LMFDB - Embedded newform 8029.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$1$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80590 q^{2} -0.0132385 q^{3} +5.87308 q^{4} -3.56068 q^{5} +0.0371460 q^{6} +1.00000 q^{7} -10.8675 q^{8} -2.99982 q^{9} +O(q^{10})$	\(q-2.80590 q^{2} -0.0132385 q^{3} +5.87308 q^{4} -3.56068 q^{5} +0.0371460 q^{6} +1.00000 q^{7} -10.8675 q^{8} -2.99982 q^{9} +9.99092 q^{10} -0.637573 q^{11} -0.0777509 q^{12} +0.863746 q^{13} -2.80590 q^{14} +0.0471382 q^{15} +18.7469 q^{16} -6.01284 q^{17} +8.41721 q^{18} -3.62084 q^{19} -20.9122 q^{20} -0.0132385 q^{21} +1.78897 q^{22} -1.95921 q^{23} +0.143869 q^{24} +7.67846 q^{25} -2.42358 q^{26} +0.0794288 q^{27} +5.87308 q^{28} +1.94856 q^{29} -0.132265 q^{30} +1.00000 q^{31} -30.8669 q^{32} +0.00844052 q^{33} +16.8714 q^{34} -3.56068 q^{35} -17.6182 q^{36} -1.00000 q^{37} +10.1597 q^{38} -0.0114347 q^{39} +38.6956 q^{40} -0.663475 q^{41} +0.0371460 q^{42} +11.3918 q^{43} -3.74451 q^{44} +10.6814 q^{45} +5.49735 q^{46} -0.475940 q^{47} -0.248181 q^{48} +1.00000 q^{49} -21.5450 q^{50} +0.0796011 q^{51} +5.07285 q^{52} +13.7924 q^{53} -0.222869 q^{54} +2.27019 q^{55} -10.8675 q^{56} +0.0479345 q^{57} -5.46747 q^{58} +3.24490 q^{59} +0.276846 q^{60} -12.6208 q^{61} -2.80590 q^{62} -2.99982 q^{63} +49.1158 q^{64} -3.07552 q^{65} -0.0236833 q^{66} -1.17626 q^{67} -35.3139 q^{68} +0.0259371 q^{69} +9.99092 q^{70} +0.0167723 q^{71} +32.6005 q^{72} +7.56825 q^{73} +2.80590 q^{74} -0.101652 q^{75} -21.2655 q^{76} -0.637573 q^{77} +0.0320847 q^{78} -5.58904 q^{79} -66.7517 q^{80} +8.99842 q^{81} +1.86164 q^{82} -10.9163 q^{83} -0.0777509 q^{84} +21.4098 q^{85} -31.9643 q^{86} -0.0257961 q^{87} +6.92880 q^{88} -10.1553 q^{89} -29.9710 q^{90} +0.863746 q^{91} -11.5066 q^{92} -0.0132385 q^{93} +1.33544 q^{94} +12.8927 q^{95} +0.408633 q^{96} +11.0153 q^{97} -2.80590 q^{98} +1.91261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) $ 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * 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 $

$2$	−2.80590	−1.98407	−0.992036	−	0.125958i	$-0.959800\pi$
$2$	−2.80590	−1.98407	−0.992036	+	0.125958i	$0.959800\pi$
$3$	−0.0132385	−0.00764327	−0.00382163	−	0.999993i	$-0.501216\pi$
$3$	−0.0132385	−0.00764327	−0.00382163	+	0.999993i	$0.501216\pi$
$4$	5.87308	2.93654
$5$	−3.56068	−1.59239	−0.796193	−	0.605043i	$-0.793156\pi$
$5$	−3.56068	−1.59239	−0.796193	+	0.605043i	$0.793156\pi$
$6$	0.0371460	0.0151648
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.8675	−3.84223
$9$	−2.99982	−0.999942
$10$	9.99092	3.15941
$11$	−0.637573	−0.192235	−0.0961177	−	0.995370i	$-0.530643\pi$
$11$	−0.637573	−0.192235	−0.0961177	+	0.995370i	$0.530643\pi$
$12$	−0.0777509	−0.0224447
$13$	0.863746	0.239560	0.119780	−	0.992800i	$-0.461781\pi$
$13$	0.863746	0.239560	0.119780	+	0.992800i	$0.461781\pi$
$14$	−2.80590	−0.749908
$15$	0.0471382	0.0121710
$16$	18.7469	4.68672
$17$	−6.01284	−1.45833	−0.729164	−	0.684339i	$-0.760091\pi$
$17$	−6.01284	−1.45833	−0.729164	+	0.684339i	$0.760091\pi$
$18$	8.41721	1.98396
$19$	−3.62084	−0.830677	−0.415338	−	0.909667i	$-0.636337\pi$
$19$	−3.62084	−0.830677	−0.415338	+	0.909667i	$0.636337\pi$
$20$	−20.9122	−4.67610
$21$	−0.0132385	−0.00288888
$22$	1.78897	0.381409
$23$	−1.95921	−0.408524	−0.204262	−	0.978916i	$-0.565479\pi$
$23$	−1.95921	−0.408524	−0.204262	+	0.978916i	$0.565479\pi$
$24$	0.143869	0.0293672
$25$	7.67846	1.53569
$26$	−2.42358	−0.475304
$27$	0.0794288	0.0152861
$28$	5.87308	1.10991
$29$	1.94856	0.361839	0.180919	−	0.983498i	$-0.442093\pi$
$29$	1.94856	0.361839	0.180919	+	0.983498i	$0.442093\pi$
$30$	−0.132265	−0.0241482
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−30.8669	−5.45656
$33$	0.00844052	0.00146931
$34$	16.8714	2.89342
$35$	−3.56068	−0.601865
$36$	−17.6182	−2.93637
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	10.1597	1.64812
$39$	−0.0114347	−0.00183102
$40$	38.6956	6.11831
$41$	−0.663475	−0.103617	−0.0518087	−	0.998657i	$-0.516499\pi$
$41$	−0.663475	−0.103617	−0.0518087	+	0.998657i	$0.516499\pi$
$42$	0.0371460	0.00573175
$43$	11.3918	1.73724	0.868619	−	0.495480i	$-0.165008\pi$
$43$	11.3918	1.73724	0.868619	+	0.495480i	$0.165008\pi$
$44$	−3.74451	−0.564507
$45$	10.6814	1.59229
$46$	5.49735	0.810540
$47$	−0.475940	−0.0694230	−0.0347115	−	0.999397i	$-0.511051\pi$
$47$	−0.475940	−0.0694230	−0.0347115	+	0.999397i	$0.511051\pi$
$48$	−0.248181	−0.0358218
$49$	1.00000	0.142857
$50$	−21.5450	−3.04692
$51$	0.0796011	0.0111464
$52$	5.07285	0.703477
$53$	13.7924	1.89453	0.947265	−	0.320450i	$-0.103834\pi$
$53$	13.7924	1.89453	0.947265	+	0.320450i	$0.103834\pi$
$54$	−0.222869	−0.0303287
$55$	2.27019	0.306113
$56$	−10.8675	−1.45223
$57$	0.0479345	0.00634908
$58$	−5.46747	−0.717914
$59$	3.24490	0.422450	0.211225	−	0.977438i	$-0.432255\pi$
$59$	3.24490	0.422450	0.211225	+	0.977438i	$0.432255\pi$
$60$	0.276846	0.0357407
$61$	−12.6208	−1.61592	−0.807962	−	0.589234i	$-0.799430\pi$
$61$	−12.6208	−1.61592	−0.807962	+	0.589234i	$0.799430\pi$
$62$	−2.80590	−0.356350
$63$	−2.99982	−0.377942
$64$	49.1158	6.13948
$65$	−3.07552	−0.381472
$66$	−0.0236833	−0.00291521
$67$	−1.17626	−0.143703	−0.0718513	−	0.997415i	$-0.522891\pi$
$67$	−1.17626	−0.143703	−0.0718513	+	0.997415i	$0.522891\pi$
$68$	−35.3139	−4.28243
$69$	0.0259371	0.00312245
$70$	9.99092	1.19414
$71$	0.0167723	0.00199051	0.000995254	−	1.00000i	$-0.499683\pi$
$71$	0.0167723	0.00199051	0.000995254		1.00000i	$0.499683\pi$
$72$	32.6005	3.84201
$73$	7.56825	0.885796	0.442898	−	0.896572i	$-0.353950\pi$
$73$	7.56825	0.885796	0.442898	+	0.896572i	$0.353950\pi$
$74$	2.80590	0.326179
$75$	−0.101652	−0.0117377
$76$	−21.2655	−2.43931
$77$	−0.637573	−0.0726582
$78$	0.0320847	0.00363287
$79$	−5.58904	−0.628817	−0.314408	−	0.949288i	$-0.601806\pi$
$79$	−5.58904	−0.628817	−0.314408	+	0.949288i	$0.601806\pi$
$80$	−66.7517	−7.46307
$81$	8.99842	0.999825
$82$	1.86164	0.205584
$83$	−10.9163	−1.19821	−0.599107	−	0.800669i	$-0.704478\pi$
$83$	−10.9163	−1.19821	−0.599107	+	0.800669i	$0.704478\pi$
$84$	−0.0777509	−0.00848332
$85$	21.4098	2.32222
$86$	−31.9643	−3.44680
$87$	−0.0257961	−0.00276563
$88$	6.92880	0.738613
$89$	−10.1553	−1.07646	−0.538231	−	0.842797i	$-0.680907\pi$
$89$	−10.1553	−1.07646	−0.538231	+	0.842797i	$0.680907\pi$
$90$	−29.9710	−3.15922
$91$	0.863746	0.0905452
$92$	−11.5066	−1.19965
$93$	−0.0132385	−0.00137277
$94$	1.33544	0.137740
$95$	12.8927	1.32276
$96$	0.408633	0.0417059
$97$	11.0153	1.11843	0.559216	−	0.829022i	$-0.311102\pi$
$97$	11.0153	1.11843	0.559216	+	0.829022i	$0.311102\pi$
$98$	−2.80590	−0.283439
$99$	1.91261	0.192224
$100$	45.0962	4.50962
$101$	19.4871	1.93904	0.969519	−	0.245016i	$-0.0787933\pi$
$101$	19.4871	1.93904	0.969519	+	0.245016i	$0.0787933\pi$
$102$	−0.223353	−0.0221152
$103$	−5.17631	−0.510037	−0.255019	−	0.966936i	$-0.582082\pi$
$103$	−5.17631	−0.510037	−0.255019	+	0.966936i	$0.582082\pi$
$104$	−9.38673	−0.920445
$105$	0.0471382	0.00460022
$106$	−38.7001	−3.75888
$107$	20.0126	1.93469	0.967345	−	0.253465i	$-0.0815702\pi$
$107$	20.0126	1.93469	0.967345	+	0.253465i	$0.0815702\pi$
$108$	0.466492	0.0448882
$109$	12.2397	1.17235	0.586177	−	0.810183i	$-0.300632\pi$
$109$	12.2397	1.17235	0.586177	+	0.810183i	$0.300632\pi$
$110$	−6.36994	−0.607350
$111$	0.0132385	0.00125655
$112$	18.7469	1.77141
$113$	10.6149	0.998564	0.499282	−	0.866439i	$-0.333597\pi$
$113$	10.6149	0.998564	0.499282	+	0.866439i	$0.333597\pi$
$114$	−0.134500	−0.0125970
$115$	6.97613	0.650527
$116$	11.4441	1.06255
$117$	−2.59109	−0.239546
$118$	−9.10486	−0.838170
$119$	−6.01284	−0.551196
$120$	−0.512273	−0.0467639
$121$	−10.5935	−0.963046
$122$	35.4126	3.20611
$123$	0.00878343	0.000791975 0
$124$	5.87308	0.527418
$125$	−9.53716	−0.853030
$126$	8.41721	0.749865
$127$	−3.20665	−0.284544	−0.142272	−	0.989828i	$-0.545441\pi$
$127$	−3.20665	−0.284544	−0.142272	+	0.989828i	$0.545441\pi$
$128$	−76.0802	−6.72460
$129$	−0.150811	−0.0132782
$130$	8.62962	0.756867
$131$	16.4286	1.43537	0.717686	−	0.696367i	$-0.245201\pi$
$131$	16.4286	1.43537	0.717686	+	0.696367i	$0.245201\pi$
$132$	0.0495718	0.00431468
$133$	−3.62084	−0.313966
$134$	3.30046	0.285116
$135$	−0.282821	−0.0243413
$136$	65.3443	5.60323
$137$	−4.85039	−0.414397	−0.207198	−	0.978299i	$-0.566435\pi$
$137$	−4.85039	−0.414397	−0.207198	+	0.978299i	$0.566435\pi$
$138$	−0.0727768	−0.00619517
$139$	−10.0810	−0.855057	−0.427528	−	0.904002i	$-0.640616\pi$
$139$	−10.0810	−0.855057	−0.427528	+	0.904002i	$0.640616\pi$
$140$	−20.9122	−1.76740
$141$	0.00630074	0.000530618 0
$142$	−0.0470614	−0.00394931
$143$	−0.550701	−0.0460519
$144$	−56.2374	−4.68645
$145$	−6.93821	−0.576187
$146$	−21.2357	−1.75748
$147$	−0.0132385	−0.00109190
$148$	−5.87308	−0.482764
$149$	−16.1936	−1.32663	−0.663315	−	0.748341i	$-0.730851\pi$
$149$	−16.1936	−1.32663	−0.663315	+	0.748341i	$0.730851\pi$
$150$	0.285224	0.0232884
$151$	5.03559	0.409791	0.204895	−	0.978784i	$-0.434315\pi$
$151$	5.03559	0.409791	0.204895	+	0.978784i	$0.434315\pi$
$152$	39.3493	3.19165
$153$	18.0375	1.45824
$154$	1.78897	0.144159
$155$	−3.56068	−0.286001
$156$	−0.0671570	−0.00537686
$157$	6.96326	0.555729	0.277864	−	0.960620i	$-0.410373\pi$
$157$	6.96326	0.555729	0.277864	+	0.960620i	$0.410373\pi$
$158$	15.6823	1.24762
$159$	−0.182591	−0.0144804
$160$	109.907	8.68894
$161$	−1.95921	−0.154407
$162$	−25.2487	−1.98372
$163$	−18.2946	−1.43294	−0.716471	−	0.697617i	$-0.754244\pi$
$163$	−18.2946	−1.43294	−0.716471	+	0.697617i	$0.754244\pi$
$164$	−3.89664	−0.304276
$165$	−0.0300540	−0.00233970
$166$	30.6299	2.37734
$167$	19.8933	1.53939	0.769693	−	0.638414i	$-0.220409\pi$
$167$	19.8933	1.53939	0.769693	+	0.638414i	$0.220409\pi$
$168$	0.143869	0.0110998
$169$	−12.2539	−0.942611
$170$	−60.0738	−4.60745
$171$	10.8619	0.830628
$172$	66.9051	5.10147
$173$	−1.61622	−0.122879	−0.0614394	−	0.998111i	$-0.519569\pi$
$173$	−1.61622	−0.122879	−0.0614394	+	0.998111i	$0.519569\pi$
$174$	0.0723812	0.00548721
$175$	7.67846	0.580437
$176$	−11.9525	−0.900954
$177$	−0.0429576	−0.00322889
$178$	28.4948	2.13578
$179$	4.76334	0.356029	0.178014	−	0.984028i	$-0.443033\pi$
$179$	4.76334	0.356029	0.178014	+	0.984028i	$0.443033\pi$
$180$	62.7328	4.67583
$181$	−19.7898	−1.47096	−0.735481	−	0.677545i	$-0.763044\pi$
$181$	−19.7898	−1.47096	−0.735481	+	0.677545i	$0.763044\pi$
$182$	−2.42358	−0.179648
$183$	0.167080	0.0123509
$184$	21.2917	1.56964
$185$	3.56068	0.261787
$186$	0.0371460	0.00272368
$187$	3.83362	0.280342
$188$	−2.79523	−0.203863
$189$	0.0794288	0.00577760
$190$	−36.1755	−2.62445
$191$	20.2997	1.46884	0.734419	−	0.678697i	$-0.237455\pi$
$191$	20.2997	1.46884	0.734419	+	0.678697i	$0.237455\pi$
$192$	−0.650221	−0.0469256
$193$	−16.5309	−1.18992	−0.594959	−	0.803756i	$-0.702832\pi$
$193$	−16.5309	−1.18992	−0.594959	+	0.803756i	$0.702832\pi$
$194$	−30.9078	−2.21905
$195$	0.0407154	0.00291569
$196$	5.87308	0.419506
$197$	22.7242	1.61903	0.809515	−	0.587100i	$-0.199730\pi$
$197$	22.7242	1.61903	0.809515	+	0.587100i	$0.199730\pi$
$198$	−5.36658	−0.381387
$199$	−20.7972	−1.47428	−0.737138	−	0.675742i	$-0.763823\pi$
$199$	−20.7972	−1.47428	−0.737138	+	0.675742i	$0.763823\pi$
$200$	−83.4455	−5.90049
$201$	0.0155719	0.00109836
$202$	−54.6788	−3.84719
$203$	1.94856	0.136762
$204$	0.467503	0.0327318
$205$	2.36242	0.164999
$206$	14.5242	1.01195
$207$	5.87729	0.408500
$208$	16.1925	1.12275
$209$	2.30855	0.159686
$210$	−0.132265	−0.00912716
$211$	14.4230	0.992920	0.496460	−	0.868059i	$-0.334633\pi$
$211$	14.4230	0.992920	0.496460	+	0.868059i	$0.334633\pi$
$212$	81.0038	5.56336
$213$	−0.000222041 0	−1.52140e−5 0
$214$	−56.1533	−3.83856
$215$	−40.5627	−2.76635
$216$	−0.863190	−0.0587327
$217$	1.00000	0.0678844
$218$	−34.3435	−2.32604
$219$	−0.100192	−0.00677038
$220$	13.3330	0.898913
$221$	−5.19356	−0.349357
$222$	−0.0371460	−0.00249307
$223$	−7.27242	−0.486997	−0.243499	−	0.969901i	$-0.578295\pi$
$223$	−7.27242	−0.486997	−0.243499	+	0.969901i	$0.578295\pi$
$224$	−30.8669	−2.06238
$225$	−23.0340	−1.53560
$226$	−29.7843	−1.98122
$227$	−22.3205	−1.48146	−0.740730	−	0.671803i	$-0.765520\pi$
$227$	−22.3205	−1.48146	−0.740730	+	0.671803i	$0.765520\pi$
$228$	0.281523	0.0186443
$229$	13.5876	0.897893	0.448946	−	0.893559i	$-0.351799\pi$
$229$	13.5876	0.897893	0.448946	+	0.893559i	$0.351799\pi$
$230$	−19.5743	−1.29069
$231$	0.00844052	0.000555346 0
$232$	−21.1759	−1.39027
$233$	13.2081	0.865294	0.432647	−	0.901563i	$-0.357580\pi$
$233$	13.2081	0.865294	0.432647	+	0.901563i	$0.357580\pi$
$234$	7.27033	0.475276
$235$	1.69467	0.110548
$236$	19.0575	1.24054
$237$	0.0739907	0.00480621
$238$	16.8714	1.09361
$239$	2.26015	0.146197	0.0730985	−	0.997325i	$-0.476711\pi$
$239$	2.26015	0.146197	0.0730985	+	0.997325i	$0.476711\pi$
$240$	0.883694	0.0570422
$241$	−7.05091	−0.454189	−0.227094	−	0.973873i	$-0.572923\pi$
$241$	−7.05091	−0.454189	−0.227094	+	0.973873i	$0.572923\pi$
$242$	29.7243	1.91075
$243$	−0.357412	−0.0229280
$244$	−74.1228	−4.74522
$245$	−3.56068	−0.227484
$246$	−0.0246454	−0.00157133
$247$	−3.12748	−0.198997
$248$	−10.8675	−0.690085
$249$	0.144515	0.00915827
$250$	26.7603	1.69247
$251$	−27.7605	−1.75223	−0.876113	−	0.482106i	$-0.839872\pi$
$251$	−27.7605	−1.75223	−0.876113	+	0.482106i	$0.839872\pi$
$252$	−17.6182	−1.10984
$253$	1.24914	0.0785327
$254$	8.99754	0.564556
$255$	−0.283434	−0.0177493
$256$	115.242	7.20261
$257$	29.1144	1.81610	0.908052	−	0.418858i	$-0.137569\pi$
$257$	29.1144	1.81610	0.908052	+	0.418858i	$0.137569\pi$
$258$	0.423161	0.0263448
$259$	−1.00000	−0.0621370
$260$	−18.0628	−1.12021
$261$	−5.84534	−0.361818
$262$	−46.0970	−2.84788
$263$	−26.3330	−1.62376	−0.811882	−	0.583822i	$-0.801557\pi$
$263$	−26.3330	−1.62376	−0.811882	+	0.583822i	$0.801557\pi$
$264$	−0.0917271	−0.00564541
$265$	−49.1103	−3.01682
$266$	10.1597	0.622932
$267$	0.134442	0.00822769
$268$	−6.90825	−0.421988
$269$	−25.9567	−1.58261	−0.791305	−	0.611421i	$-0.790598\pi$
$269$	−25.9567	−1.58261	−0.791305	+	0.611421i	$0.790598\pi$
$270$	0.793567	0.0482950
$271$	2.81790	0.171175	0.0855875	−	0.996331i	$-0.472723\pi$
$271$	2.81790	0.171175	0.0855875	+	0.996331i	$0.472723\pi$
$272$	−112.722	−6.83477
$273$	−0.0114347	−0.000692061 0
$274$	13.6097	0.822193
$275$	−4.89558	−0.295215
$276$	0.152330	0.00916921
$277$	−1.22037	−0.0733246	−0.0366623	−	0.999328i	$-0.511673\pi$
$277$	−1.22037	−0.0733246	−0.0366623	+	0.999328i	$0.511673\pi$
$278$	28.2862	1.69649
$279$	−2.99982	−0.179595
$280$	38.6956	2.31251
$281$	2.80612	0.167399	0.0836995	−	0.996491i	$-0.473326\pi$
$281$	2.80612	0.167399	0.0836995	+	0.996491i	$0.473326\pi$
$282$	−0.0176793	−0.00105278
$283$	16.8823	1.00355	0.501773	−	0.864999i	$-0.332681\pi$
$283$	16.8823	1.00355	0.501773	+	0.864999i	$0.332681\pi$
$284$	0.0985051	0.00584520
$285$	−0.170680	−0.0101102
$286$	1.54521	0.0913703
$287$	−0.663475	−0.0391637
$288$	92.5954	5.45624
$289$	19.1542	1.12672
$290$	19.4679	1.14320
$291$	−0.145826	−0.00854848
$292$	44.4489	2.60117
$293$	0.559865	0.0327077	0.0163538	−	0.999866i	$-0.494794\pi$
$293$	0.559865	0.0327077	0.0163538	+	0.999866i	$0.494794\pi$
$294$	0.0371460	0.00216640
$295$	−11.5540	−0.672703
$296$	10.8675	0.631659
$297$	−0.0506417	−0.00293853
$298$	45.4375	2.63213
$299$	−1.69226	−0.0978659
$300$	−0.597007	−0.0344682
$301$	11.3918	0.656614
$302$	−14.1294	−0.813054
$303$	−0.257980	−0.0148206
$304$	−67.8794	−3.89315
$305$	44.9386	2.57318
$306$	−50.6113	−2.89326
$307$	15.5624	0.888191	0.444096	−	0.895979i	$-0.353525\pi$
$307$	15.5624	0.888191	0.444096	+	0.895979i	$0.353525\pi$
$308$	−3.74451	−0.213364
$309$	0.0685268	0.00389835
$310$	9.99092	0.567446
$311$	5.26695	0.298662	0.149331	−	0.988787i	$-0.452288\pi$
$311$	5.26695	0.298662	0.149331	+	0.988787i	$0.452288\pi$
$312$	0.124266	0.00703520
$313$	−6.77027	−0.382678	−0.191339	−	0.981524i	$-0.561283\pi$
$313$	−6.77027	−0.382678	−0.191339	+	0.981524i	$0.561283\pi$
$314$	−19.5382	−1.10261
$315$	10.6814	0.601830
$316$	−32.8249	−1.84654
$317$	10.9319	0.613996	0.306998	−	0.951710i	$-0.400675\pi$
$317$	10.9319	0.613996	0.306998	+	0.951710i	$0.400675\pi$
$318$	0.512332	0.0287301
$319$	−1.24235	−0.0695582
$320$	−174.886	−9.77642
$321$	−0.264937	−0.0147873
$322$	5.49735	0.306355
$323$	21.7715	1.21140
$324$	52.8484	2.93602
$325$	6.63224	0.367891
$326$	51.3328	2.84306
$327$	−0.162036	−0.00896062
$328$	7.21029	0.398122
$329$	−0.475940	−0.0262394
$330$	0.0843286	0.00464214
$331$	10.1709	0.559043	0.279522	−	0.960139i	$-0.409824\pi$
$331$	10.1709	0.559043	0.279522	+	0.960139i	$0.409824\pi$
$332$	−64.1120	−3.51860
$333$	2.99982	0.164389
$334$	−55.8185	−3.05425
$335$	4.18828	0.228830
$336$	−0.248181	−0.0135394
$337$	22.4601	1.22348	0.611741	−	0.791058i	$-0.290470\pi$
$337$	22.4601	1.22348	0.611741	+	0.791058i	$0.290470\pi$
$338$	34.3833	1.87021
$339$	−0.140525	−0.00763229
$340$	125.741	6.81929
$341$	−0.637573	−0.0345265
$342$	−30.4773	−1.64803
$343$	1.00000	0.0539949
$344$	−123.800	−6.67487
$345$	−0.0923536	−0.00497215
$346$	4.53495	0.243800
$347$	4.95016	0.265739	0.132869	−	0.991134i	$-0.457581\pi$
$347$	4.95016	0.265739	0.132869	+	0.991134i	$0.457581\pi$
$348$	−0.151502	−0.00812138
$349$	−5.37665	−0.287805	−0.143903	−	0.989592i	$-0.545965\pi$
$349$	−5.37665	−0.287805	−0.143903	+	0.989592i	$0.545965\pi$
$350$	−21.5450	−1.15163
$351$	0.0686063	0.00366193
$352$	19.6799	1.04894
$353$	−14.3675	−0.764703	−0.382352	−	0.924017i	$-0.624886\pi$
$353$	−14.3675	−0.764703	−0.382352	+	0.924017i	$0.624886\pi$
$354$	0.120535	0.00640636
$355$	−0.0597209	−0.00316966
$356$	−59.6430	−3.16107
$357$	0.0796011	0.00421294
$358$	−13.3655	−0.706387
$359$	−10.6860	−0.563984	−0.281992	−	0.959417i	$-0.590995\pi$
$359$	−10.6860	−0.563984	−0.281992	+	0.959417i	$0.590995\pi$
$360$	−116.080	−6.11796
$361$	−5.88954	−0.309976
$362$	55.5281	2.91849
$363$	0.140242	0.00736081
$364$	5.07285	0.265889
$365$	−26.9481	−1.41053
$366$	−0.468811	−0.0245051
$367$	4.63940	0.242175	0.121087	−	0.992642i	$-0.461362\pi$
$367$	4.63940	0.242175	0.121087	+	0.992642i	$0.461362\pi$
$368$	−36.7291	−1.91464
$369$	1.99031	0.103611
$370$	−9.99092	−0.519403
$371$	13.7924	0.716065
$372$	−0.0777509	−0.00403119
$373$	−31.4469	−1.62826	−0.814130	−	0.580683i	$-0.802786\pi$
$373$	−31.4469	−1.62826	−0.814130	+	0.580683i	$0.802786\pi$
$374$	−10.7568	−0.556219
$375$	0.126258	0.00651993
$376$	5.17226	0.266739
$377$	1.68306	0.0866821
$378$	−0.222869	−0.0114632
$379$	6.89347	0.354094	0.177047	−	0.984202i	$-0.443346\pi$
$379$	6.89347	0.354094	0.177047	+	0.984202i	$0.443346\pi$
$380$	75.7195	3.88433
$381$	0.0424513	0.00217485
$382$	−56.9590	−2.91428
$383$	−7.95759	−0.406614	−0.203307	−	0.979115i	$-0.565169\pi$
$383$	−7.95759	−0.406614	−0.203307	+	0.979115i	$0.565169\pi$
$384$	1.00719	0.0513979
$385$	2.27019	0.115700
$386$	46.3840	2.36088
$387$	−34.1735	−1.73714
$388$	64.6936	3.28432
$389$	−14.9920	−0.760125	−0.380063	−	0.924961i	$-0.624098\pi$
$389$	−14.9920	−0.760125	−0.380063	+	0.924961i	$0.624098\pi$
$390$	−0.114243	−0.00578494
$391$	11.7804	0.595761
$392$	−10.8675	−0.548890
$393$	−0.217490	−0.0109709
$394$	−63.7617	−3.21227
$395$	19.9008	1.00132
$396$	11.2329	0.564474
$397$	−24.7199	−1.24065	−0.620327	−	0.784343i	$-0.713000\pi$
$397$	−24.7199	−1.24065	−0.620327	+	0.784343i	$0.713000\pi$
$398$	58.3549	2.92507
$399$	0.0479345	0.00239973
$400$	143.947	7.19736
$401$	−1.68988	−0.0843888	−0.0421944	−	0.999109i	$-0.513435\pi$
$401$	−1.68988	−0.0843888	−0.0421944	+	0.999109i	$0.513435\pi$
$402$	−0.0436932	−0.00217922
$403$	0.863746	0.0430262
$404$	114.449	5.69406
$405$	−32.0405	−1.59211
$406$	−5.46747	−0.271346
$407$	0.637573	0.0316033
$408$	−0.865062	−0.0428270
$409$	14.5082	0.717383	0.358691	−	0.933456i	$-0.383223\pi$
$409$	14.5082	0.717383	0.358691	+	0.933456i	$0.383223\pi$
$410$	−6.62872	−0.327369
$411$	0.0642120	0.00316734
$412$	−30.4009	−1.49774
$413$	3.24490	0.159671
$414$	−16.4911	−0.810493
$415$	38.8693	1.90802
$416$	−26.6612	−1.30717
$417$	0.133457	0.00653543
$418$	−6.47755	−0.316827
$419$	20.6662	1.00961	0.504805	−	0.863234i	$-0.331565\pi$
$419$	20.6662	1.00961	0.504805	+	0.863234i	$0.331565\pi$
$420$	0.276846	0.0135087
$421$	18.0488	0.879647	0.439823	−	0.898084i	$-0.355041\pi$
$421$	18.0488	0.879647	0.439823	+	0.898084i	$0.355041\pi$
$422$	−40.4695	−1.97002
$423$	1.42774	0.0694189
$424$	−149.888	−7.27922
$425$	−46.1694	−2.23954
$426$	0.000623024 0	3.01856e−5 0
$427$	−12.6208	−0.610762
$428$	117.535	5.68129
$429$	0.00729047	0.000351987 0
$430$	113.815	5.48864
$431$	5.23582	0.252201	0.126100	−	0.992017i	$-0.459754\pi$
$431$	5.23582	0.252201	0.126100	+	0.992017i	$0.459754\pi$
$432$	1.48904	0.0716416
$433$	−11.9790	−0.575673	−0.287836	−	0.957680i	$-0.592936\pi$
$433$	−11.9790	−0.575673	−0.287836	+	0.957680i	$0.592936\pi$
$434$	−2.80590	−0.134688
$435$	0.0918517	0.00440395
$436$	71.8849	3.44266
$437$	7.09398	0.339351
$438$	0.281130	0.0134329
$439$	19.9143	0.950460	0.475230	−	0.879862i	$-0.342365\pi$
$439$	19.9143	0.950460	0.475230	+	0.879862i	$0.342365\pi$
$440$	−24.6713	−1.17616
$441$	−2.99982	−0.142849
$442$	14.5726	0.693149
$443$	31.8100	1.51134	0.755670	−	0.654952i	$-0.227311\pi$
$443$	31.8100	1.51134	0.755670	+	0.654952i	$0.227311\pi$
$444$	0.0777509	0.00368989
$445$	36.1599	1.71414
$446$	20.4057	0.966237
$447$	0.214379	0.0101398
$448$	49.1158	2.32050
$449$	−27.8791	−1.31569	−0.657847	−	0.753152i	$-0.728533\pi$
$449$	−27.8791	−1.31569	−0.657847	+	0.753152i	$0.728533\pi$
$450$	64.6312	3.04675
$451$	0.423013	0.0199189
$452$	62.3420	2.93232
$453$	−0.0666638	−0.00313214
$454$	62.6290	2.93932
$455$	−3.07552	−0.144183
$456$	−0.520927	−0.0243946
$457$	−10.3589	−0.484570	−0.242285	−	0.970205i	$-0.577897\pi$
$457$	−10.3589	−0.484570	−0.242285	+	0.970205i	$0.577897\pi$
$458$	−38.1254	−1.78148
$459$	−0.477593	−0.0222921
$460$	40.9713	1.91030
$461$	−9.38857	−0.437270	−0.218635	−	0.975807i	$-0.570160\pi$
$461$	−9.38857	−0.437270	−0.218635	+	0.975807i	$0.570160\pi$
$462$	−0.0236833	−0.00110185
$463$	5.70836	0.265290	0.132645	−	0.991164i	$-0.457653\pi$
$463$	5.70836	0.265290	0.132645	+	0.991164i	$0.457653\pi$
$464$	36.5295	1.69584
$465$	0.0471382	0.00218598
$466$	−37.0607	−1.71681
$467$	38.5956	1.78599	0.892997	−	0.450063i	$-0.148599\pi$
$467$	38.5956	1.78599	0.892997	+	0.450063i	$0.148599\pi$
$468$	−15.2176	−0.703436
$469$	−1.17626	−0.0543145
$470$	−4.75508	−0.219335
$471$	−0.0921833	−0.00424758
$472$	−35.2638	−1.62315
$473$	−7.26312	−0.333959
$474$	−0.207611	−0.00953587
$475$	−27.8025	−1.27566
$476$	−35.3139	−1.61861
$477$	−41.3748	−1.89442
$478$	−6.34175	−0.290065
$479$	26.8781	1.22809	0.614047	−	0.789270i	$-0.289541\pi$
$479$	26.8781	1.22809	0.614047	+	0.789270i	$0.289541\pi$
$480$	−1.45501	−0.0664119
$481$	−0.863746	−0.0393834
$482$	19.7841	0.901143
$483$	0.0259371	0.00118018
$484$	−62.2164	−2.82802
$485$	−39.2219	−1.78098
$486$	1.00286	0.0454908
$487$	25.7111	1.16508	0.582541	−	0.812802i	$-0.302059\pi$
$487$	25.7111	1.16508	0.582541	+	0.812802i	$0.302059\pi$
$488$	137.156	6.20875
$489$	0.242193	0.0109524
$490$	9.99092	0.451344
$491$	−18.4665	−0.833381	−0.416691	−	0.909048i	$-0.636810\pi$
$491$	−18.4665	−0.833381	−0.416691	+	0.909048i	$0.636810\pi$
$492$	0.0515857	0.00232566
$493$	−11.7164	−0.527679
$494$	8.77540	0.394824
$495$	−6.81019	−0.306095
$496$	18.7469	0.841760
$497$	0.0167723	0.000752341 0
$498$	−0.405495	−0.0181707
$499$	−20.1408	−0.901627	−0.450814	−	0.892618i	$-0.648866\pi$
$499$	−20.1408	−0.901627	−0.450814	+	0.892618i	$0.648866\pi$
$500$	−56.0125	−2.50495
$501$	−0.263357	−0.0117659
$502$	77.8931	3.47654
$503$	−7.84681	−0.349872	−0.174936	−	0.984580i	$-0.555972\pi$
$503$	−7.84681	−0.349872	−0.174936	+	0.984580i	$0.555972\pi$
$504$	32.6005	1.45214
$505$	−69.3874	−3.08770
$506$	−3.50496	−0.155815
$507$	0.162224	0.00720463
$508$	−18.8329	−0.835575
$509$	6.65561	0.295005	0.147502	−	0.989062i	$-0.452877\pi$
$509$	6.65561	0.295005	0.147502	+	0.989062i	$0.452877\pi$
$510$	0.795288	0.0352160
$511$	7.56825	0.334800
$512$	−171.197	−7.56589
$513$	−0.287599	−0.0126978
$514$	−81.6920	−3.60328
$515$	18.4312	0.812176
$516$	−0.885725	−0.0389919
$517$	0.303446	0.0133456
$518$	2.80590	0.123284
$519$	0.0213964	0.000939196 0
$520$	33.4232	1.46570
$521$	−34.3388	−1.50441	−0.752204	−	0.658930i	$-0.771009\pi$
$521$	−34.3388	−1.50441	−0.752204	+	0.658930i	$0.771009\pi$
$522$	16.4015	0.717872
$523$	−20.9539	−0.916251	−0.458126	−	0.888888i	$-0.651479\pi$
$523$	−20.9539	−0.916251	−0.458126	+	0.888888i	$0.651479\pi$
$524$	96.4863	4.21502
$525$	−0.101652	−0.00443644
$526$	73.8878	3.22166
$527$	−6.01284	−0.261923
$528$	0.158233	0.00688623
$529$	−19.1615	−0.833108
$530$	137.799	5.98559
$531$	−9.73412	−0.422425
$532$	−21.2655	−0.921974
$533$	−0.573073	−0.0248226
$534$	−0.377230	−0.0163243
$535$	−71.2585	−3.08077
$536$	12.7829	0.552139
$537$	−0.0630596	−0.00272122
$538$	72.8321	3.14001
$539$	−0.637573	−0.0274622
$540$	−1.66103	−0.0714793
$541$	5.37427	0.231058	0.115529	−	0.993304i	$-0.463144\pi$
$541$	5.37427	0.231058	0.115529	+	0.993304i	$0.463144\pi$
$542$	−7.90673	−0.339623
$543$	0.261987	0.0112430
$544$	185.598	7.95744
$545$	−43.5818	−1.86684
$546$	0.0320847	0.00137310
$547$	33.9507	1.45163	0.725814	−	0.687891i	$-0.241463\pi$
$547$	33.9507	1.45163	0.725814	+	0.687891i	$0.241463\pi$
$548$	−28.4867	−1.21689
$549$	37.8601	1.61583
$550$	13.7365	0.585727
$551$	−7.05542	−0.300571
$552$	−0.281870	−0.0119972
$553$	−5.58904	−0.237670
$554$	3.42422	0.145481
$555$	−0.0471382	−0.00200090
$556$	−59.2063	−2.51091
$557$	15.9827	0.677208	0.338604	−	0.940929i	$-0.390045\pi$
$557$	15.9827	0.677208	0.338604	+	0.940929i	$0.390045\pi$
$558$	8.41721	0.356329
$559$	9.83965	0.416173
$560$	−66.7517	−2.82077
$561$	−0.0507515	−0.00214273
$562$	−7.87369	−0.332132
$563$	−36.3412	−1.53160	−0.765800	−	0.643078i	$-0.777657\pi$
$563$	−36.3412	−1.53160	−0.765800	+	0.643078i	$0.777657\pi$
$564$	0.0370047	0.00155818
$565$	−37.7962	−1.59010
$566$	−47.3699	−1.99111
$567$	8.99842	0.377898
$568$	−0.182273	−0.00764799
$569$	34.0083	1.42570	0.712851	−	0.701316i	$-0.247404\pi$
$569$	34.0083	1.42570	0.712851	+	0.701316i	$0.247404\pi$
$570$	0.478910	0.0200593
$571$	10.8398	0.453631	0.226816	−	0.973938i	$-0.427169\pi$
$571$	10.8398	0.453631	0.226816	+	0.973938i	$0.427169\pi$
$572$	−3.23431	−0.135233
$573$	−0.268739	−0.0112267
$574$	1.86164	0.0777035
$575$	−15.0437	−0.627367
$576$	−147.339	−6.13912
$577$	28.1811	1.17319	0.586597	−	0.809879i	$-0.300467\pi$
$577$	28.1811	1.17319	0.586597	+	0.809879i	$0.300467\pi$
$578$	−53.7448	−2.23549
$579$	0.218844	0.00909486
$580$	−40.7486	−1.69200
$581$	−10.9163	−0.452882
$582$	0.409174	0.0169608
$583$	−8.79365	−0.364196
$584$	−82.2477	−3.40343
$585$	9.22604	0.381450
$586$	−1.57093	−0.0648943
$587$	6.83669	0.282180	0.141090	−	0.989997i	$-0.454939\pi$
$587$	6.83669	0.282180	0.141090	+	0.989997i	$0.454939\pi$
$588$	−0.0777509	−0.00320639
$589$	−3.62084	−0.149194
$590$	32.4195	1.33469
$591$	−0.300834	−0.0123747
$592$	−18.7469	−0.770492
$593$	3.48288	0.143025	0.0715124	−	0.997440i	$-0.477217\pi$
$593$	3.48288	0.143025	0.0715124	+	0.997440i	$0.477217\pi$
$594$	0.142095	0.00583025
$595$	21.4098	0.877716
$596$	−95.1061	−3.89570
$597$	0.275324	0.0112683
$598$	4.74831	0.194173
$599$	−11.9143	−0.486806	−0.243403	−	0.969925i	$-0.578264\pi$
$599$	−11.9143	−0.486806	−0.243403	+	0.969925i	$0.578264\pi$
$600$	1.10469	0.0450990
$601$	28.4527	1.16061	0.580305	−	0.814399i	$-0.302933\pi$
$601$	28.4527	1.16061	0.580305	+	0.814399i	$0.302933\pi$
$602$	−31.9643	−1.30277
$603$	3.52856	0.143694
$604$	29.5744	1.20337
$605$	37.7201	1.53354
$606$	0.723867	0.0294051
$607$	13.3905	0.543502	0.271751	−	0.962368i	$-0.412397\pi$
$607$	13.3905	0.543502	0.271751	+	0.962368i	$0.412397\pi$
$608$	111.764	4.53264
$609$	−0.0257961	−0.00104531
$610$	−126.093	−5.10536
$611$	−0.411091	−0.0166310
$612$	105.935	4.28218
$613$	32.1371	1.29801	0.649003	−	0.760786i	$-0.275186\pi$
$613$	32.1371	1.29801	0.649003	+	0.760786i	$0.275186\pi$
$614$	−43.6665	−1.76223
$615$	−0.0312750	−0.00126113
$616$	6.92880	0.279169
$617$	33.0962	1.33240	0.666201	−	0.745772i	$-0.267919\pi$
$617$	33.0962	1.33240	0.666201	+	0.745772i	$0.267919\pi$
$618$	−0.192279	−0.00773461
$619$	−0.376129	−0.0151179	−0.00755896	−	0.999971i	$-0.502406\pi$
$619$	−0.376129	−0.0151179	−0.00755896	+	0.999971i	$0.502406\pi$
$620$	−20.9122	−0.839853
$621$	−0.155618	−0.00624473
$622$	−14.7785	−0.592566
$623$	−10.1553	−0.406865
$624$	−0.214365	−0.00858148
$625$	−4.43351	−0.177340
$626$	18.9967	0.759261
$627$	−0.0305618	−0.00122052
$628$	40.8958	1.63192
$629$	6.01284	0.239748
$630$	−29.9710	−1.19407
$631$	−38.4004	−1.52869	−0.764347	−	0.644805i	$-0.776938\pi$
$631$	−38.4004	−1.52869	−0.764347	+	0.644805i	$0.776938\pi$
$632$	60.7388	2.41606
$633$	−0.190939	−0.00758915
$634$	−30.6738	−1.21821
$635$	11.4179	0.453104
$636$	−1.07237	−0.0425223
$637$	0.863746	0.0342229
$638$	3.48591	0.138008
$639$	−0.0503140	−0.00199039
$640$	270.897	10.7082
$641$	18.4024	0.726851	0.363426	−	0.931623i	$-0.381607\pi$
$641$	18.4024	0.726851	0.363426	+	0.931623i	$0.381607\pi$
$642$	0.743387	0.0293391
$643$	13.7871	0.543709	0.271854	−	0.962338i	$-0.412363\pi$
$643$	13.7871	0.543709	0.271854	+	0.962338i	$0.412363\pi$
$644$	−11.5066	−0.453423
$645$	0.536990	0.0211440
$646$	−61.0887	−2.40350
$647$	−31.7424	−1.24792	−0.623962	−	0.781455i	$-0.714478\pi$
$647$	−31.7424	−1.24792	−0.623962	+	0.781455i	$0.714478\pi$
$648$	−97.7901	−3.84156
$649$	−2.06886	−0.0812098
$650$	−18.6094	−0.729921
$651$	−0.0132385	−0.000518859 0
$652$	−107.446	−4.20789
$653$	2.90396	0.113641	0.0568203	−	0.998384i	$-0.481904\pi$
$653$	2.90396	0.113641	0.0568203	+	0.998384i	$0.481904\pi$
$654$	0.454657	0.0177785
$655$	−58.4970	−2.28567
$656$	−12.4381	−0.485626
$657$	−22.7034	−0.885745
$658$	1.33544	0.0520609
$659$	−14.8052	−0.576729	−0.288364	−	0.957521i	$-0.593111\pi$
$659$	−14.8052	−0.576729	−0.288364	+	0.957521i	$0.593111\pi$
$660$	−0.176510	−0.00687063
$661$	−5.68123	−0.220974	−0.110487	−	0.993878i	$-0.535241\pi$
$661$	−5.68123	−0.220974	−0.110487	+	0.993878i	$0.535241\pi$
$662$	−28.5385	−1.10918
$663$	0.0687551	0.00267023
$664$	118.632	4.60382
$665$	12.8927	0.499956
$666$	−8.41721	−0.326160
$667$	−3.81764	−0.147820
$668$	116.835	4.52047
$669$	0.0962761	0.00372225
$670$	−11.7519	−0.454015
$671$	8.04666	0.310638
$672$	0.408633	0.0157634
$673$	24.7550	0.954235	0.477118	−	0.878839i	$-0.341682\pi$
$673$	24.7550	0.954235	0.477118	+	0.878839i	$0.341682\pi$
$674$	−63.0209	−2.42747
$675$	0.609891	0.0234747
$676$	−71.9684	−2.76801
$677$	4.43538	0.170466	0.0852328	−	0.996361i	$-0.472837\pi$
$677$	4.43538	0.170466	0.0852328	+	0.996361i	$0.472837\pi$
$678$	0.394300	0.0151430
$679$	11.0153	0.422728
$680$	−232.670	−8.92250
$681$	0.295490	0.0113232
$682$	1.78897	0.0685030
$683$	−26.4567	−1.01234	−0.506168	−	0.862435i	$-0.668938\pi$
$683$	−26.4567	−1.01234	−0.506168	+	0.862435i	$0.668938\pi$
$684$	63.7926	2.43917
$685$	17.2707	0.659880
$686$	−2.80590	−0.107130
$687$	−0.179880	−0.00686283
$688$	213.561	8.14195
$689$	11.9131	0.453854
$690$	0.259135	0.00986511
$691$	12.3727	0.470680	0.235340	−	0.971913i	$-0.424380\pi$
$691$	12.3727	0.470680	0.235340	+	0.971913i	$0.424380\pi$
$692$	−9.49218	−0.360838
$693$	1.91261	0.0726539
$694$	−13.8897	−0.527244
$695$	35.8951	1.36158
$696$	0.280338	0.0106262
$697$	3.98937	0.151108
$698$	15.0863	0.571027
$699$	−0.174856	−0.00661367
$700$	45.0962	1.70448
$701$	−13.9328	−0.526234	−0.263117	−	0.964764i	$-0.584751\pi$
$701$	−13.9328	−0.526234	−0.263117	+	0.964764i	$0.584751\pi$
$702$	−0.192502	−0.00726554
$703$	3.62084	0.136562
$704$	−31.3149	−1.18022
$705$	−0.0224349	−0.000844949 0
$706$	40.3137	1.51723
$707$	19.4871	0.732887
$708$	−0.252294	−0.00948177
$709$	−4.90012	−0.184028	−0.0920140	−	0.995758i	$-0.529330\pi$
$709$	−4.90012	−0.184028	−0.0920140	+	0.995758i	$0.529330\pi$
$710$	0.167571	0.00628882
$711$	16.7662	0.628780
$712$	110.363	4.13602
$713$	−1.95921	−0.0733730
$714$	−0.223353	−0.00835877
$715$	1.96087	0.0733324
$716$	27.9755	1.04549
$717$	−0.0299210	−0.00111742
$718$	29.9838	1.11899
$719$	−40.8715	−1.52425	−0.762124	−	0.647431i	$-0.775843\pi$
$719$	−40.8715	−1.52425	−0.762124	+	0.647431i	$0.775843\pi$
$720$	200.243	7.46263
$721$	−5.17631	−0.192776
$722$	16.5255	0.615014
$723$	0.0933436	0.00347149
$724$	−116.227	−4.31954
$725$	14.9620	0.555673
$726$	−0.393506	−0.0146044
$727$	16.4563	0.610332	0.305166	−	0.952299i	$-0.401288\pi$
$727$	16.4563	0.610332	0.305166	+	0.952299i	$0.401288\pi$
$728$	−9.38673	−0.347895
$729$	−26.9905	−0.999650
$730$	75.6138	2.79859
$731$	−68.4972	−2.53346
$732$	0.981276	0.0362690
$733$	−44.7084	−1.65134	−0.825672	−	0.564150i	$-0.809204\pi$
$733$	−44.7084	−1.65134	−0.825672	+	0.564150i	$0.809204\pi$
$734$	−13.0177	−0.480492
$735$	0.0471382	0.00173872
$736$	60.4748	2.22913
$737$	0.749949	0.0276247
$738$	−5.58461	−0.205572
$739$	−16.8502	−0.619843	−0.309922	−	0.950762i	$-0.600303\pi$
$739$	−16.8502	−0.619843	−0.309922	+	0.950762i	$0.600303\pi$
$740$	20.9122	0.768747
$741$	0.0414032	0.00152099
$742$	−38.7001	−1.42072
$743$	−43.7276	−1.60421	−0.802104	−	0.597184i	$-0.796286\pi$
$743$	−43.7276	−1.60421	−0.802104	+	0.597184i	$0.796286\pi$
$744$	0.143869	0.00527450
$745$	57.6602	2.11251
$746$	88.2369	3.23058
$747$	32.7468	1.19814
$748$	22.5152	0.823236
$749$	20.0126	0.731244
$750$	−0.354267	−0.0129360
$751$	20.7246	0.756252	0.378126	−	0.925754i	$-0.376569\pi$
$751$	20.7246	0.756252	0.378126	+	0.925754i	$0.376569\pi$
$752$	−8.92239	−0.325366
$753$	0.367508	0.0133927
$754$	−4.72250	−0.171983
$755$	−17.9302	−0.652545
$756$	0.466492	0.0169661
$757$	−38.3766	−1.39482	−0.697411	−	0.716672i	$-0.745665\pi$
$757$	−38.3766	−1.39482	−0.697411	+	0.716672i	$0.745665\pi$
$758$	−19.3424	−0.702547
$759$	−0.0165368	−0.000600246 0
$760$	−140.110	−5.08234
$761$	−14.2628	−0.517026	−0.258513	−	0.966008i	$-0.583233\pi$
$761$	−14.2628	−0.517026	−0.258513	+	0.966008i	$0.583233\pi$
$762$	−0.119114	−0.00431505
$763$	12.2397	0.443108
$764$	119.222	4.31330
$765$	−64.2257	−2.32208
$766$	22.3282	0.806751
$767$	2.80277	0.101202
$768$	−1.52563	−0.0550515
$769$	−18.4459	−0.665177	−0.332589	−	0.943072i	$-0.607922\pi$
$769$	−18.4459	−0.665177	−0.332589	+	0.943072i	$0.607922\pi$
$770$	−6.36994	−0.229557
$771$	−0.385431	−0.0138810
$772$	−97.0871	−3.49424
$773$	−41.5861	−1.49575	−0.747873	−	0.663842i	$-0.768925\pi$
$773$	−41.5861	−1.49575	−0.747873	+	0.663842i	$0.768925\pi$
$774$	95.8874	3.44660
$775$	7.67846	0.275819
$776$	−119.708	−4.29728
$777$	0.0132385	0.000474929 0
$778$	42.0661	1.50814
$779$	2.40233	0.0860725
$780$	0.239125	0.00856204
$781$	−0.0106936	−0.000382646 0
$782$	−33.0547	−1.18203
$783$	0.154772	0.00553110
$784$	18.7469	0.669531
$785$	−24.7940	−0.884935
$786$	0.610256	0.0217671
$787$	−32.1149	−1.14477	−0.572387	−	0.819984i	$-0.693982\pi$
$787$	−32.1149	−1.14477	−0.572387	+	0.819984i	$0.693982\pi$
$788$	133.461	4.75434
$789$	0.348610	0.0124109
$790$	−55.8397	−1.98669
$791$	10.6149	0.377422
$792$	−20.7852	−0.738570
$793$	−10.9011	−0.387111
$794$	69.3615	2.46155
$795$	0.650148	0.0230584
$796$	−122.144	−4.32927
$797$	21.4198	0.758728	0.379364	−	0.925248i	$-0.376143\pi$
$797$	21.4198	0.758728	0.379364	+	0.925248i	$0.376143\pi$
$798$	−0.134500	−0.00476123
$799$	2.86175	0.101241
$800$	−237.011	−8.37959
$801$	30.4642	1.07640
$802$	4.74165	0.167433
$803$	−4.82531	−0.170281
$804$	0.0914550	0.00322537
$805$	6.97613	0.245876
$806$	−2.42358	−0.0853671
$807$	0.343629	0.0120963
$808$	−211.775	−7.45023
$809$	17.4992	0.615238	0.307619	−	0.951510i	$-0.400468\pi$
$809$	17.4992	0.615238	0.307619	+	0.951510i	$0.400468\pi$
$810$	89.9025	3.15885
$811$	39.6188	1.39120	0.695602	−	0.718427i	$-0.255138\pi$
$811$	39.6188	1.39120	0.695602	+	0.718427i	$0.255138\pi$
$812$	11.4441	0.401607
$813$	−0.0373048	−0.00130834
$814$	−1.78897	−0.0627032
$815$	65.1412	2.28180
$816$	1.49227	0.0522400
$817$	−41.2480	−1.44308
$818$	−40.7085	−1.42334
$819$	−2.59109	−0.0905399
$820$	13.8747	0.484525
$821$	−52.3139	−1.82577	−0.912884	−	0.408220i	$-0.866150\pi$
$821$	−52.3139	−1.82577	−0.912884	+	0.408220i	$0.866150\pi$
$822$	−0.180172	−0.00628424
$823$	29.6983	1.03522	0.517609	−	0.855617i	$-0.326822\pi$
$823$	29.6983	1.03522	0.517609	+	0.855617i	$0.326822\pi$
$824$	56.2534	1.95968
$825$	0.0648103	0.00225640
$826$	−9.10486	−0.316798
$827$	−3.85946	−0.134206	−0.0671032	−	0.997746i	$-0.521376\pi$
$827$	−3.85946	−0.134206	−0.0671032	+	0.997746i	$0.521376\pi$
$828$	34.5178	1.19958
$829$	−29.9803	−1.04126	−0.520630	−	0.853782i	$-0.674303\pi$
$829$	−29.9803	−1.04126	−0.520630	+	0.853782i	$0.674303\pi$
$830$	−109.063	−3.78565
$831$	0.0161558	0.000560440 0
$832$	42.4236	1.47077
$833$	−6.01284	−0.208332
$834$	−0.374468	−0.0129667
$835$	−70.8336	−2.45130
$836$	13.5583	0.468923
$837$	0.0794288	0.00274546
$838$	−57.9873	−2.00314
$839$	8.74406	0.301879	0.150939	−	0.988543i	$-0.451770\pi$
$839$	8.74406	0.301879	0.150939	+	0.988543i	$0.451770\pi$
$840$	−0.512273	−0.0176751
$841$	−25.2031	−0.869073
$842$	−50.6433	−1.74528
$843$	−0.0371489	−0.00127947
$844$	84.7074	2.91575
$845$	43.6324	1.50100
$846$	−4.00609	−0.137732
$847$	−10.5935	−0.363997
$848$	258.564	8.87914
$849$	−0.223496	−0.00767037
$850$	129.547	4.44341
$851$	1.95921	0.0671609
$852$	−0.00130406	−4.46764e−5 0
$853$	36.9488	1.26510	0.632552	−	0.774518i	$-0.282008\pi$
$853$	36.9488	1.26510	0.632552	+	0.774518i	$0.282008\pi$
$854$	35.4126	1.21180
$855$	−38.6757	−1.32268
$856$	−217.486	−7.43352
$857$	−29.3361	−1.00210	−0.501052	−	0.865417i	$-0.667053\pi$
$857$	−29.3361	−1.00210	−0.501052	+	0.865417i	$0.667053\pi$
$858$	−0.0204563	−0.000698367 0
$859$	6.00886	0.205020	0.102510	−	0.994732i	$-0.467313\pi$
$859$	6.00886	0.205020	0.102510	+	0.994732i	$0.467313\pi$
$860$	−238.228	−8.12350
$861$	0.00878343	0.000299338 0
$862$	−14.6912	−0.500384
$863$	37.2606	1.26836	0.634182	−	0.773184i	$-0.281337\pi$
$863$	37.2606	1.26836	0.634182	+	0.773184i	$0.281337\pi$
$864$	−2.45173	−0.0834094
$865$	5.75484	0.195671
$866$	33.6118	1.14218
$867$	−0.253573	−0.00861180
$868$	5.87308	0.199345
$869$	3.56342	0.120881
$870$	−0.257727	−0.00873775
$871$	−1.01599	−0.0344254
$872$	−133.015	−4.50446
$873$	−33.0439	−1.11837
$874$	−19.9050	−0.673297
$875$	−9.53716	−0.322415
$876$	−0.588438	−0.0198815
$877$	−36.8583	−1.24462	−0.622308	−	0.782772i	$-0.713805\pi$
$877$	−36.8583	−1.24462	−0.622308	+	0.782772i	$0.713805\pi$
$878$	−55.8777	−1.88578
$879$	−0.00741179	−0.000249993 0
$880$	42.5591	1.43467
$881$	−52.6556	−1.77401	−0.887005	−	0.461759i	$-0.847219\pi$
$881$	−52.6556	−1.77401	−0.887005	+	0.461759i	$0.847219\pi$
$882$	8.41721	0.283422
$883$	−52.6774	−1.77274	−0.886368	−	0.462982i	$-0.846780\pi$
$883$	−52.6774	−1.77274	−0.886368	+	0.462982i	$0.846780\pi$
$884$	−30.5022	−1.02590
$885$	0.152959	0.00514164
$886$	−89.2558	−2.99861
$887$	4.52044	0.151782	0.0758908	−	0.997116i	$-0.475820\pi$
$887$	4.52044	0.151782	0.0758908	+	0.997116i	$0.475820\pi$
$888$	−0.143869	−0.00482794
$889$	−3.20665	−0.107548
$890$	−101.461	−3.40098
$891$	−5.73715	−0.192202
$892$	−42.7115	−1.43009
$893$	1.72330	0.0576681
$894$	−0.601526	−0.0201180
$895$	−16.9607	−0.566935
$896$	−76.0802	−2.54166
$897$	0.0224030	0.000748015 0
$898$	78.2259	2.61043
$899$	1.94856	0.0649882
$900$	−135.281	−4.50936
$901$	−82.9314	−2.76285
$902$	−1.18693	−0.0395206
$903$	−0.150811	−0.00501868
$904$	−115.357	−3.83671
$905$	70.4651	2.34234
$906$	0.187052	0.00621439
$907$	0.128933	0.00428116	0.00214058	−	0.999998i	$-0.499319\pi$
$907$	0.128933	0.00428116	0.00214058	+	0.999998i	$0.499319\pi$
$908$	−131.090	−4.35037
$909$	−58.4579	−1.93892
$910$	8.62962	0.286069
$911$	−49.3481	−1.63498	−0.817488	−	0.575945i	$-0.804634\pi$
$911$	−49.3481	−1.63498	−0.817488	+	0.575945i	$0.804634\pi$
$912$	0.898623	0.0297564
$913$	6.95990	0.230339
$914$	29.0661	0.961421
$915$	−0.594920	−0.0196675
$916$	79.8009	2.63670
$917$	16.4286	0.542519
$918$	1.34008	0.0442291
$919$	−45.2934	−1.49409	−0.747045	−	0.664773i	$-0.768528\pi$
$919$	−45.2934	−1.49409	−0.747045	+	0.664773i	$0.768528\pi$
$920$	−75.8129	−2.49948
$921$	−0.206023	−0.00678868
$922$	26.3434	0.867574
$923$	0.0144870	0.000476846 0
$924$	0.0495718	0.00163079
$925$	−7.67846	−0.252466
$926$	−16.0171	−0.526354
$927$	15.5280	0.510008
$928$	−60.1461	−1.97439
$929$	21.2204	0.696219	0.348109	−	0.937454i	$-0.386824\pi$
$929$	21.2204	0.696219	0.348109	+	0.937454i	$0.386824\pi$
$930$	−0.132265	−0.00433714
$931$	−3.62084	−0.118668
$932$	77.5725	2.54097
$933$	−0.0697267	−0.00228275
$934$	−108.296	−3.54354
$935$	−13.6503	−0.446413
$936$	28.1585	0.920391
$937$	2.07144	0.0676709	0.0338355	−	0.999427i	$-0.489228\pi$
$937$	2.07144	0.0676709	0.0338355	+	0.999427i	$0.489228\pi$
$938$	3.30046	0.107764
$939$	0.0896284	0.00292491
$940$	9.95294	0.324629
$941$	−13.4762	−0.439311	−0.219656	−	0.975577i	$-0.570493\pi$
$941$	−13.4762	−0.439311	−0.219656	+	0.975577i	$0.570493\pi$
$942$	0.258657	0.00842751
$943$	1.29989	0.0423301
$944$	60.8317	1.97990
$945$	−0.282821	−0.00920016
$946$	20.3796	0.662598
$947$	−35.4294	−1.15130	−0.575651	−	0.817696i	$-0.695251\pi$
$947$	−35.4294	−1.15130	−0.575651	+	0.817696i	$0.695251\pi$
$948$	0.434553	0.0141136
$949$	6.53704	0.212201
$950$	78.0109	2.53101
$951$	−0.144722	−0.00469294
$952$	65.3443	2.11782
$953$	−19.7176	−0.638715	−0.319357	−	0.947634i	$-0.603467\pi$
$953$	−19.7176	−0.638715	−0.319357	+	0.947634i	$0.603467\pi$
$954$	116.093	3.75866
$955$	−72.2809	−2.33896
$956$	13.2740	0.429313
$957$	0.0164469	0.000531652 0
$958$	−75.4174	−2.43662
$959$	−4.85039	−0.156627
$960$	2.31523	0.0747237
$961$	1.00000	0.0322581
$962$	2.42358	0.0781395
$963$	−60.0342	−1.93458
$964$	−41.4105	−1.33374
$965$	58.8612	1.89481
$966$	−0.0727768	−0.00234156
$967$	12.4798	0.401324	0.200662	−	0.979661i	$-0.435691\pi$
$967$	12.4798	0.401324	0.200662	+	0.979661i	$0.435691\pi$
$968$	115.125	3.70024
$969$	−0.288222	−0.00925904
$970$	110.053	3.53358
$971$	18.9504	0.608147	0.304074	−	0.952649i	$-0.401653\pi$
$971$	18.9504	0.608147	0.304074	+	0.952649i	$0.401653\pi$
$972$	−2.09911	−0.0673290
$973$	−10.0810	−0.323181
$974$	−72.1428	−2.31160
$975$	−0.0878011	−0.00281188
$976$	−236.600	−7.57339
$977$	1.95625	0.0625861	0.0312930	−	0.999510i	$-0.490037\pi$
$977$	1.95625	0.0625861	0.0312930	+	0.999510i	$0.490037\pi$
$978$	−0.679570	−0.0217303
$979$	6.47476	0.206934
$980$	−20.9122	−0.668015
$981$	−36.7171	−1.17229
$982$	51.8152	1.65349
$983$	39.9406	1.27391	0.636954	−	0.770901i	$-0.280194\pi$
$983$	39.9406	1.27391	0.636954	+	0.770901i	$0.280194\pi$
$984$	−0.0954536	−0.00304295
$985$	−80.9135	−2.57812
$986$	32.8750	1.04695
$987$	0.00630074	0.000200555 0
$988$	−18.3679	−0.584362
$989$	−22.3190	−0.709703
$990$	19.1087	0.607315
$991$	9.94572	0.315936	0.157968	−	0.987444i	$-0.449506\pi$
$991$	9.94572	0.315936	0.157968	+	0.987444i	$0.449506\pi$
$992$	−30.8669	−0.980026
$993$	−0.134648	−0.00427292
$994$	−0.0470614	−0.00149270
$995$	74.0523	2.34762
$996$	0.848748	0.0268936
$997$	1.40108	0.0443727	0.0221863	−	0.999754i	$-0.492937\pi$
$997$	1.40108	0.0443727	0.0221863	+	0.999754i	$0.492937\pi$
$998$	56.5132	1.78889
$999$	−0.0794288	−0.00251302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.d.1.1	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.d.1.1	✓	66	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80590 q^{2} -0.0132385 q^{3} +5.87308 q^{4} -3.56068 q^{5} +0.0371460 q^{6} +1.00000 q^{7} -10.8675 q^{8} -2.99982 q^{9} +O(q^{10})\)	\(q-2.80590 q^{2} -0.0132385 q^{3} +5.87308 q^{4} -3.56068 q^{5} +0.0371460 q^{6} +1.00000 q^{7} -10.8675 q^{8} -2.99982 q^{9} +9.99092 q^{10} -0.637573 q^{11} -0.0777509 q^{12} +0.863746 q^{13} -2.80590 q^{14} +0.0471382 q^{15} +18.7469 q^{16} -6.01284 q^{17} +8.41721 q^{18} -3.62084 q^{19} -20.9122 q^{20} -0.0132385 q^{21} +1.78897 q^{22} -1.95921 q^{23} +0.143869 q^{24} +7.67846 q^{25} -2.42358 q^{26} +0.0794288 q^{27} +5.87308 q^{28} +1.94856 q^{29} -0.132265 q^{30} +1.00000 q^{31} -30.8669 q^{32} +0.00844052 q^{33} +16.8714 q^{34} -3.56068 q^{35} -17.6182 q^{36} -1.00000 q^{37} +10.1597 q^{38} -0.0114347 q^{39} +38.6956 q^{40} -0.663475 q^{41} +0.0371460 q^{42} +11.3918 q^{43} -3.74451 q^{44} +10.6814 q^{45} +5.49735 q^{46} -0.475940 q^{47} -0.248181 q^{48} +1.00000 q^{49} -21.5450 q^{50} +0.0796011 q^{51} +5.07285 q^{52} +13.7924 q^{53} -0.222869 q^{54} +2.27019 q^{55} -10.8675 q^{56} +0.0479345 q^{57} -5.46747 q^{58} +3.24490 q^{59} +0.276846 q^{60} -12.6208 q^{61} -2.80590 q^{62} -2.99982 q^{63} +49.1158 q^{64} -3.07552 q^{65} -0.0236833 q^{66} -1.17626 q^{67} -35.3139 q^{68} +0.0259371 q^{69} +9.99092 q^{70} +0.0167723 q^{71} +32.6005 q^{72} +7.56825 q^{73} +2.80590 q^{74} -0.101652 q^{75} -21.2655 q^{76} -0.637573 q^{77} +0.0320847 q^{78} -5.58904 q^{79} -66.7517 q^{80} +8.99842 q^{81} +1.86164 q^{82} -10.9163 q^{83} -0.0777509 q^{84} +21.4098 q^{85} -31.9643 q^{86} -0.0257961 q^{87} +6.92880 q^{88} -10.1553 q^{89} -29.9710 q^{90} +0.863746 q^{91} -11.5066 q^{92} -0.0132385 q^{93} +1.33544 q^{94} +12.8927 q^{95} +0.408633 q^{96} +11.0153 q^{97} -2.80590 q^{98} +1.91261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9}+O(q^{10}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9	\( 66 q - 5 q^{2} - 12 q^{3} + 63 q^{4} - 26 q^{5} - 19 q^{6} + 66 q^{7} - 15 q^{8} + 66 q^{9} - 6 q^{10} - 57 q^{11} - 29 q^{12} - 28 q^{13} - 5 q^{14} - 24 q^{15} + 69 q^{16} - 47 q^{17} + 8 q^{18} - 27 q^{19} - 77 q^{20} - 12 q^{21} - 12 q^{22} - 46 q^{23} - 57 q^{24} + 72 q^{25} - 21 q^{26} - 36 q^{27} + 63 q^{28} - 62 q^{29} + 2 q^{30} + 66 q^{31} - 40 q^{32} + 4 q^{33} - 46 q^{34} - 26 q^{35} + 62 q^{36} - 66 q^{37} - 31 q^{38} - 8 q^{39} - 37 q^{40} - 33 q^{41} - 19 q^{42} - 22 q^{43} - 84 q^{44} - 77 q^{45} - 14 q^{46} - 20 q^{47} - 43 q^{48} + 66 q^{49} - 10 q^{50} - 39 q^{51} - 41 q^{52} - 47 q^{53} - 65 q^{54} - 15 q^{55} - 15 q^{56} + 5 q^{57} + 24 q^{58} - 125 q^{59} - 77 q^{60} - 57 q^{61} - 5 q^{62} + 66 q^{63} + 81 q^{64} - 40 q^{65} + 33 q^{66} - 25 q^{67} - 107 q^{68} - 72 q^{69} - 6 q^{70} - 57 q^{71} + 38 q^{72} + 5 q^{73} + 5 q^{74} - 60 q^{75} - 33 q^{76} - 57 q^{77} - 19 q^{78} - 4 q^{79} - 132 q^{80} + 58 q^{81} + 8 q^{82} - 84 q^{83} - 29 q^{84} - 33 q^{85} - 60 q^{86} - 31 q^{87} + 21 q^{88} - 132 q^{89} - 61 q^{90} - 28 q^{91} - 100 q^{92} - 12 q^{93} - 35 q^{94} + 4 q^{95} - 198 q^{96} - 39 q^{97} - 5 q^{98} - 174 q^{99}+O(q^{100}) \) 66 * q - 5 * q^2 - 12 * q^3 + 63 * q^4 - 26 * q^5 - 19 * q^6 + 66 * q^7 - 15 * q^8 + 66 * q^9 - 6 * q^10 - 57 * q^11 - 29 * q^12 - 28 * q^13 - 5 * q^14 - 24 * q^15 + 69 * q^16 - 47 * q^17 + 8 * q^18 - 27 * q^19 - 77 * q^20 - 12 * q^21 - 12 * q^22 - 46 * q^23 - 57 * q^24 + 72 * q^25 - 21 * q^26 - 36 * q^27 + 63 * q^28 - 62 * q^29 + 2 * q^30 + 66 * q^31 - 40 * q^32 + 4 * q^33 - 46 * q^34 - 26 * q^35 + 62 * q^36 - 66 * q^37 - 31 * q^38 - 8 * q^39 - 37 * q^40 - 33 * q^41 - 19 * q^42 - 22 * q^43 - 84 * q^44 - 77 * q^45 - 14 * q^46 - 20 * q^47 - 43 * q^48 + 66 * q^49 - 10 * q^50 - 39 * q^51 - 41 * q^52 - 47 * q^53 - 65 * q^54 - 15 * q^55 - 15 * q^56 + 5 * q^57 + 24 * q^58 - 125 * q^59 - 77 * q^60 - 57 * q^61 - 5 * q^62 + 66 * q^63 + 81 * q^64 - 40 * q^65 + 33 * q^66 - 25 * q^67 - 107 * q^68 - 72 * q^69 - 6 * q^70 - 57 * q^71 + 38 * q^72 + 5 * q^73 + 5 * q^74 - 60 * q^75 - 33 * q^76 - 57 * q^77 - 19 * q^78 - 4 * q^79 - 132 * q^80 + 58 * q^81 + 8 * q^82 - 84 * q^83 - 29 * q^84 - 33 * q^85 - 60 * q^86 - 31 * q^87 + 21 * q^88 - 132 * q^89 - 61 * q^90 - 28 * q^91 - 100 * q^92 - 12 * q^93 - 35 * q^94 + 4 * q^95 - 198 * q^96 - 39 * q^97 - 5 * q^98 - 174 * q^99

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