LMFDB - Embedded newform 4010.2.a.n.1.17

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			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.40993 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.40993 q^{6} +4.92260 q^{7} +1.00000 q^{8} +2.80778 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.40993 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.40993 q^{6} +4.92260 q^{7} +1.00000 q^{8} +2.80778 q^{9} +1.00000 q^{10} -1.92594 q^{11} +2.40993 q^{12} -1.63940 q^{13} +4.92260 q^{14} +2.40993 q^{15} +1.00000 q^{16} +6.34821 q^{17} +2.80778 q^{18} -0.942089 q^{19} +1.00000 q^{20} +11.8631 q^{21} -1.92594 q^{22} -7.85720 q^{23} +2.40993 q^{24} +1.00000 q^{25} -1.63940 q^{26} -0.463247 q^{27} +4.92260 q^{28} -5.38911 q^{29} +2.40993 q^{30} -0.366550 q^{31} +1.00000 q^{32} -4.64139 q^{33} +6.34821 q^{34} +4.92260 q^{35} +2.80778 q^{36} +8.44027 q^{37} -0.942089 q^{38} -3.95083 q^{39} +1.00000 q^{40} +5.10597 q^{41} +11.8631 q^{42} -6.48856 q^{43} -1.92594 q^{44} +2.80778 q^{45} -7.85720 q^{46} -0.0520240 q^{47} +2.40993 q^{48} +17.2320 q^{49} +1.00000 q^{50} +15.2988 q^{51} -1.63940 q^{52} +1.55627 q^{53} -0.463247 q^{54} -1.92594 q^{55} +4.92260 q^{56} -2.27037 q^{57} -5.38911 q^{58} -12.1489 q^{59} +2.40993 q^{60} +6.58878 q^{61} -0.366550 q^{62} +13.8216 q^{63} +1.00000 q^{64} -1.63940 q^{65} -4.64139 q^{66} +4.51013 q^{67} +6.34821 q^{68} -18.9353 q^{69} +4.92260 q^{70} -12.5467 q^{71} +2.80778 q^{72} -4.90827 q^{73} +8.44027 q^{74} +2.40993 q^{75} -0.942089 q^{76} -9.48064 q^{77} -3.95083 q^{78} -0.680334 q^{79} +1.00000 q^{80} -9.53972 q^{81} +5.10597 q^{82} -10.5234 q^{83} +11.8631 q^{84} +6.34821 q^{85} -6.48856 q^{86} -12.9874 q^{87} -1.92594 q^{88} -4.12062 q^{89} +2.80778 q^{90} -8.07009 q^{91} -7.85720 q^{92} -0.883360 q^{93} -0.0520240 q^{94} -0.942089 q^{95} +2.40993 q^{96} +15.7769 q^{97} +17.2320 q^{98} -5.40761 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * 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
$3$	2.40993	1.39138	0.695688	−	0.718344i	$-0.255100\pi$
$3$	2.40993	1.39138	0.695688	+	0.718344i	$0.255100\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.40993	0.983851
$7$	4.92260	1.86057	0.930285	−	0.366839i	$-0.119560\pi$
$7$	4.92260	1.86057	0.930285	+	0.366839i	$0.119560\pi$
$8$	1.00000	0.353553
$9$	2.80778	0.935925
$10$	1.00000	0.316228
$11$	−1.92594	−0.580693	−0.290346	−	0.956922i	$-0.593771\pi$
$11$	−1.92594	−0.580693	−0.290346	+	0.956922i	$0.593771\pi$
$12$	2.40993	0.695688
$13$	−1.63940	−0.454687	−0.227343	−	0.973815i	$-0.573004\pi$
$13$	−1.63940	−0.454687	−0.227343	+	0.973815i	$0.573004\pi$
$14$	4.92260	1.31562
$15$	2.40993	0.622242
$16$	1.00000	0.250000
$17$	6.34821	1.53967	0.769834	−	0.638244i	$-0.220339\pi$
$17$	6.34821	1.53967	0.769834	+	0.638244i	$0.220339\pi$
$18$	2.80778	0.661799
$19$	−0.942089	−0.216130	−0.108065	−	0.994144i	$-0.534465\pi$
$19$	−0.942089	−0.216130	−0.108065	+	0.994144i	$0.534465\pi$
$20$	1.00000	0.223607
$21$	11.8631	2.58875
$22$	−1.92594	−0.410612
$23$	−7.85720	−1.63834	−0.819169	−	0.573552i	$-0.805565\pi$
$23$	−7.85720	−1.63834	−0.819169	+	0.573552i	$0.805565\pi$
$24$	2.40993	0.491925
$25$	1.00000	0.200000
$26$	−1.63940	−0.321512
$27$	−0.463247	−0.0891519
$28$	4.92260	0.930285
$29$	−5.38911	−1.00073	−0.500366	−	0.865814i	$-0.666801\pi$
$29$	−5.38911	−1.00073	−0.500366	+	0.865814i	$0.666801\pi$
$30$	2.40993	0.439992
$31$	−0.366550	−0.0658342	−0.0329171	−	0.999458i	$-0.510480\pi$
$31$	−0.366550	−0.0658342	−0.0329171	+	0.999458i	$0.510480\pi$
$32$	1.00000	0.176777
$33$	−4.64139	−0.807961
$34$	6.34821	1.08871
$35$	4.92260	0.832072
$36$	2.80778	0.467963
$37$	8.44027	1.38757	0.693786	−	0.720181i	$-0.255941\pi$
$37$	8.44027	1.38757	0.693786	+	0.720181i	$0.255941\pi$
$38$	−0.942089	−0.152827
$39$	−3.95083	−0.632640
$40$	1.00000	0.158114
$41$	5.10597	0.797418	0.398709	−	0.917078i	$-0.369458\pi$
$41$	5.10597	0.797418	0.398709	+	0.917078i	$0.369458\pi$
$42$	11.8631	1.83052
$43$	−6.48856	−0.989495	−0.494748	−	0.869037i	$-0.664740\pi$
$43$	−6.48856	−0.989495	−0.494748	+	0.869037i	$0.664740\pi$
$44$	−1.92594	−0.290346
$45$	2.80778	0.418559
$46$	−7.85720	−1.15848
$47$	−0.0520240	−0.00758848	−0.00379424	−	0.999993i	$-0.501208\pi$
$47$	−0.0520240	−0.00758848	−0.00379424	+	0.999993i	$0.501208\pi$
$48$	2.40993	0.347844
$49$	17.2320	2.46172
$50$	1.00000	0.141421
$51$	15.2988	2.14226
$52$	−1.63940	−0.227343
$53$	1.55627	0.213770	0.106885	−	0.994271i	$-0.465912\pi$
$53$	1.55627	0.213770	0.106885	+	0.994271i	$0.465912\pi$
$54$	−0.463247	−0.0630399
$55$	−1.92594	−0.259694
$56$	4.92260	0.657811
$57$	−2.27037	−0.300718
$58$	−5.38911	−0.707625
$59$	−12.1489	−1.58165	−0.790827	−	0.612040i	$-0.790349\pi$
$59$	−12.1489	−1.58165	−0.790827	+	0.612040i	$0.790349\pi$
$60$	2.40993	0.311121
$61$	6.58878	0.843607	0.421804	−	0.906687i	$-0.361397\pi$
$61$	6.58878	0.843607	0.421804	+	0.906687i	$0.361397\pi$
$62$	−0.366550	−0.0465518
$63$	13.8216	1.74135
$64$	1.00000	0.125000
$65$	−1.63940	−0.203342
$66$	−4.64139	−0.571315
$67$	4.51013	0.551001	0.275500	−	0.961301i	$-0.411156\pi$
$67$	4.51013	0.551001	0.275500	+	0.961301i	$0.411156\pi$
$68$	6.34821	0.769834
$69$	−18.9353	−2.27954
$70$	4.92260	0.588364
$71$	−12.5467	−1.48902	−0.744510	−	0.667611i	$-0.767317\pi$
$71$	−12.5467	−1.48902	−0.744510	+	0.667611i	$0.767317\pi$
$72$	2.80778	0.330900
$73$	−4.90827	−0.574469	−0.287235	−	0.957860i	$-0.592736\pi$
$73$	−4.90827	−0.574469	−0.287235	+	0.957860i	$0.592736\pi$
$74$	8.44027	0.981162
$75$	2.40993	0.278275
$76$	−0.942089	−0.108065
$77$	−9.48064	−1.08042
$78$	−3.95083	−0.447344
$79$	−0.680334	−0.0765436	−0.0382718	−	0.999267i	$-0.512185\pi$
$79$	−0.680334	−0.0765436	−0.0382718	+	0.999267i	$0.512185\pi$
$80$	1.00000	0.111803
$81$	−9.53972	−1.05997
$82$	5.10597	0.563860
$83$	−10.5234	−1.15509	−0.577545	−	0.816359i	$-0.695989\pi$
$83$	−10.5234	−1.15509	−0.577545	+	0.816359i	$0.695989\pi$
$84$	11.8631	1.29437
$85$	6.34821	0.688560
$86$	−6.48856	−0.699679
$87$	−12.9874	−1.39239
$88$	−1.92594	−0.205306
$89$	−4.12062	−0.436785	−0.218392	−	0.975861i	$-0.570081\pi$
$89$	−4.12062	−0.436785	−0.218392	+	0.975861i	$0.570081\pi$
$90$	2.80778	0.295966
$91$	−8.07009	−0.845976
$92$	−7.85720	−0.819169
$93$	−0.883360	−0.0916001
$94$	−0.0520240	−0.00536587
$95$	−0.942089	−0.0966562
$96$	2.40993	0.245963
$97$	15.7769	1.60190	0.800951	−	0.598730i	$-0.204328\pi$
$97$	15.7769	1.60190	0.800951	+	0.598730i	$0.204328\pi$
$98$	17.2320	1.74070
$99$	−5.40761	−0.543485
$100$	1.00000	0.100000
$101$	14.6810	1.46081	0.730407	−	0.683012i	$-0.239330\pi$
$101$	14.6810	1.46081	0.730407	+	0.683012i	$0.239330\pi$
$102$	15.2988	1.51480
$103$	0.258573	0.0254779	0.0127390	−	0.999919i	$-0.495945\pi$
$103$	0.258573	0.0254779	0.0127390	+	0.999919i	$0.495945\pi$
$104$	−1.63940	−0.160756
$105$	11.8631	1.15772
$106$	1.55627	0.151158
$107$	−14.5114	−1.40287	−0.701437	−	0.712731i	$-0.747458\pi$
$107$	−14.5114	−1.40287	−0.701437	+	0.712731i	$0.747458\pi$
$108$	−0.463247	−0.0445760
$109$	−9.80642	−0.939284	−0.469642	−	0.882857i	$-0.655617\pi$
$109$	−9.80642	−0.939284	−0.469642	+	0.882857i	$0.655617\pi$
$110$	−1.92594	−0.183631
$111$	20.3405	1.93063
$112$	4.92260	0.465142
$113$	9.64153	0.906999	0.453499	−	0.891257i	$-0.350175\pi$
$113$	9.64153	0.906999	0.453499	+	0.891257i	$0.350175\pi$
$114$	−2.27037	−0.212640
$115$	−7.85720	−0.732687
$116$	−5.38911	−0.500366
$117$	−4.60306	−0.425553
$118$	−12.1489	−1.11840
$119$	31.2497	2.86466
$120$	2.40993	0.219996
$121$	−7.29076	−0.662796
$122$	6.58878	0.596521
$123$	12.3050	1.10951
$124$	−0.366550	−0.0329171
$125$	1.00000	0.0894427
$126$	13.8216	1.23132
$127$	−3.78056	−0.335470	−0.167735	−	0.985832i	$-0.553645\pi$
$127$	−3.78056	−0.335470	−0.167735	+	0.985832i	$0.553645\pi$
$128$	1.00000	0.0883883
$129$	−15.6370	−1.37676
$130$	−1.63940	−0.143785
$131$	2.81059	0.245562	0.122781	−	0.992434i	$-0.460819\pi$
$131$	2.81059	0.245562	0.122781	+	0.992434i	$0.460819\pi$
$132$	−4.64139	−0.403981
$133$	−4.63753	−0.402125
$134$	4.51013	0.389616
$135$	−0.463247	−0.0398700
$136$	6.34821	0.544355
$137$	1.93821	0.165593	0.0827963	−	0.996566i	$-0.473615\pi$
$137$	1.93821	0.165593	0.0827963	+	0.996566i	$0.473615\pi$
$138$	−18.9353	−1.61188
$139$	−20.9891	−1.78028	−0.890138	−	0.455691i	$-0.849392\pi$
$139$	−20.9891	−1.78028	−0.890138	+	0.455691i	$0.849392\pi$
$140$	4.92260	0.416036
$141$	−0.125374	−0.0105584
$142$	−12.5467	−1.05290
$143$	3.15738	0.264033
$144$	2.80778	0.233981
$145$	−5.38911	−0.447541
$146$	−4.90827	−0.406211
$147$	41.5280	3.42517
$148$	8.44027	0.693786
$149$	−0.676365	−0.0554100	−0.0277050	−	0.999616i	$-0.508820\pi$
$149$	−0.676365	−0.0554100	−0.0277050	+	0.999616i	$0.508820\pi$
$150$	2.40993	0.196770
$151$	2.04025	0.166033	0.0830166	−	0.996548i	$-0.473545\pi$
$151$	2.04025	0.166033	0.0830166	+	0.996548i	$0.473545\pi$
$152$	−0.942089	−0.0764135
$153$	17.8244	1.44101
$154$	−9.48064	−0.763971
$155$	−0.366550	−0.0294420
$156$	−3.95083	−0.316320
$157$	10.7203	0.855575	0.427787	−	0.903879i	$-0.359293\pi$
$157$	10.7203	0.855575	0.427787	+	0.903879i	$0.359293\pi$
$158$	−0.680334	−0.0541245
$159$	3.75050	0.297434
$160$	1.00000	0.0790569
$161$	−38.6779	−3.04824
$162$	−9.53972	−0.749511
$163$	4.37339	0.342550	0.171275	−	0.985223i	$-0.445211\pi$
$163$	4.37339	0.342550	0.171275	+	0.985223i	$0.445211\pi$
$164$	5.10597	0.398709
$165$	−4.64139	−0.361331
$166$	−10.5234	−0.816771
$167$	−7.29467	−0.564479	−0.282239	−	0.959344i	$-0.591077\pi$
$167$	−7.29467	−0.564479	−0.282239	+	0.959344i	$0.591077\pi$
$168$	11.8631	0.915261
$169$	−10.3124	−0.793260
$170$	6.34821	0.486886
$171$	−2.64517	−0.202281
$172$	−6.48856	−0.494748
$173$	20.3994	1.55093	0.775467	−	0.631388i	$-0.217514\pi$
$173$	20.3994	1.55093	0.775467	+	0.631388i	$0.217514\pi$
$174$	−12.9874	−0.984572
$175$	4.92260	0.372114
$176$	−1.92594	−0.145173
$177$	−29.2781	−2.20067
$178$	−4.12062	−0.308853
$179$	9.57165	0.715419	0.357709	−	0.933833i	$-0.383558\pi$
$179$	9.57165	0.715419	0.357709	+	0.933833i	$0.383558\pi$
$180$	2.80778	0.209279
$181$	−1.92313	−0.142945	−0.0714726	−	0.997443i	$-0.522770\pi$
$181$	−1.92313	−0.142945	−0.0714726	+	0.997443i	$0.522770\pi$
$182$	−8.07009	−0.598195
$183$	15.8785	1.17377
$184$	−7.85720	−0.579240
$185$	8.44027	0.620541
$186$	−0.883360	−0.0647711
$187$	−12.2263	−0.894074
$188$	−0.0520240	−0.00379424
$189$	−2.28038	−0.165873
$190$	−0.942089	−0.0683463
$191$	−20.9468	−1.51566	−0.757829	−	0.652453i	$-0.773740\pi$
$191$	−20.9468	−1.51566	−0.757829	+	0.652453i	$0.773740\pi$
$192$	2.40993	0.173922
$193$	21.2217	1.52757	0.763785	−	0.645471i	$-0.223339\pi$
$193$	21.2217	1.52757	0.763785	+	0.645471i	$0.223339\pi$
$194$	15.7769	1.13272
$195$	−3.95083	−0.282925
$196$	17.2320	1.23086
$197$	8.49981	0.605586	0.302793	−	0.953056i	$-0.402081\pi$
$197$	8.49981	0.605586	0.302793	+	0.953056i	$0.402081\pi$
$198$	−5.40761	−0.384302
$199$	6.43272	0.456004	0.228002	−	0.973661i	$-0.426781\pi$
$199$	6.43272	0.456004	0.228002	+	0.973661i	$0.426781\pi$
$200$	1.00000	0.0707107
$201$	10.8691	0.766649
$202$	14.6810	1.03295
$203$	−26.5284	−1.86193
$204$	15.2988	1.07113
$205$	5.10597	0.356616
$206$	0.258573	0.0180156
$207$	−22.0612	−1.53336
$208$	−1.63940	−0.113672
$209$	1.81441	0.125505
$210$	11.8631	0.818635
$211$	10.2181	0.703441	0.351720	−	0.936105i	$-0.385597\pi$
$211$	10.2181	0.703441	0.351720	+	0.936105i	$0.385597\pi$
$212$	1.55627	0.106885
$213$	−30.2367	−2.07179
$214$	−14.5114	−0.991982
$215$	−6.48856	−0.442516
$216$	−0.463247	−0.0315200
$217$	−1.80438	−0.122489
$218$	−9.80642	−0.664174
$219$	−11.8286	−0.799302
$220$	−1.92594	−0.129847
$221$	−10.4072	−0.700066
$222$	20.3405	1.36516
$223$	−8.32263	−0.557325	−0.278662	−	0.960389i	$-0.589891\pi$
$223$	−8.32263	−0.557325	−0.278662	+	0.960389i	$0.589891\pi$
$224$	4.92260	0.328905
$225$	2.80778	0.187185
$226$	9.64153	0.641345
$227$	26.8868	1.78454	0.892271	−	0.451500i	$-0.149111\pi$
$227$	26.8868	1.78454	0.892271	+	0.451500i	$0.149111\pi$
$228$	−2.27037	−0.150359
$229$	−28.1263	−1.85864	−0.929320	−	0.369275i	$-0.879606\pi$
$229$	−28.1263	−1.85864	−0.929320	+	0.369275i	$0.879606\pi$
$230$	−7.85720	−0.518088
$231$	−22.8477	−1.50327
$232$	−5.38911	−0.353812
$233$	−20.7003	−1.35612	−0.678060	−	0.735007i	$-0.737179\pi$
$233$	−20.7003	−1.35612	−0.678060	+	0.735007i	$0.737179\pi$
$234$	−4.60306	−0.300911
$235$	−0.0520240	−0.00339367
$236$	−12.1489	−0.790827
$237$	−1.63956	−0.106501
$238$	31.2497	2.02562
$239$	3.18337	0.205915	0.102958	−	0.994686i	$-0.467169\pi$
$239$	3.18337	0.205915	0.102958	+	0.994686i	$0.467169\pi$
$240$	2.40993	0.155560
$241$	−3.54778	−0.228532	−0.114266	−	0.993450i	$-0.536452\pi$
$241$	−3.54778	−0.228532	−0.114266	+	0.993450i	$0.536452\pi$
$242$	−7.29076	−0.468668
$243$	−21.6003	−1.38566
$244$	6.58878	0.421804
$245$	17.2320	1.10091
$246$	12.3050	0.784540
$247$	1.54446	0.0982714
$248$	−0.366550	−0.0232759
$249$	−25.3606	−1.60716
$250$	1.00000	0.0632456
$251$	−27.0904	−1.70993	−0.854967	−	0.518683i	$-0.826423\pi$
$251$	−27.0904	−1.70993	−0.854967	+	0.518683i	$0.826423\pi$
$252$	13.8216	0.870677
$253$	15.1325	0.951371
$254$	−3.78056	−0.237213
$255$	15.2988	0.958046
$256$	1.00000	0.0625000
$257$	10.9647	0.683960	0.341980	−	0.939707i	$-0.388903\pi$
$257$	10.9647	0.683960	0.341980	+	0.939707i	$0.388903\pi$
$258$	−15.6370	−0.973516
$259$	41.5481	2.58167
$260$	−1.63940	−0.101671
$261$	−15.1314	−0.936611
$262$	2.81059	0.173639
$263$	−4.91518	−0.303083	−0.151542	−	0.988451i	$-0.548424\pi$
$263$	−4.91518	−0.303083	−0.151542	+	0.988451i	$0.548424\pi$
$264$	−4.64139	−0.285658
$265$	1.55627	0.0956008
$266$	−4.63753	−0.284345
$267$	−9.93041	−0.607731
$268$	4.51013	0.275500
$269$	5.15521	0.314318	0.157159	−	0.987573i	$-0.449766\pi$
$269$	5.15521	0.314318	0.157159	+	0.987573i	$0.449766\pi$
$270$	−0.463247	−0.0281923
$271$	16.4176	0.997298	0.498649	−	0.866804i	$-0.333830\pi$
$271$	16.4176	0.997298	0.498649	+	0.866804i	$0.333830\pi$
$272$	6.34821	0.384917
$273$	−19.4484	−1.17707
$274$	1.93821	0.117092
$275$	−1.92594	−0.116139
$276$	−18.9353	−1.13977
$277$	7.94040	0.477093	0.238546	−	0.971131i	$-0.423329\pi$
$277$	7.94040	0.477093	0.238546	+	0.971131i	$0.423329\pi$
$278$	−20.9891	−1.25885
$279$	−1.02919	−0.0616159
$280$	4.92260	0.294182
$281$	4.45357	0.265678	0.132839	−	0.991138i	$-0.457591\pi$
$281$	4.45357	0.265678	0.132839	+	0.991138i	$0.457591\pi$
$282$	−0.125374	−0.00746594
$283$	13.2187	0.785772	0.392886	−	0.919587i	$-0.371477\pi$
$283$	13.2187	0.785772	0.392886	+	0.919587i	$0.371477\pi$
$284$	−12.5467	−0.744510
$285$	−2.27037	−0.134485
$286$	3.15738	0.186700
$287$	25.1346	1.48365
$288$	2.80778	0.165450
$289$	23.2998	1.37058
$290$	−5.38911	−0.316459
$291$	38.0213	2.22885
$292$	−4.90827	−0.287235
$293$	6.61431	0.386412	0.193206	−	0.981158i	$-0.438111\pi$
$293$	6.61431	0.386412	0.193206	+	0.981158i	$0.438111\pi$
$294$	41.5280	2.42196
$295$	−12.1489	−0.707337
$296$	8.44027	0.490581
$297$	0.892186	0.0517699
$298$	−0.676365	−0.0391808
$299$	12.8811	0.744931
$300$	2.40993	0.139138
$301$	−31.9406	−1.84102
$302$	2.04025	0.117403
$303$	35.3802	2.03254
$304$	−0.942089	−0.0540325
$305$	6.58878	0.377273
$306$	17.8244	1.01895
$307$	−4.04614	−0.230925	−0.115463	−	0.993312i	$-0.536835\pi$
$307$	−4.04614	−0.230925	−0.115463	+	0.993312i	$0.536835\pi$
$308$	−9.48064	−0.540209
$309$	0.623143	0.0354493
$310$	−0.366550	−0.0208186
$311$	19.1166	1.08400	0.542001	−	0.840378i	$-0.317667\pi$
$311$	19.1166	1.08400	0.542001	+	0.840378i	$0.317667\pi$
$312$	−3.95083	−0.223672
$313$	−15.5180	−0.877127	−0.438564	−	0.898700i	$-0.644513\pi$
$313$	−15.5180	−0.877127	−0.438564	+	0.898700i	$0.644513\pi$
$314$	10.7203	0.604983
$315$	13.8216	0.778757
$316$	−0.680334	−0.0382718
$317$	−27.4669	−1.54269	−0.771347	−	0.636414i	$-0.780417\pi$
$317$	−27.4669	−1.54269	−0.771347	+	0.636414i	$0.780417\pi$
$318$	3.75050	0.210318
$319$	10.3791	0.581118
$320$	1.00000	0.0559017
$321$	−34.9716	−1.95192
$322$	−38.6779	−2.15543
$323$	−5.98058	−0.332768
$324$	−9.53972	−0.529985
$325$	−1.63940	−0.0909373
$326$	4.37339	0.242220
$327$	−23.6328	−1.30690
$328$	5.10597	0.281930
$329$	−0.256094	−0.0141189
$330$	−4.64139	−0.255500
$331$	−9.07338	−0.498718	−0.249359	−	0.968411i	$-0.580220\pi$
$331$	−9.07338	−0.498718	−0.249359	+	0.968411i	$0.580220\pi$
$332$	−10.5234	−0.577545
$333$	23.6984	1.29866
$334$	−7.29467	−0.399147
$335$	4.51013	0.246415
$336$	11.8631	0.647187
$337$	−17.0857	−0.930716	−0.465358	−	0.885123i	$-0.654074\pi$
$337$	−17.0857	−0.930716	−0.465358	+	0.885123i	$0.654074\pi$
$338$	−10.3124	−0.560920
$339$	23.2354	1.26198
$340$	6.34821	0.344280
$341$	0.705952	0.0382295
$342$	−2.64517	−0.143035
$343$	50.3682	2.71963
$344$	−6.48856	−0.349839
$345$	−18.9353	−1.01944
$346$	20.3994	1.09668
$347$	24.2906	1.30399	0.651995	−	0.758223i	$-0.273932\pi$
$347$	24.2906	1.30399	0.651995	+	0.758223i	$0.273932\pi$
$348$	−12.9874	−0.696197
$349$	7.91193	0.423516	0.211758	−	0.977322i	$-0.432081\pi$
$349$	7.91193	0.423516	0.211758	+	0.977322i	$0.432081\pi$
$350$	4.92260	0.263124
$351$	0.759445	0.0405362
$352$	−1.92594	−0.102653
$353$	23.9224	1.27326	0.636630	−	0.771169i	$-0.280328\pi$
$353$	23.9224	1.27326	0.636630	+	0.771169i	$0.280328\pi$
$354$	−29.2781	−1.55611
$355$	−12.5467	−0.665910
$356$	−4.12062	−0.218392
$357$	75.3097	3.98581
$358$	9.57165	0.505878
$359$	−7.28928	−0.384713	−0.192357	−	0.981325i	$-0.561613\pi$
$359$	−7.28928	−0.384713	−0.192357	+	0.981325i	$0.561613\pi$
$360$	2.80778	0.147983
$361$	−18.1125	−0.953288
$362$	−1.92313	−0.101078
$363$	−17.5702	−0.922198
$364$	−8.07009	−0.422988
$365$	−4.90827	−0.256910
$366$	15.8785	0.829984
$367$	14.8491	0.775118	0.387559	−	0.921845i	$-0.373318\pi$
$367$	14.8491	0.775118	0.387559	+	0.921845i	$0.373318\pi$
$368$	−7.85720	−0.409585
$369$	14.3364	0.746324
$370$	8.44027	0.438789
$371$	7.66089	0.397734
$372$	−0.883360	−0.0458001
$373$	14.0137	0.725602	0.362801	−	0.931867i	$-0.381820\pi$
$373$	14.0137	0.725602	0.362801	+	0.931867i	$0.381820\pi$
$374$	−12.2263	−0.632205
$375$	2.40993	0.124448
$376$	−0.0520240	−0.00268293
$377$	8.83488	0.455020
$378$	−2.28038	−0.117290
$379$	7.91478	0.406555	0.203277	−	0.979121i	$-0.434841\pi$
$379$	7.91478	0.406555	0.203277	+	0.979121i	$0.434841\pi$
$380$	−0.942089	−0.0483281
$381$	−9.11089	−0.466765
$382$	−20.9468	−1.07173
$383$	33.0020	1.68632	0.843162	−	0.537659i	$-0.180691\pi$
$383$	33.0020	1.68632	0.843162	+	0.537659i	$0.180691\pi$
$384$	2.40993	0.122981
$385$	−9.48064	−0.483178
$386$	21.2217	1.08016
$387$	−18.2184	−0.926094
$388$	15.7769	0.800951
$389$	−37.4760	−1.90011	−0.950053	−	0.312087i	$-0.898972\pi$
$389$	−37.4760	−1.90011	−0.950053	+	0.312087i	$0.898972\pi$
$390$	−3.95083	−0.200058
$391$	−49.8792	−2.52250
$392$	17.2320	0.870348
$393$	6.77334	0.341670
$394$	8.49981	0.428214
$395$	−0.680334	−0.0342313
$396$	−5.40761	−0.271742
$397$	33.3960	1.67610	0.838049	−	0.545595i	$-0.183696\pi$
$397$	33.3960	1.67610	0.838049	+	0.545595i	$0.183696\pi$
$398$	6.43272	0.322443
$399$	−11.1761	−0.559506
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	10.8691	0.542102
$403$	0.600920	0.0299339
$404$	14.6810	0.730407
$405$	−9.53972	−0.474033
$406$	−26.5284	−1.31658
$407$	−16.2555	−0.805753
$408$	15.2988	0.757402
$409$	9.49883	0.469687	0.234844	−	0.972033i	$-0.424542\pi$
$409$	9.49883	0.469687	0.234844	+	0.972033i	$0.424542\pi$
$410$	5.10597	0.252166
$411$	4.67096	0.230401
$412$	0.258573	0.0127390
$413$	−59.8043	−2.94278
$414$	−22.0612	−1.08425
$415$	−10.5234	−0.516572
$416$	−1.63940	−0.0803780
$417$	−50.5824	−2.47703
$418$	1.81441	0.0887455
$419$	28.6518	1.39973	0.699866	−	0.714274i	$-0.253243\pi$
$419$	28.6518	1.39973	0.699866	+	0.714274i	$0.253243\pi$
$420$	11.8631	0.578862
$421$	−26.9745	−1.31466	−0.657330	−	0.753603i	$-0.728314\pi$
$421$	−26.9745	−1.31466	−0.657330	+	0.753603i	$0.728314\pi$
$422$	10.2181	0.497408
$423$	−0.146072	−0.00710225
$424$	1.55627	0.0755791
$425$	6.34821	0.307933
$426$	−30.2367	−1.46497
$427$	32.4340	1.56959
$428$	−14.5114	−0.701437
$429$	7.60907	0.367369
$430$	−6.48856	−0.312906
$431$	−23.1663	−1.11588	−0.557940	−	0.829881i	$-0.688408\pi$
$431$	−23.1663	−1.11588	−0.557940	+	0.829881i	$0.688408\pi$
$432$	−0.463247	−0.0222880
$433$	5.96925	0.286864	0.143432	−	0.989660i	$-0.454186\pi$
$433$	5.96925	0.286864	0.143432	+	0.989660i	$0.454186\pi$
$434$	−1.80438	−0.0866129
$435$	−12.9874	−0.622698
$436$	−9.80642	−0.469642
$437$	7.40218	0.354094
$438$	−11.8286	−0.565192
$439$	13.2198	0.630946	0.315473	−	0.948935i	$-0.397837\pi$
$439$	13.2198	0.630946	0.315473	+	0.948935i	$0.397837\pi$
$440$	−1.92594	−0.0918156
$441$	48.3837	2.30398
$442$	−10.4072	−0.495021
$443$	−8.19362	−0.389290	−0.194645	−	0.980874i	$-0.562356\pi$
$443$	−8.19362	−0.389290	−0.194645	+	0.980874i	$0.562356\pi$
$444$	20.3405	0.965317
$445$	−4.12062	−0.195336
$446$	−8.32263	−0.394088
$447$	−1.62999	−0.0770961
$448$	4.92260	0.232571
$449$	39.4647	1.86246	0.931228	−	0.364438i	$-0.118739\pi$
$449$	39.4647	1.86246	0.931228	+	0.364438i	$0.118739\pi$
$450$	2.80778	0.132360
$451$	−9.83378	−0.463055
$452$	9.64153	0.453499
$453$	4.91687	0.231015
$454$	26.8868	1.26186
$455$	−8.07009	−0.378332
$456$	−2.27037	−0.106320
$457$	27.6514	1.29348	0.646739	−	0.762712i	$-0.276132\pi$
$457$	27.6514	1.29348	0.646739	+	0.762712i	$0.276132\pi$
$458$	−28.1263	−1.31426
$459$	−2.94079	−0.137264
$460$	−7.85720	−0.366344
$461$	−27.2256	−1.26802	−0.634011	−	0.773324i	$-0.718593\pi$
$461$	−27.2256	−1.26802	−0.634011	+	0.773324i	$0.718593\pi$
$462$	−22.8477	−1.06297
$463$	−16.7899	−0.780292	−0.390146	−	0.920753i	$-0.627575\pi$
$463$	−16.7899	−0.780292	−0.390146	+	0.920753i	$0.627575\pi$
$464$	−5.38911	−0.250183
$465$	−0.883360	−0.0409648
$466$	−20.7003	−0.958921
$467$	−33.1085	−1.53208	−0.766040	−	0.642793i	$-0.777776\pi$
$467$	−33.1085	−1.53208	−0.766040	+	0.642793i	$0.777776\pi$
$468$	−4.60306	−0.212776
$469$	22.2016	1.02517
$470$	−0.0520240	−0.00239969
$471$	25.8353	1.19043
$472$	−12.1489	−0.559199
$473$	12.4966	0.574593
$474$	−1.63956	−0.0753075
$475$	−0.942089	−0.0432260
$476$	31.2497	1.43233
$477$	4.36965	0.200073
$478$	3.18337	0.145604
$479$	−24.8206	−1.13408	−0.567041	−	0.823690i	$-0.691912\pi$
$479$	−24.8206	−1.13408	−0.567041	+	0.823690i	$0.691912\pi$
$480$	2.40993	0.109998
$481$	−13.8369	−0.630911
$482$	−3.54778	−0.161597
$483$	−93.2111	−4.24125
$484$	−7.29076	−0.331398
$485$	15.7769	0.716392
$486$	−21.6003	−0.979812
$487$	−34.8987	−1.58141	−0.790705	−	0.612198i	$-0.790286\pi$
$487$	−34.8987	−1.58141	−0.790705	+	0.612198i	$0.790286\pi$
$488$	6.58878	0.298260
$489$	10.5396	0.476616
$490$	17.2320	0.778463
$491$	2.13938	0.0965490	0.0482745	−	0.998834i	$-0.484628\pi$
$491$	2.13938	0.0965490	0.0482745	+	0.998834i	$0.484628\pi$
$492$	12.3050	0.554754
$493$	−34.2112	−1.54080
$494$	1.54446	0.0694884
$495$	−5.40761	−0.243054
$496$	−0.366550	−0.0164586
$497$	−61.7624	−2.77042
$498$	−25.3606	−1.13644
$499$	13.2615	0.593667	0.296833	−	0.954929i	$-0.404069\pi$
$499$	13.2615	0.593667	0.296833	+	0.954929i	$0.404069\pi$
$500$	1.00000	0.0447214
$501$	−17.5797	−0.785402
$502$	−27.0904	−1.20911
$503$	25.1413	1.12099	0.560497	−	0.828157i	$-0.310610\pi$
$503$	25.1413	1.12099	0.560497	+	0.828157i	$0.310610\pi$
$504$	13.8216	0.615662
$505$	14.6810	0.653296
$506$	15.1325	0.672721
$507$	−24.8521	−1.10372
$508$	−3.78056	−0.167735
$509$	−42.7071	−1.89296	−0.946480	−	0.322761i	$-0.895389\pi$
$509$	−42.7071	−1.89296	−0.946480	+	0.322761i	$0.895389\pi$
$510$	15.2988	0.677441
$511$	−24.1614	−1.06884
$512$	1.00000	0.0441942
$513$	0.436420	0.0192684
$514$	10.9647	0.483633
$515$	0.258573	0.0113941
$516$	−15.6370	−0.688380
$517$	0.100195	0.00440658
$518$	41.5481	1.82552
$519$	49.1611	2.15793
$520$	−1.63940	−0.0718923
$521$	−0.366067	−0.0160377	−0.00801885	−	0.999968i	$-0.502553\pi$
$521$	−0.366067	−0.0160377	−0.00801885	+	0.999968i	$0.502553\pi$
$522$	−15.1314	−0.662284
$523$	10.3216	0.451332	0.225666	−	0.974205i	$-0.427544\pi$
$523$	10.3216	0.451332	0.225666	+	0.974205i	$0.427544\pi$
$524$	2.81059	0.122781
$525$	11.8631	0.517750
$526$	−4.91518	−0.214312
$527$	−2.32693	−0.101363
$528$	−4.64139	−0.201990
$529$	38.7355	1.68415
$530$	1.55627	0.0676000
$531$	−34.1114	−1.48031
$532$	−4.63753	−0.201062
$533$	−8.37070	−0.362575
$534$	−9.93041	−0.429731
$535$	−14.5114	−0.627384
$536$	4.51013	0.194808
$537$	23.0670	0.995416
$538$	5.15521	0.222257
$539$	−33.1878	−1.42950
$540$	−0.463247	−0.0199350
$541$	18.2594	0.785032	0.392516	−	0.919745i	$-0.371605\pi$
$541$	18.2594	0.785032	0.392516	+	0.919745i	$0.371605\pi$
$542$	16.4176	0.705196
$543$	−4.63462	−0.198890
$544$	6.34821	0.272177
$545$	−9.80642	−0.420061
$546$	−19.4484	−0.832314
$547$	4.38701	0.187575	0.0937875	−	0.995592i	$-0.470103\pi$
$547$	4.38701	0.187575	0.0937875	+	0.995592i	$0.470103\pi$
$548$	1.93821	0.0827963
$549$	18.4998	0.789554
$550$	−1.92594	−0.0821223
$551$	5.07702	0.216288
$552$	−18.9353	−0.805941
$553$	−3.34902	−0.142415
$554$	7.94040	0.337355
$555$	20.3405	0.863406
$556$	−20.9891	−0.890138
$557$	−25.6339	−1.08614	−0.543072	−	0.839686i	$-0.682739\pi$
$557$	−25.6339	−1.08614	−0.543072	+	0.839686i	$0.682739\pi$
$558$	−1.02919	−0.0435690
$559$	10.6373	0.449910
$560$	4.92260	0.208018
$561$	−29.4645	−1.24399
$562$	4.45357	0.187863
$563$	18.9064	0.796810	0.398405	−	0.917210i	$-0.369564\pi$
$563$	18.9064	0.796810	0.398405	+	0.917210i	$0.369564\pi$
$564$	−0.125374	−0.00527921
$565$	9.64153	0.405622
$566$	13.2187	0.555625
$567$	−46.9603	−1.97215
$568$	−12.5467	−0.526448
$569$	−16.1799	−0.678299	−0.339149	−	0.940733i	$-0.610139\pi$
$569$	−16.1799	−0.678299	−0.339149	+	0.940733i	$0.610139\pi$
$570$	−2.27037	−0.0950953
$571$	−2.84421	−0.119027	−0.0595133	−	0.998228i	$-0.518955\pi$
$571$	−2.84421	−0.119027	−0.0595133	+	0.998228i	$0.518955\pi$
$572$	3.15738	0.132017
$573$	−50.4804	−2.10885
$574$	25.1346	1.04910
$575$	−7.85720	−0.327668
$576$	2.80778	0.116991
$577$	47.6272	1.98275	0.991374	−	0.131064i	$-0.0418392\pi$
$577$	47.6272	1.98275	0.991374	+	0.131064i	$0.0418392\pi$
$578$	23.2998	0.969144
$579$	51.1428	2.12542
$580$	−5.38911	−0.223771
$581$	−51.8023	−2.14912
$582$	38.0213	1.57603
$583$	−2.99728	−0.124135
$584$	−4.90827	−0.203106
$585$	−4.60306	−0.190313
$586$	6.61431	0.273234
$587$	0.962093	0.0397098	0.0198549	−	0.999803i	$-0.493680\pi$
$587$	0.962093	0.0397098	0.0198549	+	0.999803i	$0.493680\pi$
$588$	41.5280	1.71259
$589$	0.345322	0.0142287
$590$	−12.1489	−0.500163
$591$	20.4840	0.842598
$592$	8.44027	0.346893
$593$	−5.98558	−0.245798	−0.122899	−	0.992419i	$-0.539219\pi$
$593$	−5.98558	−0.245798	−0.122899	+	0.992419i	$0.539219\pi$
$594$	0.892186	0.0366068
$595$	31.2497	1.28111
$596$	−0.676365	−0.0277050
$597$	15.5024	0.634472
$598$	12.8811	0.526746
$599$	14.5566	0.594765	0.297382	−	0.954758i	$-0.403886\pi$
$599$	14.5566	0.594765	0.297382	+	0.954758i	$0.403886\pi$
$600$	2.40993	0.0983851
$601$	14.1903	0.578835	0.289417	−	0.957203i	$-0.406538\pi$
$601$	14.1903	0.578835	0.289417	+	0.957203i	$0.406538\pi$
$602$	−31.9406	−1.30180
$603$	12.6634	0.515695
$604$	2.04025	0.0830166
$605$	−7.29076	−0.296411
$606$	35.3802	1.43722
$607$	−26.6596	−1.08208	−0.541039	−	0.840997i	$-0.681969\pi$
$607$	−26.6596	−1.08208	−0.541039	+	0.840997i	$0.681969\pi$
$608$	−0.942089	−0.0382067
$609$	−63.9318	−2.59065
$610$	6.58878	0.266772
$611$	0.0852879	0.00345038
$612$	17.8244	0.720507
$613$	−9.11426	−0.368122	−0.184061	−	0.982915i	$-0.558924\pi$
$613$	−9.11426	−0.368122	−0.184061	+	0.982915i	$0.558924\pi$
$614$	−4.04614	−0.163289
$615$	12.3050	0.496187
$616$	−9.48064	−0.381986
$617$	1.37818	0.0554835	0.0277417	−	0.999615i	$-0.491168\pi$
$617$	1.37818	0.0554835	0.0277417	+	0.999615i	$0.491168\pi$
$618$	0.623143	0.0250665
$619$	−6.48064	−0.260479	−0.130239	−	0.991483i	$-0.541575\pi$
$619$	−6.48064	−0.260479	−0.130239	+	0.991483i	$0.541575\pi$
$620$	−0.366550	−0.0147210
$621$	3.63982	0.146061
$622$	19.1166	0.766506
$623$	−20.2842	−0.812668
$624$	−3.95083	−0.158160
$625$	1.00000	0.0400000
$626$	−15.5180	−0.620223
$627$	4.37260	0.174625
$628$	10.7203	0.427787
$629$	53.5806	2.13640
$630$	13.8216	0.550664
$631$	2.52896	0.100676	0.0503381	−	0.998732i	$-0.483970\pi$
$631$	2.52896	0.100676	0.0503381	+	0.998732i	$0.483970\pi$
$632$	−0.680334	−0.0270623
$633$	24.6249	0.978750
$634$	−27.4669	−1.09085
$635$	−3.78056	−0.150027
$636$	3.75050	0.148717
$637$	−28.2501	−1.11931
$638$	10.3791	0.410912
$639$	−35.2283	−1.39361
$640$	1.00000	0.0395285
$641$	−13.6153	−0.537771	−0.268886	−	0.963172i	$-0.586655\pi$
$641$	−13.6153	−0.537771	−0.268886	+	0.963172i	$0.586655\pi$
$642$	−34.9716	−1.38022
$643$	−22.7745	−0.898138	−0.449069	−	0.893497i	$-0.648244\pi$
$643$	−22.7745	−0.898138	−0.449069	+	0.893497i	$0.648244\pi$
$644$	−38.6779	−1.52412
$645$	−15.6370	−0.615706
$646$	−5.98058	−0.235303
$647$	40.4368	1.58974	0.794868	−	0.606783i	$-0.207540\pi$
$647$	40.4368	1.58974	0.794868	+	0.606783i	$0.207540\pi$
$648$	−9.53972	−0.374756
$649$	23.3981	0.918455
$650$	−1.63940	−0.0643024
$651$	−4.34843	−0.170428
$652$	4.37339	0.171275
$653$	−20.4902	−0.801843	−0.400922	−	0.916112i	$-0.631310\pi$
$653$	−20.4902	−0.801843	−0.400922	+	0.916112i	$0.631310\pi$
$654$	−23.6328	−0.924116
$655$	2.81059	0.109819
$656$	5.10597	0.199354
$657$	−13.7813	−0.537660
$658$	−0.256094	−0.00998357
$659$	−46.9932	−1.83059	−0.915297	−	0.402780i	$-0.868044\pi$
$659$	−46.9932	−1.83059	−0.915297	+	0.402780i	$0.868044\pi$
$660$	−4.64139	−0.180666
$661$	7.16742	0.278780	0.139390	−	0.990238i	$-0.455486\pi$
$661$	7.16742	0.278780	0.139390	+	0.990238i	$0.455486\pi$
$662$	−9.07338	−0.352647
$663$	−25.0807	−0.974055
$664$	−10.5234	−0.408386
$665$	−4.63753	−0.179836
$666$	23.6984	0.918294
$667$	42.3433	1.63954
$668$	−7.29467	−0.282239
$669$	−20.0570	−0.775448
$670$	4.51013	0.174242
$671$	−12.6896	−0.489877
$672$	11.8631	0.457631
$673$	−7.31529	−0.281984	−0.140992	−	0.990011i	$-0.545029\pi$
$673$	−7.31529	−0.281984	−0.140992	+	0.990011i	$0.545029\pi$
$674$	−17.0857	−0.658115
$675$	−0.463247	−0.0178304
$676$	−10.3124	−0.396630
$677$	−12.0112	−0.461628	−0.230814	−	0.972998i	$-0.574139\pi$
$677$	−12.0112	−0.461628	−0.230814	+	0.972998i	$0.574139\pi$
$678$	23.2354	0.892351
$679$	77.6634	2.98045
$680$	6.34821	0.243443
$681$	64.7955	2.48297
$682$	0.705952	0.0270323
$683$	−33.7361	−1.29088	−0.645438	−	0.763813i	$-0.723325\pi$
$683$	−33.7361	−1.29088	−0.645438	+	0.763813i	$0.723325\pi$
$684$	−2.64517	−0.101141
$685$	1.93821	0.0740553
$686$	50.3682	1.92307
$687$	−67.7826	−2.58607
$688$	−6.48856	−0.247374
$689$	−2.55134	−0.0971983
$690$	−18.9353	−0.720855
$691$	40.3855	1.53634	0.768169	−	0.640247i	$-0.221168\pi$
$691$	40.3855	1.53634	0.768169	+	0.640247i	$0.221168\pi$
$692$	20.3994	0.775467
$693$	−26.6195	−1.01119
$694$	24.2906	0.922060
$695$	−20.9891	−0.796164
$696$	−12.9874	−0.492286
$697$	32.4137	1.22776
$698$	7.91193	0.299471
$699$	−49.8862	−1.88687
$700$	4.92260	0.186057
$701$	−8.29900	−0.313449	−0.156725	−	0.987642i	$-0.550093\pi$
$701$	−8.29900	−0.313449	−0.156725	+	0.987642i	$0.550093\pi$
$702$	0.759445	0.0286634
$703$	−7.95148	−0.299896
$704$	−1.92594	−0.0725866
$705$	−0.125374	−0.00472187
$706$	23.9224	0.900331
$707$	72.2688	2.71795
$708$	−29.2781	−1.10034
$709$	17.5204	0.657993	0.328997	−	0.944331i	$-0.393290\pi$
$709$	17.5204	0.657993	0.328997	+	0.944331i	$0.393290\pi$
$710$	−12.5467	−0.470869
$711$	−1.91023	−0.0716391
$712$	−4.12062	−0.154427
$713$	2.88005	0.107859
$714$	75.3097	2.81840
$715$	3.15738	0.118079
$716$	9.57165	0.357709
$717$	7.67171	0.286505
$718$	−7.28928	−0.272034
$719$	16.4679	0.614149	0.307075	−	0.951685i	$-0.400650\pi$
$719$	16.4679	0.614149	0.307075	+	0.951685i	$0.400650\pi$
$720$	2.80778	0.104640
$721$	1.27285	0.0474034
$722$	−18.1125	−0.674076
$723$	−8.54990	−0.317974
$724$	−1.92313	−0.0714726
$725$	−5.38911	−0.200146
$726$	−17.5702	−0.652093
$727$	31.5415	1.16981	0.584905	−	0.811102i	$-0.301132\pi$
$727$	31.5415	1.16981	0.584905	+	0.811102i	$0.301132\pi$
$728$	−8.07009	−0.299098
$729$	−23.4362	−0.868008
$730$	−4.90827	−0.181663
$731$	−41.1907	−1.52349
$732$	15.8785	0.586887
$733$	44.3887	1.63953	0.819766	−	0.572698i	$-0.194103\pi$
$733$	44.3887	1.63953	0.819766	+	0.572698i	$0.194103\pi$
$734$	14.8491	0.548091
$735$	41.5280	1.53178
$736$	−7.85720	−0.289620
$737$	−8.68625	−0.319962
$738$	14.3364	0.527730
$739$	−41.8657	−1.54006	−0.770028	−	0.638010i	$-0.779758\pi$
$739$	−41.8657	−1.54006	−0.770028	+	0.638010i	$0.779758\pi$
$740$	8.44027	0.310271
$741$	3.72203	0.136732
$742$	7.66089	0.281240
$743$	37.8050	1.38693	0.693466	−	0.720490i	$-0.256083\pi$
$743$	37.8050	1.38693	0.693466	+	0.720490i	$0.256083\pi$
$744$	−0.883360	−0.0323855
$745$	−0.676365	−0.0247801
$746$	14.0137	0.513078
$747$	−29.5472	−1.08108
$748$	−12.2263	−0.447037
$749$	−71.4341	−2.61014
$750$	2.40993	0.0879983
$751$	26.6230	0.971488	0.485744	−	0.874101i	$-0.338549\pi$
$751$	26.6230	0.971488	0.485744	+	0.874101i	$0.338549\pi$
$752$	−0.0520240	−0.00189712
$753$	−65.2861	−2.37916
$754$	8.83488	0.321747
$755$	2.04025	0.0742523
$756$	−2.28038	−0.0829367
$757$	−11.8026	−0.428971	−0.214486	−	0.976727i	$-0.568808\pi$
$757$	−11.8026	−0.428971	−0.214486	+	0.976727i	$0.568808\pi$
$758$	7.91478	0.287478
$759$	36.4683	1.32371
$760$	−0.942089	−0.0341731
$761$	20.7950	0.753817	0.376909	−	0.926250i	$-0.376987\pi$
$761$	20.7950	0.753817	0.376909	+	0.926250i	$0.376987\pi$
$762$	−9.11089	−0.330053
$763$	−48.2731	−1.74760
$764$	−20.9468	−0.757829
$765$	17.8244	0.644441
$766$	33.0020	1.19241
$767$	19.9169	0.719157
$768$	2.40993	0.0869610
$769$	−43.7238	−1.57672	−0.788360	−	0.615214i	$-0.789070\pi$
$769$	−43.7238	−1.57672	−0.788360	+	0.615214i	$0.789070\pi$
$770$	−9.48064	−0.341658
$771$	26.4242	0.951645
$772$	21.2217	0.763785
$773$	−11.4740	−0.412692	−0.206346	−	0.978479i	$-0.566157\pi$
$773$	−11.4740	−0.412692	−0.206346	+	0.978479i	$0.566157\pi$
$774$	−18.2184	−0.654847
$775$	−0.366550	−0.0131668
$776$	15.7769	0.566358
$777$	100.128	3.59208
$778$	−37.4760	−1.34358
$779$	−4.81027	−0.172346
$780$	−3.95083	−0.141463
$781$	24.1642	0.864663
$782$	−49.8792	−1.78367
$783$	2.49649	0.0892172
$784$	17.2320	0.615429
$785$	10.7203	0.382625
$786$	6.77334	0.241597
$787$	−30.9746	−1.10413	−0.552063	−	0.833803i	$-0.686159\pi$
$787$	−30.9746	−1.10413	−0.552063	+	0.833803i	$0.686159\pi$
$788$	8.49981	0.302793
$789$	−11.8453	−0.421702
$790$	−0.680334	−0.0242052
$791$	47.4614	1.68753
$792$	−5.40761	−0.192151
$793$	−10.8016	−0.383577
$794$	33.3960	1.18518
$795$	3.75050	0.133017
$796$	6.43272	0.228002
$797$	−30.8353	−1.09224	−0.546121	−	0.837706i	$-0.683896\pi$
$797$	−30.8353	−1.09224	−0.546121	+	0.837706i	$0.683896\pi$
$798$	−11.1761	−0.395631
$799$	−0.330259	−0.0116837
$800$	1.00000	0.0353553
$801$	−11.5698	−0.408798
$802$	1.00000	0.0353112
$803$	9.45303	0.333590
$804$	10.8691	0.383324
$805$	−38.6779	−1.36322
$806$	0.600920	0.0211665
$807$	12.4237	0.437335
$808$	14.6810	0.516476
$809$	−11.4122	−0.401233	−0.200617	−	0.979670i	$-0.564295\pi$
$809$	−11.4122	−0.401233	−0.200617	+	0.979670i	$0.564295\pi$
$810$	−9.53972	−0.335192
$811$	−52.7980	−1.85399	−0.926994	−	0.375077i	$-0.877616\pi$
$811$	−52.7980	−1.85399	−0.926994	+	0.375077i	$0.877616\pi$
$812$	−26.5284	−0.930966
$813$	39.5653	1.38762
$814$	−16.2555	−0.569753
$815$	4.37339	0.153193
$816$	15.2988	0.535564
$817$	6.11279	0.213860
$818$	9.49883	0.332119
$819$	−22.6590	−0.791770
$820$	5.10597	0.178308
$821$	23.4845	0.819616	0.409808	−	0.912172i	$-0.365596\pi$
$821$	23.4845	0.819616	0.409808	+	0.912172i	$0.365596\pi$
$822$	4.67096	0.162918
$823$	25.8371	0.900623	0.450312	−	0.892871i	$-0.351313\pi$
$823$	25.8371	0.900623	0.450312	+	0.892871i	$0.351313\pi$
$824$	0.258573	0.00900780
$825$	−4.64139	−0.161592
$826$	−59.8043	−2.08086
$827$	0.410686	0.0142810	0.00714048	−	0.999975i	$-0.497727\pi$
$827$	0.410686	0.0142810	0.00714048	+	0.999975i	$0.497727\pi$
$828$	−22.0612	−0.766681
$829$	29.6344	1.02925	0.514623	−	0.857417i	$-0.327932\pi$
$829$	29.6344	1.02925	0.514623	+	0.857417i	$0.327932\pi$
$830$	−10.5234	−0.365271
$831$	19.1358	0.663815
$832$	−1.63940	−0.0568358
$833$	109.393	3.79023
$834$	−50.5824	−1.75153
$835$	−7.29467	−0.252443
$836$	1.81441	0.0627525
$837$	0.169803	0.00586925
$838$	28.6518	0.989760
$839$	−6.57898	−0.227132	−0.113566	−	0.993530i	$-0.536227\pi$
$839$	−6.57898	−0.227132	−0.113566	+	0.993530i	$0.536227\pi$
$840$	11.8631	0.409317
$841$	0.0424989	0.00146548
$842$	−26.9745	−0.929604
$843$	10.7328	0.369658
$844$	10.2181	0.351720
$845$	−10.3124	−0.354757
$846$	−0.146072	−0.00502205
$847$	−35.8895	−1.23318
$848$	1.55627	0.0534425
$849$	31.8563	1.09330
$850$	6.34821	0.217742
$851$	−66.3169	−2.27331
$852$	−30.2367	−1.03589
$853$	−25.7019	−0.880016	−0.440008	−	0.897994i	$-0.645024\pi$
$853$	−25.7019	−0.880016	−0.440008	+	0.897994i	$0.645024\pi$
$854$	32.4340	1.10987
$855$	−2.64517	−0.0904630
$856$	−14.5114	−0.495991
$857$	51.0321	1.74322	0.871612	−	0.490197i	$-0.163075\pi$
$857$	51.0321	1.74322	0.871612	+	0.490197i	$0.163075\pi$
$858$	7.60907	0.259769
$859$	−29.4857	−1.00604	−0.503019	−	0.864275i	$-0.667777\pi$
$859$	−29.4857	−1.00604	−0.503019	+	0.864275i	$0.667777\pi$
$860$	−6.48856	−0.221258
$861$	60.5728	2.06432
$862$	−23.1663	−0.789046
$863$	6.82069	0.232179	0.116090	−	0.993239i	$-0.462964\pi$
$863$	6.82069	0.232179	0.116090	+	0.993239i	$0.462964\pi$
$864$	−0.463247	−0.0157600
$865$	20.3994	0.693599
$866$	5.96925	0.202844
$867$	56.1509	1.90699
$868$	−1.80438	−0.0612446
$869$	1.31028	0.0444483
$870$	−12.9874	−0.440314
$871$	−7.39389	−0.250533
$872$	−9.80642	−0.332087
$873$	44.2980	1.49926
$874$	7.40218	0.250382
$875$	4.92260	0.166414
$876$	−11.8286	−0.399651
$877$	39.3765	1.32965	0.664824	−	0.747000i	$-0.268506\pi$
$877$	39.3765	1.32965	0.664824	+	0.747000i	$0.268506\pi$
$878$	13.2198	0.446146
$879$	15.9400	0.537644
$880$	−1.92594	−0.0649234
$881$	−0.837220	−0.0282067	−0.0141033	−	0.999901i	$-0.504489\pi$
$881$	−0.837220	−0.0282067	−0.0141033	+	0.999901i	$0.504489\pi$
$882$	48.3837	1.62916
$883$	33.6302	1.13175	0.565873	−	0.824492i	$-0.308539\pi$
$883$	33.6302	1.13175	0.565873	+	0.824492i	$0.308539\pi$
$884$	−10.4072	−0.350033
$885$	−29.2781	−0.984172
$886$	−8.19362	−0.275270
$887$	13.5788	0.455932	0.227966	−	0.973669i	$-0.426793\pi$
$887$	13.5788	0.455932	0.227966	+	0.973669i	$0.426793\pi$
$888$	20.3405	0.682582
$889$	−18.6102	−0.624166
$890$	−4.12062	−0.138123
$891$	18.3729	0.615516
$892$	−8.32263	−0.278662
$893$	0.0490112	0.00164010
$894$	−1.62999	−0.0545152
$895$	9.57165	0.319945
$896$	4.92260	0.164453
$897$	31.0425	1.03648
$898$	39.4647	1.31695
$899$	1.97538	0.0658825
$900$	2.80778	0.0935925
$901$	9.87952	0.329135
$902$	−9.83378	−0.327429
$903$	−76.9747	−2.56156
$904$	9.64153	0.320672
$905$	−1.92313	−0.0639270
$906$	4.91687	0.163352
$907$	−53.6493	−1.78139	−0.890697	−	0.454597i	$-0.849783\pi$
$907$	−53.6493	−1.78139	−0.890697	+	0.454597i	$0.849783\pi$
$908$	26.8868	0.892271
$909$	41.2210	1.36721
$910$	−8.07009	−0.267521
$911$	−19.8790	−0.658620	−0.329310	−	0.944222i	$-0.606816\pi$
$911$	−19.8790	−0.658620	−0.329310	+	0.944222i	$0.606816\pi$
$912$	−2.27037	−0.0751795
$913$	20.2674	0.670752
$914$	27.6514	0.914626
$915$	15.8785	0.524928
$916$	−28.1263	−0.929320
$917$	13.8354	0.456886
$918$	−2.94079	−0.0970605
$919$	4.66735	0.153962	0.0769809	−	0.997033i	$-0.475472\pi$
$919$	4.66735	0.153962	0.0769809	+	0.997033i	$0.475472\pi$
$920$	−7.85720	−0.259044
$921$	−9.75092	−0.321304
$922$	−27.2256	−0.896627
$923$	20.5690	0.677037
$924$	−22.8477	−0.751634
$925$	8.44027	0.277514
$926$	−16.7899	−0.551749
$927$	0.726014	0.0238454
$928$	−5.38911	−0.176906
$929$	−17.1018	−0.561093	−0.280547	−	0.959840i	$-0.590516\pi$
$929$	−17.1018	−0.561093	−0.280547	+	0.959840i	$0.590516\pi$
$930$	−0.883360	−0.0289665
$931$	−16.2341	−0.532051
$932$	−20.7003	−0.678060
$933$	46.0697	1.50825
$934$	−33.1085	−1.08334
$935$	−12.2263	−0.399842
$936$	−4.60306	−0.150456
$937$	26.6824	0.871677	0.435838	−	0.900025i	$-0.356452\pi$
$937$	26.6824	0.871677	0.435838	+	0.900025i	$0.356452\pi$
$938$	22.2016	0.724908
$939$	−37.3973	−1.22041
$940$	−0.0520240	−0.00169684
$941$	29.2988	0.955112	0.477556	−	0.878601i	$-0.341523\pi$
$941$	29.2988	0.955112	0.477556	+	0.878601i	$0.341523\pi$
$942$	25.8353	0.841758
$943$	−40.1186	−1.30644
$944$	−12.1489	−0.395414
$945$	−2.28038	−0.0741808
$946$	12.4966	0.406298
$947$	3.32433	0.108026	0.0540131	−	0.998540i	$-0.482799\pi$
$947$	3.32433	0.108026	0.0540131	+	0.998540i	$0.482799\pi$
$948$	−1.63956	−0.0532504
$949$	8.04659	0.261203
$950$	−0.942089	−0.0305654
$951$	−66.1934	−2.14647
$952$	31.2497	1.01281
$953$	−43.5591	−1.41102	−0.705509	−	0.708701i	$-0.749282\pi$
$953$	−43.5591	−1.41102	−0.705509	+	0.708701i	$0.749282\pi$
$954$	4.36965	0.141473
$955$	−20.9468	−0.677823
$956$	3.18337	0.102958
$957$	25.0129	0.808553
$958$	−24.8206	−0.801917
$959$	9.54105	0.308096
$960$	2.40993	0.0777802
$961$	−30.8656	−0.995666
$962$	−13.8369	−0.446121
$963$	−40.7449	−1.31299
$964$	−3.54778	−0.114266
$965$	21.2217	0.683150
$966$	−93.2111	−2.99902
$967$	−15.0485	−0.483926	−0.241963	−	0.970285i	$-0.577791\pi$
$967$	−15.0485	−0.483926	−0.241963	+	0.970285i	$0.577791\pi$
$968$	−7.29076	−0.234334
$969$	−14.4128	−0.463006
$970$	15.7769	0.506566
$971$	46.5073	1.49249	0.746245	−	0.665671i	$-0.231855\pi$
$971$	46.5073	1.49249	0.746245	+	0.665671i	$0.231855\pi$
$972$	−21.6003	−0.692831
$973$	−103.321	−3.31233
$974$	−34.8987	−1.11823
$975$	−3.95083	−0.126528
$976$	6.58878	0.210902
$977$	4.42597	0.141599	0.0707996	−	0.997491i	$-0.477445\pi$
$977$	4.42597	0.141599	0.0707996	+	0.997491i	$0.477445\pi$
$978$	10.5396	0.337019
$979$	7.93606	0.253638
$980$	17.2320	0.550457
$981$	−27.5342	−0.879100
$982$	2.13938	0.0682704
$983$	−59.8724	−1.90963	−0.954816	−	0.297197i	$-0.903948\pi$
$983$	−59.8724	−1.90963	−0.954816	+	0.297197i	$0.903948\pi$
$984$	12.3050	0.392270
$985$	8.49981	0.270826
$986$	−34.2112	−1.08951
$987$	−0.617168	−0.0196447
$988$	1.54446	0.0491357
$989$	50.9819	1.62113
$990$	−5.40761	−0.171865
$991$	27.8401	0.884370	0.442185	−	0.896924i	$-0.354203\pi$
$991$	27.8401	0.884370	0.442185	+	0.896924i	$0.354203\pi$
$992$	−0.366550	−0.0116380
$993$	−21.8662	−0.693904
$994$	−61.7624	−1.95899
$995$	6.43272	0.203931
$996$	−25.3606	−0.803581
$997$	34.6994	1.09894	0.549470	−	0.835513i	$-0.314830\pi$
$997$	34.6994	1.09894	0.549470	+	0.835513i	$0.314830\pi$
$998$	13.2615	0.419786
$999$	−3.90993	−0.123705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.n.1.17	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.n.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.40993 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.40993 q^{6} +4.92260 q^{7} +1.00000 q^{8} +2.80778 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.40993 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.40993 q^{6} +4.92260 q^{7} +1.00000 q^{8} +2.80778 q^{9} +1.00000 q^{10} -1.92594 q^{11} +2.40993 q^{12} -1.63940 q^{13} +4.92260 q^{14} +2.40993 q^{15} +1.00000 q^{16} +6.34821 q^{17} +2.80778 q^{18} -0.942089 q^{19} +1.00000 q^{20} +11.8631 q^{21} -1.92594 q^{22} -7.85720 q^{23} +2.40993 q^{24} +1.00000 q^{25} -1.63940 q^{26} -0.463247 q^{27} +4.92260 q^{28} -5.38911 q^{29} +2.40993 q^{30} -0.366550 q^{31} +1.00000 q^{32} -4.64139 q^{33} +6.34821 q^{34} +4.92260 q^{35} +2.80778 q^{36} +8.44027 q^{37} -0.942089 q^{38} -3.95083 q^{39} +1.00000 q^{40} +5.10597 q^{41} +11.8631 q^{42} -6.48856 q^{43} -1.92594 q^{44} +2.80778 q^{45} -7.85720 q^{46} -0.0520240 q^{47} +2.40993 q^{48} +17.2320 q^{49} +1.00000 q^{50} +15.2988 q^{51} -1.63940 q^{52} +1.55627 q^{53} -0.463247 q^{54} -1.92594 q^{55} +4.92260 q^{56} -2.27037 q^{57} -5.38911 q^{58} -12.1489 q^{59} +2.40993 q^{60} +6.58878 q^{61} -0.366550 q^{62} +13.8216 q^{63} +1.00000 q^{64} -1.63940 q^{65} -4.64139 q^{66} +4.51013 q^{67} +6.34821 q^{68} -18.9353 q^{69} +4.92260 q^{70} -12.5467 q^{71} +2.80778 q^{72} -4.90827 q^{73} +8.44027 q^{74} +2.40993 q^{75} -0.942089 q^{76} -9.48064 q^{77} -3.95083 q^{78} -0.680334 q^{79} +1.00000 q^{80} -9.53972 q^{81} +5.10597 q^{82} -10.5234 q^{83} +11.8631 q^{84} +6.34821 q^{85} -6.48856 q^{86} -12.9874 q^{87} -1.92594 q^{88} -4.12062 q^{89} +2.80778 q^{90} -8.07009 q^{91} -7.85720 q^{92} -0.883360 q^{93} -0.0520240 q^{94} -0.942089 q^{95} +2.40993 q^{96} +15.7769 q^{97} +17.2320 q^{98} -5.40761 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9	\( 22 q + 22 q^{2} + q^{3} + 22 q^{4} + 22 q^{5} + q^{6} + 22 q^{8} + 43 q^{9} + 22 q^{10} + 12 q^{11} + q^{12} + 10 q^{13} + q^{15} + 22 q^{16} + 24 q^{17} + 43 q^{18} + 13 q^{19} + 22 q^{20} + 13 q^{21} + 12 q^{22} + 7 q^{23} + q^{24} + 22 q^{25} + 10 q^{26} - 5 q^{27} + 22 q^{29} + q^{30} + 14 q^{31} + 22 q^{32} + 31 q^{33} + 24 q^{34} + 43 q^{36} + 35 q^{37} + 13 q^{38} + 4 q^{39} + 22 q^{40} + 29 q^{41} + 13 q^{42} + 7 q^{43} + 12 q^{44} + 43 q^{45} + 7 q^{46} - 21 q^{47} + q^{48} + 32 q^{49} + 22 q^{50} - 6 q^{51} + 10 q^{52} + 29 q^{53} - 5 q^{54} + 12 q^{55} - 13 q^{57} + 22 q^{58} + 12 q^{59} + q^{60} + 24 q^{61} + 14 q^{62} - 8 q^{63} + 22 q^{64} + 10 q^{65} + 31 q^{66} + 25 q^{67} + 24 q^{68} + 3 q^{69} + 31 q^{71} + 43 q^{72} + 30 q^{73} + 35 q^{74} + q^{75} + 13 q^{76} + 10 q^{77} + 4 q^{78} + 35 q^{79} + 22 q^{80} + 74 q^{81} + 29 q^{82} - 33 q^{83} + 13 q^{84} + 24 q^{85} + 7 q^{86} - 24 q^{87} + 12 q^{88} + 38 q^{89} + 43 q^{90} - 32 q^{91} + 7 q^{92} + 3 q^{93} - 21 q^{94} + 13 q^{95} + q^{96} + 11 q^{97} + 32 q^{98} - 41 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + q^3 + 22 * q^4 + 22 * q^5 + q^6 + 22 * q^8 + 43 * q^9 + 22 * q^10 + 12 * q^11 + q^12 + 10 * q^13 + q^15 + 22 * q^16 + 24 * q^17 + 43 * q^18 + 13 * q^19 + 22 * q^20 + 13 * q^21 + 12 * q^22 + 7 * q^23 + q^24 + 22 * q^25 + 10 * q^26 - 5 * q^27 + 22 * q^29 + q^30 + 14 * q^31 + 22 * q^32 + 31 * q^33 + 24 * q^34 + 43 * q^36 + 35 * q^37 + 13 * q^38 + 4 * q^39 + 22 * q^40 + 29 * q^41 + 13 * q^42 + 7 * q^43 + 12 * q^44 + 43 * q^45 + 7 * q^46 - 21 * q^47 + q^48 + 32 * q^49 + 22 * q^50 - 6 * q^51 + 10 * q^52 + 29 * q^53 - 5 * q^54 + 12 * q^55 - 13 * q^57 + 22 * q^58 + 12 * q^59 + q^60 + 24 * q^61 + 14 * q^62 - 8 * q^63 + 22 * q^64 + 10 * q^65 + 31 * q^66 + 25 * q^67 + 24 * q^68 + 3 * q^69 + 31 * q^71 + 43 * q^72 + 30 * q^73 + 35 * q^74 + q^75 + 13 * q^76 + 10 * q^77 + 4 * q^78 + 35 * q^79 + 22 * q^80 + 74 * q^81 + 29 * q^82 - 33 * q^83 + 13 * q^84 + 24 * q^85 + 7 * q^86 - 24 * q^87 + 12 * q^88 + 38 * q^89 + 43 * q^90 - 32 * q^91 + 7 * q^92 + 3 * q^93 - 21 * q^94 + 13 * q^95 + q^96 + 11 * q^97 + 32 * q^98 - 41 * q^99

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