LMFDB - Embedded newform 8018.2.a.f.1.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.50233 q^{3} +1.00000 q^{4} +0.477403 q^{5} -1.50233 q^{6} +1.81965 q^{7} -1.00000 q^{8} -0.742990 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.50233 q^{3} +1.00000 q^{4} +0.477403 q^{5} -1.50233 q^{6} +1.81965 q^{7} -1.00000 q^{8} -0.742990 q^{9} -0.477403 q^{10} +3.72939 q^{11} +1.50233 q^{12} -2.78785 q^{13} -1.81965 q^{14} +0.717220 q^{15} +1.00000 q^{16} -6.65771 q^{17} +0.742990 q^{18} -1.00000 q^{19} +0.477403 q^{20} +2.73373 q^{21} -3.72939 q^{22} -9.04267 q^{23} -1.50233 q^{24} -4.77209 q^{25} +2.78785 q^{26} -5.62322 q^{27} +1.81965 q^{28} +10.2754 q^{29} -0.717220 q^{30} +7.70560 q^{31} -1.00000 q^{32} +5.60279 q^{33} +6.65771 q^{34} +0.868708 q^{35} -0.742990 q^{36} -2.81068 q^{37} +1.00000 q^{38} -4.18828 q^{39} -0.477403 q^{40} +0.494351 q^{41} -2.73373 q^{42} -3.56544 q^{43} +3.72939 q^{44} -0.354706 q^{45} +9.04267 q^{46} +7.49608 q^{47} +1.50233 q^{48} -3.68886 q^{49} +4.77209 q^{50} -10.0021 q^{51} -2.78785 q^{52} +10.9125 q^{53} +5.62322 q^{54} +1.78042 q^{55} -1.81965 q^{56} -1.50233 q^{57} -10.2754 q^{58} -11.3081 q^{59} +0.717220 q^{60} +3.68257 q^{61} -7.70560 q^{62} -1.35198 q^{63} +1.00000 q^{64} -1.33093 q^{65} -5.60279 q^{66} +2.58881 q^{67} -6.65771 q^{68} -13.5851 q^{69} -0.868708 q^{70} +11.4587 q^{71} +0.742990 q^{72} -1.74144 q^{73} +2.81068 q^{74} -7.16927 q^{75} -1.00000 q^{76} +6.78620 q^{77} +4.18828 q^{78} -0.328881 q^{79} +0.477403 q^{80} -6.21900 q^{81} -0.494351 q^{82} -12.1789 q^{83} +2.73373 q^{84} -3.17841 q^{85} +3.56544 q^{86} +15.4372 q^{87} -3.72939 q^{88} -13.0387 q^{89} +0.354706 q^{90} -5.07292 q^{91} -9.04267 q^{92} +11.5764 q^{93} -7.49608 q^{94} -0.477403 q^{95} -1.50233 q^{96} -8.73226 q^{97} +3.68886 q^{98} -2.77090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.50233	0.867373	0.433687	−	0.901064i	$-0.357212\pi$
$3$	1.50233	0.867373	0.433687	+	0.901064i	$0.357212\pi$
$4$	1.00000	0.500000
$5$	0.477403	0.213501	0.106751	−	0.994286i	$-0.465955\pi$
$5$	0.477403	0.213501	0.106751	+	0.994286i	$0.465955\pi$
$6$	−1.50233	−0.613326
$7$	1.81965	0.687764	0.343882	−	0.939013i	$-0.388258\pi$
$7$	1.81965	0.687764	0.343882	+	0.939013i	$0.388258\pi$
$8$	−1.00000	−0.353553
$9$	−0.742990	−0.247663
$10$	−0.477403	−0.150968
$11$	3.72939	1.12445	0.562227	−	0.826983i	$-0.309945\pi$
$11$	3.72939	1.12445	0.562227	+	0.826983i	$0.309945\pi$
$12$	1.50233	0.433687
$13$	−2.78785	−0.773210	−0.386605	−	0.922245i	$-0.626352\pi$
$13$	−2.78785	−0.773210	−0.386605	+	0.922245i	$0.626352\pi$
$14$	−1.81965	−0.486323
$15$	0.717220	0.185185
$16$	1.00000	0.250000
$17$	−6.65771	−1.61473	−0.807366	−	0.590051i	$-0.799108\pi$
$17$	−6.65771	−1.61473	−0.807366	+	0.590051i	$0.799108\pi$
$18$	0.742990	0.175124
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.477403	0.106751
$21$	2.73373	0.596548
$22$	−3.72939	−0.795109
$23$	−9.04267	−1.88553	−0.942763	−	0.333462i	$-0.891783\pi$
$23$	−9.04267	−1.88553	−0.942763	+	0.333462i	$0.891783\pi$
$24$	−1.50233	−0.306663
$25$	−4.77209	−0.954417
$26$	2.78785	0.546742
$27$	−5.62322	−1.08219
$28$	1.81965	0.343882
$29$	10.2754	1.90810	0.954051	−	0.299645i	$-0.0968683\pi$
$29$	10.2754	1.90810	0.954051	+	0.299645i	$0.0968683\pi$
$30$	−0.717220	−0.130946
$31$	7.70560	1.38397	0.691983	−	0.721914i	$-0.256737\pi$
$31$	7.70560	1.38397	0.691983	+	0.721914i	$0.256737\pi$
$32$	−1.00000	−0.176777
$33$	5.60279	0.975321
$34$	6.65771	1.14179
$35$	0.868708	0.146839
$36$	−0.742990	−0.123832
$37$	−2.81068	−0.462073	−0.231036	−	0.972945i	$-0.574212\pi$
$37$	−2.81068	−0.462073	−0.231036	+	0.972945i	$0.574212\pi$
$38$	1.00000	0.162221
$39$	−4.18828	−0.670662
$40$	−0.477403	−0.0754841
$41$	0.494351	0.0772046	0.0386023	−	0.999255i	$-0.487709\pi$
$41$	0.494351	0.0772046	0.0386023	+	0.999255i	$0.487709\pi$
$42$	−2.73373	−0.421823
$43$	−3.56544	−0.543724	−0.271862	−	0.962336i	$-0.587639\pi$
$43$	−3.56544	−0.543724	−0.271862	+	0.962336i	$0.587639\pi$
$44$	3.72939	0.562227
$45$	−0.354706	−0.0528764
$46$	9.04267	1.33327
$47$	7.49608	1.09342	0.546708	−	0.837323i	$-0.315881\pi$
$47$	7.49608	1.09342	0.546708	+	0.837323i	$0.315881\pi$
$48$	1.50233	0.216843
$49$	−3.68886	−0.526980
$50$	4.77209	0.674875
$51$	−10.0021	−1.40058
$52$	−2.78785	−0.386605
$53$	10.9125	1.49895	0.749473	−	0.662035i	$-0.230307\pi$
$53$	10.9125	1.49895	0.749473	+	0.662035i	$0.230307\pi$
$54$	5.62322	0.765224
$55$	1.78042	0.240072
$56$	−1.81965	−0.243161
$57$	−1.50233	−0.198989
$58$	−10.2754	−1.34923
$59$	−11.3081	−1.47219	−0.736096	−	0.676877i	$-0.763333\pi$
$59$	−11.3081	−1.47219	−0.736096	+	0.676877i	$0.763333\pi$
$60$	0.717220	0.0925927
$61$	3.68257	0.471504	0.235752	−	0.971813i	$-0.424245\pi$
$61$	3.68257	0.471504	0.235752	+	0.971813i	$0.424245\pi$
$62$	−7.70560	−0.978612
$63$	−1.35198	−0.170334
$64$	1.00000	0.125000
$65$	−1.33093	−0.165081
$66$	−5.60279	−0.689656
$67$	2.58881	0.316273	0.158137	−	0.987417i	$-0.449451\pi$
$67$	2.58881	0.316273	0.158137	+	0.987417i	$0.449451\pi$
$68$	−6.65771	−0.807366
$69$	−13.5851	−1.63546
$70$	−0.868708	−0.103831
$71$	11.4587	1.35990	0.679949	−	0.733259i	$-0.262002\pi$
$71$	11.4587	1.35990	0.679949	+	0.733259i	$0.262002\pi$
$72$	0.742990	0.0875622
$73$	−1.74144	−0.203820	−0.101910	−	0.994794i	$-0.532495\pi$
$73$	−1.74144	−0.203820	−0.101910	+	0.994794i	$0.532495\pi$
$74$	2.81068	0.326735
$75$	−7.16927	−0.827836
$76$	−1.00000	−0.114708
$77$	6.78620	0.773359
$78$	4.18828	0.474230
$79$	−0.328881	−0.0370021	−0.0185010	−	0.999829i	$-0.505889\pi$
$79$	−0.328881	−0.0370021	−0.0185010	+	0.999829i	$0.505889\pi$
$80$	0.477403	0.0533753
$81$	−6.21900	−0.691000
$82$	−0.494351	−0.0545919
$83$	−12.1789	−1.33681	−0.668403	−	0.743799i	$-0.733022\pi$
$83$	−12.1789	−1.33681	−0.668403	+	0.743799i	$0.733022\pi$
$84$	2.73373	0.298274
$85$	−3.17841	−0.344747
$86$	3.56544	0.384471
$87$	15.4372	1.65504
$88$	−3.72939	−0.397554
$89$	−13.0387	−1.38210	−0.691049	−	0.722808i	$-0.742851\pi$
$89$	−13.0387	−1.38210	−0.691049	+	0.722808i	$0.742851\pi$
$90$	0.354706	0.0373893
$91$	−5.07292	−0.531786
$92$	−9.04267	−0.942763
$93$	11.5764	1.20042
$94$	−7.49608	−0.773162
$95$	−0.477403	−0.0489806
$96$	−1.50233	−0.153331
$97$	−8.73226	−0.886627	−0.443313	−	0.896367i	$-0.646197\pi$
$97$	−8.73226	−0.886627	−0.443313	+	0.896367i	$0.646197\pi$
$98$	3.68886	0.372631
$99$	−2.77090	−0.278486
$100$	−4.77209	−0.477209
$101$	−16.2341	−1.61536	−0.807679	−	0.589623i	$-0.799276\pi$
$101$	−16.2341	−1.61536	−0.807679	+	0.589623i	$0.799276\pi$
$102$	10.0021	0.990357
$103$	−7.61230	−0.750062	−0.375031	−	0.927012i	$-0.622368\pi$
$103$	−7.61230	−0.750062	−0.375031	+	0.927012i	$0.622368\pi$
$104$	2.78785	0.273371
$105$	1.30509	0.127364
$106$	−10.9125	−1.05991
$107$	−15.1771	−1.46723	−0.733613	−	0.679568i	$-0.762167\pi$
$107$	−15.1771	−1.46723	−0.733613	+	0.679568i	$0.762167\pi$
$108$	−5.62322	−0.541095
$109$	1.96894	0.188591	0.0942954	−	0.995544i	$-0.469940\pi$
$109$	1.96894	0.188591	0.0942954	+	0.995544i	$0.469940\pi$
$110$	−1.78042	−0.169757
$111$	−4.22258	−0.400790
$112$	1.81965	0.171941
$113$	−16.5300	−1.55501	−0.777504	−	0.628879i	$-0.783514\pi$
$113$	−16.5300	−1.55501	−0.777504	+	0.628879i	$0.783514\pi$
$114$	1.50233	0.140707
$115$	−4.31700	−0.402562
$116$	10.2754	0.954051
$117$	2.07134	0.191496
$118$	11.3081	1.04100
$119$	−12.1147	−1.11056
$120$	−0.717220	−0.0654729
$121$	2.90835	0.264395
$122$	−3.68257	−0.333404
$123$	0.742680	0.0669652
$124$	7.70560	0.691983
$125$	−4.66523	−0.417271
$126$	1.35198	0.120444
$127$	−1.47910	−0.131249	−0.0656246	−	0.997844i	$-0.520904\pi$
$127$	−1.47910	−0.131249	−0.0656246	+	0.997844i	$0.520904\pi$
$128$	−1.00000	−0.0883883
$129$	−5.35648	−0.471612
$130$	1.33093	0.116730
$131$	10.6669	0.931973	0.465986	−	0.884792i	$-0.345700\pi$
$131$	10.6669	0.931973	0.465986	+	0.884792i	$0.345700\pi$
$132$	5.60279	0.487660
$133$	−1.81965	−0.157784
$134$	−2.58881	−0.223639
$135$	−2.68455	−0.231049
$136$	6.65771	0.570894
$137$	−4.88892	−0.417689	−0.208844	−	0.977949i	$-0.566970\pi$
$137$	−4.88892	−0.417689	−0.208844	+	0.977949i	$0.566970\pi$
$138$	13.5851	1.15644
$139$	−1.46986	−0.124672	−0.0623358	−	0.998055i	$-0.519855\pi$
$139$	−1.46986	−0.124672	−0.0623358	+	0.998055i	$0.519855\pi$
$140$	0.868708	0.0734193
$141$	11.2616	0.948400
$142$	−11.4587	−0.961593
$143$	−10.3970	−0.869439
$144$	−0.742990	−0.0619158
$145$	4.90553	0.407382
$146$	1.74144	0.144122
$147$	−5.54191	−0.457089
$148$	−2.81068	−0.231036
$149$	7.43479	0.609081	0.304541	−	0.952499i	$-0.401497\pi$
$149$	7.43479	0.609081	0.304541	+	0.952499i	$0.401497\pi$
$150$	7.16927	0.585369
$151$	4.85805	0.395342	0.197671	−	0.980268i	$-0.436662\pi$
$151$	4.85805	0.395342	0.197671	+	0.980268i	$0.436662\pi$
$152$	1.00000	0.0811107
$153$	4.94661	0.399910
$154$	−6.78620	−0.546847
$155$	3.67868	0.295478
$156$	−4.18828	−0.335331
$157$	−11.9079	−0.950354	−0.475177	−	0.879890i	$-0.657616\pi$
$157$	−11.9079	−0.950354	−0.475177	+	0.879890i	$0.657616\pi$
$158$	0.328881	0.0261644
$159$	16.3942	1.30015
$160$	−0.477403	−0.0377421
$161$	−16.4545	−1.29680
$162$	6.21900	0.488610
$163$	−10.7129	−0.839098	−0.419549	−	0.907733i	$-0.637812\pi$
$163$	−10.7129	−0.839098	−0.419549	+	0.907733i	$0.637812\pi$
$164$	0.494351	0.0386023
$165$	2.67479	0.208232
$166$	12.1789	0.945265
$167$	7.22335	0.558960	0.279480	−	0.960152i	$-0.409838\pi$
$167$	7.22335	0.558960	0.279480	+	0.960152i	$0.409838\pi$
$168$	−2.73373	−0.210912
$169$	−5.22790	−0.402146
$170$	3.17841	0.243773
$171$	0.742990	0.0568179
$172$	−3.56544	−0.271862
$173$	−6.67132	−0.507211	−0.253606	−	0.967308i	$-0.581617\pi$
$173$	−6.67132	−0.507211	−0.253606	+	0.967308i	$0.581617\pi$
$174$	−15.4372	−1.17029
$175$	−8.68354	−0.656414
$176$	3.72939	0.281113
$177$	−16.9886	−1.27694
$178$	13.0387	0.977291
$179$	5.22855	0.390800	0.195400	−	0.980724i	$-0.437399\pi$
$179$	5.22855	0.390800	0.195400	+	0.980724i	$0.437399\pi$
$180$	−0.354706	−0.0264382
$181$	5.24070	0.389538	0.194769	−	0.980849i	$-0.437604\pi$
$181$	5.24070	0.389538	0.194769	+	0.980849i	$0.437604\pi$
$182$	5.07292	0.376030
$183$	5.53245	0.408970
$184$	9.04267	0.666634
$185$	−1.34183	−0.0986532
$186$	−11.5764	−0.848822
$187$	−24.8292	−1.81569
$188$	7.49608	0.546708
$189$	−10.2323	−0.744292
$190$	0.477403	0.0346345
$191$	−1.72281	−0.124658	−0.0623290	−	0.998056i	$-0.519853\pi$
$191$	−1.72281	−0.124658	−0.0623290	+	0.998056i	$0.519853\pi$
$192$	1.50233	0.108422
$193$	−24.2033	−1.74219	−0.871096	−	0.491112i	$-0.836590\pi$
$193$	−24.2033	−1.74219	−0.871096	+	0.491112i	$0.836590\pi$
$194$	8.73226	0.626940
$195$	−1.99950	−0.143187
$196$	−3.68886	−0.263490
$197$	4.93840	0.351846	0.175923	−	0.984404i	$-0.443709\pi$
$197$	4.93840	0.351846	0.175923	+	0.984404i	$0.443709\pi$
$198$	2.77090	0.196919
$199$	16.5232	1.17130	0.585651	−	0.810563i	$-0.300839\pi$
$199$	16.5232	1.17130	0.585651	+	0.810563i	$0.300839\pi$
$200$	4.77209	0.337437
$201$	3.88925	0.274327
$202$	16.2341	1.14223
$203$	18.6977	1.31232
$204$	−10.0021	−0.700288
$205$	0.236005	0.0164833
$206$	7.61230	0.530374
$207$	6.71861	0.466976
$208$	−2.78785	−0.193303
$209$	−3.72939	−0.257967
$210$	−1.30509	−0.0900598
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	10.9125	0.749473
$213$	17.2148	1.17954
$214$	15.1771	1.03749
$215$	−1.70215	−0.116086
$216$	5.62322	0.382612
$217$	14.0215	0.951842
$218$	−1.96894	−0.133354
$219$	−2.61622	−0.176788
$220$	1.78042	0.120036
$221$	18.5607	1.24853
$222$	4.22258	0.283401
$223$	10.8053	0.723577	0.361788	−	0.932260i	$-0.382166\pi$
$223$	10.8053	0.723577	0.361788	+	0.932260i	$0.382166\pi$
$224$	−1.81965	−0.121581
$225$	3.54561	0.236374
$226$	16.5300	1.09956
$227$	11.2983	0.749897	0.374949	−	0.927046i	$-0.377660\pi$
$227$	11.2983	0.749897	0.374949	+	0.927046i	$0.377660\pi$
$228$	−1.50233	−0.0994946
$229$	−16.5741	−1.09524	−0.547622	−	0.836726i	$-0.684467\pi$
$229$	−16.5741	−1.09524	−0.547622	+	0.836726i	$0.684467\pi$
$230$	4.31700	0.284655
$231$	10.1951	0.670791
$232$	−10.2754	−0.674616
$233$	−23.1141	−1.51425	−0.757126	−	0.653269i	$-0.773397\pi$
$233$	−23.1141	−1.51425	−0.757126	+	0.653269i	$0.773397\pi$
$234$	−2.07134	−0.135408
$235$	3.57866	0.233446
$236$	−11.3081	−0.736096
$237$	−0.494090	−0.0320946
$238$	12.1147	0.785281
$239$	16.8488	1.08986	0.544930	−	0.838482i	$-0.316556\pi$
$239$	16.8488	1.08986	0.544930	+	0.838482i	$0.316556\pi$
$240$	0.717220	0.0462963
$241$	9.43534	0.607783	0.303892	−	0.952707i	$-0.401714\pi$
$241$	9.43534	0.607783	0.303892	+	0.952707i	$0.401714\pi$
$242$	−2.90835	−0.186956
$243$	7.52666	0.482835
$244$	3.68257	0.235752
$245$	−1.76108	−0.112511
$246$	−0.742680	−0.0473516
$247$	2.78785	0.177387
$248$	−7.70560	−0.489306
$249$	−18.2968	−1.15951
$250$	4.66523	0.295055
$251$	21.3849	1.34980	0.674902	−	0.737907i	$-0.264186\pi$
$251$	21.3849	1.34980	0.674902	+	0.737907i	$0.264186\pi$
$252$	−1.35198	−0.0851670
$253$	−33.7236	−2.12019
$254$	1.47910	0.0928071
$255$	−4.77504	−0.299025
$256$	1.00000	0.0625000
$257$	18.2912	1.14097	0.570486	−	0.821308i	$-0.306755\pi$
$257$	18.2912	1.14097	0.570486	+	0.821308i	$0.306755\pi$
$258$	5.35648	0.333480
$259$	−5.11446	−0.317797
$260$	−1.33093	−0.0825407
$261$	−7.63455	−0.472567
$262$	−10.6669	−0.659004
$263$	−6.06669	−0.374088	−0.187044	−	0.982352i	$-0.559891\pi$
$263$	−6.06669	−0.374088	−0.187044	+	0.982352i	$0.559891\pi$
$264$	−5.60279	−0.344828
$265$	5.20966	0.320027
$266$	1.81965	0.111570
$267$	−19.5885	−1.19880
$268$	2.58881	0.158137
$269$	−6.38956	−0.389578	−0.194789	−	0.980845i	$-0.562402\pi$
$269$	−6.38956	−0.389578	−0.194789	+	0.980845i	$0.562402\pi$
$270$	2.68455	0.163376
$271$	−21.6222	−1.31346	−0.656728	−	0.754128i	$-0.728060\pi$
$271$	−21.6222	−1.31346	−0.656728	+	0.754128i	$0.728060\pi$
$272$	−6.65771	−0.403683
$273$	−7.62122	−0.461257
$274$	4.88892	0.295351
$275$	−17.7970	−1.07320
$276$	−13.5851	−0.817728
$277$	7.46173	0.448332	0.224166	−	0.974551i	$-0.428034\pi$
$277$	7.46173	0.448332	0.224166	+	0.974551i	$0.428034\pi$
$278$	1.46986	0.0881561
$279$	−5.72518	−0.342758
$280$	−0.868708	−0.0519153
$281$	−6.86267	−0.409393	−0.204696	−	0.978826i	$-0.565621\pi$
$281$	−6.86267	−0.409393	−0.204696	+	0.978826i	$0.565621\pi$
$282$	−11.2616	−0.670620
$283$	−27.2428	−1.61941	−0.809707	−	0.586834i	$-0.800374\pi$
$283$	−27.2428	−1.61941	−0.809707	+	0.586834i	$0.800374\pi$
$284$	11.4587	0.679949
$285$	−0.717220	−0.0424844
$286$	10.3970	0.614786
$287$	0.899547	0.0530986
$288$	0.742990	0.0437811
$289$	27.3251	1.60736
$290$	−4.90553	−0.288063
$291$	−13.1188	−0.769036
$292$	−1.74144	−0.101910
$293$	8.41021	0.491330	0.245665	−	0.969355i	$-0.420994\pi$
$293$	8.41021	0.491330	0.245665	+	0.969355i	$0.420994\pi$
$294$	5.54191	0.323211
$295$	−5.39854	−0.314315
$296$	2.81068	0.163367
$297$	−20.9712	−1.21687
$298$	−7.43479	−0.430686
$299$	25.2096	1.45791
$300$	−7.16927	−0.413918
$301$	−6.48786	−0.373954
$302$	−4.85805	−0.279549
$303$	−24.3891	−1.40112
$304$	−1.00000	−0.0573539
$305$	1.75807	0.100667
$306$	−4.94661	−0.282779
$307$	−7.82912	−0.446832	−0.223416	−	0.974723i	$-0.571721\pi$
$307$	−7.82912	−0.446832	−0.223416	+	0.974723i	$0.571721\pi$
$308$	6.78620	0.386679
$309$	−11.4362	−0.650584
$310$	−3.67868	−0.208935
$311$	8.63616	0.489712	0.244856	−	0.969559i	$-0.421259\pi$
$311$	8.63616	0.489712	0.244856	+	0.969559i	$0.421259\pi$
$312$	4.18828	0.237115
$313$	−12.3352	−0.697226	−0.348613	−	0.937267i	$-0.613347\pi$
$313$	−12.3352	−0.697226	−0.348613	+	0.937267i	$0.613347\pi$
$314$	11.9079	0.672002
$315$	−0.645442	−0.0363665
$316$	−0.328881	−0.0185010
$317$	−11.3061	−0.635014	−0.317507	−	0.948256i	$-0.602846\pi$
$317$	−11.3061	−0.635014	−0.317507	+	0.948256i	$0.602846\pi$
$318$	−16.3942	−0.919341
$319$	38.3211	2.14557
$320$	0.477403	0.0266877
$321$	−22.8011	−1.27263
$322$	16.4545	0.916975
$323$	6.65771	0.370445
$324$	−6.21900	−0.345500
$325$	13.3039	0.737965
$326$	10.7129	0.593332
$327$	2.95801	0.163579
$328$	−0.494351	−0.0272959
$329$	13.6403	0.752012
$330$	−2.67479	−0.147242
$331$	21.5327	1.18355	0.591773	−	0.806105i	$-0.298428\pi$
$331$	21.5327	1.18355	0.591773	+	0.806105i	$0.298428\pi$
$332$	−12.1789	−0.668403
$333$	2.08831	0.114439
$334$	−7.22335	−0.395244
$335$	1.23591	0.0675247
$336$	2.73373	0.149137
$337$	−31.8729	−1.73623	−0.868115	−	0.496363i	$-0.834668\pi$
$337$	−31.8729	−1.73623	−0.868115	+	0.496363i	$0.834668\pi$
$338$	5.22790	0.284360
$339$	−24.8335	−1.34877
$340$	−3.17841	−0.172374
$341$	28.7372	1.55620
$342$	−0.742990	−0.0401763
$343$	−19.4500	−1.05020
$344$	3.56544	0.192235
$345$	−6.48558	−0.349172
$346$	6.67132	0.358652
$347$	8.13899	0.436924	0.218462	−	0.975845i	$-0.429896\pi$
$347$	8.13899	0.436924	0.218462	+	0.975845i	$0.429896\pi$
$348$	15.4372	0.827518
$349$	−27.0992	−1.45059	−0.725295	−	0.688439i	$-0.758296\pi$
$349$	−27.0992	−1.45059	−0.725295	+	0.688439i	$0.758296\pi$
$350$	8.68354	0.464155
$351$	15.6767	0.836760
$352$	−3.72939	−0.198777
$353$	0.844232	0.0449339	0.0224670	−	0.999748i	$-0.492848\pi$
$353$	0.844232	0.0449339	0.0224670	+	0.999748i	$0.492848\pi$
$354$	16.9886	0.902933
$355$	5.47043	0.290340
$356$	−13.0387	−0.691049
$357$	−18.2004	−0.963266
$358$	−5.22855	−0.276337
$359$	−30.3215	−1.60031	−0.800154	−	0.599794i	$-0.795249\pi$
$359$	−30.3215	−1.60031	−0.800154	+	0.599794i	$0.795249\pi$
$360$	0.354706	0.0186946
$361$	1.00000	0.0526316
$362$	−5.24070	−0.275445
$363$	4.36931	0.229330
$364$	−5.07292	−0.265893
$365$	−0.831367	−0.0435158
$366$	−5.53245	−0.289186
$367$	−14.1710	−0.739722	−0.369861	−	0.929087i	$-0.620595\pi$
$367$	−14.1710	−0.739722	−0.369861	+	0.929087i	$0.620595\pi$
$368$	−9.04267	−0.471382
$369$	−0.367298	−0.0191207
$370$	1.34183	0.0697583
$371$	19.8569	1.03092
$372$	11.5764	0.600208
$373$	−30.3434	−1.57112	−0.785560	−	0.618786i	$-0.787625\pi$
$373$	−30.3434	−1.57112	−0.785560	+	0.618786i	$0.787625\pi$
$374$	24.8292	1.28389
$375$	−7.00873	−0.361929
$376$	−7.49608	−0.386581
$377$	−28.6464	−1.47536
$378$	10.2323	0.526294
$379$	−23.4299	−1.20351	−0.601757	−	0.798679i	$-0.705533\pi$
$379$	−23.4299	−1.20351	−0.601757	+	0.798679i	$0.705533\pi$
$380$	−0.477403	−0.0244903
$381$	−2.22211	−0.113842
$382$	1.72281	0.0881466
$383$	14.5278	0.742334	0.371167	−	0.928566i	$-0.378958\pi$
$383$	14.5278	0.742334	0.371167	+	0.928566i	$0.378958\pi$
$384$	−1.50233	−0.0766657
$385$	3.23975	0.165113
$386$	24.2033	1.23192
$387$	2.64908	0.134661
$388$	−8.73226	−0.443313
$389$	15.3520	0.778379	0.389190	−	0.921158i	$-0.372755\pi$
$389$	15.3520	0.778379	0.389190	+	0.921158i	$0.372755\pi$
$390$	1.99950	0.101249
$391$	60.2035	3.04462
$392$	3.68886	0.186316
$393$	16.0253	0.808369
$394$	−4.93840	−0.248793
$395$	−0.157009	−0.00789999
$396$	−2.77090	−0.139243
$397$	26.4158	1.32577	0.662885	−	0.748721i	$-0.269332\pi$
$397$	26.4158	1.32577	0.662885	+	0.748721i	$0.269332\pi$
$398$	−16.5232	−0.828236
$399$	−2.73373	−0.136858
$400$	−4.77209	−0.238604
$401$	−6.58176	−0.328678	−0.164339	−	0.986404i	$-0.552549\pi$
$401$	−6.58176	−0.328678	−0.164339	+	0.986404i	$0.552549\pi$
$402$	−3.88925	−0.193978
$403$	−21.4820	−1.07010
$404$	−16.2341	−0.807679
$405$	−2.96897	−0.147529
$406$	−18.6977	−0.927953
$407$	−10.4821	−0.519580
$408$	10.0021	0.495178
$409$	−0.966471	−0.0477889	−0.0238945	−	0.999714i	$-0.507607\pi$
$409$	−0.966471	−0.0477889	−0.0238945	+	0.999714i	$0.507607\pi$
$410$	−0.236005	−0.0116554
$411$	−7.34480	−0.362292
$412$	−7.61230	−0.375031
$413$	−20.5769	−1.01252
$414$	−6.71861	−0.330202
$415$	−5.81424	−0.285410
$416$	2.78785	0.136686
$417$	−2.20822	−0.108137
$418$	3.72939	0.182410
$419$	23.4182	1.14406	0.572028	−	0.820234i	$-0.306157\pi$
$419$	23.4182	1.14406	0.572028	+	0.820234i	$0.306157\pi$
$420$	1.30509	0.0636819
$421$	−1.97774	−0.0963889	−0.0481945	−	0.998838i	$-0.515347\pi$
$421$	−1.97774	−0.0963889	−0.0481945	+	0.998838i	$0.515347\pi$
$422$	1.00000	0.0486792
$423$	−5.56951	−0.270799
$424$	−10.9125	−0.529957
$425$	31.7712	1.54113
$426$	−17.2148	−0.834061
$427$	6.70099	0.324284
$428$	−15.1771	−0.733613
$429$	−15.6197	−0.754128
$430$	1.70215	0.0820850
$431$	25.2296	1.21527	0.607633	−	0.794218i	$-0.292119\pi$
$431$	25.2296	1.21527	0.607633	+	0.794218i	$0.292119\pi$
$432$	−5.62322	−0.270548
$433$	5.82213	0.279794	0.139897	−	0.990166i	$-0.455323\pi$
$433$	5.82213	0.279794	0.139897	+	0.990166i	$0.455323\pi$
$434$	−14.0215	−0.673054
$435$	7.36975	0.353352
$436$	1.96894	0.0942954
$437$	9.04267	0.432570
$438$	2.61622	0.125008
$439$	14.4731	0.690761	0.345381	−	0.938463i	$-0.387750\pi$
$439$	14.4731	0.690761	0.345381	+	0.938463i	$0.387750\pi$
$440$	−1.78042	−0.0848784
$441$	2.74079	0.130514
$442$	−18.5607	−0.882842
$443$	2.24416	0.106623	0.0533116	−	0.998578i	$-0.483022\pi$
$443$	2.24416	0.106623	0.0533116	+	0.998578i	$0.483022\pi$
$444$	−4.22258	−0.200395
$445$	−6.22471	−0.295080
$446$	−10.8053	−0.511646
$447$	11.1695	0.528301
$448$	1.81965	0.0859705
$449$	−28.0791	−1.32514	−0.662568	−	0.749002i	$-0.730533\pi$
$449$	−28.0791	−1.32514	−0.662568	+	0.749002i	$0.730533\pi$
$450$	−3.54561	−0.167142
$451$	1.84363	0.0868130
$452$	−16.5300	−0.777504
$453$	7.29841	0.342909
$454$	−11.2983	−0.530257
$455$	−2.42183	−0.113537
$456$	1.50233	0.0703533
$457$	10.5461	0.493326	0.246663	−	0.969101i	$-0.420666\pi$
$457$	10.5461	0.493326	0.246663	+	0.969101i	$0.420666\pi$
$458$	16.5741	0.774455
$459$	37.4378	1.74745
$460$	−4.31700	−0.201281
$461$	−42.0384	−1.95792	−0.978962	−	0.204043i	$-0.934592\pi$
$461$	−42.0384	−1.95792	−0.978962	+	0.204043i	$0.934592\pi$
$462$	−10.1951	−0.474321
$463$	16.2752	0.756375	0.378187	−	0.925729i	$-0.376547\pi$
$463$	16.2752	0.756375	0.378187	+	0.925729i	$0.376547\pi$
$464$	10.2754	0.477025
$465$	5.52660	0.256290
$466$	23.1141	1.07074
$467$	18.4526	0.853882	0.426941	−	0.904279i	$-0.359591\pi$
$467$	18.4526	0.853882	0.426941	+	0.904279i	$0.359591\pi$
$468$	2.07134	0.0957479
$469$	4.71073	0.217521
$470$	−3.57866	−0.165071
$471$	−17.8897	−0.824312
$472$	11.3081	0.520499
$473$	−13.2969	−0.611392
$474$	0.494090	0.0226943
$475$	4.77209	0.218958
$476$	−12.1147	−0.555278
$477$	−8.10787	−0.371234
$478$	−16.8488	−0.770647
$479$	17.9958	0.822250	0.411125	−	0.911579i	$-0.365136\pi$
$479$	17.9958	0.822250	0.411125	+	0.911579i	$0.365136\pi$
$480$	−0.717220	−0.0327365
$481$	7.83575	0.357279
$482$	−9.43534	−0.429768
$483$	−24.7202	−1.12481
$484$	2.90835	0.132198
$485$	−4.16881	−0.189296
$486$	−7.52666	−0.341416
$487$	−41.8738	−1.89748	−0.948741	−	0.316055i	$-0.897642\pi$
$487$	−41.8738	−1.89748	−0.948741	+	0.316055i	$0.897642\pi$
$488$	−3.68257	−0.166702
$489$	−16.0943	−0.727812
$490$	1.76108	0.0795573
$491$	33.6671	1.51938	0.759688	−	0.650288i	$-0.225352\pi$
$491$	33.6671	1.51938	0.759688	+	0.650288i	$0.225352\pi$
$492$	0.742680	0.0334826
$493$	−68.4109	−3.08107
$494$	−2.78785	−0.125431
$495$	−1.32284	−0.0594571
$496$	7.70560	0.345991
$497$	20.8509	0.935289
$498$	18.2968	0.819898
$499$	−1.25125	−0.0560136	−0.0280068	−	0.999608i	$-0.508916\pi$
$499$	−1.25125	−0.0560136	−0.0280068	+	0.999608i	$0.508916\pi$
$500$	−4.66523	−0.208635
$501$	10.8519	0.484827
$502$	−21.3849	−0.954456
$503$	35.3258	1.57510	0.787550	−	0.616251i	$-0.211349\pi$
$503$	35.3258	1.57510	0.787550	+	0.616251i	$0.211349\pi$
$504$	1.35198	0.0602222
$505$	−7.75023	−0.344881
$506$	33.7236	1.49920
$507$	−7.85406	−0.348811
$508$	−1.47910	−0.0656246
$509$	19.5467	0.866391	0.433195	−	0.901300i	$-0.357386\pi$
$509$	19.5467	0.866391	0.433195	+	0.901300i	$0.357386\pi$
$510$	4.77504	0.211442
$511$	−3.16881	−0.140180
$512$	−1.00000	−0.0441942
$513$	5.62322	0.248271
$514$	−18.2912	−0.806788
$515$	−3.63414	−0.160139
$516$	−5.35648	−0.235806
$517$	27.9558	1.22950
$518$	5.11446	0.224717
$519$	−10.0226	−0.439941
$520$	1.33093	0.0583651
$521$	−8.21538	−0.359922	−0.179961	−	0.983674i	$-0.557597\pi$
$521$	−8.21538	−0.359922	−0.179961	+	0.983674i	$0.557597\pi$
$522$	7.63455	0.334155
$523$	−7.75531	−0.339116	−0.169558	−	0.985520i	$-0.554234\pi$
$523$	−7.75531	−0.339116	−0.169558	+	0.985520i	$0.554234\pi$
$524$	10.6669	0.465986
$525$	−13.0456	−0.569356
$526$	6.06669	0.264520
$527$	−51.3016	−2.23473
$528$	5.60279	0.243830
$529$	58.7699	2.55521
$530$	−5.20966	−0.226293
$531$	8.40182	0.364608
$532$	−1.81965	−0.0788920
$533$	−1.37817	−0.0596954
$534$	19.5885	0.847676
$535$	−7.24560	−0.313255
$536$	−2.58881	−0.111819
$537$	7.85503	0.338970
$538$	6.38956	0.275474
$539$	−13.7572	−0.592565
$540$	−2.68455	−0.115524
$541$	−17.1262	−0.736315	−0.368157	−	0.929763i	$-0.620011\pi$
$541$	−17.1262	−0.736315	−0.368157	+	0.929763i	$0.620011\pi$
$542$	21.6222	0.928753
$543$	7.87329	0.337875
$544$	6.65771	0.285447
$545$	0.939981	0.0402644
$546$	7.62122	0.326158
$547$	33.2557	1.42191	0.710955	−	0.703237i	$-0.248263\pi$
$547$	33.2557	1.42191	0.710955	+	0.703237i	$0.248263\pi$
$548$	−4.88892	−0.208844
$549$	−2.73611	−0.116774
$550$	17.7970	0.758865
$551$	−10.2754	−0.437748
$552$	13.5851	0.578221
$553$	−0.598450	−0.0254487
$554$	−7.46173	−0.317019
$555$	−2.01588	−0.0855691
$556$	−1.46986	−0.0623358
$557$	−6.16496	−0.261218	−0.130609	−	0.991434i	$-0.541693\pi$
$557$	−6.16496	−0.261218	−0.130609	+	0.991434i	$0.541693\pi$
$558$	5.72518	0.242366
$559$	9.93990	0.420413
$560$	0.868708	0.0367096
$561$	−37.3018	−1.57488
$562$	6.86267	0.289484
$563$	1.15020	0.0484752	0.0242376	−	0.999706i	$-0.492284\pi$
$563$	1.15020	0.0484752	0.0242376	+	0.999706i	$0.492284\pi$
$564$	11.2616	0.474200
$565$	−7.89146	−0.331996
$566$	27.2428	1.14510
$567$	−11.3164	−0.475245
$568$	−11.4587	−0.480797
$569$	1.75569	0.0736023	0.0368012	−	0.999323i	$-0.488283\pi$
$569$	1.75569	0.0736023	0.0368012	+	0.999323i	$0.488283\pi$
$570$	0.717220	0.0300410
$571$	24.4399	1.02278	0.511388	−	0.859350i	$-0.329131\pi$
$571$	24.4399	1.02278	0.511388	+	0.859350i	$0.329131\pi$
$572$	−10.3970	−0.434719
$573$	−2.58824	−0.108125
$574$	−0.899547	−0.0375463
$575$	43.1524	1.79958
$576$	−0.742990	−0.0309579
$577$	20.3751	0.848227	0.424114	−	0.905609i	$-0.360586\pi$
$577$	20.3751	0.848227	0.424114	+	0.905609i	$0.360586\pi$
$578$	−27.3251	−1.13658
$579$	−36.3615	−1.51113
$580$	4.90553	0.203691
$581$	−22.1613	−0.919408
$582$	13.1188	0.543791
$583$	40.6969	1.68549
$584$	1.74144	0.0720611
$585$	0.988866	0.0408846
$586$	−8.41021	−0.347422
$587$	22.8753	0.944166	0.472083	−	0.881554i	$-0.343502\pi$
$587$	22.8753	0.944166	0.472083	+	0.881554i	$0.343502\pi$
$588$	−5.54191	−0.228544
$589$	−7.70560	−0.317504
$590$	5.39854	0.222254
$591$	7.41913	0.305182
$592$	−2.81068	−0.115518
$593$	4.51557	0.185432	0.0927162	−	0.995693i	$-0.470445\pi$
$593$	4.51557	0.185432	0.0927162	+	0.995693i	$0.470445\pi$
$594$	20.9712	0.860459
$595$	−5.78361	−0.237105
$596$	7.43479	0.304541
$597$	24.8235	1.01596
$598$	−25.2096	−1.03090
$599$	−0.0856596	−0.00349995	−0.00174998	−	0.999998i	$-0.500557\pi$
$599$	−0.0856596	−0.00349995	−0.00174998	+	0.999998i	$0.500557\pi$
$600$	7.16927	0.292684
$601$	−25.6115	−1.04471	−0.522357	−	0.852727i	$-0.674947\pi$
$601$	−25.6115	−1.04471	−0.522357	+	0.852727i	$0.674947\pi$
$602$	6.48786	0.264425
$603$	−1.92346	−0.0783292
$604$	4.85805	0.197671
$605$	1.38846	0.0564488
$606$	24.3891	0.990740
$607$	46.7172	1.89619	0.948096	−	0.317984i	$-0.103006\pi$
$607$	46.7172	1.89619	0.948096	+	0.317984i	$0.103006\pi$
$608$	1.00000	0.0405554
$609$	28.0903	1.13827
$610$	−1.75807	−0.0711822
$611$	−20.8979	−0.845440
$612$	4.94661	0.199955
$613$	36.0338	1.45539	0.727695	−	0.685900i	$-0.240591\pi$
$613$	36.0338	1.45539	0.727695	+	0.685900i	$0.240591\pi$
$614$	7.82912	0.315958
$615$	0.354558	0.0142972
$616$	−6.78620	−0.273424
$617$	−1.74578	−0.0702825	−0.0351413	−	0.999382i	$-0.511188\pi$
$617$	−1.74578	−0.0702825	−0.0351413	+	0.999382i	$0.511188\pi$
$618$	11.4362	0.460032
$619$	−2.94838	−0.118505	−0.0592527	−	0.998243i	$-0.518872\pi$
$619$	−2.94838	−0.118505	−0.0592527	+	0.998243i	$0.518872\pi$
$620$	3.67868	0.147739
$621$	50.8490	2.04050
$622$	−8.63616	−0.346279
$623$	−23.7259	−0.950558
$624$	−4.18828	−0.167665
$625$	21.6332	0.865329
$626$	12.3352	0.493014
$627$	−5.60279	−0.223754
$628$	−11.9079	−0.475177
$629$	18.7127	0.746124
$630$	0.645442	0.0257150
$631$	−1.44209	−0.0574089	−0.0287044	−	0.999588i	$-0.509138\pi$
$631$	−1.44209	−0.0574089	−0.0287044	+	0.999588i	$0.509138\pi$
$632$	0.328881	0.0130822
$633$	−1.50233	−0.0597124
$634$	11.3061	0.449023
$635$	−0.706128	−0.0280219
$636$	16.3942	0.650073
$637$	10.2840	0.407467
$638$	−38.3211	−1.51715
$639$	−8.51371	−0.336797
$640$	−0.477403	−0.0188710
$641$	−17.6190	−0.695907	−0.347953	−	0.937512i	$-0.613123\pi$
$641$	−17.6190	−0.695907	−0.347953	+	0.937512i	$0.613123\pi$
$642$	22.8011	0.899887
$643$	−3.46650	−0.136705	−0.0683527	−	0.997661i	$-0.521774\pi$
$643$	−3.46650	−0.136705	−0.0683527	+	0.997661i	$0.521774\pi$
$644$	−16.4545	−0.648399
$645$	−2.55720	−0.100690
$646$	−6.65771	−0.261944
$647$	8.88818	0.349430	0.174715	−	0.984619i	$-0.444100\pi$
$647$	8.88818	0.349430	0.174715	+	0.984619i	$0.444100\pi$
$648$	6.21900	0.244305
$649$	−42.1724	−1.65541
$650$	−13.3039	−0.521820
$651$	21.0650	0.825603
$652$	−10.7129	−0.419549
$653$	−22.9425	−0.897810	−0.448905	−	0.893579i	$-0.648186\pi$
$653$	−22.9425	−0.897810	−0.448905	+	0.893579i	$0.648186\pi$
$654$	−2.95801	−0.115668
$655$	5.09242	0.198977
$656$	0.494351	0.0193011
$657$	1.29387	0.0504787
$658$	−13.6403	−0.531753
$659$	−20.7846	−0.809655	−0.404827	−	0.914393i	$-0.632668\pi$
$659$	−20.7846	−0.809655	−0.404827	+	0.914393i	$0.632668\pi$
$660$	2.67479	0.104116
$661$	8.31521	0.323424	0.161712	−	0.986838i	$-0.448298\pi$
$661$	8.31521	0.323424	0.161712	+	0.986838i	$0.448298\pi$
$662$	−21.5327	−0.836893
$663$	27.8844	1.08294
$664$	12.1789	0.472632
$665$	−0.868708	−0.0336871
$666$	−2.08831	−0.0809203
$667$	−92.9174	−3.59778
$668$	7.22335	0.279480
$669$	16.2332	0.627611
$670$	−1.23591	−0.0477472
$671$	13.7337	0.530185
$672$	−2.73373	−0.105456
$673$	49.2848	1.89979	0.949894	−	0.312572i	$-0.101191\pi$
$673$	49.2848	1.89979	0.949894	+	0.312572i	$0.101191\pi$
$674$	31.8729	1.22770
$675$	26.8345	1.03286
$676$	−5.22790	−0.201073
$677$	24.8750	0.956025	0.478012	−	0.878353i	$-0.341357\pi$
$677$	24.8750	0.956025	0.478012	+	0.878353i	$0.341357\pi$
$678$	24.8335	0.953726
$679$	−15.8897	−0.609790
$680$	3.17841	0.121887
$681$	16.9739	0.650441
$682$	−28.7372	−1.10040
$683$	−19.2023	−0.734757	−0.367379	−	0.930072i	$-0.619745\pi$
$683$	−19.2023	−0.734757	−0.367379	+	0.930072i	$0.619745\pi$
$684$	0.742990	0.0284089
$685$	−2.33399	−0.0891771
$686$	19.4500	0.742605
$687$	−24.8998	−0.949986
$688$	−3.56544	−0.135931
$689$	−30.4224	−1.15900
$690$	6.48558	0.246902
$691$	−49.5701	−1.88573	−0.942867	−	0.333169i	$-0.891882\pi$
$691$	−49.5701	−1.88573	−0.942867	+	0.333169i	$0.891882\pi$
$692$	−6.67132	−0.253606
$693$	−5.04208	−0.191533
$694$	−8.13899	−0.308952
$695$	−0.701714	−0.0266175
$696$	−15.4372	−0.585144
$697$	−3.29124	−0.124665
$698$	27.0992	1.02572
$699$	−34.7250	−1.31342
$700$	−8.68354	−0.328207
$701$	−37.3576	−1.41098	−0.705489	−	0.708721i	$-0.749273\pi$
$701$	−37.3576	−1.41098	−0.705489	+	0.708721i	$0.749273\pi$
$702$	−15.6767	−0.591679
$703$	2.81068	0.106007
$704$	3.72939	0.140557
$705$	5.37634	0.202485
$706$	−0.844232	−0.0317731
$707$	−29.5405	−1.11099
$708$	−16.9886	−0.638470
$709$	25.4152	0.954488	0.477244	−	0.878771i	$-0.341636\pi$
$709$	25.4152	0.954488	0.477244	+	0.878771i	$0.341636\pi$
$710$	−5.47043	−0.205301
$711$	0.244356	0.00916405
$712$	13.0387	0.488645
$713$	−69.6792	−2.60950
$714$	18.2004	0.681132
$715$	−4.96355	−0.185626
$716$	5.22855	0.195400
$717$	25.3126	0.945315
$718$	30.3215	1.13159
$719$	−24.7149	−0.921710	−0.460855	−	0.887475i	$-0.652457\pi$
$719$	−24.7149	−0.921710	−0.460855	+	0.887475i	$0.652457\pi$
$720$	−0.354706	−0.0132191
$721$	−13.8517	−0.515866
$722$	−1.00000	−0.0372161
$723$	14.1750	0.527175
$724$	5.24070	0.194769
$725$	−49.0353	−1.82112
$726$	−4.36931	−0.162160
$727$	2.06911	0.0767391	0.0383695	−	0.999264i	$-0.487784\pi$
$727$	2.06911	0.0767391	0.0383695	+	0.999264i	$0.487784\pi$
$728$	5.07292	0.188015
$729$	29.9645	1.10980
$730$	0.831367	0.0307703
$731$	23.7377	0.877969
$732$	5.53245	0.204485
$733$	−32.3259	−1.19398	−0.596992	−	0.802247i	$-0.703638\pi$
$733$	−32.3259	−1.19398	−0.596992	+	0.802247i	$0.703638\pi$
$734$	14.1710	0.523063
$735$	−2.64573	−0.0975891
$736$	9.04267	0.333317
$737$	9.65467	0.355634
$738$	0.367298	0.0135204
$739$	−39.0505	−1.43650	−0.718248	−	0.695787i	$-0.755056\pi$
$739$	−39.0505	−1.43650	−0.718248	+	0.695787i	$0.755056\pi$
$740$	−1.34183	−0.0493266
$741$	4.18828	0.153860
$742$	−19.8569	−0.728971
$743$	17.9407	0.658181	0.329090	−	0.944298i	$-0.393258\pi$
$743$	17.9407	0.658181	0.329090	+	0.944298i	$0.393258\pi$
$744$	−11.5764	−0.424411
$745$	3.54939	0.130040
$746$	30.3434	1.11095
$747$	9.04879	0.331078
$748$	−24.8292	−0.907846
$749$	−27.6171	−1.00911
$750$	7.00873	0.255923
$751$	21.2647	0.775959	0.387979	−	0.921668i	$-0.373173\pi$
$751$	21.2647	0.775959	0.387979	+	0.921668i	$0.373173\pi$
$752$	7.49608	0.273354
$753$	32.1273	1.17078
$754$	28.6464	1.04324
$755$	2.31925	0.0844061
$756$	−10.2323	−0.372146
$757$	−23.7681	−0.863867	−0.431933	−	0.901906i	$-0.642168\pi$
$757$	−23.7681	−0.863867	−0.431933	+	0.901906i	$0.642168\pi$
$758$	23.4299	0.851013
$759$	−50.6642	−1.83899
$760$	0.477403	0.0173172
$761$	42.8711	1.55408	0.777039	−	0.629453i	$-0.216721\pi$
$761$	42.8711	1.55408	0.777039	+	0.629453i	$0.216721\pi$
$762$	2.22211	0.0804984
$763$	3.58280	0.129706
$764$	−1.72281	−0.0623290
$765$	2.36153	0.0853813
$766$	−14.5278	−0.524909
$767$	31.5253	1.13831
$768$	1.50233	0.0542108
$769$	19.9215	0.718388	0.359194	−	0.933263i	$-0.383052\pi$
$769$	19.9215	0.718388	0.359194	+	0.933263i	$0.383052\pi$
$770$	−3.23975	−0.116753
$771$	27.4794	0.989648
$772$	−24.2033	−0.871096
$773$	−21.2037	−0.762646	−0.381323	−	0.924442i	$-0.624531\pi$
$773$	−21.2037	−0.762646	−0.381323	+	0.924442i	$0.624531\pi$
$774$	−2.64908	−0.0952194
$775$	−36.7718	−1.32088
$776$	8.73226	0.313470
$777$	−7.68364	−0.275649
$778$	−15.3520	−0.550397
$779$	−0.494351	−0.0177119
$780$	−1.99950	−0.0715936
$781$	42.7340	1.52914
$782$	−60.2035	−2.15287
$783$	−57.7811	−2.06493
$784$	−3.68886	−0.131745
$785$	−5.68487	−0.202902
$786$	−16.0253	−0.571603
$787$	−37.2901	−1.32925	−0.664625	−	0.747177i	$-0.731409\pi$
$787$	−37.2901	−1.32925	−0.664625	+	0.747177i	$0.731409\pi$
$788$	4.93840	0.175923
$789$	−9.11420	−0.324474
$790$	0.157009	0.00558613
$791$	−30.0788	−1.06948
$792$	2.77090	0.0984596
$793$	−10.2664	−0.364572
$794$	−26.4158	−0.937461
$795$	7.82665	0.277583
$796$	16.5232	0.585651
$797$	−44.1419	−1.56359	−0.781793	−	0.623538i	$-0.785695\pi$
$797$	−44.1419	−1.56359	−0.781793	+	0.623538i	$0.785695\pi$
$798$	2.73373	0.0967729
$799$	−49.9068	−1.76557
$800$	4.77209	0.168719
$801$	9.68761	0.342295
$802$	6.58176	0.232410
$803$	−6.49449	−0.229186
$804$	3.88925	0.137163
$805$	−7.85544	−0.276868
$806$	21.4820	0.756672
$807$	−9.59926	−0.337910
$808$	16.2341	0.571115
$809$	25.1728	0.885028	0.442514	−	0.896762i	$-0.354087\pi$
$809$	25.1728	0.885028	0.442514	+	0.896762i	$0.354087\pi$
$810$	2.96897	0.104319
$811$	10.3910	0.364879	0.182439	−	0.983217i	$-0.441601\pi$
$811$	10.3910	0.364879	0.182439	+	0.983217i	$0.441601\pi$
$812$	18.6977	0.656162
$813$	−32.4838	−1.13926
$814$	10.4821	0.367398
$815$	−5.11437	−0.179149
$816$	−10.0021	−0.350144
$817$	3.56544	0.124739
$818$	0.966471	0.0337919
$819$	3.76913	0.131704
$820$	0.236005	0.00824164
$821$	−30.6205	−1.06866	−0.534332	−	0.845275i	$-0.679437\pi$
$821$	−30.6205	−1.06866	−0.534332	+	0.845275i	$0.679437\pi$
$822$	7.34480	0.256179
$823$	−49.2774	−1.71770	−0.858852	−	0.512224i	$-0.828822\pi$
$823$	−49.2774	−1.71770	−0.858852	+	0.512224i	$0.828822\pi$
$824$	7.61230	0.265187
$825$	−26.7370	−0.930863
$826$	20.5769	0.715961
$827$	25.8305	0.898215	0.449108	−	0.893478i	$-0.351742\pi$
$827$	25.8305	0.898215	0.449108	+	0.893478i	$0.351742\pi$
$828$	6.71861	0.233488
$829$	−11.4653	−0.398208	−0.199104	−	0.979978i	$-0.563803\pi$
$829$	−11.4653	−0.398208	−0.199104	+	0.979978i	$0.563803\pi$
$830$	5.81424	0.201815
$831$	11.2100	0.388871
$832$	−2.78785	−0.0966513
$833$	24.5594	0.850932
$834$	2.20822	0.0764643
$835$	3.44845	0.119339
$836$	−3.72939	−0.128984
$837$	−43.3303	−1.49771
$838$	−23.4182	−0.808970
$839$	−46.9342	−1.62035	−0.810175	−	0.586188i	$-0.800628\pi$
$839$	−46.9342	−1.62035	−0.810175	+	0.586188i	$0.800628\pi$
$840$	−1.30509	−0.0450299
$841$	76.5847	2.64085
$842$	1.97774	0.0681573
$843$	−10.3100	−0.355096
$844$	−1.00000	−0.0344214
$845$	−2.49582	−0.0858587
$846$	5.56951	0.191484
$847$	5.29219	0.181842
$848$	10.9125	0.374736
$849$	−40.9278	−1.40464
$850$	−31.7712	−1.08974
$851$	25.4161	0.871251
$852$	17.2148	0.589770
$853$	18.3740	0.629113	0.314557	−	0.949239i	$-0.398144\pi$
$853$	18.3740	0.629113	0.314557	+	0.949239i	$0.398144\pi$
$854$	−6.70099	−0.229303
$855$	0.354706	0.0121307
$856$	15.1771	0.518743
$857$	15.2051	0.519397	0.259698	−	0.965690i	$-0.416377\pi$
$857$	15.2051	0.519397	0.259698	+	0.965690i	$0.416377\pi$
$858$	15.6197	0.533249
$859$	−10.6679	−0.363986	−0.181993	−	0.983300i	$-0.558255\pi$
$859$	−10.6679	−0.363986	−0.181993	+	0.983300i	$0.558255\pi$
$860$	−1.70215	−0.0580429
$861$	1.35142	0.0460563
$862$	−25.2296	−0.859323
$863$	−0.578329	−0.0196866	−0.00984328	−	0.999952i	$-0.503133\pi$
$863$	−0.578329	−0.0196866	−0.00984328	+	0.999952i	$0.503133\pi$
$864$	5.62322	0.191306
$865$	−3.18491	−0.108290
$866$	−5.82213	−0.197844
$867$	41.0515	1.39418
$868$	14.0215	0.475921
$869$	−1.22653	−0.0416071
$870$	−7.36975	−0.249858
$871$	−7.21720	−0.244546
$872$	−1.96894	−0.0666769
$873$	6.48798	0.219585
$874$	−9.04267	−0.305873
$875$	−8.48909	−0.286984
$876$	−2.61622	−0.0883939
$877$	−40.1636	−1.35623	−0.678114	−	0.734956i	$-0.737203\pi$
$877$	−40.1636	−1.35623	−0.678114	+	0.734956i	$0.737203\pi$
$878$	−14.4731	−0.488442
$879$	12.6349	0.426166
$880$	1.78042	0.0600181
$881$	20.8651	0.702963	0.351481	−	0.936195i	$-0.385678\pi$
$881$	20.8651	0.702963	0.351481	+	0.936195i	$0.385678\pi$
$882$	−2.74079	−0.0922871
$883$	−32.0948	−1.08008	−0.540038	−	0.841640i	$-0.681590\pi$
$883$	−32.0948	−1.08008	−0.540038	+	0.841640i	$0.681590\pi$
$884$	18.5607	0.624264
$885$	−8.11041	−0.272628
$886$	−2.24416	−0.0753940
$887$	23.5376	0.790316	0.395158	−	0.918613i	$-0.370690\pi$
$887$	23.5376	0.790316	0.395158	+	0.918613i	$0.370690\pi$
$888$	4.22258	0.141701
$889$	−2.69145	−0.0902684
$890$	6.22471	0.208653
$891$	−23.1931	−0.776997
$892$	10.8053	0.361788
$893$	−7.49608	−0.250847
$894$	−11.1695	−0.373565
$895$	2.49613	0.0834363
$896$	−1.81965	−0.0607903
$897$	37.8732	1.26455
$898$	28.0791	0.937012
$899$	79.1784	2.64075
$900$	3.54561	0.118187
$901$	−72.6522	−2.42040
$902$	−1.84363	−0.0613860
$903$	−9.74694	−0.324358
$904$	16.5300	0.549778
$905$	2.50193	0.0831669
$906$	−7.29841	−0.242473
$907$	−33.1958	−1.10225	−0.551124	−	0.834423i	$-0.685801\pi$
$907$	−33.1958	−1.10225	−0.551124	+	0.834423i	$0.685801\pi$
$908$	11.2983	0.374949
$909$	12.0618	0.400065
$910$	2.42183	0.0802828
$911$	−15.5029	−0.513635	−0.256817	−	0.966460i	$-0.582674\pi$
$911$	−15.5029	−0.513635	−0.256817	+	0.966460i	$0.582674\pi$
$912$	−1.50233	−0.0497473
$913$	−45.4198	−1.50318
$914$	−10.5461	−0.348834
$915$	2.64121	0.0873157
$916$	−16.5741	−0.547622
$917$	19.4101	0.640978
$918$	−37.4378	−1.23563
$919$	40.6039	1.33940	0.669699	−	0.742632i	$-0.266423\pi$
$919$	40.6039	1.33940	0.669699	+	0.742632i	$0.266423\pi$
$920$	4.31700	0.142327
$921$	−11.7620	−0.387570
$922$	42.0384	1.38446
$923$	−31.9451	−1.05149
$924$	10.1951	0.335395
$925$	13.4128	0.441010
$926$	−16.2752	−0.534838
$927$	5.65586	0.185763
$928$	−10.2754	−0.337308
$929$	25.3944	0.833162	0.416581	−	0.909099i	$-0.363228\pi$
$929$	25.3944	0.833162	0.416581	+	0.909099i	$0.363228\pi$
$930$	−5.52660	−0.181225
$931$	3.68886	0.120898
$932$	−23.1141	−0.757126
$933$	12.9744	0.424763
$934$	−18.4526	−0.603786
$935$	−11.8535	−0.387652
$936$	−2.07134	−0.0677040
$937$	15.4401	0.504406	0.252203	−	0.967674i	$-0.418845\pi$
$937$	15.4401	0.504406	0.252203	+	0.967674i	$0.418845\pi$
$938$	−4.71073	−0.153811
$939$	−18.5316	−0.604756
$940$	3.57866	0.116723
$941$	6.22860	0.203046	0.101523	−	0.994833i	$-0.467628\pi$
$941$	6.22860	0.203046	0.101523	+	0.994833i	$0.467628\pi$
$942$	17.8897	0.582877
$943$	−4.47025	−0.145571
$944$	−11.3081	−0.368048
$945$	−4.88494	−0.158907
$946$	13.2969	0.432320
$947$	41.8401	1.35962	0.679810	−	0.733388i	$-0.262062\pi$
$947$	41.8401	1.35962	0.679810	+	0.733388i	$0.262062\pi$
$948$	−0.494090	−0.0160473
$949$	4.85486	0.157595
$950$	−4.77209	−0.154827
$951$	−16.9856	−0.550794
$952$	12.1147	0.392641
$953$	37.2073	1.20526	0.602632	−	0.798019i	$-0.294119\pi$
$953$	37.2073	1.20526	0.602632	+	0.798019i	$0.294119\pi$
$954$	8.10787	0.262502
$955$	−0.822475	−0.0266147
$956$	16.8488	0.544930
$957$	57.5712	1.86101
$958$	−17.9958	−0.581419
$959$	−8.89614	−0.287272
$960$	0.717220	0.0231482
$961$	28.3762	0.915361
$962$	−7.83575	−0.252635
$963$	11.2764	0.363378
$964$	9.43534	0.303892
$965$	−11.5547	−0.371960
$966$	24.7202	0.795359
$967$	−24.2498	−0.779823	−0.389911	−	0.920852i	$-0.627494\pi$
$967$	−24.2498	−0.779823	−0.389911	+	0.920852i	$0.627494\pi$
$968$	−2.90835	−0.0934779
$969$	10.0021	0.321314
$970$	4.16881	0.133852
$971$	−29.6548	−0.951666	−0.475833	−	0.879536i	$-0.657853\pi$
$971$	−29.6548	−0.951666	−0.475833	+	0.879536i	$0.657853\pi$
$972$	7.52666	0.241418
$973$	−2.67463	−0.0857446
$974$	41.8738	1.34172
$975$	19.9868	0.640091
$976$	3.68257	0.117876
$977$	48.6719	1.55715	0.778577	−	0.627550i	$-0.215942\pi$
$977$	48.6719	1.55715	0.778577	+	0.627550i	$0.215942\pi$
$978$	16.0943	0.514641
$979$	−48.6264	−1.55410
$980$	−1.76108	−0.0562555
$981$	−1.46291	−0.0467070
$982$	−33.6671	−1.07436
$983$	51.2339	1.63411	0.817054	−	0.576562i	$-0.195606\pi$
$983$	51.2339	1.63411	0.817054	+	0.576562i	$0.195606\pi$
$984$	−0.742680	−0.0236758
$985$	2.35761	0.0751196
$986$	68.4109	2.17865
$987$	20.4923	0.652276
$988$	2.78785	0.0886933
$989$	32.2411	1.02521
$990$	1.32284	0.0420425
$991$	−37.8760	−1.20317	−0.601585	−	0.798809i	$-0.705464\pi$
$991$	−37.8760	−1.20317	−0.601585	+	0.798809i	$0.705464\pi$
$992$	−7.70560	−0.244653
$993$	32.3494	1.02658
$994$	−20.8509	−0.661350
$995$	7.88826	0.250075
$996$	−18.2968	−0.579755
$997$	26.6441	0.843826	0.421913	−	0.906636i	$-0.361359\pi$
$997$	26.6441	0.843826	0.421913	+	0.906636i	$0.361359\pi$
$998$	1.25125	0.0396076
$999$	15.8051	0.500051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.26	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.26	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.50233 q^{3} +1.00000 q^{4} +0.477403 q^{5} -1.50233 q^{6} +1.81965 q^{7} -1.00000 q^{8} -0.742990 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.50233 q^{3} +1.00000 q^{4} +0.477403 q^{5} -1.50233 q^{6} +1.81965 q^{7} -1.00000 q^{8} -0.742990 q^{9} -0.477403 q^{10} +3.72939 q^{11} +1.50233 q^{12} -2.78785 q^{13} -1.81965 q^{14} +0.717220 q^{15} +1.00000 q^{16} -6.65771 q^{17} +0.742990 q^{18} -1.00000 q^{19} +0.477403 q^{20} +2.73373 q^{21} -3.72939 q^{22} -9.04267 q^{23} -1.50233 q^{24} -4.77209 q^{25} +2.78785 q^{26} -5.62322 q^{27} +1.81965 q^{28} +10.2754 q^{29} -0.717220 q^{30} +7.70560 q^{31} -1.00000 q^{32} +5.60279 q^{33} +6.65771 q^{34} +0.868708 q^{35} -0.742990 q^{36} -2.81068 q^{37} +1.00000 q^{38} -4.18828 q^{39} -0.477403 q^{40} +0.494351 q^{41} -2.73373 q^{42} -3.56544 q^{43} +3.72939 q^{44} -0.354706 q^{45} +9.04267 q^{46} +7.49608 q^{47} +1.50233 q^{48} -3.68886 q^{49} +4.77209 q^{50} -10.0021 q^{51} -2.78785 q^{52} +10.9125 q^{53} +5.62322 q^{54} +1.78042 q^{55} -1.81965 q^{56} -1.50233 q^{57} -10.2754 q^{58} -11.3081 q^{59} +0.717220 q^{60} +3.68257 q^{61} -7.70560 q^{62} -1.35198 q^{63} +1.00000 q^{64} -1.33093 q^{65} -5.60279 q^{66} +2.58881 q^{67} -6.65771 q^{68} -13.5851 q^{69} -0.868708 q^{70} +11.4587 q^{71} +0.742990 q^{72} -1.74144 q^{73} +2.81068 q^{74} -7.16927 q^{75} -1.00000 q^{76} +6.78620 q^{77} +4.18828 q^{78} -0.328881 q^{79} +0.477403 q^{80} -6.21900 q^{81} -0.494351 q^{82} -12.1789 q^{83} +2.73373 q^{84} -3.17841 q^{85} +3.56544 q^{86} +15.4372 q^{87} -3.72939 q^{88} -13.0387 q^{89} +0.354706 q^{90} -5.07292 q^{91} -9.04267 q^{92} +11.5764 q^{93} -7.49608 q^{94} -0.477403 q^{95} -1.50233 q^{96} -8.73226 q^{97} +3.68886 q^{98} -2.77090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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