LMFDB - Embedded newform 8035.2.a.e.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.59466 q^{2} -3.04599 q^{3} +4.73224 q^{4} +1.00000 q^{5} +7.90331 q^{6} -0.447166 q^{7} -7.08923 q^{8} +6.27808 q^{9} +O(q^{10})$	\(q-2.59466 q^{2} -3.04599 q^{3} +4.73224 q^{4} +1.00000 q^{5} +7.90331 q^{6} -0.447166 q^{7} -7.08923 q^{8} +6.27808 q^{9} -2.59466 q^{10} -0.526592 q^{11} -14.4144 q^{12} -3.03214 q^{13} +1.16024 q^{14} -3.04599 q^{15} +8.92964 q^{16} +2.90689 q^{17} -16.2895 q^{18} -1.44327 q^{19} +4.73224 q^{20} +1.36206 q^{21} +1.36633 q^{22} -5.83121 q^{23} +21.5938 q^{24} +1.00000 q^{25} +7.86736 q^{26} -9.98501 q^{27} -2.11610 q^{28} +4.16733 q^{29} +7.90331 q^{30} -6.11330 q^{31} -8.99088 q^{32} +1.60400 q^{33} -7.54238 q^{34} -0.447166 q^{35} +29.7094 q^{36} +5.15081 q^{37} +3.74480 q^{38} +9.23587 q^{39} -7.08923 q^{40} -2.69925 q^{41} -3.53409 q^{42} -8.24891 q^{43} -2.49196 q^{44} +6.27808 q^{45} +15.1300 q^{46} -10.4887 q^{47} -27.1996 q^{48} -6.80004 q^{49} -2.59466 q^{50} -8.85436 q^{51} -14.3488 q^{52} -10.6720 q^{53} +25.9077 q^{54} -0.526592 q^{55} +3.17006 q^{56} +4.39620 q^{57} -10.8128 q^{58} +0.466252 q^{59} -14.4144 q^{60} +1.09388 q^{61} +15.8619 q^{62} -2.80734 q^{63} +5.46896 q^{64} -3.03214 q^{65} -4.16182 q^{66} +6.42470 q^{67} +13.7561 q^{68} +17.7618 q^{69} +1.16024 q^{70} +3.65939 q^{71} -44.5068 q^{72} -0.671565 q^{73} -13.3646 q^{74} -3.04599 q^{75} -6.82992 q^{76} +0.235474 q^{77} -23.9639 q^{78} -6.67379 q^{79} +8.92964 q^{80} +11.5800 q^{81} +7.00363 q^{82} -12.3639 q^{83} +6.44562 q^{84} +2.90689 q^{85} +21.4031 q^{86} -12.6937 q^{87} +3.73313 q^{88} +3.93445 q^{89} -16.2895 q^{90} +1.35587 q^{91} -27.5947 q^{92} +18.6211 q^{93} +27.2147 q^{94} -1.44327 q^{95} +27.3862 q^{96} +9.02693 q^{97} +17.6438 q^{98} -3.30599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.59466	−1.83470	−0.917350	−	0.398082i	$-0.869676\pi$
$2$	−2.59466	−1.83470	−0.917350	+	0.398082i	$0.869676\pi$
$3$	−3.04599	−1.75861	−0.879303	−	0.476263i	$-0.841991\pi$
$3$	−3.04599	−1.75861	−0.879303	+	0.476263i	$0.841991\pi$
$4$	4.73224	2.36612
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.90331	3.22651
$7$	−0.447166	−0.169013	−0.0845064	−	0.996423i	$-0.526931\pi$
$7$	−0.447166	−0.169013	−0.0845064	+	0.996423i	$0.526931\pi$
$8$	−7.08923	−2.50642
$9$	6.27808	2.09269
$10$	−2.59466	−0.820502
$11$	−0.526592	−0.158773	−0.0793867	−	0.996844i	$-0.525296\pi$
$11$	−0.526592	−0.158773	−0.0793867	+	0.996844i	$0.525296\pi$
$12$	−14.4144	−4.16107
$13$	−3.03214	−0.840964	−0.420482	−	0.907301i	$-0.638139\pi$
$13$	−3.03214	−0.840964	−0.420482	+	0.907301i	$0.638139\pi$
$14$	1.16024	0.310088
$15$	−3.04599	−0.786472
$16$	8.92964	2.23241
$17$	2.90689	0.705024	0.352512	−	0.935807i	$-0.385328\pi$
$17$	2.90689	0.705024	0.352512	+	0.935807i	$0.385328\pi$
$18$	−16.2895	−3.83946
$19$	−1.44327	−0.331110	−0.165555	−	0.986201i	$-0.552941\pi$
$19$	−1.44327	−0.331110	−0.165555	+	0.986201i	$0.552941\pi$
$20$	4.73224	1.05816
$21$	1.36206	0.297227
$22$	1.36633	0.291302
$23$	−5.83121	−1.21589	−0.607945	−	0.793979i	$-0.708006\pi$
$23$	−5.83121	−1.21589	−0.607945	+	0.793979i	$0.708006\pi$
$24$	21.5938	4.40781
$25$	1.00000	0.200000
$26$	7.86736	1.54292
$27$	−9.98501	−1.92162
$28$	−2.11610	−0.399905
$29$	4.16733	0.773854	0.386927	−	0.922110i	$-0.373537\pi$
$29$	4.16733	0.773854	0.386927	+	0.922110i	$0.373537\pi$
$30$	7.90331	1.44294
$31$	−6.11330	−1.09798	−0.548991	−	0.835828i	$-0.684988\pi$
$31$	−6.11330	−1.09798	−0.548991	+	0.835828i	$0.684988\pi$
$32$	−8.99088	−1.58938
$33$	1.60400	0.279220
$34$	−7.54238	−1.29351
$35$	−0.447166	−0.0755848
$36$	29.7094	4.95157
$37$	5.15081	0.846788	0.423394	−	0.905946i	$-0.360839\pi$
$37$	5.15081	0.846788	0.423394	+	0.905946i	$0.360839\pi$
$38$	3.74480	0.607487
$39$	9.23587	1.47892
$40$	−7.08923	−1.12091
$41$	−2.69925	−0.421552	−0.210776	−	0.977534i	$-0.567599\pi$
$41$	−2.69925	−0.421552	−0.210776	+	0.977534i	$0.567599\pi$
$42$	−3.53409	−0.545322
$43$	−8.24891	−1.25795	−0.628973	−	0.777427i	$-0.716524\pi$
$43$	−8.24891	−1.25795	−0.628973	+	0.777427i	$0.716524\pi$
$44$	−2.49196	−0.375677
$45$	6.27808	0.935881
$46$	15.1300	2.23079
$47$	−10.4887	−1.52994	−0.764970	−	0.644066i	$-0.777246\pi$
$47$	−10.4887	−1.52994	−0.764970	+	0.644066i	$0.777246\pi$
$48$	−27.1996	−3.92593
$49$	−6.80004	−0.971435
$50$	−2.59466	−0.366940
$51$	−8.85436	−1.23986
$52$	−14.3488	−1.98982
$53$	−10.6720	−1.46591	−0.732954	−	0.680279i	$-0.761859\pi$
$53$	−10.6720	−1.46591	−0.732954	+	0.680279i	$0.761859\pi$
$54$	25.9077	3.52559
$55$	−0.526592	−0.0710057
$56$	3.17006	0.423617
$57$	4.39620	0.582291
$58$	−10.8128	−1.41979
$59$	0.466252	0.0607008	0.0303504	−	0.999539i	$-0.490338\pi$
$59$	0.466252	0.0607008	0.0303504	+	0.999539i	$0.490338\pi$
$60$	−14.4144	−1.86089
$61$	1.09388	0.140057	0.0700285	−	0.997545i	$-0.477691\pi$
$61$	1.09388	0.140057	0.0700285	+	0.997545i	$0.477691\pi$
$62$	15.8619	2.01447
$63$	−2.80734	−0.353692
$64$	5.46896	0.683620
$65$	−3.03214	−0.376090
$66$	−4.16182	−0.512285
$67$	6.42470	0.784902	0.392451	−	0.919773i	$-0.371627\pi$
$67$	6.42470	0.784902	0.392451	+	0.919773i	$0.371627\pi$
$68$	13.7561	1.66817
$69$	17.7618	2.13827
$70$	1.16024	0.138675
$71$	3.65939	0.434290	0.217145	−	0.976139i	$-0.430326\pi$
$71$	3.65939	0.434290	0.217145	+	0.976139i	$0.430326\pi$
$72$	−44.5068	−5.24517
$73$	−0.671565	−0.0786007	−0.0393004	−	0.999227i	$-0.512513\pi$
$73$	−0.671565	−0.0786007	−0.0393004	+	0.999227i	$0.512513\pi$
$74$	−13.3646	−1.55360
$75$	−3.04599	−0.351721
$76$	−6.82992	−0.783446
$77$	0.235474	0.0268347
$78$	−23.9639	−2.71338
$79$	−6.67379	−0.750860	−0.375430	−	0.926851i	$-0.622505\pi$
$79$	−6.67379	−0.750860	−0.375430	+	0.926851i	$0.622505\pi$
$80$	8.92964	0.998364
$81$	11.5800	1.28667
$82$	7.00363	0.773422
$83$	−12.3639	−1.35711	−0.678555	−	0.734550i	$-0.737393\pi$
$83$	−12.3639	−1.35711	−0.678555	+	0.734550i	$0.737393\pi$
$84$	6.44562	0.703274
$85$	2.90689	0.315296
$86$	21.4031	2.30795
$87$	−12.6937	−1.36090
$88$	3.73313	0.397953
$89$	3.93445	0.417050	0.208525	−	0.978017i	$-0.433134\pi$
$89$	3.93445	0.417050	0.208525	+	0.978017i	$0.433134\pi$
$90$	−16.2895	−1.71706
$91$	1.35587	0.142134
$92$	−27.5947	−2.87695
$93$	18.6211	1.93092
$94$	27.2147	2.80698
$95$	−1.44327	−0.148077
$96$	27.3862	2.79509
$97$	9.02693	0.916546	0.458273	−	0.888811i	$-0.348468\pi$
$97$	9.02693	0.916546	0.458273	+	0.888811i	$0.348468\pi$
$98$	17.6438	1.78229
$99$	−3.30599	−0.332264
$100$	4.73224	0.473224
$101$	0.363640	0.0361835	0.0180918	−	0.999836i	$-0.494241\pi$
$101$	0.363640	0.0361835	0.0180918	+	0.999836i	$0.494241\pi$
$102$	22.9740	2.27477
$103$	2.85316	0.281130	0.140565	−	0.990071i	$-0.455108\pi$
$103$	2.85316	0.281130	0.140565	+	0.990071i	$0.455108\pi$
$104$	21.4955	2.10781
$105$	1.36206	0.132924
$106$	27.6901	2.68950
$107$	6.89874	0.666926	0.333463	−	0.942763i	$-0.391783\pi$
$107$	6.89874	0.666926	0.333463	+	0.942763i	$0.391783\pi$
$108$	−47.2515	−4.54678
$109$	7.92796	0.759361	0.379681	−	0.925118i	$-0.376034\pi$
$109$	7.92796	0.759361	0.379681	+	0.925118i	$0.376034\pi$
$110$	1.36633	0.130274
$111$	−15.6893	−1.48917
$112$	−3.99303	−0.377306
$113$	−5.47524	−0.515067	−0.257533	−	0.966269i	$-0.582910\pi$
$113$	−5.47524	−0.515067	−0.257533	+	0.966269i	$0.582910\pi$
$114$	−11.4066	−1.06833
$115$	−5.83121	−0.543763
$116$	19.7208	1.83103
$117$	−19.0360	−1.75988
$118$	−1.20976	−0.111368
$119$	−1.29986	−0.119158
$120$	21.5938	1.97123
$121$	−10.7227	−0.974791
$122$	−2.83824	−0.256963
$123$	8.22191	0.741344
$124$	−28.9296	−2.59796
$125$	1.00000	0.0894427
$126$	7.28409	0.648918
$127$	3.12251	0.277078	0.138539	−	0.990357i	$-0.455759\pi$
$127$	3.12251	0.277078	0.138539	+	0.990357i	$0.455759\pi$
$128$	3.79167	0.335140
$129$	25.1261	2.21223
$130$	7.86736	0.690013
$131$	8.06592	0.704723	0.352361	−	0.935864i	$-0.385379\pi$
$131$	8.06592	0.704723	0.352361	+	0.935864i	$0.385379\pi$
$132$	7.59050	0.660668
$133$	0.645382	0.0559618
$134$	−16.6699	−1.44006
$135$	−9.98501	−0.859373
$136$	−20.6076	−1.76709
$137$	17.4076	1.48723	0.743617	−	0.668605i	$-0.233108\pi$
$137$	17.4076	1.48723	0.743617	+	0.668605i	$0.233108\pi$
$138$	−46.0858	−3.92309
$139$	−1.12101	−0.0950827	−0.0475414	−	0.998869i	$-0.515139\pi$
$139$	−1.12101	−0.0950827	−0.0475414	+	0.998869i	$0.515139\pi$
$140$	−2.11610	−0.178843
$141$	31.9486	2.69056
$142$	−9.49487	−0.796792
$143$	1.59670	0.133523
$144$	56.0610	4.67175
$145$	4.16733	0.346078
$146$	1.74248	0.144209
$147$	20.7129	1.70837
$148$	24.3749	2.00360
$149$	−3.03657	−0.248765	−0.124383	−	0.992234i	$-0.539695\pi$
$149$	−3.03657	−0.248765	−0.124383	+	0.992234i	$0.539695\pi$
$150$	7.90331	0.645302
$151$	−0.427998	−0.0348299	−0.0174150	−	0.999848i	$-0.505544\pi$
$151$	−0.427998	−0.0348299	−0.0174150	+	0.999848i	$0.505544\pi$
$152$	10.2317	0.829901
$153$	18.2497	1.47540
$154$	−0.610974	−0.0492337
$155$	−6.11330	−0.491032
$156$	43.7064	3.49931
$157$	12.5778	1.00382	0.501909	−	0.864920i	$-0.332631\pi$
$157$	12.5778	1.00382	0.501909	+	0.864920i	$0.332631\pi$
$158$	17.3162	1.37760
$159$	32.5067	2.57795
$160$	−8.99088	−0.710791
$161$	2.60752	0.205501
$162$	−30.0462	−2.36065
$163$	−19.2512	−1.50787	−0.753934	−	0.656950i	$-0.771846\pi$
$163$	−19.2512	−1.50787	−0.753934	+	0.656950i	$0.771846\pi$
$164$	−12.7735	−0.997444
$165$	1.60400	0.124871
$166$	32.0800	2.48989
$167$	1.35606	0.104935	0.0524675	−	0.998623i	$-0.483291\pi$
$167$	1.35606	0.104935	0.0524675	+	0.998623i	$0.483291\pi$
$168$	−9.65599	−0.744976
$169$	−3.80614	−0.292780
$170$	−7.54238	−0.578474
$171$	−9.06099	−0.692911
$172$	−39.0358	−2.97645
$173$	−14.4768	−1.10065	−0.550327	−	0.834949i	$-0.685497\pi$
$173$	−14.4768	−1.10065	−0.550327	+	0.834949i	$0.685497\pi$
$174$	32.9357	2.49685
$175$	−0.447166	−0.0338025
$176$	−4.70228	−0.354447
$177$	−1.42020	−0.106749
$178$	−10.2085	−0.765162
$179$	8.11108	0.606250	0.303125	−	0.952951i	$-0.401970\pi$
$179$	8.11108	0.606250	0.303125	+	0.952951i	$0.401970\pi$
$180$	29.7094	2.21441
$181$	10.4243	0.774832	0.387416	−	0.921905i	$-0.373368\pi$
$181$	10.4243	0.774832	0.387416	+	0.921905i	$0.373368\pi$
$182$	−3.51801	−0.260772
$183$	−3.33195	−0.246305
$184$	41.3388	3.04754
$185$	5.15081	0.378695
$186$	−48.3153	−3.54265
$187$	−1.53074	−0.111939
$188$	−49.6352	−3.62002
$189$	4.46495	0.324778
$190$	3.74480	0.271676
$191$	22.6517	1.63902	0.819510	−	0.573065i	$-0.194246\pi$
$191$	22.6517	1.63902	0.819510	+	0.573065i	$0.194246\pi$
$192$	−16.6584	−1.20222
$193$	−4.16273	−0.299640	−0.149820	−	0.988713i	$-0.547869\pi$
$193$	−4.16273	−0.299640	−0.149820	+	0.988713i	$0.547869\pi$
$194$	−23.4218	−1.68159
$195$	9.23587	0.661395
$196$	−32.1795	−2.29853
$197$	−1.36985	−0.0975978	−0.0487989	−	0.998809i	$-0.515539\pi$
$197$	−1.36985	−0.0975978	−0.0487989	+	0.998809i	$0.515539\pi$
$198$	8.57790	0.609605
$199$	−13.3176	−0.944057	−0.472028	−	0.881583i	$-0.656478\pi$
$199$	−13.3176	−0.944057	−0.472028	+	0.881583i	$0.656478\pi$
$200$	−7.08923	−0.501284
$201$	−19.5696	−1.38033
$202$	−0.943521	−0.0663859
$203$	−1.86349	−0.130791
$204$	−41.9010	−2.93366
$205$	−2.69925	−0.188524
$206$	−7.40296	−0.515789
$207$	−36.6088	−2.54449
$208$	−27.0759	−1.87737
$209$	0.760016	0.0525714
$210$	−3.53409	−0.243875
$211$	−21.6939	−1.49347	−0.746734	−	0.665123i	$-0.768379\pi$
$211$	−21.6939	−1.49347	−0.746734	+	0.665123i	$0.768379\pi$
$212$	−50.5023	−3.46851
$213$	−11.1465	−0.763745
$214$	−17.8999	−1.22361
$215$	−8.24891	−0.562571
$216$	70.7860	4.81638
$217$	2.73366	0.185573
$218$	−20.5703	−1.39320
$219$	2.04558	0.138228
$220$	−2.49196	−0.168008
$221$	−8.81409	−0.592900
$222$	40.7084	2.73217
$223$	4.79401	0.321031	0.160515	−	0.987033i	$-0.448684\pi$
$223$	4.79401	0.321031	0.160515	+	0.987033i	$0.448684\pi$
$224$	4.02041	0.268625
$225$	6.27808	0.418539
$226$	14.2064	0.944993
$227$	10.5678	0.701410	0.350705	−	0.936486i	$-0.385942\pi$
$227$	10.5678	0.701410	0.350705	+	0.936486i	$0.385942\pi$
$228$	20.8039	1.37777
$229$	−11.7036	−0.773398	−0.386699	−	0.922206i	$-0.626385\pi$
$229$	−11.7036	−0.773398	−0.386699	+	0.922206i	$0.626385\pi$
$230$	15.1300	0.997641
$231$	−0.717252	−0.0471917
$232$	−29.5432	−1.93960
$233$	23.5118	1.54031	0.770154	−	0.637858i	$-0.220179\pi$
$233$	23.5118	1.54031	0.770154	+	0.637858i	$0.220179\pi$
$234$	49.3919	3.22885
$235$	−10.4887	−0.684210
$236$	2.20642	0.143626
$237$	20.3283	1.32047
$238$	3.37269	0.218619
$239$	4.52136	0.292462	0.146231	−	0.989250i	$-0.453286\pi$
$239$	4.52136	0.292462	0.146231	+	0.989250i	$0.453286\pi$
$240$	−27.1996	−1.75573
$241$	−27.8144	−1.79168	−0.895842	−	0.444373i	$-0.853426\pi$
$241$	−27.8144	−1.79168	−0.895842	+	0.444373i	$0.853426\pi$
$242$	27.8217	1.78845
$243$	−5.31769	−0.341130
$244$	5.17651	0.331392
$245$	−6.80004	−0.434439
$246$	−21.3330	−1.36014
$247$	4.37620	0.278451
$248$	43.3386	2.75201
$249$	37.6602	2.38662
$250$	−2.59466	−0.164100
$251$	−14.5703	−0.919667	−0.459833	−	0.888005i	$-0.652091\pi$
$251$	−14.5703	−0.919667	−0.459833	+	0.888005i	$0.652091\pi$
$252$	−13.2850	−0.836878
$253$	3.07067	0.193051
$254$	−8.10184	−0.508355
$255$	−8.85436	−0.554482
$256$	−20.7760	−1.29850
$257$	26.0470	1.62477	0.812383	−	0.583125i	$-0.198170\pi$
$257$	26.0470	1.62477	0.812383	+	0.583125i	$0.198170\pi$
$258$	−65.1936	−4.05878
$259$	−2.30326	−0.143118
$260$	−14.3488	−0.889875
$261$	26.1628	1.61944
$262$	−20.9283	−1.29295
$263$	−3.38709	−0.208857	−0.104428	−	0.994532i	$-0.533301\pi$
$263$	−3.38709	−0.208857	−0.104428	+	0.994532i	$0.533301\pi$
$264$	−11.3711	−0.699843
$265$	−10.6720	−0.655574
$266$	−1.67455	−0.102673
$267$	−11.9843	−0.733427
$268$	30.4032	1.85717
$269$	7.22310	0.440400	0.220200	−	0.975455i	$-0.429329\pi$
$269$	7.22310	0.440400	0.220200	+	0.975455i	$0.429329\pi$
$270$	25.9077	1.57669
$271$	13.2490	0.804819	0.402409	−	0.915460i	$-0.368173\pi$
$271$	13.2490	0.804819	0.402409	+	0.915460i	$0.368173\pi$
$272$	25.9575	1.57390
$273$	−4.12996	−0.249957
$274$	−45.1668	−2.72863
$275$	−0.526592	−0.0317547
$276$	84.0533	5.05941
$277$	−28.2945	−1.70005	−0.850027	−	0.526740i	$-0.823414\pi$
$277$	−28.2945	−1.70005	−0.850027	+	0.526740i	$0.823414\pi$
$278$	2.90863	0.174448
$279$	−38.3798	−2.29774
$280$	3.17006	0.189447
$281$	13.9299	0.830986	0.415493	−	0.909596i	$-0.363609\pi$
$281$	13.9299	0.830986	0.415493	+	0.909596i	$0.363609\pi$
$282$	−82.8957	−4.93637
$283$	−2.39974	−0.142650	−0.0713249	−	0.997453i	$-0.522723\pi$
$283$	−2.39974	−0.142650	−0.0713249	+	0.997453i	$0.522723\pi$
$284$	17.3171	1.02758
$285$	4.39620	0.260409
$286$	−4.14289	−0.244974
$287$	1.20701	0.0712477
$288$	−56.4454	−3.32608
$289$	−8.55000	−0.502941
$290$	−10.8128	−0.634949
$291$	−27.4960	−1.61184
$292$	−3.17801	−0.185979
$293$	1.23713	0.0722742	0.0361371	−	0.999347i	$-0.488495\pi$
$293$	1.23713	0.0722742	0.0361371	+	0.999347i	$0.488495\pi$
$294$	−53.7428	−3.13435
$295$	0.466252	0.0271462
$296$	−36.5153	−2.12241
$297$	5.25803	0.305102
$298$	7.87885	0.456409
$299$	17.6810	1.02252
$300$	−14.4144	−0.832215
$301$	3.68863	0.212609
$302$	1.11051	0.0639025
$303$	−1.10764	−0.0636325
$304$	−12.8879	−0.739172
$305$	1.09388	0.0626354
$306$	−47.3516	−2.70691
$307$	−5.35381	−0.305558	−0.152779	−	0.988260i	$-0.548822\pi$
$307$	−5.35381	−0.305558	−0.152779	+	0.988260i	$0.548822\pi$
$308$	1.11432	0.0634943
$309$	−8.69070	−0.494396
$310$	15.8619	0.900897
$311$	12.1029	0.686293	0.343147	−	0.939282i	$-0.388507\pi$
$311$	12.1029	0.686293	0.343147	+	0.939282i	$0.388507\pi$
$312$	−65.4752	−3.70681
$313$	−30.0426	−1.69811	−0.849053	−	0.528307i	$-0.822827\pi$
$313$	−30.0426	−1.69811	−0.849053	+	0.528307i	$0.822827\pi$
$314$	−32.6351	−1.84171
$315$	−2.80734	−0.158176
$316$	−31.5820	−1.77663
$317$	−0.169978	−0.00954689	−0.00477344	−	0.999989i	$-0.501519\pi$
$317$	−0.169978	−0.00954689	−0.00477344	+	0.999989i	$0.501519\pi$
$318$	−84.3438	−4.72977
$319$	−2.19448	−0.122867
$320$	5.46896	0.305724
$321$	−21.0135	−1.17286
$322$	−6.76561	−0.377033
$323$	−4.19544	−0.233440
$324$	54.7995	3.04442
$325$	−3.03214	−0.168193
$326$	49.9502	2.76649
$327$	−24.1485	−1.33542
$328$	19.1356	1.05659
$329$	4.69020	0.258579
$330$	−4.16182	−0.229101
$331$	−8.61589	−0.473572	−0.236786	−	0.971562i	$-0.576094\pi$
$331$	−8.61589	−0.473572	−0.236786	+	0.971562i	$0.576094\pi$
$332$	−58.5088	−3.21109
$333$	32.3372	1.77207
$334$	−3.51850	−0.192524
$335$	6.42470	0.351019
$336$	12.1627	0.663532
$337$	−13.2080	−0.719485	−0.359743	−	0.933052i	$-0.617135\pi$
$337$	−13.2080	−0.719485	−0.359743	+	0.933052i	$0.617135\pi$
$338$	9.87563	0.537164
$339$	16.6775	0.905799
$340$	13.7561	0.746029
$341$	3.21922	0.174330
$342$	23.5101	1.27128
$343$	6.17091	0.333198
$344$	58.4784	3.15294
$345$	17.7618	0.956264
$346$	37.5624	2.01937
$347$	14.4897	0.777848	0.388924	−	0.921270i	$-0.372847\pi$
$347$	14.4897	0.777848	0.388924	+	0.921270i	$0.372847\pi$
$348$	−60.0695	−3.22006
$349$	−3.03684	−0.162558	−0.0812790	−	0.996691i	$-0.525900\pi$
$349$	−3.03684	−0.162558	−0.0812790	+	0.996691i	$0.525900\pi$
$350$	1.16024	0.0620175
$351$	30.2759	1.61601
$352$	4.73452	0.252351
$353$	−0.797555	−0.0424496	−0.0212248	−	0.999775i	$-0.506757\pi$
$353$	−0.797555	−0.0424496	−0.0212248	+	0.999775i	$0.506757\pi$
$354$	3.68493	0.195852
$355$	3.65939	0.194220
$356$	18.6188	0.986792
$357$	3.95937	0.209552
$358$	−21.0455	−1.11229
$359$	−1.14239	−0.0602931	−0.0301465	−	0.999545i	$-0.509597\pi$
$359$	−1.14239	−0.0602931	−0.0301465	+	0.999545i	$0.509597\pi$
$360$	−44.5068	−2.34571
$361$	−16.9170	−0.890366
$362$	−27.0475	−1.42158
$363$	32.6613	1.71427
$364$	6.41630	0.336305
$365$	−0.671565	−0.0351513
$366$	8.64527	0.451896
$367$	0.209999	0.0109619	0.00548093	−	0.999985i	$-0.498255\pi$
$367$	0.209999	0.0109619	0.00548093	+	0.999985i	$0.498255\pi$
$368$	−52.0706	−2.71437
$369$	−16.9461	−0.882180
$370$	−13.3646	−0.694791
$371$	4.77214	0.247757
$372$	88.1195	4.56878
$373$	13.9461	0.722102	0.361051	−	0.932546i	$-0.382418\pi$
$373$	13.9461	0.722102	0.361051	+	0.932546i	$0.382418\pi$
$374$	3.97176	0.205375
$375$	−3.04599	−0.157294
$376$	74.3571	3.83467
$377$	−12.6359	−0.650783
$378$	−11.5850	−0.595869
$379$	−9.30438	−0.477934	−0.238967	−	0.971028i	$-0.576809\pi$
$379$	−9.30438	−0.477934	−0.238967	+	0.971028i	$0.576809\pi$
$380$	−6.82992	−0.350368
$381$	−9.51114	−0.487271
$382$	−58.7734	−3.00711
$383$	−31.6519	−1.61734	−0.808668	−	0.588266i	$-0.799811\pi$
$383$	−31.6519	−1.61734	−0.808668	+	0.588266i	$0.799811\pi$
$384$	−11.5494	−0.589378
$385$	0.235474	0.0120009
$386$	10.8008	0.549749
$387$	−51.7873	−2.63250
$388$	42.7176	2.16866
$389$	−35.8514	−1.81774	−0.908869	−	0.417082i	$-0.863053\pi$
$389$	−35.8514	−1.81774	−0.908869	+	0.417082i	$0.863053\pi$
$390$	−23.9639	−1.21346
$391$	−16.9507	−0.857232
$392$	48.2071	2.43483
$393$	−24.5687	−1.23933
$394$	3.55429	0.179063
$395$	−6.67379	−0.335795
$396$	−15.6447	−0.786177
$397$	−13.5293	−0.679018	−0.339509	−	0.940603i	$-0.610261\pi$
$397$	−13.5293	−0.679018	−0.339509	+	0.940603i	$0.610261\pi$
$398$	34.5545	1.73206
$399$	−1.96583	−0.0984146
$400$	8.92964	0.446482
$401$	7.39160	0.369119	0.184559	−	0.982821i	$-0.440914\pi$
$401$	7.39160	0.369119	0.184559	+	0.982821i	$0.440914\pi$
$402$	50.7764	2.53249
$403$	18.5364	0.923363
$404$	1.72083	0.0856146
$405$	11.5800	0.575417
$406$	4.83511	0.239962
$407$	−2.71237	−0.134447
$408$	62.7706	3.10761
$409$	6.28057	0.310554	0.155277	−	0.987871i	$-0.450373\pi$
$409$	6.28057	0.310554	0.155277	+	0.987871i	$0.450373\pi$
$410$	7.00363	0.345885
$411$	−53.0236	−2.61546
$412$	13.5018	0.665187
$413$	−0.208492	−0.0102592
$414$	94.9872	4.66837
$415$	−12.3639	−0.606918
$416$	27.2616	1.33661
$417$	3.41459	0.167213
$418$	−1.97198	−0.0964528
$419$	2.73127	0.133431	0.0667156	−	0.997772i	$-0.478748\pi$
$419$	2.73127	0.133431	0.0667156	+	0.997772i	$0.478748\pi$
$420$	6.44562	0.314514
$421$	−1.48262	−0.0722583	−0.0361291	−	0.999347i	$-0.511503\pi$
$421$	−1.48262	−0.0722583	−0.0361291	+	0.999347i	$0.511503\pi$
$422$	56.2882	2.74006
$423$	−65.8491	−3.20169
$424$	75.6560	3.67418
$425$	2.90689	0.141005
$426$	28.9213	1.40124
$427$	−0.489146	−0.0236714
$428$	32.6465	1.57803
$429$	−4.86354	−0.234814
$430$	21.4031	1.03215
$431$	−7.93114	−0.382030	−0.191015	−	0.981587i	$-0.561178\pi$
$431$	−7.93114	−0.382030	−0.191015	+	0.981587i	$0.561178\pi$
$432$	−89.1625	−4.28983
$433$	−17.5130	−0.841622	−0.420811	−	0.907148i	$-0.638254\pi$
$433$	−17.5130	−0.841622	−0.420811	+	0.907148i	$0.638254\pi$
$434$	−7.09291	−0.340470
$435$	−12.6937	−0.608614
$436$	37.5170	1.79674
$437$	8.41603	0.402593
$438$	−5.30759	−0.253606
$439$	−12.9932	−0.620131	−0.310066	−	0.950715i	$-0.600351\pi$
$439$	−12.9932	−0.620131	−0.310066	+	0.950715i	$0.600351\pi$
$440$	3.73313	0.177970
$441$	−42.6912	−2.03291
$442$	22.8695	1.08779
$443$	0.223033	0.0105966	0.00529832	−	0.999986i	$-0.498313\pi$
$443$	0.223033	0.0105966	0.00529832	+	0.999986i	$0.498313\pi$
$444$	−74.2457	−3.52355
$445$	3.93445	0.186511
$446$	−12.4388	−0.588995
$447$	9.24936	0.437480
$448$	−2.44553	−0.115541
$449$	37.3943	1.76474	0.882372	−	0.470552i	$-0.155945\pi$
$449$	37.3943	1.76474	0.882372	+	0.470552i	$0.155945\pi$
$450$	−16.2895	−0.767892
$451$	1.42140	0.0669313
$452$	−25.9101	−1.21871
$453$	1.30368	0.0612521
$454$	−27.4198	−1.28688
$455$	1.35587	0.0635641
$456$	−31.1657	−1.45947
$457$	22.7286	1.06320	0.531600	−	0.846996i	$-0.321591\pi$
$457$	22.7286	1.06320	0.531600	+	0.846996i	$0.321591\pi$
$458$	30.3669	1.41895
$459$	−29.0253	−1.35479
$460$	−27.5947	−1.28661
$461$	22.1669	1.03241	0.516207	−	0.856464i	$-0.327344\pi$
$461$	22.1669	1.03241	0.516207	+	0.856464i	$0.327344\pi$
$462$	1.86102	0.0865826
$463$	27.8894	1.29613	0.648065	−	0.761585i	$-0.275579\pi$
$463$	27.8894	1.29613	0.648065	+	0.761585i	$0.275579\pi$
$464$	37.2127	1.72756
$465$	18.6211	0.863532
$466$	−61.0050	−2.82600
$467$	−3.89609	−0.180289	−0.0901447	−	0.995929i	$-0.528733\pi$
$467$	−3.89609	−0.180289	−0.0901447	+	0.995929i	$0.528733\pi$
$468$	−90.0830	−4.16409
$469$	−2.87290	−0.132658
$470$	27.2147	1.25532
$471$	−38.3119	−1.76532
$472$	−3.30537	−0.152142
$473$	4.34381	0.199729
$474$	−52.7450	−2.42266
$475$	−1.44327	−0.0662219
$476$	−6.15126	−0.281942
$477$	−66.9994	−3.06769
$478$	−11.7314	−0.536580
$479$	−31.2021	−1.42566	−0.712830	−	0.701337i	$-0.752587\pi$
$479$	−31.2021	−1.42566	−0.712830	+	0.701337i	$0.752587\pi$
$480$	27.3862	1.25000
$481$	−15.6180	−0.712118
$482$	72.1688	3.28720
$483$	−7.94248	−0.361395
$484$	−50.7424	−2.30647
$485$	9.02693	0.409892
$486$	13.7976	0.625871
$487$	13.7078	0.621161	0.310581	−	0.950547i	$-0.399477\pi$
$487$	13.7078	0.621161	0.310581	+	0.950547i	$0.399477\pi$
$488$	−7.75477	−0.351042
$489$	58.6390	2.65175
$490$	17.6438	0.797065
$491$	18.7542	0.846367	0.423184	−	0.906044i	$-0.360913\pi$
$491$	18.7542	0.846367	0.423184	+	0.906044i	$0.360913\pi$
$492$	38.9081	1.75411
$493$	12.1140	0.545585
$494$	−11.3547	−0.510874
$495$	−3.30599	−0.148593
$496$	−54.5896	−2.45114
$497$	−1.63635	−0.0734005
$498$	−97.7154	−4.37873
$499$	−13.9627	−0.625058	−0.312529	−	0.949908i	$-0.601176\pi$
$499$	−13.9627	−0.625058	−0.312529	+	0.949908i	$0.601176\pi$
$500$	4.73224	0.211632
$501$	−4.13054	−0.184539
$502$	37.8048	1.68731
$503$	−25.5731	−1.14025	−0.570124	−	0.821559i	$-0.693105\pi$
$503$	−25.5731	−1.14025	−0.570124	+	0.821559i	$0.693105\pi$
$504$	19.9019	0.886501
$505$	0.363640	0.0161818
$506$	−7.96733	−0.354191
$507$	11.5935	0.514885
$508$	14.7765	0.655600
$509$	−20.1717	−0.894095	−0.447048	−	0.894510i	$-0.647525\pi$
$509$	−20.1717	−0.894095	−0.447048	+	0.894510i	$0.647525\pi$
$510$	22.9740	1.01731
$511$	0.300301	0.0132845
$512$	46.3233	2.04722
$513$	14.4111	0.636266
$514$	−67.5829	−2.98096
$515$	2.85316	0.125725
$516$	118.903	5.23441
$517$	5.52328	0.242914
$518$	5.97618	0.262578
$519$	44.0963	1.93561
$520$	21.4955	0.942641
$521$	−1.34970	−0.0591316	−0.0295658	−	0.999563i	$-0.509412\pi$
$521$	−1.34970	−0.0591316	−0.0295658	+	0.999563i	$0.509412\pi$
$522$	−67.8835	−2.97118
$523$	−8.42608	−0.368447	−0.184223	−	0.982884i	$-0.558977\pi$
$523$	−8.42608	−0.368447	−0.184223	+	0.982884i	$0.558977\pi$
$524$	38.1699	1.66746
$525$	1.36206	0.0594453
$526$	8.78833	0.383189
$527$	−17.7707	−0.774103
$528$	14.3231	0.623333
$529$	11.0030	0.478390
$530$	27.6901	1.20278
$531$	2.92717	0.127028
$532$	3.05411	0.132412
$533$	8.18450	0.354510
$534$	31.0951	1.34562
$535$	6.89874	0.298258
$536$	−45.5462	−1.96729
$537$	−24.7063	−1.06616
$538$	−18.7415	−0.808002
$539$	3.58085	0.154238
$540$	−47.2515	−2.03338
$541$	−7.56298	−0.325158	−0.162579	−	0.986696i	$-0.551981\pi$
$541$	−7.56298	−0.325158	−0.162579	+	0.986696i	$0.551981\pi$
$542$	−34.3766	−1.47660
$543$	−31.7523	−1.36262
$544$	−26.1355	−1.12055
$545$	7.92796	0.339597
$546$	10.7158	0.458596
$547$	24.0653	1.02896	0.514479	−	0.857503i	$-0.327985\pi$
$547$	24.0653	1.02896	0.514479	+	0.857503i	$0.327985\pi$
$548$	82.3772	3.51898
$549$	6.86747	0.293096
$550$	1.36633	0.0582603
$551$	−6.01460	−0.256230
$552$	−125.918	−5.35941
$553$	2.98429	0.126905
$554$	73.4146	3.11909
$555$	−15.6893	−0.665975
$556$	−5.30489	−0.224977
$557$	18.9519	0.803017	0.401509	−	0.915855i	$-0.368486\pi$
$557$	18.9519	0.803017	0.401509	+	0.915855i	$0.368486\pi$
$558$	99.5824	4.21566
$559$	25.0118	1.05789
$560$	−3.99303	−0.168736
$561$	4.66264	0.196857
$562$	−36.1432	−1.52461
$563$	43.4991	1.83327	0.916635	−	0.399726i	$-0.130895\pi$
$563$	43.4991	1.83327	0.916635	+	0.399726i	$0.130895\pi$
$564$	151.189	6.36619
$565$	−5.47524	−0.230345
$566$	6.22650	0.261719
$567$	−5.17819	−0.217464
$568$	−25.9423	−1.08851
$569$	−26.3909	−1.10636	−0.553182	−	0.833060i	$-0.686587\pi$
$569$	−26.3909	−1.10636	−0.553182	+	0.833060i	$0.686587\pi$
$570$	−11.4066	−0.477771
$571$	−34.2432	−1.43303	−0.716517	−	0.697570i	$-0.754265\pi$
$571$	−34.2432	−1.43303	−0.716517	+	0.697570i	$0.754265\pi$
$572$	7.55597	0.315931
$573$	−68.9969	−2.88239
$574$	−3.13178	−0.130718
$575$	−5.83121	−0.243178
$576$	34.3346	1.43061
$577$	16.2091	0.674795	0.337397	−	0.941362i	$-0.390453\pi$
$577$	16.2091	0.674795	0.337397	+	0.941362i	$0.390453\pi$
$578$	22.1843	0.922746
$579$	12.6796	0.526948
$580$	19.7208	0.818862
$581$	5.52869	0.229369
$582$	71.3426	2.95725
$583$	5.61977	0.232747
$584$	4.76088	0.197007
$585$	−19.0360	−0.787042
$586$	−3.20994	−0.132601
$587$	−21.7083	−0.895997	−0.447998	−	0.894034i	$-0.647863\pi$
$587$	−21.7083	−0.895997	−0.447998	+	0.894034i	$0.647863\pi$
$588$	98.0184	4.04221
$589$	8.82317	0.363552
$590$	−1.20976	−0.0498052
$591$	4.17256	0.171636
$592$	45.9948	1.89038
$593$	−28.3799	−1.16542	−0.582711	−	0.812680i	$-0.698008\pi$
$593$	−28.3799	−1.16542	−0.582711	+	0.812680i	$0.698008\pi$
$594$	−13.6428	−0.559770
$595$	−1.29986	−0.0532891
$596$	−14.3698	−0.588609
$597$	40.5652	1.66022
$598$	−45.8762	−1.87602
$599$	14.0896	0.575687	0.287844	−	0.957677i	$-0.407062\pi$
$599$	14.0896	0.575687	0.287844	+	0.957677i	$0.407062\pi$
$600$	21.5938	0.881561
$601$	−5.65538	−0.230688	−0.115344	−	0.993326i	$-0.536797\pi$
$601$	−5.65538	−0.230688	−0.115344	+	0.993326i	$0.536797\pi$
$602$	−9.57072	−0.390073
$603$	40.3348	1.64256
$604$	−2.02539	−0.0824119
$605$	−10.7227	−0.435940
$606$	2.87396	0.116747
$607$	−1.22678	−0.0497934	−0.0248967	−	0.999690i	$-0.507926\pi$
$607$	−1.22678	−0.0497934	−0.0248967	+	0.999690i	$0.507926\pi$
$608$	12.9763	0.526258
$609$	5.67617	0.230010
$610$	−2.83824	−0.114917
$611$	31.8033	1.28662
$612$	86.3619	3.49097
$613$	−27.3025	−1.10274	−0.551368	−	0.834262i	$-0.685894\pi$
$613$	−27.3025	−1.10274	−0.551368	+	0.834262i	$0.685894\pi$
$614$	13.8913	0.560607
$615$	8.22191	0.331539
$616$	−1.66933	−0.0672592
$617$	38.1583	1.53620	0.768098	−	0.640332i	$-0.221203\pi$
$617$	38.1583	1.53620	0.768098	+	0.640332i	$0.221203\pi$
$618$	22.5494	0.907069
$619$	−2.56929	−0.103268	−0.0516341	−	0.998666i	$-0.516443\pi$
$619$	−2.56929	−0.103268	−0.0516341	+	0.998666i	$0.516443\pi$
$620$	−28.9296	−1.16184
$621$	58.2247	2.33647
$622$	−31.4029	−1.25914
$623$	−1.75935	−0.0704868
$624$	82.4730	3.30156
$625$	1.00000	0.0400000
$626$	77.9501	3.11551
$627$	−2.31501	−0.0924524
$628$	59.5213	2.37516
$629$	14.9728	0.597006
$630$	7.28409	0.290205
$631$	12.0819	0.480972	0.240486	−	0.970653i	$-0.422693\pi$
$631$	12.0819	0.480972	0.240486	+	0.970653i	$0.422693\pi$
$632$	47.3120	1.88197
$633$	66.0794	2.62642
$634$	0.441033	0.0175157
$635$	3.12251	0.123913
$636$	153.830	6.09975
$637$	20.6187	0.816941
$638$	5.69393	0.225425
$639$	22.9740	0.908836
$640$	3.79167	0.149879
$641$	−8.41522	−0.332381	−0.166191	−	0.986094i	$-0.553147\pi$
$641$	−8.41522	−0.332381	−0.166191	+	0.986094i	$0.553147\pi$
$642$	54.5228	2.15184
$643$	6.45576	0.254590	0.127295	−	0.991865i	$-0.459370\pi$
$643$	6.45576	0.254590	0.127295	+	0.991865i	$0.459370\pi$
$644$	12.3394	0.486240
$645$	25.1261	0.989340
$646$	10.8857	0.428293
$647$	4.47445	0.175909	0.0879544	−	0.996125i	$-0.471967\pi$
$647$	4.47445	0.175909	0.0879544	+	0.996125i	$0.471967\pi$
$648$	−82.0936	−3.22494
$649$	−0.245525	−0.00963768
$650$	7.86736	0.308583
$651$	−8.32671	−0.326349
$652$	−91.1013	−3.56780
$653$	16.4975	0.645598	0.322799	−	0.946468i	$-0.395376\pi$
$653$	16.4975	0.645598	0.322799	+	0.946468i	$0.395376\pi$
$654$	62.6571	2.45009
$655$	8.06592	0.315162
$656$	−24.1033	−0.941077
$657$	−4.21614	−0.164487
$658$	−12.1695	−0.474415
$659$	44.7558	1.74344	0.871720	−	0.490004i	$-0.163005\pi$
$659$	44.7558	1.74344	0.871720	+	0.490004i	$0.163005\pi$
$660$	7.59050	0.295460
$661$	38.6038	1.50151	0.750756	−	0.660579i	$-0.229689\pi$
$661$	38.6038	1.50151	0.750756	+	0.660579i	$0.229689\pi$
$662$	22.3553	0.868863
$663$	26.8476	1.04268
$664$	87.6503	3.40149
$665$	0.645382	0.0250269
$666$	−83.9039	−3.25121
$667$	−24.3006	−0.940922
$668$	6.41720	0.248289
$669$	−14.6025	−0.564567
$670$	−16.6699	−0.644014
$671$	−0.576029	−0.0222373
$672$	−12.2461	−0.472405
$673$	26.6709	1.02809	0.514045	−	0.857763i	$-0.328147\pi$
$673$	26.6709	1.02809	0.514045	+	0.857763i	$0.328147\pi$
$674$	34.2702	1.32004
$675$	−9.98501	−0.384323
$676$	−18.0116	−0.692754
$677$	37.5231	1.44213	0.721065	−	0.692867i	$-0.243653\pi$
$677$	37.5231	1.44213	0.721065	+	0.692867i	$0.243653\pi$
$678$	−43.2725	−1.66187
$679$	−4.03653	−0.154908
$680$	−20.6076	−0.790266
$681$	−32.1895	−1.23350
$682$	−8.35276	−0.319844
$683$	6.46157	0.247245	0.123623	−	0.992329i	$-0.460549\pi$
$683$	6.46157	0.247245	0.123623	+	0.992329i	$0.460549\pi$
$684$	−42.8788	−1.63951
$685$	17.4076	0.665112
$686$	−16.0114	−0.611317
$687$	35.6492	1.36010
$688$	−73.6597	−2.80825
$689$	32.3589	1.23277
$690$	−46.0858	−1.75446
$691$	9.59956	0.365184	0.182592	−	0.983189i	$-0.441551\pi$
$691$	9.59956	0.365184	0.182592	+	0.983189i	$0.441551\pi$
$692$	−68.5079	−2.60428
$693$	1.47832	0.0561569
$694$	−37.5958	−1.42712
$695$	−1.12101	−0.0425223
$696$	89.9883	3.41100
$697$	−7.84642	−0.297205
$698$	7.87954	0.298245
$699$	−71.6168	−2.70880
$700$	−2.11610	−0.0799809
$701$	−30.7087	−1.15985	−0.579926	−	0.814669i	$-0.696919\pi$
$701$	−30.7087	−1.15985	−0.579926	+	0.814669i	$0.696919\pi$
$702$	−78.5556	−2.96489
$703$	−7.43403	−0.280380
$704$	−2.87991	−0.108541
$705$	31.9486	1.20325
$706$	2.06938	0.0778822
$707$	−0.162607	−0.00611548
$708$	−6.72073	−0.252581
$709$	16.5207	0.620449	0.310224	−	0.950663i	$-0.399596\pi$
$709$	16.5207	0.620449	0.310224	+	0.950663i	$0.399596\pi$
$710$	−9.49487	−0.356336
$711$	−41.8986	−1.57132
$712$	−27.8922	−1.04530
$713$	35.6479	1.33503
$714$	−10.2732	−0.384465
$715$	1.59670	0.0597132
$716$	38.3836	1.43446
$717$	−13.7720	−0.514326
$718$	2.96411	0.110620
$719$	31.9748	1.19246	0.596230	−	0.802814i	$-0.296665\pi$
$719$	31.9748	1.19246	0.596230	+	0.802814i	$0.296665\pi$
$720$	56.0610	2.08927
$721$	−1.27583	−0.0475145
$722$	43.8937	1.63355
$723$	84.7225	3.15086
$724$	49.3303	1.83335
$725$	4.16733	0.154771
$726$	−84.7448	−3.14517
$727$	0.587554	0.0217912	0.0108956	−	0.999941i	$-0.496532\pi$
$727$	0.587554	0.0217912	0.0108956	+	0.999941i	$0.496532\pi$
$728$	−9.61206	−0.356247
$729$	−18.5424	−0.686757
$730$	1.74248	0.0644921
$731$	−23.9786	−0.886882
$732$	−15.7676	−0.582788
$733$	45.0404	1.66361	0.831803	−	0.555071i	$-0.187309\pi$
$733$	45.0404	1.66361	0.831803	+	0.555071i	$0.187309\pi$
$734$	−0.544875	−0.0201117
$735$	20.7129	0.764006
$736$	52.4277	1.93251
$737$	−3.38319	−0.124622
$738$	43.9694	1.61853
$739$	0.119486	0.00439536	0.00219768	−	0.999998i	$-0.499300\pi$
$739$	0.119486	0.00439536	0.00219768	+	0.999998i	$0.499300\pi$
$740$	24.3749	0.896038
$741$	−13.3299	−0.489686
$742$	−12.3821	−0.454560
$743$	−24.1611	−0.886385	−0.443193	−	0.896426i	$-0.646154\pi$
$743$	−24.1611	−0.886385	−0.443193	+	0.896426i	$0.646154\pi$
$744$	−132.009	−4.83969
$745$	−3.03657	−0.111251
$746$	−36.1854	−1.32484
$747$	−77.6213	−2.84001
$748$	−7.24385	−0.264862
$749$	−3.08488	−0.112719
$750$	7.90331	0.288588
$751$	17.5941	0.642017	0.321008	−	0.947076i	$-0.395978\pi$
$751$	17.5941	0.642017	0.321008	+	0.947076i	$0.395978\pi$
$752$	−93.6606	−3.41545
$753$	44.3809	1.61733
$754$	32.7859	1.19399
$755$	−0.427998	−0.0155764
$756$	21.1292	0.768463
$757$	25.7937	0.937490	0.468745	−	0.883334i	$-0.344706\pi$
$757$	25.7937	0.937490	0.468745	+	0.883334i	$0.344706\pi$
$758$	24.1417	0.876865
$759$	−9.35323	−0.339501
$760$	10.2317	0.371143
$761$	−11.3894	−0.412864	−0.206432	−	0.978461i	$-0.566185\pi$
$761$	−11.3894	−0.412864	−0.206432	+	0.978461i	$0.566185\pi$
$762$	24.6782	0.893995
$763$	−3.54511	−0.128342
$764$	107.193	3.87812
$765$	18.2497	0.659818
$766$	82.1258	2.96732
$767$	−1.41374	−0.0510472
$768$	63.2836	2.28355
$769$	−43.2041	−1.55798	−0.778991	−	0.627036i	$-0.784268\pi$
$769$	−43.2041	−1.55798	−0.778991	+	0.627036i	$0.784268\pi$
$770$	−0.610974	−0.0220180
$771$	−79.3389	−2.85732
$772$	−19.6990	−0.708984
$773$	−8.10310	−0.291448	−0.145724	−	0.989325i	$-0.546551\pi$
$773$	−8.10310	−0.291448	−0.145724	+	0.989325i	$0.546551\pi$
$774$	134.370	4.82984
$775$	−6.11330	−0.219596
$776$	−63.9940	−2.29725
$777$	7.01573	0.251688
$778$	93.0221	3.33500
$779$	3.89576	0.139580
$780$	43.7064	1.56494
$781$	−1.92701	−0.0689537
$782$	43.9812	1.57276
$783$	−41.6108	−1.48705
$784$	−60.7219	−2.16864
$785$	12.5778	0.448921
$786$	63.7475	2.27380
$787$	14.7698	0.526486	0.263243	−	0.964730i	$-0.415208\pi$
$787$	14.7698	0.526486	0.263243	+	0.964730i	$0.415208\pi$
$788$	−6.48246	−0.230928
$789$	10.3170	0.367297
$790$	17.3162	0.616082
$791$	2.44834	0.0870529
$792$	23.4369	0.832794
$793$	−3.31680	−0.117783
$794$	35.1040	1.24579
$795$	32.5067	1.15290
$796$	−63.0219	−2.23375
$797$	−36.2454	−1.28388	−0.641939	−	0.766755i	$-0.721870\pi$
$797$	−36.2454	−1.28388	−0.641939	+	0.766755i	$0.721870\pi$
$798$	5.10066	0.180561
$799$	−30.4896	−1.07864
$800$	−8.99088	−0.317875
$801$	24.7008	0.872759
$802$	−19.1787	−0.677222
$803$	0.353641	0.0124797
$804$	−92.6080	−3.26603
$805$	2.60752	0.0919029
$806$	−48.0955	−1.69409
$807$	−22.0015	−0.774490
$808$	−2.57793	−0.0906912
$809$	−3.82482	−0.134473	−0.0672367	−	0.997737i	$-0.521418\pi$
$809$	−3.82482	−0.134473	−0.0672367	+	0.997737i	$0.521418\pi$
$810$	−30.0462	−1.05572
$811$	16.9602	0.595554	0.297777	−	0.954636i	$-0.403755\pi$
$811$	16.9602	0.595554	0.297777	+	0.954636i	$0.403755\pi$
$812$	−8.81847	−0.309468
$813$	−40.3563	−1.41536
$814$	7.03768	0.246671
$815$	−19.2512	−0.674339
$816$	−79.0662	−2.76787
$817$	11.9054	0.416518
$818$	−16.2959	−0.569774
$819$	8.51224	0.297442
$820$	−12.7735	−0.446071
$821$	45.0003	1.57052	0.785261	−	0.619165i	$-0.212529\pi$
$821$	45.0003	1.57052	0.785261	+	0.619165i	$0.212529\pi$
$822$	137.578	4.79858
$823$	24.9823	0.870830	0.435415	−	0.900230i	$-0.356602\pi$
$823$	24.9823	0.870830	0.435415	+	0.900230i	$0.356602\pi$
$824$	−20.2267	−0.704630
$825$	1.60400	0.0558440
$826$	0.540965	0.0188226
$827$	−26.9876	−0.938452	−0.469226	−	0.883078i	$-0.655467\pi$
$827$	−26.9876	−0.938452	−0.469226	+	0.883078i	$0.655467\pi$
$828$	−173.242	−6.02056
$829$	32.4619	1.12745	0.563723	−	0.825964i	$-0.309368\pi$
$829$	32.4619	1.12745	0.563723	+	0.825964i	$0.309368\pi$
$830$	32.0800	1.11351
$831$	86.1849	2.98972
$832$	−16.5826	−0.574900
$833$	−19.7670	−0.684885
$834$	−8.85968	−0.306786
$835$	1.35606	0.0469283
$836$	3.59658	0.124390
$837$	61.0414	2.10990
$838$	−7.08670	−0.244806
$839$	−43.1730	−1.49050	−0.745249	−	0.666786i	$-0.767670\pi$
$839$	−43.1730	−1.49050	−0.745249	+	0.666786i	$0.767670\pi$
$840$	−9.65599	−0.333163
$841$	−11.6334	−0.401151
$842$	3.84688	0.132572
$843$	−42.4303	−1.46138
$844$	−102.661	−3.53373
$845$	−3.80614	−0.130935
$846$	170.856	5.87414
$847$	4.79482	0.164752
$848$	−95.2968	−3.27250
$849$	7.30959	0.250865
$850$	−7.54238	−0.258701
$851$	−30.0354	−1.02960
$852$	−52.7479	−1.80711
$853$	22.1495	0.758385	0.379193	−	0.925318i	$-0.376202\pi$
$853$	22.1495	0.758385	0.379193	+	0.925318i	$0.376202\pi$
$854$	1.26917	0.0434299
$855$	−9.06099	−0.309879
$856$	−48.9067	−1.67160
$857$	−17.0655	−0.582947	−0.291474	−	0.956579i	$-0.594146\pi$
$857$	−17.0655	−0.582947	−0.291474	+	0.956579i	$0.594146\pi$
$858$	12.6192	0.430813
$859$	12.8417	0.438152	0.219076	−	0.975708i	$-0.429696\pi$
$859$	12.8417	0.438152	0.219076	+	0.975708i	$0.429696\pi$
$860$	−39.0358	−1.33111
$861$	−3.67655	−0.125297
$862$	20.5786	0.700910
$863$	37.3315	1.27078	0.635389	−	0.772192i	$-0.280840\pi$
$863$	37.3315	1.27078	0.635389	+	0.772192i	$0.280840\pi$
$864$	89.7740	3.05417
$865$	−14.4768	−0.492227
$866$	45.4403	1.54412
$867$	26.0432	0.884475
$868$	12.9363	0.439088
$869$	3.51436	0.119217
$870$	32.9357	1.11662
$871$	−19.4806	−0.660074
$872$	−56.2032	−1.90328
$873$	56.6718	1.91805
$874$	−21.8367	−0.738637
$875$	−0.447166	−0.0151170
$876$	9.68019	0.327063
$877$	−20.9514	−0.707477	−0.353738	−	0.935344i	$-0.615090\pi$
$877$	−20.9514	−0.707477	−0.353738	+	0.935344i	$0.615090\pi$
$878$	33.7129	1.13775
$879$	−3.76830	−0.127102
$880$	−4.70228	−0.158514
$881$	31.8826	1.07415	0.537076	−	0.843534i	$-0.319529\pi$
$881$	31.8826	1.07415	0.537076	+	0.843534i	$0.319529\pi$
$882$	110.769	3.72979
$883$	−34.9160	−1.17502	−0.587508	−	0.809218i	$-0.699891\pi$
$883$	−34.9160	−1.17502	−0.587508	+	0.809218i	$0.699891\pi$
$884$	−41.7104	−1.40287
$885$	−1.42020	−0.0477395
$886$	−0.578695	−0.0194416
$887$	−17.6502	−0.592636	−0.296318	−	0.955089i	$-0.595759\pi$
$887$	−17.6502	−0.592636	−0.296318	+	0.955089i	$0.595759\pi$
$888$	111.225	3.73248
$889$	−1.39628	−0.0468297
$890$	−10.2085	−0.342191
$891$	−6.09795	−0.204289
$892$	22.6864	0.759598
$893$	15.1381	0.506578
$894$	−23.9989	−0.802644
$895$	8.11108	0.271123
$896$	−1.69551	−0.0566429
$897$	−53.8563	−1.79821
$898$	−97.0253	−3.23777
$899$	−25.4761	−0.849677
$900$	29.7094	0.990313
$901$	−31.0222	−1.03350
$902$	−3.68806	−0.122799
$903$	−11.2355	−0.373895
$904$	38.8152	1.29098
$905$	10.4243	0.346515
$906$	−3.38260	−0.112379
$907$	50.3820	1.67291	0.836454	−	0.548037i	$-0.184625\pi$
$907$	50.3820	1.67291	0.836454	+	0.548037i	$0.184625\pi$
$908$	50.0094	1.65962
$909$	2.28296	0.0757210
$910$	−3.51801	−0.116621
$911$	−5.46932	−0.181207	−0.0906034	−	0.995887i	$-0.528880\pi$
$911$	−5.46932	−0.181207	−0.0906034	+	0.995887i	$0.528880\pi$
$912$	39.2565	1.29991
$913$	6.51071	0.215473
$914$	−58.9729	−1.95065
$915$	−3.33195	−0.110151
$916$	−55.3845	−1.82995
$917$	−3.60680	−0.119107
$918$	75.3107	2.48562
$919$	−21.1968	−0.699216	−0.349608	−	0.936896i	$-0.613685\pi$
$919$	−21.1968	−0.699216	−0.349608	+	0.936896i	$0.613685\pi$
$920$	41.3388	1.36290
$921$	16.3077	0.537356
$922$	−57.5154	−1.89417
$923$	−11.0958	−0.365222
$924$	−3.39421	−0.111661
$925$	5.15081	0.169358
$926$	−72.3634	−2.37801
$927$	17.9123	0.588318
$928$	−37.4679	−1.22995
$929$	−14.8202	−0.486236	−0.243118	−	0.969997i	$-0.578170\pi$
$929$	−14.8202	−0.486236	−0.243118	+	0.969997i	$0.578170\pi$
$930$	−48.3153	−1.58432
$931$	9.81432	0.321651
$932$	111.264	3.64456
$933$	−36.8654	−1.20692
$934$	10.1090	0.330777
$935$	−1.53074	−0.0500607
$936$	134.951	4.41100
$937$	43.9141	1.43461	0.717305	−	0.696759i	$-0.245375\pi$
$937$	43.9141	1.43461	0.717305	+	0.696759i	$0.245375\pi$
$938$	7.45420	0.243388
$939$	91.5095	2.98630
$940$	−49.6352	−1.61892
$941$	2.93756	0.0957616	0.0478808	−	0.998853i	$-0.484753\pi$
$941$	2.93756	0.0957616	0.0478808	+	0.998853i	$0.484753\pi$
$942$	99.4063	3.23883
$943$	15.7399	0.512562
$944$	4.16346	0.135509
$945$	4.46495	0.145245
$946$	−11.2707	−0.366442
$947$	9.95436	0.323473	0.161737	−	0.986834i	$-0.448291\pi$
$947$	9.95436	0.323473	0.161737	+	0.986834i	$0.448291\pi$
$948$	96.1985	3.12438
$949$	2.03628	0.0661004
$950$	3.74480	0.121497
$951$	0.517750	0.0167892
$952$	9.21501	0.298660
$953$	51.4352	1.66615	0.833074	−	0.553161i	$-0.186579\pi$
$953$	51.4352	1.66615	0.833074	+	0.553161i	$0.186579\pi$
$954$	173.841	5.62830
$955$	22.6517	0.732992
$956$	21.3962	0.692001
$957$	6.68438	0.216075
$958$	80.9587	2.61566
$959$	−7.78410	−0.251362
$960$	−16.6584	−0.537648
$961$	6.37247	0.205564
$962$	40.5232	1.30652
$963$	43.3108	1.39567
$964$	−131.625	−4.23934
$965$	−4.16273	−0.134003
$966$	20.6080	0.663052
$967$	−55.9389	−1.79887	−0.899437	−	0.437050i	$-0.856023\pi$
$967$	−55.9389	−1.79887	−0.899437	+	0.437050i	$0.856023\pi$
$968$	76.0157	2.44324
$969$	12.7793	0.410529
$970$	−23.4218	−0.752028
$971$	39.8119	1.27763	0.638813	−	0.769362i	$-0.279426\pi$
$971$	39.8119	1.27763	0.638813	+	0.769362i	$0.279426\pi$
$972$	−25.1646	−0.807156
$973$	0.501277	0.0160702
$974$	−35.5671	−1.13964
$975$	9.23587	0.295785
$976$	9.76795	0.312665
$977$	20.3296	0.650402	0.325201	−	0.945645i	$-0.394568\pi$
$977$	20.3296	0.650402	0.325201	+	0.945645i	$0.394568\pi$
$978$	−152.148	−4.86516
$979$	−2.07185	−0.0662166
$980$	−32.1795	−1.02793
$981$	49.7724	1.58911
$982$	−48.6608	−1.55283
$983$	−23.6556	−0.754496	−0.377248	−	0.926112i	$-0.623130\pi$
$983$	−23.6556	−0.754496	−0.377248	+	0.926112i	$0.623130\pi$
$984$	−58.2870	−1.85812
$985$	−1.36985	−0.0436471
$986$	−31.4316	−1.00099
$987$	−14.2863	−0.454739
$988$	20.7093	0.658849
$989$	48.1011	1.52953
$990$	8.57790	0.272624
$991$	−46.1214	−1.46509	−0.732547	−	0.680716i	$-0.761669\pi$
$991$	−46.1214	−1.46509	−0.732547	+	0.680716i	$0.761669\pi$
$992$	54.9639	1.74511
$993$	26.2440	0.832827
$994$	4.24578	0.134668
$995$	−13.3176	−0.422195
$996$	178.217	5.64703
$997$	16.9418	0.536551	0.268275	−	0.963342i	$-0.413546\pi$
$997$	16.9418	0.536551	0.268275	+	0.963342i	$0.413546\pi$
$998$	36.2285	1.14679
$999$	−51.4309	−1.62720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.7	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.59466 q^{2} -3.04599 q^{3} +4.73224 q^{4} +1.00000 q^{5} +7.90331 q^{6} -0.447166 q^{7} -7.08923 q^{8} +6.27808 q^{9} +O(q^{10})\)	\(q-2.59466 q^{2} -3.04599 q^{3} +4.73224 q^{4} +1.00000 q^{5} +7.90331 q^{6} -0.447166 q^{7} -7.08923 q^{8} +6.27808 q^{9} -2.59466 q^{10} -0.526592 q^{11} -14.4144 q^{12} -3.03214 q^{13} +1.16024 q^{14} -3.04599 q^{15} +8.92964 q^{16} +2.90689 q^{17} -16.2895 q^{18} -1.44327 q^{19} +4.73224 q^{20} +1.36206 q^{21} +1.36633 q^{22} -5.83121 q^{23} +21.5938 q^{24} +1.00000 q^{25} +7.86736 q^{26} -9.98501 q^{27} -2.11610 q^{28} +4.16733 q^{29} +7.90331 q^{30} -6.11330 q^{31} -8.99088 q^{32} +1.60400 q^{33} -7.54238 q^{34} -0.447166 q^{35} +29.7094 q^{36} +5.15081 q^{37} +3.74480 q^{38} +9.23587 q^{39} -7.08923 q^{40} -2.69925 q^{41} -3.53409 q^{42} -8.24891 q^{43} -2.49196 q^{44} +6.27808 q^{45} +15.1300 q^{46} -10.4887 q^{47} -27.1996 q^{48} -6.80004 q^{49} -2.59466 q^{50} -8.85436 q^{51} -14.3488 q^{52} -10.6720 q^{53} +25.9077 q^{54} -0.526592 q^{55} +3.17006 q^{56} +4.39620 q^{57} -10.8128 q^{58} +0.466252 q^{59} -14.4144 q^{60} +1.09388 q^{61} +15.8619 q^{62} -2.80734 q^{63} +5.46896 q^{64} -3.03214 q^{65} -4.16182 q^{66} +6.42470 q^{67} +13.7561 q^{68} +17.7618 q^{69} +1.16024 q^{70} +3.65939 q^{71} -44.5068 q^{72} -0.671565 q^{73} -13.3646 q^{74} -3.04599 q^{75} -6.82992 q^{76} +0.235474 q^{77} -23.9639 q^{78} -6.67379 q^{79} +8.92964 q^{80} +11.5800 q^{81} +7.00363 q^{82} -12.3639 q^{83} +6.44562 q^{84} +2.90689 q^{85} +21.4031 q^{86} -12.6937 q^{87} +3.73313 q^{88} +3.93445 q^{89} -16.2895 q^{90} +1.35587 q^{91} -27.5947 q^{92} +18.6211 q^{93} +27.2147 q^{94} -1.44327 q^{95} +27.3862 q^{96} +9.02693 q^{97} +17.6438 q^{98} -3.30599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 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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