LMFDB - Embedded newform 6019.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70229 q^{2} -1.73872 q^{3} +5.30239 q^{4} -0.220244 q^{5} +4.69853 q^{6} -4.26508 q^{7} -8.92402 q^{8} +0.0231491 q^{9} +O(q^{10})$	\(q-2.70229 q^{2} -1.73872 q^{3} +5.30239 q^{4} -0.220244 q^{5} +4.69853 q^{6} -4.26508 q^{7} -8.92402 q^{8} +0.0231491 q^{9} +0.595165 q^{10} +6.38773 q^{11} -9.21937 q^{12} +1.00000 q^{13} +11.5255 q^{14} +0.382943 q^{15} +13.5106 q^{16} -7.01519 q^{17} -0.0625557 q^{18} -3.33710 q^{19} -1.16782 q^{20} +7.41577 q^{21} -17.2615 q^{22} -7.16271 q^{23} +15.5164 q^{24} -4.95149 q^{25} -2.70229 q^{26} +5.17591 q^{27} -22.6151 q^{28} +0.641369 q^{29} -1.03483 q^{30} +1.40113 q^{31} -18.6614 q^{32} -11.1065 q^{33} +18.9571 q^{34} +0.939359 q^{35} +0.122746 q^{36} +3.86864 q^{37} +9.01783 q^{38} -1.73872 q^{39} +1.96547 q^{40} -6.89736 q^{41} -20.0396 q^{42} -8.35399 q^{43} +33.8703 q^{44} -0.00509847 q^{45} +19.3557 q^{46} -7.49573 q^{47} -23.4911 q^{48} +11.1909 q^{49} +13.3804 q^{50} +12.1974 q^{51} +5.30239 q^{52} +12.4304 q^{53} -13.9868 q^{54} -1.40686 q^{55} +38.0616 q^{56} +5.80229 q^{57} -1.73317 q^{58} +9.47518 q^{59} +2.03052 q^{60} -11.9756 q^{61} -3.78628 q^{62} -0.0987328 q^{63} +23.4075 q^{64} -0.220244 q^{65} +30.0130 q^{66} -0.485136 q^{67} -37.1972 q^{68} +12.4539 q^{69} -2.53842 q^{70} -15.3824 q^{71} -0.206583 q^{72} -10.8691 q^{73} -10.4542 q^{74} +8.60926 q^{75} -17.6946 q^{76} -27.2442 q^{77} +4.69853 q^{78} +2.10856 q^{79} -2.97562 q^{80} -9.06891 q^{81} +18.6387 q^{82} +4.97430 q^{83} +39.3213 q^{84} +1.54506 q^{85} +22.5749 q^{86} -1.11516 q^{87} -57.0043 q^{88} -9.93432 q^{89} +0.0137776 q^{90} -4.26508 q^{91} -37.9795 q^{92} -2.43618 q^{93} +20.2557 q^{94} +0.734978 q^{95} +32.4470 q^{96} -4.85176 q^{97} -30.2410 q^{98} +0.147870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.70229	−1.91081	−0.955405	−	0.295299i	$-0.904581\pi$
$2$	−2.70229	−1.91081	−0.955405	+	0.295299i	$0.904581\pi$
$3$	−1.73872	−1.00385	−0.501925	−	0.864911i	$-0.667375\pi$
$3$	−1.73872	−1.00385	−0.501925	+	0.864911i	$0.667375\pi$
$4$	5.30239	2.65119
$5$	−0.220244	−0.0984963	−0.0492481	−	0.998787i	$-0.515683\pi$
$5$	−0.220244	−0.0984963	−0.0492481	+	0.998787i	$0.515683\pi$
$6$	4.69853	1.91817
$7$	−4.26508	−1.61205	−0.806024	−	0.591883i	$-0.798385\pi$
$7$	−4.26508	−1.61205	−0.806024	+	0.591883i	$0.798385\pi$
$8$	−8.92402	−3.15512
$9$	0.0231491	0.00771638
$10$	0.595165	0.188208
$11$	6.38773	1.92597	0.962987	−	0.269547i	$-0.0868741\pi$
$11$	6.38773	1.92597	0.962987	+	0.269547i	$0.0868741\pi$
$12$	−9.21937	−2.66140
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	11.5255	3.08032
$15$	0.382943	0.0988756
$16$	13.5106	3.37764
$17$	−7.01519	−1.70143	−0.850716	−	0.525625i	$-0.823831\pi$
$17$	−7.01519	−1.70143	−0.850716	+	0.525625i	$0.823831\pi$
$18$	−0.0625557	−0.0147445
$19$	−3.33710	−0.765584	−0.382792	−	0.923835i	$-0.625037\pi$
$19$	−3.33710	−0.765584	−0.382792	+	0.923835i	$0.625037\pi$
$20$	−1.16782	−0.261133
$21$	7.41577	1.61825
$22$	−17.2615	−3.68017
$23$	−7.16271	−1.49353	−0.746764	−	0.665089i	$-0.768393\pi$
$23$	−7.16271	−1.49353	−0.746764	+	0.665089i	$0.768393\pi$
$24$	15.5164	3.16727
$25$	−4.95149	−0.990298
$26$	−2.70229	−0.529963
$27$	5.17591	0.996105
$28$	−22.6151	−4.27385
$29$	0.641369	0.119099	0.0595496	−	0.998225i	$-0.481034\pi$
$29$	0.641369	0.119099	0.0595496	+	0.998225i	$0.481034\pi$
$30$	−1.03483	−0.188932
$31$	1.40113	0.251651	0.125826	−	0.992052i	$-0.459842\pi$
$31$	1.40113	0.251651	0.125826	+	0.992052i	$0.459842\pi$
$32$	−18.6614	−3.29891
$33$	−11.1065	−1.93339
$34$	18.9571	3.25111
$35$	0.939359	0.158781
$36$	0.122746	0.0204576
$37$	3.86864	0.636000	0.318000	−	0.948091i	$-0.396989\pi$
$37$	3.86864	0.636000	0.318000	+	0.948091i	$0.396989\pi$
$38$	9.01783	1.46289
$39$	−1.73872	−0.278418
$40$	1.96547	0.310768
$41$	−6.89736	−1.07719	−0.538593	−	0.842566i	$-0.681044\pi$
$41$	−6.89736	−1.07719	−0.538593	+	0.842566i	$0.681044\pi$
$42$	−20.0396	−3.09218
$43$	−8.35399	−1.27397	−0.636986	−	0.770875i	$-0.719819\pi$
$43$	−8.35399	−1.27397	−0.636986	+	0.770875i	$0.719819\pi$
$44$	33.8703	5.10613
$45$	−0.00509847	−0.000760035 0
$46$	19.3557	2.85385
$47$	−7.49573	−1.09336	−0.546682	−	0.837340i	$-0.684109\pi$
$47$	−7.49573	−1.09336	−0.546682	+	0.837340i	$0.684109\pi$
$48$	−23.4911	−3.39064
$49$	11.1909	1.59870
$50$	13.3804	1.89227
$51$	12.1974	1.70798
$52$	5.30239	0.735309
$53$	12.4304	1.70745	0.853725	−	0.520724i	$-0.174338\pi$
$53$	12.4304	1.70745	0.853725	+	0.520724i	$0.174338\pi$
$54$	−13.9868	−1.90337
$55$	−1.40686	−0.189701
$56$	38.0616	5.08620
$57$	5.80229	0.768532
$58$	−1.73317	−0.227576
$59$	9.47518	1.23356	0.616782	−	0.787134i	$-0.288436\pi$
$59$	9.47518	1.23356	0.616782	+	0.787134i	$0.288436\pi$
$60$	2.03052	0.262138
$61$	−11.9756	−1.53332	−0.766659	−	0.642055i	$-0.778082\pi$
$61$	−11.9756	−1.53332	−0.766659	+	0.642055i	$0.778082\pi$
$62$	−3.78628	−0.480857
$63$	−0.0987328	−0.0124392
$64$	23.4075	2.92594
$65$	−0.220244	−0.0273180
$66$	30.0130	3.69434
$67$	−0.485136	−0.0592687	−0.0296344	−	0.999561i	$-0.509434\pi$
$67$	−0.485136	−0.0592687	−0.0296344	+	0.999561i	$0.509434\pi$
$68$	−37.1972	−4.51083
$69$	12.4539	1.49928
$70$	−2.53842	−0.303400
$71$	−15.3824	−1.82555	−0.912776	−	0.408460i	$-0.866066\pi$
$71$	−15.3824	−1.82555	−0.912776	+	0.408460i	$0.866066\pi$
$72$	−0.206583	−0.0243461
$73$	−10.8691	−1.27213	−0.636064	−	0.771636i	$-0.719439\pi$
$73$	−10.8691	−1.27213	−0.636064	+	0.771636i	$0.719439\pi$
$74$	−10.4542	−1.21528
$75$	8.60926	0.994112
$76$	−17.6946	−2.02971
$77$	−27.2442	−3.10476
$78$	4.69853	0.532004
$79$	2.10856	0.237231	0.118616	−	0.992940i	$-0.462154\pi$
$79$	2.10856	0.237231	0.118616	+	0.992940i	$0.462154\pi$
$80$	−2.97562	−0.332685
$81$	−9.06891	−1.00766
$82$	18.6387	2.05830
$83$	4.97430	0.546000	0.273000	−	0.962014i	$-0.411984\pi$
$83$	4.97430	0.546000	0.273000	+	0.962014i	$0.411984\pi$
$84$	39.3213	4.29031
$85$	1.54506	0.167585
$86$	22.5749	2.43432
$87$	−1.11516	−0.119558
$88$	−57.0043	−6.07668
$89$	−9.93432	−1.05304	−0.526518	−	0.850164i	$-0.676503\pi$
$89$	−9.93432	−1.05304	−0.526518	+	0.850164i	$0.676503\pi$
$90$	0.0137776	0.00145228
$91$	−4.26508	−0.447101
$92$	−37.9795	−3.95963
$93$	−2.43618	−0.252620
$94$	20.2557	2.08921
$95$	0.734978	0.0754072
$96$	32.4470	3.31161
$97$	−4.85176	−0.492621	−0.246311	−	0.969191i	$-0.579218\pi$
$97$	−4.85176	−0.492621	−0.246311	+	0.969191i	$0.579218\pi$
$98$	−30.2410	−3.05480
$99$	0.147870	0.0148615
$100$	−26.2547	−2.62547
$101$	3.12889	0.311336	0.155668	−	0.987809i	$-0.450247\pi$
$101$	3.12889	0.311336	0.155668	+	0.987809i	$0.450247\pi$
$102$	−32.9611	−3.26363
$103$	10.2989	1.01478	0.507390	−	0.861716i	$-0.330610\pi$
$103$	10.2989	1.01478	0.507390	+	0.861716i	$0.330610\pi$
$104$	−8.92402	−0.875073
$105$	−1.63328	−0.159392
$106$	−33.5907	−3.26261
$107$	−5.36761	−0.518906	−0.259453	−	0.965756i	$-0.583542\pi$
$107$	−5.36761	−0.518906	−0.259453	+	0.965756i	$0.583542\pi$
$108$	27.4447	2.64087
$109$	−15.0849	−1.44487	−0.722435	−	0.691438i	$-0.756977\pi$
$109$	−15.0849	−1.44487	−0.722435	+	0.691438i	$0.756977\pi$
$110$	3.80176	0.362483
$111$	−6.72648	−0.638450
$112$	−57.6235	−5.44491
$113$	18.0890	1.70167	0.850833	−	0.525436i	$-0.176098\pi$
$113$	18.0890	1.70167	0.850833	+	0.525436i	$0.176098\pi$
$114$	−15.6795	−1.46852
$115$	1.57755	0.147107
$116$	3.40079	0.315755
$117$	0.0231491	0.00214014
$118$	−25.6047	−2.35711
$119$	29.9203	2.74279
$120$	−3.41740	−0.311964
$121$	29.8031	2.70938
$122$	32.3616	2.92988
$123$	11.9926	1.08133
$124$	7.42936	0.667176
$125$	2.19176	0.196037
$126$	0.266805	0.0237689
$127$	3.15249	0.279738	0.139869	−	0.990170i	$-0.455332\pi$
$127$	3.15249	0.279738	0.139869	+	0.990170i	$0.455332\pi$
$128$	−25.9312	−2.29202
$129$	14.5253	1.27888
$130$	0.595165	0.0521994
$131$	−13.0568	−1.14077	−0.570387	−	0.821376i	$-0.693207\pi$
$131$	−13.0568	−1.14077	−0.570387	+	0.821376i	$0.693207\pi$
$132$	−58.8909	−5.12579
$133$	14.2330	1.23416
$134$	1.31098	0.113251
$135$	−1.13997	−0.0981126
$136$	62.6037	5.36822
$137$	−4.34098	−0.370875	−0.185437	−	0.982656i	$-0.559370\pi$
$137$	−4.34098	−0.370875	−0.185437	+	0.982656i	$0.559370\pi$
$138$	−33.6542	−2.86484
$139$	−14.8636	−1.26072	−0.630358	−	0.776305i	$-0.717092\pi$
$139$	−14.8636	−1.26072	−0.630358	+	0.776305i	$0.717092\pi$
$140$	4.98085	0.420958
$141$	13.0330	1.09757
$142$	41.5677	3.48828
$143$	6.38773	0.534169
$144$	0.312758	0.0260631
$145$	−0.141258	−0.0117308
$146$	29.3714	2.43080
$147$	−19.4578	−1.60485
$148$	20.5130	1.68616
$149$	−1.37365	−0.112534	−0.0562668	−	0.998416i	$-0.517920\pi$
$149$	−1.37365	−0.112534	−0.0562668	+	0.998416i	$0.517920\pi$
$150$	−23.2647	−1.89956
$151$	7.79347	0.634223	0.317112	−	0.948388i	$-0.397287\pi$
$151$	7.79347	0.634223	0.317112	+	0.948388i	$0.397287\pi$
$152$	29.7804	2.41551
$153$	−0.162395	−0.0131289
$154$	73.6217	5.93261
$155$	−0.308592	−0.0247867
$156$	−9.21937	−0.738141
$157$	−14.1598	−1.13008	−0.565039	−	0.825064i	$-0.691139\pi$
$157$	−14.1598	−1.13008	−0.565039	+	0.825064i	$0.691139\pi$
$158$	−5.69795	−0.453304
$159$	−21.6130	−1.71403
$160$	4.11007	0.324930
$161$	30.5495	2.40764
$162$	24.5069	1.92544
$163$	−11.3607	−0.889840	−0.444920	−	0.895570i	$-0.646768\pi$
$163$	−11.3607	−0.889840	−0.444920	+	0.895570i	$0.646768\pi$
$164$	−36.5725	−2.85583
$165$	2.44614	0.190432
$166$	−13.4420	−1.04330
$167$	−7.51084	−0.581206	−0.290603	−	0.956844i	$-0.593856\pi$
$167$	−7.51084	−0.581206	−0.290603	+	0.956844i	$0.593856\pi$
$168$	−66.1786	−5.10579
$169$	1.00000	0.0769231
$170$	−4.17519	−0.320223
$171$	−0.0772510	−0.00590753
$172$	−44.2961	−3.37755
$173$	−3.87537	−0.294639	−0.147320	−	0.989089i	$-0.547065\pi$
$173$	−3.87537	−0.294639	−0.147320	+	0.989089i	$0.547065\pi$
$174$	3.01349	0.228452
$175$	21.1185	1.59641
$176$	86.3018	6.50524
$177$	−16.4747	−1.23831
$178$	26.8454	2.01215
$179$	12.7728	0.954686	0.477343	−	0.878717i	$-0.341600\pi$
$179$	12.7728	0.954686	0.477343	+	0.878717i	$0.341600\pi$
$180$	−0.0270341	−0.00201500
$181$	−10.8629	−0.807436	−0.403718	−	0.914884i	$-0.632282\pi$
$181$	−10.8629	−0.807436	−0.403718	+	0.914884i	$0.632282\pi$
$182$	11.5255	0.854326
$183$	20.8222	1.53922
$184$	63.9202	4.71226
$185$	−0.852046	−0.0626437
$186$	6.58328	0.482709
$187$	−44.8111	−3.27691
$188$	−39.7453	−2.89872
$189$	−22.0757	−1.60577
$190$	−1.98613	−0.144089
$191$	−16.6149	−1.20221	−0.601105	−	0.799170i	$-0.705272\pi$
$191$	−16.6149	−1.20221	−0.601105	+	0.799170i	$0.705272\pi$
$192$	−40.6992	−2.93721
$193$	−5.14392	−0.370268	−0.185134	−	0.982713i	$-0.559272\pi$
$193$	−5.14392	−0.370268	−0.185134	+	0.982713i	$0.559272\pi$
$194$	13.1109	0.941305
$195$	0.382943	0.0274232
$196$	59.3384	4.23845
$197$	−4.61349	−0.328697	−0.164349	−	0.986402i	$-0.552552\pi$
$197$	−4.61349	−0.328697	−0.164349	+	0.986402i	$0.552552\pi$
$198$	−0.399589	−0.0283976
$199$	−6.20534	−0.439885	−0.219942	−	0.975513i	$-0.570587\pi$
$199$	−6.20534	−0.439885	−0.219942	+	0.975513i	$0.570587\pi$
$200$	44.1872	3.12451
$201$	0.843515	0.0594970
$202$	−8.45517	−0.594904
$203$	−2.73549	−0.191994
$204$	64.6756	4.52820
$205$	1.51910	0.106099
$206$	−27.8307	−1.93905
$207$	−0.165810	−0.0115246
$208$	13.5106	0.936788
$209$	−21.3165	−1.47449
$210$	4.41361	0.304568
$211$	−18.9780	−1.30650	−0.653250	−	0.757142i	$-0.726595\pi$
$211$	−18.9780	−1.30650	−0.653250	+	0.757142i	$0.726595\pi$
$212$	65.9110	4.52678
$213$	26.7457	1.83258
$214$	14.5048	0.991531
$215$	1.83992	0.125482
$216$	−46.1900	−3.14283
$217$	−5.97594	−0.405673
$218$	40.7638	2.76087
$219$	18.8983	1.27703
$220$	−7.45973	−0.502935
$221$	−7.01519	−0.471892
$222$	18.1769	1.21996
$223$	2.97262	0.199062	0.0995308	−	0.995034i	$-0.468266\pi$
$223$	2.97262	0.199062	0.0995308	+	0.995034i	$0.468266\pi$
$224$	79.5924	5.31799
$225$	−0.114623	−0.00764152
$226$	−48.8817	−3.25156
$227$	2.24579	0.149058	0.0745292	−	0.997219i	$-0.476255\pi$
$227$	2.24579	0.149058	0.0745292	+	0.997219i	$0.476255\pi$
$228$	30.7660	2.03753
$229$	−25.1475	−1.66179	−0.830895	−	0.556429i	$-0.812171\pi$
$229$	−25.1475	−1.66179	−0.830895	+	0.556429i	$0.812171\pi$
$230$	−4.26299	−0.281093
$231$	47.3700	3.11672
$232$	−5.72359	−0.375772
$233$	18.8558	1.23529	0.617643	−	0.786458i	$-0.288088\pi$
$233$	18.8558	1.23529	0.617643	+	0.786458i	$0.288088\pi$
$234$	−0.0625557	−0.00408940
$235$	1.65089	0.107692
$236$	50.2411	3.27042
$237$	−3.66620	−0.238145
$238$	−80.8534	−5.24095
$239$	−16.4754	−1.06570	−0.532852	−	0.846208i	$-0.678880\pi$
$239$	−16.4754	−1.06570	−0.532852	+	0.846208i	$0.678880\pi$
$240$	5.17378	0.333966
$241$	−18.8190	−1.21224	−0.606120	−	0.795373i	$-0.707275\pi$
$241$	−18.8190	−1.21224	−0.606120	+	0.795373i	$0.707275\pi$
$242$	−80.5368	−5.17710
$243$	0.240567	0.0154324
$244$	−63.4993	−4.06512
$245$	−2.46473	−0.157466
$246$	−32.4075	−2.06622
$247$	−3.33710	−0.212335
$248$	−12.5038	−0.793989
$249$	−8.64891	−0.548102
$250$	−5.92278	−0.374589
$251$	1.36962	0.0864498	0.0432249	−	0.999065i	$-0.486237\pi$
$251$	1.36962	0.0864498	0.0432249	+	0.999065i	$0.486237\pi$
$252$	−0.523520	−0.0329786
$253$	−45.7535	−2.87650
$254$	−8.51896	−0.534527
$255$	−2.68642	−0.168230
$256$	23.2586	1.45366
$257$	23.9555	1.49431	0.747153	−	0.664652i	$-0.231420\pi$
$257$	23.9555	1.49431	0.747153	+	0.664652i	$0.231420\pi$
$258$	−39.2515	−2.44369
$259$	−16.5000	−1.02526
$260$	−1.16782	−0.0724252
$261$	0.0148471	0.000919015 0
$262$	35.2832	2.17980
$263$	6.31602	0.389463	0.194731	−	0.980857i	$-0.437617\pi$
$263$	6.31602	0.389463	0.194731	+	0.980857i	$0.437617\pi$
$264$	99.1145	6.10008
$265$	−2.73773	−0.168178
$266$	−38.4617	−2.35824
$267$	17.2730	1.05709
$268$	−2.57238	−0.157133
$269$	18.2828	1.11472	0.557361	−	0.830270i	$-0.311814\pi$
$269$	18.2828	1.11472	0.557361	+	0.830270i	$0.311814\pi$
$270$	3.08052	0.187475
$271$	−29.6549	−1.80140	−0.900702	−	0.434438i	$-0.856947\pi$
$271$	−29.6549	−1.80140	−0.900702	+	0.434438i	$0.856947\pi$
$272$	−94.7790	−5.74682
$273$	7.41577	0.448823
$274$	11.7306	0.708671
$275$	−31.6288	−1.90729
$276$	66.0357	3.97488
$277$	22.8605	1.37355	0.686777	−	0.726868i	$-0.259025\pi$
$277$	22.8605	1.37355	0.686777	+	0.726868i	$0.259025\pi$
$278$	40.1659	2.40899
$279$	0.0324350	0.00194184
$280$	−8.38286	−0.500972
$281$	14.0137	0.835985	0.417992	−	0.908451i	$-0.362734\pi$
$281$	14.0137	0.835985	0.417992	+	0.908451i	$0.362734\pi$
$282$	−35.2189	−2.09726
$283$	2.26819	0.134830	0.0674149	−	0.997725i	$-0.478525\pi$
$283$	2.26819	0.134830	0.0674149	+	0.997725i	$0.478525\pi$
$284$	−81.5634	−4.83990
$285$	−1.27792	−0.0756976
$286$	−17.2615	−1.02070
$287$	29.4178	1.73648
$288$	−0.431996	−0.0254556
$289$	32.2128	1.89487
$290$	0.381720	0.0224154
$291$	8.43585	0.494518
$292$	−57.6320	−3.37266
$293$	−5.62606	−0.328678	−0.164339	−	0.986404i	$-0.552549\pi$
$293$	−5.62606	−0.328678	−0.164339	+	0.986404i	$0.552549\pi$
$294$	52.5807	3.06657
$295$	−2.08686	−0.121501
$296$	−34.5238	−2.00666
$297$	33.0623	1.91847
$298$	3.71200	0.215030
$299$	−7.16271	−0.414230
$300$	45.6497	2.63558
$301$	35.6304	2.05370
$302$	−21.0602	−1.21188
$303$	−5.44026	−0.312535
$304$	−45.0861	−2.58587
$305$	2.63756	0.151026
$306$	0.438840	0.0250868
$307$	4.99147	0.284878	0.142439	−	0.989804i	$-0.454505\pi$
$307$	4.99147	0.284878	0.142439	+	0.989804i	$0.454505\pi$
$308$	−144.459	−8.23133
$309$	−17.9069	−1.01869
$310$	0.833906	0.0473627
$311$	−1.07536	−0.0609780	−0.0304890	−	0.999535i	$-0.509706\pi$
$311$	−1.07536	−0.0609780	−0.0304890	+	0.999535i	$0.509706\pi$
$312$	15.5164	0.878442
$313$	−27.3208	−1.54426	−0.772130	−	0.635464i	$-0.780809\pi$
$313$	−27.3208	−1.54426	−0.772130	+	0.635464i	$0.780809\pi$
$314$	38.2640	2.15936
$315$	0.0217453	0.00122521
$316$	11.1804	0.628947
$317$	4.67814	0.262751	0.131375	−	0.991333i	$-0.458061\pi$
$317$	4.67814	0.262751	0.131375	+	0.991333i	$0.458061\pi$
$318$	58.4048	3.27518
$319$	4.09689	0.229382
$320$	−5.15538	−0.288195
$321$	9.33277	0.520904
$322$	−82.5537	−4.60054
$323$	23.4104	1.30259
$324$	−48.0869	−2.67149
$325$	−4.95149	−0.274659
$326$	30.7000	1.70032
$327$	26.2284	1.45043
$328$	61.5522	3.39865
$329$	31.9698	1.76255
$330$	−6.61019	−0.363879
$331$	−20.5468	−1.12936	−0.564678	−	0.825311i	$-0.691000\pi$
$331$	−20.5468	−1.12936	−0.564678	+	0.825311i	$0.691000\pi$
$332$	26.3757	1.44755
$333$	0.0895557	0.00490762
$334$	20.2965	1.11057
$335$	0.106848	0.00583775
$336$	100.191	5.46588
$337$	−31.6067	−1.72172	−0.860862	−	0.508839i	$-0.830075\pi$
$337$	−31.6067	−1.72172	−0.860862	+	0.508839i	$0.830075\pi$
$338$	−2.70229	−0.146985
$339$	−31.4516	−1.70822
$340$	8.19248	0.444300
$341$	8.95007	0.484674
$342$	0.208755	0.0112882
$343$	−17.8744	−0.965126
$344$	74.5512	4.01953
$345$	−2.74291	−0.147673
$346$	10.4724	0.562999
$347$	−29.4773	−1.58243	−0.791213	−	0.611541i	$-0.790550\pi$
$347$	−29.4773	−1.58243	−0.791213	+	0.611541i	$0.790550\pi$
$348$	−5.91302	−0.316971
$349$	10.8045	0.578352	0.289176	−	0.957276i	$-0.406619\pi$
$349$	10.8045	0.578352	0.289176	+	0.957276i	$0.406619\pi$
$350$	−57.0684	−3.05043
$351$	5.17591	0.276270
$352$	−119.204	−6.35361
$353$	−3.62193	−0.192776	−0.0963880	−	0.995344i	$-0.530729\pi$
$353$	−3.62193	−0.192776	−0.0963880	+	0.995344i	$0.530729\pi$
$354$	44.5195	2.36618
$355$	3.38788	0.179810
$356$	−52.6756	−2.79180
$357$	−52.0230	−2.75335
$358$	−34.5159	−1.82422
$359$	−2.40536	−0.126950	−0.0634751	−	0.997983i	$-0.520218\pi$
$359$	−2.40536	−0.126950	−0.0634751	+	0.997983i	$0.520218\pi$
$360$	0.0454988	0.00239800
$361$	−7.86374	−0.413881
$362$	29.3548	1.54286
$363$	−51.8193	−2.71981
$364$	−22.6151	−1.18535
$365$	2.39385	0.125300
$366$	−56.2677	−2.94116
$367$	−4.01029	−0.209336	−0.104668	−	0.994507i	$-0.533378\pi$
$367$	−4.01029	−0.209336	−0.104668	+	0.994507i	$0.533378\pi$
$368$	−96.7721	−5.04460
$369$	−0.159668	−0.00831198
$370$	2.30248	0.119700
$371$	−53.0167	−2.75249
$372$	−12.9176	−0.669745
$373$	6.70951	0.347405	0.173703	−	0.984798i	$-0.444427\pi$
$373$	6.70951	0.347405	0.173703	+	0.984798i	$0.444427\pi$
$374$	121.093	6.26156
$375$	−3.81086	−0.196792
$376$	66.8920	3.44969
$377$	0.641369	0.0330322
$378$	59.6549	3.06832
$379$	7.00795	0.359974	0.179987	−	0.983669i	$-0.442394\pi$
$379$	7.00795	0.359974	0.179987	+	0.983669i	$0.442394\pi$
$380$	3.89714	0.199919
$381$	−5.48130	−0.280816
$382$	44.8982	2.29719
$383$	−11.0696	−0.565630	−0.282815	−	0.959174i	$-0.591268\pi$
$383$	−11.0696	−0.565630	−0.282815	+	0.959174i	$0.591268\pi$
$384$	45.0871	2.30084
$385$	6.00038	0.305807
$386$	13.9004	0.707511
$387$	−0.193388	−0.00983045
$388$	−25.7259	−1.30603
$389$	21.8609	1.10839	0.554196	−	0.832387i	$-0.313026\pi$
$389$	21.8609	1.10839	0.554196	+	0.832387i	$0.313026\pi$
$390$	−1.03483	−0.0524004
$391$	50.2477	2.54114
$392$	−99.8676	−5.04408
$393$	22.7020	1.14517
$394$	12.4670	0.628078
$395$	−0.464398	−0.0233664
$396$	0.784067	0.0394008
$397$	6.25881	0.314121	0.157060	−	0.987589i	$-0.449798\pi$
$397$	6.25881	0.314121	0.157060	+	0.987589i	$0.449798\pi$
$398$	16.7686	0.840536
$399$	−24.7472	−1.23891
$400$	−66.8974	−3.34487
$401$	−9.04557	−0.451714	−0.225857	−	0.974160i	$-0.572518\pi$
$401$	−9.04557	−0.451714	−0.225857	+	0.974160i	$0.572518\pi$
$402$	−2.27943	−0.113687
$403$	1.40113	0.0697955
$404$	16.5906	0.825412
$405$	1.99738	0.0992505
$406$	7.39209	0.366863
$407$	24.7118	1.22492
$408$	−108.850	−5.38889
$409$	−14.0744	−0.695935	−0.347967	−	0.937507i	$-0.613128\pi$
$409$	−14.0744	−0.695935	−0.347967	+	0.937507i	$0.613128\pi$
$410$	−4.10507	−0.202735
$411$	7.54774	0.372303
$412$	54.6088	2.69038
$413$	−40.4124	−1.98856
$414$	0.448068	0.0220214
$415$	−1.09556	−0.0537790
$416$	−18.6614	−0.914952
$417$	25.8437	1.26557
$418$	57.6035	2.81748
$419$	−38.6597	−1.88865	−0.944326	−	0.329012i	$-0.893284\pi$
$419$	−38.6597	−1.88865	−0.944326	+	0.329012i	$0.893284\pi$
$420$	−8.66030	−0.422579
$421$	−14.1483	−0.689547	−0.344774	−	0.938686i	$-0.612044\pi$
$421$	−14.1483	−0.689547	−0.344774	+	0.938686i	$0.612044\pi$
$422$	51.2842	2.49647
$423$	−0.173520	−0.00843681
$424$	−110.929	−5.38721
$425$	34.7356	1.68493
$426$	−72.2746	−3.50172
$427$	51.0768	2.47178
$428$	−28.4611	−1.37572
$429$	−11.1065	−0.536226
$430$	−4.97200	−0.239771
$431$	−6.84580	−0.329751	−0.164875	−	0.986314i	$-0.552722\pi$
$431$	−6.84580	−0.329751	−0.164875	+	0.986314i	$0.552722\pi$
$432$	69.9294	3.36448
$433$	32.7536	1.57404	0.787018	−	0.616930i	$-0.211624\pi$
$433$	32.7536	1.57404	0.787018	+	0.616930i	$0.211624\pi$
$434$	16.1488	0.775165
$435$	0.245608	0.0117760
$436$	−79.9860	−3.83063
$437$	23.9027	1.14342
$438$	−51.0687	−2.44016
$439$	12.9795	0.619477	0.309738	−	0.950822i	$-0.399759\pi$
$439$	12.9795	0.619477	0.309738	+	0.950822i	$0.399759\pi$
$440$	12.5549	0.598530
$441$	0.259059	0.0123361
$442$	18.9571	0.901697
$443$	21.9941	1.04497	0.522485	−	0.852648i	$-0.325005\pi$
$443$	21.9941	1.04497	0.522485	+	0.852648i	$0.325005\pi$
$444$	−35.6664	−1.69265
$445$	2.18798	0.103720
$446$	−8.03290	−0.380369
$447$	2.38839	0.112967
$448$	−99.8350	−4.71676
$449$	−22.3255	−1.05361	−0.526803	−	0.849987i	$-0.676610\pi$
$449$	−22.3255	−1.05361	−0.526803	+	0.849987i	$0.676610\pi$
$450$	0.309744	0.0146015
$451$	−44.0585	−2.07463
$452$	95.9147	4.51145
$453$	−13.5507	−0.636666
$454$	−6.06879	−0.284822
$455$	0.939359	0.0440378
$456$	−51.7798	−2.42481
$457$	12.7675	0.597241	0.298620	−	0.954372i	$-0.403474\pi$
$457$	12.7675	0.597241	0.298620	+	0.954372i	$0.403474\pi$
$458$	67.9558	3.17537
$459$	−36.3100	−1.69480
$460$	8.36476	0.390009
$461$	13.5172	0.629559	0.314780	−	0.949165i	$-0.398069\pi$
$461$	13.5172	0.629559	0.314780	+	0.949165i	$0.398069\pi$
$462$	−128.008	−5.95545
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	8.66525	0.402274
$465$	0.536555	0.0248822
$466$	−50.9540	−2.36040
$467$	−1.10636	−0.0511962	−0.0255981	−	0.999672i	$-0.508149\pi$
$467$	−1.10636	−0.0511962	−0.0255981	+	0.999672i	$0.508149\pi$
$468$	0.122746	0.00567392
$469$	2.06914	0.0955440
$470$	−4.46119	−0.205780
$471$	24.6200	1.13443
$472$	−84.5568	−3.89204
$473$	−53.3631	−2.45364
$474$	9.90714	0.455050
$475$	16.5236	0.758157
$476$	158.649	7.27167
$477$	0.287754	0.0131753
$478$	44.5213	2.03636
$479$	0.602965	0.0275502	0.0137751	−	0.999905i	$-0.495615\pi$
$479$	0.602965	0.0275502	0.0137751	+	0.999905i	$0.495615\pi$
$480$	−7.14627	−0.326181
$481$	3.86864	0.176395
$482$	50.8545	2.31636
$483$	−53.1170	−2.41691
$484$	158.028	7.18308
$485$	1.06857	0.0485214
$486$	−0.650084	−0.0294884
$487$	−8.46932	−0.383782	−0.191891	−	0.981416i	$-0.561462\pi$
$487$	−8.46932	−0.383782	−0.191891	+	0.981416i	$0.561462\pi$
$488$	106.870	4.83780
$489$	19.7531	0.893267
$490$	6.66041	0.300887
$491$	26.5169	1.19669	0.598346	−	0.801238i	$-0.295825\pi$
$491$	26.5169	1.19669	0.598346	+	0.801238i	$0.295825\pi$
$492$	63.5893	2.86683
$493$	−4.49932	−0.202639
$494$	9.01783	0.405731
$495$	−0.0325676	−0.00146381
$496$	18.9301	0.849986
$497$	65.6070	2.94288
$498$	23.3719	1.04732
$499$	−21.7495	−0.973640	−0.486820	−	0.873502i	$-0.661843\pi$
$499$	−21.7495	−0.973640	−0.486820	+	0.873502i	$0.661843\pi$
$500$	11.6216	0.519732
$501$	13.0593	0.583444
$502$	−3.70112	−0.165189
$503$	−22.0851	−0.984728	−0.492364	−	0.870390i	$-0.663867\pi$
$503$	−22.0851	−0.984728	−0.492364	+	0.870390i	$0.663867\pi$
$504$	0.881094	0.0392470
$505$	−0.689120	−0.0306654
$506$	123.639	5.49644
$507$	−1.73872	−0.0772193
$508$	16.7157	0.741641
$509$	18.7849	0.832626	0.416313	−	0.909221i	$-0.363322\pi$
$509$	18.7849	0.832626	0.416313	+	0.909221i	$0.363322\pi$
$510$	7.25949	0.321456
$511$	46.3574	2.05073
$512$	−10.9892	−0.485658
$513$	−17.2726	−0.762602
$514$	−64.7349	−2.85533
$515$	−2.26828	−0.0999521
$516$	77.0186	3.39055
$517$	−47.8807	−2.10579
$518$	44.5880	1.95908
$519$	6.73819	0.295774
$520$	1.96547	0.0861914
$521$	18.0962	0.792809	0.396405	−	0.918076i	$-0.370258\pi$
$521$	18.0962	0.792809	0.396405	+	0.918076i	$0.370258\pi$
$522$	−0.0401213	−0.00175606
$523$	16.1084	0.704370	0.352185	−	0.935930i	$-0.385439\pi$
$523$	16.1084	0.704370	0.352185	+	0.935930i	$0.385439\pi$
$524$	−69.2320	−3.02441
$525$	−36.7192	−1.60256
$526$	−17.0677	−0.744189
$527$	−9.82922	−0.428167
$528$	−150.055	−6.53029
$529$	28.3044	1.23062
$530$	7.39815	0.321355
$531$	0.219342	0.00951864
$532$	75.4689	3.27199
$533$	−6.89736	−0.298758
$534$	−46.6767	−2.01990
$535$	1.18219	0.0511103
$536$	4.32936	0.187000
$537$	−22.2084	−0.958362
$538$	−49.4055	−2.13002
$539$	71.4843	3.07905
$540$	−6.04454	−0.260116
$541$	1.47697	0.0634998	0.0317499	−	0.999496i	$-0.489892\pi$
$541$	1.47697	0.0634998	0.0317499	+	0.999496i	$0.489892\pi$
$542$	80.1361	3.44214
$543$	18.8876	0.810545
$544$	130.913	5.61286
$545$	3.32236	0.142314
$546$	−20.0396	−0.857616
$547$	−5.72265	−0.244683	−0.122341	−	0.992488i	$-0.539040\pi$
$547$	−5.72265	−0.244683	−0.122341	+	0.992488i	$0.539040\pi$
$548$	−23.0175	−0.983261
$549$	−0.277225	−0.0118317
$550$	85.4703	3.64447
$551$	−2.14031	−0.0911805
$552$	−111.139	−4.73040
$553$	−8.99317	−0.382428
$554$	−61.7757	−2.62460
$555$	1.48147	0.0628849
$556$	−78.8127	−3.34240
$557$	22.5308	0.954661	0.477330	−	0.878724i	$-0.341605\pi$
$557$	22.5308	0.954661	0.477330	+	0.878724i	$0.341605\pi$
$558$	−0.0876490	−0.00371048
$559$	−8.35399	−0.353336
$560$	12.6913	0.536304
$561$	77.9140	3.28953
$562$	−37.8690	−1.59741
$563$	37.1646	1.56630	0.783151	−	0.621831i	$-0.213611\pi$
$563$	37.1646	1.56630	0.783151	+	0.621831i	$0.213611\pi$
$564$	69.1059	2.90988
$565$	−3.98399	−0.167608
$566$	−6.12931	−0.257634
$567$	38.6796	1.62439
$568$	137.273	5.75984
$569$	43.3027	1.81534	0.907672	−	0.419681i	$-0.137858\pi$
$569$	43.3027	1.81534	0.907672	+	0.419681i	$0.137858\pi$
$570$	3.45332	0.144644
$571$	8.90631	0.372718	0.186359	−	0.982482i	$-0.440331\pi$
$571$	8.90631	0.372718	0.186359	+	0.982482i	$0.440331\pi$
$572$	33.8703	1.41619
$573$	28.8886	1.20684
$574$	−79.4954	−3.31807
$575$	35.4661	1.47904
$576$	0.541864	0.0225777
$577$	−11.6713	−0.485883	−0.242942	−	0.970041i	$-0.578112\pi$
$577$	−11.6713	−0.485883	−0.242942	+	0.970041i	$0.578112\pi$
$578$	−87.0485	−3.62074
$579$	8.94384	0.371693
$580$	−0.749005	−0.0311007
$581$	−21.2158	−0.880178
$582$	−22.7961	−0.944930
$583$	79.4023	3.28851
$584$	96.9959	4.01372
$585$	−0.00509847	−0.000210796 0
$586$	15.2033	0.628041
$587$	33.9142	1.39979	0.699895	−	0.714245i	$-0.253230\pi$
$587$	33.9142	1.39979	0.699895	+	0.714245i	$0.253230\pi$
$588$	−103.173	−4.25477
$589$	−4.67573	−0.192660
$590$	5.63930	0.232166
$591$	8.02157	0.329963
$592$	52.2675	2.14818
$593$	−23.7219	−0.974142	−0.487071	−	0.873362i	$-0.661935\pi$
$593$	−23.7219	−0.974142	−0.487071	+	0.873362i	$0.661935\pi$
$594$	−89.3442	−3.66584
$595$	−6.58978	−0.270155
$596$	−7.28362	−0.298349
$597$	10.7894	0.441579
$598$	19.3557	0.791515
$599$	38.4946	1.57285	0.786424	−	0.617687i	$-0.211930\pi$
$599$	38.4946	1.57285	0.786424	+	0.617687i	$0.211930\pi$
$600$	−76.8293	−3.13654
$601$	−37.6971	−1.53770	−0.768849	−	0.639431i	$-0.779170\pi$
$601$	−37.6971	−1.53770	−0.768849	+	0.639431i	$0.779170\pi$
$602$	−96.2838	−3.92424
$603$	−0.0112305	−0.000457340 0
$604$	41.3240	1.68145
$605$	−6.56398	−0.266864
$606$	14.7012	0.597194
$607$	−23.0919	−0.937270	−0.468635	−	0.883392i	$-0.655254\pi$
$607$	−23.0919	−0.937270	−0.468635	+	0.883392i	$0.655254\pi$
$608$	62.2751	2.52559
$609$	4.75625	0.192733
$610$	−7.12745	−0.288582
$611$	−7.49573	−0.303245
$612$	−0.861084	−0.0348073
$613$	11.5773	0.467604	0.233802	−	0.972284i	$-0.424883\pi$
$613$	11.5773	0.467604	0.233802	+	0.972284i	$0.424883\pi$
$614$	−13.4884	−0.544348
$615$	−2.64130	−0.106507
$616$	243.128	9.79589
$617$	9.62746	0.387587	0.193793	−	0.981042i	$-0.437921\pi$
$617$	9.62746	0.387587	0.193793	+	0.981042i	$0.437921\pi$
$618$	48.3897	1.94652
$619$	−12.4561	−0.500653	−0.250327	−	0.968161i	$-0.580538\pi$
$619$	−12.4561	−0.500653	−0.250327	+	0.968161i	$0.580538\pi$
$620$	−1.63627	−0.0657144
$621$	−37.0735	−1.48771
$622$	2.90594	0.116517
$623$	42.3706	1.69754
$624$	−23.4911	−0.940396
$625$	24.2747	0.970990
$626$	73.8287	2.95079
$627$	37.0635	1.48017
$628$	−75.0810	−2.99606
$629$	−27.1392	−1.08211
$630$	−0.0587623	−0.00234115
$631$	0.823822	0.0327958	0.0163979	−	0.999866i	$-0.494780\pi$
$631$	0.823822	0.0327958	0.0163979	+	0.999866i	$0.494780\pi$
$632$	−18.8168	−0.748494
$633$	32.9975	1.31153
$634$	−12.6417	−0.502067
$635$	−0.694319	−0.0275532
$636$	−114.601	−4.54421
$637$	11.1909	0.443398
$638$	−11.0710	−0.438306
$639$	−0.356089	−0.0140867
$640$	5.71120	0.225755
$641$	38.5349	1.52204	0.761018	−	0.648731i	$-0.224700\pi$
$641$	38.5349	1.52204	0.761018	+	0.648731i	$0.224700\pi$
$642$	−25.2199	−0.995349
$643$	−2.79968	−0.110409	−0.0552044	−	0.998475i	$-0.517581\pi$
$643$	−2.79968	−0.110409	−0.0552044	+	0.998475i	$0.517581\pi$
$644$	161.985	6.38311
$645$	−3.19911	−0.125965
$646$	−63.2618	−2.48900
$647$	4.65219	0.182897	0.0914483	−	0.995810i	$-0.470850\pi$
$647$	4.65219	0.182897	0.0914483	+	0.995810i	$0.470850\pi$
$648$	80.9312	3.17928
$649$	60.5249	2.37581
$650$	13.3804	0.524822
$651$	10.3905	0.407236
$652$	−60.2389	−2.35914
$653$	−46.7592	−1.82983	−0.914913	−	0.403650i	$-0.867741\pi$
$653$	−46.7592	−1.82983	−0.914913	+	0.403650i	$0.867741\pi$
$654$	−70.8769	−2.77151
$655$	2.87568	0.112362
$656$	−93.1871	−3.63835
$657$	−0.251610	−0.00981622
$658$	−86.3919	−3.36791
$659$	−20.6437	−0.804163	−0.402081	−	0.915604i	$-0.631713\pi$
$659$	−20.6437	−0.804163	−0.402081	+	0.915604i	$0.631713\pi$
$660$	12.9704	0.504872
$661$	7.86212	0.305801	0.152900	−	0.988242i	$-0.451139\pi$
$661$	7.86212	0.305801	0.152900	+	0.988242i	$0.451139\pi$
$662$	55.5236	2.15799
$663$	12.1974	0.473710
$664$	−44.3907	−1.72269
$665$	−3.13474	−0.121560
$666$	−0.242006	−0.00937753
$667$	−4.59394	−0.177878
$668$	−39.8254	−1.54089
$669$	−5.16856	−0.199828
$670$	−0.288736	−0.0111548
$671$	−76.4969	−2.95313
$672$	−138.389	−5.33847
$673$	24.7514	0.954095	0.477047	−	0.878878i	$-0.341707\pi$
$673$	24.7514	0.954095	0.477047	+	0.878878i	$0.341707\pi$
$674$	85.4104	3.28989
$675$	−25.6285	−0.986441
$676$	5.30239	0.203938
$677$	19.7839	0.760356	0.380178	−	0.924913i	$-0.375863\pi$
$677$	19.7839	0.760356	0.380178	+	0.924913i	$0.375863\pi$
$678$	84.9916	3.26408
$679$	20.6931	0.794129
$680$	−13.7881	−0.528750
$681$	−3.90480	−0.149632
$682$	−24.1857	−0.926119
$683$	−45.5190	−1.74174	−0.870869	−	0.491515i	$-0.836443\pi$
$683$	−45.5190	−1.74174	−0.870869	+	0.491515i	$0.836443\pi$
$684$	−0.409615	−0.0156620
$685$	0.956076	0.0365298
$686$	48.3018	1.84417
$687$	43.7244	1.66819
$688$	−112.867	−4.30302
$689$	12.4304	0.473562
$690$	7.41215	0.282176
$691$	42.6220	1.62142	0.810710	−	0.585449i	$-0.199082\pi$
$691$	42.6220	1.62142	0.810710	+	0.585449i	$0.199082\pi$
$692$	−20.5487	−0.781145
$693$	−0.630679	−0.0239575
$694$	79.6564	3.02371
$695$	3.27363	0.124176
$696$	9.95173	0.377219
$697$	48.3863	1.83276
$698$	−29.1969	−1.10512
$699$	−32.7850	−1.24004
$700$	111.978	4.23239
$701$	50.7029	1.91502	0.957511	−	0.288395i	$-0.0931217\pi$
$701$	50.7029	1.91502	0.957511	+	0.288395i	$0.0931217\pi$
$702$	−13.9868	−0.527899
$703$	−12.9101	−0.486912
$704$	149.521	5.63529
$705$	−2.87044	−0.108107
$706$	9.78753	0.368358
$707$	−13.3449	−0.501888
$708$	−87.3552	−3.28301
$709$	36.0903	1.35540	0.677700	−	0.735338i	$-0.262977\pi$
$709$	36.0903	1.35540	0.677700	+	0.735338i	$0.262977\pi$
$710$	−9.15505	−0.343583
$711$	0.0488113	0.00183057
$712$	88.6541	3.32245
$713$	−10.0359	−0.375848
$714$	140.582	5.26113
$715$	−1.40686	−0.0526137
$716$	67.7265	2.53106
$717$	28.6461	1.06981
$718$	6.50000	0.242578
$719$	39.1537	1.46019	0.730094	−	0.683347i	$-0.239476\pi$
$719$	39.1537	1.46019	0.730094	+	0.683347i	$0.239476\pi$
$720$	−0.0688831	−0.00256712
$721$	−43.9256	−1.63587
$722$	21.2501	0.790848
$723$	32.7210	1.21691
$724$	−57.5995	−2.14067
$725$	−3.17573	−0.117944
$726$	140.031	5.19704
$727$	39.8734	1.47882	0.739410	−	0.673255i	$-0.235104\pi$
$727$	39.8734	1.47882	0.739410	+	0.673255i	$0.235104\pi$
$728$	38.0616	1.41066
$729$	26.7885	0.992165
$730$	−6.46889	−0.239424
$731$	58.6048	2.16758
$732$	110.407	4.08078
$733$	−29.2021	−1.07860	−0.539302	−	0.842112i	$-0.681312\pi$
$733$	−29.2021	−1.07860	−0.539302	+	0.842112i	$0.681312\pi$
$734$	10.8370	0.400001
$735$	4.28547	0.158072
$736$	133.666	4.92701
$737$	−3.09892	−0.114150
$738$	0.431469	0.0158826
$739$	27.4139	1.00844	0.504219	−	0.863576i	$-0.331781\pi$
$739$	27.4139	1.00844	0.504219	+	0.863576i	$0.331781\pi$
$740$	−4.51788	−0.166081
$741$	5.80229	0.213152
$742$	143.267	5.25949
$743$	1.49057	0.0546837	0.0273418	−	0.999626i	$-0.491296\pi$
$743$	1.49057	0.0546837	0.0273418	+	0.999626i	$0.491296\pi$
$744$	21.7405	0.797047
$745$	0.302538	0.0110841
$746$	−18.1311	−0.663826
$747$	0.115151	0.00421314
$748$	−237.606	−8.68774
$749$	22.8932	0.836501
$750$	10.2981	0.376032
$751$	−9.34341	−0.340946	−0.170473	−	0.985362i	$-0.554530\pi$
$751$	−9.34341	−0.340946	−0.170473	+	0.985362i	$0.554530\pi$
$752$	−101.271	−3.69299
$753$	−2.38139	−0.0867827
$754$	−1.73317	−0.0631182
$755$	−1.71647	−0.0624687
$756$	−117.054	−4.25720
$757$	−48.6890	−1.76963	−0.884816	−	0.465940i	$-0.845716\pi$
$757$	−48.6890	−1.76963	−0.884816	+	0.465940i	$0.845716\pi$
$758$	−18.9375	−0.687843
$759$	79.5525	2.88757
$760$	−6.55896	−0.237919
$761$	37.6290	1.36405	0.682025	−	0.731329i	$-0.261100\pi$
$761$	37.6290	1.36405	0.682025	+	0.731329i	$0.261100\pi$
$762$	14.8121	0.536585
$763$	64.3382	2.32920
$764$	−88.0985	−3.18729
$765$	0.0357667	0.00129315
$766$	29.9133	1.08081
$767$	9.47518	0.342129
$768$	−40.4402	−1.45926
$769$	27.5945	0.995082	0.497541	−	0.867440i	$-0.334236\pi$
$769$	27.5945	0.995082	0.497541	+	0.867440i	$0.334236\pi$
$770$	−16.2148	−0.584340
$771$	−41.6520	−1.50006
$772$	−27.2751	−0.981651
$773$	−38.1877	−1.37351	−0.686757	−	0.726887i	$-0.740967\pi$
$773$	−38.1877	−1.37351	−0.686757	+	0.726887i	$0.740967\pi$
$774$	0.522590	0.0187841
$775$	−6.93771	−0.249210
$776$	43.2972	1.55428
$777$	28.6890	1.02921
$778$	−59.0745	−2.11792
$779$	23.0172	0.824677
$780$	2.03052	0.0727041
$781$	−98.2586	−3.51597
$782$	−135.784	−4.85563
$783$	3.31967	0.118635
$784$	151.195	5.39982
$785$	3.11863	0.111309
$786$	−61.3476	−2.18820
$787$	−1.34112	−0.0478059	−0.0239029	−	0.999714i	$-0.507609\pi$
$787$	−1.34112	−0.0478059	−0.0239029	+	0.999714i	$0.507609\pi$
$788$	−24.4625	−0.871441
$789$	−10.9818	−0.390962
$790$	1.25494	0.0446488
$791$	−77.1508	−2.74317
$792$	−1.31960	−0.0468899
$793$	−11.9756	−0.425266
$794$	−16.9131	−0.600225
$795$	4.76015	0.168825
$796$	−32.9031	−1.16622
$797$	21.3360	0.755760	0.377880	−	0.925855i	$-0.376653\pi$
$797$	21.3360	0.755760	0.377880	+	0.925855i	$0.376653\pi$
$798$	66.8742	2.36732
$799$	52.5839	1.86029
$800$	92.4019	3.26690
$801$	−0.229971	−0.00812562
$802$	24.4438	0.863140
$803$	−69.4287	−2.45009
$804$	4.47265	0.157738
$805$	−6.72835	−0.237143
$806$	−3.78628	−0.133366
$807$	−31.7887	−1.11902
$808$	−27.9223	−0.982301
$809$	−24.1946	−0.850636	−0.425318	−	0.905044i	$-0.639838\pi$
$809$	−24.1946	−0.850636	−0.425318	+	0.905044i	$0.639838\pi$
$810$	−5.39750	−0.189649
$811$	−42.2558	−1.48380	−0.741901	−	0.670510i	$-0.766076\pi$
$811$	−42.2558	−1.48380	−0.741901	+	0.670510i	$0.766076\pi$
$812$	−14.5046	−0.509012
$813$	51.5615	1.80834
$814$	−66.7786	−2.34059
$815$	2.50213	0.0876459
$816$	164.794	5.76895
$817$	27.8781	0.975333
$818$	38.0332	1.32980
$819$	−0.0987328	−0.00345000
$820$	8.05489	0.281289
$821$	1.13643	0.0396617	0.0198308	−	0.999803i	$-0.493687\pi$
$821$	1.13643	0.0396617	0.0198308	+	0.999803i	$0.493687\pi$
$822$	−20.3962	−0.711400
$823$	44.0311	1.53483	0.767413	−	0.641153i	$-0.221544\pi$
$823$	44.0311	1.53483	0.767413	+	0.641153i	$0.221544\pi$
$824$	−91.9076	−3.20175
$825$	54.9937	1.91463
$826$	109.206	3.79977
$827$	16.1385	0.561190	0.280595	−	0.959826i	$-0.409468\pi$
$827$	16.1385	0.561190	0.280595	+	0.959826i	$0.409468\pi$
$828$	−0.879191	−0.0305540
$829$	43.5621	1.51297	0.756487	−	0.654009i	$-0.226914\pi$
$829$	43.5621	1.51297	0.756487	+	0.654009i	$0.226914\pi$
$830$	2.96053	0.102761
$831$	−39.7480	−1.37884
$832$	23.4075	0.811511
$833$	−78.5060	−2.72007
$834$	−69.8372	−2.41827
$835$	1.65422	0.0572467
$836$	−113.029	−3.90917
$837$	7.25215	0.250671
$838$	104.470	3.60885
$839$	−23.1120	−0.797914	−0.398957	−	0.916970i	$-0.630628\pi$
$839$	−23.1120	−0.797914	−0.398957	+	0.916970i	$0.630628\pi$
$840$	14.5755	0.502901
$841$	−28.5886	−0.985815
$842$	38.2329	1.31759
$843$	−24.3658	−0.839204
$844$	−100.629	−3.46379
$845$	−0.220244	−0.00757664
$846$	0.468901	0.0161211
$847$	−127.113	−4.36764
$848$	167.942	5.76715
$849$	−3.94375	−0.135349
$850$	−93.8659	−3.21957
$851$	−27.7099	−0.949884
$852$	141.816	4.85853
$853$	33.1923	1.13648	0.568241	−	0.822862i	$-0.307624\pi$
$853$	33.1923	1.13648	0.568241	+	0.822862i	$0.307624\pi$
$854$	−138.025	−4.72310
$855$	0.0170141	0.000581870 0
$856$	47.9007	1.63721
$857$	16.2990	0.556762	0.278381	−	0.960471i	$-0.410202\pi$
$857$	16.2990	0.556762	0.278381	+	0.960471i	$0.410202\pi$
$858$	30.0130	1.02463
$859$	11.6727	0.398268	0.199134	−	0.979972i	$-0.436187\pi$
$859$	11.6727	0.398268	0.199134	+	0.979972i	$0.436187\pi$
$860$	9.75597	0.332676
$861$	−51.1493	−1.74316
$862$	18.4994	0.630091
$863$	−30.9323	−1.05295	−0.526474	−	0.850191i	$-0.676486\pi$
$863$	−30.9323	−1.05295	−0.526474	+	0.850191i	$0.676486\pi$
$864$	−96.5899	−3.28606
$865$	0.853529	0.0290209
$866$	−88.5097	−3.00768
$867$	−56.0091	−1.90217
$868$	−31.6868	−1.07552
$869$	13.4689	0.456902
$870$	−0.663705	−0.0225017
$871$	−0.485136	−0.0164382
$872$	134.618	4.55874
$873$	−0.112314	−0.00380125
$874$	−64.5921	−2.18486
$875$	−9.34802	−0.316021
$876$	100.206	3.38565
$877$	7.89069	0.266450	0.133225	−	0.991086i	$-0.457467\pi$
$877$	7.89069	0.266450	0.133225	+	0.991086i	$0.457467\pi$
$878$	−35.0744	−1.18370
$879$	9.78214	0.329943
$880$	−19.0075	−0.640742
$881$	6.37050	0.214628	0.107314	−	0.994225i	$-0.465775\pi$
$881$	6.37050	0.214628	0.107314	+	0.994225i	$0.465775\pi$
$882$	−0.700053	−0.0235720
$883$	−20.9557	−0.705215	−0.352607	−	0.935771i	$-0.614705\pi$
$883$	−20.9557	−0.705215	−0.352607	+	0.935771i	$0.614705\pi$
$884$	−37.1972	−1.25108
$885$	3.62846	0.121969
$886$	−59.4345	−1.99674
$887$	15.9575	0.535802	0.267901	−	0.963446i	$-0.413670\pi$
$887$	15.9575	0.535802	0.267901	+	0.963446i	$0.413670\pi$
$888$	60.0273	2.01438
$889$	−13.4456	−0.450952
$890$	−5.91256	−0.198189
$891$	−57.9298	−1.94072
$892$	15.7620	0.527751
$893$	25.0140	0.837062
$894$	−6.45413	−0.215858
$895$	−2.81314	−0.0940330
$896$	110.599	3.69484
$897$	12.4539	0.415825
$898$	60.3301	2.01324
$899$	0.898644	0.0299715
$900$	−0.607774	−0.0202591
$901$	−87.2018	−2.90511
$902$	119.059	3.96423
$903$	−61.9513	−2.06161
$904$	−161.426	−5.36896
$905$	2.39250	0.0795294
$906$	36.6179	1.21655
$907$	−38.7368	−1.28623	−0.643117	−	0.765768i	$-0.722359\pi$
$907$	−38.7368	−1.28623	−0.643117	+	0.765768i	$0.722359\pi$
$908$	11.9081	0.395183
$909$	0.0724310	0.00240238
$910$	−2.53842	−0.0841479
$911$	−21.6623	−0.717704	−0.358852	−	0.933395i	$-0.616832\pi$
$911$	−21.6623	−0.717704	−0.358852	+	0.933395i	$0.616832\pi$
$912$	78.3921	2.59582
$913$	31.7745	1.05158
$914$	−34.5017	−1.14121
$915$	−4.58598	−0.151608
$916$	−133.342	−4.40573
$917$	55.6880	1.83898
$918$	98.1202	3.23845
$919$	−2.19664	−0.0724604	−0.0362302	−	0.999343i	$-0.511535\pi$
$919$	−2.19664	−0.0724604	−0.0362302	+	0.999343i	$0.511535\pi$
$920$	−14.0781	−0.464140
$921$	−8.67878	−0.285975
$922$	−36.5275	−1.20297
$923$	−15.3824	−0.506317
$924$	251.174	8.26302
$925$	−19.1555	−0.629830
$926$	2.70229	0.0888029
$927$	0.238411	0.00783043
$928$	−11.9689	−0.392897
$929$	17.9937	0.590353	0.295177	−	0.955443i	$-0.404622\pi$
$929$	17.9937	0.590353	0.295177	+	0.955443i	$0.404622\pi$
$930$	−1.44993	−0.0475451
$931$	−37.3451	−1.22394
$932$	99.9810	3.27499
$933$	1.86975	0.0612128
$934$	2.98971	0.0978261
$935$	9.86940	0.322764
$936$	−0.206583	−0.00675239
$937$	−18.6559	−0.609460	−0.304730	−	0.952439i	$-0.598566\pi$
$937$	−18.6559	−0.609460	−0.304730	+	0.952439i	$0.598566\pi$
$938$	−5.59142	−0.182566
$939$	47.5032	1.55021
$940$	8.75367	0.285513
$941$	−35.6245	−1.16132	−0.580662	−	0.814144i	$-0.697206\pi$
$941$	−35.6245	−1.16132	−0.580662	+	0.814144i	$0.697206\pi$
$942$	−66.5305	−2.16768
$943$	49.4038	1.60881
$944$	128.015	4.16653
$945$	4.86204	0.158162
$946$	144.203	4.68844
$947$	25.5585	0.830540	0.415270	−	0.909698i	$-0.363687\pi$
$947$	25.5585	0.830540	0.415270	+	0.909698i	$0.363687\pi$
$948$	−19.4396	−0.631369
$949$	−10.8691	−0.352825
$950$	−44.6517	−1.44869
$951$	−8.13398	−0.263762
$952$	−267.009	−8.65383
$953$	41.6981	1.35074	0.675368	−	0.737481i	$-0.263985\pi$
$953$	41.6981	1.35074	0.675368	+	0.737481i	$0.263985\pi$
$954$	−0.777595	−0.0251756
$955$	3.65933	0.118413
$956$	−87.3589	−2.82539
$957$	−7.12335	−0.230265
$958$	−1.62939	−0.0526431
$959$	18.5146	0.597867
$960$	8.96377	0.289304
$961$	−29.0368	−0.936672
$962$	−10.4542	−0.337057
$963$	−0.124255	−0.00400408
$964$	−99.7857	−3.21388
$965$	1.13292	0.0364700
$966$	143.538	4.61825
$967$	7.22757	0.232423	0.116212	−	0.993224i	$-0.462925\pi$
$967$	7.22757	0.232423	0.116212	+	0.993224i	$0.462925\pi$
$968$	−265.964	−8.54841
$969$	−40.7041	−1.30761
$970$	−2.88760	−0.0927151
$971$	18.5942	0.596717	0.298358	−	0.954454i	$-0.403561\pi$
$971$	18.5942	0.596717	0.298358	+	0.954454i	$0.403561\pi$
$972$	1.27558	0.0409143
$973$	63.3945	2.03233
$974$	22.8866	0.733334
$975$	8.60926	0.275717
$976$	−161.797	−5.17899
$977$	25.8003	0.825424	0.412712	−	0.910862i	$-0.364582\pi$
$977$	25.8003	0.825424	0.412712	+	0.910862i	$0.364582\pi$
$978$	−53.3787	−1.70686
$979$	−63.4578	−2.02812
$980$	−13.0689	−0.417472
$981$	−0.349202	−0.0111492
$982$	−71.6564	−2.28665
$983$	23.6172	0.753270	0.376635	−	0.926362i	$-0.377081\pi$
$983$	23.6172	0.753270	0.376635	+	0.926362i	$0.377081\pi$
$984$	−107.022	−3.41174
$985$	1.01609	0.0323755
$986$	12.1585	0.387205
$987$	−55.5866	−1.76934
$988$	−17.6946	−0.562941
$989$	59.8372	1.90271
$990$	0.0880073	0.00279706
$991$	−8.06671	−0.256247	−0.128124	−	0.991758i	$-0.540895\pi$
$991$	−8.06671	−0.256247	−0.128124	+	0.991758i	$0.540895\pi$
$992$	−26.1472	−0.830173
$993$	35.7252	1.13371
$994$	−177.289	−5.62328
$995$	1.36669	0.0433270
$996$	−45.8599	−1.45313
$997$	40.0101	1.26713	0.633566	−	0.773688i	$-0.281590\pi$
$997$	40.0101	1.26713	0.633566	+	0.773688i	$0.281590\pi$
$998$	58.7734	1.86044
$999$	20.0237	0.633523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.3	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.3	✓	130	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70229 q^{2} -1.73872 q^{3} +5.30239 q^{4} -0.220244 q^{5} +4.69853 q^{6} -4.26508 q^{7} -8.92402 q^{8} +0.0231491 q^{9} +O(q^{10})\)	\(q-2.70229 q^{2} -1.73872 q^{3} +5.30239 q^{4} -0.220244 q^{5} +4.69853 q^{6} -4.26508 q^{7} -8.92402 q^{8} +0.0231491 q^{9} +0.595165 q^{10} +6.38773 q^{11} -9.21937 q^{12} +1.00000 q^{13} +11.5255 q^{14} +0.382943 q^{15} +13.5106 q^{16} -7.01519 q^{17} -0.0625557 q^{18} -3.33710 q^{19} -1.16782 q^{20} +7.41577 q^{21} -17.2615 q^{22} -7.16271 q^{23} +15.5164 q^{24} -4.95149 q^{25} -2.70229 q^{26} +5.17591 q^{27} -22.6151 q^{28} +0.641369 q^{29} -1.03483 q^{30} +1.40113 q^{31} -18.6614 q^{32} -11.1065 q^{33} +18.9571 q^{34} +0.939359 q^{35} +0.122746 q^{36} +3.86864 q^{37} +9.01783 q^{38} -1.73872 q^{39} +1.96547 q^{40} -6.89736 q^{41} -20.0396 q^{42} -8.35399 q^{43} +33.8703 q^{44} -0.00509847 q^{45} +19.3557 q^{46} -7.49573 q^{47} -23.4911 q^{48} +11.1909 q^{49} +13.3804 q^{50} +12.1974 q^{51} +5.30239 q^{52} +12.4304 q^{53} -13.9868 q^{54} -1.40686 q^{55} +38.0616 q^{56} +5.80229 q^{57} -1.73317 q^{58} +9.47518 q^{59} +2.03052 q^{60} -11.9756 q^{61} -3.78628 q^{62} -0.0987328 q^{63} +23.4075 q^{64} -0.220244 q^{65} +30.0130 q^{66} -0.485136 q^{67} -37.1972 q^{68} +12.4539 q^{69} -2.53842 q^{70} -15.3824 q^{71} -0.206583 q^{72} -10.8691 q^{73} -10.4542 q^{74} +8.60926 q^{75} -17.6946 q^{76} -27.2442 q^{77} +4.69853 q^{78} +2.10856 q^{79} -2.97562 q^{80} -9.06891 q^{81} +18.6387 q^{82} +4.97430 q^{83} +39.3213 q^{84} +1.54506 q^{85} +22.5749 q^{86} -1.11516 q^{87} -57.0043 q^{88} -9.93432 q^{89} +0.0137776 q^{90} -4.26508 q^{91} -37.9795 q^{92} -2.43618 q^{93} +20.2557 q^{94} +0.734978 q^{95} +32.4470 q^{96} -4.85176 q^{97} -30.2410 q^{98} +0.147870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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