LMFDB - Embedded newform 7942.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.469.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 4 $ x^3 - x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.16425$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.16425 q^{3} +1.00000 q^{4} -0.683969 q^{5} +1.16425 q^{6} -0.316031 q^{7} -1.00000 q^{8} -1.64453 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.16425 q^{3} +1.00000 q^{4} -0.683969 q^{5} +1.16425 q^{6} -0.316031 q^{7} -1.00000 q^{8} -1.64453 q^{9} +0.683969 q^{10} +1.00000 q^{11} -1.16425 q^{12} +0.316031 q^{13} +0.316031 q^{14} +0.796310 q^{15} +1.00000 q^{16} -1.84822 q^{17} +1.64453 q^{18} -0.683969 q^{20} +0.367938 q^{21} -1.00000 q^{22} -4.48028 q^{23} +1.16425 q^{24} -4.53219 q^{25} -0.316031 q^{26} +5.40738 q^{27} -0.316031 q^{28} -5.49274 q^{29} -0.796310 q^{30} -0.796310 q^{31} -1.00000 q^{32} -1.16425 q^{33} +1.84822 q^{34} +0.216155 q^{35} -1.64453 q^{36} -0.632062 q^{37} -0.367938 q^{39} +0.683969 q^{40} +3.83575 q^{41} -0.367938 q^{42} +6.68397 q^{43} +1.00000 q^{44} +1.12481 q^{45} +4.48028 q^{46} -4.32850 q^{47} -1.16425 q^{48} -6.90012 q^{49} +4.53219 q^{50} +2.15178 q^{51} +0.316031 q^{52} +3.44084 q^{53} -5.40738 q^{54} -0.683969 q^{55} +0.316031 q^{56} +5.49274 q^{58} +2.80877 q^{59} +0.796310 q^{60} -12.0249 q^{61} +0.796310 q^{62} +0.519721 q^{63} +1.00000 q^{64} -0.216155 q^{65} +1.16425 q^{66} -10.7483 q^{67} -1.84822 q^{68} +5.21616 q^{69} -0.216155 q^{70} +13.0125 q^{71} +1.64453 q^{72} +3.44084 q^{73} +0.632062 q^{74} +5.27659 q^{75} -0.316031 q^{77} +0.367938 q^{78} -9.06437 q^{79} -0.683969 q^{80} -1.36195 q^{81} -3.83575 q^{82} -4.35547 q^{83} +0.367938 q^{84} +1.26412 q^{85} -6.68397 q^{86} +6.39492 q^{87} -1.00000 q^{88} +9.28905 q^{89} -1.12481 q^{90} -0.0998755 q^{91} -4.48028 q^{92} +0.927102 q^{93} +4.32850 q^{94} +1.16425 q^{96} +3.69643 q^{97} +6.90012 q^{98} -1.64453 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 3 q^{8} + 7 q^{9} - q^{10} + 3 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{14} + q^{15} + 3 q^{16} + 5 q^{17} - 7 q^{18} + q^{20} - 5 q^{21} - 3 q^{22} - 9 q^{23} - 4 q^{24} - 4 q^{26} + 19 q^{27} - 4 q^{28} + 6 q^{29} - q^{30} - q^{31} - 3 q^{32} + 4 q^{33} - 5 q^{34} - 16 q^{35} + 7 q^{36} - 8 q^{37} + 5 q^{39} - q^{40} + 19 q^{41} + 5 q^{42} + 17 q^{43} + 3 q^{44} - 13 q^{45} + 9 q^{46} + 2 q^{47} + 4 q^{48} - q^{49} + 17 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + q^{55} + 4 q^{56} - 6 q^{58} - 11 q^{59} + q^{60} + q^{62} + 6 q^{63} + 3 q^{64} + 16 q^{65} - 4 q^{66} - 2 q^{67} + 5 q^{68} - q^{69} + 16 q^{70} + 21 q^{71} - 7 q^{72} - 3 q^{73} + 8 q^{74} + 10 q^{75} - 4 q^{77} - 5 q^{78} + q^{80} + 27 q^{81} - 19 q^{82} - 25 q^{83} - 5 q^{84} + 16 q^{85} - 17 q^{86} + 40 q^{87} - 3 q^{88} + 4 q^{89} + 13 q^{90} - 20 q^{91} - 9 q^{92} + 10 q^{93} - 2 q^{94} - 4 q^{96} - 10 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 3 * q^8 + 7 * q^9 - q^10 + 3 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^14 + q^15 + 3 * q^16 + 5 * q^17 - 7 * q^18 + q^20 - 5 * q^21 - 3 * q^22 - 9 * q^23 - 4 * q^24 - 4 * q^26 + 19 * q^27 - 4 * q^28 + 6 * q^29 - q^30 - q^31 - 3 * q^32 + 4 * q^33 - 5 * q^34 - 16 * q^35 + 7 * q^36 - 8 * q^37 + 5 * q^39 - q^40 + 19 * q^41 + 5 * q^42 + 17 * q^43 + 3 * q^44 - 13 * q^45 + 9 * q^46 + 2 * q^47 + 4 * q^48 - q^49 + 17 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + q^55 + 4 * q^56 - 6 * q^58 - 11 * q^59 + q^60 + q^62 + 6 * q^63 + 3 * q^64 + 16 * q^65 - 4 * q^66 - 2 * q^67 + 5 * q^68 - q^69 + 16 * q^70 + 21 * q^71 - 7 * q^72 - 3 * q^73 + 8 * q^74 + 10 * q^75 - 4 * q^77 - 5 * q^78 + q^80 + 27 * q^81 - 19 * q^82 - 25 * q^83 - 5 * q^84 + 16 * q^85 - 17 * q^86 + 40 * q^87 - 3 * q^88 + 4 * q^89 + 13 * q^90 - 20 * q^91 - 9 * q^92 + 10 * q^93 - 2 * q^94 - 4 * q^96 - 10 * q^97 + q^98 + 7 * 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
$3$	−1.16425	−0.672179	−0.336089	−	0.941830i	$-0.609104\pi$
$3$	−1.16425	−0.672179	−0.336089	+	0.941830i	$0.609104\pi$
$4$	1.00000	0.500000
$5$	−0.683969	−0.305880	−0.152940	−	0.988235i	$-0.548874\pi$
$5$	−0.683969	−0.305880	−0.152940	+	0.988235i	$0.548874\pi$
$6$	1.16425	0.475302
$7$	−0.316031	−0.119448	−0.0597242	−	0.998215i	$-0.519022\pi$
$7$	−0.316031	−0.119448	−0.0597242	+	0.998215i	$0.519022\pi$
$8$	−1.00000	−0.353553
$9$	−1.64453	−0.548176
$10$	0.683969	0.216290
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.16425	−0.336089
$13$	0.316031	0.0876512	0.0438256	−	0.999039i	$-0.486045\pi$
$13$	0.316031	0.0876512	0.0438256	+	0.999039i	$0.486045\pi$
$14$	0.316031	0.0844628
$15$	0.796310	0.205606
$16$	1.00000	0.250000
$17$	−1.84822	−0.448258	−0.224129	−	0.974559i	$-0.571954\pi$
$17$	−1.84822	−0.448258	−0.224129	+	0.974559i	$0.571954\pi$
$18$	1.64453	0.387619
$19$	0	0
$19$	0	0
$20$	−0.683969	−0.152940
$21$	0.367938	0.0802907
$22$	−1.00000	−0.213201
$23$	−4.48028	−0.934203	−0.467101	−	0.884204i	$-0.654702\pi$
$23$	−4.48028	−0.934203	−0.467101	+	0.884204i	$0.654702\pi$
$24$	1.16425	0.237651
$25$	−4.53219	−0.906437
$26$	−0.316031	−0.0619788
$27$	5.40738	1.04065
$28$	−0.316031	−0.0597242
$29$	−5.49274	−1.01998	−0.509988	−	0.860181i	$-0.670350\pi$
$29$	−5.49274	−1.01998	−0.509988	+	0.860181i	$0.670350\pi$
$30$	−0.796310	−0.145386
$31$	−0.796310	−0.143021	−0.0715107	−	0.997440i	$-0.522782\pi$
$31$	−0.796310	−0.143021	−0.0715107	+	0.997440i	$0.522782\pi$
$32$	−1.00000	−0.176777
$33$	−1.16425	−0.202670
$34$	1.84822	0.316967
$35$	0.216155	0.0365369
$36$	−1.64453	−0.274088
$37$	−0.632062	−0.103910	−0.0519552	−	0.998649i	$-0.516545\pi$
$37$	−0.632062	−0.103910	−0.0519552	+	0.998649i	$0.516545\pi$
$38$	0	0
$39$	−0.367938	−0.0589173
$40$	0.683969	0.108145
$41$	3.83575	0.599044	0.299522	−	0.954089i	$-0.403173\pi$
$41$	3.83575	0.599044	0.299522	+	0.954089i	$0.403173\pi$
$42$	−0.367938	−0.0567741
$43$	6.68397	1.01930	0.509648	−	0.860383i	$-0.329776\pi$
$43$	6.68397	1.01930	0.509648	+	0.860383i	$0.329776\pi$
$44$	1.00000	0.150756
$45$	1.12481	0.167676
$46$	4.48028	0.660581
$47$	−4.32850	−0.631376	−0.315688	−	0.948863i	$-0.602235\pi$
$47$	−4.32850	−0.631376	−0.315688	+	0.948863i	$0.602235\pi$
$48$	−1.16425	−0.168045
$49$	−6.90012	−0.985732
$50$	4.53219	0.640948
$51$	2.15178	0.301310
$52$	0.316031	0.0438256
$53$	3.44084	0.472635	0.236318	−	0.971676i	$-0.424059\pi$
$53$	3.44084	0.472635	0.236318	+	0.971676i	$0.424059\pi$
$54$	−5.40738	−0.735851
$55$	−0.683969	−0.0922264
$56$	0.316031	0.0422314
$57$	0	0
$58$	5.49274	0.721233
$59$	2.80877	0.365671	0.182836	−	0.983143i	$-0.441472\pi$
$59$	2.80877	0.365671	0.182836	+	0.983143i	$0.441472\pi$
$60$	0.796310	0.102803
$61$	−12.0249	−1.53963	−0.769817	−	0.638264i	$-0.779653\pi$
$61$	−12.0249	−1.53963	−0.769817	+	0.638264i	$0.779653\pi$
$62$	0.796310	0.101131
$63$	0.519721	0.0654787
$64$	1.00000	0.125000
$65$	−0.216155	−0.0268108
$66$	1.16425	0.143309
$67$	−10.7483	−1.31312	−0.656559	−	0.754274i	$-0.727989\pi$
$67$	−10.7483	−1.31312	−0.656559	+	0.754274i	$0.727989\pi$
$68$	−1.84822	−0.224129
$69$	5.21616	0.627951
$70$	−0.216155	−0.0258355
$71$	13.0125	1.54430	0.772148	−	0.635443i	$-0.219183\pi$
$71$	13.0125	1.54430	0.772148	+	0.635443i	$0.219183\pi$
$72$	1.64453	0.193809
$73$	3.44084	0.402719	0.201360	−	0.979517i	$-0.435464\pi$
$73$	3.44084	0.402719	0.201360	+	0.979517i	$0.435464\pi$
$74$	0.632062	0.0734757
$75$	5.27659	0.609288
$76$	0	0
$77$	−0.316031	−0.0360151
$78$	0.367938	0.0416608
$79$	−9.06437	−1.01982	−0.509911	−	0.860227i	$-0.670322\pi$
$79$	−9.06437	−1.01982	−0.509911	+	0.860227i	$0.670322\pi$
$80$	−0.683969	−0.0764701
$81$	−1.36195	−0.151328
$82$	−3.83575	−0.423588
$83$	−4.35547	−0.478075	−0.239038	−	0.971010i	$-0.576832\pi$
$83$	−4.35547	−0.478075	−0.239038	+	0.971010i	$0.576832\pi$
$84$	0.367938	0.0401454
$85$	1.26412	0.137113
$86$	−6.68397	−0.720751
$87$	6.39492	0.685607
$88$	−1.00000	−0.106600
$89$	9.28905	0.984638	0.492319	−	0.870415i	$-0.336149\pi$
$89$	9.28905	0.984638	0.492319	+	0.870415i	$0.336149\pi$
$90$	−1.12481	−0.118565
$91$	−0.0998755	−0.0104698
$92$	−4.48028	−0.467101
$93$	0.927102	0.0961360
$94$	4.32850	0.446450
$95$	0	0
$96$	1.16425	0.118826
$97$	3.69643	0.375316	0.187658	−	0.982234i	$-0.439910\pi$
$97$	3.69643	0.375316	0.187658	+	0.982234i	$0.439910\pi$
$98$	6.90012	0.697018
$99$	−1.64453	−0.165281
$100$	−4.53219	−0.453219
$101$	−10.6570	−1.06041	−0.530205	−	0.847869i	$-0.677885\pi$
$101$	−10.6570	−1.06041	−0.530205	+	0.847869i	$0.677885\pi$
$102$	−2.15178	−0.213058
$103$	0.355473	0.0350258	0.0175129	−	0.999847i	$-0.494425\pi$
$103$	0.355473	0.0350258	0.0175129	+	0.999847i	$0.494425\pi$
$104$	−0.316031	−0.0309894
$105$	−0.251658	−0.0245593
$106$	−3.44084	−0.334204
$107$	7.51972	0.726959	0.363479	−	0.931602i	$-0.381589\pi$
$107$	7.51972	0.726959	0.363479	+	0.931602i	$0.381589\pi$
$108$	5.40738	0.520325
$109$	6.07290	0.581678	0.290839	−	0.956772i	$-0.406066\pi$
$109$	6.07290	0.581678	0.290839	+	0.956772i	$0.406066\pi$
$110$	0.683969	0.0652139
$111$	0.735877	0.0698463
$112$	−0.316031	−0.0298621
$113$	−5.06437	−0.476416	−0.238208	−	0.971214i	$-0.576560\pi$
$113$	−5.06437	−0.476416	−0.238208	+	0.971214i	$0.576560\pi$
$114$	0	0
$115$	3.06437	0.285754
$116$	−5.49274	−0.509988
$117$	−0.519721	−0.0480482
$118$	−2.80877	−0.258569
$119$	0.584094	0.0535438
$120$	−0.796310	−0.0726928
$121$	1.00000	0.0909091
$122$	12.0249	1.08869
$123$	−4.46577	−0.402665
$124$	−0.796310	−0.0715107
$125$	6.51972	0.583142
$126$	−0.519721	−0.0463004
$127$	5.67150	0.503265	0.251632	−	0.967823i	$-0.419033\pi$
$127$	5.67150	0.503265	0.251632	+	0.967823i	$0.419033\pi$
$128$	−1.00000	−0.0883883
$129$	−7.78180	−0.685149
$130$	0.216155	0.0189581
$131$	−7.20369	−0.629389	−0.314695	−	0.949193i	$-0.601902\pi$
$131$	−7.20369	−0.629389	−0.314695	+	0.949193i	$0.601902\pi$
$132$	−1.16425	−0.101335
$133$	0	0
$134$	10.7483	0.928515
$135$	−3.69848	−0.318315
$136$	1.84822	0.158483
$137$	−5.90865	−0.504810	−0.252405	−	0.967622i	$-0.581222\pi$
$137$	−5.90865	−0.504810	−0.252405	+	0.967622i	$0.581222\pi$
$138$	−5.21616	−0.444029
$139$	−4.90865	−0.416346	−0.208173	−	0.978092i	$-0.566752\pi$
$139$	−4.90865	−0.416346	−0.208173	+	0.978092i	$0.566752\pi$
$140$	0.216155	0.0182685
$141$	5.03944	0.424398
$142$	−13.0125	−1.09198
$143$	0.316031	0.0264278
$144$	−1.64453	−0.137044
$145$	3.75687	0.311991
$146$	−3.44084	−0.284766
$147$	8.03346	0.662588
$148$	−0.632062	−0.0519552
$149$	−5.61755	−0.460208	−0.230104	−	0.973166i	$-0.573907\pi$
$149$	−5.61755	−0.460208	−0.230104	+	0.973166i	$0.573907\pi$
$150$	−5.27659	−0.430832
$151$	−5.92112	−0.481854	−0.240927	−	0.970543i	$-0.577451\pi$
$151$	−5.92112	−0.481854	−0.240927	+	0.970543i	$0.577451\pi$
$152$	0	0
$153$	3.03944	0.245724
$154$	0.316031	0.0254665
$155$	0.544651	0.0437474
$156$	−0.367938	−0.0294586
$157$	−4.78778	−0.382107	−0.191053	−	0.981580i	$-0.561190\pi$
$157$	−4.78778	−0.382107	−0.191053	+	0.981580i	$0.561190\pi$
$158$	9.06437	0.721123
$159$	−4.00599	−0.317695
$160$	0.683969	0.0540725
$161$	1.41591	0.111589
$162$	1.36195	0.107005
$163$	−8.98549	−0.703798	−0.351899	−	0.936038i	$-0.614464\pi$
$163$	−8.98549	−0.703798	−0.351899	+	0.936038i	$0.614464\pi$
$164$	3.83575	0.299522
$165$	0.796310	0.0619926
$166$	4.35547	0.338050
$167$	5.34301	0.413454	0.206727	−	0.978399i	$-0.433719\pi$
$167$	5.34301	0.413454	0.206727	+	0.978399i	$0.433719\pi$
$168$	−0.367938	−0.0283871
$169$	−12.9001	−0.992317
$170$	−1.26412	−0.0969538
$171$	0	0
$172$	6.68397	0.509648
$173$	−17.3659	−1.32030	−0.660152	−	0.751132i	$-0.729508\pi$
$173$	−17.3659	−1.32030	−0.660152	+	0.751132i	$0.729508\pi$
$174$	−6.39492	−0.484797
$175$	1.43231	0.108273
$176$	1.00000	0.0753778
$177$	−3.27011	−0.245797
$178$	−9.28905	−0.696244
$179$	10.1642	0.759712	0.379856	−	0.925046i	$-0.375974\pi$
$179$	10.1642	0.759712	0.379856	+	0.925046i	$0.375974\pi$
$180$	1.12481	0.0838381
$181$	8.02493	0.596488	0.298244	−	0.954490i	$-0.403599\pi$
$181$	8.02493	0.596488	0.298244	+	0.954490i	$0.403599\pi$
$182$	0.0998755	0.00740326
$183$	14.0000	1.03491
$184$	4.48028	0.330291
$185$	0.432311	0.0317841
$186$	−0.927102	−0.0679784
$187$	−1.84822	−0.135155
$188$	−4.32850	−0.315688
$189$	−1.70890	−0.124304
$190$	0	0
$191$	15.4658	1.11906	0.559532	−	0.828809i	$-0.310981\pi$
$191$	15.4658	1.11906	0.559532	+	0.828809i	$0.310981\pi$
$192$	−1.16425	−0.0840224
$193$	−23.9730	−1.72562	−0.862808	−	0.505532i	$-0.831296\pi$
$193$	−23.9730	−1.72562	−0.862808	+	0.505532i	$0.831296\pi$
$194$	−3.69643	−0.265389
$195$	0.251658	0.0180216
$196$	−6.90012	−0.492866
$197$	16.4323	1.17075	0.585377	−	0.810761i	$-0.300947\pi$
$197$	16.4323	1.17075	0.585377	+	0.810761i	$0.300947\pi$
$198$	1.64453	0.116871
$199$	−0.376464	−0.0266868	−0.0133434	−	0.999911i	$-0.504247\pi$
$199$	−0.376464	−0.0266868	−0.0133434	+	0.999911i	$0.504247\pi$
$200$	4.53219	0.320474
$201$	12.5137	0.882651
$202$	10.6570	0.749823
$203$	1.73588	0.121835
$204$	2.15178	0.150655
$205$	−2.62354	−0.183236
$206$	−0.355473	−0.0247670
$207$	7.36794	0.512107
$208$	0.316031	0.0219128
$209$	0	0
$210$	0.251658	0.0173661
$211$	−15.4658	−1.06471	−0.532354	−	0.846522i	$-0.678692\pi$
$211$	−15.4658	−1.06471	−0.532354	+	0.846522i	$0.678692\pi$
$212$	3.44084	0.236318
$213$	−15.1497	−1.03804
$214$	−7.51972	−0.514038
$215$	−4.57163	−0.311782
$216$	−5.40738	−0.367926
$217$	0.251658	0.0170837
$218$	−6.07290	−0.411309
$219$	−4.00599	−0.270699
$220$	−0.683969	−0.0461132
$221$	−0.584094	−0.0392904
$222$	−0.735877	−0.0493888
$223$	21.6175	1.44762	0.723809	−	0.690000i	$-0.242390\pi$
$223$	21.6175	1.44762	0.723809	+	0.690000i	$0.242390\pi$
$224$	0.316031	0.0211157
$225$	7.45330	0.496887
$226$	5.06437	0.336877
$227$	1.51972	0.100867	0.0504337	−	0.998727i	$-0.483940\pi$
$227$	1.51972	0.100867	0.0504337	+	0.998727i	$0.483940\pi$
$228$	0	0
$229$	−3.22862	−0.213353	−0.106677	−	0.994294i	$-0.534021\pi$
$229$	−3.22862	−0.213353	−0.106677	+	0.994294i	$0.534021\pi$
$230$	−3.06437	−0.202059
$231$	0.367938	0.0242086
$232$	5.49274	0.360616
$233$	19.0893	1.25058	0.625291	−	0.780392i	$-0.284980\pi$
$233$	19.0893	1.25058	0.625291	+	0.780392i	$0.284980\pi$
$234$	0.519721	0.0339752
$235$	2.96056	0.193125
$236$	2.80877	0.182836
$237$	10.5532	0.685503
$238$	−0.584094	−0.0378612
$239$	1.26806	0.0820242	0.0410121	−	0.999159i	$-0.486942\pi$
$239$	1.26806	0.0820242	0.0410121	+	0.999159i	$0.486942\pi$
$240$	0.796310	0.0514016
$241$	18.7089	1.20515	0.602573	−	0.798064i	$-0.294142\pi$
$241$	18.7089	1.20515	0.602573	+	0.798064i	$0.294142\pi$
$242$	−1.00000	−0.0642824
$243$	−14.6365	−0.938931
$244$	−12.0249	−0.769817
$245$	4.71947	0.301516
$246$	4.46577	0.284727
$247$	0	0
$248$	0.796310	0.0505657
$249$	5.07085	0.321352
$250$	−6.51972	−0.412343
$251$	2.35343	0.148547	0.0742735	−	0.997238i	$-0.476336\pi$
$251$	2.35343	0.148547	0.0742735	+	0.997238i	$0.476336\pi$
$252$	0.519721	0.0327394
$253$	−4.48028	−0.281673
$254$	−5.67150	−0.355862
$255$	−1.47175	−0.0921648
$256$	1.00000	0.0625000
$257$	−11.2891	−0.704192	−0.352096	−	0.935964i	$-0.614531\pi$
$257$	−11.2891	−0.704192	−0.352096	+	0.935964i	$0.614531\pi$
$258$	7.78180	0.484474
$259$	0.199751	0.0124119
$260$	−0.216155	−0.0134054
$261$	9.03296	0.559126
$262$	7.20369	0.445045
$263$	11.2621	0.694449	0.347225	−	0.937782i	$-0.387124\pi$
$263$	11.2621	0.694449	0.347225	+	0.937782i	$0.387124\pi$
$264$	1.16425	0.0716545
$265$	−2.35343	−0.144570
$266$	0	0
$267$	−10.8148	−0.661853
$268$	−10.7483	−0.656559
$269$	1.44682	0.0882144	0.0441072	−	0.999027i	$-0.485956\pi$
$269$	1.44682	0.0882144	0.0441072	+	0.999027i	$0.485956\pi$
$270$	3.69848	0.225082
$271$	15.1977	0.923195	0.461597	−	0.887090i	$-0.347276\pi$
$271$	15.1977	0.923195	0.461597	+	0.887090i	$0.347276\pi$
$272$	−1.84822	−0.112065
$273$	0.116280	0.00703758
$274$	5.90865	0.356955
$275$	−4.53219	−0.273301
$276$	5.21616	0.313976
$277$	0.303566	0.0182395	0.00911975	−	0.999958i	$-0.497097\pi$
$277$	0.303566	0.0182395	0.00911975	+	0.999958i	$0.497097\pi$
$278$	4.90865	0.294401
$279$	1.30955	0.0784009
$280$	−0.216155	−0.0129178
$281$	13.4448	0.802048	0.401024	−	0.916068i	$-0.368654\pi$
$281$	13.4448	0.802048	0.401024	+	0.916068i	$0.368654\pi$
$282$	−5.03944	−0.300094
$283$	−12.1642	−0.723089	−0.361545	−	0.932355i	$-0.617751\pi$
$283$	−12.1642	−0.723089	−0.361545	+	0.932355i	$0.617751\pi$
$284$	13.0125	0.772148
$285$	0	0
$286$	−0.316031	−0.0186873
$287$	−1.21222	−0.0715548
$288$	1.64453	0.0969047
$289$	−13.5841	−0.799064
$290$	−3.75687	−0.220611
$291$	−4.30357	−0.252279
$292$	3.44084	0.201360
$293$	21.6051	1.26218	0.631091	−	0.775709i	$-0.282607\pi$
$293$	21.6051	1.26218	0.631091	+	0.775709i	$0.282607\pi$
$294$	−8.03346	−0.468521
$295$	−1.92112	−0.111852
$296$	0.632062	0.0367378
$297$	5.40738	0.313768
$298$	5.61755	0.325416
$299$	−1.41591	−0.0818840
$300$	5.27659	0.304644
$301$	−2.11234	−0.121753
$302$	5.92112	0.340722
$303$	12.4074	0.712785
$304$	0	0
$305$	8.22468	0.470944
$306$	−3.03944	−0.173753
$307$	−11.7214	−0.668974	−0.334487	−	0.942400i	$-0.608563\pi$
$307$	−11.7214	−0.668974	−0.334487	+	0.942400i	$0.608563\pi$
$308$	−0.316031	−0.0180075
$309$	−0.413859	−0.0235436
$310$	−0.544651	−0.0309341
$311$	−11.1622	−0.632950	−0.316475	−	0.948601i	$-0.602499\pi$
$311$	−11.1622	−0.632950	−0.316475	+	0.948601i	$0.602499\pi$
$312$	0.367938	0.0208304
$313$	13.7963	0.779814	0.389907	−	0.920854i	$-0.372507\pi$
$313$	13.7963	0.779814	0.389907	+	0.920854i	$0.372507\pi$
$314$	4.78778	0.270190
$315$	−0.355473	−0.0200286
$316$	−9.06437	−0.509911
$317$	16.1767	0.908575	0.454287	−	0.890855i	$-0.349894\pi$
$317$	16.1767	0.908575	0.454287	+	0.890855i	$0.349894\pi$
$318$	4.00599	0.224645
$319$	−5.49274	−0.307535
$320$	−0.683969	−0.0382350
$321$	−8.75482	−0.488646
$322$	−1.41591	−0.0789054
$323$	0	0
$324$	−1.36195	−0.0756640
$325$	−1.43231	−0.0794503
$326$	8.98549	0.497660
$327$	−7.07036	−0.390992
$328$	−3.83575	−0.211794
$329$	1.36794	0.0754169
$330$	−0.796310	−0.0438354
$331$	18.5820	1.02136	0.510681	−	0.859770i	$-0.329393\pi$
$331$	18.5820	1.02136	0.510681	+	0.859770i	$0.329393\pi$
$332$	−4.35547	−0.239038
$333$	1.03944	0.0569611
$334$	−5.34301	−0.292356
$335$	7.35153	0.401657
$336$	0.367938	0.0200727
$337$	25.1497	1.36999	0.684997	−	0.728546i	$-0.259804\pi$
$337$	25.1497	1.36999	0.684997	+	0.728546i	$0.259804\pi$
$338$	12.9001	0.701674
$339$	5.89619	0.320237
$340$	1.26412	0.0685567
$341$	−0.796310	−0.0431226
$342$	0	0
$343$	4.39287	0.237193
$344$	−6.68397	−0.360375
$345$	−3.56769	−0.192078
$346$	17.3659	0.933596
$347$	18.5781	0.997325	0.498663	−	0.866796i	$-0.333825\pi$
$347$	18.5781	0.997325	0.498663	+	0.866796i	$0.333825\pi$
$348$	6.39492	0.342803
$349$	−18.6819	−1.00002	−0.500010	−	0.866020i	$-0.666670\pi$
$349$	−18.6819	−1.00002	−0.500010	+	0.866020i	$0.666670\pi$
$350$	−1.43231	−0.0765602
$351$	1.70890	0.0912143
$352$	−1.00000	−0.0533002
$353$	1.92710	0.102569	0.0512846	−	0.998684i	$-0.483668\pi$
$353$	1.92710	0.102569	0.0512846	+	0.998684i	$0.483668\pi$
$354$	3.27011	0.173804
$355$	−8.90012	−0.472370
$356$	9.28905	0.492319
$357$	−0.680030	−0.0359910
$358$	−10.1642	−0.537197
$359$	5.30152	0.279803	0.139902	−	0.990165i	$-0.455321\pi$
$359$	5.30152	0.279803	0.139902	+	0.990165i	$0.455321\pi$
$360$	−1.12481	−0.0592825
$361$	0	0
$362$	−8.02493	−0.421781
$363$	−1.16425	−0.0611072
$364$	−0.0998755	−0.00523490
$365$	−2.35343	−0.123184
$366$	−14.0000	−0.731792
$367$	−8.10381	−0.423016	−0.211508	−	0.977376i	$-0.567837\pi$
$367$	−8.10381	−0.423016	−0.211508	+	0.977376i	$0.567837\pi$
$368$	−4.48028	−0.233551
$369$	−6.30800	−0.328381
$370$	−0.432311	−0.0224748
$371$	−1.08741	−0.0564555
$372$	0.927102	0.0480680
$373$	22.9645	1.18906	0.594528	−	0.804075i	$-0.297339\pi$
$373$	22.9645	1.18906	0.594528	+	0.804075i	$0.297339\pi$
$374$	1.84822	0.0955690
$375$	−7.59057	−0.391975
$376$	4.32850	0.223225
$377$	−1.73588	−0.0894022
$378$	1.70890	0.0878963
$379$	−13.1557	−0.675764	−0.337882	−	0.941188i	$-0.609710\pi$
$379$	−13.1557	−0.675764	−0.337882	+	0.941188i	$0.609710\pi$
$380$	0	0
$381$	−6.60304	−0.338284
$382$	−15.4658	−0.791297
$383$	−25.8067	−1.31866	−0.659331	−	0.751853i	$-0.729160\pi$
$383$	−25.8067	−1.31866	−0.659331	+	0.751853i	$0.729160\pi$
$384$	1.16425	0.0594128
$385$	0.216155	0.0110163
$386$	23.9730	1.22019
$387$	−10.9920	−0.558753
$388$	3.69643	0.187658
$389$	11.0125	0.558354	0.279177	−	0.960240i	$-0.409938\pi$
$389$	11.0125	0.558354	0.279177	+	0.960240i	$0.409938\pi$
$390$	−0.251658	−0.0127432
$391$	8.28053	0.418764
$392$	6.90012	0.348509
$393$	8.38688	0.423062
$394$	−16.4323	−0.827848
$395$	6.19975	0.311943
$396$	−1.64453	−0.0826406
$397$	15.5820	0.782040	0.391020	−	0.920382i	$-0.372122\pi$
$397$	15.5820	0.782040	0.391020	+	0.920382i	$0.372122\pi$
$398$	0.376464	0.0188704
$399$	0	0
$400$	−4.53219	−0.226609
$401$	−22.8817	−1.14266	−0.571328	−	0.820722i	$-0.693572\pi$
$401$	−22.8817	−1.14266	−0.571328	+	0.820722i	$0.693572\pi$
$402$	−12.5137	−0.624128
$403$	−0.251658	−0.0125360
$404$	−10.6570	−0.530205
$405$	0.931533	0.0462882
$406$	−1.73588	−0.0861501
$407$	−0.632062	−0.0313301
$408$	−2.15178	−0.106529
$409$	−19.4198	−0.960250	−0.480125	−	0.877200i	$-0.659409\pi$
$409$	−19.4198	−0.960250	−0.480125	+	0.877200i	$0.659409\pi$
$410$	2.62354	0.129567
$411$	6.87913	0.339323
$412$	0.355473	0.0175129
$413$	−0.887659	−0.0436789
$414$	−7.36794	−0.362114
$415$	2.97901	0.146234
$416$	−0.316031	−0.0154947
$417$	5.71489	0.279859
$418$	0	0
$419$	−15.2891	−0.746919	−0.373460	−	0.927646i	$-0.621829\pi$
$419$	−15.2891	−0.746919	−0.373460	+	0.927646i	$0.621829\pi$
$420$	−0.251658	−0.0122797
$421$	3.99401	0.194656	0.0973281	−	0.995252i	$-0.468970\pi$
$421$	3.99401	0.194656	0.0973281	+	0.995252i	$0.468970\pi$
$422$	15.4658	0.752862
$423$	7.11833	0.346105
$424$	−3.44084	−0.167102
$425$	8.37646	0.406318
$426$	15.1497	0.734007
$427$	3.80025	0.183907
$428$	7.51972	0.363479
$429$	−0.367938	−0.0177642
$430$	4.57163	0.220464
$431$	19.8252	0.954945	0.477473	−	0.878647i	$-0.341553\pi$
$431$	19.8252	0.954945	0.477473	+	0.878647i	$0.341553\pi$
$432$	5.40738	0.260163
$433$	16.2745	0.782105	0.391052	−	0.920368i	$-0.372111\pi$
$433$	16.2745	0.782105	0.391052	+	0.920368i	$0.372111\pi$
$434$	−0.251658	−0.0120800
$435$	−4.37392	−0.209714
$436$	6.07290	0.290839
$437$	0	0
$438$	4.00599	0.191413
$439$	−39.7463	−1.89699	−0.948494	−	0.316796i	$-0.897393\pi$
$439$	−39.7463	−1.89699	−0.948494	+	0.316796i	$0.897393\pi$
$440$	0.683969	0.0326069
$441$	11.3474	0.540354
$442$	0.584094	0.0277825
$443$	−35.0353	−1.66458	−0.832290	−	0.554341i	$-0.812970\pi$
$443$	−35.0353	−1.66458	−0.832290	+	0.554341i	$0.812970\pi$
$444$	0.735877	0.0349232
$445$	−6.35343	−0.301181
$446$	−21.6175	−1.02362
$447$	6.54022	0.309342
$448$	−0.316031	−0.0149311
$449$	26.9606	1.27235	0.636174	−	0.771546i	$-0.280516\pi$
$449$	26.9606	1.27235	0.636174	+	0.771546i	$0.280516\pi$
$450$	−7.45330	−0.351352
$451$	3.83575	0.180619
$452$	−5.06437	−0.238208
$453$	6.89365	0.323892
$454$	−1.51972	−0.0713240
$455$	0.0683118	0.00320250
$456$	0	0
$457$	3.54465	0.165812	0.0829059	−	0.996557i	$-0.473580\pi$
$457$	3.54465	0.165812	0.0829059	+	0.996557i	$0.473580\pi$
$458$	3.22862	0.150864
$459$	−9.99401	−0.466481
$460$	3.06437	0.142877
$461$	−19.1682	−0.892751	−0.446376	−	0.894846i	$-0.647286\pi$
$461$	−19.1682	−0.892751	−0.446376	+	0.894846i	$0.647286\pi$
$462$	−0.367938	−0.0171180
$463$	31.7214	1.47422	0.737108	−	0.675775i	$-0.236191\pi$
$463$	31.7214	1.47422	0.737108	+	0.675775i	$0.236191\pi$
$464$	−5.49274	−0.254994
$465$	−0.634109	−0.0294061
$466$	−19.0893	−0.884295
$467$	−3.21017	−0.148549	−0.0742744	−	0.997238i	$-0.523664\pi$
$467$	−3.21017	−0.148549	−0.0742744	+	0.997238i	$0.523664\pi$
$468$	−0.519721	−0.0240241
$469$	3.39681	0.156850
$470$	−2.96056	−0.136560
$471$	5.57417	0.256844
$472$	−2.80877	−0.129284
$473$	6.68397	0.307329
$474$	−10.5532	−0.484723
$475$	0	0
$476$	0.584094	0.0267719
$477$	−5.65855	−0.259087
$478$	−1.26806	−0.0579998
$479$	−0.243133	−0.0111090	−0.00555451	−	0.999985i	$-0.501768\pi$
$479$	−0.243133	−0.0111090	−0.00555451	+	0.999985i	$0.501768\pi$
$480$	−0.796310	−0.0363464
$481$	−0.199751	−0.00910786
$482$	−18.7089	−0.852167
$483$	−1.64847	−0.0750078
$484$	1.00000	0.0454545
$485$	−2.52825	−0.114802
$486$	14.6365	0.663925
$487$	−28.5091	−1.29187	−0.645936	−	0.763391i	$-0.723533\pi$
$487$	−28.5091	−1.29187	−0.645936	+	0.763391i	$0.723533\pi$
$488$	12.0249	0.544343
$489$	10.4613	0.473078
$490$	−4.71947	−0.213204
$491$	3.17876	0.143455	0.0717277	−	0.997424i	$-0.477149\pi$
$491$	3.17876	0.143455	0.0717277	+	0.997424i	$0.477149\pi$
$492$	−4.46577	−0.201332
$493$	10.1518	0.457213
$494$	0	0
$495$	1.12481	0.0505562
$496$	−0.796310	−0.0357554
$497$	−4.11234	−0.184464
$498$	−5.07085	−0.227230
$499$	25.1313	1.12503	0.562515	−	0.826787i	$-0.309834\pi$
$499$	25.1313	1.12503	0.562515	+	0.826787i	$0.309834\pi$
$500$	6.51972	0.291571
$501$	−6.22059	−0.277915
$502$	−2.35343	−0.105039
$503$	41.7673	1.86231	0.931156	−	0.364622i	$-0.118802\pi$
$503$	41.7673	1.86231	0.931156	+	0.364622i	$0.118802\pi$
$504$	−0.519721	−0.0231502
$505$	7.28905	0.324359
$506$	4.48028	0.199173
$507$	15.0189	0.667015
$508$	5.67150	0.251632
$509$	26.1707	1.16000	0.579999	−	0.814618i	$-0.303053\pi$
$509$	26.1707	1.16000	0.579999	+	0.814618i	$0.303053\pi$
$510$	1.47175	0.0651703
$511$	−1.08741	−0.0481042
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	11.2891	0.497939
$515$	−0.243133	−0.0107137
$516$	−7.78180	−0.342575
$517$	−4.32850	−0.190367
$518$	−0.199751	−0.00877656
$519$	20.2182	0.887481
$520$	0.216155	0.00947904
$521$	−14.0249	−0.614443	−0.307222	−	0.951638i	$-0.599399\pi$
$521$	−14.0249	−0.614443	−0.307222	+	0.951638i	$0.599399\pi$
$522$	−9.03296	−0.395362
$523$	26.0978	1.14118	0.570589	−	0.821236i	$-0.306715\pi$
$523$	26.0978	1.14118	0.570589	+	0.821236i	$0.306715\pi$
$524$	−7.20369	−0.314695
$525$	−1.66756	−0.0727785
$526$	−11.2621	−0.491050
$527$	1.47175	0.0641106
$528$	−1.16425	−0.0506674
$529$	−2.92710	−0.127265
$530$	2.35343	0.102226
$531$	−4.61911	−0.200452
$532$	0	0
$533$	1.21222	0.0525069
$534$	10.8148	0.468000
$535$	−5.14326	−0.222362
$536$	10.7483	0.464258
$537$	−11.8337	−0.510662
$538$	−1.44682	−0.0623770
$539$	−6.90012	−0.297209
$540$	−3.69848	−0.159157
$541$	16.0000	0.687894	0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000	0.687894	0.343947	+	0.938989i	$0.388236\pi$
$542$	−15.1977	−0.652797
$543$	−9.34301	−0.400947
$544$	1.84822	0.0792417
$545$	−4.15367	−0.177924
$546$	−0.116280	−0.00497632
$547$	−0.760807	−0.0325297	−0.0162649	−	0.999868i	$-0.505177\pi$
$547$	−0.760807	−0.0325297	−0.0162649	+	0.999868i	$0.505177\pi$
$548$	−5.90865	−0.252405
$549$	19.7753	0.843990
$550$	4.53219	0.193253
$551$	0	0
$552$	−5.21616	−0.222014
$553$	2.86462	0.121816
$554$	−0.303566	−0.0128973
$555$	−0.503317	−0.0213646
$556$	−4.90865	−0.208173
$557$	23.0104	0.974983	0.487491	−	0.873128i	$-0.337912\pi$
$557$	23.0104	0.974983	0.487491	+	0.873128i	$0.337912\pi$
$558$	−1.30955	−0.0554378
$559$	2.11234	0.0893425
$560$	0.216155	0.00913423
$561$	2.15178	0.0908483
$562$	−13.4448	−0.567134
$563$	10.4074	0.438619	0.219309	−	0.975655i	$-0.429620\pi$
$563$	10.4074	0.438619	0.219309	+	0.975655i	$0.429620\pi$
$564$	5.03944	0.212199
$565$	3.46387	0.145726
$566$	12.1642	0.511301
$567$	0.430419	0.0180759
$568$	−13.0125	−0.545991
$569$	−13.7818	−0.577763	−0.288881	−	0.957365i	$-0.593283\pi$
$569$	−13.7818	−0.577763	−0.288881	+	0.957365i	$0.593283\pi$
$570$	0	0
$571$	−36.8212	−1.54092	−0.770460	−	0.637488i	$-0.779974\pi$
$571$	−36.8212	−1.54092	−0.770460	+	0.637488i	$0.779974\pi$
$572$	0.316031	0.0132139
$573$	−18.0060	−0.752211
$574$	1.21222	0.0505969
$575$	20.3055	0.846796
$576$	−1.64453	−0.0685219
$577$	38.4697	1.60151	0.800757	−	0.598989i	$-0.204431\pi$
$577$	38.4697	1.60151	0.800757	+	0.598989i	$0.204431\pi$
$578$	13.5841	0.565024
$579$	27.9105	1.15992
$580$	3.75687	0.155995
$581$	1.37646	0.0571053
$582$	4.30357	0.178389
$583$	3.44084	0.142505
$584$	−3.44084	−0.142383
$585$	0.355473	0.0146970
$586$	−21.6051	−0.892498
$587$	30.2326	1.24783	0.623916	−	0.781492i	$-0.285541\pi$
$587$	30.2326	1.24783	0.623916	+	0.781492i	$0.285541\pi$
$588$	8.03346	0.331294
$589$	0	0
$590$	1.92112	0.0790911
$591$	−19.1313	−0.786956
$592$	−0.632062	−0.0259776
$593$	7.64248	0.313839	0.156920	−	0.987611i	$-0.449844\pi$
$593$	7.64248	0.313839	0.156920	+	0.987611i	$0.449844\pi$
$594$	−5.40738	−0.221868
$595$	−0.399502	−0.0163780
$596$	−5.61755	−0.230104
$597$	0.438297	0.0179383
$598$	1.41591	0.0579007
$599$	−0.804835	−0.0328847	−0.0164423	−	0.999865i	$-0.505234\pi$
$599$	−0.804835	−0.0328847	−0.0164423	+	0.999865i	$0.505234\pi$
$600$	−5.27659	−0.215416
$601$	14.0854	0.574554	0.287277	−	0.957848i	$-0.407250\pi$
$601$	14.0854	0.574554	0.287277	+	0.957848i	$0.407250\pi$
$602$	2.11234	0.0860926
$603$	17.6759	0.719820
$604$	−5.92112	−0.240927
$605$	−0.683969	−0.0278073
$606$	−12.4074	−0.504015
$607$	24.4323	0.991677	0.495838	−	0.868415i	$-0.334861\pi$
$607$	24.4323	0.991677	0.495838	+	0.868415i	$0.334861\pi$
$608$	0	0
$609$	−2.02099	−0.0818947
$610$	−8.22468	−0.333008
$611$	−1.36794	−0.0553409
$612$	3.03944	0.122862
$613$	10.7857	0.435632	0.217816	−	0.975990i	$-0.430107\pi$
$613$	10.7857	0.435632	0.217816	+	0.975990i	$0.430107\pi$
$614$	11.7214	0.473036
$615$	3.05445	0.123167
$616$	0.316031	0.0127332
$617$	−1.68996	−0.0680351	−0.0340175	−	0.999421i	$-0.510830\pi$
$617$	−1.68996	−0.0680351	−0.0340175	+	0.999421i	$0.510830\pi$
$618$	0.413859	0.0166479
$619$	31.0353	1.24742	0.623708	−	0.781657i	$-0.285625\pi$
$619$	31.0353	1.24742	0.623708	+	0.781657i	$0.285625\pi$
$620$	0.544651	0.0218737
$621$	−24.2266	−0.972179
$622$	11.1622	0.447563
$623$	−2.93563	−0.117613
$624$	−0.367938	−0.0147293
$625$	18.2016	0.728066
$626$	−13.7963	−0.551411
$627$	0	0
$628$	−4.78778	−0.191053
$629$	1.16819	0.0465787
$630$	0.355473	0.0141624
$631$	35.6674	1.41990	0.709949	−	0.704254i	$-0.248718\pi$
$631$	35.6674	1.41990	0.709949	+	0.704254i	$0.248718\pi$
$632$	9.06437	0.360561
$633$	18.0060	0.715674
$634$	−16.1767	−0.642459
$635$	−3.87913	−0.153939
$636$	−4.00599	−0.158848
$637$	−2.18065	−0.0864006
$638$	5.49274	0.217460
$639$	−21.3993	−0.846545
$640$	0.683969	0.0270363
$641$	12.1707	0.480715	0.240357	−	0.970684i	$-0.422735\pi$
$641$	12.1707	0.480715	0.240357	+	0.970684i	$0.422735\pi$
$642$	8.75482	0.345525
$643$	14.8028	0.583765	0.291882	−	0.956454i	$-0.405718\pi$
$643$	14.8028	0.583765	0.291882	+	0.956454i	$0.405718\pi$
$644$	1.41591	0.0557945
$645$	5.32251	0.209574
$646$	0	0
$647$	−49.1871	−1.93375	−0.966873	−	0.255259i	$-0.917839\pi$
$647$	−49.1871	−1.93375	−0.966873	+	0.255259i	$0.917839\pi$
$648$	1.36195	0.0535025
$649$	2.80877	0.110254
$650$	1.43231	0.0561798
$651$	−0.292993	−0.0114833
$652$	−8.98549	−0.351899
$653$	−11.8358	−0.463169	−0.231584	−	0.972815i	$-0.574391\pi$
$653$	−11.8358	−0.463169	−0.231584	+	0.972815i	$0.574391\pi$
$654$	7.07036	0.276473
$655$	4.92710	0.192518
$656$	3.83575	0.149761
$657$	−5.65855	−0.220761
$658$	−1.36794	−0.0533278
$659$	−37.6194	−1.46545	−0.732723	−	0.680527i	$-0.761751\pi$
$659$	−37.6194	−1.46545	−0.732723	+	0.680527i	$0.761751\pi$
$660$	0.796310	0.0309963
$661$	26.6879	1.03804	0.519020	−	0.854762i	$-0.326297\pi$
$661$	26.6879	1.03804	0.519020	+	0.854762i	$0.326297\pi$
$662$	−18.5820	−0.722212
$663$	0.680030	0.0264102
$664$	4.35547	0.169025
$665$	0	0
$666$	−1.03944	−0.0402776
$667$	24.6090	0.952865
$668$	5.34301	0.206727
$669$	−25.1682	−0.973058
$670$	−7.35153	−0.284015
$671$	−12.0249	−0.464217
$672$	−0.367938	−0.0141935
$673$	33.1747	1.27879	0.639395	−	0.768879i	$-0.279185\pi$
$673$	33.1747	1.27879	0.639395	+	0.768879i	$0.279185\pi$
$674$	−25.1497	−0.968732
$675$	−24.5073	−0.943285
$676$	−12.9001	−0.496159
$677$	48.7818	1.87484	0.937418	−	0.348205i	$-0.113209\pi$
$677$	48.7818	1.87484	0.937418	+	0.348205i	$0.113209\pi$
$678$	−5.89619	−0.226442
$679$	−1.16819	−0.0448309
$680$	−1.26412	−0.0484769
$681$	−1.76933	−0.0678010
$682$	0.796310	0.0304923
$683$	1.47175	0.0563151	0.0281575	−	0.999603i	$-0.491036\pi$
$683$	1.47175	0.0563151	0.0281575	+	0.999603i	$0.491036\pi$
$684$	0	0
$685$	4.04133	0.154411
$686$	−4.39287	−0.167720
$687$	3.75891	0.143412
$688$	6.68397	0.254824
$689$	1.08741	0.0414270
$690$	3.56769	0.135820
$691$	18.9066	0.719241	0.359621	−	0.933099i	$-0.382906\pi$
$691$	18.9066	0.719241	0.359621	+	0.933099i	$0.382906\pi$
$692$	−17.3659	−0.660152
$693$	0.519721	0.0197426
$694$	−18.5781	−0.705215
$695$	3.35737	0.127352
$696$	−6.39492	−0.242399
$697$	−7.08930	−0.268526
$698$	18.6819	0.707121
$699$	−22.2247	−0.840615
$700$	1.43231	0.0541363
$701$	29.0353	1.09665	0.548325	−	0.836265i	$-0.315266\pi$
$701$	29.0353	1.09665	0.548325	+	0.836265i	$0.315266\pi$
$702$	−1.70890	−0.0644982
$703$	0	0
$704$	1.00000	0.0376889
$705$	−3.44682	−0.129815
$706$	−1.92710	−0.0725274
$707$	3.36794	0.126664
$708$	−3.27011	−0.122898
$709$	15.6531	0.587863	0.293931	−	0.955827i	$-0.405036\pi$
$709$	15.6531	0.587863	0.293931	+	0.955827i	$0.405036\pi$
$710$	8.90012	0.334016
$711$	14.9066	0.559041
$712$	−9.28905	−0.348122
$713$	3.56769	0.133611
$714$	0.680030	0.0254495
$715$	−0.216155	−0.00808375
$716$	10.1642	0.379856
$717$	−1.47634	−0.0551349
$718$	−5.30152	−0.197851
$719$	24.4553	0.912031	0.456015	−	0.889972i	$-0.349276\pi$
$719$	24.4553	0.912031	0.456015	+	0.889972i	$0.349276\pi$
$720$	1.12481	0.0419190
$721$	−0.112341	−0.00418378
$722$	0	0
$723$	−21.7818	−0.810074
$724$	8.02493	0.298244
$725$	24.8941	0.924545
$726$	1.16425	0.0432093
$727$	2.75891	0.102322	0.0511612	−	0.998690i	$-0.483708\pi$
$727$	2.75891	0.102322	0.0511612	+	0.998690i	$0.483708\pi$
$728$	0.0998755	0.00370163
$729$	21.1264	0.782458
$730$	2.35343	0.0871042
$731$	−12.3534	−0.456908
$732$	14.0000	0.517455
$733$	−17.0394	−0.629366	−0.314683	−	0.949197i	$-0.601898\pi$
$733$	−17.0394	−0.629366	−0.314683	+	0.949197i	$0.601898\pi$
$734$	8.10381	0.299117
$735$	−5.49464	−0.202673
$736$	4.48028	0.165145
$737$	−10.7483	−0.395920
$738$	6.30800	0.232201
$739$	−29.5656	−1.08759	−0.543795	−	0.839218i	$-0.683013\pi$
$739$	−29.5656	−1.08759	−0.543795	+	0.839218i	$0.683013\pi$
$740$	0.432311	0.0158921
$741$	0	0
$742$	1.08741	0.0399201
$743$	33.6175	1.23331	0.616654	−	0.787234i	$-0.288488\pi$
$743$	33.6175	1.23331	0.616654	+	0.787234i	$0.288488\pi$
$744$	−0.927102	−0.0339892
$745$	3.84223	0.140768
$746$	−22.9645	−0.840790
$747$	7.16269	0.262069
$748$	−1.84822	−0.0675775
$749$	−2.37646	−0.0868341
$750$	7.59057	0.277168
$751$	−51.7463	−1.88825	−0.944125	−	0.329589i	$-0.893090\pi$
$751$	−51.7463	−1.88825	−0.944125	+	0.329589i	$0.893090\pi$
$752$	−4.32850	−0.157844
$753$	−2.73997	−0.0998501
$754$	1.73588	0.0632169
$755$	4.04986	0.147389
$756$	−1.70890	−0.0621521
$757$	5.23715	0.190347	0.0951737	−	0.995461i	$-0.469659\pi$
$757$	5.23715	0.190347	0.0951737	+	0.995461i	$0.469659\pi$
$758$	13.1557	0.477837
$759$	5.21616	0.189334
$760$	0	0
$761$	38.8047	1.40667	0.703334	−	0.710859i	$-0.251694\pi$
$761$	38.8047	1.40667	0.703334	+	0.710859i	$0.251694\pi$
$762$	6.60304	0.239203
$763$	−1.91922	−0.0694805
$764$	15.4658	0.559532
$765$	−2.07888	−0.0751622
$766$	25.8067	0.932435
$767$	0.887659	0.0320515
$768$	−1.16425	−0.0420112
$769$	10.1767	0.366982	0.183491	−	0.983021i	$-0.441260\pi$
$769$	10.1767	0.366982	0.183491	+	0.983021i	$0.441260\pi$
$770$	−0.216155	−0.00778970
$771$	13.1433	0.473343
$772$	−23.9730	−0.862808
$773$	38.3055	1.37775	0.688876	−	0.724879i	$-0.258105\pi$
$773$	38.3055	1.37775	0.688876	+	0.724879i	$0.258105\pi$
$774$	10.9920	0.395098
$775$	3.60902	0.129640
$776$	−3.69643	−0.132694
$777$	−0.232560	−0.00834303
$778$	−11.0125	−0.394816
$779$	0	0
$780$	0.251658	0.00901082
$781$	13.0125	0.465623
$782$	−8.28053	−0.296111
$783$	−29.7014	−1.06144
$784$	−6.90012	−0.246433
$785$	3.27470	0.116879
$786$	−8.38688	−0.299150
$787$	15.7523	0.561508	0.280754	−	0.959780i	$-0.409415\pi$
$787$	15.7523	0.561508	0.280754	+	0.959780i	$0.409415\pi$
$788$	16.4323	0.585377
$789$	−13.1118	−0.466794
$790$	−6.19975	−0.220577
$791$	1.60050	0.0569072
$792$	1.64453	0.0584357
$793$	−3.80025	−0.134951
$794$	−15.5820	−0.552986
$795$	2.73997	0.0971768
$796$	−0.376464	−0.0133434
$797$	−34.0439	−1.20590	−0.602948	−	0.797781i	$-0.706007\pi$
$797$	−34.0439	−1.20590	−0.602948	+	0.797781i	$0.706007\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	4.53219	0.160237
$801$	−15.2761	−0.539754
$802$	22.8817	0.807980
$803$	3.44084	0.121424
$804$	12.5137	0.441325
$805$	−0.968436	−0.0341329
$806$	0.251658	0.00886429
$807$	−1.68446	−0.0592958
$808$	10.6570	0.374912
$809$	20.7050	0.727948	0.363974	−	0.931409i	$-0.381420\pi$
$809$	20.7050	0.727948	0.363974	+	0.931409i	$0.381420\pi$
$810$	−0.931533	−0.0327307
$811$	−10.1228	−0.355458	−0.177729	−	0.984079i	$-0.556875\pi$
$811$	−10.1228	−0.355458	−0.177729	+	0.984079i	$0.556875\pi$
$812$	1.73588	0.0609173
$813$	−17.6939	−0.620552
$814$	0.632062	0.0221538
$815$	6.14580	0.215278
$816$	2.15178	0.0753275
$817$	0	0
$818$	19.4198	0.678999
$819$	0.164248	0.00573929
$820$	−2.62354	−0.0916179
$821$	14.7779	0.515751	0.257875	−	0.966178i	$-0.416978\pi$
$821$	14.7779	0.515751	0.257875	+	0.966178i	$0.416978\pi$
$822$	−6.87913	−0.239937
$823$	4.25560	0.148341	0.0741704	−	0.997246i	$-0.476369\pi$
$823$	4.25560	0.148341	0.0741704	+	0.997246i	$0.476369\pi$
$824$	−0.355473	−0.0123835
$825$	5.27659	0.183707
$826$	0.887659	0.0308856
$827$	8.48028	0.294888	0.147444	−	0.989070i	$-0.452895\pi$
$827$	8.48028	0.294888	0.147444	+	0.989070i	$0.452895\pi$
$828$	7.36794	0.256054
$829$	−39.5447	−1.37344	−0.686721	−	0.726921i	$-0.740951\pi$
$829$	−39.5447	−1.37344	−0.686721	+	0.726921i	$0.740951\pi$
$830$	−2.97901	−0.103403
$831$	−0.353426	−0.0122602
$832$	0.316031	0.0109564
$833$	12.7529	0.441863
$834$	−5.71489	−0.197890
$835$	−3.65445	−0.126468
$836$	0	0
$837$	−4.30595	−0.148835
$838$	15.2891	0.528152
$839$	33.5237	1.15737	0.578683	−	0.815553i	$-0.303567\pi$
$839$	33.5237	1.15737	0.578683	+	0.815553i	$0.303567\pi$
$840$	0.251658	0.00868304
$841$	1.17023	0.0403529
$842$	−3.99401	−0.137643
$843$	−15.6531	−0.539120
$844$	−15.4658	−0.532354
$845$	8.82329	0.303530
$846$	−7.11833	−0.244733
$847$	−0.316031	−0.0108589
$848$	3.44084	0.118159
$849$	14.1622	0.486045
$850$	−8.37646	−0.287310
$851$	2.83181	0.0970733
$852$	−15.1497	−0.519021
$853$	−15.3679	−0.526188	−0.263094	−	0.964770i	$-0.584743\pi$
$853$	−15.3679	−0.526188	−0.263094	+	0.964770i	$0.584743\pi$
$854$	−3.80025	−0.130042
$855$	0	0
$856$	−7.51972	−0.257019
$857$	13.5861	0.464094	0.232047	−	0.972705i	$-0.425458\pi$
$857$	13.5861	0.464094	0.232047	+	0.972705i	$0.425458\pi$
$858$	0.367938	0.0125612
$859$	48.0748	1.64029	0.820145	−	0.572155i	$-0.193893\pi$
$859$	48.0748	1.64029	0.820145	+	0.572155i	$0.193893\pi$
$860$	−4.57163	−0.155891
$861$	1.41132	0.0480977
$862$	−19.8252	−0.675248
$863$	21.9894	0.748529	0.374264	−	0.927322i	$-0.377895\pi$
$863$	21.9894	0.748529	0.374264	+	0.927322i	$0.377895\pi$
$864$	−5.40738	−0.183963
$865$	11.8777	0.403855
$866$	−16.2745	−0.553031
$867$	15.8153	0.537114
$868$	0.251658	0.00854184
$869$	−9.06437	−0.307488
$870$	4.37392	0.148290
$871$	−3.39681	−0.115096
$872$	−6.07290	−0.205654
$873$	−6.07888	−0.205739
$874$	0	0
$875$	−2.06043	−0.0696554
$876$	−4.00599	−0.135350
$877$	10.3075	0.348060	0.174030	−	0.984740i	$-0.444321\pi$
$877$	10.3075	0.348060	0.174030	+	0.984740i	$0.444321\pi$
$878$	39.7463	1.34137
$879$	−25.1537	−0.848412
$880$	−0.683969	−0.0230566
$881$	39.8317	1.34196	0.670981	−	0.741474i	$-0.265873\pi$
$881$	39.8317	1.34196	0.670981	+	0.741474i	$0.265873\pi$
$882$	−11.3474	−0.382088
$883$	−13.6715	−0.460083	−0.230041	−	0.973181i	$-0.573886\pi$
$883$	−13.6715	−0.460083	−0.230041	+	0.973181i	$0.573886\pi$
$884$	−0.584094	−0.0196452
$885$	2.23665	0.0751843
$886$	35.0353	1.17704
$887$	4.63206	0.155529	0.0777647	−	0.996972i	$-0.475222\pi$
$887$	4.63206	0.155529	0.0777647	+	0.996972i	$0.475222\pi$
$888$	−0.735877	−0.0246944
$889$	−1.79237	−0.0601142
$890$	6.35343	0.212967
$891$	−1.36195	−0.0456271
$892$	21.6175	0.723809
$893$	0	0
$894$	−6.54022	−0.218738
$895$	−6.95203	−0.232381
$896$	0.316031	0.0105579
$897$	1.64847	0.0550407
$898$	−26.9606	−0.899685
$899$	4.37392	0.145879
$900$	7.45330	0.248443
$901$	−6.35941	−0.211863
$902$	−3.83575	−0.127717
$903$	2.45929	0.0818400
$904$	5.06437	0.168439
$905$	−5.48880	−0.182454
$906$	−6.89365	−0.229026
$907$	15.1622	0.503453	0.251726	−	0.967798i	$-0.419002\pi$
$907$	15.1622	0.503453	0.251726	+	0.967798i	$0.419002\pi$
$908$	1.51972	0.0504337
$909$	17.5257	0.581291
$910$	−0.0683118	−0.00226451
$911$	28.4992	0.944221	0.472111	−	0.881539i	$-0.343492\pi$
$911$	28.4992	0.944221	0.472111	+	0.881539i	$0.343492\pi$
$912$	0	0
$913$	−4.35547	−0.144145
$914$	−3.54465	−0.117247
$915$	−9.57557	−0.316559
$916$	−3.22862	−0.106677
$917$	2.27659	0.0751796
$918$	9.99401	0.329852
$919$	−3.13522	−0.103421	−0.0517107	−	0.998662i	$-0.516467\pi$
$919$	−3.13522	−0.103421	−0.0517107	+	0.998662i	$0.516467\pi$
$920$	−3.06437	−0.101029
$921$	13.6466	0.449670
$922$	19.1682	0.631271
$923$	4.11234	0.135359
$924$	0.367938	0.0121043
$925$	2.86462	0.0941882
$926$	−31.7214	−1.04243
$927$	−0.584585	−0.0192003
$928$	5.49274	0.180308
$929$	3.38040	0.110907	0.0554537	−	0.998461i	$-0.482339\pi$
$929$	3.38040	0.110907	0.0554537	+	0.998461i	$0.482339\pi$
$930$	0.634109	0.0207933
$931$	0	0
$932$	19.0893	0.625291
$933$	12.9956	0.425456
$934$	3.21017	0.105040
$935$	1.26412	0.0413413
$936$	0.519721	0.0169876
$937$	−44.5011	−1.45379	−0.726894	−	0.686750i	$-0.759037\pi$
$937$	−44.5011	−1.45379	−0.726894	+	0.686750i	$0.759037\pi$
$938$	−3.39681	−0.110910
$939$	−16.0623	−0.524174
$940$	2.96056	0.0965627
$941$	43.7403	1.42589	0.712947	−	0.701218i	$-0.247360\pi$
$941$	43.7403	1.42589	0.712947	+	0.701218i	$0.247360\pi$
$942$	−5.57417	−0.181616
$943$	−17.1852	−0.559628
$944$	2.80877	0.0914178
$945$	1.16883	0.0380222
$946$	−6.68397	−0.217315
$947$	49.0603	1.59424	0.797122	−	0.603818i	$-0.206355\pi$
$947$	49.0603	1.59424	0.797122	+	0.603818i	$0.206355\pi$
$948$	10.5532	0.342751
$949$	1.08741	0.0352988
$950$	0	0
$951$	−18.8337	−0.610725
$952$	−0.584094	−0.0189306
$953$	49.0893	1.59016	0.795079	−	0.606506i	$-0.207429\pi$
$953$	49.0893	1.59016	0.795079	+	0.606506i	$0.207429\pi$
$954$	5.65855	0.183202
$955$	−10.5781	−0.342300
$956$	1.26806	0.0410121
$957$	6.39492	0.206718
$958$	0.243133	0.00785526
$959$	1.86732	0.0602988
$960$	0.796310	0.0257008
$961$	−30.3659	−0.979545
$962$	0.199751	0.00644023
$963$	−12.3664	−0.398501
$964$	18.7089	0.602573
$965$	16.3968	0.527832
$966$	1.64847	0.0530385
$967$	−0.764901	−0.0245976	−0.0122988	−	0.999924i	$-0.503915\pi$
$967$	−0.764901	−0.0245976	−0.0122988	+	0.999924i	$0.503915\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	2.52825	0.0811771
$971$	−38.8127	−1.24556	−0.622780	−	0.782397i	$-0.713997\pi$
$971$	−38.8127	−1.24556	−0.622780	+	0.782397i	$0.713997\pi$
$972$	−14.6365	−0.469466
$973$	1.55128	0.0497319
$974$	28.5091	0.913492
$975$	1.66756	0.0534048
$976$	−12.0249	−0.384909
$977$	2.00000	0.0639857	0.0319928	−	0.999488i	$-0.489815\pi$
$977$	2.00000	0.0639857	0.0319928	+	0.999488i	$0.489815\pi$
$978$	−10.4613	−0.334517
$979$	9.28905	0.296879
$980$	4.71947	0.150758
$981$	−9.98704	−0.318862
$982$	−3.17876	−0.101438
$983$	−34.4388	−1.09843	−0.549213	−	0.835682i	$-0.685073\pi$
$983$	−34.4388	−1.09843	−0.549213	+	0.835682i	$0.685073\pi$
$984$	4.46577	0.142363
$985$	−11.2392	−0.358110
$986$	−10.1518	−0.323299
$987$	−1.59262	−0.0506936
$988$	0	0
$989$	−29.9460	−0.952229
$990$	−1.12481	−0.0357487
$991$	12.5426	0.398429	0.199214	−	0.979956i	$-0.436161\pi$
$991$	12.5426	0.398429	0.199214	+	0.979956i	$0.436161\pi$
$992$	0.796310	0.0252829
$993$	−21.6341	−0.686538
$994$	4.11234	0.130436
$995$	0.257490	0.00816297
$996$	5.07085	0.160676
$997$	15.4468	0.489206	0.244603	−	0.969623i	$-0.421342\pi$
$997$	15.4468	0.489206	0.244603	+	0.969623i	$0.421342\pi$
$998$	−25.1313	−0.795517
$999$	−3.41780	−0.108134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bf.1.1	✓	3
19.18	odd	2		7942.2.a.bg.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.bf.1.1	✓	3	1.1	even	1	trivial
7942.2.a.bg.1.3	yes	3	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.16425 q^{3} +1.00000 q^{4} -0.683969 q^{5} +1.16425 q^{6} -0.316031 q^{7} -1.00000 q^{8} -1.64453 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.16425 q^{3} +1.00000 q^{4} -0.683969 q^{5} +1.16425 q^{6} -0.316031 q^{7} -1.00000 q^{8} -1.64453 q^{9} +0.683969 q^{10} +1.00000 q^{11} -1.16425 q^{12} +0.316031 q^{13} +0.316031 q^{14} +0.796310 q^{15} +1.00000 q^{16} -1.84822 q^{17} +1.64453 q^{18} -0.683969 q^{20} +0.367938 q^{21} -1.00000 q^{22} -4.48028 q^{23} +1.16425 q^{24} -4.53219 q^{25} -0.316031 q^{26} +5.40738 q^{27} -0.316031 q^{28} -5.49274 q^{29} -0.796310 q^{30} -0.796310 q^{31} -1.00000 q^{32} -1.16425 q^{33} +1.84822 q^{34} +0.216155 q^{35} -1.64453 q^{36} -0.632062 q^{37} -0.367938 q^{39} +0.683969 q^{40} +3.83575 q^{41} -0.367938 q^{42} +6.68397 q^{43} +1.00000 q^{44} +1.12481 q^{45} +4.48028 q^{46} -4.32850 q^{47} -1.16425 q^{48} -6.90012 q^{49} +4.53219 q^{50} +2.15178 q^{51} +0.316031 q^{52} +3.44084 q^{53} -5.40738 q^{54} -0.683969 q^{55} +0.316031 q^{56} +5.49274 q^{58} +2.80877 q^{59} +0.796310 q^{60} -12.0249 q^{61} +0.796310 q^{62} +0.519721 q^{63} +1.00000 q^{64} -0.216155 q^{65} +1.16425 q^{66} -10.7483 q^{67} -1.84822 q^{68} +5.21616 q^{69} -0.216155 q^{70} +13.0125 q^{71} +1.64453 q^{72} +3.44084 q^{73} +0.632062 q^{74} +5.27659 q^{75} -0.316031 q^{77} +0.367938 q^{78} -9.06437 q^{79} -0.683969 q^{80} -1.36195 q^{81} -3.83575 q^{82} -4.35547 q^{83} +0.367938 q^{84} +1.26412 q^{85} -6.68397 q^{86} +6.39492 q^{87} -1.00000 q^{88} +9.28905 q^{89} -1.12481 q^{90} -0.0998755 q^{91} -4.48028 q^{92} +0.927102 q^{93} +4.32850 q^{94} +1.16425 q^{96} +3.69643 q^{97} +6.90012 q^{98} -1.64453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} + 4 q^{3} + 3 q^{4} + q^{5} - 4 q^{6} - 4 q^{7} - 3 q^{8} + 7 q^{9} - q^{10} + 3 q^{11} + 4 q^{12} + 4 q^{13} + 4 q^{14} + q^{15} + 3 q^{16} + 5 q^{17} - 7 q^{18} + q^{20} - 5 q^{21} - 3 q^{22} - 9 q^{23} - 4 q^{24} - 4 q^{26} + 19 q^{27} - 4 q^{28} + 6 q^{29} - q^{30} - q^{31} - 3 q^{32} + 4 q^{33} - 5 q^{34} - 16 q^{35} + 7 q^{36} - 8 q^{37} + 5 q^{39} - q^{40} + 19 q^{41} + 5 q^{42} + 17 q^{43} + 3 q^{44} - 13 q^{45} + 9 q^{46} + 2 q^{47} + 4 q^{48} - q^{49} + 17 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + q^{55} + 4 q^{56} - 6 q^{58} - 11 q^{59} + q^{60} + q^{62} + 6 q^{63} + 3 q^{64} + 16 q^{65} - 4 q^{66} - 2 q^{67} + 5 q^{68} - q^{69} + 16 q^{70} + 21 q^{71} - 7 q^{72} - 3 q^{73} + 8 q^{74} + 10 q^{75} - 4 q^{77} - 5 q^{78} + q^{80} + 27 q^{81} - 19 q^{82} - 25 q^{83} - 5 q^{84} + 16 q^{85} - 17 q^{86} + 40 q^{87} - 3 q^{88} + 4 q^{89} + 13 q^{90} - 20 q^{91} - 9 q^{92} + 10 q^{93} - 2 q^{94} - 4 q^{96} - 10 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 4 * q^3 + 3 * q^4 + q^5 - 4 * q^6 - 4 * q^7 - 3 * q^8 + 7 * q^9 - q^10 + 3 * q^11 + 4 * q^12 + 4 * q^13 + 4 * q^14 + q^15 + 3 * q^16 + 5 * q^17 - 7 * q^18 + q^20 - 5 * q^21 - 3 * q^22 - 9 * q^23 - 4 * q^24 - 4 * q^26 + 19 * q^27 - 4 * q^28 + 6 * q^29 - q^30 - q^31 - 3 * q^32 + 4 * q^33 - 5 * q^34 - 16 * q^35 + 7 * q^36 - 8 * q^37 + 5 * q^39 - q^40 + 19 * q^41 + 5 * q^42 + 17 * q^43 + 3 * q^44 - 13 * q^45 + 9 * q^46 + 2 * q^47 + 4 * q^48 - q^49 + 17 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + q^55 + 4 * q^56 - 6 * q^58 - 11 * q^59 + q^60 + q^62 + 6 * q^63 + 3 * q^64 + 16 * q^65 - 4 * q^66 - 2 * q^67 + 5 * q^68 - q^69 + 16 * q^70 + 21 * q^71 - 7 * q^72 - 3 * q^73 + 8 * q^74 + 10 * q^75 - 4 * q^77 - 5 * q^78 + q^80 + 27 * q^81 - 19 * q^82 - 25 * q^83 - 5 * q^84 + 16 * q^85 - 17 * q^86 + 40 * q^87 - 3 * q^88 + 4 * q^89 + 13 * q^90 - 20 * q^91 - 9 * q^92 + 10 * q^93 - 2 * q^94 - 4 * q^96 - 10 * q^97 + q^98 + 7 * q^99

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