LMFDB - Embedded newform 2001.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
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} - x^{6} - 9x^{5} + 10x^{4} + 19x^{3} - 20x^{2} - 5x + 1 $ x^7 - x^6 - 9x^5 + 10x^4 + 19x^3 - 20x^2 - 5*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.136094$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.17088 q^{2} +1.00000 q^{3} -0.629030 q^{4} +0.418864 q^{5} +1.17088 q^{6} +1.98148 q^{7} -3.07829 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.17088 q^{2} +1.00000 q^{3} -0.629030 q^{4} +0.418864 q^{5} +1.17088 q^{6} +1.98148 q^{7} -3.07829 q^{8} +1.00000 q^{9} +0.490441 q^{10} -5.41188 q^{11} -0.629030 q^{12} -1.43970 q^{13} +2.32008 q^{14} +0.418864 q^{15} -2.34626 q^{16} -6.03721 q^{17} +1.17088 q^{18} -6.20121 q^{19} -0.263478 q^{20} +1.98148 q^{21} -6.33668 q^{22} -1.00000 q^{23} -3.07829 q^{24} -4.82455 q^{25} -1.68572 q^{26} +1.00000 q^{27} -1.24641 q^{28} +1.00000 q^{29} +0.490441 q^{30} -6.35355 q^{31} +3.40938 q^{32} -5.41188 q^{33} -7.06888 q^{34} +0.829970 q^{35} -0.629030 q^{36} +4.47112 q^{37} -7.26090 q^{38} -1.43970 q^{39} -1.28939 q^{40} +8.27534 q^{41} +2.32008 q^{42} +6.28106 q^{43} +3.40424 q^{44} +0.418864 q^{45} -1.17088 q^{46} +6.99741 q^{47} -2.34626 q^{48} -3.07374 q^{49} -5.64899 q^{50} -6.03721 q^{51} +0.905613 q^{52} +5.10879 q^{53} +1.17088 q^{54} -2.26684 q^{55} -6.09957 q^{56} -6.20121 q^{57} +1.17088 q^{58} +9.51627 q^{59} -0.263478 q^{60} -4.79680 q^{61} -7.43927 q^{62} +1.98148 q^{63} +8.68451 q^{64} -0.603037 q^{65} -6.33668 q^{66} -12.2420 q^{67} +3.79759 q^{68} -1.00000 q^{69} +0.971799 q^{70} -7.30808 q^{71} -3.07829 q^{72} -4.61997 q^{73} +5.23516 q^{74} -4.82455 q^{75} +3.90075 q^{76} -10.7235 q^{77} -1.68572 q^{78} -4.07417 q^{79} -0.982764 q^{80} +1.00000 q^{81} +9.68946 q^{82} +3.71419 q^{83} -1.24641 q^{84} -2.52877 q^{85} +7.35439 q^{86} +1.00000 q^{87} +16.6593 q^{88} -0.547294 q^{89} +0.490441 q^{90} -2.85273 q^{91} +0.629030 q^{92} -6.35355 q^{93} +8.19315 q^{94} -2.59746 q^{95} +3.40938 q^{96} -8.58637 q^{97} -3.59900 q^{98} -5.41188 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9} - 11 q^{10} - 12 q^{11} + 7 q^{12} - 13 q^{13} - 3 q^{14} - 5 q^{15} - 13 q^{16} - 12 q^{17} - q^{18} - 5 q^{19} - 8 q^{20} - 5 q^{21} - q^{22} - 7 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} + 7 q^{27} - 21 q^{28} + 7 q^{29} - 11 q^{30} - 8 q^{31} - 5 q^{32} - 12 q^{33} - 28 q^{34} + 5 q^{35} + 7 q^{36} - 24 q^{37} - 6 q^{38} - 13 q^{39} - 20 q^{40} + 9 q^{41} - 3 q^{42} - q^{43} - 23 q^{44} - 5 q^{45} + q^{46} + 27 q^{47} - 13 q^{48} - 14 q^{49} + 7 q^{50} - 12 q^{51} - 9 q^{52} - q^{53} - q^{54} - 11 q^{55} - 20 q^{56} - 5 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + q^{61} - 5 q^{63} + 3 q^{64} + 12 q^{65} - q^{66} - 16 q^{67} + 15 q^{68} - 7 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} - 23 q^{73} - 8 q^{74} - 4 q^{75} - 2 q^{76} + 13 q^{77} + 2 q^{78} - 44 q^{79} + 30 q^{80} + 7 q^{81} - 10 q^{82} + 21 q^{83} - 21 q^{84} + 6 q^{86} + 7 q^{87} + 21 q^{88} - 5 q^{89} - 11 q^{90} - 18 q^{91} - 7 q^{92} - 8 q^{93} + 28 q^{94} + 9 q^{95} - 5 q^{96} - 55 q^{97} + 36 q^{98} - 12 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9 - 11 * q^10 - 12 * q^11 + 7 * q^12 - 13 * q^13 - 3 * q^14 - 5 * q^15 - 13 * q^16 - 12 * q^17 - q^18 - 5 * q^19 - 8 * q^20 - 5 * q^21 - q^22 - 7 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 + 7 * q^27 - 21 * q^28 + 7 * q^29 - 11 * q^30 - 8 * q^31 - 5 * q^32 - 12 * q^33 - 28 * q^34 + 5 * q^35 + 7 * q^36 - 24 * q^37 - 6 * q^38 - 13 * q^39 - 20 * q^40 + 9 * q^41 - 3 * q^42 - q^43 - 23 * q^44 - 5 * q^45 + q^46 + 27 * q^47 - 13 * q^48 - 14 * q^49 + 7 * q^50 - 12 * q^51 - 9 * q^52 - q^53 - q^54 - 11 * q^55 - 20 * q^56 - 5 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + q^61 - 5 * q^63 + 3 * q^64 + 12 * q^65 - q^66 - 16 * q^67 + 15 * q^68 - 7 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 - 23 * q^73 - 8 * q^74 - 4 * q^75 - 2 * q^76 + 13 * q^77 + 2 * q^78 - 44 * q^79 + 30 * q^80 + 7 * q^81 - 10 * q^82 + 21 * q^83 - 21 * q^84 + 6 * q^86 + 7 * q^87 + 21 * q^88 - 5 * q^89 - 11 * q^90 - 18 * q^91 - 7 * q^92 - 8 * q^93 + 28 * q^94 + 9 * q^95 - 5 * q^96 - 55 * q^97 + 36 * q^98 - 12 * 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 $

$2$	1.17088	0.827940	0.413970	−	0.910291i	$-0.364142\pi$
$2$	1.17088	0.827940	0.413970	+	0.910291i	$0.364142\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.629030	−0.314515
$5$	0.418864	0.187322	0.0936609	−	0.995604i	$-0.470143\pi$
$5$	0.418864	0.187322	0.0936609	+	0.995604i	$0.470143\pi$
$6$	1.17088	0.478011
$7$	1.98148	0.748928	0.374464	−	0.927241i	$-0.377827\pi$
$7$	1.98148	0.748928	0.374464	+	0.927241i	$0.377827\pi$
$8$	−3.07829	−1.08834
$9$	1.00000	0.333333
$10$	0.490441	0.155091
$11$	−5.41188	−1.63174	−0.815871	−	0.578234i	$-0.803742\pi$
$11$	−5.41188	−1.63174	−0.815871	+	0.578234i	$0.803742\pi$
$12$	−0.629030	−0.181585
$13$	−1.43970	−0.399300	−0.199650	−	0.979867i	$-0.563980\pi$
$13$	−1.43970	−0.399300	−0.199650	+	0.979867i	$0.563980\pi$
$14$	2.32008	0.620068
$15$	0.418864	0.108150
$16$	−2.34626	−0.586565
$17$	−6.03721	−1.46424	−0.732120	−	0.681176i	$-0.761469\pi$
$17$	−6.03721	−1.46424	−0.732120	+	0.681176i	$0.761469\pi$
$18$	1.17088	0.275980
$19$	−6.20121	−1.42265	−0.711327	−	0.702861i	$-0.751906\pi$
$19$	−6.20121	−1.42265	−0.711327	+	0.702861i	$0.751906\pi$
$20$	−0.263478	−0.0589155
$21$	1.98148	0.432394
$22$	−6.33668	−1.35098
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.07829	−0.628353
$25$	−4.82455	−0.964911
$26$	−1.68572	−0.330596
$27$	1.00000	0.192450
$28$	−1.24641	−0.235549
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.490441	0.0895419
$31$	−6.35355	−1.14113	−0.570566	−	0.821252i	$-0.693276\pi$
$31$	−6.35355	−1.14113	−0.570566	+	0.821252i	$0.693276\pi$
$32$	3.40938	0.602699
$33$	−5.41188	−0.942087
$34$	−7.06888	−1.21230
$35$	0.829970	0.140291
$36$	−0.629030	−0.104838
$37$	4.47112	0.735048	0.367524	−	0.930014i	$-0.380206\pi$
$37$	4.47112	0.735048	0.367524	+	0.930014i	$0.380206\pi$
$38$	−7.26090	−1.17787
$39$	−1.43970	−0.230536
$40$	−1.28939	−0.203870
$41$	8.27534	1.29239	0.646195	−	0.763172i	$-0.276359\pi$
$41$	8.27534	1.29239	0.646195	+	0.763172i	$0.276359\pi$
$42$	2.32008	0.357996
$43$	6.28106	0.957852	0.478926	−	0.877855i	$-0.341026\pi$
$43$	6.28106	0.957852	0.478926	+	0.877855i	$0.341026\pi$
$44$	3.40424	0.513208
$45$	0.418864	0.0624406
$46$	−1.17088	−0.172637
$47$	6.99741	1.02068	0.510338	−	0.859974i	$-0.329520\pi$
$47$	6.99741	1.02068	0.510338	+	0.859974i	$0.329520\pi$
$48$	−2.34626	−0.338653
$49$	−3.07374	−0.439106
$50$	−5.64899	−0.798888
$51$	−6.03721	−0.845379
$52$	0.905613	0.125586
$53$	5.10879	0.701747	0.350873	−	0.936423i	$-0.385885\pi$
$53$	5.10879	0.701747	0.350873	+	0.936423i	$0.385885\pi$
$54$	1.17088	0.159337
$55$	−2.26684	−0.305661
$56$	−6.09957	−0.815089
$57$	−6.20121	−0.821370
$58$	1.17088	0.153745
$59$	9.51627	1.23891	0.619457	−	0.785031i	$-0.287353\pi$
$59$	9.51627	1.23891	0.619457	+	0.785031i	$0.287353\pi$
$60$	−0.263478	−0.0340149
$61$	−4.79680	−0.614168	−0.307084	−	0.951682i	$-0.599353\pi$
$61$	−4.79680	−0.614168	−0.307084	+	0.951682i	$0.599353\pi$
$62$	−7.43927	−0.944788
$63$	1.98148	0.249643
$64$	8.68451	1.08556
$65$	−0.603037	−0.0747975
$66$	−6.33668	−0.779991
$67$	−12.2420	−1.49560	−0.747801	−	0.663923i	$-0.768890\pi$
$67$	−12.2420	−1.49560	−0.747801	+	0.663923i	$0.768890\pi$
$68$	3.79759	0.460526
$69$	−1.00000	−0.120386
$70$	0.971799	0.116152
$71$	−7.30808	−0.867309	−0.433655	−	0.901079i	$-0.642776\pi$
$71$	−7.30808	−0.867309	−0.433655	+	0.901079i	$0.642776\pi$
$72$	−3.07829	−0.362780
$73$	−4.61997	−0.540727	−0.270364	−	0.962758i	$-0.587144\pi$
$73$	−4.61997	−0.540727	−0.270364	+	0.962758i	$0.587144\pi$
$74$	5.23516	0.608576
$75$	−4.82455	−0.557091
$76$	3.90075	0.447447
$77$	−10.7235	−1.22206
$78$	−1.68572	−0.190870
$79$	−4.07417	−0.458380	−0.229190	−	0.973382i	$-0.573608\pi$
$79$	−4.07417	−0.458380	−0.229190	+	0.973382i	$0.573608\pi$
$80$	−0.982764	−0.109876
$81$	1.00000	0.111111
$82$	9.68946	1.07002
$83$	3.71419	0.407686	0.203843	−	0.979004i	$-0.434657\pi$
$83$	3.71419	0.407686	0.203843	+	0.979004i	$0.434657\pi$
$84$	−1.24641	−0.135995
$85$	−2.52877	−0.274284
$86$	7.35439	0.793044
$87$	1.00000	0.107211
$88$	16.6593	1.77589
$89$	−0.547294	−0.0580131	−0.0290065	−	0.999579i	$-0.509234\pi$
$89$	−0.547294	−0.0580131	−0.0290065	+	0.999579i	$0.509234\pi$
$90$	0.490441	0.0516971
$91$	−2.85273	−0.299047
$92$	0.629030	0.0655810
$93$	−6.35355	−0.658832
$94$	8.19315	0.845059
$95$	−2.59746	−0.266494
$96$	3.40938	0.347969
$97$	−8.58637	−0.871814	−0.435907	−	0.899992i	$-0.643572\pi$
$97$	−8.58637	−0.871814	−0.435907	+	0.899992i	$0.643572\pi$
$98$	−3.59900	−0.363554
$99$	−5.41188	−0.543914
$100$	3.03479	0.303479
$101$	15.6455	1.55678	0.778392	−	0.627779i	$-0.216036\pi$
$101$	15.6455	1.55678	0.778392	+	0.627779i	$0.216036\pi$
$102$	−7.06888	−0.699923
$103$	−0.736275	−0.0725474	−0.0362737	−	0.999342i	$-0.511549\pi$
$103$	−0.736275	−0.0725474	−0.0362737	+	0.999342i	$0.511549\pi$
$104$	4.43180	0.434574
$105$	0.829970	0.0809968
$106$	5.98180	0.581004
$107$	−15.9928	−1.54608	−0.773040	−	0.634357i	$-0.781265\pi$
$107$	−15.9928	−1.54608	−0.773040	+	0.634357i	$0.781265\pi$
$108$	−0.629030	−0.0605285
$109$	−2.90116	−0.277881	−0.138940	−	0.990301i	$-0.544370\pi$
$109$	−2.90116	−0.277881	−0.138940	+	0.990301i	$0.544370\pi$
$110$	−2.65421	−0.253069
$111$	4.47112	0.424380
$112$	−4.64906	−0.439295
$113$	−4.66285	−0.438644	−0.219322	−	0.975652i	$-0.570385\pi$
$113$	−4.66285	−0.438644	−0.219322	+	0.975652i	$0.570385\pi$
$114$	−7.26090	−0.680045
$115$	−0.418864	−0.0390593
$116$	−0.629030	−0.0584040
$117$	−1.43970	−0.133100
$118$	11.1425	1.02575
$119$	−11.9626	−1.09661
$120$	−1.28939	−0.117704
$121$	18.2884	1.66258
$122$	−5.61650	−0.508494
$123$	8.27534	0.746162
$124$	3.99658	0.358903
$125$	−4.11515	−0.368070
$126$	2.32008	0.206689
$127$	2.45509	0.217854	0.108927	−	0.994050i	$-0.465259\pi$
$127$	2.45509	0.217854	0.108927	+	0.994050i	$0.465259\pi$
$128$	3.34979	0.296083
$129$	6.28106	0.553016
$130$	−0.706087	−0.0619279
$131$	−6.30415	−0.550796	−0.275398	−	0.961330i	$-0.588810\pi$
$131$	−6.30415	−0.550796	−0.275398	+	0.961330i	$0.588810\pi$
$132$	3.40424	0.296301
$133$	−12.2876	−1.06547
$134$	−14.3340	−1.23827
$135$	0.418864	0.0360501
$136$	18.5843	1.59359
$137$	−11.1580	−0.953294	−0.476647	−	0.879095i	$-0.658148\pi$
$137$	−11.1580	−0.953294	−0.476647	+	0.879095i	$0.658148\pi$
$138$	−1.17088	−0.0996723
$139$	−19.7370	−1.67407	−0.837036	−	0.547148i	$-0.815713\pi$
$139$	−19.7370	−1.67407	−0.837036	+	0.547148i	$0.815713\pi$
$140$	−0.522077	−0.0441235
$141$	6.99741	0.589288
$142$	−8.55691	−0.718080
$143$	7.79146	0.651555
$144$	−2.34626	−0.195522
$145$	0.418864	0.0347848
$146$	−5.40945	−0.447690
$147$	−3.07374	−0.253518
$148$	−2.81247	−0.231184
$149$	22.6974	1.85945	0.929723	−	0.368260i	$-0.120046\pi$
$149$	22.6974	1.85945	0.929723	+	0.368260i	$0.120046\pi$
$150$	−5.64899	−0.461238
$151$	10.5126	0.855507	0.427754	−	0.903895i	$-0.359305\pi$
$151$	10.5126	0.855507	0.427754	+	0.903895i	$0.359305\pi$
$152$	19.0891	1.54833
$153$	−6.03721	−0.488080
$154$	−12.5560	−1.01179
$155$	−2.66127	−0.213759
$156$	0.905613	0.0725070
$157$	18.9413	1.51168	0.755840	−	0.654756i	$-0.227229\pi$
$157$	18.9413	1.51168	0.755840	+	0.654756i	$0.227229\pi$
$158$	−4.77038	−0.379511
$159$	5.10879	0.405154
$160$	1.42807	0.112899
$161$	−1.98148	−0.156162
$162$	1.17088	0.0919933
$163$	1.36439	0.106868	0.0534338	−	0.998571i	$-0.482983\pi$
$163$	1.36439	0.106868	0.0534338	+	0.998571i	$0.482983\pi$
$164$	−5.20544	−0.406477
$165$	−2.26684	−0.176473
$166$	4.34889	0.337539
$167$	14.9947	1.16032	0.580162	−	0.814501i	$-0.302989\pi$
$167$	14.9947	1.16032	0.580162	+	0.814501i	$0.302989\pi$
$168$	−6.09957	−0.470592
$169$	−10.9273	−0.840560
$170$	−2.96090	−0.227091
$171$	−6.20121	−0.474218
$172$	−3.95098	−0.301259
$173$	−24.0572	−1.82903	−0.914516	−	0.404551i	$-0.867428\pi$
$173$	−24.0572	−1.82903	−0.914516	+	0.404551i	$0.867428\pi$
$174$	1.17088	0.0887645
$175$	−9.55975	−0.722649
$176$	12.6977	0.957123
$177$	9.51627	0.715287
$178$	−0.640818	−0.0480313
$179$	−15.0638	−1.12592	−0.562960	−	0.826484i	$-0.690337\pi$
$179$	−15.0638	−1.12592	−0.562960	+	0.826484i	$0.690337\pi$
$180$	−0.263478	−0.0196385
$181$	−4.16684	−0.309719	−0.154859	−	0.987937i	$-0.549492\pi$
$181$	−4.16684	−0.309719	−0.154859	+	0.987937i	$0.549492\pi$
$182$	−3.34021	−0.247593
$183$	−4.79680	−0.354590
$184$	3.07829	0.226935
$185$	1.87279	0.137690
$186$	−7.43927	−0.545474
$187$	32.6727	2.38926
$188$	−4.40158	−0.321018
$189$	1.98148	0.144131
$190$	−3.04133	−0.220641
$191$	21.6210	1.56444	0.782219	−	0.623003i	$-0.214088\pi$
$191$	21.6210	1.56444	0.782219	+	0.623003i	$0.214088\pi$
$192$	8.68451	0.626751
$193$	20.6563	1.48688	0.743438	−	0.668805i	$-0.233194\pi$
$193$	20.6563	1.48688	0.743438	+	0.668805i	$0.233194\pi$
$194$	−10.0536	−0.721810
$195$	−0.603037	−0.0431844
$196$	1.93348	0.138106
$197$	−13.3639	−0.952135	−0.476068	−	0.879409i	$-0.657938\pi$
$197$	−13.3639	−0.952135	−0.476068	+	0.879409i	$0.657938\pi$
$198$	−6.33668	−0.450328
$199$	0.555384	0.0393701	0.0196851	−	0.999806i	$-0.493734\pi$
$199$	0.555384	0.0393701	0.0196851	+	0.999806i	$0.493734\pi$
$200$	14.8514	1.05015
$201$	−12.2420	−0.863486
$202$	18.3190	1.28892
$203$	1.98148	0.139073
$204$	3.79759	0.265885
$205$	3.46624	0.242093
$206$	−0.862093	−0.0600649
$207$	−1.00000	−0.0695048
$208$	3.37790	0.234215
$209$	33.5602	2.32141
$210$	0.971799	0.0670605
$211$	−17.5831	−1.21047	−0.605236	−	0.796046i	$-0.706921\pi$
$211$	−17.5831	−1.21047	−0.605236	+	0.796046i	$0.706921\pi$
$212$	−3.21359	−0.220710
$213$	−7.30808	−0.500741
$214$	−18.7257	−1.28006
$215$	2.63091	0.179427
$216$	−3.07829	−0.209451
$217$	−12.5894	−0.854626
$218$	−3.39692	−0.230069
$219$	−4.61997	−0.312189
$220$	1.42591	0.0961350
$221$	8.69176	0.584671
$222$	5.23516	0.351361
$223$	−4.80810	−0.321974	−0.160987	−	0.986957i	$-0.551468\pi$
$223$	−4.80810	−0.321974	−0.160987	+	0.986957i	$0.551468\pi$
$224$	6.75562	0.451379
$225$	−4.82455	−0.321637
$226$	−5.45966	−0.363171
$227$	−9.02664	−0.599119	−0.299560	−	0.954078i	$-0.596840\pi$
$227$	−9.02664	−0.599119	−0.299560	+	0.954078i	$0.596840\pi$
$228$	3.90075	0.258333
$229$	−9.33240	−0.616702	−0.308351	−	0.951273i	$-0.599777\pi$
$229$	−9.33240	−0.616702	−0.308351	+	0.951273i	$0.599777\pi$
$230$	−0.490441	−0.0323387
$231$	−10.7235	−0.705556
$232$	−3.07829	−0.202100
$233$	1.59220	0.104309	0.0521543	−	0.998639i	$-0.483391\pi$
$233$	1.59220	0.104309	0.0521543	+	0.998639i	$0.483391\pi$
$234$	−1.68572	−0.110199
$235$	2.93096	0.191195
$236$	−5.98603	−0.389657
$237$	−4.07417	−0.264646
$238$	−14.0068	−0.907928
$239$	−14.9035	−0.964030	−0.482015	−	0.876163i	$-0.660095\pi$
$239$	−14.9035	−0.964030	−0.482015	+	0.876163i	$0.660095\pi$
$240$	−0.982764	−0.0634371
$241$	−14.3190	−0.922370	−0.461185	−	0.887304i	$-0.652575\pi$
$241$	−14.3190	−0.922370	−0.461185	+	0.887304i	$0.652575\pi$
$242$	21.4136	1.37652
$243$	1.00000	0.0641500
$244$	3.01734	0.193165
$245$	−1.28748	−0.0822541
$246$	9.68946	0.617778
$247$	8.92786	0.568066
$248$	19.5581	1.24194
$249$	3.71419	0.235377
$250$	−4.81837	−0.304740
$251$	6.91890	0.436717	0.218358	−	0.975869i	$-0.429930\pi$
$251$	6.91890	0.436717	0.218358	+	0.975869i	$0.429930\pi$
$252$	−1.24641	−0.0785165
$253$	5.41188	0.340242
$254$	2.87463	0.180370
$255$	−2.52877	−0.158358
$256$	−13.4468	−0.840425
$257$	22.2006	1.38484	0.692418	−	0.721497i	$-0.256545\pi$
$257$	22.2006	1.38484	0.692418	+	0.721497i	$0.256545\pi$
$258$	7.35439	0.457864
$259$	8.85943	0.550498
$260$	0.379329	0.0235250
$261$	1.00000	0.0618984
$262$	−7.38143	−0.456026
$263$	20.0295	1.23507	0.617535	−	0.786544i	$-0.288132\pi$
$263$	20.0295	1.23507	0.617535	+	0.786544i	$0.288132\pi$
$264$	16.6593	1.02531
$265$	2.13989	0.131452
$266$	−14.3873	−0.882143
$267$	−0.547294	−0.0334939
$268$	7.70060	0.470389
$269$	17.7058	1.07954	0.539772	−	0.841811i	$-0.318511\pi$
$269$	17.7058	1.07954	0.539772	+	0.841811i	$0.318511\pi$
$270$	0.490441	0.0298473
$271$	23.5873	1.43283	0.716414	−	0.697675i	$-0.245782\pi$
$271$	23.5873	1.43283	0.716414	+	0.697675i	$0.245782\pi$
$272$	14.1649	0.858872
$273$	−2.85273	−0.172655
$274$	−13.0647	−0.789270
$275$	26.1099	1.57449
$276$	0.629030	0.0378632
$277$	9.80130	0.588903	0.294451	−	0.955666i	$-0.404863\pi$
$277$	9.80130	0.588903	0.294451	+	0.955666i	$0.404863\pi$
$278$	−23.1098	−1.38603
$279$	−6.35355	−0.380377
$280$	−2.55489	−0.152684
$281$	−27.4425	−1.63708	−0.818542	−	0.574447i	$-0.805217\pi$
$281$	−27.4425	−1.63708	−0.818542	+	0.574447i	$0.805217\pi$
$282$	8.19315	0.487895
$283$	0.0818159	0.00486345	0.00243173	−	0.999997i	$-0.499226\pi$
$283$	0.0818159	0.00486345	0.00243173	+	0.999997i	$0.499226\pi$
$284$	4.59700	0.272782
$285$	−2.59746	−0.153860
$286$	9.12290	0.539448
$287$	16.3974	0.967908
$288$	3.40938	0.200900
$289$	19.4480	1.14400
$290$	0.490441	0.0287997
$291$	−8.58637	−0.503342
$292$	2.90610	0.170067
$293$	15.5146	0.906370	0.453185	−	0.891417i	$-0.350288\pi$
$293$	15.5146	0.906370	0.453185	+	0.891417i	$0.350288\pi$
$294$	−3.59900	−0.209898
$295$	3.98603	0.232075
$296$	−13.7634	−0.799982
$297$	−5.41188	−0.314029
$298$	26.5761	1.53951
$299$	1.43970	0.0832598
$300$	3.03479	0.175214
$301$	12.4458	0.717363
$302$	12.3091	0.708309
$303$	15.6455	0.898809
$304$	14.5496	0.834479
$305$	−2.00921	−0.115047
$306$	−7.06888	−0.404101
$307$	−31.5596	−1.80120	−0.900600	−	0.434649i	$-0.856873\pi$
$307$	−31.5596	−1.80120	−0.900600	+	0.434649i	$0.856873\pi$
$308$	6.74542	0.384356
$309$	−0.736275	−0.0418852
$310$	−3.11604	−0.176979
$311$	5.49672	0.311691	0.155845	−	0.987781i	$-0.450190\pi$
$311$	5.49672	0.311691	0.155845	+	0.987781i	$0.450190\pi$
$312$	4.43180	0.250901
$313$	−24.9161	−1.40834	−0.704170	−	0.710031i	$-0.748681\pi$
$313$	−24.9161	−1.40834	−0.704170	+	0.710031i	$0.748681\pi$
$314$	22.1781	1.25158
$315$	0.829970	0.0467635
$316$	2.56278	0.144167
$317$	−18.0990	−1.01654	−0.508270	−	0.861198i	$-0.669715\pi$
$317$	−18.0990	−1.01654	−0.508270	+	0.861198i	$0.669715\pi$
$318$	5.98180	0.335443
$319$	−5.41188	−0.303007
$320$	3.63763	0.203350
$321$	−15.9928	−0.892630
$322$	−2.32008	−0.129293
$323$	37.4380	2.08311
$324$	−0.629030	−0.0349461
$325$	6.94589	0.385289
$326$	1.59755	0.0884799
$327$	−2.90116	−0.160434
$328$	−25.4739	−1.40656
$329$	13.8652	0.764414
$330$	−2.65421	−0.146109
$331$	19.9928	1.09891	0.549453	−	0.835525i	$-0.314836\pi$
$331$	19.9928	1.09891	0.549453	+	0.835525i	$0.314836\pi$
$332$	−2.33634	−0.128223
$333$	4.47112	0.245016
$334$	17.5570	0.960678
$335$	−5.12774	−0.280159
$336$	−4.64906	−0.253627
$337$	6.05071	0.329603	0.164802	−	0.986327i	$-0.447302\pi$
$337$	6.05071	0.329603	0.164802	+	0.986327i	$0.447302\pi$
$338$	−12.7946	−0.695933
$339$	−4.66285	−0.253251
$340$	1.59067	0.0862665
$341$	34.3846	1.86203
$342$	−7.26090	−0.392624
$343$	−19.9609	−1.07779
$344$	−19.3349	−1.04247
$345$	−0.418864	−0.0225509
$346$	−28.1681	−1.51433
$347$	−5.26287	−0.282526	−0.141263	−	0.989972i	$-0.545116\pi$
$347$	−5.26287	−0.282526	−0.141263	+	0.989972i	$0.545116\pi$
$348$	−0.629030	−0.0337196
$349$	−14.6134	−0.782238	−0.391119	−	0.920340i	$-0.627912\pi$
$349$	−14.6134	−0.782238	−0.391119	+	0.920340i	$0.627912\pi$
$350$	−11.1934	−0.598310
$351$	−1.43970	−0.0768453
$352$	−18.4512	−0.983450
$353$	−21.6900	−1.15444	−0.577221	−	0.816588i	$-0.695863\pi$
$353$	−21.6900	−1.15444	−0.577221	+	0.816588i	$0.695863\pi$
$354$	11.1425	0.592215
$355$	−3.06109	−0.162466
$356$	0.344265	0.0182460
$357$	−11.9626	−0.633129
$358$	−17.6379	−0.932194
$359$	13.7538	0.725899	0.362949	−	0.931809i	$-0.381770\pi$
$359$	13.7538	0.725899	0.362949	+	0.931809i	$0.381770\pi$
$360$	−1.28939	−0.0679566
$361$	19.4550	1.02395
$362$	−4.87889	−0.256429
$363$	18.2884	0.959893
$364$	1.79445	0.0940549
$365$	−1.93514	−0.101290
$366$	−5.61650	−0.293579
$367$	−25.2233	−1.31664	−0.658322	−	0.752737i	$-0.728733\pi$
$367$	−25.2233	−1.31664	−0.658322	+	0.752737i	$0.728733\pi$
$368$	2.34626	0.122307
$369$	8.27534	0.430797
$370$	2.19282	0.113999
$371$	10.1230	0.525558
$372$	3.99658	0.207213
$373$	12.2050	0.631950	0.315975	−	0.948767i	$-0.397668\pi$
$373$	12.2050	0.631950	0.315975	+	0.948767i	$0.397668\pi$
$374$	38.2559	1.97817
$375$	−4.11515	−0.212506
$376$	−21.5401	−1.11084
$377$	−1.43970	−0.0741481
$378$	2.32008	0.119332
$379$	−24.4364	−1.25522	−0.627608	−	0.778530i	$-0.715966\pi$
$379$	−24.4364	−1.25522	−0.627608	+	0.778530i	$0.715966\pi$
$380$	1.63388	0.0838165
$381$	2.45509	0.125778
$382$	25.3157	1.29526
$383$	−1.23449	−0.0630793	−0.0315397	−	0.999503i	$-0.510041\pi$
$383$	−1.23449	−0.0630793	−0.0315397	+	0.999503i	$0.510041\pi$
$384$	3.34979	0.170943
$385$	−4.49170	−0.228918
$386$	24.1862	1.23104
$387$	6.28106	0.319284
$388$	5.40109	0.274199
$389$	19.5460	0.991023	0.495511	−	0.868602i	$-0.334981\pi$
$389$	19.5460	0.991023	0.495511	+	0.868602i	$0.334981\pi$
$390$	−0.706087	−0.0357541
$391$	6.03721	0.305315
$392$	9.46187	0.477897
$393$	−6.30415	−0.318002
$394$	−15.6475	−0.788311
$395$	−1.70652	−0.0858645
$396$	3.40424	0.171069
$397$	2.21872	0.111354	0.0556771	−	0.998449i	$-0.482268\pi$
$397$	2.21872	0.111354	0.0556771	+	0.998449i	$0.482268\pi$
$398$	0.650290	0.0325961
$399$	−12.2876	−0.615147
$400$	11.3197	0.565983
$401$	−1.79468	−0.0896219	−0.0448110	−	0.998995i	$-0.514269\pi$
$401$	−1.79468	−0.0896219	−0.0448110	+	0.998995i	$0.514269\pi$
$402$	−14.3340	−0.714914
$403$	9.14718	0.455654
$404$	−9.84148	−0.489632
$405$	0.418864	0.0208135
$406$	2.32008	0.115144
$407$	−24.1972	−1.19941
$408$	18.5843	0.920060
$409$	−20.6359	−1.02038	−0.510190	−	0.860062i	$-0.670425\pi$
$409$	−20.6359	−1.02038	−0.510190	+	0.860062i	$0.670425\pi$
$410$	4.05857	0.200438
$411$	−11.1580	−0.550385
$412$	0.463140	0.0228173
$413$	18.8563	0.927857
$414$	−1.17088	−0.0575458
$415$	1.55574	0.0763684
$416$	−4.90847	−0.240658
$417$	−19.7370	−0.966526
$418$	39.2951	1.92198
$419$	−13.8247	−0.675379	−0.337689	−	0.941258i	$-0.609645\pi$
$419$	−13.8247	−0.675379	−0.337689	+	0.941258i	$0.609645\pi$
$420$	−0.522077	−0.0254747
$421$	8.29062	0.404060	0.202030	−	0.979379i	$-0.435246\pi$
$421$	8.29062	0.404060	0.202030	+	0.979379i	$0.435246\pi$
$422$	−20.5878	−1.00220
$423$	6.99741	0.340226
$424$	−15.7263	−0.763739
$425$	29.1269	1.41286
$426$	−8.55691	−0.414584
$427$	−9.50477	−0.459968
$428$	10.0599	0.486266
$429$	7.79146	0.376175
$430$	3.08049	0.148554
$431$	−28.2247	−1.35953	−0.679767	−	0.733428i	$-0.737919\pi$
$431$	−28.2247	−1.35953	−0.679767	+	0.733428i	$0.737919\pi$
$432$	−2.34626	−0.112884
$433$	2.28751	0.109931	0.0549654	−	0.998488i	$-0.482495\pi$
$433$	2.28751	0.109931	0.0549654	+	0.998488i	$0.482495\pi$
$434$	−14.7408	−0.707579
$435$	0.418864	0.0200830
$436$	1.82492	0.0873977
$437$	6.20121	0.296644
$438$	−5.40945	−0.258474
$439$	−9.84200	−0.469733	−0.234866	−	0.972028i	$-0.575465\pi$
$439$	−9.84200	−0.469733	−0.234866	+	0.972028i	$0.575465\pi$
$440$	6.97799	0.332663
$441$	−3.07374	−0.146369
$442$	10.1770	0.484072
$443$	−12.8680	−0.611376	−0.305688	−	0.952132i	$-0.598886\pi$
$443$	−12.8680	−0.611376	−0.305688	+	0.952132i	$0.598886\pi$
$444$	−2.81247	−0.133474
$445$	−0.229242	−0.0108671
$446$	−5.62973	−0.266575
$447$	22.6974	1.07355
$448$	17.2082	0.813010
$449$	11.4040	0.538189	0.269094	−	0.963114i	$-0.413276\pi$
$449$	11.4040	0.538189	0.269094	+	0.963114i	$0.413276\pi$
$450$	−5.64899	−0.266296
$451$	−44.7851	−2.10885
$452$	2.93308	0.137960
$453$	10.5126	0.493927
$454$	−10.5691	−0.496035
$455$	−1.19491	−0.0560180
$456$	19.0891	0.893930
$457$	−25.5939	−1.19723	−0.598617	−	0.801035i	$-0.704283\pi$
$457$	−25.5939	−1.19723	−0.598617	+	0.801035i	$0.704283\pi$
$458$	−10.9272	−0.510593
$459$	−6.03721	−0.281793
$460$	0.263478	0.0122847
$461$	35.5432	1.65541	0.827707	−	0.561161i	$-0.189645\pi$
$461$	35.5432	1.65541	0.827707	+	0.561161i	$0.189645\pi$
$462$	−12.5560	−0.584158
$463$	−8.53051	−0.396446	−0.198223	−	0.980157i	$-0.563517\pi$
$463$	−8.53051	−0.396446	−0.198223	+	0.980157i	$0.563517\pi$
$464$	−2.34626	−0.108922
$465$	−2.66127	−0.123414
$466$	1.86428	0.0863612
$467$	14.1441	0.654513	0.327257	−	0.944936i	$-0.393876\pi$
$467$	14.1441	0.654513	0.327257	+	0.944936i	$0.393876\pi$
$468$	0.905613	0.0418620
$469$	−24.2573	−1.12010
$470$	3.43182	0.158298
$471$	18.9413	0.872769
$472$	−29.2938	−1.34836
$473$	−33.9923	−1.56297
$474$	−4.77038	−0.219111
$475$	29.9181	1.37273
$476$	7.52485	0.344901
$477$	5.10879	0.233916
$478$	−17.4503	−0.798159
$479$	15.6742	0.716170	0.358085	−	0.933689i	$-0.383430\pi$
$479$	15.6742	0.716170	0.358085	+	0.933689i	$0.383430\pi$
$480$	1.42807	0.0651821
$481$	−6.43706	−0.293504
$482$	−16.7659	−0.763667
$483$	−1.98148	−0.0901604
$484$	−11.5040	−0.522908
$485$	−3.59652	−0.163310
$486$	1.17088	0.0531124
$487$	40.9182	1.85418	0.927091	−	0.374836i	$-0.122301\pi$
$487$	40.9182	1.85418	0.927091	+	0.374836i	$0.122301\pi$
$488$	14.7660	0.668423
$489$	1.36439	0.0617000
$490$	−1.50749	−0.0681015
$491$	23.9426	1.08052	0.540258	−	0.841500i	$-0.318327\pi$
$491$	23.9426	1.08052	0.540258	+	0.841500i	$0.318327\pi$
$492$	−5.20544	−0.234679
$493$	−6.03721	−0.271902
$494$	10.4535	0.470325
$495$	−2.26684	−0.101887
$496$	14.9071	0.669348
$497$	−14.4808	−0.649553
$498$	4.34889	0.194878
$499$	−17.0774	−0.764489	−0.382244	−	0.924061i	$-0.624849\pi$
$499$	−17.0774	−0.764489	−0.382244	+	0.924061i	$0.624849\pi$
$500$	2.58856	0.115764
$501$	14.9947	0.669913
$502$	8.10123	0.361575
$503$	−24.9975	−1.11458	−0.557291	−	0.830317i	$-0.688159\pi$
$503$	−24.9975	−1.11458	−0.557291	+	0.830317i	$0.688159\pi$
$504$	−6.09957	−0.271696
$505$	6.55333	0.291619
$506$	6.33668	0.281700
$507$	−10.9273	−0.485297
$508$	−1.54433	−0.0685184
$509$	−30.2846	−1.34234	−0.671170	−	0.741303i	$-0.734208\pi$
$509$	−30.2846	−1.34234	−0.671170	+	0.741303i	$0.734208\pi$
$510$	−2.96090	−0.131111
$511$	−9.15438	−0.404966
$512$	−22.4442	−0.991904
$513$	−6.20121	−0.273790
$514$	25.9943	1.14656
$515$	−0.308399	−0.0135897
$516$	−3.95098	−0.173932
$517$	−37.8691	−1.66548
$518$	10.3734	0.455780
$519$	−24.0572	−1.05599
$520$	1.85632	0.0814052
$521$	−32.0208	−1.40286	−0.701429	−	0.712740i	$-0.747454\pi$
$521$	−32.0208	−1.40286	−0.701429	+	0.712740i	$0.747454\pi$
$522$	1.17088	0.0512482
$523$	−22.1259	−0.967500	−0.483750	−	0.875206i	$-0.660726\pi$
$523$	−22.1259	−0.967500	−0.483750	+	0.875206i	$0.660726\pi$
$524$	3.96550	0.173234
$525$	−9.55975	−0.417222
$526$	23.4522	1.02256
$527$	38.3577	1.67089
$528$	12.6977	0.552595
$529$	1.00000	0.0434783
$530$	2.50556	0.108835
$531$	9.51627	0.412971
$532$	7.72925	0.335105
$533$	−11.9140	−0.516052
$534$	−0.640818	−0.0277309
$535$	−6.69880	−0.289614
$536$	37.6845	1.62772
$537$	−15.0638	−0.650050
$538$	20.7315	0.893797
$539$	16.6347	0.716508
$540$	−0.263478	−0.0113383
$541$	15.9859	0.687289	0.343645	−	0.939100i	$-0.388338\pi$
$541$	15.9859	0.687289	0.343645	+	0.939100i	$0.388338\pi$
$542$	27.6180	1.18630
$543$	−4.16684	−0.178816
$544$	−20.5832	−0.882496
$545$	−1.21519	−0.0520531
$546$	−3.34021	−0.142948
$547$	−9.89012	−0.422871	−0.211436	−	0.977392i	$-0.567814\pi$
$547$	−9.89012	−0.422871	−0.211436	+	0.977392i	$0.567814\pi$
$548$	7.01873	0.299825
$549$	−4.79680	−0.204723
$550$	30.5717	1.30358
$551$	−6.20121	−0.264180
$552$	3.07829	0.131021
$553$	−8.07288	−0.343294
$554$	11.4762	0.487576
$555$	1.87279	0.0794956
$556$	12.4152	0.526521
$557$	−13.0049	−0.551036	−0.275518	−	0.961296i	$-0.588849\pi$
$557$	−13.0049	−0.551036	−0.275518	+	0.961296i	$0.588849\pi$
$558$	−7.43927	−0.314929
$559$	−9.04282	−0.382470
$560$	−1.94733	−0.0822895
$561$	32.6727	1.37944
$562$	−32.1320	−1.35541
$563$	−45.4359	−1.91490	−0.957448	−	0.288606i	$-0.906808\pi$
$563$	−45.4359	−1.91490	−0.957448	+	0.288606i	$0.906808\pi$
$564$	−4.40158	−0.185340
$565$	−1.95310	−0.0821676
$566$	0.0957970	0.00402665
$567$	1.98148	0.0832143
$568$	22.4964	0.943927
$569$	33.2297	1.39306	0.696530	−	0.717527i	$-0.254726\pi$
$569$	33.2297	1.39306	0.696530	+	0.717527i	$0.254726\pi$
$570$	−3.04133	−0.127387
$571$	−2.25155	−0.0942246	−0.0471123	−	0.998890i	$-0.515002\pi$
$571$	−2.25155	−0.0942246	−0.0471123	+	0.998890i	$0.515002\pi$
$572$	−4.90106	−0.204924
$573$	21.6210	0.903229
$574$	19.1995	0.801370
$575$	4.82455	0.201198
$576$	8.68451	0.361855
$577$	30.7244	1.27907	0.639537	−	0.768760i	$-0.279126\pi$
$577$	30.7244	1.27907	0.639537	+	0.768760i	$0.279126\pi$
$578$	22.7713	0.947162
$579$	20.6563	0.858448
$580$	−0.263478	−0.0109403
$581$	7.35960	0.305327
$582$	−10.0536	−0.416737
$583$	−27.6482	−1.14507
$584$	14.2216	0.588495
$585$	−0.603037	−0.0249325
$586$	18.1657	0.750420
$587$	11.0766	0.457180	0.228590	−	0.973523i	$-0.426589\pi$
$587$	11.0766	0.457180	0.228590	+	0.973523i	$0.426589\pi$
$588$	1.93348	0.0797353
$589$	39.3997	1.62344
$590$	4.66717	0.192145
$591$	−13.3639	−0.549716
$592$	−10.4904	−0.431153
$593$	−0.411473	−0.0168972	−0.00844860	−	0.999964i	$-0.502689\pi$
$593$	−0.411473	−0.0168972	−0.00844860	+	0.999964i	$0.502689\pi$
$594$	−6.33668	−0.259997
$595$	−5.01071	−0.205419
$596$	−14.2774	−0.584824
$597$	0.555384	0.0227303
$598$	1.68572	0.0689341
$599$	−16.1494	−0.659845	−0.329923	−	0.944008i	$-0.607023\pi$
$599$	−16.1494	−0.659845	−0.329923	+	0.944008i	$0.607023\pi$
$600$	14.8514	0.606305
$601$	4.83308	0.197146	0.0985728	−	0.995130i	$-0.468572\pi$
$601$	4.83308	0.197146	0.0985728	+	0.995130i	$0.468572\pi$
$602$	14.5726	0.593934
$603$	−12.2420	−0.498534
$604$	−6.61277	−0.269070
$605$	7.66036	0.311438
$606$	18.3190	0.744160
$607$	28.1431	1.14229	0.571147	−	0.820848i	$-0.306499\pi$
$607$	28.1431	1.14229	0.571147	+	0.820848i	$0.306499\pi$
$608$	−21.1423	−0.857433
$609$	1.98148	0.0802936
$610$	−2.35255	−0.0952520
$611$	−10.0741	−0.407556
$612$	3.79759	0.153509
$613$	−7.28446	−0.294216	−0.147108	−	0.989120i	$-0.546997\pi$
$613$	−7.28446	−0.294216	−0.147108	+	0.989120i	$0.546997\pi$
$614$	−36.9526	−1.49129
$615$	3.46624	0.139772
$616$	33.0101	1.33001
$617$	−49.2391	−1.98229	−0.991145	−	0.132782i	$-0.957609\pi$
$617$	−49.2391	−1.98229	−0.991145	+	0.132782i	$0.957609\pi$
$618$	−0.862093	−0.0346785
$619$	14.5176	0.583513	0.291757	−	0.956493i	$-0.405760\pi$
$619$	14.5176	0.583513	0.291757	+	0.956493i	$0.405760\pi$
$620$	1.67402	0.0672303
$621$	−1.00000	−0.0401286
$622$	6.43603	0.258061
$623$	−1.08445	−0.0434476
$624$	3.37790	0.135224
$625$	22.3991	0.895963
$626$	−29.1739	−1.16602
$627$	33.5602	1.34026
$628$	−11.9147	−0.475446
$629$	−26.9931	−1.07629
$630$	0.971799	0.0387174
$631$	2.60365	0.103649	0.0518247	−	0.998656i	$-0.483496\pi$
$631$	2.60365	0.103649	0.0518247	+	0.998656i	$0.483496\pi$
$632$	12.5415	0.498873
$633$	−17.5831	−0.698866
$634$	−21.1918	−0.841635
$635$	1.02835	0.0408088
$636$	−3.21359	−0.127427
$637$	4.42526	0.175335
$638$	−6.33668	−0.250872
$639$	−7.30808	−0.289103
$640$	1.40311	0.0554627
$641$	−3.11790	−0.123150	−0.0615749	−	0.998102i	$-0.519612\pi$
$641$	−3.11790	−0.123150	−0.0615749	+	0.998102i	$0.519612\pi$
$642$	−18.7257	−0.739044
$643$	−46.1556	−1.82020	−0.910100	−	0.414390i	$-0.863995\pi$
$643$	−46.1556	−1.82020	−0.910100	+	0.414390i	$0.863995\pi$
$644$	1.24641	0.0491154
$645$	2.63091	0.103592
$646$	43.8356	1.72469
$647$	22.7429	0.894114	0.447057	−	0.894505i	$-0.352472\pi$
$647$	22.7429	0.894114	0.447057	+	0.894505i	$0.352472\pi$
$648$	−3.07829	−0.120927
$649$	−51.5009	−2.02159
$650$	8.13283	0.318996
$651$	−12.5894	−0.493418
$652$	−0.858245	−0.0336115
$653$	4.52151	0.176940	0.0884701	−	0.996079i	$-0.471802\pi$
$653$	4.52151	0.176940	0.0884701	+	0.996079i	$0.471802\pi$
$654$	−3.39692	−0.132830
$655$	−2.64058	−0.103176
$656$	−19.4161	−0.758071
$657$	−4.61997	−0.180242
$658$	16.2346	0.632889
$659$	10.2697	0.400050	0.200025	−	0.979791i	$-0.435898\pi$
$659$	10.2697	0.400050	0.200025	+	0.979791i	$0.435898\pi$
$660$	1.42591	0.0555036
$661$	8.53689	0.332047	0.166023	−	0.986122i	$-0.446907\pi$
$661$	8.53689	0.332047	0.166023	+	0.986122i	$0.446907\pi$
$662$	23.4093	0.909829
$663$	8.69176	0.337560
$664$	−11.4334	−0.443701
$665$	−5.14682	−0.199585
$666$	5.23516	0.202859
$667$	−1.00000	−0.0387202
$668$	−9.43211	−0.364939
$669$	−4.80810	−0.185892
$670$	−6.00399	−0.231955
$671$	25.9597	1.00216
$672$	6.75562	0.260604
$673$	11.0930	0.427605	0.213803	−	0.976877i	$-0.431415\pi$
$673$	11.0930	0.427605	0.213803	+	0.976877i	$0.431415\pi$
$674$	7.08468	0.272892
$675$	−4.82455	−0.185697
$676$	6.87359	0.264369
$677$	12.0257	0.462186	0.231093	−	0.972932i	$-0.425770\pi$
$677$	12.0257	0.462186	0.231093	+	0.972932i	$0.425770\pi$
$678$	−5.45966	−0.209677
$679$	−17.0137	−0.652926
$680$	7.78430	0.298514
$681$	−9.02664	−0.345902
$682$	40.2604	1.54165
$683$	36.4023	1.39289	0.696447	−	0.717608i	$-0.254763\pi$
$683$	36.4023	1.39289	0.696447	+	0.717608i	$0.254763\pi$
$684$	3.90075	0.149149
$685$	−4.67369	−0.178573
$686$	−23.3719	−0.892344
$687$	−9.33240	−0.356053
$688$	−14.7370	−0.561843
$689$	−7.35511	−0.280207
$690$	−0.490441	−0.0186708
$691$	42.5117	1.61722	0.808611	−	0.588344i	$-0.200220\pi$
$691$	42.5117	1.61722	0.808611	+	0.588344i	$0.200220\pi$
$692$	15.1327	0.575258
$693$	−10.7235	−0.407353
$694$	−6.16221	−0.233914
$695$	−8.26713	−0.313590
$696$	−3.07829	−0.116682
$697$	−49.9600	−1.89237
$698$	−17.1106	−0.647646
$699$	1.59220	0.0602226
$700$	6.01337	0.227284
$701$	25.5766	0.966016	0.483008	−	0.875616i	$-0.339544\pi$
$701$	25.5766	0.966016	0.483008	+	0.875616i	$0.339544\pi$
$702$	−1.68572	−0.0636233
$703$	−27.7264	−1.04572
$704$	−46.9995	−1.77136
$705$	2.93096	0.110386
$706$	−25.3965	−0.955809
$707$	31.0012	1.16592
$708$	−5.98603	−0.224969
$709$	35.7447	1.34242	0.671210	−	0.741267i	$-0.265775\pi$
$709$	35.7447	1.34242	0.671210	+	0.741267i	$0.265775\pi$
$710$	−3.58418	−0.134512
$711$	−4.07417	−0.152793
$712$	1.68473	0.0631379
$713$	6.35355	0.237942
$714$	−14.0068	−0.524192
$715$	3.26356	0.122050
$716$	9.47557	0.354119
$717$	−14.9035	−0.556583
$718$	16.1041	0.601001
$719$	−10.3233	−0.384994	−0.192497	−	0.981298i	$-0.561659\pi$
$719$	−10.3233	−0.384994	−0.192497	+	0.981298i	$0.561659\pi$
$720$	−0.982764	−0.0366255
$721$	−1.45891	−0.0543328
$722$	22.7795	0.847766
$723$	−14.3190	−0.532530
$724$	2.62107	0.0974113
$725$	−4.82455	−0.179179
$726$	21.4136	0.794734
$727$	−35.6565	−1.32243	−0.661213	−	0.750199i	$-0.729958\pi$
$727$	−35.6565	−1.32243	−0.661213	+	0.750199i	$0.729958\pi$
$728$	8.78152	0.325465
$729$	1.00000	0.0370370
$730$	−2.26583	−0.0838620
$731$	−37.9201	−1.40253
$732$	3.01734	0.111524
$733$	32.2388	1.19077	0.595385	−	0.803441i	$-0.297000\pi$
$733$	32.2388	1.19077	0.595385	+	0.803441i	$0.297000\pi$
$734$	−29.5335	−1.09010
$735$	−1.28748	−0.0474894
$736$	−3.40938	−0.125671
$737$	66.2523	2.44044
$738$	9.68946	0.356674
$739$	−0.631756	−0.0232395	−0.0116198	−	0.999932i	$-0.503699\pi$
$739$	−0.631756	−0.0232395	−0.0116198	+	0.999932i	$0.503699\pi$
$740$	−1.17804	−0.0433057
$741$	8.92786	0.327973
$742$	11.8528	0.435131
$743$	−19.9139	−0.730570	−0.365285	−	0.930896i	$-0.619028\pi$
$743$	−19.9139	−0.730570	−0.365285	+	0.930896i	$0.619028\pi$
$744$	19.5581	0.717033
$745$	9.50714	0.348315
$746$	14.2906	0.523217
$747$	3.71419	0.135895
$748$	−20.5521	−0.751459
$749$	−31.6893	−1.15790
$750$	−4.81837	−0.175942
$751$	−26.2402	−0.957517	−0.478759	−	0.877947i	$-0.658913\pi$
$751$	−26.2402	−0.957517	−0.478759	+	0.877947i	$0.658913\pi$
$752$	−16.4177	−0.598693
$753$	6.91890	0.252139
$754$	−1.68572	−0.0613902
$755$	4.40337	0.160255
$756$	−1.24641	−0.0453315
$757$	−20.9477	−0.761357	−0.380679	−	0.924707i	$-0.624310\pi$
$757$	−20.9477	−0.761357	−0.380679	+	0.924707i	$0.624310\pi$
$758$	−28.6122	−1.03924
$759$	5.41188	0.196439
$760$	7.99575	0.290036
$761$	−16.9578	−0.614720	−0.307360	−	0.951593i	$-0.599446\pi$
$761$	−16.9578	−0.614720	−0.307360	+	0.951593i	$0.599446\pi$
$762$	2.87463	0.104137
$763$	−5.74858	−0.208113
$764$	−13.6003	−0.492040
$765$	−2.52877	−0.0914280
$766$	−1.44544	−0.0522259
$767$	−13.7005	−0.494698
$768$	−13.4468	−0.485220
$769$	−14.0287	−0.505889	−0.252944	−	0.967481i	$-0.581399\pi$
$769$	−14.0287	−0.505889	−0.252944	+	0.967481i	$0.581399\pi$
$770$	−5.25926	−0.189530
$771$	22.2006	0.799535
$772$	−12.9935	−0.467645
$773$	−6.44609	−0.231850	−0.115925	−	0.993258i	$-0.536983\pi$
$773$	−6.44609	−0.231850	−0.115925	+	0.993258i	$0.536983\pi$
$774$	7.35439	0.264348
$775$	30.6530	1.10109
$776$	26.4313	0.948830
$777$	8.85943	0.317830
$778$	22.8861	0.820507
$779$	−51.3171	−1.83863
$780$	0.379329	0.0135821
$781$	39.5504	1.41523
$782$	7.06888	0.252783
$783$	1.00000	0.0357371
$784$	7.21180	0.257564
$785$	7.93383	0.283170
$786$	−7.38143	−0.263287
$787$	33.2754	1.18614	0.593069	−	0.805151i	$-0.297916\pi$
$787$	33.2754	1.18614	0.593069	+	0.805151i	$0.297916\pi$
$788$	8.40627	0.299461
$789$	20.0295	0.713068
$790$	−1.99814	−0.0710907
$791$	−9.23934	−0.328513
$792$	16.6593	0.591963
$793$	6.90594	0.245237
$794$	2.59786	0.0921946
$795$	2.13989	0.0758941
$796$	−0.349353	−0.0123825
$797$	17.1250	0.606600	0.303300	−	0.952895i	$-0.401912\pi$
$797$	17.1250	0.606600	0.303300	+	0.952895i	$0.401912\pi$
$798$	−14.3873	−0.509305
$799$	−42.2449	−1.49452
$800$	−16.4487	−0.581551
$801$	−0.547294	−0.0193377
$802$	−2.10136	−0.0742016
$803$	25.0027	0.882327
$804$	7.70060	0.271579
$805$	−0.829970	−0.0292526
$806$	10.7103	0.377254
$807$	17.7058	0.623275
$808$	−48.1613	−1.69431
$809$	24.7592	0.870487	0.435244	−	0.900313i	$-0.356662\pi$
$809$	24.7592	0.870487	0.435244	+	0.900313i	$0.356662\pi$
$810$	0.490441	0.0172324
$811$	56.3750	1.97959	0.989797	−	0.142481i	$-0.0455081\pi$
$811$	56.3750	1.97959	0.989797	+	0.142481i	$0.0455081\pi$
$812$	−1.24641	−0.0437404
$813$	23.5873	0.827244
$814$	−28.3321	−0.993038
$815$	0.571495	0.0200186
$816$	14.1649	0.495870
$817$	−38.9501	−1.36269
$818$	−24.1622	−0.844813
$819$	−2.85273	−0.0996824
$820$	−2.18037	−0.0761419
$821$	29.7906	1.03970	0.519849	−	0.854258i	$-0.325988\pi$
$821$	29.7906	1.03970	0.519849	+	0.854258i	$0.325988\pi$
$822$	−13.0647	−0.455685
$823$	−23.2267	−0.809631	−0.404816	−	0.914398i	$-0.632664\pi$
$823$	−23.2267	−0.809631	−0.404816	+	0.914398i	$0.632664\pi$
$824$	2.26647	0.0789562
$825$	26.1099	0.909030
$826$	22.0785	0.768210
$827$	39.9652	1.38973	0.694863	−	0.719142i	$-0.255465\pi$
$827$	39.9652	1.38973	0.694863	+	0.719142i	$0.255465\pi$
$828$	0.629030	0.0218603
$829$	−12.4272	−0.431614	−0.215807	−	0.976436i	$-0.569238\pi$
$829$	−12.4272	−0.431614	−0.215807	+	0.976436i	$0.569238\pi$
$830$	1.82159	0.0632285
$831$	9.80130	0.340003
$832$	−12.5031	−0.433466
$833$	18.5568	0.642957
$834$	−23.1098	−0.800225
$835$	6.28073	0.217354
$836$	−21.1104	−0.730117
$837$	−6.35355	−0.219611
$838$	−16.1871	−0.559173
$839$	−14.5525	−0.502409	−0.251205	−	0.967934i	$-0.580827\pi$
$839$	−14.5525	−0.502409	−0.251205	+	0.967934i	$0.580827\pi$
$840$	−2.55489	−0.0881521
$841$	1.00000	0.0344828
$842$	9.70735	0.334537
$843$	−27.4425	−0.945171
$844$	11.0603	0.380712
$845$	−4.57704	−0.157455
$846$	8.19315	0.281686
$847$	36.2381	1.24516
$848$	−11.9866	−0.411620
$849$	0.0818159	0.00280792
$850$	34.1042	1.16976
$851$	−4.47112	−0.153268
$852$	4.59700	0.157491
$853$	−12.2748	−0.420280	−0.210140	−	0.977671i	$-0.567392\pi$
$853$	−12.2748	−0.420280	−0.210140	+	0.977671i	$0.567392\pi$
$854$	−11.1290	−0.380826
$855$	−2.59746	−0.0888314
$856$	49.2304	1.68266
$857$	−56.8515	−1.94201	−0.971005	−	0.239059i	$-0.923161\pi$
$857$	−56.8515	−1.94201	−0.971005	+	0.239059i	$0.923161\pi$
$858$	9.12290	0.311451
$859$	11.8379	0.403902	0.201951	−	0.979396i	$-0.435272\pi$
$859$	11.8379	0.403902	0.201951	+	0.979396i	$0.435272\pi$
$860$	−1.65492	−0.0564324
$861$	16.3974	0.558822
$862$	−33.0478	−1.12561
$863$	24.4196	0.831252	0.415626	−	0.909536i	$-0.363563\pi$
$863$	24.4196	0.831252	0.415626	+	0.909536i	$0.363563\pi$
$864$	3.40938	0.115990
$865$	−10.0767	−0.342617
$866$	2.67841	0.0910161
$867$	19.4480	0.660487
$868$	7.91913	0.268793
$869$	22.0489	0.747958
$870$	0.490441	0.0166275
$871$	17.6248	0.597193
$872$	8.93061	0.302429
$873$	−8.58637	−0.290605
$874$	7.26090	0.245603
$875$	−8.15409	−0.275658
$876$	2.90610	0.0981882
$877$	−32.9055	−1.11114	−0.555570	−	0.831470i	$-0.687500\pi$
$877$	−32.9055	−1.11114	−0.555570	+	0.831470i	$0.687500\pi$
$878$	−11.5238	−0.388911
$879$	15.5146	0.523293
$880$	5.31860	0.179290
$881$	32.6832	1.10113	0.550563	−	0.834794i	$-0.314413\pi$
$881$	32.6832	1.10113	0.550563	+	0.834794i	$0.314413\pi$
$882$	−3.59900	−0.121185
$883$	14.0627	0.473247	0.236624	−	0.971601i	$-0.423959\pi$
$883$	14.0627	0.473247	0.236624	+	0.971601i	$0.423959\pi$
$884$	−5.46738	−0.183888
$885$	3.98603	0.133989
$886$	−15.0669	−0.506182
$887$	32.0083	1.07473	0.537367	−	0.843348i	$-0.319419\pi$
$887$	32.0083	1.07473	0.537367	+	0.843348i	$0.319419\pi$
$888$	−13.7634	−0.461870
$889$	4.86471	0.163157
$890$	−0.268416	−0.00899731
$891$	−5.41188	−0.181305
$892$	3.02444	0.101266
$893$	−43.3924	−1.45207
$894$	26.5761	0.888836
$895$	−6.30967	−0.210909
$896$	6.63754	0.221745
$897$	1.43970	0.0480701
$898$	13.3528	0.445588
$899$	−6.35355	−0.211903
$900$	3.03479	0.101160
$901$	−30.8429	−1.02753
$902$	−52.4382	−1.74600
$903$	12.4458	0.414170
$904$	14.3536	0.477394
$905$	−1.74534	−0.0580171
$906$	12.3091	0.408942
$907$	15.8519	0.526355	0.263177	−	0.964747i	$-0.415230\pi$
$907$	15.8519	0.526355	0.263177	+	0.964747i	$0.415230\pi$
$908$	5.67803	0.188432
$909$	15.6455	0.518928
$910$	−1.39910	−0.0463796
$911$	−18.8578	−0.624786	−0.312393	−	0.949953i	$-0.601131\pi$
$911$	−18.8578	−0.624786	−0.312393	+	0.949953i	$0.601131\pi$
$912$	14.5496	0.481787
$913$	−20.1008	−0.665238
$914$	−29.9675	−0.991238
$915$	−2.00921	−0.0664224
$916$	5.87036	0.193962
$917$	−12.4915	−0.412507
$918$	−7.06888	−0.233308
$919$	−54.8856	−1.81051	−0.905254	−	0.424870i	$-0.860320\pi$
$919$	−54.8856	−1.81051	−0.905254	+	0.424870i	$0.860320\pi$
$920$	1.28939	0.0425098
$921$	−31.5596	−1.03992
$922$	41.6170	1.37058
$923$	10.5214	0.346317
$924$	6.74542	0.221908
$925$	−21.5712	−0.709255
$926$	−9.98824	−0.328234
$927$	−0.736275	−0.0241825
$928$	3.40938	0.111918
$929$	29.6410	0.972488	0.486244	−	0.873823i	$-0.338367\pi$
$929$	29.6410	0.972488	0.486244	+	0.873823i	$0.338367\pi$
$930$	−3.11604	−0.102179
$931$	19.0609	0.624696
$932$	−1.00154	−0.0328066
$933$	5.49672	0.179955
$934$	16.5612	0.541898
$935$	13.6854	0.447561
$936$	4.43180	0.144858
$937$	7.03873	0.229945	0.114973	−	0.993369i	$-0.463322\pi$
$937$	7.03873	0.229945	0.114973	+	0.993369i	$0.463322\pi$
$938$	−28.4025	−0.927374
$939$	−24.9161	−0.813106
$940$	−1.84367	−0.0601337
$941$	−19.4424	−0.633804	−0.316902	−	0.948458i	$-0.602643\pi$
$941$	−19.4424	−0.633804	−0.316902	+	0.948458i	$0.602643\pi$
$942$	22.1781	0.722600
$943$	−8.27534	−0.269482
$944$	−22.3277	−0.726703
$945$	0.829970	0.0269989
$946$	−39.8011	−1.29404
$947$	−60.2582	−1.95813	−0.979065	−	0.203550i	$-0.934752\pi$
$947$	−60.2582	−1.95813	−0.979065	+	0.203550i	$0.934752\pi$
$948$	2.56278	0.0832351
$949$	6.65136	0.215912
$950$	35.0306	1.13654
$951$	−18.0990	−0.586900
$952$	36.8244	1.19349
$953$	34.8557	1.12909	0.564543	−	0.825404i	$-0.309052\pi$
$953$	34.8557	1.12909	0.564543	+	0.825404i	$0.309052\pi$
$954$	5.98180	0.193668
$955$	9.05625	0.293053
$956$	9.37479	0.303202
$957$	−5.41188	−0.174941
$958$	18.3526	0.592946
$959$	−22.1094	−0.713949
$960$	3.63763	0.117404
$961$	9.36758	0.302180
$962$	−7.53705	−0.243004
$963$	−15.9928	−0.515360
$964$	9.00710	0.290099
$965$	8.65220	0.278524
$966$	−2.32008	−0.0746474
$967$	−50.9108	−1.63718	−0.818591	−	0.574377i	$-0.805245\pi$
$967$	−50.9108	−1.63718	−0.818591	+	0.574377i	$0.805245\pi$
$968$	−56.2970	−1.80946
$969$	37.4380	1.20268
$970$	−4.21111	−0.135211
$971$	9.00540	0.288997	0.144498	−	0.989505i	$-0.453843\pi$
$971$	9.00540	0.288997	0.144498	+	0.989505i	$0.453843\pi$
$972$	−0.629030	−0.0201762
$973$	−39.1085	−1.25376
$974$	47.9105	1.53515
$975$	6.94589	0.222447
$976$	11.2546	0.360249
$977$	−13.1636	−0.421142	−0.210571	−	0.977579i	$-0.567532\pi$
$977$	−13.1636	−0.421142	−0.210571	+	0.977579i	$0.567532\pi$
$978$	1.59755	0.0510839
$979$	2.96189	0.0946624
$980$	0.809864	0.0258702
$981$	−2.90116	−0.0926269
$982$	28.0340	0.894602
$983$	−49.6509	−1.58362	−0.791809	−	0.610769i	$-0.790861\pi$
$983$	−49.6509	−1.58362	−0.791809	+	0.610769i	$0.790861\pi$
$984$	−25.4739	−0.812078
$985$	−5.59764	−0.178356
$986$	−7.06888	−0.225119
$987$	13.8652	0.441335
$988$	−5.61589	−0.178665
$989$	−6.28106	−0.199726
$990$	−2.65421	−0.0843563
$991$	−11.4473	−0.363634	−0.181817	−	0.983332i	$-0.558198\pi$
$991$	−11.4473	−0.363634	−0.181817	+	0.983332i	$0.558198\pi$
$992$	−21.6617	−0.687759
$993$	19.9928	0.634454
$994$	−16.9553	−0.537791
$995$	0.232630	0.00737488
$996$	−2.33634	−0.0740298
$997$	−3.23372	−0.102413	−0.0512064	−	0.998688i	$-0.516307\pi$
$997$	−3.23372	−0.102413	−0.0512064	+	0.998688i	$0.516307\pi$
$998$	−19.9956	−0.632951
$999$	4.47112	0.141460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.j.1.5	✓	7
3.2	odd	2		6003.2.a.i.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.j.1.5	✓	7	1.1	even	1	trivial
6003.2.a.i.1.3		7	3.2	odd	2

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+1.17088 q^{2} +1.00000 q^{3} -0.629030 q^{4} +0.418864 q^{5} +1.17088 q^{6} +1.98148 q^{7} -3.07829 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.17088 q^{2} +1.00000 q^{3} -0.629030 q^{4} +0.418864 q^{5} +1.17088 q^{6} +1.98148 q^{7} -3.07829 q^{8} +1.00000 q^{9} +0.490441 q^{10} -5.41188 q^{11} -0.629030 q^{12} -1.43970 q^{13} +2.32008 q^{14} +0.418864 q^{15} -2.34626 q^{16} -6.03721 q^{17} +1.17088 q^{18} -6.20121 q^{19} -0.263478 q^{20} +1.98148 q^{21} -6.33668 q^{22} -1.00000 q^{23} -3.07829 q^{24} -4.82455 q^{25} -1.68572 q^{26} +1.00000 q^{27} -1.24641 q^{28} +1.00000 q^{29} +0.490441 q^{30} -6.35355 q^{31} +3.40938 q^{32} -5.41188 q^{33} -7.06888 q^{34} +0.829970 q^{35} -0.629030 q^{36} +4.47112 q^{37} -7.26090 q^{38} -1.43970 q^{39} -1.28939 q^{40} +8.27534 q^{41} +2.32008 q^{42} +6.28106 q^{43} +3.40424 q^{44} +0.418864 q^{45} -1.17088 q^{46} +6.99741 q^{47} -2.34626 q^{48} -3.07374 q^{49} -5.64899 q^{50} -6.03721 q^{51} +0.905613 q^{52} +5.10879 q^{53} +1.17088 q^{54} -2.26684 q^{55} -6.09957 q^{56} -6.20121 q^{57} +1.17088 q^{58} +9.51627 q^{59} -0.263478 q^{60} -4.79680 q^{61} -7.43927 q^{62} +1.98148 q^{63} +8.68451 q^{64} -0.603037 q^{65} -6.33668 q^{66} -12.2420 q^{67} +3.79759 q^{68} -1.00000 q^{69} +0.971799 q^{70} -7.30808 q^{71} -3.07829 q^{72} -4.61997 q^{73} +5.23516 q^{74} -4.82455 q^{75} +3.90075 q^{76} -10.7235 q^{77} -1.68572 q^{78} -4.07417 q^{79} -0.982764 q^{80} +1.00000 q^{81} +9.68946 q^{82} +3.71419 q^{83} -1.24641 q^{84} -2.52877 q^{85} +7.35439 q^{86} +1.00000 q^{87} +16.6593 q^{88} -0.547294 q^{89} +0.490441 q^{90} -2.85273 q^{91} +0.629030 q^{92} -6.35355 q^{93} +8.19315 q^{94} -2.59746 q^{95} +3.40938 q^{96} -8.58637 q^{97} -3.59900 q^{98} -5.41188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9	\( 7 q - q^{2} + 7 q^{3} + 7 q^{4} - 5 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 7 q^{9} - 11 q^{10} - 12 q^{11} + 7 q^{12} - 13 q^{13} - 3 q^{14} - 5 q^{15} - 13 q^{16} - 12 q^{17} - q^{18} - 5 q^{19} - 8 q^{20} - 5 q^{21} - q^{22} - 7 q^{23} + 3 q^{24} - 4 q^{25} + 2 q^{26} + 7 q^{27} - 21 q^{28} + 7 q^{29} - 11 q^{30} - 8 q^{31} - 5 q^{32} - 12 q^{33} - 28 q^{34} + 5 q^{35} + 7 q^{36} - 24 q^{37} - 6 q^{38} - 13 q^{39} - 20 q^{40} + 9 q^{41} - 3 q^{42} - q^{43} - 23 q^{44} - 5 q^{45} + q^{46} + 27 q^{47} - 13 q^{48} - 14 q^{49} + 7 q^{50} - 12 q^{51} - 9 q^{52} - q^{53} - q^{54} - 11 q^{55} - 20 q^{56} - 5 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + q^{61} - 5 q^{63} + 3 q^{64} + 12 q^{65} - q^{66} - 16 q^{67} + 15 q^{68} - 7 q^{69} + 40 q^{70} - 13 q^{71} + 3 q^{72} - 23 q^{73} - 8 q^{74} - 4 q^{75} - 2 q^{76} + 13 q^{77} + 2 q^{78} - 44 q^{79} + 30 q^{80} + 7 q^{81} - 10 q^{82} + 21 q^{83} - 21 q^{84} + 6 q^{86} + 7 q^{87} + 21 q^{88} - 5 q^{89} - 11 q^{90} - 18 q^{91} - 7 q^{92} - 8 q^{93} + 28 q^{94} + 9 q^{95} - 5 q^{96} - 55 q^{97} + 36 q^{98} - 12 q^{99}+O(q^{100}) \) 7 * q - q^2 + 7 * q^3 + 7 * q^4 - 5 * q^5 - q^6 - 5 * q^7 + 3 * q^8 + 7 * q^9 - 11 * q^10 - 12 * q^11 + 7 * q^12 - 13 * q^13 - 3 * q^14 - 5 * q^15 - 13 * q^16 - 12 * q^17 - q^18 - 5 * q^19 - 8 * q^20 - 5 * q^21 - q^22 - 7 * q^23 + 3 * q^24 - 4 * q^25 + 2 * q^26 + 7 * q^27 - 21 * q^28 + 7 * q^29 - 11 * q^30 - 8 * q^31 - 5 * q^32 - 12 * q^33 - 28 * q^34 + 5 * q^35 + 7 * q^36 - 24 * q^37 - 6 * q^38 - 13 * q^39 - 20 * q^40 + 9 * q^41 - 3 * q^42 - q^43 - 23 * q^44 - 5 * q^45 + q^46 + 27 * q^47 - 13 * q^48 - 14 * q^49 + 7 * q^50 - 12 * q^51 - 9 * q^52 - q^53 - q^54 - 11 * q^55 - 20 * q^56 - 5 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + q^61 - 5 * q^63 + 3 * q^64 + 12 * q^65 - q^66 - 16 * q^67 + 15 * q^68 - 7 * q^69 + 40 * q^70 - 13 * q^71 + 3 * q^72 - 23 * q^73 - 8 * q^74 - 4 * q^75 - 2 * q^76 + 13 * q^77 + 2 * q^78 - 44 * q^79 + 30 * q^80 + 7 * q^81 - 10 * q^82 + 21 * q^83 - 21 * q^84 + 6 * q^86 + 7 * q^87 + 21 * q^88 - 5 * q^89 - 11 * q^90 - 18 * q^91 - 7 * q^92 - 8 * q^93 + 28 * q^94 + 9 * q^95 - 5 * q^96 - 55 * q^97 + 36 * q^98 - 12 * q^99

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