LMFDB - Embedded newform 6035.2.a.g.1.19

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:	$58$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-1.22809 q^{2} +1.74628 q^{3} -0.491793 q^{4} +1.00000 q^{5} -2.14460 q^{6} +4.49008 q^{7} +3.06015 q^{8} +0.0495068 q^{9} +O(q^{10})$	\(q-1.22809 q^{2} +1.74628 q^{3} -0.491793 q^{4} +1.00000 q^{5} -2.14460 q^{6} +4.49008 q^{7} +3.06015 q^{8} +0.0495068 q^{9} -1.22809 q^{10} +3.79225 q^{11} -0.858810 q^{12} +0.918173 q^{13} -5.51423 q^{14} +1.74628 q^{15} -2.77455 q^{16} +1.00000 q^{17} -0.0607989 q^{18} +4.05614 q^{19} -0.491793 q^{20} +7.84096 q^{21} -4.65723 q^{22} +0.887348 q^{23} +5.34389 q^{24} +1.00000 q^{25} -1.12760 q^{26} -5.15240 q^{27} -2.20819 q^{28} -3.54752 q^{29} -2.14460 q^{30} -4.76166 q^{31} -2.71289 q^{32} +6.62235 q^{33} -1.22809 q^{34} +4.49008 q^{35} -0.0243471 q^{36} -1.86425 q^{37} -4.98130 q^{38} +1.60339 q^{39} +3.06015 q^{40} +3.10500 q^{41} -9.62941 q^{42} +12.0774 q^{43} -1.86500 q^{44} +0.0495068 q^{45} -1.08974 q^{46} +6.08988 q^{47} -4.84516 q^{48} +13.1609 q^{49} -1.22809 q^{50} +1.74628 q^{51} -0.451551 q^{52} +6.14926 q^{53} +6.32761 q^{54} +3.79225 q^{55} +13.7403 q^{56} +7.08317 q^{57} +4.35668 q^{58} +6.26327 q^{59} -0.858810 q^{60} -10.1251 q^{61} +5.84775 q^{62} +0.222290 q^{63} +8.88079 q^{64} +0.918173 q^{65} -8.13285 q^{66} -0.712305 q^{67} -0.491793 q^{68} +1.54956 q^{69} -5.51423 q^{70} +1.00000 q^{71} +0.151498 q^{72} +10.0495 q^{73} +2.28946 q^{74} +1.74628 q^{75} -1.99478 q^{76} +17.0275 q^{77} -1.96911 q^{78} -3.23450 q^{79} -2.77455 q^{80} -9.14607 q^{81} -3.81322 q^{82} -11.1906 q^{83} -3.85613 q^{84} +1.00000 q^{85} -14.8322 q^{86} -6.19498 q^{87} +11.6049 q^{88} -0.418157 q^{89} -0.0607989 q^{90} +4.12267 q^{91} -0.436391 q^{92} -8.31521 q^{93} -7.47893 q^{94} +4.05614 q^{95} -4.73748 q^{96} -12.5160 q^{97} -16.1627 q^{98} +0.187742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) $ 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * 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 $

$2$	−1.22809	−0.868391	−0.434196	−	0.900819i	$-0.642967\pi$
$2$	−1.22809	−0.868391	−0.434196	+	0.900819i	$0.642967\pi$
$3$	1.74628	1.00822	0.504109	−	0.863640i	$-0.331821\pi$
$3$	1.74628	1.00822	0.504109	+	0.863640i	$0.331821\pi$
$4$	−0.491793	−0.245896
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.14460	−0.875527
$7$	4.49008	1.69709	0.848546	−	0.529121i	$-0.177478\pi$
$7$	4.49008	1.69709	0.848546	+	0.529121i	$0.177478\pi$
$8$	3.06015	1.08193
$9$	0.0495068	0.0165023
$10$	−1.22809	−0.388356
$11$	3.79225	1.14341	0.571704	−	0.820460i	$-0.306283\pi$
$11$	3.79225	1.14341	0.571704	+	0.820460i	$0.306283\pi$
$12$	−0.858810	−0.247917
$13$	0.918173	0.254655	0.127328	−	0.991861i	$-0.459360\pi$
$13$	0.918173	0.254655	0.127328	+	0.991861i	$0.459360\pi$
$14$	−5.51423	−1.47374
$15$	1.74628	0.450889
$16$	−2.77455	−0.693639
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0607989	−0.0143304
$19$	4.05614	0.930542	0.465271	−	0.885168i	$-0.345957\pi$
$19$	4.05614	0.930542	0.465271	+	0.885168i	$0.345957\pi$
$20$	−0.491793	−0.109968
$21$	7.84096	1.71104
$22$	−4.65723	−0.992926
$23$	0.887348	0.185025	0.0925124	−	0.995712i	$-0.470510\pi$
$23$	0.887348	0.185025	0.0925124	+	0.995712i	$0.470510\pi$
$24$	5.34389	1.09082
$25$	1.00000	0.200000
$26$	−1.12760	−0.221141
$27$	−5.15240	−0.991579
$28$	−2.20819	−0.417309
$29$	−3.54752	−0.658759	−0.329379	−	0.944198i	$-0.606839\pi$
$29$	−3.54752	−0.658759	−0.329379	+	0.944198i	$0.606839\pi$
$30$	−2.14460	−0.391548
$31$	−4.76166	−0.855219	−0.427609	−	0.903964i	$-0.640644\pi$
$31$	−4.76166	−0.855219	−0.427609	+	0.903964i	$0.640644\pi$
$32$	−2.71289	−0.479576
$33$	6.62235	1.15280
$34$	−1.22809	−0.210616
$35$	4.49008	0.758963
$36$	−0.0243471	−0.00405785
$37$	−1.86425	−0.306480	−0.153240	−	0.988189i	$-0.548971\pi$
$37$	−1.86425	−0.306480	−0.153240	+	0.988189i	$0.548971\pi$
$38$	−4.98130	−0.808074
$39$	1.60339	0.256748
$40$	3.06015	0.483852
$41$	3.10500	0.484919	0.242460	−	0.970161i	$-0.422046\pi$
$41$	3.10500	0.484919	0.242460	+	0.970161i	$0.422046\pi$
$42$	−9.62941	−1.48585
$43$	12.0774	1.84179	0.920895	−	0.389811i	$-0.127460\pi$
$43$	12.0774	1.84179	0.920895	+	0.389811i	$0.127460\pi$
$44$	−1.86500	−0.281160
$45$	0.0495068	0.00738004
$46$	−1.08974	−0.160674
$47$	6.08988	0.888301	0.444150	−	0.895952i	$-0.353506\pi$
$47$	6.08988	0.888301	0.444150	+	0.895952i	$0.353506\pi$
$48$	−4.84516	−0.699339
$49$	13.1609	1.88012
$50$	−1.22809	−0.173678
$51$	1.74628	0.244529
$52$	−0.451551	−0.0626188
$53$	6.14926	0.844665	0.422333	−	0.906441i	$-0.361211\pi$
$53$	6.14926	0.844665	0.422333	+	0.906441i	$0.361211\pi$
$54$	6.32761	0.861079
$55$	3.79225	0.511348
$56$	13.7403	1.83613
$57$	7.08317	0.938188
$58$	4.35668	0.572060
$59$	6.26327	0.815409	0.407704	−	0.913114i	$-0.366329\pi$
$59$	6.26327	0.815409	0.407704	+	0.913114i	$0.366329\pi$
$60$	−0.858810	−0.110872
$61$	−10.1251	−1.29639	−0.648194	−	0.761476i	$-0.724475\pi$
$61$	−10.1251	−1.29639	−0.648194	+	0.761476i	$0.724475\pi$
$62$	5.84775	0.742665
$63$	0.222290	0.0280059
$64$	8.88079	1.11010
$65$	0.918173	0.113885
$66$	−8.13285	−1.00108
$67$	−0.712305	−0.0870219	−0.0435110	−	0.999053i	$-0.513854\pi$
$67$	−0.712305	−0.0870219	−0.0435110	+	0.999053i	$0.513854\pi$
$68$	−0.491793	−0.0596386
$69$	1.54956	0.186545
$70$	−5.51423	−0.659077
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	0.151498	0.0178542
$73$	10.0495	1.17620	0.588100	−	0.808788i	$-0.299876\pi$
$73$	10.0495	1.17620	0.588100	+	0.808788i	$0.299876\pi$
$74$	2.28946	0.266145
$75$	1.74628	0.201643
$76$	−1.99478	−0.228817
$77$	17.0275	1.94047
$78$	−1.96911	−0.222958
$79$	−3.23450	−0.363910	−0.181955	−	0.983307i	$-0.558243\pi$
$79$	−3.23450	−0.363910	−0.181955	+	0.983307i	$0.558243\pi$
$80$	−2.77455	−0.310205
$81$	−9.14607	−1.01623
$82$	−3.81322	−0.421100
$83$	−11.1906	−1.22832	−0.614161	−	0.789180i	$-0.710506\pi$
$83$	−11.1906	−1.22832	−0.614161	+	0.789180i	$0.710506\pi$
$84$	−3.85613	−0.420738
$85$	1.00000	0.108465
$86$	−14.8322	−1.59939
$87$	−6.19498	−0.664172
$88$	11.6049	1.23708
$89$	−0.418157	−0.0443246	−0.0221623	−	0.999754i	$-0.507055\pi$
$89$	−0.418157	−0.0443246	−0.0221623	+	0.999754i	$0.507055\pi$
$90$	−0.0607989	−0.00640876
$91$	4.12267	0.432174
$92$	−0.436391	−0.0454969
$93$	−8.31521	−0.862247
$94$	−7.47893	−0.771393
$95$	4.05614	0.416151
$96$	−4.73748	−0.483517
$97$	−12.5160	−1.27081	−0.635403	−	0.772181i	$-0.719166\pi$
$97$	−12.5160	−1.27081	−0.635403	+	0.772181i	$0.719166\pi$
$98$	−16.1627	−1.63268
$99$	0.187742	0.0188688
$100$	−0.491793	−0.0491793
$101$	−5.35220	−0.532563	−0.266282	−	0.963895i	$-0.585795\pi$
$101$	−5.35220	−0.532563	−0.266282	+	0.963895i	$0.585795\pi$
$102$	−2.14460	−0.212347
$103$	1.37664	0.135644	0.0678222	−	0.997697i	$-0.478395\pi$
$103$	1.37664	0.135644	0.0678222	+	0.997697i	$0.478395\pi$
$104$	2.80975	0.275518
$105$	7.84096	0.765199
$106$	−7.55185	−0.733500
$107$	3.35161	0.324013	0.162006	−	0.986790i	$-0.448203\pi$
$107$	3.35161	0.324013	0.162006	+	0.986790i	$0.448203\pi$
$108$	2.53391	0.243826
$109$	−4.44210	−0.425476	−0.212738	−	0.977109i	$-0.568238\pi$
$109$	−4.44210	−0.425476	−0.212738	+	0.977109i	$0.568238\pi$
$110$	−4.65723	−0.444050
$111$	−3.25550	−0.308998
$112$	−12.4580	−1.17717
$113$	−0.286808	−0.0269806	−0.0134903	−	0.999909i	$-0.504294\pi$
$113$	−0.286808	−0.0269806	−0.0134903	+	0.999909i	$0.504294\pi$
$114$	−8.69877	−0.814715
$115$	0.887348	0.0827456
$116$	1.74465	0.161986
$117$	0.0454558	0.00420239
$118$	−7.69187	−0.708094
$119$	4.49008	0.411605
$120$	5.34389	0.487828
$121$	3.38120	0.307381
$122$	12.4346	1.12577
$123$	5.42221	0.488904
$124$	2.34175	0.210295
$125$	1.00000	0.0894427
$126$	−0.272992	−0.0243201
$127$	17.5825	1.56020	0.780099	−	0.625656i	$-0.215168\pi$
$127$	17.5825	1.56020	0.780099	+	0.625656i	$0.215168\pi$
$128$	−5.48063	−0.484424
$129$	21.0906	1.85692
$130$	−1.12760	−0.0988971
$131$	−15.7048	−1.37214	−0.686069	−	0.727536i	$-0.740665\pi$
$131$	−15.7048	−1.37214	−0.686069	+	0.727536i	$0.740665\pi$
$132$	−3.25682	−0.283470
$133$	18.2124	1.57922
$134$	0.874775	0.0755691
$135$	−5.15240	−0.443448
$136$	3.06015	0.262406
$137$	−11.8639	−1.01360	−0.506802	−	0.862063i	$-0.669172\pi$
$137$	−11.8639	−1.01360	−0.506802	+	0.862063i	$0.669172\pi$
$138$	−1.90300	−0.161994
$139$	1.97305	0.167352	0.0836758	−	0.996493i	$-0.473334\pi$
$139$	1.97305	0.167352	0.0836758	+	0.996493i	$0.473334\pi$
$140$	−2.20819	−0.186626
$141$	10.6347	0.895600
$142$	−1.22809	−0.103059
$143$	3.48195	0.291175
$144$	−0.137359	−0.0114466
$145$	−3.54752	−0.294606
$146$	−12.3416	−1.02140
$147$	22.9826	1.89557
$148$	0.916822	0.0753623
$149$	3.22926	0.264552	0.132276	−	0.991213i	$-0.457772\pi$
$149$	3.22926	0.264552	0.132276	+	0.991213i	$0.457772\pi$
$150$	−2.14460	−0.175105
$151$	6.55583	0.533506	0.266753	−	0.963765i	$-0.414049\pi$
$151$	6.55583	0.533506	0.266753	+	0.963765i	$0.414049\pi$
$152$	12.4124	1.00678
$153$	0.0495068	0.00400239
$154$	−20.9114	−1.68509
$155$	−4.76166	−0.382466
$156$	−0.788536	−0.0631334
$157$	−3.80094	−0.303348	−0.151674	−	0.988431i	$-0.548466\pi$
$157$	−3.80094	−0.303348	−0.151674	+	0.988431i	$0.548466\pi$
$158$	3.97227	0.316017
$159$	10.7383	0.851606
$160$	−2.71289	−0.214473
$161$	3.98427	0.314004
$162$	11.2322	0.882485
$163$	8.87082	0.694816	0.347408	−	0.937714i	$-0.387062\pi$
$163$	8.87082	0.694816	0.347408	+	0.937714i	$0.387062\pi$
$164$	−1.52702	−0.119240
$165$	6.62235	0.515549
$166$	13.7430	1.06667
$167$	−12.5725	−0.972893	−0.486446	−	0.873710i	$-0.661707\pi$
$167$	−12.5725	−0.972893	−0.486446	+	0.873710i	$0.661707\pi$
$168$	23.9945	1.85122
$169$	−12.1570	−0.935151
$170$	−1.22809	−0.0941903
$171$	0.200806	0.0153560
$172$	−5.93959	−0.452889
$173$	13.4369	1.02159	0.510793	−	0.859704i	$-0.329352\pi$
$173$	13.4369	1.02159	0.510793	+	0.859704i	$0.329352\pi$
$174$	7.60800	0.576761
$175$	4.49008	0.339418
$176$	−10.5218	−0.793112
$177$	10.9375	0.822109
$178$	0.513535	0.0384911
$179$	−25.5236	−1.90772	−0.953862	−	0.300245i	$-0.902932\pi$
$179$	−25.5236	−1.90772	−0.953862	+	0.300245i	$0.902932\pi$
$180$	−0.0243471	−0.00181472
$181$	−15.6896	−1.16620	−0.583099	−	0.812401i	$-0.698160\pi$
$181$	−15.6896	−1.16620	−0.583099	+	0.812401i	$0.698160\pi$
$182$	−5.06302	−0.375296
$183$	−17.6813	−1.30704
$184$	2.71542	0.200183
$185$	−1.86425	−0.137062
$186$	10.2118	0.748768
$187$	3.79225	0.277317
$188$	−2.99496	−0.218430
$189$	−23.1347	−1.68280
$190$	−4.98130	−0.361382
$191$	−5.98397	−0.432985	−0.216492	−	0.976284i	$-0.569462\pi$
$191$	−5.98397	−0.432985	−0.216492	+	0.976284i	$0.569462\pi$
$192$	15.5084	1.11922
$193$	−18.1936	−1.30961	−0.654803	−	0.755800i	$-0.727248\pi$
$193$	−18.1936	−1.30961	−0.654803	+	0.755800i	$0.727248\pi$
$194$	15.3708	1.10356
$195$	1.60339	0.114821
$196$	−6.47241	−0.462315
$197$	16.0812	1.14573	0.572867	−	0.819648i	$-0.305831\pi$
$197$	16.0812	1.14573	0.572867	+	0.819648i	$0.305831\pi$
$198$	−0.230565	−0.0163855
$199$	0.225119	0.0159583	0.00797913	−	0.999968i	$-0.497460\pi$
$199$	0.225119	0.0159583	0.00797913	+	0.999968i	$0.497460\pi$
$200$	3.06015	0.216385
$201$	−1.24389	−0.0877370
$202$	6.57298	0.462474
$203$	−15.9287	−1.11797
$204$	−0.858810	−0.0601287
$205$	3.10500	0.216863
$206$	−1.69064	−0.117792
$207$	0.0439298	0.00305333
$208$	−2.54752	−0.176639
$209$	15.3819	1.06399
$210$	−9.62941	−0.664493
$211$	12.0094	0.826763	0.413381	−	0.910558i	$-0.364348\pi$
$211$	12.0094	0.826763	0.413381	+	0.910558i	$0.364348\pi$
$212$	−3.02416	−0.207700
$213$	1.74628	0.119653
$214$	−4.11609	−0.281370
$215$	12.0774	0.823674
$216$	−15.7671	−1.07282
$217$	−21.3802	−1.45139
$218$	5.45530	0.369479
$219$	17.5492	1.18586
$220$	−1.86500	−0.125738
$221$	0.918173	0.0617630
$222$	3.99805	0.268332
$223$	21.0312	1.40836	0.704178	−	0.710023i	$-0.251316\pi$
$223$	21.0312	1.40836	0.704178	+	0.710023i	$0.251316\pi$
$224$	−12.1811	−0.813885
$225$	0.0495068	0.00330045
$226$	0.352226	0.0234297
$227$	15.0126	0.996424	0.498212	−	0.867055i	$-0.333990\pi$
$227$	15.0126	0.996424	0.498212	+	0.867055i	$0.333990\pi$
$228$	−3.48345	−0.230697
$229$	−8.97407	−0.593023	−0.296512	−	0.955029i	$-0.595823\pi$
$229$	−8.97407	−0.593023	−0.296512	+	0.955029i	$0.595823\pi$
$230$	−1.08974	−0.0718556
$231$	29.7349	1.95641
$232$	−10.8559	−0.712728
$233$	2.85136	0.186799	0.0933995	−	0.995629i	$-0.470227\pi$
$233$	2.85136	0.186799	0.0933995	+	0.995629i	$0.470227\pi$
$234$	−0.0558239	−0.00364932
$235$	6.08988	0.397260
$236$	−3.08023	−0.200506
$237$	−5.64836	−0.366901
$238$	−5.51423	−0.357435
$239$	−27.5798	−1.78399	−0.891996	−	0.452043i	$-0.850695\pi$
$239$	−27.5798	−1.78399	−0.891996	+	0.452043i	$0.850695\pi$
$240$	−4.84516	−0.312754
$241$	−18.6441	−1.20097	−0.600485	−	0.799636i	$-0.705026\pi$
$241$	−18.6441	−1.20097	−0.600485	+	0.799636i	$0.705026\pi$
$242$	−4.15242	−0.266927
$243$	−0.514438	−0.0330012
$244$	4.97945	0.318777
$245$	13.1609	0.840816
$246$	−6.65897	−0.424560
$247$	3.72424	0.236967
$248$	−14.5714	−0.925283
$249$	−19.5419	−1.23842
$250$	−1.22809	−0.0776713
$251$	−15.5719	−0.982888	−0.491444	−	0.870909i	$-0.663531\pi$
$251$	−15.5719	−0.982888	−0.491444	+	0.870909i	$0.663531\pi$
$252$	−0.109320	−0.00688654
$253$	3.36505	0.211559
$254$	−21.5930	−1.35486
$255$	1.74628	0.109357
$256$	−11.0309	−0.689429
$257$	5.75944	0.359264	0.179632	−	0.983734i	$-0.442509\pi$
$257$	5.75944	0.359264	0.179632	+	0.983734i	$0.442509\pi$
$258$	−25.9012	−1.61254
$259$	−8.37062	−0.520125
$260$	−0.451551	−0.0280040
$261$	−0.175627	−0.0108710
$262$	19.2870	1.19155
$263$	25.6431	1.58122	0.790612	−	0.612318i	$-0.209763\pi$
$263$	25.6431	1.58122	0.790612	+	0.612318i	$0.209763\pi$
$264$	20.2654	1.24725
$265$	6.14926	0.377746
$266$	−22.3665	−1.37138
$267$	−0.730221	−0.0446888
$268$	0.350306	0.0213984
$269$	3.70012	0.225600	0.112800	−	0.993618i	$-0.464018\pi$
$269$	3.70012	0.225600	0.112800	+	0.993618i	$0.464018\pi$
$270$	6.32761	0.385086
$271$	19.8140	1.20361	0.601806	−	0.798642i	$-0.294448\pi$
$271$	19.8140	1.20361	0.601806	+	0.798642i	$0.294448\pi$
$272$	−2.77455	−0.168232
$273$	7.19936	0.435725
$274$	14.5700	0.880205
$275$	3.79225	0.228682
$276$	−0.762063	−0.0458708
$277$	−4.81765	−0.289465	−0.144732	−	0.989471i	$-0.546232\pi$
$277$	−4.81765	−0.289465	−0.144732	+	0.989471i	$0.546232\pi$
$278$	−2.42308	−0.145327
$279$	−0.235734	−0.0141131
$280$	13.7403	0.821141
$281$	−20.8406	−1.24325	−0.621624	−	0.783315i	$-0.713527\pi$
$281$	−20.8406	−1.24325	−0.621624	+	0.783315i	$0.713527\pi$
$282$	−13.0603	−0.777732
$283$	19.7130	1.17181	0.585907	−	0.810379i	$-0.300739\pi$
$283$	19.7130	1.17181	0.585907	+	0.810379i	$0.300739\pi$
$284$	−0.491793	−0.0291825
$285$	7.08317	0.419571
$286$	−4.27615	−0.252854
$287$	13.9417	0.822953
$288$	−0.134307	−0.00791409
$289$	1.00000	0.0588235
$290$	4.35668	0.255833
$291$	−21.8565	−1.28125
$292$	−4.94225	−0.289223
$293$	20.1518	1.17728	0.588640	−	0.808395i	$-0.299664\pi$
$293$	20.1518	1.17728	0.588640	+	0.808395i	$0.299664\pi$
$294$	−28.2247	−1.64610
$295$	6.26327	0.364662
$296$	−5.70487	−0.331589
$297$	−19.5392	−1.13378
$298$	−3.96583	−0.229734
$299$	0.814739	0.0471176
$300$	−0.858810	−0.0495834
$301$	54.2287	3.12569
$302$	−8.05116	−0.463292
$303$	−9.34645	−0.536940
$304$	−11.2540	−0.645460
$305$	−10.1251	−0.579762
$306$	−0.0607989	−0.00347564
$307$	8.53990	0.487398	0.243699	−	0.969851i	$-0.421639\pi$
$307$	8.53990	0.487398	0.243699	+	0.969851i	$0.421639\pi$
$308$	−8.37402	−0.477154
$309$	2.40401	0.136759
$310$	5.84775	0.332130
$311$	15.6607	0.888037	0.444019	−	0.896018i	$-0.353552\pi$
$311$	15.6607	0.888037	0.444019	+	0.896018i	$0.353552\pi$
$312$	4.90661	0.277782
$313$	10.8867	0.615355	0.307678	−	0.951491i	$-0.400448\pi$
$313$	10.8867	0.615355	0.307678	+	0.951491i	$0.400448\pi$
$314$	4.66790	0.263425
$315$	0.222290	0.0125246
$316$	1.59071	0.0894842
$317$	−10.1848	−0.572038	−0.286019	−	0.958224i	$-0.592332\pi$
$317$	−10.1848	−0.572038	−0.286019	+	0.958224i	$0.592332\pi$
$318$	−13.1877	−0.739528
$319$	−13.4531	−0.753230
$320$	8.88079	0.496451
$321$	5.85287	0.326675
$322$	−4.89304	−0.272679
$323$	4.05614	0.225689
$324$	4.49797	0.249887
$325$	0.918173	0.0509311
$326$	−10.8942	−0.603373
$327$	−7.75716	−0.428972
$328$	9.50176	0.524647
$329$	27.3441	1.50753
$330$	−8.13285	−0.447699
$331$	−15.6249	−0.858824	−0.429412	−	0.903109i	$-0.641279\pi$
$331$	−15.6249	−0.858824	−0.429412	+	0.903109i	$0.641279\pi$
$332$	5.50343	0.302040
$333$	−0.0922928	−0.00505762
$334$	15.4402	0.844852
$335$	−0.712305	−0.0389174
$336$	−21.7552	−1.18684
$337$	−2.59907	−0.141580	−0.0707902	−	0.997491i	$-0.522552\pi$
$337$	−2.59907	−0.141580	−0.0707902	+	0.997491i	$0.522552\pi$
$338$	14.9298	0.812077
$339$	−0.500848	−0.0272023
$340$	−0.491793	−0.0266712
$341$	−18.0574	−0.977864
$342$	−0.246608	−0.0133351
$343$	27.6628	1.49365
$344$	36.9587	1.99268
$345$	1.54956	0.0834256
$346$	−16.5017	−0.887136
$347$	2.05982	0.110577	0.0552885	−	0.998470i	$-0.482392\pi$
$347$	2.05982	0.110577	0.0552885	+	0.998470i	$0.482392\pi$
$348$	3.04665	0.163317
$349$	−18.0482	−0.966098	−0.483049	−	0.875593i	$-0.660471\pi$
$349$	−18.0482	−0.966098	−0.483049	+	0.875593i	$0.660471\pi$
$350$	−5.51423	−0.294748
$351$	−4.73079	−0.252511
$352$	−10.2880	−0.548351
$353$	−25.8276	−1.37466	−0.687332	−	0.726344i	$-0.741218\pi$
$353$	−25.8276	−1.37466	−0.687332	+	0.726344i	$0.741218\pi$
$354$	−13.4322	−0.713913
$355$	1.00000	0.0530745
$356$	0.205647	0.0108993
$357$	7.84096	0.414988
$358$	31.3453	1.65665
$359$	29.4572	1.55469	0.777347	−	0.629072i	$-0.216565\pi$
$359$	29.4572	1.55469	0.777347	+	0.629072i	$0.216565\pi$
$360$	0.151498	0.00798465
$361$	−2.54775	−0.134092
$362$	19.2682	1.01272
$363$	5.90453	0.309907
$364$	−2.02750	−0.106270
$365$	10.0495	0.526012
$366$	21.7143	1.13502
$367$	−22.0829	−1.15272	−0.576359	−	0.817196i	$-0.695527\pi$
$367$	−22.0829	−1.15272	−0.576359	+	0.817196i	$0.695527\pi$
$368$	−2.46200	−0.128340
$369$	0.153719	0.00800227
$370$	2.28946	0.119023
$371$	27.6107	1.43348
$372$	4.08936	0.212023
$373$	0.293972	0.0152213	0.00761066	−	0.999971i	$-0.497577\pi$
$373$	0.293972	0.0152213	0.00761066	+	0.999971i	$0.497577\pi$
$374$	−4.65723	−0.240820
$375$	1.74628	0.0901777
$376$	18.6359	0.961076
$377$	−3.25724	−0.167756
$378$	28.4115	1.46133
$379$	−1.74214	−0.0894877	−0.0447439	−	0.998998i	$-0.514247\pi$
$379$	−1.74214	−0.0894877	−0.0447439	+	0.998998i	$0.514247\pi$
$380$	−1.99478	−0.102330
$381$	30.7041	1.57302
$382$	7.34885	0.376000
$383$	−12.1408	−0.620368	−0.310184	−	0.950677i	$-0.600391\pi$
$383$	−12.1408	−0.620368	−0.310184	+	0.950677i	$0.600391\pi$
$384$	−9.57074	−0.488405
$385$	17.0275	0.867804
$386$	22.3434	1.13725
$387$	0.597915	0.0303937
$388$	6.15527	0.312487
$389$	24.0771	1.22076	0.610379	−	0.792109i	$-0.291017\pi$
$389$	24.0771	1.22076	0.610379	+	0.792109i	$0.291017\pi$
$390$	−1.96911	−0.0997097
$391$	0.887348	0.0448751
$392$	40.2742	2.03415
$393$	−27.4251	−1.38341
$394$	−19.7491	−0.994946
$395$	−3.23450	−0.162746
$396$	−0.0923304	−0.00463977
$397$	−12.0622	−0.605384	−0.302692	−	0.953088i	$-0.597885\pi$
$397$	−12.0622	−0.605384	−0.302692	+	0.953088i	$0.597885\pi$
$398$	−0.276467	−0.0138580
$399$	31.8040	1.59219
$400$	−2.77455	−0.138728
$401$	−3.90205	−0.194859	−0.0974295	−	0.995242i	$-0.531062\pi$
$401$	−3.90205	−0.194859	−0.0974295	+	0.995242i	$0.531062\pi$
$402$	1.52761	0.0761901
$403$	−4.37203	−0.217786
$404$	2.63217	0.130955
$405$	−9.14607	−0.454472
$406$	19.5619	0.970839
$407$	−7.06969	−0.350432
$408$	5.34389	0.264562
$409$	21.4662	1.06144	0.530719	−	0.847548i	$-0.321922\pi$
$409$	21.4662	1.06144	0.530719	+	0.847548i	$0.321922\pi$
$410$	−3.81322	−0.188322
$411$	−20.7178	−1.02193
$412$	−0.677022	−0.0333545
$413$	28.1226	1.38382
$414$	−0.0539498	−0.00265149
$415$	−11.1906	−0.549323
$416$	−2.49090	−0.122127
$417$	3.44550	0.168727
$418$	−18.8904	−0.923959
$419$	7.07898	0.345831	0.172915	−	0.984937i	$-0.444681\pi$
$419$	7.07898	0.345831	0.172915	+	0.984937i	$0.444681\pi$
$420$	−3.85613	−0.188160
$421$	16.9894	0.828012	0.414006	−	0.910274i	$-0.364129\pi$
$421$	16.9894	0.828012	0.414006	+	0.910274i	$0.364129\pi$
$422$	−14.7487	−0.717954
$423$	0.301491	0.0146590
$424$	18.8176	0.913865
$425$	1.00000	0.0485071
$426$	−2.14460	−0.103906
$427$	−45.4626	−2.20009
$428$	−1.64830	−0.0796736
$429$	6.08047	0.293568
$430$	−14.8322	−0.715271
$431$	−8.08299	−0.389344	−0.194672	−	0.980868i	$-0.562364\pi$
$431$	−8.08299	−0.389344	−0.194672	+	0.980868i	$0.562364\pi$
$432$	14.2956	0.687798
$433$	−13.9141	−0.668669	−0.334335	−	0.942454i	$-0.608512\pi$
$433$	−13.9141	−0.668669	−0.334335	+	0.942454i	$0.608512\pi$
$434$	26.2569	1.26037
$435$	−6.19498	−0.297027
$436$	2.18459	0.104623
$437$	3.59921	0.172173
$438$	−21.5520	−1.02979
$439$	30.9949	1.47931	0.739654	−	0.672988i	$-0.234989\pi$
$439$	30.9949	1.47931	0.739654	+	0.672988i	$0.234989\pi$
$440$	11.6049	0.553240
$441$	0.651552	0.0310263
$442$	−1.12760	−0.0536345
$443$	−4.70972	−0.223765	−0.111883	−	0.993721i	$-0.535688\pi$
$443$	−4.70972	−0.223765	−0.111883	+	0.993721i	$0.535688\pi$
$444$	1.60103	0.0759816
$445$	−0.418157	−0.0198226
$446$	−25.8283	−1.22300
$447$	5.63921	0.266725
$448$	39.8755	1.88394
$449$	−24.1384	−1.13916	−0.569580	−	0.821936i	$-0.692894\pi$
$449$	−24.1384	−1.13916	−0.569580	+	0.821936i	$0.692894\pi$
$450$	−0.0607989	−0.00286609
$451$	11.7749	0.554461
$452$	0.141050	0.00663443
$453$	11.4483	0.537890
$454$	−18.4369	−0.865286
$455$	4.12267	0.193274
$456$	21.6755	1.01505
$457$	5.88560	0.275317	0.137658	−	0.990480i	$-0.456042\pi$
$457$	5.88560	0.275317	0.137658	+	0.990480i	$0.456042\pi$
$458$	11.0210	0.514976
$459$	−5.15240	−0.240493
$460$	−0.436391	−0.0203469
$461$	−35.9477	−1.67425	−0.837126	−	0.547011i	$-0.815766\pi$
$461$	−35.9477	−1.67425	−0.837126	+	0.547011i	$0.815766\pi$
$462$	−36.5172	−1.69893
$463$	−6.88387	−0.319920	−0.159960	−	0.987123i	$-0.551137\pi$
$463$	−6.88387	−0.319920	−0.159960	+	0.987123i	$0.551137\pi$
$464$	9.84280	0.456940
$465$	−8.31521	−0.385608
$466$	−3.50173	−0.162215
$467$	−33.0787	−1.53070	−0.765349	−	0.643615i	$-0.777434\pi$
$467$	−33.0787	−1.53070	−0.765349	+	0.643615i	$0.777434\pi$
$468$	−0.0223548	−0.00103335
$469$	−3.19831	−0.147684
$470$	−7.47893	−0.344977
$471$	−6.63752	−0.305841
$472$	19.1665	0.882212
$473$	45.8007	2.10592
$474$	6.93670	0.318613
$475$	4.05614	0.186108
$476$	−2.20819	−0.101212
$477$	0.304430	0.0139389
$478$	33.8706	1.54920
$479$	10.0648	0.459872	0.229936	−	0.973206i	$-0.426148\pi$
$479$	10.0648	0.459872	0.229936	+	0.973206i	$0.426148\pi$
$480$	−4.73748	−0.216235
$481$	−1.71170	−0.0780468
$482$	22.8966	1.04291
$483$	6.95766	0.316585
$484$	−1.66285	−0.0755840
$485$	−12.5160	−0.568322
$486$	0.631776	0.0286579
$487$	5.52936	0.250559	0.125280	−	0.992121i	$-0.460017\pi$
$487$	5.52936	0.250559	0.125280	+	0.992121i	$0.460017\pi$
$488$	−30.9843	−1.40259
$489$	15.4910	0.700526
$490$	−16.1627	−0.730158
$491$	37.2409	1.68066	0.840330	−	0.542075i	$-0.182361\pi$
$491$	37.2409	1.68066	0.840330	+	0.542075i	$0.182361\pi$
$492$	−2.66660	−0.120220
$493$	−3.54752	−0.159772
$494$	−4.57370	−0.205780
$495$	0.187742	0.00843839
$496$	13.2115	0.593213
$497$	4.49008	0.201408
$498$	23.9992	1.07543
$499$	25.3954	1.13686	0.568428	−	0.822733i	$-0.307552\pi$
$499$	25.3954	1.13686	0.568428	+	0.822733i	$0.307552\pi$
$500$	−0.491793	−0.0219936
$501$	−21.9552	−0.980887
$502$	19.1237	0.853531
$503$	10.4668	0.466693	0.233347	−	0.972394i	$-0.425032\pi$
$503$	10.4668	0.466693	0.233347	+	0.972394i	$0.425032\pi$
$504$	0.680239	0.0303003
$505$	−5.35220	−0.238170
$506$	−4.13259	−0.183716
$507$	−21.2295	−0.942835
$508$	−8.64697	−0.383647
$509$	4.16817	0.184751	0.0923754	−	0.995724i	$-0.470554\pi$
$509$	4.16817	0.184751	0.0923754	+	0.995724i	$0.470554\pi$
$510$	−2.14460	−0.0949643
$511$	45.1229	1.99612
$512$	24.5082	1.08312
$513$	−20.8988	−0.922706
$514$	−7.07312	−0.311982
$515$	1.37664	0.0606621
$516$	−10.3722	−0.456611
$517$	23.0944	1.01569
$518$	10.2799	0.451672
$519$	23.4646	1.02998
$520$	2.80975	0.123215
$521$	31.4871	1.37948	0.689738	−	0.724059i	$-0.257726\pi$
$521$	31.4871	1.37948	0.689738	+	0.724059i	$0.257726\pi$
$522$	0.215685	0.00944029
$523$	29.4597	1.28818	0.644092	−	0.764948i	$-0.277236\pi$
$523$	29.4597	1.28818	0.644092	+	0.764948i	$0.277236\pi$
$524$	7.72352	0.337404
$525$	7.84096	0.342208
$526$	−31.4921	−1.37312
$527$	−4.76166	−0.207421
$528$	−18.3741	−0.799629
$529$	−22.2126	−0.965766
$530$	−7.55185	−0.328031
$531$	0.310075	0.0134561
$532$	−8.95672	−0.388323
$533$	2.85093	0.123487
$534$	0.896778	0.0388074
$535$	3.35161	0.144903
$536$	−2.17976	−0.0941512
$537$	−44.5715	−1.92340
$538$	−4.54408	−0.195909
$539$	49.9093	2.14975
$540$	2.53391	0.109042
$541$	−23.2456	−0.999406	−0.499703	−	0.866197i	$-0.666558\pi$
$541$	−23.2456	−0.999406	−0.499703	+	0.866197i	$0.666558\pi$
$542$	−24.3333	−1.04521
$543$	−27.3985	−1.17578
$544$	−2.71289	−0.116314
$545$	−4.44210	−0.190278
$546$	−8.84147	−0.378380
$547$	11.9828	0.512348	0.256174	−	0.966631i	$-0.417538\pi$
$547$	11.9828	0.512348	0.256174	+	0.966631i	$0.417538\pi$
$548$	5.83459	0.249241
$549$	−0.501262	−0.0213933
$550$	−4.65723	−0.198585
$551$	−14.3892	−0.613002
$552$	4.74189	0.201828
$553$	−14.5232	−0.617589
$554$	5.91651	0.251368
$555$	−3.25550	−0.138188
$556$	−0.970330	−0.0411512
$557$	−21.4481	−0.908784	−0.454392	−	0.890802i	$-0.650143\pi$
$557$	−21.4481	−0.908784	−0.454392	+	0.890802i	$0.650143\pi$
$558$	0.289503	0.0122557
$559$	11.0892	0.469022
$560$	−12.4580	−0.526446
$561$	6.62235	0.279596
$562$	25.5942	1.07963
$563$	27.6867	1.16686	0.583428	−	0.812165i	$-0.301711\pi$
$563$	27.6867	1.16686	0.583428	+	0.812165i	$0.301711\pi$
$564$	−5.23005	−0.220225
$565$	−0.286808	−0.0120661
$566$	−24.2093	−1.01759
$567$	−41.0666	−1.72464
$568$	3.06015	0.128401
$569$	−4.55642	−0.191015	−0.0955076	−	0.995429i	$-0.530447\pi$
$569$	−4.55642	−0.191015	−0.0955076	+	0.995429i	$0.530447\pi$
$570$	−8.69877	−0.364351
$571$	25.7988	1.07965	0.539824	−	0.841778i	$-0.318491\pi$
$571$	25.7988	1.07965	0.539824	+	0.841778i	$0.318491\pi$
$572$	−1.71240	−0.0715989
$573$	−10.4497	−0.436543
$574$	−17.1217	−0.714645
$575$	0.887348	0.0370050
$576$	0.439659	0.0183191
$577$	39.8462	1.65882	0.829410	−	0.558641i	$-0.188677\pi$
$577$	39.8462	1.65882	0.829410	+	0.558641i	$0.188677\pi$
$578$	−1.22809	−0.0510818
$579$	−31.7712	−1.32037
$580$	1.74465	0.0724425
$581$	−50.2465	−2.08458
$582$	26.8417	1.11263
$583$	23.3195	0.965797
$584$	30.7528	1.27256
$585$	0.0454558	0.00187937
$586$	−24.7482	−1.02234
$587$	−20.0188	−0.826264	−0.413132	−	0.910671i	$-0.635565\pi$
$587$	−20.0188	−0.826264	−0.413132	+	0.910671i	$0.635565\pi$
$588$	−11.3027	−0.466114
$589$	−19.3139	−0.795817
$590$	−7.69187	−0.316669
$591$	28.0823	1.15515
$592$	5.17245	0.212586
$593$	−26.6416	−1.09404	−0.547019	−	0.837120i	$-0.684238\pi$
$593$	−26.6416	−1.09404	−0.547019	+	0.837120i	$0.684238\pi$
$594$	23.9959	0.984565
$595$	4.49008	0.184076
$596$	−1.58813	−0.0650523
$597$	0.393122	0.0160894
$598$	−1.00057	−0.0409165
$599$	−13.2628	−0.541905	−0.270953	−	0.962593i	$-0.587339\pi$
$599$	−13.2628	−0.541905	−0.270953	+	0.962593i	$0.587339\pi$
$600$	5.34389	0.218163
$601$	−46.3304	−1.88986	−0.944929	−	0.327276i	$-0.893869\pi$
$601$	−46.3304	−1.88986	−0.944929	+	0.327276i	$0.893869\pi$
$602$	−66.5977	−2.71432
$603$	−0.0352639	−0.00143606
$604$	−3.22411	−0.131187
$605$	3.38120	0.137465
$606$	11.4783	0.466274
$607$	−11.2154	−0.455221	−0.227610	−	0.973752i	$-0.573091\pi$
$607$	−11.2154	−0.455221	−0.227610	+	0.973752i	$0.573091\pi$
$608$	−11.0039	−0.446265
$609$	−27.8160	−1.12716
$610$	12.4346	0.503460
$611$	5.59157	0.226211
$612$	−0.0243471	−0.000984173 0
$613$	34.2471	1.38323	0.691613	−	0.722268i	$-0.256900\pi$
$613$	34.2471	1.38323	0.691613	+	0.722268i	$0.256900\pi$
$614$	−10.4878	−0.423252
$615$	5.42221	0.218645
$616$	52.1068	2.09944
$617$	−3.28483	−0.132242	−0.0661212	−	0.997812i	$-0.521062\pi$
$617$	−3.28483	−0.132242	−0.0661212	+	0.997812i	$0.521062\pi$
$618$	−2.95234	−0.118760
$619$	19.5132	0.784300	0.392150	−	0.919901i	$-0.371731\pi$
$619$	19.5132	0.784300	0.392150	+	0.919901i	$0.371731\pi$
$620$	2.34175	0.0940469
$621$	−4.57197	−0.183467
$622$	−19.2328	−0.771164
$623$	−1.87756	−0.0752229
$624$	−4.44869	−0.178090
$625$	1.00000	0.0400000
$626$	−13.3699	−0.534369
$627$	26.8612	1.07273
$628$	1.86927	0.0745922
$629$	−1.86425	−0.0743323
$630$	−0.272992	−0.0108763
$631$	42.2081	1.68028	0.840140	−	0.542370i	$-0.182473\pi$
$631$	42.2081	1.68028	0.840140	+	0.542370i	$0.182473\pi$
$632$	−9.89806	−0.393724
$633$	20.9719	0.833557
$634$	12.5079	0.496752
$635$	17.5825	0.697742
$636$	−5.28104	−0.209407
$637$	12.0839	0.478783
$638$	16.5216	0.654098
$639$	0.0495068	0.00195846
$640$	−5.48063	−0.216641
$641$	−3.29027	−0.129958	−0.0649790	−	0.997887i	$-0.520698\pi$
$641$	−3.29027	−0.129958	−0.0649790	+	0.997887i	$0.520698\pi$
$642$	−7.18786	−0.283682
$643$	−22.0348	−0.868969	−0.434484	−	0.900679i	$-0.643069\pi$
$643$	−22.0348	−0.868969	−0.434484	+	0.900679i	$0.643069\pi$
$644$	−1.95943	−0.0772125
$645$	21.0906	0.830442
$646$	−4.98130	−0.195987
$647$	−41.0564	−1.61409	−0.807047	−	0.590488i	$-0.798935\pi$
$647$	−41.0564	−1.61409	−0.807047	+	0.590488i	$0.798935\pi$
$648$	−27.9883	−1.09949
$649$	23.7519	0.932345
$650$	−1.12760	−0.0442281
$651$	−37.3360	−1.46331
$652$	−4.36261	−0.170853
$653$	−43.6872	−1.70961	−0.854806	−	0.518948i	$-0.826324\pi$
$653$	−43.6872	−1.70961	−0.854806	+	0.518948i	$0.826324\pi$
$654$	9.52650	0.372515
$655$	−15.7048	−0.613639
$656$	−8.61499	−0.336359
$657$	0.497516	0.0194100
$658$	−33.5810	−1.30912
$659$	−37.3036	−1.45314	−0.726571	−	0.687092i	$-0.758887\pi$
$659$	−37.3036	−1.45314	−0.726571	+	0.687092i	$0.758887\pi$
$660$	−3.25682	−0.126772
$661$	28.7159	1.11692	0.558460	−	0.829531i	$-0.311392\pi$
$661$	28.7159	1.11692	0.558460	+	0.829531i	$0.311392\pi$
$662$	19.1888	0.745795
$663$	1.60339	0.0622705
$664$	−34.2448	−1.32895
$665$	18.2124	0.706246
$666$	0.113344	0.00439199
$667$	−3.14789	−0.121887
$668$	6.18309	0.239231
$669$	36.7265	1.41993
$670$	0.874775	0.0337955
$671$	−38.3970	−1.48230
$672$	−21.2717	−0.820573
$673$	−17.9904	−0.693479	−0.346740	−	0.937961i	$-0.612711\pi$
$673$	−17.9904	−0.693479	−0.346740	+	0.937961i	$0.612711\pi$
$674$	3.19189	0.122947
$675$	−5.15240	−0.198316
$676$	5.97870	0.229950
$677$	−46.7657	−1.79735	−0.898676	−	0.438613i	$-0.855470\pi$
$677$	−46.7657	−1.79735	−0.898676	+	0.438613i	$0.855470\pi$
$678$	0.615086	0.0236222
$679$	−56.1978	−2.15668
$680$	3.06015	0.117351
$681$	26.2163	1.00461
$682$	22.1762	0.849169
$683$	48.5466	1.85758	0.928792	−	0.370603i	$-0.120849\pi$
$683$	48.5466	1.85758	0.928792	+	0.370603i	$0.120849\pi$
$684$	−0.0987551	−0.00377600
$685$	−11.8639	−0.453297
$686$	−33.9724	−1.29707
$687$	−15.6713	−0.597896
$688$	−33.5095	−1.27754
$689$	5.64608	0.215099
$690$	−1.90300	−0.0724461
$691$	6.32044	0.240441	0.120220	−	0.992747i	$-0.461640\pi$
$691$	6.32044	0.240441	0.120220	+	0.992747i	$0.461640\pi$
$692$	−6.60815	−0.251204
$693$	0.842979	0.0320221
$694$	−2.52965	−0.0960242
$695$	1.97305	0.0748419
$696$	−18.9576	−0.718585
$697$	3.10500	0.117610
$698$	22.1648	0.838951
$699$	4.97929	0.188334
$700$	−2.20819	−0.0834618
$701$	28.6893	1.08358	0.541790	−	0.840514i	$-0.317747\pi$
$701$	28.6893	1.08358	0.541790	+	0.840514i	$0.317747\pi$
$702$	5.80984	0.219278
$703$	−7.56163	−0.285192
$704$	33.6782	1.26929
$705$	10.6347	0.400525
$706$	31.7186	1.19375
$707$	−24.0318	−0.903809
$708$	−5.37896	−0.202154
$709$	−20.7769	−0.780292	−0.390146	−	0.920753i	$-0.627575\pi$
$709$	−20.7769	−0.780292	−0.390146	+	0.920753i	$0.627575\pi$
$710$	−1.22809	−0.0460894
$711$	−0.160130	−0.00600534
$712$	−1.27962	−0.0479559
$713$	−4.22525	−0.158237
$714$	−9.62941	−0.360372
$715$	3.48195	0.130217
$716$	12.5523	0.469102
$717$	−48.1622	−1.79865
$718$	−36.1762	−1.35008
$719$	−4.97940	−0.185700	−0.0928501	−	0.995680i	$-0.529598\pi$
$719$	−4.97940	−0.185700	−0.0928501	+	0.995680i	$0.529598\pi$
$720$	−0.137359	−0.00511908
$721$	6.18123	0.230201
$722$	3.12887	0.116445
$723$	−32.5578	−1.21084
$724$	7.71603	0.286764
$725$	−3.54752	−0.131752
$726$	−7.25129	−0.269121
$727$	7.55948	0.280366	0.140183	−	0.990126i	$-0.455231\pi$
$727$	7.55948	0.280366	0.140183	+	0.990126i	$0.455231\pi$
$728$	12.6160	0.467580
$729$	26.5399	0.982958
$730$	−12.3416	−0.456785
$731$	12.0774	0.446700
$732$	8.69554	0.321396
$733$	28.1898	1.04122	0.520608	−	0.853796i	$-0.325705\pi$
$733$	28.1898	1.04122	0.520608	+	0.853796i	$0.325705\pi$
$734$	27.1198	1.00101
$735$	22.9826	0.847726
$736$	−2.40728	−0.0887335
$737$	−2.70124	−0.0995015
$738$	−0.188780	−0.00694910
$739$	13.2047	0.485742	0.242871	−	0.970059i	$-0.421911\pi$
$739$	13.2047	0.485742	0.242871	+	0.970059i	$0.421911\pi$
$740$	0.916822	0.0337031
$741$	6.50357	0.238915
$742$	−33.9084	−1.24482
$743$	19.3143	0.708572	0.354286	−	0.935137i	$-0.384724\pi$
$743$	19.3143	0.708572	0.354286	+	0.935137i	$0.384724\pi$
$744$	−25.4458	−0.932887
$745$	3.22926	0.118311
$746$	−0.361025	−0.0132181
$747$	−0.554009	−0.0202701
$748$	−1.86500	−0.0681913
$749$	15.0490	0.549880
$750$	−2.14460	−0.0783095
$751$	25.5601	0.932700	0.466350	−	0.884600i	$-0.345569\pi$
$751$	25.5601	0.932700	0.466350	+	0.884600i	$0.345569\pi$
$752$	−16.8967	−0.616160
$753$	−27.1929	−0.990965
$754$	4.00019	0.145678
$755$	6.55583	0.238591
$756$	11.3775	0.413795
$757$	−44.3514	−1.61198	−0.805990	−	0.591929i	$-0.798367\pi$
$757$	−44.3514	−1.61198	−0.805990	+	0.591929i	$0.798367\pi$
$758$	2.13951	0.0777104
$759$	5.87633	0.213297
$760$	12.4124	0.450244
$761$	29.6223	1.07381	0.536903	−	0.843644i	$-0.319594\pi$
$761$	29.6223	1.07381	0.536903	+	0.843644i	$0.319594\pi$
$762$	−37.7074	−1.36600
$763$	−19.9454	−0.722071
$764$	2.94287	0.106469
$765$	0.0495068	0.00178992
$766$	14.9101	0.538722
$767$	5.75077	0.207648
$768$	−19.2630	−0.695094
$769$	33.4733	1.20708	0.603538	−	0.797334i	$-0.293757\pi$
$769$	33.4733	1.20708	0.603538	+	0.797334i	$0.293757\pi$
$770$	−20.9114	−0.753594
$771$	10.0576	0.362216
$772$	8.94749	0.322027
$773$	−50.5959	−1.81981	−0.909904	−	0.414820i	$-0.863845\pi$
$773$	−50.5959	−1.81981	−0.909904	+	0.414820i	$0.863845\pi$
$774$	−0.734294	−0.0263936
$775$	−4.76166	−0.171044
$776$	−38.3008	−1.37492
$777$	−14.6175	−0.524399
$778$	−29.5689	−1.06010
$779$	12.5943	0.451238
$780$	−0.788536	−0.0282341
$781$	3.79225	0.135698
$782$	−1.08974	−0.0389692
$783$	18.2783	0.653212
$784$	−36.5155	−1.30413
$785$	−3.80094	−0.135661
$786$	33.6805	1.20134
$787$	32.2438	1.14937	0.574684	−	0.818375i	$-0.305125\pi$
$787$	32.2438	1.14937	0.574684	+	0.818375i	$0.305125\pi$
$788$	−7.90859	−0.281732
$789$	44.7802	1.59422
$790$	3.97227	0.141327
$791$	−1.28779	−0.0457886
$792$	0.574520	0.0204147
$793$	−9.29660	−0.330132
$794$	14.8135	0.525710
$795$	10.7383	0.380850
$796$	−0.110712	−0.00392408
$797$	−0.436409	−0.0154584	−0.00772921	−	0.999970i	$-0.502460\pi$
$797$	−0.436409	−0.0154584	−0.00772921	+	0.999970i	$0.502460\pi$
$798$	−39.0582	−1.38265
$799$	6.08988	0.215445
$800$	−2.71289	−0.0959152
$801$	−0.0207016	−0.000731456 0
$802$	4.79207	0.169214
$803$	38.1101	1.34488
$804$	0.611734	0.0215742
$805$	3.98427	0.140427
$806$	5.36925	0.189124
$807$	6.46146	0.227454
$808$	−16.3785	−0.576194
$809$	−0.204432	−0.00718744	−0.00359372	−	0.999994i	$-0.501144\pi$
$809$	−0.204432	−0.00718744	−0.00359372	+	0.999994i	$0.501144\pi$
$810$	11.2322	0.394659
$811$	41.4571	1.45575	0.727877	−	0.685708i	$-0.240507\pi$
$811$	41.4571	1.45575	0.727877	+	0.685708i	$0.240507\pi$
$812$	7.83361	0.274906
$813$	34.6008	1.21350
$814$	8.68223	0.304312
$815$	8.87082	0.310731
$816$	−4.84516	−0.169615
$817$	48.9877	1.71386
$818$	−26.3625	−0.921743
$819$	0.204100	0.00713185
$820$	−1.52702	−0.0533257
$821$	29.0136	1.01258	0.506291	−	0.862363i	$-0.331016\pi$
$821$	29.0136	1.01258	0.506291	+	0.862363i	$0.331016\pi$
$822$	25.4433	0.887438
$823$	53.9849	1.88180	0.940898	−	0.338689i	$-0.109984\pi$
$823$	53.9849	1.88180	0.940898	+	0.338689i	$0.109984\pi$
$824$	4.21273	0.146757
$825$	6.62235	0.230561
$826$	−34.5371	−1.20170
$827$	19.1737	0.666734	0.333367	−	0.942797i	$-0.391815\pi$
$827$	19.1737	0.666734	0.333367	+	0.942797i	$0.391815\pi$
$828$	−0.0216043	−0.000750803 0
$829$	−6.25273	−0.217166	−0.108583	−	0.994087i	$-0.534631\pi$
$829$	−6.25273	−0.217166	−0.108583	+	0.994087i	$0.534631\pi$
$830$	13.7430	0.477027
$831$	−8.41298	−0.291843
$832$	8.15410	0.282692
$833$	13.1609	0.455997
$834$	−4.23139	−0.146521
$835$	−12.5725	−0.435091
$836$	−7.56471	−0.261631
$837$	24.5340	0.848018
$838$	−8.69363	−0.300317
$839$	39.2729	1.35585	0.677925	−	0.735131i	$-0.262879\pi$
$839$	39.2729	1.35585	0.677925	+	0.735131i	$0.262879\pi$
$840$	23.9945	0.827889
$841$	−16.4151	−0.566037
$842$	−20.8645	−0.719038
$843$	−36.3937	−1.25346
$844$	−5.90615	−0.203298
$845$	−12.1570	−0.418212
$846$	−0.370258	−0.0127297
$847$	15.1819	0.521655
$848$	−17.0614	−0.585892
$849$	34.4244	1.18144
$850$	−1.22809	−0.0421232
$851$	−1.65423	−0.0567064
$852$	−0.858810	−0.0294223
$853$	32.2502	1.10423	0.552113	−	0.833769i	$-0.313822\pi$
$853$	32.2502	1.10423	0.552113	+	0.833769i	$0.313822\pi$
$854$	55.8322	1.91054
$855$	0.200806	0.00686743
$856$	10.2564	0.350558
$857$	−29.6186	−1.01175	−0.505876	−	0.862606i	$-0.668831\pi$
$857$	−29.6186	−1.01175	−0.505876	+	0.862606i	$0.668831\pi$
$858$	−7.46736	−0.254932
$859$	23.7790	0.811331	0.405665	−	0.914022i	$-0.367040\pi$
$859$	23.7790	0.811331	0.405665	+	0.914022i	$0.367040\pi$
$860$	−5.93959	−0.202538
$861$	24.3462	0.829716
$862$	9.92665	0.338103
$863$	26.8070	0.912520	0.456260	−	0.889847i	$-0.349189\pi$
$863$	26.8070	0.912520	0.456260	+	0.889847i	$0.349189\pi$
$864$	13.9779	0.475538
$865$	13.4369	0.456867
$866$	17.0878	0.580667
$867$	1.74628	0.0593069
$868$	10.5146	0.356890
$869$	−12.2661	−0.416098
$870$	7.60800	0.257935
$871$	−0.654019	−0.0221606
$872$	−13.5935	−0.460333
$873$	−0.619627	−0.0209712
$874$	−4.42015	−0.149514
$875$	4.49008	0.151793
$876$	−8.63057	−0.291600
$877$	13.3216	0.449839	0.224920	−	0.974377i	$-0.427788\pi$
$877$	13.3216	0.449839	0.224920	+	0.974377i	$0.427788\pi$
$878$	−38.0646	−1.28462
$879$	35.1907	1.18695
$880$	−10.5218	−0.354690
$881$	−24.1105	−0.812303	−0.406151	−	0.913806i	$-0.633129\pi$
$881$	−24.1105	−0.812303	−0.406151	+	0.913806i	$0.633129\pi$
$882$	−0.800165	−0.0269430
$883$	−38.5490	−1.29728	−0.648638	−	0.761097i	$-0.724661\pi$
$883$	−38.5490	−1.29728	−0.648638	+	0.761097i	$0.724661\pi$
$884$	−0.451551	−0.0151873
$885$	10.9375	0.367658
$886$	5.78396	0.194316
$887$	30.4956	1.02394	0.511971	−	0.859002i	$-0.328915\pi$
$887$	30.4956	1.02394	0.511971	+	0.859002i	$0.328915\pi$
$888$	−9.96232	−0.334313
$889$	78.9471	2.64780
$890$	0.513535	0.0172137
$891$	−34.6842	−1.16197
$892$	−10.3430	−0.346310
$893$	24.7014	0.826601
$894$	−6.92546	−0.231622
$895$	−25.5236	−0.853160
$896$	−24.6085	−0.822112
$897$	1.42277	0.0475048
$898$	29.6441	0.989238
$899$	16.8921	0.563383
$900$	−0.0243471	−0.000811570 0
$901$	6.14926	0.204861
$902$	−14.4607	−0.481489
$903$	94.6986	3.15137
$904$	−0.877674	−0.0291910
$905$	−15.6896	−0.521540
$906$	−14.0596	−0.467099
$907$	−41.1763	−1.36724	−0.683619	−	0.729839i	$-0.739595\pi$
$907$	−41.1763	−1.36724	−0.683619	+	0.729839i	$0.739595\pi$
$908$	−7.38311	−0.245017
$909$	−0.264970	−0.00878850
$910$	−5.06302	−0.167837
$911$	−40.5680	−1.34408	−0.672039	−	0.740516i	$-0.734581\pi$
$911$	−40.5680	−1.34408	−0.672039	+	0.740516i	$0.734581\pi$
$912$	−19.6526	−0.650764
$913$	−42.4374	−1.40447
$914$	−7.22805	−0.239083
$915$	−17.6813	−0.584526
$916$	4.41338	0.145822
$917$	−70.5160	−2.32865
$918$	6.32761	0.208842
$919$	−2.23421	−0.0736999	−0.0368499	−	0.999321i	$-0.511732\pi$
$919$	−2.23421	−0.0736999	−0.0368499	+	0.999321i	$0.511732\pi$
$920$	2.71542	0.0895246
$921$	14.9131	0.491403
$922$	44.1470	1.45391
$923$	0.918173	0.0302220
$924$	−14.6234	−0.481075
$925$	−1.86425	−0.0612960
$926$	8.45401	0.277816
$927$	0.0681531	0.00223844
$928$	9.62405	0.315925
$929$	−10.5369	−0.345705	−0.172852	−	0.984948i	$-0.555298\pi$
$929$	−10.5369	−0.345705	−0.172852	+	0.984948i	$0.555298\pi$
$930$	10.2118	0.334859
$931$	53.3822	1.74953
$932$	−1.40228	−0.0459332
$933$	27.3480	0.895335
$934$	40.6236	1.32925
$935$	3.79225	0.124020
$936$	0.139102	0.00454668
$937$	−42.4464	−1.38666	−0.693332	−	0.720618i	$-0.743858\pi$
$937$	−42.4464	−1.38666	−0.693332	+	0.720618i	$0.743858\pi$
$938$	3.92782	0.128248
$939$	19.0114	0.620412
$940$	−2.99496	−0.0976848
$941$	−20.1245	−0.656039	−0.328020	−	0.944671i	$-0.606381\pi$
$941$	−20.1245	−0.656039	−0.328020	+	0.944671i	$0.606381\pi$
$942$	8.15148	0.265589
$943$	2.75522	0.0897221
$944$	−17.3778	−0.565599
$945$	−23.1347	−0.752572
$946$	−56.2474	−1.82876
$947$	−54.5368	−1.77221	−0.886104	−	0.463486i	$-0.846599\pi$
$947$	−54.5368	−1.77221	−0.886104	+	0.463486i	$0.846599\pi$
$948$	2.77782	0.0902195
$949$	9.22714	0.299526
$950$	−4.98130	−0.161615
$951$	−17.7856	−0.576738
$952$	13.7403	0.445326
$953$	−48.3764	−1.56707	−0.783533	−	0.621351i	$-0.786584\pi$
$953$	−48.3764	−1.56707	−0.783533	+	0.621351i	$0.786584\pi$
$954$	−0.373868	−0.0121044
$955$	−5.98397	−0.193637
$956$	13.5636	0.438677
$957$	−23.4930	−0.759419
$958$	−12.3605	−0.399349
$959$	−53.2700	−1.72018
$960$	15.5084	0.500531
$961$	−8.32662	−0.268601
$962$	2.10212	0.0677752
$963$	0.165928	0.00534695
$964$	9.16902	0.295314
$965$	−18.1936	−0.585673
$966$	−8.54464	−0.274919
$967$	18.0046	0.578988	0.289494	−	0.957180i	$-0.406513\pi$
$967$	18.0046	0.578988	0.289494	+	0.957180i	$0.406513\pi$
$968$	10.3470	0.332564
$969$	7.08317	0.227544
$970$	15.3708	0.493526
$971$	−31.8750	−1.02292	−0.511459	−	0.859308i	$-0.670895\pi$
$971$	−31.8750	−1.02292	−0.511459	+	0.859308i	$0.670895\pi$
$972$	0.252997	0.00811487
$973$	8.85915	0.284011
$974$	−6.79056	−0.217584
$975$	1.60339	0.0513496
$976$	28.0927	0.899224
$977$	−14.7371	−0.471483	−0.235741	−	0.971816i	$-0.575752\pi$
$977$	−14.7371	−0.471483	−0.235741	+	0.971816i	$0.575752\pi$
$978$	−19.0243	−0.608331
$979$	−1.58576	−0.0506811
$980$	−6.47241	−0.206754
$981$	−0.219914	−0.00702131
$982$	−45.7352	−1.45947
$983$	−12.8401	−0.409534	−0.204767	−	0.978811i	$-0.565644\pi$
$983$	−12.8401	−0.409534	−0.204767	+	0.978811i	$0.565644\pi$
$984$	16.5928	0.528958
$985$	16.0812	0.512388
$986$	4.35668	0.138745
$987$	47.7505	1.51992
$988$	−1.83155	−0.0582694
$989$	10.7169	0.340777
$990$	−0.230565	−0.00732783
$991$	−10.5630	−0.335545	−0.167773	−	0.985826i	$-0.553657\pi$
$991$	−10.5630	−0.335545	−0.167773	+	0.985826i	$0.553657\pi$
$992$	12.9179	0.410142
$993$	−27.2856	−0.865881
$994$	−5.51423	−0.174901
$995$	0.225119	0.00713675
$996$	9.61056	0.304522
$997$	−15.4641	−0.489752	−0.244876	−	0.969554i	$-0.578747\pi$
$997$	−15.4641	−0.489752	−0.244876	+	0.969554i	$0.578747\pi$
$998$	−31.1879	−0.987236
$999$	9.60533	0.303899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.g.1.19	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.g.1.19	✓	58	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)

\(f(q)\)	\(=\)	\(q-1.22809 q^{2} +1.74628 q^{3} -0.491793 q^{4} +1.00000 q^{5} -2.14460 q^{6} +4.49008 q^{7} +3.06015 q^{8} +0.0495068 q^{9} +O(q^{10})\)	\(q-1.22809 q^{2} +1.74628 q^{3} -0.491793 q^{4} +1.00000 q^{5} -2.14460 q^{6} +4.49008 q^{7} +3.06015 q^{8} +0.0495068 q^{9} -1.22809 q^{10} +3.79225 q^{11} -0.858810 q^{12} +0.918173 q^{13} -5.51423 q^{14} +1.74628 q^{15} -2.77455 q^{16} +1.00000 q^{17} -0.0607989 q^{18} +4.05614 q^{19} -0.491793 q^{20} +7.84096 q^{21} -4.65723 q^{22} +0.887348 q^{23} +5.34389 q^{24} +1.00000 q^{25} -1.12760 q^{26} -5.15240 q^{27} -2.20819 q^{28} -3.54752 q^{29} -2.14460 q^{30} -4.76166 q^{31} -2.71289 q^{32} +6.62235 q^{33} -1.22809 q^{34} +4.49008 q^{35} -0.0243471 q^{36} -1.86425 q^{37} -4.98130 q^{38} +1.60339 q^{39} +3.06015 q^{40} +3.10500 q^{41} -9.62941 q^{42} +12.0774 q^{43} -1.86500 q^{44} +0.0495068 q^{45} -1.08974 q^{46} +6.08988 q^{47} -4.84516 q^{48} +13.1609 q^{49} -1.22809 q^{50} +1.74628 q^{51} -0.451551 q^{52} +6.14926 q^{53} +6.32761 q^{54} +3.79225 q^{55} +13.7403 q^{56} +7.08317 q^{57} +4.35668 q^{58} +6.26327 q^{59} -0.858810 q^{60} -10.1251 q^{61} +5.84775 q^{62} +0.222290 q^{63} +8.88079 q^{64} +0.918173 q^{65} -8.13285 q^{66} -0.712305 q^{67} -0.491793 q^{68} +1.54956 q^{69} -5.51423 q^{70} +1.00000 q^{71} +0.151498 q^{72} +10.0495 q^{73} +2.28946 q^{74} +1.74628 q^{75} -1.99478 q^{76} +17.0275 q^{77} -1.96911 q^{78} -3.23450 q^{79} -2.77455 q^{80} -9.14607 q^{81} -3.81322 q^{82} -11.1906 q^{83} -3.85613 q^{84} +1.00000 q^{85} -14.8322 q^{86} -6.19498 q^{87} +11.6049 q^{88} -0.418157 q^{89} -0.0607989 q^{90} +4.12267 q^{91} -0.436391 q^{92} -8.31521 q^{93} -7.47893 q^{94} +4.05614 q^{95} -4.73748 q^{96} -12.5160 q^{97} -16.1627 q^{98} +0.187742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * q^99

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