LMFDB - Embedded newform 4010.2.a.l.1.14

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 $ x^17 - 3x^16 - 24x^15 + 70x^14 + 228x^13 - 638x^12 - 1075x^11 + 2854x^10 + 2544x^9 - 6415x^8 - 2573x^7 + 6456x^6 + 485x^5 - 1839x^4 + 67x^3 + 136x^2 - 8x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.15213$ of defining polynomial
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.15213 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15213 q^{6} -4.40972 q^{7} -1.00000 q^{8} +1.63168 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.15213 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15213 q^{6} -4.40972 q^{7} -1.00000 q^{8} +1.63168 q^{9} +1.00000 q^{10} +3.46745 q^{11} +2.15213 q^{12} -2.43182 q^{13} +4.40972 q^{14} -2.15213 q^{15} +1.00000 q^{16} +4.79853 q^{17} -1.63168 q^{18} -6.67647 q^{19} -1.00000 q^{20} -9.49031 q^{21} -3.46745 q^{22} -0.931214 q^{23} -2.15213 q^{24} +1.00000 q^{25} +2.43182 q^{26} -2.94480 q^{27} -4.40972 q^{28} +6.55653 q^{29} +2.15213 q^{30} -4.82923 q^{31} -1.00000 q^{32} +7.46241 q^{33} -4.79853 q^{34} +4.40972 q^{35} +1.63168 q^{36} +8.15269 q^{37} +6.67647 q^{38} -5.23361 q^{39} +1.00000 q^{40} -0.0826739 q^{41} +9.49031 q^{42} +1.98104 q^{43} +3.46745 q^{44} -1.63168 q^{45} +0.931214 q^{46} +11.6223 q^{47} +2.15213 q^{48} +12.4456 q^{49} -1.00000 q^{50} +10.3271 q^{51} -2.43182 q^{52} -5.51735 q^{53} +2.94480 q^{54} -3.46745 q^{55} +4.40972 q^{56} -14.3687 q^{57} -6.55653 q^{58} +10.7443 q^{59} -2.15213 q^{60} -13.5180 q^{61} +4.82923 q^{62} -7.19527 q^{63} +1.00000 q^{64} +2.43182 q^{65} -7.46241 q^{66} +11.5935 q^{67} +4.79853 q^{68} -2.00410 q^{69} -4.40972 q^{70} +15.4391 q^{71} -1.63168 q^{72} +5.98090 q^{73} -8.15269 q^{74} +2.15213 q^{75} -6.67647 q^{76} -15.2905 q^{77} +5.23361 q^{78} -10.6192 q^{79} -1.00000 q^{80} -11.2327 q^{81} +0.0826739 q^{82} +9.12066 q^{83} -9.49031 q^{84} -4.79853 q^{85} -1.98104 q^{86} +14.1105 q^{87} -3.46745 q^{88} -9.01860 q^{89} +1.63168 q^{90} +10.7237 q^{91} -0.931214 q^{92} -10.3931 q^{93} -11.6223 q^{94} +6.67647 q^{95} -2.15213 q^{96} +7.88077 q^{97} -12.4456 q^{98} +5.65777 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.15213	1.24254	0.621268	−	0.783598i	$-0.286618\pi$
$3$	2.15213	1.24254	0.621268	+	0.783598i	$0.286618\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.15213	−0.878605
$7$	−4.40972	−1.66672	−0.833359	−	0.552733i	$-0.813585\pi$
$7$	−4.40972	−1.66672	−0.833359	+	0.552733i	$0.813585\pi$
$8$	−1.00000	−0.353553
$9$	1.63168	0.543894
$10$	1.00000	0.316228
$11$	3.46745	1.04547	0.522737	−	0.852494i	$-0.324911\pi$
$11$	3.46745	1.04547	0.522737	+	0.852494i	$0.324911\pi$
$12$	2.15213	0.621268
$13$	−2.43182	−0.674466	−0.337233	−	0.941421i	$-0.609491\pi$
$13$	−2.43182	−0.674466	−0.337233	+	0.941421i	$0.609491\pi$
$14$	4.40972	1.17855
$15$	−2.15213	−0.555679
$16$	1.00000	0.250000
$17$	4.79853	1.16381	0.581907	−	0.813255i	$-0.302307\pi$
$17$	4.79853	1.16381	0.581907	+	0.813255i	$0.302307\pi$
$18$	−1.63168	−0.384591
$19$	−6.67647	−1.53169	−0.765844	−	0.643026i	$-0.777679\pi$
$19$	−6.67647	−1.53169	−0.765844	+	0.643026i	$0.777679\pi$
$20$	−1.00000	−0.223607
$21$	−9.49031	−2.07096
$22$	−3.46745	−0.739262
$23$	−0.931214	−0.194172	−0.0970858	−	0.995276i	$-0.530952\pi$
$23$	−0.931214	−0.194172	−0.0970858	+	0.995276i	$0.530952\pi$
$24$	−2.15213	−0.439303
$25$	1.00000	0.200000
$26$	2.43182	0.476920
$27$	−2.94480	−0.566727
$28$	−4.40972	−0.833359
$29$	6.55653	1.21752	0.608759	−	0.793355i	$-0.291668\pi$
$29$	6.55653	1.21752	0.608759	+	0.793355i	$0.291668\pi$
$30$	2.15213	0.392924
$31$	−4.82923	−0.867355	−0.433677	−	0.901068i	$-0.642784\pi$
$31$	−4.82923	−0.867355	−0.433677	+	0.901068i	$0.642784\pi$
$32$	−1.00000	−0.176777
$33$	7.46241	1.29904
$34$	−4.79853	−0.822941
$35$	4.40972	0.745379
$36$	1.63168	0.271947
$37$	8.15269	1.34029	0.670147	−	0.742229i	$-0.266231\pi$
$37$	8.15269	1.34029	0.670147	+	0.742229i	$0.266231\pi$
$38$	6.67647	1.08307
$39$	−5.23361	−0.838048
$40$	1.00000	0.158114
$41$	−0.0826739	−0.0129115	−0.00645575	−	0.999979i	$-0.502055\pi$
$41$	−0.0826739	−0.0129115	−0.00645575	+	0.999979i	$0.502055\pi$
$42$	9.49031	1.46439
$43$	1.98104	0.302106	0.151053	−	0.988526i	$-0.451734\pi$
$43$	1.98104	0.302106	0.151053	+	0.988526i	$0.451734\pi$
$44$	3.46745	0.522737
$45$	−1.63168	−0.243237
$46$	0.931214	0.137300
$47$	11.6223	1.69529	0.847646	−	0.530562i	$-0.178019\pi$
$47$	11.6223	1.69529	0.847646	+	0.530562i	$0.178019\pi$
$48$	2.15213	0.310634
$49$	12.4456	1.77795
$50$	−1.00000	−0.141421
$51$	10.3271	1.44608
$52$	−2.43182	−0.337233
$53$	−5.51735	−0.757866	−0.378933	−	0.925424i	$-0.623709\pi$
$53$	−5.51735	−0.757866	−0.378933	+	0.925424i	$0.623709\pi$
$54$	2.94480	0.400737
$55$	−3.46745	−0.467550
$56$	4.40972	0.589274
$57$	−14.3687	−1.90318
$58$	−6.55653	−0.860915
$59$	10.7443	1.39879	0.699393	−	0.714737i	$-0.253454\pi$
$59$	10.7443	1.39879	0.699393	+	0.714737i	$0.253454\pi$
$60$	−2.15213	−0.277839
$61$	−13.5180	−1.73080	−0.865401	−	0.501080i	$-0.832936\pi$
$61$	−13.5180	−1.73080	−0.865401	+	0.501080i	$0.832936\pi$
$62$	4.82923	0.613312
$63$	−7.19527	−0.906518
$64$	1.00000	0.125000
$65$	2.43182	0.301630
$66$	−7.46241	−0.918559
$67$	11.5935	1.41638	0.708188	−	0.706024i	$-0.249513\pi$
$67$	11.5935	1.41638	0.708188	+	0.706024i	$0.249513\pi$
$68$	4.79853	0.581907
$69$	−2.00410	−0.241265
$70$	−4.40972	−0.527062
$71$	15.4391	1.83228	0.916142	−	0.400855i	$-0.131287\pi$
$71$	15.4391	1.83228	0.916142	+	0.400855i	$0.131287\pi$
$72$	−1.63168	−0.192296
$73$	5.98090	0.700011	0.350005	−	0.936748i	$-0.386180\pi$
$73$	5.98090	0.700011	0.350005	+	0.936748i	$0.386180\pi$
$74$	−8.15269	−0.947731
$75$	2.15213	0.248507
$76$	−6.67647	−0.765844
$77$	−15.2905	−1.74251
$78$	5.23361	0.592590
$79$	−10.6192	−1.19476	−0.597379	−	0.801959i	$-0.703791\pi$
$79$	−10.6192	−1.19476	−0.597379	+	0.801959i	$0.703791\pi$
$80$	−1.00000	−0.111803
$81$	−11.2327	−1.24807
$82$	0.0826739	0.00912981
$83$	9.12066	1.00112	0.500561	−	0.865701i	$-0.333127\pi$
$83$	9.12066	1.00112	0.500561	+	0.865701i	$0.333127\pi$
$84$	−9.49031	−1.03548
$85$	−4.79853	−0.520474
$86$	−1.98104	−0.213621
$87$	14.1105	1.51281
$88$	−3.46745	−0.369631
$89$	−9.01860	−0.955970	−0.477985	−	0.878368i	$-0.658633\pi$
$89$	−9.01860	−0.955970	−0.477985	+	0.878368i	$0.658633\pi$
$90$	1.63168	0.171995
$91$	10.7237	1.12414
$92$	−0.931214	−0.0970858
$93$	−10.3931	−1.07772
$94$	−11.6223	−1.19875
$95$	6.67647	0.684992
$96$	−2.15213	−0.219651
$97$	7.88077	0.800171	0.400086	−	0.916478i	$-0.368980\pi$
$97$	7.88077	0.800171	0.400086	+	0.916478i	$0.368980\pi$
$98$	−12.4456	−1.25720
$99$	5.65777	0.568628
$100$	1.00000	0.100000
$101$	−12.8713	−1.28074	−0.640369	−	0.768067i	$-0.721219\pi$
$101$	−12.8713	−1.28074	−0.640369	+	0.768067i	$0.721219\pi$
$102$	−10.3271	−1.02253
$103$	−7.57098	−0.745991	−0.372996	−	0.927833i	$-0.621669\pi$
$103$	−7.57098	−0.745991	−0.372996	+	0.927833i	$0.621669\pi$
$104$	2.43182	0.238460
$105$	9.49031	0.926159
$106$	5.51735	0.535892
$107$	14.6280	1.41414	0.707071	−	0.707142i	$-0.250016\pi$
$107$	14.6280	1.41414	0.707071	+	0.707142i	$0.250016\pi$
$108$	−2.94480	−0.283364
$109$	3.10204	0.297122	0.148561	−	0.988903i	$-0.452536\pi$
$109$	3.10204	0.297122	0.148561	+	0.988903i	$0.452536\pi$
$110$	3.46745	0.330608
$111$	17.5457	1.66536
$112$	−4.40972	−0.416679
$113$	18.2558	1.71736	0.858681	−	0.512511i	$-0.171285\pi$
$113$	18.2558	1.71736	0.858681	+	0.512511i	$0.171285\pi$
$114$	14.3687	1.34575
$115$	0.931214	0.0868361
$116$	6.55653	0.608759
$117$	−3.96796	−0.366838
$118$	−10.7443	−0.989092
$119$	−21.1602	−1.93975
$120$	2.15213	0.196462
$121$	1.02318	0.0930160
$122$	13.5180	1.22386
$123$	−0.177925	−0.0160430
$124$	−4.82923	−0.433677
$125$	−1.00000	−0.0894427
$126$	7.19527	0.641005
$127$	14.0072	1.24294	0.621471	−	0.783437i	$-0.286535\pi$
$127$	14.0072	1.24294	0.621471	+	0.783437i	$0.286535\pi$
$128$	−1.00000	−0.0883883
$129$	4.26347	0.375378
$130$	−2.43182	−0.213285
$131$	−20.3081	−1.77433	−0.887165	−	0.461451i	$-0.847329\pi$
$131$	−20.3081	−1.77433	−0.887165	+	0.461451i	$0.847329\pi$
$132$	7.46241	0.649519
$133$	29.4414	2.55289
$134$	−11.5935	−1.00153
$135$	2.94480	0.253448
$136$	−4.79853	−0.411471
$137$	2.07544	0.177317	0.0886584	−	0.996062i	$-0.471742\pi$
$137$	2.07544	0.177317	0.0886584	+	0.996062i	$0.471742\pi$
$138$	2.00410	0.170600
$139$	6.92751	0.587584	0.293792	−	0.955869i	$-0.405083\pi$
$139$	6.92751	0.587584	0.293792	+	0.955869i	$0.405083\pi$
$140$	4.40972	0.372689
$141$	25.0128	2.10646
$142$	−15.4391	−1.29562
$143$	−8.43221	−0.705137
$144$	1.63168	0.135974
$145$	−6.55653	−0.544490
$146$	−5.98090	−0.494982
$147$	26.7847	2.20916
$148$	8.15269	0.670147
$149$	18.5148	1.51679	0.758396	−	0.651794i	$-0.225983\pi$
$149$	18.5148	1.51679	0.758396	+	0.651794i	$0.225983\pi$
$150$	−2.15213	−0.175721
$151$	10.2224	0.831883	0.415942	−	0.909391i	$-0.363452\pi$
$151$	10.2224	0.831883	0.415942	+	0.909391i	$0.363452\pi$
$152$	6.67647	0.541534
$153$	7.82968	0.632992
$154$	15.2905	1.23214
$155$	4.82923	0.387893
$156$	−5.23361	−0.419024
$157$	2.44008	0.194740	0.0973698	−	0.995248i	$-0.468957\pi$
$157$	2.44008	0.194740	0.0973698	+	0.995248i	$0.468957\pi$
$158$	10.6192	0.844821
$159$	−11.8741	−0.941675
$160$	1.00000	0.0790569
$161$	4.10639	0.323629
$162$	11.2327	0.882521
$163$	10.5301	0.824784	0.412392	−	0.911006i	$-0.364693\pi$
$163$	10.5301	0.824784	0.412392	+	0.911006i	$0.364693\pi$
$164$	−0.0826739	−0.00645575
$165$	−7.46241	−0.580948
$166$	−9.12066	−0.707900
$167$	22.0520	1.70644	0.853219	−	0.521554i	$-0.174647\pi$
$167$	22.0520	1.70644	0.853219	+	0.521554i	$0.174647\pi$
$168$	9.49031	0.732193
$169$	−7.08624	−0.545095
$170$	4.79853	0.368030
$171$	−10.8939	−0.833077
$172$	1.98104	0.151053
$173$	−6.99836	−0.532076	−0.266038	−	0.963963i	$-0.585715\pi$
$173$	−6.99836	−0.532076	−0.266038	+	0.963963i	$0.585715\pi$
$174$	−14.1105	−1.06972
$175$	−4.40972	−0.333343
$176$	3.46745	0.261369
$177$	23.1232	1.73804
$178$	9.01860	0.675973
$179$	24.9744	1.86668	0.933338	−	0.358999i	$-0.116882\pi$
$179$	24.9744	1.86668	0.933338	+	0.358999i	$0.116882\pi$
$180$	−1.63168	−0.121619
$181$	−5.63024	−0.418492	−0.209246	−	0.977863i	$-0.567101\pi$
$181$	−5.63024	−0.418492	−0.209246	+	0.977863i	$0.567101\pi$
$182$	−10.7237	−0.794890
$183$	−29.0925	−2.15058
$184$	0.931214	0.0686500
$185$	−8.15269	−0.599397
$186$	10.3931	0.762062
$187$	16.6386	1.21674
$188$	11.6223	0.847646
$189$	12.9857	0.944574
$190$	−6.67647	−0.484362
$191$	−8.02334	−0.580549	−0.290274	−	0.956943i	$-0.593747\pi$
$191$	−8.02334	−0.580549	−0.290274	+	0.956943i	$0.593747\pi$
$192$	2.15213	0.155317
$193$	−9.60240	−0.691196	−0.345598	−	0.938383i	$-0.612324\pi$
$193$	−9.60240	−0.691196	−0.345598	+	0.938383i	$0.612324\pi$
$194$	−7.88077	−0.565807
$195$	5.23361	0.374787
$196$	12.4456	0.888973
$197$	4.73915	0.337650	0.168825	−	0.985646i	$-0.446003\pi$
$197$	4.73915	0.337650	0.168825	+	0.985646i	$0.446003\pi$
$198$	−5.65777	−0.402080
$199$	6.77589	0.480330	0.240165	−	0.970732i	$-0.422798\pi$
$199$	6.77589	0.480330	0.240165	+	0.970732i	$0.422798\pi$
$200$	−1.00000	−0.0707107
$201$	24.9508	1.75990
$202$	12.8713	0.905619
$203$	−28.9125	−2.02926
$204$	10.3271	0.723040
$205$	0.0826739	0.00577420
$206$	7.57098	0.527495
$207$	−1.51945	−0.105609
$208$	−2.43182	−0.168617
$209$	−23.1503	−1.60134
$210$	−9.49031	−0.654894
$211$	−4.97267	−0.342333	−0.171166	−	0.985242i	$-0.554754\pi$
$211$	−4.97267	−0.342333	−0.171166	+	0.985242i	$0.554754\pi$
$212$	−5.51735	−0.378933
$213$	33.2270	2.27668
$214$	−14.6280	−0.999950
$215$	−1.98104	−0.135106
$216$	2.94480	0.200368
$217$	21.2955	1.44563
$218$	−3.10204	−0.210097
$219$	12.8717	0.869788
$220$	−3.46745	−0.233775
$221$	−11.6692	−0.784954
$222$	−17.5457	−1.17759
$223$	−16.9371	−1.13419	−0.567096	−	0.823652i	$-0.691933\pi$
$223$	−16.9371	−1.13419	−0.567096	+	0.823652i	$0.691933\pi$
$224$	4.40972	0.294637
$225$	1.63168	0.108779
$226$	−18.2558	−1.21436
$227$	−2.04807	−0.135935	−0.0679675	−	0.997688i	$-0.521651\pi$
$227$	−2.04807	−0.135935	−0.0679675	+	0.997688i	$0.521651\pi$
$228$	−14.3687	−0.951588
$229$	2.04352	0.135040	0.0675198	−	0.997718i	$-0.478491\pi$
$229$	2.04352	0.135040	0.0675198	+	0.997718i	$0.478491\pi$
$230$	−0.931214	−0.0614024
$231$	−32.9071	−2.16513
$232$	−6.55653	−0.430457
$233$	−18.1255	−1.18744	−0.593722	−	0.804671i	$-0.702342\pi$
$233$	−18.1255	−1.18744	−0.593722	+	0.804671i	$0.702342\pi$
$234$	3.96796	0.259394
$235$	−11.6223	−0.758158
$236$	10.7443	0.699393
$237$	−22.8540	−1.48453
$238$	21.1602	1.37161
$239$	−18.3347	−1.18598	−0.592988	−	0.805212i	$-0.702052\pi$
$239$	−18.3347	−1.18598	−0.592988	+	0.805212i	$0.702052\pi$
$240$	−2.15213	−0.138920
$241$	28.9759	1.86650	0.933252	−	0.359222i	$-0.116958\pi$
$241$	28.9759	1.86650	0.933252	+	0.359222i	$0.116958\pi$
$242$	−1.02318	−0.0657722
$243$	−15.3398	−0.984048
$244$	−13.5180	−0.865401
$245$	−12.4456	−0.795122
$246$	0.177925	0.0113441
$247$	16.2360	1.03307
$248$	4.82923	0.306656
$249$	19.6289	1.24393
$250$	1.00000	0.0632456
$251$	22.6586	1.43020	0.715101	−	0.699022i	$-0.246381\pi$
$251$	22.6586	1.43020	0.715101	+	0.699022i	$0.246381\pi$
$252$	−7.19527	−0.453259
$253$	−3.22893	−0.203001
$254$	−14.0072	−0.878892
$255$	−10.3271	−0.646707
$256$	1.00000	0.0625000
$257$	26.1168	1.62912	0.814561	−	0.580078i	$-0.196978\pi$
$257$	26.1168	1.62912	0.814561	+	0.580078i	$0.196978\pi$
$258$	−4.26347	−0.265432
$259$	−35.9511	−2.23389
$260$	2.43182	0.150815
$261$	10.6982	0.662201
$262$	20.3081	1.25464
$263$	1.18678	0.0731799	0.0365900	−	0.999330i	$-0.488350\pi$
$263$	1.18678	0.0731799	0.0365900	+	0.999330i	$0.488350\pi$
$264$	−7.46241	−0.459280
$265$	5.51735	0.338928
$266$	−29.4414	−1.80517
$267$	−19.4092	−1.18783
$268$	11.5935	0.708188
$269$	−2.59446	−0.158187	−0.0790935	−	0.996867i	$-0.525203\pi$
$269$	−2.59446	−0.158187	−0.0790935	+	0.996867i	$0.525203\pi$
$270$	−2.94480	−0.179215
$271$	−19.7248	−1.19820	−0.599099	−	0.800675i	$-0.704475\pi$
$271$	−19.7248	−1.19820	−0.599099	+	0.800675i	$0.704475\pi$
$272$	4.79853	0.290954
$273$	23.0787	1.39679
$274$	−2.07544	−0.125382
$275$	3.46745	0.209095
$276$	−2.00410	−0.120632
$277$	24.9859	1.50126	0.750629	−	0.660724i	$-0.229750\pi$
$277$	24.9859	1.50126	0.750629	+	0.660724i	$0.229750\pi$
$278$	−6.92751	−0.415484
$279$	−7.87977	−0.471749
$280$	−4.40972	−0.263531
$281$	9.29610	0.554559	0.277279	−	0.960789i	$-0.410567\pi$
$281$	9.29610	0.554559	0.277279	+	0.960789i	$0.410567\pi$
$282$	−25.0128	−1.48949
$283$	10.8220	0.643302	0.321651	−	0.946858i	$-0.395762\pi$
$283$	10.8220	0.643302	0.321651	+	0.946858i	$0.395762\pi$
$284$	15.4391	0.916142
$285$	14.3687	0.851127
$286$	8.43221	0.498607
$287$	0.364569	0.0215198
$288$	−1.63168	−0.0961479
$289$	6.02590	0.354464
$290$	6.55653	0.385013
$291$	16.9605	0.994241
$292$	5.98090	0.350005
$293$	−23.2472	−1.35812	−0.679058	−	0.734085i	$-0.737612\pi$
$293$	−23.2472	−1.35812	−0.679058	+	0.734085i	$0.737612\pi$
$294$	−26.7847	−1.56211
$295$	−10.7443	−0.625557
$296$	−8.15269	−0.473865
$297$	−10.2109	−0.592499
$298$	−18.5148	−1.07253
$299$	2.26455	0.130962
$300$	2.15213	0.124254
$301$	−8.73584	−0.503526
$302$	−10.2224	−0.588230
$303$	−27.7007	−1.59136
$304$	−6.67647	−0.382922
$305$	13.5180	0.774038
$306$	−7.82968	−0.447593
$307$	−9.50961	−0.542742	−0.271371	−	0.962475i	$-0.587477\pi$
$307$	−9.50961	−0.542742	−0.271371	+	0.962475i	$0.587477\pi$
$308$	−15.2905	−0.871255
$309$	−16.2938	−0.926920
$310$	−4.82923	−0.274282
$311$	0.632277	0.0358531	0.0179266	−	0.999839i	$-0.494293\pi$
$311$	0.632277	0.0358531	0.0179266	+	0.999839i	$0.494293\pi$
$312$	5.23361	0.296295
$313$	−20.3452	−1.14998	−0.574990	−	0.818160i	$-0.694994\pi$
$313$	−20.3452	−1.14998	−0.574990	+	0.818160i	$0.694994\pi$
$314$	−2.44008	−0.137702
$315$	7.19527	0.405407
$316$	−10.6192	−0.597379
$317$	−35.2623	−1.98053	−0.990265	−	0.139192i	$-0.955549\pi$
$317$	−35.2623	−1.98053	−0.990265	+	0.139192i	$0.955549\pi$
$318$	11.8741	0.665865
$319$	22.7344	1.27288
$320$	−1.00000	−0.0559017
$321$	31.4814	1.75712
$322$	−4.10639	−0.228840
$323$	−32.0373	−1.78260
$324$	−11.2327	−0.624037
$325$	−2.43182	−0.134893
$326$	−10.5301	−0.583211
$327$	6.67601	0.369184
$328$	0.0826739	0.00456490
$329$	−51.2513	−2.82557
$330$	7.46241	0.410792
$331$	10.6941	0.587799	0.293899	−	0.955836i	$-0.405047\pi$
$331$	10.6941	0.587799	0.293899	+	0.955836i	$0.405047\pi$
$332$	9.12066	0.500561
$333$	13.3026	0.728978
$334$	−22.0520	−1.20663
$335$	−11.5935	−0.633422
$336$	−9.49031	−0.517739
$337$	−24.6450	−1.34250	−0.671249	−	0.741232i	$-0.734242\pi$
$337$	−24.6450	−1.34250	−0.671249	+	0.741232i	$0.734242\pi$
$338$	7.08624	0.385441
$339$	39.2889	2.13388
$340$	−4.79853	−0.260237
$341$	−16.7451	−0.906797
$342$	10.8939	0.589074
$343$	−24.0137	−1.29662
$344$	−1.98104	−0.106811
$345$	2.00410	0.107897
$346$	6.99836	0.376234
$347$	9.99727	0.536682	0.268341	−	0.963324i	$-0.413525\pi$
$347$	9.99727	0.536682	0.268341	+	0.963324i	$0.413525\pi$
$348$	14.1105	0.756404
$349$	12.2481	0.655627	0.327814	−	0.944742i	$-0.393688\pi$
$349$	12.2481	0.655627	0.327814	+	0.944742i	$0.393688\pi$
$350$	4.40972	0.235709
$351$	7.16123	0.382238
$352$	−3.46745	−0.184815
$353$	−4.98404	−0.265274	−0.132637	−	0.991165i	$-0.542344\pi$
$353$	−4.98404	−0.265274	−0.132637	+	0.991165i	$0.542344\pi$
$354$	−23.1232	−1.22898
$355$	−15.4391	−0.819422
$356$	−9.01860	−0.477985
$357$	−45.5395	−2.41021
$358$	−24.9744	−1.31994
$359$	32.0394	1.69098	0.845488	−	0.533995i	$-0.179310\pi$
$359$	32.0394	1.69098	0.845488	+	0.533995i	$0.179310\pi$
$360$	1.63168	0.0859973
$361$	25.5753	1.34607
$362$	5.63024	0.295919
$363$	2.20201	0.115576
$364$	10.7237	0.562072
$365$	−5.98090	−0.313054
$366$	29.0925	1.52069
$367$	26.6423	1.39072	0.695359	−	0.718662i	$-0.255245\pi$
$367$	26.6423	1.39072	0.695359	+	0.718662i	$0.255245\pi$
$368$	−0.931214	−0.0485429
$369$	−0.134898	−0.00702249
$370$	8.15269	0.423838
$371$	24.3300	1.26315
$372$	−10.3931	−0.538859
$373$	−2.41595	−0.125093	−0.0625466	−	0.998042i	$-0.519922\pi$
$373$	−2.41595	−0.125093	−0.0625466	+	0.998042i	$0.519922\pi$
$374$	−16.6386	−0.860364
$375$	−2.15213	−0.111136
$376$	−11.6223	−0.599377
$377$	−15.9443	−0.821174
$378$	−12.9857	−0.667915
$379$	−15.0140	−0.771219	−0.385610	−	0.922662i	$-0.626009\pi$
$379$	−15.0140	−0.771219	−0.385610	+	0.922662i	$0.626009\pi$
$380$	6.67647	0.342496
$381$	30.1455	1.54440
$382$	8.02334	0.410510
$383$	−3.77917	−0.193107	−0.0965533	−	0.995328i	$-0.530782\pi$
$383$	−3.77917	−0.193107	−0.0965533	+	0.995328i	$0.530782\pi$
$384$	−2.15213	−0.109826
$385$	15.2905	0.779274
$386$	9.60240	0.488749
$387$	3.23243	0.164314
$388$	7.88077	0.400086
$389$	16.0079	0.811632	0.405816	−	0.913955i	$-0.366987\pi$
$389$	16.0079	0.811632	0.405816	+	0.913955i	$0.366987\pi$
$390$	−5.23361	−0.265014
$391$	−4.46846	−0.225980
$392$	−12.4456	−0.628599
$393$	−43.7059	−2.20467
$394$	−4.73915	−0.238755
$395$	10.6192	0.534312
$396$	5.65777	0.284314
$397$	22.9613	1.15240	0.576198	−	0.817310i	$-0.304536\pi$
$397$	22.9613	1.15240	0.576198	+	0.817310i	$0.304536\pi$
$398$	−6.77589	−0.339644
$399$	63.3618	3.17206
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−24.9508	−1.24443
$403$	11.7438	0.585001
$404$	−12.8713	−0.640369
$405$	11.2327	0.558155
$406$	28.9125	1.43490
$407$	28.2690	1.40124
$408$	−10.3271	−0.511267
$409$	−2.56055	−0.126611	−0.0633054	−	0.997994i	$-0.520164\pi$
$409$	−2.56055	−0.126611	−0.0633054	+	0.997994i	$0.520164\pi$
$410$	−0.0826739	−0.00408298
$411$	4.46663	0.220322
$412$	−7.57098	−0.372996
$413$	−47.3793	−2.33138
$414$	1.51945	0.0746767
$415$	−9.12066	−0.447715
$416$	2.43182	0.119230
$417$	14.9089	0.730094
$418$	23.1503	1.13232
$419$	−30.6276	−1.49626	−0.748129	−	0.663553i	$-0.769048\pi$
$419$	−30.6276	−1.49626	−0.748129	+	0.663553i	$0.769048\pi$
$420$	9.49031	0.463080
$421$	37.2917	1.81749	0.908743	−	0.417356i	$-0.137043\pi$
$421$	37.2917	1.81749	0.908743	+	0.417356i	$0.137043\pi$
$422$	4.97267	0.242066
$423$	18.9640	0.922060
$424$	5.51735	0.267946
$425$	4.79853	0.232763
$426$	−33.2270	−1.60985
$427$	59.6106	2.88476
$428$	14.6280	0.707071
$429$	−18.1473	−0.876158
$430$	1.98104	0.0955344
$431$	−21.7748	−1.04885	−0.524427	−	0.851456i	$-0.675720\pi$
$431$	−21.7748	−1.04885	−0.524427	+	0.851456i	$0.675720\pi$
$432$	−2.94480	−0.141682
$433$	−27.6818	−1.33030	−0.665151	−	0.746709i	$-0.731633\pi$
$433$	−27.6818	−1.33030	−0.665151	+	0.746709i	$0.731633\pi$
$434$	−21.2955	−1.02222
$435$	−14.1105	−0.676549
$436$	3.10204	0.148561
$437$	6.21722	0.297410
$438$	−12.8717	−0.615033
$439$	−4.06381	−0.193955	−0.0969776	−	0.995287i	$-0.530918\pi$
$439$	−4.06381	−0.193955	−0.0969776	+	0.995287i	$0.530918\pi$
$440$	3.46745	0.165304
$441$	20.3073	0.967015
$442$	11.6692	0.555046
$443$	−5.79090	−0.275134	−0.137567	−	0.990492i	$-0.543928\pi$
$443$	−5.79090	−0.275134	−0.137567	+	0.990492i	$0.543928\pi$
$444$	17.5457	0.832681
$445$	9.01860	0.427523
$446$	16.9371	0.801995
$447$	39.8463	1.88467
$448$	−4.40972	−0.208340
$449$	11.5422	0.544708	0.272354	−	0.962197i	$-0.412198\pi$
$449$	11.5422	0.544708	0.272354	+	0.962197i	$0.412198\pi$
$450$	−1.63168	−0.0769183
$451$	−0.286667	−0.0134986
$452$	18.2558	0.858681
$453$	21.9999	1.03364
$454$	2.04807	0.0961205
$455$	−10.7237	−0.502733
$456$	14.3687	0.672875
$457$	29.2402	1.36780	0.683900	−	0.729576i	$-0.260283\pi$
$457$	29.2402	1.36780	0.683900	+	0.729576i	$0.260283\pi$
$458$	−2.04352	−0.0954873
$459$	−14.1307	−0.659566
$460$	0.931214	0.0434181
$461$	−30.8494	−1.43680	−0.718400	−	0.695631i	$-0.755125\pi$
$461$	−30.8494	−1.43680	−0.718400	+	0.695631i	$0.755125\pi$
$462$	32.9071	1.53098
$463$	28.7096	1.33425	0.667125	−	0.744946i	$-0.267525\pi$
$463$	28.7096	1.33425	0.667125	+	0.744946i	$0.267525\pi$
$464$	6.55653	0.304379
$465$	10.3931	0.481971
$466$	18.1255	0.839649
$467$	−3.13314	−0.144985	−0.0724923	−	0.997369i	$-0.523095\pi$
$467$	−3.13314	−0.144985	−0.0724923	+	0.997369i	$0.523095\pi$
$468$	−3.96796	−0.183419
$469$	−51.1242	−2.36070
$470$	11.6223	0.536099
$471$	5.25138	0.241971
$472$	−10.7443	−0.494546
$473$	6.86916	0.315844
$474$	22.8540	1.04972
$475$	−6.67647	−0.306338
$476$	−21.1602	−0.969875
$477$	−9.00257	−0.412199
$478$	18.3347	0.838611
$479$	28.5029	1.30233	0.651165	−	0.758936i	$-0.274280\pi$
$479$	28.5029	1.30233	0.651165	+	0.758936i	$0.274280\pi$
$480$	2.15213	0.0982311
$481$	−19.8259	−0.903983
$482$	−28.9759	−1.31982
$483$	8.83751	0.402121
$484$	1.02318	0.0465080
$485$	−7.88077	−0.357848
$486$	15.3398	0.695827
$487$	−33.4999	−1.51803	−0.759013	−	0.651075i	$-0.774318\pi$
$487$	−33.4999	−1.51803	−0.759013	+	0.651075i	$0.774318\pi$
$488$	13.5180	0.611931
$489$	22.6623	1.02482
$490$	12.4456	0.562236
$491$	−29.8201	−1.34576	−0.672881	−	0.739751i	$-0.734943\pi$
$491$	−29.8201	−1.34576	−0.672881	+	0.739751i	$0.734943\pi$
$492$	−0.177925	−0.00802150
$493$	31.4617	1.41696
$494$	−16.2360	−0.730492
$495$	−5.65777	−0.254298
$496$	−4.82923	−0.216839
$497$	−68.0821	−3.05390
$498$	−19.6289	−0.879591
$499$	31.0553	1.39023	0.695114	−	0.718899i	$-0.255354\pi$
$499$	31.0553	1.39023	0.695114	+	0.718899i	$0.255354\pi$
$500$	−1.00000	−0.0447214
$501$	47.4589	2.12031
$502$	−22.6586	−1.01130
$503$	6.72531	0.299867	0.149933	−	0.988696i	$-0.452094\pi$
$503$	6.72531	0.299867	0.149933	+	0.988696i	$0.452094\pi$
$504$	7.19527	0.320503
$505$	12.8713	0.572764
$506$	3.22893	0.143544
$507$	−15.2505	−0.677300
$508$	14.0072	0.621471
$509$	−4.87672	−0.216157	−0.108078	−	0.994142i	$-0.534470\pi$
$509$	−4.87672	−0.216157	−0.108078	+	0.994142i	$0.534470\pi$
$510$	10.3271	0.457291
$511$	−26.3741	−1.16672
$512$	−1.00000	−0.0441942
$513$	19.6609	0.868050
$514$	−26.1168	−1.15196
$515$	7.57098	0.333617
$516$	4.26347	0.187689
$517$	40.2998	1.77238
$518$	35.9511	1.57960
$519$	−15.0614	−0.661123
$520$	−2.43182	−0.106642
$521$	−26.0269	−1.14026	−0.570129	−	0.821555i	$-0.693107\pi$
$521$	−26.0269	−1.14026	−0.570129	+	0.821555i	$0.693107\pi$
$522$	−10.6982	−0.468247
$523$	−3.22399	−0.140975	−0.0704877	−	0.997513i	$-0.522456\pi$
$523$	−3.22399	−0.140975	−0.0704877	+	0.997513i	$0.522456\pi$
$524$	−20.3081	−0.887165
$525$	−9.49031	−0.414191
$526$	−1.18678	−0.0517460
$527$	−23.1732	−1.00944
$528$	7.46241	0.324760
$529$	−22.1328	−0.962297
$530$	−5.51735	−0.239658
$531$	17.5313	0.760793
$532$	29.4414	1.27645
$533$	0.201048	0.00870837
$534$	19.4092	0.839920
$535$	−14.6280	−0.632424
$536$	−11.5935	−0.500764
$537$	53.7483	2.31941
$538$	2.59446	0.111855
$539$	43.1545	1.85880
$540$	2.94480	0.126724
$541$	−33.9837	−1.46107	−0.730537	−	0.682873i	$-0.760730\pi$
$541$	−33.9837	−1.46107	−0.730537	+	0.682873i	$0.760730\pi$
$542$	19.7248	0.847255
$543$	−12.1170	−0.519992
$544$	−4.79853	−0.205735
$545$	−3.10204	−0.132877
$546$	−23.0787	−0.987679
$547$	−9.62648	−0.411598	−0.205799	−	0.978594i	$-0.565979\pi$
$547$	−9.62648	−0.411598	−0.205799	+	0.978594i	$0.565979\pi$
$548$	2.07544	0.0886584
$549$	−22.0571	−0.941373
$550$	−3.46745	−0.147852
$551$	−43.7745	−1.86486
$552$	2.00410	0.0853001
$553$	46.8279	1.99132
$554$	−24.9859	−1.06155
$555$	−17.5457	−0.744773
$556$	6.92751	0.293792
$557$	9.92615	0.420585	0.210292	−	0.977639i	$-0.432558\pi$
$557$	9.92615	0.420585	0.210292	+	0.977639i	$0.432558\pi$
$558$	7.87977	0.333577
$559$	−4.81754	−0.203760
$560$	4.40972	0.186345
$561$	35.8086	1.51184
$562$	−9.29610	−0.392132
$563$	16.8071	0.708335	0.354168	−	0.935182i	$-0.384764\pi$
$563$	16.8071	0.708335	0.354168	+	0.935182i	$0.384764\pi$
$564$	25.0128	1.05323
$565$	−18.2558	−0.768027
$566$	−10.8220	−0.454883
$567$	49.5329	2.08019
$568$	−15.4391	−0.647810
$569$	−19.5970	−0.821549	−0.410775	−	0.911737i	$-0.634742\pi$
$569$	−19.5970	−0.821549	−0.410775	+	0.911737i	$0.634742\pi$
$570$	−14.3687	−0.601837
$571$	24.4096	1.02151	0.510755	−	0.859726i	$-0.329366\pi$
$571$	24.4096	1.02151	0.510755	+	0.859726i	$0.329366\pi$
$572$	−8.43221	−0.352568
$573$	−17.2673	−0.721352
$574$	−0.364569	−0.0152168
$575$	−0.931214	−0.0388343
$576$	1.63168	0.0679868
$577$	−5.57481	−0.232082	−0.116041	−	0.993244i	$-0.537020\pi$
$577$	−5.57481	−0.232082	−0.116041	+	0.993244i	$0.537020\pi$
$578$	−6.02590	−0.250644
$579$	−20.6657	−0.858835
$580$	−6.55653	−0.272245
$581$	−40.2195	−1.66859
$582$	−16.9605	−0.703035
$583$	−19.1311	−0.792329
$584$	−5.98090	−0.247491
$585$	3.96796	0.164055
$586$	23.2472	0.960333
$587$	8.03347	0.331577	0.165788	−	0.986161i	$-0.446983\pi$
$587$	8.03347	0.331577	0.165788	+	0.986161i	$0.446983\pi$
$588$	26.7847	1.10458
$589$	32.2422	1.32852
$590$	10.7443	0.442335
$591$	10.1993	0.419543
$592$	8.15269	0.335073
$593$	30.0881	1.23557	0.617785	−	0.786347i	$-0.288030\pi$
$593$	30.0881	1.23557	0.617785	+	0.786347i	$0.288030\pi$
$594$	10.2109	0.418960
$595$	21.1602	0.867483
$596$	18.5148	0.758396
$597$	14.5826	0.596827
$598$	−2.26455	−0.0926042
$599$	13.6904	0.559376	0.279688	−	0.960091i	$-0.409769\pi$
$599$	13.6904	0.559376	0.279688	+	0.960091i	$0.409769\pi$
$600$	−2.15213	−0.0878605
$601$	4.51699	0.184252	0.0921260	−	0.995747i	$-0.470634\pi$
$601$	4.51699	0.184252	0.0921260	+	0.995747i	$0.470634\pi$
$602$	8.73584	0.356046
$603$	18.9170	0.770359
$604$	10.2224	0.415942
$605$	−1.02318	−0.0415980
$606$	27.7007	1.12526
$607$	−27.0474	−1.09782	−0.548911	−	0.835881i	$-0.684957\pi$
$607$	−27.0474	−1.09782	−0.548911	+	0.835881i	$0.684957\pi$
$608$	6.67647	0.270767
$609$	−62.2235	−2.52142
$610$	−13.5180	−0.547327
$611$	−28.2635	−1.14342
$612$	7.82968	0.316496
$613$	23.4893	0.948724	0.474362	−	0.880330i	$-0.342679\pi$
$613$	23.4893	0.948724	0.474362	+	0.880330i	$0.342679\pi$
$614$	9.50961	0.383777
$615$	0.177925	0.00717465
$616$	15.2905	0.616070
$617$	−30.7710	−1.23879	−0.619396	−	0.785079i	$-0.712623\pi$
$617$	−30.7710	−1.23879	−0.619396	+	0.785079i	$0.712623\pi$
$618$	16.2938	0.655432
$619$	23.2436	0.934237	0.467119	−	0.884195i	$-0.345292\pi$
$619$	23.2436	0.934237	0.467119	+	0.884195i	$0.345292\pi$
$620$	4.82923	0.193946
$621$	2.74224	0.110042
$622$	−0.632277	−0.0253520
$623$	39.7695	1.59333
$624$	−5.23361	−0.209512
$625$	1.00000	0.0400000
$626$	20.3452	0.813159
$627$	−49.8226	−1.98972
$628$	2.44008	0.0973698
$629$	39.1209	1.55985
$630$	−7.19527	−0.286666
$631$	46.2842	1.84254	0.921272	−	0.388918i	$-0.127151\pi$
$631$	46.2842	1.84254	0.921272	+	0.388918i	$0.127151\pi$
$632$	10.6192	0.422411
$633$	−10.7019	−0.425361
$634$	35.2623	1.40045
$635$	−14.0072	−0.555860
$636$	−11.8741	−0.470838
$637$	−30.2656	−1.19916
$638$	−22.7344	−0.900064
$639$	25.1917	0.996569
$640$	1.00000	0.0395285
$641$	5.18150	0.204657	0.102328	−	0.994751i	$-0.467371\pi$
$641$	5.18150	0.204657	0.102328	+	0.994751i	$0.467371\pi$
$642$	−31.4814	−1.24247
$643$	27.5627	1.08697	0.543484	−	0.839420i	$-0.317105\pi$
$643$	27.5627	1.08697	0.543484	+	0.839420i	$0.317105\pi$
$644$	4.10639	0.161815
$645$	−4.26347	−0.167874
$646$	32.0373	1.26049
$647$	−31.4338	−1.23579	−0.617895	−	0.786261i	$-0.712014\pi$
$647$	−31.4338	−1.23579	−0.617895	+	0.786261i	$0.712014\pi$
$648$	11.2327	0.441261
$649$	37.2552	1.46240
$650$	2.43182	0.0953839
$651$	45.8309	1.79625
$652$	10.5301	0.412392
$653$	38.3897	1.50230	0.751152	−	0.660129i	$-0.229499\pi$
$653$	38.3897	1.50230	0.751152	+	0.660129i	$0.229499\pi$
$654$	−6.67601	−0.261053
$655$	20.3081	0.793505
$656$	−0.0826739	−0.00322788
$657$	9.75893	0.380732
$658$	51.2513	1.99798
$659$	−6.96887	−0.271469	−0.135734	−	0.990745i	$-0.543339\pi$
$659$	−6.96887	−0.271469	−0.135734	+	0.990745i	$0.543339\pi$
$660$	−7.46241	−0.290474
$661$	−28.9996	−1.12796	−0.563978	−	0.825790i	$-0.690730\pi$
$661$	−28.9996	−1.12796	−0.563978	+	0.825790i	$0.690730\pi$
$662$	−10.6941	−0.415637
$663$	−25.1136	−0.975333
$664$	−9.12066	−0.353950
$665$	−29.4414	−1.14169
$666$	−13.3026	−0.515465
$667$	−6.10553	−0.236407
$668$	22.0520	0.853219
$669$	−36.4509	−1.40927
$670$	11.5935	0.447897
$671$	−46.8729	−1.80951
$672$	9.49031	0.366097
$673$	−8.14549	−0.313986	−0.156993	−	0.987600i	$-0.550180\pi$
$673$	−8.14549	−0.313986	−0.156993	+	0.987600i	$0.550180\pi$
$674$	24.6450	0.949290
$675$	−2.94480	−0.113345
$676$	−7.08624	−0.272548
$677$	−0.905278	−0.0347927	−0.0173963	−	0.999849i	$-0.505538\pi$
$677$	−0.905278	−0.0347927	−0.0173963	+	0.999849i	$0.505538\pi$
$678$	−39.2889	−1.50888
$679$	−34.7520	−1.33366
$680$	4.79853	0.184015
$681$	−4.40772	−0.168904
$682$	16.7451	0.641202
$683$	4.86594	0.186190	0.0930951	−	0.995657i	$-0.470324\pi$
$683$	4.86594	0.186190	0.0930951	+	0.995657i	$0.470324\pi$
$684$	−10.8939	−0.416538
$685$	−2.07544	−0.0792985
$686$	24.0137	0.916847
$687$	4.39793	0.167791
$688$	1.98104	0.0755265
$689$	13.4172	0.511155
$690$	−2.00410	−0.0762947
$691$	−12.9474	−0.492542	−0.246271	−	0.969201i	$-0.579205\pi$
$691$	−12.9474	−0.492542	−0.246271	+	0.969201i	$0.579205\pi$
$692$	−6.99836	−0.266038
$693$	−24.9492	−0.947741
$694$	−9.99727	−0.379491
$695$	−6.92751	−0.262775
$696$	−14.1105	−0.534859
$697$	−0.396713	−0.0150266
$698$	−12.2481	−0.463598
$699$	−39.0086	−1.47544
$700$	−4.40972	−0.166672
$701$	9.73753	0.367782	0.183891	−	0.982947i	$-0.441131\pi$
$701$	9.73753	0.367782	0.183891	+	0.982947i	$0.441131\pi$
$702$	−7.16123	−0.270283
$703$	−54.4312	−2.05291
$704$	3.46745	0.130684
$705$	−25.0128	−0.942038
$706$	4.98404	0.187577
$707$	56.7587	2.13463
$708$	23.1232	0.869021
$709$	−38.3392	−1.43986	−0.719930	−	0.694047i	$-0.755826\pi$
$709$	−38.3392	−1.43986	−0.719930	+	0.694047i	$0.755826\pi$
$710$	15.4391	0.579419
$711$	−17.3272	−0.649822
$712$	9.01860	0.337986
$713$	4.49704	0.168416
$714$	45.5395	1.70427
$715$	8.43221	0.315347
$716$	24.9744	0.933338
$717$	−39.4588	−1.47362
$718$	−32.0394	−1.19570
$719$	−26.7985	−0.999416	−0.499708	−	0.866194i	$-0.666559\pi$
$719$	−26.7985	−0.999416	−0.499708	+	0.866194i	$0.666559\pi$
$720$	−1.63168	−0.0608093
$721$	33.3859	1.24336
$722$	−25.5753	−0.951814
$723$	62.3601	2.31920
$724$	−5.63024	−0.209246
$725$	6.55653	0.243504
$726$	−2.20201	−0.0817243
$727$	−10.1345	−0.375868	−0.187934	−	0.982182i	$-0.560179\pi$
$727$	−10.1345	−0.375868	−0.187934	+	0.982182i	$0.560179\pi$
$728$	−10.7237	−0.397445
$729$	0.684683	0.0253586
$730$	5.98090	0.221363
$731$	9.50609	0.351596
$732$	−29.0925	−1.07529
$733$	−27.3842	−1.01146	−0.505730	−	0.862692i	$-0.668777\pi$
$733$	−27.3842	−1.01146	−0.505730	+	0.862692i	$0.668777\pi$
$734$	−26.6423	−0.983387
$735$	−26.7847	−0.987967
$736$	0.931214	0.0343250
$737$	40.1999	1.48078
$738$	0.134898	0.00496565
$739$	−31.5324	−1.15994	−0.579969	−	0.814638i	$-0.696936\pi$
$739$	−31.5324	−1.15994	−0.579969	+	0.814638i	$0.696936\pi$
$740$	−8.15269	−0.299699
$741$	34.9421	1.28363
$742$	−24.3300	−0.893181
$743$	−3.96578	−0.145490	−0.0727452	−	0.997351i	$-0.523176\pi$
$743$	−3.96578	−0.145490	−0.0727452	+	0.997351i	$0.523176\pi$
$744$	10.3931	0.381031
$745$	−18.5148	−0.678330
$746$	2.41595	0.0884542
$747$	14.8820	0.544505
$748$	16.6386	0.608369
$749$	−64.5054	−2.35698
$750$	2.15213	0.0785848
$751$	43.2721	1.57902	0.789511	−	0.613737i	$-0.210334\pi$
$751$	43.2721	1.57902	0.789511	+	0.613737i	$0.210334\pi$
$752$	11.6223	0.423823
$753$	48.7645	1.77708
$754$	15.9443	0.580658
$755$	−10.2224	−0.372029
$756$	12.9857	0.472287
$757$	1.81395	0.0659291	0.0329646	−	0.999457i	$-0.489505\pi$
$757$	1.81395	0.0659291	0.0329646	+	0.999457i	$0.489505\pi$
$758$	15.0140	0.545334
$759$	−6.94910	−0.252236
$760$	−6.67647	−0.242181
$761$	−6.77729	−0.245677	−0.122838	−	0.992427i	$-0.539200\pi$
$761$	−6.77729	−0.245677	−0.122838	+	0.992427i	$0.539200\pi$
$762$	−30.1455	−1.09205
$763$	−13.6791	−0.495218
$764$	−8.02334	−0.290274
$765$	−7.82968	−0.283083
$766$	3.77917	0.136547
$767$	−26.1282	−0.943435
$768$	2.15213	0.0776585
$769$	17.3853	0.626929	0.313464	−	0.949600i	$-0.398510\pi$
$769$	17.3853	0.626929	0.313464	+	0.949600i	$0.398510\pi$
$770$	−15.2905	−0.551030
$771$	56.2069	2.02424
$772$	−9.60240	−0.345598
$773$	21.9761	0.790426	0.395213	−	0.918590i	$-0.370671\pi$
$773$	21.9761	0.790426	0.395213	+	0.918590i	$0.370671\pi$
$774$	−3.23243	−0.116187
$775$	−4.82923	−0.173471
$776$	−7.88077	−0.282903
$777$	−77.3715	−2.77569
$778$	−16.0079	−0.573910
$779$	0.551970	0.0197764
$780$	5.23361	0.187393
$781$	53.5342	1.91560
$782$	4.46846	0.159792
$783$	−19.3077	−0.690000
$784$	12.4456	0.444487
$785$	−2.44008	−0.0870902
$786$	43.7059	1.55894
$787$	25.9506	0.925040	0.462520	−	0.886609i	$-0.346945\pi$
$787$	25.9506	0.925040	0.462520	+	0.886609i	$0.346945\pi$
$788$	4.73915	0.168825
$789$	2.55411	0.0909286
$790$	−10.6192	−0.377816
$791$	−80.5030	−2.86236
$792$	−5.65777	−0.201040
$793$	32.8734	1.16737
$794$	−22.9613	−0.814867
$795$	11.8741	0.421130
$796$	6.77589	0.240165
$797$	−45.3858	−1.60765	−0.803824	−	0.594867i	$-0.797205\pi$
$797$	−45.3858	−1.60765	−0.803824	+	0.594867i	$0.797205\pi$
$798$	−63.3618	−2.24298
$799$	55.7702	1.97301
$800$	−1.00000	−0.0353553
$801$	−14.7155	−0.519947
$802$	−1.00000	−0.0353112
$803$	20.7384	0.731843
$804$	24.9508	0.879948
$805$	−4.10639	−0.144731
$806$	−11.7438	−0.413658
$807$	−5.58363	−0.196553
$808$	12.8713	0.452810
$809$	40.5574	1.42592	0.712960	−	0.701204i	$-0.247354\pi$
$809$	40.5574	1.42592	0.712960	+	0.701204i	$0.247354\pi$
$810$	−11.2327	−0.394675
$811$	−27.1581	−0.953652	−0.476826	−	0.878998i	$-0.658213\pi$
$811$	−27.1581	−0.953652	−0.476826	+	0.878998i	$0.658213\pi$
$812$	−28.9125	−1.01463
$813$	−42.4505	−1.48880
$814$	−28.2690	−0.990828
$815$	−10.5301	−0.368855
$816$	10.3271	0.361520
$817$	−13.2264	−0.462732
$818$	2.56055	0.0895274
$819$	17.4976	0.611416
$820$	0.0826739	0.00288710
$821$	43.3239	1.51201	0.756007	−	0.654563i	$-0.227148\pi$
$821$	43.3239	1.51201	0.756007	+	0.654563i	$0.227148\pi$
$822$	−4.46663	−0.155792
$823$	−6.06111	−0.211277	−0.105639	−	0.994405i	$-0.533689\pi$
$823$	−6.06111	−0.211277	−0.105639	+	0.994405i	$0.533689\pi$
$824$	7.57098	0.263748
$825$	7.46241	0.259808
$826$	47.3793	1.64854
$827$	45.8403	1.59402	0.797011	−	0.603965i	$-0.206413\pi$
$827$	45.8403	1.59402	0.797011	+	0.603965i	$0.206413\pi$
$828$	−1.51945	−0.0528044
$829$	31.0200	1.07737	0.538685	−	0.842507i	$-0.318921\pi$
$829$	31.0200	1.07737	0.538685	+	0.842507i	$0.318921\pi$
$830$	9.12066	0.316583
$831$	53.7731	1.86537
$832$	−2.43182	−0.0843083
$833$	59.7207	2.06920
$834$	−14.9089	−0.516254
$835$	−22.0520	−0.763142
$836$	−23.1503	−0.800670
$837$	14.2211	0.491554
$838$	30.6276	1.05801
$839$	15.7606	0.544116	0.272058	−	0.962281i	$-0.412296\pi$
$839$	15.7606	0.544116	0.272058	+	0.962281i	$0.412296\pi$
$840$	−9.49031	−0.327447
$841$	13.9881	0.482349
$842$	−37.2917	−1.28516
$843$	20.0065	0.689059
$844$	−4.97267	−0.171166
$845$	7.08624	0.243774
$846$	−18.9640	−0.651995
$847$	−4.51192	−0.155031
$848$	−5.51735	−0.189467
$849$	23.2904	0.799325
$850$	−4.79853	−0.164588
$851$	−7.59189	−0.260247
$852$	33.2270	1.13834
$853$	−33.6925	−1.15361	−0.576805	−	0.816882i	$-0.695701\pi$
$853$	−33.6925	−1.15361	−0.576805	+	0.816882i	$0.695701\pi$
$854$	−59.6106	−2.03983
$855$	10.8939	0.372563
$856$	−14.6280	−0.499975
$857$	−23.4255	−0.800198	−0.400099	−	0.916472i	$-0.631024\pi$
$857$	−23.4255	−0.800198	−0.400099	+	0.916472i	$0.631024\pi$
$858$	18.1473	0.619537
$859$	−18.6509	−0.636361	−0.318181	−	0.948030i	$-0.603072\pi$
$859$	−18.6509	−0.636361	−0.318181	+	0.948030i	$0.603072\pi$
$860$	−1.98104	−0.0675530
$861$	0.784601	0.0267391
$862$	21.7748	0.741651
$863$	−22.4982	−0.765849	−0.382924	−	0.923780i	$-0.625083\pi$
$863$	−22.4982	−0.765849	−0.382924	+	0.923780i	$0.625083\pi$
$864$	2.94480	0.100184
$865$	6.99836	0.237951
$866$	27.6818	0.940665
$867$	12.9685	0.440435
$868$	21.2955	0.722817
$869$	−36.8216	−1.24909
$870$	14.1105	0.478392
$871$	−28.1934	−0.955297
$872$	−3.10204	−0.105048
$873$	12.8589	0.435209
$874$	−6.21722	−0.210301
$875$	4.40972	0.149076
$876$	12.8717	0.434894
$877$	−39.5636	−1.33597	−0.667983	−	0.744176i	$-0.732842\pi$
$877$	−39.5636	−1.33597	−0.667983	+	0.744176i	$0.732842\pi$
$878$	4.06381	0.137147
$879$	−50.0311	−1.68751
$880$	−3.46745	−0.116888
$881$	−37.7811	−1.27288	−0.636438	−	0.771328i	$-0.719593\pi$
$881$	−37.7811	−1.27288	−0.636438	+	0.771328i	$0.719593\pi$
$882$	−20.3073	−0.683783
$883$	−9.33027	−0.313988	−0.156994	−	0.987600i	$-0.550180\pi$
$883$	−9.33027	−0.313988	−0.156994	+	0.987600i	$0.550180\pi$
$884$	−11.6692	−0.392477
$885$	−23.1232	−0.777276
$886$	5.79090	0.194549
$887$	9.03773	0.303457	0.151729	−	0.988422i	$-0.451516\pi$
$887$	9.03773	0.303457	0.151729	+	0.988422i	$0.451516\pi$
$888$	−17.5457	−0.588794
$889$	−61.7680	−2.07163
$890$	−9.01860	−0.302304
$891$	−38.9486	−1.30483
$892$	−16.9371	−0.567096
$893$	−77.5963	−2.59666
$894$	−39.8463	−1.33266
$895$	−24.9744	−0.834803
$896$	4.40972	0.147318
$897$	4.87361	0.162725
$898$	−11.5422	−0.385167
$899$	−31.6630	−1.05602
$900$	1.63168	0.0543894
$901$	−26.4752	−0.882016
$902$	0.286667	0.00954498
$903$	−18.8007	−0.625648
$904$	−18.2558	−0.607179
$905$	5.63024	0.187155
$906$	−21.9999	−0.730897
$907$	4.85636	0.161253	0.0806264	−	0.996744i	$-0.474308\pi$
$907$	4.85636	0.161253	0.0806264	+	0.996744i	$0.474308\pi$
$908$	−2.04807	−0.0679675
$909$	−21.0018	−0.696587
$910$	10.7237	0.355486
$911$	−40.8202	−1.35243	−0.676216	−	0.736703i	$-0.736381\pi$
$911$	−40.8202	−1.35243	−0.676216	+	0.736703i	$0.736381\pi$
$912$	−14.3687	−0.475794
$913$	31.6254	1.04665
$914$	−29.2402	−0.967180
$915$	29.0925	0.961770
$916$	2.04352	0.0675198
$917$	89.5532	2.95731
$918$	14.1307	0.466383
$919$	11.2809	0.372122	0.186061	−	0.982538i	$-0.440428\pi$
$919$	11.2809	0.372122	0.186061	+	0.982538i	$0.440428\pi$
$920$	−0.931214	−0.0307012
$921$	−20.4660	−0.674376
$922$	30.8494	1.01597
$923$	−37.5451	−1.23581
$924$	−32.9071	−1.08257
$925$	8.15269	0.268059
$926$	−28.7096	−0.943457
$927$	−12.3534	−0.405740
$928$	−6.55653	−0.215229
$929$	25.7575	0.845077	0.422538	−	0.906345i	$-0.361139\pi$
$929$	25.7575	0.845077	0.422538	+	0.906345i	$0.361139\pi$
$930$	−10.3931	−0.340805
$931$	−83.0929	−2.72326
$932$	−18.1255	−0.593722
$933$	1.36074	0.0445488
$934$	3.13314	0.102520
$935$	−16.6386	−0.544142
$936$	3.96796	0.129697
$937$	−51.6744	−1.68813	−0.844064	−	0.536242i	$-0.819843\pi$
$937$	−51.6744	−1.68813	−0.844064	+	0.536242i	$0.819843\pi$
$938$	51.1242	1.66927
$939$	−43.7857	−1.42889
$940$	−11.6223	−0.379079
$941$	−46.5175	−1.51643	−0.758214	−	0.652006i	$-0.773928\pi$
$941$	−46.5175	−1.51643	−0.758214	+	0.652006i	$0.773928\pi$
$942$	−5.25138	−0.171099
$943$	0.0769871	0.00250705
$944$	10.7443	0.349697
$945$	−12.9857	−0.422426
$946$	−6.86916	−0.223336
$947$	−24.5315	−0.797167	−0.398583	−	0.917132i	$-0.630498\pi$
$947$	−24.5315	−0.797167	−0.398583	+	0.917132i	$0.630498\pi$
$948$	−22.8540	−0.742264
$949$	−14.5445	−0.472134
$950$	6.67647	0.216613
$951$	−75.8893	−2.46088
$952$	21.1602	0.685805
$953$	59.0228	1.91194	0.955968	−	0.293469i	$-0.0948099\pi$
$953$	59.0228	1.91194	0.955968	+	0.293469i	$0.0948099\pi$
$954$	9.00257	0.291469
$955$	8.02334	0.259629
$956$	−18.3347	−0.592988
$957$	48.9275	1.58160
$958$	−28.5029	−0.920887
$959$	−9.15211	−0.295537
$960$	−2.15213	−0.0694598
$961$	−7.67858	−0.247696
$962$	19.8259	0.639212
$963$	23.8683	0.769144
$964$	28.9759	0.933252
$965$	9.60240	0.309112
$966$	−8.83751	−0.284342
$967$	17.0618	0.548669	0.274335	−	0.961634i	$-0.411542\pi$
$967$	17.0618	0.548669	0.274335	+	0.961634i	$0.411542\pi$
$968$	−1.02318	−0.0328861
$969$	−68.9485	−2.21495
$970$	7.88077	0.253036
$971$	1.62035	0.0519995	0.0259997	−	0.999662i	$-0.491723\pi$
$971$	1.62035	0.0519995	0.0259997	+	0.999662i	$0.491723\pi$
$972$	−15.3398	−0.492024
$973$	−30.5484	−0.979336
$974$	33.4999	1.07341
$975$	−5.23361	−0.167610
$976$	−13.5180	−0.432700
$977$	8.03328	0.257007	0.128504	−	0.991709i	$-0.458983\pi$
$977$	8.03328	0.257007	0.128504	+	0.991709i	$0.458983\pi$
$978$	−22.6623	−0.724660
$979$	−31.2715	−0.999441
$980$	−12.4456	−0.397561
$981$	5.06155	0.161603
$982$	29.8201	0.951597
$983$	26.3578	0.840684	0.420342	−	0.907366i	$-0.361910\pi$
$983$	26.3578	0.840684	0.420342	+	0.907366i	$0.361910\pi$
$984$	0.177925	0.00567206
$985$	−4.73915	−0.151002
$986$	−31.4617	−1.00195
$987$	−110.300	−3.51088
$988$	16.2360	0.516536
$989$	−1.84477	−0.0586604
$990$	5.65777	0.179816
$991$	15.3012	0.486059	0.243030	−	0.970019i	$-0.421859\pi$
$991$	15.3012	0.486059	0.243030	+	0.970019i	$0.421859\pi$
$992$	4.82923	0.153328
$993$	23.0151	0.730361
$994$	68.0821	2.15943
$995$	−6.77589	−0.214810
$996$	19.6289	0.621965
$997$	4.24414	0.134413	0.0672066	−	0.997739i	$-0.478591\pi$
$997$	4.24414	0.134413	0.0672066	+	0.997739i	$0.478591\pi$
$998$	−31.0553	−0.983040
$999$	−24.0080	−0.759581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.l.1.14	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.l.1.14	✓	17	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.15213 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15213 q^{6} -4.40972 q^{7} -1.00000 q^{8} +1.63168 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.15213 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.15213 q^{6} -4.40972 q^{7} -1.00000 q^{8} +1.63168 q^{9} +1.00000 q^{10} +3.46745 q^{11} +2.15213 q^{12} -2.43182 q^{13} +4.40972 q^{14} -2.15213 q^{15} +1.00000 q^{16} +4.79853 q^{17} -1.63168 q^{18} -6.67647 q^{19} -1.00000 q^{20} -9.49031 q^{21} -3.46745 q^{22} -0.931214 q^{23} -2.15213 q^{24} +1.00000 q^{25} +2.43182 q^{26} -2.94480 q^{27} -4.40972 q^{28} +6.55653 q^{29} +2.15213 q^{30} -4.82923 q^{31} -1.00000 q^{32} +7.46241 q^{33} -4.79853 q^{34} +4.40972 q^{35} +1.63168 q^{36} +8.15269 q^{37} +6.67647 q^{38} -5.23361 q^{39} +1.00000 q^{40} -0.0826739 q^{41} +9.49031 q^{42} +1.98104 q^{43} +3.46745 q^{44} -1.63168 q^{45} +0.931214 q^{46} +11.6223 q^{47} +2.15213 q^{48} +12.4456 q^{49} -1.00000 q^{50} +10.3271 q^{51} -2.43182 q^{52} -5.51735 q^{53} +2.94480 q^{54} -3.46745 q^{55} +4.40972 q^{56} -14.3687 q^{57} -6.55653 q^{58} +10.7443 q^{59} -2.15213 q^{60} -13.5180 q^{61} +4.82923 q^{62} -7.19527 q^{63} +1.00000 q^{64} +2.43182 q^{65} -7.46241 q^{66} +11.5935 q^{67} +4.79853 q^{68} -2.00410 q^{69} -4.40972 q^{70} +15.4391 q^{71} -1.63168 q^{72} +5.98090 q^{73} -8.15269 q^{74} +2.15213 q^{75} -6.67647 q^{76} -15.2905 q^{77} +5.23361 q^{78} -10.6192 q^{79} -1.00000 q^{80} -11.2327 q^{81} +0.0826739 q^{82} +9.12066 q^{83} -9.49031 q^{84} -4.79853 q^{85} -1.98104 q^{86} +14.1105 q^{87} -3.46745 q^{88} -9.01860 q^{89} +1.63168 q^{90} +10.7237 q^{91} -0.931214 q^{92} -10.3931 q^{93} -11.6223 q^{94} +6.67647 q^{95} -2.15213 q^{96} +7.88077 q^{97} -12.4456 q^{98} +5.65777 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9	\( 17 q - 17 q^{2} + 3 q^{3} + 17 q^{4} - 17 q^{5} - 3 q^{6} + 4 q^{7} - 17 q^{8} + 6 q^{9} + 17 q^{10} - 8 q^{11} + 3 q^{12} + 14 q^{13} - 4 q^{14} - 3 q^{15} + 17 q^{16} - 8 q^{17} - 6 q^{18} + 7 q^{19} - 17 q^{20} - 11 q^{21} + 8 q^{22} + q^{23} - 3 q^{24} + 17 q^{25} - 14 q^{26} + 15 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 8 q^{31} - 17 q^{32} + 3 q^{33} + 8 q^{34} - 4 q^{35} + 6 q^{36} + 49 q^{37} - 7 q^{38} - 12 q^{39} + 17 q^{40} - 23 q^{41} + 11 q^{42} + 35 q^{43} - 8 q^{44} - 6 q^{45} - q^{46} + 11 q^{47} + 3 q^{48} + 27 q^{49} - 17 q^{50} - 16 q^{51} + 14 q^{52} - 3 q^{53} - 15 q^{54} + 8 q^{55} - 4 q^{56} + 9 q^{57} + 18 q^{58} - 6 q^{59} - 3 q^{60} + 6 q^{61} - 8 q^{62} + 10 q^{63} + 17 q^{64} - 14 q^{65} - 3 q^{66} + 55 q^{67} - 8 q^{68} - q^{69} + 4 q^{70} + 5 q^{71} - 6 q^{72} + 62 q^{73} - 49 q^{74} + 3 q^{75} + 7 q^{76} + 2 q^{77} + 12 q^{78} - 3 q^{79} - 17 q^{80} - 15 q^{81} + 23 q^{82} + 7 q^{83} - 11 q^{84} + 8 q^{85} - 35 q^{86} + 10 q^{87} + 8 q^{88} - 18 q^{89} + 6 q^{90} + 18 q^{91} + q^{92} + 33 q^{93} - 11 q^{94} - 7 q^{95} - 3 q^{96} + 63 q^{97} - 27 q^{98} - 11 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 3 * q^3 + 17 * q^4 - 17 * q^5 - 3 * q^6 + 4 * q^7 - 17 * q^8 + 6 * q^9 + 17 * q^10 - 8 * q^11 + 3 * q^12 + 14 * q^13 - 4 * q^14 - 3 * q^15 + 17 * q^16 - 8 * q^17 - 6 * q^18 + 7 * q^19 - 17 * q^20 - 11 * q^21 + 8 * q^22 + q^23 - 3 * q^24 + 17 * q^25 - 14 * q^26 + 15 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 8 * q^31 - 17 * q^32 + 3 * q^33 + 8 * q^34 - 4 * q^35 + 6 * q^36 + 49 * q^37 - 7 * q^38 - 12 * q^39 + 17 * q^40 - 23 * q^41 + 11 * q^42 + 35 * q^43 - 8 * q^44 - 6 * q^45 - q^46 + 11 * q^47 + 3 * q^48 + 27 * q^49 - 17 * q^50 - 16 * q^51 + 14 * q^52 - 3 * q^53 - 15 * q^54 + 8 * q^55 - 4 * q^56 + 9 * q^57 + 18 * q^58 - 6 * q^59 - 3 * q^60 + 6 * q^61 - 8 * q^62 + 10 * q^63 + 17 * q^64 - 14 * q^65 - 3 * q^66 + 55 * q^67 - 8 * q^68 - q^69 + 4 * q^70 + 5 * q^71 - 6 * q^72 + 62 * q^73 - 49 * q^74 + 3 * q^75 + 7 * q^76 + 2 * q^77 + 12 * q^78 - 3 * q^79 - 17 * q^80 - 15 * q^81 + 23 * q^82 + 7 * q^83 - 11 * q^84 + 8 * q^85 - 35 * q^86 + 10 * q^87 + 8 * q^88 - 18 * q^89 + 6 * q^90 + 18 * q^91 + q^92 + 33 * q^93 - 11 * q^94 - 7 * q^95 - 3 * q^96 + 63 * q^97 - 27 * q^98 - 11 * q^99

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