LMFDB - Embedded newform 6005.2.a.e.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.89204 q^{2} +0.756696 q^{3} +1.57982 q^{4} +1.00000 q^{5} -1.43170 q^{6} +1.91014 q^{7} +0.794996 q^{8} -2.42741 q^{9} +O(q^{10})$	\(q-1.89204 q^{2} +0.756696 q^{3} +1.57982 q^{4} +1.00000 q^{5} -1.43170 q^{6} +1.91014 q^{7} +0.794996 q^{8} -2.42741 q^{9} -1.89204 q^{10} +2.49389 q^{11} +1.19544 q^{12} -2.55585 q^{13} -3.61406 q^{14} +0.756696 q^{15} -4.66381 q^{16} -4.47228 q^{17} +4.59276 q^{18} -4.64851 q^{19} +1.57982 q^{20} +1.44539 q^{21} -4.71854 q^{22} -1.64112 q^{23} +0.601570 q^{24} +1.00000 q^{25} +4.83578 q^{26} -4.10690 q^{27} +3.01767 q^{28} -2.91138 q^{29} -1.43170 q^{30} +8.89011 q^{31} +7.23412 q^{32} +1.88711 q^{33} +8.46174 q^{34} +1.91014 q^{35} -3.83488 q^{36} +9.68950 q^{37} +8.79518 q^{38} -1.93400 q^{39} +0.794996 q^{40} +9.36663 q^{41} -2.73474 q^{42} +3.56525 q^{43} +3.93990 q^{44} -2.42741 q^{45} +3.10507 q^{46} -0.376518 q^{47} -3.52908 q^{48} -3.35138 q^{49} -1.89204 q^{50} -3.38415 q^{51} -4.03779 q^{52} -1.94607 q^{53} +7.77042 q^{54} +2.49389 q^{55} +1.51855 q^{56} -3.51751 q^{57} +5.50845 q^{58} +6.92242 q^{59} +1.19544 q^{60} -8.61881 q^{61} -16.8205 q^{62} -4.63669 q^{63} -4.35965 q^{64} -2.55585 q^{65} -3.57050 q^{66} -7.74089 q^{67} -7.06540 q^{68} -1.24183 q^{69} -3.61406 q^{70} -11.5080 q^{71} -1.92978 q^{72} -7.07811 q^{73} -18.3329 q^{74} +0.756696 q^{75} -7.34382 q^{76} +4.76367 q^{77} +3.65921 q^{78} +0.605622 q^{79} -4.66381 q^{80} +4.17456 q^{81} -17.7220 q^{82} -0.362354 q^{83} +2.28346 q^{84} -4.47228 q^{85} -6.74560 q^{86} -2.20303 q^{87} +1.98263 q^{88} -10.2309 q^{89} +4.59276 q^{90} -4.88202 q^{91} -2.59268 q^{92} +6.72711 q^{93} +0.712387 q^{94} -4.64851 q^{95} +5.47403 q^{96} +0.592516 q^{97} +6.34095 q^{98} -6.05369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) $ 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * 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 $

$2$	−1.89204	−1.33788	−0.668938	−	0.743318i	$-0.733251\pi$
$2$	−1.89204	−1.33788	−0.668938	+	0.743318i	$0.733251\pi$
$3$	0.756696	0.436878	0.218439	−	0.975851i	$-0.429903\pi$
$3$	0.756696	0.436878	0.218439	+	0.975851i	$0.429903\pi$
$4$	1.57982	0.789910
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.43170	−0.584489
$7$	1.91014	0.721964	0.360982	−	0.932573i	$-0.382442\pi$
$7$	1.91014	0.721964	0.360982	+	0.932573i	$0.382442\pi$
$8$	0.794996	0.281074
$9$	−2.42741	−0.809137
$10$	−1.89204	−0.598316
$11$	2.49389	0.751936	0.375968	−	0.926633i	$-0.377310\pi$
$11$	2.49389	0.751936	0.375968	+	0.926633i	$0.377310\pi$
$12$	1.19544	0.345095
$13$	−2.55585	−0.708865	−0.354433	−	0.935082i	$-0.615326\pi$
$13$	−2.55585	−0.708865	−0.354433	+	0.935082i	$0.615326\pi$
$14$	−3.61406	−0.965898
$15$	0.756696	0.195378
$16$	−4.66381	−1.16595
$17$	−4.47228	−1.08469	−0.542343	−	0.840157i	$-0.682463\pi$
$17$	−4.47228	−1.08469	−0.542343	+	0.840157i	$0.682463\pi$
$18$	4.59276	1.08252
$19$	−4.64851	−1.06644	−0.533221	−	0.845976i	$-0.679019\pi$
$19$	−4.64851	−1.06644	−0.533221	+	0.845976i	$0.679019\pi$
$20$	1.57982	0.353259
$21$	1.44539	0.315410
$22$	−4.71854	−1.00600
$23$	−1.64112	−0.342197	−0.171099	−	0.985254i	$-0.554732\pi$
$23$	−1.64112	−0.342197	−0.171099	+	0.985254i	$0.554732\pi$
$24$	0.601570	0.122795
$25$	1.00000	0.200000
$26$	4.83578	0.948374
$27$	−4.10690	−0.790373
$28$	3.01767	0.570287
$29$	−2.91138	−0.540630	−0.270315	−	0.962772i	$-0.587128\pi$
$29$	−2.91138	−0.540630	−0.270315	+	0.962772i	$0.587128\pi$
$30$	−1.43170	−0.261391
$31$	8.89011	1.59671	0.798356	−	0.602186i	$-0.205703\pi$
$31$	8.89011	1.59671	0.798356	+	0.602186i	$0.205703\pi$
$32$	7.23412	1.27882
$33$	1.88711	0.328504
$34$	8.46174	1.45118
$35$	1.91014	0.322872
$36$	−3.83488	−0.639146
$37$	9.68950	1.59294	0.796472	−	0.604675i	$-0.206697\pi$
$37$	9.68950	1.59294	0.796472	+	0.604675i	$0.206697\pi$
$38$	8.79518	1.42677
$39$	−1.93400	−0.309688
$40$	0.794996	0.125700
$41$	9.36663	1.46282	0.731411	−	0.681937i	$-0.238862\pi$
$41$	9.36663	1.46282	0.731411	+	0.681937i	$0.238862\pi$
$42$	−2.73474	−0.421980
$43$	3.56525	0.543695	0.271848	−	0.962340i	$-0.412365\pi$
$43$	3.56525	0.543695	0.271848	+	0.962340i	$0.412365\pi$
$44$	3.93990	0.593962
$45$	−2.42741	−0.361857
$46$	3.10507	0.457818
$47$	−0.376518	−0.0549208	−0.0274604	−	0.999623i	$-0.508742\pi$
$47$	−0.376518	−0.0549208	−0.0274604	+	0.999623i	$0.508742\pi$
$48$	−3.52908	−0.509379
$49$	−3.35138	−0.478768
$50$	−1.89204	−0.267575
$51$	−3.38415	−0.473876
$52$	−4.03779	−0.559940
$53$	−1.94607	−0.267313	−0.133657	−	0.991028i	$-0.542672\pi$
$53$	−1.94607	−0.267313	−0.133657	+	0.991028i	$0.542672\pi$
$54$	7.77042	1.05742
$55$	2.49389	0.336276
$56$	1.51855	0.202925
$57$	−3.51751	−0.465906
$58$	5.50845	0.723295
$59$	6.92242	0.901223	0.450611	−	0.892720i	$-0.351206\pi$
$59$	6.92242	0.901223	0.450611	+	0.892720i	$0.351206\pi$
$60$	1.19544	0.154331
$61$	−8.61881	−1.10353	−0.551763	−	0.834001i	$-0.686045\pi$
$61$	−8.61881	−1.10353	−0.551763	+	0.834001i	$0.686045\pi$
$62$	−16.8205	−2.13620
$63$	−4.63669	−0.584168
$64$	−4.35965	−0.544956
$65$	−2.55585	−0.317014
$66$	−3.57050	−0.439498
$67$	−7.74089	−0.945700	−0.472850	−	0.881143i	$-0.656775\pi$
$67$	−7.74089	−0.945700	−0.472850	+	0.881143i	$0.656775\pi$
$68$	−7.06540	−0.856805
$69$	−1.24183	−0.149499
$70$	−3.61406	−0.431963
$71$	−11.5080	−1.36575	−0.682877	−	0.730533i	$-0.739272\pi$
$71$	−11.5080	−1.36575	−0.682877	+	0.730533i	$0.739272\pi$
$72$	−1.92978	−0.227427
$73$	−7.07811	−0.828430	−0.414215	−	0.910179i	$-0.635944\pi$
$73$	−7.07811	−0.828430	−0.414215	+	0.910179i	$0.635944\pi$
$74$	−18.3329	−2.13116
$75$	0.756696	0.0873757
$76$	−7.34382	−0.842394
$77$	4.76367	0.542870
$78$	3.65921	0.414324
$79$	0.605622	0.0681378	0.0340689	−	0.999419i	$-0.489153\pi$
$79$	0.605622	0.0681378	0.0340689	+	0.999419i	$0.489153\pi$
$80$	−4.66381	−0.521430
$81$	4.17456	0.463840
$82$	−17.7220	−1.95707
$83$	−0.362354	−0.0397736	−0.0198868	−	0.999802i	$-0.506331\pi$
$83$	−0.362354	−0.0397736	−0.0198868	+	0.999802i	$0.506331\pi$
$84$	2.28346	0.249146
$85$	−4.47228	−0.485087
$86$	−6.74560	−0.727397
$87$	−2.20303	−0.236189
$88$	1.98263	0.211349
$89$	−10.2309	−1.08447	−0.542237	−	0.840226i	$-0.682422\pi$
$89$	−10.2309	−1.08447	−0.542237	+	0.840226i	$0.682422\pi$
$90$	4.59276	0.484120
$91$	−4.88202	−0.511775
$92$	−2.59268	−0.270305
$93$	6.72711	0.697569
$94$	0.712387	0.0734771
$95$	−4.64851	−0.476927
$96$	5.47403	0.558691
$97$	0.592516	0.0601609	0.0300805	−	0.999547i	$-0.490424\pi$
$97$	0.592516	0.0601609	0.0300805	+	0.999547i	$0.490424\pi$
$98$	6.34095	0.640532
$99$	−6.05369	−0.608419
$100$	1.57982	0.157982
$101$	−19.0123	−1.89179	−0.945896	−	0.324471i	$-0.894814\pi$
$101$	−19.0123	−1.89179	−0.945896	+	0.324471i	$0.894814\pi$
$102$	6.40296	0.633987
$103$	10.3814	1.02291	0.511456	−	0.859309i	$-0.329106\pi$
$103$	10.3814	1.02291	0.511456	+	0.859309i	$0.329106\pi$
$104$	−2.03189	−0.199243
$105$	1.44539	0.141056
$106$	3.68205	0.357632
$107$	6.89457	0.666523	0.333262	−	0.942834i	$-0.391851\pi$
$107$	6.89457	0.666523	0.333262	+	0.942834i	$0.391851\pi$
$108$	−6.48816	−0.624324
$109$	−12.1395	−1.16275	−0.581377	−	0.813635i	$-0.697486\pi$
$109$	−12.1395	−1.16275	−0.581377	+	0.813635i	$0.697486\pi$
$110$	−4.71854	−0.449895
$111$	7.33200	0.695923
$112$	−8.90851	−0.841775
$113$	4.77745	0.449425	0.224712	−	0.974425i	$-0.427856\pi$
$113$	4.77745	0.449425	0.224712	+	0.974425i	$0.427856\pi$
$114$	6.65527	0.623323
$115$	−1.64112	−0.153035
$116$	−4.59946	−0.427049
$117$	6.20410	0.573569
$118$	−13.0975	−1.20572
$119$	−8.54266	−0.783105
$120$	0.601570	0.0549156
$121$	−4.78052	−0.434593
$122$	16.3072	1.47638
$123$	7.08769	0.639075
$124$	14.0448	1.26126
$125$	1.00000	0.0894427
$126$	8.77281	0.781544
$127$	−1.15319	−0.102329	−0.0511646	−	0.998690i	$-0.516293\pi$
$127$	−1.15319	−0.102329	−0.0511646	+	0.998690i	$0.516293\pi$
$128$	−6.21961	−0.549741
$129$	2.69781	0.237529
$130$	4.83578	0.424126
$131$	8.26697	0.722289	0.361144	−	0.932510i	$-0.382386\pi$
$131$	8.26697	0.722289	0.361144	+	0.932510i	$0.382386\pi$
$132$	2.98130	0.259489
$133$	−8.87930	−0.769933
$134$	14.6461	1.26523
$135$	−4.10690	−0.353466
$136$	−3.55544	−0.304877
$137$	−12.5948	−1.07605	−0.538023	−	0.842930i	$-0.680829\pi$
$137$	−12.5948	−1.07605	−0.538023	+	0.842930i	$0.680829\pi$
$138$	2.34959	0.200011
$139$	−6.12952	−0.519899	−0.259950	−	0.965622i	$-0.583706\pi$
$139$	−6.12952	−0.519899	−0.259950	+	0.965622i	$0.583706\pi$
$140$	3.01767	0.255040
$141$	−0.284909	−0.0239937
$142$	21.7737	1.82721
$143$	−6.37401	−0.533021
$144$	11.3210	0.943415
$145$	−2.91138	−0.241777
$146$	13.3921	1.10834
$147$	−2.53597	−0.209163
$148$	15.3077	1.25828
$149$	22.3533	1.83125	0.915626	−	0.402031i	$-0.131696\pi$
$149$	22.3533	1.83125	0.915626	+	0.402031i	$0.131696\pi$
$150$	−1.43170	−0.116898
$151$	12.9786	1.05618	0.528091	−	0.849188i	$-0.322908\pi$
$151$	12.9786	1.05618	0.528091	+	0.849188i	$0.322908\pi$
$152$	−3.69555	−0.299749
$153$	10.8561	0.877660
$154$	−9.01306	−0.726293
$155$	8.89011	0.714071
$156$	−3.05537	−0.244626
$157$	−14.1872	−1.13226	−0.566132	−	0.824314i	$-0.691561\pi$
$157$	−14.1872	−1.13226	−0.566132	+	0.824314i	$0.691561\pi$
$158$	−1.14586	−0.0911599
$159$	−1.47258	−0.116783
$160$	7.23412	0.571908
$161$	−3.13477	−0.247054
$162$	−7.89845	−0.620561
$163$	−10.7641	−0.843112	−0.421556	−	0.906802i	$-0.638516\pi$
$163$	−10.7641	−0.843112	−0.421556	+	0.906802i	$0.638516\pi$
$164$	14.7976	1.15550
$165$	1.88711	0.146912
$166$	0.685589	0.0532121
$167$	−0.695963	−0.0538552	−0.0269276	−	0.999637i	$-0.508572\pi$
$167$	−0.695963	−0.0538552	−0.0269276	+	0.999637i	$0.508572\pi$
$168$	1.14908	0.0886536
$169$	−6.46763	−0.497510
$170$	8.46174	0.648985
$171$	11.2839	0.862898
$172$	5.63245	0.429471
$173$	4.07485	0.309805	0.154903	−	0.987930i	$-0.450494\pi$
$173$	4.07485	0.309805	0.154903	+	0.987930i	$0.450494\pi$
$174$	4.16822	0.315992
$175$	1.91014	0.144393
$176$	−11.6310	−0.876721
$177$	5.23817	0.393725
$178$	19.3573	1.45089
$179$	−21.0439	−1.57290	−0.786448	−	0.617657i	$-0.788082\pi$
$179$	−21.0439	−1.57290	−0.786448	+	0.617657i	$0.788082\pi$
$180$	−3.83488	−0.285835
$181$	12.5542	0.933145	0.466573	−	0.884483i	$-0.345489\pi$
$181$	12.5542	0.933145	0.466573	+	0.884483i	$0.345489\pi$
$182$	9.23699	0.684691
$183$	−6.52182	−0.482107
$184$	−1.30469	−0.0961827
$185$	9.68950	0.712386
$186$	−12.7280	−0.933260
$187$	−11.1534	−0.815615
$188$	−0.594831	−0.0433825
$189$	−7.84474	−0.570621
$190$	8.79518	0.638069
$191$	−4.11019	−0.297403	−0.148702	−	0.988882i	$-0.547509\pi$
$191$	−4.11019	−0.297403	−0.148702	+	0.988882i	$0.547509\pi$
$192$	−3.29893	−0.238080
$193$	−8.42490	−0.606437	−0.303219	−	0.952921i	$-0.598061\pi$
$193$	−8.42490	−0.606437	−0.303219	+	0.952921i	$0.598061\pi$
$194$	−1.12107	−0.0804878
$195$	−1.93400	−0.138497
$196$	−5.29458	−0.378184
$197$	−14.3469	−1.02218	−0.511088	−	0.859529i	$-0.670757\pi$
$197$	−14.3469	−1.02218	−0.511088	+	0.859529i	$0.670757\pi$
$198$	11.4538	0.813989
$199$	−11.6234	−0.823963	−0.411982	−	0.911192i	$-0.635163\pi$
$199$	−11.6234	−0.823963	−0.411982	+	0.911192i	$0.635163\pi$
$200$	0.794996	0.0562147
$201$	−5.85749	−0.413156
$202$	35.9720	2.53098
$203$	−5.56113	−0.390315
$204$	−5.34636	−0.374320
$205$	9.36663	0.654194
$206$	−19.6421	−1.36853
$207$	3.98368	0.276885
$208$	11.9200	0.826503
$209$	−11.5929	−0.801896
$210$	−2.73474	−0.188715
$211$	8.11749	0.558831	0.279415	−	0.960170i	$-0.409859\pi$
$211$	8.11749	0.558831	0.279415	+	0.960170i	$0.409859\pi$
$212$	−3.07444	−0.211154
$213$	−8.70809	−0.596668
$214$	−13.0448	−0.891725
$215$	3.56525	0.243148
$216$	−3.26497	−0.222153
$217$	16.9813	1.15277
$218$	22.9684	1.55562
$219$	−5.35598	−0.361923
$220$	3.93990	0.265628
$221$	11.4305	0.768897
$222$	−13.8725	−0.931058
$223$	−7.31809	−0.490056	−0.245028	−	0.969516i	$-0.578797\pi$
$223$	−7.31809	−0.490056	−0.245028	+	0.969516i	$0.578797\pi$
$224$	13.8182	0.923265
$225$	−2.42741	−0.161827
$226$	−9.03913	−0.601274
$227$	10.3026	0.683805	0.341903	−	0.939735i	$-0.388929\pi$
$227$	10.3026	0.683805	0.341903	+	0.939735i	$0.388929\pi$
$228$	−5.55703	−0.368024
$229$	−18.3410	−1.21201	−0.606005	−	0.795461i	$-0.707229\pi$
$229$	−18.3410	−1.21201	−0.606005	+	0.795461i	$0.707229\pi$
$230$	3.10507	0.204742
$231$	3.60465	0.237168
$232$	−2.31454	−0.151957
$233$	−21.2649	−1.39311	−0.696554	−	0.717505i	$-0.745284\pi$
$233$	−21.2649	−1.39311	−0.696554	+	0.717505i	$0.745284\pi$
$234$	−11.7384	−0.767364
$235$	−0.376518	−0.0245613
$236$	10.9362	0.711885
$237$	0.458272	0.0297679
$238$	16.1631	1.04770
$239$	15.1248	0.978345	0.489173	−	0.872187i	$-0.337299\pi$
$239$	15.1248	0.978345	0.489173	+	0.872187i	$0.337299\pi$
$240$	−3.52908	−0.227801
$241$	23.8750	1.53793	0.768963	−	0.639294i	$-0.220773\pi$
$241$	23.8750	1.53793	0.768963	+	0.639294i	$0.220773\pi$
$242$	9.04494	0.581431
$243$	15.4796	0.993015
$244$	−13.6162	−0.871687
$245$	−3.35138	−0.214112
$246$	−13.4102	−0.855003
$247$	11.8809	0.755964
$248$	7.06761	0.448794
$249$	−0.274192	−0.0173762
$250$	−1.89204	−0.119663
$251$	−11.5332	−0.727970	−0.363985	−	0.931405i	$-0.618584\pi$
$251$	−11.5332	−0.727970	−0.363985	+	0.931405i	$0.618584\pi$
$252$	−7.32514	−0.461440
$253$	−4.09277	−0.257310
$254$	2.18189	0.136904
$255$	−3.38415	−0.211924
$256$	20.4871	1.28044
$257$	−22.5220	−1.40488	−0.702441	−	0.711742i	$-0.747906\pi$
$257$	−22.5220	−1.40488	−0.702441	+	0.711742i	$0.747906\pi$
$258$	−5.10436	−0.317784
$259$	18.5083	1.15005
$260$	−4.03779	−0.250413
$261$	7.06712	0.437444
$262$	−15.6415	−0.966333
$263$	−28.6588	−1.76718	−0.883588	−	0.468266i	$-0.844879\pi$
$263$	−28.6588	−1.76718	−0.883588	+	0.468266i	$0.844879\pi$
$264$	1.50025	0.0923339
$265$	−1.94607	−0.119546
$266$	16.8000	1.03007
$267$	−7.74168	−0.473783
$268$	−12.2292	−0.747018
$269$	−2.49500	−0.152123	−0.0760615	−	0.997103i	$-0.524235\pi$
$269$	−2.49500	−0.152123	−0.0760615	+	0.997103i	$0.524235\pi$
$270$	7.77042	0.472893
$271$	4.94600	0.300448	0.150224	−	0.988652i	$-0.452001\pi$
$271$	4.94600	0.300448	0.150224	+	0.988652i	$0.452001\pi$
$272$	20.8578	1.26469
$273$	−3.69421	−0.223584
$274$	23.8299	1.43962
$275$	2.49389	0.150387
$276$	−1.96187	−0.118091
$277$	−23.3309	−1.40182	−0.700910	−	0.713249i	$-0.747223\pi$
$277$	−23.3309	−1.40182	−0.700910	+	0.713249i	$0.747223\pi$
$278$	11.5973	0.695560
$279$	−21.5800	−1.29196
$280$	1.51855	0.0907508
$281$	25.6903	1.53256	0.766279	−	0.642508i	$-0.222106\pi$
$281$	25.6903	1.53256	0.766279	+	0.642508i	$0.222106\pi$
$282$	0.539060	0.0321006
$283$	−32.7448	−1.94648	−0.973238	−	0.229799i	$-0.926193\pi$
$283$	−32.7448	−1.94648	−0.973238	+	0.229799i	$0.926193\pi$
$284$	−18.1807	−1.07882
$285$	−3.51751	−0.208359
$286$	12.0599	0.713116
$287$	17.8915	1.05610
$288$	−17.5602	−1.03474
$289$	3.00127	0.176545
$290$	5.50845	0.323467
$291$	0.448355	0.0262830
$292$	−11.1822	−0.654386
$293$	−7.60371	−0.444214	−0.222107	−	0.975022i	$-0.571293\pi$
$293$	−7.60371	−0.444214	−0.222107	+	0.975022i	$0.571293\pi$
$294$	4.79817	0.279835
$295$	6.92242	0.403039
$296$	7.70312	0.447735
$297$	−10.2421	−0.594310
$298$	−42.2933	−2.44999
$299$	4.19446	0.242572
$300$	1.19544	0.0690190
$301$	6.81011	0.392528
$302$	−24.5560	−1.41304
$303$	−14.3865	−0.826483
$304$	21.6798	1.24342
$305$	−8.61881	−0.493512
$306$	−20.5401	−1.17420
$307$	32.3219	1.84471	0.922354	−	0.386345i	$-0.126263\pi$
$307$	32.3219	1.84471	0.922354	+	0.386345i	$0.126263\pi$
$308$	7.52574	0.428819
$309$	7.85558	0.446888
$310$	−16.8205	−0.955338
$311$	8.61861	0.488716	0.244358	−	0.969685i	$-0.421423\pi$
$311$	8.61861	0.488716	0.244358	+	0.969685i	$0.421423\pi$
$312$	−1.53752	−0.0870451
$313$	−7.53406	−0.425850	−0.212925	−	0.977068i	$-0.568299\pi$
$313$	−7.53406	−0.425850	−0.212925	+	0.977068i	$0.568299\pi$
$314$	26.8428	1.51483
$315$	−4.63669	−0.261248
$316$	0.956775	0.0538228
$317$	−15.3740	−0.863488	−0.431744	−	0.901996i	$-0.642102\pi$
$317$	−15.3740	−0.863488	−0.431744	+	0.901996i	$0.642102\pi$
$318$	2.78619	0.156242
$319$	−7.26065	−0.406519
$320$	−4.35965	−0.243712
$321$	5.21709	0.291190
$322$	5.93111	0.330528
$323$	20.7894	1.15676
$324$	6.59506	0.366392
$325$	−2.55585	−0.141773
$326$	20.3662	1.12798
$327$	−9.18591	−0.507982
$328$	7.44643	0.411161
$329$	−0.719201	−0.0396508
$330$	−3.57050	−0.196549
$331$	−35.4662	−1.94940	−0.974699	−	0.223522i	$-0.928244\pi$
$331$	−35.4662	−1.94940	−0.974699	+	0.223522i	$0.928244\pi$
$332$	−0.572455	−0.0314175
$333$	−23.5204	−1.28891
$334$	1.31679	0.0720516
$335$	−7.74089	−0.422930
$336$	−6.74103	−0.367753
$337$	22.6698	1.23490	0.617452	−	0.786609i	$-0.288165\pi$
$337$	22.6698	1.23490	0.617452	+	0.786609i	$0.288165\pi$
$338$	12.2370	0.665606
$339$	3.61508	0.196344
$340$	−7.06540	−0.383175
$341$	22.1709	1.20062
$342$	−21.3495	−1.15445
$343$	−19.7725	−1.06762
$344$	2.83436	0.152818
$345$	−1.24183	−0.0668578
$346$	−7.70979	−0.414481
$347$	−5.72381	−0.307270	−0.153635	−	0.988128i	$-0.549098\pi$
$347$	−5.72381	−0.307270	−0.153635	+	0.988128i	$0.549098\pi$
$348$	−3.48039	−0.186568
$349$	11.1249	0.595503	0.297752	−	0.954643i	$-0.403763\pi$
$349$	11.1249	0.595503	0.297752	+	0.954643i	$0.403763\pi$
$350$	−3.61406	−0.193180
$351$	10.4966	0.560268
$352$	18.0411	0.961594
$353$	−20.2179	−1.07609	−0.538046	−	0.842916i	$-0.680837\pi$
$353$	−20.2179	−1.07609	−0.538046	+	0.842916i	$0.680837\pi$
$354$	−9.91083	−0.526755
$355$	−11.5080	−0.610784
$356$	−16.1630	−0.856637
$357$	−6.46419	−0.342121
$358$	39.8160	2.10434
$359$	11.6324	0.613935	0.306968	−	0.951720i	$-0.400686\pi$
$359$	11.6324	0.613935	0.306968	+	0.951720i	$0.400686\pi$
$360$	−1.92978	−0.101709
$361$	2.60868	0.137299
$362$	−23.7530	−1.24843
$363$	−3.61740	−0.189864
$364$	−7.71272	−0.404257
$365$	−7.07811	−0.370485
$366$	12.3395	0.644999
$367$	3.61973	0.188948	0.0944741	−	0.995527i	$-0.469883\pi$
$367$	3.61973	0.188948	0.0944741	+	0.995527i	$0.469883\pi$
$368$	7.65387	0.398986
$369$	−22.7367	−1.18362
$370$	−18.3329	−0.953084
$371$	−3.71726	−0.192991
$372$	10.6276	0.551017
$373$	−32.6154	−1.68876	−0.844380	−	0.535745i	$-0.820031\pi$
$373$	−32.6154	−1.68876	−0.844380	+	0.535745i	$0.820031\pi$
$374$	21.1026	1.09119
$375$	0.756696	0.0390756
$376$	−0.299330	−0.0154368
$377$	7.44105	0.383234
$378$	14.8426	0.763419
$379$	24.9850	1.28339	0.641696	−	0.766959i	$-0.278231\pi$
$379$	24.9850	1.28339	0.641696	+	0.766959i	$0.278231\pi$
$380$	−7.34382	−0.376730
$381$	−0.872615	−0.0447054
$382$	7.77666	0.397888
$383$	30.0507	1.53552	0.767759	−	0.640739i	$-0.221372\pi$
$383$	30.0507	1.53552	0.767759	+	0.640739i	$0.221372\pi$
$384$	−4.70635	−0.240170
$385$	4.76367	0.242779
$386$	15.9403	0.811338
$387$	−8.65433	−0.439924
$388$	0.936070	0.0475217
$389$	39.0008	1.97742	0.988710	−	0.149840i	$-0.0478757\pi$
$389$	39.0008	1.97742	0.988710	+	0.149840i	$0.0478757\pi$
$390$	3.65921	0.185291
$391$	7.33955	0.371177
$392$	−2.66433	−0.134569
$393$	6.25558	0.315552
$394$	27.1450	1.36754
$395$	0.605622	0.0304722
$396$	−9.56375	−0.480597
$397$	−20.1085	−1.00922	−0.504609	−	0.863348i	$-0.668363\pi$
$397$	−20.1085	−1.00922	−0.504609	+	0.863348i	$0.668363\pi$
$398$	21.9920	1.10236
$399$	−6.71892	−0.336367
$400$	−4.66381	−0.233190
$401$	28.4264	1.41955	0.709773	−	0.704431i	$-0.248798\pi$
$401$	28.4264	1.41955	0.709773	+	0.704431i	$0.248798\pi$
$402$	11.0826	0.552751
$403$	−22.7218	−1.13185
$404$	−30.0360	−1.49435
$405$	4.17456	0.207436
$406$	10.5219	0.522193
$407$	24.1645	1.19779
$408$	−2.69039	−0.133194
$409$	−34.7586	−1.71870	−0.859352	−	0.511384i	$-0.829133\pi$
$409$	−34.7586	−1.71870	−0.859352	+	0.511384i	$0.829133\pi$
$410$	−17.7220	−0.875230
$411$	−9.53042	−0.470101
$412$	16.4008	0.808009
$413$	13.2228	0.650650
$414$	−7.53728	−0.370437
$415$	−0.362354	−0.0177873
$416$	−18.4893	−0.906515
$417$	−4.63818	−0.227133
$418$	21.9342	1.07284
$419$	−4.36478	−0.213234	−0.106617	−	0.994300i	$-0.534002\pi$
$419$	−4.36478	−0.213234	−0.106617	+	0.994300i	$0.534002\pi$
$420$	2.28346	0.111421
$421$	−27.5126	−1.34088	−0.670440	−	0.741963i	$-0.733895\pi$
$421$	−27.5126	−1.34088	−0.670440	+	0.741963i	$0.733895\pi$
$422$	−15.3586	−0.747646
$423$	0.913964	0.0444384
$424$	−1.54712	−0.0751348
$425$	−4.47228	−0.216937
$426$	16.4761	0.798268
$427$	−16.4631	−0.796706
$428$	10.8922	0.526494
$429$	−4.82318	−0.232865
$430$	−6.74560	−0.325302
$431$	−16.7790	−0.808216	−0.404108	−	0.914711i	$-0.632418\pi$
$431$	−16.7790	−0.808216	−0.404108	+	0.914711i	$0.632418\pi$
$432$	19.1538	0.921537
$433$	−30.3204	−1.45710	−0.728552	−	0.684991i	$-0.759806\pi$
$433$	−30.3204	−1.45710	−0.728552	+	0.684991i	$0.759806\pi$
$434$	−32.1294	−1.54226
$435$	−2.20303	−0.105627
$436$	−19.1782	−0.918471
$437$	7.62877	0.364934
$438$	10.1337	0.484208
$439$	21.0011	1.00233	0.501163	−	0.865353i	$-0.332906\pi$
$439$	21.0011	1.00233	0.501163	+	0.865353i	$0.332906\pi$
$440$	1.98263	0.0945183
$441$	8.13517	0.387389
$442$	−21.6269	−1.02869
$443$	10.3392	0.491231	0.245616	−	0.969367i	$-0.421010\pi$
$443$	10.3392	0.491231	0.245616	+	0.969367i	$0.421010\pi$
$444$	11.5833	0.549717
$445$	−10.2309	−0.484991
$446$	13.8461	0.655633
$447$	16.9146	0.800035
$448$	−8.32753	−0.393439
$449$	1.13161	0.0534042	0.0267021	−	0.999643i	$-0.491499\pi$
$449$	1.13161	0.0534042	0.0267021	+	0.999643i	$0.491499\pi$
$450$	4.59276	0.216505
$451$	23.3593	1.09995
$452$	7.54751	0.355005
$453$	9.82083	0.461423
$454$	−19.4929	−0.914846
$455$	−4.88202	−0.228873
$456$	−2.79641	−0.130954
$457$	−10.4663	−0.489594	−0.244797	−	0.969574i	$-0.578721\pi$
$457$	−10.4663	−0.489594	−0.244797	+	0.969574i	$0.578721\pi$
$458$	34.7020	1.62152
$459$	18.3672	0.857307
$460$	−2.59268	−0.120884
$461$	−12.1854	−0.567532	−0.283766	−	0.958894i	$-0.591584\pi$
$461$	−12.1854	−0.567532	−0.283766	+	0.958894i	$0.591584\pi$
$462$	−6.82014	−0.317302
$463$	−35.8376	−1.66552	−0.832758	−	0.553637i	$-0.813240\pi$
$463$	−35.8376	−1.66552	−0.832758	+	0.553637i	$0.813240\pi$
$464$	13.5781	0.630348
$465$	6.72711	0.311962
$466$	40.2340	1.86380
$467$	19.9701	0.924106	0.462053	−	0.886852i	$-0.347113\pi$
$467$	19.9701	0.924106	0.462053	+	0.886852i	$0.347113\pi$
$468$	9.80137	0.453068
$469$	−14.7862	−0.682761
$470$	0.712387	0.0328600
$471$	−10.7354	−0.494662
$472$	5.50330	0.253310
$473$	8.89133	0.408824
$474$	−0.867069	−0.0398258
$475$	−4.64851	−0.213288
$476$	−13.4959	−0.618582
$477$	4.72392	0.216293
$478$	−28.6168	−1.30890
$479$	−42.4070	−1.93763	−0.968813	−	0.247794i	$-0.920295\pi$
$479$	−42.4070	−1.93763	−0.968813	+	0.247794i	$0.920295\pi$
$480$	5.47403	0.249854
$481$	−24.7649	−1.12918
$482$	−45.1725	−2.05755
$483$	−2.37206	−0.107933
$484$	−7.55237	−0.343289
$485$	0.592516	0.0269048
$486$	−29.2880	−1.32853
$487$	8.47448	0.384015	0.192008	−	0.981393i	$-0.438500\pi$
$487$	8.47448	0.384015	0.192008	+	0.981393i	$0.438500\pi$
$488$	−6.85192	−0.310172
$489$	−8.14517	−0.368337
$490$	6.34095	0.286455
$491$	17.1233	0.772764	0.386382	−	0.922339i	$-0.373725\pi$
$491$	17.1233	0.772764	0.386382	+	0.922339i	$0.373725\pi$
$492$	11.1973	0.504812
$493$	13.0205	0.586414
$494$	−22.4792	−1.01139
$495$	−6.05369	−0.272093
$496$	−41.4618	−1.86169
$497$	−21.9819	−0.986025
$498$	0.518782	0.0232472
$499$	3.72866	0.166918	0.0834588	−	0.996511i	$-0.473403\pi$
$499$	3.72866	0.166918	0.0834588	+	0.996511i	$0.473403\pi$
$500$	1.57982	0.0706517
$501$	−0.526632	−0.0235282
$502$	21.8213	0.973933
$503$	21.5334	0.960127	0.480064	−	0.877234i	$-0.340614\pi$
$503$	21.5334	0.960127	0.480064	+	0.877234i	$0.340614\pi$
$504$	−3.68615	−0.164194
$505$	−19.0123	−0.846035
$506$	7.74370	0.344249
$507$	−4.89403	−0.217351
$508$	−1.82184	−0.0808309
$509$	−21.5888	−0.956905	−0.478453	−	0.878113i	$-0.658802\pi$
$509$	−21.5888	−0.956905	−0.478453	+	0.878113i	$0.658802\pi$
$510$	6.40296	0.283528
$511$	−13.5202	−0.598097
$512$	−26.3231	−1.16333
$513$	19.0910	0.842887
$514$	42.6125	1.87956
$515$	10.3814	0.457460
$516$	4.26205	0.187626
$517$	−0.938993	−0.0412969
$518$	−35.0184	−1.53862
$519$	3.08342	0.135347
$520$	−2.03189	−0.0891043
$521$	13.0284	0.570785	0.285392	−	0.958411i	$-0.407876\pi$
$521$	13.0284	0.570785	0.285392	+	0.958411i	$0.407876\pi$
$522$	−13.3713	−0.585245
$523$	−6.53023	−0.285547	−0.142773	−	0.989755i	$-0.545602\pi$
$523$	−6.53023	−0.285547	−0.142773	+	0.989755i	$0.545602\pi$
$524$	13.0603	0.570544
$525$	1.44539	0.0630821
$526$	54.2236	2.36426
$527$	−39.7591	−1.73193
$528$	−8.80114	−0.383020
$529$	−20.3067	−0.882901
$530$	3.68205	0.159938
$531$	−16.8036	−0.729213
$532$	−14.0277	−0.608178
$533$	−23.9397	−1.03694
$534$	14.6476	0.633862
$535$	6.89457	0.298078
$536$	−6.15398	−0.265811
$537$	−15.9238	−0.687164
$538$	4.72065	0.203522
$539$	−8.35796	−0.360003
$540$	−6.48816	−0.279206
$541$	−2.07326	−0.0891362	−0.0445681	−	0.999006i	$-0.514191\pi$
$541$	−2.07326	−0.0891362	−0.0445681	+	0.999006i	$0.514191\pi$
$542$	−9.35803	−0.401962
$543$	9.49970	0.407671
$544$	−32.3530	−1.38712
$545$	−12.1395	−0.519999
$546$	6.98959	0.299127
$547$	−27.4515	−1.17374	−0.586871	−	0.809681i	$-0.699640\pi$
$547$	−27.4515	−1.17374	−0.586871	+	0.809681i	$0.699640\pi$
$548$	−19.8975	−0.849980
$549$	20.9214	0.892904
$550$	−4.71854	−0.201199
$551$	13.5336	0.576550
$552$	−0.987250	−0.0420201
$553$	1.15682	0.0491930
$554$	44.1431	1.87546
$555$	7.33200	0.311226
$556$	−9.68354	−0.410674
$557$	−9.82616	−0.416348	−0.208174	−	0.978092i	$-0.566752\pi$
$557$	−9.82616	−0.416348	−0.208174	+	0.978092i	$0.566752\pi$
$558$	40.8302	1.72848
$559$	−9.11224	−0.385407
$560$	−8.90851	−0.376453
$561$	−8.43970	−0.356324
$562$	−48.6072	−2.05037
$563$	32.0962	1.35269	0.676346	−	0.736584i	$-0.263562\pi$
$563$	32.0962	1.35269	0.676346	+	0.736584i	$0.263562\pi$
$564$	−0.450106	−0.0189529
$565$	4.77745	0.200989
$566$	61.9545	2.60414
$567$	7.97399	0.334876
$568$	−9.14886	−0.383878
$569$	44.1902	1.85255	0.926276	−	0.376846i	$-0.122992\pi$
$569$	44.1902	1.85255	0.926276	+	0.376846i	$0.122992\pi$
$570$	6.65527	0.278759
$571$	47.3752	1.98259	0.991296	−	0.131652i	$-0.0420280\pi$
$571$	47.3752	1.98259	0.991296	+	0.131652i	$0.0420280\pi$
$572$	−10.0698	−0.421039
$573$	−3.11017	−0.129929
$574$	−33.8515	−1.41294
$575$	−1.64112	−0.0684395
$576$	10.5827	0.440944
$577$	1.15079	0.0479079	0.0239540	−	0.999713i	$-0.492374\pi$
$577$	1.15079	0.0479079	0.0239540	+	0.999713i	$0.492374\pi$
$578$	−5.67853	−0.236196
$579$	−6.37508	−0.264939
$580$	−4.59946	−0.190982
$581$	−0.692146	−0.0287151
$582$	−0.848305	−0.0351634
$583$	−4.85328	−0.201003
$584$	−5.62707	−0.232850
$585$	6.20410	0.256508
$586$	14.3865	0.594302
$587$	−5.73954	−0.236896	−0.118448	−	0.992960i	$-0.537792\pi$
$587$	−5.73954	−0.236896	−0.118448	+	0.992960i	$0.537792\pi$
$588$	−4.00638	−0.165220
$589$	−41.3258	−1.70280
$590$	−13.0975	−0.539216
$591$	−10.8562	−0.446566
$592$	−45.1900	−1.85730
$593$	−40.9799	−1.68284	−0.841422	−	0.540378i	$-0.818281\pi$
$593$	−40.9799	−1.68284	−0.841422	+	0.540378i	$0.818281\pi$
$594$	19.3786	0.795112
$595$	−8.54266	−0.350215
$596$	35.3142	1.44653
$597$	−8.79540	−0.359972
$598$	−7.93609	−0.324531
$599$	−6.01631	−0.245820	−0.122910	−	0.992418i	$-0.539223\pi$
$599$	−6.01631	−0.245820	−0.122910	+	0.992418i	$0.539223\pi$
$600$	0.601570	0.0245590
$601$	22.8598	0.932472	0.466236	−	0.884660i	$-0.345610\pi$
$601$	22.8598	0.932472	0.466236	+	0.884660i	$0.345610\pi$
$602$	−12.8850	−0.525154
$603$	18.7903	0.765201
$604$	20.5038	0.834288
$605$	−4.78052	−0.194356
$606$	27.2199	1.10573
$607$	−15.2593	−0.619355	−0.309677	−	0.950842i	$-0.600221\pi$
$607$	−15.2593	−0.619355	−0.309677	+	0.950842i	$0.600221\pi$
$608$	−33.6279	−1.36379
$609$	−4.20808	−0.170520
$610$	16.3072	0.660257
$611$	0.962323	0.0389314
$612$	17.1506	0.693273
$613$	−9.52547	−0.384730	−0.192365	−	0.981323i	$-0.561616\pi$
$613$	−9.52547	−0.384730	−0.192365	+	0.981323i	$0.561616\pi$
$614$	−61.1544	−2.46799
$615$	7.08769	0.285803
$616$	3.78710	0.152587
$617$	31.4482	1.26606	0.633029	−	0.774128i	$-0.281811\pi$
$617$	31.4482	1.26606	0.633029	+	0.774128i	$0.281811\pi$
$618$	−14.8631	−0.597881
$619$	1.04362	0.0419467	0.0209733	−	0.999780i	$-0.493323\pi$
$619$	1.04362	0.0419467	0.0209733	+	0.999780i	$0.493323\pi$
$620$	14.0448	0.564052
$621$	6.73992	0.270464
$622$	−16.3068	−0.653842
$623$	−19.5424	−0.782950
$624$	9.01981	0.361081
$625$	1.00000	0.0400000
$626$	14.2548	0.569735
$627$	−8.77228	−0.350331
$628$	−22.4133	−0.894387
$629$	−43.3341	−1.72785
$630$	8.77281	0.349517
$631$	27.2225	1.08371	0.541856	−	0.840471i	$-0.317722\pi$
$631$	27.2225	1.08371	0.541856	+	0.840471i	$0.317722\pi$
$632$	0.481467	0.0191517
$633$	6.14247	0.244141
$634$	29.0882	1.15524
$635$	−1.15319	−0.0457630
$636$	−2.32642	−0.0922485
$637$	8.56562	0.339382
$638$	13.7375	0.543871
$639$	27.9348	1.10508
$640$	−6.21961	−0.245852
$641$	−22.6226	−0.893537	−0.446769	−	0.894649i	$-0.647425\pi$
$641$	−22.6226	−0.893537	−0.446769	+	0.894649i	$0.647425\pi$
$642$	−9.87095	−0.389575
$643$	20.4039	0.804652	0.402326	−	0.915497i	$-0.368202\pi$
$643$	20.4039	0.804652	0.402326	+	0.915497i	$0.368202\pi$
$644$	−4.95237	−0.195151
$645$	2.69781	0.106226
$646$	−39.3345	−1.54759
$647$	30.6791	1.20612	0.603059	−	0.797697i	$-0.293948\pi$
$647$	30.6791	1.20612	0.603059	+	0.797697i	$0.293948\pi$
$648$	3.31876	0.130373
$649$	17.2638	0.677661
$650$	4.83578	0.189675
$651$	12.8497	0.503619
$652$	−17.0054	−0.665983
$653$	36.9648	1.44654	0.723272	−	0.690564i	$-0.242637\pi$
$653$	36.9648	1.44654	0.723272	+	0.690564i	$0.242637\pi$
$654$	17.3801	0.679616
$655$	8.26697	0.323017
$656$	−43.6841	−1.70558
$657$	17.1815	0.670314
$658$	1.36076	0.0530478
$659$	21.9028	0.853211	0.426605	−	0.904438i	$-0.359709\pi$
$659$	21.9028	0.853211	0.426605	+	0.904438i	$0.359709\pi$
$660$	2.98130	0.116047
$661$	−3.95599	−0.153870	−0.0769352	−	0.997036i	$-0.524513\pi$
$661$	−3.95599	−0.153870	−0.0769352	+	0.997036i	$0.524513\pi$
$662$	67.1035	2.60805
$663$	8.64939	0.335914
$664$	−0.288070	−0.0111793
$665$	−8.87930	−0.344324
$666$	44.5016	1.72440
$667$	4.77793	0.185002
$668$	−1.09950	−0.0425408
$669$	−5.53757	−0.214095
$670$	14.6461	0.565827
$671$	−21.4944	−0.829780
$672$	10.4561	0.403355
$673$	25.5175	0.983627	0.491814	−	0.870701i	$-0.336334\pi$
$673$	25.5175	0.983627	0.491814	+	0.870701i	$0.336334\pi$
$674$	−42.8922	−1.65215
$675$	−4.10690	−0.158075
$676$	−10.2177	−0.392988
$677$	−12.6776	−0.487238	−0.243619	−	0.969871i	$-0.578335\pi$
$677$	−12.6776	−0.487238	−0.243619	+	0.969871i	$0.578335\pi$
$678$	−6.83987	−0.262684
$679$	1.13179	0.0434340
$680$	−3.55544	−0.136345
$681$	7.79591	0.298740
$682$	−41.9484	−1.60629
$683$	5.39356	0.206379	0.103189	−	0.994662i	$-0.467095\pi$
$683$	5.39356	0.206379	0.103189	+	0.994662i	$0.467095\pi$
$684$	17.8265	0.681612
$685$	−12.5948	−0.481222
$686$	37.4105	1.42834
$687$	−13.8786	−0.529501
$688$	−16.6276	−0.633923
$689$	4.97387	0.189489
$690$	2.34959	0.0894475
$691$	−30.5967	−1.16395	−0.581976	−	0.813206i	$-0.697720\pi$
$691$	−30.5967	−1.16395	−0.581976	+	0.813206i	$0.697720\pi$
$692$	6.43754	0.244718
$693$	−11.5634	−0.439257
$694$	10.8297	0.411089
$695$	−6.12952	−0.232506
$696$	−1.75140	−0.0663866
$697$	−41.8902	−1.58670
$698$	−21.0488	−0.796709
$699$	−16.0910	−0.608619
$700$	3.01767	0.114057
$701$	30.9171	1.16772	0.583861	−	0.811854i	$-0.301541\pi$
$701$	30.9171	1.16772	0.583861	+	0.811854i	$0.301541\pi$
$702$	−19.8600	−0.749569
$703$	−45.0418	−1.69878
$704$	−10.8725	−0.409772
$705$	−0.284909	−0.0107303
$706$	38.2531	1.43968
$707$	−36.3160	−1.36581
$708$	8.27537	0.311007
$709$	−34.8100	−1.30732	−0.653659	−	0.756789i	$-0.726767\pi$
$709$	−34.8100	−1.30732	−0.653659	+	0.756789i	$0.726767\pi$
$710$	21.7737	0.817153
$711$	−1.47009	−0.0551329
$712$	−8.13353	−0.304817
$713$	−14.5898	−0.546391
$714$	12.2305	0.457716
$715$	−6.37401	−0.238374
$716$	−33.2456	−1.24245
$717$	11.4449	0.427418
$718$	−22.0090	−0.821369
$719$	37.3072	1.39132	0.695662	−	0.718369i	$-0.255111\pi$
$719$	37.3072	1.39132	0.695662	+	0.718369i	$0.255111\pi$
$720$	11.3210	0.421908
$721$	19.8299	0.738506
$722$	−4.93572	−0.183689
$723$	18.0661	0.671886
$724$	19.8334	0.737101
$725$	−2.91138	−0.108126
$726$	6.84427	0.254015
$727$	−37.1754	−1.37876	−0.689379	−	0.724401i	$-0.742116\pi$
$727$	−37.1754	−1.37876	−0.689379	+	0.724401i	$0.742116\pi$
$728$	−3.88119	−0.143847
$729$	−0.810369	−0.0300137
$730$	13.3921	0.495663
$731$	−15.9448	−0.589739
$732$	−10.3033	−0.380821
$733$	−37.4194	−1.38212	−0.691058	−	0.722799i	$-0.742855\pi$
$733$	−37.4194	−1.38212	−0.691058	+	0.722799i	$0.742855\pi$
$734$	−6.84868	−0.252789
$735$	−2.53597	−0.0935408
$736$	−11.8721	−0.437611
$737$	−19.3049	−0.711105
$738$	43.0187	1.58354
$739$	−33.0873	−1.21714	−0.608568	−	0.793502i	$-0.708256\pi$
$739$	−33.0873	−1.21714	−0.608568	+	0.793502i	$0.708256\pi$
$740$	15.3077	0.562721
$741$	8.99023	0.330264
$742$	7.03321	0.258197
$743$	41.7712	1.53244	0.766219	−	0.642580i	$-0.222136\pi$
$743$	41.7712	1.53244	0.766219	+	0.642580i	$0.222136\pi$
$744$	5.34803	0.196068
$745$	22.3533	0.818961
$746$	61.7096	2.25935
$747$	0.879583	0.0321823
$748$	−17.6203	−0.644262
$749$	13.1696	0.481206
$750$	−1.43170	−0.0522783
$751$	33.9448	1.23866	0.619332	−	0.785129i	$-0.287404\pi$
$751$	33.9448	1.23866	0.619332	+	0.785129i	$0.287404\pi$
$752$	1.75601	0.0640350
$753$	−8.72713	−0.318034
$754$	−14.0788	−0.512719
$755$	12.9786	0.472339
$756$	−12.3933	−0.450739
$757$	21.8426	0.793882	0.396941	−	0.917844i	$-0.370072\pi$
$757$	21.8426	0.793882	0.396941	+	0.917844i	$0.370072\pi$
$758$	−47.2726	−1.71702
$759$	−3.09698	−0.112413
$760$	−3.69555	−0.134052
$761$	0.137147	0.00497158	0.00248579	−	0.999997i	$-0.499209\pi$
$761$	0.137147	0.00497158	0.00248579	+	0.999997i	$0.499209\pi$
$762$	1.65102	0.0598103
$763$	−23.1881	−0.839466
$764$	−6.49337	−0.234922
$765$	10.8561	0.392502
$766$	−56.8571	−2.05433
$767$	−17.6927	−0.638846
$768$	15.5025	0.559397
$769$	2.21221	0.0797742	0.0398871	−	0.999204i	$-0.487300\pi$
$769$	2.21221	0.0797742	0.0398871	+	0.999204i	$0.487300\pi$
$770$	−9.01306	−0.324808
$771$	−17.0423	−0.613762
$772$	−13.3098	−0.479031
$773$	19.4610	0.699964	0.349982	−	0.936756i	$-0.386188\pi$
$773$	19.4610	0.699964	0.349982	+	0.936756i	$0.386188\pi$
$774$	16.3743	0.588564
$775$	8.89011	0.319342
$776$	0.471048	0.0169097
$777$	14.0051	0.502431
$778$	−73.7912	−2.64554
$779$	−43.5409	−1.56001
$780$	−3.05537	−0.109400
$781$	−28.6998	−1.02696
$782$	−13.8867	−0.496589
$783$	11.9567	0.427299
$784$	15.6302	0.558221
$785$	−14.1872	−0.506364
$786$	−11.8358	−0.422170
$787$	−33.2744	−1.18610	−0.593052	−	0.805164i	$-0.702077\pi$
$787$	−33.2744	−1.18610	−0.593052	+	0.805164i	$0.702077\pi$
$788$	−22.6656	−0.807427
$789$	−21.6860	−0.772041
$790$	−1.14586	−0.0407680
$791$	9.12558	0.324468
$792$	−4.81266	−0.171011
$793$	22.0284	0.782251
$794$	38.0461	1.35021
$795$	−1.47258	−0.0522272
$796$	−18.3629	−0.650857
$797$	−6.68804	−0.236902	−0.118451	−	0.992960i	$-0.537793\pi$
$797$	−6.68804	−0.236902	−0.118451	+	0.992960i	$0.537793\pi$
$798$	12.7125	0.450017
$799$	1.68389	0.0595718
$800$	7.23412	0.255765
$801$	24.8346	0.877488
$802$	−53.7839	−1.89917
$803$	−17.6520	−0.622926
$804$	−9.25379	−0.326356
$805$	−3.13477	−0.110486
$806$	42.9906	1.51428
$807$	−1.88796	−0.0664592
$808$	−15.1147	−0.531733
$809$	−30.8092	−1.08319	−0.541597	−	0.840638i	$-0.682180\pi$
$809$	−30.8092	−1.08319	−0.541597	+	0.840638i	$0.682180\pi$
$810$	−7.89845	−0.277523
$811$	53.2390	1.86948	0.934738	−	0.355338i	$-0.115634\pi$
$811$	53.2390	1.86948	0.934738	+	0.355338i	$0.115634\pi$
$812$	−8.78559	−0.308314
$813$	3.74261	0.131259
$814$	−45.7203	−1.60250
$815$	−10.7641	−0.377051
$816$	15.7830	0.552517
$817$	−16.5731	−0.579820
$818$	65.7648	2.29941
$819$	11.8507	0.414096
$820$	14.7976	0.516754
$821$	1.56067	0.0544677	0.0272339	−	0.999629i	$-0.491330\pi$
$821$	1.56067	0.0544677	0.0272339	+	0.999629i	$0.491330\pi$
$822$	18.0320	0.628937
$823$	−38.6523	−1.34733	−0.673667	−	0.739035i	$-0.735282\pi$
$823$	−38.6523	−1.34733	−0.673667	+	0.739035i	$0.735282\pi$
$824$	8.25320	0.287514
$825$	1.88711	0.0657009
$826$	−25.0180	−0.870489
$827$	−33.1917	−1.15419	−0.577094	−	0.816678i	$-0.695813\pi$
$827$	−33.1917	−1.15419	−0.577094	+	0.816678i	$0.695813\pi$
$828$	6.29350	0.218714
$829$	−52.0597	−1.80811	−0.904053	−	0.427420i	$-0.859423\pi$
$829$	−52.0597	−1.80811	−0.904053	+	0.427420i	$0.859423\pi$
$830$	0.685589	0.0237972
$831$	−17.6544	−0.612425
$832$	11.1426	0.386301
$833$	14.9883	0.519314
$834$	8.77563	0.303875
$835$	−0.695963	−0.0240848
$836$	−18.3147	−0.633426
$837$	−36.5108	−1.26200
$838$	8.25835	0.285280
$839$	3.49117	0.120528	0.0602642	−	0.998182i	$-0.480806\pi$
$839$	3.49117	0.120528	0.0602642	+	0.998182i	$0.480806\pi$
$840$	1.14908	0.0396471
$841$	−20.5239	−0.707720
$842$	52.0549	1.79393
$843$	19.4398	0.669541
$844$	12.8242	0.441426
$845$	−6.46763	−0.222493
$846$	−1.72926	−0.0594531
$847$	−9.13145	−0.313760
$848$	9.07610	0.311675
$849$	−24.7778	−0.850373
$850$	8.46174	0.290235
$851$	−15.9016	−0.545101
$852$	−13.7572	−0.471315
$853$	−34.1322	−1.16867	−0.584333	−	0.811514i	$-0.698644\pi$
$853$	−34.1322	−1.16867	−0.584333	+	0.811514i	$0.698644\pi$
$854$	31.1489	1.06589
$855$	11.2839	0.385900
$856$	5.48116	0.187342
$857$	37.7280	1.28876	0.644382	−	0.764703i	$-0.277115\pi$
$857$	37.7280	1.28876	0.644382	+	0.764703i	$0.277115\pi$
$858$	9.12566	0.311545
$859$	4.46102	0.152208	0.0761041	−	0.997100i	$-0.475752\pi$
$859$	4.46102	0.152208	0.0761041	+	0.997100i	$0.475752\pi$
$860$	5.63245	0.192065
$861$	13.5384	0.461389
$862$	31.7466	1.08129
$863$	−19.0539	−0.648601	−0.324300	−	0.945954i	$-0.605129\pi$
$863$	−19.0539	−0.648601	−0.324300	+	0.945954i	$0.605129\pi$
$864$	−29.7098	−1.01075
$865$	4.07485	0.138549
$866$	57.3674	1.94942
$867$	2.27105	0.0771288
$868$	26.8275	0.910583
$869$	1.51035	0.0512353
$870$	4.16822	0.141316
$871$	19.7845	0.670374
$872$	−9.65086	−0.326819
$873$	−1.43828	−0.0486785
$874$	−14.4340	−0.488236
$875$	1.91014	0.0645744
$876$	−8.46148	−0.285887
$877$	−23.2583	−0.785379	−0.392689	−	0.919671i	$-0.628455\pi$
$877$	−23.2583	−0.785379	−0.392689	+	0.919671i	$0.628455\pi$
$878$	−39.7349	−1.34099
$879$	−5.75369	−0.194067
$880$	−11.6310	−0.392081
$881$	8.02827	0.270479	0.135240	−	0.990813i	$-0.456820\pi$
$881$	8.02827	0.270479	0.135240	+	0.990813i	$0.456820\pi$
$882$	−15.3921	−0.518278
$883$	41.5928	1.39971	0.699854	−	0.714286i	$-0.253248\pi$
$883$	41.5928	1.39971	0.699854	+	0.714286i	$0.253248\pi$
$884$	18.0581	0.607360
$885$	5.23817	0.176079
$886$	−19.5622	−0.657206
$887$	−56.7507	−1.90550	−0.952751	−	0.303752i	$-0.901760\pi$
$887$	−56.7507	−1.90550	−0.952751	+	0.303752i	$0.901760\pi$
$888$	5.82892	0.195606
$889$	−2.20275	−0.0738780
$890$	19.3573	0.648858
$891$	10.4109	0.348778
$892$	−11.5613	−0.387100
$893$	1.75025	0.0585698
$894$	−32.0032	−1.07035
$895$	−21.0439	−0.703420
$896$	−11.8803	−0.396893
$897$	3.17393	0.105974
$898$	−2.14106	−0.0714481
$899$	−25.8825	−0.863229
$900$	−3.83488	−0.127829
$901$	8.70337	0.289951
$902$	−44.1968	−1.47159
$903$	5.15318	0.171487
$904$	3.79806	0.126321
$905$	12.5542	0.417315
$906$	−18.5814	−0.617326
$907$	−31.6334	−1.05037	−0.525185	−	0.850988i	$-0.676004\pi$
$907$	−31.6334	−1.05037	−0.525185	+	0.850988i	$0.676004\pi$
$908$	16.2762	0.540145
$909$	46.1506	1.53072
$910$	9.23699	0.306203
$911$	33.1446	1.09813	0.549064	−	0.835780i	$-0.314984\pi$
$911$	33.1446	1.09813	0.549064	+	0.835780i	$0.314984\pi$
$912$	16.4050	0.543223
$913$	−0.903671	−0.0299072
$914$	19.8027	0.655015
$915$	−6.52182	−0.215605
$916$	−28.9756	−0.957380
$917$	15.7911	0.521466
$918$	−34.7515	−1.14697
$919$	44.7369	1.47573	0.737867	−	0.674946i	$-0.235833\pi$
$919$	44.7369	1.47573	0.737867	+	0.674946i	$0.235833\pi$
$920$	−1.30469	−0.0430142
$921$	24.4578	0.805913
$922$	23.0553	0.759287
$923$	29.4129	0.968136
$924$	5.69470	0.187342
$925$	9.68950	0.318589
$926$	67.8063	2.22825
$927$	−25.2000	−0.827677
$928$	−21.0613	−0.691370
$929$	6.54620	0.214774	0.107387	−	0.994217i	$-0.465752\pi$
$929$	6.54620	0.214774	0.107387	+	0.994217i	$0.465752\pi$
$930$	−12.7280	−0.417367
$931$	15.5789	0.510579
$932$	−33.5947	−1.10043
$933$	6.52166	0.213510
$934$	−37.7843	−1.23634
$935$	−11.1534	−0.364754
$936$	4.93224	0.161215
$937$	−20.9532	−0.684510	−0.342255	−	0.939607i	$-0.611191\pi$
$937$	−20.9532	−0.684510	−0.342255	+	0.939607i	$0.611191\pi$
$938$	27.9760	0.913449
$939$	−5.70099	−0.186045
$940$	−0.594831	−0.0194012
$941$	−9.09019	−0.296332	−0.148166	−	0.988963i	$-0.547337\pi$
$941$	−9.09019	−0.296332	−0.148166	+	0.988963i	$0.547337\pi$
$942$	20.3119	0.661796
$943$	−15.3718	−0.500574
$944$	−32.2849	−1.05078
$945$	−7.84474	−0.255189
$946$	−16.8228	−0.546955
$947$	−36.9202	−1.19974	−0.599872	−	0.800096i	$-0.704782\pi$
$947$	−36.9202	−1.19974	−0.599872	+	0.800096i	$0.704782\pi$
$948$	0.723987	0.0235140
$949$	18.0906	0.587246
$950$	8.79518	0.285353
$951$	−11.6334	−0.377239
$952$	−6.79139	−0.220110
$953$	51.1743	1.65770	0.828849	−	0.559472i	$-0.188996\pi$
$953$	51.1743	1.65770	0.828849	+	0.559472i	$0.188996\pi$
$954$	−8.93785	−0.289373
$955$	−4.11019	−0.133003
$956$	23.8946	0.772805
$957$	−5.49411	−0.177599
$958$	80.2358	2.59230
$959$	−24.0578	−0.776866
$960$	−3.29893	−0.106472
$961$	48.0341	1.54949
$962$	46.8563	1.51071
$963$	−16.7360	−0.539309
$964$	37.7183	1.21482
$965$	−8.42490	−0.271207
$966$	4.48804	0.144400
$967$	12.9986	0.418007	0.209003	−	0.977915i	$-0.432978\pi$
$967$	12.9986	0.418007	0.209003	+	0.977915i	$0.432978\pi$
$968$	−3.80050	−0.122153
$969$	15.7313	0.505362
$970$	−1.12107	−0.0359952
$971$	42.2474	1.35579	0.677893	−	0.735161i	$-0.262893\pi$
$971$	42.2474	1.35579	0.677893	+	0.735161i	$0.262893\pi$
$972$	24.4549	0.784393
$973$	−11.7082	−0.375348
$974$	−16.0341	−0.513764
$975$	−1.93400	−0.0619376
$976$	40.1965	1.28666
$977$	−49.5232	−1.58439	−0.792193	−	0.610271i	$-0.791061\pi$
$977$	−49.5232	−1.58439	−0.792193	+	0.610271i	$0.791061\pi$
$978$	15.4110	0.492789
$979$	−25.5147	−0.815454
$980$	−5.29458	−0.169129
$981$	29.4676	0.940827
$982$	−32.3980	−1.03386
$983$	30.6185	0.976579	0.488289	−	0.872682i	$-0.337621\pi$
$983$	30.6185	0.976579	0.488289	+	0.872682i	$0.337621\pi$
$984$	5.63468	0.179627
$985$	−14.3469	−0.457131
$986$	−24.6353	−0.784548
$987$	−0.544216	−0.0173226
$988$	18.7697	0.597144
$989$	−5.85101	−0.186051
$990$	11.4538	0.364027
$991$	−35.7220	−1.13475	−0.567373	−	0.823461i	$-0.692040\pi$
$991$	−35.7220	−1.13475	−0.567373	+	0.823461i	$0.692040\pi$
$992$	64.3122	2.04191
$993$	−26.8371	−0.851650
$994$	41.5908	1.31918
$995$	−11.6234	−0.368488
$996$	−0.433174	−0.0137256
$997$	23.5707	0.746493	0.373246	−	0.927732i	$-0.378245\pi$
$997$	23.5707	0.746493	0.373246	+	0.927732i	$0.378245\pi$
$998$	−7.05477	−0.223315
$999$	−39.7938	−1.25902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.e.1.20	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.e.1.20	✓	88	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.89204 q^{2} +0.756696 q^{3} +1.57982 q^{4} +1.00000 q^{5} -1.43170 q^{6} +1.91014 q^{7} +0.794996 q^{8} -2.42741 q^{9} +O(q^{10})\)	\(q-1.89204 q^{2} +0.756696 q^{3} +1.57982 q^{4} +1.00000 q^{5} -1.43170 q^{6} +1.91014 q^{7} +0.794996 q^{8} -2.42741 q^{9} -1.89204 q^{10} +2.49389 q^{11} +1.19544 q^{12} -2.55585 q^{13} -3.61406 q^{14} +0.756696 q^{15} -4.66381 q^{16} -4.47228 q^{17} +4.59276 q^{18} -4.64851 q^{19} +1.57982 q^{20} +1.44539 q^{21} -4.71854 q^{22} -1.64112 q^{23} +0.601570 q^{24} +1.00000 q^{25} +4.83578 q^{26} -4.10690 q^{27} +3.01767 q^{28} -2.91138 q^{29} -1.43170 q^{30} +8.89011 q^{31} +7.23412 q^{32} +1.88711 q^{33} +8.46174 q^{34} +1.91014 q^{35} -3.83488 q^{36} +9.68950 q^{37} +8.79518 q^{38} -1.93400 q^{39} +0.794996 q^{40} +9.36663 q^{41} -2.73474 q^{42} +3.56525 q^{43} +3.93990 q^{44} -2.42741 q^{45} +3.10507 q^{46} -0.376518 q^{47} -3.52908 q^{48} -3.35138 q^{49} -1.89204 q^{50} -3.38415 q^{51} -4.03779 q^{52} -1.94607 q^{53} +7.77042 q^{54} +2.49389 q^{55} +1.51855 q^{56} -3.51751 q^{57} +5.50845 q^{58} +6.92242 q^{59} +1.19544 q^{60} -8.61881 q^{61} -16.8205 q^{62} -4.63669 q^{63} -4.35965 q^{64} -2.55585 q^{65} -3.57050 q^{66} -7.74089 q^{67} -7.06540 q^{68} -1.24183 q^{69} -3.61406 q^{70} -11.5080 q^{71} -1.92978 q^{72} -7.07811 q^{73} -18.3329 q^{74} +0.756696 q^{75} -7.34382 q^{76} +4.76367 q^{77} +3.65921 q^{78} +0.605622 q^{79} -4.66381 q^{80} +4.17456 q^{81} -17.7220 q^{82} -0.362354 q^{83} +2.28346 q^{84} -4.47228 q^{85} -6.74560 q^{86} -2.20303 q^{87} +1.98263 q^{88} -10.2309 q^{89} +4.59276 q^{90} -4.88202 q^{91} -2.59268 q^{92} +6.72711 q^{93} +0.712387 q^{94} -4.64851 q^{95} +5.47403 q^{96} +0.592516 q^{97} +6.34095 q^{98} -6.05369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9}+O(q^{10}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9	\( 88 q - 14 q^{2} - 34 q^{3} + 66 q^{4} + 88 q^{5} - q^{6} - 35 q^{7} - 39 q^{8} + 72 q^{9} - 14 q^{10} - 26 q^{11} - 64 q^{12} - 31 q^{13} - 17 q^{14} - 34 q^{15} + 34 q^{16} - 31 q^{17} - 42 q^{18} - 56 q^{19} + 66 q^{20} - q^{21} - 49 q^{22} - 74 q^{23} - 3 q^{24} + 88 q^{25} - q^{26} - 130 q^{27} - 57 q^{28} - 6 q^{29} - q^{30} - 37 q^{31} - 87 q^{32} - 43 q^{33} - 35 q^{34} - 35 q^{35} + 53 q^{36} - 67 q^{37} - 40 q^{38} - 21 q^{39} - 39 q^{40} + 2 q^{41} - 15 q^{42} - 136 q^{43} - 15 q^{44} + 72 q^{45} - 16 q^{46} - 139 q^{47} - 71 q^{48} + 41 q^{49} - 14 q^{50} - 71 q^{51} - 71 q^{52} - 75 q^{53} + 26 q^{54} - 26 q^{55} - 22 q^{56} - 34 q^{57} - 65 q^{58} - 41 q^{59} - 64 q^{60} - 11 q^{61} - 30 q^{62} - 114 q^{63} - 33 q^{64} - 31 q^{65} + 24 q^{66} - 209 q^{67} - 42 q^{68} - 22 q^{69} - 17 q^{70} - 43 q^{71} - 80 q^{72} - 50 q^{73} + 9 q^{74} - 34 q^{75} - 62 q^{76} - 49 q^{77} - 19 q^{78} - 77 q^{79} + 34 q^{80} + 72 q^{81} - 107 q^{82} - 113 q^{83} + 19 q^{84} - 31 q^{85} + 14 q^{86} - 87 q^{87} - 107 q^{88} - 5 q^{89} - 42 q^{90} - 159 q^{91} - 100 q^{92} - 82 q^{93} - 31 q^{94} - 56 q^{95} + 58 q^{96} - 105 q^{97} - 29 q^{98} - 68 q^{99}+O(q^{100}) \) 88 * q - 14 * q^2 - 34 * q^3 + 66 * q^4 + 88 * q^5 - q^6 - 35 * q^7 - 39 * q^8 + 72 * q^9 - 14 * q^10 - 26 * q^11 - 64 * q^12 - 31 * q^13 - 17 * q^14 - 34 * q^15 + 34 * q^16 - 31 * q^17 - 42 * q^18 - 56 * q^19 + 66 * q^20 - q^21 - 49 * q^22 - 74 * q^23 - 3 * q^24 + 88 * q^25 - q^26 - 130 * q^27 - 57 * q^28 - 6 * q^29 - q^30 - 37 * q^31 - 87 * q^32 - 43 * q^33 - 35 * q^34 - 35 * q^35 + 53 * q^36 - 67 * q^37 - 40 * q^38 - 21 * q^39 - 39 * q^40 + 2 * q^41 - 15 * q^42 - 136 * q^43 - 15 * q^44 + 72 * q^45 - 16 * q^46 - 139 * q^47 - 71 * q^48 + 41 * q^49 - 14 * q^50 - 71 * q^51 - 71 * q^52 - 75 * q^53 + 26 * q^54 - 26 * q^55 - 22 * q^56 - 34 * q^57 - 65 * q^58 - 41 * q^59 - 64 * q^60 - 11 * q^61 - 30 * q^62 - 114 * q^63 - 33 * q^64 - 31 * q^65 + 24 * q^66 - 209 * q^67 - 42 * q^68 - 22 * q^69 - 17 * q^70 - 43 * q^71 - 80 * q^72 - 50 * q^73 + 9 * q^74 - 34 * q^75 - 62 * q^76 - 49 * q^77 - 19 * q^78 - 77 * q^79 + 34 * q^80 + 72 * q^81 - 107 * q^82 - 113 * q^83 + 19 * q^84 - 31 * q^85 + 14 * q^86 - 87 * q^87 - 107 * q^88 - 5 * q^89 - 42 * q^90 - 159 * q^91 - 100 * q^92 - 82 * q^93 - 31 * q^94 - 56 * q^95 + 58 * q^96 - 105 * q^97 - 29 * q^98 - 68 * q^99

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