LMFDB - Embedded newform 2671.2.a.b.1.73

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.73
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.836398 q^{2} +2.44549 q^{3} -1.30044 q^{4} -1.82035 q^{5} +2.04541 q^{6} +3.51126 q^{7} -2.76048 q^{8} +2.98044 q^{9} +O(q^{10})$	\(q+0.836398 q^{2} +2.44549 q^{3} -1.30044 q^{4} -1.82035 q^{5} +2.04541 q^{6} +3.51126 q^{7} -2.76048 q^{8} +2.98044 q^{9} -1.52254 q^{10} +0.215499 q^{11} -3.18021 q^{12} +5.69704 q^{13} +2.93681 q^{14} -4.45166 q^{15} +0.292017 q^{16} -1.80783 q^{17} +2.49283 q^{18} -4.63369 q^{19} +2.36726 q^{20} +8.58675 q^{21} +0.180243 q^{22} +6.40057 q^{23} -6.75074 q^{24} -1.68631 q^{25} +4.76500 q^{26} -0.0478394 q^{27} -4.56617 q^{28} +5.52048 q^{29} -3.72336 q^{30} +6.56087 q^{31} +5.76520 q^{32} +0.527001 q^{33} -1.51207 q^{34} -6.39173 q^{35} -3.87588 q^{36} -6.47893 q^{37} -3.87561 q^{38} +13.9321 q^{39} +5.02505 q^{40} -0.808442 q^{41} +7.18194 q^{42} +10.0892 q^{43} -0.280243 q^{44} -5.42545 q^{45} +5.35342 q^{46} +6.79408 q^{47} +0.714125 q^{48} +5.32891 q^{49} -1.41043 q^{50} -4.42104 q^{51} -7.40865 q^{52} +10.3441 q^{53} -0.0400128 q^{54} -0.392284 q^{55} -9.69275 q^{56} -11.3317 q^{57} +4.61732 q^{58} -5.56766 q^{59} +5.78912 q^{60} +0.298748 q^{61} +5.48750 q^{62} +10.4651 q^{63} +4.23797 q^{64} -10.3706 q^{65} +0.440782 q^{66} +1.60738 q^{67} +2.35098 q^{68} +15.6525 q^{69} -5.34603 q^{70} +7.04414 q^{71} -8.22744 q^{72} -0.663013 q^{73} -5.41896 q^{74} -4.12386 q^{75} +6.02583 q^{76} +0.756671 q^{77} +11.6528 q^{78} -8.95363 q^{79} -0.531574 q^{80} -9.05830 q^{81} -0.676179 q^{82} +1.26360 q^{83} -11.1665 q^{84} +3.29090 q^{85} +8.43858 q^{86} +13.5003 q^{87} -0.594880 q^{88} -1.63051 q^{89} -4.53784 q^{90} +20.0038 q^{91} -8.32355 q^{92} +16.0446 q^{93} +5.68255 q^{94} +8.43495 q^{95} +14.0988 q^{96} -3.87168 q^{97} +4.45709 q^{98} +0.642280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.836398	0.591423	0.295711	−	0.955277i	$-0.404443\pi$
$2$	0.836398	0.591423	0.295711	+	0.955277i	$0.404443\pi$
$3$	2.44549	1.41191	0.705953	−	0.708259i	$-0.250519\pi$
$3$	2.44549	1.41191	0.705953	+	0.708259i	$0.250519\pi$
$4$	−1.30044	−0.650219
$5$	−1.82035	−0.814087	−0.407044	−	0.913409i	$-0.633440\pi$
$5$	−1.82035	−0.814087	−0.407044	+	0.913409i	$0.633440\pi$
$6$	2.04541	0.835033
$7$	3.51126	1.32713	0.663565	−	0.748119i	$-0.269043\pi$
$7$	3.51126	1.32713	0.663565	+	0.748119i	$0.269043\pi$
$8$	−2.76048	−0.975977
$9$	2.98044	0.993479
$10$	−1.52254	−0.481470
$11$	0.215499	0.0649753	0.0324876	−	0.999472i	$-0.489657\pi$
$11$	0.215499	0.0649753	0.0324876	+	0.999472i	$0.489657\pi$
$12$	−3.18021	−0.918049
$13$	5.69704	1.58008	0.790038	−	0.613058i	$-0.210061\pi$
$13$	5.69704	1.58008	0.790038	+	0.613058i	$0.210061\pi$
$14$	2.93681	0.784895
$15$	−4.45166	−1.14941
$16$	0.292017	0.0730042
$17$	−1.80783	−0.438464	−0.219232	−	0.975673i	$-0.570355\pi$
$17$	−1.80783	−0.438464	−0.219232	+	0.975673i	$0.570355\pi$
$18$	2.49283	0.587566
$19$	−4.63369	−1.06304	−0.531520	−	0.847045i	$-0.678379\pi$
$19$	−4.63369	−1.06304	−0.531520	+	0.847045i	$0.678379\pi$
$20$	2.36726	0.529335
$21$	8.58675	1.87378
$22$	0.180243	0.0384279
$23$	6.40057	1.33461	0.667305	−	0.744784i	$-0.267448\pi$
$23$	6.40057	1.33461	0.667305	+	0.744784i	$0.267448\pi$
$24$	−6.75074	−1.37799
$25$	−1.68631	−0.337262
$26$	4.76500	0.934493
$27$	−0.0478394	−0.00920670
$28$	−4.56617	−0.862925
$29$	5.52048	1.02513	0.512563	−	0.858649i	$-0.328696\pi$
$29$	5.52048	1.02513	0.512563	+	0.858649i	$0.328696\pi$
$30$	−3.72336	−0.679790
$31$	6.56087	1.17837	0.589183	−	0.807999i	$-0.299450\pi$
$31$	6.56087	1.17837	0.589183	+	0.807999i	$0.299450\pi$
$32$	5.76520	1.01915
$33$	0.527001	0.0917390
$34$	−1.51207	−0.259318
$35$	−6.39173	−1.08040
$36$	−3.87588	−0.645979
$37$	−6.47893	−1.06513	−0.532565	−	0.846389i	$-0.678772\pi$
$37$	−6.47893	−1.06513	−0.532565	+	0.846389i	$0.678772\pi$
$38$	−3.87561	−0.628706
$39$	13.9321	2.23092
$40$	5.02505	0.794531
$41$	−0.808442	−0.126257	−0.0631287	−	0.998005i	$-0.520108\pi$
$41$	−0.808442	−0.126257	−0.0631287	+	0.998005i	$0.520108\pi$
$42$	7.18194	1.10820
$43$	10.0892	1.53859	0.769294	−	0.638895i	$-0.220608\pi$
$43$	10.0892	1.53859	0.769294	+	0.638895i	$0.220608\pi$
$44$	−0.280243	−0.0422482
$45$	−5.42545	−0.808779
$46$	5.35342	0.789319
$47$	6.79408	0.991018	0.495509	−	0.868603i	$-0.334982\pi$
$47$	6.79408	0.991018	0.495509	+	0.868603i	$0.334982\pi$
$48$	0.714125	0.103075
$49$	5.32891	0.761274
$50$	−1.41043	−0.199464
$51$	−4.42104	−0.619070
$52$	−7.40865	−1.02740
$53$	10.3441	1.42087	0.710435	−	0.703762i	$-0.248498\pi$
$53$	10.3441	1.42087	0.710435	+	0.703762i	$0.248498\pi$
$54$	−0.0400128	−0.00544505
$55$	−0.392284	−0.0528956
$56$	−9.69275	−1.29525
$57$	−11.3317	−1.50091
$58$	4.61732	0.606283
$59$	−5.56766	−0.724848	−0.362424	−	0.932013i	$-0.618051\pi$
$59$	−5.56766	−0.724848	−0.362424	+	0.932013i	$0.618051\pi$
$60$	5.78912	0.747372
$61$	0.298748	0.0382507	0.0191254	−	0.999817i	$-0.493912\pi$
$61$	0.298748	0.0382507	0.0191254	+	0.999817i	$0.493912\pi$
$62$	5.48750	0.696913
$63$	10.4651	1.31848
$64$	4.23797	0.529746
$65$	−10.3706	−1.28632
$66$	0.440782	0.0542565
$67$	1.60738	0.196372	0.0981862	−	0.995168i	$-0.468696\pi$
$67$	1.60738	0.196372	0.0981862	+	0.995168i	$0.468696\pi$
$68$	2.35098	0.285098
$69$	15.6525	1.88435
$70$	−5.34603	−0.638973
$71$	7.04414	0.835985	0.417993	−	0.908450i	$-0.362734\pi$
$71$	7.04414	0.835985	0.417993	+	0.908450i	$0.362734\pi$
$72$	−8.22744	−0.969613
$73$	−0.663013	−0.0775998	−0.0387999	−	0.999247i	$-0.512353\pi$
$73$	−0.663013	−0.0775998	−0.0387999	+	0.999247i	$0.512353\pi$
$74$	−5.41896	−0.629942
$75$	−4.12386	−0.476182
$76$	6.02583	0.691210
$77$	0.756671	0.0862306
$78$	11.6528	1.31942
$79$	−8.95363	−1.00736	−0.503681	−	0.863890i	$-0.668021\pi$
$79$	−8.95363	−1.00736	−0.503681	+	0.863890i	$0.668021\pi$
$80$	−0.531574	−0.0594318
$81$	−9.05830	−1.00648
$82$	−0.676179	−0.0746715
$83$	1.26360	0.138698	0.0693491	−	0.997592i	$-0.477908\pi$
$83$	1.26360	0.138698	0.0693491	+	0.997592i	$0.477908\pi$
$84$	−11.1665	−1.21837
$85$	3.29090	0.356948
$86$	8.43858	0.909956
$87$	13.5003	1.44738
$88$	−0.594880	−0.0634144
$89$	−1.63051	−0.172833	−0.0864166	−	0.996259i	$-0.527542\pi$
$89$	−1.63051	−0.172833	−0.0864166	+	0.996259i	$0.527542\pi$
$90$	−4.53784	−0.478330
$91$	20.0038	2.09697
$92$	−8.32355	−0.867790
$93$	16.0446	1.66374
$94$	5.68255	0.586111
$95$	8.43495	0.865408
$96$	14.0988	1.43895
$97$	−3.87168	−0.393109	−0.196555	−	0.980493i	$-0.562975\pi$
$97$	−3.87168	−0.393109	−0.196555	+	0.980493i	$0.562975\pi$
$98$	4.45709	0.450234
$99$	0.642280	0.0645516
$100$	2.19294	0.219294
$101$	13.5687	1.35013	0.675066	−	0.737757i	$-0.264115\pi$
$101$	13.5687	1.35013	0.675066	+	0.737757i	$0.264115\pi$
$102$	−3.69775	−0.366132
$103$	−7.49557	−0.738561	−0.369280	−	0.929318i	$-0.620396\pi$
$103$	−7.49557	−0.738561	−0.369280	+	0.929318i	$0.620396\pi$
$104$	−15.7266	−1.54212
$105$	−15.6309	−1.52542
$106$	8.65178	0.840335
$107$	−11.6420	−1.12547	−0.562735	−	0.826637i	$-0.690251\pi$
$107$	−11.6420	−1.12547	−0.562735	+	0.826637i	$0.690251\pi$
$108$	0.0622122	0.00598637
$109$	2.44046	0.233754	0.116877	−	0.993146i	$-0.462712\pi$
$109$	2.44046	0.233754	0.116877	+	0.993146i	$0.462712\pi$
$110$	−0.328105	−0.0312836
$111$	−15.8442	−1.50386
$112$	1.02535	0.0968860
$113$	12.2217	1.14972	0.574860	−	0.818252i	$-0.305057\pi$
$113$	12.2217	1.14972	0.574860	+	0.818252i	$0.305057\pi$
$114$	−9.47777	−0.887675
$115$	−11.6513	−1.08649
$116$	−7.17904	−0.666557
$117$	16.9797	1.56977
$118$	−4.65678	−0.428692
$119$	−6.34776	−0.581899
$120$	12.2887	1.12180
$121$	−10.9536	−0.995778
$122$	0.249872	0.0226223
$123$	−1.97704	−0.178264
$124$	−8.53201	−0.766197
$125$	12.1715	1.08865
$126$	8.75297	0.779777
$127$	−1.34431	−0.119289	−0.0596443	−	0.998220i	$-0.518997\pi$
$127$	−1.34431	−0.119289	−0.0596443	+	0.998220i	$0.518997\pi$
$128$	−7.98577	−0.705849
$129$	24.6731	2.17234
$130$	−8.67398	−0.760758
$131$	10.3131	0.901060	0.450530	−	0.892761i	$-0.351235\pi$
$131$	10.3131	0.901060	0.450530	+	0.892761i	$0.351235\pi$
$132$	−0.685332	−0.0596505
$133$	−16.2701	−1.41079
$134$	1.34441	0.116139
$135$	0.0870847	0.00749506
$136$	4.99049	0.427931
$137$	−18.2714	−1.56103	−0.780514	−	0.625138i	$-0.785043\pi$
$137$	−18.2714	−1.56103	−0.780514	+	0.625138i	$0.785043\pi$
$138$	13.0918	1.11444
$139$	−9.35879	−0.793802	−0.396901	−	0.917861i	$-0.629914\pi$
$139$	−9.35879	−0.793802	−0.396901	+	0.917861i	$0.629914\pi$
$140$	8.31205	0.702496
$141$	16.6149	1.39922
$142$	5.89170	0.494421
$143$	1.22771	0.102666
$144$	0.870338	0.0725282
$145$	−10.0492	−0.834543
$146$	−0.554543	−0.0458943
$147$	13.0318	1.07485
$148$	8.42545	0.692568
$149$	12.9676	1.06235	0.531174	−	0.847263i	$-0.321751\pi$
$149$	12.9676	1.06235	0.531174	+	0.847263i	$0.321751\pi$
$150$	−3.44919	−0.281625
$151$	−22.0368	−1.79333	−0.896663	−	0.442713i	$-0.854016\pi$
$151$	−22.0368	−1.79333	−0.896663	+	0.442713i	$0.854016\pi$
$152$	12.7912	1.03750
$153$	−5.38813	−0.435605
$154$	0.632878	0.0509988
$155$	−11.9431	−0.959293
$156$	−18.1178	−1.45059
$157$	1.87507	0.149647	0.0748233	−	0.997197i	$-0.476161\pi$
$157$	1.87507	0.149647	0.0748233	+	0.997197i	$0.476161\pi$
$158$	−7.48880	−0.595777
$159$	25.2964	2.00614
$160$	−10.4947	−0.829680
$161$	22.4740	1.77120
$162$	−7.57635	−0.595254
$163$	7.85406	0.615177	0.307589	−	0.951519i	$-0.400478\pi$
$163$	7.85406	0.615177	0.307589	+	0.951519i	$0.400478\pi$
$164$	1.05133	0.0820950
$165$	−0.959328	−0.0746836
$166$	1.05687	0.0820293
$167$	19.5378	1.51188	0.755939	−	0.654642i	$-0.227181\pi$
$167$	19.5378	1.51188	0.755939	+	0.654642i	$0.227181\pi$
$168$	−23.7036	−1.82877
$169$	19.4563	1.49664
$170$	2.75250	0.211107
$171$	−13.8104	−1.05611
$172$	−13.1204	−1.00042
$173$	−0.404874	−0.0307820	−0.0153910	−	0.999882i	$-0.504899\pi$
$173$	−0.404874	−0.0307820	−0.0153910	+	0.999882i	$0.504899\pi$
$174$	11.2916	0.856015
$175$	−5.92106	−0.447590
$176$	0.0629292	0.00474347
$177$	−13.6157	−1.02342
$178$	−1.36375	−0.102218
$179$	2.35743	0.176203	0.0881015	−	0.996112i	$-0.471920\pi$
$179$	2.35743	0.176203	0.0881015	+	0.996112i	$0.471920\pi$
$180$	7.05547	0.525883
$181$	0.596253	0.0443192	0.0221596	−	0.999754i	$-0.492946\pi$
$181$	0.596253	0.0443192	0.0221596	+	0.999754i	$0.492946\pi$
$182$	16.7311	1.24019
$183$	0.730585	0.0540064
$184$	−17.6686	−1.30255
$185$	11.7939	0.867108
$186$	13.4196	0.983976
$187$	−0.389586	−0.0284893
$188$	−8.83528	−0.644379
$189$	−0.167976	−0.0122185
$190$	7.05498	0.511822
$191$	−11.2604	−0.814777	−0.407388	−	0.913255i	$-0.633560\pi$
$191$	−11.2604	−0.814777	−0.407388	+	0.913255i	$0.633560\pi$
$192$	10.3639	0.747952
$193$	−1.58958	−0.114421	−0.0572104	−	0.998362i	$-0.518221\pi$
$193$	−1.58958	−0.114421	−0.0572104	+	0.998362i	$0.518221\pi$
$194$	−3.23826	−0.232494
$195$	−25.3613	−1.81616
$196$	−6.92992	−0.494995
$197$	14.1815	1.01039	0.505193	−	0.863006i	$-0.331421\pi$
$197$	14.1815	1.01039	0.505193	+	0.863006i	$0.331421\pi$
$198$	0.537202	0.0381773
$199$	22.6994	1.60912	0.804558	−	0.593874i	$-0.202402\pi$
$199$	22.6994	1.60912	0.804558	+	0.593874i	$0.202402\pi$
$200$	4.65502	0.329160
$201$	3.93083	0.277260
$202$	11.3488	0.798499
$203$	19.3838	1.36048
$204$	5.74930	0.402531
$205$	1.47165	0.102785
$206$	−6.26928	−0.436802
$207$	19.0765	1.32591
$208$	1.66363	0.115352
$209$	−0.998553	−0.0690714
$210$	−13.0737	−0.902170
$211$	−18.9889	−1.30725	−0.653626	−	0.756818i	$-0.726753\pi$
$211$	−18.9889	−1.30725	−0.653626	+	0.756818i	$0.726753\pi$
$212$	−13.4519	−0.923878
$213$	17.2264	1.18033
$214$	−9.73731	−0.665629
$215$	−18.3659	−1.25254
$216$	0.132060	0.00898553
$217$	23.0369	1.56385
$218$	2.04120	0.138247
$219$	−1.62139	−0.109564
$220$	0.510141	0.0343937
$221$	−10.2993	−0.692806
$222$	−13.2520	−0.889419
$223$	−20.1951	−1.35236	−0.676182	−	0.736734i	$-0.736367\pi$
$223$	−20.1951	−1.35236	−0.676182	+	0.736734i	$0.736367\pi$
$224$	20.2431	1.35255
$225$	−5.02594	−0.335063
$226$	10.2222	0.679970
$227$	25.4971	1.69230	0.846152	−	0.532941i	$-0.178913\pi$
$227$	25.4971	1.69230	0.846152	+	0.532941i	$0.178913\pi$
$228$	14.7361	0.975923
$229$	−14.6917	−0.970855	−0.485427	−	0.874277i	$-0.661336\pi$
$229$	−14.6917	−0.970855	−0.485427	+	0.874277i	$0.661336\pi$
$230$	−9.74513	−0.642575
$231$	1.85043	0.121750
$232$	−15.2392	−1.00050
$233$	−21.3900	−1.40131	−0.700653	−	0.713502i	$-0.747108\pi$
$233$	−21.3900	−1.40131	−0.700653	+	0.713502i	$0.747108\pi$
$234$	14.2018	0.928399
$235$	−12.3676	−0.806775
$236$	7.24040	0.471310
$237$	−21.8960	−1.42230
$238$	−5.30926	−0.344148
$239$	21.4399	1.38683	0.693416	−	0.720538i	$-0.256105\pi$
$239$	21.4399	1.38683	0.693416	+	0.720538i	$0.256105\pi$
$240$	−1.29996	−0.0839121
$241$	−24.5722	−1.58284	−0.791418	−	0.611276i	$-0.790657\pi$
$241$	−24.5722	−1.58284	−0.791418	+	0.611276i	$0.790657\pi$
$242$	−9.16154	−0.588926
$243$	−22.0085	−1.41185
$244$	−0.388503	−0.0248713
$245$	−9.70051	−0.619743
$246$	−1.65359	−0.105429
$247$	−26.3983	−1.67968
$248$	−18.1111	−1.15006
$249$	3.09013	0.195829
$250$	10.1802	0.643851
$251$	−12.2557	−0.773570	−0.386785	−	0.922170i	$-0.626414\pi$
$251$	−12.2557	−0.773570	−0.386785	+	0.922170i	$0.626414\pi$
$252$	−13.6092	−0.857298
$253$	1.37931	0.0867167
$254$	−1.12438	−0.0705500
$255$	8.04787	0.503977
$256$	−15.1552	−0.947202
$257$	−14.7742	−0.921588	−0.460794	−	0.887507i	$-0.652435\pi$
$257$	−14.7742	−0.921588	−0.460794	+	0.887507i	$0.652435\pi$
$258$	20.6365	1.28477
$259$	−22.7492	−1.41356
$260$	13.4864	0.836390
$261$	16.4534	1.01844
$262$	8.62586	0.532907
$263$	6.19885	0.382237	0.191119	−	0.981567i	$-0.438788\pi$
$263$	6.19885	0.382237	0.191119	+	0.981567i	$0.438788\pi$
$264$	−1.45477	−0.0895352
$265$	−18.8299	−1.15671
$266$	−13.6082	−0.834375
$267$	−3.98739	−0.244024
$268$	−2.09030	−0.127685
$269$	−20.8784	−1.27298	−0.636488	−	0.771287i	$-0.719613\pi$
$269$	−20.8784	−1.27298	−0.636488	+	0.771287i	$0.719613\pi$
$270$	0.0728375	0.00443275
$271$	3.42850	0.208266	0.104133	−	0.994563i	$-0.466793\pi$
$271$	3.42850	0.208266	0.104133	+	0.994563i	$0.466793\pi$
$272$	−0.527918	−0.0320097
$273$	48.9191	2.96072
$274$	−15.2821	−0.923227
$275$	−0.363397	−0.0219137
$276$	−20.3552	−1.22524
$277$	−23.4213	−1.40725	−0.703624	−	0.710572i	$-0.748436\pi$
$277$	−23.4213	−1.40725	−0.703624	+	0.710572i	$0.748436\pi$
$278$	−7.82767	−0.469473
$279$	19.5543	1.17068
$280$	17.6442	1.05445
$281$	26.8256	1.60028	0.800140	−	0.599813i	$-0.204758\pi$
$281$	26.8256	1.60028	0.800140	+	0.599813i	$0.204758\pi$
$282$	13.8966	0.827533
$283$	−7.74690	−0.460505	−0.230253	−	0.973131i	$-0.573955\pi$
$283$	−7.74690	−0.460505	−0.230253	+	0.973131i	$0.573955\pi$
$284$	−9.16046	−0.543574
$285$	20.6276	1.22187
$286$	1.02685	0.0607189
$287$	−2.83865	−0.167560
$288$	17.1828	1.01251
$289$	−13.7317	−0.807749
$290$	−8.40515	−0.493567
$291$	−9.46816	−0.555033
$292$	0.862207	0.0504569
$293$	−20.7748	−1.21367	−0.606837	−	0.794826i	$-0.707562\pi$
$293$	−20.7748	−1.21367	−0.606837	+	0.794826i	$0.707562\pi$
$294$	10.8998	0.635689
$295$	10.1351	0.590090
$296$	17.8850	1.03954
$297$	−0.0103093	−0.000598208 0
$298$	10.8461	0.628297
$299$	36.4643	2.10879
$300$	5.36282	0.309623
$301$	35.4257	2.04191
$302$	−18.4315	−1.06061
$303$	33.1821	1.90626
$304$	−1.35311	−0.0776064
$305$	−0.543827	−0.0311394
$306$	−4.50662	−0.257627
$307$	−7.65186	−0.436715	−0.218357	−	0.975869i	$-0.570070\pi$
$307$	−7.65186	−0.436715	−0.218357	+	0.975869i	$0.570070\pi$
$308$	−0.984004	−0.0560688
$309$	−18.3304	−1.04278
$310$	−9.98919	−0.567348
$311$	−16.2573	−0.921869	−0.460934	−	0.887434i	$-0.652486\pi$
$311$	−16.2573	−0.921869	−0.460934	+	0.887434i	$0.652486\pi$
$312$	−38.4592	−2.17733
$313$	27.5525	1.55736	0.778679	−	0.627423i	$-0.215890\pi$
$313$	27.5525	1.55736	0.778679	+	0.627423i	$0.215890\pi$
$314$	1.56830	0.0885044
$315$	−19.0502	−1.07335
$316$	11.6436	0.655006
$317$	−18.8590	−1.05922	−0.529612	−	0.848240i	$-0.677663\pi$
$317$	−18.8590	−1.05922	−0.529612	+	0.848240i	$0.677663\pi$
$318$	21.1579	1.18647
$319$	1.18966	0.0666079
$320$	−7.71461	−0.431260
$321$	−28.4703	−1.58906
$322$	18.7972	1.04753
$323$	8.37693	0.466105
$324$	11.7798	0.654431
$325$	−9.60698	−0.532899
$326$	6.56912	0.363830
$327$	5.96813	0.330038
$328$	2.23169	0.123224
$329$	23.8557	1.31521
$330$	−0.802380	−0.0441696
$331$	−30.8742	−1.69700	−0.848499	−	0.529196i	$-0.822493\pi$
$331$	−30.8742	−1.69700	−0.848499	+	0.529196i	$0.822493\pi$
$332$	−1.64324	−0.0901842
$333$	−19.3100	−1.05818
$334$	16.3413	0.894159
$335$	−2.92600	−0.159864
$336$	2.50748	0.136794
$337$	−33.4365	−1.82140	−0.910702	−	0.413065i	$-0.864458\pi$
$337$	−33.4365	−1.82140	−0.910702	+	0.413065i	$0.864458\pi$
$338$	16.2732	0.885146
$339$	29.8880	1.62330
$340$	−4.27961	−0.232094
$341$	1.41386	0.0765647
$342$	−11.5510	−0.624607
$343$	−5.86761	−0.316821
$344$	−27.8510	−1.50163
$345$	−28.4932	−1.53402
$346$	−0.338636	−0.0182052
$347$	−22.2206	−1.19286	−0.596432	−	0.802664i	$-0.703415\pi$
$347$	−22.2206	−1.19286	−0.596432	+	0.802664i	$0.703415\pi$
$348$	−17.5563	−0.941116
$349$	−26.6528	−1.42669	−0.713346	−	0.700812i	$-0.752821\pi$
$349$	−26.6528	−1.42669	−0.713346	+	0.700812i	$0.752821\pi$
$350$	−4.95237	−0.264715
$351$	−0.272543	−0.0145473
$352$	1.24239	0.0662198
$353$	−28.1649	−1.49907	−0.749533	−	0.661967i	$-0.769722\pi$
$353$	−28.1649	−1.49907	−0.749533	+	0.661967i	$0.769722\pi$
$354$	−11.3881	−0.605272
$355$	−12.8228	−0.680565
$356$	2.12037	0.112380
$357$	−15.5234	−0.821586
$358$	1.97175	0.104210
$359$	24.0221	1.26784	0.633918	−	0.773400i	$-0.281446\pi$
$359$	24.0221	1.26784	0.633918	+	0.773400i	$0.281446\pi$
$360$	14.9769	0.789350
$361$	2.47106	0.130056
$362$	0.498705	0.0262114
$363$	−26.7869	−1.40595
$364$	−26.0137	−1.36349
$365$	1.20692	0.0631730
$366$	0.611060	0.0319406
$367$	32.0461	1.67279	0.836397	−	0.548124i	$-0.184658\pi$
$367$	32.0461	1.67279	0.836397	+	0.548124i	$0.184658\pi$
$368$	1.86907	0.0974322
$369$	−2.40951	−0.125434
$370$	9.86443	0.512827
$371$	36.3208	1.88568
$372$	−20.8650	−1.08180
$373$	−4.12639	−0.213656	−0.106828	−	0.994277i	$-0.534069\pi$
$373$	−4.12639	−0.213656	−0.106828	+	0.994277i	$0.534069\pi$
$374$	−0.325849	−0.0168492
$375$	29.7652	1.53707
$376$	−18.7549	−0.967211
$377$	31.4504	1.61978
$378$	−0.140495	−0.00722629
$379$	−11.4960	−0.590511	−0.295255	−	0.955418i	$-0.595405\pi$
$379$	−11.4960	−0.590511	−0.295255	+	0.955418i	$0.595405\pi$
$380$	−10.9691	−0.562705
$381$	−3.28751	−0.168424
$382$	−9.41821	−0.481877
$383$	18.7781	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$383$	18.7781	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$384$	−19.5292	−0.996593
$385$	−1.37741	−0.0701993
$386$	−1.32952	−0.0676710
$387$	30.0702	1.52856
$388$	5.03488	0.255607
$389$	−35.5687	−1.80341	−0.901703	−	0.432356i	$-0.857682\pi$
$389$	−35.5687	−1.80341	−0.901703	+	0.432356i	$0.857682\pi$
$390$	−21.2122	−1.07412
$391$	−11.5712	−0.585179
$392$	−14.7104	−0.742985
$393$	25.2206	1.27221
$394$	11.8613	0.597566
$395$	16.2988	0.820081
$396$	−0.835246	−0.0419727
$397$	−11.3296	−0.568616	−0.284308	−	0.958733i	$-0.591764\pi$
$397$	−11.3296	−0.568616	−0.284308	+	0.958733i	$0.591764\pi$
$398$	18.9857	0.951668
$399$	−39.7883	−1.99191
$400$	−0.492431	−0.0246215
$401$	−29.6003	−1.47817	−0.739085	−	0.673612i	$-0.764742\pi$
$401$	−29.6003	−1.47817	−0.739085	+	0.673612i	$0.764742\pi$
$402$	3.28774	0.163978
$403$	37.3776	1.86191
$404$	−17.6452	−0.877882
$405$	16.4893	0.819361
$406$	16.2126	0.804616
$407$	−1.39620	−0.0692071
$408$	12.2042	0.604198
$409$	36.5444	1.80701	0.903503	−	0.428582i	$-0.140987\pi$
$409$	36.5444	1.80701	0.903503	+	0.428582i	$0.140987\pi$
$410$	1.23089	0.0607891
$411$	−44.6825	−2.20403
$412$	9.74753	0.480227
$413$	−19.5495	−0.961967
$414$	15.9555	0.784172
$415$	−2.30020	−0.112912
$416$	32.8446	1.61034
$417$	−22.8869	−1.12077
$418$	−0.835188	−0.0408504
$419$	4.27013	0.208610	0.104305	−	0.994545i	$-0.466738\pi$
$419$	4.27013	0.208610	0.104305	+	0.994545i	$0.466738\pi$
$420$	20.3271	0.991859
$421$	28.4389	1.38603	0.693014	−	0.720924i	$-0.256282\pi$
$421$	28.4389	1.38603	0.693014	+	0.720924i	$0.256282\pi$
$422$	−15.8823	−0.773138
$423$	20.2493	0.984556
$424$	−28.5547	−1.38674
$425$	3.04857	0.147877
$426$	14.4081	0.698076
$427$	1.04898	0.0507637
$428$	15.1396	0.731802
$429$	3.00234	0.144955
$430$	−15.3612	−0.740783
$431$	3.68418	0.177461	0.0887304	−	0.996056i	$-0.471719\pi$
$431$	3.68418	0.177461	0.0887304	+	0.996056i	$0.471719\pi$
$432$	−0.0139699	−0.000672128 0
$433$	10.5456	0.506789	0.253394	−	0.967363i	$-0.418453\pi$
$433$	10.5456	0.506789	0.253394	+	0.967363i	$0.418453\pi$
$434$	19.2680	0.924894
$435$	−24.5753	−1.17830
$436$	−3.17367	−0.151991
$437$	−29.6582	−1.41875
$438$	−1.35613	−0.0647984
$439$	−27.3166	−1.30375	−0.651874	−	0.758327i	$-0.726017\pi$
$439$	−27.3166	−1.30375	−0.651874	+	0.758327i	$0.726017\pi$
$440$	1.08289	0.0516248
$441$	15.8825	0.756309
$442$	−8.61432	−0.409741
$443$	5.48890	0.260785	0.130393	−	0.991462i	$-0.458376\pi$
$443$	5.48890	0.260785	0.130393	+	0.991462i	$0.458376\pi$
$444$	20.6044	0.977840
$445$	2.96810	0.140701
$446$	−16.8911	−0.799819
$447$	31.7122	1.49994
$448$	14.8806	0.703042
$449$	−5.99234	−0.282796	−0.141398	−	0.989953i	$-0.545160\pi$
$449$	−5.99234	−0.282796	−0.141398	+	0.989953i	$0.545160\pi$
$450$	−4.20369	−0.198164
$451$	−0.174218	−0.00820361
$452$	−15.8935	−0.747569
$453$	−53.8908	−2.53201
$454$	21.3258	1.00087
$455$	−36.4140	−1.70711
$456$	31.2808	1.46486
$457$	19.4070	0.907819	0.453910	−	0.891048i	$-0.350029\pi$
$457$	19.4070	0.907819	0.453910	+	0.891048i	$0.350029\pi$
$458$	−12.2881	−0.574186
$459$	0.0864857	0.00403681
$460$	15.1518	0.706456
$461$	−22.1661	−1.03238	−0.516189	−	0.856475i	$-0.672650\pi$
$461$	−22.1661	−1.03238	−0.516189	+	0.856475i	$0.672650\pi$
$462$	1.54770	0.0720055
$463$	26.0730	1.21172	0.605859	−	0.795572i	$-0.292830\pi$
$463$	26.0730	1.21172	0.605859	+	0.795572i	$0.292830\pi$
$464$	1.61207	0.0748385
$465$	−29.2068	−1.35443
$466$	−17.8906	−0.828764
$467$	20.6740	0.956680	0.478340	−	0.878175i	$-0.341239\pi$
$467$	20.6740	0.956680	0.478340	+	0.878175i	$0.341239\pi$
$468$	−22.0810	−1.02070
$469$	5.64391	0.260612
$470$	−10.3443	−0.477145
$471$	4.58546	0.211287
$472$	15.3694	0.707435
$473$	2.17421	0.0999702
$474$	−18.3138	−0.841181
$475$	7.81383	0.358523
$476$	8.25488	0.378362
$477$	30.8299	1.41161
$478$	17.9323	0.820204
$479$	−6.69809	−0.306043	−0.153022	−	0.988223i	$-0.548900\pi$
$479$	−6.69809	−0.306043	−0.153022	+	0.988223i	$0.548900\pi$
$480$	−25.6647	−1.17143
$481$	−36.9107	−1.68298
$482$	−20.5522	−0.936125
$483$	54.9601	2.50077
$484$	14.2444	0.647474
$485$	7.04782	0.320025
$486$	−18.4079	−0.834998
$487$	21.8220	0.988848	0.494424	−	0.869221i	$-0.335379\pi$
$487$	21.8220	0.988848	0.494424	+	0.869221i	$0.335379\pi$
$488$	−0.824687	−0.0373318
$489$	19.2070	0.868573
$490$	−8.11349	−0.366530
$491$	−40.2083	−1.81457	−0.907286	−	0.420513i	$-0.861850\pi$
$491$	−40.2083	−1.81457	−0.907286	+	0.420513i	$0.861850\pi$
$492$	2.57102	0.115910
$493$	−9.98010	−0.449481
$494$	−22.0795	−0.993404
$495$	−1.16918	−0.0525506
$496$	1.91588	0.0860257
$497$	24.7338	1.10946
$498$	2.58458	0.115818
$499$	13.2315	0.592325	0.296163	−	0.955138i	$-0.404293\pi$
$499$	13.2315	0.592325	0.296163	+	0.955138i	$0.404293\pi$
$500$	−15.8282	−0.707860
$501$	47.7795	2.13463
$502$	−10.2506	−0.457507
$503$	−20.1686	−0.899272	−0.449636	−	0.893212i	$-0.648446\pi$
$503$	−20.1686	−0.899272	−0.449636	+	0.893212i	$0.648446\pi$
$504$	−28.8886	−1.28680
$505$	−24.6998	−1.09912
$506$	1.15366	0.0512862
$507$	47.5803	2.11311
$508$	1.74820	0.0775638
$509$	11.9672	0.530436	0.265218	−	0.964188i	$-0.414556\pi$
$509$	11.9672	0.530436	0.265218	+	0.964188i	$0.414556\pi$
$510$	6.73122	0.298063
$511$	−2.32801	−0.102985
$512$	3.29575	0.145653
$513$	0.221673	0.00978710
$514$	−12.3571	−0.545048
$515$	13.6446	0.601253
$516$	−32.0858	−1.41250
$517$	1.46411	0.0643917
$518$	−19.0274	−0.836014
$519$	−0.990117	−0.0434613
$520$	28.6279	1.25542
$521$	−2.91967	−0.127913	−0.0639566	−	0.997953i	$-0.520372\pi$
$521$	−2.91967	−0.127913	−0.0639566	+	0.997953i	$0.520372\pi$
$522$	13.7616	0.602330
$523$	6.78424	0.296654	0.148327	−	0.988938i	$-0.452611\pi$
$523$	6.78424	0.296654	0.148327	+	0.988938i	$0.452611\pi$
$524$	−13.4116	−0.585887
$525$	−14.4799	−0.631956
$526$	5.18471	0.226064
$527$	−11.8610	−0.516671
$528$	0.153893	0.00669733
$529$	17.9673	0.781186
$530$	−15.7493	−0.684106
$531$	−16.5941	−0.720121
$532$	21.1582	0.917325
$533$	−4.60573	−0.199496
$534$	−3.33505	−0.144322
$535$	21.1925	0.916231
$536$	−4.43713	−0.191655
$537$	5.76509	0.248782
$538$	−17.4626	−0.752867
$539$	1.14837	0.0494640
$540$	−0.113248	−0.00487343
$541$	13.8150	0.593953	0.296976	−	0.954885i	$-0.404022\pi$
$541$	13.8150	0.593953	0.296976	+	0.954885i	$0.404022\pi$
$542$	2.86759	0.123174
$543$	1.45813	0.0625745
$544$	−10.4225	−0.446862
$545$	−4.44250	−0.190296
$546$	40.9158	1.75104
$547$	10.4167	0.445388	0.222694	−	0.974888i	$-0.428515\pi$
$547$	10.4167	0.445388	0.222694	+	0.974888i	$0.428515\pi$
$548$	23.7608	1.01501
$549$	0.890399	0.0380013
$550$	−0.303945	−0.0129603
$551$	−25.5802	−1.08975
$552$	−43.2085	−1.83908
$553$	−31.4385	−1.33690
$554$	−19.5895	−0.832278
$555$	28.8420	1.22428
$556$	12.1705	0.516145
$557$	26.5424	1.12464	0.562319	−	0.826920i	$-0.309909\pi$
$557$	26.5424	1.12464	0.562319	+	0.826920i	$0.309909\pi$
$558$	16.3551	0.692369
$559$	57.4786	2.43108
$560$	−1.86649	−0.0788737
$561$	−0.952729	−0.0402243
$562$	22.4369	0.946442
$563$	5.66655	0.238817	0.119408	−	0.992845i	$-0.461900\pi$
$563$	5.66655	0.238817	0.119408	+	0.992845i	$0.461900\pi$
$564$	−21.6066	−0.909803
$565$	−22.2478	−0.935972
$566$	−6.47949	−0.272353
$567$	−31.8060	−1.33573
$568$	−19.4452	−0.815902
$569$	−10.9054	−0.457177	−0.228589	−	0.973523i	$-0.573411\pi$
$569$	−10.9054	−0.457177	−0.228589	+	0.973523i	$0.573411\pi$
$570$	17.2529	0.722645
$571$	15.8415	0.662948	0.331474	−	0.943464i	$-0.392454\pi$
$571$	15.8415	0.662948	0.331474	+	0.943464i	$0.392454\pi$
$572$	−1.59655	−0.0667553
$573$	−27.5373	−1.15039
$574$	−2.37424	−0.0990988
$575$	−10.7933	−0.450113
$576$	12.6310	0.526292
$577$	−38.0385	−1.58356	−0.791782	−	0.610804i	$-0.790846\pi$
$577$	−38.0385	−1.58356	−0.791782	+	0.610804i	$0.790846\pi$
$578$	−11.4852	−0.477721
$579$	−3.88732	−0.161551
$580$	13.0684	0.542636
$581$	4.43683	0.184071
$582$	−7.91915	−0.328259
$583$	2.22914	0.0923215
$584$	1.83023	0.0757356
$585$	−30.9090	−1.27793
$586$	−17.3760	−0.717795
$587$	5.46289	0.225478	0.112739	−	0.993625i	$-0.464038\pi$
$587$	5.46289	0.225478	0.112739	+	0.993625i	$0.464038\pi$
$588$	−16.9471	−0.698886
$589$	−30.4010	−1.25265
$590$	8.47699	0.348992
$591$	34.6806	1.42657
$592$	−1.89196	−0.0777589
$593$	31.1062	1.27738	0.638690	−	0.769464i	$-0.279477\pi$
$593$	31.1062	1.27738	0.638690	+	0.769464i	$0.279477\pi$
$594$	−0.00862270	−0.000353794 0
$595$	11.5552	0.473716
$596$	−16.8636	−0.690760
$597$	55.5112	2.27192
$598$	30.4987	1.24718
$599$	18.5740	0.758912	0.379456	−	0.925210i	$-0.376111\pi$
$599$	18.5740	0.758912	0.379456	+	0.925210i	$0.376111\pi$
$600$	11.3838	0.464743
$601$	−5.49417	−0.224112	−0.112056	−	0.993702i	$-0.535744\pi$
$601$	−5.49417	−0.224112	−0.112056	+	0.993702i	$0.535744\pi$
$602$	29.6300	1.20763
$603$	4.79069	0.195092
$604$	28.6575	1.16606
$605$	19.9394	0.810650
$606$	27.7534	1.12741
$607$	18.3724	0.745711	0.372856	−	0.927889i	$-0.378379\pi$
$607$	18.3724	0.745711	0.372856	+	0.927889i	$0.378379\pi$
$608$	−26.7141	−1.08340
$609$	47.4030	1.92086
$610$	−0.454855	−0.0184166
$611$	38.7062	1.56588
$612$	7.00694	0.283239
$613$	14.0057	0.565686	0.282843	−	0.959166i	$-0.408722\pi$
$613$	14.0057	0.565686	0.282843	+	0.959166i	$0.408722\pi$
$614$	−6.40000	−0.258283
$615$	3.59891	0.145122
$616$	−2.08877	−0.0841591
$617$	30.6600	1.23432	0.617162	−	0.786836i	$-0.288282\pi$
$617$	30.6600	1.23432	0.617162	+	0.786836i	$0.288282\pi$
$618$	−15.3315	−0.616723
$619$	21.8293	0.877393	0.438697	−	0.898635i	$-0.355440\pi$
$619$	21.8293	0.877393	0.438697	+	0.898635i	$0.355440\pi$
$620$	15.5313	0.623751
$621$	−0.306199	−0.0122874
$622$	−13.5976	−0.545214
$623$	−5.72512	−0.229372
$624$	4.06840	0.162866
$625$	−13.7248	−0.548992
$626$	23.0448	0.921056
$627$	−2.44196	−0.0975223
$628$	−2.43841	−0.0973031
$629$	11.7128	0.467021
$630$	−15.9335	−0.634806
$631$	24.2875	0.966869	0.483434	−	0.875381i	$-0.339389\pi$
$631$	24.2875	0.966869	0.483434	+	0.875381i	$0.339389\pi$
$632$	24.7163	0.983162
$633$	−46.4373	−1.84572
$634$	−15.7736	−0.626449
$635$	2.44713	0.0971114
$636$	−32.8964	−1.30443
$637$	30.3591	1.20287
$638$	0.995025	0.0393934
$639$	20.9946	0.830534
$640$	14.5369	0.574623
$641$	28.9285	1.14261	0.571303	−	0.820739i	$-0.306438\pi$
$641$	28.9285	1.14261	0.571303	+	0.820739i	$0.306438\pi$
$642$	−23.8125	−0.939805
$643$	8.66785	0.341827	0.170913	−	0.985286i	$-0.445328\pi$
$643$	8.66785	0.341827	0.170913	+	0.985286i	$0.445328\pi$
$644$	−29.2261	−1.15167
$645$	−44.9137	−1.76848
$646$	7.00645	0.275665
$647$	−2.08735	−0.0820623	−0.0410311	−	0.999158i	$-0.513064\pi$
$647$	−2.08735	−0.0820623	−0.0410311	+	0.999158i	$0.513064\pi$
$648$	25.0053	0.982300
$649$	−1.19982	−0.0470972
$650$	−8.03526	−0.315169
$651$	56.3366	2.20800
$652$	−10.2137	−0.400000
$653$	−39.6099	−1.55005	−0.775027	−	0.631928i	$-0.782264\pi$
$653$	−39.6099	−1.55005	−0.775027	+	0.631928i	$0.782264\pi$
$654$	4.99173	0.195192
$655$	−18.7735	−0.733541
$656$	−0.236079	−0.00921732
$657$	−1.97607	−0.0770938
$658$	19.9529	0.777845
$659$	5.48193	0.213546	0.106773	−	0.994283i	$-0.465948\pi$
$659$	5.48193	0.213546	0.106773	+	0.994283i	$0.465948\pi$
$660$	1.24755	0.0485607
$661$	1.10211	0.0428672	0.0214336	−	0.999770i	$-0.493177\pi$
$661$	1.10211	0.0428672	0.0214336	+	0.999770i	$0.493177\pi$
$662$	−25.8231	−1.00364
$663$	−25.1869	−0.978177
$664$	−3.48814	−0.135366
$665$	29.6173	1.14851
$666$	−16.1509	−0.625834
$667$	35.3342	1.36815
$668$	−25.4077	−0.983052
$669$	−49.3870	−1.90941
$670$	−2.44730	−0.0945474
$671$	0.0643797	0.00248535
$672$	49.5044	1.90967
$673$	20.2620	0.781041	0.390521	−	0.920594i	$-0.372295\pi$
$673$	20.2620	0.781041	0.390521	+	0.920594i	$0.372295\pi$
$674$	−27.9662	−1.07722
$675$	0.0806721	0.00310507
$676$	−25.3017	−0.973143
$677$	15.9278	0.612156	0.306078	−	0.952006i	$-0.400983\pi$
$677$	15.9278	0.612156	0.306078	+	0.952006i	$0.400983\pi$
$678$	24.9983	0.960054
$679$	−13.5944	−0.521707
$680$	−9.08446	−0.348373
$681$	62.3531	2.38938
$682$	1.18255	0.0452821
$683$	−13.2077	−0.505379	−0.252689	−	0.967547i	$-0.581315\pi$
$683$	−13.2077	−0.505379	−0.252689	+	0.967547i	$0.581315\pi$
$684$	17.9596	0.686702
$685$	33.2604	1.27081
$686$	−4.90766	−0.187375
$687$	−35.9285	−1.37076
$688$	2.94621	0.112323
$689$	58.9308	2.24508
$690$	−23.8316	−0.907255
$691$	22.6144	0.860291	0.430146	−	0.902759i	$-0.358462\pi$
$691$	22.6144	0.860291	0.430146	+	0.902759i	$0.358462\pi$
$692$	0.526514	0.0200151
$693$	2.25521	0.0856684
$694$	−18.5853	−0.705487
$695$	17.0363	0.646224
$696$	−37.2673	−1.41261
$697$	1.46153	0.0553593
$698$	−22.2923	−0.843778
$699$	−52.3091	−1.97851
$700$	7.69998	0.291032
$701$	−46.4758	−1.75537	−0.877684	−	0.479240i	$-0.840912\pi$
$701$	−46.4758	−1.75537	−0.877684	+	0.479240i	$0.840912\pi$
$702$	−0.227955	−0.00860359
$703$	30.0213	1.13228
$704$	0.913277	0.0344204
$705$	−30.2450	−1.13909
$706$	−23.5571	−0.886582
$707$	47.6430	1.79180
$708$	17.7064	0.665446
$709$	−36.2750	−1.36234	−0.681168	−	0.732127i	$-0.738528\pi$
$709$	−36.2750	−1.36234	−0.681168	+	0.732127i	$0.738528\pi$
$710$	−10.7250	−0.402501
$711$	−26.6857	−1.00079
$712$	4.50098	0.168681
$713$	41.9933	1.57266
$714$	−12.9838	−0.485905
$715$	−2.23486	−0.0835790
$716$	−3.06570	−0.114571
$717$	52.4311	1.95808
$718$	20.0920	0.749827
$719$	18.2777	0.681645	0.340822	−	0.940128i	$-0.389294\pi$
$719$	18.2777	0.681645	0.340822	+	0.940128i	$0.389294\pi$
$720$	−1.58432	−0.0590442
$721$	−26.3189	−0.980166
$722$	2.06679	0.0769179
$723$	−60.0912	−2.23482
$724$	−0.775391	−0.0288172
$725$	−9.30923	−0.345736
$726$	−22.4045	−0.831508
$727$	−0.813076	−0.0301553	−0.0150777	−	0.999886i	$-0.504800\pi$
$727$	−0.813076	−0.0301553	−0.0150777	+	0.999886i	$0.504800\pi$
$728$	−55.2200	−2.04659
$729$	−26.6467	−0.986916
$730$	1.00946	0.0373619
$731$	−18.2396	−0.674615
$732$	−0.950081	−0.0351160
$733$	−37.6751	−1.39156	−0.695781	−	0.718254i	$-0.744941\pi$
$733$	−37.6751	−1.39156	−0.695781	+	0.718254i	$0.744941\pi$
$734$	26.8033	0.989329
$735$	−23.7225	−0.875019
$736$	36.9006	1.36017
$737$	0.346388	0.0127594
$738$	−2.01531	−0.0741846
$739$	−1.15947	−0.0426517	−0.0213259	−	0.999773i	$-0.506789\pi$
$739$	−1.15947	−0.0426517	−0.0213259	+	0.999773i	$0.506789\pi$
$740$	−15.3373	−0.563810
$741$	−64.5569	−2.37156
$742$	30.3786	1.11523
$743$	22.3381	0.819505	0.409753	−	0.912197i	$-0.365615\pi$
$743$	22.3381	0.819505	0.409753	+	0.912197i	$0.365615\pi$
$744$	−44.2907	−1.62378
$745$	−23.6057	−0.864845
$746$	−3.45130	−0.126361
$747$	3.76608	0.137794
$748$	0.506632	0.0185243
$749$	−40.8779	−1.49365
$750$	24.8956	0.909057
$751$	15.7579	0.575015	0.287508	−	0.957778i	$-0.407173\pi$
$751$	15.7579	0.575015	0.287508	+	0.957778i	$0.407173\pi$
$752$	1.98399	0.0723485
$753$	−29.9711	−1.09221
$754$	26.3050	0.957973
$755$	40.1147	1.45992
$756$	0.218443	0.00794469
$757$	6.09282	0.221447	0.110724	−	0.993851i	$-0.464683\pi$
$757$	6.09282	0.221447	0.110724	+	0.993851i	$0.464683\pi$
$758$	−9.61524	−0.349241
$759$	3.37310	0.122436
$760$	−23.2845	−0.844618
$761$	−32.6925	−1.18510	−0.592552	−	0.805532i	$-0.701879\pi$
$761$	−32.6925	−1.18510	−0.592552	+	0.805532i	$0.701879\pi$
$762$	−2.74967	−0.0996100
$763$	8.56908	0.310222
$764$	14.6435	0.529783
$765$	9.80831	0.354620
$766$	15.7059	0.567479
$767$	−31.7192	−1.14531
$768$	−37.0620	−1.33736
$769$	−23.1267	−0.833971	−0.416986	−	0.908913i	$-0.636913\pi$
$769$	−23.1267	−0.833971	−0.416986	+	0.908913i	$0.636913\pi$
$770$	−1.15206	−0.0415174
$771$	−36.1302	−1.30120
$772$	2.06716	0.0743985
$773$	50.7828	1.82653	0.913266	−	0.407364i	$-0.133552\pi$
$773$	50.7828	1.82653	0.913266	+	0.407364i	$0.133552\pi$
$774$	25.1507	0.904022
$775$	−11.0637	−0.397418
$776$	10.6877	0.383666
$777$	−55.6330	−1.99582
$778$	−29.7496	−1.06658
$779$	3.74607	0.134217
$780$	32.9808	1.18090
$781$	1.51800	0.0543184
$782$	−9.67810	−0.346088
$783$	−0.264096	−0.00943803
$784$	1.55613	0.0555762
$785$	−3.41329	−0.121825
$786$	21.0945	0.752415
$787$	−46.9113	−1.67221	−0.836103	−	0.548572i	$-0.815172\pi$
$787$	−46.9113	−1.67221	−0.836103	+	0.548572i	$0.815172\pi$
$788$	−18.4421	−0.656973
$789$	15.1592	0.539683
$790$	13.6323	0.485014
$791$	42.9134	1.52583
$792$	−1.77300	−0.0630009
$793$	1.70198	0.0604390
$794$	−9.47604	−0.336292
$795$	−46.0485	−1.63317
$796$	−29.5192	−1.04628
$797$	10.0698	0.356692	0.178346	−	0.983968i	$-0.442925\pi$
$797$	10.0698	0.356692	0.178346	+	0.983968i	$0.442925\pi$
$798$	−33.2789	−1.17806
$799$	−12.2826	−0.434526
$800$	−9.72192	−0.343722
$801$	−4.85962	−0.171706
$802$	−24.7577	−0.874224
$803$	−0.142878	−0.00504207
$804$	−5.11181	−0.180279
$805$	−40.9107	−1.44191
$806$	31.2625	1.10118
$807$	−51.0579	−1.79732
$808$	−37.4560	−1.31770
$809$	−11.1705	−0.392733	−0.196367	−	0.980531i	$-0.562914\pi$
$809$	−11.1705	−0.392733	−0.196367	+	0.980531i	$0.562914\pi$
$810$	13.7916	0.484589
$811$	−27.3271	−0.959584	−0.479792	−	0.877382i	$-0.659288\pi$
$811$	−27.3271	−0.959584	−0.479792	+	0.877382i	$0.659288\pi$
$812$	−25.2074	−0.884608
$813$	8.38437	0.294053
$814$	−1.16778	−0.0409306
$815$	−14.2972	−0.500808
$816$	−1.29102	−0.0451947
$817$	−46.7502	−1.63558
$818$	30.5657	1.06870
$819$	59.6200	2.08329
$820$	−1.91379	−0.0668325
$821$	−4.03674	−0.140883	−0.0704415	−	0.997516i	$-0.522441\pi$
$821$	−4.03674	−0.140883	−0.0704415	+	0.997516i	$0.522441\pi$
$822$	−37.3724	−1.30351
$823$	29.9903	1.04540	0.522698	−	0.852518i	$-0.324926\pi$
$823$	29.9903	1.04540	0.522698	+	0.852518i	$0.324926\pi$
$824$	20.6914	0.720819
$825$	−0.888686	−0.0309401
$826$	−16.3512	−0.568929
$827$	29.4084	1.02263	0.511316	−	0.859393i	$-0.329158\pi$
$827$	29.4084	1.02263	0.511316	+	0.859393i	$0.329158\pi$
$828$	−24.8078	−0.862131
$829$	8.00242	0.277936	0.138968	−	0.990297i	$-0.455622\pi$
$829$	8.00242	0.277936	0.138968	+	0.990297i	$0.455622\pi$
$830$	−1.92388	−0.0667790
$831$	−57.2766	−1.98690
$832$	24.1439	0.837039
$833$	−9.63379	−0.333791
$834$	−19.1425	−0.662851
$835$	−35.5657	−1.23080
$836$	1.29856	0.0449115
$837$	−0.313868	−0.0108489
$838$	3.57153	0.123376
$839$	−27.5082	−0.949690	−0.474845	−	0.880069i	$-0.657496\pi$
$839$	−27.5082	−0.949690	−0.474845	+	0.880069i	$0.657496\pi$
$840$	43.1489	1.48878
$841$	1.47565	0.0508847
$842$	23.7863	0.819729
$843$	65.6018	2.25945
$844$	24.6939	0.850000
$845$	−35.4174	−1.21839
$846$	16.9365	0.582289
$847$	−38.4607	−1.32153
$848$	3.02065	0.103730
$849$	−18.9450	−0.650190
$850$	2.54982	0.0874579
$851$	−41.4688	−1.42153
$852$	−22.4019	−0.767475
$853$	4.68397	0.160376	0.0801880	−	0.996780i	$-0.474448\pi$
$853$	4.68397	0.160376	0.0801880	+	0.996780i	$0.474448\pi$
$854$	0.877364	0.0300228
$855$	25.1399	0.859765
$856$	32.1374	1.09843
$857$	−16.9265	−0.578199	−0.289099	−	0.957299i	$-0.593356\pi$
$857$	−16.9265	−0.578199	−0.289099	+	0.957299i	$0.593356\pi$
$858$	2.51116	0.0857294
$859$	28.6576	0.977785	0.488892	−	0.872344i	$-0.337401\pi$
$859$	28.6576	0.977785	0.488892	+	0.872344i	$0.337401\pi$
$860$	23.8837	0.814429
$861$	−6.94189	−0.236579
$862$	3.08144	0.104954
$863$	−25.7441	−0.876338	−0.438169	−	0.898893i	$-0.644373\pi$
$863$	−25.7441	−0.876338	−0.438169	+	0.898893i	$0.644373\pi$
$864$	−0.275804	−0.00938304
$865$	0.737014	0.0250592
$866$	8.82031	0.299726
$867$	−33.5809	−1.14047
$868$	−29.9581	−1.01684
$869$	−1.92950	−0.0654537
$870$	−20.5547	−0.696871
$871$	9.15730	0.310283
$872$	−6.73684	−0.228138
$873$	−11.5393	−0.390546
$874$	−24.8061	−0.839079
$875$	42.7371	1.44478
$876$	2.10852	0.0712404
$877$	12.7081	0.429120	0.214560	−	0.976711i	$-0.431168\pi$
$877$	12.7081	0.429120	0.214560	+	0.976711i	$0.431168\pi$
$878$	−22.8475	−0.771067
$879$	−50.8045	−1.71359
$880$	−0.114553	−0.00386160
$881$	23.0607	0.776933	0.388467	−	0.921463i	$-0.373005\pi$
$881$	23.0607	0.776933	0.388467	+	0.921463i	$0.373005\pi$
$882$	13.2841	0.447299
$883$	−6.42543	−0.216233	−0.108117	−	0.994138i	$-0.534482\pi$
$883$	−6.42543	−0.216233	−0.108117	+	0.994138i	$0.534482\pi$
$884$	13.3936	0.450476
$885$	24.7854	0.833151
$886$	4.59090	0.154234
$887$	−22.0777	−0.741296	−0.370648	−	0.928773i	$-0.620864\pi$
$887$	−22.0777	−0.741296	−0.370648	+	0.928773i	$0.620864\pi$
$888$	43.7375	1.46774
$889$	−4.72023	−0.158312
$890$	2.48251	0.0832140
$891$	−1.95205	−0.0653962
$892$	26.2625	0.879333
$893$	−31.4816	−1.05349
$894$	26.5240	0.887097
$895$	−4.29137	−0.143445
$896$	−28.0401	−0.936754
$897$	89.1732	2.97741
$898$	−5.01198	−0.167252
$899$	36.2191	1.20798
$900$	6.53593	0.217864
$901$	−18.7004	−0.623001
$902$	−0.145716	−0.00485180
$903$	86.6334	2.88298
$904$	−33.7377	−1.12210
$905$	−1.08539	−0.0360797
$906$	−45.0741	−1.49749
$907$	−10.9071	−0.362165	−0.181083	−	0.983468i	$-0.557960\pi$
$907$	−10.9071	−0.362165	−0.181083	+	0.983468i	$0.557960\pi$
$908$	−33.1575	−1.10037
$909$	40.4405	1.34133
$910$	−30.4566	−1.00963
$911$	19.3047	0.639594	0.319797	−	0.947486i	$-0.396385\pi$
$911$	19.3047	0.639594	0.319797	+	0.947486i	$0.396385\pi$
$912$	−3.30903	−0.109573
$913$	0.272304	0.00901196
$914$	16.2319	0.536905
$915$	−1.32992	−0.0439659
$916$	19.1057	0.631269
$917$	36.2119	1.19582
$918$	0.0723364	0.00238746
$919$	0.560673	0.0184949	0.00924745	−	0.999957i	$-0.497056\pi$
$919$	0.560673	0.0184949	0.00924745	+	0.999957i	$0.497056\pi$
$920$	32.1632	1.06039
$921$	−18.7126	−0.616600
$922$	−18.5397	−0.610572
$923$	40.1307	1.32092
$924$	−2.40637	−0.0791639
$925$	10.9255	0.359228
$926$	21.8074	0.716637
$927$	−22.3401	−0.733745
$928$	31.8267	1.04476
$929$	−53.6574	−1.76044	−0.880221	−	0.474563i	$-0.842606\pi$
$929$	−53.6574	−1.76044	−0.880221	+	0.474563i	$0.842606\pi$
$930$	−24.4285	−0.801042
$931$	−24.6925	−0.809265
$932$	27.8164	0.911156
$933$	−39.7572	−1.30159
$934$	17.2917	0.565802
$935$	0.709184	0.0231928
$936$	−46.8721	−1.53206
$937$	−13.5866	−0.443854	−0.221927	−	0.975063i	$-0.571235\pi$
$937$	−13.5866	−0.443854	−0.221927	+	0.975063i	$0.571235\pi$
$938$	4.72056	0.154132
$939$	67.3794	2.19884
$940$	16.0833	0.524581
$941$	2.14325	0.0698679	0.0349340	−	0.999390i	$-0.488878\pi$
$941$	2.14325	0.0698679	0.0349340	+	0.999390i	$0.488878\pi$
$942$	3.83527	0.124960
$943$	−5.17449	−0.168505
$944$	−1.62585	−0.0529169
$945$	0.305777	0.00994691
$946$	1.81850	0.0591246
$947$	40.9848	1.33183	0.665914	−	0.746029i	$-0.268042\pi$
$947$	40.9848	1.33183	0.665914	+	0.746029i	$0.268042\pi$
$948$	28.4745	0.924807
$949$	−3.77721	−0.122614
$950$	6.53547	0.212039
$951$	−46.1195	−1.49553
$952$	17.5229	0.567920
$953$	10.3856	0.336423	0.168211	−	0.985751i	$-0.446201\pi$
$953$	10.3856	0.336423	0.168211	+	0.985751i	$0.446201\pi$
$954$	25.7861	0.834856
$955$	20.4980	0.663299
$956$	−27.8813	−0.901745
$957$	2.90929	0.0940441
$958$	−5.60227	−0.181001
$959$	−64.1554	−2.07169
$960$	−18.8660	−0.608898
$961$	12.0450	0.388549
$962$	−30.8721	−0.995355
$963$	−34.6981	−1.11813
$964$	31.9547	1.02919
$965$	2.89361	0.0931484
$966$	45.9685	1.47901
$967$	36.1982	1.16406	0.582028	−	0.813169i	$-0.302259\pi$
$967$	36.1982	1.16406	0.582028	+	0.813169i	$0.302259\pi$
$968$	30.2371	0.971857
$969$	20.4857	0.658097
$970$	5.89479	0.189270
$971$	−39.7969	−1.27714	−0.638572	−	0.769562i	$-0.720475\pi$
$971$	−39.7969	−1.27714	−0.638572	+	0.769562i	$0.720475\pi$
$972$	28.6207	0.918010
$973$	−32.8611	−1.05348
$974$	18.2519	0.584827
$975$	−23.4938	−0.752404
$976$	0.0872393	0.00279246
$977$	24.4118	0.781003	0.390502	−	0.920602i	$-0.372302\pi$
$977$	24.4118	0.781003	0.390502	+	0.920602i	$0.372302\pi$
$978$	16.0647	0.513694
$979$	−0.351372	−0.0112299
$980$	12.6149	0.402969
$981$	7.27364	0.232229
$982$	−33.6301	−1.07318
$983$	−36.7573	−1.17237	−0.586187	−	0.810175i	$-0.699372\pi$
$983$	−36.7573	−1.17237	−0.586187	+	0.810175i	$0.699372\pi$
$984$	5.45758	0.173981
$985$	−25.8153	−0.822543
$986$	−8.34734	−0.265833
$987$	58.3391	1.85695
$988$	34.3294	1.09216
$989$	64.5766	2.05342
$990$	−0.977898	−0.0310796
$991$	−41.1901	−1.30845	−0.654223	−	0.756302i	$-0.727004\pi$
$991$	−41.1901	−1.30845	−0.654223	+	0.756302i	$0.727004\pi$
$992$	37.8247	1.20094
$993$	−75.5026	−2.39600
$994$	20.6873	0.656160
$995$	−41.3209	−1.30996
$996$	−4.01852	−0.127332
$997$	27.0415	0.856413	0.428207	−	0.903681i	$-0.359146\pi$
$997$	27.0415	0.856413	0.428207	+	0.903681i	$0.359146\pi$
$998$	11.0668	0.350314
$999$	0.309948	0.00980633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.73	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.73	✓	122	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q+0.836398 q^{2} +2.44549 q^{3} -1.30044 q^{4} -1.82035 q^{5} +2.04541 q^{6} +3.51126 q^{7} -2.76048 q^{8} +2.98044 q^{9} +O(q^{10})\)	\(q+0.836398 q^{2} +2.44549 q^{3} -1.30044 q^{4} -1.82035 q^{5} +2.04541 q^{6} +3.51126 q^{7} -2.76048 q^{8} +2.98044 q^{9} -1.52254 q^{10} +0.215499 q^{11} -3.18021 q^{12} +5.69704 q^{13} +2.93681 q^{14} -4.45166 q^{15} +0.292017 q^{16} -1.80783 q^{17} +2.49283 q^{18} -4.63369 q^{19} +2.36726 q^{20} +8.58675 q^{21} +0.180243 q^{22} +6.40057 q^{23} -6.75074 q^{24} -1.68631 q^{25} +4.76500 q^{26} -0.0478394 q^{27} -4.56617 q^{28} +5.52048 q^{29} -3.72336 q^{30} +6.56087 q^{31} +5.76520 q^{32} +0.527001 q^{33} -1.51207 q^{34} -6.39173 q^{35} -3.87588 q^{36} -6.47893 q^{37} -3.87561 q^{38} +13.9321 q^{39} +5.02505 q^{40} -0.808442 q^{41} +7.18194 q^{42} +10.0892 q^{43} -0.280243 q^{44} -5.42545 q^{45} +5.35342 q^{46} +6.79408 q^{47} +0.714125 q^{48} +5.32891 q^{49} -1.41043 q^{50} -4.42104 q^{51} -7.40865 q^{52} +10.3441 q^{53} -0.0400128 q^{54} -0.392284 q^{55} -9.69275 q^{56} -11.3317 q^{57} +4.61732 q^{58} -5.56766 q^{59} +5.78912 q^{60} +0.298748 q^{61} +5.48750 q^{62} +10.4651 q^{63} +4.23797 q^{64} -10.3706 q^{65} +0.440782 q^{66} +1.60738 q^{67} +2.35098 q^{68} +15.6525 q^{69} -5.34603 q^{70} +7.04414 q^{71} -8.22744 q^{72} -0.663013 q^{73} -5.41896 q^{74} -4.12386 q^{75} +6.02583 q^{76} +0.756671 q^{77} +11.6528 q^{78} -8.95363 q^{79} -0.531574 q^{80} -9.05830 q^{81} -0.676179 q^{82} +1.26360 q^{83} -11.1665 q^{84} +3.29090 q^{85} +8.43858 q^{86} +13.5003 q^{87} -0.594880 q^{88} -1.63051 q^{89} -4.53784 q^{90} +20.0038 q^{91} -8.32355 q^{92} +16.0446 q^{93} +5.68255 q^{94} +8.43495 q^{95} +14.0988 q^{96} -3.87168 q^{97} +4.45709 q^{98} +0.642280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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