LMFDB - Embedded newform 4010.2.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.88307 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.88307 q^{6} -0.867210 q^{7} +1.00000 q^{8} +5.31208 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.88307 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.88307 q^{6} -0.867210 q^{7} +1.00000 q^{8} +5.31208 q^{9} -1.00000 q^{10} +1.33015 q^{11} -2.88307 q^{12} +6.72854 q^{13} -0.867210 q^{14} +2.88307 q^{15} +1.00000 q^{16} -1.82114 q^{17} +5.31208 q^{18} -4.13067 q^{19} -1.00000 q^{20} +2.50022 q^{21} +1.33015 q^{22} -4.99847 q^{23} -2.88307 q^{24} +1.00000 q^{25} +6.72854 q^{26} -6.66587 q^{27} -0.867210 q^{28} +2.06922 q^{29} +2.88307 q^{30} -1.12902 q^{31} +1.00000 q^{32} -3.83491 q^{33} -1.82114 q^{34} +0.867210 q^{35} +5.31208 q^{36} +6.71256 q^{37} -4.13067 q^{38} -19.3988 q^{39} -1.00000 q^{40} +4.80486 q^{41} +2.50022 q^{42} +4.78483 q^{43} +1.33015 q^{44} -5.31208 q^{45} -4.99847 q^{46} -2.03479 q^{47} -2.88307 q^{48} -6.24795 q^{49} +1.00000 q^{50} +5.25046 q^{51} +6.72854 q^{52} +1.92550 q^{53} -6.66587 q^{54} -1.33015 q^{55} -0.867210 q^{56} +11.9090 q^{57} +2.06922 q^{58} -2.26064 q^{59} +2.88307 q^{60} -13.5186 q^{61} -1.12902 q^{62} -4.60668 q^{63} +1.00000 q^{64} -6.72854 q^{65} -3.83491 q^{66} -3.49264 q^{67} -1.82114 q^{68} +14.4109 q^{69} +0.867210 q^{70} -9.07288 q^{71} +5.31208 q^{72} +8.67245 q^{73} +6.71256 q^{74} -2.88307 q^{75} -4.13067 q^{76} -1.15352 q^{77} -19.3988 q^{78} +2.83838 q^{79} -1.00000 q^{80} +3.28192 q^{81} +4.80486 q^{82} +4.99821 q^{83} +2.50022 q^{84} +1.82114 q^{85} +4.78483 q^{86} -5.96569 q^{87} +1.33015 q^{88} -7.52201 q^{89} -5.31208 q^{90} -5.83506 q^{91} -4.99847 q^{92} +3.25505 q^{93} -2.03479 q^{94} +4.13067 q^{95} -2.88307 q^{96} +8.45750 q^{97} -6.24795 q^{98} +7.06586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - 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
$3$	−2.88307	−1.66454	−0.832270	−	0.554371i	$-0.812959\pi$
$3$	−2.88307	−1.66454	−0.832270	+	0.554371i	$0.812959\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.88307	−1.17701
$7$	−0.867210	−0.327775	−0.163887	−	0.986479i	$-0.552403\pi$
$7$	−0.867210	−0.327775	−0.163887	+	0.986479i	$0.552403\pi$
$8$	1.00000	0.353553
$9$	5.31208	1.77069
$10$	−1.00000	−0.316228
$11$	1.33015	0.401055	0.200528	−	0.979688i	$-0.435734\pi$
$11$	1.33015	0.401055	0.200528	+	0.979688i	$0.435734\pi$
$12$	−2.88307	−0.832270
$13$	6.72854	1.86616	0.933081	−	0.359667i	$-0.117110\pi$
$13$	6.72854	1.86616	0.933081	+	0.359667i	$0.117110\pi$
$14$	−0.867210	−0.231772
$15$	2.88307	0.744405
$16$	1.00000	0.250000
$17$	−1.82114	−0.441691	−0.220845	−	0.975309i	$-0.570882\pi$
$17$	−1.82114	−0.441691	−0.220845	+	0.975309i	$0.570882\pi$
$18$	5.31208	1.25207
$19$	−4.13067	−0.947641	−0.473820	−	0.880622i	$-0.657125\pi$
$19$	−4.13067	−0.947641	−0.473820	+	0.880622i	$0.657125\pi$
$20$	−1.00000	−0.223607
$21$	2.50022	0.545594
$22$	1.33015	0.283589
$23$	−4.99847	−1.04225	−0.521127	−	0.853479i	$-0.674488\pi$
$23$	−4.99847	−1.04225	−0.521127	+	0.853479i	$0.674488\pi$
$24$	−2.88307	−0.588504
$25$	1.00000	0.200000
$26$	6.72854	1.31958
$27$	−6.66587	−1.28285
$28$	−0.867210	−0.163887
$29$	2.06922	0.384244	0.192122	−	0.981371i	$-0.438463\pi$
$29$	2.06922	0.384244	0.192122	+	0.981371i	$0.438463\pi$
$30$	2.88307	0.526374
$31$	−1.12902	−0.202779	−0.101389	−	0.994847i	$-0.532329\pi$
$31$	−1.12902	−0.202779	−0.101389	+	0.994847i	$0.532329\pi$
$32$	1.00000	0.176777
$33$	−3.83491	−0.667572
$34$	−1.82114	−0.312322
$35$	0.867210	0.146585
$36$	5.31208	0.885346
$37$	6.71256	1.10354	0.551769	−	0.833997i	$-0.313953\pi$
$37$	6.71256	1.10354	0.551769	+	0.833997i	$0.313953\pi$
$38$	−4.13067	−0.670083
$39$	−19.3988	−3.10630
$40$	−1.00000	−0.158114
$41$	4.80486	0.750393	0.375196	−	0.926945i	$-0.377575\pi$
$41$	4.80486	0.750393	0.375196	+	0.926945i	$0.377575\pi$
$42$	2.50022	0.385793
$43$	4.78483	0.729680	0.364840	−	0.931070i	$-0.381124\pi$
$43$	4.78483	0.729680	0.364840	+	0.931070i	$0.381124\pi$
$44$	1.33015	0.200528
$45$	−5.31208	−0.791877
$46$	−4.99847	−0.736985
$47$	−2.03479	−0.296804	−0.148402	−	0.988927i	$-0.547413\pi$
$47$	−2.03479	−0.296804	−0.148402	+	0.988927i	$0.547413\pi$
$48$	−2.88307	−0.416135
$49$	−6.24795	−0.892564
$50$	1.00000	0.141421
$51$	5.25046	0.735212
$52$	6.72854	0.933081
$53$	1.92550	0.264488	0.132244	−	0.991217i	$-0.457782\pi$
$53$	1.92550	0.264488	0.132244	+	0.991217i	$0.457782\pi$
$54$	−6.66587	−0.907110
$55$	−1.33015	−0.179357
$56$	−0.867210	−0.115886
$57$	11.9090	1.57739
$58$	2.06922	0.271701
$59$	−2.26064	−0.294310	−0.147155	−	0.989113i	$-0.547012\pi$
$59$	−2.26064	−0.294310	−0.147155	+	0.989113i	$0.547012\pi$
$60$	2.88307	0.372202
$61$	−13.5186	−1.73088	−0.865440	−	0.501013i	$-0.832961\pi$
$61$	−13.5186	−1.73088	−0.865440	+	0.501013i	$0.832961\pi$
$62$	−1.12902	−0.143386
$63$	−4.60668	−0.580388
$64$	1.00000	0.125000
$65$	−6.72854	−0.834573
$66$	−3.83491	−0.472045
$67$	−3.49264	−0.426694	−0.213347	−	0.976976i	$-0.568437\pi$
$67$	−3.49264	−0.426694	−0.213347	+	0.976976i	$0.568437\pi$
$68$	−1.82114	−0.220845
$69$	14.4109	1.73487
$70$	0.867210	0.103651
$71$	−9.07288	−1.07675	−0.538376	−	0.842705i	$-0.680962\pi$
$71$	−9.07288	−1.07675	−0.538376	+	0.842705i	$0.680962\pi$
$72$	5.31208	0.626034
$73$	8.67245	1.01503	0.507517	−	0.861642i	$-0.330564\pi$
$73$	8.67245	1.01503	0.507517	+	0.861642i	$0.330564\pi$
$74$	6.71256	0.780319
$75$	−2.88307	−0.332908
$76$	−4.13067	−0.473820
$77$	−1.15352	−0.131456
$78$	−19.3988	−2.19649
$79$	2.83838	0.319343	0.159672	−	0.987170i	$-0.448956\pi$
$79$	2.83838	0.319343	0.159672	+	0.987170i	$0.448956\pi$
$80$	−1.00000	−0.111803
$81$	3.28192	0.364658
$82$	4.80486	0.530608
$83$	4.99821	0.548625	0.274313	−	0.961641i	$-0.411550\pi$
$83$	4.99821	0.548625	0.274313	+	0.961641i	$0.411550\pi$
$84$	2.50022	0.272797
$85$	1.82114	0.197530
$86$	4.78483	0.515962
$87$	−5.96569	−0.639589
$88$	1.33015	0.141794
$89$	−7.52201	−0.797331	−0.398666	−	0.917096i	$-0.630527\pi$
$89$	−7.52201	−0.797331	−0.398666	+	0.917096i	$0.630527\pi$
$90$	−5.31208	−0.559942
$91$	−5.83506	−0.611680
$92$	−4.99847	−0.521127
$93$	3.25505	0.337533
$94$	−2.03479	−0.209872
$95$	4.13067	0.423798
$96$	−2.88307	−0.294252
$97$	8.45750	0.858729	0.429364	−	0.903131i	$-0.358738\pi$
$97$	8.45750	0.858729	0.429364	+	0.903131i	$0.358738\pi$
$98$	−6.24795	−0.631138
$99$	7.06586	0.710145
$100$	1.00000	0.100000
$101$	6.44945	0.641745	0.320872	−	0.947122i	$-0.396024\pi$
$101$	6.44945	0.641745	0.320872	+	0.947122i	$0.396024\pi$
$102$	5.25046	0.519873
$103$	9.27004	0.913404	0.456702	−	0.889620i	$-0.349031\pi$
$103$	9.27004	0.913404	0.456702	+	0.889620i	$0.349031\pi$
$104$	6.72854	0.659788
$105$	−2.50022	−0.243997
$106$	1.92550	0.187022
$107$	4.30195	0.415885	0.207942	−	0.978141i	$-0.433323\pi$
$107$	4.30195	0.415885	0.207942	+	0.978141i	$0.433323\pi$
$108$	−6.66587	−0.641424
$109$	5.40382	0.517592	0.258796	−	0.965932i	$-0.416674\pi$
$109$	5.40382	0.517592	0.258796	+	0.965932i	$0.416674\pi$
$110$	−1.33015	−0.126825
$111$	−19.3528	−1.83688
$112$	−0.867210	−0.0819436
$113$	12.6752	1.19238	0.596190	−	0.802844i	$-0.296681\pi$
$113$	12.6752	1.19238	0.596190	+	0.802844i	$0.296681\pi$
$114$	11.9090	1.11538
$115$	4.99847	0.466110
$116$	2.06922	0.192122
$117$	35.7425	3.30440
$118$	−2.26064	−0.208109
$119$	1.57931	0.144775
$120$	2.88307	0.263187
$121$	−9.23070	−0.839155
$122$	−13.5186	−1.22392
$123$	−13.8527	−1.24906
$124$	−1.12902	−0.101389
$125$	−1.00000	−0.0894427
$126$	−4.60668	−0.410396
$127$	17.1104	1.51831	0.759153	−	0.650913i	$-0.225614\pi$
$127$	17.1104	1.51831	0.759153	+	0.650913i	$0.225614\pi$
$128$	1.00000	0.0883883
$129$	−13.7950	−1.21458
$130$	−6.72854	−0.590132
$131$	−5.47195	−0.478087	−0.239043	−	0.971009i	$-0.576834\pi$
$131$	−5.47195	−0.478087	−0.239043	+	0.971009i	$0.576834\pi$
$132$	−3.83491	−0.333786
$133$	3.58216	0.310612
$134$	−3.49264	−0.301718
$135$	6.66587	0.573707
$136$	−1.82114	−0.156161
$137$	6.72773	0.574789	0.287394	−	0.957812i	$-0.407211\pi$
$137$	6.72773	0.574789	0.287394	+	0.957812i	$0.407211\pi$
$138$	14.4109	1.22674
$139$	19.1929	1.62792	0.813962	−	0.580918i	$-0.197306\pi$
$139$	19.1929	1.62792	0.813962	+	0.580918i	$0.197306\pi$
$140$	0.867210	0.0732926
$141$	5.86643	0.494043
$142$	−9.07288	−0.761379
$143$	8.94996	0.748434
$144$	5.31208	0.442673
$145$	−2.06922	−0.171839
$146$	8.67245	0.717737
$147$	18.0132	1.48571
$148$	6.71256	0.551769
$149$	23.5386	1.92835	0.964177	−	0.265258i	$-0.0854571\pi$
$149$	23.5386	1.92835	0.964177	+	0.265258i	$0.0854571\pi$
$150$	−2.88307	−0.235401
$151$	1.48896	0.121170	0.0605849	−	0.998163i	$-0.480703\pi$
$151$	1.48896	0.121170	0.0605849	+	0.998163i	$0.480703\pi$
$152$	−4.13067	−0.335042
$153$	−9.67402	−0.782098
$154$	−1.15352	−0.0929532
$155$	1.12902	0.0906854
$156$	−19.3988	−1.55315
$157$	17.0685	1.36221	0.681105	−	0.732185i	$-0.261500\pi$
$157$	17.0685	1.36221	0.681105	+	0.732185i	$0.261500\pi$
$158$	2.83838	0.225810
$159$	−5.55136	−0.440251
$160$	−1.00000	−0.0790569
$161$	4.33473	0.341624
$162$	3.28192	0.257852
$163$	−13.1841	−1.03266	−0.516328	−	0.856391i	$-0.672701\pi$
$163$	−13.1841	−1.03266	−0.516328	+	0.856391i	$0.672701\pi$
$164$	4.80486	0.375196
$165$	3.83491	0.298547
$166$	4.99821	0.387937
$167$	−11.1734	−0.864621	−0.432311	−	0.901725i	$-0.642302\pi$
$167$	−11.1734	−0.864621	−0.432311	+	0.901725i	$0.642302\pi$
$168$	2.50022	0.192897
$169$	32.2732	2.48256
$170$	1.82114	0.139675
$171$	−21.9424	−1.67798
$172$	4.78483	0.364840
$173$	−7.93368	−0.603187	−0.301593	−	0.953437i	$-0.597519\pi$
$173$	−7.93368	−0.603187	−0.301593	+	0.953437i	$0.597519\pi$
$174$	−5.96569	−0.452258
$175$	−0.867210	−0.0655549
$176$	1.33015	0.100264
$177$	6.51758	0.489891
$178$	−7.52201	−0.563798
$179$	19.4425	1.45320	0.726601	−	0.687060i	$-0.241099\pi$
$179$	19.4425	1.45320	0.726601	+	0.687060i	$0.241099\pi$
$180$	−5.31208	−0.395939
$181$	1.31845	0.0980000	0.0490000	−	0.998799i	$-0.484397\pi$
$181$	1.31845	0.0980000	0.0490000	+	0.998799i	$0.484397\pi$
$182$	−5.83506	−0.432523
$183$	38.9750	2.88112
$184$	−4.99847	−0.368492
$185$	−6.71256	−0.493517
$186$	3.25505	0.238672
$187$	−2.42239	−0.177142
$188$	−2.03479	−0.148402
$189$	5.78071	0.420485
$190$	4.13067	0.299670
$191$	4.21485	0.304976	0.152488	−	0.988305i	$-0.451272\pi$
$191$	4.21485	0.304976	0.152488	+	0.988305i	$0.451272\pi$
$192$	−2.88307	−0.208067
$193$	16.5579	1.19186	0.595931	−	0.803036i	$-0.296783\pi$
$193$	16.5579	1.19186	0.595931	+	0.803036i	$0.296783\pi$
$194$	8.45750	0.607213
$195$	19.3988	1.38918
$196$	−6.24795	−0.446282
$197$	2.67413	0.190524	0.0952619	−	0.995452i	$-0.469631\pi$
$197$	2.67413	0.190524	0.0952619	+	0.995452i	$0.469631\pi$
$198$	7.06586	0.502148
$199$	19.0834	1.35279	0.676393	−	0.736541i	$-0.263542\pi$
$199$	19.0834	1.35279	0.676393	+	0.736541i	$0.263542\pi$
$200$	1.00000	0.0707107
$201$	10.0695	0.710249
$202$	6.44945	0.453782
$203$	−1.79444	−0.125945
$204$	5.25046	0.367606
$205$	−4.80486	−0.335586
$206$	9.27004	0.645874
$207$	−26.5523	−1.84551
$208$	6.72854	0.466540
$209$	−5.49441	−0.380056
$210$	−2.50022	−0.172532
$211$	5.41807	0.372995	0.186497	−	0.982455i	$-0.440286\pi$
$211$	5.41807	0.372995	0.186497	+	0.982455i	$0.440286\pi$
$212$	1.92550	0.132244
$213$	26.1577	1.79230
$214$	4.30195	0.294075
$215$	−4.78483	−0.326323
$216$	−6.66587	−0.453555
$217$	0.979101	0.0664657
$218$	5.40382	0.365993
$219$	−25.0032	−1.68956
$220$	−1.33015	−0.0896787
$221$	−12.2536	−0.824266
$222$	−19.3528	−1.29887
$223$	20.6570	1.38329	0.691647	−	0.722236i	$-0.256885\pi$
$223$	20.6570	1.38329	0.691647	+	0.722236i	$0.256885\pi$
$224$	−0.867210	−0.0579429
$225$	5.31208	0.354138
$226$	12.6752	0.843140
$227$	−18.6037	−1.23477	−0.617384	−	0.786662i	$-0.711808\pi$
$227$	−18.6037	−1.23477	−0.617384	+	0.786662i	$0.711808\pi$
$228$	11.9090	0.788693
$229$	−13.0044	−0.859355	−0.429677	−	0.902983i	$-0.641373\pi$
$229$	−13.0044	−0.859355	−0.429677	+	0.902983i	$0.641373\pi$
$230$	4.99847	0.329590
$231$	3.32567	0.218813
$232$	2.06922	0.135851
$233$	−3.00108	−0.196607	−0.0983035	−	0.995156i	$-0.531342\pi$
$233$	−3.00108	−0.196607	−0.0983035	+	0.995156i	$0.531342\pi$
$234$	35.7425	2.33656
$235$	2.03479	0.132735
$236$	−2.26064	−0.147155
$237$	−8.18325	−0.531559
$238$	1.57931	0.102371
$239$	28.8344	1.86514	0.932572	−	0.360983i	$-0.117559\pi$
$239$	28.8344	1.86514	0.932572	+	0.360983i	$0.117559\pi$
$240$	2.88307	0.186101
$241$	7.55019	0.486350	0.243175	−	0.969982i	$-0.421811\pi$
$241$	7.55019	0.486350	0.243175	+	0.969982i	$0.421811\pi$
$242$	−9.23070	−0.593372
$243$	10.5356	0.675860
$244$	−13.5186	−0.865440
$245$	6.24795	0.399167
$246$	−13.8527	−0.883218
$247$	−27.7934	−1.76845
$248$	−1.12902	−0.0716931
$249$	−14.4102	−0.913208
$250$	−1.00000	−0.0632456
$251$	−21.3752	−1.34919	−0.674597	−	0.738186i	$-0.735682\pi$
$251$	−21.3752	−1.34919	−0.674597	+	0.738186i	$0.735682\pi$
$252$	−4.60668	−0.290194
$253$	−6.64872	−0.418001
$254$	17.1104	1.07360
$255$	−5.25046	−0.328797
$256$	1.00000	0.0625000
$257$	−3.97971	−0.248248	−0.124124	−	0.992267i	$-0.539612\pi$
$257$	−3.97971	−0.248248	−0.124124	+	0.992267i	$0.539612\pi$
$258$	−13.7950	−0.858839
$259$	−5.82120	−0.361712
$260$	−6.72854	−0.417286
$261$	10.9918	0.680377
$262$	−5.47195	−0.338058
$263$	20.8581	1.28617	0.643083	−	0.765796i	$-0.277655\pi$
$263$	20.8581	1.28617	0.643083	+	0.765796i	$0.277655\pi$
$264$	−3.83491	−0.236022
$265$	−1.92550	−0.118283
$266$	3.58216	0.219636
$267$	21.6864	1.32719
$268$	−3.49264	−0.213347
$269$	−13.8566	−0.844850	−0.422425	−	0.906398i	$-0.638821\pi$
$269$	−13.8566	−0.844850	−0.422425	+	0.906398i	$0.638821\pi$
$270$	6.66587	0.405672
$271$	−5.82559	−0.353879	−0.176940	−	0.984222i	$-0.556620\pi$
$271$	−5.82559	−0.353879	−0.176940	+	0.984222i	$0.556620\pi$
$272$	−1.82114	−0.110423
$273$	16.8229	1.01817
$274$	6.72773	0.406437
$275$	1.33015	0.0802110
$276$	14.4109	0.867436
$277$	7.12203	0.427921	0.213961	−	0.976842i	$-0.431364\pi$
$277$	7.12203	0.427921	0.213961	+	0.976842i	$0.431364\pi$
$278$	19.1929	1.15112
$279$	−5.99746	−0.359059
$280$	0.867210	0.0518257
$281$	33.0700	1.97279	0.986396	−	0.164387i	$-0.0525646\pi$
$281$	33.0700	1.97279	0.986396	+	0.164387i	$0.0525646\pi$
$282$	5.86643	0.349341
$283$	7.07732	0.420703	0.210351	−	0.977626i	$-0.432539\pi$
$283$	7.07732	0.420703	0.210351	+	0.977626i	$0.432539\pi$
$284$	−9.07288	−0.538376
$285$	−11.9090	−0.705428
$286$	8.94996	0.529223
$287$	−4.16682	−0.245960
$288$	5.31208	0.313017
$289$	−13.6835	−0.804909
$290$	−2.06922	−0.121509
$291$	−24.3835	−1.42939
$292$	8.67245	0.507517
$293$	−22.2386	−1.29919	−0.649596	−	0.760280i	$-0.725062\pi$
$293$	−22.2386	−1.29919	−0.649596	+	0.760280i	$0.725062\pi$
$294$	18.0132	1.05055
$295$	2.26064	0.131620
$296$	6.71256	0.390160
$297$	−8.86660	−0.514492
$298$	23.5386	1.36355
$299$	−33.6324	−1.94501
$300$	−2.88307	−0.166454
$301$	−4.14946	−0.239171
$302$	1.48896	0.0856800
$303$	−18.5942	−1.06821
$304$	−4.13067	−0.236910
$305$	13.5186	0.774073
$306$	−9.67402	−0.553027
$307$	14.4414	0.824217	0.412108	−	0.911135i	$-0.364793\pi$
$307$	14.4414	0.824217	0.412108	+	0.911135i	$0.364793\pi$
$308$	−1.15352	−0.0657278
$309$	−26.7261	−1.52040
$310$	1.12902	0.0641243
$311$	−12.9454	−0.734065	−0.367033	−	0.930208i	$-0.619626\pi$
$311$	−12.9454	−0.734065	−0.367033	+	0.930208i	$0.619626\pi$
$312$	−19.3988	−1.09824
$313$	12.8709	0.727506	0.363753	−	0.931495i	$-0.381495\pi$
$313$	12.8709	0.727506	0.363753	+	0.931495i	$0.381495\pi$
$314$	17.0685	0.963229
$315$	4.60668	0.259557
$316$	2.83838	0.159672
$317$	−23.6880	−1.33045	−0.665224	−	0.746644i	$-0.731664\pi$
$317$	−23.6880	−1.33045	−0.665224	+	0.746644i	$0.731664\pi$
$318$	−5.55136	−0.311305
$319$	2.75237	0.154103
$320$	−1.00000	−0.0559017
$321$	−12.4028	−0.692257
$322$	4.33473	0.241565
$323$	7.52252	0.418564
$324$	3.28192	0.182329
$325$	6.72854	0.373232
$326$	−13.1841	−0.730198
$327$	−15.5796	−0.861552
$328$	4.80486	0.265304
$329$	1.76459	0.0972850
$330$	3.83491	0.211105
$331$	−3.21129	−0.176509	−0.0882543	−	0.996098i	$-0.528129\pi$
$331$	−3.21129	−0.176509	−0.0882543	+	0.996098i	$0.528129\pi$
$332$	4.99821	0.274313
$333$	35.6576	1.95403
$334$	−11.1734	−0.611379
$335$	3.49264	0.190823
$336$	2.50022	0.136398
$337$	−10.1369	−0.552190	−0.276095	−	0.961130i	$-0.589040\pi$
$337$	−10.1369	−0.552190	−0.276095	+	0.961130i	$0.589040\pi$
$338$	32.2732	1.75543
$339$	−36.5434	−1.98476
$340$	1.82114	0.0987650
$341$	−1.50177	−0.0813255
$342$	−21.9424	−1.18651
$343$	11.4888	0.620334
$344$	4.78483	0.257981
$345$	−14.4109	−0.775859
$346$	−7.93368	−0.426517
$347$	−30.7883	−1.65280	−0.826400	−	0.563083i	$-0.809615\pi$
$347$	−30.7883	−1.65280	−0.826400	+	0.563083i	$0.809615\pi$
$348$	−5.96569	−0.319794
$349$	−23.6495	−1.26593	−0.632965	−	0.774180i	$-0.718162\pi$
$349$	−23.6495	−1.26593	−0.632965	+	0.774180i	$0.718162\pi$
$350$	−0.867210	−0.0463543
$351$	−44.8516	−2.39400
$352$	1.33015	0.0708972
$353$	13.4017	0.713299	0.356650	−	0.934238i	$-0.383919\pi$
$353$	13.4017	0.713299	0.356650	+	0.934238i	$0.383919\pi$
$354$	6.51758	0.346405
$355$	9.07288	0.481538
$356$	−7.52201	−0.398666
$357$	−4.55325	−0.240984
$358$	19.4425	1.02757
$359$	20.1426	1.06308	0.531542	−	0.847032i	$-0.321613\pi$
$359$	20.1426	1.06308	0.531542	+	0.847032i	$0.321613\pi$
$360$	−5.31208	−0.279971
$361$	−1.93757	−0.101977
$362$	1.31845	0.0692964
$363$	26.6127	1.39681
$364$	−5.83506	−0.305840
$365$	−8.67245	−0.453937
$366$	38.9750	2.03726
$367$	5.95908	0.311061	0.155531	−	0.987831i	$-0.450291\pi$
$367$	5.95908	0.311061	0.155531	+	0.987831i	$0.450291\pi$
$368$	−4.99847	−0.260563
$369$	25.5238	1.32871
$370$	−6.71256	−0.348969
$371$	−1.66982	−0.0866926
$372$	3.25505	0.168767
$373$	10.4266	0.539871	0.269935	−	0.962878i	$-0.412998\pi$
$373$	10.4266	0.539871	0.269935	+	0.962878i	$0.412998\pi$
$374$	−2.42239	−0.125259
$375$	2.88307	0.148881
$376$	−2.03479	−0.104936
$377$	13.9228	0.717061
$378$	5.78071	0.297328
$379$	−12.3032	−0.631974	−0.315987	−	0.948764i	$-0.602336\pi$
$379$	−12.3032	−0.631974	−0.315987	+	0.948764i	$0.602336\pi$
$380$	4.13067	0.211899
$381$	−49.3305	−2.52728
$382$	4.21485	0.215650
$383$	3.36706	0.172049	0.0860245	−	0.996293i	$-0.472584\pi$
$383$	3.36706	0.172049	0.0860245	+	0.996293i	$0.472584\pi$
$384$	−2.88307	−0.147126
$385$	1.15352	0.0587888
$386$	16.5579	0.842773
$387$	25.4174	1.29204
$388$	8.45750	0.429364
$389$	12.0923	0.613105	0.306552	−	0.951854i	$-0.400825\pi$
$389$	12.0923	0.613105	0.306552	+	0.951854i	$0.400825\pi$
$390$	19.3988	0.982298
$391$	9.10291	0.460354
$392$	−6.24795	−0.315569
$393$	15.7760	0.795794
$394$	2.67413	0.134721
$395$	−2.83838	−0.142815
$396$	7.06586	0.355073
$397$	14.4221	0.723827	0.361913	−	0.932212i	$-0.382124\pi$
$397$	14.4221	0.723827	0.361913	+	0.932212i	$0.382124\pi$
$398$	19.0834	0.956564
$399$	−10.3276	−0.517027
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	10.0695	0.502222
$403$	−7.59668	−0.378418
$404$	6.44945	0.320872
$405$	−3.28192	−0.163080
$406$	−1.79444	−0.0890568
$407$	8.92871	0.442580
$408$	5.25046	0.259937
$409$	4.28102	0.211683	0.105842	−	0.994383i	$-0.466246\pi$
$409$	4.28102	0.211683	0.105842	+	0.994383i	$0.466246\pi$
$410$	−4.80486	−0.237295
$411$	−19.3965	−0.956758
$412$	9.27004	0.456702
$413$	1.96045	0.0964674
$414$	−26.5523	−1.30497
$415$	−4.99821	−0.245353
$416$	6.72854	0.329894
$417$	−55.3345	−2.70974
$418$	−5.49441	−0.268740
$419$	−1.76386	−0.0861700	−0.0430850	−	0.999071i	$-0.513719\pi$
$419$	−1.76386	−0.0861700	−0.0430850	+	0.999071i	$0.513719\pi$
$420$	−2.50022	−0.121998
$421$	−32.4043	−1.57929	−0.789645	−	0.613564i	$-0.789735\pi$
$421$	−32.4043	−1.57929	−0.789645	+	0.613564i	$0.789735\pi$
$422$	5.41807	0.263747
$423$	−10.8090	−0.525549
$424$	1.92550	0.0935108
$425$	−1.82114	−0.0883381
$426$	26.1577	1.26735
$427$	11.7235	0.567338
$428$	4.30195	0.207942
$429$	−25.8033	−1.24580
$430$	−4.78483	−0.230745
$431$	−22.1266	−1.06580	−0.532900	−	0.846178i	$-0.678898\pi$
$431$	−22.1266	−1.06580	−0.532900	+	0.846178i	$0.678898\pi$
$432$	−6.66587	−0.320712
$433$	−33.9538	−1.63171	−0.815857	−	0.578253i	$-0.803735\pi$
$433$	−33.9538	−1.63171	−0.815857	+	0.578253i	$0.803735\pi$
$434$	0.979101	0.0469983
$435$	5.96569	0.286033
$436$	5.40382	0.258796
$437$	20.6470	0.987682
$438$	−25.0032	−1.19470
$439$	−21.5548	−1.02875	−0.514377	−	0.857564i	$-0.671977\pi$
$439$	−21.5548	−1.02875	−0.514377	+	0.857564i	$0.671977\pi$
$440$	−1.33015	−0.0634124
$441$	−33.1896	−1.58046
$442$	−12.2536	−0.582844
$443$	19.4900	0.925999	0.462999	−	0.886359i	$-0.346773\pi$
$443$	19.4900	0.925999	0.462999	+	0.886359i	$0.346773\pi$
$444$	−19.3528	−0.918441
$445$	7.52201	0.356577
$446$	20.6570	0.978137
$447$	−67.8633	−3.20982
$448$	−0.867210	−0.0409718
$449$	23.8264	1.12444	0.562219	−	0.826988i	$-0.309948\pi$
$449$	23.8264	1.12444	0.562219	+	0.826988i	$0.309948\pi$
$450$	5.31208	0.250414
$451$	6.39118	0.300949
$452$	12.6752	0.596190
$453$	−4.29277	−0.201692
$454$	−18.6037	−0.873113
$455$	5.83506	0.273552
$456$	11.9090	0.557690
$457$	10.3737	0.485262	0.242631	−	0.970119i	$-0.421990\pi$
$457$	10.3737	0.485262	0.242631	+	0.970119i	$0.421990\pi$
$458$	−13.0044	−0.607655
$459$	12.1395	0.566622
$460$	4.99847	0.233055
$461$	−9.75474	−0.454324	−0.227162	−	0.973857i	$-0.572945\pi$
$461$	−9.75474	−0.454324	−0.227162	+	0.973857i	$0.572945\pi$
$462$	3.32567	0.154724
$463$	−27.9235	−1.29772	−0.648858	−	0.760910i	$-0.724753\pi$
$463$	−27.9235	−1.29772	−0.648858	+	0.760910i	$0.724753\pi$
$464$	2.06922	0.0960609
$465$	−3.25505	−0.150949
$466$	−3.00108	−0.139022
$467$	−3.89002	−0.180009	−0.0900043	−	0.995941i	$-0.528688\pi$
$467$	−3.89002	−0.180009	−0.0900043	+	0.995941i	$0.528688\pi$
$468$	35.7425	1.65220
$469$	3.02885	0.139860
$470$	2.03479	0.0938578
$471$	−49.2095	−2.26745
$472$	−2.26064	−0.104054
$473$	6.36455	0.292642
$474$	−8.18325	−0.375869
$475$	−4.13067	−0.189528
$476$	1.57931	0.0723875
$477$	10.2284	0.468327
$478$	28.8344	1.31886
$479$	−10.4030	−0.475326	−0.237663	−	0.971348i	$-0.576381\pi$
$479$	−10.4030	−0.475326	−0.237663	+	0.971348i	$0.576381\pi$
$480$	2.88307	0.131593
$481$	45.1657	2.05938
$482$	7.55019	0.343902
$483$	−12.4973	−0.568647
$484$	−9.23070	−0.419577
$485$	−8.45750	−0.384035
$486$	10.5356	0.477905
$487$	5.91522	0.268044	0.134022	−	0.990978i	$-0.457211\pi$
$487$	5.91522	0.268044	0.134022	+	0.990978i	$0.457211\pi$
$488$	−13.5186	−0.611959
$489$	38.0106	1.71890
$490$	6.24795	0.282253
$491$	13.0351	0.588265	0.294133	−	0.955765i	$-0.404969\pi$
$491$	13.0351	0.588265	0.294133	+	0.955765i	$0.404969\pi$
$492$	−13.8527	−0.624529
$493$	−3.76833	−0.169717
$494$	−27.7934	−1.25048
$495$	−7.06586	−0.317587
$496$	−1.12902	−0.0506947
$497$	7.86809	0.352932
$498$	−14.4102	−0.645736
$499$	41.2790	1.84790	0.923950	−	0.382513i	$-0.124941\pi$
$499$	41.2790	1.84790	0.923950	+	0.382513i	$0.124941\pi$
$500$	−1.00000	−0.0447214
$501$	32.2136	1.43920
$502$	−21.3752	−0.954024
$503$	4.80820	0.214387	0.107194	−	0.994238i	$-0.465814\pi$
$503$	4.80820	0.214387	0.107194	+	0.994238i	$0.465814\pi$
$504$	−4.60668	−0.205198
$505$	−6.44945	−0.286997
$506$	−6.64872	−0.295572
$507$	−93.0459	−4.13231
$508$	17.1104	0.759153
$509$	−41.0305	−1.81864	−0.909321	−	0.416094i	$-0.863399\pi$
$509$	−41.0305	−1.81864	−0.909321	+	0.416094i	$0.863399\pi$
$510$	−5.25046	−0.232494
$511$	−7.52083	−0.332702
$512$	1.00000	0.0441942
$513$	27.5345	1.21568
$514$	−3.97971	−0.175538
$515$	−9.27004	−0.408487
$516$	−13.7950	−0.607291
$517$	−2.70657	−0.119035
$518$	−5.82120	−0.255769
$519$	22.8733	1.00403
$520$	−6.72854	−0.295066
$521$	−12.4256	−0.544374	−0.272187	−	0.962244i	$-0.587747\pi$
$521$	−12.4256	−0.544374	−0.272187	+	0.962244i	$0.587747\pi$
$522$	10.9918	0.481099
$523$	−1.93702	−0.0847002	−0.0423501	−	0.999103i	$-0.513484\pi$
$523$	−1.93702	−0.0847002	−0.0423501	+	0.999103i	$0.513484\pi$
$524$	−5.47195	−0.239043
$525$	2.50022	0.109119
$526$	20.8581	0.909457
$527$	2.05611	0.0895655
$528$	−3.83491	−0.166893
$529$	1.98473	0.0862927
$530$	−1.92550	−0.0836386
$531$	−12.0087	−0.521133
$532$	3.58216	0.155306
$533$	32.3297	1.40035
$534$	21.6864	0.938464
$535$	−4.30195	−0.185989
$536$	−3.49264	−0.150859
$537$	−56.0541	−2.41891
$538$	−13.8566	−0.597399
$539$	−8.31070	−0.357967
$540$	6.66587	0.286853
$541$	39.2345	1.68682	0.843412	−	0.537268i	$-0.180544\pi$
$541$	39.2345	1.68682	0.843412	+	0.537268i	$0.180544\pi$
$542$	−5.82559	−0.250231
$543$	−3.80119	−0.163125
$544$	−1.82114	−0.0780806
$545$	−5.40382	−0.231474
$546$	16.8229	0.719952
$547$	−33.0997	−1.41524	−0.707621	−	0.706592i	$-0.750232\pi$
$547$	−33.0997	−1.41524	−0.707621	+	0.706592i	$0.750232\pi$
$548$	6.72773	0.287394
$549$	−71.8119	−3.06486
$550$	1.33015	0.0567178
$551$	−8.54725	−0.364125
$552$	14.4109	0.613370
$553$	−2.46148	−0.104673
$554$	7.12203	0.302586
$555$	19.3528	0.821479
$556$	19.1929	0.813962
$557$	17.1689	0.727471	0.363736	−	0.931502i	$-0.381501\pi$
$557$	17.1689	0.727471	0.363736	+	0.931502i	$0.381501\pi$
$558$	−5.99746	−0.253893
$559$	32.1950	1.36170
$560$	0.867210	0.0366463
$561$	6.98390	0.294860
$562$	33.0700	1.39497
$563$	28.0977	1.18418	0.592088	−	0.805873i	$-0.298304\pi$
$563$	28.0977	1.18418	0.592088	+	0.805873i	$0.298304\pi$
$564$	5.86643	0.247021
$565$	−12.6752	−0.533248
$566$	7.07732	0.297482
$567$	−2.84611	−0.119526
$568$	−9.07288	−0.380689
$569$	29.0827	1.21921	0.609605	−	0.792706i	$-0.291328\pi$
$569$	29.0827	1.21921	0.609605	+	0.792706i	$0.291328\pi$
$570$	−11.9090	−0.498813
$571$	19.1249	0.800351	0.400176	−	0.916438i	$-0.368949\pi$
$571$	19.1249	0.800351	0.400176	+	0.916438i	$0.368949\pi$
$572$	8.94996	0.374217
$573$	−12.1517	−0.507644
$574$	−4.16682	−0.173920
$575$	−4.99847	−0.208451
$576$	5.31208	0.221336
$577$	41.0525	1.70904	0.854520	−	0.519419i	$-0.173851\pi$
$577$	41.0525	1.70904	0.854520	+	0.519419i	$0.173851\pi$
$578$	−13.6835	−0.569157
$579$	−47.7374	−1.98390
$580$	−2.06922	−0.0859195
$581$	−4.33450	−0.179825
$582$	−24.3835	−1.01073
$583$	2.56121	0.106074
$584$	8.67245	0.358868
$585$	−35.7425	−1.47777
$586$	−22.2386	−0.918668
$587$	−5.29864	−0.218698	−0.109349	−	0.994003i	$-0.534877\pi$
$587$	−5.29864	−0.218698	−0.109349	+	0.994003i	$0.534877\pi$
$588$	18.0132	0.742854
$589$	4.66363	0.192161
$590$	2.26064	0.0930691
$591$	−7.70969	−0.317134
$592$	6.71256	0.275885
$593$	8.53086	0.350320	0.175160	−	0.984540i	$-0.443956\pi$
$593$	8.53086	0.350320	0.175160	+	0.984540i	$0.443956\pi$
$594$	−8.86660	−0.363801
$595$	−1.57931	−0.0647453
$596$	23.5386	0.964177
$597$	−55.0187	−2.25177
$598$	−33.6324	−1.37533
$599$	−23.5964	−0.964122	−0.482061	−	0.876138i	$-0.660112\pi$
$599$	−23.5964	−0.964122	−0.482061	+	0.876138i	$0.660112\pi$
$600$	−2.88307	−0.117701
$601$	−12.5855	−0.513373	−0.256687	−	0.966495i	$-0.582631\pi$
$601$	−12.5855	−0.513373	−0.256687	+	0.966495i	$0.582631\pi$
$602$	−4.14946	−0.169119
$603$	−18.5532	−0.755544
$604$	1.48896	0.0605849
$605$	9.23070	0.375281
$606$	−18.5942	−0.755338
$607$	13.7700	0.558905	0.279453	−	0.960159i	$-0.409847\pi$
$607$	13.7700	0.558905	0.279453	+	0.960159i	$0.409847\pi$
$608$	−4.13067	−0.167521
$609$	5.17350	0.209641
$610$	13.5186	0.547352
$611$	−13.6912	−0.553885
$612$	−9.67402	−0.391049
$613$	39.9101	1.61196	0.805978	−	0.591946i	$-0.201640\pi$
$613$	39.9101	1.61196	0.805978	+	0.591946i	$0.201640\pi$
$614$	14.4414	0.582809
$615$	13.8527	0.558596
$616$	−1.15352	−0.0464766
$617$	15.2976	0.615858	0.307929	−	0.951409i	$-0.400364\pi$
$617$	15.2976	0.615858	0.307929	+	0.951409i	$0.400364\pi$
$618$	−26.7261	−1.07508
$619$	20.7530	0.834133	0.417066	−	0.908876i	$-0.363058\pi$
$619$	20.7530	0.834133	0.417066	+	0.908876i	$0.363058\pi$
$620$	1.12902	0.0453427
$621$	33.3192	1.33705
$622$	−12.9454	−0.519063
$623$	6.52316	0.261345
$624$	−19.3988	−0.776575
$625$	1.00000	0.0400000
$626$	12.8709	0.514425
$627$	15.8407	0.632619
$628$	17.0685	0.681105
$629$	−12.2245	−0.487422
$630$	4.60668	0.183535
$631$	23.6234	0.940433	0.470217	−	0.882551i	$-0.344176\pi$
$631$	23.6234	0.940433	0.470217	+	0.882551i	$0.344176\pi$
$632$	2.83838	0.112905
$633$	−15.6206	−0.620865
$634$	−23.6880	−0.940769
$635$	−17.1104	−0.679007
$636$	−5.55136	−0.220126
$637$	−42.0396	−1.66567
$638$	2.75237	0.108967
$639$	−48.1958	−1.90660
$640$	−1.00000	−0.0395285
$641$	48.0161	1.89652	0.948262	−	0.317490i	$-0.102840\pi$
$641$	48.0161	1.89652	0.948262	+	0.317490i	$0.102840\pi$
$642$	−12.4028	−0.489499
$643$	−23.4094	−0.923175	−0.461588	−	0.887095i	$-0.652720\pi$
$643$	−23.4094	−0.923175	−0.461588	+	0.887095i	$0.652720\pi$
$644$	4.33473	0.170812
$645$	13.7950	0.543178
$646$	7.52252	0.295969
$647$	5.68923	0.223667	0.111833	−	0.993727i	$-0.464328\pi$
$647$	5.68923	0.223667	0.111833	+	0.993727i	$0.464328\pi$
$648$	3.28192	0.128926
$649$	−3.00699	−0.118035
$650$	6.72854	0.263915
$651$	−2.82281	−0.110635
$652$	−13.1841	−0.516328
$653$	10.4953	0.410713	0.205356	−	0.978687i	$-0.434165\pi$
$653$	10.4953	0.410713	0.205356	+	0.978687i	$0.434165\pi$
$654$	−15.5796	−0.609209
$655$	5.47195	0.213807
$656$	4.80486	0.187598
$657$	46.0687	1.79731
$658$	1.76459	0.0687909
$659$	9.88452	0.385046	0.192523	−	0.981292i	$-0.438333\pi$
$659$	9.88452	0.385046	0.192523	+	0.981292i	$0.438333\pi$
$660$	3.83491	0.149274
$661$	−5.27083	−0.205012	−0.102506	−	0.994732i	$-0.532686\pi$
$661$	−5.27083	−0.205012	−0.102506	+	0.994732i	$0.532686\pi$
$662$	−3.21129	−0.124810
$663$	35.3279	1.37202
$664$	4.99821	0.193968
$665$	−3.58216	−0.138910
$666$	35.6576	1.38170
$667$	−10.3429	−0.400480
$668$	−11.1734	−0.432311
$669$	−59.5555	−2.30255
$670$	3.49264	0.134933
$671$	−17.9818	−0.694178
$672$	2.50022	0.0964483
$673$	20.9723	0.808422	0.404211	−	0.914666i	$-0.367546\pi$
$673$	20.9723	0.808422	0.404211	+	0.914666i	$0.367546\pi$
$674$	−10.1369	−0.390457
$675$	−6.66587	−0.256569
$676$	32.2732	1.24128
$677$	9.63787	0.370414	0.185207	−	0.982700i	$-0.440705\pi$
$677$	9.63787	0.370414	0.185207	+	0.982700i	$0.440705\pi$
$678$	−36.5434	−1.40344
$679$	−7.33443	−0.281469
$680$	1.82114	0.0698374
$681$	53.6356	2.05532
$682$	−1.50177	−0.0575058
$683$	−1.38530	−0.0530069	−0.0265034	−	0.999649i	$-0.508437\pi$
$683$	−1.38530	−0.0530069	−0.0265034	+	0.999649i	$0.508437\pi$
$684$	−21.9424	−0.838990
$685$	−6.72773	−0.257053
$686$	11.4888	0.438643
$687$	37.4925	1.43043
$688$	4.78483	0.182420
$689$	12.9558	0.493578
$690$	−14.4109	−0.548615
$691$	−23.5986	−0.897735	−0.448867	−	0.893598i	$-0.648172\pi$
$691$	−23.5986	−0.897735	−0.448867	+	0.893598i	$0.648172\pi$
$692$	−7.93368	−0.301593
$693$	−6.12758	−0.232768
$694$	−30.7883	−1.16871
$695$	−19.1929	−0.728030
$696$	−5.96569	−0.226129
$697$	−8.75031	−0.331441
$698$	−23.6495	−0.895148
$699$	8.65230	0.327260
$700$	−0.867210	−0.0327775
$701$	−10.6557	−0.402459	−0.201230	−	0.979544i	$-0.564494\pi$
$701$	−10.6557	−0.402459	−0.201230	+	0.979544i	$0.564494\pi$
$702$	−44.8516	−1.69281
$703$	−27.7274	−1.04576
$704$	1.33015	0.0501319
$705$	−5.86643	−0.220943
$706$	13.4017	0.504379
$707$	−5.59303	−0.210348
$708$	6.51758	0.244946
$709$	−20.8849	−0.784347	−0.392174	−	0.919891i	$-0.628277\pi$
$709$	−20.8849	−0.784347	−0.392174	+	0.919891i	$0.628277\pi$
$710$	9.07288	0.340499
$711$	15.0777	0.565458
$712$	−7.52201	−0.281899
$713$	5.64340	0.211347
$714$	−4.55325	−0.170401
$715$	−8.94996	−0.334710
$716$	19.4425	0.726601
$717$	−83.1316	−3.10461
$718$	20.1426	0.751713
$719$	−29.3590	−1.09491	−0.547454	−	0.836836i	$-0.684403\pi$
$719$	−29.3590	−1.09491	−0.547454	+	0.836836i	$0.684403\pi$
$720$	−5.31208	−0.197969
$721$	−8.03907	−0.299391
$722$	−1.93757	−0.0721088
$723$	−21.7677	−0.809550
$724$	1.31845	0.0490000
$725$	2.06922	0.0768488
$726$	26.6127	0.987691
$727$	42.8112	1.58778	0.793889	−	0.608062i	$-0.208053\pi$
$727$	42.8112	1.58778	0.793889	+	0.608062i	$0.208053\pi$
$728$	−5.83506	−0.216262
$729$	−40.2206	−1.48965
$730$	−8.67245	−0.320982
$731$	−8.71384	−0.322293
$732$	38.9750	1.44056
$733$	33.0769	1.22172	0.610861	−	0.791738i	$-0.290823\pi$
$733$	33.0769	1.22172	0.610861	+	0.791738i	$0.290823\pi$
$734$	5.95908	0.219954
$735$	−18.0132	−0.664429
$736$	−4.99847	−0.184246
$737$	−4.64574	−0.171128
$738$	25.5238	0.939543
$739$	23.4370	0.862142	0.431071	−	0.902318i	$-0.358136\pi$
$739$	23.4370	0.862142	0.431071	+	0.902318i	$0.358136\pi$
$740$	−6.71256	−0.246759
$741$	80.1302	2.94366
$742$	−1.66982	−0.0613009
$743$	−12.9298	−0.474349	−0.237175	−	0.971467i	$-0.576221\pi$
$743$	−12.9298	−0.474349	−0.237175	+	0.971467i	$0.576221\pi$
$744$	3.25505	0.119336
$745$	−23.5386	−0.862387
$746$	10.4266	0.381746
$747$	26.5509	0.971446
$748$	−2.42239	−0.0885712
$749$	−3.73069	−0.136316
$750$	2.88307	0.105275
$751$	−37.7029	−1.37580	−0.687899	−	0.725806i	$-0.741467\pi$
$751$	−37.7029	−1.37580	−0.687899	+	0.725806i	$0.741467\pi$
$752$	−2.03479	−0.0742011
$753$	61.6263	2.24579
$754$	13.9228	0.507039
$755$	−1.48896	−0.0541888
$756$	5.78071	0.210242
$757$	21.5487	0.783201	0.391600	−	0.920135i	$-0.371922\pi$
$757$	21.5487	0.783201	0.391600	+	0.920135i	$0.371922\pi$
$758$	−12.3032	−0.446873
$759$	19.1687	0.695780
$760$	4.13067	0.149835
$761$	20.8529	0.755918	0.377959	−	0.925822i	$-0.376626\pi$
$761$	20.8529	0.755918	0.377959	+	0.925822i	$0.376626\pi$
$762$	−49.3305	−1.78706
$763$	−4.68625	−0.169653
$764$	4.21485	0.152488
$765$	9.67402	0.349765
$766$	3.36706	0.121657
$767$	−15.2108	−0.549230
$768$	−2.88307	−0.104034
$769$	17.4031	0.627573	0.313786	−	0.949494i	$-0.398402\pi$
$769$	17.4031	0.627573	0.313786	+	0.949494i	$0.398402\pi$
$770$	1.15352	0.0415699
$771$	11.4738	0.413218
$772$	16.5579	0.595931
$773$	10.6926	0.384587	0.192293	−	0.981338i	$-0.438408\pi$
$773$	10.6926	0.384587	0.192293	+	0.981338i	$0.438408\pi$
$774$	25.4174	0.913610
$775$	−1.12902	−0.0405557
$776$	8.45750	0.303606
$777$	16.7829	0.602083
$778$	12.0923	0.433530
$779$	−19.8473	−0.711103
$780$	19.3988	0.694590
$781$	−12.0683	−0.431837
$782$	9.10291	0.325519
$783$	−13.7931	−0.492926
$784$	−6.24795	−0.223141
$785$	−17.0685	−0.609199
$786$	15.7760	0.562711
$787$	12.0817	0.430665	0.215332	−	0.976541i	$-0.430916\pi$
$787$	12.0817	0.430665	0.215332	+	0.976541i	$0.430916\pi$
$788$	2.67413	0.0952619
$789$	−60.1353	−2.14088
$790$	−2.83838	−0.100985
$791$	−10.9920	−0.390832
$792$	7.06586	0.251074
$793$	−90.9605	−3.23010
$794$	14.4221	0.511823
$795$	5.55136	0.196886
$796$	19.0834	0.676393
$797$	−5.74200	−0.203392	−0.101696	−	0.994816i	$-0.532427\pi$
$797$	−5.74200	−0.203392	−0.101696	+	0.994816i	$0.532427\pi$
$798$	−10.3276	−0.365593
$799$	3.70563	0.131096
$800$	1.00000	0.0353553
$801$	−39.9575	−1.41183
$802$	−1.00000	−0.0353112
$803$	11.5357	0.407084
$804$	10.0695	0.355125
$805$	−4.33473	−0.152779
$806$	−7.59668	−0.267582
$807$	39.9494	1.40629
$808$	6.44945	0.226891
$809$	17.8718	0.628340	0.314170	−	0.949367i	$-0.398274\pi$
$809$	17.8718	0.628340	0.314170	+	0.949367i	$0.398274\pi$
$810$	−3.28192	−0.115315
$811$	3.82692	0.134381	0.0671906	−	0.997740i	$-0.478596\pi$
$811$	3.82692	0.134381	0.0671906	+	0.997740i	$0.478596\pi$
$812$	−1.79444	−0.0629727
$813$	16.7956	0.589046
$814$	8.92871	0.312951
$815$	13.1841	0.461818
$816$	5.25046	0.183803
$817$	−19.7646	−0.691475
$818$	4.28102	0.149683
$819$	−30.9963	−1.08310
$820$	−4.80486	−0.167793
$821$	−11.0102	−0.384258	−0.192129	−	0.981370i	$-0.561539\pi$
$821$	−11.0102	−0.384258	−0.192129	+	0.981370i	$0.561539\pi$
$822$	−19.3965	−0.676530
$823$	40.8900	1.42533	0.712667	−	0.701502i	$-0.247487\pi$
$823$	40.8900	1.42533	0.712667	+	0.701502i	$0.247487\pi$
$824$	9.27004	0.322937
$825$	−3.83491	−0.133514
$826$	1.96045	0.0682128
$827$	−36.4534	−1.26761	−0.633804	−	0.773494i	$-0.718507\pi$
$827$	−36.4534	−1.26761	−0.633804	+	0.773494i	$0.718507\pi$
$828$	−26.5523	−0.922755
$829$	−5.32337	−0.184888	−0.0924441	−	0.995718i	$-0.529468\pi$
$829$	−5.32337	−0.184888	−0.0924441	+	0.995718i	$0.529468\pi$
$830$	−4.99821	−0.173491
$831$	−20.5333	−0.712292
$832$	6.72854	0.233270
$833$	11.3784	0.394237
$834$	−55.3345	−1.91608
$835$	11.1734	0.386670
$836$	−5.49441	−0.190028
$837$	7.52593	0.260134
$838$	−1.76386	−0.0609314
$839$	−10.5226	−0.363282	−0.181641	−	0.983365i	$-0.558141\pi$
$839$	−10.5226	−0.363282	−0.181641	+	0.983365i	$0.558141\pi$
$840$	−2.50022	−0.0862659
$841$	−24.7183	−0.852357
$842$	−32.4043	−1.11673
$843$	−95.3431	−3.28379
$844$	5.41807	0.186497
$845$	−32.2732	−1.11023
$846$	−10.8090	−0.371619
$847$	8.00496	0.275054
$848$	1.92550	0.0661221
$849$	−20.4044	−0.700276
$850$	−1.82114	−0.0624645
$851$	−33.5525	−1.15017
$852$	26.1577	0.896149
$853$	4.05556	0.138860	0.0694298	−	0.997587i	$-0.477882\pi$
$853$	4.05556	0.138860	0.0694298	+	0.997587i	$0.477882\pi$
$854$	11.7235	0.401169
$855$	21.9424	0.750415
$856$	4.30195	0.147037
$857$	25.9909	0.887831	0.443915	−	0.896069i	$-0.353589\pi$
$857$	25.9909	0.887831	0.443915	+	0.896069i	$0.353589\pi$
$858$	−25.8033	−0.880912
$859$	17.8006	0.607350	0.303675	−	0.952776i	$-0.401786\pi$
$859$	17.8006	0.607350	0.303675	+	0.952776i	$0.401786\pi$
$860$	−4.78483	−0.163162
$861$	12.0132	0.409410
$862$	−22.1266	−0.753634
$863$	25.1619	0.856522	0.428261	−	0.903655i	$-0.359126\pi$
$863$	25.1619	0.856522	0.428261	+	0.903655i	$0.359126\pi$
$864$	−6.66587	−0.226777
$865$	7.93368	0.269753
$866$	−33.9538	−1.15380
$867$	39.4503	1.33980
$868$	0.979101	0.0332329
$869$	3.77548	0.128074
$870$	5.96569	0.202256
$871$	−23.5004	−0.796280
$872$	5.40382	0.182996
$873$	44.9269	1.52054
$874$	20.6470	0.698397
$875$	0.867210	0.0293170
$876$	−25.0032	−0.844782
$877$	−45.7856	−1.54607	−0.773036	−	0.634363i	$-0.781263\pi$
$877$	−45.7856	−1.54607	−0.773036	+	0.634363i	$0.781263\pi$
$878$	−21.5548	−0.727440
$879$	64.1153	2.16256
$880$	−1.33015	−0.0448393
$881$	−41.3856	−1.39432	−0.697158	−	0.716918i	$-0.745552\pi$
$881$	−41.3856	−1.39432	−0.697158	+	0.716918i	$0.745552\pi$
$882$	−33.1896	−1.11755
$883$	−38.1461	−1.28372	−0.641859	−	0.766823i	$-0.721837\pi$
$883$	−38.1461	−1.28372	−0.641859	+	0.766823i	$0.721837\pi$
$884$	−12.2536	−0.412133
$885$	−6.51758	−0.219086
$886$	19.4900	0.654780
$887$	−3.19217	−0.107183	−0.0535913	−	0.998563i	$-0.517067\pi$
$887$	−3.19217	−0.107183	−0.0535913	+	0.998563i	$0.517067\pi$
$888$	−19.3528	−0.649436
$889$	−14.8383	−0.497662
$890$	7.52201	0.252138
$891$	4.36544	0.146248
$892$	20.6570	0.691647
$893$	8.40504	0.281264
$894$	−67.8633	−2.26969
$895$	−19.4425	−0.649892
$896$	−0.867210	−0.0289715
$897$	96.9645	3.23755
$898$	23.8264	0.795098
$899$	−2.33619	−0.0779165
$900$	5.31208	0.177069
$901$	−3.50661	−0.116822
$902$	6.39118	0.212803
$903$	11.9632	0.398109
$904$	12.6752	0.421570
$905$	−1.31845	−0.0438269
$906$	−4.29277	−0.142618
$907$	−28.2757	−0.938880	−0.469440	−	0.882964i	$-0.655544\pi$
$907$	−28.2757	−0.938880	−0.469440	+	0.882964i	$0.655544\pi$
$908$	−18.6037	−0.617384
$909$	34.2600	1.13633
$910$	5.83506	0.193430
$911$	−11.7244	−0.388447	−0.194223	−	0.980957i	$-0.562219\pi$
$911$	−11.7244	−0.388447	−0.194223	+	0.980957i	$0.562219\pi$
$912$	11.9090	0.394346
$913$	6.64837	0.220029
$914$	10.3737	0.343132
$915$	−38.9750	−1.28848
$916$	−13.0044	−0.429677
$917$	4.74533	0.156705
$918$	12.1395	0.400662
$919$	2.30087	0.0758988	0.0379494	−	0.999280i	$-0.487917\pi$
$919$	2.30087	0.0758988	0.0379494	+	0.999280i	$0.487917\pi$
$920$	4.99847	0.164795
$921$	−41.6356	−1.37194
$922$	−9.75474	−0.321255
$923$	−61.0472	−2.00939
$924$	3.32567	0.109407
$925$	6.71256	0.220708
$926$	−27.9235	−0.917623
$927$	49.2432	1.61736
$928$	2.06922	0.0679253
$929$	1.09251	0.0358442	0.0179221	−	0.999839i	$-0.494295\pi$
$929$	1.09251	0.0358442	0.0179221	+	0.999839i	$0.494295\pi$
$930$	−3.25505	−0.106737
$931$	25.8082	0.845830
$932$	−3.00108	−0.0983035
$933$	37.3224	1.22188
$934$	−3.89002	−0.127285
$935$	2.42239	0.0792205
$936$	35.7425	1.16828
$937$	−11.5093	−0.375991	−0.187995	−	0.982170i	$-0.560199\pi$
$937$	−11.5093	−0.375991	−0.187995	+	0.982170i	$0.560199\pi$
$938$	3.02885	0.0988956
$939$	−37.1077	−1.21096
$940$	2.03479	0.0663675
$941$	−44.7211	−1.45787	−0.728933	−	0.684585i	$-0.759983\pi$
$941$	−44.7211	−1.45787	−0.728933	+	0.684585i	$0.759983\pi$
$942$	−49.2095	−1.60333
$943$	−24.0170	−0.782100
$944$	−2.26064	−0.0735776
$945$	−5.78071	−0.188046
$946$	6.36455	0.206929
$947$	−32.3918	−1.05259	−0.526296	−	0.850301i	$-0.676420\pi$
$947$	−32.3918	−1.05259	−0.526296	+	0.850301i	$0.676420\pi$
$948$	−8.18325	−0.265780
$949$	58.3529	1.89422
$950$	−4.13067	−0.134017
$951$	68.2940	2.21458
$952$	1.57931	0.0511857
$953$	44.0015	1.42535	0.712675	−	0.701494i	$-0.247483\pi$
$953$	44.0015	1.42535	0.712675	+	0.701494i	$0.247483\pi$
$954$	10.2284	0.331157
$955$	−4.21485	−0.136389
$956$	28.8344	0.932572
$957$	−7.93526	−0.256510
$958$	−10.4030	−0.336106
$959$	−5.83435	−0.188401
$960$	2.88307	0.0930506
$961$	−29.7253	−0.958881
$962$	45.1657	1.45620
$963$	22.8523	0.736404
$964$	7.55019	0.243175
$965$	−16.5579	−0.533016
$966$	−12.4973	−0.402094
$967$	−21.9491	−0.705836	−0.352918	−	0.935654i	$-0.614810\pi$
$967$	−21.9491	−0.705836	−0.352918	+	0.935654i	$0.614810\pi$
$968$	−9.23070	−0.296686
$969$	−21.6879	−0.696716
$970$	−8.45750	−0.271554
$971$	−27.4175	−0.879869	−0.439935	−	0.898030i	$-0.644998\pi$
$971$	−27.4175	−0.879869	−0.439935	+	0.898030i	$0.644998\pi$
$972$	10.5356	0.337930
$973$	−16.6443	−0.533592
$974$	5.91522	0.189536
$975$	−19.3988	−0.621260
$976$	−13.5186	−0.432720
$977$	−54.9519	−1.75807	−0.879033	−	0.476761i	$-0.841811\pi$
$977$	−54.9519	−1.75807	−0.879033	+	0.476761i	$0.841811\pi$
$978$	38.0106	1.21544
$979$	−10.0054	−0.319774
$980$	6.24795	0.199583
$981$	28.7055	0.916496
$982$	13.0351	0.415966
$983$	−0.228649	−0.00729276	−0.00364638	−	0.999993i	$-0.501161\pi$
$983$	−0.228649	−0.00729276	−0.00364638	+	0.999993i	$0.501161\pi$
$984$	−13.8527	−0.441609
$985$	−2.67413	−0.0852048
$986$	−3.76833	−0.120008
$987$	−5.08743	−0.161935
$988$	−27.7934	−0.884225
$989$	−23.9169	−0.760512
$990$	−7.06586	−0.224568
$991$	10.1393	0.322084	0.161042	−	0.986948i	$-0.448515\pi$
$991$	10.1393	0.322084	0.161042	+	0.986948i	$0.448515\pi$
$992$	−1.12902	−0.0358466
$993$	9.25837	0.293805
$994$	7.86809	0.249561
$995$	−19.0834	−0.604984
$996$	−14.4102	−0.456604
$997$	−0.825970	−0.0261587	−0.0130794	−	0.999914i	$-0.504163\pi$
$997$	−0.825970	−0.0261587	−0.0130794	+	0.999914i	$0.504163\pi$
$998$	41.2790	1.30666
$999$	−44.7450	−1.41567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.3	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.3	✓	22	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.88307 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.88307 q^{6} -0.867210 q^{7} +1.00000 q^{8} +5.31208 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.88307 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.88307 q^{6} -0.867210 q^{7} +1.00000 q^{8} +5.31208 q^{9} -1.00000 q^{10} +1.33015 q^{11} -2.88307 q^{12} +6.72854 q^{13} -0.867210 q^{14} +2.88307 q^{15} +1.00000 q^{16} -1.82114 q^{17} +5.31208 q^{18} -4.13067 q^{19} -1.00000 q^{20} +2.50022 q^{21} +1.33015 q^{22} -4.99847 q^{23} -2.88307 q^{24} +1.00000 q^{25} +6.72854 q^{26} -6.66587 q^{27} -0.867210 q^{28} +2.06922 q^{29} +2.88307 q^{30} -1.12902 q^{31} +1.00000 q^{32} -3.83491 q^{33} -1.82114 q^{34} +0.867210 q^{35} +5.31208 q^{36} +6.71256 q^{37} -4.13067 q^{38} -19.3988 q^{39} -1.00000 q^{40} +4.80486 q^{41} +2.50022 q^{42} +4.78483 q^{43} +1.33015 q^{44} -5.31208 q^{45} -4.99847 q^{46} -2.03479 q^{47} -2.88307 q^{48} -6.24795 q^{49} +1.00000 q^{50} +5.25046 q^{51} +6.72854 q^{52} +1.92550 q^{53} -6.66587 q^{54} -1.33015 q^{55} -0.867210 q^{56} +11.9090 q^{57} +2.06922 q^{58} -2.26064 q^{59} +2.88307 q^{60} -13.5186 q^{61} -1.12902 q^{62} -4.60668 q^{63} +1.00000 q^{64} -6.72854 q^{65} -3.83491 q^{66} -3.49264 q^{67} -1.82114 q^{68} +14.4109 q^{69} +0.867210 q^{70} -9.07288 q^{71} +5.31208 q^{72} +8.67245 q^{73} +6.71256 q^{74} -2.88307 q^{75} -4.13067 q^{76} -1.15352 q^{77} -19.3988 q^{78} +2.83838 q^{79} -1.00000 q^{80} +3.28192 q^{81} +4.80486 q^{82} +4.99821 q^{83} +2.50022 q^{84} +1.82114 q^{85} +4.78483 q^{86} -5.96569 q^{87} +1.33015 q^{88} -7.52201 q^{89} -5.31208 q^{90} -5.83506 q^{91} -4.99847 q^{92} +3.25505 q^{93} -2.03479 q^{94} +4.13067 q^{95} -2.88307 q^{96} +8.45750 q^{97} -6.24795 q^{98} +7.06586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - q^99

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