LMFDB - Embedded newform 8018.2.a.d.1.10

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:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.46114 q^{3} +1.00000 q^{4} +1.82408 q^{5} -1.46114 q^{6} -2.77663 q^{7} +1.00000 q^{8} -0.865063 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.46114 q^{3} +1.00000 q^{4} +1.82408 q^{5} -1.46114 q^{6} -2.77663 q^{7} +1.00000 q^{8} -0.865063 q^{9} +1.82408 q^{10} -1.21614 q^{11} -1.46114 q^{12} +1.42796 q^{13} -2.77663 q^{14} -2.66525 q^{15} +1.00000 q^{16} +4.88240 q^{17} -0.865063 q^{18} +1.00000 q^{19} +1.82408 q^{20} +4.05705 q^{21} -1.21614 q^{22} +7.05784 q^{23} -1.46114 q^{24} -1.67272 q^{25} +1.42796 q^{26} +5.64741 q^{27} -2.77663 q^{28} -10.2436 q^{29} -2.66525 q^{30} -7.99282 q^{31} +1.00000 q^{32} +1.77695 q^{33} +4.88240 q^{34} -5.06481 q^{35} -0.865063 q^{36} -7.54026 q^{37} +1.00000 q^{38} -2.08645 q^{39} +1.82408 q^{40} -0.862262 q^{41} +4.05705 q^{42} -5.82798 q^{43} -1.21614 q^{44} -1.57795 q^{45} +7.05784 q^{46} +8.09691 q^{47} -1.46114 q^{48} +0.709678 q^{49} -1.67272 q^{50} -7.13388 q^{51} +1.42796 q^{52} +2.56029 q^{53} +5.64741 q^{54} -2.21834 q^{55} -2.77663 q^{56} -1.46114 q^{57} -10.2436 q^{58} -3.58628 q^{59} -2.66525 q^{60} -3.47477 q^{61} -7.99282 q^{62} +2.40196 q^{63} +1.00000 q^{64} +2.60472 q^{65} +1.77695 q^{66} +14.8212 q^{67} +4.88240 q^{68} -10.3125 q^{69} -5.06481 q^{70} -0.424097 q^{71} -0.865063 q^{72} +8.16655 q^{73} -7.54026 q^{74} +2.44408 q^{75} +1.00000 q^{76} +3.37677 q^{77} -2.08645 q^{78} +10.3349 q^{79} +1.82408 q^{80} -5.65648 q^{81} -0.862262 q^{82} -10.4403 q^{83} +4.05705 q^{84} +8.90591 q^{85} -5.82798 q^{86} +14.9674 q^{87} -1.21614 q^{88} +6.13887 q^{89} -1.57795 q^{90} -3.96492 q^{91} +7.05784 q^{92} +11.6786 q^{93} +8.09691 q^{94} +1.82408 q^{95} -1.46114 q^{96} -9.03631 q^{97} +0.709678 q^{98} +1.05204 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	−1.46114	−0.843591	−0.421795	−	0.906691i	$-0.638600\pi$
$3$	−1.46114	−0.843591	−0.421795	+	0.906691i	$0.638600\pi$
$4$	1.00000	0.500000
$5$	1.82408	0.815755	0.407878	−	0.913037i	$-0.366269\pi$
$5$	1.82408	0.815755	0.407878	+	0.913037i	$0.366269\pi$
$6$	−1.46114	−0.596509
$7$	−2.77663	−1.04947	−0.524734	−	0.851266i	$-0.675835\pi$
$7$	−2.77663	−1.04947	−0.524734	+	0.851266i	$0.675835\pi$
$8$	1.00000	0.353553
$9$	−0.865063	−0.288354
$10$	1.82408	0.576826
$11$	−1.21614	−0.366680	−0.183340	−	0.983050i	$-0.558691\pi$
$11$	−1.21614	−0.366680	−0.183340	+	0.983050i	$0.558691\pi$
$12$	−1.46114	−0.421795
$13$	1.42796	0.396045	0.198022	−	0.980197i	$-0.436548\pi$
$13$	1.42796	0.396045	0.198022	+	0.980197i	$0.436548\pi$
$14$	−2.77663	−0.742086
$15$	−2.66525	−0.688164
$16$	1.00000	0.250000
$17$	4.88240	1.18416	0.592078	−	0.805881i	$-0.298308\pi$
$17$	4.88240	1.18416	0.592078	+	0.805881i	$0.298308\pi$
$18$	−0.865063	−0.203897
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.82408	0.407878
$21$	4.05705	0.885321
$22$	−1.21614	−0.259282
$23$	7.05784	1.47166	0.735830	−	0.677166i	$-0.236792\pi$
$23$	7.05784	1.47166	0.735830	+	0.677166i	$0.236792\pi$
$24$	−1.46114	−0.298254
$25$	−1.67272	−0.334543
$26$	1.42796	0.280046
$27$	5.64741	1.08684
$28$	−2.77663	−0.524734
$29$	−10.2436	−1.90219	−0.951097	−	0.308893i	$-0.900042\pi$
$29$	−10.2436	−1.90219	−0.951097	+	0.308893i	$0.900042\pi$
$30$	−2.66525	−0.486605
$31$	−7.99282	−1.43555	−0.717776	−	0.696274i	$-0.754840\pi$
$31$	−7.99282	−1.43555	−0.717776	+	0.696274i	$0.754840\pi$
$32$	1.00000	0.176777
$33$	1.77695	0.309328
$34$	4.88240	0.837325
$35$	−5.06481	−0.856109
$36$	−0.865063	−0.144177
$37$	−7.54026	−1.23961	−0.619805	−	0.784756i	$-0.712788\pi$
$37$	−7.54026	−1.23961	−0.619805	+	0.784756i	$0.712788\pi$
$38$	1.00000	0.162221
$39$	−2.08645	−0.334100
$40$	1.82408	0.288413
$41$	−0.862262	−0.134663	−0.0673313	−	0.997731i	$-0.521448\pi$
$41$	−0.862262	−0.134663	−0.0673313	+	0.997731i	$0.521448\pi$
$42$	4.05705	0.626017
$43$	−5.82798	−0.888758	−0.444379	−	0.895839i	$-0.646576\pi$
$43$	−5.82798	−0.888758	−0.444379	+	0.895839i	$0.646576\pi$
$44$	−1.21614	−0.183340
$45$	−1.57795	−0.235227
$46$	7.05784	1.04062
$47$	8.09691	1.18106	0.590528	−	0.807017i	$-0.298920\pi$
$47$	8.09691	1.18106	0.590528	+	0.807017i	$0.298920\pi$
$48$	−1.46114	−0.210898
$49$	0.709678	0.101383
$50$	−1.67272	−0.236558
$51$	−7.13388	−0.998943
$52$	1.42796	0.198022
$53$	2.56029	0.351683	0.175841	−	0.984419i	$-0.443735\pi$
$53$	2.56029	0.351683	0.175841	+	0.984419i	$0.443735\pi$
$54$	5.64741	0.768515
$55$	−2.21834	−0.299121
$56$	−2.77663	−0.371043
$57$	−1.46114	−0.193533
$58$	−10.2436	−1.34505
$59$	−3.58628	−0.466894	−0.233447	−	0.972370i	$-0.575000\pi$
$59$	−3.58628	−0.466894	−0.233447	+	0.972370i	$0.575000\pi$
$60$	−2.66525	−0.344082
$61$	−3.47477	−0.444899	−0.222450	−	0.974944i	$-0.571405\pi$
$61$	−3.47477	−0.444899	−0.222450	+	0.974944i	$0.571405\pi$
$62$	−7.99282	−1.01509
$63$	2.40196	0.302619
$64$	1.00000	0.125000
$65$	2.60472	0.323076
$66$	1.77695	0.218728
$67$	14.8212	1.81069	0.905347	−	0.424673i	$-0.139611\pi$
$67$	14.8212	1.81069	0.905347	+	0.424673i	$0.139611\pi$
$68$	4.88240	0.592078
$69$	−10.3125	−1.24148
$70$	−5.06481	−0.605360
$71$	−0.424097	−0.0503310	−0.0251655	−	0.999683i	$-0.508011\pi$
$71$	−0.424097	−0.0503310	−0.0251655	+	0.999683i	$0.508011\pi$
$72$	−0.865063	−0.101949
$73$	8.16655	0.955822	0.477911	−	0.878408i	$-0.341394\pi$
$73$	8.16655	0.955822	0.477911	+	0.878408i	$0.341394\pi$
$74$	−7.54026	−0.876537
$75$	2.44408	0.282218
$76$	1.00000	0.114708
$77$	3.37677	0.384818
$78$	−2.08645	−0.236244
$79$	10.3349	1.16277	0.581386	−	0.813628i	$-0.302511\pi$
$79$	10.3349	1.16277	0.581386	+	0.813628i	$0.302511\pi$
$80$	1.82408	0.203939
$81$	−5.65648	−0.628497
$82$	−0.862262	−0.0952209
$83$	−10.4403	−1.14597	−0.572983	−	0.819567i	$-0.694214\pi$
$83$	−10.4403	−1.14597	−0.572983	+	0.819567i	$0.694214\pi$
$84$	4.05705	0.442661
$85$	8.90591	0.965981
$86$	−5.82798	−0.628447
$87$	14.9674	1.60467
$88$	−1.21614	−0.129641
$89$	6.13887	0.650719	0.325359	−	0.945590i	$-0.394515\pi$
$89$	6.13887	0.650719	0.325359	+	0.945590i	$0.394515\pi$
$90$	−1.57795	−0.166330
$91$	−3.96492	−0.415636
$92$	7.05784	0.735830
$93$	11.6786	1.21102
$94$	8.09691	0.835133
$95$	1.82408	0.187147
$96$	−1.46114	−0.149127
$97$	−9.03631	−0.917499	−0.458749	−	0.888566i	$-0.651702\pi$
$97$	−9.03631	−0.917499	−0.458749	+	0.888566i	$0.651702\pi$
$98$	0.709678	0.0716883
$99$	1.05204	0.105734
$100$	−1.67272	−0.167272
$101$	−15.2409	−1.51653	−0.758265	−	0.651947i	$-0.773952\pi$
$101$	−15.2409	−1.51653	−0.758265	+	0.651947i	$0.773952\pi$
$102$	−7.13388	−0.706359
$103$	−1.13743	−0.112075	−0.0560373	−	0.998429i	$-0.517847\pi$
$103$	−1.13743	−0.112075	−0.0560373	+	0.998429i	$0.517847\pi$
$104$	1.42796	0.140023
$105$	7.40041	0.722206
$106$	2.56029	0.248677
$107$	−3.71361	−0.359008	−0.179504	−	0.983757i	$-0.557449\pi$
$107$	−3.71361	−0.359008	−0.179504	+	0.983757i	$0.557449\pi$
$108$	5.64741	0.543422
$109$	−7.68678	−0.736260	−0.368130	−	0.929774i	$-0.620002\pi$
$109$	−7.68678	−0.736260	−0.368130	+	0.929774i	$0.620002\pi$
$110$	−2.21834	−0.211510
$111$	11.0174	1.04572
$112$	−2.77663	−0.262367
$113$	3.56486	0.335354	0.167677	−	0.985842i	$-0.446374\pi$
$113$	3.56486	0.335354	0.167677	+	0.985842i	$0.446374\pi$
$114$	−1.46114	−0.136849
$115$	12.8741	1.20052
$116$	−10.2436	−0.951097
$117$	−1.23528	−0.114201
$118$	−3.58628	−0.330144
$119$	−13.5566	−1.24273
$120$	−2.66525	−0.243303
$121$	−9.52101	−0.865546
$122$	−3.47477	−0.314591
$123$	1.25989	0.113600
$124$	−7.99282	−0.717776
$125$	−12.1716	−1.08866
$126$	2.40196	0.213984
$127$	12.0562	1.06981	0.534906	−	0.844911i	$-0.320347\pi$
$127$	12.0562	1.06981	0.534906	+	0.844911i	$0.320347\pi$
$128$	1.00000	0.0883883
$129$	8.51550	0.749748
$130$	2.60472	0.228449
$131$	−5.02274	−0.438839	−0.219419	−	0.975631i	$-0.570416\pi$
$131$	−5.02274	−0.438839	−0.219419	+	0.975631i	$0.570416\pi$
$132$	1.77695	0.154664
$133$	−2.77663	−0.240764
$134$	14.8212	1.28035
$135$	10.3013	0.886599
$136$	4.88240	0.418662
$137$	6.60500	0.564303	0.282152	−	0.959370i	$-0.408952\pi$
$137$	6.60500	0.564303	0.282152	+	0.959370i	$0.408952\pi$
$138$	−10.3125	−0.877859
$139$	−8.51196	−0.721975	−0.360987	−	0.932571i	$-0.617560\pi$
$139$	−8.51196	−0.721975	−0.360987	+	0.932571i	$0.617560\pi$
$140$	−5.06481	−0.428054
$141$	−11.8307	−0.996328
$142$	−0.424097	−0.0355894
$143$	−1.73660	−0.145222
$144$	−0.865063	−0.0720886
$145$	−18.6852	−1.55172
$146$	8.16655	0.675869
$147$	−1.03694	−0.0855254
$148$	−7.54026	−0.619805
$149$	−19.5391	−1.60071	−0.800353	−	0.599529i	$-0.795355\pi$
$149$	−19.5391	−1.60071	−0.800353	+	0.599529i	$0.795355\pi$
$150$	2.44408	0.199558
$151$	10.5323	0.857109	0.428555	−	0.903516i	$-0.359023\pi$
$151$	10.5323	0.857109	0.428555	+	0.903516i	$0.359023\pi$
$152$	1.00000	0.0811107
$153$	−4.22358	−0.341457
$154$	3.37677	0.272108
$155$	−14.5796	−1.17106
$156$	−2.08645	−0.167050
$157$	−10.4380	−0.833045	−0.416522	−	0.909125i	$-0.636751\pi$
$157$	−10.4380	−0.833045	−0.416522	+	0.909125i	$0.636751\pi$
$158$	10.3349	0.822204
$159$	−3.74095	−0.296676
$160$	1.82408	0.144207
$161$	−19.5970	−1.54446
$162$	−5.65648	−0.444415
$163$	18.4883	1.44811	0.724057	−	0.689740i	$-0.242275\pi$
$163$	18.4883	1.44811	0.724057	+	0.689740i	$0.242275\pi$
$164$	−0.862262	−0.0673313
$165$	3.24131	0.252336
$166$	−10.4403	−0.810321
$167$	−6.60100	−0.510801	−0.255400	−	0.966835i	$-0.582207\pi$
$167$	−6.60100	−0.510801	−0.255400	+	0.966835i	$0.582207\pi$
$168$	4.05705	0.313008
$169$	−10.9609	−0.843148
$170$	8.90591	0.683052
$171$	−0.865063	−0.0661530
$172$	−5.82798	−0.444379
$173$	12.6258	0.959918	0.479959	−	0.877291i	$-0.340651\pi$
$173$	12.6258	0.959918	0.479959	+	0.877291i	$0.340651\pi$
$174$	14.9674	1.13468
$175$	4.64451	0.351092
$176$	−1.21614	−0.0916699
$177$	5.24006	0.393867
$178$	6.13887	0.460128
$179$	−15.6437	−1.16927	−0.584634	−	0.811297i	$-0.698762\pi$
$179$	−15.6437	−1.16927	−0.584634	+	0.811297i	$0.698762\pi$
$180$	−1.57795	−0.117613
$181$	12.5304	0.931375	0.465687	−	0.884949i	$-0.345807\pi$
$181$	12.5304	0.931375	0.465687	+	0.884949i	$0.345807\pi$
$182$	−3.96492	−0.293899
$183$	5.07714	0.375313
$184$	7.05784	0.520311
$185$	−13.7541	−1.01122
$186$	11.6786	0.856320
$187$	−5.93768	−0.434206
$188$	8.09691	0.590528
$189$	−15.6808	−1.14061
$190$	1.82408	0.132333
$191$	−26.2653	−1.90049	−0.950245	−	0.311505i	$-0.899167\pi$
$191$	−26.2653	−1.90049	−0.950245	+	0.311505i	$0.899167\pi$
$192$	−1.46114	−0.105449
$193$	−1.16834	−0.0840989	−0.0420494	−	0.999116i	$-0.513389\pi$
$193$	−1.16834	−0.0840989	−0.0420494	+	0.999116i	$0.513389\pi$
$194$	−9.03631	−0.648769
$195$	−3.80587	−0.272544
$196$	0.709678	0.0506913
$197$	−2.55178	−0.181807	−0.0909035	−	0.995860i	$-0.528975\pi$
$197$	−2.55178	−0.181807	−0.0909035	+	0.995860i	$0.528975\pi$
$198$	1.05204	0.0747650
$199$	−8.74578	−0.619972	−0.309986	−	0.950741i	$-0.600324\pi$
$199$	−8.74578	−0.619972	−0.309986	+	0.950741i	$0.600324\pi$
$200$	−1.67272	−0.118279
$201$	−21.6558	−1.52748
$202$	−15.2409	−1.07235
$203$	28.4428	1.99629
$204$	−7.13388	−0.499472
$205$	−1.57284	−0.109852
$206$	−1.13743	−0.0792487
$207$	−6.10547	−0.424360
$208$	1.42796	0.0990112
$209$	−1.21614	−0.0841221
$210$	7.40041	0.510677
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	2.56029	0.175841
$213$	0.619665	0.0424588
$214$	−3.71361	−0.253857
$215$	−10.6307	−0.725009
$216$	5.64741	0.384257
$217$	22.1931	1.50657
$218$	−7.68678	−0.520615
$219$	−11.9325	−0.806323
$220$	−2.21834	−0.149560
$221$	6.97187	0.468979
$222$	11.0174	0.739439
$223$	4.84894	0.324709	0.162355	−	0.986732i	$-0.448091\pi$
$223$	4.84894	0.324709	0.162355	+	0.986732i	$0.448091\pi$
$224$	−2.77663	−0.185521
$225$	1.44700	0.0964670
$226$	3.56486	0.237131
$227$	−14.6540	−0.972622	−0.486311	−	0.873786i	$-0.661658\pi$
$227$	−14.6540	−0.972622	−0.486311	+	0.873786i	$0.661658\pi$
$228$	−1.46114	−0.0967665
$229$	−27.3808	−1.80937	−0.904686	−	0.426078i	$-0.859895\pi$
$229$	−27.3808	−1.80937	−0.904686	+	0.426078i	$0.859895\pi$
$230$	12.8741	0.848892
$231$	−4.93394	−0.324629
$232$	−10.2436	−0.672527
$233$	−11.7025	−0.766657	−0.383329	−	0.923612i	$-0.625222\pi$
$233$	−11.7025	−0.766657	−0.383329	+	0.923612i	$0.625222\pi$
$234$	−1.23528	−0.0807525
$235$	14.7695	0.963453
$236$	−3.58628	−0.233447
$237$	−15.1008	−0.980904
$238$	−13.5566	−0.878745
$239$	13.8794	0.897781	0.448891	−	0.893587i	$-0.351819\pi$
$239$	13.8794	0.897781	0.448891	+	0.893587i	$0.351819\pi$
$240$	−2.66525	−0.172041
$241$	−16.4042	−1.05669	−0.528343	−	0.849031i	$-0.677186\pi$
$241$	−16.4042	−1.05669	−0.528343	+	0.849031i	$0.677186\pi$
$242$	−9.52101	−0.612033
$243$	−8.67731	−0.556649
$244$	−3.47477	−0.222450
$245$	1.29451	0.0827033
$246$	1.25989	0.0803275
$247$	1.42796	0.0908590
$248$	−7.99282	−0.507544
$249$	15.2547	0.966727
$250$	−12.1716	−0.769799
$251$	−19.6656	−1.24128	−0.620642	−	0.784094i	$-0.713128\pi$
$251$	−19.6656	−1.24128	−0.620642	+	0.784094i	$0.713128\pi$
$252$	2.40196	0.151309
$253$	−8.58331	−0.539628
$254$	12.0562	0.756472
$255$	−13.0128	−0.814893
$256$	1.00000	0.0625000
$257$	−12.8680	−0.802683	−0.401341	−	0.915929i	$-0.631456\pi$
$257$	−12.8680	−0.802683	−0.401341	+	0.915929i	$0.631456\pi$
$258$	8.51550	0.530152
$259$	20.9365	1.30093
$260$	2.60472	0.161538
$261$	8.86138	0.548506
$262$	−5.02274	−0.310306
$263$	−14.0847	−0.868501	−0.434250	−	0.900792i	$-0.642987\pi$
$263$	−14.0847	−0.868501	−0.434250	+	0.900792i	$0.642987\pi$
$264$	1.77695	0.109364
$265$	4.67018	0.286887
$266$	−2.77663	−0.170246
$267$	−8.96976	−0.548940
$268$	14.8212	0.905347
$269$	−7.22519	−0.440528	−0.220264	−	0.975440i	$-0.570692\pi$
$269$	−7.22519	−0.440528	−0.220264	+	0.975440i	$0.570692\pi$
$270$	10.3013	0.626920
$271$	−14.7499	−0.895990	−0.447995	−	0.894036i	$-0.647862\pi$
$271$	−14.7499	−0.895990	−0.447995	+	0.894036i	$0.647862\pi$
$272$	4.88240	0.296039
$273$	5.79331	0.350627
$274$	6.60500	0.399023
$275$	2.03425	0.122670
$276$	−10.3125	−0.620740
$277$	−6.43726	−0.386777	−0.193389	−	0.981122i	$-0.561948\pi$
$277$	−6.43726	−0.386777	−0.193389	+	0.981122i	$0.561948\pi$
$278$	−8.51196	−0.510513
$279$	6.91429	0.413948
$280$	−5.06481	−0.302680
$281$	13.9676	0.833240	0.416620	−	0.909081i	$-0.363215\pi$
$281$	13.9676	0.833240	0.416620	+	0.909081i	$0.363215\pi$
$282$	−11.8307	−0.704510
$283$	−6.75138	−0.401328	−0.200664	−	0.979660i	$-0.564310\pi$
$283$	−6.75138	−0.401328	−0.200664	+	0.979660i	$0.564310\pi$
$284$	−0.424097	−0.0251655
$285$	−2.66525	−0.157876
$286$	−1.73660	−0.102687
$287$	2.39418	0.141324
$288$	−0.865063	−0.0509743
$289$	6.83782	0.402225
$290$	−18.6852	−1.09724
$291$	13.2033	0.773993
$292$	8.16655	0.477911
$293$	−5.13724	−0.300121	−0.150060	−	0.988677i	$-0.547947\pi$
$293$	−5.13724	−0.300121	−0.150060	+	0.988677i	$0.547947\pi$
$294$	−1.03694	−0.0604756
$295$	−6.54167	−0.380871
$296$	−7.54026	−0.438269
$297$	−6.86803	−0.398524
$298$	−19.5391	−1.13187
$299$	10.0783	0.582844
$300$	2.44408	0.141109
$301$	16.1821	0.932723
$302$	10.5323	0.606068
$303$	22.2692	1.27933
$304$	1.00000	0.0573539
$305$	−6.33828	−0.362929
$306$	−4.22358	−0.241446
$307$	−19.8146	−1.13088	−0.565440	−	0.824790i	$-0.691294\pi$
$307$	−19.8146	−1.13088	−0.565440	+	0.824790i	$0.691294\pi$
$308$	3.37677	0.192409
$309$	1.66195	0.0945451
$310$	−14.5796	−0.828064
$311$	14.9239	0.846255	0.423127	−	0.906070i	$-0.360932\pi$
$311$	14.9239	0.846255	0.423127	+	0.906070i	$0.360932\pi$
$312$	−2.08645	−0.118122
$313$	−18.1988	−1.02866	−0.514328	−	0.857594i	$-0.671959\pi$
$313$	−18.1988	−1.02866	−0.514328	+	0.857594i	$0.671959\pi$
$314$	−10.4380	−0.589052
$315$	4.38138	0.246863
$316$	10.3349	0.581386
$317$	−29.2845	−1.64478	−0.822391	−	0.568922i	$-0.807361\pi$
$317$	−29.2845	−1.64478	−0.822391	+	0.568922i	$0.807361\pi$
$318$	−3.74095	−0.209782
$319$	12.4577	0.697496
$320$	1.82408	0.101969
$321$	5.42611	0.302856
$322$	−19.5970	−1.09210
$323$	4.88240	0.271664
$324$	−5.65648	−0.314249
$325$	−2.38857	−0.132494
$326$	18.4883	1.02397
$327$	11.2315	0.621102
$328$	−0.862262	−0.0476104
$329$	−22.4821	−1.23948
$330$	3.24131	0.178428
$331$	−11.3759	−0.625278	−0.312639	−	0.949872i	$-0.601213\pi$
$331$	−11.3759	−0.625278	−0.312639	+	0.949872i	$0.601213\pi$
$332$	−10.4403	−0.572983
$333$	6.52280	0.357447
$334$	−6.60100	−0.361191
$335$	27.0351	1.47708
$336$	4.05705	0.221330
$337$	2.84687	0.155079	0.0775394	−	0.996989i	$-0.475294\pi$
$337$	2.84687	0.155079	0.0775394	+	0.996989i	$0.475294\pi$
$338$	−10.9609	−0.596196
$339$	−5.20876	−0.282901
$340$	8.90591	0.482991
$341$	9.72038	0.526388
$342$	−0.865063	−0.0467773
$343$	17.4659	0.943070
$344$	−5.82798	−0.314223
$345$	−18.8109	−1.01274
$346$	12.6258	0.678765
$347$	−7.03087	−0.377437	−0.188718	−	0.982031i	$-0.560433\pi$
$347$	−7.03087	−0.377437	−0.188718	+	0.982031i	$0.560433\pi$
$348$	14.9674	0.802337
$349$	16.1992	0.867123	0.433561	−	0.901124i	$-0.357257\pi$
$349$	16.1992	0.867123	0.433561	+	0.901124i	$0.357257\pi$
$350$	4.64451	0.248260
$351$	8.06427	0.430439
$352$	−1.21614	−0.0648204
$353$	22.9606	1.22207	0.611034	−	0.791604i	$-0.290754\pi$
$353$	22.9606	1.22207	0.611034	+	0.791604i	$0.290754\pi$
$354$	5.24006	0.278506
$355$	−0.773588	−0.0410578
$356$	6.13887	0.325359
$357$	19.8082	1.04836
$358$	−15.6437	−0.826798
$359$	36.5391	1.92846	0.964229	−	0.265071i	$-0.0853953\pi$
$359$	36.5391	1.92846	0.964229	+	0.265071i	$0.0853953\pi$
$360$	−1.57795	−0.0831652
$361$	1.00000	0.0526316
$362$	12.5304	0.658582
$363$	13.9115	0.730167
$364$	−3.96492	−0.207818
$365$	14.8965	0.779717
$366$	5.07714	0.265386
$367$	25.3408	1.32278	0.661389	−	0.750043i	$-0.269967\pi$
$367$	25.3408	1.32278	0.661389	+	0.750043i	$0.269967\pi$
$368$	7.05784	0.367915
$369$	0.745911	0.0388306
$370$	−13.7541	−0.715040
$371$	−7.10898	−0.369080
$372$	11.6786	0.605510
$373$	−21.0985	−1.09244	−0.546219	−	0.837642i	$-0.683933\pi$
$373$	−21.0985	−1.09244	−0.546219	+	0.837642i	$0.683933\pi$
$374$	−5.93768	−0.307030
$375$	17.7844	0.918384
$376$	8.09691	0.417566
$377$	−14.6275	−0.753354
$378$	−15.6808	−0.806531
$379$	24.4401	1.25540	0.627701	−	0.778455i	$-0.283996\pi$
$379$	24.4401	1.25540	0.627701	+	0.778455i	$0.283996\pi$
$380$	1.82408	0.0935736
$381$	−17.6158	−0.902484
$382$	−26.2653	−1.34385
$383$	−25.8701	−1.32190	−0.660951	−	0.750429i	$-0.729847\pi$
$383$	−25.8701	−1.32190	−0.660951	+	0.750429i	$0.729847\pi$
$384$	−1.46114	−0.0745636
$385$	6.15951	0.313918
$386$	−1.16834	−0.0594669
$387$	5.04157	0.256277
$388$	−9.03631	−0.458749
$389$	16.4882	0.835983	0.417992	−	0.908451i	$-0.362734\pi$
$389$	16.4882	0.835983	0.417992	+	0.908451i	$0.362734\pi$
$390$	−3.80587	−0.192718
$391$	34.4592	1.74268
$392$	0.709678	0.0358441
$393$	7.33894	0.370201
$394$	−2.55178	−0.128557
$395$	18.8518	0.948537
$396$	1.05204	0.0528668
$397$	35.6965	1.79156	0.895778	−	0.444502i	$-0.146619\pi$
$397$	35.6965	1.79156	0.895778	+	0.444502i	$0.146619\pi$
$398$	−8.74578	−0.438386
$399$	4.05705	0.203107
$400$	−1.67272	−0.0836358
$401$	−19.5734	−0.977447	−0.488724	−	0.872439i	$-0.662537\pi$
$401$	−19.5734	−0.977447	−0.488724	+	0.872439i	$0.662537\pi$
$402$	−21.6558	−1.08009
$403$	−11.4134	−0.568543
$404$	−15.2409	−0.758265
$405$	−10.3179	−0.512700
$406$	28.4428	1.41159
$407$	9.17000	0.454540
$408$	−7.13388	−0.353180
$409$	24.6509	1.21891	0.609454	−	0.792821i	$-0.291389\pi$
$409$	24.6509	1.21891	0.609454	+	0.792821i	$0.291389\pi$
$410$	−1.57284	−0.0776770
$411$	−9.65085	−0.476041
$412$	−1.13743	−0.0560373
$413$	9.95777	0.489990
$414$	−6.10547	−0.300068
$415$	−19.0439	−0.934828
$416$	1.42796	0.0700115
$417$	12.4372	0.609051
$418$	−1.21614	−0.0594833
$419$	−32.3414	−1.57998	−0.789989	−	0.613120i	$-0.789914\pi$
$419$	−32.3414	−1.57998	−0.789989	+	0.613120i	$0.789914\pi$
$420$	7.40041	0.361103
$421$	−17.8218	−0.868581	−0.434291	−	0.900773i	$-0.643001\pi$
$421$	−17.8218	−0.868581	−0.434291	+	0.900773i	$0.643001\pi$
$422$	−1.00000	−0.0486792
$423$	−7.00434	−0.340563
$424$	2.56029	0.124339
$425$	−8.16687	−0.396151
$426$	0.619665	0.0300229
$427$	9.64816	0.466907
$428$	−3.71361	−0.179504
$429$	2.53742	0.122508
$430$	−10.6307	−0.512659
$431$	28.4446	1.37013	0.685064	−	0.728483i	$-0.259774\pi$
$431$	28.4446	1.37013	0.685064	+	0.728483i	$0.259774\pi$
$432$	5.64741	0.271711
$433$	9.12218	0.438384	0.219192	−	0.975682i	$-0.429658\pi$
$433$	9.12218	0.438384	0.219192	+	0.975682i	$0.429658\pi$
$434$	22.1931	1.06530
$435$	27.3018	1.30902
$436$	−7.68678	−0.368130
$437$	7.05784	0.337622
$438$	−11.9325	−0.570157
$439$	−25.1019	−1.19805	−0.599023	−	0.800732i	$-0.704444\pi$
$439$	−25.1019	−1.19805	−0.599023	+	0.800732i	$0.704444\pi$
$440$	−2.21834	−0.105755
$441$	−0.613916	−0.0292341
$442$	6.97187	0.331618
$443$	10.1470	0.482098	0.241049	−	0.970513i	$-0.422508\pi$
$443$	10.1470	0.482098	0.241049	+	0.970513i	$0.422508\pi$
$444$	11.0174	0.522862
$445$	11.1978	0.530827
$446$	4.84894	0.229604
$447$	28.5494	1.35034
$448$	−2.77663	−0.131183
$449$	5.78601	0.273059	0.136529	−	0.990636i	$-0.456405\pi$
$449$	5.78601	0.273059	0.136529	+	0.990636i	$0.456405\pi$
$450$	1.44700	0.0682125
$451$	1.04863	0.0493781
$452$	3.56486	0.167677
$453$	−15.3892	−0.723050
$454$	−14.6540	−0.687748
$455$	−7.23235	−0.339058
$456$	−1.46114	−0.0684243
$457$	−23.9897	−1.12219	−0.561095	−	0.827751i	$-0.689620\pi$
$457$	−23.9897	−1.12219	−0.561095	+	0.827751i	$0.689620\pi$
$458$	−27.3808	−1.27942
$459$	27.5729	1.28699
$460$	12.8741	0.600258
$461$	−34.5981	−1.61139	−0.805696	−	0.592329i	$-0.798209\pi$
$461$	−34.5981	−1.61139	−0.805696	+	0.592329i	$0.798209\pi$
$462$	−4.93394	−0.229548
$463$	−6.30630	−0.293079	−0.146539	−	0.989205i	$-0.546813\pi$
$463$	−6.30630	−0.293079	−0.146539	+	0.989205i	$0.546813\pi$
$464$	−10.2436	−0.475548
$465$	21.3028	0.987895
$466$	−11.7025	−0.542108
$467$	7.16190	0.331413	0.165707	−	0.986175i	$-0.447010\pi$
$467$	7.16190	0.331413	0.165707	+	0.986175i	$0.447010\pi$
$468$	−1.23528	−0.0571007
$469$	−41.1529	−1.90026
$470$	14.7695	0.681264
$471$	15.2514	0.702749
$472$	−3.58628	−0.165072
$473$	7.08763	0.325890
$474$	−15.1008	−0.693604
$475$	−1.67272	−0.0767495
$476$	−13.5566	−0.621367
$477$	−2.21481	−0.101409
$478$	13.8794	0.634827
$479$	−26.1422	−1.19447	−0.597234	−	0.802067i	$-0.703733\pi$
$479$	−26.1422	−1.19447	−0.597234	+	0.802067i	$0.703733\pi$
$480$	−2.66525	−0.121651
$481$	−10.7672	−0.490942
$482$	−16.4042	−0.747190
$483$	28.6340	1.30289
$484$	−9.52101	−0.432773
$485$	−16.4830	−0.748454
$486$	−8.67731	−0.393611
$487$	22.2984	1.01044	0.505218	−	0.862992i	$-0.331412\pi$
$487$	22.2984	1.01044	0.505218	+	0.862992i	$0.331412\pi$
$488$	−3.47477	−0.157296
$489$	−27.0140	−1.22162
$490$	1.29451	0.0584801
$491$	25.7119	1.16036	0.580180	−	0.814488i	$-0.302982\pi$
$491$	25.7119	1.16036	0.580180	+	0.814488i	$0.302982\pi$
$492$	1.25989	0.0568001
$493$	−50.0135	−2.25249
$494$	1.42796	0.0642470
$495$	1.91900	0.0862528
$496$	−7.99282	−0.358888
$497$	1.17756	0.0528208
$498$	15.2547	0.683579
$499$	−34.0529	−1.52442	−0.762209	−	0.647331i	$-0.775885\pi$
$499$	−34.0529	−1.52442	−0.762209	+	0.647331i	$0.775885\pi$
$500$	−12.1716	−0.544330
$501$	9.64500	0.430907
$502$	−19.6656	−0.877721
$503$	13.7182	0.611666	0.305833	−	0.952085i	$-0.401065\pi$
$503$	13.7182	0.611666	0.305833	+	0.952085i	$0.401065\pi$
$504$	2.40196	0.106992
$505$	−27.8007	−1.23712
$506$	−8.58331	−0.381575
$507$	16.0155	0.711272
$508$	12.0562	0.534906
$509$	−28.2094	−1.25036	−0.625179	−	0.780481i	$-0.714974\pi$
$509$	−28.2094	−1.25036	−0.625179	+	0.780481i	$0.714974\pi$
$510$	−13.0128	−0.576217
$511$	−22.6755	−1.00310
$512$	1.00000	0.0441942
$513$	5.64741	0.249339
$514$	−12.8680	−0.567582
$515$	−2.07477	−0.0914254
$516$	8.51550	0.374874
$517$	−9.84697	−0.433069
$518$	20.9365	0.919897
$519$	−18.4480	−0.809778
$520$	2.60472	0.114225
$521$	6.67300	0.292349	0.146175	−	0.989259i	$-0.453304\pi$
$521$	6.67300	0.292349	0.146175	+	0.989259i	$0.453304\pi$
$522$	8.86138	0.387852
$523$	27.8938	1.21971	0.609854	−	0.792513i	$-0.291228\pi$
$523$	27.8938	1.21971	0.609854	+	0.792513i	$0.291228\pi$
$524$	−5.02274	−0.219419
$525$	−6.78630	−0.296178
$526$	−14.0847	−0.614123
$527$	−39.0241	−1.69992
$528$	1.77695	0.0773319
$529$	26.8131	1.16578
$530$	4.67018	0.202860
$531$	3.10236	0.134631
$532$	−2.77663	−0.120382
$533$	−1.23128	−0.0533325
$534$	−8.96976	−0.388160
$535$	−6.77393	−0.292863
$536$	14.8212	0.640177
$537$	22.8577	0.986384
$538$	−7.22519	−0.311500
$539$	−0.863067	−0.0371749
$540$	10.3013	0.443299
$541$	−8.33901	−0.358522	−0.179261	−	0.983802i	$-0.557371\pi$
$541$	−8.33901	−0.358522	−0.179261	+	0.983802i	$0.557371\pi$
$542$	−14.7499	−0.633561
$543$	−18.3087	−0.785699
$544$	4.88240	0.209331
$545$	−14.0213	−0.600608
$546$	5.79331	0.247931
$547$	8.05012	0.344198	0.172099	−	0.985080i	$-0.444945\pi$
$547$	8.05012	0.344198	0.172099	+	0.985080i	$0.444945\pi$
$548$	6.60500	0.282152
$549$	3.00590	0.128289
$550$	2.03425	0.0867409
$551$	−10.2436	−0.436393
$552$	−10.3125	−0.438929
$553$	−28.6963	−1.22029
$554$	−6.43726	−0.273493
$555$	20.0967	0.853055
$556$	−8.51196	−0.360987
$557$	27.6121	1.16996	0.584980	−	0.811048i	$-0.301102\pi$
$557$	27.6121	1.16996	0.584980	+	0.811048i	$0.301102\pi$
$558$	6.91429	0.292705
$559$	−8.32212	−0.351988
$560$	−5.06481	−0.214027
$561$	8.67579	0.366292
$562$	13.9676	0.589190
$563$	30.0167	1.26505	0.632526	−	0.774539i	$-0.282018\pi$
$563$	30.0167	1.26505	0.632526	+	0.774539i	$0.282018\pi$
$564$	−11.8307	−0.498164
$565$	6.50260	0.273566
$566$	−6.75138	−0.283782
$567$	15.7059	0.659588
$568$	−0.424097	−0.0177947
$569$	4.88122	0.204631	0.102316	−	0.994752i	$-0.467375\pi$
$569$	4.88122	0.204631	0.102316	+	0.994752i	$0.467375\pi$
$570$	−2.66525	−0.111635
$571$	−14.4168	−0.603323	−0.301662	−	0.953415i	$-0.597541\pi$
$571$	−14.4168	−0.603323	−0.301662	+	0.953415i	$0.597541\pi$
$572$	−1.73660	−0.0726108
$573$	38.3773	1.60324
$574$	2.39418	0.0999313
$575$	−11.8058	−0.492334
$576$	−0.865063	−0.0360443
$577$	−36.0190	−1.49949	−0.749745	−	0.661727i	$-0.769824\pi$
$577$	−36.0190	−1.49949	−0.749745	+	0.661727i	$0.769824\pi$
$578$	6.83782	0.284416
$579$	1.70711	0.0709450
$580$	−18.6852	−0.775862
$581$	28.9887	1.20266
$582$	13.2033	0.547296
$583$	−3.11367	−0.128955
$584$	8.16655	0.337934
$585$	−2.25325	−0.0931603
$586$	−5.13724	−0.212217
$587$	19.9494	0.823400	0.411700	−	0.911319i	$-0.364935\pi$
$587$	19.9494	0.823400	0.411700	+	0.911319i	$0.364935\pi$
$588$	−1.03694	−0.0427627
$589$	−7.99282	−0.329338
$590$	−6.54167	−0.269316
$591$	3.72852	0.153371
$592$	−7.54026	−0.309903
$593$	−39.4333	−1.61933	−0.809665	−	0.586892i	$-0.800351\pi$
$593$	−39.4333	−1.61933	−0.809665	+	0.586892i	$0.800351\pi$
$594$	−6.86803	−0.281799
$595$	−24.7284	−1.01377
$596$	−19.5391	−0.800353
$597$	12.7788	0.523003
$598$	10.0783	0.412133
$599$	−12.9656	−0.529760	−0.264880	−	0.964281i	$-0.585332\pi$
$599$	−12.9656	−0.529760	−0.264880	+	0.964281i	$0.585332\pi$
$600$	2.44408	0.0997790
$601$	42.6830	1.74107	0.870537	−	0.492102i	$-0.163771\pi$
$601$	42.6830	1.74107	0.870537	+	0.492102i	$0.163771\pi$
$602$	16.1821	0.659535
$603$	−12.8212	−0.522122
$604$	10.5323	0.428555
$605$	−17.3671	−0.706074
$606$	22.2692	0.904623
$607$	−12.4908	−0.506985	−0.253493	−	0.967337i	$-0.581579\pi$
$607$	−12.4908	−0.506985	−0.253493	+	0.967337i	$0.581579\pi$
$608$	1.00000	0.0405554
$609$	−41.5589	−1.68405
$610$	−6.33828	−0.256629
$611$	11.5621	0.467751
$612$	−4.22358	−0.170728
$613$	9.86462	0.398428	0.199214	−	0.979956i	$-0.436161\pi$
$613$	9.86462	0.398428	0.199214	+	0.979956i	$0.436161\pi$
$614$	−19.8146	−0.799653
$615$	2.29814	0.0926700
$616$	3.37677	0.136054
$617$	−45.9061	−1.84811	−0.924054	−	0.382262i	$-0.875145\pi$
$617$	−45.9061	−1.84811	−0.924054	+	0.382262i	$0.875145\pi$
$618$	1.66195	0.0668534
$619$	−31.1519	−1.25210	−0.626050	−	0.779783i	$-0.715329\pi$
$619$	−31.1519	−1.25210	−0.626050	+	0.779783i	$0.715329\pi$
$620$	−14.5796	−0.585530
$621$	39.8585	1.59947
$622$	14.9239	0.598392
$623$	−17.0454	−0.682908
$624$	−2.08645	−0.0835250
$625$	−13.8384	−0.553538
$626$	−18.1988	−0.727369
$627$	1.77695	0.0709646
$628$	−10.4380	−0.416522
$629$	−36.8146	−1.46789
$630$	4.38138	0.174558
$631$	29.8730	1.18923	0.594613	−	0.804012i	$-0.297305\pi$
$631$	29.8730	1.18923	0.594613	+	0.804012i	$0.297305\pi$
$632$	10.3349	0.411102
$633$	1.46114	0.0580752
$634$	−29.2845	−1.16304
$635$	21.9915	0.872705
$636$	−3.74095	−0.148338
$637$	1.01339	0.0401520
$638$	12.4577	0.493204
$639$	0.366870	0.0145132
$640$	1.82408	0.0721033
$641$	−33.7213	−1.33191	−0.665956	−	0.745991i	$-0.731976\pi$
$641$	−33.7213	−1.33191	−0.665956	+	0.745991i	$0.731976\pi$
$642$	5.42611	0.214151
$643$	27.0639	1.06730	0.533648	−	0.845707i	$-0.320821\pi$
$643$	27.0639	1.06730	0.533648	+	0.845707i	$0.320821\pi$
$644$	−19.5970	−0.772230
$645$	15.5330	0.611611
$646$	4.88240	0.192095
$647$	25.4824	1.00182	0.500909	−	0.865500i	$-0.332999\pi$
$647$	25.4824	1.00182	0.500909	+	0.865500i	$0.332999\pi$
$648$	−5.65648	−0.222207
$649$	4.36141	0.171200
$650$	−2.38857	−0.0936875
$651$	−32.4273	−1.27093
$652$	18.4883	0.724057
$653$	29.7431	1.16394	0.581968	−	0.813212i	$-0.302283\pi$
$653$	29.7431	1.16394	0.581968	+	0.813212i	$0.302283\pi$
$654$	11.2315	0.439186
$655$	−9.16191	−0.357985
$656$	−0.862262	−0.0336657
$657$	−7.06458	−0.275616
$658$	−22.4821	−0.876445
$659$	−1.40224	−0.0546234	−0.0273117	−	0.999627i	$-0.508695\pi$
$659$	−1.40224	−0.0546234	−0.0273117	+	0.999627i	$0.508695\pi$
$660$	3.24131	0.126168
$661$	23.4190	0.910892	0.455446	−	0.890263i	$-0.349480\pi$
$661$	23.4190	0.910892	0.455446	+	0.890263i	$0.349480\pi$
$662$	−11.3759	−0.442139
$663$	−10.1869	−0.395626
$664$	−10.4403	−0.405160
$665$	−5.06481	−0.196405
$666$	6.52280	0.252753
$667$	−72.2978	−2.79938
$668$	−6.60100	−0.255400
$669$	−7.08499	−0.273922
$670$	27.0351	1.04446
$671$	4.22581	0.163135
$672$	4.05705	0.156504
$673$	−12.2858	−0.473585	−0.236792	−	0.971560i	$-0.576096\pi$
$673$	−12.2858	−0.473585	−0.236792	+	0.971560i	$0.576096\pi$
$674$	2.84687	0.109657
$675$	−9.44651	−0.363596
$676$	−10.9609	−0.421574
$677$	47.2914	1.81756	0.908778	−	0.417280i	$-0.137017\pi$
$677$	47.2914	1.81756	0.908778	+	0.417280i	$0.137017\pi$
$678$	−5.20876	−0.200041
$679$	25.0905	0.962885
$680$	8.90591	0.341526
$681$	21.4116	0.820495
$682$	9.72038	0.372212
$683$	−31.2861	−1.19713	−0.598564	−	0.801075i	$-0.704262\pi$
$683$	−31.2861	−1.19713	−0.598564	+	0.801075i	$0.704262\pi$
$684$	−0.865063	−0.0330765
$685$	12.0481	0.460334
$686$	17.4659	0.666851
$687$	40.0072	1.52637
$688$	−5.82798	−0.222190
$689$	3.65599	0.139282
$690$	−18.8109	−0.716118
$691$	8.50326	0.323479	0.161740	−	0.986833i	$-0.448290\pi$
$691$	8.50326	0.323479	0.161740	+	0.986833i	$0.448290\pi$
$692$	12.6258	0.479959
$693$	−2.92112	−0.110964
$694$	−7.03087	−0.266888
$695$	−15.5265	−0.588955
$696$	14.9674	0.567338
$697$	−4.20991	−0.159462
$698$	16.1992	0.613149
$699$	17.0990	0.646745
$700$	4.64451	0.175546
$701$	−1.01268	−0.0382483	−0.0191242	−	0.999817i	$-0.506088\pi$
$701$	−1.01268	−0.0382483	−0.0191242	+	0.999817i	$0.506088\pi$
$702$	8.06427	0.304366
$703$	−7.54026	−0.284386
$704$	−1.21614	−0.0458350
$705$	−21.5803	−0.812760
$706$	22.9606	0.864132
$707$	42.3184	1.59155
$708$	5.24006	0.196934
$709$	−9.19588	−0.345358	−0.172679	−	0.984978i	$-0.555242\pi$
$709$	−9.19588	−0.345358	−0.172679	+	0.984978i	$0.555242\pi$
$710$	−0.773588	−0.0290322
$711$	−8.94038	−0.335290
$712$	6.13887	0.230064
$713$	−56.4120	−2.11265
$714$	19.8082	0.741301
$715$	−3.16770	−0.118465
$716$	−15.6437	−0.584634
$717$	−20.2797	−0.757360
$718$	36.5391	1.36363
$719$	37.4818	1.39784	0.698918	−	0.715202i	$-0.253665\pi$
$719$	37.4818	1.39784	0.698918	+	0.715202i	$0.253665\pi$
$720$	−1.57795	−0.0588067
$721$	3.15823	0.117619
$722$	1.00000	0.0372161
$723$	23.9688	0.891411
$724$	12.5304	0.465687
$725$	17.1347	0.636366
$726$	13.9115	0.516306
$727$	−19.1272	−0.709387	−0.354694	−	0.934983i	$-0.615415\pi$
$727$	−19.1272	−0.709387	−0.354694	+	0.934983i	$0.615415\pi$
$728$	−3.96492	−0.146950
$729$	29.6482	1.09808
$730$	14.8965	0.551343
$731$	−28.4545	−1.05243
$732$	5.07714	0.187656
$733$	21.2864	0.786232	0.393116	−	0.919489i	$-0.371397\pi$
$733$	21.2864	0.786232	0.393116	+	0.919489i	$0.371397\pi$
$734$	25.3408	0.935346
$735$	−1.89147	−0.0697678
$736$	7.05784	0.260155
$737$	−18.0246	−0.663945
$738$	0.745911	0.0274574
$739$	25.6648	0.944095	0.472047	−	0.881573i	$-0.343515\pi$
$739$	25.6648	0.944095	0.472047	+	0.881573i	$0.343515\pi$
$740$	−13.7541	−0.505610
$741$	−2.08645	−0.0766478
$742$	−7.10898	−0.260979
$743$	14.3271	0.525609	0.262804	−	0.964849i	$-0.415353\pi$
$743$	14.3271	0.525609	0.262804	+	0.964849i	$0.415353\pi$
$744$	11.6786	0.428160
$745$	−35.6410	−1.30578
$746$	−21.0985	−0.772470
$747$	9.03148	0.330445
$748$	−5.93768	−0.217103
$749$	10.3113	0.376767
$750$	17.7844	0.649396
$751$	13.2594	0.483841	0.241921	−	0.970296i	$-0.422223\pi$
$751$	13.2594	0.483841	0.241921	+	0.970296i	$0.422223\pi$
$752$	8.09691	0.295264
$753$	28.7343	1.04714
$754$	−14.6275	−0.532702
$755$	19.2119	0.699192
$756$	−15.6808	−0.570304
$757$	19.9743	0.725977	0.362989	−	0.931794i	$-0.381756\pi$
$757$	19.9743	0.725977	0.362989	+	0.931794i	$0.381756\pi$
$758$	24.4401	0.887703
$759$	12.5414	0.455225
$760$	1.82408	0.0661665
$761$	−29.0655	−1.05362	−0.526812	−	0.849982i	$-0.676613\pi$
$761$	−29.0655	−1.05362	−0.526812	+	0.849982i	$0.676613\pi$
$762$	−17.6158	−0.638153
$763$	21.3434	0.772681
$764$	−26.2653	−0.950245
$765$	−7.70417	−0.278545
$766$	−25.8701	−0.934726
$767$	−5.12106	−0.184911
$768$	−1.46114	−0.0527244
$769$	40.5879	1.46364	0.731819	−	0.681499i	$-0.238672\pi$
$769$	40.5879	1.46364	0.731819	+	0.681499i	$0.238672\pi$
$770$	6.15951	0.221973
$771$	18.8019	0.677136
$772$	−1.16834	−0.0420494
$773$	38.5180	1.38540	0.692699	−	0.721227i	$-0.256422\pi$
$773$	38.5180	1.38540	0.692699	+	0.721227i	$0.256422\pi$
$774$	5.04157	0.181215
$775$	13.3697	0.480254
$776$	−9.03631	−0.324385
$777$	−30.5912	−1.09745
$778$	16.4882	0.591129
$779$	−0.862262	−0.0308937
$780$	−3.80587	−0.136272
$781$	0.515760	0.0184554
$782$	34.4592	1.23226
$783$	−57.8499	−2.06739
$784$	0.709678	0.0253456
$785$	−19.0398	−0.679561
$786$	7.33894	0.261771
$787$	12.7039	0.452845	0.226422	−	0.974029i	$-0.427297\pi$
$787$	12.7039	0.452845	0.226422	+	0.974029i	$0.427297\pi$
$788$	−2.55178	−0.0909035
$789$	20.5798	0.732659
$790$	18.8518	0.670717
$791$	−9.89829	−0.351943
$792$	1.05204	0.0373825
$793$	−4.96184	−0.176200
$794$	35.6965	1.26682
$795$	−6.82380	−0.242015
$796$	−8.74578	−0.309986
$797$	−6.89626	−0.244278	−0.122139	−	0.992513i	$-0.538975\pi$
$797$	−6.89626	−0.244278	−0.122139	+	0.992513i	$0.538975\pi$
$798$	4.05705	0.143618
$799$	39.5324	1.39855
$800$	−1.67272	−0.0591394
$801$	−5.31051	−0.187638
$802$	−19.5734	−0.691159
$803$	−9.93166	−0.350481
$804$	−21.6558	−0.763742
$805$	−35.7466	−1.25990
$806$	−11.4134	−0.402021
$807$	10.5570	0.371625
$808$	−15.2409	−0.536174
$809$	−38.1999	−1.34304	−0.671518	−	0.740989i	$-0.734357\pi$
$809$	−38.1999	−1.34304	−0.671518	+	0.740989i	$0.734357\pi$
$810$	−10.3179	−0.362534
$811$	−21.7735	−0.764569	−0.382285	−	0.924045i	$-0.624863\pi$
$811$	−21.7735	−0.764569	−0.382285	+	0.924045i	$0.624863\pi$
$812$	28.4428	0.998145
$813$	21.5516	0.755849
$814$	9.17000	0.321408
$815$	33.7242	1.18131
$816$	−7.13388	−0.249736
$817$	−5.82798	−0.203895
$818$	24.6509	0.861898
$819$	3.42991	0.119851
$820$	−1.57284	−0.0549259
$821$	1.08513	0.0378713	0.0189357	−	0.999821i	$-0.493972\pi$
$821$	1.08513	0.0378713	0.0189357	+	0.999821i	$0.493972\pi$
$822$	−9.65085	−0.336612
$823$	−26.8699	−0.936626	−0.468313	−	0.883563i	$-0.655138\pi$
$823$	−26.8699	−0.936626	−0.468313	+	0.883563i	$0.655138\pi$
$824$	−1.13743	−0.0396243
$825$	−2.97234	−0.103483
$826$	9.95777	0.346475
$827$	22.8594	0.794901	0.397450	−	0.917624i	$-0.369895\pi$
$827$	22.8594	0.794901	0.397450	+	0.917624i	$0.369895\pi$
$828$	−6.10547	−0.212180
$829$	−36.0596	−1.25240	−0.626201	−	0.779662i	$-0.715391\pi$
$829$	−36.0596	−1.25240	−0.626201	+	0.779662i	$0.715391\pi$
$830$	−19.0439	−0.661024
$831$	9.40575	0.326282
$832$	1.42796	0.0495056
$833$	3.46493	0.120053
$834$	12.4372	0.430664
$835$	−12.0408	−0.416688
$836$	−1.21614	−0.0420610
$837$	−45.1387	−1.56022
$838$	−32.3414	−1.11721
$839$	−31.6285	−1.09194	−0.545968	−	0.837806i	$-0.683838\pi$
$839$	−31.6285	−1.09194	−0.545968	+	0.837806i	$0.683838\pi$
$840$	7.40041	0.255338
$841$	75.9319	2.61834
$842$	−17.8218	−0.614180
$843$	−20.4087	−0.702914
$844$	−1.00000	−0.0344214
$845$	−19.9937	−0.687803
$846$	−7.00434	−0.240814
$847$	26.4363	0.908363
$848$	2.56029	0.0879207
$849$	9.86473	0.338557
$850$	−8.16687	−0.280121
$851$	−53.2179	−1.82429
$852$	0.619665	0.0212294
$853$	12.8704	0.440673	0.220336	−	0.975424i	$-0.429284\pi$
$853$	12.8704	0.440673	0.220336	+	0.975424i	$0.429284\pi$
$854$	9.64816	0.330153
$855$	−1.57795	−0.0539647
$856$	−3.71361	−0.126928
$857$	−38.5153	−1.31566	−0.657829	−	0.753168i	$-0.728525\pi$
$857$	−38.5153	−1.31566	−0.657829	+	0.753168i	$0.728525\pi$
$858$	2.53742	0.0866260
$859$	−21.8526	−0.745602	−0.372801	−	0.927911i	$-0.621603\pi$
$859$	−21.8526	−0.745602	−0.372801	+	0.927911i	$0.621603\pi$
$860$	−10.6307	−0.362505
$861$	−3.49824	−0.119220
$862$	28.4446	0.968827
$863$	2.74159	0.0933248	0.0466624	−	0.998911i	$-0.485141\pi$
$863$	2.74159	0.0933248	0.0466624	+	0.998911i	$0.485141\pi$
$864$	5.64741	0.192129
$865$	23.0304	0.783059
$866$	9.12218	0.309984
$867$	−9.99103	−0.339313
$868$	22.1931	0.753283
$869$	−12.5687	−0.426365
$870$	27.3018	0.925618
$871$	21.1640	0.717116
$872$	−7.68678	−0.260307
$873$	7.81698	0.264565
$874$	7.05784	0.238735
$875$	33.7960	1.14251
$876$	−11.9325	−0.403162
$877$	−57.1209	−1.92884	−0.964418	−	0.264382i	$-0.914832\pi$
$877$	−57.1209	−1.92884	−0.964418	+	0.264382i	$0.914832\pi$
$878$	−25.1019	−0.847147
$879$	7.50623	0.253179
$880$	−2.21834	−0.0747802
$881$	−31.5977	−1.06455	−0.532277	−	0.846570i	$-0.678664\pi$
$881$	−31.5977	−1.06455	−0.532277	+	0.846570i	$0.678664\pi$
$882$	−0.613916	−0.0206716
$883$	−20.7145	−0.697100	−0.348550	−	0.937290i	$-0.613326\pi$
$883$	−20.7145	−0.697100	−0.348550	+	0.937290i	$0.613326\pi$
$884$	6.97187	0.234489
$885$	9.55832	0.321299
$886$	10.1470	0.340895
$887$	33.8950	1.13808	0.569041	−	0.822309i	$-0.307314\pi$
$887$	33.8950	1.13808	0.569041	+	0.822309i	$0.307314\pi$
$888$	11.0174	0.369719
$889$	−33.4755	−1.12273
$890$	11.1978	0.375352
$891$	6.87906	0.230457
$892$	4.84894	0.162355
$893$	8.09691	0.270953
$894$	28.5494	0.954835
$895$	−28.5355	−0.953837
$896$	−2.77663	−0.0927607
$897$	−14.7258	−0.491682
$898$	5.78601	0.193082
$899$	81.8754	2.73070
$900$	1.44700	0.0482335
$901$	12.5004	0.416447
$902$	1.04863	0.0349156
$903$	−23.6444	−0.786837
$904$	3.56486	0.118565
$905$	22.8565	0.759774
$906$	−15.3892	−0.511273
$907$	−12.9369	−0.429563	−0.214781	−	0.976662i	$-0.568904\pi$
$907$	−12.9369	−0.429563	−0.214781	+	0.976662i	$0.568904\pi$
$908$	−14.6540	−0.486311
$909$	13.1844	0.437298
$910$	−7.23235	−0.239750
$911$	11.8616	0.392994	0.196497	−	0.980504i	$-0.437043\pi$
$911$	11.8616	0.392994	0.196497	+	0.980504i	$0.437043\pi$
$912$	−1.46114	−0.0483833
$913$	12.6968	0.420203
$914$	−23.9897	−0.793509
$915$	9.26113	0.306164
$916$	−27.3808	−0.904686
$917$	13.9463	0.460547
$918$	27.5729	0.910041
$919$	38.9994	1.28647	0.643235	−	0.765669i	$-0.277592\pi$
$919$	38.9994	1.28647	0.643235	+	0.765669i	$0.277592\pi$
$920$	12.8741	0.424446
$921$	28.9520	0.954000
$922$	−34.5981	−1.13943
$923$	−0.605593	−0.0199333
$924$	−4.93394	−0.162315
$925$	12.6127	0.414703
$926$	−6.30630	−0.207238
$927$	0.983951	0.0323172
$928$	−10.2436	−0.336263
$929$	−5.05712	−0.165919	−0.0829594	−	0.996553i	$-0.526437\pi$
$929$	−5.05712	−0.165919	−0.0829594	+	0.996553i	$0.526437\pi$
$930$	21.3028	0.698547
$931$	0.709678	0.0232587
$932$	−11.7025	−0.383329
$933$	−21.8059	−0.713893
$934$	7.16190	0.234344
$935$	−10.8308	−0.354206
$936$	−1.23528	−0.0403763
$937$	46.6251	1.52317	0.761587	−	0.648062i	$-0.224420\pi$
$937$	46.6251	1.52317	0.761587	+	0.648062i	$0.224420\pi$
$938$	−41.1529	−1.34369
$939$	26.5910	0.867765
$940$	14.7695	0.481726
$941$	57.4611	1.87318	0.936589	−	0.350429i	$-0.113964\pi$
$941$	57.4611	1.87318	0.936589	+	0.350429i	$0.113964\pi$
$942$	15.2514	0.496919
$943$	−6.08570	−0.198178
$944$	−3.58628	−0.116723
$945$	−28.6030	−0.930457
$946$	7.08763	0.230439
$947$	−13.2264	−0.429800	−0.214900	−	0.976636i	$-0.568943\pi$
$947$	−13.2264	−0.429800	−0.214900	+	0.976636i	$0.568943\pi$
$948$	−15.1008	−0.490452
$949$	11.6615	0.378549
$950$	−1.67272	−0.0542701
$951$	42.7889	1.38752
$952$	−13.5566	−0.439373
$953$	32.1059	1.04001	0.520007	−	0.854162i	$-0.325929\pi$
$953$	32.1059	1.04001	0.520007	+	0.854162i	$0.325929\pi$
$954$	−2.21481	−0.0717072
$955$	−47.9101	−1.55033
$956$	13.8794	0.448891
$957$	−18.2024	−0.588401
$958$	−26.1422	−0.844616
$959$	−18.3397	−0.592218
$960$	−2.66525	−0.0860205
$961$	32.8851	1.06081
$962$	−10.7672	−0.347148
$963$	3.21250	0.103522
$964$	−16.4042	−0.528343
$965$	−2.13115	−0.0686041
$966$	28.6340	0.921284
$967$	−6.13235	−0.197203	−0.0986015	−	0.995127i	$-0.531437\pi$
$967$	−6.13235	−0.197203	−0.0986015	+	0.995127i	$0.531437\pi$
$968$	−9.52101	−0.306017
$969$	−7.13388	−0.229173
$970$	−16.4830	−0.529237
$971$	47.2746	1.51711	0.758556	−	0.651607i	$-0.225905\pi$
$971$	47.2746	1.51711	0.758556	+	0.651607i	$0.225905\pi$
$972$	−8.67731	−0.278325
$973$	23.6346	0.757689
$974$	22.2984	0.714486
$975$	3.49004	0.111771
$976$	−3.47477	−0.111225
$977$	23.7397	0.759502	0.379751	−	0.925089i	$-0.376010\pi$
$977$	23.7397	0.759502	0.379751	+	0.925089i	$0.376010\pi$
$978$	−27.0140	−0.863812
$979$	−7.46572	−0.238605
$980$	1.29451	0.0413517
$981$	6.64955	0.212304
$982$	25.7119	0.820498
$983$	−11.0704	−0.353092	−0.176546	−	0.984292i	$-0.556492\pi$
$983$	−11.0704	−0.353092	−0.176546	+	0.984292i	$0.556492\pi$
$984$	1.25989	0.0401637
$985$	−4.65467	−0.148310
$986$	−50.0135	−1.59275
$987$	32.8496	1.04561
$988$	1.42796	0.0454295
$989$	−41.1329	−1.30795
$990$	1.91900	0.0609900
$991$	3.96292	0.125886	0.0629431	−	0.998017i	$-0.479951\pi$
$991$	3.96292	0.125886	0.0629431	+	0.998017i	$0.479951\pi$
$992$	−7.99282	−0.253772
$993$	16.6219	0.527479
$994$	1.17756	0.0373499
$995$	−15.9530	−0.505745
$996$	15.2547	0.483364
$997$	31.6596	1.00267	0.501335	−	0.865253i	$-0.332842\pi$
$997$	31.6596	1.00267	0.501335	+	0.865253i	$0.332842\pi$
$998$	−34.0529	−1.07793
$999$	−42.5829	−1.34726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.10	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.10	✓	30	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.46114 q^{3} +1.00000 q^{4} +1.82408 q^{5} -1.46114 q^{6} -2.77663 q^{7} +1.00000 q^{8} -0.865063 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.46114 q^{3} +1.00000 q^{4} +1.82408 q^{5} -1.46114 q^{6} -2.77663 q^{7} +1.00000 q^{8} -0.865063 q^{9} +1.82408 q^{10} -1.21614 q^{11} -1.46114 q^{12} +1.42796 q^{13} -2.77663 q^{14} -2.66525 q^{15} +1.00000 q^{16} +4.88240 q^{17} -0.865063 q^{18} +1.00000 q^{19} +1.82408 q^{20} +4.05705 q^{21} -1.21614 q^{22} +7.05784 q^{23} -1.46114 q^{24} -1.67272 q^{25} +1.42796 q^{26} +5.64741 q^{27} -2.77663 q^{28} -10.2436 q^{29} -2.66525 q^{30} -7.99282 q^{31} +1.00000 q^{32} +1.77695 q^{33} +4.88240 q^{34} -5.06481 q^{35} -0.865063 q^{36} -7.54026 q^{37} +1.00000 q^{38} -2.08645 q^{39} +1.82408 q^{40} -0.862262 q^{41} +4.05705 q^{42} -5.82798 q^{43} -1.21614 q^{44} -1.57795 q^{45} +7.05784 q^{46} +8.09691 q^{47} -1.46114 q^{48} +0.709678 q^{49} -1.67272 q^{50} -7.13388 q^{51} +1.42796 q^{52} +2.56029 q^{53} +5.64741 q^{54} -2.21834 q^{55} -2.77663 q^{56} -1.46114 q^{57} -10.2436 q^{58} -3.58628 q^{59} -2.66525 q^{60} -3.47477 q^{61} -7.99282 q^{62} +2.40196 q^{63} +1.00000 q^{64} +2.60472 q^{65} +1.77695 q^{66} +14.8212 q^{67} +4.88240 q^{68} -10.3125 q^{69} -5.06481 q^{70} -0.424097 q^{71} -0.865063 q^{72} +8.16655 q^{73} -7.54026 q^{74} +2.44408 q^{75} +1.00000 q^{76} +3.37677 q^{77} -2.08645 q^{78} +10.3349 q^{79} +1.82408 q^{80} -5.65648 q^{81} -0.862262 q^{82} -10.4403 q^{83} +4.05705 q^{84} +8.90591 q^{85} -5.82798 q^{86} +14.9674 q^{87} -1.21614 q^{88} +6.13887 q^{89} -1.57795 q^{90} -3.96492 q^{91} +7.05784 q^{92} +11.6786 q^{93} +8.09691 q^{94} +1.82408 q^{95} -1.46114 q^{96} -9.03631 q^{97} +0.709678 q^{98} +1.05204 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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