LMFDB - Embedded newform 6035.2.a.h.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.15770 q^{2} +0.151800 q^{3} -0.659734 q^{4} +1.00000 q^{5} -0.175739 q^{6} -1.47605 q^{7} +3.07917 q^{8} -2.97696 q^{9} +O(q^{10})$	\(q-1.15770 q^{2} +0.151800 q^{3} -0.659734 q^{4} +1.00000 q^{5} -0.175739 q^{6} -1.47605 q^{7} +3.07917 q^{8} -2.97696 q^{9} -1.15770 q^{10} -4.09881 q^{11} -0.100148 q^{12} -5.73266 q^{13} +1.70882 q^{14} +0.151800 q^{15} -2.24528 q^{16} -1.00000 q^{17} +3.44642 q^{18} +5.48494 q^{19} -0.659734 q^{20} -0.224064 q^{21} +4.74519 q^{22} -3.36468 q^{23} +0.467418 q^{24} +1.00000 q^{25} +6.63669 q^{26} -0.907301 q^{27} +0.973799 q^{28} -8.71953 q^{29} -0.175739 q^{30} +6.73056 q^{31} -3.55898 q^{32} -0.622200 q^{33} +1.15770 q^{34} -1.47605 q^{35} +1.96400 q^{36} -4.36855 q^{37} -6.34991 q^{38} -0.870217 q^{39} +3.07917 q^{40} -9.70355 q^{41} +0.259398 q^{42} +6.38894 q^{43} +2.70413 q^{44} -2.97696 q^{45} +3.89529 q^{46} -4.07299 q^{47} -0.340834 q^{48} -4.82128 q^{49} -1.15770 q^{50} -0.151800 q^{51} +3.78203 q^{52} -7.85015 q^{53} +1.05038 q^{54} -4.09881 q^{55} -4.54500 q^{56} +0.832613 q^{57} +10.0946 q^{58} +11.6314 q^{59} -0.100148 q^{60} -11.0078 q^{61} -7.79196 q^{62} +4.39413 q^{63} +8.61079 q^{64} -5.73266 q^{65} +0.720320 q^{66} -9.09646 q^{67} +0.659734 q^{68} -0.510758 q^{69} +1.70882 q^{70} -1.00000 q^{71} -9.16656 q^{72} +13.4496 q^{73} +5.05747 q^{74} +0.151800 q^{75} -3.61860 q^{76} +6.05005 q^{77} +1.00745 q^{78} -14.7955 q^{79} -2.24528 q^{80} +8.79314 q^{81} +11.2338 q^{82} -1.40893 q^{83} +0.147823 q^{84} -1.00000 q^{85} -7.39646 q^{86} -1.32362 q^{87} -12.6209 q^{88} -2.80115 q^{89} +3.44642 q^{90} +8.46167 q^{91} +2.21980 q^{92} +1.02170 q^{93} +4.71529 q^{94} +5.48494 q^{95} -0.540253 q^{96} +3.94992 q^{97} +5.58159 q^{98} +12.2020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.15770	−0.818616	−0.409308	−	0.912396i	$-0.634230\pi$
$2$	−1.15770	−0.818616	−0.409308	+	0.912396i	$0.634230\pi$
$3$	0.151800	0.0876417	0.0438209	−	0.999039i	$-0.486047\pi$
$3$	0.151800	0.0876417	0.0438209	+	0.999039i	$0.486047\pi$
$4$	−0.659734	−0.329867
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.175739	−0.0717449
$7$	−1.47605	−0.557894	−0.278947	−	0.960307i	$-0.589985\pi$
$7$	−1.47605	−0.557894	−0.278947	+	0.960307i	$0.589985\pi$
$8$	3.07917	1.08865
$9$	−2.97696	−0.992319
$10$	−1.15770	−0.366096
$11$	−4.09881	−1.23584	−0.617920	−	0.786241i	$-0.712024\pi$
$11$	−4.09881	−1.23584	−0.617920	+	0.786241i	$0.712024\pi$
$12$	−0.100148	−0.0289101
$13$	−5.73266	−1.58995	−0.794976	−	0.606641i	$-0.792517\pi$
$13$	−5.73266	−1.58995	−0.794976	+	0.606641i	$0.792517\pi$
$14$	1.70882	0.456701
$15$	0.151800	0.0391946
$16$	−2.24528	−0.561320
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.44642	0.812329
$19$	5.48494	1.25833	0.629166	−	0.777271i	$-0.283397\pi$
$19$	5.48494	1.25833	0.629166	+	0.777271i	$0.283397\pi$
$20$	−0.659734	−0.147521
$21$	−0.224064	−0.0488948
$22$	4.74519	1.01168
$23$	−3.36468	−0.701585	−0.350792	−	0.936453i	$-0.614088\pi$
$23$	−3.36468	−0.701585	−0.350792	+	0.936453i	$0.614088\pi$
$24$	0.467418	0.0954112
$25$	1.00000	0.200000
$26$	6.63669	1.30156
$27$	−0.907301	−0.174610
$28$	0.973799	0.184031
$29$	−8.71953	−1.61918	−0.809588	−	0.586999i	$-0.800309\pi$
$29$	−8.71953	−1.61918	−0.809588	+	0.586999i	$0.800309\pi$
$30$	−0.175739	−0.0320853
$31$	6.73056	1.20884	0.604422	−	0.796664i	$-0.293404\pi$
$31$	6.73056	1.20884	0.604422	+	0.796664i	$0.293404\pi$
$32$	−3.55898	−0.629145
$33$	−0.622200	−0.108311
$34$	1.15770	0.198544
$35$	−1.47605	−0.249498
$36$	1.96400	0.327333
$37$	−4.36855	−0.718186	−0.359093	−	0.933302i	$-0.616914\pi$
$37$	−4.36855	−0.718186	−0.359093	+	0.933302i	$0.616914\pi$
$38$	−6.34991	−1.03009
$39$	−0.870217	−0.139346
$40$	3.07917	0.486860
$41$	−9.70355	−1.51544	−0.757720	−	0.652580i	$-0.773687\pi$
$41$	−9.70355	−1.51544	−0.757720	+	0.652580i	$0.773687\pi$
$42$	0.259398	0.0400260
$43$	6.38894	0.974304	0.487152	−	0.873317i	$-0.338036\pi$
$43$	6.38894	0.974304	0.487152	+	0.873317i	$0.338036\pi$
$44$	2.70413	0.407663
$45$	−2.97696	−0.443779
$46$	3.89529	0.574329
$47$	−4.07299	−0.594107	−0.297053	−	0.954861i	$-0.596004\pi$
$47$	−4.07299	−0.594107	−0.297053	+	0.954861i	$0.596004\pi$
$48$	−0.340834	−0.0491951
$49$	−4.82128	−0.688755
$50$	−1.15770	−0.163723
$51$	−0.151800	−0.0212562
$52$	3.78203	0.524473
$53$	−7.85015	−1.07830	−0.539150	−	0.842210i	$-0.681255\pi$
$53$	−7.85015	−1.07830	−0.539150	+	0.842210i	$0.681255\pi$
$54$	1.05038	0.142939
$55$	−4.09881	−0.552684
$56$	−4.54500	−0.607352
$57$	0.832613	0.110282
$58$	10.0946	1.32548
$59$	11.6314	1.51428	0.757142	−	0.653251i	$-0.226595\pi$
$59$	11.6314	1.51428	0.757142	+	0.653251i	$0.226595\pi$
$60$	−0.100148	−0.0129290
$61$	−11.0078	−1.40941	−0.704704	−	0.709502i	$-0.748920\pi$
$61$	−11.0078	−1.40941	−0.704704	+	0.709502i	$0.748920\pi$
$62$	−7.79196	−0.989579
$63$	4.39413	0.553608
$64$	8.61079	1.07635
$65$	−5.73266	−0.711048
$66$	0.720320	0.0886652
$67$	−9.09646	−1.11131	−0.555655	−	0.831413i	$-0.687532\pi$
$67$	−9.09646	−1.11131	−0.555655	+	0.831413i	$0.687532\pi$
$68$	0.659734	0.0800045
$69$	−0.510758	−0.0614881
$70$	1.70882	0.204243
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−9.16656	−1.08029
$73$	13.4496	1.57416	0.787081	−	0.616850i	$-0.211591\pi$
$73$	13.4496	1.57416	0.787081	+	0.616850i	$0.211591\pi$
$74$	5.05747	0.587918
$75$	0.151800	0.0175283
$76$	−3.61860	−0.415082
$77$	6.05005	0.689467
$78$	1.00745	0.114071
$79$	−14.7955	−1.66462	−0.832311	−	0.554309i	$-0.812982\pi$
$79$	−14.7955	−1.66462	−0.832311	+	0.554309i	$0.812982\pi$
$80$	−2.24528	−0.251030
$81$	8.79314	0.977016
$82$	11.2338	1.24056
$83$	−1.40893	−0.154650	−0.0773250	−	0.997006i	$-0.524638\pi$
$83$	−1.40893	−0.154650	−0.0773250	+	0.997006i	$0.524638\pi$
$84$	0.147823	0.0161288
$85$	−1.00000	−0.108465
$86$	−7.39646	−0.797581
$87$	−1.32362	−0.141907
$88$	−12.6209	−1.34540
$89$	−2.80115	−0.296921	−0.148461	−	0.988918i	$-0.547432\pi$
$89$	−2.80115	−0.296921	−0.148461	+	0.988918i	$0.547432\pi$
$90$	3.44642	0.363284
$91$	8.46167	0.887024
$92$	2.21980	0.231430
$93$	1.02170	0.105945
$94$	4.71529	0.486345
$95$	5.48494	0.562743
$96$	−0.540253	−0.0551393
$97$	3.94992	0.401054	0.200527	−	0.979688i	$-0.435735\pi$
$97$	3.94992	0.401054	0.200527	+	0.979688i	$0.435735\pi$
$98$	5.58159	0.563826
$99$	12.2020	1.22635
$100$	−0.659734	−0.0659734
$101$	0.977567	0.0972715	0.0486358	−	0.998817i	$-0.484513\pi$
$101$	0.977567	0.0972715	0.0486358	+	0.998817i	$0.484513\pi$
$102$	0.175739	0.0174007
$103$	4.31890	0.425553	0.212777	−	0.977101i	$-0.431749\pi$
$103$	4.31890	0.425553	0.212777	+	0.977101i	$0.431749\pi$
$104$	−17.6518	−1.73090
$105$	−0.224064	−0.0218664
$106$	9.08810	0.882715
$107$	−2.92255	−0.282534	−0.141267	−	0.989972i	$-0.545118\pi$
$107$	−2.92255	−0.282534	−0.141267	+	0.989972i	$0.545118\pi$
$108$	0.598578	0.0575982
$109$	16.5691	1.58703	0.793515	−	0.608551i	$-0.208249\pi$
$109$	16.5691	1.58703	0.793515	+	0.608551i	$0.208249\pi$
$110$	4.74519	0.452436
$111$	−0.663146	−0.0629430
$112$	3.31414	0.313157
$113$	−16.8621	−1.58626	−0.793128	−	0.609055i	$-0.791549\pi$
$113$	−16.8621	−1.58626	−0.793128	+	0.609055i	$0.791549\pi$
$114$	−0.963915	−0.0902789
$115$	−3.36468	−0.313758
$116$	5.75257	0.534113
$117$	17.0659	1.57774
$118$	−13.4657	−1.23962
$119$	1.47605	0.135309
$120$	0.467418	0.0426692
$121$	5.80028	0.527298
$122$	12.7437	1.15376
$123$	−1.47300	−0.132816
$124$	−4.44038	−0.398758
$125$	1.00000	0.0894427
$126$	−5.08708	−0.453193
$127$	19.0368	1.68925	0.844623	−	0.535361i	$-0.179824\pi$
$127$	19.0368	1.68925	0.844623	+	0.535361i	$0.179824\pi$
$128$	−2.85074	−0.251972
$129$	0.969840	0.0853896
$130$	6.63669	0.582076
$131$	13.3959	1.17040	0.585201	−	0.810888i	$-0.301015\pi$
$131$	13.3959	1.17040	0.585201	+	0.810888i	$0.301015\pi$
$132$	0.410486	0.0357283
$133$	−8.09603	−0.702015
$134$	10.5310	0.909736
$135$	−0.907301	−0.0780881
$136$	−3.07917	−0.264037
$137$	−7.28653	−0.622530	−0.311265	−	0.950323i	$-0.600753\pi$
$137$	−7.28653	−0.622530	−0.311265	+	0.950323i	$0.600753\pi$
$138$	0.591304	0.0503352
$139$	−14.8162	−1.25670	−0.628349	−	0.777932i	$-0.716269\pi$
$139$	−14.8162	−1.25670	−0.628349	+	0.777932i	$0.716269\pi$
$140$	0.973799	0.0823011
$141$	−0.618280	−0.0520685
$142$	1.15770	0.0971519
$143$	23.4971	1.96493
$144$	6.68411	0.557009
$145$	−8.71953	−0.724117
$146$	−15.5706	−1.28864
$147$	−0.731870	−0.0603636
$148$	2.88208	0.236906
$149$	−4.55578	−0.373224	−0.186612	−	0.982434i	$-0.559751\pi$
$149$	−4.55578	−0.373224	−0.186612	+	0.982434i	$0.559751\pi$
$150$	−0.175739	−0.0143490
$151$	5.54180	0.450986	0.225493	−	0.974245i	$-0.427601\pi$
$151$	5.54180	0.450986	0.225493	+	0.974245i	$0.427601\pi$
$152$	16.8891	1.36988
$153$	2.97696	0.240673
$154$	−7.00413	−0.564409
$155$	6.73056	0.540611
$156$	0.574112	0.0459657
$157$	−4.39543	−0.350793	−0.175397	−	0.984498i	$-0.556121\pi$
$157$	−4.39543	−0.350793	−0.175397	+	0.984498i	$0.556121\pi$
$158$	17.1287	1.36269
$159$	−1.19165	−0.0945041
$160$	−3.55898	−0.281362
$161$	4.96643	0.391410
$162$	−10.1798	−0.799801
$163$	0.745707	0.0584083	0.0292041	−	0.999573i	$-0.490703\pi$
$163$	0.745707	0.0584083	0.0292041	+	0.999573i	$0.490703\pi$
$164$	6.40176	0.499894
$165$	−0.622200	−0.0484382
$166$	1.63111	0.126599
$167$	0.971474	0.0751749	0.0375875	−	0.999293i	$-0.488033\pi$
$167$	0.971474	0.0751749	0.0375875	+	0.999293i	$0.488033\pi$
$168$	−0.689931	−0.0532293
$169$	19.8633	1.52795
$170$	1.15770	0.0887914
$171$	−16.3284	−1.24867
$172$	−4.21500	−0.321391
$173$	23.9302	1.81938	0.909691	−	0.415286i	$-0.136318\pi$
$173$	23.9302	1.81938	0.909691	+	0.415286i	$0.136318\pi$
$174$	1.53236	0.116168
$175$	−1.47605	−0.111579
$176$	9.20299	0.693702
$177$	1.76565	0.132714
$178$	3.24289	0.243065
$179$	16.5703	1.23852	0.619262	−	0.785184i	$-0.287432\pi$
$179$	16.5703	1.23852	0.619262	+	0.785184i	$0.287432\pi$
$180$	1.96400	0.146388
$181$	−9.83681	−0.731164	−0.365582	−	0.930779i	$-0.619130\pi$
$181$	−9.83681	−0.731164	−0.365582	+	0.930779i	$0.619130\pi$
$182$	−9.79607	−0.726133
$183$	−1.67099	−0.123523
$184$	−10.3604	−0.763781
$185$	−4.36855	−0.321182
$186$	−1.18282	−0.0867284
$187$	4.09881	0.299735
$188$	2.68709	0.195976
$189$	1.33922	0.0974139
$190$	−6.34991	−0.460671
$191$	10.0393	0.726418	0.363209	−	0.931708i	$-0.381681\pi$
$191$	10.0393	0.726418	0.363209	+	0.931708i	$0.381681\pi$
$192$	1.30712	0.0943331
$193$	−19.2531	−1.38587	−0.692934	−	0.721001i	$-0.743682\pi$
$193$	−19.2531	−1.38587	−0.692934	+	0.721001i	$0.743682\pi$
$194$	−4.57282	−0.328309
$195$	−0.870217	−0.0623175
$196$	3.18077	0.227198
$197$	−15.7549	−1.12249	−0.561244	−	0.827650i	$-0.689677\pi$
$197$	−15.7549	−1.12249	−0.561244	+	0.827650i	$0.689677\pi$
$198$	−14.1262	−1.00391
$199$	13.2291	0.937790	0.468895	−	0.883254i	$-0.344652\pi$
$199$	13.2291	0.937790	0.468895	+	0.883254i	$0.344652\pi$
$200$	3.07917	0.217730
$201$	−1.38084	−0.0973970
$202$	−1.13173	−0.0796281
$203$	12.8704	0.903328
$204$	0.100148	0.00701174
$205$	−9.70355	−0.677725
$206$	−4.99998	−0.348365
$207$	10.0165	0.696196
$208$	12.8714	0.892473
$209$	−22.4818	−1.55510
$210$	0.259398	0.0179002
$211$	−20.8357	−1.43439	−0.717194	−	0.696874i	$-0.754574\pi$
$211$	−20.8357	−1.43439	−0.717194	+	0.696874i	$0.754574\pi$
$212$	5.17901	0.355696
$213$	−0.151800	−0.0104012
$214$	3.38343	0.231287
$215$	6.38894	0.435722
$216$	−2.79374	−0.190090
$217$	−9.93462	−0.674406
$218$	−19.1820	−1.29917
$219$	2.04166	0.137962
$220$	2.70413	0.182312
$221$	5.73266	0.385620
$222$	0.767723	0.0515262
$223$	12.7865	0.856248	0.428124	−	0.903720i	$-0.359175\pi$
$223$	12.7865	0.856248	0.428124	+	0.903720i	$0.359175\pi$
$224$	5.25323	0.350996
$225$	−2.97696	−0.198464
$226$	19.5213	1.29853
$227$	−10.7144	−0.711137	−0.355568	−	0.934650i	$-0.615713\pi$
$227$	−10.7144	−0.711137	−0.355568	+	0.934650i	$0.615713\pi$
$228$	−0.549304	−0.0363785
$229$	15.4229	1.01917	0.509587	−	0.860419i	$-0.329798\pi$
$229$	15.4229	1.01917	0.509587	+	0.860419i	$0.329798\pi$
$230$	3.89529	0.256848
$231$	0.918396	0.0604261
$232$	−26.8489	−1.76272
$233$	16.5277	1.08276	0.541382	−	0.840777i	$-0.317901\pi$
$233$	16.5277	1.08276	0.541382	+	0.840777i	$0.317901\pi$
$234$	−19.7571	−1.29156
$235$	−4.07299	−0.265693
$236$	−7.67365	−0.499512
$237$	−2.24595	−0.145890
$238$	−1.70882	−0.110766
$239$	0.768666	0.0497209	0.0248604	−	0.999691i	$-0.492086\pi$
$239$	0.768666	0.0497209	0.0248604	+	0.999691i	$0.492086\pi$
$240$	−0.340834	−0.0220007
$241$	−27.5507	−1.77469	−0.887347	−	0.461102i	$-0.847454\pi$
$241$	−27.5507	−1.77469	−0.887347	+	0.461102i	$0.847454\pi$
$242$	−6.71498	−0.431655
$243$	4.05670	0.260238
$244$	7.26224	0.464917
$245$	−4.82128	−0.308020
$246$	1.70529	0.108725
$247$	−31.4433	−2.00069
$248$	20.7245	1.31601
$249$	−0.213875	−0.0135538
$250$	−1.15770	−0.0732193
$251$	10.0953	0.637207	0.318604	−	0.947888i	$-0.396786\pi$
$251$	10.0953	0.637207	0.318604	+	0.947888i	$0.396786\pi$
$252$	−2.89896	−0.182617
$253$	13.7912	0.867046
$254$	−22.0389	−1.38285
$255$	−0.151800	−0.00950608
$256$	−13.9213	−0.870081
$257$	−12.2657	−0.765111	−0.382556	−	0.923932i	$-0.624956\pi$
$257$	−12.2657	−0.765111	−0.382556	+	0.923932i	$0.624956\pi$
$258$	−1.12278	−0.0699014
$259$	6.44819	0.400671
$260$	3.78203	0.234552
$261$	25.9577	1.60674
$262$	−15.5084	−0.958111
$263$	−7.39317	−0.455882	−0.227941	−	0.973675i	$-0.573199\pi$
$263$	−7.39317	−0.455882	−0.227941	+	0.973675i	$0.573199\pi$
$264$	−1.91586	−0.117913
$265$	−7.85015	−0.482231
$266$	9.37277	0.574681
$267$	−0.425214	−0.0260227
$268$	6.00125	0.366584
$269$	−29.9787	−1.82783	−0.913916	−	0.405902i	$-0.866957\pi$
$269$	−29.9787	−1.82783	−0.913916	+	0.405902i	$0.866957\pi$
$270$	1.05038	0.0639242
$271$	−8.42753	−0.511936	−0.255968	−	0.966685i	$-0.582394\pi$
$271$	−8.42753	−0.511936	−0.255968	+	0.966685i	$0.582394\pi$
$272$	2.24528	0.136140
$273$	1.28448	0.0777403
$274$	8.43560	0.509613
$275$	−4.09881	−0.247168
$276$	0.336965	0.0202829
$277$	24.2133	1.45484	0.727419	−	0.686193i	$-0.240720\pi$
$277$	24.2133	1.45484	0.727419	+	0.686193i	$0.240720\pi$
$278$	17.1527	1.02875
$279$	−20.0366	−1.19956
$280$	−4.54500	−0.271616
$281$	18.9774	1.13210	0.566050	−	0.824371i	$-0.308471\pi$
$281$	18.9774	1.13210	0.566050	+	0.824371i	$0.308471\pi$
$282$	0.715781	0.0426242
$283$	2.22120	0.132037	0.0660184	−	0.997818i	$-0.478970\pi$
$283$	2.22120	0.132037	0.0660184	+	0.997818i	$0.478970\pi$
$284$	0.659734	0.0391480
$285$	0.832613	0.0493198
$286$	−27.2025	−1.60852
$287$	14.3229	0.845454
$288$	10.5949	0.624312
$289$	1.00000	0.0588235
$290$	10.0946	0.592774
$291$	0.599598	0.0351491
$292$	−8.87319	−0.519264
$293$	9.51258	0.555731	0.277865	−	0.960620i	$-0.410373\pi$
$293$	9.51258	0.555731	0.277865	+	0.960620i	$0.410373\pi$
$294$	0.847285	0.0494147
$295$	11.6314	0.677208
$296$	−13.4515	−0.781853
$297$	3.71886	0.215790
$298$	5.27422	0.305527
$299$	19.2886	1.11549
$300$	−0.100148	−0.00578202
$301$	−9.43038	−0.543558
$302$	−6.41574	−0.369184
$303$	0.148395	0.00852504
$304$	−12.3152	−0.706327
$305$	−11.0078	−0.630306
$306$	−3.44642	−0.197019
$307$	−14.4644	−0.825524	−0.412762	−	0.910839i	$-0.635436\pi$
$307$	−14.4644	−0.825524	−0.412762	+	0.910839i	$0.635436\pi$
$308$	−3.99142	−0.227432
$309$	0.655608	0.0372962
$310$	−7.79196	−0.442553
$311$	−21.4243	−1.21486	−0.607431	−	0.794373i	$-0.707800\pi$
$311$	−21.4243	−1.21486	−0.607431	+	0.794373i	$0.707800\pi$
$312$	−2.67954	−0.151699
$313$	11.8014	0.667053	0.333526	−	0.942741i	$-0.391761\pi$
$313$	11.8014	0.667053	0.333526	+	0.942741i	$0.391761\pi$
$314$	5.08858	0.287165
$315$	4.39413	0.247581
$316$	9.76108	0.549104
$317$	−12.0401	−0.676240	−0.338120	−	0.941103i	$-0.609791\pi$
$317$	−12.0401	−0.676240	−0.338120	+	0.941103i	$0.609791\pi$
$318$	1.37957	0.0773626
$319$	35.7397	2.00104
$320$	8.61079	0.481358
$321$	−0.443643	−0.0247617
$322$	−5.74963	−0.320414
$323$	−5.48494	−0.305190
$324$	−5.80114	−0.322285
$325$	−5.73266	−0.317991
$326$	−0.863304	−0.0478140
$327$	2.51518	0.139090
$328$	−29.8789	−1.64978
$329$	6.01193	0.331448
$330$	0.720320	0.0396523
$331$	12.9434	0.711433	0.355717	−	0.934594i	$-0.384237\pi$
$331$	12.9434	0.711433	0.355717	+	0.934594i	$0.384237\pi$
$332$	0.929518	0.0510139
$333$	13.0050	0.712669
$334$	−1.12467	−0.0615394
$335$	−9.09646	−0.496993
$336$	0.503087	0.0274456
$337$	1.07493	0.0585550	0.0292775	−	0.999571i	$-0.490679\pi$
$337$	1.07493	0.0585550	0.0292775	+	0.999571i	$0.490679\pi$
$338$	−22.9958	−1.25080
$339$	−2.55967	−0.139022
$340$	0.659734	0.0357791
$341$	−27.5873	−1.49394
$342$	18.9034	1.02218
$343$	17.4488	0.942146
$344$	19.6726	1.06068
$345$	−0.510758	−0.0274983
$346$	−27.7040	−1.48938
$347$	−10.6266	−0.570468	−0.285234	−	0.958458i	$-0.592071\pi$
$347$	−10.6266	−0.570468	−0.285234	+	0.958458i	$0.592071\pi$
$348$	0.873240	0.0468106
$349$	9.56382	0.511940	0.255970	−	0.966685i	$-0.417605\pi$
$349$	9.56382	0.511940	0.255970	+	0.966685i	$0.417605\pi$
$350$	1.70882	0.0913402
$351$	5.20125	0.277622
$352$	14.5876	0.777522
$353$	4.55188	0.242272	0.121136	−	0.992636i	$-0.461346\pi$
$353$	4.55188	0.242272	0.121136	+	0.992636i	$0.461346\pi$
$354$	−2.04409	−0.108642
$355$	−1.00000	−0.0530745
$356$	1.84802	0.0979446
$357$	0.224064	0.0118587
$358$	−19.1834	−1.01388
$359$	28.9977	1.53044	0.765219	−	0.643770i	$-0.222630\pi$
$359$	28.9977	1.53044	0.765219	+	0.643770i	$0.222630\pi$
$360$	−9.16656	−0.483120
$361$	11.0846	0.583398
$362$	11.3881	0.598543
$363$	0.880482	0.0462133
$364$	−5.58246	−0.292600
$365$	13.4496	0.703987
$366$	1.93450	0.101118
$367$	−6.10835	−0.318853	−0.159427	−	0.987210i	$-0.550965\pi$
$367$	−6.10835	−0.318853	−0.159427	+	0.987210i	$0.550965\pi$
$368$	7.55466	0.393814
$369$	28.8870	1.50380
$370$	5.05747	0.262925
$371$	11.5872	0.601577
$372$	−0.674049	−0.0349478
$373$	−16.6483	−0.862014	−0.431007	−	0.902349i	$-0.641842\pi$
$373$	−16.6483	−0.862014	−0.431007	+	0.902349i	$0.641842\pi$
$374$	−4.74519	−0.245368
$375$	0.151800	0.00783891
$376$	−12.5414	−0.646775
$377$	49.9860	2.57441
$378$	−1.55041	−0.0797447
$379$	28.8558	1.48222	0.741111	−	0.671383i	$-0.234299\pi$
$379$	28.8558	1.48222	0.741111	+	0.671383i	$0.234299\pi$
$380$	−3.61860	−0.185630
$381$	2.88979	0.148049
$382$	−11.6225	−0.594658
$383$	11.9375	0.609979	0.304990	−	0.952356i	$-0.401347\pi$
$383$	11.9375	0.609979	0.304990	+	0.952356i	$0.401347\pi$
$384$	−0.432742	−0.0220832
$385$	6.05005	0.308339
$386$	22.2893	1.13449
$387$	−19.0196	−0.966820
$388$	−2.60590	−0.132295
$389$	27.1499	1.37655	0.688277	−	0.725448i	$-0.258368\pi$
$389$	27.1499	1.37655	0.688277	+	0.725448i	$0.258368\pi$
$390$	1.00745	0.0510141
$391$	3.36468	0.170159
$392$	−14.8456	−0.749814
$393$	2.03349	0.102576
$394$	18.2394	0.918888
$395$	−14.7955	−0.744441
$396$	−8.05007	−0.404531
$397$	33.9603	1.70442	0.852210	−	0.523201i	$-0.175262\pi$
$397$	33.9603	1.70442	0.852210	+	0.523201i	$0.175262\pi$
$398$	−15.3154	−0.767690
$399$	−1.22898	−0.0615258
$400$	−2.24528	−0.112264
$401$	−22.5847	−1.12783	−0.563914	−	0.825834i	$-0.690705\pi$
$401$	−22.5847	−1.12783	−0.563914	+	0.825834i	$0.690705\pi$
$402$	1.59860	0.0797308
$403$	−38.5840	−1.92200
$404$	−0.644934	−0.0320867
$405$	8.79314	0.436935
$406$	−14.9001	−0.739479
$407$	17.9059	0.887562
$408$	−0.467418	−0.0231406
$409$	3.25935	0.161165	0.0805823	−	0.996748i	$-0.474322\pi$
$409$	3.25935	0.161165	0.0805823	+	0.996748i	$0.474322\pi$
$410$	11.2338	0.554797
$411$	−1.10609	−0.0545596
$412$	−2.84932	−0.140376
$413$	−17.1685	−0.844809
$414$	−11.5961	−0.569917
$415$	−1.40893	−0.0691615
$416$	20.4024	1.00031
$417$	−2.24910	−0.110139
$418$	26.0271	1.27303
$419$	−7.59851	−0.371211	−0.185606	−	0.982624i	$-0.559425\pi$
$419$	−7.59851	−0.371211	−0.185606	+	0.982624i	$0.559425\pi$
$420$	0.147823	0.00721301
$421$	10.6622	0.519644	0.259822	−	0.965657i	$-0.416336\pi$
$421$	10.6622	0.519644	0.259822	+	0.965657i	$0.416336\pi$
$422$	24.1214	1.17421
$423$	12.1251	0.589543
$424$	−24.1719	−1.17389
$425$	−1.00000	−0.0485071
$426$	0.175739	0.00851456
$427$	16.2481	0.786299
$428$	1.92811	0.0931986
$429$	3.56686	0.172209
$430$	−7.39646	−0.356689
$431$	12.8435	0.618649	0.309324	−	0.950957i	$-0.399897\pi$
$431$	12.8435	0.618649	0.309324	+	0.950957i	$0.399897\pi$
$432$	2.03715	0.0980123
$433$	0.748898	0.0359898	0.0179949	−	0.999838i	$-0.494272\pi$
$433$	0.748898	0.0359898	0.0179949	+	0.999838i	$0.494272\pi$
$434$	11.5013	0.552080
$435$	−1.32362	−0.0634629
$436$	−10.9312	−0.523509
$437$	−18.4551	−0.882826
$438$	−2.36362	−0.112938
$439$	11.6843	0.557661	0.278830	−	0.960340i	$-0.410053\pi$
$439$	11.6843	0.557661	0.278830	+	0.960340i	$0.410053\pi$
$440$	−12.6209	−0.601680
$441$	14.3528	0.683464
$442$	−6.63669	−0.315675
$443$	5.27224	0.250492	0.125246	−	0.992126i	$-0.460028\pi$
$443$	5.27224	0.250492	0.125246	+	0.992126i	$0.460028\pi$
$444$	0.437500	0.0207628
$445$	−2.80115	−0.132787
$446$	−14.8029	−0.700939
$447$	−0.691567	−0.0327100
$448$	−12.7099	−0.600488
$449$	34.9399	1.64892	0.824459	−	0.565922i	$-0.191480\pi$
$449$	34.9399	1.64892	0.824459	+	0.565922i	$0.191480\pi$
$450$	3.44642	0.162466
$451$	39.7730	1.87284
$452$	11.1245	0.523254
$453$	0.841245	0.0395252
$454$	12.4040	0.582148
$455$	8.46167	0.396689
$456$	2.56376	0.120059
$457$	−19.3672	−0.905958	−0.452979	−	0.891521i	$-0.649639\pi$
$457$	−19.3672	−0.905958	−0.452979	+	0.891521i	$0.649639\pi$
$458$	−17.8551	−0.834312
$459$	0.907301	0.0423492
$460$	2.21980	0.103499
$461$	26.5221	1.23526	0.617629	−	0.786470i	$-0.288093\pi$
$461$	26.5221	1.23526	0.617629	+	0.786470i	$0.288093\pi$
$462$	−1.06323	−0.0494658
$463$	2.65966	0.123605	0.0618024	−	0.998088i	$-0.480315\pi$
$463$	2.65966	0.123605	0.0618024	+	0.998088i	$0.480315\pi$
$464$	19.5778	0.908876
$465$	1.02170	0.0473801
$466$	−19.1341	−0.886369
$467$	−35.8575	−1.65929	−0.829643	−	0.558294i	$-0.811456\pi$
$467$	−35.8575	−1.65929	−0.829643	+	0.558294i	$0.811456\pi$
$468$	−11.2589	−0.520445
$469$	13.4268	0.619992
$470$	4.71529	0.217500
$471$	−0.667225	−0.0307441
$472$	35.8152	1.64853
$473$	−26.1871	−1.20408
$474$	2.60014	0.119428
$475$	5.48494	0.251666
$476$	−0.973799	−0.0446340
$477$	23.3695	1.07002
$478$	−0.889884	−0.0407023
$479$	34.9971	1.59906	0.799529	−	0.600627i	$-0.205082\pi$
$479$	34.9971	1.59906	0.799529	+	0.600627i	$0.205082\pi$
$480$	−0.540253	−0.0246591
$481$	25.0434	1.14188
$482$	31.8954	1.45279
$483$	0.753904	0.0343038
$484$	−3.82664	−0.173938
$485$	3.94992	0.179357
$486$	−4.69644	−0.213035
$487$	−23.0879	−1.04621	−0.523106	−	0.852268i	$-0.675227\pi$
$487$	−23.0879	−1.04621	−0.523106	+	0.852268i	$0.675227\pi$
$488$	−33.8950	−1.53435
$489$	0.113198	0.00511900
$490$	5.58159	0.252151
$491$	2.15966	0.0974643	0.0487322	−	0.998812i	$-0.484482\pi$
$491$	2.15966	0.0974643	0.0487322	+	0.998812i	$0.484482\pi$
$492$	0.971787	0.0438115
$493$	8.71953	0.392708
$494$	36.4018	1.63780
$495$	12.2020	0.548439
$496$	−15.1120	−0.678549
$497$	1.47605	0.0662098
$498$	0.247603	0.0110954
$499$	13.4900	0.603897	0.301948	−	0.953324i	$-0.402363\pi$
$499$	13.4900	0.603897	0.301948	+	0.953324i	$0.402363\pi$
$500$	−0.659734	−0.0295042
$501$	0.147470	0.00658846
$502$	−11.6873	−0.521628
$503$	21.9109	0.976959	0.488480	−	0.872575i	$-0.337552\pi$
$503$	21.9109	0.976959	0.488480	+	0.872575i	$0.337552\pi$
$504$	13.5303	0.602686
$505$	0.977567	0.0435012
$506$	−15.9661	−0.709778
$507$	3.01525	0.133912
$508$	−12.5593	−0.557227
$509$	33.0965	1.46697	0.733487	−	0.679703i	$-0.237891\pi$
$509$	33.0965	1.46697	0.733487	+	0.679703i	$0.237891\pi$
$510$	0.175739	0.00778183
$511$	−19.8523	−0.878215
$512$	21.8181	0.964234
$513$	−4.97649	−0.219718
$514$	14.1999	0.626333
$515$	4.31890	0.190313
$516$	−0.639837	−0.0281672
$517$	16.6944	0.734220
$518$	−7.46506	−0.327996
$519$	3.63261	0.159454
$520$	−17.6518	−0.774084
$521$	−16.8229	−0.737026	−0.368513	−	0.929623i	$-0.620133\pi$
$521$	−16.8229	−0.737026	−0.368513	+	0.929623i	$0.620133\pi$
$522$	−30.0511	−1.31530
$523$	−25.7380	−1.12544	−0.562722	−	0.826646i	$-0.690246\pi$
$523$	−25.7380	−1.12544	−0.562722	+	0.826646i	$0.690246\pi$
$524$	−8.83772	−0.386077
$525$	−0.224064	−0.00977895
$526$	8.55906	0.373193
$527$	−6.73056	−0.293188
$528$	1.39701	0.0607972
$529$	−11.6789	−0.507779
$530$	9.08810	0.394762
$531$	−34.6263	−1.50265
$532$	5.34123	0.231572
$533$	55.6271	2.40948
$534$	0.492270	0.0213026
$535$	−2.92255	−0.126353
$536$	−28.0095	−1.20983
$537$	2.51537	0.108546
$538$	34.7063	1.49629
$539$	19.7615	0.851190
$540$	0.598578	0.0257587
$541$	23.5698	1.01335	0.506673	−	0.862138i	$-0.330875\pi$
$541$	23.5698	1.01335	0.506673	+	0.862138i	$0.330875\pi$
$542$	9.75654	0.419079
$543$	−1.49323	−0.0640805
$544$	3.55898	0.152590
$545$	16.5691	0.709741
$546$	−1.48704	−0.0636395
$547$	−35.7871	−1.53015	−0.765073	−	0.643943i	$-0.777297\pi$
$547$	−35.7871	−1.53015	−0.765073	+	0.643943i	$0.777297\pi$
$548$	4.80717	0.205352
$549$	32.7698	1.39858
$550$	4.74519	0.202336
$551$	−47.8261	−2.03746
$552$	−1.57271	−0.0669391
$553$	21.8388	0.928682
$554$	−28.0317	−1.19095
$555$	−0.663146	−0.0281490
$556$	9.77479	0.414543
$557$	37.5404	1.59064	0.795319	−	0.606191i	$-0.207303\pi$
$557$	37.5404	1.59064	0.795319	+	0.606191i	$0.207303\pi$
$558$	23.1963	0.981978
$559$	−36.6256	−1.54910
$560$	3.31414	0.140048
$561$	0.622200	0.0262693
$562$	−21.9702	−0.926755
$563$	−32.3454	−1.36320	−0.681598	−	0.731727i	$-0.738715\pi$
$563$	−32.3454	−1.36320	−0.681598	+	0.731727i	$0.738715\pi$
$564$	0.407900	0.0171757
$565$	−16.8621	−0.709395
$566$	−2.57148	−0.108088
$567$	−12.9791	−0.545071
$568$	−3.07917	−0.129199
$569$	17.7609	0.744574	0.372287	−	0.928118i	$-0.378574\pi$
$569$	17.7609	0.744574	0.372287	+	0.928118i	$0.378574\pi$
$570$	−0.963915	−0.0403740
$571$	−27.0173	−1.13064	−0.565320	−	0.824872i	$-0.691247\pi$
$571$	−27.0173	−1.13064	−0.565320	+	0.824872i	$0.691247\pi$
$572$	−15.5018	−0.648164
$573$	1.52397	0.0636646
$574$	−16.5816	−0.692103
$575$	−3.36468	−0.140317
$576$	−25.6340	−1.06808
$577$	27.1207	1.12905	0.564525	−	0.825416i	$-0.309059\pi$
$577$	27.1207	1.12905	0.564525	+	0.825416i	$0.309059\pi$
$578$	−1.15770	−0.0481539
$579$	−2.92262	−0.121460
$580$	5.75257	0.238863
$581$	2.07964	0.0862782
$582$	−0.694154	−0.0287736
$583$	32.1763	1.33261
$584$	41.4138	1.71371
$585$	17.0659	0.705587
$586$	−11.0127	−0.454930
$587$	−18.0790	−0.746198	−0.373099	−	0.927791i	$-0.621705\pi$
$587$	−18.0790	−0.746198	−0.373099	+	0.927791i	$0.621705\pi$
$588$	0.482840	0.0199120
$589$	36.9167	1.52113
$590$	−13.4657	−0.554374
$591$	−2.39159	−0.0983769
$592$	9.80863	0.403132
$593$	−26.7489	−1.09845	−0.549223	−	0.835676i	$-0.685076\pi$
$593$	−26.7489	−1.09845	−0.549223	+	0.835676i	$0.685076\pi$
$594$	−4.30532	−0.176649
$595$	1.47605	0.0605121
$596$	3.00560	0.123114
$597$	2.00818	0.0821895
$598$	−22.3303	−0.913155
$599$	−15.3732	−0.628131	−0.314065	−	0.949401i	$-0.601691\pi$
$599$	−15.3732	−0.628131	−0.314065	+	0.949401i	$0.601691\pi$
$600$	0.467418	0.0190822
$601$	3.63501	0.148275	0.0741376	−	0.997248i	$-0.476380\pi$
$601$	3.63501	0.148275	0.0741376	+	0.997248i	$0.476380\pi$
$602$	10.9175	0.444965
$603$	27.0798	1.10277
$604$	−3.65612	−0.148765
$605$	5.80028	0.235815
$606$	−0.171796	−0.00697874
$607$	−19.0075	−0.771491	−0.385746	−	0.922605i	$-0.626056\pi$
$607$	−19.0075	−0.771491	−0.385746	+	0.922605i	$0.626056\pi$
$608$	−19.5208	−0.791673
$609$	1.95373	0.0791692
$610$	12.7437	0.515979
$611$	23.3490	0.944601
$612$	−1.96400	−0.0793900
$613$	7.88599	0.318512	0.159256	−	0.987237i	$-0.449090\pi$
$613$	7.88599	0.318512	0.159256	+	0.987237i	$0.449090\pi$
$614$	16.7454	0.675788
$615$	−1.47300	−0.0593970
$616$	18.6291	0.750589
$617$	−13.4858	−0.542917	−0.271459	−	0.962450i	$-0.587506\pi$
$617$	−13.4858	−0.542917	−0.271459	+	0.962450i	$0.587506\pi$
$618$	−0.758996	−0.0305313
$619$	39.8374	1.60120	0.800600	−	0.599199i	$-0.204514\pi$
$619$	39.8374	1.60120	0.800600	+	0.599199i	$0.204514\pi$
$620$	−4.44038	−0.178330
$621$	3.05278	0.122504
$622$	24.8029	0.994505
$623$	4.13463	0.165651
$624$	1.95388	0.0782179
$625$	1.00000	0.0400000
$626$	−13.6624	−0.546060
$627$	−3.41273	−0.136291
$628$	2.89981	0.115715
$629$	4.36855	0.174186
$630$	−5.08708	−0.202674
$631$	−1.04849	−0.0417399	−0.0208699	−	0.999782i	$-0.506644\pi$
$631$	−1.04849	−0.0417399	−0.0208699	+	0.999782i	$0.506644\pi$
$632$	−45.5578	−1.81219
$633$	−3.16285	−0.125712
$634$	13.9388	0.553581
$635$	19.0368	0.755454
$636$	0.786173	0.0311738
$637$	27.6388	1.09509
$638$	−41.3758	−1.63808
$639$	2.97696	0.117767
$640$	−2.85074	−0.112685
$641$	−0.724711	−0.0286244	−0.0143122	−	0.999898i	$-0.504556\pi$
$641$	−0.724711	−0.0286244	−0.0143122	+	0.999898i	$0.504556\pi$
$642$	0.513605	0.0202704
$643$	−9.66968	−0.381335	−0.190667	−	0.981655i	$-0.561065\pi$
$643$	−9.66968	−0.381335	−0.190667	+	0.981655i	$0.561065\pi$
$644$	−3.27653	−0.129113
$645$	0.969840	0.0381874
$646$	6.34991	0.249834
$647$	−47.6875	−1.87479	−0.937395	−	0.348268i	$-0.886770\pi$
$647$	−47.6875	−1.87479	−0.937395	+	0.348268i	$0.886770\pi$
$648$	27.0756	1.06363
$649$	−47.6751	−1.87141
$650$	6.63669	0.260312
$651$	−1.50808	−0.0591061
$652$	−0.491969	−0.0192670
$653$	32.0511	1.25426	0.627128	−	0.778916i	$-0.284230\pi$
$653$	32.0511	1.25426	0.627128	+	0.778916i	$0.284230\pi$
$654$	−2.91182	−0.113861
$655$	13.3959	0.523420
$656$	21.7872	0.850647
$657$	−40.0390	−1.56207
$658$	−6.96000	−0.271329
$659$	15.7770	0.614585	0.307292	−	0.951615i	$-0.400577\pi$
$659$	15.7770	0.614585	0.307292	+	0.951615i	$0.400577\pi$
$660$	0.410486	0.0159782
$661$	27.5288	1.07075	0.535373	−	0.844615i	$-0.320171\pi$
$661$	27.5288	1.07075	0.535373	+	0.844615i	$0.320171\pi$
$662$	−14.9845	−0.582391
$663$	0.870217	0.0337964
$664$	−4.33833	−0.168360
$665$	−8.09603	−0.313951
$666$	−15.0559	−0.583403
$667$	29.3384	1.13599
$668$	−0.640915	−0.0247977
$669$	1.94099	0.0750430
$670$	10.5310	0.406846
$671$	45.1190	1.74180
$672$	0.797439	0.0307619
$673$	−33.0681	−1.27468	−0.637341	−	0.770582i	$-0.719966\pi$
$673$	−33.0681	−1.27468	−0.637341	+	0.770582i	$0.719966\pi$
$674$	−1.24444	−0.0479340
$675$	−0.907301	−0.0349220
$676$	−13.1045	−0.504020
$677$	−29.2432	−1.12391	−0.561954	−	0.827168i	$-0.689950\pi$
$677$	−29.2432	−1.12391	−0.561954	+	0.827168i	$0.689950\pi$
$678$	2.96333	0.113806
$679$	−5.83028	−0.223746
$680$	−3.07917	−0.118081
$681$	−1.62644	−0.0623253
$682$	31.9378	1.22296
$683$	−4.31884	−0.165256	−0.0826280	−	0.996580i	$-0.526331\pi$
$683$	−4.31884	−0.165256	−0.0826280	+	0.996580i	$0.526331\pi$
$684$	10.7724	0.411894
$685$	−7.28653	−0.278404
$686$	−20.2004	−0.771256
$687$	2.34119	0.0893221
$688$	−14.3450	−0.546897
$689$	45.0022	1.71445
$690$	0.591304	0.0225106
$691$	35.8062	1.36213	0.681067	−	0.732221i	$-0.261516\pi$
$691$	35.8062	1.36213	0.681067	+	0.732221i	$0.261516\pi$
$692$	−15.7876	−0.600154
$693$	−18.0107	−0.684171
$694$	12.3025	0.466995
$695$	−14.8162	−0.562012
$696$	−4.07566	−0.154488
$697$	9.70355	0.367548
$698$	−11.0720	−0.419082
$699$	2.50890	0.0948953
$700$	0.973799	0.0368062
$701$	−42.2640	−1.59629	−0.798146	−	0.602465i	$-0.794185\pi$
$701$	−42.2640	−1.59629	−0.798146	+	0.602465i	$0.794185\pi$
$702$	−6.02148	−0.227266
$703$	−23.9612	−0.903715
$704$	−35.2940	−1.33019
$705$	−0.618280	−0.0232858
$706$	−5.26970	−0.198328
$707$	−1.44294	−0.0542672
$708$	−1.16486	−0.0437781
$709$	−21.2871	−0.799454	−0.399727	−	0.916634i	$-0.630895\pi$
$709$	−21.2871	−0.799454	−0.399727	+	0.916634i	$0.630895\pi$
$710$	1.15770	0.0434476
$711$	44.0455	1.65184
$712$	−8.62522	−0.323244
$713$	−22.6462	−0.848106
$714$	−0.259398	−0.00970774
$715$	23.4971	0.878741
$716$	−10.9320	−0.408548
$717$	0.116683	0.00435762
$718$	−33.5706	−1.25284
$719$	−24.8455	−0.926582	−0.463291	−	0.886206i	$-0.653332\pi$
$719$	−24.8455	−0.926582	−0.463291	+	0.886206i	$0.653332\pi$
$720$	6.68411	0.249102
$721$	−6.37490	−0.237414
$722$	−12.8326	−0.477579
$723$	−4.18219	−0.155537
$724$	6.48968	0.241187
$725$	−8.71953	−0.323835
$726$	−1.01933	−0.0378310
$727$	20.2370	0.750550	0.375275	−	0.926914i	$-0.377548\pi$
$727$	20.2370	0.750550	0.375275	+	0.926914i	$0.377548\pi$
$728$	26.0549	0.965660
$729$	−25.7636	−0.954208
$730$	−15.5706	−0.576295
$731$	−6.38894	−0.236303
$732$	1.10241	0.0407461
$733$	53.2556	1.96704	0.983521	−	0.180794i	$-0.0578667\pi$
$733$	53.2556	1.96704	0.983521	+	0.180794i	$0.0578667\pi$
$734$	7.07163	0.261019
$735$	−0.731870	−0.0269954
$736$	11.9748	0.441398
$737$	37.2847	1.37340
$738$	−33.4425	−1.23103
$739$	36.4562	1.34106	0.670531	−	0.741881i	$-0.266066\pi$
$739$	36.4562	1.34106	0.670531	+	0.741881i	$0.266066\pi$
$740$	2.88208	0.105948
$741$	−4.77309	−0.175344
$742$	−13.4145	−0.492461
$743$	27.2013	0.997921	0.498960	−	0.866625i	$-0.333715\pi$
$743$	27.2013	0.997921	0.498960	+	0.866625i	$0.333715\pi$
$744$	3.14598	0.115337
$745$	−4.55578	−0.166911
$746$	19.2737	0.705659
$747$	4.19432	0.153462
$748$	−2.70413	−0.0988727
$749$	4.31382	0.157624
$750$	−0.175739	−0.00641706
$751$	33.6346	1.22734	0.613672	−	0.789561i	$-0.289692\pi$
$751$	33.6346	1.22734	0.613672	+	0.789561i	$0.289692\pi$
$752$	9.14501	0.333484
$753$	1.53246	0.0558459
$754$	−57.8688	−2.10746
$755$	5.54180	0.201687
$756$	−0.883530	−0.0321337
$757$	6.03145	0.219217	0.109608	−	0.993975i	$-0.465040\pi$
$757$	6.03145	0.219217	0.109608	+	0.993975i	$0.465040\pi$
$758$	−33.4063	−1.21337
$759$	2.09350	0.0759894
$760$	16.8891	0.612631
$761$	−40.3720	−1.46348	−0.731742	−	0.681582i	$-0.761292\pi$
$761$	−40.3720	−1.46348	−0.731742	+	0.681582i	$0.761292\pi$
$762$	−3.34551	−0.121195
$763$	−24.4568	−0.885394
$764$	−6.62327	−0.239622
$765$	2.97696	0.107632
$766$	−13.8201	−0.499339
$767$	−66.6790	−2.40764
$768$	−2.11325	−0.0762553
$769$	1.03516	0.0373289	0.0186645	−	0.999826i	$-0.494059\pi$
$769$	1.03516	0.0373289	0.0186645	+	0.999826i	$0.494059\pi$
$770$	−7.00413	−0.252411
$771$	−1.86193	−0.0670557
$772$	12.7019	0.457153
$773$	−40.5052	−1.45687	−0.728435	−	0.685115i	$-0.759752\pi$
$773$	−40.5052	−1.45687	−0.728435	+	0.685115i	$0.759752\pi$
$774$	22.0189	0.791455
$775$	6.73056	0.241769
$776$	12.1625	0.436608
$777$	0.978835	0.0351155
$778$	−31.4314	−1.12687
$779$	−53.2234	−1.90693
$780$	0.574112	0.0205565
$781$	4.09881	0.146667
$782$	−3.89529	−0.139295
$783$	7.91124	0.282725
$784$	10.8251	0.386612
$785$	−4.39543	−0.156880
$786$	−2.35417	−0.0839705
$787$	−7.56303	−0.269593	−0.134797	−	0.990873i	$-0.543038\pi$
$787$	−7.56303	−0.269593	−0.134797	+	0.990873i	$0.543038\pi$
$788$	10.3940	0.370272
$789$	−1.12228	−0.0399543
$790$	17.1287	0.609412
$791$	24.8893	0.884962
$792$	37.5720	1.33506
$793$	63.1040	2.24089
$794$	−39.3158	−1.39527
$795$	−1.19165	−0.0422635
$796$	−8.72772	−0.309346
$797$	−31.4107	−1.11263	−0.556313	−	0.830973i	$-0.687784\pi$
$797$	−31.4107	−1.11263	−0.556313	+	0.830973i	$0.687784\pi$
$798$	1.42278	0.0503660
$799$	4.07299	0.144092
$800$	−3.55898	−0.125829
$801$	8.33891	0.294641
$802$	26.1463	0.923258
$803$	−55.1276	−1.94541
$804$	0.910989	0.0321281
$805$	4.96643	0.175044
$806$	44.6686	1.57338
$807$	−4.55076	−0.160194
$808$	3.01009	0.105895
$809$	−0.970581	−0.0341238	−0.0170619	−	0.999854i	$-0.505431\pi$
$809$	−0.970581	−0.0341238	−0.0170619	+	0.999854i	$0.505431\pi$
$810$	−10.1798	−0.357682
$811$	−6.45318	−0.226602	−0.113301	−	0.993561i	$-0.536142\pi$
$811$	−6.45318	−0.226602	−0.113301	+	0.993561i	$0.536142\pi$
$812$	−8.49107	−0.297978
$813$	−1.27930	−0.0448670
$814$	−20.7296	−0.726573
$815$	0.745707	0.0261210
$816$	0.340834	0.0119316
$817$	35.0429	1.22600
$818$	−3.77335	−0.131932
$819$	−25.1900	−0.880211
$820$	6.40176	0.223559
$821$	−11.3431	−0.395877	−0.197939	−	0.980214i	$-0.563425\pi$
$821$	−11.3431	−0.395877	−0.197939	+	0.980214i	$0.563425\pi$
$822$	1.28052	0.0446634
$823$	−40.6223	−1.41600	−0.708002	−	0.706211i	$-0.750403\pi$
$823$	−40.6223	−1.41600	−0.708002	+	0.706211i	$0.750403\pi$
$824$	13.2986	0.463279
$825$	−0.622200	−0.0216622
$826$	19.8760	0.691575
$827$	−36.4889	−1.26884	−0.634421	−	0.772988i	$-0.718761\pi$
$827$	−36.4889	−1.26884	−0.634421	+	0.772988i	$0.718761\pi$
$828$	−6.60824	−0.229652
$829$	47.6259	1.65412	0.827059	−	0.562116i	$-0.190012\pi$
$829$	47.6259	1.65412	0.827059	+	0.562116i	$0.190012\pi$
$830$	1.63111	0.0566168
$831$	3.67558	0.127505
$832$	−49.3627	−1.71134
$833$	4.82128	0.167048
$834$	2.60379	0.0901617
$835$	0.971474	0.0336192
$836$	14.8320	0.512975
$837$	−6.10664	−0.211077
$838$	8.79678	0.303880
$839$	−12.8907	−0.445036	−0.222518	−	0.974929i	$-0.571428\pi$
$839$	−12.8907	−0.445036	−0.222518	+	0.974929i	$0.571428\pi$
$840$	−0.689931	−0.0238049
$841$	47.0301	1.62173
$842$	−12.3436	−0.425389
$843$	2.88077	0.0992191
$844$	13.7460	0.473157
$845$	19.8633	0.683320
$846$	−14.0372	−0.482610
$847$	−8.56149	−0.294176
$848$	17.6258	0.605272
$849$	0.337178	0.0115719
$850$	1.15770	0.0397087
$851$	14.6988	0.503868
$852$	0.100148	0.00343100
$853$	18.5042	0.633571	0.316786	−	0.948497i	$-0.397396\pi$
$853$	18.5042	0.633571	0.316786	+	0.948497i	$0.397396\pi$
$854$	−18.8104	−0.643677
$855$	−16.3284	−0.558420
$856$	−8.99903	−0.307580
$857$	8.04437	0.274791	0.137395	−	0.990516i	$-0.456127\pi$
$857$	8.04437	0.274791	0.137395	+	0.990516i	$0.456127\pi$
$858$	−4.12934	−0.140973
$859$	4.85350	0.165599	0.0827996	−	0.996566i	$-0.473614\pi$
$859$	4.85350	0.165599	0.0827996	+	0.996566i	$0.473614\pi$
$860$	−4.21500	−0.143730
$861$	2.17421	0.0740970
$862$	−14.8689	−0.506436
$863$	−21.8261	−0.742970	−0.371485	−	0.928439i	$-0.621151\pi$
$863$	−21.8261	−0.742970	−0.371485	+	0.928439i	$0.621151\pi$
$864$	3.22907	0.109855
$865$	23.9302	0.813652
$866$	−0.866998	−0.0294618
$867$	0.151800	0.00515540
$868$	6.55421	0.222464
$869$	60.6439	2.05720
$870$	1.53236	0.0519518
$871$	52.1469	1.76693
$872$	51.0190	1.72772
$873$	−11.7588	−0.397974
$874$	21.3654	0.722696
$875$	−1.47605	−0.0498995
$876$	−1.34695	−0.0455092
$877$	17.7722	0.600124	0.300062	−	0.953920i	$-0.402993\pi$
$877$	17.7722	0.600124	0.300062	+	0.953920i	$0.402993\pi$
$878$	−13.5269	−0.456510
$879$	1.44401	0.0487052
$880$	9.20299	0.310233
$881$	−14.6027	−0.491976	−0.245988	−	0.969273i	$-0.579112\pi$
$881$	−14.6027	−0.491976	−0.245988	+	0.969273i	$0.579112\pi$
$882$	−16.6162	−0.559495
$883$	−11.3781	−0.382903	−0.191451	−	0.981502i	$-0.561319\pi$
$883$	−11.3781	−0.382903	−0.191451	+	0.981502i	$0.561319\pi$
$884$	−3.78203	−0.127203
$885$	1.76565	0.0593517
$886$	−6.10366	−0.205056
$887$	−41.3562	−1.38861	−0.694303	−	0.719683i	$-0.744287\pi$
$887$	−41.3562	−1.38861	−0.694303	+	0.719683i	$0.744287\pi$
$888$	−2.04194	−0.0685230
$889$	−28.0993	−0.942420
$890$	3.24289	0.108702
$891$	−36.0415	−1.20743
$892$	−8.43570	−0.282448
$893$	−22.3401	−0.747583
$894$	0.800626	0.0267769
$895$	16.5703	0.553885
$896$	4.20782	0.140574
$897$	2.92800	0.0977631
$898$	−40.4499	−1.34983
$899$	−58.6873	−1.95733
$900$	1.96400	0.0654667
$901$	7.85015	0.261526
$902$	−46.0452	−1.53314
$903$	−1.43153	−0.0476383
$904$	−51.9214	−1.72688
$905$	−9.83681	−0.326987
$906$	−0.973909	−0.0323559
$907$	−12.1415	−0.403150	−0.201575	−	0.979473i	$-0.564606\pi$
$907$	−12.1415	−0.403150	−0.201575	+	0.979473i	$0.564606\pi$
$908$	7.06863	0.234581
$909$	−2.91017	−0.0965244
$910$	−9.79607	−0.324736
$911$	53.1580	1.76120	0.880602	−	0.473857i	$-0.157138\pi$
$911$	53.1580	1.76120	0.880602	+	0.473857i	$0.157138\pi$
$912$	−1.86945	−0.0619037
$913$	5.77493	0.191122
$914$	22.4213	0.741632
$915$	−1.67099	−0.0552411
$916$	−10.1750	−0.336192
$917$	−19.7729	−0.652960
$918$	−1.05038	−0.0346678
$919$	16.1909	0.534090	0.267045	−	0.963684i	$-0.413953\pi$
$919$	16.1909	0.534090	0.267045	+	0.963684i	$0.413953\pi$
$920$	−10.3604	−0.341573
$921$	−2.19569	−0.0723504
$922$	−30.7046	−1.01120
$923$	5.73266	0.188693
$924$	−0.605898	−0.0199326
$925$	−4.36855	−0.143637
$926$	−3.07908	−0.101185
$927$	−12.8572	−0.422285
$928$	31.0326	1.01870
$929$	52.5084	1.72274	0.861372	−	0.507975i	$-0.169606\pi$
$929$	52.5084	1.72274	0.861372	+	0.507975i	$0.169606\pi$
$930$	−1.18282	−0.0387861
$931$	−26.4444	−0.866682
$932$	−10.9039	−0.357168
$933$	−3.25221	−0.106473
$934$	41.5122	1.35832
$935$	4.09881	0.134046
$936$	52.5487	1.71761
$937$	52.3087	1.70885	0.854425	−	0.519575i	$-0.173910\pi$
$937$	52.3087	1.70885	0.854425	+	0.519575i	$0.173910\pi$
$938$	−15.5442	−0.507536
$939$	1.79145	0.0584617
$940$	2.68709	0.0876433
$941$	−25.3883	−0.827633	−0.413817	−	0.910360i	$-0.635805\pi$
$941$	−25.3883	−0.827633	−0.413817	+	0.910360i	$0.635805\pi$
$942$	0.772446	0.0251676
$943$	32.6494	1.06321
$944$	−26.1158	−0.849998
$945$	1.33922	0.0435648
$946$	30.3167	0.985682
$947$	35.0209	1.13803	0.569014	−	0.822328i	$-0.307325\pi$
$947$	35.0209	1.13803	0.569014	+	0.822328i	$0.307325\pi$
$948$	1.48173	0.0481244
$949$	−77.1022	−2.50284
$950$	−6.34991	−0.206018
$951$	−1.82769	−0.0592668
$952$	4.54500	0.147304
$953$	12.2931	0.398212	0.199106	−	0.979978i	$-0.436196\pi$
$953$	12.2931	0.398212	0.199106	+	0.979978i	$0.436196\pi$
$954$	−27.0549	−0.875934
$955$	10.0393	0.324864
$956$	−0.507115	−0.0164013
$957$	5.42529	0.175375
$958$	−40.5161	−1.30902
$959$	10.7553	0.347306
$960$	1.30712	0.0421870
$961$	14.3004	0.461303
$962$	−28.9927	−0.934762
$963$	8.70031	0.280363
$964$	18.1761	0.585413
$965$	−19.2531	−0.619779
$966$	−0.872793	−0.0280817
$967$	40.4865	1.30196	0.650980	−	0.759095i	$-0.274358\pi$
$967$	40.4865	1.30196	0.650980	+	0.759095i	$0.274358\pi$
$968$	17.8601	0.574044
$969$	−0.832613	−0.0267474
$970$	−4.57282	−0.146824
$971$	−39.3382	−1.26242	−0.631212	−	0.775611i	$-0.717442\pi$
$971$	−39.3382	−1.26242	−0.631212	+	0.775611i	$0.717442\pi$
$972$	−2.67635	−0.0858438
$973$	21.8695	0.701104
$974$	26.7288	0.856446
$975$	−0.870217	−0.0278692
$976$	24.7157	0.791129
$977$	−57.1638	−1.82883	−0.914416	−	0.404776i	$-0.867350\pi$
$977$	−57.1638	−1.82883	−0.914416	+	0.404776i	$0.867350\pi$
$978$	−0.131049	−0.00419050
$979$	11.4814	0.366947
$980$	3.18077	0.101606
$981$	−49.3254	−1.57484
$982$	−2.50024	−0.0797859
$983$	39.1281	1.24799	0.623996	−	0.781428i	$-0.285508\pi$
$983$	39.1281	1.24799	0.623996	+	0.781428i	$0.285508\pi$
$984$	−4.53561	−0.144590
$985$	−15.7549	−0.501992
$986$	−10.0946	−0.321477
$987$	0.912610	0.0290487
$988$	20.7442	0.659961
$989$	−21.4967	−0.683557
$990$	−14.1262	−0.448961
$991$	2.77429	0.0881282	0.0440641	−	0.999029i	$-0.485969\pi$
$991$	2.77429	0.0881282	0.0440641	+	0.999029i	$0.485969\pi$
$992$	−23.9539	−0.760538
$993$	1.96481	0.0623512
$994$	−1.70882	−0.0542004
$995$	13.2291	0.419392
$996$	0.141101	0.00447095
$997$	−55.8457	−1.76865	−0.884325	−	0.466872i	$-0.845381\pi$
$997$	−55.8457	−1.76865	−0.884325	+	0.466872i	$0.845381\pi$
$998$	−15.6174	−0.494360
$999$	3.96359	0.125403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.20	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.20	✓	59	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-1.15770 q^{2} +0.151800 q^{3} -0.659734 q^{4} +1.00000 q^{5} -0.175739 q^{6} -1.47605 q^{7} +3.07917 q^{8} -2.97696 q^{9} +O(q^{10})\)	\(q-1.15770 q^{2} +0.151800 q^{3} -0.659734 q^{4} +1.00000 q^{5} -0.175739 q^{6} -1.47605 q^{7} +3.07917 q^{8} -2.97696 q^{9} -1.15770 q^{10} -4.09881 q^{11} -0.100148 q^{12} -5.73266 q^{13} +1.70882 q^{14} +0.151800 q^{15} -2.24528 q^{16} -1.00000 q^{17} +3.44642 q^{18} +5.48494 q^{19} -0.659734 q^{20} -0.224064 q^{21} +4.74519 q^{22} -3.36468 q^{23} +0.467418 q^{24} +1.00000 q^{25} +6.63669 q^{26} -0.907301 q^{27} +0.973799 q^{28} -8.71953 q^{29} -0.175739 q^{30} +6.73056 q^{31} -3.55898 q^{32} -0.622200 q^{33} +1.15770 q^{34} -1.47605 q^{35} +1.96400 q^{36} -4.36855 q^{37} -6.34991 q^{38} -0.870217 q^{39} +3.07917 q^{40} -9.70355 q^{41} +0.259398 q^{42} +6.38894 q^{43} +2.70413 q^{44} -2.97696 q^{45} +3.89529 q^{46} -4.07299 q^{47} -0.340834 q^{48} -4.82128 q^{49} -1.15770 q^{50} -0.151800 q^{51} +3.78203 q^{52} -7.85015 q^{53} +1.05038 q^{54} -4.09881 q^{55} -4.54500 q^{56} +0.832613 q^{57} +10.0946 q^{58} +11.6314 q^{59} -0.100148 q^{60} -11.0078 q^{61} -7.79196 q^{62} +4.39413 q^{63} +8.61079 q^{64} -5.73266 q^{65} +0.720320 q^{66} -9.09646 q^{67} +0.659734 q^{68} -0.510758 q^{69} +1.70882 q^{70} -1.00000 q^{71} -9.16656 q^{72} +13.4496 q^{73} +5.05747 q^{74} +0.151800 q^{75} -3.61860 q^{76} +6.05005 q^{77} +1.00745 q^{78} -14.7955 q^{79} -2.24528 q^{80} +8.79314 q^{81} +11.2338 q^{82} -1.40893 q^{83} +0.147823 q^{84} -1.00000 q^{85} -7.39646 q^{86} -1.32362 q^{87} -12.6209 q^{88} -2.80115 q^{89} +3.44642 q^{90} +8.46167 q^{91} +2.21980 q^{92} +1.02170 q^{93} +4.71529 q^{94} +5.48494 q^{95} -0.540253 q^{96} +3.94992 q^{97} +5.58159 q^{98} +12.2020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 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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