LMFDB - Embedded newform 4033.2.a.d.1.59

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			1.59
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)

$f(q)$	$=$	$q+1.36683 q^{2} -1.35767 q^{3} -0.131769 q^{4} -3.35463 q^{5} -1.85571 q^{6} +0.187605 q^{7} -2.91377 q^{8} -1.15672 q^{9} +O(q^{10})$	\(q+1.36683 q^{2} -1.35767 q^{3} -0.131769 q^{4} -3.35463 q^{5} -1.85571 q^{6} +0.187605 q^{7} -2.91377 q^{8} -1.15672 q^{9} -4.58522 q^{10} +3.88280 q^{11} +0.178900 q^{12} +2.16883 q^{13} +0.256425 q^{14} +4.55450 q^{15} -3.71910 q^{16} +5.37477 q^{17} -1.58105 q^{18} +5.11965 q^{19} +0.442038 q^{20} -0.254707 q^{21} +5.30714 q^{22} -6.17876 q^{23} +3.95595 q^{24} +6.25357 q^{25} +2.96443 q^{26} +5.64347 q^{27} -0.0247206 q^{28} -3.55860 q^{29} +6.22523 q^{30} -4.97257 q^{31} +0.744158 q^{32} -5.27158 q^{33} +7.34641 q^{34} -0.629347 q^{35} +0.152421 q^{36} -1.00000 q^{37} +6.99770 q^{38} -2.94456 q^{39} +9.77464 q^{40} +0.281174 q^{41} -0.348141 q^{42} +4.35948 q^{43} -0.511634 q^{44} +3.88038 q^{45} -8.44533 q^{46} +10.6360 q^{47} +5.04932 q^{48} -6.96480 q^{49} +8.54758 q^{50} -7.29718 q^{51} -0.285785 q^{52} +2.07149 q^{53} +7.71368 q^{54} -13.0254 q^{55} -0.546639 q^{56} -6.95081 q^{57} -4.86401 q^{58} +7.25928 q^{59} -0.600143 q^{60} -12.0140 q^{61} -6.79667 q^{62} -0.217007 q^{63} +8.45534 q^{64} -7.27563 q^{65} -7.20536 q^{66} -13.1088 q^{67} -0.708229 q^{68} +8.38874 q^{69} -0.860211 q^{70} -1.96858 q^{71} +3.37043 q^{72} +0.287921 q^{73} -1.36683 q^{74} -8.49030 q^{75} -0.674613 q^{76} +0.728434 q^{77} -4.02472 q^{78} +6.57383 q^{79} +12.4762 q^{80} -4.19182 q^{81} +0.384317 q^{82} -9.01294 q^{83} +0.0335625 q^{84} -18.0304 q^{85} +5.95868 q^{86} +4.83142 q^{87} -11.3136 q^{88} +2.10679 q^{89} +5.30383 q^{90} +0.406884 q^{91} +0.814170 q^{92} +6.75112 q^{93} +14.5376 q^{94} -17.1746 q^{95} -1.01032 q^{96} +8.99215 q^{97} -9.51972 q^{98} -4.49132 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.36683	0.966496	0.483248	−	0.875483i	$-0.339457\pi$
$2$	1.36683	0.966496	0.483248	+	0.875483i	$0.339457\pi$
$3$	−1.35767	−0.783853	−0.391927	−	0.919997i	$-0.628191\pi$
$3$	−1.35767	−0.783853	−0.391927	+	0.919997i	$0.628191\pi$
$4$	−0.131769	−0.0658846
$5$	−3.35463	−1.50024	−0.750119	−	0.661303i	$-0.770004\pi$
$5$	−3.35463	−1.50024	−0.750119	+	0.661303i	$0.770004\pi$
$6$	−1.85571	−0.757591
$7$	0.187605	0.0709081	0.0354540	−	0.999371i	$-0.488712\pi$
$7$	0.187605	0.0709081	0.0354540	+	0.999371i	$0.488712\pi$
$8$	−2.91377	−1.03017
$9$	−1.15672	−0.385574
$10$	−4.58522	−1.44997
$11$	3.88280	1.17071	0.585354	−	0.810778i	$-0.300955\pi$
$11$	3.88280	1.17071	0.585354	+	0.810778i	$0.300955\pi$
$12$	0.178900	0.0516439
$13$	2.16883	0.601525	0.300763	−	0.953699i	$-0.402759\pi$
$13$	2.16883	0.601525	0.300763	+	0.953699i	$0.402759\pi$
$14$	0.256425	0.0685324
$15$	4.55450	1.17597
$16$	−3.71910	−0.929775
$17$	5.37477	1.30357	0.651786	−	0.758403i	$-0.274020\pi$
$17$	5.37477	1.30357	0.651786	+	0.758403i	$0.274020\pi$
$18$	−1.58105	−0.372656
$19$	5.11965	1.17453	0.587264	−	0.809395i	$-0.300205\pi$
$19$	5.11965	1.17453	0.587264	+	0.809395i	$0.300205\pi$
$20$	0.442038	0.0988426
$21$	−0.254707	−0.0555815
$22$	5.30714	1.13149
$23$	−6.17876	−1.28836	−0.644180	−	0.764874i	$-0.722801\pi$
$23$	−6.17876	−1.28836	−0.644180	+	0.764874i	$0.722801\pi$
$24$	3.95595	0.807505
$25$	6.25357	1.25071
$26$	2.96443	0.581372
$27$	5.64347	1.08609
$28$	−0.0247206	−0.00467175
$29$	−3.55860	−0.660816	−0.330408	−	0.943838i	$-0.607186\pi$
$29$	−3.55860	−0.660816	−0.330408	+	0.943838i	$0.607186\pi$
$30$	6.22523	1.13657
$31$	−4.97257	−0.893100	−0.446550	−	0.894759i	$-0.647347\pi$
$31$	−4.97257	−0.893100	−0.446550	+	0.894759i	$0.647347\pi$
$32$	0.744158	0.131550
$33$	−5.27158	−0.917663
$34$	7.34641	1.25990
$35$	−0.629347	−0.106379
$36$	0.152421	0.0254034
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	6.99770	1.13518
$39$	−2.94456	−0.471507
$40$	9.77464	1.54551
$41$	0.281174	0.0439120	0.0219560	−	0.999759i	$-0.493011\pi$
$41$	0.281174	0.0439120	0.0219560	+	0.999759i	$0.493011\pi$
$42$	−0.348141	−0.0537194
$43$	4.35948	0.664815	0.332407	−	0.943136i	$-0.392139\pi$
$43$	4.35948	0.664815	0.332407	+	0.943136i	$0.392139\pi$
$44$	−0.511634	−0.0771317
$45$	3.88038	0.578453
$46$	−8.44533	−1.24520
$47$	10.6360	1.55142	0.775708	−	0.631091i	$-0.217393\pi$
$47$	10.6360	1.55142	0.775708	+	0.631091i	$0.217393\pi$
$48$	5.04932	0.728807
$49$	−6.96480	−0.994972
$50$	8.54758	1.20881
$51$	−7.29718	−1.02181
$52$	−0.285785	−0.0396313
$53$	2.07149	0.284541	0.142271	−	0.989828i	$-0.454560\pi$
$53$	2.07149	0.284541	0.142271	+	0.989828i	$0.454560\pi$
$54$	7.71368	1.04970
$55$	−13.0254	−1.75634
$56$	−0.546639	−0.0730477
$57$	−6.95081	−0.920658
$58$	−4.86401	−0.638676
$59$	7.25928	0.945078	0.472539	−	0.881310i	$-0.343338\pi$
$59$	7.25928	0.945078	0.472539	+	0.881310i	$0.343338\pi$
$60$	−0.600143	−0.0774781
$61$	−12.0140	−1.53824	−0.769118	−	0.639107i	$-0.779304\pi$
$61$	−12.0140	−1.53824	−0.769118	+	0.639107i	$0.779304\pi$
$62$	−6.79667	−0.863178
$63$	−0.217007	−0.0273403
$64$	8.45534	1.05692
$65$	−7.27563	−0.902431
$66$	−7.20536	−0.886918
$67$	−13.1088	−1.60149	−0.800745	−	0.599005i	$-0.795563\pi$
$67$	−13.1088	−1.60149	−0.800745	+	0.599005i	$0.795563\pi$
$68$	−0.708229	−0.0858854
$69$	8.38874	1.00989
$70$	−0.860211	−0.102815
$71$	−1.96858	−0.233627	−0.116813	−	0.993154i	$-0.537268\pi$
$71$	−1.96858	−0.233627	−0.116813	+	0.993154i	$0.537268\pi$
$72$	3.37043	0.397209
$73$	0.287921	0.0336986	0.0168493	−	0.999858i	$-0.494636\pi$
$73$	0.287921	0.0336986	0.0168493	+	0.999858i	$0.494636\pi$
$74$	−1.36683	−0.158891
$75$	−8.49030	−0.980376
$76$	−0.674613	−0.0773834
$77$	0.728434	0.0830127
$78$	−4.02472	−0.455710
$79$	6.57383	0.739614	0.369807	−	0.929109i	$-0.379424\pi$
$79$	6.57383	0.739614	0.369807	+	0.929109i	$0.379424\pi$
$80$	12.4762	1.39488
$81$	−4.19182	−0.465758
$82$	0.384317	0.0424408
$83$	−9.01294	−0.989298	−0.494649	−	0.869093i	$-0.664703\pi$
$83$	−9.01294	−0.989298	−0.494649	+	0.869093i	$0.664703\pi$
$84$	0.0335625	0.00366197
$85$	−18.0304	−1.95567
$86$	5.95868	0.642541
$87$	4.83142	0.517982
$88$	−11.3136	−1.20603
$89$	2.10679	0.223319	0.111659	−	0.993747i	$-0.464383\pi$
$89$	2.10679	0.223319	0.111659	+	0.993747i	$0.464383\pi$
$90$	5.30383	0.559073
$91$	0.406884	0.0426530
$92$	0.814170	0.0848831
$93$	6.75112	0.700059
$94$	14.5376	1.49944
$95$	−17.1746	−1.76207
$96$	−1.01032	−0.103116
$97$	8.99215	0.913014	0.456507	−	0.889720i	$-0.349100\pi$
$97$	8.99215	0.913014	0.456507	+	0.889720i	$0.349100\pi$
$98$	−9.51972	−0.961637
$99$	−4.49132	−0.451395
$100$	−0.824028	−0.0824028
$101$	−12.3102	−1.22491	−0.612454	−	0.790507i	$-0.709817\pi$
$101$	−12.3102	−1.22491	−0.612454	+	0.790507i	$0.709817\pi$
$102$	−9.97402	−0.987575
$103$	1.68424	0.165953	0.0829765	−	0.996552i	$-0.473557\pi$
$103$	1.68424	0.165953	0.0829765	+	0.996552i	$0.473557\pi$
$104$	−6.31948	−0.619676
$105$	0.854447	0.0833855
$106$	2.83138	0.275008
$107$	−9.98277	−0.965071	−0.482535	−	0.875876i	$-0.660284\pi$
$107$	−9.98277	−0.965071	−0.482535	+	0.875876i	$0.660284\pi$
$108$	−0.743636	−0.0715564
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−17.8035	−1.69750
$111$	1.35767	0.128865
$112$	−0.697722	−0.0659285
$113$	1.49758	0.140881	0.0704403	−	0.997516i	$-0.477560\pi$
$113$	1.49758	0.140881	0.0704403	+	0.997516i	$0.477560\pi$
$114$	−9.50060	−0.889812
$115$	20.7275	1.93285
$116$	0.468914	0.0435376
$117$	−2.50874	−0.231933
$118$	9.92222	0.913414
$119$	1.00833	0.0924339
$120$	−13.2708	−1.21145
$121$	4.07614	0.370558
$122$	−16.4211	−1.48670
$123$	−0.381742	−0.0344205
$124$	0.655232	0.0588415
$125$	−4.20526	−0.376130
$126$	−0.296613	−0.0264243
$127$	−17.3908	−1.54318	−0.771591	−	0.636120i	$-0.780539\pi$
$127$	−17.3908	−1.54318	−0.771591	+	0.636120i	$0.780539\pi$
$128$	10.0687	0.889957
$129$	−5.91875	−0.521117
$130$	−9.94457	−0.872196
$131$	−16.3759	−1.43077	−0.715383	−	0.698732i	$-0.753748\pi$
$131$	−16.3759	−1.43077	−0.715383	+	0.698732i	$0.753748\pi$
$132$	0.694631	0.0604599
$133$	0.960473	0.0832836
$134$	−17.9175	−1.54783
$135$	−18.9318	−1.62939
$136$	−15.6608	−1.34291
$137$	−14.4669	−1.23599	−0.617996	−	0.786181i	$-0.712055\pi$
$137$	−14.4669	−1.23599	−0.617996	+	0.786181i	$0.712055\pi$
$138$	11.4660	0.976050
$139$	−8.65939	−0.734479	−0.367240	−	0.930126i	$-0.619697\pi$
$139$	−8.65939	−0.734479	−0.367240	+	0.930126i	$0.619697\pi$
$140$	0.0829285	0.00700874
$141$	−14.4402	−1.21608
$142$	−2.69071	−0.225800
$143$	8.42114	0.704211
$144$	4.30197	0.358497
$145$	11.9378	0.991380
$146$	0.393539	0.0325695
$147$	9.45593	0.779912
$148$	0.131769	0.0108314
$149$	−5.05631	−0.414229	−0.207114	−	0.978317i	$-0.566407\pi$
$149$	−5.05631	−0.414229	−0.207114	+	0.978317i	$0.566407\pi$
$150$	−11.6048	−0.947529
$151$	8.18641	0.666201	0.333100	−	0.942891i	$-0.391905\pi$
$151$	8.18641	0.666201	0.333100	+	0.942891i	$0.391905\pi$
$152$	−14.9175	−1.20997
$153$	−6.21712	−0.502624
$154$	0.995647	0.0802315
$155$	16.6811	1.33986
$156$	0.388003	0.0310651
$157$	−14.4695	−1.15479	−0.577395	−	0.816465i	$-0.695931\pi$
$157$	−14.4695	−1.15479	−0.577395	+	0.816465i	$0.695931\pi$
$158$	8.98533	0.714834
$159$	−2.81241	−0.223039
$160$	−2.49638	−0.197356
$161$	−1.15917	−0.0913552
$162$	−5.72952	−0.450154
$163$	19.5578	1.53189	0.765944	−	0.642907i	$-0.222272\pi$
$163$	19.5578	1.53189	0.765944	+	0.642907i	$0.222272\pi$
$164$	−0.0370500	−0.00289312
$165$	17.6842	1.37671
$166$	−12.3192	−0.956153
$167$	−4.99834	−0.386783	−0.193391	−	0.981122i	$-0.561949\pi$
$167$	−4.99834	−0.386783	−0.193391	+	0.981122i	$0.561949\pi$
$168$	0.742157	0.0572586
$169$	−8.29617	−0.638167
$170$	−24.6445	−1.89015
$171$	−5.92202	−0.452868
$172$	−0.574446	−0.0438011
$173$	−8.65311	−0.657884	−0.328942	−	0.944350i	$-0.606692\pi$
$173$	−8.65311	−0.657884	−0.328942	+	0.944350i	$0.606692\pi$
$174$	6.60374	0.500628
$175$	1.17320	0.0886857
$176$	−14.4405	−1.08849
$177$	−9.85573	−0.740802
$178$	2.87962	0.215837
$179$	5.01244	0.374647	0.187324	−	0.982298i	$-0.440019\pi$
$179$	5.01244	0.374647	0.187324	+	0.982298i	$0.440019\pi$
$180$	−0.511315	−0.0381112
$181$	−12.7997	−0.951396	−0.475698	−	0.879609i	$-0.657804\pi$
$181$	−12.7997	−0.951396	−0.475698	+	0.879609i	$0.657804\pi$
$182$	0.556142	0.0412240
$183$	16.3111	1.20575
$184$	18.0035	1.32723
$185$	3.35463	0.246638
$186$	9.22766	0.676605
$187$	20.8692	1.52610
$188$	−1.40149	−0.102215
$189$	1.05874	0.0770123
$190$	−23.4747	−1.70304
$191$	−16.7087	−1.20900	−0.604499	−	0.796606i	$-0.706626\pi$
$191$	−16.7087	−1.20900	−0.604499	+	0.796606i	$0.706626\pi$
$192$	−11.4796	−0.828468
$193$	17.1337	1.23331	0.616655	−	0.787233i	$-0.288487\pi$
$193$	17.1337	1.23331	0.616655	+	0.787233i	$0.288487\pi$
$194$	12.2908	0.882425
$195$	9.87793	0.707373
$196$	0.917747	0.0655534
$197$	−13.0762	−0.931637	−0.465819	−	0.884880i	$-0.654240\pi$
$197$	−13.0762	−0.931637	−0.465819	+	0.884880i	$0.654240\pi$
$198$	−6.13889	−0.436272
$199$	19.0255	1.34868	0.674339	−	0.738421i	$-0.264428\pi$
$199$	19.0255	1.34868	0.674339	+	0.738421i	$0.264428\pi$
$200$	−18.2215	−1.28845
$201$	17.7974	1.25533
$202$	−16.8259	−1.18387
$203$	−0.667612	−0.0468572
$204$	0.961544	0.0673215
$205$	−0.943235	−0.0658784
$206$	2.30207	0.160393
$207$	7.14711	0.496759
$208$	−8.06609	−0.559283
$209$	19.8786	1.37503
$210$	1.16789	0.0805918
$211$	11.2414	0.773893	0.386947	−	0.922102i	$-0.373530\pi$
$211$	11.2414	0.773893	0.386947	+	0.922102i	$0.373530\pi$
$212$	−0.272959	−0.0187469
$213$	2.67268	0.183129
$214$	−13.6448	−0.932737
$215$	−14.6245	−0.997380
$216$	−16.4438	−1.11886
$217$	−0.932880	−0.0633280
$218$	−1.36683	−0.0925736
$219$	−0.390902	−0.0264147
$220$	1.71634	0.115716
$221$	11.6570	0.784132
$222$	1.85571	0.124547
$223$	5.00452	0.335128	0.167564	−	0.985861i	$-0.446410\pi$
$223$	5.00452	0.335128	0.167564	+	0.985861i	$0.446410\pi$
$224$	0.139608	0.00932795
$225$	−7.23364	−0.482243
$226$	2.04694	0.136161
$227$	23.1809	1.53857	0.769284	−	0.638907i	$-0.220613\pi$
$227$	23.1809	1.53857	0.769284	+	0.638907i	$0.220613\pi$
$228$	0.915903	0.0606572
$229$	3.34886	0.221299	0.110649	−	0.993859i	$-0.464707\pi$
$229$	3.34886	0.221299	0.110649	+	0.993859i	$0.464707\pi$
$230$	28.3310	1.86809
$231$	−0.988975	−0.0650698
$232$	10.3689	0.680755
$233$	8.84043	0.579156	0.289578	−	0.957154i	$-0.406485\pi$
$233$	8.84043	0.579156	0.289578	+	0.957154i	$0.406485\pi$
$234$	−3.42902	−0.224162
$235$	−35.6798	−2.32749
$236$	−0.956550	−0.0622661
$237$	−8.92512	−0.579749
$238$	1.37822	0.0893370
$239$	−16.2841	−1.05333	−0.526665	−	0.850073i	$-0.676558\pi$
$239$	−16.2841	−1.05333	−0.526665	+	0.850073i	$0.676558\pi$
$240$	−16.9386	−1.09338
$241$	−15.7797	−1.01646	−0.508229	−	0.861222i	$-0.669700\pi$
$241$	−15.7797	−1.01646	−0.508229	+	0.861222i	$0.669700\pi$
$242$	5.57140	0.358143
$243$	−11.2393	−0.721001
$244$	1.58308	0.101346
$245$	23.3644	1.49269
$246$	−0.521777	−0.0332673
$247$	11.1037	0.706509
$248$	14.4889	0.920048
$249$	12.2366	0.775465
$250$	−5.74788	−0.363528
$251$	−1.77584	−0.112090	−0.0560451	−	0.998428i	$-0.517849\pi$
$251$	−1.77584	−0.112090	−0.0560451	+	0.998428i	$0.517849\pi$
$252$	0.0285949	0.00180131
$253$	−23.9909	−1.50829
$254$	−23.7703	−1.49148
$255$	24.4794	1.53296
$256$	−3.14843	−0.196777
$257$	−29.0283	−1.81074	−0.905368	−	0.424628i	$-0.860405\pi$
$257$	−29.0283	−1.81074	−0.905368	+	0.424628i	$0.860405\pi$
$258$	−8.08994	−0.503658
$259$	−0.187605	−0.0116572
$260$	0.958704	0.0594563
$261$	4.11632	0.254794
$262$	−22.3831	−1.38283
$263$	29.3886	1.81218	0.906090	−	0.423084i	$-0.139053\pi$
$263$	29.3886	1.81218	0.906090	+	0.423084i	$0.139053\pi$
$264$	15.3602	0.945353
$265$	−6.94909	−0.426880
$266$	1.31281	0.0804933
$267$	−2.86033	−0.175049
$268$	1.72733	0.105514
$269$	2.54322	0.155063	0.0775313	−	0.996990i	$-0.475296\pi$
$269$	2.54322	0.155063	0.0775313	+	0.996990i	$0.475296\pi$
$270$	−25.8766	−1.57480
$271$	−6.33814	−0.385014	−0.192507	−	0.981296i	$-0.561662\pi$
$271$	−6.33814	−0.385014	−0.192507	+	0.981296i	$0.561662\pi$
$272$	−19.9893	−1.21203
$273$	−0.552415	−0.0334337
$274$	−19.7739	−1.19458
$275$	24.2814	1.46422
$276$	−1.10538	−0.0665359
$277$	28.1588	1.69190	0.845949	−	0.533264i	$-0.179035\pi$
$277$	28.1588	1.69190	0.845949	+	0.533264i	$0.179035\pi$
$278$	−11.8359	−0.709872
$279$	5.75188	0.344356
$280$	1.83377	0.109589
$281$	−12.3264	−0.735331	−0.367665	−	0.929958i	$-0.619843\pi$
$281$	−12.3264	−0.735331	−0.367665	+	0.929958i	$0.619843\pi$
$282$	−19.7373	−1.17534
$283$	0.551490	0.0327827	0.0163913	−	0.999866i	$-0.494782\pi$
$283$	0.551490	0.0327827	0.0163913	+	0.999866i	$0.494782\pi$
$284$	0.259398	0.0153924
$285$	23.3174	1.38121
$286$	11.5103	0.680617
$287$	0.0527497	0.00311371
$288$	−0.860785	−0.0507222
$289$	11.8881	0.699302
$290$	16.3170	0.958166
$291$	−12.2084	−0.715669
$292$	−0.0379391	−0.00222022
$293$	−1.86230	−0.108797	−0.0543984	−	0.998519i	$-0.517324\pi$
$293$	−1.86230	−0.108797	−0.0543984	+	0.998519i	$0.517324\pi$
$294$	12.9247	0.753782
$295$	−24.3522	−1.41784
$296$	2.91377	0.169360
$297$	21.9125	1.27149
$298$	−6.91112	−0.400351
$299$	−13.4007	−0.774981
$300$	1.11876	0.0645917
$301$	0.817861	0.0471407
$302$	11.1895	0.643881
$303$	16.7132	0.960147
$304$	−19.0405	−1.09205
$305$	40.3026	2.30772
$306$	−8.49776	−0.485785
$307$	−13.3187	−0.760141	−0.380071	−	0.924958i	$-0.624100\pi$
$307$	−13.3187	−0.760141	−0.380071	+	0.924958i	$0.624100\pi$
$308$	−0.0959851	−0.00546926
$309$	−2.28665	−0.130083
$310$	22.8003	1.29497
$311$	25.4224	1.44157	0.720785	−	0.693159i	$-0.243782\pi$
$311$	25.4224	1.44157	0.720785	+	0.693159i	$0.243782\pi$
$312$	8.57978	0.485735
$313$	−5.82865	−0.329455	−0.164727	−	0.986339i	$-0.552674\pi$
$313$	−5.82865	−0.329455	−0.164727	+	0.986339i	$0.552674\pi$
$314$	−19.7773	−1.11610
$315$	0.727980	0.0410170
$316$	−0.866229	−0.0487292
$317$	−2.92286	−0.164164	−0.0820822	−	0.996626i	$-0.526157\pi$
$317$	−2.92286	−0.164164	−0.0820822	+	0.996626i	$0.526157\pi$
$318$	−3.84409	−0.215566
$319$	−13.8173	−0.773622
$320$	−28.3646	−1.58563
$321$	13.5533	0.756474
$322$	−1.58439	−0.0882944
$323$	27.5169	1.53108
$324$	0.552353	0.0306863
$325$	13.5629	0.752336
$326$	26.7323	1.48056
$327$	1.35767	0.0750795
$328$	−0.819276	−0.0452369
$329$	1.99536	0.110008
$330$	24.1713	1.33059
$331$	1.16340	0.0639461	0.0319730	−	0.999489i	$-0.489821\pi$
$331$	1.16340	0.0639461	0.0319730	+	0.999489i	$0.489821\pi$
$332$	1.18763	0.0651795
$333$	1.15672	0.0633880
$334$	−6.83189	−0.373824
$335$	43.9751	2.40262
$336$	0.947279	0.0516783
$337$	34.3043	1.86867	0.934337	−	0.356392i	$-0.115993\pi$
$337$	34.3043	1.86867	0.934337	+	0.356392i	$0.115993\pi$
$338$	−11.3395	−0.616786
$339$	−2.03323	−0.110430
$340$	2.37585	0.128849
$341$	−19.3075	−1.04556
$342$	−8.09441	−0.437695
$343$	−2.61987	−0.141460
$344$	−12.7025	−0.684875
$345$	−28.1411	−1.51507
$346$	−11.8274	−0.635843
$347$	0.797050	0.0427879	0.0213939	−	0.999771i	$-0.493190\pi$
$347$	0.797050	0.0427879	0.0213939	+	0.999771i	$0.493190\pi$
$348$	−0.636632	−0.0341271
$349$	26.7856	1.43380	0.716899	−	0.697177i	$-0.245561\pi$
$349$	26.7856	1.43380	0.716899	+	0.697177i	$0.245561\pi$
$350$	1.60357	0.0857144
$351$	12.2397	0.653309
$352$	2.88942	0.154007
$353$	−5.26224	−0.280081	−0.140040	−	0.990146i	$-0.544723\pi$
$353$	−5.26224	−0.280081	−0.140040	+	0.990146i	$0.544723\pi$
$354$	−13.4711	−0.715983
$355$	6.60385	0.350496
$356$	−0.277610	−0.0147133
$357$	−1.36899	−0.0724546
$358$	6.85116	0.362095
$359$	−12.2077	−0.644299	−0.322150	−	0.946689i	$-0.604405\pi$
$359$	−12.2077	−0.644299	−0.322150	+	0.946689i	$0.604405\pi$
$360$	−11.3065	−0.595907
$361$	7.21083	0.379517
$362$	−17.4951	−0.919521
$363$	−5.53407	−0.290463
$364$	−0.0536148	−0.00281018
$365$	−0.965868	−0.0505558
$366$	22.2945	1.16535
$367$	−31.5485	−1.64682	−0.823409	−	0.567448i	$-0.807931\pi$
$367$	−31.5485	−1.64682	−0.823409	+	0.567448i	$0.807931\pi$
$368$	22.9794	1.19788
$369$	−0.325240	−0.0169313
$370$	4.58522	0.238374
$371$	0.388623	0.0201763
$372$	−0.889591	−0.0461231
$373$	15.6350	0.809549	0.404775	−	0.914416i	$-0.367350\pi$
$373$	15.6350	0.809549	0.404775	+	0.914416i	$0.367350\pi$
$374$	28.5246	1.47497
$375$	5.70937	0.294830
$376$	−30.9908	−1.59823
$377$	−7.71800	−0.397497
$378$	1.44713	0.0744322
$379$	28.8328	1.48104	0.740521	−	0.672033i	$-0.234579\pi$
$379$	28.8328	1.48104	0.740521	+	0.672033i	$0.234579\pi$
$380$	2.26308	0.116093
$381$	23.6110	1.20963
$382$	−22.8380	−1.16849
$383$	−26.7145	−1.36505	−0.682525	−	0.730863i	$-0.739118\pi$
$383$	−26.7145	−1.36505	−0.682525	+	0.730863i	$0.739118\pi$
$384$	−13.6700	−0.697595
$385$	−2.44363	−0.124539
$386$	23.4189	1.19199
$387$	−5.04271	−0.256335
$388$	−1.18489	−0.0601536
$389$	−30.0816	−1.52520	−0.762598	−	0.646873i	$-0.776076\pi$
$389$	−30.0816	−1.52520	−0.762598	+	0.646873i	$0.776076\pi$
$390$	13.5015	0.683674
$391$	−33.2094	−1.67947
$392$	20.2938	1.02499
$393$	22.2331	1.12151
$394$	−17.8729	−0.900424
$395$	−22.0528	−1.10960
$396$	0.591818	0.0297400
$397$	−4.45709	−0.223695	−0.111847	−	0.993725i	$-0.535677\pi$
$397$	−4.45709	−0.223695	−0.111847	+	0.993725i	$0.535677\pi$
$398$	26.0046	1.30349
$399$	−1.30401	−0.0652821
$400$	−23.2576	−1.16288
$401$	0.249566	0.0124627	0.00623136	−	0.999981i	$-0.498016\pi$
$401$	0.249566	0.0124627	0.00623136	+	0.999981i	$0.498016\pi$
$402$	24.3261	1.21327
$403$	−10.7847	−0.537222
$404$	1.62210	0.0807025
$405$	14.0620	0.698748
$406$	−0.912514	−0.0452873
$407$	−3.88280	−0.192463
$408$	21.2623	1.05264
$409$	−11.6562	−0.576363	−0.288182	−	0.957576i	$-0.593051\pi$
$409$	−11.6562	−0.576363	−0.288182	+	0.957576i	$0.593051\pi$
$410$	−1.28924	−0.0636712
$411$	19.6413	0.968836
$412$	−0.221931	−0.0109337
$413$	1.36188	0.0670137
$414$	9.76890	0.480115
$415$	30.2351	1.48418
$416$	1.61395	0.0791306
$417$	11.7566	0.575724
$418$	27.1707	1.32896
$419$	3.01213	0.147152	0.0735761	−	0.997290i	$-0.476559\pi$
$419$	3.01213	0.147152	0.0735761	+	0.997290i	$0.476559\pi$
$420$	−0.112590	−0.00549382
$421$	−12.3769	−0.603213	−0.301607	−	0.953432i	$-0.597523\pi$
$421$	−12.3769	−0.603213	−0.301607	+	0.953432i	$0.597523\pi$
$422$	15.3652	0.747965
$423$	−12.3029	−0.598186
$424$	−6.03585	−0.293127
$425$	33.6115	1.63040
$426$	3.65311	0.176994
$427$	−2.25389	−0.109073
$428$	1.31542	0.0635833
$429$	−11.4332	−0.551998
$430$	−19.9892	−0.963964
$431$	−9.98206	−0.480819	−0.240409	−	0.970672i	$-0.577282\pi$
$431$	−9.98206	−0.480819	−0.240409	+	0.970672i	$0.577282\pi$
$432$	−20.9886	−1.00982
$433$	−7.82269	−0.375934	−0.187967	−	0.982175i	$-0.560190\pi$
$433$	−7.82269	−0.375934	−0.187967	+	0.982175i	$0.560190\pi$
$434$	−1.27509	−0.0612063
$435$	−16.2076	−0.777097
$436$	0.131769	0.00631060
$437$	−31.6331	−1.51322
$438$	−0.534298	−0.0255297
$439$	39.2449	1.87306	0.936528	−	0.350594i	$-0.114020\pi$
$439$	39.2449	1.87306	0.936528	+	0.350594i	$0.114020\pi$
$440$	37.9530	1.80934
$441$	8.05635	0.383636
$442$	15.9331	0.757861
$443$	−15.0031	−0.712821	−0.356411	−	0.934329i	$-0.616000\pi$
$443$	−15.0031	−0.712821	−0.356411	+	0.934329i	$0.616000\pi$
$444$	−0.178900	−0.00849020
$445$	−7.06750	−0.335032
$446$	6.84034	0.323900
$447$	6.86481	0.324694
$448$	1.58627	0.0749440
$449$	−39.5349	−1.86577	−0.932885	−	0.360175i	$-0.882717\pi$
$449$	−39.5349	−1.86577	−0.932885	+	0.360175i	$0.882717\pi$
$450$	−9.88718	−0.466086
$451$	1.09174	0.0514081
$452$	−0.197335	−0.00928187
$453$	−11.1145	−0.522204
$454$	31.6844	1.48702
$455$	−1.36495	−0.0639897
$456$	20.2531	0.948437
$457$	−30.6647	−1.43444	−0.717218	−	0.696849i	$-0.754585\pi$
$457$	−30.6647	−1.43444	−0.717218	+	0.696849i	$0.754585\pi$
$458$	4.57733	0.213885
$459$	30.3324	1.41579
$460$	−2.73124	−0.127345
$461$	−19.9093	−0.927266	−0.463633	−	0.886027i	$-0.653454\pi$
$461$	−19.9093	−0.927266	−0.463633	+	0.886027i	$0.653454\pi$
$462$	−1.35176	−0.0628897
$463$	−37.3558	−1.73607	−0.868036	−	0.496500i	$-0.834618\pi$
$463$	−37.3558	−1.73607	−0.868036	+	0.496500i	$0.834618\pi$
$464$	13.2348	0.614410
$465$	−22.6475	−1.05025
$466$	12.0834	0.559752
$467$	−10.4620	−0.484126	−0.242063	−	0.970261i	$-0.577824\pi$
$467$	−10.4620	−0.484126	−0.242063	+	0.970261i	$0.577824\pi$
$468$	0.330574	0.0152808
$469$	−2.45927	−0.113559
$470$	−48.7683	−2.24951
$471$	19.6448	0.905186
$472$	−21.1519	−0.973594
$473$	16.9270	0.778304
$474$	−12.1991	−0.560325
$475$	32.0161	1.46900
$476$	−0.132867	−0.00608997
$477$	−2.39614	−0.109712
$478$	−22.2576	−1.01804
$479$	−23.2752	−1.06347	−0.531736	−	0.846910i	$-0.678460\pi$
$479$	−23.2752	−1.06347	−0.531736	+	0.846910i	$0.678460\pi$
$480$	3.38927	0.154698
$481$	−2.16883	−0.0988902
$482$	−21.5682	−0.982403
$483$	1.57377	0.0716090
$484$	−0.537110	−0.0244141
$485$	−30.1654	−1.36974
$486$	−15.3622	−0.696845
$487$	11.0128	0.499039	0.249519	−	0.968370i	$-0.419727\pi$
$487$	11.0128	0.499039	0.249519	+	0.968370i	$0.419727\pi$
$488$	35.0061	1.58465
$489$	−26.5532	−1.20078
$490$	31.9352	1.44268
$491$	19.0674	0.860502	0.430251	−	0.902709i	$-0.358425\pi$
$491$	19.0674	0.860502	0.430251	+	0.902709i	$0.358425\pi$
$492$	0.0503019	0.00226778
$493$	−19.1267	−0.861421
$494$	15.1768	0.682838
$495$	15.0667	0.677200
$496$	18.4935	0.830381
$497$	−0.369315	−0.0165660
$498$	16.7254	0.749484
$499$	−36.4642	−1.63236	−0.816181	−	0.577797i	$-0.803913\pi$
$499$	−36.4642	−1.63236	−0.816181	+	0.577797i	$0.803913\pi$
$500$	0.554124	0.0247812
$501$	6.78611	0.303181
$502$	−2.42728	−0.108335
$503$	−40.0567	−1.78604	−0.893020	−	0.450017i	$-0.851418\pi$
$503$	−40.0567	−1.78604	−0.893020	+	0.450017i	$0.851418\pi$
$504$	0.632309	0.0281653
$505$	41.2961	1.83765
$506$	−32.7915	−1.45776
$507$	11.2635	0.500229
$508$	2.29157	0.101672
$509$	2.36119	0.104658	0.0523290	−	0.998630i	$-0.483336\pi$
$509$	2.36119	0.104658	0.0523290	+	0.998630i	$0.483336\pi$
$510$	33.4592	1.48160
$511$	0.0540154	0.00238950
$512$	−24.4408	−1.08014
$513$	28.8926	1.27564
$514$	−39.6768	−1.75007
$515$	−5.65000	−0.248969
$516$	0.779909	0.0343336
$517$	41.2974	1.81626
$518$	−0.256425	−0.0112667
$519$	11.7481	0.515684
$520$	21.1995	0.929661
$521$	−16.8886	−0.739901	−0.369950	−	0.929051i	$-0.620625\pi$
$521$	−16.8886	−0.739901	−0.369950	+	0.929051i	$0.620625\pi$
$522$	5.62631	0.246257
$523$	35.9691	1.57282	0.786410	−	0.617705i	$-0.211937\pi$
$523$	35.9691	1.57282	0.786410	+	0.617705i	$0.211937\pi$
$524$	2.15784	0.0942655
$525$	−1.59282	−0.0695166
$526$	40.1693	1.75147
$527$	−26.7264	−1.16422
$528$	19.6055	0.853220
$529$	15.1770	0.659872
$530$	−9.49825	−0.412578
$531$	−8.39698	−0.364398
$532$	−0.126561	−0.00548711
$533$	0.609818	0.0264142
$534$	−3.90959	−0.169185
$535$	33.4885	1.44784
$536$	38.1959	1.64981
$537$	−6.80526	−0.293668
$538$	3.47615	0.149868
$539$	−27.0429	−1.16482
$540$	2.49463	0.107352
$541$	15.1090	0.649588	0.324794	−	0.945785i	$-0.394705\pi$
$541$	15.1090	0.649588	0.324794	+	0.945785i	$0.394705\pi$
$542$	−8.66317	−0.372115
$543$	17.3778	0.745755
$544$	3.99968	0.171485
$545$	3.35463	0.143697
$546$	−0.755059	−0.0323136
$547$	−3.28445	−0.140433	−0.0702165	−	0.997532i	$-0.522369\pi$
$547$	−3.28445	−0.140433	−0.0702165	+	0.997532i	$0.522369\pi$
$548$	1.90629	0.0814329
$549$	13.8969	0.593104
$550$	33.1885	1.41516
$551$	−18.2188	−0.776147
$552$	−24.4429	−1.04036
$553$	1.23329	0.0524446
$554$	38.4883	1.63521
$555$	−4.55450	−0.193328
$556$	1.14104	0.0483909
$557$	6.68295	0.283165	0.141583	−	0.989926i	$-0.454781\pi$
$557$	6.68295	0.283165	0.141583	+	0.989926i	$0.454781\pi$
$558$	7.86186	0.332819
$559$	9.45498	0.399903
$560$	2.34060	0.0989085
$561$	−28.3335	−1.19624
$562$	−16.8481	−0.710695
$563$	−26.5874	−1.12053	−0.560263	−	0.828314i	$-0.689300\pi$
$563$	−26.5874	−1.12053	−0.560263	+	0.828314i	$0.689300\pi$
$564$	1.90277	0.0801212
$565$	−5.02384	−0.211355
$566$	0.753794	0.0316843
$567$	−0.786408	−0.0330260
$568$	5.73598	0.240676
$569$	14.6582	0.614505	0.307253	−	0.951628i	$-0.400590\pi$
$569$	14.6582	0.614505	0.307253	+	0.951628i	$0.400590\pi$
$570$	31.8710	1.33493
$571$	20.1109	0.841614	0.420807	−	0.907150i	$-0.361747\pi$
$571$	20.1109	0.841614	0.420807	+	0.907150i	$0.361747\pi$
$572$	−1.10965	−0.0463967
$573$	22.6849	0.947676
$574$	0.0720999	0.00300939
$575$	−38.6393	−1.61137
$576$	−9.78048	−0.407520
$577$	0.0716347	0.00298219	0.00149110	−	0.999999i	$-0.499525\pi$
$577$	0.0716347	0.00298219	0.00149110	+	0.999999i	$0.499525\pi$
$578$	16.2491	0.675873
$579$	−23.2620	−0.966734
$580$	−1.57304	−0.0653167
$581$	−1.69087	−0.0701493
$582$	−16.6868	−0.691692
$583$	8.04319	0.333115
$584$	−0.838935	−0.0347154
$585$	8.41589	0.347954
$586$	−2.54546	−0.105152
$587$	−8.13809	−0.335895	−0.167948	−	0.985796i	$-0.553714\pi$
$587$	−8.13809	−0.335895	−0.167948	+	0.985796i	$0.553714\pi$
$588$	−1.24600	−0.0513842
$589$	−25.4578	−1.04897
$590$	−33.2854	−1.37034
$591$	17.7531	0.730267
$592$	3.71910	0.152854
$593$	−23.2514	−0.954819	−0.477409	−	0.878681i	$-0.658424\pi$
$593$	−23.2514	−0.954819	−0.477409	+	0.878681i	$0.658424\pi$
$594$	29.9507	1.22889
$595$	−3.38259	−0.138673
$596$	0.666266	0.0272913
$597$	−25.8304	−1.05717
$598$	−18.3165	−0.749017
$599$	24.9520	1.01951	0.509755	−	0.860319i	$-0.329736\pi$
$599$	24.9520	1.01951	0.509755	+	0.860319i	$0.329736\pi$
$600$	24.7388	1.00996
$601$	−1.42647	−0.0581868	−0.0290934	−	0.999577i	$-0.509262\pi$
$601$	−1.42647	−0.0581868	−0.0290934	+	0.999577i	$0.509262\pi$
$602$	1.11788	0.0455614
$603$	15.1632	0.617493
$604$	−1.07872	−0.0438924
$605$	−13.6740	−0.555925
$606$	22.8441	0.927979
$607$	−27.2877	−1.10757	−0.553786	−	0.832659i	$-0.686818\pi$
$607$	−27.2877	−1.10757	−0.553786	+	0.832659i	$0.686818\pi$
$608$	3.80983	0.154509
$609$	0.906399	0.0367291
$610$	55.0869	2.23040
$611$	23.0676	0.933217
$612$	0.819225	0.0331152
$613$	19.0439	0.769177	0.384588	−	0.923088i	$-0.374343\pi$
$613$	19.0439	0.769177	0.384588	+	0.923088i	$0.374343\pi$
$614$	−18.2045	−0.734674
$615$	1.28060	0.0516390
$616$	−2.12249	−0.0855175
$617$	−40.4498	−1.62845	−0.814224	−	0.580550i	$-0.802837\pi$
$617$	−40.4498	−1.62845	−0.814224	+	0.580550i	$0.802837\pi$
$618$	−3.12546	−0.125724
$619$	37.4626	1.50575	0.752874	−	0.658164i	$-0.228667\pi$
$619$	37.4626	1.50575	0.752874	+	0.658164i	$0.228667\pi$
$620$	−2.19806	−0.0882763
$621$	−34.8696	−1.39927
$622$	34.7481	1.39327
$623$	0.395244	0.0158351
$624$	10.9511	0.438396
$625$	−17.1607	−0.686429
$626$	−7.96679	−0.318417
$627$	−26.9886	−1.07782
$628$	1.90663	0.0760829
$629$	−5.37477	−0.214306
$630$	0.995026	0.0396428
$631$	31.5301	1.25519	0.627596	−	0.778539i	$-0.284039\pi$
$631$	31.5301	1.25519	0.627596	+	0.778539i	$0.284039\pi$
$632$	−19.1547	−0.761931
$633$	−15.2622	−0.606619
$634$	−3.99507	−0.158664
$635$	58.3397	2.31514
$636$	0.370589	0.0146948
$637$	−15.1055	−0.598501
$638$	−18.8860	−0.747703
$639$	2.27710	0.0900805
$640$	−33.7768	−1.33515
$641$	28.1252	1.11088	0.555438	−	0.831558i	$-0.312550\pi$
$641$	28.1252	1.11088	0.555438	+	0.831558i	$0.312550\pi$
$642$	18.5251	0.731129
$643$	−20.0237	−0.789657	−0.394829	−	0.918755i	$-0.629196\pi$
$643$	−20.0237	−0.789657	−0.394829	+	0.918755i	$0.629196\pi$
$644$	0.152743	0.00601890
$645$	19.8552	0.781799
$646$	37.6110	1.47979
$647$	−22.2690	−0.875486	−0.437743	−	0.899100i	$-0.644222\pi$
$647$	−22.2690	−0.875486	−0.437743	+	0.899100i	$0.644222\pi$
$648$	12.2140	0.479812
$649$	28.1863	1.10641
$650$	18.5382	0.727130
$651$	1.26655	0.0496399
$652$	−2.57712	−0.100928
$653$	10.7938	0.422394	0.211197	−	0.977444i	$-0.432264\pi$
$653$	10.7938	0.422394	0.211197	+	0.977444i	$0.432264\pi$
$654$	1.85571	0.0725641
$655$	54.9350	2.14649
$656$	−1.04571	−0.0408282
$657$	−0.333044	−0.0129933
$658$	2.72733	0.106322
$659$	−5.82091	−0.226750	−0.113375	−	0.993552i	$-0.536166\pi$
$659$	−5.82091	−0.226750	−0.113375	+	0.993552i	$0.536166\pi$
$660$	−2.33023	−0.0907042
$661$	−41.2378	−1.60396	−0.801982	−	0.597348i	$-0.796221\pi$
$661$	−41.2378	−1.60396	−0.801982	+	0.597348i	$0.796221\pi$
$662$	1.59017	0.0618037
$663$	−15.8263	−0.614644
$664$	26.2616	1.01915
$665$	−3.22204	−0.124945
$666$	1.58105	0.0612643
$667$	21.9877	0.851368
$668$	0.658627	0.0254830
$669$	−6.79451	−0.262691
$670$	60.1066	2.32212
$671$	−46.6480	−1.80083
$672$	−0.189542	−0.00731174
$673$	4.61595	0.177932	0.0889659	−	0.996035i	$-0.471644\pi$
$673$	4.61595	0.177932	0.0889659	+	0.996035i	$0.471644\pi$
$674$	46.8882	1.80607
$675$	35.2918	1.35838
$676$	1.09318	0.0420454
$677$	31.4453	1.20854	0.604270	−	0.796779i	$-0.293465\pi$
$677$	31.4453	1.20854	0.604270	+	0.796779i	$0.293465\pi$
$678$	−2.77908	−0.106730
$679$	1.68697	0.0647401
$680$	52.5364	2.01468
$681$	−31.4721	−1.20601
$682$	−26.3901	−1.01053
$683$	−30.3037	−1.15954	−0.579769	−	0.814781i	$-0.696857\pi$
$683$	−30.3037	−1.15954	−0.579769	+	0.814781i	$0.696857\pi$
$684$	0.780340	0.0298370
$685$	48.5312	1.85428
$686$	−3.58092	−0.136720
$687$	−4.54666	−0.173466
$688$	−16.2133	−0.618128
$689$	4.49271	0.171159
$690$	−38.4642	−1.46431
$691$	−20.9525	−0.797070	−0.398535	−	0.917153i	$-0.630481\pi$
$691$	−20.9525	−0.797070	−0.398535	+	0.917153i	$0.630481\pi$
$692$	1.14021	0.0433444
$693$	−0.842596	−0.0320076
$694$	1.08943	0.0413543
$695$	29.0491	1.10189
$696$	−14.0776	−0.533612
$697$	1.51124	0.0572424
$698$	36.6114	1.38576
$699$	−12.0024	−0.453973
$700$	−0.154592	−0.00584302
$701$	−44.9765	−1.69874	−0.849369	−	0.527800i	$-0.823017\pi$
$701$	−44.9765	−1.69874	−0.849369	+	0.527800i	$0.823017\pi$
$702$	16.7297	0.631421
$703$	−5.11965	−0.193091
$704$	32.8304	1.23734
$705$	48.4415	1.82441
$706$	−7.19259	−0.270697
$707$	−2.30945	−0.0868558
$708$	1.29868	0.0488075
$709$	−5.92931	−0.222680	−0.111340	−	0.993782i	$-0.535514\pi$
$709$	−5.92931	−0.222680	−0.111340	+	0.993782i	$0.535514\pi$
$710$	9.02635	0.338753
$711$	−7.60411	−0.285176
$712$	−6.13870	−0.230057
$713$	30.7243	1.15063
$714$	−1.87118	−0.0700271
$715$	−28.2498	−1.05648
$716$	−0.660485	−0.0246835
$717$	22.1085	0.825656
$718$	−16.6859	−0.622713
$719$	7.89895	0.294581	0.147291	−	0.989093i	$-0.452945\pi$
$719$	7.89895	0.294581	0.147291	+	0.989093i	$0.452945\pi$
$720$	−14.4315	−0.537831
$721$	0.315972	0.0117674
$722$	9.85599	0.366802
$723$	21.4236	0.796754
$724$	1.68661	0.0626824
$725$	−22.2539	−0.826491
$726$	−7.56414	−0.280732
$727$	−26.0540	−0.966288	−0.483144	−	0.875541i	$-0.660505\pi$
$727$	−26.0540	−0.966288	−0.483144	+	0.875541i	$0.660505\pi$
$728$	−1.18557	−0.0439400
$729$	27.8348	1.03092
$730$	−1.32018	−0.0488620
$731$	23.4312	0.866634
$732$	−2.14930	−0.0794404
$733$	−45.2174	−1.67014	−0.835072	−	0.550141i	$-0.814574\pi$
$733$	−45.2174	−1.67014	−0.835072	+	0.550141i	$0.814574\pi$
$734$	−43.1215	−1.59164
$735$	−31.7212	−1.17005
$736$	−4.59797	−0.169484
$737$	−50.8987	−1.87488
$738$	−0.444549	−0.0163641
$739$	0.761077	0.0279967	0.0139983	−	0.999902i	$-0.495544\pi$
$739$	0.761077	0.0279967	0.0139983	+	0.999902i	$0.495544\pi$
$740$	−0.442038	−0.0162496
$741$	−15.0751	−0.553799
$742$	0.531182	0.0195003
$743$	−53.0651	−1.94677	−0.973385	−	0.229176i	$-0.926397\pi$
$743$	−53.0651	−1.94677	−0.973385	+	0.229176i	$0.926397\pi$
$744$	−19.6712	−0.721182
$745$	16.9621	0.621442
$746$	21.3704	0.782427
$747$	10.4255	0.381448
$748$	−2.74991	−0.100547
$749$	−1.87282	−0.0684313
$750$	7.80375	0.284953
$751$	30.1768	1.10117	0.550583	−	0.834780i	$-0.314405\pi$
$751$	30.1768	1.10117	0.550583	+	0.834780i	$0.314405\pi$
$752$	−39.5562	−1.44247
$753$	2.41101	0.0878622
$754$	−10.5492	−0.384180
$755$	−27.4624	−0.999460
$756$	−0.139510	−0.00507393
$757$	−37.0441	−1.34639	−0.673195	−	0.739465i	$-0.735079\pi$
$757$	−37.0441	−1.34639	−0.673195	+	0.739465i	$0.735079\pi$
$758$	39.4096	1.43142
$759$	32.5718	1.18228
$760$	50.0427	1.81524
$761$	25.4650	0.923106	0.461553	−	0.887113i	$-0.347292\pi$
$761$	25.4650	0.923106	0.461553	+	0.887113i	$0.347292\pi$
$762$	32.2723	1.16910
$763$	−0.187605	−0.00679176
$764$	2.20169	0.0796543
$765$	20.8562	0.754056
$766$	−36.5143	−1.31932
$767$	15.7441	0.568488
$768$	4.27454	0.154244
$769$	21.4888	0.774906	0.387453	−	0.921889i	$-0.373355\pi$
$769$	21.4888	0.774906	0.387453	+	0.921889i	$0.373355\pi$
$770$	−3.34003	−0.120366
$771$	39.4110	1.41935
$772$	−2.25769	−0.0812562
$773$	−44.8206	−1.61208	−0.806042	−	0.591858i	$-0.798395\pi$
$773$	−44.8206	−1.61208	−0.806042	+	0.591858i	$0.798395\pi$
$774$	−6.89254	−0.247747
$775$	−31.0963	−1.11701
$776$	−26.2011	−0.940563
$777$	0.254707	0.00913755
$778$	−41.1165	−1.47410
$779$	1.43951	0.0515758
$780$	−1.30161	−0.0466050
$781$	−7.64359	−0.273509
$782$	−45.3917	−1.62320
$783$	−20.0829	−0.717703
$784$	25.9028	0.925100
$785$	48.5398	1.73246
$786$	30.3889	1.08394
$787$	−14.7459	−0.525634	−0.262817	−	0.964846i	$-0.584651\pi$
$787$	−14.7459	−0.525634	−0.262817	+	0.964846i	$0.584651\pi$
$788$	1.72303	0.0613806
$789$	−39.9002	−1.42048
$790$	−30.1425	−1.07242
$791$	0.280954	0.00998958
$792$	13.0867	0.465015
$793$	−26.0563	−0.925288
$794$	−6.09209	−0.216200
$795$	9.43460	0.334611
$796$	−2.50697	−0.0888572
$797$	5.29190	0.187449	0.0937244	−	0.995598i	$-0.470123\pi$
$797$	5.29190	0.187449	0.0937244	+	0.995598i	$0.470123\pi$
$798$	−1.78236	−0.0630949
$799$	57.1659	2.02239
$800$	4.65364	0.164531
$801$	−2.43697	−0.0861061
$802$	0.341115	0.0120452
$803$	1.11794	0.0394512
$804$	−2.34515	−0.0827071
$805$	3.88858	0.137054
$806$	−14.7408	−0.519223
$807$	−3.45286	−0.121546
$808$	35.8690	1.26187
$809$	23.7800	0.836061	0.418030	−	0.908433i	$-0.362721\pi$
$809$	23.7800	0.836061	0.418030	+	0.908433i	$0.362721\pi$
$810$	19.2204	0.675337
$811$	−19.7727	−0.694315	−0.347157	−	0.937807i	$-0.612853\pi$
$811$	−19.7727	−0.694315	−0.347157	+	0.937807i	$0.612853\pi$
$812$	0.0879707	0.00308717
$813$	8.60512	0.301795
$814$	−5.30714	−0.186015
$815$	−65.6094	−2.29820
$816$	27.1389	0.950053
$817$	22.3190	0.780844
$818$	−15.9321	−0.557053
$819$	−0.470652	−0.0164459
$820$	0.124289	0.00434037
$821$	−11.1999	−0.390880	−0.195440	−	0.980716i	$-0.562613\pi$
$821$	−11.1999	−0.390880	−0.195440	+	0.980716i	$0.562613\pi$
$822$	26.8464	0.936377
$823$	−35.7462	−1.24603	−0.623016	−	0.782209i	$-0.714093\pi$
$823$	−35.7462	−1.24603	−0.623016	+	0.782209i	$0.714093\pi$
$824$	−4.90748	−0.170960
$825$	−32.9661	−1.14773
$826$	1.86146	0.0647685
$827$	27.2347	0.947045	0.473522	−	0.880782i	$-0.342982\pi$
$827$	27.2347	0.947045	0.473522	+	0.880782i	$0.342982\pi$
$828$	−0.941769	−0.0327288
$829$	−19.5072	−0.677513	−0.338756	−	0.940874i	$-0.610006\pi$
$829$	−19.5072	−0.677513	−0.338756	+	0.940874i	$0.610006\pi$
$830$	41.3263	1.43446
$831$	−38.2304	−1.32620
$832$	18.3382	0.635762
$833$	−37.4342	−1.29702
$834$	16.0693	0.556435
$835$	16.7676	0.580266
$836$	−2.61939	−0.0905934
$837$	−28.0626	−0.969984
$838$	4.11708	0.142222
$839$	−52.2527	−1.80396	−0.901981	−	0.431776i	$-0.857887\pi$
$839$	−52.2527	−1.80396	−0.901981	+	0.431776i	$0.857887\pi$
$840$	−2.48966	−0.0859016
$841$	−16.3364	−0.563323
$842$	−16.9171	−0.583003
$843$	16.7352	0.576391
$844$	−1.48128	−0.0509877
$845$	27.8306	0.957403
$846$	−16.8160	−0.578145
$847$	0.764705	0.0262756
$848$	−7.70408	−0.264559
$849$	−0.748743	−0.0256968
$850$	45.9413	1.57577
$851$	6.17876	0.211805
$852$	−0.352177	−0.0120654
$853$	4.78039	0.163677	0.0818387	−	0.996646i	$-0.473921\pi$
$853$	4.78039	0.163677	0.0818387	+	0.996646i	$0.473921\pi$
$854$	−3.08069	−0.105419
$855$	19.8662	0.679410
$856$	29.0875	0.994190
$857$	30.8728	1.05459	0.527297	−	0.849681i	$-0.323205\pi$
$857$	30.8728	1.05459	0.527297	+	0.849681i	$0.323205\pi$
$858$	−15.6272	−0.533504
$859$	4.88556	0.166693	0.0833465	−	0.996521i	$-0.473439\pi$
$859$	4.88556	0.166693	0.0833465	+	0.996521i	$0.473439\pi$
$860$	1.92705	0.0657120
$861$	−0.0716168	−0.00244069
$862$	−13.6438	−0.464710
$863$	30.2712	1.03044	0.515222	−	0.857057i	$-0.327709\pi$
$863$	30.2712	1.03044	0.515222	+	0.857057i	$0.327709\pi$
$864$	4.19964	0.142875
$865$	29.0280	0.986983
$866$	−10.6923	−0.363339
$867$	−16.1402	−0.548150
$868$	0.122925	0.00417234
$869$	25.5249	0.865873
$870$	−22.1531	−0.751061
$871$	−28.4307	−0.963337
$872$	2.91377	0.0986727
$873$	−10.4014	−0.352035
$874$	−43.2371	−1.46252
$875$	−0.788928	−0.0266706
$876$	0.0515089	0.00174032
$877$	23.6018	0.796974	0.398487	−	0.917174i	$-0.369535\pi$
$877$	23.6018	0.796974	0.398487	+	0.917174i	$0.369535\pi$
$878$	53.6412	1.81030
$879$	2.52840	0.0852808
$880$	48.4426	1.63300
$881$	39.9954	1.34748	0.673740	−	0.738968i	$-0.264687\pi$
$881$	39.9954	1.34748	0.673740	+	0.738968i	$0.264687\pi$
$882$	11.0117	0.370783
$883$	18.4295	0.620201	0.310101	−	0.950704i	$-0.399637\pi$
$883$	18.4295	0.620201	0.310101	+	0.950704i	$0.399637\pi$
$884$	−1.53603	−0.0516623
$885$	33.0624	1.11138
$886$	−20.5068	−0.688939
$887$	−19.1730	−0.643766	−0.321883	−	0.946779i	$-0.604316\pi$
$887$	−19.1730	−0.643766	−0.321883	+	0.946779i	$0.604316\pi$
$888$	−3.95595	−0.132753
$889$	−3.26260	−0.109424
$890$	−9.66009	−0.323807
$891$	−16.2760	−0.545267
$892$	−0.659442	−0.0220798
$893$	54.4525	1.82218
$894$	9.38305	0.313816
$895$	−16.8149	−0.562060
$896$	1.88894	0.0631051
$897$	18.1937	0.607471
$898$	−54.0376	−1.80326
$899$	17.6954	0.590174
$900$	0.953172	0.0317724
$901$	11.1338	0.370920
$902$	1.49223	0.0496857
$903$	−1.11039	−0.0369514
$904$	−4.36361	−0.145132
$905$	42.9384	1.42732
$906$	−15.1916	−0.504708
$907$	38.4412	1.27642	0.638209	−	0.769863i	$-0.279675\pi$
$907$	38.4412	1.27642	0.638209	+	0.769863i	$0.279675\pi$
$908$	−3.05453	−0.101368
$909$	14.2395	0.472293
$910$	−1.86565	−0.0618458
$911$	24.3129	0.805521	0.402761	−	0.915305i	$-0.368051\pi$
$911$	24.3129	0.805521	0.402761	+	0.915305i	$0.368051\pi$
$912$	25.8508	0.856004
$913$	−34.9954	−1.15818
$914$	−41.9136	−1.38638
$915$	−54.7177	−1.80891
$916$	−0.441277	−0.0145802
$917$	−3.07220	−0.101453
$918$	41.4593	1.36836
$919$	−29.1779	−0.962491	−0.481246	−	0.876586i	$-0.659815\pi$
$919$	−29.1779	−0.962491	−0.481246	+	0.876586i	$0.659815\pi$
$920$	−60.3951	−1.99117
$921$	18.0825	0.595839
$922$	−27.2126	−0.896200
$923$	−4.26951	−0.140533
$924$	0.130316	0.00428710
$925$	−6.25357	−0.205616
$926$	−51.0592	−1.67791
$927$	−1.94820	−0.0639872
$928$	−2.64816	−0.0869302
$929$	−43.0198	−1.41143	−0.705717	−	0.708494i	$-0.749375\pi$
$929$	−43.0198	−1.41143	−0.705717	+	0.708494i	$0.749375\pi$
$930$	−30.9554	−1.01507
$931$	−35.6574	−1.16862
$932$	−1.16490	−0.0381574
$933$	−34.5153	−1.12998
$934$	−14.2999	−0.467906
$935$	−70.0084	−2.28952
$936$	7.30988	0.238931
$937$	49.0430	1.60216	0.801082	−	0.598554i	$-0.204258\pi$
$937$	49.0430	1.60216	0.801082	+	0.598554i	$0.204258\pi$
$938$	−3.36141	−0.109754
$939$	7.91340	0.258244
$940$	4.70150	0.153346
$941$	50.1446	1.63467	0.817333	−	0.576166i	$-0.195452\pi$
$941$	50.1446	1.63467	0.817333	+	0.576166i	$0.195452\pi$
$942$	26.8512	0.874859
$943$	−1.73730	−0.0565744
$944$	−26.9980	−0.878709
$945$	−3.55170	−0.115537
$946$	23.1364	0.752228
$947$	−5.65186	−0.183661	−0.0918304	−	0.995775i	$-0.529272\pi$
$947$	−5.65186	−0.183661	−0.0918304	+	0.995775i	$0.529272\pi$
$948$	1.17606	0.0381965
$949$	0.624451	0.0202705
$950$	43.7606	1.41978
$951$	3.96829	0.128681
$952$	−2.93806	−0.0952230
$953$	32.6417	1.05737	0.528684	−	0.848819i	$-0.322686\pi$
$953$	32.6417	1.05737	0.528684	+	0.848819i	$0.322686\pi$
$954$	−3.27512	−0.106036
$955$	56.0515	1.81378
$956$	2.14574	0.0693983
$957$	18.7594	0.606406
$958$	−31.8133	−1.02784
$959$	−2.71407	−0.0876419
$960$	38.5098	1.24290
$961$	−6.27356	−0.202373
$962$	−2.96443	−0.0955770
$963$	11.5473	0.372106
$964$	2.07928	0.0669689
$965$	−57.4773	−1.85026
$966$	2.15108	0.0692099
$967$	−22.0363	−0.708638	−0.354319	−	0.935125i	$-0.615287\pi$
$967$	−22.0363	−0.708638	−0.354319	+	0.935125i	$0.615287\pi$
$968$	−11.8769	−0.381739
$969$	−37.3590	−1.20014
$970$	−41.2310	−1.32385
$971$	46.7250	1.49948	0.749738	−	0.661734i	$-0.230179\pi$
$971$	46.7250	1.49948	0.749738	+	0.661734i	$0.230179\pi$
$972$	1.48099	0.0475029
$973$	−1.62455	−0.0520805
$974$	15.0527	0.482319
$975$	−18.4140	−0.589721
$976$	44.6813	1.43021
$977$	29.1808	0.933575	0.466788	−	0.884369i	$-0.345411\pi$
$977$	29.1808	0.933575	0.466788	+	0.884369i	$0.345411\pi$
$978$	−36.2937	−1.16054
$979$	8.18023	0.261441
$980$	−3.07870	−0.0983456
$981$	1.15672	0.0369313
$982$	26.0620	0.831672
$983$	−6.12631	−0.195399	−0.0976994	−	0.995216i	$-0.531148\pi$
$983$	−6.12631	−0.195399	−0.0976994	+	0.995216i	$0.531148\pi$
$984$	1.11231	0.0354591
$985$	43.8657	1.39768
$986$	−26.1429	−0.832561
$987$	−2.70905	−0.0862301
$988$	−1.46312	−0.0465481
$989$	−26.9362	−0.856521
$990$	20.5937	0.654511
$991$	35.2493	1.11973	0.559866	−	0.828583i	$-0.310853\pi$
$991$	35.2493	1.11973	0.559866	+	0.828583i	$0.310853\pi$
$992$	−3.70038	−0.117487
$993$	−1.57951	−0.0501243
$994$	−0.504792	−0.0160110
$995$	−63.8234	−2.02334
$996$	−1.61241	−0.0510912
$997$	44.6999	1.41566	0.707830	−	0.706383i	$-0.249674\pi$
$997$	44.6999	1.41566	0.707830	+	0.706383i	$0.249674\pi$
$998$	−49.8404	−1.57767
$999$	−5.64347	−0.178552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.59	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.59	✓	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)

\(f(q)\)	\(=\)	\(q+1.36683 q^{2} -1.35767 q^{3} -0.131769 q^{4} -3.35463 q^{5} -1.85571 q^{6} +0.187605 q^{7} -2.91377 q^{8} -1.15672 q^{9} +O(q^{10})\)	\(q+1.36683 q^{2} -1.35767 q^{3} -0.131769 q^{4} -3.35463 q^{5} -1.85571 q^{6} +0.187605 q^{7} -2.91377 q^{8} -1.15672 q^{9} -4.58522 q^{10} +3.88280 q^{11} +0.178900 q^{12} +2.16883 q^{13} +0.256425 q^{14} +4.55450 q^{15} -3.71910 q^{16} +5.37477 q^{17} -1.58105 q^{18} +5.11965 q^{19} +0.442038 q^{20} -0.254707 q^{21} +5.30714 q^{22} -6.17876 q^{23} +3.95595 q^{24} +6.25357 q^{25} +2.96443 q^{26} +5.64347 q^{27} -0.0247206 q^{28} -3.55860 q^{29} +6.22523 q^{30} -4.97257 q^{31} +0.744158 q^{32} -5.27158 q^{33} +7.34641 q^{34} -0.629347 q^{35} +0.152421 q^{36} -1.00000 q^{37} +6.99770 q^{38} -2.94456 q^{39} +9.77464 q^{40} +0.281174 q^{41} -0.348141 q^{42} +4.35948 q^{43} -0.511634 q^{44} +3.88038 q^{45} -8.44533 q^{46} +10.6360 q^{47} +5.04932 q^{48} -6.96480 q^{49} +8.54758 q^{50} -7.29718 q^{51} -0.285785 q^{52} +2.07149 q^{53} +7.71368 q^{54} -13.0254 q^{55} -0.546639 q^{56} -6.95081 q^{57} -4.86401 q^{58} +7.25928 q^{59} -0.600143 q^{60} -12.0140 q^{61} -6.79667 q^{62} -0.217007 q^{63} +8.45534 q^{64} -7.27563 q^{65} -7.20536 q^{66} -13.1088 q^{67} -0.708229 q^{68} +8.38874 q^{69} -0.860211 q^{70} -1.96858 q^{71} +3.37043 q^{72} +0.287921 q^{73} -1.36683 q^{74} -8.49030 q^{75} -0.674613 q^{76} +0.728434 q^{77} -4.02472 q^{78} +6.57383 q^{79} +12.4762 q^{80} -4.19182 q^{81} +0.384317 q^{82} -9.01294 q^{83} +0.0335625 q^{84} -18.0304 q^{85} +5.95868 q^{86} +4.83142 q^{87} -11.3136 q^{88} +2.10679 q^{89} +5.30383 q^{90} +0.406884 q^{91} +0.814170 q^{92} +6.75112 q^{93} +14.5376 q^{94} -17.1746 q^{95} -1.01032 q^{96} +8.99215 q^{97} -9.51972 q^{98} -4.49132 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 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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