LMFDB - Embedded newform 6035.2.a.h.1.8

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			1.8
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)

$f(q)$	$=$	$q-2.42937 q^{2} -1.27159 q^{3} +3.90183 q^{4} +1.00000 q^{5} +3.08915 q^{6} -3.98798 q^{7} -4.62024 q^{8} -1.38307 q^{9} +O(q^{10})$	\(q-2.42937 q^{2} -1.27159 q^{3} +3.90183 q^{4} +1.00000 q^{5} +3.08915 q^{6} -3.98798 q^{7} -4.62024 q^{8} -1.38307 q^{9} -2.42937 q^{10} +3.67662 q^{11} -4.96151 q^{12} -2.50375 q^{13} +9.68828 q^{14} -1.27159 q^{15} +3.42060 q^{16} -1.00000 q^{17} +3.35999 q^{18} -5.80938 q^{19} +3.90183 q^{20} +5.07106 q^{21} -8.93185 q^{22} +0.315035 q^{23} +5.87503 q^{24} +1.00000 q^{25} +6.08252 q^{26} +5.57345 q^{27} -15.5604 q^{28} -1.97085 q^{29} +3.08915 q^{30} +2.19873 q^{31} +0.930573 q^{32} -4.67513 q^{33} +2.42937 q^{34} -3.98798 q^{35} -5.39650 q^{36} -11.3424 q^{37} +14.1131 q^{38} +3.18373 q^{39} -4.62024 q^{40} -4.51969 q^{41} -12.3195 q^{42} -2.11503 q^{43} +14.3455 q^{44} -1.38307 q^{45} -0.765336 q^{46} +2.18566 q^{47} -4.34959 q^{48} +8.90401 q^{49} -2.42937 q^{50} +1.27159 q^{51} -9.76919 q^{52} +3.21188 q^{53} -13.5400 q^{54} +3.67662 q^{55} +18.4254 q^{56} +7.38712 q^{57} +4.78791 q^{58} +6.78510 q^{59} -4.96151 q^{60} -8.68708 q^{61} -5.34152 q^{62} +5.51566 q^{63} -9.10191 q^{64} -2.50375 q^{65} +11.3576 q^{66} -8.74432 q^{67} -3.90183 q^{68} -0.400594 q^{69} +9.68828 q^{70} -1.00000 q^{71} +6.39012 q^{72} -12.6319 q^{73} +27.5549 q^{74} -1.27159 q^{75} -22.6672 q^{76} -14.6623 q^{77} -7.73445 q^{78} -0.759044 q^{79} +3.42060 q^{80} -2.93790 q^{81} +10.9800 q^{82} -14.7822 q^{83} +19.7864 q^{84} -1.00000 q^{85} +5.13819 q^{86} +2.50610 q^{87} -16.9868 q^{88} +6.70253 q^{89} +3.35999 q^{90} +9.98491 q^{91} +1.22921 q^{92} -2.79587 q^{93} -5.30978 q^{94} -5.80938 q^{95} -1.18330 q^{96} -8.88965 q^{97} -21.6311 q^{98} -5.08502 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.42937	−1.71782	−0.858911	−	0.512125i	$-0.828859\pi$
$2$	−2.42937	−1.71782	−0.858911	+	0.512125i	$0.828859\pi$
$3$	−1.27159	−0.734150	−0.367075	−	0.930191i	$-0.619641\pi$
$3$	−1.27159	−0.734150	−0.367075	+	0.930191i	$0.619641\pi$
$4$	3.90183	1.95091
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.08915	1.26114
$7$	−3.98798	−1.50732	−0.753658	−	0.657267i	$-0.771712\pi$
$7$	−3.98798	−1.50732	−0.753658	+	0.657267i	$0.771712\pi$
$8$	−4.62024	−1.63350
$9$	−1.38307	−0.461024
$10$	−2.42937	−0.768234
$11$	3.67662	1.10854	0.554271	−	0.832336i	$-0.312997\pi$
$11$	3.67662	1.10854	0.554271	+	0.832336i	$0.312997\pi$
$12$	−4.96151	−1.43226
$13$	−2.50375	−0.694415	−0.347207	−	0.937788i	$-0.612870\pi$
$13$	−2.50375	−0.694415	−0.347207	+	0.937788i	$0.612870\pi$
$14$	9.68828	2.58930
$15$	−1.27159	−0.328322
$16$	3.42060	0.855151
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.35999	0.791957
$19$	−5.80938	−1.33276	−0.666382	−	0.745611i	$-0.732158\pi$
$19$	−5.80938	−1.33276	−0.666382	+	0.745611i	$0.732158\pi$
$20$	3.90183	0.872475
$21$	5.07106	1.10660
$22$	−8.93185	−1.90428
$23$	0.315035	0.0656893	0.0328447	−	0.999460i	$-0.489543\pi$
$23$	0.315035	0.0656893	0.0328447	+	0.999460i	$0.489543\pi$
$24$	5.87503	1.19923
$25$	1.00000	0.200000
$26$	6.08252	1.19288
$27$	5.57345	1.07261
$28$	−15.5604	−2.94064
$29$	−1.97085	−0.365977	−0.182988	−	0.983115i	$-0.558577\pi$
$29$	−1.97085	−0.365977	−0.182988	+	0.983115i	$0.558577\pi$
$30$	3.08915	0.563999
$31$	2.19873	0.394904	0.197452	−	0.980313i	$-0.436733\pi$
$31$	2.19873	0.394904	0.197452	+	0.980313i	$0.436733\pi$
$32$	0.930573	0.164504
$33$	−4.67513	−0.813836
$34$	2.42937	0.416633
$35$	−3.98798	−0.674092
$36$	−5.39650	−0.899417
$37$	−11.3424	−1.86468	−0.932342	−	0.361578i	$-0.882238\pi$
$37$	−11.3424	−1.86468	−0.932342	+	0.361578i	$0.882238\pi$
$38$	14.1131	2.28945
$39$	3.18373	0.509805
$40$	−4.62024	−0.730524
$41$	−4.51969	−0.705856	−0.352928	−	0.935650i	$-0.614814\pi$
$41$	−4.51969	−0.705856	−0.352928	+	0.935650i	$0.614814\pi$
$42$	−12.3195	−1.90094
$43$	−2.11503	−0.322540	−0.161270	−	0.986910i	$-0.551559\pi$
$43$	−2.11503	−0.322540	−0.161270	+	0.986910i	$0.551559\pi$
$44$	14.3455	2.16267
$45$	−1.38307	−0.206176
$46$	−0.765336	−0.112843
$47$	2.18566	0.318812	0.159406	−	0.987213i	$-0.449042\pi$
$47$	2.18566	0.318812	0.159406	+	0.987213i	$0.449042\pi$
$48$	−4.34959	−0.627809
$49$	8.90401	1.27200
$50$	−2.42937	−0.343564
$51$	1.27159	0.178058
$52$	−9.76919	−1.35474
$53$	3.21188	0.441186	0.220593	−	0.975366i	$-0.429201\pi$
$53$	3.21188	0.441186	0.220593	+	0.975366i	$0.429201\pi$
$54$	−13.5400	−1.84255
$55$	3.67662	0.495755
$56$	18.4254	2.46220
$57$	7.38712	0.978449
$58$	4.78791	0.628683
$59$	6.78510	0.883345	0.441672	−	0.897176i	$-0.354385\pi$
$59$	6.78510	0.883345	0.441672	+	0.897176i	$0.354385\pi$
$60$	−4.96151	−0.640528
$61$	−8.68708	−1.11227	−0.556133	−	0.831093i	$-0.687715\pi$
$61$	−8.68708	−1.11227	−0.556133	+	0.831093i	$0.687715\pi$
$62$	−5.34152	−0.678374
$63$	5.51566	0.694908
$64$	−9.10191	−1.13774
$65$	−2.50375	−0.310552
$66$	11.3576	1.39803
$67$	−8.74432	−1.06829	−0.534144	−	0.845393i	$-0.679366\pi$
$67$	−8.74432	−1.06829	−0.534144	+	0.845393i	$0.679366\pi$
$68$	−3.90183	−0.473166
$69$	−0.400594	−0.0482258
$70$	9.68828	1.15797
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	6.39012	0.753083
$73$	−12.6319	−1.47845	−0.739225	−	0.673458i	$-0.764808\pi$
$73$	−12.6319	−1.47845	−0.739225	+	0.673458i	$0.764808\pi$
$74$	27.5549	3.20319
$75$	−1.27159	−0.146830
$76$	−22.6672	−2.60011
$77$	−14.6623	−1.67092
$78$	−7.73445	−0.875754
$79$	−0.759044	−0.0853991	−0.0426995	−	0.999088i	$-0.513596\pi$
$79$	−0.759044	−0.0853991	−0.0426995	+	0.999088i	$0.513596\pi$
$80$	3.42060	0.382435
$81$	−2.93790	−0.326434
$82$	10.9800	1.21254
$83$	−14.7822	−1.62256	−0.811278	−	0.584660i	$-0.801228\pi$
$83$	−14.7822	−1.62256	−0.811278	+	0.584660i	$0.801228\pi$
$84$	19.7864	2.15887
$85$	−1.00000	−0.108465
$86$	5.13819	0.554066
$87$	2.50610	0.268682
$88$	−16.9868	−1.81080
$89$	6.70253	0.710467	0.355234	−	0.934778i	$-0.384401\pi$
$89$	6.70253	0.710467	0.355234	+	0.934778i	$0.384401\pi$
$90$	3.35999	0.354174
$91$	9.98491	1.04670
$92$	1.22921	0.128154
$93$	−2.79587	−0.289918
$94$	−5.30978	−0.547662
$95$	−5.80938	−0.596030
$96$	−1.18330	−0.120770
$97$	−8.88965	−0.902607	−0.451304	−	0.892371i	$-0.649041\pi$
$97$	−8.88965	−0.902607	−0.451304	+	0.892371i	$0.649041\pi$
$98$	−21.6311	−2.18507
$99$	−5.08502	−0.511064
$100$	3.90183	0.390183
$101$	3.48671	0.346941	0.173470	−	0.984839i	$-0.444502\pi$
$101$	3.48671	0.346941	0.173470	+	0.984839i	$0.444502\pi$
$102$	−3.08915	−0.305871
$103$	1.15960	0.114258	0.0571292	−	0.998367i	$-0.481805\pi$
$103$	1.15960	0.114258	0.0571292	+	0.998367i	$0.481805\pi$
$104$	11.5679	1.13433
$105$	5.07106	0.494885
$106$	−7.80284	−0.757879
$107$	−17.7237	−1.71341	−0.856707	−	0.515803i	$-0.827494\pi$
$107$	−17.7237	−1.71341	−0.856707	+	0.515803i	$0.827494\pi$
$108$	21.7466	2.09257
$109$	17.6055	1.68630	0.843149	−	0.537681i	$-0.180699\pi$
$109$	17.6055	1.68630	0.843149	+	0.537681i	$0.180699\pi$
$110$	−8.93185	−0.851619
$111$	14.4229	1.36896
$112$	−13.6413	−1.28898
$113$	3.45839	0.325338	0.162669	−	0.986681i	$-0.447990\pi$
$113$	3.45839	0.325338	0.162669	+	0.986681i	$0.447990\pi$
$114$	−17.9460	−1.68080
$115$	0.315035	0.0293772
$116$	−7.68990	−0.713989
$117$	3.46286	0.320142
$118$	−16.4835	−1.51743
$119$	3.98798	0.365578
$120$	5.87503	0.536314
$121$	2.51750	0.228864
$122$	21.1041	1.91068
$123$	5.74717	0.518204
$124$	8.57907	0.770423
$125$	1.00000	0.0894427
$126$	−13.3996	−1.19373
$127$	−10.7869	−0.957183	−0.478592	−	0.878038i	$-0.658853\pi$
$127$	−10.7869	−0.957183	−0.478592	+	0.878038i	$0.658853\pi$
$128$	20.2507	1.78993
$129$	2.68944	0.236792
$130$	6.08252	0.533473
$131$	12.2627	1.07140	0.535701	−	0.844408i	$-0.320048\pi$
$131$	12.2627	1.07140	0.535701	+	0.844408i	$0.320048\pi$
$132$	−18.2416	−1.58772
$133$	23.1677	2.00890
$134$	21.2432	1.83513
$135$	5.57345	0.479686
$136$	4.62024	0.396182
$137$	−6.39130	−0.546046	−0.273023	−	0.962008i	$-0.588023\pi$
$137$	−6.39130	−0.546046	−0.273023	+	0.962008i	$0.588023\pi$
$138$	0.973190	0.0828434
$139$	16.7839	1.42359	0.711796	−	0.702386i	$-0.247882\pi$
$139$	16.7839	1.42359	0.711796	+	0.702386i	$0.247882\pi$
$140$	−15.5604	−1.31510
$141$	−2.77926	−0.234056
$142$	2.42937	0.203868
$143$	−9.20532	−0.769788
$144$	−4.73094	−0.394245
$145$	−1.97085	−0.163670
$146$	30.6875	2.53972
$147$	−11.3222	−0.933840
$148$	−44.2562	−3.63784
$149$	−6.05220	−0.495815	−0.247908	−	0.968784i	$-0.579743\pi$
$149$	−6.05220	−0.495815	−0.247908	+	0.968784i	$0.579743\pi$
$150$	3.08915	0.252228
$151$	−10.3766	−0.844437	−0.422219	−	0.906494i	$-0.638749\pi$
$151$	−10.3766	−0.844437	−0.422219	+	0.906494i	$0.638749\pi$
$152$	26.8407	2.17707
$153$	1.38307	0.111815
$154$	35.6201	2.87035
$155$	2.19873	0.176606
$156$	12.4224	0.994585
$157$	20.7199	1.65363	0.826814	−	0.562476i	$-0.190151\pi$
$157$	20.7199	1.65363	0.826814	+	0.562476i	$0.190151\pi$
$158$	1.84400	0.146700
$159$	−4.08418	−0.323897
$160$	0.930573	0.0735682
$161$	−1.25635	−0.0990146
$162$	7.13724	0.560755
$163$	5.01205	0.392574	0.196287	−	0.980546i	$-0.437112\pi$
$163$	5.01205	0.392574	0.196287	+	0.980546i	$0.437112\pi$
$164$	−17.6350	−1.37706
$165$	−4.67513	−0.363958
$166$	35.9114	2.78726
$167$	−1.99111	−0.154076	−0.0770382	−	0.997028i	$-0.524546\pi$
$167$	−1.99111	−0.154076	−0.0770382	+	0.997028i	$0.524546\pi$
$168$	−23.4295	−1.80763
$169$	−6.73125	−0.517788
$170$	2.42937	0.186324
$171$	8.03479	0.614436
$172$	−8.25249	−0.629247
$173$	−13.7311	−1.04396	−0.521980	−	0.852958i	$-0.674806\pi$
$173$	−13.7311	−1.04396	−0.521980	+	0.852958i	$0.674806\pi$
$174$	−6.08823	−0.461548
$175$	−3.98798	−0.301463
$176$	12.5762	0.947970
$177$	−8.62783	−0.648508
$178$	−16.2829	−1.22046
$179$	13.3360	0.996780	0.498390	−	0.866953i	$-0.333925\pi$
$179$	13.3360	0.996780	0.498390	+	0.866953i	$0.333925\pi$
$180$	−5.39650	−0.402232
$181$	16.4765	1.22469	0.612343	−	0.790593i	$-0.290227\pi$
$181$	16.4765	1.22469	0.612343	+	0.790593i	$0.290227\pi$
$182$	−24.2570	−1.79805
$183$	11.0464	0.816570
$184$	−1.45554	−0.107304
$185$	−11.3424	−0.833912
$186$	6.79220	0.498028
$187$	−3.67662	−0.268861
$188$	8.52808	0.621974
$189$	−22.2268	−1.61676
$190$	14.1131	1.02387
$191$	−25.4205	−1.83936	−0.919680	−	0.392669i	$-0.871552\pi$
$191$	−25.4205	−1.83936	−0.919680	+	0.392669i	$0.871552\pi$
$192$	11.5739	0.835271
$193$	22.3825	1.61113	0.805563	−	0.592510i	$-0.201863\pi$
$193$	22.3825	1.61113	0.805563	+	0.592510i	$0.201863\pi$
$194$	21.5962	1.55052
$195$	3.18373	0.227992
$196$	34.7419	2.48157
$197$	−10.5691	−0.753016	−0.376508	−	0.926413i	$-0.622875\pi$
$197$	−10.5691	−0.753016	−0.376508	+	0.926413i	$0.622875\pi$
$198$	12.3534	0.877917
$199$	−15.1807	−1.07613	−0.538066	−	0.842903i	$-0.680845\pi$
$199$	−15.1807	−1.07613	−0.538066	+	0.842903i	$0.680845\pi$
$200$	−4.62024	−0.326700
$201$	11.1191	0.784284
$202$	−8.47050	−0.595982
$203$	7.85970	0.551643
$204$	4.96151	0.347375
$205$	−4.51969	−0.315669
$206$	−2.81708	−0.196276
$207$	−0.435716	−0.0302843
$208$	−8.56433	−0.593829
$209$	−21.3589	−1.47742
$210$	−12.3195	−0.850124
$211$	−6.31119	−0.434480	−0.217240	−	0.976118i	$-0.569705\pi$
$211$	−6.31119	−0.434480	−0.217240	+	0.976118i	$0.569705\pi$
$212$	12.5322	0.860716
$213$	1.27159	0.0871276
$214$	43.0574	2.94334
$215$	−2.11503	−0.144244
$216$	−25.7507	−1.75211
$217$	−8.76850	−0.595244
$218$	−42.7701	−2.89676
$219$	16.0625	1.08540
$220$	14.3455	0.967175
$221$	2.50375	0.168420
$222$	−35.0384	−2.35163
$223$	1.60405	0.107415	0.0537074	−	0.998557i	$-0.482896\pi$
$223$	1.60405	0.107415	0.0537074	+	0.998557i	$0.482896\pi$
$224$	−3.71111	−0.247959
$225$	−1.38307	−0.0922047
$226$	−8.40170	−0.558873
$227$	−9.39286	−0.623426	−0.311713	−	0.950176i	$-0.600903\pi$
$227$	−9.39286	−0.623426	−0.311713	+	0.950176i	$0.600903\pi$
$228$	28.8233	1.90887
$229$	−10.4355	−0.689599	−0.344799	−	0.938676i	$-0.612053\pi$
$229$	−10.4355	−0.689599	−0.344799	+	0.938676i	$0.612053\pi$
$230$	−0.765336	−0.0504647
$231$	18.6443	1.22671
$232$	9.10578	0.597824
$233$	16.5127	1.08178	0.540891	−	0.841093i	$-0.318087\pi$
$233$	16.5127	1.08178	0.540891	+	0.841093i	$0.318087\pi$
$234$	−8.41256	−0.549946
$235$	2.18566	0.142577
$236$	26.4743	1.72333
$237$	0.965189	0.0626957
$238$	−9.68828	−0.627998
$239$	−8.89834	−0.575586	−0.287793	−	0.957693i	$-0.592922\pi$
$239$	−8.89834	−0.575586	−0.287793	+	0.957693i	$0.592922\pi$
$240$	−4.34959	−0.280765
$241$	−9.79857	−0.631181	−0.315591	−	0.948895i	$-0.602203\pi$
$241$	−9.79857	−0.631181	−0.315591	+	0.948895i	$0.602203\pi$
$242$	−6.11594	−0.393148
$243$	−12.9846	−0.832959
$244$	−33.8955	−2.16994
$245$	8.90401	0.568856
$246$	−13.9620	−0.890183
$247$	14.5452	0.925491
$248$	−10.1587	−0.645075
$249$	18.7968	1.19120
$250$	−2.42937	−0.153647
$251$	−5.08523	−0.320977	−0.160489	−	0.987038i	$-0.551307\pi$
$251$	−5.08523	−0.320977	−0.160489	+	0.987038i	$0.551307\pi$
$252$	21.5212	1.35571
$253$	1.15826	0.0728193
$254$	26.2054	1.64427
$255$	1.27159	0.0796298
$256$	−30.9927	−1.93704
$257$	−20.5715	−1.28322	−0.641608	−	0.767033i	$-0.721732\pi$
$257$	−20.5715	−1.28322	−0.641608	+	0.767033i	$0.721732\pi$
$258$	−6.53365	−0.406767
$259$	45.2334	2.81067
$260$	−9.76919	−0.605860
$261$	2.72582	0.168724
$262$	−29.7907	−1.84048
$263$	24.8829	1.53434	0.767172	−	0.641441i	$-0.221663\pi$
$263$	24.8829	1.53434	0.767172	+	0.641441i	$0.221663\pi$
$264$	21.6002	1.32940
$265$	3.21188	0.197304
$266$	−56.2829	−3.45093
$267$	−8.52284	−0.521590
$268$	−34.1188	−2.08414
$269$	−11.0662	−0.674721	−0.337361	−	0.941376i	$-0.609534\pi$
$269$	−11.0662	−0.674721	−0.337361	+	0.941376i	$0.609534\pi$
$270$	−13.5400	−0.824015
$271$	−25.8353	−1.56939	−0.784693	−	0.619885i	$-0.787179\pi$
$271$	−25.8353	−1.56939	−0.784693	+	0.619885i	$0.787179\pi$
$272$	−3.42060	−0.207405
$273$	−12.6967	−0.768437
$274$	15.5268	0.938009
$275$	3.67662	0.221708
$276$	−1.56305	−0.0940844
$277$	0.680683	0.0408983	0.0204491	−	0.999791i	$-0.493490\pi$
$277$	0.680683	0.0408983	0.0204491	+	0.999791i	$0.493490\pi$
$278$	−40.7743	−2.44548
$279$	−3.04100	−0.182060
$280$	18.4254	1.10113
$281$	−14.9418	−0.891353	−0.445676	−	0.895194i	$-0.647037\pi$
$281$	−14.9418	−0.891353	−0.445676	+	0.895194i	$0.647037\pi$
$282$	6.75184	0.402066
$283$	−22.3943	−1.33120	−0.665602	−	0.746307i	$-0.731825\pi$
$283$	−22.3943	−1.33120	−0.665602	+	0.746307i	$0.731825\pi$
$284$	−3.90183	−0.231531
$285$	7.38712	0.437575
$286$	22.3631	1.32236
$287$	18.0244	1.06395
$288$	−1.28705	−0.0758400
$289$	1.00000	0.0588235
$290$	4.78791	0.281156
$291$	11.3039	0.662649
$292$	−49.2875	−2.88433
$293$	17.0867	0.998218	0.499109	−	0.866539i	$-0.333661\pi$
$293$	17.0867	0.998218	0.499109	+	0.866539i	$0.333661\pi$
$294$	27.5058	1.60417
$295$	6.78510	0.395044
$296$	52.4047	3.04596
$297$	20.4914	1.18903
$298$	14.7030	0.851722
$299$	−0.788768	−0.0456156
$300$	−4.96151	−0.286453
$301$	8.43472	0.486169
$302$	25.2086	1.45059
$303$	−4.43365	−0.254706
$304$	−19.8716	−1.13971
$305$	−8.68708	−0.497420
$306$	−3.35999	−0.192078
$307$	−13.4110	−0.765405	−0.382702	−	0.923872i	$-0.625006\pi$
$307$	−13.4110	−0.765405	−0.382702	+	0.923872i	$0.625006\pi$
$308$	−57.2097	−3.25983
$309$	−1.47452	−0.0838828
$310$	−5.34152	−0.303378
$311$	−0.131895	−0.00747905	−0.00373953	−	0.999993i	$-0.501190\pi$
$311$	−0.131895	−0.00747905	−0.00373953	+	0.999993i	$0.501190\pi$
$312$	−14.7096	−0.832767
$313$	30.1108	1.70197	0.850983	−	0.525194i	$-0.176007\pi$
$313$	30.1108	1.70197	0.850983	+	0.525194i	$0.176007\pi$
$314$	−50.3362	−2.84064
$315$	5.51566	0.310772
$316$	−2.96166	−0.166606
$317$	9.66390	0.542779	0.271389	−	0.962470i	$-0.412517\pi$
$317$	9.66390	0.542779	0.271389	+	0.962470i	$0.412517\pi$
$318$	9.92198	0.556397
$319$	−7.24604	−0.405701
$320$	−9.10191	−0.508812
$321$	22.5372	1.25790
$322$	3.05215	0.170089
$323$	5.80938	0.323243
$324$	−11.4632	−0.636844
$325$	−2.50375	−0.138883
$326$	−12.1761	−0.674373
$327$	−22.3868	−1.23800
$328$	20.8820	1.15302
$329$	−8.71639	−0.480550
$330$	11.3576	0.625216
$331$	−17.9664	−0.987523	−0.493762	−	0.869597i	$-0.664378\pi$
$331$	−17.9664	−0.987523	−0.493762	+	0.869597i	$0.664378\pi$
$332$	−57.6776	−3.16547
$333$	15.6874	0.859663
$334$	4.83713	0.264676
$335$	−8.74432	−0.477753
$336$	17.3461	0.946307
$337$	0.271535	0.0147914	0.00739572	−	0.999973i	$-0.497646\pi$
$337$	0.271535	0.0147914	0.00739572	+	0.999973i	$0.497646\pi$
$338$	16.3527	0.889468
$339$	−4.39764	−0.238847
$340$	−3.90183	−0.211606
$341$	8.08389	0.437767
$342$	−19.5195	−1.05549
$343$	−7.59316	−0.409992
$344$	9.77196	0.526869
$345$	−0.400594	−0.0215672
$346$	33.3580	1.79334
$347$	−0.428586	−0.0230077	−0.0115039	−	0.999934i	$-0.503662\pi$
$347$	−0.428586	−0.0230077	−0.0115039	+	0.999934i	$0.503662\pi$
$348$	9.77836	0.524175
$349$	−20.5964	−1.10250	−0.551249	−	0.834341i	$-0.685848\pi$
$349$	−20.5964	−1.10250	−0.551249	+	0.834341i	$0.685848\pi$
$350$	9.68828	0.517860
$351$	−13.9545	−0.744837
$352$	3.42136	0.182359
$353$	29.7977	1.58597	0.792986	−	0.609240i	$-0.208525\pi$
$353$	29.7977	1.58597	0.792986	+	0.609240i	$0.208525\pi$
$354$	20.9602	1.11402
$355$	−1.00000	−0.0530745
$356$	26.1521	1.38606
$357$	−5.07106	−0.268389
$358$	−32.3981	−1.71229
$359$	−17.7215	−0.935306	−0.467653	−	0.883912i	$-0.654900\pi$
$359$	−17.7215	−0.935306	−0.467653	+	0.883912i	$0.654900\pi$
$360$	6.39012	0.336789
$361$	14.7489	0.776259
$362$	−40.0274	−2.10379
$363$	−3.20122	−0.168021
$364$	38.9594	2.04203
$365$	−12.6319	−0.661183
$366$	−26.8357	−1.40272
$367$	22.2123	1.15947	0.579737	−	0.814803i	$-0.303155\pi$
$367$	22.2123	1.15947	0.579737	+	0.814803i	$0.303155\pi$
$368$	1.07761	0.0561743
$369$	6.25105	0.325416
$370$	27.5549	1.43251
$371$	−12.8089	−0.665006
$372$	−10.9090	−0.565606
$373$	30.4656	1.57745	0.788725	−	0.614746i	$-0.210742\pi$
$373$	30.4656	1.57745	0.788725	+	0.614746i	$0.210742\pi$
$374$	8.93185	0.461855
$375$	−1.27159	−0.0656644
$376$	−10.0983	−0.520779
$377$	4.93450	0.254140
$378$	53.9971	2.77731
$379$	−25.3078	−1.29998	−0.649988	−	0.759944i	$-0.725226\pi$
$379$	−25.3078	−1.29998	−0.649988	+	0.759944i	$0.725226\pi$
$380$	−22.6672	−1.16280
$381$	13.7165	0.702716
$382$	61.7556	3.15969
$383$	34.3133	1.75333	0.876665	−	0.481102i	$-0.159763\pi$
$383$	34.3133	1.75333	0.876665	+	0.481102i	$0.159763\pi$
$384$	−25.7505	−1.31408
$385$	−14.6623	−0.747259
$386$	−54.3753	−2.76763
$387$	2.92524	0.148698
$388$	−34.6859	−1.76091
$389$	7.49829	0.380178	0.190089	−	0.981767i	$-0.439122\pi$
$389$	7.49829	0.380178	0.190089	+	0.981767i	$0.439122\pi$
$390$	−7.73445	−0.391649
$391$	−0.315035	−0.0159320
$392$	−41.1387	−2.07782
$393$	−15.5931	−0.786569
$394$	25.6762	1.29355
$395$	−0.759044	−0.0381916
$396$	−19.8409	−0.997041
$397$	−23.2300	−1.16588	−0.582941	−	0.812515i	$-0.698098\pi$
$397$	−23.2300	−1.16588	−0.582941	+	0.812515i	$0.698098\pi$
$398$	36.8795	1.84860
$399$	−29.4597	−1.47483
$400$	3.42060	0.171030
$401$	30.5623	1.52621	0.763104	−	0.646276i	$-0.223674\pi$
$401$	30.5623	1.52621	0.763104	+	0.646276i	$0.223674\pi$
$402$	−27.0125	−1.34726
$403$	−5.50507	−0.274227
$404$	13.6045	0.676851
$405$	−2.93790	−0.145986
$406$	−19.0941	−0.947624
$407$	−41.7017	−2.06708
$408$	−5.87503	−0.290857
$409$	3.66443	0.181194	0.0905972	−	0.995888i	$-0.471122\pi$
$409$	3.66443	0.181194	0.0905972	+	0.995888i	$0.471122\pi$
$410$	10.9800	0.542262
$411$	8.12708	0.400879
$412$	4.52454	0.222908
$413$	−27.0589	−1.33148
$414$	1.05851	0.0520231
$415$	−14.7822	−0.725629
$416$	−2.32992	−0.114234
$417$	−21.3422	−1.04513
$418$	51.8885	2.53795
$419$	−36.7487	−1.79529	−0.897645	−	0.440720i	$-0.854723\pi$
$419$	−36.7487	−1.79529	−0.897645	+	0.440720i	$0.854723\pi$
$420$	19.7864	0.965478
$421$	29.9058	1.45752	0.728761	−	0.684768i	$-0.240097\pi$
$421$	29.9058	1.45752	0.728761	+	0.684768i	$0.240097\pi$
$422$	15.3322	0.746360
$423$	−3.02293	−0.146980
$424$	−14.8397	−0.720678
$425$	−1.00000	−0.0485071
$426$	−3.08915	−0.149670
$427$	34.6439	1.67654
$428$	−69.1548	−3.34272
$429$	11.7053	0.565140
$430$	5.13819	0.247786
$431$	−13.9002	−0.669548	−0.334774	−	0.942298i	$-0.608660\pi$
$431$	−13.9002	−0.669548	−0.334774	+	0.942298i	$0.608660\pi$
$432$	19.0646	0.917244
$433$	3.93595	0.189150	0.0945750	−	0.995518i	$-0.469851\pi$
$433$	3.93595	0.189150	0.0945750	+	0.995518i	$0.469851\pi$
$434$	21.3019	1.02252
$435$	2.50610	0.120158
$436$	68.6935	3.28982
$437$	−1.83016	−0.0875483
$438$	−39.0218	−1.86453
$439$	−13.1527	−0.627742	−0.313871	−	0.949466i	$-0.601626\pi$
$439$	−13.1527	−0.627742	−0.313871	+	0.949466i	$0.601626\pi$
$440$	−16.9868	−0.809816
$441$	−12.3149	−0.586423
$442$	−6.08252	−0.289316
$443$	−6.48561	−0.308141	−0.154070	−	0.988060i	$-0.549238\pi$
$443$	−6.48561	−0.308141	−0.154070	+	0.988060i	$0.549238\pi$
$444$	56.2755	2.67072
$445$	6.70253	0.317731
$446$	−3.89682	−0.184520
$447$	7.69588	0.364003
$448$	36.2983	1.71493
$449$	15.8165	0.746429	0.373214	−	0.927745i	$-0.378256\pi$
$449$	15.8165	0.746429	0.373214	+	0.927745i	$0.378256\pi$
$450$	3.35999	0.158391
$451$	−16.6171	−0.782471
$452$	13.4940	0.634706
$453$	13.1948	0.619944
$454$	22.8187	1.07093
$455$	9.98491	0.468100
$456$	−34.1303	−1.59830
$457$	16.4752	0.770676	0.385338	−	0.922776i	$-0.374085\pi$
$457$	16.4752	0.770676	0.385338	+	0.922776i	$0.374085\pi$
$458$	25.3517	1.18461
$459$	−5.57345	−0.260146
$460$	1.22921	0.0573123
$461$	21.8741	1.01878	0.509390	−	0.860536i	$-0.329871\pi$
$461$	21.8741	1.01878	0.509390	+	0.860536i	$0.329871\pi$
$462$	−45.2940	−2.10727
$463$	−9.32393	−0.433320	−0.216660	−	0.976247i	$-0.569516\pi$
$463$	−9.32393	−0.433320	−0.216660	+	0.976247i	$0.569516\pi$
$464$	−6.74148	−0.312965
$465$	−2.79587	−0.129655
$466$	−40.1154	−1.85831
$467$	−26.7561	−1.23813	−0.619063	−	0.785341i	$-0.712488\pi$
$467$	−26.7561	−1.23813	−0.619063	+	0.785341i	$0.712488\pi$
$468$	13.5115	0.624569
$469$	34.8722	1.61025
$470$	−5.30978	−0.244922
$471$	−26.3471	−1.21401
$472$	−31.3488	−1.44294
$473$	−7.77616	−0.357548
$474$	−2.34480	−0.107700
$475$	−5.80938	−0.266553
$476$	15.5604	0.713211
$477$	−4.44226	−0.203397
$478$	21.6174	0.988755
$479$	−8.98994	−0.410761	−0.205380	−	0.978682i	$-0.565843\pi$
$479$	−8.98994	−0.410761	−0.205380	+	0.978682i	$0.565843\pi$
$480$	−1.18330	−0.0540101
$481$	28.3986	1.29486
$482$	23.8043	1.08426
$483$	1.59756	0.0726916
$484$	9.82287	0.446494
$485$	−8.88965	−0.403658
$486$	31.5443	1.43088
$487$	−22.4248	−1.01616	−0.508082	−	0.861308i	$-0.669645\pi$
$487$	−22.4248	−1.01616	−0.508082	+	0.861308i	$0.669645\pi$
$488$	40.1364	1.81689
$489$	−6.37325	−0.288208
$490$	−21.6311	−0.977194
$491$	34.0485	1.53659	0.768295	−	0.640096i	$-0.221106\pi$
$491$	34.0485	1.53659	0.768295	+	0.640096i	$0.221106\pi$
$492$	22.4244	1.01097
$493$	1.97085	0.0887624
$494$	−35.3357	−1.58983
$495$	−5.08502	−0.228555
$496$	7.52098	0.337702
$497$	3.98798	0.178885
$498$	−45.6644	−2.04627
$499$	30.4220	1.36187	0.680937	−	0.732342i	$-0.261573\pi$
$499$	30.4220	1.36187	0.680937	+	0.732342i	$0.261573\pi$
$500$	3.90183	0.174495
$501$	2.53186	0.113115
$502$	12.3539	0.551382
$503$	23.4692	1.04644	0.523220	−	0.852198i	$-0.324731\pi$
$503$	23.4692	1.04644	0.523220	+	0.852198i	$0.324731\pi$
$504$	−25.4837	−1.13513
$505$	3.48671	0.155157
$506$	−2.81385	−0.125091
$507$	8.55935	0.380134
$508$	−42.0887	−1.86738
$509$	−19.5988	−0.868699	−0.434350	−	0.900744i	$-0.643022\pi$
$509$	−19.5988	−0.868699	−0.434350	+	0.900744i	$0.643022\pi$
$510$	−3.08915	−0.136790
$511$	50.3758	2.22849
$512$	34.7911	1.53757
$513$	−32.3783	−1.42954
$514$	49.9758	2.20434
$515$	1.15960	0.0510979
$516$	10.4938	0.461962
$517$	8.03585	0.353416
$518$	−109.889	−4.82823
$519$	17.4603	0.766423
$520$	11.5679	0.507287
$521$	−13.4498	−0.589245	−0.294622	−	0.955614i	$-0.595194\pi$
$521$	−13.4498	−0.589245	−0.294622	+	0.955614i	$0.595194\pi$
$522$	−6.62202	−0.289838
$523$	17.2159	0.752798	0.376399	−	0.926458i	$-0.377162\pi$
$523$	17.2159	0.752798	0.376399	+	0.926458i	$0.377162\pi$
$524$	47.8471	2.09021
$525$	5.07106	0.221319
$526$	−60.4497	−2.63573
$527$	−2.19873	−0.0957782
$528$	−15.9918	−0.695952
$529$	−22.9008	−0.995685
$530$	−7.80284	−0.338934
$531$	−9.38427	−0.407243
$532$	90.3964	3.91918
$533$	11.3162	0.490157
$534$	20.7051	0.895998
$535$	−17.7237	−0.766262
$536$	40.4008	1.74505
$537$	−16.9579	−0.731786
$538$	26.8840	1.15905
$539$	32.7366	1.41007
$540$	21.7466	0.935826
$541$	24.1222	1.03709	0.518547	−	0.855049i	$-0.326473\pi$
$541$	24.1222	1.03709	0.518547	+	0.855049i	$0.326473\pi$
$542$	62.7636	2.69593
$543$	−20.9512	−0.899103
$544$	−0.930573	−0.0398980
$545$	17.6055	0.754135
$546$	30.8449	1.32004
$547$	−8.68344	−0.371277	−0.185638	−	0.982618i	$-0.559435\pi$
$547$	−8.68344	−0.371277	−0.185638	+	0.982618i	$0.559435\pi$
$548$	−24.9377	−1.06529
$549$	12.0148	0.512781
$550$	−8.93185	−0.380855
$551$	11.4494	0.487761
$552$	1.85084	0.0787769
$553$	3.02705	0.128723
$554$	−1.65363	−0.0702560
$555$	14.4229	0.612216
$556$	65.4879	2.77730
$557$	24.7365	1.04812	0.524060	−	0.851682i	$-0.324417\pi$
$557$	24.7365	1.04812	0.524060	+	0.851682i	$0.324417\pi$
$558$	7.38771	0.312747
$559$	5.29551	0.223976
$560$	−13.6413	−0.576451
$561$	4.67513	0.197384
$562$	36.2991	1.53119
$563$	−13.3070	−0.560825	−0.280413	−	0.959880i	$-0.590471\pi$
$563$	−13.3070	−0.560825	−0.280413	+	0.959880i	$0.590471\pi$
$564$	−10.8442	−0.456623
$565$	3.45839	0.145496
$566$	54.4040	2.28677
$567$	11.7163	0.492039
$568$	4.62024	0.193861
$569$	−4.32511	−0.181318	−0.0906589	−	0.995882i	$-0.528897\pi$
$569$	−4.32511	−0.181318	−0.0906589	+	0.995882i	$0.528897\pi$
$570$	−17.9460	−0.751677
$571$	29.1181	1.21855	0.609277	−	0.792958i	$-0.291460\pi$
$571$	29.1181	1.21855	0.609277	+	0.792958i	$0.291460\pi$
$572$	−35.9176	−1.50179
$573$	32.3243	1.35037
$574$	−43.7880	−1.82767
$575$	0.315035	0.0131379
$576$	12.5886	0.524525
$577$	40.9318	1.70401	0.852007	−	0.523530i	$-0.175385\pi$
$577$	40.9318	1.70401	0.852007	+	0.523530i	$0.175385\pi$
$578$	−2.42937	−0.101048
$579$	−28.4612	−1.18281
$580$	−7.68990	−0.319306
$581$	58.9512	2.44571
$582$	−27.4614	−1.13831
$583$	11.8089	0.489073
$584$	58.3623	2.41505
$585$	3.46286	0.143172
$586$	−41.5100	−1.71476
$587$	9.75288	0.402545	0.201272	−	0.979535i	$-0.435492\pi$
$587$	9.75288	0.402545	0.201272	+	0.979535i	$0.435492\pi$
$588$	−44.1773	−1.82184
$589$	−12.7733	−0.526313
$590$	−16.4835	−0.678615
$591$	13.4395	0.552827
$592$	−38.7979	−1.59459
$593$	0.440354	0.0180832	0.00904159	−	0.999959i	$-0.497122\pi$
$593$	0.440354	0.0180832	0.00904159	+	0.999959i	$0.497122\pi$
$594$	−49.7812	−2.04255
$595$	3.98798	0.163491
$596$	−23.6146	−0.967293
$597$	19.3036	0.790042
$598$	1.91621	0.0783596
$599$	−20.1581	−0.823637	−0.411818	−	0.911266i	$-0.635106\pi$
$599$	−20.1581	−0.823637	−0.411818	+	0.911266i	$0.635106\pi$
$600$	5.87503	0.239847
$601$	12.4295	0.507011	0.253506	−	0.967334i	$-0.418416\pi$
$601$	12.4295	0.507011	0.253506	+	0.967334i	$0.418416\pi$
$602$	−20.4910	−0.835152
$603$	12.0940	0.492506
$604$	−40.4878	−1.64742
$605$	2.51750	0.102351
$606$	10.7710	0.437540
$607$	42.5471	1.72694	0.863468	−	0.504404i	$-0.168288\pi$
$607$	42.5471	1.72694	0.863468	+	0.504404i	$0.168288\pi$
$608$	−5.40605	−0.219244
$609$	−9.99428	−0.404989
$610$	21.1041	0.854480
$611$	−5.47235	−0.221388
$612$	5.39650	0.218141
$613$	−44.8811	−1.81273	−0.906365	−	0.422496i	$-0.861154\pi$
$613$	−44.8811	−1.81273	−0.906365	+	0.422496i	$0.861154\pi$
$614$	32.5802	1.31483
$615$	5.74717	0.231748
$616$	67.7432	2.72945
$617$	−2.61918	−0.105444	−0.0527221	−	0.998609i	$-0.516790\pi$
$617$	−2.61918	−0.105444	−0.0527221	+	0.998609i	$0.516790\pi$
$618$	3.58216	0.144096
$619$	15.1738	0.609885	0.304943	−	0.952371i	$-0.401363\pi$
$619$	15.1738	0.609885	0.304943	+	0.952371i	$0.401363\pi$
$620$	8.57907	0.344544
$621$	1.75583	0.0704591
$622$	0.320420	0.0128477
$623$	−26.7296	−1.07090
$624$	10.8903	0.435960
$625$	1.00000	0.0400000
$626$	−73.1503	−2.92367
$627$	27.1596	1.08465
$628$	80.8454	3.22608
$629$	11.3424	0.452252
$630$	−13.3996	−0.533852
$631$	−19.4791	−0.775449	−0.387725	−	0.921775i	$-0.626739\pi$
$631$	−19.4791	−0.775449	−0.387725	+	0.921775i	$0.626739\pi$
$632$	3.50696	0.139500
$633$	8.02522	0.318974
$634$	−23.4772	−0.932398
$635$	−10.7869	−0.428065
$636$	−15.9358	−0.631894
$637$	−22.2934	−0.883297
$638$	17.6033	0.696921
$639$	1.38307	0.0547134
$640$	20.2507	0.800481
$641$	40.8595	1.61385	0.806927	−	0.590652i	$-0.201129\pi$
$641$	40.8595	1.61385	0.806927	+	0.590652i	$0.201129\pi$
$642$	−54.7511	−2.16085
$643$	33.6589	1.32738	0.663688	−	0.748009i	$-0.268990\pi$
$643$	33.6589	1.32738	0.663688	+	0.748009i	$0.268990\pi$
$644$	−4.90208	−0.193169
$645$	2.68944	0.105897
$646$	−14.1131	−0.555273
$647$	39.4066	1.54923	0.774616	−	0.632432i	$-0.217943\pi$
$647$	39.4066	1.54923	0.774616	+	0.632432i	$0.217943\pi$
$648$	13.5738	0.533230
$649$	24.9462	0.979224
$650$	6.08252	0.238576
$651$	11.1499	0.436999
$652$	19.5562	0.765879
$653$	5.23312	0.204788	0.102394	−	0.994744i	$-0.467350\pi$
$653$	5.23312	0.204788	0.102394	+	0.994744i	$0.467350\pi$
$654$	54.3859	2.12666
$655$	12.2627	0.479145
$656$	−15.4601	−0.603614
$657$	17.4708	0.681601
$658$	21.1753	0.825500
$659$	23.1726	0.902677	0.451339	−	0.892353i	$-0.350947\pi$
$659$	23.1726	0.902677	0.451339	+	0.892353i	$0.350947\pi$
$660$	−18.2416	−0.710052
$661$	44.1494	1.71721	0.858607	−	0.512635i	$-0.171331\pi$
$661$	44.1494	1.71721	0.858607	+	0.512635i	$0.171331\pi$
$662$	43.6470	1.69639
$663$	−3.18373	−0.123646
$664$	68.2973	2.65045
$665$	23.1677	0.898406
$666$	−38.1104	−1.47675
$667$	−0.620885	−0.0240408
$668$	−7.76895	−0.300590
$669$	−2.03968	−0.0788586
$670$	21.2432	0.820695
$671$	−31.9390	−1.23299
$672$	4.71899	0.182039
$673$	22.3455	0.861354	0.430677	−	0.902506i	$-0.358275\pi$
$673$	22.3455	0.861354	0.430677	+	0.902506i	$0.358275\pi$
$674$	−0.659658	−0.0254091
$675$	5.57345	0.214522
$676$	−26.2642	−1.01016
$677$	−16.2816	−0.625752	−0.312876	−	0.949794i	$-0.601292\pi$
$677$	−16.2816	−0.625752	−0.312876	+	0.949794i	$0.601292\pi$
$678$	10.6835	0.410297
$679$	35.4518	1.36051
$680$	4.62024	0.177178
$681$	11.9438	0.457688
$682$	−19.6387	−0.752006
$683$	33.9755	1.30004	0.650019	−	0.759918i	$-0.274761\pi$
$683$	33.9755	1.30004	0.650019	+	0.759918i	$0.274761\pi$
$684$	31.3504	1.19871
$685$	−6.39130	−0.244199
$686$	18.4466	0.704294
$687$	13.2697	0.506269
$688$	−7.23469	−0.275820
$689$	−8.04174	−0.306366
$690$	0.973190	0.0370487
$691$	0.104224	0.00396488	0.00198244	−	0.999998i	$-0.499369\pi$
$691$	0.104224	0.00396488	0.00198244	+	0.999998i	$0.499369\pi$
$692$	−53.5765	−2.03667
$693$	20.2790	0.770335
$694$	1.04119	0.0395232
$695$	16.7839	0.636649
$696$	−11.5788	−0.438892
$697$	4.51969	0.171195
$698$	50.0361	1.89389
$699$	−20.9973	−0.794190
$700$	−15.5604	−0.588129
$701$	13.7168	0.518075	0.259038	−	0.965867i	$-0.416595\pi$
$701$	13.7168	0.518075	0.259038	+	0.965867i	$0.416595\pi$
$702$	33.9006	1.27950
$703$	65.8925	2.48518
$704$	−33.4642	−1.26123
$705$	−2.77926	−0.104673
$706$	−72.3896	−2.72442
$707$	−13.9049	−0.522949
$708$	−33.6643	−1.26518
$709$	32.3565	1.21517	0.607586	−	0.794254i	$-0.292138\pi$
$709$	32.3565	1.21517	0.607586	+	0.794254i	$0.292138\pi$
$710$	2.42937	0.0911725
$711$	1.04981	0.0393710
$712$	−30.9673	−1.16055
$713$	0.692677	0.0259409
$714$	12.3195	0.461045
$715$	−9.20532	−0.344259
$716$	52.0348	1.94463
$717$	11.3150	0.422567
$718$	43.0521	1.60669
$719$	28.7133	1.07082	0.535412	−	0.844591i	$-0.320156\pi$
$719$	28.7133	1.07082	0.535412	+	0.844591i	$0.320156\pi$
$720$	−4.73094	−0.176312
$721$	−4.62445	−0.172223
$722$	−35.8305	−1.33347
$723$	12.4597	0.463382
$724$	64.2883	2.38926
$725$	−1.97085	−0.0731954
$726$	7.77694	0.288629
$727$	46.2823	1.71652	0.858258	−	0.513218i	$-0.171547\pi$
$727$	46.2823	1.71652	0.858258	+	0.513218i	$0.171547\pi$
$728$	−46.1326	−1.70979
$729$	25.3247	0.937951
$730$	30.6875	1.13580
$731$	2.11503	0.0782273
$732$	43.1010	1.59306
$733$	10.2472	0.378488	0.189244	−	0.981930i	$-0.439396\pi$
$733$	10.2472	0.378488	0.189244	+	0.981930i	$0.439396\pi$
$734$	−53.9620	−1.99177
$735$	−11.3222	−0.417626
$736$	0.293163	0.0108061
$737$	−32.1495	−1.18424
$738$	−15.1861	−0.559008
$739$	19.7132	0.725163	0.362581	−	0.931952i	$-0.381896\pi$
$739$	19.7132	0.725163	0.362581	+	0.931952i	$0.381896\pi$
$740$	−44.2562	−1.62689
$741$	−18.4955	−0.679449
$742$	31.1176	1.14236
$743$	−38.6227	−1.41693	−0.708466	−	0.705745i	$-0.750612\pi$
$743$	−38.6227	−1.41693	−0.708466	+	0.705745i	$0.750612\pi$
$744$	12.9176	0.473582
$745$	−6.05220	−0.221735
$746$	−74.0122	−2.70978
$747$	20.4448	0.748037
$748$	−14.3455	−0.524524
$749$	70.6818	2.58266
$750$	3.08915	0.112800
$751$	−7.83646	−0.285957	−0.142978	−	0.989726i	$-0.545668\pi$
$751$	−7.83646	−0.285957	−0.142978	+	0.989726i	$0.545668\pi$
$752$	7.47629	0.272632
$753$	6.46631	0.235645
$754$	−11.9877	−0.436567
$755$	−10.3766	−0.377644
$756$	−86.7252	−3.15417
$757$	20.4472	0.743165	0.371583	−	0.928400i	$-0.378815\pi$
$757$	20.4472	0.743165	0.371583	+	0.928400i	$0.378815\pi$
$758$	61.4821	2.23313
$759$	−1.47283	−0.0534603
$760$	26.8407	0.973616
$761$	22.9474	0.831844	0.415922	−	0.909400i	$-0.363459\pi$
$761$	22.9474	0.831844	0.415922	+	0.909400i	$0.363459\pi$
$762$	−33.3224	−1.20714
$763$	−70.2103	−2.54178
$764$	−99.1863	−3.58843
$765$	1.38307	0.0500050
$766$	−83.3597	−3.01191
$767$	−16.9882	−0.613408
$768$	39.4098	1.42208
$769$	4.10090	0.147882	0.0739411	−	0.997263i	$-0.476442\pi$
$769$	4.10090	0.147882	0.0739411	+	0.997263i	$0.476442\pi$
$770$	35.6201	1.28366
$771$	26.1584	0.942073
$772$	87.3325	3.14317
$773$	14.5582	0.523622	0.261811	−	0.965119i	$-0.415680\pi$
$773$	14.5582	0.523622	0.261811	+	0.965119i	$0.415680\pi$
$774$	−7.10649	−0.255437
$775$	2.19873	0.0789807
$776$	41.0723	1.47441
$777$	−57.5181	−2.06345
$778$	−18.2161	−0.653079
$779$	26.2566	0.940740
$780$	12.4224	0.444792
$781$	−3.67662	−0.131560
$782$	0.765336	0.0273683
$783$	−10.9844	−0.392551
$784$	30.4571	1.08775
$785$	20.7199	0.739525
$786$	37.8814	1.35119
$787$	−41.5895	−1.48251	−0.741254	−	0.671225i	$-0.765768\pi$
$787$	−41.5895	−1.48251	−0.741254	+	0.671225i	$0.765768\pi$
$788$	−41.2387	−1.46907
$789$	−31.6407	−1.12644
$790$	1.84400	0.0656064
$791$	−13.7920	−0.490387
$792$	23.4940	0.834823
$793$	21.7502	0.772374
$794$	56.4343	2.00278
$795$	−4.08418	−0.144851
$796$	−59.2325	−2.09944
$797$	12.8541	0.455316	0.227658	−	0.973741i	$-0.426893\pi$
$797$	12.8541	0.455316	0.227658	+	0.973741i	$0.426893\pi$
$798$	71.5685	2.53350
$799$	−2.18566	−0.0773232
$800$	0.930573	0.0329007
$801$	−9.27008	−0.327542
$802$	−74.2470	−2.62175
$803$	−46.4426	−1.63892
$804$	43.3850	1.53007
$805$	−1.25635	−0.0442807
$806$	13.3738	0.471073
$807$	14.0717	0.495347
$808$	−16.1094	−0.566728
$809$	−0.328729	−0.0115575	−0.00577875	−	0.999983i	$-0.501839\pi$
$809$	−0.328729	−0.0115575	−0.00577875	+	0.999983i	$0.501839\pi$
$810$	7.13724	0.250777
$811$	17.8007	0.625067	0.312534	−	0.949907i	$-0.398822\pi$
$811$	17.8007	0.625067	0.312534	+	0.949907i	$0.398822\pi$
$812$	30.6672	1.07621
$813$	32.8518	1.15216
$814$	101.309	3.55087
$815$	5.01205	0.175565
$816$	4.34959	0.152266
$817$	12.2870	0.429869
$818$	−8.90225	−0.311260
$819$	−13.8098	−0.482555
$820$	−17.6350	−0.615842
$821$	−34.7271	−1.21199	−0.605993	−	0.795470i	$-0.707224\pi$
$821$	−34.7271	−1.21199	−0.605993	+	0.795470i	$0.707224\pi$
$822$	−19.7437	−0.688640
$823$	38.6959	1.34885	0.674427	−	0.738341i	$-0.264391\pi$
$823$	38.6959	1.34885	0.674427	+	0.738341i	$0.264391\pi$
$824$	−5.35761	−0.186641
$825$	−4.67513	−0.162767
$826$	65.7359	2.28725
$827$	−30.8123	−1.07145	−0.535724	−	0.844393i	$-0.679961\pi$
$827$	−30.8123	−1.07145	−0.535724	+	0.844393i	$0.679961\pi$
$828$	−1.70009	−0.0590821
$829$	−35.9839	−1.24977	−0.624886	−	0.780716i	$-0.714855\pi$
$829$	−35.9839	−1.24977	−0.624886	+	0.780716i	$0.714855\pi$
$830$	35.9114	1.24650
$831$	−0.865546	−0.0300255
$832$	22.7889	0.790063
$833$	−8.90401	−0.308506
$834$	51.8479	1.79535
$835$	−1.99111	−0.0689051
$836$	−83.3386	−2.88233
$837$	12.2545	0.423578
$838$	89.2760	3.08399
$839$	−6.56823	−0.226761	−0.113380	−	0.993552i	$-0.536168\pi$
$839$	−6.56823	−0.226761	−0.113380	+	0.993552i	$0.536168\pi$
$840$	−23.4295	−0.808395
$841$	−25.1158	−0.866061
$842$	−72.6523	−2.50376
$843$	18.9998	0.654387
$844$	−24.6252	−0.847634
$845$	−6.73125	−0.231562
$846$	7.34380	0.252485
$847$	−10.0398	−0.344970
$848$	10.9866	0.377281
$849$	28.4763	0.977303
$850$	2.42937	0.0833266
$851$	−3.57326	−0.122490
$852$	4.96151	0.169978
$853$	46.8920	1.60555	0.802776	−	0.596281i	$-0.203355\pi$
$853$	46.8920	1.60555	0.802776	+	0.596281i	$0.203355\pi$
$854$	−84.1628	−2.87999
$855$	8.03479	0.274784
$856$	81.8877	2.79886
$857$	−20.5622	−0.702392	−0.351196	−	0.936302i	$-0.614225\pi$
$857$	−20.5622	−0.702392	−0.351196	+	0.936302i	$0.614225\pi$
$858$	−28.4366	−0.970809
$859$	−40.8446	−1.39360	−0.696800	−	0.717266i	$-0.745393\pi$
$859$	−40.8446	−1.39360	−0.696800	+	0.717266i	$0.745393\pi$
$860$	−8.25249	−0.281408
$861$	−22.9196	−0.781098
$862$	33.7686	1.15016
$863$	4.41429	0.150264	0.0751321	−	0.997174i	$-0.476062\pi$
$863$	4.41429	0.150264	0.0751321	+	0.997174i	$0.476062\pi$
$864$	5.18650	0.176448
$865$	−13.7311	−0.466873
$866$	−9.56188	−0.324926
$867$	−1.27159	−0.0431853
$868$	−34.2132	−1.16127
$869$	−2.79071	−0.0946684
$870$	−6.08823	−0.206410
$871$	21.8936	0.741835
$872$	−81.3414	−2.75457
$873$	12.2950	0.416123
$874$	4.44613	0.150393
$875$	−3.98798	−0.134818
$876$	62.6732	2.11753
$877$	−31.2970	−1.05682	−0.528412	−	0.848988i	$-0.677212\pi$
$877$	−31.2970	−1.05682	−0.528412	+	0.848988i	$0.677212\pi$
$878$	31.9527	1.07835
$879$	−21.7273	−0.732842
$880$	12.5762	0.423945
$881$	−52.5351	−1.76995	−0.884977	−	0.465635i	$-0.845826\pi$
$881$	−52.5351	−1.76995	−0.884977	+	0.465635i	$0.845826\pi$
$882$	29.9174	1.00737
$883$	41.8291	1.40766	0.703831	−	0.710367i	$-0.251471\pi$
$883$	41.8291	1.40766	0.703831	+	0.710367i	$0.251471\pi$
$884$	9.76919	0.328574
$885$	−8.62783	−0.290021
$886$	15.7559	0.529331
$887$	−30.4898	−1.02375	−0.511874	−	0.859060i	$-0.671049\pi$
$887$	−30.4898	−1.02375	−0.511874	+	0.859060i	$0.671049\pi$
$888$	−66.6371	−2.23619
$889$	43.0180	1.44278
$890$	−16.2829	−0.545805
$891$	−10.8015	−0.361865
$892$	6.25871	0.209557
$893$	−12.6974	−0.424901
$894$	−18.6961	−0.625292
$895$	13.3360	0.445774
$896$	−80.7596	−2.69799
$897$	1.00299	0.0334887
$898$	−38.4242	−1.28223
$899$	−4.33336	−0.144526
$900$	−5.39650	−0.179883
$901$	−3.21188	−0.107003
$902$	40.3692	1.34415
$903$	−10.7255	−0.356921
$904$	−15.9786	−0.531440
$905$	16.4765	0.547696
$906$	−32.0549	−1.06495
$907$	0.577997	0.0191921	0.00959603	−	0.999954i	$-0.496945\pi$
$907$	0.577997	0.0191921	0.00959603	+	0.999954i	$0.496945\pi$
$908$	−36.6493	−1.21625
$909$	−4.82237	−0.159948
$910$	−24.2570	−0.804112
$911$	−5.21004	−0.172616	−0.0863082	−	0.996268i	$-0.527507\pi$
$911$	−5.21004	−0.172616	−0.0863082	+	0.996268i	$0.527507\pi$
$912$	25.2684	0.836721
$913$	−54.3485	−1.79867
$914$	−40.0242	−1.32388
$915$	11.0464	0.365181
$916$	−40.7176	−1.34535
$917$	−48.9036	−1.61494
$918$	13.5400	0.446885
$919$	−29.9307	−0.987323	−0.493661	−	0.869654i	$-0.664342\pi$
$919$	−29.9307	−0.987323	−0.493661	+	0.869654i	$0.664342\pi$
$920$	−1.45554	−0.0479876
$921$	17.0532	0.561922
$922$	−53.1403	−1.75008
$923$	2.50375	0.0824119
$924$	72.7470	2.39320
$925$	−11.3424	−0.372937
$926$	22.6512	0.744366
$927$	−1.60380	−0.0526758
$928$	−1.83402	−0.0602045
$929$	17.8034	0.584112	0.292056	−	0.956401i	$-0.405661\pi$
$929$	17.8034	0.584112	0.292056	+	0.956401i	$0.405661\pi$
$930$	6.79220	0.222725
$931$	−51.7268	−1.69528
$932$	64.4296	2.11046
$933$	0.167715	0.00549075
$934$	65.0005	2.12688
$935$	−3.67662	−0.120238
$936$	−15.9992	−0.522952
$937$	36.2100	1.18293	0.591464	−	0.806331i	$-0.298550\pi$
$937$	36.2100	1.18293	0.591464	+	0.806331i	$0.298550\pi$
$938$	−84.7174	−2.76612
$939$	−38.2885	−1.24950
$940$	8.52808	0.278155
$941$	38.8131	1.26527	0.632636	−	0.774449i	$-0.281973\pi$
$941$	38.8131	1.26527	0.632636	+	0.774449i	$0.281973\pi$
$942$	64.0068	2.08545
$943$	−1.42386	−0.0463672
$944$	23.2091	0.755393
$945$	−22.2268	−0.723038
$946$	18.8912	0.614205
$947$	7.06061	0.229439	0.114719	−	0.993398i	$-0.463403\pi$
$947$	7.06061	0.229439	0.114719	+	0.993398i	$0.463403\pi$
$948$	3.76600	0.122314
$949$	31.6271	1.02666
$950$	14.1131	0.457890
$951$	−12.2885	−0.398481
$952$	−18.4254	−0.597172
$953$	−25.2314	−0.817325	−0.408663	−	0.912686i	$-0.634005\pi$
$953$	−25.2314	−0.817325	−0.408663	+	0.912686i	$0.634005\pi$
$954$	10.7919	0.349400
$955$	−25.4205	−0.822587
$956$	−34.7198	−1.12292
$957$	9.21396	0.297845
$958$	21.8399	0.705614
$959$	25.4884	0.823063
$960$	11.5739	0.373545
$961$	−26.1656	−0.844051
$962$	−68.9906	−2.22435
$963$	24.5131	0.789924
$964$	−38.2323	−1.23138
$965$	22.3825	0.720517
$966$	−3.88106	−0.124871
$967$	−23.0484	−0.741186	−0.370593	−	0.928795i	$-0.620846\pi$
$967$	−23.0484	−0.741186	−0.370593	+	0.928795i	$0.620846\pi$
$968$	−11.6315	−0.373850
$969$	−7.38712	−0.237309
$970$	21.5962	0.693413
$971$	−39.8325	−1.27829	−0.639143	−	0.769088i	$-0.720711\pi$
$971$	−39.8325	−1.27829	−0.639143	+	0.769088i	$0.720711\pi$
$972$	−50.6635	−1.62503
$973$	−66.9339	−2.14580
$974$	54.4781	1.74559
$975$	3.18373	0.101961
$976$	−29.7150	−0.951155
$977$	−25.0608	−0.801765	−0.400882	−	0.916130i	$-0.631296\pi$
$977$	−25.0608	−0.801765	−0.400882	+	0.916130i	$0.631296\pi$
$978$	15.4830	0.495091
$979$	24.6426	0.787582
$980$	34.7419	1.10979
$981$	−24.3496	−0.777423
$982$	−82.7164	−2.63959
$983$	−14.5345	−0.463579	−0.231790	−	0.972766i	$-0.574458\pi$
$983$	−14.5345	−0.463579	−0.231790	+	0.972766i	$0.574458\pi$
$984$	−26.5533	−0.846488
$985$	−10.5691	−0.336759
$986$	−4.78791	−0.152478
$987$	11.0836	0.352796
$988$	56.7530	1.80555
$989$	−0.666309	−0.0211874
$990$	12.3534	0.392616
$991$	−25.8689	−0.821753	−0.410876	−	0.911691i	$-0.634777\pi$
$991$	−25.8689	−0.821753	−0.410876	+	0.911691i	$0.634777\pi$
$992$	2.04608	0.0649630
$993$	22.8458	0.724990
$994$	−9.68828	−0.307294
$995$	−15.1807	−0.481261
$996$	73.3420	2.32393
$997$	7.04268	0.223044	0.111522	−	0.993762i	$-0.464427\pi$
$997$	7.04268	0.223044	0.111522	+	0.993762i	$0.464427\pi$
$998$	−73.9061	−2.33946
$999$	−63.2164	−2.00008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.8	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-2.42937 q^{2} -1.27159 q^{3} +3.90183 q^{4} +1.00000 q^{5} +3.08915 q^{6} -3.98798 q^{7} -4.62024 q^{8} -1.38307 q^{9} +O(q^{10})\)	\(q-2.42937 q^{2} -1.27159 q^{3} +3.90183 q^{4} +1.00000 q^{5} +3.08915 q^{6} -3.98798 q^{7} -4.62024 q^{8} -1.38307 q^{9} -2.42937 q^{10} +3.67662 q^{11} -4.96151 q^{12} -2.50375 q^{13} +9.68828 q^{14} -1.27159 q^{15} +3.42060 q^{16} -1.00000 q^{17} +3.35999 q^{18} -5.80938 q^{19} +3.90183 q^{20} +5.07106 q^{21} -8.93185 q^{22} +0.315035 q^{23} +5.87503 q^{24} +1.00000 q^{25} +6.08252 q^{26} +5.57345 q^{27} -15.5604 q^{28} -1.97085 q^{29} +3.08915 q^{30} +2.19873 q^{31} +0.930573 q^{32} -4.67513 q^{33} +2.42937 q^{34} -3.98798 q^{35} -5.39650 q^{36} -11.3424 q^{37} +14.1131 q^{38} +3.18373 q^{39} -4.62024 q^{40} -4.51969 q^{41} -12.3195 q^{42} -2.11503 q^{43} +14.3455 q^{44} -1.38307 q^{45} -0.765336 q^{46} +2.18566 q^{47} -4.34959 q^{48} +8.90401 q^{49} -2.42937 q^{50} +1.27159 q^{51} -9.76919 q^{52} +3.21188 q^{53} -13.5400 q^{54} +3.67662 q^{55} +18.4254 q^{56} +7.38712 q^{57} +4.78791 q^{58} +6.78510 q^{59} -4.96151 q^{60} -8.68708 q^{61} -5.34152 q^{62} +5.51566 q^{63} -9.10191 q^{64} -2.50375 q^{65} +11.3576 q^{66} -8.74432 q^{67} -3.90183 q^{68} -0.400594 q^{69} +9.68828 q^{70} -1.00000 q^{71} +6.39012 q^{72} -12.6319 q^{73} +27.5549 q^{74} -1.27159 q^{75} -22.6672 q^{76} -14.6623 q^{77} -7.73445 q^{78} -0.759044 q^{79} +3.42060 q^{80} -2.93790 q^{81} +10.9800 q^{82} -14.7822 q^{83} +19.7864 q^{84} -1.00000 q^{85} +5.13819 q^{86} +2.50610 q^{87} -16.9868 q^{88} +6.70253 q^{89} +3.35999 q^{90} +9.98491 q^{91} +1.22921 q^{92} -2.79587 q^{93} -5.30978 q^{94} -5.80938 q^{95} -1.18330 q^{96} -8.88965 q^{97} -21.6311 q^{98} -5.08502 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 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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