LMFDB - Embedded newform 6041.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77588 q^{2} -2.45572 q^{3} +1.15374 q^{4} +3.79745 q^{5} +4.36107 q^{6} +1.00000 q^{7} +1.50285 q^{8} +3.03058 q^{9} +O(q^{10})$	\(q-1.77588 q^{2} -2.45572 q^{3} +1.15374 q^{4} +3.79745 q^{5} +4.36107 q^{6} +1.00000 q^{7} +1.50285 q^{8} +3.03058 q^{9} -6.74380 q^{10} -3.93143 q^{11} -2.83328 q^{12} -2.72283 q^{13} -1.77588 q^{14} -9.32548 q^{15} -4.97636 q^{16} -7.29722 q^{17} -5.38194 q^{18} +4.42633 q^{19} +4.38128 q^{20} -2.45572 q^{21} +6.98175 q^{22} +2.06972 q^{23} -3.69058 q^{24} +9.42059 q^{25} +4.83542 q^{26} -0.0750949 q^{27} +1.15374 q^{28} +4.44108 q^{29} +16.5609 q^{30} -5.61549 q^{31} +5.83172 q^{32} +9.65452 q^{33} +12.9590 q^{34} +3.79745 q^{35} +3.49652 q^{36} +1.49082 q^{37} -7.86063 q^{38} +6.68652 q^{39} +5.70698 q^{40} -0.159373 q^{41} +4.36107 q^{42} -2.02229 q^{43} -4.53587 q^{44} +11.5085 q^{45} -3.67556 q^{46} +5.64206 q^{47} +12.2206 q^{48} +1.00000 q^{49} -16.7298 q^{50} +17.9200 q^{51} -3.14145 q^{52} +4.77808 q^{53} +0.133359 q^{54} -14.9294 q^{55} +1.50285 q^{56} -10.8699 q^{57} -7.88682 q^{58} -5.77842 q^{59} -10.7592 q^{60} +3.30941 q^{61} +9.97244 q^{62} +3.03058 q^{63} -0.403706 q^{64} -10.3398 q^{65} -17.1453 q^{66} -7.50876 q^{67} -8.41913 q^{68} -5.08265 q^{69} -6.74380 q^{70} -8.09341 q^{71} +4.55450 q^{72} +5.87661 q^{73} -2.64752 q^{74} -23.1344 q^{75} +5.10686 q^{76} -3.93143 q^{77} -11.8744 q^{78} -1.33605 q^{79} -18.8975 q^{80} -8.90733 q^{81} +0.283027 q^{82} +8.82471 q^{83} -2.83328 q^{84} -27.7108 q^{85} +3.59135 q^{86} -10.9061 q^{87} -5.90834 q^{88} +13.9342 q^{89} -20.4376 q^{90} -2.72283 q^{91} +2.38792 q^{92} +13.7901 q^{93} -10.0196 q^{94} +16.8088 q^{95} -14.3211 q^{96} -13.4883 q^{97} -1.77588 q^{98} -11.9145 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * 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 $

$2$	−1.77588	−1.25574	−0.627868	−	0.778320i	$-0.716072\pi$
$2$	−1.77588	−1.25574	−0.627868	+	0.778320i	$0.716072\pi$
$3$	−2.45572	−1.41781	−0.708906	−	0.705303i	$-0.750811\pi$
$3$	−2.45572	−1.41781	−0.708906	+	0.705303i	$0.750811\pi$
$4$	1.15374	0.576872
$5$	3.79745	1.69827	0.849135	−	0.528177i	$-0.177124\pi$
$5$	3.79745	1.69827	0.849135	+	0.528177i	$0.177124\pi$
$6$	4.36107	1.78040
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.50285	0.531336
$9$	3.03058	1.01019
$10$	−6.74380	−2.13258
$11$	−3.93143	−1.18537	−0.592686	−	0.805434i	$-0.701933\pi$
$11$	−3.93143	−1.18537	−0.592686	+	0.805434i	$0.701933\pi$
$12$	−2.83328	−0.817897
$13$	−2.72283	−0.755177	−0.377589	−	0.925973i	$-0.623247\pi$
$13$	−2.72283	−0.755177	−0.377589	+	0.925973i	$0.623247\pi$
$14$	−1.77588	−0.474624
$15$	−9.32548	−2.40783
$16$	−4.97636	−1.24409
$17$	−7.29722	−1.76984	−0.884918	−	0.465746i	$-0.845786\pi$
$17$	−7.29722	−1.76984	−0.884918	+	0.465746i	$0.845786\pi$
$18$	−5.38194	−1.26854
$19$	4.42633	1.01547	0.507735	−	0.861513i	$-0.330483\pi$
$19$	4.42633	1.01547	0.507735	+	0.861513i	$0.330483\pi$
$20$	4.38128	0.979685
$21$	−2.45572	−0.535883
$22$	6.98175	1.48851
$23$	2.06972	0.431566	0.215783	−	0.976441i	$-0.430770\pi$
$23$	2.06972	0.431566	0.215783	+	0.976441i	$0.430770\pi$
$24$	−3.69058	−0.753336
$25$	9.42059	1.88412
$26$	4.83542	0.948303
$27$	−0.0750949	−0.0144520
$28$	1.15374	0.218037
$29$	4.44108	0.824688	0.412344	−	0.911028i	$-0.364710\pi$
$29$	4.44108	0.824688	0.412344	+	0.911028i	$0.364710\pi$
$30$	16.5609	3.02360
$31$	−5.61549	−1.00857	−0.504286	−	0.863537i	$-0.668244\pi$
$31$	−5.61549	−1.00857	−0.504286	+	0.863537i	$0.668244\pi$
$32$	5.83172	1.03091
$33$	9.65452	1.68064
$34$	12.9590	2.22245
$35$	3.79745	0.641885
$36$	3.49652	0.582753
$37$	1.49082	0.245090	0.122545	−	0.992463i	$-0.460894\pi$
$37$	1.49082	0.245090	0.122545	+	0.992463i	$0.460894\pi$
$38$	−7.86063	−1.27516
$39$	6.68652	1.07070
$40$	5.70698	0.902352
$41$	−0.159373	−0.0248899	−0.0124449	−	0.999923i	$-0.503961\pi$
$41$	−0.159373	−0.0248899	−0.0124449	+	0.999923i	$0.503961\pi$
$42$	4.36107	0.672927
$43$	−2.02229	−0.308397	−0.154198	−	0.988040i	$-0.549280\pi$
$43$	−2.02229	−0.308397	−0.154198	+	0.988040i	$0.549280\pi$
$44$	−4.53587	−0.683808
$45$	11.5085	1.71558
$46$	−3.67556	−0.541932
$47$	5.64206	0.822979	0.411489	−	0.911415i	$-0.365009\pi$
$47$	5.64206	0.822979	0.411489	+	0.911415i	$0.365009\pi$
$48$	12.2206	1.76389
$49$	1.00000	0.142857
$50$	−16.7298	−2.36595
$51$	17.9200	2.50930
$52$	−3.14145	−0.435641
$53$	4.77808	0.656320	0.328160	−	0.944622i	$-0.393571\pi$
$53$	4.77808	0.656320	0.328160	+	0.944622i	$0.393571\pi$
$54$	0.133359	0.0181479
$55$	−14.9294	−2.01308
$56$	1.50285	0.200826
$57$	−10.8699	−1.43975
$58$	−7.88682	−1.03559
$59$	−5.77842	−0.752286	−0.376143	−	0.926562i	$-0.622750\pi$
$59$	−5.77842	−0.752286	−0.376143	+	0.926562i	$0.622750\pi$
$60$	−10.7592	−1.38901
$61$	3.30941	0.423727	0.211864	−	0.977299i	$-0.432047\pi$
$61$	3.30941	0.423727	0.211864	+	0.977299i	$0.432047\pi$
$62$	9.97244	1.26650
$63$	3.03058	0.381817
$64$	−0.403706	−0.0504633
$65$	−10.3398	−1.28249
$66$	−17.1453	−2.11043
$67$	−7.50876	−0.917341	−0.458671	−	0.888606i	$-0.651674\pi$
$67$	−7.50876	−0.917341	−0.458671	+	0.888606i	$0.651674\pi$
$68$	−8.41913	−1.02097
$69$	−5.08265	−0.611879
$70$	−6.74380	−0.806038
$71$	−8.09341	−0.960511	−0.480255	−	0.877129i	$-0.659456\pi$
$71$	−8.09341	−0.960511	−0.480255	+	0.877129i	$0.659456\pi$
$72$	4.55450	0.536752
$73$	5.87661	0.687805	0.343903	−	0.939005i	$-0.388251\pi$
$73$	5.87661	0.687805	0.343903	+	0.939005i	$0.388251\pi$
$74$	−2.64752	−0.307768
$75$	−23.1344	−2.67133
$76$	5.10686	0.585797
$77$	−3.93143	−0.448029
$78$	−11.8744	−1.34452
$79$	−1.33605	−0.150318	−0.0751589	−	0.997172i	$-0.523946\pi$
$79$	−1.33605	−0.150318	−0.0751589	+	0.997172i	$0.523946\pi$
$80$	−18.8975	−2.11280
$81$	−8.90733	−0.989703
$82$	0.283027	0.0312551
$83$	8.82471	0.968638	0.484319	−	0.874892i	$-0.339067\pi$
$83$	8.82471	0.968638	0.484319	+	0.874892i	$0.339067\pi$
$84$	−2.83328	−0.309136
$85$	−27.7108	−3.00566
$86$	3.59135	0.387265
$87$	−10.9061	−1.16925
$88$	−5.90834	−0.629831
$89$	13.9342	1.47702	0.738509	−	0.674244i	$-0.235530\pi$
$89$	13.9342	1.47702	0.738509	+	0.674244i	$0.235530\pi$
$90$	−20.4376	−2.15431
$91$	−2.72283	−0.285430
$92$	2.38792	0.248958
$93$	13.7901	1.42997
$94$	−10.0196	−1.03344
$95$	16.8088	1.72454
$96$	−14.3211	−1.46164
$97$	−13.4883	−1.36953	−0.684764	−	0.728764i	$-0.740095\pi$
$97$	−13.4883	−1.36953	−0.684764	+	0.728764i	$0.740095\pi$
$98$	−1.77588	−0.179391
$99$	−11.9145	−1.19745
$100$	10.8690	1.08690
$101$	4.51086	0.448847	0.224423	−	0.974492i	$-0.427950\pi$
$101$	4.51086	0.448847	0.224423	+	0.974492i	$0.427950\pi$
$102$	−31.8237	−3.15101
$103$	5.63424	0.555158	0.277579	−	0.960703i	$-0.410468\pi$
$103$	5.63424	0.555158	0.277579	+	0.960703i	$0.410468\pi$
$104$	−4.09200	−0.401253
$105$	−9.32548	−0.910073
$106$	−8.48530	−0.824165
$107$	−13.1722	−1.27340	−0.636701	−	0.771111i	$-0.719702\pi$
$107$	−13.1722	−1.27340	−0.636701	+	0.771111i	$0.719702\pi$
$108$	−0.0866404	−0.00833698
$109$	−0.250074	−0.0239527	−0.0119763	−	0.999928i	$-0.503812\pi$
$109$	−0.250074	−0.0239527	−0.0119763	+	0.999928i	$0.503812\pi$
$110$	26.5128	2.52790
$111$	−3.66105	−0.347492
$112$	−4.97636	−0.470222
$113$	5.38090	0.506193	0.253096	−	0.967441i	$-0.418551\pi$
$113$	5.38090	0.506193	0.253096	+	0.967441i	$0.418551\pi$
$114$	19.3035	1.80794
$115$	7.85963	0.732914
$116$	5.12387	0.475740
$117$	−8.25175	−0.762875
$118$	10.2618	0.944672
$119$	−7.29722	−0.668935
$120$	−14.0148	−1.27937
$121$	4.45618	0.405107
$122$	−5.87712	−0.532089
$123$	0.391376	0.0352892
$124$	−6.47885	−0.581818
$125$	16.7869	1.50147
$126$	−5.38194	−0.479461
$127$	11.9700	1.06216	0.531082	−	0.847320i	$-0.321786\pi$
$127$	11.9700	1.06216	0.531082	+	0.847320i	$0.321786\pi$
$128$	−10.9465	−0.967544
$129$	4.96619	0.437249
$130$	18.3622	1.61047
$131$	−17.9572	−1.56893	−0.784466	−	0.620172i	$-0.787063\pi$
$131$	−17.9572	−1.56893	−0.784466	+	0.620172i	$0.787063\pi$
$132$	11.1388	0.969512
$133$	4.42633	0.383812
$134$	13.3346	1.15194
$135$	−0.285169	−0.0245434
$136$	−10.9666	−0.940379
$137$	7.23963	0.618524	0.309262	−	0.950977i	$-0.399918\pi$
$137$	7.23963	0.618524	0.309262	+	0.950977i	$0.399918\pi$
$138$	9.02617	0.768359
$139$	−1.61566	−0.137039	−0.0685194	−	0.997650i	$-0.521827\pi$
$139$	−1.61566	−0.137039	−0.0685194	+	0.997650i	$0.521827\pi$
$140$	4.38128	0.370286
$141$	−13.8553	−1.16683
$142$	14.3729	1.20615
$143$	10.7046	0.895166
$144$	−15.0813	−1.25677
$145$	16.8648	1.40054
$146$	−10.4361	−0.863702
$147$	−2.45572	−0.202545
$148$	1.72003	0.141386
$149$	−4.47423	−0.366543	−0.183272	−	0.983062i	$-0.558669\pi$
$149$	−4.47423	−0.366543	−0.183272	+	0.983062i	$0.558669\pi$
$150$	41.0838	3.35448
$151$	−9.29377	−0.756316	−0.378158	−	0.925741i	$-0.623442\pi$
$151$	−9.29377	−0.756316	−0.378158	+	0.925741i	$0.623442\pi$
$152$	6.65210	0.539556
$153$	−22.1148	−1.78788
$154$	6.98175	0.562606
$155$	−21.3245	−1.71283
$156$	7.71454	0.617657
$157$	3.37326	0.269216	0.134608	−	0.990899i	$-0.457023\pi$
$157$	3.37326	0.269216	0.134608	+	0.990899i	$0.457023\pi$
$158$	2.37267	0.188759
$159$	−11.7337	−0.930539
$160$	22.1456	1.75077
$161$	2.06972	0.163116
$162$	15.8183	1.24281
$163$	−2.69644	−0.211201	−0.105601	−	0.994409i	$-0.533676\pi$
$163$	−2.69644	−0.211201	−0.105601	+	0.994409i	$0.533676\pi$
$164$	−0.183876	−0.0143583
$165$	36.6625	2.85417
$166$	−15.6716	−1.21635
$167$	−10.3687	−0.802352	−0.401176	−	0.916001i	$-0.631398\pi$
$167$	−10.3687	−0.802352	−0.401176	+	0.916001i	$0.631398\pi$
$168$	−3.69058	−0.284734
$169$	−5.58620	−0.429707
$170$	49.2110	3.77431
$171$	13.4144	1.02582
$172$	−2.33321	−0.177906
$173$	12.7319	0.967987	0.483993	−	0.875072i	$-0.339186\pi$
$173$	12.7319	0.967987	0.483993	+	0.875072i	$0.339186\pi$
$174$	19.3679	1.46827
$175$	9.42059	0.712130
$176$	19.5642	1.47471
$177$	14.1902	1.06660
$178$	−24.7454	−1.85474
$179$	−3.13411	−0.234255	−0.117127	−	0.993117i	$-0.537369\pi$
$179$	−3.13411	−0.234255	−0.117127	+	0.993117i	$0.537369\pi$
$180$	13.2778	0.989671
$181$	18.2963	1.35995	0.679976	−	0.733234i	$-0.261990\pi$
$181$	18.2963	1.35995	0.679976	+	0.733234i	$0.261990\pi$
$182$	4.83542	0.358425
$183$	−8.12701	−0.600766
$184$	3.11047	0.229307
$185$	5.66132	0.416229
$186$	−24.4895	−1.79566
$187$	28.6886	2.09792
$188$	6.50949	0.474754
$189$	−0.0750949	−0.00546235
$190$	−29.8503	−2.16557
$191$	−14.3129	−1.03565	−0.517823	−	0.855488i	$-0.673258\pi$
$191$	−14.3129	−1.03565	−0.517823	+	0.855488i	$0.673258\pi$
$192$	0.991392	0.0715475
$193$	−7.30612	−0.525906	−0.262953	−	0.964809i	$-0.584696\pi$
$193$	−7.30612	−0.525906	−0.262953	+	0.964809i	$0.584696\pi$
$194$	23.9536	1.71977
$195$	25.3917	1.81834
$196$	1.15374	0.0824103
$197$	−13.3565	−0.951610	−0.475805	−	0.879551i	$-0.657843\pi$
$197$	−13.3565	−0.951610	−0.475805	+	0.879551i	$0.657843\pi$
$198$	21.1588	1.50369
$199$	−14.8528	−1.05289	−0.526444	−	0.850210i	$-0.676475\pi$
$199$	−14.8528	−1.05289	−0.526444	+	0.850210i	$0.676475\pi$
$200$	14.1577	1.00110
$201$	18.4394	1.30062
$202$	−8.01073	−0.563633
$203$	4.44108	0.311703
$204$	20.6751	1.44754
$205$	−0.605211	−0.0422697
$206$	−10.0057	−0.697131
$207$	6.27244	0.435965
$208$	13.5498	0.939509
$209$	−17.4018	−1.20371
$210$	16.5609	1.14281
$211$	27.9221	1.92224	0.961118	−	0.276137i	$-0.0890544\pi$
$211$	27.9221	1.92224	0.961118	+	0.276137i	$0.0890544\pi$
$212$	5.51269	0.378613
$213$	19.8752	1.36182
$214$	23.3922	1.59906
$215$	−7.67955	−0.523741
$216$	−0.112856	−0.00767889
$217$	−5.61549	−0.381205
$218$	0.444100	0.0300783
$219$	−14.4313	−0.975179
$220$	−17.2247	−1.16129
$221$	19.8691	1.33654
$222$	6.50159	0.436358
$223$	20.5058	1.37317	0.686585	−	0.727049i	$-0.259109\pi$
$223$	20.5058	1.37317	0.686585	+	0.727049i	$0.259109\pi$
$224$	5.83172	0.389648
$225$	28.5498	1.90332
$226$	−9.55583	−0.635644
$227$	−19.6976	−1.30737	−0.653686	−	0.756765i	$-0.726778\pi$
$227$	−19.6976	−1.30737	−0.653686	+	0.756765i	$0.726778\pi$
$228$	−12.5410	−0.830550
$229$	−25.2467	−1.66835	−0.834174	−	0.551501i	$-0.814055\pi$
$229$	−25.2467	−1.66835	−0.834174	+	0.551501i	$0.814055\pi$
$230$	−13.9578	−0.920347
$231$	9.65452	0.635221
$232$	6.67426	0.438187
$233$	12.8568	0.842279	0.421140	−	0.906996i	$-0.361630\pi$
$233$	12.8568	0.842279	0.421140	+	0.906996i	$0.361630\pi$
$234$	14.6541	0.957969
$235$	21.4254	1.39764
$236$	−6.66682	−0.433973
$237$	3.28098	0.213122
$238$	12.9590	0.840006
$239$	26.1158	1.68929	0.844644	−	0.535328i	$-0.179812\pi$
$239$	26.1158	1.68929	0.844644	+	0.535328i	$0.179812\pi$
$240$	46.4070	2.99556
$241$	6.80367	0.438263	0.219131	−	0.975695i	$-0.429678\pi$
$241$	6.80367	0.438263	0.219131	+	0.975695i	$0.429678\pi$
$242$	−7.91363	−0.508708
$243$	22.0992	1.41767
$244$	3.81822	0.244436
$245$	3.79745	0.242610
$246$	−0.695037	−0.0443139
$247$	−12.0522	−0.766860
$248$	−8.43923	−0.535891
$249$	−21.6710	−1.37335
$250$	−29.8116	−1.88545
$251$	−30.3255	−1.91413	−0.957063	−	0.289879i	$-0.906385\pi$
$251$	−30.3255	−1.91413	−0.957063	+	0.289879i	$0.906385\pi$
$252$	3.49652	0.220260
$253$	−8.13695	−0.511566
$254$	−21.2572	−1.33380
$255$	68.0501	4.26146
$256$	20.2471	1.26544
$257$	−5.73473	−0.357723	−0.178861	−	0.983874i	$-0.557241\pi$
$257$	−5.73473	−0.357723	−0.178861	+	0.983874i	$0.557241\pi$
$258$	−8.81936	−0.549069
$259$	1.49082	0.0926353
$260$	−11.9295	−0.739835
$261$	13.4591	0.833094
$262$	31.8899	1.97016
$263$	−8.10630	−0.499856	−0.249928	−	0.968264i	$-0.580407\pi$
$263$	−8.10630	−0.499856	−0.249928	+	0.968264i	$0.580407\pi$
$264$	14.5093	0.892983
$265$	18.1445	1.11461
$266$	−7.86063	−0.481966
$267$	−34.2184	−2.09413
$268$	−8.66320	−0.529189
$269$	−15.9064	−0.969830	−0.484915	−	0.874561i	$-0.661149\pi$
$269$	−15.9064	−0.969830	−0.484915	+	0.874561i	$0.661149\pi$
$270$	0.506425	0.0308201
$271$	0.772761	0.0469419	0.0234709	−	0.999725i	$-0.492528\pi$
$271$	0.772761	0.0469419	0.0234709	+	0.999725i	$0.492528\pi$
$272$	36.3136	2.20184
$273$	6.68652	0.404687
$274$	−12.8567	−0.776702
$275$	−37.0364	−2.23338
$276$	−5.86408	−0.352976
$277$	−13.2059	−0.793464	−0.396732	−	0.917934i	$-0.629856\pi$
$277$	−13.2059	−0.793464	−0.396732	+	0.917934i	$0.629856\pi$
$278$	2.86922	0.172084
$279$	−17.0182	−1.01885
$280$	5.70698	0.341057
$281$	−19.8370	−1.18337	−0.591687	−	0.806168i	$-0.701538\pi$
$281$	−19.8370	−1.18337	−0.591687	+	0.806168i	$0.701538\pi$
$282$	24.6054	1.46523
$283$	−11.6095	−0.690110	−0.345055	−	0.938582i	$-0.612140\pi$
$283$	−11.6095	−0.690110	−0.345055	+	0.938582i	$0.612140\pi$
$284$	−9.33773	−0.554092
$285$	−41.2777	−2.44508
$286$	−19.0101	−1.12409
$287$	−0.159373	−0.00940750
$288$	17.6735	1.04142
$289$	36.2495	2.13232
$290$	−29.9498	−1.75871
$291$	33.1235	1.94174
$292$	6.78011	0.396776
$293$	21.4996	1.25602	0.628010	−	0.778205i	$-0.283870\pi$
$293$	21.4996	1.25602	0.628010	+	0.778205i	$0.283870\pi$
$294$	4.36107	0.254343
$295$	−21.9432	−1.27758
$296$	2.24048	0.130225
$297$	0.295231	0.0171310
$298$	7.94569	0.460282
$299$	−5.63549	−0.325909
$300$	−26.6912	−1.54101
$301$	−2.02229	−0.116563
$302$	16.5046	0.949733
$303$	−11.0774	−0.636381
$304$	−22.0270	−1.26334
$305$	12.5673	0.719603
$306$	39.2732	2.24510
$307$	−3.14445	−0.179463	−0.0897317	−	0.995966i	$-0.528601\pi$
$307$	−3.14445	−0.179463	−0.0897317	+	0.995966i	$0.528601\pi$
$308$	−4.53587	−0.258455
$309$	−13.8361	−0.787110
$310$	37.8698	2.15086
$311$	6.11563	0.346785	0.173393	−	0.984853i	$-0.444527\pi$
$311$	6.11563	0.346785	0.173393	+	0.984853i	$0.444527\pi$
$312$	10.0488	0.568902
$313$	10.3205	0.583350	0.291675	−	0.956517i	$-0.405787\pi$
$313$	10.3205	0.583350	0.291675	+	0.956517i	$0.405787\pi$
$314$	−5.99050	−0.338064
$315$	11.5085	0.648428
$316$	−1.54146	−0.0867142
$317$	21.2784	1.19511	0.597556	−	0.801827i	$-0.296139\pi$
$317$	21.2784	1.19511	0.597556	+	0.801827i	$0.296139\pi$
$318$	20.8375	1.16851
$319$	−17.4598	−0.977562
$320$	−1.53305	−0.0857003
$321$	32.3472	1.80545
$322$	−3.67556	−0.204831
$323$	−32.2999	−1.79722
$324$	−10.2768	−0.570932
$325$	−25.6507	−1.42284
$326$	4.78854	0.265213
$327$	0.614112	0.0339604
$328$	−0.239513	−0.0132249
$329$	5.64206	0.311057
$330$	−65.1082	−3.58409
$331$	−34.9264	−1.91973	−0.959863	−	0.280469i	$-0.909510\pi$
$331$	−34.9264	−1.91973	−0.959863	+	0.280469i	$0.909510\pi$
$332$	10.1815	0.558780
$333$	4.51806	0.247588
$334$	18.4135	1.00754
$335$	−28.5141	−1.55789
$336$	12.2206	0.666687
$337$	5.63701	0.307068	0.153534	−	0.988143i	$-0.450935\pi$
$337$	5.63701	0.307068	0.153534	+	0.988143i	$0.450935\pi$
$338$	9.92040	0.539599
$339$	−13.2140	−0.717686
$340$	−31.9712	−1.73388
$341$	22.0769	1.19553
$342$	−23.8223	−1.28816
$343$	1.00000	0.0539949
$344$	−3.03920	−0.163863
$345$	−19.3011	−1.03914
$346$	−22.6103	−1.21554
$347$	−14.3899	−0.772490	−0.386245	−	0.922396i	$-0.626228\pi$
$347$	−14.3899	−0.772490	−0.386245	+	0.922396i	$0.626228\pi$
$348$	−12.5828	−0.674510
$349$	−28.2781	−1.51369	−0.756845	−	0.653595i	$-0.773260\pi$
$349$	−28.2781	−1.51369	−0.756845	+	0.653595i	$0.773260\pi$
$350$	−16.7298	−0.894247
$351$	0.204471	0.0109138
$352$	−22.9270	−1.22202
$353$	−32.9459	−1.75354	−0.876768	−	0.480914i	$-0.840305\pi$
$353$	−32.9459	−1.75354	−0.876768	+	0.480914i	$0.840305\pi$
$354$	−25.2001	−1.33937
$355$	−30.7343	−1.63121
$356$	16.0765	0.852051
$357$	17.9200	0.948425
$358$	5.56580	0.294162
$359$	−19.7629	−1.04305	−0.521523	−	0.853237i	$-0.674636\pi$
$359$	−19.7629	−1.04305	−0.521523	+	0.853237i	$0.674636\pi$
$360$	17.2954	0.911550
$361$	0.592425	0.0311803
$362$	−32.4920	−1.70774
$363$	−10.9431	−0.574366
$364$	−3.14145	−0.164657
$365$	22.3161	1.16808
$366$	14.4326	0.754403
$367$	6.79269	0.354575	0.177288	−	0.984159i	$-0.443268\pi$
$367$	6.79269	0.354575	0.177288	+	0.984159i	$0.443268\pi$
$368$	−10.2997	−0.536907
$369$	−0.482993	−0.0251436
$370$	−10.0538	−0.522673
$371$	4.77808	0.248066
$372$	15.9103	0.824908
$373$	−11.8238	−0.612214	−0.306107	−	0.951997i	$-0.599027\pi$
$373$	−11.8238	−0.612214	−0.306107	+	0.951997i	$0.599027\pi$
$374$	−50.9474	−2.63443
$375$	−41.2241	−2.12880
$376$	8.47915	0.437279
$377$	−12.0923	−0.622786
$378$	0.133359	0.00685927
$379$	9.39251	0.482461	0.241230	−	0.970468i	$-0.422449\pi$
$379$	9.39251	0.482461	0.241230	+	0.970468i	$0.422449\pi$
$380$	19.3930	0.994841
$381$	−29.3950	−1.50595
$382$	25.4180	1.30050
$383$	−1.21364	−0.0620140	−0.0310070	−	0.999519i	$-0.509871\pi$
$383$	−1.21364	−0.0620140	−0.0310070	+	0.999519i	$0.509871\pi$
$384$	26.8816	1.37180
$385$	−14.9294	−0.760873
$386$	12.9748	0.660399
$387$	−6.12872	−0.311540
$388$	−15.5621	−0.790043
$389$	25.8727	1.31180	0.655899	−	0.754849i	$-0.272290\pi$
$389$	25.8727	1.31180	0.655899	+	0.754849i	$0.272290\pi$
$390$	−45.0926	−2.28335
$391$	−15.1032	−0.763801
$392$	1.50285	0.0759052
$393$	44.0980	2.22445
$394$	23.7195	1.19497
$395$	−5.07359	−0.255280
$396$	−13.7463	−0.690779
$397$	−11.4390	−0.574106	−0.287053	−	0.957915i	$-0.592676\pi$
$397$	−11.4390	−0.574106	−0.287053	+	0.957915i	$0.592676\pi$
$398$	26.3768	1.32215
$399$	−10.8699	−0.544173
$400$	−46.8803	−2.34401
$401$	9.96748	0.497752	0.248876	−	0.968535i	$-0.419939\pi$
$401$	9.96748	0.497752	0.248876	+	0.968535i	$0.419939\pi$
$402$	−32.7462	−1.63323
$403$	15.2900	0.761651
$404$	5.20438	0.258927
$405$	−33.8251	−1.68078
$406$	−7.88682	−0.391416
$407$	−5.86108	−0.290523
$408$	26.9310	1.33328
$409$	18.9057	0.934827	0.467413	−	0.884039i	$-0.345186\pi$
$409$	18.9057	0.934827	0.467413	+	0.884039i	$0.345186\pi$
$410$	1.07478	0.0530796
$411$	−17.7785	−0.876951
$412$	6.50047	0.320255
$413$	−5.77842	−0.284337
$414$	−11.1391	−0.547456
$415$	33.5113	1.64501
$416$	−15.8788	−0.778522
$417$	3.96762	0.194295
$418$	30.9036	1.51154
$419$	−34.7050	−1.69545	−0.847726	−	0.530434i	$-0.822029\pi$
$419$	−34.7050	−1.69545	−0.847726	+	0.530434i	$0.822029\pi$
$420$	−10.7592	−0.524996
$421$	−3.71750	−0.181180	−0.0905899	−	0.995888i	$-0.528875\pi$
$421$	−3.71750	−0.181180	−0.0905899	+	0.995888i	$0.528875\pi$
$422$	−49.5863	−2.41382
$423$	17.0987	0.831367
$424$	7.18073	0.348727
$425$	−68.7441	−3.33458
$426$	−35.2959	−1.71009
$427$	3.30941	0.160154
$428$	−15.1973	−0.734591
$429$	−26.2876	−1.26918
$430$	13.6379	0.657680
$431$	3.05152	0.146986	0.0734932	−	0.997296i	$-0.476585\pi$
$431$	3.05152	0.146986	0.0734932	+	0.997296i	$0.476585\pi$
$432$	0.373700	0.0179796
$433$	−8.76309	−0.421127	−0.210564	−	0.977580i	$-0.567530\pi$
$433$	−8.76309	−0.421127	−0.210564	+	0.977580i	$0.567530\pi$
$434$	9.97244	0.478692
$435$	−41.4152	−1.98571
$436$	−0.288521	−0.0138177
$437$	9.16125	0.438242
$438$	25.6283	1.22457
$439$	−26.6646	−1.27263	−0.636315	−	0.771429i	$-0.719542\pi$
$439$	−26.6646	−1.27263	−0.636315	+	0.771429i	$0.719542\pi$
$440$	−22.4366	−1.06962
$441$	3.03058	0.144313
$442$	−35.2851	−1.67834
$443$	39.0708	1.85631	0.928156	−	0.372192i	$-0.121394\pi$
$443$	39.0708	1.85631	0.928156	+	0.372192i	$0.121394\pi$
$444$	−4.22392	−0.200458
$445$	52.9142	2.50837
$446$	−36.4158	−1.72434
$447$	10.9875	0.519690
$448$	−0.403706	−0.0190733
$449$	16.1619	0.762727	0.381364	−	0.924425i	$-0.375455\pi$
$449$	16.1619	0.762727	0.381364	+	0.924425i	$0.375455\pi$
$450$	−50.7011	−2.39007
$451$	0.626565	0.0295038
$452$	6.20819	0.292009
$453$	22.8229	1.07231
$454$	34.9805	1.64171
$455$	−10.3398	−0.484737
$456$	−16.3357	−0.764990
$457$	3.01968	0.141255	0.0706274	−	0.997503i	$-0.477500\pi$
$457$	3.01968	0.141255	0.0706274	+	0.997503i	$0.477500\pi$
$458$	44.8351	2.09501
$459$	0.547985	0.0255777
$460$	9.06801	0.422798
$461$	12.3378	0.574629	0.287314	−	0.957836i	$-0.407238\pi$
$461$	12.3378	0.574629	0.287314	+	0.957836i	$0.407238\pi$
$462$	−17.1453	−0.797669
$463$	7.46397	0.346880	0.173440	−	0.984844i	$-0.444512\pi$
$463$	7.46397	0.346880	0.173440	+	0.984844i	$0.444512\pi$
$464$	−22.1004	−1.02599
$465$	52.3672	2.42847
$466$	−22.8322	−1.05768
$467$	−29.1346	−1.34819	−0.674094	−	0.738646i	$-0.735466\pi$
$467$	−29.1346	−1.34819	−0.674094	+	0.738646i	$0.735466\pi$
$468$	−9.52042	−0.440081
$469$	−7.50876	−0.346722
$470$	−38.0489	−1.75507
$471$	−8.28380	−0.381697
$472$	−8.68407	−0.399717
$473$	7.95052	0.365565
$474$	−5.82662	−0.267625
$475$	41.6987	1.91327
$476$	−8.41913	−0.385890
$477$	14.4804	0.663010
$478$	−46.3784	−2.12130
$479$	31.5870	1.44325	0.721624	−	0.692285i	$-0.243396\pi$
$479$	31.5870	1.44325	0.721624	+	0.692285i	$0.243396\pi$
$480$	−54.3836	−2.48226
$481$	−4.05926	−0.185086
$482$	−12.0825	−0.550342
$483$	−5.08265	−0.231269
$484$	5.14129	0.233695
$485$	−51.2211	−2.32583
$486$	−39.2455	−1.78021
$487$	−28.6971	−1.30039	−0.650195	−	0.759768i	$-0.725313\pi$
$487$	−28.6971	−1.30039	−0.650195	+	0.759768i	$0.725313\pi$
$488$	4.97354	0.225142
$489$	6.62170	0.299444
$490$	−6.74380	−0.304654
$491$	12.7145	0.573797	0.286899	−	0.957961i	$-0.407376\pi$
$491$	12.7145	0.573797	0.286899	+	0.957961i	$0.407376\pi$
$492$	0.451548	0.0203574
$493$	−32.4076	−1.45956
$494$	21.4032	0.962974
$495$	−45.2448	−2.03360
$496$	27.9447	1.25476
$497$	−8.09341	−0.363039
$498$	38.4852	1.72456
$499$	3.71358	0.166243	0.0831213	−	0.996539i	$-0.473511\pi$
$499$	3.71358	0.166243	0.0831213	+	0.996539i	$0.473511\pi$
$500$	19.3678	0.866157
$501$	25.4626	1.13758
$502$	53.8544	2.40364
$503$	9.60133	0.428102	0.214051	−	0.976822i	$-0.431334\pi$
$503$	9.60133	0.428102	0.214051	+	0.976822i	$0.431334\pi$
$504$	4.55450	0.202873
$505$	17.1297	0.762263
$506$	14.4502	0.642392
$507$	13.7182	0.609245
$508$	13.8103	0.612733
$509$	4.40519	0.195257	0.0976284	−	0.995223i	$-0.468874\pi$
$509$	4.40519	0.195257	0.0976284	+	0.995223i	$0.468874\pi$
$510$	−120.849	−5.35127
$511$	5.87661	0.259966
$512$	−14.0633	−0.621518
$513$	−0.332395	−0.0146756
$514$	10.1842	0.449205
$515$	21.3957	0.942807
$516$	5.72972	0.252237
$517$	−22.1814	−0.975536
$518$	−2.64752	−0.116325
$519$	−31.2660	−1.37242
$520$	−15.5391	−0.681436
$521$	−0.381395	−0.0167092	−0.00835460	−	0.999965i	$-0.502659\pi$
$521$	−0.381395	−0.0167092	−0.00835460	+	0.999965i	$0.502659\pi$
$522$	−23.9016	−1.04615
$523$	−38.6725	−1.69103	−0.845516	−	0.533950i	$-0.820707\pi$
$523$	−38.6725	−1.69103	−0.845516	+	0.533950i	$0.820707\pi$
$524$	−20.7181	−0.905073
$525$	−23.1344	−1.00967
$526$	14.3958	0.627687
$527$	40.9775	1.78501
$528$	−48.0444	−2.09086
$529$	−18.7163	−0.813751
$530$	−32.2225	−1.39965
$531$	−17.5119	−0.759954
$532$	5.10686	0.221410
$533$	0.433946	0.0187963
$534$	60.7678	2.62968
$535$	−50.0206	−2.16258
$536$	−11.2845	−0.487417
$537$	7.69652	0.332129
$538$	28.2478	1.21785
$539$	−3.93143	−0.169339
$540$	−0.329012	−0.0141584
$541$	−17.9126	−0.770122	−0.385061	−	0.922891i	$-0.625820\pi$
$541$	−17.9126	−0.770122	−0.385061	+	0.922891i	$0.625820\pi$
$542$	−1.37233	−0.0589466
$543$	−44.9306	−1.92816
$544$	−42.5554	−1.82455
$545$	−0.949640	−0.0406781
$546$	−11.8744	−0.508179
$547$	−31.2348	−1.33550	−0.667751	−	0.744385i	$-0.732743\pi$
$547$	−31.2348	−1.33550	−0.667751	+	0.744385i	$0.732743\pi$
$548$	8.35269	0.356809
$549$	10.0294	0.428046
$550$	65.7722	2.80454
$551$	19.6577	0.837446
$552$	−7.63844	−0.325114
$553$	−1.33605	−0.0568148
$554$	23.4520	0.996381
$555$	−13.9026	−0.590135
$556$	−1.86406	−0.0790539
$557$	11.0758	0.469296	0.234648	−	0.972080i	$-0.424606\pi$
$557$	11.0758	0.469296	0.234648	+	0.972080i	$0.424606\pi$
$558$	30.2223	1.27941
$559$	5.50636	0.232894
$560$	−18.8975	−0.798564
$561$	−70.4512	−2.97445
$562$	35.2280	1.48601
$563$	38.2690	1.61285	0.806423	−	0.591340i	$-0.201401\pi$
$563$	38.2690	1.61285	0.806423	+	0.591340i	$0.201401\pi$
$564$	−15.9855	−0.673112
$565$	20.4337	0.859651
$566$	20.6170	0.866596
$567$	−8.90733	−0.374073
$568$	−12.1631	−0.510354
$569$	14.1025	0.591209	0.295605	−	0.955310i	$-0.404479\pi$
$569$	14.1025	0.591209	0.295605	+	0.955310i	$0.404479\pi$
$570$	73.3041	3.07037
$571$	−21.1302	−0.884273	−0.442136	−	0.896948i	$-0.645779\pi$
$571$	−21.1302	−0.884273	−0.442136	+	0.896948i	$0.645779\pi$
$572$	12.3504	0.516397
$573$	35.1486	1.46835
$574$	0.283027	0.0118133
$575$	19.4979	0.813120
$576$	−1.22346	−0.0509777
$577$	11.0735	0.460995	0.230497	−	0.973073i	$-0.425965\pi$
$577$	11.0735	0.460995	0.230497	+	0.973073i	$0.425965\pi$
$578$	−64.3747	−2.67763
$579$	17.9418	0.745636
$580$	19.4576	0.807934
$581$	8.82471	0.366111
$582$	−58.8234	−2.43831
$583$	−18.7847	−0.777984
$584$	8.83164	0.365456
$585$	−31.3356	−1.29557
$586$	−38.1807	−1.57723
$587$	21.5064	0.887663	0.443831	−	0.896110i	$-0.353619\pi$
$587$	21.5064	0.887663	0.443831	+	0.896110i	$0.353619\pi$
$588$	−2.83328	−0.116842
$589$	−24.8560	−1.02418
$590$	38.9685	1.60431
$591$	32.7998	1.34920
$592$	−7.41888	−0.304914
$593$	3.34751	0.137466	0.0687328	−	0.997635i	$-0.478104\pi$
$593$	3.34751	0.137466	0.0687328	+	0.997635i	$0.478104\pi$
$594$	−0.524294	−0.0215120
$595$	−27.7108	−1.13603
$596$	−5.16212	−0.211449
$597$	36.4744	1.49280
$598$	10.0079	0.409255
$599$	20.6706	0.844578	0.422289	−	0.906461i	$-0.361227\pi$
$599$	20.6706	0.844578	0.422289	+	0.906461i	$0.361227\pi$
$600$	−34.7674	−1.41937
$601$	−0.996994	−0.0406682	−0.0203341	−	0.999793i	$-0.506473\pi$
$601$	−0.996994	−0.0406682	−0.0203341	+	0.999793i	$0.506473\pi$
$602$	3.59135	0.146372
$603$	−22.7559	−0.926692
$604$	−10.7226	−0.436298
$605$	16.9221	0.687981
$606$	19.6721	0.799126
$607$	−29.5002	−1.19737	−0.598687	−	0.800983i	$-0.704311\pi$
$607$	−29.5002	−1.19737	−0.598687	+	0.800983i	$0.704311\pi$
$608$	25.8131	1.04686
$609$	−10.9061	−0.441936
$610$	−22.3180	−0.903631
$611$	−15.3624	−0.621495
$612$	−25.5149	−1.03138
$613$	2.70792	0.109372	0.0546860	−	0.998504i	$-0.482584\pi$
$613$	2.70792	0.109372	0.0546860	+	0.998504i	$0.482584\pi$
$614$	5.58417	0.225359
$615$	1.48623	0.0599306
$616$	−5.90834	−0.238054
$617$	−22.9584	−0.924270	−0.462135	−	0.886810i	$-0.652916\pi$
$617$	−22.9584	−0.924270	−0.462135	+	0.886810i	$0.652916\pi$
$618$	24.5713	0.988402
$619$	7.38401	0.296788	0.148394	−	0.988928i	$-0.452590\pi$
$619$	7.38401	0.296788	0.148394	+	0.988928i	$0.452590\pi$
$620$	−24.6031	−0.988083
$621$	−0.155425	−0.00623700
$622$	−10.8606	−0.435471
$623$	13.9342	0.558260
$624$	−33.2745	−1.33205
$625$	16.6446	0.665782
$626$	−18.3280	−0.732534
$627$	42.7341	1.70664
$628$	3.89188	0.155303
$629$	−10.8789	−0.433769
$630$	−20.4376	−0.814255
$631$	−42.8434	−1.70557	−0.852785	−	0.522262i	$-0.825088\pi$
$631$	−42.8434	−1.70557	−0.852785	+	0.522262i	$0.825088\pi$
$632$	−2.00788	−0.0798693
$633$	−68.5690	−2.72537
$634$	−37.7878	−1.50074
$635$	45.4554	1.80384
$636$	−13.5376	−0.536803
$637$	−2.72283	−0.107882
$638$	31.0065	1.22756
$639$	−24.5277	−0.970301
$640$	−41.5688	−1.64315
$641$	−21.0514	−0.831480	−0.415740	−	0.909484i	$-0.636477\pi$
$641$	−21.0514	−0.831480	−0.415740	+	0.909484i	$0.636477\pi$
$642$	−57.4448	−2.26716
$643$	28.1612	1.11057	0.555286	−	0.831660i	$-0.312609\pi$
$643$	28.1612	1.11057	0.555286	+	0.831660i	$0.312609\pi$
$644$	2.38792	0.0940974
$645$	18.8589	0.742567
$646$	57.3608	2.25683
$647$	27.2127	1.06984	0.534920	−	0.844903i	$-0.320342\pi$
$647$	27.2127	1.06984	0.534920	+	0.844903i	$0.320342\pi$
$648$	−13.3863	−0.525865
$649$	22.7175	0.891739
$650$	45.5525	1.78671
$651$	13.7901	0.540477
$652$	−3.11100	−0.121836
$653$	−11.2925	−0.441909	−0.220954	−	0.975284i	$-0.570917\pi$
$653$	−11.2925	−0.441909	−0.220954	+	0.975284i	$0.570917\pi$
$654$	−1.09059	−0.0426453
$655$	−68.1916	−2.66447
$656$	0.793098	0.0309653
$657$	17.8095	0.694816
$658$	−10.0196	−0.390605
$659$	27.0458	1.05355	0.526776	−	0.850004i	$-0.323401\pi$
$659$	27.0458	1.05355	0.526776	+	0.850004i	$0.323401\pi$
$660$	42.2992	1.64649
$661$	−22.3412	−0.868972	−0.434486	−	0.900679i	$-0.643070\pi$
$661$	−22.3412	−0.868972	−0.434486	+	0.900679i	$0.643070\pi$
$662$	62.0250	2.41067
$663$	−48.7930	−1.89496
$664$	13.2622	0.514673
$665$	16.8088	0.651816
$666$	−8.02353	−0.310905
$667$	9.19178	0.355907
$668$	−11.9628	−0.462855
$669$	−50.3566	−1.94690
$670$	50.6376	1.95630
$671$	−13.0107	−0.502274
$672$	−14.3211	−0.552448
$673$	−25.3629	−0.977667	−0.488833	−	0.872377i	$-0.662577\pi$
$673$	−25.3629	−0.977667	−0.488833	+	0.872377i	$0.662577\pi$
$674$	−10.0106	−0.385596
$675$	−0.707439	−0.0272293
$676$	−6.44504	−0.247886
$677$	4.35309	0.167303	0.0836514	−	0.996495i	$-0.473342\pi$
$677$	4.35309	0.167303	0.0836514	+	0.996495i	$0.473342\pi$
$678$	23.4665	0.901225
$679$	−13.4883	−0.517633
$680$	−41.6451	−1.59702
$681$	48.3718	1.85361
$682$	−39.2060	−1.50127
$683$	−6.46747	−0.247471	−0.123735	−	0.992315i	$-0.539487\pi$
$683$	−6.46747	−0.247471	−0.123735	+	0.992315i	$0.539487\pi$
$684$	15.4767	0.591768
$685$	27.4921	1.05042
$686$	−1.77588	−0.0678034
$687$	61.9989	2.36541
$688$	10.0637	0.383674
$689$	−13.0099	−0.495638
$690$	34.2764	1.30488
$691$	−16.5215	−0.628509	−0.314254	−	0.949339i	$-0.601754\pi$
$691$	−16.5215	−0.628509	−0.314254	+	0.949339i	$0.601754\pi$
$692$	14.6893	0.558405
$693$	−11.9145	−0.452595
$694$	25.5547	0.970043
$695$	−6.13539	−0.232729
$696$	−16.3901	−0.621267
$697$	1.16298	0.0440511
$698$	50.2184	1.90079
$699$	−31.5728	−1.19419
$700$	10.8690	0.410808
$701$	−40.1973	−1.51823	−0.759116	−	0.650956i	$-0.774368\pi$
$701$	−40.1973	−1.51823	−0.759116	+	0.650956i	$0.774368\pi$
$702$	−0.363115	−0.0137049
$703$	6.59889	0.248882
$704$	1.58715	0.0598178
$705$	−52.6149	−1.98159
$706$	58.5080	2.20198
$707$	4.51086	0.169648
$708$	16.3719	0.615292
$709$	−0.387279	−0.0145446	−0.00727229	−	0.999974i	$-0.502315\pi$
$709$	−0.387279	−0.0145446	−0.00727229	+	0.999974i	$0.502315\pi$
$710$	54.5803	2.04836
$711$	−4.04902	−0.151850
$712$	20.9409	0.784793
$713$	−11.6225	−0.435265
$714$	−31.8237	−1.19097
$715$	40.6502	1.52023
$716$	−3.61597	−0.135135
$717$	−64.1331	−2.39510
$718$	35.0965	1.30979
$719$	−9.47849	−0.353488	−0.176744	−	0.984257i	$-0.556556\pi$
$719$	−9.47849	−0.353488	−0.176744	+	0.984257i	$0.556556\pi$
$720$	−57.2703	−2.13434
$721$	5.63424	0.209830
$722$	−1.05207	−0.0391542
$723$	−16.7079	−0.621375
$724$	21.1092	0.784519
$725$	41.8376	1.55381
$726$	19.4337	0.721252
$727$	−13.0875	−0.485390	−0.242695	−	0.970103i	$-0.578031\pi$
$727$	−13.0875	−0.485390	−0.242695	+	0.970103i	$0.578031\pi$
$728$	−4.09200	−0.151659
$729$	−27.5476	−1.02028
$730$	−39.6307	−1.46680
$731$	14.7571	0.545812
$732$	−9.37649	−0.346565
$733$	9.45256	0.349138	0.174569	−	0.984645i	$-0.444147\pi$
$733$	9.45256	0.349138	0.174569	+	0.984645i	$0.444147\pi$
$734$	−12.0630	−0.445253
$735$	−9.32548	−0.343975
$736$	12.0700	0.444906
$737$	29.5202	1.08739
$738$	0.857737	0.0315737
$739$	−9.94234	−0.365735	−0.182867	−	0.983138i	$-0.558538\pi$
$739$	−9.94234	−0.365735	−0.182867	+	0.983138i	$0.558538\pi$
$740$	6.53172	0.240111
$741$	29.5968	1.08726
$742$	−8.48530	−0.311505
$743$	−34.9617	−1.28262	−0.641310	−	0.767282i	$-0.721609\pi$
$743$	−34.9617	−1.28262	−0.641310	+	0.767282i	$0.721609\pi$
$744$	20.7244	0.759794
$745$	−16.9907	−0.622489
$746$	20.9977	0.768779
$747$	26.7440	0.978511
$748$	33.0993	1.21023
$749$	−13.1722	−0.481301
$750$	73.2090	2.67321
$751$	−28.9130	−1.05505	−0.527526	−	0.849539i	$-0.676880\pi$
$751$	−28.9130	−1.05505	−0.527526	+	0.849539i	$0.676880\pi$
$752$	−28.0769	−1.02386
$753$	74.4710	2.71387
$754$	21.4745	0.782054
$755$	−35.2926	−1.28443
$756$	−0.0866404	−0.00315108
$757$	35.4421	1.28817	0.644083	−	0.764956i	$-0.277239\pi$
$757$	35.4421	1.28817	0.644083	+	0.764956i	$0.277239\pi$
$758$	−16.6800	−0.605843
$759$	19.9821	0.725305
$760$	25.2610	0.916312
$761$	−19.5898	−0.710131	−0.355066	−	0.934841i	$-0.615541\pi$
$761$	−19.5898	−0.710131	−0.355066	+	0.934841i	$0.615541\pi$
$762$	52.2019	1.89108
$763$	−0.250074	−0.00905327
$764$	−16.5135	−0.597436
$765$	−83.9798	−3.03630
$766$	2.15527	0.0778732
$767$	15.7336	0.568109
$768$	−49.7213	−1.79416
$769$	1.48996	0.0537292	0.0268646	−	0.999639i	$-0.491448\pi$
$769$	1.48996	0.0537292	0.0268646	+	0.999639i	$0.491448\pi$
$770$	26.5128	0.955456
$771$	14.0829	0.507184
$772$	−8.42939	−0.303381
$773$	5.34512	0.192251	0.0961253	−	0.995369i	$-0.469355\pi$
$773$	5.34512	0.192251	0.0961253	+	0.995369i	$0.469355\pi$
$774$	10.8839	0.391212
$775$	−52.9013	−1.90027
$776$	−20.2708	−0.727681
$777$	−3.66105	−0.131340
$778$	−45.9468	−1.64727
$779$	−0.705438	−0.0252750
$780$	29.2955	1.04895
$781$	31.8187	1.13856
$782$	26.8214	0.959132
$783$	−0.333503	−0.0119184
$784$	−4.97636	−0.177727
$785$	12.8098	0.457201
$786$	−78.3127	−2.79332
$787$	46.2542	1.64878	0.824391	−	0.566020i	$-0.191518\pi$
$787$	46.2542	1.64878	0.824391	+	0.566020i	$0.191518\pi$
$788$	−15.4100	−0.548957
$789$	19.9068	0.708702
$790$	9.01008	0.320564
$791$	5.38090	0.191323
$792$	−17.9057	−0.636251
$793$	−9.01097	−0.319989
$794$	20.3143	0.720926
$795$	−44.5579	−1.58031
$796$	−17.1363	−0.607382
$797$	12.6251	0.447204	0.223602	−	0.974681i	$-0.428218\pi$
$797$	12.6251	0.447204	0.223602	+	0.974681i	$0.428218\pi$
$798$	19.3035	0.683338
$799$	−41.1714	−1.45654
$800$	54.9383	1.94236
$801$	42.2286	1.49207
$802$	−17.7010	−0.625045
$803$	−23.1035	−0.815305
$804$	21.2744	0.750291
$805$	7.85963	0.277016
$806$	−27.1532	−0.956432
$807$	39.0617	1.37504
$808$	6.77912	0.238489
$809$	−19.9407	−0.701079	−0.350540	−	0.936548i	$-0.614002\pi$
$809$	−19.9407	−0.701079	−0.350540	+	0.936548i	$0.614002\pi$
$810$	60.0692	2.11062
$811$	−12.8648	−0.451743	−0.225872	−	0.974157i	$-0.572523\pi$
$811$	−12.8648	−0.451743	−0.225872	+	0.974157i	$0.572523\pi$
$812$	5.12387	0.179813
$813$	−1.89769	−0.0665548
$814$	10.4086	0.364820
$815$	−10.2396	−0.358676
$816$	−89.1762	−3.12179
$817$	−8.95135	−0.313168
$818$	−33.5742	−1.17390
$819$	−8.25175	−0.288340
$820$	−0.698259	−0.0243842
$821$	34.0293	1.18763	0.593815	−	0.804601i	$-0.297621\pi$
$821$	34.0293	1.18763	0.593815	+	0.804601i	$0.297621\pi$
$822$	31.5725	1.10122
$823$	−28.3781	−0.989200	−0.494600	−	0.869121i	$-0.664685\pi$
$823$	−28.3781	−0.989200	−0.494600	+	0.869121i	$0.664685\pi$
$824$	8.46739	0.294976
$825$	90.9512	3.16652
$826$	10.2618	0.357052
$827$	−50.7391	−1.76437	−0.882186	−	0.470901i	$-0.843929\pi$
$827$	−50.7391	−1.76437	−0.882186	+	0.470901i	$0.843929\pi$
$828$	7.23679	0.251496
$829$	−2.63507	−0.0915199	−0.0457600	−	0.998952i	$-0.514571\pi$
$829$	−2.63507	−0.0915199	−0.0457600	+	0.998952i	$0.514571\pi$
$830$	−59.5121	−2.06569
$831$	32.4300	1.12498
$832$	1.09922	0.0381087
$833$	−7.29722	−0.252834
$834$	−7.04602	−0.243984
$835$	−39.3745	−1.36261
$836$	−20.0773	−0.694387
$837$	0.421695	0.0145759
$838$	61.6320	2.12904
$839$	−2.88734	−0.0996820	−0.0498410	−	0.998757i	$-0.515871\pi$
$839$	−2.88734	−0.0996820	−0.0498410	+	0.998757i	$0.515871\pi$
$840$	−14.0148	−0.483555
$841$	−9.27679	−0.319889
$842$	6.60183	0.227514
$843$	48.7141	1.67780
$844$	32.2150	1.10889
$845$	−21.2133	−0.729759
$846$	−30.3652	−1.04398
$847$	4.45618	0.153116
$848$	−23.7775	−0.816522
$849$	28.5096	0.978447
$850$	122.081	4.18735
$851$	3.08558	0.105772
$852$	22.9309	0.785599
$853$	4.46798	0.152981	0.0764903	−	0.997070i	$-0.475629\pi$
$853$	4.46798	0.152981	0.0764903	+	0.997070i	$0.475629\pi$
$854$	−5.87712	−0.201111
$855$	50.9403	1.74212
$856$	−19.7958	−0.676605
$857$	19.4388	0.664016	0.332008	−	0.943277i	$-0.392274\pi$
$857$	19.4388	0.664016	0.332008	+	0.943277i	$0.392274\pi$
$858$	46.6836	1.59375
$859$	−2.13295	−0.0727753	−0.0363876	−	0.999338i	$-0.511585\pi$
$859$	−2.13295	−0.0727753	−0.0363876	+	0.999338i	$0.511585\pi$
$860$	−8.86024	−0.302132
$861$	0.391376	0.0133381
$862$	−5.41912	−0.184576
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−0.437933	−0.0148988
$865$	48.3486	1.64390
$866$	15.5622	0.528825
$867$	−89.0187	−3.02323
$868$	−6.47885	−0.219906
$869$	5.25261	0.178182
$870$	73.5484	2.49352
$871$	20.4451	0.692755
$872$	−0.375822	−0.0127269
$873$	−40.8774	−1.38349
$874$	−16.2693	−0.550316
$875$	16.7869	0.567502
$876$	−16.6501	−0.562554
$877$	−56.8078	−1.91826	−0.959132	−	0.282958i	$-0.908684\pi$
$877$	−56.8078	−1.91826	−0.959132	+	0.282958i	$0.908684\pi$
$878$	47.3530	1.59809
$879$	−52.7971	−1.78080
$880$	74.2941	2.50446
$881$	19.8945	0.670261	0.335131	−	0.942172i	$-0.391220\pi$
$881$	19.8945	0.670261	0.335131	+	0.942172i	$0.391220\pi$
$882$	−5.38194	−0.181219
$883$	−39.9695	−1.34508	−0.672540	−	0.740060i	$-0.734797\pi$
$883$	−39.9695	−1.34508	−0.672540	+	0.740060i	$0.734797\pi$
$884$	22.9239	0.771013
$885$	53.8865	1.81137
$886$	−69.3851	−2.33104
$887$	−22.2323	−0.746487	−0.373243	−	0.927734i	$-0.621754\pi$
$887$	−22.2323	−0.746487	−0.373243	+	0.927734i	$0.621754\pi$
$888$	−5.50200	−0.184635
$889$	11.9700	0.401460
$890$	−93.9692	−3.14985
$891$	35.0186	1.17317
$892$	23.6585	0.792144
$893$	24.9736	0.835711
$894$	−19.5124	−0.652593
$895$	−11.9016	−0.397827
$896$	−10.9465	−0.365697
$897$	13.8392	0.462077
$898$	−28.7016	−0.957784
$899$	−24.9389	−0.831758
$900$	32.9392	1.09797
$901$	−34.8668	−1.16158
$902$	−1.11270	−0.0370490
$903$	4.96619	0.165265
$904$	8.08667	0.268959
$905$	69.4791	2.30956
$906$	−40.5308	−1.34654
$907$	−9.46897	−0.314412	−0.157206	−	0.987566i	$-0.550249\pi$
$907$	−9.46897	−0.314412	−0.157206	+	0.987566i	$0.550249\pi$
$908$	−22.7260	−0.754187
$909$	13.6705	0.453422
$910$	18.3622	0.608702
$911$	−50.3827	−1.66925	−0.834627	−	0.550815i	$-0.814317\pi$
$911$	−50.3827	−1.66925	−0.834627	+	0.550815i	$0.814317\pi$
$912$	54.0923	1.79118
$913$	−34.6938	−1.14820
$914$	−5.36259	−0.177379
$915$	−30.8619	−1.02026
$916$	−29.1282	−0.962424
$917$	−17.9572	−0.593000
$918$	−0.973154	−0.0321189
$919$	−44.5952	−1.47106	−0.735530	−	0.677492i	$-0.763067\pi$
$919$	−44.5952	−1.47106	−0.735530	+	0.677492i	$0.763067\pi$
$920$	11.8118	0.389424
$921$	7.72191	0.254445
$922$	−21.9104	−0.721582
$923$	22.0370	0.725356
$924$	11.1388	0.366441
$925$	14.0444	0.461778
$926$	−13.2551	−0.435590
$927$	17.0750	0.560817
$928$	25.8992	0.850181
$929$	−10.0779	−0.330644	−0.165322	−	0.986240i	$-0.552866\pi$
$929$	−10.0779	−0.330644	−0.165322	+	0.986240i	$0.552866\pi$
$930$	−92.9977	−3.04952
$931$	4.42633	0.145067
$932$	14.8335	0.485888
$933$	−15.0183	−0.491677
$934$	51.7395	1.69297
$935$	108.943	3.56282
$936$	−12.4011	−0.405343
$937$	43.1967	1.41117	0.705587	−	0.708623i	$-0.250683\pi$
$937$	43.1967	1.41117	0.705587	+	0.708623i	$0.250683\pi$
$938$	13.3346	0.435392
$939$	−25.3444	−0.827082
$940$	24.7194	0.806259
$941$	−56.3024	−1.83541	−0.917703	−	0.397267i	$-0.869959\pi$
$941$	−56.3024	−1.83541	−0.917703	+	0.397267i	$0.869959\pi$
$942$	14.7110	0.479311
$943$	−0.329857	−0.0107416
$944$	28.7555	0.935912
$945$	−0.285169	−0.00927654
$946$	−14.1192	−0.459053
$947$	38.2828	1.24402	0.622012	−	0.783008i	$-0.286315\pi$
$947$	38.2828	1.24402	0.622012	+	0.783008i	$0.286315\pi$
$948$	3.78541	0.122944
$949$	−16.0010	−0.519415
$950$	−74.0518	−2.40256
$951$	−52.2538	−1.69444
$952$	−10.9666	−0.355430
$953$	5.95334	0.192848	0.0964238	−	0.995340i	$-0.469260\pi$
$953$	5.95334	0.192848	0.0964238	+	0.995340i	$0.469260\pi$
$954$	−25.7154	−0.832566
$955$	−54.3525	−1.75881
$956$	30.1309	0.974504
$957$	42.8765	1.38600
$958$	−56.0947	−1.81234
$959$	7.23963	0.233780
$960$	3.76475	0.121507
$961$	0.533771	0.0172184
$962$	7.20876	0.232420
$963$	−39.9193	−1.28638
$964$	7.84970	0.252822
$965$	−27.7446	−0.893129
$966$	9.02617	0.290412
$967$	50.6711	1.62947	0.814736	−	0.579832i	$-0.196882\pi$
$967$	50.6711	1.62947	0.814736	+	0.579832i	$0.196882\pi$
$968$	6.69695	0.215248
$969$	79.3197	2.54812
$970$	90.9624	2.92063
$971$	−53.2975	−1.71040	−0.855199	−	0.518300i	$-0.826565\pi$
$971$	−53.2975	−1.71040	−0.855199	+	0.518300i	$0.826565\pi$
$972$	25.4969	0.817812
$973$	−1.61566	−0.0517958
$974$	50.9626	1.63295
$975$	62.9909	2.01732
$976$	−16.4688	−0.527155
$977$	−8.73166	−0.279351	−0.139675	−	0.990197i	$-0.544606\pi$
$977$	−8.73166	−0.279351	−0.139675	+	0.990197i	$0.544606\pi$
$978$	−11.7593	−0.376022
$979$	−54.7812	−1.75082
$980$	4.38128	0.139955
$981$	−0.757868	−0.0241969
$982$	−22.5794	−0.720538
$983$	29.3197	0.935154	0.467577	−	0.883952i	$-0.345127\pi$
$983$	29.3197	0.935154	0.467577	+	0.883952i	$0.345127\pi$
$984$	0.588179	0.0187504
$985$	−50.7205	−1.61609
$986$	57.5519	1.83283
$987$	−13.8553	−0.441020
$988$	−13.9051	−0.442380
$989$	−4.18557	−0.133093
$990$	80.3492	2.55367
$991$	−55.0749	−1.74951	−0.874755	−	0.484565i	$-0.838978\pi$
$991$	−55.0749	−1.74951	−0.874755	+	0.484565i	$0.838978\pi$
$992$	−32.7480	−1.03975
$993$	85.7695	2.72181
$994$	14.3729	0.455881
$995$	−56.4027	−1.78809
$996$	−25.0029	−0.792246
$997$	31.9901	1.01314	0.506568	−	0.862200i	$-0.330914\pi$
$997$	31.9901	1.01314	0.506568	+	0.862200i	$0.330914\pi$
$998$	−6.59487	−0.208757
$999$	−0.111953	−0.00354205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.19	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.19	✓	83	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.77588 q^{2} -2.45572 q^{3} +1.15374 q^{4} +3.79745 q^{5} +4.36107 q^{6} +1.00000 q^{7} +1.50285 q^{8} +3.03058 q^{9} +O(q^{10})\)	\(q-1.77588 q^{2} -2.45572 q^{3} +1.15374 q^{4} +3.79745 q^{5} +4.36107 q^{6} +1.00000 q^{7} +1.50285 q^{8} +3.03058 q^{9} -6.74380 q^{10} -3.93143 q^{11} -2.83328 q^{12} -2.72283 q^{13} -1.77588 q^{14} -9.32548 q^{15} -4.97636 q^{16} -7.29722 q^{17} -5.38194 q^{18} +4.42633 q^{19} +4.38128 q^{20} -2.45572 q^{21} +6.98175 q^{22} +2.06972 q^{23} -3.69058 q^{24} +9.42059 q^{25} +4.83542 q^{26} -0.0750949 q^{27} +1.15374 q^{28} +4.44108 q^{29} +16.5609 q^{30} -5.61549 q^{31} +5.83172 q^{32} +9.65452 q^{33} +12.9590 q^{34} +3.79745 q^{35} +3.49652 q^{36} +1.49082 q^{37} -7.86063 q^{38} +6.68652 q^{39} +5.70698 q^{40} -0.159373 q^{41} +4.36107 q^{42} -2.02229 q^{43} -4.53587 q^{44} +11.5085 q^{45} -3.67556 q^{46} +5.64206 q^{47} +12.2206 q^{48} +1.00000 q^{49} -16.7298 q^{50} +17.9200 q^{51} -3.14145 q^{52} +4.77808 q^{53} +0.133359 q^{54} -14.9294 q^{55} +1.50285 q^{56} -10.8699 q^{57} -7.88682 q^{58} -5.77842 q^{59} -10.7592 q^{60} +3.30941 q^{61} +9.97244 q^{62} +3.03058 q^{63} -0.403706 q^{64} -10.3398 q^{65} -17.1453 q^{66} -7.50876 q^{67} -8.41913 q^{68} -5.08265 q^{69} -6.74380 q^{70} -8.09341 q^{71} +4.55450 q^{72} +5.87661 q^{73} -2.64752 q^{74} -23.1344 q^{75} +5.10686 q^{76} -3.93143 q^{77} -11.8744 q^{78} -1.33605 q^{79} -18.8975 q^{80} -8.90733 q^{81} +0.283027 q^{82} +8.82471 q^{83} -2.83328 q^{84} -27.7108 q^{85} +3.59135 q^{86} -10.9061 q^{87} -5.90834 q^{88} +13.9342 q^{89} -20.4376 q^{90} -2.72283 q^{91} +2.38792 q^{92} +13.7901 q^{93} -10.0196 q^{94} +16.8088 q^{95} -14.3211 q^{96} -13.4883 q^{97} -1.77588 q^{98} -11.9145 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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