LMFDB - Embedded newform 6035.2.a.h.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27257 q^{2} +0.337599 q^{3} -0.380563 q^{4} +1.00000 q^{5} -0.429619 q^{6} -3.22826 q^{7} +3.02944 q^{8} -2.88603 q^{9} +O(q^{10})$	\(q-1.27257 q^{2} +0.337599 q^{3} -0.380563 q^{4} +1.00000 q^{5} -0.429619 q^{6} -3.22826 q^{7} +3.02944 q^{8} -2.88603 q^{9} -1.27257 q^{10} +5.86941 q^{11} -0.128478 q^{12} +5.87183 q^{13} +4.10820 q^{14} +0.337599 q^{15} -3.09405 q^{16} -1.00000 q^{17} +3.67267 q^{18} -1.15278 q^{19} -0.380563 q^{20} -1.08986 q^{21} -7.46924 q^{22} +5.98677 q^{23} +1.02274 q^{24} +1.00000 q^{25} -7.47233 q^{26} -1.98712 q^{27} +1.22856 q^{28} -5.17557 q^{29} -0.429619 q^{30} -4.45421 q^{31} -2.12148 q^{32} +1.98151 q^{33} +1.27257 q^{34} -3.22826 q^{35} +1.09831 q^{36} +9.18517 q^{37} +1.46700 q^{38} +1.98233 q^{39} +3.02944 q^{40} +0.830550 q^{41} +1.38692 q^{42} +3.80639 q^{43} -2.23368 q^{44} -2.88603 q^{45} -7.61859 q^{46} +1.20804 q^{47} -1.04455 q^{48} +3.42169 q^{49} -1.27257 q^{50} -0.337599 q^{51} -2.23460 q^{52} +10.7170 q^{53} +2.52875 q^{54} +5.86941 q^{55} -9.77982 q^{56} -0.389179 q^{57} +6.58628 q^{58} +10.2801 q^{59} -0.128478 q^{60} +3.99447 q^{61} +5.66830 q^{62} +9.31686 q^{63} +8.88782 q^{64} +5.87183 q^{65} -2.52161 q^{66} -3.74312 q^{67} +0.380563 q^{68} +2.02113 q^{69} +4.10820 q^{70} -1.00000 q^{71} -8.74303 q^{72} -12.5152 q^{73} -11.6888 q^{74} +0.337599 q^{75} +0.438707 q^{76} -18.9480 q^{77} -2.52265 q^{78} -16.5348 q^{79} -3.09405 q^{80} +7.98723 q^{81} -1.05693 q^{82} +5.36542 q^{83} +0.414760 q^{84} -1.00000 q^{85} -4.84391 q^{86} -1.74727 q^{87} +17.7810 q^{88} +16.4034 q^{89} +3.67267 q^{90} -18.9558 q^{91} -2.27834 q^{92} -1.50374 q^{93} -1.53731 q^{94} -1.15278 q^{95} -0.716209 q^{96} -12.0695 q^{97} -4.35435 q^{98} -16.9393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * 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 $

$2$	−1.27257	−0.899844	−0.449922	−	0.893068i	$-0.648548\pi$
$2$	−1.27257	−0.899844	−0.449922	+	0.893068i	$0.648548\pi$
$3$	0.337599	0.194913	0.0974566	−	0.995240i	$-0.468929\pi$
$3$	0.337599	0.194913	0.0974566	+	0.995240i	$0.468929\pi$
$4$	−0.380563	−0.190281
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.429619	−0.175391
$7$	−3.22826	−1.22017	−0.610085	−	0.792336i	$-0.708865\pi$
$7$	−3.22826	−1.22017	−0.610085	+	0.792336i	$0.708865\pi$
$8$	3.02944	1.07107
$9$	−2.88603	−0.962009
$10$	−1.27257	−0.402422
$11$	5.86941	1.76969	0.884846	−	0.465883i	$-0.154263\pi$
$11$	5.86941	1.76969	0.884846	+	0.465883i	$0.154263\pi$
$12$	−0.128478	−0.0370883
$13$	5.87183	1.62855	0.814277	−	0.580477i	$-0.197134\pi$
$13$	5.87183	1.62855	0.814277	+	0.580477i	$0.197134\pi$
$14$	4.10820	1.09796
$15$	0.337599	0.0871678
$16$	−3.09405	−0.773512
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.67267	0.865658
$19$	−1.15278	−0.264467	−0.132233	−	0.991219i	$-0.542215\pi$
$19$	−1.15278	−0.264467	−0.132233	+	0.991219i	$0.542215\pi$
$20$	−0.380563	−0.0850964
$21$	−1.08986	−0.237827
$22$	−7.46924	−1.59245
$23$	5.98677	1.24833	0.624164	−	0.781293i	$-0.285440\pi$
$23$	5.98677	1.24833	0.624164	+	0.781293i	$0.285440\pi$
$24$	1.02274	0.208765
$25$	1.00000	0.200000
$26$	−7.47233	−1.46544
$27$	−1.98712	−0.382421
$28$	1.22856	0.232175
$29$	−5.17557	−0.961078	−0.480539	−	0.876973i	$-0.659559\pi$
$29$	−5.17557	−0.961078	−0.480539	+	0.876973i	$0.659559\pi$
$30$	−0.429619	−0.0784374
$31$	−4.45421	−0.800000	−0.400000	−	0.916515i	$-0.630990\pi$
$31$	−4.45421	−0.800000	−0.400000	+	0.916515i	$0.630990\pi$
$32$	−2.12148	−0.375028
$33$	1.98151	0.344936
$34$	1.27257	0.218244
$35$	−3.22826	−0.545676
$36$	1.09831	0.183052
$37$	9.18517	1.51003	0.755017	−	0.655706i	$-0.227629\pi$
$37$	9.18517	1.51003	0.755017	+	0.655706i	$0.227629\pi$
$38$	1.46700	0.237979
$39$	1.98233	0.317427
$40$	3.02944	0.478996
$41$	0.830550	0.129710	0.0648551	−	0.997895i	$-0.479341\pi$
$41$	0.830550	0.129710	0.0648551	+	0.997895i	$0.479341\pi$
$42$	1.38692	0.214007
$43$	3.80639	0.580470	0.290235	−	0.956955i	$-0.406267\pi$
$43$	3.80639	0.580470	0.290235	+	0.956955i	$0.406267\pi$
$44$	−2.23368	−0.336739
$45$	−2.88603	−0.430223
$46$	−7.61859	−1.12330
$47$	1.20804	0.176210	0.0881052	−	0.996111i	$-0.471919\pi$
$47$	1.20804	0.176210	0.0881052	+	0.996111i	$0.471919\pi$
$48$	−1.04455	−0.150768
$49$	3.42169	0.488813
$50$	−1.27257	−0.179969
$51$	−0.337599	−0.0472734
$52$	−2.23460	−0.309883
$53$	10.7170	1.47209	0.736043	−	0.676935i	$-0.236692\pi$
$53$	10.7170	1.47209	0.736043	+	0.676935i	$0.236692\pi$
$54$	2.52875	0.344119
$55$	5.86941	0.791430
$56$	−9.77982	−1.30688
$57$	−0.389179	−0.0515481
$58$	6.58628	0.864820
$59$	10.2801	1.33836	0.669179	−	0.743101i	$-0.266646\pi$
$59$	10.2801	1.33836	0.669179	+	0.743101i	$0.266646\pi$
$60$	−0.128478	−0.0165864
$61$	3.99447	0.511439	0.255719	−	0.966751i	$-0.417688\pi$
$61$	3.99447	0.511439	0.255719	+	0.966751i	$0.417688\pi$
$62$	5.66830	0.719875
$63$	9.31686	1.17381
$64$	8.88782	1.11098
$65$	5.87183	0.728311
$66$	−2.52161	−0.310389
$67$	−3.74312	−0.457295	−0.228647	−	0.973509i	$-0.573430\pi$
$67$	−3.74312	−0.457295	−0.228647	+	0.973509i	$0.573430\pi$
$68$	0.380563	0.0461500
$69$	2.02113	0.243316
$70$	4.10820	0.491023
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−8.74303	−1.03038
$73$	−12.5152	−1.46479	−0.732394	−	0.680881i	$-0.761597\pi$
$73$	−12.5152	−1.46479	−0.732394	+	0.680881i	$0.761597\pi$
$74$	−11.6888	−1.35879
$75$	0.337599	0.0389826
$76$	0.438707	0.0503231
$77$	−18.9480	−2.15932
$78$	−2.52265	−0.285634
$79$	−16.5348	−1.86031	−0.930155	−	0.367168i	$-0.880327\pi$
$79$	−16.5348	−1.86031	−0.930155	+	0.367168i	$0.880327\pi$
$80$	−3.09405	−0.345925
$81$	7.98723	0.887470
$82$	−1.05693	−0.116719
$83$	5.36542	0.588931	0.294465	−	0.955662i	$-0.404858\pi$
$83$	5.36542	0.588931	0.294465	+	0.955662i	$0.404858\pi$
$84$	0.414760	0.0452541
$85$	−1.00000	−0.108465
$86$	−4.84391	−0.522332
$87$	−1.74727	−0.187327
$88$	17.7810	1.89546
$89$	16.4034	1.73875	0.869376	−	0.494151i	$-0.164521\pi$
$89$	16.4034	1.73875	0.869376	+	0.494151i	$0.164521\pi$
$90$	3.67267	0.387134
$91$	−18.9558	−1.98711
$92$	−2.27834	−0.237534
$93$	−1.50374	−0.155931
$94$	−1.53731	−0.158562
$95$	−1.15278	−0.118273
$96$	−0.716209	−0.0730978
$97$	−12.0695	−1.22547	−0.612734	−	0.790290i	$-0.709930\pi$
$97$	−12.0695	−1.22547	−0.612734	+	0.790290i	$0.709930\pi$
$98$	−4.35435	−0.439855
$99$	−16.9393	−1.70246
$100$	−0.380563	−0.0380563
$101$	3.19386	0.317801	0.158901	−	0.987295i	$-0.449205\pi$
$101$	3.19386	0.317801	0.158901	+	0.987295i	$0.449205\pi$
$102$	0.429619	0.0425387
$103$	−10.8152	−1.06565	−0.532827	−	0.846224i	$-0.678870\pi$
$103$	−10.8152	−1.06565	−0.532827	+	0.846224i	$0.678870\pi$
$104$	17.7883	1.74429
$105$	−1.08986	−0.106359
$106$	−13.6381	−1.32465
$107$	5.76952	0.557761	0.278880	−	0.960326i	$-0.410037\pi$
$107$	5.76952	0.557761	0.278880	+	0.960326i	$0.410037\pi$
$108$	0.756224	0.0727676
$109$	−4.47956	−0.429064	−0.214532	−	0.976717i	$-0.568823\pi$
$109$	−4.47956	−0.429064	−0.214532	+	0.976717i	$0.568823\pi$
$110$	−7.46924	−0.712164
$111$	3.10091	0.294325
$112$	9.98840	0.943815
$113$	−17.8871	−1.68267	−0.841336	−	0.540512i	$-0.818231\pi$
$113$	−17.8871	−1.68267	−0.841336	+	0.540512i	$0.818231\pi$
$114$	0.495258	0.0463852
$115$	5.98677	0.558269
$116$	1.96963	0.182875
$117$	−16.9463	−1.56668
$118$	−13.0822	−1.20431
$119$	3.22826	0.295935
$120$	1.02274	0.0933626
$121$	23.4499	2.13181
$122$	−5.08324	−0.460215
$123$	0.280393	0.0252822
$124$	1.69511	0.152225
$125$	1.00000	0.0894427
$126$	−11.8564	−1.05625
$127$	−4.04593	−0.359018	−0.179509	−	0.983756i	$-0.557451\pi$
$127$	−4.04593	−0.359018	−0.179509	+	0.983756i	$0.557451\pi$
$128$	−7.06743	−0.624679
$129$	1.28504	0.113141
$130$	−7.47233	−0.655366
$131$	−13.9551	−1.21926	−0.609631	−	0.792685i	$-0.708683\pi$
$131$	−13.9551	−1.21926	−0.609631	+	0.792685i	$0.708683\pi$
$132$	−0.754088	−0.0656349
$133$	3.72149	0.322694
$134$	4.76339	0.411494
$135$	−1.98712	−0.171024
$136$	−3.02944	−0.259772
$137$	3.39428	0.289993	0.144997	−	0.989432i	$-0.453683\pi$
$137$	3.39428	0.289993	0.144997	+	0.989432i	$0.453683\pi$
$138$	−2.57203	−0.218946
$139$	−0.911726	−0.0773316	−0.0386658	−	0.999252i	$-0.512311\pi$
$139$	−0.911726	−0.0773316	−0.0386658	+	0.999252i	$0.512311\pi$
$140$	1.22856	0.103832
$141$	0.407833	0.0343457
$142$	1.27257	0.106792
$143$	34.4642	2.88204
$144$	8.92950	0.744125
$145$	−5.17557	−0.429807
$146$	15.9264	1.31808
$147$	1.15516	0.0952761
$148$	−3.49553	−0.287331
$149$	7.69870	0.630702	0.315351	−	0.948975i	$-0.397878\pi$
$149$	7.69870	0.630702	0.315351	+	0.948975i	$0.397878\pi$
$150$	−0.429619	−0.0350783
$151$	−14.1874	−1.15455	−0.577276	−	0.816549i	$-0.695884\pi$
$151$	−14.1874	−1.15455	−0.577276	+	0.816549i	$0.695884\pi$
$152$	−3.49229	−0.283262
$153$	2.88603	0.233321
$154$	24.1127	1.94305
$155$	−4.45421	−0.357771
$156$	−0.754400	−0.0604004
$157$	−3.39395	−0.270867	−0.135433	−	0.990786i	$-0.543243\pi$
$157$	−3.39395	−0.270867	−0.135433	+	0.990786i	$0.543243\pi$
$158$	21.0417	1.67399
$159$	3.61804	0.286929
$160$	−2.12148	−0.167717
$161$	−19.3269	−1.52317
$162$	−10.1643	−0.798584
$163$	14.4047	1.12827	0.564133	−	0.825684i	$-0.309210\pi$
$163$	14.4047	1.12827	0.564133	+	0.825684i	$0.309210\pi$
$164$	−0.316076	−0.0246814
$165$	1.98151	0.154260
$166$	−6.82787	−0.529946
$167$	−5.75602	−0.445414	−0.222707	−	0.974885i	$-0.571489\pi$
$167$	−5.75602	−0.445414	−0.222707	+	0.974885i	$0.571489\pi$
$168$	−3.30166	−0.254729
$169$	21.4784	1.65219
$170$	1.27257	0.0976018
$171$	3.32697	0.254419
$172$	−1.44857	−0.110453
$173$	−17.5794	−1.33654	−0.668270	−	0.743919i	$-0.732965\pi$
$173$	−17.5794	−1.33654	−0.668270	+	0.743919i	$0.732965\pi$
$174$	2.22352	0.168565
$175$	−3.22826	−0.244034
$176$	−18.1602	−1.36888
$177$	3.47056	0.260864
$178$	−20.8744	−1.56460
$179$	6.73734	0.503573	0.251786	−	0.967783i	$-0.418982\pi$
$179$	6.73734	0.503573	0.251786	+	0.967783i	$0.418982\pi$
$180$	1.09831	0.0818635
$181$	7.56702	0.562452	0.281226	−	0.959642i	$-0.409259\pi$
$181$	7.56702	0.562452	0.281226	+	0.959642i	$0.409259\pi$
$182$	24.1226	1.78809
$183$	1.34853	0.0996862
$184$	18.1365	1.33704
$185$	9.18517	0.675307
$186$	1.91362	0.140313
$187$	−5.86941	−0.429213
$188$	−0.459734	−0.0335295
$189$	6.41495	0.466619
$190$	1.46700	0.106427
$191$	16.9482	1.22633	0.613164	−	0.789956i	$-0.289897\pi$
$191$	16.9482	1.22633	0.613164	+	0.789956i	$0.289897\pi$
$192$	3.00052	0.216544
$193$	−22.1445	−1.59400	−0.796998	−	0.603982i	$-0.793580\pi$
$193$	−22.1445	−1.59400	−0.796998	+	0.603982i	$0.793580\pi$
$194$	15.3592	1.10273
$195$	1.98233	0.141957
$196$	−1.30217	−0.0930120
$197$	17.8575	1.27229	0.636146	−	0.771568i	$-0.280527\pi$
$197$	17.8575	1.27229	0.636146	+	0.771568i	$0.280527\pi$
$198$	21.5564	1.53195
$199$	13.3543	0.946658	0.473329	−	0.880886i	$-0.343052\pi$
$199$	13.3543	0.946658	0.473329	+	0.880886i	$0.343052\pi$
$200$	3.02944	0.214213
$201$	−1.26368	−0.0891328
$202$	−4.06442	−0.285971
$203$	16.7081	1.17268
$204$	0.128478	0.00899524
$205$	0.830550	0.0580081
$206$	13.7631	0.958922
$207$	−17.2780	−1.20090
$208$	−18.1677	−1.25971
$209$	−6.76616	−0.468025
$210$	1.38692	0.0957069
$211$	−5.21992	−0.359354	−0.179677	−	0.983726i	$-0.557505\pi$
$211$	−5.21992	−0.359354	−0.179677	+	0.983726i	$0.557505\pi$
$212$	−4.07847	−0.280111
$213$	−0.337599	−0.0231319
$214$	−7.34213	−0.501897
$215$	3.80639	0.259594
$216$	−6.01985	−0.409599
$217$	14.3794	0.976135
$218$	5.70056	0.386090
$219$	−4.22511	−0.285506
$220$	−2.23368	−0.150594
$221$	−5.87183	−0.394982
$222$	−3.94613	−0.264847
$223$	−0.885735	−0.0593132	−0.0296566	−	0.999560i	$-0.509441\pi$
$223$	−0.885735	−0.0593132	−0.0296566	+	0.999560i	$0.509441\pi$
$224$	6.84869	0.457597
$225$	−2.88603	−0.192402
$226$	22.7625	1.51414
$227$	13.7887	0.915187	0.457593	−	0.889162i	$-0.348712\pi$
$227$	13.7887	0.915187	0.457593	+	0.889162i	$0.348712\pi$
$228$	0.148107	0.00980864
$229$	7.08786	0.468379	0.234190	−	0.972191i	$-0.424756\pi$
$229$	7.08786	0.468379	0.234190	+	0.972191i	$0.424756\pi$
$230$	−7.61859	−0.502355
$231$	−6.39683	−0.420881
$232$	−15.6790	−1.02938
$233$	7.66767	0.502326	0.251163	−	0.967945i	$-0.419187\pi$
$233$	7.66767	0.502326	0.251163	+	0.967945i	$0.419187\pi$
$234$	21.5653	1.40977
$235$	1.20804	0.0788036
$236$	−3.91223	−0.254665
$237$	−5.58214	−0.362599
$238$	−4.10820	−0.266295
$239$	17.6920	1.14440	0.572199	−	0.820115i	$-0.306090\pi$
$239$	17.6920	1.14440	0.572199	+	0.820115i	$0.306090\pi$
$240$	−1.04455	−0.0674253
$241$	8.20554	0.528565	0.264283	−	0.964445i	$-0.414865\pi$
$241$	8.20554	0.528565	0.264283	+	0.964445i	$0.414865\pi$
$242$	−29.8417	−1.91830
$243$	8.65784	0.555401
$244$	−1.52014	−0.0973173
$245$	3.42169	0.218604
$246$	−0.356820	−0.0227500
$247$	−6.76896	−0.430699
$248$	−13.4937	−0.856854
$249$	1.81136	0.114790
$250$	−1.27257	−0.0804845
$251$	31.6059	1.99495	0.997474	−	0.0710310i	$-0.0226289\pi$
$251$	31.6059	1.99495	0.997474	+	0.0710310i	$0.0226289\pi$
$252$	−3.54565	−0.223355
$253$	35.1388	2.20916
$254$	5.14873	0.323060
$255$	−0.337599	−0.0211413
$256$	−8.78183	−0.548865
$257$	2.79029	0.174054	0.0870268	−	0.996206i	$-0.472263\pi$
$257$	2.79029	0.174054	0.0870268	+	0.996206i	$0.472263\pi$
$258$	−1.63530	−0.101809
$259$	−29.6522	−1.84250
$260$	−2.23460	−0.138584
$261$	14.9368	0.924566
$262$	17.7589	1.09715
$263$	−10.3937	−0.640904	−0.320452	−	0.947265i	$-0.603835\pi$
$263$	−10.3937	−0.640904	−0.320452	+	0.947265i	$0.603835\pi$
$264$	6.00285	0.369450
$265$	10.7170	0.658337
$266$	−4.73586	−0.290374
$267$	5.53776	0.338906
$268$	1.42449	0.0870147
$269$	−17.6866	−1.07837	−0.539185	−	0.842188i	$-0.681267\pi$
$269$	−17.6866	−1.07837	−0.539185	+	0.842188i	$0.681267\pi$
$270$	2.52875	0.153895
$271$	−4.35618	−0.264619	−0.132310	−	0.991208i	$-0.542239\pi$
$271$	−4.35618	−0.264619	−0.132310	+	0.991208i	$0.542239\pi$
$272$	3.09405	0.187604
$273$	−6.39948	−0.387314
$274$	−4.31947	−0.260948
$275$	5.86941	0.353938
$276$	−0.769167	−0.0462984
$277$	20.1846	1.21278	0.606389	−	0.795168i	$-0.292618\pi$
$277$	20.1846	1.21278	0.606389	+	0.795168i	$0.292618\pi$
$278$	1.16024	0.0695863
$279$	12.8550	0.769607
$280$	−9.77982	−0.584456
$281$	9.95562	0.593902	0.296951	−	0.954893i	$-0.404030\pi$
$281$	9.95562	0.593902	0.296951	+	0.954893i	$0.404030\pi$
$282$	−0.518996	−0.0309058
$283$	7.96809	0.473654	0.236827	−	0.971552i	$-0.423893\pi$
$283$	7.96809	0.473654	0.236827	+	0.971552i	$0.423893\pi$
$284$	0.380563	0.0225822
$285$	−0.389179	−0.0230530
$286$	−43.8581	−2.59339
$287$	−2.68124	−0.158268
$288$	6.12264	0.360780
$289$	1.00000	0.0588235
$290$	6.58628	0.386759
$291$	−4.07464	−0.238860
$292$	4.76280	0.278722
$293$	19.8259	1.15824	0.579120	−	0.815242i	$-0.303396\pi$
$293$	19.8259	1.15824	0.579120	+	0.815242i	$0.303396\pi$
$294$	−1.47003	−0.0857336
$295$	10.2801	0.598532
$296$	27.8259	1.61735
$297$	−11.6632	−0.676768
$298$	−9.79714	−0.567533
$299$	35.1533	2.03297
$300$	−0.128478	−0.00741767
$301$	−12.2880	−0.708271
$302$	18.0544	1.03892
$303$	1.07825	0.0619436
$304$	3.56677	0.204568
$305$	3.99447	0.228722
$306$	−3.67267	−0.209953
$307$	−32.2798	−1.84231	−0.921153	−	0.389201i	$-0.872751\pi$
$307$	−32.2798	−1.84231	−0.921153	+	0.389201i	$0.872751\pi$
$308$	7.21090	0.410879
$309$	−3.65121	−0.207710
$310$	5.66830	0.321938
$311$	30.2566	1.71569	0.857847	−	0.513904i	$-0.171801\pi$
$311$	30.2566	1.71569	0.857847	+	0.513904i	$0.171801\pi$
$312$	6.00534	0.339985
$313$	5.12744	0.289820	0.144910	−	0.989445i	$-0.453711\pi$
$313$	5.12744	0.289820	0.144910	+	0.989445i	$0.453711\pi$
$314$	4.31905	0.243738
$315$	9.31686	0.524945
$316$	6.29252	0.353982
$317$	18.2026	1.02236	0.511179	−	0.859474i	$-0.329209\pi$
$317$	18.2026	1.02236	0.511179	+	0.859474i	$0.329209\pi$
$318$	−4.60421	−0.258191
$319$	−30.3775	−1.70081
$320$	8.88782	0.496844
$321$	1.94779	0.108715
$322$	24.5948	1.37062
$323$	1.15278	0.0641426
$324$	−3.03964	−0.168869
$325$	5.87183	0.325711
$326$	−18.3311	−1.01526
$327$	−1.51230	−0.0836302
$328$	2.51610	0.138928
$329$	−3.89986	−0.215006
$330$	−2.52161	−0.138810
$331$	24.1254	1.32605	0.663025	−	0.748597i	$-0.269272\pi$
$331$	24.1254	1.32605	0.663025	+	0.748597i	$0.269272\pi$
$332$	−2.04188	−0.112063
$333$	−26.5087	−1.45267
$334$	7.32494	0.400803
$335$	−3.74312	−0.204508
$336$	3.37208	0.183962
$337$	−17.9452	−0.977537	−0.488769	−	0.872413i	$-0.662554\pi$
$337$	−17.9452	−0.977537	−0.488769	+	0.872413i	$0.662554\pi$
$338$	−27.3328	−1.48671
$339$	−6.03866	−0.327975
$340$	0.380563	0.0206389
$341$	−26.1436	−1.41575
$342$	−4.23380	−0.228938
$343$	11.5517	0.623734
$344$	11.5312	0.621722
$345$	2.02113	0.108814
$346$	22.3711	1.20268
$347$	32.5771	1.74883	0.874414	−	0.485180i	$-0.161246\pi$
$347$	32.5771	1.74883	0.874414	+	0.485180i	$0.161246\pi$
$348$	0.664945	0.0356448
$349$	13.1267	0.702658	0.351329	−	0.936252i	$-0.385730\pi$
$349$	13.1267	0.702658	0.351329	+	0.936252i	$0.385730\pi$
$350$	4.10820	0.219592
$351$	−11.6680	−0.622794
$352$	−12.4518	−0.663683
$353$	16.3060	0.867881	0.433940	−	0.900942i	$-0.357123\pi$
$353$	16.3060	0.867881	0.433940	+	0.900942i	$0.357123\pi$
$354$	−4.41654	−0.234736
$355$	−1.00000	−0.0530745
$356$	−6.24250	−0.330852
$357$	1.08986	0.0576815
$358$	−8.57375	−0.453137
$359$	−28.1828	−1.48743	−0.743715	−	0.668497i	$-0.766938\pi$
$359$	−28.1828	−1.48743	−0.743715	+	0.668497i	$0.766938\pi$
$360$	−8.74303	−0.460798
$361$	−17.6711	−0.930057
$362$	−9.62957	−0.506119
$363$	7.91668	0.415518
$364$	7.21388	0.378110
$365$	−12.5152	−0.655073
$366$	−1.71610	−0.0897020
$367$	−2.14334	−0.111882	−0.0559408	−	0.998434i	$-0.517816\pi$
$367$	−2.14334	−0.111882	−0.0559408	+	0.998434i	$0.517816\pi$
$368$	−18.5234	−0.965596
$369$	−2.39699	−0.124782
$370$	−11.6888	−0.607671
$371$	−34.5972	−1.79619
$372$	0.572267	0.0296707
$373$	−23.8548	−1.23515	−0.617577	−	0.786511i	$-0.711885\pi$
$373$	−23.8548	−1.23515	−0.617577	+	0.786511i	$0.711885\pi$
$374$	7.46924	0.386225
$375$	0.337599	0.0174336
$376$	3.65967	0.188733
$377$	−30.3901	−1.56517
$378$	−8.16348	−0.419884
$379$	0.237486	0.0121988	0.00609941	−	0.999981i	$-0.498058\pi$
$379$	0.237486	0.0121988	0.00609941	+	0.999981i	$0.498058\pi$
$380$	0.438707	0.0225052
$381$	−1.36590	−0.0699773
$382$	−21.5678	−1.10350
$383$	−17.5382	−0.896162	−0.448081	−	0.893993i	$-0.647892\pi$
$383$	−17.5382	−0.896162	−0.448081	+	0.893993i	$0.647892\pi$
$384$	−2.38596	−0.121758
$385$	−18.9480	−0.965679
$386$	28.1804	1.43435
$387$	−10.9854	−0.558417
$388$	4.59318	0.233184
$389$	17.1988	0.872013	0.436007	−	0.899943i	$-0.356392\pi$
$389$	17.1988	0.872013	0.436007	+	0.899943i	$0.356392\pi$
$390$	−2.52265	−0.127740
$391$	−5.98677	−0.302764
$392$	10.3658	0.523552
$393$	−4.71123	−0.237650
$394$	−22.7249	−1.14486
$395$	−16.5348	−0.831955
$396$	6.44645	0.323946
$397$	14.2319	0.714279	0.357139	−	0.934051i	$-0.383752\pi$
$397$	14.2319	0.714279	0.357139	+	0.934051i	$0.383752\pi$
$398$	−16.9942	−0.851844
$399$	1.25637	0.0628974
$400$	−3.09405	−0.154702
$401$	7.19842	0.359472	0.179736	−	0.983715i	$-0.442476\pi$
$401$	7.19842	0.359472	0.179736	+	0.983715i	$0.442476\pi$
$402$	1.60812	0.0802056
$403$	−26.1544	−1.30284
$404$	−1.21546	−0.0604716
$405$	7.98723	0.396889
$406$	−21.2622	−1.05523
$407$	53.9115	2.67229
$408$	−1.02274	−0.0506330
$409$	−7.04846	−0.348524	−0.174262	−	0.984699i	$-0.555754\pi$
$409$	−7.04846	−0.348524	−0.174262	+	0.984699i	$0.555754\pi$
$410$	−1.05693	−0.0521983
$411$	1.14591	0.0565235
$412$	4.11587	0.202774
$413$	−33.1870	−1.63302
$414$	21.9875	1.08062
$415$	5.36542	0.263378
$416$	−12.4570	−0.610753
$417$	−0.307798	−0.0150729
$418$	8.61042	0.421149
$419$	−31.3895	−1.53348	−0.766740	−	0.641958i	$-0.778122\pi$
$419$	−31.3895	−1.53348	−0.766740	+	0.641958i	$0.778122\pi$
$420$	0.414760	0.0202382
$421$	12.2569	0.597367	0.298683	−	0.954352i	$-0.403453\pi$
$421$	12.2569	0.597367	0.298683	+	0.954352i	$0.403453\pi$
$422$	6.64272	0.323363
$423$	−3.48643	−0.169516
$424$	32.4663	1.57670
$425$	−1.00000	−0.0485071
$426$	0.429619	0.0208151
$427$	−12.8952	−0.624042
$428$	−2.19566	−0.106131
$429$	11.6351	0.561747
$430$	−4.84391	−0.233594
$431$	11.4468	0.551374	0.275687	−	0.961247i	$-0.411095\pi$
$431$	11.4468	0.551374	0.275687	+	0.961247i	$0.411095\pi$
$432$	6.14824	0.295807
$433$	21.5457	1.03542	0.517711	−	0.855556i	$-0.326784\pi$
$433$	21.5457	1.03542	0.517711	+	0.855556i	$0.326784\pi$
$434$	−18.2988	−0.878369
$435$	−1.74727	−0.0837751
$436$	1.70475	0.0816429
$437$	−6.90146	−0.330141
$438$	5.37675	0.256911
$439$	11.1990	0.534498	0.267249	−	0.963628i	$-0.413885\pi$
$439$	11.1990	0.534498	0.267249	+	0.963628i	$0.413885\pi$
$440$	17.7810	0.847675
$441$	−9.87510	−0.470243
$442$	7.47233	0.355422
$443$	23.4136	1.11241	0.556206	−	0.831044i	$-0.312257\pi$
$443$	23.4136	1.11241	0.556206	+	0.831044i	$0.312257\pi$
$444$	−1.18009	−0.0560046
$445$	16.4034	0.777593
$446$	1.12716	0.0533726
$447$	2.59908	0.122932
$448$	−28.6922	−1.35558
$449$	−13.1544	−0.620794	−0.310397	−	0.950607i	$-0.600462\pi$
$449$	−13.1544	−0.620794	−0.310397	+	0.950607i	$0.600462\pi$
$450$	3.67267	0.173132
$451$	4.87484	0.229547
$452$	6.80715	0.320181
$453$	−4.78965	−0.225037
$454$	−17.5471	−0.823525
$455$	−18.9558	−0.888663
$456$	−1.17899	−0.0552114
$457$	11.3029	0.528728	0.264364	−	0.964423i	$-0.414838\pi$
$457$	11.3029	0.528728	0.264364	+	0.964423i	$0.414838\pi$
$458$	−9.01981	−0.421468
$459$	1.98712	0.0927508
$460$	−2.27834	−0.106228
$461$	35.2666	1.64253	0.821264	−	0.570549i	$-0.193270\pi$
$461$	35.2666	1.64253	0.821264	+	0.570549i	$0.193270\pi$
$462$	8.14042	0.378727
$463$	−10.4005	−0.483353	−0.241677	−	0.970357i	$-0.577697\pi$
$463$	−10.4005	−0.483353	−0.241677	+	0.970357i	$0.577697\pi$
$464$	16.0134	0.743405
$465$	−1.50374	−0.0697342
$466$	−9.75766	−0.452015
$467$	21.7086	1.00455	0.502276	−	0.864707i	$-0.332496\pi$
$467$	21.7086	1.00455	0.502276	+	0.864707i	$0.332496\pi$
$468$	6.44912	0.298111
$469$	12.0838	0.557977
$470$	−1.53731	−0.0709110
$471$	−1.14580	−0.0527955
$472$	31.1430	1.43347
$473$	22.3413	1.02725
$474$	7.10366	0.326282
$475$	−1.15278	−0.0528934
$476$	−1.22856	−0.0563108
$477$	−30.9294	−1.41616
$478$	−22.5143	−1.02978
$479$	22.7469	1.03933	0.519666	−	0.854370i	$-0.326056\pi$
$479$	22.7469	1.03933	0.519666	+	0.854370i	$0.326056\pi$
$480$	−0.716209	−0.0326903
$481$	53.9338	2.45917
$482$	−10.4421	−0.475626
$483$	−6.52474	−0.296886
$484$	−8.92417	−0.405644
$485$	−12.0695	−0.548046
$486$	−11.0177	−0.499774
$487$	10.9760	0.497369	0.248684	−	0.968585i	$-0.420002\pi$
$487$	10.9760	0.497369	0.248684	+	0.968585i	$0.420002\pi$
$488$	12.1010	0.547785
$489$	4.86303	0.219914
$490$	−4.35435	−0.196709
$491$	−2.80460	−0.126570	−0.0632849	−	0.997996i	$-0.520158\pi$
$491$	−2.80460	−0.126570	−0.0632849	+	0.997996i	$0.520158\pi$
$492$	−0.106707	−0.00481073
$493$	5.17557	0.233096
$494$	8.61398	0.387561
$495$	−16.9393	−0.761363
$496$	13.7815	0.618809
$497$	3.22826	0.144807
$498$	−2.30509	−0.103293
$499$	−9.89967	−0.443170	−0.221585	−	0.975141i	$-0.571123\pi$
$499$	−9.89967	−0.443170	−0.221585	+	0.975141i	$0.571123\pi$
$500$	−0.380563	−0.0170193
$501$	−1.94323	−0.0868170
$502$	−40.2208	−1.79514
$503$	−26.2041	−1.16838	−0.584192	−	0.811615i	$-0.698589\pi$
$503$	−26.2041	−1.16838	−0.584192	+	0.811615i	$0.698589\pi$
$504$	28.2248	1.25723
$505$	3.19386	0.142125
$506$	−44.7166	−1.98790
$507$	7.25111	0.322033
$508$	1.53973	0.0683144
$509$	−9.96280	−0.441593	−0.220797	−	0.975320i	$-0.570866\pi$
$509$	−9.96280	−0.441593	−0.220797	+	0.975320i	$0.570866\pi$
$510$	0.429619	0.0190239
$511$	40.4022	1.78729
$512$	25.3104	1.11857
$513$	2.29072	0.101138
$514$	−3.55084	−0.156621
$515$	−10.8152	−0.476575
$516$	−0.489037	−0.0215287
$517$	7.09046	0.311838
$518$	37.7345	1.65796
$519$	−5.93481	−0.260509
$520$	17.7883	0.780070
$521$	21.8350	0.956608	0.478304	−	0.878194i	$-0.341252\pi$
$521$	21.8350	0.956608	0.478304	+	0.878194i	$0.341252\pi$
$522$	−19.0082	−0.831965
$523$	6.74454	0.294918	0.147459	−	0.989068i	$-0.452891\pi$
$523$	6.74454	0.294918	0.147459	+	0.989068i	$0.452891\pi$
$524$	5.31079	0.232003
$525$	−1.08986	−0.0475654
$526$	13.2267	0.576713
$527$	4.45421	0.194029
$528$	−6.13088	−0.266812
$529$	12.8414	0.558323
$530$	−13.6381	−0.592400
$531$	−29.6687	−1.28751
$532$	−1.41626	−0.0614027
$533$	4.87685	0.211240
$534$	−7.04720	−0.304962
$535$	5.76952	0.249438
$536$	−11.3395	−0.489794
$537$	2.27452	0.0981529
$538$	22.5074	0.970364
$539$	20.0833	0.865049
$540$	0.756224	0.0325427
$541$	−18.2284	−0.783700	−0.391850	−	0.920029i	$-0.628165\pi$
$541$	−18.2284	−0.783700	−0.391850	+	0.920029i	$0.628165\pi$
$542$	5.54355	0.238116
$543$	2.55462	0.109629
$544$	2.12148	0.0909576
$545$	−4.47956	−0.191883
$546$	8.14379	0.348522
$547$	27.0661	1.15726	0.578631	−	0.815589i	$-0.303587\pi$
$547$	27.0661	1.15726	0.578631	+	0.815589i	$0.303587\pi$
$548$	−1.29174	−0.0551803
$549$	−11.5281	−0.492009
$550$	−7.46924	−0.318489
$551$	5.96631	0.254173
$552$	6.12289	0.260607
$553$	53.3787	2.26989
$554$	−25.6864	−1.09131
$555$	3.10091	0.131626
$556$	0.346969	0.0147148
$557$	23.8903	1.01226	0.506132	−	0.862456i	$-0.331075\pi$
$557$	23.8903	1.01226	0.506132	+	0.862456i	$0.331075\pi$
$558$	−16.3589	−0.692526
$559$	22.3505	0.945326
$560$	9.98840	0.422087
$561$	−1.98151	−0.0836593
$562$	−12.6692	−0.534419
$563$	−1.17816	−0.0496536	−0.0248268	−	0.999692i	$-0.507903\pi$
$563$	−1.17816	−0.0496536	−0.0248268	+	0.999692i	$0.507903\pi$
$564$	−0.155206	−0.00653535
$565$	−17.8871	−0.752514
$566$	−10.1400	−0.426214
$567$	−25.7849	−1.08286
$568$	−3.02944	−0.127112
$569$	10.7108	0.449021	0.224511	−	0.974472i	$-0.427922\pi$
$569$	10.7108	0.449021	0.224511	+	0.974472i	$0.427922\pi$
$570$	0.495258	0.0207441
$571$	32.0002	1.33917	0.669584	−	0.742737i	$-0.266473\pi$
$571$	32.0002	1.33917	0.669584	+	0.742737i	$0.266473\pi$
$572$	−13.1158	−0.548398
$573$	5.72170	0.239027
$574$	3.41206	0.142417
$575$	5.98677	0.249666
$576$	−25.6505	−1.06877
$577$	−7.78397	−0.324051	−0.162025	−	0.986787i	$-0.551803\pi$
$577$	−7.78397	−0.324051	−0.162025	+	0.986787i	$0.551803\pi$
$578$	−1.27257	−0.0529320
$579$	−7.47597	−0.310691
$580$	1.96963	0.0817843
$581$	−17.3210	−0.718596
$582$	5.18527	0.214936
$583$	62.9021	2.60514
$584$	−37.9138	−1.56889
$585$	−16.9463	−0.700642
$586$	−25.2298	−1.04223
$587$	−17.1422	−0.707536	−0.353768	−	0.935333i	$-0.615100\pi$
$587$	−17.1422	−0.707536	−0.353768	+	0.935333i	$0.615100\pi$
$588$	−0.439611	−0.0181293
$589$	5.13475	0.211573
$590$	−13.0822	−0.538585
$591$	6.02868	0.247987
$592$	−28.4194	−1.16803
$593$	12.7502	0.523588	0.261794	−	0.965124i	$-0.415686\pi$
$593$	12.7502	0.523588	0.261794	+	0.965124i	$0.415686\pi$
$594$	14.8423	0.608985
$595$	3.22826	0.132346
$596$	−2.92984	−0.120011
$597$	4.50839	0.184516
$598$	−44.7351	−1.82935
$599$	−30.0767	−1.22890	−0.614449	−	0.788956i	$-0.710622\pi$
$599$	−30.0767	−1.22890	−0.614449	+	0.788956i	$0.710622\pi$
$600$	1.02274	0.0417530
$601$	41.1510	1.67858	0.839291	−	0.543682i	$-0.182970\pi$
$601$	41.1510	1.67858	0.839291	+	0.543682i	$0.182970\pi$
$602$	15.6374	0.637334
$603$	10.8027	0.439922
$604$	5.39919	0.219690
$605$	23.4499	0.953375
$606$	−1.37214	−0.0557396
$607$	−14.8488	−0.602694	−0.301347	−	0.953515i	$-0.597436\pi$
$607$	−14.8488	−0.602694	−0.301347	+	0.953515i	$0.597436\pi$
$608$	2.44560	0.0991824
$609$	5.64064	0.228570
$610$	−5.08324	−0.205814
$611$	7.09339	0.286968
$612$	−1.09831	−0.0443967
$613$	−39.2117	−1.58375	−0.791874	−	0.610685i	$-0.790894\pi$
$613$	−39.2117	−1.58375	−0.791874	+	0.610685i	$0.790894\pi$
$614$	41.0784	1.65779
$615$	0.280393	0.0113065
$616$	−57.4017	−2.31278
$617$	−35.4969	−1.42905	−0.714525	−	0.699610i	$-0.753357\pi$
$617$	−35.4969	−1.42905	−0.714525	+	0.699610i	$0.753357\pi$
$618$	4.64642	0.186907
$619$	10.8519	0.436173	0.218087	−	0.975929i	$-0.430018\pi$
$619$	10.8519	0.436173	0.218087	+	0.975929i	$0.430018\pi$
$620$	1.69511	0.0680771
$621$	−11.8964	−0.477387
$622$	−38.5037	−1.54386
$623$	−52.9544	−2.12157
$624$	−6.13342	−0.245533
$625$	1.00000	0.0400000
$626$	−6.52503	−0.260793
$627$	−2.28425	−0.0912242
$628$	1.29161	0.0515409
$629$	−9.18517	−0.366237
$630$	−11.8564	−0.472369
$631$	6.96650	0.277332	0.138666	−	0.990339i	$-0.455719\pi$
$631$	6.96650	0.277332	0.138666	+	0.990339i	$0.455719\pi$
$632$	−50.0911	−1.99252
$633$	−1.76224	−0.0700428
$634$	−23.1641	−0.919962
$635$	−4.04593	−0.160558
$636$	−1.37689	−0.0545972
$637$	20.0916	0.796059
$638$	38.6575	1.53047
$639$	2.88603	0.114169
$640$	−7.06743	−0.279365
$641$	−35.2341	−1.39166	−0.695831	−	0.718206i	$-0.744964\pi$
$641$	−35.2341	−1.39166	−0.695831	+	0.718206i	$0.744964\pi$
$642$	−2.47870	−0.0978264
$643$	−5.44519	−0.214737	−0.107369	−	0.994219i	$-0.534243\pi$
$643$	−5.44519	−0.214737	−0.107369	+	0.994219i	$0.534243\pi$
$644$	7.35509	0.289831
$645$	1.28504	0.0505983
$646$	−1.46700	−0.0577183
$647$	−48.6119	−1.91113	−0.955566	−	0.294778i	$-0.904754\pi$
$647$	−48.6119	−1.91113	−0.955566	+	0.294778i	$0.904754\pi$
$648$	24.1968	0.950540
$649$	60.3382	2.36848
$650$	−7.47233	−0.293089
$651$	4.85447	0.190262
$652$	−5.48191	−0.214688
$653$	3.91385	0.153161	0.0765803	−	0.997063i	$-0.475600\pi$
$653$	3.91385	0.153161	0.0765803	+	0.997063i	$0.475600\pi$
$654$	1.92451	0.0752541
$655$	−13.9551	−0.545271
$656$	−2.56976	−0.100332
$657$	36.1191	1.40914
$658$	4.96285	0.193472
$659$	−9.49337	−0.369809	−0.184905	−	0.982756i	$-0.559198\pi$
$659$	−9.49337	−0.369809	−0.184905	+	0.982756i	$0.559198\pi$
$660$	−0.754088	−0.0293528
$661$	20.9295	0.814064	0.407032	−	0.913414i	$-0.366564\pi$
$661$	20.9295	0.814064	0.407032	+	0.913414i	$0.366564\pi$
$662$	−30.7012	−1.19324
$663$	−1.98233	−0.0769872
$664$	16.2542	0.630785
$665$	3.72149	0.144313
$666$	33.7341	1.30717
$667$	−30.9849	−1.19974
$668$	2.19052	0.0847539
$669$	−0.299024	−0.0115609
$670$	4.76339	0.184026
$671$	23.4451	0.905090
$672$	2.31211	0.0891917
$673$	30.6986	1.18334	0.591672	−	0.806179i	$-0.298468\pi$
$673$	30.6986	1.18334	0.591672	+	0.806179i	$0.298468\pi$
$674$	22.8365	0.879631
$675$	−1.98712	−0.0764843
$676$	−8.17389	−0.314381
$677$	−3.29935	−0.126804	−0.0634022	−	0.997988i	$-0.520195\pi$
$677$	−3.29935	−0.126804	−0.0634022	+	0.997988i	$0.520195\pi$
$678$	7.68462	0.295126
$679$	38.9634	1.49528
$680$	−3.02944	−0.116174
$681$	4.65505	0.178382
$682$	33.2696	1.27396
$683$	−2.75054	−0.105246	−0.0526232	−	0.998614i	$-0.516758\pi$
$683$	−2.75054	−0.105246	−0.0526232	+	0.998614i	$0.516758\pi$
$684$	−1.26612	−0.0484113
$685$	3.39428	0.129689
$686$	−14.7004	−0.561264
$687$	2.39286	0.0912932
$688$	−11.7772	−0.449000
$689$	62.9282	2.39737
$690$	−2.57203	−0.0979156
$691$	47.7193	1.81533	0.907664	−	0.419697i	$-0.137864\pi$
$691$	47.7193	1.81533	0.907664	+	0.419697i	$0.137864\pi$
$692$	6.69008	0.254319
$693$	54.6844	2.07729
$694$	−41.4566	−1.57367
$695$	−0.911726	−0.0345837
$696$	−5.29324	−0.200640
$697$	−0.830550	−0.0314593
$698$	−16.7047	−0.632282
$699$	2.58860	0.0979099
$700$	1.22856	0.0464351
$701$	8.50339	0.321169	0.160584	−	0.987022i	$-0.448662\pi$
$701$	8.50339	0.321169	0.160584	+	0.987022i	$0.448662\pi$
$702$	14.8484	0.560417
$703$	−10.5885	−0.399354
$704$	52.1662	1.96609
$705$	0.407833	0.0153599
$706$	−20.7505	−0.780957
$707$	−10.3106	−0.387771
$708$	−1.32077	−0.0496375
$709$	−28.2298	−1.06019	−0.530096	−	0.847938i	$-0.677844\pi$
$709$	−28.2298	−1.06019	−0.530096	+	0.847938i	$0.677844\pi$
$710$	1.27257	0.0477587
$711$	47.7198	1.78963
$712$	49.6929	1.86232
$713$	−26.6663	−0.998663
$714$	−1.38692	−0.0519044
$715$	34.4642	1.28889
$716$	−2.56398	−0.0958205
$717$	5.97280	0.223058
$718$	35.8646	1.33845
$719$	29.0258	1.08248	0.541240	−	0.840868i	$-0.317955\pi$
$719$	29.0258	1.08248	0.541240	+	0.840868i	$0.317955\pi$
$720$	8.92950	0.332783
$721$	34.9144	1.30028
$722$	22.4877	0.836906
$723$	2.77019	0.103024
$724$	−2.87972	−0.107024
$725$	−5.17557	−0.192216
$726$	−10.0745	−0.373901
$727$	40.1887	1.49052	0.745258	−	0.666776i	$-0.232326\pi$
$727$	40.1887	1.49052	0.745258	+	0.666776i	$0.232326\pi$
$728$	−57.4255	−2.12833
$729$	−21.0388	−0.779215
$730$	15.9264	0.589463
$731$	−3.80639	−0.140785
$732$	−0.513200	−0.0189684
$733$	24.2480	0.895621	0.447810	−	0.894129i	$-0.352204\pi$
$733$	24.2480	0.895621	0.447810	+	0.894129i	$0.352204\pi$
$734$	2.72756	0.100676
$735$	1.15516	0.0426088
$736$	−12.7008	−0.468158
$737$	−21.9699	−0.809271
$738$	3.05034	0.112285
$739$	−16.7701	−0.616898	−0.308449	−	0.951241i	$-0.599810\pi$
$739$	−16.7701	−0.616898	−0.308449	+	0.951241i	$0.599810\pi$
$740$	−3.49553	−0.128498
$741$	−2.28520	−0.0839488
$742$	44.0273	1.61629
$743$	24.8609	0.912057	0.456028	−	0.889965i	$-0.349272\pi$
$743$	24.8609	0.912057	0.456028	+	0.889965i	$0.349272\pi$
$744$	−4.55548	−0.167012
$745$	7.69870	0.282059
$746$	30.3569	1.11144
$747$	−15.4847	−0.566557
$748$	2.23368	0.0816713
$749$	−18.6255	−0.680562
$750$	−0.429619	−0.0156875
$751$	31.6001	1.15310	0.576552	−	0.817060i	$-0.304398\pi$
$751$	31.6001	1.15310	0.576552	+	0.817060i	$0.304398\pi$
$752$	−3.73772	−0.136301
$753$	10.6701	0.388842
$754$	38.6735	1.40841
$755$	−14.1874	−0.516332
$756$	−2.44129	−0.0887888
$757$	51.0067	1.85387	0.926935	−	0.375223i	$-0.122434\pi$
$757$	51.0067	1.85387	0.926935	+	0.375223i	$0.122434\pi$
$758$	−0.302217	−0.0109770
$759$	11.8628	0.430594
$760$	−3.49229	−0.126679
$761$	36.4452	1.32114	0.660569	−	0.750765i	$-0.270315\pi$
$761$	36.4452	1.32114	0.660569	+	0.750765i	$0.270315\pi$
$762$	1.73821	0.0629687
$763$	14.4612	0.523531
$764$	−6.44985	−0.233347
$765$	2.88603	0.104345
$766$	22.3187	0.806406
$767$	60.3632	2.17959
$768$	−2.96474	−0.106981
$769$	24.1240	0.869933	0.434967	−	0.900447i	$-0.356760\pi$
$769$	24.1240	0.869933	0.434967	+	0.900447i	$0.356760\pi$
$770$	24.1127	0.868960
$771$	0.942001	0.0339253
$772$	8.42737	0.303308
$773$	−15.2051	−0.546890	−0.273445	−	0.961888i	$-0.588163\pi$
$773$	−15.2051	−0.546890	−0.273445	+	0.961888i	$0.588163\pi$
$774$	13.9796	0.502488
$775$	−4.45421	−0.160000
$776$	−36.5636	−1.31256
$777$	−10.0106	−0.359127
$778$	−21.8867	−0.784676
$779$	−0.957445	−0.0343040
$780$	−0.754400	−0.0270119
$781$	−5.86941	−0.210024
$782$	7.61859	0.272440
$783$	10.2845	0.367537
$784$	−10.5869	−0.378103
$785$	−3.39395	−0.121135
$786$	5.99538	0.213848
$787$	−43.2331	−1.54109	−0.770547	−	0.637383i	$-0.780017\pi$
$787$	−43.2331	−1.54109	−0.770547	+	0.637383i	$0.780017\pi$
$788$	−6.79589	−0.242094
$789$	−3.50891	−0.124921
$790$	21.0417	0.748630
$791$	57.7441	2.05315
$792$	−51.3164	−1.82345
$793$	23.4548	0.832906
$794$	−18.1111	−0.642739
$795$	3.61804	0.128319
$796$	−5.08213	−0.180131
$797$	−11.0646	−0.391928	−0.195964	−	0.980611i	$-0.562784\pi$
$797$	−11.0646	−0.391928	−0.195964	+	0.980611i	$0.562784\pi$
$798$	−1.59883	−0.0565978
$799$	−1.20804	−0.0427373
$800$	−2.12148	−0.0750055
$801$	−47.3405	−1.67269
$802$	−9.16050	−0.323468
$803$	−73.4565	−2.59222
$804$	0.480908	0.0169603
$805$	−19.3269	−0.681183
$806$	33.2833	1.17236
$807$	−5.97098	−0.210188
$808$	9.67560	0.340386
$809$	14.9362	0.525131	0.262565	−	0.964914i	$-0.415431\pi$
$809$	14.9362	0.525131	0.262565	+	0.964914i	$0.415431\pi$
$810$	−10.1643	−0.357138
$811$	−12.6566	−0.444433	−0.222216	−	0.974997i	$-0.571329\pi$
$811$	−12.6566	−0.444433	−0.222216	+	0.974997i	$0.571329\pi$
$812$	−6.35848	−0.223139
$813$	−1.47064	−0.0515777
$814$	−68.6062	−2.40465
$815$	14.4047	0.504576
$816$	1.04455	0.0365665
$817$	−4.38795	−0.153515
$818$	8.96967	0.313617
$819$	54.7070	1.91162
$820$	−0.316076	−0.0110379
$821$	−6.96528	−0.243090	−0.121545	−	0.992586i	$-0.538785\pi$
$821$	−6.96528	−0.243090	−0.121545	+	0.992586i	$0.538785\pi$
$822$	−1.45825	−0.0508623
$823$	−55.3958	−1.93098	−0.965488	−	0.260449i	$-0.916130\pi$
$823$	−55.3958	−1.93098	−0.965488	+	0.260449i	$0.916130\pi$
$824$	−32.7640	−1.14139
$825$	1.98151	0.0689873
$826$	42.2328	1.46947
$827$	−44.2933	−1.54023	−0.770115	−	0.637905i	$-0.779801\pi$
$827$	−44.2933	−1.54023	−0.770115	+	0.637905i	$0.779801\pi$
$828$	6.57536	0.228509
$829$	−54.2801	−1.88522	−0.942612	−	0.333889i	$-0.891639\pi$
$829$	−54.2801	−1.88522	−0.942612	+	0.333889i	$0.891639\pi$
$830$	−6.82787	−0.236999
$831$	6.81432	0.236386
$832$	52.1878	1.80929
$833$	−3.42169	−0.118555
$834$	0.391695	0.0135633
$835$	−5.75602	−0.199195
$836$	2.57495	0.0890564
$837$	8.85105	0.305937
$838$	39.9454	1.37989
$839$	15.9942	0.552181	0.276091	−	0.961132i	$-0.410961\pi$
$839$	15.9942	0.552181	0.276091	+	0.961132i	$0.410961\pi$
$840$	−3.30166	−0.113918
$841$	−2.21352	−0.0763282
$842$	−15.5978	−0.537537
$843$	3.36101	0.115759
$844$	1.98651	0.0683784
$845$	21.4784	0.738881
$846$	4.43673	0.152538
$847$	−75.7026	−2.60117
$848$	−33.1587	−1.13868
$849$	2.69002	0.0923214
$850$	1.27257	0.0436488
$851$	54.9895	1.88502
$852$	0.128478	0.00440158
$853$	−14.9503	−0.511888	−0.255944	−	0.966692i	$-0.582386\pi$
$853$	−14.9503	−0.511888	−0.255944	+	0.966692i	$0.582386\pi$
$854$	16.4100	0.561540
$855$	3.32697	0.113780
$856$	17.4784	0.597399
$857$	−11.1088	−0.379470	−0.189735	−	0.981835i	$-0.560763\pi$
$857$	−11.1088	−0.379470	−0.189735	+	0.981835i	$0.560763\pi$
$858$	−14.8065	−0.505485
$859$	39.6451	1.35267	0.676337	−	0.736592i	$-0.263566\pi$
$859$	39.6451	1.35267	0.676337	+	0.736592i	$0.263566\pi$
$860$	−1.44857	−0.0493959
$861$	−0.905184	−0.0308486
$862$	−14.5669	−0.496150
$863$	8.52322	0.290134	0.145067	−	0.989422i	$-0.453660\pi$
$863$	8.52322	0.290134	0.145067	+	0.989422i	$0.453660\pi$
$864$	4.21563	0.143419
$865$	−17.5794	−0.597719
$866$	−27.4185	−0.931717
$867$	0.337599	0.0114655
$868$	−5.47225	−0.185740
$869$	−97.0494	−3.29217
$870$	2.22352	0.0753845
$871$	−21.9790	−0.744729
$872$	−13.5705	−0.459556
$873$	34.8328	1.17891
$874$	8.78259	0.297076
$875$	−3.22826	−0.109135
$876$	1.60792	0.0543265
$877$	7.66079	0.258686	0.129343	−	0.991600i	$-0.458713\pi$
$877$	7.66079	0.258686	0.129343	+	0.991600i	$0.458713\pi$
$878$	−14.2515	−0.480964
$879$	6.69320	0.225756
$880$	−18.1602	−0.612181
$881$	−14.3327	−0.482880	−0.241440	−	0.970416i	$-0.577620\pi$
$881$	−14.3327	−0.482880	−0.241440	+	0.970416i	$0.577620\pi$
$882$	12.5668	0.423145
$883$	−10.4269	−0.350893	−0.175446	−	0.984489i	$-0.556137\pi$
$883$	−10.4269	−0.350893	−0.175446	+	0.984489i	$0.556137\pi$
$884$	2.23460	0.0751578
$885$	3.47056	0.116662
$886$	−29.7954	−1.00100
$887$	−5.95401	−0.199916	−0.0999580	−	0.994992i	$-0.531871\pi$
$887$	−5.95401	−0.199916	−0.0999580	+	0.994992i	$0.531871\pi$
$888$	9.39400	0.315242
$889$	13.0613	0.438063
$890$	−20.8744	−0.699713
$891$	46.8803	1.57055
$892$	0.337078	0.0112862
$893$	−1.39261	−0.0466018
$894$	−3.30751	−0.110620
$895$	6.73734	0.225205
$896$	22.8155	0.762214
$897$	11.8677	0.396253
$898$	16.7399	0.558617
$899$	23.0531	0.768863
$900$	1.09831	0.0366105
$901$	−10.7170	−0.357033
$902$	−6.20358	−0.206556
$903$	−4.14844	−0.138051
$904$	−54.1877	−1.80226
$905$	7.56702	0.251536
$906$	6.09517	0.202499
$907$	−3.87371	−0.128624	−0.0643122	−	0.997930i	$-0.520485\pi$
$907$	−3.87371	−0.128624	−0.0643122	+	0.997930i	$0.520485\pi$
$908$	−5.24746	−0.174143
$909$	−9.21757	−0.305728
$910$	24.1226	0.799658
$911$	−39.2971	−1.30197	−0.650985	−	0.759091i	$-0.725644\pi$
$911$	−39.2971	−1.30197	−0.650985	+	0.759091i	$0.725644\pi$
$912$	1.20414	0.0398730
$913$	31.4918	1.04223
$914$	−14.3838	−0.475773
$915$	1.34853	0.0445810
$916$	−2.69738	−0.0891238
$917$	45.0508	1.48771
$918$	−2.52875	−0.0834612
$919$	7.26096	0.239517	0.119759	−	0.992803i	$-0.461788\pi$
$919$	7.26096	0.239517	0.119759	+	0.992803i	$0.461788\pi$
$920$	18.1365	0.597944
$921$	−10.8976	−0.359090
$922$	−44.8792	−1.47802
$923$	−5.87183	−0.193274
$924$	2.43440	0.0800857
$925$	9.18517	0.302007
$926$	13.2354	0.434942
$927$	31.2130	1.02517
$928$	10.9798	0.360431
$929$	47.2676	1.55080	0.775400	−	0.631470i	$-0.217548\pi$
$929$	47.2676	1.55080	0.775400	+	0.631470i	$0.217548\pi$
$930$	1.91362	0.0627499
$931$	−3.94447	−0.129275
$932$	−2.91803	−0.0955833
$933$	10.2146	0.334411
$934$	−27.6257	−0.903940
$935$	−5.86941	−0.191950
$936$	−51.3376	−1.67802
$937$	−8.70300	−0.284315	−0.142157	−	0.989844i	$-0.545404\pi$
$937$	−8.70300	−0.284315	−0.142157	+	0.989844i	$0.545404\pi$
$938$	−15.3775	−0.502092
$939$	1.73102	0.0564897
$940$	−0.459734	−0.0149949
$941$	34.4777	1.12394	0.561971	−	0.827157i	$-0.310043\pi$
$941$	34.4777	1.12394	0.561971	+	0.827157i	$0.310043\pi$
$942$	1.45811	0.0475077
$943$	4.97231	0.161921
$944$	−31.8072	−1.03524
$945$	6.41495	0.208678
$946$	−28.4309	−0.924367
$947$	−26.2627	−0.853423	−0.426712	−	0.904388i	$-0.640328\pi$
$947$	−26.2627	−0.853423	−0.426712	+	0.904388i	$0.640328\pi$
$948$	2.12435	0.0689958
$949$	−73.4869	−2.38549
$950$	1.46700	0.0475958
$951$	6.14518	0.199271
$952$	9.77982	0.316966
$953$	−52.2036	−1.69104	−0.845520	−	0.533943i	$-0.820710\pi$
$953$	−52.2036	−1.69104	−0.845520	+	0.533943i	$0.820710\pi$
$954$	39.3599	1.27432
$955$	16.9482	0.548430
$956$	−6.73290	−0.217758
$957$	−10.2554	−0.331511
$958$	−28.9470	−0.935236
$959$	−10.9576	−0.353841
$960$	3.00052	0.0968415
$961$	−11.1600	−0.360000
$962$	−68.6346	−2.21287
$963$	−16.6510	−0.536571
$964$	−3.12272	−0.100576
$965$	−22.1445	−0.712857
$966$	8.30320	0.267151
$967$	−6.63601	−0.213400	−0.106700	−	0.994291i	$-0.534028\pi$
$967$	−6.63601	−0.213400	−0.106700	+	0.994291i	$0.534028\pi$
$968$	71.0400	2.28331
$969$	0.389179	0.0125022
$970$	15.3592	0.493155
$971$	−28.2267	−0.905838	−0.452919	−	0.891552i	$-0.649617\pi$
$971$	−28.2267	−0.905838	−0.452919	+	0.891552i	$0.649617\pi$
$972$	−3.29485	−0.105682
$973$	2.94329	0.0943576
$974$	−13.9677	−0.447554
$975$	1.98233	0.0634853
$976$	−12.3591	−0.395604
$977$	−22.0592	−0.705738	−0.352869	−	0.935673i	$-0.614794\pi$
$977$	−22.0592	−0.705738	−0.352869	+	0.935673i	$0.614794\pi$
$978$	−6.18856	−0.197888
$979$	96.2779	3.07706
$980$	−1.30217	−0.0415962
$981$	12.9281	0.412763
$982$	3.56905	0.113893
$983$	19.2776	0.614859	0.307429	−	0.951571i	$-0.400531\pi$
$983$	19.2776	0.614859	0.307429	+	0.951571i	$0.400531\pi$
$984$	0.849433	0.0270789
$985$	17.8575	0.568987
$986$	−6.58628	−0.209750
$987$	−1.31659	−0.0419076
$988$	2.57601	0.0819539
$989$	22.7880	0.724617
$990$	21.5564	0.685108
$991$	15.0669	0.478617	0.239309	−	0.970944i	$-0.423079\pi$
$991$	15.0669	0.478617	0.239309	+	0.970944i	$0.423079\pi$
$992$	9.44950	0.300022
$993$	8.14471	0.258465
$994$	−4.10820	−0.130304
$995$	13.3543	0.423358
$996$	−0.689337	−0.0218425
$997$	32.8272	1.03965	0.519825	−	0.854273i	$-0.325997\pi$
$997$	32.8272	1.03965	0.519825	+	0.854273i	$0.325997\pi$
$998$	12.5980	0.398784
$999$	−18.2520	−0.577469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.18	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.18	✓	59	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.27257 q^{2} +0.337599 q^{3} -0.380563 q^{4} +1.00000 q^{5} -0.429619 q^{6} -3.22826 q^{7} +3.02944 q^{8} -2.88603 q^{9} +O(q^{10})\)	\(q-1.27257 q^{2} +0.337599 q^{3} -0.380563 q^{4} +1.00000 q^{5} -0.429619 q^{6} -3.22826 q^{7} +3.02944 q^{8} -2.88603 q^{9} -1.27257 q^{10} +5.86941 q^{11} -0.128478 q^{12} +5.87183 q^{13} +4.10820 q^{14} +0.337599 q^{15} -3.09405 q^{16} -1.00000 q^{17} +3.67267 q^{18} -1.15278 q^{19} -0.380563 q^{20} -1.08986 q^{21} -7.46924 q^{22} +5.98677 q^{23} +1.02274 q^{24} +1.00000 q^{25} -7.47233 q^{26} -1.98712 q^{27} +1.22856 q^{28} -5.17557 q^{29} -0.429619 q^{30} -4.45421 q^{31} -2.12148 q^{32} +1.98151 q^{33} +1.27257 q^{34} -3.22826 q^{35} +1.09831 q^{36} +9.18517 q^{37} +1.46700 q^{38} +1.98233 q^{39} +3.02944 q^{40} +0.830550 q^{41} +1.38692 q^{42} +3.80639 q^{43} -2.23368 q^{44} -2.88603 q^{45} -7.61859 q^{46} +1.20804 q^{47} -1.04455 q^{48} +3.42169 q^{49} -1.27257 q^{50} -0.337599 q^{51} -2.23460 q^{52} +10.7170 q^{53} +2.52875 q^{54} +5.86941 q^{55} -9.77982 q^{56} -0.389179 q^{57} +6.58628 q^{58} +10.2801 q^{59} -0.128478 q^{60} +3.99447 q^{61} +5.66830 q^{62} +9.31686 q^{63} +8.88782 q^{64} +5.87183 q^{65} -2.52161 q^{66} -3.74312 q^{67} +0.380563 q^{68} +2.02113 q^{69} +4.10820 q^{70} -1.00000 q^{71} -8.74303 q^{72} -12.5152 q^{73} -11.6888 q^{74} +0.337599 q^{75} +0.438707 q^{76} -18.9480 q^{77} -2.52265 q^{78} -16.5348 q^{79} -3.09405 q^{80} +7.98723 q^{81} -1.05693 q^{82} +5.36542 q^{83} +0.414760 q^{84} -1.00000 q^{85} -4.84391 q^{86} -1.74727 q^{87} +17.7810 q^{88} +16.4034 q^{89} +3.67267 q^{90} -18.9558 q^{91} -2.27834 q^{92} -1.50374 q^{93} -1.53731 q^{94} -1.15278 q^{95} -0.716209 q^{96} -12.0695 q^{97} -4.35435 q^{98} -16.9393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

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