LMFDB - Embedded newform 4033.2.a.d.1.39

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:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
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)

$f(q)$	$=$	$q-0.258525 q^{2} +2.73396 q^{3} -1.93316 q^{4} +0.131458 q^{5} -0.706797 q^{6} -5.26098 q^{7} +1.01682 q^{8} +4.47453 q^{9} +O(q^{10})$	\(q-0.258525 q^{2} +2.73396 q^{3} -1.93316 q^{4} +0.131458 q^{5} -0.706797 q^{6} -5.26098 q^{7} +1.01682 q^{8} +4.47453 q^{9} -0.0339852 q^{10} +0.331440 q^{11} -5.28519 q^{12} -0.368513 q^{13} +1.36010 q^{14} +0.359400 q^{15} +3.60346 q^{16} -0.0419886 q^{17} -1.15678 q^{18} +7.98216 q^{19} -0.254130 q^{20} -14.3833 q^{21} -0.0856857 q^{22} -0.769458 q^{23} +2.77995 q^{24} -4.98272 q^{25} +0.0952698 q^{26} +4.03131 q^{27} +10.1703 q^{28} +3.96180 q^{29} -0.0929140 q^{30} +2.67524 q^{31} -2.96523 q^{32} +0.906145 q^{33} +0.0108551 q^{34} -0.691596 q^{35} -8.65000 q^{36} -1.00000 q^{37} -2.06359 q^{38} -1.00750 q^{39} +0.133669 q^{40} -5.70460 q^{41} +3.71844 q^{42} -8.15928 q^{43} -0.640729 q^{44} +0.588212 q^{45} +0.198924 q^{46} -6.54630 q^{47} +9.85170 q^{48} +20.6779 q^{49} +1.28816 q^{50} -0.114795 q^{51} +0.712396 q^{52} -12.0752 q^{53} -1.04219 q^{54} +0.0435704 q^{55} -5.34948 q^{56} +21.8229 q^{57} -1.02422 q^{58} -7.42797 q^{59} -0.694780 q^{60} -0.0525192 q^{61} -0.691616 q^{62} -23.5404 q^{63} -6.44032 q^{64} -0.0484438 q^{65} -0.234261 q^{66} -2.07676 q^{67} +0.0811708 q^{68} -2.10367 q^{69} +0.178795 q^{70} -2.79766 q^{71} +4.54980 q^{72} +0.167895 q^{73} +0.258525 q^{74} -13.6225 q^{75} -15.4308 q^{76} -1.74370 q^{77} +0.260464 q^{78} -9.34397 q^{79} +0.473702 q^{80} -2.40217 q^{81} +1.47478 q^{82} -10.9990 q^{83} +27.8053 q^{84} -0.00551973 q^{85} +2.10938 q^{86} +10.8314 q^{87} +0.337016 q^{88} +13.8760 q^{89} -0.152068 q^{90} +1.93874 q^{91} +1.48749 q^{92} +7.31399 q^{93} +1.69238 q^{94} +1.04932 q^{95} -8.10681 q^{96} -8.58543 q^{97} -5.34575 q^{98} +1.48304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−0.258525	−0.182805	−0.0914025	−	0.995814i	$-0.529135\pi$
$2$	−0.258525	−0.182805	−0.0914025	+	0.995814i	$0.529135\pi$
$3$	2.73396	1.57845	0.789226	−	0.614103i	$-0.210482\pi$
$3$	2.73396	1.57845	0.789226	+	0.614103i	$0.210482\pi$
$4$	−1.93316	−0.966582
$5$	0.131458	0.0587897	0.0293949	−	0.999568i	$-0.490642\pi$
$5$	0.131458	0.0587897	0.0293949	+	0.999568i	$0.490642\pi$
$6$	−0.706797	−0.288549
$7$	−5.26098	−1.98846	−0.994231	−	0.107260i	$-0.965792\pi$
$7$	−5.26098	−1.98846	−0.994231	+	0.107260i	$0.965792\pi$
$8$	1.01682	0.359501
$9$	4.47453	1.49151
$10$	−0.0339852	−0.0107471
$11$	0.331440	0.0999331	0.0499665	−	0.998751i	$-0.484089\pi$
$11$	0.331440	0.0999331	0.0499665	+	0.998751i	$0.484089\pi$
$12$	−5.28519	−1.52570
$13$	−0.368513	−0.102207	−0.0511035	−	0.998693i	$-0.516274\pi$
$13$	−0.368513	−0.102207	−0.0511035	+	0.998693i	$0.516274\pi$
$14$	1.36010	0.363501
$15$	0.359400	0.0927967
$16$	3.60346	0.900864
$17$	−0.0419886	−0.0101837	−0.00509186	−	0.999987i	$-0.501621\pi$
$17$	−0.0419886	−0.0101837	−0.00509186	+	0.999987i	$0.501621\pi$
$18$	−1.15678	−0.272655
$19$	7.98216	1.83123	0.915616	−	0.402053i	$-0.131703\pi$
$19$	7.98216	1.83123	0.915616	+	0.402053i	$0.131703\pi$
$20$	−0.254130	−0.0568251
$21$	−14.3833	−3.13869
$22$	−0.0856857	−0.0182683
$23$	−0.769458	−0.160443	−0.0802215	−	0.996777i	$-0.525563\pi$
$23$	−0.769458	−0.160443	−0.0802215	+	0.996777i	$0.525563\pi$
$24$	2.77995	0.567455
$25$	−4.98272	−0.996544
$26$	0.0952698	0.0186840
$27$	4.03131	0.775825
$28$	10.1703	1.92201
$29$	3.96180	0.735687	0.367844	−	0.929888i	$-0.380096\pi$
$29$	3.96180	0.735687	0.367844	+	0.929888i	$0.380096\pi$
$30$	−0.0929140	−0.0169637
$31$	2.67524	0.480487	0.240243	−	0.970713i	$-0.422773\pi$
$31$	2.67524	0.480487	0.240243	+	0.970713i	$0.422773\pi$
$32$	−2.96523	−0.524183
$33$	0.906145	0.157740
$34$	0.0108551	0.00186164
$35$	−0.691596	−0.116901
$36$	−8.65000	−1.44167
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−2.06359	−0.334759
$39$	−1.00750	−0.161329
$40$	0.133669	0.0211350
$41$	−5.70460	−0.890909	−0.445455	−	0.895304i	$-0.646958\pi$
$41$	−5.70460	−0.890909	−0.445455	+	0.895304i	$0.646958\pi$
$42$	3.71844	0.573768
$43$	−8.15928	−1.24428	−0.622140	−	0.782906i	$-0.713736\pi$
$43$	−8.15928	−1.24428	−0.622140	+	0.782906i	$0.713736\pi$
$44$	−0.640729	−0.0965935
$45$	0.588212	0.0876854
$46$	0.198924	0.0293298
$47$	−6.54630	−0.954876	−0.477438	−	0.878666i	$-0.658434\pi$
$47$	−6.54630	−0.954876	−0.477438	+	0.878666i	$0.658434\pi$
$48$	9.85170	1.42197
$49$	20.6779	2.95398
$50$	1.28816	0.182173
$51$	−0.114795	−0.0160745
$52$	0.712396	0.0987915
$53$	−12.0752	−1.65865	−0.829327	−	0.558764i	$-0.811276\pi$
$53$	−12.0752	−1.65865	−0.829327	+	0.558764i	$0.811276\pi$
$54$	−1.04219	−0.141825
$55$	0.0435704	0.00587504
$56$	−5.34948	−0.714854
$57$	21.8229	2.89051
$58$	−1.02422	−0.134487
$59$	−7.42797	−0.967039	−0.483519	−	0.875334i	$-0.660642\pi$
$59$	−7.42797	−0.967039	−0.483519	+	0.875334i	$0.660642\pi$
$60$	−0.694780	−0.0896957
$61$	−0.0525192	−0.00672440	−0.00336220	−	0.999994i	$-0.501070\pi$
$61$	−0.0525192	−0.00672440	−0.00336220	+	0.999994i	$0.501070\pi$
$62$	−0.691616	−0.0878353
$63$	−23.5404	−2.96581
$64$	−6.44032	−0.805040
$65$	−0.0484438	−0.00600872
$66$	−0.234261	−0.0288356
$67$	−2.07676	−0.253717	−0.126859	−	0.991921i	$-0.540489\pi$
$67$	−2.07676	−0.253717	−0.126859	+	0.991921i	$0.540489\pi$
$68$	0.0811708	0.00984341
$69$	−2.10367	−0.253252
$70$	0.178795	0.0213701
$71$	−2.79766	−0.332021	−0.166010	−	0.986124i	$-0.553089\pi$
$71$	−2.79766	−0.332021	−0.166010	+	0.986124i	$0.553089\pi$
$72$	4.54980	0.536199
$73$	0.167895	0.0196506	0.00982531	−	0.999952i	$-0.496872\pi$
$73$	0.167895	0.0196506	0.00982531	+	0.999952i	$0.496872\pi$
$74$	0.258525	0.0300530
$75$	−13.6225	−1.57300
$76$	−15.4308	−1.77004
$77$	−1.74370	−0.198713
$78$	0.260464	0.0294917
$79$	−9.34397	−1.05128	−0.525640	−	0.850707i	$-0.676174\pi$
$79$	−9.34397	−1.05128	−0.525640	+	0.850707i	$0.676174\pi$
$80$	0.473702	0.0529615
$81$	−2.40217	−0.266907
$82$	1.47478	0.162863
$83$	−10.9990	−1.20729	−0.603646	−	0.797252i	$-0.706286\pi$
$83$	−10.9990	−1.20729	−0.603646	+	0.797252i	$0.706286\pi$
$84$	27.8053	3.03380
$85$	−0.00551973	−0.000598698 0
$86$	2.10938	0.227460
$87$	10.8314	1.16125
$88$	0.337016	0.0359260
$89$	13.8760	1.47086	0.735428	−	0.677603i	$-0.236981\pi$
$89$	13.8760	1.47086	0.735428	+	0.677603i	$0.236981\pi$
$90$	−0.152068	−0.0160293
$91$	1.93874	0.203235
$92$	1.48749	0.155081
$93$	7.31399	0.758425
$94$	1.69238	0.174556
$95$	1.04932	0.107658
$96$	−8.10681	−0.827398
$97$	−8.58543	−0.871719	−0.435859	−	0.900015i	$-0.643555\pi$
$97$	−8.58543	−0.871719	−0.435859	+	0.900015i	$0.643555\pi$
$98$	−5.34575	−0.540002
$99$	1.48304	0.149051
$100$	9.63242	0.963242
$101$	−10.0105	−0.996082	−0.498041	−	0.867153i	$-0.665947\pi$
$101$	−10.0105	−0.996082	−0.498041	+	0.867153i	$0.665947\pi$
$102$	0.0296774	0.00293850
$103$	0.955365	0.0941349	0.0470675	−	0.998892i	$-0.485012\pi$
$103$	0.955365	0.0941349	0.0470675	+	0.998892i	$0.485012\pi$
$104$	−0.374712	−0.0367435
$105$	−1.89080	−0.184523
$106$	3.12174	0.303210
$107$	9.23809	0.893080	0.446540	−	0.894764i	$-0.352656\pi$
$107$	9.23809	0.893080	0.446540	+	0.894764i	$0.352656\pi$
$108$	−7.79318	−0.749899
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−0.0112641	−0.00107399
$111$	−2.73396	−0.259496
$112$	−18.9577	−1.79133
$113$	2.99810	0.282037	0.141019	−	0.990007i	$-0.454962\pi$
$113$	2.99810	0.282037	0.141019	+	0.990007i	$0.454962\pi$
$114$	−5.64177	−0.528400
$115$	−0.101151	−0.00943240
$116$	−7.65881	−0.711102
$117$	−1.64892	−0.152443
$118$	1.92032	0.176780
$119$	0.220901	0.0202500
$120$	0.365446	0.0333605
$121$	−10.8901	−0.990013
$122$	0.0135775	0.00122925
$123$	−15.5962	−1.40626
$124$	−5.17167	−0.464430
$125$	−1.31231	−0.117376
$126$	6.08579	0.542165
$127$	−11.9869	−1.06366	−0.531831	−	0.846850i	$-0.678496\pi$
$127$	−11.9869	−1.06366	−0.531831	+	0.846850i	$0.678496\pi$
$128$	7.59545	0.671349
$129$	−22.3071	−1.96403
$130$	0.0125240	0.00109842
$131$	7.56617	0.661059	0.330530	−	0.943796i	$-0.392773\pi$
$131$	7.56617	0.661059	0.330530	+	0.943796i	$0.392773\pi$
$132$	−1.75173	−0.152468
$133$	−41.9939	−3.64134
$134$	0.536896	0.0463807
$135$	0.529947	0.0456105
$136$	−0.0426949	−0.00366106
$137$	−11.6258	−0.993263	−0.496631	−	0.867962i	$-0.665430\pi$
$137$	−11.6258	−0.993263	−0.496631	+	0.867962i	$0.665430\pi$
$138$	0.543851	0.0462957
$139$	−6.33087	−0.536977	−0.268489	−	0.963283i	$-0.586524\pi$
$139$	−6.33087	−0.536977	−0.268489	+	0.963283i	$0.586524\pi$
$140$	1.33697	0.112995
$141$	−17.8973	−1.50723
$142$	0.723265	0.0606951
$143$	−0.122140	−0.0102139
$144$	16.1238	1.34365
$145$	0.520809	0.0432508
$146$	−0.0434051	−0.00359223
$147$	56.5324	4.66272
$148$	1.93316	0.158905
$149$	19.1031	1.56499	0.782493	−	0.622660i	$-0.213948\pi$
$149$	19.1031	1.56499	0.782493	+	0.622660i	$0.213948\pi$
$150$	3.52177	0.287552
$151$	−9.76081	−0.794323	−0.397162	−	0.917749i	$-0.630005\pi$
$151$	−9.76081	−0.794323	−0.397162	+	0.917749i	$0.630005\pi$
$152$	8.11644	0.658330
$153$	−0.187879	−0.0151891
$154$	0.450791	0.0363257
$155$	0.351681	0.0282477
$156$	1.94766	0.155938
$157$	0.0760018	0.00606560	0.00303280	−	0.999995i	$-0.499035\pi$
$157$	0.0760018	0.00606560	0.00303280	+	0.999995i	$0.499035\pi$
$158$	2.41565	0.192179
$159$	−33.0130	−2.61810
$160$	−0.389802	−0.0308166
$161$	4.04810	0.319035
$162$	0.621021	0.0487920
$163$	−6.27783	−0.491717	−0.245859	−	0.969306i	$-0.579070\pi$
$163$	−6.27783	−0.491717	−0.245859	+	0.969306i	$0.579070\pi$
$164$	11.0279	0.861137
$165$	0.119120	0.00927346
$166$	2.84351	0.220699
$167$	−21.0207	−1.62663	−0.813316	−	0.581822i	$-0.802340\pi$
$167$	−21.0207	−1.62663	−0.813316	+	0.581822i	$0.802340\pi$
$168$	−14.6253	−1.12836
$169$	−12.8642	−0.989554
$170$	0.00142699	0.000109445 0
$171$	35.7164	2.73130
$172$	15.7732	1.20270
$173$	6.18435	0.470187	0.235094	−	0.971973i	$-0.424460\pi$
$173$	6.18435	0.470187	0.235094	+	0.971973i	$0.424460\pi$
$174$	−2.80019	−0.212282
$175$	26.2140	1.98159
$176$	1.19433	0.0900261
$177$	−20.3078	−1.52642
$178$	−3.58730	−0.268880
$179$	23.1004	1.72660	0.863302	−	0.504688i	$-0.168393\pi$
$179$	23.1004	1.72660	0.863302	+	0.504688i	$0.168393\pi$
$180$	−1.13711	−0.0847552
$181$	0.761895	0.0566312	0.0283156	−	0.999599i	$-0.490986\pi$
$181$	0.761895	0.0566312	0.0283156	+	0.999599i	$0.490986\pi$
$182$	−0.501212	−0.0371523
$183$	−0.143585	−0.0106141
$184$	−0.782402	−0.0576794
$185$	−0.131458	−0.00966497
$186$	−1.89085	−0.138644
$187$	−0.0139167	−0.00101769
$188$	12.6551	0.922966
$189$	−21.2086	−1.54270
$190$	−0.271275	−0.0196804
$191$	2.09906	0.151883	0.0759413	−	0.997112i	$-0.475804\pi$
$191$	2.09906	0.151883	0.0759413	+	0.997112i	$0.475804\pi$
$192$	−17.6076	−1.27072
$193$	15.3727	1.10655	0.553275	−	0.832998i	$-0.313378\pi$
$193$	15.3727	1.10655	0.553275	+	0.832998i	$0.313378\pi$
$194$	2.21955	0.159354
$195$	−0.132443	−0.00948448
$196$	−39.9737	−2.85527
$197$	−22.2016	−1.58180	−0.790901	−	0.611944i	$-0.790388\pi$
$197$	−22.2016	−1.58180	−0.790901	+	0.611944i	$0.790388\pi$
$198$	−0.383403	−0.0272473
$199$	4.21481	0.298780	0.149390	−	0.988778i	$-0.452269\pi$
$199$	4.21481	0.298780	0.149390	+	0.988778i	$0.452269\pi$
$200$	−5.06654	−0.358259
$201$	−5.67779	−0.400480
$202$	2.58797	0.182089
$203$	−20.8429	−1.46289
$204$	0.221918	0.0155373
$205$	−0.749914	−0.0523763
$206$	−0.246986	−0.0172083
$207$	−3.44296	−0.239302
$208$	−1.32792	−0.0920746
$209$	2.64561	0.183001
$210$	0.488818	0.0337317
$211$	−9.74020	−0.670543	−0.335272	−	0.942122i	$-0.608828\pi$
$211$	−9.74020	−0.670543	−0.335272	+	0.942122i	$0.608828\pi$
$212$	23.3433	1.60322
$213$	−7.64868	−0.524079
$214$	−2.38828	−0.163259
$215$	−1.07260	−0.0731508
$216$	4.09912	0.278910
$217$	−14.0744	−0.955429
$218$	0.258525	0.0175095
$219$	0.459018	0.0310175
$220$	−0.0842288	−0.00567871
$221$	0.0154733	0.00104085
$222$	0.706797	0.0474371
$223$	−16.7583	−1.12222	−0.561111	−	0.827741i	$-0.689626\pi$
$223$	−16.7583	−1.12222	−0.561111	+	0.827741i	$0.689626\pi$
$224$	15.6000	1.04232
$225$	−22.2953	−1.48636
$226$	−0.775084	−0.0515578
$227$	17.8104	1.18212	0.591058	−	0.806629i	$-0.298710\pi$
$227$	17.8104	1.18212	0.591058	+	0.806629i	$0.298710\pi$
$228$	−42.1873	−2.79392
$229$	10.4364	0.689654	0.344827	−	0.938666i	$-0.387938\pi$
$229$	10.4364	0.689654	0.344827	+	0.938666i	$0.387938\pi$
$230$	0.0261501	0.00172429
$231$	−4.76720	−0.313659
$232$	4.02844	0.264480
$233$	−2.27569	−0.149085	−0.0745427	−	0.997218i	$-0.523750\pi$
$233$	−2.27569	−0.149085	−0.0745427	+	0.997218i	$0.523750\pi$
$234$	0.426288	0.0278673
$235$	−0.860562	−0.0561369
$236$	14.3595	0.934723
$237$	−25.5460	−1.65939
$238$	−0.0571085	−0.00370179
$239$	7.50113	0.485207	0.242604	−	0.970125i	$-0.421999\pi$
$239$	7.50113	0.485207	0.242604	+	0.970125i	$0.421999\pi$
$240$	1.29508	0.0835972
$241$	−0.703068	−0.0452886	−0.0226443	−	0.999744i	$-0.507209\pi$
$241$	−0.703068	−0.0452886	−0.0226443	+	0.999744i	$0.507209\pi$
$242$	2.81538	0.180979
$243$	−18.6613	−1.19713
$244$	0.101528	0.00649969
$245$	2.71827	0.173664
$246$	4.03200	0.257071
$247$	−2.94153	−0.187165
$248$	2.72024	0.172735
$249$	−30.0707	−1.90565
$250$	0.339264	0.0214570
$251$	−5.34397	−0.337308	−0.168654	−	0.985675i	$-0.553942\pi$
$251$	−5.34397	−0.337308	−0.168654	+	0.985675i	$0.553942\pi$
$252$	45.5075	2.86670
$253$	−0.255030	−0.0160336
$254$	3.09891	0.194443
$255$	−0.0150907	−0.000945016 0
$256$	10.9170	0.682314
$257$	8.35235	0.521005	0.260502	−	0.965473i	$-0.416112\pi$
$257$	8.35235	0.521005	0.260502	+	0.965473i	$0.416112\pi$
$258$	5.76696	0.359035
$259$	5.26098	0.326901
$260$	0.0936499	0.00580792
$261$	17.7272	1.09729
$262$	−1.95605	−0.120845
$263$	−16.2273	−1.00062	−0.500310	−	0.865847i	$-0.666780\pi$
$263$	−16.2273	−1.00062	−0.500310	+	0.865847i	$0.666780\pi$
$264$	0.921388	0.0567075
$265$	−1.58738	−0.0975117
$266$	10.8565	0.665655
$267$	37.9365	2.32168
$268$	4.01473	0.245238
$269$	−21.8512	−1.33229	−0.666146	−	0.745821i	$-0.732057\pi$
$269$	−21.8512	−1.33229	−0.666146	+	0.745821i	$0.732057\pi$
$270$	−0.137005	−0.00833783
$271$	2.76264	0.167818	0.0839092	−	0.996473i	$-0.473259\pi$
$271$	2.76264	0.167818	0.0839092	+	0.996473i	$0.473259\pi$
$272$	−0.151304	−0.00917415
$273$	5.30042	0.320796
$274$	3.00557	0.181573
$275$	−1.65147	−0.0995877
$276$	4.06673	0.244789
$277$	−1.74293	−0.104722	−0.0523611	−	0.998628i	$-0.516675\pi$
$277$	−1.74293	−0.104722	−0.0523611	+	0.998628i	$0.516675\pi$
$278$	1.63669	0.0981622
$279$	11.9704	0.716651
$280$	−0.703231	−0.0420261
$281$	−2.35646	−0.140575	−0.0702874	−	0.997527i	$-0.522392\pi$
$281$	−2.35646	−0.140575	−0.0702874	+	0.997527i	$0.522392\pi$
$282$	4.62691	0.275528
$283$	26.5639	1.57906	0.789531	−	0.613710i	$-0.210324\pi$
$283$	26.5639	1.57906	0.789531	+	0.613710i	$0.210324\pi$
$284$	5.40833	0.320926
$285$	2.86879	0.169932
$286$	0.0315763	0.00186714
$287$	30.0118	1.77154
$288$	−13.2680	−0.781825
$289$	−16.9982	−0.999896
$290$	−0.134642	−0.00790647
$291$	−23.4722	−1.37597
$292$	−0.324569	−0.0189939
$293$	1.54973	0.0905363	0.0452682	−	0.998975i	$-0.485586\pi$
$293$	1.54973	0.0905363	0.0452682	+	0.998975i	$0.485586\pi$
$294$	−14.6151	−0.852368
$295$	−0.976464	−0.0568519
$296$	−1.01682	−0.0591016
$297$	1.33614	0.0775306
$298$	−4.93863	−0.286087
$299$	0.283555	0.0163984
$300$	26.3346	1.52043
$301$	42.9258	2.47420
$302$	2.52342	0.145206
$303$	−27.3683	−1.57227
$304$	28.7634	1.64969
$305$	−0.00690406	−0.000395325 0
$306$	0.0485715	0.00277665
$307$	22.4480	1.28118	0.640588	−	0.767885i	$-0.278691\pi$
$307$	22.4480	1.28118	0.640588	+	0.767885i	$0.278691\pi$
$308$	3.37086	0.192073
$309$	2.61193	0.148587
$310$	−0.0909183	−0.00516381
$311$	26.3420	1.49372	0.746860	−	0.664981i	$-0.231561\pi$
$311$	26.3420	1.49372	0.746860	+	0.664981i	$0.231561\pi$
$312$	−1.02445	−0.0579979
$313$	−17.6125	−0.995517	−0.497758	−	0.867316i	$-0.665843\pi$
$313$	−17.6125	−0.995517	−0.497758	+	0.867316i	$0.665843\pi$
$314$	−0.0196484	−0.00110882
$315$	−3.09457	−0.174359
$316$	18.0634	1.01615
$317$	−5.72190	−0.321374	−0.160687	−	0.987005i	$-0.551371\pi$
$317$	−5.72190	−0.321374	−0.160687	+	0.987005i	$0.551371\pi$
$318$	8.53471	0.478602
$319$	1.31310	0.0735195
$320$	−0.846631	−0.0473281
$321$	25.2566	1.40968
$322$	−1.04654	−0.0583212
$323$	−0.335160	−0.0186488
$324$	4.64379	0.257988
$325$	1.83619	0.101854
$326$	1.62298	0.0898884
$327$	−2.73396	−0.151188
$328$	−5.80057	−0.320283
$329$	34.4399	1.89873
$330$	−0.0307955	−0.00169523
$331$	34.4181	1.89179	0.945895	−	0.324471i	$-0.105186\pi$
$331$	34.4181	1.89179	0.945895	+	0.324471i	$0.105186\pi$
$332$	21.2628	1.16695
$333$	−4.47453	−0.245203
$334$	5.43439	0.297357
$335$	−0.273007	−0.0149160
$336$	−51.8295	−2.82753
$337$	11.2283	0.611644	0.305822	−	0.952089i	$-0.401069\pi$
$337$	11.2283	0.611644	0.305822	+	0.952089i	$0.401069\pi$
$338$	3.32572	0.180895
$339$	8.19668	0.445182
$340$	0.0106705	0.000578691 0
$341$	0.886682	0.0480165
$342$	−9.23360	−0.499296
$343$	−71.9589	−3.88542
$344$	−8.29654	−0.447320
$345$	−0.276543	−0.0148886
$346$	−1.59881	−0.0859526
$347$	27.0977	1.45468	0.727341	−	0.686276i	$-0.240756\pi$
$347$	27.0977	1.45468	0.727341	+	0.686276i	$0.240756\pi$
$348$	−20.9389	−1.12244
$349$	−15.8481	−0.848332	−0.424166	−	0.905585i	$-0.639433\pi$
$349$	−15.8481	−0.848332	−0.424166	+	0.905585i	$0.639433\pi$
$350$	−6.77697	−0.362244
$351$	−1.48559	−0.0792948
$352$	−0.982797	−0.0523833
$353$	12.7838	0.680411	0.340206	−	0.940351i	$-0.389503\pi$
$353$	12.7838	0.680411	0.340206	+	0.940351i	$0.389503\pi$
$354$	5.25007	0.279038
$355$	−0.367774	−0.0195194
$356$	−26.8246	−1.42170
$357$	0.603934	0.0319636
$358$	−5.97203	−0.315632
$359$	−22.2489	−1.17425	−0.587125	−	0.809496i	$-0.699740\pi$
$359$	−22.2489	−1.17425	−0.587125	+	0.809496i	$0.699740\pi$
$360$	0.598107	0.0315230
$361$	44.7149	2.35341
$362$	−0.196969	−0.0103525
$363$	−29.7732	−1.56269
$364$	−3.74790	−0.196443
$365$	0.0220711	0.00115525
$366$	0.0371205	0.00194032
$367$	27.8487	1.45369	0.726844	−	0.686802i	$-0.240986\pi$
$367$	27.8487	1.45369	0.726844	+	0.686802i	$0.240986\pi$
$368$	−2.77271	−0.144537
$369$	−25.5254	−1.32880
$370$	0.0339852	0.00176680
$371$	63.5272	3.29817
$372$	−14.1391	−0.733080
$373$	2.15874	0.111775	0.0558876	−	0.998437i	$-0.482201\pi$
$373$	2.15874	0.111775	0.0558876	+	0.998437i	$0.482201\pi$
$374$	0.00359782	0.000186039 0
$375$	−3.58779	−0.185273
$376$	−6.65642	−0.343279
$377$	−1.45997	−0.0751924
$378$	5.48296	0.282013
$379$	4.46592	0.229399	0.114700	−	0.993400i	$-0.463409\pi$
$379$	4.46592	0.229399	0.114700	+	0.993400i	$0.463409\pi$
$380$	−2.02850	−0.104060
$381$	−32.7716	−1.67894
$382$	−0.542660	−0.0277649
$383$	3.40813	0.174147	0.0870735	−	0.996202i	$-0.472248\pi$
$383$	3.40813	0.174147	0.0870735	+	0.996202i	$0.472248\pi$
$384$	20.7656	1.05969
$385$	−0.229223	−0.0116823
$386$	−3.97423	−0.202283
$387$	−36.5090	−1.85586
$388$	16.5971	0.842588
$389$	−8.58002	−0.435024	−0.217512	−	0.976058i	$-0.569794\pi$
$389$	−8.58002	−0.435024	−0.217512	+	0.976058i	$0.569794\pi$
$390$	0.0342400	0.00173381
$391$	0.0323084	0.00163391
$392$	21.0257	1.06196
$393$	20.6856	1.04345
$394$	5.73969	0.289161
$395$	−1.22834	−0.0618044
$396$	−2.86696	−0.144070
$397$	14.8504	0.745322	0.372661	−	0.927967i	$-0.378445\pi$
$397$	14.8504	0.745322	0.372661	+	0.927967i	$0.378445\pi$
$398$	−1.08963	−0.0546184
$399$	−114.810	−5.74768
$400$	−17.9550	−0.897750
$401$	−29.5824	−1.47727	−0.738637	−	0.674103i	$-0.764530\pi$
$401$	−29.5824	−1.47727	−0.738637	+	0.674103i	$0.764530\pi$
$402$	1.46785	0.0732098
$403$	−0.985858	−0.0491091
$404$	19.3520	0.962796
$405$	−0.315784	−0.0156914
$406$	5.38842	0.267423
$407$	−0.331440	−0.0164289
$408$	−0.116726	−0.00577881
$409$	22.2862	1.10198	0.550991	−	0.834511i	$-0.314250\pi$
$409$	22.2862	1.10198	0.550991	+	0.834511i	$0.314250\pi$
$410$	0.193872	0.00957465
$411$	−31.7846	−1.56782
$412$	−1.84688	−0.0909891
$413$	39.0783	1.92292
$414$	0.890093	0.0437457
$415$	−1.44590	−0.0709764
$416$	1.09272	0.0535752
$417$	−17.3083	−0.847593
$418$	−0.683957	−0.0334534
$419$	−18.6441	−0.910822	−0.455411	−	0.890281i	$-0.650508\pi$
$419$	−18.6441	−0.910822	−0.455411	+	0.890281i	$0.650508\pi$
$420$	3.65522	0.178356
$421$	30.9241	1.50715	0.753574	−	0.657363i	$-0.228328\pi$
$421$	30.9241	1.50715	0.753574	+	0.657363i	$0.228328\pi$
$422$	2.51809	0.122579
$423$	−29.2916	−1.42421
$424$	−12.2783	−0.596288
$425$	0.209217	0.0101485
$426$	1.97738	0.0958042
$427$	0.276302	0.0133712
$428$	−17.8588	−0.863235
$429$	−0.333926	−0.0161221
$430$	0.277295	0.0133723
$431$	−11.4900	−0.553456	−0.276728	−	0.960948i	$-0.589250\pi$
$431$	−11.4900	−0.553456	−0.276728	+	0.960948i	$0.589250\pi$
$432$	14.5266	0.698913
$433$	−14.1233	−0.678724	−0.339362	−	0.940656i	$-0.610211\pi$
$433$	−14.1233	−0.678724	−0.339362	+	0.940656i	$0.610211\pi$
$434$	3.63858	0.174657
$435$	1.42387	0.0682694
$436$	1.93316	0.0925818
$437$	−6.14194	−0.293809
$438$	−0.118668	−0.00567016
$439$	−4.04403	−0.193011	−0.0965055	−	0.995332i	$-0.530767\pi$
$439$	−4.04403	−0.193011	−0.0965055	+	0.995332i	$0.530767\pi$
$440$	0.0443034	0.00211208
$441$	92.5237	4.40589
$442$	−0.00400024	−0.000190272 0
$443$	−14.0472	−0.667404	−0.333702	−	0.942679i	$-0.608298\pi$
$443$	−14.0472	−0.667404	−0.333702	+	0.942679i	$0.608298\pi$
$444$	5.28519	0.250824
$445$	1.82411	0.0864712
$446$	4.33245	0.205148
$447$	52.2270	2.47025
$448$	33.8824	1.60079
$449$	9.22340	0.435279	0.217640	−	0.976029i	$-0.430164\pi$
$449$	9.22340	0.435279	0.217640	+	0.976029i	$0.430164\pi$
$450$	5.76391	0.271713
$451$	−1.89074	−0.0890313
$452$	−5.79582	−0.272612
$453$	−26.6856	−1.25380
$454$	−4.60444	−0.216097
$455$	0.254862	0.0119481
$456$	22.1900	1.03914
$457$	1.80604	0.0844832	0.0422416	−	0.999107i	$-0.486550\pi$
$457$	1.80604	0.0844832	0.0422416	+	0.999107i	$0.486550\pi$
$458$	−2.69806	−0.126072
$459$	−0.169269	−0.00790079
$460$	0.195542	0.00911719
$461$	34.9906	1.62968	0.814838	−	0.579689i	$-0.196826\pi$
$461$	34.9906	1.62968	0.814838	+	0.579689i	$0.196826\pi$
$462$	1.23244	0.0573384
$463$	−29.6526	−1.37807	−0.689037	−	0.724726i	$-0.741966\pi$
$463$	−29.6526	−1.37807	−0.689037	+	0.724726i	$0.741966\pi$
$464$	14.2762	0.662754
$465$	0.961480	0.0445876
$466$	0.588323	0.0272536
$467$	−16.6326	−0.769666	−0.384833	−	0.922986i	$-0.625741\pi$
$467$	−16.6326	−0.769666	−0.384833	+	0.922986i	$0.625741\pi$
$468$	3.18764	0.147349
$469$	10.9258	0.504507
$470$	0.222477	0.0102621
$471$	0.207786	0.00957426
$472$	−7.55292	−0.347651
$473$	−2.70432	−0.124345
$474$	6.60430	0.303345
$475$	−39.7729	−1.82490
$476$	−0.427038	−0.0195732
$477$	−54.0308	−2.47390
$478$	−1.93923	−0.0886983
$479$	16.7259	0.764228	0.382114	−	0.924115i	$-0.375196\pi$
$479$	16.7259	0.764228	0.382114	+	0.924115i	$0.375196\pi$
$480$	−1.06570	−0.0486425
$481$	0.368513	0.0168027
$482$	0.181761	0.00827898
$483$	11.0673	0.503581
$484$	21.0524	0.956929
$485$	−1.12862	−0.0512481
$486$	4.82443	0.218841
$487$	−18.6178	−0.843651	−0.421826	−	0.906677i	$-0.638611\pi$
$487$	−18.6178	−0.843651	−0.421826	+	0.906677i	$0.638611\pi$
$488$	−0.0534027	−0.00241743
$489$	−17.1633	−0.776152
$490$	−0.702741	−0.0317466
$491$	−28.6498	−1.29295	−0.646474	−	0.762936i	$-0.723757\pi$
$491$	−28.6498	−1.29295	−0.646474	+	0.762936i	$0.723757\pi$
$492$	30.1499	1.35926
$493$	−0.166350	−0.00749204
$494$	0.760459	0.0342147
$495$	0.194957	0.00876268
$496$	9.64009	0.432853
$497$	14.7184	0.660211
$498$	7.77404	0.348363
$499$	5.22314	0.233820	0.116910	−	0.993143i	$-0.462701\pi$
$499$	5.22314	0.233820	0.116910	+	0.993143i	$0.462701\pi$
$500$	2.53690	0.113454
$501$	−57.4698	−2.56756
$502$	1.38155	0.0616616
$503$	2.57489	0.114809	0.0574044	−	0.998351i	$-0.481718\pi$
$503$	2.57489	0.114809	0.0574044	+	0.998351i	$0.481718\pi$
$504$	−23.9364	−1.06621
$505$	−1.31596	−0.0585594
$506$	0.0659316	0.00293102
$507$	−35.1702	−1.56196
$508$	23.1726	1.02812
$509$	43.3283	1.92049	0.960246	−	0.279155i	$-0.0900544\pi$
$509$	43.3283	1.92049	0.960246	+	0.279155i	$0.0900544\pi$
$510$	0.00390133	0.000172754 0
$511$	−0.883291	−0.0390745
$512$	−18.0132	−0.796079
$513$	32.1785	1.42072
$514$	−2.15929	−0.0952423
$515$	0.125590	0.00553416
$516$	43.1234	1.89840
$517$	−2.16971	−0.0954236
$518$	−1.36010	−0.0597592
$519$	16.9078	0.742168
$520$	−0.0492588	−0.00216014
$521$	37.0069	1.62130	0.810650	−	0.585530i	$-0.199114\pi$
$521$	37.0069	1.62130	0.810650	+	0.585530i	$0.199114\pi$
$522$	−4.58292	−0.200589
$523$	−14.5676	−0.636998	−0.318499	−	0.947923i	$-0.603179\pi$
$523$	−14.5676	−0.636998	−0.318499	+	0.947923i	$0.603179\pi$
$524$	−14.6266	−0.638968
$525$	71.6679	3.12784
$526$	4.19517	0.182918
$527$	−0.112329	−0.00489314
$528$	3.26525	0.142102
$529$	−22.4079	−0.974258
$530$	0.410377	0.0178256
$531$	−33.2367	−1.44235
$532$	81.1812	3.51965
$533$	2.10222	0.0910572
$534$	−9.80754	−0.424414
$535$	1.21442	0.0525039
$536$	−2.11170	−0.0912116
$537$	63.1555	2.72536
$538$	5.64909	0.243550
$539$	6.85348	0.295200
$540$	−1.02447	−0.0440863
$541$	−16.1000	−0.692194	−0.346097	−	0.938199i	$-0.612493\pi$
$541$	−16.1000	−0.692194	−0.346097	+	0.938199i	$0.612493\pi$
$542$	−0.714212	−0.0306780
$543$	2.08299	0.0893896
$544$	0.124506	0.00533814
$545$	−0.131458	−0.00563103
$546$	−1.37029	−0.0586432
$547$	−17.3539	−0.741998	−0.370999	−	0.928633i	$-0.620985\pi$
$547$	−17.3539	−0.741998	−0.370999	+	0.928633i	$0.620985\pi$
$548$	22.4747	0.960070
$549$	−0.234999	−0.0100295
$550$	0.426948	0.0182051
$551$	31.6237	1.34721
$552$	−2.13906	−0.0910442
$553$	49.1584	2.09043
$554$	0.450590	0.0191438
$555$	−0.359400	−0.0152557
$556$	12.2386	0.519033
$557$	−29.8400	−1.26436	−0.632181	−	0.774821i	$-0.717840\pi$
$557$	−29.8400	−1.26436	−0.632181	+	0.774821i	$0.717840\pi$
$558$	−3.09466	−0.131007
$559$	3.00680	0.127174
$560$	−2.49214	−0.105312
$561$	−0.0380477	−0.00160638
$562$	0.609205	0.0256978
$563$	−14.5781	−0.614393	−0.307197	−	0.951646i	$-0.599391\pi$
$563$	−14.5781	−0.614393	−0.307197	+	0.951646i	$0.599391\pi$
$564$	34.5984	1.45686
$565$	0.394123	0.0165809
$566$	−6.86745	−0.288661
$567$	12.6377	0.530735
$568$	−2.84472	−0.119362
$569$	38.0042	1.59322	0.796609	−	0.604494i	$-0.206625\pi$
$569$	38.0042	1.59322	0.796609	+	0.604494i	$0.206625\pi$
$570$	−0.741655	−0.0310645
$571$	6.96810	0.291606	0.145803	−	0.989314i	$-0.453423\pi$
$571$	6.96810	0.291606	0.145803	+	0.989314i	$0.453423\pi$
$572$	0.236117	0.00987254
$573$	5.73874	0.239739
$574$	−7.75880	−0.323846
$575$	3.83399	0.159889
$576$	−28.8174	−1.20073
$577$	12.5242	0.521388	0.260694	−	0.965422i	$-0.416049\pi$
$577$	12.5242	0.521388	0.260694	+	0.965422i	$0.416049\pi$
$578$	4.39447	0.182786
$579$	42.0283	1.74664
$580$	−1.00681	−0.0418055
$581$	57.8653	2.40066
$582$	6.06816	0.251533
$583$	−4.00220	−0.165754
$584$	0.170719	0.00706442
$585$	−0.216763	−0.00896207
$586$	−0.400645	−0.0165505
$587$	−29.6045	−1.22191	−0.610955	−	0.791665i	$-0.709214\pi$
$587$	−29.6045	−1.22191	−0.610955	+	0.791665i	$0.709214\pi$
$588$	−109.287	−4.50690
$589$	21.3542	0.879883
$590$	0.252441	0.0103928
$591$	−60.6984	−2.49680
$592$	−3.60346	−0.148101
$593$	5.46348	0.224358	0.112179	−	0.993688i	$-0.464217\pi$
$593$	5.46348	0.224358	0.112179	+	0.993688i	$0.464217\pi$
$594$	−0.345425	−0.0141730
$595$	0.0290391	0.00119049
$596$	−36.9294	−1.51269
$597$	11.5231	0.471610
$598$	−0.0733061	−0.00299771
$599$	−43.2712	−1.76801	−0.884006	−	0.467476i	$-0.845163\pi$
$599$	−43.2712	−1.76801	−0.884006	+	0.467476i	$0.845163\pi$
$600$	−13.8517	−0.565494
$601$	−2.23211	−0.0910497	−0.0455249	−	0.998963i	$-0.514496\pi$
$601$	−2.23211	−0.0910497	−0.0455249	+	0.998963i	$0.514496\pi$
$602$	−11.0974	−0.452296
$603$	−9.29254	−0.378422
$604$	18.8692	0.767779
$605$	−1.43159	−0.0582026
$606$	7.07540	0.287418
$607$	−10.3308	−0.419313	−0.209656	−	0.977775i	$-0.567235\pi$
$607$	−10.3308	−0.419313	−0.209656	+	0.977775i	$0.567235\pi$
$608$	−23.6689	−0.959902
$609$	−56.9837	−2.30910
$610$	0.00178487	7.22675e−5 0
$611$	2.41239	0.0975950
$612$	0.363201	0.0146815
$613$	−26.8274	−1.08355	−0.541773	−	0.840525i	$-0.682247\pi$
$613$	−26.8274	−1.08355	−0.541773	+	0.840525i	$0.682247\pi$
$614$	−5.80338	−0.234205
$615$	−2.05024	−0.0826735
$616$	−1.77303	−0.0714376
$617$	−6.46096	−0.260108	−0.130054	−	0.991507i	$-0.541515\pi$
$617$	−6.46096	−0.260108	−0.130054	+	0.991507i	$0.541515\pi$
$618$	−0.675250	−0.0271625
$619$	−35.0762	−1.40983	−0.704916	−	0.709290i	$-0.749016\pi$
$619$	−35.0762	−1.40983	−0.704916	+	0.709290i	$0.749016\pi$
$620$	−0.679856	−0.0273037
$621$	−3.10192	−0.124476
$622$	−6.81008	−0.273059
$623$	−73.0014	−2.92474
$624$	−3.63047	−0.145335
$625$	24.7411	0.989643
$626$	4.55327	0.181985
$627$	7.23299	0.288858
$628$	−0.146924	−0.00586291
$629$	0.0419886	0.00167419
$630$	0.800024	0.0318737
$631$	14.1994	0.565269	0.282635	−	0.959228i	$-0.408792\pi$
$631$	14.1994	0.565269	0.282635	+	0.959228i	$0.408792\pi$
$632$	−9.50116	−0.377936
$633$	−26.6293	−1.05842
$634$	1.47926	0.0587488
$635$	−1.57577	−0.0625324
$636$	63.8196	2.53061
$637$	−7.62005	−0.301918
$638$	−0.339470	−0.0134397
$639$	−12.5182	−0.495213
$640$	0.998480	0.0394684
$641$	−1.99547	−0.0788161	−0.0394081	−	0.999223i	$-0.512547\pi$
$641$	−1.99547	−0.0788161	−0.0394081	+	0.999223i	$0.512547\pi$
$642$	−6.52946	−0.257697
$643$	−11.2079	−0.441995	−0.220998	−	0.975274i	$-0.570931\pi$
$643$	−11.2079	−0.441995	−0.220998	+	0.975274i	$0.570931\pi$
$644$	−7.82564	−0.308374
$645$	−2.93245	−0.115465
$646$	0.0866472	0.00340909
$647$	−43.7977	−1.72187	−0.860933	−	0.508719i	$-0.830119\pi$
$647$	−43.7977	−1.72187	−0.860933	+	0.508719i	$0.830119\pi$
$648$	−2.44258	−0.0959535
$649$	−2.46193	−0.0966391
$650$	−0.474703	−0.0186194
$651$	−38.4787	−1.50810
$652$	12.1361	0.475285
$653$	−40.9925	−1.60416	−0.802080	−	0.597217i	$-0.796273\pi$
$653$	−40.9925	−1.60416	−0.802080	+	0.597217i	$0.796273\pi$
$654$	0.706797	0.0276380
$655$	0.994632	0.0388635
$656$	−20.5563	−0.802588
$657$	0.751251	0.0293091
$658$	−8.90359	−0.347098
$659$	45.1753	1.75978	0.879889	−	0.475179i	$-0.157617\pi$
$659$	45.1753	1.75978	0.879889	+	0.475179i	$0.157617\pi$
$660$	−0.230278	−0.00896356
$661$	−34.7264	−1.35070	−0.675351	−	0.737497i	$-0.736008\pi$
$661$	−34.7264	−1.35070	−0.675351	+	0.737497i	$0.736008\pi$
$662$	−8.89795	−0.345829
$663$	0.0423034	0.00164293
$664$	−11.1840	−0.434023
$665$	−5.52043	−0.214073
$666$	1.15678	0.0448243
$667$	−3.04844	−0.118036
$668$	40.6365	1.57227
$669$	−45.8166	−1.77137
$670$	0.0705791	0.00272671
$671$	−0.0174070	−0.000671990 0
$672$	42.6498	1.64525
$673$	10.4127	0.401381	0.200690	−	0.979655i	$-0.435682\pi$
$673$	10.4127	0.401381	0.200690	+	0.979655i	$0.435682\pi$
$674$	−2.90280	−0.111812
$675$	−20.0869	−0.773144
$676$	24.8686	0.956485
$677$	−8.88212	−0.341367	−0.170684	−	0.985326i	$-0.554598\pi$
$677$	−8.88212	−0.341367	−0.170684	+	0.985326i	$0.554598\pi$
$678$	−2.11905	−0.0813816
$679$	45.1677	1.73338
$680$	−0.00561258	−0.000215233 0
$681$	48.6929	1.86591
$682$	−0.229230	−0.00877765
$683$	1.44313	0.0552199	0.0276099	−	0.999619i	$-0.491210\pi$
$683$	1.44313	0.0552199	0.0276099	+	0.999619i	$0.491210\pi$
$684$	−69.0457	−2.64003
$685$	−1.52831	−0.0583936
$686$	18.6032	0.710274
$687$	28.5326	1.08859
$688$	−29.4016	−1.12093
$689$	4.44986	0.169526
$690$	0.0714934	0.00272171
$691$	35.8543	1.36396	0.681981	−	0.731370i	$-0.261119\pi$
$691$	35.8543	1.36396	0.681981	+	0.731370i	$0.261119\pi$
$692$	−11.9554	−0.454475
$693$	−7.80224	−0.296383
$694$	−7.00545	−0.265923
$695$	−0.832242	−0.0315687
$696$	11.0136	0.417469
$697$	0.239528	0.00907278
$698$	4.09715	0.155079
$699$	−6.22164	−0.235324
$700$	−50.6759	−1.91537
$701$	43.5491	1.64483	0.822413	−	0.568890i	$-0.192627\pi$
$701$	43.5491	1.64483	0.822413	+	0.568890i	$0.192627\pi$
$702$	0.384062	0.0144955
$703$	−7.98216	−0.301053
$704$	−2.13458	−0.0804502
$705$	−2.35274	−0.0886093
$706$	−3.30493	−0.124383
$707$	52.6650	1.98067
$708$	39.2582	1.47541
$709$	−26.5387	−0.996680	−0.498340	−	0.866982i	$-0.666057\pi$
$709$	−26.5387	−0.996680	−0.498340	+	0.866982i	$0.666057\pi$
$710$	0.0950788	0.00356825
$711$	−41.8099	−1.56799
$712$	14.1095	0.528774
$713$	−2.05848	−0.0770907
$714$	−0.156132	−0.00584310
$715$	−0.0160563	−0.000600470 0
$716$	−44.6568	−1.66890
$717$	20.5078	0.765877
$718$	5.75189	0.214659
$719$	−30.7632	−1.14727	−0.573637	−	0.819110i	$-0.694468\pi$
$719$	−30.7632	−1.14727	−0.573637	+	0.819110i	$0.694468\pi$
$720$	2.11959	0.0789926
$721$	−5.02615	−0.187184
$722$	−11.5599	−0.430216
$723$	−1.92216	−0.0714859
$724$	−1.47287	−0.0547387
$725$	−19.7405	−0.733145
$726$	7.69713	0.285667
$727$	−2.77697	−0.102992	−0.0514961	−	0.998673i	$-0.516399\pi$
$727$	−2.77697	−0.102992	−0.0514961	+	0.998673i	$0.516399\pi$
$728$	1.97135	0.0730631
$729$	−43.8128	−1.62270
$730$	−0.00570594	−0.000211186 0
$731$	0.342597	0.0126714
$732$	0.277574	0.0102594
$733$	−17.8354	−0.658766	−0.329383	−	0.944196i	$-0.606841\pi$
$733$	−17.8354	−0.658766	−0.329383	+	0.944196i	$0.606841\pi$
$734$	−7.19958	−0.265741
$735$	7.43163	0.274120
$736$	2.28162	0.0841016
$737$	−0.688324	−0.0253547
$738$	6.59897	0.242911
$739$	−22.5867	−0.830863	−0.415432	−	0.909624i	$-0.636369\pi$
$739$	−22.5867	−0.830863	−0.415432	+	0.909624i	$0.636369\pi$
$740$	0.254130	0.00934199
$741$	−8.04201	−0.295431
$742$	−16.4234	−0.602922
$743$	33.3637	1.22400	0.611998	−	0.790859i	$-0.290366\pi$
$743$	33.3637	1.22400	0.611998	+	0.790859i	$0.290366\pi$
$744$	7.43702	0.272655
$745$	2.51125	0.0920051
$746$	−0.558089	−0.0204331
$747$	−49.2152	−1.80069
$748$	0.0269033	0.000983682 0
$749$	−48.6014	−1.77586
$750$	0.927535	0.0338688
$751$	−51.7658	−1.88896	−0.944481	−	0.328567i	$-0.893434\pi$
$751$	−51.7658	−1.88896	−0.944481	+	0.328567i	$0.893434\pi$
$752$	−23.5893	−0.860213
$753$	−14.6102	−0.532425
$754$	0.377440	0.0137455
$755$	−1.28313	−0.0466980
$756$	40.9997	1.49115
$757$	−26.5615	−0.965395	−0.482698	−	0.875787i	$-0.660343\pi$
$757$	−26.5615	−0.965395	−0.482698	+	0.875787i	$0.660343\pi$
$758$	−1.15455	−0.0419353
$759$	−0.697240	−0.0253082
$760$	1.06697	0.0387030
$761$	11.0897	0.402002	0.201001	−	0.979591i	$-0.435581\pi$
$761$	11.0897	0.402002	0.201001	+	0.979591i	$0.435581\pi$
$762$	8.47229	0.306919
$763$	5.26098	0.190460
$764$	−4.05783	−0.146807
$765$	−0.0246982	−0.000892965 0
$766$	−0.881087	−0.0318350
$767$	2.73730	0.0988381
$768$	29.8467	1.07700
$769$	27.6463	0.996952	0.498476	−	0.866903i	$-0.333893\pi$
$769$	27.6463	0.996952	0.498476	+	0.866903i	$0.333893\pi$
$770$	0.0592599	0.00213558
$771$	22.8350	0.822381
$772$	−29.7179	−1.06957
$773$	4.89548	0.176078	0.0880392	−	0.996117i	$-0.471940\pi$
$773$	4.89548	0.176078	0.0880392	+	0.996117i	$0.471940\pi$
$774$	9.43849	0.339260
$775$	−13.3299	−0.478826
$776$	−8.72986	−0.313384
$777$	14.3833	0.515998
$778$	2.21815	0.0795246
$779$	−45.5351	−1.63146
$780$	0.256035	0.00916753
$781$	−0.927257	−0.0331799
$782$	−0.00835255	−0.000298687 0
$783$	15.9712	0.570765
$784$	74.5118	2.66113
$785$	0.00999103	0.000356595 0
$786$	−5.34775	−0.190748
$787$	0.248889	0.00887193	0.00443596	−	0.999990i	$-0.498588\pi$
$787$	0.248889	0.00887193	0.00443596	+	0.999990i	$0.498588\pi$
$788$	42.9194	1.52894
$789$	−44.3648	−1.57943
$790$	0.317556	0.0112982
$791$	−15.7729	−0.560821
$792$	1.50799	0.0535841
$793$	0.0193540	0.000687281 0
$794$	−3.83922	−0.136249
$795$	−4.33982	−0.153918
$796$	−8.14792	−0.288795
$797$	24.3345	0.861971	0.430985	−	0.902359i	$-0.358166\pi$
$797$	24.3345	0.861971	0.430985	+	0.902359i	$0.358166\pi$
$798$	29.6812	1.05070
$799$	0.274870	0.00972419
$800$	14.7749	0.522372
$801$	62.0887	2.19380
$802$	7.64780	0.270053
$803$	0.0556472	0.00196375
$804$	10.9761	0.387097
$805$	0.532154	0.0187560
$806$	0.254869	0.00897739
$807$	−59.7403	−2.10296
$808$	−10.1789	−0.358093
$809$	30.2503	1.06355	0.531773	−	0.846887i	$-0.321526\pi$
$809$	30.2503	1.06355	0.531773	+	0.846887i	$0.321526\pi$
$810$	0.0816380	0.00286847
$811$	5.60837	0.196937	0.0984683	−	0.995140i	$-0.468606\pi$
$811$	5.60837	0.196937	0.0984683	+	0.995140i	$0.468606\pi$
$812$	40.2928	1.41400
$813$	7.55294	0.264893
$814$	0.0856857	0.00300328
$815$	−0.825269	−0.0289079
$816$	−0.413659	−0.0144810
$817$	−65.1287	−2.27857
$818$	−5.76155	−0.201448
$819$	8.67493	0.303127
$820$	1.44971	0.0506260
$821$	44.9374	1.56833	0.784163	−	0.620555i	$-0.213093\pi$
$821$	44.9374	1.56833	0.784163	+	0.620555i	$0.213093\pi$
$822$	8.21711	0.286605
$823$	−12.4536	−0.434105	−0.217053	−	0.976160i	$-0.569644\pi$
$823$	−12.4536	−0.434105	−0.217053	+	0.976160i	$0.569644\pi$
$824$	0.971437	0.0338416
$825$	−4.51506	−0.157194
$826$	−10.1027	−0.351519
$827$	−4.48831	−0.156074	−0.0780369	−	0.996950i	$-0.524865\pi$
$827$	−4.48831	−0.156074	−0.0780369	+	0.996950i	$0.524865\pi$
$828$	6.65581	0.231306
$829$	17.8137	0.618696	0.309348	−	0.950949i	$-0.399889\pi$
$829$	17.8137	0.618696	0.309348	+	0.950949i	$0.399889\pi$
$830$	0.373801	0.0129748
$831$	−4.76509	−0.165299
$832$	2.37334	0.0822808
$833$	−0.868234	−0.0300825
$834$	4.47464	0.154944
$835$	−2.76334	−0.0956293
$836$	−5.11440	−0.176885
$837$	10.7847	0.372774
$838$	4.81996	0.166503
$839$	−0.537968	−0.0185727	−0.00928636	−	0.999957i	$-0.502956\pi$
$839$	−0.537968	−0.0185727	−0.00928636	+	0.999957i	$0.502956\pi$
$840$	−1.92260	−0.0663361
$841$	−13.3042	−0.458764
$842$	−7.99466	−0.275514
$843$	−6.44247	−0.221891
$844$	18.8294	0.648135
$845$	−1.69110	−0.0581756
$846$	7.57262	0.260352
$847$	57.2928	1.96860
$848$	−43.5124	−1.49422
$849$	72.6247	2.49247
$850$	−0.0540880	−0.00185520
$851$	0.769458	0.0263767
$852$	14.7862	0.506565
$853$	−30.2356	−1.03525	−0.517623	−	0.855609i	$-0.673183\pi$
$853$	−30.2356	−1.03525	−0.517623	+	0.855609i	$0.673183\pi$
$854$	−0.0714312	−0.00244432
$855$	4.69520	0.160572
$856$	9.39350	0.321063
$857$	−24.2769	−0.829283	−0.414642	−	0.909985i	$-0.636093\pi$
$857$	−24.2769	−0.829283	−0.414642	+	0.909985i	$0.636093\pi$
$858$	0.0863282	0.00294720
$859$	−12.2241	−0.417082	−0.208541	−	0.978014i	$-0.566871\pi$
$859$	−12.2241	−0.417082	−0.208541	+	0.978014i	$0.566871\pi$
$860$	2.07352	0.0707063
$861$	82.0510	2.79629
$862$	2.97047	0.101174
$863$	12.6714	0.431338	0.215669	−	0.976467i	$-0.430807\pi$
$863$	12.6714	0.431338	0.215669	+	0.976467i	$0.430807\pi$
$864$	−11.9537	−0.406675
$865$	0.812981	0.0276422
$866$	3.65124	0.124074
$867$	−46.4725	−1.57829
$868$	27.2080	0.923501
$869$	−3.09697	−0.105058
$870$	−0.368107	−0.0124800
$871$	0.765314	0.0259317
$872$	−1.01682	−0.0344340
$873$	−38.4158	−1.30018
$874$	1.58785	0.0537097
$875$	6.90401	0.233398
$876$	−0.887357	−0.0299810
$877$	26.2367	0.885949	0.442974	−	0.896534i	$-0.353923\pi$
$877$	26.2367	0.885949	0.442974	+	0.896534i	$0.353923\pi$
$878$	1.04548	0.0352834
$879$	4.23690	0.142907
$880$	0.157004	0.00529261
$881$	−4.12088	−0.138836	−0.0694180	−	0.997588i	$-0.522114\pi$
$881$	−4.12088	−0.138836	−0.0694180	+	0.997588i	$0.522114\pi$
$882$	−23.9197	−0.805419
$883$	7.53365	0.253528	0.126764	−	0.991933i	$-0.459541\pi$
$883$	7.53365	0.253528	0.126764	+	0.991933i	$0.459541\pi$
$884$	−0.0299125	−0.00100607
$885$	−2.66961	−0.0897380
$886$	3.63157	0.122005
$887$	19.9816	0.670918	0.335459	−	0.942055i	$-0.391109\pi$
$887$	19.9816	0.670918	0.335459	+	0.942055i	$0.391109\pi$
$888$	−2.77995	−0.0932890
$889$	63.0626	2.11505
$890$	−0.471579	−0.0158074
$891$	−0.796176	−0.0266729
$892$	32.3966	1.08472
$893$	−52.2536	−1.74860
$894$	−13.5020	−0.451575
$895$	3.03672	0.101506
$896$	−39.9595	−1.33495
$897$	0.775228	0.0258841
$898$	−2.38448	−0.0795712
$899$	10.5987	0.353488
$900$	43.1005	1.43668
$901$	0.507020	0.0168913
$902$	0.488803	0.0162754
$903$	117.357	3.90541
$904$	3.04853	0.101393
$905$	0.100157	0.00332933
$906$	6.89891	0.229201
$907$	−5.73563	−0.190448	−0.0952242	−	0.995456i	$-0.530357\pi$
$907$	−5.73563	−0.190448	−0.0952242	+	0.995456i	$0.530357\pi$
$908$	−34.4304	−1.14261
$909$	−44.7923	−1.48567
$910$	−0.0658883	−0.00218417
$911$	19.7041	0.652826	0.326413	−	0.945227i	$-0.394160\pi$
$911$	19.7041	0.652826	0.326413	+	0.945227i	$0.394160\pi$
$912$	78.6378	2.60396
$913$	−3.64550	−0.120648
$914$	−0.466908	−0.0154439
$915$	−0.0188754	−0.000624002 0
$916$	−20.1752	−0.666607
$917$	−39.8054	−1.31449
$918$	0.0437603	0.00144430
$919$	45.9787	1.51670	0.758348	−	0.651849i	$-0.226007\pi$
$919$	45.9787	1.51670	0.758348	+	0.651849i	$0.226007\pi$
$920$	−0.102853	−0.00339096
$921$	61.3720	2.02228
$922$	−9.04596	−0.297913
$923$	1.03097	0.0339349
$924$	9.21579	0.303177
$925$	4.98272	0.163831
$926$	7.66595	0.251919
$927$	4.27481	0.140403
$928$	−11.7476	−0.385635
$929$	12.4913	0.409826	0.204913	−	0.978780i	$-0.434309\pi$
$929$	12.4913	0.409826	0.204913	+	0.978780i	$0.434309\pi$
$930$	−0.248567	−0.00815083
$931$	165.054	5.40943
$932$	4.39928	0.144103
$933$	72.0180	2.35776
$934$	4.29995	0.140699
$935$	−0.00182946	−5.98298e−5 0
$936$	−1.67666	−0.0548033
$937$	42.9624	1.40352	0.701760	−	0.712413i	$-0.252398\pi$
$937$	42.9624	1.40352	0.701760	+	0.712413i	$0.252398\pi$
$938$	−2.82460	−0.0922263
$939$	−48.1518	−1.57138
$940$	1.66361	0.0542609
$941$	−34.8738	−1.13685	−0.568426	−	0.822734i	$-0.692447\pi$
$941$	−34.8738	−1.13685	−0.568426	+	0.822734i	$0.692447\pi$
$942$	−0.0537179	−0.00175022
$943$	4.38945	0.142940
$944$	−26.7663	−0.871170
$945$	−2.78804	−0.0906948
$946$	0.699134	0.0227308
$947$	−4.01790	−0.130564	−0.0652822	−	0.997867i	$-0.520795\pi$
$947$	−4.01790	−0.130564	−0.0652822	+	0.997867i	$0.520795\pi$
$948$	49.3847	1.60394
$949$	−0.0618714	−0.00200843
$950$	10.2823	0.333602
$951$	−15.6434	−0.507274
$952$	0.224617	0.00727988
$953$	−9.34681	−0.302773	−0.151386	−	0.988475i	$-0.548374\pi$
$953$	−9.34681	−0.302773	−0.151386	+	0.988475i	$0.548374\pi$
$954$	13.9683	0.452241
$955$	0.275938	0.00892913
$956$	−14.5009	−0.468993
$957$	3.58996	0.116047
$958$	−4.32408	−0.139705
$959$	61.1633	1.97506
$960$	−2.31465	−0.0747051
$961$	−23.8431	−0.769133
$962$	−0.0952698	−0.00307162
$963$	41.3361	1.33204
$964$	1.35915	0.0437752
$965$	2.02086	0.0650538
$966$	−2.86119	−0.0920572
$967$	54.5512	1.75425	0.877124	−	0.480264i	$-0.159459\pi$
$967$	54.5512	1.75425	0.877124	+	0.480264i	$0.159459\pi$
$968$	−11.0733	−0.355911
$969$	−0.916312	−0.0294362
$970$	0.291777	0.00936840
$971$	−21.0107	−0.674267	−0.337134	−	0.941457i	$-0.609457\pi$
$971$	−21.0107	−0.674267	−0.337134	+	0.941457i	$0.609457\pi$
$972$	36.0755	1.15712
$973$	33.3066	1.06776
$974$	4.81316	0.154224
$975$	5.02008	0.160771
$976$	−0.189251	−0.00605777
$977$	−50.8794	−1.62778	−0.813888	−	0.581021i	$-0.802653\pi$
$977$	−50.8794	−1.62778	−0.813888	+	0.581021i	$0.802653\pi$
$978$	4.43715	0.141884
$979$	4.59908	0.146987
$980$	−5.25486	−0.167860
$981$	−4.47453	−0.142861
$982$	7.40670	0.236357
$983$	54.4112	1.73545	0.867724	−	0.497047i	$-0.165582\pi$
$983$	54.4112	1.73545	0.867724	+	0.497047i	$0.165582\pi$
$984$	−15.8585	−0.505551
$985$	−2.91858	−0.0929937
$986$	0.0430057	0.00136958
$987$	94.1573	2.99706
$988$	5.68646	0.180910
$989$	6.27823	0.199636
$990$	−0.0504014	−0.00160186
$991$	19.1229	0.607459	0.303730	−	0.952758i	$-0.401768\pi$
$991$	19.1229	0.607459	0.303730	+	0.952758i	$0.401768\pi$
$992$	−7.93269	−0.251863
$993$	94.0977	2.98610
$994$	−3.80508	−0.120690
$995$	0.554069	0.0175652
$996$	58.1316	1.84197
$997$	−34.1851	−1.08265	−0.541327	−	0.840812i	$-0.682078\pi$
$997$	−34.1851	−1.08265	−0.541327	+	0.840812i	$0.682078\pi$
$998$	−1.35031	−0.0427434
$999$	−4.03131	−0.127545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.39	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.39	✓	79	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)

\(f(q)\)	\(=\)	\(q-0.258525 q^{2} +2.73396 q^{3} -1.93316 q^{4} +0.131458 q^{5} -0.706797 q^{6} -5.26098 q^{7} +1.01682 q^{8} +4.47453 q^{9} +O(q^{10})\)	\(q-0.258525 q^{2} +2.73396 q^{3} -1.93316 q^{4} +0.131458 q^{5} -0.706797 q^{6} -5.26098 q^{7} +1.01682 q^{8} +4.47453 q^{9} -0.0339852 q^{10} +0.331440 q^{11} -5.28519 q^{12} -0.368513 q^{13} +1.36010 q^{14} +0.359400 q^{15} +3.60346 q^{16} -0.0419886 q^{17} -1.15678 q^{18} +7.98216 q^{19} -0.254130 q^{20} -14.3833 q^{21} -0.0856857 q^{22} -0.769458 q^{23} +2.77995 q^{24} -4.98272 q^{25} +0.0952698 q^{26} +4.03131 q^{27} +10.1703 q^{28} +3.96180 q^{29} -0.0929140 q^{30} +2.67524 q^{31} -2.96523 q^{32} +0.906145 q^{33} +0.0108551 q^{34} -0.691596 q^{35} -8.65000 q^{36} -1.00000 q^{37} -2.06359 q^{38} -1.00750 q^{39} +0.133669 q^{40} -5.70460 q^{41} +3.71844 q^{42} -8.15928 q^{43} -0.640729 q^{44} +0.588212 q^{45} +0.198924 q^{46} -6.54630 q^{47} +9.85170 q^{48} +20.6779 q^{49} +1.28816 q^{50} -0.114795 q^{51} +0.712396 q^{52} -12.0752 q^{53} -1.04219 q^{54} +0.0435704 q^{55} -5.34948 q^{56} +21.8229 q^{57} -1.02422 q^{58} -7.42797 q^{59} -0.694780 q^{60} -0.0525192 q^{61} -0.691616 q^{62} -23.5404 q^{63} -6.44032 q^{64} -0.0484438 q^{65} -0.234261 q^{66} -2.07676 q^{67} +0.0811708 q^{68} -2.10367 q^{69} +0.178795 q^{70} -2.79766 q^{71} +4.54980 q^{72} +0.167895 q^{73} +0.258525 q^{74} -13.6225 q^{75} -15.4308 q^{76} -1.74370 q^{77} +0.260464 q^{78} -9.34397 q^{79} +0.473702 q^{80} -2.40217 q^{81} +1.47478 q^{82} -10.9990 q^{83} +27.8053 q^{84} -0.00551973 q^{85} +2.10938 q^{86} +10.8314 q^{87} +0.337016 q^{88} +13.8760 q^{89} -0.152068 q^{90} +1.93874 q^{91} +1.48749 q^{92} +7.31399 q^{93} +1.69238 q^{94} +1.04932 q^{95} -8.10681 q^{96} -8.58543 q^{97} -5.34575 q^{98} +1.48304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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