LMFDB - Embedded newform 8033.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, 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("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.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:	$64.1438279437$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52594 q^{2} -2.31351 q^{3} +4.38038 q^{4} +1.97796 q^{5} +5.84380 q^{6} -1.35042 q^{7} -6.01269 q^{8} +2.35235 q^{9} +O(q^{10})$	\(q-2.52594 q^{2} -2.31351 q^{3} +4.38038 q^{4} +1.97796 q^{5} +5.84380 q^{6} -1.35042 q^{7} -6.01269 q^{8} +2.35235 q^{9} -4.99621 q^{10} +4.37458 q^{11} -10.1341 q^{12} -2.14019 q^{13} +3.41108 q^{14} -4.57604 q^{15} +6.42695 q^{16} +4.82219 q^{17} -5.94189 q^{18} -7.69516 q^{19} +8.66421 q^{20} +3.12422 q^{21} -11.0499 q^{22} -1.66907 q^{23} +13.9104 q^{24} -1.08767 q^{25} +5.40600 q^{26} +1.49836 q^{27} -5.91536 q^{28} -1.00000 q^{29} +11.5588 q^{30} -4.68291 q^{31} -4.20871 q^{32} -10.1206 q^{33} -12.1806 q^{34} -2.67108 q^{35} +10.3042 q^{36} -4.26938 q^{37} +19.4375 q^{38} +4.95137 q^{39} -11.8929 q^{40} -11.8213 q^{41} -7.89159 q^{42} +1.74065 q^{43} +19.1623 q^{44} +4.65285 q^{45} +4.21596 q^{46} +3.93132 q^{47} -14.8688 q^{48} -5.17636 q^{49} +2.74740 q^{50} -11.1562 q^{51} -9.37485 q^{52} +8.44876 q^{53} -3.78476 q^{54} +8.65274 q^{55} +8.11967 q^{56} +17.8029 q^{57} +2.52594 q^{58} -0.646581 q^{59} -20.0448 q^{60} -3.17744 q^{61} +11.8288 q^{62} -3.17666 q^{63} -2.22294 q^{64} -4.23321 q^{65} +25.5642 q^{66} -3.88783 q^{67} +21.1230 q^{68} +3.86141 q^{69} +6.74699 q^{70} -12.6910 q^{71} -14.1439 q^{72} -7.46441 q^{73} +10.7842 q^{74} +2.51635 q^{75} -33.7077 q^{76} -5.90752 q^{77} -12.5069 q^{78} -6.04746 q^{79} +12.7123 q^{80} -10.5235 q^{81} +29.8599 q^{82} +16.2995 q^{83} +13.6853 q^{84} +9.53810 q^{85} -4.39678 q^{86} +2.31351 q^{87} -26.3030 q^{88} -3.13821 q^{89} -11.7528 q^{90} +2.89016 q^{91} -7.31114 q^{92} +10.8340 q^{93} -9.93027 q^{94} -15.2207 q^{95} +9.73692 q^{96} -0.778266 q^{97} +13.0752 q^{98} +10.2905 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) $ 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * 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 $

$2$	−2.52594	−1.78611	−0.893055	−	0.449948i	$-0.851443\pi$
$2$	−2.52594	−1.78611	−0.893055	+	0.449948i	$0.851443\pi$
$3$	−2.31351	−1.33571	−0.667854	−	0.744292i	$-0.732787\pi$
$3$	−2.31351	−1.33571	−0.667854	+	0.744292i	$0.732787\pi$
$4$	4.38038	2.19019
$5$	1.97796	0.884571	0.442285	−	0.896874i	$-0.354168\pi$
$5$	1.97796	0.884571	0.442285	+	0.896874i	$0.354168\pi$
$6$	5.84380	2.38572
$7$	−1.35042	−0.510411	−0.255206	−	0.966887i	$-0.582143\pi$
$7$	−1.35042	−0.510411	−0.255206	+	0.966887i	$0.582143\pi$
$8$	−6.01269	−2.12581
$9$	2.35235	0.784115
$10$	−4.99621	−1.57994
$11$	4.37458	1.31898	0.659492	−	0.751711i	$-0.270771\pi$
$11$	4.37458	1.31898	0.659492	+	0.751711i	$0.270771\pi$
$12$	−10.1341	−2.92545
$13$	−2.14019	−0.593583	−0.296791	−	0.954942i	$-0.595917\pi$
$13$	−2.14019	−0.593583	−0.296791	+	0.954942i	$0.595917\pi$
$14$	3.41108	0.911651
$15$	−4.57604	−1.18153
$16$	6.42695	1.60674
$17$	4.82219	1.16955	0.584777	−	0.811194i	$-0.301182\pi$
$17$	4.82219	1.16955	0.584777	+	0.811194i	$0.301182\pi$
$18$	−5.94189	−1.40052
$19$	−7.69516	−1.76539	−0.882695	−	0.469945i	$-0.844274\pi$
$19$	−7.69516	−1.76539	−0.882695	+	0.469945i	$0.844274\pi$
$20$	8.66421	1.93738
$21$	3.12422	0.681760
$22$	−11.0499	−2.35585
$23$	−1.66907	−0.348024	−0.174012	−	0.984744i	$-0.555673\pi$
$23$	−1.66907	−0.348024	−0.174012	+	0.984744i	$0.555673\pi$
$24$	13.9104	2.83946
$25$	−1.08767	−0.217535
$26$	5.40600	1.06020
$27$	1.49836	0.288359
$28$	−5.91536	−1.11790
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	11.5588	2.11034
$31$	−4.68291	−0.841076	−0.420538	−	0.907275i	$-0.638159\pi$
$31$	−4.68291	−0.841076	−0.420538	+	0.907275i	$0.638159\pi$
$32$	−4.20871	−0.744002
$33$	−10.1206	−1.76178
$34$	−12.1806	−2.08895
$35$	−2.67108	−0.451495
$36$	10.3042	1.71736
$37$	−4.26938	−0.701882	−0.350941	−	0.936398i	$-0.614138\pi$
$37$	−4.26938	−0.701882	−0.350941	+	0.936398i	$0.614138\pi$
$38$	19.4375	3.15318
$39$	4.95137	0.792853
$40$	−11.8929	−1.88043
$41$	−11.8213	−1.84617	−0.923087	−	0.384592i	$-0.874342\pi$
$41$	−11.8213	−1.84617	−0.923087	+	0.384592i	$0.874342\pi$
$42$	−7.89159	−1.21770
$43$	1.74065	0.265447	0.132723	−	0.991153i	$-0.457628\pi$
$43$	1.74065	0.265447	0.132723	+	0.991153i	$0.457628\pi$
$44$	19.1623	2.88883
$45$	4.65285	0.693605
$46$	4.21596	0.621610
$47$	3.93132	0.573441	0.286721	−	0.958014i	$-0.407435\pi$
$47$	3.93132	0.573441	0.286721	+	0.958014i	$0.407435\pi$
$48$	−14.8688	−2.14613
$49$	−5.17636	−0.739480
$50$	2.74740	0.388541
$51$	−11.1562	−1.56218
$52$	−9.37485	−1.30006
$53$	8.44876	1.16053	0.580263	−	0.814429i	$-0.302950\pi$
$53$	8.44876	1.16053	0.580263	+	0.814429i	$0.302950\pi$
$54$	−3.78476	−0.515040
$55$	8.65274	1.16674
$56$	8.11967	1.08504
$57$	17.8029	2.35805
$58$	2.52594	0.331672
$59$	−0.646581	−0.0841777	−0.0420889	−	0.999114i	$-0.513401\pi$
$59$	−0.646581	−0.0841777	−0.0420889	+	0.999114i	$0.513401\pi$
$60$	−20.0448	−2.58777
$61$	−3.17744	−0.406829	−0.203415	−	0.979093i	$-0.565204\pi$
$61$	−3.17744	−0.406829	−0.203415	+	0.979093i	$0.565204\pi$
$62$	11.8288	1.50225
$63$	−3.17666	−0.400221
$64$	−2.22294	−0.277868
$65$	−4.23321	−0.525066
$66$	25.5642	3.14673
$67$	−3.88783	−0.474974	−0.237487	−	0.971391i	$-0.576324\pi$
$67$	−3.88783	−0.474974	−0.237487	+	0.971391i	$0.576324\pi$
$68$	21.1230	2.56154
$69$	3.86141	0.464859
$70$	6.74699	0.806419
$71$	−12.6910	−1.50614	−0.753071	−	0.657939i	$-0.771429\pi$
$71$	−12.6910	−1.50614	−0.753071	+	0.657939i	$0.771429\pi$
$72$	−14.1439	−1.66688
$73$	−7.46441	−0.873643	−0.436822	−	0.899548i	$-0.643896\pi$
$73$	−7.46441	−0.873643	−0.436822	+	0.899548i	$0.643896\pi$
$74$	10.7842	1.25364
$75$	2.51635	0.290563
$76$	−33.7077	−3.86654
$77$	−5.90752	−0.673225
$78$	−12.5069	−1.41612
$79$	−6.04746	−0.680393	−0.340196	−	0.940354i	$-0.610494\pi$
$79$	−6.04746	−0.680393	−0.340196	+	0.940354i	$0.610494\pi$
$80$	12.7123	1.42127
$81$	−10.5235	−1.16928
$82$	29.8599	3.29747
$83$	16.2995	1.78910	0.894552	−	0.446965i	$-0.147495\pi$
$83$	16.2995	1.78910	0.894552	+	0.446965i	$0.147495\pi$
$84$	13.6853	1.49318
$85$	9.53810	1.03455
$86$	−4.39678	−0.474117
$87$	2.31351	0.248035
$88$	−26.3030	−2.80391
$89$	−3.13821	−0.332649	−0.166325	−	0.986071i	$-0.553190\pi$
$89$	−3.13821	−0.332649	−0.166325	+	0.986071i	$0.553190\pi$
$90$	−11.7528	−1.23886
$91$	2.89016	0.302971
$92$	−7.31114	−0.762239
$93$	10.8340	1.12343
$94$	−9.93027	−1.02423
$95$	−15.2207	−1.56161
$96$	9.73692	0.993770
$97$	−0.778266	−0.0790209	−0.0395105	−	0.999219i	$-0.512580\pi$
$97$	−0.778266	−0.0790209	−0.0395105	+	0.999219i	$0.512580\pi$
$98$	13.0752	1.32079
$99$	10.2905	1.03424
$100$	−4.76443	−0.476443
$101$	9.64904	0.960116	0.480058	−	0.877237i	$-0.340616\pi$
$101$	9.64904	0.960116	0.480058	+	0.877237i	$0.340616\pi$
$102$	28.1799	2.79023
$103$	18.9024	1.86251	0.931254	−	0.364370i	$-0.118716\pi$
$103$	18.9024	1.86251	0.931254	+	0.364370i	$0.118716\pi$
$104$	12.8683	1.26184
$105$	6.17958	0.603065
$106$	−21.3411	−2.07283
$107$	0.686385	0.0663554	0.0331777	−	0.999449i	$-0.489437\pi$
$107$	0.686385	0.0663554	0.0331777	+	0.999449i	$0.489437\pi$
$108$	6.56336	0.631560
$109$	0.358126	0.0343023	0.0171511	−	0.999853i	$-0.494540\pi$
$109$	0.358126	0.0343023	0.0171511	+	0.999853i	$0.494540\pi$
$110$	−21.8563	−2.08392
$111$	9.87727	0.937509
$112$	−8.67909	−0.820097
$113$	−2.54295	−0.239221	−0.119610	−	0.992821i	$-0.538165\pi$
$113$	−2.54295	−0.239221	−0.119610	+	0.992821i	$0.538165\pi$
$114$	−44.9690	−4.21173
$115$	−3.30134	−0.307852
$116$	−4.38038	−0.406708
$117$	−5.03447	−0.465437
$118$	1.63323	0.150351
$119$	−6.51199	−0.596953
$120$	27.5143	2.51170
$121$	8.13693	0.739721
$122$	8.02602	0.726642
$123$	27.3487	2.46595
$124$	−20.5129	−1.84212
$125$	−12.0412	−1.07700
$126$	8.02405	0.714839
$127$	−3.64859	−0.323760	−0.161880	−	0.986810i	$-0.551756\pi$
$127$	−3.64859	−0.323760	−0.161880	+	0.986810i	$0.551756\pi$
$128$	14.0324	1.24030
$129$	−4.02702	−0.354559
$130$	10.6929	0.937825
$131$	10.3115	0.900918	0.450459	−	0.892797i	$-0.351260\pi$
$131$	10.3115	0.900918	0.450459	+	0.892797i	$0.351260\pi$
$132$	−44.3323	−3.85863
$133$	10.3917	0.901075
$134$	9.82043	0.848356
$135$	2.96369	0.255074
$136$	−28.9944	−2.48625
$137$	−18.5751	−1.58698	−0.793490	−	0.608583i	$-0.791738\pi$
$137$	−18.5751	−1.58698	−0.793490	+	0.608583i	$0.791738\pi$
$138$	−9.75368	−0.830289
$139$	11.6668	0.989562	0.494781	−	0.869018i	$-0.335248\pi$
$139$	11.6668	0.989562	0.494781	+	0.869018i	$0.335248\pi$
$140$	−11.7003	−0.988859
$141$	−9.09516	−0.765950
$142$	32.0567	2.69014
$143$	−9.36244	−0.782927
$144$	15.1184	1.25987
$145$	−1.97796	−0.164261
$146$	18.8547	1.56042
$147$	11.9756	0.987730
$148$	−18.7015	−1.53725
$149$	9.82734	0.805087	0.402544	−	0.915401i	$-0.368126\pi$
$149$	9.82734	0.805087	0.402544	+	0.915401i	$0.368126\pi$
$150$	−6.35615	−0.518978
$151$	3.66245	0.298046	0.149023	−	0.988834i	$-0.452387\pi$
$151$	3.66245	0.298046	0.149023	+	0.988834i	$0.452387\pi$
$152$	46.2686	3.75288
$153$	11.3435	0.917065
$154$	14.9221	1.20245
$155$	−9.26262	−0.743991
$156$	21.6888	1.73650
$157$	9.83106	0.784604	0.392302	−	0.919837i	$-0.371679\pi$
$157$	9.83106	0.784604	0.392302	+	0.919837i	$0.371679\pi$
$158$	15.2755	1.21526
$159$	−19.5463	−1.55012
$160$	−8.32467	−0.658123
$161$	2.25394	0.177635
$162$	26.5818	2.08846
$163$	23.0249	1.80345	0.901723	−	0.432315i	$-0.142303\pi$
$163$	23.0249	1.80345	0.901723	+	0.432315i	$0.142303\pi$
$164$	−51.7817	−4.04347
$165$	−20.0182	−1.55842
$166$	−41.1716	−3.19553
$167$	9.30128	0.719755	0.359878	−	0.933000i	$-0.382818\pi$
$167$	9.30128	0.719755	0.359878	+	0.933000i	$0.382818\pi$
$168$	−18.7850	−1.44929
$169$	−8.41958	−0.647660
$170$	−24.0927	−1.84782
$171$	−18.1017	−1.38427
$172$	7.62471	0.581378
$173$	2.63209	0.200114	0.100057	−	0.994982i	$-0.468098\pi$
$173$	2.63209	0.200114	0.100057	+	0.994982i	$0.468098\pi$
$174$	−5.84380	−0.443017
$175$	1.46882	0.111032
$176$	28.1152	2.11926
$177$	1.49587	0.112437
$178$	7.92693	0.594148
$179$	22.7208	1.69823	0.849116	−	0.528206i	$-0.177135\pi$
$179$	22.7208	1.69823	0.849116	+	0.528206i	$0.177135\pi$
$180$	20.3812	1.51913
$181$	20.8265	1.54802	0.774009	−	0.633174i	$-0.218248\pi$
$181$	20.8265	1.54802	0.774009	+	0.633174i	$0.218248\pi$
$182$	−7.30038	−0.541140
$183$	7.35105	0.543405
$184$	10.0356	0.739833
$185$	−8.44466	−0.620864
$186$	−27.3660	−2.00657
$187$	21.0951	1.54262
$188$	17.2207	1.25595
$189$	−2.02341	−0.147182
$190$	38.4466	2.78921
$191$	14.3629	1.03926	0.519631	−	0.854391i	$-0.326069\pi$
$191$	14.3629	1.03926	0.519631	+	0.854391i	$0.326069\pi$
$192$	5.14280	0.371150
$193$	−20.1891	−1.45324	−0.726622	−	0.687037i	$-0.758911\pi$
$193$	−20.1891	−1.45324	−0.726622	+	0.687037i	$0.758911\pi$
$194$	1.96585	0.141140
$195$	9.79360	0.701334
$196$	−22.6744	−1.61960
$197$	12.0051	0.855331	0.427666	−	0.903937i	$-0.359336\pi$
$197$	12.0051	0.855331	0.427666	+	0.903937i	$0.359336\pi$
$198$	−25.9933	−1.84726
$199$	7.67976	0.544403	0.272202	−	0.962240i	$-0.412248\pi$
$199$	7.67976	0.544403	0.272202	+	0.962240i	$0.412248\pi$
$200$	6.53986	0.462438
$201$	8.99455	0.634426
$202$	−24.3729	−1.71487
$203$	1.35042	0.0947810
$204$	−48.8684	−3.42147
$205$	−23.3820	−1.63307
$206$	−47.7463	−3.32664
$207$	−3.92622	−0.272891
$208$	−13.7549	−0.953732
$209$	−33.6631	−2.32852
$210$	−15.6092	−1.07714
$211$	3.47868	0.239482	0.119741	−	0.992805i	$-0.461794\pi$
$211$	3.47868	0.239482	0.119741	+	0.992805i	$0.461794\pi$
$212$	37.0088	2.54177
$213$	29.3608	2.01177
$214$	−1.73377	−0.118518
$215$	3.44294	0.234806
$216$	−9.00915	−0.612995
$217$	6.32391	0.429295
$218$	−0.904606	−0.0612676
$219$	17.2690	1.16693
$220$	37.9023	2.55537
$221$	−10.3204	−0.694227
$222$	−24.9494	−1.67449
$223$	2.67647	0.179229	0.0896147	−	0.995977i	$-0.471436\pi$
$223$	2.67647	0.179229	0.0896147	+	0.995977i	$0.471436\pi$
$224$	5.68354	0.379747
$225$	−2.55859	−0.170573
$226$	6.42335	0.427275
$227$	−27.7955	−1.84485	−0.922426	−	0.386174i	$-0.873796\pi$
$227$	−27.7955	−1.84485	−0.922426	+	0.386174i	$0.873796\pi$
$228$	77.9832	5.16457
$229$	−23.7298	−1.56811	−0.784056	−	0.620690i	$-0.786852\pi$
$229$	−23.7298	−1.56811	−0.784056	+	0.620690i	$0.786852\pi$
$230$	8.33900	0.549857
$231$	13.6671	0.899232
$232$	6.01269	0.394753
$233$	25.4553	1.66763	0.833815	−	0.552044i	$-0.186152\pi$
$233$	25.4553	1.66763	0.833815	+	0.552044i	$0.186152\pi$
$234$	12.7168	0.831322
$235$	7.77599	0.507249
$236$	−2.83227	−0.184365
$237$	13.9909	0.908806
$238$	16.4489	1.06622
$239$	17.0968	1.10590	0.552950	−	0.833215i	$-0.313502\pi$
$239$	17.0968	1.10590	0.552950	+	0.833215i	$0.313502\pi$
$240$	−29.4100	−1.89841
$241$	9.02746	0.581510	0.290755	−	0.956798i	$-0.406094\pi$
$241$	9.02746	0.581510	0.290755	+	0.956798i	$0.406094\pi$
$242$	−20.5534	−1.32122
$243$	19.8512	1.27346
$244$	−13.9184	−0.891033
$245$	−10.2386	−0.654122
$246$	−69.0812	−4.40446
$247$	16.4691	1.04791
$248$	28.1569	1.78797
$249$	−37.7091	−2.38972
$250$	30.4153	1.92363
$251$	4.60472	0.290647	0.145324	−	0.989384i	$-0.453578\pi$
$251$	4.60472	0.290647	0.145324	+	0.989384i	$0.453578\pi$
$252$	−13.9150	−0.876560
$253$	−7.30146	−0.459039
$254$	9.21611	0.578270
$255$	−22.0665	−1.38186
$256$	−30.9992	−1.93745
$257$	9.42990	0.588221	0.294110	−	0.955771i	$-0.404977\pi$
$257$	9.42990	0.588221	0.294110	+	0.955771i	$0.404977\pi$
$258$	10.1720	0.633282
$259$	5.76546	0.358248
$260$	−18.5431	−1.14999
$261$	−2.35235	−0.145607
$262$	−26.0462	−1.60914
$263$	−19.2845	−1.18913	−0.594566	−	0.804047i	$-0.702676\pi$
$263$	−19.2845	−1.18913	−0.594566	+	0.804047i	$0.702676\pi$
$264$	60.8523	3.74520
$265$	16.7113	1.02657
$266$	−26.2488	−1.60942
$267$	7.26029	0.444322
$268$	−17.0302	−1.04028
$269$	−28.8974	−1.76191	−0.880953	−	0.473203i	$-0.843098\pi$
$269$	−28.8974	−1.76191	−0.880953	+	0.473203i	$0.843098\pi$
$270$	−7.48610	−0.455590
$271$	−16.7333	−1.01647	−0.508237	−	0.861217i	$-0.669703\pi$
$271$	−16.7333	−1.01647	−0.508237	+	0.861217i	$0.669703\pi$
$272$	30.9920	1.87917
$273$	−6.68643	−0.404681
$274$	46.9197	2.83452
$275$	−4.75812	−0.286925
$276$	16.9144	1.01813
$277$	1.00000	0.0600842
$277$	1.00000	0.0600842
$278$	−29.4696	−1.76747
$279$	−11.0158	−0.659501
$280$	16.0604	0.959791
$281$	−17.9454	−1.07053	−0.535266	−	0.844684i	$-0.679789\pi$
$281$	−17.9454	−1.07053	−0.535266	+	0.844684i	$0.679789\pi$
$282$	22.9738	1.36807
$283$	−26.1553	−1.55477	−0.777386	−	0.629024i	$-0.783455\pi$
$283$	−26.1553	−1.55477	−0.777386	+	0.629024i	$0.783455\pi$
$284$	−55.5913	−3.29874
$285$	35.2133	2.08586
$286$	23.6490	1.39839
$287$	15.9637	0.942308
$288$	−9.90035	−0.583384
$289$	6.25354	0.367855
$290$	4.99621	0.293388
$291$	1.80053	0.105549
$292$	−32.6969	−1.91344
$293$	3.40873	0.199140	0.0995700	−	0.995031i	$-0.468253\pi$
$293$	3.40873	0.199140	0.0995700	+	0.995031i	$0.468253\pi$
$294$	−30.2496	−1.76419
$295$	−1.27891	−0.0744611
$296$	25.6705	1.49207
$297$	6.55468	0.380341
$298$	−24.8233	−1.43797
$299$	3.57212	0.206581
$300$	11.0226	0.636388
$301$	−2.35061	−0.135487
$302$	−9.25112	−0.532342
$303$	−22.3232	−1.28243
$304$	−49.4564	−2.83652
$305$	−6.28485	−0.359869
$306$	−28.6529	−1.63798
$307$	−10.6145	−0.605803	−0.302901	−	0.953022i	$-0.597955\pi$
$307$	−10.6145	−0.605803	−0.302901	+	0.953022i	$0.597955\pi$
$308$	−25.8772	−1.47449
$309$	−43.7310	−2.48777
$310$	23.3968	1.32885
$311$	−27.0651	−1.53472	−0.767359	−	0.641217i	$-0.778430\pi$
$311$	−27.0651	−1.53472	−0.767359	+	0.641217i	$0.778430\pi$
$312$	−29.7710	−1.68545
$313$	−6.06107	−0.342592	−0.171296	−	0.985220i	$-0.554795\pi$
$313$	−6.06107	−0.342592	−0.171296	+	0.985220i	$0.554795\pi$
$314$	−24.8327	−1.40139
$315$	−6.28330	−0.354024
$316$	−26.4902	−1.49019
$317$	−2.81388	−0.158043	−0.0790215	−	0.996873i	$-0.525180\pi$
$317$	−2.81388	−0.158043	−0.0790215	+	0.996873i	$0.525180\pi$
$318$	49.3729	2.76869
$319$	−4.37458	−0.244929
$320$	−4.39689	−0.245793
$321$	−1.58796	−0.0886314
$322$	−5.69332	−0.317277
$323$	−37.1075	−2.06472
$324$	−46.0969	−2.56094
$325$	2.32783	0.129125
$326$	−58.1594	−3.22115
$327$	−0.828530	−0.0458178
$328$	71.0777	3.92461
$329$	−5.30893	−0.292691
$330$	50.5649	2.78350
$331$	−8.54085	−0.469448	−0.234724	−	0.972062i	$-0.575419\pi$
$331$	−8.54085	−0.469448	−0.234724	+	0.972062i	$0.575419\pi$
$332$	71.3980	3.91847
$333$	−10.0431	−0.550356
$334$	−23.4945	−1.28556
$335$	−7.68997	−0.420148
$336$	20.0792	1.09541
$337$	1.64948	0.0898528	0.0449264	−	0.998990i	$-0.485695\pi$
$337$	1.64948	0.0898528	0.0449264	+	0.998990i	$0.485695\pi$
$338$	21.2674	1.15679
$339$	5.88316	0.319529
$340$	41.7805	2.26587
$341$	−20.4858	−1.10937
$342$	45.7238	2.47246
$343$	16.4432	0.887850
$344$	−10.4660	−0.564289
$345$	7.63771	0.411200
$346$	−6.64849	−0.357425
$347$	13.2743	0.712601	0.356301	−	0.934371i	$-0.384038\pi$
$347$	13.2743	0.712601	0.356301	+	0.934371i	$0.384038\pi$
$348$	10.1341	0.543243
$349$	23.4293	1.25414	0.627071	−	0.778962i	$-0.284253\pi$
$349$	23.4293	1.25414	0.627071	+	0.778962i	$0.284253\pi$
$350$	−3.71015	−0.198316
$351$	−3.20677	−0.171165
$352$	−18.4113	−0.981328
$353$	−8.46924	−0.450772	−0.225386	−	0.974270i	$-0.572364\pi$
$353$	−8.46924	−0.450772	−0.225386	+	0.974270i	$0.572364\pi$
$354$	−3.77849	−0.200825
$355$	−25.1023	−1.33229
$356$	−13.7465	−0.728565
$357$	15.0656	0.797355
$358$	−57.3914	−3.03323
$359$	12.3181	0.650126	0.325063	−	0.945692i	$-0.394615\pi$
$359$	12.3181	0.650126	0.325063	+	0.945692i	$0.394615\pi$
$360$	−27.9761	−1.47447
$361$	40.2155	2.11661
$362$	−52.6064	−2.76493
$363$	−18.8249	−0.988051
$364$	12.6600	0.663564
$365$	−14.7643	−0.772799
$366$	−18.5683	−0.970581
$367$	20.0042	1.04421	0.522105	−	0.852881i	$-0.325147\pi$
$367$	20.0042	1.04421	0.522105	+	0.852881i	$0.325147\pi$
$368$	−10.7270	−0.559184
$369$	−27.8077	−1.44761
$370$	21.3307	1.10893
$371$	−11.4094	−0.592346
$372$	47.4570	2.46053
$373$	24.9989	1.29439	0.647196	−	0.762323i	$-0.275941\pi$
$373$	24.9989	1.29439	0.647196	+	0.762323i	$0.275941\pi$
$374$	−53.2849	−2.75529
$375$	27.8574	1.43855
$376$	−23.6378	−1.21903
$377$	2.14019	0.110226
$378$	5.11102	0.262882
$379$	13.2105	0.678580	0.339290	−	0.940682i	$-0.389813\pi$
$379$	13.2105	0.678580	0.339290	+	0.940682i	$0.389813\pi$
$380$	−66.6725	−3.42023
$381$	8.44105	0.432448
$382$	−36.2798	−1.85624
$383$	6.14546	0.314018	0.157009	−	0.987597i	$-0.449815\pi$
$383$	6.14546	0.314018	0.157009	+	0.987597i	$0.449815\pi$
$384$	−32.4643	−1.65668
$385$	−11.6848	−0.595515
$386$	50.9965	2.59565
$387$	4.09461	0.208141
$388$	−3.40910	−0.173071
$389$	−13.1889	−0.668705	−0.334352	−	0.942448i	$-0.608518\pi$
$389$	−13.1889	−0.668705	−0.334352	+	0.942448i	$0.608518\pi$
$390$	−24.7381	−1.25266
$391$	−8.04855	−0.407033
$392$	31.1239	1.57199
$393$	−23.8557	−1.20336
$394$	−30.3243	−1.52772
$395$	−11.9616	−0.601855
$396$	45.0764	2.26517
$397$	−36.7383	−1.84384	−0.921922	−	0.387375i	$-0.873382\pi$
$397$	−36.7383	−1.84384	−0.921922	+	0.387375i	$0.873382\pi$
$398$	−19.3986	−0.972364
$399$	−24.0414	−1.20357
$400$	−6.99043	−0.349522
$401$	−32.7923	−1.63757	−0.818784	−	0.574101i	$-0.805352\pi$
$401$	−32.7923	−1.63757	−0.818784	+	0.574101i	$0.805352\pi$
$402$	−22.7197	−1.13316
$403$	10.0223	0.499248
$404$	42.2664	2.10283
$405$	−20.8151	−1.03431
$406$	−3.41108	−0.169289
$407$	−18.6767	−0.925771
$408$	67.0788	3.32090
$409$	21.2227	1.04939	0.524697	−	0.851289i	$-0.324179\pi$
$409$	21.2227	1.04939	0.524697	+	0.851289i	$0.324179\pi$
$410$	59.0616	2.91684
$411$	42.9738	2.11974
$412$	82.7996	4.07924
$413$	0.873157	0.0429653
$414$	9.91740	0.487414
$415$	32.2398	1.58259
$416$	9.00746	0.441627
$417$	−26.9912	−1.32177
$418$	85.0310	4.15900
$419$	2.58474	0.126273	0.0631365	−	0.998005i	$-0.479890\pi$
$419$	2.58474	0.126273	0.0631365	+	0.998005i	$0.479890\pi$
$420$	27.0689	1.32083
$421$	−30.1742	−1.47060	−0.735301	−	0.677741i	$-0.762959\pi$
$421$	−30.1742	−1.47060	−0.735301	+	0.677741i	$0.762959\pi$
$422$	−8.78695	−0.427742
$423$	9.24782	0.449644
$424$	−50.7998	−2.46706
$425$	−5.24498	−0.254419
$426$	−74.1636	−3.59324
$427$	4.29088	0.207650
$428$	3.00663	0.145331
$429$	21.6601	1.04576
$430$	−8.69665	−0.419390
$431$	12.9495	0.623757	0.311878	−	0.950122i	$-0.399042\pi$
$431$	12.9495	0.623757	0.311878	+	0.950122i	$0.399042\pi$
$432$	9.62986	0.463317
$433$	23.8721	1.14722	0.573609	−	0.819129i	$-0.305543\pi$
$433$	23.8721	1.14722	0.573609	+	0.819129i	$0.305543\pi$
$434$	−15.9738	−0.766768
$435$	4.57604	0.219404
$436$	1.56873	0.0751284
$437$	12.8437	0.614399
$438$	−43.6205	−2.08427
$439$	26.0016	1.24099	0.620495	−	0.784210i	$-0.286932\pi$
$439$	26.0016	1.24099	0.620495	+	0.784210i	$0.286932\pi$
$440$	−52.0263	−2.48025
$441$	−12.1766	−0.579838
$442$	26.0688	1.23996
$443$	31.3848	1.49114	0.745569	−	0.666429i	$-0.232178\pi$
$443$	31.3848	1.49114	0.745569	+	0.666429i	$0.232178\pi$
$444$	43.2662	2.05332
$445$	−6.20725	−0.294252
$446$	−6.76060	−0.320123
$447$	−22.7357	−1.07536
$448$	3.00191	0.141827
$449$	21.2886	1.00467	0.502336	−	0.864673i	$-0.332474\pi$
$449$	21.2886	1.00467	0.502336	+	0.864673i	$0.332474\pi$
$450$	6.46284	0.304661
$451$	−51.7131	−2.43508
$452$	−11.1391	−0.523939
$453$	−8.47312	−0.398102
$454$	70.2098	3.29511
$455$	5.71662	0.267999
$456$	−107.043	−5.01275
$457$	17.2663	0.807684	0.403842	−	0.914829i	$-0.367675\pi$
$457$	17.2663	0.807684	0.403842	+	0.914829i	$0.367675\pi$
$458$	59.9402	2.80082
$459$	7.22536	0.337251
$460$	−14.4611	−0.674254
$461$	5.74262	0.267460	0.133730	−	0.991018i	$-0.457304\pi$
$461$	5.74262	0.267460	0.133730	+	0.991018i	$0.457304\pi$
$462$	−34.5224	−1.60613
$463$	−10.7696	−0.500506	−0.250253	−	0.968180i	$-0.580514\pi$
$463$	−10.7696	−0.500506	−0.250253	+	0.968180i	$0.580514\pi$
$464$	−6.42695	−0.298364
$465$	21.4292	0.993755
$466$	−64.2985	−2.97857
$467$	−3.67916	−0.170251	−0.0851257	−	0.996370i	$-0.527129\pi$
$467$	−3.67916	−0.170251	−0.0851257	+	0.996370i	$0.527129\pi$
$468$	−22.0529	−1.01940
$469$	5.25021	0.242432
$470$	−19.6417	−0.906003
$471$	−22.7443	−1.04800
$472$	3.88769	0.178946
$473$	7.61461	0.350120
$474$	−35.3402	−1.62323
$475$	8.36983	0.384034
$476$	−28.5250	−1.30744
$477$	19.8744	0.909987
$478$	−43.1855	−1.97526
$479$	−29.7382	−1.35877	−0.679387	−	0.733781i	$-0.737754\pi$
$479$	−29.7382	−1.35877	−0.679387	+	0.733781i	$0.737754\pi$
$480$	19.2592	0.879060
$481$	9.13730	0.416625
$482$	−22.8028	−1.03864
$483$	−5.21453	−0.237269
$484$	35.6428	1.62013
$485$	−1.53938	−0.0698996
$486$	−50.1430	−2.27453
$487$	−37.6458	−1.70589	−0.852947	−	0.521997i	$-0.825187\pi$
$487$	−37.6458	−1.70589	−0.852947	+	0.521997i	$0.825187\pi$
$488$	19.1050	0.864841
$489$	−53.2683	−2.40888
$490$	25.8622	1.16833
$491$	3.81272	0.172066	0.0860329	−	0.996292i	$-0.472581\pi$
$491$	3.81272	0.172066	0.0860329	+	0.996292i	$0.472581\pi$
$492$	119.798	5.40089
$493$	−4.82219	−0.217181
$494$	−41.6000	−1.87167
$495$	20.3542	0.914855
$496$	−30.0969	−1.35139
$497$	17.1382	0.768752
$498$	95.2510	4.26830
$499$	37.9452	1.69866	0.849331	−	0.527860i	$-0.177006\pi$
$499$	37.9452	1.69866	0.849331	+	0.527860i	$0.177006\pi$
$500$	−52.7449	−2.35882
$501$	−21.5187	−0.961382
$502$	−11.6312	−0.519128
$503$	−30.2807	−1.35015	−0.675076	−	0.737748i	$-0.735889\pi$
$503$	−30.2807	−1.35015	−0.675076	+	0.737748i	$0.735889\pi$
$504$	19.1003	0.850794
$505$	19.0854	0.849290
$506$	18.4431	0.819894
$507$	19.4788	0.865084
$508$	−15.9822	−0.709095
$509$	37.7543	1.67343	0.836715	−	0.547638i	$-0.184473\pi$
$509$	37.7543	1.67343	0.836715	+	0.547638i	$0.184473\pi$
$510$	55.7388	2.46815
$511$	10.0801	0.445917
$512$	50.2374	2.22020
$513$	−11.5301	−0.509066
$514$	−23.8194	−1.05063
$515$	37.3882	1.64752
$516$	−17.6399	−0.776552
$517$	17.1979	0.756361
$518$	−14.5632	−0.639871
$519$	−6.08937	−0.267294
$520$	25.4530	1.11619
$521$	−6.75120	−0.295776	−0.147888	−	0.989004i	$-0.547247\pi$
$521$	−6.75120	−0.295776	−0.147888	+	0.989004i	$0.547247\pi$
$522$	5.94189	0.260069
$523$	5.63324	0.246324	0.123162	−	0.992387i	$-0.460696\pi$
$523$	5.63324	0.246324	0.123162	+	0.992387i	$0.460696\pi$
$524$	45.1681	1.97318
$525$	−3.39813	−0.148307
$526$	48.7115	2.12392
$527$	−22.5819	−0.983684
$528$	−65.0449	−2.83072
$529$	−20.2142	−0.878879
$530$	−42.2118	−1.83356
$531$	−1.52098	−0.0660050
$532$	45.5196	1.97353
$533$	25.2998	1.09586
$534$	−18.3391	−0.793609
$535$	1.35764	0.0586960
$536$	23.3763	1.00970
$537$	−52.5649	−2.26834
$538$	72.9932	3.14696
$539$	−22.6444	−0.975363
$540$	12.9821	0.558659
$541$	−37.7598	−1.62342	−0.811709	−	0.584061i	$-0.801463\pi$
$541$	−37.7598	−1.62342	−0.811709	+	0.584061i	$0.801463\pi$
$542$	42.2673	1.81553
$543$	−48.1823	−2.06770
$544$	−20.2952	−0.870151
$545$	0.708359	0.0303428
$546$	16.8895	0.722805
$547$	12.9123	0.552089	0.276044	−	0.961145i	$-0.410976\pi$
$547$	12.9123	0.552089	0.276044	+	0.961145i	$0.410976\pi$
$548$	−81.3661	−3.47579
$549$	−7.47444	−0.319001
$550$	12.0187	0.512480
$551$	7.69516	0.327825
$552$	−23.2174	−0.988200
$553$	8.16662	0.347280
$554$	−2.52594	−0.107317
$555$	19.5368	0.829293
$556$	51.1048	2.16733
$557$	13.6711	0.579262	0.289631	−	0.957138i	$-0.406467\pi$
$557$	13.6711	0.579262	0.289631	+	0.957138i	$0.406467\pi$
$558$	27.8254	1.17794
$559$	−3.72533	−0.157565
$560$	−17.1669	−0.725434
$561$	−48.8037	−2.06049
$562$	45.3290	1.91209
$563$	−28.4966	−1.20099	−0.600495	−	0.799629i	$-0.705030\pi$
$563$	−28.4966	−1.20099	−0.600495	+	0.799629i	$0.705030\pi$
$564$	−39.8402	−1.67758
$565$	−5.02986	−0.211608
$566$	66.0668	2.77699
$567$	14.2112	0.596813
$568$	76.3070	3.20177
$569$	14.6781	0.615337	0.307669	−	0.951494i	$-0.400451\pi$
$569$	14.6781	0.615337	0.307669	+	0.951494i	$0.400451\pi$
$570$	−88.9468	−3.72557
$571$	42.5277	1.77973	0.889864	−	0.456226i	$-0.150799\pi$
$571$	42.5277	1.77973	0.889864	+	0.456226i	$0.150799\pi$
$572$	−41.0110	−1.71476
$573$	−33.2287	−1.38815
$574$	−40.3234	−1.68307
$575$	1.81540	0.0757074
$576$	−5.22913	−0.217880
$577$	36.0730	1.50174	0.750869	−	0.660451i	$-0.229635\pi$
$577$	36.0730	1.50174	0.750869	+	0.660451i	$0.229635\pi$
$578$	−15.7961	−0.657030
$579$	46.7078	1.94111
$580$	−8.66421	−0.359762
$581$	−22.0112	−0.913178
$582$	−4.54803	−0.188522
$583$	36.9598	1.53072
$584$	44.8812	1.85720
$585$	−9.95799	−0.411712
$586$	−8.61025	−0.355686
$587$	13.0275	0.537703	0.268851	−	0.963182i	$-0.413356\pi$
$587$	13.0275	0.537703	0.268851	+	0.963182i	$0.413356\pi$
$588$	52.4576	2.16331
$589$	36.0358	1.48483
$590$	3.23046	0.132996
$591$	−27.7741	−1.14247
$592$	−27.4391	−1.12774
$593$	−25.2322	−1.03616	−0.518082	−	0.855331i	$-0.673354\pi$
$593$	−25.2322	−1.03616	−0.518082	+	0.855331i	$0.673354\pi$
$594$	−16.5567	−0.679331
$595$	−12.8805	−0.528047
$596$	43.0475	1.76329
$597$	−17.7672	−0.727164
$598$	−9.02297	−0.368977
$599$	22.1308	0.904241	0.452121	−	0.891957i	$-0.350668\pi$
$599$	22.1308	0.904241	0.452121	+	0.891957i	$0.350668\pi$
$600$	−15.1300	−0.617682
$601$	−9.97396	−0.406846	−0.203423	−	0.979091i	$-0.565207\pi$
$601$	−9.97396	−0.406846	−0.203423	+	0.979091i	$0.565207\pi$
$602$	5.93751	0.241995
$603$	−9.14552	−0.372434
$604$	16.0429	0.652776
$605$	16.0945	0.654336
$606$	56.3871	2.29057
$607$	−33.3839	−1.35501	−0.677505	−	0.735518i	$-0.736939\pi$
$607$	−33.3839	−1.35501	−0.677505	+	0.735518i	$0.736939\pi$
$608$	32.3867	1.31346
$609$	−3.12422	−0.126600
$610$	15.8752	0.642766
$611$	−8.41377	−0.340385
$612$	49.6887	2.00855
$613$	−25.2244	−1.01880	−0.509401	−	0.860529i	$-0.670133\pi$
$613$	−25.2244	−1.01880	−0.509401	+	0.860529i	$0.670133\pi$
$614$	26.8117	1.08203
$615$	54.0946	2.18131
$616$	35.5201	1.43115
$617$	28.3622	1.14182	0.570909	−	0.821013i	$-0.306591\pi$
$617$	28.3622	1.14182	0.570909	+	0.821013i	$0.306591\pi$
$618$	110.462	4.44343
$619$	−13.5087	−0.542960	−0.271480	−	0.962444i	$-0.587513\pi$
$619$	−13.5087	−0.542960	−0.271480	+	0.962444i	$0.587513\pi$
$620$	−40.5738	−1.62948
$621$	−2.50085	−0.100356
$622$	68.3647	2.74118
$623$	4.23790	0.169788
$624$	31.8222	1.27391
$625$	−18.3786	−0.735144
$626$	15.3099	0.611906
$627$	77.8800	3.11023
$628$	43.0637	1.71843
$629$	−20.5878	−0.820888
$630$	15.8713	0.632326
$631$	−33.1106	−1.31811	−0.659056	−	0.752094i	$-0.729044\pi$
$631$	−33.1106	−1.31811	−0.659056	+	0.752094i	$0.729044\pi$
$632$	36.3615	1.44638
$633$	−8.04798	−0.319879
$634$	7.10769	0.282282
$635$	−7.21676	−0.286388
$636$	−85.6203	−3.39507
$637$	11.0784	0.438943
$638$	11.0499	0.437471
$639$	−29.8536	−1.18099
$640$	27.7556	1.09714
$641$	18.7495	0.740561	0.370280	−	0.928920i	$-0.379262\pi$
$641$	18.7495	0.740561	0.370280	+	0.928920i	$0.379262\pi$
$642$	4.01110	0.158305
$643$	−1.36312	−0.0537562	−0.0268781	−	0.999639i	$-0.508557\pi$
$643$	−1.36312	−0.0537562	−0.0268781	+	0.999639i	$0.508557\pi$
$644$	9.87312	0.389055
$645$	−7.96528	−0.313633
$646$	93.7315	3.68782
$647$	37.6814	1.48141	0.740704	−	0.671831i	$-0.234492\pi$
$647$	37.6814	1.48141	0.740704	+	0.671831i	$0.234492\pi$
$648$	63.2746	2.48566
$649$	−2.82852	−0.111029
$650$	−5.87997	−0.230631
$651$	−14.6304	−0.573413
$652$	100.858	3.94989
$653$	−27.6162	−1.08071	−0.540353	−	0.841438i	$-0.681709\pi$
$653$	−27.6162	−1.08071	−0.540353	+	0.841438i	$0.681709\pi$
$654$	2.09282	0.0818356
$655$	20.3957	0.796925
$656$	−75.9748	−2.96632
$657$	−17.5589	−0.685037
$658$	13.4101	0.522778
$659$	30.1475	1.17438	0.587191	−	0.809449i	$-0.300234\pi$
$659$	30.1475	1.17438	0.587191	+	0.809449i	$0.300234\pi$
$660$	−87.6874	−3.41323
$661$	−11.6249	−0.452156	−0.226078	−	0.974109i	$-0.572590\pi$
$661$	−11.6249	−0.452156	−0.226078	+	0.974109i	$0.572590\pi$
$662$	21.5737	0.838485
$663$	23.8764	0.927284
$664$	−98.0039	−3.80329
$665$	20.5544	0.797065
$666$	25.3682	0.982997
$667$	1.66907	0.0646265
$668$	40.7431	1.57640
$669$	−6.19204	−0.239398
$670$	19.4244	0.750430
$671$	−13.9000	−0.536602
$672$	−13.1489	−0.507231
$673$	18.7219	0.721675	0.360838	−	0.932629i	$-0.382491\pi$
$673$	18.7219	0.721675	0.360838	+	0.932629i	$0.382491\pi$
$674$	−4.16648	−0.160487
$675$	−1.62972	−0.0627281
$676$	−36.8809	−1.41850
$677$	−41.4291	−1.59225	−0.796125	−	0.605133i	$-0.793120\pi$
$677$	−41.4291	−1.59225	−0.796125	+	0.605133i	$0.793120\pi$
$678$	−14.8605	−0.570714
$679$	1.05099	0.0403332
$680$	−57.3497	−2.19926
$681$	64.3053	2.46418
$682$	51.7459	1.98145
$683$	−40.2900	−1.54165	−0.770827	−	0.637045i	$-0.780157\pi$
$683$	−40.2900	−1.54165	−0.770827	+	0.637045i	$0.780157\pi$
$684$	−79.2922	−3.03181
$685$	−36.7409	−1.40380
$686$	−41.5346	−1.58580
$687$	54.8993	2.09454
$688$	11.1871	0.426503
$689$	−18.0820	−0.688869
$690$	−19.2924	−0.734449
$691$	−16.0496	−0.610554	−0.305277	−	0.952264i	$-0.598749\pi$
$691$	−16.0496	−0.610554	−0.305277	+	0.952264i	$0.598749\pi$
$692$	11.5295	0.438287
$693$	−13.8965	−0.527886
$694$	−33.5301	−1.27278
$695$	23.0764	0.875337
$696$	−13.9104	−0.527274
$697$	−57.0045	−2.15920
$698$	−59.1811	−2.24004
$699$	−58.8911	−2.22747
$700$	6.43398	0.243182
$701$	29.6886	1.12132	0.560662	−	0.828045i	$-0.310547\pi$
$701$	29.6886	1.12132	0.560662	+	0.828045i	$0.310547\pi$
$702$	8.10011	0.305719
$703$	32.8536	1.23910
$704$	−9.72443	−0.366503
$705$	−17.9899	−0.677537
$706$	21.3928	0.805128
$707$	−13.0303	−0.490054
$708$	6.55250	0.246258
$709$	5.92977	0.222697	0.111349	−	0.993781i	$-0.464483\pi$
$709$	5.92977	0.222697	0.111349	+	0.993781i	$0.464483\pi$
$710$	63.4068	2.37962
$711$	−14.2257	−0.533506
$712$	18.8691	0.707149
$713$	7.81609	0.292715
$714$	−38.0548	−1.42416
$715$	−18.5185	−0.692554
$716$	99.5257	3.71945
$717$	−39.5537	−1.47716
$718$	−31.1149	−1.16120
$719$	23.4442	0.874322	0.437161	−	0.899383i	$-0.355984\pi$
$719$	23.4442	0.874322	0.437161	+	0.899383i	$0.355984\pi$
$720$	29.9036	1.11444
$721$	−25.5262	−0.950645
$722$	−101.582	−3.78049
$723$	−20.8852	−0.776727
$724$	91.2277	3.39045
$725$	1.08767	0.0403952
$726$	47.5506	1.76477
$727$	17.7047	0.656633	0.328316	−	0.944568i	$-0.393519\pi$
$727$	17.7047	0.656633	0.328316	+	0.944568i	$0.393519\pi$
$728$	−17.3777	−0.644059
$729$	−14.3555	−0.531686
$730$	37.2938	1.38030
$731$	8.39375	0.310454
$732$	32.2004	1.19016
$733$	48.8325	1.80367	0.901835	−	0.432080i	$-0.142220\pi$
$733$	48.8325	1.80367	0.901835	+	0.432080i	$0.142220\pi$
$734$	−50.5294	−1.86507
$735$	23.6872	0.873717
$736$	7.02462	0.258931
$737$	−17.0076	−0.626483
$738$	70.2407	2.58560
$739$	7.74175	0.284785	0.142392	−	0.989810i	$-0.454521\pi$
$739$	7.74175	0.284785	0.142392	+	0.989810i	$0.454521\pi$
$740$	−36.9908	−1.35981
$741$	−38.1016	−1.39970
$742$	28.8194	1.05800
$743$	27.2877	1.00109	0.500544	−	0.865711i	$-0.333133\pi$
$743$	27.2877	1.00109	0.500544	+	0.865711i	$0.333133\pi$
$744$	−65.1414	−2.38820
$745$	19.4381	0.712157
$746$	−63.1457	−2.31193
$747$	38.3421	1.40286
$748$	92.4043	3.37864
$749$	−0.926909	−0.0338685
$750$	−70.3662	−2.56941
$751$	10.8827	0.397115	0.198557	−	0.980089i	$-0.436374\pi$
$751$	10.8827	0.397115	0.198557	+	0.980089i	$0.436374\pi$
$752$	25.2664	0.921370
$753$	−10.6531	−0.388220
$754$	−5.40600	−0.196875
$755$	7.24417	0.263642
$756$	−8.86331	−0.322355
$757$	16.3520	0.594322	0.297161	−	0.954827i	$-0.403960\pi$
$757$	16.3520	0.594322	0.297161	+	0.954827i	$0.403960\pi$
$758$	−33.3691	−1.21202
$759$	16.8920	0.613142
$760$	91.5175	3.31969
$761$	53.4147	1.93628	0.968142	−	0.250404i	$-0.0805633\pi$
$761$	53.4147	1.93628	0.968142	+	0.250404i	$0.0805633\pi$
$762$	−21.3216	−0.772400
$763$	−0.483621	−0.0175083
$764$	62.9148	2.27618
$765$	22.4369	0.811209
$766$	−15.5231	−0.560871
$767$	1.38381	0.0499664
$768$	71.7172	2.58787
$769$	39.5106	1.42479	0.712394	−	0.701779i	$-0.247611\pi$
$769$	39.5106	1.42479	0.712394	+	0.701779i	$0.247611\pi$
$770$	29.5152	1.06365
$771$	−21.8162	−0.785691
$772$	−88.4360	−3.18288
$773$	46.7860	1.68278	0.841388	−	0.540432i	$-0.181739\pi$
$773$	46.7860	1.68278	0.841388	+	0.540432i	$0.181739\pi$
$774$	−10.3427	−0.371762
$775$	5.09349	0.182964
$776$	4.67947	0.167983
$777$	−13.3385	−0.478515
$778$	33.3144	1.19438
$779$	90.9666	3.25922
$780$	42.8997	1.53605
$781$	−55.5177	−1.98658
$782$	20.3302	0.727006
$783$	−1.49836	−0.0535469
$784$	−33.2682	−1.18815
$785$	19.4454	0.694037
$786$	60.2582	2.14934
$787$	−12.5452	−0.447189	−0.223595	−	0.974682i	$-0.571779\pi$
$787$	−12.5452	−0.447189	−0.223595	+	0.974682i	$0.571779\pi$
$788$	52.5871	1.87334
$789$	44.6149	1.58833
$790$	30.2144	1.07498
$791$	3.43406	0.122101
$792$	−61.8737	−2.19859
$793$	6.80033	0.241487
$794$	92.7989	3.29331
$795$	−38.6619	−1.37119
$796$	33.6402	1.19235
$797$	−10.4118	−0.368804	−0.184402	−	0.982851i	$-0.559035\pi$
$797$	−10.4118	−0.368804	−0.184402	+	0.982851i	$0.559035\pi$
$798$	60.7271	2.14971
$799$	18.9576	0.670670
$800$	4.57771	0.161847
$801$	−7.38215	−0.260835
$802$	82.8314	2.92488
$803$	−32.6536	−1.15232
$804$	39.3995	1.38951
$805$	4.45821	0.157131
$806$	−25.3158	−0.891712
$807$	66.8546	2.35339
$808$	−58.0167	−2.04102
$809$	9.35240	0.328813	0.164406	−	0.986393i	$-0.447429\pi$
$809$	9.35240	0.328813	0.164406	+	0.986393i	$0.447429\pi$
$810$	52.5776	1.84739
$811$	−17.4092	−0.611320	−0.305660	−	0.952141i	$-0.598877\pi$
$811$	−17.4092	−0.611320	−0.305660	+	0.952141i	$0.598877\pi$
$812$	5.91536	0.207588
$813$	38.7127	1.35771
$814$	47.1763	1.65353
$815$	45.5422	1.59527
$816$	−71.7004	−2.51002
$817$	−13.3946	−0.468617
$818$	−53.6072	−1.87433
$819$	6.79866	0.237564
$820$	−102.422	−3.57673
$821$	−46.2374	−1.61370	−0.806848	−	0.590758i	$-0.798829\pi$
$821$	−46.2374	−1.61370	−0.806848	+	0.590758i	$0.798829\pi$
$822$	−108.549	−3.78609
$823$	−23.3161	−0.812749	−0.406374	−	0.913707i	$-0.633207\pi$
$823$	−23.3161	−0.812749	−0.406374	+	0.913707i	$0.633207\pi$
$824$	−113.654	−3.95933
$825$	11.0080	0.383248
$826$	−2.20554	−0.0767407
$827$	19.0685	0.663076	0.331538	−	0.943442i	$-0.392432\pi$
$827$	19.0685	0.663076	0.331538	+	0.943442i	$0.392432\pi$
$828$	−17.1983	−0.597683
$829$	20.1054	0.698288	0.349144	−	0.937069i	$-0.386472\pi$
$829$	20.1054	0.698288	0.349144	+	0.937069i	$0.386472\pi$
$830$	−81.4357	−2.82668
$831$	−2.31351	−0.0802549
$832$	4.75752	0.164937
$833$	−24.9614	−0.864862
$834$	68.1782	2.36082
$835$	18.3976	0.636674
$836$	−147.457	−5.09991
$837$	−7.01667	−0.242532
$838$	−6.52891	−0.225537
$839$	−2.43610	−0.0841036	−0.0420518	−	0.999115i	$-0.513389\pi$
$839$	−2.43610	−0.0841036	−0.0420518	+	0.999115i	$0.513389\pi$
$840$	−37.1559	−1.28200
$841$	1.00000	0.0344828
$842$	76.2183	2.62666
$843$	41.5169	1.42992
$844$	15.2379	0.524512
$845$	−16.6536	−0.572901
$846$	−23.3594	−0.803114
$847$	−10.9883	−0.377562
$848$	54.2998	1.86466
$849$	60.5107	2.07672
$850$	13.2485	0.454420
$851$	7.12588	0.244272
$852$	128.611	4.40615
$853$	−13.4249	−0.459659	−0.229829	−	0.973231i	$-0.573817\pi$
$853$	−13.4249	−0.459659	−0.229829	+	0.973231i	$0.573817\pi$
$854$	−10.8385	−0.370886
$855$	−35.8044	−1.22448
$856$	−4.12702	−0.141059
$857$	39.7980	1.35947	0.679736	−	0.733456i	$-0.262094\pi$
$857$	39.7980	1.35947	0.679736	+	0.733456i	$0.262094\pi$
$858$	−54.7122	−1.86784
$859$	56.5299	1.92877	0.964387	−	0.264495i	$-0.0852051\pi$
$859$	56.5299	1.92877	0.964387	+	0.264495i	$0.0852051\pi$
$860$	15.0814	0.514270
$861$	−36.9323	−1.25865
$862$	−32.7097	−1.11410
$863$	23.4103	0.796896	0.398448	−	0.917191i	$-0.369549\pi$
$863$	23.4103	0.796896	0.398448	+	0.917191i	$0.369549\pi$
$864$	−6.30615	−0.214540
$865$	5.20616	0.177015
$866$	−60.2994	−2.04906
$867$	−14.4676	−0.491347
$868$	27.7011	0.940237
$869$	−26.4551	−0.897428
$870$	−11.5588	−0.391880
$871$	8.32070	0.281936
$872$	−2.15330	−0.0729200
$873$	−1.83075	−0.0619615
$874$	−32.4425	−1.09738
$875$	16.2607	0.549711
$876$	75.6448	2.55580
$877$	17.7632	0.599820	0.299910	−	0.953968i	$-0.403043\pi$
$877$	17.7632	0.599820	0.299910	+	0.953968i	$0.403043\pi$
$878$	−65.6786	−2.21654
$879$	−7.88614	−0.265993
$880$	55.6107	1.87464
$881$	5.93446	0.199937	0.0999685	−	0.994991i	$-0.468126\pi$
$881$	5.93446	0.199937	0.0999685	+	0.994991i	$0.468126\pi$
$882$	30.7574	1.03565
$883$	25.6105	0.861860	0.430930	−	0.902385i	$-0.358186\pi$
$883$	25.6105	0.861860	0.430930	+	0.902385i	$0.358186\pi$
$884$	−45.2073	−1.52049
$885$	2.95878	0.0994583
$886$	−79.2762	−2.66334
$887$	2.44186	0.0819895	0.0409948	−	0.999159i	$-0.486947\pi$
$887$	2.44186	0.0819895	0.0409948	+	0.999159i	$0.486947\pi$
$888$	−59.3890	−1.99296
$889$	4.92713	0.165251
$890$	15.6791	0.525566
$891$	−46.0359	−1.54226
$892$	11.7239	0.392546
$893$	−30.2521	−1.01235
$894$	57.4290	1.92071
$895$	44.9408	1.50221
$896$	−18.9497	−0.633065
$897$	−8.26415	−0.275932
$898$	−53.7738	−1.79445
$899$	4.68291	0.156184
$900$	−11.2076	−0.373586
$901$	40.7416	1.35730
$902$	130.624	4.34931
$903$	5.43817	0.180971
$904$	15.2900	0.508538
$905$	41.1939	1.36933
$906$	21.4026	0.711054
$907$	−11.8555	−0.393656	−0.196828	−	0.980438i	$-0.563064\pi$
$907$	−11.8555	−0.393656	−0.196828	+	0.980438i	$0.563064\pi$
$908$	−121.755	−4.04057
$909$	22.6979	0.752841
$910$	−14.4399	−0.478676
$911$	−14.8517	−0.492058	−0.246029	−	0.969262i	$-0.579126\pi$
$911$	−14.8517	−0.492058	−0.246029	+	0.969262i	$0.579126\pi$
$912$	114.418	3.78876
$913$	71.3035	2.35980
$914$	−43.6137	−1.44261
$915$	14.5401	0.480680
$916$	−103.946	−3.43446
$917$	−13.9248	−0.459839
$918$	−18.2508	−0.602367
$919$	48.5239	1.60066	0.800328	−	0.599562i	$-0.204659\pi$
$919$	48.5239	1.60066	0.800328	+	0.599562i	$0.204659\pi$
$920$	19.8500	0.654434
$921$	24.5568	0.809175
$922$	−14.5055	−0.477714
$923$	27.1612	0.894020
$924$	59.8672	1.96949
$925$	4.64370	0.152684
$926$	27.2034	0.893959
$927$	44.4650	1.46042
$928$	4.20871	0.138158
$929$	−30.3489	−0.995716	−0.497858	−	0.867259i	$-0.665880\pi$
$929$	−30.3489	−0.995716	−0.497858	+	0.867259i	$0.665880\pi$
$930$	−54.1289	−1.77496
$931$	39.8329	1.30547
$932$	111.504	3.65242
$933$	62.6154	2.04994
$934$	9.29335	0.304088
$935$	41.7252	1.36456
$936$	30.2707	0.989430
$937$	39.8221	1.30093	0.650466	−	0.759535i	$-0.274573\pi$
$937$	39.8221	1.30093	0.650466	+	0.759535i	$0.274573\pi$
$938$	−13.2617	−0.433010
$939$	14.0224	0.457602
$940$	34.0618	1.11097
$941$	−16.4689	−0.536872	−0.268436	−	0.963297i	$-0.586507\pi$
$941$	−16.4689	−0.536872	−0.268436	+	0.963297i	$0.586507\pi$
$942$	57.4507	1.87185
$943$	19.7305	0.642513
$944$	−4.15555	−0.135251
$945$	−4.00223	−0.130192
$946$	−19.2341	−0.625353
$947$	−10.7382	−0.348945	−0.174472	−	0.984662i	$-0.555822\pi$
$947$	−10.7382	−0.348945	−0.174472	+	0.984662i	$0.555822\pi$
$948$	61.2854	1.99046
$949$	15.9753	0.518579
$950$	−21.1417	−0.685928
$951$	6.50994	0.211099
$952$	39.1546	1.26901
$953$	0.882870	0.0285990	0.0142995	−	0.999898i	$-0.495448\pi$
$953$	0.882870	0.0285990	0.0142995	+	0.999898i	$0.495448\pi$
$954$	−50.2016	−1.62534
$955$	28.4092	0.919300
$956$	74.8904	2.42213
$957$	10.1206	0.327154
$958$	75.1169	2.42692
$959$	25.0843	0.810013
$960$	10.1723	0.328308
$961$	−9.07031	−0.292591
$962$	−23.0803	−0.744138
$963$	1.61462	0.0520303
$964$	39.5437	1.27362
$965$	−39.9333	−1.28550
$966$	13.1716	0.423789
$967$	22.6006	0.726787	0.363394	−	0.931636i	$-0.381618\pi$
$967$	22.6006	0.726787	0.363394	+	0.931636i	$0.381618\pi$
$968$	−48.9249	−1.57251
$969$	85.8488	2.75786
$970$	3.88838	0.124848
$971$	21.2880	0.683164	0.341582	−	0.939852i	$-0.389037\pi$
$971$	21.2880	0.683164	0.341582	+	0.939852i	$0.389037\pi$
$972$	86.9558	2.78911
$973$	−15.7550	−0.505084
$974$	95.0911	3.04692
$975$	−5.38548	−0.172473
$976$	−20.4212	−0.653668
$977$	−15.2015	−0.486338	−0.243169	−	0.969984i	$-0.578187\pi$
$977$	−15.2015	−0.486338	−0.243169	+	0.969984i	$0.578187\pi$
$978$	134.553	4.30252
$979$	−13.7283	−0.438759
$980$	−44.8491	−1.43265
$981$	0.842437	0.0268969
$982$	−9.63071	−0.307328
$983$	−10.5018	−0.334955	−0.167477	−	0.985876i	$-0.553562\pi$
$983$	−10.5018	−0.334955	−0.167477	+	0.985876i	$0.553562\pi$
$984$	−164.439	−5.24213
$985$	23.7457	0.756601
$986$	12.1806	0.387908
$987$	12.2823	0.390950
$988$	72.1410	2.29511
$989$	−2.90526	−0.0923819
$990$	−51.4136	−1.63403
$991$	−13.7416	−0.436515	−0.218257	−	0.975891i	$-0.570037\pi$
$991$	−13.7416	−0.436515	−0.218257	+	0.975891i	$0.570037\pi$
$992$	19.7090	0.625763
$993$	19.7594	0.627045
$994$	−43.2900	−1.37308
$995$	15.1902	0.481563
$996$	−165.180	−5.23394
$997$	44.2088	1.40011	0.700053	−	0.714091i	$-0.253160\pi$
$997$	44.2088	1.40011	0.700053	+	0.714091i	$0.253160\pi$
$998$	−95.8474	−3.03400
$999$	−6.39705	−0.202394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.e.1.13	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.e.1.13	✓	169	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52594 q^{2} -2.31351 q^{3} +4.38038 q^{4} +1.97796 q^{5} +5.84380 q^{6} -1.35042 q^{7} -6.01269 q^{8} +2.35235 q^{9} +O(q^{10})\)	\(q-2.52594 q^{2} -2.31351 q^{3} +4.38038 q^{4} +1.97796 q^{5} +5.84380 q^{6} -1.35042 q^{7} -6.01269 q^{8} +2.35235 q^{9} -4.99621 q^{10} +4.37458 q^{11} -10.1341 q^{12} -2.14019 q^{13} +3.41108 q^{14} -4.57604 q^{15} +6.42695 q^{16} +4.82219 q^{17} -5.94189 q^{18} -7.69516 q^{19} +8.66421 q^{20} +3.12422 q^{21} -11.0499 q^{22} -1.66907 q^{23} +13.9104 q^{24} -1.08767 q^{25} +5.40600 q^{26} +1.49836 q^{27} -5.91536 q^{28} -1.00000 q^{29} +11.5588 q^{30} -4.68291 q^{31} -4.20871 q^{32} -10.1206 q^{33} -12.1806 q^{34} -2.67108 q^{35} +10.3042 q^{36} -4.26938 q^{37} +19.4375 q^{38} +4.95137 q^{39} -11.8929 q^{40} -11.8213 q^{41} -7.89159 q^{42} +1.74065 q^{43} +19.1623 q^{44} +4.65285 q^{45} +4.21596 q^{46} +3.93132 q^{47} -14.8688 q^{48} -5.17636 q^{49} +2.74740 q^{50} -11.1562 q^{51} -9.37485 q^{52} +8.44876 q^{53} -3.78476 q^{54} +8.65274 q^{55} +8.11967 q^{56} +17.8029 q^{57} +2.52594 q^{58} -0.646581 q^{59} -20.0448 q^{60} -3.17744 q^{61} +11.8288 q^{62} -3.17666 q^{63} -2.22294 q^{64} -4.23321 q^{65} +25.5642 q^{66} -3.88783 q^{67} +21.1230 q^{68} +3.86141 q^{69} +6.74699 q^{70} -12.6910 q^{71} -14.1439 q^{72} -7.46441 q^{73} +10.7842 q^{74} +2.51635 q^{75} -33.7077 q^{76} -5.90752 q^{77} -12.5069 q^{78} -6.04746 q^{79} +12.7123 q^{80} -10.5235 q^{81} +29.8599 q^{82} +16.2995 q^{83} +13.6853 q^{84} +9.53810 q^{85} -4.39678 q^{86} +2.31351 q^{87} -26.3030 q^{88} -3.13821 q^{89} -11.7528 q^{90} +2.89016 q^{91} -7.31114 q^{92} +10.8340 q^{93} -9.93027 q^{94} -15.2207 q^{95} +9.73692 q^{96} -0.778266 q^{97} +13.0752 q^{98} +10.2905 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9}+O(q^{10}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9	\( 169 q + 3 q^{2} + 8 q^{3} + 183 q^{4} + 13 q^{5} + 17 q^{6} + 76 q^{7} + 6 q^{8} + 181 q^{9} + 30 q^{10} + 2 q^{11} + 25 q^{12} + 63 q^{13} - 3 q^{14} + 26 q^{15} + 219 q^{16} + 14 q^{17} + 31 q^{18} + 51 q^{19} + 49 q^{20} + 16 q^{21} + 53 q^{22} + 50 q^{23} + 43 q^{24} + 214 q^{25} - 2 q^{26} + 23 q^{27} + 149 q^{28} - 169 q^{29} + 26 q^{30} + 65 q^{31} + 25 q^{32} + 57 q^{33} + 60 q^{34} + 60 q^{35} + 218 q^{36} + 52 q^{37} + 35 q^{38} + 49 q^{39} + 72 q^{40} + 3 q^{41} + 78 q^{42} + 132 q^{43} + 64 q^{45} + 32 q^{46} + 54 q^{47} + 76 q^{48} + 245 q^{49} - 6 q^{50} + 44 q^{51} + 193 q^{52} + 58 q^{53} + 54 q^{54} + 213 q^{55} + 12 q^{56} + 52 q^{57} - 3 q^{58} + 25 q^{59} + 32 q^{60} + 100 q^{61} + 78 q^{62} + 227 q^{63} + 292 q^{64} + 37 q^{65} + 59 q^{66} + 110 q^{67} + 24 q^{68} - 20 q^{69} + 47 q^{70} + 44 q^{71} + 71 q^{72} + 139 q^{73} + 35 q^{74} + 53 q^{75} + 92 q^{76} + 22 q^{77} + 83 q^{78} + 137 q^{79} + 90 q^{80} + 177 q^{81} + 91 q^{82} + 126 q^{83} + 36 q^{84} + 95 q^{85} + 21 q^{86} - 8 q^{87} + 75 q^{88} + 19 q^{89} + 130 q^{90} + 102 q^{91} + 68 q^{92} + 22 q^{93} + 82 q^{94} + 37 q^{95} + 107 q^{96} + 116 q^{97} - 13 q^{98} - 11 q^{99}+O(q^{100}) \) 169 * q + 3 * q^2 + 8 * q^3 + 183 * q^4 + 13 * q^5 + 17 * q^6 + 76 * q^7 + 6 * q^8 + 181 * q^9 + 30 * q^10 + 2 * q^11 + 25 * q^12 + 63 * q^13 - 3 * q^14 + 26 * q^15 + 219 * q^16 + 14 * q^17 + 31 * q^18 + 51 * q^19 + 49 * q^20 + 16 * q^21 + 53 * q^22 + 50 * q^23 + 43 * q^24 + 214 * q^25 - 2 * q^26 + 23 * q^27 + 149 * q^28 - 169 * q^29 + 26 * q^30 + 65 * q^31 + 25 * q^32 + 57 * q^33 + 60 * q^34 + 60 * q^35 + 218 * q^36 + 52 * q^37 + 35 * q^38 + 49 * q^39 + 72 * q^40 + 3 * q^41 + 78 * q^42 + 132 * q^43 + 64 * q^45 + 32 * q^46 + 54 * q^47 + 76 * q^48 + 245 * q^49 - 6 * q^50 + 44 * q^51 + 193 * q^52 + 58 * q^53 + 54 * q^54 + 213 * q^55 + 12 * q^56 + 52 * q^57 - 3 * q^58 + 25 * q^59 + 32 * q^60 + 100 * q^61 + 78 * q^62 + 227 * q^63 + 292 * q^64 + 37 * q^65 + 59 * q^66 + 110 * q^67 + 24 * q^68 - 20 * q^69 + 47 * q^70 + 44 * q^71 + 71 * q^72 + 139 * q^73 + 35 * q^74 + 53 * q^75 + 92 * q^76 + 22 * q^77 + 83 * q^78 + 137 * q^79 + 90 * q^80 + 177 * q^81 + 91 * q^82 + 126 * q^83 + 36 * q^84 + 95 * q^85 + 21 * q^86 - 8 * q^87 + 75 * q^88 + 19 * q^89 + 130 * q^90 + 102 * q^91 + 68 * q^92 + 22 * q^93 + 82 * q^94 + 37 * q^95 + 107 * q^96 + 116 * q^97 - 13 * q^98 - 11 * q^99

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