LMFDB - Embedded newform 8035.2.a.c.1.1

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:	$127$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.73873 q^{2} +0.672106 q^{3} +5.50064 q^{4} -1.00000 q^{5} -1.84072 q^{6} -4.04942 q^{7} -9.58729 q^{8} -2.54827 q^{9} +O(q^{10})$	\(q-2.73873 q^{2} +0.672106 q^{3} +5.50064 q^{4} -1.00000 q^{5} -1.84072 q^{6} -4.04942 q^{7} -9.58729 q^{8} -2.54827 q^{9} +2.73873 q^{10} +0.460312 q^{11} +3.69701 q^{12} +4.70974 q^{13} +11.0903 q^{14} -0.672106 q^{15} +15.2557 q^{16} +1.88989 q^{17} +6.97903 q^{18} -0.896877 q^{19} -5.50064 q^{20} -2.72164 q^{21} -1.26067 q^{22} +7.89725 q^{23} -6.44367 q^{24} +1.00000 q^{25} -12.8987 q^{26} -3.72903 q^{27} -22.2744 q^{28} +2.07462 q^{29} +1.84072 q^{30} -7.14822 q^{31} -22.6067 q^{32} +0.309378 q^{33} -5.17590 q^{34} +4.04942 q^{35} -14.0171 q^{36} -7.38534 q^{37} +2.45630 q^{38} +3.16545 q^{39} +9.58729 q^{40} -4.34092 q^{41} +7.45383 q^{42} +5.12899 q^{43} +2.53201 q^{44} +2.54827 q^{45} -21.6284 q^{46} +11.3612 q^{47} +10.2535 q^{48} +9.39780 q^{49} -2.73873 q^{50} +1.27021 q^{51} +25.9066 q^{52} -2.32300 q^{53} +10.2128 q^{54} -0.460312 q^{55} +38.8230 q^{56} -0.602796 q^{57} -5.68182 q^{58} -12.4749 q^{59} -3.69701 q^{60} -8.13512 q^{61} +19.5770 q^{62} +10.3190 q^{63} +31.4022 q^{64} -4.70974 q^{65} -0.847303 q^{66} +10.8075 q^{67} +10.3956 q^{68} +5.30779 q^{69} -11.0903 q^{70} +0.719061 q^{71} +24.4310 q^{72} -3.20538 q^{73} +20.2265 q^{74} +0.672106 q^{75} -4.93339 q^{76} -1.86400 q^{77} -8.66930 q^{78} +7.37343 q^{79} -15.2557 q^{80} +5.13852 q^{81} +11.8886 q^{82} +3.92971 q^{83} -14.9707 q^{84} -1.88989 q^{85} -14.0469 q^{86} +1.39436 q^{87} -4.41315 q^{88} -12.8480 q^{89} -6.97903 q^{90} -19.0717 q^{91} +43.4399 q^{92} -4.80436 q^{93} -31.1152 q^{94} +0.896877 q^{95} -15.1941 q^{96} -6.91020 q^{97} -25.7380 q^{98} -1.17300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) $ 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * 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 $

$2$	−2.73873	−1.93657	−0.968287	−	0.249841i	$-0.919622\pi$
$2$	−2.73873	−1.93657	−0.968287	+	0.249841i	$0.919622\pi$
$3$	0.672106	0.388040	0.194020	−	0.980998i	$-0.437847\pi$
$3$	0.672106	0.388040	0.194020	+	0.980998i	$0.437847\pi$
$4$	5.50064	2.75032
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.84072	−0.751469
$7$	−4.04942	−1.53054	−0.765268	−	0.643711i	$-0.777394\pi$
$7$	−4.04942	−1.53054	−0.765268	+	0.643711i	$0.777394\pi$
$8$	−9.58729	−3.38962
$9$	−2.54827	−0.849425
$10$	2.73873	0.866062
$11$	0.460312	0.138789	0.0693946	−	0.997589i	$-0.477893\pi$
$11$	0.460312	0.138789	0.0693946	+	0.997589i	$0.477893\pi$
$12$	3.69701	1.06723
$13$	4.70974	1.30625	0.653124	−	0.757251i	$-0.273458\pi$
$13$	4.70974	1.30625	0.653124	+	0.757251i	$0.273458\pi$
$14$	11.0903	2.96400
$15$	−0.672106	−0.173537
$16$	15.2557	3.81393
$17$	1.88989	0.458366	0.229183	−	0.973383i	$-0.426395\pi$
$17$	1.88989	0.458366	0.229183	+	0.973383i	$0.426395\pi$
$18$	6.97903	1.64497
$19$	−0.896877	−0.205758	−0.102879	−	0.994694i	$-0.532805\pi$
$19$	−0.896877	−0.205758	−0.102879	+	0.994694i	$0.532805\pi$
$20$	−5.50064	−1.22998
$21$	−2.72164	−0.593910
$22$	−1.26067	−0.268776
$23$	7.89725	1.64669	0.823346	−	0.567540i	$-0.192105\pi$
$23$	7.89725	1.64669	0.823346	+	0.567540i	$0.192105\pi$
$24$	−6.44367	−1.31531
$25$	1.00000	0.200000
$26$	−12.8987	−2.52964
$27$	−3.72903	−0.717652
$28$	−22.2744	−4.20946
$29$	2.07462	0.385247	0.192624	−	0.981273i	$-0.438300\pi$
$29$	2.07462	0.385247	0.192624	+	0.981273i	$0.438300\pi$
$30$	1.84072	0.336067
$31$	−7.14822	−1.28386	−0.641929	−	0.766764i	$-0.721866\pi$
$31$	−7.14822	−1.28386	−0.641929	+	0.766764i	$0.721866\pi$
$32$	−22.6067	−3.99634
$33$	0.309378	0.0538558
$34$	−5.17590	−0.887660
$35$	4.04942	0.684477
$36$	−14.0171	−2.33619
$37$	−7.38534	−1.21414	−0.607071	−	0.794647i	$-0.707656\pi$
$37$	−7.38534	−1.21414	−0.607071	+	0.794647i	$0.707656\pi$
$38$	2.45630	0.398465
$39$	3.16545	0.506877
$40$	9.58729	1.51588
$41$	−4.34092	−0.677938	−0.338969	−	0.940798i	$-0.610078\pi$
$41$	−4.34092	−0.677938	−0.338969	+	0.940798i	$0.610078\pi$
$42$	7.45383	1.15015
$43$	5.12899	0.782163	0.391082	−	0.920356i	$-0.372101\pi$
$43$	5.12899	0.782163	0.391082	+	0.920356i	$0.372101\pi$
$44$	2.53201	0.381715
$45$	2.54827	0.379874
$46$	−21.6284	−3.18894
$47$	11.3612	1.65720	0.828598	−	0.559844i	$-0.189139\pi$
$47$	11.3612	1.65720	0.828598	+	0.559844i	$0.189139\pi$
$48$	10.2535	1.47996
$49$	9.39780	1.34254
$50$	−2.73873	−0.387315
$51$	1.27021	0.177865
$52$	25.9066	3.59260
$53$	−2.32300	−0.319089	−0.159544	−	0.987191i	$-0.551003\pi$
$53$	−2.32300	−0.319089	−0.159544	+	0.987191i	$0.551003\pi$
$54$	10.2128	1.38979
$55$	−0.460312	−0.0620685
$56$	38.8230	5.18794
$57$	−0.602796	−0.0798423
$58$	−5.68182	−0.746060
$59$	−12.4749	−1.62409	−0.812044	−	0.583596i	$-0.801645\pi$
$59$	−12.4749	−1.62409	−0.812044	+	0.583596i	$0.801645\pi$
$60$	−3.69701	−0.477282
$61$	−8.13512	−1.04160	−0.520798	−	0.853680i	$-0.674365\pi$
$61$	−8.13512	−1.04160	−0.520798	+	0.853680i	$0.674365\pi$
$62$	19.5770	2.48629
$63$	10.3190	1.30008
$64$	31.4022	3.92527
$65$	−4.70974	−0.584172
$66$	−0.847303	−0.104296
$67$	10.8075	1.32035	0.660173	−	0.751113i	$-0.270483\pi$
$67$	10.8075	1.32035	0.660173	+	0.751113i	$0.270483\pi$
$68$	10.3956	1.26065
$69$	5.30779	0.638983
$70$	−11.0903	−1.32554
$71$	0.719061	0.0853369	0.0426684	−	0.999089i	$-0.486414\pi$
$71$	0.719061	0.0853369	0.0426684	+	0.999089i	$0.486414\pi$
$72$	24.4310	2.87923
$73$	−3.20538	−0.375162	−0.187581	−	0.982249i	$-0.560065\pi$
$73$	−3.20538	−0.375162	−0.187581	+	0.982249i	$0.560065\pi$
$74$	20.2265	2.35128
$75$	0.672106	0.0776081
$76$	−4.93339	−0.565899
$77$	−1.86400	−0.212422
$78$	−8.66930	−0.981604
$79$	7.37343	0.829576	0.414788	−	0.909918i	$-0.363856\pi$
$79$	7.37343	0.829576	0.414788	+	0.909918i	$0.363856\pi$
$80$	−15.2557	−1.70564
$81$	5.13852	0.570947
$82$	11.8886	1.31288
$83$	3.92971	0.431341	0.215671	−	0.976466i	$-0.430806\pi$
$83$	3.92971	0.431341	0.215671	+	0.976466i	$0.430806\pi$
$84$	−14.9707	−1.63344
$85$	−1.88989	−0.204988
$86$	−14.0469	−1.51472
$87$	1.39436	0.149492
$88$	−4.41315	−0.470443
$89$	−12.8480	−1.36189	−0.680945	−	0.732335i	$-0.738431\pi$
$89$	−12.8480	−1.36189	−0.680945	+	0.732335i	$0.738431\pi$
$90$	−6.97903	−0.735655
$91$	−19.0717	−1.99926
$92$	43.4399	4.52892
$93$	−4.80436	−0.498189
$94$	−31.1152	−3.20928
$95$	0.896877	0.0920176
$96$	−15.1941	−1.55074
$97$	−6.91020	−0.701625	−0.350812	−	0.936446i	$-0.614094\pi$
$97$	−6.91020	−0.701625	−0.350812	+	0.936446i	$0.614094\pi$
$98$	−25.7380	−2.59993
$99$	−1.17300	−0.117891
$100$	5.50064	0.550064
$101$	−5.64649	−0.561847	−0.280924	−	0.959730i	$-0.590641\pi$
$101$	−5.64649	−0.561847	−0.280924	+	0.959730i	$0.590641\pi$
$102$	−3.47875	−0.344448
$103$	5.65716	0.557417	0.278708	−	0.960376i	$-0.410094\pi$
$103$	5.65716	0.557417	0.278708	+	0.960376i	$0.410094\pi$
$104$	−45.1537	−4.42768
$105$	2.72164	0.265605
$106$	6.36207	0.617939
$107$	−0.267149	−0.0258263	−0.0129132	−	0.999917i	$-0.504110\pi$
$107$	−0.267149	−0.0258263	−0.0129132	+	0.999917i	$0.504110\pi$
$108$	−20.5120	−1.97377
$109$	−4.45431	−0.426645	−0.213323	−	0.976982i	$-0.568429\pi$
$109$	−4.45431	−0.426645	−0.213323	+	0.976982i	$0.568429\pi$
$110$	1.26067	0.120200
$111$	−4.96373	−0.471137
$112$	−61.7768	−5.83736
$113$	8.67867	0.816421	0.408210	−	0.912888i	$-0.366153\pi$
$113$	8.67867	0.816421	0.408210	+	0.912888i	$0.366153\pi$
$114$	1.65089	0.154620
$115$	−7.89725	−0.736423
$116$	11.4117	1.05955
$117$	−12.0017	−1.10956
$118$	34.1653	3.14517
$119$	−7.65297	−0.701546
$120$	6.44367	0.588224
$121$	−10.7881	−0.980738
$122$	22.2799	2.01713
$123$	−2.91756	−0.263067
$124$	−39.3197	−3.53102
$125$	−1.00000	−0.0894427
$126$	−28.2610	−2.51769
$127$	−17.9999	−1.59724	−0.798618	−	0.601838i	$-0.794435\pi$
$127$	−17.9999	−1.59724	−0.798618	+	0.601838i	$0.794435\pi$
$128$	−40.7887	−3.60524
$129$	3.44722	0.303511
$130$	12.8987	1.13129
$131$	10.6006	0.926175	0.463087	−	0.886313i	$-0.346742\pi$
$131$	10.6006	0.926175	0.463087	+	0.886313i	$0.346742\pi$
$132$	1.70178	0.148121
$133$	3.63183	0.314920
$134$	−29.5988	−2.55695
$135$	3.72903	0.320944
$136$	−18.1190	−1.55369
$137$	0.399871	0.0341633	0.0170816	−	0.999854i	$-0.494562\pi$
$137$	0.399871	0.0341633	0.0170816	+	0.999854i	$0.494562\pi$
$138$	−14.5366	−1.23744
$139$	5.78024	0.490273	0.245137	−	0.969489i	$-0.421167\pi$
$139$	5.78024	0.490273	0.245137	+	0.969489i	$0.421167\pi$
$140$	22.2744	1.88253
$141$	7.63590	0.643059
$142$	−1.96931	−0.165261
$143$	2.16795	0.181293
$144$	−38.8758	−3.23965
$145$	−2.07462	−0.172288
$146$	8.77868	0.726529
$147$	6.31631	0.520961
$148$	−40.6241	−3.33928
$149$	10.5286	0.862533	0.431267	−	0.902224i	$-0.358067\pi$
$149$	10.5286	0.862533	0.431267	+	0.902224i	$0.358067\pi$
$150$	−1.84072	−0.150294
$151$	−2.14284	−0.174382	−0.0871910	−	0.996192i	$-0.527789\pi$
$151$	−2.14284	−0.174382	−0.0871910	+	0.996192i	$0.527789\pi$
$152$	8.59862	0.697440
$153$	−4.81596	−0.389348
$154$	5.10498	0.411371
$155$	7.14822	0.574159
$156$	17.4120	1.39407
$157$	−20.1647	−1.60932	−0.804658	−	0.593739i	$-0.797651\pi$
$157$	−20.1647	−1.60932	−0.804658	+	0.593739i	$0.797651\pi$
$158$	−20.1938	−1.60653
$159$	−1.56130	−0.123819
$160$	22.6067	1.78722
$161$	−31.9793	−2.52032
$162$	−14.0730	−1.10568
$163$	0.0189603	0.00148508	0.000742542	−	1.00000i	$-0.499764\pi$
$163$	0.0189603	0.00148508	0.000742542		1.00000i	$0.499764\pi$
$164$	−23.8778	−1.86455
$165$	−0.309378	−0.0240851
$166$	−10.7624	−0.835324
$167$	−14.2128	−1.09982	−0.549908	−	0.835225i	$-0.685337\pi$
$167$	−14.2128	−1.09982	−0.549908	+	0.835225i	$0.685337\pi$
$168$	26.0931	2.01313
$169$	9.18168	0.706283
$170$	5.17590	0.396974
$171$	2.28549	0.174776
$172$	28.2127	2.15120
$173$	8.49028	0.645504	0.322752	−	0.946484i	$-0.395392\pi$
$173$	8.49028	0.645504	0.322752	+	0.946484i	$0.395392\pi$
$174$	−3.81878	−0.289501
$175$	−4.04942	−0.306107
$176$	7.02239	0.529333
$177$	−8.38443	−0.630212
$178$	35.1873	2.63740
$179$	3.15156	0.235559	0.117779	−	0.993040i	$-0.462422\pi$
$179$	3.15156	0.235559	0.117779	+	0.993040i	$0.462422\pi$
$180$	14.0171	1.04477
$181$	−13.9785	−1.03901	−0.519507	−	0.854466i	$-0.673884\pi$
$181$	−13.9785	−1.03901	−0.519507	+	0.854466i	$0.673884\pi$
$182$	52.2323	3.87171
$183$	−5.46766	−0.404181
$184$	−75.7133	−5.58166
$185$	7.38534	0.542981
$186$	13.1578	0.964779
$187$	0.869940	0.0636163
$188$	62.4936	4.55782
$189$	15.1004	1.09839
$190$	−2.45630	−0.178199
$191$	9.49051	0.686709	0.343355	−	0.939206i	$-0.388437\pi$
$191$	9.49051	0.686709	0.343355	+	0.939206i	$0.388437\pi$
$192$	21.1056	1.52317
$193$	7.53441	0.542338	0.271169	−	0.962532i	$-0.412590\pi$
$193$	7.53441	0.542338	0.271169	+	0.962532i	$0.412590\pi$
$194$	18.9252	1.35875
$195$	−3.16545	−0.226682
$196$	51.6939	3.69242
$197$	18.6098	1.32589	0.662946	−	0.748667i	$-0.269306\pi$
$197$	18.6098	1.32589	0.662946	+	0.748667i	$0.269306\pi$
$198$	3.21253	0.228305
$199$	−3.59780	−0.255041	−0.127521	−	0.991836i	$-0.540702\pi$
$199$	−3.59780	−0.255041	−0.127521	+	0.991836i	$0.540702\pi$
$200$	−9.58729	−0.677924
$201$	7.26379	0.512348
$202$	15.4642	1.08806
$203$	−8.40101	−0.589635
$204$	6.98695	0.489184
$205$	4.34092	0.303183
$206$	−15.4934	−1.07948
$207$	−20.1244	−1.39874
$208$	71.8505	4.98194
$209$	−0.412843	−0.0285569
$210$	−7.45383	−0.514363
$211$	11.7418	0.808338	0.404169	−	0.914684i	$-0.367561\pi$
$211$	11.7418	0.808338	0.404169	+	0.914684i	$0.367561\pi$
$212$	−12.7780	−0.877596
$213$	0.483285	0.0331142
$214$	0.731650	0.0500145
$215$	−5.12899	−0.349794
$216$	35.7513	2.43257
$217$	28.9461	1.96499
$218$	12.1991	0.826230
$219$	−2.15436	−0.145578
$220$	−2.53201	−0.170708
$221$	8.90091	0.598740
$222$	13.5943	0.912391
$223$	−7.30162	−0.488952	−0.244476	−	0.969655i	$-0.578616\pi$
$223$	−7.30162	−0.488952	−0.244476	+	0.969655i	$0.578616\pi$
$224$	91.5440	6.11654
$225$	−2.54827	−0.169885
$226$	−23.7685	−1.58106
$227$	8.94938	0.593991	0.296995	−	0.954879i	$-0.404015\pi$
$227$	8.94938	0.593991	0.296995	+	0.954879i	$0.404015\pi$
$228$	−3.31576	−0.219592
$229$	−9.91003	−0.654873	−0.327437	−	0.944873i	$-0.606185\pi$
$229$	−9.91003	−0.654873	−0.327437	+	0.944873i	$0.606185\pi$
$230$	21.6284	1.42614
$231$	−1.25280	−0.0824284
$232$	−19.8900	−1.30584
$233$	−11.4368	−0.749248	−0.374624	−	0.927177i	$-0.622228\pi$
$233$	−11.4368	−0.749248	−0.374624	+	0.927177i	$0.622228\pi$
$234$	32.8694	2.14874
$235$	−11.3612	−0.741121
$236$	−68.6197	−4.46676
$237$	4.95573	0.321909
$238$	20.9594	1.35860
$239$	16.9253	1.09481	0.547405	−	0.836868i	$-0.315616\pi$
$239$	16.9253	1.09481	0.547405	+	0.836868i	$0.315616\pi$
$240$	−10.2535	−0.661858
$241$	−10.3712	−0.668065	−0.334033	−	0.942562i	$-0.608410\pi$
$241$	−10.3712	−0.668065	−0.334033	+	0.942562i	$0.608410\pi$
$242$	29.5457	1.89927
$243$	14.6407	0.939202
$244$	−44.7483	−2.86472
$245$	−9.39780	−0.600403
$246$	7.99040	0.509449
$247$	−4.22406	−0.268770
$248$	68.5320	4.35179
$249$	2.64118	0.167378
$250$	2.73873	0.173212
$251$	−24.0454	−1.51773	−0.758865	−	0.651248i	$-0.774246\pi$
$251$	−24.0454	−1.51773	−0.758865	+	0.651248i	$0.774246\pi$
$252$	56.7612	3.57562
$253$	3.63520	0.228543
$254$	49.2970	3.09317
$255$	−1.27021	−0.0795435
$256$	48.9048	3.05655
$257$	15.6555	0.976562	0.488281	−	0.872686i	$-0.337624\pi$
$257$	15.6555	0.976562	0.488281	+	0.872686i	$0.337624\pi$
$258$	−9.44100	−0.587771
$259$	29.9064	1.85829
$260$	−25.9066	−1.60666
$261$	−5.28670	−0.327239
$262$	−29.0320	−1.79361
$263$	−3.58626	−0.221138	−0.110569	−	0.993868i	$-0.535267\pi$
$263$	−3.58626	−0.221138	−0.110569	+	0.993868i	$0.535267\pi$
$264$	−2.96610	−0.182551
$265$	2.32300	0.142701
$266$	−9.94660	−0.609865
$267$	−8.63524	−0.528468
$268$	59.4481	3.63137
$269$	23.0733	1.40680	0.703401	−	0.710793i	$-0.251664\pi$
$269$	23.0733	1.40680	0.703401	+	0.710793i	$0.251664\pi$
$270$	−10.2128	−0.621531
$271$	−24.3432	−1.47874	−0.739372	−	0.673297i	$-0.764877\pi$
$271$	−24.3432	−1.47874	−0.739372	+	0.673297i	$0.764877\pi$
$272$	28.8317	1.74818
$273$	−12.8182	−0.775794
$274$	−1.09514	−0.0661597
$275$	0.460312	0.0277579
$276$	29.1962	1.75741
$277$	9.41866	0.565912	0.282956	−	0.959133i	$-0.408685\pi$
$277$	9.41866	0.565912	0.282956	+	0.959133i	$0.408685\pi$
$278$	−15.8305	−0.949451
$279$	18.2156	1.09054
$280$	−38.8230	−2.32012
$281$	22.8523	1.36326	0.681628	−	0.731699i	$-0.261272\pi$
$281$	22.8523	1.36326	0.681628	+	0.731699i	$0.261272\pi$
$282$	−20.9127	−1.24533
$283$	−10.8492	−0.644917	−0.322458	−	0.946584i	$-0.604509\pi$
$283$	−10.8492	−0.644917	−0.322458	+	0.946584i	$0.604509\pi$
$284$	3.95530	0.234704
$285$	0.602796	0.0357065
$286$	−5.93743	−0.351088
$287$	17.5782	1.03761
$288$	57.6081	3.39459
$289$	−13.4283	−0.789900
$290$	5.68182	0.333648
$291$	−4.64439	−0.272259
$292$	−17.6317	−1.03181
$293$	−7.24594	−0.423312	−0.211656	−	0.977344i	$-0.567886\pi$
$293$	−7.24594	−0.423312	−0.211656	+	0.977344i	$0.567886\pi$
$294$	−17.2987	−1.00888
$295$	12.4749	0.726315
$296$	70.8054	4.11548
$297$	−1.71652	−0.0996023
$298$	−28.8349	−1.67036
$299$	37.1940	2.15099
$300$	3.69701	0.213447
$301$	−20.7694	−1.19713
$302$	5.86866	0.337704
$303$	−3.79504	−0.218019
$304$	−13.6825	−0.784745
$305$	8.13512	0.465816
$306$	13.1896	0.754000
$307$	−6.32300	−0.360873	−0.180436	−	0.983587i	$-0.557751\pi$
$307$	−6.32300	−0.360873	−0.180436	+	0.983587i	$0.557751\pi$
$308$	−10.2532	−0.584228
$309$	3.80221	0.216300
$310$	−19.5770	−1.11190
$311$	19.9361	1.13047	0.565237	−	0.824929i	$-0.308785\pi$
$311$	19.9361	1.13047	0.565237	+	0.824929i	$0.308785\pi$
$312$	−30.3480	−1.71812
$313$	−23.2465	−1.31397	−0.656986	−	0.753903i	$-0.728169\pi$
$313$	−23.2465	−1.31397	−0.656986	+	0.753903i	$0.728169\pi$
$314$	55.2256	3.11656
$315$	−10.3190	−0.581411
$316$	40.5586	2.28160
$317$	1.33149	0.0747839	0.0373919	−	0.999301i	$-0.488095\pi$
$317$	1.33149	0.0747839	0.0373919	+	0.999301i	$0.488095\pi$
$318$	4.27599	0.239785
$319$	0.954972	0.0534682
$320$	−31.4022	−1.75544
$321$	−0.179553	−0.0100216
$322$	87.5826	4.88079
$323$	−1.69500	−0.0943123
$324$	28.2651	1.57029
$325$	4.70974	0.261250
$326$	−0.0519271	−0.00287597
$327$	−2.99377	−0.165556
$328$	41.6177	2.29795
$329$	−46.0061	−2.53640
$330$	0.847303	0.0466425
$331$	2.80261	0.154045	0.0770227	−	0.997029i	$-0.475459\pi$
$331$	2.80261	0.154045	0.0770227	+	0.997029i	$0.475459\pi$
$332$	21.6159	1.18633
$333$	18.8199	1.03132
$334$	38.9249	2.12988
$335$	−10.8075	−0.590477
$336$	−41.5206	−2.26513
$337$	35.5167	1.93472	0.967360	−	0.253407i	$-0.0815512\pi$
$337$	35.5167	1.93472	0.967360	+	0.253407i	$0.0815512\pi$
$338$	−25.1461	−1.36777
$339$	5.83299	0.316804
$340$	−10.3956	−0.563781
$341$	−3.29041	−0.178186
$342$	−6.25933	−0.338466
$343$	−9.70969	−0.524274
$344$	−49.1731	−2.65124
$345$	−5.30779	−0.285762
$346$	−23.2526	−1.25007
$347$	−22.5308	−1.20952	−0.604759	−	0.796408i	$-0.706731\pi$
$347$	−22.5308	−1.20952	−0.604759	+	0.796408i	$0.706731\pi$
$348$	7.66989	0.411149
$349$	−0.523580	−0.0280266	−0.0140133	−	0.999902i	$-0.504461\pi$
$349$	−0.523580	−0.0280266	−0.0140133	+	0.999902i	$0.504461\pi$
$350$	11.0903	0.592799
$351$	−17.5628	−0.937431
$352$	−10.4061	−0.554649
$353$	24.9522	1.32807	0.664036	−	0.747701i	$-0.268842\pi$
$353$	24.9522	1.32807	0.664036	+	0.747701i	$0.268842\pi$
$354$	22.9627	1.22045
$355$	−0.719061	−0.0381638
$356$	−70.6724	−3.74563
$357$	−5.14360	−0.272228
$358$	−8.63128	−0.456177
$359$	8.80305	0.464607	0.232304	−	0.972643i	$-0.425374\pi$
$359$	8.80305	0.464607	0.232304	+	0.972643i	$0.425374\pi$
$360$	−24.4310	−1.28763
$361$	−18.1956	−0.957664
$362$	38.2833	2.01213
$363$	−7.25075	−0.380566
$364$	−104.907	−5.49860
$365$	3.20538	0.167778
$366$	14.9744	0.782726
$367$	37.0035	1.93157	0.965785	−	0.259345i	$-0.0835067\pi$
$367$	37.0035	1.93157	0.965785	+	0.259345i	$0.0835067\pi$
$368$	120.478	6.28037
$369$	11.0619	0.575857
$370$	−20.2265	−1.05152
$371$	9.40681	0.488377
$372$	−26.4270	−1.37018
$373$	24.5833	1.27287	0.636437	−	0.771329i	$-0.280408\pi$
$373$	24.5833	1.27287	0.636437	+	0.771329i	$0.280408\pi$
$374$	−2.38253	−0.123198
$375$	−0.672106	−0.0347074
$376$	−108.923	−5.61727
$377$	9.77093	0.503228
$378$	−41.3559	−2.12712
$379$	12.3545	0.634609	0.317305	−	0.948324i	$-0.397222\pi$
$379$	12.3545	0.634609	0.317305	+	0.948324i	$0.397222\pi$
$380$	4.93339	0.253078
$381$	−12.0979	−0.619792
$382$	−25.9919	−1.32986
$383$	−21.6173	−1.10459	−0.552295	−	0.833649i	$-0.686248\pi$
$383$	−21.6173	−1.10459	−0.552295	+	0.833649i	$0.686248\pi$
$384$	−27.4143	−1.39898
$385$	1.86400	0.0949980
$386$	−20.6347	−1.05028
$387$	−13.0701	−0.664389
$388$	−38.0105	−1.92969
$389$	35.5079	1.80032	0.900160	−	0.435560i	$-0.143450\pi$
$389$	35.5079	1.80032	0.900160	+	0.435560i	$0.143450\pi$
$390$	8.66930	0.438987
$391$	14.9250	0.754788
$392$	−90.0995	−4.55071
$393$	7.12469	0.359393
$394$	−50.9671	−2.56769
$395$	−7.37343	−0.370998
$396$	−6.45225	−0.324238
$397$	−9.49768	−0.476675	−0.238337	−	0.971182i	$-0.576602\pi$
$397$	−9.49768	−0.476675	−0.238337	+	0.971182i	$0.576602\pi$
$398$	9.85340	0.493907
$399$	2.44097	0.122202
$400$	15.2557	0.762786
$401$	32.3349	1.61473	0.807364	−	0.590053i	$-0.200893\pi$
$401$	32.3349	1.61473	0.807364	+	0.590053i	$0.200893\pi$
$402$	−19.8935	−0.992200
$403$	−33.6663	−1.67704
$404$	−31.0593	−1.54526
$405$	−5.13852	−0.255335
$406$	23.0081	1.14187
$407$	−3.39956	−0.168510
$408$	−12.1778	−0.602893
$409$	38.0241	1.88017	0.940085	−	0.340940i	$-0.110745\pi$
$409$	38.0241	1.88017	0.940085	+	0.340940i	$0.110745\pi$
$410$	−11.8886	−0.587137
$411$	0.268756	0.0132567
$412$	31.1180	1.53307
$413$	50.5160	2.48573
$414$	55.1152	2.70876
$415$	−3.92971	−0.192902
$416$	−106.472	−5.22021
$417$	3.88493	0.190246
$418$	1.13067	0.0553026
$419$	−29.8806	−1.45976	−0.729881	−	0.683574i	$-0.760425\pi$
$419$	−29.8806	−1.45976	−0.729881	+	0.683574i	$0.760425\pi$
$420$	14.9707	0.730497
$421$	−0.946480	−0.0461286	−0.0230643	−	0.999734i	$-0.507342\pi$
$421$	−0.946480	−0.0461286	−0.0230643	+	0.999734i	$0.507342\pi$
$422$	−32.1576	−1.56541
$423$	−28.9514	−1.40766
$424$	22.2713	1.08159
$425$	1.88989	0.0916732
$426$	−1.32359	−0.0641280
$427$	32.9425	1.59420
$428$	−1.46949	−0.0710306
$429$	1.45709	0.0703491
$430$	14.0469	0.677402
$431$	6.21771	0.299497	0.149748	−	0.988724i	$-0.452154\pi$
$431$	6.21771	0.299497	0.149748	+	0.988724i	$0.452154\pi$
$432$	−56.8890	−2.73707
$433$	5.32847	0.256070	0.128035	−	0.991770i	$-0.459133\pi$
$433$	5.32847	0.256070	0.128035	+	0.991770i	$0.459133\pi$
$434$	−79.2756	−3.80535
$435$	−1.39436	−0.0668546
$436$	−24.5015	−1.17341
$437$	−7.08286	−0.338819
$438$	5.90020	0.281922
$439$	−27.1930	−1.29785	−0.648925	−	0.760853i	$-0.724781\pi$
$439$	−27.1930	−1.29785	−0.648925	+	0.760853i	$0.724781\pi$
$440$	4.41315	0.210388
$441$	−23.9482	−1.14039
$442$	−24.3772	−1.15950
$443$	19.6402	0.933136	0.466568	−	0.884485i	$-0.345490\pi$
$443$	19.6402	0.933136	0.466568	+	0.884485i	$0.345490\pi$
$444$	−27.3037	−1.29578
$445$	12.8480	0.609055
$446$	19.9971	0.946892
$447$	7.07631	0.334698
$448$	−127.161	−6.00778
$449$	23.2975	1.09948	0.549738	−	0.835337i	$-0.314727\pi$
$449$	23.2975	1.09948	0.549738	+	0.835337i	$0.314727\pi$
$450$	6.97903	0.328995
$451$	−1.99818	−0.0940906
$452$	47.7382	2.24542
$453$	−1.44022	−0.0676673
$454$	−24.5099	−1.15031
$455$	19.0717	0.894096
$456$	5.77918	0.270635
$457$	−0.782267	−0.0365929	−0.0182965	−	0.999833i	$-0.505824\pi$
$457$	−0.782267	−0.0365929	−0.0182965	+	0.999833i	$0.505824\pi$
$458$	27.1409	1.26821
$459$	−7.04746	−0.328947
$460$	−43.4399	−2.02540
$461$	−1.66376	−0.0774889	−0.0387444	−	0.999249i	$-0.512336\pi$
$461$	−1.66376	−0.0774889	−0.0387444	+	0.999249i	$0.512336\pi$
$462$	3.43109	0.159629
$463$	−2.28043	−0.105981	−0.0529903	−	0.998595i	$-0.516875\pi$
$463$	−2.28043	−0.105981	−0.0529903	+	0.998595i	$0.516875\pi$
$464$	31.6498	1.46931
$465$	4.80436	0.222797
$466$	31.3222	1.45097
$467$	−26.9150	−1.24548	−0.622739	−	0.782430i	$-0.713980\pi$
$467$	−26.9150	−1.24548	−0.622739	+	0.782430i	$0.713980\pi$
$468$	−66.0171	−3.05164
$469$	−43.7641	−2.02084
$470$	31.1152	1.43523
$471$	−13.5528	−0.624479
$472$	119.600	5.50504
$473$	2.36093	0.108556
$474$	−13.5724	−0.623401
$475$	−0.896877	−0.0411515
$476$	−42.0962	−1.92948
$477$	5.91965	0.271042
$478$	−46.3539	−2.12018
$479$	−21.9265	−1.00185	−0.500923	−	0.865492i	$-0.667006\pi$
$479$	−21.9265	−1.00185	−0.500923	+	0.865492i	$0.667006\pi$
$480$	15.1941	0.693513
$481$	−34.7831	−1.58597
$482$	28.4038	1.29376
$483$	−21.4935	−0.977987
$484$	−59.3415	−2.69734
$485$	6.91020	0.313776
$486$	−40.0969	−1.81883
$487$	3.14742	0.142623	0.0713116	−	0.997454i	$-0.477282\pi$
$487$	3.14742	0.142623	0.0713116	+	0.997454i	$0.477282\pi$
$488$	77.9938	3.53061
$489$	0.0127433	0.000576272 0
$490$	25.7380	1.16273
$491$	−10.0092	−0.451710	−0.225855	−	0.974161i	$-0.572518\pi$
$491$	−10.0092	−0.451710	−0.225855	+	0.974161i	$0.572518\pi$
$492$	−16.0484	−0.723519
$493$	3.92081	0.176584
$494$	11.5685	0.520494
$495$	1.17300	0.0527225
$496$	−109.051	−4.89654
$497$	−2.91178	−0.130611
$498$	−7.23347	−0.324139
$499$	−9.43387	−0.422318	−0.211159	−	0.977452i	$-0.567724\pi$
$499$	−9.43387	−0.422318	−0.211159	+	0.977452i	$0.567724\pi$
$500$	−5.50064	−0.245996
$501$	−9.55248	−0.426773
$502$	65.8538	2.93920
$503$	−11.8360	−0.527740	−0.263870	−	0.964558i	$-0.584999\pi$
$503$	−11.8360	−0.527740	−0.263870	+	0.964558i	$0.584999\pi$
$504$	−98.9316	−4.40676
$505$	5.64649	0.251266
$506$	−9.95583	−0.442591
$507$	6.17106	0.274066
$508$	−99.0111	−4.39291
$509$	4.80814	0.213117	0.106559	−	0.994306i	$-0.466017\pi$
$509$	4.80814	0.213117	0.106559	+	0.994306i	$0.466017\pi$
$510$	3.47875	0.154042
$511$	12.9799	0.574199
$512$	−52.3595	−2.31399
$513$	3.34448	0.147662
$514$	−42.8761	−1.89119
$515$	−5.65716	−0.249284
$516$	18.9619	0.834751
$517$	5.22968	0.230001
$518$	−81.9054	−3.59872
$519$	5.70636	0.250482
$520$	45.1537	1.98012
$521$	12.8214	0.561714	0.280857	−	0.959750i	$-0.409381\pi$
$521$	12.8214	0.561714	0.280857	+	0.959750i	$0.409381\pi$
$522$	14.4788	0.633722
$523$	30.8274	1.34799	0.673994	−	0.738737i	$-0.264577\pi$
$523$	30.8274	1.34799	0.673994	+	0.738737i	$0.264577\pi$
$524$	58.3098	2.54728
$525$	−2.72164	−0.118782
$526$	9.82180	0.428251
$527$	−13.5094	−0.588477
$528$	4.71979	0.205403
$529$	39.3666	1.71159
$530$	−6.36207	−0.276351
$531$	31.7894	1.37954
$532$	19.9774	0.866129
$533$	−20.4446	−0.885555
$534$	23.6496	1.02342
$535$	0.267149	0.0115499
$536$	−103.615	−4.47547
$537$	2.11818	0.0914064
$538$	−63.1914	−2.72438
$539$	4.32592	0.186331
$540$	20.5120	0.882697
$541$	12.2282	0.525730	0.262865	−	0.964833i	$-0.415333\pi$
$541$	12.2282	0.525730	0.262865	+	0.964833i	$0.415333\pi$
$542$	66.6694	2.86370
$543$	−9.39503	−0.403179
$544$	−42.7242	−1.83179
$545$	4.45431	0.190802
$546$	35.1056	1.50238
$547$	43.6996	1.86846	0.934230	−	0.356671i	$-0.116088\pi$
$547$	43.6996	1.86846	0.934230	+	0.356671i	$0.116088\pi$
$548$	2.19955	0.0939599
$549$	20.7305	0.884757
$550$	−1.26067	−0.0537551
$551$	−1.86068	−0.0792675
$552$	−50.8873	−2.16591
$553$	−29.8581	−1.26970
$554$	−25.7952	−1.09593
$555$	4.96373	0.210699
$556$	31.7950	1.34841
$557$	43.5075	1.84347	0.921736	−	0.387818i	$-0.126771\pi$
$557$	43.5075	1.84347	0.921736	+	0.387818i	$0.126771\pi$
$558$	−49.8876	−2.11191
$559$	24.1562	1.02170
$560$	61.7768	2.61055
$561$	0.584692	0.0246857
$562$	−62.5863	−2.64004
$563$	11.9258	0.502614	0.251307	−	0.967907i	$-0.419140\pi$
$563$	11.9258	0.502614	0.251307	+	0.967907i	$0.419140\pi$
$564$	42.0023	1.76862
$565$	−8.67867	−0.365114
$566$	29.7130	1.24893
$567$	−20.8080	−0.873855
$568$	−6.89385	−0.289260
$569$	35.3402	1.48154	0.740768	−	0.671761i	$-0.234462\pi$
$569$	35.3402	1.48154	0.740768	+	0.671761i	$0.234462\pi$
$570$	−1.65089	−0.0691484
$571$	5.79538	0.242529	0.121265	−	0.992620i	$-0.461305\pi$
$571$	5.79538	0.242529	0.121265	+	0.992620i	$0.461305\pi$
$572$	11.9251	0.498614
$573$	6.37863	0.266471
$574$	−48.1420	−2.00941
$575$	7.89725	0.329338
$576$	−80.0214	−3.33422
$577$	10.1655	0.423196	0.211598	−	0.977357i	$-0.432133\pi$
$577$	10.1655	0.423196	0.211598	+	0.977357i	$0.432133\pi$
$578$	36.7765	1.52970
$579$	5.06392	0.210449
$580$	−11.4117	−0.473846
$581$	−15.9130	−0.660184
$582$	12.7197	0.527249
$583$	−1.06931	−0.0442861
$584$	30.7310	1.27166
$585$	12.0017	0.496210
$586$	19.8447	0.819775
$587$	−3.40191	−0.140412	−0.0702059	−	0.997533i	$-0.522366\pi$
$587$	−3.40191	−0.140412	−0.0702059	+	0.997533i	$0.522366\pi$
$588$	34.7437	1.43281
$589$	6.41107	0.264163
$590$	−34.1653	−1.40656
$591$	12.5077	0.514499
$592$	−112.669	−4.63066
$593$	−29.6990	−1.21959	−0.609797	−	0.792558i	$-0.708749\pi$
$593$	−29.6990	−1.21959	−0.609797	+	0.792558i	$0.708749\pi$
$594$	4.70107	0.192887
$595$	7.65297	0.313741
$596$	57.9138	2.37224
$597$	−2.41810	−0.0989664
$598$	−101.864	−4.16554
$599$	−21.4711	−0.877286	−0.438643	−	0.898661i	$-0.644541\pi$
$599$	−21.4711	−0.877286	−0.438643	+	0.898661i	$0.644541\pi$
$600$	−6.44367	−0.263062
$601$	−40.7889	−1.66381	−0.831906	−	0.554917i	$-0.812750\pi$
$601$	−40.7889	−1.66381	−0.831906	+	0.554917i	$0.812750\pi$
$602$	56.8818	2.31833
$603$	−27.5405	−1.12154
$604$	−11.7870	−0.479606
$605$	10.7881	0.438599
$606$	10.3936	0.422211
$607$	15.3212	0.621869	0.310935	−	0.950431i	$-0.399358\pi$
$607$	15.3212	0.621869	0.310935	+	0.950431i	$0.399358\pi$
$608$	20.2754	0.822277
$609$	−5.64636	−0.228802
$610$	−22.2799	−0.902086
$611$	53.5082	2.16471
$612$	−26.4909	−1.07083
$613$	31.8329	1.28572	0.642860	−	0.765983i	$-0.277748\pi$
$613$	31.8329	1.28572	0.642860	+	0.765983i	$0.277748\pi$
$614$	17.3170	0.698856
$615$	2.91756	0.117647
$616$	17.8707	0.720030
$617$	−13.4029	−0.539581	−0.269791	−	0.962919i	$-0.586955\pi$
$617$	−13.4029	−0.539581	−0.269791	+	0.962919i	$0.586955\pi$
$618$	−10.4132	−0.418881
$619$	16.8705	0.678084	0.339042	−	0.940771i	$-0.389897\pi$
$619$	16.8705	0.678084	0.339042	+	0.940771i	$0.389897\pi$
$620$	39.3197	1.57912
$621$	−29.4491	−1.18175
$622$	−54.5996	−2.18925
$623$	52.0271	2.08442
$624$	48.2912	1.93319
$625$	1.00000	0.0400000
$626$	63.6660	2.54460
$627$	−0.277474	−0.0110813
$628$	−110.918	−4.42613
$629$	−13.9575	−0.556522
$630$	28.2610	1.12595
$631$	−0.508434	−0.0202404	−0.0101202	−	0.999949i	$-0.503221\pi$
$631$	−0.508434	−0.0202404	−0.0101202	+	0.999949i	$0.503221\pi$
$632$	−70.6913	−2.81195
$633$	7.89172	0.313668
$634$	−3.64659	−0.144825
$635$	17.9999	0.714306
$636$	−8.58816	−0.340543
$637$	44.2612	1.75369
$638$	−2.61541	−0.103545
$639$	−1.83237	−0.0724873
$640$	40.7887	1.61231
$641$	35.0735	1.38532	0.692661	−	0.721264i	$-0.256438\pi$
$641$	35.0735	1.38532	0.692661	+	0.721264i	$0.256438\pi$
$642$	0.491746	0.0194077
$643$	6.74671	0.266064	0.133032	−	0.991112i	$-0.457529\pi$
$643$	6.74671	0.266064	0.133032	+	0.991112i	$0.457529\pi$
$644$	−175.906	−6.93169
$645$	−3.44722	−0.135734
$646$	4.64215	0.182643
$647$	−36.0223	−1.41618	−0.708092	−	0.706121i	$-0.750444\pi$
$647$	−36.0223	−1.41618	−0.708092	+	0.706121i	$0.750444\pi$
$648$	−49.2645	−1.93529
$649$	−5.74233	−0.225406
$650$	−12.8987	−0.505929
$651$	19.4549	0.762496
$652$	0.104294	0.00408445
$653$	29.9839	1.17336	0.586679	−	0.809819i	$-0.300435\pi$
$653$	29.9839	1.17336	0.586679	+	0.809819i	$0.300435\pi$
$654$	8.19911	0.320611
$655$	−10.6006	−0.414198
$656$	−66.2239	−2.58561
$657$	8.16820	0.318672
$658$	125.998	4.91193
$659$	30.5409	1.18970	0.594852	−	0.803836i	$-0.297211\pi$
$659$	30.5409	1.18970	0.594852	+	0.803836i	$0.297211\pi$
$660$	−1.70178	−0.0662416
$661$	44.2137	1.71971	0.859856	−	0.510536i	$-0.170553\pi$
$661$	44.2137	1.71971	0.859856	+	0.510536i	$0.170553\pi$
$662$	−7.67559	−0.298320
$663$	5.98235	0.232335
$664$	−37.6752	−1.46208
$665$	−3.63183	−0.140836
$666$	−51.5425	−1.99723
$667$	16.3838	0.634383
$668$	−78.1792	−3.02485
$669$	−4.90746	−0.189733
$670$	29.5988	1.14350
$671$	−3.74469	−0.144562
$672$	61.5273	2.37347
$673$	32.9221	1.26906	0.634528	−	0.772900i	$-0.281195\pi$
$673$	32.9221	1.26906	0.634528	+	0.772900i	$0.281195\pi$
$674$	−97.2707	−3.74673
$675$	−3.72903	−0.143530
$676$	50.5051	1.94250
$677$	26.6989	1.02612	0.513061	−	0.858352i	$-0.328511\pi$
$677$	26.6989	1.02612	0.513061	+	0.858352i	$0.328511\pi$
$678$	−15.9750	−0.613515
$679$	27.9823	1.07386
$680$	18.1190	0.694830
$681$	6.01493	0.230492
$682$	9.01154	0.345070
$683$	−29.8544	−1.14235	−0.571174	−	0.820829i	$-0.693512\pi$
$683$	−29.8544	−1.14235	−0.571174	+	0.820829i	$0.693512\pi$
$684$	12.5716	0.480688
$685$	−0.399871	−0.0152783
$686$	26.5922	1.01530
$687$	−6.66059	−0.254117
$688$	78.2464	2.98312
$689$	−10.9407	−0.416809
$690$	14.5366	0.553399
$691$	−16.2706	−0.618962	−0.309481	−	0.950906i	$-0.600155\pi$
$691$	−16.2706	−0.618962	−0.309481	+	0.950906i	$0.600155\pi$
$692$	46.7019	1.77534
$693$	4.74997	0.180437
$694$	61.7058	2.34232
$695$	−5.78024	−0.219257
$696$	−13.3682	−0.506719
$697$	−8.20388	−0.310744
$698$	1.43394	0.0542756
$699$	−7.68672	−0.290738
$700$	−22.2744	−0.841893
$701$	30.4616	1.15052	0.575260	−	0.817971i	$-0.304901\pi$
$701$	30.4616	1.15052	0.575260	+	0.817971i	$0.304901\pi$
$702$	48.0996	1.81540
$703$	6.62374	0.249819
$704$	14.4548	0.544786
$705$	−7.63590	−0.287585
$706$	−68.3373	−2.57191
$707$	22.8650	0.859928
$708$	−46.1197	−1.73328
$709$	−22.8481	−0.858079	−0.429039	−	0.903286i	$-0.641148\pi$
$709$	−22.8481	−0.858079	−0.429039	+	0.903286i	$0.641148\pi$
$710$	1.96931	0.0739070
$711$	−18.7895	−0.704662
$712$	123.178	4.61629
$713$	−56.4513	−2.11412
$714$	14.0869	0.527190
$715$	−2.16795	−0.0810768
$716$	17.3356	0.647862
$717$	11.3756	0.424830
$718$	−24.1092	−0.899747
$719$	43.7155	1.63031	0.815157	−	0.579240i	$-0.196651\pi$
$719$	43.7155	1.63031	0.815157	+	0.579240i	$0.196651\pi$
$720$	38.8758	1.44881
$721$	−22.9082	−0.853147
$722$	49.8328	1.85459
$723$	−6.97051	−0.259236
$724$	−76.8906	−2.85762
$725$	2.07462	0.0770494
$726$	19.8578	0.736994
$727$	−48.5020	−1.79884	−0.899420	−	0.437086i	$-0.856011\pi$
$727$	−48.5020	−1.79884	−0.899420	+	0.437086i	$0.856011\pi$
$728$	182.846	6.77673
$729$	−5.57546	−0.206499
$730$	−8.77868	−0.324914
$731$	9.69323	0.358517
$732$	−30.0756	−1.11163
$733$	−41.9950	−1.55112	−0.775560	−	0.631274i	$-0.782532\pi$
$733$	−41.9950	−1.55112	−0.775560	+	0.631274i	$0.782532\pi$
$734$	−101.343	−3.74063
$735$	−6.31631	−0.232981
$736$	−178.531	−6.58074
$737$	4.97482	0.183250
$738$	−30.2954	−1.11519
$739$	49.3188	1.81422	0.907111	−	0.420891i	$-0.138283\pi$
$739$	49.3188	1.81422	0.907111	+	0.420891i	$0.138283\pi$
$740$	40.6241	1.49337
$741$	−2.83901	−0.104294
$742$	−25.7627	−0.945779
$743$	2.34627	0.0860764	0.0430382	−	0.999073i	$-0.486296\pi$
$743$	2.34627	0.0860764	0.0430382	+	0.999073i	$0.486296\pi$
$744$	46.0608	1.68867
$745$	−10.5286	−0.385737
$746$	−67.3269	−2.46501
$747$	−10.0140	−0.366392
$748$	4.78522	0.174965
$749$	1.08180	0.0395281
$750$	1.84072	0.0672134
$751$	−14.1416	−0.516035	−0.258018	−	0.966140i	$-0.583069\pi$
$751$	−14.1416	−0.516035	−0.258018	+	0.966140i	$0.583069\pi$
$752$	173.323	6.32043
$753$	−16.1610	−0.588941
$754$	−26.7599	−0.974539
$755$	2.14284	0.0779860
$756$	83.0618	3.02093
$757$	−26.3013	−0.955937	−0.477968	−	0.878377i	$-0.658627\pi$
$757$	−26.3013	−0.955937	−0.477968	+	0.878377i	$0.658627\pi$
$758$	−33.8357	−1.22897
$759$	2.44324	0.0886840
$760$	−8.59862	−0.311905
$761$	30.8457	1.11816	0.559079	−	0.829115i	$-0.311155\pi$
$761$	30.8457	1.11816	0.559079	+	0.829115i	$0.311155\pi$
$762$	33.1328	1.20027
$763$	18.0374	0.652996
$764$	52.2039	1.88867
$765$	4.81596	0.174122
$766$	59.2038	2.13912
$767$	−58.7534	−2.12146
$768$	32.8692	1.18606
$769$	23.5947	0.850847	0.425423	−	0.904994i	$-0.360125\pi$
$769$	23.5947	0.850847	0.425423	+	0.904994i	$0.360125\pi$
$770$	−5.10498	−0.183971
$771$	10.5221	0.378946
$772$	41.4440	1.49160
$773$	48.4171	1.74144	0.870722	−	0.491776i	$-0.163652\pi$
$773$	48.4171	1.74144	0.870722	+	0.491776i	$0.163652\pi$
$774$	35.7954	1.28664
$775$	−7.14822	−0.256772
$776$	66.2501	2.37824
$777$	20.1002	0.721092
$778$	−97.2464	−3.48645
$779$	3.89327	0.139491
$780$	−17.4120	−0.623448
$781$	0.330993	0.0118438
$782$	−40.8754	−1.46170
$783$	−7.73631	−0.276473
$784$	143.370	5.12037
$785$	20.1647	0.719708
$786$	−19.5126	−0.695992
$787$	−28.6413	−1.02095	−0.510475	−	0.859892i	$-0.670531\pi$
$787$	−28.6413	−1.02095	−0.510475	+	0.859892i	$0.670531\pi$
$788$	102.366	3.64662
$789$	−2.41035	−0.0858106
$790$	20.1938	0.718464
$791$	−35.1436	−1.24956
$792$	11.2459	0.399606
$793$	−38.3143	−1.36058
$794$	26.0116	0.923116
$795$	1.56130	0.0553737
$796$	−19.7902	−0.701445
$797$	−4.42056	−0.156584	−0.0782921	−	0.996930i	$-0.524947\pi$
$797$	−4.42056	−0.156584	−0.0782921	+	0.996930i	$0.524947\pi$
$798$	−6.68516	−0.236652
$799$	21.4714	0.759603
$800$	−22.6067	−0.799268
$801$	32.7403	1.15682
$802$	−88.5566	−3.12704
$803$	−1.47548	−0.0520685
$804$	39.9554	1.40912
$805$	31.9793	1.12712
$806$	92.2028	3.24770
$807$	15.5077	0.545896
$808$	54.1346	1.90445
$809$	−20.4813	−0.720085	−0.360043	−	0.932936i	$-0.617238\pi$
$809$	−20.4813	−0.720085	−0.360043	+	0.932936i	$0.617238\pi$
$810$	14.0730	0.494475
$811$	30.0703	1.05591	0.527956	−	0.849272i	$-0.322959\pi$
$811$	30.0703	1.05591	0.527956	+	0.849272i	$0.322959\pi$
$812$	−46.2109	−1.62168
$813$	−16.3612	−0.573812
$814$	9.31048	0.326332
$815$	−0.0189603	−0.000664150 0
$816$	19.3779	0.678363
$817$	−4.60007	−0.160936
$818$	−104.138	−3.64109
$819$	48.6000	1.69822
$820$	23.8778	0.833850
$821$	−42.4145	−1.48027	−0.740137	−	0.672456i	$-0.765240\pi$
$821$	−42.4145	−1.48027	−0.740137	+	0.672456i	$0.765240\pi$
$822$	−0.736049	−0.0256727
$823$	46.7809	1.63068	0.815339	−	0.578984i	$-0.196550\pi$
$823$	46.7809	1.63068	0.815339	+	0.578984i	$0.196550\pi$
$824$	−54.2369	−1.88943
$825$	0.309378	0.0107712
$826$	−138.350	−4.81380
$827$	7.12302	0.247692	0.123846	−	0.992301i	$-0.460477\pi$
$827$	7.12302	0.247692	0.123846	+	0.992301i	$0.460477\pi$
$828$	−110.697	−3.84698
$829$	27.6045	0.958745	0.479372	−	0.877612i	$-0.340864\pi$
$829$	27.6045	0.958745	0.479372	+	0.877612i	$0.340864\pi$
$830$	10.7624	0.373568
$831$	6.33033	0.219597
$832$	147.896	5.12738
$833$	17.7608	0.615376
$834$	−10.6398	−0.368425
$835$	14.2128	0.491853
$836$	−2.27090	−0.0785407
$837$	26.6559	0.921362
$838$	81.8348	2.82694
$839$	−5.35738	−0.184957	−0.0924787	−	0.995715i	$-0.529479\pi$
$839$	−5.35738	−0.184957	−0.0924787	+	0.995715i	$0.529479\pi$
$840$	−26.0931	−0.900299
$841$	−24.6960	−0.851585
$842$	2.59215	0.0893315
$843$	15.3592	0.528998
$844$	64.5873	2.22319
$845$	−9.18168	−0.315859
$846$	79.2899	2.72604
$847$	43.6856	1.50105
$848$	−35.4391	−1.21698
$849$	−7.29180	−0.250254
$850$	−5.17590	−0.177532
$851$	−58.3239	−1.99932
$852$	2.65838	0.0910745
$853$	20.1372	0.689483	0.344742	−	0.938698i	$-0.387967\pi$
$853$	20.1372	0.689483	0.344742	+	0.938698i	$0.387967\pi$
$854$	−90.2206	−3.08729
$855$	−2.28549	−0.0781620
$856$	2.56124	0.0875414
$857$	33.8129	1.15503	0.577513	−	0.816381i	$-0.304023\pi$
$857$	33.8129	1.15503	0.577513	+	0.816381i	$0.304023\pi$
$858$	−3.99058	−0.136236
$859$	−32.5718	−1.11134	−0.555668	−	0.831404i	$-0.687538\pi$
$859$	−32.5718	−1.11134	−0.555668	+	0.831404i	$0.687538\pi$
$860$	−28.2127	−0.962045
$861$	11.8144	0.402634
$862$	−17.0286	−0.579997
$863$	−37.1210	−1.26361	−0.631806	−	0.775126i	$-0.717686\pi$
$863$	−37.1210	−1.26361	−0.631806	+	0.775126i	$0.717686\pi$
$864$	84.3010	2.86798
$865$	−8.49028	−0.288678
$866$	−14.5932	−0.495899
$867$	−9.02524	−0.306513
$868$	159.222	5.40435
$869$	3.39408	0.115136
$870$	3.81878	0.129469
$871$	50.9006	1.72470
$872$	42.7048	1.44617
$873$	17.6091	0.595977
$874$	19.3980	0.656148
$875$	4.04942	0.136895
$876$	−11.8503	−0.400386
$877$	31.8501	1.07550	0.537750	−	0.843104i	$-0.319274\pi$
$877$	31.8501	1.07550	0.537750	+	0.843104i	$0.319274\pi$
$878$	74.4742	2.51338
$879$	−4.87004	−0.164262
$880$	−7.02239	−0.236725
$881$	17.4896	0.589238	0.294619	−	0.955615i	$-0.404807\pi$
$881$	17.4896	0.589238	0.294619	+	0.955615i	$0.404807\pi$
$882$	65.5875	2.20845
$883$	−28.0966	−0.945526	−0.472763	−	0.881190i	$-0.656743\pi$
$883$	−28.0966	−0.945526	−0.472763	+	0.881190i	$0.656743\pi$
$884$	48.9606	1.64672
$885$	8.38443	0.281839
$886$	−53.7893	−1.80709
$887$	21.9904	0.738367	0.369183	−	0.929357i	$-0.379637\pi$
$887$	21.9904	0.738367	0.369183	+	0.929357i	$0.379637\pi$
$888$	47.5887	1.59697
$889$	72.8893	2.44463
$890$	−35.1873	−1.17948
$891$	2.36532	0.0792413
$892$	−40.1635	−1.34477
$893$	−10.1896	−0.340981
$894$	−19.3801	−0.648167
$895$	−3.15156	−0.105345
$896$	165.171	5.51796
$897$	24.9983	0.834670
$898$	−63.8055	−2.12922
$899$	−14.8298	−0.494603
$900$	−14.0171	−0.467238
$901$	−4.39022	−0.146260
$902$	5.47247	0.182213
$903$	−13.9592	−0.464535
$904$	−83.2050	−2.76736
$905$	13.9785	0.464661
$906$	3.94436	0.131043
$907$	0.890858	0.0295805	0.0147902	−	0.999891i	$-0.495292\pi$
$907$	0.890858	0.0295805	0.0147902	+	0.999891i	$0.495292\pi$
$908$	49.2273	1.63366
$909$	14.3888	0.477247
$910$	−52.2323	−1.73148
$911$	3.78776	0.125494	0.0627471	−	0.998029i	$-0.480014\pi$
$911$	3.78776	0.125494	0.0627471	+	0.998029i	$0.480014\pi$
$912$	−9.19609	−0.304513
$913$	1.80889	0.0598655
$914$	2.14242	0.0708649
$915$	5.46766	0.180755
$916$	−54.5115	−1.80111
$917$	−42.9261	−1.41754
$918$	19.3011	0.637030
$919$	−40.5919	−1.33900	−0.669501	−	0.742811i	$-0.733492\pi$
$919$	−40.5919	−1.33900	−0.669501	+	0.742811i	$0.733492\pi$
$920$	75.7133	2.49619
$921$	−4.24972	−0.140033
$922$	4.55658	0.150063
$923$	3.38659	0.111471
$924$	−6.89121	−0.226704
$925$	−7.38534	−0.242829
$926$	6.24548	0.205239
$927$	−14.4160	−0.473483
$928$	−46.9003	−1.53958
$929$	26.7517	0.877693	0.438847	−	0.898562i	$-0.355387\pi$
$929$	26.7517	0.877693	0.438847	+	0.898562i	$0.355387\pi$
$930$	−13.1578	−0.431462
$931$	−8.42867	−0.276238
$932$	−62.9095	−2.06067
$933$	13.3992	0.438670
$934$	73.7129	2.41196
$935$	−0.869940	−0.0284501
$936$	115.064	3.76098
$937$	12.9994	0.424672	0.212336	−	0.977197i	$-0.431893\pi$
$937$	12.9994	0.424672	0.212336	+	0.977197i	$0.431893\pi$
$938$	119.858	3.91350
$939$	−15.6241	−0.509874
$940$	−62.4936	−2.03832
$941$	−2.50205	−0.0815644	−0.0407822	−	0.999168i	$-0.512985\pi$
$941$	−2.50205	−0.0815644	−0.0407822	+	0.999168i	$0.512985\pi$
$942$	37.1174	1.20935
$943$	−34.2814	−1.11635
$944$	−190.313	−6.19416
$945$	−15.1004	−0.491216
$946$	−6.46596	−0.210226
$947$	3.70137	0.120279	0.0601393	−	0.998190i	$-0.480846\pi$
$947$	3.70137	0.120279	0.0601393	+	0.998190i	$0.480846\pi$
$948$	27.2596	0.885352
$949$	−15.0965	−0.490054
$950$	2.45630	0.0796930
$951$	0.894902	0.0290192
$952$	73.3712	2.37798
$953$	−16.9425	−0.548822	−0.274411	−	0.961613i	$-0.588483\pi$
$953$	−16.9425	−0.548822	−0.274411	+	0.961613i	$0.588483\pi$
$954$	−16.2123	−0.524893
$955$	−9.49051	−0.307106
$956$	93.1002	3.01107
$957$	0.641842	0.0207478
$958$	60.0507	1.94015
$959$	−1.61925	−0.0522882
$960$	−21.1056	−0.681180
$961$	20.0970	0.648290
$962$	95.2614	3.07135
$963$	0.680770	0.0219375
$964$	−57.0480	−1.83739
$965$	−7.53441	−0.242541
$966$	58.8648	1.89394
$967$	45.6881	1.46923	0.734615	−	0.678485i	$-0.237363\pi$
$967$	45.6881	1.46923	0.734615	+	0.678485i	$0.237363\pi$
$968$	103.429	3.32433
$969$	−1.13922	−0.0365970
$970$	−18.9252	−0.607651
$971$	24.2798	0.779176	0.389588	−	0.920989i	$-0.372617\pi$
$971$	24.2798	0.779176	0.389588	+	0.920989i	$0.372617\pi$
$972$	80.5332	2.58310
$973$	−23.4066	−0.750381
$974$	−8.61993	−0.276200
$975$	3.16545	0.101375
$976$	−124.107	−3.97257
$977$	18.6640	0.597116	0.298558	−	0.954392i	$-0.403494\pi$
$977$	18.6640	0.597116	0.298558	+	0.954392i	$0.403494\pi$
$978$	−0.0349005	−0.00111599
$979$	−5.91411	−0.189016
$980$	−51.6939	−1.65130
$981$	11.3508	0.362403
$982$	27.4125	0.874769
$983$	9.71230	0.309774	0.154887	−	0.987932i	$-0.450499\pi$
$983$	9.71230	0.309774	0.154887	+	0.987932i	$0.450499\pi$
$984$	27.9715	0.891699
$985$	−18.6098	−0.592957
$986$	−10.7380	−0.341969
$987$	−30.9210	−0.984226
$988$	−23.2350	−0.739204
$989$	40.5049	1.28798
$990$	−3.21253	−0.102101
$991$	−10.3712	−0.329451	−0.164725	−	0.986339i	$-0.552674\pi$
$991$	−10.3712	−0.329451	−0.164725	+	0.986339i	$0.552674\pi$
$992$	161.598	5.13073
$993$	1.88365	0.0597758
$994$	7.97458	0.252938
$995$	3.59780	0.114058
$996$	14.5282	0.460342
$997$	35.0517	1.11010	0.555049	−	0.831818i	$-0.312700\pi$
$997$	35.0517	1.11010	0.555049	+	0.831818i	$0.312700\pi$
$998$	25.8368	0.817850
$999$	27.5401	0.871331

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.c.1.1	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.c.1.1	✓	127	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)

\(f(q)\)	\(=\)	\(q-2.73873 q^{2} +0.672106 q^{3} +5.50064 q^{4} -1.00000 q^{5} -1.84072 q^{6} -4.04942 q^{7} -9.58729 q^{8} -2.54827 q^{9} +O(q^{10})\)	\(q-2.73873 q^{2} +0.672106 q^{3} +5.50064 q^{4} -1.00000 q^{5} -1.84072 q^{6} -4.04942 q^{7} -9.58729 q^{8} -2.54827 q^{9} +2.73873 q^{10} +0.460312 q^{11} +3.69701 q^{12} +4.70974 q^{13} +11.0903 q^{14} -0.672106 q^{15} +15.2557 q^{16} +1.88989 q^{17} +6.97903 q^{18} -0.896877 q^{19} -5.50064 q^{20} -2.72164 q^{21} -1.26067 q^{22} +7.89725 q^{23} -6.44367 q^{24} +1.00000 q^{25} -12.8987 q^{26} -3.72903 q^{27} -22.2744 q^{28} +2.07462 q^{29} +1.84072 q^{30} -7.14822 q^{31} -22.6067 q^{32} +0.309378 q^{33} -5.17590 q^{34} +4.04942 q^{35} -14.0171 q^{36} -7.38534 q^{37} +2.45630 q^{38} +3.16545 q^{39} +9.58729 q^{40} -4.34092 q^{41} +7.45383 q^{42} +5.12899 q^{43} +2.53201 q^{44} +2.54827 q^{45} -21.6284 q^{46} +11.3612 q^{47} +10.2535 q^{48} +9.39780 q^{49} -2.73873 q^{50} +1.27021 q^{51} +25.9066 q^{52} -2.32300 q^{53} +10.2128 q^{54} -0.460312 q^{55} +38.8230 q^{56} -0.602796 q^{57} -5.68182 q^{58} -12.4749 q^{59} -3.69701 q^{60} -8.13512 q^{61} +19.5770 q^{62} +10.3190 q^{63} +31.4022 q^{64} -4.70974 q^{65} -0.847303 q^{66} +10.8075 q^{67} +10.3956 q^{68} +5.30779 q^{69} -11.0903 q^{70} +0.719061 q^{71} +24.4310 q^{72} -3.20538 q^{73} +20.2265 q^{74} +0.672106 q^{75} -4.93339 q^{76} -1.86400 q^{77} -8.66930 q^{78} +7.37343 q^{79} -15.2557 q^{80} +5.13852 q^{81} +11.8886 q^{82} +3.92971 q^{83} -14.9707 q^{84} -1.88989 q^{85} -14.0469 q^{86} +1.39436 q^{87} -4.41315 q^{88} -12.8480 q^{89} -6.97903 q^{90} -19.0717 q^{91} +43.4399 q^{92} -4.80436 q^{93} -31.1152 q^{94} +0.896877 q^{95} -15.1941 q^{96} -6.91020 q^{97} -25.7380 q^{98} -1.17300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9	\( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 127 * q + 19 * q^2 + 10 * q^3 + 125 * q^4 - 127 * q^5 + 13 * q^7 + 54 * q^8 + 123 * q^9 - 19 * q^10 + 30 * q^11 + 35 * q^12 + 30 * q^13 + 39 * q^14 - 10 * q^15 + 121 * q^16 + 63 * q^17 + 53 * q^18 - 35 * q^19 - 125 * q^20 + 33 * q^21 + 49 * q^22 + 61 * q^23 - 5 * q^24 + 127 * q^25 + 10 * q^26 + 40 * q^27 + 32 * q^28 + 134 * q^29 - 25 * q^31 + 122 * q^32 + 48 * q^33 - 21 * q^34 - 13 * q^35 + 133 * q^36 + 60 * q^37 + 33 * q^38 + 26 * q^39 - 54 * q^40 + 9 * q^41 + 45 * q^42 + 48 * q^43 + 85 * q^44 - 123 * q^45 - 11 * q^46 + 57 * q^47 + 71 * q^48 + 70 * q^49 + 19 * q^50 + 45 * q^51 + 68 * q^52 + 182 * q^53 - 29 * q^54 - 30 * q^55 + 96 * q^56 + 74 * q^57 + 47 * q^58 + 19 * q^59 - 35 * q^60 + 16 * q^61 + 43 * q^62 + 73 * q^63 + 110 * q^64 - 30 * q^65 + 8 * q^66 + 40 * q^67 + 129 * q^68 + 2 * q^69 - 39 * q^70 + 48 * q^71 + 151 * q^72 + 30 * q^73 + 117 * q^74 + 10 * q^75 - 98 * q^76 + 134 * q^77 + 54 * q^78 + 23 * q^79 - 121 * q^80 + 111 * q^81 + 4 * q^82 + 92 * q^83 + 48 * q^84 - 63 * q^85 + 42 * q^86 + 69 * q^87 + 121 * q^88 + 12 * q^89 - 53 * q^90 - 30 * q^91 + 175 * q^92 + 82 * q^93 - 23 * q^94 + 35 * q^95 + 6 * q^96 + 67 * q^97 + 122 * q^98 + 73 * q^99

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