LMFDB - Embedded newform 2005.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.667454 q^{2} -3.21238 q^{3} -1.55450 q^{4} -1.00000 q^{5} +2.14411 q^{6} +2.82900 q^{7} +2.37247 q^{8} +7.31937 q^{9} +O(q^{10})$	\(q-0.667454 q^{2} -3.21238 q^{3} -1.55450 q^{4} -1.00000 q^{5} +2.14411 q^{6} +2.82900 q^{7} +2.37247 q^{8} +7.31937 q^{9} +0.667454 q^{10} +3.25570 q^{11} +4.99366 q^{12} -2.24560 q^{13} -1.88823 q^{14} +3.21238 q^{15} +1.52550 q^{16} +3.79206 q^{17} -4.88534 q^{18} +5.30414 q^{19} +1.55450 q^{20} -9.08782 q^{21} -2.17303 q^{22} +0.878564 q^{23} -7.62127 q^{24} +1.00000 q^{25} +1.49884 q^{26} -13.8754 q^{27} -4.39770 q^{28} +7.11004 q^{29} -2.14411 q^{30} -5.86275 q^{31} -5.76314 q^{32} -10.4585 q^{33} -2.53103 q^{34} -2.82900 q^{35} -11.3780 q^{36} +2.00833 q^{37} -3.54027 q^{38} +7.21372 q^{39} -2.37247 q^{40} -1.02655 q^{41} +6.06571 q^{42} +11.4997 q^{43} -5.06100 q^{44} -7.31937 q^{45} -0.586401 q^{46} -13.4765 q^{47} -4.90047 q^{48} +1.00326 q^{49} -0.667454 q^{50} -12.1815 q^{51} +3.49080 q^{52} -5.78974 q^{53} +9.26123 q^{54} -3.25570 q^{55} +6.71172 q^{56} -17.0389 q^{57} -4.74562 q^{58} +10.8109 q^{59} -4.99366 q^{60} +0.286602 q^{61} +3.91311 q^{62} +20.7065 q^{63} +0.795639 q^{64} +2.24560 q^{65} +6.98060 q^{66} +5.54705 q^{67} -5.89478 q^{68} -2.82228 q^{69} +1.88823 q^{70} -7.06353 q^{71} +17.3650 q^{72} +9.09931 q^{73} -1.34047 q^{74} -3.21238 q^{75} -8.24531 q^{76} +9.21039 q^{77} -4.81483 q^{78} +1.95042 q^{79} -1.52550 q^{80} +22.6151 q^{81} +0.685178 q^{82} -5.44511 q^{83} +14.1271 q^{84} -3.79206 q^{85} -7.67555 q^{86} -22.8401 q^{87} +7.72405 q^{88} +12.6982 q^{89} +4.88534 q^{90} -6.35281 q^{91} -1.36573 q^{92} +18.8334 q^{93} +8.99495 q^{94} -5.30414 q^{95} +18.5134 q^{96} -9.29054 q^{97} -0.669627 q^{98} +23.8297 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) $ 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.667454	−0.471961	−0.235981	−	0.971758i	$-0.575830\pi$
$2$	−0.667454	−0.471961	−0.235981	+	0.971758i	$0.575830\pi$
$3$	−3.21238	−1.85467	−0.927334	−	0.374236i	$-0.877905\pi$
$3$	−3.21238	−1.85467	−0.927334	+	0.374236i	$0.877905\pi$
$4$	−1.55450	−0.777252
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.14411	0.875331
$7$	2.82900	1.06926	0.534631	−	0.845085i	$-0.320451\pi$
$7$	2.82900	1.06926	0.534631	+	0.845085i	$0.320451\pi$
$8$	2.37247	0.838795
$9$	7.31937	2.43979
$10$	0.667454	0.211068
$11$	3.25570	0.981631	0.490816	−	0.871264i	$-0.336699\pi$
$11$	3.25570	0.981631	0.490816	+	0.871264i	$0.336699\pi$
$12$	4.99366	1.44154
$13$	−2.24560	−0.622818	−0.311409	−	0.950276i	$-0.600801\pi$
$13$	−2.24560	−0.622818	−0.311409	+	0.950276i	$0.600801\pi$
$14$	−1.88823	−0.504651
$15$	3.21238	0.829432
$16$	1.52550	0.381374
$17$	3.79206	0.919710	0.459855	−	0.887994i	$-0.347901\pi$
$17$	3.79206	0.919710	0.459855	+	0.887994i	$0.347901\pi$
$18$	−4.88534	−1.15149
$19$	5.30414	1.21685	0.608427	−	0.793610i	$-0.291801\pi$
$19$	5.30414	1.21685	0.608427	+	0.793610i	$0.291801\pi$
$20$	1.55450	0.347598
$21$	−9.08782	−1.98313
$22$	−2.17303	−0.463292
$23$	0.878564	0.183193	0.0915967	−	0.995796i	$-0.470803\pi$
$23$	0.878564	0.183193	0.0915967	+	0.995796i	$0.470803\pi$
$24$	−7.62127	−1.55568
$25$	1.00000	0.200000
$26$	1.49884	0.293946
$27$	−13.8754	−2.67033
$28$	−4.39770	−0.831087
$29$	7.11004	1.32030	0.660150	−	0.751134i	$-0.270493\pi$
$29$	7.11004	1.32030	0.660150	+	0.751134i	$0.270493\pi$
$30$	−2.14411	−0.391460
$31$	−5.86275	−1.05298	−0.526490	−	0.850181i	$-0.676492\pi$
$31$	−5.86275	−1.05298	−0.526490	+	0.850181i	$0.676492\pi$
$32$	−5.76314	−1.01879
$33$	−10.4585	−1.82060
$34$	−2.53103	−0.434068
$35$	−2.82900	−0.478189
$36$	−11.3780	−1.89633
$37$	2.00833	0.330167	0.165083	−	0.986280i	$-0.447211\pi$
$37$	2.00833	0.330167	0.165083	+	0.986280i	$0.447211\pi$
$38$	−3.54027	−0.574308
$39$	7.21372	1.15512
$40$	−2.37247	−0.375120
$41$	−1.02655	−0.160321	−0.0801604	−	0.996782i	$-0.525543\pi$
$41$	−1.02655	−0.160321	−0.0801604	+	0.996782i	$0.525543\pi$
$42$	6.06571	0.935959
$43$	11.4997	1.75369	0.876847	−	0.480770i	$-0.159643\pi$
$43$	11.4997	1.75369	0.876847	+	0.480770i	$0.159643\pi$
$44$	−5.06100	−0.762975
$45$	−7.31937	−1.09111
$46$	−0.586401	−0.0864602
$47$	−13.4765	−1.96575	−0.982875	−	0.184274i	$-0.941007\pi$
$47$	−13.4765	−1.96575	−0.982875	+	0.184274i	$0.941007\pi$
$48$	−4.90047	−0.707321
$49$	1.00326	0.143322
$50$	−0.667454	−0.0943923
$51$	−12.1815	−1.70576
$52$	3.49080	0.484086
$53$	−5.78974	−0.795281	−0.397641	−	0.917541i	$-0.630171\pi$
$53$	−5.78974	−0.795281	−0.397641	+	0.917541i	$0.630171\pi$
$54$	9.26123	1.26029
$55$	−3.25570	−0.438999
$56$	6.71172	0.896892
$57$	−17.0389	−2.25686
$58$	−4.74562	−0.623131
$59$	10.8109	1.40745	0.703727	−	0.710471i	$-0.251518\pi$
$59$	10.8109	1.40745	0.703727	+	0.710471i	$0.251518\pi$
$60$	−4.99366	−0.644678
$61$	0.286602	0.0366956	0.0183478	−	0.999832i	$-0.494159\pi$
$61$	0.286602	0.0366956	0.0183478	+	0.999832i	$0.494159\pi$
$62$	3.91311	0.496966
$63$	20.7065	2.60878
$64$	0.795639	0.0994549
$65$	2.24560	0.278532
$66$	6.98060	0.859252
$67$	5.54705	0.677680	0.338840	−	0.940844i	$-0.389965\pi$
$67$	5.54705	0.677680	0.338840	+	0.940844i	$0.389965\pi$
$68$	−5.89478	−0.714847
$69$	−2.82228	−0.339763
$70$	1.88823	0.225687
$71$	−7.06353	−0.838287	−0.419144	−	0.907920i	$-0.637670\pi$
$71$	−7.06353	−0.838287	−0.419144	+	0.907920i	$0.637670\pi$
$72$	17.3650	2.04648
$73$	9.09931	1.06499	0.532497	−	0.846432i	$-0.321254\pi$
$73$	9.09931	1.06499	0.532497	+	0.846432i	$0.321254\pi$
$74$	−1.34047	−0.155826
$75$	−3.21238	−0.370933
$76$	−8.24531	−0.945802
$77$	9.21039	1.04962
$78$	−4.81483	−0.545172
$79$	1.95042	0.219439	0.109720	−	0.993963i	$-0.465005\pi$
$79$	1.95042	0.219439	0.109720	+	0.993963i	$0.465005\pi$
$80$	−1.52550	−0.170556
$81$	22.6151	2.51279
$82$	0.685178	0.0756652
$83$	−5.44511	−0.597678	−0.298839	−	0.954303i	$-0.596599\pi$
$83$	−5.44511	−0.597678	−0.298839	+	0.954303i	$0.596599\pi$
$84$	14.1271	1.54139
$85$	−3.79206	−0.411307
$86$	−7.67555	−0.827676
$87$	−22.8401	−2.44872
$88$	7.72405	0.823387
$89$	12.6982	1.34601	0.673003	−	0.739640i	$-0.265004\pi$
$89$	12.6982	1.34601	0.673003	+	0.739640i	$0.265004\pi$
$90$	4.88534	0.514961
$91$	−6.35281	−0.665955
$92$	−1.36573	−0.142387
$93$	18.8334	1.95293
$94$	8.99495	0.927758
$95$	−5.30414	−0.544193
$96$	18.5134	1.88951
$97$	−9.29054	−0.943311	−0.471656	−	0.881783i	$-0.656343\pi$
$97$	−9.29054	−0.943311	−0.471656	+	0.881783i	$0.656343\pi$
$98$	−0.669627	−0.0676425
$99$	23.8297	2.39497
$100$	−1.55450	−0.155450
$101$	14.1191	1.40490	0.702451	−	0.711732i	$-0.252089\pi$
$101$	14.1191	1.40490	0.702451	+	0.711732i	$0.252089\pi$
$102$	8.13061	0.805051
$103$	−4.59544	−0.452802	−0.226401	−	0.974034i	$-0.572696\pi$
$103$	−4.59544	−0.452802	−0.226401	+	0.974034i	$0.572696\pi$
$104$	−5.32762	−0.522416
$105$	9.08782	0.886881
$106$	3.86438	0.375342
$107$	9.12956	0.882587	0.441294	−	0.897363i	$-0.354520\pi$
$107$	9.12956	0.882587	0.441294	+	0.897363i	$0.354520\pi$
$108$	21.5695	2.07552
$109$	−10.0425	−0.961895	−0.480947	−	0.876749i	$-0.659707\pi$
$109$	−10.0425	−0.961895	−0.480947	+	0.876749i	$0.659707\pi$
$110$	2.17303	0.207190
$111$	−6.45150	−0.612349
$112$	4.31563	0.407789
$113$	−12.8208	−1.20607	−0.603037	−	0.797713i	$-0.706043\pi$
$113$	−12.8208	−1.20607	−0.603037	+	0.797713i	$0.706043\pi$
$114$	11.3727	1.06515
$115$	−0.878564	−0.0819266
$116$	−11.0526	−1.02621
$117$	−16.4364	−1.51954
$118$	−7.21575	−0.664264
$119$	10.7277	0.983411
$120$	7.62127	0.695723
$121$	−0.400406	−0.0364005
$122$	−0.191293	−0.0173189
$123$	3.29768	0.297342
$124$	9.11367	0.818431
$125$	−1.00000	−0.0894427
$126$	−13.8207	−1.23124
$127$	3.93630	0.349290	0.174645	−	0.984631i	$-0.444122\pi$
$127$	3.93630	0.349290	0.174645	+	0.984631i	$0.444122\pi$
$128$	10.9952	0.971849
$129$	−36.9415	−3.25252
$130$	−1.49884	−0.131457
$131$	7.90807	0.690931	0.345466	−	0.938431i	$-0.387721\pi$
$131$	7.90807	0.690931	0.345466	+	0.938431i	$0.387721\pi$
$132$	16.2579	1.41506
$133$	15.0054	1.30114
$134$	−3.70240	−0.319839
$135$	13.8754	1.19421
$136$	8.99655	0.771448
$137$	17.0644	1.45791	0.728954	−	0.684563i	$-0.240007\pi$
$137$	17.0644	1.45791	0.728954	+	0.684563i	$0.240007\pi$
$138$	1.88374	0.160355
$139$	9.33204	0.791534	0.395767	−	0.918351i	$-0.370479\pi$
$139$	9.33204	0.791534	0.395767	+	0.918351i	$0.370479\pi$
$140$	4.39770	0.371673
$141$	43.2916	3.64581
$142$	4.71459	0.395639
$143$	−7.31101	−0.611377
$144$	11.1657	0.930472
$145$	−7.11004	−0.590456
$146$	−6.07337	−0.502636
$147$	−3.22284	−0.265815
$148$	−3.12195	−0.256623
$149$	21.6483	1.77350	0.886749	−	0.462252i	$-0.152959\pi$
$149$	21.6483	1.77350	0.886749	+	0.462252i	$0.152959\pi$
$150$	2.14411	0.175066
$151$	12.7655	1.03884	0.519421	−	0.854519i	$-0.326148\pi$
$151$	12.7655	1.03884	0.519421	+	0.854519i	$0.326148\pi$
$152$	12.5839	1.02069
$153$	27.7555	2.24390
$154$	−6.14751	−0.495381
$155$	5.86275	0.470907
$156$	−11.2138	−0.897819
$157$	−14.1190	−1.12682	−0.563410	−	0.826177i	$-0.690511\pi$
$157$	−14.1190	−1.12682	−0.563410	+	0.826177i	$0.690511\pi$
$158$	−1.30181	−0.103567
$159$	18.5988	1.47498
$160$	5.76314	0.455616
$161$	2.48546	0.195882
$162$	−15.0945	−1.18594
$163$	−2.18558	−0.171188	−0.0855940	−	0.996330i	$-0.527279\pi$
$163$	−2.18558	−0.171188	−0.0855940	+	0.996330i	$0.527279\pi$
$164$	1.59578	0.124610
$165$	10.4585	0.814197
$166$	3.63436	0.282081
$167$	−16.4531	−1.27318	−0.636590	−	0.771202i	$-0.719656\pi$
$167$	−16.4531	−1.27318	−0.636590	+	0.771202i	$0.719656\pi$
$168$	−21.5606	−1.66344
$169$	−7.95728	−0.612098
$170$	2.53103	0.194121
$171$	38.8230	2.96887
$172$	−17.8764	−1.36306
$173$	−20.5096	−1.55932	−0.779659	−	0.626205i	$-0.784607\pi$
$173$	−20.5096	−1.55932	−0.779659	+	0.626205i	$0.784607\pi$
$174$	15.2447	1.15570
$175$	2.82900	0.213852
$176$	4.96656	0.374368
$177$	−34.7286	−2.61036
$178$	−8.47546	−0.635263
$179$	5.37186	0.401511	0.200756	−	0.979641i	$-0.435660\pi$
$179$	5.37186	0.401511	0.200756	+	0.979641i	$0.435660\pi$
$180$	11.3780	0.848066
$181$	−22.1293	−1.64486	−0.822430	−	0.568867i	$-0.807382\pi$
$181$	−22.1293	−1.64486	−0.822430	+	0.568867i	$0.807382\pi$
$182$	4.24021	0.314305
$183$	−0.920673	−0.0680581
$184$	2.08437	0.153662
$185$	−2.00833	−0.147655
$186$	−12.5704	−0.921707
$187$	12.3458	0.902816
$188$	20.9493	1.52788
$189$	−39.2537	−2.85529
$190$	3.54027	0.256838
$191$	9.68490	0.700775	0.350387	−	0.936605i	$-0.386050\pi$
$191$	9.68490	0.700775	0.350387	+	0.936605i	$0.386050\pi$
$192$	−2.55589	−0.184456
$193$	−15.2046	−1.09445	−0.547225	−	0.836986i	$-0.684316\pi$
$193$	−15.2046	−1.09445	−0.547225	+	0.836986i	$0.684316\pi$
$194$	6.20101	0.445207
$195$	−7.21372	−0.516585
$196$	−1.55957	−0.111398
$197$	−17.1349	−1.22081	−0.610404	−	0.792090i	$-0.708993\pi$
$197$	−17.1349	−1.22081	−0.610404	+	0.792090i	$0.708993\pi$
$198$	−15.9052	−1.13034
$199$	6.37923	0.452212	0.226106	−	0.974103i	$-0.427400\pi$
$199$	6.37923	0.452212	0.226106	+	0.974103i	$0.427400\pi$
$200$	2.37247	0.167759
$201$	−17.8192	−1.25687
$202$	−9.42384	−0.663059
$203$	20.1143	1.41175
$204$	18.9362	1.32580
$205$	1.02655	0.0716977
$206$	3.06725	0.213705
$207$	6.43054	0.446953
$208$	−3.42565	−0.237526
$209$	17.2687	1.19450
$210$	−6.06571	−0.418574
$211$	14.3149	0.985476	0.492738	−	0.870178i	$-0.335996\pi$
$211$	14.3149	0.985476	0.492738	+	0.870178i	$0.335996\pi$
$212$	9.00017	0.618134
$213$	22.6907	1.55474
$214$	−6.09356	−0.416547
$215$	−11.4997	−0.784276
$216$	−32.9191	−2.23986
$217$	−16.5857	−1.12591
$218$	6.70289	0.453977
$219$	−29.2304	−1.97521
$220$	5.06100	0.341213
$221$	−8.51545	−0.572811
$222$	4.30608	0.289005
$223$	−10.3387	−0.692331	−0.346166	−	0.938173i	$-0.612516\pi$
$223$	−10.3387	−0.692331	−0.346166	+	0.938173i	$0.612516\pi$
$224$	−16.3039	−1.08935
$225$	7.31937	0.487958
$226$	8.55727	0.569221
$227$	10.8444	0.719766	0.359883	−	0.932997i	$-0.382817\pi$
$227$	10.8444	0.719766	0.359883	+	0.932997i	$0.382817\pi$
$228$	26.4871	1.75415
$229$	−22.4028	−1.48042	−0.740210	−	0.672375i	$-0.765274\pi$
$229$	−22.4028	−1.48042	−0.740210	+	0.672375i	$0.765274\pi$
$230$	0.586401	0.0386662
$231$	−29.5872	−1.94670
$232$	16.8683	1.10746
$233$	−3.08377	−0.202024	−0.101012	−	0.994885i	$-0.532208\pi$
$233$	−3.08377	−0.202024	−0.101012	+	0.994885i	$0.532208\pi$
$234$	10.9705	0.717166
$235$	13.4765	0.879110
$236$	−16.8055	−1.09395
$237$	−6.26548	−0.406986
$238$	−7.16028	−0.464132
$239$	24.7857	1.60326	0.801628	−	0.597823i	$-0.203967\pi$
$239$	24.7857	1.60326	0.801628	+	0.597823i	$0.203967\pi$
$240$	4.90047	0.316324
$241$	−6.39171	−0.411726	−0.205863	−	0.978581i	$-0.566000\pi$
$241$	−6.39171	−0.411726	−0.205863	+	0.978581i	$0.566000\pi$
$242$	0.267253	0.0171796
$243$	−31.0218	−1.99005
$244$	−0.445524	−0.0285217
$245$	−1.00326	−0.0640956
$246$	−2.20105	−0.140334
$247$	−11.9110	−0.757878
$248$	−13.9092	−0.883234
$249$	17.4918	1.10849
$250$	0.667454	0.0422135
$251$	−7.54077	−0.475969	−0.237985	−	0.971269i	$-0.576487\pi$
$251$	−7.54077	−0.475969	−0.237985	+	0.971269i	$0.576487\pi$
$252$	−32.1884	−2.02768
$253$	2.86034	0.179828
$254$	−2.62730	−0.164852
$255$	12.1815	0.762837
$256$	−8.93008	−0.558130
$257$	15.7451	0.982153	0.491077	−	0.871116i	$-0.336603\pi$
$257$	15.7451	0.982153	0.491077	+	0.871116i	$0.336603\pi$
$258$	24.6568	1.53506
$259$	5.68156	0.353035
$260$	−3.49080	−0.216490
$261$	52.0410	3.22126
$262$	−5.27827	−0.326093
$263$	−8.16498	−0.503474	−0.251737	−	0.967796i	$-0.581002\pi$
$263$	−8.16498	−0.503474	−0.251737	+	0.967796i	$0.581002\pi$
$264$	−24.8126	−1.52711
$265$	5.78974	0.355661
$266$	−10.0154	−0.614086
$267$	−40.7914	−2.49639
$268$	−8.62292	−0.526728
$269$	20.8306	1.27006	0.635031	−	0.772487i	$-0.280987\pi$
$269$	20.8306	1.27006	0.635031	+	0.772487i	$0.280987\pi$
$270$	−9.26123	−0.563620
$271$	−16.5149	−1.00321	−0.501606	−	0.865096i	$-0.667257\pi$
$271$	−16.5149	−1.00321	−0.501606	+	0.865096i	$0.667257\pi$
$272$	5.78477	0.350753
$273$	20.4076	1.23513
$274$	−11.3897	−0.688076
$275$	3.25570	0.196326
$276$	4.38725	0.264081
$277$	−2.00220	−0.120300	−0.0601501	−	0.998189i	$-0.519158\pi$
$277$	−2.00220	−0.120300	−0.0601501	+	0.998189i	$0.519158\pi$
$278$	−6.22871	−0.373573
$279$	−42.9116	−2.56905
$280$	−6.71172	−0.401102
$281$	−22.2038	−1.32457	−0.662285	−	0.749252i	$-0.730413\pi$
$281$	−22.2038	−1.32457	−0.662285	+	0.749252i	$0.730413\pi$
$282$	−28.8952	−1.72068
$283$	22.3883	1.33085	0.665424	−	0.746466i	$-0.268251\pi$
$283$	22.3883	1.33085	0.665424	+	0.746466i	$0.268251\pi$
$284$	10.9803	0.651561
$285$	17.0389	1.00930
$286$	4.87976	0.288546
$287$	−2.90412	−0.171425
$288$	−42.1825	−2.48563
$289$	−2.62028	−0.154134
$290$	4.74562	0.278673
$291$	29.8447	1.74953
$292$	−14.1449	−0.827769
$293$	−8.26885	−0.483071	−0.241536	−	0.970392i	$-0.577651\pi$
$293$	−8.26885	−0.483071	−0.241536	+	0.970392i	$0.577651\pi$
$294$	2.15109	0.125454
$295$	−10.8109	−0.629432
$296$	4.76469	0.276942
$297$	−45.1743	−2.62128
$298$	−14.4492	−0.837022
$299$	−1.97290	−0.114096
$300$	4.99366	0.288309
$301$	32.5328	1.87516
$302$	−8.52038	−0.490293
$303$	−45.3558	−2.60562
$304$	8.09144	0.464076
$305$	−0.286602	−0.0164108
$306$	−18.5255	−1.05903
$307$	4.72377	0.269600	0.134800	−	0.990873i	$-0.456961\pi$
$307$	4.72377	0.269600	0.134800	+	0.990873i	$0.456961\pi$
$308$	−14.3176	−0.815821
$309$	14.7623	0.839797
$310$	−3.91311	−0.222250
$311$	12.0054	0.680765	0.340383	−	0.940287i	$-0.389443\pi$
$311$	12.0054	0.680765	0.340383	+	0.940287i	$0.389443\pi$
$312$	17.1143	0.968908
$313$	19.3260	1.09237	0.546185	−	0.837665i	$-0.316080\pi$
$313$	19.3260	1.09237	0.546185	+	0.837665i	$0.316080\pi$
$314$	9.42380	0.531816
$315$	−20.7065	−1.16668
$316$	−3.03193	−0.170560
$317$	19.4719	1.09365	0.546826	−	0.837246i	$-0.315836\pi$
$317$	19.4719	1.09365	0.546826	+	0.837246i	$0.315836\pi$
$318$	−12.4139	−0.696135
$319$	23.1482	1.29605
$320$	−0.795639	−0.0444776
$321$	−29.3276	−1.63691
$322$	−1.65893	−0.0924486
$323$	20.1136	1.11915
$324$	−35.1552	−1.95307
$325$	−2.24560	−0.124564
$326$	1.45878	0.0807941
$327$	32.2602	1.78399
$328$	−2.43547	−0.134476
$329$	−38.1251	−2.10190
$330$	−6.98060	−0.384269
$331$	−3.77898	−0.207711	−0.103856	−	0.994592i	$-0.533118\pi$
$331$	−3.77898	−0.207711	−0.103856	+	0.994592i	$0.533118\pi$
$332$	8.46445	0.464547
$333$	14.6997	0.805538
$334$	10.9817	0.600892
$335$	−5.54705	−0.303068
$336$	−13.8634	−0.756312
$337$	−2.02773	−0.110457	−0.0552287	−	0.998474i	$-0.517589\pi$
$337$	−2.02773	−0.110457	−0.0552287	+	0.998474i	$0.517589\pi$
$338$	5.31112	0.288887
$339$	41.1851	2.23687
$340$	5.89478	0.319689
$341$	−19.0874	−1.03364
$342$	−25.9126	−1.40119
$343$	−16.9648	−0.916013
$344$	27.2828	1.47099
$345$	2.82228	0.151946
$346$	13.6892	0.735938
$347$	36.6002	1.96480	0.982402	−	0.186778i	$-0.0598046\pi$
$347$	36.6002	1.96480	0.982402	+	0.186778i	$0.0598046\pi$
$348$	35.5051	1.90327
$349$	−2.38879	−0.127869	−0.0639345	−	0.997954i	$-0.520365\pi$
$349$	−2.38879	−0.127869	−0.0639345	+	0.997954i	$0.520365\pi$
$350$	−1.88823	−0.100930
$351$	31.1587	1.66313
$352$	−18.7631	−1.00007
$353$	7.48397	0.398331	0.199166	−	0.979966i	$-0.436177\pi$
$353$	7.48397	0.398331	0.199166	+	0.979966i	$0.436177\pi$
$354$	23.1797	1.23199
$355$	7.06353	0.374893
$356$	−19.7394	−1.04619
$357$	−34.4616	−1.82390
$358$	−3.58547	−0.189498
$359$	−5.53220	−0.291978	−0.145989	−	0.989286i	$-0.546636\pi$
$359$	−5.53220	−0.291978	−0.145989	+	0.989286i	$0.546636\pi$
$360$	−17.3650	−0.915215
$361$	9.13392	0.480733
$362$	14.7703	0.776310
$363$	1.28626	0.0675109
$364$	9.87547	0.517616
$365$	−9.09931	−0.476280
$366$	0.614507	0.0321208
$367$	31.2744	1.63251	0.816254	−	0.577693i	$-0.196047\pi$
$367$	31.2744	1.63251	0.816254	+	0.577693i	$0.196047\pi$
$368$	1.34025	0.0698651
$369$	−7.51373	−0.391149
$370$	1.34047	0.0696875
$371$	−16.3792	−0.850364
$372$	−29.2765	−1.51792
$373$	−2.64606	−0.137008	−0.0685040	−	0.997651i	$-0.521823\pi$
$373$	−2.64606	−0.137008	−0.0685040	+	0.997651i	$0.521823\pi$
$374$	−8.24027	−0.426094
$375$	3.21238	0.165886
$376$	−31.9726	−1.64886
$377$	−15.9663	−0.822306
$378$	26.2000	1.34758
$379$	6.59242	0.338630	0.169315	−	0.985562i	$-0.445845\pi$
$379$	6.59242	0.338630	0.169315	+	0.985562i	$0.445845\pi$
$380$	8.24531	0.422976
$381$	−12.6449	−0.647817
$382$	−6.46423	−0.330739
$383$	20.1841	1.03136	0.515679	−	0.856782i	$-0.327540\pi$
$383$	20.1841	1.03136	0.515679	+	0.856782i	$0.327540\pi$
$384$	−35.3208	−1.80246
$385$	−9.21039	−0.469405
$386$	10.1484	0.516538
$387$	84.1708	4.27864
$388$	14.4422	0.733191
$389$	28.0119	1.42026	0.710130	−	0.704071i	$-0.248636\pi$
$389$	28.0119	1.42026	0.710130	+	0.704071i	$0.248636\pi$
$390$	4.81483	0.243808
$391$	3.33157	0.168485
$392$	2.38019	0.120218
$393$	−25.4037	−1.28145
$394$	11.4367	0.576174
$395$	−1.95042	−0.0981361
$396$	−37.0434	−1.86150
$397$	−22.1799	−1.11318	−0.556589	−	0.830788i	$-0.687890\pi$
$397$	−22.1799	−1.11318	−0.556589	+	0.830788i	$0.687890\pi$
$398$	−4.25785	−0.213427
$399$	−48.2031	−2.41317
$400$	1.52550	0.0762748
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	11.8935	0.593195
$403$	13.1654	0.655815
$404$	−21.9482	−1.09196
$405$	−22.6151	−1.12375
$406$	−13.4254	−0.666290
$407$	6.53851	0.324102
$408$	−28.9003	−1.43078
$409$	27.1553	1.34274	0.671372	−	0.741120i	$-0.265705\pi$
$409$	27.1553	1.34274	0.671372	+	0.741120i	$0.265705\pi$
$410$	−0.685178	−0.0338385
$411$	−54.8172	−2.70393
$412$	7.14363	0.351942
$413$	30.5839	1.50494
$414$	−4.29209	−0.210945
$415$	5.44511	0.267290
$416$	12.9417	0.634519
$417$	−29.9780	−1.46803
$418$	−11.5261	−0.563758
$419$	15.8959	0.776568	0.388284	−	0.921540i	$-0.373068\pi$
$419$	15.8959	0.776568	0.388284	+	0.921540i	$0.373068\pi$
$420$	−14.1271	−0.689330
$421$	7.02056	0.342161	0.171081	−	0.985257i	$-0.445274\pi$
$421$	7.02056	0.342161	0.171081	+	0.985257i	$0.445274\pi$
$422$	−9.55452	−0.465107
$423$	−98.6395	−4.79602
$424$	−13.7360	−0.667078
$425$	3.79206	0.183942
$426$	−15.1450	−0.733779
$427$	0.810797	0.0392372
$428$	−14.1919	−0.685993
$429$	23.4857	1.13390
$430$	7.67555	0.370148
$431$	14.0731	0.677878	0.338939	−	0.940808i	$-0.389932\pi$
$431$	14.0731	0.677878	0.338939	+	0.940808i	$0.389932\pi$
$432$	−21.1669	−1.01839
$433$	7.87924	0.378652	0.189326	−	0.981914i	$-0.439370\pi$
$433$	7.87924	0.378652	0.189326	+	0.981914i	$0.439370\pi$
$434$	11.0702	0.531387
$435$	22.8401	1.09510
$436$	15.6111	0.747635
$437$	4.66003	0.222919
$438$	19.5100	0.932222
$439$	30.9691	1.47807	0.739037	−	0.673665i	$-0.235281\pi$
$439$	30.9691	1.47807	0.739037	+	0.673665i	$0.235281\pi$
$440$	−7.72405	−0.368230
$441$	7.34320	0.349676
$442$	5.68368	0.270345
$443$	4.82657	0.229317	0.114659	−	0.993405i	$-0.463423\pi$
$443$	4.82657	0.229317	0.114659	+	0.993405i	$0.463423\pi$
$444$	10.0289	0.475950
$445$	−12.6982	−0.601952
$446$	6.90061	0.326754
$447$	−69.5425	−3.28925
$448$	2.25087	0.106343
$449$	−15.5729	−0.734930	−0.367465	−	0.930037i	$-0.619774\pi$
$449$	−15.5729	−0.734930	−0.367465	+	0.930037i	$0.619774\pi$
$450$	−4.88534	−0.230297
$451$	−3.34215	−0.157376
$452$	19.9299	0.937425
$453$	−41.0076	−1.92670
$454$	−7.23812	−0.339702
$455$	6.35281	0.297824
$456$	−40.4243	−1.89304
$457$	28.9636	1.35486	0.677430	−	0.735587i	$-0.263093\pi$
$457$	28.9636	1.35486	0.677430	+	0.735587i	$0.263093\pi$
$458$	14.9529	0.698701
$459$	−52.6165	−2.45593
$460$	1.36573	0.0636776
$461$	−6.40160	−0.298152	−0.149076	−	0.988826i	$-0.547630\pi$
$461$	−6.40160	−0.298152	−0.149076	+	0.988826i	$0.547630\pi$
$462$	19.7481	0.918766
$463$	−30.4032	−1.41296	−0.706479	−	0.707734i	$-0.749717\pi$
$463$	−30.4032	−1.41296	−0.706479	+	0.707734i	$0.749717\pi$
$464$	10.8463	0.503528
$465$	−18.8334	−0.873376
$466$	2.05827	0.0953477
$467$	−17.7983	−0.823609	−0.411804	−	0.911272i	$-0.635101\pi$
$467$	−17.7983	−0.823609	−0.411804	+	0.911272i	$0.635101\pi$
$468$	25.5504	1.18107
$469$	15.6926	0.724618
$470$	−8.99495	−0.414906
$471$	45.3556	2.08988
$472$	25.6484	1.18056
$473$	37.4397	1.72148
$474$	4.18192	0.192082
$475$	5.30414	0.243371
$476$	−16.6763	−0.764359
$477$	−42.3772	−1.94032
$478$	−16.5433	−0.756675
$479$	−35.0620	−1.60202	−0.801012	−	0.598648i	$-0.795705\pi$
$479$	−35.0620	−1.60202	−0.801012	+	0.598648i	$0.795705\pi$
$480$	−18.5134	−0.845016
$481$	−4.50990	−0.205634
$482$	4.26617	0.194319
$483$	−7.98424	−0.363295
$484$	0.622433	0.0282924
$485$	9.29054	0.421862
$486$	20.7056	0.939227
$487$	3.84000	0.174007	0.0870034	−	0.996208i	$-0.472271\pi$
$487$	3.84000	0.174007	0.0870034	+	0.996208i	$0.472271\pi$
$488$	0.679954	0.0307800
$489$	7.02092	0.317497
$490$	0.669627	0.0302507
$491$	24.9978	1.12813	0.564066	−	0.825729i	$-0.309236\pi$
$491$	24.9978	1.12813	0.564066	+	0.825729i	$0.309236\pi$
$492$	−5.12626	−0.231110
$493$	26.9617	1.21429
$494$	7.95004	0.357689
$495$	−23.8297	−1.07106
$496$	−8.94359	−0.401579
$497$	−19.9828	−0.896349
$498$	−11.6749	−0.523167
$499$	−35.7808	−1.60177	−0.800885	−	0.598819i	$-0.795637\pi$
$499$	−35.7808	−1.60177	−0.800885	+	0.598819i	$0.795637\pi$
$500$	1.55450	0.0695196
$501$	52.8536	2.36132
$502$	5.03312	0.224639
$503$	36.2480	1.61622	0.808109	−	0.589033i	$-0.200491\pi$
$503$	36.2480	1.61622	0.808109	+	0.589033i	$0.200491\pi$
$504$	49.1256	2.18823
$505$	−14.1191	−0.628291
$506$	−1.90915	−0.0848720
$507$	25.5618	1.13524
$508$	−6.11900	−0.271487
$509$	−23.1254	−1.02501	−0.512507	−	0.858683i	$-0.671283\pi$
$509$	−23.1254	−1.02501	−0.512507	+	0.858683i	$0.671283\pi$
$510$	−8.13061	−0.360030
$511$	25.7420	1.13876
$512$	−16.0300	−0.708433
$513$	−73.5974	−3.24940
$514$	−10.5091	−0.463538
$515$	4.59544	0.202499
$516$	57.4257	2.52803
$517$	−43.8755	−1.92964
$518$	−3.79218	−0.166619
$519$	65.8846	2.89202
$520$	5.32762	0.233632
$521$	15.2132	0.666504	0.333252	−	0.942838i	$-0.391854\pi$
$521$	15.2132	0.666504	0.333252	+	0.942838i	$0.391854\pi$
$522$	−34.7350	−1.52031
$523$	40.7584	1.78224	0.891121	−	0.453766i	$-0.149920\pi$
$523$	40.7584	1.78224	0.891121	+	0.453766i	$0.149920\pi$
$524$	−12.2931	−0.537028
$525$	−9.08782	−0.396625
$526$	5.44975	0.237620
$527$	−22.2319	−0.968436
$528$	−15.9545	−0.694329
$529$	−22.2281	−0.966440
$530$	−3.86438	−0.167858
$531$	79.1287	3.43389
$532$	−23.3260	−1.01131
$533$	2.30523	0.0998506
$534$	27.2264	1.17820
$535$	−9.12956	−0.394705
$536$	13.1602	0.568434
$537$	−17.2564	−0.744670
$538$	−13.9034	−0.599420
$539$	3.26630	0.140690
$540$	−21.5695	−0.928202
$541$	25.8941	1.11327	0.556637	−	0.830756i	$-0.312091\pi$
$541$	25.8941	1.11327	0.556637	+	0.830756i	$0.312091\pi$
$542$	11.0230	0.473477
$543$	71.0877	3.05067
$544$	−21.8542	−0.936990
$545$	10.0425	0.430172
$546$	−13.6212	−0.582932
$547$	24.3851	1.04263	0.521316	−	0.853364i	$-0.325441\pi$
$547$	24.3851	1.04263	0.521316	+	0.853364i	$0.325441\pi$
$548$	−26.5267	−1.13316
$549$	2.09774	0.0895295
$550$	−2.17303	−0.0926584
$551$	37.7126	1.60661
$552$	−6.69577	−0.284991
$553$	5.51773	0.234638
$554$	1.33637	0.0567771
$555$	6.45150	0.273851
$556$	−14.5067	−0.615221
$557$	2.31914	0.0982651	0.0491326	−	0.998792i	$-0.484354\pi$
$557$	2.31914	0.0982651	0.0491326	+	0.998792i	$0.484354\pi$
$558$	28.6415	1.21249
$559$	−25.8238	−1.09223
$560$	−4.31563	−0.182369
$561$	−39.6594	−1.67442
$562$	14.8201	0.625146
$563$	−5.95982	−0.251177	−0.125588	−	0.992082i	$-0.540082\pi$
$563$	−5.95982	−0.251177	−0.125588	+	0.992082i	$0.540082\pi$
$564$	−67.2970	−2.83372
$565$	12.8208	0.539373
$566$	−14.9432	−0.628109
$567$	63.9781	2.68683
$568$	−16.7580	−0.703151
$569$	35.9990	1.50916	0.754578	−	0.656210i	$-0.227842\pi$
$569$	35.9990	1.50916	0.754578	+	0.656210i	$0.227842\pi$
$570$	−11.3727	−0.476350
$571$	9.06765	0.379469	0.189735	−	0.981835i	$-0.439237\pi$
$571$	9.06765	0.379469	0.189735	+	0.981835i	$0.439237\pi$
$572$	11.3650	0.475194
$573$	−31.1116	−1.29970
$574$	1.93837	0.0809060
$575$	0.878564	0.0366387
$576$	5.82358	0.242649
$577$	−22.3796	−0.931673	−0.465837	−	0.884871i	$-0.654247\pi$
$577$	−22.3796	−0.931673	−0.465837	+	0.884871i	$0.654247\pi$
$578$	1.74891	0.0727453
$579$	48.8429	2.02984
$580$	11.0526	0.458934
$581$	−15.4042	−0.639075
$582$	−19.9200	−0.825710
$583$	−18.8497	−0.780673
$584$	21.5878	0.893311
$585$	16.4364	0.679561
$586$	5.51908	0.227991
$587$	40.6003	1.67575	0.837877	−	0.545860i	$-0.183797\pi$
$587$	40.6003	1.67575	0.837877	+	0.545860i	$0.183797\pi$
$588$	5.00991	0.206605
$589$	−31.0968	−1.28132
$590$	7.21575	0.297068
$591$	55.0436	2.26419
$592$	3.06369	0.125917
$593$	10.2761	0.421989	0.210994	−	0.977487i	$-0.432330\pi$
$593$	10.2761	0.421989	0.210994	+	0.977487i	$0.432330\pi$
$594$	30.1518	1.23714
$595$	−10.7277	−0.439795
$596$	−33.6524	−1.37845
$597$	−20.4925	−0.838702
$598$	1.31682	0.0538489
$599$	−11.6513	−0.476058	−0.238029	−	0.971258i	$-0.576501\pi$
$599$	−11.6513	−0.476058	−0.238029	+	0.971258i	$0.576501\pi$
$600$	−7.62127	−0.311137
$601$	−19.9760	−0.814836	−0.407418	−	0.913242i	$-0.633571\pi$
$601$	−19.9760	−0.814836	−0.407418	+	0.913242i	$0.633571\pi$
$602$	−21.7141	−0.885003
$603$	40.6009	1.65340
$604$	−19.8440	−0.807442
$605$	0.400406	0.0162788
$606$	30.2729	1.22975
$607$	−46.0854	−1.87055	−0.935274	−	0.353926i	$-0.884847\pi$
$607$	−46.0854	−1.87055	−0.935274	+	0.353926i	$0.884847\pi$
$608$	−30.5685	−1.23972
$609$	−64.6148	−2.61832
$610$	0.191293	0.00774525
$611$	30.2628	1.22430
$612$	−43.1461	−1.74408
$613$	−27.4120	−1.10716	−0.553579	−	0.832796i	$-0.686738\pi$
$613$	−27.4120	−1.10716	−0.553579	+	0.832796i	$0.686738\pi$
$614$	−3.15290	−0.127241
$615$	−3.29768	−0.132975
$616$	21.8514	0.880417
$617$	23.8006	0.958175	0.479088	−	0.877767i	$-0.340968\pi$
$617$	23.8006	0.958175	0.479088	+	0.877767i	$0.340968\pi$
$618$	−9.85315	−0.396352
$619$	−30.8955	−1.24179	−0.620897	−	0.783892i	$-0.713232\pi$
$619$	−30.8955	−1.24179	−0.620897	+	0.783892i	$0.713232\pi$
$620$	−9.11367	−0.366014
$621$	−12.1905	−0.489187
$622$	−8.01307	−0.321295
$623$	35.9232	1.43923
$624$	11.0045	0.440532
$625$	1.00000	0.0400000
$626$	−12.8992	−0.515556
$627$	−55.4736	−2.21540
$628$	21.9481	0.875824
$629$	7.61569	0.303658
$630$	13.8207	0.550628
$631$	26.6166	1.05959	0.529795	−	0.848126i	$-0.322269\pi$
$631$	26.6166	1.05959	0.529795	+	0.848126i	$0.322269\pi$
$632$	4.62730	0.184064
$633$	−45.9848	−1.82773
$634$	−12.9966	−0.516161
$635$	−3.93630	−0.156207
$636$	−28.9120	−1.14643
$637$	−2.25291	−0.0892636
$638$	−15.4503	−0.611685
$639$	−51.7006	−2.04525
$640$	−10.9952	−0.434624
$641$	39.3962	1.55606	0.778029	−	0.628229i	$-0.216220\pi$
$641$	39.3962	1.55606	0.778029	+	0.628229i	$0.216220\pi$
$642$	19.5748	0.772556
$643$	23.2079	0.915229	0.457615	−	0.889151i	$-0.348704\pi$
$643$	23.2079	0.915229	0.457615	+	0.889151i	$0.348704\pi$
$644$	−3.86366	−0.152250
$645$	36.9415	1.45457
$646$	−13.4249	−0.528197
$647$	−6.18877	−0.243305	−0.121653	−	0.992573i	$-0.538819\pi$
$647$	−6.18877	−0.243305	−0.121653	+	0.992573i	$0.538819\pi$
$648$	53.6536	2.10771
$649$	35.1969	1.38160
$650$	1.49884	0.0587892
$651$	53.2796	2.08819
$652$	3.39750	0.133056
$653$	−3.27878	−0.128309	−0.0641543	−	0.997940i	$-0.520435\pi$
$653$	−3.27878	−0.128309	−0.0641543	+	0.997940i	$0.520435\pi$
$654$	−21.5322	−0.841977
$655$	−7.90807	−0.308994
$656$	−1.56600	−0.0611422
$657$	66.6012	2.59836
$658$	25.4467	0.992017
$659$	30.2426	1.17808	0.589042	−	0.808102i	$-0.299505\pi$
$659$	30.2426	1.17808	0.589042	+	0.808102i	$0.299505\pi$
$660$	−16.2579	−0.632836
$661$	−9.78983	−0.380780	−0.190390	−	0.981709i	$-0.560975\pi$
$661$	−9.78983	−0.380780	−0.190390	+	0.981709i	$0.560975\pi$
$662$	2.52229	0.0980317
$663$	27.3549	1.06237
$664$	−12.9184	−0.501329
$665$	−15.0054	−0.581886
$666$	−9.81136	−0.380183
$667$	6.24662	0.241870
$668$	25.5764	0.989582
$669$	33.2118	1.28404
$670$	3.70240	0.143036
$671$	0.933089	0.0360215
$672$	52.3744	2.02039
$673$	−44.7335	−1.72435	−0.862174	−	0.506612i	$-0.830898\pi$
$673$	−44.7335	−1.72435	−0.862174	+	0.506612i	$0.830898\pi$
$674$	1.35341	0.0521316
$675$	−13.8754	−0.534066
$676$	12.3696	0.475755
$677$	21.3473	0.820442	0.410221	−	0.911986i	$-0.365452\pi$
$677$	21.3473	0.820442	0.410221	+	0.911986i	$0.365452\pi$
$678$	−27.4892	−1.05572
$679$	−26.2830	−1.00865
$680$	−8.99655	−0.345002
$681$	−34.8362	−1.33493
$682$	12.7399	0.487837
$683$	19.5100	0.746531	0.373266	−	0.927725i	$-0.378238\pi$
$683$	19.5100	0.746531	0.373266	+	0.927725i	$0.378238\pi$
$684$	−60.3505	−2.30756
$685$	−17.0644	−0.651996
$686$	11.3232	0.432323
$687$	71.9663	2.74569
$688$	17.5428	0.668813
$689$	13.0014	0.495315
$690$	−1.88374	−0.0717129
$691$	−39.8643	−1.51651	−0.758255	−	0.651958i	$-0.773948\pi$
$691$	−39.8643	−1.51651	−0.758255	+	0.651958i	$0.773948\pi$
$692$	31.8823	1.21198
$693$	67.4142	2.56086
$694$	−24.4290	−0.927312
$695$	−9.33204	−0.353985
$696$	−54.1875	−2.05397
$697$	−3.89276	−0.147449
$698$	1.59441	0.0603492
$699$	9.90623	0.374688
$700$	−4.39770	−0.166217
$701$	−38.9457	−1.47096	−0.735479	−	0.677548i	$-0.763043\pi$
$701$	−38.9457	−1.47096	−0.735479	+	0.677548i	$0.763043\pi$
$702$	−20.7970	−0.784933
$703$	10.6524	0.401765
$704$	2.59036	0.0976280
$705$	−43.2916	−1.63046
$706$	−4.99520	−0.187997
$707$	39.9429	1.50221
$708$	53.9857	2.02891
$709$	−13.5550	−0.509070	−0.254535	−	0.967064i	$-0.581922\pi$
$709$	−13.5550	−0.509070	−0.254535	+	0.967064i	$0.581922\pi$
$710$	−4.71459	−0.176935
$711$	14.2758	0.535385
$712$	30.1261	1.12902
$713$	−5.15080	−0.192899
$714$	23.0015	0.860811
$715$	7.31101	0.273416
$716$	−8.35058	−0.312076
$717$	−79.6212	−2.97351
$718$	3.69249	0.137802
$719$	−49.4830	−1.84540	−0.922702	−	0.385514i	$-0.874024\pi$
$719$	−49.4830	−1.84540	−0.922702	+	0.385514i	$0.874024\pi$
$720$	−11.1657	−0.416120
$721$	−13.0005	−0.484164
$722$	−6.09647	−0.226887
$723$	20.5326	0.763615
$724$	34.4001	1.27847
$725$	7.11004	0.264060
$726$	−0.858516	−0.0318625
$727$	28.5395	1.05847	0.529235	−	0.848475i	$-0.322479\pi$
$727$	28.5395	1.05847	0.529235	+	0.848475i	$0.322479\pi$
$728$	−15.0718	−0.558600
$729$	31.8085	1.17809
$730$	6.07337	0.224786
$731$	43.6077	1.61289
$732$	1.43119	0.0528983
$733$	5.31362	0.196263	0.0981316	−	0.995173i	$-0.468713\pi$
$733$	5.31362	0.196263	0.0981316	+	0.995173i	$0.468713\pi$
$734$	−20.8742	−0.770481
$735$	3.22284	0.118876
$736$	−5.06329	−0.186635
$737$	18.0595	0.665232
$738$	5.01507	0.184607
$739$	−23.5291	−0.865533	−0.432766	−	0.901506i	$-0.642462\pi$
$739$	−23.5291	−0.865533	−0.432766	+	0.901506i	$0.642462\pi$
$740$	3.12195	0.114765
$741$	38.2626	1.40561
$742$	10.9324	0.401339
$743$	−3.96082	−0.145308	−0.0726542	−	0.997357i	$-0.523147\pi$
$743$	−3.96082	−0.145308	−0.0726542	+	0.997357i	$0.523147\pi$
$744$	44.6816	1.63811
$745$	−21.6483	−0.793132
$746$	1.76613	0.0646625
$747$	−39.8548	−1.45821
$748$	−19.1916	−0.701716
$749$	25.8275	0.943718
$750$	−2.14411	−0.0782920
$751$	−21.5715	−0.787156	−0.393578	−	0.919291i	$-0.628763\pi$
$751$	−21.5715	−0.787156	−0.393578	+	0.919291i	$0.628763\pi$
$752$	−20.5583	−0.749686
$753$	24.2238	0.882765
$754$	10.6568	0.388097
$755$	−12.7655	−0.464584
$756$	61.0200	2.21928
$757$	−16.9016	−0.614299	−0.307149	−	0.951661i	$-0.599375\pi$
$757$	−16.9016	−0.614299	−0.307149	+	0.951661i	$0.599375\pi$
$758$	−4.40014	−0.159820
$759$	−9.18850	−0.333522
$760$	−12.5839	−0.456467
$761$	−52.8353	−1.91528	−0.957639	−	0.287971i	$-0.907019\pi$
$761$	−52.8353	−1.91528	−0.957639	+	0.287971i	$0.907019\pi$
$762$	8.43988	0.305745
$763$	−28.4102	−1.02852
$764$	−15.0552	−0.544679
$765$	−27.7555	−1.00350
$766$	−13.4719	−0.486761
$767$	−24.2769	−0.876587
$768$	28.6868	1.03515
$769$	3.55278	0.128117	0.0640583	−	0.997946i	$-0.479596\pi$
$769$	3.55278	0.128117	0.0640583	+	0.997946i	$0.479596\pi$
$770$	6.14751	0.221541
$771$	−50.5793	−1.82157
$772$	23.6356	0.850664
$773$	8.26693	0.297341	0.148670	−	0.988887i	$-0.452501\pi$
$773$	8.26693	0.297341	0.148670	+	0.988887i	$0.452501\pi$
$774$	−56.1802	−2.01936
$775$	−5.86275	−0.210596
$776$	−22.0415	−0.791245
$777$	−18.2513	−0.654762
$778$	−18.6967	−0.670308
$779$	−5.44499	−0.195087
$780$	11.2138	0.401517
$781$	−22.9968	−0.822889
$782$	−2.22367	−0.0795183
$783$	−98.6549	−3.52564
$784$	1.53046	0.0546593
$785$	14.1190	0.503930
$786$	16.9558	0.604794
$787$	7.05063	0.251328	0.125664	−	0.992073i	$-0.459894\pi$
$787$	7.05063	0.251328	0.125664	+	0.992073i	$0.459894\pi$
$788$	26.6362	0.948876
$789$	26.2290	0.933777
$790$	1.30181	0.0463165
$791$	−36.2699	−1.28961
$792$	56.5352	2.00889
$793$	−0.643593	−0.0228547
$794$	14.8041	0.525377
$795$	−18.5988	−0.659632
$796$	−9.91655	−0.351483
$797$	21.0784	0.746635	0.373318	−	0.927704i	$-0.378220\pi$
$797$	21.0784	0.746635	0.373318	+	0.927704i	$0.378220\pi$
$798$	32.1734	1.13892
$799$	−51.1037	−1.80792
$800$	−5.76314	−0.203758
$801$	92.9428	3.28397
$802$	−0.667454	−0.0235686
$803$	29.6246	1.04543
$804$	27.7001	0.976906
$805$	−2.48546	−0.0876010
$806$	−8.78729	−0.309519
$807$	−66.9156	−2.35554
$808$	33.4971	1.17842
$809$	11.1487	0.391968	0.195984	−	0.980607i	$-0.437210\pi$
$809$	11.1487	0.391968	0.195984	+	0.980607i	$0.437210\pi$
$810$	15.0945	0.530368
$811$	35.0040	1.22916	0.614578	−	0.788856i	$-0.289326\pi$
$811$	35.0040	1.22916	0.614578	+	0.788856i	$0.289326\pi$
$812$	−31.2678	−1.09728
$813$	53.0523	1.86062
$814$	−4.36416	−0.152964
$815$	2.18558	0.0765576
$816$	−18.5829	−0.650530
$817$	60.9962	2.13399
$818$	−18.1249	−0.633724
$819$	−46.4986	−1.62479
$820$	−1.59578	−0.0557272
$821$	2.60183	0.0908046	0.0454023	−	0.998969i	$-0.485543\pi$
$821$	2.60183	0.0908046	0.0454023	+	0.998969i	$0.485543\pi$
$822$	36.5880	1.27615
$823$	−7.29027	−0.254123	−0.127061	−	0.991895i	$-0.540555\pi$
$823$	−7.29027	−0.254123	−0.127061	+	0.991895i	$0.540555\pi$
$824$	−10.9025	−0.379808
$825$	−10.4585	−0.364120
$826$	−20.4134	−0.710272
$827$	−55.4252	−1.92732	−0.963661	−	0.267129i	$-0.913925\pi$
$827$	−55.4252	−1.92732	−0.963661	+	0.267129i	$0.913925\pi$
$828$	−9.99630	−0.347396
$829$	−50.0894	−1.73968	−0.869838	−	0.493338i	$-0.835777\pi$
$829$	−50.0894	−1.73968	−0.869838	+	0.493338i	$0.835777\pi$
$830$	−3.63436	−0.126151
$831$	6.43181	0.223117
$832$	−1.78669	−0.0619423
$833$	3.80441	0.131815
$834$	20.0090	0.692854
$835$	16.4531	0.569383
$836$	−26.8443	−0.928429
$837$	81.3482	2.81181
$838$	−10.6098	−0.366510
$839$	25.1665	0.868845	0.434422	−	0.900709i	$-0.356953\pi$
$839$	25.1665	0.868845	0.434422	+	0.900709i	$0.356953\pi$
$840$	21.5606	0.743911
$841$	21.5526	0.743193
$842$	−4.68590	−0.161487
$843$	71.3271	2.45664
$844$	−22.2525	−0.765964
$845$	7.95728	0.273739
$846$	65.8374	2.26354
$847$	−1.13275	−0.0389217
$848$	−8.83221	−0.303299
$849$	−71.9197	−2.46828
$850$	−2.53103	−0.0868135
$851$	1.76444	0.0604843
$852$	−35.2729	−1.20843
$853$	27.2703	0.933719	0.466859	−	0.884332i	$-0.345385\pi$
$853$	27.2703	0.933719	0.466859	+	0.884332i	$0.345385\pi$
$854$	−0.541170	−0.0185184
$855$	−38.8230	−1.32772
$856$	21.6596	0.740309
$857$	36.8272	1.25799	0.628996	−	0.777408i	$-0.283466\pi$
$857$	36.8272	1.25799	0.628996	+	0.777408i	$0.283466\pi$
$858$	−15.6756	−0.535157
$859$	35.4536	1.20966	0.604831	−	0.796354i	$-0.293241\pi$
$859$	35.4536	1.20966	0.604831	+	0.796354i	$0.293241\pi$
$860$	17.8764	0.609580
$861$	9.32915	0.317936
$862$	−9.39315	−0.319932
$863$	−31.3793	−1.06816	−0.534082	−	0.845432i	$-0.679343\pi$
$863$	−31.3793	−1.06816	−0.534082	+	0.845432i	$0.679343\pi$
$864$	79.9661	2.72050
$865$	20.5096	0.697348
$866$	−5.25903	−0.178709
$867$	8.41732	0.285867
$868$	25.7826	0.875118
$869$	6.34998	0.215408
$870$	−15.2447	−0.516845
$871$	−12.4565	−0.422071
$872$	−23.8255	−0.806832
$873$	−68.0009	−2.30148
$874$	−3.11036	−0.105209
$875$	−2.82900	−0.0956377
$876$	45.4388	1.53524
$877$	35.4343	1.19653	0.598266	−	0.801298i	$-0.295857\pi$
$877$	35.4343	1.19653	0.598266	+	0.801298i	$0.295857\pi$
$878$	−20.6705	−0.697594
$879$	26.5627	0.895936
$880$	−4.96656	−0.167423
$881$	0.499253	0.0168203	0.00841014	−	0.999965i	$-0.497323\pi$
$881$	0.499253	0.0168203	0.00841014	+	0.999965i	$0.497323\pi$
$882$	−4.90125	−0.165034
$883$	21.3985	0.720118	0.360059	−	0.932930i	$-0.382757\pi$
$883$	21.3985	0.720118	0.360059	+	0.932930i	$0.382757\pi$
$884$	13.2373	0.445219
$885$	34.7286	1.16739
$886$	−3.22152	−0.108229
$887$	−4.12484	−0.138498	−0.0692492	−	0.997599i	$-0.522060\pi$
$887$	−4.12484	−0.138498	−0.0692492	+	0.997599i	$0.522060\pi$
$888$	−15.3060	−0.513635
$889$	11.1358	0.373483
$890$	8.47546	0.284098
$891$	73.6279	2.46663
$892$	16.0716	0.538116
$893$	−71.4813	−2.39203
$894$	46.4164	1.55240
$895$	−5.37186	−0.179561
$896$	31.1055	1.03916
$897$	6.33772	0.211610
$898$	10.3942	0.346858
$899$	−41.6843	−1.39025
$900$	−11.3780	−0.379267
$901$	−21.9550	−0.731428
$902$	2.23074	0.0742754
$903$	−104.508	−3.47780
$904$	−30.4168	−1.01165
$905$	22.1293	0.735604
$906$	27.3707	0.909330
$907$	20.4605	0.679378	0.339689	−	0.940538i	$-0.389678\pi$
$907$	20.4605	0.679378	0.339689	+	0.940538i	$0.389678\pi$
$908$	−16.8576	−0.559440
$909$	103.343	3.42766
$910$	−4.24021	−0.140562
$911$	−51.3454	−1.70115	−0.850575	−	0.525854i	$-0.823746\pi$
$911$	−51.3454	−1.70115	−0.850575	+	0.525854i	$0.823746\pi$
$912$	−25.9928	−0.860707
$913$	−17.7277	−0.586700
$914$	−19.3319	−0.639442
$915$	0.920673	0.0304365
$916$	34.8253	1.15066
$917$	22.3719	0.738787
$918$	35.1191	1.15910
$919$	27.2159	0.897769	0.448884	−	0.893590i	$-0.351822\pi$
$919$	27.2159	0.897769	0.448884	+	0.893590i	$0.351822\pi$
$920$	−2.08437	−0.0687195
$921$	−15.1745	−0.500017
$922$	4.27278	0.140716
$923$	15.8619	0.522100
$924$	45.9935	1.51308
$925$	2.00833	0.0660333
$926$	20.2928	0.666861
$927$	−33.6357	−1.10474
$928$	−40.9761	−1.34511
$929$	−4.78652	−0.157040	−0.0785202	−	0.996913i	$-0.525020\pi$
$929$	−4.78652	−0.157040	−0.0785202	+	0.996913i	$0.525020\pi$
$930$	12.5704	0.412200
$931$	5.32141	0.174402
$932$	4.79373	0.157024
$933$	−38.5660	−1.26259
$934$	11.8796	0.388712
$935$	−12.3458	−0.403751
$936$	−38.9948	−1.27459
$937$	3.09137	0.100991	0.0504954	−	0.998724i	$-0.483920\pi$
$937$	3.09137	0.100991	0.0504954	+	0.998724i	$0.483920\pi$
$938$	−10.4741	−0.341992
$939$	−62.0824	−2.02598
$940$	−20.9493	−0.683290
$941$	−19.5465	−0.637196	−0.318598	−	0.947890i	$-0.603212\pi$
$941$	−19.5465	−0.637196	−0.318598	+	0.947890i	$0.603212\pi$
$942$	−30.2728	−0.986341
$943$	−0.901894	−0.0293697
$944$	16.4919	0.536766
$945$	39.2537	1.27692
$946$	−24.9893	−0.812472
$947$	−28.9035	−0.939236	−0.469618	−	0.882870i	$-0.655608\pi$
$947$	−28.9035	−0.939236	−0.469618	+	0.882870i	$0.655608\pi$
$948$	9.73971	0.316331
$949$	−20.4334	−0.663297
$950$	−3.54027	−0.114862
$951$	−62.5512	−2.02836
$952$	25.4513	0.824880
$953$	27.3907	0.887271	0.443635	−	0.896207i	$-0.353689\pi$
$953$	27.3907	0.887271	0.443635	+	0.896207i	$0.353689\pi$
$954$	28.2849	0.915756
$955$	−9.68490	−0.313396
$956$	−38.5296	−1.24613
$957$	−74.3606	−2.40374
$958$	23.4023	0.756093
$959$	48.2752	1.55889
$960$	2.55589	0.0824911
$961$	3.37179	0.108767
$962$	3.01015	0.0970511
$963$	66.8226	2.15333
$964$	9.93594	0.320015
$965$	15.2046	0.489453
$966$	5.32911	0.171461
$967$	27.5316	0.885356	0.442678	−	0.896681i	$-0.354029\pi$
$967$	27.5316	0.885356	0.442678	+	0.896681i	$0.354029\pi$
$968$	−0.949951	−0.0305326
$969$	−64.6126	−2.07565
$970$	−6.20101	−0.199102
$971$	−17.5702	−0.563855	−0.281927	−	0.959436i	$-0.590974\pi$
$971$	−17.5702	−0.563855	−0.281927	+	0.959436i	$0.590974\pi$
$972$	48.2236	1.54677
$973$	26.4004	0.846357
$974$	−2.56302	−0.0821245
$975$	7.21372	0.231024
$976$	0.437209	0.0139947
$977$	−33.0875	−1.05856	−0.529282	−	0.848446i	$-0.677539\pi$
$977$	−33.0875	−1.05856	−0.529282	+	0.848446i	$0.677539\pi$
$978$	−4.68614	−0.149846
$979$	41.3415	1.32128
$980$	1.55957	0.0498185
$981$	−73.5046	−2.34682
$982$	−16.6849	−0.532435
$983$	4.54154	0.144853	0.0724263	−	0.997374i	$-0.476926\pi$
$983$	4.54154	0.144853	0.0724263	+	0.997374i	$0.476926\pi$
$984$	7.82364	0.249409
$985$	17.1349	0.545962
$986$	−17.9957	−0.573100
$987$	122.472	3.89833
$988$	18.5157	0.589062
$989$	10.1033	0.321265
$990$	15.9052	0.505501
$991$	−18.1869	−0.577727	−0.288863	−	0.957370i	$-0.593277\pi$
$991$	−18.1869	−0.577727	−0.288863	+	0.957370i	$0.593277\pi$
$992$	33.7878	1.07276
$993$	12.1395	0.385235
$994$	13.3376	0.423042
$995$	−6.37923	−0.202235
$996$	−27.1910	−0.861580
$997$	32.6612	1.03439	0.517196	−	0.855867i	$-0.326976\pi$
$997$	32.6612	1.03439	0.517196	+	0.855867i	$0.326976\pi$
$998$	23.8821	0.755973
$999$	−27.8664	−0.881655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.f.1.14	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.f.1.14	✓	37	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:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-0.667454 q^{2} -3.21238 q^{3} -1.55450 q^{4} -1.00000 q^{5} +2.14411 q^{6} +2.82900 q^{7} +2.37247 q^{8} +7.31937 q^{9} +O(q^{10})\)	\(q-0.667454 q^{2} -3.21238 q^{3} -1.55450 q^{4} -1.00000 q^{5} +2.14411 q^{6} +2.82900 q^{7} +2.37247 q^{8} +7.31937 q^{9} +0.667454 q^{10} +3.25570 q^{11} +4.99366 q^{12} -2.24560 q^{13} -1.88823 q^{14} +3.21238 q^{15} +1.52550 q^{16} +3.79206 q^{17} -4.88534 q^{18} +5.30414 q^{19} +1.55450 q^{20} -9.08782 q^{21} -2.17303 q^{22} +0.878564 q^{23} -7.62127 q^{24} +1.00000 q^{25} +1.49884 q^{26} -13.8754 q^{27} -4.39770 q^{28} +7.11004 q^{29} -2.14411 q^{30} -5.86275 q^{31} -5.76314 q^{32} -10.4585 q^{33} -2.53103 q^{34} -2.82900 q^{35} -11.3780 q^{36} +2.00833 q^{37} -3.54027 q^{38} +7.21372 q^{39} -2.37247 q^{40} -1.02655 q^{41} +6.06571 q^{42} +11.4997 q^{43} -5.06100 q^{44} -7.31937 q^{45} -0.586401 q^{46} -13.4765 q^{47} -4.90047 q^{48} +1.00326 q^{49} -0.667454 q^{50} -12.1815 q^{51} +3.49080 q^{52} -5.78974 q^{53} +9.26123 q^{54} -3.25570 q^{55} +6.71172 q^{56} -17.0389 q^{57} -4.74562 q^{58} +10.8109 q^{59} -4.99366 q^{60} +0.286602 q^{61} +3.91311 q^{62} +20.7065 q^{63} +0.795639 q^{64} +2.24560 q^{65} +6.98060 q^{66} +5.54705 q^{67} -5.89478 q^{68} -2.82228 q^{69} +1.88823 q^{70} -7.06353 q^{71} +17.3650 q^{72} +9.09931 q^{73} -1.34047 q^{74} -3.21238 q^{75} -8.24531 q^{76} +9.21039 q^{77} -4.81483 q^{78} +1.95042 q^{79} -1.52550 q^{80} +22.6151 q^{81} +0.685178 q^{82} -5.44511 q^{83} +14.1271 q^{84} -3.79206 q^{85} -7.67555 q^{86} -22.8401 q^{87} +7.72405 q^{88} +12.6982 q^{89} +4.88534 q^{90} -6.35281 q^{91} -1.36573 q^{92} +18.8334 q^{93} +8.99495 q^{94} -5.30414 q^{95} +18.5134 q^{96} -9.29054 q^{97} -0.669627 q^{98} +23.8297 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9}+O(q^{10}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9	\( 37 q + 7 q^{2} + 3 q^{3} + 43 q^{4} - 37 q^{5} + 8 q^{6} - 16 q^{7} + 21 q^{8} + 54 q^{9} - 7 q^{10} + 42 q^{11} - 13 q^{13} + 14 q^{14} - 3 q^{15} + 63 q^{16} + 18 q^{17} + 22 q^{18} + 22 q^{19} - 43 q^{20} + 16 q^{21} - 10 q^{22} + 23 q^{23} + 23 q^{24} + 37 q^{25} + 21 q^{26} + 3 q^{27} - 18 q^{28} + 33 q^{29} - 8 q^{30} + 11 q^{31} + 54 q^{32} + 2 q^{33} + 8 q^{34} + 16 q^{35} + 91 q^{36} - 11 q^{37} + 29 q^{38} + 25 q^{39} - 21 q^{40} + 24 q^{41} + 4 q^{42} + 25 q^{43} + 84 q^{44} - 54 q^{45} + 31 q^{46} + 7 q^{47} + 4 q^{48} + 45 q^{49} + 7 q^{50} + 94 q^{51} - 43 q^{52} + 49 q^{53} + 38 q^{54} - 42 q^{55} + 46 q^{56} + 6 q^{57} + 15 q^{58} + 69 q^{59} + 9 q^{61} + 17 q^{62} - 38 q^{63} + 107 q^{64} + 13 q^{65} + 74 q^{66} + 13 q^{67} + 86 q^{68} - 14 q^{70} + 51 q^{71} + 81 q^{72} - 47 q^{73} + 79 q^{74} + 3 q^{75} + 59 q^{76} + 2 q^{77} + 20 q^{78} + 67 q^{79} - 63 q^{80} + 125 q^{81} - 24 q^{82} + 80 q^{83} + 50 q^{84} - 18 q^{85} + 69 q^{86} - 32 q^{87} - 12 q^{88} + 34 q^{89} - 22 q^{90} + 39 q^{91} + 85 q^{92} + q^{93} + 12 q^{94} - 22 q^{95} + 77 q^{96} - 14 q^{97} + 40 q^{98} + 133 q^{99}+O(q^{100}) \) 37 * q + 7 * q^2 + 3 * q^3 + 43 * q^4 - 37 * q^5 + 8 * q^6 - 16 * q^7 + 21 * q^8 + 54 * q^9 - 7 * q^10 + 42 * q^11 - 13 * q^13 + 14 * q^14 - 3 * q^15 + 63 * q^16 + 18 * q^17 + 22 * q^18 + 22 * q^19 - 43 * q^20 + 16 * q^21 - 10 * q^22 + 23 * q^23 + 23 * q^24 + 37 * q^25 + 21 * q^26 + 3 * q^27 - 18 * q^28 + 33 * q^29 - 8 * q^30 + 11 * q^31 + 54 * q^32 + 2 * q^33 + 8 * q^34 + 16 * q^35 + 91 * q^36 - 11 * q^37 + 29 * q^38 + 25 * q^39 - 21 * q^40 + 24 * q^41 + 4 * q^42 + 25 * q^43 + 84 * q^44 - 54 * q^45 + 31 * q^46 + 7 * q^47 + 4 * q^48 + 45 * q^49 + 7 * q^50 + 94 * q^51 - 43 * q^52 + 49 * q^53 + 38 * q^54 - 42 * q^55 + 46 * q^56 + 6 * q^57 + 15 * q^58 + 69 * q^59 + 9 * q^61 + 17 * q^62 - 38 * q^63 + 107 * q^64 + 13 * q^65 + 74 * q^66 + 13 * q^67 + 86 * q^68 - 14 * q^70 + 51 * q^71 + 81 * q^72 - 47 * q^73 + 79 * q^74 + 3 * q^75 + 59 * q^76 + 2 * q^77 + 20 * q^78 + 67 * q^79 - 63 * q^80 + 125 * q^81 - 24 * q^82 + 80 * q^83 + 50 * q^84 - 18 * q^85 + 69 * q^86 - 32 * q^87 - 12 * q^88 + 34 * q^89 - 22 * q^90 + 39 * q^91 + 85 * q^92 + q^93 + 12 * q^94 - 22 * q^95 + 77 * q^96 - 14 * q^97 + 40 * q^98 + 133 * q^99

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