LMFDB - Embedded newform 2671.2.a.a.1.83

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:	$1$
Dimension:	$100$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.83
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)

$f(q)$	$=$	$q+1.83621 q^{2} -3.13452 q^{3} +1.37166 q^{4} -1.62430 q^{5} -5.75564 q^{6} -0.0838203 q^{7} -1.15376 q^{8} +6.82524 q^{9} +O(q^{10})$	\(q+1.83621 q^{2} -3.13452 q^{3} +1.37166 q^{4} -1.62430 q^{5} -5.75564 q^{6} -0.0838203 q^{7} -1.15376 q^{8} +6.82524 q^{9} -2.98256 q^{10} -0.105193 q^{11} -4.29950 q^{12} +1.56218 q^{13} -0.153911 q^{14} +5.09142 q^{15} -4.86187 q^{16} +4.28053 q^{17} +12.5326 q^{18} +4.70130 q^{19} -2.22799 q^{20} +0.262737 q^{21} -0.193156 q^{22} +1.89252 q^{23} +3.61649 q^{24} -2.36164 q^{25} +2.86848 q^{26} -11.9903 q^{27} -0.114973 q^{28} -2.79796 q^{29} +9.34890 q^{30} +0.413744 q^{31} -6.61988 q^{32} +0.329729 q^{33} +7.85994 q^{34} +0.136150 q^{35} +9.36191 q^{36} +8.60096 q^{37} +8.63256 q^{38} -4.89668 q^{39} +1.87406 q^{40} -6.45932 q^{41} +0.482439 q^{42} -10.7990 q^{43} -0.144289 q^{44} -11.0863 q^{45} +3.47505 q^{46} +0.310364 q^{47} +15.2396 q^{48} -6.99297 q^{49} -4.33646 q^{50} -13.4174 q^{51} +2.14277 q^{52} -0.295681 q^{53} -22.0167 q^{54} +0.170865 q^{55} +0.0967086 q^{56} -14.7363 q^{57} -5.13763 q^{58} +10.8011 q^{59} +6.98370 q^{60} -14.5372 q^{61} +0.759719 q^{62} -0.572093 q^{63} -2.43174 q^{64} -2.53745 q^{65} +0.605451 q^{66} +13.4438 q^{67} +5.87143 q^{68} -5.93214 q^{69} +0.249999 q^{70} -3.11105 q^{71} -7.87470 q^{72} -16.3905 q^{73} +15.7932 q^{74} +7.40262 q^{75} +6.44859 q^{76} +0.00881727 q^{77} -8.99132 q^{78} +9.15910 q^{79} +7.89715 q^{80} +17.1082 q^{81} -11.8607 q^{82} -16.8886 q^{83} +0.360386 q^{84} -6.95287 q^{85} -19.8293 q^{86} +8.77026 q^{87} +0.121367 q^{88} -17.0071 q^{89} -20.3567 q^{90} -0.130942 q^{91} +2.59589 q^{92} -1.29689 q^{93} +0.569893 q^{94} -7.63633 q^{95} +20.7502 q^{96} +7.26705 q^{97} -12.8406 q^{98} -0.717965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) $ 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * 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 $

$2$	1.83621	1.29840	0.649198	−	0.760620i	$-0.275105\pi$
$2$	1.83621	1.29840	0.649198	+	0.760620i	$0.275105\pi$
$3$	−3.13452	−1.80972	−0.904859	−	0.425711i	$-0.860024\pi$
$3$	−3.13452	−1.80972	−0.904859	+	0.425711i	$0.860024\pi$
$4$	1.37166	0.685830
$5$	−1.62430	−0.726410	−0.363205	−	0.931709i	$-0.618318\pi$
$5$	−1.62430	−0.726410	−0.363205	+	0.931709i	$0.618318\pi$
$6$	−5.75564	−2.34973
$7$	−0.0838203	−0.0316811	−0.0158405	−	0.999875i	$-0.505042\pi$
$7$	−0.0838203	−0.0316811	−0.0158405	+	0.999875i	$0.505042\pi$
$8$	−1.15376	−0.407916
$9$	6.82524	2.27508
$10$	−2.98256	−0.943168
$11$	−0.105193	−0.0317168	−0.0158584	−	0.999874i	$-0.505048\pi$
$11$	−0.105193	−0.0317168	−0.0158584	+	0.999874i	$0.505048\pi$
$12$	−4.29950	−1.24116
$13$	1.56218	0.433269	0.216635	−	0.976253i	$-0.430492\pi$
$13$	1.56218	0.433269	0.216635	+	0.976253i	$0.430492\pi$
$14$	−0.153911	−0.0411346
$15$	5.09142	1.31460
$16$	−4.86187	−1.21547
$17$	4.28053	1.03818	0.519090	−	0.854719i	$-0.326271\pi$
$17$	4.28053	1.03818	0.519090	+	0.854719i	$0.326271\pi$
$18$	12.5326	2.95395
$19$	4.70130	1.07855	0.539276	−	0.842129i	$-0.318698\pi$
$19$	4.70130	1.07855	0.539276	+	0.842129i	$0.318698\pi$
$20$	−2.22799	−0.498194
$21$	0.262737	0.0573338
$22$	−0.193156	−0.0411809
$23$	1.89252	0.394617	0.197308	−	0.980341i	$-0.436780\pi$
$23$	1.89252	0.394617	0.197308	+	0.980341i	$0.436780\pi$
$24$	3.61649	0.738213
$25$	−2.36164	−0.472328
$26$	2.86848	0.562555
$27$	−11.9903	−2.30753
$28$	−0.114973	−0.0217279
$29$	−2.79796	−0.519567	−0.259784	−	0.965667i	$-0.583651\pi$
$29$	−2.79796	−0.519567	−0.259784	+	0.965667i	$0.583651\pi$
$30$	9.34890	1.70687
$31$	0.413744	0.0743105	0.0371553	−	0.999310i	$-0.488170\pi$
$31$	0.413744	0.0743105	0.0371553	+	0.999310i	$0.488170\pi$
$32$	−6.61988	−1.17024
$33$	0.329729	0.0573984
$34$	7.85994	1.34797
$35$	0.136150	0.0230135
$36$	9.36191	1.56032
$37$	8.60096	1.41399	0.706995	−	0.707219i	$-0.250050\pi$
$37$	8.60096	1.41399	0.706995	+	0.707219i	$0.250050\pi$
$38$	8.63256	1.40039
$39$	−4.89668	−0.784096
$40$	1.87406	0.296315
$41$	−6.45932	−1.00878	−0.504388	−	0.863477i	$-0.668282\pi$
$41$	−6.45932	−1.00878	−0.504388	+	0.863477i	$0.668282\pi$
$42$	0.482439	0.0744420
$43$	−10.7990	−1.64684	−0.823418	−	0.567436i	$-0.807936\pi$
$43$	−10.7990	−1.64684	−0.823418	+	0.567436i	$0.807936\pi$
$44$	−0.144289	−0.0217523
$45$	−11.0863	−1.65264
$46$	3.47505	0.512369
$47$	0.310364	0.0452712	0.0226356	−	0.999744i	$-0.492794\pi$
$47$	0.310364	0.0452712	0.0226356	+	0.999744i	$0.492794\pi$
$48$	15.2396	2.19965
$49$	−6.99297	−0.998996
$50$	−4.33646	−0.613268
$51$	−13.4174	−1.87881
$52$	2.14277	0.297149
$53$	−0.295681	−0.0406149	−0.0203075	−	0.999794i	$-0.506465\pi$
$53$	−0.295681	−0.0406149	−0.0203075	+	0.999794i	$0.506465\pi$
$54$	−22.0167	−2.99609
$55$	0.170865	0.0230394
$56$	0.0967086	0.0129232
$57$	−14.7363	−1.95187
$58$	−5.13763	−0.674604
$59$	10.8011	1.40619	0.703093	−	0.711098i	$-0.251802\pi$
$59$	10.8011	1.40619	0.703093	+	0.711098i	$0.251802\pi$
$60$	6.98370	0.901591
$61$	−14.5372	−1.86130	−0.930649	−	0.365914i	$-0.880756\pi$
$61$	−14.5372	−1.86130	−0.930649	+	0.365914i	$0.880756\pi$
$62$	0.759719	0.0964844
$63$	−0.572093	−0.0720770
$64$	−2.43174	−0.303968
$65$	−2.53745	−0.314731
$66$	0.605451	0.0745258
$67$	13.4438	1.64242	0.821211	−	0.570625i	$-0.193299\pi$
$67$	13.4438	1.64242	0.821211	+	0.570625i	$0.193299\pi$
$68$	5.87143	0.712016
$69$	−5.93214	−0.714146
$70$	0.249999	0.0298806
$71$	−3.11105	−0.369213	−0.184607	−	0.982812i	$-0.559101\pi$
$71$	−3.11105	−0.369213	−0.184607	+	0.982812i	$0.559101\pi$
$72$	−7.87470	−0.928042
$73$	−16.3905	−1.91836	−0.959182	−	0.282788i	$-0.908741\pi$
$73$	−16.3905	−1.91836	−0.959182	+	0.282788i	$0.908741\pi$
$74$	15.7932	1.83592
$75$	7.40262	0.854781
$76$	6.44859	0.739704
$77$	0.00881727	0.00100482
$78$	−8.99132	−1.01807
$79$	9.15910	1.03048	0.515239	−	0.857046i	$-0.327703\pi$
$79$	9.15910	1.03048	0.515239	+	0.857046i	$0.327703\pi$
$80$	7.89715	0.882928
$81$	17.1082	1.90091
$82$	−11.8607	−1.30979
$83$	−16.8886	−1.85376	−0.926880	−	0.375359i	$-0.877520\pi$
$83$	−16.8886	−1.85376	−0.926880	+	0.375359i	$0.877520\pi$
$84$	0.360386	0.0393213
$85$	−6.95287	−0.754145
$86$	−19.8293	−2.13824
$87$	8.77026	0.940271
$88$	0.121367	0.0129378
$89$	−17.0071	−1.80275	−0.901376	−	0.433038i	$-0.857442\pi$
$89$	−17.0071	−1.80275	−0.901376	+	0.433038i	$0.857442\pi$
$90$	−20.3567	−2.14578
$91$	−0.130942	−0.0137264
$92$	2.59589	0.270640
$93$	−1.29689	−0.134481
$94$	0.569893	0.0587800
$95$	−7.63633	−0.783471
$96$	20.7502	2.11781
$97$	7.26705	0.737857	0.368929	−	0.929458i	$-0.379725\pi$
$97$	7.26705	0.737857	0.368929	+	0.929458i	$0.379725\pi$
$98$	−12.8406	−1.29709
$99$	−0.717965	−0.0721582
$100$	−3.23937	−0.323937
$101$	−14.4630	−1.43912	−0.719559	−	0.694431i	$-0.755656\pi$
$101$	−14.4630	−1.43912	−0.719559	+	0.694431i	$0.755656\pi$
$102$	−24.6372	−2.43944
$103$	−12.9831	−1.27926	−0.639631	−	0.768682i	$-0.720913\pi$
$103$	−12.9831	−1.27926	−0.639631	+	0.768682i	$0.720913\pi$
$104$	−1.80238	−0.176738
$105$	−0.426764	−0.0416479
$106$	−0.542932	−0.0527342
$107$	12.5389	1.21218	0.606088	−	0.795397i	$-0.292738\pi$
$107$	12.5389	1.21218	0.606088	+	0.795397i	$0.292738\pi$
$108$	−16.4466	−1.58258
$109$	12.7652	1.22269	0.611343	−	0.791365i	$-0.290629\pi$
$109$	12.7652	1.22269	0.611343	+	0.791365i	$0.290629\pi$
$110$	0.313743	0.0299142
$111$	−26.9599	−2.55892
$112$	0.407523	0.0385073
$113$	−5.16512	−0.485894	−0.242947	−	0.970040i	$-0.578114\pi$
$113$	−5.16512	−0.485894	−0.242947	+	0.970040i	$0.578114\pi$
$114$	−27.0590	−2.53430
$115$	−3.07402	−0.286654
$116$	−3.83785	−0.356335
$117$	10.6622	0.985723
$118$	19.8331	1.82579
$119$	−0.358795	−0.0328907
$120$	−5.87428	−0.536246
$121$	−10.9889	−0.998994
$122$	−26.6933	−2.41670
$123$	20.2469	1.82560
$124$	0.567516	0.0509644
$125$	11.9575	1.06951
$126$	−1.05048	−0.0935844
$127$	−15.7292	−1.39574	−0.697871	−	0.716223i	$-0.745869\pi$
$127$	−15.7292	−1.39574	−0.697871	+	0.716223i	$0.745869\pi$
$128$	8.77457	0.775570
$129$	33.8498	2.98031
$130$	−4.65928	−0.408646
$131$	4.74341	0.414434	0.207217	−	0.978295i	$-0.433559\pi$
$131$	4.74341	0.414434	0.207217	+	0.978295i	$0.433559\pi$
$132$	0.452276	0.0393656
$133$	−0.394064	−0.0341697
$134$	24.6856	2.13251
$135$	19.4759	1.67622
$136$	−4.93871	−0.423491
$137$	−16.3725	−1.39880	−0.699399	−	0.714731i	$-0.746549\pi$
$137$	−16.3725	−1.39880	−0.699399	+	0.714731i	$0.746549\pi$
$138$	−10.8926	−0.927243
$139$	1.57267	0.133392	0.0666960	−	0.997773i	$-0.478754\pi$
$139$	1.57267	0.133392	0.0666960	+	0.997773i	$0.478754\pi$
$140$	0.186751	0.0157833
$141$	−0.972843	−0.0819282
$142$	−5.71253	−0.479385
$143$	−0.164329	−0.0137419
$144$	−33.1834	−2.76528
$145$	4.54473	0.377419
$146$	−30.0964	−2.49080
$147$	21.9196	1.80790
$148$	11.7976	0.969757
$149$	8.03235	0.658036	0.329018	−	0.944324i	$-0.393282\pi$
$149$	8.03235	0.658036	0.329018	+	0.944324i	$0.393282\pi$
$150$	13.5927	1.10984
$151$	15.6720	1.27537	0.637683	−	0.770299i	$-0.279893\pi$
$151$	15.6720	1.27537	0.637683	+	0.770299i	$0.279893\pi$
$152$	−5.42418	−0.439959
$153$	29.2156	2.36194
$154$	0.0161904	0.00130466
$155$	−0.672045	−0.0539799
$156$	−6.71658	−0.537757
$157$	−9.03054	−0.720715	−0.360358	−	0.932814i	$-0.617345\pi$
$157$	−9.03054	−0.720715	−0.360358	+	0.932814i	$0.617345\pi$
$158$	16.8180	1.33797
$159$	0.926819	0.0735016
$160$	10.7527	0.850075
$161$	−0.158631	−0.0125019
$162$	31.4142	2.46813
$163$	10.6650	0.835351	0.417676	−	0.908596i	$-0.362845\pi$
$163$	10.6650	0.835351	0.417676	+	0.908596i	$0.362845\pi$
$164$	−8.86000	−0.691850
$165$	−0.535579	−0.0416948
$166$	−31.0109	−2.40691
$167$	5.20020	0.402404	0.201202	−	0.979550i	$-0.435515\pi$
$167$	5.20020	0.402404	0.201202	+	0.979550i	$0.435515\pi$
$168$	−0.303135	−0.0233874
$169$	−10.5596	−0.812278
$170$	−12.7669	−0.979178
$171$	32.0875	2.45379
$172$	−14.8126	−1.12945
$173$	−19.8440	−1.50871	−0.754357	−	0.656465i	$-0.772051\pi$
$173$	−19.8440	−1.50871	−0.754357	+	0.656465i	$0.772051\pi$
$174$	16.1040	1.22084
$175$	0.197953	0.0149639
$176$	0.511433	0.0385507
$177$	−33.8564	−2.54480
$178$	−31.2286	−2.34068
$179$	11.8749	0.887572	0.443786	−	0.896133i	$-0.353635\pi$
$179$	11.8749	0.887572	0.443786	+	0.896133i	$0.353635\pi$
$180$	−15.2066	−1.13343
$181$	1.98374	0.147450	0.0737250	−	0.997279i	$-0.476511\pi$
$181$	1.98374	0.147450	0.0737250	+	0.997279i	$0.476511\pi$
$182$	−0.240437	−0.0178224
$183$	45.5672	3.36842
$184$	−2.18351	−0.160971
$185$	−13.9706	−1.02714
$186$	−2.38136	−0.174610
$187$	−0.450280	−0.0329277
$188$	0.425714	0.0310484
$189$	1.00503	0.0731052
$190$	−14.0219	−1.01726
$191$	−13.5299	−0.978990	−0.489495	−	0.872006i	$-0.662819\pi$
$191$	−13.5299	−0.978990	−0.489495	+	0.872006i	$0.662819\pi$
$192$	7.62235	0.550096
$193$	−2.27804	−0.163977	−0.0819884	−	0.996633i	$-0.526127\pi$
$193$	−2.27804	−0.163977	−0.0819884	+	0.996633i	$0.526127\pi$
$194$	13.3438	0.958030
$195$	7.95368	0.569575
$196$	−9.59199	−0.685142
$197$	20.0658	1.42963	0.714815	−	0.699314i	$-0.246511\pi$
$197$	20.0658	1.42963	0.714815	+	0.699314i	$0.246511\pi$
$198$	−1.31833	−0.0936898
$199$	0.388522	0.0275416	0.0137708	−	0.999905i	$-0.495616\pi$
$199$	0.388522	0.0275416	0.0137708	+	0.999905i	$0.495616\pi$
$200$	2.72477	0.192670
$201$	−42.1399	−2.97232
$202$	−26.5570	−1.86854
$203$	0.234525	0.0164605
$204$	−18.4041	−1.28855
$205$	10.4919	0.732786
$206$	−23.8397	−1.66099
$207$	12.9169	0.897785
$208$	−7.59509	−0.526625
$209$	−0.494542	−0.0342082
$210$	−0.783627	−0.0540754
$211$	−19.8300	−1.36516	−0.682578	−	0.730813i	$-0.739141\pi$
$211$	−19.8300	−1.36516	−0.682578	+	0.730813i	$0.739141\pi$
$212$	−0.405574	−0.0278550
$213$	9.75165	0.668172
$214$	23.0240	1.57388
$215$	17.5409	1.19628
$216$	13.8339	0.941281
$217$	−0.0346801	−0.00235424
$218$	23.4396	1.58753
$219$	51.3765	3.47170
$220$	0.234368	0.0158011
$221$	6.68693	0.449812
$222$	−49.5040	−3.32249
$223$	−22.8511	−1.53022	−0.765111	−	0.643899i	$-0.777316\pi$
$223$	−22.8511	−1.53022	−0.765111	+	0.643899i	$0.777316\pi$
$224$	0.554880	0.0370745
$225$	−16.1188	−1.07458
$226$	−9.48423	−0.630882
$227$	−21.7704	−1.44495	−0.722476	−	0.691395i	$-0.756996\pi$
$227$	−21.7704	−1.44495	−0.722476	+	0.691395i	$0.756996\pi$
$228$	−20.2132	−1.33865
$229$	−4.97008	−0.328432	−0.164216	−	0.986424i	$-0.552509\pi$
$229$	−4.97008	−0.328432	−0.164216	+	0.986424i	$0.552509\pi$
$230$	−5.64454	−0.372190
$231$	−0.0276380	−0.00181844
$232$	3.22817	0.211940
$233$	−1.26679	−0.0829901	−0.0414950	−	0.999139i	$-0.513212\pi$
$233$	−1.26679	−0.0829901	−0.0414950	+	0.999139i	$0.513212\pi$
$234$	19.5781	1.27986
$235$	−0.504125	−0.0328855
$236$	14.8155	0.964405
$237$	−28.7094	−1.86488
$238$	−0.658822	−0.0427051
$239$	−9.93534	−0.642664	−0.321332	−	0.946967i	$-0.604131\pi$
$239$	−9.93534	−0.642664	−0.321332	+	0.946967i	$0.604131\pi$
$240$	−24.7538	−1.59785
$241$	19.9444	1.28473	0.642365	−	0.766399i	$-0.277953\pi$
$241$	19.9444	1.28473	0.642365	+	0.766399i	$0.277953\pi$
$242$	−20.1780	−1.29709
$243$	−17.6551	−1.13257
$244$	−19.9401	−1.27653
$245$	11.3587	0.725681
$246$	37.1775	2.37035
$247$	7.34425	0.467304
$248$	−0.477361	−0.0303125
$249$	52.9376	3.35478
$250$	21.9565	1.38865
$251$	−1.35737	−0.0856764	−0.0428382	−	0.999082i	$-0.513640\pi$
$251$	−1.35737	−0.0856764	−0.0428382	+	0.999082i	$0.513640\pi$
$252$	−0.784718	−0.0494326
$253$	−0.199079	−0.0125160
$254$	−28.8821	−1.81223
$255$	21.7939	1.36479
$256$	20.9754	1.31096
$257$	29.1044	1.81548	0.907742	−	0.419530i	$-0.137805\pi$
$257$	29.1044	1.81548	0.907742	+	0.419530i	$0.137805\pi$
$258$	62.1553	3.86962
$259$	−0.720935	−0.0447967
$260$	−3.48052	−0.215852
$261$	−19.0967	−1.18206
$262$	8.70989	0.538099
$263$	−23.9044	−1.47401	−0.737006	−	0.675886i	$-0.763761\pi$
$263$	−23.9044	−1.47401	−0.737006	+	0.675886i	$0.763761\pi$
$264$	−0.380428	−0.0234137
$265$	0.480276	0.0295031
$266$	−0.723584	−0.0443658
$267$	53.3092	3.26247
$268$	18.4403	1.12642
$269$	−21.2361	−1.29479	−0.647395	−	0.762155i	$-0.724141\pi$
$269$	−21.2361	−1.29479	−0.647395	+	0.762155i	$0.724141\pi$
$270$	35.7618	2.17639
$271$	−5.29778	−0.321817	−0.160909	−	0.986969i	$-0.551442\pi$
$271$	−5.29778	−0.321817	−0.160909	+	0.986969i	$0.551442\pi$
$272$	−20.8114	−1.26187
$273$	0.410441	0.0248410
$274$	−30.0634	−1.81619
$275$	0.248427	0.0149807
$276$	−8.13688	−0.489783
$277$	2.69004	0.161629	0.0808144	−	0.996729i	$-0.474248\pi$
$277$	2.69004	0.161629	0.0808144	+	0.996729i	$0.474248\pi$
$278$	2.88775	0.173196
$279$	2.82390	0.169062
$280$	−0.157084	−0.00938757
$281$	−7.50836	−0.447911	−0.223956	−	0.974599i	$-0.571897\pi$
$281$	−7.50836	−0.447911	−0.223956	+	0.974599i	$0.571897\pi$
$282$	−1.78634	−0.106375
$283$	32.5941	1.93752	0.968760	−	0.247999i	$-0.0797731\pi$
$283$	32.5941	1.93752	0.968760	+	0.247999i	$0.0797731\pi$
$284$	−4.26730	−0.253218
$285$	23.9363	1.41786
$286$	−0.301743	−0.0178424
$287$	0.541422	0.0319591
$288$	−45.1823	−2.66239
$289$	1.32292	0.0778187
$290$	8.34507	0.490039
$291$	−22.7787	−1.33531
$292$	−22.4822	−1.31567
$293$	−4.31712	−0.252209	−0.126104	−	0.992017i	$-0.540247\pi$
$293$	−4.31712	−0.252209	−0.126104	+	0.992017i	$0.540247\pi$
$294$	40.2490	2.34737
$295$	−17.5443	−1.02147
$296$	−9.92346	−0.576789
$297$	1.26129	0.0731875
$298$	14.7491	0.854390
$299$	2.95644	0.170976
$300$	10.1539	0.586235
$301$	0.905177	0.0521735
$302$	28.7770	1.65593
$303$	45.3345	2.60440
$304$	−22.8571	−1.31094
$305$	23.6128	1.35207
$306$	53.6460	3.06674
$307$	13.6393	0.778436	0.389218	−	0.921146i	$-0.372745\pi$
$307$	13.6393	0.778436	0.389218	+	0.921146i	$0.372745\pi$
$308$	0.0120943	0.000689137 0
$309$	40.6958	2.31510
$310$	−1.23401	−0.0700873
$311$	−21.4135	−1.21425	−0.607124	−	0.794607i	$-0.707677\pi$
$311$	−21.4135	−1.21425	−0.607124	+	0.794607i	$0.707677\pi$
$312$	5.64960	0.319845
$313$	19.8552	1.12228	0.561141	−	0.827721i	$-0.310363\pi$
$313$	19.8552	1.12228	0.561141	+	0.827721i	$0.310363\pi$
$314$	−16.5820	−0.935774
$315$	0.929253	0.0523575
$316$	12.5632	0.706734
$317$	−14.5811	−0.818954	−0.409477	−	0.912321i	$-0.634289\pi$
$317$	−14.5811	−0.818954	−0.409477	+	0.912321i	$0.634289\pi$
$318$	1.70183	0.0954341
$319$	0.294324	0.0164790
$320$	3.94989	0.220805
$321$	−39.3033	−2.19370
$322$	−0.291280	−0.0162324
$323$	20.1240	1.11973
$324$	23.4666	1.30370
$325$	−3.68930	−0.204645
$326$	19.5833	1.08462
$327$	−40.0129	−2.21272
$328$	7.45252	0.411496
$329$	−0.0260148	−0.00143424
$330$	−0.983435	−0.0541363
$331$	26.5107	1.45716	0.728579	−	0.684962i	$-0.240181\pi$
$331$	26.5107	1.45716	0.728579	+	0.684962i	$0.240181\pi$
$332$	−23.1654	−1.27136
$333$	58.7036	3.21694
$334$	9.54866	0.522479
$335$	−21.8368	−1.19307
$336$	−1.27739	−0.0696874
$337$	32.6416	1.77810	0.889051	−	0.457808i	$-0.151365\pi$
$337$	32.6416	1.77810	0.889051	+	0.457808i	$0.151365\pi$
$338$	−19.3896	−1.05466
$339$	16.1902	0.879330
$340$	−9.53699	−0.517216
$341$	−0.0435228	−0.00235689
$342$	58.9193	3.18599
$343$	1.17289	0.0633304
$344$	12.4595	0.671771
$345$	9.63559	0.518763
$346$	−36.4378	−1.95891
$347$	−5.75890	−0.309154	−0.154577	−	0.987981i	$-0.549401\pi$
$347$	−5.75890	−0.309154	−0.154577	+	0.987981i	$0.549401\pi$
$348$	12.0298	0.644866
$349$	−5.38053	−0.288013	−0.144007	−	0.989577i	$-0.545999\pi$
$349$	−5.38053	−0.288013	−0.144007	+	0.989577i	$0.545999\pi$
$350$	0.363483	0.0194290
$351$	−18.7310	−0.999784
$352$	0.696362	0.0371162
$353$	−19.6921	−1.04810	−0.524051	−	0.851687i	$-0.675580\pi$
$353$	−19.6921	−1.04810	−0.524051	+	0.851687i	$0.675580\pi$
$354$	−62.1673	−3.30416
$355$	5.05328	0.268200
$356$	−23.3280	−1.23638
$357$	1.12465	0.0595229
$358$	21.8048	1.15242
$359$	−22.5177	−1.18844	−0.594219	−	0.804303i	$-0.702539\pi$
$359$	−22.5177	−1.18844	−0.594219	+	0.804303i	$0.702539\pi$
$360$	12.7909	0.674139
$361$	3.10220	0.163274
$362$	3.64255	0.191448
$363$	34.4451	1.80790
$364$	−0.179608	−0.00941402
$365$	26.6232	1.39352
$366$	83.6709	4.37355
$367$	−26.5820	−1.38757	−0.693785	−	0.720182i	$-0.744058\pi$
$367$	−26.5820	−1.38757	−0.693785	+	0.720182i	$0.744058\pi$
$368$	−9.20117	−0.479644
$369$	−44.0864	−2.29505
$370$	−25.6529	−1.33363
$371$	0.0247841	0.00128672
$372$	−1.77889	−0.0922312
$373$	−4.72669	−0.244739	−0.122369	−	0.992485i	$-0.539049\pi$
$373$	−4.72669	−0.244739	−0.122369	+	0.992485i	$0.539049\pi$
$374$	−0.826808	−0.0427532
$375$	−37.4812	−1.93552
$376$	−0.358086	−0.0184669
$377$	−4.37090	−0.225113
$378$	1.84545	0.0949195
$379$	−22.0726	−1.13379	−0.566896	−	0.823789i	$-0.691856\pi$
$379$	−22.0726	−1.13379	−0.566896	+	0.823789i	$0.691856\pi$
$380$	−10.4745	−0.537328
$381$	49.3036	2.52590
$382$	−24.8437	−1.27112
$383$	13.2909	0.679133	0.339566	−	0.940582i	$-0.389720\pi$
$383$	13.2909	0.679133	0.339566	+	0.940582i	$0.389720\pi$
$384$	−27.5041	−1.40356
$385$	−0.0143219	−0.000729913 0
$386$	−4.18295	−0.212907
$387$	−73.7059	−3.74668
$388$	9.96793	0.506045
$389$	6.85656	0.347641	0.173821	−	0.984777i	$-0.444389\pi$
$389$	6.85656	0.347641	0.173821	+	0.984777i	$0.444389\pi$
$390$	14.6046	0.739534
$391$	8.10097	0.409684
$392$	8.06822	0.407507
$393$	−14.8683	−0.750008
$394$	36.8450	1.85622
$395$	−14.8771	−0.748550
$396$	−0.984804	−0.0494883
$397$	7.50799	0.376815	0.188408	−	0.982091i	$-0.439667\pi$
$397$	7.50799	0.376815	0.188408	+	0.982091i	$0.439667\pi$
$398$	0.713407	0.0357598
$399$	1.23520	0.0618375
$400$	11.4820	0.574099
$401$	−19.7173	−0.984635	−0.492317	−	0.870416i	$-0.663850\pi$
$401$	−19.7173	−0.984635	−0.492317	+	0.870416i	$0.663850\pi$
$402$	−77.3777	−3.85925
$403$	0.646340	0.0321965
$404$	−19.8383	−0.986991
$405$	−27.7888	−1.38084
$406$	0.430638	0.0213722
$407$	−0.904758	−0.0448472
$408$	15.4805	0.766399
$409$	−35.5368	−1.75718	−0.878590	−	0.477577i	$-0.841515\pi$
$409$	−35.5368	−1.75718	−0.878590	+	0.477577i	$0.841515\pi$
$410$	19.2653	0.951446
$411$	51.3200	2.53143
$412$	−17.8084	−0.877357
$413$	−0.905353	−0.0445495
$414$	23.7181	1.16568
$415$	27.4321	1.34659
$416$	−10.3414	−0.507029
$417$	−4.92957	−0.241402
$418$	−0.908082	−0.0444157
$419$	−30.3875	−1.48452	−0.742262	−	0.670110i	$-0.766247\pi$
$419$	−30.3875	−1.48452	−0.742262	+	0.670110i	$0.766247\pi$
$420$	−0.585375	−0.0285634
$421$	21.1009	1.02840	0.514199	−	0.857671i	$-0.328089\pi$
$421$	21.1009	1.02840	0.514199	+	0.857671i	$0.328089\pi$
$422$	−36.4121	−1.77251
$423$	2.11831	0.102996
$424$	0.341145	0.0165675
$425$	−10.1091	−0.490362
$426$	17.9061	0.867552
$427$	1.21851	0.0589679
$428$	17.1991	0.831348
$429$	0.515094	0.0248690
$430$	32.2087	1.55324
$431$	19.5589	0.942120	0.471060	−	0.882101i	$-0.343872\pi$
$431$	19.5589	0.942120	0.471060	+	0.882101i	$0.343872\pi$
$432$	58.2953	2.80473
$433$	15.7638	0.757561	0.378780	−	0.925487i	$-0.376344\pi$
$433$	15.7638	0.757561	0.378780	+	0.925487i	$0.376344\pi$
$434$	−0.0636799	−0.00305673
$435$	−14.2456	−0.683022
$436$	17.5096	0.838556
$437$	8.89728	0.425615
$438$	94.3379	4.50764
$439$	8.24970	0.393737	0.196868	−	0.980430i	$-0.436923\pi$
$439$	8.24970	0.393737	0.196868	+	0.980430i	$0.436923\pi$
$440$	−0.197137	−0.00939814
$441$	−47.7287	−2.27280
$442$	12.2786	0.584034
$443$	29.5672	1.40478	0.702390	−	0.711793i	$-0.252116\pi$
$443$	29.5672	1.40478	0.702390	+	0.711793i	$0.252116\pi$
$444$	−36.9799	−1.75499
$445$	27.6247	1.30954
$446$	−41.9593	−1.98683
$447$	−25.1776	−1.19086
$448$	0.203829	0.00963003
$449$	−5.35407	−0.252674	−0.126337	−	0.991987i	$-0.540322\pi$
$449$	−5.35407	−0.252674	−0.126337	+	0.991987i	$0.540322\pi$
$450$	−29.5974	−1.39523
$451$	0.679473	0.0319951
$452$	−7.08479	−0.333241
$453$	−49.1241	−2.30805
$454$	−39.9750	−1.87612
$455$	0.212689	0.00997103
$456$	17.0022	0.796201
$457$	15.6128	0.730337	0.365168	−	0.930942i	$-0.381011\pi$
$457$	15.6128	0.730337	0.365168	+	0.930942i	$0.381011\pi$
$458$	−9.12611	−0.426435
$459$	−51.3248	−2.39564
$460$	−4.21651	−0.196596
$461$	−17.2659	−0.804155	−0.402078	−	0.915606i	$-0.631712\pi$
$461$	−17.2659	−0.804155	−0.402078	+	0.915606i	$0.631712\pi$
$462$	−0.0507490	−0.00236106
$463$	9.68339	0.450025	0.225013	−	0.974356i	$-0.427758\pi$
$463$	9.68339	0.450025	0.225013	+	0.974356i	$0.427758\pi$
$464$	13.6033	0.631517
$465$	2.10654	0.0976885
$466$	−2.32609	−0.107754
$467$	15.5215	0.718247	0.359124	−	0.933290i	$-0.383076\pi$
$467$	15.5215	0.718247	0.359124	+	0.933290i	$0.383076\pi$
$468$	14.6250	0.676039
$469$	−1.12686	−0.0520337
$470$	−0.925679	−0.0426984
$471$	28.3064	1.30429
$472$	−12.4619	−0.573606
$473$	1.13598	0.0522323
$474$	−52.7164	−2.42135
$475$	−11.1028	−0.509430
$476$	−0.492145	−0.0225574
$477$	−2.01809	−0.0924022
$478$	−18.2434	−0.834432
$479$	0.0111021	0.000507266 0	0.000253633	−	1.00000i	$-0.499919\pi$
$479$	0.0111021	0.000507266 0	0.000253633		1.00000i	$0.499919\pi$
$480$	−33.7046	−1.53840
$481$	13.4362	0.612639
$482$	36.6220	1.66809
$483$	0.497233	0.0226249
$484$	−15.0731	−0.685141
$485$	−11.8039	−0.535987
$486$	−32.4184	−1.47053
$487$	−7.88763	−0.357423	−0.178711	−	0.983902i	$-0.557193\pi$
$487$	−7.88763	−0.357423	−0.178711	+	0.983902i	$0.557193\pi$
$488$	16.7725	0.759253
$489$	−33.4299	−1.51175
$490$	20.8570	0.942221
$491$	−30.4198	−1.37283	−0.686414	−	0.727211i	$-0.740816\pi$
$491$	−30.4198	−1.37283	−0.686414	+	0.727211i	$0.740816\pi$
$492$	27.7719	1.25205
$493$	−11.9767	−0.539405
$494$	13.4856	0.606745
$495$	1.16619	0.0524164
$496$	−2.01157	−0.0903220
$497$	0.260769	0.0116971
$498$	97.2044	4.35583
$499$	20.6899	0.926206	0.463103	−	0.886305i	$-0.346736\pi$
$499$	20.6899	0.926206	0.463103	+	0.886305i	$0.346736\pi$
$500$	16.4017	0.733505
$501$	−16.3002	−0.728238
$502$	−2.49241	−0.111242
$503$	22.4461	1.00082	0.500412	−	0.865788i	$-0.333182\pi$
$503$	22.4461	1.00082	0.500412	+	0.865788i	$0.333182\pi$
$504$	0.660059	0.0294014
$505$	23.4922	1.04539
$506$	−0.365550	−0.0162507
$507$	33.0993	1.46999
$508$	−21.5752	−0.957243
$509$	−15.9686	−0.707797	−0.353898	−	0.935284i	$-0.615144\pi$
$509$	−15.9686	−0.707797	−0.353898	+	0.935284i	$0.615144\pi$
$510$	40.0182	1.77204
$511$	1.37386	0.0607759
$512$	20.9661	0.926580
$513$	−56.3700	−2.48880
$514$	53.4418	2.35722
$515$	21.0885	0.929269
$516$	46.4304	2.04399
$517$	−0.0326480	−0.00143586
$518$	−1.32379	−0.0581639
$519$	62.2016	2.73035
$520$	2.92761	0.128384
$521$	15.7899	0.691766	0.345883	−	0.938278i	$-0.387579\pi$
$521$	15.7899	0.691766	0.345883	+	0.938278i	$0.387579\pi$
$522$	−35.0656	−1.53478
$523$	−32.1926	−1.40769	−0.703843	−	0.710356i	$-0.748534\pi$
$523$	−32.1926	−1.40769	−0.703843	+	0.710356i	$0.748534\pi$
$524$	6.50635	0.284231
$525$	−0.620489	−0.0270804
$526$	−43.8935	−1.91385
$527$	1.77104	0.0771477
$528$	−1.60310	−0.0697659
$529$	−19.4184	−0.844277
$530$	0.881886	0.0383067
$531$	73.7202	3.19918
$532$	−0.540522	−0.0234346
$533$	−10.0906	−0.437072
$534$	97.8869	4.23598
$535$	−20.3669	−0.880538
$536$	−15.5109	−0.669970
$537$	−37.2222	−1.60626
$538$	−38.9939	−1.68115
$539$	0.735609	0.0316849
$540$	26.7143	1.14960
$541$	−39.6904	−1.70642	−0.853211	−	0.521565i	$-0.825348\pi$
$541$	−39.6904	−1.70642	−0.853211	+	0.521565i	$0.825348\pi$
$542$	−9.72784	−0.417846
$543$	−6.21807	−0.266843
$544$	−28.3366	−1.21492
$545$	−20.7346	−0.888172
$546$	0.753655	0.0322534
$547$	12.3402	0.527628	0.263814	−	0.964574i	$-0.415020\pi$
$547$	12.3402	0.527628	0.263814	+	0.964574i	$0.415020\pi$
$548$	−22.4575	−0.959339
$549$	−99.2198	−4.23460
$550$	0.456164	0.0194509
$551$	−13.1540	−0.560380
$552$	6.84427	0.291312
$553$	−0.767718	−0.0326467
$554$	4.93947	0.209858
$555$	43.7911	1.85883
$556$	2.15717	0.0914843
$557$	18.1157	0.767585	0.383793	−	0.923419i	$-0.374618\pi$
$557$	18.1157	0.767585	0.383793	+	0.923419i	$0.374618\pi$
$558$	5.18527	0.219510
$559$	−16.8700	−0.713524
$560$	−0.661941	−0.0279721
$561$	1.41141	0.0595899
$562$	−13.7869	−0.581566
$563$	−5.82289	−0.245406	−0.122703	−	0.992443i	$-0.539156\pi$
$563$	−5.82289	−0.245406	−0.122703	+	0.992443i	$0.539156\pi$
$564$	−1.33441	−0.0561888
$565$	8.38972	0.352958
$566$	59.8496	2.51567
$567$	−1.43401	−0.0602228
$568$	3.58941	0.150608
$569$	−21.5416	−0.903069	−0.451535	−	0.892254i	$-0.649123\pi$
$569$	−21.5416	−0.903069	−0.451535	+	0.892254i	$0.649123\pi$
$570$	43.9520	1.84095
$571$	16.2384	0.679556	0.339778	−	0.940506i	$-0.389648\pi$
$571$	16.2384	0.679556	0.339778	+	0.940506i	$0.389648\pi$
$572$	−0.225404	−0.00942462
$573$	42.4098	1.77170
$574$	0.994164	0.0414956
$575$	−4.46944	−0.186389
$576$	−16.5972	−0.691551
$577$	−12.8132	−0.533418	−0.266709	−	0.963777i	$-0.585936\pi$
$577$	−12.8132	−0.533418	−0.266709	+	0.963777i	$0.585936\pi$
$578$	2.42915	0.101039
$579$	7.14056	0.296752
$580$	6.23383	0.258846
$581$	1.41560	0.0587291
$582$	−41.8265	−1.73376
$583$	0.0311035	0.00128817
$584$	18.9107	0.782532
$585$	−17.3187	−0.716039
$586$	−7.92714	−0.327467
$587$	20.9216	0.863526	0.431763	−	0.901987i	$-0.357892\pi$
$587$	20.9216	0.863526	0.431763	+	0.901987i	$0.357892\pi$
$588$	30.0663	1.23991
$589$	1.94513	0.0801477
$590$	−32.2150	−1.32627
$591$	−62.8968	−2.58723
$592$	−41.8168	−1.71866
$593$	−15.1565	−0.622401	−0.311201	−	0.950344i	$-0.600731\pi$
$593$	−15.1565	−0.622401	−0.311201	+	0.950344i	$0.600731\pi$
$594$	2.31599	0.0950264
$595$	0.582792	0.0238921
$596$	11.0177	0.451301
$597$	−1.21783	−0.0498425
$598$	5.42864	0.221994
$599$	−4.40010	−0.179783	−0.0898916	−	0.995952i	$-0.528652\pi$
$599$	−4.40010	−0.179783	−0.0898916	+	0.995952i	$0.528652\pi$
$600$	−8.54085	−0.348679
$601$	0.555161	0.0226455	0.0113227	−	0.999936i	$-0.496396\pi$
$601$	0.555161	0.0226455	0.0113227	+	0.999936i	$0.496396\pi$
$602$	1.66209	0.0677419
$603$	91.7571	3.73664
$604$	21.4966	0.874685
$605$	17.8494	0.725680
$606$	83.2436	3.38154
$607$	−0.580343	−0.0235554	−0.0117777	−	0.999931i	$-0.503749\pi$
$607$	−0.580343	−0.0235554	−0.0117777	+	0.999931i	$0.503749\pi$
$608$	−31.1220	−1.26216
$609$	−0.735126	−0.0297888
$610$	43.3580	1.75552
$611$	0.484843	0.0196146
$612$	40.0739	1.61989
$613$	−36.8733	−1.48930	−0.744648	−	0.667457i	$-0.767383\pi$
$613$	−36.8733	−1.48930	−0.744648	+	0.667457i	$0.767383\pi$
$614$	25.0446	1.01072
$615$	−32.8871	−1.32614
$616$	−0.0101730	−0.000409883 0
$617$	1.07856	0.0434211	0.0217106	−	0.999764i	$-0.493089\pi$
$617$	1.07856	0.0434211	0.0217106	+	0.999764i	$0.493089\pi$
$618$	74.7260	3.00592
$619$	−20.8928	−0.839752	−0.419876	−	0.907582i	$-0.637926\pi$
$619$	−20.8928	−0.839752	−0.419876	+	0.907582i	$0.637926\pi$
$620$	−0.921818	−0.0370211
$621$	−22.6918	−0.910592
$622$	−39.3197	−1.57657
$623$	1.42554	0.0571131
$624$	23.8070	0.953042
$625$	−7.61446	−0.304578
$626$	36.4582	1.45716
$627$	1.55015	0.0619071
$628$	−12.3868	−0.494289
$629$	36.8167	1.46798
$630$	1.70630	0.0679807
$631$	39.5037	1.57262	0.786309	−	0.617833i	$-0.211989\pi$
$631$	39.5037	1.57262	0.786309	+	0.617833i	$0.211989\pi$
$632$	−10.5674	−0.420349
$633$	62.1577	2.47055
$634$	−26.7739	−1.06333
$635$	25.5490	1.01388
$636$	1.27128	0.0504096
$637$	−10.9243	−0.432835
$638$	0.540441	0.0213963
$639$	−21.2336	−0.839990
$640$	−14.2526	−0.563382
$641$	39.7835	1.57135	0.785676	−	0.618638i	$-0.212315\pi$
$641$	39.7835	1.57135	0.785676	+	0.618638i	$0.212315\pi$
$642$	−72.1691	−2.84829
$643$	45.1790	1.78169	0.890843	−	0.454312i	$-0.150115\pi$
$643$	45.1790	1.78169	0.890843	+	0.454312i	$0.150115\pi$
$644$	−0.217588	−0.00857418
$645$	−54.9823	−2.16493
$646$	36.9519	1.45385
$647$	26.9210	1.05837	0.529186	−	0.848506i	$-0.322497\pi$
$647$	26.9210	1.05837	0.529186	+	0.848506i	$0.322497\pi$
$648$	−19.7387	−0.775411
$649$	−1.13620	−0.0445997
$650$	−6.77432	−0.265711
$651$	0.108706	0.00426051
$652$	14.6288	0.572909
$653$	−37.5612	−1.46988	−0.734941	−	0.678131i	$-0.762790\pi$
$653$	−37.5612	−1.46988	−0.734941	+	0.678131i	$0.762790\pi$
$654$	−73.4720	−2.87298
$655$	−7.70474	−0.301049
$656$	31.4044	1.22613
$657$	−111.869	−4.36443
$658$	−0.0477686	−0.00186221
$659$	12.9039	0.502664	0.251332	−	0.967901i	$-0.419131\pi$
$659$	12.9039	0.502664	0.251332	+	0.967901i	$0.419131\pi$
$660$	−0.734633	−0.0285956
$661$	2.33642	0.0908763	0.0454381	−	0.998967i	$-0.485532\pi$
$661$	2.33642	0.0908763	0.0454381	+	0.998967i	$0.485532\pi$
$662$	48.6791	1.89197
$663$	−20.9604	−0.814033
$664$	19.4854	0.756179
$665$	0.640079	0.0248212
$666$	107.792	4.17686
$667$	−5.29518	−0.205030
$668$	7.13292	0.275981
$669$	71.6272	2.76927
$670$	−40.0969	−1.54908
$671$	1.52921	0.0590343
$672$	−1.73928	−0.0670944
$673$	−4.37419	−0.168613	−0.0843064	−	0.996440i	$-0.526867\pi$
$673$	−4.37419	−0.168613	−0.0843064	+	0.996440i	$0.526867\pi$
$674$	59.9368	2.30868
$675$	28.3168	1.08991
$676$	−14.4842	−0.557085
$677$	−8.51759	−0.327357	−0.163679	−	0.986514i	$-0.552336\pi$
$677$	−8.51759	−0.327357	−0.163679	+	0.986514i	$0.552336\pi$
$678$	29.7286	1.14172
$679$	−0.609126	−0.0233761
$680$	8.02196	0.307628
$681$	68.2399	2.61496
$682$	−0.0799169	−0.00306017
$683$	−7.44998	−0.285065	−0.142533	−	0.989790i	$-0.545525\pi$
$683$	−7.44998	−0.285065	−0.142533	+	0.989790i	$0.545525\pi$
$684$	44.0131	1.68288
$685$	26.5939	1.01610
$686$	2.15368	0.0822279
$687$	15.5788	0.594370
$688$	52.5034	2.00167
$689$	−0.461906	−0.0175972
$690$	17.6929	0.673559
$691$	−3.19339	−0.121482	−0.0607412	−	0.998154i	$-0.519346\pi$
$691$	−3.19339	−0.121482	−0.0607412	+	0.998154i	$0.519346\pi$
$692$	−27.2193	−1.03472
$693$	0.0601800	0.00228605
$694$	−10.5745	−0.401404
$695$	−2.55449	−0.0968974
$696$	−10.1188	−0.383552
$697$	−27.6493	−1.04729
$698$	−9.87978	−0.373955
$699$	3.97078	0.150189
$700$	0.271525	0.0102627
$701$	−40.7399	−1.53872	−0.769362	−	0.638813i	$-0.779426\pi$
$701$	−40.7399	−1.53872	−0.769362	+	0.638813i	$0.779426\pi$
$702$	−34.3939	−1.29812
$703$	40.4357	1.52506
$704$	0.255801	0.00964087
$705$	1.58019	0.0595135
$706$	−36.1587	−1.36085
$707$	1.21229	0.0455928
$708$	−46.4394	−1.74530
$709$	39.4880	1.48300	0.741501	−	0.670952i	$-0.234114\pi$
$709$	39.4880	1.48300	0.741501	+	0.670952i	$0.234114\pi$
$710$	9.27888	0.348230
$711$	62.5130	2.34442
$712$	19.6222	0.735372
$713$	0.783016	0.0293242
$714$	2.06509	0.0772842
$715$	0.266921	0.00998226
$716$	16.2883	0.608724
$717$	31.1426	1.16304
$718$	−41.3472	−1.54306
$719$	−51.6607	−1.92662	−0.963309	−	0.268395i	$-0.913507\pi$
$719$	−51.6607	−1.92662	−0.963309	+	0.268395i	$0.913507\pi$
$720$	53.8999	2.00873
$721$	1.08825	0.0405284
$722$	5.69628	0.211994
$723$	−62.5161	−2.32500
$724$	2.72101	0.101126
$725$	6.60777	0.245406
$726$	63.2483	2.34737
$727$	41.2738	1.53076	0.765381	−	0.643577i	$-0.222551\pi$
$727$	41.2738	1.53076	0.765381	+	0.643577i	$0.222551\pi$
$728$	0.151076	0.00559924
$729$	4.01568	0.148729
$730$	48.8857	1.80934
$731$	−46.2255	−1.70971
$732$	62.5027	2.31017
$733$	−26.4858	−0.978276	−0.489138	−	0.872207i	$-0.662688\pi$
$733$	−26.4858	−0.978276	−0.489138	+	0.872207i	$0.662688\pi$
$734$	−48.8101	−1.80161
$735$	−35.6041	−1.31328
$736$	−12.5282	−0.461797
$737$	−1.41419	−0.0520923
$738$	−80.9519	−2.97988
$739$	−12.9719	−0.477180	−0.238590	−	0.971120i	$-0.576685\pi$
$739$	−12.9719	−0.477180	−0.238590	+	0.971120i	$0.576685\pi$
$740$	−19.1629	−0.704442
$741$	−23.0207	−0.845688
$742$	0.0455087	0.00167068
$743$	−3.80111	−0.139449	−0.0697246	−	0.997566i	$-0.522212\pi$
$743$	−3.80111	−0.139449	−0.0697246	+	0.997566i	$0.522212\pi$
$744$	1.49630	0.0548570
$745$	−13.0470	−0.478004
$746$	−8.67919	−0.317768
$747$	−115.268	−4.21745
$748$	−0.617631	−0.0225828
$749$	−1.05101	−0.0384031
$750$	−68.8232	−2.51307
$751$	13.7722	0.502556	0.251278	−	0.967915i	$-0.419149\pi$
$751$	13.7722	0.502556	0.251278	+	0.967915i	$0.419149\pi$
$752$	−1.50895	−0.0550257
$753$	4.25470	0.155050
$754$	−8.02588	−0.292285
$755$	−25.4560	−0.926439
$756$	1.37856	0.0501378
$757$	28.8911	1.05006	0.525032	−	0.851083i	$-0.324054\pi$
$757$	28.8911	1.05006	0.525032	+	0.851083i	$0.324054\pi$
$758$	−40.5299	−1.47211
$759$	0.624017	0.0226504
$760$	8.81050	0.319591
$761$	−2.19773	−0.0796675	−0.0398338	−	0.999206i	$-0.512683\pi$
$761$	−2.19773	−0.0796675	−0.0398338	+	0.999206i	$0.512683\pi$
$762$	90.5317	3.27962
$763$	−1.06998	−0.0387360
$764$	−18.5584	−0.671421
$765$	−47.4550	−1.71574
$766$	24.4048	0.881783
$767$	16.8732	0.609257
$768$	−65.7480	−2.37248
$769$	−13.2801	−0.478893	−0.239447	−	0.970910i	$-0.576966\pi$
$769$	−13.2801	−0.478893	−0.239447	+	0.970910i	$0.576966\pi$
$770$	−0.0262980	−0.000947715 0
$771$	−91.2285	−3.28551
$772$	−3.12470	−0.112460
$773$	41.8762	1.50618	0.753090	−	0.657917i	$-0.228562\pi$
$773$	41.8762	1.50618	0.753090	+	0.657917i	$0.228562\pi$
$774$	−135.339	−4.86467
$775$	−0.977113	−0.0350989
$776$	−8.38444	−0.300984
$777$	2.25979	0.0810695
$778$	12.5901	0.451376
$779$	−30.3672	−1.08802
$780$	10.9098	0.390632
$781$	0.327259	0.0117103
$782$	14.8751	0.531931
$783$	33.5483	1.19892
$784$	33.9989	1.21425
$785$	14.6683	0.523535
$786$	−27.3014	−0.973807
$787$	−10.2471	−0.365269	−0.182634	−	0.983181i	$-0.558462\pi$
$787$	−10.2471	−0.365269	−0.182634	+	0.983181i	$0.558462\pi$
$788$	27.5235	0.980484
$789$	74.9291	2.66755
$790$	−27.3175	−0.971914
$791$	0.432942	0.0153936
$792$	0.828360	0.0294345
$793$	−22.7097	−0.806443
$794$	13.7862	0.489255
$795$	−1.50544	−0.0533923
$796$	0.532920	0.0188888
$797$	−35.2544	−1.24878	−0.624388	−	0.781114i	$-0.714652\pi$
$797$	−35.2544	−1.24878	−0.624388	+	0.781114i	$0.714652\pi$
$798$	2.26809	0.0802895
$799$	1.32852	0.0469997
$800$	15.6338	0.552737
$801$	−116.078	−4.10140
$802$	−36.2051	−1.27845
$803$	1.72416	0.0608443
$804$	−57.8017	−2.03851
$805$	0.257665	0.00908151
$806$	1.18681	0.0418038
$807$	66.5651	2.34320
$808$	16.6868	0.587040
$809$	24.4444	0.859419	0.429710	−	0.902967i	$-0.358616\pi$
$809$	24.4444	0.859419	0.429710	+	0.902967i	$0.358616\pi$
$810$	−51.0261	−1.79287
$811$	6.70508	0.235447	0.117724	−	0.993046i	$-0.462440\pi$
$811$	6.70508	0.235447	0.117724	+	0.993046i	$0.462440\pi$
$812$	0.321689	0.0112891
$813$	16.6060	0.582399
$814$	−1.66132	−0.0582294
$815$	−17.3233	−0.606808
$816$	65.2337	2.28364
$817$	−50.7694	−1.77620
$818$	−65.2529	−2.28151
$819$	−0.893710	−0.0312288
$820$	14.3913	0.502567
$821$	−43.5300	−1.51921	−0.759603	−	0.650387i	$-0.774607\pi$
$821$	−43.5300	−1.51921	−0.759603	+	0.650387i	$0.774607\pi$
$822$	94.2343	3.28680
$823$	−2.51483	−0.0876614	−0.0438307	−	0.999039i	$-0.513956\pi$
$823$	−2.51483	−0.0876614	−0.0438307	+	0.999039i	$0.513956\pi$
$824$	14.9794	0.521832
$825$	−0.778701	−0.0271109
$826$	−1.66242	−0.0578429
$827$	−9.69393	−0.337091	−0.168545	−	0.985694i	$-0.553907\pi$
$827$	−9.69393	−0.337091	−0.168545	+	0.985694i	$0.553907\pi$
$828$	17.7176	0.615728
$829$	7.25243	0.251887	0.125944	−	0.992037i	$-0.459804\pi$
$829$	7.25243	0.251887	0.125944	+	0.992037i	$0.459804\pi$
$830$	50.3711	1.74841
$831$	−8.43200	−0.292503
$832$	−3.79881	−0.131700
$833$	−29.9336	−1.03714
$834$	−9.05172	−0.313435
$835$	−8.44671	−0.292310
$836$	−0.678344	−0.0234610
$837$	−4.96091	−0.171474
$838$	−55.7977	−1.92750
$839$	8.32760	0.287501	0.143750	−	0.989614i	$-0.454084\pi$
$839$	8.32760	0.287501	0.143750	+	0.989614i	$0.454084\pi$
$840$	0.492384	0.0169889
$841$	−21.1714	−0.730050
$842$	38.7457	1.33527
$843$	23.5351	0.810593
$844$	−27.2001	−0.936265
$845$	17.1520	0.590047
$846$	3.88965	0.133729
$847$	0.921095	0.0316492
$848$	1.43756	0.0493661
$849$	−102.167	−3.50637
$850$	−18.5623	−0.636683
$851$	16.2775	0.557984
$852$	13.3760	0.458253
$853$	35.9781	1.23187	0.615934	−	0.787798i	$-0.288779\pi$
$853$	35.9781	1.23187	0.615934	+	0.787798i	$0.288779\pi$
$854$	2.23744	0.0765637
$855$	−52.1198	−1.78246
$856$	−14.4668	−0.494467
$857$	−22.9011	−0.782286	−0.391143	−	0.920330i	$-0.627920\pi$
$857$	−22.9011	−0.782286	−0.391143	+	0.920330i	$0.627920\pi$
$858$	0.945820	0.0322898
$859$	−38.0294	−1.29755	−0.648774	−	0.760981i	$-0.724718\pi$
$859$	−38.0294	−1.29755	−0.648774	+	0.760981i	$0.724718\pi$
$860$	24.0601	0.820444
$861$	−1.69710	−0.0578370
$862$	35.9142	1.22324
$863$	42.9950	1.46357	0.731783	−	0.681538i	$-0.238689\pi$
$863$	42.9950	1.46357	0.731783	+	0.681538i	$0.238689\pi$
$864$	79.3744	2.70037
$865$	32.2327	1.09595
$866$	28.9457	0.983614
$867$	−4.14672	−0.140830
$868$	−0.0475693	−0.00161461
$869$	−0.963469	−0.0326835
$870$	−26.1578	−0.886833
$871$	21.0016	0.711611
$872$	−14.7280	−0.498754
$873$	49.5994	1.67868
$874$	16.3373	0.552616
$875$	−1.00228	−0.0338834
$876$	70.4711	2.38100
$877$	34.7462	1.17329	0.586647	−	0.809843i	$-0.300448\pi$
$877$	34.7462	1.17329	0.586647	+	0.809843i	$0.300448\pi$
$878$	15.1482	0.511226
$879$	13.5321	0.456427
$880$	−0.830722	−0.0280036
$881$	−24.8569	−0.837449	−0.418724	−	0.908113i	$-0.637523\pi$
$881$	−24.8569	−0.837449	−0.418724	+	0.908113i	$0.637523\pi$
$882$	−87.6399	−2.95099
$883$	−3.90556	−0.131433	−0.0657163	−	0.997838i	$-0.520933\pi$
$883$	−3.90556	−0.131433	−0.0657163	+	0.997838i	$0.520933\pi$
$884$	9.17221	0.308495
$885$	54.9930	1.84857
$886$	54.2915	1.82396
$887$	−39.1417	−1.31425	−0.657125	−	0.753782i	$-0.728228\pi$
$887$	−39.1417	−1.31425	−0.657125	+	0.753782i	$0.728228\pi$
$888$	31.1053	1.04383
$889$	1.31843	0.0442186
$890$	50.7247	1.70030
$891$	−1.79965	−0.0602906
$892$	−31.3439	−1.04947
$893$	1.45911	0.0488274
$894$	−46.2313	−1.54621
$895$	−19.2884	−0.644742
$896$	−0.735487	−0.0245709
$897$	−9.26704	−0.309417
$898$	−9.83118	−0.328071
$899$	−1.15764	−0.0386093
$900$	−22.1095	−0.736982
$901$	−1.26567	−0.0421656
$902$	1.24765	0.0415423
$903$	−2.83730	−0.0944194
$904$	5.95931	0.198204
$905$	−3.22219	−0.107109
$906$	−90.2021	−2.99676
$907$	2.15744	0.0716367	0.0358183	−	0.999358i	$-0.488596\pi$
$907$	2.15744	0.0716367	0.0358183	+	0.999358i	$0.488596\pi$
$908$	−29.8616	−0.990993
$909$	−98.7131	−3.27411
$910$	0.390542	0.0129463
$911$	9.38288	0.310869	0.155434	−	0.987846i	$-0.450322\pi$
$911$	9.38288	0.310869	0.155434	+	0.987846i	$0.450322\pi$
$912$	71.6461	2.37244
$913$	1.77655	0.0587953
$914$	28.6684	0.948266
$915$	−74.0149	−2.44686
$916$	−6.81727	−0.225249
$917$	−0.397594	−0.0131297
$918$	−94.2431	−3.11048
$919$	−42.3369	−1.39656	−0.698282	−	0.715823i	$-0.746052\pi$
$919$	−42.3369	−1.39656	−0.698282	+	0.715823i	$0.746052\pi$
$920$	3.54669	0.116931
$921$	−42.7527	−1.40875
$922$	−31.7039	−1.04411
$923$	−4.86000	−0.159969
$924$	−0.0379099	−0.00124714
$925$	−20.3124	−0.667867
$926$	17.7807	0.584311
$927$	−88.6127	−2.91042
$928$	18.5221	0.608019
$929$	−50.1017	−1.64378	−0.821891	−	0.569645i	$-0.807081\pi$
$929$	−50.1017	−1.64378	−0.821891	+	0.569645i	$0.807081\pi$
$930$	3.86805	0.126838
$931$	−32.8761	−1.07747
$932$	−1.73760	−0.0569171
$933$	67.1211	2.19745
$934$	28.5006	0.932569
$935$	0.731391	0.0239190
$936$	−12.3017	−0.402092
$937$	11.5667	0.377868	0.188934	−	0.981990i	$-0.439497\pi$
$937$	11.5667	0.377868	0.188934	+	0.981990i	$0.439497\pi$
$938$	−2.06916	−0.0675603
$939$	−62.2365	−2.03101
$940$	−0.691489	−0.0225539
$941$	−21.9083	−0.714191	−0.357096	−	0.934068i	$-0.616233\pi$
$941$	−21.9083	−0.714191	−0.357096	+	0.934068i	$0.616233\pi$
$942$	51.9765	1.69349
$943$	−12.2244	−0.398080
$944$	−52.5136	−1.70917
$945$	−1.63247	−0.0531044
$946$	2.08589	0.0678182
$947$	14.9394	0.485466	0.242733	−	0.970093i	$-0.421956\pi$
$947$	14.9394	0.485466	0.242733	+	0.970093i	$0.421956\pi$
$948$	−39.3796	−1.27899
$949$	−25.6049	−0.831169
$950$	−20.3870	−0.661442
$951$	45.7047	1.48208
$952$	0.413964	0.0134166
$953$	20.7004	0.670551	0.335276	−	0.942120i	$-0.391171\pi$
$953$	20.7004	0.670551	0.335276	+	0.942120i	$0.391171\pi$
$954$	−3.70564	−0.119975
$955$	21.9767	0.711148
$956$	−13.6279	−0.440758
$957$	−0.922567	−0.0298223
$958$	0.0203857	0.000658632 0
$959$	1.37235	0.0443155
$960$	−12.3810	−0.399595
$961$	−30.8288	−0.994478
$962$	24.6717	0.795447
$963$	85.5807	2.75780
$964$	27.3569	0.881107
$965$	3.70022	0.119114
$966$	0.913024	0.0293761
$967$	10.8298	0.348263	0.174131	−	0.984722i	$-0.444288\pi$
$967$	10.8298	0.348263	0.174131	+	0.984722i	$0.444288\pi$
$968$	12.6786	0.407506
$969$	−63.0793	−2.02640
$970$	−21.6744	−0.695923
$971$	−17.9858	−0.577192	−0.288596	−	0.957451i	$-0.593188\pi$
$971$	−17.9858	−0.577192	−0.288596	+	0.957451i	$0.593188\pi$
$972$	−24.2167	−0.776753
$973$	−0.131822	−0.00422601
$974$	−14.4833	−0.464076
$975$	11.5642	0.370350
$976$	70.6779	2.26235
$977$	21.0385	0.673081	0.336540	−	0.941669i	$-0.390743\pi$
$977$	21.0385	0.673081	0.336540	+	0.941669i	$0.390743\pi$
$978$	−61.3842	−1.96285
$979$	1.78902	0.0571775
$980$	15.5803	0.497694
$981$	87.1257	2.78171
$982$	−55.8572	−1.78247
$983$	11.4648	0.365670	0.182835	−	0.983144i	$-0.441473\pi$
$983$	11.4648	0.365670	0.182835	+	0.983144i	$0.441473\pi$
$984$	−23.3601	−0.744693
$985$	−32.5930	−1.03850
$986$	−21.9918	−0.700361
$987$	0.0815440	0.00259557
$988$	10.0738	0.320491
$989$	−20.4373	−0.649869
$990$	2.14137	0.0680573
$991$	50.1020	1.59154	0.795772	−	0.605597i	$-0.207066\pi$
$991$	50.1020	1.59154	0.795772	+	0.605597i	$0.207066\pi$
$992$	−2.73893	−0.0869612
$993$	−83.0983	−2.63704
$994$	0.478826	0.0151874
$995$	−0.631077	−0.0200065
$996$	72.6124	2.30081
$997$	−30.3175	−0.960166	−0.480083	−	0.877223i	$-0.659393\pi$
$997$	−30.3175	−0.960166	−0.480083	+	0.877223i	$0.659393\pi$
$998$	37.9909	1.20258
$999$	−103.128	−3.26283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.a.1.83	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.a.1.83	✓	100	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)

\(f(q)\)	\(=\)	\(q+1.83621 q^{2} -3.13452 q^{3} +1.37166 q^{4} -1.62430 q^{5} -5.75564 q^{6} -0.0838203 q^{7} -1.15376 q^{8} +6.82524 q^{9} +O(q^{10})\)	\(q+1.83621 q^{2} -3.13452 q^{3} +1.37166 q^{4} -1.62430 q^{5} -5.75564 q^{6} -0.0838203 q^{7} -1.15376 q^{8} +6.82524 q^{9} -2.98256 q^{10} -0.105193 q^{11} -4.29950 q^{12} +1.56218 q^{13} -0.153911 q^{14} +5.09142 q^{15} -4.86187 q^{16} +4.28053 q^{17} +12.5326 q^{18} +4.70130 q^{19} -2.22799 q^{20} +0.262737 q^{21} -0.193156 q^{22} +1.89252 q^{23} +3.61649 q^{24} -2.36164 q^{25} +2.86848 q^{26} -11.9903 q^{27} -0.114973 q^{28} -2.79796 q^{29} +9.34890 q^{30} +0.413744 q^{31} -6.61988 q^{32} +0.329729 q^{33} +7.85994 q^{34} +0.136150 q^{35} +9.36191 q^{36} +8.60096 q^{37} +8.63256 q^{38} -4.89668 q^{39} +1.87406 q^{40} -6.45932 q^{41} +0.482439 q^{42} -10.7990 q^{43} -0.144289 q^{44} -11.0863 q^{45} +3.47505 q^{46} +0.310364 q^{47} +15.2396 q^{48} -6.99297 q^{49} -4.33646 q^{50} -13.4174 q^{51} +2.14277 q^{52} -0.295681 q^{53} -22.0167 q^{54} +0.170865 q^{55} +0.0967086 q^{56} -14.7363 q^{57} -5.13763 q^{58} +10.8011 q^{59} +6.98370 q^{60} -14.5372 q^{61} +0.759719 q^{62} -0.572093 q^{63} -2.43174 q^{64} -2.53745 q^{65} +0.605451 q^{66} +13.4438 q^{67} +5.87143 q^{68} -5.93214 q^{69} +0.249999 q^{70} -3.11105 q^{71} -7.87470 q^{72} -16.3905 q^{73} +15.7932 q^{74} +7.40262 q^{75} +6.44859 q^{76} +0.00881727 q^{77} -8.99132 q^{78} +9.15910 q^{79} +7.89715 q^{80} +17.1082 q^{81} -11.8607 q^{82} -16.8886 q^{83} +0.360386 q^{84} -6.95287 q^{85} -19.8293 q^{86} +8.77026 q^{87} +0.121367 q^{88} -17.0071 q^{89} -20.3567 q^{90} -0.130942 q^{91} +2.59589 q^{92} -1.29689 q^{93} +0.569893 q^{94} -7.63633 q^{95} +20.7502 q^{96} +7.26705 q^{97} -12.8406 q^{98} -0.717965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9}+O(q^{10}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9	\( 100 q - 15 q^{2} - 12 q^{3} + 89 q^{4} - 33 q^{5} - 28 q^{6} - 14 q^{7} - 45 q^{8} + 60 q^{9} - 18 q^{10} - 47 q^{11} - 27 q^{12} - 29 q^{13} - 51 q^{14} - 36 q^{15} + 71 q^{16} - 99 q^{17} - 27 q^{18} - 45 q^{19} - 75 q^{20} - 79 q^{21} - 2 q^{22} - 25 q^{23} - 66 q^{24} + 67 q^{25} - 73 q^{26} - 42 q^{27} - 31 q^{28} - 78 q^{29} - 29 q^{30} - 41 q^{31} - 95 q^{32} - 83 q^{33} - 44 q^{34} - 45 q^{35} + 23 q^{36} - 16 q^{37} - 29 q^{38} - 42 q^{39} - 37 q^{40} - 235 q^{41} + 16 q^{42} - 6 q^{43} - 122 q^{44} - 79 q^{45} - 17 q^{46} - 67 q^{47} - 25 q^{48} + 30 q^{49} - 68 q^{50} - 18 q^{51} - 41 q^{52} - 69 q^{53} - 63 q^{54} - 32 q^{55} - 120 q^{56} - 63 q^{57} - 7 q^{58} - 118 q^{59} - 49 q^{60} - 60 q^{61} - 23 q^{62} - 43 q^{63} + 43 q^{64} - 181 q^{65} - 4 q^{66} - 18 q^{67} - 130 q^{68} - 80 q^{69} + 12 q^{70} - 77 q^{71} - 40 q^{72} - 64 q^{73} - 48 q^{74} - 18 q^{75} - 134 q^{76} - 87 q^{77} + 65 q^{78} - 48 q^{79} - 95 q^{80} - 20 q^{81} + 45 q^{82} - 108 q^{83} - 97 q^{84} - 21 q^{85} - 73 q^{86} - 3 q^{87} + 23 q^{88} - 325 q^{89} + 6 q^{90} - 17 q^{91} - 19 q^{92} + 2 q^{93} - 5 q^{94} - 54 q^{95} - 105 q^{96} - 81 q^{97} - 61 q^{98} - 76 q^{99}+O(q^{100}) \) 100 * q - 15 * q^2 - 12 * q^3 + 89 * q^4 - 33 * q^5 - 28 * q^6 - 14 * q^7 - 45 * q^8 + 60 * q^9 - 18 * q^10 - 47 * q^11 - 27 * q^12 - 29 * q^13 - 51 * q^14 - 36 * q^15 + 71 * q^16 - 99 * q^17 - 27 * q^18 - 45 * q^19 - 75 * q^20 - 79 * q^21 - 2 * q^22 - 25 * q^23 - 66 * q^24 + 67 * q^25 - 73 * q^26 - 42 * q^27 - 31 * q^28 - 78 * q^29 - 29 * q^30 - 41 * q^31 - 95 * q^32 - 83 * q^33 - 44 * q^34 - 45 * q^35 + 23 * q^36 - 16 * q^37 - 29 * q^38 - 42 * q^39 - 37 * q^40 - 235 * q^41 + 16 * q^42 - 6 * q^43 - 122 * q^44 - 79 * q^45 - 17 * q^46 - 67 * q^47 - 25 * q^48 + 30 * q^49 - 68 * q^50 - 18 * q^51 - 41 * q^52 - 69 * q^53 - 63 * q^54 - 32 * q^55 - 120 * q^56 - 63 * q^57 - 7 * q^58 - 118 * q^59 - 49 * q^60 - 60 * q^61 - 23 * q^62 - 43 * q^63 + 43 * q^64 - 181 * q^65 - 4 * q^66 - 18 * q^67 - 130 * q^68 - 80 * q^69 + 12 * q^70 - 77 * q^71 - 40 * q^72 - 64 * q^73 - 48 * q^74 - 18 * q^75 - 134 * q^76 - 87 * q^77 + 65 * q^78 - 48 * q^79 - 95 * q^80 - 20 * q^81 + 45 * q^82 - 108 * q^83 - 97 * q^84 - 21 * q^85 - 73 * q^86 - 3 * q^87 + 23 * q^88 - 325 * q^89 + 6 * q^90 - 17 * q^91 - 19 * q^92 + 2 * q^93 - 5 * q^94 - 54 * q^95 - 105 * q^96 - 81 * q^97 - 61 * q^98 - 76 * q^99

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