LMFDB - Embedded newform 6005.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72268 q^{2} +3.38210 q^{3} +5.41301 q^{4} +1.00000 q^{5} -9.20838 q^{6} +2.13000 q^{7} -9.29255 q^{8} +8.43858 q^{9} +O(q^{10})$	\(q-2.72268 q^{2} +3.38210 q^{3} +5.41301 q^{4} +1.00000 q^{5} -9.20838 q^{6} +2.13000 q^{7} -9.29255 q^{8} +8.43858 q^{9} -2.72268 q^{10} +2.82240 q^{11} +18.3073 q^{12} +5.37809 q^{13} -5.79931 q^{14} +3.38210 q^{15} +14.4747 q^{16} +0.761062 q^{17} -22.9756 q^{18} +7.81894 q^{19} +5.41301 q^{20} +7.20386 q^{21} -7.68451 q^{22} -6.36227 q^{23} -31.4283 q^{24} +1.00000 q^{25} -14.6428 q^{26} +18.3938 q^{27} +11.5297 q^{28} -8.09464 q^{29} -9.20838 q^{30} -3.42478 q^{31} -20.8248 q^{32} +9.54563 q^{33} -2.07213 q^{34} +2.13000 q^{35} +45.6781 q^{36} +3.57720 q^{37} -21.2885 q^{38} +18.1892 q^{39} -9.29255 q^{40} -11.2882 q^{41} -19.6138 q^{42} -5.98637 q^{43} +15.2777 q^{44} +8.43858 q^{45} +17.3224 q^{46} +5.73598 q^{47} +48.9547 q^{48} -2.46311 q^{49} -2.72268 q^{50} +2.57398 q^{51} +29.1116 q^{52} +3.55954 q^{53} -50.0805 q^{54} +2.82240 q^{55} -19.7931 q^{56} +26.4444 q^{57} +22.0391 q^{58} -1.19857 q^{59} +18.3073 q^{60} +7.65980 q^{61} +9.32460 q^{62} +17.9741 q^{63} +27.7501 q^{64} +5.37809 q^{65} -25.9897 q^{66} +1.20832 q^{67} +4.11964 q^{68} -21.5178 q^{69} -5.79931 q^{70} +0.858507 q^{71} -78.4159 q^{72} +6.34868 q^{73} -9.73959 q^{74} +3.38210 q^{75} +42.3240 q^{76} +6.01170 q^{77} -49.5235 q^{78} -10.4294 q^{79} +14.4747 q^{80} +36.8939 q^{81} +30.7343 q^{82} -7.42527 q^{83} +38.9945 q^{84} +0.761062 q^{85} +16.2990 q^{86} -27.3768 q^{87} -26.2273 q^{88} +1.90809 q^{89} -22.9756 q^{90} +11.4553 q^{91} -34.4390 q^{92} -11.5829 q^{93} -15.6173 q^{94} +7.81894 q^{95} -70.4316 q^{96} -17.7354 q^{97} +6.70628 q^{98} +23.8171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * 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 $

$2$	−2.72268	−1.92523	−0.962614	−	0.270876i	$-0.912687\pi$
$2$	−2.72268	−1.92523	−0.962614	+	0.270876i	$0.912687\pi$
$3$	3.38210	1.95265	0.976327	−	0.216298i	$-0.0693984\pi$
$3$	3.38210	1.95265	0.976327	+	0.216298i	$0.0693984\pi$
$4$	5.41301	2.70651
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−9.20838	−3.75931
$7$	2.13000	0.805063	0.402532	−	0.915406i	$-0.368130\pi$
$7$	2.13000	0.805063	0.402532	+	0.915406i	$0.368130\pi$
$8$	−9.29255	−3.28541
$9$	8.43858	2.81286
$10$	−2.72268	−0.860988
$11$	2.82240	0.850986	0.425493	−	0.904962i	$-0.360101\pi$
$11$	2.82240	0.850986	0.425493	+	0.904962i	$0.360101\pi$
$12$	18.3073	5.28487
$13$	5.37809	1.49161	0.745807	−	0.666163i	$-0.232064\pi$
$13$	5.37809	1.49161	0.745807	+	0.666163i	$0.232064\pi$
$14$	−5.79931	−1.54993
$15$	3.38210	0.873254
$16$	14.4747	3.61867
$17$	0.761062	0.184585	0.0922923	−	0.995732i	$-0.470581\pi$
$17$	0.761062	0.184585	0.0922923	+	0.995732i	$0.470581\pi$
$18$	−22.9756	−5.41540
$19$	7.81894	1.79379	0.896894	−	0.442246i	$-0.145818\pi$
$19$	7.81894	1.79379	0.896894	+	0.442246i	$0.145818\pi$
$20$	5.41301	1.21039
$21$	7.20386	1.57201
$22$	−7.68451	−1.63834
$23$	−6.36227	−1.32662	−0.663312	−	0.748343i	$-0.730850\pi$
$23$	−6.36227	−1.32662	−0.663312	+	0.748343i	$0.730850\pi$
$24$	−31.4283	−6.41528
$25$	1.00000	0.200000
$26$	−14.6428	−2.87170
$27$	18.3938	3.53989
$28$	11.5297	2.17891
$29$	−8.09464	−1.50314	−0.751568	−	0.659655i	$-0.770702\pi$
$29$	−8.09464	−1.50314	−0.751568	+	0.659655i	$0.770702\pi$
$30$	−9.20838	−1.68121
$31$	−3.42478	−0.615109	−0.307554	−	0.951531i	$-0.599511\pi$
$31$	−3.42478	−0.615109	−0.307554	+	0.951531i	$0.599511\pi$
$32$	−20.8248	−3.68135
$33$	9.54563	1.66168
$34$	−2.07213	−0.355368
$35$	2.13000	0.360035
$36$	45.6781	7.61302
$37$	3.57720	0.588088	0.294044	−	0.955792i	$-0.404999\pi$
$37$	3.57720	0.588088	0.294044	+	0.955792i	$0.404999\pi$
$38$	−21.2885	−3.45345
$39$	18.1892	2.91261
$40$	−9.29255	−1.46928
$41$	−11.2882	−1.76293	−0.881463	−	0.472252i	$-0.843441\pi$
$41$	−11.2882	−1.76293	−0.881463	+	0.472252i	$0.843441\pi$
$42$	−19.6138	−3.02648
$43$	−5.98637	−0.912914	−0.456457	−	0.889746i	$-0.650882\pi$
$43$	−5.98637	−0.912914	−0.456457	+	0.889746i	$0.650882\pi$
$44$	15.2777	2.30320
$45$	8.43858	1.25795
$46$	17.3224	2.55406
$47$	5.73598	0.836678	0.418339	−	0.908291i	$-0.362612\pi$
$47$	5.73598	0.836678	0.418339	+	0.908291i	$0.362612\pi$
$48$	48.9547	7.06601
$49$	−2.46311	−0.351874
$50$	−2.72268	−0.385046
$51$	2.57398	0.360430
$52$	29.1116	4.03706
$53$	3.55954	0.488940	0.244470	−	0.969657i	$-0.421386\pi$
$53$	3.55954	0.488940	0.244470	+	0.969657i	$0.421386\pi$
$54$	−50.0805	−6.81510
$55$	2.82240	0.380572
$56$	−19.7931	−2.64496
$57$	26.4444	3.50265
$58$	22.0391	2.89388
$59$	−1.19857	−0.156040	−0.0780201	−	0.996952i	$-0.524860\pi$
$59$	−1.19857	−0.156040	−0.0780201	+	0.996952i	$0.524860\pi$
$60$	18.3073	2.36347
$61$	7.65980	0.980737	0.490368	−	0.871515i	$-0.336862\pi$
$61$	7.65980	0.980737	0.490368	+	0.871515i	$0.336862\pi$
$62$	9.32460	1.18422
$63$	17.9741	2.26453
$64$	27.7501	3.46877
$65$	5.37809	0.667070
$66$	−25.9897	−3.19912
$67$	1.20832	0.147620	0.0738101	−	0.997272i	$-0.476484\pi$
$67$	1.20832	0.147620	0.0738101	+	0.997272i	$0.476484\pi$
$68$	4.11964	0.499579
$69$	−21.5178	−2.59044
$70$	−5.79931	−0.693150
$71$	0.858507	0.101886	0.0509430	−	0.998702i	$-0.483777\pi$
$71$	0.858507	0.101886	0.0509430	+	0.998702i	$0.483777\pi$
$72$	−78.4159	−9.24141
$73$	6.34868	0.743056	0.371528	−	0.928422i	$-0.378834\pi$
$73$	6.34868	0.743056	0.371528	+	0.928422i	$0.378834\pi$
$74$	−9.73959	−1.13220
$75$	3.38210	0.390531
$76$	42.3240	4.85489
$77$	6.01170	0.685097
$78$	−49.5235	−5.60743
$79$	−10.4294	−1.17340	−0.586698	−	0.809806i	$-0.699572\pi$
$79$	−10.4294	−1.17340	−0.586698	+	0.809806i	$0.699572\pi$
$80$	14.4747	1.61832
$81$	36.8939	4.09932
$82$	30.7343	3.39404
$83$	−7.42527	−0.815029	−0.407515	−	0.913199i	$-0.633604\pi$
$83$	−7.42527	−0.815029	−0.407515	+	0.913199i	$0.633604\pi$
$84$	38.9945	4.25465
$85$	0.761062	0.0825487
$86$	16.2990	1.75757
$87$	−27.3768	−2.93511
$88$	−26.2273	−2.79584
$89$	1.90809	0.202257	0.101129	−	0.994873i	$-0.467755\pi$
$89$	1.90809	0.202257	0.101129	+	0.994873i	$0.467755\pi$
$90$	−22.9756	−2.42184
$91$	11.4553	1.20084
$92$	−34.4390	−3.59052
$93$	−11.5829	−1.20109
$94$	−15.6173	−1.61080
$95$	7.81894	0.802206
$96$	−70.4316	−7.18840
$97$	−17.7354	−1.80076	−0.900378	−	0.435109i	$-0.856710\pi$
$97$	−17.7354	−1.80076	−0.900378	+	0.435109i	$0.856710\pi$
$98$	6.70628	0.677437
$99$	23.8171	2.39370
$100$	5.41301	0.541301
$101$	−14.1385	−1.40684	−0.703419	−	0.710776i	$-0.748344\pi$
$101$	−14.1385	−1.40684	−0.703419	+	0.710776i	$0.748344\pi$
$102$	−7.00815	−0.693910
$103$	10.2450	1.00947	0.504735	−	0.863274i	$-0.331590\pi$
$103$	10.2450	1.00947	0.504735	+	0.863274i	$0.331590\pi$
$104$	−49.9762	−4.90056
$105$	7.20386	0.703024
$106$	−9.69151	−0.941322
$107$	15.1389	1.46354	0.731768	−	0.681554i	$-0.238696\pi$
$107$	15.1389	1.46354	0.731768	+	0.681554i	$0.238696\pi$
$108$	99.5659	9.58073
$109$	−8.55422	−0.819346	−0.409673	−	0.912233i	$-0.634357\pi$
$109$	−8.55422	−0.819346	−0.409673	+	0.912233i	$0.634357\pi$
$110$	−7.68451	−0.732689
$111$	12.0984	1.14833
$112$	30.8310	2.91325
$113$	14.2018	1.33600	0.667999	−	0.744162i	$-0.267151\pi$
$113$	14.2018	1.33600	0.667999	+	0.744162i	$0.267151\pi$
$114$	−71.9998	−6.74340
$115$	−6.36227	−0.593284
$116$	−43.8164	−4.06825
$117$	45.3834	4.19570
$118$	3.26332	0.300413
$119$	1.62106	0.148602
$120$	−31.4283	−2.86900
$121$	−3.03406	−0.275823
$122$	−20.8552	−1.88814
$123$	−38.1779	−3.44239
$124$	−18.5384	−1.66480
$125$	1.00000	0.0894427
$126$	−48.9379	−4.35974
$127$	−20.1328	−1.78650	−0.893250	−	0.449560i	$-0.851581\pi$
$127$	−20.1328	−1.78650	−0.893250	+	0.449560i	$0.851581\pi$
$128$	−33.9052	−2.99682
$129$	−20.2465	−1.78260
$130$	−14.6428	−1.28426
$131$	5.66618	0.495056	0.247528	−	0.968881i	$-0.420382\pi$
$131$	5.66618	0.495056	0.247528	+	0.968881i	$0.420382\pi$
$132$	51.6706	4.49735
$133$	16.6543	1.44411
$134$	−3.28988	−0.284203
$135$	18.3938	1.58309
$136$	−7.07221	−0.606437
$137$	−11.3346	−0.968383	−0.484192	−	0.874962i	$-0.660886\pi$
$137$	−11.3346	−0.968383	−0.484192	+	0.874962i	$0.660886\pi$
$138$	58.5862	4.98719
$139$	−20.9002	−1.77273	−0.886366	−	0.462986i	$-0.846778\pi$
$139$	−20.9002	−1.77273	−0.886366	+	0.462986i	$0.846778\pi$
$140$	11.5297	0.974437
$141$	19.3996	1.63374
$142$	−2.33744	−0.196154
$143$	15.1791	1.26934
$144$	122.146	10.1788
$145$	−8.09464	−0.672223
$146$	−17.2854	−1.43055
$147$	−8.33049	−0.687087
$148$	19.3634	1.59166
$149$	−10.9556	−0.897516	−0.448758	−	0.893653i	$-0.648133\pi$
$149$	−10.9556	−0.897516	−0.448758	+	0.893653i	$0.648133\pi$
$150$	−9.20838	−0.751861
$151$	−4.18079	−0.340228	−0.170114	−	0.985424i	$-0.554414\pi$
$151$	−4.18079	−0.340228	−0.170114	+	0.985424i	$0.554414\pi$
$152$	−72.6579	−5.89333
$153$	6.42228	0.519211
$154$	−16.3680	−1.31897
$155$	−3.42478	−0.275085
$156$	98.4584	7.88298
$157$	−12.5129	−0.998636	−0.499318	−	0.866419i	$-0.666416\pi$
$157$	−12.5129	−0.998636	−0.499318	+	0.866419i	$0.666416\pi$
$158$	28.3959	2.25905
$159$	12.0387	0.954732
$160$	−20.8248	−1.64635
$161$	−13.5516	−1.06802
$162$	−100.450	−7.89213
$163$	−20.9847	−1.64365	−0.821823	−	0.569742i	$-0.807043\pi$
$163$	−20.9847	−1.64365	−0.821823	+	0.569742i	$0.807043\pi$
$164$	−61.1034	−4.77137
$165$	9.54563	0.743126
$166$	20.2167	1.56912
$167$	−2.82749	−0.218798	−0.109399	−	0.993998i	$-0.534893\pi$
$167$	−2.82749	−0.218798	−0.109399	+	0.993998i	$0.534893\pi$
$168$	−66.9422	−5.16470
$169$	15.9238	1.22491
$170$	−2.07213	−0.158925
$171$	65.9807	5.04567
$172$	−32.4043	−2.47081
$173$	12.8273	0.975244	0.487622	−	0.873055i	$-0.337864\pi$
$173$	12.8273	0.975244	0.487622	+	0.873055i	$0.337864\pi$
$174$	74.5385	5.65075
$175$	2.13000	0.161013
$176$	40.8533	3.07943
$177$	−4.05367	−0.304693
$178$	−5.19513	−0.389391
$179$	−4.97979	−0.372207	−0.186104	−	0.982530i	$-0.559586\pi$
$179$	−4.97979	−0.372207	−0.186104	+	0.982530i	$0.559586\pi$
$180$	45.6781	3.40465
$181$	−1.65874	−0.123293	−0.0616466	−	0.998098i	$-0.519635\pi$
$181$	−1.65874	−0.123293	−0.0616466	+	0.998098i	$0.519635\pi$
$182$	−31.1892	−2.31190
$183$	25.9062	1.91504
$184$	59.1217	4.35851
$185$	3.57720	0.263001
$186$	31.5367	2.31238
$187$	2.14802	0.157079
$188$	31.0489	2.26447
$189$	39.1787	2.84983
$190$	−21.2885	−1.54443
$191$	6.47155	0.468265	0.234132	−	0.972205i	$-0.424775\pi$
$191$	6.47155	0.468265	0.234132	+	0.972205i	$0.424775\pi$
$192$	93.8537	6.77331
$193$	−7.06584	−0.508610	−0.254305	−	0.967124i	$-0.581847\pi$
$193$	−7.06584	−0.508610	−0.254305	+	0.967124i	$0.581847\pi$
$194$	48.2879	3.46687
$195$	18.1892	1.30256
$196$	−13.3329	−0.952348
$197$	5.48708	0.390938	0.195469	−	0.980710i	$-0.437377\pi$
$197$	5.48708	0.390938	0.195469	+	0.980710i	$0.437377\pi$
$198$	−64.8463	−4.60843
$199$	7.21856	0.511710	0.255855	−	0.966715i	$-0.417643\pi$
$199$	7.21856	0.511710	0.255855	+	0.966715i	$0.417643\pi$
$200$	−9.29255	−0.657083
$201$	4.08667	0.288251
$202$	38.4948	2.70848
$203$	−17.2415	−1.21012
$204$	13.9330	0.975506
$205$	−11.2882	−0.788405
$206$	−27.8939	−1.94346
$207$	−53.6885	−3.73161
$208$	77.8460	5.39765
$209$	22.0682	1.52649
$210$	−19.6138	−1.35348
$211$	17.3407	1.19378	0.596891	−	0.802323i	$-0.296403\pi$
$211$	17.3407	1.19378	0.596891	+	0.802323i	$0.296403\pi$
$212$	19.2678	1.32332
$213$	2.90355	0.198948
$214$	−41.2185	−2.81764
$215$	−5.98637	−0.408267
$216$	−170.925	−11.6300
$217$	−7.29477	−0.495201
$218$	23.2904	1.57743
$219$	21.4718	1.45093
$220$	15.2777	1.03002
$221$	4.09306	0.275329
$222$	−32.9402	−2.21080
$223$	−19.3033	−1.29265	−0.646323	−	0.763064i	$-0.723694\pi$
$223$	−19.3033	−1.29265	−0.646323	+	0.763064i	$0.723694\pi$
$224$	−44.3568	−2.96372
$225$	8.43858	0.562572
$226$	−38.6671	−2.57210
$227$	−7.94855	−0.527564	−0.263782	−	0.964582i	$-0.584970\pi$
$227$	−7.94855	−0.527564	−0.263782	+	0.964582i	$0.584970\pi$
$228$	143.144	9.47993
$229$	6.46293	0.427082	0.213541	−	0.976934i	$-0.431500\pi$
$229$	6.46293	0.427082	0.213541	+	0.976934i	$0.431500\pi$
$230$	17.3224	1.14221
$231$	20.3322	1.33776
$232$	75.2198	4.93842
$233$	7.64664	0.500948	0.250474	−	0.968123i	$-0.419414\pi$
$233$	7.64664	0.500948	0.250474	+	0.968123i	$0.419414\pi$
$234$	−123.565	−8.07768
$235$	5.73598	0.374174
$236$	−6.48786	−0.422324
$237$	−35.2731	−2.29124
$238$	−4.41363	−0.286093
$239$	−15.7764	−1.02049	−0.510245	−	0.860029i	$-0.670445\pi$
$239$	−15.7764	−1.02049	−0.510245	+	0.860029i	$0.670445\pi$
$240$	48.9547	3.16001
$241$	−2.81071	−0.181054	−0.0905268	−	0.995894i	$-0.528855\pi$
$241$	−2.81071	−0.181054	−0.0905268	+	0.995894i	$0.528855\pi$
$242$	8.26078	0.531023
$243$	69.5973	4.46467
$244$	41.4626	2.65437
$245$	−2.46311	−0.157363
$246$	103.946	6.62738
$247$	42.0509	2.67564
$248$	31.8249	2.02089
$249$	−25.1130	−1.59147
$250$	−2.72268	−0.172198
$251$	−14.4792	−0.913919	−0.456960	−	0.889487i	$-0.651062\pi$
$251$	−14.4792	−0.913919	−0.456960	+	0.889487i	$0.651062\pi$
$252$	97.2943	6.12896
$253$	−17.9569	−1.12894
$254$	54.8154	3.43942
$255$	2.57398	0.161189
$256$	36.8129	2.30080
$257$	14.9717	0.933906	0.466953	−	0.884282i	$-0.345352\pi$
$257$	14.9717	0.933906	0.466953	+	0.884282i	$0.345352\pi$
$258$	55.1248	3.43192
$259$	7.61942	0.473448
$260$	29.1116	1.80543
$261$	−68.3073	−4.22811
$262$	−15.4272	−0.953097
$263$	−22.1080	−1.36324	−0.681619	−	0.731707i	$-0.738724\pi$
$263$	−22.1080	−1.36324	−0.681619	+	0.731707i	$0.738724\pi$
$264$	−88.7033	−5.45931
$265$	3.55954	0.218661
$266$	−45.3444	−2.78025
$267$	6.45335	0.394939
$268$	6.54067	0.399535
$269$	12.0130	0.732443	0.366222	−	0.930528i	$-0.380651\pi$
$269$	12.0130	0.732443	0.366222	+	0.930528i	$0.380651\pi$
$270$	−50.0805	−3.04780
$271$	−1.60960	−0.0977763	−0.0488882	−	0.998804i	$-0.515568\pi$
$271$	−1.60960	−0.0977763	−0.0488882	+	0.998804i	$0.515568\pi$
$272$	11.0161	0.667950
$273$	38.7430	2.34483
$274$	30.8606	1.86436
$275$	2.82240	0.170197
$276$	−116.476	−7.01104
$277$	−6.51928	−0.391706	−0.195853	−	0.980633i	$-0.562747\pi$
$277$	−6.51928	−0.391706	−0.195853	+	0.980633i	$0.562747\pi$
$278$	56.9046	3.41291
$279$	−28.9003	−1.73021
$280$	−19.7931	−1.18286
$281$	−13.4884	−0.804653	−0.402327	−	0.915496i	$-0.631798\pi$
$281$	−13.4884	−0.804653	−0.402327	+	0.915496i	$0.631798\pi$
$282$	−52.8191	−3.14533
$283$	−23.6507	−1.40589	−0.702943	−	0.711246i	$-0.748131\pi$
$283$	−23.6507	−1.40589	−0.702943	+	0.711246i	$0.748131\pi$
$284$	4.64711	0.275755
$285$	26.4444	1.56643
$286$	−41.3279	−2.44377
$287$	−24.0439	−1.41927
$288$	−175.732	−10.3551
$289$	−16.4208	−0.965929
$290$	22.0391	1.29418
$291$	−59.9828	−3.51625
$292$	34.3655	2.01109
$293$	3.84120	0.224405	0.112203	−	0.993685i	$-0.464209\pi$
$293$	3.84120	0.224405	0.112203	+	0.993685i	$0.464209\pi$
$294$	22.6813	1.32280
$295$	−1.19857	−0.0697833
$296$	−33.2413	−1.93211
$297$	51.9147	3.01240
$298$	29.8286	1.72792
$299$	−34.2168	−1.97881
$300$	18.3073	1.05697
$301$	−12.7510	−0.734953
$302$	11.3830	0.655016
$303$	−47.8179	−2.74707
$304$	113.176	6.49112
$305$	7.65980	0.438599
$306$	−17.4858	−0.999599
$307$	29.9636	1.71011	0.855055	−	0.518537i	$-0.173523\pi$
$307$	29.9636	1.71011	0.855055	+	0.518537i	$0.173523\pi$
$308$	32.5414	1.85422
$309$	34.6496	1.97115
$310$	9.32460	0.529601
$311$	−32.4220	−1.83848	−0.919241	−	0.393695i	$-0.871197\pi$
$311$	−32.4220	−1.83848	−0.919241	+	0.393695i	$0.871197\pi$
$312$	−169.024	−9.56911
$313$	25.4291	1.43734	0.718669	−	0.695352i	$-0.244752\pi$
$313$	25.4291	1.43734	0.718669	+	0.695352i	$0.244752\pi$
$314$	34.0686	1.92260
$315$	17.9741	1.01273
$316$	−56.4543	−3.17580
$317$	12.8795	0.723386	0.361693	−	0.932297i	$-0.382199\pi$
$317$	12.8795	0.723386	0.361693	+	0.932297i	$0.382199\pi$
$318$	−32.7776	−1.83808
$319$	−22.8463	−1.27915
$320$	27.7501	1.55128
$321$	51.2013	2.85778
$322$	36.8967	2.05618
$323$	5.95069	0.331105
$324$	199.707	11.0948
$325$	5.37809	0.298323
$326$	57.1347	3.16440
$327$	−28.9312	−1.59990
$328$	104.897	5.79194
$329$	12.2176	0.673579
$330$	−25.9897	−1.43069
$331$	6.59737	0.362624	0.181312	−	0.983426i	$-0.441966\pi$
$331$	6.59737	0.362624	0.181312	+	0.983426i	$0.441966\pi$
$332$	−40.1931	−2.20588
$333$	30.1865	1.65421
$334$	7.69836	0.421235
$335$	1.20832	0.0660178
$336$	104.273	5.68858
$337$	−15.6928	−0.854840	−0.427420	−	0.904053i	$-0.640577\pi$
$337$	−15.6928	−0.854840	−0.427420	+	0.904053i	$0.640577\pi$
$338$	−43.3555	−2.35823
$339$	48.0320	2.60874
$340$	4.11964	0.223419
$341$	−9.66610	−0.523449
$342$	−179.645	−9.71407
$343$	−20.1564	−1.08834
$344$	55.6287	2.99930
$345$	−21.5178	−1.15848
$346$	−34.9248	−1.87757
$347$	26.5969	1.42780	0.713898	−	0.700250i	$-0.246928\pi$
$347$	26.5969	1.42780	0.713898	+	0.700250i	$0.246928\pi$
$348$	−148.191	−7.94388
$349$	12.9996	0.695854	0.347927	−	0.937522i	$-0.386886\pi$
$349$	12.9996	0.695854	0.347927	+	0.937522i	$0.386886\pi$
$350$	−5.79931	−0.309986
$351$	98.9235	5.28015
$352$	−58.7760	−3.13277
$353$	−3.51589	−0.187132	−0.0935661	−	0.995613i	$-0.529827\pi$
$353$	−3.51589	−0.187132	−0.0935661	+	0.995613i	$0.529827\pi$
$354$	11.0369	0.586603
$355$	0.858507	0.0455648
$356$	10.3285	0.547410
$357$	5.48258	0.290169
$358$	13.5584	0.716584
$359$	−18.4691	−0.974764	−0.487382	−	0.873189i	$-0.662048\pi$
$359$	−18.4691	−0.974764	−0.487382	+	0.873189i	$0.662048\pi$
$360$	−78.4159	−4.13288
$361$	42.1358	2.21767
$362$	4.51623	0.237368
$363$	−10.2615	−0.538588
$364$	62.0077	3.25009
$365$	6.34868	0.332305
$366$	−70.5343	−3.68689
$367$	34.4443	1.79798	0.898990	−	0.437970i	$-0.144302\pi$
$367$	34.4443	1.79798	0.898990	+	0.437970i	$0.144302\pi$
$368$	−92.0917	−4.80061
$369$	−95.2567	−4.95887
$370$	−9.73959	−0.506337
$371$	7.58181	0.393628
$372$	−62.6986	−3.25077
$373$	−0.974043	−0.0504340	−0.0252170	−	0.999682i	$-0.508028\pi$
$373$	−0.974043	−0.0504340	−0.0252170	+	0.999682i	$0.508028\pi$
$374$	−5.84838	−0.302413
$375$	3.38210	0.174651
$376$	−53.3019	−2.74883
$377$	−43.5337	−2.24210
$378$	−106.671	−5.48658
$379$	4.06326	0.208716	0.104358	−	0.994540i	$-0.466721\pi$
$379$	4.06326	0.208716	0.104358	+	0.994540i	$0.466721\pi$
$380$	42.3240	2.17117
$381$	−68.0912	−3.48842
$382$	−17.6200	−0.901517
$383$	−2.24274	−0.114599	−0.0572993	−	0.998357i	$-0.518249\pi$
$383$	−2.24274	−0.114599	−0.0572993	+	0.998357i	$0.518249\pi$
$384$	−114.671	−5.85176
$385$	6.01170	0.306385
$386$	19.2380	0.979191
$387$	−50.5165	−2.56790
$388$	−96.0018	−4.87375
$389$	−10.3482	−0.524675	−0.262337	−	0.964976i	$-0.584493\pi$
$389$	−10.3482	−0.524675	−0.262337	+	0.964976i	$0.584493\pi$
$390$	−49.5235	−2.50772
$391$	−4.84208	−0.244874
$392$	22.8886	1.15605
$393$	19.1636	0.966674
$394$	−14.9396	−0.752645
$395$	−10.4294	−0.524758
$396$	128.922	6.47857
$397$	−25.9980	−1.30480	−0.652400	−	0.757875i	$-0.726238\pi$
$397$	−25.9980	−1.30480	−0.652400	+	0.757875i	$0.726238\pi$
$398$	−19.6538	−0.985158
$399$	56.3265	2.81985
$400$	14.4747	0.723733
$401$	−18.5534	−0.926514	−0.463257	−	0.886224i	$-0.653319\pi$
$401$	−18.5534	−0.926514	−0.463257	+	0.886224i	$0.653319\pi$
$402$	−11.1267	−0.554950
$403$	−18.4188	−0.917504
$404$	−76.5321	−3.80761
$405$	36.8939	1.83327
$406$	46.9433	2.32976
$407$	10.0963	0.500454
$408$	−23.9189	−1.18416
$409$	−1.96497	−0.0971613	−0.0485807	−	0.998819i	$-0.515470\pi$
$409$	−1.96497	−0.0971613	−0.0485807	+	0.998819i	$0.515470\pi$
$410$	30.7343	1.51786
$411$	−38.3348	−1.89092
$412$	55.4563	2.73213
$413$	−2.55294	−0.125622
$414$	146.177	7.18420
$415$	−7.42527	−0.364492
$416$	−111.998	−5.49114
$417$	−70.6865	−3.46153
$418$	−60.0847	−2.93884
$419$	11.5017	0.561895	0.280947	−	0.959723i	$-0.409351\pi$
$419$	11.5017	0.561895	0.280947	+	0.959723i	$0.409351\pi$
$420$	38.9945	1.90274
$421$	−6.36409	−0.310167	−0.155083	−	0.987901i	$-0.549565\pi$
$421$	−6.36409	−0.310167	−0.155083	+	0.987901i	$0.549565\pi$
$422$	−47.2132	−2.29830
$423$	48.4035	2.35346
$424$	−33.0772	−1.60637
$425$	0.761062	0.0369169
$426$	−7.90546	−0.383021
$427$	16.3153	0.789555
$428$	81.9472	3.96107
$429$	51.3372	2.47859
$430$	16.2990	0.786008
$431$	−27.0421	−1.30257	−0.651285	−	0.758833i	$-0.725770\pi$
$431$	−27.0421	−1.30257	−0.651285	+	0.758833i	$0.725770\pi$
$432$	266.244	12.8097
$433$	3.64771	0.175298	0.0876489	−	0.996151i	$-0.472065\pi$
$433$	3.64771	0.175298	0.0876489	+	0.996151i	$0.472065\pi$
$434$	19.8614	0.953376
$435$	−27.3768	−1.31262
$436$	−46.3041	−2.21756
$437$	−49.7462	−2.37968
$438$	−58.4611	−2.79338
$439$	5.54277	0.264542	0.132271	−	0.991214i	$-0.457773\pi$
$439$	5.54277	0.264542	0.132271	+	0.991214i	$0.457773\pi$
$440$	−26.2273	−1.25034
$441$	−20.7852	−0.989771
$442$	−11.1441	−0.530071
$443$	40.0796	1.90424	0.952119	−	0.305728i	$-0.0988998\pi$
$443$	40.0796	1.90424	0.952119	+	0.305728i	$0.0988998\pi$
$444$	65.4890	3.10797
$445$	1.90809	0.0904522
$446$	52.5568	2.48864
$447$	−37.0528	−1.75254
$448$	59.1077	2.79258
$449$	−2.95359	−0.139389	−0.0696943	−	0.997568i	$-0.522202\pi$
$449$	−2.95359	−0.139389	−0.0696943	+	0.997568i	$0.522202\pi$
$450$	−22.9756	−1.08308
$451$	−31.8599	−1.50023
$452$	76.8748	3.61588
$453$	−14.1398	−0.664348
$454$	21.6414	1.01568
$455$	11.4553	0.537033
$456$	−245.736	−11.5076
$457$	−23.8831	−1.11720	−0.558602	−	0.829436i	$-0.688662\pi$
$457$	−23.8831	−1.11720	−0.558602	+	0.829436i	$0.688662\pi$
$458$	−17.5965	−0.822231
$459$	13.9988	0.653409
$460$	−34.4390	−1.60573
$461$	−17.5564	−0.817684	−0.408842	−	0.912605i	$-0.634067\pi$
$461$	−17.5564	−0.817684	−0.408842	+	0.912605i	$0.634067\pi$
$462$	−55.3581	−2.57549
$463$	8.47412	0.393826	0.196913	−	0.980421i	$-0.436908\pi$
$463$	8.47412	0.393826	0.196913	+	0.980421i	$0.436908\pi$
$464$	−117.167	−5.43935
$465$	−11.5829	−0.537146
$466$	−20.8194	−0.964439
$467$	32.8393	1.51962	0.759811	−	0.650144i	$-0.225292\pi$
$467$	32.8393	1.51962	0.759811	+	0.650144i	$0.225292\pi$
$468$	245.661	11.3557
$469$	2.57372	0.118844
$470$	−15.6173	−0.720371
$471$	−42.3197	−1.94999
$472$	11.1377	0.512656
$473$	−16.8959	−0.776876
$474$	96.0376	4.41115
$475$	7.81894	0.358757
$476$	8.77481	0.402193
$477$	30.0375	1.37532
$478$	42.9542	1.96468
$479$	−12.2982	−0.561920	−0.280960	−	0.959720i	$-0.590653\pi$
$479$	−12.2982	−0.561920	−0.280960	+	0.959720i	$0.590653\pi$
$480$	−70.4316	−3.21475
$481$	19.2385	0.877200
$482$	7.65267	0.348570
$483$	−45.8328	−2.08547
$484$	−16.4234	−0.746517
$485$	−17.7354	−0.805322
$486$	−189.492	−8.59551
$487$	18.0855	0.819534	0.409767	−	0.912190i	$-0.365610\pi$
$487$	18.0855	0.819534	0.409767	+	0.912190i	$0.365610\pi$
$488$	−71.1791	−3.22212
$489$	−70.9722	−3.20947
$490$	6.70628	0.302959
$491$	21.0048	0.947933	0.473966	−	0.880543i	$-0.342822\pi$
$491$	21.0048	0.947933	0.473966	+	0.880543i	$0.342822\pi$
$492$	−206.658	−9.31684
$493$	−6.16052	−0.277456
$494$	−114.491	−5.15121
$495$	23.8171	1.07050
$496$	−49.5725	−2.22587
$497$	1.82862	0.0820247
$498$	68.3747	3.06394
$499$	5.87509	0.263005	0.131503	−	0.991316i	$-0.458020\pi$
$499$	5.87509	0.263005	0.131503	+	0.991316i	$0.458020\pi$
$500$	5.41301	0.242077
$501$	−9.56284	−0.427236
$502$	39.4223	1.75950
$503$	18.3821	0.819617	0.409809	−	0.912172i	$-0.365595\pi$
$503$	18.3821	0.819617	0.409809	+	0.912172i	$0.365595\pi$
$504$	−167.026	−7.43992
$505$	−14.1385	−0.629157
$506$	48.8909	2.17346
$507$	53.8559	2.39183
$508$	−108.979	−4.83517
$509$	13.8004	0.611692	0.305846	−	0.952081i	$-0.401061\pi$
$509$	13.8004	0.611692	0.305846	+	0.952081i	$0.401061\pi$
$510$	−7.00815	−0.310326
$511$	13.5227	0.598207
$512$	−32.4194	−1.43275
$513$	143.820	6.34981
$514$	−40.7631	−1.79798
$515$	10.2450	0.451448
$516$	−109.595	−4.82463
$517$	16.1892	0.712001
$518$	−20.7453	−0.911495
$519$	43.3833	1.90432
$520$	−49.9762	−2.19160
$521$	22.0615	0.966532	0.483266	−	0.875474i	$-0.339450\pi$
$521$	22.0615	0.966532	0.483266	+	0.875474i	$0.339450\pi$
$522$	185.979	8.14008
$523$	−3.32680	−0.145471	−0.0727355	−	0.997351i	$-0.523173\pi$
$523$	−3.32680	−0.145471	−0.0727355	+	0.997351i	$0.523173\pi$
$524$	30.6711	1.33987
$525$	7.20386	0.314402
$526$	60.1931	2.62455
$527$	−2.60647	−0.113540
$528$	138.170	6.01307
$529$	17.4784	0.759932
$530$	−9.69151	−0.420972
$531$	−10.1142	−0.438919
$532$	90.1500	3.90850
$533$	−60.7091	−2.62960
$534$	−17.5704	−0.760347
$535$	15.1389	0.654513
$536$	−11.2284	−0.484993
$537$	−16.8421	−0.726792
$538$	−32.7075	−1.41012
$539$	−6.95190	−0.299439
$540$	99.5659	4.28463
$541$	39.4652	1.69674	0.848371	−	0.529402i	$-0.177583\pi$
$541$	39.4652	1.69674	0.848371	+	0.529402i	$0.177583\pi$
$542$	4.38244	0.188242
$543$	−5.61002	−0.240749
$544$	−15.8490	−0.679520
$545$	−8.55422	−0.366422
$546$	−105.485	−4.51434
$547$	18.2621	0.780829	0.390415	−	0.920639i	$-0.372332\pi$
$547$	18.2621	0.780829	0.390415	+	0.920639i	$0.372332\pi$
$548$	−61.3545	−2.62094
$549$	64.6378	2.75867
$550$	−7.68451	−0.327668
$551$	−63.2915	−2.69631
$552$	199.955	8.51066
$553$	−22.2145	−0.944657
$554$	17.7499	0.754123
$555$	12.0984	0.513550
$556$	−113.133	−4.79791
$557$	−35.6198	−1.50926	−0.754630	−	0.656150i	$-0.772184\pi$
$557$	−35.6198	−1.50926	−0.754630	+	0.656150i	$0.772184\pi$
$558$	78.6864	3.33106
$559$	−32.1952	−1.36171
$560$	30.8310	1.30285
$561$	7.26482	0.306721
$562$	36.7248	1.54914
$563$	7.75825	0.326971	0.163486	−	0.986546i	$-0.447726\pi$
$563$	7.75825	0.326971	0.163486	+	0.986546i	$0.447726\pi$
$564$	105.010	4.42174
$565$	14.2018	0.597476
$566$	64.3933	2.70665
$567$	78.5839	3.30021
$568$	−7.97772	−0.334738
$569$	33.8329	1.41835	0.709174	−	0.705034i	$-0.249068\pi$
$569$	33.8329	1.41835	0.709174	+	0.705034i	$0.249068\pi$
$570$	−71.9998	−3.01574
$571$	4.13386	0.172997	0.0864983	−	0.996252i	$-0.472432\pi$
$571$	4.13386	0.172997	0.0864983	+	0.996252i	$0.472432\pi$
$572$	82.1647	3.43548
$573$	21.8874	0.914359
$574$	65.4640	2.73241
$575$	−6.36227	−0.265325
$576$	234.172	9.75716
$577$	−4.81498	−0.200450	−0.100225	−	0.994965i	$-0.531956\pi$
$577$	−4.81498	−0.200450	−0.100225	+	0.994965i	$0.531956\pi$
$578$	44.7086	1.85963
$579$	−23.8973	−0.993140
$580$	−43.8164	−1.81938
$581$	−15.8158	−0.656150
$582$	163.314	6.76959
$583$	10.0464	0.416081
$584$	−58.9954	−2.44125
$585$	45.3834	1.87637
$586$	−10.4584	−0.432032
$587$	−19.1167	−0.789032	−0.394516	−	0.918889i	$-0.629088\pi$
$587$	−19.1167	−0.789032	−0.394516	+	0.918889i	$0.629088\pi$
$588$	−45.0930	−1.85961
$589$	−26.7781	−1.10337
$590$	3.26332	0.134349
$591$	18.5578	0.763367
$592$	51.7788	2.12809
$593$	35.6831	1.46533	0.732665	−	0.680590i	$-0.238276\pi$
$593$	35.6831	1.46533	0.732665	+	0.680590i	$0.238276\pi$
$594$	−141.347	−5.79955
$595$	1.62106	0.0664569
$596$	−59.3027	−2.42913
$597$	24.4139	0.999193
$598$	93.1616	3.80966
$599$	12.9534	0.529261	0.264631	−	0.964350i	$-0.414750\pi$
$599$	12.9534	0.529261	0.264631	+	0.964350i	$0.414750\pi$
$600$	−31.4283	−1.28306
$601$	−19.7547	−0.805811	−0.402905	−	0.915242i	$-0.632000\pi$
$601$	−19.7547	−0.805811	−0.402905	+	0.915242i	$0.632000\pi$
$602$	34.7168	1.41495
$603$	10.1965	0.415235
$604$	−22.6307	−0.920829
$605$	−3.03406	−0.123352
$606$	130.193	5.28873
$607$	−4.29736	−0.174424	−0.0872122	−	0.996190i	$-0.527796\pi$
$607$	−4.29736	−0.174424	−0.0872122	+	0.996190i	$0.527796\pi$
$608$	−162.828	−6.60355
$609$	−58.3126	−2.36295
$610$	−20.8552	−0.844403
$611$	30.8486	1.24800
$612$	34.7639	1.40525
$613$	26.6328	1.07569	0.537844	−	0.843044i	$-0.319239\pi$
$613$	26.6328	1.07569	0.537844	+	0.843044i	$0.319239\pi$
$614$	−81.5813	−3.29235
$615$	−38.1779	−1.53948
$616$	−55.8641	−2.25083
$617$	7.24705	0.291755	0.145878	−	0.989303i	$-0.453399\pi$
$617$	7.24705	0.291755	0.145878	+	0.989303i	$0.453399\pi$
$618$	−94.3399	−3.79491
$619$	15.5467	0.624873	0.312437	−	0.949939i	$-0.398855\pi$
$619$	15.5467	0.624873	0.312437	+	0.949939i	$0.398855\pi$
$620$	−18.5384	−0.744519
$621$	−117.026	−4.69610
$622$	88.2748	3.53950
$623$	4.06423	0.162830
$624$	263.283	10.5397
$625$	1.00000	0.0400000
$626$	−69.2355	−2.76721
$627$	74.6367	2.98070
$628$	−67.7323	−2.70281
$629$	2.72247	0.108552
$630$	−48.9379	−1.94973
$631$	35.7808	1.42441	0.712206	−	0.701970i	$-0.247696\pi$
$631$	35.7808	1.42441	0.712206	+	0.701970i	$0.247696\pi$
$632$	96.9154	3.85509
$633$	58.6479	2.33104
$634$	−35.0669	−1.39268
$635$	−20.1328	−0.798947
$636$	65.1657	2.58399
$637$	−13.2468	−0.524859
$638$	62.2033	2.46265
$639$	7.24458	0.286591
$640$	−33.9052	−1.34022
$641$	36.0122	1.42240	0.711198	−	0.702992i	$-0.248153\pi$
$641$	36.0122	1.42240	0.711198	+	0.702992i	$0.248153\pi$
$642$	−139.405	−5.50188
$643$	34.1320	1.34603	0.673017	−	0.739627i	$-0.264998\pi$
$643$	34.1320	1.34603	0.673017	+	0.739627i	$0.264998\pi$
$644$	−73.3550	−2.89059
$645$	−20.2465	−0.797205
$646$	−16.2019	−0.637454
$647$	−1.83324	−0.0720720	−0.0360360	−	0.999350i	$-0.511473\pi$
$647$	−1.83324	−0.0720720	−0.0360360	+	0.999350i	$0.511473\pi$
$648$	−342.838	−13.4680
$649$	−3.38284	−0.132788
$650$	−14.6428	−0.574339
$651$	−24.6716	−0.966957
$652$	−113.590	−4.44854
$653$	11.1070	0.434651	0.217325	−	0.976099i	$-0.430267\pi$
$653$	11.1070	0.434651	0.217325	+	0.976099i	$0.430267\pi$
$654$	78.7705	3.08017
$655$	5.66618	0.221396
$656$	−163.393	−6.37944
$657$	53.5738	2.09011
$658$	−33.2647	−1.29679
$659$	5.97707	0.232833	0.116417	−	0.993200i	$-0.462859\pi$
$659$	5.97707	0.232833	0.116417	+	0.993200i	$0.462859\pi$
$660$	51.6706	2.01128
$661$	−40.3921	−1.57107	−0.785535	−	0.618817i	$-0.787612\pi$
$661$	−40.3921	−1.57107	−0.785535	+	0.618817i	$0.787612\pi$
$662$	−17.9626	−0.698134
$663$	13.8431	0.537622
$664$	68.9997	2.67771
$665$	16.6543	0.645826
$666$	−82.1883	−3.18473
$667$	51.5002	1.99410
$668$	−15.3052	−0.592177
$669$	−65.2857	−2.52409
$670$	−3.28988	−0.127099
$671$	21.6190	0.834593
$672$	−150.019	−5.78711
$673$	18.5258	0.714116	0.357058	−	0.934082i	$-0.383780\pi$
$673$	18.5258	0.714116	0.357058	+	0.934082i	$0.383780\pi$
$674$	42.7265	1.64576
$675$	18.3938	0.707978
$676$	86.1958	3.31522
$677$	−7.00911	−0.269382	−0.134691	−	0.990888i	$-0.543004\pi$
$677$	−7.00911	−0.269382	−0.134691	+	0.990888i	$0.543004\pi$
$678$	−130.776	−5.02242
$679$	−37.7763	−1.44972
$680$	−7.07221	−0.271207
$681$	−26.8828	−1.03015
$682$	26.3177	1.00776
$683$	46.7942	1.79053	0.895265	−	0.445535i	$-0.146986\pi$
$683$	46.7942	1.79053	0.895265	+	0.445535i	$0.146986\pi$
$684$	357.154	13.6561
$685$	−11.3346	−0.433074
$686$	54.8795	2.09531
$687$	21.8583	0.833945
$688$	−86.6508	−3.30353
$689$	19.1435	0.729310
$690$	58.5862	2.23034
$691$	−18.9231	−0.719868	−0.359934	−	0.932978i	$-0.617201\pi$
$691$	−18.9231	−0.719868	−0.359934	+	0.932978i	$0.617201\pi$
$692$	69.4345	2.63950
$693$	50.7302	1.92708
$694$	−72.4150	−2.74883
$695$	−20.9002	−0.792790
$696$	254.401	9.64304
$697$	−8.59105	−0.325409
$698$	−35.3939	−1.33968
$699$	25.8617	0.978178
$700$	11.5297	0.435781
$701$	1.72466	0.0651397	0.0325698	−	0.999469i	$-0.489631\pi$
$701$	1.72466	0.0651397	0.0325698	+	0.999469i	$0.489631\pi$
$702$	−269.337	−10.1655
$703$	27.9699	1.05490
$704$	78.3220	2.95187
$705$	19.3996	0.730633
$706$	9.57267	0.360272
$707$	−30.1150	−1.13259
$708$	−21.9426	−0.824652
$709$	−28.6190	−1.07481	−0.537405	−	0.843324i	$-0.680595\pi$
$709$	−28.6190	−1.07481	−0.537405	+	0.843324i	$0.680595\pi$
$710$	−2.33744	−0.0877227
$711$	−88.0091	−3.30060
$712$	−17.7310	−0.664499
$713$	21.7894	0.816018
$714$	−14.9273	−0.558641
$715$	15.1791	0.567667
$716$	−26.9557	−1.00738
$717$	−53.3573	−1.99267
$718$	50.2856	1.87664
$719$	−35.1644	−1.31141	−0.655705	−	0.755017i	$-0.727629\pi$
$719$	−35.1644	−1.31141	−0.655705	+	0.755017i	$0.727629\pi$
$720$	122.146	4.55210
$721$	21.8218	0.812687
$722$	−114.722	−4.26953
$723$	−9.50609	−0.353535
$724$	−8.97878	−0.333694
$725$	−8.09464	−0.300627
$726$	27.9388	1.03690
$727$	8.21134	0.304542	0.152271	−	0.988339i	$-0.451341\pi$
$727$	8.21134	0.304542	0.152271	+	0.988339i	$0.451341\pi$
$728$	−106.449	−3.94526
$729$	124.703	4.61864
$730$	−17.2854	−0.639763
$731$	−4.55600	−0.168510
$732$	140.230	5.18307
$733$	28.1952	1.04142	0.520708	−	0.853735i	$-0.325668\pi$
$733$	28.1952	1.04142	0.520708	+	0.853735i	$0.325668\pi$
$734$	−93.7810	−3.46152
$735$	−8.33049	−0.307275
$736$	132.493	4.88376
$737$	3.41037	0.125623
$738$	259.354	9.54695
$739$	49.0577	1.80462	0.902309	−	0.431091i	$-0.141871\pi$
$739$	49.0577	1.80462	0.902309	+	0.431091i	$0.141871\pi$
$740$	19.3634	0.711814
$741$	142.220	5.22459
$742$	−20.6429	−0.757824
$743$	2.43244	0.0892377	0.0446188	−	0.999004i	$-0.485793\pi$
$743$	2.43244	0.0892377	0.0446188	+	0.999004i	$0.485793\pi$
$744$	107.635	3.94609
$745$	−10.9556	−0.401381
$746$	2.65201	0.0970970
$747$	−62.6587	−2.29256
$748$	11.6273	0.425135
$749$	32.2459	1.17824
$750$	−9.20838	−0.336243
$751$	12.9237	0.471593	0.235796	−	0.971803i	$-0.424230\pi$
$751$	12.9237	0.471593	0.235796	+	0.971803i	$0.424230\pi$
$752$	83.0264	3.02766
$753$	−48.9701	−1.78457
$754$	118.528	4.31655
$755$	−4.18079	−0.152155
$756$	212.075	7.71309
$757$	−19.4901	−0.708380	−0.354190	−	0.935174i	$-0.615243\pi$
$757$	−19.4901	−0.708380	−0.354190	+	0.935174i	$0.615243\pi$
$758$	−11.0630	−0.401825
$759$	−60.7319	−2.20443
$760$	−72.6579	−2.63558
$761$	52.0215	1.88578	0.942889	−	0.333107i	$-0.108097\pi$
$761$	52.0215	1.88578	0.942889	+	0.333107i	$0.108097\pi$
$762$	185.391	6.71600
$763$	−18.2205	−0.659625
$764$	35.0306	1.26736
$765$	6.42228	0.232198
$766$	6.10627	0.220628
$767$	−6.44600	−0.232752
$768$	124.505	4.49268
$769$	12.8789	0.464427	0.232213	−	0.972665i	$-0.425403\pi$
$769$	12.8789	0.464427	0.232213	+	0.972665i	$0.425403\pi$
$770$	−16.3680	−0.589861
$771$	50.6356	1.82360
$772$	−38.2475	−1.37656
$773$	32.3380	1.16312	0.581558	−	0.813505i	$-0.302443\pi$
$773$	32.3380	1.16312	0.581558	+	0.813505i	$0.302443\pi$
$774$	137.541	4.94379
$775$	−3.42478	−0.123022
$776$	164.807	5.91623
$777$	25.7696	0.924480
$778$	28.1749	1.01012
$779$	−88.2620	−3.16232
$780$	98.4584	3.52538
$781$	2.42305	0.0867035
$782$	13.1835	0.471439
$783$	−148.891	−5.32094
$784$	−35.6528	−1.27331
$785$	−12.5129	−0.446603
$786$	−52.1763	−1.86107
$787$	−35.7703	−1.27507	−0.637536	−	0.770421i	$-0.720046\pi$
$787$	−35.7703	−1.27507	−0.637536	+	0.770421i	$0.720046\pi$
$788$	29.7016	1.05808
$789$	−74.7714	−2.66193
$790$	28.3959	1.01028
$791$	30.2499	1.07556
$792$	−221.321	−7.86431
$793$	41.1951	1.46288
$794$	70.7843	2.51204
$795$	12.0387	0.426969
$796$	39.0741	1.38495
$797$	33.6546	1.19211	0.596053	−	0.802945i	$-0.296735\pi$
$797$	33.6546	1.19211	0.596053	+	0.802945i	$0.296735\pi$
$798$	−153.359	−5.42886
$799$	4.36543	0.154438
$800$	−20.8248	−0.736269
$801$	16.1016	0.568921
$802$	50.5152	1.78375
$803$	17.9185	0.632330
$804$	22.1212	0.780154
$805$	−13.5516	−0.477631
$806$	50.1485	1.76641
$807$	40.6290	1.43021
$808$	131.383	4.62204
$809$	−30.6068	−1.07608	−0.538039	−	0.842920i	$-0.680835\pi$
$809$	−30.6068	−1.07608	−0.538039	+	0.842920i	$0.680835\pi$
$810$	−100.450	−3.52947
$811$	−0.335342	−0.0117755	−0.00588773	−	0.999983i	$-0.501874\pi$
$811$	−0.335342	−0.0117755	−0.00588773	+	0.999983i	$0.501874\pi$
$812$	−93.3287	−3.27520
$813$	−5.44383	−0.190923
$814$	−27.4890	−0.963489
$815$	−20.9847	−0.735061
$816$	37.2576	1.30428
$817$	−46.8071	−1.63757
$818$	5.34998	0.187058
$819$	96.6665	3.37780
$820$	−61.1034	−2.13382
$821$	−32.7532	−1.14310	−0.571548	−	0.820569i	$-0.693657\pi$
$821$	−32.7532	−1.14310	−0.571548	+	0.820569i	$0.693657\pi$
$822$	104.374	3.64045
$823$	31.5171	1.09862	0.549308	−	0.835620i	$-0.314891\pi$
$823$	31.5171	1.09862	0.549308	+	0.835620i	$0.314891\pi$
$824$	−95.2022	−3.31652
$825$	9.54563	0.332336
$826$	6.95086	0.241851
$827$	−16.3491	−0.568513	−0.284257	−	0.958748i	$-0.591747\pi$
$827$	−16.3491	−0.568513	−0.284257	+	0.958748i	$0.591747\pi$
$828$	−290.616	−10.0996
$829$	4.84764	0.168365	0.0841827	−	0.996450i	$-0.473172\pi$
$829$	4.84764	0.168365	0.0841827	+	0.996450i	$0.473172\pi$
$830$	20.2167	0.701731
$831$	−22.0488	−0.764866
$832$	149.243	5.17406
$833$	−1.87458	−0.0649504
$834$	192.457	6.66424
$835$	−2.82749	−0.0978493
$836$	119.455	4.13145
$837$	−62.9948	−2.17742
$838$	−31.3155	−1.08178
$839$	−41.9581	−1.44856	−0.724278	−	0.689508i	$-0.757827\pi$
$839$	−41.9581	−1.44856	−0.724278	+	0.689508i	$0.757827\pi$
$840$	−66.9422	−2.30973
$841$	36.5232	1.25942
$842$	17.3274	0.597142
$843$	−45.6192	−1.57121
$844$	93.8653	3.23098
$845$	15.9238	0.547796
$846$	−131.788	−4.53095
$847$	−6.46253	−0.222055
$848$	51.5232	1.76931
$849$	−79.9889	−2.74521
$850$	−2.07213	−0.0710735
$851$	−22.7591	−0.780172
$852$	15.7170	0.538454
$853$	−21.5815	−0.738936	−0.369468	−	0.929243i	$-0.620460\pi$
$853$	−21.5815	−0.738936	−0.369468	+	0.929243i	$0.620460\pi$
$854$	−44.4215	−1.52007
$855$	65.9807	2.25649
$856$	−140.679	−4.80832
$857$	17.7043	0.604769	0.302384	−	0.953186i	$-0.402217\pi$
$857$	17.7043	0.604769	0.302384	+	0.953186i	$0.402217\pi$
$858$	−139.775	−4.77184
$859$	−36.2877	−1.23812	−0.619060	−	0.785344i	$-0.712486\pi$
$859$	−36.2877	−1.23812	−0.619060	+	0.785344i	$0.712486\pi$
$860$	−32.4043	−1.10498
$861$	−81.3188	−2.77134
$862$	73.6270	2.50774
$863$	40.5850	1.38153	0.690765	−	0.723079i	$-0.257274\pi$
$863$	40.5850	1.38153	0.690765	+	0.723079i	$0.257274\pi$
$864$	−383.048	−13.0316
$865$	12.8273	0.436142
$866$	−9.93157	−0.337488
$867$	−55.5367	−1.88612
$868$	−39.4867	−1.34026
$869$	−29.4359	−0.998543
$870$	74.5385	2.52709
$871$	6.49847	0.220192
$872$	79.4905	2.69189
$873$	−149.661	−5.06527
$874$	135.443	4.58143
$875$	2.13000	0.0720070
$876$	116.227	3.92696
$877$	15.5006	0.523417	0.261708	−	0.965147i	$-0.415714\pi$
$877$	15.5006	0.523417	0.261708	+	0.965147i	$0.415714\pi$
$878$	−15.0912	−0.509304
$879$	12.9913	0.438186
$880$	40.8533	1.37716
$881$	42.3720	1.42755	0.713775	−	0.700375i	$-0.246984\pi$
$881$	42.3720	1.42755	0.713775	+	0.700375i	$0.246984\pi$
$882$	56.5915	1.90554
$883$	26.9629	0.907372	0.453686	−	0.891162i	$-0.350109\pi$
$883$	26.9629	0.907372	0.453686	+	0.891162i	$0.350109\pi$
$884$	22.1558	0.745179
$885$	−4.05367	−0.136263
$886$	−109.124	−3.66609
$887$	29.4205	0.987843	0.493922	−	0.869506i	$-0.335563\pi$
$887$	29.4205	0.987843	0.493922	+	0.869506i	$0.335563\pi$
$888$	−112.425	−3.77275
$889$	−42.8829	−1.43825
$890$	−5.19513	−0.174141
$891$	104.129	3.48846
$892$	−104.489	−3.49855
$893$	44.8493	1.50082
$894$	100.883	3.37404
$895$	−4.97979	−0.166456
$896$	−72.2180	−2.41263
$897$	−115.725	−3.86393
$898$	8.04170	0.268355
$899$	27.7224	0.924592
$900$	45.6781	1.52260
$901$	2.70903	0.0902509
$902$	86.7445	2.88828
$903$	−43.1250	−1.43511
$904$	−131.971	−4.38930
$905$	−1.65874	−0.0551384
$906$	38.4983	1.27902
$907$	45.1512	1.49922	0.749610	−	0.661880i	$-0.230241\pi$
$907$	45.1512	1.49922	0.749610	+	0.661880i	$0.230241\pi$
$908$	−43.0256	−1.42785
$909$	−119.309	−3.95724
$910$	−31.1892	−1.03391
$911$	0.938771	0.0311029	0.0155514	−	0.999879i	$-0.495050\pi$
$911$	0.938771	0.0311029	0.0155514	+	0.999879i	$0.495050\pi$
$912$	382.774	12.6749
$913$	−20.9571	−0.693578
$914$	65.0261	2.15087
$915$	25.9062	0.856432
$916$	34.9839	1.15590
$917$	12.0689	0.398552
$918$	−38.1144	−1.25796
$919$	16.4364	0.542188	0.271094	−	0.962553i	$-0.412615\pi$
$919$	16.4364	0.542188	0.271094	+	0.962553i	$0.412615\pi$
$920$	59.1217	1.94918
$921$	101.340	3.33926
$922$	47.8006	1.57423
$923$	4.61712	0.151974
$924$	110.058	3.62065
$925$	3.57720	0.117618
$926$	−23.0724	−0.758205
$927$	86.4532	2.83950
$928$	168.570	5.53357
$929$	45.2806	1.48561	0.742804	−	0.669509i	$-0.233495\pi$
$929$	45.2806	1.48561	0.742804	+	0.669509i	$0.233495\pi$
$930$	31.5367	1.03413
$931$	−19.2589	−0.631186
$932$	41.3913	1.35582
$933$	−109.654	−3.58992
$934$	−89.4111	−2.92562
$935$	2.14802	0.0702478
$936$	−421.728	−13.7846
$937$	29.0808	0.950027	0.475013	−	0.879979i	$-0.342443\pi$
$937$	29.0808	0.950027	0.475013	+	0.879979i	$0.342443\pi$
$938$	−7.00744	−0.228801
$939$	86.0037	2.80663
$940$	31.0489	1.01270
$941$	−7.29798	−0.237907	−0.118954	−	0.992900i	$-0.537954\pi$
$941$	−7.29798	−0.237907	−0.118954	+	0.992900i	$0.537954\pi$
$942$	115.223	3.75418
$943$	71.8188	2.33874
$944$	−17.3489	−0.564657
$945$	39.1787	1.27448
$946$	46.0023	1.49566
$947$	−56.9429	−1.85040	−0.925198	−	0.379484i	$-0.876102\pi$
$947$	−56.9429	−1.85040	−0.925198	+	0.379484i	$0.876102\pi$
$948$	−190.934	−6.20124
$949$	34.1437	1.10835
$950$	−21.2885	−0.690690
$951$	43.5598	1.41252
$952$	−15.0638	−0.488220
$953$	−8.60909	−0.278876	−0.139438	−	0.990231i	$-0.544530\pi$
$953$	−8.60909	−0.278876	−0.139438	+	0.990231i	$0.544530\pi$
$954$	−81.7826	−2.64781
$955$	6.47155	0.209414
$956$	−85.3979	−2.76196
$957$	−77.2684	−2.49773
$958$	33.4842	1.08182
$959$	−24.1427	−0.779610
$960$	93.8537	3.02911
$961$	−19.2709	−0.621641
$962$	−52.3803	−1.68881
$963$	127.751	4.11672
$964$	−15.2144	−0.490023
$965$	−7.06584	−0.227457
$966$	124.788	4.01500
$967$	−26.9992	−0.868237	−0.434119	−	0.900856i	$-0.642940\pi$
$967$	−26.9992	−0.868237	−0.434119	+	0.900856i	$0.642940\pi$
$968$	28.1941	0.906194
$969$	20.1258	0.646535
$970$	48.2879	1.55043
$971$	−34.0616	−1.09309	−0.546544	−	0.837431i	$-0.684057\pi$
$971$	−34.0616	−1.09309	−0.546544	+	0.837431i	$0.684057\pi$
$972$	376.731	12.0837
$973$	−44.5173	−1.42716
$974$	−49.2412	−1.57779
$975$	18.1892	0.582521
$976$	110.873	3.54896
$977$	3.42367	0.109533	0.0547665	−	0.998499i	$-0.482559\pi$
$977$	3.42367	0.109533	0.0547665	+	0.998499i	$0.482559\pi$
$978$	193.235	6.17897
$979$	5.38540	0.172118
$980$	−13.3329	−0.425903
$981$	−72.1855	−2.30470
$982$	−57.1894	−1.82499
$983$	39.6326	1.26408	0.632042	−	0.774934i	$-0.282217\pi$
$983$	39.6326	1.26408	0.632042	+	0.774934i	$0.282217\pi$
$984$	354.770	11.3097
$985$	5.48708	0.174833
$986$	16.7732	0.534166
$987$	41.3212	1.31527
$988$	227.622	7.24162
$989$	38.0869	1.21109
$990$	−64.8463	−2.06095
$991$	−28.0532	−0.891139	−0.445570	−	0.895247i	$-0.646999\pi$
$991$	−28.0532	−0.891139	−0.445570	+	0.895247i	$0.646999\pi$
$992$	71.3205	2.26443
$993$	22.3129	0.708080
$994$	−4.97875	−0.157916
$995$	7.21856	0.228844
$996$	−135.937	−4.30732
$997$	−35.4524	−1.12279	−0.561395	−	0.827548i	$-0.689735\pi$
$997$	−35.4524	−1.12279	−0.561395	+	0.827548i	$0.689735\pi$
$998$	−15.9960	−0.506345
$999$	65.7983	2.08177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.2	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.2	✓	111	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72268 q^{2} +3.38210 q^{3} +5.41301 q^{4} +1.00000 q^{5} -9.20838 q^{6} +2.13000 q^{7} -9.29255 q^{8} +8.43858 q^{9} +O(q^{10})\)	\(q-2.72268 q^{2} +3.38210 q^{3} +5.41301 q^{4} +1.00000 q^{5} -9.20838 q^{6} +2.13000 q^{7} -9.29255 q^{8} +8.43858 q^{9} -2.72268 q^{10} +2.82240 q^{11} +18.3073 q^{12} +5.37809 q^{13} -5.79931 q^{14} +3.38210 q^{15} +14.4747 q^{16} +0.761062 q^{17} -22.9756 q^{18} +7.81894 q^{19} +5.41301 q^{20} +7.20386 q^{21} -7.68451 q^{22} -6.36227 q^{23} -31.4283 q^{24} +1.00000 q^{25} -14.6428 q^{26} +18.3938 q^{27} +11.5297 q^{28} -8.09464 q^{29} -9.20838 q^{30} -3.42478 q^{31} -20.8248 q^{32} +9.54563 q^{33} -2.07213 q^{34} +2.13000 q^{35} +45.6781 q^{36} +3.57720 q^{37} -21.2885 q^{38} +18.1892 q^{39} -9.29255 q^{40} -11.2882 q^{41} -19.6138 q^{42} -5.98637 q^{43} +15.2777 q^{44} +8.43858 q^{45} +17.3224 q^{46} +5.73598 q^{47} +48.9547 q^{48} -2.46311 q^{49} -2.72268 q^{50} +2.57398 q^{51} +29.1116 q^{52} +3.55954 q^{53} -50.0805 q^{54} +2.82240 q^{55} -19.7931 q^{56} +26.4444 q^{57} +22.0391 q^{58} -1.19857 q^{59} +18.3073 q^{60} +7.65980 q^{61} +9.32460 q^{62} +17.9741 q^{63} +27.7501 q^{64} +5.37809 q^{65} -25.9897 q^{66} +1.20832 q^{67} +4.11964 q^{68} -21.5178 q^{69} -5.79931 q^{70} +0.858507 q^{71} -78.4159 q^{72} +6.34868 q^{73} -9.73959 q^{74} +3.38210 q^{75} +42.3240 q^{76} +6.01170 q^{77} -49.5235 q^{78} -10.4294 q^{79} +14.4747 q^{80} +36.8939 q^{81} +30.7343 q^{82} -7.42527 q^{83} +38.9945 q^{84} +0.761062 q^{85} +16.2990 q^{86} -27.3768 q^{87} -26.2273 q^{88} +1.90809 q^{89} -22.9756 q^{90} +11.4553 q^{91} -34.4390 q^{92} -11.5829 q^{93} -15.6173 q^{94} +7.81894 q^{95} -70.4316 q^{96} -17.7354 q^{97} +6.70628 q^{98} +23.8171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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