LMFDB - Embedded newform 6035.2.a.b.1.5

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:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29064 q^{2} +1.47549 q^{3} +3.24701 q^{4} +1.00000 q^{5} -3.37981 q^{6} +2.13493 q^{7} -2.85645 q^{8} -0.822934 q^{9} +O(q^{10})$	\(q-2.29064 q^{2} +1.47549 q^{3} +3.24701 q^{4} +1.00000 q^{5} -3.37981 q^{6} +2.13493 q^{7} -2.85645 q^{8} -0.822934 q^{9} -2.29064 q^{10} -0.291105 q^{11} +4.79093 q^{12} -3.13120 q^{13} -4.89035 q^{14} +1.47549 q^{15} +0.0490540 q^{16} -1.00000 q^{17} +1.88504 q^{18} +4.57063 q^{19} +3.24701 q^{20} +3.15007 q^{21} +0.666815 q^{22} +1.45160 q^{23} -4.21465 q^{24} +1.00000 q^{25} +7.17243 q^{26} -5.64069 q^{27} +6.93215 q^{28} -3.26953 q^{29} -3.37981 q^{30} -2.50942 q^{31} +5.60053 q^{32} -0.429522 q^{33} +2.29064 q^{34} +2.13493 q^{35} -2.67207 q^{36} -9.23957 q^{37} -10.4696 q^{38} -4.62004 q^{39} -2.85645 q^{40} -8.92497 q^{41} -7.21566 q^{42} -7.61724 q^{43} -0.945220 q^{44} -0.822934 q^{45} -3.32508 q^{46} +3.76522 q^{47} +0.0723786 q^{48} -2.44206 q^{49} -2.29064 q^{50} -1.47549 q^{51} -10.1670 q^{52} +11.3006 q^{53} +12.9208 q^{54} -0.291105 q^{55} -6.09832 q^{56} +6.74391 q^{57} +7.48931 q^{58} +2.28543 q^{59} +4.79093 q^{60} +15.0184 q^{61} +5.74817 q^{62} -1.75691 q^{63} -12.9269 q^{64} -3.13120 q^{65} +0.983877 q^{66} +2.30632 q^{67} -3.24701 q^{68} +2.14182 q^{69} -4.89035 q^{70} +1.00000 q^{71} +2.35067 q^{72} +2.51175 q^{73} +21.1645 q^{74} +1.47549 q^{75} +14.8409 q^{76} -0.621489 q^{77} +10.5828 q^{78} -10.3435 q^{79} +0.0490540 q^{80} -5.85398 q^{81} +20.4439 q^{82} -6.23747 q^{83} +10.2283 q^{84} -1.00000 q^{85} +17.4483 q^{86} -4.82416 q^{87} +0.831524 q^{88} -5.63891 q^{89} +1.88504 q^{90} -6.68489 q^{91} +4.71335 q^{92} -3.70262 q^{93} -8.62475 q^{94} +4.57063 q^{95} +8.26351 q^{96} -7.72883 q^{97} +5.59387 q^{98} +0.239560 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.29064	−1.61972	−0.809862	−	0.586621i	$-0.800458\pi$
$2$	−2.29064	−1.61972	−0.809862	+	0.586621i	$0.800458\pi$
$3$	1.47549	0.851874	0.425937	−	0.904753i	$-0.359945\pi$
$3$	1.47549	0.851874	0.425937	+	0.904753i	$0.359945\pi$
$4$	3.24701	1.62351
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.37981	−1.37980
$7$	2.13493	0.806929	0.403464	−	0.914995i	$-0.367806\pi$
$7$	2.13493	0.806929	0.403464	+	0.914995i	$0.367806\pi$
$8$	−2.85645	−1.00991
$9$	−0.822934	−0.274311
$10$	−2.29064	−0.724362
$11$	−0.291105	−0.0877714	−0.0438857	−	0.999037i	$-0.513974\pi$
$11$	−0.291105	−0.0877714	−0.0438857	+	0.999037i	$0.513974\pi$
$12$	4.79093	1.38302
$13$	−3.13120	−0.868437	−0.434219	−	0.900808i	$-0.642975\pi$
$13$	−3.13120	−0.868437	−0.434219	+	0.900808i	$0.642975\pi$
$14$	−4.89035	−1.30700
$15$	1.47549	0.380969
$16$	0.0490540	0.0122635
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.88504	0.444308
$19$	4.57063	1.04857	0.524287	−	0.851541i	$-0.324332\pi$
$19$	4.57063	1.04857	0.524287	+	0.851541i	$0.324332\pi$
$20$	3.24701	0.726054
$21$	3.15007	0.687401
$22$	0.666815	0.142165
$23$	1.45160	0.302679	0.151340	−	0.988482i	$-0.451641\pi$
$23$	1.45160	0.302679	0.151340	+	0.988482i	$0.451641\pi$
$24$	−4.21465	−0.860312
$25$	1.00000	0.200000
$26$	7.17243	1.40663
$27$	−5.64069	−1.08555
$28$	6.93215	1.31005
$29$	−3.26953	−0.607137	−0.303568	−	0.952810i	$-0.598178\pi$
$29$	−3.26953	−0.607137	−0.303568	+	0.952810i	$0.598178\pi$
$30$	−3.37981	−0.617065
$31$	−2.50942	−0.450705	−0.225353	−	0.974277i	$-0.572353\pi$
$31$	−2.50942	−0.450705	−0.225353	+	0.974277i	$0.572353\pi$
$32$	5.60053	0.990042
$33$	−0.429522	−0.0747701
$34$	2.29064	0.392841
$35$	2.13493	0.360870
$36$	−2.67207	−0.445346
$37$	−9.23957	−1.51898	−0.759488	−	0.650521i	$-0.774551\pi$
$37$	−9.23957	−1.51898	−0.759488	+	0.650521i	$0.774551\pi$
$38$	−10.4696	−1.69840
$39$	−4.62004	−0.739799
$40$	−2.85645	−0.451644
$41$	−8.92497	−1.39385	−0.696923	−	0.717146i	$-0.745448\pi$
$41$	−8.92497	−1.39385	−0.696923	+	0.717146i	$0.745448\pi$
$42$	−7.21566	−1.11340
$43$	−7.61724	−1.16162	−0.580809	−	0.814040i	$-0.697264\pi$
$43$	−7.61724	−1.16162	−0.580809	+	0.814040i	$0.697264\pi$
$44$	−0.945220	−0.142497
$45$	−0.822934	−0.122676
$46$	−3.32508	−0.490256
$47$	3.76522	0.549214	0.274607	−	0.961557i	$-0.411452\pi$
$47$	3.76522	0.549214	0.274607	+	0.961557i	$0.411452\pi$
$48$	0.0723786	0.0104469
$49$	−2.44206	−0.348866
$50$	−2.29064	−0.323945
$51$	−1.47549	−0.206610
$52$	−10.1670	−1.40991
$53$	11.3006	1.55226	0.776129	−	0.630574i	$-0.217181\pi$
$53$	11.3006	1.55226	0.776129	+	0.630574i	$0.217181\pi$
$54$	12.9208	1.75829
$55$	−0.291105	−0.0392525
$56$	−6.09832	−0.814922
$57$	6.74391	0.893253
$58$	7.48931	0.983394
$59$	2.28543	0.297538	0.148769	−	0.988872i	$-0.452469\pi$
$59$	2.28543	0.297538	0.148769	+	0.988872i	$0.452469\pi$
$60$	4.79093	0.618506
$61$	15.0184	1.92291	0.961457	−	0.274956i	$-0.0886631\pi$
$61$	15.0184	1.92291	0.961457	+	0.274956i	$0.0886631\pi$
$62$	5.74817	0.730018
$63$	−1.75691	−0.221350
$64$	−12.9269	−1.61586
$65$	−3.13120	−0.388377
$66$	0.983877	0.121107
$67$	2.30632	0.281762	0.140881	−	0.990027i	$-0.455006\pi$
$67$	2.30632	0.281762	0.140881	+	0.990027i	$0.455006\pi$
$68$	−3.24701	−0.393758
$69$	2.14182	0.257844
$70$	−4.89035	−0.584509
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	2.35067	0.277029
$73$	2.51175	0.293978	0.146989	−	0.989138i	$-0.453042\pi$
$73$	2.51175	0.293978	0.146989	+	0.989138i	$0.453042\pi$
$74$	21.1645	2.46032
$75$	1.47549	0.170375
$76$	14.8409	1.70237
$77$	−0.621489	−0.0708252
$78$	10.5828	1.19827
$79$	−10.3435	−1.16373	−0.581866	−	0.813285i	$-0.697677\pi$
$79$	−10.3435	−1.16373	−0.581866	+	0.813285i	$0.697677\pi$
$80$	0.0490540	0.00548440
$81$	−5.85398	−0.650442
$82$	20.4439	2.25765
$83$	−6.23747	−0.684652	−0.342326	−	0.939581i	$-0.611215\pi$
$83$	−6.23747	−0.684652	−0.342326	+	0.939581i	$0.611215\pi$
$84$	10.2283	1.11600
$85$	−1.00000	−0.108465
$86$	17.4483	1.88150
$87$	−4.82416	−0.517204
$88$	0.831524	0.0886408
$89$	−5.63891	−0.597724	−0.298862	−	0.954296i	$-0.596607\pi$
$89$	−5.63891	−0.597724	−0.298862	+	0.954296i	$0.596607\pi$
$90$	1.88504	0.198701
$91$	−6.68489	−0.700767
$92$	4.71335	0.491401
$93$	−3.70262	−0.383944
$94$	−8.62475	−0.889575
$95$	4.57063	0.468937
$96$	8.26351	0.843391
$97$	−7.72883	−0.784743	−0.392372	−	0.919807i	$-0.628345\pi$
$97$	−7.72883	−0.784743	−0.392372	+	0.919807i	$0.628345\pi$
$98$	5.59387	0.565066
$99$	0.239560	0.0240767
$100$	3.24701	0.324701
$101$	−7.65917	−0.762116	−0.381058	−	0.924551i	$-0.624440\pi$
$101$	−7.65917	−0.762116	−0.381058	+	0.924551i	$0.624440\pi$
$102$	3.37981	0.334651
$103$	7.36668	0.725860	0.362930	−	0.931816i	$-0.381776\pi$
$103$	7.36668	0.725860	0.362930	+	0.931816i	$0.381776\pi$
$104$	8.94409	0.877040
$105$	3.15007	0.307415
$106$	−25.8856	−2.51423
$107$	−9.56371	−0.924559	−0.462280	−	0.886734i	$-0.652968\pi$
$107$	−9.56371	−0.924559	−0.462280	+	0.886734i	$0.652968\pi$
$108$	−18.3154	−1.76240
$109$	−2.47223	−0.236797	−0.118399	−	0.992966i	$-0.537776\pi$
$109$	−2.47223	−0.236797	−0.118399	+	0.992966i	$0.537776\pi$
$110$	0.666815	0.0635783
$111$	−13.6329	−1.29398
$112$	0.104727	0.00989576
$113$	−19.9065	−1.87265	−0.936324	−	0.351138i	$-0.885795\pi$
$113$	−19.9065	−1.87265	−0.936324	+	0.351138i	$0.885795\pi$
$114$	−15.4478	−1.44682
$115$	1.45160	0.135362
$116$	−10.6162	−0.985690
$117$	2.57677	0.238222
$118$	−5.23509	−0.481930
$119$	−2.13493	−0.195709
$120$	−4.21465	−0.384743
$121$	−10.9153	−0.992296
$122$	−34.4018	−3.11459
$123$	−13.1687	−1.18738
$124$	−8.14812	−0.731722
$125$	1.00000	0.0894427
$126$	4.02444	0.358525
$127$	−7.46071	−0.662031	−0.331015	−	0.943625i	$-0.607391\pi$
$127$	−7.46071	−0.662031	−0.331015	+	0.943625i	$0.607391\pi$
$128$	18.4097	1.62720
$129$	−11.2392	−0.989552
$130$	7.17243	0.629063
$131$	−2.31713	−0.202448	−0.101224	−	0.994864i	$-0.532276\pi$
$131$	−2.31713	−0.202448	−0.101224	+	0.994864i	$0.532276\pi$
$132$	−1.39466	−0.121390
$133$	9.75799	0.846125
$134$	−5.28295	−0.456377
$135$	−5.64069	−0.485474
$136$	2.85645	0.244938
$137$	4.62071	0.394774	0.197387	−	0.980326i	$-0.436755\pi$
$137$	4.62071	0.394774	0.197387	+	0.980326i	$0.436755\pi$
$138$	−4.90612	−0.417636
$139$	9.33720	0.791971	0.395986	−	0.918257i	$-0.370403\pi$
$139$	9.33720	0.791971	0.395986	+	0.918257i	$0.370403\pi$
$140$	6.93215	0.585873
$141$	5.55554	0.467861
$142$	−2.29064	−0.192226
$143$	0.911505	0.0762239
$144$	−0.0403682	−0.00336401
$145$	−3.26953	−0.271520
$146$	−5.75350	−0.476163
$147$	−3.60323	−0.297190
$148$	−30.0010	−2.46607
$149$	21.1025	1.72878	0.864392	−	0.502818i	$-0.167703\pi$
$149$	21.1025	1.72878	0.864392	+	0.502818i	$0.167703\pi$
$150$	−3.37981	−0.275960
$151$	−16.3341	−1.32925	−0.664624	−	0.747178i	$-0.731408\pi$
$151$	−16.3341	−1.32925	−0.664624	+	0.747178i	$0.731408\pi$
$152$	−13.0558	−1.05896
$153$	0.822934	0.0665303
$154$	1.42360	0.114717
$155$	−2.50942	−0.201562
$156$	−15.0013	−1.20107
$157$	−3.69533	−0.294919	−0.147460	−	0.989068i	$-0.547110\pi$
$157$	−3.69533	−0.294919	−0.147460	+	0.989068i	$0.547110\pi$
$158$	23.6931	1.88492
$159$	16.6739	1.32233
$160$	5.60053	0.442760
$161$	3.09906	0.244240
$162$	13.4093	1.05354
$163$	−16.9582	−1.32827	−0.664135	−	0.747613i	$-0.731200\pi$
$163$	−16.9582	−1.32827	−0.664135	+	0.747613i	$0.731200\pi$
$164$	−28.9795	−2.26292
$165$	−0.429522	−0.0334382
$166$	14.2878	1.10895
$167$	14.3639	1.11151	0.555754	−	0.831347i	$-0.312430\pi$
$167$	14.3639	1.11151	0.555754	+	0.831347i	$0.312430\pi$
$168$	−8.99800	−0.694211
$169$	−3.19562	−0.245817
$170$	2.29064	0.175684
$171$	−3.76133	−0.287636
$172$	−24.7333	−1.88589
$173$	16.2357	1.23437	0.617187	−	0.786817i	$-0.288272\pi$
$173$	16.2357	1.23437	0.617187	+	0.786817i	$0.288272\pi$
$174$	11.0504	0.837728
$175$	2.13493	0.161386
$176$	−0.0142798	−0.00107638
$177$	3.37213	0.253465
$178$	12.9167	0.968147
$179$	13.0418	0.974791	0.487395	−	0.873181i	$-0.337947\pi$
$179$	13.0418	0.974791	0.487395	+	0.873181i	$0.337947\pi$
$180$	−2.67207	−0.199165
$181$	−1.20261	−0.0893895	−0.0446948	−	0.999001i	$-0.514232\pi$
$181$	−1.20261	−0.0893895	−0.0446948	+	0.999001i	$0.514232\pi$
$182$	15.3126	1.13505
$183$	22.1595	1.63808
$184$	−4.14641	−0.305677
$185$	−9.23957	−0.679307
$186$	8.48136	0.621883
$187$	0.291105	0.0212877
$188$	12.2257	0.891652
$189$	−12.0425	−0.875963
$190$	−10.4696	−0.759548
$191$	−2.48642	−0.179911	−0.0899555	−	0.995946i	$-0.528672\pi$
$191$	−2.48642	−0.179911	−0.0899555	+	0.995946i	$0.528672\pi$
$192$	−19.0734	−1.37651
$193$	−19.1018	−1.37498	−0.687489	−	0.726194i	$-0.741287\pi$
$193$	−19.1018	−1.37498	−0.687489	+	0.726194i	$0.741287\pi$
$194$	17.7039	1.27107
$195$	−4.62004	−0.330848
$196$	−7.92940	−0.566386
$197$	−21.0086	−1.49680	−0.748401	−	0.663246i	$-0.769178\pi$
$197$	−21.0086	−1.49680	−0.748401	+	0.663246i	$0.769178\pi$
$198$	−0.548744	−0.0389976
$199$	−9.27536	−0.657513	−0.328756	−	0.944415i	$-0.606629\pi$
$199$	−9.27536	−0.657513	−0.328756	+	0.944415i	$0.606629\pi$
$200$	−2.85645	−0.201981
$201$	3.40296	0.240026
$202$	17.5444	1.23442
$203$	−6.98023	−0.489916
$204$	−4.79093	−0.335432
$205$	−8.92497	−0.623347
$206$	−16.8744	−1.17569
$207$	−1.19457	−0.0830283
$208$	−0.153598	−0.0106501
$209$	−1.33053	−0.0920348
$210$	−7.21566	−0.497928
$211$	−18.0591	−1.24324	−0.621621	−	0.783318i	$-0.713526\pi$
$211$	−18.0591	−1.24324	−0.621621	+	0.783318i	$0.713526\pi$
$212$	36.6932	2.52010
$213$	1.47549	0.101099
$214$	21.9070	1.49753
$215$	−7.61724	−0.519492
$216$	16.1123	1.09631
$217$	−5.35745	−0.363687
$218$	5.66299	0.383546
$219$	3.70606	0.250432
$220$	−0.945220	−0.0637267
$221$	3.13120	0.210627
$222$	31.2280	2.09588
$223$	−3.77114	−0.252534	−0.126267	−	0.991996i	$-0.540300\pi$
$223$	−3.77114	−0.252534	−0.126267	+	0.991996i	$0.540300\pi$
$224$	11.9567	0.798894
$225$	−0.822934	−0.0548623
$226$	45.5986	3.03317
$227$	−1.53437	−0.101840	−0.0509198	−	0.998703i	$-0.516215\pi$
$227$	−1.53437	−0.101840	−0.0509198	+	0.998703i	$0.516215\pi$
$228$	21.8976	1.45020
$229$	−15.9741	−1.05560	−0.527800	−	0.849369i	$-0.676983\pi$
$229$	−15.9741	−1.05560	−0.527800	+	0.849369i	$0.676983\pi$
$230$	−3.32508	−0.219249
$231$	−0.917000	−0.0603341
$232$	9.33924	0.613151
$233$	−6.38033	−0.417989	−0.208995	−	0.977917i	$-0.567019\pi$
$233$	−6.38033	−0.417989	−0.208995	+	0.977917i	$0.567019\pi$
$234$	−5.90243	−0.385854
$235$	3.76522	0.245616
$236$	7.42083	0.483055
$237$	−15.2617	−0.991352
$238$	4.89035	0.316994
$239$	−2.61022	−0.168841	−0.0844207	−	0.996430i	$-0.526904\pi$
$239$	−2.61022	−0.168841	−0.0844207	+	0.996430i	$0.526904\pi$
$240$	0.0723786	0.00467202
$241$	10.4429	0.672688	0.336344	−	0.941739i	$-0.390809\pi$
$241$	10.4429	0.672688	0.336344	+	0.941739i	$0.390809\pi$
$242$	25.0029	1.60725
$243$	8.28461	0.531458
$244$	48.7650	3.12186
$245$	−2.44206	−0.156018
$246$	30.1647	1.92323
$247$	−14.3115	−0.910621
$248$	7.16802	0.455170
$249$	−9.20332	−0.583237
$250$	−2.29064	−0.144872
$251$	−17.5203	−1.10587	−0.552936	−	0.833223i	$-0.686493\pi$
$251$	−17.5203	−1.10587	−0.552936	+	0.833223i	$0.686493\pi$
$252$	−5.70470	−0.359362
$253$	−0.422567	−0.0265665
$254$	17.0898	1.07231
$255$	−1.47549	−0.0923987
$256$	−16.3162	−1.01976
$257$	22.1492	1.38163	0.690814	−	0.723032i	$-0.257252\pi$
$257$	22.1492	1.38163	0.690814	+	0.723032i	$0.257252\pi$
$258$	25.7448	1.60280
$259$	−19.7259	−1.22571
$260$	−10.1670	−0.630532
$261$	2.69061	0.166545
$262$	5.30770	0.327911
$263$	−14.6674	−0.904432	−0.452216	−	0.891909i	$-0.649366\pi$
$263$	−14.6674	−0.904432	−0.452216	+	0.891909i	$0.649366\pi$
$264$	1.22690	0.0755108
$265$	11.3006	0.694191
$266$	−22.3520	−1.37049
$267$	−8.32015	−0.509185
$268$	7.48866	0.457443
$269$	24.4008	1.48775	0.743873	−	0.668321i	$-0.232987\pi$
$269$	24.4008	1.48775	0.743873	+	0.668321i	$0.232987\pi$
$270$	12.9208	0.786333
$271$	−23.5020	−1.42765	−0.713823	−	0.700326i	$-0.753038\pi$
$271$	−23.5020	−1.42765	−0.713823	+	0.700326i	$0.753038\pi$
$272$	−0.0490540	−0.00297433
$273$	−9.86348	−0.596965
$274$	−10.5844	−0.639424
$275$	−0.291105	−0.0175543
$276$	6.95450	0.418611
$277$	27.0676	1.62633	0.813167	−	0.582030i	$-0.197742\pi$
$277$	27.0676	1.62633	0.813167	+	0.582030i	$0.197742\pi$
$278$	−21.3881	−1.28277
$279$	2.06509	0.123634
$280$	−6.09832	−0.364444
$281$	−14.6824	−0.875876	−0.437938	−	0.899005i	$-0.644291\pi$
$281$	−14.6824	−0.875876	−0.437938	+	0.899005i	$0.644291\pi$
$282$	−12.7257	−0.757806
$283$	20.6087	1.22506	0.612531	−	0.790447i	$-0.290151\pi$
$283$	20.6087	1.22506	0.612531	+	0.790447i	$0.290151\pi$
$284$	3.24701	0.192675
$285$	6.74391	0.399475
$286$	−2.08793	−0.123462
$287$	−19.0542	−1.12473
$288$	−4.60886	−0.271580
$289$	1.00000	0.0588235
$290$	7.48931	0.439787
$291$	−11.4038	−0.668502
$292$	8.15567	0.477275
$293$	28.2918	1.65283	0.826413	−	0.563064i	$-0.190378\pi$
$293$	28.2918	1.65283	0.826413	+	0.563064i	$0.190378\pi$
$294$	8.25369	0.481365
$295$	2.28543	0.133063
$296$	26.3923	1.53402
$297$	1.64203	0.0952804
$298$	−48.3382	−2.80015
$299$	−4.54523	−0.262858
$300$	4.79093	0.276604
$301$	−16.2623	−0.937343
$302$	37.4154	2.15301
$303$	−11.3010	−0.649226
$304$	0.224208	0.0128592
$305$	15.0184	0.859953
$306$	−1.88504	−0.107761
$307$	18.2953	1.04417	0.522084	−	0.852894i	$-0.325155\pi$
$307$	18.2953	1.04417	0.522084	+	0.852894i	$0.325155\pi$
$308$	−2.01798	−0.114985
$309$	10.8694	0.618341
$310$	5.74817	0.326474
$311$	1.31146	0.0743663	0.0371831	−	0.999308i	$-0.488162\pi$
$311$	1.31146	0.0743663	0.0371831	+	0.999308i	$0.488162\pi$
$312$	13.1969	0.747127
$313$	−12.1440	−0.686420	−0.343210	−	0.939259i	$-0.611514\pi$
$313$	−12.1440	−0.686420	−0.343210	+	0.939259i	$0.611514\pi$
$314$	8.46464	0.477688
$315$	−1.75691	−0.0989906
$316$	−33.5854	−1.88932
$317$	33.5936	1.88681	0.943403	−	0.331648i	$-0.107604\pi$
$317$	33.5936	1.88681	0.943403	+	0.331648i	$0.107604\pi$
$318$	−38.1939	−2.14181
$319$	0.951776	0.0532892
$320$	−12.9269	−0.722634
$321$	−14.1111	−0.787608
$322$	−7.09882	−0.395602
$323$	−4.57063	−0.254317
$324$	−19.0079	−1.05600
$325$	−3.13120	−0.173687
$326$	38.8451	2.15143
$327$	−3.64775	−0.201721
$328$	25.4937	1.40765
$329$	8.03850	0.443177
$330$	0.983877	0.0541607
$331$	−26.4007	−1.45111	−0.725556	−	0.688163i	$-0.758417\pi$
$331$	−26.4007	−1.45111	−0.725556	+	0.688163i	$0.758417\pi$
$332$	−20.2531	−1.11154
$333$	7.60356	0.416672
$334$	−32.9023	−1.80034
$335$	2.30632	0.126008
$336$	0.154523	0.00842994
$337$	0.346503	0.0188752	0.00943760	−	0.999955i	$-0.496996\pi$
$337$	0.346503	0.0188752	0.00943760	+	0.999955i	$0.496996\pi$
$338$	7.31999	0.398155
$339$	−29.3718	−1.59526
$340$	−3.24701	−0.176094
$341$	0.730504	0.0395590
$342$	8.61583	0.465891
$343$	−20.1582	−1.08844
$344$	21.7582	1.17313
$345$	2.14182	0.115311
$346$	−37.1900	−1.99934
$347$	7.47758	0.401417	0.200709	−	0.979651i	$-0.435676\pi$
$347$	7.47758	0.401417	0.200709	+	0.979651i	$0.435676\pi$
$348$	−15.6641	−0.839683
$349$	−6.03937	−0.323280	−0.161640	−	0.986850i	$-0.551678\pi$
$349$	−6.03937	−0.323280	−0.161640	+	0.986850i	$0.551678\pi$
$350$	−4.89035	−0.261400
$351$	17.6621	0.942734
$352$	−1.63034	−0.0868974
$353$	11.2626	0.599448	0.299724	−	0.954026i	$-0.403105\pi$
$353$	11.2626	0.599448	0.299724	+	0.954026i	$0.403105\pi$
$354$	−7.72432	−0.410543
$355$	1.00000	0.0530745
$356$	−18.3096	−0.970407
$357$	−3.15007	−0.166719
$358$	−29.8740	−1.57889
$359$	−5.53819	−0.292295	−0.146147	−	0.989263i	$-0.546687\pi$
$359$	−5.53819	−0.292295	−0.146147	+	0.989263i	$0.546687\pi$
$360$	2.35067	0.123891
$361$	1.89067	0.0995089
$362$	2.75475	0.144786
$363$	−16.1053	−0.845311
$364$	−21.7059	−1.13770
$365$	2.51175	0.131471
$366$	−50.7594	−2.65324
$367$	12.9927	0.678214	0.339107	−	0.940748i	$-0.389875\pi$
$367$	12.9927	0.678214	0.339107	+	0.940748i	$0.389875\pi$
$368$	0.0712066	0.00371190
$369$	7.34466	0.382348
$370$	21.1645	1.10029
$371$	24.1260	1.25256
$372$	−12.0225	−0.623335
$373$	−5.02700	−0.260288	−0.130144	−	0.991495i	$-0.541544\pi$
$373$	−5.02700	−0.260288	−0.130144	+	0.991495i	$0.541544\pi$
$374$	−0.666815	−0.0344802
$375$	1.47549	0.0761939
$376$	−10.7552	−0.554655
$377$	10.2375	0.527260
$378$	27.5850	1.41882
$379$	17.8455	0.916662	0.458331	−	0.888782i	$-0.348447\pi$
$379$	17.8455	0.916662	0.458331	+	0.888782i	$0.348447\pi$
$380$	14.8409	0.761321
$381$	−11.0082	−0.563967
$382$	5.69548	0.291406
$383$	3.78094	0.193197	0.0965984	−	0.995323i	$-0.469204\pi$
$383$	3.78094	0.193197	0.0965984	+	0.995323i	$0.469204\pi$
$384$	27.1633	1.38617
$385$	−0.621489	−0.0316740
$386$	43.7553	2.22709
$387$	6.26849	0.318645
$388$	−25.0956	−1.27403
$389$	−27.1470	−1.37641	−0.688203	−	0.725518i	$-0.741600\pi$
$389$	−27.1470	−1.37641	−0.688203	+	0.725518i	$0.741600\pi$
$390$	10.5828	0.535882
$391$	−1.45160	−0.0734104
$392$	6.97562	0.352322
$393$	−3.41890	−0.172461
$394$	48.1231	2.42441
$395$	−10.3435	−0.520437
$396$	0.777853	0.0390886
$397$	12.9710	0.650995	0.325497	−	0.945543i	$-0.394468\pi$
$397$	12.9710	0.650995	0.325497	+	0.945543i	$0.394468\pi$
$398$	21.2465	1.06499
$399$	14.3978	0.720792
$400$	0.0490540	0.00245270
$401$	20.8395	1.04068	0.520338	−	0.853960i	$-0.325806\pi$
$401$	20.8395	1.04068	0.520338	+	0.853960i	$0.325806\pi$
$402$	−7.79493	−0.388776
$403$	7.85749	0.391409
$404$	−24.8694	−1.23730
$405$	−5.85398	−0.290887
$406$	15.9892	0.793529
$407$	2.68968	0.133323
$408$	4.21465	0.208656
$409$	15.7739	0.779969	0.389985	−	0.920821i	$-0.372480\pi$
$409$	15.7739	0.779969	0.389985	+	0.920821i	$0.372480\pi$
$410$	20.4439	1.00965
$411$	6.81780	0.336297
$412$	23.9197	1.17844
$413$	4.87925	0.240092
$414$	2.73632	0.134483
$415$	−6.23747	−0.306185
$416$	−17.5363	−0.859790
$417$	13.7769	0.674659
$418$	3.04776	0.149071
$419$	−31.5598	−1.54179	−0.770897	−	0.636959i	$-0.780192\pi$
$419$	−31.5598	−1.54179	−0.770897	+	0.636959i	$0.780192\pi$
$420$	10.2283	0.499090
$421$	−12.1744	−0.593343	−0.296672	−	0.954980i	$-0.595877\pi$
$421$	−12.1744	−0.593343	−0.296672	+	0.954980i	$0.595877\pi$
$422$	41.3669	2.01371
$423$	−3.09853	−0.150656
$424$	−32.2796	−1.56763
$425$	−1.00000	−0.0485071
$426$	−3.37981	−0.163752
$427$	32.0634	1.55165
$428$	−31.0535	−1.50103
$429$	1.34492	0.0649331
$430$	17.4483	0.841433
$431$	3.96345	0.190913	0.0954564	−	0.995434i	$-0.469569\pi$
$431$	3.96345	0.190913	0.0954564	+	0.995434i	$0.469569\pi$
$432$	−0.276698	−0.0133127
$433$	12.1725	0.584971	0.292486	−	0.956270i	$-0.405518\pi$
$433$	12.1725	0.584971	0.292486	+	0.956270i	$0.405518\pi$
$434$	12.2720	0.589073
$435$	−4.82416	−0.231301
$436$	−8.02737	−0.384441
$437$	6.63472	0.317382
$438$	−8.48922	−0.405631
$439$	32.7900	1.56498	0.782491	−	0.622662i	$-0.213949\pi$
$439$	32.7900	1.56498	0.782491	+	0.622662i	$0.213949\pi$
$440$	0.831524	0.0396414
$441$	2.00966	0.0956979
$442$	−7.17243	−0.341158
$443$	9.29088	0.441423	0.220712	−	0.975339i	$-0.429162\pi$
$443$	9.29088	0.441423	0.220712	+	0.975339i	$0.429162\pi$
$444$	−44.2661	−2.10078
$445$	−5.63891	−0.267310
$446$	8.63831	0.409036
$447$	31.1365	1.47271
$448$	−27.5980	−1.30388
$449$	−24.1207	−1.13833	−0.569164	−	0.822224i	$-0.692733\pi$
$449$	−24.1207	−1.13833	−0.569164	+	0.822224i	$0.692733\pi$
$450$	1.88504	0.0888617
$451$	2.59810	0.122340
$452$	−64.6366	−3.04025
$453$	−24.1007	−1.13235
$454$	3.51467	0.164952
$455$	−6.68489	−0.313393
$456$	−19.2636	−0.902102
$457$	20.9781	0.981312	0.490656	−	0.871353i	$-0.336757\pi$
$457$	20.9781	0.981312	0.490656	+	0.871353i	$0.336757\pi$
$458$	36.5909	1.70978
$459$	5.64069	0.263285
$460$	4.71335	0.219761
$461$	−17.7366	−0.826076	−0.413038	−	0.910714i	$-0.635532\pi$
$461$	−17.7366	−0.826076	−0.413038	+	0.910714i	$0.635532\pi$
$462$	2.10051	0.0977247
$463$	−21.6998	−1.00847	−0.504237	−	0.863565i	$-0.668226\pi$
$463$	−21.6998	−1.00847	−0.504237	+	0.863565i	$0.668226\pi$
$464$	−0.160384	−0.00744562
$465$	−3.70262	−0.171705
$466$	14.6150	0.677027
$467$	32.3763	1.49820	0.749098	−	0.662459i	$-0.230487\pi$
$467$	32.3763	1.49820	0.749098	+	0.662459i	$0.230487\pi$
$468$	8.36679	0.386755
$469$	4.92385	0.227362
$470$	−8.62475	−0.397830
$471$	−5.45241	−0.251234
$472$	−6.52822	−0.300485
$473$	2.21741	0.101957
$474$	34.9589	1.60572
$475$	4.57063	0.209715
$476$	−6.93215	−0.317734
$477$	−9.29965	−0.425802
$478$	5.97907	0.273476
$479$	−22.2064	−1.01463	−0.507317	−	0.861759i	$-0.669363\pi$
$479$	−22.2064	−1.01463	−0.507317	+	0.861759i	$0.669363\pi$
$480$	8.26351	0.377176
$481$	28.9309	1.31914
$482$	−23.9210	−1.08957
$483$	4.57263	0.208062
$484$	−35.4420	−1.61100
$485$	−7.72883	−0.350948
$486$	−18.9770	−0.860815
$487$	−17.2805	−0.783056	−0.391528	−	0.920166i	$-0.628053\pi$
$487$	−17.2805	−0.783056	−0.391528	+	0.920166i	$0.628053\pi$
$488$	−42.8993	−1.94196
$489$	−25.0216	−1.13152
$490$	5.59387	0.252705
$491$	−11.3478	−0.512121	−0.256060	−	0.966661i	$-0.582425\pi$
$491$	−11.3478	−0.512121	−0.256060	+	0.966661i	$0.582425\pi$
$492$	−42.7589	−1.92772
$493$	3.26953	0.147252
$494$	32.7825	1.47495
$495$	0.239560	0.0107674
$496$	−0.123097	−0.00552722
$497$	2.13493	0.0957648
$498$	21.0814	0.944682
$499$	−34.3948	−1.53972	−0.769862	−	0.638210i	$-0.779675\pi$
$499$	−34.3948	−1.53972	−0.769862	+	0.638210i	$0.779675\pi$
$500$	3.24701	0.145211
$501$	21.1937	0.946865
$502$	40.1327	1.79121
$503$	−10.0456	−0.447913	−0.223957	−	0.974599i	$-0.571897\pi$
$503$	−10.0456	−0.447913	−0.223957	+	0.974599i	$0.571897\pi$
$504$	5.01851	0.223542
$505$	−7.65917	−0.340828
$506$	0.967946	0.0430305
$507$	−4.71510	−0.209405
$508$	−24.2250	−1.07481
$509$	−1.38289	−0.0612954	−0.0306477	−	0.999530i	$-0.509757\pi$
$509$	−1.38289	−0.0612954	−0.0306477	+	0.999530i	$0.509757\pi$
$510$	3.37981	0.149660
$511$	5.36241	0.237219
$512$	0.554968	0.0245263
$513$	−25.7815	−1.13828
$514$	−50.7357	−2.23786
$515$	7.36668	0.324615
$516$	−36.4936	−1.60654
$517$	−1.09607	−0.0482053
$518$	45.1848	1.98530
$519$	23.9555	1.05153
$520$	8.94409	0.392224
$521$	28.8576	1.26428	0.632138	−	0.774856i	$-0.282178\pi$
$521$	28.8576	1.26428	0.632138	+	0.774856i	$0.282178\pi$
$522$	−6.16320	−0.269756
$523$	4.09527	0.179074	0.0895368	−	0.995984i	$-0.471461\pi$
$523$	4.09527	0.179074	0.0895368	+	0.995984i	$0.471461\pi$
$524$	−7.52374	−0.328676
$525$	3.15007	0.137480
$526$	33.5977	1.46493
$527$	2.50942	0.109312
$528$	−0.0210697	−0.000916943 0
$529$	−20.8929	−0.908385
$530$	−25.8856	−1.12440
$531$	−1.88076	−0.0816181
$532$	31.6843	1.37369
$533$	27.9458	1.21047
$534$	19.0584	0.824739
$535$	−9.56371	−0.413475
$536$	−6.58789	−0.284554
$537$	19.2430	0.830399
$538$	−55.8934	−2.40974
$539$	0.710896	0.0306204
$540$	−18.3154	−0.788169
$541$	−34.4653	−1.48178	−0.740890	−	0.671626i	$-0.765596\pi$
$541$	−34.4653	−1.48178	−0.740890	+	0.671626i	$0.765596\pi$
$542$	53.8346	2.31239
$543$	−1.77444	−0.0761486
$544$	−5.60053	−0.240121
$545$	−2.47223	−0.105899
$546$	22.5936	0.966918
$547$	29.5318	1.26269	0.631345	−	0.775502i	$-0.282503\pi$
$547$	29.5318	1.26269	0.631345	+	0.775502i	$0.282503\pi$
$548$	15.0035	0.640917
$549$	−12.3592	−0.527477
$550$	0.666815	0.0284331
$551$	−14.9438	−0.636628
$552$	−6.11798	−0.260398
$553$	−22.0826	−0.939049
$554$	−62.0020	−2.63421
$555$	−13.6329	−0.578684
$556$	30.3180	1.28577
$557$	−8.69384	−0.368370	−0.184185	−	0.982892i	$-0.558965\pi$
$557$	−8.69384	−0.368370	−0.184185	+	0.982892i	$0.558965\pi$
$558$	−4.73036	−0.200252
$559$	23.8511	1.00879
$560$	0.104727	0.00442552
$561$	0.429522	0.0181344
$562$	33.6319	1.41868
$563$	25.5963	1.07875	0.539377	−	0.842065i	$-0.318660\pi$
$563$	25.5963	1.07875	0.539377	+	0.842065i	$0.318660\pi$
$564$	18.0389	0.759575
$565$	−19.9065	−0.837473
$566$	−47.2071	−1.98426
$567$	−12.4979	−0.524860
$568$	−2.85645	−0.119854
$569$	−31.2297	−1.30922	−0.654609	−	0.755968i	$-0.727167\pi$
$569$	−31.2297	−1.30922	−0.654609	+	0.755968i	$0.727167\pi$
$570$	−15.4478	−0.647039
$571$	9.86986	0.413041	0.206520	−	0.978442i	$-0.433786\pi$
$571$	9.86986	0.413041	0.206520	+	0.978442i	$0.433786\pi$
$572$	2.95967	0.123750
$573$	−3.66868	−0.153262
$574$	43.6463	1.82176
$575$	1.45160	0.0605358
$576$	10.6380	0.443248
$577$	−25.3858	−1.05682	−0.528412	−	0.848988i	$-0.677212\pi$
$577$	−25.3858	−1.05682	−0.528412	+	0.848988i	$0.677212\pi$
$578$	−2.29064	−0.0952779
$579$	−28.1845	−1.17131
$580$	−10.6162	−0.440814
$581$	−13.3166	−0.552465
$582$	26.1219	1.08279
$583$	−3.28966	−0.136244
$584$	−7.17467	−0.296890
$585$	2.57677	0.106536
$586$	−64.8063	−2.67712
$587$	−38.8938	−1.60532	−0.802659	−	0.596438i	$-0.796582\pi$
$587$	−38.8938	−1.60532	−0.802659	+	0.596438i	$0.796582\pi$
$588$	−11.6997	−0.482489
$589$	−11.4696	−0.472598
$590$	−5.23509	−0.215525
$591$	−30.9980	−1.27509
$592$	−0.453238	−0.0186280
$593$	−6.03235	−0.247719	−0.123860	−	0.992300i	$-0.539527\pi$
$593$	−6.03235	−0.247719	−0.123860	+	0.992300i	$0.539527\pi$
$594$	−3.76130	−0.154328
$595$	−2.13493	−0.0875237
$596$	68.5201	2.80669
$597$	−13.6857	−0.560118
$598$	10.4115	0.425757
$599$	−9.33856	−0.381563	−0.190782	−	0.981632i	$-0.561102\pi$
$599$	−9.33856	−0.381563	−0.190782	+	0.981632i	$0.561102\pi$
$600$	−4.21465	−0.172062
$601$	4.03005	0.164389	0.0821945	−	0.996616i	$-0.473807\pi$
$601$	4.03005	0.164389	0.0821945	+	0.996616i	$0.473807\pi$
$602$	37.2510	1.51824
$603$	−1.89795	−0.0772906
$604$	−53.0369	−2.15804
$605$	−10.9153	−0.443768
$606$	25.8865	1.05157
$607$	−23.0046	−0.933728	−0.466864	−	0.884329i	$-0.654616\pi$
$607$	−23.0046	−0.933728	−0.466864	+	0.884329i	$0.654616\pi$
$608$	25.5979	1.03813
$609$	−10.2993	−0.417347
$610$	−34.4018	−1.39289
$611$	−11.7896	−0.476958
$612$	2.67207	0.108012
$613$	−21.3515	−0.862380	−0.431190	−	0.902261i	$-0.641906\pi$
$613$	−21.3515	−0.862380	−0.431190	+	0.902261i	$0.641906\pi$
$614$	−41.9078	−1.69126
$615$	−13.1687	−0.531013
$616$	1.77525	0.0715268
$617$	42.5762	1.71405	0.857026	−	0.515273i	$-0.172310\pi$
$617$	42.5762	1.71405	0.857026	+	0.515273i	$0.172310\pi$
$618$	−24.8979	−1.00154
$619$	−39.6761	−1.59472	−0.797358	−	0.603506i	$-0.793770\pi$
$619$	−39.6761	−1.59472	−0.797358	+	0.603506i	$0.793770\pi$
$620$	−8.14812	−0.327236
$621$	−8.18802	−0.328574
$622$	−3.00408	−0.120453
$623$	−12.0387	−0.482320
$624$	−0.226631	−0.00907252
$625$	1.00000	0.0400000
$626$	27.8175	1.11181
$627$	−1.96318	−0.0784020
$628$	−11.9988	−0.478803
$629$	9.23957	0.368406
$630$	4.02444	0.160337
$631$	19.4823	0.775576	0.387788	−	0.921749i	$-0.373239\pi$
$631$	19.4823	0.775576	0.387788	+	0.921749i	$0.373239\pi$
$632$	29.5456	1.17526
$633$	−26.6460	−1.05909
$634$	−76.9508	−3.05611
$635$	−7.46071	−0.296069
$636$	54.1404	2.14681
$637$	7.64657	0.302968
$638$	−2.18017	−0.0863138
$639$	−0.822934	−0.0325548
$640$	18.4097	0.727707
$641$	−4.12878	−0.163077	−0.0815385	−	0.996670i	$-0.525983\pi$
$641$	−4.12878	−0.163077	−0.0815385	+	0.996670i	$0.525983\pi$
$642$	32.3235	1.27571
$643$	−18.0269	−0.710912	−0.355456	−	0.934693i	$-0.615674\pi$
$643$	−18.0269	−0.710912	−0.355456	+	0.934693i	$0.615674\pi$
$644$	10.0627	0.396526
$645$	−11.2392	−0.442541
$646$	10.4696	0.411923
$647$	−14.8324	−0.583123	−0.291562	−	0.956552i	$-0.594175\pi$
$647$	−14.8324	−0.583123	−0.291562	+	0.956552i	$0.594175\pi$
$648$	16.7216	0.656885
$649$	−0.665300	−0.0261153
$650$	7.17243	0.281326
$651$	−7.90485	−0.309815
$652$	−55.0635	−2.15645
$653$	11.6432	0.455635	0.227818	−	0.973704i	$-0.426841\pi$
$653$	11.6432	0.455635	0.227818	+	0.973704i	$0.426841\pi$
$654$	8.35567	0.326733
$655$	−2.31713	−0.0905377
$656$	−0.437805	−0.0170934
$657$	−2.06700	−0.0806415
$658$	−18.4133	−0.717824
$659$	−31.0571	−1.20981	−0.604906	−	0.796297i	$-0.706789\pi$
$659$	−31.0571	−1.20981	−0.604906	+	0.796297i	$0.706789\pi$
$660$	−1.39466	−0.0542871
$661$	32.4934	1.26385	0.631924	−	0.775030i	$-0.282266\pi$
$661$	32.4934	1.26385	0.631924	+	0.775030i	$0.282266\pi$
$662$	60.4743	2.35040
$663$	4.62004	0.179428
$664$	17.8170	0.691434
$665$	9.75799	0.378399
$666$	−17.4170	−0.674894
$667$	−4.74605	−0.183768
$668$	46.6396	1.80454
$669$	−5.56427	−0.215127
$670$	−5.28295	−0.204098
$671$	−4.37194	−0.168777
$672$	17.6420	0.680556
$673$	11.2768	0.434691	0.217345	−	0.976095i	$-0.430260\pi$
$673$	11.2768	0.434691	0.217345	+	0.976095i	$0.430260\pi$
$674$	−0.793711	−0.0305726
$675$	−5.64069	−0.217110
$676$	−10.3762	−0.399085
$677$	28.0812	1.07925	0.539625	−	0.841905i	$-0.318566\pi$
$677$	28.0812	1.07925	0.539625	+	0.841905i	$0.318566\pi$
$678$	67.2802	2.58388
$679$	−16.5005	−0.633232
$680$	2.85645	0.109540
$681$	−2.26394	−0.0867544
$682$	−1.67332	−0.0640747
$683$	1.52602	0.0583914	0.0291957	−	0.999574i	$-0.490705\pi$
$683$	1.52602	0.0583914	0.0291957	+	0.999574i	$0.490705\pi$
$684$	−12.2131	−0.466978
$685$	4.62071	0.176548
$686$	46.1750	1.76297
$687$	−23.5696	−0.899237
$688$	−0.373656	−0.0142455
$689$	−35.3844	−1.34804
$690$	−4.90612	−0.186773
$691$	3.27995	0.124775	0.0623875	−	0.998052i	$-0.480129\pi$
$691$	3.27995	0.124775	0.0623875	+	0.998052i	$0.480129\pi$
$692$	52.7173	2.00401
$693$	0.511444	0.0194282
$694$	−17.1284	−0.650185
$695$	9.33720	0.354180
$696$	13.7799	0.522327
$697$	8.92497	0.338057
$698$	13.8340	0.523624
$699$	−9.41410	−0.356074
$700$	6.93215	0.262011
$701$	−41.9318	−1.58374	−0.791871	−	0.610689i	$-0.790893\pi$
$701$	−41.9318	−1.58374	−0.791871	+	0.610689i	$0.790893\pi$
$702$	−40.4575	−1.52697
$703$	−42.2307	−1.59276
$704$	3.76307	0.141826
$705$	5.55554	0.209234
$706$	−25.7985	−0.970940
$707$	−16.3518	−0.614973
$708$	10.9493	0.411502
$709$	37.4393	1.40606	0.703032	−	0.711158i	$-0.251829\pi$
$709$	37.4393	1.40606	0.703032	+	0.711158i	$0.251829\pi$
$710$	−2.29064	−0.0859660
$711$	8.51199	0.319225
$712$	16.1072	0.603645
$713$	−3.64267	−0.136419
$714$	7.21566	0.270039
$715$	0.911505	0.0340884
$716$	42.3469	1.58258
$717$	−3.85135	−0.143831
$718$	12.6860	0.473436
$719$	−16.2769	−0.607025	−0.303512	−	0.952827i	$-0.598159\pi$
$719$	−16.2769	−0.607025	−0.303512	+	0.952827i	$0.598159\pi$
$720$	−0.0403682	−0.00150443
$721$	15.7274	0.585717
$722$	−4.33083	−0.161177
$723$	15.4084	0.573046
$724$	−3.90490	−0.145124
$725$	−3.26953	−0.121427
$726$	36.8915	1.36917
$727$	52.4144	1.94394	0.971971	−	0.235100i	$-0.0755419\pi$
$727$	52.4144	1.94394	0.971971	+	0.235100i	$0.0755419\pi$
$728$	19.0950	0.707709
$729$	29.7858	1.10318
$730$	−5.75350	−0.212947
$731$	7.61724	0.281734
$732$	71.9522	2.65943
$733$	−47.0574	−1.73810	−0.869052	−	0.494721i	$-0.835270\pi$
$733$	−47.0574	−1.73810	−0.869052	+	0.494721i	$0.835270\pi$
$734$	−29.7615	−1.09852
$735$	−3.60323	−0.132907
$736$	8.12971	0.299665
$737$	−0.671382	−0.0247307
$738$	−16.8239	−0.619298
$739$	24.9070	0.916219	0.458110	−	0.888896i	$-0.348527\pi$
$739$	24.9070	0.916219	0.458110	+	0.888896i	$0.348527\pi$
$740$	−30.0010	−1.10286
$741$	−21.1165	−0.775734
$742$	−55.2639	−2.02880
$743$	18.5786	0.681584	0.340792	−	0.940139i	$-0.389305\pi$
$743$	18.5786	0.681584	0.340792	+	0.940139i	$0.389305\pi$
$744$	10.5763	0.387747
$745$	21.1025	0.773136
$746$	11.5150	0.421595
$747$	5.13303	0.187808
$748$	0.945220	0.0345607
$749$	−20.4179	−0.746053
$750$	−3.37981	−0.123413
$751$	−40.6369	−1.48286	−0.741431	−	0.671029i	$-0.765853\pi$
$751$	−40.6369	−1.48286	−0.741431	+	0.671029i	$0.765853\pi$
$752$	0.184699	0.00673528
$753$	−25.8510	−0.942064
$754$	−23.4505	−0.854016
$755$	−16.3341	−0.594458
$756$	−39.1021	−1.42213
$757$	−35.4838	−1.28968	−0.644841	−	0.764317i	$-0.723076\pi$
$757$	−35.4838	−1.28968	−0.644841	+	0.764317i	$0.723076\pi$
$758$	−40.8775	−1.48474
$759$	−0.623492	−0.0226313
$760$	−13.0558	−0.473582
$761$	26.8853	0.974591	0.487296	−	0.873237i	$-0.337983\pi$
$761$	26.8853	0.974591	0.487296	+	0.873237i	$0.337983\pi$
$762$	25.2158	0.913470
$763$	−5.27805	−0.191078
$764$	−8.07343	−0.292087
$765$	0.822934	0.0297532
$766$	−8.66075	−0.312926
$767$	−7.15614	−0.258393
$768$	−24.0743	−0.868706
$769$	18.8811	0.680871	0.340435	−	0.940268i	$-0.389426\pi$
$769$	18.8811	0.680871	0.340435	+	0.940268i	$0.389426\pi$
$770$	1.42360	0.0513031
$771$	32.6809	1.17697
$772$	−62.0238	−2.23228
$773$	−9.15886	−0.329421	−0.164711	−	0.986342i	$-0.552669\pi$
$773$	−9.15886	−0.329421	−0.164711	+	0.986342i	$0.552669\pi$
$774$	−14.3588	−0.516117
$775$	−2.50942	−0.0901411
$776$	22.0770	0.792517
$777$	−29.1053	−1.04415
$778$	62.1838	2.22940
$779$	−40.7928	−1.46155
$780$	−15.0013	−0.537134
$781$	−0.291105	−0.0104165
$782$	3.32508	0.118905
$783$	18.4424	0.659079
$784$	−0.119793	−0.00427831
$785$	−3.69533	−0.131892
$786$	7.83145	0.279338
$787$	40.8765	1.45709	0.728545	−	0.684998i	$-0.240197\pi$
$787$	40.8765	1.45709	0.728545	+	0.684998i	$0.240197\pi$
$788$	−68.2152	−2.43007
$789$	−21.6416	−0.770461
$790$	23.6931	0.842964
$791$	−42.4991	−1.51109
$792$	−0.684290	−0.0243152
$793$	−47.0257	−1.66993
$794$	−29.7118	−1.05443
$795$	16.6739	0.591363
$796$	−30.1172	−1.06747
$797$	46.7371	1.65551	0.827757	−	0.561087i	$-0.189617\pi$
$797$	46.7371	1.65551	0.827757	+	0.561087i	$0.189617\pi$
$798$	−32.9801	−1.16748
$799$	−3.76522	−0.133204
$800$	5.60053	0.198008
$801$	4.64045	0.163962
$802$	−47.7357	−1.68561
$803$	−0.731182	−0.0258028
$804$	11.0494	0.389683
$805$	3.09906	0.109228
$806$	−17.9986	−0.633975
$807$	36.0032	1.26737
$808$	21.8780	0.769665
$809$	−20.8043	−0.731439	−0.365720	−	0.930725i	$-0.619177\pi$
$809$	−20.8043	−0.731439	−0.365720	+	0.930725i	$0.619177\pi$
$810$	13.4093	0.471156
$811$	−17.8681	−0.627434	−0.313717	−	0.949517i	$-0.601574\pi$
$811$	−17.8681	−0.627434	−0.313717	+	0.949517i	$0.601574\pi$
$812$	−22.6649	−0.795381
$813$	−34.6770	−1.21617
$814$	−6.16108	−0.215946
$815$	−16.9582	−0.594020
$816$	−0.0723786	−0.00253376
$817$	−34.8156	−1.21804
$818$	−36.1323	−1.26333
$819$	5.50122	0.192228
$820$	−28.9795	−1.01201
$821$	27.8683	0.972611	0.486305	−	0.873789i	$-0.338344\pi$
$821$	27.8683	0.972611	0.486305	+	0.873789i	$0.338344\pi$
$822$	−15.6171	−0.544709
$823$	−45.4193	−1.58322	−0.791609	−	0.611028i	$-0.790756\pi$
$823$	−45.4193	−1.58322	−0.791609	+	0.611028i	$0.790756\pi$
$824$	−21.0425	−0.733050
$825$	−0.429522	−0.0149540
$826$	−11.1766	−0.388883
$827$	39.3143	1.36709	0.683546	−	0.729908i	$-0.260437\pi$
$827$	39.3143	1.36709	0.683546	+	0.729908i	$0.260437\pi$
$828$	−3.87878	−0.134797
$829$	27.2045	0.944851	0.472426	−	0.881371i	$-0.343379\pi$
$829$	27.2045	0.944851	0.472426	+	0.881371i	$0.343379\pi$
$830$	14.2878	0.495936
$831$	39.9379	1.38543
$832$	40.4765	1.40327
$833$	2.44206	0.0846124
$834$	−31.5579	−1.09276
$835$	14.3639	0.497082
$836$	−4.32025	−0.149419
$837$	14.1549	0.489264
$838$	72.2919	2.49728
$839$	−0.387496	−0.0133779	−0.00668893	−	0.999978i	$-0.502129\pi$
$839$	−0.387496	−0.0133779	−0.00668893	+	0.999978i	$0.502129\pi$
$840$	−8.99800	−0.310460
$841$	−18.3102	−0.631385
$842$	27.8871	0.961052
$843$	−21.6636	−0.746135
$844$	−58.6382	−2.01841
$845$	−3.19562	−0.109933
$846$	7.09760	0.244021
$847$	−23.3033	−0.800712
$848$	0.554340	0.0190361
$849$	30.4079	1.04360
$850$	2.29064	0.0785681
$851$	−13.4121	−0.459762
$852$	4.79093	0.164134
$853$	−28.3275	−0.969915	−0.484957	−	0.874538i	$-0.661165\pi$
$853$	−28.3275	−0.969915	−0.484957	+	0.874538i	$0.661165\pi$
$854$	−73.4455	−2.51325
$855$	−3.76133	−0.128635
$856$	27.3182	0.933718
$857$	37.6664	1.28666	0.643329	−	0.765590i	$-0.277553\pi$
$857$	37.6664	1.28666	0.643329	+	0.765590i	$0.277553\pi$
$858$	−3.08071	−0.105174
$859$	7.02659	0.239744	0.119872	−	0.992789i	$-0.461752\pi$
$859$	7.02659	0.239744	0.119872	+	0.992789i	$0.461752\pi$
$860$	−24.7333	−0.843397
$861$	−28.1143	−0.958132
$862$	−9.07882	−0.309226
$863$	17.1807	0.584837	0.292418	−	0.956290i	$-0.405540\pi$
$863$	17.1807	0.584837	0.292418	+	0.956290i	$0.405540\pi$
$864$	−31.5909	−1.07474
$865$	16.2357	0.552029
$866$	−27.8827	−0.947492
$867$	1.47549	0.0501102
$868$	−17.3957	−0.590448
$869$	3.01103	0.102142
$870$	11.0504	0.374643
$871$	−7.22155	−0.244693
$872$	7.06180	0.239143
$873$	6.36031	0.215264
$874$	−15.1977	−0.514070
$875$	2.13493	0.0721739
$876$	12.0336	0.406578
$877$	20.0733	0.677827	0.338914	−	0.940817i	$-0.389941\pi$
$877$	20.0733	0.677827	0.338914	+	0.940817i	$0.389941\pi$
$878$	−75.1100	−2.53484
$879$	41.7443	1.40800
$880$	−0.0142798	−0.000481373 0
$881$	−48.8877	−1.64707	−0.823535	−	0.567266i	$-0.808001\pi$
$881$	−48.8877	−1.64707	−0.823535	+	0.567266i	$0.808001\pi$
$882$	−4.60339	−0.155004
$883$	−41.8672	−1.40894	−0.704471	−	0.709733i	$-0.748816\pi$
$883$	−41.8672	−1.40894	−0.704471	+	0.709733i	$0.748816\pi$
$884$	10.1670	0.341954
$885$	3.37213	0.113353
$886$	−21.2820	−0.714983
$887$	17.2666	0.579756	0.289878	−	0.957064i	$-0.406385\pi$
$887$	17.2666	0.579756	0.289878	+	0.957064i	$0.406385\pi$
$888$	38.9416	1.30679
$889$	−15.9281	−0.534212
$890$	12.9167	0.432969
$891$	1.70412	0.0570902
$892$	−12.2449	−0.409991
$893$	17.2094	0.575892
$894$	−71.3224	−2.38538
$895$	13.0418	0.435940
$896$	39.3035	1.31304
$897$	−6.70644	−0.223922
$898$	55.2518	1.84378
$899$	8.20463	0.273640
$900$	−2.67207	−0.0890691
$901$	−11.3006	−0.376478
$902$	−5.95130	−0.198157
$903$	−23.9948	−0.798498
$904$	56.8619	1.89120
$905$	−1.20261	−0.0399762
$906$	55.2060	1.83410
$907$	−51.9974	−1.72655	−0.863273	−	0.504736i	$-0.831590\pi$
$907$	−51.9974	−1.72655	−0.863273	+	0.504736i	$0.831590\pi$
$908$	−4.98210	−0.165337
$909$	6.30299	0.209057
$910$	15.3126	0.507609
$911$	0.780321	0.0258532	0.0129266	−	0.999916i	$-0.495885\pi$
$911$	0.780321	0.0258532	0.0129266	+	0.999916i	$0.495885\pi$
$912$	0.330816	0.0109544
$913$	1.81576	0.0600928
$914$	−48.0531	−1.58945
$915$	22.1595	0.732572
$916$	−51.8681	−1.71377
$917$	−4.94691	−0.163362
$918$	−12.9208	−0.426449
$919$	13.1042	0.432269	0.216134	−	0.976364i	$-0.430655\pi$
$919$	13.1042	0.432269	0.216134	+	0.976364i	$0.430655\pi$
$920$	−4.14641	−0.136703
$921$	26.9945	0.889499
$922$	40.6281	1.33802
$923$	−3.13120	−0.103065
$924$	−2.97751	−0.0979528
$925$	−9.23957	−0.303795
$926$	49.7063	1.63345
$927$	−6.06229	−0.199112
$928$	−18.3111	−0.601091
$929$	−4.73806	−0.155451	−0.0777254	−	0.996975i	$-0.524766\pi$
$929$	−4.73806	−0.155451	−0.0777254	+	0.996975i	$0.524766\pi$
$930$	8.48136	0.278115
$931$	−11.1618	−0.365812
$932$	−20.7170	−0.678608
$933$	1.93505	0.0633507
$934$	−74.1623	−2.42666
$935$	0.291105	0.00952014
$936$	−7.36039	−0.240582
$937$	45.3007	1.47991	0.739955	−	0.672656i	$-0.234847\pi$
$937$	45.3007	1.47991	0.739955	+	0.672656i	$0.234847\pi$
$938$	−11.2787	−0.368264
$939$	−17.9183	−0.584743
$940$	12.2257	0.398759
$941$	−26.5669	−0.866057	−0.433028	−	0.901380i	$-0.642555\pi$
$941$	−26.5669	−0.866057	−0.433028	+	0.901380i	$0.642555\pi$
$942$	12.4895	0.406929
$943$	−12.9555	−0.421888
$944$	0.112110	0.00364886
$945$	−12.0425	−0.391743
$946$	−5.07929	−0.165142
$947$	21.4021	0.695476	0.347738	−	0.937592i	$-0.386950\pi$
$947$	21.4021	0.695476	0.347738	+	0.937592i	$0.386950\pi$
$948$	−49.5548	−1.60947
$949$	−7.86478	−0.255301
$950$	−10.4696	−0.339680
$951$	49.5670	1.60732
$952$	6.09832	0.197648
$953$	46.0030	1.49018	0.745091	−	0.666963i	$-0.232406\pi$
$953$	46.0030	1.49018	0.745091	+	0.666963i	$0.232406\pi$
$954$	21.3021	0.689681
$955$	−2.48642	−0.0804587
$956$	−8.47542	−0.274115
$957$	1.40433	0.0453957
$958$	50.8667	1.64343
$959$	9.86490	0.318554
$960$	−19.0734	−0.615593
$961$	−24.7028	−0.796865
$962$	−66.2701	−2.13664
$963$	7.87030	0.253617
$964$	33.9083	1.09211
$965$	−19.1018	−0.614909
$966$	−10.4742	−0.337003
$967$	−42.0093	−1.35093	−0.675463	−	0.737394i	$-0.736056\pi$
$967$	−42.0093	−1.35093	−0.675463	+	0.737394i	$0.736056\pi$
$968$	31.1788	1.00213
$969$	−6.74391	−0.216646
$970$	17.7039	0.568439
$971$	30.9096	0.991935	0.495968	−	0.868341i	$-0.334813\pi$
$971$	30.9096	0.991935	0.495968	+	0.868341i	$0.334813\pi$
$972$	26.9002	0.862824
$973$	19.9343	0.639064
$974$	39.5834	1.26834
$975$	−4.62004	−0.147960
$976$	0.736714	0.0235816
$977$	−33.1696	−1.06119	−0.530595	−	0.847626i	$-0.678031\pi$
$977$	−33.1696	−1.06119	−0.530595	+	0.847626i	$0.678031\pi$
$978$	57.3155	1.83275
$979$	1.64151	0.0524630
$980$	−7.92940	−0.253295
$981$	2.03448	0.0649561
$982$	25.9938	0.829494
$983$	−0.557967	−0.0177964	−0.00889820	−	0.999960i	$-0.502832\pi$
$983$	−0.557967	−0.0177964	−0.00889820	+	0.999960i	$0.502832\pi$
$984$	37.6157	1.19914
$985$	−21.0086	−0.669390
$986$	−7.48931	−0.238508
$987$	11.8607	0.377531
$988$	−46.4697	−1.47840
$989$	−11.0572	−0.351598
$990$	−0.548744	−0.0174402
$991$	−4.00628	−0.127264	−0.0636318	−	0.997973i	$-0.520268\pi$
$991$	−4.00628	−0.127264	−0.0636318	+	0.997973i	$0.520268\pi$
$992$	−14.0541	−0.446217
$993$	−38.9539	−1.23616
$994$	−4.89035	−0.155113
$995$	−9.27536	−0.294049
$996$	−29.8833	−0.946888
$997$	−18.3237	−0.580316	−0.290158	−	0.956979i	$-0.593708\pi$
$997$	−18.3237	−0.580316	−0.290158	+	0.956979i	$0.593708\pi$
$998$	78.7860	2.49393
$999$	52.1176	1.64893

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.b.1.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.b.1.5	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.29064 q^{2} +1.47549 q^{3} +3.24701 q^{4} +1.00000 q^{5} -3.37981 q^{6} +2.13493 q^{7} -2.85645 q^{8} -0.822934 q^{9} +O(q^{10})\)	\(q-2.29064 q^{2} +1.47549 q^{3} +3.24701 q^{4} +1.00000 q^{5} -3.37981 q^{6} +2.13493 q^{7} -2.85645 q^{8} -0.822934 q^{9} -2.29064 q^{10} -0.291105 q^{11} +4.79093 q^{12} -3.13120 q^{13} -4.89035 q^{14} +1.47549 q^{15} +0.0490540 q^{16} -1.00000 q^{17} +1.88504 q^{18} +4.57063 q^{19} +3.24701 q^{20} +3.15007 q^{21} +0.666815 q^{22} +1.45160 q^{23} -4.21465 q^{24} +1.00000 q^{25} +7.17243 q^{26} -5.64069 q^{27} +6.93215 q^{28} -3.26953 q^{29} -3.37981 q^{30} -2.50942 q^{31} +5.60053 q^{32} -0.429522 q^{33} +2.29064 q^{34} +2.13493 q^{35} -2.67207 q^{36} -9.23957 q^{37} -10.4696 q^{38} -4.62004 q^{39} -2.85645 q^{40} -8.92497 q^{41} -7.21566 q^{42} -7.61724 q^{43} -0.945220 q^{44} -0.822934 q^{45} -3.32508 q^{46} +3.76522 q^{47} +0.0723786 q^{48} -2.44206 q^{49} -2.29064 q^{50} -1.47549 q^{51} -10.1670 q^{52} +11.3006 q^{53} +12.9208 q^{54} -0.291105 q^{55} -6.09832 q^{56} +6.74391 q^{57} +7.48931 q^{58} +2.28543 q^{59} +4.79093 q^{60} +15.0184 q^{61} +5.74817 q^{62} -1.75691 q^{63} -12.9269 q^{64} -3.13120 q^{65} +0.983877 q^{66} +2.30632 q^{67} -3.24701 q^{68} +2.14182 q^{69} -4.89035 q^{70} +1.00000 q^{71} +2.35067 q^{72} +2.51175 q^{73} +21.1645 q^{74} +1.47549 q^{75} +14.8409 q^{76} -0.621489 q^{77} +10.5828 q^{78} -10.3435 q^{79} +0.0490540 q^{80} -5.85398 q^{81} +20.4439 q^{82} -6.23747 q^{83} +10.2283 q^{84} -1.00000 q^{85} +17.4483 q^{86} -4.82416 q^{87} +0.831524 q^{88} -5.63891 q^{89} +1.88504 q^{90} -6.68489 q^{91} +4.71335 q^{92} -3.70262 q^{93} -8.62475 q^{94} +4.57063 q^{95} +8.26351 q^{96} -7.72883 q^{97} +5.59387 q^{98} +0.239560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9	\( 36 q - q^{2} - 4 q^{3} + 23 q^{4} + 36 q^{5} - 2 q^{6} - 7 q^{7} - 3 q^{8} + 10 q^{9} - q^{10} - 22 q^{11} - 14 q^{12} - 15 q^{13} - 28 q^{14} - 4 q^{15} + q^{16} - 36 q^{17} - 12 q^{18} - 23 q^{19} + 23 q^{20} - 21 q^{21} + 2 q^{23} - 13 q^{24} + 36 q^{25} - 18 q^{26} - 13 q^{27} - 20 q^{28} - 4 q^{29} - 2 q^{30} - 43 q^{31} - 2 q^{32} - 19 q^{33} + q^{34} - 7 q^{35} - 35 q^{36} - 30 q^{37} - 11 q^{38} - 20 q^{39} - 3 q^{40} - 39 q^{41} + 2 q^{42} - 7 q^{43} - 45 q^{44} + 10 q^{45} - 52 q^{46} - 12 q^{47} - 12 q^{48} - 15 q^{49} - q^{50} + 4 q^{51} - 19 q^{52} - 31 q^{53} + 48 q^{54} - 22 q^{55} - 30 q^{56} + 18 q^{57} - 12 q^{58} - 66 q^{59} - 14 q^{60} - 93 q^{61} - 7 q^{62} - 22 q^{63} - 41 q^{64} - 15 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 73 q^{69} - 28 q^{70} + 36 q^{71} - q^{72} - 47 q^{73} - 27 q^{74} - 4 q^{75} - 56 q^{76} - 9 q^{77} - 78 q^{78} - 21 q^{79} + q^{80} - 40 q^{81} - 15 q^{82} - 8 q^{83} - 54 q^{84} - 36 q^{85} - 17 q^{86} - 32 q^{87} - 13 q^{88} - 62 q^{89} - 12 q^{90} - 33 q^{91} + 42 q^{92} - 24 q^{93} - 40 q^{94} - 23 q^{95} + 21 q^{96} - 60 q^{97} + 11 q^{98} - 65 q^{99}+O(q^{100}) \) 36 * q - q^2 - 4 * q^3 + 23 * q^4 + 36 * q^5 - 2 * q^6 - 7 * q^7 - 3 * q^8 + 10 * q^9 - q^10 - 22 * q^11 - 14 * q^12 - 15 * q^13 - 28 * q^14 - 4 * q^15 + q^16 - 36 * q^17 - 12 * q^18 - 23 * q^19 + 23 * q^20 - 21 * q^21 + 2 * q^23 - 13 * q^24 + 36 * q^25 - 18 * q^26 - 13 * q^27 - 20 * q^28 - 4 * q^29 - 2 * q^30 - 43 * q^31 - 2 * q^32 - 19 * q^33 + q^34 - 7 * q^35 - 35 * q^36 - 30 * q^37 - 11 * q^38 - 20 * q^39 - 3 * q^40 - 39 * q^41 + 2 * q^42 - 7 * q^43 - 45 * q^44 + 10 * q^45 - 52 * q^46 - 12 * q^47 - 12 * q^48 - 15 * q^49 - q^50 + 4 * q^51 - 19 * q^52 - 31 * q^53 + 48 * q^54 - 22 * q^55 - 30 * q^56 + 18 * q^57 - 12 * q^58 - 66 * q^59 - 14 * q^60 - 93 * q^61 - 7 * q^62 - 22 * q^63 - 41 * q^64 - 15 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 73 * q^69 - 28 * q^70 + 36 * q^71 - q^72 - 47 * q^73 - 27 * q^74 - 4 * q^75 - 56 * q^76 - 9 * q^77 - 78 * q^78 - 21 * q^79 + q^80 - 40 * q^81 - 15 * q^82 - 8 * q^83 - 54 * q^84 - 36 * q^85 - 17 * q^86 - 32 * q^87 - 13 * q^88 - 62 * q^89 - 12 * q^90 - 33 * q^91 + 42 * q^92 - 24 * q^93 - 40 * q^94 - 23 * q^95 + 21 * q^96 - 60 * q^97 + 11 * q^98 - 65 * q^99

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