LMFDB - Embedded newform 722.4.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,4,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	722.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:	$42.5993790241$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.6719782761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 75x^{4} + 135x^{3} + 1857x^{2} - 1425x - 14797 $ x^6 - 3x^5 - 75x^4 + 135x^3 + 1857x^2 - 1425*x - 14797
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 19 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$7.04755$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} -4.98337 q^{3} +4.00000 q^{4} +2.34989 q^{5} -9.96675 q^{6} +2.84316 q^{7} +8.00000 q^{8} -2.16599 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} -4.98337 q^{3} +4.00000 q^{4} +2.34989 q^{5} -9.96675 q^{6} +2.84316 q^{7} +8.00000 q^{8} -2.16599 q^{9} +4.69977 q^{10} +3.80193 q^{11} -19.9335 q^{12} +16.3926 q^{13} +5.68632 q^{14} -11.7104 q^{15} +16.0000 q^{16} -74.7965 q^{17} -4.33198 q^{18} +9.39954 q^{20} -14.1685 q^{21} +7.60386 q^{22} +35.0510 q^{23} -39.8670 q^{24} -119.478 q^{25} +32.7852 q^{26} +145.345 q^{27} +11.3726 q^{28} +78.1681 q^{29} -23.4207 q^{30} -229.733 q^{31} +32.0000 q^{32} -18.9464 q^{33} -149.593 q^{34} +6.68110 q^{35} -8.66397 q^{36} +401.456 q^{37} -81.6905 q^{39} +18.7991 q^{40} -64.8351 q^{41} -28.3370 q^{42} -77.8702 q^{43} +15.2077 q^{44} -5.08983 q^{45} +70.1021 q^{46} -465.436 q^{47} -79.7340 q^{48} -334.916 q^{49} -238.956 q^{50} +372.739 q^{51} +65.5705 q^{52} -70.9500 q^{53} +290.690 q^{54} +8.93410 q^{55} +22.7453 q^{56} +156.336 q^{58} -663.483 q^{59} -46.8414 q^{60} -157.946 q^{61} -459.466 q^{62} -6.15826 q^{63} +64.0000 q^{64} +38.5208 q^{65} -37.8929 q^{66} +89.6525 q^{67} -299.186 q^{68} -174.672 q^{69} +13.3622 q^{70} -631.227 q^{71} -17.3279 q^{72} -758.971 q^{73} +802.912 q^{74} +595.404 q^{75} +10.8095 q^{77} -163.381 q^{78} -824.356 q^{79} +37.5982 q^{80} -665.827 q^{81} -129.670 q^{82} -132.745 q^{83} -56.6741 q^{84} -175.763 q^{85} -155.740 q^{86} -389.541 q^{87} +30.4154 q^{88} +1411.22 q^{89} -10.1797 q^{90} +46.6068 q^{91} +140.204 q^{92} +1144.85 q^{93} -930.872 q^{94} -159.468 q^{96} -1320.52 q^{97} -669.833 q^{98} -8.23495 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9}+O(q^{10}) $ 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9	\( 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9} - 54 q^{10} + 9 q^{11} - 36 q^{12} - 24 q^{13} - 42 q^{14} + 96 q^{16} - 102 q^{17} + 66 q^{18} - 108 q^{20} - 51 q^{21} + 18 q^{22} - 264 q^{23} - 72 q^{24} + 177 q^{25} - 48 q^{26} - 189 q^{27} - 84 q^{28} - 483 q^{29} - 72 q^{31} + 192 q^{32} - 387 q^{33} - 204 q^{34} + 135 q^{35} + 132 q^{36} + 558 q^{37} - 624 q^{39} - 216 q^{40} - 396 q^{41} - 102 q^{42} - 2064 q^{43} + 36 q^{44} - 1296 q^{45} - 528 q^{46} + 858 q^{47} - 144 q^{48} - 1413 q^{49} + 354 q^{50} + 1272 q^{51} - 96 q^{52} - 762 q^{53} - 378 q^{54} - 1107 q^{55} - 168 q^{56} - 966 q^{58} - 393 q^{59} - 627 q^{61} - 144 q^{62} - 84 q^{63} + 384 q^{64} - 495 q^{65} - 774 q^{66} - 2028 q^{67} - 408 q^{68} + 237 q^{69} + 270 q^{70} - 1284 q^{71} + 264 q^{72} - 2688 q^{73} + 1116 q^{74} - 927 q^{75} - 708 q^{77} - 1248 q^{78} - 969 q^{79} - 432 q^{80} - 1398 q^{81} - 792 q^{82} - 927 q^{83} - 204 q^{84} + 396 q^{85} - 4128 q^{86} - 2892 q^{87} + 72 q^{88} + 1257 q^{89} - 2592 q^{90} + 1323 q^{91} - 1056 q^{92} - 1368 q^{93} + 1716 q^{94} - 288 q^{96} + 2403 q^{97} - 2826 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9 - 54 * q^10 + 9 * q^11 - 36 * q^12 - 24 * q^13 - 42 * q^14 + 96 * q^16 - 102 * q^17 + 66 * q^18 - 108 * q^20 - 51 * q^21 + 18 * q^22 - 264 * q^23 - 72 * q^24 + 177 * q^25 - 48 * q^26 - 189 * q^27 - 84 * q^28 - 483 * q^29 - 72 * q^31 + 192 * q^32 - 387 * q^33 - 204 * q^34 + 135 * q^35 + 132 * q^36 + 558 * q^37 - 624 * q^39 - 216 * q^40 - 396 * q^41 - 102 * q^42 - 2064 * q^43 + 36 * q^44 - 1296 * q^45 - 528 * q^46 + 858 * q^47 - 144 * q^48 - 1413 * q^49 + 354 * q^50 + 1272 * q^51 - 96 * q^52 - 762 * q^53 - 378 * q^54 - 1107 * q^55 - 168 * q^56 - 966 * q^58 - 393 * q^59 - 627 * q^61 - 144 * q^62 - 84 * q^63 + 384 * q^64 - 495 * q^65 - 774 * q^66 - 2028 * q^67 - 408 * q^68 + 237 * q^69 + 270 * q^70 - 1284 * q^71 + 264 * q^72 - 2688 * q^73 + 1116 * q^74 - 927 * q^75 - 708 * q^77 - 1248 * q^78 - 969 * q^79 - 432 * q^80 - 1398 * q^81 - 792 * q^82 - 927 * q^83 - 204 * q^84 + 396 * q^85 - 4128 * q^86 - 2892 * q^87 + 72 * q^88 + 1257 * q^89 - 2592 * q^90 + 1323 * q^91 - 1056 * q^92 - 1368 * q^93 + 1716 * q^94 - 288 * q^96 + 2403 * q^97 - 2826 * q^98 + 567 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−4.98337	−0.959051	−0.479525	−	0.877528i	$-0.659191\pi$
$3$	−4.98337	−0.959051	−0.479525	+	0.877528i	$0.659191\pi$
$4$	4.00000	0.500000
$5$	2.34989	0.210180	0.105090	−	0.994463i	$-0.466487\pi$
$5$	2.34989	0.210180	0.105090	+	0.994463i	$0.466487\pi$
$6$	−9.96675	−0.678151
$7$	2.84316	0.153516	0.0767581	−	0.997050i	$-0.475543\pi$
$7$	2.84316	0.153516	0.0767581	+	0.997050i	$0.475543\pi$
$8$	8.00000	0.353553
$9$	−2.16599	−0.0802219
$10$	4.69977	0.148620
$11$	3.80193	0.104211	0.0521057	−	0.998642i	$-0.483407\pi$
$11$	3.80193	0.104211	0.0521057	+	0.998642i	$0.483407\pi$
$12$	−19.9335	−0.479525
$13$	16.3926	0.349730	0.174865	−	0.984592i	$-0.444051\pi$
$13$	16.3926	0.349730	0.174865	+	0.984592i	$0.444051\pi$
$14$	5.68632	0.108552
$15$	−11.7104	−0.201573
$16$	16.0000	0.250000
$17$	−74.7965	−1.06711	−0.533553	−	0.845767i	$-0.679144\pi$
$17$	−74.7965	−1.06711	−0.533553	+	0.845767i	$0.679144\pi$
$18$	−4.33198	−0.0567255
$19$	0	0
$19$	0	0
$20$	9.39954	0.105090
$21$	−14.1685	−0.147230
$22$	7.60386	0.0736886
$23$	35.0510	0.317767	0.158884	−	0.987297i	$-0.449211\pi$
$23$	35.0510	0.317767	0.158884	+	0.987297i	$0.449211\pi$
$24$	−39.8670	−0.339076
$25$	−119.478	−0.955824
$26$	32.7852	0.247297
$27$	145.345	1.03599
$28$	11.3726	0.0767581
$29$	78.1681	0.500533	0.250266	−	0.968177i	$-0.419482\pi$
$29$	78.1681	0.500533	0.250266	+	0.968177i	$0.419482\pi$
$30$	−23.4207	−0.142534
$31$	−229.733	−1.33101	−0.665504	−	0.746394i	$-0.731784\pi$
$31$	−229.733	−1.33101	−0.665504	+	0.746394i	$0.731784\pi$
$32$	32.0000	0.176777
$33$	−18.9464	−0.0999440
$34$	−149.593	−0.754558
$35$	6.68110	0.0322660
$36$	−8.66397	−0.0401110
$37$	401.456	1.78376	0.891878	−	0.452276i	$-0.149388\pi$
$37$	401.456	1.78376	0.891878	+	0.452276i	$0.149388\pi$
$38$	0	0
$39$	−81.6905	−0.335409
$40$	18.7991	0.0743099
$41$	−64.8351	−0.246964	−0.123482	−	0.992347i	$-0.539406\pi$
$41$	−64.8351	−0.246964	−0.123482	+	0.992347i	$0.539406\pi$
$42$	−28.3370	−0.104107
$43$	−77.8702	−0.276165	−0.138082	−	0.990421i	$-0.544094\pi$
$43$	−77.8702	−0.276165	−0.138082	+	0.990421i	$0.544094\pi$
$44$	15.2077	0.0521057
$45$	−5.08983	−0.0168611
$46$	70.1021	0.224695
$47$	−465.436	−1.44449	−0.722243	−	0.691640i	$-0.756889\pi$
$47$	−465.436	−1.44449	−0.722243	+	0.691640i	$0.756889\pi$
$48$	−79.7340	−0.239763
$49$	−334.916	−0.976433
$50$	−238.956	−0.675870
$51$	372.739	1.02341
$52$	65.5705	0.174865
$53$	−70.9500	−0.183882	−0.0919409	−	0.995764i	$-0.529307\pi$
$53$	−70.9500	−0.183882	−0.0919409	+	0.995764i	$0.529307\pi$
$54$	290.690	0.732554
$55$	8.93410	0.0219032
$56$	22.7453	0.0542761
$57$	0	0
$58$	156.336	0.353930
$59$	−663.483	−1.46404	−0.732018	−	0.681286i	$-0.761421\pi$
$59$	−663.483	−1.46404	−0.732018	+	0.681286i	$0.761421\pi$
$60$	−46.8414	−0.100787
$61$	−157.946	−0.331523	−0.165761	−	0.986166i	$-0.553008\pi$
$61$	−157.946	−0.331523	−0.165761	+	0.986166i	$0.553008\pi$
$62$	−459.466	−0.941165
$63$	−6.15826	−0.0123154
$64$	64.0000	0.125000
$65$	38.5208	0.0735064
$66$	−37.8929	−0.0706710
$67$	89.6525	0.163474	0.0817372	−	0.996654i	$-0.473953\pi$
$67$	89.6525	0.163474	0.0817372	+	0.996654i	$0.473953\pi$
$68$	−299.186	−0.533553
$69$	−174.672	−0.304755
$70$	13.3622	0.0228155
$71$	−631.227	−1.05511	−0.527556	−	0.849520i	$-0.676891\pi$
$71$	−631.227	−1.05511	−0.527556	+	0.849520i	$0.676891\pi$
$72$	−17.3279	−0.0283627
$73$	−758.971	−1.21686	−0.608431	−	0.793607i	$-0.708201\pi$
$73$	−758.971	−1.21686	−0.608431	+	0.793607i	$0.708201\pi$
$74$	802.912	1.26131
$75$	595.404	0.916684
$76$	0	0
$77$	10.8095	0.0159981
$78$	−163.381	−0.237170
$79$	−824.356	−1.17402	−0.587008	−	0.809581i	$-0.699694\pi$
$79$	−824.356	−1.17402	−0.587008	+	0.809581i	$0.699694\pi$
$80$	37.5982	0.0525450
$81$	−665.827	−0.913343
$82$	−129.670	−0.174630
$83$	−132.745	−0.175551	−0.0877753	−	0.996140i	$-0.527976\pi$
$83$	−132.745	−0.175551	−0.0877753	+	0.996140i	$0.527976\pi$
$84$	−56.6741	−0.0736149
$85$	−175.763	−0.224285
$86$	−155.740	−0.195278
$87$	−389.541	−0.480036
$88$	30.4154	0.0368443
$89$	1411.22	1.68077	0.840385	−	0.541990i	$-0.182329\pi$
$89$	1411.22	1.68077	0.840385	+	0.541990i	$0.182329\pi$
$90$	−10.1797	−0.0119226
$91$	46.6068	0.0536892
$92$	140.204	0.158884
$93$	1144.85	1.27650
$94$	−930.872	−1.02141
$95$	0	0
$96$	−159.468	−0.169538
$97$	−1320.52	−1.38225	−0.691127	−	0.722733i	$-0.742885\pi$
$97$	−1320.52	−1.38225	−0.691127	+	0.722733i	$0.742885\pi$
$98$	−669.833	−0.690442
$99$	−8.23495	−0.00836004
$100$	−477.912	−0.477912
$101$	−290.376	−0.286074	−0.143037	−	0.989717i	$-0.545687\pi$
$101$	−290.376	−0.286074	−0.143037	+	0.989717i	$0.545687\pi$
$102$	745.477	0.723659
$103$	606.177	0.579887	0.289943	−	0.957044i	$-0.406364\pi$
$103$	606.177	0.579887	0.289943	+	0.957044i	$0.406364\pi$
$104$	131.141	0.123648
$105$	−33.2944	−0.0309448
$106$	−141.900	−0.130024
$107$	728.733	0.658405	0.329202	−	0.944259i	$-0.393220\pi$
$107$	728.733	0.658405	0.329202	+	0.944259i	$0.393220\pi$
$108$	581.380	0.517994
$109$	−1500.04	−1.31815	−0.659073	−	0.752079i	$-0.729051\pi$
$109$	−1500.04	−1.31815	−0.659073	+	0.752079i	$0.729051\pi$
$110$	17.8682	0.0154879
$111$	−2000.61	−1.71071
$112$	45.4905	0.0383790
$113$	−1048.77	−0.873094	−0.436547	−	0.899681i	$-0.643799\pi$
$113$	−1048.77	−0.873094	−0.436547	+	0.899681i	$0.643799\pi$
$114$	0	0
$115$	82.3660	0.0667884
$116$	312.672	0.250266
$117$	−35.5063	−0.0280560
$118$	−1326.97	−1.03523
$119$	−212.658	−0.163818
$120$	−93.6829	−0.0712670
$121$	−1316.55	−0.989140
$122$	−315.892	−0.234422
$123$	323.097	0.236851
$124$	−918.932	−0.665504
$125$	−574.495	−0.411075
$126$	−12.3165	−0.00870827
$127$	2362.95	1.65101	0.825503	−	0.564398i	$-0.190892\pi$
$127$	2362.95	1.65101	0.825503	+	0.564398i	$0.190892\pi$
$128$	128.000	0.0883883
$129$	388.056	0.264856
$130$	77.0415	0.0519769
$131$	1775.83	1.18439	0.592196	−	0.805794i	$-0.298261\pi$
$131$	1775.83	1.18439	0.592196	+	0.805794i	$0.298261\pi$
$132$	−75.7857	−0.0499720
$133$	0	0
$134$	179.305	0.115594
$135$	341.544	0.217744
$136$	−598.372	−0.377279
$137$	−1895.68	−1.18218	−0.591091	−	0.806605i	$-0.701303\pi$
$137$	−1895.68	−1.18218	−0.591091	+	0.806605i	$0.701303\pi$
$138$	−349.345	−0.215494
$139$	−188.521	−0.115037	−0.0575185	−	0.998344i	$-0.518319\pi$
$139$	−188.521	−0.115037	−0.0575185	+	0.998344i	$0.518319\pi$
$140$	26.7244	0.0161330
$141$	2319.44	1.38533
$142$	−1262.45	−0.746076
$143$	62.3236	0.0364459
$144$	−34.6559	−0.0200555
$145$	183.686	0.105202
$146$	−1517.94	−0.860451
$147$	1669.01	0.936448
$148$	1605.82	0.891878
$149$	−2478.55	−1.36276	−0.681378	−	0.731932i	$-0.738619\pi$
$149$	−2478.55	−1.36276	−0.681378	+	0.731932i	$0.738619\pi$
$150$	1190.81	0.648193
$151$	885.978	0.477483	0.238741	−	0.971083i	$-0.423265\pi$
$151$	885.978	0.477483	0.238741	+	0.971083i	$0.423265\pi$
$152$	0	0
$153$	162.009	0.0856053
$154$	21.6190	0.0113124
$155$	−539.846	−0.279752
$156$	−326.762	−0.167705
$157$	−1229.42	−0.624957	−0.312478	−	0.949925i	$-0.601159\pi$
$157$	−1229.42	−0.624957	−0.312478	+	0.949925i	$0.601159\pi$
$158$	−1648.71	−0.830155
$159$	353.570	0.176352
$160$	75.1963	0.0371550
$161$	99.6557	0.0487824
$162$	−1331.65	−0.645831
$163$	466.845	0.224332	0.112166	−	0.993689i	$-0.464221\pi$
$163$	466.845	0.224332	0.112166	+	0.993689i	$0.464221\pi$
$164$	−259.340	−0.123482
$165$	−44.5219	−0.0210062
$166$	−265.491	−0.124133
$167$	−3590.87	−1.66389	−0.831946	−	0.554857i	$-0.812773\pi$
$167$	−3590.87	−1.66389	−0.831946	+	0.554857i	$0.812773\pi$
$168$	−113.348	−0.0520536
$169$	−1928.28	−0.877689
$170$	−351.526	−0.158593
$171$	0	0
$172$	−311.481	−0.138082
$173$	288.595	0.126829	0.0634147	−	0.997987i	$-0.479801\pi$
$173$	288.595	0.126829	0.0634147	+	0.997987i	$0.479801\pi$
$174$	−779.081	−0.339437
$175$	−339.695	−0.146734
$176$	60.8309	0.0260528
$177$	3306.38	1.40408
$178$	2822.43	1.18848
$179$	3975.75	1.66012	0.830060	−	0.557675i	$-0.188306\pi$
$179$	3975.75	1.66012	0.830060	+	0.557675i	$0.188306\pi$
$180$	−20.3593	−0.00843053
$181$	691.246	0.283867	0.141933	−	0.989876i	$-0.454668\pi$
$181$	691.246	0.283867	0.141933	+	0.989876i	$0.454668\pi$
$182$	93.2136	0.0379640
$183$	787.103	0.317947
$184$	280.408	0.112348
$185$	943.376	0.374910
$186$	2289.69	0.902625
$187$	−284.371	−0.111205
$188$	−1861.74	−0.722243
$189$	413.239	0.159041
$190$	0	0
$191$	2235.13	0.846746	0.423373	−	0.905955i	$-0.360846\pi$
$191$	2235.13	0.846746	0.423373	+	0.905955i	$0.360846\pi$
$192$	−318.936	−0.119881
$193$	4000.95	1.49220	0.746101	−	0.665833i	$-0.231924\pi$
$193$	4000.95	1.49220	0.746101	+	0.665833i	$0.231924\pi$
$194$	−2641.04	−0.977401
$195$	−191.963	−0.0704963
$196$	−1339.67	−0.488216
$197$	−2097.94	−0.758741	−0.379371	−	0.925245i	$-0.623859\pi$
$197$	−2097.94	−0.758741	−0.379371	+	0.925245i	$0.623859\pi$
$198$	−16.4699	−0.00591144
$199$	−1891.56	−0.673813	−0.336907	−	0.941538i	$-0.609381\pi$
$199$	−1891.56	−0.673813	−0.336907	+	0.941538i	$0.609381\pi$
$200$	−955.824	−0.337935
$201$	−446.772	−0.156780
$202$	−580.751	−0.202285
$203$	222.244	0.0768398
$204$	1490.95	0.511704
$205$	−152.355	−0.0519070
$206$	1212.35	0.410042
$207$	−75.9203	−0.0254919
$208$	262.282	0.0874326
$209$	0	0
$210$	−66.5888	−0.0218813
$211$	2066.89	0.674362	0.337181	−	0.941440i	$-0.390527\pi$
$211$	2066.89	0.674362	0.337181	+	0.941440i	$0.390527\pi$
$212$	−283.800	−0.0919409
$213$	3145.64	1.01191
$214$	1457.47	0.465562
$215$	−182.986	−0.0580444
$216$	1162.76	0.366277
$217$	−653.167	−0.204331
$218$	−3000.08	−0.932069
$219$	3782.24	1.16703
$220$	35.7364	0.0109516
$221$	−1226.11	−0.373199
$222$	−4001.21	−1.20966
$223$	1154.37	0.346648	0.173324	−	0.984865i	$-0.444549\pi$
$223$	1154.37	0.346648	0.173324	+	0.984865i	$0.444549\pi$
$224$	90.9811	0.0271381
$225$	258.789	0.0766781
$226$	−2097.53	−0.617371
$227$	829.315	0.242483	0.121241	−	0.992623i	$-0.461312\pi$
$227$	829.315	0.242483	0.121241	+	0.992623i	$0.461312\pi$
$228$	0	0
$229$	5032.36	1.45217	0.726087	−	0.687603i	$-0.241337\pi$
$229$	5032.36	1.45217	0.726087	+	0.687603i	$0.241337\pi$
$230$	164.732	0.0472265
$231$	−53.8677	−0.0153430
$232$	625.344	0.176965
$233$	1248.88	0.351146	0.175573	−	0.984466i	$-0.443822\pi$
$233$	1248.88	0.351146	0.175573	+	0.984466i	$0.443822\pi$
$234$	−71.0126	−0.0198386
$235$	−1093.72	−0.303602
$236$	−2653.93	−0.732018
$237$	4108.07	1.12594
$238$	−425.316	−0.115837
$239$	4728.37	1.27972	0.639859	−	0.768492i	$-0.278993\pi$
$239$	4728.37	1.27972	0.639859	+	0.768492i	$0.278993\pi$
$240$	−187.366	−0.0503934
$241$	404.199	0.108036	0.0540182	−	0.998540i	$-0.482797\pi$
$241$	404.199	0.108036	0.0540182	+	0.998540i	$0.482797\pi$
$242$	−2633.09	−0.699428
$243$	−606.253	−0.160046
$244$	−631.783	−0.165761
$245$	−787.015	−0.205227
$246$	646.195	0.167479
$247$	0	0
$248$	−1837.86	−0.470583
$249$	661.520	0.168362
$250$	−1148.99	−0.290674
$251$	6355.08	1.59812	0.799062	−	0.601249i	$-0.205330\pi$
$251$	6355.08	1.59812	0.799062	+	0.601249i	$0.205330\pi$
$252$	−24.6330	−0.00615768
$253$	133.262	0.0331150
$254$	4725.89	1.16744
$255$	875.893	0.215100
$256$	256.000	0.0625000
$257$	4341.68	1.05380	0.526899	−	0.849928i	$-0.323354\pi$
$257$	4341.68	1.05380	0.526899	+	0.849928i	$0.323354\pi$
$258$	776.113	0.187282
$259$	1141.40	0.273835
$260$	154.083	0.0367532
$261$	−169.311	−0.0401537
$262$	3551.67	0.837491
$263$	6125.12	1.43609	0.718044	−	0.695997i	$-0.245038\pi$
$263$	6125.12	1.43609	0.718044	+	0.695997i	$0.245038\pi$
$264$	−151.571	−0.0353355
$265$	−166.724	−0.0386483
$266$	0	0
$267$	−7032.61	−1.61194
$268$	358.610	0.0817372
$269$	5933.56	1.34489	0.672445	−	0.740147i	$-0.265244\pi$
$269$	5933.56	1.34489	0.672445	+	0.740147i	$0.265244\pi$
$270$	683.088	0.153968
$271$	6490.40	1.45485	0.727424	−	0.686188i	$-0.240717\pi$
$271$	6490.40	1.45485	0.727424	+	0.686188i	$0.240717\pi$
$272$	−1196.74	−0.266777
$273$	−232.259	−0.0514907
$274$	−3791.36	−0.835929
$275$	−454.247	−0.0996077
$276$	−698.690	−0.152377
$277$	−2374.41	−0.515033	−0.257517	−	0.966274i	$-0.582904\pi$
$277$	−2374.41	−0.515033	−0.257517	+	0.966274i	$0.582904\pi$
$278$	−377.042	−0.0813434
$279$	497.600	0.106776
$280$	53.4488	0.0114078
$281$	−4657.08	−0.988676	−0.494338	−	0.869270i	$-0.664589\pi$
$281$	−4657.08	−0.988676	−0.494338	+	0.869270i	$0.664589\pi$
$282$	4638.88	0.979579
$283$	−3054.18	−0.641528	−0.320764	−	0.947159i	$-0.603940\pi$
$283$	−3054.18	−0.641528	−0.320764	+	0.947159i	$0.603940\pi$
$284$	−2524.91	−0.527556
$285$	0	0
$286$	124.647	0.0257711
$287$	−184.336	−0.0379130
$288$	−69.3118	−0.0141814
$289$	681.509	0.138716
$290$	367.372	0.0743891
$291$	6580.65	1.32565
$292$	−3035.88	−0.608431
$293$	−9656.83	−1.92545	−0.962727	−	0.270475i	$-0.912819\pi$
$293$	−9656.83	−1.92545	−0.962727	+	0.270475i	$0.912819\pi$
$294$	3338.03	0.662169
$295$	−1559.11	−0.307711
$296$	3211.65	0.630653
$297$	552.592	0.107962
$298$	−4957.10	−0.963614
$299$	574.578	0.111133
$300$	2381.61	0.458342
$301$	−221.397	−0.0423958
$302$	1771.96	0.337631
$303$	1447.05	0.274359
$304$	0	0
$305$	−371.155	−0.0696795
$306$	324.017	0.0605321
$307$	−1270.66	−0.236223	−0.118111	−	0.993000i	$-0.537684\pi$
$307$	−1270.66	−0.236223	−0.118111	+	0.993000i	$0.537684\pi$
$308$	43.2379	0.00799906
$309$	−3020.80	−0.556141
$310$	−1079.69	−0.197814
$311$	−5187.37	−0.945817	−0.472908	−	0.881112i	$-0.656796\pi$
$311$	−5187.37	−0.945817	−0.472908	+	0.881112i	$0.656796\pi$
$312$	−653.524	−0.118585
$313$	7771.34	1.40339	0.701697	−	0.712476i	$-0.252426\pi$
$313$	7771.34	1.40339	0.701697	+	0.712476i	$0.252426\pi$
$314$	−2458.83	−0.441911
$315$	−14.4712	−0.00258844
$316$	−3297.42	−0.587008
$317$	−6527.45	−1.15652	−0.578262	−	0.815851i	$-0.696269\pi$
$317$	−6527.45	−1.15652	−0.578262	+	0.815851i	$0.696269\pi$
$318$	707.141	0.124700
$319$	297.189	0.0521612
$320$	150.393	0.0262725
$321$	−3631.55	−0.631443
$322$	199.311	0.0344944
$323$	0	0
$324$	−2663.31	−0.456671
$325$	−1958.56	−0.334281
$326$	933.691	0.158627
$327$	7475.26	1.26417
$328$	−518.681	−0.0873151
$329$	−1323.31	−0.221752
$330$	−89.0439	−0.0148537
$331$	−8483.47	−1.40874	−0.704371	−	0.709832i	$-0.748771\pi$
$331$	−8483.47	−1.40874	−0.704371	+	0.709832i	$0.748771\pi$
$332$	−530.982	−0.0877753
$333$	−869.551	−0.143096
$334$	−7181.74	−1.17655
$335$	210.673	0.0343591
$336$	−226.696	−0.0368074
$337$	−5530.84	−0.894017	−0.447009	−	0.894530i	$-0.647511\pi$
$337$	−5530.84	−0.894017	−0.447009	+	0.894530i	$0.647511\pi$
$338$	−3856.56	−0.620620
$339$	5226.39	0.837341
$340$	−703.052	−0.112142
$341$	−873.429	−0.138706
$342$	0	0
$343$	−1927.42	−0.303414
$344$	−622.962	−0.0976391
$345$	−410.460	−0.0640534
$346$	577.190	0.0896819
$347$	9309.18	1.44018	0.720090	−	0.693880i	$-0.244100\pi$
$347$	9309.18	1.44018	0.720090	+	0.693880i	$0.244100\pi$
$348$	−1558.16	−0.240018
$349$	−8657.85	−1.32792	−0.663960	−	0.747768i	$-0.731125\pi$
$349$	−8657.85	−1.32792	−0.663960	+	0.747768i	$0.731125\pi$
$350$	−679.390	−0.103757
$351$	2382.59	0.362316
$352$	121.662	0.0184221
$353$	3142.73	0.473855	0.236928	−	0.971527i	$-0.423860\pi$
$353$	3142.73	0.473855	0.236928	+	0.971527i	$0.423860\pi$
$354$	6612.76	0.992837
$355$	−1483.31	−0.221763
$356$	5644.86	0.840385
$357$	1059.75	0.157110
$358$	7951.50	1.17388
$359$	5571.82	0.819136	0.409568	−	0.912280i	$-0.365680\pi$
$359$	5571.82	0.819136	0.409568	+	0.912280i	$0.365680\pi$
$360$	−40.7187	−0.00596129
$361$	0	0
$362$	1382.49	0.200724
$363$	6560.84	0.948635
$364$	186.427	0.0268446
$365$	−1783.50	−0.255760
$366$	1574.21	0.224823
$367$	−755.678	−0.107482	−0.0537412	−	0.998555i	$-0.517115\pi$
$367$	−755.678	−0.107482	−0.0537412	+	0.998555i	$0.517115\pi$
$368$	560.817	0.0794418
$369$	140.432	0.0198120
$370$	1886.75	0.265102
$371$	−201.722	−0.0282288
$372$	4579.38	0.638252
$373$	502.406	0.0697416	0.0348708	−	0.999392i	$-0.488898\pi$
$373$	502.406	0.0697416	0.0348708	+	0.999392i	$0.488898\pi$
$374$	−568.742	−0.0786335
$375$	2862.93	0.394242
$376$	−3723.49	−0.510703
$377$	1281.38	0.175051
$378$	826.478	0.112459
$379$	2045.80	0.277270	0.138635	−	0.990344i	$-0.455728\pi$
$379$	2045.80	0.277270	0.138635	+	0.990344i	$0.455728\pi$
$380$	0	0
$381$	−11775.4	−1.58340
$382$	4470.27	0.598740
$383$	−5337.35	−0.712077	−0.356039	−	0.934471i	$-0.615873\pi$
$383$	−5337.35	−0.712077	−0.356039	+	0.934471i	$0.615873\pi$
$384$	−637.872	−0.0847689
$385$	25.4011	0.00336249
$386$	8001.91	1.05515
$387$	168.666	0.0221545
$388$	−5282.09	−0.691127
$389$	−99.0642	−0.0129120	−0.00645598	−	0.999979i	$-0.502055\pi$
$389$	−99.0642	−0.0129120	−0.00645598	+	0.999979i	$0.502055\pi$
$390$	−383.927	−0.0498484
$391$	−2621.69	−0.339091
$392$	−2679.33	−0.345221
$393$	−8849.64	−1.13589
$394$	−4195.88	−0.536511
$395$	−1937.14	−0.246755
$396$	−32.9398	−0.00418002
$397$	−11627.5	−1.46994	−0.734971	−	0.678098i	$-0.762804\pi$
$397$	−11627.5	−1.46994	−0.734971	+	0.678098i	$0.762804\pi$
$398$	−3783.11	−0.476458
$399$	0	0
$400$	−1911.65	−0.238956
$401$	−5727.53	−0.713265	−0.356633	−	0.934245i	$-0.616075\pi$
$401$	−5727.53	−0.713265	−0.356633	+	0.934245i	$0.616075\pi$
$402$	−893.543	−0.110860
$403$	−3765.93	−0.465494
$404$	−1161.50	−0.143037
$405$	−1564.62	−0.191966
$406$	444.488	0.0543340
$407$	1526.31	0.185888
$408$	2981.91	0.361830
$409$	−6443.90	−0.779047	−0.389524	−	0.921016i	$-0.627360\pi$
$409$	−6443.90	−0.779047	−0.389524	+	0.921016i	$0.627360\pi$
$410$	−304.710	−0.0367038
$411$	9446.89	1.13377
$412$	2424.71	0.289943
$413$	−1886.39	−0.224753
$414$	−151.841	−0.0180255
$415$	−311.937	−0.0368973
$416$	524.564	0.0618242
$417$	939.470	0.110326
$418$	0	0
$419$	2695.30	0.314258	0.157129	−	0.987578i	$-0.449776\pi$
$419$	2695.30	0.314258	0.157129	+	0.987578i	$0.449776\pi$
$420$	−133.178	−0.0154724
$421$	16386.8	1.89702	0.948510	−	0.316747i	$-0.102591\pi$
$421$	16386.8	1.89702	0.948510	+	0.316747i	$0.102591\pi$
$422$	4133.77	0.476846
$423$	1008.13	0.115879
$424$	−567.600	−0.0650120
$425$	8936.53	1.01997
$426$	6291.28	0.715525
$427$	−449.065	−0.0508941
$428$	2914.93	0.329202
$429$	−310.582	−0.0349534
$430$	−365.972	−0.0410436
$431$	−175.095	−0.0195685	−0.00978423	−	0.999952i	$-0.503114\pi$
$431$	−175.095	−0.0195685	−0.00978423	+	0.999952i	$0.503114\pi$
$432$	2325.52	0.258997
$433$	12222.1	1.35648	0.678242	−	0.734839i	$-0.262742\pi$
$433$	12222.1	1.35648	0.678242	+	0.734839i	$0.262742\pi$
$434$	−1306.33	−0.144484
$435$	−915.376	−0.100894
$436$	−6000.16	−0.659073
$437$	0	0
$438$	7564.47	0.825216
$439$	3241.27	0.352386	0.176193	−	0.984356i	$-0.443622\pi$
$439$	3241.27	0.352386	0.176193	+	0.984356i	$0.443622\pi$
$440$	71.4728	0.00774394
$441$	725.426	0.0783313
$442$	−2452.22	−0.263892
$443$	−8349.56	−0.895485	−0.447742	−	0.894163i	$-0.647772\pi$
$443$	−8349.56	−0.895485	−0.447742	+	0.894163i	$0.647772\pi$
$444$	−8002.42	−0.855356
$445$	3316.19	0.353264
$446$	2308.74	0.245117
$447$	12351.5	1.30695
$448$	181.962	0.0191895
$449$	−11364.5	−1.19448	−0.597242	−	0.802061i	$-0.703737\pi$
$449$	−11364.5	−1.19448	−0.597242	+	0.802061i	$0.703737\pi$
$450$	517.577	0.0542196
$451$	−246.498	−0.0257365
$452$	−4195.06	−0.436547
$453$	−4415.16	−0.457930
$454$	1658.63	0.171461
$455$	109.521	0.0112844
$456$	0	0
$457$	12215.7	1.25038	0.625192	−	0.780471i	$-0.285021\pi$
$457$	12215.7	1.25038	0.625192	+	0.780471i	$0.285021\pi$
$458$	10064.7	1.02684
$459$	−10871.3	−1.10551
$460$	329.464	0.0333942
$461$	8377.50	0.846375	0.423188	−	0.906042i	$-0.360911\pi$
$461$	8377.50	0.846375	0.423188	+	0.906042i	$0.360911\pi$
$462$	−107.735	−0.0108491
$463$	6231.80	0.625521	0.312761	−	0.949832i	$-0.398746\pi$
$463$	6231.80	0.625521	0.312761	+	0.949832i	$0.398746\pi$
$464$	1250.69	0.125133
$465$	2690.26	0.268296
$466$	2497.76	0.248298
$467$	12437.0	1.23237	0.616185	−	0.787601i	$-0.288677\pi$
$467$	12437.0	1.23237	0.616185	+	0.787601i	$0.288677\pi$
$468$	−142.025	−0.0140280
$469$	254.896	0.0250960
$470$	−2187.44	−0.214679
$471$	6126.65	0.599365
$472$	−5307.86	−0.517615
$473$	−296.057	−0.0287795
$474$	8216.15	0.796161
$475$	0	0
$476$	−850.633	−0.0819090
$477$	153.677	0.0147514
$478$	9456.74	0.904898
$479$	−6328.21	−0.603640	−0.301820	−	0.953365i	$-0.597594\pi$
$479$	−6328.21	−0.603640	−0.301820	+	0.953365i	$0.597594\pi$
$480$	−374.731	−0.0356335
$481$	6580.92	0.623834
$482$	808.398	0.0763932
$483$	−496.621	−0.0467848
$484$	−5266.18	−0.494570
$485$	−3103.07	−0.290522
$486$	−1212.51	−0.113169
$487$	3598.56	0.334838	0.167419	−	0.985886i	$-0.446457\pi$
$487$	3598.56	0.334838	0.167419	+	0.985886i	$0.446457\pi$
$488$	−1263.57	−0.117211
$489$	−2326.46	−0.215146
$490$	−1574.03	−0.145117
$491$	−4272.10	−0.392663	−0.196331	−	0.980538i	$-0.562903\pi$
$491$	−4272.10	−0.392663	−0.196331	+	0.980538i	$0.562903\pi$
$492$	1292.39	0.118426
$493$	−5846.69	−0.534121
$494$	0	0
$495$	−19.3512	−0.00175711
$496$	−3675.73	−0.332752
$497$	−1794.68	−0.161977
$498$	1323.04	0.119050
$499$	−2325.72	−0.208644	−0.104322	−	0.994544i	$-0.533267\pi$
$499$	−2325.72	−0.208644	−0.104322	+	0.994544i	$0.533267\pi$
$500$	−2297.98	−0.205538
$501$	17894.6	1.59576
$502$	12710.2	1.13004
$503$	−22395.0	−1.98518	−0.992588	−	0.121525i	$-0.961221\pi$
$503$	−22395.0	−1.98518	−0.992588	+	0.121525i	$0.961221\pi$
$504$	−49.2661	−0.00435414
$505$	−682.349	−0.0601270
$506$	266.523	0.0234158
$507$	9609.35	0.841748
$508$	9451.79	0.825503
$509$	−8136.64	−0.708546	−0.354273	−	0.935142i	$-0.615272\pi$
$509$	−8136.64	−0.708546	−0.354273	+	0.935142i	$0.615272\pi$
$510$	1751.79	0.152099
$511$	−2157.88	−0.186808
$512$	512.000	0.0441942
$513$	0	0
$514$	8683.35	0.745148
$515$	1424.45	0.121881
$516$	1552.23	0.132428
$517$	−1769.55	−0.150532
$518$	2282.81	0.193631
$519$	−1438.18	−0.121636
$520$	308.166	0.0259884
$521$	13381.4	1.12524	0.562620	−	0.826716i	$-0.309794\pi$
$521$	13381.4	1.12524	0.562620	+	0.826716i	$0.309794\pi$
$522$	−338.623	−0.0283929
$523$	−12504.7	−1.04549	−0.522746	−	0.852489i	$-0.675092\pi$
$523$	−12504.7	−1.04549	−0.522746	+	0.852489i	$0.675092\pi$
$524$	7103.33	0.592196
$525$	1692.83	0.140726
$526$	12250.2	1.01547
$527$	17183.2	1.42033
$528$	−303.143	−0.0249860
$529$	−10938.4	−0.899024
$530$	−333.449	−0.0273285
$531$	1437.10	0.117448
$532$	0	0
$533$	−1062.82	−0.0863709
$534$	−14065.2	−1.13982
$535$	1712.44	0.138384
$536$	717.220	0.0577970
$537$	−19812.6	−1.59214
$538$	11867.1	0.950981
$539$	−1273.33	−0.101755
$540$	1366.18	0.108872
$541$	−4297.82	−0.341548	−0.170774	−	0.985310i	$-0.554627\pi$
$541$	−4297.82	−0.341548	−0.170774	+	0.985310i	$0.554627\pi$
$542$	12980.8	1.02873
$543$	−3444.74	−0.272243
$544$	−2393.49	−0.188639
$545$	−3524.92	−0.277048
$546$	−464.518	−0.0364094
$547$	16921.8	1.32271	0.661356	−	0.750072i	$-0.269981\pi$
$547$	16921.8	1.32271	0.661356	+	0.750072i	$0.269981\pi$
$548$	−7582.72	−0.591091
$549$	342.110	0.0265954
$550$	−908.494	−0.0704333
$551$	0	0
$552$	−1397.38	−0.107747
$553$	−2343.77	−0.180230
$554$	−4748.81	−0.364184
$555$	−4701.19	−0.359558
$556$	−754.084	−0.0575185
$557$	−6635.35	−0.504756	−0.252378	−	0.967629i	$-0.581213\pi$
$557$	−6635.35	−0.504756	−0.252378	+	0.967629i	$0.581213\pi$
$558$	995.200	0.0755021
$559$	−1276.50	−0.0965833
$560$	106.898	0.00806651
$561$	1417.13	0.106651
$562$	−9314.15	−0.699099
$563$	−3621.85	−0.271124	−0.135562	−	0.990769i	$-0.543284\pi$
$563$	−3621.85	−0.271124	−0.135562	+	0.990769i	$0.543284\pi$
$564$	9277.76	0.692667
$565$	−2464.48	−0.183507
$566$	−6108.36	−0.453628
$567$	−1893.05	−0.140213
$568$	−5049.82	−0.373038
$569$	4576.86	0.337209	0.168604	−	0.985684i	$-0.446074\pi$
$569$	4576.86	0.337209	0.168604	+	0.985684i	$0.446074\pi$
$570$	0	0
$571$	18109.2	1.32723	0.663614	−	0.748075i	$-0.269022\pi$
$571$	18109.2	1.32723	0.663614	+	0.748075i	$0.269022\pi$
$572$	249.294	0.0182229
$573$	−11138.5	−0.812073
$574$	−368.673	−0.0268085
$575$	−4187.83	−0.303730
$576$	−138.624	−0.0100277
$577$	−1497.73	−0.108061	−0.0540304	−	0.998539i	$-0.517207\pi$
$577$	−1497.73	−0.108061	−0.0540304	+	0.998539i	$0.517207\pi$
$578$	1363.02	0.0980867
$579$	−19938.2	−1.43110
$580$	734.744	0.0526010
$581$	−377.416	−0.0269498
$582$	13161.3	0.937377
$583$	−269.747	−0.0191626
$584$	−6071.77	−0.430225
$585$	−83.4357	−0.00589682
$586$	−19313.7	−1.36150
$587$	21042.7	1.47960	0.739800	−	0.672827i	$-0.234920\pi$
$587$	21042.7	1.47960	0.739800	+	0.672827i	$0.234920\pi$
$588$	6676.05	0.468224
$589$	0	0
$590$	−3118.22	−0.217585
$591$	10454.8	0.727671
$592$	6423.30	0.445939
$593$	−21290.8	−1.47438	−0.737191	−	0.675684i	$-0.763848\pi$
$593$	−21290.8	−1.47438	−0.737191	+	0.675684i	$0.763848\pi$
$594$	1105.18	0.0763404
$595$	−499.722	−0.0344313
$596$	−9914.19	−0.681378
$597$	9426.33	0.646221
$598$	1149.16	0.0785828
$599$	−7839.64	−0.534756	−0.267378	−	0.963592i	$-0.586157\pi$
$599$	−7839.64	−0.534756	−0.267378	+	0.963592i	$0.586157\pi$
$600$	4763.23	0.324097
$601$	−16076.7	−1.09115	−0.545576	−	0.838062i	$-0.683689\pi$
$601$	−16076.7	−1.09115	−0.545576	+	0.838062i	$0.683689\pi$
$602$	−442.795	−0.0299783
$603$	−194.187	−0.0131142
$604$	3543.91	0.238741
$605$	−3093.73	−0.207898
$606$	2894.10	0.194001
$607$	−11810.5	−0.789741	−0.394870	−	0.918737i	$-0.629210\pi$
$607$	−11810.5	−0.789741	−0.394870	+	0.918737i	$0.629210\pi$
$608$	0	0
$609$	−1107.53	−0.0736933
$610$	−742.309	−0.0492709
$611$	−7629.71	−0.505180
$612$	648.034	0.0428027
$613$	−22373.0	−1.47412	−0.737062	−	0.675825i	$-0.763787\pi$
$613$	−22373.0	−1.47412	−0.737062	+	0.675825i	$0.763787\pi$
$614$	−2541.32	−0.167035
$615$	759.242	0.0497815
$616$	86.4759	0.00565619
$617$	13120.7	0.856110	0.428055	−	0.903753i	$-0.359199\pi$
$617$	13120.7	0.856110	0.428055	+	0.903753i	$0.359199\pi$
$618$	−6041.61	−0.393251
$619$	−26582.6	−1.72608	−0.863041	−	0.505134i	$-0.831443\pi$
$619$	−26582.6	−1.72608	−0.863041	+	0.505134i	$0.831443\pi$
$620$	−2159.39	−0.139876
$621$	5094.50	0.329203
$622$	−10374.7	−0.668793
$623$	4012.31	0.258025
$624$	−1307.05	−0.0838523
$625$	13584.8	0.869424
$626$	15542.7	0.992349
$627$	0	0
$628$	−4917.67	−0.312478
$629$	−30027.5	−1.90346
$630$	−28.9424	−0.00183031
$631$	−9678.86	−0.610633	−0.305316	−	0.952251i	$-0.598762\pi$
$631$	−9678.86	−0.610633	−0.305316	+	0.952251i	$0.598762\pi$
$632$	−6594.85	−0.415078
$633$	−10300.1	−0.646747
$634$	−13054.9	−0.817786
$635$	5552.66	0.347009
$636$	1414.28	0.0881760
$637$	−5490.16	−0.341488
$638$	594.379	0.0368835
$639$	1367.23	0.0846431
$640$	300.785	0.0185775
$641$	−3851.50	−0.237324	−0.118662	−	0.992935i	$-0.537861\pi$
$641$	−3851.50	−0.237324	−0.118662	+	0.992935i	$0.537861\pi$
$642$	−7263.10	−0.446498
$643$	19708.1	1.20873	0.604365	−	0.796708i	$-0.293427\pi$
$643$	19708.1	1.20873	0.604365	+	0.796708i	$0.293427\pi$
$644$	398.623	0.0243912
$645$	911.888	0.0556675
$646$	0	0
$647$	−15500.5	−0.941867	−0.470933	−	0.882169i	$-0.656083\pi$
$647$	−15500.5	−0.941867	−0.470933	+	0.882169i	$0.656083\pi$
$648$	−5326.61	−0.322915
$649$	−2522.51	−0.152569
$650$	−3917.12	−0.236372
$651$	3254.98	0.195964
$652$	1867.38	0.112166
$653$	29753.6	1.78308	0.891538	−	0.452945i	$-0.149627\pi$
$653$	29753.6	1.78308	0.891538	+	0.452945i	$0.149627\pi$
$654$	14950.5	0.893902
$655$	4173.01	0.248936
$656$	−1037.36	−0.0617411
$657$	1643.93	0.0976190
$658$	−2646.62	−0.156802
$659$	22331.5	1.32005	0.660025	−	0.751244i	$-0.270546\pi$
$659$	22331.5	1.32005	0.660025	+	0.751244i	$0.270546\pi$
$660$	−178.088	−0.0105031
$661$	−18354.4	−1.08004	−0.540018	−	0.841654i	$-0.681582\pi$
$661$	−18354.4	−1.08004	−0.540018	+	0.841654i	$0.681582\pi$
$662$	−16966.9	−0.996131
$663$	6110.16	0.357917
$664$	−1061.96	−0.0620665
$665$	0	0
$666$	−1739.10	−0.101184
$667$	2739.87	0.159053
$668$	−14363.5	−0.831946
$669$	−5752.67	−0.332453
$670$	421.346	0.0242955
$671$	−600.499	−0.0345484
$672$	−453.393	−0.0260268
$673$	−18320.3	−1.04932	−0.524661	−	0.851311i	$-0.675808\pi$
$673$	−18320.3	−1.04932	−0.524661	+	0.851311i	$0.675808\pi$
$674$	−11061.7	−0.632166
$675$	−17365.5	−0.990222
$676$	−7713.13	−0.438844
$677$	15480.5	0.878826	0.439413	−	0.898285i	$-0.355187\pi$
$677$	15480.5	0.878826	0.439413	+	0.898285i	$0.355187\pi$
$678$	10452.8	0.592090
$679$	−3754.45	−0.212198
$680$	−1406.10	−0.0792966
$681$	−4132.79	−0.232553
$682$	−1746.86	−0.0980801
$683$	−27505.7	−1.54096	−0.770481	−	0.637463i	$-0.779984\pi$
$683$	−27505.7	−1.54096	−0.770481	+	0.637463i	$0.779984\pi$
$684$	0	0
$685$	−4454.63	−0.248471
$686$	−3854.85	−0.214546
$687$	−25078.1	−1.39271
$688$	−1245.92	−0.0690412
$689$	−1163.06	−0.0643090
$690$	−820.921	−0.0452926
$691$	−34067.4	−1.87552	−0.937761	−	0.347282i	$-0.887105\pi$
$691$	−34067.4	−1.87552	−0.937761	+	0.347282i	$0.887105\pi$
$692$	1154.38	0.0634147
$693$	−23.4133	−0.00128340
$694$	18618.4	1.01836
$695$	−443.003	−0.0241785
$696$	−3116.32	−0.169718
$697$	4849.43	0.263537
$698$	−17315.7	−0.938981
$699$	−6223.65	−0.336767
$700$	−1358.78	−0.0733672
$701$	32317.5	1.74125	0.870625	−	0.491948i	$-0.163715\pi$
$701$	32317.5	1.74125	0.870625	+	0.491948i	$0.163715\pi$
$702$	4765.17	0.256196
$703$	0	0
$704$	243.323	0.0130264
$705$	5450.42	0.291170
$706$	6285.47	0.335066
$707$	−825.584	−0.0439169
$708$	13225.5	0.702042
$709$	−12452.6	−0.659613	−0.329807	−	0.944048i	$-0.606984\pi$
$709$	−12452.6	−0.659613	−0.329807	+	0.944048i	$0.606984\pi$
$710$	−2966.62	−0.156810
$711$	1785.55	0.0941819
$712$	11289.7	0.594242
$713$	−8052.38	−0.422951
$714$	2119.51	0.111093
$715$	146.453	0.00766020
$716$	15903.0	0.830060
$717$	−23563.2	−1.22731
$718$	11143.6	0.579216
$719$	18461.4	0.957574	0.478787	−	0.877931i	$-0.341077\pi$
$719$	18461.4	0.957574	0.478787	+	0.877931i	$0.341077\pi$
$720$	−81.4374	−0.00421527
$721$	1723.46	0.0890220
$722$	0	0
$723$	−2014.28	−0.103612
$724$	2764.98	0.141933
$725$	−9339.37	−0.478421
$726$	13121.7	0.670786
$727$	−24404.6	−1.24500	−0.622501	−	0.782619i	$-0.713883\pi$
$727$	−24404.6	−1.24500	−0.622501	+	0.782619i	$0.713883\pi$
$728$	372.854	0.0189820
$729$	20998.5	1.06683
$730$	−3566.99	−0.180850
$731$	5824.41	0.294697
$732$	3148.41	0.158974
$733$	−17753.1	−0.894579	−0.447290	−	0.894389i	$-0.647611\pi$
$733$	−17753.1	−0.894579	−0.447290	+	0.894389i	$0.647611\pi$
$734$	−1511.36	−0.0760016
$735$	3921.99	0.196823
$736$	1121.63	0.0561739
$737$	340.852	0.0170359
$738$	280.865	0.0140092
$739$	815.608	0.0405990	0.0202995	−	0.999794i	$-0.493538\pi$
$739$	815.608	0.0405990	0.0202995	+	0.999794i	$0.493538\pi$
$740$	3773.50	0.187455
$741$	0	0
$742$	−403.444	−0.0199608
$743$	2620.75	0.129402	0.0647011	−	0.997905i	$-0.479391\pi$
$743$	2620.75	0.129402	0.0647011	+	0.997905i	$0.479391\pi$
$744$	9158.76	0.451313
$745$	−5824.30	−0.286424
$746$	1004.81	0.0493147
$747$	287.526	0.0140830
$748$	−1137.48	−0.0556023
$749$	2071.90	0.101076
$750$	5725.85	0.278771
$751$	12801.9	0.622035	0.311018	−	0.950404i	$-0.399330\pi$
$751$	12801.9	0.622035	0.311018	+	0.950404i	$0.399330\pi$
$752$	−7446.98	−0.361121
$753$	−31669.7	−1.53268
$754$	2562.76	0.123780
$755$	2081.95	0.100357
$756$	1652.96	0.0795204
$757$	−4000.26	−0.192063	−0.0960317	−	0.995378i	$-0.530615\pi$
$757$	−4000.26	−0.192063	−0.0960317	+	0.995378i	$0.530615\pi$
$758$	4091.59	0.196060
$759$	−664.092	−0.0317589
$760$	0	0
$761$	−12934.0	−0.616104	−0.308052	−	0.951369i	$-0.599677\pi$
$761$	−12934.0	−0.616104	−0.308052	+	0.951369i	$0.599677\pi$
$762$	−23550.9	−1.11963
$763$	−4264.85	−0.202356
$764$	8940.53	0.423373
$765$	380.702	0.0179925
$766$	−10674.7	−0.503515
$767$	−10876.2	−0.512017
$768$	−1275.74	−0.0599407
$769$	29993.7	1.40650	0.703250	−	0.710942i	$-0.251731\pi$
$769$	29993.7	1.40650	0.703250	+	0.710942i	$0.251731\pi$
$770$	50.8021	0.00237764
$771$	−21636.2	−1.01065
$772$	16003.8	0.746101
$773$	−25764.9	−1.19884	−0.599418	−	0.800436i	$-0.704601\pi$
$773$	−25764.9	−1.19884	−0.599418	+	0.800436i	$0.704601\pi$
$774$	337.333	0.0156656
$775$	27448.1	1.27221
$776$	−10564.2	−0.488701
$777$	−5688.04	−0.262622
$778$	−198.128	−0.00913014
$779$	0	0
$780$	−767.854	−0.0352482
$781$	−2399.88	−0.109955
$782$	−5243.39	−0.239774
$783$	11361.3	0.518545
$784$	−5358.66	−0.244108
$785$	−2888.99	−0.131353
$786$	−17699.3	−0.803197
$787$	−16133.2	−0.730734	−0.365367	−	0.930864i	$-0.619056\pi$
$787$	−16133.2	−0.730734	−0.365367	+	0.930864i	$0.619056\pi$
$788$	−8391.76	−0.379371
$789$	−30523.8	−1.37728
$790$	−3874.29	−0.174482
$791$	−2981.81	−0.134034
$792$	−65.8796	−0.00295572
$793$	−2589.15	−0.115944
$794$	−23255.0	−1.03941
$795$	830.850	0.0370657
$796$	−7566.23	−0.336907
$797$	19210.4	0.853786	0.426893	−	0.904302i	$-0.359608\pi$
$797$	19210.4	0.853786	0.426893	+	0.904302i	$0.359608\pi$
$798$	0	0
$799$	34813.0	1.54142
$800$	−3823.30	−0.168967
$801$	−3056.68	−0.134835
$802$	−11455.1	−0.504355
$803$	−2885.55	−0.126811
$804$	−1787.09	−0.0783902
$805$	234.179	0.0102531
$806$	−7531.85	−0.329154
$807$	−29569.1	−1.28982
$808$	−2323.00	−0.101142
$809$	34345.9	1.49263	0.746316	−	0.665592i	$-0.231821\pi$
$809$	34345.9	1.49263	0.746316	+	0.665592i	$0.231821\pi$
$810$	−3129.23	−0.135741
$811$	−2591.60	−0.112211	−0.0561056	−	0.998425i	$-0.517868\pi$
$811$	−2591.60	−0.112211	−0.0561056	+	0.998425i	$0.517868\pi$
$812$	888.977	0.0384199
$813$	−32344.1	−1.39527
$814$	3052.62	0.131442
$815$	1097.03	0.0471502
$816$	5963.82	0.255852
$817$	0	0
$818$	−12887.8	−0.550870
$819$	−100.950	−0.00430705
$820$	−609.420	−0.0259535
$821$	37178.0	1.58041	0.790207	−	0.612840i	$-0.209973\pi$
$821$	37178.0	1.58041	0.790207	+	0.612840i	$0.209973\pi$
$822$	18893.8	0.801698
$823$	5196.26	0.220085	0.110043	−	0.993927i	$-0.464901\pi$
$823$	5196.26	0.220085	0.110043	+	0.993927i	$0.464901\pi$
$824$	4849.41	0.205021
$825$	2263.68	0.0955289
$826$	−3772.77	−0.158924
$827$	30713.6	1.29144	0.645718	−	0.763576i	$-0.276558\pi$
$827$	30713.6	1.29144	0.645718	+	0.763576i	$0.276558\pi$
$828$	−303.681	−0.0127460
$829$	1697.82	0.0711309	0.0355655	−	0.999367i	$-0.488677\pi$
$829$	1697.82	0.0711309	0.0355655	+	0.999367i	$0.488677\pi$
$830$	−623.873	−0.0260903
$831$	11832.5	0.493943
$832$	1049.13	0.0437163
$833$	25050.6	1.04196
$834$	1878.94	0.0780124
$835$	−8438.13	−0.349717
$836$	0	0
$837$	−33390.6	−1.37891
$838$	5390.61	0.222214
$839$	3064.91	0.126117	0.0630586	−	0.998010i	$-0.479915\pi$
$839$	3064.91	0.126117	0.0630586	+	0.998010i	$0.479915\pi$
$840$	−266.355	−0.0109406
$841$	−18278.8	−0.749467
$842$	32773.7	1.34140
$843$	23208.0	0.948190
$844$	8267.55	0.337181
$845$	−4531.24	−0.184473
$846$	2016.26	0.0819391
$847$	−3743.15	−0.151849
$848$	−1135.20	−0.0459704
$849$	15220.1	0.615257
$850$	17873.1	0.721225
$851$	14071.5	0.566819
$852$	12582.6	0.505953
$853$	−28283.9	−1.13531	−0.567657	−	0.823265i	$-0.692150\pi$
$853$	−28283.9	−1.13531	−0.567657	+	0.823265i	$0.692150\pi$
$854$	−898.130	−0.0359876
$855$	0	0
$856$	5829.87	0.232781
$857$	−29128.6	−1.16104	−0.580522	−	0.814244i	$-0.697152\pi$
$857$	−29128.6	−1.16104	−0.580522	+	0.814244i	$0.697152\pi$
$858$	−621.163	−0.0247158
$859$	−18260.4	−0.725305	−0.362652	−	0.931924i	$-0.618129\pi$
$859$	−18260.4	−0.725305	−0.362652	+	0.931924i	$0.618129\pi$
$860$	−731.944	−0.0290222
$861$	918.617	0.0363605
$862$	−350.189	−0.0138370
$863$	−18631.9	−0.734920	−0.367460	−	0.930039i	$-0.619773\pi$
$863$	−18631.9	−0.734920	−0.367460	+	0.930039i	$0.619773\pi$
$864$	4651.04	0.183138
$865$	678.166	0.0266570
$866$	24444.2	0.959179
$867$	−3396.22	−0.133035
$868$	−2612.67	−0.102166
$869$	−3134.14	−0.122346
$870$	−1830.75	−0.0713429
$871$	1469.64	0.0571720
$872$	−12000.3	−0.466035
$873$	2860.24	0.110887
$874$	0	0
$875$	−1633.38	−0.0631067
$876$	15128.9	0.583516
$877$	49911.8	1.92178	0.960890	−	0.276929i	$-0.0893167\pi$
$877$	49911.8	1.92178	0.960890	+	0.276929i	$0.0893167\pi$
$878$	6482.55	0.249175
$879$	48123.6	1.84661
$880$	142.946	0.00547579
$881$	28777.8	1.10051	0.550254	−	0.834997i	$-0.314531\pi$
$881$	28777.8	1.10051	0.550254	+	0.834997i	$0.314531\pi$
$882$	1450.85	0.0553886
$883$	−21200.1	−0.807972	−0.403986	−	0.914765i	$-0.632375\pi$
$883$	−21200.1	−0.807972	−0.403986	+	0.914765i	$0.632375\pi$
$884$	−4904.44	−0.186600
$885$	7769.62	0.295111
$886$	−16699.1	−0.633203
$887$	−16075.6	−0.608531	−0.304265	−	0.952587i	$-0.598411\pi$
$887$	−16075.6	−0.608531	−0.304265	+	0.952587i	$0.598411\pi$
$888$	−16004.8	−0.604828
$889$	6718.23	0.253456
$890$	6632.39	0.249796
$891$	−2531.43	−0.0951807
$892$	4617.49	0.173324
$893$	0	0
$894$	24703.1	0.924154
$895$	9342.55	0.348924
$896$	363.924	0.0135690
$897$	−2863.34	−0.106582
$898$	−22729.0	−0.844628
$899$	−17957.8	−0.666213
$900$	1035.15	0.0383390
$901$	5306.81	0.196221
$902$	−492.997	−0.0181984
$903$	1103.31	0.0406597
$904$	−8390.13	−0.308685
$905$	1624.35	0.0596632
$906$	−8830.32	−0.323805
$907$	36155.9	1.32364	0.661818	−	0.749664i	$-0.269785\pi$
$907$	36155.9	1.32364	0.661818	+	0.749664i	$0.269785\pi$
$908$	3317.26	0.121241
$909$	628.951	0.0229494
$910$	219.041	0.00797928
$911$	38879.0	1.41396	0.706981	−	0.707232i	$-0.250057\pi$
$911$	38879.0	1.41396	0.706981	+	0.707232i	$0.250057\pi$
$912$	0	0
$913$	−504.689	−0.0182944
$914$	24431.3	0.884154
$915$	1849.60	0.0668262
$916$	20129.4	0.726087
$917$	5048.98	0.181823
$918$	−21742.6	−0.781713
$919$	−41320.3	−1.48317	−0.741584	−	0.670861i	$-0.765925\pi$
$919$	−41320.3	−1.48317	−0.741584	+	0.670861i	$0.765925\pi$
$920$	658.928	0.0236133
$921$	6332.17	0.226549
$922$	16755.0	0.598478
$923$	−10347.5	−0.369004
$924$	−215.471	−0.00767150
$925$	−47965.2	−1.70496
$926$	12463.6	0.442310
$927$	−1312.97	−0.0465196
$928$	2501.38	0.0884825
$929$	−25241.1	−0.891424	−0.445712	−	0.895176i	$-0.647049\pi$
$929$	−25241.1	−0.891424	−0.445712	+	0.895176i	$0.647049\pi$
$930$	5380.51	0.189714
$931$	0	0
$932$	4995.53	0.175573
$933$	25850.6	0.907086
$934$	24874.1	0.871417
$935$	−668.239	−0.0233730
$936$	−284.050	−0.00991931
$937$	45059.2	1.57099	0.785497	−	0.618866i	$-0.212407\pi$
$937$	45059.2	1.57099	0.785497	+	0.618866i	$0.212407\pi$
$938$	509.792	0.0177455
$939$	−38727.5	−1.34593
$940$	−4374.88	−0.151801
$941$	18314.8	0.634480	0.317240	−	0.948345i	$-0.397244\pi$
$941$	18314.8	0.634480	0.317240	+	0.948345i	$0.397244\pi$
$942$	12253.3	0.423815
$943$	−2272.54	−0.0784772
$944$	−10615.7	−0.366009
$945$	971.064	0.0334272
$946$	−592.114	−0.0203502
$947$	1162.44	0.0398882	0.0199441	−	0.999801i	$-0.493651\pi$
$947$	1162.44	0.0398882	0.0199441	+	0.999801i	$0.493651\pi$
$948$	16432.3	0.562971
$949$	−12441.5	−0.425573
$950$	0	0
$951$	32528.7	1.10917
$952$	−1701.27	−0.0579184
$953$	−19549.6	−0.664506	−0.332253	−	0.943190i	$-0.607809\pi$
$953$	−19549.6	−0.664506	−0.332253	+	0.943190i	$0.607809\pi$
$954$	307.354	0.0104308
$955$	5252.31	0.177969
$956$	18913.5	0.639859
$957$	−1481.01	−0.0500252
$958$	−12656.4	−0.426838
$959$	−5389.72	−0.181484
$960$	−749.463	−0.0251967
$961$	22986.3	0.771584
$962$	13161.8	0.441117
$963$	−1578.43	−0.0528185
$964$	1616.80	0.0540182
$965$	9401.78	0.313631
$966$	−993.243	−0.0330818
$967$	−54854.1	−1.82419	−0.912093	−	0.409983i	$-0.865534\pi$
$967$	−54854.1	−1.82419	−0.912093	+	0.409983i	$0.865534\pi$
$968$	−10532.4	−0.349714
$969$	0	0
$970$	−6206.15	−0.205430
$971$	34845.1	1.15163	0.575815	−	0.817580i	$-0.304685\pi$
$971$	34845.1	1.15163	0.575815	+	0.817580i	$0.304685\pi$
$972$	−2425.01	−0.0800229
$973$	−535.995	−0.0176600
$974$	7197.12	0.236767
$975$	9760.22	0.320592
$976$	−2527.13	−0.0828807
$977$	49706.3	1.62768	0.813842	−	0.581087i	$-0.197372\pi$
$977$	49706.3	1.62768	0.813842	+	0.581087i	$0.197372\pi$
$978$	−4652.93	−0.152131
$979$	5365.34	0.175155
$980$	−3148.06	−0.102613
$981$	3249.08	0.105744
$982$	−8544.21	−0.277654
$983$	27547.2	0.893816	0.446908	−	0.894580i	$-0.352525\pi$
$983$	27547.2	0.893816	0.446908	+	0.894580i	$0.352525\pi$
$984$	2584.78	0.0837396
$985$	−4929.92	−0.159472
$986$	−11693.4	−0.377681
$987$	6594.54	0.212671
$988$	0	0
$989$	−2729.43	−0.0877562
$990$	−38.7024	−0.00124247
$991$	48726.5	1.56191	0.780953	−	0.624589i	$-0.214734\pi$
$991$	48726.5	1.56191	0.780953	+	0.624589i	$0.214734\pi$
$992$	−7351.46	−0.235291
$993$	42276.3	1.35105
$994$	−3589.36	−0.114535
$995$	−4444.94	−0.141622
$996$	2646.08	0.0841810
$997$	20321.9	0.645537	0.322769	−	0.946478i	$-0.395386\pi$
$997$	20321.9	0.645537	0.322769	+	0.946478i	$0.395386\pi$
$998$	−4651.44	−0.147534
$999$	58349.6	1.84795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.4.a.p.1.3		6
19.4	even	9		38.4.e.a.35.2	yes	12
19.5	even	9		38.4.e.a.25.2	✓	12
19.18	odd	2		722.4.a.o.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.4.e.a.25.2	✓	12	19.5	even	9
38.4.e.a.35.2	yes	12	19.4	even	9
722.4.a.o.1.4		6	19.18	odd	2
722.4.a.p.1.3		6	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -4.98337 q^{3} +4.00000 q^{4} +2.34989 q^{5} -9.96675 q^{6} +2.84316 q^{7} +8.00000 q^{8} -2.16599 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} -4.98337 q^{3} +4.00000 q^{4} +2.34989 q^{5} -9.96675 q^{6} +2.84316 q^{7} +8.00000 q^{8} -2.16599 q^{9} +4.69977 q^{10} +3.80193 q^{11} -19.9335 q^{12} +16.3926 q^{13} +5.68632 q^{14} -11.7104 q^{15} +16.0000 q^{16} -74.7965 q^{17} -4.33198 q^{18} +9.39954 q^{20} -14.1685 q^{21} +7.60386 q^{22} +35.0510 q^{23} -39.8670 q^{24} -119.478 q^{25} +32.7852 q^{26} +145.345 q^{27} +11.3726 q^{28} +78.1681 q^{29} -23.4207 q^{30} -229.733 q^{31} +32.0000 q^{32} -18.9464 q^{33} -149.593 q^{34} +6.68110 q^{35} -8.66397 q^{36} +401.456 q^{37} -81.6905 q^{39} +18.7991 q^{40} -64.8351 q^{41} -28.3370 q^{42} -77.8702 q^{43} +15.2077 q^{44} -5.08983 q^{45} +70.1021 q^{46} -465.436 q^{47} -79.7340 q^{48} -334.916 q^{49} -238.956 q^{50} +372.739 q^{51} +65.5705 q^{52} -70.9500 q^{53} +290.690 q^{54} +8.93410 q^{55} +22.7453 q^{56} +156.336 q^{58} -663.483 q^{59} -46.8414 q^{60} -157.946 q^{61} -459.466 q^{62} -6.15826 q^{63} +64.0000 q^{64} +38.5208 q^{65} -37.8929 q^{66} +89.6525 q^{67} -299.186 q^{68} -174.672 q^{69} +13.3622 q^{70} -631.227 q^{71} -17.3279 q^{72} -758.971 q^{73} +802.912 q^{74} +595.404 q^{75} +10.8095 q^{77} -163.381 q^{78} -824.356 q^{79} +37.5982 q^{80} -665.827 q^{81} -129.670 q^{82} -132.745 q^{83} -56.6741 q^{84} -175.763 q^{85} -155.740 q^{86} -389.541 q^{87} +30.4154 q^{88} +1411.22 q^{89} -10.1797 q^{90} +46.6068 q^{91} +140.204 q^{92} +1144.85 q^{93} -930.872 q^{94} -159.468 q^{96} -1320.52 q^{97} -669.833 q^{98} -8.23495 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9}+O(q^{10}) \) 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9	\( 6 q + 12 q^{2} - 9 q^{3} + 24 q^{4} - 27 q^{5} - 18 q^{6} - 21 q^{7} + 48 q^{8} + 33 q^{9} - 54 q^{10} + 9 q^{11} - 36 q^{12} - 24 q^{13} - 42 q^{14} + 96 q^{16} - 102 q^{17} + 66 q^{18} - 108 q^{20} - 51 q^{21} + 18 q^{22} - 264 q^{23} - 72 q^{24} + 177 q^{25} - 48 q^{26} - 189 q^{27} - 84 q^{28} - 483 q^{29} - 72 q^{31} + 192 q^{32} - 387 q^{33} - 204 q^{34} + 135 q^{35} + 132 q^{36} + 558 q^{37} - 624 q^{39} - 216 q^{40} - 396 q^{41} - 102 q^{42} - 2064 q^{43} + 36 q^{44} - 1296 q^{45} - 528 q^{46} + 858 q^{47} - 144 q^{48} - 1413 q^{49} + 354 q^{50} + 1272 q^{51} - 96 q^{52} - 762 q^{53} - 378 q^{54} - 1107 q^{55} - 168 q^{56} - 966 q^{58} - 393 q^{59} - 627 q^{61} - 144 q^{62} - 84 q^{63} + 384 q^{64} - 495 q^{65} - 774 q^{66} - 2028 q^{67} - 408 q^{68} + 237 q^{69} + 270 q^{70} - 1284 q^{71} + 264 q^{72} - 2688 q^{73} + 1116 q^{74} - 927 q^{75} - 708 q^{77} - 1248 q^{78} - 969 q^{79} - 432 q^{80} - 1398 q^{81} - 792 q^{82} - 927 q^{83} - 204 q^{84} + 396 q^{85} - 4128 q^{86} - 2892 q^{87} + 72 q^{88} + 1257 q^{89} - 2592 q^{90} + 1323 q^{91} - 1056 q^{92} - 1368 q^{93} + 1716 q^{94} - 288 q^{96} + 2403 q^{97} - 2826 q^{98} + 567 q^{99}+O(q^{100}) \) 6 * q + 12 * q^2 - 9 * q^3 + 24 * q^4 - 27 * q^5 - 18 * q^6 - 21 * q^7 + 48 * q^8 + 33 * q^9 - 54 * q^10 + 9 * q^11 - 36 * q^12 - 24 * q^13 - 42 * q^14 + 96 * q^16 - 102 * q^17 + 66 * q^18 - 108 * q^20 - 51 * q^21 + 18 * q^22 - 264 * q^23 - 72 * q^24 + 177 * q^25 - 48 * q^26 - 189 * q^27 - 84 * q^28 - 483 * q^29 - 72 * q^31 + 192 * q^32 - 387 * q^33 - 204 * q^34 + 135 * q^35 + 132 * q^36 + 558 * q^37 - 624 * q^39 - 216 * q^40 - 396 * q^41 - 102 * q^42 - 2064 * q^43 + 36 * q^44 - 1296 * q^45 - 528 * q^46 + 858 * q^47 - 144 * q^48 - 1413 * q^49 + 354 * q^50 + 1272 * q^51 - 96 * q^52 - 762 * q^53 - 378 * q^54 - 1107 * q^55 - 168 * q^56 - 966 * q^58 - 393 * q^59 - 627 * q^61 - 144 * q^62 - 84 * q^63 + 384 * q^64 - 495 * q^65 - 774 * q^66 - 2028 * q^67 - 408 * q^68 + 237 * q^69 + 270 * q^70 - 1284 * q^71 + 264 * q^72 - 2688 * q^73 + 1116 * q^74 - 927 * q^75 - 708 * q^77 - 1248 * q^78 - 969 * q^79 - 432 * q^80 - 1398 * q^81 - 792 * q^82 - 927 * q^83 - 204 * q^84 + 396 * q^85 - 4128 * q^86 - 2892 * q^87 + 72 * q^88 + 1257 * q^89 - 2592 * q^90 + 1323 * q^91 - 1056 * q^92 - 1368 * q^93 + 1716 * q^94 - 288 * q^96 + 2403 * q^97 - 2826 * q^98 + 567 * q^99

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