LMFDB - Embedded newform 841.2.a.k.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(1,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("841.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.12.32268092290502656.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 78x^{8} - 169x^{6} + 148x^{4} - 36x^{2} + 1 $ x^12 - 15x^10 + 78x^8 - 169x^6 + 148x^4 - 36*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.572821$ of defining polynomial
Character	$\chi$	$=$	841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.26775 q^{2} +2.84057 q^{3} +3.14268 q^{4} +0.0578828 q^{5} +6.44169 q^{6} -1.56196 q^{7} +2.59131 q^{8} +5.06883 q^{9} +0.131264 q^{10} -3.97289 q^{11} +8.92699 q^{12} +0.404986 q^{13} -3.54213 q^{14} +0.164420 q^{15} -0.408929 q^{16} +5.16843 q^{17} +11.4948 q^{18} -3.45088 q^{19} +0.181907 q^{20} -4.43685 q^{21} -9.00950 q^{22} +0.230185 q^{23} +7.36078 q^{24} -4.99665 q^{25} +0.918405 q^{26} +5.87665 q^{27} -4.90874 q^{28} +0.372863 q^{30} +4.31832 q^{31} -6.10996 q^{32} -11.2853 q^{33} +11.7207 q^{34} -0.0904106 q^{35} +15.9297 q^{36} +5.37070 q^{37} -7.82573 q^{38} +1.15039 q^{39} +0.149992 q^{40} -1.46294 q^{41} -10.0617 q^{42} +6.48316 q^{43} -12.4855 q^{44} +0.293398 q^{45} +0.522001 q^{46} -9.57399 q^{47} -1.16159 q^{48} -4.56028 q^{49} -11.3311 q^{50} +14.6813 q^{51} +1.27274 q^{52} -1.78879 q^{53} +13.3268 q^{54} -0.229962 q^{55} -4.04752 q^{56} -9.80247 q^{57} -1.05216 q^{59} +0.516719 q^{60} -3.18937 q^{61} +9.79287 q^{62} -7.91731 q^{63} -13.0380 q^{64} +0.0234417 q^{65} -25.5921 q^{66} +10.8726 q^{67} +16.2427 q^{68} +0.653856 q^{69} -0.205028 q^{70} +13.4529 q^{71} +13.1349 q^{72} -7.01563 q^{73} +12.1794 q^{74} -14.1933 q^{75} -10.8450 q^{76} +6.20549 q^{77} +2.60879 q^{78} +4.78464 q^{79} -0.0236700 q^{80} +1.48654 q^{81} -3.31758 q^{82} +8.42345 q^{83} -13.9436 q^{84} +0.299163 q^{85} +14.7022 q^{86} -10.2950 q^{88} -1.13267 q^{89} +0.665353 q^{90} -0.632571 q^{91} +0.723397 q^{92} +12.2665 q^{93} -21.7114 q^{94} -0.199747 q^{95} -17.3558 q^{96} -17.2131 q^{97} -10.3416 q^{98} -20.1379 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} + 8 q^{5} + 24 q^{6} + 10 q^{7} + 10 q^{9} + 12 q^{13} + 16 q^{16} + 24 q^{20} - 38 q^{22} + 30 q^{23} + 10 q^{24} - 8 q^{25} - 12 q^{28} + 2 q^{30} - 4 q^{33} + 6 q^{34} + 44 q^{35} + 16 q^{36}+ \cdots - 58 q^{96}+O(q^{100}) $ 12 * q + 8 * q^4 + 8 * q^5 + 24 * q^6 + 10 * q^7 + 10 * q^9 + 12 * q^13 + 16 * q^16 + 24 * q^20 - 38 * q^22 + 30 * q^23 + 10 * q^24 - 8 * q^25 - 12 * q^28 + 2 * q^30 - 4 * q^33 + 6 * q^34 + 44 * q^35 + 16 * q^36 + 6 * q^42 - 12 * q^45 + 6 * q^49 + 8 * q^51 - 6 * q^52 + 32 * q^53 + 32 * q^54 + 14 * q^57 + 44 * q^59 - 16 * q^62 + 34 * q^63 - 2 * q^64 + 8 * q^65 + 30 * q^67 + 70 * q^71 + 56 * q^74 - 4 * q^78 + 34 * q^80 + 8 * q^81 - 62 * q^82 + 82 * q^83 + 44 * q^86 - 66 * q^88 - 32 * q^91 - 22 * q^92 - 12 * q^93 + 10 * q^94 - 58 * q^96

Coefficient data

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

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

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

$2$	2.26775	1.60354	0.801770	−	0.597633i	$-0.203892\pi$
$2$	2.26775	1.60354	0.801770	+	0.597633i	$0.203892\pi$
$3$	2.84057	1.64000	0.820001	−	0.572361i	$-0.193973\pi$
$3$	2.84057	1.64000	0.820001	+	0.572361i	$0.193973\pi$
$4$	3.14268	1.57134
$5$	0.0578828	0.0258860	0.0129430	−	0.999916i	$-0.495880\pi$
$5$	0.0578828	0.0258860	0.0129430	+	0.999916i	$0.495880\pi$
$6$	6.44169	2.62981
$7$	−1.56196	−0.590365	−0.295183	−	0.955441i	$-0.595381\pi$
$7$	−1.56196	−0.590365	−0.295183	+	0.955441i	$0.595381\pi$
$8$	2.59131	0.916165
$9$	5.06883	1.68961
$10$	0.131264	0.0415092
$11$	−3.97289	−1.19787	−0.598935	−	0.800798i	$-0.704409\pi$
$11$	−3.97289	−1.19787	−0.598935	+	0.800798i	$0.704409\pi$
$12$	8.92699	2.57700
$13$	0.404986	0.112323	0.0561614	−	0.998422i	$-0.482114\pi$
$13$	0.404986	0.112323	0.0561614	+	0.998422i	$0.482114\pi$
$14$	−3.54213	−0.946674
$15$	0.164420	0.0424531
$16$	−0.408929	−0.102232
$17$	5.16843	1.25353	0.626764	−	0.779209i	$-0.284379\pi$
$17$	5.16843	1.25353	0.626764	+	0.779209i	$0.284379\pi$
$18$	11.4948	2.70936
$19$	−3.45088	−0.791687	−0.395844	−	0.918318i	$-0.629548\pi$
$19$	−3.45088	−0.791687	−0.395844	+	0.918318i	$0.629548\pi$
$20$	0.181907	0.0406757
$21$	−4.43685	−0.968201
$22$	−9.00950	−1.92083
$23$	0.230185	0.0479968	0.0239984	−	0.999712i	$-0.492360\pi$
$23$	0.230185	0.0479968	0.0239984	+	0.999712i	$0.492360\pi$
$24$	7.36078	1.50251
$25$	−4.99665	−0.999330
$26$	0.918405	0.180114
$27$	5.87665	1.13096
$28$	−4.90874	−0.927664
$29$	0	0
$29$	0	0
$30$	0.372863	0.0680752
$31$	4.31832	0.775594	0.387797	−	0.921745i	$-0.373236\pi$
$31$	4.31832	0.775594	0.387797	+	0.921745i	$0.373236\pi$
$32$	−6.10996	−1.08010
$33$	−11.2853	−1.96451
$34$	11.7207	2.01008
$35$	−0.0904106	−0.0152822
$36$	15.9297	2.65495
$37$	5.37070	0.882937	0.441469	−	0.897277i	$-0.354458\pi$
$37$	5.37070	0.882937	0.441469	+	0.897277i	$0.354458\pi$
$38$	−7.82573	−1.26950
$39$	1.15039	0.184210
$40$	0.149992	0.0237158
$41$	−1.46294	−0.228473	−0.114237	−	0.993454i	$-0.536442\pi$
$41$	−1.46294	−0.228473	−0.114237	+	0.993454i	$0.536442\pi$
$42$	−10.0617	−1.55255
$43$	6.48316	0.988672	0.494336	−	0.869271i	$-0.335411\pi$
$43$	6.48316	0.988672	0.494336	+	0.869271i	$0.335411\pi$
$44$	−12.4855	−1.88226
$45$	0.293398	0.0437372
$46$	0.522001	0.0769648
$47$	−9.57399	−1.39651	−0.698255	−	0.715849i	$-0.746040\pi$
$47$	−9.57399	−1.39651	−0.698255	+	0.715849i	$0.746040\pi$
$48$	−1.16159	−0.167661
$49$	−4.56028	−0.651469
$50$	−11.3311	−1.60247
$51$	14.6813	2.05579
$52$	1.27274	0.176497
$53$	−1.78879	−0.245710	−0.122855	−	0.992425i	$-0.539205\pi$
$53$	−1.78879	−0.245710	−0.122855	+	0.992425i	$0.539205\pi$
$54$	13.3268	1.81354
$55$	−0.229962	−0.0310080
$56$	−4.04752	−0.540872
$57$	−9.80247	−1.29837
$58$	0	0
$59$	−1.05216	−0.136980	−0.0684900	−	0.997652i	$-0.521818\pi$
$59$	−1.05216	−0.136980	−0.0684900	+	0.997652i	$0.521818\pi$
$60$	0.516719	0.0667082
$61$	−3.18937	−0.408357	−0.204178	−	0.978934i	$-0.565452\pi$
$61$	−3.18937	−0.408357	−0.204178	+	0.978934i	$0.565452\pi$
$62$	9.79287	1.24370
$63$	−7.91731	−0.997487
$64$	−13.0380	−1.62975
$65$	0.0234417	0.00290759
$66$	−25.5921	−3.15017
$67$	10.8726	1.32830	0.664148	−	0.747601i	$-0.268795\pi$
$67$	10.8726	1.32830	0.664148	+	0.747601i	$0.268795\pi$
$68$	16.2427	1.96972
$69$	0.653856	0.0787150
$70$	−0.205028	−0.0245056
$71$	13.4529	1.59656	0.798281	−	0.602285i	$-0.205743\pi$
$71$	13.4529	1.59656	0.798281	+	0.602285i	$0.205743\pi$
$72$	13.1349	1.54796
$73$	−7.01563	−0.821118	−0.410559	−	0.911834i	$-0.634666\pi$
$73$	−7.01563	−0.821118	−0.410559	+	0.911834i	$0.634666\pi$
$74$	12.1794	1.41582
$75$	−14.1933	−1.63890
$76$	−10.8450	−1.24401
$77$	6.20549	0.707181
$78$	2.60879	0.295388
$79$	4.78464	0.538314	0.269157	−	0.963096i	$-0.413255\pi$
$79$	4.78464	0.538314	0.269157	+	0.963096i	$0.413255\pi$
$80$	−0.0236700	−0.00264638
$81$	1.48654	0.165171
$82$	−3.31758	−0.366366
$83$	8.42345	0.924594	0.462297	−	0.886725i	$-0.347025\pi$
$83$	8.42345	0.924594	0.462297	+	0.886725i	$0.347025\pi$
$84$	−13.9436	−1.52137
$85$	0.299163	0.0324488
$86$	14.7022	1.58537
$87$	0	0
$88$	−10.2950	−1.09745
$89$	−1.13267	−0.120063	−0.0600314	−	0.998196i	$-0.519120\pi$
$89$	−1.13267	−0.120063	−0.0600314	+	0.998196i	$0.519120\pi$
$90$	0.665353	0.0701343
$91$	−0.632571	−0.0663115
$92$	0.723397	0.0754193
$93$	12.2665	1.27198
$94$	−21.7114	−2.23936
$95$	−0.199747	−0.0204936
$96$	−17.3558	−1.77136
$97$	−17.2131	−1.74773	−0.873864	−	0.486170i	$-0.838393\pi$
$97$	−17.2131	−1.74773	−0.873864	+	0.486170i	$0.838393\pi$
$98$	−10.3416	−1.04466
$99$	−20.1379	−2.02393
$100$	−15.7029	−1.57029
$101$	−6.23958	−0.620862	−0.310431	−	0.950596i	$-0.600473\pi$
$101$	−6.23958	−0.620862	−0.310431	+	0.950596i	$0.600473\pi$
$102$	33.2934	3.29654
$103$	13.2105	1.30167	0.650833	−	0.759221i	$-0.274420\pi$
$103$	13.2105	1.30167	0.650833	+	0.759221i	$0.274420\pi$
$104$	1.04944	0.102906
$105$	−0.256818	−0.0250628
$106$	−4.05653	−0.394005
$107$	9.26822	0.895993	0.447996	−	0.894035i	$-0.352138\pi$
$107$	9.26822	0.895993	0.447996	+	0.894035i	$0.352138\pi$
$108$	18.4684	1.77712
$109$	−5.75542	−0.551269	−0.275634	−	0.961263i	$-0.588888\pi$
$109$	−5.75542	−0.551269	−0.275634	+	0.961263i	$0.588888\pi$
$110$	−0.521495	−0.0497226
$111$	15.2558	1.44802
$112$	0.638731	0.0603544
$113$	8.06227	0.758434	0.379217	−	0.925308i	$-0.376193\pi$
$113$	8.06227	0.758434	0.379217	+	0.925308i	$0.376193\pi$
$114$	−22.2295	−2.08199
$115$	0.0133237	0.00124245
$116$	0	0
$117$	2.05280	0.189782
$118$	−2.38604	−0.219653
$119$	−8.07288	−0.740039
$120$	0.426063	0.0388940
$121$	4.78382	0.434893
$122$	−7.23268	−0.654816
$123$	−4.15559	−0.374697
$124$	13.5711	1.21872
$125$	−0.578634	−0.0517546
$126$	−17.9545	−1.59951
$127$	17.5737	1.55941	0.779706	−	0.626146i	$-0.215369\pi$
$127$	17.5737	1.55941	0.779706	+	0.626146i	$0.215369\pi$
$128$	−17.3469	−1.53327
$129$	18.4158	1.62143
$130$	0.0531599	0.00466243
$131$	3.34792	0.292509	0.146255	−	0.989247i	$-0.453278\pi$
$131$	3.34792	0.292509	0.146255	+	0.989247i	$0.453278\pi$
$132$	−35.4659	−3.08691
$133$	5.39014	0.467385
$134$	24.6562	2.12997
$135$	0.340157	0.0292760
$136$	13.3930	1.14844
$137$	−5.52060	−0.471657	−0.235828	−	0.971795i	$-0.575780\pi$
$137$	−5.52060	−0.471657	−0.235828	+	0.971795i	$0.575780\pi$
$138$	1.48278	0.126223
$139$	−0.597509	−0.0506801	−0.0253400	−	0.999679i	$-0.508067\pi$
$139$	−0.597509	−0.0506801	−0.0253400	+	0.999679i	$0.508067\pi$
$140$	−0.284132	−0.0240135
$141$	−27.1956	−2.29028
$142$	30.5077	2.56015
$143$	−1.60896	−0.134548
$144$	−2.07279	−0.172733
$145$	0	0
$146$	−15.9097	−1.31669
$147$	−12.9538	−1.06841
$148$	16.8784	1.38739
$149$	5.10908	0.418552	0.209276	−	0.977857i	$-0.432889\pi$
$149$	5.10908	0.418552	0.209276	+	0.977857i	$0.432889\pi$
$150$	−32.1869	−2.62805
$151$	−7.80026	−0.634776	−0.317388	−	0.948296i	$-0.602806\pi$
$151$	−7.80026	−0.634776	−0.317388	+	0.948296i	$0.602806\pi$
$152$	−8.94230	−0.725316
$153$	26.1979	2.11797
$154$	14.0725	1.13399
$155$	0.249957	0.0200770
$156$	3.61530	0.289456
$157$	18.8577	1.50501	0.752504	−	0.658588i	$-0.228846\pi$
$157$	18.8577	1.50501	0.752504	+	0.658588i	$0.228846\pi$
$158$	10.8504	0.863208
$159$	−5.08119	−0.402965
$160$	−0.353662	−0.0279594
$161$	−0.359539	−0.0283357
$162$	3.37109	0.264858
$163$	−2.26200	−0.177173	−0.0885867	−	0.996068i	$-0.528235\pi$
$163$	−2.26200	−0.177173	−0.0885867	+	0.996068i	$0.528235\pi$
$164$	−4.59756	−0.359009
$165$	−0.653222	−0.0508533
$166$	19.1023	1.48262
$167$	11.7349	0.908075	0.454037	−	0.890983i	$-0.349983\pi$
$167$	11.7349	0.908075	0.454037	+	0.890983i	$0.349983\pi$
$168$	−11.4972	−0.887032
$169$	−12.8360	−0.987384
$170$	0.678426	0.0520329
$171$	−17.4919	−1.33764
$172$	20.3745	1.55354
$173$	19.2889	1.46651	0.733254	−	0.679954i	$-0.238000\pi$
$173$	19.2889	1.46651	0.733254	+	0.679954i	$0.238000\pi$
$174$	0	0
$175$	7.80457	0.589970
$176$	1.62463	0.122461
$177$	−2.98874	−0.224648
$178$	−2.56861	−0.192526
$179$	0.910387	0.0680455	0.0340228	−	0.999421i	$-0.489168\pi$
$179$	0.910387	0.0680455	0.0340228	+	0.999421i	$0.489168\pi$
$180$	0.922056	0.0687260
$181$	5.26219	0.391136	0.195568	−	0.980690i	$-0.437345\pi$
$181$	5.26219	0.391136	0.195568	+	0.980690i	$0.437345\pi$
$182$	−1.43451	−0.106333
$183$	−9.05962	−0.669706
$184$	0.596479	0.0439730
$185$	0.310871	0.0228557
$186$	27.8173	2.03966
$187$	−20.5336	−1.50156
$188$	−30.0880	−2.19439
$189$	−9.17909	−0.667680
$190$	−0.452975	−0.0328623
$191$	−10.3088	−0.745920	−0.372960	−	0.927847i	$-0.621657\pi$
$191$	−10.3088	−0.745920	−0.372960	+	0.927847i	$0.621657\pi$
$192$	−37.0353	−2.67279
$193$	−2.70997	−0.195068	−0.0975340	−	0.995232i	$-0.531095\pi$
$193$	−2.70997	−0.195068	−0.0975340	+	0.995232i	$0.531095\pi$
$194$	−39.0350	−2.80255
$195$	0.0665878	0.00476845
$196$	−14.3315	−1.02368
$197$	−14.7786	−1.05293	−0.526466	−	0.850196i	$-0.676483\pi$
$197$	−14.7786	−1.05293	−0.526466	+	0.850196i	$0.676483\pi$
$198$	−45.6676	−3.24546
$199$	15.0031	1.06354	0.531770	−	0.846889i	$-0.321527\pi$
$199$	15.0031	1.06354	0.531770	+	0.846889i	$0.321527\pi$
$200$	−12.9478	−0.915551
$201$	30.8843	2.17841
$202$	−14.1498	−0.995577
$203$	0	0
$204$	46.1385	3.23034
$205$	−0.0846792	−0.00591425
$206$	29.9580	2.08727
$207$	1.16677	0.0810959
$208$	−0.165611	−0.0114830
$209$	13.7100	0.948338
$210$	−0.582397	−0.0401892
$211$	−11.9730	−0.824257	−0.412128	−	0.911126i	$-0.635214\pi$
$211$	−11.9730	−0.824257	−0.412128	+	0.911126i	$0.635214\pi$
$212$	−5.62161	−0.386093
$213$	38.2138	2.61837
$214$	21.0180	1.43676
$215$	0.375263	0.0255927
$216$	15.2282	1.03615
$217$	−6.74505	−0.457884
$218$	−13.0518	−0.883981
$219$	−19.9284	−1.34664
$220$	−0.722696	−0.0487241
$221$	2.09314	0.140800
$222$	34.5964	2.32196
$223$	13.3713	0.895406	0.447703	−	0.894182i	$-0.352242\pi$
$223$	13.3713	0.895406	0.447703	+	0.894182i	$0.352242\pi$
$224$	9.54351	0.637653
$225$	−25.3272	−1.68848
$226$	18.2832	1.21618
$227$	−2.12231	−0.140862	−0.0704312	−	0.997517i	$-0.522438\pi$
$227$	−2.12231	−0.140862	−0.0704312	+	0.997517i	$0.522438\pi$
$228$	−30.8060	−2.04018
$229$	−27.3896	−1.80996	−0.904979	−	0.425456i	$-0.860114\pi$
$229$	−27.3896	−1.80996	−0.904979	+	0.425456i	$0.860114\pi$
$230$	0.0302149	0.00199231
$231$	17.6271	1.15978
$232$	0	0
$233$	17.4774	1.14498	0.572492	−	0.819910i	$-0.305977\pi$
$233$	17.4774	1.14498	0.572492	+	0.819910i	$0.305977\pi$
$234$	4.65524	0.304322
$235$	−0.554169	−0.0361500
$236$	−3.30661	−0.215242
$237$	13.5911	0.882837
$238$	−18.3072	−1.18668
$239$	17.2524	1.11597	0.557984	−	0.829852i	$-0.311575\pi$
$239$	17.2524	1.11597	0.557984	+	0.829852i	$0.311575\pi$
$240$	−0.0672362	−0.00434008
$241$	21.9867	1.41629	0.708143	−	0.706069i	$-0.249533\pi$
$241$	21.9867	1.41629	0.708143	+	0.706069i	$0.249533\pi$
$242$	10.8485	0.697368
$243$	−13.4073	−0.860081
$244$	−10.0232	−0.641667
$245$	−0.263962	−0.0168639
$246$	−9.42382	−0.600841
$247$	−1.39756	−0.0889245
$248$	11.1901	0.710572
$249$	23.9274	1.51634
$250$	−1.31220	−0.0829906
$251$	−9.77072	−0.616722	−0.308361	−	0.951269i	$-0.599781\pi$
$251$	−9.77072	−0.616722	−0.308361	+	0.951269i	$0.599781\pi$
$252$	−24.8815	−1.56739
$253$	−0.914498	−0.0574940
$254$	39.8526	2.50058
$255$	0.849793	0.0532161
$256$	−13.2625	−0.828907
$257$	−15.4022	−0.960766	−0.480383	−	0.877059i	$-0.659502\pi$
$257$	−15.4022	−0.960766	−0.480383	+	0.877059i	$0.659502\pi$
$258$	41.7625	2.60002
$259$	−8.38881	−0.521256
$260$	0.0736698	0.00456880
$261$	0	0
$262$	7.59225	0.469050
$263$	−30.9933	−1.91113	−0.955564	−	0.294784i	$-0.904752\pi$
$263$	−30.9933	−1.91113	−0.955564	+	0.294784i	$0.904752\pi$
$264$	−29.2435	−1.79982
$265$	−0.103540	−0.00636044
$266$	12.2235	0.749470
$267$	−3.21743	−0.196903
$268$	34.1690	2.08720
$269$	−13.8549	−0.844751	−0.422375	−	0.906421i	$-0.638804\pi$
$269$	−13.8549	−0.844751	−0.422375	+	0.906421i	$0.638804\pi$
$270$	0.771390	0.0469453
$271$	−26.8382	−1.63030	−0.815152	−	0.579247i	$-0.803347\pi$
$271$	−26.8382	−1.63030	−0.815152	+	0.579247i	$0.803347\pi$
$272$	−2.11352	−0.128151
$273$	−1.79686	−0.108751
$274$	−12.5193	−0.756320
$275$	19.8511	1.19707
$276$	2.05486	0.123688
$277$	−22.5563	−1.35528	−0.677639	−	0.735395i	$-0.736997\pi$
$277$	−22.5563	−1.35528	−0.677639	+	0.735395i	$0.736997\pi$
$278$	−1.35500	−0.0812675
$279$	21.8888	1.31045
$280$	−0.234282	−0.0140010
$281$	−3.30007	−0.196866	−0.0984328	−	0.995144i	$-0.531383\pi$
$281$	−3.30007	−0.196866	−0.0984328	+	0.995144i	$0.531383\pi$
$282$	−61.6727	−3.67255
$283$	−17.6686	−1.05029	−0.525144	−	0.851013i	$-0.675989\pi$
$283$	−17.6686	−1.05029	−0.525144	+	0.851013i	$0.675989\pi$
$284$	42.2780	2.50874
$285$	−0.567395	−0.0336096
$286$	−3.64872	−0.215753
$287$	2.28506	0.134883
$288$	−30.9703	−1.82494
$289$	9.71265	0.571332
$290$	0	0
$291$	−48.8951	−2.86628
$292$	−22.0479	−1.29025
$293$	13.5342	0.790675	0.395338	−	0.918536i	$-0.370628\pi$
$293$	13.5342	0.790675	0.395338	+	0.918536i	$0.370628\pi$
$294$	−29.3759	−1.71324
$295$	−0.0609022	−0.00354586
$296$	13.9171	0.808916
$297$	−23.3472	−1.35474
$298$	11.5861	0.671165
$299$	0.0932216	0.00539114
$300$	−44.6051	−2.57527
$301$	−10.1264	−0.583678
$302$	−17.6890	−1.01789
$303$	−17.7240	−1.01822
$304$	1.41117	0.0809360
$305$	−0.184610	−0.0105707
$306$	59.4102	3.39625
$307$	6.51865	0.372039	0.186020	−	0.982546i	$-0.440441\pi$
$307$	6.51865	0.372039	0.186020	+	0.982546i	$0.440441\pi$
$308$	19.5019	1.11122
$309$	37.5252	2.13474
$310$	0.566839	0.0321943
$311$	24.5460	1.39187	0.695937	−	0.718102i	$-0.254989\pi$
$311$	24.5460	1.39187	0.695937	+	0.718102i	$0.254989\pi$
$312$	2.98101	0.168767
$313$	1.97447	0.111604	0.0558018	−	0.998442i	$-0.482229\pi$
$313$	1.97447	0.111604	0.0558018	+	0.998442i	$0.482229\pi$
$314$	42.7645	2.41334
$315$	−0.458276	−0.0258209
$316$	15.0366	0.845875
$317$	−29.6808	−1.66704	−0.833519	−	0.552491i	$-0.813678\pi$
$317$	−29.6808	−1.66704	−0.833519	+	0.552491i	$0.813678\pi$
$318$	−11.5229	−0.646170
$319$	0	0
$320$	−0.754675	−0.0421876
$321$	26.3270	1.46943
$322$	−0.815345	−0.0454374
$323$	−17.8356	−0.992402
$324$	4.67170	0.259539
$325$	−2.02357	−0.112248
$326$	−5.12964	−0.284105
$327$	−16.3486	−0.904082
$328$	−3.79093	−0.209319
$329$	14.9542	0.824451
$330$	−1.48134	−0.0815452
$331$	−28.3740	−1.55958	−0.779788	−	0.626044i	$-0.784673\pi$
$331$	−28.3740	−1.55958	−0.779788	+	0.626044i	$0.784673\pi$
$332$	26.4722	1.45285
$333$	27.2231	1.49182
$334$	26.6118	1.45613
$335$	0.629335	0.0343842
$336$	1.81436	0.0989814
$337$	−4.01726	−0.218834	−0.109417	−	0.993996i	$-0.534898\pi$
$337$	−4.01726	−0.218834	−0.109417	+	0.993996i	$0.534898\pi$
$338$	−29.1088	−1.58331
$339$	22.9014	1.24383
$340$	0.940173	0.0509881
$341$	−17.1562	−0.929061
$342$	−39.6673	−2.14496
$343$	18.0567	0.974970
$344$	16.7998	0.905787
$345$	0.0378470	0.00203761
$346$	43.7424	2.35160
$347$	−3.55272	−0.190720	−0.0953601	−	0.995443i	$-0.530400\pi$
$347$	−3.55272	−0.190720	−0.0953601	+	0.995443i	$0.530400\pi$
$348$	0	0
$349$	3.34203	0.178895	0.0894473	−	0.995992i	$-0.471490\pi$
$349$	3.34203	0.178895	0.0894473	+	0.995992i	$0.471490\pi$
$350$	17.6988	0.946040
$351$	2.37996	0.127033
$352$	24.2742	1.29382
$353$	12.5154	0.666125	0.333063	−	0.942905i	$-0.391918\pi$
$353$	12.5154	0.666125	0.333063	+	0.942905i	$0.391918\pi$
$354$	−6.77771	−0.360231
$355$	0.778690	0.0413286
$356$	−3.55962	−0.188659
$357$	−22.9316	−1.21367
$358$	2.06453	0.109114
$359$	18.3959	0.970899	0.485450	−	0.874265i	$-0.338656\pi$
$359$	18.3959	0.970899	0.485450	+	0.874265i	$0.338656\pi$
$360$	0.760284	0.0400705
$361$	−7.09140	−0.373231
$362$	11.9333	0.627202
$363$	13.5888	0.713225
$364$	−1.98797	−0.104198
$365$	−0.406084	−0.0212554
$366$	−20.5449	−1.07390
$367$	9.83019	0.513132	0.256566	−	0.966527i	$-0.417409\pi$
$367$	9.83019	0.513132	0.256566	+	0.966527i	$0.417409\pi$
$368$	−0.0941293	−0.00490683
$369$	−7.41540	−0.386030
$370$	0.704977	0.0366500
$371$	2.79403	0.145059
$372$	38.5496	1.99871
$373$	22.1796	1.14842	0.574209	−	0.818709i	$-0.305310\pi$
$373$	22.1796	1.14842	0.574209	+	0.818709i	$0.305310\pi$
$374$	−46.5650	−2.40782
$375$	−1.64365	−0.0848777
$376$	−24.8091	−1.27943
$377$	0	0
$378$	−20.8159	−1.07065
$379$	8.70022	0.446900	0.223450	−	0.974715i	$-0.428268\pi$
$379$	8.70022	0.446900	0.223450	+	0.974715i	$0.428268\pi$
$380$	−0.627740	−0.0322024
$381$	49.9192	2.55744
$382$	−23.3778	−1.19611
$383$	5.08621	0.259893	0.129947	−	0.991521i	$-0.458519\pi$
$383$	5.08621	0.259893	0.129947	+	0.991521i	$0.458519\pi$
$384$	−49.2752	−2.51456
$385$	0.359191	0.0183061
$386$	−6.14553	−0.312799
$387$	32.8620	1.67047
$388$	−54.0953	−2.74627
$389$	29.8408	1.51299	0.756494	−	0.654000i	$-0.226910\pi$
$389$	29.8408	1.51299	0.756494	+	0.654000i	$0.226910\pi$
$390$	0.151004	0.00764640
$391$	1.18969	0.0601654
$392$	−11.8171	−0.596853
$393$	9.51001	0.479716
$394$	−33.5142	−1.68842
$395$	0.276949	0.0139348
$396$	−63.2869	−3.18028
$397$	−2.92259	−0.146680	−0.0733402	−	0.997307i	$-0.523366\pi$
$397$	−2.92259	−0.146680	−0.0733402	+	0.997307i	$0.523366\pi$
$398$	34.0232	1.70543
$399$	15.3111	0.766512
$400$	2.04328	0.102164
$401$	−20.4408	−1.02076	−0.510382	−	0.859948i	$-0.670496\pi$
$401$	−20.4408	−1.02076	−0.510382	+	0.859948i	$0.670496\pi$
$402$	70.0377	3.49316
$403$	1.74886	0.0871169
$404$	−19.6090	−0.975585
$405$	0.0860448	0.00427560
$406$	0	0
$407$	−21.3372	−1.05764
$408$	38.0437	1.88344
$409$	−33.6119	−1.66200	−0.831001	−	0.556271i	$-0.812232\pi$
$409$	−33.6119	−1.66200	−0.831001	+	0.556271i	$0.812232\pi$
$410$	−0.192031	−0.00948374
$411$	−15.6816	−0.773518
$412$	41.5163	2.04536
$413$	1.64344	0.0808683
$414$	2.64593	0.130041
$415$	0.487573	0.0239340
$416$	−2.47445	−0.121320
$417$	−1.69727	−0.0831154
$418$	31.0907	1.52070
$419$	−7.53000	−0.367865	−0.183932	−	0.982939i	$-0.558883\pi$
$419$	−7.53000	−0.367865	−0.183932	+	0.982939i	$0.558883\pi$
$420$	−0.807095	−0.0393822
$421$	−20.3755	−0.993041	−0.496521	−	0.868025i	$-0.665389\pi$
$421$	−20.3755	−0.993041	−0.496521	+	0.868025i	$0.665389\pi$
$422$	−27.1518	−1.32173
$423$	−48.5289	−2.35956
$424$	−4.63531	−0.225111
$425$	−25.8248	−1.25269
$426$	86.6592	4.19865
$427$	4.98167	0.241080
$428$	29.1270	1.40791
$429$	−4.57037	−0.220659
$430$	0.851002	0.0410390
$431$	11.8352	0.570081	0.285040	−	0.958516i	$-0.407993\pi$
$431$	11.8352	0.570081	0.285040	+	0.958516i	$0.407993\pi$
$432$	−2.40313	−0.115621
$433$	−17.0972	−0.821637	−0.410818	−	0.911717i	$-0.634757\pi$
$433$	−17.0972	−0.821637	−0.410818	+	0.911717i	$0.634757\pi$
$434$	−15.2961	−0.734235
$435$	0	0
$436$	−18.0874	−0.866230
$437$	−0.794341	−0.0379985
$438$	−45.1925	−2.15938
$439$	18.7510	0.894934	0.447467	−	0.894300i	$-0.352326\pi$
$439$	18.7510	0.894934	0.447467	+	0.894300i	$0.352326\pi$
$440$	−0.595901	−0.0284085
$441$	−23.1153	−1.10073
$442$	4.74671	0.225778
$443$	3.40383	0.161721	0.0808603	−	0.996725i	$-0.474233\pi$
$443$	3.40383	0.161721	0.0808603	+	0.996725i	$0.474233\pi$
$444$	47.9442	2.27533
$445$	−0.0655622	−0.00310794
$446$	30.3227	1.43582
$447$	14.5127	0.686427
$448$	20.3648	0.962147
$449$	0.139283	0.00657317	0.00328658	−	0.999995i	$-0.498954\pi$
$449$	0.139283	0.00657317	0.00328658	+	0.999995i	$0.498954\pi$
$450$	−57.4356	−2.70754
$451$	5.81210	0.273681
$452$	25.3371	1.19176
$453$	−22.1572	−1.04104
$454$	−4.81285	−0.225878
$455$	−0.0366150	−0.00171654
$456$	−25.4012	−1.18952
$457$	32.0795	1.50062	0.750308	−	0.661088i	$-0.229905\pi$
$457$	32.0795	1.50062	0.750308	+	0.661088i	$0.229905\pi$
$458$	−62.1128	−2.90234
$459$	30.3730	1.41769
$460$	0.0418722	0.00195230
$461$	−0.725509	−0.0337903	−0.0168952	−	0.999857i	$-0.505378\pi$
$461$	−0.725509	−0.0337903	−0.0168952	+	0.999857i	$0.505378\pi$
$462$	39.9738	1.85975
$463$	−9.14813	−0.425150	−0.212575	−	0.977145i	$-0.568185\pi$
$463$	−9.14813	−0.425150	−0.212575	+	0.977145i	$0.568185\pi$
$464$	0	0
$465$	0.710019	0.0329263
$466$	39.6344	1.83603
$467$	30.6641	1.41897	0.709483	−	0.704722i	$-0.248928\pi$
$467$	30.6641	1.41897	0.709483	+	0.704722i	$0.248928\pi$
$468$	6.45130	0.298211
$469$	−16.9825	−0.784180
$470$	−1.25672	−0.0579680
$471$	53.5666	2.46822
$472$	−2.72648	−0.125496
$473$	−25.7568	−1.18430
$474$	30.8212	1.41566
$475$	17.2429	0.791157
$476$	−25.3705	−1.16285
$477$	−9.06709	−0.415154
$478$	39.1242	1.78950
$479$	5.29729	0.242039	0.121020	−	0.992650i	$-0.461384\pi$
$479$	5.29729	0.242039	0.121020	+	0.992650i	$0.461384\pi$
$480$	−1.00460	−0.0458535
$481$	2.17506	0.0991740
$482$	49.8602	2.27107
$483$	−1.02130	−0.0464706
$484$	15.0340	0.683364
$485$	−0.996344	−0.0452417
$486$	−30.4045	−1.37917
$487$	−3.48158	−0.157766	−0.0788828	−	0.996884i	$-0.525135\pi$
$487$	−3.48158	−0.157766	−0.0788828	+	0.996884i	$0.525135\pi$
$488$	−8.26463	−0.374122
$489$	−6.42536	−0.290565
$490$	−0.598599	−0.0270419
$491$	5.85160	0.264079	0.132039	−	0.991244i	$-0.457847\pi$
$491$	5.85160	0.264079	0.132039	+	0.991244i	$0.457847\pi$
$492$	−13.0597	−0.588776
$493$	0	0
$494$	−3.16931	−0.142594
$495$	−1.16564	−0.0523915
$496$	−1.76589	−0.0792908
$497$	−21.0128	−0.942555
$498$	54.2613	2.43151
$499$	−23.7183	−1.06178	−0.530889	−	0.847441i	$-0.678142\pi$
$499$	−23.7183	−1.06178	−0.530889	+	0.847441i	$0.678142\pi$
$500$	−1.81846	−0.0813240
$501$	33.3338	1.48924
$502$	−22.1575	−0.988939
$503$	−19.3361	−0.862154	−0.431077	−	0.902315i	$-0.641866\pi$
$503$	−19.3361	−0.862154	−0.431077	+	0.902315i	$0.641866\pi$
$504$	−20.5162	−0.913863
$505$	−0.361165	−0.0160716
$506$	−2.07385	−0.0921939
$507$	−36.4615	−1.61931
$508$	55.2284	2.45036
$509$	38.8356	1.72136	0.860678	−	0.509149i	$-0.170040\pi$
$509$	38.8356	1.72136	0.860678	+	0.509149i	$0.170040\pi$
$510$	1.92712	0.0853342
$511$	10.9581	0.484759
$512$	4.61786	0.204083
$513$	−20.2796	−0.895368
$514$	−34.9284	−1.54063
$515$	0.764659	0.0336949
$516$	57.8751	2.54781
$517$	38.0364	1.67284
$518$	−19.0237	−0.835854
$519$	54.7915	2.40508
$520$	0.0607446	0.00266383
$521$	−33.3472	−1.46097	−0.730484	−	0.682930i	$-0.760706\pi$
$521$	−33.3472	−1.46097	−0.730484	+	0.682930i	$0.760706\pi$
$522$	0	0
$523$	31.8103	1.39097	0.695484	−	0.718542i	$-0.255190\pi$
$523$	31.8103	1.39097	0.695484	+	0.718542i	$0.255190\pi$
$524$	10.5214	0.459632
$525$	22.1694	0.967552
$526$	−70.2849	−3.06457
$527$	22.3189	0.972229
$528$	4.61487	0.200836
$529$	−22.9470	−0.997696
$530$	−0.234804	−0.0101992
$531$	−5.33324	−0.231443
$532$	16.9395	0.734420
$533$	−0.592471	−0.0256628
$534$	−7.29632	−0.315742
$535$	0.536471	0.0231937
$536$	28.1741	1.21694
$537$	2.58602	0.111595
$538$	−31.4195	−1.35459
$539$	18.1175	0.780375
$540$	1.06900	0.0460026
$541$	38.7402	1.66557	0.832785	−	0.553596i	$-0.186745\pi$
$541$	38.7402	1.66557	0.832785	+	0.553596i	$0.186745\pi$
$542$	−60.8622	−2.61426
$543$	14.9476	0.641464
$544$	−31.5789	−1.35393
$545$	−0.333140	−0.0142701
$546$	−4.07483	−0.174387
$547$	5.99056	0.256138	0.128069	−	0.991765i	$-0.459122\pi$
$547$	5.99056	0.256138	0.128069	+	0.991765i	$0.459122\pi$
$548$	−17.3495	−0.741132
$549$	−16.1664	−0.689964
$550$	45.0173	1.91954
$551$	0	0
$552$	1.69434	0.0721159
$553$	−7.47342	−0.317802
$554$	−51.1520	−2.17324
$555$	0.883050	0.0374834
$556$	−1.87778	−0.0796356
$557$	1.87739	0.0795478	0.0397739	−	0.999209i	$-0.487336\pi$
$557$	1.87739	0.0795478	0.0397739	+	0.999209i	$0.487336\pi$
$558$	49.6384	2.10136
$559$	2.62559	0.111050
$560$	0.0369716	0.00156233
$561$	−58.3270	−2.46257
$562$	−7.48372	−0.315682
$563$	26.4739	1.11574	0.557872	−	0.829927i	$-0.311618\pi$
$563$	26.4739	1.11574	0.557872	+	0.829927i	$0.311618\pi$
$564$	−85.4669	−3.59881
$565$	0.466667	0.0196328
$566$	−40.0679	−1.68418
$567$	−2.32191	−0.0975110
$568$	34.8605	1.46271
$569$	−12.7851	−0.535980	−0.267990	−	0.963422i	$-0.586359\pi$
$569$	−12.7851	−0.535980	−0.267990	+	0.963422i	$0.586359\pi$
$570$	−1.28671	−0.0538943
$571$	−38.0544	−1.59253	−0.796263	−	0.604951i	$-0.793193\pi$
$571$	−38.0544	−1.59253	−0.796263	+	0.604951i	$0.793193\pi$
$572$	−5.05645	−0.211421
$573$	−29.2829	−1.22331
$574$	5.18193	0.216290
$575$	−1.15015	−0.0479647
$576$	−66.0873	−2.75364
$577$	0.102256	0.00425695	0.00212848	−	0.999998i	$-0.499322\pi$
$577$	0.102256	0.00425695	0.00212848	+	0.999998i	$0.499322\pi$
$578$	22.0258	0.916154
$579$	−7.69786	−0.319912
$580$	0	0
$581$	−13.1571	−0.545848
$582$	−110.882	−4.59619
$583$	7.10668	0.294328
$584$	−18.1796	−0.752279
$585$	0.118822	0.00491269
$586$	30.6921	1.26788
$587$	−0.735311	−0.0303495	−0.0151748	−	0.999885i	$-0.504830\pi$
$587$	−0.735311	−0.0303495	−0.0151748	+	0.999885i	$0.504830\pi$
$588$	−40.7096	−1.67884
$589$	−14.9020	−0.614028
$590$	−0.138111	−0.00568593
$591$	−41.9797	−1.72681
$592$	−2.19624	−0.0902647
$593$	44.7555	1.83789	0.918944	−	0.394388i	$-0.129043\pi$
$593$	44.7555	1.83789	0.918944	+	0.394388i	$0.129043\pi$
$594$	−52.9457	−2.17239
$595$	−0.467281	−0.0191566
$596$	16.0562	0.657687
$597$	42.6173	1.74421
$598$	0.211403	0.00864491
$599$	4.06004	0.165889	0.0829444	−	0.996554i	$-0.473568\pi$
$599$	4.06004	0.165889	0.0829444	+	0.996554i	$0.473568\pi$
$600$	−36.7792	−1.50151
$601$	−44.4331	−1.81246	−0.906232	−	0.422781i	$-0.861054\pi$
$601$	−44.4331	−1.81246	−0.906232	+	0.422781i	$0.861054\pi$
$602$	−22.9642	−0.935950
$603$	55.1112	2.24430
$604$	−24.5137	−0.997449
$605$	0.276901	0.0112576
$606$	−40.1935	−1.63275
$607$	−9.70174	−0.393781	−0.196891	−	0.980425i	$-0.563084\pi$
$607$	−9.70174	−0.393781	−0.196891	+	0.980425i	$0.563084\pi$
$608$	21.0848	0.855100
$609$	0	0
$610$	−0.418648	−0.0169506
$611$	−3.87733	−0.156860
$612$	82.3315	3.32805
$613$	−1.78505	−0.0720975	−0.0360488	−	0.999350i	$-0.511477\pi$
$613$	−1.78505	−0.0720975	−0.0360488	+	0.999350i	$0.511477\pi$
$614$	14.7827	0.596580
$615$	−0.240537	−0.00969939
$616$	16.0803	0.647894
$617$	8.71009	0.350655	0.175327	−	0.984510i	$-0.443902\pi$
$617$	8.71009	0.350655	0.175327	+	0.984510i	$0.443902\pi$
$618$	85.0978	3.42313
$619$	14.2041	0.570911	0.285456	−	0.958392i	$-0.407855\pi$
$619$	14.2041	0.570911	0.285456	+	0.958392i	$0.407855\pi$
$620$	0.785534	0.0315478
$621$	1.35272	0.0542826
$622$	55.6641	2.23193
$623$	1.76919	0.0708810
$624$	−0.470428	−0.0188322
$625$	24.9498	0.997990
$626$	4.47759	0.178961
$627$	38.9441	1.55528
$628$	59.2637	2.36488
$629$	27.7581	1.10679
$630$	−1.03925	−0.0414049
$631$	16.5703	0.659653	0.329827	−	0.944042i	$-0.393010\pi$
$631$	16.5703	0.659653	0.329827	+	0.944042i	$0.393010\pi$
$632$	12.3985	0.493185
$633$	−34.0102	−1.35178
$634$	−67.3085	−2.67316
$635$	1.01721	0.0403669
$636$	−15.9686	−0.633194
$637$	−1.84685	−0.0731748
$638$	0	0
$639$	68.1903	2.69757
$640$	−1.00409	−0.0396901
$641$	−7.29754	−0.288236	−0.144118	−	0.989561i	$-0.546034\pi$
$641$	−7.29754	−0.288236	−0.144118	+	0.989561i	$0.546034\pi$
$642$	59.7030	2.35629
$643$	−33.8706	−1.33573	−0.667863	−	0.744284i	$-0.732791\pi$
$643$	−33.8706	−1.33573	−0.667863	+	0.744284i	$0.732791\pi$
$644$	−1.12992	−0.0445250
$645$	1.06596	0.0419722
$646$	−40.4467	−1.59136
$647$	33.4448	1.31485	0.657425	−	0.753520i	$-0.271646\pi$
$647$	33.4448	1.31485	0.657425	+	0.753520i	$0.271646\pi$
$648$	3.85207	0.151324
$649$	4.18013	0.164084
$650$	−4.58895	−0.179993
$651$	−19.1598	−0.750931
$652$	−7.10874	−0.278400
$653$	23.7557	0.929633	0.464817	−	0.885407i	$-0.346120\pi$
$653$	23.7557	0.929633	0.464817	+	0.885407i	$0.346120\pi$
$654$	−37.0746	−1.44973
$655$	0.193787	0.00757189
$656$	0.598240	0.0233573
$657$	−35.5610	−1.38737
$658$	33.9123	1.32204
$659$	−4.93124	−0.192094	−0.0960469	−	0.995377i	$-0.530620\pi$
$659$	−4.93124	−0.192094	−0.0960469	+	0.995377i	$0.530620\pi$
$660$	−2.05287	−0.0799077
$661$	−23.4731	−0.912998	−0.456499	−	0.889724i	$-0.650897\pi$
$661$	−23.4731	−0.912998	−0.456499	+	0.889724i	$0.650897\pi$
$662$	−64.3450	−2.50084
$663$	5.94571	0.230912
$664$	21.8277	0.847081
$665$	0.311997	0.0120987
$666$	61.7352	2.39219
$667$	0	0
$668$	36.8790	1.42689
$669$	37.9820	1.46847
$670$	1.42717	0.0551365
$671$	12.6710	0.489158
$672$	27.1090	1.04575
$673$	29.9293	1.15369	0.576846	−	0.816853i	$-0.304283\pi$
$673$	29.9293	1.15369	0.576846	+	0.816853i	$0.304283\pi$
$674$	−9.11013	−0.350909
$675$	−29.3636	−1.13020
$676$	−40.3394	−1.55151
$677$	22.0163	0.846154	0.423077	−	0.906094i	$-0.360950\pi$
$677$	22.0163	0.846154	0.423077	+	0.906094i	$0.360950\pi$
$678$	51.9346	1.99454
$679$	26.8862	1.03180
$680$	0.775223	0.0297285
$681$	−6.02856	−0.231015
$682$	−38.9059	−1.48979
$683$	−4.61710	−0.176668	−0.0883341	−	0.996091i	$-0.528154\pi$
$683$	−4.61710	−0.176668	−0.0883341	+	0.996091i	$0.528154\pi$
$684$	−54.9715	−2.10189
$685$	−0.319548	−0.0122093
$686$	40.9480	1.56340
$687$	−77.8022	−2.96834
$688$	−2.65115	−0.101074
$689$	−0.724436	−0.0275988
$690$	0.0858274	0.00326739
$691$	−35.7459	−1.35984	−0.679919	−	0.733287i	$-0.737985\pi$
$691$	−35.7459	−1.35984	−0.679919	+	0.733287i	$0.737985\pi$
$692$	60.6188	2.30438
$693$	31.4546	1.19486
$694$	−8.05668	−0.305827
$695$	−0.0345855	−0.00131190
$696$	0	0
$697$	−7.56111	−0.286398
$698$	7.57887	0.286865
$699$	49.6458	1.87778
$700$	24.5272	0.927043
$701$	−3.64465	−0.137656	−0.0688282	−	0.997629i	$-0.521926\pi$
$701$	−3.64465	−0.137656	−0.0688282	+	0.997629i	$0.521926\pi$
$702$	5.39714	0.203702
$703$	−18.5337	−0.699010
$704$	51.7984	1.95223
$705$	−1.57416	−0.0592861
$706$	28.3817	1.06816
$707$	9.74598	0.366535
$708$	−9.39266	−0.352998
$709$	−20.9910	−0.788334	−0.394167	−	0.919039i	$-0.628967\pi$
$709$	−20.9910	−0.788334	−0.394167	+	0.919039i	$0.628967\pi$
$710$	1.76587	0.0662720
$711$	24.2525	0.909541
$712$	−2.93510	−0.109997
$713$	0.994013	0.0372261
$714$	−52.0030	−1.94616
$715$	−0.0931312	−0.00348291
$716$	2.86105	0.106923
$717$	49.0067	1.83019
$718$	41.7173	1.55688
$719$	24.2529	0.904480	0.452240	−	0.891896i	$-0.350625\pi$
$719$	24.2529	0.904480	0.452240	+	0.891896i	$0.350625\pi$
$720$	−0.119979	−0.00447136
$721$	−20.6342	−0.768459
$722$	−16.0815	−0.598491
$723$	62.4547	2.32271
$724$	16.5374	0.614607
$725$	0	0
$726$	30.8159	1.14368
$727$	30.9357	1.14734	0.573672	−	0.819085i	$-0.305519\pi$
$727$	30.9357	1.14734	0.573672	+	0.819085i	$0.305519\pi$
$728$	−1.63919	−0.0607523
$729$	−42.5441	−1.57571
$730$	−0.920897	−0.0340839
$731$	33.5077	1.23933
$732$	−28.4715	−1.05234
$733$	−18.5100	−0.683681	−0.341841	−	0.939758i	$-0.611050\pi$
$733$	−18.5100	−0.683681	−0.341841	+	0.939758i	$0.611050\pi$
$734$	22.2924	0.822827
$735$	−0.749802	−0.0276569
$736$	−1.40642	−0.0518413
$737$	−43.1955	−1.59113
$738$	−16.8163	−0.619015
$739$	−34.0491	−1.25251	−0.626257	−	0.779616i	$-0.715414\pi$
$739$	−34.0491	−1.25251	−0.626257	+	0.779616i	$0.715414\pi$
$740$	0.976968	0.0359140
$741$	−3.96986	−0.145837
$742$	6.33614	0.232607
$743$	−34.8269	−1.27768	−0.638838	−	0.769342i	$-0.720584\pi$
$743$	−34.8269	−1.27768	−0.638838	+	0.769342i	$0.720584\pi$
$744$	31.7862	1.16534
$745$	0.295728	0.0108346
$746$	50.2978	1.84153
$747$	42.6970	1.56220
$748$	−64.5304	−2.35947
$749$	−14.4766	−0.528963
$750$	−3.72738	−0.136105
$751$	−48.5887	−1.77303	−0.886513	−	0.462703i	$-0.846880\pi$
$751$	−48.5887	−1.77303	−0.886513	+	0.462703i	$0.846880\pi$
$752$	3.91508	0.142768
$753$	−27.7544	−1.01143
$754$	0	0
$755$	−0.451501	−0.0164318
$756$	−28.8469	−1.04915
$757$	−30.0918	−1.09371	−0.546853	−	0.837229i	$-0.684174\pi$
$757$	−30.0918	−1.09371	−0.546853	+	0.837229i	$0.684174\pi$
$758$	19.7299	0.716622
$759$	−2.59769	−0.0942903
$760$	−0.517605	−0.0187755
$761$	−9.82865	−0.356288	−0.178144	−	0.984004i	$-0.557009\pi$
$761$	−9.82865	−0.356288	−0.178144	+	0.984004i	$0.557009\pi$
$762$	113.204	4.10095
$763$	8.98973	0.325450
$764$	−32.3973	−1.17209
$765$	1.51641	0.0548258
$766$	11.5342	0.416749
$767$	−0.426111	−0.0153860
$768$	−37.6731	−1.35941
$769$	29.9752	1.08093	0.540466	−	0.841366i	$-0.318248\pi$
$769$	29.9752	1.08093	0.540466	+	0.841366i	$0.318248\pi$
$770$	0.814555	0.0293545
$771$	−43.7511	−1.57566
$772$	−8.51656	−0.306518
$773$	−16.9149	−0.608388	−0.304194	−	0.952610i	$-0.598387\pi$
$773$	−16.9149	−0.608388	−0.304194	+	0.952610i	$0.598387\pi$
$774$	74.5227	2.67866
$775$	−21.5772	−0.775074
$776$	−44.6045	−1.60121
$777$	−23.8290	−0.854861
$778$	67.6714	2.42614
$779$	5.04844	0.180879
$780$	0.209264	0.00749285
$781$	−53.4467	−1.91247
$782$	2.69792	0.0964776
$783$	0	0
$784$	1.86483	0.0666012
$785$	1.09154	0.0389586
$786$	21.5663	0.769244
$787$	−19.9957	−0.712769	−0.356384	−	0.934339i	$-0.615991\pi$
$787$	−19.9957	−0.712769	−0.356384	+	0.934339i	$0.615991\pi$
$788$	−46.4444	−1.65451
$789$	−88.0386	−3.13426
$790$	0.628049	0.0223450
$791$	−12.5929	−0.447753
$792$	−52.1834	−1.85426
$793$	−1.29165	−0.0458678
$794$	−6.62769	−0.235208
$795$	−0.294114	−0.0104311
$796$	47.1499	1.67118
$797$	40.3008	1.42753	0.713764	−	0.700387i	$-0.246989\pi$
$797$	40.3008	1.42753	0.713764	+	0.700387i	$0.246989\pi$
$798$	34.7216	1.22913
$799$	−49.4825	−1.75056
$800$	30.5293	1.07937
$801$	−5.74131	−0.202859
$802$	−46.3545	−1.63684
$803$	27.8723	0.983592
$804$	97.0593	3.42302
$805$	−0.0208112	−0.000733497 0
$806$	3.96597	0.139695
$807$	−39.3559	−1.38539
$808$	−16.1687	−0.568812
$809$	50.1152	1.76196	0.880978	−	0.473157i	$-0.156886\pi$
$809$	50.1152	1.76196	0.880978	+	0.473157i	$0.156886\pi$
$810$	0.195128	0.00685610
$811$	−24.7764	−0.870017	−0.435009	−	0.900426i	$-0.643255\pi$
$811$	−24.7764	−0.870017	−0.435009	+	0.900426i	$0.643255\pi$
$812$	0	0
$813$	−76.2357	−2.67370
$814$	−48.3873	−1.69597
$815$	−0.130931	−0.00458631
$816$	−6.00360	−0.210168
$817$	−22.3726	−0.782719
$818$	−76.2233	−2.66509
$819$	−3.20640	−0.112041
$820$	−0.266120	−0.00929330
$821$	−35.5876	−1.24202	−0.621008	−	0.783804i	$-0.713277\pi$
$821$	−35.5876	−1.24202	−0.621008	+	0.783804i	$0.713277\pi$
$822$	−35.5620	−1.24037
$823$	−15.4039	−0.536947	−0.268474	−	0.963287i	$-0.586519\pi$
$823$	−15.4039	−0.536947	−0.268474	+	0.963287i	$0.586519\pi$
$824$	34.2324	1.19254
$825$	56.3885	1.96319
$826$	3.72690	0.129675
$827$	−41.4272	−1.44056	−0.720282	−	0.693682i	$-0.755987\pi$
$827$	−41.4272	−1.44056	−0.720282	+	0.693682i	$0.755987\pi$
$828$	3.66677	0.127429
$829$	−4.64043	−0.161169	−0.0805844	−	0.996748i	$-0.525679\pi$
$829$	−4.64043	−0.161169	−0.0805844	+	0.996748i	$0.525679\pi$
$830$	1.10569	0.0383791
$831$	−64.0728	−2.22266
$832$	−5.28020	−0.183058
$833$	−23.5695	−0.816634
$834$	−3.84897	−0.133279
$835$	0.679249	0.0235064
$836$	43.0860	1.49016
$837$	25.3773	0.877167
$838$	−17.0761	−0.589886
$839$	35.4256	1.22303	0.611514	−	0.791233i	$-0.290561\pi$
$839$	35.4256	1.22303	0.611514	+	0.791233i	$0.290561\pi$
$840$	−0.665493	−0.0229617
$841$	0	0
$842$	−46.2065	−1.59238
$843$	−9.37407	−0.322860
$844$	−37.6273	−1.29519
$845$	−0.742983	−0.0255594
$846$	−110.051	−3.78364
$847$	−7.47213	−0.256746
$848$	0.731490	0.0251195
$849$	−50.1888	−1.72248
$850$	−58.5642	−2.00873
$851$	1.23625	0.0423782
$852$	120.094	4.11434
$853$	−25.5045	−0.873256	−0.436628	−	0.899642i	$-0.643827\pi$
$853$	−25.5045	−0.873256	−0.436628	+	0.899642i	$0.643827\pi$
$854$	11.2972	0.386581
$855$	−1.01248	−0.0346262
$856$	24.0168	0.820877
$857$	−35.7869	−1.22246	−0.611228	−	0.791455i	$-0.709324\pi$
$857$	−35.7869	−1.22246	−0.611228	+	0.791455i	$0.709324\pi$
$858$	−10.3644	−0.353836
$859$	29.5758	1.00911	0.504556	−	0.863379i	$-0.331656\pi$
$859$	29.5758	1.00911	0.504556	+	0.863379i	$0.331656\pi$
$860$	1.17933	0.0402149
$861$	6.49086	0.221208
$862$	26.8392	0.914147
$863$	−40.2058	−1.36862	−0.684310	−	0.729191i	$-0.739896\pi$
$863$	−40.2058	−1.36862	−0.684310	+	0.729191i	$0.739896\pi$
$864$	−35.9061	−1.22155
$865$	1.11650	0.0379620
$866$	−38.7720	−1.31753
$867$	27.5894	0.936987
$868$	−21.1975	−0.719491
$869$	−19.0088	−0.644831
$870$	0	0
$871$	4.40323	0.149198
$872$	−14.9140	−0.505053
$873$	−87.2504	−2.95298
$874$	−1.80137	−0.0609321
$875$	0.903803	0.0305541
$876$	−62.6285	−2.11602
$877$	−52.1025	−1.75938	−0.879688	−	0.475552i	$-0.842248\pi$
$877$	−52.1025	−1.75938	−0.879688	+	0.475552i	$0.842248\pi$
$878$	42.5224	1.43506
$879$	38.4448	1.29671
$880$	0.0940381	0.00317002
$881$	−45.2608	−1.52487	−0.762437	−	0.647063i	$-0.775997\pi$
$881$	−45.2608	−1.52487	−0.762437	+	0.647063i	$0.775997\pi$
$882$	−52.4196	−1.76506
$883$	−33.8980	−1.14076	−0.570379	−	0.821382i	$-0.693204\pi$
$883$	−33.8980	−1.14076	−0.570379	+	0.821382i	$0.693204\pi$
$884$	6.57806	0.221244
$885$	−0.172997	−0.00581522
$886$	7.71902	0.259326
$887$	30.4108	1.02110	0.510548	−	0.859850i	$-0.329443\pi$
$887$	30.4108	1.02110	0.510548	+	0.859850i	$0.329443\pi$
$888$	39.5325	1.32662
$889$	−27.4494	−0.920622
$890$	−0.148678	−0.00498371
$891$	−5.90583	−0.197853
$892$	42.0216	1.40699
$893$	33.0387	1.10560
$894$	32.9111	1.10071
$895$	0.0526958	0.00176142
$896$	27.0952	0.905188
$897$	0.264802	0.00884149
$898$	0.315858	0.0105403
$899$	0	0
$900$	−79.5951	−2.65317
$901$	−9.24525	−0.308004
$902$	13.1804	0.438859
$903$	−28.7648	−0.957233
$904$	20.8918	0.694851
$905$	0.304591	0.0101249
$906$	−50.2469	−1.66934
$907$	15.8825	0.527368	0.263684	−	0.964609i	$-0.415062\pi$
$907$	15.8825	0.527368	0.263684	+	0.964609i	$0.415062\pi$
$908$	−6.66973	−0.221343
$909$	−31.6274	−1.04901
$910$	−0.0830336	−0.00275254
$911$	−24.9672	−0.827199	−0.413600	−	0.910459i	$-0.635729\pi$
$911$	−24.9672	−0.827199	−0.413600	+	0.910459i	$0.635729\pi$
$912$	4.00852	0.132735
$913$	−33.4654	−1.10754
$914$	72.7482	2.40630
$915$	−0.524396	−0.0173360
$916$	−86.0768	−2.84406
$917$	−5.22932	−0.172687
$918$	68.8784	2.27332
$919$	13.4638	0.444131	0.222065	−	0.975032i	$-0.428720\pi$
$919$	13.4638	0.444131	0.222065	+	0.975032i	$0.428720\pi$
$920$	0.0345259	0.00113828
$921$	18.5167	0.610145
$922$	−1.64527	−0.0541841
$923$	5.44822	0.179330
$924$	55.3963	1.82241
$925$	−26.8355	−0.882345
$926$	−20.7456	−0.681744
$927$	66.9616	2.19931
$928$	0	0
$929$	7.53667	0.247270	0.123635	−	0.992328i	$-0.460545\pi$
$929$	7.53667	0.247270	0.123635	+	0.992328i	$0.460545\pi$
$930$	1.61014	0.0527987
$931$	15.7370	0.515759
$932$	54.9259	1.79916
$933$	69.7245	2.28268
$934$	69.5385	2.27537
$935$	−1.18854	−0.0388694
$936$	5.31944	0.173871
$937$	−36.4635	−1.19121	−0.595605	−	0.803277i	$-0.703088\pi$
$937$	−36.4635	−1.19121	−0.595605	+	0.803277i	$0.703088\pi$
$938$	−38.5121	−1.25746
$939$	5.60861	0.183030
$940$	−1.74158	−0.0568039
$941$	−35.1767	−1.14673	−0.573364	−	0.819301i	$-0.694362\pi$
$941$	−35.1767	−1.14673	−0.573364	+	0.819301i	$0.694362\pi$
$942$	121.475	3.95788
$943$	−0.336747	−0.0109660
$944$	0.430261	0.0140038
$945$	−0.531311	−0.0172836
$946$	−58.4100	−1.89907
$947$	−10.3967	−0.337848	−0.168924	−	0.985629i	$-0.554029\pi$
$947$	−10.3967	−0.337848	−0.168924	+	0.985629i	$0.554029\pi$
$948$	42.7125	1.38724
$949$	−2.84123	−0.0922303
$950$	39.1025	1.26865
$951$	−84.3103	−2.73395
$952$	−20.9193	−0.677998
$953$	53.8152	1.74325	0.871623	−	0.490178i	$-0.163068\pi$
$953$	53.8152	1.74325	0.871623	+	0.490178i	$0.163068\pi$
$954$	−20.5619	−0.665715
$955$	−0.596703	−0.0193089
$956$	54.2189	1.75356
$957$	0	0
$958$	12.0129	0.388119
$959$	8.62295	0.278450
$960$	−2.14371	−0.0691878
$961$	−12.3521	−0.398454
$962$	4.93248	0.159029
$963$	46.9790	1.51388
$964$	69.0970	2.22547
$965$	−0.156861	−0.00504952
$966$	−2.31604	−0.0745174
$967$	−11.8947	−0.382508	−0.191254	−	0.981541i	$-0.561255\pi$
$967$	−11.8947	−0.382508	−0.191254	+	0.981541i	$0.561255\pi$
$968$	12.3963	0.398433
$969$	−50.6634	−1.62754
$970$	−2.25946	−0.0725468
$971$	−50.0900	−1.60746	−0.803732	−	0.594991i	$-0.797156\pi$
$971$	−50.0900	−1.60746	−0.803732	+	0.594991i	$0.797156\pi$
$972$	−42.1350	−1.35148
$973$	0.933285	0.0299197
$974$	−7.89535	−0.252983
$975$	−5.74809	−0.184086
$976$	1.30423	0.0417473
$977$	13.8116	0.441871	0.220936	−	0.975288i	$-0.429089\pi$
$977$	13.8116	0.441871	0.220936	+	0.975288i	$0.429089\pi$
$978$	−14.5711	−0.465932
$979$	4.49997	0.143820
$980$	−0.829547	−0.0264989
$981$	−29.1732	−0.931429
$982$	13.2699	0.423461
$983$	11.6553	0.371746	0.185873	−	0.982574i	$-0.440489\pi$
$983$	11.6553	0.371746	0.185873	+	0.982574i	$0.440489\pi$
$984$	−10.7684	−0.343284
$985$	−0.855428	−0.0272562
$986$	0	0
$987$	42.4784	1.35210
$988$	−4.39208	−0.139731
$989$	1.49232	0.0474531
$990$	−2.64337	−0.0840118
$991$	6.93524	0.220305	0.110153	−	0.993915i	$-0.464866\pi$
$991$	6.93524	0.220305	0.110153	+	0.993915i	$0.464866\pi$
$992$	−26.3848	−0.837718
$993$	−80.5983	−2.55771
$994$	−47.6518	−1.51142
$995$	0.868420	0.0275308
$996$	75.1961	2.38268
$997$	23.9700	0.759136	0.379568	−	0.925164i	$-0.376073\pi$
$997$	23.9700	0.759136	0.379568	+	0.925164i	$0.376073\pi$
$998$	−53.7872	−1.70260
$999$	31.5617	0.998568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.a.k.1.11		12
3.2	odd	2		7569.2.a.bp.1.2		12
29.2	odd	28		841.2.e.i.236.2		12
29.3	odd	28		841.2.e.h.270.2		12
29.4	even	14		841.2.d.l.190.4		24
29.5	even	14		841.2.d.m.605.4		24
29.6	even	14		841.2.d.m.645.4		24
29.7	even	7		841.2.d.l.571.1		24
29.8	odd	28		841.2.e.e.267.2		12
29.9	even	14		841.2.d.k.574.1		24
29.10	odd	28		841.2.e.h.651.2		12
29.11	odd	28		841.2.e.e.63.2		12
29.12	odd	4		841.2.b.e.840.11		12
29.13	even	14		841.2.d.k.778.1		24
29.14	odd	28		29.2.e.a.22.1	yes	12
29.15	odd	28		841.2.e.i.196.2		12
29.16	even	7		841.2.d.k.778.4		24
29.17	odd	4		841.2.b.e.840.2		12
29.18	odd	28		841.2.e.f.63.1		12
29.19	odd	28		841.2.e.a.651.1		12
29.20	even	7		841.2.d.k.574.4		24
29.21	odd	28		841.2.e.f.267.1		12
29.22	even	14		841.2.d.l.571.4		24
29.23	even	7		841.2.d.m.645.1		24
29.24	even	7		841.2.d.m.605.1		24
29.25	even	7		841.2.d.l.190.1		24
29.26	odd	28		841.2.e.a.270.1		12
29.27	odd	28		29.2.e.a.4.1	✓	12
29.28	even	2	inner	841.2.a.k.1.2		12
87.14	even	28		261.2.o.a.109.2		12
87.56	even	28		261.2.o.a.91.2		12
87.86	odd	2		7569.2.a.bp.1.11		12
116.27	even	28		464.2.y.d.33.2		12
116.43	even	28		464.2.y.d.225.2		12
145.14	odd	28		725.2.q.a.51.2		12
145.27	even	28		725.2.p.a.149.4		24
145.43	even	28		725.2.p.a.399.4		24
145.72	even	28		725.2.p.a.399.1		24
145.114	odd	28		725.2.q.a.526.2		12
145.143	even	28		725.2.p.a.149.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.4.1	✓	12	29.27	odd	28
29.2.e.a.22.1	yes	12	29.14	odd	28
261.2.o.a.91.2		12	87.56	even	28
261.2.o.a.109.2		12	87.14	even	28
464.2.y.d.33.2		12	116.27	even	28
464.2.y.d.225.2		12	116.43	even	28
725.2.p.a.149.1		24	145.143	even	28
725.2.p.a.149.4		24	145.27	even	28
725.2.p.a.399.1		24	145.72	even	28
725.2.p.a.399.4		24	145.43	even	28
725.2.q.a.51.2		12	145.14	odd	28
725.2.q.a.526.2		12	145.114	odd	28
841.2.a.k.1.2		12	29.28	even	2	inner
841.2.a.k.1.11		12	1.1	even	1	trivial
841.2.b.e.840.2		12	29.17	odd	4
841.2.b.e.840.11		12	29.12	odd	4
841.2.d.k.574.1		24	29.9	even	14
841.2.d.k.574.4		24	29.20	even	7
841.2.d.k.778.1		24	29.13	even	14
841.2.d.k.778.4		24	29.16	even	7
841.2.d.l.190.1		24	29.25	even	7
841.2.d.l.190.4		24	29.4	even	14
841.2.d.l.571.1		24	29.7	even	7
841.2.d.l.571.4		24	29.22	even	14
841.2.d.m.605.1		24	29.24	even	7
841.2.d.m.605.4		24	29.5	even	14
841.2.d.m.645.1		24	29.23	even	7
841.2.d.m.645.4		24	29.6	even	14
841.2.e.a.270.1		12	29.26	odd	28
841.2.e.a.651.1		12	29.19	odd	28
841.2.e.e.63.2		12	29.11	odd	28
841.2.e.e.267.2		12	29.8	odd	28
841.2.e.f.63.1		12	29.18	odd	28
841.2.e.f.267.1		12	29.21	odd	28
841.2.e.h.270.2		12	29.3	odd	28
841.2.e.h.651.2		12	29.10	odd	28
841.2.e.i.196.2		12	29.15	odd	28
841.2.e.i.236.2		12	29.2	odd	28
7569.2.a.bp.1.2		12	3.2	odd	2
7569.2.a.bp.1.11		12	87.86	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26775 q^{2} +2.84057 q^{3} +3.14268 q^{4} +0.0578828 q^{5} +6.44169 q^{6} -1.56196 q^{7} +2.59131 q^{8} +5.06883 q^{9} +0.131264 q^{10} -3.97289 q^{11} +8.92699 q^{12} +0.404986 q^{13} -3.54213 q^{14} +0.164420 q^{15} -0.408929 q^{16} +5.16843 q^{17} +11.4948 q^{18} -3.45088 q^{19} +0.181907 q^{20} -4.43685 q^{21} -9.00950 q^{22} +0.230185 q^{23} +7.36078 q^{24} -4.99665 q^{25} +0.918405 q^{26} +5.87665 q^{27} -4.90874 q^{28} +0.372863 q^{30} +4.31832 q^{31} -6.10996 q^{32} -11.2853 q^{33} +11.7207 q^{34} -0.0904106 q^{35} +15.9297 q^{36} +5.37070 q^{37} -7.82573 q^{38} +1.15039 q^{39} +0.149992 q^{40} -1.46294 q^{41} -10.0617 q^{42} +6.48316 q^{43} -12.4855 q^{44} +0.293398 q^{45} +0.522001 q^{46} -9.57399 q^{47} -1.16159 q^{48} -4.56028 q^{49} -11.3311 q^{50} +14.6813 q^{51} +1.27274 q^{52} -1.78879 q^{53} +13.3268 q^{54} -0.229962 q^{55} -4.04752 q^{56} -9.80247 q^{57} -1.05216 q^{59} +0.516719 q^{60} -3.18937 q^{61} +9.79287 q^{62} -7.91731 q^{63} -13.0380 q^{64} +0.0234417 q^{65} -25.5921 q^{66} +10.8726 q^{67} +16.2427 q^{68} +0.653856 q^{69} -0.205028 q^{70} +13.4529 q^{71} +13.1349 q^{72} -7.01563 q^{73} +12.1794 q^{74} -14.1933 q^{75} -10.8450 q^{76} +6.20549 q^{77} +2.60879 q^{78} +4.78464 q^{79} -0.0236700 q^{80} +1.48654 q^{81} -3.31758 q^{82} +8.42345 q^{83} -13.9436 q^{84} +0.299163 q^{85} +14.7022 q^{86} -10.2950 q^{88} -1.13267 q^{89} +0.665353 q^{90} -0.632571 q^{91} +0.723397 q^{92} +12.2665 q^{93} -21.7114 q^{94} -0.199747 q^{95} -17.3558 q^{96} -17.2131 q^{97} -10.3416 q^{98} -20.1379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} + 8 q^{5} + 24 q^{6} + 10 q^{7} + 10 q^{9} + 12 q^{13} + 16 q^{16} + 24 q^{20} - 38 q^{22} + 30 q^{23} + 10 q^{24} - 8 q^{25} - 12 q^{28} + 2 q^{30} - 4 q^{33} + 6 q^{34} + 44 q^{35} + 16 q^{36}+ \cdots - 58 q^{96}+O(q^{100}) \) 12 * q + 8 * q^4 + 8 * q^5 + 24 * q^6 + 10 * q^7 + 10 * q^9 + 12 * q^13 + 16 * q^16 + 24 * q^20 - 38 * q^22 + 30 * q^23 + 10 * q^24 - 8 * q^25 - 12 * q^28 + 2 * q^30 - 4 * q^33 + 6 * q^34 + 44 * q^35 + 16 * q^36 + 6 * q^42 - 12 * q^45 + 6 * q^49 + 8 * q^51 - 6 * q^52 + 32 * q^53 + 32 * q^54 + 14 * q^57 + 44 * q^59 - 16 * q^62 + 34 * q^63 - 2 * q^64 + 8 * q^65 + 30 * q^67 + 70 * q^71 + 56 * q^74 - 4 * q^78 + 34 * q^80 + 8 * q^81 - 62 * q^82 + 82 * q^83 + 44 * q^86 - 66 * q^88 - 32 * q^91 - 22 * q^92 - 12 * q^93 + 10 * q^94 - 58 * q^96

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