LMFDB - Embedded newform 6034.2.a.m.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.893081 q^{3} +1.00000 q^{4} +0.353208 q^{5} +0.893081 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.20241 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.893081 q^{3} +1.00000 q^{4} +0.353208 q^{5} +0.893081 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.20241 q^{9} +0.353208 q^{10} +3.54260 q^{11} +0.893081 q^{12} -5.84013 q^{13} +1.00000 q^{14} +0.315443 q^{15} +1.00000 q^{16} -2.29269 q^{17} -2.20241 q^{18} -1.48572 q^{19} +0.353208 q^{20} +0.893081 q^{21} +3.54260 q^{22} -5.37874 q^{23} +0.893081 q^{24} -4.87524 q^{25} -5.84013 q^{26} -4.64617 q^{27} +1.00000 q^{28} -2.93890 q^{29} +0.315443 q^{30} -3.17498 q^{31} +1.00000 q^{32} +3.16383 q^{33} -2.29269 q^{34} +0.353208 q^{35} -2.20241 q^{36} -1.67842 q^{37} -1.48572 q^{38} -5.21570 q^{39} +0.353208 q^{40} -10.5695 q^{41} +0.893081 q^{42} -9.01137 q^{43} +3.54260 q^{44} -0.777908 q^{45} -5.37874 q^{46} +5.71630 q^{47} +0.893081 q^{48} +1.00000 q^{49} -4.87524 q^{50} -2.04756 q^{51} -5.84013 q^{52} +13.0641 q^{53} -4.64617 q^{54} +1.25127 q^{55} +1.00000 q^{56} -1.32687 q^{57} -2.93890 q^{58} +14.0020 q^{59} +0.315443 q^{60} -1.80992 q^{61} -3.17498 q^{62} -2.20241 q^{63} +1.00000 q^{64} -2.06278 q^{65} +3.16383 q^{66} -6.91403 q^{67} -2.29269 q^{68} -4.80365 q^{69} +0.353208 q^{70} -14.5351 q^{71} -2.20241 q^{72} -8.03976 q^{73} -1.67842 q^{74} -4.35399 q^{75} -1.48572 q^{76} +3.54260 q^{77} -5.21570 q^{78} -13.6697 q^{79} +0.353208 q^{80} +2.45781 q^{81} -10.5695 q^{82} +0.0637516 q^{83} +0.893081 q^{84} -0.809797 q^{85} -9.01137 q^{86} -2.62468 q^{87} +3.54260 q^{88} +4.11184 q^{89} -0.777908 q^{90} -5.84013 q^{91} -5.37874 q^{92} -2.83552 q^{93} +5.71630 q^{94} -0.524767 q^{95} +0.893081 q^{96} +4.51949 q^{97} +1.00000 q^{98} -7.80224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.893081	0.515621	0.257810	−	0.966196i	$-0.416999\pi$
$3$	0.893081	0.515621	0.257810	+	0.966196i	$0.416999\pi$
$4$	1.00000	0.500000
$5$	0.353208	0.157959	0.0789797	−	0.996876i	$-0.474834\pi$
$5$	0.353208	0.157959	0.0789797	+	0.996876i	$0.474834\pi$
$6$	0.893081	0.364599
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.20241	−0.734135
$10$	0.353208	0.111694
$11$	3.54260	1.06813	0.534067	−	0.845442i	$-0.320663\pi$
$11$	3.54260	1.06813	0.534067	+	0.845442i	$0.320663\pi$
$12$	0.893081	0.257810
$13$	−5.84013	−1.61976	−0.809880	−	0.586596i	$-0.800468\pi$
$13$	−5.84013	−1.61976	−0.809880	+	0.586596i	$0.800468\pi$
$14$	1.00000	0.267261
$15$	0.315443	0.0814471
$16$	1.00000	0.250000
$17$	−2.29269	−0.556060	−0.278030	−	0.960572i	$-0.589681\pi$
$17$	−2.29269	−0.556060	−0.278030	+	0.960572i	$0.589681\pi$
$18$	−2.20241	−0.519112
$19$	−1.48572	−0.340847	−0.170424	−	0.985371i	$-0.554514\pi$
$19$	−1.48572	−0.340847	−0.170424	+	0.985371i	$0.554514\pi$
$20$	0.353208	0.0789797
$21$	0.893081	0.194886
$22$	3.54260	0.755285
$23$	−5.37874	−1.12155	−0.560773	−	0.827970i	$-0.689496\pi$
$23$	−5.37874	−1.12155	−0.560773	+	0.827970i	$0.689496\pi$
$24$	0.893081	0.182299
$25$	−4.87524	−0.975049
$26$	−5.84013	−1.14534
$27$	−4.64617	−0.894156
$28$	1.00000	0.188982
$29$	−2.93890	−0.545740	−0.272870	−	0.962051i	$-0.587973\pi$
$29$	−2.93890	−0.545740	−0.272870	+	0.962051i	$0.587973\pi$
$30$	0.315443	0.0575918
$31$	−3.17498	−0.570244	−0.285122	−	0.958491i	$-0.592034\pi$
$31$	−3.17498	−0.570244	−0.285122	+	0.958491i	$0.592034\pi$
$32$	1.00000	0.176777
$33$	3.16383	0.550752
$34$	−2.29269	−0.393194
$35$	0.353208	0.0597030
$36$	−2.20241	−0.367068
$37$	−1.67842	−0.275931	−0.137965	−	0.990437i	$-0.544056\pi$
$37$	−1.67842	−0.275931	−0.137965	+	0.990437i	$0.544056\pi$
$38$	−1.48572	−0.241015
$39$	−5.21570	−0.835181
$40$	0.353208	0.0558471
$41$	−10.5695	−1.65068	−0.825342	−	0.564633i	$-0.809018\pi$
$41$	−10.5695	−1.65068	−0.825342	+	0.564633i	$0.809018\pi$
$42$	0.893081	0.137805
$43$	−9.01137	−1.37422	−0.687110	−	0.726553i	$-0.741121\pi$
$43$	−9.01137	−1.37422	−0.687110	+	0.726553i	$0.741121\pi$
$44$	3.54260	0.534067
$45$	−0.777908	−0.115964
$46$	−5.37874	−0.793052
$47$	5.71630	0.833809	0.416904	−	0.908950i	$-0.363115\pi$
$47$	5.71630	0.833809	0.416904	+	0.908950i	$0.363115\pi$
$48$	0.893081	0.128905
$49$	1.00000	0.142857
$50$	−4.87524	−0.689464
$51$	−2.04756	−0.286716
$52$	−5.84013	−0.809880
$53$	13.0641	1.79449	0.897247	−	0.441529i	$-0.145564\pi$
$53$	13.0641	1.79449	0.897247	+	0.441529i	$0.145564\pi$
$54$	−4.64617	−0.632264
$55$	1.25127	0.168722
$56$	1.00000	0.133631
$57$	−1.32687	−0.175748
$58$	−2.93890	−0.385896
$59$	14.0020	1.82291	0.911456	−	0.411398i	$-0.134959\pi$
$59$	14.0020	1.82291	0.911456	+	0.411398i	$0.134959\pi$
$60$	0.315443	0.0407236
$61$	−1.80992	−0.231737	−0.115869	−	0.993265i	$-0.536965\pi$
$61$	−1.80992	−0.231737	−0.115869	+	0.993265i	$0.536965\pi$
$62$	−3.17498	−0.403223
$63$	−2.20241	−0.277477
$64$	1.00000	0.125000
$65$	−2.06278	−0.255856
$66$	3.16383	0.389440
$67$	−6.91403	−0.844684	−0.422342	−	0.906437i	$-0.638792\pi$
$67$	−6.91403	−0.844684	−0.422342	+	0.906437i	$0.638792\pi$
$68$	−2.29269	−0.278030
$69$	−4.80365	−0.578292
$70$	0.353208	0.0422164
$71$	−14.5351	−1.72500	−0.862502	−	0.506053i	$-0.831104\pi$
$71$	−14.5351	−1.72500	−0.862502	+	0.506053i	$0.831104\pi$
$72$	−2.20241	−0.259556
$73$	−8.03976	−0.940982	−0.470491	−	0.882405i	$-0.655923\pi$
$73$	−8.03976	−0.940982	−0.470491	+	0.882405i	$0.655923\pi$
$74$	−1.67842	−0.195113
$75$	−4.35399	−0.502755
$76$	−1.48572	−0.170424
$77$	3.54260	0.403717
$78$	−5.21570	−0.590562
$79$	−13.6697	−1.53796	−0.768979	−	0.639274i	$-0.779235\pi$
$79$	−13.6697	−1.53796	−0.768979	+	0.639274i	$0.779235\pi$
$80$	0.353208	0.0394899
$81$	2.45781	0.273090
$82$	−10.5695	−1.16721
$83$	0.0637516	0.00699764	0.00349882	−	0.999994i	$-0.498886\pi$
$83$	0.0637516	0.00699764	0.00349882	+	0.999994i	$0.498886\pi$
$84$	0.893081	0.0974431
$85$	−0.809797	−0.0878349
$86$	−9.01137	−0.971721
$87$	−2.62468	−0.281395
$88$	3.54260	0.377642
$89$	4.11184	0.435854	0.217927	−	0.975965i	$-0.430070\pi$
$89$	4.11184	0.435854	0.217927	+	0.975965i	$0.430070\pi$
$90$	−0.777908	−0.0819987
$91$	−5.84013	−0.612211
$92$	−5.37874	−0.560773
$93$	−2.83552	−0.294029
$94$	5.71630	0.589592
$95$	−0.524767	−0.0538400
$96$	0.893081	0.0911497
$97$	4.51949	0.458885	0.229443	−	0.973322i	$-0.426310\pi$
$97$	4.51949	0.458885	0.229443	+	0.973322i	$0.426310\pi$
$98$	1.00000	0.101015
$99$	−7.80224	−0.784155
$100$	−4.87524	−0.487524
$101$	19.9981	1.98989	0.994944	−	0.100428i	$-0.0320211\pi$
$101$	19.9981	1.98989	0.994944	+	0.100428i	$0.0320211\pi$
$102$	−2.04756	−0.202739
$103$	17.7753	1.75146	0.875728	−	0.482805i	$-0.160382\pi$
$103$	17.7753	1.75146	0.875728	+	0.482805i	$0.160382\pi$
$104$	−5.84013	−0.572671
$105$	0.315443	0.0307841
$106$	13.0641	1.26890
$107$	4.76513	0.460663	0.230331	−	0.973112i	$-0.426019\pi$
$107$	4.76513	0.460663	0.230331	+	0.973112i	$0.426019\pi$
$108$	−4.64617	−0.447078
$109$	−1.35849	−0.130120	−0.0650598	−	0.997881i	$-0.520724\pi$
$109$	−1.35849	−0.130120	−0.0650598	+	0.997881i	$0.520724\pi$
$110$	1.25127	0.119304
$111$	−1.49897	−0.142276
$112$	1.00000	0.0944911
$113$	12.4122	1.16764	0.583820	−	0.811883i	$-0.301557\pi$
$113$	12.4122	1.16764	0.583820	+	0.811883i	$0.301557\pi$
$114$	−1.32687	−0.124272
$115$	−1.89981	−0.177159
$116$	−2.93890	−0.272870
$117$	12.8623	1.18912
$118$	14.0020	1.28899
$119$	−2.29269	−0.210171
$120$	0.315443	0.0287959
$121$	1.55001	0.140910
$122$	−1.80992	−0.163863
$123$	−9.43945	−0.851127
$124$	−3.17498	−0.285122
$125$	−3.48802	−0.311978
$126$	−2.20241	−0.196206
$127$	7.94926	0.705383	0.352692	−	0.935740i	$-0.385266\pi$
$127$	7.94926	0.705383	0.352692	+	0.935740i	$0.385266\pi$
$128$	1.00000	0.0883883
$129$	−8.04788	−0.708576
$130$	−2.06278	−0.180918
$131$	20.3272	1.77599	0.887996	−	0.459851i	$-0.152097\pi$
$131$	20.3272	1.77599	0.887996	+	0.459851i	$0.152097\pi$
$132$	3.16383	0.275376
$133$	−1.48572	−0.128828
$134$	−6.91403	−0.597282
$135$	−1.64106	−0.141240
$136$	−2.29269	−0.196597
$137$	−14.0886	−1.20367	−0.601834	−	0.798621i	$-0.705563\pi$
$137$	−14.0886	−1.20367	−0.601834	+	0.798621i	$0.705563\pi$
$138$	−4.80365	−0.408914
$139$	8.20184	0.695671	0.347835	−	0.937556i	$-0.386917\pi$
$139$	8.20184	0.695671	0.347835	+	0.937556i	$0.386917\pi$
$140$	0.353208	0.0298515
$141$	5.10512	0.429929
$142$	−14.5351	−1.21976
$143$	−20.6892	−1.73012
$144$	−2.20241	−0.183534
$145$	−1.03804	−0.0862048
$146$	−8.03976	−0.665375
$147$	0.893081	0.0736601
$148$	−1.67842	−0.137965
$149$	7.96897	0.652843	0.326422	−	0.945224i	$-0.394157\pi$
$149$	7.96897	0.652843	0.326422	+	0.945224i	$0.394157\pi$
$150$	−4.35399	−0.355502
$151$	−10.1540	−0.826325	−0.413162	−	0.910657i	$-0.635576\pi$
$151$	−10.1540	−0.826325	−0.413162	+	0.910657i	$0.635576\pi$
$152$	−1.48572	−0.120508
$153$	5.04944	0.408223
$154$	3.54260	0.285471
$155$	−1.12143	−0.0900754
$156$	−5.21570	−0.417591
$157$	−6.63284	−0.529358	−0.264679	−	0.964337i	$-0.585266\pi$
$157$	−6.63284	−0.529358	−0.264679	+	0.964337i	$0.585266\pi$
$158$	−13.6697	−1.08750
$159$	11.6673	0.925278
$160$	0.353208	0.0279235
$161$	−5.37874	−0.423904
$162$	2.45781	0.193104
$163$	−16.0328	−1.25579	−0.627893	−	0.778299i	$-0.716083\pi$
$163$	−16.0328	−1.25579	−0.627893	+	0.778299i	$0.716083\pi$
$164$	−10.5695	−0.825342
$165$	1.11749	0.0869964
$166$	0.0637516	0.00494808
$167$	−6.28286	−0.486182	−0.243091	−	0.970003i	$-0.578161\pi$
$167$	−6.28286	−0.486182	−0.243091	+	0.970003i	$0.578161\pi$
$168$	0.893081	0.0689027
$169$	21.1071	1.62362
$170$	−0.809797	−0.0621086
$171$	3.27215	0.250228
$172$	−9.01137	−0.687110
$173$	−18.5193	−1.40800	−0.704000	−	0.710200i	$-0.748604\pi$
$173$	−18.5193	−1.40800	−0.704000	+	0.710200i	$0.748604\pi$
$174$	−2.62468	−0.198976
$175$	−4.87524	−0.368534
$176$	3.54260	0.267033
$177$	12.5050	0.939931
$178$	4.11184	0.308196
$179$	−8.66311	−0.647511	−0.323756	−	0.946141i	$-0.604946\pi$
$179$	−8.66311	−0.647511	−0.323756	+	0.946141i	$0.604946\pi$
$180$	−0.777908	−0.0579818
$181$	−1.19297	−0.0886725	−0.0443362	−	0.999017i	$-0.514117\pi$
$181$	−1.19297	−0.0886725	−0.0443362	+	0.999017i	$0.514117\pi$
$182$	−5.84013	−0.432899
$183$	−1.61641	−0.119488
$184$	−5.37874	−0.396526
$185$	−0.592832	−0.0435859
$186$	−2.83552	−0.207910
$187$	−8.12209	−0.593946
$188$	5.71630	0.416904
$189$	−4.64617	−0.337959
$190$	−0.524767	−0.0380706
$191$	−12.5319	−0.906779	−0.453389	−	0.891313i	$-0.649785\pi$
$191$	−12.5319	−0.906779	−0.453389	+	0.891313i	$0.649785\pi$
$192$	0.893081	0.0644526
$193$	12.3231	0.887037	0.443519	−	0.896265i	$-0.353730\pi$
$193$	12.3231	0.887037	0.443519	+	0.896265i	$0.353730\pi$
$194$	4.51949	0.324481
$195$	−1.84223	−0.131925
$196$	1.00000	0.0714286
$197$	0.627958	0.0447401	0.0223701	−	0.999750i	$-0.492879\pi$
$197$	0.627958	0.0447401	0.0223701	+	0.999750i	$0.492879\pi$
$198$	−7.80224	−0.554481
$199$	3.72282	0.263904	0.131952	−	0.991256i	$-0.457876\pi$
$199$	3.72282	0.263904	0.131952	+	0.991256i	$0.457876\pi$
$200$	−4.87524	−0.344732
$201$	−6.17479	−0.435536
$202$	19.9981	1.40706
$203$	−2.93890	−0.206270
$204$	−2.04756	−0.143358
$205$	−3.73325	−0.260741
$206$	17.7753	1.23847
$207$	11.8462	0.823366
$208$	−5.84013	−0.404940
$209$	−5.26330	−0.364070
$210$	0.315443	0.0217677
$211$	15.8092	1.08835	0.544177	−	0.838971i	$-0.316842\pi$
$211$	15.8092	1.08835	0.544177	+	0.838971i	$0.316842\pi$
$212$	13.0641	0.897247
$213$	−12.9811	−0.889448
$214$	4.76513	0.325738
$215$	−3.18289	−0.217071
$216$	−4.64617	−0.316132
$217$	−3.17498	−0.215532
$218$	−1.35849	−0.0920084
$219$	−7.18015	−0.485190
$220$	1.25127	0.0843609
$221$	13.3896	0.900683
$222$	−1.49897	−0.100604
$223$	−24.0780	−1.61238	−0.806191	−	0.591655i	$-0.798475\pi$
$223$	−24.0780	−1.61238	−0.806191	+	0.591655i	$0.798475\pi$
$224$	1.00000	0.0668153
$225$	10.7373	0.715818
$226$	12.4122	0.825646
$227$	3.58007	0.237618	0.118809	−	0.992917i	$-0.462092\pi$
$227$	3.58007	0.237618	0.118809	+	0.992917i	$0.462092\pi$
$228$	−1.32687	−0.0878739
$229$	22.5188	1.48809	0.744043	−	0.668131i	$-0.232906\pi$
$229$	22.5188	1.48809	0.744043	+	0.668131i	$0.232906\pi$
$230$	−1.89981	−0.125270
$231$	3.16383	0.208165
$232$	−2.93890	−0.192948
$233$	30.3850	1.99059	0.995294	−	0.0968982i	$-0.0308921\pi$
$233$	30.3850	1.99059	0.995294	+	0.0968982i	$0.0308921\pi$
$234$	12.8623	0.840837
$235$	2.01904	0.131708
$236$	14.0020	0.911456
$237$	−12.2081	−0.793003
$238$	−2.29269	−0.148613
$239$	−16.1706	−1.04599	−0.522994	−	0.852336i	$-0.675185\pi$
$239$	−16.1706	−1.04599	−0.522994	+	0.852336i	$0.675185\pi$
$240$	0.315443	0.0203618
$241$	3.72273	0.239802	0.119901	−	0.992786i	$-0.461742\pi$
$241$	3.72273	0.239802	0.119901	+	0.992786i	$0.461742\pi$
$242$	1.55001	0.0996382
$243$	16.1335	1.03497
$244$	−1.80992	−0.115869
$245$	0.353208	0.0225656
$246$	−9.43945	−0.601838
$247$	8.67678	0.552090
$248$	−3.17498	−0.201612
$249$	0.0569353	0.00360813
$250$	−3.48802	−0.220601
$251$	−13.9398	−0.879873	−0.439936	−	0.898029i	$-0.644999\pi$
$251$	−13.9398	−0.879873	−0.439936	+	0.898029i	$0.644999\pi$
$252$	−2.20241	−0.138739
$253$	−19.0547	−1.19796
$254$	7.94926	0.498781
$255$	−0.723215	−0.0452895
$256$	1.00000	0.0625000
$257$	2.39449	0.149364	0.0746822	−	0.997207i	$-0.476206\pi$
$257$	2.39449	0.149364	0.0746822	+	0.997207i	$0.476206\pi$
$258$	−8.04788	−0.501039
$259$	−1.67842	−0.104292
$260$	−2.06278	−0.127928
$261$	6.47265	0.400647
$262$	20.3272	1.25582
$263$	−9.84124	−0.606837	−0.303418	−	0.952857i	$-0.598128\pi$
$263$	−9.84124	−0.606837	−0.303418	+	0.952857i	$0.598128\pi$
$264$	3.16383	0.194720
$265$	4.61435	0.283457
$266$	−1.48572	−0.0910952
$267$	3.67221	0.224735
$268$	−6.91403	−0.422342
$269$	−5.15765	−0.314468	−0.157234	−	0.987561i	$-0.550258\pi$
$269$	−5.15765	−0.314468	−0.157234	+	0.987561i	$0.550258\pi$
$270$	−1.64106	−0.0998720
$271$	−15.2379	−0.925637	−0.462819	−	0.886453i	$-0.653162\pi$
$271$	−15.2379	−0.925637	−0.462819	+	0.886453i	$0.653162\pi$
$272$	−2.29269	−0.139015
$273$	−5.21570	−0.315669
$274$	−14.0886	−0.851122
$275$	−17.2710	−1.04148
$276$	−4.80365	−0.289146
$277$	17.6573	1.06092	0.530462	−	0.847709i	$-0.322019\pi$
$277$	17.6573	1.06092	0.530462	+	0.847709i	$0.322019\pi$
$278$	8.20184	0.491914
$279$	6.99260	0.418636
$280$	0.353208	0.0211082
$281$	−33.5029	−1.99862	−0.999308	−	0.0371936i	$-0.988158\pi$
$281$	−33.5029	−1.99862	−0.999308	+	0.0371936i	$0.988158\pi$
$282$	5.10512	0.304006
$283$	−4.17530	−0.248196	−0.124098	−	0.992270i	$-0.539604\pi$
$283$	−4.17530	−0.248196	−0.124098	+	0.992270i	$0.539604\pi$
$284$	−14.5351	−0.862502
$285$	−0.468660	−0.0277610
$286$	−20.6892	−1.22338
$287$	−10.5695	−0.623900
$288$	−2.20241	−0.129778
$289$	−11.7436	−0.690798
$290$	−1.03804	−0.0609560
$291$	4.03627	0.236611
$292$	−8.03976	−0.470491
$293$	6.82017	0.398439	0.199219	−	0.979955i	$-0.436159\pi$
$293$	6.82017	0.398439	0.199219	+	0.979955i	$0.436159\pi$
$294$	0.893081	0.0520855
$295$	4.94564	0.287946
$296$	−1.67842	−0.0975563
$297$	−16.4595	−0.955078
$298$	7.96897	0.461630
$299$	31.4125	1.81663
$300$	−4.35399	−0.251378
$301$	−9.01137	−0.519407
$302$	−10.1540	−0.584300
$303$	17.8600	1.02603
$304$	−1.48572	−0.0852118
$305$	−0.639280	−0.0366051
$306$	5.04944	0.288657
$307$	7.87260	0.449313	0.224656	−	0.974438i	$-0.427874\pi$
$307$	7.87260	0.449313	0.224656	+	0.974438i	$0.427874\pi$
$308$	3.54260	0.201858
$309$	15.8748	0.903087
$310$	−1.12143	−0.0636929
$311$	5.22877	0.296496	0.148248	−	0.988950i	$-0.452637\pi$
$311$	5.22877	0.296496	0.148248	+	0.988950i	$0.452637\pi$
$312$	−5.21570	−0.295281
$313$	−2.27692	−0.128699	−0.0643497	−	0.997927i	$-0.520497\pi$
$313$	−2.27692	−0.128699	−0.0643497	+	0.997927i	$0.520497\pi$
$314$	−6.63284	−0.374313
$315$	−0.777908	−0.0438301
$316$	−13.6697	−0.768979
$317$	15.9874	0.897941	0.448970	−	0.893547i	$-0.351791\pi$
$317$	15.9874	0.897941	0.448970	+	0.893547i	$0.351791\pi$
$318$	11.6673	0.654270
$319$	−10.4113	−0.582923
$320$	0.353208	0.0197449
$321$	4.25565	0.237527
$322$	−5.37874	−0.299746
$323$	3.40629	0.189531
$324$	2.45781	0.136545
$325$	28.4720	1.57934
$326$	−16.0328	−0.887975
$327$	−1.21324	−0.0670923
$328$	−10.5695	−0.583605
$329$	5.71630	0.315150
$330$	1.11749	0.0615158
$331$	−15.7450	−0.865423	−0.432711	−	0.901533i	$-0.642443\pi$
$331$	−15.7450	−0.865423	−0.432711	+	0.901533i	$0.642443\pi$
$332$	0.0637516	0.00349882
$333$	3.69657	0.202571
$334$	−6.28286	−0.343783
$335$	−2.44209	−0.133426
$336$	0.893081	0.0487216
$337$	−33.2569	−1.81162	−0.905808	−	0.423688i	$-0.860735\pi$
$337$	−33.2569	−1.81162	−0.905808	+	0.423688i	$0.860735\pi$
$338$	21.1071	1.14807
$339$	11.0851	0.602059
$340$	−0.809797	−0.0439174
$341$	−11.2477	−0.609097
$342$	3.27215	0.176938
$343$	1.00000	0.0539949
$344$	−9.01137	−0.485860
$345$	−1.69669	−0.0913466
$346$	−18.5193	−0.995606
$347$	−0.398569	−0.0213963	−0.0106982	−	0.999943i	$-0.503405\pi$
$347$	−0.398569	−0.0213963	−0.0106982	+	0.999943i	$0.503405\pi$
$348$	−2.62468	−0.140697
$349$	11.3936	0.609887	0.304944	−	0.952370i	$-0.401362\pi$
$349$	11.3936	0.609887	0.304944	+	0.952370i	$0.401362\pi$
$350$	−4.87524	−0.260593
$351$	27.1342	1.44832
$352$	3.54260	0.188821
$353$	−25.7126	−1.36854	−0.684271	−	0.729228i	$-0.739880\pi$
$353$	−25.7126	−1.36854	−0.684271	+	0.729228i	$0.739880\pi$
$354$	12.5050	0.664631
$355$	−5.13393	−0.272481
$356$	4.11184	0.217927
$357$	−2.04756	−0.108368
$358$	−8.66311	−0.457860
$359$	−6.73239	−0.355322	−0.177661	−	0.984092i	$-0.556853\pi$
$359$	−6.73239	−0.355322	−0.177661	+	0.984092i	$0.556853\pi$
$360$	−0.777908	−0.0409993
$361$	−16.7926	−0.883823
$362$	−1.19297	−0.0627009
$363$	1.38428	0.0726560
$364$	−5.84013	−0.306106
$365$	−2.83971	−0.148637
$366$	−1.61641	−0.0844910
$367$	3.68966	0.192599	0.0962993	−	0.995352i	$-0.469299\pi$
$367$	3.68966	0.192599	0.0962993	+	0.995352i	$0.469299\pi$
$368$	−5.37874	−0.280386
$369$	23.2784	1.21183
$370$	−0.592832	−0.0308199
$371$	13.0641	0.678255
$372$	−2.83552	−0.147015
$373$	10.5528	0.546404	0.273202	−	0.961957i	$-0.411917\pi$
$373$	10.5528	0.546404	0.273202	+	0.961957i	$0.411917\pi$
$374$	−8.12209	−0.419983
$375$	−3.11508	−0.160862
$376$	5.71630	0.294796
$377$	17.1635	0.883967
$378$	−4.64617	−0.238973
$379$	2.24981	0.115565	0.0577825	−	0.998329i	$-0.481597\pi$
$379$	2.24981	0.115565	0.0577825	+	0.998329i	$0.481597\pi$
$380$	−0.524767	−0.0269200
$381$	7.09934	0.363710
$382$	−12.5319	−0.641189
$383$	10.5853	0.540883	0.270442	−	0.962736i	$-0.412830\pi$
$383$	10.5853	0.540883	0.270442	+	0.962736i	$0.412830\pi$
$384$	0.893081	0.0455748
$385$	1.25127	0.0637708
$386$	12.3231	0.627230
$387$	19.8467	1.00886
$388$	4.51949	0.229443
$389$	14.7788	0.749314	0.374657	−	0.927164i	$-0.377761\pi$
$389$	14.7788	0.749314	0.374657	+	0.927164i	$0.377761\pi$
$390$	−1.84223	−0.0932849
$391$	12.3318	0.623646
$392$	1.00000	0.0505076
$393$	18.1538	0.915738
$394$	0.627958	0.0316360
$395$	−4.82824	−0.242935
$396$	−7.80224	−0.392077
$397$	−9.42891	−0.473223	−0.236612	−	0.971604i	$-0.576037\pi$
$397$	−9.42891	−0.473223	−0.236612	+	0.971604i	$0.576037\pi$
$398$	3.72282	0.186608
$399$	−1.32687	−0.0664264
$400$	−4.87524	−0.243762
$401$	−6.28737	−0.313976	−0.156988	−	0.987600i	$-0.550178\pi$
$401$	−6.28737	−0.313976	−0.156988	+	0.987600i	$0.550178\pi$
$402$	−6.17479	−0.307971
$403$	18.5423	0.923658
$404$	19.9981	0.994944
$405$	0.868119	0.0431372
$406$	−2.93890	−0.145855
$407$	−5.94598	−0.294731
$408$	−2.04756	−0.101369
$409$	17.5931	0.869925	0.434962	−	0.900449i	$-0.356762\pi$
$409$	17.5931	0.869925	0.434962	+	0.900449i	$0.356762\pi$
$410$	−3.73325	−0.184372
$411$	−12.5822	−0.620636
$412$	17.7753	0.875728
$413$	14.0020	0.688996
$414$	11.8462	0.582208
$415$	0.0225176	0.00110534
$416$	−5.84013	−0.286336
$417$	7.32490	0.358702
$418$	−5.26330	−0.257437
$419$	−24.0645	−1.17563	−0.587815	−	0.808996i	$-0.700012\pi$
$419$	−24.0645	−1.17563	−0.587815	+	0.808996i	$0.700012\pi$
$420$	0.315443	0.0153921
$421$	−28.4912	−1.38857	−0.694287	−	0.719698i	$-0.744280\pi$
$421$	−28.4912	−1.38857	−0.694287	+	0.719698i	$0.744280\pi$
$422$	15.8092	0.769582
$423$	−12.5896	−0.612129
$424$	13.0641	0.634449
$425$	11.1774	0.542185
$426$	−12.9811	−0.628935
$427$	−1.80992	−0.0875884
$428$	4.76513	0.230331
$429$	−18.4771	−0.892085
$430$	−3.18289	−0.153492
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−4.64617	−0.223539
$433$	−7.09859	−0.341136	−0.170568	−	0.985346i	$-0.554560\pi$
$433$	−7.09859	−0.341136	−0.170568	+	0.985346i	$0.554560\pi$
$434$	−3.17498	−0.152404
$435$	−0.927056	−0.0444490
$436$	−1.35849	−0.0650598
$437$	7.99129	0.382275
$438$	−7.18015	−0.343081
$439$	−36.6284	−1.74818	−0.874089	−	0.485767i	$-0.838540\pi$
$439$	−36.6284	−1.74818	−0.874089	+	0.485767i	$0.838540\pi$
$440$	1.25127	0.0596522
$441$	−2.20241	−0.104876
$442$	13.3896	0.636879
$443$	−17.8282	−0.847042	−0.423521	−	0.905886i	$-0.639206\pi$
$443$	−17.8282	−0.847042	−0.423521	+	0.905886i	$0.639206\pi$
$444$	−1.49897	−0.0711378
$445$	1.45234	0.0688473
$446$	−24.0780	−1.14013
$447$	7.11693	0.336619
$448$	1.00000	0.0472456
$449$	41.3730	1.95251	0.976257	−	0.216614i	$-0.0695012\pi$
$449$	41.3730	1.95251	0.976257	+	0.216614i	$0.0695012\pi$
$450$	10.7373	0.506160
$451$	−37.4436	−1.76315
$452$	12.4122	0.583820
$453$	−9.06839	−0.426070
$454$	3.58007	0.168021
$455$	−2.06278	−0.0967046
$456$	−1.32687	−0.0621362
$457$	18.3445	0.858119	0.429059	−	0.903276i	$-0.358845\pi$
$457$	18.3445	0.858119	0.429059	+	0.903276i	$0.358845\pi$
$458$	22.5188	1.05224
$459$	10.6522	0.497204
$460$	−1.89981	−0.0885793
$461$	14.7629	0.687577	0.343788	−	0.939047i	$-0.388290\pi$
$461$	14.7629	0.687577	0.343788	+	0.939047i	$0.388290\pi$
$462$	3.16383	0.147195
$463$	21.4847	0.998478	0.499239	−	0.866464i	$-0.333613\pi$
$463$	21.4847	0.998478	0.499239	+	0.866464i	$0.333613\pi$
$464$	−2.93890	−0.136435
$465$	−1.00153	−0.0464447
$466$	30.3850	1.40756
$467$	16.8320	0.778893	0.389446	−	0.921049i	$-0.372666\pi$
$467$	16.8320	0.778893	0.389446	+	0.921049i	$0.372666\pi$
$468$	12.8623	0.594561
$469$	−6.91403	−0.319260
$470$	2.01904	0.0931316
$471$	−5.92366	−0.272948
$472$	14.0020	0.644497
$473$	−31.9237	−1.46785
$474$	−12.2081	−0.560738
$475$	7.24324	0.332343
$476$	−2.29269	−0.105085
$477$	−28.7725	−1.31740
$478$	−16.1706	−0.739626
$479$	41.8906	1.91403	0.957014	−	0.290040i	$-0.0936688\pi$
$479$	41.8906	1.91403	0.957014	+	0.290040i	$0.0936688\pi$
$480$	0.315443	0.0143980
$481$	9.80219	0.446942
$482$	3.72273	0.169565
$483$	−4.80365	−0.218574
$484$	1.55001	0.0704549
$485$	1.59632	0.0724852
$486$	16.1335	0.731832
$487$	−24.4558	−1.10820	−0.554098	−	0.832451i	$-0.686937\pi$
$487$	−24.4558	−1.10820	−0.554098	+	0.832451i	$0.686937\pi$
$488$	−1.80992	−0.0819314
$489$	−14.3186	−0.647509
$490$	0.353208	0.0159563
$491$	−38.3170	−1.72922	−0.864610	−	0.502443i	$-0.832435\pi$
$491$	−38.3170	−1.72922	−0.864610	+	0.502443i	$0.832435\pi$
$492$	−9.43945	−0.425563
$493$	6.73799	0.303464
$494$	8.67678	0.390387
$495$	−2.75581	−0.123865
$496$	−3.17498	−0.142561
$497$	−14.5351	−0.651990
$498$	0.0569353	0.00255133
$499$	−39.3900	−1.76334	−0.881669	−	0.471868i	$-0.843580\pi$
$499$	−39.3900	−1.76334	−0.881669	+	0.471868i	$0.843580\pi$
$500$	−3.48802	−0.155989
$501$	−5.61110	−0.250685
$502$	−13.9398	−0.622164
$503$	4.55103	0.202920	0.101460	−	0.994840i	$-0.467649\pi$
$503$	4.55103	0.202920	0.101460	+	0.994840i	$0.467649\pi$
$504$	−2.20241	−0.0981030
$505$	7.06350	0.314322
$506$	−19.0547	−0.847086
$507$	18.8503	0.837172
$508$	7.94926	0.352692
$509$	−34.4865	−1.52859	−0.764293	−	0.644869i	$-0.776912\pi$
$509$	−34.4865	−1.52859	−0.764293	+	0.644869i	$0.776912\pi$
$510$	−0.723215	−0.0320245
$511$	−8.03976	−0.355658
$512$	1.00000	0.0441942
$513$	6.90290	0.304770
$514$	2.39449	0.105617
$515$	6.27839	0.276659
$516$	−8.04788	−0.354288
$517$	20.2506	0.890619
$518$	−1.67842	−0.0737456
$519$	−16.5393	−0.725994
$520$	−2.06278	−0.0904588
$521$	−11.4356	−0.501003	−0.250501	−	0.968116i	$-0.580595\pi$
$521$	−11.4356	−0.501003	−0.250501	+	0.968116i	$0.580595\pi$
$522$	6.47265	0.283300
$523$	10.5306	0.460473	0.230236	−	0.973135i	$-0.426050\pi$
$523$	10.5306	0.460473	0.230236	+	0.973135i	$0.426050\pi$
$524$	20.3272	0.887996
$525$	−4.35399	−0.190024
$526$	−9.84124	−0.429098
$527$	7.27926	0.317090
$528$	3.16383	0.137688
$529$	5.93086	0.257864
$530$	4.61435	0.200434
$531$	−30.8382	−1.33826
$532$	−1.48572	−0.0644140
$533$	61.7274	2.67371
$534$	3.67221	0.158912
$535$	1.68308	0.0727660
$536$	−6.91403	−0.298641
$537$	−7.73686	−0.333870
$538$	−5.15765	−0.222362
$539$	3.54260	0.152591
$540$	−1.64106	−0.0706202
$541$	−37.4565	−1.61038	−0.805190	−	0.593017i	$-0.797937\pi$
$541$	−37.4565	−1.61038	−0.805190	+	0.593017i	$0.797937\pi$
$542$	−15.2379	−0.654524
$543$	−1.06542	−0.0457214
$544$	−2.29269	−0.0982984
$545$	−0.479829	−0.0205536
$546$	−5.21570	−0.223212
$547$	−0.150766	−0.00644629	−0.00322314	−	0.999995i	$-0.501026\pi$
$547$	−0.150766	−0.00644629	−0.00322314	+	0.999995i	$0.501026\pi$
$548$	−14.0886	−0.601834
$549$	3.98619	0.170126
$550$	−17.2710	−0.736439
$551$	4.36638	0.186014
$552$	−4.80365	−0.204457
$553$	−13.6697	−0.581293
$554$	17.6573	0.750186
$555$	−0.529447	−0.0224738
$556$	8.20184	0.347835
$557$	18.9205	0.801687	0.400844	−	0.916146i	$-0.368717\pi$
$557$	18.9205	0.801687	0.400844	+	0.916146i	$0.368717\pi$
$558$	6.99260	0.296020
$559$	52.6275	2.22591
$560$	0.353208	0.0149258
$561$	−7.25368	−0.306251
$562$	−33.5029	−1.41324
$563$	−15.9552	−0.672431	−0.336216	−	0.941785i	$-0.609147\pi$
$563$	−15.9552	−0.672431	−0.336216	+	0.941785i	$0.609147\pi$
$564$	5.10512	0.214964
$565$	4.38408	0.184440
$566$	−4.17530	−0.175501
$567$	2.45781	0.103218
$568$	−14.5351	−0.609881
$569$	11.4244	0.478935	0.239467	−	0.970904i	$-0.423027\pi$
$569$	11.4244	0.478935	0.239467	+	0.970904i	$0.423027\pi$
$570$	−0.468660	−0.0196300
$571$	36.9451	1.54610	0.773051	−	0.634344i	$-0.218730\pi$
$571$	36.9451	1.54610	0.773051	+	0.634344i	$0.218730\pi$
$572$	−20.6892	−0.865060
$573$	−11.1920	−0.467554
$574$	−10.5695	−0.441164
$575$	26.2227	1.09356
$576$	−2.20241	−0.0917669
$577$	−33.9320	−1.41261	−0.706304	−	0.707909i	$-0.749639\pi$
$577$	−33.9320	−1.41261	−0.706304	+	0.707909i	$0.749639\pi$
$578$	−11.7436	−0.488468
$579$	11.0055	0.457375
$580$	−1.03804	−0.0431024
$581$	0.0637516	0.00264486
$582$	4.03627	0.167309
$583$	46.2809	1.91676
$584$	−8.03976	−0.332687
$585$	4.54308	0.187833
$586$	6.82017	0.281739
$587$	−10.0606	−0.415245	−0.207623	−	0.978209i	$-0.566573\pi$
$587$	−10.0606	−0.415245	−0.207623	+	0.978209i	$0.566573\pi$
$588$	0.893081	0.0368300
$589$	4.71713	0.194366
$590$	4.94564	0.203609
$591$	0.560817	0.0230689
$592$	−1.67842	−0.0689827
$593$	20.9863	0.861802	0.430901	−	0.902399i	$-0.358196\pi$
$593$	20.9863	0.861802	0.430901	+	0.902399i	$0.358196\pi$
$594$	−16.4595	−0.675342
$595$	−0.809797	−0.0331985
$596$	7.96897	0.326422
$597$	3.32478	0.136074
$598$	31.4125	1.28455
$599$	5.60927	0.229188	0.114594	−	0.993412i	$-0.463443\pi$
$599$	5.60927	0.229188	0.114594	+	0.993412i	$0.463443\pi$
$600$	−4.35399	−0.177751
$601$	10.4147	0.424826	0.212413	−	0.977180i	$-0.431868\pi$
$601$	10.4147	0.424826	0.212413	+	0.977180i	$0.431868\pi$
$602$	−9.01137	−0.367276
$603$	15.2275	0.620112
$604$	−10.1540	−0.413162
$605$	0.547475	0.0222580
$606$	17.8600	0.725511
$607$	−27.9718	−1.13534	−0.567669	−	0.823257i	$-0.692155\pi$
$607$	−27.9718	−1.13534	−0.567669	+	0.823257i	$0.692155\pi$
$608$	−1.48572	−0.0602538
$609$	−2.62468	−0.106357
$610$	−0.639280	−0.0258837
$611$	−33.3839	−1.35057
$612$	5.04944	0.204112
$613$	−4.19754	−0.169537	−0.0847685	−	0.996401i	$-0.527015\pi$
$613$	−4.19754	−0.169537	−0.0847685	+	0.996401i	$0.527015\pi$
$614$	7.87260	0.317712
$615$	−3.33409	−0.134443
$616$	3.54260	0.142735
$617$	−45.4866	−1.83122	−0.915611	−	0.402065i	$-0.868293\pi$
$617$	−45.4866	−1.83122	−0.915611	+	0.402065i	$0.868293\pi$
$618$	15.8748	0.638579
$619$	−24.0890	−0.968220	−0.484110	−	0.875007i	$-0.660856\pi$
$619$	−24.0890	−0.968220	−0.484110	+	0.875007i	$0.660856\pi$
$620$	−1.12143	−0.0450377
$621$	24.9905	1.00284
$622$	5.22877	0.209655
$623$	4.11184	0.164737
$624$	−5.21570	−0.208795
$625$	23.1442	0.925769
$626$	−2.27692	−0.0910042
$627$	−4.70055	−0.187722
$628$	−6.63284	−0.264679
$629$	3.84811	0.153434
$630$	−0.777908	−0.0309926
$631$	7.45349	0.296719	0.148359	−	0.988934i	$-0.452601\pi$
$631$	7.45349	0.296719	0.148359	+	0.988934i	$0.452601\pi$
$632$	−13.6697	−0.543750
$633$	14.1189	0.561177
$634$	15.9874	0.634940
$635$	2.80774	0.111422
$636$	11.6673	0.462639
$637$	−5.84013	−0.231394
$638$	−10.4113	−0.412189
$639$	32.0123	1.26639
$640$	0.353208	0.0139618
$641$	−12.1726	−0.480788	−0.240394	−	0.970675i	$-0.577277\pi$
$641$	−12.1726	−0.480788	−0.240394	+	0.970675i	$0.577277\pi$
$642$	4.25565	0.167957
$643$	−17.8284	−0.703084	−0.351542	−	0.936172i	$-0.614343\pi$
$643$	−17.8284	−0.703084	−0.351542	+	0.936172i	$0.614343\pi$
$644$	−5.37874	−0.211952
$645$	−2.84258	−0.111926
$646$	3.40629	0.134019
$647$	40.1680	1.57917	0.789584	−	0.613643i	$-0.210296\pi$
$647$	40.1680	1.57917	0.789584	+	0.613643i	$0.210296\pi$
$648$	2.45781	0.0965520
$649$	49.6036	1.94711
$650$	28.4720	1.11677
$651$	−2.83552	−0.111133
$652$	−16.0328	−0.627893
$653$	34.6152	1.35460	0.677299	−	0.735708i	$-0.263150\pi$
$653$	34.6152	1.35460	0.677299	+	0.735708i	$0.263150\pi$
$654$	−1.21324	−0.0474414
$655$	7.17972	0.280535
$656$	−10.5695	−0.412671
$657$	17.7068	0.690808
$658$	5.71630	0.222845
$659$	17.6974	0.689393	0.344697	−	0.938714i	$-0.387982\pi$
$659$	17.6974	0.689393	0.344697	+	0.938714i	$0.387982\pi$
$660$	1.11749	0.0434982
$661$	−44.0630	−1.71385	−0.856927	−	0.515438i	$-0.827629\pi$
$661$	−44.0630	−1.71385	−0.856927	+	0.515438i	$0.827629\pi$
$662$	−15.7450	−0.611946
$663$	11.9580	0.464411
$664$	0.0637516	0.00247404
$665$	−0.524767	−0.0203496
$666$	3.69657	0.143239
$667$	15.8076	0.612072
$668$	−6.28286	−0.243091
$669$	−21.5036	−0.831377
$670$	−2.44209	−0.0943463
$671$	−6.41184	−0.247526
$672$	0.893081	0.0344513
$673$	−9.02211	−0.347777	−0.173888	−	0.984765i	$-0.555633\pi$
$673$	−9.02211	−0.347777	−0.173888	+	0.984765i	$0.555633\pi$
$674$	−33.2569	−1.28101
$675$	22.6512	0.871846
$676$	21.1071	0.811810
$677$	40.4733	1.55551	0.777757	−	0.628565i	$-0.216358\pi$
$677$	40.4733	1.55551	0.777757	+	0.628565i	$0.216358\pi$
$678$	11.0851	0.425720
$679$	4.51949	0.173442
$680$	−0.809797	−0.0310543
$681$	3.19729	0.122520
$682$	−11.2477	−0.430696
$683$	−7.22874	−0.276600	−0.138300	−	0.990390i	$-0.544164\pi$
$683$	−7.22874	−0.276600	−0.138300	+	0.990390i	$0.544164\pi$
$684$	3.27215	0.125114
$685$	−4.97620	−0.190131
$686$	1.00000	0.0381802
$687$	20.1111	0.767288
$688$	−9.01137	−0.343555
$689$	−76.2960	−2.90665
$690$	−1.69669	−0.0645918
$691$	−10.9435	−0.416309	−0.208155	−	0.978096i	$-0.566746\pi$
$691$	−10.9435	−0.416309	−0.208155	+	0.978096i	$0.566746\pi$
$692$	−18.5193	−0.704000
$693$	−7.80224	−0.296383
$694$	−0.398569	−0.0151295
$695$	2.89695	0.109888
$696$	−2.62468	−0.0994881
$697$	24.2327	0.917879
$698$	11.3936	0.431255
$699$	27.1363	1.02639
$700$	−4.87524	−0.184267
$701$	8.16989	0.308572	0.154286	−	0.988026i	$-0.450692\pi$
$701$	8.16989	0.308572	0.154286	+	0.988026i	$0.450692\pi$
$702$	27.1342	1.02411
$703$	2.49366	0.0940502
$704$	3.54260	0.133517
$705$	1.80317	0.0679113
$706$	−25.7126	−0.967706
$707$	19.9981	0.752107
$708$	12.5050	0.469965
$709$	3.59587	0.135046	0.0675228	−	0.997718i	$-0.478490\pi$
$709$	3.59587	0.135046	0.0675228	+	0.997718i	$0.478490\pi$
$710$	−5.13393	−0.192673
$711$	30.1062	1.12907
$712$	4.11184	0.154098
$713$	17.0774	0.639554
$714$	−2.04756	−0.0766280
$715$	−7.30760	−0.273289
$716$	−8.66311	−0.323756
$717$	−14.4417	−0.539333
$718$	−6.73239	−0.251251
$719$	−17.3268	−0.646179	−0.323090	−	0.946368i	$-0.604722\pi$
$719$	−17.3268	−0.646179	−0.323090	+	0.946368i	$0.604722\pi$
$720$	−0.777908	−0.0289909
$721$	17.7753	0.661988
$722$	−16.7926	−0.624957
$723$	3.32470	0.123647
$724$	−1.19297	−0.0443362
$725$	14.3279	0.532123
$726$	1.38428	0.0513755
$727$	20.1102	0.745845	0.372923	−	0.927862i	$-0.378356\pi$
$727$	20.1102	0.745845	0.372923	+	0.927862i	$0.378356\pi$
$728$	−5.84013	−0.216449
$729$	7.03511	0.260560
$730$	−2.83971	−0.105102
$731$	20.6603	0.764149
$732$	−1.61641	−0.0597442
$733$	17.5614	0.648646	0.324323	−	0.945946i	$-0.394864\pi$
$733$	17.5614	0.648646	0.324323	+	0.945946i	$0.394864\pi$
$734$	3.68966	0.136188
$735$	0.315443	0.0116353
$736$	−5.37874	−0.198263
$737$	−24.4937	−0.902235
$738$	23.2784	0.856890
$739$	25.9747	0.955494	0.477747	−	0.878498i	$-0.341454\pi$
$739$	25.9747	0.955494	0.477747	+	0.878498i	$0.341454\pi$
$740$	−0.592832	−0.0217929
$741$	7.74907	0.284669
$742$	13.0641	0.479599
$743$	40.5064	1.48603	0.743017	−	0.669272i	$-0.233394\pi$
$743$	40.5064	1.48603	0.743017	+	0.669272i	$0.233394\pi$
$744$	−2.83552	−0.103955
$745$	2.81470	0.103123
$746$	10.5528	0.386366
$747$	−0.140407	−0.00513722
$748$	−8.12209	−0.296973
$749$	4.76513	0.174114
$750$	−3.11508	−0.113747
$751$	−0.854494	−0.0311809	−0.0155905	−	0.999878i	$-0.504963\pi$
$751$	−0.854494	−0.0311809	−0.0155905	+	0.999878i	$0.504963\pi$
$752$	5.71630	0.208452
$753$	−12.4494	−0.453681
$754$	17.1635	0.625059
$755$	−3.58649	−0.130526
$756$	−4.64617	−0.168980
$757$	−30.9955	−1.12655	−0.563275	−	0.826269i	$-0.690459\pi$
$757$	−30.9955	−1.12655	−0.563275	+	0.826269i	$0.690459\pi$
$758$	2.24981	0.0817168
$759$	−17.0174	−0.617693
$760$	−0.524767	−0.0190353
$761$	−34.9812	−1.26807	−0.634033	−	0.773306i	$-0.718602\pi$
$761$	−34.9812	−1.26807	−0.634033	+	0.773306i	$0.718602\pi$
$762$	7.09934	0.257182
$763$	−1.35849	−0.0491806
$764$	−12.5319	−0.453389
$765$	1.78350	0.0644827
$766$	10.5853	0.382462
$767$	−81.7737	−2.95268
$768$	0.893081	0.0322263
$769$	−26.3501	−0.950208	−0.475104	−	0.879930i	$-0.657589\pi$
$769$	−26.3501	−0.950208	−0.475104	+	0.879930i	$0.657589\pi$
$770$	1.25127	0.0450928
$771$	2.13848	0.0770154
$772$	12.3231	0.443519
$773$	14.5656	0.523887	0.261944	−	0.965083i	$-0.415637\pi$
$773$	14.5656	0.523887	0.261944	+	0.965083i	$0.415637\pi$
$774$	19.8467	0.713375
$775$	15.4788	0.556015
$776$	4.51949	0.162240
$777$	−1.49897	−0.0537751
$778$	14.7788	0.529845
$779$	15.7033	0.562631
$780$	−1.84223	−0.0659624
$781$	−51.4922	−1.84254
$782$	12.3318	0.440984
$783$	13.6546	0.487977
$784$	1.00000	0.0357143
$785$	−2.34277	−0.0836171
$786$	18.1538	0.647525
$787$	−49.9781	−1.78153	−0.890763	−	0.454468i	$-0.849829\pi$
$787$	−49.9781	−1.78153	−0.890763	+	0.454468i	$0.849829\pi$
$788$	0.627958	0.0223701
$789$	−8.78902	−0.312898
$790$	−4.82824	−0.171781
$791$	12.4122	0.441326
$792$	−7.80224	−0.277241
$793$	10.5702	0.375358
$794$	−9.42891	−0.334619
$795$	4.12099	0.146156
$796$	3.72282	0.131952
$797$	10.5750	0.374586	0.187293	−	0.982304i	$-0.440029\pi$
$797$	10.5750	0.374586	0.187293	+	0.982304i	$0.440029\pi$
$798$	−1.32687	−0.0469706
$799$	−13.1057	−0.463647
$800$	−4.87524	−0.172366
$801$	−9.05595	−0.319976
$802$	−6.28737	−0.222015
$803$	−28.4816	−1.00509
$804$	−6.17479	−0.217768
$805$	−1.89981	−0.0669597
$806$	18.5423	0.653125
$807$	−4.60620	−0.162146
$808$	19.9981	0.703532
$809$	−41.0158	−1.44204	−0.721019	−	0.692915i	$-0.756326\pi$
$809$	−41.0158	−1.44204	−0.721019	+	0.692915i	$0.756326\pi$
$810$	0.868119	0.0305026
$811$	52.3867	1.83955	0.919773	−	0.392450i	$-0.128373\pi$
$811$	52.3867	1.83955	0.919773	+	0.392450i	$0.128373\pi$
$812$	−2.93890	−0.103135
$813$	−13.6087	−0.477277
$814$	−5.94598	−0.208406
$815$	−5.66292	−0.198363
$816$	−2.04756	−0.0716789
$817$	13.3883	0.468399
$818$	17.5931	0.615130
$819$	12.8623	0.449446
$820$	−3.73325	−0.130371
$821$	−26.0918	−0.910612	−0.455306	−	0.890335i	$-0.650470\pi$
$821$	−26.0918	−0.910612	−0.455306	+	0.890335i	$0.650470\pi$
$822$	−12.5822	−0.438856
$823$	28.1336	0.980677	0.490339	−	0.871532i	$-0.336873\pi$
$823$	28.1336	0.980677	0.490339	+	0.871532i	$0.336873\pi$
$824$	17.7753	0.619233
$825$	−15.4244	−0.537010
$826$	14.0020	0.487194
$827$	29.2461	1.01698	0.508492	−	0.861066i	$-0.330203\pi$
$827$	29.2461	1.01698	0.508492	+	0.861066i	$0.330203\pi$
$828$	11.8462	0.411683
$829$	−23.5567	−0.818158	−0.409079	−	0.912499i	$-0.634150\pi$
$829$	−23.5567	−0.818158	−0.409079	+	0.912499i	$0.634150\pi$
$830$	0.0225176	0.000781596 0
$831$	15.7694	0.547034
$832$	−5.84013	−0.202470
$833$	−2.29269	−0.0794371
$834$	7.32490	0.253641
$835$	−2.21916	−0.0767970
$836$	−5.26330	−0.182035
$837$	14.7515	0.509887
$838$	−24.0645	−0.831296
$839$	33.8745	1.16948	0.584739	−	0.811221i	$-0.301197\pi$
$839$	33.8745	1.16948	0.584739	+	0.811221i	$0.301197\pi$
$840$	0.315443	0.0108838
$841$	−20.3629	−0.702168
$842$	−28.4912	−0.981870
$843$	−29.9208	−1.03053
$844$	15.8092	0.544177
$845$	7.45518	0.256466
$846$	−12.5896	−0.432840
$847$	1.55001	0.0532589
$848$	13.0641	0.448623
$849$	−3.72888	−0.127975
$850$	11.1774	0.383383
$851$	9.02780	0.309469
$852$	−12.9811	−0.444724
$853$	30.0846	1.03008	0.515038	−	0.857168i	$-0.327778\pi$
$853$	30.0846	1.03008	0.515038	+	0.857168i	$0.327778\pi$
$854$	−1.80992	−0.0619343
$855$	1.15575	0.0395259
$856$	4.76513	0.162869
$857$	25.3671	0.866524	0.433262	−	0.901268i	$-0.357362\pi$
$857$	25.3671	0.866524	0.433262	+	0.901268i	$0.357362\pi$
$858$	−18.4771	−0.630799
$859$	35.2785	1.20369	0.601844	−	0.798614i	$-0.294433\pi$
$859$	35.2785	1.20369	0.601844	+	0.798614i	$0.294433\pi$
$860$	−3.18289	−0.108536
$861$	−9.43945	−0.321696
$862$	−1.00000	−0.0340601
$863$	−48.7502	−1.65947	−0.829737	−	0.558154i	$-0.811510\pi$
$863$	−48.7502	−1.65947	−0.829737	+	0.558154i	$0.811510\pi$
$864$	−4.64617	−0.158066
$865$	−6.54118	−0.222407
$866$	−7.09859	−0.241220
$867$	−10.4879	−0.356189
$868$	−3.17498	−0.107766
$869$	−48.4262	−1.64274
$870$	−0.927056	−0.0314302
$871$	40.3788	1.36818
$872$	−1.35849	−0.0460042
$873$	−9.95376	−0.336884
$874$	7.99129	0.270310
$875$	−3.48802	−0.117916
$876$	−7.18015	−0.242595
$877$	−31.7679	−1.07273	−0.536363	−	0.843987i	$-0.680202\pi$
$877$	−31.7679	−1.07273	−0.536363	+	0.843987i	$0.680202\pi$
$878$	−36.6284	−1.23615
$879$	6.09096	0.205443
$880$	1.25127	0.0421804
$881$	−35.7447	−1.20427	−0.602134	−	0.798395i	$-0.705683\pi$
$881$	−35.7447	−1.20427	−0.602134	+	0.798395i	$0.705683\pi$
$882$	−2.20241	−0.0741589
$883$	17.5233	0.589706	0.294853	−	0.955543i	$-0.404729\pi$
$883$	17.5233	0.589706	0.294853	+	0.955543i	$0.404729\pi$
$884$	13.3896	0.450341
$885$	4.41685	0.148471
$886$	−17.8282	−0.598949
$887$	−44.3743	−1.48994	−0.744971	−	0.667096i	$-0.767537\pi$
$887$	−44.3743	−1.48994	−0.744971	+	0.667096i	$0.767537\pi$
$888$	−1.49897	−0.0503020
$889$	7.94926	0.266610
$890$	1.45234	0.0486824
$891$	8.70705	0.291697
$892$	−24.0780	−0.806191
$893$	−8.49282	−0.284201
$894$	7.11693	0.238026
$895$	−3.05988	−0.102281
$896$	1.00000	0.0334077
$897$	28.0539	0.936693
$898$	41.3730	1.38064
$899$	9.33096	0.311205
$900$	10.7373	0.357909
$901$	−29.9520	−0.997846
$902$	−37.4436	−1.24674
$903$	−8.04788	−0.267817
$904$	12.4122	0.412823
$905$	−0.421365	−0.0140067
$906$	−9.06839	−0.301277
$907$	37.9458	1.25997	0.629985	−	0.776608i	$-0.283061\pi$
$907$	37.9458	1.25997	0.629985	+	0.776608i	$0.283061\pi$
$908$	3.58007	0.118809
$909$	−44.0440	−1.46085
$910$	−2.06278	−0.0683805
$911$	−1.95861	−0.0648916	−0.0324458	−	0.999473i	$-0.510330\pi$
$911$	−1.95861	−0.0648916	−0.0324458	+	0.999473i	$0.510330\pi$
$912$	−1.32687	−0.0439369
$913$	0.225846	0.00747442
$914$	18.3445	0.606782
$915$	−0.570929	−0.0188743
$916$	22.5188	0.744043
$917$	20.3272	0.671262
$918$	10.6522	0.351576
$919$	−5.91428	−0.195094	−0.0975470	−	0.995231i	$-0.531100\pi$
$919$	−5.91428	−0.195094	−0.0975470	+	0.995231i	$0.531100\pi$
$920$	−1.89981	−0.0626350
$921$	7.03087	0.231675
$922$	14.7629	0.486190
$923$	84.8871	2.79409
$924$	3.16383	0.104082
$925$	8.18272	0.269046
$926$	21.4847	0.706030
$927$	−39.1485	−1.28581
$928$	−2.93890	−0.0964741
$929$	−7.93695	−0.260403	−0.130201	−	0.991488i	$-0.541562\pi$
$929$	−7.93695	−0.260403	−0.130201	+	0.991488i	$0.541562\pi$
$930$	−1.00153	−0.0328414
$931$	−1.48572	−0.0486924
$932$	30.3850	0.995294
$933$	4.66972	0.152880
$934$	16.8320	0.550760
$935$	−2.86879	−0.0938194
$936$	12.8623	0.420418
$937$	28.5845	0.933814	0.466907	−	0.884306i	$-0.345368\pi$
$937$	28.5845	0.933814	0.466907	+	0.884306i	$0.345368\pi$
$938$	−6.91403	−0.225751
$939$	−2.03348	−0.0663601
$940$	2.01904	0.0658540
$941$	−55.7304	−1.81676	−0.908379	−	0.418148i	$-0.862679\pi$
$941$	−55.7304	−1.81676	−0.908379	+	0.418148i	$0.862679\pi$
$942$	−5.92366	−0.193003
$943$	56.8508	1.85132
$944$	14.0020	0.455728
$945$	−1.64106	−0.0533838
$946$	−31.9237	−1.03793
$947$	−16.1087	−0.523464	−0.261732	−	0.965141i	$-0.584294\pi$
$947$	−16.1087	−0.523464	−0.261732	+	0.965141i	$0.584294\pi$
$948$	−12.2081	−0.396501
$949$	46.9532	1.52416
$950$	7.24324	0.235002
$951$	14.2780	0.462997
$952$	−2.29269	−0.0743066
$953$	−52.5407	−1.70196	−0.850980	−	0.525198i	$-0.823991\pi$
$953$	−52.5407	−1.70196	−0.850980	+	0.525198i	$0.823991\pi$
$954$	−28.7725	−0.931544
$955$	−4.42638	−0.143234
$956$	−16.1706	−0.522994
$957$	−9.29817	−0.300567
$958$	41.8906	1.35342
$959$	−14.0886	−0.454944
$960$	0.315443	0.0101809
$961$	−20.9195	−0.674822
$962$	9.80219	0.316035
$963$	−10.4948	−0.338189
$964$	3.72273	0.119901
$965$	4.35262	0.140116
$966$	−4.80365	−0.154555
$967$	−29.8007	−0.958324	−0.479162	−	0.877726i	$-0.659059\pi$
$967$	−29.8007	−0.958324	−0.479162	+	0.877726i	$0.659059\pi$
$968$	1.55001	0.0498191
$969$	3.04210	0.0977262
$970$	1.59632	0.0512548
$971$	24.3756	0.782252	0.391126	−	0.920337i	$-0.372086\pi$
$971$	24.3756	0.782252	0.391126	+	0.920337i	$0.372086\pi$
$972$	16.1335	0.517483
$973$	8.20184	0.262939
$974$	−24.4558	−0.783613
$975$	25.4278	0.814342
$976$	−1.80992	−0.0579343
$977$	−8.03669	−0.257117	−0.128558	−	0.991702i	$-0.541035\pi$
$977$	−8.03669	−0.257117	−0.128558	+	0.991702i	$0.541035\pi$
$978$	−14.3186	−0.457858
$979$	14.5666	0.465551
$980$	0.353208	0.0112828
$981$	2.99194	0.0955254
$982$	−38.3170	−1.22274
$983$	−10.3483	−0.330060	−0.165030	−	0.986289i	$-0.552772\pi$
$983$	−10.3483	−0.330060	−0.165030	+	0.986289i	$0.552772\pi$
$984$	−9.43945	−0.300919
$985$	0.221800	0.00706712
$986$	6.73799	0.214581
$987$	5.10512	0.162498
$988$	8.67678	0.276045
$989$	48.4698	1.54125
$990$	−2.75581	−0.0875855
$991$	−25.5648	−0.812094	−0.406047	−	0.913852i	$-0.633093\pi$
$991$	−25.5648	−0.812094	−0.406047	+	0.913852i	$0.633093\pi$
$992$	−3.17498	−0.100806
$993$	−14.0615	−0.446230
$994$	−14.5351	−0.461027
$995$	1.31493	0.0416861
$996$	0.0569353	0.00180406
$997$	47.0352	1.48962	0.744810	−	0.667277i	$-0.232540\pi$
$997$	47.0352	1.48962	0.744810	+	0.667277i	$0.232540\pi$
$998$	−39.3900	−1.24687
$999$	7.79823	0.246725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.16	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.16	✓	21	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.893081 q^{3} +1.00000 q^{4} +0.353208 q^{5} +0.893081 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.20241 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.893081 q^{3} +1.00000 q^{4} +0.353208 q^{5} +0.893081 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.20241 q^{9} +0.353208 q^{10} +3.54260 q^{11} +0.893081 q^{12} -5.84013 q^{13} +1.00000 q^{14} +0.315443 q^{15} +1.00000 q^{16} -2.29269 q^{17} -2.20241 q^{18} -1.48572 q^{19} +0.353208 q^{20} +0.893081 q^{21} +3.54260 q^{22} -5.37874 q^{23} +0.893081 q^{24} -4.87524 q^{25} -5.84013 q^{26} -4.64617 q^{27} +1.00000 q^{28} -2.93890 q^{29} +0.315443 q^{30} -3.17498 q^{31} +1.00000 q^{32} +3.16383 q^{33} -2.29269 q^{34} +0.353208 q^{35} -2.20241 q^{36} -1.67842 q^{37} -1.48572 q^{38} -5.21570 q^{39} +0.353208 q^{40} -10.5695 q^{41} +0.893081 q^{42} -9.01137 q^{43} +3.54260 q^{44} -0.777908 q^{45} -5.37874 q^{46} +5.71630 q^{47} +0.893081 q^{48} +1.00000 q^{49} -4.87524 q^{50} -2.04756 q^{51} -5.84013 q^{52} +13.0641 q^{53} -4.64617 q^{54} +1.25127 q^{55} +1.00000 q^{56} -1.32687 q^{57} -2.93890 q^{58} +14.0020 q^{59} +0.315443 q^{60} -1.80992 q^{61} -3.17498 q^{62} -2.20241 q^{63} +1.00000 q^{64} -2.06278 q^{65} +3.16383 q^{66} -6.91403 q^{67} -2.29269 q^{68} -4.80365 q^{69} +0.353208 q^{70} -14.5351 q^{71} -2.20241 q^{72} -8.03976 q^{73} -1.67842 q^{74} -4.35399 q^{75} -1.48572 q^{76} +3.54260 q^{77} -5.21570 q^{78} -13.6697 q^{79} +0.353208 q^{80} +2.45781 q^{81} -10.5695 q^{82} +0.0637516 q^{83} +0.893081 q^{84} -0.809797 q^{85} -9.01137 q^{86} -2.62468 q^{87} +3.54260 q^{88} +4.11184 q^{89} -0.777908 q^{90} -5.84013 q^{91} -5.37874 q^{92} -2.83552 q^{93} +5.71630 q^{94} -0.524767 q^{95} +0.893081 q^{96} +4.51949 q^{97} +1.00000 q^{98} -7.80224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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