LMFDB - Embedded newform 4025.2.a.bd.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.817573 q^{2} -1.89500 q^{3} -1.33157 q^{4} +1.54930 q^{6} -1.00000 q^{7} +2.72381 q^{8} +0.591014 q^{9} +O(q^{10})$	\(q-0.817573 q^{2} -1.89500 q^{3} -1.33157 q^{4} +1.54930 q^{6} -1.00000 q^{7} +2.72381 q^{8} +0.591014 q^{9} +2.12866 q^{11} +2.52333 q^{12} -5.55212 q^{13} +0.817573 q^{14} +0.436240 q^{16} +0.145218 q^{17} -0.483197 q^{18} -3.23410 q^{19} +1.89500 q^{21} -1.74033 q^{22} -1.00000 q^{23} -5.16160 q^{24} +4.53926 q^{26} +4.56502 q^{27} +1.33157 q^{28} +3.26934 q^{29} +0.223549 q^{31} -5.80427 q^{32} -4.03380 q^{33} -0.118727 q^{34} -0.786979 q^{36} +1.16019 q^{37} +2.64411 q^{38} +10.5213 q^{39} -2.79850 q^{41} -1.54930 q^{42} -11.5742 q^{43} -2.83447 q^{44} +0.817573 q^{46} -2.13898 q^{47} -0.826674 q^{48} +1.00000 q^{49} -0.275188 q^{51} +7.39306 q^{52} -7.28007 q^{53} -3.73224 q^{54} -2.72381 q^{56} +6.12860 q^{57} -2.67292 q^{58} +4.72568 q^{59} +2.99427 q^{61} -0.182767 q^{62} -0.591014 q^{63} +3.87293 q^{64} +3.29793 q^{66} -12.8063 q^{67} -0.193369 q^{68} +1.89500 q^{69} +1.35757 q^{71} +1.60981 q^{72} -5.64692 q^{73} -0.948542 q^{74} +4.30644 q^{76} -2.12866 q^{77} -8.60189 q^{78} -15.8310 q^{79} -10.4237 q^{81} +2.28798 q^{82} +16.1543 q^{83} -2.52333 q^{84} +9.46273 q^{86} -6.19539 q^{87} +5.79805 q^{88} +5.37869 q^{89} +5.55212 q^{91} +1.33157 q^{92} -0.423624 q^{93} +1.74877 q^{94} +10.9991 q^{96} -10.2405 q^{97} -0.817573 q^{98} +1.25807 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	$ 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) $ 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * 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 $

$2$	−0.817573	−0.578111	−0.289056	−	0.957312i	$-0.593341\pi$
$2$	−0.817573	−0.578111	−0.289056	+	0.957312i	$0.593341\pi$
$3$	−1.89500	−1.09408	−0.547039	−	0.837107i	$-0.684245\pi$
$3$	−1.89500	−1.09408	−0.547039	+	0.837107i	$0.684245\pi$
$4$	−1.33157	−0.665787
$5$	0	0
$5$	0	0
$6$	1.54930	0.632498
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.72381	0.963011
$9$	0.591014	0.197005
$10$	0	0
$11$	2.12866	0.641814	0.320907	−	0.947111i	$-0.396012\pi$
$11$	2.12866	0.641814	0.320907	+	0.947111i	$0.396012\pi$
$12$	2.52333	0.728423
$13$	−5.55212	−1.53988	−0.769940	−	0.638116i	$-0.779714\pi$
$13$	−5.55212	−1.53988	−0.769940	+	0.638116i	$0.779714\pi$
$14$	0.817573	0.218506
$15$	0	0
$16$	0.436240	0.109060
$17$	0.145218	0.0352206	0.0176103	−	0.999845i	$-0.494394\pi$
$17$	0.145218	0.0352206	0.0176103	+	0.999845i	$0.494394\pi$
$18$	−0.483197	−0.113891
$19$	−3.23410	−0.741953	−0.370976	−	0.928642i	$-0.620977\pi$
$19$	−3.23410	−0.741953	−0.370976	+	0.928642i	$0.620977\pi$
$20$	0	0
$21$	1.89500	0.413522
$22$	−1.74033	−0.371040
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−5.16160	−1.05361
$25$	0	0
$26$	4.53926	0.890223
$27$	4.56502	0.878539
$28$	1.33157	0.251644
$29$	3.26934	0.607101	0.303551	−	0.952815i	$-0.401828\pi$
$29$	3.26934	0.607101	0.303551	+	0.952815i	$0.401828\pi$
$30$	0	0
$31$	0.223549	0.0401506	0.0200753	−	0.999798i	$-0.493609\pi$
$31$	0.223549	0.0401506	0.0200753	+	0.999798i	$0.493609\pi$
$32$	−5.80427	−1.02606
$33$	−4.03380	−0.702194
$34$	−0.118727	−0.0203614
$35$	0	0
$36$	−0.786979	−0.131163
$37$	1.16019	0.190734	0.0953672	−	0.995442i	$-0.469597\pi$
$37$	1.16019	0.190734	0.0953672	+	0.995442i	$0.469597\pi$
$38$	2.64411	0.428931
$39$	10.5213	1.68475
$40$	0	0
$41$	−2.79850	−0.437052	−0.218526	−	0.975831i	$-0.570125\pi$
$41$	−2.79850	−0.437052	−0.218526	+	0.975831i	$0.570125\pi$
$42$	−1.54930	−0.239062
$43$	−11.5742	−1.76504	−0.882522	−	0.470271i	$-0.844156\pi$
$43$	−11.5742	−1.76504	−0.882522	+	0.470271i	$0.844156\pi$
$44$	−2.83447	−0.427312
$45$	0	0
$46$	0.817573	0.120545
$47$	−2.13898	−0.312002	−0.156001	−	0.987757i	$-0.549860\pi$
$47$	−2.13898	−0.312002	−0.156001	+	0.987757i	$0.549860\pi$
$48$	−0.826674	−0.119320
$49$	1.00000	0.142857
$50$	0	0
$51$	−0.275188	−0.0385341
$52$	7.39306	1.02523
$53$	−7.28007	−0.999995	−0.499998	−	0.866027i	$-0.666666\pi$
$53$	−7.28007	−0.999995	−0.499998	+	0.866027i	$0.666666\pi$
$54$	−3.73224	−0.507893
$55$	0	0
$56$	−2.72381	−0.363984
$57$	6.12860	0.811753
$58$	−2.67292	−0.350972
$59$	4.72568	0.615232	0.307616	−	0.951511i	$-0.400469\pi$
$59$	4.72568	0.615232	0.307616	+	0.951511i	$0.400469\pi$
$60$	0	0
$61$	2.99427	0.383377	0.191688	−	0.981456i	$-0.438604\pi$
$61$	2.99427	0.383377	0.191688	+	0.981456i	$0.438604\pi$
$62$	−0.182767	−0.0232115
$63$	−0.591014	−0.0744608
$64$	3.87293	0.484117
$65$	0	0
$66$	3.29793	0.405947
$67$	−12.8063	−1.56454	−0.782269	−	0.622941i	$-0.785938\pi$
$67$	−12.8063	−1.56454	−0.782269	+	0.622941i	$0.785938\pi$
$68$	−0.193369	−0.0234494
$69$	1.89500	0.228131
$70$	0	0
$71$	1.35757	0.161113	0.0805567	−	0.996750i	$-0.474330\pi$
$71$	1.35757	0.161113	0.0805567	+	0.996750i	$0.474330\pi$
$72$	1.60981	0.189718
$73$	−5.64692	−0.660922	−0.330461	−	0.943820i	$-0.607204\pi$
$73$	−5.64692	−0.660922	−0.330461	+	0.943820i	$0.607204\pi$
$74$	−0.948542	−0.110266
$75$	0	0
$76$	4.30644	0.493983
$77$	−2.12866	−0.242583
$78$	−8.60189	−0.973972
$79$	−15.8310	−1.78113	−0.890564	−	0.454858i	$-0.849690\pi$
$79$	−15.8310	−1.78113	−0.890564	+	0.454858i	$0.849690\pi$
$80$	0	0
$81$	−10.4237	−1.15819
$82$	2.28798	0.252665
$83$	16.1543	1.77317	0.886584	−	0.462568i	$-0.153072\pi$
$83$	16.1543	1.77317	0.886584	+	0.462568i	$0.153072\pi$
$84$	−2.52333	−0.275318
$85$	0	0
$86$	9.46273	1.02039
$87$	−6.19539	−0.664216
$88$	5.79805	0.618074
$89$	5.37869	0.570140	0.285070	−	0.958507i	$-0.407983\pi$
$89$	5.37869	0.570140	0.285070	+	0.958507i	$0.407983\pi$
$90$	0	0
$91$	5.55212	0.582020
$92$	1.33157	0.138826
$93$	−0.423624	−0.0439278
$94$	1.74877	0.180372
$95$	0	0
$96$	10.9991	1.12259
$97$	−10.2405	−1.03977	−0.519884	−	0.854237i	$-0.674025\pi$
$97$	−10.2405	−1.03977	−0.519884	+	0.854237i	$0.674025\pi$
$98$	−0.817573	−0.0825873
$99$	1.25807	0.126440
$100$	0	0
$101$	9.36317	0.931671	0.465835	−	0.884871i	$-0.345754\pi$
$101$	9.36317	0.931671	0.465835	+	0.884871i	$0.345754\pi$
$102$	0.224986	0.0222770
$103$	−6.45952	−0.636475	−0.318238	−	0.948011i	$-0.603091\pi$
$103$	−6.45952	−0.636475	−0.318238	+	0.948011i	$0.603091\pi$
$104$	−15.1229	−1.48292
$105$	0	0
$106$	5.95199	0.578109
$107$	−13.6196	−1.31665	−0.658326	−	0.752733i	$-0.728735\pi$
$107$	−13.6196	−1.31665	−0.658326	+	0.752733i	$0.728735\pi$
$108$	−6.07867	−0.584920
$109$	−19.7751	−1.89411	−0.947055	−	0.321073i	$-0.895957\pi$
$109$	−19.7751	−1.89411	−0.947055	+	0.321073i	$0.895957\pi$
$110$	0	0
$111$	−2.19856	−0.208678
$112$	−0.436240	−0.0412208
$113$	6.01223	0.565583	0.282792	−	0.959181i	$-0.408739\pi$
$113$	6.01223	0.565583	0.282792	+	0.959181i	$0.408739\pi$
$114$	−5.01058	−0.469284
$115$	0	0
$116$	−4.35337	−0.404200
$117$	−3.28138	−0.303364
$118$	−3.86359	−0.355672
$119$	−0.145218	−0.0133121
$120$	0	0
$121$	−6.46882	−0.588074
$122$	−2.44803	−0.221634
$123$	5.30315	0.478169
$124$	−0.297672	−0.0267317
$125$	0	0
$126$	0.483197	0.0430466
$127$	4.25574	0.377636	0.188818	−	0.982012i	$-0.439534\pi$
$127$	4.25574	0.377636	0.188818	+	0.982012i	$0.439534\pi$
$128$	8.44213	0.746186
$129$	21.9330	1.93109
$130$	0	0
$131$	5.53859	0.483909	0.241955	−	0.970288i	$-0.422212\pi$
$131$	5.53859	0.483909	0.241955	+	0.970288i	$0.422212\pi$
$132$	5.37131	0.467512
$133$	3.23410	0.280432
$134$	10.4701	0.904477
$135$	0	0
$136$	0.395546	0.0339178
$137$	−17.7030	−1.51247	−0.756236	−	0.654299i	$-0.772964\pi$
$137$	−17.7030	−1.51247	−0.756236	+	0.654299i	$0.772964\pi$
$138$	−1.54930	−0.131885
$139$	9.23566	0.783358	0.391679	−	0.920102i	$-0.371894\pi$
$139$	9.23566	0.783358	0.391679	+	0.920102i	$0.371894\pi$
$140$	0	0
$141$	4.05335	0.341354
$142$	−1.10991	−0.0931414
$143$	−11.8186	−0.988318
$144$	0.257824	0.0214853
$145$	0	0
$146$	4.61677	0.382086
$147$	−1.89500	−0.156297
$148$	−1.54488	−0.126989
$149$	4.06403	0.332939	0.166469	−	0.986047i	$-0.446763\pi$
$149$	4.06403	0.332939	0.166469	+	0.986047i	$0.446763\pi$
$150$	0	0
$151$	−3.18853	−0.259479	−0.129739	−	0.991548i	$-0.541414\pi$
$151$	−3.18853	−0.259479	−0.129739	+	0.991548i	$0.541414\pi$
$152$	−8.80905	−0.714508
$153$	0.0858260	0.00693862
$154$	1.74033	0.140240
$155$	0	0
$156$	−14.0098	−1.12168
$157$	−17.1593	−1.36946	−0.684732	−	0.728795i	$-0.740081\pi$
$157$	−17.1593	−1.36946	−0.684732	+	0.728795i	$0.740081\pi$
$158$	12.9430	1.02969
$159$	13.7957	1.09407
$160$	0	0
$161$	1.00000	0.0788110
$162$	8.52217	0.669565
$163$	−10.8914	−0.853078	−0.426539	−	0.904469i	$-0.640267\pi$
$163$	−10.8914	−0.853078	−0.426539	+	0.904469i	$0.640267\pi$
$164$	3.72641	0.290984
$165$	0	0
$166$	−13.2073	−1.02509
$167$	5.62878	0.435568	0.217784	−	0.975997i	$-0.430117\pi$
$167$	5.62878	0.435568	0.217784	+	0.975997i	$0.430117\pi$
$168$	5.16160	0.398226
$169$	17.8260	1.37123
$170$	0	0
$171$	−1.91140	−0.146168
$172$	15.4119	1.17514
$173$	20.1921	1.53518	0.767590	−	0.640941i	$-0.221456\pi$
$173$	20.1921	1.53518	0.767590	+	0.640941i	$0.221456\pi$
$174$	5.06518	0.383991
$175$	0	0
$176$	0.928606	0.0699963
$177$	−8.95516	−0.673111
$178$	−4.39747	−0.329605
$179$	−0.0487966	−0.00364723	−0.00182361	−	0.999998i	$-0.500580\pi$
$179$	−0.0487966	−0.00364723	−0.00182361	+	0.999998i	$0.500580\pi$
$180$	0	0
$181$	11.0147	0.818717	0.409358	−	0.912374i	$-0.365753\pi$
$181$	11.0147	0.818717	0.409358	+	0.912374i	$0.365753\pi$
$182$	−4.53926	−0.336473
$183$	−5.67413	−0.419444
$184$	−2.72381	−0.200802
$185$	0	0
$186$	0.346344	0.0253952
$187$	0.309120	0.0226051
$188$	2.84821	0.207727
$189$	−4.56502	−0.332056
$190$	0	0
$191$	13.6292	0.986177	0.493088	−	0.869979i	$-0.335868\pi$
$191$	13.6292	0.986177	0.493088	+	0.869979i	$0.335868\pi$
$192$	−7.33920	−0.529661
$193$	8.24539	0.593516	0.296758	−	0.954953i	$-0.404095\pi$
$193$	8.24539	0.593516	0.296758	+	0.954953i	$0.404095\pi$
$194$	8.37238	0.601102
$195$	0	0
$196$	−1.33157	−0.0951125
$197$	6.23251	0.444048	0.222024	−	0.975041i	$-0.428734\pi$
$197$	6.23251	0.444048	0.222024	+	0.975041i	$0.428734\pi$
$198$	−1.02856	−0.0730967
$199$	7.76075	0.550145	0.275073	−	0.961423i	$-0.411298\pi$
$199$	7.76075	0.550145	0.275073	+	0.961423i	$0.411298\pi$
$200$	0	0
$201$	24.2679	1.71173
$202$	−7.65508	−0.538609
$203$	−3.26934	−0.229463
$204$	0.366434	0.0256555
$205$	0	0
$206$	5.28113	0.367954
$207$	−0.591014	−0.0410783
$208$	−2.42206	−0.167939
$209$	−6.88428	−0.476196
$210$	0	0
$211$	10.0472	0.691678	0.345839	−	0.938294i	$-0.387594\pi$
$211$	10.0472	0.691678	0.345839	+	0.938294i	$0.387594\pi$
$212$	9.69396	0.665784
$213$	−2.57258	−0.176270
$214$	11.1350	0.761172
$215$	0	0
$216$	12.4342	0.846042
$217$	−0.223549	−0.0151755
$218$	16.1676	1.09501
$219$	10.7009	0.723100
$220$	0	0
$221$	−0.806269	−0.0542355
$222$	1.79748	0.120639
$223$	16.1886	1.08407	0.542034	−	0.840356i	$-0.317654\pi$
$223$	16.1886	1.08407	0.542034	+	0.840356i	$0.317654\pi$
$224$	5.80427	0.387814
$225$	0	0
$226$	−4.91544	−0.326970
$227$	19.1412	1.27044	0.635222	−	0.772329i	$-0.280908\pi$
$227$	19.1412	1.27044	0.635222	+	0.772329i	$0.280908\pi$
$228$	−8.16069	−0.540455
$229$	−8.64191	−0.571074	−0.285537	−	0.958368i	$-0.592172\pi$
$229$	−8.64191	−0.571074	−0.285537	+	0.958368i	$0.592172\pi$
$230$	0	0
$231$	4.03380	0.265405
$232$	8.90505	0.584645
$233$	25.5478	1.67369	0.836846	−	0.547439i	$-0.184397\pi$
$233$	25.5478	1.67369	0.836846	+	0.547439i	$0.184397\pi$
$234$	2.68277	0.175378
$235$	0	0
$236$	−6.29260	−0.409613
$237$	29.9997	1.94869
$238$	0.118727	0.00769590
$239$	29.9879	1.93976	0.969879	−	0.243587i	$-0.0783243\pi$
$239$	29.9879	1.93976	0.969879	+	0.243587i	$0.0783243\pi$
$240$	0	0
$241$	1.47944	0.0952994	0.0476497	−	0.998864i	$-0.484827\pi$
$241$	1.47944	0.0952994	0.0476497	+	0.998864i	$0.484827\pi$
$242$	5.28873	0.339972
$243$	6.05790	0.388615
$244$	−3.98709	−0.255247
$245$	0	0
$246$	−4.33571	−0.276435
$247$	17.9561	1.14252
$248$	0.608903	0.0386654
$249$	−30.6124	−1.93998
$250$	0	0
$251$	−19.5809	−1.23593	−0.617967	−	0.786204i	$-0.712043\pi$
$251$	−19.5809	−1.23593	−0.617967	+	0.786204i	$0.712043\pi$
$252$	0.786979	0.0495750
$253$	−2.12866	−0.133828
$254$	−3.47938	−0.218316
$255$	0	0
$256$	−14.6479	−0.915495
$257$	9.42026	0.587620	0.293810	−	0.955864i	$-0.405077\pi$
$257$	9.42026	0.587620	0.293810	+	0.955864i	$0.405077\pi$
$258$	−17.9318	−1.11639
$259$	−1.16019	−0.0720908
$260$	0	0
$261$	1.93223	0.119602
$262$	−4.52820	−0.279753
$263$	2.39107	0.147440	0.0737200	−	0.997279i	$-0.476513\pi$
$263$	2.39107	0.147440	0.0737200	+	0.997279i	$0.476513\pi$
$264$	−10.9873	−0.676221
$265$	0	0
$266$	−2.64411	−0.162121
$267$	−10.1926	−0.623778
$268$	17.0525	1.04165
$269$	17.8491	1.08828	0.544141	−	0.838994i	$-0.316856\pi$
$269$	17.8491	1.08828	0.544141	+	0.838994i	$0.316856\pi$
$270$	0	0
$271$	16.6951	1.01415	0.507077	−	0.861901i	$-0.330726\pi$
$271$	16.6951	1.01415	0.507077	+	0.861901i	$0.330726\pi$
$272$	0.0633500	0.00384116
$273$	−10.5213	−0.636775
$274$	14.4735	0.874378
$275$	0	0
$276$	−2.52333	−0.151887
$277$	−28.0654	−1.68628	−0.843142	−	0.537691i	$-0.819297\pi$
$277$	−28.0654	−1.68628	−0.843142	+	0.537691i	$0.819297\pi$
$278$	−7.55082	−0.452868
$279$	0.132121	0.00790985
$280$	0	0
$281$	−22.2279	−1.32601	−0.663004	−	0.748616i	$-0.730719\pi$
$281$	−22.2279	−1.32601	−0.663004	+	0.748616i	$0.730719\pi$
$282$	−3.31391	−0.197341
$283$	−11.0420	−0.656379	−0.328190	−	0.944612i	$-0.606439\pi$
$283$	−11.0420	−0.656379	−0.328190	+	0.944612i	$0.606439\pi$
$284$	−1.80770	−0.107267
$285$	0	0
$286$	9.66254	0.571358
$287$	2.79850	0.165190
$288$	−3.43040	−0.202139
$289$	−16.9789	−0.998760
$290$	0	0
$291$	19.4058	1.13759
$292$	7.51930	0.440033
$293$	8.90419	0.520188	0.260094	−	0.965583i	$-0.416246\pi$
$293$	8.90419	0.520188	0.260094	+	0.965583i	$0.416246\pi$
$294$	1.54930	0.0903569
$295$	0	0
$296$	3.16014	0.183679
$297$	9.71737	0.563859
$298$	−3.32264	−0.192476
$299$	5.55212	0.321087
$300$	0	0
$301$	11.5742	0.667124
$302$	2.60685	0.150008
$303$	−17.7432	−1.01932
$304$	−1.41084	−0.0809174
$305$	0	0
$306$	−0.0701690	−0.00401130
$307$	−3.40251	−0.194192	−0.0970958	−	0.995275i	$-0.530955\pi$
$307$	−3.40251	−0.194192	−0.0970958	+	0.995275i	$0.530955\pi$
$308$	2.83447	0.161509
$309$	12.2408	0.696353
$310$	0	0
$311$	−21.5337	−1.22107	−0.610533	−	0.791991i	$-0.709045\pi$
$311$	−21.5337	−1.22107	−0.610533	+	0.791991i	$0.709045\pi$
$312$	28.6578	1.62243
$313$	24.4624	1.38270	0.691348	−	0.722522i	$-0.257017\pi$
$313$	24.4624	1.38270	0.691348	+	0.722522i	$0.257017\pi$
$314$	14.0290	0.791703
$315$	0	0
$316$	21.0802	1.18585
$317$	10.9401	0.614457	0.307228	−	0.951636i	$-0.400598\pi$
$317$	10.9401	0.614457	0.307228	+	0.951636i	$0.400598\pi$
$318$	−11.2790	−0.632495
$319$	6.95931	0.389646
$320$	0	0
$321$	25.8090	1.44052
$322$	−0.817573	−0.0455616
$323$	−0.469650	−0.0261320
$324$	13.8800	0.771111
$325$	0	0
$326$	8.90449	0.493174
$327$	37.4737	2.07230
$328$	−7.62257	−0.420886
$329$	2.13898	0.117926
$330$	0	0
$331$	31.4654	1.72949	0.864747	−	0.502207i	$-0.167478\pi$
$331$	31.4654	1.72949	0.864747	+	0.502207i	$0.167478\pi$
$332$	−21.5107	−1.18055
$333$	0.685690	0.0375756
$334$	−4.60194	−0.251807
$335$	0	0
$336$	0.826674	0.0450987
$337$	35.5298	1.93543	0.967717	−	0.252040i	$-0.0811014\pi$
$337$	35.5298	1.93543	0.967717	+	0.252040i	$0.0811014\pi$
$338$	−14.5741	−0.792726
$339$	−11.3932	−0.618792
$340$	0	0
$341$	0.475859	0.0257692
$342$	1.56271	0.0845015
$343$	−1.00000	−0.0539949
$344$	−31.5258	−1.69976
$345$	0	0
$346$	−16.5085	−0.887505
$347$	29.9862	1.60974	0.804870	−	0.593451i	$-0.202235\pi$
$347$	29.9862	1.60974	0.804870	+	0.593451i	$0.202235\pi$
$348$	8.24963	0.442226
$349$	9.56989	0.512264	0.256132	−	0.966642i	$-0.417552\pi$
$349$	9.56989	0.512264	0.256132	+	0.966642i	$0.417552\pi$
$350$	0	0
$351$	−25.3455	−1.35285
$352$	−12.3553	−0.658540
$353$	1.92987	0.102717	0.0513584	−	0.998680i	$-0.483645\pi$
$353$	1.92987	0.102717	0.0513584	+	0.998680i	$0.483645\pi$
$354$	7.32149	0.389133
$355$	0	0
$356$	−7.16213	−0.379592
$357$	0.275188	0.0145645
$358$	0.0398947	0.00210850
$359$	−27.4206	−1.44720	−0.723602	−	0.690217i	$-0.757515\pi$
$359$	−27.4206	−1.44720	−0.723602	+	0.690217i	$0.757515\pi$
$360$	0	0
$361$	−8.54062	−0.449506
$362$	−9.00532	−0.473309
$363$	12.2584	0.643399
$364$	−7.39306	−0.387502
$365$	0	0
$366$	4.63901	0.242485
$367$	28.8264	1.50472	0.752362	−	0.658750i	$-0.228915\pi$
$367$	28.8264	1.50472	0.752362	+	0.658750i	$0.228915\pi$
$368$	−0.436240	−0.0227406
$369$	−1.65395	−0.0861013
$370$	0	0
$371$	7.28007	0.377963
$372$	0.564087	0.0292466
$373$	−5.41771	−0.280518	−0.140259	−	0.990115i	$-0.544794\pi$
$373$	−5.41771	−0.280518	−0.140259	+	0.990115i	$0.544794\pi$
$374$	−0.252728	−0.0130683
$375$	0	0
$376$	−5.82615	−0.300461
$377$	−18.1518	−0.934864
$378$	3.73224	0.191966
$379$	6.96741	0.357892	0.178946	−	0.983859i	$-0.442731\pi$
$379$	6.96741	0.357892	0.178946	+	0.983859i	$0.442731\pi$
$380$	0	0
$381$	−8.06462	−0.413163
$382$	−11.1429	−0.570120
$383$	−11.7539	−0.600598	−0.300299	−	0.953845i	$-0.597086\pi$
$383$	−11.7539	−0.600598	−0.300299	+	0.953845i	$0.597086\pi$
$384$	−15.9978	−0.816385
$385$	0	0
$386$	−6.74120	−0.343118
$387$	−6.84050	−0.347722
$388$	13.6360	0.692265
$389$	−37.4964	−1.90114	−0.950572	−	0.310506i	$-0.899502\pi$
$389$	−37.4964	−1.90114	−0.950572	+	0.310506i	$0.899502\pi$
$390$	0	0
$391$	−0.145218	−0.00734400
$392$	2.72381	0.137573
$393$	−10.4956	−0.529434
$394$	−5.09553	−0.256709
$395$	0	0
$396$	−1.67521	−0.0841824
$397$	−7.47066	−0.374941	−0.187471	−	0.982270i	$-0.560029\pi$
$397$	−7.47066	−0.374941	−0.187471	+	0.982270i	$0.560029\pi$
$398$	−6.34498	−0.318045
$399$	−6.12860	−0.306814
$400$	0	0
$401$	18.9575	0.946695	0.473347	−	0.880876i	$-0.343046\pi$
$401$	18.9575	0.946695	0.473347	+	0.880876i	$0.343046\pi$
$402$	−19.8408	−0.989568
$403$	−1.24117	−0.0618271
$404$	−12.4678	−0.620294
$405$	0	0
$406$	2.67292	0.132655
$407$	2.46965	0.122416
$408$	−0.749559	−0.0371087
$409$	12.6697	0.626478	0.313239	−	0.949674i	$-0.398586\pi$
$409$	12.6697	0.626478	0.313239	+	0.949674i	$0.398586\pi$
$410$	0	0
$411$	33.5472	1.65476
$412$	8.60133	0.423757
$413$	−4.72568	−0.232536
$414$	0.483197	0.0237478
$415$	0	0
$416$	32.2260	1.58001
$417$	−17.5015	−0.857054
$418$	5.62840	0.275294
$419$	9.45883	0.462094	0.231047	−	0.972943i	$-0.425785\pi$
$419$	9.45883	0.462094	0.231047	+	0.972943i	$0.425785\pi$
$420$	0	0
$421$	3.83766	0.187036	0.0935180	−	0.995618i	$-0.470189\pi$
$421$	3.83766	0.187036	0.0935180	+	0.995618i	$0.470189\pi$
$422$	−8.21433	−0.399867
$423$	−1.26416	−0.0614658
$424$	−19.8295	−0.963006
$425$	0	0
$426$	2.10327	0.101904
$427$	−2.99427	−0.144903
$428$	18.1355	0.876610
$429$	22.3961	1.08130
$430$	0	0
$431$	−8.26552	−0.398136	−0.199068	−	0.979986i	$-0.563791\pi$
$431$	−8.26552	−0.398136	−0.199068	+	0.979986i	$0.563791\pi$
$432$	1.99144	0.0958134
$433$	19.8987	0.956271	0.478136	−	0.878286i	$-0.341313\pi$
$433$	19.8987	0.956271	0.478136	+	0.878286i	$0.341313\pi$
$434$	0.182767	0.00877312
$435$	0	0
$436$	26.3320	1.26107
$437$	3.23410	0.154708
$438$	−8.74876	−0.418032
$439$	−6.12702	−0.292427	−0.146213	−	0.989253i	$-0.546709\pi$
$439$	−6.12702	−0.292427	−0.146213	+	0.989253i	$0.546709\pi$
$440$	0	0
$441$	0.591014	0.0281435
$442$	0.659184	0.0313542
$443$	−6.22440	−0.295730	−0.147865	−	0.989008i	$-0.547240\pi$
$443$	−6.22440	−0.295730	−0.147865	+	0.989008i	$0.547240\pi$
$444$	2.92755	0.138935
$445$	0	0
$446$	−13.2354	−0.626713
$447$	−7.70133	−0.364260
$448$	−3.87293	−0.182979
$449$	12.0155	0.567045	0.283523	−	0.958966i	$-0.408497\pi$
$449$	12.0155	0.567045	0.283523	+	0.958966i	$0.408497\pi$
$450$	0	0
$451$	−5.95705	−0.280506
$452$	−8.00574	−0.376558
$453$	6.04225	0.283890
$454$	−15.6493	−0.734459
$455$	0	0
$456$	16.6931	0.781727
$457$	−3.26533	−0.152746	−0.0763728	−	0.997079i	$-0.524334\pi$
$457$	−3.26533	−0.152746	−0.0763728	+	0.997079i	$0.524334\pi$
$458$	7.06539	0.330144
$459$	0.662924	0.0309427
$460$	0	0
$461$	−15.7704	−0.734502	−0.367251	−	0.930122i	$-0.619701\pi$
$461$	−15.7704	−0.734502	−0.367251	+	0.930122i	$0.619701\pi$
$462$	−3.29793	−0.153433
$463$	36.2016	1.68243	0.841215	−	0.540700i	$-0.181841\pi$
$463$	36.2016	1.68243	0.841215	+	0.540700i	$0.181841\pi$
$464$	1.42622	0.0662105
$465$	0	0
$466$	−20.8872	−0.967580
$467$	−27.2801	−1.26237	−0.631187	−	0.775631i	$-0.717432\pi$
$467$	−27.2801	−1.26237	−0.631187	+	0.775631i	$0.717432\pi$
$468$	4.36940	0.201976
$469$	12.8063	0.591340
$470$	0	0
$471$	32.5169	1.49830
$472$	12.8718	0.592475
$473$	−24.6374	−1.13283
$474$	−24.5270	−1.12656
$475$	0	0
$476$	0.193369	0.00886305
$477$	−4.30263	−0.197004
$478$	−24.5173	−1.12140
$479$	−2.24978	−0.102795	−0.0513976	−	0.998678i	$-0.516368\pi$
$479$	−2.24978	−0.102795	−0.0513976	+	0.998678i	$0.516368\pi$
$480$	0	0
$481$	−6.44153	−0.293708
$482$	−1.20955	−0.0550937
$483$	−1.89500	−0.0862254
$484$	8.61371	0.391532
$485$	0	0
$486$	−4.95278	−0.224662
$487$	29.1879	1.32263	0.661314	−	0.750109i	$-0.269999\pi$
$487$	29.1879	1.32263	0.661314	+	0.750109i	$0.269999\pi$
$488$	8.15580	0.369196
$489$	20.6391	0.933333
$490$	0	0
$491$	−8.72378	−0.393698	−0.196849	−	0.980434i	$-0.563071\pi$
$491$	−8.72378	−0.393698	−0.196849	+	0.980434i	$0.563071\pi$
$492$	−7.06154	−0.318359
$493$	0.474768	0.0213825
$494$	−14.6804	−0.660503
$495$	0	0
$496$	0.0975209	0.00437882
$497$	−1.35757	−0.0608951
$498$	25.0279	1.12153
$499$	15.1622	0.678752	0.339376	−	0.940651i	$-0.389784\pi$
$499$	15.1622	0.678752	0.339376	+	0.940651i	$0.389784\pi$
$500$	0	0
$501$	−10.6665	−0.476545
$502$	16.0088	0.714507
$503$	21.9258	0.977622	0.488811	−	0.872390i	$-0.337431\pi$
$503$	21.9258	0.977622	0.488811	+	0.872390i	$0.337431\pi$
$504$	−1.60981	−0.0717065
$505$	0	0
$506$	1.74033	0.0773672
$507$	−33.7803	−1.50024
$508$	−5.66684	−0.251425
$509$	−35.3864	−1.56848	−0.784238	−	0.620461i	$-0.786946\pi$
$509$	−35.3864	−1.56848	−0.784238	+	0.620461i	$0.786946\pi$
$510$	0	0
$511$	5.64692	0.249805
$512$	−4.90852	−0.216928
$513$	−14.7637	−0.651834
$514$	−7.70175	−0.339710
$515$	0	0
$516$	−29.2054	−1.28570
$517$	−4.55315	−0.200247
$518$	0.948542	0.0416765
$519$	−38.2640	−1.67960
$520$	0	0
$521$	−2.41956	−0.106003	−0.0530015	−	0.998594i	$-0.516879\pi$
$521$	−2.41956	−0.106003	−0.0530015	+	0.998594i	$0.516879\pi$
$522$	−1.57974	−0.0691432
$523$	8.41047	0.367764	0.183882	−	0.982948i	$-0.441134\pi$
$523$	8.41047	0.367764	0.183882	+	0.982948i	$0.441134\pi$
$524$	−7.37505	−0.322180
$525$	0	0
$526$	−1.95488	−0.0852367
$527$	0.0324634	0.00141413
$528$	−1.75970	−0.0765813
$529$	1.00000	0.0434783
$530$	0	0
$531$	2.79295	0.121204
$532$	−4.30644	−0.186708
$533$	15.5376	0.673008
$534$	8.33320	0.360613
$535$	0	0
$536$	−34.8819	−1.50667
$537$	0.0924693	0.00399035
$538$	−14.5930	−0.629148
$539$	2.12866	0.0916878
$540$	0	0
$541$	−42.1387	−1.81168	−0.905842	−	0.423617i	$-0.860760\pi$
$541$	−42.1387	−1.81168	−0.905842	+	0.423617i	$0.860760\pi$
$542$	−13.6495	−0.586294
$543$	−20.8728	−0.895739
$544$	−0.842886	−0.0361384
$545$	0	0
$546$	8.60189	0.368127
$547$	39.6226	1.69414	0.847069	−	0.531482i	$-0.178365\pi$
$547$	39.6226	1.69414	0.847069	+	0.531482i	$0.178365\pi$
$548$	23.5729	1.00698
$549$	1.76965	0.0755270
$550$	0	0
$551$	−10.5734	−0.450441
$552$	5.16160	0.219692
$553$	15.8310	0.673203
$554$	22.9455	0.974860
$555$	0	0
$556$	−12.2980	−0.521550
$557$	−17.2373	−0.730368	−0.365184	−	0.930935i	$-0.618994\pi$
$557$	−17.2373	−0.730368	−0.365184	+	0.930935i	$0.618994\pi$
$558$	−0.108018	−0.00457277
$559$	64.2612	2.71796
$560$	0	0
$561$	−0.585781	−0.0247317
$562$	18.1730	0.766580
$563$	−40.4377	−1.70425	−0.852123	−	0.523341i	$-0.824685\pi$
$563$	−40.4377	−1.70425	−0.852123	+	0.523341i	$0.824685\pi$
$564$	−5.39734	−0.227269
$565$	0	0
$566$	9.02765	0.379460
$567$	10.4237	0.437756
$568$	3.69774	0.155154
$569$	23.0934	0.968126	0.484063	−	0.875033i	$-0.339161\pi$
$569$	23.0934	0.968126	0.484063	+	0.875033i	$0.339161\pi$
$570$	0	0
$571$	−4.95672	−0.207432	−0.103716	−	0.994607i	$-0.533073\pi$
$571$	−4.95672	−0.207432	−0.103716	+	0.994607i	$0.533073\pi$
$572$	15.7373	0.658009
$573$	−25.8274	−1.07895
$574$	−2.28798	−0.0954983
$575$	0	0
$576$	2.28896	0.0953732
$577$	−21.6383	−0.900815	−0.450408	−	0.892823i	$-0.648721\pi$
$577$	−21.6383	−0.900815	−0.450408	+	0.892823i	$0.648721\pi$
$578$	13.8815	0.577394
$579$	−15.6250	−0.649352
$580$	0	0
$581$	−16.1543	−0.670194
$582$	−15.8656	−0.657652
$583$	−15.4968	−0.641811
$584$	−15.3811	−0.636475
$585$	0	0
$586$	−7.27982	−0.300727
$587$	22.8051	0.941268	0.470634	−	0.882329i	$-0.344025\pi$
$587$	22.8051	0.941268	0.470634	+	0.882329i	$0.344025\pi$
$588$	2.52333	0.104060
$589$	−0.722979	−0.0297898
$590$	0	0
$591$	−11.8106	−0.485823
$592$	0.506122	0.0208015
$593$	−15.9010	−0.652976	−0.326488	−	0.945201i	$-0.605865\pi$
$593$	−15.9010	−0.652976	−0.326488	+	0.945201i	$0.605865\pi$
$594$	−7.94466	−0.325973
$595$	0	0
$596$	−5.41156	−0.221666
$597$	−14.7066	−0.601901
$598$	−4.53926	−0.185624
$599$	−20.5273	−0.838725	−0.419362	−	0.907819i	$-0.637746\pi$
$599$	−20.5273	−0.838725	−0.419362	+	0.907819i	$0.637746\pi$
$600$	0	0
$601$	−31.6529	−1.29115	−0.645575	−	0.763697i	$-0.723382\pi$
$601$	−31.6529	−1.29115	−0.645575	+	0.763697i	$0.723382\pi$
$602$	−9.46273	−0.385672
$603$	−7.56870	−0.308221
$604$	4.24576	0.172758
$605$	0	0
$606$	14.5063	0.589280
$607$	15.7128	0.637762	0.318881	−	0.947795i	$-0.396693\pi$
$607$	15.7128	0.637762	0.318881	+	0.947795i	$0.396693\pi$
$608$	18.7716	0.761287
$609$	6.19539	0.251050
$610$	0	0
$611$	11.8759	0.480445
$612$	−0.114284	−0.00461965
$613$	−35.5774	−1.43696	−0.718479	−	0.695549i	$-0.755161\pi$
$613$	−35.5774	−1.43696	−0.718479	+	0.695549i	$0.755161\pi$
$614$	2.78180	0.112264
$615$	0	0
$616$	−5.79805	−0.233610
$617$	−6.23170	−0.250879	−0.125439	−	0.992101i	$-0.540034\pi$
$617$	−6.23170	−0.250879	−0.125439	+	0.992101i	$0.540034\pi$
$618$	−10.0077	−0.402570
$619$	−33.4737	−1.34542	−0.672712	−	0.739905i	$-0.734870\pi$
$619$	−33.4737	−1.34542	−0.672712	+	0.739905i	$0.734870\pi$
$620$	0	0
$621$	−4.56502	−0.183188
$622$	17.6054	0.705912
$623$	−5.37869	−0.215493
$624$	4.58979	0.183739
$625$	0	0
$626$	−19.9998	−0.799353
$627$	13.0457	0.520995
$628$	22.8489	0.911772
$629$	0.168481	0.00671778
$630$	0	0
$631$	4.34219	0.172860	0.0864299	−	0.996258i	$-0.472454\pi$
$631$	4.34219	0.172860	0.0864299	+	0.996258i	$0.472454\pi$
$632$	−43.1206	−1.71525
$633$	−19.0394	−0.756749
$634$	−8.94432	−0.355224
$635$	0	0
$636$	−18.3700	−0.728419
$637$	−5.55212	−0.219983
$638$	−5.68974	−0.225259
$639$	0.802340	0.0317401
$640$	0	0
$641$	13.5873	0.536667	0.268334	−	0.963326i	$-0.413527\pi$
$641$	13.5873	0.536667	0.268334	+	0.963326i	$0.413527\pi$
$642$	−21.1008	−0.832780
$643$	27.3763	1.07962	0.539808	−	0.841788i	$-0.318497\pi$
$643$	27.3763	1.07962	0.539808	+	0.841788i	$0.318497\pi$
$644$	−1.33157	−0.0524714
$645$	0	0
$646$	0.383973	0.0151072
$647$	40.8194	1.60478	0.802389	−	0.596802i	$-0.203562\pi$
$647$	40.8194	1.60478	0.802389	+	0.596802i	$0.203562\pi$
$648$	−28.3922	−1.11535
$649$	10.0594	0.394865
$650$	0	0
$651$	0.423624	0.0166031
$652$	14.5027	0.567969
$653$	18.3223	0.717007	0.358504	−	0.933528i	$-0.383287\pi$
$653$	18.3223	0.717007	0.358504	+	0.933528i	$0.383287\pi$
$654$	−30.6375	−1.19802
$655$	0	0
$656$	−1.22082	−0.0476649
$657$	−3.33741	−0.130205
$658$	−1.74877	−0.0681741
$659$	38.4961	1.49960	0.749798	−	0.661667i	$-0.230151\pi$
$659$	38.4961	1.49960	0.749798	+	0.661667i	$0.230151\pi$
$660$	0	0
$661$	21.0492	0.818720	0.409360	−	0.912373i	$-0.365752\pi$
$661$	21.0492	0.818720	0.409360	+	0.912373i	$0.365752\pi$
$662$	−25.7253	−0.999841
$663$	1.52788	0.0593379
$664$	44.0012	1.70758
$665$	0	0
$666$	−0.560602	−0.0217229
$667$	−3.26934	−0.126589
$668$	−7.49514	−0.289996
$669$	−30.6774	−1.18606
$670$	0	0
$671$	6.37377	0.246057
$672$	−10.9991	−0.424298
$673$	0.230881	0.00889982	0.00444991	−	0.999990i	$-0.498584\pi$
$673$	0.230881	0.00889982	0.00444991	+	0.999990i	$0.498584\pi$
$674$	−29.0482	−1.11890
$675$	0	0
$676$	−23.7367	−0.912950
$677$	33.4150	1.28424	0.642121	−	0.766603i	$-0.278055\pi$
$677$	33.4150	1.28424	0.642121	+	0.766603i	$0.278055\pi$
$678$	9.31474	0.357731
$679$	10.2405	0.392995
$680$	0	0
$681$	−36.2725	−1.38996
$682$	−0.389049	−0.0148975
$683$	27.2707	1.04348	0.521742	−	0.853103i	$-0.325282\pi$
$683$	27.2707	1.04348	0.521742	+	0.853103i	$0.325282\pi$
$684$	2.54517	0.0973169
$685$	0	0
$686$	0.817573	0.0312151
$687$	16.3764	0.624799
$688$	−5.04912	−0.192496
$689$	40.4198	1.53987
$690$	0	0
$691$	−21.1761	−0.805576	−0.402788	−	0.915293i	$-0.631959\pi$
$691$	−21.1761	−0.805576	−0.402788	+	0.915293i	$0.631959\pi$
$692$	−26.8873	−1.02210
$693$	−1.25807	−0.0477900
$694$	−24.5159	−0.930609
$695$	0	0
$696$	−16.8750	−0.639647
$697$	−0.406393	−0.0153932
$698$	−7.82408	−0.296146
$699$	−48.4130	−1.83115
$700$	0	0
$701$	−11.6727	−0.440873	−0.220436	−	0.975401i	$-0.570748\pi$
$701$	−11.6727	−0.440873	−0.220436	+	0.975401i	$0.570748\pi$
$702$	20.7218	0.782095
$703$	−3.75217	−0.141516
$704$	8.24415	0.310713
$705$	0	0
$706$	−1.57781	−0.0593818
$707$	−9.36317	−0.352138
$708$	11.9245	0.448149
$709$	5.69291	0.213802	0.106901	−	0.994270i	$-0.465907\pi$
$709$	5.69291	0.213802	0.106901	+	0.994270i	$0.465907\pi$
$710$	0	0
$711$	−9.35635	−0.350891
$712$	14.6505	0.549051
$713$	−0.223549	−0.00837197
$714$	−0.224986	−0.00841990
$715$	0	0
$716$	0.0649763	0.00242828
$717$	−56.8270	−2.12224
$718$	22.4183	0.836645
$719$	2.96662	0.110636	0.0553181	−	0.998469i	$-0.482383\pi$
$719$	2.96662	0.110636	0.0553181	+	0.998469i	$0.482383\pi$
$720$	0	0
$721$	6.45952	0.240565
$722$	6.98258	0.259865
$723$	−2.80354	−0.104265
$724$	−14.6669	−0.545091
$725$	0	0
$726$	−10.0221	−0.371956
$727$	−18.3570	−0.680822	−0.340411	−	0.940277i	$-0.610566\pi$
$727$	−18.3570	−0.680822	−0.340411	+	0.940277i	$0.610566\pi$
$728$	15.1229	0.560492
$729$	19.7915	0.733020
$730$	0	0
$731$	−1.68078	−0.0621659
$732$	7.55553	0.279260
$733$	9.59697	0.354472	0.177236	−	0.984168i	$-0.443284\pi$
$733$	9.59697	0.354472	0.177236	+	0.984168i	$0.443284\pi$
$734$	−23.5676	−0.869898
$735$	0	0
$736$	5.80427	0.213948
$737$	−27.2602	−1.00414
$738$	1.35223	0.0497762
$739$	36.6324	1.34754	0.673772	−	0.738939i	$-0.264673\pi$
$739$	36.6324	1.34754	0.673772	+	0.738939i	$0.264673\pi$
$740$	0	0
$741$	−34.0267	−1.25000
$742$	−5.95199	−0.218504
$743$	−11.6543	−0.427554	−0.213777	−	0.976882i	$-0.568577\pi$
$743$	−11.6543	−0.427554	−0.213777	+	0.976882i	$0.568577\pi$
$744$	−1.15387	−0.0423029
$745$	0	0
$746$	4.42937	0.162171
$747$	9.54743	0.349322
$748$	−0.411616	−0.0150502
$749$	13.6196	0.497648
$750$	0	0
$751$	−18.9424	−0.691216	−0.345608	−	0.938379i	$-0.612327\pi$
$751$	−18.9424	−0.691216	−0.345608	+	0.938379i	$0.612327\pi$
$752$	−0.933107	−0.0340269
$753$	37.1057	1.35221
$754$	14.8404	0.540455
$755$	0	0
$756$	6.07867	0.221079
$757$	−17.4475	−0.634139	−0.317070	−	0.948402i	$-0.602699\pi$
$757$	−17.4475	−0.634139	−0.317070	+	0.948402i	$0.602699\pi$
$758$	−5.69636	−0.206901
$759$	4.03380	0.146418
$760$	0	0
$761$	40.5646	1.47046	0.735232	−	0.677816i	$-0.237073\pi$
$761$	40.5646	1.47046	0.735232	+	0.677816i	$0.237073\pi$
$762$	6.59341	0.238854
$763$	19.7751	0.715906
$764$	−18.1483	−0.656584
$765$	0	0
$766$	9.60969	0.347212
$767$	−26.2376	−0.947383
$768$	27.7578	1.00162
$769$	24.6548	0.889076	0.444538	−	0.895760i	$-0.353368\pi$
$769$	24.6548	0.889076	0.444538	+	0.895760i	$0.353368\pi$
$770$	0	0
$771$	−17.8514	−0.642902
$772$	−10.9793	−0.395155
$773$	−13.7942	−0.496144	−0.248072	−	0.968742i	$-0.579797\pi$
$773$	−13.7942	−0.496144	−0.248072	+	0.968742i	$0.579797\pi$
$774$	5.59260	0.201022
$775$	0	0
$776$	−27.8932	−1.00131
$777$	2.19856	0.0788729
$778$	30.6560	1.09907
$779$	9.05062	0.324272
$780$	0	0
$781$	2.88979	0.103405
$782$	0.118727	0.00424565
$783$	14.9246	0.533362
$784$	0.436240	0.0155800
$785$	0	0
$786$	8.58093	0.306072
$787$	27.0967	0.965892	0.482946	−	0.875650i	$-0.339567\pi$
$787$	27.0967	0.965892	0.482946	+	0.875650i	$0.339567\pi$
$788$	−8.29905	−0.295641
$789$	−4.53108	−0.161311
$790$	0	0
$791$	−6.01223	−0.213770
$792$	3.42673	0.121763
$793$	−16.6245	−0.590355
$794$	6.10781	0.216758
$795$	0	0
$796$	−10.3340	−0.366280
$797$	0.804834	0.0285087	0.0142543	−	0.999898i	$-0.495463\pi$
$797$	0.804834	0.0285087	0.0142543	+	0.999898i	$0.495463\pi$
$798$	5.01058	0.177373
$799$	−0.310618	−0.0109889
$800$	0	0
$801$	3.17888	0.112320
$802$	−15.4992	−0.547295
$803$	−12.0204	−0.424189
$804$	−32.3145	−1.13964
$805$	0	0
$806$	1.01475	0.0357429
$807$	−33.8241	−1.19066
$808$	25.5035	0.897209
$809$	−15.2092	−0.534725	−0.267363	−	0.963596i	$-0.586152\pi$
$809$	−15.2092	−0.534725	−0.267363	+	0.963596i	$0.586152\pi$
$810$	0	0
$811$	−47.1011	−1.65394	−0.826972	−	0.562243i	$-0.809939\pi$
$811$	−47.1011	−1.65394	−0.826972	+	0.562243i	$0.809939\pi$
$812$	4.35337	0.152773
$813$	−31.6372	−1.10956
$814$	−2.01912	−0.0707701
$815$	0	0
$816$	−0.120048	−0.00420252
$817$	37.4320	1.30958
$818$	−10.3584	−0.362174
$819$	3.28138	0.114661
$820$	0	0
$821$	35.4688	1.23787	0.618935	−	0.785442i	$-0.287565\pi$
$821$	35.4688	1.23787	0.618935	+	0.785442i	$0.287565\pi$
$822$	−27.4273	−0.956636
$823$	21.9442	0.764928	0.382464	−	0.923970i	$-0.375076\pi$
$823$	21.9442	0.764928	0.382464	+	0.923970i	$0.375076\pi$
$824$	−17.5945	−0.612932
$825$	0	0
$826$	3.86359	0.134432
$827$	−24.1922	−0.841244	−0.420622	−	0.907236i	$-0.638188\pi$
$827$	−24.1922	−0.841244	−0.420622	+	0.907236i	$0.638188\pi$
$828$	0.786979	0.0273494
$829$	33.2183	1.15372	0.576860	−	0.816843i	$-0.304278\pi$
$829$	33.2183	1.15372	0.576860	+	0.816843i	$0.304278\pi$
$830$	0	0
$831$	53.1838	1.84493
$832$	−21.5030	−0.745482
$833$	0.145218	0.00503151
$834$	14.3088	0.495473
$835$	0	0
$836$	9.16694	0.317045
$837$	1.02051	0.0352738
$838$	−7.73328	−0.267142
$839$	−25.8544	−0.892592	−0.446296	−	0.894885i	$-0.647257\pi$
$839$	−25.8544	−0.892592	−0.446296	+	0.894885i	$0.647257\pi$
$840$	0	0
$841$	−18.3114	−0.631428
$842$	−3.13757	−0.108128
$843$	42.1219	1.45075
$844$	−13.3786	−0.460511
$845$	0	0
$846$	1.03355	0.0355341
$847$	6.46882	0.222271
$848$	−3.17586	−0.109059
$849$	20.9246	0.718130
$850$	0	0
$851$	−1.16019	−0.0397709
$852$	3.42558	0.117359
$853$	10.3145	0.353162	0.176581	−	0.984286i	$-0.443496\pi$
$853$	10.3145	0.353162	0.176581	+	0.984286i	$0.443496\pi$
$854$	2.44803	0.0837700
$855$	0	0
$856$	−37.0970	−1.26795
$857$	−47.4897	−1.62222	−0.811109	−	0.584896i	$-0.801135\pi$
$857$	−47.4897	−1.62222	−0.811109	+	0.584896i	$0.801135\pi$
$858$	−18.3105	−0.625109
$859$	−37.5321	−1.28058	−0.640289	−	0.768134i	$-0.721185\pi$
$859$	−37.5321	−1.28058	−0.640289	+	0.768134i	$0.721185\pi$
$860$	0	0
$861$	−5.30315	−0.180731
$862$	6.75767	0.230167
$863$	−29.7998	−1.01440	−0.507199	−	0.861829i	$-0.669319\pi$
$863$	−29.7998	−1.01440	−0.507199	+	0.861829i	$0.669319\pi$
$864$	−26.4966	−0.901433
$865$	0	0
$866$	−16.2686	−0.552831
$867$	32.1750	1.09272
$868$	0.297672	0.0101036
$869$	−33.6988	−1.14315
$870$	0	0
$871$	71.1021	2.40920
$872$	−53.8635	−1.82405
$873$	−6.05230	−0.204839
$874$	−2.64411	−0.0894383
$875$	0	0
$876$	−14.2490	−0.481431
$877$	−36.3203	−1.22645	−0.613225	−	0.789908i	$-0.710128\pi$
$877$	−36.3203	−1.22645	−0.613225	+	0.789908i	$0.710128\pi$
$878$	5.00929	0.169055
$879$	−16.8734	−0.569126
$880$	0	0
$881$	−11.1876	−0.376920	−0.188460	−	0.982081i	$-0.560350\pi$
$881$	−11.1876	−0.376920	−0.188460	+	0.982081i	$0.560350\pi$
$882$	−0.483197	−0.0162701
$883$	−36.6756	−1.23423	−0.617116	−	0.786872i	$-0.711699\pi$
$883$	−36.6756	−1.23423	−0.617116	+	0.786872i	$0.711699\pi$
$884$	1.07361	0.0361093
$885$	0	0
$886$	5.08890	0.170965
$887$	52.6936	1.76928	0.884639	−	0.466276i	$-0.154405\pi$
$887$	52.6936	1.76928	0.884639	+	0.466276i	$0.154405\pi$
$888$	−5.98845	−0.200959
$889$	−4.25574	−0.142733
$890$	0	0
$891$	−22.1886	−0.743346
$892$	−21.5563	−0.721759
$893$	6.91765	0.231490
$894$	6.29640	0.210583
$895$	0	0
$896$	−8.44213	−0.282032
$897$	−10.5213	−0.351294
$898$	−9.82352	−0.327815
$899$	0.730857	0.0243755
$900$	0	0
$901$	−1.05720	−0.0352204
$902$	4.87032	0.162164
$903$	−21.9330	−0.729885
$904$	16.3762	0.544663
$905$	0	0
$906$	−4.93998	−0.164120
$907$	−25.9227	−0.860750	−0.430375	−	0.902650i	$-0.641619\pi$
$907$	−25.9227	−0.860750	−0.430375	+	0.902650i	$0.641619\pi$
$908$	−25.4879	−0.845846
$909$	5.53377	0.183543
$910$	0	0
$911$	41.5021	1.37503	0.687513	−	0.726172i	$-0.258703\pi$
$911$	41.5021	1.37503	0.687513	+	0.726172i	$0.258703\pi$
$912$	2.67354	0.0885298
$913$	34.3870	1.13804
$914$	2.66965	0.0883040
$915$	0	0
$916$	11.5073	0.380214
$917$	−5.53859	−0.182900
$918$	−0.541989	−0.0178883
$919$	12.7219	0.419656	0.209828	−	0.977738i	$-0.432710\pi$
$919$	12.7219	0.419656	0.209828	+	0.977738i	$0.432710\pi$
$920$	0	0
$921$	6.44775	0.212461
$922$	12.8935	0.424624
$923$	−7.53736	−0.248095
$924$	−5.37131	−0.176703
$925$	0	0
$926$	−29.5974	−0.972632
$927$	−3.81767	−0.125389
$928$	−18.9761	−0.622922
$929$	−16.7846	−0.550686	−0.275343	−	0.961346i	$-0.588791\pi$
$929$	−16.7846	−0.550686	−0.275343	+	0.961346i	$0.588791\pi$
$930$	0	0
$931$	−3.23410	−0.105993
$932$	−34.0188	−1.11432
$933$	40.8063	1.33594
$934$	22.3035	0.729793
$935$	0	0
$936$	−8.93784	−0.292143
$937$	−36.2327	−1.18367	−0.591835	−	0.806059i	$-0.701596\pi$
$937$	−36.2327	−1.18367	−0.591835	+	0.806059i	$0.701596\pi$
$938$	−10.4701	−0.341860
$939$	−46.3562	−1.51278
$940$	0	0
$941$	−3.57666	−0.116596	−0.0582979	−	0.998299i	$-0.518567\pi$
$941$	−3.57666	−0.116596	−0.0582979	+	0.998299i	$0.518567\pi$
$942$	−26.5849	−0.866184
$943$	2.79850	0.0911317
$944$	2.06153	0.0670972
$945$	0	0
$946$	20.1429	0.654902
$947$	−1.14066	−0.0370664	−0.0185332	−	0.999828i	$-0.505900\pi$
$947$	−1.14066	−0.0370664	−0.0185332	+	0.999828i	$0.505900\pi$
$948$	−39.9469	−1.29741
$949$	31.3524	1.01774
$950$	0	0
$951$	−20.7314	−0.672263
$952$	−0.395546	−0.0128197
$953$	−26.0443	−0.843659	−0.421830	−	0.906675i	$-0.638612\pi$
$953$	−26.0443	−0.843659	−0.421830	+	0.906675i	$0.638612\pi$
$954$	3.51771	0.113890
$955$	0	0
$956$	−39.9312	−1.29147
$957$	−13.1879	−0.426303
$958$	1.83936	0.0594271
$959$	17.7030	0.571661
$960$	0	0
$961$	−30.9500	−0.998388
$962$	5.26642	0.169796
$963$	−8.04935	−0.259387
$964$	−1.96999	−0.0634491
$965$	0	0
$966$	1.54930	0.0498479
$967$	40.4020	1.29924	0.649620	−	0.760259i	$-0.274928\pi$
$967$	40.4020	1.29924	0.649620	+	0.760259i	$0.274928\pi$
$968$	−17.6198	−0.566322
$969$	0.889985	0.0285904
$970$	0	0
$971$	−9.75233	−0.312967	−0.156484	−	0.987681i	$-0.550016\pi$
$971$	−9.75233	−0.312967	−0.156484	+	0.987681i	$0.550016\pi$
$972$	−8.06655	−0.258735
$973$	−9.23566	−0.296082
$974$	−23.8632	−0.764626
$975$	0	0
$976$	1.30622	0.0418111
$977$	18.1309	0.580060	0.290030	−	0.957018i	$-0.406335\pi$
$977$	18.1309	0.580060	0.290030	+	0.957018i	$0.406335\pi$
$978$	−16.8740	−0.539571
$979$	11.4494	0.365924
$980$	0	0
$981$	−11.6874	−0.373148
$982$	7.13232	0.227602
$983$	13.1228	0.418552	0.209276	−	0.977857i	$-0.432889\pi$
$983$	13.1228	0.418552	0.209276	+	0.977857i	$0.432889\pi$
$984$	14.4447	0.460482
$985$	0	0
$986$	−0.388158	−0.0123615
$987$	−4.05335	−0.129020
$988$	−23.9099	−0.760674
$989$	11.5742	0.368037
$990$	0	0
$991$	44.3779	1.40971	0.704855	−	0.709351i	$-0.251012\pi$
$991$	44.3779	1.40971	0.704855	+	0.709351i	$0.251012\pi$
$992$	−1.29754	−0.0411969
$993$	−59.6268	−1.89220
$994$	1.10991	0.0352042
$995$	0	0
$996$	40.7627	1.29162
$997$	−10.0458	−0.318152	−0.159076	−	0.987266i	$-0.550852\pi$
$997$	−10.0458	−0.318152	−0.159076	+	0.987266i	$0.550852\pi$
$998$	−12.3962	−0.392394
$999$	5.29630	0.167568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.bd.1.9		21
5.2	odd	4		805.2.c.c.484.16	✓	42
5.3	odd	4		805.2.c.c.484.27	yes	42
5.4	even	2		4025.2.a.be.1.13		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.16	✓	42	5.2	odd	4
805.2.c.c.484.27	yes	42	5.3	odd	4
4025.2.a.bd.1.9		21	1.1	even	1	trivial
4025.2.a.be.1.13		21	5.4	even	2

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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:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.817573 q^{2} -1.89500 q^{3} -1.33157 q^{4} +1.54930 q^{6} -1.00000 q^{7} +2.72381 q^{8} +0.591014 q^{9} +O(q^{10})\)	\(q-0.817573 q^{2} -1.89500 q^{3} -1.33157 q^{4} +1.54930 q^{6} -1.00000 q^{7} +2.72381 q^{8} +0.591014 q^{9} +2.12866 q^{11} +2.52333 q^{12} -5.55212 q^{13} +0.817573 q^{14} +0.436240 q^{16} +0.145218 q^{17} -0.483197 q^{18} -3.23410 q^{19} +1.89500 q^{21} -1.74033 q^{22} -1.00000 q^{23} -5.16160 q^{24} +4.53926 q^{26} +4.56502 q^{27} +1.33157 q^{28} +3.26934 q^{29} +0.223549 q^{31} -5.80427 q^{32} -4.03380 q^{33} -0.118727 q^{34} -0.786979 q^{36} +1.16019 q^{37} +2.64411 q^{38} +10.5213 q^{39} -2.79850 q^{41} -1.54930 q^{42} -11.5742 q^{43} -2.83447 q^{44} +0.817573 q^{46} -2.13898 q^{47} -0.826674 q^{48} +1.00000 q^{49} -0.275188 q^{51} +7.39306 q^{52} -7.28007 q^{53} -3.73224 q^{54} -2.72381 q^{56} +6.12860 q^{57} -2.67292 q^{58} +4.72568 q^{59} +2.99427 q^{61} -0.182767 q^{62} -0.591014 q^{63} +3.87293 q^{64} +3.29793 q^{66} -12.8063 q^{67} -0.193369 q^{68} +1.89500 q^{69} +1.35757 q^{71} +1.60981 q^{72} -5.64692 q^{73} -0.948542 q^{74} +4.30644 q^{76} -2.12866 q^{77} -8.60189 q^{78} -15.8310 q^{79} -10.4237 q^{81} +2.28798 q^{82} +16.1543 q^{83} -2.52333 q^{84} +9.46273 q^{86} -6.19539 q^{87} +5.79805 q^{88} +5.37869 q^{89} +5.55212 q^{91} +1.33157 q^{92} -0.423624 q^{93} +1.74877 q^{94} +10.9991 q^{96} -10.2405 q^{97} -0.817573 q^{98} +1.25807 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9}+O(q^{10}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9	\( 21 q - 2 q^{2} + q^{3} + 30 q^{4} + 6 q^{6} - 21 q^{7} - 6 q^{8} + 30 q^{9} + 7 q^{11} + 22 q^{12} + 3 q^{13} + 2 q^{14} + 56 q^{16} - 7 q^{17} + 24 q^{19} - q^{21} - 4 q^{22} - 21 q^{23} + 24 q^{24} - 2 q^{26} + 19 q^{27} - 30 q^{28} + 11 q^{29} + 46 q^{31} + 6 q^{32} + 3 q^{33} + 28 q^{34} + 58 q^{36} - 24 q^{37} + 4 q^{38} + 31 q^{39} + 14 q^{41} - 6 q^{42} - 18 q^{43} + 12 q^{44} + 2 q^{46} + 25 q^{47} + 36 q^{48} + 21 q^{49} + 17 q^{51} + 8 q^{52} - 22 q^{53} - 6 q^{54} + 6 q^{56} - 40 q^{57} - 6 q^{58} + 10 q^{59} + 38 q^{61} + 54 q^{62} - 30 q^{63} + 100 q^{64} + 38 q^{66} - 12 q^{67} - 18 q^{68} - q^{69} + 56 q^{71} - 42 q^{72} + 40 q^{73} - 20 q^{74} + 60 q^{76} - 7 q^{77} - 38 q^{78} + 49 q^{79} + 57 q^{81} - 16 q^{82} + 2 q^{83} - 22 q^{84} + 16 q^{86} + 23 q^{87} - 12 q^{88} + 28 q^{89} - 3 q^{91} - 30 q^{92} + 30 q^{93} + 66 q^{94} + 46 q^{96} + q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 21 * q - 2 * q^2 + q^3 + 30 * q^4 + 6 * q^6 - 21 * q^7 - 6 * q^8 + 30 * q^9 + 7 * q^11 + 22 * q^12 + 3 * q^13 + 2 * q^14 + 56 * q^16 - 7 * q^17 + 24 * q^19 - q^21 - 4 * q^22 - 21 * q^23 + 24 * q^24 - 2 * q^26 + 19 * q^27 - 30 * q^28 + 11 * q^29 + 46 * q^31 + 6 * q^32 + 3 * q^33 + 28 * q^34 + 58 * q^36 - 24 * q^37 + 4 * q^38 + 31 * q^39 + 14 * q^41 - 6 * q^42 - 18 * q^43 + 12 * q^44 + 2 * q^46 + 25 * q^47 + 36 * q^48 + 21 * q^49 + 17 * q^51 + 8 * q^52 - 22 * q^53 - 6 * q^54 + 6 * q^56 - 40 * q^57 - 6 * q^58 + 10 * q^59 + 38 * q^61 + 54 * q^62 - 30 * q^63 + 100 * q^64 + 38 * q^66 - 12 * q^67 - 18 * q^68 - q^69 + 56 * q^71 - 42 * q^72 + 40 * q^73 - 20 * q^74 + 60 * q^76 - 7 * q^77 - 38 * q^78 + 49 * q^79 + 57 * q^81 - 16 * q^82 + 2 * q^83 - 22 * q^84 + 16 * q^86 + 23 * q^87 - 12 * q^88 + 28 * q^89 - 3 * q^91 - 30 * q^92 + 30 * q^93 + 66 * q^94 + 46 * q^96 + q^97 - 2 * q^98 - 2 * q^99

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