LMFDB - Embedded newform 8035.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42652 q^{2} +0.577409 q^{3} +3.88800 q^{4} -1.00000 q^{5} -1.40110 q^{6} +3.20436 q^{7} -4.58127 q^{8} -2.66660 q^{9} +O(q^{10})$	\(q-2.42652 q^{2} +0.577409 q^{3} +3.88800 q^{4} -1.00000 q^{5} -1.40110 q^{6} +3.20436 q^{7} -4.58127 q^{8} -2.66660 q^{9} +2.42652 q^{10} -0.907853 q^{11} +2.24497 q^{12} +0.116422 q^{13} -7.77543 q^{14} -0.577409 q^{15} +3.34053 q^{16} +3.58420 q^{17} +6.47055 q^{18} -4.76735 q^{19} -3.88800 q^{20} +1.85023 q^{21} +2.20292 q^{22} +6.47164 q^{23} -2.64527 q^{24} +1.00000 q^{25} -0.282500 q^{26} -3.27195 q^{27} +12.4585 q^{28} -5.78943 q^{29} +1.40110 q^{30} -0.789726 q^{31} +1.05666 q^{32} -0.524203 q^{33} -8.69713 q^{34} -3.20436 q^{35} -10.3677 q^{36} +2.11088 q^{37} +11.5681 q^{38} +0.0672230 q^{39} +4.58127 q^{40} -10.2168 q^{41} -4.48961 q^{42} +10.4617 q^{43} -3.52973 q^{44} +2.66660 q^{45} -15.7036 q^{46} -1.01621 q^{47} +1.92886 q^{48} +3.26790 q^{49} -2.42652 q^{50} +2.06955 q^{51} +0.452648 q^{52} -8.48653 q^{53} +7.93945 q^{54} +0.907853 q^{55} -14.6800 q^{56} -2.75272 q^{57} +14.0482 q^{58} +3.26630 q^{59} -2.24497 q^{60} +6.23607 q^{61} +1.91629 q^{62} -8.54473 q^{63} -9.24507 q^{64} -0.116422 q^{65} +1.27199 q^{66} -13.0118 q^{67} +13.9354 q^{68} +3.73678 q^{69} +7.77543 q^{70} +3.72602 q^{71} +12.2164 q^{72} +11.3992 q^{73} -5.12209 q^{74} +0.577409 q^{75} -18.5355 q^{76} -2.90908 q^{77} -0.163118 q^{78} +11.7235 q^{79} -3.34053 q^{80} +6.11054 q^{81} +24.7914 q^{82} -14.4183 q^{83} +7.19367 q^{84} -3.58420 q^{85} -25.3856 q^{86} -3.34287 q^{87} +4.15911 q^{88} +3.43339 q^{89} -6.47055 q^{90} +0.373057 q^{91} +25.1617 q^{92} -0.455995 q^{93} +2.46586 q^{94} +4.76735 q^{95} +0.610124 q^{96} -0.792195 q^{97} -7.92962 q^{98} +2.42088 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * 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 $

$2$	−2.42652	−1.71581	−0.857904	−	0.513810i	$-0.828234\pi$
$2$	−2.42652	−1.71581	−0.857904	+	0.513810i	$0.828234\pi$
$3$	0.577409	0.333367	0.166684	−	0.986010i	$-0.446694\pi$
$3$	0.577409	0.333367	0.166684	+	0.986010i	$0.446694\pi$
$4$	3.88800	1.94400
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.40110	−0.571995
$7$	3.20436	1.21113	0.605566	−	0.795795i	$-0.292947\pi$
$7$	3.20436	1.21113	0.605566	+	0.795795i	$0.292947\pi$
$8$	−4.58127	−1.61972
$9$	−2.66660	−0.888866
$10$	2.42652	0.767333
$11$	−0.907853	−0.273728	−0.136864	−	0.990590i	$-0.543702\pi$
$11$	−0.907853	−0.273728	−0.136864	+	0.990590i	$0.543702\pi$
$12$	2.24497	0.648066
$13$	0.116422	0.0322896	0.0161448	−	0.999870i	$-0.494861\pi$
$13$	0.116422	0.0322896	0.0161448	+	0.999870i	$0.494861\pi$
$14$	−7.77543	−2.07807
$15$	−0.577409	−0.149086
$16$	3.34053	0.835134
$17$	3.58420	0.869296	0.434648	−	0.900600i	$-0.356873\pi$
$17$	3.58420	0.869296	0.434648	+	0.900600i	$0.356873\pi$
$18$	6.47055	1.52512
$19$	−4.76735	−1.09371	−0.546853	−	0.837229i	$-0.684174\pi$
$19$	−4.76735	−1.09371	−0.546853	+	0.837229i	$0.684174\pi$
$20$	−3.88800	−0.869383
$21$	1.85023	0.403752
$22$	2.20292	0.469665
$23$	6.47164	1.34943	0.674715	−	0.738079i	$-0.264267\pi$
$23$	6.47164	1.34943	0.674715	+	0.738079i	$0.264267\pi$
$24$	−2.64527	−0.539963
$25$	1.00000	0.200000
$26$	−0.282500	−0.0554027
$27$	−3.27195	−0.629687
$28$	12.4585	2.35444
$29$	−5.78943	−1.07507	−0.537535	−	0.843241i	$-0.680644\pi$
$29$	−5.78943	−1.07507	−0.537535	+	0.843241i	$0.680644\pi$
$30$	1.40110	0.255804
$31$	−0.789726	−0.141839	−0.0709195	−	0.997482i	$-0.522593\pi$
$31$	−0.789726	−0.141839	−0.0709195	+	0.997482i	$0.522593\pi$
$32$	1.05666	0.186792
$33$	−0.524203	−0.0912520
$34$	−8.69713	−1.49155
$35$	−3.20436	−0.541635
$36$	−10.3677	−1.72795
$37$	2.11088	0.347027	0.173513	−	0.984832i	$-0.444488\pi$
$37$	2.11088	0.347027	0.173513	+	0.984832i	$0.444488\pi$
$38$	11.5681	1.87659
$39$	0.0672230	0.0107643
$40$	4.58127	0.724362
$41$	−10.2168	−1.59560	−0.797801	−	0.602921i	$-0.794004\pi$
$41$	−10.2168	−1.59560	−0.797801	+	0.602921i	$0.794004\pi$
$42$	−4.48961	−0.692762
$43$	10.4617	1.59540	0.797699	−	0.603056i	$-0.206050\pi$
$43$	10.4617	1.59540	0.797699	+	0.603056i	$0.206050\pi$
$44$	−3.52973	−0.532127
$45$	2.66660	0.397513
$46$	−15.7036	−2.31536
$47$	−1.01621	−0.148230	−0.0741149	−	0.997250i	$-0.523613\pi$
$47$	−1.01621	−0.148230	−0.0741149	+	0.997250i	$0.523613\pi$
$48$	1.92886	0.278406
$49$	3.26790	0.466843
$50$	−2.42652	−0.343162
$51$	2.06955	0.289795
$52$	0.452648	0.0627709
$53$	−8.48653	−1.16571	−0.582857	−	0.812574i	$-0.698065\pi$
$53$	−8.48653	−1.16571	−0.582857	+	0.812574i	$0.698065\pi$
$54$	7.93945	1.08042
$55$	0.907853	0.122415
$56$	−14.6800	−1.96170
$57$	−2.75272	−0.364606
$58$	14.0482	1.84461
$59$	3.26630	0.425236	0.212618	−	0.977135i	$-0.431801\pi$
$59$	3.26630	0.425236	0.212618	+	0.977135i	$0.431801\pi$
$60$	−2.24497	−0.289824
$61$	6.23607	0.798447	0.399223	−	0.916854i	$-0.369280\pi$
$61$	6.23607	0.798447	0.399223	+	0.916854i	$0.369280\pi$
$62$	1.91629	0.243369
$63$	−8.54473	−1.07653
$64$	−9.24507	−1.15563
$65$	−0.116422	−0.0144403
$66$	1.27199	0.156571
$67$	−13.0118	−1.58964	−0.794822	−	0.606843i	$-0.792436\pi$
$67$	−13.0118	−1.58964	−0.794822	+	0.606843i	$0.792436\pi$
$68$	13.9354	1.68991
$69$	3.73678	0.449856
$70$	7.77543	0.929342
$71$	3.72602	0.442198	0.221099	−	0.975251i	$-0.429036\pi$
$71$	3.72602	0.442198	0.221099	+	0.975251i	$0.429036\pi$
$72$	12.2164	1.43972
$73$	11.3992	1.33417	0.667086	−	0.744981i	$-0.267541\pi$
$73$	11.3992	1.33417	0.667086	+	0.744981i	$0.267541\pi$
$74$	−5.12209	−0.595431
$75$	0.577409	0.0666735
$76$	−18.5355	−2.12616
$77$	−2.90908	−0.331521
$78$	−0.163118	−0.0184695
$79$	11.7235	1.31899	0.659496	−	0.751708i	$-0.270770\pi$
$79$	11.7235	1.31899	0.659496	+	0.751708i	$0.270770\pi$
$80$	−3.34053	−0.373483
$81$	6.11054	0.678949
$82$	24.7914	2.73775
$83$	−14.4183	−1.58261	−0.791304	−	0.611422i	$-0.790598\pi$
$83$	−14.4183	−1.58261	−0.791304	+	0.611422i	$0.790598\pi$
$84$	7.19367	0.784894
$85$	−3.58420	−0.388761
$86$	−25.3856	−2.73740
$87$	−3.34287	−0.358393
$88$	4.15911	0.443363
$89$	3.43339	0.363938	0.181969	−	0.983304i	$-0.441753\pi$
$89$	3.43339	0.363938	0.181969	+	0.983304i	$0.441753\pi$
$90$	−6.47055	−0.682056
$91$	0.373057	0.0391070
$92$	25.1617	2.62329
$93$	−0.455995	−0.0472845
$94$	2.46586	0.254334
$95$	4.76735	0.489120
$96$	0.610124	0.0622705
$97$	−0.792195	−0.0804352	−0.0402176	−	0.999191i	$-0.512805\pi$
$97$	−0.792195	−0.0804352	−0.0402176	+	0.999191i	$0.512805\pi$
$98$	−7.92962	−0.801013
$99$	2.42088	0.243307
$100$	3.88800	0.388800
$101$	−4.89727	−0.487296	−0.243648	−	0.969864i	$-0.578344\pi$
$101$	−4.89727	−0.487296	−0.243648	+	0.969864i	$0.578344\pi$
$102$	−5.02180	−0.497233
$103$	−1.02785	−0.101277	−0.0506384	−	0.998717i	$-0.516126\pi$
$103$	−1.02785	−0.101277	−0.0506384	+	0.998717i	$0.516126\pi$
$104$	−0.533359	−0.0523001
$105$	−1.85023	−0.180564
$106$	20.5927	2.00014
$107$	−5.52986	−0.534591	−0.267296	−	0.963615i	$-0.586130\pi$
$107$	−5.52986	−0.534591	−0.267296	+	0.963615i	$0.586130\pi$
$108$	−12.7213	−1.22411
$109$	14.8419	1.42159	0.710796	−	0.703398i	$-0.248335\pi$
$109$	14.8419	1.42159	0.710796	+	0.703398i	$0.248335\pi$
$110$	−2.20292	−0.210040
$111$	1.21884	0.115687
$112$	10.7043	1.01146
$113$	−6.55595	−0.616732	−0.308366	−	0.951268i	$-0.599782\pi$
$113$	−6.55595	−0.616732	−0.308366	+	0.951268i	$0.599782\pi$
$114$	6.67952	0.625594
$115$	−6.47164	−0.603483
$116$	−22.5093	−2.08994
$117$	−0.310450	−0.0287011
$118$	−7.92574	−0.729623
$119$	11.4850	1.05283
$120$	2.64527	0.241479
$121$	−10.1758	−0.925073
$122$	−15.1319	−1.36998
$123$	−5.89930	−0.531922
$124$	−3.07045	−0.275735
$125$	−1.00000	−0.0894427
$126$	20.7340	1.84713
$127$	10.9389	0.970674	0.485337	−	0.874327i	$-0.338697\pi$
$127$	10.9389	0.970674	0.485337	+	0.874327i	$0.338697\pi$
$128$	20.3200	1.79605
$129$	6.04070	0.531854
$130$	0.282500	0.0247769
$131$	−11.7559	−1.02711	−0.513557	−	0.858056i	$-0.671672\pi$
$131$	−11.7559	−1.02711	−0.513557	+	0.858056i	$0.671672\pi$
$132$	−2.03810	−0.177394
$133$	−15.2763	−1.32462
$134$	31.5734	2.72752
$135$	3.27195	0.281604
$136$	−16.4202	−1.40802
$137$	7.12139	0.608422	0.304211	−	0.952605i	$-0.401607\pi$
$137$	7.12139	0.608422	0.304211	+	0.952605i	$0.401607\pi$
$138$	−9.06738	−0.771867
$139$	−12.3112	−1.04422	−0.522111	−	0.852877i	$-0.674855\pi$
$139$	−12.3112	−1.04422	−0.522111	+	0.852877i	$0.674855\pi$
$140$	−12.4585	−1.05294
$141$	−0.586771	−0.0494150
$142$	−9.04127	−0.758727
$143$	−0.105694	−0.00883856
$144$	−8.90786	−0.742322
$145$	5.78943	0.480786
$146$	−27.6603	−2.28918
$147$	1.88692	0.155630
$148$	8.20710	0.674619
$149$	0.737794	0.0604424	0.0302212	−	0.999543i	$-0.490379\pi$
$149$	0.737794	0.0604424	0.0302212	+	0.999543i	$0.490379\pi$
$150$	−1.40110	−0.114399
$151$	−2.83778	−0.230935	−0.115468	−	0.993311i	$-0.536837\pi$
$151$	−2.83778	−0.230935	−0.115468	+	0.993311i	$0.536837\pi$
$152$	21.8405	1.77150
$153$	−9.55762	−0.772688
$154$	7.05895	0.568826
$155$	0.789726	0.0634324
$156$	0.261363	0.0209258
$157$	−23.0729	−1.84142	−0.920708	−	0.390251i	$-0.872388\pi$
$157$	−23.0729	−1.84142	−0.920708	+	0.390251i	$0.872388\pi$
$158$	−28.4472	−2.26314
$159$	−4.90020	−0.388611
$160$	−1.05666	−0.0835361
$161$	20.7374	1.63434
$162$	−14.8274	−1.16495
$163$	8.67563	0.679528	0.339764	−	0.940511i	$-0.389653\pi$
$163$	8.67563	0.679528	0.339764	+	0.940511i	$0.389653\pi$
$164$	−39.7231	−3.10185
$165$	0.524203	0.0408091
$166$	34.9862	2.71545
$167$	−17.2030	−1.33121	−0.665605	−	0.746304i	$-0.731826\pi$
$167$	−17.2030	−1.33121	−0.665605	+	0.746304i	$0.731826\pi$
$168$	−8.47637	−0.653966
$169$	−12.9864	−0.998957
$170$	8.69713	0.667039
$171$	12.7126	0.972158
$172$	40.6752	3.10145
$173$	8.60854	0.654495	0.327248	−	0.944939i	$-0.393879\pi$
$173$	8.60854	0.654495	0.327248	+	0.944939i	$0.393879\pi$
$174$	8.11154	0.614934
$175$	3.20436	0.242227
$176$	−3.03271	−0.228599
$177$	1.88599	0.141760
$178$	−8.33119	−0.624449
$179$	−2.89348	−0.216269	−0.108135	−	0.994136i	$-0.534488\pi$
$179$	−2.89348	−0.216269	−0.108135	+	0.994136i	$0.534488\pi$
$180$	10.3677	0.772765
$181$	−0.557253	−0.0414203	−0.0207102	−	0.999786i	$-0.506593\pi$
$181$	−0.557253	−0.0414203	−0.0207102	+	0.999786i	$0.506593\pi$
$182$	−0.905230	−0.0671001
$183$	3.60077	0.266176
$184$	−29.6483	−2.18570
$185$	−2.11088	−0.155195
$186$	1.10648	0.0811312
$187$	−3.25392	−0.237950
$188$	−3.95103	−0.288159
$189$	−10.4845	−0.762634
$190$	−11.5681	−0.839237
$191$	2.64586	0.191447	0.0957237	−	0.995408i	$-0.469483\pi$
$191$	2.64586	0.191447	0.0957237	+	0.995408i	$0.469483\pi$
$192$	−5.33819	−0.385251
$193$	−2.78757	−0.200654	−0.100327	−	0.994955i	$-0.531989\pi$
$193$	−2.78757	−0.200654	−0.100327	+	0.994955i	$0.531989\pi$
$194$	1.92228	0.138011
$195$	−0.0672230	−0.00481394
$196$	12.7056	0.907542
$197$	−1.17527	−0.0837344	−0.0418672	−	0.999123i	$-0.513331\pi$
$197$	−1.17527	−0.0837344	−0.0418672	+	0.999123i	$0.513331\pi$
$198$	−5.87431	−0.417469
$199$	−6.23414	−0.441926	−0.220963	−	0.975282i	$-0.570920\pi$
$199$	−6.23414	−0.441926	−0.220963	+	0.975282i	$0.570920\pi$
$200$	−4.58127	−0.323944
$201$	−7.51313	−0.529936
$202$	11.8833	0.836107
$203$	−18.5514	−1.30205
$204$	8.04641	0.563361
$205$	10.2168	0.713575
$206$	2.49409	0.173772
$207$	−17.2573	−1.19946
$208$	0.388911	0.0269661
$209$	4.32806	0.299378
$210$	4.48961	0.309812
$211$	−3.32027	−0.228577	−0.114288	−	0.993448i	$-0.536459\pi$
$211$	−3.32027	−0.228577	−0.114288	+	0.993448i	$0.536459\pi$
$212$	−32.9956	−2.26615
$213$	2.15144	0.147414
$214$	13.4183	0.917257
$215$	−10.4617	−0.713484
$216$	14.9897	1.01992
$217$	−2.53056	−0.171786
$218$	−36.0141	−2.43918
$219$	6.58199	0.444770
$220$	3.52973	0.237974
$221$	0.417279	0.0280692
$222$	−2.95754	−0.198497
$223$	5.46898	0.366230	0.183115	−	0.983092i	$-0.441382\pi$
$223$	5.46898	0.366230	0.183115	+	0.983092i	$0.441382\pi$
$224$	3.38591	0.226230
$225$	−2.66660	−0.177773
$226$	15.9082	1.05819
$227$	−14.3337	−0.951358	−0.475679	−	0.879619i	$-0.657798\pi$
$227$	−14.3337	−0.951358	−0.475679	+	0.879619i	$0.657798\pi$
$228$	−10.7026	−0.708794
$229$	17.0373	1.12586	0.562930	−	0.826505i	$-0.309674\pi$
$229$	17.0373	1.12586	0.562930	+	0.826505i	$0.309674\pi$
$230$	15.7036	1.03546
$231$	−1.67973	−0.110518
$232$	26.5229	1.74131
$233$	−25.2709	−1.65555	−0.827774	−	0.561061i	$-0.810393\pi$
$233$	−25.2709	−1.65555	−0.827774	+	0.561061i	$0.810393\pi$
$234$	0.753313	0.0492456
$235$	1.01621	0.0662904
$236$	12.6994	0.826658
$237$	6.76924	0.439709
$238$	−27.8687	−1.80646
$239$	8.15197	0.527307	0.263653	−	0.964617i	$-0.415072\pi$
$239$	8.15197	0.527307	0.263653	+	0.964617i	$0.415072\pi$
$240$	−1.92886	−0.124507
$241$	3.68667	0.237479	0.118740	−	0.992925i	$-0.462115\pi$
$241$	3.68667	0.237479	0.118740	+	0.992925i	$0.462115\pi$
$242$	24.6918	1.58725
$243$	13.3441	0.856026
$244$	24.2458	1.55218
$245$	−3.26790	−0.208778
$246$	14.3148	0.912676
$247$	−0.555024	−0.0353153
$248$	3.61795	0.229740
$249$	−8.32524	−0.527590
$250$	2.42652	0.153467
$251$	19.0032	1.19947	0.599735	−	0.800199i	$-0.295273\pi$
$251$	19.0032	1.19947	0.599735	+	0.800199i	$0.295273\pi$
$252$	−33.2219	−2.09278
$253$	−5.87529	−0.369376
$254$	−26.5436	−1.66549
$255$	−2.06955	−0.129600
$256$	−30.8168	−1.92605
$257$	3.83953	0.239503	0.119752	−	0.992804i	$-0.461790\pi$
$257$	3.83953	0.239503	0.119752	+	0.992804i	$0.461790\pi$
$258$	−14.6579	−0.912560
$259$	6.76401	0.420295
$260$	−0.452648	−0.0280720
$261$	15.4381	0.955593
$262$	28.5258	1.76233
$263$	−14.5144	−0.894996	−0.447498	−	0.894285i	$-0.647685\pi$
$263$	−14.5144	−0.894996	−0.447498	+	0.894285i	$0.647685\pi$
$264$	2.40151	0.147803
$265$	8.48653	0.521323
$266$	37.0682	2.27280
$267$	1.98247	0.121325
$268$	−50.5898	−3.09027
$269$	−30.4412	−1.85603	−0.928015	−	0.372542i	$-0.878486\pi$
$269$	−30.4412	−1.85603	−0.928015	+	0.372542i	$0.878486\pi$
$270$	−7.93945	−0.483179
$271$	13.4677	0.818105	0.409053	−	0.912511i	$-0.365859\pi$
$271$	13.4677	0.818105	0.409053	+	0.912511i	$0.365859\pi$
$272$	11.9731	0.725978
$273$	0.215407	0.0130370
$274$	−17.2802	−1.04393
$275$	−0.907853	−0.0547456
$276$	14.5286	0.874519
$277$	−1.67376	−0.100566	−0.0502832	−	0.998735i	$-0.516012\pi$
$277$	−1.67376	−0.100566	−0.0502832	+	0.998735i	$0.516012\pi$
$278$	29.8734	1.79169
$279$	2.10588	0.126076
$280$	14.6800	0.877298
$281$	−6.12993	−0.365681	−0.182840	−	0.983143i	$-0.558529\pi$
$281$	−6.12993	−0.365681	−0.182840	+	0.983143i	$0.558529\pi$
$282$	1.42381	0.0847867
$283$	−3.04519	−0.181018	−0.0905088	−	0.995896i	$-0.528849\pi$
$283$	−3.04519	−0.181018	−0.0905088	+	0.995896i	$0.528849\pi$
$284$	14.4868	0.859632
$285$	2.75272	0.163057
$286$	0.256468	0.0151653
$287$	−32.7384	−1.93249
$288$	−2.81768	−0.166033
$289$	−4.15352	−0.244325
$290$	−14.0482	−0.824937
$291$	−0.457421	−0.0268145
$292$	44.3200	2.59363
$293$	7.34275	0.428968	0.214484	−	0.976727i	$-0.431193\pi$
$293$	7.34275	0.428968	0.214484	+	0.976727i	$0.431193\pi$
$294$	−4.57864	−0.267032
$295$	−3.26630	−0.190171
$296$	−9.67050	−0.562086
$297$	2.97045	0.172363
$298$	−1.79027	−0.103708
$299$	0.753439	0.0435725
$300$	2.24497	0.129613
$301$	33.5231	1.93224
$302$	6.88593	0.396241
$303$	−2.82773	−0.162449
$304$	−15.9255	−0.913391
$305$	−6.23607	−0.357076
$306$	23.1917	1.32578
$307$	1.59191	0.0908550	0.0454275	−	0.998968i	$-0.485535\pi$
$307$	1.59191	0.0908550	0.0454275	+	0.998968i	$0.485535\pi$
$308$	−11.3105	−0.644476
$309$	−0.593489	−0.0337624
$310$	−1.91629	−0.108838
$311$	−11.8207	−0.670291	−0.335146	−	0.942166i	$-0.608785\pi$
$311$	−11.8207	−0.670291	−0.335146	+	0.942166i	$0.608785\pi$
$312$	−0.307966	−0.0174352
$313$	1.48113	0.0837183	0.0418592	−	0.999124i	$-0.486672\pi$
$313$	1.48113	0.0837183	0.0418592	+	0.999124i	$0.486672\pi$
$314$	55.9868	3.15952
$315$	8.54473	0.481441
$316$	45.5808	2.56412
$317$	−16.7189	−0.939029	−0.469515	−	0.882925i	$-0.655571\pi$
$317$	−16.7189	−0.939029	−0.469515	+	0.882925i	$0.655571\pi$
$318$	11.8904	0.666783
$319$	5.25595	0.294277
$320$	9.24507	0.516815
$321$	−3.19299	−0.178215
$322$	−50.3198	−2.80421
$323$	−17.0871	−0.950754
$324$	23.7578	1.31988
$325$	0.116422	0.00645792
$326$	−21.0516	−1.16594
$327$	8.56983	0.473913
$328$	46.8061	2.58443
$329$	−3.25631	−0.179526
$330$	−1.27199	−0.0700207
$331$	−23.3832	−1.28526	−0.642628	−	0.766178i	$-0.722156\pi$
$331$	−23.3832	−1.28526	−0.642628	+	0.766178i	$0.722156\pi$
$332$	−56.0581	−3.07659
$333$	−5.62887	−0.308460
$334$	41.7435	2.28410
$335$	13.0118	0.710910
$336$	6.18074	0.337187
$337$	0.594693	0.0323950	0.0161975	−	0.999869i	$-0.494844\pi$
$337$	0.594693	0.0323950	0.0161975	+	0.999869i	$0.494844\pi$
$338$	31.5119	1.71402
$339$	−3.78547	−0.205599
$340$	−13.9354	−0.755751
$341$	0.716955	0.0388253
$342$	−30.8474	−1.66804
$343$	−11.9590	−0.645724
$344$	−47.9279	−2.58410
$345$	−3.73678	−0.201182
$346$	−20.8888	−1.12299
$347$	13.4588	0.722504	0.361252	−	0.932468i	$-0.382349\pi$
$347$	13.4588	0.722504	0.361252	+	0.932468i	$0.382349\pi$
$348$	−12.9971	−0.696716
$349$	−10.5261	−0.563447	−0.281723	−	0.959496i	$-0.590906\pi$
$349$	−10.5261	−0.563447	−0.281723	+	0.959496i	$0.590906\pi$
$350$	−7.77543	−0.415614
$351$	−0.380926	−0.0203323
$352$	−0.959289	−0.0511303
$353$	30.0925	1.60166	0.800831	−	0.598891i	$-0.204392\pi$
$353$	30.0925	1.60166	0.800831	+	0.598891i	$0.204392\pi$
$354$	−4.57639	−0.243233
$355$	−3.72602	−0.197757
$356$	13.3490	0.707496
$357$	6.63157	0.350980
$358$	7.02110	0.371077
$359$	−4.03267	−0.212836	−0.106418	−	0.994321i	$-0.533938\pi$
$359$	−4.03267	−0.212836	−0.106418	+	0.994321i	$0.533938\pi$
$360$	−12.2164	−0.643861
$361$	3.72767	0.196193
$362$	1.35219	0.0710693
$363$	−5.87560	−0.308389
$364$	1.45044	0.0760239
$365$	−11.3992	−0.596660
$366$	−8.73733	−0.456708
$367$	13.9987	0.730727	0.365364	−	0.930865i	$-0.380945\pi$
$367$	13.9987	0.730727	0.365364	+	0.930865i	$0.380945\pi$
$368$	21.6187	1.12695
$369$	27.2442	1.41828
$370$	5.12209	0.266285
$371$	−27.1939	−1.41184
$372$	−1.77291	−0.0919211
$373$	12.4633	0.645326	0.322663	−	0.946514i	$-0.395422\pi$
$373$	12.4633	0.645326	0.322663	+	0.946514i	$0.395422\pi$
$374$	7.89571	0.408277
$375$	−0.577409	−0.0298173
$376$	4.65554	0.240091
$377$	−0.674015	−0.0347136
$378$	25.4408	1.30853
$379$	−28.6722	−1.47279	−0.736395	−	0.676552i	$-0.763473\pi$
$379$	−28.6722	−1.47279	−0.736395	+	0.676552i	$0.763473\pi$
$380$	18.5355	0.950849
$381$	6.31625	0.323591
$382$	−6.42022	−0.328487
$383$	27.8014	1.42058	0.710292	−	0.703907i	$-0.248563\pi$
$383$	27.8014	1.42058	0.710292	+	0.703907i	$0.248563\pi$
$384$	11.7330	0.598746
$385$	2.90908	0.148261
$386$	6.76410	0.344284
$387$	−27.8972	−1.41810
$388$	−3.08005	−0.156366
$389$	0.818877	0.0415187	0.0207594	−	0.999785i	$-0.493392\pi$
$389$	0.818877	0.0415187	0.0207594	+	0.999785i	$0.493392\pi$
$390$	0.163118	0.00825980
$391$	23.1956	1.17305
$392$	−14.9711	−0.756155
$393$	−6.78794	−0.342406
$394$	2.85181	0.143672
$395$	−11.7235	−0.589872
$396$	9.41237	0.472989
$397$	3.17103	0.159149	0.0795747	−	0.996829i	$-0.474644\pi$
$397$	3.17103	0.159149	0.0795747	+	0.996829i	$0.474644\pi$
$398$	15.1273	0.758261
$399$	−8.82068	−0.441586
$400$	3.34053	0.167027
$401$	−9.77934	−0.488357	−0.244178	−	0.969730i	$-0.578518\pi$
$401$	−9.77934	−0.488357	−0.244178	+	0.969730i	$0.578518\pi$
$402$	18.2308	0.909268
$403$	−0.0919413	−0.00457992
$404$	−19.0406	−0.947303
$405$	−6.11054	−0.303635
$406$	45.0153	2.23407
$407$	−1.91637	−0.0949908
$408$	−9.48116	−0.469387
$409$	15.3258	0.757810	0.378905	−	0.925436i	$-0.376301\pi$
$409$	15.3258	0.757810	0.378905	+	0.925436i	$0.376301\pi$
$410$	−24.7914	−1.22436
$411$	4.11196	0.202828
$412$	−3.99627	−0.196882
$413$	10.4664	0.515017
$414$	41.8751	2.05805
$415$	14.4183	0.707764
$416$	0.123018	0.00603145
$417$	−7.10860	−0.348110
$418$	−10.5021	−0.513675
$419$	−18.6265	−0.909966	−0.454983	−	0.890500i	$-0.650355\pi$
$419$	−18.6265	−0.909966	−0.454983	+	0.890500i	$0.650355\pi$
$420$	−7.19367	−0.351015
$421$	16.9940	0.828239	0.414119	−	0.910223i	$-0.364090\pi$
$421$	16.9940	0.828239	0.414119	+	0.910223i	$0.364090\pi$
$422$	8.05671	0.392194
$423$	2.70983	0.131757
$424$	38.8791	1.88813
$425$	3.58420	0.173859
$426$	−5.22052	−0.252935
$427$	19.9826	0.967025
$428$	−21.5001	−1.03925
$429$	−0.0610286	−0.00294649
$430$	25.3856	1.22420
$431$	2.13644	0.102909	0.0514545	−	0.998675i	$-0.483614\pi$
$431$	2.13644	0.102909	0.0514545	+	0.998675i	$0.483614\pi$
$432$	−10.9301	−0.525872
$433$	7.70729	0.370389	0.185194	−	0.982702i	$-0.440709\pi$
$433$	7.70729	0.370389	0.185194	+	0.982702i	$0.440709\pi$
$434$	6.14047	0.294752
$435$	3.34287	0.160278
$436$	57.7051	2.76357
$437$	−30.8526	−1.47588
$438$	−15.9713	−0.763140
$439$	−16.5557	−0.790159	−0.395080	−	0.918647i	$-0.629283\pi$
$439$	−16.5557	−0.790159	−0.395080	+	0.918647i	$0.629283\pi$
$440$	−4.15911	−0.198278
$441$	−8.71417	−0.414961
$442$	−1.01253	−0.0481614
$443$	−4.73966	−0.225188	−0.112594	−	0.993641i	$-0.535916\pi$
$443$	−4.73966	−0.225188	−0.112594	+	0.993641i	$0.535916\pi$
$444$	4.73886	0.224896
$445$	−3.43339	−0.162758
$446$	−13.2706	−0.628381
$447$	0.426009	0.0201495
$448$	−29.6245	−1.39963
$449$	−18.9037	−0.892119	−0.446059	−	0.895003i	$-0.647173\pi$
$449$	−18.9037	−0.892119	−0.446059	+	0.895003i	$0.647173\pi$
$450$	6.47055	0.305025
$451$	9.27538	0.436761
$452$	−25.4895	−1.19893
$453$	−1.63856	−0.0769863
$454$	34.7809	1.63235
$455$	−0.373057	−0.0174892
$456$	12.6109	0.590560
$457$	16.1498	0.755456	0.377728	−	0.925917i	$-0.376705\pi$
$457$	16.1498	0.755456	0.377728	+	0.925917i	$0.376705\pi$
$458$	−41.3414	−1.93176
$459$	−11.7273	−0.547384
$460$	−25.1617	−1.17317
$461$	9.03721	0.420905	0.210453	−	0.977604i	$-0.432506\pi$
$461$	9.03721	0.420905	0.210453	+	0.977604i	$0.432506\pi$
$462$	4.07590	0.189628
$463$	37.0570	1.72219	0.861093	−	0.508447i	$-0.169780\pi$
$463$	37.0570	1.72219	0.861093	+	0.508447i	$0.169780\pi$
$464$	−19.3398	−0.897827
$465$	0.455995	0.0211463
$466$	61.3202	2.84060
$467$	−30.6586	−1.41871	−0.709355	−	0.704851i	$-0.751014\pi$
$467$	−30.6586	−1.41871	−0.709355	+	0.704851i	$0.751014\pi$
$468$	−1.20703	−0.0557949
$469$	−41.6944	−1.92527
$470$	−2.46586	−0.113742
$471$	−13.3225	−0.613868
$472$	−14.9638	−0.688764
$473$	−9.49771	−0.436705
$474$	−16.4257	−0.754457
$475$	−4.76735	−0.218741
$476$	44.6538	2.04671
$477$	22.6302	1.03616
$478$	−19.7809	−0.904758
$479$	18.2040	0.831762	0.415881	−	0.909419i	$-0.363473\pi$
$479$	18.2040	0.831762	0.415881	+	0.909419i	$0.363473\pi$
$480$	−0.610124	−0.0278482
$481$	0.245752	0.0112053
$482$	−8.94577	−0.407469
$483$	11.9740	0.544835
$484$	−39.5635	−1.79834
$485$	0.792195	0.0359717
$486$	−32.3798	−1.46878
$487$	−20.7226	−0.939031	−0.469516	−	0.882924i	$-0.655571\pi$
$487$	−20.7226	−0.939031	−0.469516	+	0.882924i	$0.655571\pi$
$488$	−28.5691	−1.29326
$489$	5.00939	0.226532
$490$	7.92962	0.358224
$491$	−12.0126	−0.542122	−0.271061	−	0.962562i	$-0.587375\pi$
$491$	−12.0126	−0.542122	−0.271061	+	0.962562i	$0.587375\pi$
$492$	−22.9365	−1.03406
$493$	−20.7505	−0.934554
$494$	1.34678	0.0605943
$495$	−2.42088	−0.108810
$496$	−2.63811	−0.118455
$497$	11.9395	0.535560
$498$	20.2013	0.905244
$499$	7.02325	0.314404	0.157202	−	0.987566i	$-0.449753\pi$
$499$	7.02325	0.314404	0.157202	+	0.987566i	$0.449753\pi$
$500$	−3.88800	−0.173877
$501$	−9.93319	−0.443782
$502$	−46.1116	−2.05806
$503$	1.79268	0.0799315	0.0399658	−	0.999201i	$-0.487275\pi$
$503$	1.79268	0.0799315	0.0399658	+	0.999201i	$0.487275\pi$
$504$	39.1457	1.74369
$505$	4.89727	0.217925
$506$	14.2565	0.633779
$507$	−7.49850	−0.333020
$508$	42.5306	1.88699
$509$	−8.40411	−0.372506	−0.186253	−	0.982502i	$-0.559634\pi$
$509$	−8.40411	−0.372506	−0.186253	+	0.982502i	$0.559634\pi$
$510$	5.02180	0.222369
$511$	36.5270	1.61586
$512$	34.1376	1.50868
$513$	15.5985	0.688692
$514$	−9.31669	−0.410942
$515$	1.02785	0.0452924
$516$	23.4862	1.03392
$517$	0.922572	0.0405746
$518$	−16.4130	−0.721146
$519$	4.97065	0.218187
$520$	0.533359	0.0233893
$521$	−10.2058	−0.447123	−0.223562	−	0.974690i	$-0.571768\pi$
$521$	−10.2058	−0.447123	−0.223562	+	0.974690i	$0.571768\pi$
$522$	−37.4608	−1.63962
$523$	20.5975	0.900667	0.450333	−	0.892860i	$-0.351305\pi$
$523$	20.5975	0.900667	0.450333	+	0.892860i	$0.351305\pi$
$524$	−45.7067	−1.99671
$525$	1.85023	0.0807505
$526$	35.2195	1.53564
$527$	−2.83054	−0.123300
$528$	−1.75112	−0.0762076
$529$	18.8821	0.820960
$530$	−20.5927	−0.894491
$531$	−8.70990	−0.377978
$532$	−59.3942	−2.57507
$533$	−1.18946	−0.0515213
$534$	−4.81051	−0.208171
$535$	5.52986	0.239077
$536$	59.6105	2.57478
$537$	−1.67073	−0.0720971
$538$	73.8661	3.18459
$539$	−2.96677	−0.127788
$540$	12.7213	0.547439
$541$	1.53835	0.0661386	0.0330693	−	0.999453i	$-0.489472\pi$
$541$	1.53835	0.0661386	0.0330693	+	0.999453i	$0.489472\pi$
$542$	−32.6797	−1.40371
$543$	−0.321763	−0.0138082
$544$	3.78727	0.162378
$545$	−14.8419	−0.635755
$546$	−0.522688	−0.0223690
$547$	−24.6058	−1.05207	−0.526034	−	0.850464i	$-0.676322\pi$
$547$	−24.6058	−1.05207	−0.526034	+	0.850464i	$0.676322\pi$
$548$	27.6880	1.18277
$549$	−16.6291	−0.709712
$550$	2.20292	0.0939329
$551$	27.6003	1.17581
$552$	−17.1192	−0.728641
$553$	37.5662	1.59748
$554$	4.06141	0.172553
$555$	−1.21884	−0.0517370
$556$	−47.8659	−2.02997
$557$	−20.8693	−0.884261	−0.442131	−	0.896951i	$-0.645777\pi$
$557$	−20.8693	−0.884261	−0.442131	+	0.896951i	$0.645777\pi$
$558$	−5.10997	−0.216322
$559$	1.21797	0.0515147
$560$	−10.7043	−0.452338
$561$	−1.87885	−0.0793250
$562$	14.8744	0.627439
$563$	−10.4972	−0.442402	−0.221201	−	0.975228i	$-0.570998\pi$
$563$	−10.4972	−0.442402	−0.221201	+	0.975228i	$0.570998\pi$
$564$	−2.28136	−0.0960628
$565$	6.55595	0.275811
$566$	7.38921	0.310592
$567$	19.5804	0.822298
$568$	−17.0699	−0.716237
$569$	−10.1887	−0.427131	−0.213566	−	0.976929i	$-0.568508\pi$
$569$	−10.1887	−0.427131	−0.213566	+	0.976929i	$0.568508\pi$
$570$	−6.67952	−0.279774
$571$	−22.8911	−0.957963	−0.478981	−	0.877825i	$-0.658994\pi$
$571$	−22.8911	−0.957963	−0.478981	+	0.877825i	$0.658994\pi$
$572$	−0.410937	−0.0171822
$573$	1.52774	0.0638224
$574$	79.4404	3.31578
$575$	6.47164	0.269886
$576$	24.6529	1.02720
$577$	−3.74935	−0.156088	−0.0780438	−	0.996950i	$-0.524867\pi$
$577$	−3.74935	−0.156088	−0.0780438	+	0.996950i	$0.524867\pi$
$578$	10.0786	0.419215
$579$	−1.60957	−0.0668915
$580$	22.5093	0.934647
$581$	−46.2012	−1.91675
$582$	1.10994	0.0460085
$583$	7.70452	0.319089
$584$	−52.2226	−2.16099
$585$	0.310450	0.0128355
$586$	−17.8173	−0.736027
$587$	−7.69760	−0.317714	−0.158857	−	0.987302i	$-0.550781\pi$
$587$	−7.69760	−0.317714	−0.158857	+	0.987302i	$0.550781\pi$
$588$	7.33633	0.302545
$589$	3.76491	0.155130
$590$	7.92574	0.326297
$591$	−0.678611	−0.0279143
$592$	7.05147	0.289814
$593$	−11.2758	−0.463042	−0.231521	−	0.972830i	$-0.574370\pi$
$593$	−11.2758	−0.463042	−0.231521	+	0.972830i	$0.574370\pi$
$594$	−7.20785	−0.295742
$595$	−11.4850	−0.470841
$596$	2.86854	0.117500
$597$	−3.59965	−0.147324
$598$	−1.82824	−0.0747621
$599$	−43.9011	−1.79375	−0.896875	−	0.442284i	$-0.854168\pi$
$599$	−43.9011	−1.79375	−0.896875	+	0.442284i	$0.854168\pi$
$600$	−2.64527	−0.107993
$601$	18.6972	0.762676	0.381338	−	0.924436i	$-0.375463\pi$
$601$	18.6972	0.762676	0.381338	+	0.924436i	$0.375463\pi$
$602$	−81.3445	−3.31535
$603$	34.6972	1.41298
$604$	−11.0333	−0.448938
$605$	10.1758	0.413705
$606$	6.86154	0.278731
$607$	−9.37822	−0.380650	−0.190325	−	0.981721i	$-0.560954\pi$
$607$	−9.37822	−0.380650	−0.190325	+	0.981721i	$0.560954\pi$
$608$	−5.03746	−0.204296
$609$	−10.7117	−0.434062
$610$	15.1319	0.612675
$611$	−0.118309	−0.00478628
$612$	−37.1600	−1.50210
$613$	−4.29579	−0.173505	−0.0867527	−	0.996230i	$-0.527649\pi$
$613$	−4.29579	−0.173505	−0.0867527	+	0.996230i	$0.527649\pi$
$614$	−3.86280	−0.155890
$615$	5.89930	0.237883
$616$	13.3273	0.536972
$617$	9.28646	0.373859	0.186929	−	0.982373i	$-0.440146\pi$
$617$	9.28646	0.373859	0.186929	+	0.982373i	$0.440146\pi$
$618$	1.44011	0.0579299
$619$	21.1663	0.850746	0.425373	−	0.905018i	$-0.360143\pi$
$619$	21.1663	0.850746	0.425373	+	0.905018i	$0.360143\pi$
$620$	3.07045	0.123312
$621$	−21.1749	−0.849718
$622$	28.6832	1.15009
$623$	11.0018	0.440778
$624$	0.224561	0.00898963
$625$	1.00000	0.0400000
$626$	−3.59399	−0.143645
$627$	2.49906	0.0998028
$628$	−89.7073	−3.57971
$629$	7.56581	0.301669
$630$	−20.7340	−0.826061
$631$	−20.3018	−0.808202	−0.404101	−	0.914714i	$-0.632416\pi$
$631$	−20.3018	−0.808202	−0.404101	+	0.914714i	$0.632416\pi$
$632$	−53.7083	−2.13640
$633$	−1.91716	−0.0762001
$634$	40.5688	1.61119
$635$	−10.9389	−0.434099
$636$	−19.0520	−0.755460
$637$	0.380455	0.0150742
$638$	−12.7537	−0.504922
$639$	−9.93581	−0.393055
$640$	−20.3200	−0.803220
$641$	−8.60419	−0.339845	−0.169923	−	0.985457i	$-0.554352\pi$
$641$	−8.60419	−0.339845	−0.169923	+	0.985457i	$0.554352\pi$
$642$	7.74786	0.305784
$643$	26.1941	1.03299	0.516497	−	0.856289i	$-0.327236\pi$
$643$	26.1941	1.03299	0.516497	+	0.856289i	$0.327236\pi$
$644$	80.6271	3.17715
$645$	−6.04070	−0.237852
$646$	41.4623	1.63131
$647$	7.59192	0.298469	0.149235	−	0.988802i	$-0.452319\pi$
$647$	7.59192	0.298469	0.149235	+	0.988802i	$0.452319\pi$
$648$	−27.9940	−1.09971
$649$	−2.96532	−0.116399
$650$	−0.282500	−0.0110805
$651$	−1.46117	−0.0572678
$652$	33.7308	1.32100
$653$	6.80048	0.266123	0.133062	−	0.991108i	$-0.457519\pi$
$653$	6.80048	0.266123	0.133062	+	0.991108i	$0.457519\pi$
$654$	−20.7949	−0.813143
$655$	11.7559	0.459339
$656$	−34.1297	−1.33254
$657$	−30.3970	−1.18590
$658$	7.90150	0.308032
$659$	−22.2596	−0.867112	−0.433556	−	0.901127i	$-0.642741\pi$
$659$	−22.2596	−0.867112	−0.433556	+	0.901127i	$0.642741\pi$
$660$	2.03810	0.0793329
$661$	33.8419	1.31630	0.658149	−	0.752888i	$-0.271340\pi$
$661$	33.8419	1.31630	0.658149	+	0.752888i	$0.271340\pi$
$662$	56.7398	2.20525
$663$	0.240941	0.00935736
$664$	66.0538	2.56339
$665$	15.2763	0.592390
$666$	13.6586	0.529259
$667$	−37.4671	−1.45073
$668$	−66.8853	−2.58787
$669$	3.15784	0.122089
$670$	−31.5734	−1.21979
$671$	−5.66143	−0.218557
$672$	1.95505	0.0754179
$673$	26.5136	1.02202	0.511012	−	0.859573i	$-0.329271\pi$
$673$	26.5136	1.02202	0.511012	+	0.859573i	$0.329271\pi$
$674$	−1.44303	−0.0555836
$675$	−3.27195	−0.125937
$676$	−50.4913	−1.94197
$677$	1.18521	0.0455512	0.0227756	−	0.999741i	$-0.492750\pi$
$677$	1.18521	0.0455512	0.0227756	+	0.999741i	$0.492750\pi$
$678$	9.18552	0.352768
$679$	−2.53847	−0.0974177
$680$	16.4202	0.629685
$681$	−8.27639	−0.317152
$682$	−1.73971	−0.0666168
$683$	−39.9783	−1.52973	−0.764864	−	0.644192i	$-0.777194\pi$
$683$	−39.9783	−1.52973	−0.764864	+	0.644192i	$0.777194\pi$
$684$	49.4266	1.88987
$685$	−7.12139	−0.272094
$686$	29.0187	1.10794
$687$	9.83752	0.375325
$688$	34.9478	1.33237
$689$	−0.988017	−0.0376404
$690$	9.06738	0.345189
$691$	−47.6166	−1.81142	−0.905711	−	0.423895i	$-0.860663\pi$
$691$	−47.6166	−1.81142	−0.905711	+	0.423895i	$0.860663\pi$
$692$	33.4700	1.27234
$693$	7.75736	0.294678
$694$	−32.6580	−1.23968
$695$	12.3112	0.466991
$696$	15.3146	0.580498
$697$	−36.6192	−1.38705
$698$	25.5417	0.966767
$699$	−14.5916	−0.551906
$700$	12.4585	0.470888
$701$	39.0988	1.47674	0.738371	−	0.674395i	$-0.235596\pi$
$701$	39.0988	1.47674	0.738371	+	0.674395i	$0.235596\pi$
$702$	0.924324	0.0348864
$703$	−10.0633	−0.379545
$704$	8.39316	0.316329
$705$	0.586771	0.0220991
$706$	−73.0200	−2.74814
$707$	−15.6926	−0.590180
$708$	7.33273	0.275581
$709$	−2.10455	−0.0790379	−0.0395189	−	0.999219i	$-0.512583\pi$
$709$	−2.10455	−0.0790379	−0.0395189	+	0.999219i	$0.512583\pi$
$710$	9.04127	0.339313
$711$	−31.2618	−1.17241
$712$	−15.7293	−0.589479
$713$	−5.11082	−0.191402
$714$	−16.0916	−0.602215
$715$	0.105694	0.00395272
$716$	−11.2499	−0.420427
$717$	4.70702	0.175787
$718$	9.78536	0.365186
$719$	35.6306	1.32880	0.664399	−	0.747378i	$-0.268687\pi$
$719$	35.6306	1.32880	0.664399	+	0.747378i	$0.268687\pi$
$720$	8.90786	0.331976
$721$	−3.29359	−0.122660
$722$	−9.04526	−0.336630
$723$	2.12872	0.0791678
$724$	−2.16660	−0.0805210
$725$	−5.78943	−0.215014
$726$	14.2573	0.529137
$727$	11.4530	0.424768	0.212384	−	0.977186i	$-0.431877\pi$
$727$	11.4530	0.424768	0.212384	+	0.977186i	$0.431877\pi$
$728$	−1.70907	−0.0633424
$729$	−10.6266	−0.393578
$730$	27.6603	1.02375
$731$	37.4969	1.38687
$732$	13.9998	0.517446
$733$	−1.13223	−0.0418200	−0.0209100	−	0.999781i	$-0.506656\pi$
$733$	−1.13223	−0.0418200	−0.0209100	+	0.999781i	$0.506656\pi$
$734$	−33.9682	−1.25379
$735$	−1.88692	−0.0695999
$736$	6.83830	0.252063
$737$	11.8128	0.435130
$738$	−66.1086	−2.43349
$739$	16.4441	0.604906	0.302453	−	0.953164i	$-0.402194\pi$
$739$	16.4441	0.604906	0.302453	+	0.953164i	$0.402194\pi$
$740$	−8.20710	−0.301699
$741$	−0.320476	−0.0117730
$742$	65.9865	2.42244
$743$	18.0807	0.663317	0.331659	−	0.943400i	$-0.392392\pi$
$743$	18.0807	0.663317	0.331659	+	0.943400i	$0.392392\pi$
$744$	2.08904	0.0765878
$745$	−0.737794	−0.0270307
$746$	−30.2425	−1.10726
$747$	38.4477	1.40673
$748$	−12.6513	−0.462576
$749$	−17.7196	−0.647461
$750$	1.40110	0.0511608
$751$	−21.3940	−0.780679	−0.390340	−	0.920671i	$-0.627642\pi$
$751$	−21.3940	−0.780679	−0.390340	+	0.920671i	$0.627642\pi$
$752$	−3.39469	−0.123792
$753$	10.9726	0.399864
$754$	1.63551	0.0595618
$755$	2.83778	0.103277
$756$	−40.7637	−1.48256
$757$	12.1309	0.440907	0.220453	−	0.975398i	$-0.429246\pi$
$757$	12.1309	0.440907	0.220453	+	0.975398i	$0.429246\pi$
$758$	69.5736	2.52703
$759$	−3.39245	−0.123138
$760$	−21.8405	−0.792239
$761$	−43.2675	−1.56844	−0.784222	−	0.620480i	$-0.786938\pi$
$761$	−43.2675	−1.56844	−0.784222	+	0.620480i	$0.786938\pi$
$762$	−15.3265	−0.555221
$763$	47.5586	1.72174
$764$	10.2871	0.372174
$765$	9.55762	0.345556
$766$	−67.4606	−2.43745
$767$	0.380268	0.0137307
$768$	−17.7939	−0.642083
$769$	−9.47258	−0.341590	−0.170795	−	0.985307i	$-0.554634\pi$
$769$	−9.47258	−0.341590	−0.170795	+	0.985307i	$0.554634\pi$
$770$	−7.05895	−0.254387
$771$	2.21698	0.0798426
$772$	−10.8381	−0.390071
$773$	−3.36303	−0.120960	−0.0604799	−	0.998169i	$-0.519263\pi$
$773$	−3.36303	−0.120960	−0.0604799	+	0.998169i	$0.519263\pi$
$774$	67.6932	2.43318
$775$	−0.789726	−0.0283678
$776$	3.62925	0.130283
$777$	3.90560	0.140113
$778$	−1.98702	−0.0712382
$779$	48.7073	1.74512
$780$	−0.261363	−0.00935830
$781$	−3.38268	−0.121042
$782$	−56.2846	−2.01273
$783$	18.9427	0.676957
$784$	10.9165	0.389876
$785$	23.0729	0.823507
$786$	16.4711	0.587504
$787$	−32.6539	−1.16399	−0.581994	−	0.813193i	$-0.697727\pi$
$787$	−32.6539	−1.16399	−0.581994	+	0.813193i	$0.697727\pi$
$788$	−4.56944	−0.162780
$789$	−8.38075	−0.298362
$790$	28.4472	1.01211
$791$	−21.0076	−0.746945
$792$	−11.0907	−0.394090
$793$	0.726014	0.0257815
$794$	−7.69456	−0.273070
$795$	4.90020	0.173792
$796$	−24.2383	−0.859104
$797$	−3.89217	−0.137868	−0.0689338	−	0.997621i	$-0.521960\pi$
$797$	−3.89217	−0.137868	−0.0689338	+	0.997621i	$0.521960\pi$
$798$	21.4036	0.757678
$799$	−3.64231	−0.128856
$800$	1.05666	0.0373585
$801$	−9.15547	−0.323493
$802$	23.7298	0.837927
$803$	−10.3488	−0.365200
$804$	−29.2110	−1.03019
$805$	−20.7374	−0.730898
$806$	0.223097	0.00785827
$807$	−17.5770	−0.618740
$808$	22.4357	0.789284
$809$	−5.48230	−0.192748	−0.0963738	−	0.995345i	$-0.530724\pi$
$809$	−5.48230	−0.192748	−0.0963738	+	0.995345i	$0.530724\pi$
$810$	14.8274	0.520980
$811$	−47.8854	−1.68148	−0.840742	−	0.541437i	$-0.817881\pi$
$811$	−47.8854	−1.68148	−0.840742	+	0.541437i	$0.817881\pi$
$812$	−72.1278	−2.53119
$813$	7.77639	0.272730
$814$	4.65011	0.162986
$815$	−8.67563	−0.303894
$816$	6.91340	0.242018
$817$	−49.8748	−1.74490
$818$	−37.1883	−1.30026
$819$	−0.994793	−0.0347609
$820$	39.7231	1.38719
$821$	27.9651	0.975990	0.487995	−	0.872846i	$-0.337728\pi$
$821$	27.9651	0.975990	0.487995	+	0.872846i	$0.337728\pi$
$822$	−9.97775	−0.348014
$823$	−12.4221	−0.433009	−0.216504	−	0.976282i	$-0.569466\pi$
$823$	−12.4221	−0.433009	−0.216504	+	0.976282i	$0.569466\pi$
$824$	4.70884	0.164040
$825$	−0.524203	−0.0182504
$826$	−25.3969	−0.883671
$827$	21.1189	0.734376	0.367188	−	0.930147i	$-0.380321\pi$
$827$	21.1189	0.734376	0.367188	+	0.930147i	$0.380321\pi$
$828$	−67.0962	−2.33175
$829$	6.45833	0.224307	0.112154	−	0.993691i	$-0.464225\pi$
$829$	6.45833	0.224307	0.112154	+	0.993691i	$0.464225\pi$
$830$	−34.9862	−1.21439
$831$	−0.966444	−0.0335256
$832$	−1.07633	−0.0373149
$833$	11.7128	0.405824
$834$	17.2492	0.597290
$835$	17.2030	0.595335
$836$	16.8275	0.581990
$837$	2.58394	0.0893141
$838$	45.1976	1.56133
$839$	1.45785	0.0503307	0.0251654	−	0.999683i	$-0.491989\pi$
$839$	1.45785	0.0503307	0.0251654	+	0.999683i	$0.491989\pi$
$840$	8.47637	0.292463
$841$	4.51749	0.155775
$842$	−41.2364	−1.42110
$843$	−3.53948	−0.121906
$844$	−12.9092	−0.444353
$845$	12.9864	0.446747
$846$	−6.57546	−0.226069
$847$	−32.6069	−1.12039
$848$	−28.3496	−0.973528
$849$	−1.75832	−0.0603454
$850$	−8.69713	−0.298309
$851$	13.6608	0.468288
$852$	8.36480	0.286573
$853$	−16.8655	−0.577464	−0.288732	−	0.957410i	$-0.593234\pi$
$853$	−16.8655	−0.577464	−0.288732	+	0.957410i	$0.593234\pi$
$854$	−48.4881	−1.65923
$855$	−12.7126	−0.434762
$856$	25.3337	0.865890
$857$	−18.9376	−0.646897	−0.323449	−	0.946246i	$-0.604842\pi$
$857$	−18.9376	−0.646897	−0.323449	+	0.946246i	$0.604842\pi$
$858$	0.148087	0.00505561
$859$	−37.8216	−1.29046	−0.645228	−	0.763990i	$-0.723238\pi$
$859$	−37.8216	−1.29046	−0.645228	+	0.763990i	$0.723238\pi$
$860$	−40.6752	−1.38701
$861$	−18.9035	−0.644228
$862$	−5.18413	−0.176572
$863$	−14.0169	−0.477139	−0.238570	−	0.971125i	$-0.576679\pi$
$863$	−14.0169	−0.477139	−0.238570	+	0.971125i	$0.576679\pi$
$864$	−3.45733	−0.117621
$865$	−8.60854	−0.292699
$866$	−18.7019	−0.635516
$867$	−2.39828	−0.0814500
$868$	−9.83883	−0.333952
$869$	−10.6432	−0.361045
$870$	−8.11154	−0.275007
$871$	−1.51486	−0.0513289
$872$	−67.9945	−2.30258
$873$	2.11246	0.0714961
$874$	74.8644	2.53233
$875$	−3.20436	−0.108327
$876$	25.5908	0.864632
$877$	−0.356129	−0.0120256	−0.00601281	−	0.999982i	$-0.501914\pi$
$877$	−0.356129	−0.0120256	−0.00601281	+	0.999982i	$0.501914\pi$
$878$	40.1727	1.35576
$879$	4.23977	0.143004
$880$	3.03271	0.102233
$881$	6.05025	0.203838	0.101919	−	0.994793i	$-0.467502\pi$
$881$	6.05025	0.203838	0.101919	+	0.994793i	$0.467502\pi$
$882$	21.1451	0.711993
$883$	−20.9533	−0.705135	−0.352567	−	0.935786i	$-0.614691\pi$
$883$	−20.9533	−0.705135	−0.352567	+	0.935786i	$0.614691\pi$
$884$	1.62238	0.0545665
$885$	−1.88599	−0.0633969
$886$	11.5009	0.386380
$887$	−48.6786	−1.63447	−0.817233	−	0.576307i	$-0.804493\pi$
$887$	−48.6786	−1.63447	−0.817233	+	0.576307i	$0.804493\pi$
$888$	−5.58384	−0.187381
$889$	35.0523	1.17562
$890$	8.33119	0.279262
$891$	−5.54747	−0.185847
$892$	21.2634	0.711951
$893$	4.84465	0.162120
$894$	−1.03372	−0.0345727
$895$	2.89348	0.0967185
$896$	65.1126	2.17526
$897$	0.435043	0.0145257
$898$	45.8701	1.53070
$899$	4.57207	0.152487
$900$	−10.3677	−0.345591
$901$	−30.4174	−1.01335
$902$	−22.5069	−0.749398
$903$	19.3566	0.644146
$904$	30.0346	0.998935
$905$	0.557253	0.0185237
$906$	3.97600	0.132094
$907$	−36.7682	−1.22087	−0.610434	−	0.792067i	$-0.709005\pi$
$907$	−36.7682	−1.22087	−0.610434	+	0.792067i	$0.709005\pi$
$908$	−55.7292	−1.84944
$909$	13.0590	0.433141
$910$	0.905230	0.0300081
$911$	−27.7537	−0.919521	−0.459760	−	0.888043i	$-0.652065\pi$
$911$	−27.7537	−0.919521	−0.459760	+	0.888043i	$0.652065\pi$
$912$	−9.19554	−0.304495
$913$	13.0897	0.433204
$914$	−39.1878	−1.29622
$915$	−3.60077	−0.119038
$916$	66.2412	2.18867
$917$	−37.6699	−1.24397
$918$	28.4565	0.939206
$919$	25.3883	0.837482	0.418741	−	0.908106i	$-0.362471\pi$
$919$	25.3883	0.837482	0.418741	+	0.908106i	$0.362471\pi$
$920$	29.6483	0.977475
$921$	0.919183	0.0302881
$922$	−21.9290	−0.722192
$923$	0.433790	0.0142784
$924$	−6.53080	−0.214847
$925$	2.11088	0.0694053
$926$	−89.9196	−2.95494
$927$	2.74086	0.0900216
$928$	−6.11744	−0.200815
$929$	−40.2700	−1.32122	−0.660609	−	0.750730i	$-0.729702\pi$
$929$	−40.2700	−1.32122	−0.660609	+	0.750730i	$0.729702\pi$
$930$	−1.10648	−0.0362830
$931$	−15.5792	−0.510589
$932$	−98.2530	−3.21839
$933$	−6.82539	−0.223453
$934$	74.3937	2.43424
$935$	3.25392	0.106415
$936$	1.42225	0.0464878
$937$	−9.01523	−0.294515	−0.147257	−	0.989098i	$-0.547045\pi$
$937$	−9.01523	−0.294515	−0.147257	+	0.989098i	$0.547045\pi$
$938$	101.172	3.30339
$939$	0.855218	0.0279090
$940$	3.95103	0.128869
$941$	26.0692	0.849830	0.424915	−	0.905233i	$-0.360304\pi$
$941$	26.0692	0.849830	0.424915	+	0.905233i	$0.360304\pi$
$942$	32.3273	1.05328
$943$	−66.1197	−2.15315
$944$	10.9112	0.355129
$945$	10.4845	0.341060
$946$	23.0464	0.749302
$947$	−38.2931	−1.24436	−0.622180	−	0.782874i	$-0.713753\pi$
$947$	−38.2931	−1.24436	−0.622180	+	0.782874i	$0.713753\pi$
$948$	26.3188	0.854795
$949$	1.32711	0.0430799
$950$	11.5681	0.375318
$951$	−9.65368	−0.313042
$952$	−52.6161	−1.70530
$953$	−49.2569	−1.59559	−0.797794	−	0.602930i	$-0.794000\pi$
$953$	−49.2569	−1.59559	−0.797794	+	0.602930i	$0.794000\pi$
$954$	−54.9126	−1.77786
$955$	−2.64586	−0.0856179
$956$	31.6948	1.02508
$957$	3.03483	0.0981023
$958$	−44.1724	−1.42714
$959$	22.8195	0.736879
$960$	5.33819	0.172289
$961$	−30.3763	−0.979882
$962$	−0.596323	−0.0192262
$963$	14.7459	0.475180
$964$	14.3338	0.461659
$965$	2.78757	0.0897351
$966$	−29.0551	−0.934833
$967$	−46.8419	−1.50633	−0.753167	−	0.657830i	$-0.771475\pi$
$967$	−46.8419	−1.50633	−0.753167	+	0.657830i	$0.771475\pi$
$968$	46.6181	1.49836
$969$	−9.86628	−0.316950
$970$	−1.92228	−0.0617206
$971$	32.7351	1.05052	0.525260	−	0.850942i	$-0.323968\pi$
$971$	32.7351	1.05052	0.525260	+	0.850942i	$0.323968\pi$
$972$	51.8819	1.66411
$973$	−39.4495	−1.26469
$974$	50.2838	1.61120
$975$	0.0672230	0.00215286
$976$	20.8318	0.666810
$977$	−49.4330	−1.58150	−0.790751	−	0.612138i	$-0.790310\pi$
$977$	−49.4330	−1.58150	−0.790751	+	0.612138i	$0.790310\pi$
$978$	−12.1554	−0.388686
$979$	−3.11701	−0.0996201
$980$	−12.7056	−0.405865
$981$	−39.5773	−1.26361
$982$	29.1489	0.930178
$983$	20.7205	0.660882	0.330441	−	0.943827i	$-0.392802\pi$
$983$	20.7205	0.660882	0.330441	+	0.943827i	$0.392802\pi$
$984$	27.0263	0.861566
$985$	1.17527	0.0374472
$986$	50.3514	1.60352
$987$	−1.88022	−0.0598482
$988$	−2.15793	−0.0686529
$989$	67.7045	2.15288
$990$	5.87431	0.186698
$991$	6.46099	0.205240	0.102620	−	0.994721i	$-0.467277\pi$
$991$	6.46099	0.205240	0.102620	+	0.994721i	$0.467277\pi$
$992$	−0.834470	−0.0264945
$993$	−13.5017	−0.428463
$994$	−28.9715	−0.918919
$995$	6.23414	0.197635
$996$	−32.3685	−1.02564
$997$	−19.4035	−0.614515	−0.307258	−	0.951626i	$-0.599411\pi$
$997$	−19.4035	−0.614515	−0.307258	+	0.951626i	$0.599411\pi$
$998$	−17.0421	−0.539457
$999$	−6.90669	−0.218518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.16	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.16	✓	140	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42652 q^{2} +0.577409 q^{3} +3.88800 q^{4} -1.00000 q^{5} -1.40110 q^{6} +3.20436 q^{7} -4.58127 q^{8} -2.66660 q^{9} +O(q^{10})\)	\(q-2.42652 q^{2} +0.577409 q^{3} +3.88800 q^{4} -1.00000 q^{5} -1.40110 q^{6} +3.20436 q^{7} -4.58127 q^{8} -2.66660 q^{9} +2.42652 q^{10} -0.907853 q^{11} +2.24497 q^{12} +0.116422 q^{13} -7.77543 q^{14} -0.577409 q^{15} +3.34053 q^{16} +3.58420 q^{17} +6.47055 q^{18} -4.76735 q^{19} -3.88800 q^{20} +1.85023 q^{21} +2.20292 q^{22} +6.47164 q^{23} -2.64527 q^{24} +1.00000 q^{25} -0.282500 q^{26} -3.27195 q^{27} +12.4585 q^{28} -5.78943 q^{29} +1.40110 q^{30} -0.789726 q^{31} +1.05666 q^{32} -0.524203 q^{33} -8.69713 q^{34} -3.20436 q^{35} -10.3677 q^{36} +2.11088 q^{37} +11.5681 q^{38} +0.0672230 q^{39} +4.58127 q^{40} -10.2168 q^{41} -4.48961 q^{42} +10.4617 q^{43} -3.52973 q^{44} +2.66660 q^{45} -15.7036 q^{46} -1.01621 q^{47} +1.92886 q^{48} +3.26790 q^{49} -2.42652 q^{50} +2.06955 q^{51} +0.452648 q^{52} -8.48653 q^{53} +7.93945 q^{54} +0.907853 q^{55} -14.6800 q^{56} -2.75272 q^{57} +14.0482 q^{58} +3.26630 q^{59} -2.24497 q^{60} +6.23607 q^{61} +1.91629 q^{62} -8.54473 q^{63} -9.24507 q^{64} -0.116422 q^{65} +1.27199 q^{66} -13.0118 q^{67} +13.9354 q^{68} +3.73678 q^{69} +7.77543 q^{70} +3.72602 q^{71} +12.2164 q^{72} +11.3992 q^{73} -5.12209 q^{74} +0.577409 q^{75} -18.5355 q^{76} -2.90908 q^{77} -0.163118 q^{78} +11.7235 q^{79} -3.34053 q^{80} +6.11054 q^{81} +24.7914 q^{82} -14.4183 q^{83} +7.19367 q^{84} -3.58420 q^{85} -25.3856 q^{86} -3.34287 q^{87} +4.15911 q^{88} +3.43339 q^{89} -6.47055 q^{90} +0.373057 q^{91} +25.1617 q^{92} -0.455995 q^{93} +2.46586 q^{94} +4.76735 q^{95} +0.610124 q^{96} -0.792195 q^{97} -7.92962 q^{98} +2.42088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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