LMFDB - Embedded newform 6005.2.a.g.1.9

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:	$113$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.61532 q^{2} +0.118458 q^{3} +4.83989 q^{4} -1.00000 q^{5} -0.309805 q^{6} -0.279288 q^{7} -7.42721 q^{8} -2.98597 q^{9} +O(q^{10})$	\(q-2.61532 q^{2} +0.118458 q^{3} +4.83989 q^{4} -1.00000 q^{5} -0.309805 q^{6} -0.279288 q^{7} -7.42721 q^{8} -2.98597 q^{9} +2.61532 q^{10} +1.51228 q^{11} +0.573322 q^{12} +6.55978 q^{13} +0.730428 q^{14} -0.118458 q^{15} +9.74474 q^{16} -0.741439 q^{17} +7.80926 q^{18} +6.45376 q^{19} -4.83989 q^{20} -0.0330839 q^{21} -3.95510 q^{22} -5.49802 q^{23} -0.879811 q^{24} +1.00000 q^{25} -17.1559 q^{26} -0.709084 q^{27} -1.35173 q^{28} +4.96614 q^{29} +0.309805 q^{30} +6.47632 q^{31} -10.6312 q^{32} +0.179142 q^{33} +1.93910 q^{34} +0.279288 q^{35} -14.4517 q^{36} +9.53849 q^{37} -16.8786 q^{38} +0.777057 q^{39} +7.42721 q^{40} -0.762472 q^{41} +0.0865249 q^{42} +5.30011 q^{43} +7.31927 q^{44} +2.98597 q^{45} +14.3791 q^{46} +0.739734 q^{47} +1.15434 q^{48} -6.92200 q^{49} -2.61532 q^{50} -0.0878292 q^{51} +31.7486 q^{52} +1.95913 q^{53} +1.85448 q^{54} -1.51228 q^{55} +2.07433 q^{56} +0.764498 q^{57} -12.9880 q^{58} -0.941317 q^{59} -0.573322 q^{60} +3.97162 q^{61} -16.9376 q^{62} +0.833946 q^{63} +8.31442 q^{64} -6.55978 q^{65} -0.468512 q^{66} -4.16986 q^{67} -3.58848 q^{68} -0.651283 q^{69} -0.730428 q^{70} +9.91347 q^{71} +22.1774 q^{72} -8.63925 q^{73} -24.9462 q^{74} +0.118458 q^{75} +31.2355 q^{76} -0.422363 q^{77} -2.03225 q^{78} +2.17004 q^{79} -9.74474 q^{80} +8.87391 q^{81} +1.99411 q^{82} -8.60261 q^{83} -0.160122 q^{84} +0.741439 q^{85} -13.8615 q^{86} +0.588278 q^{87} -11.2320 q^{88} -3.17906 q^{89} -7.80926 q^{90} -1.83207 q^{91} -26.6098 q^{92} +0.767171 q^{93} -1.93464 q^{94} -6.45376 q^{95} -1.25935 q^{96} -12.4135 q^{97} +18.1032 q^{98} -4.51562 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) $ 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * 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 $

$2$	−2.61532	−1.84931	−0.924655	−	0.380807i	$-0.875646\pi$
$2$	−2.61532	−1.84931	−0.924655	+	0.380807i	$0.875646\pi$
$3$	0.118458	0.0683916	0.0341958	−	0.999415i	$-0.489113\pi$
$3$	0.118458	0.0683916	0.0341958	+	0.999415i	$0.489113\pi$
$4$	4.83989	2.41994
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.309805	−0.126477
$7$	−0.279288	−0.105561	−0.0527806	−	0.998606i	$-0.516808\pi$
$7$	−0.279288	−0.105561	−0.0527806	+	0.998606i	$0.516808\pi$
$8$	−7.42721	−2.62592
$9$	−2.98597	−0.995323
$10$	2.61532	0.827036
$11$	1.51228	0.455970	0.227985	−	0.973665i	$-0.426786\pi$
$11$	1.51228	0.455970	0.227985	+	0.973665i	$0.426786\pi$
$12$	0.573322	0.165504
$13$	6.55978	1.81936	0.909678	−	0.415314i	$-0.136328\pi$
$13$	6.55978	1.81936	0.909678	+	0.415314i	$0.136328\pi$
$14$	0.730428	0.195215
$15$	−0.118458	−0.0305857
$16$	9.74474	2.43618
$17$	−0.741439	−0.179825	−0.0899127	−	0.995950i	$-0.528659\pi$
$17$	−0.741439	−0.179825	−0.0899127	+	0.995950i	$0.528659\pi$
$18$	7.80926	1.84066
$19$	6.45376	1.48059	0.740297	−	0.672280i	$-0.234685\pi$
$19$	6.45376	1.48059	0.740297	+	0.672280i	$0.234685\pi$
$20$	−4.83989	−1.08223
$21$	−0.0330839	−0.00721950
$22$	−3.95510	−0.843230
$23$	−5.49802	−1.14642	−0.573208	−	0.819410i	$-0.694301\pi$
$23$	−5.49802	−1.14642	−0.573208	+	0.819410i	$0.694301\pi$
$24$	−0.879811	−0.179591
$25$	1.00000	0.200000
$26$	−17.1559	−3.36455
$27$	−0.709084	−0.136463
$28$	−1.35173	−0.255452
$29$	4.96614	0.922190	0.461095	−	0.887351i	$-0.347457\pi$
$29$	4.96614	0.922190	0.461095	+	0.887351i	$0.347457\pi$
$30$	0.309805	0.0565623
$31$	6.47632	1.16318	0.581591	−	0.813481i	$-0.302430\pi$
$31$	6.47632	1.16318	0.581591	+	0.813481i	$0.302430\pi$
$32$	−10.6312	−1.87934
$33$	0.179142	0.0311845
$34$	1.93910	0.332553
$35$	0.279288	0.0472084
$36$	−14.4517	−2.40862
$37$	9.53849	1.56812	0.784059	−	0.620686i	$-0.213146\pi$
$37$	9.53849	1.56812	0.784059	+	0.620686i	$0.213146\pi$
$38$	−16.8786	−2.73807
$39$	0.777057	0.124429
$40$	7.42721	1.17435
$41$	−0.762472	−0.119078	−0.0595391	−	0.998226i	$-0.518963\pi$
$41$	−0.762472	−0.119078	−0.0595391	+	0.998226i	$0.518963\pi$
$42$	0.0865249	0.0133511
$43$	5.30011	0.808259	0.404129	−	0.914702i	$-0.367575\pi$
$43$	5.30011	0.808259	0.404129	+	0.914702i	$0.367575\pi$
$44$	7.31927	1.10342
$45$	2.98597	0.445122
$46$	14.3791	2.12008
$47$	0.739734	0.107901	0.0539507	−	0.998544i	$-0.482819\pi$
$47$	0.739734	0.107901	0.0539507	+	0.998544i	$0.482819\pi$
$48$	1.15434	0.166615
$49$	−6.92200	−0.988857
$50$	−2.61532	−0.369862
$51$	−0.0878292	−0.0122986
$52$	31.7486	4.40274
$53$	1.95913	0.269108	0.134554	−	0.990906i	$-0.457040\pi$
$53$	1.95913	0.269108	0.134554	+	0.990906i	$0.457040\pi$
$54$	1.85448	0.252363
$55$	−1.51228	−0.203916
$56$	2.07433	0.277195
$57$	0.764498	0.101260
$58$	−12.9880	−1.70541
$59$	−0.941317	−0.122549	−0.0612745	−	0.998121i	$-0.519517\pi$
$59$	−0.941317	−0.122549	−0.0612745	+	0.998121i	$0.519517\pi$
$60$	−0.573322	−0.0740156
$61$	3.97162	0.508514	0.254257	−	0.967137i	$-0.418169\pi$
$61$	3.97162	0.508514	0.254257	+	0.967137i	$0.418169\pi$
$62$	−16.9376	−2.15108
$63$	0.833946	0.105067
$64$	8.31442	1.03930
$65$	−6.55978	−0.813641
$66$	−0.468512	−0.0576698
$67$	−4.16986	−0.509430	−0.254715	−	0.967016i	$-0.581982\pi$
$67$	−4.16986	−0.509430	−0.254715	+	0.967016i	$0.581982\pi$
$68$	−3.58848	−0.435167
$69$	−0.651283	−0.0784053
$70$	−0.730428	−0.0873029
$71$	9.91347	1.17651	0.588256	−	0.808674i	$-0.299815\pi$
$71$	9.91347	1.17651	0.588256	+	0.808674i	$0.299815\pi$
$72$	22.1774	2.61363
$73$	−8.63925	−1.01115	−0.505574	−	0.862783i	$-0.668719\pi$
$73$	−8.63925	−1.01115	−0.505574	+	0.862783i	$0.668719\pi$
$74$	−24.9462	−2.89993
$75$	0.118458	0.0136783
$76$	31.2355	3.58295
$77$	−0.422363	−0.0481327
$78$	−2.03225	−0.230107
$79$	2.17004	0.244148	0.122074	−	0.992521i	$-0.461045\pi$
$79$	2.17004	0.244148	0.122074	+	0.992521i	$0.461045\pi$
$80$	−9.74474	−1.08950
$81$	8.87391	0.985990
$82$	1.99411	0.220212
$83$	−8.60261	−0.944259	−0.472130	−	0.881529i	$-0.656515\pi$
$83$	−8.60261	−0.944259	−0.472130	+	0.881529i	$0.656515\pi$
$84$	−0.160122	−0.0174708
$85$	0.741439	0.0804204
$86$	−13.8615	−1.49472
$87$	0.588278	0.0630701
$88$	−11.2320	−1.19734
$89$	−3.17906	−0.336980	−0.168490	−	0.985703i	$-0.553889\pi$
$89$	−3.17906	−0.336980	−0.168490	+	0.985703i	$0.553889\pi$
$90$	−7.80926	−0.823168
$91$	−1.83207	−0.192053
$92$	−26.6098	−2.77426
$93$	0.767171	0.0795519
$94$	−1.93464	−0.199543
$95$	−6.45376	−0.662141
$96$	−1.25935	−0.128531
$97$	−12.4135	−1.26040	−0.630201	−	0.776432i	$-0.717027\pi$
$97$	−12.4135	−1.26040	−0.630201	+	0.776432i	$0.717027\pi$
$98$	18.1032	1.82870
$99$	−4.51562	−0.453837
$100$	4.83989	0.483989
$101$	−1.97009	−0.196031	−0.0980156	−	0.995185i	$-0.531249\pi$
$101$	−1.97009	−0.196031	−0.0980156	+	0.995185i	$0.531249\pi$
$102$	0.229701	0.0227438
$103$	−16.3803	−1.61400	−0.806998	−	0.590554i	$-0.798909\pi$
$103$	−16.3803	−1.61400	−0.806998	+	0.590554i	$0.798909\pi$
$104$	−48.7209	−4.77747
$105$	0.0330839	0.00322866
$106$	−5.12376	−0.497664
$107$	−1.81964	−0.175912	−0.0879558	−	0.996124i	$-0.528033\pi$
$107$	−1.81964	−0.175912	−0.0879558	+	0.996124i	$0.528033\pi$
$108$	−3.43189	−0.330234
$109$	6.87812	0.658805	0.329402	−	0.944190i	$-0.393153\pi$
$109$	6.87812	0.658805	0.329402	+	0.944190i	$0.393153\pi$
$110$	3.95510	0.377104
$111$	1.12991	0.107246
$112$	−2.72159	−0.257166
$113$	−3.07854	−0.289605	−0.144803	−	0.989461i	$-0.546255\pi$
$113$	−3.07854	−0.289605	−0.144803	+	0.989461i	$0.546255\pi$
$114$	−1.99940	−0.187261
$115$	5.49802	0.512693
$116$	24.0356	2.23165
$117$	−19.5873	−1.81085
$118$	2.46184	0.226631
$119$	0.207075	0.0189826
$120$	0.879811	0.0803154
$121$	−8.71300	−0.792091
$122$	−10.3871	−0.940399
$123$	−0.0903207	−0.00814395
$124$	31.3447	2.81484
$125$	−1.00000	−0.0894427
$126$	−2.18104	−0.194302
$127$	1.49768	0.132897	0.0664486	−	0.997790i	$-0.478833\pi$
$127$	1.49768	0.132897	0.0664486	+	0.997790i	$0.478833\pi$
$128$	−0.482499	−0.0426473
$129$	0.627839	0.0552781
$130$	17.1559	1.50467
$131$	12.3212	1.07651	0.538255	−	0.842782i	$-0.319084\pi$
$131$	12.3212	1.07651	0.538255	+	0.842782i	$0.319084\pi$
$132$	0.867025	0.0754648
$133$	−1.80246	−0.156293
$134$	10.9055	0.942093
$135$	0.709084	0.0610283
$136$	5.50682	0.472206
$137$	8.99734	0.768695	0.384347	−	0.923189i	$-0.374426\pi$
$137$	8.99734	0.768695	0.384347	+	0.923189i	$0.374426\pi$
$138$	1.70331	0.144996
$139$	4.13543	0.350763	0.175381	−	0.984501i	$-0.443884\pi$
$139$	4.13543	0.350763	0.175381	+	0.984501i	$0.443884\pi$
$140$	1.35173	0.114242
$141$	0.0876273	0.00737955
$142$	−25.9269	−2.17574
$143$	9.92024	0.829572
$144$	−29.0975	−2.42479
$145$	−4.96614	−0.412416
$146$	22.5944	1.86992
$147$	−0.819964	−0.0676295
$148$	46.1652	3.79476
$149$	20.1522	1.65093	0.825467	−	0.564450i	$-0.190912\pi$
$149$	20.1522	1.65093	0.825467	+	0.564450i	$0.190912\pi$
$150$	−0.309805	−0.0252955
$151$	18.4128	1.49841	0.749205	−	0.662338i	$-0.230436\pi$
$151$	18.4128	1.49841	0.749205	+	0.662338i	$0.230436\pi$
$152$	−47.9334	−3.88791
$153$	2.21391	0.178984
$154$	1.10461	0.0890123
$155$	−6.47632	−0.520191
$156$	3.76087	0.301111
$157$	17.9733	1.43443	0.717213	−	0.696854i	$-0.245417\pi$
$157$	17.9733	1.43443	0.717213	+	0.696854i	$0.245417\pi$
$158$	−5.67534	−0.451506
$159$	0.232075	0.0184047
$160$	10.6312	0.840468
$161$	1.53553	0.121017
$162$	−23.2081	−1.82340
$163$	−21.8261	−1.70955	−0.854777	−	0.518996i	$-0.826306\pi$
$163$	−21.8261	−1.70955	−0.854777	+	0.518996i	$0.826306\pi$
$164$	−3.69028	−0.288162
$165$	−0.179142	−0.0139461
$166$	22.4986	1.74623
$167$	15.3719	1.18952	0.594758	−	0.803905i	$-0.297248\pi$
$167$	15.3719	1.18952	0.594758	+	0.803905i	$0.297248\pi$
$168$	0.245721	0.0189578
$169$	30.0307	2.31006
$170$	−1.93910	−0.148722
$171$	−19.2707	−1.47367
$172$	25.6519	1.95594
$173$	−10.9101	−0.829480	−0.414740	−	0.909940i	$-0.636127\pi$
$173$	−10.9101	−0.829480	−0.414740	+	0.909940i	$0.636127\pi$
$174$	−1.53854	−0.116636
$175$	−0.279288	−0.0211122
$176$	14.7368	1.11083
$177$	−0.111506	−0.00838133
$178$	8.31427	0.623181
$179$	−19.5892	−1.46417	−0.732084	−	0.681215i	$-0.761452\pi$
$179$	−19.5892	−1.46417	−0.732084	+	0.681215i	$0.761452\pi$
$180$	14.4517	1.07717
$181$	−22.0686	−1.64035	−0.820173	−	0.572116i	$-0.806123\pi$
$181$	−22.0686	−1.64035	−0.820173	+	0.572116i	$0.806123\pi$
$182$	4.79145	0.355166
$183$	0.470469	0.0347781
$184$	40.8349	3.01039
$185$	−9.53849	−0.701284
$186$	−2.00640	−0.147116
$187$	−1.12126	−0.0819950
$188$	3.58023	0.261115
$189$	0.198039	0.0144052
$190$	16.8786	1.22450
$191$	−2.68413	−0.194217	−0.0971084	−	0.995274i	$-0.530959\pi$
$191$	−2.68413	−0.194217	−0.0971084	+	0.995274i	$0.530959\pi$
$192$	0.984907	0.0710796
$193$	−3.97277	−0.285966	−0.142983	−	0.989725i	$-0.545669\pi$
$193$	−3.97277	−0.285966	−0.142983	+	0.989725i	$0.545669\pi$
$194$	32.4653	2.33087
$195$	−0.777057	−0.0556462
$196$	−33.5017	−2.39298
$197$	−5.53698	−0.394493	−0.197247	−	0.980354i	$-0.563200\pi$
$197$	−5.53698	−0.394493	−0.197247	+	0.980354i	$0.563200\pi$
$198$	11.8098	0.839285
$199$	−4.47579	−0.317280	−0.158640	−	0.987336i	$-0.550711\pi$
$199$	−4.47579	−0.317280	−0.158640	+	0.987336i	$0.550711\pi$
$200$	−7.42721	−0.525183
$201$	−0.493952	−0.0348407
$202$	5.15241	0.362522
$203$	−1.38699	−0.0973474
$204$	−0.425084	−0.0297618
$205$	0.762472	0.0532534
$206$	42.8396	2.98478
$207$	16.4169	1.14105
$208$	63.9234	4.43229
$209$	9.75990	0.675106
$210$	−0.0865249	−0.00597079
$211$	6.10286	0.420138	0.210069	−	0.977687i	$-0.432631\pi$
$211$	6.10286	0.420138	0.210069	+	0.977687i	$0.432631\pi$
$212$	9.48199	0.651226
$213$	1.17433	0.0804636
$214$	4.75895	0.325315
$215$	−5.30011	−0.361464
$216$	5.26652	0.358341
$217$	−1.80876	−0.122787
$218$	−17.9885	−1.21833
$219$	−1.02339	−0.0691540
$220$	−7.31927	−0.493465
$221$	−4.86368	−0.327166
$222$	−2.95507	−0.198331
$223$	2.22308	0.148868	0.0744342	−	0.997226i	$-0.476285\pi$
$223$	2.22308	0.148868	0.0744342	+	0.997226i	$0.476285\pi$
$224$	2.96916	0.198386
$225$	−2.98597	−0.199065
$226$	8.05137	0.535569
$227$	5.57369	0.369939	0.184970	−	0.982744i	$-0.440781\pi$
$227$	5.57369	0.369939	0.184970	+	0.982744i	$0.440781\pi$
$228$	3.70008	0.245044
$229$	5.29187	0.349697	0.174848	−	0.984595i	$-0.444056\pi$
$229$	5.29187	0.349697	0.174848	+	0.984595i	$0.444056\pi$
$230$	−14.3791	−0.948128
$231$	−0.0500322	−0.00329187
$232$	−36.8846	−2.42159
$233$	12.5227	0.820389	0.410195	−	0.911998i	$-0.365461\pi$
$233$	12.5227	0.820389	0.410195	+	0.911998i	$0.365461\pi$
$234$	51.2270	3.34881
$235$	−0.739734	−0.0482549
$236$	−4.55587	−0.296562
$237$	0.257058	0.0166977
$238$	−0.541568	−0.0351046
$239$	18.5363	1.19901	0.599507	−	0.800370i	$-0.295363\pi$
$239$	18.5363	1.19901	0.599507	+	0.800370i	$0.295363\pi$
$240$	−1.15434	−0.0745123
$241$	15.4564	0.995635	0.497817	−	0.867282i	$-0.334135\pi$
$241$	15.4564	0.995635	0.497817	+	0.867282i	$0.334135\pi$
$242$	22.7873	1.46482
$243$	3.17844	0.203897
$244$	19.2222	1.23058
$245$	6.92200	0.442230
$246$	0.236217	0.0150607
$247$	42.3352	2.69373
$248$	−48.1010	−3.05442
$249$	−1.01905	−0.0645794
$250$	2.61532	0.165407
$251$	0.373574	0.0235798	0.0117899	−	0.999930i	$-0.496247\pi$
$251$	0.373574	0.0235798	0.0117899	+	0.999930i	$0.496247\pi$
$252$	4.03621	0.254257
$253$	−8.31455	−0.522732
$254$	−3.91690	−0.245768
$255$	0.0878292	0.00550008
$256$	−15.3669	−0.960434
$257$	−4.10876	−0.256297	−0.128149	−	0.991755i	$-0.540903\pi$
$257$	−4.10876	−0.256297	−0.128149	+	0.991755i	$0.540903\pi$
$258$	−1.64200	−0.102226
$259$	−2.66399	−0.165532
$260$	−31.7486	−1.96896
$261$	−14.8287	−0.917876
$262$	−32.2239	−1.99080
$263$	−2.69563	−0.166220	−0.0831098	−	0.996540i	$-0.526485\pi$
$263$	−2.69563	−0.166220	−0.0831098	+	0.996540i	$0.526485\pi$
$264$	−1.33052	−0.0818879
$265$	−1.95913	−0.120349
$266$	4.71401	0.289034
$267$	−0.376585	−0.0230466
$268$	−20.1817	−1.23279
$269$	−12.7290	−0.776100	−0.388050	−	0.921638i	$-0.626851\pi$
$269$	−12.7290	−0.776100	−0.388050	+	0.921638i	$0.626851\pi$
$270$	−1.85448	−0.112860
$271$	−7.97865	−0.484668	−0.242334	−	0.970193i	$-0.577913\pi$
$271$	−7.97865	−0.484668	−0.242334	+	0.970193i	$0.577913\pi$
$272$	−7.22513	−0.438088
$273$	−0.217023	−0.0131348
$274$	−23.5309	−1.42155
$275$	1.51228	0.0911940
$276$	−3.15214	−0.189736
$277$	16.3796	0.984154	0.492077	−	0.870552i	$-0.336238\pi$
$277$	16.3796	0.984154	0.492077	+	0.870552i	$0.336238\pi$
$278$	−10.8155	−0.648669
$279$	−19.3381	−1.15774
$280$	−2.07433	−0.123965
$281$	31.4911	1.87860	0.939302	−	0.343093i	$-0.111475\pi$
$281$	31.4911	1.87860	0.939302	+	0.343093i	$0.111475\pi$
$282$	−0.229173	−0.0136471
$283$	20.3435	1.20929	0.604647	−	0.796494i	$-0.293314\pi$
$283$	20.3435	1.20929	0.604647	+	0.796494i	$0.293314\pi$
$284$	47.9801	2.84710
$285$	−0.764498	−0.0452849
$286$	−25.9446	−1.53413
$287$	0.212950	0.0125700
$288$	31.7443	1.87055
$289$	−16.4503	−0.967663
$290$	12.9880	0.762684
$291$	−1.47048	−0.0862009
$292$	−41.8130	−2.44692
$293$	−22.3943	−1.30829	−0.654145	−	0.756369i	$-0.726972\pi$
$293$	−22.3943	−1.30829	−0.654145	+	0.756369i	$0.726972\pi$
$294$	2.14447	0.125068
$295$	0.941317	0.0548056
$296$	−70.8444	−4.11774
$297$	−1.07234	−0.0622232
$298$	−52.7045	−3.05309
$299$	−36.0658	−2.08574
$300$	0.573322	0.0331008
$301$	−1.48026	−0.0853207
$302$	−48.1553	−2.77102
$303$	−0.233372	−0.0134069
$304$	62.8902	3.60700
$305$	−3.97162	−0.227414
$306$	−5.79009	−0.330997
$307$	−29.2444	−1.66907	−0.834534	−	0.550956i	$-0.814263\pi$
$307$	−29.2444	−1.66907	−0.834534	+	0.550956i	$0.814263\pi$
$308$	−2.04419	−0.116478
$309$	−1.94037	−0.110384
$310$	16.9376	0.961994
$311$	22.5771	1.28023	0.640116	−	0.768278i	$-0.278886\pi$
$311$	22.5771	1.28023	0.640116	+	0.768278i	$0.278886\pi$
$312$	−5.77137	−0.326739
$313$	−5.21125	−0.294558	−0.147279	−	0.989095i	$-0.547051\pi$
$313$	−5.21125	−0.294558	−0.147279	+	0.989095i	$0.547051\pi$
$314$	−47.0059	−2.65270
$315$	−0.833946	−0.0469876
$316$	10.5027	0.590826
$317$	−8.82631	−0.495735	−0.247867	−	0.968794i	$-0.579730\pi$
$317$	−8.82631	−0.495735	−0.247867	+	0.968794i	$0.579730\pi$
$318$	−0.606949	−0.0340360
$319$	7.51021	0.420491
$320$	−8.31442	−0.464790
$321$	−0.215551	−0.0120309
$322$	−4.01591	−0.223798
$323$	−4.78507	−0.266248
$324$	42.9487	2.38604
$325$	6.55978	0.363871
$326$	57.0822	3.16149
$327$	0.814767	0.0450567
$328$	5.66304	0.312689
$329$	−0.206599	−0.0113902
$330$	0.468512	0.0257907
$331$	−18.8474	−1.03595	−0.517973	−	0.855397i	$-0.673313\pi$
$331$	−18.8474	−1.03595	−0.517973	+	0.855397i	$0.673313\pi$
$332$	−41.6357	−2.28505
$333$	−28.4816	−1.56078
$334$	−40.2025	−2.19978
$335$	4.16986	0.227824
$336$	−0.322394	−0.0175880
$337$	−30.8338	−1.67962	−0.839812	−	0.542878i	$-0.817335\pi$
$337$	−30.8338	−1.67962	−0.839812	+	0.542878i	$0.817335\pi$
$338$	−78.5399	−4.27201
$339$	−0.364678	−0.0198066
$340$	3.58848	0.194613
$341$	9.79403	0.530376
$342$	50.3990	2.72527
$343$	3.88825	0.209946
$344$	−39.3650	−2.12242
$345$	0.651283	0.0350639
$346$	28.5334	1.53396
$347$	19.3210	1.03720	0.518602	−	0.855016i	$-0.326453\pi$
$347$	19.3210	1.03720	0.518602	+	0.855016i	$0.326453\pi$
$348$	2.84720	0.152626
$349$	−2.71159	−0.145148	−0.0725741	−	0.997363i	$-0.523121\pi$
$349$	−2.71159	−0.145148	−0.0725741	+	0.997363i	$0.523121\pi$
$350$	0.730428	0.0390430
$351$	−4.65144	−0.248275
$352$	−16.0773	−0.856924
$353$	−16.3992	−0.872841	−0.436421	−	0.899743i	$-0.643754\pi$
$353$	−16.3992	−0.872841	−0.436421	+	0.899743i	$0.643754\pi$
$354$	0.291624	0.0154997
$355$	−9.91347	−0.526153
$356$	−15.3863	−0.815473
$357$	0.0245297	0.00129825
$358$	51.2321	2.70770
$359$	28.4828	1.50327	0.751633	−	0.659582i	$-0.229267\pi$
$359$	28.4828	1.50327	0.751633	+	0.659582i	$0.229267\pi$
$360$	−22.1774	−1.16885
$361$	22.6510	1.19216
$362$	57.7164	3.03351
$363$	−1.03212	−0.0541724
$364$	−8.86702	−0.464758
$365$	8.63925	0.452199
$366$	−1.23043	−0.0643154
$367$	3.72089	0.194229	0.0971145	−	0.995273i	$-0.469039\pi$
$367$	3.72089	0.194229	0.0971145	+	0.995273i	$0.469039\pi$
$368$	−53.5768	−2.79288
$369$	2.27672	0.118521
$370$	24.9462	1.29689
$371$	−0.547164	−0.0284073
$372$	3.71302	0.192511
$373$	−15.6753	−0.811638	−0.405819	−	0.913953i	$-0.633014\pi$
$373$	−15.6753	−0.811638	−0.405819	+	0.913953i	$0.633014\pi$
$374$	2.93246	0.151634
$375$	−0.118458	−0.00611713
$376$	−5.49416	−0.283340
$377$	32.5768	1.67779
$378$	−0.517935	−0.0266397
$379$	−32.0622	−1.64692	−0.823461	−	0.567373i	$-0.807960\pi$
$379$	−32.0622	−1.64692	−0.823461	+	0.567373i	$0.807960\pi$
$380$	−31.2355	−1.60235
$381$	0.177411	0.00908906
$382$	7.01985	0.359167
$383$	6.31227	0.322542	0.161271	−	0.986910i	$-0.448441\pi$
$383$	6.31227	0.322542	0.161271	+	0.986910i	$0.448441\pi$
$384$	−0.0571558	−0.00291672
$385$	0.422363	0.0215256
$386$	10.3900	0.528839
$387$	−15.8259	−0.804478
$388$	−60.0800	−3.05010
$389$	1.26300	0.0640367	0.0320183	−	0.999487i	$-0.489807\pi$
$389$	1.26300	0.0640367	0.0320183	+	0.999487i	$0.489807\pi$
$390$	2.03225	0.102907
$391$	4.07645	0.206155
$392$	51.4111	2.59665
$393$	1.45955	0.0736243
$394$	14.4810	0.729540
$395$	−2.17004	−0.109186
$396$	−21.8551	−1.09826
$397$	26.5356	1.33179	0.665893	−	0.746048i	$-0.268051\pi$
$397$	26.5356	1.33179	0.665893	+	0.746048i	$0.268051\pi$
$398$	11.7056	0.586749
$399$	−0.213515	−0.0106891
$400$	9.74474	0.487237
$401$	−8.33771	−0.416365	−0.208183	−	0.978090i	$-0.566755\pi$
$401$	−8.33771	−0.416365	−0.208183	+	0.978090i	$0.566755\pi$
$402$	1.29184	0.0644313
$403$	42.4833	2.11624
$404$	−9.53501	−0.474384
$405$	−8.87391	−0.440948
$406$	3.62741	0.180025
$407$	14.4249	0.715015
$408$	0.652326	0.0322950
$409$	5.64629	0.279191	0.139596	−	0.990209i	$-0.455420\pi$
$409$	5.64629	0.279191	0.139596	+	0.990209i	$0.455420\pi$
$410$	−1.99411	−0.0984819
$411$	1.06581	0.0525723
$412$	−79.2787	−3.90578
$413$	0.262899	0.0129364
$414$	−42.9354	−2.11016
$415$	8.60261	0.422286
$416$	−69.7382	−3.41919
$417$	0.489874	0.0239892
$418$	−25.5252	−1.24848
$419$	−15.7006	−0.767024	−0.383512	−	0.923536i	$-0.625286\pi$
$419$	−15.7006	−0.767024	−0.383512	+	0.923536i	$0.625286\pi$
$420$	0.160122	0.00781317
$421$	36.5135	1.77956	0.889780	−	0.456389i	$-0.150858\pi$
$421$	36.5135	1.77956	0.889780	+	0.456389i	$0.150858\pi$
$422$	−15.9609	−0.776965
$423$	−2.20882	−0.107397
$424$	−14.5509	−0.706654
$425$	−0.741439	−0.0359651
$426$	−3.07124	−0.148802
$427$	−1.10923	−0.0536793
$428$	−8.80687	−0.425696
$429$	1.17513	0.0567358
$430$	13.8615	0.668459
$431$	−10.8974	−0.524910	−0.262455	−	0.964944i	$-0.584532\pi$
$431$	−10.8974	−0.524910	−0.262455	+	0.964944i	$0.584532\pi$
$432$	−6.90984	−0.332450
$433$	27.9739	1.34434	0.672169	−	0.740397i	$-0.265363\pi$
$433$	27.9739	1.34434	0.672169	+	0.740397i	$0.265363\pi$
$434$	4.73049	0.227071
$435$	−0.588278	−0.0282058
$436$	33.2893	1.59427
$437$	−35.4829	−1.69738
$438$	2.67648	0.127887
$439$	21.8510	1.04289	0.521445	−	0.853285i	$-0.325393\pi$
$439$	21.8510	1.04289	0.521445	+	0.853285i	$0.325393\pi$
$440$	11.2320	0.535466
$441$	20.6689	0.984232
$442$	12.7201	0.605032
$443$	−15.0769	−0.716323	−0.358161	−	0.933660i	$-0.616596\pi$
$443$	−15.0769	−0.716323	−0.358161	+	0.933660i	$0.616596\pi$
$444$	5.46863	0.259530
$445$	3.17906	0.150702
$446$	−5.81406	−0.275304
$447$	2.38719	0.112910
$448$	−2.32212	−0.109710
$449$	14.3108	0.675367	0.337684	−	0.941260i	$-0.390357\pi$
$449$	14.3108	0.675367	0.337684	+	0.941260i	$0.390357\pi$
$450$	7.80926	0.368132
$451$	−1.15307	−0.0542961
$452$	−14.8998	−0.700828
$453$	2.18114	0.102479
$454$	−14.5770	−0.684132
$455$	1.83207	0.0858888
$456$	−5.67808	−0.265901
$457$	−1.70430	−0.0797239	−0.0398620	−	0.999205i	$-0.512692\pi$
$457$	−1.70430	−0.0797239	−0.0398620	+	0.999205i	$0.512692\pi$
$458$	−13.8399	−0.646698
$459$	0.525743	0.0245396
$460$	26.6098	1.24069
$461$	0.550936	0.0256597	0.0128298	−	0.999918i	$-0.495916\pi$
$461$	0.550936	0.0256597	0.0128298	+	0.999918i	$0.495916\pi$
$462$	0.130850	0.00608769
$463$	18.7403	0.870935	0.435468	−	0.900204i	$-0.356583\pi$
$463$	18.7403	0.870935	0.435468	+	0.900204i	$0.356583\pi$
$464$	48.3938	2.24663
$465$	−0.767171	−0.0355767
$466$	−32.7508	−1.51715
$467$	13.6825	0.633152	0.316576	−	0.948567i	$-0.397467\pi$
$467$	13.6825	0.633152	0.316576	+	0.948567i	$0.397467\pi$
$468$	−94.8003	−4.38215
$469$	1.16459	0.0537760
$470$	1.93464	0.0892383
$471$	2.12908	0.0981028
$472$	6.99136	0.321803
$473$	8.01525	0.368542
$474$	−0.672288	−0.0308792
$475$	6.45376	0.296119
$476$	1.00222	0.0459368
$477$	−5.84991	−0.267849
$478$	−48.4783	−2.21735
$479$	−8.60356	−0.393107	−0.196553	−	0.980493i	$-0.562975\pi$
$479$	−8.60356	−0.393107	−0.196553	+	0.980493i	$0.562975\pi$
$480$	1.25935	0.0574810
$481$	62.5704	2.85296
$482$	−40.4234	−1.84124
$483$	0.181896	0.00827655
$484$	−42.1700	−1.91682
$485$	12.4135	0.563669
$486$	−8.31262	−0.377068
$487$	20.1234	0.911880	0.455940	−	0.890010i	$-0.349303\pi$
$487$	20.1234	0.911880	0.455940	+	0.890010i	$0.349303\pi$
$488$	−29.4981	−1.33531
$489$	−2.58547	−0.116919
$490$	−18.1032	−0.817820
$491$	26.1547	1.18035	0.590174	−	0.807276i	$-0.299059\pi$
$491$	26.1547	1.18035	0.590174	+	0.807276i	$0.299059\pi$
$492$	−0.437142	−0.0197079
$493$	−3.68209	−0.165833
$494$	−110.720	−4.98153
$495$	4.51562	0.202962
$496$	63.1101	2.83373
$497$	−2.76872	−0.124194
$498$	2.66513	0.119427
$499$	14.3347	0.641711	0.320855	−	0.947128i	$-0.396030\pi$
$499$	14.3347	0.641711	0.320855	+	0.947128i	$0.396030\pi$
$500$	−4.83989	−0.216446
$501$	1.82092	0.0813529
$502$	−0.977016	−0.0436063
$503$	−34.3232	−1.53040	−0.765199	−	0.643794i	$-0.777359\pi$
$503$	−34.3232	−1.53040	−0.765199	+	0.643794i	$0.777359\pi$
$504$	−6.19390	−0.275898
$505$	1.97009	0.0876678
$506$	21.7452	0.966692
$507$	3.55737	0.157988
$508$	7.24858	0.321604
$509$	−8.40853	−0.372702	−0.186351	−	0.982483i	$-0.559666\pi$
$509$	−8.40853	−0.372702	−0.186351	+	0.982483i	$0.559666\pi$
$510$	−0.229701	−0.0101713
$511$	2.41284	0.106738
$512$	41.1544	1.81879
$513$	−4.57626	−0.202047
$514$	10.7457	0.473973
$515$	16.3803	0.721801
$516$	3.03867	0.133770
$517$	1.11869	0.0491998
$518$	6.96718	0.306120
$519$	−1.29239	−0.0567295
$520$	48.7209	2.13655
$521$	25.7944	1.13007	0.565036	−	0.825066i	$-0.308862\pi$
$521$	25.7944	1.13007	0.565036	+	0.825066i	$0.308862\pi$
$522$	38.7819	1.69744
$523$	30.8178	1.34757	0.673785	−	0.738927i	$-0.264667\pi$
$523$	30.8178	1.34757	0.673785	+	0.738927i	$0.264667\pi$
$524$	59.6334	2.60510
$525$	−0.0330839	−0.00144390
$526$	7.04992	0.307391
$527$	−4.80180	−0.209170
$528$	1.74569	0.0759713
$529$	7.22822	0.314270
$530$	5.12376	0.222562
$531$	2.81074	0.121976
$532$	−8.72370	−0.378221
$533$	−5.00165	−0.216646
$534$	0.984889	0.0426203
$535$	1.81964	0.0786700
$536$	30.9704	1.33772
$537$	−2.32050	−0.100137
$538$	33.2904	1.43525
$539$	−10.4680	−0.450889
$540$	3.43189	0.147685
$541$	−7.56113	−0.325078	−0.162539	−	0.986702i	$-0.551968\pi$
$541$	−7.56113	−0.325078	−0.162539	+	0.986702i	$0.551968\pi$
$542$	20.8667	0.896302
$543$	−2.61420	−0.112186
$544$	7.88237	0.337954
$545$	−6.87812	−0.294626
$546$	0.567584	0.0242904
$547$	−27.9688	−1.19586	−0.597929	−	0.801549i	$-0.704010\pi$
$547$	−27.9688	−1.19586	−0.597929	+	0.801549i	$0.704010\pi$
$548$	43.5461	1.86020
$549$	−11.8591	−0.506135
$550$	−3.95510	−0.168646
$551$	32.0503	1.36539
$552$	4.83722	0.205886
$553$	−0.606067	−0.0257726
$554$	−42.8378	−1.82000
$555$	−1.12991	−0.0479619
$556$	20.0150	0.848826
$557$	36.6286	1.55200	0.776001	−	0.630732i	$-0.217245\pi$
$557$	36.6286	1.55200	0.776001	+	0.630732i	$0.217245\pi$
$558$	50.5753	2.14102
$559$	34.7675	1.47051
$560$	2.72159	0.115008
$561$	−0.132823	−0.00560777
$562$	−82.3593	−3.47412
$563$	12.5777	0.530089	0.265044	−	0.964236i	$-0.414613\pi$
$563$	12.5777	0.530089	0.265044	+	0.964236i	$0.414613\pi$
$564$	0.424106	0.0178581
$565$	3.07854	0.129515
$566$	−53.2046	−2.23636
$567$	−2.47838	−0.104082
$568$	−73.6294	−3.08942
$569$	−13.6128	−0.570677	−0.285338	−	0.958427i	$-0.592106\pi$
$569$	−13.6128	−0.570677	−0.285338	+	0.958427i	$0.592106\pi$
$570$	1.99940	0.0837458
$571$	−17.7723	−0.743749	−0.371874	−	0.928283i	$-0.621285\pi$
$571$	−17.7723	−0.743749	−0.371874	+	0.928283i	$0.621285\pi$
$572$	48.0128	2.00752
$573$	−0.317956	−0.0132828
$574$	−0.556931	−0.0232459
$575$	−5.49802	−0.229283
$576$	−24.8266	−1.03444
$577$	19.8260	0.825368	0.412684	−	0.910874i	$-0.364591\pi$
$577$	19.8260	0.825368	0.412684	+	0.910874i	$0.364591\pi$
$578$	43.0227	1.78951
$579$	−0.470605	−0.0195577
$580$	−24.0356	−0.998023
$581$	2.40261	0.0996771
$582$	3.84577	0.159412
$583$	2.96276	0.122705
$584$	64.1655	2.65519
$585$	19.5873	0.809835
$586$	58.5683	2.41943
$587$	−12.9028	−0.532554	−0.266277	−	0.963897i	$-0.585794\pi$
$587$	−12.9028	−0.532554	−0.266277	+	0.963897i	$0.585794\pi$
$588$	−3.96854	−0.163660
$589$	41.7966	1.72220
$590$	−2.46184	−0.101352
$591$	−0.655898	−0.0269800
$592$	92.9501	3.82022
$593$	−7.95355	−0.326613	−0.163307	−	0.986575i	$-0.552216\pi$
$593$	−7.95355	−0.326613	−0.163307	+	0.986575i	$0.552216\pi$
$594$	2.80450	0.115070
$595$	−0.207075	−0.00848926
$596$	97.5345	3.99517
$597$	−0.530192	−0.0216993
$598$	94.3235	3.85718
$599$	−38.9132	−1.58995	−0.794976	−	0.606641i	$-0.792517\pi$
$599$	−38.9132	−1.58995	−0.794976	+	0.606641i	$0.792517\pi$
$600$	−0.879811	−0.0359181
$601$	33.5487	1.36848	0.684240	−	0.729257i	$-0.260134\pi$
$601$	33.5487	1.36848	0.684240	+	0.729257i	$0.260134\pi$
$602$	3.87135	0.157784
$603$	12.4511	0.507047
$604$	89.1158	3.62607
$605$	8.71300	0.354234
$606$	0.610343	0.0247935
$607$	22.8389	0.927004	0.463502	−	0.886096i	$-0.346593\pi$
$607$	22.8389	0.927004	0.463502	+	0.886096i	$0.346593\pi$
$608$	−68.6110	−2.78254
$609$	−0.164299	−0.00665775
$610$	10.3871	0.420559
$611$	4.85250	0.196311
$612$	10.7151	0.433132
$613$	10.6870	0.431645	0.215823	−	0.976433i	$-0.430757\pi$
$613$	10.6870	0.431645	0.215823	+	0.976433i	$0.430757\pi$
$614$	76.4835	3.08662
$615$	0.0903207	0.00364208
$616$	3.13698	0.126392
$617$	0.302797	0.0121901	0.00609507	−	0.999981i	$-0.498060\pi$
$617$	0.302797	0.0121901	0.00609507	+	0.999981i	$0.498060\pi$
$618$	5.07469	0.204134
$619$	−31.7873	−1.27764	−0.638819	−	0.769357i	$-0.720577\pi$
$619$	−31.7873	−1.27764	−0.638819	+	0.769357i	$0.720577\pi$
$620$	−31.3447	−1.25883
$621$	3.89856	0.156444
$622$	−59.0464	−2.36755
$623$	0.887876	0.0355720
$624$	7.57222	0.303131
$625$	1.00000	0.0400000
$626$	13.6291	0.544728
$627$	1.15614	0.0461716
$628$	86.9888	3.47123
$629$	−7.07221	−0.281987
$630$	2.18104	0.0868945
$631$	42.5377	1.69340	0.846700	−	0.532070i	$-0.178586\pi$
$631$	42.5377	1.69340	0.846700	+	0.532070i	$0.178586\pi$
$632$	−16.1173	−0.641113
$633$	0.722931	0.0287339
$634$	23.0836	0.916767
$635$	−1.49768	−0.0594334
$636$	1.12322	0.0445384
$637$	−45.4068	−1.79908
$638$	−19.6416	−0.777618
$639$	−29.6013	−1.17101
$640$	0.482499	0.0190724
$641$	−14.1949	−0.560664	−0.280332	−	0.959903i	$-0.590445\pi$
$641$	−14.1949	−0.560664	−0.280332	+	0.959903i	$0.590445\pi$
$642$	0.563734	0.0222488
$643$	−39.9835	−1.57679	−0.788397	−	0.615167i	$-0.789089\pi$
$643$	−39.9835	−1.57679	−0.788397	+	0.615167i	$0.789089\pi$
$644$	7.43181	0.292854
$645$	−0.627839	−0.0247211
$646$	12.5145	0.492375
$647$	8.98189	0.353115	0.176557	−	0.984290i	$-0.443504\pi$
$647$	8.98189	0.353115	0.176557	+	0.984290i	$0.443504\pi$
$648$	−65.9084	−2.58913
$649$	−1.42354	−0.0558787
$650$	−17.1559	−0.672910
$651$	−0.214262	−0.00839759
$652$	−105.636	−4.13702
$653$	−17.9587	−0.702778	−0.351389	−	0.936229i	$-0.614291\pi$
$653$	−17.9587	−0.702778	−0.351389	+	0.936229i	$0.614291\pi$
$654$	−2.13087	−0.0833238
$655$	−12.3212	−0.481430
$656$	−7.43009	−0.290096
$657$	25.7965	1.00642
$658$	0.540323	0.0210640
$659$	27.4719	1.07015	0.535076	−	0.844804i	$-0.320283\pi$
$659$	27.4719	1.07015	0.535076	+	0.844804i	$0.320283\pi$
$660$	−0.867025	−0.0337489
$661$	44.3414	1.72468	0.862340	−	0.506329i	$-0.168998\pi$
$661$	44.3414	1.72468	0.862340	+	0.506329i	$0.168998\pi$
$662$	49.2919	1.91578
$663$	−0.576141	−0.0223754
$664$	63.8934	2.47955
$665$	1.80246	0.0698964
$666$	74.4885	2.88637
$667$	−27.3040	−1.05721
$668$	74.3984	2.87856
$669$	0.263341	0.0101814
$670$	−10.9055	−0.421317
$671$	6.00621	0.231867
$672$	0.351721	0.0135679
$673$	−15.4183	−0.594333	−0.297167	−	0.954826i	$-0.596042\pi$
$673$	−15.4183	−0.594333	−0.297167	+	0.954826i	$0.596042\pi$
$674$	80.6402	3.10614
$675$	−0.709084	−0.0272927
$676$	145.345	5.59021
$677$	43.2144	1.66086	0.830432	−	0.557120i	$-0.188094\pi$
$677$	43.2144	1.66086	0.830432	+	0.557120i	$0.188094\pi$
$678$	0.953748	0.0366285
$679$	3.46695	0.133049
$680$	−5.50682	−0.211177
$681$	0.660247	0.0253007
$682$	−25.6145	−0.980830
$683$	30.0745	1.15077	0.575384	−	0.817883i	$-0.304853\pi$
$683$	30.0745	1.15077	0.575384	+	0.817883i	$0.304853\pi$
$684$	−93.2681	−3.56619
$685$	−8.99734	−0.343771
$686$	−10.1690	−0.388255
$687$	0.626864	0.0239163
$688$	51.6482	1.96907
$689$	12.8515	0.489603
$690$	−1.70331	−0.0648440
$691$	−18.1932	−0.692103	−0.346051	−	0.938216i	$-0.612478\pi$
$691$	−18.1932	−0.692103	−0.346051	+	0.938216i	$0.612478\pi$
$692$	−52.8037	−2.00729
$693$	1.26116	0.0479076
$694$	−50.5305	−1.91811
$695$	−4.13543	−0.156866
$696$	−4.36927	−0.165617
$697$	0.565327	0.0214133
$698$	7.09167	0.268424
$699$	1.48341	0.0561078
$700$	−1.35173	−0.0510904
$701$	−11.3631	−0.429179	−0.214589	−	0.976704i	$-0.568841\pi$
$701$	−11.3631	−0.429179	−0.214589	+	0.976704i	$0.568841\pi$
$702$	12.1650	0.459138
$703$	61.5591	2.32174
$704$	12.5737	0.473891
$705$	−0.0876273	−0.00330023
$706$	42.8891	1.61415
$707$	0.550223	0.0206933
$708$	−0.539678	−0.0202823
$709$	−18.0988	−0.679715	−0.339858	−	0.940477i	$-0.610379\pi$
$709$	−18.0988	−0.679715	−0.339858	+	0.940477i	$0.610379\pi$
$710$	25.9269	0.973019
$711$	−6.47967	−0.243006
$712$	23.6116	0.884881
$713$	−35.6070	−1.33349
$714$	−0.0641530	−0.00240086
$715$	−9.92024	−0.370996
$716$	−94.8097	−3.54320
$717$	2.19577	0.0820025
$718$	−74.4916	−2.78000
$719$	13.8478	0.516434	0.258217	−	0.966087i	$-0.416865\pi$
$719$	13.8478	0.516434	0.258217	+	0.966087i	$0.416865\pi$
$720$	29.0975	1.08440
$721$	4.57482	0.170375
$722$	−59.2395	−2.20467
$723$	1.83093	0.0680931
$724$	−106.810	−3.96954
$725$	4.96614	0.184438
$726$	2.69933	0.100182
$727$	−24.0125	−0.890573	−0.445286	−	0.895388i	$-0.646898\pi$
$727$	−24.0125	−0.890573	−0.445286	+	0.895388i	$0.646898\pi$
$728$	13.6072	0.504316
$729$	−26.2452	−0.972045
$730$	−22.5944	−0.836256
$731$	−3.92971	−0.145345
$732$	2.27702	0.0841610
$733$	−47.5012	−1.75450	−0.877248	−	0.480037i	$-0.840623\pi$
$733$	−47.5012	−1.75450	−0.877248	+	0.480037i	$0.840623\pi$
$734$	−9.73132	−0.359190
$735$	0.819964	0.0302448
$736$	58.4504	2.15451
$737$	−6.30600	−0.232285
$738$	−5.95434	−0.219182
$739$	34.3220	1.26256	0.631278	−	0.775557i	$-0.282531\pi$
$739$	34.3220	1.26256	0.631278	+	0.775557i	$0.282531\pi$
$740$	−46.1652	−1.69707
$741$	5.01494	0.184228
$742$	1.43101	0.0525339
$743$	20.8467	0.764791	0.382396	−	0.923999i	$-0.375099\pi$
$743$	20.8467	0.764791	0.382396	+	0.923999i	$0.375099\pi$
$744$	−5.69794	−0.208897
$745$	−20.1522	−0.738321
$746$	40.9960	1.50097
$747$	25.6871	0.939843
$748$	−5.42680	−0.198423
$749$	0.508205	0.0185694
$750$	0.309805	0.0113125
$751$	32.7478	1.19499	0.597493	−	0.801874i	$-0.296164\pi$
$751$	32.7478	1.19499	0.597493	+	0.801874i	$0.296164\pi$
$752$	7.20852	0.262868
$753$	0.0442528	0.00161266
$754$	−85.1987	−3.10276
$755$	−18.4128	−0.670110
$756$	0.958487	0.0348598
$757$	29.4133	1.06904	0.534522	−	0.845155i	$-0.320492\pi$
$757$	29.4133	1.06904	0.534522	+	0.845155i	$0.320492\pi$
$758$	83.8527	3.04567
$759$	−0.984924	−0.0357505
$760$	47.9334	1.73873
$761$	10.2652	0.372112	0.186056	−	0.982539i	$-0.440429\pi$
$761$	10.2652	0.372112	0.186056	+	0.982539i	$0.440429\pi$
$762$	−0.463987	−0.0168085
$763$	−1.92098	−0.0695442
$764$	−12.9909	−0.469994
$765$	−2.21391	−0.0800442
$766$	−16.5086	−0.596480
$767$	−6.17483	−0.222960
$768$	−1.82033	−0.0656857
$769$	2.71480	0.0978983	0.0489491	−	0.998801i	$-0.484413\pi$
$769$	2.71480	0.0978983	0.0489491	+	0.998801i	$0.484413\pi$
$770$	−1.10461	−0.0398075
$771$	−0.486714	−0.0175286
$772$	−19.2277	−0.692022
$773$	−3.32873	−0.119726	−0.0598631	−	0.998207i	$-0.519066\pi$
$773$	−3.32873	−0.119726	−0.0598631	+	0.998207i	$0.519066\pi$
$774$	41.3899	1.48773
$775$	6.47632	0.232636
$776$	92.1978	3.30971
$777$	−0.315570	−0.0113210
$778$	−3.30315	−0.118424
$779$	−4.92081	−0.176306
$780$	−3.76087	−0.134661
$781$	14.9920	0.536455
$782$	−10.6612	−0.381244
$783$	−3.52142	−0.125845
$784$	−67.4531	−2.40904
$785$	−17.9733	−0.641495
$786$	−3.81718	−0.136154
$787$	3.58306	0.127722	0.0638611	−	0.997959i	$-0.479659\pi$
$787$	3.58306	0.127722	0.0638611	+	0.997959i	$0.479659\pi$
$788$	−26.7983	−0.954651
$789$	−0.319318	−0.0113680
$790$	5.67534	0.201920
$791$	0.859802	0.0305710
$792$	33.5385	1.19174
$793$	26.0530	0.925168
$794$	−69.3991	−2.46288
$795$	−0.232075	−0.00823084
$796$	−21.6623	−0.767800
$797$	4.78301	0.169423	0.0847115	−	0.996406i	$-0.473003\pi$
$797$	4.78301	0.169423	0.0847115	+	0.996406i	$0.473003\pi$
$798$	0.558411	0.0197675
$799$	−0.548468	−0.0194034
$800$	−10.6312	−0.375869
$801$	9.49259	0.335404
$802$	21.8058	0.769988
$803$	−13.0650	−0.461053
$804$	−2.39067	−0.0843126
$805$	−1.53553	−0.0541204
$806$	−111.107	−3.91359
$807$	−1.50785	−0.0530788
$808$	14.6323	0.514761
$809$	9.36288	0.329181	0.164591	−	0.986362i	$-0.447370\pi$
$809$	9.36288	0.329181	0.164591	+	0.986362i	$0.447370\pi$
$810$	23.2081	0.815449
$811$	−25.0300	−0.878921	−0.439460	−	0.898262i	$-0.644830\pi$
$811$	−25.0300	−0.878921	−0.439460	+	0.898262i	$0.644830\pi$
$812$	−6.71286	−0.235575
$813$	−0.945133	−0.0331473
$814$	−37.7256	−1.32228
$815$	21.8261	0.764536
$816$	−0.855873	−0.0299615
$817$	34.2056	1.19670
$818$	−14.7668	−0.516311
$819$	5.47051	0.191155
$820$	3.69028	0.128870
$821$	14.5447	0.507614	0.253807	−	0.967255i	$-0.418317\pi$
$821$	14.5447	0.507614	0.253807	+	0.967255i	$0.418317\pi$
$822$	−2.78742	−0.0972224
$823$	36.6903	1.27894	0.639472	−	0.768815i	$-0.279153\pi$
$823$	36.6903	1.27894	0.639472	+	0.768815i	$0.279153\pi$
$824$	121.660	4.23822
$825$	0.179142	0.00623691
$826$	−0.687564	−0.0239234
$827$	51.3346	1.78508	0.892539	−	0.450971i	$-0.148922\pi$
$827$	51.3346	1.78508	0.892539	+	0.450971i	$0.148922\pi$
$828$	79.4560	2.76129
$829$	27.9729	0.971538	0.485769	−	0.874087i	$-0.338540\pi$
$829$	27.9729	0.971538	0.485769	+	0.874087i	$0.338540\pi$
$830$	−22.4986	−0.780937
$831$	1.94029	0.0673079
$832$	54.5408	1.89086
$833$	5.13224	0.177822
$834$	−1.28118	−0.0443635
$835$	−15.3719	−0.531968
$836$	47.2368	1.63372
$837$	−4.59226	−0.158732
$838$	41.0621	1.41847
$839$	−45.7798	−1.58049	−0.790247	−	0.612789i	$-0.790048\pi$
$839$	−45.7798	−1.58049	−0.790247	+	0.612789i	$0.790048\pi$
$840$	−0.245721	−0.00847818
$841$	−4.33741	−0.149566
$842$	−95.4945	−3.29096
$843$	3.73037	0.128481
$844$	29.5372	1.01671
$845$	−30.0307	−1.03309
$846$	5.77677	0.198610
$847$	2.43344	0.0836140
$848$	19.0913	0.655596
$849$	2.40984	0.0827056
$850$	1.93910	0.0665106
$851$	−52.4428	−1.79772
$852$	5.68362	0.194717
$853$	20.7914	0.711884	0.355942	−	0.934508i	$-0.384160\pi$
$853$	20.7914	0.711884	0.355942	+	0.934508i	$0.384160\pi$
$854$	2.90098	0.0992696
$855$	19.2707	0.659044
$856$	13.5149	0.461929
$857$	5.65503	0.193172	0.0965860	−	0.995325i	$-0.469208\pi$
$857$	5.65503	0.193172	0.0965860	+	0.995325i	$0.469208\pi$
$858$	−3.07334	−0.104922
$859$	48.1201	1.64184	0.820918	−	0.571046i	$-0.193462\pi$
$859$	48.1201	1.64184	0.820918	+	0.571046i	$0.193462\pi$
$860$	−25.6519	−0.874723
$861$	0.0252255	0.000859684 0
$862$	28.5002	0.970721
$863$	7.66337	0.260864	0.130432	−	0.991457i	$-0.458364\pi$
$863$	7.66337	0.260864	0.130432	+	0.991457i	$0.458364\pi$
$864$	7.53840	0.256462
$865$	10.9101	0.370955
$866$	−73.1606	−2.48610
$867$	−1.94866	−0.0661800
$868$	−8.75421	−0.297137
$869$	3.28171	0.111324
$870$	1.53854	0.0521612
$871$	−27.3534	−0.926834
$872$	−51.0853	−1.72997
$873$	37.0664	1.25451
$874$	92.7990	3.13897
$875$	0.279288	0.00944167
$876$	−4.95308	−0.167349
$877$	−41.6004	−1.40475	−0.702373	−	0.711809i	$-0.747876\pi$
$877$	−41.6004	−1.40475	−0.702373	+	0.711809i	$0.747876\pi$
$878$	−57.1472	−1.92863
$879$	−2.65278	−0.0894761
$880$	−14.7368	−0.496777
$881$	−17.5846	−0.592439	−0.296219	−	0.955120i	$-0.595726\pi$
$881$	−17.5846	−0.592439	−0.296219	+	0.955120i	$0.595726\pi$
$882$	−54.0556	−1.82015
$883$	28.2835	0.951817	0.475908	−	0.879495i	$-0.342119\pi$
$883$	28.2835	0.951817	0.475908	+	0.879495i	$0.342119\pi$
$884$	−23.5397	−0.791724
$885$	0.111506	0.00374824
$886$	39.4308	1.32470
$887$	−53.5989	−1.79967	−0.899837	−	0.436227i	$-0.856315\pi$
$887$	−53.5989	−1.79967	−0.899837	+	0.436227i	$0.856315\pi$
$888$	−8.39206	−0.281619
$889$	−0.418284	−0.0140288
$890$	−8.31427	−0.278695
$891$	13.4198	0.449582
$892$	10.7595	0.360253
$893$	4.77407	0.159758
$894$	−6.24326	−0.208806
$895$	19.5892	0.654796
$896$	0.134756	0.00450190
$897$	−4.27227	−0.142647
$898$	−37.4272	−1.24896
$899$	32.1624	1.07267
$900$	−14.4517	−0.481725
$901$	−1.45258	−0.0483924
$902$	3.01565	0.100410
$903$	−0.175348	−0.00583522
$904$	22.8650	0.760478
$905$	22.0686	0.733585
$906$	−5.70437	−0.189515
$907$	1.75657	0.0583260	0.0291630	−	0.999575i	$-0.490716\pi$
$907$	1.75657	0.0583260	0.0291630	+	0.999575i	$0.490716\pi$
$908$	26.9761	0.895232
$909$	5.88262	0.195114
$910$	−4.79145	−0.158835
$911$	−11.0519	−0.366166	−0.183083	−	0.983097i	$-0.558608\pi$
$911$	−11.0519	−0.366166	−0.183083	+	0.983097i	$0.558608\pi$
$912$	7.44983	0.246689
$913$	−13.0096	−0.430554
$914$	4.45729	0.147434
$915$	−0.470469	−0.0155532
$916$	25.6121	0.846247
$917$	−3.44118	−0.113638
$918$	−1.37499	−0.0453813
$919$	−6.28211	−0.207228	−0.103614	−	0.994618i	$-0.533041\pi$
$919$	−6.28211	−0.207228	−0.103614	+	0.994618i	$0.533041\pi$
$920$	−40.8349	−1.34629
$921$	−3.46423	−0.114150
$922$	−1.44087	−0.0474526
$923$	65.0302	2.14050
$924$	−0.242150	−0.00796615
$925$	9.53849	0.313624
$926$	−49.0118	−1.61063
$927$	48.9110	1.60645
$928$	−52.7959	−1.73311
$929$	−40.6871	−1.33490	−0.667450	−	0.744654i	$-0.732614\pi$
$929$	−40.6871	−1.33490	−0.667450	+	0.744654i	$0.732614\pi$
$930$	2.00640	0.0657923
$931$	−44.6729	−1.46409
$932$	60.6085	1.98530
$933$	2.67444	0.0875572
$934$	−35.7842	−1.17089
$935$	1.12126	0.0366693
$936$	145.479	4.75513
$937$	40.2511	1.31495	0.657474	−	0.753478i	$-0.271625\pi$
$937$	40.2511	1.31495	0.657474	+	0.753478i	$0.271625\pi$
$938$	−3.04578	−0.0994484
$939$	−0.617314	−0.0201453
$940$	−3.58023	−0.116774
$941$	48.6555	1.58612	0.793061	−	0.609142i	$-0.208486\pi$
$941$	48.6555	1.58612	0.793061	+	0.609142i	$0.208486\pi$
$942$	−5.56822	−0.181422
$943$	4.19209	0.136513
$944$	−9.17289	−0.298552
$945$	−0.198039	−0.00644221
$946$	−20.9624	−0.681548
$947$	−5.43721	−0.176685	−0.0883427	−	0.996090i	$-0.528157\pi$
$947$	−5.43721	−0.176685	−0.0883427	+	0.996090i	$0.528157\pi$
$948$	1.24413	0.0404075
$949$	−56.6716	−1.83964
$950$	−16.8786	−0.547615
$951$	−1.04555	−0.0339041
$952$	−1.53799	−0.0498466
$953$	32.0220	1.03729	0.518647	−	0.854989i	$-0.326436\pi$
$953$	32.0220	1.03729	0.518647	+	0.854989i	$0.326436\pi$
$954$	15.2994	0.495336
$955$	2.68413	0.0868564
$956$	89.7136	2.90155
$957$	0.889643	0.0287581
$958$	22.5010	0.726976
$959$	−2.51285	−0.0811443
$960$	−0.984907	−0.0317877
$961$	10.9428	0.352993
$962$	−163.641	−5.27601
$963$	5.43340	0.175089
$964$	74.8073	2.40938
$965$	3.97277	0.127888
$966$	−0.475716	−0.0153059
$967$	−29.7935	−0.958095	−0.479048	−	0.877789i	$-0.659018\pi$
$967$	−29.7935	−0.958095	−0.479048	+	0.877789i	$0.659018\pi$
$968$	64.7133	2.07996
$969$	−0.566829	−0.0182092
$970$	−32.4653	−1.04240
$971$	−5.88500	−0.188859	−0.0944293	−	0.995532i	$-0.530103\pi$
$971$	−5.88500	−0.188859	−0.0944293	+	0.995532i	$0.530103\pi$
$972$	15.3833	0.493419
$973$	−1.15498	−0.0370269
$974$	−52.6292	−1.68635
$975$	0.777057	0.0248857
$976$	38.7024	1.23883
$977$	26.1253	0.835824	0.417912	−	0.908488i	$-0.362762\pi$
$977$	26.1253	0.835824	0.417912	+	0.908488i	$0.362762\pi$
$978$	6.76183	0.216220
$979$	−4.80764	−0.153653
$980$	33.5017	1.07017
$981$	−20.5379	−0.655723
$982$	−68.4030	−2.18283
$983$	5.91246	0.188578	0.0942891	−	0.995545i	$-0.469942\pi$
$983$	5.91246	0.188578	0.0942891	+	0.995545i	$0.469942\pi$
$984$	0.670831	0.0213853
$985$	5.53698	0.176423
$986$	9.62985	0.306677
$987$	−0.0244733	−0.000778993 0
$988$	204.898	6.51867
$989$	−29.1401	−0.926601
$990$	−11.8098	−0.375340
$991$	33.0205	1.04893	0.524465	−	0.851432i	$-0.324265\pi$
$991$	33.0205	1.04893	0.524465	+	0.851432i	$0.324265\pi$
$992$	−68.8509	−2.18602
$993$	−2.23262	−0.0708500
$994$	7.24108	0.229673
$995$	4.47579	0.141892
$996$	−4.93207	−0.156279
$997$	−51.4054	−1.62803	−0.814013	−	0.580847i	$-0.802721\pi$
$997$	−51.4054	−1.62803	−0.814013	+	0.580847i	$0.802721\pi$
$998$	−37.4899	−1.18672
$999$	−6.76359	−0.213991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.g.1.9	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.g.1.9	✓	113	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)

\(f(q)\)	\(=\)	\(q-2.61532 q^{2} +0.118458 q^{3} +4.83989 q^{4} -1.00000 q^{5} -0.309805 q^{6} -0.279288 q^{7} -7.42721 q^{8} -2.98597 q^{9} +O(q^{10})\)	\(q-2.61532 q^{2} +0.118458 q^{3} +4.83989 q^{4} -1.00000 q^{5} -0.309805 q^{6} -0.279288 q^{7} -7.42721 q^{8} -2.98597 q^{9} +2.61532 q^{10} +1.51228 q^{11} +0.573322 q^{12} +6.55978 q^{13} +0.730428 q^{14} -0.118458 q^{15} +9.74474 q^{16} -0.741439 q^{17} +7.80926 q^{18} +6.45376 q^{19} -4.83989 q^{20} -0.0330839 q^{21} -3.95510 q^{22} -5.49802 q^{23} -0.879811 q^{24} +1.00000 q^{25} -17.1559 q^{26} -0.709084 q^{27} -1.35173 q^{28} +4.96614 q^{29} +0.309805 q^{30} +6.47632 q^{31} -10.6312 q^{32} +0.179142 q^{33} +1.93910 q^{34} +0.279288 q^{35} -14.4517 q^{36} +9.53849 q^{37} -16.8786 q^{38} +0.777057 q^{39} +7.42721 q^{40} -0.762472 q^{41} +0.0865249 q^{42} +5.30011 q^{43} +7.31927 q^{44} +2.98597 q^{45} +14.3791 q^{46} +0.739734 q^{47} +1.15434 q^{48} -6.92200 q^{49} -2.61532 q^{50} -0.0878292 q^{51} +31.7486 q^{52} +1.95913 q^{53} +1.85448 q^{54} -1.51228 q^{55} +2.07433 q^{56} +0.764498 q^{57} -12.9880 q^{58} -0.941317 q^{59} -0.573322 q^{60} +3.97162 q^{61} -16.9376 q^{62} +0.833946 q^{63} +8.31442 q^{64} -6.55978 q^{65} -0.468512 q^{66} -4.16986 q^{67} -3.58848 q^{68} -0.651283 q^{69} -0.730428 q^{70} +9.91347 q^{71} +22.1774 q^{72} -8.63925 q^{73} -24.9462 q^{74} +0.118458 q^{75} +31.2355 q^{76} -0.422363 q^{77} -2.03225 q^{78} +2.17004 q^{79} -9.74474 q^{80} +8.87391 q^{81} +1.99411 q^{82} -8.60261 q^{83} -0.160122 q^{84} +0.741439 q^{85} -13.8615 q^{86} +0.588278 q^{87} -11.2320 q^{88} -3.17906 q^{89} -7.80926 q^{90} -1.83207 q^{91} -26.6098 q^{92} +0.767171 q^{93} -1.93464 q^{94} -6.45376 q^{95} -1.25935 q^{96} -12.4135 q^{97} +18.1032 q^{98} -4.51562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9}+O(q^{10}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9	\( 113 q - 3 q^{2} + 6 q^{3} + 141 q^{4} - 113 q^{5} + 7 q^{6} + 7 q^{7} - 12 q^{8} + 141 q^{9} + 3 q^{10} + 38 q^{11} - 4 q^{12} + 17 q^{13} + 23 q^{14} - 6 q^{15} + 193 q^{16} - 11 q^{17} - 3 q^{18} + 76 q^{19} - 141 q^{20} + 19 q^{21} + 41 q^{22} - 28 q^{23} + 29 q^{24} + 113 q^{25} + 21 q^{26} + 18 q^{27} + 29 q^{28} + 24 q^{29} - 7 q^{30} + 59 q^{31} - 22 q^{32} + 3 q^{33} + 55 q^{34} - 7 q^{35} + 232 q^{36} + 41 q^{37} - 6 q^{38} + 55 q^{39} + 12 q^{40} + 24 q^{41} + 17 q^{42} + 136 q^{43} + 85 q^{44} - 141 q^{45} + 84 q^{46} - 91 q^{47} - 19 q^{48} + 198 q^{49} - 3 q^{50} + 97 q^{51} + 45 q^{52} + 9 q^{53} + 54 q^{54} - 38 q^{55} + 98 q^{56} + 22 q^{57} + 69 q^{58} + 59 q^{59} + 4 q^{60} + 51 q^{61} - 30 q^{62} - 22 q^{63} + 298 q^{64} - 17 q^{65} + 76 q^{66} + 201 q^{67} - 34 q^{68} + 42 q^{69} - 23 q^{70} + 69 q^{71} - 7 q^{72} + 30 q^{73} + 35 q^{74} + 6 q^{75} + 170 q^{76} - 37 q^{77} - 11 q^{78} + 143 q^{79} - 193 q^{80} + 197 q^{81} + 55 q^{82} - 15 q^{83} + 83 q^{84} + 11 q^{85} + 78 q^{86} - 51 q^{87} + 113 q^{88} + 53 q^{89} + 3 q^{90} + 217 q^{91} - 40 q^{92} + 36 q^{93} + 81 q^{94} - 76 q^{95} + 66 q^{96} + 63 q^{97} - 62 q^{98} + 184 q^{99}+O(q^{100}) \) 113 * q - 3 * q^2 + 6 * q^3 + 141 * q^4 - 113 * q^5 + 7 * q^6 + 7 * q^7 - 12 * q^8 + 141 * q^9 + 3 * q^10 + 38 * q^11 - 4 * q^12 + 17 * q^13 + 23 * q^14 - 6 * q^15 + 193 * q^16 - 11 * q^17 - 3 * q^18 + 76 * q^19 - 141 * q^20 + 19 * q^21 + 41 * q^22 - 28 * q^23 + 29 * q^24 + 113 * q^25 + 21 * q^26 + 18 * q^27 + 29 * q^28 + 24 * q^29 - 7 * q^30 + 59 * q^31 - 22 * q^32 + 3 * q^33 + 55 * q^34 - 7 * q^35 + 232 * q^36 + 41 * q^37 - 6 * q^38 + 55 * q^39 + 12 * q^40 + 24 * q^41 + 17 * q^42 + 136 * q^43 + 85 * q^44 - 141 * q^45 + 84 * q^46 - 91 * q^47 - 19 * q^48 + 198 * q^49 - 3 * q^50 + 97 * q^51 + 45 * q^52 + 9 * q^53 + 54 * q^54 - 38 * q^55 + 98 * q^56 + 22 * q^57 + 69 * q^58 + 59 * q^59 + 4 * q^60 + 51 * q^61 - 30 * q^62 - 22 * q^63 + 298 * q^64 - 17 * q^65 + 76 * q^66 + 201 * q^67 - 34 * q^68 + 42 * q^69 - 23 * q^70 + 69 * q^71 - 7 * q^72 + 30 * q^73 + 35 * q^74 + 6 * q^75 + 170 * q^76 - 37 * q^77 - 11 * q^78 + 143 * q^79 - 193 * q^80 + 197 * q^81 + 55 * q^82 - 15 * q^83 + 83 * q^84 + 11 * q^85 + 78 * q^86 - 51 * q^87 + 113 * q^88 + 53 * q^89 + 3 * q^90 + 217 * q^91 - 40 * q^92 + 36 * q^93 + 81 * q^94 - 76 * q^95 + 66 * q^96 + 63 * q^97 - 62 * q^98 + 184 * q^99

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