LMFDB - Embedded newform 354.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.24914 q^{5} +1.00000 q^{6} +2.71982 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.24914 q^{5} +1.00000 q^{6} +2.71982 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.24914 q^{10} +2.83709 q^{11} +1.00000 q^{12} +0.470683 q^{13} +2.71982 q^{14} -2.24914 q^{15} +1.00000 q^{16} -3.77846 q^{17} +1.00000 q^{18} +5.55691 q^{19} -2.24914 q^{20} +2.71982 q^{21} +2.83709 q^{22} -3.05863 q^{23} +1.00000 q^{24} +0.0586332 q^{25} +0.470683 q^{26} +1.00000 q^{27} +2.71982 q^{28} -5.30777 q^{29} -2.24914 q^{30} -3.30777 q^{31} +1.00000 q^{32} +2.83709 q^{33} -3.77846 q^{34} -6.11727 q^{35} +1.00000 q^{36} -8.52588 q^{37} +5.55691 q^{38} +0.470683 q^{39} -2.24914 q^{40} +1.89572 q^{41} +2.71982 q^{42} -4.83709 q^{43} +2.83709 q^{44} -2.24914 q^{45} -3.05863 q^{46} +2.61555 q^{47} +1.00000 q^{48} +0.397442 q^{49} +0.0586332 q^{50} -3.77846 q^{51} +0.470683 q^{52} -8.36641 q^{53} +1.00000 q^{54} -6.38101 q^{55} +2.71982 q^{56} +5.55691 q^{57} -5.30777 q^{58} +1.00000 q^{59} -2.24914 q^{60} +14.3043 q^{61} -3.30777 q^{62} +2.71982 q^{63} +1.00000 q^{64} -1.05863 q^{65} +2.83709 q^{66} -2.61555 q^{67} -3.77846 q^{68} -3.05863 q^{69} -6.11727 q^{70} -3.41205 q^{71} +1.00000 q^{72} +9.32238 q^{73} -8.52588 q^{74} +0.0586332 q^{75} +5.55691 q^{76} +7.71639 q^{77} +0.470683 q^{78} +2.27674 q^{79} -2.24914 q^{80} +1.00000 q^{81} +1.89572 q^{82} +6.27674 q^{83} +2.71982 q^{84} +8.49828 q^{85} -4.83709 q^{86} -5.30777 q^{87} +2.83709 q^{88} -17.4948 q^{89} -2.24914 q^{90} +1.28018 q^{91} -3.05863 q^{92} -3.30777 q^{93} +2.61555 q^{94} -12.4983 q^{95} +1.00000 q^{96} +9.05863 q^{97} +0.397442 q^{98} +2.83709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + q^{13} - q^{14} + 2 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 2 q^{20} - q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + q^{25} + q^{26} + 3 q^{27} - q^{28} - 8 q^{29} + 2 q^{30} - 2 q^{31} + 3 q^{32} + q^{33} - 3 q^{34} - 20 q^{35} + 3 q^{36} + 9 q^{37} + q^{39} + 2 q^{40} - q^{41} - q^{42} - 7 q^{43} + q^{44} + 2 q^{45} - 10 q^{46} - 8 q^{47} + 3 q^{48} + 12 q^{49} + q^{50} - 3 q^{51} + q^{52} - 18 q^{53} + 3 q^{54} - q^{56} - 8 q^{58} + 3 q^{59} + 2 q^{60} - 2 q^{62} - q^{63} + 3 q^{64} - 4 q^{65} + q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 20 q^{70} - 9 q^{71} + 3 q^{72} + 8 q^{73} + 9 q^{74} + q^{75} - 21 q^{77} + q^{78} - 19 q^{79} + 2 q^{80} + 3 q^{81} - q^{82} - 7 q^{83} - q^{84} + 8 q^{85} - 7 q^{86} - 8 q^{87} + q^{88} + 2 q^{90} + 13 q^{91} - 10 q^{92} - 2 q^{93} - 8 q^{94} - 20 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + q^11 + 3 * q^12 + q^13 - q^14 + 2 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 2 * q^20 - q^21 + q^22 - 10 * q^23 + 3 * q^24 + q^25 + q^26 + 3 * q^27 - q^28 - 8 * q^29 + 2 * q^30 - 2 * q^31 + 3 * q^32 + q^33 - 3 * q^34 - 20 * q^35 + 3 * q^36 + 9 * q^37 + q^39 + 2 * q^40 - q^41 - q^42 - 7 * q^43 + q^44 + 2 * q^45 - 10 * q^46 - 8 * q^47 + 3 * q^48 + 12 * q^49 + q^50 - 3 * q^51 + q^52 - 18 * q^53 + 3 * q^54 - q^56 - 8 * q^58 + 3 * q^59 + 2 * q^60 - 2 * q^62 - q^63 + 3 * q^64 - 4 * q^65 + q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 20 * q^70 - 9 * q^71 + 3 * q^72 + 8 * q^73 + 9 * q^74 + q^75 - 21 * q^77 + q^78 - 19 * q^79 + 2 * q^80 + 3 * q^81 - q^82 - 7 * q^83 - q^84 + 8 * q^85 - 7 * q^86 - 8 * q^87 + q^88 + 2 * q^90 + 13 * q^91 - 10 * q^92 - 2 * q^93 - 8 * q^94 - 20 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.24914	−1.00585	−0.502923	−	0.864331i	$-0.667742\pi$
$5$	−2.24914	−1.00585	−0.502923	+	0.864331i	$0.667742\pi$
$6$	1.00000	0.408248
$7$	2.71982	1.02800	0.513998	−	0.857791i	$-0.328164\pi$
$7$	2.71982	1.02800	0.513998	+	0.857791i	$0.328164\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.24914	−0.711241
$11$	2.83709	0.855415	0.427707	−	0.903917i	$-0.359321\pi$
$11$	2.83709	0.855415	0.427707	+	0.903917i	$0.359321\pi$
$12$	1.00000	0.288675
$13$	0.470683	0.130544	0.0652720	−	0.997868i	$-0.479208\pi$
$13$	0.470683	0.130544	0.0652720	+	0.997868i	$0.479208\pi$
$14$	2.71982	0.726904
$15$	−2.24914	−0.580726
$16$	1.00000	0.250000
$17$	−3.77846	−0.916410	−0.458205	−	0.888846i	$-0.651508\pi$
$17$	−3.77846	−0.916410	−0.458205	+	0.888846i	$0.651508\pi$
$18$	1.00000	0.235702
$19$	5.55691	1.27484	0.637422	−	0.770515i	$-0.280001\pi$
$19$	5.55691	1.27484	0.637422	+	0.770515i	$0.280001\pi$
$20$	−2.24914	−0.502923
$21$	2.71982	0.593514
$22$	2.83709	0.604870
$23$	−3.05863	−0.637769	−0.318885	−	0.947794i	$-0.603308\pi$
$23$	−3.05863	−0.637769	−0.318885	+	0.947794i	$0.603308\pi$
$24$	1.00000	0.204124
$25$	0.0586332	0.0117266
$26$	0.470683	0.0923086
$27$	1.00000	0.192450
$28$	2.71982	0.513998
$29$	−5.30777	−0.985629	−0.492814	−	0.870134i	$-0.664032\pi$
$29$	−5.30777	−0.985629	−0.492814	+	0.870134i	$0.664032\pi$
$30$	−2.24914	−0.410635
$31$	−3.30777	−0.594094	−0.297047	−	0.954863i	$-0.596002\pi$
$31$	−3.30777	−0.594094	−0.297047	+	0.954863i	$0.596002\pi$
$32$	1.00000	0.176777
$33$	2.83709	0.493874
$34$	−3.77846	−0.648000
$35$	−6.11727	−1.03401
$36$	1.00000	0.166667
$37$	−8.52588	−1.40165	−0.700823	−	0.713335i	$-0.747184\pi$
$37$	−8.52588	−1.40165	−0.700823	+	0.713335i	$0.747184\pi$
$38$	5.55691	0.901451
$39$	0.470683	0.0753697
$40$	−2.24914	−0.355620
$41$	1.89572	0.296062	0.148031	−	0.988983i	$-0.452706\pi$
$41$	1.89572	0.296062	0.148031	+	0.988983i	$0.452706\pi$
$42$	2.71982	0.419678
$43$	−4.83709	−0.737649	−0.368825	−	0.929499i	$-0.620240\pi$
$43$	−4.83709	−0.737649	−0.368825	+	0.929499i	$0.620240\pi$
$44$	2.83709	0.427707
$45$	−2.24914	−0.335282
$46$	−3.05863	−0.450971
$47$	2.61555	0.381517	0.190758	−	0.981637i	$-0.438905\pi$
$47$	2.61555	0.381517	0.190758	+	0.981637i	$0.438905\pi$
$48$	1.00000	0.144338
$49$	0.397442	0.0567775
$50$	0.0586332	0.00829198
$51$	−3.77846	−0.529090
$52$	0.470683	0.0652720
$53$	−8.36641	−1.14921	−0.574607	−	0.818429i	$-0.694845\pi$
$53$	−8.36641	−1.14921	−0.574607	+	0.818429i	$0.694845\pi$
$54$	1.00000	0.136083
$55$	−6.38101	−0.860416
$56$	2.71982	0.363452
$57$	5.55691	0.736031
$58$	−5.30777	−0.696945
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−2.24914	−0.290363
$61$	14.3043	1.83148	0.915741	−	0.401769i	$-0.131604\pi$
$61$	14.3043	1.83148	0.915741	+	0.401769i	$0.131604\pi$
$62$	−3.30777	−0.420088
$63$	2.71982	0.342666
$64$	1.00000	0.125000
$65$	−1.05863	−0.131307
$66$	2.83709	0.349222
$67$	−2.61555	−0.319540	−0.159770	−	0.987154i	$-0.551075\pi$
$67$	−2.61555	−0.319540	−0.159770	+	0.987154i	$0.551075\pi$
$68$	−3.77846	−0.458205
$69$	−3.05863	−0.368216
$70$	−6.11727	−0.731153
$71$	−3.41205	−0.404936	−0.202468	−	0.979289i	$-0.564896\pi$
$71$	−3.41205	−0.404936	−0.202468	+	0.979289i	$0.564896\pi$
$72$	1.00000	0.117851
$73$	9.32238	1.09110	0.545551	−	0.838078i	$-0.316320\pi$
$73$	9.32238	1.09110	0.545551	+	0.838078i	$0.316320\pi$
$74$	−8.52588	−0.991113
$75$	0.0586332	0.00677037
$76$	5.55691	0.637422
$77$	7.71639	0.879364
$78$	0.470683	0.0532944
$79$	2.27674	0.256153	0.128077	−	0.991764i	$-0.459120\pi$
$79$	2.27674	0.256153	0.128077	+	0.991764i	$0.459120\pi$
$80$	−2.24914	−0.251462
$81$	1.00000	0.111111
$82$	1.89572	0.209348
$83$	6.27674	0.688962	0.344481	−	0.938793i	$-0.388055\pi$
$83$	6.27674	0.688962	0.344481	+	0.938793i	$0.388055\pi$
$84$	2.71982	0.296757
$85$	8.49828	0.921768
$86$	−4.83709	−0.521597
$87$	−5.30777	−0.569053
$88$	2.83709	0.302435
$89$	−17.4948	−1.85445	−0.927225	−	0.374505i	$-0.877813\pi$
$89$	−17.4948	−1.85445	−0.927225	+	0.374505i	$0.877813\pi$
$90$	−2.24914	−0.237080
$91$	1.28018	0.134199
$92$	−3.05863	−0.318885
$93$	−3.30777	−0.343000
$94$	2.61555	0.269773
$95$	−12.4983	−1.28230
$96$	1.00000	0.102062
$97$	9.05863	0.919765	0.459882	−	0.887980i	$-0.347892\pi$
$97$	9.05863	0.919765	0.459882	+	0.887980i	$0.347892\pi$
$98$	0.397442	0.0401477
$99$	2.83709	0.285138
$100$	0.0586332	0.00586332
$101$	7.77846	0.773985	0.386993	−	0.922083i	$-0.373514\pi$
$101$	7.77846	0.773985	0.386993	+	0.922083i	$0.373514\pi$
$102$	−3.77846	−0.374123
$103$	−9.68879	−0.954665	−0.477332	−	0.878723i	$-0.658396\pi$
$103$	−9.68879	−0.954665	−0.477332	+	0.878723i	$0.658396\pi$
$104$	0.470683	0.0461543
$105$	−6.11727	−0.596984
$106$	−8.36641	−0.812617
$107$	−13.9379	−1.34743	−0.673715	−	0.738991i	$-0.735303\pi$
$107$	−13.9379	−1.34743	−0.673715	+	0.738991i	$0.735303\pi$
$108$	1.00000	0.0962250
$109$	−3.68879	−0.353322	−0.176661	−	0.984272i	$-0.556530\pi$
$109$	−3.68879	−0.353322	−0.176661	+	0.984272i	$0.556530\pi$
$110$	−6.38101	−0.608406
$111$	−8.52588	−0.809241
$112$	2.71982	0.256999
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	5.55691	0.520453
$115$	6.87930	0.641498
$116$	−5.30777	−0.492814
$117$	0.470683	0.0435147
$118$	1.00000	0.0920575
$119$	−10.2767	−0.942067
$120$	−2.24914	−0.205318
$121$	−2.95092	−0.268265
$122$	14.3043	1.29505
$123$	1.89572	0.170932
$124$	−3.30777	−0.297047
$125$	11.1138	0.994051
$126$	2.71982	0.242301
$127$	−4.49828	−0.399158	−0.199579	−	0.979882i	$-0.563957\pi$
$127$	−4.49828	−0.399158	−0.199579	+	0.979882i	$0.563957\pi$
$128$	1.00000	0.0883883
$129$	−4.83709	−0.425882
$130$	−1.05863	−0.0928483
$131$	9.32238	0.814500	0.407250	−	0.913317i	$-0.366488\pi$
$131$	9.32238	0.814500	0.407250	+	0.913317i	$0.366488\pi$
$132$	2.83709	0.246937
$133$	15.1138	1.31054
$134$	−2.61555	−0.225949
$135$	−2.24914	−0.193575
$136$	−3.77846	−0.324000
$137$	22.6578	1.93578	0.967891	−	0.251369i	$-0.0808809\pi$
$137$	22.6578	1.93578	0.967891	+	0.251369i	$0.0808809\pi$
$138$	−3.05863	−0.260368
$139$	9.55691	0.810607	0.405303	−	0.914182i	$-0.367166\pi$
$139$	9.55691	0.810607	0.405303	+	0.914182i	$0.367166\pi$
$140$	−6.11727	−0.517003
$141$	2.61555	0.220269
$142$	−3.41205	−0.286333
$143$	1.33537	0.111669
$144$	1.00000	0.0833333
$145$	11.9379	0.991391
$146$	9.32238	0.771526
$147$	0.397442	0.0327805
$148$	−8.52588	−0.700823
$149$	10.3940	0.851510	0.425755	−	0.904838i	$-0.360009\pi$
$149$	10.3940	0.851510	0.425755	+	0.904838i	$0.360009\pi$
$150$	0.0586332	0.00478738
$151$	−21.7440	−1.76950	−0.884750	−	0.466066i	$-0.845671\pi$
$151$	−21.7440	−1.76950	−0.884750	+	0.466066i	$0.845671\pi$
$152$	5.55691	0.450725
$153$	−3.77846	−0.305470
$154$	7.71639	0.621804
$155$	7.43965	0.597567
$156$	0.470683	0.0376848
$157$	23.1905	1.85080	0.925402	−	0.378987i	$-0.123728\pi$
$157$	23.1905	1.85080	0.925402	+	0.378987i	$0.123728\pi$
$158$	2.27674	0.181128
$159$	−8.36641	−0.663499
$160$	−2.24914	−0.177810
$161$	−8.31894	−0.655625
$162$	1.00000	0.0785674
$163$	15.2311	1.19299	0.596496	−	0.802616i	$-0.296559\pi$
$163$	15.2311	1.19299	0.596496	+	0.802616i	$0.296559\pi$
$164$	1.89572	0.148031
$165$	−6.38101	−0.496761
$166$	6.27674	0.487169
$167$	0.193945	0.0150079	0.00750397	−	0.999972i	$-0.497611\pi$
$167$	0.193945	0.0150079	0.00750397	+	0.999972i	$0.497611\pi$
$168$	2.71982	0.209839
$169$	−12.7785	−0.982958
$170$	8.49828	0.651788
$171$	5.55691	0.424948
$172$	−4.83709	−0.368825
$173$	−22.0061	−1.67309	−0.836547	−	0.547895i	$-0.815429\pi$
$173$	−22.0061	−1.67309	−0.836547	+	0.547895i	$0.815429\pi$
$174$	−5.30777	−0.402381
$175$	0.159472	0.0120549
$176$	2.83709	0.213854
$177$	1.00000	0.0751646
$178$	−17.4948	−1.31129
$179$	4.60256	0.344011	0.172006	−	0.985096i	$-0.444975\pi$
$179$	4.60256	0.344011	0.172006	+	0.985096i	$0.444975\pi$
$180$	−2.24914	−0.167641
$181$	11.8827	0.883237	0.441618	−	0.897203i	$-0.354405\pi$
$181$	11.8827	0.883237	0.441618	+	0.897203i	$0.354405\pi$
$182$	1.28018	0.0948930
$183$	14.3043	1.05741
$184$	−3.05863	−0.225485
$185$	19.1759	1.40984
$186$	−3.30777	−0.242538
$187$	−10.7198	−0.783911
$188$	2.61555	0.190758
$189$	2.71982	0.197838
$190$	−12.4983	−0.906721
$191$	5.38445	0.389605	0.194803	−	0.980842i	$-0.437593\pi$
$191$	5.38445	0.389605	0.194803	+	0.980842i	$0.437593\pi$
$192$	1.00000	0.0721688
$193$	10.8371	0.780071	0.390035	−	0.920800i	$-0.372463\pi$
$193$	10.8371	0.780071	0.390035	+	0.920800i	$0.372463\pi$
$194$	9.05863	0.650372
$195$	−1.05863	−0.0758103
$196$	0.397442	0.0283887
$197$	7.24570	0.516235	0.258117	−	0.966114i	$-0.416898\pi$
$197$	7.24570	0.516235	0.258117	+	0.966114i	$0.416898\pi$
$198$	2.83709	0.201623
$199$	−19.6121	−1.39027	−0.695133	−	0.718881i	$-0.744654\pi$
$199$	−19.6121	−1.39027	−0.695133	+	0.718881i	$0.744654\pi$
$200$	0.0586332	0.00414599
$201$	−2.61555	−0.184486
$202$	7.77846	0.547290
$203$	−14.4362	−1.01322
$204$	−3.77846	−0.264545
$205$	−4.26375	−0.297793
$206$	−9.68879	−0.675050
$207$	−3.05863	−0.212590
$208$	0.470683	0.0326360
$209$	15.7655	1.09052
$210$	−6.11727	−0.422131
$211$	24.2147	1.66701	0.833503	−	0.552515i	$-0.186332\pi$
$211$	24.2147	1.66701	0.833503	+	0.552515i	$0.186332\pi$
$212$	−8.36641	−0.574607
$213$	−3.41205	−0.233790
$214$	−13.9379	−0.952777
$215$	10.8793	0.741962
$216$	1.00000	0.0680414
$217$	−8.99656	−0.610726
$218$	−3.68879	−0.249836
$219$	9.32238	0.629948
$220$	−6.38101	−0.430208
$221$	−1.77846	−0.119632
$222$	−8.52588	−0.572220
$223$	−13.2802	−0.889306	−0.444653	−	0.895703i	$-0.646673\pi$
$223$	−13.2802	−0.889306	−0.444653	+	0.895703i	$0.646673\pi$
$224$	2.71982	0.181726
$225$	0.0586332	0.00390888
$226$	−2.00000	−0.133038
$227$	9.04564	0.600380	0.300190	−	0.953879i	$-0.402950\pi$
$227$	9.04564	0.600380	0.300190	+	0.953879i	$0.402950\pi$
$228$	5.55691	0.368016
$229$	−4.96896	−0.328358	−0.164179	−	0.986431i	$-0.552498\pi$
$229$	−4.96896	−0.328358	−0.164179	+	0.986431i	$0.552498\pi$
$230$	6.87930	0.453607
$231$	7.71639	0.507701
$232$	−5.30777	−0.348472
$233$	6.85008	0.448764	0.224382	−	0.974501i	$-0.427964\pi$
$233$	6.85008	0.448764	0.224382	+	0.974501i	$0.427964\pi$
$234$	0.470683	0.0307695
$235$	−5.88273	−0.383747
$236$	1.00000	0.0650945
$237$	2.27674	0.147890
$238$	−10.2767	−0.666142
$239$	23.1544	1.49773	0.748867	−	0.662720i	$-0.230598\pi$
$239$	23.1544	1.49773	0.748867	+	0.662720i	$0.230598\pi$
$240$	−2.24914	−0.145181
$241$	17.3354	1.11667	0.558335	−	0.829616i	$-0.311440\pi$
$241$	17.3354	1.11667	0.558335	+	0.829616i	$0.311440\pi$
$242$	−2.95092	−0.189692
$243$	1.00000	0.0641500
$244$	14.3043	0.915741
$245$	−0.893904	−0.0571094
$246$	1.89572	0.120867
$247$	2.61555	0.166423
$248$	−3.30777	−0.210044
$249$	6.27674	0.397772
$250$	11.1138	0.702900
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	2.71982	0.171333
$253$	−8.67762	−0.545557
$254$	−4.49828	−0.282247
$255$	8.49828	0.532183
$256$	1.00000	0.0625000
$257$	−26.9475	−1.68094	−0.840469	−	0.541860i	$-0.817720\pi$
$257$	−26.9475	−1.68094	−0.840469	+	0.541860i	$0.817720\pi$
$258$	−4.83709	−0.301144
$259$	−23.1889	−1.44089
$260$	−1.05863	−0.0656536
$261$	−5.30777	−0.328543
$262$	9.32238	0.575939
$263$	0.144864	0.00893270	0.00446635	−	0.999990i	$-0.498578\pi$
$263$	0.144864	0.00893270	0.00446635	+	0.999990i	$0.498578\pi$
$264$	2.83709	0.174611
$265$	18.8172	1.15593
$266$	15.1138	0.926688
$267$	−17.4948	−1.07067
$268$	−2.61555	−0.159770
$269$	3.83365	0.233742	0.116871	−	0.993147i	$-0.462714\pi$
$269$	3.83365	0.233742	0.116871	+	0.993147i	$0.462714\pi$
$270$	−2.24914	−0.136878
$271$	−16.6026	−1.00853	−0.504267	−	0.863548i	$-0.668237\pi$
$271$	−16.6026	−1.00853	−0.504267	+	0.863548i	$0.668237\pi$
$272$	−3.77846	−0.229103
$273$	1.28018	0.0774798
$274$	22.6578	1.36880
$275$	0.166348	0.0100311
$276$	−3.05863	−0.184108
$277$	−28.7259	−1.72597	−0.862987	−	0.505226i	$-0.831409\pi$
$277$	−28.7259	−1.72597	−0.862987	+	0.505226i	$0.831409\pi$
$278$	9.55691	0.573186
$279$	−3.30777	−0.198031
$280$	−6.11727	−0.365577
$281$	23.5991	1.40781	0.703903	−	0.710296i	$-0.251439\pi$
$281$	23.5991	1.40781	0.703903	+	0.710296i	$0.251439\pi$
$282$	2.61555	0.155754
$283$	−4.60256	−0.273594	−0.136797	−	0.990599i	$-0.543681\pi$
$283$	−4.60256	−0.273594	−0.136797	+	0.990599i	$0.543681\pi$
$284$	−3.41205	−0.202468
$285$	−12.4983	−0.740334
$286$	1.33537	0.0789622
$287$	5.15603	0.304351
$288$	1.00000	0.0589256
$289$	−2.72326	−0.160192
$290$	11.9379	0.701019
$291$	9.05863	0.531026
$292$	9.32238	0.545551
$293$	−0.366407	−0.0214057	−0.0107029	−	0.999943i	$-0.503407\pi$
$293$	−0.366407	−0.0214057	−0.0107029	+	0.999943i	$0.503407\pi$
$294$	0.397442	0.0231793
$295$	−2.24914	−0.130950
$296$	−8.52588	−0.495557
$297$	2.83709	0.164625
$298$	10.3940	0.602109
$299$	−1.43965	−0.0832570
$300$	0.0586332	0.00338519
$301$	−13.1560	−0.758301
$302$	−21.7440	−1.25123
$303$	7.77846	0.446861
$304$	5.55691	0.318711
$305$	−32.1725	−1.84219
$306$	−3.77846	−0.216000
$307$	10.2345	0.584116	0.292058	−	0.956401i	$-0.405660\pi$
$307$	10.2345	0.584116	0.292058	+	0.956401i	$0.405660\pi$
$308$	7.71639	0.439682
$309$	−9.68879	−0.551176
$310$	7.43965	0.422544
$311$	−10.0828	−0.571743	−0.285871	−	0.958268i	$-0.592283\pi$
$311$	−10.0828	−0.571743	−0.285871	+	0.958268i	$0.592283\pi$
$312$	0.470683	0.0266472
$313$	−21.6121	−1.22159	−0.610794	−	0.791789i	$-0.709150\pi$
$313$	−21.6121	−1.22159	−0.610794	+	0.791789i	$0.709150\pi$
$314$	23.1905	1.30872
$315$	−6.11727	−0.344669
$316$	2.27674	0.128077
$317$	19.9785	1.12211	0.561053	−	0.827780i	$-0.310397\pi$
$317$	19.9785	1.12211	0.561053	+	0.827780i	$0.310397\pi$
$318$	−8.36641	−0.469165
$319$	−15.0586	−0.843122
$320$	−2.24914	−0.125731
$321$	−13.9379	−0.777939
$322$	−8.31894	−0.463597
$323$	−20.9966	−1.16828
$324$	1.00000	0.0555556
$325$	0.0275977	0.00153084
$326$	15.2311	0.843572
$327$	−3.68879	−0.203990
$328$	1.89572	0.104674
$329$	7.11383	0.392198
$330$	−6.38101	−0.351263
$331$	−19.8827	−1.09285	−0.546427	−	0.837507i	$-0.684012\pi$
$331$	−19.8827	−1.09285	−0.546427	+	0.837507i	$0.684012\pi$
$332$	6.27674	0.344481
$333$	−8.52588	−0.467215
$334$	0.193945	0.0106122
$335$	5.88273	0.321408
$336$	2.71982	0.148379
$337$	15.2311	0.829691	0.414845	−	0.909892i	$-0.363836\pi$
$337$	15.2311	0.829691	0.414845	+	0.909892i	$0.363836\pi$
$338$	−12.7785	−0.695056
$339$	−2.00000	−0.108625
$340$	8.49828	0.460884
$341$	−9.38445	−0.508197
$342$	5.55691	0.300484
$343$	−17.9578	−0.969630
$344$	−4.83709	−0.260798
$345$	6.87930	0.370369
$346$	−22.0061	−1.18306
$347$	10.7880	0.579131	0.289565	−	0.957158i	$-0.406489\pi$
$347$	10.7880	0.579131	0.289565	+	0.957158i	$0.406489\pi$
$348$	−5.30777	−0.284527
$349$	−19.2948	−1.03283	−0.516413	−	0.856340i	$-0.672733\pi$
$349$	−19.2948	−1.03283	−0.516413	+	0.856340i	$0.672733\pi$
$350$	0.159472	0.00852413
$351$	0.470683	0.0251232
$352$	2.83709	0.151217
$353$	−4.56035	−0.242723	−0.121362	−	0.992608i	$-0.538726\pi$
$353$	−4.56035	−0.242723	−0.121362	+	0.992608i	$0.538726\pi$
$354$	1.00000	0.0531494
$355$	7.67418	0.407303
$356$	−17.4948	−0.927225
$357$	−10.2767	−0.543903
$358$	4.60256	0.243253
$359$	12.1741	0.642523	0.321262	−	0.946990i	$-0.395893\pi$
$359$	12.1741	0.642523	0.321262	+	0.946990i	$0.395893\pi$
$360$	−2.24914	−0.118540
$361$	11.8793	0.625226
$362$	11.8827	0.624543
$363$	−2.95092	−0.154883
$364$	1.28018	0.0670995
$365$	−20.9673	−1.09748
$366$	14.3043	0.747700
$367$	2.15785	0.112639	0.0563195	−	0.998413i	$-0.482063\pi$
$367$	2.15785	0.112639	0.0563195	+	0.998413i	$0.482063\pi$
$368$	−3.05863	−0.159442
$369$	1.89572	0.0986874
$370$	19.1759	0.996908
$371$	−22.7552	−1.18139
$372$	−3.30777	−0.171500
$373$	−21.6673	−1.12189	−0.560945	−	0.827853i	$-0.689562\pi$
$373$	−21.6673	−1.12189	−0.560945	+	0.827853i	$0.689562\pi$
$374$	−10.7198	−0.554309
$375$	11.1138	0.573916
$376$	2.61555	0.134887
$377$	−2.49828	−0.128668
$378$	2.71982	0.139893
$379$	−36.7880	−1.88967	−0.944837	−	0.327542i	$-0.893780\pi$
$379$	−36.7880	−1.88967	−0.944837	+	0.327542i	$0.893780\pi$
$380$	−12.4983	−0.641148
$381$	−4.49828	−0.230454
$382$	5.38445	0.275493
$383$	−29.8190	−1.52368	−0.761841	−	0.647764i	$-0.775704\pi$
$383$	−29.8190	−1.52368	−0.761841	+	0.647764i	$0.775704\pi$
$384$	1.00000	0.0510310
$385$	−17.3552	−0.884505
$386$	10.8371	0.551593
$387$	−4.83709	−0.245883
$388$	9.05863	0.459882
$389$	−5.69566	−0.288782	−0.144391	−	0.989521i	$-0.546122\pi$
$389$	−5.69566	−0.288782	−0.144391	+	0.989521i	$0.546122\pi$
$390$	−1.05863	−0.0536060
$391$	11.5569	0.584458
$392$	0.397442	0.0200739
$393$	9.32238	0.470252
$394$	7.24570	0.365033
$395$	−5.12070	−0.257651
$396$	2.83709	0.142569
$397$	26.5681	1.33341	0.666707	−	0.745320i	$-0.267703\pi$
$397$	26.5681	1.33341	0.666707	+	0.745320i	$0.267703\pi$
$398$	−19.6121	−0.983066
$399$	15.1138	0.756638
$400$	0.0586332	0.00293166
$401$	−4.96735	−0.248057	−0.124029	−	0.992279i	$-0.539581\pi$
$401$	−4.96735	−0.248057	−0.124029	+	0.992279i	$0.539581\pi$
$402$	−2.61555	−0.130452
$403$	−1.55691	−0.0775554
$404$	7.77846	0.386993
$405$	−2.24914	−0.111761
$406$	−14.4362	−0.716457
$407$	−24.1887	−1.19899
$408$	−3.77846	−0.187062
$409$	8.85008	0.437608	0.218804	−	0.975769i	$-0.429784\pi$
$409$	8.85008	0.437608	0.218804	+	0.975769i	$0.429784\pi$
$410$	−4.26375	−0.210572
$411$	22.6578	1.11762
$412$	−9.68879	−0.477332
$413$	2.71982	0.133834
$414$	−3.05863	−0.150324
$415$	−14.1173	−0.692989
$416$	0.470683	0.0230772
$417$	9.55691	0.468004
$418$	15.7655	0.771114
$419$	30.0682	1.46893	0.734463	−	0.678648i	$-0.237434\pi$
$419$	30.0682	1.46893	0.734463	+	0.678648i	$0.237434\pi$
$420$	−6.11727	−0.298492
$421$	15.0862	0.735258	0.367629	−	0.929973i	$-0.380170\pi$
$421$	15.0862	0.735258	0.367629	+	0.929973i	$0.380170\pi$
$422$	24.2147	1.17875
$423$	2.61555	0.127172
$424$	−8.36641	−0.406309
$425$	−0.221543	−0.0107464
$426$	−3.41205	−0.165314
$427$	38.9053	1.88276
$428$	−13.9379	−0.673715
$429$	1.33537	0.0644723
$430$	10.8793	0.524646
$431$	32.1656	1.54936	0.774681	−	0.632352i	$-0.217911\pi$
$431$	32.1656	1.54936	0.774681	+	0.632352i	$0.217911\pi$
$432$	1.00000	0.0481125
$433$	−12.1043	−0.581694	−0.290847	−	0.956770i	$-0.593937\pi$
$433$	−12.1043	−0.581694	−0.290847	+	0.956770i	$0.593937\pi$
$434$	−8.99656	−0.431849
$435$	11.9379	0.572380
$436$	−3.68879	−0.176661
$437$	−16.9966	−0.813056
$438$	9.32238	0.445441
$439$	−2.22154	−0.106028	−0.0530142	−	0.998594i	$-0.516883\pi$
$439$	−2.22154	−0.106028	−0.0530142	+	0.998594i	$0.516883\pi$
$440$	−6.38101	−0.304203
$441$	0.397442	0.0189258
$442$	−1.77846	−0.0845926
$443$	32.9475	1.56538	0.782691	−	0.622410i	$-0.213847\pi$
$443$	32.9475	1.56538	0.782691	+	0.622410i	$0.213847\pi$
$444$	−8.52588	−0.404620
$445$	39.3484	1.86529
$446$	−13.2802	−0.628835
$447$	10.3940	0.491620
$448$	2.71982	0.128500
$449$	−39.8888	−1.88247	−0.941236	−	0.337751i	$-0.890334\pi$
$449$	−39.8888	−1.88247	−0.941236	+	0.337751i	$0.890334\pi$
$450$	0.0586332	0.00276399
$451$	5.37834	0.253256
$452$	−2.00000	−0.0940721
$453$	−21.7440	−1.02162
$454$	9.04564	0.424533
$455$	−2.87930	−0.134983
$456$	5.55691	0.260226
$457$	−0.0620710	−0.00290356	−0.00145178	−	0.999999i	$-0.500462\pi$
$457$	−0.0620710	−0.00290356	−0.00145178	+	0.999999i	$0.500462\pi$
$458$	−4.96896	−0.232184
$459$	−3.77846	−0.176363
$460$	6.87930	0.320749
$461$	18.1250	0.844165	0.422083	−	0.906557i	$-0.361299\pi$
$461$	18.1250	0.844165	0.422083	+	0.906557i	$0.361299\pi$
$462$	7.71639	0.358999
$463$	−22.9199	−1.06518	−0.532589	−	0.846374i	$-0.678781\pi$
$463$	−22.9199	−1.06518	−0.532589	+	0.846374i	$0.678781\pi$
$464$	−5.30777	−0.246407
$465$	7.43965	0.345005
$466$	6.85008	0.317324
$467$	−19.8337	−0.917792	−0.458896	−	0.888490i	$-0.651755\pi$
$467$	−19.8337	−0.917792	−0.458896	+	0.888490i	$0.651755\pi$
$468$	0.470683	0.0217573
$469$	−7.11383	−0.328486
$470$	−5.88273	−0.271350
$471$	23.1905	1.06856
$472$	1.00000	0.0460287
$473$	−13.7233	−0.630996
$474$	2.27674	0.104574
$475$	0.325819	0.0149496
$476$	−10.2767	−0.471034
$477$	−8.36641	−0.383071
$478$	23.1544	1.05906
$479$	−6.91988	−0.316178	−0.158089	−	0.987425i	$-0.550533\pi$
$479$	−6.91988	−0.316178	−0.158089	+	0.987425i	$0.550533\pi$
$480$	−2.24914	−0.102659
$481$	−4.01299	−0.182977
$482$	17.3354	0.789605
$483$	−8.31894	−0.378525
$484$	−2.95092	−0.134133
$485$	−20.3741	−0.925142
$486$	1.00000	0.0453609
$487$	7.19213	0.325906	0.162953	−	0.986634i	$-0.447898\pi$
$487$	7.19213	0.325906	0.162953	+	0.986634i	$0.447898\pi$
$488$	14.3043	0.647527
$489$	15.2311	0.688774
$490$	−0.893904	−0.0403825
$491$	33.9379	1.53160	0.765799	−	0.643080i	$-0.222344\pi$
$491$	33.9379	1.53160	0.765799	+	0.643080i	$0.222344\pi$
$492$	1.89572	0.0854658
$493$	20.0552	0.903241
$494$	2.61555	0.117679
$495$	−6.38101	−0.286805
$496$	−3.30777	−0.148523
$497$	−9.28018	−0.416273
$498$	6.27674	0.281267
$499$	−14.4622	−0.647417	−0.323708	−	0.946157i	$-0.604930\pi$
$499$	−14.4622	−0.647417	−0.323708	+	0.946157i	$0.604930\pi$
$500$	11.1138	0.497026
$501$	0.193945	0.00866483
$502$	20.0000	0.892644
$503$	−20.0552	−0.894217	−0.447108	−	0.894480i	$-0.647546\pi$
$503$	−20.0552	−0.894217	−0.447108	+	0.894480i	$0.647546\pi$
$504$	2.71982	0.121151
$505$	−17.4948	−0.778510
$506$	−8.67762	−0.385767
$507$	−12.7785	−0.567511
$508$	−4.49828	−0.199579
$509$	0.615547	0.0272837	0.0136418	−	0.999907i	$-0.495658\pi$
$509$	0.615547	0.0272837	0.0136418	+	0.999907i	$0.495658\pi$
$510$	8.49828	0.376310
$511$	25.3552	1.12165
$512$	1.00000	0.0441942
$513$	5.55691	0.245344
$514$	−26.9475	−1.18860
$515$	21.7914	0.960246
$516$	−4.83709	−0.212941
$517$	7.42054	0.326355
$518$	−23.1889	−1.01886
$519$	−22.0061	−0.965961
$520$	−1.05863	−0.0464241
$521$	32.2569	1.41320	0.706600	−	0.707614i	$-0.250228\pi$
$521$	32.2569	1.41320	0.706600	+	0.707614i	$0.250228\pi$
$522$	−5.30777	−0.232315
$523$	2.22766	0.0974086	0.0487043	−	0.998813i	$-0.484491\pi$
$523$	2.22766	0.0974086	0.0487043	+	0.998813i	$0.484491\pi$
$524$	9.32238	0.407250
$525$	0.159472	0.00695992
$526$	0.144864	0.00631637
$527$	12.4983	0.544434
$528$	2.83709	0.123469
$529$	−13.6448	−0.593251
$530$	18.8172	0.817368
$531$	1.00000	0.0433963
$532$	15.1138	0.655268
$533$	0.892286	0.0386492
$534$	−17.4948	−0.757076
$535$	31.3484	1.35531
$536$	−2.61555	−0.112974
$537$	4.60256	0.198615
$538$	3.83365	0.165280
$539$	1.12758	0.0485683
$540$	−2.24914	−0.0967876
$541$	−5.17752	−0.222599	−0.111299	−	0.993787i	$-0.535501\pi$
$541$	−5.17752	−0.222599	−0.111299	+	0.993787i	$0.535501\pi$
$542$	−16.6026	−0.713141
$543$	11.8827	0.509937
$544$	−3.77846	−0.162000
$545$	8.29660	0.355387
$546$	1.28018	0.0547865
$547$	31.1982	1.33394	0.666970	−	0.745084i	$-0.267591\pi$
$547$	31.1982	1.33394	0.666970	+	0.745084i	$0.267591\pi$
$548$	22.6578	0.967891
$549$	14.3043	0.610494
$550$	0.166348	0.00709308
$551$	−29.4948	−1.25652
$552$	−3.05863	−0.130184
$553$	6.19233	0.263325
$554$	−28.7259	−1.22045
$555$	19.1759	0.813972
$556$	9.55691	0.405303
$557$	−22.4837	−0.952664	−0.476332	−	0.879266i	$-0.658034\pi$
$557$	−22.4837	−0.952664	−0.476332	+	0.879266i	$0.658034\pi$
$558$	−3.30777	−0.140029
$559$	−2.27674	−0.0962958
$560$	−6.11727	−0.258502
$561$	−10.7198	−0.452591
$562$	23.5991	0.995469
$563$	31.4396	1.32502	0.662512	−	0.749052i	$-0.269491\pi$
$563$	31.4396	1.32502	0.662512	+	0.749052i	$0.269491\pi$
$564$	2.61555	0.110134
$565$	4.49828	0.189244
$566$	−4.60256	−0.193460
$567$	2.71982	0.114222
$568$	−3.41205	−0.143166
$569$	15.2311	0.638521	0.319260	−	0.947667i	$-0.396566\pi$
$569$	15.2311	0.638521	0.319260	+	0.947667i	$0.396566\pi$
$570$	−12.4983	−0.523495
$571$	32.7620	1.37105	0.685524	−	0.728050i	$-0.259573\pi$
$571$	32.7620	1.37105	0.685524	+	0.728050i	$0.259573\pi$
$572$	1.33537	0.0558347
$573$	5.38445	0.224939
$574$	5.15603	0.215209
$575$	−0.179337	−0.00747888
$576$	1.00000	0.0416667
$577$	8.13026	0.338467	0.169233	−	0.985576i	$-0.445871\pi$
$577$	8.13026	0.338467	0.169233	+	0.985576i	$0.445871\pi$
$578$	−2.72326	−0.113273
$579$	10.8371	0.450374
$580$	11.9379	0.495696
$581$	17.0716	0.708250
$582$	9.05863	0.375492
$583$	−23.7363	−0.983055
$584$	9.32238	0.385763
$585$	−1.05863	−0.0437691
$586$	−0.366407	−0.0151361
$587$	−45.1751	−1.86458	−0.932289	−	0.361715i	$-0.882191\pi$
$587$	−45.1751	−1.86458	−0.932289	+	0.361715i	$0.882191\pi$
$588$	0.397442	0.0163902
$589$	−18.3810	−0.757377
$590$	−2.24914	−0.0925957
$591$	7.24570	0.298048
$592$	−8.52588	−0.350411
$593$	18.1104	0.743705	0.371852	−	0.928292i	$-0.378723\pi$
$593$	18.1104	0.743705	0.371852	+	0.928292i	$0.378723\pi$
$594$	2.83709	0.116407
$595$	23.1138	0.947575
$596$	10.3940	0.425755
$597$	−19.6121	−0.802670
$598$	−1.43965	−0.0588716
$599$	36.6724	1.49839	0.749196	−	0.662348i	$-0.230440\pi$
$599$	36.6724	1.49839	0.749196	+	0.662348i	$0.230440\pi$
$600$	0.0586332	0.00239369
$601$	−0.436210	−0.0177934	−0.00889669	−	0.999960i	$-0.502832\pi$
$601$	−0.436210	−0.0177934	−0.00889669	+	0.999960i	$0.502832\pi$
$602$	−13.1560	−0.536200
$603$	−2.61555	−0.106513
$604$	−21.7440	−0.884750
$605$	6.63703	0.269834
$606$	7.77846	0.315978
$607$	−4.33881	−0.176107	−0.0880534	−	0.996116i	$-0.528065\pi$
$607$	−4.33881	−0.176107	−0.0880534	+	0.996116i	$0.528065\pi$
$608$	5.55691	0.225363
$609$	−14.4362	−0.584985
$610$	−32.1725	−1.30262
$611$	1.23109	0.0498048
$612$	−3.77846	−0.152735
$613$	42.0467	1.69825	0.849125	−	0.528192i	$-0.177130\pi$
$613$	42.0467	1.69825	0.849125	+	0.528192i	$0.177130\pi$
$614$	10.2345	0.413032
$615$	−4.26375	−0.171931
$616$	7.71639	0.310902
$617$	18.5044	0.744959	0.372479	−	0.928040i	$-0.378508\pi$
$617$	18.5044	0.744959	0.372479	+	0.928040i	$0.378508\pi$
$618$	−9.68879	−0.389740
$619$	−0.762030	−0.0306286	−0.0153143	−	0.999883i	$-0.504875\pi$
$619$	−0.762030	−0.0306286	−0.0153143	+	0.999883i	$0.504875\pi$
$620$	7.43965	0.298783
$621$	−3.05863	−0.122739
$622$	−10.0828	−0.404283
$623$	−47.5829	−1.90637
$624$	0.470683	0.0188424
$625$	−25.2897	−1.01159
$626$	−21.6121	−0.863794
$627$	15.7655	0.629612
$628$	23.1905	0.925402
$629$	32.2147	1.28448
$630$	−6.11727	−0.243718
$631$	49.9700	1.98928	0.994638	−	0.103422i	$-0.0329791\pi$
$631$	49.9700	1.98928	0.994638	+	0.103422i	$0.0329791\pi$
$632$	2.27674	0.0905638
$633$	24.2147	0.962447
$634$	19.9785	0.793448
$635$	10.1173	0.401491
$636$	−8.36641	−0.331750
$637$	0.187070	0.00741196
$638$	−15.0586	−0.596177
$639$	−3.41205	−0.134979
$640$	−2.24914	−0.0889051
$641$	−20.4914	−0.809362	−0.404681	−	0.914458i	$-0.632617\pi$
$641$	−20.4914	−0.809362	−0.404681	+	0.914458i	$0.632617\pi$
$642$	−13.9379	−0.550086
$643$	−27.2242	−1.07362	−0.536809	−	0.843704i	$-0.680371\pi$
$643$	−27.2242	−1.07362	−0.536809	+	0.843704i	$0.680371\pi$
$644$	−8.31894	−0.327812
$645$	10.8793	0.428372
$646$	−20.9966	−0.826099
$647$	−25.5354	−1.00390	−0.501951	−	0.864896i	$-0.667384\pi$
$647$	−25.5354	−1.00390	−0.501951	+	0.864896i	$0.667384\pi$
$648$	1.00000	0.0392837
$649$	2.83709	0.111366
$650$	0.0275977	0.00108247
$651$	−8.99656	−0.352603
$652$	15.2311	0.596496
$653$	−29.1284	−1.13988	−0.569942	−	0.821685i	$-0.693034\pi$
$653$	−29.1284	−1.13988	−0.569942	+	0.821685i	$0.693034\pi$
$654$	−3.68879	−0.144243
$655$	−20.9673	−0.819262
$656$	1.89572	0.0740156
$657$	9.32238	0.363701
$658$	7.11383	0.277326
$659$	−3.00344	−0.116997	−0.0584987	−	0.998287i	$-0.518631\pi$
$659$	−3.00344	−0.116997	−0.0584987	+	0.998287i	$0.518631\pi$
$660$	−6.38101	−0.248381
$661$	47.5241	1.84847	0.924236	−	0.381822i	$-0.124703\pi$
$661$	47.5241	1.84847	0.924236	+	0.381822i	$0.124703\pi$
$662$	−19.8827	−0.772764
$663$	−1.77846	−0.0690696
$664$	6.27674	0.243585
$665$	−33.9931	−1.31820
$666$	−8.52588	−0.330371
$667$	16.2345	0.628604
$668$	0.193945	0.00750397
$669$	−13.2802	−0.513441
$670$	5.88273	0.227270
$671$	40.5827	1.56668
$672$	2.71982	0.104919
$673$	−30.7328	−1.18466	−0.592331	−	0.805694i	$-0.701792\pi$
$673$	−30.7328	−1.18466	−0.592331	+	0.805694i	$0.701792\pi$
$674$	15.2311	0.586680
$675$	0.0586332	0.00225679
$676$	−12.7785	−0.491479
$677$	6.74742	0.259324	0.129662	−	0.991558i	$-0.458611\pi$
$677$	6.74742	0.259324	0.129662	+	0.991558i	$0.458611\pi$
$678$	−2.00000	−0.0768095
$679$	24.6379	0.945515
$680$	8.49828	0.325894
$681$	9.04564	0.346630
$682$	−9.38445	−0.359349
$683$	−47.7095	−1.82555	−0.912777	−	0.408459i	$-0.866066\pi$
$683$	−47.7095	−1.82555	−0.912777	+	0.408459i	$0.866066\pi$
$684$	5.55691	0.212474
$685$	−50.9605	−1.94710
$686$	−17.9578	−0.685632
$687$	−4.96896	−0.189578
$688$	−4.83709	−0.184412
$689$	−3.93793	−0.150023
$690$	6.87930	0.261890
$691$	32.4492	1.23443	0.617213	−	0.786796i	$-0.288262\pi$
$691$	32.4492	1.23443	0.617213	+	0.786796i	$0.288262\pi$
$692$	−22.0061	−0.836547
$693$	7.71639	0.293121
$694$	10.7880	0.409507
$695$	−21.4948	−0.815346
$696$	−5.30777	−0.201191
$697$	−7.16291	−0.271315
$698$	−19.2948	−0.730318
$699$	6.85008	0.259094
$700$	0.159472	0.00602747
$701$	−26.3388	−0.994803	−0.497402	−	0.867520i	$-0.665712\pi$
$701$	−26.3388	−0.994803	−0.497402	+	0.867520i	$0.665712\pi$
$702$	0.470683	0.0177648
$703$	−47.3776	−1.78688
$704$	2.83709	0.106927
$705$	−5.88273	−0.221557
$706$	−4.56035	−0.171631
$707$	21.1560	0.795655
$708$	1.00000	0.0375823
$709$	0.644763	0.0242146	0.0121073	−	0.999927i	$-0.496146\pi$
$709$	0.644763	0.0242146	0.0121073	+	0.999927i	$0.496146\pi$
$710$	7.67418	0.288007
$711$	2.27674	0.0853844
$712$	−17.4948	−0.655647
$713$	10.1173	0.378895
$714$	−10.2767	−0.384597
$715$	−3.00344	−0.112322
$716$	4.60256	0.172006
$717$	23.1544	0.864718
$718$	12.1741	0.454333
$719$	29.0777	1.08442	0.542208	−	0.840244i	$-0.317588\pi$
$719$	29.0777	1.08442	0.542208	+	0.840244i	$0.317588\pi$
$720$	−2.24914	−0.0838205
$721$	−26.3518	−0.981392
$722$	11.8793	0.442102
$723$	17.3354	0.644709
$724$	11.8827	0.441618
$725$	−0.311212	−0.0115581
$726$	−2.95092	−0.109519
$727$	−5.30939	−0.196914	−0.0984572	−	0.995141i	$-0.531391\pi$
$727$	−5.30939	−0.196914	−0.0984572	+	0.995141i	$0.531391\pi$
$728$	1.28018	0.0474465
$729$	1.00000	0.0370370
$730$	−20.9673	−0.776036
$731$	18.2767	0.675990
$732$	14.3043	0.528703
$733$	−44.4914	−1.64333	−0.821664	−	0.569972i	$-0.806954\pi$
$733$	−44.4914	−1.64333	−0.821664	+	0.569972i	$0.806954\pi$
$734$	2.15785	0.0796478
$735$	−0.893904	−0.0329721
$736$	−3.05863	−0.112743
$737$	−7.42054	−0.273339
$738$	1.89572	0.0697825
$739$	−17.5731	−0.646438	−0.323219	−	0.946324i	$-0.604765\pi$
$739$	−17.5731	−0.646438	−0.323219	+	0.946324i	$0.604765\pi$
$740$	19.1759	0.704920
$741$	2.61555	0.0960845
$742$	−22.7552	−0.835368
$743$	−7.46113	−0.273722	−0.136861	−	0.990590i	$-0.543701\pi$
$743$	−7.46113	−0.273722	−0.136861	+	0.990590i	$0.543701\pi$
$744$	−3.30777	−0.121269
$745$	−23.3776	−0.856488
$746$	−21.6673	−0.793296
$747$	6.27674	0.229654
$748$	−10.7198	−0.391956
$749$	−37.9087	−1.38515
$750$	11.1138	0.405820
$751$	44.0958	1.60908	0.804539	−	0.593900i	$-0.202412\pi$
$751$	44.0958	1.60908	0.804539	+	0.593900i	$0.202412\pi$
$752$	2.61555	0.0953792
$753$	20.0000	0.728841
$754$	−2.49828	−0.0909820
$755$	48.9053	1.77985
$756$	2.71982	0.0989190
$757$	−6.78801	−0.246714	−0.123357	−	0.992362i	$-0.539366\pi$
$757$	−6.78801	−0.246714	−0.123357	+	0.992362i	$0.539366\pi$
$758$	−36.7880	−1.33620
$759$	−8.67762	−0.314978
$760$	−12.4983	−0.453360
$761$	−41.7225	−1.51244	−0.756220	−	0.654318i	$-0.772956\pi$
$761$	−41.7225	−1.51244	−0.756220	+	0.654318i	$0.772956\pi$
$762$	−4.49828	−0.162956
$763$	−10.0329	−0.363214
$764$	5.38445	0.194803
$765$	8.49828	0.307256
$766$	−29.8190	−1.07741
$767$	0.470683	0.0169954
$768$	1.00000	0.0360844
$769$	−29.6121	−1.06784	−0.533920	−	0.845535i	$-0.679282\pi$
$769$	−29.6121	−1.06784	−0.533920	+	0.845535i	$0.679282\pi$
$770$	−17.3552	−0.625439
$771$	−26.9475	−0.970490
$772$	10.8371	0.390035
$773$	−37.4880	−1.34835	−0.674174	−	0.738572i	$-0.735500\pi$
$773$	−37.4880	−1.34835	−0.674174	+	0.738572i	$0.735500\pi$
$774$	−4.83709	−0.173866
$775$	−0.193945	−0.00696672
$776$	9.05863	0.325186
$777$	−23.1889	−0.831897
$778$	−5.69566	−0.204199
$779$	10.5344	0.377433
$780$	−1.05863	−0.0379051
$781$	−9.68029	−0.346388
$782$	11.5569	0.413274
$783$	−5.30777	−0.189684
$784$	0.397442	0.0141944
$785$	−52.1587	−1.86162
$786$	9.32238	0.332518
$787$	−36.1035	−1.28695	−0.643476	−	0.765467i	$-0.722508\pi$
$787$	−36.1035	−1.28695	−0.643476	+	0.765467i	$0.722508\pi$
$788$	7.24570	0.258117
$789$	0.144864	0.00515729
$790$	−5.12070	−0.182186
$791$	−5.43965	−0.193412
$792$	2.83709	0.100812
$793$	6.73281	0.239089
$794$	26.5681	0.942866
$795$	18.8172	0.667378
$796$	−19.6121	−0.695133
$797$	24.2767	0.859926	0.429963	−	0.902846i	$-0.358527\pi$
$797$	24.2767	0.859926	0.429963	+	0.902846i	$0.358527\pi$
$798$	15.1138	0.535024
$799$	−9.88273	−0.349626
$800$	0.0586332	0.00207300
$801$	−17.4948	−0.618150
$802$	−4.96735	−0.175403
$803$	26.4484	0.933345
$804$	−2.61555	−0.0922432
$805$	18.7105	0.659458
$806$	−1.55691	−0.0548400
$807$	3.83365	0.134951
$808$	7.77846	0.273645
$809$	−10.9605	−0.385350	−0.192675	−	0.981263i	$-0.561716\pi$
$809$	−10.9605	−0.385350	−0.192675	+	0.981263i	$0.561716\pi$
$810$	−2.24914	−0.0790267
$811$	−36.4492	−1.27990	−0.639952	−	0.768415i	$-0.721046\pi$
$811$	−36.4492	−1.27990	−0.639952	+	0.768415i	$0.721046\pi$
$812$	−14.4362	−0.506612
$813$	−16.6026	−0.582277
$814$	−24.1887	−0.847813
$815$	−34.2569	−1.19997
$816$	−3.77846	−0.132272
$817$	−26.8793	−0.940388
$818$	8.85008	0.309436
$819$	1.28018	0.0447330
$820$	−4.26375	−0.148897
$821$	34.0613	1.18875	0.594374	−	0.804189i	$-0.297400\pi$
$821$	34.0613	1.18875	0.594374	+	0.804189i	$0.297400\pi$
$822$	22.6578	0.790280
$823$	47.7631	1.66492	0.832458	−	0.554088i	$-0.186933\pi$
$823$	47.7631	1.66492	0.832458	+	0.554088i	$0.186933\pi$
$824$	−9.68879	−0.337525
$825$	0.166348	0.00579148
$826$	2.71982	0.0946348
$827$	−19.7914	−0.688216	−0.344108	−	0.938930i	$-0.611819\pi$
$827$	−19.7914	−0.688216	−0.344108	+	0.938930i	$0.611819\pi$
$828$	−3.05863	−0.106295
$829$	40.4362	1.40441	0.702204	−	0.711976i	$-0.252200\pi$
$829$	40.4362	1.40441	0.702204	+	0.711976i	$0.252200\pi$
$830$	−14.1173	−0.490017
$831$	−28.7259	−0.996492
$832$	0.470683	0.0163180
$833$	−1.50172	−0.0520315
$834$	9.55691	0.330929
$835$	−0.436210	−0.0150957
$836$	15.7655	0.545260
$837$	−3.30777	−0.114333
$838$	30.0682	1.03869
$839$	22.0621	0.761667	0.380834	−	0.924644i	$-0.375637\pi$
$839$	22.0621	0.761667	0.380834	+	0.924644i	$0.375637\pi$
$840$	−6.11727	−0.211066
$841$	−0.827538	−0.0285358
$842$	15.0862	0.519906
$843$	23.5991	0.812797
$844$	24.2147	0.833503
$845$	28.7405	0.988705
$846$	2.61555	0.0899244
$847$	−8.02598	−0.275776
$848$	−8.36641	−0.287304
$849$	−4.60256	−0.157959
$850$	−0.221543	−0.00759886
$851$	26.0775	0.893926
$852$	−3.41205	−0.116895
$853$	44.2829	1.51622	0.758108	−	0.652129i	$-0.226124\pi$
$853$	44.2829	1.51622	0.758108	+	0.652129i	$0.226124\pi$
$854$	38.9053	1.33131
$855$	−12.4983	−0.427432
$856$	−13.9379	−0.476389
$857$	26.9345	0.920065	0.460032	−	0.887902i	$-0.347838\pi$
$857$	26.9345	0.920065	0.460032	+	0.887902i	$0.347838\pi$
$858$	1.33537	0.0455888
$859$	39.7225	1.35531	0.677657	−	0.735378i	$-0.262995\pi$
$859$	39.7225	1.35531	0.677657	+	0.735378i	$0.262995\pi$
$860$	10.8793	0.370981
$861$	5.15603	0.175717
$862$	32.1656	1.09556
$863$	14.3810	0.489535	0.244768	−	0.969582i	$-0.421288\pi$
$863$	14.3810	0.489535	0.244768	+	0.969582i	$0.421288\pi$
$864$	1.00000	0.0340207
$865$	49.4948	1.68288
$866$	−12.1043	−0.411320
$867$	−2.72326	−0.0924868
$868$	−8.99656	−0.305363
$869$	6.45931	0.219117
$870$	11.9379	0.404734
$871$	−1.23109	−0.0417141
$872$	−3.68879	−0.124918
$873$	9.05863	0.306588
$874$	−16.9966	−0.574917
$875$	30.2277	1.02188
$876$	9.32238	0.314974
$877$	−18.8310	−0.635877	−0.317938	−	0.948111i	$-0.602991\pi$
$877$	−18.8310	−0.635877	−0.317938	+	0.948111i	$0.602991\pi$
$878$	−2.22154	−0.0749734
$879$	−0.366407	−0.0123586
$880$	−6.38101	−0.215104
$881$	35.4036	1.19278	0.596388	−	0.802696i	$-0.296602\pi$
$881$	35.4036	1.19278	0.596388	+	0.802696i	$0.296602\pi$
$882$	0.397442	0.0133826
$883$	−34.7552	−1.16960	−0.584802	−	0.811176i	$-0.698828\pi$
$883$	−34.7552	−1.16960	−0.584802	+	0.811176i	$0.698828\pi$
$884$	−1.77846	−0.0598160
$885$	−2.24914	−0.0756040
$886$	32.9475	1.10689
$887$	−8.31894	−0.279323	−0.139661	−	0.990199i	$-0.544601\pi$
$887$	−8.31894	−0.279323	−0.139661	+	0.990199i	$0.544601\pi$
$888$	−8.52588	−0.286110
$889$	−12.2345	−0.410333
$890$	39.3484	1.31896
$891$	2.83709	0.0950461
$892$	−13.2802	−0.444653
$893$	14.5344	0.486374
$894$	10.3940	0.347628
$895$	−10.3518	−0.346022
$896$	2.71982	0.0908629
$897$	−1.43965	−0.0480684
$898$	−39.8888	−1.33111
$899$	17.5569	0.585556
$900$	0.0586332	0.00195444
$901$	31.6121	1.05315
$902$	5.37834	0.179079
$903$	−13.1560	−0.437805
$904$	−2.00000	−0.0665190
$905$	−26.7259	−0.888400
$906$	−21.7440	−0.722395
$907$	−1.90184	−0.0631495	−0.0315747	−	0.999501i	$-0.510052\pi$
$907$	−1.90184	−0.0631495	−0.0315747	+	0.999501i	$0.510052\pi$
$908$	9.04564	0.300190
$909$	7.77846	0.257995
$910$	−2.87930	−0.0954477
$911$	−16.1741	−0.535871	−0.267936	−	0.963437i	$-0.586341\pi$
$911$	−16.1741	−0.535871	−0.267936	+	0.963437i	$0.586341\pi$
$912$	5.55691	0.184008
$913$	17.8077	0.589348
$914$	−0.0620710	−0.00205313
$915$	−32.1725	−1.06359
$916$	−4.96896	−0.164179
$917$	25.3552	0.837304
$918$	−3.77846	−0.124708
$919$	−54.3234	−1.79196	−0.895982	−	0.444089i	$-0.853527\pi$
$919$	−54.3234	−1.79196	−0.895982	+	0.444089i	$0.853527\pi$
$920$	6.87930	0.226804
$921$	10.2345	0.337239
$922$	18.1250	0.596915
$923$	−1.60600	−0.0528620
$924$	7.71639	0.253850
$925$	−0.499899	−0.0164366
$926$	−22.9199	−0.753194
$927$	−9.68879	−0.318222
$928$	−5.30777	−0.174236
$929$	14.6155	0.479521	0.239760	−	0.970832i	$-0.422931\pi$
$929$	14.6155	0.479521	0.239760	+	0.970832i	$0.422931\pi$
$930$	7.43965	0.243956
$931$	2.20855	0.0723824
$932$	6.85008	0.224382
$933$	−10.0828	−0.330096
$934$	−19.8337	−0.648977
$935$	24.1104	0.788494
$936$	0.470683	0.0153848
$937$	43.4519	1.41951	0.709755	−	0.704448i	$-0.248805\pi$
$937$	43.4519	1.41951	0.709755	+	0.704448i	$0.248805\pi$
$938$	−7.11383	−0.232275
$939$	−21.6121	−0.705285
$940$	−5.88273	−0.191874
$941$	−10.2637	−0.334589	−0.167294	−	0.985907i	$-0.553503\pi$
$941$	−10.2637	−0.334589	−0.167294	+	0.985907i	$0.553503\pi$
$942$	23.1905	0.755588
$943$	−5.79832	−0.188819
$944$	1.00000	0.0325472
$945$	−6.11727	−0.198995
$946$	−13.7233	−0.446182
$947$	−39.1950	−1.27367	−0.636833	−	0.771002i	$-0.719756\pi$
$947$	−39.1950	−1.27367	−0.636833	+	0.771002i	$0.719756\pi$
$948$	2.27674	0.0739450
$949$	4.38789	0.142437
$950$	0.325819	0.0105710
$951$	19.9785	0.647848
$952$	−10.2767	−0.333071
$953$	49.0940	1.59031	0.795155	−	0.606407i	$-0.207390\pi$
$953$	49.0940	1.59031	0.795155	+	0.606407i	$0.207390\pi$
$954$	−8.36641	−0.270872
$955$	−12.1104	−0.391883
$956$	23.1544	0.748867
$957$	−15.0586	−0.486776
$958$	−6.91988	−0.223571
$959$	61.6251	1.98998
$960$	−2.24914	−0.0725907
$961$	−20.0586	−0.647053
$962$	−4.01299	−0.129384
$963$	−13.9379	−0.449143
$964$	17.3354	0.558335
$965$	−24.3741	−0.784631
$966$	−8.31894	−0.267658
$967$	−11.8061	−0.379657	−0.189829	−	0.981817i	$-0.560793\pi$
$967$	−11.8061	−0.379657	−0.189829	+	0.981817i	$0.560793\pi$
$968$	−2.95092	−0.0948461
$969$	−20.9966	−0.674507
$970$	−20.3741	−0.654174
$971$	−33.5208	−1.07573	−0.537867	−	0.843030i	$-0.680770\pi$
$971$	−33.5208	−1.07573	−0.537867	+	0.843030i	$0.680770\pi$
$972$	1.00000	0.0320750
$973$	25.9931	0.833301
$974$	7.19213	0.230451
$975$	0.0275977	0.000883832 0
$976$	14.3043	0.457871
$977$	2.78801	0.0891963	0.0445982	−	0.999005i	$-0.485799\pi$
$977$	2.78801	0.0891963	0.0445982	+	0.999005i	$0.485799\pi$
$978$	15.2311	0.487037
$979$	−49.6344	−1.58632
$980$	−0.893904	−0.0285547
$981$	−3.68879	−0.117774
$982$	33.9379	1.08300
$983$	33.0518	1.05419	0.527094	−	0.849807i	$-0.323282\pi$
$983$	33.0518	1.05419	0.527094	+	0.849807i	$0.323282\pi$
$984$	1.89572	0.0604335
$985$	−16.2966	−0.519253
$986$	20.0552	0.638688
$987$	7.11383	0.226436
$988$	2.61555	0.0832116
$989$	14.7949	0.470450
$990$	−6.38101	−0.202802
$991$	−8.41473	−0.267303	−0.133651	−	0.991028i	$-0.542670\pi$
$991$	−8.41473	−0.267303	−0.133651	+	0.991028i	$0.542670\pi$
$992$	−3.30777	−0.105022
$993$	−19.8827	−0.630959
$994$	−9.28018	−0.294349
$995$	44.1104	1.39839
$996$	6.27674	0.198886
$997$	47.0518	1.49014	0.745072	−	0.666984i	$-0.232415\pi$
$997$	47.0518	1.49014	0.745072	+	0.666984i	$0.232415\pi$
$998$	−14.4622	−0.457793
$999$	−8.52588	−0.269747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.a.h.1.1	✓	3
3.2	odd	2		1062.2.a.n.1.3		3
4.3	odd	2		2832.2.a.r.1.1		3
5.4	even	2		8850.2.a.bu.1.1		3
12.11	even	2		8496.2.a.bi.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.a.h.1.1	✓	3	1.1	even	1	trivial
1062.2.a.n.1.3		3	3.2	odd	2
2832.2.a.r.1.1		3	4.3	odd	2
8496.2.a.bi.1.3		3	12.11	even	2
8850.2.a.bu.1.1		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.24914 q^{5} +1.00000 q^{6} +2.71982 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.24914 q^{5} +1.00000 q^{6} +2.71982 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.24914 q^{10} +2.83709 q^{11} +1.00000 q^{12} +0.470683 q^{13} +2.71982 q^{14} -2.24914 q^{15} +1.00000 q^{16} -3.77846 q^{17} +1.00000 q^{18} +5.55691 q^{19} -2.24914 q^{20} +2.71982 q^{21} +2.83709 q^{22} -3.05863 q^{23} +1.00000 q^{24} +0.0586332 q^{25} +0.470683 q^{26} +1.00000 q^{27} +2.71982 q^{28} -5.30777 q^{29} -2.24914 q^{30} -3.30777 q^{31} +1.00000 q^{32} +2.83709 q^{33} -3.77846 q^{34} -6.11727 q^{35} +1.00000 q^{36} -8.52588 q^{37} +5.55691 q^{38} +0.470683 q^{39} -2.24914 q^{40} +1.89572 q^{41} +2.71982 q^{42} -4.83709 q^{43} +2.83709 q^{44} -2.24914 q^{45} -3.05863 q^{46} +2.61555 q^{47} +1.00000 q^{48} +0.397442 q^{49} +0.0586332 q^{50} -3.77846 q^{51} +0.470683 q^{52} -8.36641 q^{53} +1.00000 q^{54} -6.38101 q^{55} +2.71982 q^{56} +5.55691 q^{57} -5.30777 q^{58} +1.00000 q^{59} -2.24914 q^{60} +14.3043 q^{61} -3.30777 q^{62} +2.71982 q^{63} +1.00000 q^{64} -1.05863 q^{65} +2.83709 q^{66} -2.61555 q^{67} -3.77846 q^{68} -3.05863 q^{69} -6.11727 q^{70} -3.41205 q^{71} +1.00000 q^{72} +9.32238 q^{73} -8.52588 q^{74} +0.0586332 q^{75} +5.55691 q^{76} +7.71639 q^{77} +0.470683 q^{78} +2.27674 q^{79} -2.24914 q^{80} +1.00000 q^{81} +1.89572 q^{82} +6.27674 q^{83} +2.71982 q^{84} +8.49828 q^{85} -4.83709 q^{86} -5.30777 q^{87} +2.83709 q^{88} -17.4948 q^{89} -2.24914 q^{90} +1.28018 q^{91} -3.05863 q^{92} -3.30777 q^{93} +2.61555 q^{94} -12.4983 q^{95} +1.00000 q^{96} +9.05863 q^{97} +0.397442 q^{98} +2.83709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 3 q^{6} - q^{7} + 3 q^{8} + 3 q^{9} + 2 q^{10} + q^{11} + 3 q^{12} + q^{13} - q^{14} + 2 q^{15} + 3 q^{16} - 3 q^{17} + 3 q^{18} + 2 q^{20} - q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + q^{25} + q^{26} + 3 q^{27} - q^{28} - 8 q^{29} + 2 q^{30} - 2 q^{31} + 3 q^{32} + q^{33} - 3 q^{34} - 20 q^{35} + 3 q^{36} + 9 q^{37} + q^{39} + 2 q^{40} - q^{41} - q^{42} - 7 q^{43} + q^{44} + 2 q^{45} - 10 q^{46} - 8 q^{47} + 3 q^{48} + 12 q^{49} + q^{50} - 3 q^{51} + q^{52} - 18 q^{53} + 3 q^{54} - q^{56} - 8 q^{58} + 3 q^{59} + 2 q^{60} - 2 q^{62} - q^{63} + 3 q^{64} - 4 q^{65} + q^{66} + 8 q^{67} - 3 q^{68} - 10 q^{69} - 20 q^{70} - 9 q^{71} + 3 q^{72} + 8 q^{73} + 9 q^{74} + q^{75} - 21 q^{77} + q^{78} - 19 q^{79} + 2 q^{80} + 3 q^{81} - q^{82} - 7 q^{83} - q^{84} + 8 q^{85} - 7 q^{86} - 8 q^{87} + q^{88} + 2 q^{90} + 13 q^{91} - 10 q^{92} - 2 q^{93} - 8 q^{94} - 20 q^{95} + 3 q^{96} + 28 q^{97} + 12 q^{98} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 3 * q^6 - q^7 + 3 * q^8 + 3 * q^9 + 2 * q^10 + q^11 + 3 * q^12 + q^13 - q^14 + 2 * q^15 + 3 * q^16 - 3 * q^17 + 3 * q^18 + 2 * q^20 - q^21 + q^22 - 10 * q^23 + 3 * q^24 + q^25 + q^26 + 3 * q^27 - q^28 - 8 * q^29 + 2 * q^30 - 2 * q^31 + 3 * q^32 + q^33 - 3 * q^34 - 20 * q^35 + 3 * q^36 + 9 * q^37 + q^39 + 2 * q^40 - q^41 - q^42 - 7 * q^43 + q^44 + 2 * q^45 - 10 * q^46 - 8 * q^47 + 3 * q^48 + 12 * q^49 + q^50 - 3 * q^51 + q^52 - 18 * q^53 + 3 * q^54 - q^56 - 8 * q^58 + 3 * q^59 + 2 * q^60 - 2 * q^62 - q^63 + 3 * q^64 - 4 * q^65 + q^66 + 8 * q^67 - 3 * q^68 - 10 * q^69 - 20 * q^70 - 9 * q^71 + 3 * q^72 + 8 * q^73 + 9 * q^74 + q^75 - 21 * q^77 + q^78 - 19 * q^79 + 2 * q^80 + 3 * q^81 - q^82 - 7 * q^83 - q^84 + 8 * q^85 - 7 * q^86 - 8 * q^87 + q^88 + 2 * q^90 + 13 * q^91 - 10 * q^92 - 2 * q^93 - 8 * q^94 - 20 * q^95 + 3 * q^96 + 28 * q^97 + 12 * q^98 + q^99

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