LMFDB - Embedded newform 6035.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.174528 q^{2} +1.77073 q^{3} -1.96954 q^{4} +1.00000 q^{5} -0.309043 q^{6} -0.0296109 q^{7} +0.692797 q^{8} +0.135502 q^{9} +O(q^{10})$	\(q-0.174528 q^{2} +1.77073 q^{3} -1.96954 q^{4} +1.00000 q^{5} -0.309043 q^{6} -0.0296109 q^{7} +0.692797 q^{8} +0.135502 q^{9} -0.174528 q^{10} -1.11057 q^{11} -3.48753 q^{12} -3.59151 q^{13} +0.00516794 q^{14} +1.77073 q^{15} +3.81817 q^{16} +1.00000 q^{17} -0.0236490 q^{18} -3.20572 q^{19} -1.96954 q^{20} -0.0524331 q^{21} +0.193825 q^{22} -2.84794 q^{23} +1.22676 q^{24} +1.00000 q^{25} +0.626819 q^{26} -5.07227 q^{27} +0.0583199 q^{28} +6.90282 q^{29} -0.309043 q^{30} +9.20689 q^{31} -2.05197 q^{32} -1.96652 q^{33} -0.174528 q^{34} -0.0296109 q^{35} -0.266877 q^{36} +2.24109 q^{37} +0.559489 q^{38} -6.35961 q^{39} +0.692797 q^{40} +1.03856 q^{41} +0.00915106 q^{42} +11.6250 q^{43} +2.18730 q^{44} +0.135502 q^{45} +0.497046 q^{46} +11.1717 q^{47} +6.76096 q^{48} -6.99912 q^{49} -0.174528 q^{50} +1.77073 q^{51} +7.07362 q^{52} -2.37708 q^{53} +0.885254 q^{54} -1.11057 q^{55} -0.0205144 q^{56} -5.67648 q^{57} -1.20474 q^{58} -11.6453 q^{59} -3.48753 q^{60} -6.96070 q^{61} -1.60686 q^{62} -0.00401235 q^{63} -7.27821 q^{64} -3.59151 q^{65} +0.343213 q^{66} -13.7034 q^{67} -1.96954 q^{68} -5.04295 q^{69} +0.00516794 q^{70} -1.00000 q^{71} +0.0938756 q^{72} -9.54844 q^{73} -0.391134 q^{74} +1.77073 q^{75} +6.31379 q^{76} +0.0328849 q^{77} +1.10993 q^{78} -9.95687 q^{79} +3.81817 q^{80} -9.38815 q^{81} -0.181258 q^{82} -8.79347 q^{83} +0.103269 q^{84} +1.00000 q^{85} -2.02890 q^{86} +12.2231 q^{87} -0.769396 q^{88} -13.5991 q^{89} -0.0236490 q^{90} +0.106348 q^{91} +5.60914 q^{92} +16.3030 q^{93} -1.94978 q^{94} -3.20572 q^{95} -3.63350 q^{96} +0.184984 q^{97} +1.22154 q^{98} -0.150484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * 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 $

$2$	−0.174528	−0.123410	−0.0617050	−	0.998094i	$-0.519654\pi$
$2$	−0.174528	−0.123410	−0.0617050	+	0.998094i	$0.519654\pi$
$3$	1.77073	1.02233	0.511167	−	0.859481i	$-0.329213\pi$
$3$	1.77073	1.02233	0.511167	+	0.859481i	$0.329213\pi$
$4$	−1.96954	−0.984770
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.309043	−0.126166
$7$	−0.0296109	−0.0111919	−0.00559594	−	0.999984i	$-0.501781\pi$
$7$	−0.0296109	−0.0111919	−0.00559594	+	0.999984i	$0.501781\pi$
$8$	0.692797	0.244941
$9$	0.135502	0.0451675
$10$	−0.174528	−0.0551907
$11$	−1.11057	−0.334848	−0.167424	−	0.985885i	$-0.553545\pi$
$11$	−1.11057	−0.334848	−0.167424	+	0.985885i	$0.553545\pi$
$12$	−3.48753	−1.00676
$13$	−3.59151	−0.996105	−0.498052	−	0.867147i	$-0.665951\pi$
$13$	−3.59151	−0.996105	−0.498052	+	0.867147i	$0.665951\pi$
$14$	0.00516794	0.00138119
$15$	1.77073	0.457202
$16$	3.81817	0.954542
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0236490	−0.00557412
$19$	−3.20572	−0.735443	−0.367721	−	0.929936i	$-0.619862\pi$
$19$	−3.20572	−0.735443	−0.367721	+	0.929936i	$0.619862\pi$
$20$	−1.96954	−0.440403
$21$	−0.0524331	−0.0114418
$22$	0.193825	0.0413236
$23$	−2.84794	−0.593837	−0.296918	−	0.954903i	$-0.595959\pi$
$23$	−2.84794	−0.593837	−0.296918	+	0.954903i	$0.595959\pi$
$24$	1.22676	0.250411
$25$	1.00000	0.200000
$26$	0.626819	0.122929
$27$	−5.07227	−0.976158
$28$	0.0583199	0.0110214
$29$	6.90282	1.28182	0.640911	−	0.767615i	$-0.278557\pi$
$29$	6.90282	1.28182	0.640911	+	0.767615i	$0.278557\pi$
$30$	−0.309043	−0.0564233
$31$	9.20689	1.65361	0.826803	−	0.562491i	$-0.190157\pi$
$31$	9.20689	1.65361	0.826803	+	0.562491i	$0.190157\pi$
$32$	−2.05197	−0.362741
$33$	−1.96652	−0.342327
$34$	−0.174528	−0.0299313
$35$	−0.0296109	−0.00500516
$36$	−0.266877	−0.0444795
$37$	2.24109	0.368434	0.184217	−	0.982886i	$-0.441025\pi$
$37$	2.24109	0.368434	0.184217	+	0.982886i	$0.441025\pi$
$38$	0.559489	0.0907611
$39$	−6.35961	−1.01835
$40$	0.692797	0.109541
$41$	1.03856	0.162196	0.0810980	−	0.996706i	$-0.474157\pi$
$41$	1.03856	0.162196	0.0810980	+	0.996706i	$0.474157\pi$
$42$	0.00915106	0.00141204
$43$	11.6250	1.77280	0.886400	−	0.462920i	$-0.153198\pi$
$43$	11.6250	1.77280	0.886400	+	0.462920i	$0.153198\pi$
$44$	2.18730	0.329748
$45$	0.135502	0.0201995
$46$	0.497046	0.0732855
$47$	11.1717	1.62957	0.814783	−	0.579767i	$-0.196856\pi$
$47$	11.1717	1.62957	0.814783	+	0.579767i	$0.196856\pi$
$48$	6.76096	0.975861
$49$	−6.99912	−0.999875
$50$	−0.174528	−0.0246820
$51$	1.77073	0.247952
$52$	7.07362	0.980934
$53$	−2.37708	−0.326518	−0.163259	−	0.986583i	$-0.552201\pi$
$53$	−2.37708	−0.326518	−0.163259	+	0.986583i	$0.552201\pi$
$54$	0.885254	0.120468
$55$	−1.11057	−0.149749
$56$	−0.0205144	−0.00274135
$57$	−5.67648	−0.751868
$58$	−1.20474	−0.158190
$59$	−11.6453	−1.51609	−0.758047	−	0.652200i	$-0.773846\pi$
$59$	−11.6453	−1.51609	−0.758047	+	0.652200i	$0.773846\pi$
$60$	−3.48753	−0.450239
$61$	−6.96070	−0.891227	−0.445613	−	0.895226i	$-0.647014\pi$
$61$	−6.96070	−0.891227	−0.445613	+	0.895226i	$0.647014\pi$
$62$	−1.60686	−0.204072
$63$	−0.00401235	−0.000505509 0
$64$	−7.27821	−0.909776
$65$	−3.59151	−0.445472
$66$	0.343213	0.0422466
$67$	−13.7034	−1.67414	−0.837068	−	0.547099i	$-0.815732\pi$
$67$	−13.7034	−1.67414	−0.837068	+	0.547099i	$0.815732\pi$
$68$	−1.96954	−0.238842
$69$	−5.04295	−0.607100
$70$	0.00516794	0.000617687 0
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	0.0938756	0.0110633
$73$	−9.54844	−1.11756	−0.558780	−	0.829316i	$-0.688731\pi$
$73$	−9.54844	−1.11756	−0.558780	+	0.829316i	$0.688731\pi$
$74$	−0.391134	−0.0454684
$75$	1.77073	0.204467
$76$	6.31379	0.724242
$77$	0.0328849	0.00374758
$78$	1.10993	0.125675
$79$	−9.95687	−1.12024	−0.560118	−	0.828413i	$-0.689244\pi$
$79$	−9.95687	−1.12024	−0.560118	+	0.828413i	$0.689244\pi$
$80$	3.81817	0.426884
$81$	−9.38815	−1.04313
$82$	−0.181258	−0.0200166
$83$	−8.79347	−0.965209	−0.482604	−	0.875838i	$-0.660309\pi$
$83$	−8.79347	−0.965209	−0.482604	+	0.875838i	$0.660309\pi$
$84$	0.103269	0.0112676
$85$	1.00000	0.108465
$86$	−2.02890	−0.218781
$87$	12.2231	1.31045
$88$	−0.769396	−0.0820179
$89$	−13.5991	−1.44150	−0.720752	−	0.693193i	$-0.756203\pi$
$89$	−13.5991	−1.44150	−0.720752	+	0.693193i	$0.756203\pi$
$90$	−0.0236490	−0.00249282
$91$	0.106348	0.0111483
$92$	5.60914	0.584793
$93$	16.3030	1.69054
$94$	−1.94978	−0.201105
$95$	−3.20572	−0.328900
$96$	−3.63350	−0.370842
$97$	0.184984	0.0187823	0.00939114	−	0.999956i	$-0.497011\pi$
$97$	0.184984	0.0187823	0.00939114	+	0.999956i	$0.497011\pi$
$98$	1.22154	0.123395
$99$	−0.150484	−0.0151242
$100$	−1.96954	−0.196954
$101$	−17.4203	−1.73338	−0.866692	−	0.498845i	$-0.833758\pi$
$101$	−17.4203	−1.73338	−0.866692	+	0.498845i	$0.833758\pi$
$102$	−0.309043	−0.0305998
$103$	−18.9905	−1.87119	−0.935595	−	0.353075i	$-0.885136\pi$
$103$	−18.9905	−1.87119	−0.935595	+	0.353075i	$0.885136\pi$
$104$	−2.48818	−0.243987
$105$	−0.0524331	−0.00511695
$106$	0.414868	0.0402956
$107$	4.07952	0.394382	0.197191	−	0.980365i	$-0.436818\pi$
$107$	4.07952	0.394382	0.197191	+	0.980365i	$0.436818\pi$
$108$	9.99003	0.961291
$109$	17.5919	1.68500	0.842500	−	0.538696i	$-0.181083\pi$
$109$	17.5919	1.68500	0.842500	+	0.538696i	$0.181083\pi$
$110$	0.193825	0.0184805
$111$	3.96838	0.376662
$112$	−0.113060	−0.0106831
$113$	−6.59360	−0.620274	−0.310137	−	0.950692i	$-0.600375\pi$
$113$	−6.59360	−0.620274	−0.310137	+	0.950692i	$0.600375\pi$
$114$	0.990706	0.0927881
$115$	−2.84794	−0.265572
$116$	−13.5954	−1.26230
$117$	−0.486658	−0.0449915
$118$	2.03244	0.187101
$119$	−0.0296109	−0.00271443
$120$	1.22676	0.111987
$121$	−9.76664	−0.887877
$122$	1.21484	0.109986
$123$	1.83902	0.165819
$124$	−18.1333	−1.62842
$125$	1.00000	0.0894427
$126$	0.000700269 0	6.23849e−5 0
$127$	−10.5036	−0.932047	−0.466023	−	0.884772i	$-0.654314\pi$
$127$	−10.5036	−0.932047	−0.466023	+	0.884772i	$0.654314\pi$
$128$	5.37420	0.475016
$129$	20.5848	1.81239
$130$	0.626819	0.0549757
$131$	−10.3057	−0.900415	−0.450208	−	0.892924i	$-0.648650\pi$
$131$	−10.3057	−0.900415	−0.450208	+	0.892924i	$0.648650\pi$
$132$	3.87313	0.337113
$133$	0.0949244	0.00823099
$134$	2.39163	0.206605
$135$	−5.07227	−0.436551
$136$	0.692797	0.0594068
$137$	7.61891	0.650928	0.325464	−	0.945554i	$-0.394480\pi$
$137$	7.61891	0.650928	0.325464	+	0.945554i	$0.394480\pi$
$138$	0.880137	0.0749223
$139$	−14.7850	−1.25404	−0.627022	−	0.779001i	$-0.715727\pi$
$139$	−14.7850	−1.25404	−0.627022	+	0.779001i	$0.715727\pi$
$140$	0.0583199	0.00492893
$141$	19.7822	1.66596
$142$	0.174528	0.0146461
$143$	3.98860	0.333544
$144$	0.517371	0.0431142
$145$	6.90282	0.573248
$146$	1.66647	0.137918
$147$	−12.3936	−1.02221
$148$	−4.41392	−0.362822
$149$	15.2428	1.24874	0.624368	−	0.781130i	$-0.285357\pi$
$149$	15.2428	1.24874	0.624368	+	0.781130i	$0.285357\pi$
$150$	−0.309043	−0.0252333
$151$	15.6166	1.27086	0.635429	−	0.772160i	$-0.280823\pi$
$151$	15.6166	1.27086	0.635429	+	0.772160i	$0.280823\pi$
$152$	−2.22091	−0.180140
$153$	0.135502	0.0109547
$154$	−0.00573934	−0.000462489 0
$155$	9.20689	0.739515
$156$	12.5255	1.00284
$157$	20.6993	1.65199	0.825993	−	0.563681i	$-0.190615\pi$
$157$	20.6993	1.65199	0.825993	+	0.563681i	$0.190615\pi$
$158$	1.73776	0.138248
$159$	−4.20918	−0.333810
$160$	−2.05197	−0.162223
$161$	0.0843302	0.00664615
$162$	1.63850	0.128732
$163$	−0.660376	−0.0517246	−0.0258623	−	0.999666i	$-0.508233\pi$
$163$	−0.660376	−0.0517246	−0.0258623	+	0.999666i	$0.508233\pi$
$164$	−2.04549	−0.159726
$165$	−1.96652	−0.153093
$166$	1.53471	0.119117
$167$	−5.46569	−0.422948	−0.211474	−	0.977384i	$-0.567826\pi$
$167$	−5.46569	−0.422948	−0.211474	+	0.977384i	$0.567826\pi$
$168$	−0.0363255	−0.00280257
$169$	−0.101076	−0.00777508
$170$	−0.174528	−0.0133857
$171$	−0.434383	−0.0332181
$172$	−22.8960	−1.74580
$173$	−18.0670	−1.37361	−0.686803	−	0.726843i	$-0.740987\pi$
$173$	−18.0670	−1.37361	−0.686803	+	0.726843i	$0.740987\pi$
$174$	−2.13327	−0.161723
$175$	−0.0296109	−0.00223838
$176$	−4.24032	−0.319626
$177$	−20.6208	−1.54995
$178$	2.37343	0.177896
$179$	2.33990	0.174893	0.0874463	−	0.996169i	$-0.472129\pi$
$179$	2.33990	0.174893	0.0874463	+	0.996169i	$0.472129\pi$
$180$	−0.266877	−0.0198919
$181$	18.5493	1.37876	0.689379	−	0.724401i	$-0.257883\pi$
$181$	18.5493	1.37876	0.689379	+	0.724401i	$0.257883\pi$
$182$	−0.0185607	−0.00137581
$183$	−12.3256	−0.911132
$184$	−1.97304	−0.145455
$185$	2.24109	0.164769
$186$	−2.84533	−0.208630
$187$	−1.11057	−0.0812126
$188$	−22.0032	−1.60475
$189$	0.150195	0.0109250
$190$	0.559489	0.0405896
$191$	−17.4650	−1.26373	−0.631863	−	0.775080i	$-0.717709\pi$
$191$	−17.4650	−1.26373	−0.631863	+	0.775080i	$0.717709\pi$
$192$	−12.8878	−0.930095
$193$	−18.7266	−1.34797	−0.673985	−	0.738745i	$-0.735419\pi$
$193$	−18.7266	−1.34797	−0.673985	+	0.738745i	$0.735419\pi$
$194$	−0.0322849	−0.00231792
$195$	−6.35961	−0.455421
$196$	13.7851	0.984647
$197$	−2.33270	−0.166198	−0.0830988	−	0.996541i	$-0.526482\pi$
$197$	−2.33270	−0.166198	−0.0830988	+	0.996541i	$0.526482\pi$
$198$	0.0262637	0.00186648
$199$	13.0759	0.926926	0.463463	−	0.886116i	$-0.346607\pi$
$199$	13.0759	0.926926	0.463463	+	0.886116i	$0.346607\pi$
$200$	0.692797	0.0489881
$201$	−24.2651	−1.71153
$202$	3.04033	0.213917
$203$	−0.204399	−0.0143460
$204$	−3.48753	−0.244176
$205$	1.03856	0.0725363
$206$	3.31438	0.230924
$207$	−0.385903	−0.0268221
$208$	−13.7130	−0.950824
$209$	3.56016	0.246262
$210$	0.00915106	0.000631483 0
$211$	8.93267	0.614950	0.307475	−	0.951556i	$-0.400516\pi$
$211$	8.93267	0.614950	0.307475	+	0.951556i	$0.400516\pi$
$212$	4.68176	0.321545
$213$	−1.77073	−0.121329
$214$	−0.711992	−0.0486708
$215$	11.6250	0.792820
$216$	−3.51405	−0.239101
$217$	−0.272625	−0.0185070
$218$	−3.07029	−0.207946
$219$	−16.9078	−1.14252
$220$	2.18730	0.147468
$221$	−3.59151	−0.241591
$222$	−0.692595	−0.0464839
$223$	−6.42073	−0.429964	−0.214982	−	0.976618i	$-0.568969\pi$
$223$	−6.42073	−0.429964	−0.214982	+	0.976618i	$0.568969\pi$
$224$	0.0607608	0.00405975
$225$	0.135502	0.00903349
$226$	1.15077	0.0765481
$227$	−7.29336	−0.484077	−0.242039	−	0.970267i	$-0.577816\pi$
$227$	−7.29336	−0.484077	−0.242039	+	0.970267i	$0.577816\pi$
$228$	11.1801	0.740417
$229$	−22.9370	−1.51572	−0.757860	−	0.652417i	$-0.773755\pi$
$229$	−22.9370	−1.51572	−0.757860	+	0.652417i	$0.773755\pi$
$230$	0.497046	0.0327743
$231$	0.0582304	0.00383128
$232$	4.78225	0.313970
$233$	17.3234	1.13489	0.567446	−	0.823411i	$-0.307932\pi$
$233$	17.3234	1.13489	0.567446	+	0.823411i	$0.307932\pi$
$234$	0.0849355	0.00555241
$235$	11.1717	0.728764
$236$	22.9360	1.49300
$237$	−17.6310	−1.14526
$238$	0.00516794	0.000334988 0
$239$	−21.1024	−1.36500	−0.682500	−	0.730886i	$-0.739107\pi$
$239$	−21.1024	−1.36500	−0.682500	+	0.730886i	$0.739107\pi$
$240$	6.76096	0.436418
$241$	−14.8458	−0.956300	−0.478150	−	0.878278i	$-0.658692\pi$
$241$	−14.8458	−0.956300	−0.478150	+	0.878278i	$0.658692\pi$
$242$	1.70456	0.109573
$243$	−1.40712	−0.0902668
$244$	13.7094	0.877653
$245$	−6.99912	−0.447158
$246$	−0.320960	−0.0204637
$247$	11.5134	0.732578
$248$	6.37851	0.405036
$249$	−15.5709	−0.986766
$250$	−0.174528	−0.0110381
$251$	15.4561	0.975579	0.487789	−	0.872961i	$-0.337803\pi$
$251$	15.4561	0.975579	0.487789	+	0.872961i	$0.337803\pi$
$252$	0.00790249	0.000497810 0
$253$	3.16283	0.198845
$254$	1.83318	0.115024
$255$	1.77073	0.110888
$256$	13.6185	0.851154
$257$	−3.62726	−0.226262	−0.113131	−	0.993580i	$-0.536088\pi$
$257$	−3.62726	−0.226262	−0.113131	+	0.993580i	$0.536088\pi$
$258$	−3.59264	−0.223668
$259$	−0.0663609	−0.00412347
$260$	7.07362	0.438687
$261$	0.935349	0.0578966
$262$	1.79864	0.111120
$263$	10.1725	0.627262	0.313631	−	0.949545i	$-0.398455\pi$
$263$	10.1725	0.627262	0.313631	+	0.949545i	$0.398455\pi$
$264$	−1.36240	−0.0838497
$265$	−2.37708	−0.146023
$266$	−0.0165670	−0.00101579
$267$	−24.0804	−1.47370
$268$	26.9894	1.64864
$269$	17.0735	1.04099	0.520496	−	0.853864i	$-0.325747\pi$
$269$	17.0735	1.04099	0.520496	+	0.853864i	$0.325747\pi$
$270$	0.885254	0.0538748
$271$	15.2143	0.924205	0.462103	−	0.886827i	$-0.347095\pi$
$271$	15.2143	0.924205	0.462103	+	0.886827i	$0.347095\pi$
$272$	3.81817	0.231510
$273$	0.188314	0.0113973
$274$	−1.32972	−0.0803311
$275$	−1.11057	−0.0669696
$276$	9.93229	0.597854
$277$	8.58564	0.515861	0.257930	−	0.966163i	$-0.416959\pi$
$277$	8.58564	0.515861	0.257930	+	0.966163i	$0.416959\pi$
$278$	2.58039	0.154762
$279$	1.24756	0.0746892
$280$	−0.0205144	−0.00122597
$281$	−1.54657	−0.0922609	−0.0461304	−	0.998935i	$-0.514689\pi$
$281$	−1.54657	−0.0922609	−0.0461304	+	0.998935i	$0.514689\pi$
$282$	−3.45255	−0.205596
$283$	17.9622	1.06774	0.533870	−	0.845567i	$-0.320737\pi$
$283$	17.9622	1.06774	0.533870	+	0.845567i	$0.320737\pi$
$284$	1.96954	0.116871
$285$	−5.67648	−0.336246
$286$	−0.696124	−0.0411627
$287$	−0.0307528	−0.00181528
$288$	−0.278047	−0.0163841
$289$	1.00000	0.0588235
$290$	−1.20474	−0.0707446
$291$	0.327558	0.0192018
$292$	18.8060	1.10054
$293$	−24.4632	−1.42916	−0.714578	−	0.699556i	$-0.753381\pi$
$293$	−24.4632	−1.42916	−0.714578	+	0.699556i	$0.753381\pi$
$294$	2.16303	0.126151
$295$	−11.6453	−0.678018
$296$	1.55262	0.0902444
$297$	5.63308	0.326865
$298$	−2.66029	−0.154107
$299$	10.2284	0.591524
$300$	−3.48753	−0.201353
$301$	−0.344228	−0.0198410
$302$	−2.72553	−0.156837
$303$	−30.8467	−1.77210
$304$	−12.2400	−0.702011
$305$	−6.96070	−0.398569
$306$	−0.0236490	−0.00135192
$307$	−27.7435	−1.58340	−0.791702	−	0.610907i	$-0.790805\pi$
$307$	−27.7435	−1.58340	−0.791702	+	0.610907i	$0.790805\pi$
$308$	−0.0647681	−0.00369050
$309$	−33.6272	−1.91298
$310$	−1.60686	−0.0912637
$311$	13.5576	0.768779	0.384389	−	0.923171i	$-0.374412\pi$
$311$	13.5576	0.768779	0.384389	+	0.923171i	$0.374412\pi$
$312$	−4.40592	−0.249436
$313$	−26.0530	−1.47260	−0.736301	−	0.676654i	$-0.763429\pi$
$313$	−26.0530	−1.47260	−0.736301	+	0.676654i	$0.763429\pi$
$314$	−3.61262	−0.203872
$315$	−0.00401235	−0.000226070 0
$316$	19.6105	1.10317
$317$	−0.154078	−0.00865387	−0.00432694	−	0.999991i	$-0.501377\pi$
$317$	−0.154078	−0.00865387	−0.00432694	+	0.999991i	$0.501377\pi$
$318$	0.734622	0.0411955
$319$	−7.66604	−0.429216
$320$	−7.27821	−0.406864
$321$	7.22375	0.403191
$322$	−0.0147180	−0.000820202 0
$323$	−3.20572	−0.178371
$324$	18.4903	1.02724
$325$	−3.59151	−0.199221
$326$	0.115254	0.00638334
$327$	31.1506	1.72263
$328$	0.719512	0.0397284
$329$	−0.330806	−0.0182379
$330$	0.343213	0.0188932
$331$	27.0524	1.48694	0.743468	−	0.668771i	$-0.233179\pi$
$331$	27.0524	1.48694	0.743468	+	0.668771i	$0.233179\pi$
$332$	17.3191	0.950509
$333$	0.303674	0.0166412
$334$	0.953917	0.0521960
$335$	−13.7034	−0.748696
$336$	−0.200198	−0.0109217
$337$	24.4995	1.33457	0.667287	−	0.744801i	$-0.267456\pi$
$337$	24.4995	1.33457	0.667287	+	0.744801i	$0.267456\pi$
$338$	0.0176406	0.000959523 0
$339$	−11.6755	−0.634127
$340$	−1.96954	−0.106813
$341$	−10.2249	−0.553707
$342$	0.0758120	0.00409945
$343$	0.414527	0.0223824
$344$	8.05378	0.434231
$345$	−5.04295	−0.271503
$346$	3.15320	0.169517
$347$	−26.1669	−1.40471	−0.702356	−	0.711826i	$-0.747868\pi$
$347$	−26.1669	−1.40471	−0.702356	+	0.711826i	$0.747868\pi$
$348$	−24.0738	−1.29049
$349$	10.1252	0.541989	0.270995	−	0.962581i	$-0.412647\pi$
$349$	10.1252	0.541989	0.270995	+	0.962581i	$0.412647\pi$
$350$	0.00516794	0.000276238 0
$351$	18.2171	0.972356
$352$	2.27885	0.121463
$353$	−9.12399	−0.485621	−0.242811	−	0.970074i	$-0.578069\pi$
$353$	−9.12399	−0.485621	−0.242811	+	0.970074i	$0.578069\pi$
$354$	3.59891	0.191280
$355$	−1.00000	−0.0530745
$356$	26.7840	1.41955
$357$	−0.0524331	−0.00277505
$358$	−0.408379	−0.0215835
$359$	2.26387	0.119482	0.0597412	−	0.998214i	$-0.480972\pi$
$359$	2.26387	0.119482	0.0597412	+	0.998214i	$0.480972\pi$
$360$	0.0938756	0.00494768
$361$	−8.72336	−0.459124
$362$	−3.23738	−0.170153
$363$	−17.2941	−0.907707
$364$	−0.209456	−0.0109785
$365$	−9.54844	−0.499788
$366$	2.15116	0.112443
$367$	6.30044	0.328880	0.164440	−	0.986387i	$-0.447418\pi$
$367$	6.30044	0.328880	0.164440	+	0.986387i	$0.447418\pi$
$368$	−10.8739	−0.566842
$369$	0.140728	0.00732598
$370$	−0.391134	−0.0203341
$371$	0.0703877	0.00365435
$372$	−32.1093	−1.66479
$373$	15.0709	0.780341	0.390170	−	0.920743i	$-0.372416\pi$
$373$	15.0709	0.780341	0.390170	+	0.920743i	$0.372416\pi$
$374$	0.193825	0.0100225
$375$	1.77073	0.0914404
$376$	7.73974	0.399147
$377$	−24.7915	−1.27683
$378$	−0.0262132	−0.00134826
$379$	18.4924	0.949892	0.474946	−	0.880015i	$-0.342468\pi$
$379$	18.4924	0.949892	0.474946	+	0.880015i	$0.342468\pi$
$380$	6.31379	0.323891
$381$	−18.5991	−0.952863
$382$	3.04814	0.155956
$383$	−17.9219	−0.915766	−0.457883	−	0.889013i	$-0.651392\pi$
$383$	−17.9219	−0.915766	−0.457883	+	0.889013i	$0.651392\pi$
$384$	9.51628	0.485625
$385$	0.0328849	0.00167597
$386$	3.26832	0.166353
$387$	1.57522	0.0800729
$388$	−0.364333	−0.0184962
$389$	−8.15095	−0.413270	−0.206635	−	0.978418i	$-0.566251\pi$
$389$	−8.15095	−0.413270	−0.206635	+	0.978418i	$0.566251\pi$
$390$	1.10993	0.0562035
$391$	−2.84794	−0.144027
$392$	−4.84897	−0.244910
$393$	−18.2487	−0.920525
$394$	0.407121	0.0205105
$395$	−9.95687	−0.500985
$396$	0.296385	0.0148939
$397$	−12.3688	−0.620773	−0.310387	−	0.950610i	$-0.600459\pi$
$397$	−12.3688	−0.620773	−0.310387	+	0.950610i	$0.600459\pi$
$398$	−2.28211	−0.114392
$399$	0.168086	0.00841482
$400$	3.81817	0.190908
$401$	−8.91351	−0.445120	−0.222560	−	0.974919i	$-0.571441\pi$
$401$	−8.91351	−0.445120	−0.222560	+	0.974919i	$0.571441\pi$
$402$	4.23494	0.211220
$403$	−33.0666	−1.64717
$404$	34.3099	1.70698
$405$	−9.38815	−0.466501
$406$	0.0356734	0.00177044
$407$	−2.48888	−0.123369
$408$	1.22676	0.0607336
$409$	−31.2310	−1.54427	−0.772137	−	0.635456i	$-0.780812\pi$
$409$	−31.2310	−1.54427	−0.772137	+	0.635456i	$0.780812\pi$
$410$	−0.181258	−0.00895171
$411$	13.4911	0.665466
$412$	37.4026	1.84269
$413$	0.344829	0.0169679
$414$	0.0673509	0.00331012
$415$	−8.79347	−0.431655
$416$	7.36967	0.361328
$417$	−26.1803	−1.28205
$418$	−0.621349	−0.0303912
$419$	−24.1010	−1.17741	−0.588706	−	0.808348i	$-0.700362\pi$
$419$	−24.1010	−1.17741	−0.588706	+	0.808348i	$0.700362\pi$
$420$	0.103269	0.00503902
$421$	−35.3570	−1.72319	−0.861597	−	0.507594i	$-0.830535\pi$
$421$	−35.3570	−1.72319	−0.861597	+	0.507594i	$0.830535\pi$
$422$	−1.55900	−0.0758911
$423$	1.51380	0.0736033
$424$	−1.64684	−0.0799774
$425$	1.00000	0.0485071
$426$	0.309043	0.0149732
$427$	0.206113	0.00997450
$428$	−8.03478	−0.388376
$429$	7.06276	0.340993
$430$	−2.02890	−0.0978420
$431$	31.6523	1.52464	0.762318	−	0.647202i	$-0.224061\pi$
$431$	31.6523	1.52464	0.762318	+	0.647202i	$0.224061\pi$
$432$	−19.3668	−0.931784
$433$	32.0091	1.53826	0.769130	−	0.639092i	$-0.220690\pi$
$433$	32.0091	1.53826	0.769130	+	0.639092i	$0.220690\pi$
$434$	0.0475807	0.00228395
$435$	12.2231	0.586051
$436$	−34.6480	−1.65934
$437$	9.12971	0.436733
$438$	2.95088	0.140999
$439$	16.3103	0.778448	0.389224	−	0.921143i	$-0.372743\pi$
$439$	16.3103	0.778448	0.389224	+	0.921143i	$0.372743\pi$
$440$	−0.769396	−0.0366795
$441$	−0.948398	−0.0451618
$442$	0.626819	0.0298148
$443$	16.6631	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$443$	16.6631	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$444$	−7.81589	−0.370926
$445$	−13.5991	−0.644660
$446$	1.12060	0.0530619
$447$	26.9909	1.27663
$448$	0.215515	0.0101821
$449$	−9.94266	−0.469223	−0.234612	−	0.972089i	$-0.575382\pi$
$449$	−9.94266	−0.469223	−0.234612	+	0.972089i	$0.575382\pi$
$450$	−0.0236490	−0.00111482
$451$	−1.15339	−0.0543110
$452$	12.9864	0.610827
$453$	27.6528	1.29924
$454$	1.27290	0.0597400
$455$	0.106348	0.00498567
$456$	−3.93265	−0.184163
$457$	7.95714	0.372219	0.186110	−	0.982529i	$-0.440412\pi$
$457$	7.95714	0.372219	0.186110	+	0.982529i	$0.440412\pi$
$458$	4.00316	0.187055
$459$	−5.07227	−0.236753
$460$	5.60914	0.261527
$461$	0.407807	0.0189935	0.00949674	−	0.999955i	$-0.496977\pi$
$461$	0.407807	0.0189935	0.00949674	+	0.999955i	$0.496977\pi$
$462$	−0.0101628	−0.000472818 0
$463$	4.72489	0.219584	0.109792	−	0.993955i	$-0.464982\pi$
$463$	4.72489	0.219584	0.109792	+	0.993955i	$0.464982\pi$
$464$	26.3561	1.22355
$465$	16.3030	0.756032
$466$	−3.02342	−0.140057
$467$	30.2544	1.40001	0.700003	−	0.714140i	$-0.253182\pi$
$467$	30.2544	1.40001	0.700003	+	0.714140i	$0.253182\pi$
$468$	0.958492	0.0443063
$469$	0.405770	0.0187367
$470$	−1.94978	−0.0899368
$471$	36.6530	1.68888
$472$	−8.06785	−0.371353
$473$	−12.9104	−0.593619
$474$	3.07710	0.141336
$475$	−3.20572	−0.147089
$476$	0.0583199	0.00267309
$477$	−0.322100	−0.0147480
$478$	3.68296	0.168455
$479$	0.523217	0.0239064	0.0119532	−	0.999929i	$-0.496195\pi$
$479$	0.523217	0.0239064	0.0119532	+	0.999929i	$0.496195\pi$
$480$	−3.63350	−0.165846
$481$	−8.04891	−0.366998
$482$	2.59101	0.118017
$483$	0.149326	0.00679459
$484$	19.2358	0.874354
$485$	0.184984	0.00839969
$486$	0.245582	0.0111398
$487$	−19.0909	−0.865091	−0.432546	−	0.901612i	$-0.642385\pi$
$487$	−19.0909	−0.865091	−0.432546	+	0.901612i	$0.642385\pi$
$488$	−4.82235	−0.218298
$489$	−1.16935	−0.0528799
$490$	1.22154	0.0551838
$491$	−31.0192	−1.39988	−0.699939	−	0.714203i	$-0.746789\pi$
$491$	−31.0192	−1.39988	−0.699939	+	0.714203i	$0.746789\pi$
$492$	−3.62202	−0.163293
$493$	6.90282	0.310888
$494$	−2.00941	−0.0904075
$495$	−0.150484	−0.00676376
$496$	35.1535	1.57844
$497$	0.0296109	0.00132823
$498$	2.71756	0.121777
$499$	12.0120	0.537731	0.268865	−	0.963178i	$-0.413351\pi$
$499$	12.0120	0.537731	0.268865	+	0.963178i	$0.413351\pi$
$500$	−1.96954	−0.0880805
$501$	−9.67829	−0.432394
$502$	−2.69752	−0.120396
$503$	−17.2808	−0.770514	−0.385257	−	0.922809i	$-0.625887\pi$
$503$	−17.2808	−0.770514	−0.385257	+	0.922809i	$0.625887\pi$
$504$	−0.00277974	−0.000123820 0
$505$	−17.4203	−0.775192
$506$	−0.552002	−0.0245395
$507$	−0.178979	−0.00794873
$508$	20.6873	0.917851
$509$	−38.9365	−1.72583	−0.862914	−	0.505351i	$-0.831363\pi$
$509$	−38.9365	−1.72583	−0.862914	+	0.505351i	$0.831363\pi$
$510$	−0.309043	−0.0136847
$511$	0.282738	0.0125076
$512$	−13.1252	−0.580057
$513$	16.2603	0.717908
$514$	0.633059	0.0279231
$515$	−18.9905	−0.836822
$516$	−40.5427	−1.78479
$517$	−12.4069	−0.545657
$518$	0.0115818	0.000508877 0
$519$	−31.9918	−1.40429
$520$	−2.48818	−0.109114
$521$	33.2563	1.45699	0.728493	−	0.685054i	$-0.240221\pi$
$521$	33.2563	1.45699	0.728493	+	0.685054i	$0.240221\pi$
$522$	−0.163245	−0.00714503
$523$	18.0153	0.787752	0.393876	−	0.919163i	$-0.371134\pi$
$523$	18.0153	0.787752	0.393876	+	0.919163i	$0.371134\pi$
$524$	20.2975	0.886702
$525$	−0.0524331	−0.00228837
$526$	−1.77538	−0.0774104
$527$	9.20689	0.401059
$528$	−7.50849	−0.326765
$529$	−14.8892	−0.647358
$530$	0.414868	0.0180207
$531$	−1.57797	−0.0684781
$532$	−0.186957	−0.00810563
$533$	−3.73000	−0.161564
$534$	4.20271	0.181869
$535$	4.07952	0.176373
$536$	−9.49367	−0.410064
$537$	4.14335	0.178799
$538$	−2.97981	−0.128469
$539$	7.77298	0.334806
$540$	9.99003	0.429902
$541$	43.9322	1.88879	0.944396	−	0.328810i	$-0.106647\pi$
$541$	43.9322	1.88879	0.944396	+	0.328810i	$0.106647\pi$
$542$	−2.65533	−0.114056
$543$	32.8459	1.40955
$544$	−2.05197	−0.0879776
$545$	17.5919	0.753555
$546$	−0.0328661	−0.00140654
$547$	−7.56791	−0.323581	−0.161790	−	0.986825i	$-0.551727\pi$
$547$	−7.56791	−0.323581	−0.161790	+	0.986825i	$0.551727\pi$
$548$	−15.0058	−0.641014
$549$	−0.943192	−0.0402544
$550$	0.193825	0.00826473
$551$	−22.1285	−0.942707
$552$	−3.49374	−0.148703
$553$	0.294832	0.0125375
$554$	−1.49844	−0.0636625
$555$	3.96838	0.168449
$556$	29.1196	1.23495
$557$	25.1668	1.06635	0.533175	−	0.846005i	$-0.320999\pi$
$557$	25.1668	1.06635	0.533175	+	0.846005i	$0.320999\pi$
$558$	−0.217734	−0.00921740
$559$	−41.7514	−1.76589
$560$	−0.113060	−0.00477764
$561$	−1.96652	−0.0830264
$562$	0.269921	0.0113859
$563$	1.86097	0.0784305	0.0392153	−	0.999231i	$-0.487514\pi$
$563$	1.86097	0.0784305	0.0392153	+	0.999231i	$0.487514\pi$
$564$	−38.9618	−1.64059
$565$	−6.59360	−0.277395
$566$	−3.13490	−0.131770
$567$	0.277992	0.0116746
$568$	−0.692797	−0.0290691
$569$	10.7565	0.450937	0.225468	−	0.974251i	$-0.427609\pi$
$569$	10.7565	0.450937	0.225468	+	0.974251i	$0.427609\pi$
$570$	0.990706	0.0414961
$571$	−13.4526	−0.562973	−0.281486	−	0.959565i	$-0.590827\pi$
$571$	−13.4526	−0.562973	−0.281486	+	0.959565i	$0.590827\pi$
$572$	−7.85571	−0.328464
$573$	−30.9259	−1.29195
$574$	0.00536723	0.000224024 0
$575$	−2.84794	−0.118767
$576$	−0.986214	−0.0410923
$577$	−9.95027	−0.414235	−0.207118	−	0.978316i	$-0.566408\pi$
$577$	−9.95027	−0.414235	−0.207118	+	0.978316i	$0.566408\pi$
$578$	−0.174528	−0.00725942
$579$	−33.1598	−1.37808
$580$	−13.5954	−0.564518
$581$	0.260383	0.0108025
$582$	−0.0571680	−0.00236969
$583$	2.63991	0.109334
$584$	−6.61513	−0.273736
$585$	−0.486658	−0.0201208
$586$	4.26952	0.176372
$587$	−8.34625	−0.344486	−0.172243	−	0.985054i	$-0.555102\pi$
$587$	−8.34625	−0.344486	−0.172243	+	0.985054i	$0.555102\pi$
$588$	24.4097	1.00664
$589$	−29.5147	−1.21613
$590$	2.03244	0.0836742
$591$	−4.13059	−0.169910
$592$	8.55687	0.351685
$593$	−35.8493	−1.47216	−0.736078	−	0.676897i	$-0.763324\pi$
$593$	−35.8493	−1.47216	−0.736078	+	0.676897i	$0.763324\pi$
$594$	−0.983132	−0.0403384
$595$	−0.0296109	−0.00121393
$596$	−30.0212	−1.22972
$597$	23.1540	0.947628
$598$	−1.78515	−0.0730000
$599$	−15.1992	−0.621021	−0.310511	−	0.950570i	$-0.600500\pi$
$599$	−15.1992	−0.621021	−0.310511	+	0.950570i	$0.600500\pi$
$600$	1.22676	0.0500822
$601$	16.9997	0.693434	0.346717	−	0.937970i	$-0.387297\pi$
$601$	16.9997	0.693434	0.346717	+	0.937970i	$0.387297\pi$
$602$	0.0600775	0.00244858
$603$	−1.85684	−0.0756164
$604$	−30.7574	−1.25150
$605$	−9.76664	−0.397071
$606$	5.38362	0.218695
$607$	16.1393	0.655072	0.327536	−	0.944839i	$-0.393782\pi$
$607$	16.1393	0.655072	0.327536	+	0.944839i	$0.393782\pi$
$608$	6.57805	0.266775
$609$	−0.361937	−0.0146664
$610$	1.21484	0.0491874
$611$	−40.1234	−1.62322
$612$	−0.266877	−0.0107879
$613$	23.4559	0.947374	0.473687	−	0.880693i	$-0.342923\pi$
$613$	23.4559	0.947374	0.473687	+	0.880693i	$0.342923\pi$
$614$	4.84202	0.195408
$615$	1.83902	0.0741563
$616$	0.0227825	0.000917935 0
$617$	45.3424	1.82542	0.912708	−	0.408612i	$-0.133987\pi$
$617$	45.3424	1.82542	0.912708	+	0.408612i	$0.133987\pi$
$618$	5.86889	0.236081
$619$	−15.6687	−0.629779	−0.314890	−	0.949128i	$-0.601968\pi$
$619$	−15.6687	−0.629779	−0.314890	+	0.949128i	$0.601968\pi$
$620$	−18.1333	−0.728253
$621$	14.4455	0.579679
$622$	−2.36618	−0.0948751
$623$	0.402682	0.0161331
$624$	−24.2820	−0.972060
$625$	1.00000	0.0400000
$626$	4.54698	0.181734
$627$	6.30410	0.251762
$628$	−40.7681	−1.62683
$629$	2.24109	0.0893583
$630$	0.000700269 0	2.78994e−5 0
$631$	45.6272	1.81639	0.908195	−	0.418546i	$-0.137460\pi$
$631$	45.6272	1.81639	0.908195	+	0.418546i	$0.137460\pi$
$632$	−6.89809	−0.274391
$633$	15.8174	0.628685
$634$	0.0268909	0.00106798
$635$	−10.5036	−0.416824
$636$	8.29016	0.328726
$637$	25.1374	0.995980
$638$	1.33794	0.0529695
$639$	−0.135502	−0.00536039
$640$	5.37420	0.212434
$641$	38.5674	1.52332	0.761661	−	0.647976i	$-0.224384\pi$
$641$	38.5674	1.52332	0.761661	+	0.647976i	$0.224384\pi$
$642$	−1.26075	−0.0497578
$643$	18.2313	0.718970	0.359485	−	0.933151i	$-0.382952\pi$
$643$	18.2313	0.718970	0.359485	+	0.933151i	$0.382952\pi$
$644$	−0.166092	−0.00654493
$645$	20.5848	0.810527
$646$	0.559489	0.0220128
$647$	−9.58263	−0.376732	−0.188366	−	0.982099i	$-0.560319\pi$
$647$	−9.58263	−0.376732	−0.188366	+	0.982099i	$0.560319\pi$
$648$	−6.50408	−0.255504
$649$	12.9329	0.507661
$650$	0.626819	0.0245859
$651$	−0.482746	−0.0189203
$652$	1.30064	0.0509368
$653$	−8.78149	−0.343646	−0.171823	−	0.985128i	$-0.554966\pi$
$653$	−8.78149	−0.343646	−0.171823	+	0.985128i	$0.554966\pi$
$654$	−5.43666	−0.212590
$655$	−10.3057	−0.402678
$656$	3.96540	0.154823
$657$	−1.29384	−0.0504774
$658$	0.0577349	0.00225074
$659$	−9.66743	−0.376590	−0.188295	−	0.982113i	$-0.560296\pi$
$659$	−9.66743	−0.376590	−0.188295	+	0.982113i	$0.560296\pi$
$660$	3.87313	0.150761
$661$	−28.2399	−1.09840	−0.549202	−	0.835690i	$-0.685068\pi$
$661$	−28.2399	−1.09840	−0.549202	+	0.835690i	$0.685068\pi$
$662$	−4.72141	−0.183503
$663$	−6.35961	−0.246987
$664$	−6.09209	−0.236419
$665$	0.0949244	0.00368101
$666$	−0.0529996	−0.00205369
$667$	−19.6588	−0.761193
$668$	10.7649	0.416506
$669$	−11.3694	−0.439567
$670$	2.39163	0.0923967
$671$	7.73031	0.298425
$672$	0.107591	0.00415042
$673$	15.4646	0.596116	0.298058	−	0.954548i	$-0.403661\pi$
$673$	15.4646	0.596116	0.298058	+	0.954548i	$0.403661\pi$
$674$	−4.27586	−0.164700
$675$	−5.07227	−0.195232
$676$	0.199073	0.00765667
$677$	−48.4814	−1.86329	−0.931645	−	0.363369i	$-0.881626\pi$
$677$	−48.4814	−1.86329	−0.931645	+	0.363369i	$0.881626\pi$
$678$	2.03771	0.0782577
$679$	−0.00547755	−0.000210209 0
$680$	0.692797	0.0265675
$681$	−12.9146	−0.494889
$682$	1.78453	0.0683330
$683$	43.4904	1.66411	0.832057	−	0.554691i	$-0.187163\pi$
$683$	43.4904	1.66411	0.832057	+	0.554691i	$0.187163\pi$
$684$	0.855534	0.0327122
$685$	7.61891	0.291104
$686$	−0.0723467	−0.00276221
$687$	−40.6154	−1.54957
$688$	44.3863	1.69221
$689$	8.53731	0.325246
$690$	0.880137	0.0335063
$691$	−11.6797	−0.444318	−0.222159	−	0.975010i	$-0.571310\pi$
$691$	−11.6797	−0.444318	−0.222159	+	0.975010i	$0.571310\pi$
$692$	35.5836	1.35269
$693$	0.00445598	0.000169269 0
$694$	4.56686	0.173356
$695$	−14.7850	−0.560826
$696$	8.46811	0.320983
$697$	1.03856	0.0393383
$698$	−1.76713	−0.0668869
$699$	30.6751	1.16024
$700$	0.0583199	0.00220429
$701$	18.7608	0.708585	0.354293	−	0.935135i	$-0.384722\pi$
$701$	18.7608	0.708585	0.354293	+	0.935135i	$0.384722\pi$
$702$	−3.17939	−0.119999
$703$	−7.18432	−0.270962
$704$	8.08292	0.304637
$705$	19.7822	0.745040
$706$	1.59239	0.0599306
$707$	0.515831	0.0193998
$708$	40.6135	1.52635
$709$	47.1597	1.77112	0.885560	−	0.464525i	$-0.153775\pi$
$709$	47.1597	1.77112	0.885560	+	0.464525i	$0.153775\pi$
$710$	0.174528	0.00654993
$711$	−1.34918	−0.0505982
$712$	−9.42142	−0.353083
$713$	−26.2207	−0.981973
$714$	0.00915106	0.000342470 0
$715$	3.98860	0.149165
$716$	−4.60853	−0.172229
$717$	−37.3667	−1.39549
$718$	−0.395109	−0.0147453
$719$	−19.7502	−0.736559	−0.368279	−	0.929715i	$-0.620053\pi$
$719$	−19.7502	−0.736559	−0.368279	+	0.929715i	$0.620053\pi$
$720$	0.517371	0.0192813
$721$	0.562327	0.0209421
$722$	1.52247	0.0566605
$723$	−26.2879	−0.977658
$724$	−36.5336	−1.35776
$725$	6.90282	0.256364
$726$	3.01832	0.112020
$727$	0.536915	0.0199131	0.00995654	−	0.999950i	$-0.496831\pi$
$727$	0.536915	0.0199131	0.00995654	+	0.999950i	$0.496831\pi$
$728$	0.0736775	0.00273067
$729$	25.6728	0.950844
$730$	1.66647	0.0616789
$731$	11.6250	0.429967
$732$	24.2757	0.897255
$733$	−24.0463	−0.888172	−0.444086	−	0.895984i	$-0.646472\pi$
$733$	−24.0463	−0.888172	−0.444086	+	0.895984i	$0.646472\pi$
$734$	−1.09960	−0.0405872
$735$	−12.3936	−0.457145
$736$	5.84390	0.215409
$737$	15.2185	0.560581
$738$	−0.0245609	−0.000904100 0
$739$	−13.2973	−0.489149	−0.244575	−	0.969630i	$-0.578648\pi$
$739$	−13.2973	−0.489149	−0.244575	+	0.969630i	$0.578648\pi$
$740$	−4.41392	−0.162259
$741$	20.3871	0.748940
$742$	−0.0122846	−0.000450983 0
$743$	19.3390	0.709477	0.354739	−	0.934966i	$-0.384570\pi$
$743$	19.3390	0.709477	0.354739	+	0.934966i	$0.384570\pi$
$744$	11.2946	0.414082
$745$	15.2428	0.558452
$746$	−2.63029	−0.0963019
$747$	−1.19154	−0.0435960
$748$	2.18730	0.0799757
$749$	−0.120798	−0.00441388
$750$	−0.309043	−0.0112847
$751$	−20.4420	−0.745941	−0.372970	−	0.927843i	$-0.621661\pi$
$751$	−20.4420	−0.745941	−0.372970	+	0.927843i	$0.621661\pi$
$752$	42.6556	1.55549
$753$	27.3686	0.997368
$754$	4.32682	0.157574
$755$	15.6166	0.568345
$756$	−0.295814	−0.0107587
$757$	20.2642	0.736515	0.368257	−	0.929724i	$-0.379955\pi$
$757$	20.2642	0.736515	0.368257	+	0.929724i	$0.379955\pi$
$758$	−3.22745	−0.117226
$759$	5.60053	0.203286
$760$	−2.22091	−0.0805610
$761$	9.80113	0.355291	0.177645	−	0.984095i	$-0.443152\pi$
$761$	9.80113	0.355291	0.177645	+	0.984095i	$0.443152\pi$
$762$	3.24608	0.117593
$763$	−0.520913	−0.0188583
$764$	34.3981	1.24448
$765$	0.135502	0.00489910
$766$	3.12788	0.113015
$767$	41.8243	1.51019
$768$	24.1147	0.870164
$769$	−14.5152	−0.523430	−0.261715	−	0.965145i	$-0.584288\pi$
$769$	−14.5152	−0.523430	−0.261715	+	0.965145i	$0.584288\pi$
$770$	−0.00573934	−0.000206831 0
$771$	−6.42292	−0.231316
$772$	36.8828	1.32744
$773$	31.2764	1.12493	0.562466	−	0.826820i	$-0.309853\pi$
$773$	31.2764	1.12493	0.562466	+	0.826820i	$0.309853\pi$
$774$	−0.274920	−0.00988180
$775$	9.20689	0.330721
$776$	0.128156	0.00460054
$777$	−0.117508	−0.00421556
$778$	1.42257	0.0510017
$779$	−3.32934	−0.119286
$780$	12.5255	0.448485
$781$	1.11057	0.0397391
$782$	0.497046	0.0177743
$783$	−35.0130	−1.25126
$784$	−26.7238	−0.954422
$785$	20.6993	0.738791
$786$	3.18491	0.113602
$787$	−26.2413	−0.935403	−0.467702	−	0.883886i	$-0.654918\pi$
$787$	−26.2413	−0.935403	−0.467702	+	0.883886i	$0.654918\pi$
$788$	4.59434	0.163666
$789$	18.0128	0.641271
$790$	1.73776	0.0618266
$791$	0.195243	0.00694203
$792$	−0.104255	−0.00370454
$793$	24.9994	0.887755
$794$	2.15871	0.0766097
$795$	−4.20918	−0.149284
$796$	−25.7535	−0.912809
$797$	29.2740	1.03694	0.518468	−	0.855097i	$-0.326502\pi$
$797$	29.2740	1.03694	0.518468	+	0.855097i	$0.326502\pi$
$798$	−0.0293357	−0.00103847
$799$	11.1717	0.395228
$800$	−2.05197	−0.0725482
$801$	−1.84271	−0.0651090
$802$	1.55566	0.0549323
$803$	10.6042	0.374213
$804$	47.7910	1.68546
$805$	0.0843302	0.00297225
$806$	5.77106	0.203277
$807$	30.2327	1.06424
$808$	−12.0687	−0.424576
$809$	11.3699	0.399745	0.199872	−	0.979822i	$-0.435947\pi$
$809$	11.3699	0.399745	0.199872	+	0.979822i	$0.435947\pi$
$810$	1.63850	0.0575709
$811$	26.7860	0.940582	0.470291	−	0.882511i	$-0.344149\pi$
$811$	26.7860	0.940582	0.470291	+	0.882511i	$0.344149\pi$
$812$	0.402572	0.0141275
$813$	26.9406	0.944847
$814$	0.434380	0.0152250
$815$	−0.660376	−0.0231320
$816$	6.76096	0.236681
$817$	−37.2666	−1.30379
$818$	5.45069	0.190579
$819$	0.0144104	0.000503540 0
$820$	−2.04549	−0.0714316
$821$	−49.5529	−1.72941	−0.864705	−	0.502280i	$-0.832495\pi$
$821$	−49.5529	−1.72941	−0.864705	+	0.502280i	$0.832495\pi$
$822$	−2.35457	−0.0821252
$823$	−23.5658	−0.821452	−0.410726	−	0.911759i	$-0.634725\pi$
$823$	−23.5658	−0.821452	−0.410726	+	0.911759i	$0.634725\pi$
$824$	−13.1566	−0.458331
$825$	−1.96652	−0.0684653
$826$	−0.0601824	−0.00209402
$827$	32.3737	1.12574	0.562872	−	0.826544i	$-0.309697\pi$
$827$	32.3737	1.12574	0.562872	+	0.826544i	$0.309697\pi$
$828$	0.760051	0.0264136
$829$	−28.2157	−0.979972	−0.489986	−	0.871730i	$-0.662998\pi$
$829$	−28.2157	−0.979972	−0.489986	+	0.871730i	$0.662998\pi$
$830$	1.53471	0.0532705
$831$	15.2029	0.527382
$832$	26.1397	0.906232
$833$	−6.99912	−0.242505
$834$	4.56919	0.158218
$835$	−5.46569	−0.189148
$836$	−7.01188	−0.242511
$837$	−46.6998	−1.61418
$838$	4.20631	0.145304
$839$	1.66710	0.0575545	0.0287773	−	0.999586i	$-0.490839\pi$
$839$	1.66710	0.0575545	0.0287773	+	0.999586i	$0.490839\pi$
$840$	−0.0363255	−0.00125335
$841$	18.6490	0.643068
$842$	6.17079	0.212659
$843$	−2.73857	−0.0943215
$844$	−17.5933	−0.605585
$845$	−0.101076	−0.00347712
$846$	−0.264200	−0.00908339
$847$	0.289199	0.00993701
$848$	−9.07610	−0.311675
$849$	31.8062	1.09159
$850$	−0.174528	−0.00598627
$851$	−6.38251	−0.218789
$852$	3.48753	0.119481
$853$	6.11398	0.209339	0.104669	−	0.994507i	$-0.466622\pi$
$853$	6.11398	0.209339	0.104669	+	0.994507i	$0.466622\pi$
$854$	−0.0359725	−0.00123095
$855$	−0.434383	−0.0148556
$856$	2.82628	0.0966003
$857$	25.0792	0.856690	0.428345	−	0.903615i	$-0.359097\pi$
$857$	25.0792	0.856690	0.428345	+	0.903615i	$0.359097\pi$
$858$	−1.23265	−0.0420820
$859$	−2.16123	−0.0737403	−0.0368701	−	0.999320i	$-0.511739\pi$
$859$	−2.16123	−0.0737403	−0.0368701	+	0.999320i	$0.511739\pi$
$860$	−22.8960	−0.780746
$861$	−0.0544550	−0.00185582
$862$	−5.52422	−0.188156
$863$	38.1579	1.29891	0.649455	−	0.760400i	$-0.274997\pi$
$863$	38.1579	1.29891	0.649455	+	0.760400i	$0.274997\pi$
$864$	10.4081	0.354092
$865$	−18.0670	−0.614296
$866$	−5.58649	−0.189837
$867$	1.77073	0.0601373
$868$	0.536945	0.0182251
$869$	11.0578	0.375109
$870$	−2.13327	−0.0723247
$871$	49.2158	1.66761
$872$	12.1876	0.412725
$873$	0.0250658	0.000848347 0
$874$	−1.59339	−0.0538973
$875$	−0.0296109	−0.00100103
$876$	33.3005	1.12512
$877$	−9.34681	−0.315619	−0.157810	−	0.987470i	$-0.550443\pi$
$877$	−9.34681	−0.315619	−0.157810	+	0.987470i	$0.550443\pi$
$878$	−2.84661	−0.0960683
$879$	−43.3179	−1.46108
$880$	−4.24032	−0.142941
$881$	−25.4713	−0.858151	−0.429076	−	0.903269i	$-0.641161\pi$
$881$	−25.4713	−0.858151	−0.429076	+	0.903269i	$0.641161\pi$
$882$	0.165522	0.00557342
$883$	−3.24725	−0.109279	−0.0546393	−	0.998506i	$-0.517401\pi$
$883$	−3.24725	−0.109279	−0.0546393	+	0.998506i	$0.517401\pi$
$884$	7.07362	0.237911
$885$	−20.6208	−0.693161
$886$	−2.90818	−0.0977021
$887$	11.2333	0.377177	0.188589	−	0.982056i	$-0.439609\pi$
$887$	11.2333	0.377177	0.188589	+	0.982056i	$0.439609\pi$
$888$	2.74928	0.0922599
$889$	0.311022	0.0104314
$890$	2.37343	0.0795575
$891$	10.4261	0.349289
$892$	12.6459	0.423416
$893$	−35.8135	−1.19845
$894$	−4.71067	−0.157548
$895$	2.33990	0.0782143
$896$	−0.159135	−0.00531633
$897$	18.1118	0.604735
$898$	1.73528	0.0579069
$899$	63.5536	2.11963
$900$	−0.266877	−0.00889591
$901$	−2.37708	−0.0791921
$902$	0.201299	0.00670253
$903$	−0.609536	−0.0202841
$904$	−4.56803	−0.151930
$905$	18.5493	0.616600
$906$	−4.82619	−0.160339
$907$	−55.1530	−1.83133	−0.915663	−	0.401946i	$-0.868334\pi$
$907$	−55.1530	−1.83133	−0.915663	+	0.401946i	$0.868334\pi$
$908$	14.3646	0.476705
$909$	−2.36049	−0.0782925
$910$	−0.0185607	−0.000615282 0
$911$	32.9311	1.09106	0.545528	−	0.838092i	$-0.316329\pi$
$911$	32.9311	1.09106	0.545528	+	0.838092i	$0.316329\pi$
$912$	−21.6738	−0.717690
$913$	9.76572	0.323198
$914$	−1.38875	−0.0459356
$915$	−12.3256	−0.407470
$916$	45.1754	1.49264
$917$	0.305162	0.0100773
$918$	0.885254	0.0292177
$919$	−49.4192	−1.63019	−0.815095	−	0.579328i	$-0.803315\pi$
$919$	−49.4192	−1.63019	−0.815095	+	0.579328i	$0.803315\pi$
$920$	−1.97304	−0.0650494
$921$	−49.1263	−1.61877
$922$	−0.0711739	−0.00234399
$923$	3.59151	0.118216
$924$	−0.114687	−0.00377293
$925$	2.24109	0.0736867
$926$	−0.824626	−0.0270989
$927$	−2.57326	−0.0845169
$928$	−14.1644	−0.464969
$929$	27.0770	0.888369	0.444184	−	0.895935i	$-0.353494\pi$
$929$	27.0770	0.888369	0.444184	+	0.895935i	$0.353494\pi$
$930$	−2.84533	−0.0933020
$931$	22.4372	0.735351
$932$	−34.1191	−1.11761
$933$	24.0069	0.785949
$934$	−5.28025	−0.172775
$935$	−1.11057	−0.0363194
$936$	−0.337155	−0.0110203
$937$	−56.7744	−1.85474	−0.927369	−	0.374149i	$-0.877935\pi$
$937$	−56.7744	−1.85474	−0.927369	+	0.374149i	$0.877935\pi$
$938$	−0.0708184	−0.00231230
$939$	−46.1329	−1.50549
$940$	−22.0032	−0.717665
$941$	16.3663	0.533526	0.266763	−	0.963762i	$-0.414046\pi$
$941$	16.3663	0.533526	0.266763	+	0.963762i	$0.414046\pi$
$942$	−6.39699	−0.208425
$943$	−2.95776	−0.0963180
$944$	−44.4638	−1.44717
$945$	0.150195	0.00488583
$946$	2.25322	0.0732585
$947$	−37.8554	−1.23014	−0.615068	−	0.788474i	$-0.710871\pi$
$947$	−37.8554	−1.23014	−0.615068	+	0.788474i	$0.710871\pi$
$948$	34.7249	1.12781
$949$	34.2933	1.11321
$950$	0.559489	0.0181522
$951$	−0.272831	−0.00884715
$952$	−0.0205144	−0.000664874 0
$953$	−21.0976	−0.683418	−0.341709	−	0.939806i	$-0.611006\pi$
$953$	−21.0976	−0.683418	−0.341709	+	0.939806i	$0.611006\pi$
$954$	0.0562156	0.00182005
$955$	−17.4650	−0.565155
$956$	41.5620	1.34421
$957$	−13.5745	−0.438802
$958$	−0.0913161	−0.00295029
$959$	−0.225603	−0.00728511
$960$	−12.8878	−0.415951
$961$	53.7669	1.73442
$962$	1.40476	0.0452913
$963$	0.552785	0.0178132
$964$	29.2393	0.941735
$965$	−18.7266	−0.602830
$966$	−0.0260617	−0.000838521 0
$967$	−54.4805	−1.75197	−0.875987	−	0.482334i	$-0.839789\pi$
$967$	−54.4805	−1.75197	−0.875987	+	0.482334i	$0.839789\pi$
$968$	−6.76630	−0.217477
$969$	−5.67648	−0.182355
$970$	−0.0322849	−0.00103661
$971$	23.3040	0.747861	0.373930	−	0.927457i	$-0.378010\pi$
$971$	23.3040	0.747861	0.373930	+	0.927457i	$0.378010\pi$
$972$	2.77138	0.0888920
$973$	0.437797	0.0140351
$974$	3.33190	0.106761
$975$	−6.35961	−0.203670
$976$	−26.5771	−0.850713
$977$	−23.6368	−0.756207	−0.378104	−	0.925763i	$-0.623424\pi$
$977$	−23.6368	−0.756207	−0.378104	+	0.925763i	$0.623424\pi$
$978$	0.204085	0.00652591
$979$	15.1027	0.482684
$980$	13.7851	0.440347
$981$	2.38375	0.0761071
$982$	5.41373	0.172759
$983$	−36.9314	−1.17793	−0.588964	−	0.808159i	$-0.700464\pi$
$983$	−36.9314	−1.17793	−0.588964	+	0.808159i	$0.700464\pi$
$984$	1.27407	0.0406157
$985$	−2.33270	−0.0743259
$986$	−1.20474	−0.0383667
$987$	−0.585769	−0.0186452
$988$	−22.6760	−0.721421
$989$	−33.1074	−1.05275
$990$	0.0262637	0.000834716 0
$991$	−37.1821	−1.18113	−0.590564	−	0.806991i	$-0.701095\pi$
$991$	−37.1821	−1.18113	−0.590564	+	0.806991i	$0.701095\pi$
$992$	−18.8923	−0.599831
$993$	47.9027	1.52015
$994$	−0.00516794	−0.000163917 0
$995$	13.0759	0.414534
$996$	30.6675	0.971738
$997$	−1.45531	−0.0460903	−0.0230451	−	0.999734i	$-0.507336\pi$
$997$	−1.45531	−0.0460903	−0.0230451	+	0.999734i	$0.507336\pi$
$998$	−2.09643	−0.0663614
$999$	−11.3674	−0.359649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.18	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-0.174528 q^{2} +1.77073 q^{3} -1.96954 q^{4} +1.00000 q^{5} -0.309043 q^{6} -0.0296109 q^{7} +0.692797 q^{8} +0.135502 q^{9} +O(q^{10})\)	\(q-0.174528 q^{2} +1.77073 q^{3} -1.96954 q^{4} +1.00000 q^{5} -0.309043 q^{6} -0.0296109 q^{7} +0.692797 q^{8} +0.135502 q^{9} -0.174528 q^{10} -1.11057 q^{11} -3.48753 q^{12} -3.59151 q^{13} +0.00516794 q^{14} +1.77073 q^{15} +3.81817 q^{16} +1.00000 q^{17} -0.0236490 q^{18} -3.20572 q^{19} -1.96954 q^{20} -0.0524331 q^{21} +0.193825 q^{22} -2.84794 q^{23} +1.22676 q^{24} +1.00000 q^{25} +0.626819 q^{26} -5.07227 q^{27} +0.0583199 q^{28} +6.90282 q^{29} -0.309043 q^{30} +9.20689 q^{31} -2.05197 q^{32} -1.96652 q^{33} -0.174528 q^{34} -0.0296109 q^{35} -0.266877 q^{36} +2.24109 q^{37} +0.559489 q^{38} -6.35961 q^{39} +0.692797 q^{40} +1.03856 q^{41} +0.00915106 q^{42} +11.6250 q^{43} +2.18730 q^{44} +0.135502 q^{45} +0.497046 q^{46} +11.1717 q^{47} +6.76096 q^{48} -6.99912 q^{49} -0.174528 q^{50} +1.77073 q^{51} +7.07362 q^{52} -2.37708 q^{53} +0.885254 q^{54} -1.11057 q^{55} -0.0205144 q^{56} -5.67648 q^{57} -1.20474 q^{58} -11.6453 q^{59} -3.48753 q^{60} -6.96070 q^{61} -1.60686 q^{62} -0.00401235 q^{63} -7.27821 q^{64} -3.59151 q^{65} +0.343213 q^{66} -13.7034 q^{67} -1.96954 q^{68} -5.04295 q^{69} +0.00516794 q^{70} -1.00000 q^{71} +0.0938756 q^{72} -9.54844 q^{73} -0.391134 q^{74} +1.77073 q^{75} +6.31379 q^{76} +0.0328849 q^{77} +1.10993 q^{78} -9.95687 q^{79} +3.81817 q^{80} -9.38815 q^{81} -0.181258 q^{82} -8.79347 q^{83} +0.103269 q^{84} +1.00000 q^{85} -2.02890 q^{86} +12.2231 q^{87} -0.769396 q^{88} -13.5991 q^{89} -0.0236490 q^{90} +0.106348 q^{91} +5.60914 q^{92} +16.3030 q^{93} -1.94978 q^{94} -3.20572 q^{95} -3.63350 q^{96} +0.184984 q^{97} +1.22154 q^{98} -0.150484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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