LMFDB - Embedded newform 8035.2.a.d.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:	$1$
Dimension:	$140$
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)

$f(q)$	$=$	$q-2.70407 q^{2} -1.94382 q^{3} +5.31198 q^{4} -1.00000 q^{5} +5.25623 q^{6} -4.62711 q^{7} -8.95580 q^{8} +0.778451 q^{9} +O(q^{10})$	\(q-2.70407 q^{2} -1.94382 q^{3} +5.31198 q^{4} -1.00000 q^{5} +5.25623 q^{6} -4.62711 q^{7} -8.95580 q^{8} +0.778451 q^{9} +2.70407 q^{10} -5.66830 q^{11} -10.3255 q^{12} -2.68098 q^{13} +12.5120 q^{14} +1.94382 q^{15} +13.5931 q^{16} +3.56729 q^{17} -2.10498 q^{18} +2.05675 q^{19} -5.31198 q^{20} +8.99429 q^{21} +15.3275 q^{22} -7.42227 q^{23} +17.4085 q^{24} +1.00000 q^{25} +7.24955 q^{26} +4.31830 q^{27} -24.5791 q^{28} -5.99990 q^{29} -5.25623 q^{30} +2.66060 q^{31} -18.8451 q^{32} +11.0182 q^{33} -9.64619 q^{34} +4.62711 q^{35} +4.13511 q^{36} -4.95311 q^{37} -5.56159 q^{38} +5.21136 q^{39} +8.95580 q^{40} -5.55037 q^{41} -24.3211 q^{42} -11.0930 q^{43} -30.1099 q^{44} -0.778451 q^{45} +20.0703 q^{46} +2.15138 q^{47} -26.4227 q^{48} +14.4101 q^{49} -2.70407 q^{50} -6.93418 q^{51} -14.2413 q^{52} -12.2741 q^{53} -11.6770 q^{54} +5.66830 q^{55} +41.4395 q^{56} -3.99796 q^{57} +16.2241 q^{58} +10.5191 q^{59} +10.3255 q^{60} -11.9526 q^{61} -7.19443 q^{62} -3.60198 q^{63} +23.7722 q^{64} +2.68098 q^{65} -29.7939 q^{66} +5.77467 q^{67} +18.9494 q^{68} +14.4276 q^{69} -12.5120 q^{70} -1.23348 q^{71} -6.97165 q^{72} -10.0104 q^{73} +13.3935 q^{74} -1.94382 q^{75} +10.9254 q^{76} +26.2279 q^{77} -14.0919 q^{78} +15.5007 q^{79} -13.5931 q^{80} -10.7294 q^{81} +15.0086 q^{82} -4.08411 q^{83} +47.7774 q^{84} -3.56729 q^{85} +29.9963 q^{86} +11.6628 q^{87} +50.7642 q^{88} +14.6258 q^{89} +2.10498 q^{90} +12.4052 q^{91} -39.4269 q^{92} -5.17173 q^{93} -5.81748 q^{94} -2.05675 q^{95} +36.6316 q^{96} +13.1275 q^{97} -38.9660 q^{98} -4.41249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.70407	−1.91206	−0.956032	−	0.293263i	$-0.905259\pi$
$2$	−2.70407	−1.91206	−0.956032	+	0.293263i	$0.905259\pi$
$3$	−1.94382	−1.12227	−0.561134	−	0.827725i	$-0.689635\pi$
$3$	−1.94382	−1.12227	−0.561134	+	0.827725i	$0.689635\pi$
$4$	5.31198	2.65599
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	5.25623	2.14585
$7$	−4.62711	−1.74888	−0.874442	−	0.485131i	$-0.838772\pi$
$7$	−4.62711	−1.74888	−0.874442	+	0.485131i	$0.838772\pi$
$8$	−8.95580	−3.16635
$9$	0.778451	0.259484
$10$	2.70407	0.855101
$11$	−5.66830	−1.70906	−0.854529	−	0.519404i	$-0.826154\pi$
$11$	−5.66830	−1.70906	−0.854529	+	0.519404i	$0.826154\pi$
$12$	−10.3255	−2.98073
$13$	−2.68098	−0.743571	−0.371785	−	0.928319i	$-0.621254\pi$
$13$	−2.68098	−0.743571	−0.371785	+	0.928319i	$0.621254\pi$
$14$	12.5120	3.34398
$15$	1.94382	0.501893
$16$	13.5931	3.39828
$17$	3.56729	0.865195	0.432597	−	0.901587i	$-0.357597\pi$
$17$	3.56729	0.865195	0.432597	+	0.901587i	$0.357597\pi$
$18$	−2.10498	−0.496149
$19$	2.05675	0.471851	0.235925	−	0.971771i	$-0.424188\pi$
$19$	2.05675	0.471851	0.235925	+	0.971771i	$0.424188\pi$
$20$	−5.31198	−1.18779
$21$	8.99429	1.96271
$22$	15.3275	3.26783
$23$	−7.42227	−1.54765	−0.773825	−	0.633400i	$-0.781659\pi$
$23$	−7.42227	−1.54765	−0.773825	+	0.633400i	$0.781659\pi$
$24$	17.4085	3.55350
$25$	1.00000	0.200000
$26$	7.24955	1.42175
$27$	4.31830	0.831057
$28$	−24.5791	−4.64501
$29$	−5.99990	−1.11415	−0.557077	−	0.830461i	$-0.688077\pi$
$29$	−5.99990	−1.11415	−0.557077	+	0.830461i	$0.688077\pi$
$30$	−5.25623	−0.959652
$31$	2.66060	0.477857	0.238929	−	0.971037i	$-0.423204\pi$
$31$	2.66060	0.477857	0.238929	+	0.971037i	$0.423204\pi$
$32$	−18.8451	−3.33138
$33$	11.0182	1.91802
$34$	−9.64619	−1.65431
$35$	4.62711	0.782124
$36$	4.13511	0.689185
$37$	−4.95311	−0.814286	−0.407143	−	0.913365i	$-0.633475\pi$
$37$	−4.95311	−0.814286	−0.407143	+	0.913365i	$0.633475\pi$
$38$	−5.56159	−0.902209
$39$	5.21136	0.834485
$40$	8.95580	1.41604
$41$	−5.55037	−0.866821	−0.433411	−	0.901197i	$-0.642690\pi$
$41$	−5.55037	−0.866821	−0.433411	+	0.901197i	$0.642690\pi$
$42$	−24.3211	−3.75283
$43$	−11.0930	−1.69167	−0.845836	−	0.533442i	$-0.820898\pi$
$43$	−11.0930	−1.69167	−0.845836	+	0.533442i	$0.820898\pi$
$44$	−30.1099	−4.53924
$45$	−0.778451	−0.116045
$46$	20.0703	2.95920
$47$	2.15138	0.313811	0.156906	−	0.987614i	$-0.449848\pi$
$47$	2.15138	0.313811	0.156906	+	0.987614i	$0.449848\pi$
$48$	−26.4227	−3.81378
$49$	14.4101	2.05859
$50$	−2.70407	−0.382413
$51$	−6.93418	−0.970980
$52$	−14.2413	−1.97491
$53$	−12.2741	−1.68598	−0.842991	−	0.537928i	$-0.819207\pi$
$53$	−12.2741	−1.68598	−0.842991	+	0.537928i	$0.819207\pi$
$54$	−11.6770	−1.58903
$55$	5.66830	0.764314
$56$	41.4395	5.53758
$57$	−3.99796	−0.529543
$58$	16.2241	2.13033
$59$	10.5191	1.36947	0.684737	−	0.728791i	$-0.259917\pi$
$59$	10.5191	1.36947	0.684737	+	0.728791i	$0.259917\pi$
$60$	10.3255	1.33302
$61$	−11.9526	−1.53038	−0.765189	−	0.643806i	$-0.777354\pi$
$61$	−11.9526	−1.53038	−0.765189	+	0.643806i	$0.777354\pi$
$62$	−7.19443	−0.913693
$63$	−3.60198	−0.453806
$64$	23.7722	2.97153
$65$	2.68098	0.332535
$66$	−29.7939	−3.66737
$67$	5.77467	0.705488	0.352744	−	0.935720i	$-0.385249\pi$
$67$	5.77467	0.705488	0.352744	+	0.935720i	$0.385249\pi$
$68$	18.9494	2.29795
$69$	14.4276	1.73688
$70$	−12.5120	−1.49547
$71$	−1.23348	−0.146387	−0.0731937	−	0.997318i	$-0.523319\pi$
$71$	−1.23348	−0.146387	−0.0731937	+	0.997318i	$0.523319\pi$
$72$	−6.97165	−0.821617
$73$	−10.0104	−1.17163	−0.585815	−	0.810445i	$-0.699226\pi$
$73$	−10.0104	−1.17163	−0.585815	+	0.810445i	$0.699226\pi$
$74$	13.3935	1.55697
$75$	−1.94382	−0.224453
$76$	10.9254	1.25323
$77$	26.2279	2.98894
$78$	−14.0919	−1.59559
$79$	15.5007	1.74397	0.871984	−	0.489535i	$-0.162833\pi$
$79$	15.5007	1.74397	0.871984	+	0.489535i	$0.162833\pi$
$80$	−13.5931	−1.51976
$81$	−10.7294	−1.19215
$82$	15.0086	1.65742
$83$	−4.08411	−0.448290	−0.224145	−	0.974556i	$-0.571959\pi$
$83$	−4.08411	−0.448290	−0.224145	+	0.974556i	$0.571959\pi$
$84$	47.7774	5.21294
$85$	−3.56729	−0.386927
$86$	29.9963	3.23459
$87$	11.6628	1.25038
$88$	50.7642	5.41148
$89$	14.6258	1.55033	0.775164	−	0.631761i	$-0.217667\pi$
$89$	14.6258	1.55033	0.775164	+	0.631761i	$0.217667\pi$
$90$	2.10498	0.221885
$91$	12.4052	1.30042
$92$	−39.4269	−4.11054
$93$	−5.17173	−0.536283
$94$	−5.81748	−0.600027
$95$	−2.05675	−0.211018
$96$	36.6316	3.73870
$97$	13.1275	1.33290	0.666450	−	0.745550i	$-0.267813\pi$
$97$	13.1275	1.33290	0.666450	+	0.745550i	$0.267813\pi$
$98$	−38.9660	−3.93616
$99$	−4.41249	−0.443472
$100$	5.31198	0.531198
$101$	−13.4871	−1.34202	−0.671009	−	0.741449i	$-0.734139\pi$
$101$	−13.4871	−1.34202	−0.671009	+	0.741449i	$0.734139\pi$
$102$	18.7505	1.85658
$103$	11.1202	1.09570	0.547852	−	0.836575i	$-0.315446\pi$
$103$	11.1202	1.09570	0.547852	+	0.836575i	$0.315446\pi$
$104$	24.0103	2.35441
$105$	−8.99429	−0.877752
$106$	33.1901	3.22371
$107$	1.72016	0.166294	0.0831470	−	0.996537i	$-0.473503\pi$
$107$	1.72016	0.166294	0.0831470	+	0.996537i	$0.473503\pi$
$108$	22.9387	2.20728
$109$	−8.98407	−0.860518	−0.430259	−	0.902705i	$-0.641578\pi$
$109$	−8.98407	−0.860518	−0.430259	+	0.902705i	$0.641578\pi$
$110$	−15.3275	−1.46142
$111$	9.62796	0.913846
$112$	−62.8969	−5.94320
$113$	6.39683	0.601763	0.300882	−	0.953662i	$-0.402719\pi$
$113$	6.39683	0.601763	0.300882	+	0.953662i	$0.402719\pi$
$114$	10.8107	1.01252
$115$	7.42227	0.692130
$116$	−31.8713	−2.95918
$117$	−2.08701	−0.192944
$118$	−28.4444	−2.61852
$119$	−16.5062	−1.51312
$120$	−17.4085	−1.58917
$121$	21.1296	1.92088
$122$	32.3207	2.92618
$123$	10.7889	0.972805
$124$	14.1330	1.26918
$125$	−1.00000	−0.0894427
$126$	9.73998	0.867707
$127$	18.8827	1.67557	0.837785	−	0.546001i	$-0.183850\pi$
$127$	18.8827	1.67557	0.837785	+	0.546001i	$0.183850\pi$
$128$	−26.5914	−2.35037
$129$	21.5629	1.89851
$130$	−7.24955	−0.635828
$131$	−16.2010	−1.41549	−0.707744	−	0.706469i	$-0.750287\pi$
$131$	−16.2010	−1.41549	−0.707744	+	0.706469i	$0.750287\pi$
$132$	58.5283	5.09423
$133$	−9.51681	−0.825212
$134$	−15.6151	−1.34894
$135$	−4.31830	−0.371660
$136$	−31.9479	−2.73951
$137$	2.35757	0.201421	0.100711	−	0.994916i	$-0.467888\pi$
$137$	2.35757	0.201421	0.100711	+	0.994916i	$0.467888\pi$
$138$	−39.0131	−3.32102
$139$	−8.27027	−0.701475	−0.350738	−	0.936474i	$-0.614069\pi$
$139$	−8.27027	−0.701475	−0.350738	+	0.936474i	$0.614069\pi$
$140$	24.5791	2.07731
$141$	−4.18191	−0.352180
$142$	3.33542	0.279902
$143$	15.1966	1.27080
$144$	10.5816	0.881799
$145$	5.99990	0.498265
$146$	27.0688	2.24023
$147$	−28.0108	−2.31029
$148$	−26.3108	−2.16273
$149$	10.1003	0.827449	0.413725	−	0.910402i	$-0.364228\pi$
$149$	10.1003	0.827449	0.413725	+	0.910402i	$0.364228\pi$
$150$	5.25623	0.429169
$151$	23.3710	1.90190	0.950952	−	0.309339i	$-0.100108\pi$
$151$	23.3710	1.90190	0.950952	+	0.309339i	$0.100108\pi$
$152$	−18.4198	−1.49405
$153$	2.77696	0.224504
$154$	−70.9219	−5.71505
$155$	−2.66060	−0.213704
$156$	27.6826	2.21638
$157$	−14.9527	−1.19335	−0.596677	−	0.802481i	$-0.703513\pi$
$157$	−14.9527	−1.19335	−0.596677	+	0.802481i	$0.703513\pi$
$158$	−41.9150	−3.33458
$159$	23.8588	1.89212
$160$	18.8451	1.48984
$161$	34.3436	2.70666
$162$	29.0129	2.27947
$163$	17.3820	1.36147	0.680733	−	0.732532i	$-0.261662\pi$
$163$	17.3820	1.36147	0.680733	+	0.732532i	$0.261662\pi$
$164$	−29.4834	−2.30227
$165$	−11.0182	−0.857764
$166$	11.0437	0.857158
$167$	−1.82022	−0.140853	−0.0704265	−	0.997517i	$-0.522436\pi$
$167$	−1.82022	−0.140853	−0.0704265	+	0.997517i	$0.522436\pi$
$168$	−80.5510	−6.21465
$169$	−5.81234	−0.447103
$170$	9.64619	0.739829
$171$	1.60108	0.122438
$172$	−58.9260	−4.49306
$173$	4.88363	0.371296	0.185648	−	0.982616i	$-0.440562\pi$
$173$	4.88363	0.371296	0.185648	+	0.982616i	$0.440562\pi$
$174$	−31.5369	−2.39080
$175$	−4.62711	−0.349777
$176$	−77.0500	−5.80786
$177$	−20.4473	−1.53691
$178$	−39.5490	−2.96432
$179$	−12.0555	−0.901069	−0.450535	−	0.892759i	$-0.648767\pi$
$179$	−12.0555	−0.901069	−0.450535	+	0.892759i	$0.648767\pi$
$180$	−4.13511	−0.308213
$181$	−14.6848	−1.09152	−0.545758	−	0.837943i	$-0.683758\pi$
$181$	−14.6848	−1.09152	−0.545758	+	0.837943i	$0.683758\pi$
$182$	−33.5445	−2.48648
$183$	23.2338	1.71749
$184$	66.4723	4.90041
$185$	4.95311	0.364160
$186$	13.9847	1.02541
$187$	−20.2205	−1.47867
$188$	11.4281	0.833479
$189$	−19.9813	−1.45342
$190$	5.56159	0.403480
$191$	5.41865	0.392080	0.196040	−	0.980596i	$-0.437192\pi$
$191$	5.41865	0.392080	0.196040	+	0.980596i	$0.437192\pi$
$192$	−46.2090	−3.33485
$193$	−0.461095	−0.0331903	−0.0165952	−	0.999862i	$-0.505283\pi$
$193$	−0.461095	−0.0331903	−0.0165952	+	0.999862i	$0.505283\pi$
$194$	−35.4977	−2.54859
$195$	−5.21136	−0.373193
$196$	76.5463	5.46760
$197$	22.2946	1.58842	0.794211	−	0.607642i	$-0.207884\pi$
$197$	22.2946	1.58842	0.794211	+	0.607642i	$0.207884\pi$
$198$	11.9317	0.847947
$199$	21.0990	1.49567	0.747834	−	0.663885i	$-0.231094\pi$
$199$	21.0990	1.49567	0.747834	+	0.663885i	$0.231094\pi$
$200$	−8.95580	−0.633271
$201$	−11.2249	−0.791746
$202$	36.4701	2.56602
$203$	27.7622	1.94852
$204$	−36.8342	−2.57891
$205$	5.55037	0.387654
$206$	−30.0697	−2.09506
$207$	−5.77787	−0.401590
$208$	−36.4429	−2.52686
$209$	−11.6583	−0.806420
$210$	24.3211	1.67832
$211$	22.9949	1.58303	0.791516	−	0.611148i	$-0.209292\pi$
$211$	22.9949	1.58303	0.791516	+	0.611148i	$0.209292\pi$
$212$	−65.1999	−4.47795
$213$	2.39767	0.164286
$214$	−4.65143	−0.317965
$215$	11.0930	0.756539
$216$	−38.6738	−2.63142
$217$	−12.3109	−0.835716
$218$	24.2935	1.64537
$219$	19.4585	1.31488
$220$	30.1099	2.03001
$221$	−9.56384	−0.643334
$222$	−26.0347	−1.74733
$223$	2.51123	0.168164	0.0840821	−	0.996459i	$-0.473204\pi$
$223$	2.51123	0.168164	0.0840821	+	0.996459i	$0.473204\pi$
$224$	87.1985	5.82619
$225$	0.778451	0.0518967
$226$	−17.2975	−1.15061
$227$	0.115893	0.00769210	0.00384605	−	0.999993i	$-0.498776\pi$
$227$	0.115893	0.00769210	0.00384605	+	0.999993i	$0.498776\pi$
$228$	−21.2371	−1.40646
$229$	12.8099	0.846500	0.423250	−	0.906013i	$-0.360889\pi$
$229$	12.8099	0.846500	0.423250	+	0.906013i	$0.360889\pi$
$230$	−20.0703	−1.32340
$231$	−50.9823	−3.35439
$232$	53.7339	3.52781
$233$	−8.78160	−0.575302	−0.287651	−	0.957735i	$-0.592874\pi$
$233$	−8.78160	−0.575302	−0.287651	+	0.957735i	$0.592874\pi$
$234$	5.64342	0.368922
$235$	−2.15138	−0.140341
$236$	55.8773	3.63730
$237$	−30.1307	−1.95720
$238$	44.6340	2.89319
$239$	−13.1523	−0.850752	−0.425376	−	0.905017i	$-0.639858\pi$
$239$	−13.1523	−0.850752	−0.425376	+	0.905017i	$0.639858\pi$
$240$	26.4227	1.70557
$241$	29.0921	1.87399	0.936993	−	0.349348i	$-0.113597\pi$
$241$	29.0921	1.87399	0.936993	+	0.349348i	$0.113597\pi$
$242$	−57.1360	−3.67284
$243$	7.90110	0.506856
$244$	−63.4921	−4.06466
$245$	−14.4101	−0.920631
$246$	−29.1740	−1.86007
$247$	−5.51411	−0.350854
$248$	−23.8278	−1.51306
$249$	7.93879	0.503101
$250$	2.70407	0.171020
$251$	12.0855	0.762828	0.381414	−	0.924404i	$-0.375437\pi$
$251$	12.0855	0.762828	0.381414	+	0.924404i	$0.375437\pi$
$252$	−19.1336	−1.20530
$253$	42.0716	2.64502
$254$	−51.0601	−3.20380
$255$	6.93418	0.434235
$256$	24.3605	1.52253
$257$	−4.87795	−0.304278	−0.152139	−	0.988359i	$-0.548616\pi$
$257$	−4.87795	−0.304278	−0.152139	+	0.988359i	$0.548616\pi$
$258$	−58.3076	−3.63007
$259$	22.9186	1.42409
$260$	14.2413	0.883209
$261$	−4.67063	−0.289105
$262$	43.8086	2.70650
$263$	14.6248	0.901803	0.450901	−	0.892574i	$-0.351103\pi$
$263$	14.6248	0.901803	0.450901	+	0.892574i	$0.351103\pi$
$264$	−98.6766	−6.07313
$265$	12.2741	0.753994
$266$	25.7341	1.57786
$267$	−28.4299	−1.73988
$268$	30.6749	1.87377
$269$	−19.6096	−1.19562	−0.597808	−	0.801639i	$-0.703962\pi$
$269$	−19.6096	−1.19562	−0.597808	+	0.801639i	$0.703962\pi$
$270$	11.6770	0.710638
$271$	−30.1229	−1.82984	−0.914919	−	0.403638i	$-0.867745\pi$
$271$	−30.1229	−1.82984	−0.914919	+	0.403638i	$0.867745\pi$
$272$	48.4907	2.94018
$273$	−24.1135	−1.45942
$274$	−6.37504	−0.385130
$275$	−5.66830	−0.341811
$276$	76.6389	4.61312
$277$	−11.1181	−0.668020	−0.334010	−	0.942570i	$-0.608402\pi$
$277$	−11.1181	−0.668020	−0.334010	+	0.942570i	$0.608402\pi$
$278$	22.3634	1.34127
$279$	2.07114	0.123996
$280$	−41.4395	−2.47648
$281$	−11.5988	−0.691926	−0.345963	−	0.938248i	$-0.612448\pi$
$281$	−11.5988	−0.691926	−0.345963	+	0.938248i	$0.612448\pi$
$282$	11.3081	0.673390
$283$	2.98077	0.177189	0.0885943	−	0.996068i	$-0.471763\pi$
$283$	2.98077	0.177189	0.0885943	+	0.996068i	$0.471763\pi$
$284$	−6.55223	−0.388803
$285$	3.99796	0.236819
$286$	−41.0927	−2.42986
$287$	25.6822	1.51597
$288$	−14.6700	−0.864438
$289$	−4.27444	−0.251438
$290$	−16.2241	−0.952714
$291$	−25.5176	−1.49587
$292$	−53.1751	−3.11184
$293$	−4.40942	−0.257601	−0.128801	−	0.991671i	$-0.541113\pi$
$293$	−4.40942	−0.257601	−0.128801	+	0.991671i	$0.541113\pi$
$294$	75.7430	4.41742
$295$	−10.5191	−0.612447
$296$	44.3590	2.57832
$297$	−24.4774	−1.42032
$298$	−27.3119	−1.58214
$299$	19.8990	1.15079
$300$	−10.3255	−0.596146
$301$	51.3287	2.95854
$302$	−63.1967	−3.63656
$303$	26.2166	1.50610
$304$	27.9577	1.60348
$305$	11.9526	0.684406
$306$	−7.50908	−0.429266
$307$	−21.1945	−1.20963	−0.604816	−	0.796365i	$-0.706754\pi$
$307$	−21.1945	−1.20963	−0.604816	+	0.796365i	$0.706754\pi$
$308$	139.322	7.93859
$309$	−21.6157	−1.22967
$310$	7.19443	0.408616
$311$	12.1359	0.688161	0.344081	−	0.938940i	$-0.388191\pi$
$311$	12.1359	0.688161	0.344081	+	0.938940i	$0.388191\pi$
$312$	−46.6719	−2.64227
$313$	−1.59953	−0.0904105	−0.0452053	−	0.998978i	$-0.514394\pi$
$313$	−1.59953	−0.0904105	−0.0452053	+	0.998978i	$0.514394\pi$
$314$	40.4330	2.28177
$315$	3.60198	0.202948
$316$	82.3395	4.63196
$317$	7.62059	0.428015	0.214007	−	0.976832i	$-0.431348\pi$
$317$	7.62059	0.428015	0.214007	+	0.976832i	$0.431348\pi$
$318$	−64.5157	−3.61786
$319$	34.0093	1.90415
$320$	−23.7722	−1.32891
$321$	−3.34369	−0.186626
$322$	−92.8675	−5.17530
$323$	7.33702	0.408243
$324$	−56.9941	−3.16634
$325$	−2.68098	−0.148714
$326$	−47.0022	−2.60321
$327$	17.4635	0.965731
$328$	49.7080	2.74466
$329$	−9.95468	−0.548819
$330$	29.7939	1.64010
$331$	32.9519	1.81120	0.905600	−	0.424133i	$-0.139421\pi$
$331$	32.9519	1.81120	0.905600	+	0.424133i	$0.139421\pi$
$332$	−21.6947	−1.19065
$333$	−3.85575	−0.211294
$334$	4.92200	0.269320
$335$	−5.77467	−0.315504
$336$	122.261	6.66986
$337$	13.9792	0.761494	0.380747	−	0.924679i	$-0.375667\pi$
$337$	13.9792	0.761494	0.380747	+	0.924679i	$0.375667\pi$
$338$	15.7169	0.854889
$339$	−12.4343	−0.675339
$340$	−18.9494	−1.02767
$341$	−15.0811	−0.816685
$342$	−4.32942	−0.234108
$343$	−34.2876	−1.85135
$344$	99.3471	5.35644
$345$	−14.4276	−0.776755
$346$	−13.2057	−0.709941
$347$	17.6133	0.945532	0.472766	−	0.881188i	$-0.343256\pi$
$347$	17.6133	0.945532	0.472766	+	0.881188i	$0.343256\pi$
$348$	61.9522	3.32099
$349$	1.90958	0.102218	0.0511088	−	0.998693i	$-0.483724\pi$
$349$	1.90958	0.102218	0.0511088	+	0.998693i	$0.483724\pi$
$350$	12.5120	0.668795
$351$	−11.5773	−0.617950
$352$	106.820	5.69352
$353$	−10.8897	−0.579598	−0.289799	−	0.957087i	$-0.593589\pi$
$353$	−10.8897	−0.579598	−0.289799	+	0.957087i	$0.593589\pi$
$354$	55.2909	2.93868
$355$	1.23348	0.0654665
$356$	77.6917	4.11765
$357$	32.0852	1.69813
$358$	32.5988	1.72290
$359$	−31.9369	−1.68556	−0.842781	−	0.538256i	$-0.819083\pi$
$359$	−31.9369	−1.68556	−0.842781	+	0.538256i	$0.819083\pi$
$360$	6.97165	0.367438
$361$	−14.7698	−0.777357
$362$	39.7088	2.08705
$363$	−41.0723	−2.15574
$364$	65.8961	3.45389
$365$	10.0104	0.523969
$366$	−62.8257	−3.28395
$367$	20.5003	1.07011	0.535055	−	0.844818i	$-0.320291\pi$
$367$	20.5003	1.07011	0.535055	+	0.844818i	$0.320291\pi$
$368$	−100.892	−5.25935
$369$	−4.32069	−0.224926
$370$	−13.3935	−0.696296
$371$	56.7938	2.94859
$372$	−27.4721	−1.42436
$373$	3.97013	0.205566	0.102783	−	0.994704i	$-0.467225\pi$
$373$	3.97013	0.205566	0.102783	+	0.994704i	$0.467225\pi$
$374$	54.6775	2.82731
$375$	1.94382	0.100379
$376$	−19.2673	−0.993637
$377$	16.0856	0.828452
$378$	54.0306	2.77904
$379$	16.5106	0.848094	0.424047	−	0.905640i	$-0.360609\pi$
$379$	16.5106	0.848094	0.424047	+	0.905640i	$0.360609\pi$
$380$	−10.9254	−0.560461
$381$	−36.7047	−1.88044
$382$	−14.6524	−0.749682
$383$	9.20369	0.470287	0.235143	−	0.971961i	$-0.424444\pi$
$383$	9.20369	0.470287	0.235143	+	0.971961i	$0.424444\pi$
$384$	51.6890	2.63774
$385$	−26.2279	−1.33670
$386$	1.24683	0.0634620
$387$	−8.63538	−0.438961
$388$	69.7332	3.54017
$389$	11.0467	0.560092	0.280046	−	0.959987i	$-0.409650\pi$
$389$	11.0467	0.560092	0.280046	+	0.959987i	$0.409650\pi$
$390$	14.0919	0.713569
$391$	−26.4774	−1.33902
$392$	−129.054	−6.51823
$393$	31.4919	1.58856
$394$	−60.2860	−3.03717
$395$	−15.5007	−0.779926
$396$	−23.4391	−1.17786
$397$	−36.7611	−1.84499	−0.922494	−	0.386011i	$-0.873853\pi$
$397$	−36.7611	−1.84499	−0.922494	+	0.386011i	$0.873853\pi$
$398$	−57.0531	−2.85981
$399$	18.4990	0.926108
$400$	13.5931	0.679657
$401$	−10.6643	−0.532550	−0.266275	−	0.963897i	$-0.585793\pi$
$401$	−10.6643	−0.532550	−0.266275	+	0.963897i	$0.585793\pi$
$402$	30.3530	1.51387
$403$	−7.13301	−0.355320
$404$	−71.6432	−3.56438
$405$	10.7294	0.533147
$406$	−75.0708	−3.72570
$407$	28.0757	1.39166
$408$	62.1012	3.07447
$409$	−2.58623	−0.127881	−0.0639403	−	0.997954i	$-0.520367\pi$
$409$	−2.58623	−0.127881	−0.0639403	+	0.997954i	$0.520367\pi$
$410$	−15.0086	−0.741220
$411$	−4.58271	−0.226048
$412$	59.0701	2.91018
$413$	−48.6731	−2.39505
$414$	15.6237	0.767865
$415$	4.08411	0.200481
$416$	50.5235	2.47712
$417$	16.0760	0.787243
$418$	31.5248	1.54193
$419$	36.0154	1.75947	0.879733	−	0.475468i	$-0.157721\pi$
$419$	36.0154	1.75947	0.879733	+	0.475468i	$0.157721\pi$
$420$	−47.7774	−2.33130
$421$	−10.7303	−0.522964	−0.261482	−	0.965208i	$-0.584211\pi$
$421$	−10.7303	−0.522964	−0.261482	+	0.965208i	$0.584211\pi$
$422$	−62.1797	−3.02686
$423$	1.67474	0.0814288
$424$	109.925	5.33842
$425$	3.56729	0.173039
$426$	−6.48347	−0.314125
$427$	55.3061	2.67645
$428$	9.13745	0.441675
$429$	−29.5395	−1.42618
$430$	−29.9963	−1.44655
$431$	12.1389	0.584711	0.292356	−	0.956310i	$-0.405561\pi$
$431$	12.1389	0.584711	0.292356	+	0.956310i	$0.405561\pi$
$432$	58.6992	2.82417
$433$	2.14195	0.102935	0.0514677	−	0.998675i	$-0.483610\pi$
$433$	2.14195	0.102935	0.0514677	+	0.998675i	$0.483610\pi$
$434$	33.2894	1.59794
$435$	−11.6628	−0.559186
$436$	−47.7232	−2.28553
$437$	−15.2657	−0.730260
$438$	−52.6170	−2.51414
$439$	3.15397	0.150531	0.0752654	−	0.997164i	$-0.476020\pi$
$439$	3.15397	0.150531	0.0752654	+	0.997164i	$0.476020\pi$
$440$	−50.7642	−2.42009
$441$	11.2176	0.534171
$442$	25.8613	1.23009
$443$	−19.8190	−0.941627	−0.470814	−	0.882233i	$-0.656040\pi$
$443$	−19.8190	−0.941627	−0.470814	+	0.882233i	$0.656040\pi$
$444$	51.1435	2.42716
$445$	−14.6258	−0.693327
$446$	−6.79052	−0.321541
$447$	−19.6332	−0.928619
$448$	−109.997	−5.19685
$449$	1.73415	0.0818398	0.0409199	−	0.999162i	$-0.486971\pi$
$449$	1.73415	0.0818398	0.0409199	+	0.999162i	$0.486971\pi$
$450$	−2.10498	−0.0992298
$451$	31.4611	1.48145
$452$	33.9798	1.59828
$453$	−45.4291	−2.13444
$454$	−0.313383	−0.0147078
$455$	−12.4052	−0.581565
$456$	35.8049	1.67672
$457$	32.5976	1.52485	0.762427	−	0.647075i	$-0.224008\pi$
$457$	32.5976	1.52485	0.762427	+	0.647075i	$0.224008\pi$
$458$	−34.6387	−1.61856
$459$	15.4046	0.719027
$460$	39.4269	1.83829
$461$	41.5033	1.93300	0.966500	−	0.256666i	$-0.0826242\pi$
$461$	41.5033	1.93300	0.966500	+	0.256666i	$0.0826242\pi$
$462$	137.860	6.41381
$463$	33.4513	1.55461	0.777306	−	0.629122i	$-0.216585\pi$
$463$	33.4513	1.55461	0.777306	+	0.629122i	$0.216585\pi$
$464$	−81.5575	−3.78621
$465$	5.17173	0.239833
$466$	23.7460	1.10001
$467$	9.00942	0.416906	0.208453	−	0.978032i	$-0.433157\pi$
$467$	9.00942	0.416906	0.208453	+	0.978032i	$0.433157\pi$
$468$	−11.0862	−0.512458
$469$	−26.7200	−1.23382
$470$	5.81748	0.268340
$471$	29.0654	1.33926
$472$	−94.2072	−4.33624
$473$	62.8787	2.89117
$474$	81.4753	3.74229
$475$	2.05675	0.0943702
$476$	−87.6808	−4.01884
$477$	−9.55481	−0.437485
$478$	35.5647	1.62669
$479$	−22.3135	−1.01953	−0.509766	−	0.860313i	$-0.670268\pi$
$479$	−22.3135	−1.01953	−0.509766	+	0.860313i	$0.670268\pi$
$480$	−36.6316	−1.67200
$481$	13.2792	0.605479
$482$	−78.6669	−3.58318
$483$	−66.7580	−3.03759
$484$	112.240	5.10183
$485$	−13.1275	−0.596091
$486$	−21.3651	−0.969140
$487$	12.0899	0.547846	0.273923	−	0.961752i	$-0.411679\pi$
$487$	12.0899	0.547846	0.273923	+	0.961752i	$0.411679\pi$
$488$	107.045	4.84572
$489$	−33.7876	−1.52793
$490$	38.9660	1.76030
$491$	−4.41724	−0.199347	−0.0996737	−	0.995020i	$-0.531780\pi$
$491$	−4.41724	−0.199347	−0.0996737	+	0.995020i	$0.531780\pi$
$492$	57.3105	2.58376
$493$	−21.4034	−0.963960
$494$	14.9105	0.670856
$495$	4.41249	0.198327
$496$	36.1658	1.62389
$497$	5.70746	0.256015
$498$	−21.4670	−0.961961
$499$	−29.5931	−1.32477	−0.662384	−	0.749164i	$-0.730455\pi$
$499$	−29.5931	−1.32477	−0.662384	+	0.749164i	$0.730455\pi$
$500$	−5.31198	−0.237559
$501$	3.53819	0.158075
$502$	−32.6799	−1.45858
$503$	−32.2148	−1.43639	−0.718193	−	0.695844i	$-0.755030\pi$
$503$	−32.2148	−1.43639	−0.718193	+	0.695844i	$0.755030\pi$
$504$	32.2586	1.43691
$505$	13.4871	0.600169
$506$	−113.765	−5.05745
$507$	11.2982	0.501769
$508$	100.304	4.45029
$509$	−2.88137	−0.127714	−0.0638572	−	0.997959i	$-0.520340\pi$
$509$	−2.88137	−0.127714	−0.0638572	+	0.997959i	$0.520340\pi$
$510$	−18.7505	−0.830286
$511$	46.3193	2.04904
$512$	−12.6896	−0.560804
$513$	8.88166	0.392135
$514$	13.1903	0.581799
$515$	−11.1202	−0.490014
$516$	114.542	5.04242
$517$	−12.1947	−0.536321
$518$	−61.9733	−2.72295
$519$	−9.49292	−0.416693
$520$	−24.0103	−1.05292
$521$	−34.4065	−1.50738	−0.753688	−	0.657233i	$-0.771727\pi$
$521$	−34.4065	−1.50738	−0.753688	+	0.657233i	$0.771727\pi$
$522$	12.6297	0.552786
$523$	1.90031	0.0830950	0.0415475	−	0.999137i	$-0.486771\pi$
$523$	1.90031	0.0830950	0.0415475	+	0.999137i	$0.486771\pi$
$524$	−86.0593	−3.75952
$525$	8.99429	0.392543
$526$	−39.5464	−1.72430
$527$	9.49112	0.413439
$528$	149.772	6.51797
$529$	32.0900	1.39522
$530$	−33.1901	−1.44168
$531$	8.18862	0.355356
$532$	−50.5531	−2.19175
$533$	14.8804	0.644543
$534$	76.8763	3.32676
$535$	−1.72016	−0.0743690
$536$	−51.7168	−2.23383
$537$	23.4337	1.01124
$538$	53.0256	2.28610
$539$	−81.6811	−3.51825
$540$	−22.9387	−0.987125
$541$	−40.3970	−1.73680	−0.868402	−	0.495860i	$-0.834853\pi$
$541$	−40.3970	−1.73680	−0.868402	+	0.495860i	$0.834853\pi$
$542$	81.4544	3.49877
$543$	28.5448	1.22497
$544$	−67.2261	−2.88229
$545$	8.98407	0.384835
$546$	65.2046	2.79050
$547$	−28.9456	−1.23762	−0.618812	−	0.785539i	$-0.712386\pi$
$547$	−28.9456	−1.23762	−0.618812	+	0.785539i	$0.712386\pi$
$548$	12.5234	0.534972
$549$	−9.30453	−0.397108
$550$	15.3275	0.653565
$551$	−12.3403	−0.525714
$552$	−129.211	−5.49956
$553$	−71.7236	−3.05000
$554$	30.0640	1.27730
$555$	−9.62796	−0.408684
$556$	−43.9315	−1.86311
$557$	−39.1064	−1.65699	−0.828497	−	0.559994i	$-0.810803\pi$
$557$	−39.1064	−1.65699	−0.828497	+	0.559994i	$0.810803\pi$
$558$	−5.60051	−0.237088
$559$	29.7402	1.25788
$560$	62.8969	2.65788
$561$	39.3050	1.65946
$562$	31.3639	1.32301
$563$	−11.5472	−0.486658	−0.243329	−	0.969944i	$-0.578239\pi$
$563$	−11.5472	−0.486658	−0.243329	+	0.969944i	$0.578239\pi$
$564$	−22.2142	−0.935386
$565$	−6.39683	−0.269117
$566$	−8.06021	−0.338796
$567$	49.6460	2.08493
$568$	11.0468	0.463515
$569$	4.78000	0.200388	0.100194	−	0.994968i	$-0.468054\pi$
$569$	4.78000	0.200388	0.100194	+	0.994968i	$0.468054\pi$
$570$	−10.8107	−0.452812
$571$	−9.72213	−0.406859	−0.203429	−	0.979090i	$-0.565209\pi$
$571$	−9.72213	−0.406859	−0.203429	+	0.979090i	$0.565209\pi$
$572$	80.7240	3.37524
$573$	−10.5329	−0.440019
$574$	−69.4462	−2.89863
$575$	−7.42227	−0.309530
$576$	18.5055	0.771063
$577$	−6.86691	−0.285873	−0.142937	−	0.989732i	$-0.545655\pi$
$577$	−6.86691	−0.285873	−0.142937	+	0.989732i	$0.545655\pi$
$578$	11.5584	0.480765
$579$	0.896287	0.0372484
$580$	31.8713	1.32338
$581$	18.8976	0.784006
$582$	69.0014	2.86020
$583$	69.5735	2.88144
$584$	89.6513	3.70980
$585$	2.08701	0.0862873
$586$	11.9234	0.492550
$587$	−2.36104	−0.0974507	−0.0487253	−	0.998812i	$-0.515516\pi$
$587$	−2.36104	−0.0974507	−0.0487253	+	0.998812i	$0.515516\pi$
$588$	−148.793	−6.13610
$589$	5.47218	0.225477
$590$	28.4444	1.17104
$591$	−43.3367	−1.78263
$592$	−67.3282	−2.76717
$593$	9.73144	0.399623	0.199811	−	0.979834i	$-0.435967\pi$
$593$	9.73144	0.399623	0.199811	+	0.979834i	$0.435967\pi$
$594$	66.1886	2.71575
$595$	16.5062	0.676690
$596$	53.6526	2.19770
$597$	−41.0127	−1.67854
$598$	−53.8081	−2.20038
$599$	12.9225	0.527998	0.263999	−	0.964523i	$-0.414958\pi$
$599$	12.9225	0.527998	0.263999	+	0.964523i	$0.414958\pi$
$600$	17.4085	0.710699
$601$	8.96589	0.365726	0.182863	−	0.983138i	$-0.441463\pi$
$601$	8.96589	0.365726	0.182863	+	0.983138i	$0.441463\pi$
$602$	−138.796	−5.65691
$603$	4.49530	0.183063
$604$	124.146	5.05143
$605$	−21.1296	−0.859042
$606$	−70.8914	−2.87977
$607$	−44.7205	−1.81515	−0.907574	−	0.419892i	$-0.862068\pi$
$607$	−44.7205	−1.81515	−0.907574	+	0.419892i	$0.862068\pi$
$608$	−38.7597	−1.57191
$609$	−53.9648	−2.18677
$610$	−32.3207	−1.30863
$611$	−5.76781	−0.233341
$612$	14.7511	0.596280
$613$	31.1830	1.25947	0.629734	−	0.776811i	$-0.283164\pi$
$613$	31.1830	1.25947	0.629734	+	0.776811i	$0.283164\pi$
$614$	57.3113	2.31290
$615$	−10.7889	−0.435052
$616$	−234.891	−9.46405
$617$	−16.0879	−0.647675	−0.323837	−	0.946113i	$-0.604973\pi$
$617$	−16.0879	−0.647675	−0.323837	+	0.946113i	$0.604973\pi$
$618$	58.4502	2.35121
$619$	12.1011	0.486382	0.243191	−	0.969978i	$-0.421806\pi$
$619$	12.1011	0.486382	0.243191	+	0.969978i	$0.421806\pi$
$620$	−14.1330	−0.567596
$621$	−32.0516	−1.28619
$622$	−32.8162	−1.31581
$623$	−67.6750	−2.71134
$624$	70.8387	2.83582
$625$	1.00000	0.0400000
$626$	4.32522	0.172871
$627$	22.6616	0.905019
$628$	−79.4283	−3.16953
$629$	−17.6692	−0.704516
$630$	−9.73998	−0.388050
$631$	−18.0795	−0.719734	−0.359867	−	0.933004i	$-0.617178\pi$
$631$	−18.0795	−0.719734	−0.359867	+	0.933004i	$0.617178\pi$
$632$	−138.821	−5.52202
$633$	−44.6980	−1.77658
$634$	−20.6066	−0.818391
$635$	−18.8827	−0.749337
$636$	126.737	5.02545
$637$	−38.6333	−1.53071
$638$	−91.9633	−3.64086
$639$	−0.960206	−0.0379851
$640$	26.5914	1.05112
$641$	−28.9108	−1.14191	−0.570955	−	0.820981i	$-0.693427\pi$
$641$	−28.9108	−1.14191	−0.570955	+	0.820981i	$0.693427\pi$
$642$	9.04155	0.356842
$643$	−4.53179	−0.178716	−0.0893581	−	0.996000i	$-0.528482\pi$
$643$	−4.53179	−0.178716	−0.0893581	+	0.996000i	$0.528482\pi$
$644$	182.433	7.18885
$645$	−21.5629	−0.849039
$646$	−19.8398	−0.780587
$647$	8.96821	0.352577	0.176288	−	0.984339i	$-0.443591\pi$
$647$	8.96821	0.352577	0.176288	+	0.984339i	$0.443591\pi$
$648$	96.0901	3.77477
$649$	−59.6256	−2.34051
$650$	7.24955	0.284351
$651$	23.9302	0.937897
$652$	92.3329	3.61604
$653$	35.8665	1.40357	0.701783	−	0.712391i	$-0.252388\pi$
$653$	35.8665	1.40357	0.701783	+	0.712391i	$0.252388\pi$
$654$	−47.2223	−1.84654
$655$	16.2010	0.633026
$656$	−75.4469	−2.94570
$657$	−7.79261	−0.304019
$658$	26.9181	1.04938
$659$	−40.5639	−1.58014	−0.790072	−	0.613014i	$-0.789957\pi$
$659$	−40.5639	−1.58014	−0.790072	+	0.613014i	$0.789957\pi$
$660$	−58.5283	−2.27821
$661$	−5.49332	−0.213665	−0.106833	−	0.994277i	$-0.534071\pi$
$661$	−5.49332	−0.213665	−0.106833	+	0.994277i	$0.534071\pi$
$662$	−89.1041	−3.46313
$663$	18.5904	0.721992
$664$	36.5765	1.41944
$665$	9.51681	0.369046
$666$	10.4262	0.404007
$667$	44.5329	1.72432
$668$	−9.66897	−0.374104
$669$	−4.88138	−0.188725
$670$	15.6151	0.603264
$671$	67.7511	2.61550
$672$	−169.498	−6.53855
$673$	−13.8481	−0.533805	−0.266902	−	0.963724i	$-0.586000\pi$
$673$	−13.8481	−0.533805	−0.266902	+	0.963724i	$0.586000\pi$
$674$	−37.8006	−1.45603
$675$	4.31830	0.166211
$676$	−30.8750	−1.18750
$677$	−1.23976	−0.0476477	−0.0238239	−	0.999716i	$-0.507584\pi$
$677$	−1.23976	−0.0476477	−0.0238239	+	0.999716i	$0.507584\pi$
$678$	33.6232	1.29129
$679$	−60.7426	−2.33109
$680$	31.9479	1.22515
$681$	−0.225276	−0.00863259
$682$	40.7802	1.56155
$683$	24.5329	0.938725	0.469362	−	0.883006i	$-0.344484\pi$
$683$	24.5329	0.938725	0.469362	+	0.883006i	$0.344484\pi$
$684$	8.50489	0.325193
$685$	−2.35757	−0.0900783
$686$	92.7159	3.53991
$687$	−24.9001	−0.949999
$688$	−150.789	−5.74878
$689$	32.9067	1.25365
$690$	39.0131	1.48520
$691$	19.9315	0.758231	0.379116	−	0.925349i	$-0.376228\pi$
$691$	19.9315	0.758231	0.379116	+	0.925349i	$0.376228\pi$
$692$	25.9417	0.986157
$693$	20.4171	0.775581
$694$	−47.6276	−1.80792
$695$	8.27027	0.313709
$696$	−104.449	−3.95914
$697$	−19.7998	−0.749970
$698$	−5.16363	−0.195446
$699$	17.0699	0.645642
$700$	−24.5791	−0.929002
$701$	5.42710	0.204979	0.102489	−	0.994734i	$-0.467319\pi$
$701$	5.42710	0.204979	0.102489	+	0.994734i	$0.467319\pi$
$702$	31.3057	1.18156
$703$	−10.1873	−0.384221
$704$	−134.748	−5.07851
$705$	4.18191	0.157500
$706$	29.4464	1.10823
$707$	62.4064	2.34703
$708$	−108.616	−4.08203
$709$	−22.7657	−0.854984	−0.427492	−	0.904019i	$-0.640603\pi$
$709$	−22.7657	−0.854984	−0.427492	+	0.904019i	$0.640603\pi$
$710$	−3.33542	−0.125176
$711$	12.0665	0.452531
$712$	−130.985	−4.90889
$713$	−19.7476	−0.739555
$714$	−86.7606	−3.24693
$715$	−15.1966	−0.568321
$716$	−64.0385	−2.39323
$717$	25.5658	0.954771
$718$	86.3594	3.22290
$719$	−14.3626	−0.535636	−0.267818	−	0.963470i	$-0.586303\pi$
$719$	−14.3626	−0.535636	−0.267818	+	0.963470i	$0.586303\pi$
$720$	−10.5816	−0.394352
$721$	−51.4543	−1.91626
$722$	39.9385	1.48636
$723$	−56.5499	−2.10311
$724$	−78.0055	−2.89905
$725$	−5.99990	−0.222831
$726$	111.062	4.12191
$727$	6.57900	0.244002	0.122001	−	0.992530i	$-0.461069\pi$
$727$	6.57900	0.244002	0.122001	+	0.992530i	$0.461069\pi$
$728$	−111.098	−4.11758
$729$	16.8298	0.623324
$730$	−27.0688	−1.00186
$731$	−39.5721	−1.46363
$732$	123.417	4.56164
$733$	35.5569	1.31332	0.656662	−	0.754185i	$-0.271968\pi$
$733$	35.5569	1.31332	0.656662	+	0.754185i	$0.271968\pi$
$734$	−55.4343	−2.04612
$735$	28.0108	1.03319
$736$	139.874	5.15581
$737$	−32.7326	−1.20572
$738$	11.6834	0.430073
$739$	12.1329	0.446318	0.223159	−	0.974782i	$-0.428363\pi$
$739$	12.1329	0.446318	0.223159	+	0.974782i	$0.428363\pi$
$740$	26.3108	0.967203
$741$	10.7185	0.393752
$742$	−153.574	−5.63788
$743$	17.8079	0.653309	0.326655	−	0.945144i	$-0.394079\pi$
$743$	17.8079	0.653309	0.326655	+	0.945144i	$0.394079\pi$
$744$	46.3170	1.69806
$745$	−10.1003	−0.370047
$746$	−10.7355	−0.393054
$747$	−3.17928	−0.116324
$748$	−107.411	−3.92732
$749$	−7.95937	−0.290829
$750$	−5.25623	−0.191930
$751$	−40.7257	−1.48610	−0.743051	−	0.669235i	$-0.766622\pi$
$751$	−40.7257	−1.48610	−0.743051	+	0.669235i	$0.766622\pi$
$752$	29.2440	1.06642
$753$	−23.4920	−0.856097
$754$	−43.4966	−1.58405
$755$	−23.3710	−0.850557
$756$	−106.140	−3.86027
$757$	2.78265	0.101137	0.0505686	−	0.998721i	$-0.483897\pi$
$757$	2.78265	0.101137	0.0505686	+	0.998721i	$0.483897\pi$
$758$	−44.6459	−1.62161
$759$	−81.7799	−2.96842
$760$	18.4198	0.668158
$761$	−31.9798	−1.15927	−0.579633	−	0.814877i	$-0.696804\pi$
$761$	−31.9798	−1.15927	−0.579633	+	0.814877i	$0.696804\pi$
$762$	99.2518	3.59551
$763$	41.5703	1.50495
$764$	28.7838	1.04136
$765$	−2.77696	−0.100401
$766$	−24.8874	−0.899218
$767$	−28.2016	−1.01830
$768$	−47.3525	−1.70869
$769$	35.7274	1.28836	0.644181	−	0.764873i	$-0.277199\pi$
$769$	35.7274	1.28836	0.644181	+	0.764873i	$0.277199\pi$
$770$	70.9219	2.55585
$771$	9.48188	0.341481
$772$	−2.44932	−0.0881531
$773$	−6.54254	−0.235319	−0.117659	−	0.993054i	$-0.537539\pi$
$773$	−6.54254	−0.235319	−0.117659	+	0.993054i	$0.537539\pi$
$774$	23.3507	0.839322
$775$	2.66060	0.0955714
$776$	−117.568	−4.22043
$777$	−44.5497	−1.59821
$778$	−29.8711	−1.07093
$779$	−11.4157	−0.409010
$780$	−27.6826	−0.991196
$781$	6.99175	0.250185
$782$	71.5966	2.56029
$783$	−25.9094	−0.925926
$784$	195.879	6.99568
$785$	14.9527	0.533684
$786$	−85.1562	−3.03742
$787$	22.4452	0.800085	0.400042	−	0.916497i	$-0.368995\pi$
$787$	22.4452	0.800085	0.400042	+	0.916497i	$0.368995\pi$
$788$	118.428	4.21883
$789$	−28.4280	−1.01206
$790$	41.9150	1.49127
$791$	−29.5988	−1.05241
$792$	39.5174	1.40419
$793$	32.0448	1.13794
$794$	99.4045	3.52774
$795$	−23.8588	−0.846183
$796$	112.077	3.97248
$797$	32.7407	1.15974	0.579868	−	0.814710i	$-0.303104\pi$
$797$	32.7407	1.15974	0.579868	+	0.814710i	$0.303104\pi$
$798$	−50.0225	−1.77078
$799$	7.67460	0.271508
$800$	−18.8451	−0.666276
$801$	11.3854	0.402284
$802$	28.8370	1.01827
$803$	56.7421	2.00238
$804$	−59.6266	−2.10287
$805$	−34.3436	−1.21045
$806$	19.2881	0.679395
$807$	38.1176	1.34180
$808$	120.788	4.24931
$809$	−40.8477	−1.43613	−0.718065	−	0.695976i	$-0.754972\pi$
$809$	−40.8477	−1.43613	−0.718065	+	0.695976i	$0.754972\pi$
$810$	−29.0129	−1.01941
$811$	28.5223	1.00155	0.500777	−	0.865576i	$-0.333048\pi$
$811$	28.5223	1.00155	0.500777	+	0.865576i	$0.333048\pi$
$812$	147.472	5.17526
$813$	58.5537	2.05357
$814$	−75.9186	−2.66094
$815$	−17.3820	−0.608866
$816$	−94.2573	−3.29966
$817$	−22.8156	−0.798217
$818$	6.99333	0.244516
$819$	9.65684	0.337437
$820$	29.4834	1.02961
$821$	−0.387300	−0.0135169	−0.00675843	−	0.999977i	$-0.502151\pi$
$821$	−0.387300	−0.0135169	−0.00675843	+	0.999977i	$0.502151\pi$
$822$	12.3919	0.432219
$823$	−27.7850	−0.968523	−0.484262	−	0.874923i	$-0.660912\pi$
$823$	−27.7850	−0.968523	−0.484262	+	0.874923i	$0.660912\pi$
$824$	−99.5901	−3.46939
$825$	11.0182	0.383604
$826$	131.615	4.57949
$827$	43.5641	1.51487	0.757436	−	0.652909i	$-0.226452\pi$
$827$	43.5641	1.51487	0.757436	+	0.652909i	$0.226452\pi$
$828$	−30.6919	−1.06662
$829$	−29.0648	−1.00946	−0.504732	−	0.863276i	$-0.668409\pi$
$829$	−29.0648	−1.00946	−0.504732	+	0.863276i	$0.668409\pi$
$830$	−11.0437	−0.383333
$831$	21.6116	0.749696
$832$	−63.7329	−2.20954
$833$	51.4052	1.78108
$834$	−43.4704	−1.50526
$835$	1.82022	0.0629914
$836$	−61.9285	−2.14184
$837$	11.4892	0.397127
$838$	−97.3880	−3.36421
$839$	15.0055	0.518048	0.259024	−	0.965871i	$-0.416599\pi$
$839$	15.0055	0.518048	0.259024	+	0.965871i	$0.416599\pi$
$840$	80.5510	2.77928
$841$	6.99881	0.241338
$842$	29.0155	0.999940
$843$	22.5460	0.776525
$844$	122.148	4.20451
$845$	5.81234	0.199950
$846$	−4.52862	−0.155697
$847$	−97.7692	−3.35939
$848$	−166.844	−5.72944
$849$	−5.79410	−0.198853
$850$	−9.64619	−0.330862
$851$	36.7633	1.26023
$852$	12.7364	0.436341
$853$	44.3906	1.51991	0.759953	−	0.649979i	$-0.225222\pi$
$853$	44.3906	1.51991	0.759953	+	0.649979i	$0.225222\pi$
$854$	−149.551	−5.11755
$855$	−1.60108	−0.0547557
$856$	−15.4054	−0.526546
$857$	41.4264	1.41510	0.707550	−	0.706663i	$-0.249800\pi$
$857$	41.4264	1.41510	0.707550	+	0.706663i	$0.249800\pi$
$858$	79.8769	2.72695
$859$	46.2566	1.57826	0.789128	−	0.614229i	$-0.210533\pi$
$859$	46.2566	1.57826	0.789128	+	0.614229i	$0.210533\pi$
$860$	58.9260	2.00936
$861$	−49.9216	−1.70132
$862$	−32.8244	−1.11800
$863$	24.0228	0.817746	0.408873	−	0.912591i	$-0.365922\pi$
$863$	24.0228	0.817746	0.408873	+	0.912591i	$0.365922\pi$
$864$	−81.3789	−2.76857
$865$	−4.88363	−0.166049
$866$	−5.79197	−0.196819
$867$	8.30876	0.282180
$868$	−65.3950	−2.21965
$869$	−87.8628	−2.98054
$870$	31.5369	1.06920
$871$	−15.4818	−0.524580
$872$	80.4596	2.72470
$873$	10.2191	0.345866
$874$	41.2796	1.39630
$875$	4.62711	0.156425
$876$	103.363	3.49231
$877$	−16.5584	−0.559138	−0.279569	−	0.960126i	$-0.590192\pi$
$877$	−16.5584	−0.559138	−0.279569	+	0.960126i	$0.590192\pi$
$878$	−8.52855	−0.287824
$879$	8.57114	0.289097
$880$	77.0500	2.59735
$881$	30.8670	1.03993	0.519967	−	0.854186i	$-0.325944\pi$
$881$	30.8670	1.03993	0.519967	+	0.854186i	$0.325944\pi$
$882$	−30.3331	−1.02137
$883$	−15.8176	−0.532304	−0.266152	−	0.963931i	$-0.585752\pi$
$883$	−15.8176	−0.532304	−0.266152	+	0.963931i	$0.585752\pi$
$884$	−50.8029	−1.70869
$885$	20.4473	0.687329
$886$	53.5918	1.80045
$887$	−43.7016	−1.46736	−0.733678	−	0.679498i	$-0.762198\pi$
$887$	−43.7016	−1.46736	−0.733678	+	0.679498i	$0.762198\pi$
$888$	−86.2261	−2.89356
$889$	−87.3724	−2.93038
$890$	39.5490	1.32569
$891$	60.8173	2.03746
$892$	13.3396	0.446642
$893$	4.42485	0.148072
$894$	53.0895	1.77558
$895$	12.0555	0.402971
$896$	123.041	4.11052
$897$	−38.6801	−1.29149
$898$	−4.68927	−0.156483
$899$	−15.9633	−0.532406
$900$	4.13511	0.137837
$901$	−43.7854	−1.45870
$902$	−85.0730	−2.83262
$903$	−99.7740	−3.32027
$904$	−57.2887	−1.90540
$905$	14.6848	0.488141
$906$	122.843	4.08119
$907$	−19.7155	−0.654642	−0.327321	−	0.944913i	$-0.606146\pi$
$907$	−19.7155	−0.654642	−0.327321	+	0.944913i	$0.606146\pi$
$908$	0.615621	0.0204301
$909$	−10.4991	−0.348232
$910$	33.5445	1.11199
$911$	24.9811	0.827661	0.413830	−	0.910354i	$-0.364191\pi$
$911$	24.9811	0.827661	0.413830	+	0.910354i	$0.364191\pi$
$912$	−54.3448	−1.79954
$913$	23.1500	0.766153
$914$	−88.1462	−2.91562
$915$	−23.2338	−0.768086
$916$	68.0457	2.24829
$917$	74.9638	2.47552
$918$	−41.6551	−1.37482
$919$	−16.5628	−0.546357	−0.273178	−	0.961963i	$-0.588075\pi$
$919$	−16.5628	−0.546357	−0.273178	+	0.961963i	$0.588075\pi$
$920$	−66.4723	−2.19153
$921$	41.1983	1.35753
$922$	−112.228	−3.69602
$923$	3.30695	0.108849
$924$	−270.817	−8.90922
$925$	−4.95311	−0.162857
$926$	−90.4545	−2.97252
$927$	8.65651	0.284317
$928$	113.069	3.71167
$929$	−17.5646	−0.576274	−0.288137	−	0.957589i	$-0.593036\pi$
$929$	−17.5646	−0.576274	−0.288137	+	0.957589i	$0.593036\pi$
$930$	−13.9847	−0.458576
$931$	29.6381	0.971348
$932$	−46.6476	−1.52799
$933$	−23.5900	−0.772301
$934$	−24.3621	−0.797152
$935$	20.2205	0.661280
$936$	18.6909	0.610930
$937$	44.4375	1.45171	0.725856	−	0.687847i	$-0.241444\pi$
$937$	44.4375	1.45171	0.725856	+	0.687847i	$0.241444\pi$
$938$	72.2528	2.35914
$939$	3.10920	0.101465
$940$	−11.4281	−0.372743
$941$	−43.6048	−1.42148	−0.710738	−	0.703457i	$-0.751639\pi$
$941$	−43.6048	−1.42148	−0.710738	+	0.703457i	$0.751639\pi$
$942$	−78.5947	−2.56075
$943$	41.1963	1.34154
$944$	142.988	4.65386
$945$	19.9813	0.649990
$946$	−170.028	−5.52809
$947$	−20.3440	−0.661090	−0.330545	−	0.943790i	$-0.607233\pi$
$947$	−20.3440	−0.661090	−0.330545	+	0.943790i	$0.607233\pi$
$948$	−160.053	−5.19829
$949$	26.8377	0.871190
$950$	−5.56159	−0.180442
$951$	−14.8131	−0.480347
$952$	147.827	4.79109
$953$	−10.8683	−0.352058	−0.176029	−	0.984385i	$-0.556325\pi$
$953$	−10.8683	−0.352058	−0.176029	+	0.984385i	$0.556325\pi$
$954$	25.8368	0.836498
$955$	−5.41865	−0.175344
$956$	−69.8647	−2.25959
$957$	−66.1080	−2.13697
$958$	60.3373	1.94941
$959$	−10.9088	−0.352262
$960$	46.2090	1.49139
$961$	−23.9212	−0.771653
$962$	−35.9078	−1.15771
$963$	1.33906	0.0431506
$964$	154.536	4.97728
$965$	0.461095	0.0148432
$966$	180.518	5.80807
$967$	−55.2203	−1.77577	−0.887883	−	0.460069i	$-0.847825\pi$
$967$	−55.2203	−1.77577	−0.887883	+	0.460069i	$0.847825\pi$
$968$	−189.233	−6.08218
$969$	−14.2619	−0.458158
$970$	35.4977	1.13976
$971$	−20.3343	−0.652557	−0.326279	−	0.945274i	$-0.605795\pi$
$971$	−20.3343	−0.652557	−0.326279	+	0.945274i	$0.605795\pi$
$972$	41.9704	1.34620
$973$	38.2675	1.22680
$974$	−32.6919	−1.04752
$975$	5.21136	0.166897
$976$	−162.474	−5.20066
$977$	26.5092	0.848103	0.424052	−	0.905638i	$-0.360608\pi$
$977$	26.5092	0.848103	0.424052	+	0.905638i	$0.360608\pi$
$978$	91.3639	2.92150
$979$	−82.9032	−2.64960
$980$	−76.5463	−2.44518
$981$	−6.99366	−0.223290
$982$	11.9445	0.381165
$983$	−47.4881	−1.51464	−0.757318	−	0.653046i	$-0.773491\pi$
$983$	−47.4881	−1.51464	−0.757318	+	0.653046i	$0.773491\pi$
$984$	−96.6235	−3.08025
$985$	−22.2946	−0.710364
$986$	57.8762	1.84315
$987$	19.3501	0.615922
$988$	−29.2908	−0.931865
$989$	82.3355	2.61812
$990$	−11.9317	−0.379214
$991$	46.1414	1.46573	0.732865	−	0.680374i	$-0.238183\pi$
$991$	46.1414	1.46573	0.732865	+	0.680374i	$0.238183\pi$
$992$	−50.1393	−1.59192
$993$	−64.0527	−2.03265
$994$	−15.4334	−0.489516
$995$	−21.0990	−0.668883
$996$	42.1707	1.33623
$997$	14.4134	0.456477	0.228239	−	0.973605i	$-0.426703\pi$
$997$	14.4134	0.456477	0.228239	+	0.973605i	$0.426703\pi$
$998$	80.0217	2.53304
$999$	−21.3890	−0.676718

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.7	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.7	✓	140	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70407 q^{2} -1.94382 q^{3} +5.31198 q^{4} -1.00000 q^{5} +5.25623 q^{6} -4.62711 q^{7} -8.95580 q^{8} +0.778451 q^{9} +O(q^{10})\)	\(q-2.70407 q^{2} -1.94382 q^{3} +5.31198 q^{4} -1.00000 q^{5} +5.25623 q^{6} -4.62711 q^{7} -8.95580 q^{8} +0.778451 q^{9} +2.70407 q^{10} -5.66830 q^{11} -10.3255 q^{12} -2.68098 q^{13} +12.5120 q^{14} +1.94382 q^{15} +13.5931 q^{16} +3.56729 q^{17} -2.10498 q^{18} +2.05675 q^{19} -5.31198 q^{20} +8.99429 q^{21} +15.3275 q^{22} -7.42227 q^{23} +17.4085 q^{24} +1.00000 q^{25} +7.24955 q^{26} +4.31830 q^{27} -24.5791 q^{28} -5.99990 q^{29} -5.25623 q^{30} +2.66060 q^{31} -18.8451 q^{32} +11.0182 q^{33} -9.64619 q^{34} +4.62711 q^{35} +4.13511 q^{36} -4.95311 q^{37} -5.56159 q^{38} +5.21136 q^{39} +8.95580 q^{40} -5.55037 q^{41} -24.3211 q^{42} -11.0930 q^{43} -30.1099 q^{44} -0.778451 q^{45} +20.0703 q^{46} +2.15138 q^{47} -26.4227 q^{48} +14.4101 q^{49} -2.70407 q^{50} -6.93418 q^{51} -14.2413 q^{52} -12.2741 q^{53} -11.6770 q^{54} +5.66830 q^{55} +41.4395 q^{56} -3.99796 q^{57} +16.2241 q^{58} +10.5191 q^{59} +10.3255 q^{60} -11.9526 q^{61} -7.19443 q^{62} -3.60198 q^{63} +23.7722 q^{64} +2.68098 q^{65} -29.7939 q^{66} +5.77467 q^{67} +18.9494 q^{68} +14.4276 q^{69} -12.5120 q^{70} -1.23348 q^{71} -6.97165 q^{72} -10.0104 q^{73} +13.3935 q^{74} -1.94382 q^{75} +10.9254 q^{76} +26.2279 q^{77} -14.0919 q^{78} +15.5007 q^{79} -13.5931 q^{80} -10.7294 q^{81} +15.0086 q^{82} -4.08411 q^{83} +47.7774 q^{84} -3.56729 q^{85} +29.9963 q^{86} +11.6628 q^{87} +50.7642 q^{88} +14.6258 q^{89} +2.10498 q^{90} +12.4052 q^{91} -39.4269 q^{92} -5.17173 q^{93} -5.81748 q^{94} -2.05675 q^{95} +36.6316 q^{96} +13.1275 q^{97} -38.9660 q^{98} -4.41249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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