LMFDB - Embedded newform 6031.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05458 q^{2} +0.484378 q^{3} +2.22130 q^{4} -1.81809 q^{5} -0.995193 q^{6} -4.27361 q^{7} -0.454677 q^{8} -2.76538 q^{9} +O(q^{10})$	\(q-2.05458 q^{2} +0.484378 q^{3} +2.22130 q^{4} -1.81809 q^{5} -0.995193 q^{6} -4.27361 q^{7} -0.454677 q^{8} -2.76538 q^{9} +3.73540 q^{10} +2.30129 q^{11} +1.07595 q^{12} -6.64958 q^{13} +8.78047 q^{14} -0.880640 q^{15} -3.50843 q^{16} +0.288851 q^{17} +5.68169 q^{18} -2.80501 q^{19} -4.03851 q^{20} -2.07004 q^{21} -4.72818 q^{22} +7.92686 q^{23} -0.220235 q^{24} -1.69457 q^{25} +13.6621 q^{26} -2.79262 q^{27} -9.49297 q^{28} +2.79620 q^{29} +1.80935 q^{30} +2.84918 q^{31} +8.11770 q^{32} +1.11469 q^{33} -0.593468 q^{34} +7.76979 q^{35} -6.14273 q^{36} +1.00000 q^{37} +5.76312 q^{38} -3.22091 q^{39} +0.826641 q^{40} +5.21581 q^{41} +4.25307 q^{42} +8.33510 q^{43} +5.11185 q^{44} +5.02769 q^{45} -16.2864 q^{46} +1.07114 q^{47} -1.69940 q^{48} +11.2637 q^{49} +3.48162 q^{50} +0.139913 q^{51} -14.7707 q^{52} +13.7206 q^{53} +5.73766 q^{54} -4.18394 q^{55} +1.94311 q^{56} -1.35868 q^{57} -5.74503 q^{58} -0.462463 q^{59} -1.95616 q^{60} -8.30532 q^{61} -5.85388 q^{62} +11.8181 q^{63} -9.66161 q^{64} +12.0895 q^{65} -2.29023 q^{66} -13.1382 q^{67} +0.641625 q^{68} +3.83959 q^{69} -15.9636 q^{70} +15.8523 q^{71} +1.25735 q^{72} +5.56374 q^{73} -2.05458 q^{74} -0.820810 q^{75} -6.23077 q^{76} -9.83482 q^{77} +6.61762 q^{78} -7.83484 q^{79} +6.37862 q^{80} +6.94345 q^{81} -10.7163 q^{82} -4.75478 q^{83} -4.59818 q^{84} -0.525156 q^{85} -17.1251 q^{86} +1.35442 q^{87} -1.04634 q^{88} -7.59979 q^{89} -10.3298 q^{90} +28.4177 q^{91} +17.6079 q^{92} +1.38008 q^{93} -2.20073 q^{94} +5.09975 q^{95} +3.93203 q^{96} +15.9962 q^{97} -23.1423 q^{98} -6.36394 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) $ 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * 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 $

$2$	−2.05458	−1.45281	−0.726404	−	0.687268i	$-0.758810\pi$
$2$	−2.05458	−1.45281	−0.726404	+	0.687268i	$0.758810\pi$
$3$	0.484378	0.279656	0.139828	−	0.990176i	$-0.455345\pi$
$3$	0.484378	0.279656	0.139828	+	0.990176i	$0.455345\pi$
$4$	2.22130	1.11065
$5$	−1.81809	−0.813072	−0.406536	−	0.913635i	$-0.633264\pi$
$5$	−1.81809	−0.813072	−0.406536	+	0.913635i	$0.633264\pi$
$6$	−0.995193	−0.406286
$7$	−4.27361	−1.61527	−0.807636	−	0.589681i	$-0.799254\pi$
$7$	−4.27361	−1.61527	−0.807636	+	0.589681i	$0.799254\pi$
$8$	−0.454677	−0.160752
$9$	−2.76538	−0.921793
$10$	3.73540	1.18124
$11$	2.30129	0.693865	0.346933	−	0.937890i	$-0.387223\pi$
$11$	2.30129	0.693865	0.346933	+	0.937890i	$0.387223\pi$
$12$	1.07595	0.310599
$13$	−6.64958	−1.84426	−0.922131	−	0.386877i	$-0.873554\pi$
$13$	−6.64958	−1.84426	−0.922131	+	0.386877i	$0.873554\pi$
$14$	8.78047	2.34668
$15$	−0.880640	−0.227380
$16$	−3.50843	−0.877107
$17$	0.288851	0.0700567	0.0350283	−	0.999386i	$-0.488848\pi$
$17$	0.288851	0.0700567	0.0350283	+	0.999386i	$0.488848\pi$
$18$	5.68169	1.33919
$19$	−2.80501	−0.643514	−0.321757	−	0.946822i	$-0.604273\pi$
$19$	−2.80501	−0.643514	−0.321757	+	0.946822i	$0.604273\pi$
$20$	−4.03851	−0.903039
$21$	−2.07004	−0.451720
$22$	−4.72818	−1.00805
$23$	7.92686	1.65286	0.826432	−	0.563037i	$-0.190367\pi$
$23$	7.92686	1.65286	0.826432	+	0.563037i	$0.190367\pi$
$24$	−0.220235	−0.0449553
$25$	−1.69457	−0.338913
$26$	13.6621	2.67936
$27$	−2.79262	−0.537440
$28$	−9.49297	−1.79400
$29$	2.79620	0.519242	0.259621	−	0.965711i	$-0.416402\pi$
$29$	2.79620	0.519242	0.259621	+	0.965711i	$0.416402\pi$
$30$	1.80935	0.330340
$31$	2.84918	0.511729	0.255864	−	0.966713i	$-0.417640\pi$
$31$	2.84918	0.511729	0.255864	+	0.966713i	$0.417640\pi$
$32$	8.11770	1.43502
$33$	1.11469	0.194043
$34$	−0.593468	−0.101779
$35$	7.76979	1.31333
$36$	−6.14273	−1.02379
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	5.76312	0.934901
$39$	−3.22091	−0.515758
$40$	0.826641	0.130703
$41$	5.21581	0.814572	0.407286	−	0.913301i	$-0.366475\pi$
$41$	5.21581	0.814572	0.407286	+	0.913301i	$0.366475\pi$
$42$	4.25307	0.656262
$43$	8.33510	1.27109	0.635546	−	0.772063i	$-0.280775\pi$
$43$	8.33510	1.27109	0.635546	+	0.772063i	$0.280775\pi$
$44$	5.11185	0.770641
$45$	5.02769	0.749484
$46$	−16.2864	−2.40129
$47$	1.07114	0.156241	0.0781206	−	0.996944i	$-0.475108\pi$
$47$	1.07114	0.156241	0.0781206	+	0.996944i	$0.475108\pi$
$48$	−1.69940	−0.245288
$49$	11.2637	1.60911
$50$	3.48162	0.492376
$51$	0.139913	0.0195917
$52$	−14.7707	−2.04833
$53$	13.7206	1.88468	0.942338	−	0.334664i	$-0.108623\pi$
$53$	13.7206	1.88468	0.942338	+	0.334664i	$0.108623\pi$
$54$	5.73766	0.780797
$55$	−4.18394	−0.564163
$56$	1.94311	0.259659
$57$	−1.35868	−0.179962
$58$	−5.74503	−0.754359
$59$	−0.462463	−0.0602075	−0.0301038	−	0.999547i	$-0.509584\pi$
$59$	−0.462463	−0.0602075	−0.0301038	+	0.999547i	$0.509584\pi$
$60$	−1.95616	−0.252540
$61$	−8.30532	−1.06339	−0.531694	−	0.846937i	$-0.678444\pi$
$61$	−8.30532	−1.06339	−0.531694	+	0.846937i	$0.678444\pi$
$62$	−5.85388	−0.743443
$63$	11.8181	1.48895
$64$	−9.66161	−1.20770
$65$	12.0895	1.49952
$66$	−2.29023	−0.281907
$67$	−13.1382	−1.60508	−0.802542	−	0.596596i	$-0.796519\pi$
$67$	−13.1382	−1.60508	−0.802542	+	0.596596i	$0.796519\pi$
$68$	0.641625	0.0778084
$69$	3.83959	0.462233
$70$	−15.9636	−1.90802
$71$	15.8523	1.88132	0.940659	−	0.339354i	$-0.110208\pi$
$71$	15.8523	1.88132	0.940659	+	0.339354i	$0.110208\pi$
$72$	1.25735	0.148180
$73$	5.56374	0.651186	0.325593	−	0.945510i	$-0.394436\pi$
$73$	5.56374	0.651186	0.325593	+	0.945510i	$0.394436\pi$
$74$	−2.05458	−0.238840
$75$	−0.820810	−0.0947790
$76$	−6.23077	−0.714718
$77$	−9.83482	−1.12078
$78$	6.61762	0.749298
$79$	−7.83484	−0.881488	−0.440744	−	0.897633i	$-0.645285\pi$
$79$	−7.83484	−0.881488	−0.440744	+	0.897633i	$0.645285\pi$
$80$	6.37862	0.713152
$81$	6.94345	0.771495
$82$	−10.7163	−1.18342
$83$	−4.75478	−0.521905	−0.260953	−	0.965352i	$-0.584037\pi$
$83$	−4.75478	−0.521905	−0.260953	+	0.965352i	$0.584037\pi$
$84$	−4.59818	−0.501703
$85$	−0.525156	−0.0569612
$86$	−17.1251	−1.84665
$87$	1.35442	0.145209
$88$	−1.04634	−0.111541
$89$	−7.59979	−0.805577	−0.402788	−	0.915293i	$-0.631959\pi$
$89$	−7.59979	−0.805577	−0.402788	+	0.915293i	$0.631959\pi$
$90$	−10.3298	−1.08886
$91$	28.4177	2.97899
$92$	17.6079	1.83575
$93$	1.38008	0.143108
$94$	−2.20073	−0.226988
$95$	5.09975	0.523223
$96$	3.93203	0.401311
$97$	15.9962	1.62417	0.812085	−	0.583539i	$-0.198332\pi$
$97$	15.9962	1.62417	0.812085	+	0.583539i	$0.198332\pi$
$98$	−23.1423	−2.33772
$99$	−6.36394	−0.639600
$100$	−3.76414	−0.376414
$101$	−11.0471	−1.09923	−0.549615	−	0.835418i	$-0.685226\pi$
$101$	−11.0471	−1.09923	−0.549615	+	0.835418i	$0.685226\pi$
$102$	−0.287463	−0.0284630
$103$	−16.5560	−1.63131	−0.815657	−	0.578536i	$-0.803624\pi$
$103$	−16.5560	−1.63131	−0.815657	+	0.578536i	$0.803624\pi$
$104$	3.02341	0.296470
$105$	3.76351	0.367281
$106$	−28.1902	−2.73807
$107$	18.3110	1.77020	0.885098	−	0.465405i	$-0.154091\pi$
$107$	18.3110	1.77020	0.885098	+	0.465405i	$0.154091\pi$
$108$	−6.20325	−0.596908
$109$	9.59899	0.919416	0.459708	−	0.888070i	$-0.347954\pi$
$109$	9.59899	0.919416	0.459708	+	0.888070i	$0.347954\pi$
$110$	8.59624	0.819620
$111$	0.484378	0.0459751
$112$	14.9937	1.41677
$113$	−2.31495	−0.217772	−0.108886	−	0.994054i	$-0.534728\pi$
$113$	−2.31495	−0.217772	−0.108886	+	0.994054i	$0.534728\pi$
$114$	2.79153	0.261450
$115$	−14.4117	−1.34390
$116$	6.21121	0.576696
$117$	18.3886	1.70003
$118$	0.950167	0.0874699
$119$	−1.23444	−0.113161
$120$	0.400406	0.0365519
$121$	−5.70406	−0.518551
$122$	17.0639	1.54490
$123$	2.52642	0.227800
$124$	6.32889	0.568351
$125$	12.1713	1.08863
$126$	−24.2813	−2.16315
$127$	2.04434	0.181406	0.0907028	−	0.995878i	$-0.471089\pi$
$127$	2.04434	0.181406	0.0907028	+	0.995878i	$0.471089\pi$
$128$	3.61515	0.319537
$129$	4.03734	0.355468
$130$	−24.8389	−2.17851
$131$	−9.19590	−0.803450	−0.401725	−	0.915760i	$-0.631589\pi$
$131$	−9.19590	−0.803450	−0.401725	+	0.915760i	$0.631589\pi$
$132$	2.47607	0.215514
$133$	11.9875	1.03945
$134$	26.9934	2.33188
$135$	5.07722	0.436978
$136$	−0.131334	−0.0112618
$137$	−14.6187	−1.24896	−0.624478	−	0.781042i	$-0.714688\pi$
$137$	−14.6187	−1.24896	−0.624478	+	0.781042i	$0.714688\pi$
$138$	−7.88875	−0.671535
$139$	15.3189	1.29933	0.649664	−	0.760221i	$-0.274910\pi$
$139$	15.3189	1.29933	0.649664	+	0.760221i	$0.274910\pi$
$140$	17.2590	1.45865
$141$	0.518834	0.0436937
$142$	−32.5697	−2.73319
$143$	−15.3026	−1.27967
$144$	9.70213	0.808511
$145$	−5.08374	−0.422182
$146$	−11.4311	−0.946048
$147$	5.45590	0.449995
$148$	2.22130	0.182590
$149$	−14.6410	−1.19944	−0.599718	−	0.800211i	$-0.704721\pi$
$149$	−14.6410	−1.19944	−0.599718	+	0.800211i	$0.704721\pi$
$150$	1.68642	0.137696
$151$	−4.33329	−0.352638	−0.176319	−	0.984333i	$-0.556419\pi$
$151$	−4.33329	−0.352638	−0.176319	+	0.984333i	$0.556419\pi$
$152$	1.27537	0.103446
$153$	−0.798783	−0.0645777
$154$	20.2064	1.62828
$155$	−5.18006	−0.416072
$156$	−7.15460	−0.572827
$157$	4.34284	0.346596	0.173298	−	0.984869i	$-0.444558\pi$
$157$	4.34284	0.346596	0.173298	+	0.984869i	$0.444558\pi$
$158$	16.0973	1.28063
$159$	6.64597	0.527060
$160$	−14.7587	−1.16678
$161$	−33.8763	−2.66983
$162$	−14.2659	−1.12083
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	11.5859	0.904704
$165$	−2.02661	−0.157771
$166$	9.76908	0.758228
$167$	−2.56295	−0.198327	−0.0991634	−	0.995071i	$-0.531617\pi$
$167$	−2.56295	−0.198327	−0.0991634	+	0.995071i	$0.531617\pi$
$168$	0.941199	0.0726151
$169$	31.2170	2.40130
$170$	1.07898	0.0827536
$171$	7.75692	0.593186
$172$	18.5148	1.41174
$173$	−9.06215	−0.688983	−0.344491	−	0.938790i	$-0.611949\pi$
$173$	−9.06215	−0.688983	−0.344491	+	0.938790i	$0.611949\pi$
$174$	−2.78276	−0.210961
$175$	7.24191	0.547437
$176$	−8.07391	−0.608594
$177$	−0.224007	−0.0168374
$178$	15.6144	1.17035
$179$	−21.0918	−1.57647	−0.788237	−	0.615372i	$-0.789006\pi$
$179$	−21.0918	−1.57647	−0.788237	+	0.615372i	$0.789006\pi$
$180$	11.1680	0.832414
$181$	−16.8034	−1.24898	−0.624492	−	0.781031i	$-0.714694\pi$
$181$	−16.8034	−1.24898	−0.624492	+	0.781031i	$0.714694\pi$
$182$	−58.3865	−4.32789
$183$	−4.02291	−0.297382
$184$	−3.60416	−0.265702
$185$	−1.81809	−0.133668
$186$	−2.83549	−0.207908
$187$	0.664730	0.0486099
$188$	2.37931	0.173529
$189$	11.9346	0.868112
$190$	−10.4778	−0.760143
$191$	9.18287	0.664449	0.332225	−	0.943200i	$-0.392201\pi$
$191$	9.18287	0.664449	0.332225	+	0.943200i	$0.392201\pi$
$192$	−4.67987	−0.337740
$193$	2.32341	0.167242	0.0836212	−	0.996498i	$-0.473351\pi$
$193$	2.32341	0.167242	0.0836212	+	0.996498i	$0.473351\pi$
$194$	−32.8655	−2.35961
$195$	5.85589	0.419349
$196$	25.0201	1.78715
$197$	12.9928	0.925699	0.462850	−	0.886437i	$-0.346827\pi$
$197$	12.9928	0.925699	0.462850	+	0.886437i	$0.346827\pi$
$198$	13.0752	0.929215
$199$	12.3984	0.878899	0.439450	−	0.898267i	$-0.355174\pi$
$199$	12.3984	0.878899	0.439450	+	0.898267i	$0.355174\pi$
$200$	0.770479	0.0544811
$201$	−6.36384	−0.448870
$202$	22.6972	1.59697
$203$	−11.9499	−0.838718
$204$	0.310789	0.0217596
$205$	−9.48278	−0.662306
$206$	34.0157	2.36998
$207$	−21.9208	−1.52360
$208$	23.3296	1.61762
$209$	−6.45514	−0.446512
$210$	−7.73244	−0.533589
$211$	−17.8564	−1.22929	−0.614644	−	0.788805i	$-0.710700\pi$
$211$	−17.8564	−1.22929	−0.614644	+	0.788805i	$0.710700\pi$
$212$	30.4776	2.09321
$213$	7.67848	0.526121
$214$	−37.6215	−2.57175
$215$	−15.1539	−1.03349
$216$	1.26974	0.0863948
$217$	−12.1763	−0.826581
$218$	−19.7219	−1.33573
$219$	2.69495	0.182108
$220$	−9.29379	−0.626587
$221$	−1.92074	−0.129203
$222$	−0.995193	−0.0667930
$223$	−6.39217	−0.428051	−0.214026	−	0.976828i	$-0.568658\pi$
$223$	−6.39217	−0.428051	−0.214026	+	0.976828i	$0.568658\pi$
$224$	−34.6919	−2.31795
$225$	4.68611	0.312408
$226$	4.75624	0.316381
$227$	6.87242	0.456138	0.228069	−	0.973645i	$-0.426759\pi$
$227$	6.87242	0.456138	0.228069	+	0.973645i	$0.426759\pi$
$228$	−3.01805	−0.199875
$229$	18.4374	1.21837	0.609187	−	0.793026i	$-0.291496\pi$
$229$	18.4374	1.21837	0.609187	+	0.793026i	$0.291496\pi$
$230$	29.6100	1.95242
$231$	−4.76377	−0.313433
$232$	−1.27137	−0.0834695
$233$	−3.30906	−0.216784	−0.108392	−	0.994108i	$-0.534570\pi$
$233$	−3.30906	−0.216784	−0.108392	+	0.994108i	$0.534570\pi$
$234$	−37.7809	−2.46981
$235$	−1.94742	−0.127035
$236$	−1.02727	−0.0668695
$237$	−3.79502	−0.246513
$238$	2.53625	0.164401
$239$	−18.2677	−1.18164	−0.590821	−	0.806803i	$-0.701196\pi$
$239$	−18.2677	−1.18164	−0.590821	+	0.806803i	$0.701196\pi$
$240$	3.08966	0.199437
$241$	−24.1839	−1.55782	−0.778909	−	0.627136i	$-0.784227\pi$
$241$	−24.1839	−1.55782	−0.778909	+	0.627136i	$0.784227\pi$
$242$	11.7195	0.753355
$243$	11.7411	0.753193
$244$	−18.4486	−1.18105
$245$	−20.4784	−1.30832
$246$	−5.19073	−0.330949
$247$	18.6522	1.18681
$248$	−1.29546	−0.0822616
$249$	−2.30311	−0.145954
$250$	−25.0069	−1.58157
$251$	−19.8987	−1.25599	−0.627997	−	0.778216i	$-0.716125\pi$
$251$	−19.8987	−1.25599	−0.627997	+	0.778216i	$0.716125\pi$
$252$	26.2516	1.65370
$253$	18.2420	1.14686
$254$	−4.20026	−0.263547
$255$	−0.254374	−0.0159295
$256$	11.8956	0.743476
$257$	7.54424	0.470597	0.235298	−	0.971923i	$-0.424393\pi$
$257$	7.54424	0.470597	0.235298	+	0.971923i	$0.424393\pi$
$258$	−8.29503	−0.516426
$259$	−4.27361	−0.265549
$260$	26.8544	1.66544
$261$	−7.73256	−0.478634
$262$	18.8937	1.16726
$263$	9.54568	0.588612	0.294306	−	0.955711i	$-0.404912\pi$
$263$	9.54568	0.588612	0.294306	+	0.955711i	$0.404912\pi$
$264$	−0.506825	−0.0311929
$265$	−24.9453	−1.53238
$266$	−24.6293	−1.51012
$267$	−3.68117	−0.225284
$268$	−29.1838	−1.78268
$269$	22.0115	1.34207	0.671034	−	0.741427i	$-0.265851\pi$
$269$	22.0115	1.34207	0.671034	+	0.741427i	$0.265851\pi$
$270$	−10.4316	−0.634845
$271$	−22.6244	−1.37433	−0.687166	−	0.726501i	$-0.741145\pi$
$271$	−22.6244	−1.37433	−0.687166	+	0.726501i	$0.741145\pi$
$272$	−1.01341	−0.0614472
$273$	13.7649	0.833090
$274$	30.0352	1.81449
$275$	−3.89969	−0.235160
$276$	8.52888	0.513378
$277$	27.2954	1.64002	0.820012	−	0.572346i	$-0.193967\pi$
$277$	27.2954	1.64002	0.820012	+	0.572346i	$0.193967\pi$
$278$	−31.4738	−1.88767
$279$	−7.87907	−0.471708
$280$	−3.53274	−0.211122
$281$	20.7234	1.23625	0.618127	−	0.786078i	$-0.287892\pi$
$281$	20.7234	1.23625	0.618127	+	0.786078i	$0.287892\pi$
$282$	−1.06599	−0.0634785
$283$	−17.2615	−1.02609	−0.513044	−	0.858362i	$-0.671482\pi$
$283$	−17.2615	−1.02609	−0.513044	+	0.858362i	$0.671482\pi$
$284$	35.2126	2.08948
$285$	2.47020	0.146322
$286$	31.4405	1.85911
$287$	−22.2903	−1.31576
$288$	−22.4485	−1.32279
$289$	−16.9166	−0.995092
$290$	10.4449	0.613348
$291$	7.74821	0.454208
$292$	12.3587	0.723240
$293$	24.4781	1.43003	0.715014	−	0.699111i	$-0.246420\pi$
$293$	24.4781	1.43003	0.715014	+	0.699111i	$0.246420\pi$
$294$	−11.2096	−0.653757
$295$	0.840797	0.0489531
$296$	−0.454677	−0.0264275
$297$	−6.42663	−0.372911
$298$	30.0811	1.74255
$299$	−52.7103	−3.04831
$300$	−1.82326	−0.105266
$301$	−35.6210	−2.05316
$302$	8.90310	0.512316
$303$	−5.35098	−0.307406
$304$	9.84118	0.564430
$305$	15.0998	0.864611
$306$	1.64116	0.0938190
$307$	−6.24777	−0.356579	−0.178289	−	0.983978i	$-0.557056\pi$
$307$	−6.24777	−0.356579	−0.178289	+	0.983978i	$0.557056\pi$
$308$	−21.8461	−1.24480
$309$	−8.01937	−0.456206
$310$	10.6428	0.604473
$311$	24.1016	1.36668	0.683339	−	0.730101i	$-0.260527\pi$
$311$	24.1016	1.36668	0.683339	+	0.730101i	$0.260527\pi$
$312$	1.46447	0.0829094
$313$	−27.5097	−1.55494	−0.777470	−	0.628919i	$-0.783498\pi$
$313$	−27.5097	−1.55494	−0.777470	+	0.628919i	$0.783498\pi$
$314$	−8.92271	−0.503538
$315$	−21.4864	−1.21062
$316$	−17.4035	−0.979024
$317$	−1.27101	−0.0713868	−0.0356934	−	0.999363i	$-0.511364\pi$
$317$	−1.27101	−0.0713868	−0.0356934	+	0.999363i	$0.511364\pi$
$318$	−13.6547	−0.765717
$319$	6.43488	0.360284
$320$	17.5656	0.981948
$321$	8.86946	0.495045
$322$	69.6015	3.87874
$323$	−0.810231	−0.0450824
$324$	15.4235	0.856860
$325$	11.2682	0.625045
$326$	−2.05458	−0.113793
$327$	4.64954	0.257120
$328$	−2.37151	−0.130944
$329$	−4.57761	−0.252372
$330$	4.16383	0.229211
$331$	−2.99464	−0.164600	−0.0823001	−	0.996608i	$-0.526227\pi$
$331$	−2.99464	−0.164600	−0.0823001	+	0.996608i	$0.526227\pi$
$332$	−10.5618	−0.579654
$333$	−2.76538	−0.151542
$334$	5.26578	0.288131
$335$	23.8863	1.30505
$336$	7.26259	0.396207
$337$	−17.6982	−0.964081	−0.482040	−	0.876149i	$-0.660104\pi$
$337$	−17.6982	−0.964081	−0.482040	+	0.876149i	$0.660104\pi$
$338$	−64.1377	−3.48863
$339$	−1.12131	−0.0609011
$340$	−1.16653	−0.0632639
$341$	6.55680	0.355071
$342$	−15.9372	−0.861785
$343$	−18.2216	−0.983872
$344$	−3.78978	−0.204331
$345$	−6.98071	−0.375829
$346$	18.6189	1.00096
$347$	−0.583025	−0.0312984	−0.0156492	−	0.999878i	$-0.504981\pi$
$347$	−0.583025	−0.0312984	−0.0156492	+	0.999878i	$0.504981\pi$
$348$	3.00857	0.161276
$349$	22.7142	1.21586	0.607930	−	0.793990i	$-0.292000\pi$
$349$	22.7142	1.21586	0.607930	+	0.793990i	$0.292000\pi$
$350$	−14.8791	−0.795321
$351$	18.5698	0.991181
$352$	18.6812	0.995710
$353$	30.0830	1.60116	0.800579	−	0.599227i	$-0.204525\pi$
$353$	30.0830	1.60116	0.800579	+	0.599227i	$0.204525\pi$
$354$	0.460240	0.0244615
$355$	−28.8208	−1.52965
$356$	−16.8814	−0.894713
$357$	−0.597934	−0.0316460
$358$	43.3348	2.29031
$359$	16.2150	0.855797	0.427899	−	0.903827i	$-0.359254\pi$
$359$	16.2150	0.855797	0.427899	+	0.903827i	$0.359254\pi$
$360$	−2.28597	−0.120481
$361$	−11.1319	−0.585890
$362$	34.5238	1.81453
$363$	−2.76292	−0.145016
$364$	63.1243	3.30861
$365$	−10.1154	−0.529462
$366$	8.26539	0.432039
$367$	−26.9437	−1.40645	−0.703224	−	0.710969i	$-0.748257\pi$
$367$	−26.9437	−1.40645	−0.703224	+	0.710969i	$0.748257\pi$
$368$	−27.8108	−1.44974
$369$	−14.4237	−0.750867
$370$	3.73540	0.194194
$371$	−58.6367	−3.04426
$372$	3.06557	0.158943
$373$	11.2311	0.581526	0.290763	−	0.956795i	$-0.406091\pi$
$373$	11.2311	0.581526	0.290763	+	0.956795i	$0.406091\pi$
$374$	−1.36574	−0.0706208
$375$	5.89550	0.304442
$376$	−0.487020	−0.0251161
$377$	−18.5936	−0.957619
$378$	−24.5205	−1.26120
$379$	24.8500	1.27646	0.638229	−	0.769846i	$-0.279667\pi$
$379$	24.8500	1.27646	0.638229	+	0.769846i	$0.279667\pi$
$380$	11.3281	0.581118
$381$	0.990232	0.0507311
$382$	−18.8669	−0.965317
$383$	23.2709	1.18909	0.594543	−	0.804064i	$-0.297333\pi$
$383$	23.2709	1.18909	0.594543	+	0.804064i	$0.297333\pi$
$384$	1.75110	0.0893603
$385$	17.8805	0.911276
$386$	−4.77362	−0.242971
$387$	−23.0497	−1.17168
$388$	35.5324	1.80388
$389$	0.711711	0.0360852	0.0180426	−	0.999837i	$-0.494257\pi$
$389$	0.711711	0.0360852	0.0180426	+	0.999837i	$0.494257\pi$
$390$	−12.0314	−0.609233
$391$	2.28968	0.115794
$392$	−5.12136	−0.258668
$393$	−4.45429	−0.224689
$394$	−26.6948	−1.34486
$395$	14.2444	0.716714
$396$	−14.1362	−0.710371
$397$	−8.84535	−0.443935	−0.221968	−	0.975054i	$-0.571248\pi$
$397$	−8.84535	−0.443935	−0.221968	+	0.975054i	$0.571248\pi$
$398$	−25.4735	−1.27687
$399$	5.80649	0.290688
$400$	5.94526	0.297263
$401$	23.8728	1.19215	0.596076	−	0.802928i	$-0.296726\pi$
$401$	23.8728	1.19215	0.596076	+	0.802928i	$0.296726\pi$
$402$	13.0750	0.652122
$403$	−18.9459	−0.943762
$404$	−24.5390	−1.22086
$405$	−12.6238	−0.627281
$406$	24.5520	1.21850
$407$	2.30129	0.114071
$408$	−0.0636152	−0.00314942
$409$	−26.2441	−1.29769	−0.648843	−	0.760922i	$-0.724747\pi$
$409$	−26.2441	−1.29769	−0.648843	+	0.760922i	$0.724747\pi$
$410$	19.4831	0.962203
$411$	−7.08096	−0.349278
$412$	−36.7759	−1.81182
$413$	1.97639	0.0972516
$414$	45.0379	2.21349
$415$	8.64460	0.424347
$416$	−53.9793	−2.64655
$417$	7.42011	0.363364
$418$	13.2626	0.648695
$419$	9.59250	0.468624	0.234312	−	0.972161i	$-0.424716\pi$
$419$	9.59250	0.468624	0.234312	+	0.972161i	$0.424716\pi$
$420$	8.35988	0.407921
$421$	38.5079	1.87676	0.938379	−	0.345608i	$-0.112327\pi$
$421$	38.5079	1.87676	0.938379	+	0.345608i	$0.112327\pi$
$422$	36.6875	1.78592
$423$	−2.96209	−0.144022
$424$	−6.23846	−0.302966
$425$	−0.489477	−0.0237431
$426$	−15.7761	−0.764353
$427$	35.4937	1.71766
$428$	40.6743	1.96607
$429$	−7.41225	−0.357867
$430$	31.1350	1.50146
$431$	−38.6645	−1.86240	−0.931201	−	0.364506i	$-0.881238\pi$
$431$	−38.6645	−1.86240	−0.931201	+	0.364506i	$0.881238\pi$
$432$	9.79771	0.471393
$433$	17.4178	0.837044	0.418522	−	0.908207i	$-0.362548\pi$
$433$	17.4178	0.837044	0.418522	+	0.908207i	$0.362548\pi$
$434$	25.0172	1.20086
$435$	−2.46245	−0.118065
$436$	21.3222	1.02115
$437$	−22.2349	−1.06364
$438$	−5.53699	−0.264568
$439$	−8.36678	−0.399325	−0.199662	−	0.979865i	$-0.563985\pi$
$439$	−8.36678	−0.399325	−0.199662	+	0.979865i	$0.563985\pi$
$440$	1.90234	0.0906905
$441$	−31.1485	−1.48326
$442$	3.94631	0.187707
$443$	9.10961	0.432811	0.216405	−	0.976304i	$-0.430567\pi$
$443$	9.10961	0.432811	0.216405	+	0.976304i	$0.430567\pi$
$444$	1.07595	0.0510622
$445$	13.8171	0.654992
$446$	13.1332	0.621876
$447$	−7.09177	−0.335429
$448$	41.2899	1.95077
$449$	14.7523	0.696204	0.348102	−	0.937457i	$-0.386826\pi$
$449$	14.7523	0.696204	0.348102	+	0.937457i	$0.386826\pi$
$450$	−9.62800	−0.453868
$451$	12.0031	0.565203
$452$	−5.14219	−0.241868
$453$	−2.09895	−0.0986173
$454$	−14.1199	−0.662681
$455$	−51.6658	−2.42213
$456$	0.617762	0.0289294
$457$	−24.5453	−1.14818	−0.574091	−	0.818791i	$-0.694645\pi$
$457$	−24.5453	−1.14818	−0.574091	+	0.818791i	$0.694645\pi$
$458$	−37.8810	−1.77006
$459$	−0.806652	−0.0376513
$460$	−32.0127	−1.49260
$461$	21.7357	1.01233	0.506167	−	0.862436i	$-0.331062\pi$
$461$	21.7357	1.01233	0.506167	+	0.862436i	$0.331062\pi$
$462$	9.78754	0.455357
$463$	18.4562	0.857731	0.428865	−	0.903368i	$-0.358913\pi$
$463$	18.4562	0.857731	0.428865	+	0.903368i	$0.358913\pi$
$464$	−9.81028	−0.455431
$465$	−2.50911	−0.116357
$466$	6.79873	0.314945
$467$	1.42005	0.0657119	0.0328559	−	0.999460i	$-0.489540\pi$
$467$	1.42005	0.0657119	0.0328559	+	0.999460i	$0.489540\pi$
$468$	40.8466	1.88814
$469$	56.1474	2.59265
$470$	4.00112	0.184558
$471$	2.10357	0.0969276
$472$	0.210271	0.00967851
$473$	19.1815	0.881966
$474$	7.79717	0.358136
$475$	4.75327	0.218095
$476$	−2.74205	−0.125682
$477$	−37.9428	−1.73728
$478$	37.5325	1.71670
$479$	14.7075	0.672005	0.336003	−	0.941861i	$-0.390925\pi$
$479$	14.7075	0.672005	0.336003	+	0.941861i	$0.390925\pi$
$480$	−7.14877	−0.326295
$481$	−6.64958	−0.303195
$482$	49.6877	2.26321
$483$	−16.4089	−0.746632
$484$	−12.6704	−0.575929
$485$	−29.0825	−1.32057
$486$	−24.1231	−1.09424
$487$	8.85526	0.401270	0.200635	−	0.979666i	$-0.435699\pi$
$487$	8.85526	0.401270	0.200635	+	0.979666i	$0.435699\pi$
$488$	3.77623	0.170942
$489$	0.484378	0.0219043
$490$	42.0746	1.90074
$491$	−31.9863	−1.44352	−0.721761	−	0.692143i	$-0.756667\pi$
$491$	−31.9863	−1.44352	−0.721761	+	0.692143i	$0.756667\pi$
$492$	5.61194	0.253006
$493$	0.807687	0.0363764
$494$	−38.3223	−1.72420
$495$	11.5702	0.520041
$496$	−9.99616	−0.448841
$497$	−67.7464	−3.03884
$498$	4.73192	0.212043
$499$	12.9214	0.578440	0.289220	−	0.957263i	$-0.406604\pi$
$499$	12.9214	0.578440	0.289220	+	0.957263i	$0.406604\pi$
$500$	27.0361	1.20909
$501$	−1.24143	−0.0554632
$502$	40.8834	1.82472
$503$	29.0892	1.29702	0.648511	−	0.761205i	$-0.275392\pi$
$503$	29.0892	1.29702	0.648511	+	0.761205i	$0.275392\pi$
$504$	−5.37344	−0.239352
$505$	20.0846	0.893754
$506$	−37.4796	−1.66617
$507$	15.1208	0.671538
$508$	4.54109	0.201478
$509$	−33.3090	−1.47640	−0.738199	−	0.674583i	$-0.764323\pi$
$509$	−33.3090	−1.47640	−0.738199	+	0.674583i	$0.764323\pi$
$510$	0.522631	0.0231425
$511$	−23.7772	−1.05184
$512$	−31.6708	−1.39966
$513$	7.83333	0.345850
$514$	−15.5002	−0.683687
$515$	30.1003	1.32638
$516$	8.96813	0.394800
$517$	2.46499	0.108410
$518$	8.78047	0.385792
$519$	−4.38950	−0.192678
$520$	−5.49682	−0.241051
$521$	−37.4731	−1.64173	−0.820863	−	0.571125i	$-0.806507\pi$
$521$	−37.4731	−1.64173	−0.820863	+	0.571125i	$0.806507\pi$
$522$	15.8872	0.695363
$523$	−35.1560	−1.53726	−0.768632	−	0.639692i	$-0.779062\pi$
$523$	−35.1560	−1.53726	−0.768632	+	0.639692i	$0.779062\pi$
$524$	−20.4268	−0.892351
$525$	3.50782	0.153094
$526$	−19.6124	−0.855140
$527$	0.822990	0.0358500
$528$	−3.91082	−0.170197
$529$	39.8350	1.73196
$530$	51.2521	2.22625
$531$	1.27888	0.0554989
$532$	26.6279	1.15446
$533$	−34.6829	−1.50228
$534$	7.56326	0.327294
$535$	−33.2910	−1.43930
$536$	5.97362	0.258021
$537$	−10.2164	−0.440870
$538$	−45.2245	−1.94977
$539$	25.9211	1.11650
$540$	11.2780	0.485329
$541$	−4.09467	−0.176044	−0.0880219	−	0.996119i	$-0.528055\pi$
$541$	−4.09467	−0.176044	−0.0880219	+	0.996119i	$0.528055\pi$
$542$	46.4835	1.99664
$543$	−8.13917	−0.349285
$544$	2.34481	0.100533
$545$	−17.4518	−0.747552
$546$	−28.2811	−1.21032
$547$	40.5796	1.73506	0.867529	−	0.497387i	$-0.165707\pi$
$547$	40.5796	1.73506	0.867529	+	0.497387i	$0.165707\pi$
$548$	−32.4724	−1.38715
$549$	22.9673	0.980223
$550$	8.01222	0.341642
$551$	−7.84338	−0.334139
$552$	−1.74577	−0.0743050
$553$	33.4830	1.42384
$554$	−56.0807	−2.38264
$555$	−0.880640	−0.0373811
$556$	34.0278	1.44310
$557$	14.9842	0.634901	0.317450	−	0.948275i	$-0.397173\pi$
$557$	14.9842	0.634901	0.317450	+	0.948275i	$0.397173\pi$
$558$	16.1882	0.685300
$559$	−55.4249	−2.34423
$560$	−27.2597	−1.15193
$561$	0.321980	0.0135940
$562$	−42.5779	−1.79604
$563$	32.7164	1.37883	0.689417	−	0.724365i	$-0.257867\pi$
$563$	32.7164	1.37883	0.689417	+	0.724365i	$0.257867\pi$
$564$	1.15249	0.0485284
$565$	4.20877	0.177064
$566$	35.4651	1.49071
$567$	−29.6736	−1.24617
$568$	−7.20766	−0.302426
$569$	11.8185	0.495459	0.247729	−	0.968829i	$-0.420316\pi$
$569$	11.8185	0.495459	0.247729	+	0.968829i	$0.420316\pi$
$570$	−5.07523	−0.212578
$571$	−2.08460	−0.0872377	−0.0436189	−	0.999048i	$-0.513889\pi$
$571$	−2.08460	−0.0872377	−0.0436189	+	0.999048i	$0.513889\pi$
$572$	−33.9917	−1.42126
$573$	4.44798	0.185817
$574$	45.7973	1.91154
$575$	−13.4326	−0.560177
$576$	26.7180	1.11325
$577$	27.9670	1.16428	0.582140	−	0.813088i	$-0.302215\pi$
$577$	27.9670	1.16428	0.582140	+	0.813088i	$0.302215\pi$
$578$	34.7564	1.44568
$579$	1.12541	0.0467703
$580$	−11.2925	−0.468896
$581$	20.3201	0.843019
$582$	−15.9193	−0.659877
$583$	31.5752	1.30771
$584$	−2.52970	−0.104680
$585$	−33.4321	−1.38225
$586$	−50.2923	−2.07755
$587$	−24.8377	−1.02516	−0.512582	−	0.858639i	$-0.671311\pi$
$587$	−24.8377	−1.02516	−0.512582	+	0.858639i	$0.671311\pi$
$588$	12.1192	0.499787
$589$	−7.99199	−0.329304
$590$	−1.72748	−0.0711194
$591$	6.29343	0.258877
$592$	−3.50843	−0.144196
$593$	1.84089	0.0755963	0.0377982	−	0.999285i	$-0.487966\pi$
$593$	1.84089	0.0755963	0.0377982	+	0.999285i	$0.487966\pi$
$594$	13.2040	0.541768
$595$	2.24431	0.0920078
$596$	−32.5220	−1.33215
$597$	6.00551	0.245789
$598$	108.297	4.42861
$599$	−20.2359	−0.826817	−0.413408	−	0.910546i	$-0.635662\pi$
$599$	−20.2359	−0.826817	−0.413408	+	0.910546i	$0.635662\pi$
$600$	0.373203	0.0152360
$601$	−32.9414	−1.34371	−0.671855	−	0.740683i	$-0.734502\pi$
$601$	−32.9414	−1.34371	−0.671855	+	0.740683i	$0.734502\pi$
$602$	73.1861	2.98284
$603$	36.3320	1.47955
$604$	−9.62554	−0.391658
$605$	10.3705	0.421620
$606$	10.9940	0.446602
$607$	−40.1439	−1.62939	−0.814695	−	0.579889i	$-0.803096\pi$
$607$	−40.1439	−1.62939	−0.814695	+	0.579889i	$0.803096\pi$
$608$	−22.7702	−0.923455
$609$	−5.78826	−0.234552
$610$	−31.0237	−1.25611
$611$	−7.12260	−0.288150
$612$	−1.77434	−0.0717232
$613$	26.4198	1.06708	0.533542	−	0.845773i	$-0.320860\pi$
$613$	26.4198	1.06708	0.533542	+	0.845773i	$0.320860\pi$
$614$	12.8365	0.518040
$615$	−4.59325	−0.185218
$616$	4.47166	0.180168
$617$	−27.3814	−1.10234	−0.551168	−	0.834394i	$-0.685818\pi$
$617$	−27.3814	−1.10234	−0.551168	+	0.834394i	$0.685818\pi$
$618$	16.4764	0.662779
$619$	−14.5594	−0.585191	−0.292595	−	0.956236i	$-0.594519\pi$
$619$	−14.5594	−0.585191	−0.292595	+	0.956236i	$0.594519\pi$
$620$	−11.5065	−0.462111
$621$	−22.1367	−0.888315
$622$	−49.5187	−1.98552
$623$	32.4786	1.30123
$624$	11.3003	0.452375
$625$	−13.6556	−0.546225
$626$	56.5209	2.25903
$627$	−3.12673	−0.124869
$628$	9.64674	0.384947
$629$	0.288851	0.0115172
$630$	44.1455	1.75880
$631$	−28.9740	−1.15344	−0.576719	−	0.816943i	$-0.695667\pi$
$631$	−28.9740	−1.15344	−0.576719	+	0.816943i	$0.695667\pi$
$632$	3.56232	0.141701
$633$	−8.64926	−0.343777
$634$	2.61138	0.103711
$635$	−3.71678	−0.147496
$636$	14.7627	0.585379
$637$	−74.8992	−2.96761
$638$	−13.2210	−0.523423
$639$	−43.8375	−1.73419
$640$	−6.57264	−0.259807
$641$	−14.4521	−0.570822	−0.285411	−	0.958405i	$-0.592130\pi$
$641$	−14.4521	−0.570822	−0.285411	+	0.958405i	$0.592130\pi$
$642$	−18.2230	−0.719205
$643$	−22.1850	−0.874893	−0.437446	−	0.899245i	$-0.644117\pi$
$643$	−22.1850	−0.874893	−0.437446	+	0.899245i	$0.644117\pi$
$644$	−75.2494	−2.96524
$645$	−7.34022	−0.289021
$646$	1.66468	0.0654961
$647$	13.6772	0.537708	0.268854	−	0.963181i	$-0.413355\pi$
$647$	13.6772	0.537708	0.268854	+	0.963181i	$0.413355\pi$
$648$	−3.15703	−0.124020
$649$	−1.06426	−0.0417759
$650$	−23.1513	−0.908070
$651$	−5.89793	−0.231158
$652$	2.22130	0.0869928
$653$	−9.63721	−0.377133	−0.188567	−	0.982060i	$-0.560384\pi$
$653$	−9.63721	−0.377133	−0.188567	+	0.982060i	$0.560384\pi$
$654$	−9.55284	−0.373546
$655$	16.7189	0.653263
$656$	−18.2993	−0.714467
$657$	−15.3858	−0.600259
$658$	9.40507	0.366648
$659$	7.65313	0.298124	0.149062	−	0.988828i	$-0.452375\pi$
$659$	7.65313	0.298124	0.149062	+	0.988828i	$0.452375\pi$
$660$	−4.50170	−0.175229
$661$	−8.29438	−0.322614	−0.161307	−	0.986904i	$-0.551571\pi$
$661$	−8.29438	−0.322614	−0.161307	+	0.986904i	$0.551571\pi$
$662$	6.15273	0.239132
$663$	−0.930363	−0.0361323
$664$	2.16189	0.0838975
$665$	−21.7943	−0.845148
$666$	5.68169	0.220161
$667$	22.1651	0.858237
$668$	−5.69307	−0.220271
$669$	−3.09622	−0.119707
$670$	−49.0764	−1.89598
$671$	−19.1129	−0.737847
$672$	−16.8040	−0.648227
$673$	14.7011	0.566687	0.283344	−	0.959018i	$-0.408556\pi$
$673$	14.7011	0.566687	0.283344	+	0.959018i	$0.408556\pi$
$674$	36.3623	1.40062
$675$	4.73228	0.182145
$676$	69.3422	2.66701
$677$	−5.14114	−0.197590	−0.0987950	−	0.995108i	$-0.531499\pi$
$677$	−5.14114	−0.197590	−0.0987950	+	0.995108i	$0.531499\pi$
$678$	2.30382	0.0884776
$679$	−68.3616	−2.62348
$680$	0.238776	0.00915665
$681$	3.32884	0.127562
$682$	−13.4715	−0.515849
$683$	25.0071	0.956869	0.478435	−	0.878123i	$-0.341204\pi$
$683$	25.0071	0.956869	0.478435	+	0.878123i	$0.341204\pi$
$684$	17.2304	0.658822
$685$	26.5780	1.01549
$686$	37.4376	1.42938
$687$	8.93064	0.340725
$688$	−29.2431	−1.11488
$689$	−91.2365	−3.47584
$690$	14.3424	0.546007
$691$	−44.1952	−1.68127	−0.840633	−	0.541605i	$-0.817817\pi$
$691$	−44.1952	−1.68127	−0.840633	+	0.541605i	$0.817817\pi$
$692$	−20.1297	−0.765218
$693$	27.1970	1.03313
$694$	1.19787	0.0454706
$695$	−27.8510	−1.05645
$696$	−0.615823	−0.0233427
$697$	1.50659	0.0570662
$698$	−46.6680	−1.76641
$699$	−1.60284	−0.0606248
$700$	16.0865	0.608011
$701$	−8.81752	−0.333033	−0.166517	−	0.986039i	$-0.553252\pi$
$701$	−8.81752	−0.333033	−0.166517	+	0.986039i	$0.553252\pi$
$702$	−38.1531	−1.43999
$703$	−2.80501	−0.105793
$704$	−22.2342	−0.837982
$705$	−0.943284	−0.0355261
$706$	−61.8080	−2.32618
$707$	47.2111	1.77556
$708$	−0.497586	−0.0187004
$709$	−21.6232	−0.812077	−0.406038	−	0.913856i	$-0.633090\pi$
$709$	−21.6232	−0.812077	−0.406038	+	0.913856i	$0.633090\pi$
$710$	59.2146	2.22228
$711$	21.6663	0.812549
$712$	3.45545	0.129498
$713$	22.5851	0.845817
$714$	1.22850	0.0459756
$715$	27.8215	1.04046
$716$	−46.8512	−1.75091
$717$	−8.84848	−0.330453
$718$	−33.3151	−1.24331
$719$	−41.6266	−1.55241	−0.776205	−	0.630480i	$-0.782858\pi$
$719$	−41.6266	−1.55241	−0.776205	+	0.630480i	$0.782858\pi$
$720$	−17.6393	−0.657378
$721$	70.7540	2.63502
$722$	22.8714	0.851186
$723$	−11.7141	−0.435653
$724$	−37.3253	−1.38718
$725$	−4.73835	−0.175978
$726$	5.67664	0.210680
$727$	22.8961	0.849170	0.424585	−	0.905388i	$-0.360420\pi$
$727$	22.8961	0.849170	0.424585	+	0.905388i	$0.360420\pi$
$728$	−12.9209	−0.478879
$729$	−15.1432	−0.560860
$730$	20.7828	0.769206
$731$	2.40760	0.0890484
$732$	−8.93609	−0.330287
$733$	0.724734	0.0267687	0.0133843	−	0.999910i	$-0.495740\pi$
$733$	0.724734	0.0267687	0.0133843	+	0.999910i	$0.495740\pi$
$734$	55.3579	2.04330
$735$	−9.91930	−0.365879
$736$	64.3478	2.37189
$737$	−30.2347	−1.11371
$738$	29.6346	1.09086
$739$	−19.8369	−0.729711	−0.364855	−	0.931064i	$-0.618882\pi$
$739$	−19.8369	−0.729711	−0.364855	+	0.931064i	$0.618882\pi$
$740$	−4.03851	−0.148459
$741$	9.03469	0.331898
$742$	120.474	4.42273
$743$	−6.73886	−0.247225	−0.123612	−	0.992331i	$-0.539448\pi$
$743$	−6.73886	−0.247225	−0.123612	+	0.992331i	$0.539448\pi$
$744$	−0.627491	−0.0230049
$745$	26.6186	0.975229
$746$	−23.0753	−0.844846
$747$	13.1488	0.481088
$748$	1.47656	0.0539885
$749$	−78.2543	−2.85935
$750$	−12.1128	−0.442296
$751$	−53.0664	−1.93642	−0.968209	−	0.250141i	$-0.919523\pi$
$751$	−53.0664	−1.93642	−0.968209	+	0.250141i	$0.919523\pi$
$752$	−3.75800	−0.137040
$753$	−9.63848	−0.351246
$754$	38.2020	1.39124
$755$	7.87830	0.286721
$756$	26.5103	0.964168
$757$	−39.6205	−1.44003	−0.720015	−	0.693959i	$-0.755865\pi$
$757$	−39.6205	−1.44003	−0.720015	+	0.693959i	$0.755865\pi$
$758$	−51.0563	−1.85445
$759$	8.83601	0.320727
$760$	−2.31874	−0.0841094
$761$	−39.7471	−1.44083	−0.720415	−	0.693543i	$-0.756049\pi$
$761$	−39.7471	−1.44083	−0.720415	+	0.693543i	$0.756049\pi$
$762$	−2.03451	−0.0737025
$763$	−41.0223	−1.48511
$764$	20.3979	0.737970
$765$	1.45226	0.0525064
$766$	−47.8119	−1.72751
$767$	3.07518	0.111038
$768$	5.76197	0.207917
$769$	30.3831	1.09564	0.547821	−	0.836595i	$-0.315457\pi$
$769$	30.3831	1.09564	0.547821	+	0.836595i	$0.315457\pi$
$770$	−36.7370	−1.32391
$771$	3.65426	0.131605
$772$	5.16098	0.185748
$773$	1.91987	0.0690530	0.0345265	−	0.999404i	$-0.489008\pi$
$773$	1.91987	0.0690530	0.0345265	+	0.999404i	$0.489008\pi$
$774$	47.3575	1.70223
$775$	−4.82813	−0.173432
$776$	−7.27311	−0.261089
$777$	−2.07004	−0.0742623
$778$	−1.46227	−0.0524248
$779$	−14.6304	−0.524188
$780$	13.0077	0.465750
$781$	36.4807	1.30538
$782$	−4.70433	−0.168227
$783$	−7.80874	−0.279062
$784$	−39.5180	−1.41136
$785$	−7.89565	−0.281808
$786$	9.15169	0.326430
$787$	−33.4432	−1.19212	−0.596060	−	0.802940i	$-0.703268\pi$
$787$	−33.4432	−1.19212	−0.596060	+	0.802940i	$0.703268\pi$
$788$	28.8609	1.02813
$789$	4.62372	0.164609
$790$	−29.2663	−1.04125
$791$	9.89318	0.351761
$792$	2.89353	0.102817
$793$	55.2269	1.96117
$794$	18.1735	0.644952
$795$	−12.0829	−0.428538
$796$	27.5405	0.976149
$797$	−32.6226	−1.15555	−0.577775	−	0.816196i	$-0.696079\pi$
$797$	−32.6226	−1.15555	−0.577775	+	0.816196i	$0.696079\pi$
$798$	−11.9299	−0.422314
$799$	0.309399	0.0109457
$800$	−13.7560	−0.486347
$801$	21.0163	0.742575
$802$	−49.0486	−1.73197
$803$	12.8038	0.451835
$804$	−14.1360	−0.498538
$805$	61.5900	2.17076
$806$	38.9258	1.37110
$807$	10.6619	0.375317
$808$	5.02287	0.176704
$809$	−15.8929	−0.558764	−0.279382	−	0.960180i	$-0.590130\pi$
$809$	−15.8929	−0.558764	−0.279382	+	0.960180i	$0.590130\pi$
$810$	25.9366	0.911319
$811$	30.9412	1.08649	0.543246	−	0.839573i	$-0.317195\pi$
$811$	30.9412	1.08649	0.543246	+	0.839573i	$0.317195\pi$
$812$	−26.5443	−0.931521
$813$	−10.9587	−0.384340
$814$	−4.72818	−0.165723
$815$	−1.81809	−0.0636848
$816$	−0.490875	−0.0171841
$817$	−23.3800	−0.817964
$818$	53.9206	1.88529
$819$	−78.5857	−2.74601
$820$	−21.0641	−0.735590
$821$	−21.8851	−0.763795	−0.381898	−	0.924205i	$-0.624729\pi$
$821$	−21.8851	−0.763795	−0.381898	+	0.924205i	$0.624729\pi$
$822$	14.5484	0.507433
$823$	21.8518	0.761705	0.380852	−	0.924636i	$-0.375631\pi$
$823$	21.8518	0.761705	0.380852	+	0.924636i	$0.375631\pi$
$824$	7.52764	0.262238
$825$	−1.88892	−0.0657638
$826$	−4.06064	−0.141288
$827$	6.91131	0.240330	0.120165	−	0.992754i	$-0.461658\pi$
$827$	6.91131	0.240330	0.120165	+	0.992754i	$0.461658\pi$
$828$	−48.6926	−1.69218
$829$	32.1620	1.11703	0.558516	−	0.829494i	$-0.311371\pi$
$829$	32.1620	1.11703	0.558516	+	0.829494i	$0.311371\pi$
$830$	−17.7610	−0.616494
$831$	13.2213	0.458642
$832$	64.2457	2.22732
$833$	3.25354	0.112729
$834$	−15.2452	−0.527898
$835$	4.65965	0.161254
$836$	−14.3388	−0.495918
$837$	−7.95669	−0.275023
$838$	−19.7086	−0.680821
$839$	−24.2246	−0.836326	−0.418163	−	0.908372i	$-0.637326\pi$
$839$	−24.2246	−0.836326	−0.418163	+	0.908372i	$0.637326\pi$
$840$	−1.71118	−0.0590413
$841$	−21.1812	−0.730388
$842$	−79.1175	−2.72657
$843$	10.0379	0.345725
$844$	−39.6645	−1.36531
$845$	−56.7551	−1.95243
$846$	6.08586	0.209236
$847$	24.3769	0.837602
$848$	−48.1379	−1.65306
$849$	−8.36107	−0.286951
$850$	1.00567	0.0344942
$851$	7.92686	0.271729
$852$	17.0562	0.584336
$853$	19.0426	0.652007	0.326003	−	0.945369i	$-0.394298\pi$
$853$	19.0426	0.652007	0.326003	+	0.945369i	$0.394298\pi$
$854$	−72.9246	−2.49543
$855$	−14.1027	−0.482303
$856$	−8.32561	−0.284563
$857$	−15.4693	−0.528421	−0.264211	−	0.964465i	$-0.585111\pi$
$857$	−15.4693	−0.528421	−0.264211	+	0.964465i	$0.585111\pi$
$858$	15.2291	0.519911
$859$	1.97885	0.0675174	0.0337587	−	0.999430i	$-0.489252\pi$
$859$	1.97885	0.0675174	0.0337587	+	0.999430i	$0.489252\pi$
$860$	−33.6614	−1.14784
$861$	−10.7969	−0.367959
$862$	79.4392	2.70571
$863$	−4.11891	−0.140209	−0.0701046	−	0.997540i	$-0.522333\pi$
$863$	−4.11891	−0.140209	−0.0701046	+	0.997540i	$0.522333\pi$
$864$	−22.6697	−0.771237
$865$	16.4758	0.560193
$866$	−35.7862	−1.21606
$867$	−8.19401	−0.278283
$868$	−27.0472	−0.918042
$869$	−18.0302	−0.611634
$870$	5.05930	0.171526
$871$	87.3634	2.96019
$872$	−4.36444	−0.147798
$873$	−44.2356	−1.49715
$874$	45.6834	1.54526
$875$	−52.0153	−1.75844
$876$	5.98629	0.202258
$877$	−21.5542	−0.727835	−0.363917	−	0.931431i	$-0.618561\pi$
$877$	−21.5542	−0.727835	−0.363917	+	0.931431i	$0.618561\pi$
$878$	17.1902	0.580142
$879$	11.8567	0.399915
$880$	14.6791	0.494831
$881$	25.8661	0.871453	0.435726	−	0.900079i	$-0.356492\pi$
$881$	25.8661	0.871453	0.435726	+	0.900079i	$0.356492\pi$
$882$	63.9971	2.15489
$883$	51.0192	1.71693	0.858466	−	0.512870i	$-0.171418\pi$
$883$	51.0192	1.71693	0.858466	+	0.512870i	$0.171418\pi$
$884$	−4.26654	−0.143499
$885$	0.407263	0.0136900
$886$	−18.7164	−0.628791
$887$	7.88085	0.264613	0.132306	−	0.991209i	$-0.457762\pi$
$887$	7.88085	0.264613	0.132306	+	0.991209i	$0.457762\pi$
$888$	−0.220235	−0.00739061
$889$	−8.73670	−0.293020
$890$	−28.3883	−0.951577
$891$	15.9789	0.535313
$892$	−14.1989	−0.475415
$893$	−3.00455	−0.100543
$894$	14.5706	0.487314
$895$	38.3467	1.28179
$896$	−15.4497	−0.516139
$897$	−25.5317	−0.852478
$898$	−30.3098	−1.01145
$899$	7.96690	0.265711
$900$	10.4093	0.346975
$901$	3.96322	0.132034
$902$	−24.6613	−0.821131
$903$	−17.2540	−0.574177
$904$	1.05255	0.0350074
$905$	30.5499	1.01551
$906$	4.31246	0.143272
$907$	−2.04831	−0.0680129	−0.0340064	−	0.999422i	$-0.510827\pi$
$907$	−2.04831	−0.0680129	−0.0340064	+	0.999422i	$0.510827\pi$
$908$	15.2657	0.506610
$909$	30.5495	1.01326
$910$	106.152	3.51889
$911$	45.0374	1.49216	0.746078	−	0.665858i	$-0.231934\pi$
$911$	45.0374	1.49216	0.746078	+	0.665858i	$0.231934\pi$
$912$	4.76685	0.157846
$913$	−10.9421	−0.362132
$914$	50.4304	1.66809
$915$	7.31400	0.241793
$916$	40.9549	1.35319
$917$	39.2997	1.29779
$918$	1.65733	0.0547001
$919$	−34.7395	−1.14595	−0.572975	−	0.819573i	$-0.694211\pi$
$919$	−34.7395	−1.14595	−0.572975	+	0.819573i	$0.694211\pi$
$920$	6.55266	0.216035
$921$	−3.02628	−0.0997193
$922$	−44.6578	−1.47073
$923$	−105.411	−3.46964
$924$	−10.5817	−0.348114
$925$	−1.69457	−0.0557170
$926$	−37.9197	−1.24612
$927$	45.7837	1.50373
$928$	22.6988	0.745123
$929$	−0.593923	−0.0194860	−0.00974299	−	0.999953i	$-0.503101\pi$
$929$	−0.593923	−0.0194860	−0.00974299	+	0.999953i	$0.503101\pi$
$930$	5.15516	0.169044
$931$	−31.5949	−1.03548
$932$	−7.35041	−0.240771
$933$	11.6743	0.382199
$934$	−2.91760	−0.0954667
$935$	−1.20854	−0.0395234
$936$	−8.36087	−0.273284
$937$	−45.5447	−1.48788	−0.743940	−	0.668247i	$-0.767045\pi$
$937$	−45.5447	−1.48788	−0.743940	+	0.668247i	$0.767045\pi$
$938$	−115.359	−3.76662
$939$	−13.3251	−0.434848
$940$	−4.32579	−0.141092
$941$	8.06988	0.263071	0.131535	−	0.991311i	$-0.458009\pi$
$941$	8.06988	0.263071	0.131535	+	0.991311i	$0.458009\pi$
$942$	−4.32196	−0.140817
$943$	41.3449	1.34638
$944$	1.62252	0.0528084
$945$	−21.6981	−0.705838
$946$	−39.4099	−1.28133
$947$	−26.1428	−0.849526	−0.424763	−	0.905305i	$-0.639643\pi$
$947$	−26.1428	−0.849526	−0.424763	+	0.905305i	$0.639643\pi$
$948$	−8.42988	−0.273790
$949$	−36.9965	−1.20096
$950$	−9.76598	−0.316850
$951$	−0.615647	−0.0199637
$952$	0.561270	0.0181909
$953$	13.3180	0.431413	0.215707	−	0.976458i	$-0.430794\pi$
$953$	13.3180	0.431413	0.215707	+	0.976458i	$0.430794\pi$
$954$	77.9564	2.52393
$955$	−16.6952	−0.540245
$956$	−40.5781	−1.31239
$957$	3.11691	0.100755
$958$	−30.2178	−0.976294
$959$	62.4745	2.01741
$960$	8.50840	0.274607
$961$	−22.8822	−0.738134
$962$	13.6621	0.440484
$963$	−50.6370	−1.63175
$964$	−53.7196	−1.73019
$965$	−4.22415	−0.135980
$966$	33.7134	1.08471
$967$	−19.9051	−0.640105	−0.320053	−	0.947400i	$-0.603701\pi$
$967$	−19.9051	−0.640105	−0.320053	+	0.947400i	$0.603701\pi$
$968$	2.59350	0.0833584
$969$	−0.392458	−0.0126076
$970$	59.7523	1.91853
$971$	45.3928	1.45672	0.728361	−	0.685193i	$-0.240282\pi$
$971$	45.3928	1.45672	0.728361	+	0.685193i	$0.240282\pi$
$972$	26.0805	0.836533
$973$	−65.4668	−2.09877
$974$	−18.1938	−0.582968
$975$	5.45804	0.174797
$976$	29.1386	0.932704
$977$	−38.7571	−1.23995	−0.619975	−	0.784622i	$-0.712857\pi$
$977$	−38.7571	−1.23995	−0.619975	+	0.784622i	$0.712857\pi$
$978$	−0.995193	−0.0318228
$979$	−17.4893	−0.558961
$980$	−45.4887	−1.45308
$981$	−26.5448	−0.847511
$982$	65.7184	2.09716
$983$	28.4097	0.906127	0.453064	−	0.891478i	$-0.350331\pi$
$983$	28.4097	0.906127	0.453064	+	0.891478i	$0.350331\pi$
$984$	−1.14870	−0.0366194
$985$	−23.6220	−0.752661
$986$	−1.65946	−0.0528479
$987$	−2.21729	−0.0705772
$988$	41.4320	1.31813
$989$	66.0711	2.10094
$990$	−23.7719	−0.755519
$991$	−7.29674	−0.231788	−0.115894	−	0.993262i	$-0.536973\pi$
$991$	−7.29674	−0.231788	−0.115894	+	0.993262i	$0.536973\pi$
$992$	23.1288	0.734341
$993$	−1.45054	−0.0460314
$994$	139.190	4.41485
$995$	−22.5413	−0.714609
$996$	−5.11590	−0.162103
$997$	−45.4474	−1.43933	−0.719667	−	0.694320i	$-0.755705\pi$
$997$	−45.4474	−1.43933	−0.719667	+	0.694320i	$0.755705\pi$
$998$	−26.5480	−0.840363
$999$	−2.79262	−0.0883546

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.b.1.19	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.b.1.19	✓	109	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05458 q^{2} +0.484378 q^{3} +2.22130 q^{4} -1.81809 q^{5} -0.995193 q^{6} -4.27361 q^{7} -0.454677 q^{8} -2.76538 q^{9} +O(q^{10})\)	\(q-2.05458 q^{2} +0.484378 q^{3} +2.22130 q^{4} -1.81809 q^{5} -0.995193 q^{6} -4.27361 q^{7} -0.454677 q^{8} -2.76538 q^{9} +3.73540 q^{10} +2.30129 q^{11} +1.07595 q^{12} -6.64958 q^{13} +8.78047 q^{14} -0.880640 q^{15} -3.50843 q^{16} +0.288851 q^{17} +5.68169 q^{18} -2.80501 q^{19} -4.03851 q^{20} -2.07004 q^{21} -4.72818 q^{22} +7.92686 q^{23} -0.220235 q^{24} -1.69457 q^{25} +13.6621 q^{26} -2.79262 q^{27} -9.49297 q^{28} +2.79620 q^{29} +1.80935 q^{30} +2.84918 q^{31} +8.11770 q^{32} +1.11469 q^{33} -0.593468 q^{34} +7.76979 q^{35} -6.14273 q^{36} +1.00000 q^{37} +5.76312 q^{38} -3.22091 q^{39} +0.826641 q^{40} +5.21581 q^{41} +4.25307 q^{42} +8.33510 q^{43} +5.11185 q^{44} +5.02769 q^{45} -16.2864 q^{46} +1.07114 q^{47} -1.69940 q^{48} +11.2637 q^{49} +3.48162 q^{50} +0.139913 q^{51} -14.7707 q^{52} +13.7206 q^{53} +5.73766 q^{54} -4.18394 q^{55} +1.94311 q^{56} -1.35868 q^{57} -5.74503 q^{58} -0.462463 q^{59} -1.95616 q^{60} -8.30532 q^{61} -5.85388 q^{62} +11.8181 q^{63} -9.66161 q^{64} +12.0895 q^{65} -2.29023 q^{66} -13.1382 q^{67} +0.641625 q^{68} +3.83959 q^{69} -15.9636 q^{70} +15.8523 q^{71} +1.25735 q^{72} +5.56374 q^{73} -2.05458 q^{74} -0.820810 q^{75} -6.23077 q^{76} -9.83482 q^{77} +6.61762 q^{78} -7.83484 q^{79} +6.37862 q^{80} +6.94345 q^{81} -10.7163 q^{82} -4.75478 q^{83} -4.59818 q^{84} -0.525156 q^{85} -17.1251 q^{86} +1.35442 q^{87} -1.04634 q^{88} -7.59979 q^{89} -10.3298 q^{90} +28.4177 q^{91} +17.6079 q^{92} +1.38008 q^{93} -2.20073 q^{94} +5.09975 q^{95} +3.93203 q^{96} +15.9962 q^{97} -23.1423 q^{98} -6.36394 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9}+O(q^{10}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9	\( 109 q - 11 q^{2} - 14 q^{3} + 99 q^{4} - 28 q^{5} - 14 q^{6} - 16 q^{7} - 27 q^{8} + 65 q^{9} - 21 q^{10} - 35 q^{11} - 34 q^{12} - 15 q^{13} - 19 q^{14} - 9 q^{15} + 67 q^{16} - 82 q^{17} - 7 q^{18} - 21 q^{19} - 49 q^{20} - 38 q^{21} + 8 q^{22} - 28 q^{23} - 45 q^{24} + 63 q^{25} - 59 q^{26} - 32 q^{27} - 44 q^{28} - 69 q^{29} - 10 q^{31} - 45 q^{32} - 53 q^{33} - 35 q^{34} - 40 q^{35} + 5 q^{36} + 109 q^{37} - 34 q^{38} - 18 q^{39} - 61 q^{40} - 158 q^{41} + 5 q^{42} - q^{43} - 89 q^{44} - 49 q^{45} - 28 q^{46} - 50 q^{47} - 39 q^{48} + 13 q^{49} - 56 q^{50} - 33 q^{51} - 35 q^{52} - 79 q^{53} - 57 q^{54} - 33 q^{55} - 21 q^{56} - 57 q^{57} + 3 q^{58} - 105 q^{59} - 10 q^{60} - 51 q^{61} - 100 q^{62} - 61 q^{63} + 63 q^{64} - 120 q^{65} - 37 q^{66} - 9 q^{67} - 109 q^{68} - 80 q^{69} + q^{70} - 46 q^{71} + 36 q^{72} - 81 q^{73} - 11 q^{74} - 37 q^{75} - 22 q^{76} - 111 q^{77} - 46 q^{78} - 22 q^{79} - 116 q^{80} - 59 q^{81} - 82 q^{83} - 113 q^{84} - 26 q^{85} - 70 q^{86} - 56 q^{87} - 9 q^{88} - 171 q^{89} - 84 q^{90} + 11 q^{91} - 32 q^{92} + 42 q^{93} - 123 q^{94} - 42 q^{95} - 99 q^{96} - 28 q^{97} - 81 q^{98} - 45 q^{99}+O(q^{100}) \) 109 * q - 11 * q^2 - 14 * q^3 + 99 * q^4 - 28 * q^5 - 14 * q^6 - 16 * q^7 - 27 * q^8 + 65 * q^9 - 21 * q^10 - 35 * q^11 - 34 * q^12 - 15 * q^13 - 19 * q^14 - 9 * q^15 + 67 * q^16 - 82 * q^17 - 7 * q^18 - 21 * q^19 - 49 * q^20 - 38 * q^21 + 8 * q^22 - 28 * q^23 - 45 * q^24 + 63 * q^25 - 59 * q^26 - 32 * q^27 - 44 * q^28 - 69 * q^29 - 10 * q^31 - 45 * q^32 - 53 * q^33 - 35 * q^34 - 40 * q^35 + 5 * q^36 + 109 * q^37 - 34 * q^38 - 18 * q^39 - 61 * q^40 - 158 * q^41 + 5 * q^42 - q^43 - 89 * q^44 - 49 * q^45 - 28 * q^46 - 50 * q^47 - 39 * q^48 + 13 * q^49 - 56 * q^50 - 33 * q^51 - 35 * q^52 - 79 * q^53 - 57 * q^54 - 33 * q^55 - 21 * q^56 - 57 * q^57 + 3 * q^58 - 105 * q^59 - 10 * q^60 - 51 * q^61 - 100 * q^62 - 61 * q^63 + 63 * q^64 - 120 * q^65 - 37 * q^66 - 9 * q^67 - 109 * q^68 - 80 * q^69 + q^70 - 46 * q^71 + 36 * q^72 - 81 * q^73 - 11 * q^74 - 37 * q^75 - 22 * q^76 - 111 * q^77 - 46 * q^78 - 22 * q^79 - 116 * q^80 - 59 * q^81 - 82 * q^83 - 113 * q^84 - 26 * q^85 - 70 * q^86 - 56 * q^87 - 9 * q^88 - 171 * q^89 - 84 * q^90 + 11 * q^91 - 32 * q^92 + 42 * q^93 - 123 * q^94 - 42 * q^95 - 99 * q^96 - 28 * q^97 - 81 * q^98 - 45 * q^99

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