LMFDB - Embedded newform 9898.2.a.t.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9898,2,Mod(1,9898)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9898, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9898.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9898 = 2 \cdot 7^{2} \cdot 101 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9898.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:	$79.0359279207$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.301909.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 5x^{2} + 6x - 1 $ x^5 - x^4 - 6x^3 + 5x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1414)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.151154$ of defining polynomial
Character	$\chi$	$=$	9898.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.601164 q^{3} +1.00000 q^{4} -1.03744 q^{5} +0.601164 q^{6} -1.00000 q^{8} -2.63860 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.601164 q^{3} +1.00000 q^{4} -1.03744 q^{5} +0.601164 q^{6} -1.00000 q^{8} -2.63860 q^{9} +1.03744 q^{10} -0.156813 q^{11} -0.601164 q^{12} +0.692032 q^{13} +0.623670 q^{15} +1.00000 q^{16} +7.16574 q^{17} +2.63860 q^{18} +3.66918 q^{19} -1.03744 q^{20} +0.156813 q^{22} -0.963758 q^{23} +0.601164 q^{24} -3.92372 q^{25} -0.692032 q^{26} +3.38972 q^{27} -2.22518 q^{29} -0.623670 q^{30} +2.92372 q^{31} -1.00000 q^{32} +0.0942705 q^{33} -7.16574 q^{34} -2.63860 q^{36} +8.78030 q^{37} -3.66918 q^{38} -0.416025 q^{39} +1.03744 q^{40} -0.578316 q^{41} -10.5360 q^{43} -0.156813 q^{44} +2.73739 q^{45} +0.963758 q^{46} +5.32152 q^{47} -0.601164 q^{48} +3.92372 q^{50} -4.30779 q^{51} +0.692032 q^{52} +4.61010 q^{53} -3.38972 q^{54} +0.162684 q^{55} -2.20578 q^{57} +2.22518 q^{58} +9.06802 q^{59} +0.623670 q^{60} -8.91546 q^{61} -2.92372 q^{62} +1.00000 q^{64} -0.717941 q^{65} -0.0942705 q^{66} +5.00086 q^{67} +7.16574 q^{68} +0.579377 q^{69} -8.27035 q^{71} +2.63860 q^{72} -4.38181 q^{73} -8.78030 q^{74} +2.35880 q^{75} +3.66918 q^{76} +0.416025 q^{78} +8.89176 q^{79} -1.03744 q^{80} +5.87803 q^{81} +0.578316 q^{82} -14.7641 q^{83} -7.43402 q^{85} +10.5360 q^{86} +1.33769 q^{87} +0.156813 q^{88} +1.51035 q^{89} -2.73739 q^{90} -0.963758 q^{92} -1.75764 q^{93} -5.32152 q^{94} -3.80655 q^{95} +0.601164 q^{96} +18.8369 q^{97} +0.413768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{8} + q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^8 + q^9	$ 5 q - 5 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{8} + q^{9} - 6 q^{10} - 5 q^{11} - q^{13} - 4 q^{15} + 5 q^{16} + 12 q^{17} - q^{18} + q^{19} + 6 q^{20} + 5 q^{22} - 4 q^{23} + 3 q^{25} + q^{26} + 12 q^{27} - 18 q^{29} + 4 q^{30} - 8 q^{31} - 5 q^{32} - 13 q^{33} - 12 q^{34} + q^{36} + 5 q^{37} - q^{38} - 14 q^{39} - 6 q^{40} + 13 q^{41} + q^{43} - 5 q^{44} + 18 q^{45} + 4 q^{46} - 3 q^{50} + 10 q^{51} - q^{52} - 8 q^{53} - 12 q^{54} + 6 q^{55} - 9 q^{57} + 18 q^{58} + 31 q^{59} - 4 q^{60} + 15 q^{61} + 8 q^{62} + 5 q^{64} + 17 q^{65} + 13 q^{66} - 4 q^{67} + 12 q^{68} + 15 q^{69} - 21 q^{71} - q^{72} + 3 q^{73} - 5 q^{74} - 7 q^{75} + q^{76} + 14 q^{78} + q^{79} + 6 q^{80} - 19 q^{81} - 13 q^{82} + 22 q^{83} - 13 q^{85} - q^{86} + 37 q^{87} + 5 q^{88} + 22 q^{89} - 18 q^{90} - 4 q^{92} + 7 q^{93} + 19 q^{95} - 4 q^{97} - 2 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^8 + q^9 - 6 * q^10 - 5 * q^11 - q^13 - 4 * q^15 + 5 * q^16 + 12 * q^17 - q^18 + q^19 + 6 * q^20 + 5 * q^22 - 4 * q^23 + 3 * q^25 + q^26 + 12 * q^27 - 18 * q^29 + 4 * q^30 - 8 * q^31 - 5 * q^32 - 13 * q^33 - 12 * q^34 + q^36 + 5 * q^37 - q^38 - 14 * q^39 - 6 * q^40 + 13 * q^41 + q^43 - 5 * q^44 + 18 * q^45 + 4 * q^46 - 3 * q^50 + 10 * q^51 - q^52 - 8 * q^53 - 12 * q^54 + 6 * q^55 - 9 * q^57 + 18 * q^58 + 31 * q^59 - 4 * q^60 + 15 * q^61 + 8 * q^62 + 5 * q^64 + 17 * q^65 + 13 * q^66 - 4 * q^67 + 12 * q^68 + 15 * q^69 - 21 * q^71 - q^72 + 3 * q^73 - 5 * q^74 - 7 * q^75 + q^76 + 14 * q^78 + q^79 + 6 * q^80 - 19 * q^81 - 13 * q^82 + 22 * q^83 - 13 * q^85 - q^86 + 37 * q^87 + 5 * q^88 + 22 * q^89 - 18 * q^90 - 4 * q^92 + 7 * q^93 + 19 * q^95 - 4 * q^97 - 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.601164	−0.347082	−0.173541	−	0.984827i	$-0.555521\pi$
$3$	−0.601164	−0.347082	−0.173541	+	0.984827i	$0.555521\pi$
$4$	1.00000	0.500000
$5$	−1.03744	−0.463956	−0.231978	−	0.972721i	$-0.574520\pi$
$5$	−1.03744	−0.463956	−0.231978	+	0.972721i	$0.574520\pi$
$6$	0.601164	0.245424
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	−2.63860	−0.879534
$10$	1.03744	0.328067
$11$	−0.156813	−0.0472810	−0.0236405	−	0.999721i	$-0.507526\pi$
$11$	−0.156813	−0.0472810	−0.0236405	+	0.999721i	$0.507526\pi$
$12$	−0.601164	−0.173541
$13$	0.692032	0.191935	0.0959676	−	0.995384i	$-0.469405\pi$
$13$	0.692032	0.191935	0.0959676	+	0.995384i	$0.469405\pi$
$14$	0	0
$15$	0.623670	0.161031
$16$	1.00000	0.250000
$17$	7.16574	1.73795	0.868974	−	0.494857i	$-0.164780\pi$
$17$	7.16574	1.73795	0.868974	+	0.494857i	$0.164780\pi$
$18$	2.63860	0.621924
$19$	3.66918	0.841769	0.420884	−	0.907114i	$-0.361720\pi$
$19$	3.66918	0.841769	0.420884	+	0.907114i	$0.361720\pi$
$20$	−1.03744	−0.231978
$21$	0	0
$22$	0.156813	0.0334327
$23$	−0.963758	−0.200958	−0.100479	−	0.994939i	$-0.532037\pi$
$23$	−0.963758	−0.200958	−0.100479	+	0.994939i	$0.532037\pi$
$24$	0.601164	0.122712
$25$	−3.92372	−0.784744
$26$	−0.692032	−0.135719
$27$	3.38972	0.652353
$28$	0	0
$29$	−2.22518	−0.413205	−0.206602	−	0.978425i	$-0.566241\pi$
$29$	−2.22518	−0.413205	−0.206602	+	0.978425i	$0.566241\pi$
$30$	−0.623670	−0.113866
$31$	2.92372	0.525116	0.262558	−	0.964916i	$-0.415434\pi$
$31$	2.92372	0.525116	0.262558	+	0.964916i	$0.415434\pi$
$32$	−1.00000	−0.176777
$33$	0.0942705	0.0164104
$34$	−7.16574	−1.22892
$35$	0	0
$36$	−2.63860	−0.439767
$37$	8.78030	1.44347	0.721736	−	0.692168i	$-0.243344\pi$
$37$	8.78030	1.44347	0.721736	+	0.692168i	$0.243344\pi$
$38$	−3.66918	−0.595220
$39$	−0.416025	−0.0666173
$40$	1.03744	0.164033
$41$	−0.578316	−0.0903178	−0.0451589	−	0.998980i	$-0.514379\pi$
$41$	−0.578316	−0.0903178	−0.0451589	+	0.998980i	$0.514379\pi$
$42$	0	0
$43$	−10.5360	−1.60673	−0.803364	−	0.595488i	$-0.796959\pi$
$43$	−10.5360	−1.60673	−0.803364	+	0.595488i	$0.796959\pi$
$44$	−0.156813	−0.0236405
$45$	2.73739	0.408065
$46$	0.963758	0.142098
$47$	5.32152	0.776224	0.388112	−	0.921612i	$-0.373127\pi$
$47$	5.32152	0.776224	0.388112	+	0.921612i	$0.373127\pi$
$48$	−0.601164	−0.0867705
$49$	0	0
$50$	3.92372	0.554898
$51$	−4.30779	−0.603211
$52$	0.692032	0.0959676
$53$	4.61010	0.633245	0.316623	−	0.948552i	$-0.397451\pi$
$53$	4.61010	0.633245	0.316623	+	0.948552i	$0.397451\pi$
$54$	−3.38972	−0.461283
$55$	0.162684	0.0219363
$56$	0	0
$57$	−2.20578	−0.292163
$58$	2.22518	0.292180
$59$	9.06802	1.18056	0.590278	−	0.807200i	$-0.299018\pi$
$59$	9.06802	1.18056	0.590278	+	0.807200i	$0.299018\pi$
$60$	0.623670	0.0805155
$61$	−8.91546	−1.14151	−0.570754	−	0.821121i	$-0.693349\pi$
$61$	−8.91546	−1.14151	−0.570754	+	0.821121i	$0.693349\pi$
$62$	−2.92372	−0.371313
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.717941	−0.0890496
$66$	−0.0942705	−0.0116039
$67$	5.00086	0.610952	0.305476	−	0.952200i	$-0.401184\pi$
$67$	5.00086	0.610952	0.305476	+	0.952200i	$0.401184\pi$
$68$	7.16574	0.868974
$69$	0.579377	0.0697488
$70$	0	0
$71$	−8.27035	−0.981510	−0.490755	−	0.871298i	$-0.663279\pi$
$71$	−8.27035	−0.981510	−0.490755	+	0.871298i	$0.663279\pi$
$72$	2.63860	0.310962
$73$	−4.38181	−0.512852	−0.256426	−	0.966564i	$-0.582545\pi$
$73$	−4.38181	−0.512852	−0.256426	+	0.966564i	$0.582545\pi$
$74$	−8.78030	−1.02069
$75$	2.35880	0.272371
$76$	3.66918	0.420884
$77$	0	0
$78$	0.416025	0.0471055
$79$	8.89176	1.00040	0.500201	−	0.865910i	$-0.333260\pi$
$79$	8.89176	1.00040	0.500201	+	0.865910i	$0.333260\pi$
$80$	−1.03744	−0.115989
$81$	5.87803	0.653114
$82$	0.578316	0.0638643
$83$	−14.7641	−1.62057	−0.810287	−	0.586033i	$-0.800689\pi$
$83$	−14.7641	−1.62057	−0.810287	+	0.586033i	$0.800689\pi$
$84$	0	0
$85$	−7.43402	−0.806332
$86$	10.5360	1.13613
$87$	1.33769	0.143416
$88$	0.156813	0.0167164
$89$	1.51035	0.160096	0.0800482	−	0.996791i	$-0.474493\pi$
$89$	1.51035	0.160096	0.0800482	+	0.996791i	$0.474493\pi$
$90$	−2.73739	−0.288546
$91$	0	0
$92$	−0.963758	−0.100479
$93$	−1.75764	−0.182258
$94$	−5.32152	−0.548873
$95$	−3.80655	−0.390544
$96$	0.601164	0.0613560
$97$	18.8369	1.91260	0.956300	−	0.292387i	$-0.0944494\pi$
$97$	18.8369	1.91260	0.956300	+	0.292387i	$0.0944494\pi$
$98$	0	0
$99$	0.413768	0.0415852
$100$	−3.92372	−0.392372
$101$	−1.00000	−0.0995037
$101$	−1.00000	−0.0995037
$102$	4.30779	0.426534
$103$	−17.6777	−1.74184	−0.870919	−	0.491427i	$-0.836476\pi$
$103$	−17.6777	−1.74184	−0.870919	+	0.491427i	$0.836476\pi$
$104$	−0.692032	−0.0678594
$105$	0	0
$106$	−4.61010	−0.447772
$107$	0.772909	0.0747199	0.0373600	−	0.999302i	$-0.488105\pi$
$107$	0.772909	0.0747199	0.0373600	+	0.999302i	$0.488105\pi$
$108$	3.38972	0.326176
$109$	−7.92032	−0.758629	−0.379315	−	0.925268i	$-0.623840\pi$
$109$	−7.92032	−0.758629	−0.379315	+	0.925268i	$0.623840\pi$
$110$	−0.162684	−0.0155113
$111$	−5.27840	−0.501004
$112$	0	0
$113$	−14.9428	−1.40570	−0.702849	−	0.711339i	$-0.748089\pi$
$113$	−14.9428	−1.40570	−0.702849	+	0.711339i	$0.748089\pi$
$114$	2.20578	0.206590
$115$	0.999840	0.0932355
$116$	−2.22518	−0.206602
$117$	−1.82600	−0.168814
$118$	−9.06802	−0.834779
$119$	0	0
$120$	−0.623670	−0.0569331
$121$	−10.9754	−0.997765
$122$	8.91546	0.807168
$123$	0.347663	0.0313477
$124$	2.92372	0.262558
$125$	9.25781	0.828044
$126$	0	0
$127$	2.46000	0.218290	0.109145	−	0.994026i	$-0.465189\pi$
$127$	2.46000	0.218290	0.109145	+	0.994026i	$0.465189\pi$
$128$	−1.00000	−0.0883883
$129$	6.33388	0.557667
$130$	0.717941	0.0629676
$131$	11.5215	1.00664	0.503318	−	0.864101i	$-0.332112\pi$
$131$	11.5215	1.00664	0.503318	+	0.864101i	$0.332112\pi$
$132$	0.0942705	0.00820519
$133$	0	0
$134$	−5.00086	−0.432008
$135$	−3.51663	−0.302663
$136$	−7.16574	−0.614458
$137$	−14.3939	−1.22975	−0.614875	−	0.788625i	$-0.710793\pi$
$137$	−14.3939	−1.22975	−0.614875	+	0.788625i	$0.710793\pi$
$138$	−0.579377	−0.0493198
$139$	−4.17348	−0.353990	−0.176995	−	0.984212i	$-0.556638\pi$
$139$	−4.17348	−0.353990	−0.176995	+	0.984212i	$0.556638\pi$
$140$	0	0
$141$	−3.19911	−0.269413
$142$	8.27035	0.694032
$143$	−0.108520	−0.00907489
$144$	−2.63860	−0.219884
$145$	2.30848	0.191709
$146$	4.38181	0.362641
$147$	0	0
$148$	8.78030	0.721736
$149$	15.5850	1.27677	0.638386	−	0.769716i	$-0.279602\pi$
$149$	15.5850	1.27677	0.638386	+	0.769716i	$0.279602\pi$
$150$	−2.35880	−0.192595
$151$	13.5972	1.10652	0.553262	−	0.833007i	$-0.313383\pi$
$151$	13.5972	1.10652	0.553262	+	0.833007i	$0.313383\pi$
$152$	−3.66918	−0.297610
$153$	−18.9075	−1.52858
$154$	0	0
$155$	−3.03318	−0.243631
$156$	−0.416025	−0.0333086
$157$	−12.1293	−0.968021	−0.484011	−	0.875062i	$-0.660820\pi$
$157$	−12.1293	−0.968021	−0.484011	+	0.875062i	$0.660820\pi$
$158$	−8.89176	−0.707391
$159$	−2.77142	−0.219788
$160$	1.03744	0.0820167
$161$	0	0
$162$	−5.87803	−0.461821
$163$	−12.7050	−0.995136	−0.497568	−	0.867425i	$-0.665773\pi$
$163$	−12.7050	−0.995136	−0.497568	+	0.867425i	$0.665773\pi$
$164$	−0.578316	−0.0451589
$165$	−0.0977998	−0.00761370
$166$	14.7641	1.14592
$167$	12.9972	1.00575	0.502876	−	0.864359i	$-0.332275\pi$
$167$	12.9972	1.00575	0.502876	+	0.864359i	$0.332275\pi$
$168$	0	0
$169$	−12.5211	−0.963161
$170$	7.43402	0.570163
$171$	−9.68152	−0.740364
$172$	−10.5360	−0.803364
$173$	5.70883	0.434034	0.217017	−	0.976168i	$-0.430367\pi$
$173$	5.70883	0.434034	0.217017	+	0.976168i	$0.430367\pi$
$174$	−1.33769	−0.101410
$175$	0	0
$176$	−0.156813	−0.0118202
$177$	−5.45137	−0.409750
$178$	−1.51035	−0.113205
$179$	−13.1518	−0.983014	−0.491507	−	0.870874i	$-0.663554\pi$
$179$	−13.1518	−0.983014	−0.491507	+	0.870874i	$0.663554\pi$
$180$	2.73739	0.204033
$181$	16.3129	1.21253	0.606265	−	0.795263i	$-0.292667\pi$
$181$	16.3129	1.21253	0.606265	+	0.795263i	$0.292667\pi$
$182$	0	0
$183$	5.35966	0.396197
$184$	0.963758	0.0710492
$185$	−9.10902	−0.669709
$186$	1.75764	0.128876
$187$	−1.12368	−0.0821719
$188$	5.32152	0.388112
$189$	0	0
$190$	3.80655	0.276156
$191$	14.9452	1.08139	0.540697	−	0.841217i	$-0.318160\pi$
$191$	14.9452	1.08139	0.540697	+	0.841217i	$0.318160\pi$
$192$	−0.601164	−0.0433853
$193$	−14.7074	−1.05866	−0.529332	−	0.848415i	$-0.677557\pi$
$193$	−14.7074	−1.05866	−0.529332	+	0.848415i	$0.677557\pi$
$194$	−18.8369	−1.35241
$195$	0.431600	0.0309075
$196$	0	0
$197$	−5.49552	−0.391540	−0.195770	−	0.980650i	$-0.562721\pi$
$197$	−5.49552	−0.391540	−0.195770	+	0.980650i	$0.562721\pi$
$198$	−0.413768	−0.0294052
$199$	17.9898	1.27527	0.637633	−	0.770341i	$-0.279914\pi$
$199$	17.9898	1.27527	0.637633	+	0.770341i	$0.279914\pi$
$200$	3.92372	0.277449
$201$	−3.00633	−0.212050
$202$	1.00000	0.0703598
$203$	0	0
$204$	−4.30779	−0.301605
$205$	0.599967	0.0419035
$206$	17.6777	1.23167
$207$	2.54297	0.176749
$208$	0.692032	0.0479838
$209$	−0.575377	−0.0397997
$210$	0	0
$211$	28.1674	1.93912	0.969561	−	0.244849i	$-0.0787383\pi$
$211$	28.1674	1.93912	0.969561	+	0.244849i	$0.0787383\pi$
$212$	4.61010	0.316623
$213$	4.97183	0.340664
$214$	−0.772909	−0.0528350
$215$	10.9305	0.745452
$216$	−3.38972	−0.230641
$217$	0	0
$218$	7.92032	0.536432
$219$	2.63418	0.178002
$220$	0.162684	0.0109682
$221$	4.95893	0.333574
$222$	5.27840	0.354263
$223$	−27.3041	−1.82842	−0.914210	−	0.405241i	$-0.867188\pi$
$223$	−27.3041	−1.82842	−0.914210	+	0.405241i	$0.867188\pi$
$224$	0	0
$225$	10.3531	0.690209
$226$	14.9428	0.993979
$227$	1.82997	0.121460	0.0607298	−	0.998154i	$-0.480657\pi$
$227$	1.82997	0.121460	0.0607298	+	0.998154i	$0.480657\pi$
$228$	−2.20578	−0.146081
$229$	−3.55552	−0.234955	−0.117478	−	0.993076i	$-0.537481\pi$
$229$	−3.55552	−0.234955	−0.117478	+	0.993076i	$0.537481\pi$
$230$	−0.999840	−0.0659275
$231$	0	0
$232$	2.22518	0.146090
$233$	28.6071	1.87411	0.937057	−	0.349177i	$-0.113539\pi$
$233$	28.6071	1.87411	0.937057	+	0.349177i	$0.113539\pi$
$234$	1.82600	0.119369
$235$	−5.52075	−0.360134
$236$	9.06802	0.590278
$237$	−5.34541	−0.347221
$238$	0	0
$239$	−12.0472	−0.779267	−0.389633	−	0.920970i	$-0.627398\pi$
$239$	−12.0472	−0.779267	−0.389633	+	0.920970i	$0.627398\pi$
$240$	0.623670	0.0402577
$241$	27.6898	1.78365	0.891827	−	0.452376i	$-0.149423\pi$
$241$	27.6898	1.78365	0.891827	+	0.452376i	$0.149423\pi$
$242$	10.9754	0.705526
$243$	−13.7028	−0.879037
$244$	−8.91546	−0.570754
$245$	0	0
$246$	−0.347663	−0.0221662
$247$	2.53919	0.161565
$248$	−2.92372	−0.185657
$249$	8.87566	0.562472
$250$	−9.25781	−0.585515
$251$	−20.7873	−1.31208	−0.656042	−	0.754724i	$-0.727771\pi$
$251$	−20.7873	−1.31208	−0.656042	+	0.754724i	$0.727771\pi$
$252$	0	0
$253$	0.151130	0.00950147
$254$	−2.46000	−0.154354
$255$	4.46906	0.279864
$256$	1.00000	0.0625000
$257$	28.8387	1.79891	0.899453	−	0.437017i	$-0.143965\pi$
$257$	28.8387	1.79891	0.899453	+	0.437017i	$0.143965\pi$
$258$	−6.33388	−0.394330
$259$	0	0
$260$	−0.717941	−0.0445248
$261$	5.87135	0.363428
$262$	−11.5215	−0.711800
$263$	15.1701	0.935426	0.467713	−	0.883881i	$-0.345078\pi$
$263$	15.1701	0.935426	0.467713	+	0.883881i	$0.345078\pi$
$264$	−0.0942705	−0.00580195
$265$	−4.78269	−0.293798
$266$	0	0
$267$	−0.907966	−0.0555666
$268$	5.00086	0.305476
$269$	−0.958955	−0.0584685	−0.0292343	−	0.999573i	$-0.509307\pi$
$269$	−0.958955	−0.0584685	−0.0292343	+	0.999573i	$0.509307\pi$
$270$	3.51663	0.214015
$271$	−22.0305	−1.33826	−0.669130	−	0.743145i	$-0.733333\pi$
$271$	−22.0305	−1.33826	−0.669130	+	0.743145i	$0.733333\pi$
$272$	7.16574	0.434487
$273$	0	0
$274$	14.3939	0.869564
$275$	0.615292	0.0371035
$276$	0.579377	0.0348744
$277$	18.0065	1.08191	0.540953	−	0.841053i	$-0.318064\pi$
$277$	18.0065	1.08191	0.540953	+	0.841053i	$0.318064\pi$
$278$	4.17348	0.250309
$279$	−7.71454	−0.461857
$280$	0	0
$281$	−24.0836	−1.43671	−0.718354	−	0.695678i	$-0.755104\pi$
$281$	−24.0836	−1.43671	−0.718354	+	0.695678i	$0.755104\pi$
$282$	3.19911	0.190504
$283$	16.2342	0.965025	0.482512	−	0.875889i	$-0.339724\pi$
$283$	16.2342	0.965025	0.482512	+	0.875889i	$0.339724\pi$
$284$	−8.27035	−0.490755
$285$	2.28836	0.135551
$286$	0.108520	0.00641691
$287$	0	0
$288$	2.63860	0.155481
$289$	34.3479	2.02046
$290$	−2.30848	−0.135559
$291$	−11.3241	−0.663829
$292$	−4.38181	−0.256426
$293$	16.4833	0.962963	0.481481	−	0.876456i	$-0.340099\pi$
$293$	16.4833	0.962963	0.481481	+	0.876456i	$0.340099\pi$
$294$	0	0
$295$	−9.40751	−0.547726
$296$	−8.78030	−0.510345
$297$	−0.531554	−0.0308439
$298$	−15.5850	−0.902814
$299$	−0.666952	−0.0385708
$300$	2.35880	0.136185
$301$	0	0
$302$	−13.5972	−0.782430
$303$	0.601164	0.0345360
$304$	3.66918	0.210442
$305$	9.24924	0.529610
$306$	18.9075	1.08087
$307$	−23.6040	−1.34715	−0.673577	−	0.739117i	$-0.735243\pi$
$307$	−23.6040	−1.34715	−0.673577	+	0.739117i	$0.735243\pi$
$308$	0	0
$309$	10.6272	0.604561
$310$	3.03318	0.172273
$311$	25.1019	1.42340	0.711698	−	0.702486i	$-0.247927\pi$
$311$	25.1019	1.42340	0.711698	+	0.702486i	$0.247927\pi$
$312$	0.416025	0.0235528
$313$	−17.2675	−0.976019	−0.488010	−	0.872838i	$-0.662277\pi$
$313$	−17.2675	−0.976019	−0.488010	+	0.872838i	$0.662277\pi$
$314$	12.1293	0.684494
$315$	0	0
$316$	8.89176	0.500201
$317$	−1.31329	−0.0737615	−0.0368807	−	0.999320i	$-0.511742\pi$
$317$	−1.31329	−0.0737615	−0.0368807	+	0.999320i	$0.511742\pi$
$318$	2.77142	0.155414
$319$	0.348937	0.0195367
$320$	−1.03744	−0.0579946
$321$	−0.464645	−0.0259339
$322$	0	0
$323$	26.2924	1.46295
$324$	5.87803	0.326557
$325$	−2.71534	−0.150620
$326$	12.7050	0.703667
$327$	4.76141	0.263307
$328$	0.578316	0.0319322
$329$	0	0
$330$	0.0977998	0.00538370
$331$	17.3189	0.951934	0.475967	−	0.879463i	$-0.342098\pi$
$331$	17.3189	0.951934	0.475967	+	0.879463i	$0.342098\pi$
$332$	−14.7641	−0.810287
$333$	−23.1677	−1.26958
$334$	−12.9972	−0.711173
$335$	−5.18808	−0.283455
$336$	0	0
$337$	35.1621	1.91540	0.957701	−	0.287766i	$-0.0929124\pi$
$337$	35.1621	1.91540	0.957701	+	0.287766i	$0.0929124\pi$
$338$	12.5211	0.681058
$339$	8.98306	0.487893
$340$	−7.43402	−0.403166
$341$	−0.458478	−0.0248280
$342$	9.68152	0.523517
$343$	0	0
$344$	10.5360	0.568064
$345$	−0.601067	−0.0323604
$346$	−5.70883	−0.306909
$347$	23.3211	1.25194	0.625972	−	0.779846i	$-0.284702\pi$
$347$	23.3211	1.25194	0.625972	+	0.779846i	$0.284702\pi$
$348$	1.33769	0.0717080
$349$	−1.13757	−0.0608929	−0.0304464	−	0.999536i	$-0.509693\pi$
$349$	−1.13757	−0.0608929	−0.0304464	+	0.999536i	$0.509693\pi$
$350$	0	0
$351$	2.34580	0.125209
$352$	0.156813	0.00835818
$353$	7.22564	0.384582	0.192291	−	0.981338i	$-0.438408\pi$
$353$	7.22564	0.384582	0.192291	+	0.981338i	$0.438408\pi$
$354$	5.45137	0.289737
$355$	8.57998	0.455378
$356$	1.51035	0.0800482
$357$	0	0
$358$	13.1518	0.695096
$359$	8.40766	0.443739	0.221870	−	0.975076i	$-0.428784\pi$
$359$	8.40766	0.443739	0.221870	+	0.975076i	$0.428784\pi$
$360$	−2.73739	−0.144273
$361$	−5.53708	−0.291425
$362$	−16.3129	−0.857388
$363$	6.59802	0.346306
$364$	0	0
$365$	4.54585	0.237941
$366$	−5.35966	−0.280154
$367$	−11.8397	−0.618028	−0.309014	−	0.951058i	$-0.599999\pi$
$367$	−11.8397	−0.618028	−0.309014	+	0.951058i	$0.599999\pi$
$368$	−0.963758	−0.0502394
$369$	1.52595	0.0794376
$370$	9.10902	0.473555
$371$	0	0
$372$	−1.75764	−0.0911292
$373$	−25.2380	−1.30678	−0.653388	−	0.757023i	$-0.726653\pi$
$373$	−25.2380	−1.30678	−0.653388	+	0.757023i	$0.726653\pi$
$374$	1.12368	0.0581043
$375$	−5.56546	−0.287399
$376$	−5.32152	−0.274437
$377$	−1.53989	−0.0793085
$378$	0	0
$379$	−11.8038	−0.606322	−0.303161	−	0.952939i	$-0.598042\pi$
$379$	−11.8038	−0.606322	−0.303161	+	0.952939i	$0.598042\pi$
$380$	−3.80655	−0.195272
$381$	−1.47886	−0.0757645
$382$	−14.9452	−0.764661
$383$	2.84184	0.145211	0.0726055	−	0.997361i	$-0.476869\pi$
$383$	2.84184	0.145211	0.0726055	+	0.997361i	$0.476869\pi$
$384$	0.601164	0.0306780
$385$	0	0
$386$	14.7074	0.748588
$387$	27.8004	1.41317
$388$	18.8369	0.956300
$389$	−8.55049	−0.433527	−0.216764	−	0.976224i	$-0.569550\pi$
$389$	−8.55049	−0.433527	−0.216764	+	0.976224i	$0.569550\pi$
$390$	−0.431600	−0.0218549
$391$	−6.90605	−0.349254
$392$	0	0
$393$	−6.92630	−0.349386
$394$	5.49552	0.276860
$395$	−9.22465	−0.464143
$396$	0.413768	0.0207926
$397$	5.04110	0.253005	0.126503	−	0.991966i	$-0.459625\pi$
$397$	5.04110	0.253005	0.126503	+	0.991966i	$0.459625\pi$
$398$	−17.9898	−0.901749
$399$	0	0
$400$	−3.92372	−0.196186
$401$	13.2401	0.661180	0.330590	−	0.943774i	$-0.392752\pi$
$401$	13.2401	0.661180	0.330590	+	0.943774i	$0.392752\pi$
$402$	3.00633	0.149942
$403$	2.02331	0.100788
$404$	−1.00000	−0.0497519
$405$	−6.09809	−0.303016
$406$	0	0
$407$	−1.37687	−0.0682488
$408$	4.30779	0.213267
$409$	−2.04364	−0.101052	−0.0505258	−	0.998723i	$-0.516090\pi$
$409$	−2.04364	−0.101052	−0.0505258	+	0.998723i	$0.516090\pi$
$410$	−0.599967	−0.0296303
$411$	8.65306	0.426824
$412$	−17.6777	−0.870919
$413$	0	0
$414$	−2.54297	−0.124980
$415$	15.3169	0.751876
$416$	−0.692032	−0.0339297
$417$	2.50895	0.122864
$418$	0.575377	0.0281426
$419$	31.1171	1.52017	0.760085	−	0.649823i	$-0.225157\pi$
$419$	31.1171	1.52017	0.760085	+	0.649823i	$0.225157\pi$
$420$	0	0
$421$	26.0933	1.27171	0.635856	−	0.771808i	$-0.280647\pi$
$421$	26.0933	1.27171	0.635856	+	0.771808i	$0.280647\pi$
$422$	−28.1674	−1.37117
$423$	−14.0414	−0.682715
$424$	−4.61010	−0.223886
$425$	−28.1164	−1.36385
$426$	−4.97183	−0.240886
$427$	0	0
$428$	0.772909	0.0373600
$429$	0.0652382	0.00314973
$430$	−10.9305	−0.527114
$431$	3.11726	0.150153	0.0750767	−	0.997178i	$-0.476080\pi$
$431$	3.11726	0.150153	0.0750767	+	0.997178i	$0.476080\pi$
$432$	3.38972	0.163088
$433$	−6.52478	−0.313561	−0.156780	−	0.987633i	$-0.550111\pi$
$433$	−6.52478	−0.313561	−0.156780	+	0.987633i	$0.550111\pi$
$434$	0	0
$435$	−1.38778	−0.0665388
$436$	−7.92032	−0.379315
$437$	−3.53621	−0.169160
$438$	−2.63418	−0.125866
$439$	−19.3256	−0.922359	−0.461180	−	0.887307i	$-0.652574\pi$
$439$	−19.3256	−0.922359	−0.461180	+	0.887307i	$0.652574\pi$
$440$	−0.162684	−0.00775566
$441$	0	0
$442$	−4.95893	−0.235872
$443$	15.0917	0.717028	0.358514	−	0.933524i	$-0.383284\pi$
$443$	15.0917	0.717028	0.358514	+	0.933524i	$0.383284\pi$
$444$	−5.27840	−0.250502
$445$	−1.56689	−0.0742778
$446$	27.3041	1.29289
$447$	−9.36913	−0.443145
$448$	0	0
$449$	9.90581	0.467484	0.233742	−	0.972299i	$-0.424903\pi$
$449$	9.90581	0.467484	0.233742	+	0.972299i	$0.424903\pi$
$450$	−10.3531	−0.488052
$451$	0.0906877	0.00427032
$452$	−14.9428	−0.702849
$453$	−8.17414	−0.384055
$454$	−1.82997	−0.0858849
$455$	0	0
$456$	2.20578	0.103295
$457$	5.07758	0.237519	0.118760	−	0.992923i	$-0.462108\pi$
$457$	5.07758	0.237519	0.118760	+	0.992923i	$0.462108\pi$
$458$	3.55552	0.166139
$459$	24.2899	1.13376
$460$	0.999840	0.0466178
$461$	−32.4161	−1.50977	−0.754884	−	0.655858i	$-0.772307\pi$
$461$	−32.4161	−1.50977	−0.754884	+	0.655858i	$0.772307\pi$
$462$	0	0
$463$	−6.74008	−0.313238	−0.156619	−	0.987659i	$-0.550059\pi$
$463$	−6.74008	−0.313238	−0.156619	+	0.987659i	$0.550059\pi$
$464$	−2.22518	−0.103301
$465$	1.82344	0.0845599
$466$	−28.6071	−1.32520
$467$	−0.820155	−0.0379522	−0.0189761	−	0.999820i	$-0.506041\pi$
$467$	−0.820155	−0.0379522	−0.0189761	+	0.999820i	$0.506041\pi$
$468$	−1.82600	−0.0844068
$469$	0	0
$470$	5.52075	0.254653
$471$	7.29168	0.335983
$472$	−9.06802	−0.417389
$473$	1.65219	0.0759677
$474$	5.34541	0.245523
$475$	−14.3969	−0.660573
$476$	0	0
$477$	−12.1642	−0.556961
$478$	12.0472	0.551025
$479$	38.0623	1.73911	0.869555	−	0.493836i	$-0.164406\pi$
$479$	38.0623	1.73911	0.869555	+	0.493836i	$0.164406\pi$
$480$	−0.623670	−0.0284665
$481$	6.07625	0.277053
$482$	−27.6898	−1.26123
$483$	0	0
$484$	−10.9754	−0.498882
$485$	−19.5422	−0.887363
$486$	13.7028	0.621573
$487$	9.37994	0.425046	0.212523	−	0.977156i	$-0.431832\pi$
$487$	9.37994	0.425046	0.212523	+	0.977156i	$0.431832\pi$
$488$	8.91546	0.403584
$489$	7.63781	0.345394
$490$	0	0
$491$	−19.9754	−0.901478	−0.450739	−	0.892656i	$-0.648839\pi$
$491$	−19.9754	−0.901478	−0.450739	+	0.892656i	$0.648839\pi$
$492$	0.347663	0.0156738
$493$	−15.9450	−0.718128
$494$	−2.53919	−0.114244
$495$	−0.429259	−0.0192937
$496$	2.92372	0.131279
$497$	0	0
$498$	−8.87566	−0.397728
$499$	10.9983	0.492353	0.246177	−	0.969225i	$-0.420826\pi$
$499$	10.9983	0.492353	0.246177	+	0.969225i	$0.420826\pi$
$500$	9.25781	0.414022
$501$	−7.81343	−0.349078
$502$	20.7873	0.927783
$503$	−10.7741	−0.480395	−0.240197	−	0.970724i	$-0.577212\pi$
$503$	−10.7741	−0.480395	−0.240197	+	0.970724i	$0.577212\pi$
$504$	0	0
$505$	1.03744	0.0461654
$506$	−0.151130	−0.00671855
$507$	7.52723	0.334296
$508$	2.46000	0.109145
$509$	20.5626	0.911421	0.455710	−	0.890128i	$-0.349385\pi$
$509$	20.5626	0.911421	0.455710	+	0.890128i	$0.349385\pi$
$510$	−4.46906	−0.197893
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	12.4375	0.549130
$514$	−28.8387	−1.27202
$515$	18.3395	0.808137
$516$	6.33388	0.278833
$517$	−0.834485	−0.0367006
$518$	0	0
$519$	−3.43194	−0.150645
$520$	0.717941	0.0314838
$521$	17.6930	0.775144	0.387572	−	0.921840i	$-0.373314\pi$
$521$	17.6930	0.775144	0.387572	+	0.921840i	$0.373314\pi$
$522$	−5.87135	−0.256982
$523$	14.1195	0.617401	0.308701	−	0.951159i	$-0.400106\pi$
$523$	14.1195	0.617401	0.308701	+	0.951159i	$0.400106\pi$
$524$	11.5215	0.503318
$525$	0	0
$526$	−15.1701	−0.661446
$527$	20.9506	0.912624
$528$	0.0942705	0.00410260
$529$	−22.0712	−0.959616
$530$	4.78269	0.207747
$531$	−23.9269	−1.03834
$532$	0	0
$533$	−0.400214	−0.0173352
$534$	0.907966	0.0392915
$535$	−0.801845	−0.0346668
$536$	−5.00086	−0.216004
$537$	7.90640	0.341187
$538$	0.958955	0.0413435
$539$	0	0
$540$	−3.51663	−0.151332
$541$	11.0221	0.473878	0.236939	−	0.971525i	$-0.423856\pi$
$541$	11.0221	0.473878	0.236939	+	0.971525i	$0.423856\pi$
$542$	22.0305	0.946293
$543$	−9.80674	−0.420847
$544$	−7.16574	−0.307229
$545$	8.21684	0.351971
$546$	0	0
$547$	−11.6781	−0.499321	−0.249661	−	0.968333i	$-0.580319\pi$
$547$	−11.6781	−0.499321	−0.249661	+	0.968333i	$0.580319\pi$
$548$	−14.3939	−0.614875
$549$	23.5244	1.00400
$550$	−0.615292	−0.0262361
$551$	−8.16458	−0.347823
$552$	−0.579377	−0.0246599
$553$	0	0
$554$	−18.0065	−0.765023
$555$	5.47601	0.232444
$556$	−4.17348	−0.176995
$557$	7.47491	0.316722	0.158361	−	0.987381i	$-0.449379\pi$
$557$	7.47491	0.316722	0.158361	+	0.987381i	$0.449379\pi$
$558$	7.71454	0.326582
$559$	−7.29127	−0.308388
$560$	0	0
$561$	0.675518	0.0285204
$562$	24.0836	1.01591
$563$	18.2784	0.770342	0.385171	−	0.922845i	$-0.374142\pi$
$563$	18.2784	0.770342	0.385171	+	0.922845i	$0.374142\pi$
$564$	−3.19911	−0.134707
$565$	15.5022	0.652183
$566$	−16.2342	−0.682376
$567$	0	0
$568$	8.27035	0.347016
$569$	−34.0082	−1.42570	−0.712849	−	0.701318i	$-0.752595\pi$
$569$	−34.0082	−1.42570	−0.712849	+	0.701318i	$0.752595\pi$
$570$	−2.28836	−0.0958489
$571$	−16.7657	−0.701624	−0.350812	−	0.936446i	$-0.614094\pi$
$571$	−16.7657	−0.701624	−0.350812	+	0.936446i	$0.614094\pi$
$572$	−0.108520	−0.00453744
$573$	−8.98449	−0.375333
$574$	0	0
$575$	3.78152	0.157700
$576$	−2.63860	−0.109942
$577$	−24.9025	−1.03670	−0.518352	−	0.855168i	$-0.673454\pi$
$577$	−24.9025	−1.03670	−0.518352	+	0.855168i	$0.673454\pi$
$578$	−34.3479	−1.42868
$579$	8.84157	0.367443
$580$	2.30848	0.0958545
$581$	0	0
$582$	11.3241	0.469398
$583$	−0.722924	−0.0299405
$584$	4.38181	0.181320
$585$	1.89436	0.0783221
$586$	−16.4833	−0.680917
$587$	30.3705	1.25352	0.626762	−	0.779211i	$-0.284380\pi$
$587$	30.3705	1.25352	0.626762	+	0.779211i	$0.284380\pi$
$588$	0	0
$589$	10.7277	0.442026
$590$	9.40751	0.387301
$591$	3.30371	0.135896
$592$	8.78030	0.360868
$593$	−13.0158	−0.534495	−0.267247	−	0.963628i	$-0.586114\pi$
$593$	−13.0158	−0.534495	−0.267247	+	0.963628i	$0.586114\pi$
$594$	0.531554	0.0218099
$595$	0	0
$596$	15.5850	0.638386
$597$	−10.8148	−0.442622
$598$	0.666952	0.0272737
$599$	−16.9134	−0.691064	−0.345532	−	0.938407i	$-0.612302\pi$
$599$	−16.9134	−0.691064	−0.345532	+	0.938407i	$0.612302\pi$
$600$	−2.35880	−0.0962976
$601$	23.3454	0.952278	0.476139	−	0.879370i	$-0.342036\pi$
$601$	23.3454	0.952278	0.476139	+	0.879370i	$0.342036\pi$
$602$	0	0
$603$	−13.1953	−0.537353
$604$	13.5972	0.553262
$605$	11.3863	0.462919
$606$	−0.601164	−0.0244206
$607$	4.42357	0.179547	0.0897736	−	0.995962i	$-0.471386\pi$
$607$	4.42357	0.179547	0.0897736	+	0.995962i	$0.471386\pi$
$608$	−3.66918	−0.148805
$609$	0	0
$610$	−9.24924	−0.374491
$611$	3.68267	0.148985
$612$	−18.9075	−0.764292
$613$	−21.6392	−0.873998	−0.436999	−	0.899462i	$-0.643959\pi$
$613$	−21.6392	−0.873998	−0.436999	+	0.899462i	$0.643959\pi$
$614$	23.6040	0.952582
$615$	−0.360679	−0.0145440
$616$	0	0
$617$	−2.54806	−0.102581	−0.0512905	−	0.998684i	$-0.516333\pi$
$617$	−2.54806	−0.102581	−0.0512905	+	0.998684i	$0.516333\pi$
$618$	−10.6272	−0.427489
$619$	6.97436	0.280323	0.140162	−	0.990129i	$-0.455238\pi$
$619$	6.97436	0.280323	0.140162	+	0.990129i	$0.455238\pi$
$620$	−3.03318	−0.121815
$621$	−3.26687	−0.131095
$622$	−25.1019	−1.00649
$623$	0	0
$624$	−0.416025	−0.0166543
$625$	10.0142	0.400568
$626$	17.2675	0.690150
$627$	0.345896	0.0138137
$628$	−12.1293	−0.484011
$629$	62.9174	2.50868
$630$	0	0
$631$	−48.5719	−1.93362	−0.966808	−	0.255504i	$-0.917759\pi$
$631$	−48.5719	−1.93362	−0.966808	+	0.255504i	$0.917759\pi$
$632$	−8.89176	−0.353695
$633$	−16.9332	−0.673035
$634$	1.31329	0.0521572
$635$	−2.55210	−0.101277
$636$	−2.77142	−0.109894
$637$	0	0
$638$	−0.348937	−0.0138146
$639$	21.8222	0.863271
$640$	1.03744	0.0410083
$641$	−2.08742	−0.0824479	−0.0412240	−	0.999150i	$-0.513126\pi$
$641$	−2.08742	−0.0824479	−0.0412240	+	0.999150i	$0.513126\pi$
$642$	0.464645	0.0183381
$643$	−19.7578	−0.779170	−0.389585	−	0.920990i	$-0.627382\pi$
$643$	−19.7578	−0.779170	−0.389585	+	0.920990i	$0.627382\pi$
$644$	0	0
$645$	−6.57100	−0.258733
$646$	−26.2924	−1.03446
$647$	9.30590	0.365852	0.182926	−	0.983127i	$-0.441443\pi$
$647$	9.30590	0.365852	0.182926	+	0.983127i	$0.441443\pi$
$648$	−5.87803	−0.230911
$649$	−1.42199	−0.0558178
$650$	2.71534	0.106505
$651$	0	0
$652$	−12.7050	−0.497568
$653$	39.6708	1.55244	0.776219	−	0.630463i	$-0.217135\pi$
$653$	39.6708	1.55244	0.776219	+	0.630463i	$0.217135\pi$
$654$	−4.76141	−0.186186
$655$	−11.9528	−0.467036
$656$	−0.578316	−0.0225795
$657$	11.5618	0.451071
$658$	0	0
$659$	14.1565	0.551458	0.275729	−	0.961235i	$-0.411081\pi$
$659$	14.1565	0.551458	0.275729	+	0.961235i	$0.411081\pi$
$660$	−0.0977998	−0.00380685
$661$	21.4168	0.833016	0.416508	−	0.909132i	$-0.363254\pi$
$661$	21.4168	0.833016	0.416508	+	0.909132i	$0.363254\pi$
$662$	−17.3189	−0.673119
$663$	−2.98113	−0.115777
$664$	14.7641	0.572959
$665$	0	0
$666$	23.1677	0.897731
$667$	2.14453	0.0830366
$668$	12.9972	0.502876
$669$	16.4143	0.634612
$670$	5.18808	0.200433
$671$	1.39806	0.0539716
$672$	0	0
$673$	40.7135	1.56939	0.784696	−	0.619881i	$-0.212819\pi$
$673$	40.7135	1.56939	0.784696	+	0.619881i	$0.212819\pi$
$674$	−35.1621	−1.35439
$675$	−13.3003	−0.511930
$676$	−12.5211	−0.481580
$677$	25.4628	0.978615	0.489308	−	0.872111i	$-0.337250\pi$
$677$	25.4628	0.978615	0.489308	+	0.872111i	$0.337250\pi$
$678$	−8.98306	−0.344992
$679$	0	0
$680$	7.43402	0.285082
$681$	−1.10011	−0.0421565
$682$	0.458478	0.0175560
$683$	21.9752	0.840858	0.420429	−	0.907325i	$-0.361879\pi$
$683$	21.9752	0.840858	0.420429	+	0.907325i	$0.361879\pi$
$684$	−9.68152	−0.370182
$685$	14.9327	0.570550
$686$	0	0
$687$	2.13745	0.0815488
$688$	−10.5360	−0.401682
$689$	3.19034	0.121542
$690$	0.601067	0.0228822
$691$	0.135760	0.00516455	0.00258228	−	0.999997i	$-0.499178\pi$
$691$	0.135760	0.00516455	0.00258228	+	0.999997i	$0.499178\pi$
$692$	5.70883	0.217017
$693$	0	0
$694$	−23.3211	−0.885258
$695$	4.32973	0.164236
$696$	−1.33769	−0.0507052
$697$	−4.14407	−0.156968
$698$	1.13757	0.0430578
$699$	−17.1976	−0.650471
$700$	0	0
$701$	−33.7096	−1.27319	−0.636597	−	0.771197i	$-0.719658\pi$
$701$	−33.7096	−1.27319	−0.636597	+	0.771197i	$0.719658\pi$
$702$	−2.34580	−0.0885365
$703$	32.2166	1.21507
$704$	−0.156813	−0.00591012
$705$	3.31888	0.124996
$706$	−7.22564	−0.271940
$707$	0	0
$708$	−5.45137	−0.204875
$709$	−32.7672	−1.23060	−0.615300	−	0.788293i	$-0.710965\pi$
$709$	−32.7672	−1.23060	−0.615300	+	0.788293i	$0.710965\pi$
$710$	−8.57998	−0.322001
$711$	−23.4618	−0.879887
$712$	−1.51035	−0.0566026
$713$	−2.81776	−0.105526
$714$	0	0
$715$	0.112583	0.00421035
$716$	−13.1518	−0.491507
$717$	7.24233	0.270470
$718$	−8.40766	−0.313771
$719$	5.10731	0.190470	0.0952352	−	0.995455i	$-0.469640\pi$
$719$	5.10731	0.190470	0.0952352	+	0.995455i	$0.469640\pi$
$720$	2.73739	0.102016
$721$	0	0
$722$	5.53708	0.206069
$723$	−16.6461	−0.619075
$724$	16.3129	0.606265
$725$	8.73097	0.324260
$726$	−6.59802	−0.244875
$727$	37.1433	1.37757	0.688785	−	0.724966i	$-0.258145\pi$
$727$	37.1433	1.37757	0.688785	+	0.724966i	$0.258145\pi$
$728$	0	0
$729$	−9.39644	−0.348016
$730$	−4.54585	−0.168250
$731$	−75.4985	−2.79241
$732$	5.35966	0.198099
$733$	37.4336	1.38264	0.691322	−	0.722547i	$-0.257029\pi$
$733$	37.4336	1.38264	0.691322	+	0.722547i	$0.257029\pi$
$734$	11.8397	0.437012
$735$	0	0
$736$	0.963758	0.0355246
$737$	−0.784201	−0.0288864
$738$	−1.52595	−0.0561709
$739$	1.61846	0.0595359	0.0297680	−	0.999557i	$-0.490523\pi$
$739$	1.61846	0.0595359	0.0297680	+	0.999557i	$0.490523\pi$
$740$	−9.10902	−0.334854
$741$	−1.52647	−0.0560764
$742$	0	0
$743$	24.4207	0.895909	0.447955	−	0.894056i	$-0.352153\pi$
$743$	24.4207	0.895909	0.447955	+	0.894056i	$0.352153\pi$
$744$	1.75764	0.0644381
$745$	−16.1685	−0.592367
$746$	25.2380	0.924030
$747$	38.9567	1.42535
$748$	−1.12368	−0.0410860
$749$	0	0
$750$	5.56546	0.203222
$751$	43.4949	1.58715	0.793576	−	0.608471i	$-0.208217\pi$
$751$	43.4949	1.58715	0.793576	+	0.608471i	$0.208217\pi$
$752$	5.32152	0.194056
$753$	12.4966	0.455401
$754$	1.53989	0.0560796
$755$	−14.1062	−0.513379
$756$	0	0
$757$	0.479655	0.0174334	0.00871669	−	0.999962i	$-0.497225\pi$
$757$	0.479655	0.0174334	0.00871669	+	0.999962i	$0.497225\pi$
$758$	11.8038	0.428734
$759$	−0.0908540	−0.00329779
$760$	3.80655	0.138078
$761$	13.7635	0.498926	0.249463	−	0.968384i	$-0.419746\pi$
$761$	13.7635	0.498926	0.249463	+	0.968384i	$0.419746\pi$
$762$	1.47886	0.0535736
$763$	0	0
$764$	14.9452	0.540697
$765$	19.6154	0.709197
$766$	−2.84184	−0.102680
$767$	6.27536	0.226590
$768$	−0.601164	−0.0216926
$769$	18.6446	0.672341	0.336170	−	0.941801i	$-0.390868\pi$
$769$	18.6446	0.672341	0.336170	+	0.941801i	$0.390868\pi$
$770$	0	0
$771$	−17.3368	−0.624368
$772$	−14.7074	−0.529332
$773$	23.9426	0.861157	0.430579	−	0.902553i	$-0.358310\pi$
$773$	23.9426	0.861157	0.430579	+	0.902553i	$0.358310\pi$
$774$	−27.8004	−0.999264
$775$	−11.4719	−0.412082
$776$	−18.8369	−0.676206
$777$	0	0
$778$	8.55049	0.306550
$779$	−2.12195	−0.0760267
$780$	0.431600	0.0154538
$781$	1.29690	0.0464067
$782$	6.90605	0.246960
$783$	−7.54273	−0.269555
$784$	0	0
$785$	12.5834	0.449120
$786$	6.92630	0.247053
$787$	29.6555	1.05710	0.528552	−	0.848901i	$-0.322735\pi$
$787$	29.6555	1.05710	0.528552	+	0.848901i	$0.322735\pi$
$788$	−5.49552	−0.195770
$789$	−9.11969	−0.324669
$790$	9.22465	0.328198
$791$	0	0
$792$	−0.413768	−0.0147026
$793$	−6.16979	−0.219096
$794$	−5.04110	−0.178902
$795$	2.87518	0.101972
$796$	17.9898	0.637633
$797$	25.2546	0.894566	0.447283	−	0.894393i	$-0.352392\pi$
$797$	25.2546	0.894566	0.447283	+	0.894393i	$0.352392\pi$
$798$	0	0
$799$	38.1327	1.34904
$800$	3.92372	0.138725
$801$	−3.98520	−0.140810
$802$	−13.2401	−0.467525
$803$	0.687126	0.0242481
$804$	−3.00633	−0.106025
$805$	0	0
$806$	−2.02331	−0.0712681
$807$	0.576489	0.0202934
$808$	1.00000	0.0351799
$809$	32.2569	1.13409	0.567047	−	0.823686i	$-0.308086\pi$
$809$	32.2569	1.13409	0.567047	+	0.823686i	$0.308086\pi$
$810$	6.09809	0.214265
$811$	19.2975	0.677626	0.338813	−	0.940854i	$-0.389975\pi$
$811$	19.2975	0.677626	0.338813	+	0.940854i	$0.389975\pi$
$812$	0	0
$813$	13.2440	0.464486
$814$	1.37687	0.0482592
$815$	13.1807	0.461700
$816$	−4.30779	−0.150803
$817$	−38.6586	−1.35249
$818$	2.04364	0.0714543
$819$	0	0
$820$	0.599967	0.0209518
$821$	−0.104785	−0.00365701	−0.00182850	−	0.999998i	$-0.500582\pi$
$821$	−0.104785	−0.00365701	−0.00182850	+	0.999998i	$0.500582\pi$
$822$	−8.65306	−0.301810
$823$	25.7754	0.898476	0.449238	−	0.893412i	$-0.351696\pi$
$823$	25.7754	0.898476	0.449238	+	0.893412i	$0.351696\pi$
$824$	17.6777	0.615833
$825$	−0.369891	−0.0128780
$826$	0	0
$827$	52.5656	1.82788	0.913942	−	0.405846i	$-0.133023\pi$
$827$	52.5656	1.82788	0.913942	+	0.405846i	$0.133023\pi$
$828$	2.54297	0.0883745
$829$	18.7081	0.649758	0.324879	−	0.945756i	$-0.394676\pi$
$829$	18.7081	0.649758	0.324879	+	0.945756i	$0.394676\pi$
$830$	−15.3169	−0.531656
$831$	−10.8249	−0.375510
$832$	0.692032	0.0239919
$833$	0	0
$834$	−2.50895	−0.0868777
$835$	−13.4838	−0.466625
$836$	−0.575377	−0.0198998
$837$	9.91061	0.342561
$838$	−31.1171	−1.07492
$839$	2.61552	0.0902978	0.0451489	−	0.998980i	$-0.485624\pi$
$839$	2.61552	0.0902978	0.0451489	+	0.998980i	$0.485624\pi$
$840$	0	0
$841$	−24.0486	−0.829262
$842$	−26.0933	−0.899236
$843$	14.4782	0.498655
$844$	28.1674	0.969561
$845$	12.9899	0.446865
$846$	14.0414	0.482753
$847$	0	0
$848$	4.61010	0.158311
$849$	−9.75943	−0.334943
$850$	28.1164	0.964384
$851$	−8.46209	−0.290077
$852$	4.97183	0.170332
$853$	−53.5609	−1.83389	−0.916945	−	0.399014i	$-0.869352\pi$
$853$	−53.5609	−1.83389	−0.916945	+	0.399014i	$0.869352\pi$
$854$	0	0
$855$	10.0440	0.343497
$856$	−0.772909	−0.0264175
$857$	51.8927	1.77262	0.886310	−	0.463093i	$-0.153260\pi$
$857$	51.8927	1.77262	0.886310	+	0.463093i	$0.153260\pi$
$858$	−0.0652382	−0.00222720
$859$	10.3463	0.353010	0.176505	−	0.984300i	$-0.443521\pi$
$859$	10.3463	0.353010	0.176505	+	0.984300i	$0.443521\pi$
$860$	10.9305	0.372726
$861$	0	0
$862$	−3.11726	−0.106174
$863$	32.1807	1.09544	0.547722	−	0.836661i	$-0.315495\pi$
$863$	32.1807	1.09544	0.547722	+	0.836661i	$0.315495\pi$
$864$	−3.38972	−0.115321
$865$	−5.92256	−0.201373
$866$	6.52478	0.221721
$867$	−20.6487	−0.701267
$868$	0	0
$869$	−1.39435	−0.0473000
$870$	1.38778	0.0470500
$871$	3.46075	0.117263
$872$	7.92032	0.268216
$873$	−49.7032	−1.68220
$874$	3.53621	0.119614
$875$	0	0
$876$	2.63418	0.0890008
$877$	−40.9449	−1.38261	−0.691305	−	0.722563i	$-0.742964\pi$
$877$	−40.9449	−1.38261	−0.691305	+	0.722563i	$0.742964\pi$
$878$	19.3256	0.652207
$879$	−9.90914	−0.334227
$880$	0.162684	0.00548408
$881$	−8.14253	−0.274329	−0.137164	−	0.990548i	$-0.543799\pi$
$881$	−8.14253	−0.274329	−0.137164	+	0.990548i	$0.543799\pi$
$882$	0	0
$883$	50.9606	1.71496	0.857480	−	0.514517i	$-0.172029\pi$
$883$	50.9606	1.71496	0.857480	+	0.514517i	$0.172029\pi$
$884$	4.95893	0.166787
$885$	5.65546	0.190106
$886$	−15.0917	−0.507015
$887$	−6.66563	−0.223810	−0.111905	−	0.993719i	$-0.535695\pi$
$887$	−6.66563	−0.223810	−0.111905	+	0.993719i	$0.535695\pi$
$888$	5.27840	0.177132
$889$	0	0
$890$	1.56689	0.0525223
$891$	−0.921753	−0.0308799
$892$	−27.3041	−0.914210
$893$	19.5256	0.653401
$894$	9.36913	0.313351
$895$	13.6442	0.456076
$896$	0	0
$897$	0.400947	0.0133872
$898$	−9.90581	−0.330561
$899$	−6.50579	−0.216980
$900$	10.3531	0.345105
$901$	33.0348	1.10055
$902$	−0.0906877	−0.00301957
$903$	0	0
$904$	14.9428	0.496989
$905$	−16.9236	−0.562561
$906$	8.17414	0.271568
$907$	49.1086	1.63062	0.815312	−	0.579022i	$-0.196565\pi$
$907$	49.1086	1.63062	0.815312	+	0.579022i	$0.196565\pi$
$908$	1.82997	0.0607298
$909$	2.63860	0.0875169
$910$	0	0
$911$	−7.95027	−0.263404	−0.131702	−	0.991289i	$-0.542044\pi$
$911$	−7.95027	−0.263404	−0.131702	+	0.991289i	$0.542044\pi$
$912$	−2.20578	−0.0730407
$913$	2.31521	0.0766223
$914$	−5.07758	−0.167952
$915$	−5.56031	−0.183818
$916$	−3.55552	−0.117478
$917$	0	0
$918$	−24.2899	−0.801686
$919$	−55.6046	−1.83423	−0.917113	−	0.398628i	$-0.869486\pi$
$919$	−55.6046	−1.83423	−0.917113	+	0.398628i	$0.869486\pi$
$920$	−0.999840	−0.0329637
$921$	14.1899	0.467573
$922$	32.4161	1.06757
$923$	−5.72335	−0.188386
$924$	0	0
$925$	−34.4515	−1.13276
$926$	6.74008	0.221493
$927$	46.6445	1.53201
$928$	2.22518	0.0730450
$929$	−4.15485	−0.136316	−0.0681580	−	0.997675i	$-0.521712\pi$
$929$	−4.15485	−0.136316	−0.0681580	+	0.997675i	$0.521712\pi$
$930$	−1.82344	−0.0597929
$931$	0	0
$932$	28.6071	0.937057
$933$	−15.0903	−0.494035
$934$	0.820155	0.0268363
$935$	1.16575	0.0381242
$936$	1.82600	0.0596846
$937$	24.3019	0.793909	0.396954	−	0.917838i	$-0.370067\pi$
$937$	24.3019	0.793909	0.396954	+	0.917838i	$0.370067\pi$
$938$	0	0
$939$	10.3806	0.338759
$940$	−5.52075	−0.180067
$941$	−49.5634	−1.61572	−0.807861	−	0.589374i	$-0.799375\pi$
$941$	−49.5634	−1.61572	−0.807861	+	0.589374i	$0.799375\pi$
$942$	−7.29168	−0.237576
$943$	0.557357	0.0181500
$944$	9.06802	0.295139
$945$	0	0
$946$	−1.65219	−0.0537173
$947$	−25.4718	−0.827721	−0.413861	−	0.910340i	$-0.635820\pi$
$947$	−25.4718	−0.827721	−0.413861	+	0.910340i	$0.635820\pi$
$948$	−5.34541	−0.173611
$949$	−3.03235	−0.0984343
$950$	14.3969	0.467096
$951$	0.789500	0.0256013
$952$	0	0
$953$	49.1150	1.59099	0.795495	−	0.605960i	$-0.207211\pi$
$953$	49.1150	1.59099	0.795495	+	0.605960i	$0.207211\pi$
$954$	12.1642	0.393831
$955$	−15.5047	−0.501720
$956$	−12.0472	−0.389633
$957$	−0.209768	−0.00678085
$958$	−38.0623	−1.22974
$959$	0	0
$960$	0.623670	0.0201289
$961$	−22.4518	−0.724253
$962$	−6.07625	−0.195906
$963$	−2.03940	−0.0657187
$964$	27.6898	0.891827
$965$	15.2580	0.491174
$966$	0	0
$967$	50.1361	1.61227	0.806134	−	0.591732i	$-0.201556\pi$
$967$	50.1361	1.61227	0.806134	+	0.591732i	$0.201556\pi$
$968$	10.9754	0.352763
$969$	−15.8061	−0.507764
$970$	19.5422	0.627461
$971$	28.5294	0.915551	0.457776	−	0.889068i	$-0.348646\pi$
$971$	28.5294	0.915551	0.457776	+	0.889068i	$0.348646\pi$
$972$	−13.7028	−0.439518
$973$	0	0
$974$	−9.37994	−0.300553
$975$	1.63237	0.0522775
$976$	−8.91546	−0.285377
$977$	−23.5743	−0.754209	−0.377105	−	0.926171i	$-0.623080\pi$
$977$	−23.5743	−0.754209	−0.377105	+	0.926171i	$0.623080\pi$
$978$	−7.63781	−0.244230
$979$	−0.236842	−0.00756952
$980$	0	0
$981$	20.8986	0.667240
$982$	19.9754	0.637441
$983$	21.1951	0.676020	0.338010	−	0.941143i	$-0.390246\pi$
$983$	21.1951	0.676020	0.338010	+	0.941143i	$0.390246\pi$
$984$	−0.347663	−0.0110831
$985$	5.70127	0.181657
$986$	15.9450	0.507793
$987$	0	0
$988$	2.53919	0.0807825
$989$	10.1542	0.322884
$990$	0.429259	0.0136427
$991$	14.2025	0.451156	0.225578	−	0.974225i	$-0.427573\pi$
$991$	14.2025	0.451156	0.225578	+	0.974225i	$0.427573\pi$
$992$	−2.92372	−0.0928283
$993$	−10.4115	−0.330399
$994$	0	0
$995$	−18.6633	−0.591667
$996$	8.87566	0.281236
$997$	5.61590	0.177857	0.0889286	−	0.996038i	$-0.471656\pi$
$997$	5.61590	0.177857	0.0889286	+	0.996038i	$0.471656\pi$
$998$	−10.9983	−0.348146
$999$	29.7628	0.941653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9898.2.a.t.1.3		5
7.6	odd	2		1414.2.a.e.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1414.2.a.e.1.3	✓	5	7.6	odd	2
9898.2.a.t.1.3		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9898 = 2 \cdot 7^{2} \cdot 101 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9898.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.601164 q^{3} +1.00000 q^{4} -1.03744 q^{5} +0.601164 q^{6} -1.00000 q^{8} -2.63860 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.601164 q^{3} +1.00000 q^{4} -1.03744 q^{5} +0.601164 q^{6} -1.00000 q^{8} -2.63860 q^{9} +1.03744 q^{10} -0.156813 q^{11} -0.601164 q^{12} +0.692032 q^{13} +0.623670 q^{15} +1.00000 q^{16} +7.16574 q^{17} +2.63860 q^{18} +3.66918 q^{19} -1.03744 q^{20} +0.156813 q^{22} -0.963758 q^{23} +0.601164 q^{24} -3.92372 q^{25} -0.692032 q^{26} +3.38972 q^{27} -2.22518 q^{29} -0.623670 q^{30} +2.92372 q^{31} -1.00000 q^{32} +0.0942705 q^{33} -7.16574 q^{34} -2.63860 q^{36} +8.78030 q^{37} -3.66918 q^{38} -0.416025 q^{39} +1.03744 q^{40} -0.578316 q^{41} -10.5360 q^{43} -0.156813 q^{44} +2.73739 q^{45} +0.963758 q^{46} +5.32152 q^{47} -0.601164 q^{48} +3.92372 q^{50} -4.30779 q^{51} +0.692032 q^{52} +4.61010 q^{53} -3.38972 q^{54} +0.162684 q^{55} -2.20578 q^{57} +2.22518 q^{58} +9.06802 q^{59} +0.623670 q^{60} -8.91546 q^{61} -2.92372 q^{62} +1.00000 q^{64} -0.717941 q^{65} -0.0942705 q^{66} +5.00086 q^{67} +7.16574 q^{68} +0.579377 q^{69} -8.27035 q^{71} +2.63860 q^{72} -4.38181 q^{73} -8.78030 q^{74} +2.35880 q^{75} +3.66918 q^{76} +0.416025 q^{78} +8.89176 q^{79} -1.03744 q^{80} +5.87803 q^{81} +0.578316 q^{82} -14.7641 q^{83} -7.43402 q^{85} +10.5360 q^{86} +1.33769 q^{87} +0.156813 q^{88} +1.51035 q^{89} -2.73739 q^{90} -0.963758 q^{92} -1.75764 q^{93} -5.32152 q^{94} -3.80655 q^{95} +0.601164 q^{96} +18.8369 q^{97} +0.413768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{8} + q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^8 + q^9	\( 5 q - 5 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{8} + q^{9} - 6 q^{10} - 5 q^{11} - q^{13} - 4 q^{15} + 5 q^{16} + 12 q^{17} - q^{18} + q^{19} + 6 q^{20} + 5 q^{22} - 4 q^{23} + 3 q^{25} + q^{26} + 12 q^{27} - 18 q^{29} + 4 q^{30} - 8 q^{31} - 5 q^{32} - 13 q^{33} - 12 q^{34} + q^{36} + 5 q^{37} - q^{38} - 14 q^{39} - 6 q^{40} + 13 q^{41} + q^{43} - 5 q^{44} + 18 q^{45} + 4 q^{46} - 3 q^{50} + 10 q^{51} - q^{52} - 8 q^{53} - 12 q^{54} + 6 q^{55} - 9 q^{57} + 18 q^{58} + 31 q^{59} - 4 q^{60} + 15 q^{61} + 8 q^{62} + 5 q^{64} + 17 q^{65} + 13 q^{66} - 4 q^{67} + 12 q^{68} + 15 q^{69} - 21 q^{71} - q^{72} + 3 q^{73} - 5 q^{74} - 7 q^{75} + q^{76} + 14 q^{78} + q^{79} + 6 q^{80} - 19 q^{81} - 13 q^{82} + 22 q^{83} - 13 q^{85} - q^{86} + 37 q^{87} + 5 q^{88} + 22 q^{89} - 18 q^{90} - 4 q^{92} + 7 q^{93} + 19 q^{95} - 4 q^{97} - 2 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^8 + q^9 - 6 * q^10 - 5 * q^11 - q^13 - 4 * q^15 + 5 * q^16 + 12 * q^17 - q^18 + q^19 + 6 * q^20 + 5 * q^22 - 4 * q^23 + 3 * q^25 + q^26 + 12 * q^27 - 18 * q^29 + 4 * q^30 - 8 * q^31 - 5 * q^32 - 13 * q^33 - 12 * q^34 + q^36 + 5 * q^37 - q^38 - 14 * q^39 - 6 * q^40 + 13 * q^41 + q^43 - 5 * q^44 + 18 * q^45 + 4 * q^46 - 3 * q^50 + 10 * q^51 - q^52 - 8 * q^53 - 12 * q^54 + 6 * q^55 - 9 * q^57 + 18 * q^58 + 31 * q^59 - 4 * q^60 + 15 * q^61 + 8 * q^62 + 5 * q^64 + 17 * q^65 + 13 * q^66 - 4 * q^67 + 12 * q^68 + 15 * q^69 - 21 * q^71 - q^72 + 3 * q^73 - 5 * q^74 - 7 * q^75 + q^76 + 14 * q^78 + q^79 + 6 * q^80 - 19 * q^81 - 13 * q^82 + 22 * q^83 - 13 * q^85 - q^86 + 37 * q^87 + 5 * q^88 + 22 * q^89 - 18 * q^90 - 4 * q^92 + 7 * q^93 + 19 * q^95 - 4 * q^97 - 2 * q^99

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