LMFDB - Embedded newform 671.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2661761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 3x^{3} + 9x^{2} - x - 1 $ x^6 - x^5 - 6x^4 + 3x^3 + 9*x^2 - 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			1.2
Root			$-1.68584$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.57580 q^{2} +1.68584 q^{3} +0.483130 q^{4} -0.593176 q^{5} -2.65654 q^{6} -2.68584 q^{7} +2.39028 q^{8} -0.157941 q^{9} +O(q^{10})$	\(q-1.57580 q^{2} +1.68584 q^{3} +0.483130 q^{4} -0.593176 q^{5} -2.65654 q^{6} -2.68584 q^{7} +2.39028 q^{8} -0.157941 q^{9} +0.934724 q^{10} -1.00000 q^{11} +0.814481 q^{12} +3.82551 q^{13} +4.23233 q^{14} -1.00000 q^{15} -4.73285 q^{16} -2.31103 q^{17} +0.248883 q^{18} -0.611770 q^{19} -0.286581 q^{20} -4.52790 q^{21} +1.57580 q^{22} -1.73817 q^{23} +4.02962 q^{24} -4.64814 q^{25} -6.02822 q^{26} -5.32379 q^{27} -1.29761 q^{28} -1.70444 q^{29} +1.57580 q^{30} -2.23029 q^{31} +2.67744 q^{32} -1.68584 q^{33} +3.64171 q^{34} +1.59318 q^{35} -0.0763062 q^{36} -10.8462 q^{37} +0.964025 q^{38} +6.44920 q^{39} -1.41785 q^{40} +2.81590 q^{41} +7.13504 q^{42} +2.17858 q^{43} -0.483130 q^{44} +0.0936869 q^{45} +2.73901 q^{46} -2.48074 q^{47} -7.97882 q^{48} +0.213740 q^{49} +7.32452 q^{50} -3.89603 q^{51} +1.84822 q^{52} +0.251951 q^{53} +8.38920 q^{54} +0.593176 q^{55} -6.41990 q^{56} -1.03135 q^{57} +2.68584 q^{58} +2.34462 q^{59} -0.483130 q^{60} -1.00000 q^{61} +3.51448 q^{62} +0.424205 q^{63} +5.24659 q^{64} -2.26920 q^{65} +2.65654 q^{66} -5.63241 q^{67} -1.11653 q^{68} -2.93029 q^{69} -2.51052 q^{70} +2.24195 q^{71} -0.377523 q^{72} -9.37446 q^{73} +17.0913 q^{74} -7.83603 q^{75} -0.295565 q^{76} +2.68584 q^{77} -10.1626 q^{78} -2.23186 q^{79} +2.80741 q^{80} -8.50123 q^{81} -4.43728 q^{82} +5.01950 q^{83} -2.18757 q^{84} +1.37085 q^{85} -3.43300 q^{86} -2.87341 q^{87} -2.39028 q^{88} -5.69160 q^{89} -0.147631 q^{90} -10.2747 q^{91} -0.839765 q^{92} -3.75991 q^{93} +3.90914 q^{94} +0.362887 q^{95} +4.51374 q^{96} -10.7213 q^{97} -0.336811 q^{98} +0.157941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * 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 $

$2$	−1.57580	−1.11426	−0.557128	−	0.830427i	$-0.688097\pi$
$2$	−1.57580	−1.11426	−0.557128	+	0.830427i	$0.688097\pi$
$3$	1.68584	0.973321	0.486660	−	0.873591i	$-0.338215\pi$
$3$	1.68584	0.973321	0.486660	+	0.873591i	$0.338215\pi$
$4$	0.483130	0.241565
$5$	−0.593176	−0.265276	−0.132638	−	0.991165i	$-0.542345\pi$
$5$	−0.593176	−0.265276	−0.132638	+	0.991165i	$0.542345\pi$
$6$	−2.65654	−1.08453
$7$	−2.68584	−1.01515	−0.507576	−	0.861607i	$-0.669458\pi$
$7$	−2.68584	−1.01515	−0.507576	+	0.861607i	$0.669458\pi$
$8$	2.39028	0.845090
$9$	−0.157941	−0.0526471
$10$	0.934724	0.295586
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.814481	0.235120
$13$	3.82551	1.06101	0.530503	−	0.847683i	$-0.322003\pi$
$13$	3.82551	1.06101	0.530503	+	0.847683i	$0.322003\pi$
$14$	4.23233	1.13114
$15$	−1.00000	−0.258199
$16$	−4.73285	−1.18321
$17$	−2.31103	−0.560508	−0.280254	−	0.959926i	$-0.590419\pi$
$17$	−2.31103	−0.560508	−0.280254	+	0.959926i	$0.590419\pi$
$18$	0.248883	0.0586623
$19$	−0.611770	−0.140350	−0.0701749	−	0.997535i	$-0.522356\pi$
$19$	−0.611770	−0.140350	−0.0701749	+	0.997535i	$0.522356\pi$
$20$	−0.286581	−0.0640815
$21$	−4.52790	−0.988069
$22$	1.57580	0.335961
$23$	−1.73817	−0.362434	−0.181217	−	0.983443i	$-0.558004\pi$
$23$	−1.73817	−0.362434	−0.181217	+	0.983443i	$0.558004\pi$
$24$	4.02962	0.822544
$25$	−4.64814	−0.929628
$26$	−6.02822	−1.18223
$27$	−5.32379	−1.02456
$28$	−1.29761	−0.245225
$29$	−1.70444	−0.316506	−0.158253	−	0.987399i	$-0.550586\pi$
$29$	−1.70444	−0.316506	−0.158253	+	0.987399i	$0.550586\pi$
$30$	1.57580	0.287700
$31$	−2.23029	−0.400572	−0.200286	−	0.979738i	$-0.564187\pi$
$31$	−2.23029	−0.400572	−0.200286	+	0.979738i	$0.564187\pi$
$32$	2.67744	0.473310
$33$	−1.68584	−0.293467
$34$	3.64171	0.624549
$35$	1.59318	0.269296
$36$	−0.0763062	−0.0127177
$37$	−10.8462	−1.78310	−0.891548	−	0.452926i	$-0.850380\pi$
$37$	−10.8462	−1.78310	−0.891548	+	0.452926i	$0.850380\pi$
$38$	0.964025	0.156385
$39$	6.44920	1.03270
$40$	−1.41785	−0.224182
$41$	2.81590	0.439770	0.219885	−	0.975526i	$-0.429432\pi$
$41$	2.81590	0.439770	0.219885	+	0.975526i	$0.429432\pi$
$42$	7.13504	1.10096
$43$	2.17858	0.332231	0.166115	−	0.986106i	$-0.446878\pi$
$43$	2.17858	0.332231	0.166115	+	0.986106i	$0.446878\pi$
$44$	−0.483130	−0.0728346
$45$	0.0936869	0.0139660
$46$	2.73901	0.403845
$47$	−2.48074	−0.361853	−0.180926	−	0.983497i	$-0.557910\pi$
$47$	−2.48074	−0.361853	−0.180926	+	0.983497i	$0.557910\pi$
$48$	−7.97882	−1.15164
$49$	0.213740	0.0305343
$50$	7.32452	1.03584
$51$	−3.89603	−0.545554
$52$	1.84822	0.256302
$53$	0.251951	0.0346082	0.0173041	−	0.999850i	$-0.494492\pi$
$53$	0.251951	0.0346082	0.0173041	+	0.999850i	$0.494492\pi$
$54$	8.38920	1.14162
$55$	0.593176	0.0799838
$56$	−6.41990	−0.857895
$57$	−1.03135	−0.136605
$58$	2.68584	0.352668
$59$	2.34462	0.305243	0.152622	−	0.988285i	$-0.451228\pi$
$59$	2.34462	0.305243	0.152622	+	0.988285i	$0.451228\pi$
$60$	−0.483130	−0.0623719
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	3.51448	0.446339
$63$	0.424205	0.0534448
$64$	5.24659	0.655824
$65$	−2.26920	−0.281460
$66$	2.65654	0.326997
$67$	−5.63241	−0.688109	−0.344054	−	0.938950i	$-0.611800\pi$
$67$	−5.63241	−0.688109	−0.344054	+	0.938950i	$0.611800\pi$
$68$	−1.11653	−0.135399
$69$	−2.93029	−0.352765
$70$	−2.51052	−0.300064
$71$	2.24195	0.266070	0.133035	−	0.991111i	$-0.457528\pi$
$71$	2.24195	0.266070	0.133035	+	0.991111i	$0.457528\pi$
$72$	−0.377523	−0.0444915
$73$	−9.37446	−1.09720	−0.548599	−	0.836086i	$-0.684839\pi$
$73$	−9.37446	−1.09720	−0.548599	+	0.836086i	$0.684839\pi$
$74$	17.0913	1.98682
$75$	−7.83603	−0.904827
$76$	−0.295565	−0.0339036
$77$	2.68584	0.306080
$78$	−10.1626	−1.15069
$79$	−2.23186	−0.251103	−0.125552	−	0.992087i	$-0.540070\pi$
$79$	−2.23186	−0.251103	−0.125552	+	0.992087i	$0.540070\pi$
$80$	2.80741	0.313878
$81$	−8.50123	−0.944581
$82$	−4.43728	−0.490016
$83$	5.01950	0.550962	0.275481	−	0.961306i	$-0.411163\pi$
$83$	5.01950	0.550962	0.275481	+	0.961306i	$0.411163\pi$
$84$	−2.18757	−0.238683
$85$	1.37085	0.148689
$86$	−3.43300	−0.370190
$87$	−2.87341	−0.308061
$88$	−2.39028	−0.254804
$89$	−5.69160	−0.603308	−0.301654	−	0.953417i	$-0.597539\pi$
$89$	−5.69160	−0.603308	−0.301654	+	0.953417i	$0.597539\pi$
$90$	−0.147631	−0.0155617
$91$	−10.2747	−1.07708
$92$	−0.839765	−0.0875515
$93$	−3.75991	−0.389885
$94$	3.90914	0.403197
$95$	0.362887	0.0372315
$96$	4.51374	0.460682
$97$	−10.7213	−1.08859	−0.544293	−	0.838895i	$-0.683202\pi$
$97$	−10.7213	−1.08859	−0.544293	+	0.838895i	$0.683202\pi$
$98$	−0.336811	−0.0340230
$99$	0.157941	0.0158737
$100$	−2.24566	−0.224566
$101$	−5.82418	−0.579528	−0.289764	−	0.957098i	$-0.593577\pi$
$101$	−5.82418	−0.579528	−0.289764	+	0.957098i	$0.593577\pi$
$102$	6.13935	0.607886
$103$	5.58228	0.550038	0.275019	−	0.961439i	$-0.411316\pi$
$103$	5.58228	0.550038	0.275019	+	0.961439i	$0.411316\pi$
$104$	9.14403	0.896645
$105$	2.68584	0.262111
$106$	−0.397024	−0.0385623
$107$	−1.10743	−0.107059	−0.0535297	−	0.998566i	$-0.517047\pi$
$107$	−1.10743	−0.107059	−0.0535297	+	0.998566i	$0.517047\pi$
$108$	−2.57208	−0.247499
$109$	−1.40184	−0.134272	−0.0671360	−	0.997744i	$-0.521386\pi$
$109$	−1.40184	−0.134272	−0.0671360	+	0.997744i	$0.521386\pi$
$110$	−0.934724	−0.0891224
$111$	−18.2849	−1.73552
$112$	12.7117	1.20114
$113$	5.66009	0.532456	0.266228	−	0.963910i	$-0.414223\pi$
$113$	5.66009	0.532456	0.266228	+	0.963910i	$0.414223\pi$
$114$	1.62519	0.152213
$115$	1.03104	0.0961453
$116$	−0.823464	−0.0764567
$117$	−0.604206	−0.0558588
$118$	−3.69463	−0.340119
$119$	6.20707	0.569001
$120$	−2.39028	−0.218201
$121$	1.00000	0.0909091
$122$	1.57580	0.142666
$123$	4.74716	0.428037
$124$	−1.07752	−0.0967641
$125$	5.72305	0.511885
$126$	−0.668460	−0.0595511
$127$	12.5426	1.11297	0.556487	−	0.830856i	$-0.312149\pi$
$127$	12.5426	1.11297	0.556487	+	0.830856i	$0.312149\pi$
$128$	−13.6224	−1.20406
$129$	3.67274	0.323367
$130$	3.57580	0.313618
$131$	13.0303	1.13846	0.569230	−	0.822178i	$-0.307241\pi$
$131$	13.0303	1.13846	0.569230	+	0.822178i	$0.307241\pi$
$132$	−0.814481	−0.0708914
$133$	1.64312	0.142476
$134$	8.87553	0.766729
$135$	3.15794	0.271792
$136$	−5.52401	−0.473680
$137$	17.6380	1.50691	0.753456	−	0.657498i	$-0.228385\pi$
$137$	17.6380	1.50691	0.753456	+	0.657498i	$0.228385\pi$
$138$	4.61753	0.393070
$139$	−15.2721	−1.29536	−0.647681	−	0.761912i	$-0.724261\pi$
$139$	−15.2721	−1.29536	−0.647681	+	0.761912i	$0.724261\pi$
$140$	0.769712	0.0650525
$141$	−4.18213	−0.352199
$142$	−3.53285	−0.296470
$143$	−3.82551	−0.319905
$144$	0.747511	0.0622926
$145$	1.01103	0.0839615
$146$	14.7722	1.22256
$147$	0.360332	0.0297197
$148$	−5.24010	−0.430734
$149$	10.3172	0.845220	0.422610	−	0.906312i	$-0.361114\pi$
$149$	10.3172	0.845220	0.422610	+	0.906312i	$0.361114\pi$
$150$	12.3480	1.00821
$151$	−9.92195	−0.807437	−0.403718	−	0.914883i	$-0.632282\pi$
$151$	−9.92195	−0.807437	−0.403718	+	0.914883i	$0.632282\pi$
$152$	−1.46230	−0.118608
$153$	0.365007	0.0295091
$154$	−4.23233	−0.341051
$155$	1.32295	0.106262
$156$	3.11580	0.249464
$157$	−4.01611	−0.320521	−0.160260	−	0.987075i	$-0.551233\pi$
$157$	−4.01611	−0.320521	−0.160260	+	0.987075i	$0.551233\pi$
$158$	3.51695	0.279793
$159$	0.424750	0.0336848
$160$	−1.58819	−0.125558
$161$	4.66846	0.367926
$162$	13.3962	1.05250
$163$	−3.55586	−0.278516	−0.139258	−	0.990256i	$-0.544472\pi$
$163$	−3.55586	−0.278516	−0.139258	+	0.990256i	$0.544472\pi$
$164$	1.36045	0.106233
$165$	1.00000	0.0778499
$166$	−7.90971	−0.613913
$167$	22.4774	1.73936	0.869678	−	0.493620i	$-0.164327\pi$
$167$	22.4774	1.73936	0.869678	+	0.493620i	$0.164327\pi$
$168$	−10.8229	−0.835007
$169$	1.63453	0.125733
$170$	−2.16018	−0.165678
$171$	0.0966237	0.00738900
$172$	1.05254	0.0802553
$173$	21.7995	1.65738	0.828691	−	0.559706i	$-0.189086\pi$
$173$	21.7995	1.65738	0.828691	+	0.559706i	$0.189086\pi$
$174$	4.52790	0.343259
$175$	12.4842	0.943715
$176$	4.73285	0.356752
$177$	3.95265	0.297099
$178$	8.96880	0.672240
$179$	−8.12879	−0.607574	−0.303787	−	0.952740i	$-0.598251\pi$
$179$	−8.12879	−0.607574	−0.303787	+	0.952740i	$0.598251\pi$
$180$	0.0452630	0.00337370
$181$	3.26150	0.242426	0.121213	−	0.992627i	$-0.461322\pi$
$181$	3.26150	0.242426	0.121213	+	0.992627i	$0.461322\pi$
$182$	16.1908	1.20014
$183$	−1.68584	−0.124621
$184$	−4.15472	−0.306290
$185$	6.43368	0.473013
$186$	5.92485	0.434431
$187$	2.31103	0.168999
$188$	−1.19852	−0.0874110
$189$	14.2988	1.04009
$190$	−0.571836	−0.0414854
$191$	16.2889	1.17862	0.589310	−	0.807907i	$-0.299400\pi$
$191$	16.2889	1.17862	0.589310	+	0.807907i	$0.299400\pi$
$192$	8.84491	0.638327
$193$	16.4615	1.18492	0.592462	−	0.805598i	$-0.298156\pi$
$193$	16.4615	1.18492	0.592462	+	0.805598i	$0.298156\pi$
$194$	16.8946	1.21296
$195$	−3.82551	−0.273951
$196$	0.103264	0.00737603
$197$	7.91897	0.564203	0.282102	−	0.959385i	$-0.408969\pi$
$197$	7.91897	0.564203	0.282102	+	0.959385i	$0.408969\pi$
$198$	−0.248883	−0.0176873
$199$	11.4404	0.810987	0.405494	−	0.914098i	$-0.367100\pi$
$199$	11.4404	0.810987	0.405494	+	0.914098i	$0.367100\pi$
$200$	−11.1103	−0.785620
$201$	−9.49535	−0.669750
$202$	9.17772	0.645742
$203$	4.57784	0.321301
$204$	−1.88229	−0.131787
$205$	−1.67032	−0.116660
$206$	−8.79653	−0.612883
$207$	0.274529	0.0190811
$208$	−18.1056	−1.25539
$209$	0.611770	0.0423170
$210$	−4.23233	−0.292059
$211$	9.01799	0.620824	0.310412	−	0.950602i	$-0.399533\pi$
$211$	9.01799	0.620824	0.310412	+	0.950602i	$0.399533\pi$
$212$	0.121725	0.00836013
$213$	3.77956	0.258971
$214$	1.74509	0.119292
$215$	−1.29228	−0.0881329
$216$	−12.7253	−0.865848
$217$	5.99020	0.406641
$218$	2.20901	0.149613
$219$	−15.8038	−1.06793
$220$	0.286581	0.0193213
$221$	−8.84088	−0.594702
$222$	28.8132	1.93382
$223$	−12.4564	−0.834142	−0.417071	−	0.908874i	$-0.636943\pi$
$223$	−12.4564	−0.834142	−0.417071	+	0.908874i	$0.636943\pi$
$224$	−7.19119	−0.480481
$225$	0.734133	0.0489422
$226$	−8.91914	−0.593292
$227$	−25.5971	−1.69894	−0.849469	−	0.527638i	$-0.823078\pi$
$227$	−25.5971	−1.69894	−0.849469	+	0.527638i	$0.823078\pi$
$228$	−0.498275	−0.0329991
$229$	−22.6172	−1.49459	−0.747293	−	0.664494i	$-0.768647\pi$
$229$	−22.6172	−1.49459	−0.747293	+	0.664494i	$0.768647\pi$
$230$	−1.62471	−0.107130
$231$	4.52790	0.297914
$232$	−4.07407	−0.267476
$233$	−15.7537	−1.03206	−0.516030	−	0.856571i	$-0.672591\pi$
$233$	−15.7537	−1.03206	−0.516030	+	0.856571i	$0.672591\pi$
$234$	0.952104	0.0622410
$235$	1.47151	0.0959910
$236$	1.13276	0.0737361
$237$	−3.76255	−0.244404
$238$	−9.78106	−0.634012
$239$	14.0223	0.907028	0.453514	−	0.891249i	$-0.350170\pi$
$239$	14.0223	0.907028	0.453514	+	0.891249i	$0.350170\pi$
$240$	4.73285	0.305504
$241$	−2.81475	−0.181314	−0.0906571	−	0.995882i	$-0.528897\pi$
$241$	−2.81475	−0.181314	−0.0906571	+	0.995882i	$0.528897\pi$
$242$	−1.57580	−0.101296
$243$	1.63964	0.105183
$244$	−0.483130	−0.0309292
$245$	−0.126786	−0.00810003
$246$	−7.48055	−0.476942
$247$	−2.34033	−0.148912
$248$	−5.33100	−0.338519
$249$	8.46208	0.536263
$250$	−9.01835	−0.570370
$251$	−20.3473	−1.28431	−0.642155	−	0.766575i	$-0.721960\pi$
$251$	−20.3473	−1.28431	−0.642155	+	0.766575i	$0.721960\pi$
$252$	0.204946	0.0129104
$253$	1.73817	0.109278
$254$	−19.7645	−1.24014
$255$	2.31103	0.144722
$256$	10.9730	0.685812
$257$	16.9461	1.05707	0.528533	−	0.848913i	$-0.322742\pi$
$257$	16.9461	1.05707	0.528533	+	0.848913i	$0.322742\pi$
$258$	−5.78749	−0.360313
$259$	29.1310	1.81011
$260$	−1.09632	−0.0679909
$261$	0.269201	0.0166631
$262$	−20.5330	−1.26853
$263$	7.64661	0.471510	0.235755	−	0.971813i	$-0.424244\pi$
$263$	7.64661	0.471510	0.235755	+	0.971813i	$0.424244\pi$
$264$	−4.02962	−0.248006
$265$	−0.149451	−0.00918073
$266$	−2.58922	−0.158755
$267$	−9.59513	−0.587212
$268$	−2.72119	−0.166223
$269$	−10.2826	−0.626943	−0.313472	−	0.949598i	$-0.601492\pi$
$269$	−10.2826	−0.626943	−0.313472	+	0.949598i	$0.601492\pi$
$270$	−4.97627	−0.302846
$271$	−19.8949	−1.20853	−0.604264	−	0.796784i	$-0.706533\pi$
$271$	−19.8949	−1.20853	−0.604264	+	0.796784i	$0.706533\pi$
$272$	10.9378	0.663199
$273$	−17.3215	−1.04835
$274$	−27.7938	−1.67909
$275$	4.64814	0.280294
$276$	−1.41571	−0.0852157
$277$	3.84860	0.231240	0.115620	−	0.993294i	$-0.463115\pi$
$277$	3.84860	0.231240	0.115620	+	0.993294i	$0.463115\pi$
$278$	24.0657	1.44336
$279$	0.352254	0.0210889
$280$	3.80813	0.227579
$281$	−1.40392	−0.0837509	−0.0418754	−	0.999123i	$-0.513333\pi$
$281$	−1.40392	−0.0837509	−0.0418754	+	0.999123i	$0.513333\pi$
$282$	6.59018	0.392439
$283$	7.44746	0.442706	0.221353	−	0.975194i	$-0.428953\pi$
$283$	7.44746	0.442706	0.221353	+	0.975194i	$0.428953\pi$
$284$	1.08315	0.0642732
$285$	0.611770	0.0362381
$286$	6.02822	0.356456
$287$	−7.56306	−0.446433
$288$	−0.422879	−0.0249184
$289$	−11.6591	−0.685831
$290$	−1.59318	−0.0935545
$291$	−18.0744	−1.05954
$292$	−4.52909	−0.265045
$293$	−26.4331	−1.54424	−0.772120	−	0.635476i	$-0.780804\pi$
$293$	−26.4331	−1.54424	−0.772120	+	0.635476i	$0.780804\pi$
$294$	−0.567809	−0.0331153
$295$	−1.39077	−0.0809737
$296$	−25.9253	−1.50688
$297$	5.32379	0.308917
$298$	−16.2578	−0.941791
$299$	−6.64941	−0.384545
$300$	−3.78582	−0.218575
$301$	−5.85132	−0.337265
$302$	15.6350	0.899691
$303$	−9.81865	−0.564067
$304$	2.89541	0.166063
$305$	0.593176	0.0339652
$306$	−0.575177	−0.0328807
$307$	16.1342	0.920830	0.460415	−	0.887704i	$-0.347701\pi$
$307$	16.1342	0.920830	0.460415	+	0.887704i	$0.347701\pi$
$308$	1.29761	0.0739383
$309$	9.41083	0.535364
$310$	−2.08470	−0.118403
$311$	30.2092	1.71301	0.856503	−	0.516143i	$-0.172633\pi$
$311$	30.2092	1.71301	0.856503	+	0.516143i	$0.172633\pi$
$312$	15.4154	0.872723
$313$	5.78029	0.326721	0.163361	−	0.986566i	$-0.447767\pi$
$313$	5.78029	0.326721	0.163361	+	0.986566i	$0.447767\pi$
$314$	6.32857	0.357142
$315$	−0.251628	−0.0141776
$316$	−1.07828	−0.0606578
$317$	2.87499	0.161476	0.0807378	−	0.996735i	$-0.474272\pi$
$317$	2.87499	0.161476	0.0807378	+	0.996735i	$0.474272\pi$
$318$	−0.669319	−0.0375335
$319$	1.70444	0.0954300
$320$	−3.11215	−0.173974
$321$	−1.86695	−0.104203
$322$	−7.35654	−0.409964
$323$	1.41382	0.0786671
$324$	−4.10720	−0.228178
$325$	−17.7815	−0.986341
$326$	5.60330	0.310338
$327$	−2.36328	−0.130690
$328$	6.73078	0.371645
$329$	6.66287	0.367336
$330$	−1.57580	−0.0867447
$331$	−8.21236	−0.451392	−0.225696	−	0.974198i	$-0.572466\pi$
$331$	−8.21236	−0.451392	−0.225696	+	0.974198i	$0.572466\pi$
$332$	2.42507	0.133093
$333$	1.71305	0.0938748
$334$	−35.4198	−1.93809
$335$	3.34101	0.182539
$336$	21.4298	1.16909
$337$	13.2041	0.719272	0.359636	−	0.933093i	$-0.382901\pi$
$337$	13.2041	0.719272	0.359636	+	0.933093i	$0.382901\pi$
$338$	−2.57569	−0.140099
$339$	9.54201	0.518251
$340$	0.662299	0.0359182
$341$	2.23029	0.120777
$342$	−0.152259	−0.00823324
$343$	18.2268	0.984155
$344$	5.20741	0.280765
$345$	1.73817	0.0935802
$346$	−34.3515	−1.84675
$347$	−24.2850	−1.30368	−0.651842	−	0.758354i	$-0.726004\pi$
$347$	−24.2850	−1.30368	−0.651842	+	0.758354i	$0.726004\pi$
$348$	−1.38823	−0.0744169
$349$	−23.0451	−1.23358	−0.616788	−	0.787129i	$-0.711566\pi$
$349$	−23.0451	−1.23358	−0.616788	+	0.787129i	$0.711566\pi$
$350$	−19.6725	−1.05154
$351$	−20.3662	−1.08707
$352$	−2.67744	−0.142708
$353$	−27.1319	−1.44409	−0.722043	−	0.691848i	$-0.756797\pi$
$353$	−27.1319	−1.44409	−0.722043	+	0.691848i	$0.756797\pi$
$354$	−6.22857	−0.331045
$355$	−1.32987	−0.0705821
$356$	−2.74978	−0.145738
$357$	10.4641	0.553820
$358$	12.8093	0.676993
$359$	−22.2024	−1.17180	−0.585899	−	0.810384i	$-0.699258\pi$
$359$	−22.2024	−1.17180	−0.585899	+	0.810384i	$0.699258\pi$
$360$	0.223938	0.0118025
$361$	−18.6257	−0.980302
$362$	−5.13946	−0.270124
$363$	1.68584	0.0884837
$364$	−4.96402	−0.260186
$365$	5.56070	0.291061
$366$	2.65654	0.138860
$367$	6.56689	0.342789	0.171395	−	0.985202i	$-0.445173\pi$
$367$	6.56689	0.342789	0.171395	+	0.985202i	$0.445173\pi$
$368$	8.22651	0.428837
$369$	−0.444747	−0.0231526
$370$	−10.1382	−0.527058
$371$	−0.676701	−0.0351326
$372$	−1.81653	−0.0941825
$373$	−15.4407	−0.799488	−0.399744	−	0.916627i	$-0.630901\pi$
$373$	−15.4407	−0.799488	−0.399744	+	0.916627i	$0.630901\pi$
$374$	−3.64171	−0.188309
$375$	9.64814	0.498228
$376$	−5.92965	−0.305798
$377$	−6.52033	−0.335814
$378$	−22.5320	−1.15892
$379$	7.40520	0.380380	0.190190	−	0.981747i	$-0.439090\pi$
$379$	7.40520	0.380380	0.190190	+	0.981747i	$0.439090\pi$
$380$	0.175322	0.00899382
$381$	21.1448	1.08328
$382$	−25.6679	−1.31328
$383$	11.7590	0.600855	0.300428	−	0.953805i	$-0.402871\pi$
$383$	11.7590	0.600855	0.300428	+	0.953805i	$0.402871\pi$
$384$	−22.9653	−1.17194
$385$	−1.59318	−0.0811958
$386$	−25.9399	−1.32031
$387$	−0.344088	−0.0174910
$388$	−5.17980	−0.262964
$389$	0.203891	0.0103377	0.00516883	−	0.999987i	$-0.498355\pi$
$389$	0.203891	0.0103377	0.00516883	+	0.999987i	$0.498355\pi$
$390$	6.02822	0.305251
$391$	4.01698	0.203147
$392$	0.510898	0.0258042
$393$	21.9670	1.10809
$394$	−12.4787	−0.628666
$395$	1.32388	0.0666118
$396$	0.0763062	0.00383453
$397$	−5.50308	−0.276192	−0.138096	−	0.990419i	$-0.544098\pi$
$397$	−5.50308	−0.276192	−0.138096	+	0.990419i	$0.544098\pi$
$398$	−18.0277	−0.903647
$399$	2.77003	0.138675
$400$	21.9989	1.09995
$401$	−24.4262	−1.21979	−0.609894	−	0.792483i	$-0.708788\pi$
$401$	−24.4262	−1.21979	−0.609894	+	0.792483i	$0.708788\pi$
$402$	14.9627	0.746273
$403$	−8.53199	−0.425009
$404$	−2.81384	−0.139994
$405$	5.04273	0.250575
$406$	−7.21374	−0.358012
$407$	10.8462	0.537624
$408$	−9.31259	−0.461042
$409$	0.691297	0.0341824	0.0170912	−	0.999854i	$-0.494559\pi$
$409$	0.691297	0.0341824	0.0170912	+	0.999854i	$0.494559\pi$
$410$	2.63209	0.129990
$411$	29.7348	1.46671
$412$	2.69697	0.132870
$413$	−6.29727	−0.309868
$414$	−0.432602	−0.0212612
$415$	−2.97745	−0.146157
$416$	10.2426	0.502184
$417$	−25.7463	−1.26080
$418$	−0.964025	−0.0471520
$419$	−18.8404	−0.920413	−0.460207	−	0.887812i	$-0.652225\pi$
$419$	−18.8404	−0.920413	−0.460207	+	0.887812i	$0.652225\pi$
$420$	1.29761	0.0633169
$421$	40.0749	1.95313	0.976565	−	0.215222i	$-0.0690474\pi$
$421$	40.0749	1.95313	0.976565	+	0.215222i	$0.0690474\pi$
$422$	−14.2105	−0.691757
$423$	0.391811	0.0190505
$424$	0.602233	0.0292470
$425$	10.7420	0.521064
$426$	−5.95582	−0.288560
$427$	2.68584	0.129977
$428$	−0.535034	−0.0258618
$429$	−6.44920	−0.311370
$430$	2.03637	0.0982026
$431$	−36.2326	−1.74526	−0.872631	−	0.488380i	$-0.837588\pi$
$431$	−36.2326	−1.74526	−0.872631	+	0.488380i	$0.837588\pi$
$432$	25.1967	1.21227
$433$	11.4905	0.552200	0.276100	−	0.961129i	$-0.410958\pi$
$433$	11.4905	0.552200	0.276100	+	0.961129i	$0.410958\pi$
$434$	−9.43933	−0.453102
$435$	1.70444	0.0817214
$436$	−0.677272	−0.0324354
$437$	1.06336	0.0508676
$438$	24.9036	1.18994
$439$	35.5117	1.69488	0.847440	−	0.530892i	$-0.178143\pi$
$439$	35.5117	1.69488	0.847440	+	0.530892i	$0.178143\pi$
$440$	1.41785	0.0675935
$441$	−0.0337584	−0.00160754
$442$	13.9314	0.662650
$443$	13.5182	0.642268	0.321134	−	0.947034i	$-0.395936\pi$
$443$	13.5182	0.642268	0.321134	+	0.947034i	$0.395936\pi$
$444$	−8.83398	−0.419242
$445$	3.37612	0.160043
$446$	19.6287	0.929447
$447$	17.3932	0.822670
$448$	−14.0915	−0.665761
$449$	−1.79816	−0.0848604	−0.0424302	−	0.999099i	$-0.513510\pi$
$449$	−1.79816	−0.0848604	−0.0424302	+	0.999099i	$0.513510\pi$
$450$	−1.15684	−0.0545341
$451$	−2.81590	−0.132596
$452$	2.73456	0.128623
$453$	−16.7268	−0.785895
$454$	40.3358	1.89305
$455$	6.09471	0.285724
$456$	−2.46520	−0.115444
$457$	−29.4512	−1.37767	−0.688836	−	0.724918i	$-0.741878\pi$
$457$	−29.4512	−1.37767	−0.688836	+	0.724918i	$0.741878\pi$
$458$	35.6401	1.66535
$459$	12.3034	0.574276
$460$	0.498128	0.0232253
$461$	28.0084	1.30448	0.652241	−	0.758012i	$-0.273829\pi$
$461$	28.0084	1.30448	0.652241	+	0.758012i	$0.273829\pi$
$462$	−7.13504	−0.331952
$463$	22.5775	1.04927	0.524633	−	0.851328i	$-0.324202\pi$
$463$	22.5775	1.04927	0.524633	+	0.851328i	$0.324202\pi$
$464$	8.06683	0.374493
$465$	2.23029	0.103427
$466$	24.8246	1.14998
$467$	−9.17259	−0.424457	−0.212228	−	0.977220i	$-0.568072\pi$
$467$	−9.17259	−0.424457	−0.212228	+	0.977220i	$0.568072\pi$
$468$	−0.291910	−0.0134935
$469$	15.1278	0.698535
$470$	−2.31880	−0.106958
$471$	−6.77052	−0.311969
$472$	5.60428	0.257958
$473$	−2.17858	−0.100171
$474$	5.92901	0.272329
$475$	2.84360	0.130473
$476$	2.99882	0.137451
$477$	−0.0397935	−0.00182202
$478$	−22.0963	−1.01066
$479$	−4.16575	−0.190338	−0.0951691	−	0.995461i	$-0.530339\pi$
$479$	−4.16575	−0.190338	−0.0951691	+	0.995461i	$0.530339\pi$
$480$	−2.67744	−0.122208
$481$	−41.4921	−1.89188
$482$	4.43547	0.202030
$483$	7.87028	0.358110
$484$	0.483130	0.0219605
$485$	6.35963	0.288776
$486$	−2.58373	−0.117200
$487$	34.0913	1.54482	0.772411	−	0.635123i	$-0.219051\pi$
$487$	34.0913	1.54482	0.772411	+	0.635123i	$0.219051\pi$
$488$	−2.39028	−0.108203
$489$	−5.99461	−0.271085
$490$	0.199788	0.00902550
$491$	−34.1115	−1.53943	−0.769715	−	0.638388i	$-0.779602\pi$
$491$	−34.1115	−1.53943	−0.769715	+	0.638388i	$0.779602\pi$
$492$	2.29350	0.103399
$493$	3.93901	0.177404
$494$	3.68789	0.165926
$495$	−0.0936869	−0.00421091
$496$	10.5556	0.473961
$497$	−6.02151	−0.270102
$498$	−13.3345	−0.597534
$499$	11.6968	0.523621	0.261810	−	0.965119i	$-0.415680\pi$
$499$	11.6968	0.523621	0.261810	+	0.965119i	$0.415680\pi$
$500$	2.76498	0.123654
$501$	37.8934	1.69295
$502$	32.0632	1.43105
$503$	5.52484	0.246341	0.123170	−	0.992386i	$-0.460694\pi$
$503$	5.52484	0.246341	0.123170	+	0.992386i	$0.460694\pi$
$504$	1.01397	0.0451657
$505$	3.45477	0.153735
$506$	−2.73901	−0.121764
$507$	2.75556	0.122379
$508$	6.05970	0.268856
$509$	−22.5924	−1.00139	−0.500696	−	0.865623i	$-0.666923\pi$
$509$	−22.5924	−1.00139	−0.500696	+	0.865623i	$0.666923\pi$
$510$	−3.64171	−0.161258
$511$	25.1783	1.11382
$512$	9.95369	0.439895
$513$	3.25693	0.143797
$514$	−26.7035	−1.17784
$515$	−3.31127	−0.145912
$516$	1.77441	0.0781142
$517$	2.48074	0.109103
$518$	−45.9045	−2.01693
$519$	36.7504	1.61316
$520$	−5.42402	−0.237859
$521$	−3.26564	−0.143070	−0.0715351	−	0.997438i	$-0.522790\pi$
$521$	−3.26564	−0.143070	−0.0715351	+	0.997438i	$0.522790\pi$
$522$	−0.424205	−0.0185669
$523$	−25.7294	−1.12507	−0.562534	−	0.826774i	$-0.690174\pi$
$523$	−25.7294	−1.12507	−0.562534	+	0.826774i	$0.690174\pi$
$524$	6.29532	0.275012
$525$	21.0463	0.918537
$526$	−12.0495	−0.525382
$527$	5.15427	0.224524
$528$	7.97882	0.347234
$529$	−19.9787	−0.868641
$530$	0.235505	0.0102297
$531$	−0.370311	−0.0160701
$532$	0.793840	0.0344173
$533$	10.7723	0.466598
$534$	15.1200	0.654305
$535$	0.656902	0.0284003
$536$	−13.4630	−0.581514
$537$	−13.7038	−0.591364
$538$	16.2033	0.698575
$539$	−0.213740	−0.00920644
$540$	1.52570	0.0656556
$541$	−16.8026	−0.722399	−0.361200	−	0.932489i	$-0.617633\pi$
$541$	−16.8026	−0.722399	−0.361200	+	0.932489i	$0.617633\pi$
$542$	31.3503	1.34661
$543$	5.49838	0.235958
$544$	−6.18766	−0.265294
$545$	0.831538	0.0356192
$546$	27.2952	1.16813
$547$	21.5825	0.922801	0.461400	−	0.887192i	$-0.347347\pi$
$547$	21.5825	0.922801	0.461400	+	0.887192i	$0.347347\pi$
$548$	8.52143	0.364018
$549$	0.157941	0.00674077
$550$	−7.32452	−0.312319
$551$	1.04272	0.0444215
$552$	−7.00419	−0.298118
$553$	5.99441	0.254908
$554$	−6.06460	−0.257660
$555$	10.8462	0.460393
$556$	−7.37841	−0.312914
$557$	4.67595	0.198126	0.0990632	−	0.995081i	$-0.468415\pi$
$557$	4.67595	0.198126	0.0990632	+	0.995081i	$0.468415\pi$
$558$	−0.555081	−0.0234984
$559$	8.33419	0.352499
$560$	−7.54026	−0.318634
$561$	3.89603	0.164491
$562$	2.21229	0.0933199
$563$	10.3120	0.434599	0.217299	−	0.976105i	$-0.430275\pi$
$563$	10.3120	0.434599	0.217299	+	0.976105i	$0.430275\pi$
$564$	−2.02051	−0.0850790
$565$	−3.35743	−0.141248
$566$	−11.7357	−0.493287
$567$	22.8330	0.958894
$568$	5.35887	0.224853
$569$	−14.6516	−0.614228	−0.307114	−	0.951673i	$-0.599363\pi$
$569$	−14.6516	−0.614228	−0.307114	+	0.951673i	$0.599363\pi$
$570$	−0.964025	−0.0403786
$571$	35.7154	1.49464	0.747322	−	0.664462i	$-0.231339\pi$
$571$	35.7154	1.49464	0.747322	+	0.664462i	$0.231339\pi$
$572$	−1.84822	−0.0772780
$573$	27.4604	1.14717
$574$	11.9178	0.497441
$575$	8.07928	0.336929
$576$	−0.828652	−0.0345272
$577$	−33.6593	−1.40126	−0.700628	−	0.713527i	$-0.747097\pi$
$577$	−33.6593	−1.40126	−0.700628	+	0.713527i	$0.747097\pi$
$578$	18.3724	0.764191
$579$	27.7515	1.15331
$580$	0.488459	0.0202822
$581$	−13.4816	−0.559311
$582$	28.4816	1.18060
$583$	−0.251951	−0.0104348
$584$	−22.4076	−0.927231
$585$	0.358400	0.0148180
$586$	41.6532	1.72068
$587$	12.4648	0.514476	0.257238	−	0.966348i	$-0.417188\pi$
$587$	12.4648	0.514476	0.257238	+	0.966348i	$0.417188\pi$
$588$	0.174087	0.00717924
$589$	1.36442	0.0562201
$590$	2.19157	0.0902254
$591$	13.3501	0.549150
$592$	51.3332	2.10978
$593$	−41.9350	−1.72207	−0.861033	−	0.508549i	$-0.830182\pi$
$593$	−41.9350	−1.72207	−0.861033	+	0.508549i	$0.830182\pi$
$594$	−8.38920	−0.344213
$595$	−3.68188	−0.150942
$596$	4.98457	0.204176
$597$	19.2867	0.789350
$598$	10.4781	0.428481
$599$	−30.9262	−1.26361	−0.631805	−	0.775127i	$-0.717686\pi$
$599$	−30.9262	−1.26361	−0.631805	+	0.775127i	$0.717686\pi$
$600$	−18.7303	−0.764660
$601$	−16.0105	−0.653081	−0.326540	−	0.945183i	$-0.605883\pi$
$601$	−16.0105	−0.653081	−0.326540	+	0.945183i	$0.605883\pi$
$602$	9.22049	0.375799
$603$	0.889590	0.0362269
$604$	−4.79359	−0.195049
$605$	−0.593176	−0.0241160
$606$	15.4722	0.628514
$607$	23.9459	0.971934	0.485967	−	0.873977i	$-0.338467\pi$
$607$	23.9459	0.971934	0.485967	+	0.873977i	$0.338467\pi$
$608$	−1.63798	−0.0664289
$609$	7.71751	0.312729
$610$	−0.934724	−0.0378459
$611$	−9.49009	−0.383928
$612$	0.176346	0.00712837
$613$	−14.0470	−0.567352	−0.283676	−	0.958920i	$-0.591554\pi$
$613$	−14.0470	−0.567352	−0.283676	+	0.958920i	$0.591554\pi$
$614$	−25.4243	−1.02604
$615$	−2.81590	−0.113548
$616$	6.41990	0.258665
$617$	−13.0423	−0.525063	−0.262532	−	0.964923i	$-0.584557\pi$
$617$	−13.0423	−0.525063	−0.262532	+	0.964923i	$0.584557\pi$
$618$	−14.8295	−0.596532
$619$	−31.7416	−1.27580	−0.637902	−	0.770118i	$-0.720197\pi$
$619$	−31.7416	−1.27580	−0.637902	+	0.770118i	$0.720197\pi$
$620$	0.639159	0.0256692
$621$	9.25367	0.371337
$622$	−47.6035	−1.90873
$623$	15.2867	0.612450
$624$	−30.5231	−1.22190
$625$	19.8459	0.793838
$626$	−9.10855	−0.364051
$627$	1.03135	0.0411880
$628$	−1.94030	−0.0774266
$629$	25.0658	0.999439
$630$	0.396514	0.0157975
$631$	−29.8048	−1.18651	−0.593255	−	0.805015i	$-0.702157\pi$
$631$	−29.8048	−1.18651	−0.593255	+	0.805015i	$0.702157\pi$
$632$	−5.33475	−0.212205
$633$	15.2029	0.604261
$634$	−4.53040	−0.179925
$635$	−7.43996	−0.295246
$636$	0.205209	0.00813708
$637$	0.817665	0.0323971
$638$	−2.68584	−0.106333
$639$	−0.354096	−0.0140078
$640$	8.08050	0.319410
$641$	−17.2622	−0.681817	−0.340909	−	0.940096i	$-0.610735\pi$
$641$	−17.2622	−0.681817	−0.340909	+	0.940096i	$0.610735\pi$
$642$	2.94194	0.116109
$643$	−2.96377	−0.116879	−0.0584397	−	0.998291i	$-0.518613\pi$
$643$	−2.96377	−0.116879	−0.0584397	+	0.998291i	$0.518613\pi$
$644$	2.25547	0.0888781
$645$	−2.17858	−0.0857816
$646$	−2.22789	−0.0876553
$647$	27.8857	1.09630	0.548150	−	0.836380i	$-0.315332\pi$
$647$	27.8857	1.09630	0.548150	+	0.836380i	$0.315332\pi$
$648$	−20.3203	−0.798256
$649$	−2.34462	−0.0920342
$650$	28.0200	1.09904
$651$	10.0985	0.395792
$652$	−1.71794	−0.0672798
$653$	−35.9930	−1.40852	−0.704258	−	0.709945i	$-0.748720\pi$
$653$	−35.9930	−1.40852	−0.704258	+	0.709945i	$0.748720\pi$
$654$	3.72405	0.145622
$655$	−7.72924	−0.302006
$656$	−13.3272	−0.520340
$657$	1.48061	0.0577642
$658$	−10.4993	−0.409306
$659$	−4.30703	−0.167778	−0.0838890	−	0.996475i	$-0.526734\pi$
$659$	−4.30703	−0.167778	−0.0838890	+	0.996475i	$0.526734\pi$
$660$	0.483130	0.0188058
$661$	−40.2176	−1.56428	−0.782141	−	0.623102i	$-0.785872\pi$
$661$	−40.2176	−1.56428	−0.782141	+	0.623102i	$0.785872\pi$
$662$	12.9410	0.502966
$663$	−14.9043	−0.578836
$664$	11.9980	0.465613
$665$	−0.974658	−0.0377956
$666$	−2.69942	−0.104600
$667$	2.96261	0.114713
$668$	10.8595	0.420168
$669$	−20.9995	−0.811887
$670$	−5.26475	−0.203395
$671$	1.00000	0.0386046
$672$	−12.1232	−0.467662
$673$	−27.8395	−1.07313	−0.536567	−	0.843857i	$-0.680279\pi$
$673$	−27.8395	−1.07313	−0.536567	+	0.843857i	$0.680279\pi$
$674$	−20.8069	−0.801453
$675$	24.7457	0.952463
$676$	0.789691	0.0303727
$677$	8.94205	0.343671	0.171835	−	0.985126i	$-0.445030\pi$
$677$	8.94205	0.343671	0.171835	+	0.985126i	$0.445030\pi$
$678$	−15.0362	−0.577464
$679$	28.7958	1.10508
$680$	3.27671	0.125656
$681$	−43.1526	−1.65361
$682$	−3.51448	−0.134576
$683$	35.0297	1.34038	0.670188	−	0.742192i	$-0.266214\pi$
$683$	35.0297	1.34038	0.670188	+	0.742192i	$0.266214\pi$
$684$	0.0466819	0.00178493
$685$	−10.4624	−0.399748
$686$	−28.7217	−1.09660
$687$	−38.1290	−1.45471
$688$	−10.3109	−0.393099
$689$	0.963842	0.0367195
$690$	−2.73901	−0.104272
$691$	−7.78662	−0.296217	−0.148108	−	0.988971i	$-0.547318\pi$
$691$	−7.78662	−0.296217	−0.148108	+	0.988971i	$0.547318\pi$
$692$	10.5320	0.400366
$693$	−0.424205	−0.0161142
$694$	38.2681	1.45264
$695$	9.05904	0.343629
$696$	−6.86823	−0.260340
$697$	−6.50764	−0.246494
$698$	36.3144	1.37452
$699$	−26.5582	−1.00453
$700$	6.03148	0.227969
$701$	36.9275	1.39473	0.697366	−	0.716715i	$-0.254355\pi$
$701$	36.9275	1.39473	0.697366	+	0.716715i	$0.254355\pi$
$702$	32.0930	1.21127
$703$	6.63535	0.250257
$704$	−5.24659	−0.197738
$705$	2.48074	0.0934300
$706$	42.7543	1.60908
$707$	15.6428	0.588309
$708$	1.90964	0.0717688
$709$	−15.0036	−0.563471	−0.281736	−	0.959492i	$-0.590910\pi$
$709$	−15.0036	−0.563471	−0.281736	+	0.959492i	$0.590910\pi$
$710$	2.09560	0.0786465
$711$	0.352502	0.0132199
$712$	−13.6045	−0.509850
$713$	3.87663	0.145181
$714$	−16.4893	−0.617097
$715$	2.26920	0.0848633
$716$	−3.92726	−0.146769
$717$	23.6394	0.882829
$718$	34.9864	1.30568
$719$	−42.7464	−1.59417	−0.797086	−	0.603866i	$-0.793626\pi$
$719$	−42.7464	−1.59417	−0.797086	+	0.603866i	$0.793626\pi$
$720$	−0.443406	−0.0165248
$721$	−14.9931	−0.558373
$722$	29.3503	1.09231
$723$	−4.74522	−0.176477
$724$	1.57573	0.0585616
$725$	7.92246	0.294233
$726$	−2.65654	−0.0985934
$727$	25.5349	0.947038	0.473519	−	0.880784i	$-0.342984\pi$
$727$	25.5349	0.947038	0.473519	+	0.880784i	$0.342984\pi$
$728$	−24.5594	−0.910232
$729$	28.2679	1.04696
$730$	−8.76253	−0.324316
$731$	−5.03477	−0.186218
$732$	−0.814481	−0.0301041
$733$	−9.38650	−0.346698	−0.173349	−	0.984860i	$-0.555459\pi$
$733$	−9.38650	−0.346698	−0.173349	+	0.984860i	$0.555459\pi$
$734$	−10.3481	−0.381955
$735$	−0.213740	−0.00788393
$736$	−4.65386	−0.171544
$737$	5.63241	0.207473
$738$	0.700829	0.0257979
$739$	−45.5958	−1.67727	−0.838634	−	0.544696i	$-0.816645\pi$
$739$	−45.5958	−1.67727	−0.838634	+	0.544696i	$0.816645\pi$
$740$	3.10830	0.114264
$741$	−3.94543	−0.144939
$742$	1.06634	0.0391467
$743$	−17.8019	−0.653088	−0.326544	−	0.945182i	$-0.605884\pi$
$743$	−17.8019	−0.653088	−0.326544	+	0.945182i	$0.605884\pi$
$744$	−8.98722	−0.329488
$745$	−6.11993	−0.224217
$746$	24.3314	0.890834
$747$	−0.792786	−0.0290065
$748$	1.11653	0.0408244
$749$	2.97439	0.108682
$750$	−15.2035	−0.555153
$751$	39.3389	1.43550	0.717748	−	0.696303i	$-0.245173\pi$
$751$	39.3389	1.43550	0.717748	+	0.696303i	$0.245173\pi$
$752$	11.7410	0.428148
$753$	−34.3023	−1.25005
$754$	10.2747	0.374183
$755$	5.88546	0.214194
$756$	6.90820	0.251249
$757$	−37.8192	−1.37456	−0.687280	−	0.726392i	$-0.741196\pi$
$757$	−37.8192	−1.37456	−0.687280	+	0.726392i	$0.741196\pi$
$758$	−11.6691	−0.423840
$759$	2.93029	0.106363
$760$	0.867401	0.0314639
$761$	0.981032	0.0355624	0.0177812	−	0.999842i	$-0.494340\pi$
$761$	0.981032	0.0355624	0.0177812	+	0.999842i	$0.494340\pi$
$762$	−33.3199	−1.20705
$763$	3.76512	0.136307
$764$	7.86964	0.284713
$765$	−0.216514	−0.00782806
$766$	−18.5297	−0.669506
$767$	8.96935	0.323865
$768$	18.4987	0.667515
$769$	−24.8659	−0.896686	−0.448343	−	0.893862i	$-0.647986\pi$
$769$	−24.8659	−0.896686	−0.448343	+	0.893862i	$0.647986\pi$
$770$	2.51052	0.0904728
$771$	28.5683	1.02886
$772$	7.95305	0.286236
$773$	15.0912	0.542791	0.271395	−	0.962468i	$-0.412515\pi$
$773$	15.0912	0.542791	0.271395	+	0.962468i	$0.412515\pi$
$774$	0.542212	0.0194894
$775$	10.3667	0.372383
$776$	−25.6269	−0.919953
$777$	49.1103	1.76182
$778$	−0.321290	−0.0115188
$779$	−1.72268	−0.0617216
$780$	−1.84822	−0.0661769
$781$	−2.24195	−0.0802231
$782$	−6.32994	−0.226358
$783$	9.07405	0.324280
$784$	−1.01160	−0.0361285
$785$	2.38226	0.0850265
$786$	−34.6154	−1.23469
$787$	−15.0701	−0.537191	−0.268596	−	0.963253i	$-0.586560\pi$
$787$	−15.0701	−0.537191	−0.268596	+	0.963253i	$0.586560\pi$
$788$	3.82589	0.136292
$789$	12.8910	0.458930
$790$	−2.08617	−0.0742225
$791$	−15.2021	−0.540524
$792$	0.377523	0.0134147
$793$	−3.82551	−0.135848
$794$	8.67173	0.307748
$795$	−0.251951	−0.00893579
$796$	5.52719	0.195906
$797$	0.00173753	6.15463e−5 0	3.07732e−5	−	1.00000i	$-0.499990\pi$
$797$	0.00173753	6.15463e−5 0	3.07732e−5		1.00000i	$0.499990\pi$
$798$	−4.36501	−0.154520
$799$	5.73307	0.202821
$800$	−12.4451	−0.440002
$801$	0.898938	0.0317624
$802$	38.4907	1.35916
$803$	9.37446	0.330818
$804$	−4.58749	−0.161788
$805$	−2.76922	−0.0976021
$806$	13.4447	0.473568
$807$	−17.3349	−0.610217
$808$	−13.9214	−0.489753
$809$	24.2936	0.854118	0.427059	−	0.904224i	$-0.359550\pi$
$809$	24.2936	0.854118	0.427059	+	0.904224i	$0.359550\pi$
$810$	−7.94630	−0.279205
$811$	−24.6215	−0.864579	−0.432290	−	0.901735i	$-0.642294\pi$
$811$	−24.6215	−0.864579	−0.432290	+	0.901735i	$0.642294\pi$
$812$	2.21169	0.0776152
$813$	−33.5396	−1.17629
$814$	−17.0913	−0.599050
$815$	2.10925	0.0738837
$816$	18.4393	0.645505
$817$	−1.33279	−0.0466285
$818$	−1.08934	−0.0380879
$819$	1.62280	0.0567052
$820$	−0.806984	−0.0281811
$821$	−3.38143	−0.118013	−0.0590064	−	0.998258i	$-0.518793\pi$
$821$	−3.38143	−0.118013	−0.0590064	+	0.998258i	$0.518793\pi$
$822$	−46.8559	−1.63429
$823$	18.0045	0.627597	0.313798	−	0.949490i	$-0.398398\pi$
$823$	18.0045	0.627597	0.313798	+	0.949490i	$0.398398\pi$
$824$	13.3432	0.464832
$825$	7.83603	0.272815
$826$	9.92320	0.345272
$827$	9.18833	0.319510	0.159755	−	0.987157i	$-0.448930\pi$
$827$	9.18833	0.319510	0.159755	+	0.987157i	$0.448930\pi$
$828$	0.132633	0.00460933
$829$	55.2520	1.91898	0.959490	−	0.281743i	$-0.0909126\pi$
$829$	55.2520	1.91898	0.959490	+	0.281743i	$0.0909126\pi$
$830$	4.69185	0.162856
$831$	6.48812	0.225070
$832$	20.0709	0.695833
$833$	−0.493961	−0.0171147
$834$	40.5709	1.40486
$835$	−13.3331	−0.461410
$836$	0.295565	0.0102223
$837$	11.8736	0.410411
$838$	29.6886	1.02558
$839$	−55.2868	−1.90871	−0.954356	−	0.298671i	$-0.903457\pi$
$839$	−55.2868	−1.90871	−0.954356	+	0.298671i	$0.903457\pi$
$840$	6.41990	0.221508
$841$	−26.0949	−0.899824
$842$	−63.1498	−2.17629
$843$	−2.36679	−0.0815165
$844$	4.35687	0.149970
$845$	−0.969564	−0.0333540
$846$	−0.617413	−0.0212271
$847$	−2.68584	−0.0922866
$848$	−1.19245	−0.0409488
$849$	12.5552	0.430895
$850$	−16.9272	−0.580598
$851$	18.8525	0.646256
$852$	1.82602	0.0625585
$853$	−10.1430	−0.347288	−0.173644	−	0.984808i	$-0.555554\pi$
$853$	−10.1430	−0.347288	−0.173644	+	0.984808i	$0.555554\pi$
$854$	−4.23233	−0.144828
$855$	−0.0573149	−0.00196013
$856$	−2.64707	−0.0904749
$857$	26.1607	0.893633	0.446816	−	0.894626i	$-0.352558\pi$
$857$	26.1607	0.893633	0.446816	+	0.894626i	$0.352558\pi$
$858$	10.1626	0.346946
$859$	14.8770	0.507597	0.253799	−	0.967257i	$-0.418320\pi$
$859$	14.8770	0.507597	0.253799	+	0.967257i	$0.418320\pi$
$860$	−0.624341	−0.0212898
$861$	−12.7501	−0.434523
$862$	57.0951	1.94467
$863$	13.4935	0.459325	0.229662	−	0.973270i	$-0.426238\pi$
$863$	13.4935	0.459325	0.229662	+	0.973270i	$0.426238\pi$
$864$	−14.2541	−0.484936
$865$	−12.9309	−0.439664
$866$	−18.1067	−0.615291
$867$	−19.6554	−0.667533
$868$	2.89405	0.0982304
$869$	2.23186	0.0757105
$870$	−2.68584	−0.0910585
$871$	−21.5468	−0.730087
$872$	−3.35079	−0.113472
$873$	1.69334	0.0573108
$874$	−1.67564	−0.0566795
$875$	−15.3712	−0.519641
$876$	−7.63532	−0.257974
$877$	45.8470	1.54814	0.774072	−	0.633098i	$-0.218217\pi$
$877$	45.8470	1.54814	0.774072	+	0.633098i	$0.218217\pi$
$878$	−55.9591	−1.88853
$879$	−44.5621	−1.50304
$880$	−2.80741	−0.0946378
$881$	18.7104	0.630370	0.315185	−	0.949030i	$-0.397933\pi$
$881$	18.7104	0.630370	0.315185	+	0.949030i	$0.397933\pi$
$882$	0.0531963	0.00179121
$883$	2.02167	0.0680345	0.0340173	−	0.999421i	$-0.489170\pi$
$883$	2.02167	0.0680345	0.0340173	+	0.999421i	$0.489170\pi$
$884$	−4.27130	−0.143659
$885$	−2.34462	−0.0788134
$886$	−21.3019	−0.715651
$887$	45.3084	1.52131	0.760653	−	0.649158i	$-0.224879\pi$
$887$	45.3084	1.52131	0.760653	+	0.649158i	$0.224879\pi$
$888$	−43.7059	−1.46667
$889$	−33.6874	−1.12984
$890$	−5.32007	−0.178329
$891$	8.50123	0.284802
$892$	−6.01806	−0.201500
$893$	1.51764	0.0507860
$894$	−27.4081	−0.916665
$895$	4.82180	0.161175
$896$	36.5877	1.22231
$897$	−11.2098	−0.374286
$898$	2.83353	0.0945562
$899$	3.80138	0.126783
$900$	0.354682	0.0118227
$901$	−0.582268	−0.0193981
$902$	4.43728	0.147745
$903$	−9.86440	−0.328267
$904$	13.5292	0.449973
$905$	−1.93465	−0.0643098
$906$	26.3580	0.875687
$907$	−20.2741	−0.673192	−0.336596	−	0.941649i	$-0.609276\pi$
$907$	−20.2741	−0.673192	−0.336596	+	0.941649i	$0.609276\pi$
$908$	−12.3667	−0.410404
$909$	0.919879	0.0305104
$910$	−9.60402	−0.318370
$911$	22.0528	0.730641	0.365320	−	0.930882i	$-0.380959\pi$
$911$	22.0528	0.730641	0.365320	+	0.930882i	$0.380959\pi$
$912$	4.88121	0.161633
$913$	−5.01950	−0.166121
$914$	46.4091	1.53508
$915$	1.00000	0.0330590
$916$	−10.9271	−0.361040
$917$	−34.9972	−1.15571
$918$	−19.3877	−0.639890
$919$	14.6351	0.482768	0.241384	−	0.970430i	$-0.422399\pi$
$919$	14.6351	0.482768	0.241384	+	0.970430i	$0.422399\pi$
$920$	2.46448	0.0812514
$921$	27.1998	0.896263
$922$	−44.1355	−1.45353
$923$	8.57659	0.282302
$924$	2.18757	0.0719656
$925$	50.4145	1.65762
$926$	−35.5776	−1.16915
$927$	−0.881672	−0.0289579
$928$	−4.56353	−0.149805
$929$	−16.9651	−0.556606	−0.278303	−	0.960493i	$-0.589772\pi$
$929$	−16.9651	−0.556606	−0.278303	+	0.960493i	$0.589772\pi$
$930$	−3.51448	−0.115244
$931$	−0.130760	−0.00428548
$932$	−7.61110	−0.249310
$933$	50.9279	1.66730
$934$	14.4541	0.472953
$935$	−1.37085	−0.0448316
$936$	−1.44422	−0.0472058
$937$	12.4770	0.407606	0.203803	−	0.979012i	$-0.434670\pi$
$937$	12.4770	0.407606	0.203803	+	0.979012i	$0.434670\pi$
$938$	−23.8382	−0.778346
$939$	9.74465	0.318004
$940$	0.710933	0.0231881
$941$	6.58060	0.214522	0.107261	−	0.994231i	$-0.465792\pi$
$941$	6.58060	0.214522	0.107261	+	0.994231i	$0.465792\pi$
$942$	10.6690	0.347613
$943$	−4.89453	−0.159388
$944$	−11.0967	−0.361167
$945$	−8.48173	−0.275911
$946$	3.43300	0.111616
$947$	45.2019	1.46886	0.734432	−	0.678683i	$-0.237449\pi$
$947$	45.2019	1.46886	0.734432	+	0.678683i	$0.237449\pi$
$948$	−1.81780	−0.0590395
$949$	−35.8621	−1.16413
$950$	−4.48092	−0.145380
$951$	4.84678	0.157168
$952$	14.8366	0.480857
$953$	44.5760	1.44396	0.721980	−	0.691914i	$-0.243232\pi$
$953$	44.5760	1.44396	0.721980	+	0.691914i	$0.243232\pi$
$954$	0.0627064	0.00203019
$955$	−9.66215	−0.312660
$956$	6.77461	0.219106
$957$	2.87341	0.0928840
$958$	6.56437	0.212085
$959$	−47.3728	−1.52975
$960$	−5.24659	−0.169333
$961$	−26.0258	−0.839542
$962$	65.3830	2.10803
$963$	0.174909	0.00563637
$964$	−1.35989	−0.0437992
$965$	−9.76456	−0.314332
$966$	−12.4019	−0.399026
$967$	−19.1896	−0.617095	−0.308547	−	0.951209i	$-0.599843\pi$
$967$	−19.1896	−0.617095	−0.308547	+	0.951209i	$0.599843\pi$
$968$	2.39028	0.0768264
$969$	2.38348	0.0765683
$970$	−10.0215	−0.321770
$971$	21.0715	0.676215	0.338108	−	0.941107i	$-0.390213\pi$
$971$	21.0715	0.676215	0.338108	+	0.941107i	$0.390213\pi$
$972$	0.792158	0.0254085
$973$	41.0184	1.31499
$974$	−53.7208	−1.72133
$975$	−29.9768	−0.960026
$976$	4.73285	0.151495
$977$	−32.8951	−1.05241	−0.526204	−	0.850358i	$-0.676385\pi$
$977$	−32.8951	−1.05241	−0.526204	+	0.850358i	$0.676385\pi$
$978$	9.44627	0.302058
$979$	5.69160	0.181904
$980$	−0.0612539	−0.00195668
$981$	0.221408	0.00706903
$982$	53.7527	1.71532
$983$	17.8641	0.569777	0.284888	−	0.958561i	$-0.408043\pi$
$983$	17.8641	0.569777	0.284888	+	0.958561i	$0.408043\pi$
$984$	11.3470	0.361730
$985$	−4.69734	−0.149670
$986$	−6.20707	−0.197673
$987$	11.2325	0.357535
$988$	−1.13069	−0.0359719
$989$	−3.78676	−0.120412
$990$	0.147631	0.00469203
$991$	54.3859	1.72762	0.863812	−	0.503814i	$-0.168070\pi$
$991$	54.3859	1.72762	0.863812	+	0.503814i	$0.168070\pi$
$992$	−5.97147	−0.189594
$993$	−13.8447	−0.439349
$994$	9.48866	0.300962
$995$	−6.78616	−0.215136
$996$	4.08829	0.129542
$997$	−6.53108	−0.206841	−0.103421	−	0.994638i	$-0.532979\pi$
$997$	−6.53108	−0.206841	−0.103421	+	0.994638i	$0.532979\pi$
$998$	−18.4318	−0.583447
$999$	57.7426	1.82689

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.b.1.2	✓	6
3.2	odd	2		6039.2.a.b.1.5		6
11.10	odd	2		7381.2.a.h.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.b.1.2	✓	6	1.1	even	1	trivial
6039.2.a.b.1.5		6	3.2	odd	2
7381.2.a.h.1.5		6	11.10	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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-1.57580 q^{2} +1.68584 q^{3} +0.483130 q^{4} -0.593176 q^{5} -2.65654 q^{6} -2.68584 q^{7} +2.39028 q^{8} -0.157941 q^{9} +O(q^{10})\)	\(q-1.57580 q^{2} +1.68584 q^{3} +0.483130 q^{4} -0.593176 q^{5} -2.65654 q^{6} -2.68584 q^{7} +2.39028 q^{8} -0.157941 q^{9} +0.934724 q^{10} -1.00000 q^{11} +0.814481 q^{12} +3.82551 q^{13} +4.23233 q^{14} -1.00000 q^{15} -4.73285 q^{16} -2.31103 q^{17} +0.248883 q^{18} -0.611770 q^{19} -0.286581 q^{20} -4.52790 q^{21} +1.57580 q^{22} -1.73817 q^{23} +4.02962 q^{24} -4.64814 q^{25} -6.02822 q^{26} -5.32379 q^{27} -1.29761 q^{28} -1.70444 q^{29} +1.57580 q^{30} -2.23029 q^{31} +2.67744 q^{32} -1.68584 q^{33} +3.64171 q^{34} +1.59318 q^{35} -0.0763062 q^{36} -10.8462 q^{37} +0.964025 q^{38} +6.44920 q^{39} -1.41785 q^{40} +2.81590 q^{41} +7.13504 q^{42} +2.17858 q^{43} -0.483130 q^{44} +0.0936869 q^{45} +2.73901 q^{46} -2.48074 q^{47} -7.97882 q^{48} +0.213740 q^{49} +7.32452 q^{50} -3.89603 q^{51} +1.84822 q^{52} +0.251951 q^{53} +8.38920 q^{54} +0.593176 q^{55} -6.41990 q^{56} -1.03135 q^{57} +2.68584 q^{58} +2.34462 q^{59} -0.483130 q^{60} -1.00000 q^{61} +3.51448 q^{62} +0.424205 q^{63} +5.24659 q^{64} -2.26920 q^{65} +2.65654 q^{66} -5.63241 q^{67} -1.11653 q^{68} -2.93029 q^{69} -2.51052 q^{70} +2.24195 q^{71} -0.377523 q^{72} -9.37446 q^{73} +17.0913 q^{74} -7.83603 q^{75} -0.295565 q^{76} +2.68584 q^{77} -10.1626 q^{78} -2.23186 q^{79} +2.80741 q^{80} -8.50123 q^{81} -4.43728 q^{82} +5.01950 q^{83} -2.18757 q^{84} +1.37085 q^{85} -3.43300 q^{86} -2.87341 q^{87} -2.39028 q^{88} -5.69160 q^{89} -0.147631 q^{90} -10.2747 q^{91} -0.839765 q^{92} -3.75991 q^{93} +3.90914 q^{94} +0.362887 q^{95} +4.51374 q^{96} -10.7213 q^{97} -0.336811 q^{98} +0.157941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

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