LMFDB - Embedded newform 4025.2.a.be.1.8

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			1.8
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)

$f(q)$	$=$	$q-0.685218 q^{2} -1.12744 q^{3} -1.53048 q^{4} +0.772540 q^{6} +1.00000 q^{7} +2.41915 q^{8} -1.72889 q^{9} +O(q^{10})$	\(q-0.685218 q^{2} -1.12744 q^{3} -1.53048 q^{4} +0.772540 q^{6} +1.00000 q^{7} +2.41915 q^{8} -1.72889 q^{9} +3.79196 q^{11} +1.72551 q^{12} +4.67240 q^{13} -0.685218 q^{14} +1.40331 q^{16} +6.81684 q^{17} +1.18466 q^{18} +4.06169 q^{19} -1.12744 q^{21} -2.59832 q^{22} +1.00000 q^{23} -2.72743 q^{24} -3.20161 q^{26} +5.33152 q^{27} -1.53048 q^{28} -1.63116 q^{29} +10.8411 q^{31} -5.79987 q^{32} -4.27519 q^{33} -4.67102 q^{34} +2.64602 q^{36} -4.63921 q^{37} -2.78314 q^{38} -5.26783 q^{39} +5.91824 q^{41} +0.772540 q^{42} -8.83890 q^{43} -5.80350 q^{44} -0.685218 q^{46} -1.43881 q^{47} -1.58214 q^{48} +1.00000 q^{49} -7.68555 q^{51} -7.15099 q^{52} -5.16466 q^{53} -3.65325 q^{54} +2.41915 q^{56} -4.57930 q^{57} +1.11770 q^{58} +7.98817 q^{59} +11.4239 q^{61} -7.42853 q^{62} -1.72889 q^{63} +1.16756 q^{64} +2.92944 q^{66} -0.0790979 q^{67} -10.4330 q^{68} -1.12744 q^{69} -11.0182 q^{71} -4.18243 q^{72} +2.71064 q^{73} +3.17887 q^{74} -6.21632 q^{76} +3.79196 q^{77} +3.60961 q^{78} -8.69668 q^{79} -0.824288 q^{81} -4.05528 q^{82} -2.76989 q^{83} +1.72551 q^{84} +6.05657 q^{86} +1.83902 q^{87} +9.17330 q^{88} +7.18435 q^{89} +4.67240 q^{91} -1.53048 q^{92} -12.2227 q^{93} +0.985898 q^{94} +6.53898 q^{96} -12.6425 q^{97} -0.685218 q^{98} -6.55587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.685218	−0.484522	−0.242261	−	0.970211i	$-0.577889\pi$
$2$	−0.685218	−0.484522	−0.242261	+	0.970211i	$0.577889\pi$
$3$	−1.12744	−0.650926	−0.325463	−	0.945555i	$-0.605520\pi$
$3$	−1.12744	−0.650926	−0.325463	+	0.945555i	$0.605520\pi$
$4$	−1.53048	−0.765238
$5$	0	0
$5$	0	0
$6$	0.772540	0.315388
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.41915	0.855297
$9$	−1.72889	−0.576296
$10$	0	0
$11$	3.79196	1.14332	0.571659	−	0.820491i	$-0.306300\pi$
$11$	3.79196	1.14332	0.571659	+	0.820491i	$0.306300\pi$
$12$	1.72551	0.498113
$13$	4.67240	1.29589	0.647945	−	0.761687i	$-0.275629\pi$
$13$	4.67240	1.29589	0.647945	+	0.761687i	$0.275629\pi$
$14$	−0.685218	−0.183132
$15$	0	0
$16$	1.40331	0.350827
$17$	6.81684	1.65333	0.826663	−	0.562697i	$-0.190236\pi$
$17$	6.81684	1.65333	0.826663	+	0.562697i	$0.190236\pi$
$18$	1.18466	0.279228
$19$	4.06169	0.931815	0.465908	−	0.884833i	$-0.345728\pi$
$19$	4.06169	0.931815	0.465908	+	0.884833i	$0.345728\pi$
$20$	0	0
$21$	−1.12744	−0.246027
$22$	−2.59832	−0.553963
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.72743	−0.556735
$25$	0	0
$26$	−3.20161	−0.627888
$27$	5.33152	1.02605
$28$	−1.53048	−0.289233
$29$	−1.63116	−0.302898	−0.151449	−	0.988465i	$-0.548394\pi$
$29$	−1.63116	−0.302898	−0.151449	+	0.988465i	$0.548394\pi$
$30$	0	0
$31$	10.8411	1.94712	0.973561	−	0.228428i	$-0.0733585\pi$
$31$	10.8411	1.94712	0.973561	+	0.228428i	$0.0733585\pi$
$32$	−5.79987	−1.02528
$33$	−4.27519	−0.744215
$34$	−4.67102	−0.801074
$35$	0	0
$36$	2.64602	0.441003
$37$	−4.63921	−0.762682	−0.381341	−	0.924434i	$-0.624538\pi$
$37$	−4.63921	−0.762682	−0.381341	+	0.924434i	$0.624538\pi$
$38$	−2.78314	−0.451485
$39$	−5.26783	−0.843528
$40$	0	0
$41$	5.91824	0.924274	0.462137	−	0.886809i	$-0.347083\pi$
$41$	5.91824	0.924274	0.462137	+	0.886809i	$0.347083\pi$
$42$	0.772540	0.119206
$43$	−8.83890	−1.34792	−0.673960	−	0.738768i	$-0.735408\pi$
$43$	−8.83890	−1.34792	−0.673960	+	0.738768i	$0.735408\pi$
$44$	−5.80350	−0.874911
$45$	0	0
$46$	−0.685218	−0.101030
$47$	−1.43881	−0.209872	−0.104936	−	0.994479i	$-0.533464\pi$
$47$	−1.43881	−0.209872	−0.104936	+	0.994479i	$0.533464\pi$
$48$	−1.58214	−0.228362
$49$	1.00000	0.142857
$50$	0	0
$51$	−7.68555	−1.07619
$52$	−7.15099	−0.991665
$53$	−5.16466	−0.709421	−0.354711	−	0.934976i	$-0.615421\pi$
$53$	−5.16466	−0.709421	−0.354711	+	0.934976i	$0.615421\pi$
$54$	−3.65325	−0.497145
$55$	0	0
$56$	2.41915	0.323272
$57$	−4.57930	−0.606542
$58$	1.11770	0.146761
$59$	7.98817	1.03997	0.519985	−	0.854175i	$-0.325937\pi$
$59$	7.98817	1.03997	0.519985	+	0.854175i	$0.325937\pi$
$60$	0	0
$61$	11.4239	1.46269	0.731343	−	0.682010i	$-0.238894\pi$
$61$	11.4239	1.46269	0.731343	+	0.682010i	$0.238894\pi$
$62$	−7.42853	−0.943424
$63$	−1.72889	−0.217819
$64$	1.16756	0.145944
$65$	0	0
$66$	2.92944	0.360589
$67$	−0.0790979	−0.00966335	−0.00483167	−	0.999988i	$-0.501538\pi$
$67$	−0.0790979	−0.00966335	−0.00483167	+	0.999988i	$0.501538\pi$
$68$	−10.4330	−1.26519
$69$	−1.12744	−0.135727
$70$	0	0
$71$	−11.0182	−1.30762	−0.653811	−	0.756658i	$-0.726831\pi$
$71$	−11.0182	−1.30762	−0.653811	+	0.756658i	$0.726831\pi$
$72$	−4.18243	−0.492904
$73$	2.71064	0.317256	0.158628	−	0.987338i	$-0.449293\pi$
$73$	2.71064	0.317256	0.158628	+	0.987338i	$0.449293\pi$
$74$	3.17887	0.369536
$75$	0	0
$76$	−6.21632	−0.713060
$77$	3.79196	0.432134
$78$	3.60961	0.408708
$79$	−8.69668	−0.978452	−0.489226	−	0.872157i	$-0.662721\pi$
$79$	−8.69668	−0.978452	−0.489226	+	0.872157i	$0.662721\pi$
$80$	0	0
$81$	−0.824288	−0.0915876
$82$	−4.05528	−0.447831
$83$	−2.76989	−0.304035	−0.152017	−	0.988378i	$-0.548577\pi$
$83$	−2.76989	−0.304035	−0.152017	+	0.988378i	$0.548577\pi$
$84$	1.72551	0.188269
$85$	0	0
$86$	6.05657	0.653097
$87$	1.83902	0.197164
$88$	9.17330	0.977877
$89$	7.18435	0.761540	0.380770	−	0.924670i	$-0.375659\pi$
$89$	7.18435	0.761540	0.380770	+	0.924670i	$0.375659\pi$
$90$	0	0
$91$	4.67240	0.489801
$92$	−1.53048	−0.159563
$93$	−12.2227	−1.26743
$94$	0.985898	0.101688
$95$	0	0
$96$	6.53898	0.667382
$97$	−12.6425	−1.28365	−0.641823	−	0.766853i	$-0.721822\pi$
$97$	−12.6425	−1.28365	−0.641823	+	0.766853i	$0.721822\pi$
$98$	−0.685218	−0.0692175
$99$	−6.55587	−0.658889
$100$	0	0
$101$	−10.3783	−1.03268	−0.516340	−	0.856384i	$-0.672706\pi$
$101$	−10.3783	−1.03268	−0.516340	+	0.856384i	$0.672706\pi$
$102$	5.26628	0.521439
$103$	7.68253	0.756982	0.378491	−	0.925605i	$-0.376443\pi$
$103$	7.68253	0.756982	0.378491	+	0.925605i	$0.376443\pi$
$104$	11.3032	1.10837
$105$	0	0
$106$	3.53892	0.343730
$107$	8.25087	0.797641	0.398821	−	0.917029i	$-0.369420\pi$
$107$	8.25087	0.797641	0.398821	+	0.917029i	$0.369420\pi$
$108$	−8.15976	−0.785174
$109$	15.5344	1.48793	0.743965	−	0.668219i	$-0.232943\pi$
$109$	15.5344	1.48793	0.743965	+	0.668219i	$0.232943\pi$
$110$	0	0
$111$	5.23042	0.496449
$112$	1.40331	0.132600
$113$	11.7793	1.10810	0.554052	−	0.832482i	$-0.313081\pi$
$113$	11.7793	1.10810	0.554052	+	0.832482i	$0.313081\pi$
$114$	3.13782	0.293883
$115$	0	0
$116$	2.49644	0.231789
$117$	−8.07805	−0.746816
$118$	−5.47364	−0.503889
$119$	6.81684	0.624899
$120$	0	0
$121$	3.37895	0.307177
$122$	−7.82789	−0.708704
$123$	−6.67244	−0.601633
$124$	−16.5921	−1.49001
$125$	0	0
$126$	1.18466	0.105538
$127$	−11.1573	−0.990047	−0.495023	−	0.868880i	$-0.664841\pi$
$127$	−11.1573	−0.990047	−0.495023	+	0.868880i	$0.664841\pi$
$128$	10.7997	0.954568
$129$	9.96529	0.877395
$130$	0	0
$131$	−17.7985	−1.55506	−0.777532	−	0.628843i	$-0.783529\pi$
$131$	−17.7985	−1.55506	−0.777532	+	0.628843i	$0.783529\pi$
$132$	6.54308	0.569502
$133$	4.06169	0.352193
$134$	0.0541993	0.00468211
$135$	0	0
$136$	16.4909	1.41409
$137$	3.94173	0.336765	0.168382	−	0.985722i	$-0.446146\pi$
$137$	3.94173	0.336765	0.168382	+	0.985722i	$0.446146\pi$
$138$	0.772540	0.0657630
$139$	−0.215089	−0.0182436	−0.00912181	−	0.999958i	$-0.502904\pi$
$139$	−0.215089	−0.0182436	−0.00912181	+	0.999958i	$0.502904\pi$
$140$	0	0
$141$	1.62217	0.136611
$142$	7.54989	0.633573
$143$	17.7175	1.48162
$144$	−2.42616	−0.202180
$145$	0	0
$146$	−1.85738	−0.153718
$147$	−1.12744	−0.0929894
$148$	7.10020	0.583633
$149$	11.3139	0.926873	0.463437	−	0.886130i	$-0.346616\pi$
$149$	11.3139	0.926873	0.463437	+	0.886130i	$0.346616\pi$
$150$	0	0
$151$	3.78594	0.308096	0.154048	−	0.988063i	$-0.450769\pi$
$151$	3.78594	0.308096	0.154048	+	0.988063i	$0.450769\pi$
$152$	9.82582	0.796979
$153$	−11.7855	−0.952805
$154$	−2.59832	−0.209378
$155$	0	0
$156$	8.06229	0.645500
$157$	−17.0066	−1.35727	−0.678637	−	0.734474i	$-0.737429\pi$
$157$	−17.0066	−1.35727	−0.678637	+	0.734474i	$0.737429\pi$
$158$	5.95912	0.474082
$159$	5.82283	0.461781
$160$	0	0
$161$	1.00000	0.0788110
$162$	0.564817	0.0443762
$163$	−14.7715	−1.15699	−0.578496	−	0.815686i	$-0.696360\pi$
$163$	−14.7715	−1.15699	−0.578496	+	0.815686i	$0.696360\pi$
$164$	−9.05772	−0.707289
$165$	0	0
$166$	1.89798	0.147312
$167$	13.7736	1.06584	0.532918	−	0.846167i	$-0.321095\pi$
$167$	13.7736	1.06584	0.532918	+	0.846167i	$0.321095\pi$
$168$	−2.72743	−0.210426
$169$	8.83131	0.679332
$170$	0	0
$171$	−7.02220	−0.537001
$172$	13.5277	1.03148
$173$	−12.0383	−0.915254	−0.457627	−	0.889144i	$-0.651301\pi$
$173$	−12.0383	−0.915254	−0.457627	+	0.889144i	$0.651301\pi$
$174$	−1.26013	−0.0955304
$175$	0	0
$176$	5.32129	0.401107
$177$	−9.00615	−0.676944
$178$	−4.92285	−0.368983
$179$	17.6941	1.32252	0.661261	−	0.750156i	$-0.270022\pi$
$179$	17.6941	1.32252	0.661261	+	0.750156i	$0.270022\pi$
$180$	0	0
$181$	11.8203	0.878598	0.439299	−	0.898341i	$-0.355227\pi$
$181$	11.8203	0.878598	0.439299	+	0.898341i	$0.355227\pi$
$182$	−3.20161	−0.237319
$183$	−12.8798	−0.952099
$184$	2.41915	0.178342
$185$	0	0
$186$	8.37519	0.614099
$187$	25.8492	1.89028
$188$	2.20206	0.160602
$189$	5.33152	0.387811
$190$	0	0
$191$	9.16360	0.663055	0.331527	−	0.943446i	$-0.392436\pi$
$191$	9.16360	0.663055	0.331527	+	0.943446i	$0.392436\pi$
$192$	−1.31634	−0.0949990
$193$	5.46574	0.393433	0.196716	−	0.980460i	$-0.436972\pi$
$193$	5.46574	0.393433	0.196716	+	0.980460i	$0.436972\pi$
$194$	8.66284	0.621956
$195$	0	0
$196$	−1.53048	−0.109320
$197$	−14.7144	−1.04836	−0.524180	−	0.851607i	$-0.675628\pi$
$197$	−14.7144	−1.04836	−0.524180	+	0.851607i	$0.675628\pi$
$198$	4.49220	0.319247
$199$	10.4884	0.743505	0.371753	−	0.928332i	$-0.378757\pi$
$199$	10.4884	0.743505	0.371753	+	0.928332i	$0.378757\pi$
$200$	0	0
$201$	0.0891779	0.00629012
$202$	7.11141	0.500357
$203$	−1.63116	−0.114485
$204$	11.7626	0.823543
$205$	0	0
$206$	−5.26421	−0.366775
$207$	−1.72889	−0.120166
$208$	6.55682	0.454634
$209$	15.4018	1.06536
$210$	0	0
$211$	−24.8547	−1.71107	−0.855533	−	0.517748i	$-0.826771\pi$
$211$	−24.8547	−1.71107	−0.855533	+	0.517748i	$0.826771\pi$
$212$	7.90440	0.542876
$213$	12.4223	0.851165
$214$	−5.65364	−0.386475
$215$	0	0
$216$	12.8977	0.877579
$217$	10.8411	0.735943
$218$	−10.6445	−0.720935
$219$	−3.05607	−0.206510
$220$	0	0
$221$	31.8510	2.14253
$222$	−3.58398	−0.240541
$223$	5.56715	0.372804	0.186402	−	0.982474i	$-0.440317\pi$
$223$	5.56715	0.372804	0.186402	+	0.982474i	$0.440317\pi$
$224$	−5.79987	−0.387520
$225$	0	0
$226$	−8.07140	−0.536902
$227$	−15.9092	−1.05593	−0.527965	−	0.849266i	$-0.677045\pi$
$227$	−15.9092	−1.05593	−0.527965	+	0.849266i	$0.677045\pi$
$228$	7.00850	0.464149
$229$	7.26683	0.480206	0.240103	−	0.970747i	$-0.422819\pi$
$229$	7.26683	0.480206	0.240103	+	0.970747i	$0.422819\pi$
$230$	0	0
$231$	−4.27519	−0.281287
$232$	−3.94600	−0.259068
$233$	−3.40152	−0.222841	−0.111420	−	0.993773i	$-0.535540\pi$
$233$	−3.40152	−0.222841	−0.111420	+	0.993773i	$0.535540\pi$
$234$	5.53523	0.361849
$235$	0	0
$236$	−12.2257	−0.795825
$237$	9.80495	0.636900
$238$	−4.67102	−0.302777
$239$	−10.4775	−0.677730	−0.338865	−	0.940835i	$-0.610043\pi$
$239$	−10.4775	−0.677730	−0.338865	+	0.940835i	$0.610043\pi$
$240$	0	0
$241$	−20.6275	−1.32873	−0.664367	−	0.747406i	$-0.731299\pi$
$241$	−20.6275	−1.32873	−0.664367	+	0.747406i	$0.731299\pi$
$242$	−2.31532	−0.148834
$243$	−15.0652	−0.966435
$244$	−17.4841	−1.11930
$245$	0	0
$246$	4.57208	0.291505
$247$	18.9778	1.20753
$248$	26.2262	1.66537
$249$	3.12287	0.197904
$250$	0	0
$251$	9.64286	0.608652	0.304326	−	0.952568i	$-0.401569\pi$
$251$	9.64286	0.608652	0.304326	+	0.952568i	$0.401569\pi$
$252$	2.64602	0.166684
$253$	3.79196	0.238398
$254$	7.64516	0.479700
$255$	0	0
$256$	−9.73526	−0.608454
$257$	−10.5213	−0.656298	−0.328149	−	0.944626i	$-0.606425\pi$
$257$	−10.5213	−0.656298	−0.328149	+	0.944626i	$0.606425\pi$
$258$	−6.82840	−0.425118
$259$	−4.63921	−0.288267
$260$	0	0
$261$	2.82008	0.174559
$262$	12.1959	0.753463
$263$	−19.5323	−1.20441	−0.602206	−	0.798341i	$-0.705711\pi$
$263$	−19.5323	−1.20441	−0.602206	+	0.798341i	$0.705711\pi$
$264$	−10.3423	−0.636525
$265$	0	0
$266$	−2.78314	−0.170645
$267$	−8.09990	−0.495706
$268$	0.121057	0.00739476
$269$	−4.08923	−0.249325	−0.124662	−	0.992199i	$-0.539785\pi$
$269$	−4.08923	−0.249325	−0.124662	+	0.992199i	$0.539785\pi$
$270$	0	0
$271$	9.15043	0.555849	0.277925	−	0.960603i	$-0.410353\pi$
$271$	9.15043	0.555849	0.277925	+	0.960603i	$0.410353\pi$
$272$	9.56613	0.580032
$273$	−5.26783	−0.318824
$274$	−2.70094	−0.163170
$275$	0	0
$276$	1.72551	0.103864
$277$	29.1964	1.75424	0.877120	−	0.480272i	$-0.159462\pi$
$277$	29.1964	1.75424	0.877120	+	0.480272i	$0.159462\pi$
$278$	0.147383	0.00883945
$279$	−18.7431	−1.12212
$280$	0	0
$281$	−1.02527	−0.0611625	−0.0305813	−	0.999532i	$-0.509736\pi$
$281$	−1.02527	−0.0611625	−0.0305813	+	0.999532i	$0.509736\pi$
$282$	−1.11154	−0.0661911
$283$	29.0672	1.72787	0.863933	−	0.503607i	$-0.167994\pi$
$283$	29.0672	1.72787	0.863933	+	0.503607i	$0.167994\pi$
$284$	16.8631	1.00064
$285$	0	0
$286$	−12.1404	−0.717876
$287$	5.91824	0.349343
$288$	10.0273	0.590865
$289$	29.4693	1.73349
$290$	0	0
$291$	14.2536	0.835559
$292$	−4.14857	−0.242777
$293$	−27.7312	−1.62007	−0.810036	−	0.586380i	$-0.800552\pi$
$293$	−27.7312	−1.62007	−0.810036	+	0.586380i	$0.800552\pi$
$294$	0.772540	0.0450554
$295$	0	0
$296$	−11.2229	−0.652320
$297$	20.2169	1.17310
$298$	−7.75251	−0.449091
$299$	4.67240	0.270212
$300$	0	0
$301$	−8.83890	−0.509466
$302$	−2.59420	−0.149279
$303$	11.7009	0.672198
$304$	5.69980	0.326906
$305$	0	0
$306$	8.07567	0.461655
$307$	0.743289	0.0424218	0.0212109	−	0.999775i	$-0.493248\pi$
$307$	0.743289	0.0424218	0.0212109	+	0.999775i	$0.493248\pi$
$308$	−5.80350	−0.330685
$309$	−8.66157	−0.492739
$310$	0	0
$311$	11.3354	0.642770	0.321385	−	0.946949i	$-0.395852\pi$
$311$	11.3354	0.642770	0.321385	+	0.946949i	$0.395852\pi$
$312$	−12.7437	−0.721468
$313$	−21.3433	−1.20639	−0.603196	−	0.797593i	$-0.706106\pi$
$313$	−21.3433	−1.20639	−0.603196	+	0.797593i	$0.706106\pi$
$314$	11.6532	0.657630
$315$	0	0
$316$	13.3101	0.748749
$317$	0.645246	0.0362406	0.0181203	−	0.999836i	$-0.494232\pi$
$317$	0.645246	0.0362406	0.0181203	+	0.999836i	$0.494232\pi$
$318$	−3.98991	−0.223743
$319$	−6.18527	−0.346309
$320$	0	0
$321$	−9.30233	−0.519205
$322$	−0.685218	−0.0381857
$323$	27.6879	1.54059
$324$	1.26155	0.0700863
$325$	0	0
$326$	10.1217	0.560588
$327$	−17.5141	−0.968532
$328$	14.3171	0.790529
$329$	−1.43881	−0.0793241
$330$	0	0
$331$	28.5904	1.57147	0.785734	−	0.618565i	$-0.212285\pi$
$331$	28.5904	1.57147	0.785734	+	0.618565i	$0.212285\pi$
$332$	4.23925	0.232659
$333$	8.02068	0.439530
$334$	−9.43795	−0.516421
$335$	0	0
$336$	−1.58214	−0.0863129
$337$	−24.9382	−1.35847	−0.679234	−	0.733921i	$-0.737688\pi$
$337$	−24.9382	−1.35847	−0.679234	+	0.733921i	$0.737688\pi$
$338$	−6.05138	−0.329151
$339$	−13.2804	−0.721294
$340$	0	0
$341$	41.1091	2.22618
$342$	4.81174	0.260189
$343$	1.00000	0.0539949
$344$	−21.3826	−1.15287
$345$	0	0
$346$	8.24886	0.443461
$347$	5.73940	0.308107	0.154054	−	0.988063i	$-0.450767\pi$
$347$	5.73940	0.308107	0.154054	+	0.988063i	$0.450767\pi$
$348$	−2.81458	−0.150877
$349$	14.7334	0.788662	0.394331	−	0.918969i	$-0.370976\pi$
$349$	14.7334	0.788662	0.394331	+	0.918969i	$0.370976\pi$
$350$	0	0
$351$	24.9110	1.32965
$352$	−21.9928	−1.17222
$353$	30.9626	1.64797	0.823986	−	0.566610i	$-0.191745\pi$
$353$	30.9626	1.64797	0.823986	+	0.566610i	$0.191745\pi$
$354$	6.17118	0.327994
$355$	0	0
$356$	−10.9955	−0.582759
$357$	−7.68555	−0.406763
$358$	−12.1243	−0.640791
$359$	−0.411690	−0.0217282	−0.0108641	−	0.999941i	$-0.503458\pi$
$359$	−0.411690	−0.0217282	−0.0108641	+	0.999941i	$0.503458\pi$
$360$	0	0
$361$	−2.50269	−0.131720
$362$	−8.09950	−0.425700
$363$	−3.80955	−0.199949
$364$	−7.15099	−0.374814
$365$	0	0
$366$	8.82545	0.461313
$367$	28.9764	1.51256	0.756278	−	0.654251i	$-0.227016\pi$
$367$	28.9764	1.51256	0.756278	+	0.654251i	$0.227016\pi$
$368$	1.40331	0.0731525
$369$	−10.2320	−0.532655
$370$	0	0
$371$	−5.16466	−0.268136
$372$	18.7065	0.969887
$373$	10.3339	0.535069	0.267534	−	0.963548i	$-0.413791\pi$
$373$	10.3339	0.535069	0.267534	+	0.963548i	$0.413791\pi$
$374$	−17.7123	−0.915882
$375$	0	0
$376$	−3.48069	−0.179503
$377$	−7.62141	−0.392523
$378$	−3.65325	−0.187903
$379$	−5.48106	−0.281543	−0.140771	−	0.990042i	$-0.544958\pi$
$379$	−5.48106	−0.281543	−0.140771	+	0.990042i	$0.544958\pi$
$380$	0	0
$381$	12.5791	0.644447
$382$	−6.27906	−0.321265
$383$	28.3838	1.45035	0.725173	−	0.688567i	$-0.241760\pi$
$383$	28.3838	1.45035	0.725173	+	0.688567i	$0.241760\pi$
$384$	−12.1760	−0.621353
$385$	0	0
$386$	−3.74522	−0.190627
$387$	15.2815	0.776800
$388$	19.3490	0.982295
$389$	23.4613	1.18953	0.594767	−	0.803898i	$-0.297244\pi$
$389$	23.4613	1.18953	0.594767	+	0.803898i	$0.297244\pi$
$390$	0	0
$391$	6.81684	0.344742
$392$	2.41915	0.122185
$393$	20.0667	1.01223
$394$	10.0826	0.507954
$395$	0	0
$396$	10.0336	0.504207
$397$	−7.14229	−0.358461	−0.179231	−	0.983807i	$-0.557361\pi$
$397$	−7.14229	−0.358461	−0.179231	+	0.983807i	$0.557361\pi$
$398$	−7.18686	−0.360245
$399$	−4.57930	−0.229252
$400$	0	0
$401$	−13.8293	−0.690604	−0.345302	−	0.938492i	$-0.612224\pi$
$401$	−13.8293	−0.690604	−0.345302	+	0.938492i	$0.612224\pi$
$402$	−0.0611063	−0.00304771
$403$	50.6540	2.52326
$404$	15.8838	0.790246
$405$	0	0
$406$	1.11770	0.0554704
$407$	−17.5917	−0.871988
$408$	−18.5925	−0.920465
$409$	−7.59007	−0.375305	−0.187652	−	0.982236i	$-0.560088\pi$
$409$	−7.59007	−0.375305	−0.187652	+	0.982236i	$0.560088\pi$
$410$	0	0
$411$	−4.44405	−0.219209
$412$	−11.7579	−0.579272
$413$	7.98817	0.393072
$414$	1.18466	0.0582231
$415$	0	0
$416$	−27.0993	−1.32865
$417$	0.242499	0.0118752
$418$	−10.5536	−0.516192
$419$	−23.1421	−1.13057	−0.565283	−	0.824897i	$-0.691233\pi$
$419$	−23.1421	−1.13057	−0.565283	+	0.824897i	$0.691233\pi$
$420$	0	0
$421$	−31.0152	−1.51159	−0.755793	−	0.654810i	$-0.772749\pi$
$421$	−31.0152	−1.51159	−0.755793	+	0.654810i	$0.772749\pi$
$422$	17.0309	0.829050
$423$	2.48754	0.120948
$424$	−12.4941	−0.606766
$425$	0	0
$426$	−8.51202	−0.412409
$427$	11.4239	0.552843
$428$	−12.6278	−0.610385
$429$	−19.9754	−0.964422
$430$	0	0
$431$	7.74843	0.373229	0.186614	−	0.982433i	$-0.440249\pi$
$431$	7.74843	0.373229	0.186614	+	0.982433i	$0.440249\pi$
$432$	7.48177	0.359967
$433$	−8.61269	−0.413900	−0.206950	−	0.978352i	$-0.566354\pi$
$433$	−8.61269	−0.413900	−0.206950	+	0.978352i	$0.566354\pi$
$434$	−7.42853	−0.356581
$435$	0	0
$436$	−23.7751	−1.13862
$437$	4.06169	0.194297
$438$	2.09408	0.100059
$439$	10.1584	0.484834	0.242417	−	0.970172i	$-0.422060\pi$
$439$	10.1584	0.484834	0.242417	+	0.970172i	$0.422060\pi$
$440$	0	0
$441$	−1.72889	−0.0823280
$442$	−21.8249	−1.03810
$443$	6.59857	0.313508	0.156754	−	0.987638i	$-0.449897\pi$
$443$	6.59857	0.313508	0.156754	+	0.987638i	$0.449897\pi$
$444$	−8.00503	−0.379902
$445$	0	0
$446$	−3.81471	−0.180632
$447$	−12.7557	−0.603326
$448$	1.16756	0.0551618
$449$	−13.1607	−0.621093	−0.310547	−	0.950558i	$-0.600512\pi$
$449$	−13.1607	−0.621093	−0.310547	+	0.950558i	$0.600512\pi$
$450$	0	0
$451$	22.4417	1.05674
$452$	−18.0280	−0.847964
$453$	−4.26841	−0.200547
$454$	10.9013	0.511622
$455$	0	0
$456$	−11.0780	−0.518774
$457$	12.0973	0.565890	0.282945	−	0.959136i	$-0.408689\pi$
$457$	12.0973	0.565890	0.282945	+	0.959136i	$0.408689\pi$
$458$	−4.97936	−0.232670
$459$	36.3441	1.69640
$460$	0	0
$461$	27.9319	1.30092	0.650460	−	0.759541i	$-0.274576\pi$
$461$	27.9319	1.30092	0.650460	+	0.759541i	$0.274576\pi$
$462$	2.92944	0.136290
$463$	−20.1234	−0.935212	−0.467606	−	0.883937i	$-0.654883\pi$
$463$	−20.1234	−0.935212	−0.467606	+	0.883937i	$0.654883\pi$
$464$	−2.28901	−0.106265
$465$	0	0
$466$	2.33078	0.107971
$467$	−4.37270	−0.202344	−0.101172	−	0.994869i	$-0.532259\pi$
$467$	−4.37270	−0.202344	−0.101172	+	0.994869i	$0.532259\pi$
$468$	12.3633	0.571492
$469$	−0.0790979	−0.00365240
$470$	0	0
$471$	19.1739	0.883485
$472$	19.3245	0.889484
$473$	−33.5167	−1.54110
$474$	−6.71853	−0.308592
$475$	0	0
$476$	−10.4330	−0.478196
$477$	8.92912	0.408836
$478$	7.17934	0.328376
$479$	−23.6377	−1.08003	−0.540017	−	0.841654i	$-0.681582\pi$
$479$	−23.6377	−1.08003	−0.540017	+	0.841654i	$0.681582\pi$
$480$	0	0
$481$	−21.6763	−0.988352
$482$	14.1343	0.643801
$483$	−1.12744	−0.0513001
$484$	−5.17140	−0.235064
$485$	0	0
$486$	10.3230	0.468259
$487$	−1.44583	−0.0655167	−0.0327584	−	0.999463i	$-0.510429\pi$
$487$	−1.44583	−0.0655167	−0.0327584	+	0.999463i	$0.510429\pi$
$488$	27.6362	1.25103
$489$	16.6539	0.753115
$490$	0	0
$491$	27.2394	1.22930	0.614648	−	0.788801i	$-0.289298\pi$
$491$	27.2394	1.22930	0.614648	+	0.788801i	$0.289298\pi$
$492$	10.2120	0.460393
$493$	−11.1193	−0.500789
$494$	−13.0040	−0.585076
$495$	0	0
$496$	15.2134	0.683103
$497$	−11.0182	−0.494235
$498$	−2.13985	−0.0958889
$499$	−6.34990	−0.284261	−0.142130	−	0.989848i	$-0.545395\pi$
$499$	−6.34990	−0.284261	−0.142130	+	0.989848i	$0.545395\pi$
$500$	0	0
$501$	−15.5289	−0.693780
$502$	−6.60746	−0.294906
$503$	−19.4185	−0.865829	−0.432914	−	0.901435i	$-0.642515\pi$
$503$	−19.4185	−0.865829	−0.432914	+	0.901435i	$0.642515\pi$
$504$	−4.18243	−0.186300
$505$	0	0
$506$	−2.59832	−0.115509
$507$	−9.95674	−0.442195
$508$	17.0759	0.757621
$509$	−7.50347	−0.332585	−0.166293	−	0.986076i	$-0.553180\pi$
$509$	−7.50347	−0.332585	−0.166293	+	0.986076i	$0.553180\pi$
$510$	0	0
$511$	2.71064	0.119912
$512$	−14.9286	−0.659758
$513$	21.6550	0.956090
$514$	7.20936	0.317991
$515$	0	0
$516$	−15.2516	−0.671416
$517$	−5.45590	−0.239950
$518$	3.17887	0.139672
$519$	13.5724	0.595763
$520$	0	0
$521$	−10.0876	−0.441948	−0.220974	−	0.975280i	$-0.570924\pi$
$521$	−10.0876	−0.441948	−0.220974	+	0.975280i	$0.570924\pi$
$522$	−1.93237	−0.0845776
$523$	−32.3895	−1.41629	−0.708146	−	0.706066i	$-0.750468\pi$
$523$	−32.3895	−1.41629	−0.708146	+	0.706066i	$0.750468\pi$
$524$	27.2402	1.18999
$525$	0	0
$526$	13.3839	0.583564
$527$	73.9021	3.21923
$528$	−5.99942	−0.261091
$529$	1.00000	0.0434783
$530$	0	0
$531$	−13.8106	−0.599331
$532$	−6.21632	−0.269512
$533$	27.6524	1.19776
$534$	5.55020	0.240181
$535$	0	0
$536$	−0.191349	−0.00826504
$537$	−19.9490	−0.860863
$538$	2.80202	0.120803
$539$	3.79196	0.163331
$540$	0	0
$541$	−39.7829	−1.71040	−0.855200	−	0.518299i	$-0.826566\pi$
$541$	−39.7829	−1.71040	−0.855200	+	0.518299i	$0.826566\pi$
$542$	−6.27004	−0.269321
$543$	−13.3267	−0.571902
$544$	−39.5367	−1.69512
$545$	0	0
$546$	3.60961	0.154477
$547$	0.720409	0.0308025	0.0154012	−	0.999881i	$-0.495097\pi$
$547$	0.720409	0.0308025	0.0154012	+	0.999881i	$0.495097\pi$
$548$	−6.03272	−0.257705
$549$	−19.7507	−0.842939
$550$	0	0
$551$	−6.62524	−0.282245
$552$	−2.72743	−0.116087
$553$	−8.69668	−0.369820
$554$	−20.0059	−0.849968
$555$	0	0
$556$	0.329189	0.0139607
$557$	−13.4493	−0.569865	−0.284933	−	0.958548i	$-0.591971\pi$
$557$	−13.4493	−0.569865	−0.284933	+	0.958548i	$0.591971\pi$
$558$	12.8431	0.543691
$559$	−41.2989	−1.74676
$560$	0	0
$561$	−29.1433	−1.23043
$562$	0.702534	0.0296346
$563$	−24.9853	−1.05301	−0.526503	−	0.850174i	$-0.676497\pi$
$563$	−24.9853	−1.05301	−0.526503	+	0.850174i	$0.676497\pi$
$564$	−2.48269	−0.104540
$565$	0	0
$566$	−19.9174	−0.837190
$567$	−0.824288	−0.0346168
$568$	−26.6547	−1.11841
$569$	−12.3005	−0.515664	−0.257832	−	0.966190i	$-0.583008\pi$
$569$	−12.3005	−0.515664	−0.257832	+	0.966190i	$0.583008\pi$
$570$	0	0
$571$	−0.209274	−0.00875784	−0.00437892	−	0.999990i	$-0.501394\pi$
$571$	−0.209274	−0.00875784	−0.00437892	+	0.999990i	$0.501394\pi$
$572$	−27.1163	−1.13379
$573$	−10.3314	−0.431599
$574$	−4.05528	−0.169264
$575$	0	0
$576$	−2.01857	−0.0841071
$577$	37.8175	1.57436	0.787181	−	0.616722i	$-0.211540\pi$
$577$	37.8175	1.57436	0.787181	+	0.616722i	$0.211540\pi$
$578$	−20.1929	−0.839914
$579$	−6.16227	−0.256095
$580$	0	0
$581$	−2.76989	−0.114914
$582$	−9.76680	−0.404847
$583$	−19.5842	−0.811094
$584$	6.55743	0.271348
$585$	0	0
$586$	19.0019	0.784961
$587$	−41.3519	−1.70678	−0.853388	−	0.521276i	$-0.825456\pi$
$587$	−41.3519	−1.70678	−0.853388	+	0.521276i	$0.825456\pi$
$588$	1.72551	0.0711590
$589$	44.0332	1.81436
$590$	0	0
$591$	16.5896	0.682405
$592$	−6.51025	−0.267570
$593$	−32.8585	−1.34933	−0.674667	−	0.738122i	$-0.735713\pi$
$593$	−32.8585	−1.34933	−0.674667	+	0.738122i	$0.735713\pi$
$594$	−13.8530	−0.568395
$595$	0	0
$596$	−17.3157	−0.709278
$597$	−11.8250	−0.483967
$598$	−3.20161	−0.130924
$599$	−4.51872	−0.184630	−0.0923150	−	0.995730i	$-0.529427\pi$
$599$	−4.51872	−0.184630	−0.0923150	+	0.995730i	$0.529427\pi$
$600$	0	0
$601$	29.0616	1.18545	0.592723	−	0.805406i	$-0.298053\pi$
$601$	29.0616	1.18545	0.592723	+	0.805406i	$0.298053\pi$
$602$	6.05657	0.246847
$603$	0.136751	0.00556895
$604$	−5.79429	−0.235766
$605$	0	0
$606$	−8.01766	−0.325695
$607$	5.54681	0.225138	0.112569	−	0.993644i	$-0.464092\pi$
$607$	5.54681	0.225138	0.112569	+	0.993644i	$0.464092\pi$
$608$	−23.5572	−0.955373
$609$	1.83902	0.0745210
$610$	0	0
$611$	−6.72269	−0.271971
$612$	18.0375	0.729122
$613$	−30.2171	−1.22046	−0.610229	−	0.792225i	$-0.708923\pi$
$613$	−30.2171	−1.22046	−0.610229	+	0.792225i	$0.708923\pi$
$614$	−0.509315	−0.0205543
$615$	0	0
$616$	9.17330	0.369603
$617$	5.33177	0.214649	0.107324	−	0.994224i	$-0.465772\pi$
$617$	5.33177	0.214649	0.107324	+	0.994224i	$0.465772\pi$
$618$	5.93506	0.238743
$619$	26.7730	1.07610	0.538049	−	0.842914i	$-0.319162\pi$
$619$	26.7730	1.07610	0.538049	+	0.842914i	$0.319162\pi$
$620$	0	0
$621$	5.33152	0.213947
$622$	−7.76721	−0.311437
$623$	7.18435	0.287835
$624$	−7.39240	−0.295933
$625$	0	0
$626$	14.6248	0.584524
$627$	−17.3645	−0.693471
$628$	26.0282	1.03864
$629$	−31.6248	−1.26096
$630$	0	0
$631$	41.2665	1.64279	0.821396	−	0.570358i	$-0.193196\pi$
$631$	41.2665	1.64279	0.821396	+	0.570358i	$0.193196\pi$
$632$	−21.0385	−0.836868
$633$	28.0221	1.11378
$634$	−0.442134	−0.0175594
$635$	0	0
$636$	−8.91170	−0.353372
$637$	4.67240	0.185127
$638$	4.23826	0.167794
$639$	19.0493	0.753577
$640$	0	0
$641$	−45.9389	−1.81448	−0.907239	−	0.420616i	$-0.861814\pi$
$641$	−45.9389	−1.81448	−0.907239	+	0.420616i	$0.861814\pi$
$642$	6.37412	0.251567
$643$	48.6731	1.91948	0.959740	−	0.280890i	$-0.0906295\pi$
$643$	48.6731	1.91948	0.959740	+	0.280890i	$0.0906295\pi$
$644$	−1.53048	−0.0603092
$645$	0	0
$646$	−18.9722	−0.746453
$647$	15.8668	0.623788	0.311894	−	0.950117i	$-0.399037\pi$
$647$	15.8668	0.623788	0.311894	+	0.950117i	$0.399037\pi$
$648$	−1.99407	−0.0783346
$649$	30.2908	1.18902
$650$	0	0
$651$	−12.2227	−0.479044
$652$	22.6074	0.885374
$653$	46.0747	1.80304	0.901521	−	0.432736i	$-0.142452\pi$
$653$	46.0747	1.80304	0.901521	+	0.432736i	$0.142452\pi$
$654$	12.0010	0.469275
$655$	0	0
$656$	8.30512	0.324260
$657$	−4.68639	−0.182833
$658$	0.985898	0.0384343
$659$	13.4362	0.523402	0.261701	−	0.965149i	$-0.415717\pi$
$659$	13.4362	0.523402	0.261701	+	0.965149i	$0.415717\pi$
$660$	0	0
$661$	−14.8042	−0.575818	−0.287909	−	0.957658i	$-0.592960\pi$
$661$	−14.8042	−0.575818	−0.287909	+	0.957658i	$0.592960\pi$
$662$	−19.5906	−0.761411
$663$	−35.9100	−1.39463
$664$	−6.70076	−0.260040
$665$	0	0
$666$	−5.49591	−0.212962
$667$	−1.63116	−0.0631586
$668$	−21.0802	−0.815618
$669$	−6.27661	−0.242668
$670$	0	0
$671$	43.3191	1.67231
$672$	6.53898	0.252247
$673$	−0.275846	−0.0106331	−0.00531654	−	0.999986i	$-0.501692\pi$
$673$	−0.275846	−0.0106331	−0.00531654	+	0.999986i	$0.501692\pi$
$674$	17.0881	0.658209
$675$	0	0
$676$	−13.5161	−0.519851
$677$	−13.9584	−0.536466	−0.268233	−	0.963354i	$-0.586440\pi$
$677$	−13.9584	−0.536466	−0.268233	+	0.963354i	$0.586440\pi$
$678$	9.09999	0.349483
$679$	−12.6425	−0.485173
$680$	0	0
$681$	17.9366	0.687332
$682$	−28.1687	−1.07863
$683$	32.7626	1.25363	0.626813	−	0.779169i	$-0.284359\pi$
$683$	32.7626	1.25363	0.626813	+	0.779169i	$0.284359\pi$
$684$	10.7473	0.410934
$685$	0	0
$686$	−0.685218	−0.0261618
$687$	−8.19289	−0.312578
$688$	−12.4037	−0.472887
$689$	−24.1314	−0.919332
$690$	0	0
$691$	−2.27111	−0.0863969	−0.0431985	−	0.999067i	$-0.513755\pi$
$691$	−2.27111	−0.0863969	−0.0431985	+	0.999067i	$0.513755\pi$
$692$	18.4243	0.700387
$693$	−6.55587	−0.249037
$694$	−3.93274	−0.149285
$695$	0	0
$696$	4.44887	0.168634
$697$	40.3437	1.52813
$698$	−10.0956	−0.382124
$699$	3.83500	0.145053
$700$	0	0
$701$	−27.8289	−1.05108	−0.525541	−	0.850768i	$-0.676137\pi$
$701$	−27.8289	−1.05108	−0.525541	+	0.850768i	$0.676137\pi$
$702$	−17.0695	−0.644245
$703$	−18.8430	−0.710679
$704$	4.42732	0.166861
$705$	0	0
$706$	−21.2161	−0.798480
$707$	−10.3783	−0.390317
$708$	13.7837	0.518023
$709$	20.6902	0.777038	0.388519	−	0.921441i	$-0.372987\pi$
$709$	20.6902	0.777038	0.388519	+	0.921441i	$0.372987\pi$
$710$	0	0
$711$	15.0356	0.563878
$712$	17.3800	0.651343
$713$	10.8411	0.406003
$714$	5.26628	0.197086
$715$	0	0
$716$	−27.0804	−1.01204
$717$	11.8127	0.441152
$718$	0.282098	0.0105278
$719$	−1.89998	−0.0708574	−0.0354287	−	0.999372i	$-0.511280\pi$
$719$	−1.89998	−0.0708574	−0.0354287	+	0.999372i	$0.511280\pi$
$720$	0	0
$721$	7.68253	0.286112
$722$	1.71489	0.0638215
$723$	23.2562	0.864907
$724$	−18.0907	−0.672336
$725$	0	0
$726$	2.61037	0.0968800
$727$	−5.46587	−0.202718	−0.101359	−	0.994850i	$-0.532319\pi$
$727$	−5.46587	−0.202718	−0.101359	+	0.994850i	$0.532319\pi$
$728$	11.3032	0.418925
$729$	19.4579	0.720665
$730$	0	0
$731$	−60.2533	−2.22855
$732$	19.7122	0.728583
$733$	−2.90244	−0.107204	−0.0536021	−	0.998562i	$-0.517070\pi$
$733$	−2.90244	−0.107204	−0.0536021	+	0.998562i	$0.517070\pi$
$734$	−19.8552	−0.732867
$735$	0	0
$736$	−5.79987	−0.213786
$737$	−0.299936	−0.0110483
$738$	7.01113	0.258083
$739$	−2.56763	−0.0944519	−0.0472259	−	0.998884i	$-0.515038\pi$
$739$	−2.56763	−0.0944519	−0.0472259	+	0.998884i	$0.515038\pi$
$740$	0	0
$741$	−21.3963	−0.786013
$742$	3.53892	0.129918
$743$	12.9415	0.474777	0.237389	−	0.971415i	$-0.423708\pi$
$743$	12.9415	0.474777	0.237389	+	0.971415i	$0.423708\pi$
$744$	−29.5684	−1.08403
$745$	0	0
$746$	−7.08097	−0.259253
$747$	4.78882	0.175214
$748$	−39.5615	−1.44651
$749$	8.25087	0.301480
$750$	0	0
$751$	−28.3116	−1.03310	−0.516552	−	0.856256i	$-0.672785\pi$
$751$	−28.3116	−1.03310	−0.516552	+	0.856256i	$0.672785\pi$
$752$	−2.01909	−0.0736288
$753$	−10.8717	−0.396187
$754$	5.22233	0.190186
$755$	0	0
$756$	−8.15976	−0.296768
$757$	−44.1286	−1.60388	−0.801941	−	0.597403i	$-0.796199\pi$
$757$	−44.1286	−1.60388	−0.801941	+	0.597403i	$0.796199\pi$
$758$	3.75572	0.136414
$759$	−4.27519	−0.155180
$760$	0	0
$761$	−34.3844	−1.24643	−0.623217	−	0.782049i	$-0.714175\pi$
$761$	−34.3844	−1.24643	−0.623217	+	0.782049i	$0.714175\pi$
$762$	−8.61943	−0.312249
$763$	15.5344	0.562385
$764$	−14.0247	−0.507395
$765$	0	0
$766$	−19.4491	−0.702725
$767$	37.3239	1.34769
$768$	10.9759	0.396058
$769$	32.1250	1.15846	0.579229	−	0.815165i	$-0.303354\pi$
$769$	32.1250	1.15846	0.579229	+	0.815165i	$0.303354\pi$
$770$	0	0
$771$	11.8621	0.427202
$772$	−8.36518	−0.301070
$773$	−19.8771	−0.714930	−0.357465	−	0.933927i	$-0.616359\pi$
$773$	−19.8771	−0.714930	−0.357465	+	0.933927i	$0.616359\pi$
$774$	−10.4711	−0.376377
$775$	0	0
$776$	−30.5839	−1.09790
$777$	5.23042	0.187640
$778$	−16.0761	−0.576356
$779$	24.0380	0.861252
$780$	0	0
$781$	−41.7806	−1.49503
$782$	−4.67102	−0.167035
$783$	−8.69654	−0.310789
$784$	1.40331	0.0501182
$785$	0	0
$786$	−13.7501	−0.490449
$787$	39.2007	1.39736	0.698678	−	0.715436i	$-0.253772\pi$
$787$	39.2007	1.39736	0.698678	+	0.715436i	$0.253772\pi$
$788$	22.5201	0.802245
$789$	22.0214	0.783982
$790$	0	0
$791$	11.7793	0.418824
$792$	−15.8596	−0.563546
$793$	53.3772	1.89548
$794$	4.89403	0.173683
$795$	0	0
$796$	−16.0523	−0.568958
$797$	−53.6926	−1.90189	−0.950945	−	0.309361i	$-0.899885\pi$
$797$	−53.6926	−1.90189	−0.950945	+	0.309361i	$0.899885\pi$
$798$	3.13782	0.111077
$799$	−9.80813	−0.346987
$800$	0	0
$801$	−12.4209	−0.438872
$802$	9.47611	0.334613
$803$	10.2786	0.362725
$804$	−0.136485	−0.00481344
$805$	0	0
$806$	−34.7091	−1.22257
$807$	4.61035	0.162292
$808$	−25.1067	−0.883249
$809$	−40.5611	−1.42605	−0.713027	−	0.701137i	$-0.752676\pi$
$809$	−40.5611	−1.42605	−0.713027	+	0.701137i	$0.752676\pi$
$810$	0	0
$811$	53.9344	1.89389	0.946946	−	0.321392i	$-0.104151\pi$
$811$	53.9344	1.89389	0.946946	+	0.321392i	$0.104151\pi$
$812$	2.49644	0.0876080
$813$	−10.3165	−0.361817
$814$	12.0542	0.422498
$815$	0	0
$816$	−10.7852	−0.377558
$817$	−35.9008	−1.25601
$818$	5.20085	0.181844
$819$	−8.07805	−0.282270
$820$	0	0
$821$	−29.4903	−1.02922	−0.514610	−	0.857424i	$-0.672063\pi$
$821$	−29.4903	−1.02922	−0.514610	+	0.857424i	$0.672063\pi$
$822$	3.04514	0.106212
$823$	−3.44830	−0.120200	−0.0601001	−	0.998192i	$-0.519142\pi$
$823$	−3.44830	−0.120200	−0.0601001	+	0.998192i	$0.519142\pi$
$824$	18.5852	0.647445
$825$	0	0
$826$	−5.47364	−0.190452
$827$	−36.1262	−1.25623	−0.628115	−	0.778120i	$-0.716173\pi$
$827$	−36.1262	−1.25623	−0.628115	+	0.778120i	$0.716173\pi$
$828$	2.64602	0.0919556
$829$	34.0815	1.18370	0.591849	−	0.806049i	$-0.298398\pi$
$829$	34.0815	1.18370	0.591849	+	0.806049i	$0.298398\pi$
$830$	0	0
$831$	−32.9170	−1.14188
$832$	5.45528	0.189128
$833$	6.81684	0.236189
$834$	−0.166165	−0.00575382
$835$	0	0
$836$	−23.5720	−0.815255
$837$	57.7996	1.99785
$838$	15.8574	0.547785
$839$	45.7959	1.58105	0.790525	−	0.612429i	$-0.209808\pi$
$839$	45.7959	1.58105	0.790525	+	0.612429i	$0.209808\pi$
$840$	0	0
$841$	−26.3393	−0.908253
$842$	21.2522	0.732398
$843$	1.15593	0.0398123
$844$	38.0395	1.30937
$845$	0	0
$846$	−1.70451	−0.0586021
$847$	3.37895	0.116102
$848$	−7.24762	−0.248884
$849$	−32.7714	−1.12471
$850$	0	0
$851$	−4.63921	−0.159030
$852$	−19.0121	−0.651344
$853$	33.0902	1.13299	0.566494	−	0.824066i	$-0.308299\pi$
$853$	33.0902	1.13299	0.566494	+	0.824066i	$0.308299\pi$
$854$	−7.82789	−0.267865
$855$	0	0
$856$	19.9601	0.682221
$857$	−36.3888	−1.24302	−0.621509	−	0.783407i	$-0.713480\pi$
$857$	−36.3888	−1.24302	−0.621509	+	0.783407i	$0.713480\pi$
$858$	13.6875	0.467284
$859$	27.9870	0.954905	0.477452	−	0.878658i	$-0.341560\pi$
$859$	27.9870	0.954905	0.477452	+	0.878658i	$0.341560\pi$
$860$	0	0
$861$	−6.67244	−0.227396
$862$	−5.30937	−0.180838
$863$	−40.1991	−1.36839	−0.684196	−	0.729298i	$-0.739847\pi$
$863$	−40.1991	−1.36839	−0.684196	+	0.729298i	$0.739847\pi$
$864$	−30.9221	−1.05199
$865$	0	0
$866$	5.90157	0.200544
$867$	−33.2248	−1.12837
$868$	−16.5921	−0.563171
$869$	−32.9774	−1.11868
$870$	0	0
$871$	−0.369577	−0.0125226
$872$	37.5801	1.27262
$873$	21.8574	0.739760
$874$	−2.78314	−0.0941412
$875$	0	0
$876$	4.67725	0.158029
$877$	18.8448	0.636343	0.318172	−	0.948033i	$-0.396931\pi$
$877$	18.8448	0.636343	0.318172	+	0.948033i	$0.396931\pi$
$878$	−6.96072	−0.234913
$879$	31.2651	1.05455
$880$	0	0
$881$	−5.16443	−0.173994	−0.0869971	−	0.996209i	$-0.527727\pi$
$881$	−5.16443	−0.173994	−0.0869971	+	0.996209i	$0.527727\pi$
$882$	1.18466	0.0398897
$883$	−58.5168	−1.96925	−0.984624	−	0.174686i	$-0.944109\pi$
$883$	−58.5168	−1.96925	−0.984624	+	0.174686i	$0.944109\pi$
$884$	−48.7472	−1.63955
$885$	0	0
$886$	−4.52146	−0.151901
$887$	−6.12771	−0.205748	−0.102874	−	0.994694i	$-0.532804\pi$
$887$	−6.12771	−0.205748	−0.102874	+	0.994694i	$0.532804\pi$
$888$	12.6531	0.424612
$889$	−11.1573	−0.374202
$890$	0	0
$891$	−3.12567	−0.104714
$892$	−8.52039	−0.285284
$893$	−5.84399	−0.195562
$894$	8.74046	0.292325
$895$	0	0
$896$	10.7997	0.360793
$897$	−5.26783	−0.175888
$898$	9.01797	0.300934
$899$	−17.6835	−0.589779
$900$	0	0
$901$	−35.2067	−1.17290
$902$	−15.3775	−0.512014
$903$	9.96529	0.331624
$904$	28.4959	0.947759
$905$	0	0
$906$	2.92479	0.0971697
$907$	−25.4256	−0.844242	−0.422121	−	0.906540i	$-0.638714\pi$
$907$	−25.4256	−0.844242	−0.422121	+	0.906540i	$0.638714\pi$
$908$	24.3486	0.808038
$909$	17.9429	0.595129
$910$	0	0
$911$	34.5601	1.14503	0.572514	−	0.819895i	$-0.305968\pi$
$911$	34.5601	1.14503	0.572514	+	0.819895i	$0.305968\pi$
$912$	−6.42617	−0.212792
$913$	−10.5033	−0.347608
$914$	−8.28932	−0.274186
$915$	0	0
$916$	−11.1217	−0.367472
$917$	−17.7985	−0.587759
$918$	−24.9036	−0.821943
$919$	−50.7644	−1.67456	−0.837282	−	0.546772i	$-0.815856\pi$
$919$	−50.7644	−1.67456	−0.837282	+	0.546772i	$0.815856\pi$
$920$	0	0
$921$	−0.838011	−0.0276134
$922$	−19.1395	−0.630325
$923$	−51.4815	−1.69454
$924$	6.54308	0.215251
$925$	0	0
$926$	13.7889	0.453131
$927$	−13.2822	−0.436246
$928$	9.46048	0.310556
$929$	21.8129	0.715660	0.357830	−	0.933787i	$-0.383517\pi$
$929$	21.8129	0.715660	0.357830	+	0.933787i	$0.383517\pi$
$930$	0	0
$931$	4.06169	0.133116
$932$	5.20594	0.170526
$933$	−12.7799	−0.418396
$934$	2.99625	0.0980403
$935$	0	0
$936$	−19.5420	−0.638750
$937$	48.6228	1.58844	0.794218	−	0.607632i	$-0.207881\pi$
$937$	48.6228	1.58844	0.794218	+	0.607632i	$0.207881\pi$
$938$	0.0541993	0.00176967
$939$	24.0632	0.785272
$940$	0	0
$941$	24.4957	0.798538	0.399269	−	0.916834i	$-0.369264\pi$
$941$	24.4957	0.798538	0.399269	+	0.916834i	$0.369264\pi$
$942$	−13.1383	−0.428068
$943$	5.91824	0.192724
$944$	11.2099	0.364850
$945$	0	0
$946$	22.9663	0.746698
$947$	9.94918	0.323305	0.161653	−	0.986848i	$-0.448318\pi$
$947$	9.94918	0.323305	0.161653	+	0.986848i	$0.448318\pi$
$948$	−15.0062	−0.487380
$949$	12.6652	0.411129
$950$	0	0
$951$	−0.727474	−0.0235900
$952$	16.4909	0.534474
$953$	−9.38978	−0.304165	−0.152082	−	0.988368i	$-0.548598\pi$
$953$	−9.38978	−0.304165	−0.152082	+	0.988368i	$0.548598\pi$
$954$	−6.11840	−0.198090
$955$	0	0
$956$	16.0355	0.518625
$957$	6.97350	0.225421
$958$	16.1970	0.523301
$959$	3.94173	0.127285
$960$	0	0
$961$	86.5298	2.79128
$962$	14.8530	0.478879
$963$	−14.2648	−0.459677
$964$	31.5699	1.01680
$965$	0	0
$966$	0.772540	0.0248561
$967$	36.4082	1.17081	0.585404	−	0.810741i	$-0.300936\pi$
$967$	36.4082	1.17081	0.585404	+	0.810741i	$0.300936\pi$
$968$	8.17417	0.262728
$969$	−31.2163	−1.00281
$970$	0	0
$971$	22.2136	0.712869	0.356435	−	0.934320i	$-0.383992\pi$
$971$	22.2136	0.712869	0.356435	+	0.934320i	$0.383992\pi$
$972$	23.0570	0.739553
$973$	−0.215089	−0.00689544
$974$	0.990708	0.0317443
$975$	0	0
$976$	16.0313	0.513150
$977$	25.4082	0.812882	0.406441	−	0.913677i	$-0.366770\pi$
$977$	25.4082	0.812882	0.406441	+	0.913677i	$0.366770\pi$
$978$	−11.4116	−0.364901
$979$	27.2428	0.870683
$980$	0	0
$981$	−26.8573	−0.857488
$982$	−18.6649	−0.595622
$983$	43.0259	1.37231	0.686156	−	0.727454i	$-0.259297\pi$
$983$	43.0259	1.37231	0.686156	+	0.727454i	$0.259297\pi$
$984$	−16.1416	−0.514576
$985$	0	0
$986$	7.61916	0.242644
$987$	1.62217	0.0516341
$988$	−29.0451	−0.924048
$989$	−8.83890	−0.281061
$990$	0	0
$991$	21.7311	0.690310	0.345155	−	0.938546i	$-0.387826\pi$
$991$	21.7311	0.690310	0.345155	+	0.938546i	$0.387826\pi$
$992$	−62.8770	−1.99635
$993$	−32.2338	−1.02291
$994$	7.54989	0.239468
$995$	0	0
$996$	−4.77948	−0.151444
$997$	16.7822	0.531497	0.265748	−	0.964042i	$-0.414381\pi$
$997$	16.7822	0.531497	0.265748	+	0.964042i	$0.414381\pi$
$998$	4.35107	0.137731
$999$	−24.7341	−0.782551

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.be.1.8		21
5.2	odd	4		805.2.c.c.484.17	✓	42
5.3	odd	4		805.2.c.c.484.26	yes	42
5.4	even	2		4025.2.a.bd.1.14		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.c.c.484.17	✓	42	5.2	odd	4
805.2.c.c.484.26	yes	42	5.3	odd	4
4025.2.a.bd.1.14		21	5.4	even	2
4025.2.a.be.1.8		21	1.1	even	1	trivial

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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)

\(f(q)\)	\(=\)	\(q-0.685218 q^{2} -1.12744 q^{3} -1.53048 q^{4} +0.772540 q^{6} +1.00000 q^{7} +2.41915 q^{8} -1.72889 q^{9} +O(q^{10})\)	\(q-0.685218 q^{2} -1.12744 q^{3} -1.53048 q^{4} +0.772540 q^{6} +1.00000 q^{7} +2.41915 q^{8} -1.72889 q^{9} +3.79196 q^{11} +1.72551 q^{12} +4.67240 q^{13} -0.685218 q^{14} +1.40331 q^{16} +6.81684 q^{17} +1.18466 q^{18} +4.06169 q^{19} -1.12744 q^{21} -2.59832 q^{22} +1.00000 q^{23} -2.72743 q^{24} -3.20161 q^{26} +5.33152 q^{27} -1.53048 q^{28} -1.63116 q^{29} +10.8411 q^{31} -5.79987 q^{32} -4.27519 q^{33} -4.67102 q^{34} +2.64602 q^{36} -4.63921 q^{37} -2.78314 q^{38} -5.26783 q^{39} +5.91824 q^{41} +0.772540 q^{42} -8.83890 q^{43} -5.80350 q^{44} -0.685218 q^{46} -1.43881 q^{47} -1.58214 q^{48} +1.00000 q^{49} -7.68555 q^{51} -7.15099 q^{52} -5.16466 q^{53} -3.65325 q^{54} +2.41915 q^{56} -4.57930 q^{57} +1.11770 q^{58} +7.98817 q^{59} +11.4239 q^{61} -7.42853 q^{62} -1.72889 q^{63} +1.16756 q^{64} +2.92944 q^{66} -0.0790979 q^{67} -10.4330 q^{68} -1.12744 q^{69} -11.0182 q^{71} -4.18243 q^{72} +2.71064 q^{73} +3.17887 q^{74} -6.21632 q^{76} +3.79196 q^{77} +3.60961 q^{78} -8.69668 q^{79} -0.824288 q^{81} -4.05528 q^{82} -2.76989 q^{83} +1.72551 q^{84} +6.05657 q^{86} +1.83902 q^{87} +9.17330 q^{88} +7.18435 q^{89} +4.67240 q^{91} -1.53048 q^{92} -12.2227 q^{93} +0.985898 q^{94} +6.53898 q^{96} -12.6425 q^{97} -0.685218 q^{98} -6.55587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 30 q^{4} + 6 q^{6} + 21 q^{7} + 6 q^{8} + 30 q^{9}+O(q^{10}) \) 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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