LMFDB - Embedded newform 4033.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82466 q^{2} +0.0328358 q^{3} +1.32938 q^{4} -0.181740 q^{5} -0.0599140 q^{6} +4.41961 q^{7} +1.22366 q^{8} -2.99892 q^{9} +O(q^{10})$	\(q-1.82466 q^{2} +0.0328358 q^{3} +1.32938 q^{4} -0.181740 q^{5} -0.0599140 q^{6} +4.41961 q^{7} +1.22366 q^{8} -2.99892 q^{9} +0.331613 q^{10} -0.871253 q^{11} +0.0436510 q^{12} +3.03490 q^{13} -8.06427 q^{14} -0.00596756 q^{15} -4.89151 q^{16} +6.34816 q^{17} +5.47201 q^{18} -0.715988 q^{19} -0.241600 q^{20} +0.145121 q^{21} +1.58974 q^{22} +2.85067 q^{23} +0.0401798 q^{24} -4.96697 q^{25} -5.53765 q^{26} -0.196979 q^{27} +5.87532 q^{28} +5.73056 q^{29} +0.0108888 q^{30} +7.22926 q^{31} +6.47801 q^{32} -0.0286082 q^{33} -11.5832 q^{34} -0.803218 q^{35} -3.98669 q^{36} +1.00000 q^{37} +1.30643 q^{38} +0.0996531 q^{39} -0.222388 q^{40} -9.57735 q^{41} -0.264796 q^{42} -7.97679 q^{43} -1.15822 q^{44} +0.545023 q^{45} -5.20149 q^{46} +7.45694 q^{47} -0.160616 q^{48} +12.5329 q^{49} +9.06302 q^{50} +0.208447 q^{51} +4.03452 q^{52} +2.08916 q^{53} +0.359419 q^{54} +0.158341 q^{55} +5.40810 q^{56} -0.0235100 q^{57} -10.4563 q^{58} +9.13233 q^{59} -0.00793313 q^{60} +5.31105 q^{61} -13.1909 q^{62} -13.2541 q^{63} -2.03713 q^{64} -0.551561 q^{65} +0.0522003 q^{66} -7.64729 q^{67} +8.43909 q^{68} +0.0936038 q^{69} +1.46560 q^{70} +0.273822 q^{71} -3.66966 q^{72} +3.37228 q^{73} -1.82466 q^{74} -0.163094 q^{75} -0.951817 q^{76} -3.85059 q^{77} -0.181833 q^{78} +2.85327 q^{79} +0.888982 q^{80} +8.99030 q^{81} +17.4754 q^{82} -1.37879 q^{83} +0.192920 q^{84} -1.15371 q^{85} +14.5549 q^{86} +0.188167 q^{87} -1.06612 q^{88} -1.61133 q^{89} -0.994481 q^{90} +13.4131 q^{91} +3.78961 q^{92} +0.237378 q^{93} -13.6064 q^{94} +0.130123 q^{95} +0.212710 q^{96} +6.51903 q^{97} -22.8683 q^{98} +2.61282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.82466	−1.29023	−0.645114	−	0.764086i	$-0.723190\pi$
$2$	−1.82466	−1.29023	−0.645114	+	0.764086i	$0.723190\pi$
$3$	0.0328358	0.0189577	0.00947887	−	0.999955i	$-0.496983\pi$
$3$	0.0328358	0.0189577	0.00947887	+	0.999955i	$0.496983\pi$
$4$	1.32938	0.664688
$5$	−0.181740	−0.0812765	−0.0406382	−	0.999174i	$-0.512939\pi$
$5$	−0.181740	−0.0812765	−0.0406382	+	0.999174i	$0.512939\pi$
$6$	−0.0599140	−0.0244598
$7$	4.41961	1.67045	0.835227	−	0.549905i	$-0.185336\pi$
$7$	4.41961	1.67045	0.835227	+	0.549905i	$0.185336\pi$
$8$	1.22366	0.432629
$9$	−2.99892	−0.999641
$10$	0.331613	0.104865
$11$	−0.871253	−0.262693	−0.131346	−	0.991337i	$-0.541930\pi$
$11$	−0.871253	−0.262693	−0.131346	+	0.991337i	$0.541930\pi$
$12$	0.0436510	0.0126010
$13$	3.03490	0.841729	0.420865	−	0.907123i	$-0.361727\pi$
$13$	3.03490	0.841729	0.420865	+	0.907123i	$0.361727\pi$
$14$	−8.06427	−2.15527
$15$	−0.00596756	−0.00154082
$16$	−4.89151	−1.22288
$17$	6.34816	1.53966	0.769828	−	0.638252i	$-0.220342\pi$
$17$	6.34816	1.53966	0.769828	+	0.638252i	$0.220342\pi$
$18$	5.47201	1.28976
$19$	−0.715988	−0.164259	−0.0821294	−	0.996622i	$-0.526172\pi$
$19$	−0.715988	−0.164259	−0.0821294	+	0.996622i	$0.526172\pi$
$20$	−0.241600	−0.0540235
$21$	0.145121	0.0316680
$22$	1.58974	0.338933
$23$	2.85067	0.594405	0.297203	−	0.954814i	$-0.403946\pi$
$23$	2.85067	0.594405	0.297203	+	0.954814i	$0.403946\pi$
$24$	0.0401798	0.00820167
$25$	−4.96697	−0.993394
$26$	−5.53765	−1.08602
$27$	−0.196979	−0.0379086
$28$	5.87532	1.11033
$29$	5.73056	1.06414	0.532069	−	0.846701i	$-0.321415\pi$
$29$	5.73056	1.06414	0.532069	+	0.846701i	$0.321415\pi$
$30$	0.0108888	0.00198801
$31$	7.22926	1.29841	0.649206	−	0.760612i	$-0.275101\pi$
$31$	7.22926	1.29841	0.649206	+	0.760612i	$0.275101\pi$
$32$	6.47801	1.14516
$33$	−0.0286082	−0.00498006
$34$	−11.5832	−1.98651
$35$	−0.803218	−0.135769
$36$	−3.98669	−0.664449
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	1.30643	0.211931
$39$	0.0996531	0.0159573
$40$	−0.222388	−0.0351626
$41$	−9.57735	−1.49573	−0.747866	−	0.663850i	$-0.768921\pi$
$41$	−9.57735	−1.49573	−0.747866	+	0.663850i	$0.768921\pi$
$42$	−0.264796	−0.0408590
$43$	−7.97679	−1.21645	−0.608225	−	0.793765i	$-0.708118\pi$
$43$	−7.97679	−1.21645	−0.608225	+	0.793765i	$0.708118\pi$
$44$	−1.15822	−0.174609
$45$	0.545023	0.0812472
$46$	−5.20149	−0.766918
$47$	7.45694	1.08771	0.543853	−	0.839180i	$-0.316965\pi$
$47$	7.45694	1.08771	0.543853	+	0.839180i	$0.316965\pi$
$48$	−0.160616	−0.0231830
$49$	12.5329	1.79042
$50$	9.06302	1.28170
$51$	0.208447	0.0291884
$52$	4.03452	0.559487
$53$	2.08916	0.286968	0.143484	−	0.989653i	$-0.454169\pi$
$53$	2.08916	0.286968	0.143484	+	0.989653i	$0.454169\pi$
$54$	0.359419	0.0489108
$55$	0.158341	0.0213507
$56$	5.40810	0.722687
$57$	−0.0235100	−0.00311398
$58$	−10.4563	−1.37298
$59$	9.13233	1.18893	0.594464	−	0.804122i	$-0.297364\pi$
$59$	9.13233	1.18893	0.594464	+	0.804122i	$0.297364\pi$
$60$	−0.00793313	−0.00102416
$61$	5.31105	0.680011	0.340005	−	0.940423i	$-0.389571\pi$
$61$	5.31105	0.680011	0.340005	+	0.940423i	$0.389571\pi$
$62$	−13.1909	−1.67525
$63$	−13.2541	−1.66985
$64$	−2.03713	−0.254642
$65$	−0.551561	−0.0684128
$66$	0.0522003	0.00642541
$67$	−7.64729	−0.934266	−0.467133	−	0.884187i	$-0.654713\pi$
$67$	−7.64729	−0.934266	−0.467133	+	0.884187i	$0.654713\pi$
$68$	8.43909	1.02339
$69$	0.0936038	0.0112686
$70$	1.46560	0.175172
$71$	0.273822	0.0324967	0.0162483	−	0.999868i	$-0.494828\pi$
$71$	0.273822	0.0324967	0.0162483	+	0.999868i	$0.494828\pi$
$72$	−3.66966	−0.432474
$73$	3.37228	0.394696	0.197348	−	0.980333i	$-0.436767\pi$
$73$	3.37228	0.394696	0.197348	+	0.980333i	$0.436767\pi$
$74$	−1.82466	−0.212112
$75$	−0.163094	−0.0188325
$76$	−0.951817	−0.109181
$77$	−3.85059	−0.438816
$78$	−0.181833	−0.0205885
$79$	2.85327	0.321018	0.160509	−	0.987034i	$-0.448686\pi$
$79$	2.85327	0.321018	0.160509	+	0.987034i	$0.448686\pi$
$80$	0.888982	0.0993912
$81$	8.99030	0.998922
$82$	17.4754	1.92983
$83$	−1.37879	−0.151342	−0.0756709	−	0.997133i	$-0.524110\pi$
$83$	−1.37879	−0.151342	−0.0756709	+	0.997133i	$0.524110\pi$
$84$	0.192920	0.0210493
$85$	−1.15371	−0.125138
$86$	14.5549	1.56950
$87$	0.188167	0.0201736
$88$	−1.06612	−0.113649
$89$	−1.61133	−0.170801	−0.0854003	−	0.996347i	$-0.527217\pi$
$89$	−1.61133	−0.170801	−0.0854003	+	0.996347i	$0.527217\pi$
$90$	−0.994481	−0.104827
$91$	13.4131	1.40607
$92$	3.78961	0.395094
$93$	0.237378	0.0246150
$94$	−13.6064	−1.40339
$95$	0.130123	0.0133504
$96$	0.212710	0.0217097
$97$	6.51903	0.661907	0.330954	−	0.943647i	$-0.392630\pi$
$97$	6.51903	0.661907	0.330954	+	0.943647i	$0.392630\pi$
$98$	−22.8683	−2.31005
$99$	2.61282	0.262598
$100$	−6.60297	−0.660297
$101$	0.617612	0.0614547	0.0307274	−	0.999528i	$-0.490218\pi$
$101$	0.617612	0.0614547	0.0307274	+	0.999528i	$0.490218\pi$
$102$	−0.380344	−0.0376596
$103$	−0.111359	−0.0109725	−0.00548626	−	0.999985i	$-0.501746\pi$
$103$	−0.111359	−0.0109725	−0.00548626	+	0.999985i	$0.501746\pi$
$104$	3.71368	0.364157
$105$	−0.0263743	−0.00257386
$106$	−3.81200	−0.370254
$107$	4.25583	0.411427	0.205714	−	0.978612i	$-0.434048\pi$
$107$	4.25583	0.411427	0.205714	+	0.978612i	$0.434048\pi$
$108$	−0.261859	−0.0251974
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−0.288919	−0.0275473
$111$	0.0328358	0.00311663
$112$	−21.6186	−2.04276
$113$	−6.52506	−0.613826	−0.306913	−	0.951738i	$-0.599296\pi$
$113$	−6.52506	−0.613826	−0.306913	+	0.951738i	$0.599296\pi$
$114$	0.0428977	0.00401774
$115$	−0.518079	−0.0483111
$116$	7.61807	0.707320
$117$	−9.10142	−0.841427
$118$	−16.6634	−1.53399
$119$	28.0564	2.57192
$120$	−0.00730226	−0.000666602 0
$121$	−10.2409	−0.930993
$122$	−9.69086	−0.877369
$123$	−0.314480	−0.0283557
$124$	9.61040	0.863039
$125$	1.81139	0.162016
$126$	24.1841	2.15449
$127$	−17.5962	−1.56141	−0.780705	−	0.624900i	$-0.785140\pi$
$127$	−17.5962	−1.56141	−0.780705	+	0.624900i	$0.785140\pi$
$128$	−9.23895	−0.816616
$129$	−0.261924	−0.0230611
$130$	1.00641	0.0882680
$131$	7.64997	0.668381	0.334190	−	0.942506i	$-0.391537\pi$
$131$	7.64997	0.668381	0.334190	+	0.942506i	$0.391537\pi$
$132$	−0.0380311	−0.00331018
$133$	−3.16438	−0.274387
$134$	13.9537	1.20542
$135$	0.0357989	0.00308108
$136$	7.76799	0.666100
$137$	−3.37036	−0.287949	−0.143975	−	0.989581i	$-0.545988\pi$
$137$	−3.37036	−0.287949	−0.143975	+	0.989581i	$0.545988\pi$
$138$	−0.170795	−0.0145390
$139$	−1.28695	−0.109157	−0.0545787	−	0.998509i	$-0.517382\pi$
$139$	−1.28695	−0.109157	−0.0545787	+	0.998509i	$0.517382\pi$
$140$	−1.06778	−0.0902437
$141$	0.244854	0.0206204
$142$	−0.499631	−0.0419281
$143$	−2.64416	−0.221116
$144$	14.6693	1.22244
$145$	−1.04147	−0.0864894
$146$	−6.15327	−0.509248
$147$	0.411528	0.0339422
$148$	1.32938	0.109274
$149$	2.06500	0.169171	0.0845857	−	0.996416i	$-0.473043\pi$
$149$	2.06500	0.169171	0.0845857	+	0.996416i	$0.473043\pi$
$150$	0.297591	0.0242982
$151$	1.79641	0.146189	0.0730947	−	0.997325i	$-0.476712\pi$
$151$	1.79641	0.146189	0.0730947	+	0.997325i	$0.476712\pi$
$152$	−0.876126	−0.0710632
$153$	−19.0376	−1.53910
$154$	7.02602	0.566173
$155$	−1.31384	−0.105530
$156$	0.132476	0.0106066
$157$	−7.98701	−0.637433	−0.318717	−	0.947850i	$-0.603252\pi$
$157$	−7.98701	−0.637433	−0.318717	+	0.947850i	$0.603252\pi$
$158$	−5.20624	−0.414187
$159$	0.0685992	0.00544027
$160$	−1.17731	−0.0930747
$161$	12.5988	0.992927
$162$	−16.4042	−1.28884
$163$	−18.1570	−1.42217	−0.711083	−	0.703108i	$-0.751795\pi$
$163$	−18.1570	−1.42217	−0.711083	+	0.703108i	$0.751795\pi$
$164$	−12.7319	−0.994194
$165$	0.00519925	0.000404761 0
$166$	2.51582	0.195265
$167$	−6.29299	−0.486966	−0.243483	−	0.969905i	$-0.578290\pi$
$167$	−6.29299	−0.486966	−0.243483	+	0.969905i	$0.578290\pi$
$168$	0.177579	0.0137005
$169$	−3.78940	−0.291492
$170$	2.10513	0.161456
$171$	2.14719	0.164200
$172$	−10.6042	−0.808559
$173$	3.77449	0.286969	0.143484	−	0.989653i	$-0.454169\pi$
$173$	3.77449	0.286969	0.143484	+	0.989653i	$0.454169\pi$
$174$	−0.343341	−0.0260286
$175$	−21.9521	−1.65942
$176$	4.26174	0.321241
$177$	0.299867	0.0225394
$178$	2.94013	0.220372
$179$	17.4395	1.30349	0.651746	−	0.758437i	$-0.274037\pi$
$179$	17.4395	1.30349	0.651746	+	0.758437i	$0.274037\pi$
$180$	0.724540	0.0540041
$181$	−22.9867	−1.70859	−0.854295	−	0.519788i	$-0.826011\pi$
$181$	−22.9867	−1.70859	−0.854295	+	0.519788i	$0.826011\pi$
$182$	−24.4742	−1.81415
$183$	0.174392	0.0128915
$184$	3.48825	0.257157
$185$	−0.181740	−0.0133618
$186$	−0.433134	−0.0317589
$187$	−5.53085	−0.404456
$188$	9.91308	0.722985
$189$	−0.870570	−0.0633247
$190$	−0.237431	−0.0172250
$191$	−3.41809	−0.247325	−0.123662	−	0.992324i	$-0.539464\pi$
$191$	−3.41809	−0.247325	−0.123662	+	0.992324i	$0.539464\pi$
$192$	−0.0668909	−0.00482743
$193$	15.1226	1.08855	0.544274	−	0.838908i	$-0.316805\pi$
$193$	15.1226	1.08855	0.544274	+	0.838908i	$0.316805\pi$
$194$	−11.8950	−0.854011
$195$	−0.0181109	−0.00129695
$196$	16.6610	1.19007
$197$	6.73896	0.480131	0.240065	−	0.970757i	$-0.422831\pi$
$197$	6.73896	0.480131	0.240065	+	0.970757i	$0.422831\pi$
$198$	−4.76750	−0.338812
$199$	−20.3316	−1.44127	−0.720633	−	0.693316i	$-0.756149\pi$
$199$	−20.3316	−1.44127	−0.720633	+	0.693316i	$0.756149\pi$
$200$	−6.07788	−0.429771
$201$	−0.251105	−0.0177116
$202$	−1.12693	−0.0792906
$203$	25.3268	1.77759
$204$	0.277104	0.0194011
$205$	1.74058	0.121568
$206$	0.203192	0.0141571
$207$	−8.54893	−0.594192
$208$	−14.8452	−1.02933
$209$	0.623807	0.0431496
$210$	0.0481240	0.00332087
$211$	15.0764	1.03790	0.518950	−	0.854804i	$-0.326323\pi$
$211$	15.0764	1.03790	0.518950	+	0.854804i	$0.326323\pi$
$212$	2.77728	0.190744
$213$	0.00899115	0.000616063 0
$214$	−7.76544	−0.530835
$215$	1.44970	0.0988687
$216$	−0.241035	−0.0164004
$217$	31.9505	2.16894
$218$	1.82466	0.123581
$219$	0.110732	0.00748254
$220$	0.210495	0.0141916
$221$	19.2660	1.29597
$222$	−0.0599140	−0.00402116
$223$	−2.03558	−0.136312	−0.0681562	−	0.997675i	$-0.521712\pi$
$223$	−2.03558	−0.136312	−0.0681562	+	0.997675i	$0.521712\pi$
$224$	28.6303	1.91294
$225$	14.8956	0.993037
$226$	11.9060	0.791976
$227$	−0.447937	−0.0297306	−0.0148653	−	0.999890i	$-0.504732\pi$
$227$	−0.447937	−0.0297306	−0.0148653	+	0.999890i	$0.504732\pi$
$228$	−0.0312536	−0.00206982
$229$	13.2252	0.873948	0.436974	−	0.899474i	$-0.356050\pi$
$229$	13.2252	0.873948	0.436974	+	0.899474i	$0.356050\pi$
$230$	0.945317	0.0623324
$231$	−0.126437	−0.00831896
$232$	7.01226	0.460377
$233$	22.6912	1.48655	0.743277	−	0.668984i	$-0.233271\pi$
$233$	22.6912	1.48655	0.743277	+	0.668984i	$0.233271\pi$
$234$	16.6070	1.08563
$235$	−1.35522	−0.0884049
$236$	12.1403	0.790266
$237$	0.0936893	0.00608578
$238$	−51.1933	−3.31837
$239$	15.5780	1.00766	0.503829	−	0.863803i	$-0.331924\pi$
$239$	15.5780	1.00766	0.503829	+	0.863803i	$0.331924\pi$
$240$	0.0291904	0.00188423
$241$	−6.05548	−0.390067	−0.195034	−	0.980797i	$-0.562482\pi$
$241$	−6.05548	−0.390067	−0.195034	+	0.980797i	$0.562482\pi$
$242$	18.6862	1.20119
$243$	0.886141	0.0568459
$244$	7.06039	0.451995
$245$	−2.27773	−0.145519
$246$	0.573818	0.0365853
$247$	−2.17295	−0.138261
$248$	8.84615	0.561731
$249$	−0.0452736	−0.00286910
$250$	−3.30517	−0.209038
$251$	2.14353	0.135298	0.0676491	−	0.997709i	$-0.478450\pi$
$251$	2.14353	0.135298	0.0676491	+	0.997709i	$0.478450\pi$
$252$	−17.6196	−1.10993
$253$	−2.48365	−0.156146
$254$	32.1070	2.01458
$255$	−0.0378830	−0.00237233
$256$	20.9322	1.30826
$257$	16.8749	1.05263	0.526314	−	0.850290i	$-0.323574\pi$
$257$	16.8749	1.05263	0.526314	+	0.850290i	$0.323574\pi$
$258$	0.477922	0.0297541
$259$	4.41961	0.274621
$260$	−0.733232	−0.0454731
$261$	−17.1855	−1.06376
$262$	−13.9586	−0.862364
$263$	11.2933	0.696375	0.348188	−	0.937425i	$-0.386797\pi$
$263$	11.2933	0.696375	0.348188	+	0.937425i	$0.386797\pi$
$264$	−0.0350068	−0.00215452
$265$	−0.379683	−0.0233238
$266$	5.77392	0.354022
$267$	−0.0529092	−0.00323799
$268$	−10.1661	−0.620995
$269$	−3.05900	−0.186510	−0.0932552	−	0.995642i	$-0.529727\pi$
$269$	−3.05900	−0.186510	−0.0932552	+	0.995642i	$0.529727\pi$
$270$	−0.0653208	−0.00397530
$271$	−3.69945	−0.224726	−0.112363	−	0.993667i	$-0.535842\pi$
$271$	−3.69945	−0.224726	−0.112363	+	0.993667i	$0.535842\pi$
$272$	−31.0521	−1.88281
$273$	0.440428	0.0266559
$274$	6.14975	0.371520
$275$	4.32749	0.260957
$276$	0.124435	0.00749008
$277$	23.8011	1.43007	0.715036	−	0.699088i	$-0.246410\pi$
$277$	23.8011	1.43007	0.715036	+	0.699088i	$0.246410\pi$
$278$	2.34824	0.140838
$279$	−21.6800	−1.29795
$280$	−0.982865	−0.0587374
$281$	18.8155	1.12244	0.561220	−	0.827666i	$-0.310332\pi$
$281$	18.8155	1.12244	0.561220	+	0.827666i	$0.310332\pi$
$282$	−0.446775	−0.0266051
$283$	−2.92530	−0.173891	−0.0869456	−	0.996213i	$-0.527711\pi$
$283$	−2.92530	−0.173891	−0.0869456	+	0.996213i	$0.527711\pi$
$284$	0.364012	0.0216002
$285$	0.00427270	0.000253093 0
$286$	4.82469	0.285290
$287$	−42.3281	−2.49855
$288$	−19.4271	−1.14475
$289$	23.2991	1.37054
$290$	1.90033	0.111591
$291$	0.214057	0.0125483
$292$	4.48303	0.262350
$293$	−1.33645	−0.0780764	−0.0390382	−	0.999238i	$-0.512429\pi$
$293$	−1.33645	−0.0780764	−0.0390382	+	0.999238i	$0.512429\pi$
$294$	−0.750897	−0.0437932
$295$	−1.65971	−0.0966319
$296$	1.22366	0.0711238
$297$	0.171619	0.00995832
$298$	−3.76792	−0.218270
$299$	8.65148	0.500328
$300$	−0.216813	−0.0125177
$301$	−35.2543	−2.03202
$302$	−3.27783	−0.188618
$303$	0.0202798	0.00116504
$304$	3.50226	0.200869
$305$	−0.965229	−0.0552689
$306$	34.7372	1.98579
$307$	−23.7506	−1.35552	−0.677760	−	0.735283i	$-0.737049\pi$
$307$	−23.7506	−1.35552	−0.677760	+	0.735283i	$0.737049\pi$
$308$	−5.11889	−0.291676
$309$	−0.00365655	−0.000208014 0
$310$	2.39731	0.136158
$311$	15.3607	0.871025	0.435513	−	0.900183i	$-0.356567\pi$
$311$	15.3607	0.871025	0.435513	+	0.900183i	$0.356567\pi$
$312$	0.121942	0.00690358
$313$	23.8489	1.34802	0.674010	−	0.738723i	$-0.264571\pi$
$313$	23.8489	1.34802	0.674010	+	0.738723i	$0.264571\pi$
$314$	14.5736	0.822434
$315$	2.40879	0.135720
$316$	3.79307	0.213377
$317$	−16.1302	−0.905962	−0.452981	−	0.891520i	$-0.649639\pi$
$317$	−16.1302	−0.905962	−0.452981	+	0.891520i	$0.649639\pi$
$318$	−0.125170	−0.00701918
$319$	−4.99277	−0.279541
$320$	0.370228	0.0206964
$321$	0.139744	0.00779972
$322$	−22.9885	−1.28110
$323$	−4.54521	−0.252902
$324$	11.9515	0.663971
$325$	−15.0742	−0.836169
$326$	33.1303	1.83492
$327$	−0.0328358	−0.00181582
$328$	−11.7194	−0.647097
$329$	32.9567	1.81696
$330$	−0.00948686	−0.000522234 0
$331$	0.930539	0.0511471	0.0255735	−	0.999673i	$-0.491859\pi$
$331$	0.930539	0.0511471	0.0255735	+	0.999673i	$0.491859\pi$
$332$	−1.83293	−0.100595
$333$	−2.99892	−0.164340
$334$	11.4826	0.628297
$335$	1.38982	0.0759338
$336$	−0.709861	−0.0387261
$337$	3.85631	0.210067	0.105033	−	0.994469i	$-0.466505\pi$
$337$	3.85631	0.210067	0.105033	+	0.994469i	$0.466505\pi$
$338$	6.91435	0.376091
$339$	−0.214255	−0.0116368
$340$	−1.53372	−0.0831775
$341$	−6.29851	−0.341084
$342$	−3.91789	−0.211855
$343$	24.4533	1.32035
$344$	−9.76088	−0.526271
$345$	−0.0170115	−0.000915870 0
$346$	−6.88715	−0.370255
$347$	−2.66480	−0.143054	−0.0715271	−	0.997439i	$-0.522787\pi$
$347$	−2.66480	−0.143054	−0.0715271	+	0.997439i	$0.522787\pi$
$348$	0.250145	0.0134092
$349$	25.1905	1.34842	0.674209	−	0.738541i	$-0.264485\pi$
$349$	25.1905	1.34842	0.674209	+	0.738541i	$0.264485\pi$
$350$	40.0550	2.14103
$351$	−0.597811	−0.0319088
$352$	−5.64399	−0.300826
$353$	−13.7952	−0.734245	−0.367122	−	0.930173i	$-0.619657\pi$
$353$	−13.7952	−0.734245	−0.367122	+	0.930173i	$0.619657\pi$
$354$	−0.547155	−0.0290809
$355$	−0.0497643	−0.00264122
$356$	−2.14206	−0.113529
$357$	0.921252	0.0487578
$358$	−31.8212	−1.68180
$359$	29.8318	1.57446	0.787230	−	0.616659i	$-0.211514\pi$
$359$	29.8318	1.57446	0.787230	+	0.616659i	$0.211514\pi$
$360$	0.666923	0.0351499
$361$	−18.4874	−0.973019
$362$	41.9429	2.20447
$363$	−0.336268	−0.0176495
$364$	17.8310	0.934597
$365$	−0.612878	−0.0320795
$366$	−0.318207	−0.0166329
$367$	25.6699	1.33996	0.669978	−	0.742381i	$-0.266303\pi$
$367$	25.6699	1.33996	0.669978	+	0.742381i	$0.266303\pi$
$368$	−13.9441	−0.726885
$369$	28.7217	1.49519
$370$	0.331613	0.0172397
$371$	9.23327	0.479367
$372$	0.315565	0.0163613
$373$	7.27377	0.376622	0.188311	−	0.982109i	$-0.439699\pi$
$373$	7.27377	0.376622	0.188311	+	0.982109i	$0.439699\pi$
$374$	10.0919	0.521840
$375$	0.0594785	0.00307146
$376$	9.12476	0.470574
$377$	17.3917	0.895716
$378$	1.58849	0.0817032
$379$	−8.50299	−0.436769	−0.218385	−	0.975863i	$-0.570079\pi$
$379$	−8.50299	−0.436769	−0.218385	+	0.975863i	$0.570079\pi$
$380$	0.172983	0.00887383
$381$	−0.577785	−0.0296008
$382$	6.23685	0.319105
$383$	22.7778	1.16389	0.581945	−	0.813228i	$-0.302292\pi$
$383$	22.7778	1.16389	0.581945	+	0.813228i	$0.302292\pi$
$384$	−0.303368	−0.0154812
$385$	0.699806	0.0356654
$386$	−27.5935	−1.40447
$387$	23.9218	1.21601
$388$	8.66624	0.439962
$389$	−29.2481	−1.48294	−0.741468	−	0.670989i	$-0.765870\pi$
$389$	−29.2481	−1.48294	−0.741468	+	0.670989i	$0.765870\pi$
$390$	0.0330462	0.00167336
$391$	18.0965	0.915179
$392$	15.3360	0.774586
$393$	0.251192	0.0126710
$394$	−12.2963	−0.619478
$395$	−0.518553	−0.0260912
$396$	3.47342	0.174546
$397$	−10.3602	−0.519963	−0.259981	−	0.965614i	$-0.583716\pi$
$397$	−10.3602	−0.519963	−0.259981	+	0.965614i	$0.583716\pi$
$398$	37.0982	1.85956
$399$	−0.103905	−0.00520175
$400$	24.2960	1.21480
$401$	−1.62989	−0.0813927	−0.0406963	−	0.999172i	$-0.512958\pi$
$401$	−1.62989	−0.0813927	−0.0406963	+	0.999172i	$0.512958\pi$
$402$	0.458180	0.0228519
$403$	21.9401	1.09291
$404$	0.821039	0.0408482
$405$	−1.63389	−0.0811888
$406$	−46.2128	−2.29350
$407$	−0.871253	−0.0431864
$408$	0.255068	0.0126277
$409$	5.76426	0.285024	0.142512	−	0.989793i	$-0.454482\pi$
$409$	5.76426	0.285024	0.142512	+	0.989793i	$0.454482\pi$
$410$	−3.17597	−0.156850
$411$	−0.110668	−0.00545886
$412$	−0.148038	−0.00729330
$413$	40.3613	1.98605
$414$	15.5989	0.766643
$415$	0.250581	0.0123005
$416$	19.6601	0.963916
$417$	−0.0422579	−0.00206938
$418$	−1.13823	−0.0556728
$419$	−15.1274	−0.739024	−0.369512	−	0.929226i	$-0.620475\pi$
$419$	−15.1274	−0.739024	−0.369512	+	0.929226i	$0.620475\pi$
$420$	−0.0350613	−0.00171082
$421$	30.2113	1.47241	0.736204	−	0.676760i	$-0.236616\pi$
$421$	30.2113	1.47241	0.736204	+	0.676760i	$0.236616\pi$
$422$	−27.5092	−1.33913
$423$	−22.3628	−1.08732
$424$	2.55642	0.124151
$425$	−31.5311	−1.52948
$426$	−0.0164058	−0.000794862 0
$427$	23.4728	1.13593
$428$	5.65760	0.273471
$429$	−0.0868231	−0.00419186
$430$	−2.64521	−0.127563
$431$	−10.2120	−0.491897	−0.245949	−	0.969283i	$-0.579099\pi$
$431$	−10.2120	−0.491897	−0.245949	+	0.969283i	$0.579099\pi$
$432$	0.963526	0.0463576
$433$	19.9128	0.956950	0.478475	−	0.878101i	$-0.341190\pi$
$433$	19.9128	0.956950	0.478475	+	0.878101i	$0.341190\pi$
$434$	−58.2987	−2.79843
$435$	−0.0341975	−0.00163964
$436$	−1.32938	−0.0636655
$437$	−2.04104	−0.0976363
$438$	−0.202047	−0.00965418
$439$	26.2599	1.25331	0.626657	−	0.779295i	$-0.284423\pi$
$439$	26.2599	1.25331	0.626657	+	0.779295i	$0.284423\pi$
$440$	0.193756	0.00923695
$441$	−37.5852	−1.78977
$442$	−35.1539	−1.67210
$443$	12.7417	0.605376	0.302688	−	0.953090i	$-0.402116\pi$
$443$	12.7417	0.605376	0.302688	+	0.953090i	$0.402116\pi$
$444$	0.0436510	0.00207159
$445$	0.292843	0.0138821
$446$	3.71424	0.175874
$447$	0.0678058	0.00320711
$448$	−9.00333	−0.425368
$449$	40.9109	1.93070	0.965352	−	0.260951i	$-0.0840363\pi$
$449$	40.9109	1.93070	0.965352	+	0.260951i	$0.0840363\pi$
$450$	−27.1793	−1.28124
$451$	8.34430	0.392918
$452$	−8.67426	−0.408003
$453$	0.0589863	0.00277142
$454$	0.817332	0.0383593
$455$	−2.43768	−0.114280
$456$	−0.0287682	−0.00134720
$457$	13.7426	0.642852	0.321426	−	0.946935i	$-0.395838\pi$
$457$	13.7426	0.642852	0.321426	+	0.946935i	$0.395838\pi$
$458$	−24.1315	−1.12759
$459$	−1.25045	−0.0583662
$460$	−0.688722	−0.0321118
$461$	−12.0366	−0.560602	−0.280301	−	0.959912i	$-0.590434\pi$
$461$	−12.0366	−0.560602	−0.280301	+	0.959912i	$0.590434\pi$
$462$	0.230705	0.0107333
$463$	−19.8234	−0.921273	−0.460636	−	0.887589i	$-0.652379\pi$
$463$	−19.8234	−0.921273	−0.460636	+	0.887589i	$0.652379\pi$
$464$	−28.0311	−1.30131
$465$	−0.0431410	−0.00200062
$466$	−41.4038	−1.91799
$467$	−19.9198	−0.921777	−0.460889	−	0.887458i	$-0.652469\pi$
$467$	−19.9198	−0.921777	−0.460889	+	0.887458i	$0.652469\pi$
$468$	−12.0992	−0.559286
$469$	−33.7980	−1.56065
$470$	2.47282	0.114063
$471$	−0.262260	−0.0120843
$472$	11.1749	0.514365
$473$	6.94980	0.319552
$474$	−0.170951	−0.00785204
$475$	3.55629	0.163174
$476$	37.2974	1.70953
$477$	−6.26523	−0.286865
$478$	−28.4245	−1.30011
$479$	−6.87941	−0.314328	−0.157164	−	0.987572i	$-0.550235\pi$
$479$	−6.87941	−0.314328	−0.157164	+	0.987572i	$0.550235\pi$
$480$	−0.0386579	−0.00176449
$481$	3.03490	0.138379
$482$	11.0492	0.503276
$483$	0.413692	0.0188236
$484$	−13.6140	−0.618819
$485$	−1.18477	−0.0537975
$486$	−1.61690	−0.0733442
$487$	5.09771	0.230999	0.115500	−	0.993308i	$-0.463153\pi$
$487$	5.09771	0.230999	0.115500	+	0.993308i	$0.463153\pi$
$488$	6.49892	0.294192
$489$	−0.596199	−0.0269610
$490$	4.15607	0.187752
$491$	24.7372	1.11637	0.558186	−	0.829716i	$-0.311497\pi$
$491$	24.7372	1.11637	0.558186	+	0.829716i	$0.311497\pi$
$492$	−0.418061	−0.0188477
$493$	36.3785	1.63841
$494$	3.96489	0.178389
$495$	−0.474853	−0.0213431
$496$	−35.3620	−1.58780
$497$	1.21019	0.0542842
$498$	0.0826088	0.00370179
$499$	11.1809	0.500526	0.250263	−	0.968178i	$-0.419483\pi$
$499$	11.1809	0.500526	0.250263	+	0.968178i	$0.419483\pi$
$500$	2.40802	0.107690
$501$	−0.206635	−0.00923178
$502$	−3.91120	−0.174565
$503$	−13.1193	−0.584961	−0.292480	−	0.956272i	$-0.594481\pi$
$503$	−13.1193	−0.584961	−0.292480	+	0.956272i	$0.594481\pi$
$504$	−16.2185	−0.722427
$505$	−0.112245	−0.00499482
$506$	4.53182	0.201464
$507$	−0.124428	−0.00552603
$508$	−23.3920	−1.03785
$509$	−23.6723	−1.04926	−0.524629	−	0.851331i	$-0.675796\pi$
$509$	−23.6723	−1.04926	−0.524629	+	0.851331i	$0.675796\pi$
$510$	0.0691235	0.00306084
$511$	14.9042	0.659322
$512$	−19.7162	−0.871341
$513$	0.141035	0.00622683
$514$	−30.7909	−1.35813
$515$	0.0202383	0.000891808 0
$516$	−0.348195	−0.0153284
$517$	−6.49688	−0.285733
$518$	−8.06427	−0.354324
$519$	0.123938	0.00544028
$520$	−0.674924	−0.0295974
$521$	−21.7838	−0.954365	−0.477182	−	0.878804i	$-0.658342\pi$
$521$	−21.7838	−0.954365	−0.477182	+	0.878804i	$0.658342\pi$
$522$	31.3577	1.37249
$523$	22.5880	0.987706	0.493853	−	0.869545i	$-0.335588\pi$
$523$	22.5880	0.987706	0.493853	+	0.869545i	$0.335588\pi$
$524$	10.1697	0.444265
$525$	−0.720812	−0.0314588
$526$	−20.6064	−0.898483
$527$	45.8925	1.99911
$528$	0.139938	0.00609000
$529$	−14.8737	−0.646682
$530$	0.692792	0.0300930
$531$	−27.3872	−1.18850
$532$	−4.20665	−0.182382
$533$	−29.0663	−1.25900
$534$	0.0965413	0.00417775
$535$	−0.773454	−0.0334393
$536$	−9.35769	−0.404191
$537$	0.572640	0.0247113
$538$	5.58162	0.240641
$539$	−10.9193	−0.470329
$540$	0.0475902	0.00204796
$541$	17.9795	0.773001	0.386500	−	0.922289i	$-0.373684\pi$
$541$	17.9795	0.773001	0.386500	+	0.922289i	$0.373684\pi$
$542$	6.75024	0.289948
$543$	−0.754787	−0.0323910
$544$	41.1235	1.76315
$545$	0.181740	0.00778487
$546$	−0.803630	−0.0343922
$547$	−4.29091	−0.183466	−0.0917330	−	0.995784i	$-0.529241\pi$
$547$	−4.29091	−0.183466	−0.0917330	+	0.995784i	$0.529241\pi$
$548$	−4.48047	−0.191396
$549$	−15.9274	−0.679766
$550$	−7.89618	−0.336694
$551$	−4.10301	−0.174794
$552$	0.114539	0.00487511
$553$	12.6103	0.536246
$554$	−43.4289	−1.84512
$555$	−0.00596756	−0.000253309 0
$556$	−1.71084	−0.0725556
$557$	11.9035	0.504366	0.252183	−	0.967680i	$-0.418852\pi$
$557$	11.9035	0.504366	0.252183	+	0.967680i	$0.418852\pi$
$558$	39.5585	1.67465
$559$	−24.2087	−1.02392
$560$	3.92895	0.166028
$561$	−0.181610	−0.00766757
$562$	−34.3319	−1.44820
$563$	11.6528	0.491106	0.245553	−	0.969383i	$-0.421031\pi$
$563$	11.6528	0.491106	0.245553	+	0.969383i	$0.421031\pi$
$564$	0.325503	0.0137062
$565$	1.18586	0.0498896
$566$	5.33768	0.224359
$567$	39.7336	1.66865
$568$	0.335065	0.0140590
$569$	15.1999	0.637213	0.318607	−	0.947887i	$-0.396785\pi$
$569$	15.1999	0.637213	0.318607	+	0.947887i	$0.396785\pi$
$570$	−0.00779621	−0.000326547 0
$571$	−38.0952	−1.59424	−0.797118	−	0.603824i	$-0.793643\pi$
$571$	−38.0952	−1.59424	−0.797118	+	0.603824i	$0.793643\pi$
$572$	−3.51509	−0.146973
$573$	−0.112236	−0.00468871
$574$	77.2343	3.22370
$575$	−14.1592	−0.590479
$576$	6.10921	0.254550
$577$	32.0904	1.33594	0.667971	−	0.744188i	$-0.267163\pi$
$577$	32.0904	1.33594	0.667971	+	0.744188i	$0.267163\pi$
$578$	−42.5130	−1.76831
$579$	0.496562	0.0206364
$580$	−1.38450	−0.0574884
$581$	−6.09371	−0.252810
$582$	−0.390581	−0.0161901
$583$	−1.82019	−0.0753845
$584$	4.12653	0.170757
$585$	1.65409	0.0683882
$586$	2.43857	0.100736
$587$	18.3023	0.755419	0.377709	−	0.925924i	$-0.376712\pi$
$587$	18.3023	0.755419	0.377709	+	0.925924i	$0.376712\pi$
$588$	0.547075	0.0225610
$589$	−5.17606	−0.213276
$590$	3.02840	0.124677
$591$	0.221279	0.00910219
$592$	−4.89151	−0.201040
$593$	28.0579	1.15220	0.576099	−	0.817380i	$-0.304574\pi$
$593$	28.0579	1.15220	0.576099	+	0.817380i	$0.304574\pi$
$594$	−0.313145	−0.0128485
$595$	−5.09896	−0.209037
$596$	2.74516	0.112446
$597$	−0.667602	−0.0273231
$598$	−15.7860	−0.645537
$599$	45.3344	1.85231	0.926156	−	0.377141i	$-0.123093\pi$
$599$	45.3344	1.85231	0.926156	+	0.377141i	$0.123093\pi$
$600$	−0.199572	−0.00814749
$601$	−34.8077	−1.41984	−0.709919	−	0.704284i	$-0.751268\pi$
$601$	−34.8077	−1.41984	−0.709919	+	0.704284i	$0.751268\pi$
$602$	64.3270	2.62177
$603$	22.9336	0.933930
$604$	2.38810	0.0971703
$605$	1.86118	0.0756678
$606$	−0.0370036	−0.00150317
$607$	−22.3726	−0.908075	−0.454038	−	0.890982i	$-0.650017\pi$
$607$	−22.3726	−0.908075	−0.454038	+	0.890982i	$0.650017\pi$
$608$	−4.63818	−0.188103
$609$	0.831625	0.0336992
$610$	1.76121	0.0713094
$611$	22.6311	0.915554
$612$	−25.3082	−1.02302
$613$	−36.6986	−1.48224	−0.741121	−	0.671372i	$-0.765705\pi$
$613$	−36.6986	−1.48224	−0.741121	+	0.671372i	$0.765705\pi$
$614$	43.3368	1.74893
$615$	0.0571534	0.00230465
$616$	−4.71182	−0.189845
$617$	12.0705	0.485938	0.242969	−	0.970034i	$-0.421879\pi$
$617$	12.0705	0.485938	0.242969	+	0.970034i	$0.421879\pi$
$618$	0.00667196	0.000268386 0
$619$	26.0427	1.04675	0.523373	−	0.852104i	$-0.324674\pi$
$619$	26.0427	1.04675	0.523373	+	0.852104i	$0.324674\pi$
$620$	−1.74659	−0.0701448
$621$	−0.561522	−0.0225331
$622$	−28.0280	−1.12382
$623$	−7.12145	−0.285315
$624$	−0.487455	−0.0195138
$625$	24.5057	0.980226
$626$	−43.5161	−1.73925
$627$	0.0204832	0.000818019 0
$628$	−10.6177	−0.423694
$629$	6.34816	0.253118
$630$	−4.39521	−0.175109
$631$	−40.9046	−1.62839	−0.814193	−	0.580594i	$-0.802820\pi$
$631$	−40.9046	−1.62839	−0.814193	+	0.580594i	$0.802820\pi$
$632$	3.49143	0.138882
$633$	0.495044	0.0196762
$634$	29.4321	1.16890
$635$	3.19793	0.126906
$636$	0.0911940	0.00361608
$637$	38.0361	1.50705
$638$	9.11009	0.360672
$639$	−0.821171	−0.0324850
$640$	1.67908	0.0663717
$641$	25.7238	1.01603	0.508014	−	0.861349i	$-0.330380\pi$
$641$	25.7238	1.01603	0.508014	+	0.861349i	$0.330380\pi$
$642$	−0.254984	−0.0100634
$643$	−12.5429	−0.494643	−0.247321	−	0.968934i	$-0.579550\pi$
$643$	−12.5429	−0.494643	−0.247321	+	0.968934i	$0.579550\pi$
$644$	16.7486	0.659986
$645$	0.0476020	0.00187433
$646$	8.29344	0.326301
$647$	−15.0310	−0.590929	−0.295465	−	0.955354i	$-0.595474\pi$
$647$	−15.0310	−0.590929	−0.295465	+	0.955354i	$0.595474\pi$
$648$	11.0011	0.432163
$649$	−7.95657	−0.312323
$650$	27.5053	1.07885
$651$	1.04912	0.0411182
$652$	−24.1375	−0.945296
$653$	34.3731	1.34512	0.672561	−	0.740042i	$-0.265194\pi$
$653$	34.3731	1.34512	0.672561	+	0.740042i	$0.265194\pi$
$654$	0.0599140	0.00234282
$655$	−1.39030	−0.0543236
$656$	46.8477	1.82910
$657$	−10.1132	−0.394554
$658$	−60.1348	−2.34430
$659$	−0.887520	−0.0345729	−0.0172864	−	0.999851i	$-0.505503\pi$
$659$	−0.887520	−0.0345729	−0.0172864	+	0.999851i	$0.505503\pi$
$660$	0.00691176	0.000269040 0
$661$	−32.9833	−1.28290	−0.641451	−	0.767164i	$-0.721667\pi$
$661$	−32.9833	−1.28290	−0.641451	+	0.767164i	$0.721667\pi$
$662$	−1.69792	−0.0659914
$663$	0.632614	0.0245687
$664$	−1.68717	−0.0654749
$665$	0.575094	0.0223012
$666$	5.47201	0.212036
$667$	16.3359	0.632529
$668$	−8.36575	−0.323681
$669$	−0.0668398	−0.00258418
$670$	−2.53594	−0.0979719
$671$	−4.62727	−0.178634
$672$	0.940096	0.0362650
$673$	−7.52865	−0.290208	−0.145104	−	0.989416i	$-0.546352\pi$
$673$	−7.52865	−0.290208	−0.145104	+	0.989416i	$0.546352\pi$
$674$	−7.03644	−0.271034
$675$	0.978389	0.0376582
$676$	−5.03753	−0.193751
$677$	−0.136032	−0.00522813	−0.00261406	−	0.999997i	$-0.500832\pi$
$677$	−0.136032	−0.00522813	−0.00261406	+	0.999997i	$0.500832\pi$
$678$	0.390943	0.0150141
$679$	28.8116	1.10569
$680$	−1.41175	−0.0541382
$681$	−0.0147084	−0.000563626 0
$682$	11.4926	0.440075
$683$	−35.5764	−1.36129	−0.680646	−	0.732613i	$-0.738301\pi$
$683$	−35.5764	−1.36129	−0.680646	+	0.732613i	$0.738301\pi$
$684$	2.85442	0.109142
$685$	0.612528	0.0234035
$686$	−44.6189	−1.70356
$687$	0.434261	0.0165681
$688$	39.0186	1.48757
$689$	6.34039	0.241550
$690$	0.0310402	0.00118168
$691$	38.3542	1.45906	0.729531	−	0.683948i	$-0.239738\pi$
$691$	38.3542	1.45906	0.729531	+	0.683948i	$0.239738\pi$
$692$	5.01771	0.190745
$693$	11.5476	0.438658
$694$	4.86235	0.184572
$695$	0.233889	0.00887193
$696$	0.230253	0.00872771
$697$	−60.7986	−2.30291
$698$	−45.9641	−1.73977
$699$	0.745084	0.0281817
$700$	−29.1825	−1.10300
$701$	29.6922	1.12146	0.560729	−	0.827999i	$-0.310521\pi$
$701$	29.6922	1.12146	0.560729	+	0.827999i	$0.310521\pi$
$702$	1.09080	0.0411696
$703$	−0.715988	−0.0270040
$704$	1.77486	0.0668925
$705$	−0.0444997	−0.00167596
$706$	25.1715	0.947343
$707$	2.72960	0.102657
$708$	0.398636	0.0149817
$709$	17.8156	0.669081	0.334540	−	0.942381i	$-0.391419\pi$
$709$	17.8156	0.669081	0.334540	+	0.942381i	$0.391419\pi$
$710$	0.0908028	0.00340777
$711$	−8.55674	−0.320903
$712$	−1.97172	−0.0738934
$713$	20.6082	0.771783
$714$	−1.68097	−0.0629087
$715$	0.480549	0.0179715
$716$	23.1837	0.866415
$717$	0.511516	0.0191029
$718$	−54.4327	−2.03141
$719$	31.1727	1.16255	0.581273	−	0.813709i	$-0.302555\pi$
$719$	31.1727	1.16255	0.581273	+	0.813709i	$0.302555\pi$
$720$	−2.66599	−0.0993555
$721$	−0.492163	−0.0183291
$722$	33.7331	1.25542
$723$	−0.198836	−0.00739479
$724$	−30.5580	−1.13568
$725$	−28.4635	−1.05711
$726$	0.613574	0.0227719
$727$	−22.7175	−0.842546	−0.421273	−	0.906934i	$-0.638417\pi$
$727$	−22.7175	−0.842546	−0.421273	+	0.906934i	$0.638417\pi$
$728$	16.4130	0.608307
$729$	−26.9418	−0.997844
$730$	1.11829	0.0413899
$731$	−50.6380	−1.87291
$732$	0.231833	0.00856880
$733$	27.9900	1.03383	0.516917	−	0.856035i	$-0.327079\pi$
$733$	27.9900	1.03383	0.516917	+	0.856035i	$0.327079\pi$
$734$	−46.8387	−1.72885
$735$	−0.0747909	−0.00275870
$736$	18.4667	0.680690
$737$	6.66273	0.245425
$738$	−52.4073	−1.92914
$739$	−13.1227	−0.482726	−0.241363	−	0.970435i	$-0.577594\pi$
$739$	−13.1227	−0.482726	−0.241363	+	0.970435i	$0.577594\pi$
$740$	−0.241600	−0.00888140
$741$	−0.0713504	−0.00262112
$742$	−16.8475	−0.618493
$743$	−5.90025	−0.216459	−0.108230	−	0.994126i	$-0.534518\pi$
$743$	−5.90025	−0.216459	−0.108230	+	0.994126i	$0.534518\pi$
$744$	0.290470	0.0106492
$745$	−0.375292	−0.0137497
$746$	−13.2721	−0.485928
$747$	4.13488	0.151287
$748$	−7.35258	−0.268837
$749$	18.8091	0.687270
$750$	−0.108528	−0.00396288
$751$	12.1280	0.442556	0.221278	−	0.975211i	$-0.428977\pi$
$751$	12.1280	0.442556	0.221278	+	0.975211i	$0.428977\pi$
$752$	−36.4757	−1.33013
$753$	0.0703843	0.00256495
$754$	−31.7338	−1.15568
$755$	−0.326478	−0.0118818
$756$	−1.15731	−0.0420911
$757$	5.77583	0.209926	0.104963	−	0.994476i	$-0.466528\pi$
$757$	5.77583	0.209926	0.104963	+	0.994476i	$0.466528\pi$
$758$	15.5151	0.563532
$759$	−0.0815526	−0.00296017
$760$	0.159227	0.00577576
$761$	−42.9840	−1.55817	−0.779084	−	0.626919i	$-0.784316\pi$
$761$	−42.9840	−1.55817	−0.779084	+	0.626919i	$0.784316\pi$
$762$	1.05426	0.0381918
$763$	−4.41961	−0.160000
$764$	−4.54393	−0.164394
$765$	3.45989	0.125093
$766$	−41.5616	−1.50168
$767$	27.7157	1.00076
$768$	0.687325	0.0248017
$769$	31.6929	1.14288	0.571438	−	0.820645i	$-0.306386\pi$
$769$	31.6929	1.14288	0.571438	+	0.820645i	$0.306386\pi$
$770$	−1.27691	−0.0460165
$771$	0.554101	0.0199554
$772$	20.1036	0.723544
$773$	−15.3141	−0.550809	−0.275405	−	0.961328i	$-0.588812\pi$
$773$	−15.3141	−0.550809	−0.275405	+	0.961328i	$0.588812\pi$
$774$	−43.6491	−1.56893
$775$	−35.9075	−1.28984
$776$	7.97708	0.286360
$777$	0.145121	0.00520619
$778$	53.3677	1.91332
$779$	6.85727	0.245687
$780$	−0.0240762	−0.000862067 0
$781$	−0.238568	−0.00853664
$782$	−33.0199	−1.18079
$783$	−1.12880	−0.0403400
$784$	−61.3049	−2.18946
$785$	1.45156	0.0518083
$786$	−0.458340	−0.0163485
$787$	45.2933	1.61453	0.807265	−	0.590189i	$-0.200947\pi$
$787$	45.2933	1.61453	0.807265	+	0.590189i	$0.200947\pi$
$788$	8.95860	0.319137
$789$	0.370824	0.0132017
$790$	0.946181	0.0336636
$791$	−28.8382	−1.02537
$792$	3.19720	0.113608
$793$	16.1185	0.572385
$794$	18.9038	0.670871
$795$	−0.0124672	−0.000442166 0
$796$	−27.0283	−0.957992
$797$	−55.5884	−1.96904	−0.984522	−	0.175262i	$-0.943923\pi$
$797$	−55.5884	−1.96904	−0.984522	+	0.175262i	$0.943923\pi$
$798$	0.189591	0.00671145
$799$	47.3379	1.67469
$800$	−32.1761	−1.13760
$801$	4.83225	0.170739
$802$	2.97399	0.105015
$803$	−2.93811	−0.103684
$804$	−0.333812	−0.0117727
$805$	−2.28971	−0.0807016
$806$	−40.0331	−1.41011
$807$	−0.100444	−0.00353581
$808$	0.755747	0.0265871
$809$	2.91410	0.102454	0.0512271	−	0.998687i	$-0.483687\pi$
$809$	2.91410	0.102454	0.0512271	+	0.998687i	$0.483687\pi$
$810$	2.98130	0.104752
$811$	56.1811	1.97279	0.986393	−	0.164403i	$-0.0525698\pi$
$811$	56.1811	1.97279	0.986393	+	0.164403i	$0.0525698\pi$
$812$	33.6689	1.18155
$813$	−0.121474	−0.00426029
$814$	1.58974	0.0557203
$815$	3.29985	0.115589
$816$	−1.01962	−0.0356938
$817$	5.71129	0.199813
$818$	−10.5178	−0.367746
$819$	−40.2247	−1.40556
$820$	2.31389	0.0808046
$821$	42.0865	1.46883	0.734415	−	0.678700i	$-0.237456\pi$
$821$	42.0865	1.46883	0.734415	+	0.678700i	$0.237456\pi$
$822$	0.201932	0.00704317
$823$	−25.7167	−0.896427	−0.448214	−	0.893926i	$-0.647940\pi$
$823$	−25.7167	−0.896427	−0.448214	+	0.893926i	$0.647940\pi$
$824$	−0.136265	−0.00474703
$825$	0.142096	0.00494716
$826$	−73.6456	−2.56246
$827$	−40.9718	−1.42473	−0.712364	−	0.701810i	$-0.752375\pi$
$827$	−40.9718	−1.42473	−0.712364	+	0.701810i	$0.752375\pi$
$828$	−11.3647	−0.394952
$829$	0.208982	0.00725824	0.00362912	−	0.999993i	$-0.498845\pi$
$829$	0.208982	0.00725824	0.00362912	+	0.999993i	$0.498845\pi$
$830$	−0.457224	−0.0158705
$831$	0.781528	0.0271109
$832$	−6.18250	−0.214339
$833$	79.5610	2.75662
$834$	0.0771061	0.00266997
$835$	1.14369	0.0395789
$836$	0.829273	0.0286810
$837$	−1.42401	−0.0492211
$838$	27.6024	0.953509
$839$	−19.5696	−0.675617	−0.337808	−	0.941215i	$-0.609686\pi$
$839$	−19.5696	−0.675617	−0.337808	+	0.941215i	$0.609686\pi$
$840$	−0.0322731	−0.00111353
$841$	3.83932	0.132390
$842$	−55.1252	−1.89974
$843$	0.617822	0.0212789
$844$	20.0422	0.689880
$845$	0.688684	0.0236914
$846$	40.8044	1.40288
$847$	−45.2608	−1.55518
$848$	−10.2192	−0.350927
$849$	−0.0960546	−0.00329658
$850$	57.5335	1.97338
$851$	2.85067	0.0977196
$852$	0.0119526	0.000409490 0
$853$	−8.33474	−0.285376	−0.142688	−	0.989768i	$-0.545575\pi$
$853$	−8.33474	−0.285376	−0.142688	+	0.989768i	$0.545575\pi$
$854$	−42.8298	−1.46560
$855$	−0.390230	−0.0133456
$856$	5.20769	0.177995
$857$	53.6212	1.83166	0.915832	−	0.401562i	$-0.131533\pi$
$857$	53.6212	1.83166	0.915832	+	0.401562i	$0.131533\pi$
$858$	0.158422	0.00540845
$859$	−52.7087	−1.79840	−0.899199	−	0.437540i	$-0.855850\pi$
$859$	−52.7087	−1.79840	−0.899199	+	0.437540i	$0.855850\pi$
$860$	1.92720	0.0657168
$861$	−1.38988	−0.0473668
$862$	18.6335	0.634659
$863$	5.96238	0.202962	0.101481	−	0.994837i	$-0.467642\pi$
$863$	5.96238	0.202962	0.101481	+	0.994837i	$0.467642\pi$
$864$	−1.27603	−0.0434115
$865$	−0.685974	−0.0233238
$866$	−36.3341	−1.23468
$867$	0.765045	0.0259823
$868$	42.4742	1.44167
$869$	−2.48592	−0.0843291
$870$	0.0623987	0.00211551
$871$	−23.2088	−0.786399
$872$	−1.22366	−0.0414384
$873$	−19.5501	−0.661670
$874$	3.72420	0.125973
$875$	8.00565	0.270640
$876$	0.147204	0.00497355
$877$	−19.7094	−0.665539	−0.332770	−	0.943008i	$-0.607983\pi$
$877$	−19.7094	−0.665539	−0.332770	+	0.943008i	$0.607983\pi$
$878$	−47.9153	−1.61706
$879$	−0.0438834	−0.00148015
$880$	−0.774528	−0.0261093
$881$	22.4766	0.757255	0.378627	−	0.925549i	$-0.376396\pi$
$881$	22.4766	0.757255	0.378627	+	0.925549i	$0.376396\pi$
$882$	68.5802	2.30922
$883$	4.31252	0.145128	0.0725640	−	0.997364i	$-0.476882\pi$
$883$	4.31252	0.145128	0.0725640	+	0.997364i	$0.476882\pi$
$884$	25.6118	0.861417
$885$	−0.0544977	−0.00183192
$886$	−23.2492	−0.781073
$887$	−49.2187	−1.65260	−0.826301	−	0.563229i	$-0.809559\pi$
$887$	−49.2187	−1.65260	−0.826301	+	0.563229i	$0.809559\pi$
$888$	0.0401798	0.00134835
$889$	−77.7683	−2.60826
$890$	−0.534338	−0.0179110
$891$	−7.83282	−0.262409
$892$	−2.70605	−0.0906052
$893$	−5.33908	−0.178665
$894$	−0.123722	−0.00413790
$895$	−3.16946	−0.105943
$896$	−40.8325	−1.36412
$897$	0.284078	0.00948509
$898$	−74.6484	−2.49105
$899$	41.4277	1.38169
$900$	19.8018	0.660060
$901$	13.2623	0.441832
$902$	−15.2255	−0.506953
$903$	−1.15760	−0.0385225
$904$	−7.98446	−0.265559
$905$	4.17760	0.138868
$906$	−0.107630	−0.00357576
$907$	−39.9674	−1.32710	−0.663548	−	0.748133i	$-0.730950\pi$
$907$	−39.9674	−1.32710	−0.663548	+	0.748133i	$0.730950\pi$
$908$	−0.595477	−0.0197616
$909$	−1.85217	−0.0614326
$910$	4.44794	0.147448
$911$	−11.2248	−0.371893	−0.185946	−	0.982560i	$-0.559535\pi$
$911$	−11.2248	−0.371893	−0.185946	+	0.982560i	$0.559535\pi$
$912$	0.114999	0.00380801
$913$	1.20127	0.0397564
$914$	−25.0755	−0.829425
$915$	−0.0316940	−0.00104777
$916$	17.5813	0.580903
$917$	33.8098	1.11650
$918$	2.28165	0.0753057
$919$	−47.1611	−1.55570	−0.777850	−	0.628450i	$-0.783690\pi$
$919$	−47.1611	−1.55570	−0.777850	+	0.628450i	$0.783690\pi$
$920$	−0.633953	−0.0209008
$921$	−0.779870	−0.0256976
$922$	21.9627	0.723304
$923$	0.831022	0.0273534
$924$	−0.168082	−0.00552951
$925$	−4.96697	−0.163313
$926$	36.1710	1.18865
$927$	0.333957	0.0109686
$928$	37.1227	1.21861
$929$	−12.9394	−0.424527	−0.212263	−	0.977212i	$-0.568084\pi$
$929$	−12.9394	−0.424527	−0.212263	+	0.977212i	$0.568084\pi$
$930$	0.0787176	0.00258125
$931$	−8.97342	−0.294092
$932$	30.1652	0.988094
$933$	0.504380	0.0165127
$934$	36.3468	1.18930
$935$	1.00518	0.0328728
$936$	−11.1370	−0.364026
$937$	−45.8355	−1.49738	−0.748691	−	0.662919i	$-0.769317\pi$
$937$	−45.8355	−1.49738	−0.748691	+	0.662919i	$0.769317\pi$
$938$	61.6698	2.01359
$939$	0.783096	0.0255554
$940$	−1.80160	−0.0587617
$941$	−34.0441	−1.10980	−0.554902	−	0.831916i	$-0.687244\pi$
$941$	−34.0441	−1.10980	−0.554902	+	0.831916i	$0.687244\pi$
$942$	0.478534	0.0155915
$943$	−27.3018	−0.889070
$944$	−44.6709	−1.45391
$945$	0.158217	0.00514680
$946$	−12.6810	−0.412295
$947$	9.29654	0.302097	0.151049	−	0.988526i	$-0.451735\pi$
$947$	9.29654	0.302097	0.151049	+	0.988526i	$0.451735\pi$
$948$	0.124548	0.00404514
$949$	10.2345	0.332227
$950$	−6.48901	−0.210531
$951$	−0.529647	−0.0171750
$952$	34.3315	1.11269
$953$	−3.58126	−0.116008	−0.0580042	−	0.998316i	$-0.518474\pi$
$953$	−3.58126	−0.116008	−0.0580042	+	0.998316i	$0.518474\pi$
$954$	11.4319	0.370121
$955$	0.621203	0.0201017
$956$	20.7090	0.669778
$957$	−0.163941	−0.00529947
$958$	12.5526	0.405555
$959$	−14.8956	−0.481006
$960$	0.0121567	0.000392357 0
$961$	21.2622	0.685876
$962$	−5.53765	−0.178541
$963$	−12.7629	−0.411279
$964$	−8.05000	−0.259273
$965$	−2.74837	−0.0884733
$966$	−0.754846	−0.0242868
$967$	−10.8163	−0.347829	−0.173914	−	0.984761i	$-0.555642\pi$
$967$	−10.8163	−0.347829	−0.173914	+	0.984761i	$0.555642\pi$
$968$	−12.5314	−0.402775
$969$	−0.149245	−0.00479445
$970$	2.16179	0.0694110
$971$	−10.1285	−0.325039	−0.162519	−	0.986705i	$-0.551962\pi$
$971$	−10.1285	−0.325039	−0.162519	+	0.986705i	$0.551962\pi$
$972$	1.17801	0.0377848
$973$	−5.68780	−0.182342
$974$	−9.30157	−0.298042
$975$	−0.494974	−0.0158519
$976$	−25.9791	−0.831570
$977$	−8.29432	−0.265359	−0.132679	−	0.991159i	$-0.542358\pi$
$977$	−8.29432	−0.265359	−0.132679	+	0.991159i	$0.542358\pi$
$978$	1.08786	0.0347859
$979$	1.40388	0.0448681
$980$	−3.02796	−0.0967245
$981$	2.99892	0.0957482
$982$	−45.1369	−1.44038
$983$	28.1559	0.898035	0.449017	−	0.893523i	$-0.351774\pi$
$983$	28.1559	0.898035	0.449017	+	0.893523i	$0.351774\pi$
$984$	−0.384816	−0.0122675
$985$	−1.22474	−0.0390233
$986$	−66.3783	−2.11392
$987$	1.08216	0.0344455
$988$	−2.88867	−0.0919007
$989$	−22.7392	−0.723064
$990$	0.866444	0.0275374
$991$	−38.7204	−1.23000	−0.614998	−	0.788529i	$-0.710843\pi$
$991$	−38.7204	−1.23000	−0.614998	+	0.788529i	$0.710843\pi$
$992$	46.8312	1.48689
$993$	0.0305550	0.000969632 0
$994$	−2.20817	−0.0700390
$995$	3.69505	0.117141
$996$	−0.0601856	−0.00190705
$997$	−15.2243	−0.482157	−0.241079	−	0.970506i	$-0.577501\pi$
$997$	−15.2243	−0.482157	−0.241079	+	0.970506i	$0.577501\pi$
$998$	−20.4013	−0.645793
$999$	−0.196979	−0.00623214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.18	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.18	✓	85	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.82466 q^{2} +0.0328358 q^{3} +1.32938 q^{4} -0.181740 q^{5} -0.0599140 q^{6} +4.41961 q^{7} +1.22366 q^{8} -2.99892 q^{9} +O(q^{10})\)	\(q-1.82466 q^{2} +0.0328358 q^{3} +1.32938 q^{4} -0.181740 q^{5} -0.0599140 q^{6} +4.41961 q^{7} +1.22366 q^{8} -2.99892 q^{9} +0.331613 q^{10} -0.871253 q^{11} +0.0436510 q^{12} +3.03490 q^{13} -8.06427 q^{14} -0.00596756 q^{15} -4.89151 q^{16} +6.34816 q^{17} +5.47201 q^{18} -0.715988 q^{19} -0.241600 q^{20} +0.145121 q^{21} +1.58974 q^{22} +2.85067 q^{23} +0.0401798 q^{24} -4.96697 q^{25} -5.53765 q^{26} -0.196979 q^{27} +5.87532 q^{28} +5.73056 q^{29} +0.0108888 q^{30} +7.22926 q^{31} +6.47801 q^{32} -0.0286082 q^{33} -11.5832 q^{34} -0.803218 q^{35} -3.98669 q^{36} +1.00000 q^{37} +1.30643 q^{38} +0.0996531 q^{39} -0.222388 q^{40} -9.57735 q^{41} -0.264796 q^{42} -7.97679 q^{43} -1.15822 q^{44} +0.545023 q^{45} -5.20149 q^{46} +7.45694 q^{47} -0.160616 q^{48} +12.5329 q^{49} +9.06302 q^{50} +0.208447 q^{51} +4.03452 q^{52} +2.08916 q^{53} +0.359419 q^{54} +0.158341 q^{55} +5.40810 q^{56} -0.0235100 q^{57} -10.4563 q^{58} +9.13233 q^{59} -0.00793313 q^{60} +5.31105 q^{61} -13.1909 q^{62} -13.2541 q^{63} -2.03713 q^{64} -0.551561 q^{65} +0.0522003 q^{66} -7.64729 q^{67} +8.43909 q^{68} +0.0936038 q^{69} +1.46560 q^{70} +0.273822 q^{71} -3.66966 q^{72} +3.37228 q^{73} -1.82466 q^{74} -0.163094 q^{75} -0.951817 q^{76} -3.85059 q^{77} -0.181833 q^{78} +2.85327 q^{79} +0.888982 q^{80} +8.99030 q^{81} +17.4754 q^{82} -1.37879 q^{83} +0.192920 q^{84} -1.15371 q^{85} +14.5549 q^{86} +0.188167 q^{87} -1.06612 q^{88} -1.61133 q^{89} -0.994481 q^{90} +13.4131 q^{91} +3.78961 q^{92} +0.237378 q^{93} -13.6064 q^{94} +0.130123 q^{95} +0.212710 q^{96} +6.51903 q^{97} -22.8683 q^{98} +2.61282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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