LMFDB - Embedded newform 8035.2.a.e.1.10

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:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.54388 q^{2} +1.32249 q^{3} +4.47134 q^{4} +1.00000 q^{5} -3.36426 q^{6} +2.08615 q^{7} -6.28679 q^{8} -1.25102 q^{9} +O(q^{10})$	\(q-2.54388 q^{2} +1.32249 q^{3} +4.47134 q^{4} +1.00000 q^{5} -3.36426 q^{6} +2.08615 q^{7} -6.28679 q^{8} -1.25102 q^{9} -2.54388 q^{10} +0.221908 q^{11} +5.91330 q^{12} +6.62780 q^{13} -5.30692 q^{14} +1.32249 q^{15} +7.05017 q^{16} +6.05401 q^{17} +3.18244 q^{18} -5.99797 q^{19} +4.47134 q^{20} +2.75891 q^{21} -0.564507 q^{22} +6.32410 q^{23} -8.31422 q^{24} +1.00000 q^{25} -16.8603 q^{26} -5.62193 q^{27} +9.32787 q^{28} -1.35243 q^{29} -3.36426 q^{30} +2.37765 q^{31} -5.36124 q^{32} +0.293471 q^{33} -15.4007 q^{34} +2.08615 q^{35} -5.59372 q^{36} +4.89059 q^{37} +15.2581 q^{38} +8.76520 q^{39} -6.28679 q^{40} +4.94423 q^{41} -7.01835 q^{42} +2.04258 q^{43} +0.992223 q^{44} -1.25102 q^{45} -16.0878 q^{46} -6.47533 q^{47} +9.32379 q^{48} -2.64798 q^{49} -2.54388 q^{50} +8.00637 q^{51} +29.6351 q^{52} +8.72719 q^{53} +14.3015 q^{54} +0.221908 q^{55} -13.1152 q^{56} -7.93225 q^{57} +3.44042 q^{58} +8.15836 q^{59} +5.91330 q^{60} -0.446960 q^{61} -6.04847 q^{62} -2.60981 q^{63} -0.461994 q^{64} +6.62780 q^{65} -0.746555 q^{66} -3.27388 q^{67} +27.0695 q^{68} +8.36357 q^{69} -5.30692 q^{70} +1.68463 q^{71} +7.86488 q^{72} -7.86727 q^{73} -12.4411 q^{74} +1.32249 q^{75} -26.8189 q^{76} +0.462932 q^{77} -22.2976 q^{78} +6.87089 q^{79} +7.05017 q^{80} -3.68190 q^{81} -12.5775 q^{82} +16.1977 q^{83} +12.3360 q^{84} +6.05401 q^{85} -5.19607 q^{86} -1.78858 q^{87} -1.39509 q^{88} -10.5008 q^{89} +3.18244 q^{90} +13.8266 q^{91} +28.2772 q^{92} +3.14443 q^{93} +16.4725 q^{94} -5.99797 q^{95} -7.09019 q^{96} +14.6847 q^{97} +6.73616 q^{98} -0.277610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.54388	−1.79880	−0.899398	−	0.437130i	$-0.855995\pi$
$2$	−2.54388	−1.79880	−0.899398	+	0.437130i	$0.855995\pi$
$3$	1.32249	0.763540	0.381770	−	0.924257i	$-0.375315\pi$
$3$	1.32249	0.763540	0.381770	+	0.924257i	$0.375315\pi$
$4$	4.47134	2.23567
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.36426	−1.37345
$7$	2.08615	0.788490	0.394245	−	0.919005i	$-0.371006\pi$
$7$	2.08615	0.788490	0.394245	+	0.919005i	$0.371006\pi$
$8$	−6.28679	−2.22272
$9$	−1.25102	−0.417006
$10$	−2.54388	−0.804446
$11$	0.221908	0.0669076	0.0334538	−	0.999440i	$-0.489349\pi$
$11$	0.221908	0.0669076	0.0334538	+	0.999440i	$0.489349\pi$
$12$	5.91330	1.70702
$13$	6.62780	1.83822	0.919110	−	0.394000i	$-0.128909\pi$
$13$	6.62780	1.83822	0.919110	+	0.394000i	$0.128909\pi$
$14$	−5.30692	−1.41833
$15$	1.32249	0.341466
$16$	7.05017	1.76254
$17$	6.05401	1.46831	0.734156	−	0.678981i	$-0.237578\pi$
$17$	6.05401	1.46831	0.734156	+	0.678981i	$0.237578\pi$
$18$	3.18244	0.750109
$19$	−5.99797	−1.37603	−0.688014	−	0.725698i	$-0.741517\pi$
$19$	−5.99797	−1.37603	−0.688014	+	0.725698i	$0.741517\pi$
$20$	4.47134	0.999821
$21$	2.75891	0.602044
$22$	−0.564507	−0.120353
$23$	6.32410	1.31867	0.659333	−	0.751851i	$-0.270839\pi$
$23$	6.32410	1.31867	0.659333	+	0.751851i	$0.270839\pi$
$24$	−8.31422	−1.69713
$25$	1.00000	0.200000
$26$	−16.8603	−3.30658
$27$	−5.62193	−1.08194
$28$	9.32787	1.76280
$29$	−1.35243	−0.251140	−0.125570	−	0.992085i	$-0.540076\pi$
$29$	−1.35243	−0.251140	−0.125570	+	0.992085i	$0.540076\pi$
$30$	−3.36426	−0.614227
$31$	2.37765	0.427039	0.213520	−	0.976939i	$-0.431507\pi$
$31$	2.37765	0.427039	0.213520	+	0.976939i	$0.431507\pi$
$32$	−5.36124	−0.947742
$33$	0.293471	0.0510867
$34$	−15.4007	−2.64119
$35$	2.08615	0.352623
$36$	−5.59372	−0.932287
$37$	4.89059	0.804008	0.402004	−	0.915638i	$-0.368314\pi$
$37$	4.89059	0.804008	0.402004	+	0.915638i	$0.368314\pi$
$38$	15.2581	2.47519
$39$	8.76520	1.40356
$40$	−6.28679	−0.994028
$41$	4.94423	0.772159	0.386079	−	0.922466i	$-0.373829\pi$
$41$	4.94423	0.772159	0.386079	+	0.922466i	$0.373829\pi$
$42$	−7.01835	−1.08295
$43$	2.04258	0.311490	0.155745	−	0.987797i	$-0.450222\pi$
$43$	2.04258	0.311490	0.155745	+	0.987797i	$0.450222\pi$
$44$	0.992223	0.149583
$45$	−1.25102	−0.186491
$46$	−16.0878	−2.37201
$47$	−6.47533	−0.944524	−0.472262	−	0.881458i	$-0.656562\pi$
$47$	−6.47533	−0.944524	−0.472262	+	0.881458i	$0.656562\pi$
$48$	9.32379	1.34577
$49$	−2.64798	−0.378283
$50$	−2.54388	−0.359759
$51$	8.00637	1.12112
$52$	29.6351	4.10965
$53$	8.72719	1.19877	0.599386	−	0.800460i	$-0.295411\pi$
$53$	8.72719	1.19877	0.599386	+	0.800460i	$0.295411\pi$
$54$	14.3015	1.94619
$55$	0.221908	0.0299220
$56$	−13.1152	−1.75259
$57$	−7.93225	−1.05065
$58$	3.44042	0.451750
$59$	8.15836	1.06213	0.531064	−	0.847332i	$-0.321792\pi$
$59$	8.15836	1.06213	0.531064	+	0.847332i	$0.321792\pi$
$60$	5.91330	0.763404
$61$	−0.446960	−0.0572273	−0.0286137	−	0.999591i	$-0.509109\pi$
$61$	−0.446960	−0.0572273	−0.0286137	+	0.999591i	$0.509109\pi$
$62$	−6.04847	−0.768157
$63$	−2.60981	−0.328805
$64$	−0.461994	−0.0577492
$65$	6.62780	0.822077
$66$	−0.746555	−0.0918946
$67$	−3.27388	−0.399968	−0.199984	−	0.979799i	$-0.564089\pi$
$67$	−3.27388	−0.399968	−0.199984	+	0.979799i	$0.564089\pi$
$68$	27.0695	3.28266
$69$	8.36357	1.00686
$70$	−5.30692	−0.634298
$71$	1.68463	0.199929	0.0999643	−	0.994991i	$-0.468127\pi$
$71$	1.68463	0.199929	0.0999643	+	0.994991i	$0.468127\pi$
$72$	7.86488	0.926885
$73$	−7.86727	−0.920795	−0.460397	−	0.887713i	$-0.652293\pi$
$73$	−7.86727	−0.920795	−0.460397	+	0.887713i	$0.652293\pi$
$74$	−12.4411	−1.44625
$75$	1.32249	0.152708
$76$	−26.8189	−3.07634
$77$	0.462932	0.0527560
$78$	−22.2976	−2.52471
$79$	6.87089	0.773035	0.386518	−	0.922282i	$-0.373678\pi$
$79$	6.87089	0.773035	0.386518	+	0.922282i	$0.373678\pi$
$80$	7.05017	0.788233
$81$	−3.68190	−0.409100
$82$	−12.5775	−1.38896
$83$	16.1977	1.77793	0.888963	−	0.457979i	$-0.151426\pi$
$83$	16.1977	1.77793	0.888963	+	0.457979i	$0.151426\pi$
$84$	12.3360	1.34597
$85$	6.05401	0.656649
$86$	−5.19607	−0.560307
$87$	−1.78858	−0.191756
$88$	−1.39509	−0.148717
$89$	−10.5008	−1.11308	−0.556540	−	0.830821i	$-0.687872\pi$
$89$	−10.5008	−1.11308	−0.556540	+	0.830821i	$0.687872\pi$
$90$	3.18244	0.335459
$91$	13.8266	1.44942
$92$	28.2772	2.94810
$93$	3.14443	0.326062
$94$	16.4725	1.69901
$95$	−5.99797	−0.615378
$96$	−7.09019	−0.723639
$97$	14.6847	1.49101	0.745504	−	0.666501i	$-0.232209\pi$
$97$	14.6847	1.49101	0.745504	+	0.666501i	$0.232209\pi$
$98$	6.73616	0.680455
$99$	−0.277610	−0.0279009
$100$	4.47134	0.447134
$101$	13.3893	1.33229	0.666145	−	0.745822i	$-0.267943\pi$
$101$	13.3893	1.33229	0.666145	+	0.745822i	$0.267943\pi$
$102$	−20.3673	−2.01666
$103$	−6.67503	−0.657710	−0.328855	−	0.944380i	$-0.606663\pi$
$103$	−6.67503	−0.657710	−0.328855	+	0.944380i	$0.606663\pi$
$104$	−41.6676	−4.08584
$105$	2.75891	0.269242
$106$	−22.2010	−2.15635
$107$	−14.1506	−1.36799	−0.683997	−	0.729485i	$-0.739760\pi$
$107$	−14.1506	−1.36799	−0.683997	+	0.729485i	$0.739760\pi$
$108$	−25.1375	−2.41886
$109$	−17.0881	−1.63674	−0.818371	−	0.574691i	$-0.805122\pi$
$109$	−17.0881	−1.63674	−0.818371	+	0.574691i	$0.805122\pi$
$110$	−0.564507	−0.0538236
$111$	6.46776	0.613892
$112$	14.7077	1.38975
$113$	−7.51791	−0.707225	−0.353613	−	0.935392i	$-0.615047\pi$
$113$	−7.51791	−0.707225	−0.353613	+	0.935392i	$0.615047\pi$
$114$	20.1787	1.88991
$115$	6.32410	0.589726
$116$	−6.04717	−0.561466
$117$	−8.29149	−0.766549
$118$	−20.7539	−1.91055
$119$	12.6296	1.15775
$120$	−8.31422	−0.758981
$121$	−10.9508	−0.995523
$122$	1.13701	0.102940
$123$	6.53870	0.589575
$124$	10.6313	0.954718
$125$	1.00000	0.0894427
$126$	6.63905	0.591453
$127$	−17.2947	−1.53466	−0.767328	−	0.641255i	$-0.778414\pi$
$127$	−17.2947	−1.53466	−0.767328	+	0.641255i	$0.778414\pi$
$128$	11.8977	1.05162
$129$	2.70129	0.237835
$130$	−16.8603	−1.47875
$131$	8.65582	0.756262	0.378131	−	0.925752i	$-0.376567\pi$
$131$	8.65582	0.756262	0.378131	+	0.925752i	$0.376567\pi$
$132$	1.31221	0.114213
$133$	−12.5126	−1.08498
$134$	8.32836	0.719461
$135$	−5.62193	−0.483859
$136$	−38.0602	−3.26364
$137$	17.8284	1.52319	0.761593	−	0.648055i	$-0.224417\pi$
$137$	17.8284	1.52319	0.761593	+	0.648055i	$0.224417\pi$
$138$	−21.2759	−1.81113
$139$	−11.2816	−0.956895	−0.478448	−	0.878116i	$-0.658800\pi$
$139$	−11.2816	−0.956895	−0.478448	+	0.878116i	$0.658800\pi$
$140$	9.32787	0.788349
$141$	−8.56356	−0.721182
$142$	−4.28550	−0.359631
$143$	1.47076	0.122991
$144$	−8.81989	−0.734991
$145$	−1.35243	−0.112313
$146$	20.0134	1.65632
$147$	−3.50193	−0.288835
$148$	21.8675	1.79749
$149$	−18.9699	−1.55408	−0.777039	−	0.629453i	$-0.783279\pi$
$149$	−18.9699	−1.55408	−0.777039	+	0.629453i	$0.783279\pi$
$150$	−3.36426	−0.274691
$151$	4.83210	0.393230	0.196615	−	0.980481i	$-0.437005\pi$
$151$	4.83210	0.393230	0.196615	+	0.980481i	$0.437005\pi$
$152$	37.7079	3.05852
$153$	−7.57367	−0.612295
$154$	−1.17764	−0.0948973
$155$	2.37765	0.190978
$156$	39.1922	3.13788
$157$	15.0206	1.19877	0.599387	−	0.800460i	$-0.295411\pi$
$157$	15.0206	1.19877	0.599387	+	0.800460i	$0.295411\pi$
$158$	−17.4787	−1.39053
$159$	11.5416	0.915311
$160$	−5.36124	−0.423843
$161$	13.1930	1.03976
$162$	9.36632	0.735888
$163$	−12.1542	−0.951987	−0.475994	−	0.879449i	$-0.657911\pi$
$163$	−12.1542	−0.951987	−0.475994	+	0.879449i	$0.657911\pi$
$164$	22.1073	1.72629
$165$	0.293471	0.0228467
$166$	−41.2050	−3.19813
$167$	17.8328	1.37994	0.689970	−	0.723838i	$-0.257624\pi$
$167$	17.8328	1.37994	0.689970	+	0.723838i	$0.257624\pi$
$168$	−17.3447	−1.33817
$169$	30.9277	2.37905
$170$	−15.4007	−1.18118
$171$	7.50356	0.573812
$172$	9.13305	0.696388
$173$	−13.9536	−1.06087	−0.530436	−	0.847725i	$-0.677972\pi$
$173$	−13.9536	−1.06087	−0.530436	+	0.847725i	$0.677972\pi$
$174$	4.54993	0.344929
$175$	2.08615	0.157698
$176$	1.56449	0.117928
$177$	10.7894	0.810978
$178$	26.7128	2.00221
$179$	−16.6736	−1.24624	−0.623122	−	0.782125i	$-0.714136\pi$
$179$	−16.6736	−1.24624	−0.623122	+	0.782125i	$0.714136\pi$
$180$	−5.59372	−0.416931
$181$	13.8655	1.03061	0.515306	−	0.857006i	$-0.327678\pi$
$181$	13.8655	1.03061	0.515306	+	0.857006i	$0.327678\pi$
$182$	−35.1732	−2.60721
$183$	−0.591100	−0.0436954
$184$	−39.7583	−2.93102
$185$	4.89059	0.359563
$186$	−7.99905	−0.586519
$187$	1.34343	0.0982413
$188$	−28.9534	−2.11164
$189$	−11.7282	−0.853100
$190$	15.2581	1.10694
$191$	−5.14084	−0.371978	−0.185989	−	0.982552i	$-0.559549\pi$
$191$	−5.14084	−0.371978	−0.185989	+	0.982552i	$0.559549\pi$
$192$	−0.610982	−0.0440939
$193$	−5.87316	−0.422759	−0.211380	−	0.977404i	$-0.567796\pi$
$193$	−5.87316	−0.422759	−0.211380	+	0.977404i	$0.567796\pi$
$194$	−37.3562	−2.68202
$195$	8.76520	0.627689
$196$	−11.8400	−0.845716
$197$	23.3208	1.66154	0.830771	−	0.556615i	$-0.187900\pi$
$197$	23.3208	1.66154	0.830771	+	0.556615i	$0.187900\pi$
$198$	0.706208	0.0501880
$199$	23.6505	1.67654	0.838269	−	0.545256i	$-0.183568\pi$
$199$	23.6505	1.67654	0.838269	+	0.545256i	$0.183568\pi$
$200$	−6.28679	−0.444543
$201$	−4.32967	−0.305392
$202$	−34.0609	−2.39652
$203$	−2.82137	−0.198021
$204$	35.7992	2.50644
$205$	4.94423	0.345320
$206$	16.9805	1.18309
$207$	−7.91157	−0.549892
$208$	46.7271	3.23994
$209$	−1.33099	−0.0920668
$210$	−7.01835	−0.484312
$211$	9.68877	0.667002	0.333501	−	0.942750i	$-0.391770\pi$
$211$	9.68877	0.667002	0.333501	+	0.942750i	$0.391770\pi$
$212$	39.0222	2.68006
$213$	2.22791	0.152654
$214$	35.9976	2.46074
$215$	2.04258	0.139303
$216$	35.3439	2.40485
$217$	4.96014	0.336716
$218$	43.4701	2.94416
$219$	−10.4044	−0.703064
$220$	0.992223	0.0668957
$221$	40.1247	2.69908
$222$	−16.4532	−1.10427
$223$	−12.0672	−0.808081	−0.404040	−	0.914741i	$-0.632394\pi$
$223$	−12.0672	−0.808081	−0.404040	+	0.914741i	$0.632394\pi$
$224$	−11.1843	−0.747285
$225$	−1.25102	−0.0834012
$226$	19.1247	1.27215
$227$	−23.5017	−1.55986	−0.779931	−	0.625866i	$-0.784746\pi$
$227$	−23.5017	−1.55986	−0.779931	+	0.625866i	$0.784746\pi$
$228$	−35.4678	−2.34891
$229$	−11.8415	−0.782510	−0.391255	−	0.920282i	$-0.627959\pi$
$229$	−11.8415	−0.782510	−0.391255	+	0.920282i	$0.627959\pi$
$230$	−16.0878	−1.06080
$231$	0.612224	0.0402814
$232$	8.50244	0.558213
$233$	−6.14611	−0.402645	−0.201323	−	0.979525i	$-0.564524\pi$
$233$	−6.14611	−0.402645	−0.201323	+	0.979525i	$0.564524\pi$
$234$	21.0926	1.37887
$235$	−6.47533	−0.422404
$236$	36.4788	2.37457
$237$	9.08669	0.590244
$238$	−32.1281	−2.08256
$239$	1.35031	0.0873443	0.0436722	−	0.999046i	$-0.486094\pi$
$239$	1.35031	0.0873443	0.0436722	+	0.999046i	$0.486094\pi$
$240$	9.32379	0.601848
$241$	11.1840	0.720424	0.360212	−	0.932871i	$-0.382704\pi$
$241$	11.1840	0.720424	0.360212	+	0.932871i	$0.382704\pi$
$242$	27.8574	1.79074
$243$	11.9965	0.769577
$244$	−1.99851	−0.127941
$245$	−2.64798	−0.169173
$246$	−16.6337	−1.06052
$247$	−39.7533	−2.52944
$248$	−14.9478	−0.949187
$249$	21.4213	1.35752
$250$	−2.54388	−0.160889
$251$	10.3920	0.655935	0.327967	−	0.944689i	$-0.393636\pi$
$251$	10.3920	0.655935	0.327967	+	0.944689i	$0.393636\pi$
$252$	−11.6693	−0.735099
$253$	1.40337	0.0882289
$254$	43.9956	2.76053
$255$	8.00637	0.501378
$256$	−29.3424	−1.83390
$257$	21.2233	1.32387	0.661937	−	0.749559i	$-0.269735\pi$
$257$	21.2233	1.32387	0.661937	+	0.749559i	$0.269735\pi$
$258$	−6.87176	−0.427817
$259$	10.2025	0.633952
$260$	29.6351	1.83789
$261$	1.69192	0.104727
$262$	−22.0194	−1.36036
$263$	−8.13847	−0.501840	−0.250920	−	0.968008i	$-0.580733\pi$
$263$	−8.13847	−0.501840	−0.250920	+	0.968008i	$0.580733\pi$
$264$	−1.84499	−0.113551
$265$	8.72719	0.536107
$266$	31.8307	1.95167
$267$	−13.8872	−0.849882
$268$	−14.6386	−0.894196
$269$	23.3291	1.42240	0.711201	−	0.702989i	$-0.248152\pi$
$269$	23.3291	1.42240	0.711201	+	0.702989i	$0.248152\pi$
$270$	14.3015	0.870364
$271$	2.08322	0.126547	0.0632734	−	0.997996i	$-0.479846\pi$
$271$	2.08322	0.126547	0.0632734	+	0.997996i	$0.479846\pi$
$272$	42.6818	2.58796
$273$	18.2855	1.10669
$274$	−45.3535	−2.73990
$275$	0.221908	0.0133815
$276$	37.3963	2.25099
$277$	−9.38720	−0.564022	−0.282011	−	0.959411i	$-0.591002\pi$
$277$	−9.38720	−0.564022	−0.282011	+	0.959411i	$0.591002\pi$
$278$	28.6991	1.72126
$279$	−2.97449	−0.178078
$280$	−13.1152	−0.783782
$281$	17.3632	1.03580	0.517902	−	0.855440i	$-0.326713\pi$
$281$	17.3632	1.03580	0.517902	+	0.855440i	$0.326713\pi$
$282$	21.7847	1.29726
$283$	21.6699	1.28814	0.644071	−	0.764966i	$-0.277244\pi$
$283$	21.6699	1.28814	0.644071	+	0.764966i	$0.277244\pi$
$284$	7.53254	0.446974
$285$	−7.93225	−0.469866
$286$	−3.74144	−0.221236
$287$	10.3144	0.608840
$288$	6.70700	0.395214
$289$	19.6510	1.15594
$290$	3.44042	0.202029
$291$	19.4204	1.13845
$292$	−35.1772	−2.05859
$293$	19.5291	1.14090	0.570450	−	0.821332i	$-0.306769\pi$
$293$	19.5291	1.14090	0.570450	+	0.821332i	$0.306769\pi$
$294$	8.90851	0.519555
$295$	8.15836	0.474998
$296$	−30.7461	−1.78708
$297$	−1.24755	−0.0723902
$298$	48.2573	2.79547
$299$	41.9149	2.42400
$300$	5.91330	0.341405
$301$	4.26112	0.245607
$302$	−12.2923	−0.707341
$303$	17.7073	1.01726
$304$	−42.2867	−2.42531
$305$	−0.446960	−0.0255928
$306$	19.2665	1.10139
$307$	−23.0121	−1.31337	−0.656684	−	0.754166i	$-0.728042\pi$
$307$	−23.0121	−1.31337	−0.656684	+	0.754166i	$0.728042\pi$
$308$	2.06993	0.117945
$309$	−8.82766	−0.502188
$310$	−6.04847	−0.343530
$311$	−11.9586	−0.678112	−0.339056	−	0.940766i	$-0.610108\pi$
$311$	−11.9586	−0.678112	−0.339056	+	0.940766i	$0.610108\pi$
$312$	−55.1050	−3.11970
$313$	−23.4843	−1.32741	−0.663704	−	0.747995i	$-0.731017\pi$
$313$	−23.4843	−1.32741	−0.663704	+	0.747995i	$0.731017\pi$
$314$	−38.2106	−2.15635
$315$	−2.60981	−0.147046
$316$	30.7221	1.72825
$317$	19.6593	1.10417	0.552087	−	0.833787i	$-0.313832\pi$
$317$	19.6593	1.10417	0.552087	+	0.833787i	$0.313832\pi$
$318$	−29.3606	−1.64646
$319$	−0.300115	−0.0168032
$320$	−0.461994	−0.0258262
$321$	−18.7141	−1.04452
$322$	−33.5615	−1.87031
$323$	−36.3117	−2.02044
$324$	−16.4630	−0.914612
$325$	6.62780	0.367644
$326$	30.9188	1.71243
$327$	−22.5988	−1.24972
$328$	−31.0833	−1.71629
$329$	−13.5085	−0.744748
$330$	−0.746555	−0.0410965
$331$	−16.4886	−0.906294	−0.453147	−	0.891436i	$-0.649699\pi$
$331$	−16.4886	−0.906294	−0.453147	+	0.891436i	$0.649699\pi$
$332$	72.4253	3.97485
$333$	−6.11821	−0.335276
$334$	−45.3644	−2.48223
$335$	−3.27388	−0.178871
$336$	19.4508	1.06113
$337$	−9.93274	−0.541071	−0.270536	−	0.962710i	$-0.587201\pi$
$337$	−9.93274	−0.541071	−0.270536	+	0.962710i	$0.587201\pi$
$338$	−78.6764	−4.27943
$339$	−9.94236	−0.539995
$340$	27.0695	1.46805
$341$	0.527619	0.0285722
$342$	−19.0882	−1.03217
$343$	−20.1271	−1.08676
$344$	−12.8412	−0.692354
$345$	8.36357	0.450279
$346$	35.4963	1.90829
$347$	−14.9882	−0.804608	−0.402304	−	0.915506i	$-0.631790\pi$
$347$	−14.9882	−0.804608	−0.402304	+	0.915506i	$0.631790\pi$
$348$	−7.99733	−0.428702
$349$	−30.1832	−1.61567	−0.807836	−	0.589408i	$-0.799361\pi$
$349$	−30.1832	−1.61567	−0.807836	+	0.589408i	$0.799361\pi$
$350$	−5.30692	−0.283667
$351$	−37.2610	−1.98885
$352$	−1.18970	−0.0634112
$353$	2.33863	0.124473	0.0622364	−	0.998061i	$-0.480177\pi$
$353$	2.33863	0.124473	0.0622364	+	0.998061i	$0.480177\pi$
$354$	−27.4469	−1.45878
$355$	1.68463	0.0894108
$356$	−46.9525	−2.48848
$357$	16.7025	0.883989
$358$	42.4157	2.24174
$359$	−1.13090	−0.0596864	−0.0298432	−	0.999555i	$-0.509501\pi$
$359$	−1.13090	−0.0596864	−0.0298432	+	0.999555i	$0.509501\pi$
$360$	7.86488	0.414516
$361$	16.9756	0.893452
$362$	−35.2721	−1.85386
$363$	−14.4823	−0.760122
$364$	61.8233	3.24042
$365$	−7.86727	−0.411792
$366$	1.50369	0.0785991
$367$	9.67636	0.505102	0.252551	−	0.967584i	$-0.418730\pi$
$367$	9.67636	0.505102	0.252551	+	0.967584i	$0.418730\pi$
$368$	44.5860	2.32421
$369$	−6.18532	−0.321995
$370$	−12.4411	−0.646781
$371$	18.2062	0.945220
$372$	14.0598	0.728966
$373$	−12.7644	−0.660917	−0.330458	−	0.943821i	$-0.607203\pi$
$373$	−12.7644	−0.660917	−0.330458	+	0.943821i	$0.607203\pi$
$374$	−3.41753	−0.176716
$375$	1.32249	0.0682931
$376$	40.7090	2.09941
$377$	−8.96364	−0.461651
$378$	29.8351	1.53455
$379$	−16.0201	−0.822898	−0.411449	−	0.911433i	$-0.634977\pi$
$379$	−16.0201	−0.822898	−0.411449	+	0.911433i	$0.634977\pi$
$380$	−26.8189	−1.37578
$381$	−22.8721	−1.17177
$382$	13.0777	0.669113
$383$	−9.79174	−0.500335	−0.250167	−	0.968203i	$-0.580486\pi$
$383$	−9.79174	−0.500335	−0.250167	+	0.968203i	$0.580486\pi$
$384$	15.7346	0.802955
$385$	0.462932	0.0235932
$386$	14.9406	0.760458
$387$	−2.55530	−0.129893
$388$	65.6604	3.33340
$389$	−14.4035	−0.730287	−0.365144	−	0.930951i	$-0.618980\pi$
$389$	−14.4035	−0.730287	−0.365144	+	0.930951i	$0.618980\pi$
$390$	−22.2976	−1.12908
$391$	38.2862	1.93621
$392$	16.6473	0.840816
$393$	11.4472	0.577437
$394$	−59.3255	−2.98877
$395$	6.87089	0.345712
$396$	−1.24129	−0.0623771
$397$	25.4763	1.27862	0.639310	−	0.768949i	$-0.279220\pi$
$397$	25.4763	1.27862	0.639310	+	0.768949i	$0.279220\pi$
$398$	−60.1641	−3.01575
$399$	−16.5479	−0.828429
$400$	7.05017	0.352509
$401$	18.7393	0.935795	0.467897	−	0.883783i	$-0.345012\pi$
$401$	18.7393	0.935795	0.467897	+	0.883783i	$0.345012\pi$
$402$	11.0142	0.549337
$403$	15.7586	0.784992
$404$	59.8683	2.97856
$405$	−3.68190	−0.182955
$406$	7.17724	0.356200
$407$	1.08526	0.0537943
$408$	−50.3343	−2.49192
$409$	34.6318	1.71243	0.856217	−	0.516616i	$-0.172808\pi$
$409$	34.6318	1.71243	0.856217	+	0.516616i	$0.172808\pi$
$410$	−12.5775	−0.621160
$411$	23.5780	1.16301
$412$	−29.8463	−1.47042
$413$	17.0196	0.837477
$414$	20.1261	0.989143
$415$	16.1977	0.795113
$416$	−35.5332	−1.74216
$417$	−14.9199	−0.730628
$418$	3.38589	0.165609
$419$	26.2544	1.28261	0.641306	−	0.767285i	$-0.278393\pi$
$419$	26.2544	1.28261	0.641306	+	0.767285i	$0.278393\pi$
$420$	12.3360	0.601936
$421$	−3.03988	−0.148155	−0.0740773	−	0.997253i	$-0.523601\pi$
$421$	−3.03988	−0.148155	−0.0740773	+	0.997253i	$0.523601\pi$
$422$	−24.6471	−1.19980
$423$	8.10075	0.393872
$424$	−54.8660	−2.66453
$425$	6.05401	0.293662
$426$	−5.66753	−0.274593
$427$	−0.932425	−0.0451232
$428$	−63.2723	−3.05838
$429$	1.94506	0.0939086
$430$	−5.19607	−0.250577
$431$	−7.38388	−0.355669	−0.177835	−	0.984060i	$-0.556909\pi$
$431$	−7.38388	−0.355669	−0.177835	+	0.984060i	$0.556909\pi$
$432$	−39.6356	−1.90697
$433$	19.7002	0.946733	0.473367	−	0.880866i	$-0.343039\pi$
$433$	19.7002	0.946733	0.473367	+	0.880866i	$0.343039\pi$
$434$	−12.6180	−0.605684
$435$	−1.78858	−0.0857557
$436$	−76.4065	−3.65921
$437$	−37.9318	−1.81452
$438$	26.4676	1.26467
$439$	−3.45150	−0.164731	−0.0823655	−	0.996602i	$-0.526248\pi$
$439$	−3.45150	−0.164731	−0.0823655	+	0.996602i	$0.526248\pi$
$440$	−1.39509	−0.0665081
$441$	3.31268	0.157746
$442$	−102.073	−4.85510
$443$	−7.00964	−0.333038	−0.166519	−	0.986038i	$-0.553253\pi$
$443$	−7.00964	−0.333038	−0.166519	+	0.986038i	$0.553253\pi$
$444$	28.9195	1.37246
$445$	−10.5008	−0.497785
$446$	30.6976	1.45357
$447$	−25.0876	−1.18660
$448$	−0.963788	−0.0455347
$449$	−29.1690	−1.37657	−0.688285	−	0.725441i	$-0.741636\pi$
$449$	−29.1690	−1.37657	−0.688285	+	0.725441i	$0.741636\pi$
$450$	3.18244	0.150022
$451$	1.09716	0.0516633
$452$	−33.6151	−1.58112
$453$	6.39040	0.300247
$454$	59.7855	2.80587
$455$	13.8266	0.648200
$456$	49.8684	2.33530
$457$	−23.0305	−1.07732	−0.538660	−	0.842523i	$-0.681069\pi$
$457$	−23.0305	−1.07732	−0.538660	+	0.842523i	$0.681069\pi$
$458$	30.1234	1.40758
$459$	−34.0352	−1.58863
$460$	28.2772	1.31843
$461$	−34.7680	−1.61931	−0.809654	−	0.586907i	$-0.800345\pi$
$461$	−34.7680	−1.61931	−0.809654	+	0.586907i	$0.800345\pi$
$462$	−1.55742	−0.0724579
$463$	−4.91327	−0.228339	−0.114169	−	0.993461i	$-0.536421\pi$
$463$	−4.91327	−0.228339	−0.114169	+	0.993461i	$0.536421\pi$
$464$	−9.53487	−0.442645
$465$	3.14443	0.145819
$466$	15.6350	0.724277
$467$	−24.8579	−1.15029	−0.575144	−	0.818052i	$-0.695054\pi$
$467$	−24.8579	−1.15029	−0.575144	+	0.818052i	$0.695054\pi$
$468$	−37.0741	−1.71375
$469$	−6.82980	−0.315371
$470$	16.4725	0.759818
$471$	19.8646	0.915312
$472$	−51.2899	−2.36081
$473$	0.453263	0.0208411
$474$	−23.1155	−1.06173
$475$	−5.99797	−0.275206
$476$	56.4710	2.58834
$477$	−10.9179	−0.499895
$478$	−3.43503	−0.157115
$479$	−20.1007	−0.918423	−0.459211	−	0.888327i	$-0.651868\pi$
$479$	−20.1007	−0.918423	−0.459211	+	0.888327i	$0.651868\pi$
$480$	−7.09019	−0.323621
$481$	32.4138	1.47794
$482$	−28.4507	−1.29590
$483$	17.4476	0.793895
$484$	−48.9645	−2.22566
$485$	14.6847	0.666799
$486$	−30.5177	−1.38431
$487$	−29.3671	−1.33075	−0.665376	−	0.746509i	$-0.731729\pi$
$487$	−29.3671	−1.33075	−0.665376	+	0.746509i	$0.731729\pi$
$488$	2.80994	0.127200
$489$	−16.0738	−0.726881
$490$	6.73616	0.304309
$491$	8.53562	0.385207	0.192603	−	0.981277i	$-0.438307\pi$
$491$	8.53562	0.385207	0.192603	+	0.981277i	$0.438307\pi$
$492$	29.2367	1.31809
$493$	−8.18762	−0.368752
$494$	101.128	4.54995
$495$	−0.277610	−0.0124777
$496$	16.7629	0.752675
$497$	3.51439	0.157642
$498$	−54.4932	−2.44190
$499$	−39.5805	−1.77186	−0.885932	−	0.463814i	$-0.846480\pi$
$499$	−39.5805	−1.77186	−0.885932	+	0.463814i	$0.846480\pi$
$500$	4.47134	0.199964
$501$	23.5837	1.05364
$502$	−26.4359	−1.17989
$503$	37.0500	1.65198	0.825989	−	0.563686i	$-0.190617\pi$
$503$	37.0500	1.65198	0.825989	+	0.563686i	$0.190617\pi$
$504$	16.4073	0.730840
$505$	13.3893	0.595818
$506$	−3.57000	−0.158706
$507$	40.9016	1.81650
$508$	−77.3304	−3.43098
$509$	−23.8825	−1.05857	−0.529286	−	0.848443i	$-0.677540\pi$
$509$	−23.8825	−1.05857	−0.529286	+	0.848443i	$0.677540\pi$
$510$	−20.3673	−0.901877
$511$	−16.4123	−0.726037
$512$	50.8482	2.24720
$513$	33.7202	1.48878
$514$	−53.9896	−2.38138
$515$	−6.67503	−0.294137
$516$	12.0784	0.531721
$517$	−1.43692	−0.0631959
$518$	−25.9539	−1.14035
$519$	−18.4535	−0.810019
$520$	−41.6676	−1.82724
$521$	3.96853	0.173865	0.0869323	−	0.996214i	$-0.472294\pi$
$521$	3.96853	0.173865	0.0869323	+	0.996214i	$0.472294\pi$
$522$	−4.30403	−0.188382
$523$	16.2371	0.709997	0.354999	−	0.934867i	$-0.384481\pi$
$523$	16.2371	0.709997	0.354999	+	0.934867i	$0.384481\pi$
$524$	38.7031	1.69075
$525$	2.75891	0.120409
$526$	20.7033	0.902707
$527$	14.3943	0.627027
$528$	2.06902	0.0900425
$529$	16.9943	0.738882
$530$	−22.2010	−0.964348
$531$	−10.2063	−0.442914
$532$	−55.9483	−2.42566
$533$	32.7694	1.41940
$534$	35.3274	1.52876
$535$	−14.1506	−0.611786
$536$	20.5822	0.889015
$537$	−22.0507	−0.951558
$538$	−59.3466	−2.55861
$539$	−0.587608	−0.0253101
$540$	−25.1375	−1.08175
$541$	14.8097	0.636721	0.318360	−	0.947970i	$-0.396868\pi$
$541$	14.8097	0.636721	0.318360	+	0.947970i	$0.396868\pi$
$542$	−5.29947	−0.227632
$543$	18.3370	0.786915
$544$	−32.4570	−1.39158
$545$	−17.0881	−0.731973
$546$	−46.5162	−1.99071
$547$	32.6885	1.39766	0.698831	−	0.715287i	$-0.253704\pi$
$547$	32.6885	1.39766	0.698831	+	0.715287i	$0.253704\pi$
$548$	79.7170	3.40534
$549$	0.559155	0.0238641
$550$	−0.564507	−0.0240706
$551$	8.11183	0.345576
$552$	−52.5800	−2.23795
$553$	14.3337	0.609531
$554$	23.8799	1.01456
$555$	6.46776	0.274541
$556$	−50.4440	−2.13930
$557$	8.81007	0.373295	0.186647	−	0.982427i	$-0.440238\pi$
$557$	8.81007	0.373295	0.186647	+	0.982427i	$0.440238\pi$
$558$	7.56675	0.320326
$559$	13.5378	0.572587
$560$	14.7077	0.621514
$561$	1.77667	0.0750112
$562$	−44.1701	−1.86320
$563$	42.6698	1.79832	0.899158	−	0.437624i	$-0.144180\pi$
$563$	42.6698	1.79832	0.899158	+	0.437624i	$0.144180\pi$
$564$	−38.2906	−1.61232
$565$	−7.51791	−0.316281
$566$	−55.1257	−2.31710
$567$	−7.68099	−0.322571
$568$	−10.5909	−0.444384
$569$	7.93659	0.332719	0.166360	−	0.986065i	$-0.446799\pi$
$569$	7.93659	0.332719	0.166360	+	0.986065i	$0.446799\pi$
$570$	20.1787	0.845194
$571$	−12.8989	−0.539800	−0.269900	−	0.962888i	$-0.586991\pi$
$571$	−12.8989	−0.539800	−0.269900	+	0.962888i	$0.586991\pi$
$572$	6.57626	0.274967
$573$	−6.79871	−0.284020
$574$	−26.2386	−1.09518
$575$	6.32410	0.263733
$576$	0.577962	0.0240818
$577$	−7.28590	−0.303316	−0.151658	−	0.988433i	$-0.548461\pi$
$577$	−7.28590	−0.303316	−0.151658	+	0.988433i	$0.548461\pi$
$578$	−49.9898	−2.07930
$579$	−7.76720	−0.322794
$580$	−6.04717	−0.251095
$581$	33.7908	1.40188
$582$	−49.4033	−2.04783
$583$	1.93663	0.0802070
$584$	49.4599	2.04666
$585$	−8.29149	−0.342811
$586$	−49.6796	−2.05225
$587$	36.4444	1.50422	0.752110	−	0.659038i	$-0.229036\pi$
$587$	36.4444	1.50422	0.752110	+	0.659038i	$0.229036\pi$
$588$	−15.6583	−0.645738
$589$	−14.2611	−0.587618
$590$	−20.7539	−0.854425
$591$	30.8416	1.26865
$592$	34.4795	1.41710
$593$	−26.4906	−1.08784	−0.543920	−	0.839137i	$-0.683060\pi$
$593$	−26.4906	−1.08784	−0.543920	+	0.839137i	$0.683060\pi$
$594$	3.17362	0.130215
$595$	12.6296	0.517761
$596$	−84.8209	−3.47440
$597$	31.2776	1.28011
$598$	−106.627	−4.36028
$599$	34.8900	1.42557	0.712783	−	0.701385i	$-0.247435\pi$
$599$	34.8900	1.42557	0.712783	+	0.701385i	$0.247435\pi$
$600$	−8.31422	−0.339427
$601$	21.2304	0.866007	0.433004	−	0.901392i	$-0.357454\pi$
$601$	21.2304	0.866007	0.433004	+	0.901392i	$0.357454\pi$
$602$	−10.8398	−0.441797
$603$	4.09568	0.166789
$604$	21.6059	0.879133
$605$	−10.9508	−0.445212
$606$	−45.0453	−1.82984
$607$	3.03143	0.123042	0.0615209	−	0.998106i	$-0.480405\pi$
$607$	3.03143	0.123042	0.0615209	+	0.998106i	$0.480405\pi$
$608$	32.1565	1.30412
$609$	−3.73124	−0.151197
$610$	1.13701	0.0460363
$611$	−42.9172	−1.73624
$612$	−33.8644	−1.36889
$613$	23.8629	0.963812	0.481906	−	0.876223i	$-0.339945\pi$
$613$	23.8629	0.963812	0.481906	+	0.876223i	$0.339945\pi$
$614$	58.5400	2.36248
$615$	6.53870	0.263666
$616$	−2.91036	−0.117262
$617$	−30.9732	−1.24693	−0.623467	−	0.781850i	$-0.714276\pi$
$617$	−30.9732	−1.24693	−0.623467	+	0.781850i	$0.714276\pi$
$618$	22.4565	0.903334
$619$	14.1381	0.568258	0.284129	−	0.958786i	$-0.408296\pi$
$619$	14.1381	0.568258	0.284129	+	0.958786i	$0.408296\pi$
$620$	10.6313	0.426963
$621$	−35.5537	−1.42672
$622$	30.4214	1.21979
$623$	−21.9062	−0.877653
$624$	61.7962	2.47383
$625$	1.00000	0.0400000
$626$	59.7412	2.38774
$627$	−1.76023	−0.0702967
$628$	67.1621	2.68006
$629$	29.6076	1.18053
$630$	6.63905	0.264506
$631$	−23.4726	−0.934431	−0.467215	−	0.884144i	$-0.654743\pi$
$631$	−23.4726	−0.934431	−0.467215	+	0.884144i	$0.654743\pi$
$632$	−43.1958	−1.71824
$633$	12.8133	0.509283
$634$	−50.0108	−1.98618
$635$	−17.2947	−0.686319
$636$	51.6065	2.04633
$637$	−17.5503	−0.695368
$638$	0.763456	0.0302255
$639$	−2.10750	−0.0833714
$640$	11.8977	0.470299
$641$	0.0459485	0.00181486	0.000907428	−	1.00000i	$-0.499711\pi$
$641$	0.0459485	0.00181486	0.000907428		1.00000i	$0.499711\pi$
$642$	47.6065	1.87888
$643$	−26.2476	−1.03510	−0.517552	−	0.855652i	$-0.673156\pi$
$643$	−26.2476	−1.03510	−0.517552	+	0.855652i	$0.673156\pi$
$644$	58.9904	2.32455
$645$	2.70129	0.106363
$646$	92.3727	3.63436
$647$	−23.1078	−0.908462	−0.454231	−	0.890884i	$-0.650086\pi$
$647$	−23.1078	−0.908462	−0.454231	+	0.890884i	$0.650086\pi$
$648$	23.1473	0.909313
$649$	1.81040	0.0710645
$650$	−16.8603	−0.661317
$651$	6.55974	0.257096
$652$	−54.3453	−2.12833
$653$	26.6619	1.04336	0.521681	−	0.853141i	$-0.325305\pi$
$653$	26.6619	1.04336	0.521681	+	0.853141i	$0.325305\pi$
$654$	57.4888	2.24799
$655$	8.65582	0.338211
$656$	34.8577	1.36096
$657$	9.84210	0.383977
$658$	34.3640	1.33965
$659$	30.8921	1.20339	0.601693	−	0.798727i	$-0.294493\pi$
$659$	30.8921	1.20339	0.601693	+	0.798727i	$0.294493\pi$
$660$	1.31221	0.0510776
$661$	−46.3873	−1.80426	−0.902128	−	0.431469i	$-0.857995\pi$
$661$	−46.3873	−1.80426	−0.902128	+	0.431469i	$0.857995\pi$
$662$	41.9450	1.63024
$663$	53.0646	2.06086
$664$	−101.831	−3.95182
$665$	−12.5126	−0.485220
$666$	15.5640	0.603093
$667$	−8.55291	−0.331170
$668$	79.7363	3.08509
$669$	−15.9588	−0.617002
$670$	8.32836	0.321753
$671$	−0.0991838	−0.00382895
$672$	−14.7912	−0.570582
$673$	38.4953	1.48388	0.741942	−	0.670465i	$-0.233905\pi$
$673$	38.4953	1.48388	0.741942	+	0.670465i	$0.233905\pi$
$674$	25.2677	0.973277
$675$	−5.62193	−0.216388
$676$	138.288	5.31878
$677$	−41.2878	−1.58682	−0.793410	−	0.608688i	$-0.791696\pi$
$677$	−41.2878	−1.58682	−0.793410	+	0.608688i	$0.791696\pi$
$678$	25.2922	0.971341
$679$	30.6345	1.17565
$680$	−38.0602	−1.45954
$681$	−31.0808	−1.19102
$682$	−1.34220	−0.0513956
$683$	−20.6255	−0.789213	−0.394607	−	0.918850i	$-0.629119\pi$
$683$	−20.6255	−0.789213	−0.394607	+	0.918850i	$0.629119\pi$
$684$	33.5509	1.28285
$685$	17.8284	0.681190
$686$	51.2010	1.95486
$687$	−15.6603	−0.597478
$688$	14.4005	0.549015
$689$	57.8421	2.20361
$690$	−21.2759	−0.809961
$691$	27.3094	1.03890	0.519450	−	0.854501i	$-0.326137\pi$
$691$	27.3094	1.03890	0.519450	+	0.854501i	$0.326137\pi$
$692$	−62.3912	−2.37176
$693$	−0.579136	−0.0219996
$694$	38.1282	1.44733
$695$	−11.2816	−0.427937
$696$	11.2444	0.426218
$697$	29.9324	1.13377
$698$	76.7826	2.90626
$699$	−8.12818	−0.307436
$700$	9.32787	0.352560
$701$	−4.22255	−0.159484	−0.0797418	−	0.996816i	$-0.525410\pi$
$701$	−4.22255	−0.159484	−0.0797418	+	0.996816i	$0.525410\pi$
$702$	94.7877	3.57753
$703$	−29.3336	−1.10634
$704$	−0.102520	−0.00386386
$705$	−8.56356	−0.322522
$706$	−5.94920	−0.223901
$707$	27.9322	1.05050
$708$	48.2428	1.81308
$709$	−6.71714	−0.252268	−0.126134	−	0.992013i	$-0.540257\pi$
$709$	−6.71714	−0.252268	−0.126134	+	0.992013i	$0.540257\pi$
$710$	−4.28550	−0.160832
$711$	−8.59561	−0.322360
$712$	66.0162	2.47406
$713$	15.0365	0.563122
$714$	−42.4891	−1.59012
$715$	1.47076	0.0550033
$716$	−74.5533	−2.78619
$717$	1.78577	0.0666909
$718$	2.87687	0.107364
$719$	−34.9263	−1.30253	−0.651266	−	0.758850i	$-0.725762\pi$
$719$	−34.9263	−1.30253	−0.651266	+	0.758850i	$0.725762\pi$
$720$	−8.81989	−0.328698
$721$	−13.9251	−0.518598
$722$	−43.1839	−1.60714
$723$	14.7907	0.550073
$724$	61.9972	2.30411
$725$	−1.35243	−0.0502280
$726$	36.8412	1.36731
$727$	17.5334	0.650279	0.325140	−	0.945666i	$-0.394589\pi$
$727$	17.5334	0.650279	0.325140	+	0.945666i	$0.394589\pi$
$728$	−86.9247	−3.22164
$729$	26.9110	0.996703
$730$	20.0134	0.740730
$731$	12.3658	0.457365
$732$	−2.64301	−0.0976884
$733$	13.5415	0.500166	0.250083	−	0.968224i	$-0.419542\pi$
$733$	13.5415	0.500166	0.250083	+	0.968224i	$0.419542\pi$
$734$	−24.6155	−0.908575
$735$	−3.50193	−0.129171
$736$	−33.9050	−1.24976
$737$	−0.726498	−0.0267609
$738$	15.7347	0.579203
$739$	−13.3757	−0.492032	−0.246016	−	0.969266i	$-0.579122\pi$
$739$	−13.3757	−0.492032	−0.246016	+	0.969266i	$0.579122\pi$
$740$	21.8675	0.803864
$741$	−52.5734	−1.93133
$742$	−46.3145	−1.70026
$743$	−38.9047	−1.42728	−0.713638	−	0.700515i	$-0.752954\pi$
$743$	−38.9047	−1.42728	−0.713638	+	0.700515i	$0.752954\pi$
$744$	−19.7683	−0.724742
$745$	−18.9699	−0.695004
$746$	32.4712	1.18885
$747$	−20.2636	−0.741406
$748$	6.00693	0.219635
$749$	−29.5203	−1.07865
$750$	−3.36426	−0.122845
$751$	−32.6820	−1.19258	−0.596291	−	0.802768i	$-0.703360\pi$
$751$	−32.6820	−1.19258	−0.596291	+	0.802768i	$0.703360\pi$
$752$	−45.6522	−1.66476
$753$	13.7433	0.500833
$754$	22.8024	0.830416
$755$	4.83210	0.175858
$756$	−52.4407	−1.90725
$757$	0.666792	0.0242350	0.0121175	−	0.999927i	$-0.496143\pi$
$757$	0.666792	0.0242350	0.0121175	+	0.999927i	$0.496143\pi$
$758$	40.7533	1.48023
$759$	1.85594	0.0673663
$760$	37.7079	1.36781
$761$	26.0070	0.942754	0.471377	−	0.881932i	$-0.343757\pi$
$761$	26.0070	0.942754	0.471377	+	0.881932i	$0.343757\pi$
$762$	58.1838	2.10778
$763$	−35.6483	−1.29055
$764$	−22.9864	−0.831620
$765$	−7.57367	−0.273827
$766$	24.9090	0.900000
$767$	54.0720	1.95243
$768$	−38.8051	−1.40026
$769$	27.8025	1.00259	0.501293	−	0.865278i	$-0.332858\pi$
$769$	27.8025	1.00259	0.501293	+	0.865278i	$0.332858\pi$
$770$	−1.17764	−0.0424394
$771$	28.0676	1.01083
$772$	−26.2609	−0.945149
$773$	−18.3278	−0.659204	−0.329602	−	0.944120i	$-0.606915\pi$
$773$	−18.3278	−0.659204	−0.329602	+	0.944120i	$0.606915\pi$
$774$	6.50038	0.233651
$775$	2.37765	0.0854079
$776$	−92.3198	−3.31409
$777$	13.4927	0.484048
$778$	36.6408	1.31364
$779$	−29.6553	−1.06251
$780$	39.1922	1.40330
$781$	0.373832	0.0133768
$782$	−97.3955	−3.48285
$783$	7.60327	0.271719
$784$	−18.6687	−0.666741
$785$	15.0206	0.536108
$786$	−29.1204	−1.03869
$787$	1.87212	0.0667340	0.0333670	−	0.999443i	$-0.489377\pi$
$787$	1.87212	0.0667340	0.0333670	+	0.999443i	$0.489377\pi$
$788$	104.275	3.71465
$789$	−10.7631	−0.383175
$790$	−17.4787	−0.621865
$791$	−15.6835	−0.557640
$792$	1.74528	0.0620157
$793$	−2.96236	−0.105196
$794$	−64.8087	−2.29998
$795$	11.5416	0.409340
$796$	105.749	3.74818
$797$	12.0415	0.426531	0.213265	−	0.976994i	$-0.431590\pi$
$797$	12.0415	0.426531	0.213265	+	0.976994i	$0.431590\pi$
$798$	42.0958	1.49018
$799$	−39.2017	−1.38686
$800$	−5.36124	−0.189548
$801$	13.1367	0.464161
$802$	−47.6705	−1.68330
$803$	−1.74581	−0.0616082
$804$	−19.3594	−0.682755
$805$	13.1930	0.464993
$806$	−40.0881	−1.41204
$807$	30.8526	1.08606
$808$	−84.1760	−2.96130
$809$	−10.0810	−0.354429	−0.177215	−	0.984172i	$-0.556709\pi$
$809$	−10.0810	−0.354429	−0.177215	+	0.984172i	$0.556709\pi$
$810$	9.36632	0.329099
$811$	39.9468	1.40272	0.701361	−	0.712806i	$-0.252576\pi$
$811$	39.9468	1.40272	0.701361	+	0.712806i	$0.252576\pi$
$812$	−12.6153	−0.442710
$813$	2.75504	0.0966236
$814$	−2.76077	−0.0967649
$815$	−12.1542	−0.425742
$816$	56.4463	1.97602
$817$	−12.2513	−0.428619
$818$	−88.0993	−3.08032
$819$	−17.2973	−0.604416
$820$	22.1073	0.772021
$821$	44.2350	1.54381	0.771907	−	0.635736i	$-0.219303\pi$
$821$	44.2350	1.54381	0.771907	+	0.635736i	$0.219303\pi$
$822$	−59.9795	−2.09203
$823$	33.3225	1.16155	0.580774	−	0.814065i	$-0.302750\pi$
$823$	33.3225	1.16155	0.580774	+	0.814065i	$0.302750\pi$
$824$	41.9645	1.46190
$825$	0.293471	0.0102173
$826$	−43.2957	−1.50645
$827$	9.66698	0.336154	0.168077	−	0.985774i	$-0.446244\pi$
$827$	9.66698	0.336154	0.168077	+	0.985774i	$0.446244\pi$
$828$	−35.3753	−1.22938
$829$	29.7606	1.03363	0.516814	−	0.856098i	$-0.327118\pi$
$829$	29.7606	1.03363	0.516814	+	0.856098i	$0.327118\pi$
$830$	−41.2050	−1.43025
$831$	−12.4145	−0.430654
$832$	−3.06200	−0.106156
$833$	−16.0309	−0.555438
$834$	37.9543	1.31425
$835$	17.8328	0.617128
$836$	−5.95132	−0.205831
$837$	−13.3670	−0.462031
$838$	−66.7881	−2.30716
$839$	28.0982	0.970059	0.485029	−	0.874498i	$-0.338809\pi$
$839$	28.0982	0.970059	0.485029	+	0.874498i	$0.338809\pi$
$840$	−17.3447	−0.598449
$841$	−27.1709	−0.936929
$842$	7.73309	0.266500
$843$	22.9627	0.790879
$844$	43.3217	1.49120
$845$	30.9277	1.06395
$846$	−20.6074	−0.708496
$847$	−22.8449	−0.784960
$848$	61.5282	2.11289
$849$	28.6582	0.983548
$850$	−15.4007	−0.528239
$851$	30.9286	1.06022
$852$	9.96172	0.341283
$853$	16.4572	0.563484	0.281742	−	0.959490i	$-0.409088\pi$
$853$	16.4572	0.563484	0.281742	+	0.959490i	$0.409088\pi$
$854$	2.37198	0.0811674
$855$	7.50356	0.256616
$856$	88.9621	3.04066
$857$	24.6955	0.843582	0.421791	−	0.906693i	$-0.361402\pi$
$857$	24.6955	0.843582	0.421791	+	0.906693i	$0.361402\pi$
$858$	−4.94802	−0.168922
$859$	−12.2825	−0.419074	−0.209537	−	0.977801i	$-0.567196\pi$
$859$	−12.2825	−0.419074	−0.209537	+	0.977801i	$0.567196\pi$
$860$	9.13305	0.311434
$861$	13.6407	0.464874
$862$	18.7837	0.639776
$863$	−1.73921	−0.0592035	−0.0296017	−	0.999562i	$-0.509424\pi$
$863$	−1.73921	−0.0592035	−0.0296017	+	0.999562i	$0.509424\pi$
$864$	30.1405	1.02540
$865$	−13.9536	−0.474437
$866$	−50.1151	−1.70298
$867$	25.9882	0.882607
$868$	22.1785	0.752786
$869$	1.52470	0.0517220
$870$	4.54993	0.154257
$871$	−21.6986	−0.735229
$872$	107.429	3.63801
$873$	−18.3709	−0.621760
$874$	96.4939	3.26395
$875$	2.08615	0.0705247
$876$	−46.5215	−1.57182
$877$	−21.5185	−0.726629	−0.363314	−	0.931667i	$-0.618355\pi$
$877$	−21.5185	−0.726629	−0.363314	+	0.931667i	$0.618355\pi$
$878$	8.78021	0.296318
$879$	25.8270	0.871123
$880$	1.56449	0.0527388
$881$	14.4446	0.486652	0.243326	−	0.969945i	$-0.421762\pi$
$881$	14.4446	0.486652	0.243326	+	0.969945i	$0.421762\pi$
$882$	−8.42706	−0.283754
$883$	43.2706	1.45617	0.728085	−	0.685487i	$-0.240410\pi$
$883$	43.2706	1.45617	0.728085	+	0.685487i	$0.240410\pi$
$884$	179.411	6.03425
$885$	10.7894	0.362680
$886$	17.8317	0.599067
$887$	−47.0060	−1.57831	−0.789154	−	0.614195i	$-0.789481\pi$
$887$	−47.0060	−1.57831	−0.789154	+	0.614195i	$0.789481\pi$
$888$	−40.6614	−1.36451
$889$	−36.0793	−1.21006
$890$	26.7128	0.895413
$891$	−0.817041	−0.0273719
$892$	−53.9566	−1.80660
$893$	38.8388	1.29969
$894$	63.8198	2.13445
$895$	−16.6736	−0.557337
$896$	24.8204	0.829193
$897$	55.4320	1.85082
$898$	74.2024	2.47617
$899$	−3.21561	−0.107247
$900$	−5.59372	−0.186457
$901$	52.8345	1.76017
$902$	−2.79105	−0.0929318
$903$	5.63529	0.187531
$904$	47.2635	1.57196
$905$	13.8655	0.460904
$906$	−16.2564	−0.540084
$907$	−8.56950	−0.284545	−0.142273	−	0.989827i	$-0.545441\pi$
$907$	−8.56950	−0.284545	−0.142273	+	0.989827i	$0.545441\pi$
$908$	−105.084	−3.48733
$909$	−16.7503	−0.555573
$910$	−35.1732	−1.16598
$911$	9.03908	0.299478	0.149739	−	0.988726i	$-0.452157\pi$
$911$	9.03908	0.299478	0.149739	+	0.988726i	$0.452157\pi$
$912$	−55.9238	−1.85182
$913$	3.59439	0.118957
$914$	58.5868	1.93788
$915$	−0.591100	−0.0195412
$916$	−52.9474	−1.74943
$917$	18.0573	0.596305
$918$	86.5816	2.85762
$919$	−27.5248	−0.907961	−0.453980	−	0.891012i	$-0.649996\pi$
$919$	−27.5248	−0.907961	−0.453980	+	0.891012i	$0.649996\pi$
$920$	−39.7583	−1.31079
$921$	−30.4333	−1.00281
$922$	88.4458	2.91281
$923$	11.1654	0.367513
$924$	2.73746	0.0900557
$925$	4.89059	0.160802
$926$	12.4988	0.410735
$927$	8.35058	0.274269
$928$	7.25070	0.238016
$929$	−57.4681	−1.88547	−0.942734	−	0.333544i	$-0.891755\pi$
$929$	−57.4681	−1.88547	−0.942734	+	0.333544i	$0.891755\pi$
$930$	−7.99905	−0.262299
$931$	15.8825	0.520528
$932$	−27.4813	−0.900181
$933$	−15.8152	−0.517766
$934$	63.2356	2.06913
$935$	1.34343	0.0439348
$936$	52.1269	1.70382
$937$	16.2302	0.530217	0.265108	−	0.964219i	$-0.414592\pi$
$937$	16.2302	0.530217	0.265108	+	0.964219i	$0.414592\pi$
$938$	17.3742	0.567288
$939$	−31.0577	−1.01353
$940$	−28.9534	−0.944355
$941$	−16.0621	−0.523611	−0.261805	−	0.965121i	$-0.584318\pi$
$941$	−16.0621	−0.523611	−0.261805	+	0.965121i	$0.584318\pi$
$942$	−50.5332	−1.64646
$943$	31.2678	1.01822
$944$	57.5179	1.87205
$945$	−11.7282	−0.381518
$946$	−1.15305	−0.0374888
$947$	−30.3942	−0.987678	−0.493839	−	0.869553i	$-0.664407\pi$
$947$	−30.3942	−0.987678	−0.493839	+	0.869553i	$0.664407\pi$
$948$	40.6296	1.31959
$949$	−52.1427	−1.69262
$950$	15.2581	0.495039
$951$	25.9992	0.843081
$952$	−79.3993	−2.57335
$953$	56.9325	1.84422	0.922112	−	0.386922i	$-0.126462\pi$
$953$	56.9325	1.84422	0.922112	+	0.386922i	$0.126462\pi$
$954$	27.7738	0.899210
$955$	−5.14084	−0.166354
$956$	6.03769	0.195273
$957$	−0.396899	−0.0128299
$958$	51.1337	1.65206
$959$	37.1928	1.20102
$960$	−0.610982	−0.0197194
$961$	−25.3468	−0.817637
$962$	−82.4570	−2.65852
$963$	17.7027	0.570462
$964$	50.0074	1.61063
$965$	−5.87316	−0.189064
$966$	−44.3848	−1.42806
$967$	29.5291	0.949593	0.474796	−	0.880096i	$-0.342522\pi$
$967$	29.5291	0.949593	0.474796	+	0.880096i	$0.342522\pi$
$968$	68.8451	2.21276
$969$	−48.0219	−1.54269
$970$	−37.3562	−1.19944
$971$	31.0361	0.995997	0.497999	−	0.867178i	$-0.334068\pi$
$971$	31.0361	0.995997	0.497999	+	0.867178i	$0.334068\pi$
$972$	53.6405	1.72052
$973$	−23.5352	−0.754503
$974$	74.7065	2.39375
$975$	8.76520	0.280711
$976$	−3.15114	−0.100866
$977$	1.72349	0.0551393	0.0275696	−	0.999620i	$-0.491223\pi$
$977$	1.72349	0.0551393	0.0275696	+	0.999620i	$0.491223\pi$
$978$	40.8898	1.30751
$979$	−2.33020	−0.0744736
$980$	−11.8400	−0.378216
$981$	21.3775	0.682531
$982$	−21.7136	−0.692909
$983$	−5.02593	−0.160302	−0.0801512	−	0.996783i	$-0.525540\pi$
$983$	−5.02593	−0.160302	−0.0801512	+	0.996783i	$0.525540\pi$
$984$	−41.1074	−1.31046
$985$	23.3208	0.743064
$986$	20.8283	0.663310
$987$	−17.8649	−0.568645
$988$	−177.750	−5.65499
$989$	12.9175	0.410752
$990$	0.706208	0.0224448
$991$	−36.6578	−1.16447	−0.582237	−	0.813019i	$-0.697822\pi$
$991$	−36.6578	−1.16447	−0.582237	+	0.813019i	$0.697822\pi$
$992$	−12.7472	−0.404723
$993$	−21.8060	−0.691992
$994$	−8.94018	−0.283565
$995$	23.6505	0.749771
$996$	95.7818	3.03496
$997$	9.05228	0.286689	0.143344	−	0.989673i	$-0.454214\pi$
$997$	9.05228	0.286689	0.143344	+	0.989673i	$0.454214\pi$
$998$	100.688	3.18722
$999$	−27.4946	−0.869889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.10	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.10	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.54388 q^{2} +1.32249 q^{3} +4.47134 q^{4} +1.00000 q^{5} -3.36426 q^{6} +2.08615 q^{7} -6.28679 q^{8} -1.25102 q^{9} +O(q^{10})\)	\(q-2.54388 q^{2} +1.32249 q^{3} +4.47134 q^{4} +1.00000 q^{5} -3.36426 q^{6} +2.08615 q^{7} -6.28679 q^{8} -1.25102 q^{9} -2.54388 q^{10} +0.221908 q^{11} +5.91330 q^{12} +6.62780 q^{13} -5.30692 q^{14} +1.32249 q^{15} +7.05017 q^{16} +6.05401 q^{17} +3.18244 q^{18} -5.99797 q^{19} +4.47134 q^{20} +2.75891 q^{21} -0.564507 q^{22} +6.32410 q^{23} -8.31422 q^{24} +1.00000 q^{25} -16.8603 q^{26} -5.62193 q^{27} +9.32787 q^{28} -1.35243 q^{29} -3.36426 q^{30} +2.37765 q^{31} -5.36124 q^{32} +0.293471 q^{33} -15.4007 q^{34} +2.08615 q^{35} -5.59372 q^{36} +4.89059 q^{37} +15.2581 q^{38} +8.76520 q^{39} -6.28679 q^{40} +4.94423 q^{41} -7.01835 q^{42} +2.04258 q^{43} +0.992223 q^{44} -1.25102 q^{45} -16.0878 q^{46} -6.47533 q^{47} +9.32379 q^{48} -2.64798 q^{49} -2.54388 q^{50} +8.00637 q^{51} +29.6351 q^{52} +8.72719 q^{53} +14.3015 q^{54} +0.221908 q^{55} -13.1152 q^{56} -7.93225 q^{57} +3.44042 q^{58} +8.15836 q^{59} +5.91330 q^{60} -0.446960 q^{61} -6.04847 q^{62} -2.60981 q^{63} -0.461994 q^{64} +6.62780 q^{65} -0.746555 q^{66} -3.27388 q^{67} +27.0695 q^{68} +8.36357 q^{69} -5.30692 q^{70} +1.68463 q^{71} +7.86488 q^{72} -7.86727 q^{73} -12.4411 q^{74} +1.32249 q^{75} -26.8189 q^{76} +0.462932 q^{77} -22.2976 q^{78} +6.87089 q^{79} +7.05017 q^{80} -3.68190 q^{81} -12.5775 q^{82} +16.1977 q^{83} +12.3360 q^{84} +6.05401 q^{85} -5.19607 q^{86} -1.78858 q^{87} -1.39509 q^{88} -10.5008 q^{89} +3.18244 q^{90} +13.8266 q^{91} +28.2772 q^{92} +3.14443 q^{93} +16.4725 q^{94} -5.99797 q^{95} -7.09019 q^{96} +14.6847 q^{97} +6.73616 q^{98} -0.277610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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