LMFDB - Embedded newform 4029.2.a.k.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.97184 q^{2} +1.00000 q^{3} +1.88814 q^{4} +3.63031 q^{5} +1.97184 q^{6} +2.53951 q^{7} -0.220574 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.97184 q^{2} +1.00000 q^{3} +1.88814 q^{4} +3.63031 q^{5} +1.97184 q^{6} +2.53951 q^{7} -0.220574 q^{8} +1.00000 q^{9} +7.15837 q^{10} -3.57047 q^{11} +1.88814 q^{12} +1.93908 q^{13} +5.00750 q^{14} +3.63031 q^{15} -4.21121 q^{16} +1.00000 q^{17} +1.97184 q^{18} -1.44109 q^{19} +6.85452 q^{20} +2.53951 q^{21} -7.04038 q^{22} -1.16374 q^{23} -0.220574 q^{24} +8.17914 q^{25} +3.82354 q^{26} +1.00000 q^{27} +4.79494 q^{28} +0.504567 q^{29} +7.15837 q^{30} +8.18587 q^{31} -7.86267 q^{32} -3.57047 q^{33} +1.97184 q^{34} +9.21920 q^{35} +1.88814 q^{36} -0.0403668 q^{37} -2.84159 q^{38} +1.93908 q^{39} -0.800753 q^{40} +2.99092 q^{41} +5.00750 q^{42} +2.64554 q^{43} -6.74154 q^{44} +3.63031 q^{45} -2.29470 q^{46} +5.20651 q^{47} -4.21121 q^{48} -0.550888 q^{49} +16.1279 q^{50} +1.00000 q^{51} +3.66125 q^{52} -5.46270 q^{53} +1.97184 q^{54} -12.9619 q^{55} -0.560151 q^{56} -1.44109 q^{57} +0.994923 q^{58} +11.8437 q^{59} +6.85452 q^{60} -3.38708 q^{61} +16.1412 q^{62} +2.53951 q^{63} -7.08147 q^{64} +7.03945 q^{65} -7.04038 q^{66} -5.65903 q^{67} +1.88814 q^{68} -1.16374 q^{69} +18.1788 q^{70} +5.87958 q^{71} -0.220574 q^{72} -4.87127 q^{73} -0.0795967 q^{74} +8.17914 q^{75} -2.72098 q^{76} -9.06725 q^{77} +3.82354 q^{78} +1.00000 q^{79} -15.2880 q^{80} +1.00000 q^{81} +5.89759 q^{82} -12.5661 q^{83} +4.79494 q^{84} +3.63031 q^{85} +5.21657 q^{86} +0.504567 q^{87} +0.787554 q^{88} -0.418069 q^{89} +7.15837 q^{90} +4.92431 q^{91} -2.19730 q^{92} +8.18587 q^{93} +10.2664 q^{94} -5.23160 q^{95} -7.86267 q^{96} -8.38630 q^{97} -1.08626 q^{98} -3.57047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	1.97184	1.39430	0.697149	−	0.716926i	$-0.254451\pi$
$2$	1.97184	1.39430	0.697149	+	0.716926i	$0.254451\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.88814	0.944069
$5$	3.63031	1.62352	0.811762	−	0.583989i	$-0.198509\pi$
$5$	3.63031	1.62352	0.811762	+	0.583989i	$0.198509\pi$
$6$	1.97184	0.804999
$7$	2.53951	0.959845	0.479922	−	0.877311i	$-0.340665\pi$
$7$	2.53951	0.959845	0.479922	+	0.877311i	$0.340665\pi$
$8$	−0.220574	−0.0779848
$9$	1.00000	0.333333
$10$	7.15837	2.26368
$11$	−3.57047	−1.07654	−0.538269	−	0.842773i	$-0.680921\pi$
$11$	−3.57047	−1.07654	−0.538269	+	0.842773i	$0.680921\pi$
$12$	1.88814	0.545058
$13$	1.93908	0.537803	0.268902	−	0.963168i	$-0.413339\pi$
$13$	1.93908	0.537803	0.268902	+	0.963168i	$0.413339\pi$
$14$	5.00750	1.33831
$15$	3.63031	0.937341
$16$	−4.21121	−1.05280
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.97184	0.464766
$19$	−1.44109	−0.330609	−0.165304	−	0.986243i	$-0.552861\pi$
$19$	−1.44109	−0.330609	−0.165304	+	0.986243i	$0.552861\pi$
$20$	6.85452	1.53272
$21$	2.53951	0.554167
$22$	−7.04038	−1.50102
$23$	−1.16374	−0.242656	−0.121328	−	0.992612i	$-0.538715\pi$
$23$	−1.16374	−0.242656	−0.121328	+	0.992612i	$0.538715\pi$
$24$	−0.220574	−0.0450245
$25$	8.17914	1.63583
$26$	3.82354	0.749859
$27$	1.00000	0.192450
$28$	4.79494	0.906159
$29$	0.504567	0.0936957	0.0468478	−	0.998902i	$-0.485082\pi$
$29$	0.504567	0.0936957	0.0468478	+	0.998902i	$0.485082\pi$
$30$	7.15837	1.30693
$31$	8.18587	1.47023	0.735113	−	0.677945i	$-0.237129\pi$
$31$	8.18587	1.47023	0.735113	+	0.677945i	$0.237129\pi$
$32$	−7.86267	−1.38994
$33$	−3.57047	−0.621539
$34$	1.97184	0.338167
$35$	9.21920	1.55833
$36$	1.88814	0.314690
$37$	−0.0403668	−0.00663626	−0.00331813	−	0.999994i	$-0.501056\pi$
$37$	−0.0403668	−0.00663626	−0.00331813	+	0.999994i	$0.501056\pi$
$38$	−2.84159	−0.460967
$39$	1.93908	0.310501
$40$	−0.800753	−0.126610
$41$	2.99092	0.467102	0.233551	−	0.972344i	$-0.424965\pi$
$41$	2.99092	0.467102	0.233551	+	0.972344i	$0.424965\pi$
$42$	5.00750	0.772674
$43$	2.64554	0.403441	0.201720	−	0.979443i	$-0.435347\pi$
$43$	2.64554	0.403441	0.201720	+	0.979443i	$0.435347\pi$
$44$	−6.74154	−1.01633
$45$	3.63031	0.541174
$46$	−2.29470	−0.338335
$47$	5.20651	0.759447	0.379724	−	0.925100i	$-0.376019\pi$
$47$	5.20651	0.759447	0.379724	+	0.925100i	$0.376019\pi$
$48$	−4.21121	−0.607836
$49$	−0.550888	−0.0786984
$50$	16.1279	2.28083
$51$	1.00000	0.140028
$52$	3.66125	0.507723
$53$	−5.46270	−0.750359	−0.375180	−	0.926952i	$-0.622419\pi$
$53$	−5.46270	−0.750359	−0.375180	+	0.926952i	$0.622419\pi$
$54$	1.97184	0.268333
$55$	−12.9619	−1.74778
$56$	−0.560151	−0.0748533
$57$	−1.44109	−0.190877
$58$	0.994923	0.130640
$59$	11.8437	1.54192	0.770960	−	0.636884i	$-0.219777\pi$
$59$	11.8437	1.54192	0.770960	+	0.636884i	$0.219777\pi$
$60$	6.85452	0.884915
$61$	−3.38708	−0.433671	−0.216835	−	0.976208i	$-0.569573\pi$
$61$	−3.38708	−0.433671	−0.216835	+	0.976208i	$0.569573\pi$
$62$	16.1412	2.04993
$63$	2.53951	0.319948
$64$	−7.08147	−0.885184
$65$	7.03945	0.873136
$66$	−7.04038	−0.866611
$67$	−5.65903	−0.691361	−0.345680	−	0.938352i	$-0.612352\pi$
$67$	−5.65903	−0.691361	−0.345680	+	0.938352i	$0.612352\pi$
$68$	1.88814	0.228970
$69$	−1.16374	−0.140098
$70$	18.1788	2.17278
$71$	5.87958	0.697778	0.348889	−	0.937164i	$-0.386559\pi$
$71$	5.87958	0.697778	0.348889	+	0.937164i	$0.386559\pi$
$72$	−0.220574	−0.0259949
$73$	−4.87127	−0.570139	−0.285070	−	0.958507i	$-0.592017\pi$
$73$	−4.87127	−0.570139	−0.285070	+	0.958507i	$0.592017\pi$
$74$	−0.0795967	−0.00925293
$75$	8.17914	0.944445
$76$	−2.72098	−0.312117
$77$	−9.06725	−1.03331
$78$	3.82354	0.432931
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−15.2880	−1.70925
$81$	1.00000	0.111111
$82$	5.89759	0.651280
$83$	−12.5661	−1.37931	−0.689653	−	0.724140i	$-0.742237\pi$
$83$	−12.5661	−1.37931	−0.689653	+	0.724140i	$0.742237\pi$
$84$	4.79494	0.523171
$85$	3.63031	0.393762
$86$	5.21657	0.562517
$87$	0.504567	0.0540952
$88$	0.787554	0.0839536
$89$	−0.418069	−0.0443152	−0.0221576	−	0.999754i	$-0.507054\pi$
$89$	−0.418069	−0.0443152	−0.0221576	+	0.999754i	$0.507054\pi$
$90$	7.15837	0.754559
$91$	4.92431	0.516208
$92$	−2.19730	−0.229084
$93$	8.18587	0.848835
$94$	10.2664	1.05890
$95$	−5.23160	−0.536751
$96$	−7.86267	−0.802480
$97$	−8.38630	−0.851500	−0.425750	−	0.904841i	$-0.639990\pi$
$97$	−8.38630	−0.851500	−0.425750	+	0.904841i	$0.639990\pi$
$98$	−1.08626	−0.109729
$99$	−3.57047	−0.358846
$100$	15.4433	1.54433
$101$	15.3928	1.53165	0.765823	−	0.643052i	$-0.222332\pi$
$101$	15.3928	1.53165	0.765823	+	0.643052i	$0.222332\pi$
$102$	1.97184	0.195241
$103$	−3.67387	−0.361997	−0.180999	−	0.983483i	$-0.557933\pi$
$103$	−3.67387	−0.361997	−0.180999	+	0.983483i	$0.557933\pi$
$104$	−0.427711	−0.0419405
$105$	9.21920	0.899702
$106$	−10.7715	−1.04622
$107$	−1.47429	−0.142525	−0.0712623	−	0.997458i	$-0.522703\pi$
$107$	−1.47429	−0.142525	−0.0712623	+	0.997458i	$0.522703\pi$
$108$	1.88814	0.181686
$109$	−12.4158	−1.18921	−0.594607	−	0.804017i	$-0.702692\pi$
$109$	−12.4158	−1.18921	−0.594607	+	0.804017i	$0.702692\pi$
$110$	−25.5588	−2.43693
$111$	−0.0403668	−0.00383145
$112$	−10.6944	−1.01053
$113$	0.473155	0.0445107	0.0222553	−	0.999752i	$-0.492915\pi$
$113$	0.473155	0.0445107	0.0222553	+	0.999752i	$0.492915\pi$
$114$	−2.84159	−0.266140
$115$	−4.22473	−0.393958
$116$	0.952691	0.0884552
$117$	1.93908	0.179268
$118$	23.3538	2.14990
$119$	2.53951	0.232797
$120$	−0.800753	−0.0730984
$121$	1.74827	0.158933
$122$	−6.67876	−0.604667
$123$	2.99092	0.269682
$124$	15.4560	1.38799
$125$	11.5412	1.03228
$126$	5.00750	0.446103
$127$	−21.8195	−1.93617	−0.968083	−	0.250629i	$-0.919363\pi$
$127$	−21.8195	−1.93617	−0.968083	+	0.250629i	$0.919363\pi$
$128$	1.76183	0.155726
$129$	2.64554	0.232927
$130$	13.8806	1.21741
$131$	−21.8651	−1.91036	−0.955182	−	0.296020i	$-0.904341\pi$
$131$	−21.8651	−1.91036	−0.955182	+	0.296020i	$0.904341\pi$
$132$	−6.74154	−0.586776
$133$	−3.65966	−0.317333
$134$	−11.1587	−0.963963
$135$	3.63031	0.312447
$136$	−0.220574	−0.0189141
$137$	−21.3190	−1.82140	−0.910701	−	0.413066i	$-0.864458\pi$
$137$	−21.3190	−1.82140	−0.910701	+	0.413066i	$0.864458\pi$
$138$	−2.29470	−0.195338
$139$	−5.47855	−0.464684	−0.232342	−	0.972634i	$-0.574639\pi$
$139$	−5.47855	−0.464684	−0.232342	+	0.972634i	$0.574639\pi$
$140$	17.4071	1.47117
$141$	5.20651	0.438467
$142$	11.5936	0.972910
$143$	−6.92342	−0.578966
$144$	−4.21121	−0.350934
$145$	1.83173	0.152117
$146$	−9.60535	−0.794944
$147$	−0.550888	−0.0454365
$148$	−0.0762181	−0.00626509
$149$	13.3091	1.09032	0.545162	−	0.838330i	$-0.316468\pi$
$149$	13.3091	1.09032	0.545162	+	0.838330i	$0.316468\pi$
$150$	16.1279	1.31684
$151$	15.4183	1.25473	0.627363	−	0.778727i	$-0.284134\pi$
$151$	15.4183	1.25473	0.627363	+	0.778727i	$0.284134\pi$
$152$	0.317867	0.0257824
$153$	1.00000	0.0808452
$154$	−17.8791	−1.44074
$155$	29.7172	2.38694
$156$	3.66125	0.293134
$157$	−17.1543	−1.36907	−0.684533	−	0.728982i	$-0.739994\pi$
$157$	−17.1543	−1.36907	−0.684533	+	0.728982i	$0.739994\pi$
$158$	1.97184	0.156871
$159$	−5.46270	−0.433220
$160$	−28.5439	−2.25659
$161$	−2.95532	−0.232912
$162$	1.97184	0.154922
$163$	−1.72806	−0.135352	−0.0676760	−	0.997707i	$-0.521558\pi$
$163$	−1.72806	−0.135352	−0.0676760	+	0.997707i	$0.521558\pi$
$164$	5.64726	0.440977
$165$	−12.9619	−1.00908
$166$	−24.7783	−1.92317
$167$	6.72945	0.520740	0.260370	−	0.965509i	$-0.416155\pi$
$167$	6.72945	0.520740	0.260370	+	0.965509i	$0.416155\pi$
$168$	−0.560151	−0.0432166
$169$	−9.23998	−0.710768
$170$	7.15837	0.549022
$171$	−1.44109	−0.110203
$172$	4.99514	0.380876
$173$	−11.7040	−0.889842	−0.444921	−	0.895570i	$-0.646768\pi$
$173$	−11.7040	−0.889842	−0.444921	+	0.895570i	$0.646768\pi$
$174$	0.994923	0.0754249
$175$	20.7710	1.57014
$176$	15.0360	1.13338
$177$	11.8437	0.890228
$178$	−0.824364	−0.0617887
$179$	11.4790	0.857982	0.428991	−	0.903309i	$-0.358869\pi$
$179$	11.4790	0.857982	0.428991	+	0.903309i	$0.358869\pi$
$180$	6.85452	0.510906
$181$	−16.8280	−1.25082	−0.625408	−	0.780298i	$-0.715067\pi$
$181$	−16.8280	−1.25082	−0.625408	+	0.780298i	$0.715067\pi$
$182$	9.70993	0.719748
$183$	−3.38708	−0.250380
$184$	0.256691	0.0189235
$185$	−0.146544	−0.0107741
$186$	16.1412	1.18353
$187$	−3.57047	−0.261099
$188$	9.83060	0.716970
$189$	2.53951	0.184722
$190$	−10.3159	−0.748391
$191$	−3.81190	−0.275819	−0.137910	−	0.990445i	$-0.544038\pi$
$191$	−3.81190	−0.275819	−0.137910	+	0.990445i	$0.544038\pi$
$192$	−7.08147	−0.511061
$193$	−7.01184	−0.504723	−0.252362	−	0.967633i	$-0.581207\pi$
$193$	−7.01184	−0.504723	−0.252362	+	0.967633i	$0.581207\pi$
$194$	−16.5364	−1.18724
$195$	7.03945	0.504105
$196$	−1.04015	−0.0742967
$197$	4.27418	0.304523	0.152261	−	0.988340i	$-0.451344\pi$
$197$	4.27418	0.304523	0.152261	+	0.988340i	$0.451344\pi$
$198$	−7.04038	−0.500338
$199$	12.3226	0.873523	0.436761	−	0.899577i	$-0.356125\pi$
$199$	12.3226	0.873523	0.436761	+	0.899577i	$0.356125\pi$
$200$	−1.80411	−0.127570
$201$	−5.65903	−0.399157
$202$	30.3522	2.13557
$203$	1.28135	0.0899333
$204$	1.88814	0.132196
$205$	10.8579	0.758352
$206$	−7.24427	−0.504732
$207$	−1.16374	−0.0808854
$208$	−8.16587	−0.566201
$209$	5.14537	0.355913
$210$	18.1788	1.25445
$211$	−1.63389	−0.112482	−0.0562410	−	0.998417i	$-0.517912\pi$
$211$	−1.63389	−0.112482	−0.0562410	+	0.998417i	$0.517912\pi$
$212$	−10.3143	−0.708391
$213$	5.87958	0.402862
$214$	−2.90705	−0.198722
$215$	9.60412	0.654996
$216$	−0.220574	−0.0150082
$217$	20.7881	1.41119
$218$	−24.4818	−1.65812
$219$	−4.87127	−0.329170
$220$	−24.4739	−1.65003
$221$	1.93908	0.130436
$222$	−0.0795967	−0.00534218
$223$	−6.53396	−0.437546	−0.218773	−	0.975776i	$-0.570205\pi$
$223$	−6.53396	−0.437546	−0.218773	+	0.975776i	$0.570205\pi$
$224$	−19.9673	−1.33412
$225$	8.17914	0.545276
$226$	0.932984	0.0620612
$227$	8.29767	0.550736	0.275368	−	0.961339i	$-0.411200\pi$
$227$	8.29767	0.550736	0.275368	+	0.961339i	$0.411200\pi$
$228$	−2.72098	−0.180201
$229$	21.8562	1.44430	0.722150	−	0.691736i	$-0.243154\pi$
$229$	21.8562	1.44430	0.722150	+	0.691736i	$0.243154\pi$
$230$	−8.33047	−0.549295
$231$	−9.06725	−0.596581
$232$	−0.111294	−0.00730684
$233$	5.84118	0.382668	0.191334	−	0.981525i	$-0.438719\pi$
$233$	5.84118	0.382668	0.191334	+	0.981525i	$0.438719\pi$
$234$	3.82354	0.249953
$235$	18.9012	1.23298
$236$	22.3625	1.45568
$237$	1.00000	0.0649570
$238$	5.00750	0.324588
$239$	−5.75852	−0.372488	−0.186244	−	0.982504i	$-0.559631\pi$
$239$	−5.75852	−0.372488	−0.186244	+	0.982504i	$0.559631\pi$
$240$	−15.2880	−0.986836
$241$	−9.29987	−0.599057	−0.299529	−	0.954087i	$-0.596829\pi$
$241$	−9.29987	−0.599057	−0.299529	+	0.954087i	$0.596829\pi$
$242$	3.44730	0.221601
$243$	1.00000	0.0641500
$244$	−6.39527	−0.409415
$245$	−1.99989	−0.127769
$246$	5.89759	0.376017
$247$	−2.79438	−0.177802
$248$	−1.80559	−0.114655
$249$	−12.5661	−0.796343
$250$	22.7574	1.43931
$251$	22.6176	1.42761	0.713805	−	0.700344i	$-0.246970\pi$
$251$	22.6176	1.42761	0.713805	+	0.700344i	$0.246970\pi$
$252$	4.79494	0.302053
$253$	4.15509	0.261229
$254$	−43.0245	−2.69959
$255$	3.63031	0.227339
$256$	17.6370	1.10231
$257$	−26.5546	−1.65643	−0.828216	−	0.560408i	$-0.810644\pi$
$257$	−26.5546	−1.65643	−0.828216	+	0.560408i	$0.810644\pi$
$258$	5.21657	0.324769
$259$	−0.102512	−0.00636978
$260$	13.2914	0.824301
$261$	0.504567	0.0312319
$262$	−43.1144	−2.66362
$263$	17.1888	1.05991	0.529955	−	0.848026i	$-0.322209\pi$
$263$	17.1888	1.05991	0.529955	+	0.848026i	$0.322209\pi$
$264$	0.787554	0.0484706
$265$	−19.8313	−1.21823
$266$	−7.21625	−0.442457
$267$	−0.418069	−0.0255854
$268$	−10.6850	−0.652692
$269$	−21.8332	−1.33119	−0.665597	−	0.746312i	$-0.731823\pi$
$269$	−21.8332	−1.33119	−0.665597	+	0.746312i	$0.731823\pi$
$270$	7.15837	0.435645
$271$	7.47669	0.454176	0.227088	−	0.973874i	$-0.427079\pi$
$271$	7.47669	0.454176	0.227088	+	0.973874i	$0.427079\pi$
$272$	−4.21121	−0.255342
$273$	4.92431	0.298033
$274$	−42.0375	−2.53958
$275$	−29.2034	−1.76103
$276$	−2.19730	−0.132262
$277$	−12.1905	−0.732454	−0.366227	−	0.930526i	$-0.619351\pi$
$277$	−12.1905	−0.732454	−0.366227	+	0.930526i	$0.619351\pi$
$278$	−10.8028	−0.647908
$279$	8.18587	0.490075
$280$	−2.03352	−0.121526
$281$	21.4458	1.27935	0.639674	−	0.768646i	$-0.279069\pi$
$281$	21.4458	1.27935	0.639674	+	0.768646i	$0.279069\pi$
$282$	10.2664	0.611354
$283$	27.6229	1.64201	0.821005	−	0.570921i	$-0.193414\pi$
$283$	27.6229	1.64201	0.821005	+	0.570921i	$0.193414\pi$
$284$	11.1015	0.658750
$285$	−5.23160	−0.309893
$286$	−13.6519	−0.807251
$287$	7.59546	0.448346
$288$	−7.86267	−0.463312
$289$	1.00000	0.0588235
$290$	3.61188	0.212097
$291$	−8.38630	−0.491614
$292$	−9.19763	−0.538250
$293$	−24.7959	−1.44859	−0.724296	−	0.689489i	$-0.757835\pi$
$293$	−24.7959	−1.44859	−0.724296	+	0.689489i	$0.757835\pi$
$294$	−1.08626	−0.0633521
$295$	42.9963	2.50334
$296$	0.00890388	0.000517527 0
$297$	−3.57047	−0.207180
$298$	26.2434	1.52024
$299$	−2.25658	−0.130501
$300$	15.4433	0.891621
$301$	6.71837	0.387241
$302$	30.4024	1.74946
$303$	15.3928	0.884296
$304$	6.06873	0.348066
$305$	−12.2961	−0.704075
$306$	1.97184	0.112722
$307$	4.83005	0.275666	0.137833	−	0.990456i	$-0.455986\pi$
$307$	4.83005	0.275666	0.137833	+	0.990456i	$0.455986\pi$
$308$	−17.1202	−0.975515
$309$	−3.67387	−0.208999
$310$	58.5975	3.32811
$311$	−11.2851	−0.639919	−0.319959	−	0.947431i	$-0.603669\pi$
$311$	−11.2851	−0.639919	−0.319959	+	0.947431i	$0.603669\pi$
$312$	−0.427711	−0.0242143
$313$	−2.52734	−0.142854	−0.0714268	−	0.997446i	$-0.522755\pi$
$313$	−2.52734	−0.142854	−0.0714268	+	0.997446i	$0.522755\pi$
$314$	−33.8256	−1.90889
$315$	9.21920	0.519443
$316$	1.88814	0.106216
$317$	−4.54121	−0.255060	−0.127530	−	0.991835i	$-0.540705\pi$
$317$	−4.54121	−0.255060	−0.127530	+	0.991835i	$0.540705\pi$
$318$	−10.7715	−0.604038
$319$	−1.80154	−0.100867
$320$	−25.7079	−1.43712
$321$	−1.47429	−0.0822866
$322$	−5.82742	−0.324749
$323$	−1.44109	−0.0801844
$324$	1.88814	0.104897
$325$	15.8600	0.879753
$326$	−3.40745	−0.188721
$327$	−12.4158	−0.686593
$328$	−0.659719	−0.0364269
$329$	13.2220	0.728951
$330$	−25.5588	−1.40696
$331$	14.6638	0.805993	0.402997	−	0.915202i	$-0.367969\pi$
$331$	14.6638	0.805993	0.402997	+	0.915202i	$0.367969\pi$
$332$	−23.7265	−1.30216
$333$	−0.0403668	−0.00221209
$334$	13.2694	0.726067
$335$	−20.5440	−1.12244
$336$	−10.6944	−0.583428
$337$	2.28153	0.124283	0.0621413	−	0.998067i	$-0.480207\pi$
$337$	2.28153	0.124283	0.0621413	+	0.998067i	$0.480207\pi$
$338$	−18.2197	−0.991022
$339$	0.473155	0.0256982
$340$	6.85452	0.371739
$341$	−29.2274	−1.58275
$342$	−2.84159	−0.153656
$343$	−19.1756	−1.03538
$344$	−0.583538	−0.0314623
$345$	−4.22473	−0.227452
$346$	−23.0785	−1.24071
$347$	−13.0901	−0.702716	−0.351358	−	0.936241i	$-0.614280\pi$
$347$	−13.0901	−0.702716	−0.351358	+	0.936241i	$0.614280\pi$
$348$	0.952691	0.0510696
$349$	26.3322	1.40953	0.704764	−	0.709442i	$-0.251053\pi$
$349$	26.3322	1.40953	0.704764	+	0.709442i	$0.251053\pi$
$350$	40.9570	2.18924
$351$	1.93908	0.103500
$352$	28.0734	1.49632
$353$	−3.99391	−0.212574	−0.106287	−	0.994335i	$-0.533896\pi$
$353$	−3.99391	−0.212574	−0.106287	+	0.994335i	$0.533896\pi$
$354$	23.3538	1.24124
$355$	21.3447	1.13286
$356$	−0.789372	−0.0418366
$357$	2.53951	0.134405
$358$	22.6347	1.19628
$359$	19.7654	1.04318	0.521588	−	0.853197i	$-0.325340\pi$
$359$	19.7654	1.04318	0.521588	+	0.853197i	$0.325340\pi$
$360$	−0.800753	−0.0422034
$361$	−16.9233	−0.890698
$362$	−33.1821	−1.74401
$363$	1.74827	0.0917602
$364$	9.29777	0.487336
$365$	−17.6842	−0.925634
$366$	−6.67876	−0.349104
$367$	−4.22387	−0.220484	−0.110242	−	0.993905i	$-0.535163\pi$
$367$	−4.22387	−0.220484	−0.110242	+	0.993905i	$0.535163\pi$
$368$	4.90075	0.255469
$369$	2.99092	0.155701
$370$	−0.288961	−0.0150223
$371$	−13.8726	−0.720228
$372$	15.4560	0.801358
$373$	28.2820	1.46439	0.732193	−	0.681097i	$-0.238497\pi$
$373$	28.2820	1.46439	0.732193	+	0.681097i	$0.238497\pi$
$374$	−7.04038	−0.364050
$375$	11.5412	0.595987
$376$	−1.14842	−0.0592253
$377$	0.978394	0.0503899
$378$	5.00750	0.257558
$379$	27.9032	1.43329	0.716645	−	0.697438i	$-0.245677\pi$
$379$	27.9032	1.43329	0.716645	+	0.697438i	$0.245677\pi$
$380$	−9.87798	−0.506730
$381$	−21.8195	−1.11785
$382$	−7.51644	−0.384575
$383$	3.82136	0.195262	0.0976312	−	0.995223i	$-0.468873\pi$
$383$	3.82136	0.195262	0.0976312	+	0.995223i	$0.468873\pi$
$384$	1.76183	0.0899082
$385$	−32.9169	−1.67760
$386$	−13.8262	−0.703735
$387$	2.64554	0.134480
$388$	−15.8345	−0.803874
$389$	16.6101	0.842167	0.421084	−	0.907022i	$-0.361650\pi$
$389$	16.6101	0.842167	0.421084	+	0.907022i	$0.361650\pi$
$390$	13.8806	0.702874
$391$	−1.16374	−0.0588528
$392$	0.121512	0.00613727
$393$	−21.8651	−1.10295
$394$	8.42798	0.424596
$395$	3.63031	0.182661
$396$	−6.74154	−0.338775
$397$	−4.65852	−0.233804	−0.116902	−	0.993143i	$-0.537296\pi$
$397$	−4.65852	−0.233804	−0.116902	+	0.993143i	$0.537296\pi$
$398$	24.2981	1.21795
$399$	−3.65966	−0.183212
$400$	−34.4441	−1.72220
$401$	−25.3093	−1.26389	−0.631944	−	0.775014i	$-0.717743\pi$
$401$	−25.3093	−1.26389	−0.631944	+	0.775014i	$0.717743\pi$
$402$	−11.1587	−0.556544
$403$	15.8730	0.790692
$404$	29.0638	1.44598
$405$	3.63031	0.180391
$406$	2.52662	0.125394
$407$	0.144129	0.00714419
$408$	−0.220574	−0.0109201
$409$	−11.2783	−0.557676	−0.278838	−	0.960338i	$-0.589949\pi$
$409$	−11.2783	−0.557676	−0.278838	+	0.960338i	$0.589949\pi$
$410$	21.4101	1.05737
$411$	−21.3190	−1.05159
$412$	−6.93677	−0.341750
$413$	30.0772	1.48000
$414$	−2.29470	−0.112778
$415$	−45.6187	−2.23934
$416$	−15.2463	−0.747513
$417$	−5.47855	−0.268286
$418$	10.1458	0.496249
$419$	8.58626	0.419466	0.209733	−	0.977759i	$-0.432740\pi$
$419$	8.58626	0.419466	0.209733	+	0.977759i	$0.432740\pi$
$420$	17.4071	0.849381
$421$	−5.65344	−0.275532	−0.137766	−	0.990465i	$-0.543992\pi$
$421$	−5.65344	−0.275532	−0.137766	+	0.990465i	$0.543992\pi$
$422$	−3.22177	−0.156833
$423$	5.20651	0.253149
$424$	1.20493	0.0585166
$425$	8.17914	0.396746
$426$	11.5936	0.561710
$427$	−8.60152	−0.416257
$428$	−2.78365	−0.134553
$429$	−6.92342	−0.334266
$430$	18.9378	0.913260
$431$	25.0178	1.20506	0.602532	−	0.798095i	$-0.294159\pi$
$431$	25.0178	1.20506	0.602532	+	0.798095i	$0.294159\pi$
$432$	−4.21121	−0.202612
$433$	11.0990	0.533382	0.266691	−	0.963782i	$-0.414070\pi$
$433$	11.0990	0.533382	0.266691	+	0.963782i	$0.414070\pi$
$434$	40.9907	1.96762
$435$	1.83173	0.0878248
$436$	−23.4427	−1.12270
$437$	1.67705	0.0802242
$438$	−9.60535	−0.458961
$439$	28.8938	1.37903	0.689513	−	0.724273i	$-0.257825\pi$
$439$	28.8938	1.37903	0.689513	+	0.724273i	$0.257825\pi$
$440$	2.85906	0.136301
$441$	−0.550888	−0.0262328
$442$	3.82354	0.181867
$443$	0.542603	0.0257799	0.0128899	−	0.999917i	$-0.495897\pi$
$443$	0.542603	0.0257799	0.0128899	+	0.999917i	$0.495897\pi$
$444$	−0.0762181	−0.00361715
$445$	−1.51772	−0.0719468
$446$	−12.8839	−0.610070
$447$	13.3091	0.629499
$448$	−17.9835	−0.849639
$449$	15.2786	0.721043	0.360522	−	0.932751i	$-0.382599\pi$
$449$	15.2786	0.721043	0.360522	+	0.932751i	$0.382599\pi$
$450$	16.1279	0.760277
$451$	−10.6790	−0.502853
$452$	0.893381	0.0420211
$453$	15.4183	0.724417
$454$	16.3616	0.767890
$455$	17.8768	0.838075
$456$	0.317867	0.0148855
$457$	−29.1360	−1.36293	−0.681463	−	0.731853i	$-0.738656\pi$
$457$	−29.1360	−1.36293	−0.681463	+	0.731853i	$0.738656\pi$
$458$	43.0969	2.01379
$459$	1.00000	0.0466760
$460$	−7.97687	−0.371923
$461$	9.55971	0.445240	0.222620	−	0.974905i	$-0.428539\pi$
$461$	9.55971	0.445240	0.222620	+	0.974905i	$0.428539\pi$
$462$	−17.8791	−0.831812
$463$	7.93204	0.368633	0.184317	−	0.982867i	$-0.440993\pi$
$463$	7.93204	0.368633	0.184317	+	0.982867i	$0.440993\pi$
$464$	−2.12484	−0.0986431
$465$	29.7172	1.37810
$466$	11.5178	0.533554
$467$	12.5227	0.579483	0.289742	−	0.957105i	$-0.406431\pi$
$467$	12.5227	0.579483	0.289742	+	0.957105i	$0.406431\pi$
$468$	3.66125	0.169241
$469$	−14.3712	−0.663599
$470$	37.2701	1.71914
$471$	−17.1543	−0.790431
$472$	−2.61242	−0.120246
$473$	−9.44582	−0.434319
$474$	1.97184	0.0905694
$475$	−11.7869	−0.540819
$476$	4.79494	0.219776
$477$	−5.46270	−0.250120
$478$	−11.3549	−0.519359
$479$	−5.08316	−0.232255	−0.116128	−	0.993234i	$-0.537048\pi$
$479$	−5.08316	−0.232255	−0.116128	+	0.993234i	$0.537048\pi$
$480$	−28.5439	−1.30285
$481$	−0.0782744	−0.00356900
$482$	−18.3378	−0.835265
$483$	−2.95532	−0.134472
$484$	3.30097	0.150044
$485$	−30.4448	−1.38243
$486$	1.97184	0.0894443
$487$	−0.794211	−0.0359891	−0.0179946	−	0.999838i	$-0.505728\pi$
$487$	−0.794211	−0.0359891	−0.0179946	+	0.999838i	$0.505728\pi$
$488$	0.747102	0.0338197
$489$	−1.72806	−0.0781455
$490$	−3.94346	−0.178148
$491$	17.3970	0.785117	0.392559	−	0.919727i	$-0.371590\pi$
$491$	17.3970	0.785117	0.392559	+	0.919727i	$0.371590\pi$
$492$	5.64726	0.254598
$493$	0.504567	0.0227245
$494$	−5.51007	−0.247910
$495$	−12.9619	−0.582595
$496$	−34.4724	−1.54786
$497$	14.9312	0.669758
$498$	−24.7783	−1.11034
$499$	−21.3401	−0.955314	−0.477657	−	0.878546i	$-0.658514\pi$
$499$	−21.3401	−0.955314	−0.477657	+	0.878546i	$0.658514\pi$
$500$	21.7915	0.974544
$501$	6.72945	0.300649
$502$	44.5982	1.99052
$503$	13.4082	0.597841	0.298921	−	0.954278i	$-0.403373\pi$
$503$	13.4082	0.597841	0.298921	+	0.954278i	$0.403373\pi$
$504$	−0.560151	−0.0249511
$505$	55.8808	2.48666
$506$	8.19316	0.364231
$507$	−9.23998	−0.410362
$508$	−41.1982	−1.82787
$509$	−12.9729	−0.575014	−0.287507	−	0.957778i	$-0.592827\pi$
$509$	−12.9729	−0.575014	−0.287507	+	0.957778i	$0.592827\pi$
$510$	7.15837	0.316978
$511$	−12.3706	−0.547245
$512$	31.2536	1.38123
$513$	−1.44109	−0.0636257
$514$	−52.3614	−2.30956
$515$	−13.3373	−0.587711
$516$	4.99514	0.219899
$517$	−18.5897	−0.817574
$518$	−0.202137	−0.00888138
$519$	−11.7040	−0.513751
$520$	−1.55272	−0.0680913
$521$	1.88169	0.0824383	0.0412191	−	0.999150i	$-0.486876\pi$
$521$	1.88169	0.0824383	0.0412191	+	0.999150i	$0.486876\pi$
$522$	0.994923	0.0435466
$523$	−15.8962	−0.695092	−0.347546	−	0.937663i	$-0.612985\pi$
$523$	−15.8962	−0.695092	−0.347546	+	0.937663i	$0.612985\pi$
$524$	−41.2843	−1.80351
$525$	20.7710	0.906521
$526$	33.8936	1.47783
$527$	8.18587	0.356582
$528$	15.0360	0.654358
$529$	−21.6457	−0.941118
$530$	−39.1040	−1.69857
$531$	11.8437	0.513973
$532$	−6.90994	−0.299584
$533$	5.79962	0.251209
$534$	−0.824364	−0.0356737
$535$	−5.35211	−0.231392
$536$	1.24824	0.0539156
$537$	11.4790	0.495356
$538$	−43.0515	−1.85608
$539$	1.96693	0.0847217
$540$	6.85452	0.294972
$541$	30.9377	1.33012	0.665059	−	0.746791i	$-0.268407\pi$
$541$	30.9377	1.33012	0.665059	+	0.746791i	$0.268407\pi$
$542$	14.7428	0.633258
$543$	−16.8280	−0.722159
$544$	−7.86267	−0.337109
$545$	−45.0730	−1.93072
$546$	9.70993	0.415547
$547$	−3.35933	−0.143635	−0.0718173	−	0.997418i	$-0.522880\pi$
$547$	−3.35933	−0.143635	−0.0718173	+	0.997418i	$0.522880\pi$
$548$	−40.2531	−1.71953
$549$	−3.38708	−0.144557
$550$	−57.5843	−2.45540
$551$	−0.727126	−0.0309766
$552$	0.256691	0.0109255
$553$	2.53951	0.107991
$554$	−24.0376	−1.02126
$555$	−0.146544	−0.00622044
$556$	−10.3442	−0.438694
$557$	16.4609	0.697471	0.348735	−	0.937221i	$-0.386611\pi$
$557$	16.4609	0.697471	0.348735	+	0.937221i	$0.386611\pi$
$558$	16.1412	0.683311
$559$	5.12991	0.216972
$560$	−38.8240	−1.64061
$561$	−3.57047	−0.150745
$562$	42.2876	1.78379
$563$	−37.8012	−1.59313	−0.796566	−	0.604552i	$-0.793352\pi$
$563$	−37.8012	−1.59313	−0.796566	+	0.604552i	$0.793352\pi$
$564$	9.83060	0.413943
$565$	1.71770	0.0722641
$566$	54.4678	2.28945
$567$	2.53951	0.106649
$568$	−1.29688	−0.0544160
$569$	19.4806	0.816670	0.408335	−	0.912832i	$-0.366109\pi$
$569$	19.4806	0.816670	0.408335	+	0.912832i	$0.366109\pi$
$570$	−10.3159	−0.432084
$571$	−15.6310	−0.654139	−0.327070	−	0.945000i	$-0.606061\pi$
$571$	−15.6310	−0.654139	−0.327070	+	0.945000i	$0.606061\pi$
$572$	−13.0724	−0.546583
$573$	−3.81190	−0.159244
$574$	14.9770	0.625128
$575$	−9.51837	−0.396944
$576$	−7.08147	−0.295061
$577$	−30.6465	−1.27583	−0.637916	−	0.770106i	$-0.720203\pi$
$577$	−30.6465	−1.27583	−0.637916	+	0.770106i	$0.720203\pi$
$578$	1.97184	0.0820176
$579$	−7.01184	−0.291402
$580$	3.45856	0.143609
$581$	−31.9117	−1.32392
$582$	−16.5364	−0.685456
$583$	19.5044	0.807790
$584$	1.07448	0.0444622
$585$	7.03945	0.291045
$586$	−48.8935	−2.01977
$587$	15.3311	0.632781	0.316390	−	0.948629i	$-0.397529\pi$
$587$	15.3311	0.632781	0.316390	+	0.948629i	$0.397529\pi$
$588$	−1.04015	−0.0428952
$589$	−11.7966	−0.486069
$590$	84.7817	3.49041
$591$	4.27418	0.175816
$592$	0.169993	0.00698668
$593$	5.80406	0.238344	0.119172	−	0.992874i	$-0.461976\pi$
$593$	5.80406	0.238344	0.119172	+	0.992874i	$0.461976\pi$
$594$	−7.04038	−0.288870
$595$	9.21920	0.377951
$596$	25.1294	1.02934
$597$	12.3226	0.504329
$598$	−4.44960	−0.181958
$599$	−18.2345	−0.745040	−0.372520	−	0.928024i	$-0.621506\pi$
$599$	−18.2345	−0.745040	−0.372520	+	0.928024i	$0.621506\pi$
$600$	−1.80411	−0.0736524
$601$	5.72877	0.233681	0.116841	−	0.993151i	$-0.462723\pi$
$601$	5.72877	0.233681	0.116841	+	0.993151i	$0.462723\pi$
$602$	13.2475	0.539929
$603$	−5.65903	−0.230454
$604$	29.1120	1.18455
$605$	6.34675	0.258032
$606$	30.3522	1.23297
$607$	−32.2185	−1.30771	−0.653855	−	0.756620i	$-0.726849\pi$
$607$	−32.2185	−1.30771	−0.653855	+	0.756620i	$0.726849\pi$
$608$	11.3308	0.459525
$609$	1.28135	0.0519230
$610$	−24.2460	−0.981690
$611$	10.0958	0.408433
$612$	1.88814	0.0763234
$613$	39.7068	1.60374	0.801871	−	0.597498i	$-0.203838\pi$
$613$	39.7068	1.60374	0.801871	+	0.597498i	$0.203838\pi$
$614$	9.52407	0.384360
$615$	10.8579	0.437835
$616$	2.00000	0.0805824
$617$	13.7441	0.553318	0.276659	−	0.960968i	$-0.410773\pi$
$617$	13.7441	0.553318	0.276659	+	0.960968i	$0.410773\pi$
$618$	−7.24427	−0.291407
$619$	6.94362	0.279088	0.139544	−	0.990216i	$-0.455436\pi$
$619$	6.94362	0.279088	0.139544	+	0.990216i	$0.455436\pi$
$620$	56.1102	2.25344
$621$	−1.16374	−0.0466992
$622$	−22.2524	−0.892238
$623$	−1.06169	−0.0425357
$624$	−8.16587	−0.326896
$625$	1.00259	0.0401035
$626$	−4.98350	−0.199181
$627$	5.14537	0.205486
$628$	−32.3898	−1.29249
$629$	−0.0403668	−0.00160953
$630$	18.1788	0.724259
$631$	−23.1178	−0.920307	−0.460153	−	0.887839i	$-0.652206\pi$
$631$	−23.1178	−0.920307	−0.460153	+	0.887839i	$0.652206\pi$
$632$	−0.220574	−0.00877397
$633$	−1.63389	−0.0649415
$634$	−8.95453	−0.355630
$635$	−79.2115	−3.14341
$636$	−10.3143	−0.408989
$637$	−1.06822	−0.0423242
$638$	−3.55234	−0.140639
$639$	5.87958	0.232593
$640$	6.39600	0.252824
$641$	−16.7995	−0.663540	−0.331770	−	0.943360i	$-0.607646\pi$
$641$	−16.7995	−0.663540	−0.331770	+	0.943360i	$0.607646\pi$
$642$	−2.90705	−0.114732
$643$	28.0408	1.10582	0.552910	−	0.833241i	$-0.313517\pi$
$643$	28.0408	1.10582	0.552910	+	0.833241i	$0.313517\pi$
$644$	−5.58006	−0.219885
$645$	9.60412	0.378162
$646$	−2.84159	−0.111801
$647$	−14.4609	−0.568516	−0.284258	−	0.958748i	$-0.591747\pi$
$647$	−14.4609	−0.568516	−0.284258	+	0.958748i	$0.591747\pi$
$648$	−0.220574	−0.00866498
$649$	−42.2876	−1.65993
$650$	31.2733	1.22664
$651$	20.7881	0.814749
$652$	−3.26281	−0.127782
$653$	4.29782	0.168187	0.0840934	−	0.996458i	$-0.473201\pi$
$653$	4.29782	0.168187	0.0840934	+	0.996458i	$0.473201\pi$
$654$	−24.4818	−0.957315
$655$	−79.3771	−3.10152
$656$	−12.5954	−0.491767
$657$	−4.87127	−0.190046
$658$	26.0716	1.01638
$659$	36.8066	1.43378	0.716891	−	0.697185i	$-0.245564\pi$
$659$	36.8066	1.43378	0.716891	+	0.697185i	$0.245564\pi$
$660$	−24.4739	−0.952644
$661$	24.4284	0.950154	0.475077	−	0.879944i	$-0.342420\pi$
$661$	24.4284	0.950154	0.475077	+	0.879944i	$0.342420\pi$
$662$	28.9145	1.12380
$663$	1.93908	0.0753075
$664$	2.77175	0.107565
$665$	−13.2857	−0.515197
$666$	−0.0795967	−0.00308431
$667$	−0.587183	−0.0227358
$668$	12.7061	0.491614
$669$	−6.53396	−0.252617
$670$	−40.5095	−1.56502
$671$	12.0935	0.466863
$672$	−19.9673	−0.770257
$673$	−2.96095	−0.114136	−0.0570680	−	0.998370i	$-0.518175\pi$
$673$	−2.96095	−0.114136	−0.0570680	+	0.998370i	$0.518175\pi$
$674$	4.49880	0.173287
$675$	8.17914	0.314815
$676$	−17.4463	−0.671013
$677$	20.3654	0.782705	0.391353	−	0.920241i	$-0.372007\pi$
$677$	20.3654	0.782705	0.391353	+	0.920241i	$0.372007\pi$
$678$	0.932984	0.0358310
$679$	−21.2971	−0.817307
$680$	−0.800753	−0.0307075
$681$	8.29767	0.317967
$682$	−57.6316	−2.20683
$683$	11.5422	0.441650	0.220825	−	0.975313i	$-0.429125\pi$
$683$	11.5422	0.441650	0.220825	+	0.975313i	$0.429125\pi$
$684$	−2.72098	−0.104039
$685$	−77.3944	−2.95709
$686$	−37.8111	−1.44363
$687$	21.8562	0.833867
$688$	−11.1409	−0.424744
$689$	−10.5926	−0.403546
$690$	−8.33047	−0.317136
$691$	−18.2376	−0.693790	−0.346895	−	0.937904i	$-0.612764\pi$
$691$	−18.2376	−0.693790	−0.346895	+	0.937904i	$0.612764\pi$
$692$	−22.0989	−0.840072
$693$	−9.06725	−0.344436
$694$	−25.8116	−0.979795
$695$	−19.8888	−0.754425
$696$	−0.111294	−0.00421860
$697$	2.99092	0.113289
$698$	51.9227	1.96530
$699$	5.84118	0.220934
$700$	39.2185	1.48232
$701$	12.0566	0.455370	0.227685	−	0.973735i	$-0.426884\pi$
$701$	12.0566	0.455370	0.227685	+	0.973735i	$0.426884\pi$
$702$	3.82354	0.144310
$703$	0.0581722	0.00219401
$704$	25.2842	0.952934
$705$	18.9012	0.711861
$706$	−7.87533	−0.296392
$707$	39.0903	1.47014
$708$	22.3625	0.840436
$709$	10.3804	0.389844	0.194922	−	0.980819i	$-0.437555\pi$
$709$	10.3804	0.389844	0.194922	+	0.980819i	$0.437555\pi$
$710$	42.0882	1.57954
$711$	1.00000	0.0375029
$712$	0.0922153	0.00345591
$713$	−9.52620	−0.356759
$714$	5.00750	0.187401
$715$	−25.1342	−0.939964
$716$	21.6740	0.809994
$717$	−5.75852	−0.215056
$718$	38.9741	1.45450
$719$	−37.4206	−1.39555	−0.697777	−	0.716315i	$-0.745827\pi$
$719$	−37.4206	−1.39555	−0.697777	+	0.716315i	$0.745827\pi$
$720$	−15.2880	−0.569750
$721$	−9.32983	−0.347461
$722$	−33.3699	−1.24190
$723$	−9.29987	−0.345866
$724$	−31.7736	−1.18086
$725$	4.12692	0.153270
$726$	3.44730	0.127941
$727$	2.14751	0.0796468	0.0398234	−	0.999207i	$-0.487320\pi$
$727$	2.14751	0.0796468	0.0398234	+	0.999207i	$0.487320\pi$
$728$	−1.08618	−0.0402563
$729$	1.00000	0.0370370
$730$	−34.8704	−1.29061
$731$	2.64554	0.0978488
$732$	−6.39527	−0.236376
$733$	50.7078	1.87294	0.936468	−	0.350753i	$-0.114074\pi$
$733$	50.7078	1.87294	0.936468	+	0.350753i	$0.114074\pi$
$734$	−8.32878	−0.307421
$735$	−1.99989	−0.0737672
$736$	9.15009	0.337277
$737$	20.2054	0.744276
$738$	5.89759	0.217093
$739$	−25.8330	−0.950284	−0.475142	−	0.879909i	$-0.657603\pi$
$739$	−25.8330	−0.950284	−0.475142	+	0.879909i	$0.657603\pi$
$740$	−0.276695	−0.0101715
$741$	−2.79438	−0.102654
$742$	−27.3544	−1.00421
$743$	41.2616	1.51374	0.756872	−	0.653564i	$-0.226727\pi$
$743$	41.2616	1.51374	0.756872	+	0.653564i	$0.226727\pi$
$744$	−1.80559	−0.0661962
$745$	48.3162	1.77017
$746$	55.7674	2.04179
$747$	−12.5661	−0.459769
$748$	−6.74154	−0.246495
$749$	−3.74396	−0.136801
$750$	22.7574	0.830984
$751$	4.64366	0.169450	0.0847249	−	0.996404i	$-0.472999\pi$
$751$	4.64366	0.169450	0.0847249	+	0.996404i	$0.472999\pi$
$752$	−21.9257	−0.799548
$753$	22.6176	0.824231
$754$	1.92923	0.0702585
$755$	55.9733	2.03708
$756$	4.79494	0.174390
$757$	43.1200	1.56722	0.783612	−	0.621250i	$-0.213375\pi$
$757$	43.1200	1.56722	0.783612	+	0.621250i	$0.213375\pi$
$758$	55.0205	1.99844
$759$	4.15509	0.150820
$760$	1.15396	0.0418584
$761$	−24.6797	−0.894638	−0.447319	−	0.894374i	$-0.647621\pi$
$761$	−24.6797	−0.894638	−0.447319	+	0.894374i	$0.647621\pi$
$762$	−43.0245	−1.55861
$763$	−31.5299	−1.14146
$764$	−7.19739	−0.260392
$765$	3.63031	0.131254
$766$	7.53510	0.272254
$767$	22.9659	0.829249
$768$	17.6370	0.636420
$769$	−23.1097	−0.833357	−0.416679	−	0.909054i	$-0.636806\pi$
$769$	−23.1097	−0.833357	−0.416679	+	0.909054i	$0.636806\pi$
$770$	−64.9067	−2.33908
$771$	−26.5546	−0.956342
$772$	−13.2393	−0.476493
$773$	17.0074	0.611714	0.305857	−	0.952077i	$-0.401057\pi$
$773$	17.0074	0.611714	0.305857	+	0.952077i	$0.401057\pi$
$774$	5.21657	0.187506
$775$	66.9533	2.40503
$776$	1.84980	0.0664040
$777$	−0.102512	−0.00367759
$778$	32.7525	1.17423
$779$	−4.31018	−0.154428
$780$	13.2914	0.475910
$781$	−20.9929	−0.751184
$782$	−2.29470	−0.0820583
$783$	0.504567	0.0180317
$784$	2.31991	0.0828539
$785$	−62.2756	−2.22271
$786$	−43.1144	−1.53784
$787$	−41.5252	−1.48021	−0.740107	−	0.672489i	$-0.765225\pi$
$787$	−41.5252	−1.48021	−0.740107	+	0.672489i	$0.765225\pi$
$788$	8.07024	0.287490
$789$	17.1888	0.611939
$790$	7.15837	0.254683
$791$	1.20158	0.0427233
$792$	0.787554	0.0279845
$793$	−6.56781	−0.233230
$794$	−9.18583	−0.325993
$795$	−19.8313	−0.703343
$796$	23.2667	0.824666
$797$	−40.1927	−1.42370	−0.711849	−	0.702333i	$-0.752142\pi$
$797$	−40.1927	−1.42370	−0.711849	+	0.702333i	$0.752142\pi$
$798$	−7.21625	−0.255453
$799$	5.20651	0.184193
$800$	−64.3099	−2.27370
$801$	−0.418069	−0.0147717
$802$	−49.9059	−1.76224
$803$	17.3927	0.613776
$804$	−10.6850	−0.376832
$805$	−10.7287	−0.378138
$806$	31.2990	1.10246
$807$	−21.8332	−0.768565
$808$	−3.39527	−0.119445
$809$	−13.4335	−0.472298	−0.236149	−	0.971717i	$-0.575885\pi$
$809$	−13.4335	−0.472298	−0.236149	+	0.971717i	$0.575885\pi$
$810$	7.15837	0.251520
$811$	−1.03430	−0.0363192	−0.0181596	−	0.999835i	$-0.505781\pi$
$811$	−1.03430	−0.0363192	−0.0181596	+	0.999835i	$0.505781\pi$
$812$	2.41937	0.0849032
$813$	7.47669	0.262219
$814$	0.284198	0.00996113
$815$	−6.27339	−0.219747
$816$	−4.21121	−0.147422
$817$	−3.81246	−0.133381
$818$	−22.2390	−0.777567
$819$	4.92431	0.172069
$820$	20.5013	0.715936
$821$	20.3471	0.710119	0.355060	−	0.934844i	$-0.384461\pi$
$821$	20.3471	0.710119	0.355060	+	0.934844i	$0.384461\pi$
$822$	−42.0375	−1.46623
$823$	−16.3376	−0.569494	−0.284747	−	0.958603i	$-0.591910\pi$
$823$	−16.3376	−0.569494	−0.284747	+	0.958603i	$0.591910\pi$
$824$	0.810361	0.0282303
$825$	−29.2034	−1.01673
$826$	59.3073	2.06357
$827$	−22.6386	−0.787221	−0.393611	−	0.919277i	$-0.628774\pi$
$827$	−22.6386	−0.787221	−0.393611	+	0.919277i	$0.628774\pi$
$828$	−2.19730	−0.0763614
$829$	−30.1898	−1.04854	−0.524268	−	0.851554i	$-0.675661\pi$
$829$	−30.1898	−1.04854	−0.524268	+	0.851554i	$0.675661\pi$
$830$	−89.9527	−3.12230
$831$	−12.1905	−0.422882
$832$	−13.7315	−0.476055
$833$	−0.550888	−0.0190872
$834$	−10.8028	−0.374070
$835$	24.4300	0.845434
$836$	9.71517	0.336006
$837$	8.18587	0.282945
$838$	16.9307	0.584861
$839$	45.6128	1.57473	0.787364	−	0.616489i	$-0.211445\pi$
$839$	45.6128	1.57473	0.787364	+	0.616489i	$0.211445\pi$
$840$	−2.03352	−0.0701631
$841$	−28.7454	−0.991221
$842$	−11.1477	−0.384174
$843$	21.4458	0.738632
$844$	−3.08502	−0.106191
$845$	−33.5440	−1.15395
$846$	10.2664	0.352965
$847$	4.43974	0.152551
$848$	23.0046	0.789980
$849$	27.6229	0.948015
$850$	16.1279	0.553183
$851$	0.0469764	0.00161033
$852$	11.1015	0.380330
$853$	−38.1467	−1.30612	−0.653058	−	0.757308i	$-0.726514\pi$
$853$	−38.1467	−1.30612	−0.653058	+	0.757308i	$0.726514\pi$
$854$	−16.9608	−0.580386
$855$	−5.23160	−0.178917
$856$	0.325190	0.0111148
$857$	16.5285	0.564604	0.282302	−	0.959326i	$-0.408902\pi$
$857$	16.5285	0.564604	0.282302	+	0.959326i	$0.408902\pi$
$858$	−13.6519	−0.466067
$859$	−25.1497	−0.858098	−0.429049	−	0.903281i	$-0.641151\pi$
$859$	−25.1497	−0.858098	−0.429049	+	0.903281i	$0.641151\pi$
$860$	18.1339	0.618361
$861$	7.59546	0.258853
$862$	49.3309	1.68022
$863$	29.0872	0.990141	0.495070	−	0.868853i	$-0.335142\pi$
$863$	29.0872	0.990141	0.495070	+	0.868853i	$0.335142\pi$
$864$	−7.86267	−0.267493
$865$	−42.4893	−1.44468
$866$	21.8853	0.743694
$867$	1.00000	0.0339618
$868$	39.2508	1.33226
$869$	−3.57047	−0.121120
$870$	3.61188	0.122454
$871$	−10.9733	−0.371816
$872$	2.73860	0.0927406
$873$	−8.38630	−0.283833
$874$	3.30687	0.111857
$875$	29.3091	0.990829
$876$	−9.19763	−0.310759
$877$	−0.533779	−0.0180244	−0.00901222	−	0.999959i	$-0.502869\pi$
$877$	−0.533779	−0.0180244	−0.00901222	+	0.999959i	$0.502869\pi$
$878$	56.9738	1.92277
$879$	−24.7959	−0.836345
$880$	54.5854	1.84007
$881$	−30.4044	−1.02435	−0.512175	−	0.858881i	$-0.671160\pi$
$881$	−30.4044	−1.02435	−0.512175	+	0.858881i	$0.671160\pi$
$882$	−1.08626	−0.0365763
$883$	−51.1590	−1.72164	−0.860819	−	0.508911i	$-0.830048\pi$
$883$	−51.1590	−1.72164	−0.860819	+	0.508911i	$0.830048\pi$
$884$	3.66125	0.123141
$885$	42.9963	1.44530
$886$	1.06992	0.0359448
$887$	28.0292	0.941127	0.470564	−	0.882366i	$-0.344051\pi$
$887$	28.0292	0.941127	0.470564	+	0.882366i	$0.344051\pi$
$888$	0.00890388	0.000298795 0
$889$	−55.4108	−1.85842
$890$	−2.99269	−0.100315
$891$	−3.57047	−0.119615
$892$	−12.3370	−0.413074
$893$	−7.50304	−0.251080
$894$	26.2434	0.877710
$895$	41.6724	1.39295
$896$	4.47420	0.149472
$897$	−2.25658	−0.0753450
$898$	30.1270	1.00535
$899$	4.13032	0.137754
$900$	15.4433	0.514778
$901$	−5.46270	−0.181989
$902$	−21.0572	−0.701128
$903$	6.71837	0.223573
$904$	−0.104366	−0.00347115
$905$	−61.0909	−2.03073
$906$	30.4024	1.01005
$907$	2.95153	0.0980040	0.0490020	−	0.998799i	$-0.484396\pi$
$907$	2.95153	0.0980040	0.0490020	+	0.998799i	$0.484396\pi$
$908$	15.6671	0.519932
$909$	15.3928	0.510548
$910$	35.2500	1.16853
$911$	45.2180	1.49814	0.749069	−	0.662492i	$-0.230501\pi$
$911$	45.2180	1.49814	0.749069	+	0.662492i	$0.230501\pi$
$912$	6.06873	0.200956
$913$	44.8668	1.48488
$914$	−57.4515	−1.90033
$915$	−12.2961	−0.406498
$916$	41.2676	1.36352
$917$	−55.5267	−1.83365
$918$	1.97184	0.0650803
$919$	−43.3326	−1.42941	−0.714706	−	0.699425i	$-0.753439\pi$
$919$	−43.3326	−1.42941	−0.714706	+	0.699425i	$0.753439\pi$
$920$	0.931866	0.0307227
$921$	4.83005	0.159156
$922$	18.8502	0.620798
$923$	11.4010	0.375267
$924$	−17.1202	−0.563214
$925$	−0.330166	−0.0108558
$926$	15.6407	0.513985
$927$	−3.67387	−0.120666
$928$	−3.96724	−0.130231
$929$	−43.8919	−1.44005	−0.720023	−	0.693950i	$-0.755869\pi$
$929$	−43.8919	−1.44005	−0.720023	+	0.693950i	$0.755869\pi$
$930$	58.5975	1.92149
$931$	0.793880	0.0260184
$932$	11.0289	0.361265
$933$	−11.2851	−0.369457
$934$	24.6928	0.807973
$935$	−12.9619	−0.423900
$936$	−0.427711	−0.0139802
$937$	−21.3655	−0.697982	−0.348991	−	0.937126i	$-0.613476\pi$
$937$	−21.3655	−0.697982	−0.348991	+	0.937126i	$0.613476\pi$
$938$	−28.3376	−0.925255
$939$	−2.52734	−0.0824765
$940$	35.6881	1.16402
$941$	24.6762	0.804421	0.402211	−	0.915547i	$-0.368242\pi$
$941$	24.6762	0.804421	0.402211	+	0.915547i	$0.368242\pi$
$942$	−33.8256	−1.10210
$943$	−3.48064	−0.113345
$944$	−49.8764	−1.62334
$945$	9.21920	0.299901
$946$	−18.6256	−0.605571
$947$	11.4172	0.371010	0.185505	−	0.982643i	$-0.440608\pi$
$947$	11.4172	0.371010	0.185505	+	0.982643i	$0.440608\pi$
$948$	1.88814	0.0613239
$949$	−9.44577	−0.306623
$950$	−23.2418	−0.754063
$951$	−4.54121	−0.147259
$952$	−0.560151	−0.0181546
$953$	3.61570	0.117124	0.0585620	−	0.998284i	$-0.481348\pi$
$953$	3.61570	0.117124	0.0585620	+	0.998284i	$0.481348\pi$
$954$	−10.7715	−0.348742
$955$	−13.8384	−0.447799
$956$	−10.8729	−0.351654
$957$	−1.80154	−0.0582356
$958$	−10.0232	−0.323833
$959$	−54.1397	−1.74826
$960$	−25.7079	−0.829720
$961$	36.0084	1.16156
$962$	−0.154344	−0.00497626
$963$	−1.47429	−0.0475082
$964$	−17.5594	−0.565551
$965$	−25.4551	−0.819430
$966$	−5.82742	−0.187494
$967$	−31.7755	−1.02183	−0.510916	−	0.859631i	$-0.670694\pi$
$967$	−31.7755	−1.02183	−0.510916	+	0.859631i	$0.670694\pi$
$968$	−0.385623	−0.0123944
$969$	−1.44109	−0.0462945
$970$	−60.0322	−1.92752
$971$	−36.2879	−1.16453	−0.582267	−	0.812998i	$-0.697834\pi$
$971$	−36.2879	−1.16453	−0.582267	+	0.812998i	$0.697834\pi$
$972$	1.88814	0.0605620
$973$	−13.9128	−0.446025
$974$	−1.56605	−0.0501796
$975$	15.8600	0.507926
$976$	14.2637	0.456570
$977$	4.12547	0.131985	0.0659927	−	0.997820i	$-0.478979\pi$
$977$	4.12547	0.131985	0.0659927	+	0.997820i	$0.478979\pi$
$978$	−3.40745	−0.108958
$979$	1.49270	0.0477070
$980$	−3.77608	−0.120622
$981$	−12.4158	−0.396405
$982$	34.3041	1.09469
$983$	24.6831	0.787267	0.393634	−	0.919267i	$-0.371218\pi$
$983$	24.6831	0.787267	0.393634	+	0.919267i	$0.371218\pi$
$984$	−0.659719	−0.0210311
$985$	15.5166	0.494400
$986$	0.994923	0.0316848
$987$	13.2220	0.420860
$988$	−5.27618	−0.167858
$989$	−3.07871	−0.0978974
$990$	−25.5588	−0.812311
$991$	34.7003	1.10229	0.551146	−	0.834409i	$-0.314191\pi$
$991$	34.7003	1.10229	0.551146	+	0.834409i	$0.314191\pi$
$992$	−64.3628	−2.04352
$993$	14.6638	0.465340
$994$	29.4420	0.933843
$995$	44.7347	1.41818
$996$	−23.7265	−0.751803
$997$	55.7950	1.76705	0.883523	−	0.468388i	$-0.155165\pi$
$997$	55.7950	1.76705	0.883523	+	0.468388i	$0.155165\pi$
$998$	−42.0792	−1.33199
$999$	−0.0403668	−0.00127715

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.25	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.25	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.97184 q^{2} +1.00000 q^{3} +1.88814 q^{4} +3.63031 q^{5} +1.97184 q^{6} +2.53951 q^{7} -0.220574 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.97184 q^{2} +1.00000 q^{3} +1.88814 q^{4} +3.63031 q^{5} +1.97184 q^{6} +2.53951 q^{7} -0.220574 q^{8} +1.00000 q^{9} +7.15837 q^{10} -3.57047 q^{11} +1.88814 q^{12} +1.93908 q^{13} +5.00750 q^{14} +3.63031 q^{15} -4.21121 q^{16} +1.00000 q^{17} +1.97184 q^{18} -1.44109 q^{19} +6.85452 q^{20} +2.53951 q^{21} -7.04038 q^{22} -1.16374 q^{23} -0.220574 q^{24} +8.17914 q^{25} +3.82354 q^{26} +1.00000 q^{27} +4.79494 q^{28} +0.504567 q^{29} +7.15837 q^{30} +8.18587 q^{31} -7.86267 q^{32} -3.57047 q^{33} +1.97184 q^{34} +9.21920 q^{35} +1.88814 q^{36} -0.0403668 q^{37} -2.84159 q^{38} +1.93908 q^{39} -0.800753 q^{40} +2.99092 q^{41} +5.00750 q^{42} +2.64554 q^{43} -6.74154 q^{44} +3.63031 q^{45} -2.29470 q^{46} +5.20651 q^{47} -4.21121 q^{48} -0.550888 q^{49} +16.1279 q^{50} +1.00000 q^{51} +3.66125 q^{52} -5.46270 q^{53} +1.97184 q^{54} -12.9619 q^{55} -0.560151 q^{56} -1.44109 q^{57} +0.994923 q^{58} +11.8437 q^{59} +6.85452 q^{60} -3.38708 q^{61} +16.1412 q^{62} +2.53951 q^{63} -7.08147 q^{64} +7.03945 q^{65} -7.04038 q^{66} -5.65903 q^{67} +1.88814 q^{68} -1.16374 q^{69} +18.1788 q^{70} +5.87958 q^{71} -0.220574 q^{72} -4.87127 q^{73} -0.0795967 q^{74} +8.17914 q^{75} -2.72098 q^{76} -9.06725 q^{77} +3.82354 q^{78} +1.00000 q^{79} -15.2880 q^{80} +1.00000 q^{81} +5.89759 q^{82} -12.5661 q^{83} +4.79494 q^{84} +3.63031 q^{85} +5.21657 q^{86} +0.504567 q^{87} +0.787554 q^{88} -0.418069 q^{89} +7.15837 q^{90} +4.92431 q^{91} -2.19730 q^{92} +8.18587 q^{93} +10.2664 q^{94} -5.23160 q^{95} -7.86267 q^{96} -8.38630 q^{97} -1.08626 q^{98} -3.57047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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