LMFDB - Embedded newform 2671.2.a.b.1.24

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			1.24
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)

$f(q)$	$=$	$q-1.90000 q^{2} -1.37927 q^{3} +1.61001 q^{4} -2.16641 q^{5} +2.62062 q^{6} -0.261613 q^{7} +0.740985 q^{8} -1.09761 q^{9} +O(q^{10})$	\(q-1.90000 q^{2} -1.37927 q^{3} +1.61001 q^{4} -2.16641 q^{5} +2.62062 q^{6} -0.261613 q^{7} +0.740985 q^{8} -1.09761 q^{9} +4.11618 q^{10} -3.13891 q^{11} -2.22064 q^{12} +4.26381 q^{13} +0.497066 q^{14} +2.98806 q^{15} -4.62789 q^{16} +0.178614 q^{17} +2.08546 q^{18} -7.80236 q^{19} -3.48793 q^{20} +0.360836 q^{21} +5.96394 q^{22} +1.58813 q^{23} -1.02202 q^{24} -0.306688 q^{25} -8.10126 q^{26} +5.65172 q^{27} -0.421200 q^{28} +0.980977 q^{29} -5.67732 q^{30} -9.18758 q^{31} +7.31103 q^{32} +4.32941 q^{33} -0.339366 q^{34} +0.566760 q^{35} -1.76716 q^{36} +9.96646 q^{37} +14.8245 q^{38} -5.88096 q^{39} -1.60527 q^{40} +8.83822 q^{41} -0.685589 q^{42} -12.4936 q^{43} -5.05367 q^{44} +2.37787 q^{45} -3.01745 q^{46} -8.09342 q^{47} +6.38312 q^{48} -6.93156 q^{49} +0.582707 q^{50} -0.246357 q^{51} +6.86478 q^{52} -0.749415 q^{53} -10.7383 q^{54} +6.80015 q^{55} -0.193852 q^{56} +10.7616 q^{57} -1.86386 q^{58} -12.8946 q^{59} +4.81081 q^{60} -15.2806 q^{61} +17.4564 q^{62} +0.287149 q^{63} -4.63520 q^{64} -9.23715 q^{65} -8.22589 q^{66} -8.01673 q^{67} +0.287569 q^{68} -2.19046 q^{69} -1.07685 q^{70} -2.29953 q^{71} -0.813312 q^{72} +5.96804 q^{73} -18.9363 q^{74} +0.423006 q^{75} -12.5619 q^{76} +0.821181 q^{77} +11.1738 q^{78} +6.33362 q^{79} +10.0259 q^{80} -4.50243 q^{81} -16.7926 q^{82} -1.18976 q^{83} +0.580949 q^{84} -0.386949 q^{85} +23.7379 q^{86} -1.35303 q^{87} -2.32589 q^{88} +15.9864 q^{89} -4.51795 q^{90} -1.11547 q^{91} +2.55690 q^{92} +12.6722 q^{93} +15.3775 q^{94} +16.9031 q^{95} -10.0839 q^{96} -9.87383 q^{97} +13.1700 q^{98} +3.44530 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.90000	−1.34350	−0.671752	−	0.740776i	$-0.734458\pi$
$2$	−1.90000	−1.34350	−0.671752	+	0.740776i	$0.734458\pi$
$3$	−1.37927	−0.796323	−0.398162	−	0.917315i	$-0.630352\pi$
$3$	−1.37927	−0.796323	−0.398162	+	0.917315i	$0.630352\pi$
$4$	1.61001	0.805004
$5$	−2.16641	−0.968846	−0.484423	−	0.874834i	$-0.660970\pi$
$5$	−2.16641	−0.968846	−0.484423	+	0.874834i	$0.660970\pi$
$6$	2.62062	1.06986
$7$	−0.261613	−0.0988805	−0.0494403	−	0.998777i	$-0.515744\pi$
$7$	−0.261613	−0.0988805	−0.0494403	+	0.998777i	$0.515744\pi$
$8$	0.740985	0.261978
$9$	−1.09761	−0.365870
$10$	4.11618	1.30165
$11$	−3.13891	−0.946417	−0.473209	−	0.880950i	$-0.656904\pi$
$11$	−3.13891	−0.946417	−0.473209	+	0.880950i	$0.656904\pi$
$12$	−2.22064	−0.641043
$13$	4.26381	1.18257	0.591285	−	0.806463i	$-0.298621\pi$
$13$	4.26381	1.18257	0.591285	+	0.806463i	$0.298621\pi$
$14$	0.497066	0.132846
$15$	2.98806	0.771514
$16$	−4.62789	−1.15697
$17$	0.178614	0.0433202	0.0216601	−	0.999765i	$-0.493105\pi$
$17$	0.178614	0.0433202	0.0216601	+	0.999765i	$0.493105\pi$
$18$	2.08546	0.491547
$19$	−7.80236	−1.78998	−0.894992	−	0.446083i	$-0.852819\pi$
$19$	−7.80236	−1.78998	−0.894992	+	0.446083i	$0.852819\pi$
$20$	−3.48793	−0.779925
$21$	0.360836	0.0787408
$22$	5.96394	1.27152
$23$	1.58813	0.331148	0.165574	−	0.986197i	$-0.447052\pi$
$23$	1.58813	0.331148	0.165574	+	0.986197i	$0.447052\pi$
$24$	−1.02202	−0.208619
$25$	−0.306688	−0.0613375
$26$	−8.10126	−1.58879
$27$	5.65172	1.08767
$28$	−0.421200	−0.0795992
$29$	0.980977	0.182163	0.0910814	−	0.995843i	$-0.470968\pi$
$29$	0.980977	0.182163	0.0910814	+	0.995843i	$0.470968\pi$
$30$	−5.67732	−1.03653
$31$	−9.18758	−1.65014	−0.825069	−	0.565032i	$-0.808864\pi$
$31$	−9.18758	−1.65014	−0.825069	+	0.565032i	$0.808864\pi$
$32$	7.31103	1.29242
$33$	4.32941	0.753654
$34$	−0.339366	−0.0582008
$35$	0.566760	0.0958000
$36$	−1.76716	−0.294527
$37$	9.96646	1.63848	0.819238	−	0.573453i	$-0.194397\pi$
$37$	9.96646	1.63848	0.819238	+	0.573453i	$0.194397\pi$
$38$	14.8245	2.40485
$39$	−5.88096	−0.941707
$40$	−1.60527	−0.253816
$41$	8.83822	1.38030	0.690149	−	0.723668i	$-0.257545\pi$
$41$	8.83822	1.38030	0.690149	+	0.723668i	$0.257545\pi$
$42$	−0.685589	−0.105789
$43$	−12.4936	−1.90526	−0.952629	−	0.304136i	$-0.901632\pi$
$43$	−12.4936	−1.90526	−0.952629	+	0.304136i	$0.901632\pi$
$44$	−5.05367	−0.761870
$45$	2.37787	0.354471
$46$	−3.01745	−0.444898
$47$	−8.09342	−1.18055	−0.590273	−	0.807203i	$-0.700980\pi$
$47$	−8.09342	−1.18055	−0.590273	+	0.807203i	$0.700980\pi$
$48$	6.38312	0.921324
$49$	−6.93156	−0.990223
$50$	0.582707	0.0824073
$51$	−0.246357	−0.0344968
$52$	6.86478	0.951973
$53$	−0.749415	−0.102940	−0.0514700	−	0.998675i	$-0.516391\pi$
$53$	−0.749415	−0.102940	−0.0514700	+	0.998675i	$0.516391\pi$
$54$	−10.7383	−1.46129
$55$	6.80015	0.916932
$56$	−0.193852	−0.0259045
$57$	10.7616	1.42541
$58$	−1.86386	−0.244737
$59$	−12.8946	−1.67874	−0.839370	−	0.543561i	$-0.817076\pi$
$59$	−12.8946	−1.67874	−0.839370	+	0.543561i	$0.817076\pi$
$60$	4.81081	0.621072
$61$	−15.2806	−1.95648	−0.978241	−	0.207473i	$-0.933476\pi$
$61$	−15.2806	−1.95648	−0.978241	+	0.207473i	$0.933476\pi$
$62$	17.4564	2.21697
$63$	0.287149	0.0361774
$64$	−4.63520	−0.579399
$65$	−9.23715	−1.14573
$66$	−8.22589	−1.01254
$67$	−8.01673	−0.979400	−0.489700	−	0.871891i	$-0.662894\pi$
$67$	−8.01673	−0.979400	−0.489700	+	0.871891i	$0.662894\pi$
$68$	0.287569	0.0348729
$69$	−2.19046	−0.263701
$70$	−1.07685	−0.128708
$71$	−2.29953	−0.272905	−0.136452	−	0.990647i	$-0.543570\pi$
$71$	−2.29953	−0.272905	−0.136452	+	0.990647i	$0.543570\pi$
$72$	−0.813312	−0.0958497
$73$	5.96804	0.698507	0.349253	−	0.937028i	$-0.386435\pi$
$73$	5.96804	0.698507	0.349253	+	0.937028i	$0.386435\pi$
$74$	−18.9363	−2.20130
$75$	0.423006	0.0488445
$76$	−12.5619	−1.44094
$77$	0.821181	0.0935822
$78$	11.1738	1.26519
$79$	6.33362	0.712588	0.356294	−	0.934374i	$-0.384040\pi$
$79$	6.33362	0.712588	0.356294	+	0.934374i	$0.384040\pi$
$80$	10.0259	1.12093
$81$	−4.50243	−0.500270
$82$	−16.7926	−1.85444
$83$	−1.18976	−0.130593	−0.0652966	−	0.997866i	$-0.520799\pi$
$83$	−1.18976	−0.130593	−0.0652966	+	0.997866i	$0.520799\pi$
$84$	0.580949	0.0633867
$85$	−0.386949	−0.0419706
$86$	23.7379	2.55972
$87$	−1.35303	−0.145060
$88$	−2.32589	−0.247940
$89$	15.9864	1.69456	0.847280	−	0.531147i	$-0.178239\pi$
$89$	15.9864	1.69456	0.847280	+	0.531147i	$0.178239\pi$
$90$	−4.51795	−0.476234
$91$	−1.11547	−0.116933
$92$	2.55690	0.266575
$93$	12.6722	1.31404
$94$	15.3775	1.58607
$95$	16.9031	1.73422
$96$	−10.0839	−1.02918
$97$	−9.87383	−1.00254	−0.501268	−	0.865292i	$-0.667133\pi$
$97$	−9.87383	−1.00254	−0.501268	+	0.865292i	$0.667133\pi$
$98$	13.1700	1.33037
$99$	3.44530	0.346265
$100$	−0.493770	−0.0493770
$101$	−8.45960	−0.841762	−0.420881	−	0.907116i	$-0.638279\pi$
$101$	−8.45960	−0.841762	−0.420881	+	0.907116i	$0.638279\pi$
$102$	0.468078	0.0463466
$103$	−0.0770295	−0.00758995	−0.00379497	−	0.999993i	$-0.501208\pi$
$103$	−0.0770295	−0.00758995	−0.00379497	+	0.999993i	$0.501208\pi$
$104$	3.15942	0.309807
$105$	−0.781717	−0.0762878
$106$	1.42389	0.138300
$107$	−3.03229	−0.293143	−0.146571	−	0.989200i	$-0.546824\pi$
$107$	−3.03229	−0.293143	−0.146571	+	0.989200i	$0.546824\pi$
$108$	9.09931	0.875582
$109$	−15.3523	−1.47049	−0.735243	−	0.677803i	$-0.762932\pi$
$109$	−15.3523	−1.47049	−0.735243	+	0.677803i	$0.762932\pi$
$110$	−12.9203	−1.23190
$111$	−13.7465	−1.30476
$112$	1.21072	0.114402
$113$	−0.478243	−0.0449893	−0.0224947	−	0.999747i	$-0.507161\pi$
$113$	−0.478243	−0.0449893	−0.0224947	+	0.999747i	$0.507161\pi$
$114$	−20.4470	−1.91504
$115$	−3.44053	−0.320831
$116$	1.57938	0.146642
$117$	−4.68000	−0.432666
$118$	24.4998	2.25539
$119$	−0.0467277	−0.00428352
$120$	2.21411	0.202120
$121$	−1.14724	−0.104295
$122$	29.0332	2.62854
$123$	−12.1903	−1.09916
$124$	−14.7921	−1.32837
$125$	11.4964	1.02827
$126$	−0.545584	−0.0486045
$127$	−9.25361	−0.821125	−0.410562	−	0.911832i	$-0.634668\pi$
$127$	−9.25361	−0.821125	−0.410562	+	0.911832i	$0.634668\pi$
$128$	−5.81518	−0.513994
$129$	17.2321	1.51720
$130$	17.5506	1.53929
$131$	18.9469	1.65540	0.827699	−	0.561172i	$-0.189649\pi$
$131$	18.9469	1.65540	0.827699	+	0.561172i	$0.189649\pi$
$132$	6.97039	0.606694
$133$	2.04120	0.176995
$134$	15.2318	1.31583
$135$	−12.2439	−1.05379
$136$	0.132350	0.0113489
$137$	−11.9563	−1.02149	−0.510747	−	0.859731i	$-0.670631\pi$
$137$	−11.9563	−1.02149	−0.510747	+	0.859731i	$0.670631\pi$
$138$	4.16188	0.354283
$139$	−11.2621	−0.955238	−0.477619	−	0.878567i	$-0.658500\pi$
$139$	−11.2621	−0.955238	−0.477619	+	0.878567i	$0.658500\pi$
$140$	0.912489	0.0771194
$141$	11.1630	0.940096
$142$	4.36912	0.366648
$143$	−13.3837	−1.11920
$144$	5.07961	0.423301
$145$	−2.12519	−0.176488
$146$	−11.3393	−0.938447
$147$	9.56050	0.788537
$148$	16.0461	1.31898
$149$	14.4997	1.18786	0.593930	−	0.804517i	$-0.297576\pi$
$149$	14.4997	1.18786	0.593930	+	0.804517i	$0.297576\pi$
$150$	−0.803712	−0.0656228
$151$	10.2385	0.833197	0.416598	−	0.909091i	$-0.363222\pi$
$151$	10.2385	0.833197	0.416598	+	0.909091i	$0.363222\pi$
$152$	−5.78143	−0.468936
$153$	−0.196048	−0.0158495
$154$	−1.56025	−0.125728
$155$	19.9040	1.59873
$156$	−9.46839	−0.758078
$157$	10.7677	0.859356	0.429678	−	0.902982i	$-0.358627\pi$
$157$	10.7677	0.859356	0.429678	+	0.902982i	$0.358627\pi$
$158$	−12.0339	−0.957365
$159$	1.03365	0.0819736
$160$	−15.8387	−1.25216
$161$	−0.415476	−0.0327441
$162$	8.55462	0.672115
$163$	−11.6781	−0.914703	−0.457351	−	0.889286i	$-0.651202\pi$
$163$	−11.6781	−0.914703	−0.457351	+	0.889286i	$0.651202\pi$
$164$	14.2296	1.11115
$165$	−9.37926	−0.730174
$166$	2.26055	0.175453
$167$	9.65547	0.747163	0.373581	−	0.927597i	$-0.378130\pi$
$167$	9.65547	0.747163	0.373581	+	0.927597i	$0.378130\pi$
$168$	0.267374	0.0206284
$169$	5.18011	0.398470
$170$	0.735205	0.0563876
$171$	8.56394	0.654901
$172$	−20.1148	−1.53374
$173$	−5.22945	−0.397588	−0.198794	−	0.980041i	$-0.563702\pi$
$173$	−5.22945	−0.397588	−0.198794	+	0.980041i	$0.563702\pi$
$174$	2.57077	0.194889
$175$	0.0802336	0.00606509
$176$	14.5265	1.09498
$177$	17.7852	1.33682
$178$	−30.3743	−2.27665
$179$	−16.9938	−1.27018	−0.635089	−	0.772439i	$-0.719037\pi$
$179$	−16.9938	−1.27018	−0.635089	+	0.772439i	$0.719037\pi$
$180$	3.82838	0.285351
$181$	12.7236	0.945741	0.472870	−	0.881132i	$-0.343218\pi$
$181$	12.7236	0.945741	0.472870	+	0.881132i	$0.343218\pi$
$182$	2.11940	0.157100
$183$	21.0761	1.55799
$184$	1.17678	0.0867533
$185$	−21.5914	−1.58743
$186$	−24.0772	−1.76542
$187$	−0.560652	−0.0409989
$188$	−13.0305	−0.950345
$189$	−1.47856	−0.107550
$190$	−32.1159	−2.32993
$191$	2.98986	0.216339	0.108169	−	0.994132i	$-0.465501\pi$
$191$	2.98986	0.216339	0.108169	+	0.994132i	$0.465501\pi$
$192$	6.39319	0.461389
$193$	−8.60572	−0.619453	−0.309727	−	0.950826i	$-0.600238\pi$
$193$	−8.60572	−0.619453	−0.309727	+	0.950826i	$0.600238\pi$
$194$	18.7603	1.34691
$195$	12.7405	0.912369
$196$	−11.1599	−0.797133
$197$	16.5814	1.18138	0.590689	−	0.806899i	$-0.298856\pi$
$197$	16.5814	1.18138	0.590689	+	0.806899i	$0.298856\pi$
$198$	−6.54607	−0.465209
$199$	21.3839	1.51587	0.757934	−	0.652331i	$-0.226209\pi$
$199$	21.3839	1.51587	0.757934	+	0.652331i	$0.226209\pi$
$200$	−0.227251	−0.0160691
$201$	11.0573	0.779918
$202$	16.0733	1.13091
$203$	−0.256637	−0.0180124
$204$	−0.396636	−0.0277701
$205$	−19.1472	−1.33730
$206$	0.146356	0.0101971
$207$	−1.74314	−0.121157
$208$	−19.7325	−1.36820
$209$	24.4909	1.69407
$210$	1.48526	0.102493
$211$	25.6689	1.76712	0.883559	−	0.468319i	$-0.155140\pi$
$211$	25.6689	1.76712	0.883559	+	0.468319i	$0.155140\pi$
$212$	−1.20656	−0.0828672
$213$	3.17168	0.217320
$214$	5.76136	0.393839
$215$	27.0662	1.84590
$216$	4.18784	0.284946
$217$	2.40359	0.163167
$218$	29.1695	1.97561
$219$	−8.23156	−0.556237
$220$	10.9483	0.738134
$221$	0.761575	0.0512291
$222$	26.1183	1.75295
$223$	19.6269	1.31431	0.657157	−	0.753754i	$-0.271759\pi$
$223$	19.6269	1.31431	0.657157	+	0.753754i	$0.271759\pi$
$224$	−1.91266	−0.127795
$225$	0.336623	0.0224415
$226$	0.908663	0.0604434
$227$	−8.71830	−0.578654	−0.289327	−	0.957230i	$-0.593431\pi$
$227$	−8.71830	−0.578654	−0.289327	+	0.957230i	$0.593431\pi$
$228$	17.3262	1.14746
$229$	−16.7006	−1.10361	−0.551803	−	0.833975i	$-0.686060\pi$
$229$	−16.7006	−1.10361	−0.551803	+	0.833975i	$0.686060\pi$
$230$	6.53702	0.431038
$231$	−1.13263	−0.0745217
$232$	0.726889	0.0477226
$233$	8.31204	0.544540	0.272270	−	0.962221i	$-0.412226\pi$
$233$	8.31204	0.544540	0.272270	+	0.962221i	$0.412226\pi$
$234$	8.89201	0.581289
$235$	17.5336	1.14377
$236$	−20.7605	−1.35139
$237$	−8.73578	−0.567450
$238$	0.0887827	0.00575493
$239$	9.90227	0.640524	0.320262	−	0.947329i	$-0.396229\pi$
$239$	9.90227	0.640524	0.320262	+	0.947329i	$0.396229\pi$
$240$	−13.8284	−0.892621
$241$	9.08979	0.585525	0.292763	−	0.956185i	$-0.405425\pi$
$241$	9.08979	0.585525	0.292763	+	0.956185i	$0.405425\pi$
$242$	2.17976	0.140120
$243$	−10.7451	−0.689297
$244$	−24.6019	−1.57498
$245$	15.0166	0.959373
$246$	23.1616	1.47673
$247$	−33.2678	−2.11678
$248$	−6.80786	−0.432299
$249$	1.64100	0.103994
$250$	−21.8433	−1.38149
$251$	15.5416	0.980980	0.490490	−	0.871447i	$-0.336818\pi$
$251$	15.5416	0.980980	0.490490	+	0.871447i	$0.336818\pi$
$252$	0.462312	0.0291229
$253$	−4.98499	−0.313404
$254$	17.5819	1.10319
$255$	0.533708	0.0334221
$256$	20.3192	1.26995
$257$	4.56687	0.284873	0.142437	−	0.989804i	$-0.454506\pi$
$257$	4.56687	0.284873	0.142437	+	0.989804i	$0.454506\pi$
$258$	−32.7410	−2.03837
$259$	−2.60736	−0.162013
$260$	−14.8719	−0.922315
$261$	−1.07673	−0.0666478
$262$	−35.9992	−2.22403
$263$	15.6290	0.963728	0.481864	−	0.876246i	$-0.339960\pi$
$263$	15.6290	0.963728	0.481864	+	0.876246i	$0.339960\pi$
$264$	3.20803	0.197440
$265$	1.62354	0.0997331
$266$	−3.87829	−0.237793
$267$	−22.0496	−1.34942
$268$	−12.9070	−0.788421
$269$	−7.83660	−0.477806	−0.238903	−	0.971043i	$-0.576788\pi$
$269$	−7.83660	−0.477806	−0.238903	+	0.971043i	$0.576788\pi$
$270$	23.2635	1.41577
$271$	1.71951	0.104453	0.0522263	−	0.998635i	$-0.483368\pi$
$271$	1.71951	0.104453	0.0522263	+	0.998635i	$0.483368\pi$
$272$	−0.826604	−0.0501202
$273$	1.53854	0.0931165
$274$	22.7170	1.37238
$275$	0.962665	0.0580509
$276$	−3.52666	−0.212280
$277$	26.4380	1.58851	0.794253	−	0.607587i	$-0.207862\pi$
$277$	26.4380	1.58851	0.794253	+	0.607587i	$0.207862\pi$
$278$	21.3980	1.28337
$279$	10.0844	0.603735
$280$	0.419961	0.0250975
$281$	−29.9812	−1.78853	−0.894263	−	0.447542i	$-0.852299\pi$
$281$	−29.9812	−1.78853	−0.894263	+	0.447542i	$0.852299\pi$
$282$	−21.2098	−1.26302
$283$	11.9171	0.708398	0.354199	−	0.935170i	$-0.384754\pi$
$283$	11.9171	0.708398	0.354199	+	0.935170i	$0.384754\pi$
$284$	−3.70227	−0.219689
$285$	−23.3139	−1.38100
$286$	25.4291	1.50366
$287$	−2.31219	−0.136485
$288$	−8.02465	−0.472857
$289$	−16.9681	−0.998123
$290$	4.03787	0.237112
$291$	13.6187	0.798342
$292$	9.60860	0.562301
$293$	15.4242	0.901089	0.450545	−	0.892754i	$-0.351230\pi$
$293$	15.4242	0.901089	0.450545	+	0.892754i	$0.351230\pi$
$294$	−18.1650	−1.05940
$295$	27.9350	1.62644
$296$	7.38500	0.429244
$297$	−17.7402	−1.02939
$298$	−27.5494	−1.59589
$299$	6.77149	0.391605
$300$	0.681043	0.0393200
$301$	3.26849	0.188393
$302$	−19.4532	−1.11940
$303$	11.6681	0.670314
$304$	36.1084	2.07096
$305$	33.1040	1.89553
$306$	0.372491	0.0212939
$307$	−13.5733	−0.774668	−0.387334	−	0.921939i	$-0.626604\pi$
$307$	−13.5733	−0.774668	−0.387334	+	0.921939i	$0.626604\pi$
$308$	1.32211	0.0753341
$309$	0.106245	0.00604405
$310$	−37.8177	−2.14790
$311$	−3.90128	−0.221221	−0.110611	−	0.993864i	$-0.535281\pi$
$311$	−3.90128	−0.221221	−0.110611	+	0.993864i	$0.535281\pi$
$312$	−4.35770	−0.246706
$313$	−7.98456	−0.451314	−0.225657	−	0.974207i	$-0.572453\pi$
$313$	−7.98456	−0.451314	−0.225657	+	0.974207i	$0.572453\pi$
$314$	−20.4587	−1.15455
$315$	−0.622081	−0.0350503
$316$	10.1972	0.573636
$317$	20.6943	1.16231	0.581153	−	0.813794i	$-0.302602\pi$
$317$	20.6943	1.16231	0.581153	+	0.813794i	$0.302602\pi$
$318$	−1.96393	−0.110132
$319$	−3.07920	−0.172402
$320$	10.0417	0.561349
$321$	4.18236	0.233436
$322$	0.789405	0.0439918
$323$	−1.39361	−0.0775424
$324$	−7.24895	−0.402719
$325$	−1.30766	−0.0725359
$326$	22.1885	1.22891
$327$	21.1750	1.17098
$328$	6.54898	0.361607
$329$	2.11735	0.116733
$330$	17.8206	0.980992
$331$	15.6323	0.859228	0.429614	−	0.903013i	$-0.358650\pi$
$331$	15.6323	0.859228	0.429614	+	0.903013i	$0.358650\pi$
$332$	−1.91553	−0.105128
$333$	−10.9393	−0.599469
$334$	−18.3454	−1.00382
$335$	17.3675	0.948887
$336$	−1.66991	−0.0911010
$337$	−14.6395	−0.797465	−0.398732	−	0.917067i	$-0.630550\pi$
$337$	−14.6395	−0.797465	−0.398732	+	0.917067i	$0.630550\pi$
$338$	−9.84223	−0.535347
$339$	0.659628	0.0358261
$340$	−0.622992	−0.0337865
$341$	28.8390	1.56172
$342$	−16.2715	−0.879862
$343$	3.64468	0.196794
$344$	−9.25757	−0.499135
$345$	4.74543	0.255485
$346$	9.93597	0.534161
$347$	−22.0323	−1.18276	−0.591378	−	0.806395i	$-0.701416\pi$
$347$	−22.0323	−1.18276	−0.591378	+	0.806395i	$0.701416\pi$
$348$	−2.17840	−0.116774
$349$	−2.96658	−0.158798	−0.0793988	−	0.996843i	$-0.525300\pi$
$349$	−2.96658	−0.158798	−0.0793988	+	0.996843i	$0.525300\pi$
$350$	−0.152444	−0.00814847
$351$	24.0979	1.28625
$352$	−22.9487	−1.22317
$353$	−2.00944	−0.106952	−0.0534758	−	0.998569i	$-0.517030\pi$
$353$	−2.00944	−0.106952	−0.0534758	+	0.998569i	$0.517030\pi$
$354$	−33.7920	−1.79602
$355$	4.98172	0.264402
$356$	25.7383	1.36413
$357$	0.0644502	0.00341107
$358$	32.2883	1.70649
$359$	1.48651	0.0784549	0.0392274	−	0.999230i	$-0.487510\pi$
$359$	1.48651	0.0784549	0.0392274	+	0.999230i	$0.487510\pi$
$360$	1.76196	0.0928636
$361$	41.8768	2.20404
$362$	−24.1749	−1.27061
$363$	1.58236	0.0830523
$364$	−1.79592	−0.0941316
$365$	−12.9292	−0.676745
$366$	−40.0447	−2.09317
$367$	16.1443	0.842723	0.421362	−	0.906893i	$-0.361552\pi$
$367$	16.1443	0.842723	0.421362	+	0.906893i	$0.361552\pi$
$368$	−7.34968	−0.383129
$369$	−9.70090	−0.505009
$370$	41.0237	2.13272
$371$	0.196057	0.0101788
$372$	20.4023	1.05781
$373$	12.3076	0.637264	0.318632	−	0.947879i	$-0.396777\pi$
$373$	12.3076	0.637264	0.318632	+	0.947879i	$0.396777\pi$
$374$	1.06524	0.0550822
$375$	−15.8567	−0.818837
$376$	−5.99710	−0.309277
$377$	4.18270	0.215420
$378$	2.80928	0.144494
$379$	35.0450	1.80014	0.900070	−	0.435745i	$-0.143515\pi$
$379$	35.0450	1.80014	0.900070	+	0.435745i	$0.143515\pi$
$380$	27.2141	1.39605
$381$	12.7632	0.653881
$382$	−5.68074	−0.290652
$383$	6.66678	0.340657	0.170328	−	0.985387i	$-0.445517\pi$
$383$	6.66678	0.340657	0.170328	+	0.985387i	$0.445517\pi$
$384$	8.02072	0.409305
$385$	−1.77901	−0.0906668
$386$	16.3509	0.832238
$387$	13.7131	0.697076
$388$	−15.8969	−0.807045
$389$	−18.6128	−0.943709	−0.471854	−	0.881676i	$-0.656415\pi$
$389$	−18.6128	−0.943709	−0.471854	+	0.881676i	$0.656415\pi$
$390$	−24.2071	−1.22577
$391$	0.283661	0.0143454
$392$	−5.13618	−0.259416
$393$	−26.1329	−1.31823
$394$	−31.5047	−1.58719
$395$	−13.7212	−0.690388
$396$	5.54696	0.278745
$397$	28.2123	1.41594	0.707968	−	0.706244i	$-0.249612\pi$
$397$	28.2123	1.41594	0.707968	+	0.706244i	$0.249612\pi$
$398$	−40.6296	−2.03658
$399$	−2.81537	−0.140945
$400$	1.41932	0.0709658
$401$	16.0384	0.800920	0.400460	−	0.916314i	$-0.368850\pi$
$401$	16.0384	0.800920	0.400460	+	0.916314i	$0.368850\pi$
$402$	−21.0088	−1.04782
$403$	−39.1741	−1.95140
$404$	−13.6200	−0.677622
$405$	9.75408	0.484684
$406$	0.487610	0.0241997
$407$	−31.2838	−1.55068
$408$	−0.182547	−0.00903740
$409$	−18.4813	−0.913840	−0.456920	−	0.889508i	$-0.651047\pi$
$409$	−18.4813	−0.913840	−0.456920	+	0.889508i	$0.651047\pi$
$410$	36.3796	1.79666
$411$	16.4910	0.813440
$412$	−0.124018	−0.00610994
$413$	3.37341	0.165995
$414$	3.31198	0.162775
$415$	2.57751	0.126525
$416$	31.1729	1.52838
$417$	15.5335	0.760678
$418$	−46.5328	−2.27599
$419$	−21.1206	−1.03181	−0.515905	−	0.856646i	$-0.672544\pi$
$419$	−21.1206	−1.03181	−0.515905	+	0.856646i	$0.672544\pi$
$420$	−1.25857	−0.0614120
$421$	15.2455	0.743021	0.371510	−	0.928429i	$-0.378840\pi$
$421$	15.2455	0.743021	0.371510	+	0.928429i	$0.378840\pi$
$422$	−48.7709	−2.37413
$423$	8.88341	0.431926
$424$	−0.555305	−0.0269680
$425$	−0.0547786	−0.00265715
$426$	−6.02621	−0.291971
$427$	3.99761	0.193458
$428$	−4.88202	−0.235981
$429$	18.4598	0.891248
$430$	−51.4259	−2.47998
$431$	−26.0960	−1.25700	−0.628500	−	0.777809i	$-0.716331\pi$
$431$	−26.0960	−1.25700	−0.628500	+	0.777809i	$0.716331\pi$
$432$	−26.1555	−1.25841
$433$	23.3597	1.12260	0.561298	−	0.827614i	$-0.310302\pi$
$433$	23.3597	1.12260	0.561298	+	0.827614i	$0.310302\pi$
$434$	−4.56683	−0.219215
$435$	2.93122	0.140541
$436$	−24.7174	−1.18375
$437$	−12.3911	−0.592749
$438$	15.6400	0.747307
$439$	−16.1746	−0.771969	−0.385985	−	0.922505i	$-0.626138\pi$
$439$	−16.1746	−0.771969	−0.385985	+	0.922505i	$0.626138\pi$
$440$	5.03881	0.240216
$441$	7.60814	0.362292
$442$	−1.44699	−0.0688265
$443$	22.2832	1.05871	0.529353	−	0.848401i	$-0.322435\pi$
$443$	22.2832	1.05871	0.529353	+	0.848401i	$0.322435\pi$
$444$	−22.1319	−1.05033
$445$	−34.6331	−1.64177
$446$	−37.2911	−1.76579
$447$	−19.9990	−0.945920
$448$	1.21263	0.0572913
$449$	−14.1034	−0.665580	−0.332790	−	0.943001i	$-0.607990\pi$
$449$	−14.1034	−0.665580	−0.332790	+	0.943001i	$0.607990\pi$
$450$	−0.639585	−0.0301503
$451$	−27.7424	−1.30634
$452$	−0.769976	−0.0362166
$453$	−14.1217	−0.663494
$454$	16.5648	0.777424
$455$	2.41656	0.113290
$456$	7.97416	0.373424
$457$	−7.62487	−0.356676	−0.178338	−	0.983969i	$-0.557072\pi$
$457$	−7.62487	−0.356676	−0.178338	+	0.983969i	$0.557072\pi$
$458$	31.7311	1.48270
$459$	1.00947	0.0471182
$460$	−5.53928	−0.258270
$461$	16.4841	0.767740	0.383870	−	0.923387i	$-0.374591\pi$
$461$	16.4841	0.767740	0.383870	+	0.923387i	$0.374591\pi$
$462$	2.15200	0.100120
$463$	−7.80719	−0.362831	−0.181415	−	0.983407i	$-0.558068\pi$
$463$	−7.80719	−0.362831	−0.181415	+	0.983407i	$0.558068\pi$
$464$	−4.53985	−0.210757
$465$	−27.4531	−1.27311
$466$	−15.7929	−0.731592
$467$	−25.5161	−1.18075	−0.590373	−	0.807131i	$-0.701019\pi$
$467$	−25.5161	−1.18075	−0.590373	+	0.807131i	$0.701019\pi$
$468$	−7.53484	−0.348298
$469$	2.09728	0.0968436
$470$	−33.3139	−1.53666
$471$	−14.8516	−0.684325
$472$	−9.55474	−0.439792
$473$	39.2163	1.80317
$474$	16.5980	0.762372
$475$	2.39289	0.109793
$476$	−0.0752320	−0.00344825
$477$	0.822565	0.0376627
$478$	−18.8143	−0.860547
$479$	30.2683	1.38299	0.691496	−	0.722380i	$-0.256952\pi$
$479$	30.2683	1.38299	0.691496	+	0.722380i	$0.256952\pi$
$480$	21.8458	0.997120
$481$	42.4952	1.93761
$482$	−17.2706	−0.786656
$483$	0.573054	0.0260749
$484$	−1.84707	−0.0839577
$485$	21.3907	0.971302
$486$	20.4157	0.926074
$487$	20.8189	0.943396	0.471698	−	0.881760i	$-0.343641\pi$
$487$	20.8189	0.943396	0.471698	+	0.881760i	$0.343641\pi$
$488$	−11.3227	−0.512555
$489$	16.1073	0.728399
$490$	−28.5315	−1.28892
$491$	−35.2426	−1.59048	−0.795238	−	0.606297i	$-0.792654\pi$
$491$	−35.2426	−1.59048	−0.795238	+	0.606297i	$0.792654\pi$
$492$	−19.6265	−0.884830
$493$	0.175216	0.00789132
$494$	63.2089	2.84390
$495$	−7.46391	−0.335478
$496$	42.5191	1.90916
$497$	0.601589	0.0269849
$498$	−3.11791	−0.139717
$499$	7.25089	0.324594	0.162297	−	0.986742i	$-0.448110\pi$
$499$	7.25089	0.324594	0.162297	+	0.986742i	$0.448110\pi$
$500$	18.5094	0.827764
$501$	−13.3175	−0.594983
$502$	−29.5292	−1.31795
$503$	1.45635	0.0649356	0.0324678	−	0.999473i	$-0.489663\pi$
$503$	1.45635	0.0649356	0.0324678	+	0.999473i	$0.489663\pi$
$504$	0.212773	0.00947767
$505$	18.3269	0.815538
$506$	9.47150	0.421059
$507$	−7.14479	−0.317311
$508$	−14.8984	−0.661009
$509$	−40.5408	−1.79694	−0.898470	−	0.439035i	$-0.855321\pi$
$509$	−40.5408	−1.79694	−0.898470	+	0.439035i	$0.855321\pi$
$510$	−1.01405	−0.0449028
$511$	−1.56132	−0.0690687
$512$	−26.9763	−1.19219
$513$	−44.0967	−1.94692
$514$	−8.67706	−0.382729
$515$	0.166877	0.00735349
$516$	27.7438	1.22135
$517$	25.4045	1.11729
$518$	4.95399	0.217666
$519$	7.21283	0.316608
$520$	−6.84459	−0.300155
$521$	18.4921	0.810154	0.405077	−	0.914283i	$-0.367245\pi$
$521$	18.4921	0.810154	0.405077	+	0.914283i	$0.367245\pi$
$522$	2.04579	0.0895417
$523$	−17.6232	−0.770611	−0.385305	−	0.922789i	$-0.625904\pi$
$523$	−17.6232	−0.770611	−0.385305	+	0.922789i	$0.625904\pi$
$524$	30.5047	1.33260
$525$	−0.110664	−0.00482977
$526$	−29.6952	−1.29477
$527$	−1.64103	−0.0714842
$528$	−20.0360	−0.871957
$529$	−20.4778	−0.890341
$530$	−3.08472	−0.133992
$531$	14.1533	0.614200
$532$	3.28635	0.142481
$533$	37.6845	1.63230
$534$	41.8944	1.81295
$535$	6.56917	0.284010
$536$	−5.94028	−0.256581
$537$	23.4391	1.01147
$538$	14.8896	0.641934
$539$	21.7575	0.937164
$540$	−19.7128	−0.848304
$541$	−7.91532	−0.340306	−0.170153	−	0.985418i	$-0.554426\pi$
$541$	−7.91532	−0.340306	−0.170153	+	0.985418i	$0.554426\pi$
$542$	−3.26707	−0.140333
$543$	−17.5494	−0.753115
$544$	1.30585	0.0559878
$545$	33.2594	1.42468
$546$	−2.92322	−0.125102
$547$	−29.0398	−1.24165	−0.620827	−	0.783948i	$-0.713203\pi$
$547$	−29.0398	−1.24165	−0.620827	+	0.783948i	$0.713203\pi$
$548$	−19.2497	−0.822307
$549$	16.7721	0.715817
$550$	−1.82907	−0.0779916
$551$	−7.65393	−0.326068
$552$	−1.62310	−0.0690837
$553$	−1.65696	−0.0704611
$554$	−50.2323	−2.13417
$555$	29.7804	1.26411
$556$	−18.1321	−0.768971
$557$	37.6805	1.59657	0.798286	−	0.602278i	$-0.205740\pi$
$557$	37.6805	1.59657	0.798286	+	0.602278i	$0.205740\pi$
$558$	−19.1603	−0.811121
$559$	−53.2704	−2.25310
$560$	−2.62291	−0.110838
$561$	0.773291	0.0326484
$562$	56.9643	2.40289
$563$	−32.1869	−1.35652	−0.678259	−	0.734823i	$-0.737265\pi$
$563$	−32.1869	−1.35652	−0.678259	+	0.734823i	$0.737265\pi$
$564$	17.9726	0.756782
$565$	1.03607	0.0435877
$566$	−22.6425	−0.951736
$567$	1.17790	0.0494669
$568$	−1.70392	−0.0714949
$569$	−8.83969	−0.370579	−0.185290	−	0.982684i	$-0.559322\pi$
$569$	−8.83969	−0.370579	−0.185290	+	0.982684i	$0.559322\pi$
$570$	44.2965	1.85538
$571$	8.80616	0.368526	0.184263	−	0.982877i	$-0.441010\pi$
$571$	8.80616	0.368526	0.184263	+	0.982877i	$0.441010\pi$
$572$	−21.5479	−0.900964
$573$	−4.12383	−0.172275
$574$	4.39318	0.183368
$575$	−0.487059	−0.0203118
$576$	5.08763	0.211985
$577$	−40.3283	−1.67889	−0.839444	−	0.543446i	$-0.817119\pi$
$577$	−40.3283	−1.67889	−0.839444	+	0.543446i	$0.817119\pi$
$578$	32.2394	1.34098
$579$	11.8696	0.493285
$580$	−3.42158	−0.142073
$581$	0.311257	0.0129131
$582$	−25.8755	−1.07258
$583$	2.35235	0.0974243
$584$	4.42223	0.182993
$585$	10.1388	0.419187
$586$	−29.3059	−1.21062
$587$	43.8309	1.80910	0.904548	−	0.426373i	$-0.140209\pi$
$587$	43.8309	1.80910	0.904548	+	0.426373i	$0.140209\pi$
$588$	15.3925	0.634776
$589$	71.6848	2.95372
$590$	−53.0766	−2.18513
$591$	−22.8703	−0.940758
$592$	−46.1237	−1.89567
$593$	35.8801	1.47342	0.736710	−	0.676209i	$-0.236378\pi$
$593$	35.8801	1.47342	0.736710	+	0.676209i	$0.236378\pi$
$594$	33.7065	1.38299
$595$	0.101231	0.00415007
$596$	23.3446	0.956232
$597$	−29.4943	−1.20712
$598$	−12.8658	−0.526123
$599$	−7.61123	−0.310987	−0.155493	−	0.987837i	$-0.549697\pi$
$599$	−7.61123	−0.310987	−0.155493	+	0.987837i	$0.549697\pi$
$600$	0.313441	0.0127962
$601$	−33.7555	−1.37692	−0.688458	−	0.725276i	$-0.741712\pi$
$601$	−33.7555	−1.37692	−0.688458	+	0.725276i	$0.741712\pi$
$602$	−6.21015	−0.253107
$603$	8.79924	0.358333
$604$	16.4841	0.670727
$605$	2.48539	0.101046
$606$	−22.1694	−0.900570
$607$	6.66439	0.270499	0.135250	−	0.990812i	$-0.456816\pi$
$607$	6.66439	0.270499	0.135250	+	0.990812i	$0.456816\pi$
$608$	−57.0433	−2.31341
$609$	0.353972	0.0143437
$610$	−62.8977	−2.54665
$611$	−34.5088	−1.39608
$612$	−0.315639	−0.0127589
$613$	−2.11865	−0.0855715	−0.0427857	−	0.999084i	$-0.513623\pi$
$613$	−2.11865	−0.0855715	−0.0427857	+	0.999084i	$0.513623\pi$
$614$	25.7893	1.04077
$615$	26.4091	1.06492
$616$	0.608483	0.0245165
$617$	−14.8049	−0.596024	−0.298012	−	0.954562i	$-0.596324\pi$
$617$	−14.8049	−0.596024	−0.298012	+	0.954562i	$0.596324\pi$
$618$	−0.201865	−0.00812021
$619$	11.9037	0.478450	0.239225	−	0.970964i	$-0.423107\pi$
$619$	11.9037	0.478450	0.239225	+	0.970964i	$0.423107\pi$
$620$	32.0456	1.28698
$621$	8.97565	0.360181
$622$	7.41243	0.297211
$623$	−4.18227	−0.167559
$624$	27.2164	1.08953
$625$	−23.3725	−0.934900
$626$	15.1707	0.606342
$627$	−33.7796	−1.34903
$628$	17.3361	0.691785
$629$	1.78015	0.0709791
$630$	1.18196	0.0470903
$631$	0.702695	0.0279738	0.0139869	−	0.999902i	$-0.495548\pi$
$631$	0.702695	0.0279738	0.0139869	+	0.999902i	$0.495548\pi$
$632$	4.69312	0.186682
$633$	−35.4044	−1.40720
$634$	−39.3192	−1.56156
$635$	20.0471	0.795544
$636$	1.66418	0.0659891
$637$	−29.5549	−1.17101
$638$	5.85048	0.231623
$639$	2.52399	0.0998475
$640$	12.5980	0.497981
$641$	−16.4566	−0.649996	−0.324998	−	0.945715i	$-0.605364\pi$
$641$	−16.4566	−0.649996	−0.324998	+	0.945715i	$0.605364\pi$
$642$	−7.94649	−0.313623
$643$	−26.2916	−1.03684	−0.518420	−	0.855126i	$-0.673480\pi$
$643$	−26.2916	−1.03684	−0.518420	+	0.855126i	$0.673480\pi$
$644$	−0.668919	−0.0263591
$645$	−37.3317	−1.46993
$646$	2.64786	0.104178
$647$	−12.3165	−0.484212	−0.242106	−	0.970250i	$-0.577838\pi$
$647$	−12.3165	−0.484212	−0.242106	+	0.970250i	$0.577838\pi$
$648$	−3.33623	−0.131060
$649$	40.4751	1.58879
$650$	2.48456	0.0974523
$651$	−3.31521	−0.129933
$652$	−18.8019	−0.736340
$653$	17.4876	0.684343	0.342171	−	0.939638i	$-0.388838\pi$
$653$	17.4876	0.684343	0.342171	+	0.939638i	$0.388838\pi$
$654$	−40.2326	−1.57322
$655$	−41.0467	−1.60383
$656$	−40.9023	−1.59697
$657$	−6.55058	−0.255562
$658$	−4.02296	−0.156831
$659$	−1.51879	−0.0591637	−0.0295818	−	0.999562i	$-0.509418\pi$
$659$	−1.51879	−0.0591637	−0.0295818	+	0.999562i	$0.509418\pi$
$660$	−15.1007	−0.587793
$661$	−11.9565	−0.465056	−0.232528	−	0.972590i	$-0.574700\pi$
$661$	−11.9565	−0.465056	−0.232528	+	0.972590i	$0.574700\pi$
$662$	−29.7014	−1.15438
$663$	−1.05042	−0.0407949
$664$	−0.881595	−0.0342125
$665$	−4.42207	−0.171480
$666$	20.7847	0.805389
$667$	1.55792	0.0603228
$668$	15.5454	0.601469
$669$	−27.0708	−1.04662
$670$	−32.9983	−1.27483
$671$	47.9645	1.85165
$672$	2.63808	0.101766
$673$	−16.9977	−0.655213	−0.327607	−	0.944814i	$-0.606242\pi$
$673$	−16.9977	−0.655213	−0.327607	+	0.944814i	$0.606242\pi$
$674$	27.8151	1.07140
$675$	−1.73331	−0.0667152
$676$	8.34003	0.320770
$677$	4.01231	0.154206	0.0771028	−	0.997023i	$-0.475433\pi$
$677$	4.01231	0.154206	0.0771028	+	0.997023i	$0.475433\pi$
$678$	−1.25329	−0.0481325
$679$	2.58312	0.0991312
$680$	−0.286724	−0.0109954
$681$	12.0249	0.460795
$682$	−54.7941	−2.09818
$683$	−6.16143	−0.235761	−0.117880	−	0.993028i	$-0.537610\pi$
$683$	−6.16143	−0.235761	−0.117880	+	0.993028i	$0.537610\pi$
$684$	13.7880	0.527198
$685$	25.9022	0.989671
$686$	−6.92490	−0.264394
$687$	23.0346	0.878826
$688$	57.8190	2.20433
$689$	−3.19537	−0.121734
$690$	−9.01632	−0.343245
$691$	−5.48618	−0.208704	−0.104352	−	0.994540i	$-0.533277\pi$
$691$	−5.48618	−0.208704	−0.104352	+	0.994540i	$0.533277\pi$
$692$	−8.41946	−0.320060
$693$	−0.901335	−0.0342389
$694$	41.8614	1.58904
$695$	24.3983	0.925479
$696$	−1.00258	−0.0380026
$697$	1.57863	0.0597947
$698$	5.63652	0.213345
$699$	−11.4646	−0.433630
$700$	0.129177	0.00488242
$701$	−24.4329	−0.922819	−0.461409	−	0.887187i	$-0.652656\pi$
$701$	−24.4329	−0.922819	−0.461409	+	0.887187i	$0.652656\pi$
$702$	−45.7860	−1.72808
$703$	−77.7619	−2.93285
$704$	14.5495	0.548353
$705$	−24.1836	−0.910809
$706$	3.81793	0.143690
$707$	2.21314	0.0832339
$708$	28.6343	1.07614
$709$	−37.5623	−1.41068	−0.705341	−	0.708868i	$-0.749206\pi$
$709$	−37.5623	−1.41068	−0.705341	+	0.708868i	$0.749206\pi$
$710$	−9.46529	−0.355226
$711$	−6.95184	−0.260714
$712$	11.8457	0.443937
$713$	−14.5911	−0.546439
$714$	−0.122455	−0.00458278
$715$	28.9946	1.08434
$716$	−27.3602	−1.02250
$717$	−13.6579	−0.510064
$718$	−2.82437	−0.105404
$719$	41.5046	1.54786	0.773931	−	0.633270i	$-0.218288\pi$
$719$	41.5046	1.54786	0.773931	+	0.633270i	$0.218288\pi$
$720$	−11.0045	−0.410114
$721$	0.0201520	0.000750498 0
$722$	−79.5660	−2.96114
$723$	−12.5373	−0.466267
$724$	20.4852	0.761325
$725$	−0.300854	−0.0111734
$726$	−3.00649	−0.111581
$727$	−8.73377	−0.323918	−0.161959	−	0.986798i	$-0.551781\pi$
$727$	−8.73377	−0.323918	−0.161959	+	0.986798i	$0.551781\pi$
$728$	−0.826547	−0.0306339
$729$	28.3277	1.04917
$730$	24.5655	0.909210
$731$	−2.23153	−0.0825360
$732$	33.9327	1.25419
$733$	−19.5549	−0.722278	−0.361139	−	0.932512i	$-0.617612\pi$
$733$	−19.5549	−0.722278	−0.361139	+	0.932512i	$0.617612\pi$
$734$	−30.6741	−1.13220
$735$	−20.7119	−0.763971
$736$	11.6109	0.427982
$737$	25.1638	0.926920
$738$	18.4317	0.678482
$739$	−2.00436	−0.0737317	−0.0368659	−	0.999320i	$-0.511737\pi$
$739$	−2.00436	−0.0737317	−0.0368659	+	0.999320i	$0.511737\pi$
$740$	−34.7623	−1.27789
$741$	45.8853	1.68564
$742$	−0.372509	−0.0136752
$743$	43.7836	1.60626	0.803131	−	0.595802i	$-0.203166\pi$
$743$	43.7836	1.60626	0.803131	+	0.595802i	$0.203166\pi$
$744$	9.38989	0.344250
$745$	−31.4122	−1.15085
$746$	−23.3845	−0.856167
$747$	1.30589	0.0477801
$748$	−0.902654	−0.0330043
$749$	0.793288	0.0289861
$750$	30.1278	1.10011
$751$	−6.18958	−0.225861	−0.112931	−	0.993603i	$-0.536024\pi$
$751$	−6.18958	−0.225861	−0.112931	+	0.993603i	$0.536024\pi$
$752$	37.4555	1.36586
$753$	−21.4362	−0.781177
$754$	−7.94714	−0.289418
$755$	−22.1807	−0.807239
$756$	−2.38050	−0.0865780
$757$	−7.91630	−0.287723	−0.143861	−	0.989598i	$-0.545952\pi$
$757$	−7.91630	−0.287723	−0.143861	+	0.989598i	$0.545952\pi$
$758$	−66.5855	−2.41850
$759$	6.87566	0.249571
$760$	12.5249	0.454327
$761$	53.0628	1.92353	0.961763	−	0.273884i	$-0.0883083\pi$
$761$	53.0628	1.92353	0.961763	+	0.273884i	$0.0883083\pi$
$762$	−24.2502	−0.878492
$763$	4.01638	0.145403
$764$	4.81370	0.174154
$765$	0.424719	0.0153558
$766$	−12.6669	−0.457674
$767$	−54.9804	−1.98523
$768$	−28.0258	−1.01129
$769$	−39.8887	−1.43842	−0.719212	−	0.694790i	$-0.755497\pi$
$769$	−39.8887	−1.43842	−0.719212	+	0.694790i	$0.755497\pi$
$770$	3.38012	0.121811
$771$	−6.29895	−0.226851
$772$	−13.8553	−0.498663
$773$	28.9254	1.04038	0.520188	−	0.854052i	$-0.325862\pi$
$773$	28.9254	1.04038	0.520188	+	0.854052i	$0.325862\pi$
$774$	−26.0549	−0.936524
$775$	2.81772	0.101215
$776$	−7.31636	−0.262642
$777$	3.59626	0.129015
$778$	35.3645	1.26788
$779$	−68.9589	−2.47071
$780$	20.5124	0.734461
$781$	7.21803	0.258282
$782$	−0.538957	−0.0192731
$783$	5.54420	0.198134
$784$	32.0785	1.14566
$785$	−23.3272	−0.832583
$786$	49.6526	1.77105
$787$	11.5026	0.410023	0.205011	−	0.978760i	$-0.434277\pi$
$787$	11.5026	0.410023	0.205011	+	0.978760i	$0.434277\pi$
$788$	26.6962	0.951014
$789$	−21.5567	−0.767439
$790$	26.0703	0.927539
$791$	0.125115	0.00444857
$792$	2.55291	0.0907138
$793$	−65.1537	−2.31367
$794$	−53.6035	−1.90232
$795$	−2.23930	−0.0794198
$796$	34.4283	1.22028
$797$	53.5354	1.89632	0.948161	−	0.317791i	$-0.102941\pi$
$797$	53.5354	1.89632	0.948161	+	0.317791i	$0.102941\pi$
$798$	5.34921	0.189360
$799$	−1.44559	−0.0511415
$800$	−2.24220	−0.0792739
$801$	−17.5469	−0.619988
$802$	−30.4730	−1.07604
$803$	−18.7332	−0.661079
$804$	17.8023	0.627838
$805$	0.900089	0.0317240
$806$	74.4309	2.62172
$807$	10.8088	0.380488
$808$	−6.26844	−0.220523
$809$	31.7349	1.11574	0.557871	−	0.829928i	$-0.311619\pi$
$809$	31.7349	1.11574	0.557871	+	0.829928i	$0.311619\pi$
$810$	−18.5328	−0.651176
$811$	−41.4384	−1.45510	−0.727549	−	0.686056i	$-0.759341\pi$
$811$	−41.4384	−1.45510	−0.727549	+	0.686056i	$0.759341\pi$
$812$	−0.413187	−0.0145000
$813$	−2.37167	−0.0831780
$814$	59.4394	2.08335
$815$	25.2996	0.886206
$816$	1.14011	0.0399119
$817$	97.4796	3.41038
$818$	35.1145	1.22775
$819$	1.22435	0.0427823
$820$	−30.8271	−1.07653
$821$	10.4783	0.365696	0.182848	−	0.983141i	$-0.441468\pi$
$821$	10.4783	0.365696	0.182848	+	0.983141i	$0.441468\pi$
$822$	−31.3329	−1.09286
$823$	4.49552	0.156704	0.0783521	−	0.996926i	$-0.475034\pi$
$823$	4.49552	0.156704	0.0783521	+	0.996926i	$0.475034\pi$
$824$	−0.0570777	−0.00198840
$825$	−1.32778	−0.0462273
$826$	−6.40949	−0.223015
$827$	−42.4309	−1.47547	−0.737733	−	0.675092i	$-0.764104\pi$
$827$	−42.4309	−1.47547	−0.737733	+	0.675092i	$0.764104\pi$
$828$	−2.80648	−0.0975318
$829$	34.7429	1.20667	0.603336	−	0.797487i	$-0.293838\pi$
$829$	34.7429	1.20667	0.603336	+	0.797487i	$0.293838\pi$
$830$	−4.89727	−0.169987
$831$	−36.4652	−1.26496
$832$	−19.7636	−0.685180
$833$	−1.23807	−0.0428966
$834$	−29.5137	−1.02197
$835$	−20.9177	−0.723885
$836$	39.4306	1.36373
$837$	−51.9256	−1.79481
$838$	40.1292	1.38624
$839$	−12.0217	−0.415035	−0.207517	−	0.978231i	$-0.566538\pi$
$839$	−12.0217	−0.415035	−0.207517	+	0.978231i	$0.566538\pi$
$840$	−0.579240	−0.0199857
$841$	−28.0377	−0.966817
$842$	−28.9665	−0.998251
$843$	41.3522	1.42424
$844$	41.3271	1.42254
$845$	−11.2222	−0.386056
$846$	−16.8785	−0.580295
$847$	0.300134	0.0103127
$848$	3.46821	0.119099
$849$	−16.4369	−0.564113
$850$	0.104079	0.00356989
$851$	15.8280	0.542578
$852$	5.10644	0.174944
$853$	−26.0242	−0.891051	−0.445525	−	0.895269i	$-0.646983\pi$
$853$	−26.0242	−0.891051	−0.445525	+	0.895269i	$0.646983\pi$
$854$	−7.59547	−0.259912
$855$	−18.5530	−0.634498
$856$	−2.24688	−0.0767969
$857$	−57.8490	−1.97608	−0.988042	−	0.154187i	$-0.950724\pi$
$857$	−57.8490	−1.97608	−0.988042	+	0.154187i	$0.950724\pi$
$858$	−35.0737	−1.19740
$859$	13.2310	0.451437	0.225719	−	0.974193i	$-0.427527\pi$
$859$	13.2310	0.451437	0.225719	+	0.974193i	$0.427527\pi$
$860$	43.5768	1.48596
$861$	3.18915	0.108686
$862$	49.5825	1.68879
$863$	15.7205	0.535133	0.267566	−	0.963539i	$-0.413781\pi$
$863$	15.7205	0.535133	0.267566	+	0.963539i	$0.413781\pi$
$864$	41.3199	1.40573
$865$	11.3291	0.385201
$866$	−44.3835	−1.50821
$867$	23.4036	0.794829
$868$	3.86981	0.131350
$869$	−19.8807	−0.674405
$870$	−5.56932	−0.188818
$871$	−34.1819	−1.15821
$872$	−11.3758	−0.385235
$873$	10.8376	0.366797
$874$	23.5432	0.796361
$875$	−3.00762	−0.101676
$876$	−13.2529	−0.447773
$877$	−52.8774	−1.78554	−0.892771	−	0.450511i	$-0.851242\pi$
$877$	−52.8774	−1.78554	−0.892771	+	0.450511i	$0.851242\pi$
$878$	30.7317	1.03714
$879$	−21.2741	−0.717558
$880$	−31.4704	−1.06087
$881$	−11.5711	−0.389839	−0.194919	−	0.980819i	$-0.562445\pi$
$881$	−11.5711	−0.389839	−0.194919	+	0.980819i	$0.562445\pi$
$882$	−14.4555	−0.486741
$883$	11.6907	0.393425	0.196712	−	0.980461i	$-0.436973\pi$
$883$	11.6907	0.393425	0.196712	+	0.980461i	$0.436973\pi$
$884$	1.22614	0.0412396
$885$	−38.5300	−1.29517
$886$	−42.3381	−1.42238
$887$	16.4675	0.552924	0.276462	−	0.961025i	$-0.410838\pi$
$887$	16.4675	0.552924	0.276462	+	0.961025i	$0.410838\pi$
$888$	−10.1859	−0.341817
$889$	2.42087	0.0811933
$890$	65.8030	2.20572
$891$	14.1327	0.473464
$892$	31.5995	1.05803
$893$	63.1477	2.11316
$894$	37.9981	1.27085
$895$	36.8155	1.23061
$896$	1.52133	0.0508240
$897$	−9.33972	−0.311844
$898$	26.7965	0.894209
$899$	−9.01280	−0.300594
$900$	0.541966	0.0180655
$901$	−0.133856	−0.00445938
$902$	52.7106	1.75507
$903$	−4.50814	−0.150022
$904$	−0.354371	−0.0117862
$905$	−27.5646	−0.916277
$906$	26.8312	0.891407
$907$	21.2500	0.705593	0.352797	−	0.935700i	$-0.385231\pi$
$907$	21.2500	0.705593	0.352797	+	0.935700i	$0.385231\pi$
$908$	−14.0365	−0.465819
$909$	9.28533	0.307975
$910$	−4.59147	−0.152206
$911$	15.5062	0.513742	0.256871	−	0.966446i	$-0.417308\pi$
$911$	15.5062	0.513742	0.256871	+	0.966446i	$0.417308\pi$
$912$	−49.8034	−1.64915
$913$	3.73455	0.123596
$914$	14.4873	0.479196
$915$	−45.6594	−1.50945
$916$	−26.8881	−0.888407
$917$	−4.95676	−0.163687
$918$	−1.91800	−0.0633035
$919$	8.77108	0.289331	0.144666	−	0.989481i	$-0.453789\pi$
$919$	8.77108	0.289331	0.144666	+	0.989481i	$0.453789\pi$
$920$	−2.54938	−0.0840506
$921$	18.7213	0.616886
$922$	−31.3198	−1.03146
$923$	−9.80479	−0.322729
$924$	−1.82355	−0.0599903
$925$	−3.05659	−0.100500
$926$	14.8337	0.487465
$927$	0.0845483	0.00277693
$928$	7.17195	0.235431
$929$	23.6592	0.776234	0.388117	−	0.921610i	$-0.373126\pi$
$929$	23.6592	0.776234	0.388117	+	0.921610i	$0.373126\pi$
$930$	52.1609	1.71042
$931$	54.0825	1.77248
$932$	13.3825	0.438357
$933$	5.38092	0.176163
$934$	48.4807	1.58634
$935$	1.21460	0.0397216
$936$	−3.46781	−0.113349
$937$	−7.32662	−0.239350	−0.119675	−	0.992813i	$-0.538185\pi$
$937$	−7.32662	−0.239350	−0.119675	+	0.992813i	$0.538185\pi$
$938$	−3.98484	−0.130110
$939$	11.0129	0.359392
$940$	28.2293	0.920738
$941$	24.9980	0.814912	0.407456	−	0.913225i	$-0.366416\pi$
$941$	24.9980	0.814912	0.407456	+	0.913225i	$0.366416\pi$
$942$	28.2180	0.919393
$943$	14.0362	0.457082
$944$	59.6750	1.94226
$945$	3.20317	0.104199
$946$	−74.5111	−2.42256
$947$	−17.9647	−0.583775	−0.291888	−	0.956453i	$-0.594283\pi$
$947$	−17.9647	−0.583775	−0.291888	+	0.956453i	$0.594283\pi$
$948$	−14.0647	−0.456800
$949$	25.4466	0.826033
$950$	−4.54649	−0.147508
$951$	−28.5430	−0.925571
$952$	−0.0346245	−0.00112219
$953$	41.0931	1.33114	0.665568	−	0.746337i	$-0.268189\pi$
$953$	41.0931	1.33114	0.665568	+	0.746337i	$0.268189\pi$
$954$	−1.56287	−0.0505999
$955$	−6.47725	−0.209599
$956$	15.9427	0.515625
$957$	4.24705	0.137288
$958$	−57.5097	−1.85806
$959$	3.12792	0.101006
$960$	−13.8503	−0.447015
$961$	53.4116	1.72296
$962$	−80.7409	−2.60319
$963$	3.32827	0.107252
$964$	14.6346	0.471350
$965$	18.6435	0.600155
$966$	−1.08880	−0.0350317
$967$	36.9421	1.18798	0.593989	−	0.804473i	$-0.297552\pi$
$967$	36.9421	1.18798	0.593989	+	0.804473i	$0.297552\pi$
$968$	−0.850089	−0.0273229
$969$	1.92216	0.0617488
$970$	−40.6424	−1.30495
$971$	−14.9110	−0.478517	−0.239258	−	0.970956i	$-0.576904\pi$
$971$	−14.9110	−0.478517	−0.239258	+	0.970956i	$0.576904\pi$
$972$	−17.2997	−0.554887
$973$	2.94631	0.0944545
$974$	−39.5560	−1.26746
$975$	1.80362	0.0577620
$976$	70.7170	2.26360
$977$	42.4841	1.35919	0.679594	−	0.733589i	$-0.262156\pi$
$977$	42.4841	1.35919	0.679594	+	0.733589i	$0.262156\pi$
$978$	−30.6040	−0.978607
$979$	−50.1800	−1.60376
$980$	24.1768	0.772299
$981$	16.8509	0.538007
$982$	66.9610	2.13681
$983$	16.3463	0.521367	0.260684	−	0.965424i	$-0.416052\pi$
$983$	16.3463	0.521367	0.260684	+	0.965424i	$0.416052\pi$
$984$	−9.03283	−0.287956
$985$	−35.9221	−1.14457
$986$	−0.332910	−0.0106020
$987$	−2.92040	−0.0929572
$988$	−53.5614	−1.70402
$989$	−19.8415	−0.630922
$990$	14.1814	0.450716
$991$	46.6361	1.48144	0.740722	−	0.671811i	$-0.234483\pi$
$991$	46.6361	1.48144	0.740722	+	0.671811i	$0.234483\pi$
$992$	−67.1707	−2.13267
$993$	−21.5612	−0.684223
$994$	−1.14302	−0.0362544
$995$	−46.3263	−1.46864
$996$	2.64203	0.0837160
$997$	26.9019	0.851992	0.425996	−	0.904725i	$-0.359924\pi$
$997$	26.9019	0.851992	0.425996	+	0.904725i	$0.359924\pi$
$998$	−13.7767	−0.436094
$999$	56.3276	1.78213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.24	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.24	✓	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)

\(f(q)\)	\(=\)	\(q-1.90000 q^{2} -1.37927 q^{3} +1.61001 q^{4} -2.16641 q^{5} +2.62062 q^{6} -0.261613 q^{7} +0.740985 q^{8} -1.09761 q^{9} +O(q^{10})\)	\(q-1.90000 q^{2} -1.37927 q^{3} +1.61001 q^{4} -2.16641 q^{5} +2.62062 q^{6} -0.261613 q^{7} +0.740985 q^{8} -1.09761 q^{9} +4.11618 q^{10} -3.13891 q^{11} -2.22064 q^{12} +4.26381 q^{13} +0.497066 q^{14} +2.98806 q^{15} -4.62789 q^{16} +0.178614 q^{17} +2.08546 q^{18} -7.80236 q^{19} -3.48793 q^{20} +0.360836 q^{21} +5.96394 q^{22} +1.58813 q^{23} -1.02202 q^{24} -0.306688 q^{25} -8.10126 q^{26} +5.65172 q^{27} -0.421200 q^{28} +0.980977 q^{29} -5.67732 q^{30} -9.18758 q^{31} +7.31103 q^{32} +4.32941 q^{33} -0.339366 q^{34} +0.566760 q^{35} -1.76716 q^{36} +9.96646 q^{37} +14.8245 q^{38} -5.88096 q^{39} -1.60527 q^{40} +8.83822 q^{41} -0.685589 q^{42} -12.4936 q^{43} -5.05367 q^{44} +2.37787 q^{45} -3.01745 q^{46} -8.09342 q^{47} +6.38312 q^{48} -6.93156 q^{49} +0.582707 q^{50} -0.246357 q^{51} +6.86478 q^{52} -0.749415 q^{53} -10.7383 q^{54} +6.80015 q^{55} -0.193852 q^{56} +10.7616 q^{57} -1.86386 q^{58} -12.8946 q^{59} +4.81081 q^{60} -15.2806 q^{61} +17.4564 q^{62} +0.287149 q^{63} -4.63520 q^{64} -9.23715 q^{65} -8.22589 q^{66} -8.01673 q^{67} +0.287569 q^{68} -2.19046 q^{69} -1.07685 q^{70} -2.29953 q^{71} -0.813312 q^{72} +5.96804 q^{73} -18.9363 q^{74} +0.423006 q^{75} -12.5619 q^{76} +0.821181 q^{77} +11.1738 q^{78} +6.33362 q^{79} +10.0259 q^{80} -4.50243 q^{81} -16.7926 q^{82} -1.18976 q^{83} +0.580949 q^{84} -0.386949 q^{85} +23.7379 q^{86} -1.35303 q^{87} -2.32589 q^{88} +15.9864 q^{89} -4.51795 q^{90} -1.11547 q^{91} +2.55690 q^{92} +12.6722 q^{93} +15.3775 q^{94} +16.9031 q^{95} -10.0839 q^{96} -9.87383 q^{97} +13.1700 q^{98} +3.44530 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 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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