LMFDB - Embedded newform 6002.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.79165 q^{3} +1.00000 q^{4} +2.16923 q^{5} +1.79165 q^{6} -2.84770 q^{7} -1.00000 q^{8} +0.210015 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.79165 q^{3} +1.00000 q^{4} +2.16923 q^{5} +1.79165 q^{6} -2.84770 q^{7} -1.00000 q^{8} +0.210015 q^{9} -2.16923 q^{10} +3.81889 q^{11} -1.79165 q^{12} +5.57248 q^{13} +2.84770 q^{14} -3.88651 q^{15} +1.00000 q^{16} +5.39515 q^{17} -0.210015 q^{18} +2.46652 q^{19} +2.16923 q^{20} +5.10208 q^{21} -3.81889 q^{22} -9.16709 q^{23} +1.79165 q^{24} -0.294432 q^{25} -5.57248 q^{26} +4.99868 q^{27} -2.84770 q^{28} -4.42873 q^{29} +3.88651 q^{30} -9.81343 q^{31} -1.00000 q^{32} -6.84211 q^{33} -5.39515 q^{34} -6.17732 q^{35} +0.210015 q^{36} +2.19607 q^{37} -2.46652 q^{38} -9.98394 q^{39} -2.16923 q^{40} -4.33373 q^{41} -5.10208 q^{42} -8.39449 q^{43} +3.81889 q^{44} +0.455571 q^{45} +9.16709 q^{46} -8.90181 q^{47} -1.79165 q^{48} +1.10939 q^{49} +0.294432 q^{50} -9.66622 q^{51} +5.57248 q^{52} +3.54348 q^{53} -4.99868 q^{54} +8.28405 q^{55} +2.84770 q^{56} -4.41914 q^{57} +4.42873 q^{58} +1.12273 q^{59} -3.88651 q^{60} -0.154089 q^{61} +9.81343 q^{62} -0.598060 q^{63} +1.00000 q^{64} +12.0880 q^{65} +6.84211 q^{66} -7.77129 q^{67} +5.39515 q^{68} +16.4242 q^{69} +6.17732 q^{70} +15.8435 q^{71} -0.210015 q^{72} +2.65909 q^{73} -2.19607 q^{74} +0.527520 q^{75} +2.46652 q^{76} -10.8750 q^{77} +9.98394 q^{78} +0.173390 q^{79} +2.16923 q^{80} -9.58594 q^{81} +4.33373 q^{82} -4.42655 q^{83} +5.10208 q^{84} +11.7033 q^{85} +8.39449 q^{86} +7.93475 q^{87} -3.81889 q^{88} +7.42117 q^{89} -0.455571 q^{90} -15.8687 q^{91} -9.16709 q^{92} +17.5823 q^{93} +8.90181 q^{94} +5.35045 q^{95} +1.79165 q^{96} +0.827458 q^{97} -1.10939 q^{98} +0.802024 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.79165	−1.03441	−0.517205	−	0.855861i	$-0.673028\pi$
$3$	−1.79165	−1.03441	−0.517205	+	0.855861i	$0.673028\pi$
$4$	1.00000	0.500000
$5$	2.16923	0.970110	0.485055	−	0.874484i	$-0.338800\pi$
$5$	2.16923	0.970110	0.485055	+	0.874484i	$0.338800\pi$
$6$	1.79165	0.731439
$7$	−2.84770	−1.07633	−0.538164	−	0.842840i	$-0.680882\pi$
$7$	−2.84770	−1.07633	−0.538164	+	0.842840i	$0.680882\pi$
$8$	−1.00000	−0.353553
$9$	0.210015	0.0700050
$10$	−2.16923	−0.685971
$11$	3.81889	1.15144	0.575719	−	0.817648i	$-0.304722\pi$
$11$	3.81889	1.15144	0.575719	+	0.817648i	$0.304722\pi$
$12$	−1.79165	−0.517205
$13$	5.57248	1.54553	0.772764	−	0.634694i	$-0.218874\pi$
$13$	5.57248	1.54553	0.772764	+	0.634694i	$0.218874\pi$
$14$	2.84770	0.761079
$15$	−3.88651	−1.00349
$16$	1.00000	0.250000
$17$	5.39515	1.30852	0.654258	−	0.756272i	$-0.272981\pi$
$17$	5.39515	1.30852	0.654258	+	0.756272i	$0.272981\pi$
$18$	−0.210015	−0.0495010
$19$	2.46652	0.565858	0.282929	−	0.959141i	$-0.408694\pi$
$19$	2.46652	0.565858	0.282929	+	0.959141i	$0.408694\pi$
$20$	2.16923	0.485055
$21$	5.10208	1.11337
$22$	−3.81889	−0.814189
$23$	−9.16709	−1.91147	−0.955735	−	0.294227i	$-0.904938\pi$
$23$	−9.16709	−1.91147	−0.955735	+	0.294227i	$0.904938\pi$
$24$	1.79165	0.365719
$25$	−0.294432	−0.0588864
$26$	−5.57248	−1.09285
$27$	4.99868	0.961997
$28$	−2.84770	−0.538164
$29$	−4.42873	−0.822395	−0.411198	−	0.911546i	$-0.634889\pi$
$29$	−4.42873	−0.822395	−0.411198	+	0.911546i	$0.634889\pi$
$30$	3.88651	0.709576
$31$	−9.81343	−1.76254	−0.881272	−	0.472609i	$-0.843312\pi$
$31$	−9.81343	−1.76254	−0.881272	+	0.472609i	$0.843312\pi$
$32$	−1.00000	−0.176777
$33$	−6.84211	−1.19106
$34$	−5.39515	−0.925260
$35$	−6.17732	−1.04416
$36$	0.210015	0.0350025
$37$	2.19607	0.361032	0.180516	−	0.983572i	$-0.442223\pi$
$37$	2.19607	0.361032	0.180516	+	0.983572i	$0.442223\pi$
$38$	−2.46652	−0.400122
$39$	−9.98394	−1.59871
$40$	−2.16923	−0.342986
$41$	−4.33373	−0.676816	−0.338408	−	0.941000i	$-0.609888\pi$
$41$	−4.33373	−0.676816	−0.338408	+	0.941000i	$0.609888\pi$
$42$	−5.10208	−0.787269
$43$	−8.39449	−1.28015	−0.640074	−	0.768314i	$-0.721096\pi$
$43$	−8.39449	−1.28015	−0.640074	+	0.768314i	$0.721096\pi$
$44$	3.81889	0.575719
$45$	0.455571	0.0679126
$46$	9.16709	1.35161
$47$	−8.90181	−1.29846	−0.649231	−	0.760591i	$-0.724909\pi$
$47$	−8.90181	−1.29846	−0.649231	+	0.760591i	$0.724909\pi$
$48$	−1.79165	−0.258603
$49$	1.10939	0.158484
$50$	0.294432	0.0416390
$51$	−9.66622	−1.35354
$52$	5.57248	0.772764
$53$	3.54348	0.486735	0.243367	−	0.969934i	$-0.421748\pi$
$53$	3.54348	0.486735	0.243367	+	0.969934i	$0.421748\pi$
$54$	−4.99868	−0.680234
$55$	8.28405	1.11702
$56$	2.84770	0.380540
$57$	−4.41914	−0.585329
$58$	4.42873	0.581521
$59$	1.12273	0.146168	0.0730838	−	0.997326i	$-0.476716\pi$
$59$	1.12273	0.146168	0.0730838	+	0.997326i	$0.476716\pi$
$60$	−3.88651	−0.501746
$61$	−0.154089	−0.0197291	−0.00986454	−	0.999951i	$-0.503140\pi$
$61$	−0.154089	−0.0197291	−0.00986454	+	0.999951i	$0.503140\pi$
$62$	9.81343	1.24631
$63$	−0.598060	−0.0753484
$64$	1.00000	0.125000
$65$	12.0880	1.49933
$66$	6.84211	0.842206
$67$	−7.77129	−0.949414	−0.474707	−	0.880144i	$-0.657446\pi$
$67$	−7.77129	−0.949414	−0.474707	+	0.880144i	$0.657446\pi$
$68$	5.39515	0.654258
$69$	16.4242	1.97725
$70$	6.17732	0.738331
$71$	15.8435	1.88027	0.940137	−	0.340797i	$-0.110697\pi$
$71$	15.8435	1.88027	0.940137	+	0.340797i	$0.110697\pi$
$72$	−0.210015	−0.0247505
$73$	2.65909	0.311223	0.155612	−	0.987818i	$-0.450265\pi$
$73$	2.65909	0.311223	0.155612	+	0.987818i	$0.450265\pi$
$74$	−2.19607	−0.255289
$75$	0.527520	0.0609127
$76$	2.46652	0.282929
$77$	−10.8750	−1.23933
$78$	9.98394	1.13046
$79$	0.173390	0.0195079	0.00975395	−	0.999952i	$-0.496895\pi$
$79$	0.173390	0.0195079	0.00975395	+	0.999952i	$0.496895\pi$
$80$	2.16923	0.242528
$81$	−9.58594	−1.06510
$82$	4.33373	0.478581
$83$	−4.42655	−0.485877	−0.242939	−	0.970042i	$-0.578111\pi$
$83$	−4.42655	−0.485877	−0.242939	+	0.970042i	$0.578111\pi$
$84$	5.10208	0.556683
$85$	11.7033	1.26940
$86$	8.39449	0.905201
$87$	7.93475	0.850694
$88$	−3.81889	−0.407095
$89$	7.42117	0.786643	0.393321	−	0.919401i	$-0.371326\pi$
$89$	7.42117	0.786643	0.393321	+	0.919401i	$0.371326\pi$
$90$	−0.455571	−0.0480214
$91$	−15.8687	−1.66350
$92$	−9.16709	−0.955735
$93$	17.5823	1.82319
$94$	8.90181	0.918151
$95$	5.35045	0.548944
$96$	1.79165	0.182860
$97$	0.827458	0.0840157	0.0420078	−	0.999117i	$-0.486625\pi$
$97$	0.827458	0.0840157	0.0420078	+	0.999117i	$0.486625\pi$
$98$	−1.10939	−0.112065
$99$	0.802024	0.0806064
$100$	−0.294432	−0.0294432
$101$	9.44506	0.939819	0.469910	−	0.882715i	$-0.344287\pi$
$101$	9.44506	0.939819	0.469910	+	0.882715i	$0.344287\pi$
$102$	9.66622	0.957099
$103$	9.92896	0.978330	0.489165	−	0.872191i	$-0.337302\pi$
$103$	9.92896	0.978330	0.489165	+	0.872191i	$0.337302\pi$
$104$	−5.57248	−0.546426
$105$	11.0676	1.08009
$106$	−3.54348	−0.344174
$107$	−7.63837	−0.738430	−0.369215	−	0.929344i	$-0.620373\pi$
$107$	−7.63837	−0.738430	−0.369215	+	0.929344i	$0.620373\pi$
$108$	4.99868	0.480998
$109$	10.7274	1.02749	0.513747	−	0.857942i	$-0.328257\pi$
$109$	10.7274	1.02749	0.513747	+	0.857942i	$0.328257\pi$
$110$	−8.28405	−0.789853
$111$	−3.93460	−0.373456
$112$	−2.84770	−0.269082
$113$	−18.5341	−1.74354	−0.871772	−	0.489912i	$-0.837029\pi$
$113$	−18.5341	−1.74354	−0.871772	+	0.489912i	$0.837029\pi$
$114$	4.41914	0.413890
$115$	−19.8856	−1.85434
$116$	−4.42873	−0.411198
$117$	1.17030	0.108195
$118$	−1.12273	−0.103356
$119$	−15.3637	−1.40839
$120$	3.88651	0.354788
$121$	3.58389	0.325809
$122$	0.154089	0.0139506
$123$	7.76454	0.700105
$124$	−9.81343	−0.881272
$125$	−11.4849	−1.02724
$126$	0.598060	0.0532794
$127$	5.24842	0.465722	0.232861	−	0.972510i	$-0.425191\pi$
$127$	5.24842	0.465722	0.232861	+	0.972510i	$0.425191\pi$
$128$	−1.00000	−0.0883883
$129$	15.0400	1.32420
$130$	−12.0880	−1.06019
$131$	−4.15917	−0.363388	−0.181694	−	0.983355i	$-0.558158\pi$
$131$	−4.15917	−0.363388	−0.181694	+	0.983355i	$0.558158\pi$
$132$	−6.84211	−0.595530
$133$	−7.02390	−0.609049
$134$	7.77129	0.671337
$135$	10.8433	0.933243
$136$	−5.39515	−0.462630
$137$	−9.65904	−0.825228	−0.412614	−	0.910906i	$-0.635384\pi$
$137$	−9.65904	−0.825228	−0.412614	+	0.910906i	$0.635384\pi$
$138$	−16.4242	−1.39812
$139$	−6.10300	−0.517650	−0.258825	−	0.965924i	$-0.583335\pi$
$139$	−6.10300	−0.517650	−0.258825	+	0.965924i	$0.583335\pi$
$140$	−6.17732	−0.522079
$141$	15.9489	1.34314
$142$	−15.8435	−1.32955
$143$	21.2807	1.77958
$144$	0.210015	0.0175013
$145$	−9.60695	−0.797814
$146$	−2.65909	−0.220068
$147$	−1.98763	−0.163937
$148$	2.19607	0.180516
$149$	1.37606	0.112731	0.0563656	−	0.998410i	$-0.482049\pi$
$149$	1.37606	0.112731	0.0563656	+	0.998410i	$0.482049\pi$
$150$	−0.527520	−0.0430718
$151$	12.3337	1.00370	0.501850	−	0.864955i	$-0.332653\pi$
$151$	12.3337	1.00370	0.501850	+	0.864955i	$0.332653\pi$
$152$	−2.46652	−0.200061
$153$	1.13306	0.0916026
$154$	10.8750	0.876336
$155$	−21.2876	−1.70986
$156$	−9.98394	−0.799355
$157$	−3.56787	−0.284747	−0.142374	−	0.989813i	$-0.545473\pi$
$157$	−3.56787	−0.284747	−0.142374	+	0.989813i	$0.545473\pi$
$158$	−0.173390	−0.0137942
$159$	−6.34869	−0.503484
$160$	−2.16923	−0.171493
$161$	26.1051	2.05737
$162$	9.58594	0.753142
$163$	5.82534	0.456276	0.228138	−	0.973629i	$-0.426736\pi$
$163$	5.82534	0.456276	0.228138	+	0.973629i	$0.426736\pi$
$164$	−4.33373	−0.338408
$165$	−14.8421	−1.15546
$166$	4.42655	0.343567
$167$	−11.4852	−0.888750	−0.444375	−	0.895841i	$-0.646574\pi$
$167$	−11.4852	−0.888750	−0.444375	+	0.895841i	$0.646574\pi$
$168$	−5.10208	−0.393634
$169$	18.0525	1.38865
$170$	−11.7033	−0.897604
$171$	0.518006	0.0396129
$172$	−8.39449	−0.640074
$173$	−11.0524	−0.840300	−0.420150	−	0.907455i	$-0.638023\pi$
$173$	−11.0524	−0.840300	−0.420150	+	0.907455i	$0.638023\pi$
$174$	−7.93475	−0.601532
$175$	0.838454	0.0633811
$176$	3.81889	0.287859
$177$	−2.01155	−0.151197
$178$	−7.42117	−0.556240
$179$	−12.3857	−0.925753	−0.462877	−	0.886423i	$-0.653183\pi$
$179$	−12.3857	−0.925753	−0.462877	+	0.886423i	$0.653183\pi$
$180$	0.455571	0.0339563
$181$	−13.5542	−1.00748	−0.503738	−	0.863856i	$-0.668042\pi$
$181$	−13.5542	−1.00748	−0.503738	+	0.863856i	$0.668042\pi$
$182$	15.8687	1.17627
$183$	0.276074	0.0204080
$184$	9.16709	0.675807
$185$	4.76380	0.350241
$186$	−17.5823	−1.28919
$187$	20.6035	1.50667
$188$	−8.90181	−0.649231
$189$	−14.2347	−1.03542
$190$	−5.35045	−0.388162
$191$	7.53776	0.545413	0.272706	−	0.962097i	$-0.412081\pi$
$191$	7.53776	0.545413	0.272706	+	0.962097i	$0.412081\pi$
$192$	−1.79165	−0.129301
$193$	−18.0199	−1.29710	−0.648552	−	0.761170i	$-0.724625\pi$
$193$	−18.0199	−1.29710	−0.648552	+	0.761170i	$0.724625\pi$
$194$	−0.827458	−0.0594081
$195$	−21.6575	−1.55092
$196$	1.10939	0.0792419
$197$	6.57054	0.468132	0.234066	−	0.972221i	$-0.424797\pi$
$197$	6.57054	0.468132	0.234066	+	0.972221i	$0.424797\pi$
$198$	−0.802024	−0.0569973
$199$	−2.61903	−0.185658	−0.0928291	−	0.995682i	$-0.529591\pi$
$199$	−2.61903	−0.185658	−0.0928291	+	0.995682i	$0.529591\pi$
$200$	0.294432	0.0208195
$201$	13.9234	0.982084
$202$	−9.44506	−0.664552
$203$	12.6117	0.885168
$204$	−9.66622	−0.676771
$205$	−9.40088	−0.656586
$206$	−9.92896	−0.691784
$207$	−1.92523	−0.133813
$208$	5.57248	0.386382
$209$	9.41935	0.651550
$210$	−11.0676	−0.763737
$211$	5.15449	0.354850	0.177425	−	0.984134i	$-0.443223\pi$
$211$	5.15449	0.354850	0.177425	+	0.984134i	$0.443223\pi$
$212$	3.54348	0.243367
$213$	−28.3860	−1.94498
$214$	7.63837	0.522149
$215$	−18.2096	−1.24188
$216$	−4.99868	−0.340117
$217$	27.9457	1.89708
$218$	−10.7274	−0.726548
$219$	−4.76417	−0.321933
$220$	8.28405	0.558511
$221$	30.0643	2.02235
$222$	3.93460	0.264073
$223$	−5.94759	−0.398280	−0.199140	−	0.979971i	$-0.563815\pi$
$223$	−5.94759	−0.398280	−0.199140	+	0.979971i	$0.563815\pi$
$224$	2.84770	0.190270
$225$	−0.0618352	−0.00412234
$226$	18.5341	1.23287
$227$	−1.06397	−0.0706183	−0.0353091	−	0.999376i	$-0.511242\pi$
$227$	−1.06397	−0.0706183	−0.0353091	+	0.999376i	$0.511242\pi$
$228$	−4.41914	−0.292665
$229$	21.7206	1.43534	0.717669	−	0.696384i	$-0.245209\pi$
$229$	21.7206	1.43534	0.717669	+	0.696384i	$0.245209\pi$
$230$	19.8856	1.31121
$231$	19.4843	1.28197
$232$	4.42873	0.290761
$233$	10.5852	0.693460	0.346730	−	0.937965i	$-0.387292\pi$
$233$	10.5852	0.693460	0.346730	+	0.937965i	$0.387292\pi$
$234$	−1.17030	−0.0765052
$235$	−19.3101	−1.25965
$236$	1.12273	0.0730838
$237$	−0.310654	−0.0201792
$238$	15.3637	0.995884
$239$	−0.525498	−0.0339916	−0.0169958	−	0.999856i	$-0.505410\pi$
$239$	−0.525498	−0.0339916	−0.0169958	+	0.999856i	$0.505410\pi$
$240$	−3.88651	−0.250873
$241$	−20.1884	−1.30045	−0.650226	−	0.759741i	$-0.725326\pi$
$241$	−20.1884	−1.30045	−0.650226	+	0.759741i	$0.725326\pi$
$242$	−3.58389	−0.230381
$243$	2.17862	0.139758
$244$	−0.154089	−0.00986454
$245$	2.40652	0.153747
$246$	−7.76454	−0.495049
$247$	13.7446	0.874549
$248$	9.81343	0.623154
$249$	7.93084	0.502596
$250$	11.4849	0.726366
$251$	−13.8325	−0.873102	−0.436551	−	0.899680i	$-0.643800\pi$
$251$	−13.8325	−0.873102	−0.436551	+	0.899680i	$0.643800\pi$
$252$	−0.598060	−0.0376742
$253$	−35.0081	−2.20094
$254$	−5.24842	−0.329315
$255$	−20.9683	−1.31308
$256$	1.00000	0.0625000
$257$	18.4697	1.15211	0.576054	−	0.817411i	$-0.304592\pi$
$257$	18.4697	1.15211	0.576054	+	0.817411i	$0.304592\pi$
$258$	−15.0400	−0.936349
$259$	−6.25376	−0.388590
$260$	12.0880	0.749666
$261$	−0.930101	−0.0575718
$262$	4.15917	0.256954
$263$	6.79250	0.418844	0.209422	−	0.977825i	$-0.432842\pi$
$263$	6.79250	0.418844	0.209422	+	0.977825i	$0.432842\pi$
$264$	6.84211	0.421103
$265$	7.68664	0.472187
$266$	7.02390	0.430663
$267$	−13.2962	−0.813712
$268$	−7.77129	−0.474707
$269$	−3.43856	−0.209653	−0.104826	−	0.994491i	$-0.533429\pi$
$269$	−3.43856	−0.209653	−0.104826	+	0.994491i	$0.533429\pi$
$270$	−10.8433	−0.659902
$271$	−28.1293	−1.70874	−0.854368	−	0.519668i	$-0.826055\pi$
$271$	−28.1293	−1.70874	−0.854368	+	0.519668i	$0.826055\pi$
$272$	5.39515	0.327129
$273$	28.4312	1.72074
$274$	9.65904	0.583524
$275$	−1.12440	−0.0678040
$276$	16.4242	0.988623
$277$	−7.81147	−0.469346	−0.234673	−	0.972074i	$-0.575402\pi$
$277$	−7.81147	−0.469346	−0.234673	+	0.972074i	$0.575402\pi$
$278$	6.10300	0.366034
$279$	−2.06097	−0.123387
$280$	6.17732	0.369165
$281$	−26.2051	−1.56327	−0.781633	−	0.623739i	$-0.785613\pi$
$281$	−26.2051	−1.56327	−0.781633	+	0.623739i	$0.785613\pi$
$282$	−15.9489	−0.949745
$283$	11.4045	0.677930	0.338965	−	0.940799i	$-0.389923\pi$
$283$	11.4045	0.677930	0.338965	+	0.940799i	$0.389923\pi$
$284$	15.8435	0.940137
$285$	−9.58614	−0.567834
$286$	−21.2807	−1.25835
$287$	12.3412	0.728476
$288$	−0.210015	−0.0123753
$289$	12.1076	0.712212
$290$	9.60695	0.564140
$291$	−1.48252	−0.0869067
$292$	2.65909	0.155612
$293$	−31.0663	−1.81491	−0.907457	−	0.420145i	$-0.861979\pi$
$293$	−31.0663	−1.81491	−0.907457	+	0.420145i	$0.861979\pi$
$294$	1.98763	0.115921
$295$	2.43547	0.141799
$296$	−2.19607	−0.127644
$297$	19.0894	1.10768
$298$	−1.37606	−0.0797131
$299$	−51.0834	−2.95423
$300$	0.527520	0.0304564
$301$	23.9050	1.37786
$302$	−12.3337	−0.709723
$303$	−16.9223	−0.972159
$304$	2.46652	0.141464
$305$	−0.334255	−0.0191394
$306$	−1.13306	−0.0647728
$307$	−0.501185	−0.0286042	−0.0143021	−	0.999898i	$-0.504553\pi$
$307$	−0.501185	−0.0286042	−0.0143021	+	0.999898i	$0.504553\pi$
$308$	−10.8750	−0.619663
$309$	−17.7892	−1.01199
$310$	21.2876	1.20906
$311$	7.07408	0.401135	0.200567	−	0.979680i	$-0.435721\pi$
$311$	7.07408	0.401135	0.200567	+	0.979680i	$0.435721\pi$
$312$	9.98394	0.565229
$313$	14.8946	0.841894	0.420947	−	0.907085i	$-0.361698\pi$
$313$	14.8946	0.841894	0.420947	+	0.907085i	$0.361698\pi$
$314$	3.56787	0.201347
$315$	−1.29733	−0.0730963
$316$	0.173390	0.00975395
$317$	24.8379	1.39504	0.697519	−	0.716567i	$-0.254287\pi$
$317$	24.8379	1.39504	0.697519	+	0.716567i	$0.254287\pi$
$318$	6.34869	0.356017
$319$	−16.9128	−0.946937
$320$	2.16923	0.121264
$321$	13.6853	0.763839
$322$	−26.1051	−1.45478
$323$	13.3072	0.740434
$324$	−9.58594	−0.532552
$325$	−1.64072	−0.0910106
$326$	−5.82534	−0.322636
$327$	−19.2197	−1.06285
$328$	4.33373	0.239290
$329$	25.3497	1.39757
$330$	14.8421	0.817033
$331$	−8.00498	−0.439994	−0.219997	−	0.975501i	$-0.570605\pi$
$331$	−8.00498	−0.439994	−0.219997	+	0.975501i	$0.570605\pi$
$332$	−4.42655	−0.242939
$333$	0.461209	0.0252741
$334$	11.4852	0.628441
$335$	−16.8577	−0.921036
$336$	5.10208	0.278341
$337$	1.01253	0.0551559	0.0275779	−	0.999620i	$-0.491221\pi$
$337$	1.01253	0.0551559	0.0275779	+	0.999620i	$0.491221\pi$
$338$	−18.0525	−0.981927
$339$	33.2067	1.80354
$340$	11.7033	0.634702
$341$	−37.4764	−2.02946
$342$	−0.518006	−0.0280105
$343$	16.7747	0.905748
$344$	8.39449	0.452600
$345$	35.6280	1.91815
$346$	11.0524	0.594182
$347$	−32.7922	−1.76038	−0.880189	−	0.474623i	$-0.842585\pi$
$347$	−32.7922	−1.76038	−0.880189	+	0.474623i	$0.842585\pi$
$348$	7.93475	0.425347
$349$	−32.7021	−1.75050	−0.875252	−	0.483666i	$-0.839305\pi$
$349$	−32.7021	−1.75050	−0.875252	+	0.483666i	$0.839305\pi$
$350$	−0.838454	−0.0448172
$351$	27.8550	1.48679
$352$	−3.81889	−0.203547
$353$	−19.9729	−1.06305	−0.531524	−	0.847043i	$-0.678381\pi$
$353$	−19.9729	−1.06305	−0.531524	+	0.847043i	$0.678381\pi$
$354$	2.01155	0.106913
$355$	34.3682	1.82407
$356$	7.42117	0.393321
$357$	27.5265	1.45686
$358$	12.3857	0.654607
$359$	−17.9296	−0.946286	−0.473143	−	0.880986i	$-0.656881\pi$
$359$	−17.9296	−0.946286	−0.473143	+	0.880986i	$0.656881\pi$
$360$	−0.455571	−0.0240107
$361$	−12.9163	−0.679805
$362$	13.5542	0.712393
$363$	−6.42109	−0.337020
$364$	−15.8687	−0.831748
$365$	5.76819	0.301921
$366$	−0.276074	−0.0144306
$367$	37.6450	1.96505	0.982526	−	0.186124i	$-0.0595927\pi$
$367$	37.6450	1.96505	0.982526	+	0.186124i	$0.0595927\pi$
$368$	−9.16709	−0.477868
$369$	−0.910149	−0.0473805
$370$	−4.76380	−0.247658
$371$	−10.0908	−0.523887
$372$	17.5823	0.911597
$373$	−36.4266	−1.88610	−0.943048	−	0.332657i	$-0.892055\pi$
$373$	−36.4266	−1.88610	−0.943048	+	0.332657i	$0.892055\pi$
$374$	−20.6035	−1.06538
$375$	20.5769	1.06258
$376$	8.90181	0.459076
$377$	−24.6790	−1.27103
$378$	14.2347	0.732156
$379$	21.7252	1.11595	0.557975	−	0.829858i	$-0.311578\pi$
$379$	21.7252	1.11595	0.557975	+	0.829858i	$0.311578\pi$
$380$	5.35045	0.274472
$381$	−9.40334	−0.481748
$382$	−7.53776	−0.385665
$383$	−9.37661	−0.479123	−0.239561	−	0.970881i	$-0.577004\pi$
$383$	−9.37661	−0.479123	−0.239561	+	0.970881i	$0.577004\pi$
$384$	1.79165	0.0914298
$385$	−23.5905	−1.20228
$386$	18.0199	0.917191
$387$	−1.76297	−0.0896167
$388$	0.827458	0.0420078
$389$	−4.03940	−0.204806	−0.102403	−	0.994743i	$-0.532653\pi$
$389$	−4.03940	−0.204806	−0.102403	+	0.994743i	$0.532653\pi$
$390$	21.6575	1.09667
$391$	−49.4578	−2.50119
$392$	−1.10939	−0.0560325
$393$	7.45178	0.375893
$394$	−6.57054	−0.331019
$395$	0.376123	0.0189248
$396$	0.802024	0.0403032
$397$	−4.09433	−0.205488	−0.102744	−	0.994708i	$-0.532762\pi$
$397$	−4.09433	−0.205488	−0.102744	+	0.994708i	$0.532762\pi$
$398$	2.61903	0.131280
$399$	12.5844	0.630007
$400$	−0.294432	−0.0147216
$401$	25.3062	1.26373	0.631866	−	0.775078i	$-0.282289\pi$
$401$	25.3062	1.26373	0.631866	+	0.775078i	$0.282289\pi$
$402$	−13.9234	−0.694438
$403$	−54.6851	−2.72406
$404$	9.44506	0.469910
$405$	−20.7941	−1.03327
$406$	−12.6117	−0.625908
$407$	8.38656	0.415706
$408$	9.66622	0.478549
$409$	25.7617	1.27383	0.636916	−	0.770933i	$-0.280210\pi$
$409$	25.7617	1.27383	0.636916	+	0.770933i	$0.280210\pi$
$410$	9.40088	0.464276
$411$	17.3056	0.853624
$412$	9.92896	0.489165
$413$	−3.19721	−0.157324
$414$	1.92523	0.0946198
$415$	−9.60222	−0.471354
$416$	−5.57248	−0.273213
$417$	10.9345	0.535463
$418$	−9.41935	−0.460715
$419$	17.9396	0.876409	0.438204	−	0.898875i	$-0.355615\pi$
$419$	17.9396	0.876409	0.438204	+	0.898875i	$0.355615\pi$
$420$	11.0676	0.540044
$421$	11.8868	0.579326	0.289663	−	0.957129i	$-0.406457\pi$
$421$	11.8868	0.579326	0.289663	+	0.957129i	$0.406457\pi$
$422$	−5.15449	−0.250917
$423$	−1.86951	−0.0908988
$424$	−3.54348	−0.172087
$425$	−1.58850	−0.0770538
$426$	28.3860	1.37531
$427$	0.438799	0.0212350
$428$	−7.63837	−0.369215
$429$	−38.1275	−1.84081
$430$	18.2096	0.878145
$431$	−15.0808	−0.726416	−0.363208	−	0.931708i	$-0.618318\pi$
$431$	−15.0808	−0.726416	−0.363208	+	0.931708i	$0.618318\pi$
$432$	4.99868	0.240499
$433$	−30.2619	−1.45430	−0.727148	−	0.686480i	$-0.759155\pi$
$433$	−30.2619	−1.45430	−0.727148	+	0.686480i	$0.759155\pi$
$434$	−27.9457	−1.34144
$435$	17.2123	0.825267
$436$	10.7274	0.513747
$437$	−22.6108	−1.08162
$438$	4.76417	0.227641
$439$	−0.303058	−0.0144642	−0.00723208	−	0.999974i	$-0.502302\pi$
$439$	−0.303058	−0.0144642	−0.00723208	+	0.999974i	$0.502302\pi$
$440$	−8.28405	−0.394927
$441$	0.232988	0.0110947
$442$	−30.0643	−1.43001
$443$	14.5369	0.690668	0.345334	−	0.938480i	$-0.387766\pi$
$443$	14.5369	0.690668	0.345334	+	0.938480i	$0.387766\pi$
$444$	−3.93460	−0.186728
$445$	16.0982	0.763130
$446$	5.94759	0.281627
$447$	−2.46542	−0.116610
$448$	−2.84770	−0.134541
$449$	20.6143	0.972847	0.486424	−	0.873723i	$-0.338301\pi$
$449$	20.6143	0.972847	0.486424	+	0.873723i	$0.338301\pi$
$450$	0.0618352	0.00291494
$451$	−16.5500	−0.779311
$452$	−18.5341	−0.871772
$453$	−22.0976	−1.03824
$454$	1.06397	0.0499347
$455$	−34.4230	−1.61377
$456$	4.41914	0.206945
$457$	10.9275	0.511167	0.255583	−	0.966787i	$-0.417732\pi$
$457$	10.9275	0.511167	0.255583	+	0.966787i	$0.417732\pi$
$458$	−21.7206	−1.01494
$459$	26.9686	1.25879
$460$	−19.8856	−0.927169
$461$	−5.36723	−0.249977	−0.124988	−	0.992158i	$-0.539889\pi$
$461$	−5.36723	−0.249977	−0.124988	+	0.992158i	$0.539889\pi$
$462$	−19.4843	−0.906491
$463$	−36.8748	−1.71372	−0.856859	−	0.515550i	$-0.827588\pi$
$463$	−36.8748	−1.71372	−0.856859	+	0.515550i	$0.827588\pi$
$464$	−4.42873	−0.205599
$465$	38.1400	1.76870
$466$	−10.5852	−0.490350
$467$	−20.3414	−0.941286	−0.470643	−	0.882324i	$-0.655978\pi$
$467$	−20.3414	−0.941286	−0.470643	+	0.882324i	$0.655978\pi$
$468$	1.17030	0.0540973
$469$	22.1303	1.02188
$470$	19.3101	0.890708
$471$	6.39238	0.294545
$472$	−1.12273	−0.0516780
$473$	−32.0576	−1.47401
$474$	0.310654	0.0142688
$475$	−0.726222	−0.0333213
$476$	−15.3637	−0.704196
$477$	0.744185	0.0340739
$478$	0.525498	0.0240357
$479$	−22.1272	−1.01102	−0.505510	−	0.862821i	$-0.668695\pi$
$479$	−22.1272	−1.01102	−0.505510	+	0.862821i	$0.668695\pi$
$480$	3.88651	0.177394
$481$	12.2376	0.557986
$482$	20.1884	0.919559
$483$	−46.7713	−2.12817
$484$	3.58389	0.162904
$485$	1.79495	0.0815045
$486$	−2.17862	−0.0988242
$487$	1.76191	0.0798399	0.0399200	−	0.999203i	$-0.487290\pi$
$487$	1.76191	0.0798399	0.0399200	+	0.999203i	$0.487290\pi$
$488$	0.154089	0.00697529
$489$	−10.4370	−0.471977
$490$	−2.40652	−0.108715
$491$	5.99699	0.270641	0.135320	−	0.990802i	$-0.456794\pi$
$491$	5.99699	0.270641	0.135320	+	0.990802i	$0.456794\pi$
$492$	7.76454	0.350053
$493$	−23.8937	−1.07612
$494$	−13.7446	−0.618399
$495$	1.73978	0.0781971
$496$	−9.81343	−0.440636
$497$	−45.1174	−2.02379
$498$	−7.93084	−0.355389
$499$	29.6874	1.32899	0.664495	−	0.747293i	$-0.268647\pi$
$499$	29.6874	1.32899	0.664495	+	0.747293i	$0.268647\pi$
$500$	−11.4849	−0.513618
$501$	20.5774	0.919332
$502$	13.8325	0.617376
$503$	−0.485939	−0.0216670	−0.0108335	−	0.999941i	$-0.503448\pi$
$503$	−0.485939	−0.0216670	−0.0108335	+	0.999941i	$0.503448\pi$
$504$	0.598060	0.0266397
$505$	20.4885	0.911728
$506$	35.0081	1.55630
$507$	−32.3438	−1.43644
$508$	5.24842	0.232861
$509$	16.2402	0.719835	0.359918	−	0.932984i	$-0.382805\pi$
$509$	16.2402	0.719835	0.359918	+	0.932984i	$0.382805\pi$
$510$	20.9683	0.928491
$511$	−7.57229	−0.334979
$512$	−1.00000	−0.0441942
$513$	12.3293	0.544353
$514$	−18.4697	−0.814664
$515$	21.5382	0.949087
$516$	15.0400	0.662099
$517$	−33.9950	−1.49510
$518$	6.25376	0.274774
$519$	19.8021	0.869215
$520$	−12.0880	−0.530094
$521$	37.9179	1.66121	0.830606	−	0.556861i	$-0.187994\pi$
$521$	37.9179	1.66121	0.830606	+	0.556861i	$0.187994\pi$
$522$	0.930101	0.0407094
$523$	−8.29887	−0.362884	−0.181442	−	0.983402i	$-0.558076\pi$
$523$	−8.29887	−0.362884	−0.181442	+	0.983402i	$0.558076\pi$
$524$	−4.15917	−0.181694
$525$	−1.50222	−0.0655621
$526$	−6.79250	−0.296167
$527$	−52.9449	−2.30632
$528$	−6.84211	−0.297765
$529$	61.0356	2.65372
$530$	−7.68664	−0.333886
$531$	0.235791	0.0102325
$532$	−7.02390	−0.304525
$533$	−24.1496	−1.04604
$534$	13.2962	0.575381
$535$	−16.5694	−0.716358
$536$	7.77129	0.335669
$537$	22.1909	0.957609
$538$	3.43856	0.148247
$539$	4.23662	0.182484
$540$	10.8433	0.466621
$541$	−24.9659	−1.07337	−0.536684	−	0.843784i	$-0.680323\pi$
$541$	−24.9659	−1.07337	−0.536684	+	0.843784i	$0.680323\pi$
$542$	28.1293	1.20826
$543$	24.2844	1.04214
$544$	−5.39515	−0.231315
$545$	23.2701	0.996783
$546$	−28.4312	−1.21674
$547$	2.25358	0.0963562	0.0481781	−	0.998839i	$-0.484658\pi$
$547$	2.25358	0.0963562	0.0481781	+	0.998839i	$0.484658\pi$
$548$	−9.65904	−0.412614
$549$	−0.0323610	−0.00138113
$550$	1.12440	0.0479447
$551$	−10.9235	−0.465359
$552$	−16.4242	−0.699062
$553$	−0.493762	−0.0209969
$554$	7.81147	0.331878
$555$	−8.53506	−0.362293
$556$	−6.10300	−0.258825
$557$	4.23861	0.179596	0.0897979	−	0.995960i	$-0.471378\pi$
$557$	4.23861	0.179596	0.0897979	+	0.995960i	$0.471378\pi$
$558$	2.06097	0.0872478
$559$	−46.7781	−1.97850
$560$	−6.17732	−0.261039
$561$	−36.9142	−1.55852
$562$	26.2051	1.10540
$563$	15.3419	0.646585	0.323293	−	0.946299i	$-0.395210\pi$
$563$	15.3419	0.646585	0.323293	+	0.946299i	$0.395210\pi$
$564$	15.9489	0.671571
$565$	−40.2048	−1.69143
$566$	−11.4045	−0.479369
$567$	27.2979	1.14640
$568$	−15.8435	−0.664777
$569$	2.28740	0.0958929	0.0479464	−	0.998850i	$-0.484732\pi$
$569$	2.28740	0.0958929	0.0479464	+	0.998850i	$0.484732\pi$
$570$	9.58614	0.401519
$571$	−29.6826	−1.24218	−0.621089	−	0.783740i	$-0.713310\pi$
$571$	−29.6826	−1.24218	−0.621089	+	0.783740i	$0.713310\pi$
$572$	21.2807	0.889789
$573$	−13.5050	−0.564181
$574$	−12.3412	−0.515110
$575$	2.69909	0.112560
$576$	0.210015	0.00875063
$577$	−34.5373	−1.43781	−0.718904	−	0.695110i	$-0.755356\pi$
$577$	−34.5373	−1.43781	−0.718904	+	0.695110i	$0.755356\pi$
$578$	−12.1076	−0.503610
$579$	32.2855	1.34174
$580$	−9.60695	−0.398907
$581$	12.6055	0.522964
$582$	1.48252	0.0614523
$583$	13.5322	0.560445
$584$	−2.65909	−0.110034
$585$	2.53866	0.104961
$586$	31.0663	1.28334
$587$	−27.6712	−1.14211	−0.571056	−	0.820911i	$-0.693466\pi$
$587$	−27.6712	−1.14211	−0.571056	+	0.820911i	$0.693466\pi$
$588$	−1.98763	−0.0819687
$589$	−24.2050	−0.997350
$590$	−2.43547	−0.100267
$591$	−11.7721	−0.484240
$592$	2.19607	0.0902581
$593$	33.4162	1.37224	0.686119	−	0.727490i	$-0.259313\pi$
$593$	33.4162	1.37224	0.686119	+	0.727490i	$0.259313\pi$
$594$	−19.0894	−0.783247
$595$	−33.3275	−1.36630
$596$	1.37606	0.0563656
$597$	4.69239	0.192047
$598$	51.0834	2.08896
$599$	1.21051	0.0494602	0.0247301	−	0.999694i	$-0.492127\pi$
$599$	1.21051	0.0494602	0.0247301	+	0.999694i	$0.492127\pi$
$600$	−0.527520	−0.0215359
$601$	−16.2103	−0.661234	−0.330617	−	0.943765i	$-0.607257\pi$
$601$	−16.2103	−0.661234	−0.330617	+	0.943765i	$0.607257\pi$
$602$	−23.9050	−0.974294
$603$	−1.63209	−0.0664638
$604$	12.3337	0.501850
$605$	7.77430	0.316070
$606$	16.9223	0.687420
$607$	−29.4401	−1.19494	−0.597469	−	0.801892i	$-0.703827\pi$
$607$	−29.4401	−1.19494	−0.597469	+	0.801892i	$0.703827\pi$
$608$	−2.46652	−0.100030
$609$	−22.5958	−0.915627
$610$	0.334255	0.0135336
$611$	−49.6051	−2.00681
$612$	1.13306	0.0458013
$613$	−25.2341	−1.01920	−0.509599	−	0.860412i	$-0.670206\pi$
$613$	−25.2341	−1.01920	−0.509599	+	0.860412i	$0.670206\pi$
$614$	0.501185	0.0202262
$615$	16.8431	0.679179
$616$	10.8750	0.438168
$617$	−33.5705	−1.35150	−0.675749	−	0.737132i	$-0.736180\pi$
$617$	−33.5705	−1.35150	−0.675749	+	0.737132i	$0.736180\pi$
$618$	17.7892	0.715588
$619$	−13.0341	−0.523886	−0.261943	−	0.965083i	$-0.584363\pi$
$619$	−13.0341	−0.523886	−0.261943	+	0.965083i	$0.584363\pi$
$620$	−21.2876	−0.854931
$621$	−45.8234	−1.83883
$622$	−7.07408	−0.283645
$623$	−21.1333	−0.846686
$624$	−9.98394	−0.399677
$625$	−23.4411	−0.937646
$626$	−14.8946	−0.595309
$627$	−16.8762	−0.673970
$628$	−3.56787	−0.142374
$629$	11.8481	0.472416
$630$	1.29733	0.0516869
$631$	31.4843	1.25337	0.626685	−	0.779273i	$-0.284411\pi$
$631$	31.4843	1.25337	0.626685	+	0.779273i	$0.284411\pi$
$632$	−0.173390	−0.00689708
$633$	−9.23505	−0.367060
$634$	−24.8379	−0.986440
$635$	11.3850	0.451802
$636$	−6.34869	−0.251742
$637$	6.18203	0.244941
$638$	16.9128	0.669585
$639$	3.32737	0.131629
$640$	−2.16923	−0.0857464
$641$	26.4620	1.04519	0.522594	−	0.852582i	$-0.324964\pi$
$641$	26.4620	1.04519	0.522594	+	0.852582i	$0.324964\pi$
$642$	−13.6853	−0.540116
$643$	−3.65330	−0.144072	−0.0720360	−	0.997402i	$-0.522950\pi$
$643$	−3.65330	−0.144072	−0.0720360	+	0.997402i	$0.522950\pi$
$644$	26.1051	1.02869
$645$	32.6252	1.28462
$646$	−13.3072	−0.523566
$647$	16.0888	0.632517	0.316258	−	0.948673i	$-0.397573\pi$
$647$	16.0888	0.632517	0.316258	+	0.948673i	$0.397573\pi$
$648$	9.58594	0.376571
$649$	4.28760	0.168303
$650$	1.64072	0.0643542
$651$	−50.0690	−1.96236
$652$	5.82534	0.228138
$653$	−2.21091	−0.0865195	−0.0432598	−	0.999064i	$-0.513774\pi$
$653$	−2.21091	−0.0865195	−0.0432598	+	0.999064i	$0.513774\pi$
$654$	19.2197	0.751549
$655$	−9.02221	−0.352527
$656$	−4.33373	−0.169204
$657$	0.558449	0.0217872
$658$	−25.3497	−0.988233
$659$	11.0068	0.428762	0.214381	−	0.976750i	$-0.431227\pi$
$659$	11.0068	0.428762	0.214381	+	0.976750i	$0.431227\pi$
$660$	−14.8421	−0.577729
$661$	−5.41528	−0.210630	−0.105315	−	0.994439i	$-0.533585\pi$
$661$	−5.41528	−0.210630	−0.105315	+	0.994439i	$0.533585\pi$
$662$	8.00498	0.311122
$663$	−53.8648	−2.09194
$664$	4.42655	0.171784
$665$	−15.2365	−0.590845
$666$	−0.461209	−0.0178715
$667$	40.5986	1.57198
$668$	−11.4852	−0.444375
$669$	10.6560	0.411985
$670$	16.8577	0.651271
$671$	−0.588449	−0.0227168
$672$	−5.10208	−0.196817
$673$	42.4686	1.63704	0.818521	−	0.574476i	$-0.194794\pi$
$673$	42.4686	1.63704	0.818521	+	0.574476i	$0.194794\pi$
$674$	−1.01253	−0.0390011
$675$	−1.47177	−0.0566485
$676$	18.0525	0.694327
$677$	−41.4946	−1.59477	−0.797383	−	0.603474i	$-0.793783\pi$
$677$	−41.4946	−1.59477	−0.797383	+	0.603474i	$0.793783\pi$
$678$	−33.2067	−1.27530
$679$	−2.35635	−0.0904285
$680$	−11.7033	−0.448802
$681$	1.90627	0.0730483
$682$	37.4764	1.43505
$683$	−24.3440	−0.931498	−0.465749	−	0.884917i	$-0.654215\pi$
$683$	−24.3440	−0.931498	−0.465749	+	0.884917i	$0.654215\pi$
$684$	0.518006	0.0198064
$685$	−20.9527	−0.800562
$686$	−16.7747	−0.640461
$687$	−38.9158	−1.48473
$688$	−8.39449	−0.320037
$689$	19.7460	0.752262
$690$	−35.6280	−1.35633
$691$	13.3070	0.506224	0.253112	−	0.967437i	$-0.418546\pi$
$691$	13.3070	0.506224	0.253112	+	0.967437i	$0.418546\pi$
$692$	−11.0524	−0.420150
$693$	−2.28392	−0.0867590
$694$	32.7922	1.24478
$695$	−13.2388	−0.502178
$696$	−7.93475	−0.300766
$697$	−23.3811	−0.885624
$698$	32.7021	1.23779
$699$	−18.9650	−0.717322
$700$	0.838454	0.0316906
$701$	31.0467	1.17262	0.586310	−	0.810087i	$-0.300580\pi$
$701$	31.0467	1.17262	0.586310	+	0.810087i	$0.300580\pi$
$702$	−27.8550	−1.05132
$703$	5.41666	0.204293
$704$	3.81889	0.143930
$705$	34.5969	1.30300
$706$	19.9729	0.751689
$707$	−26.8967	−1.01155
$708$	−2.01155	−0.0755986
$709$	−50.2775	−1.88821	−0.944106	−	0.329642i	$-0.893072\pi$
$709$	−50.2775	−1.88821	−0.944106	+	0.329642i	$0.893072\pi$
$710$	−34.3682	−1.28981
$711$	0.0364145	0.00136565
$712$	−7.42117	−0.278120
$713$	89.9607	3.36905
$714$	−27.5265	−1.03015
$715$	46.1627	1.72639
$716$	−12.3857	−0.462877
$717$	0.941509	0.0351613
$718$	17.9296	0.669125
$719$	11.7291	0.437423	0.218711	−	0.975790i	$-0.429815\pi$
$719$	11.7291	0.437423	0.218711	+	0.975790i	$0.429815\pi$
$720$	0.455571	0.0169781
$721$	−28.2747	−1.05300
$722$	12.9163	0.480695
$723$	36.1707	1.34520
$724$	−13.5542	−0.503738
$725$	1.30396	0.0484279
$726$	6.42109	0.238309
$727$	−36.3348	−1.34758	−0.673792	−	0.738921i	$-0.735336\pi$
$727$	−36.3348	−1.34758	−0.673792	+	0.738921i	$0.735336\pi$
$728$	15.8687	0.588134
$729$	24.8545	0.920537
$730$	−5.76819	−0.213490
$731$	−45.2895	−1.67509
$732$	0.276074	0.0102040
$733$	16.9271	0.625218	0.312609	−	0.949882i	$-0.398797\pi$
$733$	16.9271	0.625218	0.312609	+	0.949882i	$0.398797\pi$
$734$	−37.6450	−1.38950
$735$	−4.31164	−0.159037
$736$	9.16709	0.337904
$737$	−29.6777	−1.09319
$738$	0.910149	0.0335031
$739$	10.6541	0.391917	0.195958	−	0.980612i	$-0.437218\pi$
$739$	10.6541	0.391917	0.195958	+	0.980612i	$0.437218\pi$
$740$	4.76380	0.175121
$741$	−24.6256	−0.904642
$742$	10.0908	0.370444
$743$	41.0417	1.50567	0.752837	−	0.658207i	$-0.228685\pi$
$743$	41.0417	1.50567	0.752837	+	0.658207i	$0.228685\pi$
$744$	−17.5823	−0.644597
$745$	2.98500	0.109362
$746$	36.4266	1.33367
$747$	−0.929643	−0.0340138
$748$	20.6035	0.753337
$749$	21.7518	0.794793
$750$	−20.5769	−0.751360
$751$	−8.32826	−0.303903	−0.151951	−	0.988388i	$-0.548556\pi$
$751$	−8.32826	−0.303903	−0.151951	+	0.988388i	$0.548556\pi$
$752$	−8.90181	−0.324615
$753$	24.7831	0.903146
$754$	24.6790	0.898757
$755$	26.7546	0.973699
$756$	−14.2347	−0.517712
$757$	−38.4650	−1.39804	−0.699018	−	0.715104i	$-0.746379\pi$
$757$	−38.4650	−1.39804	−0.699018	+	0.715104i	$0.746379\pi$
$758$	−21.7252	−0.789096
$759$	62.7223	2.27667
$760$	−5.35045	−0.194081
$761$	47.8740	1.73543	0.867715	−	0.497062i	$-0.165588\pi$
$761$	47.8740	1.73543	0.867715	+	0.497062i	$0.165588\pi$
$762$	9.40334	0.340647
$763$	−30.5483	−1.10592
$764$	7.53776	0.272706
$765$	2.45787	0.0888646
$766$	9.37661	0.338791
$767$	6.25641	0.225906
$768$	−1.79165	−0.0646507
$769$	−54.6576	−1.97100	−0.985502	−	0.169661i	$-0.945733\pi$
$769$	−54.6576	−1.97100	−0.985502	+	0.169661i	$0.945733\pi$
$770$	23.5905	0.850142
$771$	−33.0913	−1.19175
$772$	−18.0199	−0.648552
$773$	18.3772	0.660984	0.330492	−	0.943809i	$-0.392785\pi$
$773$	18.3772	0.660984	0.330492	+	0.943809i	$0.392785\pi$
$774$	1.76297	0.0633686
$775$	2.88939	0.103790
$776$	−0.827458	−0.0297040
$777$	11.2046	0.401961
$778$	4.03940	0.144819
$779$	−10.6892	−0.382981
$780$	−21.6575	−0.775462
$781$	60.5044	2.16502
$782$	49.4578	1.76861
$783$	−22.1378	−0.791141
$784$	1.10939	0.0396210
$785$	−7.73954	−0.276236
$786$	−7.45178	−0.265796
$787$	−27.2138	−0.970067	−0.485034	−	0.874496i	$-0.661193\pi$
$787$	−27.2138	−0.970067	−0.485034	+	0.874496i	$0.661193\pi$
$788$	6.57054	0.234066
$789$	−12.1698	−0.433256
$790$	−0.376123	−0.0133819
$791$	52.7796	1.87663
$792$	−0.802024	−0.0284987
$793$	−0.858658	−0.0304918
$794$	4.09433	0.145302
$795$	−13.7718	−0.488435
$796$	−2.61903	−0.0928291
$797$	26.5411	0.940132	0.470066	−	0.882631i	$-0.344230\pi$
$797$	26.5411	0.940132	0.470066	+	0.882631i	$0.344230\pi$
$798$	−12.5844	−0.445482
$799$	−48.0265	−1.69906
$800$	0.294432	0.0104097
$801$	1.55856	0.0550689
$802$	−25.3062	−0.893593
$803$	10.1548	0.358354
$804$	13.9234	0.491042
$805$	56.6281	1.99588
$806$	54.6851	1.92620
$807$	6.16070	0.216867
$808$	−9.44506	−0.332276
$809$	9.44806	0.332176	0.166088	−	0.986111i	$-0.446886\pi$
$809$	9.44806	0.332176	0.166088	+	0.986111i	$0.446886\pi$
$810$	20.7941	0.730631
$811$	19.7889	0.694883	0.347441	−	0.937702i	$-0.387051\pi$
$811$	19.7889	0.694883	0.347441	+	0.937702i	$0.387051\pi$
$812$	12.6117	0.442584
$813$	50.3980	1.76753
$814$	−8.38656	−0.293949
$815$	12.6365	0.442638
$816$	−9.66622	−0.338385
$817$	−20.7052	−0.724382
$818$	−25.7617	−0.900736
$819$	−3.33267	−0.116453
$820$	−9.40088	−0.328293
$821$	−25.4393	−0.887839	−0.443920	−	0.896067i	$-0.646412\pi$
$821$	−25.4393	−0.887839	−0.443920	+	0.896067i	$0.646412\pi$
$822$	−17.3056	−0.603603
$823$	−47.2853	−1.64826	−0.824131	−	0.566399i	$-0.808336\pi$
$823$	−47.2853	−1.64826	−0.824131	+	0.566399i	$0.808336\pi$
$824$	−9.92896	−0.345892
$825$	2.01454	0.0701372
$826$	3.19721	0.111245
$827$	43.3408	1.50711	0.753554	−	0.657386i	$-0.228338\pi$
$827$	43.3408	1.50711	0.753554	+	0.657386i	$0.228338\pi$
$828$	−1.92523	−0.0669063
$829$	24.2344	0.841695	0.420847	−	0.907131i	$-0.361733\pi$
$829$	24.2344	0.841695	0.420847	+	0.907131i	$0.361733\pi$
$830$	9.60222	0.333298
$831$	13.9954	0.485496
$832$	5.57248	0.193191
$833$	5.98530	0.207378
$834$	−10.9345	−0.378629
$835$	−24.9140	−0.862186
$836$	9.41935	0.325775
$837$	−49.0542	−1.69556
$838$	−17.9396	−0.619714
$839$	33.8392	1.16826	0.584129	−	0.811661i	$-0.301436\pi$
$839$	33.8392	1.16826	0.584129	+	0.811661i	$0.301436\pi$
$840$	−11.0676	−0.381869
$841$	−9.38631	−0.323666
$842$	−11.8868	−0.409645
$843$	46.9504	1.61706
$844$	5.15449	0.177425
$845$	39.1601	1.34715
$846$	1.86951	0.0642752
$847$	−10.2059	−0.350677
$848$	3.54348	0.121684
$849$	−20.4330	−0.701258
$850$	1.58850	0.0544852
$851$	−20.1316	−0.690103
$852$	−28.3860	−0.972488
$853$	−37.8044	−1.29440	−0.647199	−	0.762321i	$-0.724060\pi$
$853$	−37.8044	−1.29440	−0.647199	+	0.762321i	$0.724060\pi$
$854$	−0.438799	−0.0150154
$855$	1.12367	0.0384289
$856$	7.63837	0.261074
$857$	−34.9497	−1.19386	−0.596929	−	0.802294i	$-0.703613\pi$
$857$	−34.9497	−1.19386	−0.596929	+	0.802294i	$0.703613\pi$
$858$	38.1275	1.30165
$859$	−54.1194	−1.84653	−0.923266	−	0.384162i	$-0.874490\pi$
$859$	−54.1194	−1.84653	−0.923266	+	0.384162i	$0.874490\pi$
$860$	−18.2096	−0.620942
$861$	−22.1111	−0.753543
$862$	15.0808	0.513653
$863$	−11.2433	−0.382728	−0.191364	−	0.981519i	$-0.561291\pi$
$863$	−11.2433	−0.382728	−0.191364	+	0.981519i	$0.561291\pi$
$864$	−4.99868	−0.170059
$865$	−23.9753	−0.815184
$866$	30.2619	1.02834
$867$	−21.6926	−0.736720
$868$	27.9457	0.948539
$869$	0.662157	0.0224621
$870$	−17.2123	−0.583552
$871$	−43.3054	−1.46735
$872$	−10.7274	−0.363274
$873$	0.173779	0.00588152
$874$	22.6108	0.764821
$875$	32.7054	1.10564
$876$	−4.76417	−0.160966
$877$	14.5964	0.492887	0.246443	−	0.969157i	$-0.420738\pi$
$877$	14.5964	0.492887	0.246443	+	0.969157i	$0.420738\pi$
$878$	0.303058	0.0102277
$879$	55.6600	1.87737
$880$	8.28405	0.279255
$881$	−41.8510	−1.40999	−0.704997	−	0.709210i	$-0.749052\pi$
$881$	−41.8510	−1.40999	−0.704997	+	0.709210i	$0.749052\pi$
$882$	−0.232988	−0.00784511
$883$	−25.8230	−0.869013	−0.434507	−	0.900669i	$-0.643077\pi$
$883$	−25.8230	−0.869013	−0.434507	+	0.900669i	$0.643077\pi$
$884$	30.0643	1.01117
$885$	−4.36352	−0.146678
$886$	−14.5369	−0.488376
$887$	−33.1216	−1.11212	−0.556058	−	0.831144i	$-0.687687\pi$
$887$	−33.1216	−1.11212	−0.556058	+	0.831144i	$0.687687\pi$
$888$	3.93460	0.132037
$889$	−14.9459	−0.501270
$890$	−16.0982	−0.539615
$891$	−36.6076	−1.22640
$892$	−5.94759	−0.199140
$893$	−21.9565	−0.734745
$894$	2.46542	0.0824560
$895$	−26.8675	−0.898083
$896$	2.84770	0.0951349
$897$	91.5237	3.05589
$898$	−20.6143	−0.687907
$899$	43.4611	1.44951
$900$	−0.0618352	−0.00206117
$901$	19.1176	0.636900
$902$	16.5500	0.551056
$903$	−42.8294	−1.42527
$904$	18.5341	0.616436
$905$	−29.4022	−0.977363
$906$	22.0976	0.734145
$907$	15.6957	0.521166	0.260583	−	0.965451i	$-0.416085\pi$
$907$	15.6957	0.521166	0.260583	+	0.965451i	$0.416085\pi$
$908$	−1.06397	−0.0353091
$909$	1.98361	0.0657920
$910$	34.4230	1.14111
$911$	47.3848	1.56993	0.784965	−	0.619541i	$-0.212681\pi$
$911$	47.3848	1.56993	0.784965	+	0.619541i	$0.212681\pi$
$912$	−4.41914	−0.146332
$913$	−16.9045	−0.559457
$914$	−10.9275	−0.361449
$915$	0.598868	0.0197980
$916$	21.7206	0.717669
$917$	11.8441	0.391125
$918$	−26.9686	−0.890097
$919$	51.0657	1.68450	0.842251	−	0.539086i	$-0.181230\pi$
$919$	51.0657	1.68450	0.842251	+	0.539086i	$0.181230\pi$
$920$	19.8856	0.655607
$921$	0.897949	0.0295884
$922$	5.36723	0.176760
$923$	88.2874	2.90601
$924$	19.4843	0.640986
$925$	−0.646595	−0.0212599
$926$	36.8748	1.21178
$927$	2.08523	0.0684880
$928$	4.42873	0.145380
$929$	4.71323	0.154636	0.0773180	−	0.997006i	$-0.475364\pi$
$929$	4.71323	0.154636	0.0773180	+	0.997006i	$0.475364\pi$
$930$	−38.1400	−1.25066
$931$	2.73632	0.0896793
$932$	10.5852	0.346730
$933$	−12.6743	−0.414938
$934$	20.3414	0.665590
$935$	44.6937	1.46164
$936$	−1.17030	−0.0382526
$937$	−8.42315	−0.275172	−0.137586	−	0.990490i	$-0.543934\pi$
$937$	−8.42315	−0.275172	−0.137586	+	0.990490i	$0.543934\pi$
$938$	−22.1303	−0.722580
$939$	−26.6860	−0.870864
$940$	−19.3101	−0.629825
$941$	−3.15666	−0.102904	−0.0514520	−	0.998675i	$-0.516385\pi$
$941$	−3.15666	−0.102904	−0.0514520	+	0.998675i	$0.516385\pi$
$942$	−6.39238	−0.208275
$943$	39.7277	1.29371
$944$	1.12273	0.0365419
$945$	−30.8784	−1.00448
$946$	32.0576	1.04228
$947$	−15.2889	−0.496822	−0.248411	−	0.968655i	$-0.579908\pi$
$947$	−15.2889	−0.496822	−0.248411	+	0.968655i	$0.579908\pi$
$948$	−0.310654	−0.0100896
$949$	14.8177	0.481004
$950$	0.726222	0.0235617
$951$	−44.5009	−1.44304
$952$	15.3637	0.497942
$953$	−22.2372	−0.720333	−0.360166	−	0.932888i	$-0.617280\pi$
$953$	−22.2372	−0.720333	−0.360166	+	0.932888i	$0.617280\pi$
$954$	−0.744185	−0.0240939
$955$	16.3511	0.529111
$956$	−0.525498	−0.0169958
$957$	30.3019	0.979521
$958$	22.1272	0.714899
$959$	27.5060	0.888216
$960$	−3.88651	−0.125437
$961$	65.3035	2.10656
$962$	−12.2376	−0.394555
$963$	−1.60417	−0.0516938
$964$	−20.1884	−0.650226
$965$	−39.0894	−1.25833
$966$	46.7713	1.50484
$967$	−5.78118	−0.185910	−0.0929551	−	0.995670i	$-0.529631\pi$
$967$	−5.78118	−0.185910	−0.0929551	+	0.995670i	$0.529631\pi$
$968$	−3.58389	−0.115191
$969$	−23.8419	−0.765912
$970$	−1.79495	−0.0576324
$971$	−16.8034	−0.539248	−0.269624	−	0.962966i	$-0.586899\pi$
$971$	−16.8034	−0.539248	−0.269624	+	0.962966i	$0.586899\pi$
$972$	2.17862	0.0698792
$973$	17.3795	0.557162
$974$	−1.76191	−0.0564553
$975$	2.93959	0.0941423
$976$	−0.154089	−0.00493227
$977$	−54.6752	−1.74921	−0.874607	−	0.484832i	$-0.838881\pi$
$977$	−54.6752	−1.74921	−0.874607	+	0.484832i	$0.838881\pi$
$978$	10.4370	0.333738
$979$	28.3406	0.905770
$980$	2.40652	0.0768734
$981$	2.25291	0.0719298
$982$	−5.99699	−0.191372
$983$	−50.4958	−1.61057	−0.805283	−	0.592891i	$-0.797987\pi$
$983$	−50.4958	−1.61057	−0.805283	+	0.592891i	$0.797987\pi$
$984$	−7.76454	−0.247525
$985$	14.2530	0.454139
$986$	23.8937	0.760929
$987$	−45.4178	−1.44566
$988$	13.7446	0.437274
$989$	76.9530	2.44696
$990$	−1.73978	−0.0552937
$991$	−48.7436	−1.54839	−0.774195	−	0.632947i	$-0.781845\pi$
$991$	−48.7436	−1.54839	−0.774195	+	0.632947i	$0.781845\pi$
$992$	9.81343	0.311577
$993$	14.3421	0.455134
$994$	45.1174	1.43104
$995$	−5.68128	−0.180109
$996$	7.93084	0.251298
$997$	16.7633	0.530898	0.265449	−	0.964125i	$-0.414480\pi$
$997$	16.7633	0.530898	0.265449	+	0.964125i	$0.414480\pi$
$998$	−29.6874	−0.939737
$999$	10.9775	0.347312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.17	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.17	✓	56	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.79165 q^{3} +1.00000 q^{4} +2.16923 q^{5} +1.79165 q^{6} -2.84770 q^{7} -1.00000 q^{8} +0.210015 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.79165 q^{3} +1.00000 q^{4} +2.16923 q^{5} +1.79165 q^{6} -2.84770 q^{7} -1.00000 q^{8} +0.210015 q^{9} -2.16923 q^{10} +3.81889 q^{11} -1.79165 q^{12} +5.57248 q^{13} +2.84770 q^{14} -3.88651 q^{15} +1.00000 q^{16} +5.39515 q^{17} -0.210015 q^{18} +2.46652 q^{19} +2.16923 q^{20} +5.10208 q^{21} -3.81889 q^{22} -9.16709 q^{23} +1.79165 q^{24} -0.294432 q^{25} -5.57248 q^{26} +4.99868 q^{27} -2.84770 q^{28} -4.42873 q^{29} +3.88651 q^{30} -9.81343 q^{31} -1.00000 q^{32} -6.84211 q^{33} -5.39515 q^{34} -6.17732 q^{35} +0.210015 q^{36} +2.19607 q^{37} -2.46652 q^{38} -9.98394 q^{39} -2.16923 q^{40} -4.33373 q^{41} -5.10208 q^{42} -8.39449 q^{43} +3.81889 q^{44} +0.455571 q^{45} +9.16709 q^{46} -8.90181 q^{47} -1.79165 q^{48} +1.10939 q^{49} +0.294432 q^{50} -9.66622 q^{51} +5.57248 q^{52} +3.54348 q^{53} -4.99868 q^{54} +8.28405 q^{55} +2.84770 q^{56} -4.41914 q^{57} +4.42873 q^{58} +1.12273 q^{59} -3.88651 q^{60} -0.154089 q^{61} +9.81343 q^{62} -0.598060 q^{63} +1.00000 q^{64} +12.0880 q^{65} +6.84211 q^{66} -7.77129 q^{67} +5.39515 q^{68} +16.4242 q^{69} +6.17732 q^{70} +15.8435 q^{71} -0.210015 q^{72} +2.65909 q^{73} -2.19607 q^{74} +0.527520 q^{75} +2.46652 q^{76} -10.8750 q^{77} +9.98394 q^{78} +0.173390 q^{79} +2.16923 q^{80} -9.58594 q^{81} +4.33373 q^{82} -4.42655 q^{83} +5.10208 q^{84} +11.7033 q^{85} +8.39449 q^{86} +7.93475 q^{87} -3.81889 q^{88} +7.42117 q^{89} -0.455571 q^{90} -15.8687 q^{91} -9.16709 q^{92} +17.5823 q^{93} +8.90181 q^{94} +5.35045 q^{95} +1.79165 q^{96} +0.827458 q^{97} -1.10939 q^{98} +0.802024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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