LMFDB - Embedded newform 4029.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21432 q^{2} -1.00000 q^{3} +2.90321 q^{4} -1.68889 q^{5} +2.21432 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.21432 q^{2} -1.00000 q^{3} +2.90321 q^{4} -1.68889 q^{5} +2.21432 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} +3.73975 q^{10} +5.80642 q^{11} -2.90321 q^{12} +1.09679 q^{13} -2.21432 q^{14} +1.68889 q^{15} -1.37778 q^{16} +1.00000 q^{17} -2.21432 q^{18} +1.90321 q^{19} -4.90321 q^{20} -1.00000 q^{21} -12.8573 q^{22} -1.83654 q^{23} +2.00000 q^{24} -2.14764 q^{25} -2.42864 q^{26} -1.00000 q^{27} +2.90321 q^{28} +5.80642 q^{29} -3.73975 q^{30} -9.80642 q^{31} +7.05086 q^{32} -5.80642 q^{33} -2.21432 q^{34} -1.68889 q^{35} +2.90321 q^{36} -6.37778 q^{37} -4.21432 q^{38} -1.09679 q^{39} +3.37778 q^{40} -9.61285 q^{41} +2.21432 q^{42} -4.23506 q^{43} +16.8573 q^{44} -1.68889 q^{45} +4.06668 q^{46} +0.785680 q^{47} +1.37778 q^{48} -6.00000 q^{49} +4.75557 q^{50} -1.00000 q^{51} +3.18421 q^{52} +14.4128 q^{53} +2.21432 q^{54} -9.80642 q^{55} -2.00000 q^{56} -1.90321 q^{57} -12.8573 q^{58} -2.59210 q^{59} +4.90321 q^{60} -10.0509 q^{61} +21.7146 q^{62} +1.00000 q^{63} -12.8573 q^{64} -1.85236 q^{65} +12.8573 q^{66} +7.13828 q^{67} +2.90321 q^{68} +1.83654 q^{69} +3.73975 q^{70} -0.407896 q^{71} -2.00000 q^{72} -0.260253 q^{73} +14.1225 q^{74} +2.14764 q^{75} +5.52543 q^{76} +5.80642 q^{77} +2.42864 q^{78} +1.00000 q^{79} +2.32693 q^{80} +1.00000 q^{81} +21.2859 q^{82} +3.03011 q^{83} -2.90321 q^{84} -1.68889 q^{85} +9.37778 q^{86} -5.80642 q^{87} -11.6128 q^{88} -14.6637 q^{89} +3.73975 q^{90} +1.09679 q^{91} -5.33185 q^{92} +9.80642 q^{93} -1.73975 q^{94} -3.21432 q^{95} -7.05086 q^{96} +3.11753 q^{97} +13.2859 q^{98} +5.80642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 10 q^{13} + 5 q^{15} - 4 q^{16} + 3 q^{17} - q^{19} - 8 q^{20} - 3 q^{21} - 12 q^{22} + q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 2 q^{28} + 4 q^{29} + 2 q^{30} - 16 q^{31} + 8 q^{32} - 4 q^{33} - 5 q^{35} + 2 q^{36} - 19 q^{37} - 6 q^{38} - 10 q^{39} + 10 q^{40} - 2 q^{41} + 14 q^{43} + 24 q^{44} - 5 q^{45} + 12 q^{46} + 9 q^{47} + 4 q^{48} - 18 q^{49} + 14 q^{50} - 3 q^{51} - 4 q^{52} + 17 q^{53} - 16 q^{55} - 6 q^{56} + q^{57} - 12 q^{58} - q^{59} + 8 q^{60} - 17 q^{61} + 12 q^{62} + 3 q^{63} - 12 q^{64} - 12 q^{65} + 12 q^{66} - 12 q^{67} + 2 q^{68} - q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} - 14 q^{73} - 4 q^{74} + 10 q^{76} + 4 q^{77} - 6 q^{78} + 3 q^{79} + 20 q^{80} + 3 q^{81} + 24 q^{82} + 16 q^{83} - 2 q^{84} - 5 q^{85} + 28 q^{86} - 4 q^{87} - 8 q^{88} - 4 q^{89} - 2 q^{90} + 10 q^{91} + 4 q^{92} + 16 q^{93} + 8 q^{94} - 3 q^{95} - 8 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 10 * q^13 + 5 * q^15 - 4 * q^16 + 3 * q^17 - q^19 - 8 * q^20 - 3 * q^21 - 12 * q^22 + q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 2 * q^28 + 4 * q^29 + 2 * q^30 - 16 * q^31 + 8 * q^32 - 4 * q^33 - 5 * q^35 + 2 * q^36 - 19 * q^37 - 6 * q^38 - 10 * q^39 + 10 * q^40 - 2 * q^41 + 14 * q^43 + 24 * q^44 - 5 * q^45 + 12 * q^46 + 9 * q^47 + 4 * q^48 - 18 * q^49 + 14 * q^50 - 3 * q^51 - 4 * q^52 + 17 * q^53 - 16 * q^55 - 6 * q^56 + q^57 - 12 * q^58 - q^59 + 8 * q^60 - 17 * q^61 + 12 * q^62 + 3 * q^63 - 12 * q^64 - 12 * q^65 + 12 * q^66 - 12 * q^67 + 2 * q^68 - q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 - 14 * q^73 - 4 * q^74 + 10 * q^76 + 4 * q^77 - 6 * q^78 + 3 * q^79 + 20 * q^80 + 3 * q^81 + 24 * q^82 + 16 * q^83 - 2 * q^84 - 5 * q^85 + 28 * q^86 - 4 * q^87 - 8 * q^88 - 4 * q^89 - 2 * q^90 + 10 * q^91 + 4 * q^92 + 16 * q^93 + 8 * q^94 - 3 * q^95 - 8 * q^96 - 4 * q^97 + 4 * 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 $

$2$	−2.21432	−1.56576	−0.782880	−	0.622172i	$-0.786250\pi$
$2$	−2.21432	−1.56576	−0.782880	+	0.622172i	$0.786250\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.90321	1.45161
$5$	−1.68889	−0.755296	−0.377648	−	0.925949i	$-0.623267\pi$
$5$	−1.68889	−0.755296	−0.377648	+	0.925949i	$0.623267\pi$
$6$	2.21432	0.903992
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−2.00000	−0.707107
$9$	1.00000	0.333333
$10$	3.73975	1.18261
$11$	5.80642	1.75070	0.875351	−	0.483487i	$-0.160630\pi$
$11$	5.80642	1.75070	0.875351	+	0.483487i	$0.160630\pi$
$12$	−2.90321	−0.838085
$13$	1.09679	0.304194	0.152097	−	0.988366i	$-0.451397\pi$
$13$	1.09679	0.304194	0.152097	+	0.988366i	$0.451397\pi$
$14$	−2.21432	−0.591802
$15$	1.68889	0.436070
$16$	−1.37778	−0.344446
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.21432	−0.521920
$19$	1.90321	0.436627	0.218313	−	0.975879i	$-0.429945\pi$
$19$	1.90321	0.436627	0.218313	+	0.975879i	$0.429945\pi$
$20$	−4.90321	−1.09639
$21$	−1.00000	−0.218218
$22$	−12.8573	−2.74118
$23$	−1.83654	−0.382944	−0.191472	−	0.981498i	$-0.561326\pi$
$23$	−1.83654	−0.382944	−0.191472	+	0.981498i	$0.561326\pi$
$24$	2.00000	0.408248
$25$	−2.14764	−0.429529
$26$	−2.42864	−0.476295
$27$	−1.00000	−0.192450
$28$	2.90321	0.548655
$29$	5.80642	1.07823	0.539113	−	0.842233i	$-0.318760\pi$
$29$	5.80642	1.07823	0.539113	+	0.842233i	$0.318760\pi$
$30$	−3.73975	−0.682781
$31$	−9.80642	−1.76129	−0.880643	−	0.473781i	$-0.842889\pi$
$31$	−9.80642	−1.76129	−0.880643	+	0.473781i	$0.842889\pi$
$32$	7.05086	1.24643
$33$	−5.80642	−1.01077
$34$	−2.21432	−0.379753
$35$	−1.68889	−0.285475
$36$	2.90321	0.483869
$37$	−6.37778	−1.04850	−0.524251	−	0.851564i	$-0.675655\pi$
$37$	−6.37778	−1.04850	−0.524251	+	0.851564i	$0.675655\pi$
$38$	−4.21432	−0.683653
$39$	−1.09679	−0.175627
$40$	3.37778	0.534075
$41$	−9.61285	−1.50127	−0.750637	−	0.660715i	$-0.770253\pi$
$41$	−9.61285	−1.50127	−0.750637	+	0.660715i	$0.770253\pi$
$42$	2.21432	0.341677
$43$	−4.23506	−0.645841	−0.322921	−	0.946426i	$-0.604665\pi$
$43$	−4.23506	−0.645841	−0.322921	+	0.946426i	$0.604665\pi$
$44$	16.8573	2.54133
$45$	−1.68889	−0.251765
$46$	4.06668	0.599599
$47$	0.785680	0.114603	0.0573016	−	0.998357i	$-0.481750\pi$
$47$	0.785680	0.114603	0.0573016	+	0.998357i	$0.481750\pi$
$48$	1.37778	0.198866
$49$	−6.00000	−0.857143
$50$	4.75557	0.672539
$51$	−1.00000	−0.140028
$52$	3.18421	0.441570
$53$	14.4128	1.97975	0.989876	−	0.141932i	$-0.0453314\pi$
$53$	14.4128	1.97975	0.989876	+	0.141932i	$0.0453314\pi$
$54$	2.21432	0.301331
$55$	−9.80642	−1.32230
$56$	−2.00000	−0.267261
$57$	−1.90321	−0.252087
$58$	−12.8573	−1.68824
$59$	−2.59210	−0.337463	−0.168732	−	0.985662i	$-0.553967\pi$
$59$	−2.59210	−0.337463	−0.168732	+	0.985662i	$0.553967\pi$
$60$	4.90321	0.633002
$61$	−10.0509	−1.28688	−0.643440	−	0.765496i	$-0.722493\pi$
$61$	−10.0509	−1.28688	−0.643440	+	0.765496i	$0.722493\pi$
$62$	21.7146	2.75775
$63$	1.00000	0.125988
$64$	−12.8573	−1.60716
$65$	−1.85236	−0.229757
$66$	12.8573	1.58262
$67$	7.13828	0.872079	0.436040	−	0.899927i	$-0.356381\pi$
$67$	7.13828	0.872079	0.436040	+	0.899927i	$0.356381\pi$
$68$	2.90321	0.352066
$69$	1.83654	0.221093
$70$	3.73975	0.446985
$71$	−0.407896	−0.0484083	−0.0242042	−	0.999707i	$-0.507705\pi$
$71$	−0.407896	−0.0484083	−0.0242042	+	0.999707i	$0.507705\pi$
$72$	−2.00000	−0.235702
$73$	−0.260253	−0.0304603	−0.0152301	−	0.999884i	$-0.504848\pi$
$73$	−0.260253	−0.0304603	−0.0152301	+	0.999884i	$0.504848\pi$
$74$	14.1225	1.64170
$75$	2.14764	0.247988
$76$	5.52543	0.633810
$77$	5.80642	0.661703
$78$	2.42864	0.274989
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	2.32693	0.260159
$81$	1.00000	0.111111
$82$	21.2859	2.35064
$83$	3.03011	0.332598	0.166299	−	0.986075i	$-0.446818\pi$
$83$	3.03011	0.332598	0.166299	+	0.986075i	$0.446818\pi$
$84$	−2.90321	−0.316766
$85$	−1.68889	−0.183186
$86$	9.37778	1.01123
$87$	−5.80642	−0.622514
$88$	−11.6128	−1.23793
$89$	−14.6637	−1.55435	−0.777175	−	0.629285i	$-0.783348\pi$
$89$	−14.6637	−1.55435	−0.777175	+	0.629285i	$0.783348\pi$
$90$	3.73975	0.394204
$91$	1.09679	0.114975
$92$	−5.33185	−0.555884
$93$	9.80642	1.01688
$94$	−1.73975	−0.179441
$95$	−3.21432	−0.329782
$96$	−7.05086	−0.719625
$97$	3.11753	0.316537	0.158269	−	0.987396i	$-0.449409\pi$
$97$	3.11753	0.316537	0.158269	+	0.987396i	$0.449409\pi$
$98$	13.2859	1.34208
$99$	5.80642	0.583568
$100$	−6.23506	−0.623506
$101$	−4.21432	−0.419340	−0.209670	−	0.977772i	$-0.567239\pi$
$101$	−4.21432	−0.419340	−0.209670	+	0.977772i	$0.567239\pi$
$102$	2.21432	0.219250
$103$	−10.8825	−1.07228	−0.536141	−	0.844129i	$-0.680118\pi$
$103$	−10.8825	−1.07228	−0.536141	+	0.844129i	$0.680118\pi$
$104$	−2.19358	−0.215098
$105$	1.68889	0.164819
$106$	−31.9146	−3.09982
$107$	−5.97926	−0.578037	−0.289018	−	0.957324i	$-0.593329\pi$
$107$	−5.97926	−0.578037	−0.289018	+	0.957324i	$0.593329\pi$
$108$	−2.90321	−0.279362
$109$	14.2494	1.36484	0.682420	−	0.730960i	$-0.260927\pi$
$109$	14.2494	1.36484	0.682420	+	0.730960i	$0.260927\pi$
$110$	21.7146	2.07040
$111$	6.37778	0.605353
$112$	−1.37778	−0.130188
$113$	−5.24443	−0.493355	−0.246677	−	0.969098i	$-0.579339\pi$
$113$	−5.24443	−0.493355	−0.246677	+	0.969098i	$0.579339\pi$
$114$	4.21432	0.394707
$115$	3.10171	0.289236
$116$	16.8573	1.56516
$117$	1.09679	0.101398
$118$	5.73975	0.528387
$119$	1.00000	0.0916698
$120$	−3.37778	−0.308348
$121$	22.7146	2.06496
$122$	22.2558	2.01495
$123$	9.61285	0.866761
$124$	−28.4701	−2.55669
$125$	12.0716	1.07972
$126$	−2.21432	−0.197267
$127$	16.1082	1.42937	0.714684	−	0.699447i	$-0.246570\pi$
$127$	16.1082	1.42937	0.714684	+	0.699447i	$0.246570\pi$
$128$	14.3684	1.27000
$129$	4.23506	0.372877
$130$	4.10171	0.359744
$131$	−8.44446	−0.737796	−0.368898	−	0.929470i	$-0.620265\pi$
$131$	−8.44446	−0.737796	−0.368898	+	0.929470i	$0.620265\pi$
$132$	−16.8573	−1.46724
$133$	1.90321	0.165029
$134$	−15.8064	−1.36547
$135$	1.68889	0.145357
$136$	−2.00000	−0.171499
$137$	−0.652327	−0.0557321	−0.0278660	−	0.999612i	$-0.508871\pi$
$137$	−0.652327	−0.0557321	−0.0278660	+	0.999612i	$0.508871\pi$
$138$	−4.06668	−0.346178
$139$	−4.34122	−0.368217	−0.184109	−	0.982906i	$-0.558940\pi$
$139$	−4.34122	−0.368217	−0.184109	+	0.982906i	$0.558940\pi$
$140$	−4.90321	−0.414397
$141$	−0.785680	−0.0661662
$142$	0.903212	0.0757959
$143$	6.36842	0.532554
$144$	−1.37778	−0.114815
$145$	−9.80642	−0.814379
$146$	0.576283	0.0476935
$147$	6.00000	0.494872
$148$	−18.5161	−1.52201
$149$	−19.8780	−1.62847	−0.814236	−	0.580535i	$-0.802844\pi$
$149$	−19.8780	−1.62847	−0.814236	+	0.580535i	$0.802844\pi$
$150$	−4.75557	−0.388291
$151$	8.74620	0.711756	0.355878	−	0.934532i	$-0.384182\pi$
$151$	8.74620	0.711756	0.355878	+	0.934532i	$0.384182\pi$
$152$	−3.80642	−0.308742
$153$	1.00000	0.0808452
$154$	−12.8573	−1.03607
$155$	16.5620	1.33029
$156$	−3.18421	−0.254941
$157$	−4.68889	−0.374214	−0.187107	−	0.982340i	$-0.559911\pi$
$157$	−4.68889	−0.374214	−0.187107	+	0.982340i	$0.559911\pi$
$158$	−2.21432	−0.176162
$159$	−14.4128	−1.14301
$160$	−11.9081	−0.941421
$161$	−1.83654	−0.144739
$162$	−2.21432	−0.173973
$163$	0.301740	0.0236341	0.0118170	−	0.999930i	$-0.496238\pi$
$163$	0.301740	0.0236341	0.0118170	+	0.999930i	$0.496238\pi$
$164$	−27.9081	−2.17926
$165$	9.80642	0.763429
$166$	−6.70964	−0.520769
$167$	10.6064	0.820747	0.410374	−	0.911917i	$-0.365398\pi$
$167$	10.6064	0.820747	0.410374	+	0.911917i	$0.365398\pi$
$168$	2.00000	0.154303
$169$	−11.7971	−0.907466
$170$	3.73975	0.286826
$171$	1.90321	0.145542
$172$	−12.2953	−0.937507
$173$	−8.50961	−0.646973	−0.323487	−	0.946233i	$-0.604855\pi$
$173$	−8.50961	−0.646973	−0.323487	+	0.946233i	$0.604855\pi$
$174$	12.8573	0.974708
$175$	−2.14764	−0.162347
$176$	−8.00000	−0.603023
$177$	2.59210	0.194834
$178$	32.4701	2.43374
$179$	8.64296	0.646005	0.323003	−	0.946398i	$-0.395308\pi$
$179$	8.64296	0.646005	0.323003	+	0.946398i	$0.395308\pi$
$180$	−4.90321	−0.365464
$181$	−22.9240	−1.70392	−0.851962	−	0.523603i	$-0.824587\pi$
$181$	−22.9240	−1.70392	−0.851962	+	0.523603i	$0.824587\pi$
$182$	−2.42864	−0.180023
$183$	10.0509	0.742981
$184$	3.67307	0.270782
$185$	10.7714	0.791928
$186$	−21.7146	−1.59219
$187$	5.80642	0.424608
$188$	2.28100	0.166359
$189$	−1.00000	−0.0727393
$190$	7.11753	0.516360
$191$	−7.44938	−0.539018	−0.269509	−	0.962998i	$-0.586861\pi$
$191$	−7.44938	−0.539018	−0.269509	+	0.962998i	$0.586861\pi$
$192$	12.8573	0.927894
$193$	−23.6780	−1.70438	−0.852190	−	0.523233i	$-0.824726\pi$
$193$	−23.6780	−1.70438	−0.852190	+	0.523233i	$0.824726\pi$
$194$	−6.90321	−0.495622
$195$	1.85236	0.132650
$196$	−17.4193	−1.24423
$197$	20.6035	1.46794	0.733969	−	0.679183i	$-0.237666\pi$
$197$	20.6035	1.46794	0.733969	+	0.679183i	$0.237666\pi$
$198$	−12.8573	−0.913727
$199$	−18.0781	−1.28152	−0.640760	−	0.767742i	$-0.721380\pi$
$199$	−18.0781	−1.28152	−0.640760	+	0.767742i	$0.721380\pi$
$200$	4.29529	0.303723
$201$	−7.13828	−0.503495
$202$	9.33185	0.656587
$203$	5.80642	0.407531
$204$	−2.90321	−0.203265
$205$	16.2351	1.13391
$206$	24.0973	1.67894
$207$	−1.83654	−0.127648
$208$	−1.51114	−0.104779
$209$	11.0509	0.764404
$210$	−3.73975	−0.258067
$211$	10.2716	0.707128	0.353564	−	0.935410i	$-0.384970\pi$
$211$	10.2716	0.707128	0.353564	+	0.935410i	$0.384970\pi$
$212$	41.8435	2.87382
$213$	0.407896	0.0279486
$214$	13.2400	0.905067
$215$	7.15257	0.487801
$216$	2.00000	0.136083
$217$	−9.80642	−0.665703
$218$	−31.5526	−2.13701
$219$	0.260253	0.0175862
$220$	−28.4701	−1.91946
$221$	1.09679	0.0737779
$222$	−14.1225	−0.947837
$223$	−8.80642	−0.589722	−0.294861	−	0.955540i	$-0.595273\pi$
$223$	−8.80642	−0.589722	−0.294861	+	0.955540i	$0.595273\pi$
$224$	7.05086	0.471105
$225$	−2.14764	−0.143176
$226$	11.6128	0.772475
$227$	4.99063	0.331240	0.165620	−	0.986190i	$-0.447037\pi$
$227$	4.99063	0.331240	0.165620	+	0.986190i	$0.447037\pi$
$228$	−5.52543	−0.365930
$229$	−2.39361	−0.158174	−0.0790870	−	0.996868i	$-0.525200\pi$
$229$	−2.39361	−0.158174	−0.0790870	+	0.996868i	$0.525200\pi$
$230$	−6.86818	−0.452874
$231$	−5.80642	−0.382035
$232$	−11.6128	−0.762421
$233$	24.7862	1.62380	0.811898	−	0.583800i	$-0.198435\pi$
$233$	24.7862	1.62380	0.811898	+	0.583800i	$0.198435\pi$
$234$	−2.42864	−0.158765
$235$	−1.32693	−0.0865593
$236$	−7.52543	−0.489864
$237$	−1.00000	−0.0649570
$238$	−2.21432	−0.143533
$239$	8.48103	0.548592	0.274296	−	0.961645i	$-0.411555\pi$
$239$	8.48103	0.548592	0.274296	+	0.961645i	$0.411555\pi$
$240$	−2.32693	−0.150203
$241$	−2.95560	−0.190387	−0.0951934	−	0.995459i	$-0.530347\pi$
$241$	−2.95560	−0.190387	−0.0951934	+	0.995459i	$0.530347\pi$
$242$	−50.2973	−3.23323
$243$	−1.00000	−0.0641500
$244$	−29.1798	−1.86804
$245$	10.1334	0.647396
$246$	−21.2859	−1.35714
$247$	2.08742	0.132819
$248$	19.6128	1.24542
$249$	−3.03011	−0.192026
$250$	−26.7304	−1.69058
$251$	20.3526	1.28464	0.642322	−	0.766435i	$-0.277971\pi$
$251$	20.3526	1.28464	0.642322	+	0.766435i	$0.277971\pi$
$252$	2.90321	0.182885
$253$	−10.6637	−0.670421
$254$	−35.6686	−2.23805
$255$	1.68889	0.105763
$256$	−6.10171	−0.381357
$257$	11.5714	0.721802	0.360901	−	0.932604i	$-0.382469\pi$
$257$	11.5714	0.721802	0.360901	+	0.932604i	$0.382469\pi$
$258$	−9.37778	−0.583835
$259$	−6.37778	−0.396296
$260$	−5.37778	−0.333516
$261$	5.80642	0.359409
$262$	18.6987	1.15521
$263$	−31.6336	−1.95061	−0.975305	−	0.220861i	$-0.929113\pi$
$263$	−31.6336	−1.95061	−0.975305	+	0.220861i	$0.929113\pi$
$264$	11.6128	0.714721
$265$	−24.3417	−1.49530
$266$	−4.21432	−0.258397
$267$	14.6637	0.897404
$268$	20.7239	1.26592
$269$	−28.1432	−1.71592	−0.857961	−	0.513716i	$-0.828269\pi$
$269$	−28.1432	−1.71592	−0.857961	+	0.513716i	$0.828269\pi$
$270$	−3.73975	−0.227594
$271$	15.3842	0.934526	0.467263	−	0.884118i	$-0.345240\pi$
$271$	15.3842	0.934526	0.467263	+	0.884118i	$0.345240\pi$
$272$	−1.37778	−0.0835404
$273$	−1.09679	−0.0663806
$274$	1.44446	0.0872631
$275$	−12.4701	−0.751977
$276$	5.33185	0.320940
$277$	22.9590	1.37947	0.689736	−	0.724061i	$-0.257727\pi$
$277$	22.9590	1.37947	0.689736	+	0.724061i	$0.257727\pi$
$278$	9.61285	0.576540
$279$	−9.80642	−0.587095
$280$	3.37778	0.201861
$281$	−2.12245	−0.126615	−0.0633075	−	0.997994i	$-0.520165\pi$
$281$	−2.12245	−0.126615	−0.0633075	+	0.997994i	$0.520165\pi$
$282$	1.73975	0.103600
$283$	15.1526	0.900727	0.450363	−	0.892845i	$-0.351294\pi$
$283$	15.1526	0.900727	0.450363	+	0.892845i	$0.351294\pi$
$284$	−1.18421	−0.0702698
$285$	3.21432	0.190400
$286$	−14.1017	−0.833852
$287$	−9.61285	−0.567428
$288$	7.05086	0.415476
$289$	1.00000	0.0588235
$290$	21.7146	1.27512
$291$	−3.11753	−0.182753
$292$	−0.755569	−0.0442163
$293$	7.18268	0.419616	0.209808	−	0.977743i	$-0.432716\pi$
$293$	7.18268	0.419616	0.209808	+	0.977743i	$0.432716\pi$
$294$	−13.2859	−0.774850
$295$	4.37778	0.254884
$296$	12.7556	0.741402
$297$	−5.80642	−0.336923
$298$	44.0163	2.54980
$299$	−2.01429	−0.116489
$300$	6.23506	0.359982
$301$	−4.23506	−0.244105
$302$	−19.3669	−1.11444
$303$	4.21432	0.242106
$304$	−2.62222	−0.150394
$305$	16.9748	0.971975
$306$	−2.21432	−0.126584
$307$	−23.5877	−1.34622	−0.673109	−	0.739543i	$-0.735042\pi$
$307$	−23.5877	−1.34622	−0.673109	+	0.739543i	$0.735042\pi$
$308$	16.8573	0.960533
$309$	10.8825	0.619082
$310$	−36.6735	−2.08292
$311$	−1.63158	−0.0925186	−0.0462593	−	0.998929i	$-0.514730\pi$
$311$	−1.63158	−0.0925186	−0.0462593	+	0.998929i	$0.514730\pi$
$312$	2.19358	0.124187
$313$	21.1526	1.19561	0.597807	−	0.801640i	$-0.296039\pi$
$313$	21.1526	1.19561	0.597807	+	0.801640i	$0.296039\pi$
$314$	10.3827	0.585930
$315$	−1.68889	−0.0951583
$316$	2.90321	0.163318
$317$	−21.4449	−1.20447	−0.602234	−	0.798320i	$-0.705723\pi$
$317$	−21.4449	−1.20447	−0.602234	+	0.798320i	$0.705723\pi$
$318$	31.9146	1.78968
$319$	33.7146	1.88765
$320$	21.7146	1.21388
$321$	5.97926	0.333730
$322$	4.06668	0.226627
$323$	1.90321	0.105898
$324$	2.90321	0.161290
$325$	−2.35551	−0.130660
$326$	−0.668149	−0.0370053
$327$	−14.2494	−0.787991
$328$	19.2257	1.06156
$329$	0.785680	0.0433160
$330$	−21.7146	−1.19535
$331$	−3.99355	−0.219505	−0.109753	−	0.993959i	$-0.535006\pi$
$331$	−3.99355	−0.219505	−0.109753	+	0.993959i	$0.535006\pi$
$332$	8.79706	0.482801
$333$	−6.37778	−0.349500
$334$	−23.4859	−1.28509
$335$	−12.0558	−0.658677
$336$	1.37778	0.0751643
$337$	−20.2415	−1.10263	−0.551313	−	0.834299i	$-0.685873\pi$
$337$	−20.2415	−1.10263	−0.551313	+	0.834299i	$0.685873\pi$
$338$	26.1225	1.42087
$339$	5.24443	0.284838
$340$	−4.90321	−0.265914
$341$	−56.9403	−3.08349
$342$	−4.21432	−0.227884
$343$	−13.0000	−0.701934
$344$	8.47013	0.456679
$345$	−3.10171	−0.166990
$346$	18.8430	1.01301
$347$	10.4588	0.561455	0.280728	−	0.959787i	$-0.409424\pi$
$347$	10.4588	0.561455	0.280728	+	0.959787i	$0.409424\pi$
$348$	−16.8573	−0.903645
$349$	18.9525	1.01451	0.507253	−	0.861797i	$-0.330661\pi$
$349$	18.9525	1.01451	0.507253	+	0.861797i	$0.330661\pi$
$350$	4.75557	0.254196
$351$	−1.09679	−0.0585422
$352$	40.9403	2.18212
$353$	−5.84098	−0.310884	−0.155442	−	0.987845i	$-0.549680\pi$
$353$	−5.84098	−0.310884	−0.155442	+	0.987845i	$0.549680\pi$
$354$	−5.73975	−0.305064
$355$	0.688892	0.0365626
$356$	−42.5718	−2.25630
$357$	−1.00000	−0.0529256
$358$	−19.1383	−1.01149
$359$	−11.5067	−0.607300	−0.303650	−	0.952784i	$-0.598205\pi$
$359$	−11.5067	−0.607300	−0.303650	+	0.952784i	$0.598205\pi$
$360$	3.37778	0.178025
$361$	−15.3778	−0.809357
$362$	50.7610	2.66794
$363$	−22.7146	−1.19221
$364$	3.18421	0.166898
$365$	0.439539	0.0230065
$366$	−22.2558	−1.16333
$367$	−30.1367	−1.57313	−0.786563	−	0.617511i	$-0.788141\pi$
$367$	−30.1367	−1.57313	−0.786563	+	0.617511i	$0.788141\pi$
$368$	2.53035	0.131904
$369$	−9.61285	−0.500425
$370$	−23.8513	−1.23997
$371$	14.4128	0.748276
$372$	28.4701	1.47611
$373$	37.2321	1.92781	0.963904	−	0.266251i	$-0.0857849\pi$
$373$	37.2321	1.92781	0.963904	+	0.266251i	$0.0857849\pi$
$374$	−12.8573	−0.664834
$375$	−12.0716	−0.623375
$376$	−1.57136	−0.0810367
$377$	6.36842	0.327990
$378$	2.21432	0.113892
$379$	−1.62222	−0.0833276	−0.0416638	−	0.999132i	$-0.513266\pi$
$379$	−1.62222	−0.0833276	−0.0416638	+	0.999132i	$0.513266\pi$
$380$	−9.33185	−0.478714
$381$	−16.1082	−0.825246
$382$	16.4953	0.843974
$383$	−5.55062	−0.283623	−0.141812	−	0.989894i	$-0.545293\pi$
$383$	−5.55062	−0.283623	−0.141812	+	0.989894i	$0.545293\pi$
$384$	−14.3684	−0.733235
$385$	−9.80642	−0.499782
$386$	52.4306	2.66865
$387$	−4.23506	−0.215280
$388$	9.05086	0.459488
$389$	8.86818	0.449634	0.224817	−	0.974401i	$-0.427821\pi$
$389$	8.86818	0.449634	0.224817	+	0.974401i	$0.427821\pi$
$390$	−4.10171	−0.207698
$391$	−1.83654	−0.0928776
$392$	12.0000	0.606092
$393$	8.44446	0.425967
$394$	−45.6227	−2.29844
$395$	−1.68889	−0.0849774
$396$	16.8573	0.847110
$397$	−27.9496	−1.40275	−0.701376	−	0.712792i	$-0.747430\pi$
$397$	−27.9496	−1.40275	−0.701376	+	0.712792i	$0.747430\pi$
$398$	40.0306	2.00655
$399$	−1.90321	−0.0952798
$400$	2.95899	0.147949
$401$	−38.1639	−1.90582	−0.952908	−	0.303259i	$-0.901925\pi$
$401$	−38.1639	−1.90582	−0.952908	+	0.303259i	$0.901925\pi$
$402$	15.8064	0.788353
$403$	−10.7556	−0.535773
$404$	−12.2351	−0.608717
$405$	−1.68889	−0.0839217
$406$	−12.8573	−0.638096
$407$	−37.0321	−1.83561
$408$	2.00000	0.0990148
$409$	−3.22570	−0.159500	−0.0797502	−	0.996815i	$-0.525412\pi$
$409$	−3.22570	−0.159500	−0.0797502	+	0.996815i	$0.525412\pi$
$410$	−35.9496	−1.77543
$411$	0.652327	0.0321769
$412$	−31.5941	−1.55653
$413$	−2.59210	−0.127549
$414$	4.06668	0.199866
$415$	−5.11753	−0.251210
$416$	7.73329	0.379156
$417$	4.34122	0.212590
$418$	−24.4701	−1.19687
$419$	−28.5827	−1.39636	−0.698179	−	0.715923i	$-0.746006\pi$
$419$	−28.5827	−1.39636	−0.698179	+	0.715923i	$0.746006\pi$
$420$	4.90321	0.239252
$421$	−11.2079	−0.546238	−0.273119	−	0.961980i	$-0.588055\pi$
$421$	−11.2079	−0.546238	−0.273119	+	0.961980i	$0.588055\pi$
$422$	−22.7447	−1.10719
$423$	0.785680	0.0382011
$424$	−28.8256	−1.39990
$425$	−2.14764	−0.104176
$426$	−0.903212	−0.0437608
$427$	−10.0509	−0.486395
$428$	−17.3590	−0.839081
$429$	−6.36842	−0.307470
$430$	−15.8381	−0.763779
$431$	25.5926	1.23275	0.616376	−	0.787452i	$-0.288600\pi$
$431$	25.5926	1.23275	0.616376	+	0.787452i	$0.288600\pi$
$432$	1.37778	0.0662887
$433$	9.43356	0.453348	0.226674	−	0.973971i	$-0.427215\pi$
$433$	9.43356	0.453348	0.226674	+	0.973971i	$0.427215\pi$
$434$	21.7146	1.04233
$435$	9.80642	0.470182
$436$	41.3689	1.98121
$437$	−3.49532	−0.167204
$438$	−0.576283	−0.0275359
$439$	11.8316	0.564692	0.282346	−	0.959313i	$-0.408887\pi$
$439$	11.8316	0.564692	0.282346	+	0.959313i	$0.408887\pi$
$440$	19.6128	0.935006
$441$	−6.00000	−0.285714
$442$	−2.42864	−0.115519
$443$	−8.84146	−0.420070	−0.210035	−	0.977694i	$-0.567358\pi$
$443$	−8.84146	−0.420070	−0.210035	+	0.977694i	$0.567358\pi$
$444$	18.5161	0.878733
$445$	24.7654	1.17399
$446$	19.5002	0.923363
$447$	19.8780	0.940198
$448$	−12.8573	−0.607449
$449$	−18.7239	−0.883637	−0.441818	−	0.897105i	$-0.645666\pi$
$449$	−18.7239	−0.883637	−0.441818	+	0.897105i	$0.645666\pi$
$450$	4.75557	0.224180
$451$	−55.8163	−2.62829
$452$	−15.2257	−0.716156
$453$	−8.74620	−0.410932
$454$	−11.0509	−0.518642
$455$	−1.85236	−0.0868398
$456$	3.80642	0.178252
$457$	−33.3511	−1.56010	−0.780048	−	0.625719i	$-0.784806\pi$
$457$	−33.3511	−1.56010	−0.780048	+	0.625719i	$0.784806\pi$
$458$	5.30021	0.247662
$459$	−1.00000	−0.0466760
$460$	9.00492	0.419857
$461$	12.4242	0.578652	0.289326	−	0.957231i	$-0.406569\pi$
$461$	12.4242	0.578652	0.289326	+	0.957231i	$0.406569\pi$
$462$	12.8573	0.598175
$463$	−14.5368	−0.675583	−0.337791	−	0.941221i	$-0.609680\pi$
$463$	−14.5368	−0.675583	−0.337791	+	0.941221i	$0.609680\pi$
$464$	−8.00000	−0.371391
$465$	−16.5620	−0.768044
$466$	−54.8845	−2.54247
$467$	−10.5018	−0.485964	−0.242982	−	0.970031i	$-0.578126\pi$
$467$	−10.5018	−0.485964	−0.242982	+	0.970031i	$0.578126\pi$
$468$	3.18421	0.147190
$469$	7.13828	0.329615
$470$	2.93825	0.135531
$471$	4.68889	0.216053
$472$	5.18421	0.238623
$473$	−24.5906	−1.13068
$474$	2.21432	0.101707
$475$	−4.08742	−0.187544
$476$	2.90321	0.133069
$477$	14.4128	0.659918
$478$	−18.7797	−0.858964
$479$	17.1269	0.782548	0.391274	−	0.920274i	$-0.372034\pi$
$479$	17.1269	0.782548	0.391274	+	0.920274i	$0.372034\pi$
$480$	11.9081	0.543529
$481$	−6.99508	−0.318948
$482$	6.54464	0.298100
$483$	1.83654	0.0835653
$484$	65.9452	2.99751
$485$	−5.26517	−0.239079
$486$	2.21432	0.100444
$487$	−36.4637	−1.65233	−0.826163	−	0.563431i	$-0.809481\pi$
$487$	−36.4637	−1.65233	−0.826163	+	0.563431i	$0.809481\pi$
$488$	20.1017	0.909962
$489$	−0.301740	−0.0136451
$490$	−22.4385	−1.01367
$491$	−21.8064	−0.984110	−0.492055	−	0.870564i	$-0.663754\pi$
$491$	−21.8064	−0.984110	−0.492055	+	0.870564i	$0.663754\pi$
$492$	27.9081	1.25820
$493$	5.80642	0.261508
$494$	−4.62222	−0.207963
$495$	−9.80642	−0.440766
$496$	13.5111	0.606668
$497$	−0.407896	−0.0182966
$498$	6.70964	0.300666
$499$	−23.6414	−1.05834	−0.529168	−	0.848517i	$-0.677496\pi$
$499$	−23.6414	−1.05834	−0.529168	+	0.848517i	$0.677496\pi$
$500$	35.0464	1.56732
$501$	−10.6064	−0.473859
$502$	−45.0672	−2.01145
$503$	−1.51114	−0.0673783	−0.0336891	−	0.999432i	$-0.510726\pi$
$503$	−1.51114	−0.0673783	−0.0336891	+	0.999432i	$0.510726\pi$
$504$	−2.00000	−0.0890871
$505$	7.11753	0.316726
$506$	23.6128	1.04972
$507$	11.7971	0.523926
$508$	46.7654	2.07488
$509$	−35.2830	−1.56389	−0.781946	−	0.623346i	$-0.785773\pi$
$509$	−35.2830	−1.56389	−0.781946	+	0.623346i	$0.785773\pi$
$510$	−3.73975	−0.165599
$511$	−0.260253	−0.0115129
$512$	−15.2257	−0.672887
$513$	−1.90321	−0.0840289
$514$	−25.6227	−1.13017
$515$	18.3793	0.809889
$516$	12.2953	0.541270
$517$	4.56199	0.200636
$518$	14.1225	0.620505
$519$	8.50961	0.373530
$520$	3.70471	0.162462
$521$	24.9175	1.09166	0.545828	−	0.837897i	$-0.316215\pi$
$521$	24.9175	1.09166	0.545828	+	0.837897i	$0.316215\pi$
$522$	−12.8573	−0.562748
$523$	16.0874	0.703454	0.351727	−	0.936103i	$-0.385595\pi$
$523$	16.0874	0.703454	0.351727	+	0.936103i	$0.385595\pi$
$524$	−24.5161	−1.07099
$525$	2.14764	0.0937308
$526$	70.0469	3.05419
$527$	−9.80642	−0.427175
$528$	8.00000	0.348155
$529$	−19.6271	−0.853354
$530$	53.9003	2.34128
$531$	−2.59210	−0.112488
$532$	5.52543	0.239558
$533$	−10.5433	−0.456679
$534$	−32.4701	−1.40512
$535$	10.0983	0.436588
$536$	−14.2766	−0.616653
$537$	−8.64296	−0.372971
$538$	62.3180	2.68672
$539$	−34.8385	−1.50060
$540$	4.90321	0.211001
$541$	−10.3205	−0.443712	−0.221856	−	0.975079i	$-0.571211\pi$
$541$	−10.3205	−0.443712	−0.221856	+	0.975079i	$0.571211\pi$
$542$	−34.0656	−1.46324
$543$	22.9240	0.983761
$544$	7.05086	0.302303
$545$	−24.0656	−1.03086
$546$	2.42864	0.103936
$547$	25.9432	1.10925	0.554625	−	0.832101i	$-0.312862\pi$
$547$	25.9432	1.10925	0.554625	+	0.832101i	$0.312862\pi$
$548$	−1.89384	−0.0809010
$549$	−10.0509	−0.428960
$550$	27.6128	1.17742
$551$	11.0509	0.470782
$552$	−3.67307	−0.156336
$553$	1.00000	0.0425243
$554$	−50.8385	−2.15992
$555$	−10.7714	−0.457220
$556$	−12.6035	−0.534507
$557$	21.1526	0.896263	0.448131	−	0.893968i	$-0.352090\pi$
$557$	21.1526	0.896263	0.448131	+	0.893968i	$0.352090\pi$
$558$	21.7146	0.919251
$559$	−4.64497	−0.196461
$560$	2.32693	0.0983307
$561$	−5.80642	−0.245147
$562$	4.69979	0.198249
$563$	2.28745	0.0964045	0.0482023	−	0.998838i	$-0.484651\pi$
$563$	2.28745	0.0964045	0.0482023	+	0.998838i	$0.484651\pi$
$564$	−2.28100	−0.0960473
$565$	8.85728	0.372629
$566$	−33.5526	−1.41032
$567$	1.00000	0.0419961
$568$	0.815792	0.0342299
$569$	16.5096	0.692119	0.346059	−	0.938213i	$-0.387520\pi$
$569$	16.5096	0.692119	0.346059	+	0.938213i	$0.387520\pi$
$570$	−7.11753	−0.298121
$571$	4.85728	0.203271	0.101635	−	0.994822i	$-0.467592\pi$
$571$	4.85728	0.203271	0.101635	+	0.994822i	$0.467592\pi$
$572$	18.4889	0.773058
$573$	7.44938	0.311202
$574$	21.2859	0.888457
$575$	3.94422	0.164485
$576$	−12.8573	−0.535720
$577$	−36.1497	−1.50493	−0.752465	−	0.658632i	$-0.771135\pi$
$577$	−36.1497	−1.50493	−0.752465	+	0.658632i	$0.771135\pi$
$578$	−2.21432	−0.0921036
$579$	23.6780	0.984024
$580$	−28.4701	−1.18216
$581$	3.03011	0.125710
$582$	6.90321	0.286147
$583$	83.6869	3.46596
$584$	0.520505	0.0215387
$585$	−1.85236	−0.0765855
$586$	−15.9047	−0.657019
$587$	−6.70810	−0.276873	−0.138437	−	0.990371i	$-0.544208\pi$
$587$	−6.70810	−0.276873	−0.138437	+	0.990371i	$0.544208\pi$
$588$	17.4193	0.718359
$589$	−18.6637	−0.769024
$590$	−9.69381	−0.399088
$591$	−20.6035	−0.847514
$592$	8.78721	0.361152
$593$	8.99847	0.369523	0.184761	−	0.982783i	$-0.440849\pi$
$593$	8.99847	0.369523	0.184761	+	0.982783i	$0.440849\pi$
$594$	12.8573	0.527541
$595$	−1.68889	−0.0692378
$596$	−57.7101	−2.36390
$597$	18.0781	0.739885
$598$	4.46028	0.182395
$599$	−11.9476	−0.488166	−0.244083	−	0.969754i	$-0.578487\pi$
$599$	−11.9476	−0.488166	−0.244083	+	0.969754i	$0.578487\pi$
$600$	−4.29529	−0.175354
$601$	−42.7975	−1.74575	−0.872874	−	0.487946i	$-0.837746\pi$
$601$	−42.7975	−1.74575	−0.872874	+	0.487946i	$0.837746\pi$
$602$	9.37778	0.382210
$603$	7.13828	0.290693
$604$	25.3921	1.03319
$605$	−38.3624	−1.55965
$606$	−9.33185	−0.379081
$607$	−7.27163	−0.295146	−0.147573	−	0.989051i	$-0.547146\pi$
$607$	−7.27163	−0.295146	−0.147573	+	0.989051i	$0.547146\pi$
$608$	13.4193	0.544223
$609$	−5.80642	−0.235288
$610$	−37.5877	−1.52188
$611$	0.861725	0.0348617
$612$	2.90321	0.117355
$613$	36.7783	1.48546	0.742731	−	0.669590i	$-0.233530\pi$
$613$	36.7783	1.48546	0.742731	+	0.669590i	$0.233530\pi$
$614$	52.2306	2.10786
$615$	−16.2351	−0.654661
$616$	−11.6128	−0.467895
$617$	−6.26671	−0.252288	−0.126144	−	0.992012i	$-0.540260\pi$
$617$	−6.26671	−0.252288	−0.126144	+	0.992012i	$0.540260\pi$
$618$	−24.0973	−0.969334
$619$	−21.4331	−0.861468	−0.430734	−	0.902479i	$-0.641745\pi$
$619$	−21.4331	−0.861468	−0.430734	+	0.902479i	$0.641745\pi$
$620$	48.0830	1.93106
$621$	1.83654	0.0736976
$622$	3.61285	0.144862
$623$	−14.6637	−0.587489
$624$	1.51114	0.0604939
$625$	−9.64941	−0.385977
$626$	−46.8385	−1.87204
$627$	−11.0509	−0.441329
$628$	−13.6128	−0.543212
$629$	−6.37778	−0.254299
$630$	3.73975	0.148995
$631$	35.6128	1.41773	0.708863	−	0.705347i	$-0.249209\pi$
$631$	35.6128	1.41773	0.708863	+	0.705347i	$0.249209\pi$
$632$	−2.00000	−0.0795557
$633$	−10.2716	−0.408261
$634$	47.4859	1.88591
$635$	−27.2050	−1.07960
$636$	−41.8435	−1.65920
$637$	−6.58073	−0.260738
$638$	−74.6548	−2.95561
$639$	−0.407896	−0.0161361
$640$	−24.2667	−0.959226
$641$	37.6987	1.48901	0.744505	−	0.667617i	$-0.232685\pi$
$641$	37.6987	1.48901	0.744505	+	0.667617i	$0.232685\pi$
$642$	−13.2400	−0.522541
$643$	9.13627	0.360299	0.180150	−	0.983639i	$-0.442342\pi$
$643$	9.13627	0.360299	0.180150	+	0.983639i	$0.442342\pi$
$644$	−5.33185	−0.210104
$645$	−7.15257	−0.281632
$646$	−4.21432	−0.165810
$647$	15.7447	0.618987	0.309493	−	0.950902i	$-0.399841\pi$
$647$	15.7447	0.618987	0.309493	+	0.950902i	$0.399841\pi$
$648$	−2.00000	−0.0785674
$649$	−15.0509	−0.590798
$650$	5.21585	0.204583
$651$	9.80642	0.384344
$652$	0.876015	0.0343074
$653$	22.3022	0.872753	0.436377	−	0.899764i	$-0.356262\pi$
$653$	22.3022	0.872753	0.436377	+	0.899764i	$0.356262\pi$
$654$	31.5526	1.23381
$655$	14.2618	0.557254
$656$	13.2444	0.517108
$657$	−0.260253	−0.0101534
$658$	−1.73975	−0.0678224
$659$	23.1354	0.901226	0.450613	−	0.892719i	$-0.351205\pi$
$659$	23.1354	0.901226	0.450613	+	0.892719i	$0.351205\pi$
$660$	28.4701	1.10820
$661$	−12.6889	−0.493541	−0.246770	−	0.969074i	$-0.579369\pi$
$661$	−12.6889	−0.493541	−0.246770	+	0.969074i	$0.579369\pi$
$662$	8.84299	0.343693
$663$	−1.09679	−0.0425957
$664$	−6.06022	−0.235182
$665$	−3.21432	−0.124646
$666$	14.1225	0.547234
$667$	−10.6637	−0.412900
$668$	30.7926	1.19140
$669$	8.80642	0.340476
$670$	26.6953	1.03133
$671$	−58.3595	−2.25294
$672$	−7.05086	−0.271993
$673$	−2.94470	−0.113510	−0.0567549	−	0.998388i	$-0.518075\pi$
$673$	−2.94470	−0.113510	−0.0567549	+	0.998388i	$0.518075\pi$
$674$	44.8212	1.72645
$675$	2.14764	0.0826628
$676$	−34.2494	−1.31728
$677$	14.2924	0.549300	0.274650	−	0.961544i	$-0.411438\pi$
$677$	14.2924	0.549300	0.274650	+	0.961544i	$0.411438\pi$
$678$	−11.6128	−0.445989
$679$	3.11753	0.119640
$680$	3.37778	0.129532
$681$	−4.99063	−0.191241
$682$	126.084	4.82800
$683$	−22.0716	−0.844546	−0.422273	−	0.906469i	$-0.638768\pi$
$683$	−22.0716	−0.844546	−0.422273	+	0.906469i	$0.638768\pi$
$684$	5.52543	0.211270
$685$	1.10171	0.0420942
$686$	28.7862	1.09906
$687$	2.39361	0.0913218
$688$	5.83500	0.222457
$689$	15.8078	0.602229
$690$	6.86818	0.261467
$691$	−9.38715	−0.357104	−0.178552	−	0.983930i	$-0.557141\pi$
$691$	−9.38715	−0.357104	−0.178552	+	0.983930i	$0.557141\pi$
$692$	−24.7052	−0.939150
$693$	5.80642	0.220568
$694$	−23.1590	−0.879104
$695$	7.33185	0.278113
$696$	11.6128	0.440184
$697$	−9.61285	−0.364113
$698$	−41.9670	−1.58847
$699$	−24.7862	−0.937499
$700$	−6.23506	−0.235663
$701$	−25.8593	−0.976692	−0.488346	−	0.872650i	$-0.662400\pi$
$701$	−25.8593	−0.976692	−0.488346	+	0.872650i	$0.662400\pi$
$702$	2.42864	0.0916631
$703$	−12.1383	−0.457804
$704$	−74.6548	−2.81366
$705$	1.32693	0.0499750
$706$	12.9338	0.486770
$707$	−4.21432	−0.158496
$708$	7.52543	0.282823
$709$	40.6499	1.52664	0.763319	−	0.646021i	$-0.223568\pi$
$709$	40.6499	1.52664	0.763319	+	0.646021i	$0.223568\pi$
$710$	−1.52543	−0.0572483
$711$	1.00000	0.0375029
$712$	29.3274	1.09909
$713$	18.0098	0.674474
$714$	2.21432	0.0828688
$715$	−10.7556	−0.402235
$716$	25.0923	0.937745
$717$	−8.48103	−0.316730
$718$	25.4795	0.950886
$719$	−12.5620	−0.468483	−0.234242	−	0.972178i	$-0.575261\pi$
$719$	−12.5620	−0.468483	−0.234242	+	0.972178i	$0.575261\pi$
$720$	2.32693	0.0867195
$721$	−10.8825	−0.405284
$722$	34.0513	1.26726
$723$	2.95560	0.109920
$724$	−66.5531	−2.47343
$725$	−12.4701	−0.463129
$726$	50.2973	1.86671
$727$	−25.1575	−0.933040	−0.466520	−	0.884511i	$-0.654492\pi$
$727$	−25.1575	−0.933040	−0.466520	+	0.884511i	$0.654492\pi$
$728$	−2.19358	−0.0812993
$729$	1.00000	0.0370370
$730$	−0.973279	−0.0360227
$731$	−4.23506	−0.156639
$732$	29.1798	1.07852
$733$	−12.8163	−0.473380	−0.236690	−	0.971585i	$-0.576063\pi$
$733$	−12.8163	−0.473380	−0.236690	+	0.971585i	$0.576063\pi$
$734$	66.7324	2.46314
$735$	−10.1334	−0.373774
$736$	−12.9491	−0.477312
$737$	41.4479	1.52675
$738$	21.2859	0.783545
$739$	12.8573	0.472963	0.236481	−	0.971636i	$-0.424006\pi$
$739$	12.8573	0.472963	0.236481	+	0.971636i	$0.424006\pi$
$740$	31.2716	1.14957
$741$	−2.08742	−0.0766833
$742$	−31.9146	−1.17162
$743$	−16.2938	−0.597760	−0.298880	−	0.954291i	$-0.596613\pi$
$743$	−16.2938	−0.597760	−0.298880	+	0.954291i	$0.596613\pi$
$744$	−19.6128	−0.719042
$745$	33.5718	1.22998
$746$	−82.4439	−3.01848
$747$	3.03011	0.110866
$748$	16.8573	0.616363
$749$	−5.97926	−0.218477
$750$	26.7304	0.976055
$751$	−39.6958	−1.44852	−0.724261	−	0.689526i	$-0.757819\pi$
$751$	−39.6958	−1.44852	−0.724261	+	0.689526i	$0.757819\pi$
$752$	−1.08250	−0.0394746
$753$	−20.3526	−0.741690
$754$	−14.1017	−0.513554
$755$	−14.7714	−0.537586
$756$	−2.90321	−0.105589
$757$	−44.4750	−1.61647	−0.808237	−	0.588858i	$-0.799578\pi$
$757$	−44.4750	−1.61647	−0.808237	+	0.588858i	$0.799578\pi$
$758$	3.59210	0.130471
$759$	10.6637	0.387068
$760$	6.42864	0.233191
$761$	43.2563	1.56804	0.784020	−	0.620736i	$-0.213166\pi$
$761$	43.2563	1.56804	0.784020	+	0.620736i	$0.213166\pi$
$762$	35.6686	1.29214
$763$	14.2494	0.515861
$764$	−21.6271	−0.782442
$765$	−1.68889	−0.0610620
$766$	12.2908	0.444086
$767$	−2.84299	−0.102654
$768$	6.10171	0.220177
$769$	30.7239	1.10793	0.553967	−	0.832539i	$-0.313114\pi$
$769$	30.7239	1.10793	0.553967	+	0.832539i	$0.313114\pi$
$770$	21.7146	0.782538
$771$	−11.5714	−0.416732
$772$	−68.7422	−2.47409
$773$	2.66370	0.0958067	0.0479034	−	0.998852i	$-0.484746\pi$
$773$	2.66370	0.0958067	0.0479034	+	0.998852i	$0.484746\pi$
$774$	9.37778	0.337077
$775$	21.0607	0.756523
$776$	−6.23506	−0.223826
$777$	6.37778	0.228802
$778$	−19.6370	−0.704020
$779$	−18.2953	−0.655497
$780$	5.37778	0.192556
$781$	−2.36842	−0.0847486
$782$	4.06668	0.145424
$783$	−5.80642	−0.207505
$784$	8.26671	0.295240
$785$	7.91903	0.282642
$786$	−18.6987	−0.666962
$787$	18.0765	0.644358	0.322179	−	0.946679i	$-0.395585\pi$
$787$	18.0765	0.644358	0.322179	+	0.946679i	$0.395585\pi$
$788$	59.8163	2.13087
$789$	31.6336	1.12619
$790$	3.73975	0.133054
$791$	−5.24443	−0.186471
$792$	−11.6128	−0.412645
$793$	−11.0237	−0.391462
$794$	61.8894	2.19637
$795$	24.3417	0.863311
$796$	−52.4844	−1.86026
$797$	5.01090	0.177495	0.0887476	−	0.996054i	$-0.471714\pi$
$797$	5.01090	0.177495	0.0887476	+	0.996054i	$0.471714\pi$
$798$	4.21432	0.149185
$799$	0.785680	0.0277954
$800$	−15.1427	−0.535376
$801$	−14.6637	−0.518116
$802$	84.5072	2.98405
$803$	−1.51114	−0.0533269
$804$	−20.7239	−0.730877
$805$	3.10171	0.109321
$806$	23.8163	0.838892
$807$	28.1432	0.990687
$808$	8.42864	0.296519
$809$	40.6222	1.42820	0.714101	−	0.700043i	$-0.246836\pi$
$809$	40.6222	1.42820	0.714101	+	0.700043i	$0.246836\pi$
$810$	3.73975	0.131401
$811$	30.8508	1.08332	0.541660	−	0.840598i	$-0.317796\pi$
$811$	30.8508	1.08332	0.541660	+	0.840598i	$0.317796\pi$
$812$	16.8573	0.591575
$813$	−15.3842	−0.539549
$814$	82.0010	2.87413
$815$	−0.509606	−0.0178507
$816$	1.37778	0.0482321
$817$	−8.06022	−0.281992
$818$	7.14272	0.249739
$819$	1.09679	0.0383249
$820$	47.1338	1.64598
$821$	−21.3733	−0.745935	−0.372967	−	0.927844i	$-0.621660\pi$
$821$	−21.3733	−0.745935	−0.372967	+	0.927844i	$0.621660\pi$
$822$	−1.44446	−0.0503814
$823$	34.3832	1.19852	0.599261	−	0.800554i	$-0.295461\pi$
$823$	34.3832	1.19852	0.599261	+	0.800554i	$0.295461\pi$
$824$	21.7649	0.758217
$825$	12.4701	0.434154
$826$	5.73975	0.199711
$827$	14.7318	0.512274	0.256137	−	0.966641i	$-0.417550\pi$
$827$	14.7318	0.512274	0.256137	+	0.966641i	$0.417550\pi$
$828$	−5.33185	−0.185295
$829$	−22.3872	−0.777538	−0.388769	−	0.921335i	$-0.627100\pi$
$829$	−22.3872	−0.777538	−0.388769	+	0.921335i	$0.627100\pi$
$830$	11.3319	0.393334
$831$	−22.9590	−0.796439
$832$	−14.1017	−0.488889
$833$	−6.00000	−0.207888
$834$	−9.61285	−0.332866
$835$	−17.9131	−0.619907
$836$	32.0830	1.10961
$837$	9.80642	0.338960
$838$	63.2913	2.18636
$839$	13.5368	0.467342	0.233671	−	0.972316i	$-0.424926\pi$
$839$	13.5368	0.467342	0.233671	+	0.972316i	$0.424926\pi$
$840$	−3.37778	−0.116545
$841$	4.71456	0.162571
$842$	24.8178	0.855278
$843$	2.12245	0.0731012
$844$	29.8207	1.02647
$845$	19.9240	0.685405
$846$	−1.73975	−0.0598137
$847$	22.7146	0.780481
$848$	−19.8578	−0.681918
$849$	−15.1526	−0.520035
$850$	4.75557	0.163115
$851$	11.7130	0.401517
$852$	1.18421	0.0405703
$853$	19.2034	0.657513	0.328756	−	0.944415i	$-0.393371\pi$
$853$	19.2034	0.657513	0.328756	+	0.944415i	$0.393371\pi$
$854$	22.2558	0.761578
$855$	−3.21432	−0.109927
$856$	11.9585	0.408734
$857$	24.9175	0.851166	0.425583	−	0.904919i	$-0.360069\pi$
$857$	24.9175	0.851166	0.425583	+	0.904919i	$0.360069\pi$
$858$	14.1017	0.481424
$859$	−1.35905	−0.0463701	−0.0231851	−	0.999731i	$-0.507381\pi$
$859$	−1.35905	−0.0463701	−0.0231851	+	0.999731i	$0.507381\pi$
$860$	20.7654	0.708095
$861$	9.61285	0.327605
$862$	−56.6702	−1.93019
$863$	−21.9813	−0.748251	−0.374125	−	0.927378i	$-0.622057\pi$
$863$	−21.9813	−0.748251	−0.374125	+	0.927378i	$0.622057\pi$
$864$	−7.05086	−0.239875
$865$	14.3718	0.488656
$866$	−20.8889	−0.709834
$867$	−1.00000	−0.0339618
$868$	−28.4701	−0.966339
$869$	5.80642	0.196969
$870$	−21.7146	−0.736192
$871$	7.82918	0.265281
$872$	−28.4987	−0.965088
$873$	3.11753	0.105512
$874$	7.73975	0.261801
$875$	12.0716	0.408095
$876$	0.755569	0.0255283
$877$	5.05731	0.170773	0.0853866	−	0.996348i	$-0.472787\pi$
$877$	5.05731	0.170773	0.0853866	+	0.996348i	$0.472787\pi$
$878$	−26.1990	−0.884173
$879$	−7.18268	−0.242266
$880$	13.5111	0.455460
$881$	11.1111	0.374342	0.187171	−	0.982327i	$-0.440068\pi$
$881$	11.1111	0.374342	0.187171	+	0.982327i	$0.440068\pi$
$882$	13.2859	0.447360
$883$	−47.4193	−1.59579	−0.797893	−	0.602799i	$-0.794052\pi$
$883$	−47.4193	−1.59579	−0.797893	+	0.602799i	$0.794052\pi$
$884$	3.18421	0.107097
$885$	−4.37778	−0.147158
$886$	19.5778	0.657730
$887$	−50.3165	−1.68946	−0.844731	−	0.535190i	$-0.820240\pi$
$887$	−50.3165	−1.68946	−0.844731	+	0.535190i	$0.820240\pi$
$888$	−12.7556	−0.428049
$889$	16.1082	0.540250
$890$	−54.8385	−1.83819
$891$	5.80642	0.194523
$892$	−25.5669	−0.856044
$893$	1.49532	0.0500388
$894$	−44.0163	−1.47213
$895$	−14.5970	−0.487925
$896$	14.3684	0.480015
$897$	2.01429	0.0672552
$898$	41.4608	1.38356
$899$	−56.9403	−1.89906
$900$	−6.23506	−0.207835
$901$	14.4128	0.480161
$902$	123.595	4.11527
$903$	4.23506	0.140934
$904$	10.4889	0.348854
$905$	38.7161	1.28697
$906$	19.3669	0.643422
$907$	−10.9971	−0.365152	−0.182576	−	0.983192i	$-0.558444\pi$
$907$	−10.9971	−0.365152	−0.182576	+	0.983192i	$0.558444\pi$
$908$	14.4889	0.480830
$909$	−4.21432	−0.139780
$910$	4.10171	0.135970
$911$	20.4844	0.678679	0.339340	−	0.940664i	$-0.389796\pi$
$911$	20.4844	0.678679	0.339340	+	0.940664i	$0.389796\pi$
$912$	2.62222	0.0868302
$913$	17.5941	0.582280
$914$	73.8499	2.44274
$915$	−16.9748	−0.561170
$916$	−6.94914	−0.229606
$917$	−8.44446	−0.278861
$918$	2.21432	0.0730834
$919$	40.9447	1.35064	0.675320	−	0.737524i	$-0.264005\pi$
$919$	40.9447	1.35064	0.675320	+	0.737524i	$0.264005\pi$
$920$	−6.20342	−0.204521
$921$	23.5877	0.777240
$922$	−27.5111	−0.906031
$923$	−0.447375	−0.0147255
$924$	−16.8573	−0.554564
$925$	13.6972	0.450361
$926$	32.1891	1.05780
$927$	−10.8825	−0.357427
$928$	40.9403	1.34393
$929$	4.86818	0.159720	0.0798599	−	0.996806i	$-0.474553\pi$
$929$	4.86818	0.159720	0.0798599	+	0.996806i	$0.474553\pi$
$930$	36.6735	1.20257
$931$	−11.4193	−0.374252
$932$	71.9595	2.35711
$933$	1.63158	0.0534156
$934$	23.2543	0.760903
$935$	−9.80642	−0.320704
$936$	−2.19358	−0.0716993
$937$	−36.9151	−1.20596	−0.602981	−	0.797755i	$-0.706021\pi$
$937$	−36.9151	−1.20596	−0.602981	+	0.797755i	$0.706021\pi$
$938$	−15.8064	−0.516098
$939$	−21.1526	−0.690288
$940$	−3.85236	−0.125650
$941$	46.1260	1.50366	0.751832	−	0.659354i	$-0.229170\pi$
$941$	46.1260	1.50366	0.751832	+	0.659354i	$0.229170\pi$
$942$	−10.3827	−0.338287
$943$	17.6543	0.574904
$944$	3.57136	0.116238
$945$	1.68889	0.0549397
$946$	54.4514	1.77037
$947$	3.74620	0.121735	0.0608676	−	0.998146i	$-0.480613\pi$
$947$	3.74620	0.121735	0.0608676	+	0.998146i	$0.480613\pi$
$948$	−2.90321	−0.0942919
$949$	−0.285442	−0.00926584
$950$	9.05086	0.293649
$951$	21.4449	0.695400
$952$	−2.00000	−0.0648204
$953$	−49.2226	−1.59448	−0.797239	−	0.603664i	$-0.793707\pi$
$953$	−49.2226	−1.59448	−0.797239	+	0.603664i	$0.793707\pi$
$954$	−31.9146	−1.03327
$955$	12.5812	0.407118
$956$	24.6222	0.796339
$957$	−33.7146	−1.08984
$958$	−37.9244	−1.22528
$959$	−0.652327	−0.0210647
$960$	−21.7146	−0.700834
$961$	65.1659	2.10213
$962$	15.4893	0.499396
$963$	−5.97926	−0.192679
$964$	−8.58073	−0.276367
$965$	39.9896	1.28731
$966$	−4.06668	−0.130843
$967$	−13.2908	−0.427405	−0.213702	−	0.976899i	$-0.568552\pi$
$967$	−13.2908	−0.427405	−0.213702	+	0.976899i	$0.568552\pi$
$968$	−45.4291	−1.46015
$969$	−1.90321	−0.0611400
$970$	11.6588	0.374341
$971$	−36.5531	−1.17304	−0.586522	−	0.809933i	$-0.699503\pi$
$971$	−36.5531	−1.17304	−0.586522	+	0.809933i	$0.699503\pi$
$972$	−2.90321	−0.0931206
$973$	−4.34122	−0.139173
$974$	80.7422	2.58715
$975$	2.35551	0.0754367
$976$	13.8479	0.443261
$977$	−19.5466	−0.625353	−0.312676	−	0.949860i	$-0.601226\pi$
$977$	−19.5466	−0.625353	−0.312676	+	0.949860i	$0.601226\pi$
$978$	0.668149	0.0213650
$979$	−85.1437	−2.72120
$980$	29.4193	0.939764
$981$	14.2494	0.454947
$982$	48.2864	1.54088
$983$	17.7067	0.564757	0.282378	−	0.959303i	$-0.408877\pi$
$983$	17.7067	0.564757	0.282378	+	0.959303i	$0.408877\pi$
$984$	−19.2257	−0.612893
$985$	−34.7971	−1.10873
$986$	−12.8573	−0.409459
$987$	−0.785680	−0.0250085
$988$	6.06022	0.192801
$989$	7.77784	0.247321
$990$	21.7146	0.690134
$991$	25.7699	0.818607	0.409303	−	0.912398i	$-0.365772\pi$
$991$	25.7699	0.818607	0.409303	+	0.912398i	$0.365772\pi$
$992$	−69.1437	−2.19531
$993$	3.99355	0.126731
$994$	0.903212	0.0286481
$995$	30.5319	0.967926
$996$	−8.79706	−0.278745
$997$	42.3180	1.34023	0.670113	−	0.742259i	$-0.266246\pi$
$997$	42.3180	1.34023	0.670113	+	0.742259i	$0.266246\pi$
$998$	52.3497	1.65710
$999$	6.37778	0.201784

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.d.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.d.1.1	✓	3	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21432 q^{2} -1.00000 q^{3} +2.90321 q^{4} -1.68889 q^{5} +2.21432 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.21432 q^{2} -1.00000 q^{3} +2.90321 q^{4} -1.68889 q^{5} +2.21432 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} +3.73975 q^{10} +5.80642 q^{11} -2.90321 q^{12} +1.09679 q^{13} -2.21432 q^{14} +1.68889 q^{15} -1.37778 q^{16} +1.00000 q^{17} -2.21432 q^{18} +1.90321 q^{19} -4.90321 q^{20} -1.00000 q^{21} -12.8573 q^{22} -1.83654 q^{23} +2.00000 q^{24} -2.14764 q^{25} -2.42864 q^{26} -1.00000 q^{27} +2.90321 q^{28} +5.80642 q^{29} -3.73975 q^{30} -9.80642 q^{31} +7.05086 q^{32} -5.80642 q^{33} -2.21432 q^{34} -1.68889 q^{35} +2.90321 q^{36} -6.37778 q^{37} -4.21432 q^{38} -1.09679 q^{39} +3.37778 q^{40} -9.61285 q^{41} +2.21432 q^{42} -4.23506 q^{43} +16.8573 q^{44} -1.68889 q^{45} +4.06668 q^{46} +0.785680 q^{47} +1.37778 q^{48} -6.00000 q^{49} +4.75557 q^{50} -1.00000 q^{51} +3.18421 q^{52} +14.4128 q^{53} +2.21432 q^{54} -9.80642 q^{55} -2.00000 q^{56} -1.90321 q^{57} -12.8573 q^{58} -2.59210 q^{59} +4.90321 q^{60} -10.0509 q^{61} +21.7146 q^{62} +1.00000 q^{63} -12.8573 q^{64} -1.85236 q^{65} +12.8573 q^{66} +7.13828 q^{67} +2.90321 q^{68} +1.83654 q^{69} +3.73975 q^{70} -0.407896 q^{71} -2.00000 q^{72} -0.260253 q^{73} +14.1225 q^{74} +2.14764 q^{75} +5.52543 q^{76} +5.80642 q^{77} +2.42864 q^{78} +1.00000 q^{79} +2.32693 q^{80} +1.00000 q^{81} +21.2859 q^{82} +3.03011 q^{83} -2.90321 q^{84} -1.68889 q^{85} +9.37778 q^{86} -5.80642 q^{87} -11.6128 q^{88} -14.6637 q^{89} +3.73975 q^{90} +1.09679 q^{91} -5.33185 q^{92} +9.80642 q^{93} -1.73975 q^{94} -3.21432 q^{95} -7.05086 q^{96} +3.11753 q^{97} +13.2859 q^{98} +5.80642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 10 q^{13} + 5 q^{15} - 4 q^{16} + 3 q^{17} - q^{19} - 8 q^{20} - 3 q^{21} - 12 q^{22} + q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 2 q^{28} + 4 q^{29} + 2 q^{30} - 16 q^{31} + 8 q^{32} - 4 q^{33} - 5 q^{35} + 2 q^{36} - 19 q^{37} - 6 q^{38} - 10 q^{39} + 10 q^{40} - 2 q^{41} + 14 q^{43} + 24 q^{44} - 5 q^{45} + 12 q^{46} + 9 q^{47} + 4 q^{48} - 18 q^{49} + 14 q^{50} - 3 q^{51} - 4 q^{52} + 17 q^{53} - 16 q^{55} - 6 q^{56} + q^{57} - 12 q^{58} - q^{59} + 8 q^{60} - 17 q^{61} + 12 q^{62} + 3 q^{63} - 12 q^{64} - 12 q^{65} + 12 q^{66} - 12 q^{67} + 2 q^{68} - q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} - 14 q^{73} - 4 q^{74} + 10 q^{76} + 4 q^{77} - 6 q^{78} + 3 q^{79} + 20 q^{80} + 3 q^{81} + 24 q^{82} + 16 q^{83} - 2 q^{84} - 5 q^{85} + 28 q^{86} - 4 q^{87} - 8 q^{88} - 4 q^{89} - 2 q^{90} + 10 q^{91} + 4 q^{92} + 16 q^{93} + 8 q^{94} - 3 q^{95} - 8 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 10 * q^13 + 5 * q^15 - 4 * q^16 + 3 * q^17 - q^19 - 8 * q^20 - 3 * q^21 - 12 * q^22 + q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 2 * q^28 + 4 * q^29 + 2 * q^30 - 16 * q^31 + 8 * q^32 - 4 * q^33 - 5 * q^35 + 2 * q^36 - 19 * q^37 - 6 * q^38 - 10 * q^39 + 10 * q^40 - 2 * q^41 + 14 * q^43 + 24 * q^44 - 5 * q^45 + 12 * q^46 + 9 * q^47 + 4 * q^48 - 18 * q^49 + 14 * q^50 - 3 * q^51 - 4 * q^52 + 17 * q^53 - 16 * q^55 - 6 * q^56 + q^57 - 12 * q^58 - q^59 + 8 * q^60 - 17 * q^61 + 12 * q^62 + 3 * q^63 - 12 * q^64 - 12 * q^65 + 12 * q^66 - 12 * q^67 + 2 * q^68 - q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 - 14 * q^73 - 4 * q^74 + 10 * q^76 + 4 * q^77 - 6 * q^78 + 3 * q^79 + 20 * q^80 + 3 * q^81 + 24 * q^82 + 16 * q^83 - 2 * q^84 - 5 * q^85 + 28 * q^86 - 4 * q^87 - 8 * q^88 - 4 * q^89 - 2 * q^90 + 10 * q^91 + 4 * q^92 + 16 * q^93 + 8 * q^94 - 3 * q^95 - 8 * q^96 - 4 * q^97 + 4 * q^99

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