LMFDB - Embedded newform 8035.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.67655 q^{2} -2.96805 q^{3} +5.16395 q^{4} -1.00000 q^{5} +7.94414 q^{6} +4.47636 q^{7} -8.46847 q^{8} +5.80930 q^{9} +O(q^{10})$	\(q-2.67655 q^{2} -2.96805 q^{3} +5.16395 q^{4} -1.00000 q^{5} +7.94414 q^{6} +4.47636 q^{7} -8.46847 q^{8} +5.80930 q^{9} +2.67655 q^{10} +5.49948 q^{11} -15.3268 q^{12} -6.37713 q^{13} -11.9812 q^{14} +2.96805 q^{15} +12.3384 q^{16} +2.85612 q^{17} -15.5489 q^{18} +3.21569 q^{19} -5.16395 q^{20} -13.2860 q^{21} -14.7197 q^{22} -6.00396 q^{23} +25.1348 q^{24} +1.00000 q^{25} +17.0687 q^{26} -8.33812 q^{27} +23.1157 q^{28} -4.62827 q^{29} -7.94414 q^{30} +8.09887 q^{31} -16.0876 q^{32} -16.3227 q^{33} -7.64455 q^{34} -4.47636 q^{35} +29.9989 q^{36} +7.58232 q^{37} -8.60698 q^{38} +18.9276 q^{39} +8.46847 q^{40} +5.31425 q^{41} +35.5608 q^{42} +2.72591 q^{43} +28.3990 q^{44} -5.80930 q^{45} +16.0699 q^{46} +7.21985 q^{47} -36.6211 q^{48} +13.0378 q^{49} -2.67655 q^{50} -8.47709 q^{51} -32.9311 q^{52} -1.29128 q^{53} +22.3174 q^{54} -5.49948 q^{55} -37.9079 q^{56} -9.54433 q^{57} +12.3878 q^{58} -8.89627 q^{59} +15.3268 q^{60} -12.0638 q^{61} -21.6771 q^{62} +26.0045 q^{63} +18.3824 q^{64} +6.37713 q^{65} +43.6886 q^{66} -10.8244 q^{67} +14.7488 q^{68} +17.8200 q^{69} +11.9812 q^{70} -10.9601 q^{71} -49.1959 q^{72} +8.03524 q^{73} -20.2945 q^{74} -2.96805 q^{75} +16.6057 q^{76} +24.6176 q^{77} -50.6608 q^{78} -14.9158 q^{79} -12.3384 q^{80} +7.32004 q^{81} -14.2239 q^{82} -16.0855 q^{83} -68.6084 q^{84} -2.85612 q^{85} -7.29604 q^{86} +13.7369 q^{87} -46.5722 q^{88} +4.44024 q^{89} +15.5489 q^{90} -28.5463 q^{91} -31.0041 q^{92} -24.0378 q^{93} -19.3243 q^{94} -3.21569 q^{95} +47.7487 q^{96} +13.8508 q^{97} -34.8963 q^{98} +31.9481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.67655	−1.89261	−0.946305	−	0.323275i	$-0.895216\pi$
$2$	−2.67655	−1.89261	−0.946305	+	0.323275i	$0.895216\pi$
$3$	−2.96805	−1.71360	−0.856801	−	0.515647i	$-0.827552\pi$
$3$	−2.96805	−1.71360	−0.856801	+	0.515647i	$0.827552\pi$
$4$	5.16395	2.58197
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	7.94414	3.24318
$7$	4.47636	1.69190	0.845952	−	0.533259i	$-0.179033\pi$
$7$	4.47636	1.69190	0.845952	+	0.533259i	$0.179033\pi$
$8$	−8.46847	−2.99406
$9$	5.80930	1.93643
$10$	2.67655	0.846401
$11$	5.49948	1.65816	0.829078	−	0.559134i	$-0.188866\pi$
$11$	5.49948	1.65816	0.829078	+	0.559134i	$0.188866\pi$
$12$	−15.3268	−4.42447
$13$	−6.37713	−1.76870	−0.884349	−	0.466827i	$-0.845397\pi$
$13$	−6.37713	−1.76870	−0.884349	+	0.466827i	$0.845397\pi$
$14$	−11.9812	−3.20212
$15$	2.96805	0.766346
$16$	12.3384	3.08461
$17$	2.85612	0.692710	0.346355	−	0.938104i	$-0.387419\pi$
$17$	2.85612	0.692710	0.346355	+	0.938104i	$0.387419\pi$
$18$	−15.5489	−3.66491
$19$	3.21569	0.737731	0.368865	−	0.929483i	$-0.379746\pi$
$19$	3.21569	0.737731	0.368865	+	0.929483i	$0.379746\pi$
$20$	−5.16395	−1.15469
$21$	−13.2860	−2.89925
$22$	−14.7197	−3.13824
$23$	−6.00396	−1.25191	−0.625956	−	0.779859i	$-0.715291\pi$
$23$	−6.00396	−1.25191	−0.625956	+	0.779859i	$0.715291\pi$
$24$	25.1348	5.13062
$25$	1.00000	0.200000
$26$	17.0687	3.34745
$27$	−8.33812	−1.60467
$28$	23.1157	4.36845
$29$	−4.62827	−0.859448	−0.429724	−	0.902960i	$-0.641389\pi$
$29$	−4.62827	−0.859448	−0.429724	+	0.902960i	$0.641389\pi$
$30$	−7.94414	−1.45039
$31$	8.09887	1.45460	0.727300	−	0.686320i	$-0.240775\pi$
$31$	8.09887	1.45460	0.727300	+	0.686320i	$0.240775\pi$
$32$	−16.0876	−2.84391
$33$	−16.3227	−2.84142
$34$	−7.64455	−1.31103
$35$	−4.47636	−0.756643
$36$	29.9989	4.99982
$37$	7.58232	1.24653	0.623263	−	0.782013i	$-0.285807\pi$
$37$	7.58232	1.24653	0.623263	+	0.782013i	$0.285807\pi$
$38$	−8.60698	−1.39624
$39$	18.9276	3.03084
$40$	8.46847	1.33898
$41$	5.31425	0.829946	0.414973	−	0.909834i	$-0.363791\pi$
$41$	5.31425	0.829946	0.414973	+	0.909834i	$0.363791\pi$
$42$	35.5608	5.48715
$43$	2.72591	0.415697	0.207848	−	0.978161i	$-0.433354\pi$
$43$	2.72591	0.415697	0.207848	+	0.978161i	$0.433354\pi$
$44$	28.3990	4.28131
$45$	−5.80930	−0.865999
$46$	16.0699	2.36938
$47$	7.21985	1.05312	0.526561	−	0.850137i	$-0.323481\pi$
$47$	7.21985	1.05312	0.526561	+	0.850137i	$0.323481\pi$
$48$	−36.6211	−5.28580
$49$	13.0378	1.86254
$50$	−2.67655	−0.378522
$51$	−8.47709	−1.18703
$52$	−32.9311	−4.56673
$53$	−1.29128	−0.177372	−0.0886858	−	0.996060i	$-0.528267\pi$
$53$	−1.29128	−0.177372	−0.0886858	+	0.996060i	$0.528267\pi$
$54$	22.3174	3.03702
$55$	−5.49948	−0.741549
$56$	−37.9079	−5.06566
$57$	−9.54433	−1.26418
$58$	12.3878	1.62660
$59$	−8.89627	−1.15820	−0.579098	−	0.815258i	$-0.696595\pi$
$59$	−8.89627	−1.15820	−0.579098	+	0.815258i	$0.696595\pi$
$60$	15.3268	1.97869
$61$	−12.0638	−1.54461	−0.772304	−	0.635253i	$-0.780896\pi$
$61$	−12.0638	−1.54461	−0.772304	+	0.635253i	$0.780896\pi$
$62$	−21.6771	−2.75299
$63$	26.0045	3.27626
$64$	18.3824	2.29780
$65$	6.37713	0.790986
$66$	43.6886	5.37770
$67$	−10.8244	−1.32241	−0.661205	−	0.750205i	$-0.729955\pi$
$67$	−10.8244	−1.32241	−0.661205	+	0.750205i	$0.729955\pi$
$68$	14.7488	1.78856
$69$	17.8200	2.14528
$70$	11.9812	1.43203
$71$	−10.9601	−1.30072	−0.650361	−	0.759625i	$-0.725382\pi$
$71$	−10.9601	−1.30072	−0.650361	+	0.759625i	$0.725382\pi$
$72$	−49.1959	−5.79779
$73$	8.03524	0.940454	0.470227	−	0.882546i	$-0.344172\pi$
$73$	8.03524	0.940454	0.470227	+	0.882546i	$0.344172\pi$
$74$	−20.2945	−2.35919
$75$	−2.96805	−0.342720
$76$	16.6057	1.90480
$77$	24.6176	2.80544
$78$	−50.6608	−5.73621
$79$	−14.9158	−1.67816	−0.839080	−	0.544009i	$-0.816906\pi$
$79$	−14.9158	−1.67816	−0.839080	+	0.544009i	$0.816906\pi$
$80$	−12.3384	−1.37948
$81$	7.32004	0.813337
$82$	−14.2239	−1.57076
$83$	−16.0855	−1.76562	−0.882809	−	0.469732i	$-0.844350\pi$
$83$	−16.0855	−1.76562	−0.882809	+	0.469732i	$0.844350\pi$
$84$	−68.6084	−7.48579
$85$	−2.85612	−0.309789
$86$	−7.29604	−0.786752
$87$	13.7369	1.47275
$88$	−46.5722	−4.96461
$89$	4.44024	0.470665	0.235333	−	0.971915i	$-0.424382\pi$
$89$	4.44024	0.470665	0.235333	+	0.971915i	$0.424382\pi$
$90$	15.5489	1.63900
$91$	−28.5463	−2.99247
$92$	−31.0041	−3.23240
$93$	−24.0378	−2.49261
$94$	−19.3243	−1.99315
$95$	−3.21569	−0.329923
$96$	47.7487	4.87333
$97$	13.8508	1.40634	0.703168	−	0.711024i	$-0.251768\pi$
$97$	13.8508	1.40634	0.703168	+	0.711024i	$0.251768\pi$
$98$	−34.8963	−3.52506
$99$	31.9481	3.21090
$100$	5.16395	0.516395
$101$	−16.7732	−1.66899	−0.834496	−	0.551014i	$-0.814241\pi$
$101$	−16.7732	−1.66899	−0.834496	+	0.551014i	$0.814241\pi$
$102$	22.6894	2.24658
$103$	5.26353	0.518631	0.259315	−	0.965793i	$-0.416503\pi$
$103$	5.26353	0.518631	0.259315	+	0.965793i	$0.416503\pi$
$104$	54.0046	5.29558
$105$	13.2860	1.29658
$106$	3.45620	0.335695
$107$	5.91071	0.571409	0.285705	−	0.958318i	$-0.407772\pi$
$107$	5.91071	0.571409	0.285705	+	0.958318i	$0.407772\pi$
$108$	−43.0576	−4.14322
$109$	−5.58698	−0.535135	−0.267568	−	0.963539i	$-0.586220\pi$
$109$	−5.58698	−0.535135	−0.267568	+	0.963539i	$0.586220\pi$
$110$	14.7197	1.40346
$111$	−22.5047	−2.13605
$112$	55.2313	5.21887
$113$	−12.8147	−1.20550	−0.602751	−	0.797929i	$-0.705929\pi$
$113$	−12.8147	−1.20550	−0.602751	+	0.797929i	$0.705929\pi$
$114$	25.5459	2.39259
$115$	6.00396	0.559872
$116$	−23.9001	−2.21907
$117$	−37.0466	−3.42496
$118$	23.8114	2.19201
$119$	12.7850	1.17200
$120$	−25.1348	−2.29448
$121$	19.2443	1.74948
$122$	32.2893	2.92334
$123$	−15.7729	−1.42220
$124$	41.8221	3.75574
$125$	−1.00000	−0.0894427
$126$	−69.6024	−6.20068
$127$	−9.41388	−0.835347	−0.417673	−	0.908597i	$-0.637154\pi$
$127$	−9.41388	−0.835347	−0.417673	+	0.908597i	$0.637154\pi$
$128$	−17.0263	−1.50493
$129$	−8.09061	−0.712339
$130$	−17.0687	−1.49703
$131$	−6.51369	−0.569104	−0.284552	−	0.958661i	$-0.591845\pi$
$131$	−6.51369	−0.569104	−0.284552	+	0.958661i	$0.591845\pi$
$132$	−84.2896	−7.33646
$133$	14.3946	1.24817
$134$	28.9721	2.50281
$135$	8.33812	0.717631
$136$	−24.1870	−2.07401
$137$	1.80588	0.154286	0.0771432	−	0.997020i	$-0.475420\pi$
$137$	1.80588	0.154286	0.0771432	+	0.997020i	$0.475420\pi$
$138$	−47.6963	−4.06018
$139$	−12.1619	−1.03155	−0.515777	−	0.856723i	$-0.672497\pi$
$139$	−12.1619	−1.03155	−0.515777	+	0.856723i	$0.672497\pi$
$140$	−23.1157	−1.95363
$141$	−21.4288	−1.80463
$142$	29.3353	2.46176
$143$	−35.0709	−2.93277
$144$	71.6777	5.97314
$145$	4.62827	0.384357
$146$	−21.5068	−1.77991
$147$	−38.6967	−3.19165
$148$	39.1547	3.21849
$149$	−11.0973	−0.909127	−0.454563	−	0.890714i	$-0.650205\pi$
$149$	−11.0973	−0.909127	−0.454563	+	0.890714i	$0.650205\pi$
$150$	7.94414	0.648636
$151$	−5.66452	−0.460972	−0.230486	−	0.973076i	$-0.574032\pi$
$151$	−5.66452	−0.460972	−0.230486	+	0.973076i	$0.574032\pi$
$152$	−27.2320	−2.20881
$153$	16.5920	1.34139
$154$	−65.8904	−5.30960
$155$	−8.09887	−0.650517
$156$	97.7412	7.82556
$157$	−12.4034	−0.989903	−0.494951	−	0.868921i	$-0.664814\pi$
$157$	−12.4034	−0.989903	−0.494951	+	0.868921i	$0.664814\pi$
$158$	39.9230	3.17610
$159$	3.83259	0.303944
$160$	16.0876	1.27183
$161$	−26.8759	−2.11811
$162$	−19.5925	−1.53933
$163$	7.07949	0.554509	0.277254	−	0.960797i	$-0.410576\pi$
$163$	7.07949	0.554509	0.277254	+	0.960797i	$0.410576\pi$
$164$	27.4425	2.14290
$165$	16.3227	1.27072
$166$	43.0538	3.34163
$167$	−20.6146	−1.59520	−0.797601	−	0.603185i	$-0.793898\pi$
$167$	−20.6146	−1.59520	−0.797601	+	0.603185i	$0.793898\pi$
$168$	112.512	8.68052
$169$	27.6678	2.12829
$170$	7.64455	0.586310
$171$	18.6809	1.42857
$172$	14.0764	1.07332
$173$	2.75972	0.209818	0.104909	−	0.994482i	$-0.466545\pi$
$173$	2.75972	0.209818	0.104909	+	0.994482i	$0.466545\pi$
$174$	−36.7676	−2.78734
$175$	4.47636	0.338381
$176$	67.8550	5.11476
$177$	26.4045	1.98469
$178$	−11.8846	−0.890785
$179$	4.41290	0.329836	0.164918	−	0.986307i	$-0.447264\pi$
$179$	4.41290	0.329836	0.164918	+	0.986307i	$0.447264\pi$
$180$	−29.9989	−2.23599
$181$	3.23251	0.240271	0.120135	−	0.992758i	$-0.461667\pi$
$181$	3.23251	0.240271	0.120135	+	0.992758i	$0.461667\pi$
$182$	76.4058	5.66357
$183$	35.8058	2.64684
$184$	50.8444	3.74830
$185$	−7.58232	−0.557463
$186$	64.3385	4.71753
$187$	15.7072	1.14862
$188$	37.2829	2.71913
$189$	−37.3244	−2.71495
$190$	8.60698	0.624416
$191$	−5.67269	−0.410462	−0.205231	−	0.978714i	$-0.565794\pi$
$191$	−5.67269	−0.410462	−0.205231	+	0.978714i	$0.565794\pi$
$192$	−54.5598	−3.93751
$193$	−23.5676	−1.69643	−0.848216	−	0.529650i	$-0.822323\pi$
$193$	−23.5676	−1.69643	−0.848216	+	0.529650i	$0.822323\pi$
$194$	−37.0724	−2.66165
$195$	−18.9276	−1.35543
$196$	67.3264	4.80903
$197$	−7.34264	−0.523141	−0.261571	−	0.965184i	$-0.584240\pi$
$197$	−7.34264	−0.523141	−0.261571	+	0.965184i	$0.584240\pi$
$198$	−85.5108	−6.07699
$199$	−13.7210	−0.972653	−0.486326	−	0.873777i	$-0.661663\pi$
$199$	−13.7210	−0.972653	−0.486326	+	0.873777i	$0.661663\pi$
$200$	−8.46847	−0.598812
$201$	32.1273	2.26609
$202$	44.8943	3.15875
$203$	−20.7178	−1.45410
$204$	−43.7752	−3.06488
$205$	−5.31425	−0.371163
$206$	−14.0881	−0.981566
$207$	−34.8788	−2.42424
$208$	−78.6839	−5.45574
$209$	17.6846	1.22327
$210$	−35.5608	−2.45393
$211$	7.77799	0.535459	0.267729	−	0.963494i	$-0.413727\pi$
$211$	7.77799	0.535459	0.267729	+	0.963494i	$0.413727\pi$
$212$	−6.66813	−0.457969
$213$	32.5300	2.22892
$214$	−15.8203	−1.08146
$215$	−2.72591	−0.185905
$216$	70.6112	4.80448
$217$	36.2534	2.46104
$218$	14.9538	1.01280
$219$	−23.8490	−1.61156
$220$	−28.3990	−1.91466
$221$	−18.2138	−1.22519
$222$	60.2350	4.04271
$223$	−3.78027	−0.253146	−0.126573	−	0.991957i	$-0.540398\pi$
$223$	−3.78027	−0.253146	−0.126573	+	0.991957i	$0.540398\pi$
$224$	−72.0137	−4.81162
$225$	5.80930	0.387286
$226$	34.2992	2.28155
$227$	−20.2446	−1.34368	−0.671841	−	0.740696i	$-0.734496\pi$
$227$	−20.2446	−1.34368	−0.671841	+	0.740696i	$0.734496\pi$
$228$	−49.2864	−3.26407
$229$	1.41877	0.0937547	0.0468774	−	0.998901i	$-0.485073\pi$
$229$	1.41877	0.0937547	0.0468774	+	0.998901i	$0.485073\pi$
$230$	−16.0699	−1.05962
$231$	−73.0663	−4.80741
$232$	39.1944	2.57324
$233$	−17.9676	−1.17710	−0.588549	−	0.808461i	$-0.700301\pi$
$233$	−17.9676	−1.17710	−0.588549	+	0.808461i	$0.700301\pi$
$234$	99.1573	6.48212
$235$	−7.21985	−0.470971
$236$	−45.9399	−2.99043
$237$	44.2708	2.87570
$238$	−34.2198	−2.21814
$239$	14.9952	0.969957	0.484979	−	0.874526i	$-0.338827\pi$
$239$	14.9952	0.969957	0.484979	+	0.874526i	$0.338827\pi$
$240$	36.6211	2.36388
$241$	−9.13398	−0.588372	−0.294186	−	0.955748i	$-0.595048\pi$
$241$	−9.13398	−0.588372	−0.294186	+	0.955748i	$0.595048\pi$
$242$	−51.5083	−3.31108
$243$	3.28816	0.210936
$244$	−62.2967	−3.98814
$245$	−13.0378	−0.832953
$246$	42.2171	2.69167
$247$	−20.5069	−1.30482
$248$	−68.5851	−4.35516
$249$	47.7426	3.02557
$250$	2.67655	0.169280
$251$	17.7444	1.12002	0.560009	−	0.828486i	$-0.310798\pi$
$251$	17.7444	1.12002	0.560009	+	0.828486i	$0.310798\pi$
$252$	134.286	8.45921
$253$	−33.0186	−2.07586
$254$	25.1968	1.58099
$255$	8.47709	0.530856
$256$	8.80710	0.550444
$257$	3.98565	0.248618	0.124309	−	0.992244i	$-0.460329\pi$
$257$	3.98565	0.248618	0.124309	+	0.992244i	$0.460329\pi$
$258$	21.6550	1.34818
$259$	33.9412	2.10900
$260$	32.9311	2.04230
$261$	−26.8870	−1.66426
$262$	17.4342	1.07709
$263$	4.15005	0.255903	0.127952	−	0.991780i	$-0.459160\pi$
$263$	4.15005	0.255903	0.127952	+	0.991780i	$0.459160\pi$
$264$	138.228	8.50737
$265$	1.29128	0.0793230
$266$	−38.5279	−2.36230
$267$	−13.1789	−0.806533
$268$	−55.8966	−3.41443
$269$	−15.0842	−0.919697	−0.459849	−	0.887997i	$-0.652096\pi$
$269$	−15.0842	−0.919697	−0.459849	+	0.887997i	$0.652096\pi$
$270$	−22.3174	−1.35820
$271$	−13.5386	−0.822412	−0.411206	−	0.911542i	$-0.634892\pi$
$271$	−13.5386	−0.822412	−0.411206	+	0.911542i	$0.634892\pi$
$272$	35.2400	2.13674
$273$	84.7268	5.12790
$274$	−4.83353	−0.292004
$275$	5.49948	0.331631
$276$	92.0216	5.53905
$277$	−1.79552	−0.107882	−0.0539410	−	0.998544i	$-0.517178\pi$
$277$	−1.79552	−0.107882	−0.0539410	+	0.998544i	$0.517178\pi$
$278$	32.5519	1.95233
$279$	47.0487	2.81673
$280$	37.9079	2.26543
$281$	−0.336608	−0.0200803	−0.0100402	−	0.999950i	$-0.503196\pi$
$281$	−0.336608	−0.0200803	−0.0100402	+	0.999950i	$0.503196\pi$
$282$	57.3554	3.41547
$283$	−4.23904	−0.251985	−0.125992	−	0.992031i	$-0.540211\pi$
$283$	−4.23904	−0.251985	−0.125992	+	0.992031i	$0.540211\pi$
$284$	−56.5973	−3.35843
$285$	9.54433	0.565357
$286$	93.8691	5.55060
$287$	23.7885	1.40419
$288$	−93.4575	−5.50704
$289$	−8.84260	−0.520153
$290$	−12.3878	−0.727437
$291$	−41.1098	−2.40990
$292$	41.4935	2.42823
$293$	−31.3150	−1.82944	−0.914722	−	0.404084i	$-0.867590\pi$
$293$	−31.3150	−1.82944	−0.914722	+	0.404084i	$0.867590\pi$
$294$	103.574	6.04055
$295$	8.89627	0.517961
$296$	−64.2107	−3.73217
$297$	−45.8553	−2.66080
$298$	29.7025	1.72062
$299$	38.2880	2.21425
$300$	−15.3268	−0.884895
$301$	12.2021	0.703319
$302$	15.1614	0.872441
$303$	49.7835	2.85999
$304$	39.6767	2.27561
$305$	12.0638	0.690770
$306$	−44.4095	−2.53872
$307$	17.9927	1.02690	0.513448	−	0.858120i	$-0.328368\pi$
$307$	17.9927	1.02690	0.513448	+	0.858120i	$0.328368\pi$
$308$	127.124	7.24357
$309$	−15.6224	−0.888727
$310$	21.6771	1.23117
$311$	19.4399	1.10234	0.551168	−	0.834394i	$-0.314182\pi$
$311$	19.4399	1.10234	0.551168	+	0.834394i	$0.314182\pi$
$312$	−160.288	−9.07452
$313$	2.61596	0.147863	0.0739313	−	0.997263i	$-0.476445\pi$
$313$	2.61596	0.147863	0.0739313	+	0.997263i	$0.476445\pi$
$314$	33.1985	1.87350
$315$	−26.0045	−1.46519
$316$	−77.0244	−4.33296
$317$	27.8393	1.56361	0.781806	−	0.623522i	$-0.214299\pi$
$317$	27.8393	1.56361	0.781806	+	0.623522i	$0.214299\pi$
$318$	−10.2581	−0.575248
$319$	−25.4531	−1.42510
$320$	−18.3824	−1.02761
$321$	−17.5432	−0.979168
$322$	71.9347	4.00877
$323$	9.18440	0.511034
$324$	37.8003	2.10001
$325$	−6.37713	−0.353739
$326$	−18.9486	−1.04947
$327$	16.5824	0.917009
$328$	−45.0036	−2.48491
$329$	32.3186	1.78178
$330$	−43.6886	−2.40498
$331$	1.34705	0.0740403	0.0370202	−	0.999315i	$-0.488213\pi$
$331$	1.34705	0.0740403	0.0370202	+	0.999315i	$0.488213\pi$
$332$	−83.0649	−4.55878
$333$	44.0479	2.41381
$334$	55.1760	3.01910
$335$	10.8244	0.591400
$336$	−163.929	−8.94306
$337$	20.4925	1.11630	0.558149	−	0.829741i	$-0.311512\pi$
$337$	20.4925	1.11630	0.558149	+	0.829741i	$0.311512\pi$
$338$	−74.0543	−4.02802
$339$	38.0345	2.06575
$340$	−14.7488	−0.799868
$341$	44.5396	2.41195
$342$	−50.0005	−2.70372
$343$	27.0273	1.45934
$344$	−23.0843	−1.24462
$345$	−17.8200	−0.959398
$346$	−7.38655	−0.397103
$347$	−11.8501	−0.636145	−0.318072	−	0.948066i	$-0.603035\pi$
$347$	−11.8501	−0.636145	−0.318072	+	0.948066i	$0.603035\pi$
$348$	70.9367	3.80260
$349$	−8.41436	−0.450410	−0.225205	−	0.974311i	$-0.572305\pi$
$349$	−8.41436	−0.450410	−0.225205	+	0.974311i	$0.572305\pi$
$350$	−11.9812	−0.640423
$351$	53.1733	2.83818
$352$	−88.4733	−4.71564
$353$	−12.3525	−0.657456	−0.328728	−	0.944425i	$-0.606620\pi$
$353$	−12.3525	−0.657456	−0.328728	+	0.944425i	$0.606620\pi$
$354$	−70.6732	−3.75624
$355$	10.9601	0.581701
$356$	22.9292	1.21524
$357$	−37.9465	−2.00834
$358$	−11.8114	−0.624251
$359$	−15.7302	−0.830208	−0.415104	−	0.909774i	$-0.636255\pi$
$359$	−15.7302	−0.830208	−0.415104	+	0.909774i	$0.636255\pi$
$360$	49.1959	2.59285
$361$	−8.65931	−0.455753
$362$	−8.65199	−0.454739
$363$	−57.1178	−2.99791
$364$	−147.412	−7.72647
$365$	−8.03524	−0.420584
$366$	−95.8363	−5.00944
$367$	8.98176	0.468844	0.234422	−	0.972135i	$-0.424680\pi$
$367$	8.98176	0.468844	0.234422	+	0.972135i	$0.424680\pi$
$368$	−74.0795	−3.86166
$369$	30.8721	1.60713
$370$	20.2945	1.05506
$371$	−5.78025	−0.300096
$372$	−124.130	−6.43584
$373$	16.0116	0.829047	0.414523	−	0.910039i	$-0.363948\pi$
$373$	16.0116	0.829047	0.414523	+	0.910039i	$0.363948\pi$
$374$	−42.0411	−2.17389
$375$	2.96805	0.153269
$376$	−61.1411	−3.15311
$377$	29.5151	1.52010
$378$	99.9008	5.13834
$379$	−30.3587	−1.55942	−0.779711	−	0.626140i	$-0.784634\pi$
$379$	−30.3587	−1.55942	−0.779711	+	0.626140i	$0.784634\pi$
$380$	−16.6057	−0.851853
$381$	27.9408	1.43145
$382$	15.1833	0.776844
$383$	−3.41983	−0.174745	−0.0873726	−	0.996176i	$-0.527847\pi$
$383$	−3.41983	−0.174745	−0.0873726	+	0.996176i	$0.527847\pi$
$384$	50.5349	2.57885
$385$	−24.6176	−1.25463
$386$	63.0800	3.21069
$387$	15.8356	0.804969
$388$	71.5248	3.63112
$389$	30.1384	1.52808	0.764040	−	0.645169i	$-0.223213\pi$
$389$	30.1384	1.52808	0.764040	+	0.645169i	$0.223213\pi$
$390$	50.6608	2.56531
$391$	−17.1480	−0.867212
$392$	−110.410	−5.57655
$393$	19.3329	0.975217
$394$	19.6530	0.990103
$395$	14.9158	0.750496
$396$	164.978	8.29047
$397$	36.1249	1.81306	0.906528	−	0.422145i	$-0.138723\pi$
$397$	36.1249	1.81306	0.906528	+	0.422145i	$0.138723\pi$
$398$	36.7249	1.84085
$399$	−42.7238	−2.13887
$400$	12.3384	0.616922
$401$	−23.1835	−1.15773	−0.578863	−	0.815424i	$-0.696504\pi$
$401$	−23.1835	−1.15773	−0.578863	+	0.815424i	$0.696504\pi$
$402$	−85.9905	−4.28882
$403$	−51.6475	−2.57275
$404$	−86.6157	−4.30929
$405$	−7.32004	−0.363735
$406$	55.4523	2.75205
$407$	41.6988	2.06693
$408$	71.7880	3.55403
$409$	29.8613	1.47655	0.738273	−	0.674502i	$-0.235642\pi$
$409$	29.8613	1.47655	0.738273	+	0.674502i	$0.235642\pi$
$410$	14.2239	0.702467
$411$	−5.35993	−0.264386
$412$	27.1806	1.33909
$413$	−39.8229	−1.95956
$414$	93.3549	4.58814
$415$	16.0855	0.789608
$416$	102.593	5.03001
$417$	36.0969	1.76767
$418$	−47.3339	−2.31518
$419$	4.21800	0.206063	0.103031	−	0.994678i	$-0.467146\pi$
$419$	4.21800	0.206063	0.103031	+	0.994678i	$0.467146\pi$
$420$	68.6084	3.34775
$421$	14.8624	0.724350	0.362175	−	0.932110i	$-0.382034\pi$
$421$	14.8624	0.724350	0.362175	+	0.932110i	$0.382034\pi$
$422$	−20.8182	−1.01341
$423$	41.9422	2.03930
$424$	10.9352	0.531061
$425$	2.85612	0.138542
$426$	−87.0684	−4.21848
$427$	−54.0018	−2.61333
$428$	30.5226	1.47536
$429$	104.092	5.02561
$430$	7.29604	0.351846
$431$	−0.851847	−0.0410320	−0.0205160	−	0.999790i	$-0.506531\pi$
$431$	−0.851847	−0.0410320	−0.0205160	+	0.999790i	$0.506531\pi$
$432$	−102.879	−4.94979
$433$	6.04646	0.290574	0.145287	−	0.989390i	$-0.453589\pi$
$433$	6.04646	0.290574	0.145287	+	0.989390i	$0.453589\pi$
$434$	−97.0343	−4.65780
$435$	−13.7369	−0.658635
$436$	−28.8508	−1.38170
$437$	−19.3069	−0.923574
$438$	63.8330	3.05006
$439$	20.9134	0.998143	0.499072	−	0.866561i	$-0.333674\pi$
$439$	20.9134	0.998143	0.499072	+	0.866561i	$0.333674\pi$
$440$	46.5722	2.22024
$441$	75.7403	3.60668
$442$	48.7503	2.31882
$443$	−19.7128	−0.936581	−0.468291	−	0.883575i	$-0.655130\pi$
$443$	−19.7128	−0.936581	−0.468291	+	0.883575i	$0.655130\pi$
$444$	−116.213	−5.51522
$445$	−4.44024	−0.210488
$446$	10.1181	0.479106
$447$	32.9373	1.55788
$448$	82.2862	3.88766
$449$	−30.6878	−1.44825	−0.724123	−	0.689671i	$-0.757755\pi$
$449$	−30.6878	−1.44825	−0.724123	+	0.689671i	$0.757755\pi$
$450$	−15.5489	−0.732982
$451$	29.2256	1.37618
$452$	−66.1742	−3.11257
$453$	16.8126	0.789923
$454$	54.1858	2.54307
$455$	28.5463	1.33827
$456$	80.8259	3.78502
$457$	−23.9325	−1.11951	−0.559757	−	0.828657i	$-0.689105\pi$
$457$	−23.9325	−1.11951	−0.559757	+	0.828657i	$0.689105\pi$
$458$	−3.79741	−0.177441
$459$	−23.8146	−1.11157
$460$	31.0041	1.44557
$461$	9.87095	0.459736	0.229868	−	0.973222i	$-0.426171\pi$
$461$	9.87095	0.459736	0.229868	+	0.973222i	$0.426171\pi$
$462$	195.566	9.09855
$463$	−19.7859	−0.919530	−0.459765	−	0.888041i	$-0.652066\pi$
$463$	−19.7859	−0.919530	−0.459765	+	0.888041i	$0.652066\pi$
$464$	−57.1056	−2.65106
$465$	24.0378	1.11473
$466$	48.0913	2.22779
$467$	18.2612	0.845027	0.422513	−	0.906357i	$-0.361148\pi$
$467$	18.2612	0.845027	0.422513	+	0.906357i	$0.361148\pi$
$468$	−191.307	−8.84316
$469$	−48.4539	−2.23739
$470$	19.3243	0.891364
$471$	36.8140	1.69630
$472$	75.3379	3.46771
$473$	14.9911	0.689290
$474$	−118.493	−5.44257
$475$	3.21569	0.147546
$476$	66.0211	3.02607
$477$	−7.50146	−0.343468
$478$	−40.1354	−1.83575
$479$	−34.0970	−1.55793	−0.778967	−	0.627065i	$-0.784256\pi$
$479$	−34.0970	−1.55793	−0.778967	+	0.627065i	$0.784256\pi$
$480$	−47.7487	−2.17942
$481$	−48.3534	−2.20473
$482$	24.4476	1.11356
$483$	79.7688	3.62961
$484$	99.3763	4.51711
$485$	−13.8508	−0.628933
$486$	−8.80094	−0.399219
$487$	13.5954	0.616065	0.308033	−	0.951376i	$-0.400329\pi$
$487$	13.5954	0.616065	0.308033	+	0.951376i	$0.400329\pi$
$488$	102.162	4.62465
$489$	−21.0123	−0.950207
$490$	34.8963	1.57646
$491$	−6.48373	−0.292606	−0.146303	−	0.989240i	$-0.546738\pi$
$491$	−6.48373	−0.292606	−0.146303	+	0.989240i	$0.546738\pi$
$492$	−81.4506	−3.67208
$493$	−13.2189	−0.595348
$494$	54.8878	2.46952
$495$	−31.9481	−1.43596
$496$	99.9275	4.48688
$497$	−49.0613	−2.20070
$498$	−127.786	−5.72622
$499$	−21.3616	−0.956277	−0.478138	−	0.878285i	$-0.658688\pi$
$499$	−21.3616	−0.956277	−0.478138	+	0.878285i	$0.658688\pi$
$500$	−5.16395	−0.230939
$501$	61.1850	2.73354
$502$	−47.4940	−2.11976
$503$	22.5402	1.00502	0.502509	−	0.864572i	$-0.332410\pi$
$503$	22.5402	1.00502	0.502509	+	0.864572i	$0.332410\pi$
$504$	−220.218	−9.80931
$505$	16.7732	0.746396
$506$	88.3762	3.92880
$507$	−82.1192	−3.64704
$508$	−48.6128	−2.15684
$509$	18.1162	0.802986	0.401493	−	0.915862i	$-0.368491\pi$
$509$	18.1162	0.802986	0.401493	+	0.915862i	$0.368491\pi$
$510$	−22.6894	−1.00470
$511$	35.9686	1.59116
$512$	10.4799	0.463153
$513$	−26.8129	−1.18382
$514$	−10.6678	−0.470537
$515$	−5.26353	−0.231939
$516$	−41.7795	−1.83924
$517$	39.7054	1.74624
$518$	−90.8454	−3.99152
$519$	−8.19098	−0.359544
$520$	−54.0046	−2.36826
$521$	23.5955	1.03374	0.516869	−	0.856064i	$-0.327097\pi$
$521$	23.5955	1.03374	0.516869	+	0.856064i	$0.327097\pi$
$522$	71.9645	3.14980
$523$	19.2284	0.840801	0.420400	−	0.907339i	$-0.361890\pi$
$523$	19.2284	0.840801	0.420400	+	0.907339i	$0.361890\pi$
$524$	−33.6363	−1.46941
$525$	−13.2860	−0.579850
$526$	−11.1078	−0.484325
$527$	23.1313	1.00762
$528$	−201.397	−8.76467
$529$	13.0475	0.567283
$530$	−3.45620	−0.150128
$531$	−51.6811	−2.24277
$532$	74.3329	3.22274
$533$	−33.8897	−1.46792
$534$	35.2739	1.52645
$535$	−5.91071	−0.255542
$536$	91.6661	3.95937
$537$	−13.0977	−0.565207
$538$	40.3736	1.74063
$539$	71.7010	3.08838
$540$	43.0576	1.85290
$541$	18.7965	0.808124	0.404062	−	0.914732i	$-0.367598\pi$
$541$	18.7965	0.808124	0.404062	+	0.914732i	$0.367598\pi$
$542$	36.2368	1.55650
$543$	−9.59424	−0.411728
$544$	−45.9480	−1.97000
$545$	5.58698	0.239320
$546$	−226.776	−9.70511
$547$	−24.0321	−1.02754	−0.513770	−	0.857928i	$-0.671751\pi$
$547$	−24.0321	−1.02754	−0.513770	+	0.857928i	$0.671751\pi$
$548$	9.32545	0.398364
$549$	−70.0820	−2.99103
$550$	−14.7197	−0.627648
$551$	−14.8831	−0.634041
$552$	−150.908	−6.42309
$553$	−66.7685	−2.83929
$554$	4.80580	0.204179
$555$	22.5047	0.955270
$556$	−62.8031	−2.66345
$557$	5.57291	0.236132	0.118066	−	0.993006i	$-0.462331\pi$
$557$	5.57291	0.236132	0.118066	+	0.993006i	$0.462331\pi$
$558$	−125.929	−5.33098
$559$	−17.3835	−0.735242
$560$	−55.2313	−2.33395
$561$	−46.6195	−1.96828
$562$	0.900949	0.0380042
$563$	−2.47207	−0.104185	−0.0520927	−	0.998642i	$-0.516589\pi$
$563$	−2.47207	−0.104185	−0.0520927	+	0.998642i	$0.516589\pi$
$564$	−110.657	−4.65951
$565$	12.8147	0.539117
$566$	11.3460	0.476909
$567$	32.7671	1.37609
$568$	92.8152	3.89444
$569$	−1.62921	−0.0683001	−0.0341501	−	0.999417i	$-0.510872\pi$
$569$	−1.62921	−0.0683001	−0.0341501	+	0.999417i	$0.510872\pi$
$570$	−25.5459	−1.07000
$571$	40.7643	1.70593	0.852966	−	0.521967i	$-0.174802\pi$
$571$	40.7643	1.70593	0.852966	+	0.521967i	$0.174802\pi$
$572$	−181.104	−7.57234
$573$	16.8368	0.703368
$574$	−63.6712	−2.65758
$575$	−6.00396	−0.250382
$576$	106.789	4.44953
$577$	−47.5718	−1.98044	−0.990219	−	0.139522i	$-0.955444\pi$
$577$	−47.5718	−1.98044	−0.990219	+	0.139522i	$0.955444\pi$
$578$	23.6677	0.984446
$579$	69.9497	2.90701
$580$	23.9001	0.992399
$581$	−72.0047	−2.98726
$582$	110.033	4.56100
$583$	−7.10139	−0.294110
$584$	−68.0462	−2.81577
$585$	37.0466	1.53169
$586$	83.8164	3.46242
$587$	−40.8302	−1.68524	−0.842622	−	0.538505i	$-0.818989\pi$
$587$	−40.8302	−1.68524	−0.842622	+	0.538505i	$0.818989\pi$
$588$	−199.828	−8.24076
$589$	26.0435	1.07310
$590$	−23.8114	−0.980298
$591$	21.7933	0.896456
$592$	93.5540	3.84505
$593$	27.0847	1.11224	0.556118	−	0.831103i	$-0.312290\pi$
$593$	27.0847	1.11224	0.556118	+	0.831103i	$0.312290\pi$
$594$	122.734	5.03585
$595$	−12.7850	−0.524134
$596$	−57.3059	−2.34734
$597$	40.7244	1.66674
$598$	−102.480	−4.19072
$599$	−30.9672	−1.26528	−0.632642	−	0.774444i	$-0.718030\pi$
$599$	−30.9672	−1.26528	−0.632642	+	0.774444i	$0.718030\pi$
$600$	25.1348	1.02612
$601$	15.4366	0.629672	0.314836	−	0.949146i	$-0.398050\pi$
$601$	15.4366	0.629672	0.314836	+	0.949146i	$0.398050\pi$
$602$	−32.6597	−1.33111
$603$	−62.8821	−2.56076
$604$	−29.2513	−1.19022
$605$	−19.2443	−0.782390
$606$	−133.248	−5.41284
$607$	−31.9124	−1.29528	−0.647641	−	0.761945i	$-0.724244\pi$
$607$	−31.9124	−1.29528	−0.647641	+	0.761945i	$0.724244\pi$
$608$	−51.7327	−2.09804
$609$	61.4913	2.49175
$610$	−32.2893	−1.30736
$611$	−46.0419	−1.86266
$612$	85.6803	3.46342
$613$	14.7913	0.597415	0.298707	−	0.954345i	$-0.403445\pi$
$613$	14.7913	0.597415	0.298707	+	0.954345i	$0.403445\pi$
$614$	−48.1584	−1.94352
$615$	15.7729	0.636026
$616$	−208.474	−8.39965
$617$	30.2491	1.21778	0.608892	−	0.793253i	$-0.291614\pi$
$617$	30.2491	1.21778	0.608892	+	0.793253i	$0.291614\pi$
$618$	41.8142	1.68201
$619$	−5.16945	−0.207778	−0.103889	−	0.994589i	$-0.533129\pi$
$619$	−5.16945	−0.207778	−0.103889	+	0.994589i	$0.533129\pi$
$620$	−41.8221	−1.67962
$621$	50.0617	2.00891
$622$	−52.0320	−2.08629
$623$	19.8761	0.796320
$624$	233.537	9.34897
$625$	1.00000	0.0400000
$626$	−7.00175	−0.279846
$627$	−52.4888	−2.09620
$628$	−64.0507	−2.55590
$629$	21.6560	0.863481
$630$	69.6024	2.77303
$631$	27.1333	1.08016	0.540080	−	0.841614i	$-0.318394\pi$
$631$	27.1333	1.08016	0.540080	+	0.841614i	$0.318394\pi$
$632$	126.314	5.02451
$633$	−23.0854	−0.917564
$634$	−74.5134	−2.95931
$635$	9.41388	0.373578
$636$	19.7913	0.784776
$637$	−83.1436	−3.29427
$638$	68.1265	2.69715
$639$	−63.6704	−2.51876
$640$	17.0263	0.673024
$641$	15.7697	0.622866	0.311433	−	0.950268i	$-0.399191\pi$
$641$	15.7697	0.622866	0.311433	+	0.950268i	$0.399191\pi$
$642$	46.9555	1.85318
$643$	−15.5357	−0.612669	−0.306335	−	0.951924i	$-0.599103\pi$
$643$	−15.5357	−0.612669	−0.306335	+	0.951924i	$0.599103\pi$
$644$	−138.786	−5.46891
$645$	8.09061	0.318568
$646$	−24.5826	−0.967188
$647$	−26.8428	−1.05530	−0.527650	−	0.849462i	$-0.676927\pi$
$647$	−26.8428	−1.05530	−0.527650	+	0.849462i	$0.676927\pi$
$648$	−61.9895	−2.43518
$649$	−48.9249	−1.92047
$650$	17.0687	0.669491
$651$	−107.602	−4.21725
$652$	36.5581	1.43173
$653$	−49.4761	−1.93615	−0.968074	−	0.250663i	$-0.919351\pi$
$653$	−49.4761	−1.93615	−0.968074	+	0.250663i	$0.919351\pi$
$654$	−44.3837	−1.73554
$655$	6.51369	0.254511
$656$	65.5696	2.56006
$657$	46.6791	1.82112
$658$	−86.5025	−3.37222
$659$	−13.8356	−0.538958	−0.269479	−	0.963006i	$-0.586851\pi$
$659$	−13.8356	−0.538958	−0.269479	+	0.963006i	$0.586851\pi$
$660$	84.2896	3.28097
$661$	−30.9329	−1.20315	−0.601574	−	0.798817i	$-0.705460\pi$
$661$	−30.9329	−1.20315	−0.601574	+	0.798817i	$0.705460\pi$
$662$	−3.60544	−0.140129
$663$	54.0595	2.09950
$664$	136.220	5.28636
$665$	−14.3946	−0.558199
$666$	−117.897	−4.56840
$667$	27.7879	1.07595
$668$	−106.452	−4.11877
$669$	11.2200	0.433791
$670$	−28.9721	−1.11929
$671$	−66.3445	−2.56120
$672$	213.740	8.24520
$673$	−6.14965	−0.237052	−0.118526	−	0.992951i	$-0.537817\pi$
$673$	−6.14965	−0.237052	−0.118526	+	0.992951i	$0.537817\pi$
$674$	−54.8493	−2.11272
$675$	−8.33812	−0.320934
$676$	142.875	5.49519
$677$	−1.25932	−0.0483996	−0.0241998	−	0.999707i	$-0.507704\pi$
$677$	−1.25932	−0.0483996	−0.0241998	+	0.999707i	$0.507704\pi$
$678$	−101.801	−3.90966
$679$	62.0012	2.37939
$680$	24.1870	0.927527
$681$	60.0869	2.30254
$682$	−119.213	−4.56489
$683$	32.1978	1.23202	0.616008	−	0.787740i	$-0.288749\pi$
$683$	32.1978	1.23202	0.616008	+	0.787740i	$0.288749\pi$
$684$	96.4673	3.68852
$685$	−1.80588	−0.0689990
$686$	−72.3400	−2.76195
$687$	−4.21096	−0.160658
$688$	33.6334	1.28226
$689$	8.23469	0.313717
$690$	47.6963	1.81577
$691$	21.1331	0.803940	0.401970	−	0.915653i	$-0.368326\pi$
$691$	21.1331	0.803940	0.401970	+	0.915653i	$0.368326\pi$
$692$	14.2511	0.541744
$693$	143.011	5.43254
$694$	31.7173	1.20397
$695$	12.1619	0.461325
$696$	−116.331	−4.40950
$697$	15.1781	0.574912
$698$	22.5215	0.852451
$699$	53.3287	2.01708
$700$	23.1157	0.873690
$701$	−34.5044	−1.30321	−0.651606	−	0.758558i	$-0.725904\pi$
$701$	−34.5044	−1.30321	−0.651606	+	0.758558i	$0.725904\pi$
$702$	−142.321	−5.37157
$703$	24.3824	0.919600
$704$	101.094	3.81011
$705$	21.4288	0.807056
$706$	33.0621	1.24431
$707$	−75.0827	−2.82378
$708$	136.352	5.12441
$709$	−2.68679	−0.100905	−0.0504523	−	0.998726i	$-0.516066\pi$
$709$	−2.68679	−0.100905	−0.0504523	+	0.998726i	$0.516066\pi$
$710$	−29.3353	−1.10093
$711$	−86.6503	−3.24964
$712$	−37.6021	−1.40920
$713$	−48.6253	−1.82103
$714$	101.566	3.80100
$715$	35.0709	1.31158
$716$	22.7880	0.851627
$717$	−44.5064	−1.66212
$718$	42.1027	1.57126
$719$	44.6614	1.66559	0.832795	−	0.553581i	$-0.186739\pi$
$719$	44.6614	1.66559	0.832795	+	0.553581i	$0.186739\pi$
$720$	−71.6777	−2.67127
$721$	23.5614	0.877474
$722$	23.1771	0.862563
$723$	27.1101	1.00823
$724$	16.6925	0.620372
$725$	−4.62827	−0.171890
$726$	152.879	5.67387
$727$	−5.39878	−0.200230	−0.100115	−	0.994976i	$-0.531921\pi$
$727$	−5.39878	−0.200230	−0.100115	+	0.994976i	$0.531921\pi$
$728$	241.744	8.95962
$729$	−31.7195	−1.17480
$730$	21.5068	0.796001
$731$	7.78551	0.287957
$732$	184.899	6.83408
$733$	−15.4808	−0.571798	−0.285899	−	0.958260i	$-0.592292\pi$
$733$	−15.4808	−0.571798	−0.285899	+	0.958260i	$0.592292\pi$
$734$	−24.0402	−0.887339
$735$	38.6967	1.42735
$736$	96.5891	3.56032
$737$	−59.5285	−2.19276
$738$	−82.6307	−3.04168
$739$	52.0455	1.91452	0.957262	−	0.289224i	$-0.0933971\pi$
$739$	52.0455	1.91452	0.957262	+	0.289224i	$0.0933971\pi$
$740$	−39.1547	−1.43935
$741$	60.8654	2.23595
$742$	15.4712	0.567964
$743$	−36.5685	−1.34157	−0.670784	−	0.741653i	$-0.734042\pi$
$743$	−36.5685	−1.34157	−0.670784	+	0.741653i	$0.734042\pi$
$744$	203.564	7.46301
$745$	11.0973	0.406574
$746$	−42.8558	−1.56906
$747$	−93.4457	−3.41900
$748$	81.1109	2.96571
$749$	26.4584	0.966770
$750$	−7.94414	−0.290079
$751$	−1.63402	−0.0596261	−0.0298131	−	0.999555i	$-0.509491\pi$
$751$	−1.63402	−0.0596261	−0.0298131	+	0.999555i	$0.509491\pi$
$752$	89.0817	3.24847
$753$	−52.6663	−1.91927
$754$	−78.9987	−2.87696
$755$	5.66452	0.206153
$756$	−192.741	−7.00993
$757$	22.1422	0.804771	0.402385	−	0.915470i	$-0.368181\pi$
$757$	22.1422	0.804771	0.402385	+	0.915470i	$0.368181\pi$
$758$	81.2567	2.95138
$759$	98.0008	3.55720
$760$	27.2320	0.987810
$761$	48.2448	1.74887	0.874436	−	0.485141i	$-0.161232\pi$
$761$	48.2448	1.74887	0.874436	+	0.485141i	$0.161232\pi$
$762$	−74.7852	−2.70918
$763$	−25.0093	−0.905398
$764$	−29.2935	−1.05980
$765$	−16.5920	−0.599886
$766$	9.15337	0.330725
$767$	56.7327	2.04850
$768$	−26.1399	−0.943242
$769$	−30.6543	−1.10542	−0.552710	−	0.833373i	$-0.686406\pi$
$769$	−30.6543	−1.10542	−0.552710	+	0.833373i	$0.686406\pi$
$770$	65.8904	2.37453
$771$	−11.8296	−0.426033
$772$	−121.702	−4.38014
$773$	17.1261	0.615982	0.307991	−	0.951389i	$-0.400343\pi$
$773$	17.1261	0.615982	0.307991	+	0.951389i	$0.400343\pi$
$774$	−42.3848	−1.52349
$775$	8.09887	0.290920
$776$	−117.295	−4.21065
$777$	−100.739	−3.61399
$778$	−80.6672	−2.89206
$779$	17.0890	0.612277
$780$	−97.7412	−3.49970
$781$	−60.2747	−2.15680
$782$	45.8976	1.64129
$783$	38.5911	1.37913
$784$	160.866	5.74521
$785$	12.4034	0.442698
$786$	−51.7457	−1.84571
$787$	28.0482	0.999812	0.499906	−	0.866080i	$-0.333368\pi$
$787$	28.0482	0.999812	0.499906	+	0.866080i	$0.333368\pi$
$788$	−37.9170	−1.35074
$789$	−12.3176	−0.438516
$790$	−39.9230	−1.42040
$791$	−57.3630	−2.03959
$792$	−270.552	−9.61363
$793$	76.9322	2.73194
$794$	−96.6903	−3.43141
$795$	−3.83259	−0.135928
$796$	−70.8543	−2.51136
$797$	7.12813	0.252491	0.126246	−	0.991999i	$-0.459707\pi$
$797$	7.12813	0.252491	0.126246	+	0.991999i	$0.459707\pi$
$798$	114.353	4.04804
$799$	20.6207	0.729509
$800$	−16.0876	−0.568782
$801$	25.7947	0.911411
$802$	62.0518	2.19113
$803$	44.1896	1.55942
$804$	165.904	5.85097
$805$	26.8759	0.947250
$806$	138.237	4.86921
$807$	44.7705	1.57600
$808$	142.043	4.99706
$809$	−42.0862	−1.47967	−0.739837	−	0.672787i	$-0.765097\pi$
$809$	−42.0862	−1.47967	−0.739837	+	0.672787i	$0.765097\pi$
$810$	19.5925	0.688409
$811$	13.9603	0.490211	0.245105	−	0.969496i	$-0.421177\pi$
$811$	13.9603	0.490211	0.245105	+	0.969496i	$0.421177\pi$
$812$	−106.986	−3.75446
$813$	40.1832	1.40929
$814$	−111.609	−3.91190
$815$	−7.07949	−0.247984
$816$	−104.594	−3.66152
$817$	8.76568	0.306672
$818$	−79.9254	−2.79453
$819$	−165.834	−5.79471
$820$	−27.4425	−0.958334
$821$	−15.0871	−0.526543	−0.263271	−	0.964722i	$-0.584801\pi$
$821$	−15.0871	−0.526543	−0.263271	+	0.964722i	$0.584801\pi$
$822$	14.3461	0.500379
$823$	39.2474	1.36808	0.684040	−	0.729444i	$-0.260221\pi$
$823$	39.2474	1.36808	0.684040	+	0.729444i	$0.260221\pi$
$824$	−44.5741	−1.55281
$825$	−16.3227	−0.568284
$826$	106.588	3.70868
$827$	−0.403438	−0.0140289	−0.00701445	−	0.999975i	$-0.502233\pi$
$827$	−0.403438	−0.0140289	−0.00701445	+	0.999975i	$0.502233\pi$
$828$	−180.112	−6.25933
$829$	16.3950	0.569420	0.284710	−	0.958614i	$-0.408103\pi$
$829$	16.3950	0.569420	0.284710	+	0.958614i	$0.408103\pi$
$830$	−43.0538	−1.49442
$831$	5.32917	0.184867
$832$	−117.227	−4.06411
$833$	37.2374	1.29020
$834$	−96.6154	−3.34552
$835$	20.6146	0.713396
$836$	91.3225	3.15846
$837$	−67.5294	−2.33416
$838$	−11.2897	−0.389996
$839$	−36.1940	−1.24956	−0.624778	−	0.780802i	$-0.714811\pi$
$839$	−36.1940	−1.24956	−0.624778	+	0.780802i	$0.714811\pi$
$840$	−112.512	−3.88205
$841$	−7.57913	−0.261349
$842$	−39.7801	−1.37091
$843$	0.999067	0.0344097
$844$	40.1651	1.38254
$845$	−27.6678	−0.951800
$846$	−112.261	−3.85960
$847$	86.1442	2.95995
$848$	−15.9324	−0.547123
$849$	12.5817	0.431802
$850$	−7.64455	−0.262206
$851$	−45.5239	−1.56054
$852$	167.983	5.75501
$853$	7.64068	0.261612	0.130806	−	0.991408i	$-0.458244\pi$
$853$	7.64068	0.261612	0.130806	+	0.991408i	$0.458244\pi$
$854$	144.539	4.94601
$855$	−18.6809	−0.638874
$856$	−50.0547	−1.71083
$857$	−7.12085	−0.243243	−0.121622	−	0.992577i	$-0.538809\pi$
$857$	−7.12085	−0.243243	−0.121622	+	0.992577i	$0.538809\pi$
$858$	−278.608	−9.51152
$859$	−27.1381	−0.925938	−0.462969	−	0.886374i	$-0.653216\pi$
$859$	−27.1381	−0.925938	−0.462969	+	0.886374i	$0.653216\pi$
$860$	−14.0764	−0.480002
$861$	−70.6053	−2.40622
$862$	2.28001	0.0776576
$863$	−6.01726	−0.204830	−0.102415	−	0.994742i	$-0.532657\pi$
$863$	−6.01726	−0.204830	−0.102415	+	0.994742i	$0.532657\pi$
$864$	134.140	4.56354
$865$	−2.75972	−0.0938334
$866$	−16.1837	−0.549944
$867$	26.2452	0.891335
$868$	187.211	6.35435
$869$	−82.0292	−2.78265
$870$	36.7676	1.24654
$871$	69.0286	2.33894
$872$	47.3132	1.60223
$873$	80.4634	2.72327
$874$	51.6760	1.74797
$875$	−4.47636	−0.151329
$876$	−123.155	−4.16101
$877$	−49.8434	−1.68309	−0.841547	−	0.540184i	$-0.818355\pi$
$877$	−49.8434	−1.68309	−0.841547	+	0.540184i	$0.818355\pi$
$878$	−55.9759	−1.88910
$879$	92.9445	3.13494
$880$	−67.8550	−2.28739
$881$	53.7086	1.80949	0.904744	−	0.425955i	$-0.140062\pi$
$881$	53.7086	1.80949	0.904744	+	0.425955i	$0.140062\pi$
$882$	−202.723	−6.82604
$883$	25.5827	0.860927	0.430464	−	0.902608i	$-0.358350\pi$
$883$	25.5827	0.860927	0.430464	+	0.902608i	$0.358350\pi$
$884$	−94.0552	−3.16342
$885$	−26.4045	−0.887579
$886$	52.7623	1.77258
$887$	−9.53561	−0.320175	−0.160087	−	0.987103i	$-0.551178\pi$
$887$	−9.53561	−0.320175	−0.160087	+	0.987103i	$0.551178\pi$
$888$	190.580	6.39545
$889$	−42.1399	−1.41333
$890$	11.8846	0.398371
$891$	40.2564	1.34864
$892$	−19.5211	−0.653615
$893$	23.2168	0.776921
$894$	−88.1585	−2.94846
$895$	−4.41290	−0.147507
$896$	−76.2159	−2.54619
$897$	−113.641	−3.79435
$898$	82.1375	2.74096
$899$	−37.4837	−1.25015
$900$	29.9989	0.999963
$901$	−3.68806	−0.122867
$902$	−78.2239	−2.60457
$903$	−36.2165	−1.20521
$904$	108.521	3.60934
$905$	−3.23251	−0.107452
$906$	−44.9997	−1.49502
$907$	46.1554	1.53256	0.766282	−	0.642505i	$-0.222105\pi$
$907$	46.1554	1.53256	0.766282	+	0.642505i	$0.222105\pi$
$908$	−104.542	−3.46935
$909$	−97.4403	−3.23189
$910$	−76.4058	−2.53283
$911$	15.5522	0.515268	0.257634	−	0.966243i	$-0.417057\pi$
$911$	15.5522	0.515268	0.257634	+	0.966243i	$0.417057\pi$
$912$	−117.762	−3.89950
$913$	−88.4621	−2.92767
$914$	64.0566	2.11880
$915$	−35.8058	−1.18370
$916$	7.32643	0.242072
$917$	−29.1576	−0.962869
$918$	63.7412	2.10377
$919$	38.0019	1.25357	0.626784	−	0.779193i	$-0.284371\pi$
$919$	38.0019	1.25357	0.626784	+	0.779193i	$0.284371\pi$
$920$	−50.8444	−1.67629
$921$	−53.4031	−1.75969
$922$	−26.4201	−0.870101
$923$	69.8939	2.30058
$924$	−377.310	−12.4126
$925$	7.58232	0.249305
$926$	52.9581	1.74031
$927$	30.5774	1.00429
$928$	74.4576	2.44419
$929$	−20.9701	−0.688008	−0.344004	−	0.938968i	$-0.611783\pi$
$929$	−20.9701	−0.688008	−0.344004	+	0.938968i	$0.611783\pi$
$930$	−64.3385	−2.10974
$931$	41.9255	1.37405
$932$	−92.7839	−3.03924
$933$	−57.6986	−1.88897
$934$	−48.8770	−1.59931
$935$	−15.7072	−0.513679
$936$	313.728	10.2545
$937$	4.11386	0.134394	0.0671970	−	0.997740i	$-0.478594\pi$
$937$	4.11386	0.134394	0.0671970	+	0.997740i	$0.478594\pi$
$938$	129.689	4.23451
$939$	−7.76428	−0.253378
$940$	−37.2829	−1.21603
$941$	2.11974	0.0691015	0.0345507	−	0.999403i	$-0.489000\pi$
$941$	2.11974	0.0691015	0.0345507	+	0.999403i	$0.489000\pi$
$942$	−98.5347	−3.21043
$943$	−31.9065	−1.03902
$944$	−109.766	−3.57258
$945$	37.3244	1.21416
$946$	−40.1244	−1.30456
$947$	11.3730	0.369573	0.184786	−	0.982779i	$-0.440841\pi$
$947$	11.3730	0.369573	0.184786	+	0.982779i	$0.440841\pi$
$948$	228.612	7.42497
$949$	−51.2418	−1.66338
$950$	−8.60698	−0.279247
$951$	−82.6284	−2.67941
$952$	−108.269	−3.50903
$953$	1.18075	0.0382481	0.0191241	−	0.999817i	$-0.493912\pi$
$953$	1.18075	0.0382481	0.0191241	+	0.999817i	$0.493912\pi$
$954$	20.0781	0.650051
$955$	5.67269	0.183564
$956$	77.4343	2.50440
$957$	75.5458	2.44205
$958$	91.2626	2.94856
$959$	8.08375	0.261038
$960$	54.5598	1.76091
$961$	34.5917	1.11586
$962$	129.421	4.17269
$963$	34.3370	1.10650
$964$	−47.1674	−1.51916
$965$	23.5676	0.758668
$966$	−213.506	−6.86943
$967$	−25.0780	−0.806453	−0.403226	−	0.915100i	$-0.632111\pi$
$967$	−25.0780	−0.806453	−0.403226	+	0.915100i	$0.632111\pi$
$968$	−162.970	−5.23804
$969$	−27.2597	−0.875708
$970$	37.0724	1.19032
$971$	−10.0535	−0.322631	−0.161315	−	0.986903i	$-0.551574\pi$
$971$	−10.0535	−0.322631	−0.161315	+	0.986903i	$0.551574\pi$
$972$	16.9799	0.544630
$973$	−54.4408	−1.74529
$974$	−36.3888	−1.16597
$975$	18.9276	0.606169
$976$	−148.848	−4.76451
$977$	20.5294	0.656793	0.328396	−	0.944540i	$-0.393492\pi$
$977$	20.5294	0.656793	0.328396	+	0.944540i	$0.393492\pi$
$978$	56.2405	1.79837
$979$	24.4190	0.780436
$980$	−67.3264	−2.15066
$981$	−32.4564	−1.03625
$982$	17.3540	0.553790
$983$	41.8763	1.33565	0.667824	−	0.744319i	$-0.267226\pi$
$983$	41.8763	1.33565	0.667824	+	0.744319i	$0.267226\pi$
$984$	133.573	4.25814
$985$	7.34264	0.233956
$986$	35.3810	1.12676
$987$	−95.9231	−3.05327
$988$	−105.897	−3.36902
$989$	−16.3662	−0.520416
$990$	85.5108	2.71771
$991$	−13.2331	−0.420363	−0.210182	−	0.977662i	$-0.567406\pi$
$991$	−13.2331	−0.420363	−0.210182	+	0.977662i	$0.567406\pi$
$992$	−130.291	−4.13675
$993$	−3.99809	−0.126876
$994$	131.315	4.16506
$995$	13.7210	0.434984
$996$	246.540	7.81193
$997$	−23.2142	−0.735200	−0.367600	−	0.929984i	$-0.619820\pi$
$997$	−23.2142	−0.735200	−0.367600	+	0.929984i	$0.619820\pi$
$998$	57.1755	1.80986
$999$	−63.2223	−2.00026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.9	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.9	✓	140	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.67655 q^{2} -2.96805 q^{3} +5.16395 q^{4} -1.00000 q^{5} +7.94414 q^{6} +4.47636 q^{7} -8.46847 q^{8} +5.80930 q^{9} +O(q^{10})\)	\(q-2.67655 q^{2} -2.96805 q^{3} +5.16395 q^{4} -1.00000 q^{5} +7.94414 q^{6} +4.47636 q^{7} -8.46847 q^{8} +5.80930 q^{9} +2.67655 q^{10} +5.49948 q^{11} -15.3268 q^{12} -6.37713 q^{13} -11.9812 q^{14} +2.96805 q^{15} +12.3384 q^{16} +2.85612 q^{17} -15.5489 q^{18} +3.21569 q^{19} -5.16395 q^{20} -13.2860 q^{21} -14.7197 q^{22} -6.00396 q^{23} +25.1348 q^{24} +1.00000 q^{25} +17.0687 q^{26} -8.33812 q^{27} +23.1157 q^{28} -4.62827 q^{29} -7.94414 q^{30} +8.09887 q^{31} -16.0876 q^{32} -16.3227 q^{33} -7.64455 q^{34} -4.47636 q^{35} +29.9989 q^{36} +7.58232 q^{37} -8.60698 q^{38} +18.9276 q^{39} +8.46847 q^{40} +5.31425 q^{41} +35.5608 q^{42} +2.72591 q^{43} +28.3990 q^{44} -5.80930 q^{45} +16.0699 q^{46} +7.21985 q^{47} -36.6211 q^{48} +13.0378 q^{49} -2.67655 q^{50} -8.47709 q^{51} -32.9311 q^{52} -1.29128 q^{53} +22.3174 q^{54} -5.49948 q^{55} -37.9079 q^{56} -9.54433 q^{57} +12.3878 q^{58} -8.89627 q^{59} +15.3268 q^{60} -12.0638 q^{61} -21.6771 q^{62} +26.0045 q^{63} +18.3824 q^{64} +6.37713 q^{65} +43.6886 q^{66} -10.8244 q^{67} +14.7488 q^{68} +17.8200 q^{69} +11.9812 q^{70} -10.9601 q^{71} -49.1959 q^{72} +8.03524 q^{73} -20.2945 q^{74} -2.96805 q^{75} +16.6057 q^{76} +24.6176 q^{77} -50.6608 q^{78} -14.9158 q^{79} -12.3384 q^{80} +7.32004 q^{81} -14.2239 q^{82} -16.0855 q^{83} -68.6084 q^{84} -2.85612 q^{85} -7.29604 q^{86} +13.7369 q^{87} -46.5722 q^{88} +4.44024 q^{89} +15.5489 q^{90} -28.5463 q^{91} -31.0041 q^{92} -24.0378 q^{93} -19.3243 q^{94} -3.21569 q^{95} +47.7487 q^{96} +13.8508 q^{97} -34.8963 q^{98} +31.9481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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