LMFDB - Embedded newform 4334.2.a.f.1.12

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			1.12
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.272392 q^{3} +1.00000 q^{4} +2.45255 q^{5} +0.272392 q^{6} +2.51117 q^{7} +1.00000 q^{8} -2.92580 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.272392 q^{3} +1.00000 q^{4} +2.45255 q^{5} +0.272392 q^{6} +2.51117 q^{7} +1.00000 q^{8} -2.92580 q^{9} +2.45255 q^{10} -1.00000 q^{11} +0.272392 q^{12} +5.25164 q^{13} +2.51117 q^{14} +0.668056 q^{15} +1.00000 q^{16} -0.865339 q^{17} -2.92580 q^{18} -1.56717 q^{19} +2.45255 q^{20} +0.684022 q^{21} -1.00000 q^{22} -3.84451 q^{23} +0.272392 q^{24} +1.01500 q^{25} +5.25164 q^{26} -1.61414 q^{27} +2.51117 q^{28} +0.867546 q^{29} +0.668056 q^{30} +9.29935 q^{31} +1.00000 q^{32} -0.272392 q^{33} -0.865339 q^{34} +6.15876 q^{35} -2.92580 q^{36} +6.13732 q^{37} -1.56717 q^{38} +1.43051 q^{39} +2.45255 q^{40} -1.66271 q^{41} +0.684022 q^{42} +10.8842 q^{43} -1.00000 q^{44} -7.17567 q^{45} -3.84451 q^{46} +6.71600 q^{47} +0.272392 q^{48} -0.694050 q^{49} +1.01500 q^{50} -0.235712 q^{51} +5.25164 q^{52} -5.05335 q^{53} -1.61414 q^{54} -2.45255 q^{55} +2.51117 q^{56} -0.426885 q^{57} +0.867546 q^{58} -7.85868 q^{59} +0.668056 q^{60} +13.5594 q^{61} +9.29935 q^{62} -7.34717 q^{63} +1.00000 q^{64} +12.8799 q^{65} -0.272392 q^{66} +15.0942 q^{67} -0.865339 q^{68} -1.04722 q^{69} +6.15876 q^{70} -0.0644401 q^{71} -2.92580 q^{72} -6.49316 q^{73} +6.13732 q^{74} +0.276478 q^{75} -1.56717 q^{76} -2.51117 q^{77} +1.43051 q^{78} -16.5741 q^{79} +2.45255 q^{80} +8.33773 q^{81} -1.66271 q^{82} -10.3820 q^{83} +0.684022 q^{84} -2.12229 q^{85} +10.8842 q^{86} +0.236313 q^{87} -1.00000 q^{88} +1.26760 q^{89} -7.17567 q^{90} +13.1877 q^{91} -3.84451 q^{92} +2.53307 q^{93} +6.71600 q^{94} -3.84356 q^{95} +0.272392 q^{96} -2.08036 q^{97} -0.694050 q^{98} +2.92580 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * 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
$3$	0.272392	0.157266	0.0786329	−	0.996904i	$-0.474944\pi$
$3$	0.272392	0.157266	0.0786329	+	0.996904i	$0.474944\pi$
$4$	1.00000	0.500000
$5$	2.45255	1.09681	0.548407	−	0.836212i	$-0.315235\pi$
$5$	2.45255	1.09681	0.548407	+	0.836212i	$0.315235\pi$
$6$	0.272392	0.111204
$7$	2.51117	0.949131	0.474566	−	0.880220i	$-0.342605\pi$
$7$	2.51117	0.949131	0.474566	+	0.880220i	$0.342605\pi$
$8$	1.00000	0.353553
$9$	−2.92580	−0.975267
$10$	2.45255	0.775564
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.272392	0.0786329
$13$	5.25164	1.45654	0.728271	−	0.685289i	$-0.240324\pi$
$13$	5.25164	1.45654	0.728271	+	0.685289i	$0.240324\pi$
$14$	2.51117	0.671137
$15$	0.668056	0.172491
$16$	1.00000	0.250000
$17$	−0.865339	−0.209875	−0.104938	−	0.994479i	$-0.533464\pi$
$17$	−0.865339	−0.209875	−0.104938	+	0.994479i	$0.533464\pi$
$18$	−2.92580	−0.689618
$19$	−1.56717	−0.359533	−0.179767	−	0.983709i	$-0.557534\pi$
$19$	−1.56717	−0.359533	−0.179767	+	0.983709i	$0.557534\pi$
$20$	2.45255	0.548407
$21$	0.684022	0.149266
$22$	−1.00000	−0.213201
$23$	−3.84451	−0.801636	−0.400818	−	0.916158i	$-0.631274\pi$
$23$	−3.84451	−0.801636	−0.400818	+	0.916158i	$0.631274\pi$
$24$	0.272392	0.0556019
$25$	1.01500	0.203000
$26$	5.25164	1.02993
$27$	−1.61414	−0.310642
$28$	2.51117	0.474566
$29$	0.867546	0.161099	0.0805496	−	0.996751i	$-0.474332\pi$
$29$	0.867546	0.161099	0.0805496	+	0.996751i	$0.474332\pi$
$30$	0.668056	0.121970
$31$	9.29935	1.67021	0.835106	−	0.550089i	$-0.185406\pi$
$31$	9.29935	1.67021	0.835106	+	0.550089i	$0.185406\pi$
$32$	1.00000	0.176777
$33$	−0.272392	−0.0474174
$34$	−0.865339	−0.148404
$35$	6.15876	1.04102
$36$	−2.92580	−0.487634
$37$	6.13732	1.00897	0.504484	−	0.863421i	$-0.331683\pi$
$37$	6.13732	1.00897	0.504484	+	0.863421i	$0.331683\pi$
$38$	−1.56717	−0.254228
$39$	1.43051	0.229064
$40$	2.45255	0.387782
$41$	−1.66271	−0.259672	−0.129836	−	0.991536i	$-0.541445\pi$
$41$	−1.66271	−0.259672	−0.129836	+	0.991536i	$0.541445\pi$
$42$	0.684022	0.105547
$43$	10.8842	1.65983	0.829916	−	0.557889i	$-0.188388\pi$
$43$	10.8842	1.65983	0.829916	+	0.557889i	$0.188388\pi$
$44$	−1.00000	−0.150756
$45$	−7.17567	−1.06969
$46$	−3.84451	−0.566842
$47$	6.71600	0.979629	0.489815	−	0.871827i	$-0.337064\pi$
$47$	6.71600	0.979629	0.489815	+	0.871827i	$0.337064\pi$
$48$	0.272392	0.0393165
$49$	−0.694050	−0.0991500
$50$	1.01500	0.143542
$51$	−0.235712	−0.0330062
$52$	5.25164	0.728271
$53$	−5.05335	−0.694131	−0.347066	−	0.937841i	$-0.612822\pi$
$53$	−5.05335	−0.694131	−0.347066	+	0.937841i	$0.612822\pi$
$54$	−1.61414	−0.219657
$55$	−2.45255	−0.330702
$56$	2.51117	0.335569
$57$	−0.426885	−0.0565423
$58$	0.867546	0.113914
$59$	−7.85868	−1.02311	−0.511557	−	0.859250i	$-0.670931\pi$
$59$	−7.85868	−1.02311	−0.511557	+	0.859250i	$0.670931\pi$
$60$	0.668056	0.0862456
$61$	13.5594	1.73610	0.868049	−	0.496479i	$-0.165374\pi$
$61$	13.5594	1.73610	0.868049	+	0.496479i	$0.165374\pi$
$62$	9.29935	1.18102
$63$	−7.34717	−0.925657
$64$	1.00000	0.125000
$65$	12.8799	1.59755
$66$	−0.272392	−0.0335292
$67$	15.0942	1.84405	0.922027	−	0.387125i	$-0.126532\pi$
$67$	15.0942	1.84405	0.922027	+	0.387125i	$0.126532\pi$
$68$	−0.865339	−0.104938
$69$	−1.04722	−0.126070
$70$	6.15876	0.736112
$71$	−0.0644401	−0.00764763	−0.00382381	−	0.999993i	$-0.501217\pi$
$71$	−0.0644401	−0.00764763	−0.00382381	+	0.999993i	$0.501217\pi$
$72$	−2.92580	−0.344809
$73$	−6.49316	−0.759967	−0.379984	−	0.924993i	$-0.624070\pi$
$73$	−6.49316	−0.759967	−0.379984	+	0.924993i	$0.624070\pi$
$74$	6.13732	0.713449
$75$	0.276478	0.0319249
$76$	−1.56717	−0.179767
$77$	−2.51117	−0.286174
$78$	1.43051	0.161973
$79$	−16.5741	−1.86473	−0.932366	−	0.361517i	$-0.882259\pi$
$79$	−16.5741	−1.86473	−0.932366	+	0.361517i	$0.882259\pi$
$80$	2.45255	0.274203
$81$	8.33773	0.926414
$82$	−1.66271	−0.183616
$83$	−10.3820	−1.13957	−0.569785	−	0.821794i	$-0.692974\pi$
$83$	−10.3820	−1.13957	−0.569785	+	0.821794i	$0.692974\pi$
$84$	0.684022	0.0746330
$85$	−2.12229	−0.230194
$86$	10.8842	1.17368
$87$	0.236313	0.0253354
$88$	−1.00000	−0.106600
$89$	1.26760	0.134365	0.0671826	−	0.997741i	$-0.478599\pi$
$89$	1.26760	0.134365	0.0671826	+	0.997741i	$0.478599\pi$
$90$	−7.17567	−0.756382
$91$	13.1877	1.38245
$92$	−3.84451	−0.400818
$93$	2.53307	0.262667
$94$	6.71600	0.692702
$95$	−3.84356	−0.394341
$96$	0.272392	0.0278009
$97$	−2.08036	−0.211228	−0.105614	−	0.994407i	$-0.533681\pi$
$97$	−2.08036	−0.211228	−0.105614	+	0.994407i	$0.533681\pi$
$98$	−0.694050	−0.0701096
$99$	2.92580	0.294054
$100$	1.01500	0.101500
$101$	14.5365	1.44644	0.723220	−	0.690618i	$-0.242661\pi$
$101$	14.5365	1.44644	0.723220	+	0.690618i	$0.242661\pi$
$102$	−0.235712	−0.0233389
$103$	13.9101	1.37060	0.685302	−	0.728259i	$-0.259670\pi$
$103$	13.9101	1.37060	0.685302	+	0.728259i	$0.259670\pi$
$104$	5.25164	0.514965
$105$	1.67760	0.163717
$106$	−5.05335	−0.490825
$107$	−18.7508	−1.81271	−0.906355	−	0.422517i	$-0.861147\pi$
$107$	−18.7508	−1.81271	−0.906355	+	0.422517i	$0.861147\pi$
$108$	−1.61414	−0.155321
$109$	−8.62352	−0.825984	−0.412992	−	0.910735i	$-0.635516\pi$
$109$	−8.62352	−0.825984	−0.412992	+	0.910735i	$0.635516\pi$
$110$	−2.45255	−0.233841
$111$	1.67176	0.158676
$112$	2.51117	0.237283
$113$	1.74098	0.163778	0.0818889	−	0.996641i	$-0.473905\pi$
$113$	1.74098	0.163778	0.0818889	+	0.996641i	$0.473905\pi$
$114$	−0.426885	−0.0399814
$115$	−9.42885	−0.879245
$116$	0.867546	0.0805496
$117$	−15.3653	−1.42052
$118$	−7.85868	−0.723450
$119$	−2.17301	−0.199199
$120$	0.668056	0.0609849
$121$	1.00000	0.0909091
$122$	13.5594	1.22761
$123$	−0.452909	−0.0408375
$124$	9.29935	0.835106
$125$	−9.77341	−0.874161
$126$	−7.34717	−0.654538
$127$	6.97345	0.618794	0.309397	−	0.950933i	$-0.399873\pi$
$127$	6.97345	0.618794	0.309397	+	0.950933i	$0.399873\pi$
$128$	1.00000	0.0883883
$129$	2.96479	0.261035
$130$	12.8799	1.12964
$131$	−5.97223	−0.521796	−0.260898	−	0.965366i	$-0.584019\pi$
$131$	−5.97223	−0.521796	−0.260898	+	0.965366i	$0.584019\pi$
$132$	−0.272392	−0.0237087
$133$	−3.93542	−0.341244
$134$	15.0942	1.30394
$135$	−3.95877	−0.340716
$136$	−0.865339	−0.0742022
$137$	−7.06934	−0.603974	−0.301987	−	0.953312i	$-0.597650\pi$
$137$	−7.06934	−0.603974	−0.301987	+	0.953312i	$0.597650\pi$
$138$	−1.04722	−0.0891450
$139$	−4.87943	−0.413868	−0.206934	−	0.978355i	$-0.566349\pi$
$139$	−4.87943	−0.413868	−0.206934	+	0.978355i	$0.566349\pi$
$140$	6.15876	0.520510
$141$	1.82939	0.154062
$142$	−0.0644401	−0.00540769
$143$	−5.25164	−0.439164
$144$	−2.92580	−0.243817
$145$	2.12770	0.176696
$146$	−6.49316	−0.537378
$147$	−0.189054	−0.0155929
$148$	6.13732	0.504484
$149$	−15.7845	−1.29311	−0.646557	−	0.762865i	$-0.723792\pi$
$149$	−15.7845	−1.29311	−0.646557	+	0.762865i	$0.723792\pi$
$150$	0.276478	0.0225743
$151$	10.1254	0.823996	0.411998	−	0.911185i	$-0.364831\pi$
$151$	10.1254	0.823996	0.411998	+	0.911185i	$0.364831\pi$
$152$	−1.56717	−0.127114
$153$	2.53181	0.204685
$154$	−2.51117	−0.202355
$155$	22.8071	1.83191
$156$	1.43051	0.114532
$157$	−7.78325	−0.621171	−0.310585	−	0.950546i	$-0.600525\pi$
$157$	−7.78325	−0.621171	−0.310585	+	0.950546i	$0.600525\pi$
$158$	−16.5741	−1.31856
$159$	−1.37649	−0.109163
$160$	2.45255	0.193891
$161$	−9.65420	−0.760858
$162$	8.33773	0.655074
$163$	9.60428	0.752265	0.376133	−	0.926566i	$-0.377254\pi$
$163$	9.60428	0.752265	0.376133	+	0.926566i	$0.377254\pi$
$164$	−1.66271	−0.129836
$165$	−0.668056	−0.0520081
$166$	−10.3820	−0.805798
$167$	7.34624	0.568469	0.284235	−	0.958755i	$-0.408261\pi$
$167$	7.34624	0.568469	0.284235	+	0.958755i	$0.408261\pi$
$168$	0.684022	0.0527735
$169$	14.5797	1.12151
$170$	−2.12229	−0.162772
$171$	4.58523	0.350641
$172$	10.8842	0.829916
$173$	−0.248277	−0.0188762	−0.00943809	−	0.999955i	$-0.503004\pi$
$173$	−0.248277	−0.0188762	−0.00943809	+	0.999955i	$0.503004\pi$
$174$	0.236313	0.0179148
$175$	2.54883	0.192673
$176$	−1.00000	−0.0753778
$177$	−2.14065	−0.160901
$178$	1.26760	0.0950106
$179$	−5.47580	−0.409280	−0.204640	−	0.978837i	$-0.565602\pi$
$179$	−5.47580	−0.409280	−0.204640	+	0.978837i	$0.565602\pi$
$180$	−7.17567	−0.534843
$181$	−15.9455	−1.18522	−0.592609	−	0.805490i	$-0.701902\pi$
$181$	−15.9455	−1.18522	−0.592609	+	0.805490i	$0.701902\pi$
$182$	13.1877	0.977539
$183$	3.69347	0.273029
$184$	−3.84451	−0.283421
$185$	15.0521	1.10665
$186$	2.53307	0.185734
$187$	0.865339	0.0632798
$188$	6.71600	0.489815
$189$	−4.05338	−0.294840
$190$	−3.84356	−0.278841
$191$	15.4978	1.12138	0.560692	−	0.828024i	$-0.310535\pi$
$191$	15.4978	1.12138	0.560692	+	0.828024i	$0.310535\pi$
$192$	0.272392	0.0196582
$193$	−0.187563	−0.0135011	−0.00675055	−	0.999977i	$-0.502149\pi$
$193$	−0.187563	−0.0135011	−0.00675055	+	0.999977i	$0.502149\pi$
$194$	−2.08036	−0.149361
$195$	3.50839	0.251241
$196$	−0.694050	−0.0495750
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	2.92580	0.207928
$199$	−2.02172	−0.143316	−0.0716578	−	0.997429i	$-0.522829\pi$
$199$	−2.02172	−0.143316	−0.0716578	+	0.997429i	$0.522829\pi$
$200$	1.01500	0.0717712
$201$	4.11156	0.290007
$202$	14.5365	1.02279
$203$	2.17855	0.152904
$204$	−0.235712	−0.0165031
$205$	−4.07788	−0.284811
$206$	13.9101	0.969163
$207$	11.2483	0.781810
$208$	5.25164	0.364135
$209$	1.56717	0.108403
$210$	1.67760	0.115765
$211$	−18.2204	−1.25434	−0.627171	−	0.778881i	$-0.715787\pi$
$211$	−18.2204	−1.25434	−0.627171	+	0.778881i	$0.715787\pi$
$212$	−5.05335	−0.347066
$213$	−0.0175530	−0.00120271
$214$	−18.7508	−1.28178
$215$	26.6941	1.82053
$216$	−1.61414	−0.109829
$217$	23.3522	1.58525
$218$	−8.62352	−0.584059
$219$	−1.76869	−0.119517
$220$	−2.45255	−0.165351
$221$	−4.54444	−0.305692
$222$	1.67176	0.112201
$223$	15.1496	1.01449	0.507246	−	0.861801i	$-0.330664\pi$
$223$	15.1496	1.01449	0.507246	+	0.861801i	$0.330664\pi$
$224$	2.51117	0.167784
$225$	−2.96968	−0.197979
$226$	1.74098	0.115808
$227$	8.65275	0.574303	0.287152	−	0.957885i	$-0.407292\pi$
$227$	8.65275	0.574303	0.287152	+	0.957885i	$0.407292\pi$
$228$	−0.426885	−0.0282711
$229$	−7.59307	−0.501764	−0.250882	−	0.968018i	$-0.580721\pi$
$229$	−7.59307	−0.501764	−0.250882	+	0.968018i	$0.580721\pi$
$230$	−9.42885	−0.621720
$231$	−0.684022	−0.0450054
$232$	0.867546	0.0569572
$233$	0.428353	0.0280624	0.0140312	−	0.999902i	$-0.495534\pi$
$233$	0.428353	0.0280624	0.0140312	+	0.999902i	$0.495534\pi$
$234$	−15.3653	−1.00446
$235$	16.4713	1.07447
$236$	−7.85868	−0.511557
$237$	−4.51466	−0.293259
$238$	−2.17301	−0.140855
$239$	8.09173	0.523411	0.261705	−	0.965148i	$-0.415715\pi$
$239$	8.09173	0.523411	0.261705	+	0.965148i	$0.415715\pi$
$240$	0.668056	0.0431228
$241$	−9.79772	−0.631127	−0.315563	−	0.948905i	$-0.602193\pi$
$241$	−9.79772	−0.631127	−0.315563	+	0.948905i	$0.602193\pi$
$242$	1.00000	0.0642824
$243$	7.11357	0.456335
$244$	13.5594	0.868049
$245$	−1.70219	−0.108749
$246$	−0.452909	−0.0288765
$247$	−8.23020	−0.523675
$248$	9.29935	0.590509
$249$	−2.82797	−0.179216
$250$	−9.77341	−0.618125
$251$	−20.7019	−1.30669	−0.653347	−	0.757058i	$-0.726636\pi$
$251$	−20.7019	−1.30669	−0.653347	+	0.757058i	$0.726636\pi$
$252$	−7.34717	−0.462828
$253$	3.84451	0.241702
$254$	6.97345	0.437553
$255$	−0.578095	−0.0362017
$256$	1.00000	0.0625000
$257$	−16.4364	−1.02527	−0.512636	−	0.858606i	$-0.671331\pi$
$257$	−16.4364	−1.02527	−0.512636	+	0.858606i	$0.671331\pi$
$258$	2.96479	0.184579
$259$	15.4118	0.957644
$260$	12.8799	0.798777
$261$	−2.53827	−0.157115
$262$	−5.97223	−0.368965
$263$	−20.0238	−1.23472	−0.617360	−	0.786681i	$-0.711798\pi$
$263$	−20.0238	−1.23472	−0.617360	+	0.786681i	$0.711798\pi$
$264$	−0.272392	−0.0167646
$265$	−12.3936	−0.761332
$266$	−3.93542	−0.241296
$267$	0.345284	0.0211311
$268$	15.0942	0.922027
$269$	−17.8555	−1.08867	−0.544335	−	0.838868i	$-0.683218\pi$
$269$	−17.8555	−1.08867	−0.544335	+	0.838868i	$0.683218\pi$
$270$	−3.95877	−0.240923
$271$	−13.3366	−0.810138	−0.405069	−	0.914286i	$-0.632752\pi$
$271$	−13.3366	−0.810138	−0.405069	+	0.914286i	$0.632752\pi$
$272$	−0.865339	−0.0524689
$273$	3.59224	0.217412
$274$	−7.06934	−0.427074
$275$	−1.01500	−0.0612067
$276$	−1.04722	−0.0630350
$277$	−13.9281	−0.836859	−0.418429	−	0.908249i	$-0.637419\pi$
$277$	−13.9281	−0.836859	−0.418429	+	0.908249i	$0.637419\pi$
$278$	−4.87943	−0.292649
$279$	−27.2080	−1.62890
$280$	6.15876	0.368056
$281$	5.14228	0.306763	0.153381	−	0.988167i	$-0.450984\pi$
$281$	5.14228	0.306763	0.153381	+	0.988167i	$0.450984\pi$
$282$	1.82939	0.108938
$283$	10.8197	0.643163	0.321581	−	0.946882i	$-0.395786\pi$
$283$	10.8197	0.643163	0.321581	+	0.946882i	$0.395786\pi$
$284$	−0.0644401	−0.00382381
$285$	−1.04696	−0.0620163
$286$	−5.25164	−0.310536
$287$	−4.17534	−0.246462
$288$	−2.92580	−0.172405
$289$	−16.2512	−0.955952
$290$	2.12770	0.124943
$291$	−0.566673	−0.0332190
$292$	−6.49316	−0.379984
$293$	−2.54664	−0.148777	−0.0743883	−	0.997229i	$-0.523700\pi$
$293$	−2.54664	−0.148777	−0.0743883	+	0.997229i	$0.523700\pi$
$294$	−0.189054	−0.0110259
$295$	−19.2738	−1.12216
$296$	6.13732	0.356724
$297$	1.61414	0.0936621
$298$	−15.7845	−0.914370
$299$	−20.1900	−1.16762
$300$	0.276478	0.0159624
$301$	27.3321	1.57540
$302$	10.1254	0.582653
$303$	3.95964	0.227476
$304$	−1.56717	−0.0898833
$305$	33.2550	1.90417
$306$	2.53181	0.144734
$307$	25.2850	1.44309	0.721545	−	0.692368i	$-0.243432\pi$
$307$	25.2850	1.44309	0.721545	+	0.692368i	$0.243432\pi$
$308$	−2.51117	−0.143087
$309$	3.78901	0.215549
$310$	22.8071	1.29536
$311$	−17.6125	−0.998714	−0.499357	−	0.866396i	$-0.666430\pi$
$311$	−17.6125	−0.998714	−0.499357	+	0.866396i	$0.666430\pi$
$312$	1.43051	0.0809865
$313$	8.33046	0.470866	0.235433	−	0.971891i	$-0.424349\pi$
$313$	8.33046	0.470866	0.235433	+	0.971891i	$0.424349\pi$
$314$	−7.78325	−0.439234
$315$	−18.0193	−1.01527
$316$	−16.5741	−0.932366
$317$	−3.84931	−0.216199	−0.108099	−	0.994140i	$-0.534476\pi$
$317$	−3.84931	−0.216199	−0.108099	+	0.994140i	$0.534476\pi$
$318$	−1.37649	−0.0771900
$319$	−0.867546	−0.0485732
$320$	2.45255	0.137102
$321$	−5.10758	−0.285077
$322$	−9.65420	−0.538008
$323$	1.35613	0.0754572
$324$	8.33773	0.463207
$325$	5.33040	0.295677
$326$	9.60428	0.531932
$327$	−2.34898	−0.129899
$328$	−1.66271	−0.0918078
$329$	16.8650	0.929797
$330$	−0.668056	−0.0367753
$331$	12.0256	0.660984	0.330492	−	0.943809i	$-0.392785\pi$
$331$	12.0256	0.660984	0.330492	+	0.943809i	$0.392785\pi$
$332$	−10.3820	−0.569785
$333$	−17.9566	−0.984014
$334$	7.34624	0.401968
$335$	37.0194	2.02258
$336$	0.684022	0.0373165
$337$	−0.156299	−0.00851413	−0.00425706	−	0.999991i	$-0.501355\pi$
$337$	−0.156299	−0.00851413	−0.00425706	+	0.999991i	$0.501355\pi$
$338$	14.5797	0.793030
$339$	0.474230	0.0257567
$340$	−2.12229	−0.115097
$341$	−9.29935	−0.503588
$342$	4.58523	0.247941
$343$	−19.3210	−1.04324
$344$	10.8842	0.586839
$345$	−2.56835	−0.138275
$346$	−0.248277	−0.0133475
$347$	30.0107	1.61106	0.805530	−	0.592555i	$-0.201881\pi$
$347$	30.0107	1.61106	0.805530	+	0.592555i	$0.201881\pi$
$348$	0.236313	0.0126677
$349$	−9.11012	−0.487653	−0.243827	−	0.969819i	$-0.578403\pi$
$349$	−9.11012	−0.487653	−0.243827	+	0.969819i	$0.578403\pi$
$350$	2.54883	0.136241
$351$	−8.47690	−0.452463
$352$	−1.00000	−0.0533002
$353$	27.4504	1.46104	0.730520	−	0.682891i	$-0.239278\pi$
$353$	27.4504	1.46104	0.730520	+	0.682891i	$0.239278\pi$
$354$	−2.14065	−0.113774
$355$	−0.158042	−0.00838802
$356$	1.26760	0.0671826
$357$	−0.591911	−0.0313273
$358$	−5.47580	−0.289405
$359$	23.8301	1.25771	0.628853	−	0.777525i	$-0.283525\pi$
$359$	23.8301	1.25771	0.628853	+	0.777525i	$0.283525\pi$
$360$	−7.17567	−0.378191
$361$	−16.5440	−0.870736
$362$	−15.9455	−0.838076
$363$	0.272392	0.0142969
$364$	13.1877	0.691225
$365$	−15.9248	−0.833542
$366$	3.69347	0.193061
$367$	−7.22449	−0.377115	−0.188558	−	0.982062i	$-0.560381\pi$
$367$	−7.22449	−0.377115	−0.188558	+	0.982062i	$0.560381\pi$
$368$	−3.84451	−0.200409
$369$	4.86476	0.253249
$370$	15.0521	0.782520
$371$	−12.6898	−0.658821
$372$	2.53307	0.131334
$373$	15.1724	0.785597	0.392798	−	0.919625i	$-0.371507\pi$
$373$	15.1724	0.785597	0.392798	+	0.919625i	$0.371507\pi$
$374$	0.865339	0.0447456
$375$	−2.66220	−0.137476
$376$	6.71600	0.346351
$377$	4.55603	0.234648
$378$	−4.05338	−0.208483
$379$	6.70778	0.344555	0.172278	−	0.985048i	$-0.444887\pi$
$379$	6.70778	0.344555	0.172278	+	0.985048i	$0.444887\pi$
$380$	−3.84356	−0.197170
$381$	1.89952	0.0973152
$382$	15.4978	0.792938
$383$	−29.3371	−1.49906	−0.749529	−	0.661972i	$-0.769720\pi$
$383$	−29.3371	−1.49906	−0.749529	+	0.661972i	$0.769720\pi$
$384$	0.272392	0.0139005
$385$	−6.15876	−0.313879
$386$	−0.187563	−0.00954672
$387$	−31.8451	−1.61878
$388$	−2.08036	−0.105614
$389$	26.6454	1.35097	0.675487	−	0.737372i	$-0.263934\pi$
$389$	26.6454	1.35097	0.675487	+	0.737372i	$0.263934\pi$
$390$	3.50839	0.177654
$391$	3.32681	0.168244
$392$	−0.694050	−0.0350548
$393$	−1.62679	−0.0820607
$394$	−1.00000	−0.0503793
$395$	−40.6488	−2.04526
$396$	2.92580	0.147027
$397$	−26.1893	−1.31440	−0.657202	−	0.753714i	$-0.728260\pi$
$397$	−26.1893	−1.31440	−0.657202	+	0.753714i	$0.728260\pi$
$398$	−2.02172	−0.101339
$399$	−1.07198	−0.0536661
$400$	1.01500	0.0507499
$401$	−22.4997	−1.12358	−0.561790	−	0.827280i	$-0.689887\pi$
$401$	−22.4997	−1.12358	−0.561790	+	0.827280i	$0.689887\pi$
$402$	4.11156	0.205066
$403$	48.8368	2.43273
$404$	14.5365	0.723220
$405$	20.4487	1.01610
$406$	2.17855	0.108120
$407$	−6.13732	−0.304216
$408$	−0.235712	−0.0116695
$409$	0.432831	0.0214021	0.0107011	−	0.999943i	$-0.496594\pi$
$409$	0.432831	0.0214021	0.0107011	+	0.999943i	$0.496594\pi$
$410$	−4.07788	−0.201392
$411$	−1.92563	−0.0949845
$412$	13.9101	0.685302
$413$	−19.7344	−0.971069
$414$	11.2483	0.552823
$415$	−25.4623	−1.24990
$416$	5.25164	0.257483
$417$	−1.32912	−0.0650873
$418$	1.56717	0.0766527
$419$	−21.1346	−1.03249	−0.516246	−	0.856440i	$-0.672671\pi$
$419$	−21.1346	−1.03249	−0.516246	+	0.856440i	$0.672671\pi$
$420$	1.67760	0.0818584
$421$	5.80578	0.282956	0.141478	−	0.989941i	$-0.454815\pi$
$421$	5.80578	0.282956	0.141478	+	0.989941i	$0.454815\pi$
$422$	−18.2204	−0.886954
$423$	−19.6497	−0.955400
$424$	−5.05335	−0.245412
$425$	−0.878317	−0.0426046
$426$	−0.0175530	−0.000850445 0
$427$	34.0498	1.64778
$428$	−18.7508	−0.906355
$429$	−1.43051	−0.0690655
$430$	26.6941	1.28731
$431$	−26.9842	−1.29979	−0.649893	−	0.760026i	$-0.725186\pi$
$431$	−26.9842	−1.29979	−0.649893	+	0.760026i	$0.725186\pi$
$432$	−1.61414	−0.0776605
$433$	16.3315	0.784844	0.392422	−	0.919785i	$-0.371637\pi$
$433$	16.3315	0.784844	0.392422	+	0.919785i	$0.371637\pi$
$434$	23.3522	1.12094
$435$	0.579569	0.0277882
$436$	−8.62352	−0.412992
$437$	6.02500	0.288215
$438$	−1.76869	−0.0845112
$439$	−19.9968	−0.954394	−0.477197	−	0.878796i	$-0.658347\pi$
$439$	−19.9968	−0.954394	−0.477197	+	0.878796i	$0.658347\pi$
$440$	−2.45255	−0.116921
$441$	2.03065	0.0966978
$442$	−4.54444	−0.216157
$443$	20.2357	0.961425	0.480713	−	0.876878i	$-0.340378\pi$
$443$	20.2357	0.961425	0.480713	+	0.876878i	$0.340378\pi$
$444$	1.67176	0.0793382
$445$	3.10885	0.147374
$446$	15.1496	0.717354
$447$	−4.29957	−0.203363
$448$	2.51117	0.118641
$449$	30.6550	1.44670	0.723350	−	0.690481i	$-0.242601\pi$
$449$	30.6550	1.44670	0.723350	+	0.690481i	$0.242601\pi$
$450$	−2.96968	−0.139992
$451$	1.66271	0.0782939
$452$	1.74098	0.0818889
$453$	2.75809	0.129586
$454$	8.65275	0.406094
$455$	32.3435	1.51629
$456$	−0.426885	−0.0199907
$457$	19.6701	0.920128	0.460064	−	0.887886i	$-0.347826\pi$
$457$	19.6701	0.920128	0.460064	+	0.887886i	$0.347826\pi$
$458$	−7.59307	−0.354801
$459$	1.39678	0.0651962
$460$	−9.42885	−0.439623
$461$	−4.43175	−0.206407	−0.103204	−	0.994660i	$-0.532909\pi$
$461$	−4.43175	−0.206407	−0.103204	+	0.994660i	$0.532909\pi$
$462$	−0.684022	−0.0318236
$463$	40.4012	1.87760	0.938801	−	0.344461i	$-0.111938\pi$
$463$	40.4012	1.87760	0.938801	+	0.344461i	$0.111938\pi$
$464$	0.867546	0.0402748
$465$	6.21248	0.288097
$466$	0.428353	0.0198431
$467$	2.80076	0.129604	0.0648018	−	0.997898i	$-0.479358\pi$
$467$	2.80076	0.129604	0.0648018	+	0.997898i	$0.479358\pi$
$468$	−15.3653	−0.710259
$469$	37.9041	1.75025
$470$	16.4713	0.759765
$471$	−2.12010	−0.0976889
$472$	−7.85868	−0.361725
$473$	−10.8842	−0.500458
$474$	−4.51466	−0.207365
$475$	−1.59067	−0.0729851
$476$	−2.17301	−0.0995997
$477$	14.7851	0.676963
$478$	8.09173	0.370107
$479$	18.5177	0.846093	0.423047	−	0.906108i	$-0.360961\pi$
$479$	18.5177	0.846093	0.423047	+	0.906108i	$0.360961\pi$
$480$	0.668056	0.0304924
$481$	32.2310	1.46961
$482$	−9.79772	−0.446274
$483$	−2.62973	−0.119657
$484$	1.00000	0.0454545
$485$	−5.10218	−0.231678
$486$	7.11357	0.322678
$487$	−23.9564	−1.08557	−0.542783	−	0.839873i	$-0.682630\pi$
$487$	−23.9564	−1.08557	−0.542783	+	0.839873i	$0.682630\pi$
$488$	13.5594	0.613803
$489$	2.61613	0.118306
$490$	−1.70219	−0.0768972
$491$	7.71305	0.348085	0.174043	−	0.984738i	$-0.444317\pi$
$491$	7.71305	0.348085	0.174043	+	0.984738i	$0.444317\pi$
$492$	−0.452909	−0.0204187
$493$	−0.750721	−0.0338108
$494$	−8.23020	−0.370294
$495$	7.17567	0.322523
$496$	9.29935	0.417553
$497$	−0.161820	−0.00725860
$498$	−2.82797	−0.126725
$499$	1.79339	0.0802830	0.0401415	−	0.999194i	$-0.487219\pi$
$499$	1.79339	0.0802830	0.0401415	+	0.999194i	$0.487219\pi$
$500$	−9.77341	−0.437080
$501$	2.00106	0.0894008
$502$	−20.7019	−0.923973
$503$	−19.1536	−0.854019	−0.427009	−	0.904247i	$-0.640433\pi$
$503$	−19.1536	−0.854019	−0.427009	+	0.904247i	$0.640433\pi$
$504$	−7.34717	−0.327269
$505$	35.6516	1.58647
$506$	3.84451	0.170909
$507$	3.97140	0.176376
$508$	6.97345	0.309397
$509$	9.46509	0.419533	0.209766	−	0.977752i	$-0.432730\pi$
$509$	9.46509	0.419533	0.209766	+	0.977752i	$0.432730\pi$
$510$	−0.578095	−0.0255985
$511$	−16.3054	−0.721308
$512$	1.00000	0.0441942
$513$	2.52964	0.111686
$514$	−16.4364	−0.724977
$515$	34.1152	1.50330
$516$	2.96479	0.130517
$517$	−6.71600	−0.295369
$518$	15.4118	0.677156
$519$	−0.0676289	−0.00296858
$520$	12.8799	0.564821
$521$	−0.423009	−0.0185323	−0.00926617	−	0.999957i	$-0.502950\pi$
$521$	−0.423009	−0.0185323	−0.00926617	+	0.999957i	$0.502950\pi$
$522$	−2.53827	−0.111097
$523$	−26.2850	−1.14936	−0.574681	−	0.818378i	$-0.694874\pi$
$523$	−26.2850	−1.14936	−0.574681	+	0.818378i	$0.694874\pi$
$524$	−5.97223	−0.260898
$525$	0.694281	0.0303009
$526$	−20.0238	−0.873079
$527$	−8.04708	−0.350536
$528$	−0.272392	−0.0118544
$529$	−8.21973	−0.357379
$530$	−12.3936	−0.538343
$531$	22.9929	0.997809
$532$	−3.93542	−0.170622
$533$	−8.73194	−0.378222
$534$	0.345284	0.0149419
$535$	−45.9873	−1.98820
$536$	15.0942	0.651972
$537$	−1.49157	−0.0643658
$538$	−17.8555	−0.769806
$539$	0.694050	0.0298949
$540$	−3.95877	−0.170358
$541$	3.00246	0.129086	0.0645429	−	0.997915i	$-0.479441\pi$
$541$	3.00246	0.129086	0.0645429	+	0.997915i	$0.479441\pi$
$542$	−13.3366	−0.572854
$543$	−4.34343	−0.186394
$544$	−0.865339	−0.0371011
$545$	−21.1496	−0.905950
$546$	3.59224	0.153734
$547$	10.3324	0.441781	0.220890	−	0.975299i	$-0.429104\pi$
$547$	10.3324	0.441781	0.220890	+	0.975299i	$0.429104\pi$
$548$	−7.06934	−0.301987
$549$	−39.6720	−1.69316
$550$	−1.01500	−0.0432796
$551$	−1.35959	−0.0579205
$552$	−1.04722	−0.0445725
$553$	−41.6203	−1.76987
$554$	−13.9281	−0.591749
$555$	4.10007	0.174038
$556$	−4.87943	−0.206934
$557$	0.851220	0.0360673	0.0180337	−	0.999837i	$-0.494259\pi$
$557$	0.851220	0.0360673	0.0180337	+	0.999837i	$0.494259\pi$
$558$	−27.2080	−1.15181
$559$	57.1601	2.41761
$560$	6.15876	0.260255
$561$	0.235712	0.00995176
$562$	5.14228	0.216914
$563$	32.7169	1.37885	0.689426	−	0.724356i	$-0.257863\pi$
$563$	32.7169	1.37885	0.689426	+	0.724356i	$0.257863\pi$
$564$	1.82939	0.0770311
$565$	4.26984	0.179634
$566$	10.8197	0.454785
$567$	20.9374	0.879288
$568$	−0.0644401	−0.00270384
$569$	21.3286	0.894141	0.447071	−	0.894499i	$-0.352467\pi$
$569$	21.3286	0.894141	0.447071	+	0.894499i	$0.352467\pi$
$570$	−1.04696	−0.0438522
$571$	4.32859	0.181146	0.0905729	−	0.995890i	$-0.471130\pi$
$571$	4.32859	0.181146	0.0905729	+	0.995890i	$0.471130\pi$
$572$	−5.25164	−0.219582
$573$	4.22149	0.176355
$574$	−4.17534	−0.174275
$575$	−3.90217	−0.162732
$576$	−2.92580	−0.121908
$577$	8.05532	0.335348	0.167674	−	0.985843i	$-0.446374\pi$
$577$	8.05532	0.335348	0.167674	+	0.985843i	$0.446374\pi$
$578$	−16.2512	−0.675960
$579$	−0.0510908	−0.00212326
$580$	2.12770	0.0883479
$581$	−26.0709	−1.08160
$582$	−0.566673	−0.0234894
$583$	5.05335	0.209288
$584$	−6.49316	−0.268689
$585$	−37.6840	−1.55804
$586$	−2.54664	−0.105201
$587$	−0.773591	−0.0319295	−0.0159648	−	0.999873i	$-0.505082\pi$
$587$	−0.773591	−0.0319295	−0.0159648	+	0.999873i	$0.505082\pi$
$588$	−0.189054	−0.00779646
$589$	−14.5736	−0.600496
$590$	−19.2738	−0.793490
$591$	−0.272392	−0.0112047
$592$	6.13732	0.252242
$593$	11.9916	0.492435	0.246218	−	0.969215i	$-0.420812\pi$
$593$	11.9916	0.492435	0.246218	+	0.969215i	$0.420812\pi$
$594$	1.61414	0.0662291
$595$	−5.32941	−0.218485
$596$	−15.7845	−0.646557
$597$	−0.550700	−0.0225386
$598$	−20.1900	−0.825630
$599$	−33.7873	−1.38051	−0.690255	−	0.723566i	$-0.742502\pi$
$599$	−33.7873	−1.38051	−0.690255	+	0.723566i	$0.742502\pi$
$600$	0.276478	0.0112872
$601$	−41.7735	−1.70398	−0.851989	−	0.523560i	$-0.824604\pi$
$601$	−41.7735	−1.70398	−0.851989	+	0.523560i	$0.824604\pi$
$602$	27.3321	1.11397
$603$	−44.1628	−1.79845
$604$	10.1254	0.411998
$605$	2.45255	0.0997103
$606$	3.95964	0.160850
$607$	11.8745	0.481973	0.240986	−	0.970528i	$-0.422529\pi$
$607$	11.8745	0.481973	0.240986	+	0.970528i	$0.422529\pi$
$608$	−1.56717	−0.0635571
$609$	0.593421	0.0240466
$610$	33.2550	1.34645
$611$	35.2700	1.42687
$612$	2.53181	0.102342
$613$	−40.5505	−1.63782	−0.818910	−	0.573922i	$-0.805421\pi$
$613$	−40.5505	−1.63782	−0.818910	+	0.573922i	$0.805421\pi$
$614$	25.2850	1.02042
$615$	−1.11078	−0.0447911
$616$	−2.51117	−0.101178
$617$	28.9255	1.16450	0.582248	−	0.813011i	$-0.302173\pi$
$617$	28.9255	1.16450	0.582248	+	0.813011i	$0.302173\pi$
$618$	3.78901	0.152416
$619$	−43.1648	−1.73494	−0.867470	−	0.497489i	$-0.834256\pi$
$619$	−43.1648	−1.73494	−0.867470	+	0.497489i	$0.834256\pi$
$620$	22.8071	0.915955
$621$	6.20560	0.249022
$622$	−17.6125	−0.706197
$623$	3.18315	0.127530
$624$	1.43051	0.0572661
$625$	−29.0448	−1.16179
$626$	8.33046	0.332952
$627$	0.426885	0.0170481
$628$	−7.78325	−0.310585
$629$	−5.31086	−0.211758
$630$	−18.0193	−0.717906
$631$	−1.91961	−0.0764183	−0.0382092	−	0.999270i	$-0.512165\pi$
$631$	−1.91961	−0.0764183	−0.0382092	+	0.999270i	$0.512165\pi$
$632$	−16.5741	−0.659282
$633$	−4.96309	−0.197265
$634$	−3.84931	−0.152876
$635$	17.1027	0.678701
$636$	−1.37649	−0.0545816
$637$	−3.64490	−0.144416
$638$	−0.867546	−0.0343465
$639$	0.188539	0.00745848
$640$	2.45255	0.0969455
$641$	12.4024	0.489864	0.244932	−	0.969540i	$-0.421234\pi$
$641$	12.4024	0.489864	0.244932	+	0.969540i	$0.421234\pi$
$642$	−5.10758	−0.201580
$643$	−27.7181	−1.09309	−0.546547	−	0.837428i	$-0.684058\pi$
$643$	−27.7181	−1.09309	−0.546547	+	0.837428i	$0.684058\pi$
$644$	−9.65420	−0.380429
$645$	7.27128	0.286306
$646$	1.35613	0.0533563
$647$	−28.1541	−1.10685	−0.553427	−	0.832898i	$-0.686680\pi$
$647$	−28.1541	−1.10685	−0.553427	+	0.832898i	$0.686680\pi$
$648$	8.33773	0.327537
$649$	7.85868	0.308480
$650$	5.33040	0.209075
$651$	6.36096	0.249306
$652$	9.60428	0.376133
$653$	17.9380	0.701968	0.350984	−	0.936381i	$-0.385847\pi$
$653$	17.9380	0.701968	0.350984	+	0.936381i	$0.385847\pi$
$654$	−2.34898	−0.0918525
$655$	−14.6472	−0.572313
$656$	−1.66271	−0.0649179
$657$	18.9977	0.741171
$658$	16.8650	0.657466
$659$	−0.610935	−0.0237986	−0.0118993	−	0.999929i	$-0.503788\pi$
$659$	−0.610935	−0.0237986	−0.0118993	+	0.999929i	$0.503788\pi$
$660$	−0.668056	−0.0260040
$661$	−33.9016	−1.31862	−0.659310	−	0.751871i	$-0.729152\pi$
$661$	−33.9016	−1.31862	−0.659310	+	0.751871i	$0.729152\pi$
$662$	12.0256	0.467386
$663$	−1.23787	−0.0480750
$664$	−10.3820	−0.402899
$665$	−9.65181	−0.374281
$666$	−17.9566	−0.695803
$667$	−3.33529	−0.129143
$668$	7.34624	0.284235
$669$	4.12664	0.159545
$670$	37.0194	1.43018
$671$	−13.5594	−0.523453
$672$	0.684022	0.0263867
$673$	6.69572	0.258101	0.129051	−	0.991638i	$-0.458807\pi$
$673$	6.69572	0.258101	0.129051	+	0.991638i	$0.458807\pi$
$674$	−0.156299	−0.00602040
$675$	−1.63835	−0.0630602
$676$	14.5797	0.560757
$677$	−39.7393	−1.52731	−0.763653	−	0.645627i	$-0.776596\pi$
$677$	−39.7393	−1.52731	−0.763653	+	0.645627i	$0.776596\pi$
$678$	0.474230	0.0182127
$679$	−5.22412	−0.200483
$680$	−2.12229	−0.0813859
$681$	2.35694	0.0903183
$682$	−9.29935	−0.356090
$683$	−37.6729	−1.44151	−0.720757	−	0.693188i	$-0.756206\pi$
$683$	−37.6729	−1.44151	−0.720757	+	0.693188i	$0.756206\pi$
$684$	4.58523	0.175320
$685$	−17.3379	−0.662447
$686$	−19.3210	−0.737680
$687$	−2.06830	−0.0789104
$688$	10.8842	0.414958
$689$	−26.5384	−1.01103
$690$	−2.56835	−0.0977754
$691$	−31.0055	−1.17950	−0.589752	−	0.807584i	$-0.700775\pi$
$691$	−31.0055	−1.17950	−0.589752	+	0.807584i	$0.700775\pi$
$692$	−0.248277	−0.00943809
$693$	7.34717	0.279096
$694$	30.0107	1.13919
$695$	−11.9670	−0.453936
$696$	0.236313	0.00895742
$697$	1.43881	0.0544987
$698$	−9.11012	−0.344823
$699$	0.116680	0.00441325
$700$	2.54883	0.0963366
$701$	−42.5039	−1.60535	−0.802674	−	0.596418i	$-0.796590\pi$
$701$	−42.5039	−1.60535	−0.802674	+	0.596418i	$0.796590\pi$
$702$	−8.47690	−0.319940
$703$	−9.61821	−0.362758
$704$	−1.00000	−0.0376889
$705$	4.48666	0.168978
$706$	27.4504	1.03311
$707$	36.5036	1.37286
$708$	−2.14065	−0.0804504
$709$	−44.8926	−1.68598	−0.842989	−	0.537931i	$-0.819206\pi$
$709$	−44.8926	−1.68598	−0.842989	+	0.537931i	$0.819206\pi$
$710$	−0.158042	−0.00593123
$711$	48.4925	1.81861
$712$	1.26760	0.0475053
$713$	−35.7514	−1.33890
$714$	−0.591911	−0.0221517
$715$	−12.8799	−0.481681
$716$	−5.47580	−0.204640
$717$	2.20413	0.0823146
$718$	23.8301	0.889332
$719$	32.3744	1.20736	0.603680	−	0.797227i	$-0.293701\pi$
$719$	32.3744	1.20736	0.603680	+	0.797227i	$0.293701\pi$
$720$	−7.17567	−0.267422
$721$	34.9306	1.30088
$722$	−16.5440	−0.615703
$723$	−2.66883	−0.0992547
$724$	−15.9455	−0.592609
$725$	0.880557	0.0327031
$726$	0.272392	0.0101094
$727$	6.35391	0.235653	0.117827	−	0.993034i	$-0.462407\pi$
$727$	6.35391	0.235653	0.117827	+	0.993034i	$0.462407\pi$
$728$	13.1877	0.488770
$729$	−23.0755	−0.854648
$730$	−15.9248	−0.589403
$731$	−9.41856	−0.348358
$732$	3.69347	0.136514
$733$	23.3345	0.861881	0.430940	−	0.902380i	$-0.358182\pi$
$733$	23.3345	0.861881	0.430940	+	0.902380i	$0.358182\pi$
$734$	−7.22449	−0.266661
$735$	−0.463664	−0.0171025
$736$	−3.84451	−0.141711
$737$	−15.0942	−0.556003
$738$	4.86476	0.179074
$739$	37.0860	1.36423	0.682116	−	0.731244i	$-0.261060\pi$
$739$	37.0860	1.36423	0.682116	+	0.731244i	$0.261060\pi$
$740$	15.0521	0.553325
$741$	−2.24184	−0.0823562
$742$	−12.6898	−0.465857
$743$	5.77103	0.211719	0.105859	−	0.994381i	$-0.466241\pi$
$743$	5.77103	0.211719	0.105859	+	0.994381i	$0.466241\pi$
$744$	2.53307	0.0928669
$745$	−38.7122	−1.41831
$746$	15.1724	0.555501
$747$	30.3756	1.11139
$748$	0.865339	0.0316399
$749$	−47.0864	−1.72050
$750$	−2.66220	−0.0972100
$751$	−27.5635	−1.00581	−0.502904	−	0.864342i	$-0.667735\pi$
$751$	−27.5635	−1.00581	−0.502904	+	0.864342i	$0.667735\pi$
$752$	6.71600	0.244907
$753$	−5.63905	−0.205498
$754$	4.55603	0.165921
$755$	24.8331	0.903770
$756$	−4.05338	−0.147420
$757$	26.8506	0.975903	0.487951	−	0.872871i	$-0.337744\pi$
$757$	26.8506	0.975903	0.487951	+	0.872871i	$0.337744\pi$
$758$	6.70778	0.243637
$759$	1.04722	0.0380115
$760$	−3.84356	−0.139421
$761$	−1.56404	−0.0566964	−0.0283482	−	0.999598i	$-0.509025\pi$
$761$	−1.56404	−0.0566964	−0.0283482	+	0.999598i	$0.509025\pi$
$762$	1.89952	0.0688122
$763$	−21.6551	−0.783967
$764$	15.4978	0.560692
$765$	6.20939	0.224501
$766$	−29.3371	−1.05999
$767$	−41.2709	−1.49021
$768$	0.272392	0.00982912
$769$	−0.834878	−0.0301065	−0.0150532	−	0.999887i	$-0.504792\pi$
$769$	−0.834878	−0.0301065	−0.0150532	+	0.999887i	$0.504792\pi$
$770$	−6.15876	−0.221946
$771$	−4.47714	−0.161240
$772$	−0.187563	−0.00675055
$773$	−34.3663	−1.23607	−0.618034	−	0.786151i	$-0.712071\pi$
$773$	−34.3663	−1.23607	−0.618034	+	0.786151i	$0.712071\pi$
$774$	−31.8451	−1.14465
$775$	9.43881	0.339052
$776$	−2.08036	−0.0746804
$777$	4.19806	0.150605
$778$	26.6454	0.955283
$779$	2.60575	0.0933605
$780$	3.50839	0.125620
$781$	0.0644401	0.00230585
$782$	3.32681	0.118966
$783$	−1.40034	−0.0500442
$784$	−0.694050	−0.0247875
$785$	−19.0888	−0.681308
$786$	−1.62679	−0.0580257
$787$	12.2767	0.437617	0.218808	−	0.975768i	$-0.429783\pi$
$787$	12.2767	0.437617	0.218808	+	0.975768i	$0.429783\pi$
$788$	−1.00000	−0.0356235
$789$	−5.45433	−0.194179
$790$	−40.6488	−1.44622
$791$	4.37189	0.155447
$792$	2.92580	0.103964
$793$	71.2088	2.52870
$794$	−26.1893	−0.929424
$795$	−3.37592	−0.119732
$796$	−2.02172	−0.0716578
$797$	−20.2051	−0.715702	−0.357851	−	0.933779i	$-0.616490\pi$
$797$	−20.2051	−0.715702	−0.357851	+	0.933779i	$0.616490\pi$
$798$	−1.07198	−0.0379476
$799$	−5.81161	−0.205600
$800$	1.01500	0.0358856
$801$	−3.70874	−0.131042
$802$	−22.4997	−0.794491
$803$	6.49316	0.229139
$804$	4.11156	0.145003
$805$	−23.6774	−0.834519
$806$	48.8368	1.72020
$807$	−4.86371	−0.171211
$808$	14.5365	0.511394
$809$	−42.6286	−1.49874	−0.749370	−	0.662151i	$-0.769644\pi$
$809$	−42.6286	−1.49874	−0.749370	+	0.662151i	$0.769644\pi$
$810$	20.4487	0.718494
$811$	12.2771	0.431109	0.215554	−	0.976492i	$-0.430844\pi$
$811$	12.2771	0.431109	0.215554	+	0.976492i	$0.430844\pi$
$812$	2.17855	0.0764521
$813$	−3.63278	−0.127407
$814$	−6.13732	−0.215113
$815$	23.5550	0.825095
$816$	−0.235712	−0.00825156
$817$	−17.0574	−0.596764
$818$	0.432831	0.0151336
$819$	−38.5847	−1.34826
$820$	−4.07788	−0.142406
$821$	11.5749	0.403967	0.201984	−	0.979389i	$-0.435261\pi$
$821$	11.5749	0.403967	0.201984	+	0.979389i	$0.435261\pi$
$822$	−1.92563	−0.0671642
$823$	−6.87918	−0.239793	−0.119897	−	0.992786i	$-0.538256\pi$
$823$	−6.87918	−0.239793	−0.119897	+	0.992786i	$0.538256\pi$
$824$	13.9101	0.484582
$825$	−0.276478	−0.00962572
$826$	−19.7344	−0.686649
$827$	50.0356	1.73991	0.869954	−	0.493133i	$-0.164148\pi$
$827$	50.0356	1.73991	0.869954	+	0.493133i	$0.164148\pi$
$828$	11.2483	0.390905
$829$	−50.5484	−1.75562	−0.877809	−	0.479010i	$-0.840996\pi$
$829$	−50.5484	−1.75562	−0.877809	+	0.479010i	$0.840996\pi$
$830$	−25.4623	−0.883810
$831$	−3.79391	−0.131609
$832$	5.25164	0.182068
$833$	0.600588	0.0208092
$834$	−1.32912	−0.0460237
$835$	18.0170	0.623505
$836$	1.56717	0.0542017
$837$	−15.0105	−0.518838
$838$	−21.1346	−0.730082
$839$	−8.63717	−0.298188	−0.149094	−	0.988823i	$-0.547636\pi$
$839$	−8.63717	−0.298188	−0.149094	+	0.988823i	$0.547636\pi$
$840$	1.67760	0.0578827
$841$	−28.2474	−0.974047
$842$	5.80578	0.200080
$843$	1.40072	0.0482433
$844$	−18.2204	−0.627171
$845$	35.7574	1.23009
$846$	−19.6497	−0.675570
$847$	2.51117	0.0862847
$848$	−5.05335	−0.173533
$849$	2.94720	0.101148
$850$	−0.878317	−0.0301260
$851$	−23.5950	−0.808826
$852$	−0.0175530	−0.000601355 0
$853$	−25.8949	−0.886624	−0.443312	−	0.896367i	$-0.646197\pi$
$853$	−25.8949	−0.886624	−0.443312	+	0.896367i	$0.646197\pi$
$854$	34.0498	1.16516
$855$	11.2455	0.384588
$856$	−18.7508	−0.640890
$857$	−8.21720	−0.280694	−0.140347	−	0.990102i	$-0.544822\pi$
$857$	−8.21720	−0.280694	−0.140347	+	0.990102i	$0.544822\pi$
$858$	−1.43051	−0.0488367
$859$	−50.3635	−1.71838	−0.859190	−	0.511657i	$-0.829032\pi$
$859$	−50.3635	−1.71838	−0.859190	+	0.511657i	$0.829032\pi$
$860$	26.6941	0.910263
$861$	−1.13733	−0.0387601
$862$	−26.9842	−0.919087
$863$	39.5240	1.34541	0.672706	−	0.739910i	$-0.265132\pi$
$863$	39.5240	1.34541	0.672706	+	0.739910i	$0.265132\pi$
$864$	−1.61414	−0.0549143
$865$	−0.608913	−0.0207037
$866$	16.3315	0.554969
$867$	−4.42670	−0.150339
$868$	23.3522	0.792625
$869$	16.5741	0.562238
$870$	0.579569	0.0196492
$871$	79.2694	2.68594
$872$	−8.62352	−0.292029
$873$	6.08671	0.206004
$874$	6.02500	0.203799
$875$	−24.5427	−0.829693
$876$	−1.76869	−0.0597584
$877$	−22.1454	−0.747795	−0.373898	−	0.927470i	$-0.621979\pi$
$877$	−22.1454	−0.747795	−0.373898	+	0.927470i	$0.621979\pi$
$878$	−19.9968	−0.674858
$879$	−0.693687	−0.0233975
$880$	−2.45255	−0.0826754
$881$	−10.1652	−0.342473	−0.171236	−	0.985230i	$-0.554776\pi$
$881$	−10.1652	−0.342473	−0.171236	+	0.985230i	$0.554776\pi$
$882$	2.03065	0.0683757
$883$	−1.88587	−0.0634647	−0.0317323	−	0.999496i	$-0.510102\pi$
$883$	−1.88587	−0.0634647	−0.0317323	+	0.999496i	$0.510102\pi$
$884$	−4.54444	−0.152846
$885$	−5.25004	−0.176478
$886$	20.2357	0.679830
$887$	54.5609	1.83197	0.915987	−	0.401207i	$-0.131409\pi$
$887$	54.5609	1.83197	0.915987	+	0.401207i	$0.131409\pi$
$888$	1.67176	0.0561006
$889$	17.5115	0.587317
$890$	3.10885	0.104209
$891$	−8.33773	−0.279324
$892$	15.1496	0.507246
$893$	−10.5251	−0.352209
$894$	−4.29957	−0.143799
$895$	−13.4297	−0.448904
$896$	2.51117	0.0838921
$897$	−5.49960	−0.183626
$898$	30.6550	1.02297
$899$	8.06761	0.269070
$900$	−2.96968	−0.0989894
$901$	4.37286	0.145681
$902$	1.66271	0.0553622
$903$	7.44507	0.247756
$904$	1.74098	0.0579042
$905$	−39.1071	−1.29996
$906$	2.75809	0.0916315
$907$	22.9588	0.762334	0.381167	−	0.924506i	$-0.375522\pi$
$907$	22.9588	0.762334	0.381167	+	0.924506i	$0.375522\pi$
$908$	8.65275	0.287152
$909$	−42.5310	−1.41067
$910$	32.3435	1.07218
$911$	14.1970	0.470367	0.235184	−	0.971951i	$-0.424431\pi$
$911$	14.1970	0.470367	0.235184	+	0.971951i	$0.424431\pi$
$912$	−0.426885	−0.0141356
$913$	10.3820	0.343593
$914$	19.6701	0.650629
$915$	9.05841	0.299462
$916$	−7.59307	−0.250882
$917$	−14.9972	−0.495253
$918$	1.39678	0.0461007
$919$	−32.1584	−1.06081	−0.530404	−	0.847745i	$-0.677960\pi$
$919$	−32.1584	−1.06081	−0.530404	+	0.847745i	$0.677960\pi$
$920$	−9.42885	−0.310860
$921$	6.88744	0.226949
$922$	−4.43175	−0.145952
$923$	−0.338416	−0.0111391
$924$	−0.684022	−0.0225027
$925$	6.22936	0.204820
$926$	40.4012	1.32766
$927$	−40.6982	−1.33670
$928$	0.867546	0.0284786
$929$	−17.9029	−0.587376	−0.293688	−	0.955901i	$-0.594883\pi$
$929$	−17.9029	−0.587376	−0.293688	+	0.955901i	$0.594883\pi$
$930$	6.21248	0.203715
$931$	1.08769	0.0356477
$932$	0.428353	0.0140312
$933$	−4.79752	−0.157064
$934$	2.80076	0.0916437
$935$	2.12229	0.0694062
$936$	−15.3653	−0.502229
$937$	−28.1370	−0.919194	−0.459597	−	0.888127i	$-0.652006\pi$
$937$	−28.1370	−0.919194	−0.459597	+	0.888127i	$0.652006\pi$
$938$	37.9041	1.23761
$939$	2.26916	0.0740511
$940$	16.4713	0.537235
$941$	3.09731	0.100970	0.0504848	−	0.998725i	$-0.483923\pi$
$941$	3.09731	0.100970	0.0504848	+	0.998725i	$0.483923\pi$
$942$	−2.12010	−0.0690765
$943$	6.39231	0.208162
$944$	−7.85868	−0.255778
$945$	−9.94112	−0.323385
$946$	−10.8842	−0.353877
$947$	40.4116	1.31320	0.656601	−	0.754238i	$-0.271994\pi$
$947$	40.4116	1.31320	0.656601	+	0.754238i	$0.271994\pi$
$948$	−4.51466	−0.146629
$949$	−34.0997	−1.10692
$950$	−1.59067	−0.0516082
$951$	−1.04852	−0.0340007
$952$	−2.17301	−0.0704276
$953$	−3.73033	−0.120837	−0.0604187	−	0.998173i	$-0.519244\pi$
$953$	−3.73033	−0.120837	−0.0604187	+	0.998173i	$0.519244\pi$
$954$	14.7851	0.478685
$955$	38.0092	1.22995
$956$	8.09173	0.261705
$957$	−0.236313	−0.00763891
$958$	18.5177	0.598278
$959$	−17.7523	−0.573251
$960$	0.668056	0.0215614
$961$	55.4778	1.78961
$962$	32.2310	1.03917
$963$	54.8612	1.76788
$964$	−9.79772	−0.315563
$965$	−0.460008	−0.0148082
$966$	−2.62973	−0.0846103
$967$	−11.8083	−0.379728	−0.189864	−	0.981810i	$-0.560805\pi$
$967$	−11.8083	−0.379728	−0.189864	+	0.981810i	$0.560805\pi$
$968$	1.00000	0.0321412
$969$	0.369400	0.0118668
$970$	−5.10218	−0.163821
$971$	−9.48160	−0.304279	−0.152140	−	0.988359i	$-0.548616\pi$
$971$	−9.48160	−0.304279	−0.152140	+	0.988359i	$0.548616\pi$
$972$	7.11357	0.228168
$973$	−12.2531	−0.392815
$974$	−23.9564	−0.767611
$975$	1.45196	0.0464999
$976$	13.5594	0.434024
$977$	18.8380	0.602681	0.301340	−	0.953517i	$-0.402566\pi$
$977$	18.8380	0.602681	0.301340	+	0.953517i	$0.402566\pi$
$978$	2.61613	0.0836547
$979$	−1.26760	−0.0405126
$980$	−1.70219	−0.0543745
$981$	25.2307	0.805555
$982$	7.71305	0.246133
$983$	13.6591	0.435659	0.217829	−	0.975987i	$-0.430102\pi$
$983$	13.6591	0.435659	0.217829	+	0.975987i	$0.430102\pi$
$984$	−0.452909	−0.0144382
$985$	−2.45255	−0.0781447
$986$	−0.750721	−0.0239078
$987$	4.59389	0.146225
$988$	−8.23020	−0.261838
$989$	−41.8446	−1.33058
$990$	7.17567	0.228058
$991$	1.22518	0.0389191	0.0194595	−	0.999811i	$-0.493805\pi$
$991$	1.22518	0.0389191	0.0194595	+	0.999811i	$0.493805\pi$
$992$	9.29935	0.295255
$993$	3.27567	0.103950
$994$	−0.161820	−0.00513261
$995$	−4.95836	−0.157190
$996$	−2.82797	−0.0896078
$997$	21.9715	0.695843	0.347922	−	0.937524i	$-0.386887\pi$
$997$	21.9715	0.695843	0.347922	+	0.937524i	$0.386887\pi$
$998$	1.79339	0.0567687
$999$	−9.90651	−0.313428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.12	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.272392 q^{3} +1.00000 q^{4} +2.45255 q^{5} +0.272392 q^{6} +2.51117 q^{7} +1.00000 q^{8} -2.92580 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.272392 q^{3} +1.00000 q^{4} +2.45255 q^{5} +0.272392 q^{6} +2.51117 q^{7} +1.00000 q^{8} -2.92580 q^{9} +2.45255 q^{10} -1.00000 q^{11} +0.272392 q^{12} +5.25164 q^{13} +2.51117 q^{14} +0.668056 q^{15} +1.00000 q^{16} -0.865339 q^{17} -2.92580 q^{18} -1.56717 q^{19} +2.45255 q^{20} +0.684022 q^{21} -1.00000 q^{22} -3.84451 q^{23} +0.272392 q^{24} +1.01500 q^{25} +5.25164 q^{26} -1.61414 q^{27} +2.51117 q^{28} +0.867546 q^{29} +0.668056 q^{30} +9.29935 q^{31} +1.00000 q^{32} -0.272392 q^{33} -0.865339 q^{34} +6.15876 q^{35} -2.92580 q^{36} +6.13732 q^{37} -1.56717 q^{38} +1.43051 q^{39} +2.45255 q^{40} -1.66271 q^{41} +0.684022 q^{42} +10.8842 q^{43} -1.00000 q^{44} -7.17567 q^{45} -3.84451 q^{46} +6.71600 q^{47} +0.272392 q^{48} -0.694050 q^{49} +1.01500 q^{50} -0.235712 q^{51} +5.25164 q^{52} -5.05335 q^{53} -1.61414 q^{54} -2.45255 q^{55} +2.51117 q^{56} -0.426885 q^{57} +0.867546 q^{58} -7.85868 q^{59} +0.668056 q^{60} +13.5594 q^{61} +9.29935 q^{62} -7.34717 q^{63} +1.00000 q^{64} +12.8799 q^{65} -0.272392 q^{66} +15.0942 q^{67} -0.865339 q^{68} -1.04722 q^{69} +6.15876 q^{70} -0.0644401 q^{71} -2.92580 q^{72} -6.49316 q^{73} +6.13732 q^{74} +0.276478 q^{75} -1.56717 q^{76} -2.51117 q^{77} +1.43051 q^{78} -16.5741 q^{79} +2.45255 q^{80} +8.33773 q^{81} -1.66271 q^{82} -10.3820 q^{83} +0.684022 q^{84} -2.12229 q^{85} +10.8842 q^{86} +0.236313 q^{87} -1.00000 q^{88} +1.26760 q^{89} -7.17567 q^{90} +13.1877 q^{91} -3.84451 q^{92} +2.53307 q^{93} +6.71600 q^{94} -3.84356 q^{95} +0.272392 q^{96} -2.08036 q^{97} -0.694050 q^{98} +2.92580 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * q^99

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