LMFDB - Embedded newform 8035.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.65503 q^{2} -2.98031 q^{3} +5.04918 q^{4} +1.00000 q^{5} +7.91280 q^{6} -3.81633 q^{7} -8.09566 q^{8} +5.88223 q^{9} +O(q^{10})$	\(q-2.65503 q^{2} -2.98031 q^{3} +5.04918 q^{4} +1.00000 q^{5} +7.91280 q^{6} -3.81633 q^{7} -8.09566 q^{8} +5.88223 q^{9} -2.65503 q^{10} -5.97342 q^{11} -15.0481 q^{12} +2.24489 q^{13} +10.1325 q^{14} -2.98031 q^{15} +11.3958 q^{16} -1.94879 q^{17} -15.6175 q^{18} +0.247485 q^{19} +5.04918 q^{20} +11.3739 q^{21} +15.8596 q^{22} +2.92599 q^{23} +24.1275 q^{24} +1.00000 q^{25} -5.96024 q^{26} -8.58993 q^{27} -19.2694 q^{28} +10.2141 q^{29} +7.91280 q^{30} +4.85592 q^{31} -14.0650 q^{32} +17.8026 q^{33} +5.17410 q^{34} -3.81633 q^{35} +29.7004 q^{36} -8.83263 q^{37} -0.657079 q^{38} -6.69045 q^{39} -8.09566 q^{40} +11.0506 q^{41} -30.1979 q^{42} +7.95994 q^{43} -30.1609 q^{44} +5.88223 q^{45} -7.76858 q^{46} +8.98985 q^{47} -33.9631 q^{48} +7.56441 q^{49} -2.65503 q^{50} +5.80800 q^{51} +11.3348 q^{52} +3.51176 q^{53} +22.8065 q^{54} -5.97342 q^{55} +30.8957 q^{56} -0.737580 q^{57} -27.1187 q^{58} -8.81620 q^{59} -15.0481 q^{60} +3.39339 q^{61} -12.8926 q^{62} -22.4486 q^{63} +14.5513 q^{64} +2.24489 q^{65} -47.2665 q^{66} -8.80481 q^{67} -9.83980 q^{68} -8.72034 q^{69} +10.1325 q^{70} -5.71246 q^{71} -47.6205 q^{72} -10.4008 q^{73} +23.4509 q^{74} -2.98031 q^{75} +1.24959 q^{76} +22.7966 q^{77} +17.7633 q^{78} -11.6445 q^{79} +11.3958 q^{80} +7.95395 q^{81} -29.3396 q^{82} +4.73389 q^{83} +57.4286 q^{84} -1.94879 q^{85} -21.1339 q^{86} -30.4411 q^{87} +48.3588 q^{88} +12.4396 q^{89} -15.6175 q^{90} -8.56723 q^{91} +14.7738 q^{92} -14.4721 q^{93} -23.8683 q^{94} +0.247485 q^{95} +41.9180 q^{96} +7.20990 q^{97} -20.0837 q^{98} -35.1370 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.65503	−1.87739	−0.938694	−	0.344750i	$-0.887964\pi$
$2$	−2.65503	−1.87739	−0.938694	+	0.344750i	$0.887964\pi$
$3$	−2.98031	−1.72068	−0.860341	−	0.509720i	$-0.829749\pi$
$3$	−2.98031	−1.72068	−0.860341	+	0.509720i	$0.829749\pi$
$4$	5.04918	2.52459
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	7.91280	3.23039
$7$	−3.81633	−1.44244	−0.721220	−	0.692707i	$-0.756418\pi$
$7$	−3.81633	−1.44244	−0.721220	+	0.692707i	$0.756418\pi$
$8$	−8.09566	−2.86225
$9$	5.88223	1.96074
$10$	−2.65503	−0.839594
$11$	−5.97342	−1.80105	−0.900527	−	0.434800i	$-0.856819\pi$
$11$	−5.97342	−1.80105	−0.900527	+	0.434800i	$0.856819\pi$
$12$	−15.0481	−4.34401
$13$	2.24489	0.622619	0.311310	−	0.950309i	$-0.399232\pi$
$13$	2.24489	0.622619	0.311310	+	0.950309i	$0.399232\pi$
$14$	10.1325	2.70802
$15$	−2.98031	−0.769512
$16$	11.3958	2.84896
$17$	−1.94879	−0.472652	−0.236326	−	0.971674i	$-0.575943\pi$
$17$	−1.94879	−0.472652	−0.236326	+	0.971674i	$0.575943\pi$
$18$	−15.6175	−3.68108
$19$	0.247485	0.0567768	0.0283884	−	0.999597i	$-0.490962\pi$
$19$	0.247485	0.0567768	0.0283884	+	0.999597i	$0.490962\pi$
$20$	5.04918	1.12903
$21$	11.3739	2.48198
$22$	15.8596	3.38128
$23$	2.92599	0.610111	0.305055	−	0.952335i	$-0.401325\pi$
$23$	2.92599	0.610111	0.305055	+	0.952335i	$0.401325\pi$
$24$	24.1275	4.92501
$25$	1.00000	0.200000
$26$	−5.96024	−1.16890
$27$	−8.58993	−1.65313
$28$	−19.2694	−3.64157
$29$	10.2141	1.89671	0.948355	−	0.317212i	$-0.102747\pi$
$29$	10.2141	1.89671	0.948355	+	0.317212i	$0.102747\pi$
$30$	7.91280	1.44467
$31$	4.85592	0.872149	0.436075	−	0.899911i	$-0.356368\pi$
$31$	4.85592	0.872149	0.436075	+	0.899911i	$0.356368\pi$
$32$	−14.0650	−2.48636
$33$	17.8026	3.09904
$34$	5.17410	0.887351
$35$	−3.81633	−0.645078
$36$	29.7004	4.95007
$37$	−8.83263	−1.45208	−0.726038	−	0.687655i	$-0.758640\pi$
$37$	−8.83263	−1.45208	−0.726038	+	0.687655i	$0.758640\pi$
$38$	−0.657079	−0.106592
$39$	−6.69045	−1.07133
$40$	−8.09566	−1.28004
$41$	11.0506	1.72581	0.862905	−	0.505366i	$-0.168643\pi$
$41$	11.0506	1.72581	0.862905	+	0.505366i	$0.168643\pi$
$42$	−30.1979	−4.65964
$43$	7.95994	1.21388	0.606940	−	0.794748i	$-0.292397\pi$
$43$	7.95994	1.21388	0.606940	+	0.794748i	$0.292397\pi$
$44$	−30.1609	−4.54692
$45$	5.88223	0.876871
$46$	−7.76858	−1.14542
$47$	8.98985	1.31130	0.655652	−	0.755063i	$-0.272394\pi$
$47$	8.98985	1.31130	0.655652	+	0.755063i	$0.272394\pi$
$48$	−33.9631	−4.90215
$49$	7.56441	1.08063
$50$	−2.65503	−0.375478
$51$	5.80800	0.813283
$52$	11.3348	1.57186
$53$	3.51176	0.482377	0.241189	−	0.970478i	$-0.422463\pi$
$53$	3.51176	0.482377	0.241189	+	0.970478i	$0.422463\pi$
$54$	22.8065	3.10357
$55$	−5.97342	−0.805456
$56$	30.8957	4.12862
$57$	−0.737580	−0.0976949
$58$	−27.1187	−3.56086
$59$	−8.81620	−1.14777	−0.573886	−	0.818935i	$-0.694565\pi$
$59$	−8.81620	−1.14777	−0.573886	+	0.818935i	$0.694565\pi$
$60$	−15.0481	−1.94270
$61$	3.39339	0.434479	0.217239	−	0.976118i	$-0.430295\pi$
$61$	3.39339	0.434479	0.217239	+	0.976118i	$0.430295\pi$
$62$	−12.8926	−1.63736
$63$	−22.4486	−2.82825
$64$	14.5513	1.81891
$65$	2.24489	0.278444
$66$	−47.2665	−5.81810
$67$	−8.80481	−1.07568	−0.537839	−	0.843047i	$-0.680759\pi$
$67$	−8.80481	−1.07568	−0.537839	+	0.843047i	$0.680759\pi$
$68$	−9.83980	−1.19325
$69$	−8.72034	−1.04981
$70$	10.1325	1.21106
$71$	−5.71246	−0.677944	−0.338972	−	0.940796i	$-0.610079\pi$
$71$	−5.71246	−0.677944	−0.338972	+	0.940796i	$0.610079\pi$
$72$	−47.6205	−5.61213
$73$	−10.4008	−1.21732	−0.608658	−	0.793433i	$-0.708292\pi$
$73$	−10.4008	−1.21732	−0.608658	+	0.793433i	$0.708292\pi$
$74$	23.4509	2.72611
$75$	−2.98031	−0.344136
$76$	1.24959	0.143338
$77$	22.7966	2.59791
$78$	17.7633	2.01130
$79$	−11.6445	−1.31011	−0.655055	−	0.755581i	$-0.727355\pi$
$79$	−11.6445	−1.31011	−0.655055	+	0.755581i	$0.727355\pi$
$80$	11.3958	1.27409
$81$	7.95395	0.883772
$82$	−29.3396	−3.24002
$83$	4.73389	0.519612	0.259806	−	0.965661i	$-0.416341\pi$
$83$	4.73389	0.519612	0.259806	+	0.965661i	$0.416341\pi$
$84$	57.4286	6.26597
$85$	−1.94879	−0.211376
$86$	−21.1339	−2.27893
$87$	−30.4411	−3.26363
$88$	48.3588	5.15506
$89$	12.4396	1.31860	0.659300	−	0.751880i	$-0.270853\pi$
$89$	12.4396	1.31860	0.659300	+	0.751880i	$0.270853\pi$
$90$	−15.6175	−1.64623
$91$	−8.56723	−0.898090
$92$	14.7738	1.54028
$93$	−14.4721	−1.50069
$94$	−23.8683	−2.46183
$95$	0.247485	0.0253914
$96$	41.9180	4.27824
$97$	7.20990	0.732054	0.366027	−	0.930604i	$-0.380718\pi$
$97$	7.20990	0.732054	0.366027	+	0.930604i	$0.380718\pi$
$98$	−20.0837	−2.02876
$99$	−35.1370	−3.53141
$100$	5.04918	0.504918
$101$	8.99297	0.894834	0.447417	−	0.894325i	$-0.352344\pi$
$101$	8.99297	0.894834	0.447417	+	0.894325i	$0.352344\pi$
$102$	−15.4204	−1.52685
$103$	9.11838	0.898461	0.449230	−	0.893416i	$-0.351698\pi$
$103$	9.11838	0.898461	0.449230	+	0.893416i	$0.351698\pi$
$104$	−18.1738	−1.78209
$105$	11.3739	1.10997
$106$	−9.32382	−0.905609
$107$	−1.44306	−0.139506	−0.0697529	−	0.997564i	$-0.522221\pi$
$107$	−1.44306	−0.139506	−0.0697529	+	0.997564i	$0.522221\pi$
$108$	−43.3721	−4.17348
$109$	−4.35427	−0.417064	−0.208532	−	0.978016i	$-0.566869\pi$
$109$	−4.35427	−0.417064	−0.208532	+	0.978016i	$0.566869\pi$
$110$	15.8596	1.51215
$111$	26.3239	2.49856
$112$	−43.4904	−4.10945
$113$	4.40957	0.414817	0.207409	−	0.978254i	$-0.433497\pi$
$113$	4.40957	0.414817	0.207409	+	0.978254i	$0.433497\pi$
$114$	1.95830	0.183411
$115$	2.92599	0.272850
$116$	51.5728	4.78841
$117$	13.2049	1.22080
$118$	23.4073	2.15481
$119$	7.43724	0.681771
$120$	24.1275	2.20253
$121$	24.6818	2.24380
$122$	−9.00954	−0.815686
$123$	−32.9341	−2.96957
$124$	24.5184	2.20182
$125$	1.00000	0.0894427
$126$	59.6016	5.30973
$127$	−19.3773	−1.71946	−0.859730	−	0.510749i	$-0.829368\pi$
$127$	−19.3773	−1.71946	−0.859730	+	0.510749i	$0.829368\pi$
$128$	−10.5040	−0.928434
$129$	−23.7231	−2.08870
$130$	−5.96024	−0.522747
$131$	8.00338	0.699258	0.349629	−	0.936888i	$-0.386308\pi$
$131$	8.00338	0.699258	0.349629	+	0.936888i	$0.386308\pi$
$132$	89.8887	7.82380
$133$	−0.944484	−0.0818971
$134$	23.3770	2.01947
$135$	−8.58993	−0.739304
$136$	15.7768	1.35285
$137$	−18.2210	−1.55672	−0.778362	−	0.627815i	$-0.783949\pi$
$137$	−18.2210	−1.55672	−0.778362	+	0.627815i	$0.783949\pi$
$138$	23.1528	1.97089
$139$	−12.2402	−1.03820	−0.519101	−	0.854713i	$-0.673733\pi$
$139$	−12.2402	−1.03820	−0.519101	+	0.854713i	$0.673733\pi$
$140$	−19.2694	−1.62856
$141$	−26.7925	−2.25634
$142$	15.1667	1.27276
$143$	−13.4096	−1.12137
$144$	67.0330	5.58608
$145$	10.2141	0.848234
$146$	27.6143	2.28538
$147$	−22.5443	−1.85942
$148$	−44.5975	−3.66589
$149$	−23.7952	−1.94938	−0.974691	−	0.223556i	$-0.928233\pi$
$149$	−23.7952	−1.94938	−0.974691	+	0.223556i	$0.928233\pi$
$150$	7.91280	0.646078
$151$	−6.96534	−0.566831	−0.283416	−	0.958997i	$-0.591468\pi$
$151$	−6.96534	−0.566831	−0.283416	+	0.958997i	$0.591468\pi$
$152$	−2.00355	−0.162509
$153$	−11.4632	−0.926748
$154$	−60.5256	−4.87729
$155$	4.85592	0.390037
$156$	−33.7813	−2.70467
$157$	24.3870	1.94630	0.973148	−	0.230182i	$-0.0739320\pi$
$157$	24.3870	1.94630	0.973148	+	0.230182i	$0.0739320\pi$
$158$	30.9165	2.45959
$159$	−10.4661	−0.830017
$160$	−14.0650	−1.11193
$161$	−11.1666	−0.880048
$162$	−21.1180	−1.65918
$163$	9.42925	0.738556	0.369278	−	0.929319i	$-0.379605\pi$
$163$	9.42925	0.738556	0.369278	+	0.929319i	$0.379605\pi$
$164$	55.7963	4.35696
$165$	17.8026	1.38593
$166$	−12.5686	−0.975514
$167$	4.62383	0.357802	0.178901	−	0.983867i	$-0.442746\pi$
$167$	4.62383	0.357802	0.178901	+	0.983867i	$0.442746\pi$
$168$	−92.0788	−7.10403
$169$	−7.96049	−0.612345
$170$	5.17410	0.396835
$171$	1.45576	0.111325
$172$	40.1912	3.06455
$173$	17.4888	1.32965	0.664825	−	0.746999i	$-0.268506\pi$
$173$	17.4888	1.32965	0.664825	+	0.746999i	$0.268506\pi$
$174$	80.8221	6.12711
$175$	−3.81633	−0.288488
$176$	−68.0722	−5.13113
$177$	26.2750	1.97495
$178$	−33.0276	−2.47552
$179$	−2.04104	−0.152554	−0.0762772	−	0.997087i	$-0.524303\pi$
$179$	−2.04104	−0.152554	−0.0762772	+	0.997087i	$0.524303\pi$
$180$	29.7004	2.21374
$181$	−3.94104	−0.292936	−0.146468	−	0.989215i	$-0.546790\pi$
$181$	−3.94104	−0.292936	−0.146468	+	0.989215i	$0.546790\pi$
$182$	22.7463	1.68606
$183$	−10.1133	−0.747599
$184$	−23.6878	−1.74629
$185$	−8.83263	−0.649388
$186$	38.4239	2.81738
$187$	11.6410	0.851271
$188$	45.3914	3.31051
$189$	32.7821	2.38454
$190$	−0.657079	−0.0476695
$191$	22.2647	1.61102	0.805509	−	0.592583i	$-0.201892\pi$
$191$	22.2647	1.61102	0.805509	+	0.592583i	$0.201892\pi$
$192$	−43.3672	−3.12976
$193$	−5.97822	−0.430322	−0.215161	−	0.976579i	$-0.569028\pi$
$193$	−5.97822	−0.430322	−0.215161	+	0.976579i	$0.569028\pi$
$194$	−19.1425	−1.37435
$195$	−6.69045	−0.479113
$196$	38.1941	2.72815
$197$	12.1829	0.867998	0.433999	−	0.900913i	$-0.357102\pi$
$197$	12.1829	0.867998	0.433999	+	0.900913i	$0.357102\pi$
$198$	93.2899	6.62982
$199$	−12.9375	−0.917113	−0.458556	−	0.888665i	$-0.651633\pi$
$199$	−12.9375	−0.917113	−0.458556	+	0.888665i	$0.651633\pi$
$200$	−8.09566	−0.572449
$201$	26.2410	1.85090
$202$	−23.8766	−1.67995
$203$	−38.9804	−2.73589
$204$	29.3256	2.05320
$205$	11.0506	0.771806
$206$	−24.2096	−1.68676
$207$	17.2113	1.19627
$208$	25.5824	1.77382
$209$	−1.47833	−0.102258
$210$	−30.1979	−2.08385
$211$	16.4031	1.12923	0.564617	−	0.825353i	$-0.309024\pi$
$211$	16.4031	1.12923	0.564617	+	0.825353i	$0.309024\pi$
$212$	17.7315	1.21780
$213$	17.0249	1.16653
$214$	3.83137	0.261907
$215$	7.95994	0.542864
$216$	69.5412	4.73168
$217$	−18.5318	−1.25802
$218$	11.5607	0.782991
$219$	30.9974	2.09461
$220$	−30.1609	−2.03345
$221$	−4.37481	−0.294282
$222$	−69.8908	−4.69077
$223$	−16.1155	−1.07917	−0.539587	−	0.841930i	$-0.681420\pi$
$223$	−16.1155	−1.07917	−0.539587	+	0.841930i	$0.681420\pi$
$224$	53.6767	3.58643
$225$	5.88223	0.392149
$226$	−11.7075	−0.778774
$227$	11.0683	0.734631	0.367316	−	0.930096i	$-0.380277\pi$
$227$	11.0683	0.734631	0.367316	+	0.930096i	$0.380277\pi$
$228$	−3.72417	−0.246639
$229$	−7.68033	−0.507530	−0.253765	−	0.967266i	$-0.581669\pi$
$229$	−7.68033	−0.507530	−0.253765	+	0.967266i	$0.581669\pi$
$230$	−7.76858	−0.512245
$231$	−67.9408	−4.47018
$232$	−82.6898	−5.42885
$233$	−9.02941	−0.591536	−0.295768	−	0.955260i	$-0.595576\pi$
$233$	−9.02941	−0.591536	−0.295768	+	0.955260i	$0.595576\pi$
$234$	−35.0595	−2.29191
$235$	8.98985	0.586433
$236$	−44.5146	−2.89765
$237$	34.7042	2.25428
$238$	−19.7461	−1.27995
$239$	−4.87072	−0.315061	−0.157530	−	0.987514i	$-0.550353\pi$
$239$	−4.87072	−0.315061	−0.157530	+	0.987514i	$0.550353\pi$
$240$	−33.9631	−2.19231
$241$	−12.8906	−0.830358	−0.415179	−	0.909740i	$-0.636281\pi$
$241$	−12.8906	−0.830358	−0.415179	+	0.909740i	$0.636281\pi$
$242$	−65.5308	−4.21248
$243$	2.06459	0.132444
$244$	17.1338	1.09688
$245$	7.56441	0.483273
$246$	87.4410	5.57504
$247$	0.555574	0.0353504
$248$	−39.3119	−2.49631
$249$	−14.1085	−0.894087
$250$	−2.65503	−0.167919
$251$	11.8884	0.750387	0.375193	−	0.926947i	$-0.377576\pi$
$251$	11.8884	0.750387	0.375193	+	0.926947i	$0.377576\pi$
$252$	−113.347	−7.14018
$253$	−17.4782	−1.09884
$254$	51.4474	3.22810
$255$	5.80800	0.363711
$256$	−1.21401	−0.0758757
$257$	−29.5639	−1.84415	−0.922074	−	0.387015i	$-0.873506\pi$
$257$	−29.5639	−1.84415	−0.922074	+	0.387015i	$0.873506\pi$
$258$	62.9855	3.92130
$259$	33.7083	2.09453
$260$	11.3348	0.702956
$261$	60.0817	3.71896
$262$	−21.2492	−1.31278
$263$	18.4930	1.14033	0.570165	−	0.821531i	$-0.306879\pi$
$263$	18.4930	1.14033	0.570165	+	0.821531i	$0.306879\pi$
$264$	−144.124	−8.87022
$265$	3.51176	0.215726
$266$	2.50763	0.153753
$267$	−37.0740	−2.26889
$268$	−44.4571	−2.71565
$269$	−5.61575	−0.342398	−0.171199	−	0.985236i	$-0.554764\pi$
$269$	−5.61575	−0.342398	−0.171199	+	0.985236i	$0.554764\pi$
$270$	22.8065	1.38796
$271$	0.304439	0.0184933	0.00924666	−	0.999957i	$-0.497057\pi$
$271$	0.304439	0.0184933	0.00924666	+	0.999957i	$0.497057\pi$
$272$	−22.2081	−1.34657
$273$	25.5330	1.54533
$274$	48.3773	2.92258
$275$	−5.97342	−0.360211
$276$	−44.0306	−2.65033
$277$	−14.2658	−0.857146	−0.428573	−	0.903507i	$-0.640984\pi$
$277$	−14.2658	−0.857146	−0.428573	+	0.903507i	$0.640984\pi$
$278$	32.4982	1.94911
$279$	28.5636	1.71006
$280$	30.8957	1.84637
$281$	2.57025	0.153328	0.0766640	−	0.997057i	$-0.475573\pi$
$281$	2.57025	0.153328	0.0766640	+	0.997057i	$0.475573\pi$
$282$	71.1349	4.23602
$283$	28.1868	1.67553	0.837766	−	0.546029i	$-0.183861\pi$
$283$	28.1868	1.67553	0.837766	+	0.546029i	$0.183861\pi$
$284$	−28.8432	−1.71153
$285$	−0.737580	−0.0436905
$286$	35.6030	2.10525
$287$	−42.1727	−2.48938
$288$	−82.7335	−4.87512
$289$	−13.2022	−0.776601
$290$	−27.1187	−1.59247
$291$	−21.4877	−1.25963
$292$	−52.5152	−3.07322
$293$	−9.49328	−0.554603	−0.277302	−	0.960783i	$-0.589440\pi$
$293$	−9.49328	−0.554603	−0.277302	+	0.960783i	$0.589440\pi$
$294$	59.8557	3.49086
$295$	−8.81620	−0.513299
$296$	71.5059	4.15620
$297$	51.3113	2.97738
$298$	63.1770	3.65975
$299$	6.56851	0.379867
$300$	−15.0481	−0.868803
$301$	−30.3778	−1.75095
$302$	18.4932	1.06416
$303$	−26.8018	−1.53972
$304$	2.82030	0.161755
$305$	3.39339	0.194305
$306$	30.4352	1.73987
$307$	−5.85040	−0.333900	−0.166950	−	0.985965i	$-0.553392\pi$
$307$	−5.85040	−0.333900	−0.166950	+	0.985965i	$0.553392\pi$
$308$	115.104	6.55866
$309$	−27.1756	−1.54596
$310$	−12.8926	−0.732251
$311$	8.35482	0.473758	0.236879	−	0.971539i	$-0.423875\pi$
$311$	8.35482	0.473758	0.236879	+	0.971539i	$0.423875\pi$
$312$	54.1636	3.06641
$313$	19.7865	1.11840	0.559199	−	0.829033i	$-0.311109\pi$
$313$	19.7865	1.11840	0.559199	+	0.829033i	$0.311109\pi$
$314$	−64.7482	−3.65395
$315$	−22.4486	−1.26483
$316$	−58.7952	−3.30749
$317$	−12.9975	−0.730015	−0.365008	−	0.931005i	$-0.618934\pi$
$317$	−12.9975	−0.730015	−0.365008	+	0.931005i	$0.618934\pi$
$318$	27.7878	1.55827
$319$	−61.0131	−3.41608
$320$	14.5513	0.813440
$321$	4.30076	0.240045
$322$	29.6475	1.65219
$323$	−0.482296	−0.0268357
$324$	40.1609	2.23116
$325$	2.24489	0.124524
$326$	−25.0349	−1.38656
$327$	12.9771	0.717634
$328$	−89.4617	−4.93969
$329$	−34.3083	−1.89148
$330$	−47.2665	−2.60194
$331$	−22.6296	−1.24384	−0.621918	−	0.783083i	$-0.713646\pi$
$331$	−22.6296	−1.24384	−0.621918	+	0.783083i	$0.713646\pi$
$332$	23.9023	1.31181
$333$	−51.9556	−2.84715
$334$	−12.2764	−0.671734
$335$	−8.80481	−0.481058
$336$	129.615	7.07106
$337$	1.87499	0.102137	0.0510687	−	0.998695i	$-0.483737\pi$
$337$	1.87499	0.102137	0.0510687	+	0.998695i	$0.483737\pi$
$338$	21.1353	1.14961
$339$	−13.1419	−0.713769
$340$	−9.83980	−0.533638
$341$	−29.0065	−1.57079
$342$	−3.86509	−0.209000
$343$	−2.15399	−0.116304
$344$	−64.4410	−3.47442
$345$	−8.72034	−0.469488
$346$	−46.4333	−2.49627
$347$	−14.5547	−0.781339	−0.390670	−	0.920531i	$-0.627756\pi$
$347$	−14.5547	−0.781339	−0.390670	+	0.920531i	$0.627756\pi$
$348$	−153.703	−8.23933
$349$	2.61220	0.139828	0.0699138	−	0.997553i	$-0.477728\pi$
$349$	2.61220	0.139828	0.0699138	+	0.997553i	$0.477728\pi$
$350$	10.1325	0.541604
$351$	−19.2834	−1.02927
$352$	84.0161	4.47807
$353$	−19.7114	−1.04913	−0.524567	−	0.851369i	$-0.675773\pi$
$353$	−19.7114	−1.04913	−0.524567	+	0.851369i	$0.675773\pi$
$354$	−69.7609	−3.70775
$355$	−5.71246	−0.303186
$356$	62.8100	3.32892
$357$	−22.1653	−1.17311
$358$	5.41901	0.286404
$359$	−4.66104	−0.246000	−0.123000	−	0.992407i	$-0.539252\pi$
$359$	−4.66104	−0.246000	−0.123000	+	0.992407i	$0.539252\pi$
$360$	−47.6205	−2.50982
$361$	−18.9388	−0.996776
$362$	10.4636	0.549954
$363$	−73.5592	−3.86086
$364$	−43.2575	−2.26731
$365$	−10.4008	−0.544400
$366$	26.8512	1.40353
$367$	13.0740	0.682456	0.341228	−	0.939981i	$-0.389157\pi$
$367$	13.0740	0.682456	0.341228	+	0.939981i	$0.389157\pi$
$368$	33.3441	1.73818
$369$	65.0020	3.38387
$370$	23.4509	1.21915
$371$	−13.4020	−0.695800
$372$	−73.0724	−3.78863
$373$	29.7409	1.53993	0.769963	−	0.638089i	$-0.220275\pi$
$373$	29.7409	1.53993	0.769963	+	0.638089i	$0.220275\pi$
$374$	−30.9071	−1.59817
$375$	−2.98031	−0.153902
$376$	−72.7787	−3.75328
$377$	22.9295	1.18093
$378$	−87.0373	−4.47672
$379$	16.7370	0.859722	0.429861	−	0.902895i	$-0.358563\pi$
$379$	16.7370	0.859722	0.429861	+	0.902895i	$0.358563\pi$
$380$	1.24959	0.0641028
$381$	57.7504	2.95864
$382$	−59.1135	−3.02451
$383$	−24.4848	−1.25111	−0.625557	−	0.780178i	$-0.715128\pi$
$383$	−24.4848	−1.25111	−0.625557	+	0.780178i	$0.715128\pi$
$384$	31.3052	1.59754
$385$	22.7966	1.16182
$386$	15.8724	0.807881
$387$	46.8222	2.38011
$388$	36.4041	1.84814
$389$	−34.8170	−1.76529	−0.882646	−	0.470039i	$-0.844240\pi$
$389$	−34.8170	−1.76529	−0.882646	+	0.470039i	$0.844240\pi$
$390$	17.7633	0.899481
$391$	−5.70214	−0.288370
$392$	−61.2389	−3.09303
$393$	−23.8525	−1.20320
$394$	−32.3460	−1.62957
$395$	−11.6445	−0.585899
$396$	−177.413	−8.91535
$397$	−4.30688	−0.216156	−0.108078	−	0.994142i	$-0.534470\pi$
$397$	−4.30688	−0.216156	−0.108078	+	0.994142i	$0.534470\pi$
$398$	34.3494	1.72178
$399$	2.81485	0.140919
$400$	11.3958	0.569792
$401$	25.7850	1.28764	0.643820	−	0.765177i	$-0.277348\pi$
$401$	25.7850	1.28764	0.643820	+	0.765177i	$0.277348\pi$
$402$	−69.6707	−3.47486
$403$	10.9010	0.543017
$404$	45.4071	2.25909
$405$	7.95395	0.395235
$406$	103.494	5.13633
$407$	52.7610	2.61527
$408$	−47.0196	−2.32782
$409$	−2.22146	−0.109844	−0.0549222	−	0.998491i	$-0.517491\pi$
$409$	−2.22146	−0.109844	−0.0549222	+	0.998491i	$0.517491\pi$
$410$	−29.3396	−1.44898
$411$	54.3042	2.67863
$412$	46.0403	2.26824
$413$	33.6456	1.65559
$414$	−45.6966	−2.24587
$415$	4.73389	0.232378
$416$	−31.5743	−1.54806
$417$	36.4796	1.78642
$418$	3.92501	0.191978
$419$	10.0287	0.489932	0.244966	−	0.969532i	$-0.421223\pi$
$419$	10.0287	0.489932	0.244966	+	0.969532i	$0.421223\pi$
$420$	57.4286	2.80223
$421$	−5.81908	−0.283605	−0.141802	−	0.989895i	$-0.545290\pi$
$421$	−5.81908	−0.283605	−0.141802	+	0.989895i	$0.545290\pi$
$422$	−43.5506	−2.12001
$423$	52.8804	2.57113
$424$	−28.4300	−1.38068
$425$	−1.94879	−0.0945303
$426$	−45.2016	−2.19002
$427$	−12.9503	−0.626709
$428$	−7.28627	−0.352195
$429$	39.9649	1.92952
$430$	−21.1339	−1.01917
$431$	−12.9347	−0.623044	−0.311522	−	0.950239i	$-0.600839\pi$
$431$	−12.9347	−0.623044	−0.311522	+	0.950239i	$0.600839\pi$
$432$	−97.8896	−4.70971
$433$	−23.5359	−1.13107	−0.565533	−	0.824726i	$-0.691329\pi$
$433$	−23.5359	−1.13107	−0.565533	+	0.824726i	$0.691329\pi$
$434$	49.2025	2.36180
$435$	−30.4411	−1.45954
$436$	−21.9855	−1.05292
$437$	0.724137	0.0346402
$438$	−82.2991	−3.93240
$439$	31.3057	1.49414	0.747071	−	0.664744i	$-0.231460\pi$
$439$	31.3057	1.49414	0.747071	+	0.664744i	$0.231460\pi$
$440$	48.3588	2.30541
$441$	44.4956	2.11884
$442$	11.6153	0.552482
$443$	−16.6991	−0.793399	−0.396700	−	0.917948i	$-0.629845\pi$
$443$	−16.6991	−0.793399	−0.396700	+	0.917948i	$0.629845\pi$
$444$	132.914	6.30783
$445$	12.4396	0.589696
$446$	42.7871	2.02603
$447$	70.9171	3.35426
$448$	−55.5325	−2.62366
$449$	6.56348	0.309750	0.154875	−	0.987934i	$-0.450503\pi$
$449$	6.56348	0.309750	0.154875	+	0.987934i	$0.450503\pi$
$450$	−15.6175	−0.736216
$451$	−66.0097	−3.10828
$452$	22.2647	1.04724
$453$	20.7588	0.975336
$454$	−29.3867	−1.37919
$455$	−8.56723	−0.401638
$456$	5.97119	0.279627
$457$	−36.7531	−1.71924	−0.859618	−	0.510936i	$-0.829299\pi$
$457$	−36.7531	−1.71924	−0.859618	+	0.510936i	$0.829299\pi$
$458$	20.3915	0.952832
$459$	16.7400	0.781356
$460$	14.7738	0.688834
$461$	−1.29772	−0.0604407	−0.0302204	−	0.999543i	$-0.509621\pi$
$461$	−1.29772	−0.0604407	−0.0302204	+	0.999543i	$0.509621\pi$
$462$	180.385	8.39226
$463$	28.0446	1.30334	0.651672	−	0.758501i	$-0.274068\pi$
$463$	28.0446	1.30334	0.651672	+	0.758501i	$0.274068\pi$
$464$	116.398	5.40365
$465$	−14.4721	−0.671129
$466$	23.9733	1.11054
$467$	12.1619	0.562785	0.281392	−	0.959593i	$-0.409204\pi$
$467$	12.1619	0.562785	0.281392	+	0.959593i	$0.409204\pi$
$468$	66.6741	3.08201
$469$	33.6021	1.55160
$470$	−23.8683	−1.10096
$471$	−72.6808	−3.34895
$472$	71.3730	3.28521
$473$	−47.5481	−2.18626
$474$	−92.1407	−4.23216
$475$	0.247485	0.0113554
$476$	37.5520	1.72119
$477$	20.6570	0.945818
$478$	12.9319	0.591491
$479$	16.9027	0.772302	0.386151	−	0.922436i	$-0.373804\pi$
$479$	16.9027	0.772302	0.386151	+	0.922436i	$0.373804\pi$
$480$	41.9180	1.91329
$481$	−19.8282	−0.904090
$482$	34.2250	1.55891
$483$	33.2798	1.51428
$484$	124.623	5.66466
$485$	7.20990	0.327385
$486$	−5.48156	−0.248648
$487$	−33.8959	−1.53597	−0.767986	−	0.640467i	$-0.778741\pi$
$487$	−33.8959	−1.53597	−0.767986	+	0.640467i	$0.778741\pi$
$488$	−27.4717	−1.24359
$489$	−28.1021	−1.27082
$490$	−20.0837	−0.907291
$491$	−12.7427	−0.575071	−0.287535	−	0.957770i	$-0.592836\pi$
$491$	−12.7427	−0.575071	−0.287535	+	0.957770i	$0.592836\pi$
$492$	−166.290	−7.49694
$493$	−19.9051	−0.896483
$494$	−1.47507	−0.0663664
$495$	−35.1370	−1.57929
$496$	55.3373	2.48472
$497$	21.8007	0.977893
$498$	37.4584	1.67855
$499$	28.0565	1.25598	0.627991	−	0.778220i	$-0.283877\pi$
$499$	28.0565	1.25598	0.627991	+	0.778220i	$0.283877\pi$
$500$	5.04918	0.225806
$501$	−13.7804	−0.615664
$502$	−31.5639	−1.40877
$503$	−23.7553	−1.05920	−0.529598	−	0.848249i	$-0.677657\pi$
$503$	−23.7553	−1.05920	−0.529598	+	0.848249i	$0.677657\pi$
$504$	181.736	8.09516
$505$	8.99297	0.400182
$506$	46.4050	2.06295
$507$	23.7247	1.05365
$508$	−97.8396	−4.34093
$509$	−3.54301	−0.157041	−0.0785206	−	0.996912i	$-0.525020\pi$
$509$	−3.54301	−0.157041	−0.0785206	+	0.996912i	$0.525020\pi$
$510$	−15.4204	−0.682827
$511$	39.6927	1.75590
$512$	24.2313	1.07088
$513$	−2.12588	−0.0938597
$514$	78.4931	3.46218
$515$	9.11838	0.401804
$516$	−119.782	−5.27311
$517$	−53.7002	−2.36173
$518$	−89.4964	−3.93225
$519$	−52.1221	−2.28791
$520$	−18.1738	−0.796975
$521$	13.2057	0.578554	0.289277	−	0.957245i	$-0.406585\pi$
$521$	13.2057	0.578554	0.289277	+	0.957245i	$0.406585\pi$
$522$	−159.519	−6.98194
$523$	−31.4058	−1.37328	−0.686640	−	0.726997i	$-0.740915\pi$
$523$	−31.4058	−1.37328	−0.686640	+	0.726997i	$0.740915\pi$
$524$	40.4105	1.76534
$525$	11.3739	0.496396
$526$	−49.0995	−2.14084
$527$	−9.46318	−0.412223
$528$	202.876	8.82905
$529$	−14.4386	−0.627765
$530$	−9.32382	−0.405001
$531$	−51.8589	−2.25049
$532$	−4.76887	−0.206757
$533$	24.8073	1.07452
$534$	98.4324	4.25959
$535$	−1.44306	−0.0623889
$536$	71.2807	3.07886
$537$	6.08292	0.262497
$538$	14.9100	0.642814
$539$	−45.1854	−1.94627
$540$	−43.3721	−1.86644
$541$	45.9627	1.97609	0.988046	−	0.154158i	$-0.0492664\pi$
$541$	45.9627	1.97609	0.988046	+	0.154158i	$0.0492664\pi$
$542$	−0.808293	−0.0347192
$543$	11.7455	0.504049
$544$	27.4097	1.17518
$545$	−4.35427	−0.186517
$546$	−67.7908	−2.90118
$547$	16.4598	0.703772	0.351886	−	0.936043i	$-0.385541\pi$
$547$	16.4598	0.703772	0.351886	+	0.936043i	$0.385541\pi$
$548$	−92.0011	−3.93009
$549$	19.9607	0.851901
$550$	15.8596	0.676256
$551$	2.52783	0.107689
$552$	70.5969	3.00480
$553$	44.4394	1.88975
$554$	37.8760	1.60920
$555$	26.3239	1.11739
$556$	−61.8031	−2.62103
$557$	34.6230	1.46702	0.733511	−	0.679677i	$-0.237880\pi$
$557$	34.6230	1.46702	0.733511	+	0.679677i	$0.237880\pi$
$558$	−75.8373	−3.21045
$559$	17.8692	0.755785
$560$	−43.4904	−1.83780
$561$	−34.6936	−1.46477
$562$	−6.82408	−0.287856
$563$	10.8938	0.459121	0.229560	−	0.973294i	$-0.426271\pi$
$563$	10.8938	0.459121	0.229560	+	0.973294i	$0.426271\pi$
$564$	−135.280	−5.69632
$565$	4.40957	0.185512
$566$	−74.8368	−3.14563
$567$	−30.3549	−1.27479
$568$	46.2461	1.94044
$569$	−25.7017	−1.07747	−0.538736	−	0.842474i	$-0.681098\pi$
$569$	−25.7017	−1.07747	−0.538736	+	0.842474i	$0.681098\pi$
$570$	1.95830	0.0820240
$571$	−17.0004	−0.711443	−0.355722	−	0.934592i	$-0.615765\pi$
$571$	−17.0004	−0.711443	−0.355722	+	0.934592i	$0.615765\pi$
$572$	−67.7077	−2.83100
$573$	−66.3557	−2.77205
$574$	111.970	4.67353
$575$	2.92599	0.122022
$576$	85.5938	3.56641
$577$	−3.55652	−0.148060	−0.0740298	−	0.997256i	$-0.523586\pi$
$577$	−3.55652	−0.148060	−0.0740298	+	0.997256i	$0.523586\pi$
$578$	35.0522	1.45798
$579$	17.8169	0.740447
$580$	51.5728	2.14144
$581$	−18.0661	−0.749509
$582$	57.0505	2.36482
$583$	−20.9772	−0.868787
$584$	84.2009	3.48426
$585$	13.2049	0.545957
$586$	25.2049	1.04121
$587$	28.8139	1.18928	0.594639	−	0.803992i	$-0.297295\pi$
$587$	28.8139	1.18928	0.594639	+	0.803992i	$0.297295\pi$
$588$	−113.830	−4.69427
$589$	1.20177	0.0495179
$590$	23.4073	0.963662
$591$	−36.3089	−1.49355
$592$	−100.655	−4.13691
$593$	−1.83885	−0.0755123	−0.0377562	−	0.999287i	$-0.512021\pi$
$593$	−1.83885	−0.0755123	−0.0377562	+	0.999287i	$0.512021\pi$
$594$	−136.233	−5.58971
$595$	7.43724	0.304897
$596$	−120.146	−4.92139
$597$	38.5576	1.57806
$598$	−17.4396	−0.713157
$599$	30.4869	1.24566	0.622831	−	0.782356i	$-0.285982\pi$
$599$	30.4869	1.24566	0.622831	+	0.782356i	$0.285982\pi$
$600$	24.1275	0.985003
$601$	21.9983	0.897330	0.448665	−	0.893700i	$-0.351900\pi$
$601$	21.9983	0.897330	0.448665	+	0.893700i	$0.351900\pi$
$602$	80.6540	3.28721
$603$	−51.7919	−2.10913
$604$	−35.1692	−1.43102
$605$	24.6818	1.00346
$606$	71.1596	2.89066
$607$	22.9888	0.933087	0.466543	−	0.884498i	$-0.345499\pi$
$607$	22.9888	0.933087	0.466543	+	0.884498i	$0.345499\pi$
$608$	−3.48087	−0.141168
$609$	116.174	4.70759
$610$	−9.00954	−0.364786
$611$	20.1812	0.816443
$612$	−57.8800	−2.33966
$613$	28.7067	1.15945	0.579726	−	0.814811i	$-0.303159\pi$
$613$	28.7067	1.15945	0.579726	+	0.814811i	$0.303159\pi$
$614$	15.5330	0.626860
$615$	−32.9341	−1.32803
$616$	−184.553	−7.43586
$617$	32.7294	1.31764	0.658818	−	0.752302i	$-0.271057\pi$
$617$	32.7294	1.31764	0.658818	+	0.752302i	$0.271057\pi$
$618$	72.1519	2.90238
$619$	−7.96111	−0.319984	−0.159992	−	0.987118i	$-0.551147\pi$
$619$	−7.96111	−0.319984	−0.159992	+	0.987118i	$0.551147\pi$
$620$	24.5184	0.984683
$621$	−25.1340	−1.00859
$622$	−22.1823	−0.889429
$623$	−47.4739	−1.90200
$624$	−76.2433	−3.05218
$625$	1.00000	0.0400000
$626$	−52.5337	−2.09967
$627$	4.40588	0.175954
$628$	123.134	4.91360
$629$	17.2130	0.686326
$630$	59.6016	2.37458
$631$	1.91141	0.0760920	0.0380460	−	0.999276i	$-0.487887\pi$
$631$	1.91141	0.0760920	0.0380460	+	0.999276i	$0.487887\pi$
$632$	94.2700	3.74986
$633$	−48.8862	−1.94305
$634$	34.5089	1.37052
$635$	−19.3773	−0.768966
$636$	−52.8453	−2.09545
$637$	16.9812	0.672821
$638$	161.991	6.41330
$639$	−33.6020	−1.32927
$640$	−10.5040	−0.415208
$641$	7.71540	0.304740	0.152370	−	0.988324i	$-0.451309\pi$
$641$	7.71540	0.304740	0.152370	+	0.988324i	$0.451309\pi$
$642$	−11.4186	−0.450658
$643$	−7.09735	−0.279892	−0.139946	−	0.990159i	$-0.544693\pi$
$643$	−7.09735	−0.279892	−0.139946	+	0.990159i	$0.544693\pi$
$644$	−56.3819	−2.22176
$645$	−23.7231	−0.934095
$646$	1.28051	0.0503810
$647$	0.921504	0.0362281	0.0181140	−	0.999836i	$-0.494234\pi$
$647$	0.921504	0.0362281	0.0181140	+	0.999836i	$0.494234\pi$
$648$	−64.3924	−2.52957
$649$	52.6629	2.06720
$650$	−5.96024	−0.233780
$651$	55.2305	2.16465
$652$	47.6099	1.86455
$653$	11.2155	0.438898	0.219449	−	0.975624i	$-0.429574\pi$
$653$	11.2155	0.438898	0.219449	+	0.975624i	$0.429574\pi$
$654$	−34.4545	−1.34728
$655$	8.00338	0.312718
$656$	125.931	4.91677
$657$	−61.1796	−2.38684
$658$	91.0895	3.55104
$659$	−10.5720	−0.411825	−0.205912	−	0.978570i	$-0.566016\pi$
$659$	−10.5720	−0.411825	−0.205912	+	0.978570i	$0.566016\pi$
$660$	89.8887	3.49891
$661$	11.4559	0.445584	0.222792	−	0.974866i	$-0.428483\pi$
$661$	11.4559	0.445584	0.222792	+	0.974866i	$0.428483\pi$
$662$	60.0822	2.33516
$663$	13.0383	0.506365
$664$	−38.3240	−1.48726
$665$	−0.944484	−0.0366255
$666$	137.944	5.34520
$667$	29.8863	1.15720
$668$	23.3465	0.903304
$669$	48.0292	1.85691
$670$	23.3770	0.903133
$671$	−20.2701	−0.782520
$672$	−159.973	−6.17109
$673$	−4.34984	−0.167674	−0.0838370	−	0.996479i	$-0.526718\pi$
$673$	−4.34984	−0.167674	−0.0838370	+	0.996479i	$0.526718\pi$
$674$	−4.97816	−0.191752
$675$	−8.58993	−0.330627
$676$	−40.1939	−1.54592
$677$	0.564636	0.0217007	0.0108504	−	0.999941i	$-0.496546\pi$
$677$	0.564636	0.0217007	0.0108504	+	0.999941i	$0.496546\pi$
$678$	34.8921	1.34002
$679$	−27.5154	−1.05594
$680$	15.7768	0.605011
$681$	−32.9870	−1.26407
$682$	77.0130	2.94898
$683$	30.2367	1.15698	0.578488	−	0.815691i	$-0.303643\pi$
$683$	30.2367	1.15698	0.578488	+	0.815691i	$0.303643\pi$
$684$	7.35040	0.281050
$685$	−18.2210	−0.696189
$686$	5.71890	0.218349
$687$	22.8897	0.873298
$688$	90.7103	3.45830
$689$	7.88349	0.300337
$690$	23.1528	0.881411
$691$	−27.9321	−1.06259	−0.531294	−	0.847187i	$-0.678294\pi$
$691$	−27.9321	−1.06259	−0.531294	+	0.847187i	$0.678294\pi$
$692$	88.3042	3.35682
$693$	134.095	5.09384
$694$	38.6432	1.46688
$695$	−12.2402	−0.464298
$696$	246.441	9.34132
$697$	−21.5353	−0.815707
$698$	−6.93546	−0.262511
$699$	26.9104	1.01784
$700$	−19.2694	−0.728313
$701$	30.5685	1.15456	0.577279	−	0.816547i	$-0.304115\pi$
$701$	30.5685	1.15456	0.577279	+	0.816547i	$0.304115\pi$
$702$	51.1980	1.93235
$703$	−2.18594	−0.0824443
$704$	−86.9208	−3.27595
$705$	−26.7925	−1.00906
$706$	52.3344	1.96963
$707$	−34.3202	−1.29074
$708$	132.667	4.98594
$709$	29.7823	1.11850	0.559249	−	0.829000i	$-0.311090\pi$
$709$	29.7823	1.11850	0.559249	+	0.829000i	$0.311090\pi$
$710$	15.1667	0.569198
$711$	−68.4957	−2.56879
$712$	−100.707	−3.77416
$713$	14.2084	0.532108
$714$	58.8494	2.20238
$715$	−13.4096	−0.501492
$716$	−10.3056	−0.385137
$717$	14.5162	0.542119
$718$	12.3752	0.461838
$719$	−43.4163	−1.61915	−0.809577	−	0.587014i	$-0.800304\pi$
$719$	−43.4163	−1.61915	−0.809577	+	0.587014i	$0.800304\pi$
$720$	67.0330	2.49817
$721$	−34.7988	−1.29597
$722$	50.2829	1.87134
$723$	38.4180	1.42878
$724$	−19.8990	−0.739542
$725$	10.2141	0.379342
$726$	195.302	7.24833
$727$	−10.5941	−0.392915	−0.196458	−	0.980512i	$-0.562944\pi$
$727$	−10.5941	−0.392915	−0.196458	+	0.980512i	$0.562944\pi$
$728$	69.3574	2.57056
$729$	−30.0150	−1.11167
$730$	27.6143	1.02205
$731$	−15.5123	−0.573742
$732$	−51.0640	−1.88738
$733$	−24.7053	−0.912510	−0.456255	−	0.889849i	$-0.650809\pi$
$733$	−24.7053	−0.912510	−0.456255	+	0.889849i	$0.650809\pi$
$734$	−34.7118	−1.28124
$735$	−22.5443	−0.831558
$736$	−41.1540	−1.51696
$737$	52.5948	1.93736
$738$	−172.582	−6.35284
$739$	−41.2265	−1.51654	−0.758270	−	0.651940i	$-0.773955\pi$
$739$	−41.2265	−1.51654	−0.758270	+	0.651940i	$0.773955\pi$
$740$	−44.5975	−1.63944
$741$	−1.65578	−0.0608267
$742$	35.5828	1.30629
$743$	40.1936	1.47456	0.737280	−	0.675587i	$-0.236110\pi$
$743$	40.1936	1.47456	0.737280	+	0.675587i	$0.236110\pi$
$744$	117.161	4.29535
$745$	−23.7952	−0.871790
$746$	−78.9629	−2.89104
$747$	27.8459	1.01883
$748$	58.7773	2.14911
$749$	5.50720	0.201229
$750$	7.91280	0.288935
$751$	21.7084	0.792151	0.396076	−	0.918218i	$-0.370372\pi$
$751$	21.7084	0.792151	0.396076	+	0.918218i	$0.370372\pi$
$752$	102.447	3.73586
$753$	−35.4310	−1.29118
$754$	−60.8784	−2.21706
$755$	−6.96534	−0.253495
$756$	165.522	6.01999
$757$	−17.3965	−0.632285	−0.316143	−	0.948712i	$-0.602388\pi$
$757$	−17.3965	−0.632285	−0.316143	+	0.948712i	$0.602388\pi$
$758$	−44.4372	−1.61403
$759$	52.0903	1.89076
$760$	−2.00355	−0.0726764
$761$	−33.9211	−1.22964	−0.614819	−	0.788668i	$-0.710771\pi$
$761$	−33.9211	−1.22964	−0.614819	+	0.788668i	$0.710771\pi$
$762$	−153.329	−5.55452
$763$	16.6174	0.601589
$764$	112.419	4.06716
$765$	−11.4632	−0.414454
$766$	65.0078	2.34883
$767$	−19.7914	−0.714625
$768$	3.61812	0.130558
$769$	−1.47421	−0.0531612	−0.0265806	−	0.999647i	$-0.508462\pi$
$769$	−1.47421	−0.0531612	−0.0265806	+	0.999647i	$0.508462\pi$
$770$	−60.5256	−2.18119
$771$	88.1096	3.17319
$772$	−30.1851	−1.08639
$773$	42.4065	1.52526	0.762628	−	0.646838i	$-0.223909\pi$
$773$	42.4065	1.52526	0.762628	+	0.646838i	$0.223909\pi$
$774$	−124.314	−4.46839
$775$	4.85592	0.174430
$776$	−58.3689	−2.09532
$777$	−100.461	−3.60402
$778$	92.4401	3.31414
$779$	2.73485	0.0979861
$780$	−33.7813	−1.20956
$781$	34.1229	1.22101
$782$	15.1394	0.541382
$783$	−87.7384	−3.13551
$784$	86.2029	3.07867
$785$	24.3870	0.870410
$786$	63.3291	2.25888
$787$	−3.02005	−0.107653	−0.0538266	−	0.998550i	$-0.517142\pi$
$787$	−3.02005	−0.107653	−0.0538266	+	0.998550i	$0.517142\pi$
$788$	61.5138	2.19134
$789$	−55.1149	−1.96214
$790$	30.9165	1.09996
$791$	−16.8284	−0.598349
$792$	284.457	10.1078
$793$	7.61777	0.270515
$794$	11.4349	0.405810
$795$	−10.4661	−0.371195
$796$	−65.3236	−2.31533
$797$	−26.3177	−0.932220	−0.466110	−	0.884727i	$-0.654345\pi$
$797$	−26.3177	−0.932220	−0.466110	+	0.884727i	$0.654345\pi$
$798$	−7.47351	−0.264560
$799$	−17.5193	−0.619790
$800$	−14.0650	−0.497272
$801$	73.1729	2.58544
$802$	−68.4599	−2.41740
$803$	62.1281	2.19245
$804$	132.496	4.67276
$805$	−11.1666	−0.393569
$806$	−28.9424	−1.01945
$807$	16.7366	0.589158
$808$	−72.8040	−2.56124
$809$	15.1560	0.532855	0.266428	−	0.963855i	$-0.414157\pi$
$809$	15.1560	0.532855	0.266428	+	0.963855i	$0.414157\pi$
$810$	−21.1180	−0.742009
$811$	49.2555	1.72960	0.864798	−	0.502120i	$-0.167447\pi$
$811$	49.2555	1.72960	0.864798	+	0.502120i	$0.167447\pi$
$812$	−196.819	−6.90699
$813$	−0.907320	−0.0318211
$814$	−140.082	−4.90987
$815$	9.42925	0.330292
$816$	66.1871	2.31701
$817$	1.96996	0.0689203
$818$	5.89805	0.206221
$819$	−50.3945	−1.76092
$820$	55.7963	1.94849
$821$	−11.2850	−0.393850	−0.196925	−	0.980419i	$-0.563096\pi$
$821$	−11.2850	−0.393850	−0.196925	+	0.980419i	$0.563096\pi$
$822$	−144.179	−5.02883
$823$	4.08790	0.142495	0.0712477	−	0.997459i	$-0.477302\pi$
$823$	4.08790	0.142495	0.0712477	+	0.997459i	$0.477302\pi$
$824$	−73.8193	−2.57162
$825$	17.8026	0.619808
$826$	−89.3300	−3.10819
$827$	34.2008	1.18928	0.594639	−	0.803993i	$-0.297295\pi$
$827$	34.2008	1.18928	0.594639	+	0.803993i	$0.297295\pi$
$828$	86.9031	3.02009
$829$	33.9772	1.18008	0.590038	−	0.807375i	$-0.299113\pi$
$829$	33.9772	1.18008	0.590038	+	0.807375i	$0.299113\pi$
$830$	−12.5686	−0.436263
$831$	42.5163	1.47488
$832$	32.6659	1.13249
$833$	−14.7415	−0.510762
$834$	−96.8545	−3.35380
$835$	4.62383	0.160014
$836$	−7.46435	−0.258160
$837$	−41.7120	−1.44178
$838$	−26.6264	−0.919792
$839$	−31.5023	−1.08758	−0.543789	−	0.839222i	$-0.683011\pi$
$839$	−31.5023	−1.08758	−0.543789	+	0.839222i	$0.683011\pi$
$840$	−92.0788	−3.17702
$841$	75.3277	2.59751
$842$	15.4498	0.532436
$843$	−7.66012	−0.263829
$844$	82.8220	2.85085
$845$	−7.96049	−0.273849
$846$	−140.399	−4.82701
$847$	−94.1939	−3.23654
$848$	40.0195	1.37427
$849$	−84.0054	−2.88306
$850$	5.17410	0.177470
$851$	−25.8442	−0.885927
$852$	85.9617	2.94500
$853$	3.39342	0.116189	0.0580943	−	0.998311i	$-0.481498\pi$
$853$	3.39342	0.116189	0.0580943	+	0.998311i	$0.481498\pi$
$854$	34.3834	1.17658
$855$	1.45576	0.0497860
$856$	11.6825	0.399300
$857$	47.4311	1.62022	0.810108	−	0.586280i	$-0.199408\pi$
$857$	47.4311	1.62022	0.810108	+	0.586280i	$0.199408\pi$
$858$	−106.108	−3.62246
$859$	−23.8829	−0.814874	−0.407437	−	0.913233i	$-0.633577\pi$
$859$	−23.8829	−0.814874	−0.407437	+	0.913233i	$0.633577\pi$
$860$	40.1912	1.37051
$861$	125.688	4.28342
$862$	34.3421	1.16970
$863$	7.72664	0.263018	0.131509	−	0.991315i	$-0.458018\pi$
$863$	7.72664	0.263018	0.131509	+	0.991315i	$0.458018\pi$
$864$	120.817	4.11029
$865$	17.4888	0.594638
$866$	62.4886	2.12345
$867$	39.3466	1.33628
$868$	−93.5705	−3.17599
$869$	69.5576	2.35958
$870$	80.8221	2.74013
$871$	−19.7658	−0.669738
$872$	35.2507	1.19374
$873$	42.4103	1.43537
$874$	−1.92260	−0.0650331
$875$	−3.81633	−0.129016
$876$	156.512	5.28804
$877$	−40.2874	−1.36041	−0.680204	−	0.733022i	$-0.738109\pi$
$877$	−40.2874	−1.36041	−0.680204	+	0.733022i	$0.738109\pi$
$878$	−83.1177	−2.80509
$879$	28.2929	0.954295
$880$	−68.0722	−2.29471
$881$	16.1391	0.543739	0.271870	−	0.962334i	$-0.412358\pi$
$881$	16.1391	0.543739	0.271870	+	0.962334i	$0.412358\pi$
$882$	−118.137	−3.97789
$883$	−44.0726	−1.48316	−0.741580	−	0.670864i	$-0.765923\pi$
$883$	−44.0726	−1.48316	−0.741580	+	0.670864i	$0.765923\pi$
$884$	−22.0892	−0.742941
$885$	26.2750	0.883224
$886$	44.3367	1.48952
$887$	4.45959	0.149738	0.0748692	−	0.997193i	$-0.476146\pi$
$887$	4.45959	0.149738	0.0748692	+	0.997193i	$0.476146\pi$
$888$	−213.110	−7.15149
$889$	73.9504	2.48022
$890$	−33.0276	−1.10709
$891$	−47.5123	−1.59172
$892$	−81.3701	−2.72447
$893$	2.22485	0.0744517
$894$	−188.287	−6.29726
$895$	−2.04104	−0.0682244
$896$	40.0869	1.33921
$897$	−19.5762	−0.653629
$898$	−17.4262	−0.581521
$899$	49.5988	1.65421
$900$	29.7004	0.990014
$901$	−6.84369	−0.227996
$902$	175.258	5.83545
$903$	90.5352	3.01282
$904$	−35.6984	−1.18731
$905$	−3.94104	−0.131005
$906$	−55.1153	−1.83108
$907$	6.19036	0.205547	0.102774	−	0.994705i	$-0.467228\pi$
$907$	6.19036	0.205547	0.102774	+	0.994705i	$0.467228\pi$
$908$	55.8860	1.85464
$909$	52.8987	1.75454
$910$	22.7463	0.754031
$911$	31.8641	1.05570	0.527852	−	0.849337i	$-0.322998\pi$
$911$	31.8641	1.05570	0.527852	+	0.849337i	$0.322998\pi$
$912$	−8.40535	−0.278329
$913$	−28.2775	−0.935850
$914$	97.5805	3.22768
$915$	−10.1133	−0.334337
$916$	−38.7794	−1.28131
$917$	−30.5436	−1.00864
$918$	−44.4452	−1.46691
$919$	−20.4431	−0.674354	−0.337177	−	0.941441i	$-0.609472\pi$
$919$	−20.4431	−0.674354	−0.337177	+	0.941441i	$0.609472\pi$
$920$	−23.6878	−0.780964
$921$	17.4360	0.574535
$922$	3.44548	0.113471
$923$	−12.8238	−0.422101
$924$	−343.045	−11.2854
$925$	−8.83263	−0.290415
$926$	−74.4593	−2.44688
$927$	53.6364	1.76165
$928$	−143.661	−4.71591
$929$	−44.5783	−1.46257	−0.731283	−	0.682074i	$-0.761078\pi$
$929$	−44.5783	−1.46257	−0.731283	+	0.682074i	$0.761078\pi$
$930$	38.4239	1.25997
$931$	1.87208	0.0613548
$932$	−45.5911	−1.49339
$933$	−24.8999	−0.815187
$934$	−32.2901	−1.05657
$935$	11.6410	0.380700
$936$	−106.903	−3.49422
$937$	32.1595	1.05061	0.525303	−	0.850915i	$-0.323952\pi$
$937$	32.1595	1.05061	0.525303	+	0.850915i	$0.323952\pi$
$938$	−89.2146	−2.91296
$939$	−58.9698	−1.92441
$940$	45.3914	1.48050
$941$	−53.1108	−1.73136	−0.865682	−	0.500595i	$-0.833115\pi$
$941$	−53.1108	−1.73136	−0.865682	+	0.500595i	$0.833115\pi$
$942$	192.970	6.28729
$943$	32.3339	1.05294
$944$	−100.468	−3.26996
$945$	32.7821	1.06640
$946$	126.242	4.10447
$947$	−18.4457	−0.599404	−0.299702	−	0.954033i	$-0.596887\pi$
$947$	−18.4457	−0.599404	−0.299702	+	0.954033i	$0.596887\pi$
$948$	175.228	5.69113
$949$	−23.3485	−0.757924
$950$	−0.657079	−0.0213184
$951$	38.7367	1.25612
$952$	−60.2094	−1.95140
$953$	−0.334831	−0.0108462	−0.00542312	−	0.999985i	$-0.501726\pi$
$953$	−0.334831	−0.0108462	−0.00542312	+	0.999985i	$0.501726\pi$
$954$	−54.8449	−1.77567
$955$	22.2647	0.720469
$956$	−24.5931	−0.795399
$957$	181.838	5.87798
$958$	−44.8770	−1.44991
$959$	69.5374	2.24548
$960$	−43.3672	−1.39967
$961$	−7.42003	−0.239356
$962$	52.6445	1.69733
$963$	−8.48841	−0.273535
$964$	−65.0871	−2.09631
$965$	−5.97822	−0.192446
$966$	−88.3587	−2.84289
$967$	−51.4091	−1.65321	−0.826603	−	0.562785i	$-0.809730\pi$
$967$	−51.4091	−1.65321	−0.826603	+	0.562785i	$0.809730\pi$
$968$	−199.815	−6.42230
$969$	1.43739	0.0461756
$970$	−19.1425	−0.614628
$971$	−56.4309	−1.81096	−0.905478	−	0.424394i	$-0.860487\pi$
$971$	−56.4309	−1.81096	−0.905478	+	0.424394i	$0.860487\pi$
$972$	10.4245	0.334366
$973$	46.7128	1.49754
$974$	89.9947	2.88362
$975$	−6.69045	−0.214266
$976$	38.6705	1.23781
$977$	0.157554	0.00504059	0.00252030	−	0.999997i	$-0.499198\pi$
$977$	0.157554	0.00504059	0.00252030	+	0.999997i	$0.499198\pi$
$978$	74.6118	2.38582
$979$	−74.3072	−2.37487
$980$	38.1941	1.22006
$981$	−25.6129	−0.817755
$982$	33.8323	1.07963
$983$	48.1152	1.53464	0.767318	−	0.641267i	$-0.221591\pi$
$983$	48.1152	1.53464	0.767318	+	0.641267i	$0.221591\pi$
$984$	266.623	8.49964
$985$	12.1829	0.388181
$986$	52.8487	1.68305
$987$	102.249	3.25463
$988$	2.80519	0.0892451
$989$	23.2907	0.740601
$990$	93.2899	2.96495
$991$	−50.8853	−1.61642	−0.808212	−	0.588892i	$-0.799564\pi$
$991$	−50.8853	−1.61642	−0.808212	+	0.588892i	$0.799564\pi$
$992$	−68.2985	−2.16848
$993$	67.4432	2.14024
$994$	−57.8814	−1.83589
$995$	−12.9375	−0.410145
$996$	−71.2361	−2.25720
$997$	−61.0410	−1.93319	−0.966594	−	0.256312i	$-0.917493\pi$
$997$	−61.0410	−1.93319	−0.966594	+	0.256312i	$0.917493\pi$
$998$	−74.4909	−2.35797
$999$	75.8717	2.40047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.5	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.5	✓	153	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.65503 q^{2} -2.98031 q^{3} +5.04918 q^{4} +1.00000 q^{5} +7.91280 q^{6} -3.81633 q^{7} -8.09566 q^{8} +5.88223 q^{9} +O(q^{10})\)	\(q-2.65503 q^{2} -2.98031 q^{3} +5.04918 q^{4} +1.00000 q^{5} +7.91280 q^{6} -3.81633 q^{7} -8.09566 q^{8} +5.88223 q^{9} -2.65503 q^{10} -5.97342 q^{11} -15.0481 q^{12} +2.24489 q^{13} +10.1325 q^{14} -2.98031 q^{15} +11.3958 q^{16} -1.94879 q^{17} -15.6175 q^{18} +0.247485 q^{19} +5.04918 q^{20} +11.3739 q^{21} +15.8596 q^{22} +2.92599 q^{23} +24.1275 q^{24} +1.00000 q^{25} -5.96024 q^{26} -8.58993 q^{27} -19.2694 q^{28} +10.2141 q^{29} +7.91280 q^{30} +4.85592 q^{31} -14.0650 q^{32} +17.8026 q^{33} +5.17410 q^{34} -3.81633 q^{35} +29.7004 q^{36} -8.83263 q^{37} -0.657079 q^{38} -6.69045 q^{39} -8.09566 q^{40} +11.0506 q^{41} -30.1979 q^{42} +7.95994 q^{43} -30.1609 q^{44} +5.88223 q^{45} -7.76858 q^{46} +8.98985 q^{47} -33.9631 q^{48} +7.56441 q^{49} -2.65503 q^{50} +5.80800 q^{51} +11.3348 q^{52} +3.51176 q^{53} +22.8065 q^{54} -5.97342 q^{55} +30.8957 q^{56} -0.737580 q^{57} -27.1187 q^{58} -8.81620 q^{59} -15.0481 q^{60} +3.39339 q^{61} -12.8926 q^{62} -22.4486 q^{63} +14.5513 q^{64} +2.24489 q^{65} -47.2665 q^{66} -8.80481 q^{67} -9.83980 q^{68} -8.72034 q^{69} +10.1325 q^{70} -5.71246 q^{71} -47.6205 q^{72} -10.4008 q^{73} +23.4509 q^{74} -2.98031 q^{75} +1.24959 q^{76} +22.7966 q^{77} +17.7633 q^{78} -11.6445 q^{79} +11.3958 q^{80} +7.95395 q^{81} -29.3396 q^{82} +4.73389 q^{83} +57.4286 q^{84} -1.94879 q^{85} -21.1339 q^{86} -30.4411 q^{87} +48.3588 q^{88} +12.4396 q^{89} -15.6175 q^{90} -8.56723 q^{91} +14.7738 q^{92} -14.4721 q^{93} -23.8683 q^{94} +0.247485 q^{95} +41.9180 q^{96} +7.20990 q^{97} -20.0837 q^{98} -35.1370 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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