LMFDB - Embedded newform 4026.2.a.z.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1477718538$
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} - 18x^{5} - 10x^{4} + 91x^{3} + 90x^{2} - 66x - 56 $ x^7 - 18x^5 - 10x^4 + 91x^3 + 90x^2 - 66*x - 56
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.868643$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.19576 q^{5} +1.00000 q^{6} -0.720188 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.19576 q^{5} +1.00000 q^{6} -0.720188 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.19576 q^{10} +1.00000 q^{11} -1.00000 q^{12} +5.69929 q^{13} +0.720188 q^{14} +2.19576 q^{15} +1.00000 q^{16} +4.45702 q^{17} -1.00000 q^{18} -5.59557 q^{19} -2.19576 q^{20} +0.720188 q^{21} -1.00000 q^{22} +9.41599 q^{23} +1.00000 q^{24} -0.178658 q^{25} -5.69929 q^{26} -1.00000 q^{27} -0.720188 q^{28} +2.40527 q^{29} -2.19576 q^{30} +3.92743 q^{31} -1.00000 q^{32} -1.00000 q^{33} -4.45702 q^{34} +1.58136 q^{35} +1.00000 q^{36} -2.96854 q^{37} +5.59557 q^{38} -5.69929 q^{39} +2.19576 q^{40} -7.55529 q^{41} -0.720188 q^{42} -9.82233 q^{43} +1.00000 q^{44} -2.19576 q^{45} -9.41599 q^{46} +5.15343 q^{47} -1.00000 q^{48} -6.48133 q^{49} +0.178658 q^{50} -4.45702 q^{51} +5.69929 q^{52} +6.87538 q^{53} +1.00000 q^{54} -2.19576 q^{55} +0.720188 q^{56} +5.59557 q^{57} -2.40527 q^{58} +5.27321 q^{59} +2.19576 q^{60} -1.00000 q^{61} -3.92743 q^{62} -0.720188 q^{63} +1.00000 q^{64} -12.5143 q^{65} +1.00000 q^{66} +3.37762 q^{67} +4.45702 q^{68} -9.41599 q^{69} -1.58136 q^{70} -10.7947 q^{71} -1.00000 q^{72} -8.19894 q^{73} +2.96854 q^{74} +0.178658 q^{75} -5.59557 q^{76} -0.720188 q^{77} +5.69929 q^{78} +3.03405 q^{79} -2.19576 q^{80} +1.00000 q^{81} +7.55529 q^{82} +4.92697 q^{83} +0.720188 q^{84} -9.78653 q^{85} +9.82233 q^{86} -2.40527 q^{87} -1.00000 q^{88} -6.58979 q^{89} +2.19576 q^{90} -4.10456 q^{91} +9.41599 q^{92} -3.92743 q^{93} -5.15343 q^{94} +12.2865 q^{95} +1.00000 q^{96} -11.0029 q^{97} +6.48133 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} + 7 q^{11} - 7 q^{12} - 7 q^{13} + 4 q^{14} - 2 q^{15} + 7 q^{16} - 4 q^{17} - 7 q^{18} - 4 q^{19} + 2 q^{20} + 4 q^{21} - 7 q^{22} - q^{23} + 7 q^{24} + 5 q^{25} + 7 q^{26} - 7 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 7 q^{32} - 7 q^{33} + 4 q^{34} + 13 q^{35} + 7 q^{36} - 15 q^{37} + 4 q^{38} + 7 q^{39} - 2 q^{40} + q^{41} - 4 q^{42} - 13 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} + 11 q^{47} - 7 q^{48} + 9 q^{49} - 5 q^{50} + 4 q^{51} - 7 q^{52} + 14 q^{53} + 7 q^{54} + 2 q^{55} + 4 q^{56} + 4 q^{57} - 6 q^{58} + 39 q^{59} - 2 q^{60} - 7 q^{61} - 7 q^{62} - 4 q^{63} + 7 q^{64} - 2 q^{65} + 7 q^{66} - 3 q^{67} - 4 q^{68} + q^{69} - 13 q^{70} + 12 q^{71} - 7 q^{72} - 21 q^{73} + 15 q^{74} - 5 q^{75} - 4 q^{76} - 4 q^{77} - 7 q^{78} + 15 q^{79} + 2 q^{80} + 7 q^{81} - q^{82} + 5 q^{83} + 4 q^{84} - 34 q^{85} + 13 q^{86} - 6 q^{87} - 7 q^{88} - 8 q^{89} - 2 q^{90} + 29 q^{91} - q^{92} - 7 q^{93} - 11 q^{94} + 13 q^{95} + 7 q^{96} - 20 q^{97} - 9 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 + 7 * q^11 - 7 * q^12 - 7 * q^13 + 4 * q^14 - 2 * q^15 + 7 * q^16 - 4 * q^17 - 7 * q^18 - 4 * q^19 + 2 * q^20 + 4 * q^21 - 7 * q^22 - q^23 + 7 * q^24 + 5 * q^25 + 7 * q^26 - 7 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 7 * q^32 - 7 * q^33 + 4 * q^34 + 13 * q^35 + 7 * q^36 - 15 * q^37 + 4 * q^38 + 7 * q^39 - 2 * q^40 + q^41 - 4 * q^42 - 13 * q^43 + 7 * q^44 + 2 * q^45 + q^46 + 11 * q^47 - 7 * q^48 + 9 * q^49 - 5 * q^50 + 4 * q^51 - 7 * q^52 + 14 * q^53 + 7 * q^54 + 2 * q^55 + 4 * q^56 + 4 * q^57 - 6 * q^58 + 39 * q^59 - 2 * q^60 - 7 * q^61 - 7 * q^62 - 4 * q^63 + 7 * q^64 - 2 * q^65 + 7 * q^66 - 3 * q^67 - 4 * q^68 + q^69 - 13 * q^70 + 12 * q^71 - 7 * q^72 - 21 * q^73 + 15 * q^74 - 5 * q^75 - 4 * q^76 - 4 * q^77 - 7 * q^78 + 15 * q^79 + 2 * q^80 + 7 * q^81 - q^82 + 5 * q^83 + 4 * q^84 - 34 * q^85 + 13 * q^86 - 6 * q^87 - 7 * q^88 - 8 * q^89 - 2 * q^90 + 29 * q^91 - q^92 - 7 * q^93 - 11 * q^94 + 13 * q^95 + 7 * q^96 - 20 * q^97 - 9 * q^98 + 7 * 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
$5$	−2.19576	−0.981972	−0.490986	−	0.871168i	$-0.663363\pi$
$5$	−2.19576	−0.981972	−0.490986	+	0.871168i	$0.663363\pi$
$6$	1.00000	0.408248
$7$	−0.720188	−0.272206	−0.136103	−	0.990695i	$-0.543458\pi$
$7$	−0.720188	−0.272206	−0.136103	+	0.990695i	$0.543458\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.19576	0.694359
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	5.69929	1.58070	0.790350	−	0.612656i	$-0.209899\pi$
$13$	5.69929	1.58070	0.790350	+	0.612656i	$0.209899\pi$
$14$	0.720188	0.192478
$15$	2.19576	0.566942
$16$	1.00000	0.250000
$17$	4.45702	1.08099	0.540493	−	0.841348i	$-0.318238\pi$
$17$	4.45702	1.08099	0.540493	+	0.841348i	$0.318238\pi$
$18$	−1.00000	−0.235702
$19$	−5.59557	−1.28371	−0.641856	−	0.766826i	$-0.721835\pi$
$19$	−5.59557	−1.28371	−0.641856	+	0.766826i	$0.721835\pi$
$20$	−2.19576	−0.490986
$21$	0.720188	0.157158
$22$	−1.00000	−0.213201
$23$	9.41599	1.96337	0.981684	−	0.190514i	$-0.0610154\pi$
$23$	9.41599	1.96337	0.981684	+	0.190514i	$0.0610154\pi$
$24$	1.00000	0.204124
$25$	−0.178658	−0.0357316
$26$	−5.69929	−1.11772
$27$	−1.00000	−0.192450
$28$	−0.720188	−0.136103
$29$	2.40527	0.446648	0.223324	−	0.974744i	$-0.428309\pi$
$29$	2.40527	0.446648	0.223324	+	0.974744i	$0.428309\pi$
$30$	−2.19576	−0.400888
$31$	3.92743	0.705388	0.352694	−	0.935739i	$-0.385266\pi$
$31$	3.92743	0.705388	0.352694	+	0.935739i	$0.385266\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−4.45702	−0.764373
$35$	1.58136	0.267298
$36$	1.00000	0.166667
$37$	−2.96854	−0.488024	−0.244012	−	0.969772i	$-0.578464\pi$
$37$	−2.96854	−0.488024	−0.244012	+	0.969772i	$0.578464\pi$
$38$	5.59557	0.907721
$39$	−5.69929	−0.912617
$40$	2.19576	0.347179
$41$	−7.55529	−1.17994	−0.589969	−	0.807426i	$-0.700860\pi$
$41$	−7.55529	−1.17994	−0.589969	+	0.807426i	$0.700860\pi$
$42$	−0.720188	−0.111127
$43$	−9.82233	−1.49789	−0.748945	−	0.662632i	$-0.769440\pi$
$43$	−9.82233	−1.49789	−0.748945	+	0.662632i	$0.769440\pi$
$44$	1.00000	0.150756
$45$	−2.19576	−0.327324
$46$	−9.41599	−1.38831
$47$	5.15343	0.751705	0.375853	−	0.926679i	$-0.377350\pi$
$47$	5.15343	0.751705	0.375853	+	0.926679i	$0.377350\pi$
$48$	−1.00000	−0.144338
$49$	−6.48133	−0.925904
$50$	0.178658	0.0252661
$51$	−4.45702	−0.624108
$52$	5.69929	0.790350
$53$	6.87538	0.944406	0.472203	−	0.881490i	$-0.343459\pi$
$53$	6.87538	0.944406	0.472203	+	0.881490i	$0.343459\pi$
$54$	1.00000	0.136083
$55$	−2.19576	−0.296076
$56$	0.720188	0.0962392
$57$	5.59557	0.741151
$58$	−2.40527	−0.315828
$59$	5.27321	0.686513	0.343257	−	0.939242i	$-0.388470\pi$
$59$	5.27321	0.686513	0.343257	+	0.939242i	$0.388470\pi$
$60$	2.19576	0.283471
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−3.92743	−0.498785
$63$	−0.720188	−0.0907352
$64$	1.00000	0.125000
$65$	−12.5143	−1.55220
$66$	1.00000	0.123091
$67$	3.37762	0.412642	0.206321	−	0.978484i	$-0.433851\pi$
$67$	3.37762	0.412642	0.206321	+	0.978484i	$0.433851\pi$
$68$	4.45702	0.540493
$69$	−9.41599	−1.13355
$70$	−1.58136	−0.189008
$71$	−10.7947	−1.28109	−0.640545	−	0.767921i	$-0.721292\pi$
$71$	−10.7947	−1.28109	−0.640545	+	0.767921i	$0.721292\pi$
$72$	−1.00000	−0.117851
$73$	−8.19894	−0.959614	−0.479807	−	0.877374i	$-0.659293\pi$
$73$	−8.19894	−0.959614	−0.479807	+	0.877374i	$0.659293\pi$
$74$	2.96854	0.345085
$75$	0.178658	0.0206297
$76$	−5.59557	−0.641856
$77$	−0.720188	−0.0820731
$78$	5.69929	0.645318
$79$	3.03405	0.341357	0.170679	−	0.985327i	$-0.445404\pi$
$79$	3.03405	0.341357	0.170679	+	0.985327i	$0.445404\pi$
$80$	−2.19576	−0.245493
$81$	1.00000	0.111111
$82$	7.55529	0.834342
$83$	4.92697	0.540806	0.270403	−	0.962747i	$-0.412843\pi$
$83$	4.92697	0.540806	0.270403	+	0.962747i	$0.412843\pi$
$84$	0.720188	0.0785790
$85$	−9.78653	−1.06150
$86$	9.82233	1.05917
$87$	−2.40527	−0.257872
$88$	−1.00000	−0.106600
$89$	−6.58979	−0.698516	−0.349258	−	0.937027i	$-0.613566\pi$
$89$	−6.58979	−0.698516	−0.349258	+	0.937027i	$0.613566\pi$
$90$	2.19576	0.231453
$91$	−4.10456	−0.430275
$92$	9.41599	0.981684
$93$	−3.92743	−0.407256
$94$	−5.15343	−0.531536
$95$	12.2865	1.26057
$96$	1.00000	0.102062
$97$	−11.0029	−1.11717	−0.558587	−	0.829446i	$-0.688656\pi$
$97$	−11.0029	−1.11717	−0.558587	+	0.829446i	$0.688656\pi$
$98$	6.48133	0.654713
$99$	1.00000	0.100504
$100$	−0.178658	−0.0178658
$101$	15.3271	1.52511	0.762554	−	0.646925i	$-0.223945\pi$
$101$	15.3271	1.52511	0.762554	+	0.646925i	$0.223945\pi$
$102$	4.45702	0.441311
$103$	12.7728	1.25854	0.629270	−	0.777187i	$-0.283354\pi$
$103$	12.7728	1.25854	0.629270	+	0.777187i	$0.283354\pi$
$104$	−5.69929	−0.558862
$105$	−1.58136	−0.154325
$106$	−6.87538	−0.667796
$107$	14.3071	1.38312	0.691560	−	0.722319i	$-0.256924\pi$
$107$	14.3071	1.38312	0.691560	+	0.722319i	$0.256924\pi$
$108$	−1.00000	−0.0962250
$109$	−3.27997	−0.314164	−0.157082	−	0.987586i	$-0.550209\pi$
$109$	−3.27997	−0.314164	−0.157082	+	0.987586i	$0.550209\pi$
$110$	2.19576	0.209357
$111$	2.96854	0.281761
$112$	−0.720188	−0.0680514
$113$	0.815918	0.0767551	0.0383776	−	0.999263i	$-0.487781\pi$
$113$	0.815918	0.0767551	0.0383776	+	0.999263i	$0.487781\pi$
$114$	−5.59557	−0.524073
$115$	−20.6752	−1.92797
$116$	2.40527	0.223324
$117$	5.69929	0.526900
$118$	−5.27321	−0.485438
$119$	−3.20990	−0.294251
$120$	−2.19576	−0.200444
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	7.55529	0.681237
$124$	3.92743	0.352694
$125$	11.3711	1.01706
$126$	0.720188	0.0641595
$127$	−13.4662	−1.19494	−0.597468	−	0.801893i	$-0.703826\pi$
$127$	−13.4662	−1.19494	−0.597468	+	0.801893i	$0.703826\pi$
$128$	−1.00000	−0.0883883
$129$	9.82233	0.864808
$130$	12.5143	1.09757
$131$	14.0935	1.23136	0.615679	−	0.787997i	$-0.288882\pi$
$131$	14.0935	1.23136	0.615679	+	0.787997i	$0.288882\pi$
$132$	−1.00000	−0.0870388
$133$	4.02986	0.349433
$134$	−3.37762	−0.291782
$135$	2.19576	0.188981
$136$	−4.45702	−0.382187
$137$	−18.1394	−1.54976	−0.774878	−	0.632111i	$-0.782189\pi$
$137$	−18.1394	−1.54976	−0.774878	+	0.632111i	$0.782189\pi$
$138$	9.41599	0.801542
$139$	3.88654	0.329652	0.164826	−	0.986323i	$-0.447294\pi$
$139$	3.88654	0.329652	0.164826	+	0.986323i	$0.447294\pi$
$140$	1.58136	0.133649
$141$	−5.15343	−0.433997
$142$	10.7947	0.905868
$143$	5.69929	0.476599
$144$	1.00000	0.0833333
$145$	−5.28139	−0.438595
$146$	8.19894	0.678550
$147$	6.48133	0.534571
$148$	−2.96854	−0.244012
$149$	−1.02173	−0.0837037	−0.0418519	−	0.999124i	$-0.513326\pi$
$149$	−1.02173	−0.0837037	−0.0418519	+	0.999124i	$0.513326\pi$
$150$	−0.178658	−0.0145874
$151$	20.5874	1.67538	0.837691	−	0.546145i	$-0.183905\pi$
$151$	20.5874	1.67538	0.837691	+	0.546145i	$0.183905\pi$
$152$	5.59557	0.453860
$153$	4.45702	0.360329
$154$	0.720188	0.0580344
$155$	−8.62368	−0.692671
$156$	−5.69929	−0.456309
$157$	4.32417	0.345106	0.172553	−	0.985000i	$-0.444798\pi$
$157$	4.32417	0.345106	0.172553	+	0.985000i	$0.444798\pi$
$158$	−3.03405	−0.241376
$159$	−6.87538	−0.545253
$160$	2.19576	0.173590
$161$	−6.78128	−0.534440
$162$	−1.00000	−0.0785674
$163$	−13.3061	−1.04221	−0.521107	−	0.853491i	$-0.674481\pi$
$163$	−13.3061	−1.04221	−0.521107	+	0.853491i	$0.674481\pi$
$164$	−7.55529	−0.589969
$165$	2.19576	0.170939
$166$	−4.92697	−0.382407
$167$	3.08344	0.238604	0.119302	−	0.992858i	$-0.461934\pi$
$167$	3.08344	0.238604	0.119302	+	0.992858i	$0.461934\pi$
$168$	−0.720188	−0.0555637
$169$	19.4819	1.49861
$170$	9.78653	0.750593
$171$	−5.59557	−0.427904
$172$	−9.82233	−0.748945
$173$	−23.4543	−1.78319	−0.891597	−	0.452829i	$-0.850415\pi$
$173$	−23.4543	−1.78319	−0.891597	+	0.452829i	$0.850415\pi$
$174$	2.40527	0.182343
$175$	0.128668	0.00972635
$176$	1.00000	0.0753778
$177$	−5.27321	−0.396359
$178$	6.58979	0.493925
$179$	16.6392	1.24367	0.621835	−	0.783148i	$-0.286387\pi$
$179$	16.6392	1.24367	0.621835	+	0.783148i	$0.286387\pi$
$180$	−2.19576	−0.163662
$181$	19.7672	1.46929	0.734643	−	0.678454i	$-0.237350\pi$
$181$	19.7672	1.46929	0.734643	+	0.678454i	$0.237350\pi$
$182$	4.10456	0.304251
$183$	1.00000	0.0739221
$184$	−9.41599	−0.694156
$185$	6.51818	0.479226
$186$	3.92743	0.287973
$187$	4.45702	0.325930
$188$	5.15343	0.375853
$189$	0.720188	0.0523860
$190$	−12.2865	−0.891356
$191$	−10.1446	−0.734039	−0.367020	−	0.930213i	$-0.619622\pi$
$191$	−10.1446	−0.734039	−0.367020	+	0.930213i	$0.619622\pi$
$192$	−1.00000	−0.0721688
$193$	24.1601	1.73908	0.869542	−	0.493859i	$-0.164414\pi$
$193$	24.1601	1.73908	0.869542	+	0.493859i	$0.164414\pi$
$194$	11.0029	0.789961
$195$	12.5143	0.896164
$196$	−6.48133	−0.462952
$197$	27.5537	1.96312	0.981560	−	0.191156i	$-0.0612238\pi$
$197$	27.5537	1.96312	0.981560	+	0.191156i	$0.0612238\pi$
$198$	−1.00000	−0.0710669
$199$	3.12144	0.221273	0.110637	−	0.993861i	$-0.464711\pi$
$199$	3.12144	0.221273	0.110637	+	0.993861i	$0.464711\pi$
$200$	0.178658	0.0126330
$201$	−3.37762	−0.238239
$202$	−15.3271	−1.07841
$203$	−1.73225	−0.121580
$204$	−4.45702	−0.312054
$205$	16.5896	1.15867
$206$	−12.7728	−0.889922
$207$	9.41599	0.654456
$208$	5.69929	0.395175
$209$	−5.59557	−0.387053
$210$	1.58136	0.109124
$211$	18.2914	1.25923	0.629617	−	0.776906i	$-0.283212\pi$
$211$	18.2914	1.25923	0.629617	+	0.776906i	$0.283212\pi$
$212$	6.87538	0.472203
$213$	10.7947	0.739638
$214$	−14.3071	−0.978013
$215$	21.5674	1.47089
$216$	1.00000	0.0680414
$217$	−2.82849	−0.192011
$218$	3.27997	0.222147
$219$	8.19894	0.554033
$220$	−2.19576	−0.148038
$221$	25.4019	1.70871
$222$	−2.96854	−0.199235
$223$	3.50492	0.234707	0.117353	−	0.993090i	$-0.462559\pi$
$223$	3.50492	0.234707	0.117353	+	0.993090i	$0.462559\pi$
$224$	0.720188	0.0481196
$225$	−0.178658	−0.0119105
$226$	−0.815918	−0.0542741
$227$	10.0698	0.668358	0.334179	−	0.942510i	$-0.391541\pi$
$227$	10.0698	0.668358	0.334179	+	0.942510i	$0.391541\pi$
$228$	5.59557	0.370575
$229$	2.30032	0.152010	0.0760048	−	0.997107i	$-0.475784\pi$
$229$	2.30032	0.152010	0.0760048	+	0.997107i	$0.475784\pi$
$230$	20.6752	1.36328
$231$	0.720188	0.0473849
$232$	−2.40527	−0.157914
$233$	−8.07582	−0.529065	−0.264532	−	0.964377i	$-0.585218\pi$
$233$	−8.07582	−0.529065	−0.264532	+	0.964377i	$0.585218\pi$
$234$	−5.69929	−0.372574
$235$	−11.3157	−0.738153
$236$	5.27321	0.343257
$237$	−3.03405	−0.197083
$238$	3.20990	0.208067
$239$	−22.2075	−1.43648	−0.718240	−	0.695795i	$-0.755052\pi$
$239$	−22.2075	−1.43648	−0.718240	+	0.695795i	$0.755052\pi$
$240$	2.19576	0.141735
$241$	−12.6713	−0.816229	−0.408115	−	0.912931i	$-0.633814\pi$
$241$	−12.6713	−0.816229	−0.408115	+	0.912931i	$0.633814\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	−1.00000	−0.0640184
$245$	14.2314	0.909212
$246$	−7.55529	−0.481708
$247$	−31.8908	−2.02916
$248$	−3.92743	−0.249392
$249$	−4.92697	−0.312234
$250$	−11.3711	−0.719169
$251$	6.04672	0.381666	0.190833	−	0.981623i	$-0.438881\pi$
$251$	6.04672	0.381666	0.190833	+	0.981623i	$0.438881\pi$
$252$	−0.720188	−0.0453676
$253$	9.41599	0.591978
$254$	13.4662	0.844947
$255$	9.78653	0.612856
$256$	1.00000	0.0625000
$257$	−13.2050	−0.823703	−0.411852	−	0.911251i	$-0.635118\pi$
$257$	−13.2050	−0.823703	−0.411852	+	0.911251i	$0.635118\pi$
$258$	−9.82233	−0.611511
$259$	2.13791	0.132843
$260$	−12.5143	−0.776101
$261$	2.40527	0.148883
$262$	−14.0935	−0.870702
$263$	18.4668	1.13871	0.569356	−	0.822091i	$-0.307192\pi$
$263$	18.4668	1.13871	0.569356	+	0.822091i	$0.307192\pi$
$264$	1.00000	0.0615457
$265$	−15.0966	−0.927380
$266$	−4.02986	−0.247087
$267$	6.58979	0.403288
$268$	3.37762	0.206321
$269$	−23.2724	−1.41895	−0.709473	−	0.704733i	$-0.751067\pi$
$269$	−23.2724	−1.41895	−0.709473	+	0.704733i	$0.751067\pi$
$270$	−2.19576	−0.133629
$271$	22.7083	1.37943	0.689717	−	0.724079i	$-0.257735\pi$
$271$	22.7083	1.37943	0.689717	+	0.724079i	$0.257735\pi$
$272$	4.45702	0.270247
$273$	4.10456	0.248420
$274$	18.1394	1.09584
$275$	−0.178658	−0.0107735
$276$	−9.41599	−0.566776
$277$	−10.4501	−0.627888	−0.313944	−	0.949442i	$-0.601650\pi$
$277$	−10.4501	−0.627888	−0.313944	+	0.949442i	$0.601650\pi$
$278$	−3.88654	−0.233099
$279$	3.92743	0.235129
$280$	−1.58136	−0.0945042
$281$	−5.60417	−0.334317	−0.167158	−	0.985930i	$-0.553459\pi$
$281$	−5.60417	−0.334317	−0.167158	+	0.985930i	$0.553459\pi$
$282$	5.15343	0.306882
$283$	−18.1446	−1.07858	−0.539292	−	0.842119i	$-0.681308\pi$
$283$	−18.1446	−1.07858	−0.539292	+	0.842119i	$0.681308\pi$
$284$	−10.7947	−0.640545
$285$	−12.2865	−0.727789
$286$	−5.69929	−0.337006
$287$	5.44123	0.321186
$288$	−1.00000	−0.0589256
$289$	2.86505	0.168532
$290$	5.28139	0.310134
$291$	11.0029	0.645001
$292$	−8.19894	−0.479807
$293$	−30.5335	−1.78378	−0.891892	−	0.452249i	$-0.850622\pi$
$293$	−30.5335	−1.78378	−0.891892	+	0.452249i	$0.850622\pi$
$294$	−6.48133	−0.377999
$295$	−11.5787	−0.674137
$296$	2.96854	0.172543
$297$	−1.00000	−0.0580259
$298$	1.02173	0.0591875
$299$	53.6645	3.10350
$300$	0.178658	0.0103148
$301$	7.07393	0.407734
$302$	−20.5874	−1.18467
$303$	−15.3271	−0.880522
$304$	−5.59557	−0.320928
$305$	2.19576	0.125729
$306$	−4.45702	−0.254791
$307$	−11.6038	−0.662263	−0.331131	−	0.943585i	$-0.607430\pi$
$307$	−11.6038	−0.662263	−0.331131	+	0.943585i	$0.607430\pi$
$308$	−0.720188	−0.0410365
$309$	−12.7728	−0.726618
$310$	8.62368	0.489792
$311$	18.9583	1.07503	0.537513	−	0.843256i	$-0.319364\pi$
$311$	18.9583	1.07503	0.537513	+	0.843256i	$0.319364\pi$
$312$	5.69929	0.322659
$313$	34.3419	1.94112	0.970561	−	0.240857i	$-0.0774284\pi$
$313$	34.3419	1.94112	0.970561	+	0.240857i	$0.0774284\pi$
$314$	−4.32417	−0.244027
$315$	1.58136	0.0890994
$316$	3.03405	0.170679
$317$	17.1734	0.964555	0.482277	−	0.876019i	$-0.339810\pi$
$317$	17.1734	0.964555	0.482277	+	0.876019i	$0.339810\pi$
$318$	6.87538	0.385552
$319$	2.40527	0.134669
$320$	−2.19576	−0.122746
$321$	−14.3071	−0.798544
$322$	6.78128	0.377906
$323$	−24.9396	−1.38767
$324$	1.00000	0.0555556
$325$	−1.01823	−0.0564810
$326$	13.3061	0.736957
$327$	3.27997	0.181383
$328$	7.55529	0.417171
$329$	−3.71144	−0.204618
$330$	−2.19576	−0.120872
$331$	−7.58047	−0.416660	−0.208330	−	0.978059i	$-0.566803\pi$
$331$	−7.58047	−0.416660	−0.208330	+	0.978059i	$0.566803\pi$
$332$	4.92697	0.270403
$333$	−2.96854	−0.162675
$334$	−3.08344	−0.168718
$335$	−7.41642	−0.405203
$336$	0.720188	0.0392895
$337$	6.80393	0.370634	0.185317	−	0.982679i	$-0.440669\pi$
$337$	6.80393	0.370634	0.185317	+	0.982679i	$0.440669\pi$
$338$	−19.4819	−1.05968
$339$	−0.815918	−0.0443146
$340$	−9.78653	−0.530749
$341$	3.92743	0.212682
$342$	5.59557	0.302574
$343$	9.70910	0.524242
$344$	9.82233	0.529584
$345$	20.6752	1.11312
$346$	23.4543	1.26091
$347$	−11.4684	−0.615654	−0.307827	−	0.951442i	$-0.599602\pi$
$347$	−11.4684	−0.615654	−0.307827	+	0.951442i	$0.599602\pi$
$348$	−2.40527	−0.128936
$349$	19.6086	1.04962	0.524811	−	0.851219i	$-0.324136\pi$
$349$	19.6086	1.04962	0.524811	+	0.851219i	$0.324136\pi$
$350$	−0.128668	−0.00687757
$351$	−5.69929	−0.304206
$352$	−1.00000	−0.0533002
$353$	2.90330	0.154527	0.0772636	−	0.997011i	$-0.475382\pi$
$353$	2.90330	0.154527	0.0772636	+	0.997011i	$0.475382\pi$
$354$	5.27321	0.280268
$355$	23.7024	1.25799
$356$	−6.58979	−0.349258
$357$	3.20990	0.169886
$358$	−16.6392	−0.879408
$359$	−17.1293	−0.904049	−0.452024	−	0.892006i	$-0.649298\pi$
$359$	−17.1293	−0.904049	−0.452024	+	0.892006i	$0.649298\pi$
$360$	2.19576	0.115726
$361$	12.3104	0.647914
$362$	−19.7672	−1.03894
$363$	−1.00000	−0.0524864
$364$	−4.10456	−0.215138
$365$	18.0029	0.942314
$366$	−1.00000	−0.0522708
$367$	−28.3378	−1.47922	−0.739611	−	0.673035i	$-0.764990\pi$
$367$	−28.3378	−1.47922	−0.739611	+	0.673035i	$0.764990\pi$
$368$	9.41599	0.490842
$369$	−7.55529	−0.393313
$370$	−6.51818	−0.338864
$371$	−4.95157	−0.257073
$372$	−3.92743	−0.203628
$373$	29.8422	1.54517	0.772585	−	0.634912i	$-0.218964\pi$
$373$	29.8422	1.54517	0.772585	+	0.634912i	$0.218964\pi$
$374$	−4.45702	−0.230467
$375$	−11.3711	−0.587199
$376$	−5.15343	−0.265768
$377$	13.7083	0.706016
$378$	−0.720188	−0.0370425
$379$	12.9240	0.663863	0.331932	−	0.943303i	$-0.392300\pi$
$379$	12.9240	0.663863	0.331932	+	0.943303i	$0.392300\pi$
$380$	12.2865	0.630284
$381$	13.4662	0.689896
$382$	10.1446	0.519044
$383$	34.3072	1.75302	0.876509	−	0.481386i	$-0.159866\pi$
$383$	34.3072	1.75302	0.876509	+	0.481386i	$0.159866\pi$
$384$	1.00000	0.0510310
$385$	1.58136	0.0805934
$386$	−24.1601	−1.22972
$387$	−9.82233	−0.499297
$388$	−11.0029	−0.558587
$389$	21.6276	1.09656	0.548280	−	0.836295i	$-0.315283\pi$
$389$	21.6276	1.09656	0.548280	+	0.836295i	$0.315283\pi$
$390$	−12.5143	−0.633684
$391$	41.9673	2.12238
$392$	6.48133	0.327357
$393$	−14.0935	−0.710925
$394$	−27.5537	−1.38813
$395$	−6.66203	−0.335203
$396$	1.00000	0.0502519
$397$	1.62444	0.0815285	0.0407643	−	0.999169i	$-0.487021\pi$
$397$	1.62444	0.0815285	0.0407643	+	0.999169i	$0.487021\pi$
$398$	−3.12144	−0.156464
$399$	−4.02986	−0.201745
$400$	−0.178658	−0.00893291
$401$	16.6097	0.829449	0.414724	−	0.909947i	$-0.363878\pi$
$401$	16.6097	0.829449	0.414724	+	0.909947i	$0.363878\pi$
$402$	3.37762	0.168460
$403$	22.3836	1.11501
$404$	15.3271	0.762554
$405$	−2.19576	−0.109108
$406$	1.73225	0.0859701
$407$	−2.96854	−0.147145
$408$	4.45702	0.220655
$409$	−21.6485	−1.07045	−0.535225	−	0.844709i	$-0.679773\pi$
$409$	−21.6485	−1.07045	−0.535225	+	0.844709i	$0.679773\pi$
$410$	−16.5896	−0.819300
$411$	18.1394	0.894752
$412$	12.7728	0.629270
$413$	−3.79770	−0.186873
$414$	−9.41599	−0.462771
$415$	−10.8184	−0.531056
$416$	−5.69929	−0.279431
$417$	−3.88654	−0.190325
$418$	5.59557	0.273688
$419$	38.3846	1.87521	0.937606	−	0.347700i	$-0.113037\pi$
$419$	38.3846	1.87521	0.937606	+	0.347700i	$0.113037\pi$
$420$	−1.58136	−0.0771623
$421$	36.1761	1.76312	0.881559	−	0.472074i	$-0.156495\pi$
$421$	36.1761	1.76312	0.881559	+	0.472074i	$0.156495\pi$
$422$	−18.2914	−0.890413
$423$	5.15343	0.250568
$424$	−6.87538	−0.333898
$425$	−0.796283	−0.0386254
$426$	−10.7947	−0.523003
$427$	0.720188	0.0348524
$428$	14.3071	0.691560
$429$	−5.69929	−0.275164
$430$	−21.5674	−1.04007
$431$	−8.60726	−0.414597	−0.207299	−	0.978278i	$-0.566467\pi$
$431$	−8.60726	−0.414597	−0.207299	+	0.978278i	$0.566467\pi$
$432$	−1.00000	−0.0481125
$433$	−5.99249	−0.287981	−0.143990	−	0.989579i	$-0.545993\pi$
$433$	−5.99249	−0.287981	−0.143990	+	0.989579i	$0.545993\pi$
$434$	2.82849	0.135772
$435$	5.28139	0.253223
$436$	−3.27997	−0.157082
$437$	−52.6878	−2.52040
$438$	−8.19894	−0.391761
$439$	33.1375	1.58156	0.790782	−	0.612098i	$-0.209674\pi$
$439$	33.1375	1.58156	0.790782	+	0.612098i	$0.209674\pi$
$440$	2.19576	0.104679
$441$	−6.48133	−0.308635
$442$	−25.4019	−1.20824
$443$	27.1133	1.28819	0.644097	−	0.764944i	$-0.277233\pi$
$443$	27.1133	1.28819	0.644097	+	0.764944i	$0.277233\pi$
$444$	2.96854	0.140880
$445$	14.4696	0.685923
$446$	−3.50492	−0.165963
$447$	1.02173	0.0483264
$448$	−0.720188	−0.0340257
$449$	−24.6469	−1.16316	−0.581580	−	0.813489i	$-0.697565\pi$
$449$	−24.6469	−1.16316	−0.581580	+	0.813489i	$0.697565\pi$
$450$	0.178658	0.00842203
$451$	−7.55529	−0.355765
$452$	0.815918	0.0383776
$453$	−20.5874	−0.967282
$454$	−10.0698	−0.472600
$455$	9.01262	0.422518
$456$	−5.59557	−0.262036
$457$	−29.5167	−1.38073	−0.690366	−	0.723460i	$-0.742551\pi$
$457$	−29.5167	−1.38073	−0.690366	+	0.723460i	$0.742551\pi$
$458$	−2.30032	−0.107487
$459$	−4.45702	−0.208036
$460$	−20.6752	−0.963986
$461$	13.6061	0.633701	0.316850	−	0.948476i	$-0.397375\pi$
$461$	13.6061	0.633701	0.316850	+	0.948476i	$0.397375\pi$
$462$	−0.720188	−0.0335062
$463$	4.33603	0.201512	0.100756	−	0.994911i	$-0.467874\pi$
$463$	4.33603	0.201512	0.100756	+	0.994911i	$0.467874\pi$
$464$	2.40527	0.111662
$465$	8.62368	0.399914
$466$	8.07582	0.374105
$467$	18.1090	0.837984	0.418992	−	0.907990i	$-0.362384\pi$
$467$	18.1090	0.837984	0.418992	+	0.907990i	$0.362384\pi$
$468$	5.69929	0.263450
$469$	−2.43252	−0.112323
$470$	11.3157	0.521953
$471$	−4.32417	−0.199247
$472$	−5.27321	−0.242719
$473$	−9.82233	−0.451631
$474$	3.03405	0.139358
$475$	0.999694	0.0458691
$476$	−3.20990	−0.147125
$477$	6.87538	0.314802
$478$	22.2075	1.01575
$479$	−2.30938	−0.105518	−0.0527590	−	0.998607i	$-0.516802\pi$
$479$	−2.30938	−0.105518	−0.0527590	+	0.998607i	$0.516802\pi$
$480$	−2.19576	−0.100222
$481$	−16.9186	−0.771420
$482$	12.6713	0.577161
$483$	6.78128	0.308559
$484$	1.00000	0.0454545
$485$	24.1596	1.09703
$486$	1.00000	0.0453609
$487$	−34.6810	−1.57154	−0.785772	−	0.618516i	$-0.787734\pi$
$487$	−34.6810	−1.57154	−0.785772	+	0.618516i	$0.787734\pi$
$488$	1.00000	0.0452679
$489$	13.3061	0.601723
$490$	−14.2314	−0.642910
$491$	−6.55240	−0.295706	−0.147853	−	0.989009i	$-0.547236\pi$
$491$	−6.55240	−0.295706	−0.147853	+	0.989009i	$0.547236\pi$
$492$	7.55529	0.340619
$493$	10.7203	0.482820
$494$	31.8908	1.43483
$495$	−2.19576	−0.0986919
$496$	3.92743	0.176347
$497$	7.77419	0.348720
$498$	4.92697	0.220783
$499$	11.2422	0.503268	0.251634	−	0.967822i	$-0.419032\pi$
$499$	11.2422	0.503268	0.251634	+	0.967822i	$0.419032\pi$
$500$	11.3711	0.508530
$501$	−3.08344	−0.137758
$502$	−6.04672	−0.269878
$503$	40.9857	1.82746	0.913732	−	0.406318i	$-0.133188\pi$
$503$	40.9857	1.82746	0.913732	+	0.406318i	$0.133188\pi$
$504$	0.720188	0.0320797
$505$	−33.6547	−1.49761
$506$	−9.41599	−0.418592
$507$	−19.4819	−0.865223
$508$	−13.4662	−0.597468
$509$	38.6555	1.71337	0.856687	−	0.515837i	$-0.172519\pi$
$509$	38.6555	1.71337	0.856687	+	0.515837i	$0.172519\pi$
$510$	−9.78653	−0.433355
$511$	5.90478	0.261212
$512$	−1.00000	−0.0441942
$513$	5.59557	0.247050
$514$	13.2050	0.582446
$515$	−28.0459	−1.23585
$516$	9.82233	0.432404
$517$	5.15343	0.226648
$518$	−2.13791	−0.0939342
$519$	23.4543	1.02953
$520$	12.5143	0.548786
$521$	33.4067	1.46357	0.731787	−	0.681533i	$-0.238686\pi$
$521$	33.4067	1.46357	0.731787	+	0.681533i	$0.238686\pi$
$522$	−2.40527	−0.105276
$523$	−33.2711	−1.45485	−0.727423	−	0.686190i	$-0.759282\pi$
$523$	−33.2711	−1.45485	−0.727423	+	0.686190i	$0.759282\pi$
$524$	14.0935	0.615679
$525$	−0.128668	−0.00561551
$526$	−18.4668	−0.805191
$527$	17.5047	0.762515
$528$	−1.00000	−0.0435194
$529$	65.6608	2.85482
$530$	15.0966	0.655757
$531$	5.27321	0.228838
$532$	4.02986	0.174717
$533$	−43.0598	−1.86513
$534$	−6.58979	−0.285168
$535$	−31.4149	−1.35818
$536$	−3.37762	−0.145891
$537$	−16.6392	−0.718033
$538$	23.2724	1.00335
$539$	−6.48133	−0.279171
$540$	2.19576	0.0944903
$541$	31.5524	1.35654	0.678271	−	0.734812i	$-0.262730\pi$
$541$	31.5524	1.35654	0.678271	+	0.734812i	$0.262730\pi$
$542$	−22.7083	−0.975407
$543$	−19.7672	−0.848293
$544$	−4.45702	−0.191093
$545$	7.20200	0.308500
$546$	−4.10456	−0.175659
$547$	14.4932	0.619684	0.309842	−	0.950788i	$-0.399724\pi$
$547$	14.4932	0.619684	0.309842	+	0.950788i	$0.399724\pi$
$548$	−18.1394	−0.774878
$549$	−1.00000	−0.0426790
$550$	0.178658	0.00761801
$551$	−13.4589	−0.573367
$552$	9.41599	0.400771
$553$	−2.18509	−0.0929193
$554$	10.4501	0.443984
$555$	−6.51818	−0.276681
$556$	3.88654	0.164826
$557$	25.9734	1.10053	0.550264	−	0.834991i	$-0.314527\pi$
$557$	25.9734	1.10053	0.550264	+	0.834991i	$0.314527\pi$
$558$	−3.92743	−0.166262
$559$	−55.9803	−2.36772
$560$	1.58136	0.0668245
$561$	−4.45702	−0.188176
$562$	5.60417	0.236398
$563$	−20.1525	−0.849328	−0.424664	−	0.905351i	$-0.639608\pi$
$563$	−20.1525	−0.849328	−0.424664	+	0.905351i	$0.639608\pi$
$564$	−5.15343	−0.216999
$565$	−1.79156	−0.0753713
$566$	18.1446	0.762674
$567$	−0.720188	−0.0302451
$568$	10.7947	0.452934
$569$	35.5705	1.49119	0.745595	−	0.666399i	$-0.232165\pi$
$569$	35.5705	1.49119	0.745595	+	0.666399i	$0.232165\pi$
$570$	12.2865	0.514625
$571$	−4.47090	−0.187101	−0.0935507	−	0.995615i	$-0.529822\pi$
$571$	−4.47090	−0.187101	−0.0935507	+	0.995615i	$0.529822\pi$
$572$	5.69929	0.238299
$573$	10.1446	0.423798
$574$	−5.44123	−0.227113
$575$	−1.68224	−0.0701544
$576$	1.00000	0.0416667
$577$	26.7759	1.11469	0.557347	−	0.830280i	$-0.311819\pi$
$577$	26.7759	1.11469	0.557347	+	0.830280i	$0.311819\pi$
$578$	−2.86505	−0.119170
$579$	−24.1601	−1.00406
$580$	−5.28139	−0.219298
$581$	−3.54835	−0.147210
$582$	−11.0029	−0.456084
$583$	6.87538	0.284749
$584$	8.19894	0.339275
$585$	−12.5143	−0.517401
$586$	30.5335	1.26133
$587$	30.0886	1.24189	0.620944	−	0.783855i	$-0.286749\pi$
$587$	30.0886	1.24189	0.620944	+	0.783855i	$0.286749\pi$
$588$	6.48133	0.267285
$589$	−21.9762	−0.905514
$590$	11.5787	0.476687
$591$	−27.5537	−1.13341
$592$	−2.96854	−0.122006
$593$	34.6332	1.42221	0.711107	−	0.703084i	$-0.248194\pi$
$593$	34.6332	1.42221	0.711107	+	0.703084i	$0.248194\pi$
$594$	1.00000	0.0410305
$595$	7.04815	0.288946
$596$	−1.02173	−0.0418519
$597$	−3.12144	−0.127752
$598$	−53.6645	−2.19450
$599$	−28.0255	−1.14509	−0.572546	−	0.819873i	$-0.694044\pi$
$599$	−28.0255	−1.14509	−0.572546	+	0.819873i	$0.694044\pi$
$600$	−0.178658	−0.00729369
$601$	−11.9462	−0.487297	−0.243649	−	0.969864i	$-0.578344\pi$
$601$	−11.9462	−0.487297	−0.243649	+	0.969864i	$0.578344\pi$
$602$	−7.07393	−0.288312
$603$	3.37762	0.137547
$604$	20.5874	0.837691
$605$	−2.19576	−0.0892702
$606$	15.3271	0.622623
$607$	−4.58417	−0.186066	−0.0930328	−	0.995663i	$-0.529656\pi$
$607$	−4.58417	−0.186066	−0.0930328	+	0.995663i	$0.529656\pi$
$608$	5.59557	0.226930
$609$	1.73225	0.0701943
$610$	−2.19576	−0.0889035
$611$	29.3709	1.18822
$612$	4.45702	0.180164
$613$	−47.7681	−1.92933	−0.964667	−	0.263472i	$-0.915132\pi$
$613$	−47.7681	−1.92933	−0.964667	+	0.263472i	$0.915132\pi$
$614$	11.6038	0.468291
$615$	−16.5896	−0.668956
$616$	0.720188	0.0290172
$617$	−25.3592	−1.02092	−0.510462	−	0.859900i	$-0.670526\pi$
$617$	−25.3592	−1.02092	−0.510462	+	0.859900i	$0.670526\pi$
$618$	12.7728	0.513796
$619$	−42.6926	−1.71596	−0.857980	−	0.513683i	$-0.828281\pi$
$619$	−42.6926	−1.71596	−0.857980	+	0.513683i	$0.828281\pi$
$620$	−8.62368	−0.346335
$621$	−9.41599	−0.377851
$622$	−18.9583	−0.760158
$623$	4.74589	0.190140
$624$	−5.69929	−0.228154
$625$	−24.0748	−0.962992
$626$	−34.3419	−1.37258
$627$	5.59557	0.223465
$628$	4.32417	0.172553
$629$	−13.2308	−0.527548
$630$	−1.58136	−0.0630028
$631$	−7.77304	−0.309440	−0.154720	−	0.987958i	$-0.549448\pi$
$631$	−7.77304	−0.309440	−0.154720	+	0.987958i	$0.549448\pi$
$632$	−3.03405	−0.120688
$633$	−18.2914	−0.727019
$634$	−17.1734	−0.682043
$635$	29.5686	1.17339
$636$	−6.87538	−0.272626
$637$	−36.9390	−1.46358
$638$	−2.40527	−0.0952256
$639$	−10.7947	−0.427030
$640$	2.19576	0.0867949
$641$	−25.6532	−1.01324	−0.506621	−	0.862169i	$-0.669106\pi$
$641$	−25.6532	−1.01324	−0.506621	+	0.862169i	$0.669106\pi$
$642$	14.3071	0.564656
$643$	39.5133	1.55825	0.779125	−	0.626868i	$-0.215664\pi$
$643$	39.5133	1.55825	0.779125	+	0.626868i	$0.215664\pi$
$644$	−6.78128	−0.267220
$645$	−21.5674	−0.849217
$646$	24.9396	0.981234
$647$	−20.1515	−0.792239	−0.396119	−	0.918199i	$-0.629643\pi$
$647$	−20.1515	−0.792239	−0.396119	+	0.918199i	$0.629643\pi$
$648$	−1.00000	−0.0392837
$649$	5.27321	0.206992
$650$	1.01823	0.0399381
$651$	2.82849	0.110857
$652$	−13.3061	−0.521107
$653$	−8.89676	−0.348157	−0.174079	−	0.984732i	$-0.555695\pi$
$653$	−8.89676	−0.348157	−0.174079	+	0.984732i	$0.555695\pi$
$654$	−3.27997	−0.128257
$655$	−30.9460	−1.20916
$656$	−7.55529	−0.294984
$657$	−8.19894	−0.319871
$658$	3.71144	0.144687
$659$	−17.2195	−0.670778	−0.335389	−	0.942080i	$-0.608868\pi$
$659$	−17.2195	−0.670778	−0.335389	+	0.942080i	$0.608868\pi$
$660$	2.19576	0.0854697
$661$	−0.414710	−0.0161304	−0.00806518	−	0.999967i	$-0.502567\pi$
$661$	−0.414710	−0.0161304	−0.00806518	+	0.999967i	$0.502567\pi$
$662$	7.58047	0.294623
$663$	−25.4019	−0.986527
$664$	−4.92697	−0.191204
$665$	−8.84859	−0.343134
$666$	2.96854	0.115028
$667$	22.6480	0.876934
$668$	3.08344	0.119302
$669$	−3.50492	−0.135508
$670$	7.41642	0.286521
$671$	−1.00000	−0.0386046
$672$	−0.720188	−0.0277819
$673$	−24.4650	−0.943057	−0.471528	−	0.881851i	$-0.656298\pi$
$673$	−24.4650	−0.943057	−0.471528	+	0.881851i	$0.656298\pi$
$674$	−6.80393	−0.262078
$675$	0.178658	0.00687656
$676$	19.4819	0.749305
$677$	−37.9491	−1.45850	−0.729250	−	0.684247i	$-0.760131\pi$
$677$	−37.9491	−1.45850	−0.729250	+	0.684247i	$0.760131\pi$
$678$	0.815918	0.0313351
$679$	7.92415	0.304101
$680$	9.78653	0.375296
$681$	−10.0698	−0.385876
$682$	−3.92743	−0.150389
$683$	14.9810	0.573232	0.286616	−	0.958046i	$-0.407470\pi$
$683$	14.9810	0.573232	0.286616	+	0.958046i	$0.407470\pi$
$684$	−5.59557	−0.213952
$685$	39.8298	1.52182
$686$	−9.70910	−0.370695
$687$	−2.30032	−0.0877628
$688$	−9.82233	−0.374473
$689$	39.1848	1.49282
$690$	−20.6752	−0.787092
$691$	42.5478	1.61859	0.809297	−	0.587400i	$-0.199848\pi$
$691$	42.5478	1.61859	0.809297	+	0.587400i	$0.199848\pi$
$692$	−23.4543	−0.891597
$693$	−0.720188	−0.0273577
$694$	11.4684	0.435333
$695$	−8.53389	−0.323709
$696$	2.40527	0.0911716
$697$	−33.6741	−1.27550
$698$	−19.6086	−0.742195
$699$	8.07582	0.305456
$700$	0.128668	0.00486318
$701$	34.5606	1.30534	0.652669	−	0.757643i	$-0.273649\pi$
$701$	34.5606	1.30534	0.652669	+	0.757643i	$0.273649\pi$
$702$	5.69929	0.215106
$703$	16.6106	0.626482
$704$	1.00000	0.0376889
$705$	11.3157	0.426173
$706$	−2.90330	−0.109267
$707$	−11.0384	−0.415143
$708$	−5.27321	−0.198179
$709$	16.0418	0.602462	0.301231	−	0.953551i	$-0.402603\pi$
$709$	16.0418	0.602462	0.301231	+	0.953551i	$0.402603\pi$
$710$	−23.7024	−0.889536
$711$	3.03405	0.113786
$712$	6.58979	0.246963
$713$	36.9807	1.38494
$714$	−3.20990	−0.120127
$715$	−12.5143	−0.468007
$716$	16.6392	0.621835
$717$	22.2075	0.829353
$718$	17.1293	0.639259
$719$	−21.0838	−0.786292	−0.393146	−	0.919476i	$-0.628613\pi$
$719$	−21.0838	−0.786292	−0.393146	+	0.919476i	$0.628613\pi$
$720$	−2.19576	−0.0818310
$721$	−9.19881	−0.342581
$722$	−12.3104	−0.458144
$723$	12.6713	0.471250
$724$	19.7672	0.734643
$725$	−0.429721	−0.0159595
$726$	1.00000	0.0371135
$727$	6.73422	0.249758	0.124879	−	0.992172i	$-0.460146\pi$
$727$	6.73422	0.249758	0.124879	+	0.992172i	$0.460146\pi$
$728$	4.10456	0.152125
$729$	1.00000	0.0370370
$730$	−18.0029	−0.666316
$731$	−43.7783	−1.61920
$732$	1.00000	0.0369611
$733$	−22.7145	−0.838980	−0.419490	−	0.907760i	$-0.637791\pi$
$733$	−22.7145	−0.838980	−0.419490	+	0.907760i	$0.637791\pi$
$734$	28.3378	1.04597
$735$	−14.2314	−0.524934
$736$	−9.41599	−0.347078
$737$	3.37762	0.124416
$738$	7.55529	0.278114
$739$	−23.5358	−0.865777	−0.432888	−	0.901447i	$-0.642506\pi$
$739$	−23.5358	−0.865777	−0.432888	+	0.901447i	$0.642506\pi$
$740$	6.51818	0.239613
$741$	31.8908	1.17154
$742$	4.95157	0.181778
$743$	−1.45576	−0.0534066	−0.0267033	−	0.999643i	$-0.508501\pi$
$743$	−1.45576	−0.0534066	−0.0267033	+	0.999643i	$0.508501\pi$
$744$	3.92743	0.143987
$745$	2.24348	0.0821947
$746$	−29.8422	−1.09260
$747$	4.92697	0.180269
$748$	4.45702	0.162965
$749$	−10.3038	−0.376493
$750$	11.3711	0.415213
$751$	37.6172	1.37267	0.686336	−	0.727284i	$-0.259218\pi$
$751$	37.6172	1.37267	0.686336	+	0.727284i	$0.259218\pi$
$752$	5.15343	0.187926
$753$	−6.04672	−0.220355
$754$	−13.7083	−0.499229
$755$	−45.2050	−1.64518
$756$	0.720188	0.0261930
$757$	−3.10018	−0.112678	−0.0563389	−	0.998412i	$-0.517943\pi$
$757$	−3.10018	−0.112678	−0.0563389	+	0.998412i	$0.517943\pi$
$758$	−12.9240	−0.469422
$759$	−9.41599	−0.341779
$760$	−12.2865	−0.445678
$761$	−39.1368	−1.41871	−0.709354	−	0.704853i	$-0.751013\pi$
$761$	−39.1368	−1.41871	−0.709354	+	0.704853i	$0.751013\pi$
$762$	−13.4662	−0.487830
$763$	2.36219	0.0855171
$764$	−10.1446	−0.367020
$765$	−9.78653	−0.353833
$766$	−34.3072	−1.23957
$767$	30.0536	1.08517
$768$	−1.00000	−0.0360844
$769$	−23.2999	−0.840214	−0.420107	−	0.907474i	$-0.638008\pi$
$769$	−23.2999	−0.840214	−0.420107	+	0.907474i	$0.638008\pi$
$770$	−1.58136	−0.0569882
$771$	13.2050	0.475565
$772$	24.1601	0.869542
$773$	3.53270	0.127063	0.0635313	−	0.997980i	$-0.479764\pi$
$773$	3.53270	0.127063	0.0635313	+	0.997980i	$0.479764\pi$
$774$	9.82233	0.353056
$775$	−0.701668	−0.0252047
$776$	11.0029	0.394981
$777$	−2.13791	−0.0766969
$778$	−21.6276	−0.775385
$779$	42.2761	1.51470
$780$	12.5143	0.448082
$781$	−10.7947	−0.386263
$782$	−41.9673	−1.50075
$783$	−2.40527	−0.0859574
$784$	−6.48133	−0.231476
$785$	−9.49482	−0.338885
$786$	14.0935	0.502700
$787$	−7.45308	−0.265674	−0.132837	−	0.991138i	$-0.542409\pi$
$787$	−7.45308	−0.265674	−0.132837	+	0.991138i	$0.542409\pi$
$788$	27.5537	0.981560
$789$	−18.4668	−0.657436
$790$	6.66203	0.237024
$791$	−0.587615	−0.0208932
$792$	−1.00000	−0.0355335
$793$	−5.69929	−0.202388
$794$	−1.62444	−0.0576494
$795$	15.0966	0.535423
$796$	3.12144	0.110637
$797$	−22.5039	−0.797128	−0.398564	−	0.917141i	$-0.630491\pi$
$797$	−22.5039	−0.797128	−0.398564	+	0.917141i	$0.630491\pi$
$798$	4.02986	0.142656
$799$	22.9690	0.812583
$800$	0.178658	0.00631652
$801$	−6.58979	−0.232839
$802$	−16.6097	−0.586509
$803$	−8.19894	−0.289334
$804$	−3.37762	−0.119119
$805$	14.8900	0.524805
$806$	−22.3836	−0.788428
$807$	23.2724	0.819229
$808$	−15.3271	−0.539207
$809$	−27.8998	−0.980904	−0.490452	−	0.871468i	$-0.663168\pi$
$809$	−27.8998	−0.980904	−0.490452	+	0.871468i	$0.663168\pi$
$810$	2.19576	0.0771510
$811$	−9.67778	−0.339833	−0.169916	−	0.985458i	$-0.554350\pi$
$811$	−9.67778	−0.339833	−0.169916	+	0.985458i	$0.554350\pi$
$812$	−1.73225	−0.0607900
$813$	−22.7083	−0.796416
$814$	2.96854	0.104047
$815$	29.2170	1.02343
$816$	−4.45702	−0.156027
$817$	54.9615	1.92286
$818$	21.6485	0.756923
$819$	−4.10456	−0.143425
$820$	16.5896	0.579333
$821$	−24.1337	−0.842270	−0.421135	−	0.906998i	$-0.638368\pi$
$821$	−24.1337	−0.842270	−0.421135	+	0.906998i	$0.638368\pi$
$822$	−18.1394	−0.632685
$823$	−23.5294	−0.820182	−0.410091	−	0.912045i	$-0.634503\pi$
$823$	−23.5294	−0.820182	−0.410091	+	0.912045i	$0.634503\pi$
$824$	−12.7728	−0.444961
$825$	0.178658	0.00622008
$826$	3.79770	0.132139
$827$	37.6188	1.30813	0.654066	−	0.756437i	$-0.273062\pi$
$827$	37.6188	1.30813	0.654066	+	0.756437i	$0.273062\pi$
$828$	9.41599	0.327228
$829$	−14.5140	−0.504092	−0.252046	−	0.967715i	$-0.581103\pi$
$829$	−14.5140	−0.504092	−0.252046	+	0.967715i	$0.581103\pi$
$830$	10.8184	0.375513
$831$	10.4501	0.362511
$832$	5.69929	0.197587
$833$	−28.8874	−1.00089
$834$	3.88654	0.134580
$835$	−6.77048	−0.234302
$836$	−5.59557	−0.193527
$837$	−3.92743	−0.135752
$838$	−38.3846	−1.32597
$839$	48.2366	1.66531	0.832655	−	0.553791i	$-0.186819\pi$
$839$	48.2366	1.66531	0.832655	+	0.553791i	$0.186819\pi$
$840$	1.58136	0.0545620
$841$	−23.2147	−0.800506
$842$	−36.1761	−1.24671
$843$	5.60417	0.193018
$844$	18.2914	0.629617
$845$	−42.7776	−1.47159
$846$	−5.15343	−0.177179
$847$	−0.720188	−0.0247460
$848$	6.87538	0.236101
$849$	18.1446	0.622721
$850$	0.796283	0.0273123
$851$	−27.9517	−0.958172
$852$	10.7947	0.369819
$853$	−21.0870	−0.722005	−0.361003	−	0.932565i	$-0.617565\pi$
$853$	−21.0870	−0.722005	−0.361003	+	0.932565i	$0.617565\pi$
$854$	−0.720188	−0.0246443
$855$	12.2865	0.420189
$856$	−14.3071	−0.489007
$857$	35.4180	1.20985	0.604927	−	0.796281i	$-0.293202\pi$
$857$	35.4180	1.20985	0.604927	+	0.796281i	$0.293202\pi$
$858$	5.69929	0.194571
$859$	25.5779	0.872708	0.436354	−	0.899775i	$-0.356269\pi$
$859$	25.5779	0.872708	0.436354	+	0.899775i	$0.356269\pi$
$860$	21.5674	0.735443
$861$	−5.44123	−0.185437
$862$	8.60726	0.293164
$863$	−26.7743	−0.911407	−0.455703	−	0.890132i	$-0.650612\pi$
$863$	−26.7743	−0.911407	−0.455703	+	0.890132i	$0.650612\pi$
$864$	1.00000	0.0340207
$865$	51.4998	1.75105
$866$	5.99249	0.203633
$867$	−2.86505	−0.0973021
$868$	−2.82849	−0.0960053
$869$	3.03405	0.102923
$870$	−5.28139	−0.179056
$871$	19.2500	0.652263
$872$	3.27997	0.111074
$873$	−11.0029	−0.372391
$874$	52.6878	1.78219
$875$	−8.18931	−0.276849
$876$	8.19894	0.277017
$877$	−1.59108	−0.0537269	−0.0268634	−	0.999639i	$-0.508552\pi$
$877$	−1.59108	−0.0537269	−0.0268634	+	0.999639i	$0.508552\pi$
$878$	−33.1375	−1.11833
$879$	30.5335	1.02987
$880$	−2.19576	−0.0740189
$881$	29.3144	0.987628	0.493814	−	0.869568i	$-0.335602\pi$
$881$	29.3144	0.987628	0.493814	+	0.869568i	$0.335602\pi$
$882$	6.48133	0.218238
$883$	−18.4305	−0.620236	−0.310118	−	0.950698i	$-0.600369\pi$
$883$	−18.4305	−0.620236	−0.310118	+	0.950698i	$0.600369\pi$
$884$	25.4019	0.854357
$885$	11.5787	0.389213
$886$	−27.1133	−0.910891
$887$	27.4042	0.920143	0.460072	−	0.887882i	$-0.347824\pi$
$887$	27.4042	0.920143	0.460072	+	0.887882i	$0.347824\pi$
$888$	−2.96854	−0.0996175
$889$	9.69823	0.325268
$890$	−14.4696	−0.485021
$891$	1.00000	0.0335013
$892$	3.50492	0.117353
$893$	−28.8364	−0.964972
$894$	−1.02173	−0.0341719
$895$	−36.5356	−1.22125
$896$	0.720188	0.0240598
$897$	−53.6645	−1.79180
$898$	24.6469	0.822478
$899$	9.44654	0.315060
$900$	−0.178658	−0.00595527
$901$	30.6437	1.02089
$902$	7.55529	0.251564
$903$	−7.07393	−0.235406
$904$	−0.815918	−0.0271370
$905$	−43.4040	−1.44280
$906$	20.5874	0.683972
$907$	−0.813003	−0.0269953	−0.0134977	−	0.999909i	$-0.504297\pi$
$907$	−0.813003	−0.0269953	−0.0134977	+	0.999909i	$0.504297\pi$
$908$	10.0698	0.334179
$909$	15.3271	0.508369
$910$	−9.01262	−0.298765
$911$	−16.2991	−0.540012	−0.270006	−	0.962859i	$-0.587026\pi$
$911$	−16.2991	−0.540012	−0.270006	+	0.962859i	$0.587026\pi$
$912$	5.59557	0.185288
$913$	4.92697	0.163059
$914$	29.5167	0.976326
$915$	−2.19576	−0.0725894
$916$	2.30032	0.0760048
$917$	−10.1500	−0.335183
$918$	4.45702	0.147104
$919$	−3.25021	−0.107215	−0.0536073	−	0.998562i	$-0.517072\pi$
$919$	−3.25021	−0.107215	−0.0536073	+	0.998562i	$0.517072\pi$
$920$	20.6752	0.681641
$921$	11.6038	0.382358
$922$	−13.6061	−0.448094
$923$	−61.5219	−2.02502
$924$	0.720188	0.0236925
$925$	0.530353	0.0174379
$926$	−4.33603	−0.142491
$927$	12.7728	0.419513
$928$	−2.40527	−0.0789569
$929$	−13.9446	−0.457508	−0.228754	−	0.973484i	$-0.573465\pi$
$929$	−13.9446	−0.457508	−0.228754	+	0.973484i	$0.573465\pi$
$930$	−8.62368	−0.282782
$931$	36.2667	1.18859
$932$	−8.07582	−0.264532
$933$	−18.9583	−0.620666
$934$	−18.1090	−0.592544
$935$	−9.78653	−0.320054
$936$	−5.69929	−0.186287
$937$	19.5389	0.638309	0.319154	−	0.947703i	$-0.396601\pi$
$937$	19.5389	0.638309	0.319154	+	0.947703i	$0.396601\pi$
$938$	2.43252	0.0794246
$939$	−34.3419	−1.12071
$940$	−11.3157	−0.369077
$941$	−38.8161	−1.26537	−0.632684	−	0.774410i	$-0.718047\pi$
$941$	−38.8161	−1.26537	−0.632684	+	0.774410i	$0.718047\pi$
$942$	4.32417	0.140889
$943$	−71.1405	−2.31665
$944$	5.27321	0.171628
$945$	−1.58136	−0.0514416
$946$	9.82233	0.319351
$947$	−19.0213	−0.618109	−0.309055	−	0.951044i	$-0.600013\pi$
$947$	−19.0213	−0.618109	−0.309055	+	0.951044i	$0.600013\pi$
$948$	−3.03405	−0.0985413
$949$	−46.7282	−1.51686
$950$	−0.999694	−0.0324343
$951$	−17.1734	−0.556886
$952$	3.20990	0.104033
$953$	−28.5681	−0.925411	−0.462706	−	0.886512i	$-0.653121\pi$
$953$	−28.5681	−0.925411	−0.462706	+	0.886512i	$0.653121\pi$
$954$	−6.87538	−0.222599
$955$	22.2751	0.720806
$956$	−22.2075	−0.718240
$957$	−2.40527	−0.0777514
$958$	2.30938	0.0746126
$959$	13.0638	0.421852
$960$	2.19576	0.0708677
$961$	−15.5753	−0.502428
$962$	16.9186	0.545476
$963$	14.3071	0.461040
$964$	−12.6713	−0.408115
$965$	−53.0497	−1.70773
$966$	−6.78128	−0.218184
$967$	47.0659	1.51354	0.756769	−	0.653682i	$-0.226777\pi$
$967$	47.0659	1.51354	0.756769	+	0.653682i	$0.226777\pi$
$968$	−1.00000	−0.0321412
$969$	24.9396	0.801174
$970$	−24.1596	−0.775719
$971$	57.9769	1.86057	0.930284	−	0.366840i	$-0.119560\pi$
$971$	57.9769	1.86057	0.930284	+	0.366840i	$0.119560\pi$
$972$	−1.00000	−0.0320750
$973$	−2.79904	−0.0897331
$974$	34.6810	1.11125
$975$	1.01823	0.0326093
$976$	−1.00000	−0.0320092
$977$	−16.9435	−0.542072	−0.271036	−	0.962569i	$-0.587366\pi$
$977$	−16.9435	−0.542072	−0.271036	+	0.962569i	$0.587366\pi$
$978$	−13.3061	−0.425482
$979$	−6.58979	−0.210611
$980$	14.2314	0.454606
$981$	−3.27997	−0.104721
$982$	6.55240	0.209096
$983$	38.5294	1.22890	0.614449	−	0.788957i	$-0.289378\pi$
$983$	38.5294	1.22890	0.614449	+	0.788957i	$0.289378\pi$
$984$	−7.55529	−0.240854
$985$	−60.5012	−1.92773
$986$	−10.7203	−0.341405
$987$	3.71144	0.118136
$988$	−31.8908	−1.01458
$989$	−92.4869	−2.94091
$990$	2.19576	0.0697857
$991$	19.4044	0.616402	0.308201	−	0.951321i	$-0.400273\pi$
$991$	19.4044	0.616402	0.308201	+	0.951321i	$0.400273\pi$
$992$	−3.92743	−0.124696
$993$	7.58047	0.240559
$994$	−7.77419	−0.246582
$995$	−6.85392	−0.217284
$996$	−4.92697	−0.156117
$997$	−36.8673	−1.16760	−0.583799	−	0.811898i	$-0.698435\pi$
$997$	−36.8673	−1.16760	−0.583799	+	0.811898i	$0.698435\pi$
$998$	−11.2422	−0.355864
$999$	2.96854	0.0939203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.z.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.z.1.2	✓	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.19576 q^{5} +1.00000 q^{6} -0.720188 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.19576 q^{5} +1.00000 q^{6} -0.720188 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.19576 q^{10} +1.00000 q^{11} -1.00000 q^{12} +5.69929 q^{13} +0.720188 q^{14} +2.19576 q^{15} +1.00000 q^{16} +4.45702 q^{17} -1.00000 q^{18} -5.59557 q^{19} -2.19576 q^{20} +0.720188 q^{21} -1.00000 q^{22} +9.41599 q^{23} +1.00000 q^{24} -0.178658 q^{25} -5.69929 q^{26} -1.00000 q^{27} -0.720188 q^{28} +2.40527 q^{29} -2.19576 q^{30} +3.92743 q^{31} -1.00000 q^{32} -1.00000 q^{33} -4.45702 q^{34} +1.58136 q^{35} +1.00000 q^{36} -2.96854 q^{37} +5.59557 q^{38} -5.69929 q^{39} +2.19576 q^{40} -7.55529 q^{41} -0.720188 q^{42} -9.82233 q^{43} +1.00000 q^{44} -2.19576 q^{45} -9.41599 q^{46} +5.15343 q^{47} -1.00000 q^{48} -6.48133 q^{49} +0.178658 q^{50} -4.45702 q^{51} +5.69929 q^{52} +6.87538 q^{53} +1.00000 q^{54} -2.19576 q^{55} +0.720188 q^{56} +5.59557 q^{57} -2.40527 q^{58} +5.27321 q^{59} +2.19576 q^{60} -1.00000 q^{61} -3.92743 q^{62} -0.720188 q^{63} +1.00000 q^{64} -12.5143 q^{65} +1.00000 q^{66} +3.37762 q^{67} +4.45702 q^{68} -9.41599 q^{69} -1.58136 q^{70} -10.7947 q^{71} -1.00000 q^{72} -8.19894 q^{73} +2.96854 q^{74} +0.178658 q^{75} -5.59557 q^{76} -0.720188 q^{77} +5.69929 q^{78} +3.03405 q^{79} -2.19576 q^{80} +1.00000 q^{81} +7.55529 q^{82} +4.92697 q^{83} +0.720188 q^{84} -9.78653 q^{85} +9.82233 q^{86} -2.40527 q^{87} -1.00000 q^{88} -6.58979 q^{89} +2.19576 q^{90} -4.10456 q^{91} +9.41599 q^{92} -3.92743 q^{93} -5.15343 q^{94} +12.2865 q^{95} +1.00000 q^{96} -11.0029 q^{97} +6.48133 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 4 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} + 7 q^{11} - 7 q^{12} - 7 q^{13} + 4 q^{14} - 2 q^{15} + 7 q^{16} - 4 q^{17} - 7 q^{18} - 4 q^{19} + 2 q^{20} + 4 q^{21} - 7 q^{22} - q^{23} + 7 q^{24} + 5 q^{25} + 7 q^{26} - 7 q^{27} - 4 q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} - 7 q^{32} - 7 q^{33} + 4 q^{34} + 13 q^{35} + 7 q^{36} - 15 q^{37} + 4 q^{38} + 7 q^{39} - 2 q^{40} + q^{41} - 4 q^{42} - 13 q^{43} + 7 q^{44} + 2 q^{45} + q^{46} + 11 q^{47} - 7 q^{48} + 9 q^{49} - 5 q^{50} + 4 q^{51} - 7 q^{52} + 14 q^{53} + 7 q^{54} + 2 q^{55} + 4 q^{56} + 4 q^{57} - 6 q^{58} + 39 q^{59} - 2 q^{60} - 7 q^{61} - 7 q^{62} - 4 q^{63} + 7 q^{64} - 2 q^{65} + 7 q^{66} - 3 q^{67} - 4 q^{68} + q^{69} - 13 q^{70} + 12 q^{71} - 7 q^{72} - 21 q^{73} + 15 q^{74} - 5 q^{75} - 4 q^{76} - 4 q^{77} - 7 q^{78} + 15 q^{79} + 2 q^{80} + 7 q^{81} - q^{82} + 5 q^{83} + 4 q^{84} - 34 q^{85} + 13 q^{86} - 6 q^{87} - 7 q^{88} - 8 q^{89} - 2 q^{90} + 29 q^{91} - q^{92} - 7 q^{93} - 11 q^{94} + 13 q^{95} + 7 q^{96} - 20 q^{97} - 9 q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 4 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 + 7 * q^11 - 7 * q^12 - 7 * q^13 + 4 * q^14 - 2 * q^15 + 7 * q^16 - 4 * q^17 - 7 * q^18 - 4 * q^19 + 2 * q^20 + 4 * q^21 - 7 * q^22 - q^23 + 7 * q^24 + 5 * q^25 + 7 * q^26 - 7 * q^27 - 4 * q^28 + 6 * q^29 + 2 * q^30 + 7 * q^31 - 7 * q^32 - 7 * q^33 + 4 * q^34 + 13 * q^35 + 7 * q^36 - 15 * q^37 + 4 * q^38 + 7 * q^39 - 2 * q^40 + q^41 - 4 * q^42 - 13 * q^43 + 7 * q^44 + 2 * q^45 + q^46 + 11 * q^47 - 7 * q^48 + 9 * q^49 - 5 * q^50 + 4 * q^51 - 7 * q^52 + 14 * q^53 + 7 * q^54 + 2 * q^55 + 4 * q^56 + 4 * q^57 - 6 * q^58 + 39 * q^59 - 2 * q^60 - 7 * q^61 - 7 * q^62 - 4 * q^63 + 7 * q^64 - 2 * q^65 + 7 * q^66 - 3 * q^67 - 4 * q^68 + q^69 - 13 * q^70 + 12 * q^71 - 7 * q^72 - 21 * q^73 + 15 * q^74 - 5 * q^75 - 4 * q^76 - 4 * q^77 - 7 * q^78 + 15 * q^79 + 2 * q^80 + 7 * q^81 - q^82 + 5 * q^83 + 4 * q^84 - 34 * q^85 + 13 * q^86 - 6 * q^87 - 7 * q^88 - 8 * q^89 - 2 * q^90 + 29 * q^91 - q^92 - 7 * q^93 - 11 * q^94 + 13 * q^95 + 7 * q^96 - 20 * q^97 - 9 * q^98 + 7 * q^99

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