LMFDB - Embedded newform 4334.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.15745 q^{3} +1.00000 q^{4} +1.30451 q^{5} +2.15745 q^{6} +3.75589 q^{7} -1.00000 q^{8} +1.65457 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.15745 q^{3} +1.00000 q^{4} +1.30451 q^{5} +2.15745 q^{6} +3.75589 q^{7} -1.00000 q^{8} +1.65457 q^{9} -1.30451 q^{10} -1.00000 q^{11} -2.15745 q^{12} +6.48907 q^{13} -3.75589 q^{14} -2.81441 q^{15} +1.00000 q^{16} -6.32826 q^{17} -1.65457 q^{18} +3.82507 q^{19} +1.30451 q^{20} -8.10313 q^{21} +1.00000 q^{22} -2.37417 q^{23} +2.15745 q^{24} -3.29826 q^{25} -6.48907 q^{26} +2.90269 q^{27} +3.75589 q^{28} +8.10855 q^{29} +2.81441 q^{30} +7.24195 q^{31} -1.00000 q^{32} +2.15745 q^{33} +6.32826 q^{34} +4.89959 q^{35} +1.65457 q^{36} -2.45345 q^{37} -3.82507 q^{38} -13.9998 q^{39} -1.30451 q^{40} -2.38220 q^{41} +8.10313 q^{42} +3.54500 q^{43} -1.00000 q^{44} +2.15841 q^{45} +2.37417 q^{46} -3.61902 q^{47} -2.15745 q^{48} +7.10671 q^{49} +3.29826 q^{50} +13.6529 q^{51} +6.48907 q^{52} +10.9848 q^{53} -2.90269 q^{54} -1.30451 q^{55} -3.75589 q^{56} -8.25239 q^{57} -8.10855 q^{58} +1.96589 q^{59} -2.81441 q^{60} -2.90437 q^{61} -7.24195 q^{62} +6.21440 q^{63} +1.00000 q^{64} +8.46505 q^{65} -2.15745 q^{66} +15.6383 q^{67} -6.32826 q^{68} +5.12214 q^{69} -4.89959 q^{70} -8.30796 q^{71} -1.65457 q^{72} +3.37563 q^{73} +2.45345 q^{74} +7.11581 q^{75} +3.82507 q^{76} -3.75589 q^{77} +13.9998 q^{78} +1.08576 q^{79} +1.30451 q^{80} -11.2261 q^{81} +2.38220 q^{82} -7.44011 q^{83} -8.10313 q^{84} -8.25527 q^{85} -3.54500 q^{86} -17.4938 q^{87} +1.00000 q^{88} +13.5670 q^{89} -2.15841 q^{90} +24.3722 q^{91} -2.37417 q^{92} -15.6241 q^{93} +3.61902 q^{94} +4.98984 q^{95} +2.15745 q^{96} +14.0858 q^{97} -7.10671 q^{98} -1.65457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * 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
$3$	−2.15745	−1.24560	−0.622801	−	0.782380i	$-0.714005\pi$
$3$	−2.15745	−1.24560	−0.622801	+	0.782380i	$0.714005\pi$
$4$	1.00000	0.500000
$5$	1.30451	0.583394	0.291697	−	0.956511i	$-0.405780\pi$
$5$	1.30451	0.583394	0.291697	+	0.956511i	$0.405780\pi$
$6$	2.15745	0.880774
$7$	3.75589	1.41959	0.709797	−	0.704407i	$-0.248787\pi$
$7$	3.75589	1.41959	0.709797	+	0.704407i	$0.248787\pi$
$8$	−1.00000	−0.353553
$9$	1.65457	0.551525
$10$	−1.30451	−0.412522
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.15745	−0.622801
$13$	6.48907	1.79975	0.899873	−	0.436153i	$-0.143659\pi$
$13$	6.48907	1.79975	0.899873	+	0.436153i	$0.143659\pi$
$14$	−3.75589	−1.00380
$15$	−2.81441	−0.726677
$16$	1.00000	0.250000
$17$	−6.32826	−1.53483	−0.767414	−	0.641152i	$-0.778457\pi$
$17$	−6.32826	−1.53483	−0.767414	+	0.641152i	$0.778457\pi$
$18$	−1.65457	−0.389987
$19$	3.82507	0.877532	0.438766	−	0.898601i	$-0.355416\pi$
$19$	3.82507	0.877532	0.438766	+	0.898601i	$0.355416\pi$
$20$	1.30451	0.291697
$21$	−8.10313	−1.76825
$22$	1.00000	0.213201
$23$	−2.37417	−0.495048	−0.247524	−	0.968882i	$-0.579617\pi$
$23$	−2.37417	−0.495048	−0.247524	+	0.968882i	$0.579617\pi$
$24$	2.15745	0.440387
$25$	−3.29826	−0.659651
$26$	−6.48907	−1.27261
$27$	2.90269	0.558622
$28$	3.75589	0.709797
$29$	8.10855	1.50572	0.752860	−	0.658181i	$-0.228674\pi$
$29$	8.10855	1.50572	0.752860	+	0.658181i	$0.228674\pi$
$30$	2.81441	0.513838
$31$	7.24195	1.30069	0.650346	−	0.759638i	$-0.274624\pi$
$31$	7.24195	1.30069	0.650346	+	0.759638i	$0.274624\pi$
$32$	−1.00000	−0.176777
$33$	2.15745	0.375563
$34$	6.32826	1.08529
$35$	4.89959	0.828182
$36$	1.65457	0.275762
$37$	−2.45345	−0.403344	−0.201672	−	0.979453i	$-0.564638\pi$
$37$	−2.45345	−0.403344	−0.201672	+	0.979453i	$0.564638\pi$
$38$	−3.82507	−0.620509
$39$	−13.9998	−2.24177
$40$	−1.30451	−0.206261
$41$	−2.38220	−0.372037	−0.186019	−	0.982546i	$-0.559558\pi$
$41$	−2.38220	−0.372037	−0.186019	+	0.982546i	$0.559558\pi$
$42$	8.10313	1.25034
$43$	3.54500	0.540607	0.270304	−	0.962775i	$-0.412876\pi$
$43$	3.54500	0.540607	0.270304	+	0.962775i	$0.412876\pi$
$44$	−1.00000	−0.150756
$45$	2.15841	0.321756
$46$	2.37417	0.350052
$47$	−3.61902	−0.527889	−0.263944	−	0.964538i	$-0.585024\pi$
$47$	−3.61902	−0.527889	−0.263944	+	0.964538i	$0.585024\pi$
$48$	−2.15745	−0.311401
$49$	7.10671	1.01524
$50$	3.29826	0.466444
$51$	13.6529	1.91178
$52$	6.48907	0.899873
$53$	10.9848	1.50888	0.754442	−	0.656367i	$-0.227908\pi$
$53$	10.9848	1.50888	0.754442	+	0.656367i	$0.227908\pi$
$54$	−2.90269	−0.395005
$55$	−1.30451	−0.175900
$56$	−3.75589	−0.501902
$57$	−8.25239	−1.09306
$58$	−8.10855	−1.06470
$59$	1.96589	0.255937	0.127968	−	0.991778i	$-0.459154\pi$
$59$	1.96589	0.255937	0.127968	+	0.991778i	$0.459154\pi$
$60$	−2.81441	−0.363338
$61$	−2.90437	−0.371867	−0.185933	−	0.982562i	$-0.559531\pi$
$61$	−2.90437	−0.371867	−0.185933	+	0.982562i	$0.559531\pi$
$62$	−7.24195	−0.919729
$63$	6.21440	0.782940
$64$	1.00000	0.125000
$65$	8.46505	1.04996
$66$	−2.15745	−0.265563
$67$	15.6383	1.91052	0.955262	−	0.295761i	$-0.0955732\pi$
$67$	15.6383	1.91052	0.955262	+	0.295761i	$0.0955732\pi$
$68$	−6.32826	−0.767414
$69$	5.12214	0.616633
$70$	−4.89959	−0.585613
$71$	−8.30796	−0.985974	−0.492987	−	0.870037i	$-0.664095\pi$
$71$	−8.30796	−0.985974	−0.492987	+	0.870037i	$0.664095\pi$
$72$	−1.65457	−0.194993
$73$	3.37563	0.395088	0.197544	−	0.980294i	$-0.436704\pi$
$73$	3.37563	0.395088	0.197544	+	0.980294i	$0.436704\pi$
$74$	2.45345	0.285207
$75$	7.11581	0.821663
$76$	3.82507	0.438766
$77$	−3.75589	−0.428023
$78$	13.9998	1.58517
$79$	1.08576	0.122157	0.0610786	−	0.998133i	$-0.480546\pi$
$79$	1.08576	0.122157	0.0610786	+	0.998133i	$0.480546\pi$
$80$	1.30451	0.145849
$81$	−11.2261	−1.24735
$82$	2.38220	0.263070
$83$	−7.44011	−0.816658	−0.408329	−	0.912835i	$-0.633888\pi$
$83$	−7.44011	−0.816658	−0.408329	+	0.912835i	$0.633888\pi$
$84$	−8.10313	−0.884124
$85$	−8.25527	−0.895410
$86$	−3.54500	−0.382267
$87$	−17.4938	−1.87553
$88$	1.00000	0.106600
$89$	13.5670	1.43810	0.719050	−	0.694958i	$-0.244577\pi$
$89$	13.5670	1.43810	0.719050	+	0.694958i	$0.244577\pi$
$90$	−2.15841	−0.227516
$91$	24.3722	2.55491
$92$	−2.37417	−0.247524
$93$	−15.6241	−1.62015
$94$	3.61902	0.373274
$95$	4.98984	0.511947
$96$	2.15745	0.220193
$97$	14.0858	1.43019	0.715096	−	0.699026i	$-0.246383\pi$
$97$	14.0858	1.43019	0.715096	+	0.699026i	$0.246383\pi$
$98$	−7.10671	−0.717886
$99$	−1.65457	−0.166291
$100$	−3.29826	−0.329826
$101$	−7.50269	−0.746545	−0.373273	−	0.927722i	$-0.621764\pi$
$101$	−7.50269	−0.746545	−0.373273	+	0.927722i	$0.621764\pi$
$102$	−13.6529	−1.35184
$103$	−15.9208	−1.56872	−0.784360	−	0.620305i	$-0.787009\pi$
$103$	−15.9208	−1.56872	−0.784360	+	0.620305i	$0.787009\pi$
$104$	−6.48907	−0.636306
$105$	−10.5706	−1.03159
$106$	−10.9848	−1.06694
$107$	−6.56242	−0.634413	−0.317206	−	0.948357i	$-0.602745\pi$
$107$	−6.56242	−0.634413	−0.317206	+	0.948357i	$0.602745\pi$
$108$	2.90269	0.279311
$109$	9.96259	0.954243	0.477121	−	0.878837i	$-0.341680\pi$
$109$	9.96259	0.954243	0.477121	+	0.878837i	$0.341680\pi$
$110$	1.30451	0.124380
$111$	5.29318	0.502406
$112$	3.75589	0.354898
$113$	2.36033	0.222041	0.111021	−	0.993818i	$-0.464588\pi$
$113$	2.36033	0.222041	0.111021	+	0.993818i	$0.464588\pi$
$114$	8.25239	0.772907
$115$	−3.09712	−0.288808
$116$	8.10855	0.752860
$117$	10.7366	0.992603
$118$	−1.96589	−0.180975
$119$	−23.7682	−2.17883
$120$	2.81441	0.256919
$121$	1.00000	0.0909091
$122$	2.90437	0.262950
$123$	5.13947	0.463410
$124$	7.24195	0.650346
$125$	−10.8251	−0.968231
$126$	−6.21440	−0.553622
$127$	−16.6146	−1.47431	−0.737153	−	0.675726i	$-0.763830\pi$
$127$	−16.6146	−1.47431	−0.737153	+	0.675726i	$0.763830\pi$
$128$	−1.00000	−0.0883883
$129$	−7.64814	−0.673382
$130$	−8.46505	−0.742434
$131$	−3.66216	−0.319964	−0.159982	−	0.987120i	$-0.551144\pi$
$131$	−3.66216	−0.319964	−0.159982	+	0.987120i	$0.551144\pi$
$132$	2.15745	0.187782
$133$	14.3666	1.24574
$134$	−15.6383	−1.35094
$135$	3.78658	0.325897
$136$	6.32826	0.542644
$137$	−16.3569	−1.39746	−0.698732	−	0.715384i	$-0.746252\pi$
$137$	−16.3569	−1.39746	−0.698732	+	0.715384i	$0.746252\pi$
$138$	−5.12214	−0.436026
$139$	−15.4603	−1.31132	−0.655661	−	0.755056i	$-0.727610\pi$
$139$	−15.4603	−1.31132	−0.655661	+	0.755056i	$0.727610\pi$
$140$	4.89959	0.414091
$141$	7.80785	0.657539
$142$	8.30796	0.697189
$143$	−6.48907	−0.542644
$144$	1.65457	0.137881
$145$	10.5777	0.878428
$146$	−3.37563	−0.279369
$147$	−15.3323	−1.26459
$148$	−2.45345	−0.201672
$149$	7.99570	0.655033	0.327517	−	0.944845i	$-0.393788\pi$
$149$	7.99570	0.655033	0.327517	+	0.944845i	$0.393788\pi$
$150$	−7.11581	−0.581003
$151$	−7.52878	−0.612683	−0.306342	−	0.951922i	$-0.599105\pi$
$151$	−7.52878	−0.612683	−0.306342	+	0.951922i	$0.599105\pi$
$152$	−3.82507	−0.310254
$153$	−10.4706	−0.846495
$154$	3.75589	0.302658
$155$	9.44719	0.758816
$156$	−13.9998	−1.12088
$157$	−1.47655	−0.117841	−0.0589206	−	0.998263i	$-0.518766\pi$
$157$	−1.47655	−0.117841	−0.0589206	+	0.998263i	$0.518766\pi$
$158$	−1.08576	−0.0863782
$159$	−23.6992	−1.87947
$160$	−1.30451	−0.103130
$161$	−8.91712	−0.702767
$162$	11.2261	0.882006
$163$	−8.26509	−0.647372	−0.323686	−	0.946165i	$-0.604922\pi$
$163$	−8.26509	−0.647372	−0.323686	+	0.946165i	$0.604922\pi$
$164$	−2.38220	−0.186019
$165$	2.81441	0.219101
$166$	7.44011	0.577465
$167$	10.2135	0.790348	0.395174	−	0.918606i	$-0.370684\pi$
$167$	10.2135	0.790348	0.395174	+	0.918606i	$0.370684\pi$
$168$	8.10313	0.625170
$169$	29.1081	2.23908
$170$	8.25527	0.633150
$171$	6.32887	0.483980
$172$	3.54500	0.270304
$173$	8.04761	0.611849	0.305924	−	0.952056i	$-0.401035\pi$
$173$	8.04761	0.611849	0.305924	+	0.952056i	$0.401035\pi$
$174$	17.4938	1.32620
$175$	−12.3879	−0.936436
$176$	−1.00000	−0.0753778
$177$	−4.24130	−0.318795
$178$	−13.5670	−1.01689
$179$	−0.315782	−0.0236027	−0.0118013	−	0.999930i	$-0.503757\pi$
$179$	−0.315782	−0.0236027	−0.0118013	+	0.999930i	$0.503757\pi$
$180$	2.15841	0.160878
$181$	6.81049	0.506220	0.253110	−	0.967437i	$-0.418547\pi$
$181$	6.81049	0.506220	0.253110	+	0.967437i	$0.418547\pi$
$182$	−24.3722	−1.80659
$183$	6.26603	0.463198
$184$	2.37417	0.175026
$185$	−3.20054	−0.235309
$186$	15.6241	1.14562
$187$	6.32826	0.462768
$188$	−3.61902	−0.263944
$189$	10.9022	0.793016
$190$	−4.98984	−0.362001
$191$	1.33119	0.0963215	0.0481608	−	0.998840i	$-0.484664\pi$
$191$	1.33119	0.0963215	0.0481608	+	0.998840i	$0.484664\pi$
$192$	−2.15745	−0.155700
$193$	−1.62124	−0.116699	−0.0583497	−	0.998296i	$-0.518584\pi$
$193$	−1.62124	−0.116699	−0.0583497	+	0.998296i	$0.518584\pi$
$194$	−14.0858	−1.01130
$195$	−18.2629	−1.30783
$196$	7.10671	0.507622
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	1.65457	0.117585
$199$	14.1891	1.00584	0.502918	−	0.864334i	$-0.332260\pi$
$199$	14.1891	1.00584	0.502918	+	0.864334i	$0.332260\pi$
$200$	3.29826	0.233222
$201$	−33.7388	−2.37975
$202$	7.50269	0.527887
$203$	30.4548	2.13751
$204$	13.6529	0.955892
$205$	−3.10760	−0.217044
$206$	15.9208	1.10925
$207$	−3.92824	−0.273031
$208$	6.48907	0.449936
$209$	−3.82507	−0.264586
$210$	10.5706	0.729441
$211$	0.821899	0.0565819	0.0282909	−	0.999600i	$-0.490994\pi$
$211$	0.821899	0.0565819	0.0282909	+	0.999600i	$0.490994\pi$
$212$	10.9848	0.754442
$213$	17.9240	1.22813
$214$	6.56242	0.448597
$215$	4.62448	0.315387
$216$	−2.90269	−0.197503
$217$	27.2000	1.84645
$218$	−9.96259	−0.674752
$219$	−7.28274	−0.492122
$220$	−1.30451	−0.0879500
$221$	−41.0645	−2.76230
$222$	−5.29318	−0.355255
$223$	13.5587	0.907959	0.453980	−	0.891012i	$-0.350004\pi$
$223$	13.5587	0.907959	0.453980	+	0.891012i	$0.350004\pi$
$224$	−3.75589	−0.250951
$225$	−5.45721	−0.363814
$226$	−2.36033	−0.157007
$227$	−3.11435	−0.206707	−0.103353	−	0.994645i	$-0.532957\pi$
$227$	−3.11435	−0.206707	−0.103353	+	0.994645i	$0.532957\pi$
$228$	−8.25239	−0.546528
$229$	7.91029	0.522727	0.261363	−	0.965240i	$-0.415828\pi$
$229$	7.91029	0.522727	0.261363	+	0.965240i	$0.415828\pi$
$230$	3.09712	0.204218
$231$	8.10313	0.533147
$232$	−8.10855	−0.532352
$233$	4.67924	0.306547	0.153274	−	0.988184i	$-0.451018\pi$
$233$	4.67924	0.306547	0.153274	+	0.988184i	$0.451018\pi$
$234$	−10.7366	−0.701877
$235$	−4.72105	−0.307967
$236$	1.96589	0.127968
$237$	−2.34246	−0.152159
$238$	23.7682	1.54067
$239$	−0.0387479	−0.00250639	−0.00125320	−	0.999999i	$-0.500399\pi$
$239$	−0.0387479	−0.00250639	−0.00125320	+	0.999999i	$0.500399\pi$
$240$	−2.81441	−0.181669
$241$	−12.6230	−0.813121	−0.406560	−	0.913624i	$-0.633272\pi$
$241$	−12.6230	−0.813121	−0.406560	+	0.913624i	$0.633272\pi$
$242$	−1.00000	−0.0642824
$243$	15.5117	0.995074
$244$	−2.90437	−0.185933
$245$	9.27077	0.592288
$246$	−5.13947	−0.327681
$247$	24.8212	1.57933
$248$	−7.24195	−0.459864
$249$	16.0516	1.01723
$250$	10.8251	0.684643
$251$	17.3217	1.09333	0.546667	−	0.837350i	$-0.315896\pi$
$251$	17.3217	1.09333	0.546667	+	0.837350i	$0.315896\pi$
$252$	6.21440	0.391470
$253$	2.37417	0.149263
$254$	16.6146	1.04249
$255$	17.8103	1.11532
$256$	1.00000	0.0625000
$257$	24.4784	1.52692	0.763461	−	0.645854i	$-0.223499\pi$
$257$	24.4784	1.52692	0.763461	+	0.645854i	$0.223499\pi$
$258$	7.64814	0.476153
$259$	−9.21488	−0.572585
$260$	8.46505	0.524980
$261$	13.4162	0.830441
$262$	3.66216	0.226249
$263$	28.9863	1.78737	0.893686	−	0.448693i	$-0.148110\pi$
$263$	28.9863	1.78737	0.893686	+	0.448693i	$0.148110\pi$
$264$	−2.15745	−0.132782
$265$	14.3298	0.880274
$266$	−14.3666	−0.880870
$267$	−29.2701	−1.79130
$268$	15.6383	0.955262
$269$	−9.78788	−0.596778	−0.298389	−	0.954444i	$-0.596449\pi$
$269$	−9.78788	−0.596778	−0.298389	+	0.954444i	$0.596449\pi$
$270$	−3.78658	−0.230444
$271$	−24.9929	−1.51821	−0.759107	−	0.650966i	$-0.774364\pi$
$271$	−24.9929	−1.51821	−0.759107	+	0.650966i	$0.774364\pi$
$272$	−6.32826	−0.383707
$273$	−52.5818	−3.18240
$274$	16.3569	0.988156
$275$	3.29826	0.198892
$276$	5.12214	0.308317
$277$	6.92834	0.416284	0.208142	−	0.978099i	$-0.433258\pi$
$277$	6.92834	0.416284	0.208142	+	0.978099i	$0.433258\pi$
$278$	15.4603	0.927244
$279$	11.9823	0.717364
$280$	−4.89959	−0.292807
$281$	20.5543	1.22617	0.613084	−	0.790018i	$-0.289929\pi$
$281$	20.5543	1.22617	0.613084	+	0.790018i	$0.289929\pi$
$282$	−7.80785	−0.464951
$283$	−10.3328	−0.614223	−0.307112	−	0.951673i	$-0.599363\pi$
$283$	−10.3328	−0.614223	−0.307112	+	0.951673i	$0.599363\pi$
$284$	−8.30796	−0.492987
$285$	−10.7653	−0.637682
$286$	6.48907	0.383707
$287$	−8.94729	−0.528142
$288$	−1.65457	−0.0974967
$289$	23.0468	1.35570
$290$	−10.5777	−0.621142
$291$	−30.3893	−1.78145
$292$	3.37563	0.197544
$293$	27.9322	1.63182	0.815909	−	0.578180i	$-0.196237\pi$
$293$	27.9322	1.63182	0.815909	+	0.578180i	$0.196237\pi$
$294$	15.3323	0.894201
$295$	2.56452	0.149312
$296$	2.45345	0.142604
$297$	−2.90269	−0.168431
$298$	−7.99570	−0.463178
$299$	−15.4062	−0.890961
$300$	7.11581	0.410831
$301$	13.3146	0.767442
$302$	7.52878	0.433232
$303$	16.1866	0.929898
$304$	3.82507	0.219383
$305$	−3.78878	−0.216945
$306$	10.4706	0.598562
$307$	−16.2986	−0.930208	−0.465104	−	0.885256i	$-0.653983\pi$
$307$	−16.2986	−0.930208	−0.465104	+	0.885256i	$0.653983\pi$
$308$	−3.75589	−0.214012
$309$	34.3482	1.95400
$310$	−9.44719	−0.536564
$311$	−0.726589	−0.0412011	−0.0206005	−	0.999788i	$-0.506558\pi$
$311$	−0.726589	−0.0412011	−0.0206005	+	0.999788i	$0.506558\pi$
$312$	13.9998	0.792584
$313$	−0.824305	−0.0465924	−0.0232962	−	0.999729i	$-0.507416\pi$
$313$	−0.824305	−0.0465924	−0.0232962	+	0.999729i	$0.507416\pi$
$314$	1.47655	0.0833263
$315$	8.10674	0.456763
$316$	1.08576	0.0610786
$317$	−11.5157	−0.646785	−0.323393	−	0.946265i	$-0.604823\pi$
$317$	−11.5157	−0.646785	−0.323393	+	0.946265i	$0.604823\pi$
$318$	23.6992	1.32898
$319$	−8.10855	−0.453991
$320$	1.30451	0.0729243
$321$	14.1581	0.790226
$322$	8.91712	0.496932
$323$	−24.2060	−1.34686
$324$	−11.2261	−0.623673
$325$	−21.4026	−1.18720
$326$	8.26509	0.457761
$327$	−21.4937	−1.18861
$328$	2.38220	0.131535
$329$	−13.5927	−0.749387
$330$	−2.81441	−0.154928
$331$	−13.6447	−0.749983	−0.374991	−	0.927028i	$-0.622354\pi$
$331$	−13.6447	−0.749983	−0.374991	+	0.927028i	$0.622354\pi$
$332$	−7.44011	−0.408329
$333$	−4.05941	−0.222454
$334$	−10.2135	−0.558860
$335$	20.4003	1.11459
$336$	−8.10313	−0.442062
$337$	22.7007	1.23659	0.618294	−	0.785947i	$-0.287824\pi$
$337$	22.7007	1.23659	0.618294	+	0.785947i	$0.287824\pi$
$338$	−29.1081	−1.58327
$339$	−5.09229	−0.276575
$340$	−8.25527	−0.447705
$341$	−7.24195	−0.392174
$342$	−6.32887	−0.342226
$343$	0.400802	0.0216413
$344$	−3.54500	−0.191134
$345$	6.68188	0.359740
$346$	−8.04761	−0.432642
$347$	−25.1502	−1.35013	−0.675066	−	0.737758i	$-0.735885\pi$
$347$	−25.1502	−1.35013	−0.675066	+	0.737758i	$0.735885\pi$
$348$	−17.4938	−0.937764
$349$	31.0815	1.66375	0.831876	−	0.554961i	$-0.187267\pi$
$349$	31.0815	1.66375	0.831876	+	0.554961i	$0.187267\pi$
$350$	12.3879	0.662161
$351$	18.8357	1.00538
$352$	1.00000	0.0533002
$353$	−19.7906	−1.05335	−0.526674	−	0.850068i	$-0.676561\pi$
$353$	−19.7906	−1.05335	−0.526674	+	0.850068i	$0.676561\pi$
$354$	4.24130	0.225422
$355$	−10.8378	−0.575211
$356$	13.5670	0.719050
$357$	51.2787	2.71396
$358$	0.315782	0.0166896
$359$	22.6457	1.19520	0.597598	−	0.801796i	$-0.296122\pi$
$359$	22.6457	1.19520	0.597598	+	0.801796i	$0.296122\pi$
$360$	−2.15841	−0.113758
$361$	−4.36881	−0.229937
$362$	−6.81049	−0.357952
$363$	−2.15745	−0.113237
$364$	24.3722	1.27745
$365$	4.40354	0.230492
$366$	−6.26603	−0.327531
$367$	−25.4528	−1.32862	−0.664312	−	0.747455i	$-0.731275\pi$
$367$	−25.4528	−1.32862	−0.664312	+	0.747455i	$0.731275\pi$
$368$	−2.37417	−0.123762
$369$	−3.94153	−0.205188
$370$	3.20054	0.166388
$371$	41.2578	2.14200
$372$	−15.6241	−0.810073
$373$	16.5608	0.857485	0.428743	−	0.903427i	$-0.358957\pi$
$373$	16.5608	0.857485	0.428743	+	0.903427i	$0.358957\pi$
$374$	−6.32826	−0.327226
$375$	23.3547	1.20603
$376$	3.61902	0.186637
$377$	52.6170	2.70991
$378$	−10.9022	−0.560747
$379$	−34.2986	−1.76180	−0.880901	−	0.473301i	$-0.843062\pi$
$379$	−34.2986	−1.76180	−0.880901	+	0.473301i	$0.843062\pi$
$380$	4.98984	0.255974
$381$	35.8450	1.83640
$382$	−1.33119	−0.0681096
$383$	0.987844	0.0504765	0.0252382	−	0.999681i	$-0.491966\pi$
$383$	0.987844	0.0504765	0.0252382	+	0.999681i	$0.491966\pi$
$384$	2.15745	0.110097
$385$	−4.89959	−0.249706
$386$	1.62124	0.0825189
$387$	5.86546	0.298158
$388$	14.0858	0.715096
$389$	10.6338	0.539155	0.269578	−	0.962979i	$-0.413116\pi$
$389$	10.6338	0.539155	0.269578	+	0.962979i	$0.413116\pi$
$390$	18.2629	0.924778
$391$	15.0244	0.759814
$392$	−7.10671	−0.358943
$393$	7.90091	0.398548
$394$	−1.00000	−0.0503793
$395$	1.41638	0.0712658
$396$	−1.65457	−0.0831454
$397$	14.0988	0.707598	0.353799	−	0.935321i	$-0.384890\pi$
$397$	14.0988	0.707598	0.353799	+	0.935321i	$0.384890\pi$
$398$	−14.1891	−0.711234
$399$	−30.9951	−1.55169
$400$	−3.29826	−0.164913
$401$	19.7780	0.987667	0.493834	−	0.869556i	$-0.335595\pi$
$401$	19.7780	0.987667	0.493834	+	0.869556i	$0.335595\pi$
$402$	33.7388	1.68274
$403$	46.9935	2.34092
$404$	−7.50269	−0.373273
$405$	−14.6446	−0.727694
$406$	−30.4548	−1.51145
$407$	2.45345	0.121613
$408$	−13.6529	−0.675918
$409$	−2.13641	−0.105639	−0.0528194	−	0.998604i	$-0.516821\pi$
$409$	−2.13641	−0.105639	−0.0528194	+	0.998604i	$0.516821\pi$
$410$	3.10760	0.153474
$411$	35.2891	1.74068
$412$	−15.9208	−0.784360
$413$	7.38366	0.363326
$414$	3.92824	0.193062
$415$	−9.70569	−0.476434
$416$	−6.48907	−0.318153
$417$	33.3547	1.63338
$418$	3.82507	0.187090
$419$	8.98107	0.438754	0.219377	−	0.975640i	$-0.429598\pi$
$419$	8.98107	0.438754	0.219377	+	0.975640i	$0.429598\pi$
$420$	−10.5706	−0.515793
$421$	23.9520	1.16735	0.583675	−	0.811987i	$-0.301614\pi$
$421$	23.9520	1.16735	0.583675	+	0.811987i	$0.301614\pi$
$422$	−0.821899	−0.0400094
$423$	−5.98794	−0.291144
$424$	−10.9848	−0.533471
$425$	20.8722	1.01245
$426$	−17.9240	−0.868420
$427$	−10.9085	−0.527900
$428$	−6.56242	−0.317206
$429$	13.9998	0.675918
$430$	−4.62448	−0.223012
$431$	18.3882	0.885730	0.442865	−	0.896588i	$-0.353962\pi$
$431$	18.3882	0.885730	0.442865	+	0.896588i	$0.353962\pi$
$432$	2.90269	0.139656
$433$	−19.1755	−0.921515	−0.460758	−	0.887526i	$-0.652422\pi$
$433$	−19.1755	−0.921515	−0.460758	+	0.887526i	$0.652422\pi$
$434$	−27.2000	−1.30564
$435$	−22.8208	−1.09417
$436$	9.96259	0.477121
$437$	−9.08137	−0.434421
$438$	7.28274	0.347983
$439$	31.0343	1.48119	0.740594	−	0.671953i	$-0.234544\pi$
$439$	31.0343	1.48119	0.740594	+	0.671953i	$0.234544\pi$
$440$	1.30451	0.0621900
$441$	11.7586	0.559932
$442$	41.0645	1.95324
$443$	29.7569	1.41379	0.706896	−	0.707318i	$-0.250095\pi$
$443$	29.7569	1.41379	0.706896	+	0.707318i	$0.250095\pi$
$444$	5.29318	0.251203
$445$	17.6983	0.838979
$446$	−13.5587	−0.642024
$447$	−17.2503	−0.815911
$448$	3.75589	0.177449
$449$	−0.975997	−0.0460602	−0.0230301	−	0.999735i	$-0.507331\pi$
$449$	−0.975997	−0.0460602	−0.0230301	+	0.999735i	$0.507331\pi$
$450$	5.45721	0.257255
$451$	2.38220	0.112173
$452$	2.36033	0.111021
$453$	16.2429	0.763160
$454$	3.11435	0.146164
$455$	31.7938	1.49052
$456$	8.25239	0.386454
$457$	−8.23244	−0.385097	−0.192549	−	0.981287i	$-0.561675\pi$
$457$	−8.23244	−0.385097	−0.192549	+	0.981287i	$0.561675\pi$
$458$	−7.91029	−0.369624
$459$	−18.3689	−0.857389
$460$	−3.09712	−0.144404
$461$	40.0218	1.86400	0.932000	−	0.362458i	$-0.118062\pi$
$461$	40.0218	1.86400	0.932000	+	0.362458i	$0.118062\pi$
$462$	−8.10313	−0.376992
$463$	10.2624	0.476932	0.238466	−	0.971151i	$-0.423355\pi$
$463$	10.2624	0.476932	0.238466	+	0.971151i	$0.423355\pi$
$464$	8.10855	0.376430
$465$	−20.3818	−0.945183
$466$	−4.67924	−0.216761
$467$	35.8072	1.65696	0.828481	−	0.560018i	$-0.189206\pi$
$467$	35.8072	1.65696	0.828481	+	0.560018i	$0.189206\pi$
$468$	10.7366	0.496302
$469$	58.7358	2.71217
$470$	4.72105	0.217766
$471$	3.18557	0.146783
$472$	−1.96589	−0.0904873
$473$	−3.54500	−0.162999
$474$	2.34246	0.107593
$475$	−12.6161	−0.578865
$476$	−23.7682	−1.08942
$477$	18.1752	0.832186
$478$	0.0387479	0.00177229
$479$	18.9993	0.868099	0.434049	−	0.900889i	$-0.357084\pi$
$479$	18.9993	0.868099	0.434049	+	0.900889i	$0.357084\pi$
$480$	2.81441	0.128460
$481$	−15.9206	−0.725917
$482$	12.6230	0.574963
$483$	19.2382	0.875368
$484$	1.00000	0.0454545
$485$	18.3750	0.834366
$486$	−15.5117	−0.703623
$487$	10.4051	0.471501	0.235751	−	0.971814i	$-0.424245\pi$
$487$	10.4051	0.471501	0.235751	+	0.971814i	$0.424245\pi$
$488$	2.90437	0.131475
$489$	17.8315	0.806368
$490$	−9.27077	−0.418811
$491$	15.1440	0.683438	0.341719	−	0.939802i	$-0.388991\pi$
$491$	15.1440	0.683438	0.341719	+	0.939802i	$0.388991\pi$
$492$	5.13947	0.231705
$493$	−51.3130	−2.31102
$494$	−24.8212	−1.11676
$495$	−2.15841	−0.0970131
$496$	7.24195	0.325173
$497$	−31.2038	−1.39968
$498$	−16.0516	−0.719291
$499$	28.0146	1.25410	0.627052	−	0.778978i	$-0.284261\pi$
$499$	28.0146	1.25410	0.627052	+	0.778978i	$0.284261\pi$
$500$	−10.8251	−0.484115
$501$	−22.0352	−0.984459
$502$	−17.3217	−0.773103
$503$	−13.0208	−0.580569	−0.290284	−	0.956940i	$-0.593750\pi$
$503$	−13.0208	−0.580569	−0.290284	+	0.956940i	$0.593750\pi$
$504$	−6.21440	−0.276811
$505$	−9.78732	−0.435530
$506$	−2.37417	−0.105545
$507$	−62.7991	−2.78901
$508$	−16.6146	−0.737153
$509$	−35.6015	−1.57801	−0.789005	−	0.614386i	$-0.789404\pi$
$509$	−35.6015	−1.57801	−0.789005	+	0.614386i	$0.789404\pi$
$510$	−17.8103	−0.788653
$511$	12.6785	0.560864
$512$	−1.00000	−0.0441942
$513$	11.1030	0.490209
$514$	−24.4784	−1.07970
$515$	−20.7688	−0.915183
$516$	−7.64814	−0.336691
$517$	3.61902	0.159164
$518$	9.21488	0.404878
$519$	−17.3623	−0.762120
$520$	−8.46505	−0.371217
$521$	20.6561	0.904961	0.452480	−	0.891774i	$-0.350539\pi$
$521$	20.6561	0.904961	0.452480	+	0.891774i	$0.350539\pi$
$522$	−13.4162	−0.587211
$523$	−23.5013	−1.02764	−0.513820	−	0.857898i	$-0.671770\pi$
$523$	−23.5013	−1.02764	−0.513820	+	0.857898i	$0.671770\pi$
$524$	−3.66216	−0.159982
$525$	26.7262	1.16643
$526$	−28.9863	−1.26386
$527$	−45.8289	−1.99634
$528$	2.15745	0.0938908
$529$	−17.3633	−0.754927
$530$	−14.3298	−0.622447
$531$	3.25271	0.141155
$532$	14.3666	0.622869
$533$	−15.4583	−0.669572
$534$	29.2701	1.26664
$535$	−8.56073	−0.370113
$536$	−15.6383	−0.675472
$537$	0.681283	0.0293995
$538$	9.78788	0.421986
$539$	−7.10671	−0.306108
$540$	3.78658	0.162948
$541$	26.8412	1.15399	0.576997	−	0.816746i	$-0.304224\pi$
$541$	26.8412	1.15399	0.576997	+	0.816746i	$0.304224\pi$
$542$	24.9929	1.07354
$543$	−14.6933	−0.630549
$544$	6.32826	0.271322
$545$	12.9963	0.556700
$546$	52.5818	2.25029
$547$	−24.5824	−1.05107	−0.525533	−	0.850773i	$-0.676134\pi$
$547$	−24.5824	−1.05107	−0.525533	+	0.850773i	$0.676134\pi$
$548$	−16.3569	−0.698732
$549$	−4.80550	−0.205094
$550$	−3.29826	−0.140638
$551$	31.0158	1.32132
$552$	−5.12214	−0.218013
$553$	4.07799	0.173414
$554$	−6.92834	−0.294357
$555$	6.90500	0.293101
$556$	−15.4603	−0.655661
$557$	−41.4488	−1.75624	−0.878120	−	0.478440i	$-0.841202\pi$
$557$	−41.4488	−1.75624	−0.878120	+	0.478440i	$0.841202\pi$
$558$	−11.9823	−0.507253
$559$	23.0038	0.972955
$560$	4.89959	0.207046
$561$	−13.6529	−0.576425
$562$	−20.5543	−0.867031
$563$	−44.8885	−1.89183	−0.945913	−	0.324420i	$-0.894831\pi$
$563$	−44.8885	−1.89183	−0.945913	+	0.324420i	$0.894831\pi$
$564$	7.80785	0.328770
$565$	3.07908	0.129538
$566$	10.3328	0.434322
$567$	−42.1640	−1.77072
$568$	8.30796	0.348594
$569$	−3.02496	−0.126813	−0.0634065	−	0.997988i	$-0.520196\pi$
$569$	−3.02496	−0.126813	−0.0634065	+	0.997988i	$0.520196\pi$
$570$	10.7653	0.450909
$571$	6.74404	0.282229	0.141115	−	0.989993i	$-0.454931\pi$
$571$	6.74404	0.282229	0.141115	+	0.989993i	$0.454931\pi$
$572$	−6.48907	−0.271322
$573$	−2.87197	−0.119978
$574$	8.94729	0.373453
$575$	7.83062	0.326559
$576$	1.65457	0.0689406
$577$	−32.8218	−1.36639	−0.683194	−	0.730237i	$-0.739410\pi$
$577$	−32.8218	−1.36639	−0.683194	+	0.730237i	$0.739410\pi$
$578$	−23.0468	−0.958622
$579$	3.49774	0.145361
$580$	10.5777	0.439214
$581$	−27.9442	−1.15932
$582$	30.3893	1.25968
$583$	−10.9848	−0.454945
$584$	−3.37563	−0.139685
$585$	14.0061	0.579079
$586$	−27.9322	−1.15387
$587$	29.8605	1.23248	0.616238	−	0.787560i	$-0.288656\pi$
$587$	29.8605	1.23248	0.616238	+	0.787560i	$0.288656\pi$
$588$	−15.3323	−0.632295
$589$	27.7010	1.14140
$590$	−2.56452	−0.105580
$591$	−2.15745	−0.0887455
$592$	−2.45345	−0.100836
$593$	−34.5304	−1.41799	−0.708997	−	0.705212i	$-0.750852\pi$
$593$	−34.5304	−1.41799	−0.708997	+	0.705212i	$0.750852\pi$
$594$	2.90269	0.119099
$595$	−31.0059	−1.27112
$596$	7.99570	0.327517
$597$	−30.6121	−1.25287
$598$	15.4062	0.630005
$599$	−26.3685	−1.07739	−0.538695	−	0.842501i	$-0.681082\pi$
$599$	−26.3685	−1.07739	−0.538695	+	0.842501i	$0.681082\pi$
$600$	−7.11581	−0.290502
$601$	0.278560	0.0113627	0.00568136	−	0.999984i	$-0.498192\pi$
$601$	0.278560	0.0113627	0.00568136	+	0.999984i	$0.498192\pi$
$602$	−13.3146	−0.542664
$603$	25.8747	1.05370
$604$	−7.52878	−0.306342
$605$	1.30451	0.0530358
$606$	−16.1866	−0.657537
$607$	−11.5456	−0.468620	−0.234310	−	0.972162i	$-0.575283\pi$
$607$	−11.5456	−0.468620	−0.234310	+	0.972162i	$0.575283\pi$
$608$	−3.82507	−0.155127
$609$	−65.7046	−2.66249
$610$	3.78878	0.153403
$611$	−23.4841	−0.950065
$612$	−10.4706	−0.423248
$613$	−5.48625	−0.221587	−0.110794	−	0.993843i	$-0.535339\pi$
$613$	−5.48625	−0.221587	−0.110794	+	0.993843i	$0.535339\pi$
$614$	16.2986	0.657757
$615$	6.70449	0.270351
$616$	3.75589	0.151329
$617$	48.7863	1.96406	0.982030	−	0.188723i	$-0.0604348\pi$
$617$	48.7863	1.96406	0.982030	+	0.188723i	$0.0604348\pi$
$618$	−34.3482	−1.38169
$619$	−29.2176	−1.17435	−0.587176	−	0.809459i	$-0.699761\pi$
$619$	−29.2176	−1.17435	−0.587176	+	0.809459i	$0.699761\pi$
$620$	9.44719	0.379408
$621$	−6.89146	−0.276545
$622$	0.726589	0.0291336
$623$	50.9562	2.04152
$624$	−13.9998	−0.560442
$625$	2.36978	0.0947911
$626$	0.824305	0.0329458
$627$	8.25239	0.329569
$628$	−1.47655	−0.0589206
$629$	15.5260	0.619064
$630$	−8.10674	−0.322980
$631$	36.9407	1.47059	0.735293	−	0.677750i	$-0.237045\pi$
$631$	36.9407	1.47059	0.735293	+	0.677750i	$0.237045\pi$
$632$	−1.08576	−0.0431891
$633$	−1.77320	−0.0704785
$634$	11.5157	0.457346
$635$	−21.6739	−0.860101
$636$	−23.6992	−0.939734
$637$	46.1160	1.82718
$638$	8.10855	0.321020
$639$	−13.7461	−0.543789
$640$	−1.30451	−0.0515652
$641$	28.4825	1.12499	0.562496	−	0.826800i	$-0.309841\pi$
$641$	28.4825	1.12499	0.562496	+	0.826800i	$0.309841\pi$
$642$	−14.1581	−0.558774
$643$	15.8690	0.625811	0.312905	−	0.949784i	$-0.398698\pi$
$643$	15.8690	0.625811	0.312905	+	0.949784i	$0.398698\pi$
$644$	−8.91712	−0.351384
$645$	−9.97707	−0.392847
$646$	24.2060	0.952374
$647$	34.8219	1.36899	0.684494	−	0.729018i	$-0.260023\pi$
$647$	34.8219	1.36899	0.684494	+	0.729018i	$0.260023\pi$
$648$	11.2261	0.441003
$649$	−1.96589	−0.0771678
$650$	21.4026	0.839480
$651$	−58.6825	−2.29995
$652$	−8.26509	−0.323686
$653$	−33.1985	−1.29916	−0.649580	−	0.760294i	$-0.725055\pi$
$653$	−33.1985	−1.29916	−0.649580	+	0.760294i	$0.725055\pi$
$654$	21.4937	0.840472
$655$	−4.77732	−0.186665
$656$	−2.38220	−0.0930093
$657$	5.58523	0.217901
$658$	13.5927	0.529897
$659$	18.9213	0.737071	0.368535	−	0.929614i	$-0.379859\pi$
$659$	18.9213	0.737071	0.368535	+	0.929614i	$0.379859\pi$
$660$	2.81441	0.109551
$661$	14.6431	0.569550	0.284775	−	0.958594i	$-0.408081\pi$
$661$	14.6431	0.569550	0.284775	+	0.958594i	$0.408081\pi$
$662$	13.6447	0.530318
$663$	88.5945	3.44072
$664$	7.44011	0.288732
$665$	18.7413	0.726757
$666$	4.05941	0.157299
$667$	−19.2511	−0.745404
$668$	10.2135	0.395174
$669$	−29.2522	−1.13096
$670$	−20.4003	−0.788133
$671$	2.90437	0.112122
$672$	8.10313	0.312585
$673$	9.10397	0.350932	0.175466	−	0.984485i	$-0.443857\pi$
$673$	9.10397	0.350932	0.175466	+	0.984485i	$0.443857\pi$
$674$	−22.7007	−0.874400
$675$	−9.57380	−0.368496
$676$	29.1081	1.11954
$677$	39.8283	1.53072	0.765362	−	0.643600i	$-0.222560\pi$
$677$	39.8283	1.53072	0.765362	+	0.643600i	$0.222560\pi$
$678$	5.09229	0.195568
$679$	52.9046	2.03029
$680$	8.25527	0.316575
$681$	6.71904	0.257474
$682$	7.24195	0.277309
$683$	−14.6479	−0.560487	−0.280244	−	0.959929i	$-0.590415\pi$
$683$	−14.6479	−0.560487	−0.280244	+	0.959929i	$0.590415\pi$
$684$	6.32887	0.241990
$685$	−21.3377	−0.815272
$686$	−0.400802	−0.0153027
$687$	−17.0660	−0.651109
$688$	3.54500	0.135152
$689$	71.2814	2.71560
$690$	−6.68188	−0.254375
$691$	−14.2972	−0.543889	−0.271945	−	0.962313i	$-0.587667\pi$
$691$	−14.2972	−0.543889	−0.271945	+	0.962313i	$0.587667\pi$
$692$	8.04761	0.305924
$693$	−6.21440	−0.236065
$694$	25.1502	0.954687
$695$	−20.1680	−0.765017
$696$	17.4938	0.663099
$697$	15.0752	0.571013
$698$	−31.0815	−1.17645
$699$	−10.0952	−0.381836
$700$	−12.3879	−0.468218
$701$	−10.8602	−0.410183	−0.205092	−	0.978743i	$-0.565749\pi$
$701$	−10.8602	−0.410183	−0.205092	+	0.978743i	$0.565749\pi$
$702$	−18.8357	−0.710909
$703$	−9.38461	−0.353947
$704$	−1.00000	−0.0376889
$705$	10.1854	0.383605
$706$	19.7906	0.744829
$707$	−28.1793	−1.05979
$708$	−4.24130	−0.159398
$709$	26.7189	1.00345	0.501726	−	0.865027i	$-0.332699\pi$
$709$	26.7189	1.00345	0.501726	+	0.865027i	$0.332699\pi$
$710$	10.8378	0.406736
$711$	1.79647	0.0673727
$712$	−13.5670	−0.508445
$713$	−17.1936	−0.643906
$714$	−51.2787	−1.91906
$715$	−8.46505	−0.316575
$716$	−0.315782	−0.0118013
$717$	0.0835965	0.00312197
$718$	−22.6457	−0.845132
$719$	−35.5858	−1.32713	−0.663564	−	0.748120i	$-0.730957\pi$
$719$	−35.5858	−1.32713	−0.663564	+	0.748120i	$0.730957\pi$
$720$	2.15841	0.0804390
$721$	−59.7967	−2.22695
$722$	4.36881	0.162590
$723$	27.2335	1.01282
$724$	6.81049	0.253110
$725$	−26.7441	−0.993250
$726$	2.15745	0.0800703
$727$	−12.1928	−0.452207	−0.226104	−	0.974103i	$-0.572599\pi$
$727$	−12.1928	−0.452207	−0.226104	+	0.974103i	$0.572599\pi$
$728$	−24.3722	−0.903296
$729$	0.212740	0.00787927
$730$	−4.40354	−0.162982
$731$	−22.4337	−0.829739
$732$	6.26603	0.231599
$733$	−39.5883	−1.46223	−0.731114	−	0.682255i	$-0.760999\pi$
$733$	−39.5883	−1.46223	−0.731114	+	0.682255i	$0.760999\pi$
$734$	25.4528	0.939479
$735$	−20.0012	−0.737755
$736$	2.37417	0.0875130
$737$	−15.6383	−0.576045
$738$	3.94153	0.145090
$739$	1.37148	0.0504508	0.0252254	−	0.999682i	$-0.491970\pi$
$739$	1.37148	0.0504508	0.0252254	+	0.999682i	$0.491970\pi$
$740$	−3.20054	−0.117654
$741$	−53.5504	−1.96722
$742$	−41.2578	−1.51462
$743$	4.49385	0.164863	0.0824317	−	0.996597i	$-0.473731\pi$
$743$	4.49385	0.164863	0.0824317	+	0.996597i	$0.473731\pi$
$744$	15.6241	0.572808
$745$	10.4305	0.382143
$746$	−16.5608	−0.606334
$747$	−12.3102	−0.450407
$748$	6.32826	0.231384
$749$	−24.6477	−0.900608
$750$	−23.3547	−0.852792
$751$	−1.02148	−0.0372744	−0.0186372	−	0.999826i	$-0.505933\pi$
$751$	−1.02148	−0.0372744	−0.0186372	+	0.999826i	$0.505933\pi$
$752$	−3.61902	−0.131972
$753$	−37.3705	−1.36186
$754$	−52.6170	−1.91620
$755$	−9.82136	−0.357436
$756$	10.9022	0.396508
$757$	−46.7177	−1.69798	−0.848992	−	0.528405i	$-0.822790\pi$
$757$	−46.7177	−1.69798	−0.848992	+	0.528405i	$0.822790\pi$
$758$	34.2986	1.24578
$759$	−5.12214	−0.185922
$760$	−4.98984	−0.181001
$761$	28.8084	1.04430	0.522151	−	0.852853i	$-0.325130\pi$
$761$	28.8084	1.04430	0.522151	+	0.852853i	$0.325130\pi$
$762$	−35.8450	−1.29853
$763$	37.4184	1.35464
$764$	1.33119	0.0481608
$765$	−13.6589	−0.493840
$766$	−0.987844	−0.0356923
$767$	12.7568	0.460621
$768$	−2.15745	−0.0778501
$769$	−24.0528	−0.867365	−0.433683	−	0.901066i	$-0.642786\pi$
$769$	−24.0528	−0.867365	−0.433683	+	0.901066i	$0.642786\pi$
$770$	4.89959	0.176569
$771$	−52.8109	−1.90194
$772$	−1.62124	−0.0583497
$773$	−21.2008	−0.762539	−0.381269	−	0.924464i	$-0.624513\pi$
$773$	−21.2008	−0.762539	−0.381269	+	0.924464i	$0.624513\pi$
$774$	−5.86546	−0.210830
$775$	−23.8858	−0.858004
$776$	−14.0858	−0.505649
$777$	19.8806	0.713212
$778$	−10.6338	−0.381240
$779$	−9.11209	−0.326475
$780$	−18.2629	−0.653917
$781$	8.30796	0.297282
$782$	−15.0244	−0.537270
$783$	23.5366	0.841128
$784$	7.10671	0.253811
$785$	−1.92617	−0.0687479
$786$	−7.90091	−0.281816
$787$	47.4516	1.69147	0.845734	−	0.533605i	$-0.179163\pi$
$787$	47.4516	1.69147	0.845734	+	0.533605i	$0.179163\pi$
$788$	1.00000	0.0356235
$789$	−62.5364	−2.22635
$790$	−1.41638	−0.0503925
$791$	8.86515	0.315209
$792$	1.65457	0.0587927
$793$	−18.8467	−0.669266
$794$	−14.0988	−0.500348
$795$	−30.9158	−1.09647
$796$	14.1891	0.502918
$797$	−15.5632	−0.551276	−0.275638	−	0.961262i	$-0.588889\pi$
$797$	−15.5632	−0.551276	−0.275638	+	0.961262i	$0.588889\pi$
$798$	30.9951	1.09721
$799$	22.9021	0.810218
$800$	3.29826	0.116611
$801$	22.4476	0.793147
$802$	−19.7780	−0.698386
$803$	−3.37563	−0.119123
$804$	−33.7388	−1.18988
$805$	−11.6325	−0.409990
$806$	−46.9935	−1.65528
$807$	21.1168	0.743347
$808$	7.50269	0.263944
$809$	−25.9346	−0.911813	−0.455906	−	0.890028i	$-0.650685\pi$
$809$	−25.9346	−0.911813	−0.455906	+	0.890028i	$0.650685\pi$
$810$	14.6446	0.514557
$811$	24.1966	0.849656	0.424828	−	0.905274i	$-0.360335\pi$
$811$	24.1966	0.849656	0.424828	+	0.905274i	$0.360335\pi$
$812$	30.4548	1.06875
$813$	53.9209	1.89109
$814$	−2.45345	−0.0859932
$815$	−10.7819	−0.377673
$816$	13.6529	0.477946
$817$	13.5599	0.474400
$818$	2.13641	0.0746979
$819$	40.3257	1.40909
$820$	−3.10760	−0.108522
$821$	20.2162	0.705551	0.352775	−	0.935708i	$-0.385238\pi$
$821$	20.2162	0.705551	0.352775	+	0.935708i	$0.385238\pi$
$822$	−35.2891	−1.23085
$823$	−31.9409	−1.11339	−0.556694	−	0.830718i	$-0.687930\pi$
$823$	−31.9409	−1.11339	−0.556694	+	0.830718i	$0.687930\pi$
$824$	15.9208	0.554627
$825$	−7.11581	−0.247741
$826$	−7.38366	−0.256910
$827$	−1.86072	−0.0647035	−0.0323518	−	0.999477i	$-0.510300\pi$
$827$	−1.86072	−0.0647035	−0.0323518	+	0.999477i	$0.510300\pi$
$828$	−3.92824	−0.136516
$829$	14.8867	0.517037	0.258518	−	0.966006i	$-0.416766\pi$
$829$	14.8867	0.517037	0.258518	+	0.966006i	$0.416766\pi$
$830$	9.70569	0.336889
$831$	−14.9475	−0.518524
$832$	6.48907	0.224968
$833$	−44.9731	−1.55823
$834$	−33.3547	−1.15498
$835$	13.3237	0.461084
$836$	−3.82507	−0.132293
$837$	21.0211	0.726596
$838$	−8.98107	−0.310246
$839$	−0.924455	−0.0319157	−0.0159579	−	0.999873i	$-0.505080\pi$
$839$	−0.924455	−0.0319157	−0.0159579	+	0.999873i	$0.505080\pi$
$840$	10.5706	0.364721
$841$	36.7485	1.26719
$842$	−23.9520	−0.825441
$843$	−44.3448	−1.52732
$844$	0.821899	0.0282909
$845$	37.9717	1.30627
$846$	5.98794	0.205870
$847$	3.75589	0.129054
$848$	10.9848	0.377221
$849$	22.2925	0.765078
$850$	−20.8722	−0.715911
$851$	5.82490	0.199675
$852$	17.9240	0.614066
$853$	−6.28952	−0.215349	−0.107675	−	0.994186i	$-0.534340\pi$
$853$	−6.28952	−0.215349	−0.107675	+	0.994186i	$0.534340\pi$
$854$	10.9085	0.373281
$855$	8.25606	0.282351
$856$	6.56242	0.224299
$857$	−29.3347	−1.00205	−0.501026	−	0.865432i	$-0.667044\pi$
$857$	−29.3347	−1.00205	−0.501026	+	0.865432i	$0.667044\pi$
$858$	−13.9998	−0.477946
$859$	−25.3434	−0.864704	−0.432352	−	0.901705i	$-0.642316\pi$
$859$	−25.3434	−0.864704	−0.432352	+	0.901705i	$0.642316\pi$
$860$	4.62448	0.157694
$861$	19.3033	0.657854
$862$	−18.3882	−0.626306
$863$	31.1540	1.06049	0.530247	−	0.847844i	$-0.322099\pi$
$863$	31.1540	1.06049	0.530247	+	0.847844i	$0.322099\pi$
$864$	−2.90269	−0.0987514
$865$	10.4982	0.356949
$866$	19.1755	0.651610
$867$	−49.7223	−1.68866
$868$	27.2000	0.923227
$869$	−1.08576	−0.0368318
$870$	22.8208	0.773696
$871$	101.478	3.43846
$872$	−9.96259	−0.337376
$873$	23.3059	0.788786
$874$	9.08137	0.307182
$875$	−40.6581	−1.37449
$876$	−7.28274	−0.246061
$877$	39.0021	1.31701	0.658504	−	0.752577i	$-0.271190\pi$
$877$	39.0021	1.31701	0.658504	+	0.752577i	$0.271190\pi$
$878$	−31.0343	−1.04736
$879$	−60.2623	−2.03260
$880$	−1.30451	−0.0439750
$881$	−10.0979	−0.340206	−0.170103	−	0.985426i	$-0.554410\pi$
$881$	−10.0979	−0.340206	−0.170103	+	0.985426i	$0.554410\pi$
$882$	−11.7586	−0.395932
$883$	−52.2409	−1.75805	−0.879023	−	0.476779i	$-0.841804\pi$
$883$	−52.2409	−1.75805	−0.879023	+	0.476779i	$0.841804\pi$
$884$	−41.0645	−1.38115
$885$	−5.53281	−0.185983
$886$	−29.7569	−0.999702
$887$	−39.3031	−1.31967	−0.659835	−	0.751411i	$-0.729374\pi$
$887$	−39.3031	−1.31967	−0.659835	+	0.751411i	$0.729374\pi$
$888$	−5.29318	−0.177627
$889$	−62.4025	−2.09291
$890$	−17.6983	−0.593248
$891$	11.2261	0.376089
$892$	13.5587	0.453980
$893$	−13.8430	−0.463239
$894$	17.2503	0.576936
$895$	−0.411941	−0.0137697
$896$	−3.75589	−0.125475
$897$	33.2379	1.10978
$898$	0.975997	0.0325695
$899$	58.7217	1.95848
$900$	−5.45721	−0.181907
$901$	−69.5149	−2.31588
$902$	−2.38220	−0.0793186
$903$	−28.7256	−0.955928
$904$	−2.36033	−0.0785035
$905$	8.88435	0.295326
$906$	−16.2429	−0.539635
$907$	56.7750	1.88518	0.942592	−	0.333946i	$-0.108380\pi$
$907$	56.7750	1.88518	0.942592	+	0.333946i	$0.108380\pi$
$908$	−3.11435	−0.103353
$909$	−12.4137	−0.411738
$910$	−31.7938	−1.05395
$911$	4.70094	0.155749	0.0778745	−	0.996963i	$-0.475187\pi$
$911$	4.70094	0.155749	0.0778745	+	0.996963i	$0.475187\pi$
$912$	−8.25239	−0.273264
$913$	7.44011	0.246232
$914$	8.23244	0.272305
$915$	8.17409	0.270227
$916$	7.91029	0.261363
$917$	−13.7547	−0.454219
$918$	18.3689	0.606265
$919$	5.31705	0.175393	0.0876966	−	0.996147i	$-0.472049\pi$
$919$	5.31705	0.175393	0.0876966	+	0.996147i	$0.472049\pi$
$920$	3.09712	0.102109
$921$	35.1633	1.15867
$922$	−40.0218	−1.31805
$923$	−53.9110	−1.77450
$924$	8.10313	0.266573
$925$	8.09210	0.266066
$926$	−10.2624	−0.337242
$927$	−26.3421	−0.865188
$928$	−8.10855	−0.266176
$929$	−4.54756	−0.149201	−0.0746003	−	0.997214i	$-0.523768\pi$
$929$	−4.54756	−0.149201	−0.0746003	+	0.997214i	$0.523768\pi$
$930$	20.3818	0.668346
$931$	27.1837	0.890910
$932$	4.67924	0.153274
$933$	1.56758	0.0513202
$934$	−35.8072	−1.17165
$935$	8.25527	0.269976
$936$	−10.7366	−0.350938
$937$	10.4230	0.340506	0.170253	−	0.985400i	$-0.445542\pi$
$937$	10.4230	0.340506	0.170253	+	0.985400i	$0.445542\pi$
$938$	−58.7358	−1.91779
$939$	1.77839	0.0580356
$940$	−4.72105	−0.153984
$941$	44.2970	1.44404	0.722021	−	0.691871i	$-0.243213\pi$
$941$	44.2970	1.44404	0.722021	+	0.691871i	$0.243213\pi$
$942$	−3.18557	−0.103791
$943$	5.65575	0.184176
$944$	1.96589	0.0639842
$945$	14.2220	0.462641
$946$	3.54500	0.115258
$947$	−26.2521	−0.853078	−0.426539	−	0.904469i	$-0.640267\pi$
$947$	−26.2521	−0.853078	−0.426539	+	0.904469i	$0.640267\pi$
$948$	−2.34246	−0.0760797
$949$	21.9047	0.711057
$950$	12.6161	0.409319
$951$	24.8445	0.805637
$952$	23.7682	0.770333
$953$	16.6417	0.539079	0.269539	−	0.962989i	$-0.413129\pi$
$953$	16.6417	0.539079	0.269539	+	0.962989i	$0.413129\pi$
$954$	−18.1752	−0.588444
$955$	1.73655	0.0561934
$956$	−0.0387479	−0.00125320
$957$	17.4938	0.565493
$958$	−18.9993	−0.613838
$959$	−61.4347	−1.98383
$960$	−2.81441	−0.0908346
$961$	21.4458	0.691801
$962$	15.9206	0.513300
$963$	−10.8580	−0.349894
$964$	−12.6230	−0.406560
$965$	−2.11492	−0.0680817
$966$	−19.2382	−0.618979
$967$	26.4926	0.851946	0.425973	−	0.904736i	$-0.359932\pi$
$967$	26.4926	0.851946	0.425973	+	0.904736i	$0.359932\pi$
$968$	−1.00000	−0.0321412
$969$	52.2232	1.67765
$970$	−18.3750	−0.589986
$971$	−15.0703	−0.483630	−0.241815	−	0.970322i	$-0.577743\pi$
$971$	−15.0703	−0.483630	−0.241815	+	0.970322i	$0.577743\pi$
$972$	15.5117	0.497537
$973$	−58.0670	−1.86154
$974$	−10.4051	−0.333402
$975$	46.1750	1.47878
$976$	−2.90437	−0.0929667
$977$	−34.7677	−1.11232	−0.556158	−	0.831076i	$-0.687725\pi$
$977$	−34.7677	−1.11232	−0.556158	+	0.831076i	$0.687725\pi$
$978$	−17.8315	−0.570188
$979$	−13.5670	−0.433603
$980$	9.27077	0.296144
$981$	16.4838	0.526288
$982$	−15.1440	−0.483264
$983$	−58.3551	−1.86124	−0.930619	−	0.365989i	$-0.880731\pi$
$983$	−58.3551	−1.86124	−0.930619	+	0.365989i	$0.880731\pi$
$984$	−5.13947	−0.163840
$985$	1.30451	0.0415651
$986$	51.3130	1.63414
$987$	29.3254	0.933438
$988$	24.8212	0.789667
$989$	−8.41643	−0.267627
$990$	2.15841	0.0685986
$991$	2.25130	0.0715150	0.0357575	−	0.999360i	$-0.488616\pi$
$991$	2.25130	0.0715150	0.0357575	+	0.999360i	$0.488616\pi$
$992$	−7.24195	−0.229932
$993$	29.4378	0.934180
$994$	31.2038	0.989724
$995$	18.5098	0.586799
$996$	16.0516	0.508616
$997$	−22.3385	−0.707466	−0.353733	−	0.935346i	$-0.615088\pi$
$997$	−22.3385	−0.707466	−0.353733	+	0.935346i	$0.615088\pi$
$998$	−28.0146	−0.886785
$999$	−7.12158	−0.225317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.e.1.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.e.1.6	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.15745 q^{3} +1.00000 q^{4} +1.30451 q^{5} +2.15745 q^{6} +3.75589 q^{7} -1.00000 q^{8} +1.65457 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.15745 q^{3} +1.00000 q^{4} +1.30451 q^{5} +2.15745 q^{6} +3.75589 q^{7} -1.00000 q^{8} +1.65457 q^{9} -1.30451 q^{10} -1.00000 q^{11} -2.15745 q^{12} +6.48907 q^{13} -3.75589 q^{14} -2.81441 q^{15} +1.00000 q^{16} -6.32826 q^{17} -1.65457 q^{18} +3.82507 q^{19} +1.30451 q^{20} -8.10313 q^{21} +1.00000 q^{22} -2.37417 q^{23} +2.15745 q^{24} -3.29826 q^{25} -6.48907 q^{26} +2.90269 q^{27} +3.75589 q^{28} +8.10855 q^{29} +2.81441 q^{30} +7.24195 q^{31} -1.00000 q^{32} +2.15745 q^{33} +6.32826 q^{34} +4.89959 q^{35} +1.65457 q^{36} -2.45345 q^{37} -3.82507 q^{38} -13.9998 q^{39} -1.30451 q^{40} -2.38220 q^{41} +8.10313 q^{42} +3.54500 q^{43} -1.00000 q^{44} +2.15841 q^{45} +2.37417 q^{46} -3.61902 q^{47} -2.15745 q^{48} +7.10671 q^{49} +3.29826 q^{50} +13.6529 q^{51} +6.48907 q^{52} +10.9848 q^{53} -2.90269 q^{54} -1.30451 q^{55} -3.75589 q^{56} -8.25239 q^{57} -8.10855 q^{58} +1.96589 q^{59} -2.81441 q^{60} -2.90437 q^{61} -7.24195 q^{62} +6.21440 q^{63} +1.00000 q^{64} +8.46505 q^{65} -2.15745 q^{66} +15.6383 q^{67} -6.32826 q^{68} +5.12214 q^{69} -4.89959 q^{70} -8.30796 q^{71} -1.65457 q^{72} +3.37563 q^{73} +2.45345 q^{74} +7.11581 q^{75} +3.82507 q^{76} -3.75589 q^{77} +13.9998 q^{78} +1.08576 q^{79} +1.30451 q^{80} -11.2261 q^{81} +2.38220 q^{82} -7.44011 q^{83} -8.10313 q^{84} -8.25527 q^{85} -3.54500 q^{86} -17.4938 q^{87} +1.00000 q^{88} +13.5670 q^{89} -2.15841 q^{90} +24.3722 q^{91} -2.37417 q^{92} -15.6241 q^{93} +3.61902 q^{94} +4.98984 q^{95} +2.15745 q^{96} +14.0858 q^{97} -7.10671 q^{98} -1.65457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * q^99

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