LMFDB - Embedded newform 4002.2.a.bh.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 16x^{5} + 51x^{4} + 45x^{3} - 152x^{2} - 54x + 70 $ x^7 - 3x^6 - 16x^5 + 51x^4 + 45x^3 - 152x^2 - 54x + 70
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$2.66930$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71883 q^{5} +1.00000 q^{6} -4.60478 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71883 q^{5} +1.00000 q^{6} -4.60478 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.71883 q^{10} +2.78053 q^{11} +1.00000 q^{12} +1.37983 q^{13} -4.60478 q^{14} +3.71883 q^{15} +1.00000 q^{16} +4.93831 q^{17} +1.00000 q^{18} -7.94337 q^{19} +3.71883 q^{20} -4.60478 q^{21} +2.78053 q^{22} +1.00000 q^{23} +1.00000 q^{24} +8.82973 q^{25} +1.37983 q^{26} +1.00000 q^{27} -4.60478 q^{28} -1.00000 q^{29} +3.71883 q^{30} +3.30293 q^{31} +1.00000 q^{32} +2.78053 q^{33} +4.93831 q^{34} -17.1244 q^{35} +1.00000 q^{36} +6.62374 q^{37} -7.94337 q^{38} +1.37983 q^{39} +3.71883 q^{40} +11.1461 q^{41} -4.60478 q^{42} +2.25663 q^{43} +2.78053 q^{44} +3.71883 q^{45} +1.00000 q^{46} +2.24907 q^{47} +1.00000 q^{48} +14.2040 q^{49} +8.82973 q^{50} +4.93831 q^{51} +1.37983 q^{52} -9.83795 q^{53} +1.00000 q^{54} +10.3403 q^{55} -4.60478 q^{56} -7.94337 q^{57} -1.00000 q^{58} -8.05784 q^{59} +3.71883 q^{60} +6.65714 q^{61} +3.30293 q^{62} -4.60478 q^{63} +1.00000 q^{64} +5.13135 q^{65} +2.78053 q^{66} -4.47849 q^{67} +4.93831 q^{68} +1.00000 q^{69} -17.1244 q^{70} -12.5838 q^{71} +1.00000 q^{72} +4.28247 q^{73} +6.62374 q^{74} +8.82973 q^{75} -7.94337 q^{76} -12.8037 q^{77} +1.37983 q^{78} +7.22562 q^{79} +3.71883 q^{80} +1.00000 q^{81} +11.1461 q^{82} -0.204495 q^{83} -4.60478 q^{84} +18.3648 q^{85} +2.25663 q^{86} -1.00000 q^{87} +2.78053 q^{88} -6.34556 q^{89} +3.71883 q^{90} -6.35380 q^{91} +1.00000 q^{92} +3.30293 q^{93} +2.24907 q^{94} -29.5401 q^{95} +1.00000 q^{96} -9.98687 q^{97} +14.2040 q^{98} +2.78053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.71883	1.66311	0.831557	−	0.555440i	$-0.187450\pi$
$5$	3.71883	1.66311	0.831557	+	0.555440i	$0.187450\pi$
$6$	1.00000	0.408248
$7$	−4.60478	−1.74044	−0.870221	−	0.492661i	$-0.836024\pi$
$7$	−4.60478	−1.74044	−0.870221	+	0.492661i	$0.836024\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.71883	1.17600
$11$	2.78053	0.838360	0.419180	−	0.907903i	$-0.362318\pi$
$11$	2.78053	0.838360	0.419180	+	0.907903i	$0.362318\pi$
$12$	1.00000	0.288675
$13$	1.37983	0.382695	0.191348	−	0.981522i	$-0.438714\pi$
$13$	1.37983	0.382695	0.191348	+	0.981522i	$0.438714\pi$
$14$	−4.60478	−1.23068
$15$	3.71883	0.960199
$16$	1.00000	0.250000
$17$	4.93831	1.19772	0.598858	−	0.800855i	$-0.295621\pi$
$17$	4.93831	1.19772	0.598858	+	0.800855i	$0.295621\pi$
$18$	1.00000	0.235702
$19$	−7.94337	−1.82233	−0.911167	−	0.412037i	$-0.864818\pi$
$19$	−7.94337	−1.82233	−0.911167	+	0.412037i	$0.864818\pi$
$20$	3.71883	0.831557
$21$	−4.60478	−1.00485
$22$	2.78053	0.592810
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	8.82973	1.76595
$26$	1.37983	0.270607
$27$	1.00000	0.192450
$28$	−4.60478	−0.870221
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.71883	0.678963
$31$	3.30293	0.593223	0.296612	−	0.954998i	$-0.404143\pi$
$31$	3.30293	0.593223	0.296612	+	0.954998i	$0.404143\pi$
$32$	1.00000	0.176777
$33$	2.78053	0.484027
$34$	4.93831	0.846913
$35$	−17.1244	−2.89455
$36$	1.00000	0.166667
$37$	6.62374	1.08894	0.544468	−	0.838781i	$-0.316731\pi$
$37$	6.62374	1.08894	0.544468	+	0.838781i	$0.316731\pi$
$38$	−7.94337	−1.28859
$39$	1.37983	0.220949
$40$	3.71883	0.587999
$41$	11.1461	1.74074	0.870368	−	0.492402i	$-0.163881\pi$
$41$	11.1461	1.74074	0.870368	+	0.492402i	$0.163881\pi$
$42$	−4.60478	−0.710533
$43$	2.25663	0.344133	0.172066	−	0.985085i	$-0.444956\pi$
$43$	2.25663	0.344133	0.172066	+	0.985085i	$0.444956\pi$
$44$	2.78053	0.419180
$45$	3.71883	0.554371
$46$	1.00000	0.147442
$47$	2.24907	0.328061	0.164030	−	0.986455i	$-0.447550\pi$
$47$	2.24907	0.328061	0.164030	+	0.986455i	$0.447550\pi$
$48$	1.00000	0.144338
$49$	14.2040	2.02914
$50$	8.82973	1.24871
$51$	4.93831	0.691502
$52$	1.37983	0.191348
$53$	−9.83795	−1.35135	−0.675673	−	0.737201i	$-0.736147\pi$
$53$	−9.83795	−1.35135	−0.675673	+	0.737201i	$0.736147\pi$
$54$	1.00000	0.136083
$55$	10.3403	1.39429
$56$	−4.60478	−0.615339
$57$	−7.94337	−1.05213
$58$	−1.00000	−0.131306
$59$	−8.05784	−1.04904	−0.524521	−	0.851398i	$-0.675755\pi$
$59$	−8.05784	−1.04904	−0.524521	+	0.851398i	$0.675755\pi$
$60$	3.71883	0.480099
$61$	6.65714	0.852360	0.426180	−	0.904638i	$-0.359859\pi$
$61$	6.65714	0.852360	0.426180	+	0.904638i	$0.359859\pi$
$62$	3.30293	0.419472
$63$	−4.60478	−0.580148
$64$	1.00000	0.125000
$65$	5.13135	0.636466
$66$	2.78053	0.342259
$67$	−4.47849	−0.547135	−0.273567	−	0.961853i	$-0.588204\pi$
$67$	−4.47849	−0.547135	−0.273567	+	0.961853i	$0.588204\pi$
$68$	4.93831	0.598858
$69$	1.00000	0.120386
$70$	−17.1244	−2.04676
$71$	−12.5838	−1.49342	−0.746712	−	0.665147i	$-0.768369\pi$
$71$	−12.5838	−1.49342	−0.746712	+	0.665147i	$0.768369\pi$
$72$	1.00000	0.117851
$73$	4.28247	0.501225	0.250613	−	0.968087i	$-0.419368\pi$
$73$	4.28247	0.501225	0.250613	+	0.968087i	$0.419368\pi$
$74$	6.62374	0.769995
$75$	8.82973	1.01957
$76$	−7.94337	−0.911167
$77$	−12.8037	−1.45912
$78$	1.37983	0.156235
$79$	7.22562	0.812945	0.406473	−	0.913663i	$-0.366759\pi$
$79$	7.22562	0.812945	0.406473	+	0.913663i	$0.366759\pi$
$80$	3.71883	0.415778
$81$	1.00000	0.111111
$82$	11.1461	1.23089
$83$	−0.204495	−0.0224462	−0.0112231	−	0.999937i	$-0.503573\pi$
$83$	−0.204495	−0.0224462	−0.0112231	+	0.999937i	$0.503573\pi$
$84$	−4.60478	−0.502423
$85$	18.3648	1.99194
$86$	2.25663	0.243339
$87$	−1.00000	−0.107211
$88$	2.78053	0.296405
$89$	−6.34556	−0.672628	−0.336314	−	0.941750i	$-0.609180\pi$
$89$	−6.34556	−0.672628	−0.336314	+	0.941750i	$0.609180\pi$
$90$	3.71883	0.392000
$91$	−6.35380	−0.666059
$92$	1.00000	0.104257
$93$	3.30293	0.342498
$94$	2.24907	0.231974
$95$	−29.5401	−3.03075
$96$	1.00000	0.102062
$97$	−9.98687	−1.01401	−0.507007	−	0.861942i	$-0.669248\pi$
$97$	−9.98687	−1.01401	−0.507007	+	0.861942i	$0.669248\pi$
$98$	14.2040	1.43482
$99$	2.78053	0.279453
$100$	8.82973	0.882973
$101$	18.2379	1.81474	0.907369	−	0.420335i	$-0.138087\pi$
$101$	18.2379	1.81474	0.907369	+	0.420335i	$0.138087\pi$
$102$	4.93831	0.488965
$103$	6.97380	0.687149	0.343574	−	0.939126i	$-0.388362\pi$
$103$	6.97380	0.687149	0.343574	+	0.939126i	$0.388362\pi$
$104$	1.37983	0.135303
$105$	−17.1244	−1.67117
$106$	−9.83795	−0.955546
$107$	10.5583	1.02071	0.510355	−	0.859964i	$-0.329514\pi$
$107$	10.5583	1.02071	0.510355	+	0.859964i	$0.329514\pi$
$108$	1.00000	0.0962250
$109$	−5.19977	−0.498048	−0.249024	−	0.968497i	$-0.580110\pi$
$109$	−5.19977	−0.498048	−0.249024	+	0.968497i	$0.580110\pi$
$110$	10.3403	0.985910
$111$	6.62374	0.628698
$112$	−4.60478	−0.435111
$113$	−4.78183	−0.449837	−0.224918	−	0.974378i	$-0.572212\pi$
$113$	−4.78183	−0.449837	−0.224918	+	0.974378i	$0.572212\pi$
$114$	−7.94337	−0.743965
$115$	3.71883	0.346783
$116$	−1.00000	−0.0928477
$117$	1.37983	0.127565
$118$	−8.05784	−0.741784
$119$	−22.7398	−2.08456
$120$	3.71883	0.339482
$121$	−3.26868	−0.297153
$122$	6.65714	0.602709
$123$	11.1461	1.00501
$124$	3.30293	0.296612
$125$	14.2421	1.27385
$126$	−4.60478	−0.410226
$127$	−2.69448	−0.239097	−0.119548	−	0.992828i	$-0.538145\pi$
$127$	−2.69448	−0.239097	−0.119548	+	0.992828i	$0.538145\pi$
$128$	1.00000	0.0883883
$129$	2.25663	0.198685
$130$	5.13135	0.450049
$131$	0.996015	0.0870222	0.0435111	−	0.999053i	$-0.486146\pi$
$131$	0.996015	0.0870222	0.0435111	+	0.999053i	$0.486146\pi$
$132$	2.78053	0.242014
$133$	36.5775	3.17167
$134$	−4.47849	−0.386883
$135$	3.71883	0.320066
$136$	4.93831	0.423457
$137$	3.41580	0.291831	0.145916	−	0.989297i	$-0.453387\pi$
$137$	3.41580	0.291831	0.145916	+	0.989297i	$0.453387\pi$
$138$	1.00000	0.0851257
$139$	17.7746	1.50762	0.753811	−	0.657092i	$-0.228214\pi$
$139$	17.7746	1.50762	0.753811	+	0.657092i	$0.228214\pi$
$140$	−17.1244	−1.44728
$141$	2.24907	0.189406
$142$	−12.5838	−1.05601
$143$	3.83665	0.320836
$144$	1.00000	0.0833333
$145$	−3.71883	−0.308832
$146$	4.28247	0.354420
$147$	14.2040	1.17153
$148$	6.62374	0.544468
$149$	5.28256	0.432764	0.216382	−	0.976309i	$-0.430574\pi$
$149$	5.28256	0.432764	0.216382	+	0.976309i	$0.430574\pi$
$150$	8.82973	0.720944
$151$	−18.4191	−1.49893	−0.749463	−	0.662046i	$-0.769688\pi$
$151$	−18.4191	−1.49893	−0.749463	+	0.662046i	$0.769688\pi$
$152$	−7.94337	−0.644293
$153$	4.93831	0.399239
$154$	−12.8037	−1.03175
$155$	12.2830	0.986598
$156$	1.37983	0.110475
$157$	−21.4418	−1.71124	−0.855622	−	0.517601i	$-0.826825\pi$
$157$	−21.4418	−1.71124	−0.855622	+	0.517601i	$0.826825\pi$
$158$	7.22562	0.574839
$159$	−9.83795	−0.780200
$160$	3.71883	0.294000
$161$	−4.60478	−0.362907
$162$	1.00000	0.0785674
$163$	1.18250	0.0926208	0.0463104	−	0.998927i	$-0.485254\pi$
$163$	1.18250	0.0926208	0.0463104	+	0.998927i	$0.485254\pi$
$164$	11.1461	0.870368
$165$	10.3403	0.804992
$166$	−0.204495	−0.0158719
$167$	−2.72521	−0.210883	−0.105441	−	0.994426i	$-0.533626\pi$
$167$	−2.72521	−0.210883	−0.105441	+	0.994426i	$0.533626\pi$
$168$	−4.60478	−0.355266
$169$	−11.0961	−0.853544
$170$	18.3648	1.40851
$171$	−7.94337	−0.607445
$172$	2.25663	0.172066
$173$	−8.72763	−0.663550	−0.331775	−	0.943359i	$-0.607647\pi$
$173$	−8.72763	−0.663550	−0.331775	+	0.943359i	$0.607647\pi$
$174$	−1.00000	−0.0758098
$175$	−40.6590	−3.07353
$176$	2.78053	0.209590
$177$	−8.05784	−0.605664
$178$	−6.34556	−0.475620
$179$	−15.4069	−1.15156	−0.575782	−	0.817603i	$-0.695302\pi$
$179$	−15.4069	−1.15156	−0.575782	+	0.817603i	$0.695302\pi$
$180$	3.71883	0.277186
$181$	−17.9295	−1.33269	−0.666344	−	0.745645i	$-0.732142\pi$
$181$	−17.9295	−1.33269	−0.666344	+	0.745645i	$0.732142\pi$
$182$	−6.35380	−0.470975
$183$	6.65714	0.492110
$184$	1.00000	0.0737210
$185$	24.6326	1.81103
$186$	3.30293	0.242182
$187$	13.7311	1.00412
$188$	2.24907	0.164030
$189$	−4.60478	−0.334948
$190$	−29.5401	−2.14306
$191$	−7.71097	−0.557946	−0.278973	−	0.960299i	$-0.589994\pi$
$191$	−7.71097	−0.557946	−0.278973	+	0.960299i	$0.589994\pi$
$192$	1.00000	0.0721688
$193$	8.44722	0.608044	0.304022	−	0.952665i	$-0.401670\pi$
$193$	8.44722	0.608044	0.304022	+	0.952665i	$0.401670\pi$
$194$	−9.98687	−0.717016
$195$	5.13135	0.367464
$196$	14.2040	1.01457
$197$	−4.15297	−0.295887	−0.147944	−	0.988996i	$-0.547265\pi$
$197$	−4.15297	−0.295887	−0.147944	+	0.988996i	$0.547265\pi$
$198$	2.78053	0.197603
$199$	−15.2894	−1.08383	−0.541917	−	0.840432i	$-0.682301\pi$
$199$	−15.2894	−1.08383	−0.541917	+	0.840432i	$0.682301\pi$
$200$	8.82973	0.624356
$201$	−4.47849	−0.315888
$202$	18.2379	1.28321
$203$	4.60478	0.323192
$204$	4.93831	0.345751
$205$	41.4507	2.89504
$206$	6.97380	0.485887
$207$	1.00000	0.0695048
$208$	1.37983	0.0956738
$209$	−22.0867	−1.52777
$210$	−17.1244	−1.18170
$211$	19.2932	1.32820	0.664099	−	0.747645i	$-0.268815\pi$
$211$	19.2932	1.32820	0.664099	+	0.747645i	$0.268815\pi$
$212$	−9.83795	−0.675673
$213$	−12.5838	−0.862229
$214$	10.5583	0.721750
$215$	8.39204	0.572332
$216$	1.00000	0.0680414
$217$	−15.2093	−1.03247
$218$	−5.19977	−0.352173
$219$	4.28247	0.289383
$220$	10.3403	0.697144
$221$	6.81402	0.458360
$222$	6.62374	0.444557
$223$	29.2088	1.95597	0.977985	−	0.208677i	$-0.0669159\pi$
$223$	29.2088	1.95597	0.977985	+	0.208677i	$0.0669159\pi$
$224$	−4.60478	−0.307670
$225$	8.82973	0.588649
$226$	−4.78183	−0.318083
$227$	0.308766	0.0204935	0.0102468	−	0.999948i	$-0.496738\pi$
$227$	0.308766	0.0204935	0.0102468	+	0.999948i	$0.496738\pi$
$228$	−7.94337	−0.526063
$229$	12.6463	0.835692	0.417846	−	0.908518i	$-0.362785\pi$
$229$	12.6463	0.835692	0.417846	+	0.908518i	$0.362785\pi$
$230$	3.71883	0.245213
$231$	−12.8037	−0.842422
$232$	−1.00000	−0.0656532
$233$	−28.5421	−1.86986	−0.934928	−	0.354836i	$-0.884537\pi$
$233$	−28.5421	−1.86986	−0.934928	+	0.354836i	$0.884537\pi$
$234$	1.37983	0.0902022
$235$	8.36393	0.545602
$236$	−8.05784	−0.524521
$237$	7.22562	0.469354
$238$	−22.7398	−1.47400
$239$	14.0741	0.910375	0.455188	−	0.890396i	$-0.349572\pi$
$239$	14.0741	0.910375	0.455188	+	0.890396i	$0.349572\pi$
$240$	3.71883	0.240050
$241$	−19.9558	−1.28546	−0.642732	−	0.766091i	$-0.722199\pi$
$241$	−19.9558	−1.28546	−0.642732	+	0.766091i	$0.722199\pi$
$242$	−3.26868	−0.210119
$243$	1.00000	0.0641500
$244$	6.65714	0.426180
$245$	52.8223	3.37469
$246$	11.1461	0.710652
$247$	−10.9605	−0.697399
$248$	3.30293	0.209736
$249$	−0.204495	−0.0129593
$250$	14.2421	0.900751
$251$	−26.1076	−1.64790	−0.823949	−	0.566664i	$-0.808234\pi$
$251$	−26.1076	−1.64790	−0.823949	+	0.566664i	$0.808234\pi$
$252$	−4.60478	−0.290074
$253$	2.78053	0.174810
$254$	−2.69448	−0.169067
$255$	18.3648	1.15005
$256$	1.00000	0.0625000
$257$	−4.52071	−0.281994	−0.140997	−	0.990010i	$-0.545031\pi$
$257$	−4.52071	−0.281994	−0.140997	+	0.990010i	$0.545031\pi$
$258$	2.25663	0.140492
$259$	−30.5009	−1.89523
$260$	5.13135	0.318233
$261$	−1.00000	−0.0618984
$262$	0.996015	0.0615340
$263$	−17.0963	−1.05420	−0.527102	−	0.849802i	$-0.676722\pi$
$263$	−17.0963	−1.05420	−0.527102	+	0.849802i	$0.676722\pi$
$264$	2.78053	0.171130
$265$	−36.5857	−2.24744
$266$	36.5775	2.24271
$267$	−6.34556	−0.388342
$268$	−4.47849	−0.273567
$269$	2.10959	0.128624	0.0643119	−	0.997930i	$-0.479515\pi$
$269$	2.10959	0.128624	0.0643119	+	0.997930i	$0.479515\pi$
$270$	3.71883	0.226321
$271$	4.02444	0.244467	0.122234	−	0.992501i	$-0.460994\pi$
$271$	4.02444	0.244467	0.122234	+	0.992501i	$0.460994\pi$
$272$	4.93831	0.299429
$273$	−6.35380	−0.384550
$274$	3.41580	0.206356
$275$	24.5513	1.48050
$276$	1.00000	0.0601929
$277$	−13.7719	−0.827471	−0.413736	−	0.910397i	$-0.635776\pi$
$277$	−13.7719	−0.827471	−0.413736	+	0.910397i	$0.635776\pi$
$278$	17.7746	1.06605
$279$	3.30293	0.197741
$280$	−17.1244	−1.02338
$281$	20.7797	1.23961	0.619805	−	0.784756i	$-0.287212\pi$
$281$	20.7797	1.23961	0.619805	+	0.784756i	$0.287212\pi$
$282$	2.24907	0.133930
$283$	13.4968	0.802304	0.401152	−	0.916012i	$-0.368610\pi$
$283$	13.4968	0.802304	0.401152	+	0.916012i	$0.368610\pi$
$284$	−12.5838	−0.746712
$285$	−29.5401	−1.74980
$286$	3.83665	0.226866
$287$	−51.3255	−3.02965
$288$	1.00000	0.0589256
$289$	7.38690	0.434523
$290$	−3.71883	−0.218377
$291$	−9.98687	−0.585441
$292$	4.28247	0.250613
$293$	−7.06536	−0.412763	−0.206381	−	0.978472i	$-0.566169\pi$
$293$	−7.06536	−0.412763	−0.206381	+	0.978472i	$0.566169\pi$
$294$	14.2040	0.828393
$295$	−29.9658	−1.74467
$296$	6.62374	0.384997
$297$	2.78053	0.161342
$298$	5.28256	0.306011
$299$	1.37983	0.0797975
$300$	8.82973	0.509785
$301$	−10.3913	−0.598944
$302$	−18.4191	−1.05990
$303$	18.2379	1.04774
$304$	−7.94337	−0.455584
$305$	24.7568	1.41757
$306$	4.93831	0.282304
$307$	0.163949	0.00935709	0.00467854	−	0.999989i	$-0.498511\pi$
$307$	0.163949	0.00935709	0.00467854	+	0.999989i	$0.498511\pi$
$308$	−12.8037	−0.729559
$309$	6.97380	0.396725
$310$	12.2830	0.697630
$311$	−21.5334	−1.22105	−0.610524	−	0.791998i	$-0.709041\pi$
$311$	−21.5334	−1.22105	−0.610524	+	0.791998i	$0.709041\pi$
$312$	1.37983	0.0781174
$313$	−26.7907	−1.51430	−0.757151	−	0.653240i	$-0.773409\pi$
$313$	−26.7907	−1.51430	−0.757151	+	0.653240i	$0.773409\pi$
$314$	−21.4418	−1.21003
$315$	−17.1244	−0.964851
$316$	7.22562	0.406473
$317$	−22.0650	−1.23929	−0.619646	−	0.784881i	$-0.712724\pi$
$317$	−22.0650	−1.23929	−0.619646	+	0.784881i	$0.712724\pi$
$318$	−9.83795	−0.551685
$319$	−2.78053	−0.155680
$320$	3.71883	0.207889
$321$	10.5583	0.589307
$322$	−4.60478	−0.256614
$323$	−39.2268	−2.18264
$324$	1.00000	0.0555556
$325$	12.1835	0.675819
$326$	1.18250	0.0654928
$327$	−5.19977	−0.287548
$328$	11.1461	0.615443
$329$	−10.3565	−0.570971
$330$	10.3403	0.569216
$331$	23.9163	1.31456	0.657280	−	0.753646i	$-0.271707\pi$
$331$	23.9163	1.31456	0.657280	+	0.753646i	$0.271707\pi$
$332$	−0.204495	−0.0112231
$333$	6.62374	0.362979
$334$	−2.72521	−0.149117
$335$	−16.6548	−0.909947
$336$	−4.60478	−0.251211
$337$	28.5941	1.55762	0.778811	−	0.627259i	$-0.215823\pi$
$337$	28.5941	1.55762	0.778811	+	0.627259i	$0.215823\pi$
$338$	−11.0961	−0.603547
$339$	−4.78183	−0.259713
$340$	18.3648	0.995969
$341$	9.18388	0.497335
$342$	−7.94337	−0.429528
$343$	−33.1728	−1.79116
$344$	2.25663	0.121669
$345$	3.71883	0.200215
$346$	−8.72763	−0.469200
$347$	6.90150	0.370492	0.185246	−	0.982692i	$-0.440692\pi$
$347$	6.90150	0.370492	0.185246	+	0.982692i	$0.440692\pi$
$348$	−1.00000	−0.0536056
$349$	−3.78651	−0.202687	−0.101344	−	0.994851i	$-0.532314\pi$
$349$	−3.78651	−0.202687	−0.101344	+	0.994851i	$0.532314\pi$
$350$	−40.6590	−2.17331
$351$	1.37983	0.0736498
$352$	2.78053	0.148202
$353$	5.72830	0.304887	0.152443	−	0.988312i	$-0.451286\pi$
$353$	5.72830	0.304887	0.152443	+	0.988312i	$0.451286\pi$
$354$	−8.05784	−0.428269
$355$	−46.7971	−2.48373
$356$	−6.34556	−0.336314
$357$	−22.7398	−1.20352
$358$	−15.4069	−0.814279
$359$	15.6510	0.826026	0.413013	−	0.910725i	$-0.364476\pi$
$359$	15.6510	0.826026	0.413013	+	0.910725i	$0.364476\pi$
$360$	3.71883	0.196000
$361$	44.0972	2.32090
$362$	−17.9295	−0.942352
$363$	−3.26868	−0.171561
$364$	−6.35380	−0.333030
$365$	15.9258	0.833595
$366$	6.65714	0.347974
$367$	28.5831	1.49203	0.746013	−	0.665931i	$-0.231965\pi$
$367$	28.5831	1.49203	0.746013	+	0.665931i	$0.231965\pi$
$368$	1.00000	0.0521286
$369$	11.1461	0.580245
$370$	24.6326	1.28059
$371$	45.3016	2.35194
$372$	3.30293	0.171249
$373$	−14.0297	−0.726432	−0.363216	−	0.931705i	$-0.618321\pi$
$373$	−14.0297	−0.726432	−0.363216	+	0.931705i	$0.618321\pi$
$374$	13.7311	0.710018
$375$	14.2421	0.735460
$376$	2.24907	0.115987
$377$	−1.37983	−0.0710647
$378$	−4.60478	−0.236844
$379$	−20.8137	−1.06913	−0.534565	−	0.845128i	$-0.679524\pi$
$379$	−20.8137	−1.06913	−0.534565	+	0.845128i	$0.679524\pi$
$380$	−29.5401	−1.51537
$381$	−2.69448	−0.138043
$382$	−7.71097	−0.394528
$383$	−18.0623	−0.922942	−0.461471	−	0.887155i	$-0.652678\pi$
$383$	−18.0623	−0.922942	−0.461471	+	0.887155i	$0.652678\pi$
$384$	1.00000	0.0510310
$385$	−47.6149	−2.42668
$386$	8.44722	0.429952
$387$	2.25663	0.114711
$388$	−9.98687	−0.507007
$389$	−22.5311	−1.14237	−0.571187	−	0.820820i	$-0.693517\pi$
$389$	−22.5311	−1.14237	−0.571187	+	0.820820i	$0.693517\pi$
$390$	5.13135	0.259836
$391$	4.93831	0.249741
$392$	14.2040	0.717410
$393$	0.996015	0.0502423
$394$	−4.15297	−0.209224
$395$	26.8709	1.35202
$396$	2.78053	0.139727
$397$	−24.4105	−1.22513	−0.612564	−	0.790421i	$-0.709862\pi$
$397$	−24.4105	−1.22513	−0.612564	+	0.790421i	$0.709862\pi$
$398$	−15.2894	−0.766387
$399$	36.5775	1.83116
$400$	8.82973	0.441486
$401$	6.92862	0.345999	0.172999	−	0.984922i	$-0.444654\pi$
$401$	6.92862	0.345999	0.172999	+	0.984922i	$0.444654\pi$
$402$	−4.47849	−0.223367
$403$	4.55747	0.227024
$404$	18.2379	0.907369
$405$	3.71883	0.184790
$406$	4.60478	0.228531
$407$	18.4175	0.912921
$408$	4.93831	0.244483
$409$	−21.4966	−1.06294	−0.531468	−	0.847078i	$-0.678360\pi$
$409$	−21.4966	−1.06294	−0.531468	+	0.847078i	$0.678360\pi$
$410$	41.4507	2.04710
$411$	3.41580	0.168489
$412$	6.97380	0.343574
$413$	37.1046	1.82580
$414$	1.00000	0.0491473
$415$	−0.760483	−0.0373306
$416$	1.37983	0.0676516
$417$	17.7746	0.870426
$418$	−22.0867	−1.08030
$419$	−22.2577	−1.08736	−0.543680	−	0.839293i	$-0.682969\pi$
$419$	−22.2577	−1.08736	−0.543680	+	0.839293i	$0.682969\pi$
$420$	−17.1244	−0.835586
$421$	9.60251	0.467998	0.233999	−	0.972237i	$-0.424819\pi$
$421$	9.60251	0.467998	0.233999	+	0.972237i	$0.424819\pi$
$422$	19.2932	0.939178
$423$	2.24907	0.109354
$424$	−9.83795	−0.477773
$425$	43.6039	2.11510
$426$	−12.5838	−0.609688
$427$	−30.6547	−1.48348
$428$	10.5583	0.510355
$429$	3.83665	0.185235
$430$	8.39204	0.404700
$431$	8.01844	0.386234	0.193117	−	0.981176i	$-0.438140\pi$
$431$	8.01844	0.386234	0.193117	+	0.981176i	$0.438140\pi$
$432$	1.00000	0.0481125
$433$	−1.63085	−0.0783736	−0.0391868	−	0.999232i	$-0.512477\pi$
$433$	−1.63085	−0.0783736	−0.0391868	+	0.999232i	$0.512477\pi$
$434$	−15.2093	−0.730068
$435$	−3.71883	−0.178304
$436$	−5.19977	−0.249024
$437$	−7.94337	−0.379983
$438$	4.28247	0.204624
$439$	−24.6912	−1.17844	−0.589222	−	0.807971i	$-0.700566\pi$
$439$	−24.6912	−1.17844	−0.589222	+	0.807971i	$0.700566\pi$
$440$	10.3403	0.492955
$441$	14.2040	0.676380
$442$	6.81402	0.324110
$443$	28.2870	1.34396	0.671979	−	0.740571i	$-0.265445\pi$
$443$	28.2870	1.34396	0.671979	+	0.740571i	$0.265445\pi$
$444$	6.62374	0.314349
$445$	−23.5981	−1.11866
$446$	29.2088	1.38308
$447$	5.28256	0.249857
$448$	−4.60478	−0.217555
$449$	−1.75366	−0.0827602	−0.0413801	−	0.999143i	$-0.513175\pi$
$449$	−1.75366	−0.0827602	−0.0413801	+	0.999143i	$0.513175\pi$
$450$	8.82973	0.416237
$451$	30.9921	1.45936
$452$	−4.78183	−0.224918
$453$	−18.4191	−0.865406
$454$	0.308766	0.0144911
$455$	−23.6287	−1.10773
$456$	−7.94337	−0.371982
$457$	11.1380	0.521016	0.260508	−	0.965472i	$-0.416110\pi$
$457$	11.1380	0.521016	0.260508	+	0.965472i	$0.416110\pi$
$458$	12.6463	0.590923
$459$	4.93831	0.230501
$460$	3.71883	0.173392
$461$	33.5519	1.56267	0.781333	−	0.624114i	$-0.214540\pi$
$461$	33.5519	1.56267	0.781333	+	0.624114i	$0.214540\pi$
$462$	−12.8037	−0.595682
$463$	27.0322	1.25629	0.628147	−	0.778094i	$-0.283814\pi$
$463$	27.0322	1.25629	0.628147	+	0.778094i	$0.283814\pi$
$464$	−1.00000	−0.0464238
$465$	12.2830	0.569612
$466$	−28.5421	−1.32219
$467$	36.0487	1.66814	0.834068	−	0.551662i	$-0.186006\pi$
$467$	36.0487	1.66814	0.834068	+	0.551662i	$0.186006\pi$
$468$	1.37983	0.0637826
$469$	20.6225	0.952257
$470$	8.36393	0.385799
$471$	−21.4418	−0.987988
$472$	−8.05784	−0.370892
$473$	6.27462	0.288507
$474$	7.22562	0.331884
$475$	−70.1378	−3.21814
$476$	−22.7398	−1.04228
$477$	−9.83795	−0.450449
$478$	14.0741	0.643732
$479$	−1.47382	−0.0673404	−0.0336702	−	0.999433i	$-0.510720\pi$
$479$	−1.47382	−0.0673404	−0.0336702	+	0.999433i	$0.510720\pi$
$480$	3.71883	0.169741
$481$	9.13963	0.416731
$482$	−19.9558	−0.908960
$483$	−4.60478	−0.209525
$484$	−3.26868	−0.148576
$485$	−37.1395	−1.68642
$486$	1.00000	0.0453609
$487$	−13.9536	−0.632298	−0.316149	−	0.948709i	$-0.602390\pi$
$487$	−13.9536	−0.632298	−0.316149	+	0.948709i	$0.602390\pi$
$488$	6.65714	0.301355
$489$	1.18250	0.0534746
$490$	52.8223	2.38627
$491$	−40.4341	−1.82477	−0.912384	−	0.409336i	$-0.865760\pi$
$491$	−40.4341	−1.82477	−0.912384	+	0.409336i	$0.865760\pi$
$492$	11.1461	0.502507
$493$	−4.93831	−0.222410
$494$	−10.9605	−0.493136
$495$	10.3403	0.464763
$496$	3.30293	0.148306
$497$	57.9457	2.59922
$498$	−0.204495	−0.00916364
$499$	−25.4971	−1.14141	−0.570704	−	0.821156i	$-0.693329\pi$
$499$	−25.4971	−1.14141	−0.570704	+	0.821156i	$0.693329\pi$
$500$	14.2421	0.636927
$501$	−2.72521	−0.121753
$502$	−26.1076	−1.16524
$503$	−17.1876	−0.766359	−0.383179	−	0.923674i	$-0.625171\pi$
$503$	−17.1876	−0.766359	−0.383179	+	0.923674i	$0.625171\pi$
$504$	−4.60478	−0.205113
$505$	67.8237	3.01812
$506$	2.78053	0.123609
$507$	−11.0961	−0.492794
$508$	−2.69448	−0.119548
$509$	27.5658	1.22183	0.610915	−	0.791696i	$-0.290802\pi$
$509$	27.5658	1.22183	0.610915	+	0.791696i	$0.290802\pi$
$510$	18.3648	0.813205
$511$	−19.7198	−0.872354
$512$	1.00000	0.0441942
$513$	−7.94337	−0.350708
$514$	−4.52071	−0.199400
$515$	25.9344	1.14281
$516$	2.25663	0.0993426
$517$	6.25360	0.275033
$518$	−30.5009	−1.34013
$519$	−8.72763	−0.383100
$520$	5.13135	0.225025
$521$	39.6580	1.73745	0.868725	−	0.495296i	$-0.164940\pi$
$521$	39.6580	1.73745	0.868725	+	0.495296i	$0.164940\pi$
$522$	−1.00000	−0.0437688
$523$	1.34961	0.0590144	0.0295072	−	0.999565i	$-0.490606\pi$
$523$	1.34961	0.0590144	0.0295072	+	0.999565i	$0.490606\pi$
$524$	0.996015	0.0435111
$525$	−40.6590	−1.77450
$526$	−17.0963	−0.745435
$527$	16.3109	0.710513
$528$	2.78053	0.121007
$529$	1.00000	0.0434783
$530$	−36.5857	−1.58918
$531$	−8.05784	−0.349681
$532$	36.5775	1.58583
$533$	15.3798	0.666171
$534$	−6.34556	−0.274599
$535$	39.2646	1.69755
$536$	−4.47849	−0.193441
$537$	−15.4069	−0.664856
$538$	2.10959	0.0909508
$539$	39.4945	1.70115
$540$	3.71883	0.160033
$541$	−6.19991	−0.266555	−0.133278	−	0.991079i	$-0.542550\pi$
$541$	−6.19991	−0.266555	−0.133278	+	0.991079i	$0.542550\pi$
$542$	4.02444	0.172865
$543$	−17.9295	−0.769427
$544$	4.93831	0.211728
$545$	−19.3371	−0.828310
$546$	−6.35380	−0.271918
$547$	−29.0573	−1.24240	−0.621201	−	0.783651i	$-0.713355\pi$
$547$	−29.0573	−1.24240	−0.621201	+	0.783651i	$0.713355\pi$
$548$	3.41580	0.145916
$549$	6.65714	0.284120
$550$	24.5513	1.04687
$551$	7.94337	0.338399
$552$	1.00000	0.0425628
$553$	−33.2724	−1.41488
$554$	−13.7719	−0.585110
$555$	24.6326	1.04560
$556$	17.7746	0.753811
$557$	33.9773	1.43966	0.719832	−	0.694149i	$-0.244219\pi$
$557$	33.9773	1.43966	0.719832	+	0.694149i	$0.244219\pi$
$558$	3.30293	0.139824
$559$	3.11376	0.131698
$560$	−17.1244	−0.723638
$561$	13.7311	0.579727
$562$	20.7797	0.876537
$563$	−30.9349	−1.30375	−0.651875	−	0.758326i	$-0.726017\pi$
$563$	−30.9349	−1.30375	−0.651875	+	0.758326i	$0.726017\pi$
$564$	2.24907	0.0947030
$565$	−17.7828	−0.748130
$566$	13.4968	0.567315
$567$	−4.60478	−0.193383
$568$	−12.5838	−0.528005
$569$	−1.01798	−0.0426759	−0.0213379	−	0.999772i	$-0.506793\pi$
$569$	−1.01798	−0.0426759	−0.0213379	+	0.999772i	$0.506793\pi$
$570$	−29.5401	−1.23730
$571$	31.4205	1.31491	0.657454	−	0.753494i	$-0.271633\pi$
$571$	31.4205	1.31491	0.657454	+	0.753494i	$0.271633\pi$
$572$	3.83665	0.160418
$573$	−7.71097	−0.322130
$574$	−51.3255	−2.14229
$575$	8.82973	0.368225
$576$	1.00000	0.0416667
$577$	25.3878	1.05691	0.528453	−	0.848962i	$-0.322772\pi$
$577$	25.3878	1.05691	0.528453	+	0.848962i	$0.322772\pi$
$578$	7.38690	0.307254
$579$	8.44722	0.351055
$580$	−3.71883	−0.154416
$581$	0.941654	0.0390664
$582$	−9.98687	−0.413969
$583$	−27.3547	−1.13291
$584$	4.28247	0.177210
$585$	5.13135	0.212155
$586$	−7.06536	−0.291867
$587$	34.2879	1.41521	0.707607	−	0.706606i	$-0.249775\pi$
$587$	34.2879	1.41521	0.707607	+	0.706606i	$0.249775\pi$
$588$	14.2040	0.585763
$589$	−26.2364	−1.08105
$590$	−29.9658	−1.23367
$591$	−4.15297	−0.170830
$592$	6.62374	0.272234
$593$	−0.803400	−0.0329917	−0.0164958	−	0.999864i	$-0.505251\pi$
$593$	−0.803400	−0.0329917	−0.0164958	+	0.999864i	$0.505251\pi$
$594$	2.78053	0.114086
$595$	−84.5656	−3.46685
$596$	5.28256	0.216382
$597$	−15.2894	−0.625752
$598$	1.37983	0.0564254
$599$	12.6330	0.516168	0.258084	−	0.966122i	$-0.416909\pi$
$599$	12.6330	0.516168	0.258084	+	0.966122i	$0.416909\pi$
$600$	8.82973	0.360472
$601$	−12.9777	−0.529371	−0.264686	−	0.964335i	$-0.585268\pi$
$601$	−12.9777	−0.529371	−0.264686	+	0.964335i	$0.585268\pi$
$602$	−10.3913	−0.423517
$603$	−4.47849	−0.182378
$604$	−18.4191	−0.749463
$605$	−12.1557	−0.494199
$606$	18.2379	0.740864
$607$	−29.0337	−1.17844	−0.589221	−	0.807972i	$-0.700565\pi$
$607$	−29.0337	−1.17844	−0.589221	+	0.807972i	$0.700565\pi$
$608$	−7.94337	−0.322146
$609$	4.60478	0.186595
$610$	24.7568	1.00237
$611$	3.10333	0.125547
$612$	4.93831	0.199619
$613$	−28.5306	−1.15234	−0.576170	−	0.817330i	$-0.695453\pi$
$613$	−28.5306	−1.15234	−0.576170	+	0.817330i	$0.695453\pi$
$614$	0.163949	0.00661646
$615$	41.4507	1.67145
$616$	−12.8037	−0.515876
$617$	−42.1437	−1.69664	−0.848320	−	0.529484i	$-0.822386\pi$
$617$	−42.1437	−1.69664	−0.848320	+	0.529484i	$0.822386\pi$
$618$	6.97380	0.280527
$619$	29.1517	1.17171	0.585854	−	0.810417i	$-0.300759\pi$
$619$	29.1517	1.17171	0.585854	+	0.810417i	$0.300759\pi$
$620$	12.2830	0.493299
$621$	1.00000	0.0401286
$622$	−21.5334	−0.863411
$623$	29.2199	1.17067
$624$	1.37983	0.0552373
$625$	8.81548	0.352619
$626$	−26.7907	−1.07077
$627$	−22.0867	−0.882060
$628$	−21.4418	−0.855622
$629$	32.7101	1.30424
$630$	−17.1244	−0.682253
$631$	35.0433	1.39505	0.697525	−	0.716560i	$-0.254284\pi$
$631$	35.0433	1.39505	0.697525	+	0.716560i	$0.254284\pi$
$632$	7.22562	0.287420
$633$	19.2932	0.766836
$634$	−22.0650	−0.876312
$635$	−10.0203	−0.397645
$636$	−9.83795	−0.390100
$637$	19.5991	0.776543
$638$	−2.78053	−0.110082
$639$	−12.5838	−0.497808
$640$	3.71883	0.147000
$641$	32.3259	1.27680	0.638398	−	0.769707i	$-0.279598\pi$
$641$	32.3259	1.27680	0.638398	+	0.769707i	$0.279598\pi$
$642$	10.5583	0.416703
$643$	21.0841	0.831476	0.415738	−	0.909484i	$-0.363523\pi$
$643$	21.0841	0.831476	0.415738	+	0.909484i	$0.363523\pi$
$644$	−4.60478	−0.181454
$645$	8.39204	0.330436
$646$	−39.2268	−1.54336
$647$	18.5913	0.730898	0.365449	−	0.930831i	$-0.380915\pi$
$647$	18.5913	0.730898	0.365449	+	0.930831i	$0.380915\pi$
$648$	1.00000	0.0392837
$649$	−22.4050	−0.879474
$650$	12.1835	0.477876
$651$	−15.2093	−0.596098
$652$	1.18250	0.0463104
$653$	−27.2557	−1.06660	−0.533300	−	0.845926i	$-0.679048\pi$
$653$	−27.2557	−1.06660	−0.533300	+	0.845926i	$0.679048\pi$
$654$	−5.19977	−0.203327
$655$	3.70401	0.144728
$656$	11.1461	0.435184
$657$	4.28247	0.167075
$658$	−10.3565	−0.403738
$659$	−50.2556	−1.95768	−0.978840	−	0.204627i	$-0.934402\pi$
$659$	−50.2556	−1.95768	−0.978840	+	0.204627i	$0.934402\pi$
$660$	10.3403	0.402496
$661$	−2.74580	−0.106799	−0.0533996	−	0.998573i	$-0.517006\pi$
$661$	−2.74580	−0.106799	−0.0533996	+	0.998573i	$0.517006\pi$
$662$	23.9163	0.929535
$663$	6.81402	0.264634
$664$	−0.204495	−0.00793594
$665$	136.026	5.27484
$666$	6.62374	0.256665
$667$	−1.00000	−0.0387202
$668$	−2.72521	−0.105441
$669$	29.2088	1.12928
$670$	−16.6548	−0.643430
$671$	18.5104	0.714584
$672$	−4.60478	−0.177633
$673$	−10.6408	−0.410173	−0.205086	−	0.978744i	$-0.565748\pi$
$673$	−10.6408	−0.410173	−0.205086	+	0.978744i	$0.565748\pi$
$674$	28.5941	1.10140
$675$	8.82973	0.339856
$676$	−11.0961	−0.426772
$677$	−11.5858	−0.445277	−0.222638	−	0.974901i	$-0.571467\pi$
$677$	−11.5858	−0.445277	−0.222638	+	0.974901i	$0.571467\pi$
$678$	−4.78183	−0.183645
$679$	45.9873	1.76483
$680$	18.3648	0.704256
$681$	0.308766	0.0118320
$682$	9.18388	0.351669
$683$	10.6120	0.406057	0.203029	−	0.979173i	$-0.434922\pi$
$683$	10.6120	0.406057	0.203029	+	0.979173i	$0.434922\pi$
$684$	−7.94337	−0.303722
$685$	12.7028	0.485348
$686$	−33.1728	−1.26654
$687$	12.6463	0.482487
$688$	2.25663	0.0860332
$689$	−13.5747	−0.517154
$690$	3.71883	0.141574
$691$	−11.1751	−0.425123	−0.212561	−	0.977148i	$-0.568181\pi$
$691$	−11.1751	−0.425123	−0.212561	+	0.977148i	$0.568181\pi$
$692$	−8.72763	−0.331775
$693$	−12.8037	−0.486372
$694$	6.90150	0.261977
$695$	66.1008	2.50735
$696$	−1.00000	−0.0379049
$697$	55.0431	2.08491
$698$	−3.78651	−0.143321
$699$	−28.5421	−1.07956
$700$	−40.6590	−1.53676
$701$	−32.7324	−1.23628	−0.618142	−	0.786066i	$-0.712114\pi$
$701$	−32.7324	−1.23628	−0.618142	+	0.786066i	$0.712114\pi$
$702$	1.37983	0.0520782
$703$	−52.6149	−1.98441
$704$	2.78053	0.104795
$705$	8.36393	0.315004
$706$	5.72830	0.215587
$707$	−83.9815	−3.15845
$708$	−8.05784	−0.302832
$709$	−35.9866	−1.35151	−0.675753	−	0.737128i	$-0.736181\pi$
$709$	−35.9866	−1.35151	−0.675753	+	0.737128i	$0.736181\pi$
$710$	−46.7971	−1.75626
$711$	7.22562	0.270982
$712$	−6.34556	−0.237810
$713$	3.30293	0.123696
$714$	−22.7398	−0.851016
$715$	14.2679	0.533587
$716$	−15.4069	−0.575782
$717$	14.0741	0.525605
$718$	15.6510	0.584088
$719$	0.778740	0.0290421	0.0145210	−	0.999895i	$-0.495378\pi$
$719$	0.778740	0.0290421	0.0145210	+	0.999895i	$0.495378\pi$
$720$	3.71883	0.138593
$721$	−32.1128	−1.19594
$722$	44.0972	1.64113
$723$	−19.9558	−0.742163
$724$	−17.9295	−0.666344
$725$	−8.82973	−0.327928
$726$	−3.26868	−0.121312
$727$	−32.3786	−1.20086	−0.600428	−	0.799679i	$-0.705003\pi$
$727$	−32.3786	−1.20086	−0.600428	+	0.799679i	$0.705003\pi$
$728$	−6.35380	−0.235488
$729$	1.00000	0.0370370
$730$	15.9258	0.589440
$731$	11.1439	0.412174
$732$	6.65714	0.246055
$733$	−30.5086	−1.12686	−0.563431	−	0.826163i	$-0.690519\pi$
$733$	−30.5086	−1.12686	−0.563431	+	0.826163i	$0.690519\pi$
$734$	28.5831	1.05502
$735$	52.8223	1.94838
$736$	1.00000	0.0368605
$737$	−12.4526	−0.458696
$738$	11.1461	0.410295
$739$	21.7963	0.801789	0.400894	−	0.916124i	$-0.368699\pi$
$739$	21.7963	0.801789	0.400894	+	0.916124i	$0.368699\pi$
$740$	24.6326	0.905513
$741$	−10.9605	−0.402643
$742$	45.3016	1.66307
$743$	−12.2878	−0.450797	−0.225398	−	0.974267i	$-0.572368\pi$
$743$	−12.2878	−0.450797	−0.225398	+	0.974267i	$0.572368\pi$
$744$	3.30293	0.121091
$745$	19.6450	0.719736
$746$	−14.0297	−0.513665
$747$	−0.204495	−0.00748208
$748$	13.7311	0.502059
$749$	−48.6186	−1.77649
$750$	14.2421	0.520049
$751$	−31.1076	−1.13513	−0.567567	−	0.823327i	$-0.692115\pi$
$751$	−31.1076	−1.13513	−0.567567	+	0.823327i	$0.692115\pi$
$752$	2.24907	0.0820152
$753$	−26.1076	−0.951414
$754$	−1.37983	−0.0502504
$755$	−68.4976	−2.49288
$756$	−4.60478	−0.167474
$757$	−40.2253	−1.46201	−0.731007	−	0.682370i	$-0.760950\pi$
$757$	−40.2253	−1.46201	−0.731007	+	0.682370i	$0.760950\pi$
$758$	−20.8137	−0.755988
$759$	2.78053	0.100927
$760$	−29.5401	−1.07153
$761$	−16.2854	−0.590346	−0.295173	−	0.955444i	$-0.595377\pi$
$761$	−16.2854	−0.590346	−0.295173	+	0.955444i	$0.595377\pi$
$762$	−2.69448	−0.0976109
$763$	23.9438	0.866824
$764$	−7.71097	−0.278973
$765$	18.3648	0.663979
$766$	−18.0623	−0.652619
$767$	−11.1184	−0.401463
$768$	1.00000	0.0360844
$769$	−14.8768	−0.536471	−0.268235	−	0.963353i	$-0.586440\pi$
$769$	−14.8768	−0.536471	−0.268235	+	0.963353i	$0.586440\pi$
$770$	−47.6149	−1.71592
$771$	−4.52071	−0.162809
$772$	8.44722	0.304022
$773$	18.0707	0.649957	0.324979	−	0.945721i	$-0.394643\pi$
$773$	18.0707	0.649957	0.324979	+	0.945721i	$0.394643\pi$
$774$	2.25663	0.0811129
$775$	29.1640	1.04760
$776$	−9.98687	−0.358508
$777$	−30.5009	−1.09421
$778$	−22.5311	−0.807780
$779$	−88.5380	−3.17220
$780$	5.13135	0.183732
$781$	−34.9896	−1.25203
$782$	4.93831	0.176594
$783$	−1.00000	−0.0357371
$784$	14.2040	0.507285
$785$	−79.7386	−2.84599
$786$	0.996015	0.0355267
$787$	−4.00793	−0.142867	−0.0714337	−	0.997445i	$-0.522757\pi$
$787$	−4.00793	−0.142867	−0.0714337	+	0.997445i	$0.522757\pi$
$788$	−4.15297	−0.147944
$789$	−17.0963	−0.608645
$790$	26.8709	0.956023
$791$	22.0193	0.782915
$792$	2.78053	0.0988017
$793$	9.18571	0.326194
$794$	−24.4105	−0.866296
$795$	−36.5857	−1.29756
$796$	−15.2894	−0.541917
$797$	−14.9864	−0.530847	−0.265424	−	0.964132i	$-0.585512\pi$
$797$	−14.9864	−0.530847	−0.265424	+	0.964132i	$0.585512\pi$
$798$	36.5775	1.29483
$799$	11.1066	0.392924
$800$	8.82973	0.312178
$801$	−6.34556	−0.224209
$802$	6.92862	0.244658
$803$	11.9075	0.420207
$804$	−4.47849	−0.157944
$805$	−17.1244	−0.603556
$806$	4.55747	0.160530
$807$	2.10959	0.0742610
$808$	18.2379	0.641607
$809$	−4.52837	−0.159209	−0.0796044	−	0.996827i	$-0.525366\pi$
$809$	−4.52837	−0.159209	−0.0796044	+	0.996827i	$0.525366\pi$
$810$	3.71883	0.130667
$811$	51.1734	1.79694	0.898470	−	0.439035i	$-0.144680\pi$
$811$	51.1734	1.79694	0.898470	+	0.439035i	$0.144680\pi$
$812$	4.60478	0.161596
$813$	4.02444	0.141143
$814$	18.4175	0.645533
$815$	4.39753	0.154039
$816$	4.93831	0.172875
$817$	−17.9253	−0.627125
$818$	−21.4966	−0.751610
$819$	−6.35380	−0.222020
$820$	41.4507	1.44752
$821$	−9.15775	−0.319608	−0.159804	−	0.987149i	$-0.551086\pi$
$821$	−9.15775	−0.319608	−0.159804	+	0.987149i	$0.551086\pi$
$822$	3.41580	0.119140
$823$	23.6275	0.823604	0.411802	−	0.911273i	$-0.364900\pi$
$823$	23.6275	0.823604	0.411802	+	0.911273i	$0.364900\pi$
$824$	6.97380	0.242944
$825$	24.5513	0.854766
$826$	37.1046	1.29103
$827$	−3.64580	−0.126777	−0.0633884	−	0.997989i	$-0.520191\pi$
$827$	−3.64580	−0.126777	−0.0633884	+	0.997989i	$0.520191\pi$
$828$	1.00000	0.0347524
$829$	−20.4248	−0.709382	−0.354691	−	0.934984i	$-0.615414\pi$
$829$	−20.4248	−0.709382	−0.354691	+	0.934984i	$0.615414\pi$
$830$	−0.760483	−0.0263967
$831$	−13.7719	−0.477741
$832$	1.37983	0.0478369
$833$	70.1437	2.43033
$834$	17.7746	0.615484
$835$	−10.1346	−0.350722
$836$	−22.0867	−0.763886
$837$	3.30293	0.114166
$838$	−22.2577	−0.768879
$839$	−38.8579	−1.34153	−0.670763	−	0.741672i	$-0.734033\pi$
$839$	−38.8579	−1.34153	−0.670763	+	0.741672i	$0.734033\pi$
$840$	−17.1244	−0.590848
$841$	1.00000	0.0344828
$842$	9.60251	0.330924
$843$	20.7797	0.715689
$844$	19.2932	0.664099
$845$	−41.2645	−1.41954
$846$	2.24907	0.0773247
$847$	15.0515	0.517177
$848$	−9.83795	−0.337837
$849$	13.4968	0.463210
$850$	43.6039	1.49560
$851$	6.62374	0.227059
$852$	−12.5838	−0.431114
$853$	3.79944	0.130091	0.0650453	−	0.997882i	$-0.479281\pi$
$853$	3.79944	0.130091	0.0650453	+	0.997882i	$0.479281\pi$
$854$	−30.6547	−1.04898
$855$	−29.5401	−1.01025
$856$	10.5583	0.360875
$857$	−14.6653	−0.500958	−0.250479	−	0.968122i	$-0.580588\pi$
$857$	−14.6653	−0.500958	−0.250479	+	0.968122i	$0.580588\pi$
$858$	3.83665	0.130981
$859$	−13.5359	−0.461839	−0.230919	−	0.972973i	$-0.574173\pi$
$859$	−13.5359	−0.461839	−0.230919	+	0.972973i	$0.574173\pi$
$860$	8.39204	0.286166
$861$	−51.3255	−1.74917
$862$	8.01844	0.273109
$863$	28.2096	0.960267	0.480134	−	0.877195i	$-0.340588\pi$
$863$	28.2096	0.960267	0.480134	+	0.877195i	$0.340588\pi$
$864$	1.00000	0.0340207
$865$	−32.4566	−1.10356
$866$	−1.63085	−0.0554185
$867$	7.38690	0.250872
$868$	−15.2093	−0.516236
$869$	20.0910	0.681541
$870$	−3.71883	−0.126080
$871$	−6.17955	−0.209386
$872$	−5.19977	−0.176087
$873$	−9.98687	−0.338004
$874$	−7.94337	−0.268689
$875$	−65.5819	−2.21707
$876$	4.28247	0.144691
$877$	22.8411	0.771290	0.385645	−	0.922647i	$-0.373979\pi$
$877$	22.8411	0.771290	0.385645	+	0.922647i	$0.373979\pi$
$878$	−24.6912	−0.833286
$879$	−7.06536	−0.238309
$880$	10.3403	0.348572
$881$	−4.29668	−0.144759	−0.0723794	−	0.997377i	$-0.523059\pi$
$881$	−4.29668	−0.144759	−0.0723794	+	0.997377i	$0.523059\pi$
$882$	14.2040	0.478273
$883$	55.8399	1.87916	0.939582	−	0.342324i	$-0.111214\pi$
$883$	55.8399	1.87916	0.939582	+	0.342324i	$0.111214\pi$
$884$	6.81402	0.229180
$885$	−29.9658	−1.00729
$886$	28.2870	0.950321
$887$	20.4493	0.686622	0.343311	−	0.939222i	$-0.388452\pi$
$887$	20.4493	0.686622	0.343311	+	0.939222i	$0.388452\pi$
$888$	6.62374	0.222278
$889$	12.4075	0.416134
$890$	−23.5981	−0.791010
$891$	2.78053	0.0931511
$892$	29.2088	0.977985
$893$	−17.8652	−0.597837
$894$	5.28256	0.176675
$895$	−57.2956	−1.91518
$896$	−4.60478	−0.153835
$897$	1.37983	0.0460711
$898$	−1.75366	−0.0585203
$899$	−3.30293	−0.110159
$900$	8.82973	0.294324
$901$	−48.5829	−1.61853
$902$	30.9921	1.03193
$903$	−10.3913	−0.345800
$904$	−4.78183	−0.159041
$905$	−66.6767	−2.21641
$906$	−18.4191	−0.611934
$907$	52.5944	1.74637	0.873184	−	0.487390i	$-0.162051\pi$
$907$	52.5944	1.74637	0.873184	+	0.487390i	$0.162051\pi$
$908$	0.308766	0.0102468
$909$	18.2379	0.604913
$910$	−23.6287	−0.783285
$911$	−5.27268	−0.174692	−0.0873458	−	0.996178i	$-0.527839\pi$
$911$	−5.27268	−0.174692	−0.0873458	+	0.996178i	$0.527839\pi$
$912$	−7.94337	−0.263031
$913$	−0.568603	−0.0188180
$914$	11.1380	0.368414
$915$	24.7568	0.818435
$916$	12.6463	0.417846
$917$	−4.58643	−0.151457
$918$	4.93831	0.162988
$919$	−47.1846	−1.55648	−0.778239	−	0.627968i	$-0.783887\pi$
$919$	−47.1846	−1.55648	−0.778239	+	0.627968i	$0.783887\pi$
$920$	3.71883	0.122606
$921$	0.163949	0.00540232
$922$	33.5519	1.10497
$923$	−17.3635	−0.571527
$924$	−12.8037	−0.421211
$925$	58.4859	1.92300
$926$	27.0322	0.888334
$927$	6.97380	0.229050
$928$	−1.00000	−0.0328266
$929$	−32.4729	−1.06540	−0.532700	−	0.846304i	$-0.678823\pi$
$929$	−32.4729	−1.06540	−0.532700	+	0.846304i	$0.678823\pi$
$930$	12.2830	0.402777
$931$	−112.828	−3.69777
$932$	−28.5421	−0.934928
$933$	−21.5334	−0.704972
$934$	36.0487	1.17955
$935$	51.0637	1.66996
$936$	1.37983	0.0451011
$937$	23.6276	0.771882	0.385941	−	0.922524i	$-0.373877\pi$
$937$	23.6276	0.771882	0.385941	+	0.922524i	$0.373877\pi$
$938$	20.6225	0.673347
$939$	−26.7907	−0.874283
$940$	8.36393	0.272801
$941$	9.77868	0.318776	0.159388	−	0.987216i	$-0.449048\pi$
$941$	9.77868	0.318776	0.159388	+	0.987216i	$0.449048\pi$
$942$	−21.4418	−0.698613
$943$	11.1461	0.362968
$944$	−8.05784	−0.262260
$945$	−17.1244	−0.557057
$946$	6.27462	0.204005
$947$	−4.26283	−0.138523	−0.0692617	−	0.997599i	$-0.522064\pi$
$947$	−4.26283	−0.138523	−0.0692617	+	0.997599i	$0.522064\pi$
$948$	7.22562	0.234677
$949$	5.90907	0.191817
$950$	−70.1378	−2.27557
$951$	−22.0650	−0.715506
$952$	−22.7398	−0.737002
$953$	−26.8988	−0.871337	−0.435668	−	0.900107i	$-0.643488\pi$
$953$	−26.8988	−0.871337	−0.435668	+	0.900107i	$0.643488\pi$
$954$	−9.83795	−0.318515
$955$	−28.6758	−0.927928
$956$	14.0741	0.455188
$957$	−2.78053	−0.0898816
$958$	−1.47382	−0.0476168
$959$	−15.7290	−0.507916
$960$	3.71883	0.120025
$961$	−20.0907	−0.648086
$962$	9.13963	0.294673
$963$	10.5583	0.340236
$964$	−19.9558	−0.642732
$965$	31.4138	1.01125
$966$	−4.60478	−0.148156
$967$	34.9817	1.12494	0.562468	−	0.826819i	$-0.309852\pi$
$967$	34.9817	1.12494	0.562468	+	0.826819i	$0.309852\pi$
$968$	−3.26868	−0.105059
$969$	−39.2268	−1.26015
$970$	−37.1395	−1.19248
$971$	34.6984	1.11353	0.556763	−	0.830671i	$-0.312043\pi$
$971$	34.6984	1.11353	0.556763	+	0.830671i	$0.312043\pi$
$972$	1.00000	0.0320750
$973$	−81.8481	−2.62393
$974$	−13.9536	−0.447102
$975$	12.1835	0.390184
$976$	6.65714	0.213090
$977$	−38.1624	−1.22092	−0.610461	−	0.792046i	$-0.709016\pi$
$977$	−38.1624	−1.22092	−0.610461	+	0.792046i	$0.709016\pi$
$978$	1.18250	0.0378123
$979$	−17.6440	−0.563904
$980$	52.8223	1.68735
$981$	−5.19977	−0.166016
$982$	−40.4341	−1.29031
$983$	−56.5239	−1.80283	−0.901416	−	0.432953i	$-0.857471\pi$
$983$	−56.5239	−1.80283	−0.901416	+	0.432953i	$0.857471\pi$
$984$	11.1461	0.355326
$985$	−15.4442	−0.492094
$986$	−4.93831	−0.157268
$987$	−10.3565	−0.329650
$988$	−10.9605	−0.348699
$989$	2.25663	0.0717567
$990$	10.3403	0.328637
$991$	−32.1961	−1.02274	−0.511372	−	0.859359i	$-0.670863\pi$
$991$	−32.1961	−1.02274	−0.511372	+	0.859359i	$0.670863\pi$
$992$	3.30293	0.104868
$993$	23.9163	0.758962
$994$	57.9457	1.83793
$995$	−56.8586	−1.80254
$996$	−0.204495	−0.00647967
$997$	31.4497	0.996022	0.498011	−	0.867171i	$-0.334064\pi$
$997$	31.4497	0.996022	0.498011	+	0.867171i	$0.334064\pi$
$998$	−25.4971	−0.807097
$999$	6.62374	0.209566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bh.1.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bh.1.7	✓	7	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71883 q^{5} +1.00000 q^{6} -4.60478 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.71883 q^{5} +1.00000 q^{6} -4.60478 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.71883 q^{10} +2.78053 q^{11} +1.00000 q^{12} +1.37983 q^{13} -4.60478 q^{14} +3.71883 q^{15} +1.00000 q^{16} +4.93831 q^{17} +1.00000 q^{18} -7.94337 q^{19} +3.71883 q^{20} -4.60478 q^{21} +2.78053 q^{22} +1.00000 q^{23} +1.00000 q^{24} +8.82973 q^{25} +1.37983 q^{26} +1.00000 q^{27} -4.60478 q^{28} -1.00000 q^{29} +3.71883 q^{30} +3.30293 q^{31} +1.00000 q^{32} +2.78053 q^{33} +4.93831 q^{34} -17.1244 q^{35} +1.00000 q^{36} +6.62374 q^{37} -7.94337 q^{38} +1.37983 q^{39} +3.71883 q^{40} +11.1461 q^{41} -4.60478 q^{42} +2.25663 q^{43} +2.78053 q^{44} +3.71883 q^{45} +1.00000 q^{46} +2.24907 q^{47} +1.00000 q^{48} +14.2040 q^{49} +8.82973 q^{50} +4.93831 q^{51} +1.37983 q^{52} -9.83795 q^{53} +1.00000 q^{54} +10.3403 q^{55} -4.60478 q^{56} -7.94337 q^{57} -1.00000 q^{58} -8.05784 q^{59} +3.71883 q^{60} +6.65714 q^{61} +3.30293 q^{62} -4.60478 q^{63} +1.00000 q^{64} +5.13135 q^{65} +2.78053 q^{66} -4.47849 q^{67} +4.93831 q^{68} +1.00000 q^{69} -17.1244 q^{70} -12.5838 q^{71} +1.00000 q^{72} +4.28247 q^{73} +6.62374 q^{74} +8.82973 q^{75} -7.94337 q^{76} -12.8037 q^{77} +1.37983 q^{78} +7.22562 q^{79} +3.71883 q^{80} +1.00000 q^{81} +11.1461 q^{82} -0.204495 q^{83} -4.60478 q^{84} +18.3648 q^{85} +2.25663 q^{86} -1.00000 q^{87} +2.78053 q^{88} -6.34556 q^{89} +3.71883 q^{90} -6.35380 q^{91} +1.00000 q^{92} +3.30293 q^{93} +2.24907 q^{94} -29.5401 q^{95} +1.00000 q^{96} -9.98687 q^{97} +14.2040 q^{98} +2.78053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9	\( 7 q + 7 q^{2} + 7 q^{3} + 7 q^{4} + q^{5} + 7 q^{6} - 2 q^{7} + 7 q^{8} + 7 q^{9} + q^{10} + 11 q^{11} + 7 q^{12} - q^{13} - 2 q^{14} + q^{15} + 7 q^{16} + 18 q^{17} + 7 q^{18} + 6 q^{19} + q^{20} - 2 q^{21} + 11 q^{22} + 7 q^{23} + 7 q^{24} + 12 q^{25} - q^{26} + 7 q^{27} - 2 q^{28} - 7 q^{29} + q^{30} + 3 q^{31} + 7 q^{32} + 11 q^{33} + 18 q^{34} - 4 q^{35} + 7 q^{36} + 5 q^{37} + 6 q^{38} - q^{39} + q^{40} + 25 q^{41} - 2 q^{42} + 20 q^{43} + 11 q^{44} + q^{45} + 7 q^{46} + 7 q^{48} + 7 q^{49} + 12 q^{50} + 18 q^{51} - q^{52} - 4 q^{53} + 7 q^{54} + 17 q^{55} - 2 q^{56} + 6 q^{57} - 7 q^{58} - 17 q^{59} + q^{60} + 5 q^{61} + 3 q^{62} - 2 q^{63} + 7 q^{64} + 7 q^{65} + 11 q^{66} + 15 q^{67} + 18 q^{68} + 7 q^{69} - 4 q^{70} + 15 q^{71} + 7 q^{72} + 14 q^{73} + 5 q^{74} + 12 q^{75} + 6 q^{76} - 12 q^{77} - q^{78} - 4 q^{79} + q^{80} + 7 q^{81} + 25 q^{82} + 14 q^{83} - 2 q^{84} + 34 q^{85} + 20 q^{86} - 7 q^{87} + 11 q^{88} + 8 q^{89} + q^{90} - 6 q^{91} + 7 q^{92} + 3 q^{93} - 18 q^{95} + 7 q^{96} - 18 q^{97} + 7 q^{98} + 11 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 + 7 * q^3 + 7 * q^4 + q^5 + 7 * q^6 - 2 * q^7 + 7 * q^8 + 7 * q^9 + q^10 + 11 * q^11 + 7 * q^12 - q^13 - 2 * q^14 + q^15 + 7 * q^16 + 18 * q^17 + 7 * q^18 + 6 * q^19 + q^20 - 2 * q^21 + 11 * q^22 + 7 * q^23 + 7 * q^24 + 12 * q^25 - q^26 + 7 * q^27 - 2 * q^28 - 7 * q^29 + q^30 + 3 * q^31 + 7 * q^32 + 11 * q^33 + 18 * q^34 - 4 * q^35 + 7 * q^36 + 5 * q^37 + 6 * q^38 - q^39 + q^40 + 25 * q^41 - 2 * q^42 + 20 * q^43 + 11 * q^44 + q^45 + 7 * q^46 + 7 * q^48 + 7 * q^49 + 12 * q^50 + 18 * q^51 - q^52 - 4 * q^53 + 7 * q^54 + 17 * q^55 - 2 * q^56 + 6 * q^57 - 7 * q^58 - 17 * q^59 + q^60 + 5 * q^61 + 3 * q^62 - 2 * q^63 + 7 * q^64 + 7 * q^65 + 11 * q^66 + 15 * q^67 + 18 * q^68 + 7 * q^69 - 4 * q^70 + 15 * q^71 + 7 * q^72 + 14 * q^73 + 5 * q^74 + 12 * q^75 + 6 * q^76 - 12 * q^77 - q^78 - 4 * q^79 + q^80 + 7 * q^81 + 25 * q^82 + 14 * q^83 - 2 * q^84 + 34 * q^85 + 20 * q^86 - 7 * q^87 + 11 * q^88 + 8 * q^89 + q^90 - 6 * q^91 + 7 * q^92 + 3 * q^93 - 18 * q^95 + 7 * q^96 - 18 * q^97 + 7 * q^98 + 11 * q^99

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