LMFDB - Embedded newform 8013.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59380 q^{2} +1.00000 q^{3} +4.72779 q^{4} +3.19035 q^{5} -2.59380 q^{6} -1.98667 q^{7} -7.07533 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.59380 q^{2} +1.00000 q^{3} +4.72779 q^{4} +3.19035 q^{5} -2.59380 q^{6} -1.98667 q^{7} -7.07533 q^{8} +1.00000 q^{9} -8.27513 q^{10} +5.06836 q^{11} +4.72779 q^{12} +0.245801 q^{13} +5.15303 q^{14} +3.19035 q^{15} +8.89640 q^{16} +4.87352 q^{17} -2.59380 q^{18} +0.823783 q^{19} +15.0833 q^{20} -1.98667 q^{21} -13.1463 q^{22} +1.93066 q^{23} -7.07533 q^{24} +5.17835 q^{25} -0.637557 q^{26} +1.00000 q^{27} -9.39256 q^{28} -3.16980 q^{29} -8.27513 q^{30} -3.64138 q^{31} -8.92480 q^{32} +5.06836 q^{33} -12.6409 q^{34} -6.33818 q^{35} +4.72779 q^{36} -4.19585 q^{37} -2.13673 q^{38} +0.245801 q^{39} -22.5728 q^{40} +9.38947 q^{41} +5.15303 q^{42} +12.9096 q^{43} +23.9621 q^{44} +3.19035 q^{45} -5.00773 q^{46} +0.500259 q^{47} +8.89640 q^{48} -3.05313 q^{49} -13.4316 q^{50} +4.87352 q^{51} +1.16209 q^{52} +1.17465 q^{53} -2.59380 q^{54} +16.1699 q^{55} +14.0564 q^{56} +0.823783 q^{57} +8.22181 q^{58} -7.13919 q^{59} +15.0833 q^{60} -1.40681 q^{61} +9.44500 q^{62} -1.98667 q^{63} +5.35633 q^{64} +0.784191 q^{65} -13.1463 q^{66} +11.2667 q^{67} +23.0410 q^{68} +1.93066 q^{69} +16.4400 q^{70} +8.14403 q^{71} -7.07533 q^{72} +16.1711 q^{73} +10.8832 q^{74} +5.17835 q^{75} +3.89467 q^{76} -10.0692 q^{77} -0.637557 q^{78} -3.53457 q^{79} +28.3826 q^{80} +1.00000 q^{81} -24.3544 q^{82} -15.2846 q^{83} -9.39256 q^{84} +15.5483 q^{85} -33.4848 q^{86} -3.16980 q^{87} -35.8603 q^{88} -10.1431 q^{89} -8.27513 q^{90} -0.488325 q^{91} +9.12773 q^{92} -3.64138 q^{93} -1.29757 q^{94} +2.62816 q^{95} -8.92480 q^{96} +2.80629 q^{97} +7.91921 q^{98} +5.06836 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * 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 $

$2$	−2.59380	−1.83409	−0.917046	−	0.398781i	$-0.869433\pi$
$2$	−2.59380	−1.83409	−0.917046	+	0.398781i	$0.869433\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.72779	2.36389
$5$	3.19035	1.42677	0.713384	−	0.700773i	$-0.247161\pi$
$5$	3.19035	1.42677	0.713384	+	0.700773i	$0.247161\pi$
$6$	−2.59380	−1.05891
$7$	−1.98667	−0.750892	−0.375446	−	0.926844i	$-0.622510\pi$
$7$	−1.98667	−0.750892	−0.375446	+	0.926844i	$0.622510\pi$
$8$	−7.07533	−2.50151
$9$	1.00000	0.333333
$10$	−8.27513	−2.61683
$11$	5.06836	1.52817	0.764084	−	0.645116i	$-0.223191\pi$
$11$	5.06836	1.52817	0.764084	+	0.645116i	$0.223191\pi$
$12$	4.72779	1.36479
$13$	0.245801	0.0681728	0.0340864	−	0.999419i	$-0.489148\pi$
$13$	0.245801	0.0681728	0.0340864	+	0.999419i	$0.489148\pi$
$14$	5.15303	1.37720
$15$	3.19035	0.823745
$16$	8.89640	2.22410
$17$	4.87352	1.18200	0.591001	−	0.806671i	$-0.298733\pi$
$17$	4.87352	1.18200	0.591001	+	0.806671i	$0.298733\pi$
$18$	−2.59380	−0.611364
$19$	0.823783	0.188989	0.0944944	−	0.995525i	$-0.469877\pi$
$19$	0.823783	0.188989	0.0944944	+	0.995525i	$0.469877\pi$
$20$	15.0833	3.37273
$21$	−1.98667	−0.433527
$22$	−13.1463	−2.80280
$23$	1.93066	0.402570	0.201285	−	0.979533i	$-0.435488\pi$
$23$	1.93066	0.402570	0.201285	+	0.979533i	$0.435488\pi$
$24$	−7.07533	−1.44425
$25$	5.17835	1.03567
$26$	−0.637557	−0.125035
$27$	1.00000	0.192450
$28$	−9.39256	−1.77503
$29$	−3.16980	−0.588616	−0.294308	−	0.955711i	$-0.595089\pi$
$29$	−3.16980	−0.588616	−0.294308	+	0.955711i	$0.595089\pi$
$30$	−8.27513	−1.51082
$31$	−3.64138	−0.654011	−0.327006	−	0.945022i	$-0.606040\pi$
$31$	−3.64138	−0.654011	−0.327006	+	0.945022i	$0.606040\pi$
$32$	−8.92480	−1.57770
$33$	5.06836	0.882289
$34$	−12.6409	−2.16790
$35$	−6.33818	−1.07135
$36$	4.72779	0.787965
$37$	−4.19585	−0.689793	−0.344896	−	0.938641i	$-0.612086\pi$
$37$	−4.19585	−0.689793	−0.344896	+	0.938641i	$0.612086\pi$
$38$	−2.13673	−0.346623
$39$	0.245801	0.0393596
$40$	−22.5728	−3.56907
$41$	9.38947	1.46639	0.733194	−	0.680019i	$-0.238029\pi$
$41$	9.38947	1.46639	0.733194	+	0.680019i	$0.238029\pi$
$42$	5.15303	0.795129
$43$	12.9096	1.96869	0.984345	−	0.176254i	$-0.0563981\pi$
$43$	12.9096	1.96869	0.984345	+	0.176254i	$0.0563981\pi$
$44$	23.9621	3.61243
$45$	3.19035	0.475590
$46$	−5.00773	−0.738350
$47$	0.500259	0.0729702	0.0364851	−	0.999334i	$-0.488384\pi$
$47$	0.500259	0.0729702	0.0364851	+	0.999334i	$0.488384\pi$
$48$	8.89640	1.28408
$49$	−3.05313	−0.436162
$50$	−13.4316	−1.89951
$51$	4.87352	0.682430
$52$	1.16209	0.161153
$53$	1.17465	0.161351	0.0806756	−	0.996740i	$-0.474292\pi$
$53$	1.17465	0.161351	0.0806756	+	0.996740i	$0.474292\pi$
$54$	−2.59380	−0.352971
$55$	16.1699	2.18034
$56$	14.0564	1.87836
$57$	0.823783	0.109113
$58$	8.22181	1.07958
$59$	−7.13919	−0.929444	−0.464722	−	0.885457i	$-0.653846\pi$
$59$	−7.13919	−0.929444	−0.464722	+	0.885457i	$0.653846\pi$
$60$	15.0833	1.94725
$61$	−1.40681	−0.180123	−0.0900617	−	0.995936i	$-0.528706\pi$
$61$	−1.40681	−0.180123	−0.0900617	+	0.995936i	$0.528706\pi$
$62$	9.44500	1.19952
$63$	−1.98667	−0.250297
$64$	5.35633	0.669541
$65$	0.784191	0.0972669
$66$	−13.1463	−1.61820
$67$	11.2667	1.37645	0.688223	−	0.725499i	$-0.258391\pi$
$67$	11.2667	1.37645	0.688223	+	0.725499i	$0.258391\pi$
$68$	23.0410	2.79413
$69$	1.93066	0.232424
$70$	16.4400	1.96495
$71$	8.14403	0.966519	0.483259	−	0.875477i	$-0.339453\pi$
$71$	8.14403	0.966519	0.483259	+	0.875477i	$0.339453\pi$
$72$	−7.07533	−0.833835
$73$	16.1711	1.89269	0.946344	−	0.323161i	$-0.104745\pi$
$73$	16.1711	1.89269	0.946344	+	0.323161i	$0.104745\pi$
$74$	10.8832	1.26514
$75$	5.17835	0.597944
$76$	3.89467	0.446750
$77$	−10.0692	−1.14749
$78$	−0.637557	−0.0721891
$79$	−3.53457	−0.397671	−0.198835	−	0.980033i	$-0.563716\pi$
$79$	−3.53457	−0.397671	−0.198835	+	0.980033i	$0.563716\pi$
$80$	28.3826	3.17328
$81$	1.00000	0.111111
$82$	−24.3544	−2.68949
$83$	−15.2846	−1.67770	−0.838852	−	0.544360i	$-0.816772\pi$
$83$	−15.2846	−1.67770	−0.838852	+	0.544360i	$0.816772\pi$
$84$	−9.39256	−1.02481
$85$	15.5483	1.68644
$86$	−33.4848	−3.61076
$87$	−3.16980	−0.339838
$88$	−35.8603	−3.82272
$89$	−10.1431	−1.07517	−0.537586	−	0.843209i	$-0.680663\pi$
$89$	−10.1431	−1.07517	−0.537586	+	0.843209i	$0.680663\pi$
$90$	−8.27513	−0.872275
$91$	−0.488325	−0.0511904
$92$	9.12773	0.951632
$93$	−3.64138	−0.377594
$94$	−1.29757	−0.133834
$95$	2.62816	0.269643
$96$	−8.92480	−0.910883
$97$	2.80629	0.284936	0.142468	−	0.989799i	$-0.454496\pi$
$97$	2.80629	0.284936	0.142468	+	0.989799i	$0.454496\pi$
$98$	7.91921	0.799961
$99$	5.06836	0.509390
$100$	24.4821	2.44821
$101$	1.18833	0.118243	0.0591216	−	0.998251i	$-0.481170\pi$
$101$	1.18833	0.118243	0.0591216	+	0.998251i	$0.481170\pi$
$102$	−12.6409	−1.25164
$103$	−3.87228	−0.381547	−0.190773	−	0.981634i	$-0.561100\pi$
$103$	−3.87228	−0.381547	−0.190773	+	0.981634i	$0.561100\pi$
$104$	−1.73912	−0.170535
$105$	−6.33818	−0.618543
$106$	−3.04681	−0.295933
$107$	−3.55642	−0.343812	−0.171906	−	0.985113i	$-0.554993\pi$
$107$	−3.55642	−0.343812	−0.171906	+	0.985113i	$0.554993\pi$
$108$	4.72779	0.454932
$109$	−8.09175	−0.775049	−0.387524	−	0.921859i	$-0.626670\pi$
$109$	−8.09175	−0.775049	−0.387524	+	0.921859i	$0.626670\pi$
$110$	−41.9414	−3.99895
$111$	−4.19585	−0.398252
$112$	−17.6742	−1.67006
$113$	−3.85557	−0.362702	−0.181351	−	0.983418i	$-0.558047\pi$
$113$	−3.85557	−0.362702	−0.181351	+	0.983418i	$0.558047\pi$
$114$	−2.13673	−0.200123
$115$	6.15947	0.574374
$116$	−14.9861	−1.39143
$117$	0.245801	0.0227243
$118$	18.5176	1.70469
$119$	−9.68209	−0.887556
$120$	−22.5728	−2.06060
$121$	14.6883	1.33530
$122$	3.64898	0.330363
$123$	9.38947	0.846620
$124$	−17.2157	−1.54601
$125$	0.568991	0.0508921
$126$	5.15303	0.459068
$127$	13.0579	1.15870	0.579350	−	0.815079i	$-0.303307\pi$
$127$	13.0579	1.15870	0.579350	+	0.815079i	$0.303307\pi$
$128$	3.95636	0.349697
$129$	12.9096	1.13662
$130$	−2.03403	−0.178396
$131$	−1.51727	−0.132564	−0.0662820	−	0.997801i	$-0.521114\pi$
$131$	−1.51727	−0.132564	−0.0662820	+	0.997801i	$0.521114\pi$
$132$	23.9621	2.08564
$133$	−1.63659	−0.141910
$134$	−29.2235	−2.52453
$135$	3.19035	0.274582
$136$	−34.4818	−2.95679
$137$	−5.24947	−0.448492	−0.224246	−	0.974533i	$-0.571992\pi$
$137$	−5.24947	−0.448492	−0.224246	+	0.974533i	$0.571992\pi$
$138$	−5.00773	−0.426286
$139$	9.48475	0.804486	0.402243	−	0.915533i	$-0.368231\pi$
$139$	9.48475	0.804486	0.402243	+	0.915533i	$0.368231\pi$
$140$	−29.9656	−2.53255
$141$	0.500259	0.0421294
$142$	−21.1240	−1.77268
$143$	1.24581	0.104180
$144$	8.89640	0.741366
$145$	−10.1128	−0.839819
$146$	−41.9447	−3.47136
$147$	−3.05313	−0.251818
$148$	−19.8371	−1.63060
$149$	8.08300	0.662185	0.331093	−	0.943598i	$-0.392583\pi$
$149$	8.08300	0.662185	0.331093	+	0.943598i	$0.392583\pi$
$150$	−13.4316	−1.09668
$151$	3.82291	0.311104	0.155552	−	0.987828i	$-0.450284\pi$
$151$	3.82291	0.311104	0.155552	+	0.987828i	$0.450284\pi$
$152$	−5.82854	−0.472757
$153$	4.87352	0.394001
$154$	26.1174	2.10460
$155$	−11.6173	−0.933123
$156$	1.16209	0.0930419
$157$	7.71216	0.615497	0.307749	−	0.951468i	$-0.400424\pi$
$157$	7.71216	0.615497	0.307749	+	0.951468i	$0.400424\pi$
$158$	9.16797	0.729364
$159$	1.17465	0.0931561
$160$	−28.4732	−2.25101
$161$	−3.83558	−0.302286
$162$	−2.59380	−0.203788
$163$	−4.49641	−0.352186	−0.176093	−	0.984374i	$-0.556346\pi$
$163$	−4.49641	−0.352186	−0.176093	+	0.984374i	$0.556346\pi$
$164$	44.3914	3.46639
$165$	16.1699	1.25882
$166$	39.6452	3.07706
$167$	−1.82265	−0.141041	−0.0705205	−	0.997510i	$-0.522466\pi$
$167$	−1.82265	−0.141041	−0.0705205	+	0.997510i	$0.522466\pi$
$168$	14.0564	1.08447
$169$	−12.9396	−0.995352
$170$	−40.3290	−3.09309
$171$	0.823783	0.0629963
$172$	61.0336	4.65377
$173$	−23.5027	−1.78688	−0.893440	−	0.449183i	$-0.851715\pi$
$173$	−23.5027	−1.78688	−0.893440	+	0.449183i	$0.851715\pi$
$174$	8.22181	0.623294
$175$	−10.2877	−0.777675
$176$	45.0902	3.39880
$177$	−7.13919	−0.536615
$178$	26.3093	1.97196
$179$	8.88872	0.664374	0.332187	−	0.943213i	$-0.392213\pi$
$179$	8.88872	0.664374	0.332187	+	0.943213i	$0.392213\pi$
$180$	15.0833	1.12424
$181$	−7.96963	−0.592378	−0.296189	−	0.955129i	$-0.595716\pi$
$181$	−7.96963	−0.592378	−0.296189	+	0.955129i	$0.595716\pi$
$182$	1.26662	0.0938879
$183$	−1.40681	−0.103994
$184$	−13.6600	−1.00703
$185$	−13.3862	−0.984175
$186$	9.44500	0.692541
$187$	24.7008	1.80630
$188$	2.36512	0.172494
$189$	−1.98667	−0.144509
$190$	−6.81691	−0.494551
$191$	10.9738	0.794036	0.397018	−	0.917811i	$-0.370045\pi$
$191$	10.9738	0.794036	0.397018	+	0.917811i	$0.370045\pi$
$192$	5.35633	0.386560
$193$	14.2303	1.02432	0.512160	−	0.858890i	$-0.328845\pi$
$193$	14.2303	1.02432	0.512160	+	0.858890i	$0.328845\pi$
$194$	−7.27895	−0.522598
$195$	0.784191	0.0561571
$196$	−14.4346	−1.03104
$197$	26.3142	1.87481	0.937406	−	0.348239i	$-0.113220\pi$
$197$	26.3142	1.87481	0.937406	+	0.348239i	$0.113220\pi$
$198$	−13.1463	−0.934267
$199$	−11.8744	−0.841755	−0.420878	−	0.907117i	$-0.638278\pi$
$199$	−11.8744	−0.841755	−0.420878	+	0.907117i	$0.638278\pi$
$200$	−36.6385	−2.59073
$201$	11.2667	0.794691
$202$	−3.08229	−0.216869
$203$	6.29735	0.441987
$204$	23.0410	1.61319
$205$	29.9557	2.09220
$206$	10.0439	0.699792
$207$	1.93066	0.134190
$208$	2.18674	0.151623
$209$	4.17523	0.288807
$210$	16.4400	1.13447
$211$	−4.95086	−0.340831	−0.170416	−	0.985372i	$-0.554511\pi$
$211$	−4.95086	−0.340831	−0.170416	+	0.985372i	$0.554511\pi$
$212$	5.55351	0.381417
$213$	8.14403	0.558020
$214$	9.22464	0.630583
$215$	41.1860	2.80886
$216$	−7.07533	−0.481415
$217$	7.23423	0.491091
$218$	20.9884	1.42151
$219$	16.1711	1.09274
$220$	76.4477	5.15410
$221$	1.19791	0.0805805
$222$	10.8832	0.730431
$223$	−1.59303	−0.106677	−0.0533386	−	0.998576i	$-0.516986\pi$
$223$	−1.59303	−0.106677	−0.0533386	+	0.998576i	$0.516986\pi$
$224$	17.7306	1.18468
$225$	5.17835	0.345223
$226$	10.0006	0.665229
$227$	−25.9749	−1.72401	−0.862007	−	0.506896i	$-0.830793\pi$
$227$	−25.9749	−1.72401	−0.862007	+	0.506896i	$0.830793\pi$
$228$	3.89467	0.257931
$229$	20.9223	1.38259	0.691293	−	0.722575i	$-0.257041\pi$
$229$	20.9223	1.38259	0.691293	+	0.722575i	$0.257041\pi$
$230$	−15.9764	−1.05345
$231$	−10.0692	−0.662503
$232$	22.4273	1.47243
$233$	29.5122	1.93341	0.966703	−	0.255901i	$-0.0823720\pi$
$233$	29.5122	1.93341	0.966703	+	0.255901i	$0.0823720\pi$
$234$	−0.637557	−0.0416784
$235$	1.59600	0.104112
$236$	−33.7526	−2.19711
$237$	−3.53457	−0.229595
$238$	25.1134	1.62786
$239$	17.1530	1.10954	0.554769	−	0.832005i	$-0.312807\pi$
$239$	17.1530	1.10954	0.554769	+	0.832005i	$0.312807\pi$
$240$	28.3826	1.83209
$241$	2.52599	0.162713	0.0813565	−	0.996685i	$-0.474075\pi$
$241$	2.52599	0.162713	0.0813565	+	0.996685i	$0.474075\pi$
$242$	−38.0985	−2.44906
$243$	1.00000	0.0641500
$244$	−6.65109	−0.425793
$245$	−9.74057	−0.622302
$246$	−24.3544	−1.55278
$247$	0.202486	0.0128839
$248$	25.7640	1.63601
$249$	−15.2846	−0.968622
$250$	−1.47585	−0.0933409
$251$	−14.5430	−0.917945	−0.458973	−	0.888450i	$-0.651782\pi$
$251$	−14.5430	−0.917945	−0.458973	+	0.888450i	$0.651782\pi$
$252$	−9.39256	−0.591676
$253$	9.78526	0.615194
$254$	−33.8695	−2.12516
$255$	15.5483	0.973669
$256$	−20.9747	−1.31092
$257$	−8.04735	−0.501980	−0.250990	−	0.967990i	$-0.580756\pi$
$257$	−8.04735	−0.501980	−0.250990	+	0.967990i	$0.580756\pi$
$258$	−33.4848	−2.08467
$259$	8.33577	0.517960
$260$	3.70749	0.229929
$261$	−3.16980	−0.196205
$262$	3.93548	0.243135
$263$	−3.75214	−0.231367	−0.115683	−	0.993286i	$-0.536906\pi$
$263$	−3.75214	−0.231367	−0.115683	+	0.993286i	$0.536906\pi$
$264$	−35.8603	−2.20705
$265$	3.74756	0.230211
$266$	4.24498	0.260276
$267$	−10.1431	−0.620750
$268$	53.2665	3.25377
$269$	4.71612	0.287547	0.143773	−	0.989611i	$-0.454076\pi$
$269$	4.71612	0.287547	0.143773	+	0.989611i	$0.454076\pi$
$270$	−8.27513	−0.503608
$271$	−25.8057	−1.56759	−0.783794	−	0.621021i	$-0.786718\pi$
$271$	−25.8057	−1.56759	−0.783794	+	0.621021i	$0.786718\pi$
$272$	43.3568	2.62889
$273$	−0.488325	−0.0295548
$274$	13.6161	0.822576
$275$	26.2457	1.58268
$276$	9.12773	0.549425
$277$	−17.4050	−1.04577	−0.522883	−	0.852404i	$-0.675144\pi$
$277$	−17.4050	−1.04577	−0.522883	+	0.852404i	$0.675144\pi$
$278$	−24.6015	−1.47550
$279$	−3.64138	−0.218004
$280$	44.8447	2.67999
$281$	−18.8805	−1.12631	−0.563157	−	0.826350i	$-0.690413\pi$
$281$	−18.8805	−1.12631	−0.563157	+	0.826350i	$0.690413\pi$
$282$	−1.29757	−0.0772691
$283$	13.8879	0.825549	0.412775	−	0.910833i	$-0.364560\pi$
$283$	13.8879	0.825549	0.412775	+	0.910833i	$0.364560\pi$
$284$	38.5032	2.28475
$285$	2.62816	0.155679
$286$	−3.23137	−0.191075
$287$	−18.6538	−1.10110
$288$	−8.92480	−0.525899
$289$	6.75122	0.397130
$290$	26.2305	1.54031
$291$	2.80629	0.164508
$292$	76.4537	4.47411
$293$	−3.75980	−0.219650	−0.109825	−	0.993951i	$-0.535029\pi$
$293$	−3.75980	−0.219650	−0.109825	+	0.993951i	$0.535029\pi$
$294$	7.91921	0.461858
$295$	−22.7765	−1.32610
$296$	29.6870	1.72552
$297$	5.06836	0.294096
$298$	−20.9657	−1.21451
$299$	0.474556	0.0274443
$300$	24.4821	1.41348
$301$	−25.6471	−1.47827
$302$	−9.91585	−0.570593
$303$	1.18833	0.0682678
$304$	7.32870	0.420330
$305$	−4.48822	−0.256995
$306$	−12.6409	−0.722634
$307$	30.5207	1.74191	0.870955	−	0.491363i	$-0.163501\pi$
$307$	30.5207	1.74191	0.870955	+	0.491363i	$0.163501\pi$
$308$	−47.6049	−2.71254
$309$	−3.87228	−0.220286
$310$	30.1329	1.71143
$311$	2.13835	0.121254	0.0606272	−	0.998160i	$-0.480690\pi$
$311$	2.13835	0.121254	0.0606272	+	0.998160i	$0.480690\pi$
$312$	−1.73912	−0.0984583
$313$	−18.0403	−1.01970	−0.509850	−	0.860263i	$-0.670299\pi$
$313$	−18.0403	−1.01970	−0.509850	+	0.860263i	$0.670299\pi$
$314$	−20.0038	−1.12888
$315$	−6.33818	−0.357116
$316$	−16.7107	−0.940051
$317$	−5.53079	−0.310640	−0.155320	−	0.987864i	$-0.549641\pi$
$317$	−5.53079	−0.310640	−0.155320	+	0.987864i	$0.549641\pi$
$318$	−3.04681	−0.170857
$319$	−16.0657	−0.899505
$320$	17.0886	0.955280
$321$	−3.55642	−0.198500
$322$	9.94872	0.554420
$323$	4.01473	0.223385
$324$	4.72779	0.262655
$325$	1.27284	0.0706045
$326$	11.6628	0.645942
$327$	−8.09175	−0.447475
$328$	−66.4336	−3.66818
$329$	−0.993850	−0.0547927
$330$	−41.9414	−2.30880
$331$	11.8230	0.649851	0.324926	−	0.945740i	$-0.394661\pi$
$331$	11.8230	0.649851	0.324926	+	0.945740i	$0.394661\pi$
$332$	−72.2623	−3.96591
$333$	−4.19585	−0.229931
$334$	4.72759	0.258682
$335$	35.9447	1.96387
$336$	−17.6742	−0.964208
$337$	2.77650	0.151246	0.0756229	−	0.997136i	$-0.475905\pi$
$337$	2.77650	0.151246	0.0756229	+	0.997136i	$0.475905\pi$
$338$	33.5627	1.82557
$339$	−3.85557	−0.209406
$340$	73.5088	3.98658
$341$	−18.4558	−0.999440
$342$	−2.13673	−0.115541
$343$	19.9723	1.07840
$344$	−91.3394	−4.92469
$345$	6.15947	0.331615
$346$	60.9613	3.27730
$347$	−1.62885	−0.0874413	−0.0437207	−	0.999044i	$-0.513921\pi$
$347$	−1.62885	−0.0874413	−0.0437207	+	0.999044i	$0.513921\pi$
$348$	−14.9861	−0.803340
$349$	−14.8821	−0.796620	−0.398310	−	0.917251i	$-0.630403\pi$
$349$	−14.8821	−0.796620	−0.398310	+	0.917251i	$0.630403\pi$
$350$	26.6842	1.42633
$351$	0.245801	0.0131199
$352$	−45.2341	−2.41099
$353$	10.2288	0.544426	0.272213	−	0.962237i	$-0.412245\pi$
$353$	10.2288	0.544426	0.272213	+	0.962237i	$0.412245\pi$
$354$	18.5176	0.984201
$355$	25.9823	1.37900
$356$	−47.9546	−2.54159
$357$	−9.68209	−0.512431
$358$	−23.0555	−1.21852
$359$	19.8878	1.04964	0.524820	−	0.851213i	$-0.324133\pi$
$359$	19.8878	1.04964	0.524820	+	0.851213i	$0.324133\pi$
$360$	−22.5728	−1.18969
$361$	−18.3214	−0.964283
$362$	20.6716	1.08648
$363$	14.6883	0.770936
$364$	−2.30870	−0.121009
$365$	51.5916	2.70043
$366$	3.64898	0.190735
$367$	22.7948	1.18988	0.594941	−	0.803770i	$-0.297176\pi$
$367$	22.7948	1.18988	0.594941	+	0.803770i	$0.297176\pi$
$368$	17.1759	0.895355
$369$	9.38947	0.488796
$370$	34.7212	1.80507
$371$	−2.33365	−0.121157
$372$	−17.2157	−0.892591
$373$	31.6897	1.64083	0.820414	−	0.571770i	$-0.193743\pi$
$373$	31.6897	1.64083	0.820414	+	0.571770i	$0.193743\pi$
$374$	−64.0688	−3.31292
$375$	0.568991	0.0293826
$376$	−3.53949	−0.182535
$377$	−0.779138	−0.0401276
$378$	5.15303	0.265043
$379$	24.9493	1.28156	0.640779	−	0.767725i	$-0.278611\pi$
$379$	24.9493	1.28156	0.640779	+	0.767725i	$0.278611\pi$
$380$	12.4254	0.637408
$381$	13.0579	0.668975
$382$	−28.4638	−1.45633
$383$	−31.0206	−1.58508	−0.792539	−	0.609821i	$-0.791241\pi$
$383$	−31.0206	−1.58508	−0.792539	+	0.609821i	$0.791241\pi$
$384$	3.95636	0.201897
$385$	−32.1242	−1.63720
$386$	−36.9106	−1.87870
$387$	12.9096	0.656230
$388$	13.2675	0.673557
$389$	8.75417	0.443854	0.221927	−	0.975063i	$-0.428765\pi$
$389$	8.75417	0.443854	0.221927	+	0.975063i	$0.428765\pi$
$390$	−2.03403	−0.102997
$391$	9.40909	0.475838
$392$	21.6019	1.09106
$393$	−1.51727	−0.0765359
$394$	−68.2538	−3.43858
$395$	−11.2765	−0.567384
$396$	23.9621	1.20414
$397$	−18.7909	−0.943089	−0.471544	−	0.881842i	$-0.656303\pi$
$397$	−18.7909	−0.943089	−0.471544	+	0.881842i	$0.656303\pi$
$398$	30.7998	1.54386
$399$	−1.63659	−0.0819319
$400$	46.0686	2.30343
$401$	−2.82244	−0.140946	−0.0704730	−	0.997514i	$-0.522451\pi$
$401$	−2.82244	−0.140946	−0.0704730	+	0.997514i	$0.522451\pi$
$402$	−29.2235	−1.45754
$403$	−0.895054	−0.0445858
$404$	5.61817	0.279514
$405$	3.19035	0.158530
$406$	−16.3340	−0.810645
$407$	−21.2661	−1.05412
$408$	−34.4818	−1.70710
$409$	−29.8231	−1.47466	−0.737329	−	0.675534i	$-0.763913\pi$
$409$	−29.8231	−1.47466	−0.737329	+	0.675534i	$0.763913\pi$
$410$	−77.6991	−3.83728
$411$	−5.24947	−0.258937
$412$	−18.3073	−0.901936
$413$	14.1832	0.697911
$414$	−5.00773	−0.246117
$415$	−48.7633	−2.39369
$416$	−2.19372	−0.107556
$417$	9.48475	0.464470
$418$	−10.8297	−0.529698
$419$	−29.3549	−1.43408	−0.717042	−	0.697030i	$-0.754504\pi$
$419$	−29.3549	−1.43408	−0.717042	+	0.697030i	$0.754504\pi$
$420$	−29.9656	−1.46217
$421$	−22.8494	−1.11361	−0.556806	−	0.830642i	$-0.687973\pi$
$421$	−22.8494	−1.11361	−0.556806	+	0.830642i	$0.687973\pi$
$422$	12.8415	0.625115
$423$	0.500259	0.0243234
$424$	−8.31106	−0.403621
$425$	25.2368	1.22416
$426$	−21.1240	−1.02346
$427$	2.79487	0.135253
$428$	−16.8140	−0.812736
$429$	1.24581	0.0601481
$430$	−106.828	−5.15172
$431$	−14.2715	−0.687436	−0.343718	−	0.939073i	$-0.611686\pi$
$431$	−14.2715	−0.687436	−0.343718	+	0.939073i	$0.611686\pi$
$432$	8.89640	0.428028
$433$	7.11365	0.341860	0.170930	−	0.985283i	$-0.445323\pi$
$433$	7.11365	0.341860	0.170930	+	0.985283i	$0.445323\pi$
$434$	−18.7641	−0.900707
$435$	−10.1128	−0.484870
$436$	−38.2561	−1.83213
$437$	1.59044	0.0760812
$438$	−41.9447	−2.00419
$439$	−32.7073	−1.56103	−0.780516	−	0.625136i	$-0.785044\pi$
$439$	−32.7073	−1.56103	−0.780516	+	0.625136i	$0.785044\pi$
$440$	−114.407	−5.45414
$441$	−3.05313	−0.145387
$442$	−3.10715	−0.147792
$443$	17.8792	0.849468	0.424734	−	0.905318i	$-0.360368\pi$
$443$	17.8792	0.849468	0.424734	+	0.905318i	$0.360368\pi$
$444$	−19.8371	−0.941426
$445$	−32.3602	−1.53402
$446$	4.13200	0.195656
$447$	8.08300	0.382313
$448$	−10.6413	−0.502753
$449$	−20.7607	−0.979758	−0.489879	−	0.871790i	$-0.662959\pi$
$449$	−20.7607	−0.979758	−0.489879	+	0.871790i	$0.662959\pi$
$450$	−13.4316	−0.633171
$451$	47.5892	2.24089
$452$	−18.2283	−0.857389
$453$	3.82291	0.179616
$454$	67.3736	3.16200
$455$	−1.55793	−0.0730369
$456$	−5.82854	−0.272946
$457$	18.6577	0.872772	0.436386	−	0.899760i	$-0.356258\pi$
$457$	18.6577	0.872772	0.436386	+	0.899760i	$0.356258\pi$
$458$	−54.2683	−2.53579
$459$	4.87352	0.227477
$460$	29.1207	1.35776
$461$	3.77911	0.176011	0.0880053	−	0.996120i	$-0.471951\pi$
$461$	3.77911	0.176011	0.0880053	+	0.996120i	$0.471951\pi$
$462$	26.1174	1.21509
$463$	33.6188	1.56240	0.781198	−	0.624283i	$-0.214609\pi$
$463$	33.6188	1.56240	0.781198	+	0.624283i	$0.214609\pi$
$464$	−28.1998	−1.30914
$465$	−11.6173	−0.538739
$466$	−76.5486	−3.54604
$467$	−8.47037	−0.391962	−0.195981	−	0.980608i	$-0.562789\pi$
$467$	−8.47037	−0.391962	−0.195981	+	0.980608i	$0.562789\pi$
$468$	1.16209	0.0537178
$469$	−22.3832	−1.03356
$470$	−4.13970	−0.190950
$471$	7.71216	0.355358
$472$	50.5121	2.32501
$473$	65.4303	3.00849
$474$	9.16797	0.421099
$475$	4.26584	0.195730
$476$	−45.7749	−2.09809
$477$	1.17465	0.0537837
$478$	−44.4915	−2.03499
$479$	−17.4170	−0.795802	−0.397901	−	0.917428i	$-0.630261\pi$
$479$	−17.4170	−0.795802	−0.397901	+	0.917428i	$0.630261\pi$
$480$	−28.4732	−1.29962
$481$	−1.03134	−0.0470251
$482$	−6.55190	−0.298431
$483$	−3.83558	−0.174525
$484$	69.4432	3.15651
$485$	8.95305	0.406537
$486$	−2.59380	−0.117657
$487$	−22.1569	−1.00402	−0.502012	−	0.864861i	$-0.667407\pi$
$487$	−22.1569	−1.00402	−0.502012	+	0.864861i	$0.667407\pi$
$488$	9.95364	0.450580
$489$	−4.49641	−0.203335
$490$	25.2651	1.14136
$491$	28.9121	1.30479	0.652393	−	0.757881i	$-0.273765\pi$
$491$	28.9121	1.30479	0.652393	+	0.757881i	$0.273765\pi$
$492$	44.3914	2.00132
$493$	−15.4481	−0.695746
$494$	−0.525209	−0.0236303
$495$	16.1699	0.726781
$496$	−32.3952	−1.45459
$497$	−16.1795	−0.725751
$498$	39.6452	1.77654
$499$	30.3108	1.35690	0.678448	−	0.734649i	$-0.262653\pi$
$499$	30.3108	1.35690	0.678448	+	0.734649i	$0.262653\pi$
$500$	2.69007	0.120304
$501$	−1.82265	−0.0814300
$502$	37.7216	1.68360
$503$	−3.63230	−0.161956	−0.0809782	−	0.996716i	$-0.525804\pi$
$503$	−3.63230	−0.161956	−0.0809782	+	0.996716i	$0.525804\pi$
$504$	14.0564	0.626120
$505$	3.79119	0.168706
$506$	−25.3810	−1.12832
$507$	−12.9396	−0.574667
$508$	61.7349	2.73904
$509$	−17.1381	−0.759632	−0.379816	−	0.925062i	$-0.624013\pi$
$509$	−17.1381	−0.759632	−0.379816	+	0.925062i	$0.624013\pi$
$510$	−40.3290	−1.78580
$511$	−32.1267	−1.42120
$512$	46.4913	2.05465
$513$	0.823783	0.0363709
$514$	20.8732	0.920677
$515$	−12.3539	−0.544379
$516$	61.0336	2.68686
$517$	2.53549	0.111511
$518$	−21.6213	−0.949986
$519$	−23.5027	−1.03166
$520$	−5.54841	−0.243314
$521$	−11.1236	−0.487334	−0.243667	−	0.969859i	$-0.578350\pi$
$521$	−11.1236	−0.487334	−0.243667	+	0.969859i	$0.578350\pi$
$522$	8.22181	0.359859
$523$	6.50848	0.284596	0.142298	−	0.989824i	$-0.454551\pi$
$523$	6.50848	0.284596	0.142298	+	0.989824i	$0.454551\pi$
$524$	−7.17331	−0.313367
$525$	−10.2877	−0.448991
$526$	9.73229	0.424348
$527$	−17.7463	−0.773043
$528$	45.0902	1.96230
$529$	−19.2726	−0.837938
$530$	−9.72041	−0.422228
$531$	−7.13919	−0.309815
$532$	−7.73744	−0.335460
$533$	2.30794	0.0999679
$534$	26.3093	1.13851
$535$	−11.3462	−0.490541
$536$	−79.7156	−3.44319
$537$	8.88872	0.383577
$538$	−12.2327	−0.527388
$539$	−15.4744	−0.666529
$540$	15.0833	0.649082
$541$	−12.3854	−0.532491	−0.266245	−	0.963905i	$-0.585783\pi$
$541$	−12.3854	−0.532491	−0.266245	+	0.963905i	$0.585783\pi$
$542$	66.9349	2.87510
$543$	−7.96963	−0.342009
$544$	−43.4952	−1.86484
$545$	−25.8155	−1.10582
$546$	1.26662	0.0542062
$547$	28.6251	1.22392	0.611960	−	0.790889i	$-0.290381\pi$
$547$	28.6251	1.22392	0.611960	+	0.790889i	$0.290381\pi$
$548$	−24.8184	−1.06019
$549$	−1.40681	−0.0600412
$550$	−68.0762	−2.90278
$551$	−2.61123	−0.111242
$552$	−13.6600	−0.581409
$553$	7.02204	0.298607
$554$	45.1451	1.91803
$555$	−13.3862	−0.568214
$556$	44.8419	1.90172
$557$	−30.5013	−1.29238	−0.646191	−	0.763176i	$-0.723639\pi$
$557$	−30.5013	−1.29238	−0.646191	+	0.763176i	$0.723639\pi$
$558$	9.44500	0.399839
$559$	3.17318	0.134211
$560$	−56.3870	−2.38279
$561$	24.7008	1.04287
$562$	48.9721	2.06576
$563$	3.96459	0.167088	0.0835438	−	0.996504i	$-0.473376\pi$
$563$	3.96459	0.167088	0.0835438	+	0.996504i	$0.473376\pi$
$564$	2.36512	0.0995893
$565$	−12.3006	−0.517492
$566$	−36.0224	−1.51413
$567$	−1.98667	−0.0834324
$568$	−57.6217	−2.41775
$569$	−4.85702	−0.203617	−0.101809	−	0.994804i	$-0.532463\pi$
$569$	−4.85702	−0.203617	−0.101809	+	0.994804i	$0.532463\pi$
$570$	−6.81691	−0.285529
$571$	16.2021	0.678037	0.339018	−	0.940780i	$-0.389905\pi$
$571$	16.2021	0.678037	0.339018	+	0.940780i	$0.389905\pi$
$572$	5.88991	0.246270
$573$	10.9738	0.458437
$574$	48.3842	2.01952
$575$	9.99761	0.416929
$576$	5.35633	0.223180
$577$	24.5844	1.02346	0.511731	−	0.859146i	$-0.329005\pi$
$577$	24.5844	1.02346	0.511731	+	0.859146i	$0.329005\pi$
$578$	−17.5113	−0.728374
$579$	14.2303	0.591392
$580$	−47.8110	−1.98524
$581$	30.3655	1.25977
$582$	−7.27895	−0.301722
$583$	5.95357	0.246572
$584$	−114.416	−4.73457
$585$	0.784191	0.0324223
$586$	9.75217	0.402858
$587$	−11.3682	−0.469214	−0.234607	−	0.972090i	$-0.575380\pi$
$587$	−11.3682	−0.469214	−0.234607	+	0.972090i	$0.575380\pi$
$588$	−14.4346	−0.595271
$589$	−2.99971	−0.123601
$590$	59.0777	2.43219
$591$	26.3142	1.08242
$592$	−37.3279	−1.53417
$593$	−28.7410	−1.18025	−0.590126	−	0.807311i	$-0.700922\pi$
$593$	−28.7410	−1.18025	−0.590126	+	0.807311i	$0.700922\pi$
$594$	−13.1463	−0.539400
$595$	−30.8893	−1.26634
$596$	38.2147	1.56534
$597$	−11.8744	−0.485988
$598$	−1.23090	−0.0503354
$599$	−26.5938	−1.08659	−0.543297	−	0.839541i	$-0.682824\pi$
$599$	−26.5938	−1.08659	−0.543297	+	0.839541i	$0.682824\pi$
$600$	−36.6385	−1.49576
$601$	45.0413	1.83727	0.918636	−	0.395104i	$-0.129292\pi$
$601$	45.0413	1.83727	0.918636	+	0.395104i	$0.129292\pi$
$602$	66.5233	2.71129
$603$	11.2667	0.458815
$604$	18.0739	0.735416
$605$	46.8609	1.90517
$606$	−3.08229	−0.125209
$607$	−12.2879	−0.498752	−0.249376	−	0.968407i	$-0.580226\pi$
$607$	−12.2879	−0.498752	−0.249376	+	0.968407i	$0.580226\pi$
$608$	−7.35210	−0.298167
$609$	6.29735	0.255181
$610$	11.6415	0.471352
$611$	0.122964	0.00497459
$612$	23.0410	0.931376
$613$	1.74580	0.0705123	0.0352562	−	0.999378i	$-0.488775\pi$
$613$	1.74580	0.0705123	0.0352562	+	0.999378i	$0.488775\pi$
$614$	−79.1646	−3.19482
$615$	29.9557	1.20793
$616$	71.2427	2.87045
$617$	28.2058	1.13552	0.567761	−	0.823193i	$-0.307810\pi$
$617$	28.2058	1.13552	0.567761	+	0.823193i	$0.307810\pi$
$618$	10.0439	0.404025
$619$	−19.6488	−0.789751	−0.394876	−	0.918735i	$-0.629212\pi$
$619$	−19.6488	−0.789751	−0.394876	+	0.918735i	$0.629212\pi$
$620$	−54.9241	−2.20580
$621$	1.93066	0.0774745
$622$	−5.54644	−0.222392
$623$	20.1511	0.807337
$624$	2.18674	0.0875397
$625$	−24.0765	−0.963058
$626$	46.7930	1.87022
$627$	4.17523	0.166743
$628$	36.4615	1.45497
$629$	−20.4486	−0.815337
$630$	16.4400	0.654984
$631$	22.9566	0.913888	0.456944	−	0.889496i	$-0.348944\pi$
$631$	22.9566	0.913888	0.456944	+	0.889496i	$0.348944\pi$
$632$	25.0083	0.994775
$633$	−4.95086	−0.196779
$634$	14.3458	0.569743
$635$	41.6592	1.65320
$636$	5.55351	0.220211
$637$	−0.750462	−0.0297344
$638$	41.6711	1.64978
$639$	8.14403	0.322173
$640$	12.6222	0.498936
$641$	24.4519	0.965791	0.482895	−	0.875678i	$-0.339585\pi$
$641$	24.4519	0.965791	0.482895	+	0.875678i	$0.339585\pi$
$642$	9.22464	0.364068
$643$	0.843444	0.0332622	0.0166311	−	0.999862i	$-0.494706\pi$
$643$	0.843444	0.0332622	0.0166311	+	0.999862i	$0.494706\pi$
$644$	−18.1338	−0.714572
$645$	41.1860	1.62170
$646$	−10.4134	−0.409709
$647$	−3.98889	−0.156820	−0.0784098	−	0.996921i	$-0.524984\pi$
$647$	−3.98889	−0.156820	−0.0784098	+	0.996921i	$0.524984\pi$
$648$	−7.07533	−0.277945
$649$	−36.1840	−1.42035
$650$	−3.30149	−0.129495
$651$	7.23423	0.283532
$652$	−21.2581	−0.832531
$653$	−27.2412	−1.06603	−0.533015	−	0.846106i	$-0.678941\pi$
$653$	−27.2412	−1.06603	−0.533015	+	0.846106i	$0.678941\pi$
$654$	20.9884	0.820710
$655$	−4.84061	−0.189138
$656$	83.5324	3.26139
$657$	16.1711	0.630896
$658$	2.57785	0.100495
$659$	22.8314	0.889384	0.444692	−	0.895684i	$-0.353313\pi$
$659$	22.8314	0.889384	0.444692	+	0.895684i	$0.353313\pi$
$660$	76.4477	2.97572
$661$	12.2464	0.476328	0.238164	−	0.971225i	$-0.423454\pi$
$661$	12.2464	0.476328	0.238164	+	0.971225i	$0.423454\pi$
$662$	−30.6665	−1.19189
$663$	1.19791	0.0465232
$664$	108.144	4.19678
$665$	−5.22129	−0.202473
$666$	10.8832	0.421715
$667$	−6.11979	−0.236959
$668$	−8.61711	−0.333406
$669$	−1.59303	−0.0615901
$670$	−93.2333	−3.60192
$671$	−7.13022	−0.275259
$672$	17.7306	0.683975
$673$	−11.3608	−0.437925	−0.218963	−	0.975733i	$-0.570267\pi$
$673$	−11.3608	−0.437925	−0.218963	+	0.975733i	$0.570267\pi$
$674$	−7.20169	−0.277399
$675$	5.17835	0.199315
$676$	−61.1756	−2.35291
$677$	0.568463	0.0218478	0.0109239	−	0.999940i	$-0.496523\pi$
$677$	0.568463	0.0218478	0.0109239	+	0.999940i	$0.496523\pi$
$678$	10.0006	0.384070
$679$	−5.57518	−0.213956
$680$	−110.009	−4.21865
$681$	−25.9749	−0.995360
$682$	47.8707	1.83306
$683$	−30.5439	−1.16873	−0.584366	−	0.811490i	$-0.698657\pi$
$683$	−30.5439	−1.16873	−0.584366	+	0.811490i	$0.698657\pi$
$684$	3.89467	0.148917
$685$	−16.7477	−0.639895
$686$	−51.8041	−1.97789
$687$	20.9223	0.798236
$688$	114.849	4.37856
$689$	0.288731	0.0109998
$690$	−15.9764	−0.608212
$691$	−4.35824	−0.165795	−0.0828977	−	0.996558i	$-0.526417\pi$
$691$	−4.35824	−0.165795	−0.0828977	+	0.996558i	$0.526417\pi$
$692$	−111.116	−4.22399
$693$	−10.0692	−0.382496
$694$	4.22491	0.160375
$695$	30.2597	1.14782
$696$	22.4273	0.850106
$697$	45.7598	1.73328
$698$	38.6011	1.46107
$699$	29.5122	1.11625
$700$	−48.6380	−1.83834
$701$	−47.8527	−1.80737	−0.903685	−	0.428198i	$-0.859149\pi$
$701$	−47.8527	−1.80737	−0.903685	+	0.428198i	$0.859149\pi$
$702$	−0.637557	−0.0240630
$703$	−3.45647	−0.130363
$704$	27.1478	1.02317
$705$	1.59600	0.0601089
$706$	−26.5315	−0.998527
$707$	−2.36082	−0.0887879
$708$	−33.7526	−1.26850
$709$	−11.7029	−0.439511	−0.219755	−	0.975555i	$-0.570526\pi$
$709$	−11.7029	−0.439511	−0.219755	+	0.975555i	$0.570526\pi$
$710$	−67.3929	−2.52921
$711$	−3.53457	−0.132557
$712$	71.7661	2.68955
$713$	−7.03025	−0.263285
$714$	25.1134	0.939845
$715$	3.97456	0.148640
$716$	42.0240	1.57051
$717$	17.1530	0.640592
$718$	−51.5850	−1.92513
$719$	−26.3660	−0.983287	−0.491644	−	0.870797i	$-0.663604\pi$
$719$	−26.3660	−0.983287	−0.491644	+	0.870797i	$0.663604\pi$
$720$	28.3826	1.05776
$721$	7.69294	0.286500
$722$	47.5220	1.76858
$723$	2.52599	0.0939424
$724$	−37.6787	−1.40032
$725$	−16.4143	−0.609612
$726$	−38.0985	−1.41397
$727$	−16.9348	−0.628078	−0.314039	−	0.949410i	$-0.601682\pi$
$727$	−16.9348	−0.628078	−0.314039	+	0.949410i	$0.601682\pi$
$728$	3.45506	0.128053
$729$	1.00000	0.0370370
$730$	−133.818	−4.95283
$731$	62.9150	2.32700
$732$	−6.65109	−0.245832
$733$	−15.8156	−0.584163	−0.292082	−	0.956393i	$-0.594348\pi$
$733$	−15.8156	−0.584163	−0.292082	+	0.956393i	$0.594348\pi$
$734$	−59.1252	−2.18235
$735$	−9.74057	−0.359286
$736$	−17.2307	−0.635132
$737$	57.1037	2.10344
$738$	−24.3544	−0.896497
$739$	−30.0321	−1.10475	−0.552375	−	0.833596i	$-0.686278\pi$
$739$	−30.0321	−1.10475	−0.552375	+	0.833596i	$0.686278\pi$
$740$	−63.2872	−2.32649
$741$	0.202486	0.00743853
$742$	6.05302	0.222213
$743$	3.39514	0.124555	0.0622777	−	0.998059i	$-0.480164\pi$
$743$	3.39514	0.124555	0.0622777	+	0.998059i	$0.480164\pi$
$744$	25.7640	0.944553
$745$	25.7876	0.944786
$746$	−82.1965	−3.00943
$747$	−15.2846	−0.559234
$748$	116.780	4.26990
$749$	7.06545	0.258166
$750$	−1.47585	−0.0538904
$751$	−13.0174	−0.475010	−0.237505	−	0.971386i	$-0.576330\pi$
$751$	−13.0174	−0.475010	−0.237505	+	0.971386i	$0.576330\pi$
$752$	4.45050	0.162293
$753$	−14.5430	−0.529976
$754$	2.02093	0.0735978
$755$	12.1964	0.443873
$756$	−9.39256	−0.341604
$757$	41.2008	1.49747	0.748735	−	0.662869i	$-0.230662\pi$
$757$	41.2008	1.49747	0.748735	+	0.662869i	$0.230662\pi$
$758$	−64.7134	−2.35050
$759$	9.78526	0.355183
$760$	−18.5951	−0.674515
$761$	36.4020	1.31957	0.659785	−	0.751454i	$-0.270647\pi$
$761$	36.4020	1.31957	0.659785	+	0.751454i	$0.270647\pi$
$762$	−33.8695	−1.22696
$763$	16.0757	0.581978
$764$	51.8818	1.87702
$765$	15.5483	0.562148
$766$	80.4612	2.90718
$767$	−1.75482	−0.0633628
$768$	−20.9747	−0.756858
$769$	34.1171	1.23029	0.615147	−	0.788412i	$-0.289097\pi$
$769$	34.1171	1.23029	0.615147	+	0.788412i	$0.289097\pi$
$770$	83.3237	3.00278
$771$	−8.04735	−0.289818
$772$	67.2779	2.42139
$773$	33.7241	1.21297	0.606486	−	0.795095i	$-0.292579\pi$
$773$	33.7241	1.21297	0.606486	+	0.795095i	$0.292579\pi$
$774$	−33.4848	−1.20359
$775$	−18.8563	−0.677339
$776$	−19.8554	−0.712768
$777$	8.33577	0.299044
$778$	−22.7065	−0.814069
$779$	7.73489	0.277131
$780$	3.70749	0.132749
$781$	41.2769	1.47700
$782$	−24.4053	−0.872731
$783$	−3.16980	−0.113279
$784$	−27.1619	−0.970067
$785$	24.6045	0.878173
$786$	3.93548	0.140374
$787$	−29.6566	−1.05714	−0.528572	−	0.848889i	$-0.677272\pi$
$787$	−29.6566	−1.05714	−0.528572	+	0.848889i	$0.677272\pi$
$788$	124.408	4.43185
$789$	−3.75214	−0.133580
$790$	29.2490	1.04063
$791$	7.65976	0.272350
$792$	−35.8603	−1.27424
$793$	−0.345795	−0.0122795
$794$	48.7398	1.72971
$795$	3.74756	0.132912
$796$	−56.1397	−1.98982
$797$	−32.7636	−1.16055	−0.580273	−	0.814422i	$-0.697054\pi$
$797$	−32.7636	−1.16055	−0.580273	+	0.814422i	$0.697054\pi$
$798$	4.24498	0.150271
$799$	2.43802	0.0862510
$800$	−46.2157	−1.63397
$801$	−10.1431	−0.358390
$802$	7.32084	0.258508
$803$	81.9612	2.89235
$804$	53.2665	1.87857
$805$	−12.2369	−0.431292
$806$	2.32159	0.0817745
$807$	4.71612	0.166015
$808$	−8.40782	−0.295786
$809$	−25.4596	−0.895112	−0.447556	−	0.894256i	$-0.647705\pi$
$809$	−25.4596	−0.895112	−0.447556	+	0.894256i	$0.647705\pi$
$810$	−8.27513	−0.290758
$811$	49.0358	1.72188	0.860941	−	0.508705i	$-0.169876\pi$
$811$	49.0358	1.72188	0.860941	+	0.508705i	$0.169876\pi$
$812$	29.7725	1.04481
$813$	−25.8057	−0.905047
$814$	55.1599	1.93335
$815$	−14.3451	−0.502489
$816$	43.3568	1.51779
$817$	10.6347	0.372060
$818$	77.3551	2.70466
$819$	−0.488325	−0.0170635
$820$	141.624	4.94573
$821$	−12.3424	−0.430753	−0.215377	−	0.976531i	$-0.569098\pi$
$821$	−12.3424	−0.430753	−0.215377	+	0.976531i	$0.569098\pi$
$822$	13.6161	0.474915
$823$	24.0480	0.838261	0.419130	−	0.907926i	$-0.362335\pi$
$823$	24.0480	0.838261	0.419130	+	0.907926i	$0.362335\pi$
$824$	27.3976	0.954441
$825$	26.2457	0.913760
$826$	−36.7884	−1.28003
$827$	50.9901	1.77310	0.886550	−	0.462632i	$-0.153095\pi$
$827$	50.9901	1.77310	0.886550	+	0.462632i	$0.153095\pi$
$828$	9.12773	0.317211
$829$	−25.6581	−0.891141	−0.445571	−	0.895247i	$-0.646999\pi$
$829$	−25.6581	−0.891141	−0.445571	+	0.895247i	$0.646999\pi$
$830$	126.482	4.39026
$831$	−17.4050	−0.603774
$832$	1.31659	0.0456445
$833$	−14.8795	−0.515545
$834$	−24.6015	−0.851881
$835$	−5.81490	−0.201233
$836$	19.7396	0.682709
$837$	−3.64138	−0.125865
$838$	76.1408	2.63024
$839$	22.3736	0.772423	0.386212	−	0.922410i	$-0.373783\pi$
$839$	22.3736	0.772423	0.386212	+	0.922410i	$0.373783\pi$
$840$	44.8447	1.54729
$841$	−18.9524	−0.653531
$842$	59.2668	2.04247
$843$	−18.8805	−0.650278
$844$	−23.4066	−0.805688
$845$	−41.2818	−1.42014
$846$	−1.29757	−0.0446114
$847$	−29.1808	−1.00267
$848$	10.4502	0.358861
$849$	13.8879	0.476631
$850$	−65.4591	−2.24523
$851$	−8.10074	−0.277690
$852$	38.5032	1.31910
$853$	−8.89687	−0.304623	−0.152312	−	0.988333i	$-0.548672\pi$
$853$	−8.89687	−0.304623	−0.152312	+	0.988333i	$0.548672\pi$
$854$	−7.24932	−0.248067
$855$	2.62816	0.0898811
$856$	25.1629	0.860049
$857$	−28.7920	−0.983516	−0.491758	−	0.870732i	$-0.663646\pi$
$857$	−28.7920	−0.983516	−0.491758	+	0.870732i	$0.663646\pi$
$858$	−3.23137	−0.110317
$859$	−24.9081	−0.849854	−0.424927	−	0.905228i	$-0.639700\pi$
$859$	−24.9081	−0.849854	−0.424927	+	0.905228i	$0.639700\pi$
$860$	194.719	6.63986
$861$	−18.6538	−0.635720
$862$	37.0175	1.26082
$863$	40.0451	1.36315	0.681575	−	0.731748i	$-0.261295\pi$
$863$	40.0451	1.36315	0.681575	+	0.731748i	$0.261295\pi$
$864$	−8.92480	−0.303628
$865$	−74.9820	−2.54946
$866$	−18.4514	−0.627003
$867$	6.75122	0.229283
$868$	34.2019	1.16089
$869$	−17.9145	−0.607708
$870$	26.2305	0.889296
$871$	2.76936	0.0938362
$872$	57.2518	1.93879
$873$	2.80629	0.0949785
$874$	−4.12529	−0.139540
$875$	−1.13040	−0.0382145
$876$	76.4537	2.58313
$877$	50.4087	1.70218	0.851090	−	0.525020i	$-0.175942\pi$
$877$	50.4087	1.70218	0.851090	+	0.525020i	$0.175942\pi$
$878$	84.8360	2.86308
$879$	−3.75980	−0.126815
$880$	143.854	4.84930
$881$	27.3603	0.921793	0.460897	−	0.887454i	$-0.347528\pi$
$881$	27.3603	0.921793	0.460897	+	0.887454i	$0.347528\pi$
$882$	7.91921	0.266654
$883$	14.7610	0.496746	0.248373	−	0.968664i	$-0.420104\pi$
$883$	14.7610	0.496746	0.248373	+	0.968664i	$0.420104\pi$
$884$	5.66349	0.190484
$885$	−22.7765	−0.765625
$886$	−46.3751	−1.55800
$887$	28.3115	0.950606	0.475303	−	0.879822i	$-0.342338\pi$
$887$	28.3115	0.950606	0.475303	+	0.879822i	$0.342338\pi$
$888$	29.6870	0.996230
$889$	−25.9417	−0.870057
$890$	83.9358	2.81353
$891$	5.06836	0.169797
$892$	−7.53150	−0.252173
$893$	0.412105	0.0137906
$894$	−20.9657	−0.701197
$895$	28.3582	0.947909
$896$	−7.86000	−0.262584
$897$	0.474556	0.0158450
$898$	53.8491	1.79697
$899$	11.5424	0.384962
$900$	24.4821	0.816071
$901$	5.72470	0.190717
$902$	−123.437	−4.11000
$903$	−25.6471	−0.853481
$904$	27.2795	0.907301
$905$	−25.4259	−0.845186
$906$	−9.91585	−0.329432
$907$	29.8761	0.992021	0.496011	−	0.868317i	$-0.334798\pi$
$907$	29.8761	0.992021	0.496011	+	0.868317i	$0.334798\pi$
$908$	−122.804	−4.07539
$909$	1.18833	0.0394144
$910$	4.04096	0.133956
$911$	50.0393	1.65788	0.828938	−	0.559341i	$-0.188946\pi$
$911$	50.0393	1.65788	0.828938	+	0.559341i	$0.188946\pi$
$912$	7.32870	0.242678
$913$	−77.4679	−2.56381
$914$	−48.3944	−1.60074
$915$	−4.48822	−0.148376
$916$	98.9163	3.26829
$917$	3.01431	0.0995413
$918$	−12.6409	−0.417213
$919$	21.2316	0.700366	0.350183	−	0.936681i	$-0.386119\pi$
$919$	21.2316	0.700366	0.350183	+	0.936681i	$0.386119\pi$
$920$	−43.5803	−1.43680
$921$	30.5207	1.00569
$922$	−9.80224	−0.322820
$923$	2.00181	0.0658903
$924$	−47.6049	−1.56609
$925$	−21.7276	−0.714397
$926$	−87.2003	−2.86558
$927$	−3.87228	−0.127182
$928$	28.2898	0.928658
$929$	−0.435512	−0.0142887	−0.00714435	−	0.999974i	$-0.502274\pi$
$929$	−0.435512	−0.0142887	−0.00714435	+	0.999974i	$0.502274\pi$
$930$	30.1329	0.988096
$931$	−2.51512	−0.0824297
$932$	139.527	4.57037
$933$	2.13835	0.0700063
$934$	21.9704	0.718894
$935$	78.8042	2.57717
$936$	−1.73912	−0.0568449
$937$	11.5193	0.376320	0.188160	−	0.982138i	$-0.439748\pi$
$937$	11.5193	0.376320	0.188160	+	0.982138i	$0.439748\pi$
$938$	58.0576	1.89565
$939$	−18.0403	−0.588724
$940$	7.54555	0.246109
$941$	35.5870	1.16010	0.580051	−	0.814580i	$-0.303033\pi$
$941$	35.5870	1.16010	0.580051	+	0.814580i	$0.303033\pi$
$942$	−20.0038	−0.651759
$943$	18.1278	0.590323
$944$	−63.5131	−2.06717
$945$	−6.33818	−0.206181
$946$	−169.713	−5.51785
$947$	13.7279	0.446097	0.223048	−	0.974807i	$-0.428399\pi$
$947$	13.7279	0.446097	0.223048	+	0.974807i	$0.428399\pi$
$948$	−16.7107	−0.542739
$949$	3.97488	0.129030
$950$	−11.0647	−0.358987
$951$	−5.53079	−0.179348
$952$	68.5040	2.22023
$953$	24.9459	0.808076	0.404038	−	0.914742i	$-0.367606\pi$
$953$	24.9459	0.808076	0.404038	+	0.914742i	$0.367606\pi$
$954$	−3.04681	−0.0986443
$955$	35.0103	1.13291
$956$	81.0959	2.62283
$957$	−16.0657	−0.519330
$958$	45.1761	1.45957
$959$	10.4290	0.336769
$960$	17.0886	0.551531
$961$	−17.7404	−0.572269
$962$	2.67509	0.0862484
$963$	−3.55642	−0.114604
$964$	11.9423	0.384636
$965$	45.3997	1.46147
$966$	9.94872	0.320095
$967$	0.820836	0.0263963	0.0131981	−	0.999913i	$-0.495799\pi$
$967$	0.820836	0.0263963	0.0131981	+	0.999913i	$0.495799\pi$
$968$	−103.925	−3.34026
$969$	4.01473	0.128972
$970$	−23.2224	−0.745626
$971$	6.06879	0.194757	0.0973784	−	0.995247i	$-0.468954\pi$
$971$	6.06879	0.194757	0.0973784	+	0.995247i	$0.468954\pi$
$972$	4.72779	0.151644
$973$	−18.8431	−0.604082
$974$	57.4705	1.84147
$975$	1.27284	0.0407635
$976$	−12.5155	−0.400612
$977$	−43.8991	−1.40446	−0.702228	−	0.711952i	$-0.747811\pi$
$977$	−43.8991	−1.40446	−0.702228	+	0.711952i	$0.747811\pi$
$978$	11.6628	0.372935
$979$	−51.4091	−1.64304
$980$	−46.0513	−1.47106
$981$	−8.09175	−0.258350
$982$	−74.9923	−2.39310
$983$	−32.7990	−1.04613	−0.523063	−	0.852294i	$-0.675211\pi$
$983$	−32.7990	−1.04613	−0.523063	+	0.852294i	$0.675211\pi$
$984$	−66.4336	−2.11782
$985$	83.9517	2.67492
$986$	40.0692	1.27606
$987$	−0.993850	−0.0316346
$988$	0.957313	0.0304562
$989$	24.9239	0.792534
$990$	−41.9414	−1.33298
$991$	−41.3737	−1.31428	−0.657139	−	0.753769i	$-0.728234\pi$
$991$	−41.3737	−1.31428	−0.657139	+	0.753769i	$0.728234\pi$
$992$	32.4986	1.03183
$993$	11.8230	0.375192
$994$	41.9664	1.33109
$995$	−37.8836	−1.20099
$996$	−72.2623	−2.28972
$997$	3.39197	0.107425	0.0537124	−	0.998556i	$-0.482895\pi$
$997$	3.39197	0.107425	0.0537124	+	0.998556i	$0.482895\pi$
$998$	−78.6200	−2.48867
$999$	−4.19585	−0.132751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.7	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.7	✓	129	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59380 q^{2} +1.00000 q^{3} +4.72779 q^{4} +3.19035 q^{5} -2.59380 q^{6} -1.98667 q^{7} -7.07533 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.59380 q^{2} +1.00000 q^{3} +4.72779 q^{4} +3.19035 q^{5} -2.59380 q^{6} -1.98667 q^{7} -7.07533 q^{8} +1.00000 q^{9} -8.27513 q^{10} +5.06836 q^{11} +4.72779 q^{12} +0.245801 q^{13} +5.15303 q^{14} +3.19035 q^{15} +8.89640 q^{16} +4.87352 q^{17} -2.59380 q^{18} +0.823783 q^{19} +15.0833 q^{20} -1.98667 q^{21} -13.1463 q^{22} +1.93066 q^{23} -7.07533 q^{24} +5.17835 q^{25} -0.637557 q^{26} +1.00000 q^{27} -9.39256 q^{28} -3.16980 q^{29} -8.27513 q^{30} -3.64138 q^{31} -8.92480 q^{32} +5.06836 q^{33} -12.6409 q^{34} -6.33818 q^{35} +4.72779 q^{36} -4.19585 q^{37} -2.13673 q^{38} +0.245801 q^{39} -22.5728 q^{40} +9.38947 q^{41} +5.15303 q^{42} +12.9096 q^{43} +23.9621 q^{44} +3.19035 q^{45} -5.00773 q^{46} +0.500259 q^{47} +8.89640 q^{48} -3.05313 q^{49} -13.4316 q^{50} +4.87352 q^{51} +1.16209 q^{52} +1.17465 q^{53} -2.59380 q^{54} +16.1699 q^{55} +14.0564 q^{56} +0.823783 q^{57} +8.22181 q^{58} -7.13919 q^{59} +15.0833 q^{60} -1.40681 q^{61} +9.44500 q^{62} -1.98667 q^{63} +5.35633 q^{64} +0.784191 q^{65} -13.1463 q^{66} +11.2667 q^{67} +23.0410 q^{68} +1.93066 q^{69} +16.4400 q^{70} +8.14403 q^{71} -7.07533 q^{72} +16.1711 q^{73} +10.8832 q^{74} +5.17835 q^{75} +3.89467 q^{76} -10.0692 q^{77} -0.637557 q^{78} -3.53457 q^{79} +28.3826 q^{80} +1.00000 q^{81} -24.3544 q^{82} -15.2846 q^{83} -9.39256 q^{84} +15.5483 q^{85} -33.4848 q^{86} -3.16980 q^{87} -35.8603 q^{88} -10.1431 q^{89} -8.27513 q^{90} -0.488325 q^{91} +9.12773 q^{92} -3.64138 q^{93} -1.29757 q^{94} +2.62816 q^{95} -8.92480 q^{96} +2.80629 q^{97} +7.91921 q^{98} +5.06836 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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