LMFDB - Embedded newform 4334.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.415881$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.415881 q^{3} +1.00000 q^{4} -2.24456 q^{5} +0.415881 q^{6} +1.94686 q^{7} -1.00000 q^{8} -2.82704 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.415881 q^{3} +1.00000 q^{4} -2.24456 q^{5} +0.415881 q^{6} +1.94686 q^{7} -1.00000 q^{8} -2.82704 q^{9} +2.24456 q^{10} +1.00000 q^{11} -0.415881 q^{12} +1.65329 q^{13} -1.94686 q^{14} +0.933471 q^{15} +1.00000 q^{16} -4.04145 q^{17} +2.82704 q^{18} -7.25266 q^{19} -2.24456 q^{20} -0.809661 q^{21} -1.00000 q^{22} +8.28397 q^{23} +0.415881 q^{24} +0.0380545 q^{25} -1.65329 q^{26} +2.42336 q^{27} +1.94686 q^{28} +10.1950 q^{29} -0.933471 q^{30} +2.78382 q^{31} -1.00000 q^{32} -0.415881 q^{33} +4.04145 q^{34} -4.36984 q^{35} -2.82704 q^{36} -0.827167 q^{37} +7.25266 q^{38} -0.687573 q^{39} +2.24456 q^{40} +5.69287 q^{41} +0.809661 q^{42} +7.31501 q^{43} +1.00000 q^{44} +6.34547 q^{45} -8.28397 q^{46} -7.73976 q^{47} -0.415881 q^{48} -3.20976 q^{49} -0.0380545 q^{50} +1.68076 q^{51} +1.65329 q^{52} -7.74921 q^{53} -2.42336 q^{54} -2.24456 q^{55} -1.94686 q^{56} +3.01625 q^{57} -10.1950 q^{58} +7.99838 q^{59} +0.933471 q^{60} -8.08683 q^{61} -2.78382 q^{62} -5.50384 q^{63} +1.00000 q^{64} -3.71092 q^{65} +0.415881 q^{66} -11.4984 q^{67} -4.04145 q^{68} -3.44515 q^{69} +4.36984 q^{70} -3.83205 q^{71} +2.82704 q^{72} +0.425688 q^{73} +0.827167 q^{74} -0.0158262 q^{75} -7.25266 q^{76} +1.94686 q^{77} +0.687573 q^{78} -13.8952 q^{79} -2.24456 q^{80} +7.47330 q^{81} -5.69287 q^{82} -2.39944 q^{83} -0.809661 q^{84} +9.07128 q^{85} -7.31501 q^{86} -4.23991 q^{87} -1.00000 q^{88} +10.9318 q^{89} -6.34547 q^{90} +3.21872 q^{91} +8.28397 q^{92} -1.15774 q^{93} +7.73976 q^{94} +16.2790 q^{95} +0.415881 q^{96} +13.3160 q^{97} +3.20976 q^{98} -2.82704 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * 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
$3$	−0.415881	−0.240109	−0.120055	−	0.992767i	$-0.538307\pi$
$3$	−0.415881	−0.240109	−0.120055	+	0.992767i	$0.538307\pi$
$4$	1.00000	0.500000
$5$	−2.24456	−1.00380	−0.501899	−	0.864926i	$-0.667365\pi$
$5$	−2.24456	−1.00380	−0.501899	+	0.864926i	$0.667365\pi$
$6$	0.415881	0.169783
$7$	1.94686	0.735842	0.367921	−	0.929857i	$-0.380070\pi$
$7$	1.94686	0.735842	0.367921	+	0.929857i	$0.380070\pi$
$8$	−1.00000	−0.353553
$9$	−2.82704	−0.942348
$10$	2.24456	0.709793
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.415881	−0.120055
$13$	1.65329	0.458541	0.229270	−	0.973363i	$-0.426366\pi$
$13$	1.65329	0.458541	0.229270	+	0.973363i	$0.426366\pi$
$14$	−1.94686	−0.520319
$15$	0.933471	0.241021
$16$	1.00000	0.250000
$17$	−4.04145	−0.980196	−0.490098	−	0.871667i	$-0.663039\pi$
$17$	−4.04145	−0.980196	−0.490098	+	0.871667i	$0.663039\pi$
$18$	2.82704	0.666340
$19$	−7.25266	−1.66387	−0.831937	−	0.554870i	$-0.812768\pi$
$19$	−7.25266	−1.66387	−0.831937	+	0.554870i	$0.812768\pi$
$20$	−2.24456	−0.501899
$21$	−0.809661	−0.176682
$22$	−1.00000	−0.213201
$23$	8.28397	1.72733	0.863663	−	0.504069i	$-0.168164\pi$
$23$	8.28397	1.72733	0.863663	+	0.504069i	$0.168164\pi$
$24$	0.415881	0.0848914
$25$	0.0380545	0.00761091
$26$	−1.65329	−0.324237
$27$	2.42336	0.466375
$28$	1.94686	0.367921
$29$	10.1950	1.89316	0.946581	−	0.322466i	$-0.104512\pi$
$29$	10.1950	1.89316	0.946581	+	0.322466i	$0.104512\pi$
$30$	−0.933471	−0.170428
$31$	2.78382	0.499989	0.249994	−	0.968247i	$-0.419571\pi$
$31$	2.78382	0.499989	0.249994	+	0.968247i	$0.419571\pi$
$32$	−1.00000	−0.176777
$33$	−0.415881	−0.0723956
$34$	4.04145	0.693103
$35$	−4.36984	−0.738637
$36$	−2.82704	−0.471174
$37$	−0.827167	−0.135985	−0.0679927	−	0.997686i	$-0.521659\pi$
$37$	−0.827167	−0.135985	−0.0679927	+	0.997686i	$0.521659\pi$
$38$	7.25266	1.17654
$39$	−0.687573	−0.110100
$40$	2.24456	0.354896
$41$	5.69287	0.889077	0.444538	−	0.895760i	$-0.353368\pi$
$41$	5.69287	0.889077	0.444538	+	0.895760i	$0.353368\pi$
$42$	0.809661	0.124933
$43$	7.31501	1.11553	0.557764	−	0.830000i	$-0.311659\pi$
$43$	7.31501	1.11553	0.557764	+	0.830000i	$0.311659\pi$
$44$	1.00000	0.150756
$45$	6.34547	0.945927
$46$	−8.28397	−1.22140
$47$	−7.73976	−1.12896	−0.564480	−	0.825447i	$-0.690923\pi$
$47$	−7.73976	−1.12896	−0.564480	+	0.825447i	$0.690923\pi$
$48$	−0.415881	−0.0600273
$49$	−3.20976	−0.458536
$50$	−0.0380545	−0.00538172
$51$	1.68076	0.235354
$52$	1.65329	0.229270
$53$	−7.74921	−1.06444	−0.532218	−	0.846607i	$-0.678641\pi$
$53$	−7.74921	−1.06444	−0.532218	+	0.846607i	$0.678641\pi$
$54$	−2.42336	−0.329777
$55$	−2.24456	−0.302657
$56$	−1.94686	−0.260159
$57$	3.01625	0.399512
$58$	−10.1950	−1.33867
$59$	7.99838	1.04130	0.520650	−	0.853770i	$-0.325690\pi$
$59$	7.99838	1.04130	0.520650	+	0.853770i	$0.325690\pi$
$60$	0.933471	0.120511
$61$	−8.08683	−1.03541	−0.517706	−	0.855559i	$-0.673214\pi$
$61$	−8.08683	−1.03541	−0.517706	+	0.855559i	$0.673214\pi$
$62$	−2.78382	−0.353545
$63$	−5.50384	−0.693419
$64$	1.00000	0.125000
$65$	−3.71092	−0.460282
$66$	0.415881	0.0511915
$67$	−11.4984	−1.40475	−0.702377	−	0.711805i	$-0.747878\pi$
$67$	−11.4984	−1.40475	−0.702377	+	0.711805i	$0.747878\pi$
$68$	−4.04145	−0.490098
$69$	−3.44515	−0.414747
$70$	4.36984	0.522295
$71$	−3.83205	−0.454781	−0.227391	−	0.973804i	$-0.573019\pi$
$71$	−3.83205	−0.454781	−0.227391	+	0.973804i	$0.573019\pi$
$72$	2.82704	0.333170
$73$	0.425688	0.0498230	0.0249115	−	0.999690i	$-0.492070\pi$
$73$	0.425688	0.0498230	0.0249115	+	0.999690i	$0.492070\pi$
$74$	0.827167	0.0961562
$75$	−0.0158262	−0.00182745
$76$	−7.25266	−0.831937
$77$	1.94686	0.221865
$78$	0.687573	0.0778524
$79$	−13.8952	−1.56333	−0.781666	−	0.623698i	$-0.785630\pi$
$79$	−13.8952	−1.56333	−0.781666	+	0.623698i	$0.785630\pi$
$80$	−2.24456	−0.250950
$81$	7.47330	0.830367
$82$	−5.69287	−0.628672
$83$	−2.39944	−0.263373	−0.131686	−	0.991291i	$-0.542039\pi$
$83$	−2.39944	−0.263373	−0.131686	+	0.991291i	$0.542039\pi$
$84$	−0.809661	−0.0883412
$85$	9.07128	0.983919
$86$	−7.31501	−0.788798
$87$	−4.23991	−0.454566
$88$	−1.00000	−0.106600
$89$	10.9318	1.15877	0.579387	−	0.815053i	$-0.303292\pi$
$89$	10.9318	1.15877	0.579387	+	0.815053i	$0.303292\pi$
$90$	−6.34547	−0.668871
$91$	3.21872	0.337414
$92$	8.28397	0.863663
$93$	−1.15774	−0.120052
$94$	7.73976	0.798295
$95$	16.2790	1.67019
$96$	0.415881	0.0424457
$97$	13.3160	1.35204	0.676020	−	0.736883i	$-0.263703\pi$
$97$	13.3160	1.35204	0.676020	+	0.736883i	$0.263703\pi$
$98$	3.20976	0.324234
$99$	−2.82704	−0.284128
$100$	0.0380545	0.00380545
$101$	8.43947	0.839758	0.419879	−	0.907580i	$-0.362072\pi$
$101$	8.43947	0.839758	0.419879	+	0.907580i	$0.362072\pi$
$102$	−1.68076	−0.166420
$103$	−0.908357	−0.0895031	−0.0447516	−	0.998998i	$-0.514250\pi$
$103$	−0.908357	−0.0895031	−0.0447516	+	0.998998i	$0.514250\pi$
$104$	−1.65329	−0.162119
$105$	1.81733	0.177354
$106$	7.74921	0.752670
$107$	14.1911	1.37190	0.685951	−	0.727647i	$-0.259386\pi$
$107$	14.1911	1.37190	0.685951	+	0.727647i	$0.259386\pi$
$108$	2.42336	0.233188
$109$	4.23544	0.405681	0.202841	−	0.979212i	$-0.434983\pi$
$109$	4.23544	0.405681	0.202841	+	0.979212i	$0.434983\pi$
$110$	2.24456	0.214011
$111$	0.344003	0.0326513
$112$	1.94686	0.183961
$113$	−7.13396	−0.671106	−0.335553	−	0.942021i	$-0.608923\pi$
$113$	−7.13396	−0.671106	−0.335553	+	0.942021i	$0.608923\pi$
$114$	−3.01625	−0.282497
$115$	−18.5939	−1.73389
$116$	10.1950	0.946581
$117$	−4.67393	−0.432105
$118$	−7.99838	−0.736310
$119$	−7.86812	−0.721269
$120$	−0.933471	−0.0852139
$121$	1.00000	0.0909091
$122$	8.08683	0.732147
$123$	−2.36756	−0.213476
$124$	2.78382	0.249994
$125$	11.1374	0.996158
$126$	5.50384	0.490321
$127$	−17.6578	−1.56687	−0.783436	−	0.621472i	$-0.786535\pi$
$127$	−17.6578	−1.56687	−0.783436	+	0.621472i	$0.786535\pi$
$128$	−1.00000	−0.0883883
$129$	−3.04217	−0.267849
$130$	3.71092	0.325469
$131$	−7.73493	−0.675804	−0.337902	−	0.941181i	$-0.609717\pi$
$131$	−7.73493	−0.675804	−0.337902	+	0.941181i	$0.609717\pi$
$132$	−0.415881	−0.0361978
$133$	−14.1199	−1.22435
$134$	11.4984	0.993312
$135$	−5.43938	−0.468147
$136$	4.04145	0.346551
$137$	1.28592	0.109864	0.0549319	−	0.998490i	$-0.482506\pi$
$137$	1.28592	0.109864	0.0549319	+	0.998490i	$0.482506\pi$
$138$	3.44515	0.293270
$139$	−15.5538	−1.31925	−0.659627	−	0.751593i	$-0.729286\pi$
$139$	−15.5538	−1.31925	−0.659627	+	0.751593i	$0.729286\pi$
$140$	−4.36984	−0.369318
$141$	3.21882	0.271074
$142$	3.83205	0.321579
$143$	1.65329	0.138255
$144$	−2.82704	−0.235587
$145$	−22.8833	−1.90035
$146$	−0.425688	−0.0352302
$147$	1.33488	0.110099
$148$	−0.827167	−0.0679927
$149$	−20.2290	−1.65722	−0.828611	−	0.559825i	$-0.810868\pi$
$149$	−20.2290	−1.65722	−0.828611	+	0.559825i	$0.810868\pi$
$150$	0.0158262	0.00129220
$151$	5.49776	0.447402	0.223701	−	0.974658i	$-0.428186\pi$
$151$	5.49776	0.447402	0.223701	+	0.974658i	$0.428186\pi$
$152$	7.25266	0.588269
$153$	11.4254	0.923685
$154$	−1.94686	−0.156882
$155$	−6.24845	−0.501888
$156$	−0.687573	−0.0550499
$157$	2.13019	0.170008	0.0850039	−	0.996381i	$-0.472910\pi$
$157$	2.13019	0.170008	0.0850039	+	0.996381i	$0.472910\pi$
$158$	13.8952	1.10544
$159$	3.22275	0.255581
$160$	2.24456	0.177448
$161$	16.1277	1.27104
$162$	−7.47330	−0.587158
$163$	20.4786	1.60401	0.802005	−	0.597317i	$-0.203767\pi$
$163$	20.4786	1.60401	0.802005	+	0.597317i	$0.203767\pi$
$164$	5.69287	0.444538
$165$	0.933471	0.0726706
$166$	2.39944	0.186233
$167$	−2.86254	−0.221510	−0.110755	−	0.993848i	$-0.535327\pi$
$167$	−2.86254	−0.221510	−0.110755	+	0.993848i	$0.535327\pi$
$168$	0.809661	0.0624667
$169$	−10.2666	−0.789740
$170$	−9.07128	−0.695735
$171$	20.5036	1.56795
$172$	7.31501	0.557764
$173$	−16.6986	−1.26957	−0.634784	−	0.772690i	$-0.718911\pi$
$173$	−16.6986	−1.26957	−0.634784	+	0.772690i	$0.718911\pi$
$174$	4.23991	0.321426
$175$	0.0740866	0.00560042
$176$	1.00000	0.0753778
$177$	−3.32637	−0.250026
$178$	−10.9318	−0.819377
$179$	−23.1531	−1.73055	−0.865273	−	0.501301i	$-0.832855\pi$
$179$	−23.1531	−1.73055	−0.865273	+	0.501301i	$0.832855\pi$
$180$	6.34547	0.472963
$181$	8.37604	0.622586	0.311293	−	0.950314i	$-0.399238\pi$
$181$	8.37604	0.622586	0.311293	+	0.950314i	$0.399238\pi$
$182$	−3.21872	−0.238587
$183$	3.36316	0.248612
$184$	−8.28397	−0.610702
$185$	1.85663	0.136502
$186$	1.15774	0.0848895
$187$	−4.04145	−0.295540
$188$	−7.73976	−0.564480
$189$	4.71793	0.343179
$190$	−16.2790	−1.18101
$191$	8.39612	0.607522	0.303761	−	0.952748i	$-0.401758\pi$
$191$	8.39612	0.607522	0.303761	+	0.952748i	$0.401758\pi$
$192$	−0.415881	−0.0300136
$193$	−21.4162	−1.54157	−0.770784	−	0.637096i	$-0.780135\pi$
$193$	−21.4162	−1.54157	−0.770784	+	0.637096i	$0.780135\pi$
$194$	−13.3160	−0.956036
$195$	1.54330	0.110518
$196$	−3.20976	−0.229268
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.82704	0.200909
$199$	2.37949	0.168678	0.0843389	−	0.996437i	$-0.473122\pi$
$199$	2.37949	0.168678	0.0843389	+	0.996437i	$0.473122\pi$
$200$	−0.0380545	−0.00269086
$201$	4.78197	0.337294
$202$	−8.43947	−0.593799
$203$	19.8482	1.39307
$204$	1.68076	0.117677
$205$	−12.7780	−0.892454
$206$	0.908357	0.0632883
$207$	−23.4191	−1.62774
$208$	1.65329	0.114635
$209$	−7.25266	−0.501677
$210$	−1.81733	−0.125408
$211$	12.5858	0.866441	0.433220	−	0.901288i	$-0.357377\pi$
$211$	12.5858	0.866441	0.433220	+	0.901288i	$0.357377\pi$
$212$	−7.74921	−0.532218
$213$	1.59368	0.109197
$214$	−14.1911	−0.970082
$215$	−16.4190	−1.11977
$216$	−2.42336	−0.164889
$217$	5.41969	0.367913
$218$	−4.23544	−0.286860
$219$	−0.177036	−0.0119630
$220$	−2.24456	−0.151328
$221$	−6.68170	−0.449460
$222$	−0.344003	−0.0230880
$223$	−17.6630	−1.18280	−0.591402	−	0.806377i	$-0.701425\pi$
$223$	−17.6630	−1.18280	−0.591402	+	0.806377i	$0.701425\pi$
$224$	−1.94686	−0.130080
$225$	−0.107582	−0.00717212
$226$	7.13396	0.474544
$227$	−18.5462	−1.23096	−0.615478	−	0.788154i	$-0.711037\pi$
$227$	−18.5462	−1.23096	−0.615478	+	0.788154i	$0.711037\pi$
$228$	3.01625	0.199756
$229$	−21.5774	−1.42587	−0.712936	−	0.701229i	$-0.752635\pi$
$229$	−21.5774	−1.42587	−0.712936	+	0.701229i	$0.752635\pi$
$230$	18.5939	1.22604
$231$	−0.809661	−0.0532718
$232$	−10.1950	−0.669334
$233$	22.8480	1.49682	0.748412	−	0.663234i	$-0.230817\pi$
$233$	22.8480	1.49682	0.748412	+	0.663234i	$0.230817\pi$
$234$	4.67393	0.305544
$235$	17.3724	1.13325
$236$	7.99838	0.520650
$237$	5.77875	0.375370
$238$	7.86812	0.510014
$239$	15.0535	0.973733	0.486866	−	0.873476i	$-0.338140\pi$
$239$	15.0535	0.973733	0.486866	+	0.873476i	$0.338140\pi$
$240$	0.933471	0.0602553
$241$	−5.12265	−0.329979	−0.164989	−	0.986295i	$-0.552759\pi$
$241$	−5.12265	−0.329979	−0.164989	+	0.986295i	$0.552759\pi$
$242$	−1.00000	−0.0642824
$243$	−10.3781	−0.665754
$244$	−8.08683	−0.517706
$245$	7.20449	0.460278
$246$	2.36756	0.150950
$247$	−11.9908	−0.762954
$248$	−2.78382	−0.176773
$249$	0.997882	0.0632382
$250$	−11.1374	−0.704390
$251$	−7.34662	−0.463715	−0.231857	−	0.972750i	$-0.574480\pi$
$251$	−7.34662	−0.463715	−0.231857	+	0.972750i	$0.574480\pi$
$252$	−5.50384	−0.346709
$253$	8.28397	0.520808
$254$	17.6578	1.10795
$255$	−3.77258	−0.236248
$256$	1.00000	0.0625000
$257$	−23.0169	−1.43576	−0.717878	−	0.696169i	$-0.754886\pi$
$257$	−23.0169	−1.43576	−0.717878	+	0.696169i	$0.754886\pi$
$258$	3.04217	0.189398
$259$	−1.61037	−0.100064
$260$	−3.71092	−0.230141
$261$	−28.8217	−1.78402
$262$	7.73493	0.477865
$263$	−12.3679	−0.762636	−0.381318	−	0.924444i	$-0.624530\pi$
$263$	−12.3679	−0.762636	−0.381318	+	0.924444i	$0.624530\pi$
$264$	0.415881	0.0255957
$265$	17.3936	1.06848
$266$	14.1199	0.865745
$267$	−4.54635	−0.278232
$268$	−11.4984	−0.702377
$269$	19.0593	1.16206	0.581032	−	0.813881i	$-0.302649\pi$
$269$	19.0593	1.16206	0.581032	+	0.813881i	$0.302649\pi$
$270$	5.43938	0.331030
$271$	−27.2184	−1.65340	−0.826700	−	0.562643i	$-0.809784\pi$
$271$	−27.2184	−1.65340	−0.826700	+	0.562643i	$0.809784\pi$
$272$	−4.04145	−0.245049
$273$	−1.33861	−0.0810161
$274$	−1.28592	−0.0776854
$275$	0.0380545	0.00229477
$276$	−3.44515	−0.207373
$277$	−9.80168	−0.588926	−0.294463	−	0.955663i	$-0.595141\pi$
$277$	−9.80168	−0.588926	−0.294463	+	0.955663i	$0.595141\pi$
$278$	15.5538	0.932854
$279$	−7.86998	−0.471163
$280$	4.36984	0.261148
$281$	10.1543	0.605753	0.302876	−	0.953030i	$-0.402053\pi$
$281$	10.1543	0.605753	0.302876	+	0.953030i	$0.402053\pi$
$282$	−3.21882	−0.191678
$283$	−9.36458	−0.556667	−0.278333	−	0.960485i	$-0.589782\pi$
$283$	−9.36458	−0.556667	−0.278333	+	0.960485i	$0.589782\pi$
$284$	−3.83205	−0.227391
$285$	−6.77015	−0.401029
$286$	−1.65329	−0.0977612
$287$	11.0832	0.654220
$288$	2.82704	0.166585
$289$	−0.666685	−0.0392167
$290$	22.8833	1.34375
$291$	−5.53789	−0.324637
$292$	0.425688	0.0249115
$293$	−6.59187	−0.385101	−0.192550	−	0.981287i	$-0.561676\pi$
$293$	−6.59187	−0.385101	−0.192550	+	0.981287i	$0.561676\pi$
$294$	−1.33488	−0.0778516
$295$	−17.9528	−1.04525
$296$	0.827167	0.0480781
$297$	2.42336	0.140618
$298$	20.2290	1.17183
$299$	13.6958	0.792049
$300$	−0.0158262	−0.000913724 0
$301$	14.2413	0.820853
$302$	−5.49776	−0.316361
$303$	−3.50982	−0.201634
$304$	−7.25266	−0.415969
$305$	18.1514	1.03934
$306$	−11.4254	−0.653144
$307$	−6.82122	−0.389308	−0.194654	−	0.980872i	$-0.562358\pi$
$307$	−6.82122	−0.389308	−0.194654	+	0.980872i	$0.562358\pi$
$308$	1.94686	0.110932
$309$	0.377769	0.0214905
$310$	6.24845	0.354888
$311$	−12.7217	−0.721384	−0.360692	−	0.932685i	$-0.617459\pi$
$311$	−12.7217	−0.721384	−0.360692	+	0.932685i	$0.617459\pi$
$312$	0.687573	0.0389262
$313$	−2.87908	−0.162735	−0.0813676	−	0.996684i	$-0.525929\pi$
$313$	−2.87908	−0.162735	−0.0813676	+	0.996684i	$0.525929\pi$
$314$	−2.13019	−0.120214
$315$	12.3537	0.696053
$316$	−13.8952	−0.781666
$317$	1.25368	0.0704135	0.0352067	−	0.999380i	$-0.488791\pi$
$317$	1.25368	0.0704135	0.0352067	+	0.999380i	$0.488791\pi$
$318$	−3.22275	−0.180723
$319$	10.1950	0.570810
$320$	−2.24456	−0.125475
$321$	−5.90180	−0.329406
$322$	−16.1277	−0.898761
$323$	29.3113	1.63092
$324$	7.47330	0.415183
$325$	0.0629153	0.00348991
$326$	−20.4786	−1.13421
$327$	−1.76144	−0.0974078
$328$	−5.69287	−0.314336
$329$	−15.0682	−0.830736
$330$	−0.933471	−0.0513859
$331$	−30.0110	−1.64955	−0.824777	−	0.565458i	$-0.808700\pi$
$331$	−30.0110	−1.64955	−0.824777	+	0.565458i	$0.808700\pi$
$332$	−2.39944	−0.131686
$333$	2.33844	0.128145
$334$	2.86254	0.156631
$335$	25.8089	1.41009
$336$	−0.809661	−0.0441706
$337$	−17.6720	−0.962654	−0.481327	−	0.876541i	$-0.659845\pi$
$337$	−17.6720	−0.962654	−0.481327	+	0.876541i	$0.659845\pi$
$338$	10.2666	0.558431
$339$	2.96688	0.161139
$340$	9.07128	0.491959
$341$	2.78382	0.150752
$342$	−20.5036	−1.10871
$343$	−19.8769	−1.07325
$344$	−7.31501	−0.394399
$345$	7.73284	0.416322
$346$	16.6986	0.897720
$347$	−0.243786	−0.0130871	−0.00654355	−	0.999979i	$-0.502083\pi$
$347$	−0.243786	−0.0130871	−0.00654355	+	0.999979i	$0.502083\pi$
$348$	−4.23991	−0.227283
$349$	−34.9736	−1.87210	−0.936048	−	0.351872i	$-0.885545\pi$
$349$	−34.9736	−1.87210	−0.936048	+	0.351872i	$0.885545\pi$
$350$	−0.0740866	−0.00396010
$351$	4.00652	0.213852
$352$	−1.00000	−0.0533002
$353$	24.5306	1.30563	0.652816	−	0.757517i	$-0.273588\pi$
$353$	24.5306	1.30563	0.652816	+	0.757517i	$0.273588\pi$
$354$	3.32637	0.176795
$355$	8.60128	0.456508
$356$	10.9318	0.579387
$357$	3.27220	0.173183
$358$	23.1531	1.22368
$359$	34.5941	1.82581	0.912903	−	0.408177i	$-0.133835\pi$
$359$	34.5941	1.82581	0.912903	+	0.408177i	$0.133835\pi$
$360$	−6.34547	−0.334436
$361$	33.6011	1.76848
$362$	−8.37604	−0.440235
$363$	−0.415881	−0.0218281
$364$	3.21872	0.168707
$365$	−0.955483	−0.0500123
$366$	−3.36316	−0.175795
$367$	−16.5904	−0.866013	−0.433006	−	0.901391i	$-0.642547\pi$
$367$	−16.5904	−0.866013	−0.433006	+	0.901391i	$0.642547\pi$
$368$	8.28397	0.431832
$369$	−16.0940	−0.837819
$370$	−1.85663	−0.0965214
$371$	−15.0866	−0.783257
$372$	−1.15774	−0.0600259
$373$	31.2666	1.61892	0.809462	−	0.587172i	$-0.199759\pi$
$373$	31.2666	1.61892	0.809462	+	0.587172i	$0.199759\pi$
$374$	4.04145	0.208978
$375$	−4.63183	−0.239187
$376$	7.73976	0.399148
$377$	16.8553	0.868092
$378$	−4.71793	−0.242664
$379$	−7.45385	−0.382878	−0.191439	−	0.981504i	$-0.561315\pi$
$379$	−7.45385	−0.382878	−0.191439	+	0.981504i	$0.561315\pi$
$380$	16.2790	0.835097
$381$	7.34353	0.376221
$382$	−8.39612	−0.429583
$383$	−19.2295	−0.982582	−0.491291	−	0.870996i	$-0.663475\pi$
$383$	−19.2295	−0.982582	−0.491291	+	0.870996i	$0.663475\pi$
$384$	0.415881	0.0212229
$385$	−4.36984	−0.222707
$386$	21.4162	1.09005
$387$	−20.6798	−1.05122
$388$	13.3160	0.676020
$389$	−18.3410	−0.929926	−0.464963	−	0.885330i	$-0.653932\pi$
$389$	−18.3410	−0.929926	−0.464963	+	0.885330i	$0.653932\pi$
$390$	−1.54330	−0.0781481
$391$	−33.4792	−1.69312
$392$	3.20976	0.162117
$393$	3.21681	0.162267
$394$	−1.00000	−0.0503793
$395$	31.1886	1.56927
$396$	−2.82704	−0.142064
$397$	−5.37974	−0.270001	−0.135001	−	0.990846i	$-0.543104\pi$
$397$	−5.37974	−0.270001	−0.135001	+	0.990846i	$0.543104\pi$
$398$	−2.37949	−0.119273
$399$	5.87219	0.293977
$400$	0.0380545	0.00190273
$401$	−38.0579	−1.90052	−0.950261	−	0.311456i	$-0.899183\pi$
$401$	−38.0579	−1.90052	−0.950261	+	0.311456i	$0.899183\pi$
$402$	−4.78197	−0.238503
$403$	4.60247	0.229265
$404$	8.43947	0.419879
$405$	−16.7743	−0.833520
$406$	−19.8482	−0.985048
$407$	−0.827167	−0.0410011
$408$	−1.68076	−0.0832102
$409$	25.1927	1.24570	0.622850	−	0.782341i	$-0.285975\pi$
$409$	25.1927	1.24570	0.622850	+	0.782341i	$0.285975\pi$
$410$	12.7780	0.631060
$411$	−0.534791	−0.0263793
$412$	−0.908357	−0.0447516
$413$	15.5717	0.766232
$414$	23.4191	1.15099
$415$	5.38569	0.264373
$416$	−1.65329	−0.0810593
$417$	6.46853	0.316765
$418$	7.25266	0.354739
$419$	3.41451	0.166809	0.0834047	−	0.996516i	$-0.473421\pi$
$419$	3.41451	0.166809	0.0834047	+	0.996516i	$0.473421\pi$
$420$	1.81733	0.0886768
$421$	20.5210	1.00013	0.500067	−	0.865987i	$-0.333309\pi$
$421$	20.5210	1.00013	0.500067	+	0.865987i	$0.333309\pi$
$422$	−12.5858	−0.612666
$423$	21.8806	1.06387
$424$	7.74921	0.376335
$425$	−0.153795	−0.00746018
$426$	−1.59368	−0.0772140
$427$	−15.7439	−0.761900
$428$	14.1911	0.685951
$429$	−0.687573	−0.0331964
$430$	16.4190	0.791794
$431$	7.43175	0.357975	0.178987	−	0.983851i	$-0.442718\pi$
$431$	7.43175	0.357975	0.178987	+	0.983851i	$0.442718\pi$
$432$	2.42336	0.116594
$433$	−32.3343	−1.55389	−0.776943	−	0.629571i	$-0.783231\pi$
$433$	−32.3343	−1.55389	−0.776943	+	0.629571i	$0.783231\pi$
$434$	−5.41969	−0.260154
$435$	9.51673	0.456292
$436$	4.23544	0.202841
$437$	−60.0808	−2.87405
$438$	0.177036	0.00845909
$439$	6.87171	0.327969	0.163984	−	0.986463i	$-0.447565\pi$
$439$	6.87171	0.327969	0.163984	+	0.986463i	$0.447565\pi$
$440$	2.24456	0.107005
$441$	9.07412	0.432101
$442$	6.68170	0.317816
$443$	−2.12632	−0.101025	−0.0505124	−	0.998723i	$-0.516085\pi$
$443$	−2.12632	−0.101025	−0.0505124	+	0.998723i	$0.516085\pi$
$444$	0.344003	0.0163257
$445$	−24.5372	−1.16317
$446$	17.6630	0.836369
$447$	8.41285	0.397914
$448$	1.94686	0.0919803
$449$	−29.2391	−1.37988	−0.689939	−	0.723868i	$-0.742363\pi$
$449$	−29.2391	−1.37988	−0.689939	+	0.723868i	$0.742363\pi$
$450$	0.107582	0.00507145
$451$	5.69287	0.268067
$452$	−7.13396	−0.335553
$453$	−2.28642	−0.107425
$454$	18.5462	0.870417
$455$	−7.22461	−0.338695
$456$	−3.01625	−0.141249
$457$	−26.0219	−1.21725	−0.608626	−	0.793458i	$-0.708279\pi$
$457$	−26.0219	−1.21725	−0.608626	+	0.793458i	$0.708279\pi$
$458$	21.5774	1.00824
$459$	−9.79388	−0.457139
$460$	−18.5939	−0.866944
$461$	−22.1268	−1.03055	−0.515275	−	0.857025i	$-0.672310\pi$
$461$	−22.1268	−1.03055	−0.515275	+	0.857025i	$0.672310\pi$
$462$	0.809661	0.0376688
$463$	−18.9937	−0.882711	−0.441356	−	0.897332i	$-0.645502\pi$
$463$	−18.9937	−0.882711	−0.441356	+	0.897332i	$0.645502\pi$
$464$	10.1950	0.473291
$465$	2.59861	0.120508
$466$	−22.8480	−1.05841
$467$	20.0636	0.928433	0.464217	−	0.885722i	$-0.346336\pi$
$467$	20.0636	0.928433	0.464217	+	0.885722i	$0.346336\pi$
$468$	−4.67393	−0.216052
$469$	−22.3857	−1.03368
$470$	−17.3724	−0.801327
$471$	−0.885907	−0.0408204
$472$	−7.99838	−0.368155
$473$	7.31501	0.336344
$474$	−5.77875	−0.265427
$475$	−0.275997	−0.0126636
$476$	−7.86812	−0.360635
$477$	21.9074	1.00307
$478$	−15.0535	−0.688533
$479$	−30.9779	−1.41542	−0.707708	−	0.706505i	$-0.750271\pi$
$479$	−30.9779	−1.41542	−0.707708	+	0.706505i	$0.750271\pi$
$480$	−0.933471	−0.0426069
$481$	−1.36755	−0.0623548
$482$	5.12265	0.233330
$483$	−6.70720	−0.305188
$484$	1.00000	0.0454545
$485$	−29.8887	−1.35717
$486$	10.3781	0.470759
$487$	−40.2405	−1.82347	−0.911735	−	0.410778i	$-0.865257\pi$
$487$	−40.2405	−1.82347	−0.911735	+	0.410778i	$0.865257\pi$
$488$	8.08683	0.366073
$489$	−8.51668	−0.385137
$490$	−7.20449	−0.325466
$491$	23.9956	1.08291	0.541453	−	0.840731i	$-0.317874\pi$
$491$	23.9956	1.08291	0.541453	+	0.840731i	$0.317874\pi$
$492$	−2.36756	−0.106738
$493$	−41.2025	−1.85567
$494$	11.9908	0.539490
$495$	6.34547	0.285208
$496$	2.78382	0.124997
$497$	−7.46045	−0.334647
$498$	−0.997882	−0.0447162
$499$	10.6271	0.475733	0.237867	−	0.971298i	$-0.423552\pi$
$499$	10.6271	0.475733	0.237867	+	0.971298i	$0.423552\pi$
$500$	11.1374	0.498079
$501$	1.19048	0.0531866
$502$	7.34662	0.327896
$503$	−12.7231	−0.567297	−0.283648	−	0.958928i	$-0.591545\pi$
$503$	−12.7231	−0.567297	−0.283648	+	0.958928i	$0.591545\pi$
$504$	5.50384	0.245161
$505$	−18.9429	−0.842948
$506$	−8.28397	−0.368267
$507$	4.26970	0.189624
$508$	−17.6578	−0.783436
$509$	1.21159	0.0537026	0.0268513	−	0.999639i	$-0.491452\pi$
$509$	1.21159	0.0537026	0.0268513	+	0.999639i	$0.491452\pi$
$510$	3.77258	0.167052
$511$	0.828753	0.0366619
$512$	−1.00000	−0.0441942
$513$	−17.5758	−0.775990
$514$	23.0169	1.01523
$515$	2.03886	0.0898431
$516$	−3.04217	−0.133924
$517$	−7.73976	−0.340394
$518$	1.61037	0.0707557
$519$	6.94462	0.304835
$520$	3.71092	0.162734
$521$	10.2745	0.450133	0.225067	−	0.974343i	$-0.427740\pi$
$521$	10.2745	0.450133	0.225067	+	0.974343i	$0.427740\pi$
$522$	28.8217	1.26149
$523$	38.8472	1.69867	0.849334	−	0.527855i	$-0.177004\pi$
$523$	38.8472	1.69867	0.849334	+	0.527855i	$0.177004\pi$
$524$	−7.73493	−0.337902
$525$	−0.0308113	−0.00134471
$526$	12.3679	0.539265
$527$	−11.2507	−0.490087
$528$	−0.415881	−0.0180989
$529$	45.6241	1.98366
$530$	−17.3936	−0.755529
$531$	−22.6117	−0.981266
$532$	−14.1199	−0.612174
$533$	9.41198	0.407678
$534$	4.54635	0.196740
$535$	−31.8527	−1.37711
$536$	11.4984	0.496656
$537$	9.62895	0.415520
$538$	−19.0593	−0.821703
$539$	−3.20976	−0.138254
$540$	−5.43938	−0.234073
$541$	14.0073	0.602221	0.301111	−	0.953589i	$-0.402643\pi$
$541$	14.0073	0.602221	0.301111	+	0.953589i	$0.402643\pi$
$542$	27.2184	1.16913
$543$	−3.48344	−0.149489
$544$	4.04145	0.173276
$545$	−9.50670	−0.407222
$546$	1.33861	0.0572870
$547$	41.4133	1.77070	0.885352	−	0.464922i	$-0.153918\pi$
$547$	41.4133	1.77070	0.885352	+	0.464922i	$0.153918\pi$
$548$	1.28592	0.0549319
$549$	22.8618	0.975718
$550$	−0.0380545	−0.00162265
$551$	−73.9408	−3.14998
$552$	3.44515	0.146635
$553$	−27.0519	−1.15036
$554$	9.80168	0.416433
$555$	−0.772136	−0.0327753
$556$	−15.5538	−0.659627
$557$	12.2680	0.519814	0.259907	−	0.965634i	$-0.416308\pi$
$557$	12.2680	0.519814	0.259907	+	0.965634i	$0.416308\pi$
$558$	7.86998	0.333163
$559$	12.0938	0.511515
$560$	−4.36984	−0.184659
$561$	1.68076	0.0709619
$562$	−10.1543	−0.428332
$563$	14.1117	0.594738	0.297369	−	0.954763i	$-0.403891\pi$
$563$	14.1117	0.594738	0.297369	+	0.954763i	$0.403891\pi$
$564$	3.21882	0.135537
$565$	16.0126	0.673655
$566$	9.36458	0.393623
$567$	14.5494	0.611019
$568$	3.83205	0.160789
$569$	1.27004	0.0532428	0.0266214	−	0.999646i	$-0.491525\pi$
$569$	1.27004	0.0532428	0.0266214	+	0.999646i	$0.491525\pi$
$570$	6.77015	0.283570
$571$	−29.1426	−1.21958	−0.609789	−	0.792564i	$-0.708746\pi$
$571$	−29.1426	−1.21958	−0.609789	+	0.792564i	$0.708746\pi$
$572$	1.65329	0.0691276
$573$	−3.49179	−0.145872
$574$	−11.0832	−0.462603
$575$	0.315242	0.0131465
$576$	−2.82704	−0.117793
$577$	17.4190	0.725164	0.362582	−	0.931952i	$-0.381895\pi$
$577$	17.4190	0.725164	0.362582	+	0.931952i	$0.381895\pi$
$578$	0.666685	0.0277304
$579$	8.90658	0.370145
$580$	−22.8833	−0.950177
$581$	−4.67136	−0.193801
$582$	5.53789	0.229553
$583$	−7.74921	−0.320940
$584$	−0.425688	−0.0176151
$585$	10.4909	0.433746
$586$	6.59187	0.272307
$587$	23.4923	0.969629	0.484815	−	0.874617i	$-0.338887\pi$
$587$	23.4923	0.969629	0.484815	+	0.874617i	$0.338887\pi$
$588$	1.33488	0.0550494
$589$	−20.1901	−0.831919
$590$	17.9528	0.739107
$591$	−0.415881	−0.0171071
$592$	−0.827167	−0.0339963
$593$	−31.0519	−1.27515	−0.637575	−	0.770389i	$-0.720062\pi$
$593$	−31.0519	−1.27515	−0.637575	+	0.770389i	$0.720062\pi$
$594$	−2.42336	−0.0994316
$595$	17.6605	0.724009
$596$	−20.2290	−0.828611
$597$	−0.989587	−0.0405011
$598$	−13.6958	−0.560064
$599$	11.6353	0.475407	0.237703	−	0.971338i	$-0.423605\pi$
$599$	11.6353	0.475407	0.237703	+	0.971338i	$0.423605\pi$
$600$	0.0158262	0.000646101 0
$601$	−21.8978	−0.893230	−0.446615	−	0.894726i	$-0.647371\pi$
$601$	−21.8978	−0.893230	−0.446615	+	0.894726i	$0.647371\pi$
$602$	−14.2413	−0.580430
$603$	32.5065	1.32377
$604$	5.49776	0.223701
$605$	−2.24456	−0.0912544
$606$	3.50982	0.142577
$607$	−3.60391	−0.146278	−0.0731391	−	0.997322i	$-0.523302\pi$
$607$	−3.60391	−0.146278	−0.0731391	+	0.997322i	$0.523302\pi$
$608$	7.25266	0.294134
$609$	−8.25448	−0.334489
$610$	−18.1514	−0.734928
$611$	−12.7961	−0.517674
$612$	11.4254	0.461842
$613$	−11.8355	−0.478031	−0.239016	−	0.971016i	$-0.576825\pi$
$613$	−11.8355	−0.478031	−0.239016	+	0.971016i	$0.576825\pi$
$614$	6.82122	0.275282
$615$	5.31413	0.214286
$616$	−1.94686	−0.0784410
$617$	−11.4542	−0.461129	−0.230564	−	0.973057i	$-0.574057\pi$
$617$	−11.4542	−0.461129	−0.230564	+	0.973057i	$0.574057\pi$
$618$	−0.377769	−0.0151961
$619$	−26.2561	−1.05532	−0.527660	−	0.849455i	$-0.676931\pi$
$619$	−26.2561	−1.05532	−0.527660	+	0.849455i	$0.676931\pi$
$620$	−6.24845	−0.250944
$621$	20.0750	0.805583
$622$	12.7217	0.510095
$623$	21.2827	0.852674
$624$	−0.687573	−0.0275250
$625$	−25.1888	−1.00755
$626$	2.87908	0.115071
$627$	3.01625	0.120457
$628$	2.13019	0.0850039
$629$	3.34295	0.133292
$630$	−12.3537	−0.492184
$631$	11.1616	0.444336	0.222168	−	0.975008i	$-0.428687\pi$
$631$	11.1616	0.444336	0.222168	+	0.975008i	$0.428687\pi$
$632$	13.8952	0.552721
$633$	−5.23419	−0.208040
$634$	−1.25368	−0.0497899
$635$	39.6339	1.57282
$636$	3.22275	0.127790
$637$	−5.30666	−0.210258
$638$	−10.1950	−0.403624
$639$	10.8334	0.428562
$640$	2.24456	0.0887241
$641$	43.2448	1.70807	0.854033	−	0.520219i	$-0.174150\pi$
$641$	43.2448	1.70807	0.854033	+	0.520219i	$0.174150\pi$
$642$	5.90180	0.232926
$643$	49.6160	1.95666	0.978332	−	0.207040i	$-0.0663830\pi$
$643$	49.6160	1.95666	0.978332	+	0.207040i	$0.0663830\pi$
$644$	16.1277	0.635520
$645$	6.82835	0.268866
$646$	−29.3113	−1.15324
$647$	−28.2651	−1.11121	−0.555607	−	0.831445i	$-0.687514\pi$
$647$	−28.2651	−1.11121	−0.555607	+	0.831445i	$0.687514\pi$
$648$	−7.47330	−0.293579
$649$	7.99838	0.313964
$650$	−0.0629153	−0.00246774
$651$	−2.25395	−0.0883392
$652$	20.4786	0.802005
$653$	−15.1579	−0.593175	−0.296588	−	0.955006i	$-0.595849\pi$
$653$	−15.1579	−0.593175	−0.296588	+	0.955006i	$0.595849\pi$
$654$	1.76144	0.0688777
$655$	17.3615	0.678371
$656$	5.69287	0.222269
$657$	−1.20344	−0.0469506
$658$	15.0682	0.587419
$659$	−9.71715	−0.378526	−0.189263	−	0.981926i	$-0.560610\pi$
$659$	−9.71715	−0.378526	−0.189263	+	0.981926i	$0.560610\pi$
$660$	0.933471	0.0363353
$661$	31.9873	1.24416	0.622080	−	0.782953i	$-0.286288\pi$
$661$	31.9873	1.24416	0.622080	+	0.782953i	$0.286288\pi$
$662$	30.0110	1.16641
$663$	2.77879	0.107919
$664$	2.39944	0.0931164
$665$	31.6929	1.22900
$666$	−2.33844	−0.0906125
$667$	84.4550	3.27011
$668$	−2.86254	−0.110755
$669$	7.34572	0.284002
$670$	−25.8089	−0.997084
$671$	−8.08683	−0.312188
$672$	0.809661	0.0312333
$673$	−1.26061	−0.0485930	−0.0242965	−	0.999705i	$-0.507735\pi$
$673$	−1.26061	−0.0485930	−0.0242965	+	0.999705i	$0.507735\pi$
$674$	17.6720	0.680699
$675$	0.0922197	0.00354954
$676$	−10.2666	−0.394870
$677$	−4.77936	−0.183686	−0.0918428	−	0.995774i	$-0.529276\pi$
$677$	−4.77936	−0.183686	−0.0918428	+	0.995774i	$0.529276\pi$
$678$	−2.96688	−0.113942
$679$	25.9244	0.994888
$680$	−9.07128	−0.347868
$681$	7.71302	0.295564
$682$	−2.78382	−0.106598
$683$	29.3451	1.12286	0.561430	−	0.827524i	$-0.310251\pi$
$683$	29.3451	1.12286	0.561430	+	0.827524i	$0.310251\pi$
$684$	20.5036	0.783974
$685$	−2.88633	−0.110281
$686$	19.8769	0.758904
$687$	8.97362	0.342365
$688$	7.31501	0.278882
$689$	−12.8117	−0.488087
$690$	−7.73284	−0.294384
$691$	−34.2141	−1.30157	−0.650783	−	0.759263i	$-0.725559\pi$
$691$	−34.2141	−1.30157	−0.650783	+	0.759263i	$0.725559\pi$
$692$	−16.6986	−0.634784
$693$	−5.50384	−0.209074
$694$	0.243786	0.00925398
$695$	34.9114	1.32427
$696$	4.23991	0.160713
$697$	−23.0074	−0.871469
$698$	34.9736	1.32377
$699$	−9.50207	−0.359401
$700$	0.0740866	0.00280021
$701$	−11.5370	−0.435745	−0.217873	−	0.975977i	$-0.569912\pi$
$701$	−11.5370	−0.435745	−0.217873	+	0.975977i	$0.569912\pi$
$702$	−4.00652	−0.151216
$703$	5.99916	0.226263
$704$	1.00000	0.0376889
$705$	−7.22484	−0.272103
$706$	−24.5306	−0.923221
$707$	16.4304	0.617929
$708$	−3.32637	−0.125013
$709$	−21.8738	−0.821489	−0.410745	−	0.911750i	$-0.634731\pi$
$709$	−21.8738	−0.821489	−0.410745	+	0.911750i	$0.634731\pi$
$710$	−8.60128	−0.322800
$711$	39.2823	1.47320
$712$	−10.9318	−0.409688
$713$	23.0611	0.863644
$714$	−3.27220	−0.122459
$715$	−3.71092	−0.138780
$716$	−23.1531	−0.865273
$717$	−6.26049	−0.233802
$718$	−34.5941	−1.29104
$719$	−13.8885	−0.517953	−0.258976	−	0.965884i	$-0.583385\pi$
$719$	−13.8885	−0.517953	−0.258976	+	0.965884i	$0.583385\pi$
$720$	6.34547	0.236482
$721$	−1.76844	−0.0658601
$722$	−33.6011	−1.25050
$723$	2.13041	0.0792309
$724$	8.37604	0.311293
$725$	0.387966	0.0144087
$726$	0.415881	0.0154348
$727$	13.0964	0.485720	0.242860	−	0.970061i	$-0.421914\pi$
$727$	13.0964	0.485720	0.242860	+	0.970061i	$0.421914\pi$
$728$	−3.21872	−0.119294
$729$	−18.1038	−0.670513
$730$	0.955483	0.0353640
$731$	−29.5632	−1.09344
$732$	3.36316	0.124306
$733$	13.6829	0.505388	0.252694	−	0.967546i	$-0.418683\pi$
$733$	13.6829	0.505388	0.252694	+	0.967546i	$0.418683\pi$
$734$	16.5904	0.612364
$735$	−2.99621	−0.110517
$736$	−8.28397	−0.305351
$737$	−11.4984	−0.423549
$738$	16.0940	0.592428
$739$	−24.5625	−0.903545	−0.451773	−	0.892133i	$-0.649208\pi$
$739$	−24.5625	−0.903545	−0.451773	+	0.892133i	$0.649208\pi$
$740$	1.85663	0.0682509
$741$	4.98674	0.183192
$742$	15.0866	0.553846
$743$	31.4640	1.15430	0.577151	−	0.816637i	$-0.304164\pi$
$743$	31.4640	1.15430	0.577151	+	0.816637i	$0.304164\pi$
$744$	1.15774	0.0424448
$745$	45.4051	1.66352
$746$	−31.2666	−1.14475
$747$	6.78332	0.248189
$748$	−4.04145	−0.147770
$749$	27.6280	1.00950
$750$	4.63183	0.169131
$751$	1.88471	0.0687740	0.0343870	−	0.999409i	$-0.489052\pi$
$751$	1.88471	0.0687740	0.0343870	+	0.999409i	$0.489052\pi$
$752$	−7.73976	−0.282240
$753$	3.05532	0.111342
$754$	−16.8553	−0.613834
$755$	−12.3401	−0.449101
$756$	4.71793	0.171589
$757$	9.73585	0.353856	0.176928	−	0.984224i	$-0.443384\pi$
$757$	9.73585	0.353856	0.176928	+	0.984224i	$0.443384\pi$
$758$	7.45385	0.270736
$759$	−3.44515	−0.125051
$760$	−16.2790	−0.590503
$761$	−3.78408	−0.137173	−0.0685863	−	0.997645i	$-0.521849\pi$
$761$	−3.78408	−0.137173	−0.0685863	+	0.997645i	$0.521849\pi$
$762$	−7.34353	−0.266028
$763$	8.24578	0.298517
$764$	8.39612	0.303761
$765$	−25.6449	−0.927193
$766$	19.2295	0.694790
$767$	13.2237	0.477478
$768$	−0.415881	−0.0150068
$769$	22.9503	0.827608	0.413804	−	0.910366i	$-0.364200\pi$
$769$	22.9503	0.827608	0.413804	+	0.910366i	$0.364200\pi$
$770$	4.36984	0.157478
$771$	9.57231	0.344738
$772$	−21.4162	−0.770784
$773$	−24.2586	−0.872523	−0.436261	−	0.899820i	$-0.643698\pi$
$773$	−24.2586	−0.872523	−0.436261	+	0.899820i	$0.643698\pi$
$774$	20.6798	0.743321
$775$	0.105937	0.00380537
$776$	−13.3160	−0.478018
$777$	0.669724	0.0240262
$778$	18.3410	0.657557
$779$	−41.2885	−1.47931
$780$	1.54330	0.0552590
$781$	−3.83205	−0.137122
$782$	33.4792	1.19721
$783$	24.7061	0.882925
$784$	−3.20976	−0.114634
$785$	−4.78135	−0.170654
$786$	−3.21681	−0.114740
$787$	−46.0669	−1.64211	−0.821054	−	0.570850i	$-0.806614\pi$
$787$	−46.0669	−1.64211	−0.821054	+	0.570850i	$0.806614\pi$
$788$	1.00000	0.0356235
$789$	5.14357	0.183116
$790$	−31.1886	−1.10964
$791$	−13.8888	−0.493828
$792$	2.82704	0.100455
$793$	−13.3699	−0.474779
$794$	5.37974	0.190920
$795$	−7.23366	−0.256552
$796$	2.37949	0.0843389
$797$	43.5713	1.54337	0.771687	−	0.636003i	$-0.219413\pi$
$797$	43.5713	1.54337	0.771687	+	0.636003i	$0.219413\pi$
$798$	−5.87219	−0.207873
$799$	31.2798	1.10660
$800$	−0.0380545	−0.00134543
$801$	−30.9048	−1.09197
$802$	38.0579	1.34387
$803$	0.425688	0.0150222
$804$	4.78197	0.168647
$805$	−36.1996	−1.27587
$806$	−4.60247	−0.162115
$807$	−7.92639	−0.279022
$808$	−8.43947	−0.296899
$809$	−15.7310	−0.553071	−0.276536	−	0.961004i	$-0.589186\pi$
$809$	−15.7310	−0.553071	−0.276536	+	0.961004i	$0.589186\pi$
$810$	16.7743	0.589388
$811$	20.9510	0.735689	0.367845	−	0.929887i	$-0.380096\pi$
$811$	20.9510	0.735689	0.367845	+	0.929887i	$0.380096\pi$
$812$	19.8482	0.696534
$813$	11.3196	0.396996
$814$	0.827167	0.0289922
$815$	−45.9655	−1.61010
$816$	1.68076	0.0588385
$817$	−53.0533	−1.85610
$818$	−25.1927	−0.880843
$819$	−9.09946	−0.317961
$820$	−12.7780	−0.446227
$821$	21.6596	0.755924	0.377962	−	0.925821i	$-0.376625\pi$
$821$	21.6596	0.755924	0.377962	+	0.925821i	$0.376625\pi$
$822$	0.534791	0.0186530
$823$	51.1991	1.78469	0.892344	−	0.451355i	$-0.149059\pi$
$823$	51.1991	1.78469	0.892344	+	0.451355i	$0.149059\pi$
$824$	0.908357	0.0316441
$825$	−0.0158262	−0.000550996 0
$826$	−15.5717	−0.541808
$827$	39.9638	1.38968	0.694839	−	0.719166i	$-0.255476\pi$
$827$	39.9638	1.38968	0.694839	+	0.719166i	$0.255476\pi$
$828$	−23.4191	−0.813871
$829$	8.72748	0.303118	0.151559	−	0.988448i	$-0.451571\pi$
$829$	8.72748	0.303118	0.151559	+	0.988448i	$0.451571\pi$
$830$	−5.38569	−0.186940
$831$	4.07634	0.141406
$832$	1.65329	0.0573176
$833$	12.9721	0.449455
$834$	−6.46853	−0.223987
$835$	6.42514	0.222351
$836$	−7.25266	−0.250839
$837$	6.74619	0.233183
$838$	−3.41451	−0.117952
$839$	−28.0173	−0.967265	−0.483632	−	0.875271i	$-0.660683\pi$
$839$	−28.0173	−0.967265	−0.483632	+	0.875271i	$0.660683\pi$
$840$	−1.81733	−0.0627039
$841$	74.9378	2.58406
$842$	−20.5210	−0.707202
$843$	−4.22297	−0.145447
$844$	12.5858	0.433220
$845$	23.0441	0.792740
$846$	−21.8806	−0.752271
$847$	1.94686	0.0668947
$848$	−7.74921	−0.266109
$849$	3.89456	0.133661
$850$	0.153795	0.00527514
$851$	−6.85222	−0.234891
$852$	1.59368	0.0545985
$853$	35.2276	1.20617	0.603085	−	0.797677i	$-0.293938\pi$
$853$	35.2276	1.20617	0.603085	+	0.797677i	$0.293938\pi$
$854$	15.7439	0.538744
$855$	−46.0215	−1.57390
$856$	−14.1911	−0.485041
$857$	−17.6481	−0.602848	−0.301424	−	0.953490i	$-0.597462\pi$
$857$	−17.6481	−0.602848	−0.301424	+	0.953490i	$0.597462\pi$
$858$	0.687573	0.0234734
$859$	−0.698490	−0.0238322	−0.0119161	−	0.999929i	$-0.503793\pi$
$859$	−0.698490	−0.0238322	−0.0119161	+	0.999929i	$0.503793\pi$
$860$	−16.4190	−0.559883
$861$	−4.60929	−0.157084
$862$	−7.43175	−0.253126
$863$	5.07840	0.172871	0.0864354	−	0.996257i	$-0.472452\pi$
$863$	5.07840	0.172871	0.0864354	+	0.996257i	$0.472452\pi$
$864$	−2.42336	−0.0824443
$865$	37.4809	1.27439
$866$	32.3343	1.09876
$867$	0.277262	0.00941630
$868$	5.41969	0.183956
$869$	−13.8952	−0.471362
$870$	−9.51673	−0.322647
$871$	−19.0102	−0.644137
$872$	−4.23544	−0.143430
$873$	−37.6450	−1.27409
$874$	60.0808	2.03226
$875$	21.6829	0.733015
$876$	−0.177036	−0.00598148
$877$	3.11728	0.105263	0.0526315	−	0.998614i	$-0.483239\pi$
$877$	3.11728	0.105263	0.0526315	+	0.998614i	$0.483239\pi$
$878$	−6.87171	−0.231909
$879$	2.74143	0.0924663
$880$	−2.24456	−0.0756641
$881$	−54.2647	−1.82822	−0.914112	−	0.405462i	$-0.867111\pi$
$881$	−54.2647	−1.82822	−0.914112	+	0.405462i	$0.867111\pi$
$882$	−9.07412	−0.305541
$883$	43.3020	1.45723	0.728614	−	0.684924i	$-0.240165\pi$
$883$	43.3020	1.45723	0.728614	+	0.684924i	$0.240165\pi$
$884$	−6.68170	−0.224730
$885$	7.46625	0.250975
$886$	2.12632	0.0714353
$887$	3.68238	0.123642	0.0618210	−	0.998087i	$-0.480309\pi$
$887$	3.68238	0.123642	0.0618210	+	0.998087i	$0.480309\pi$
$888$	−0.344003	−0.0115440
$889$	−34.3771	−1.15297
$890$	24.5372	0.822489
$891$	7.47330	0.250365
$892$	−17.6630	−0.591402
$893$	56.1338	1.87845
$894$	−8.41285	−0.281368
$895$	51.9686	1.73712
$896$	−1.94686	−0.0650399
$897$	−5.69583	−0.190178
$898$	29.2391	0.975721
$899$	28.3810	0.946560
$900$	−0.107582	−0.00358606
$901$	31.3180	1.04336
$902$	−5.69287	−0.189552
$903$	−5.92267	−0.197094
$904$	7.13396	0.237272
$905$	−18.8005	−0.624951
$906$	2.28642	0.0759611
$907$	−9.34926	−0.310437	−0.155218	−	0.987880i	$-0.549608\pi$
$907$	−9.34926	−0.310437	−0.155218	+	0.987880i	$0.549608\pi$
$908$	−18.5462	−0.615478
$909$	−23.8587	−0.791344
$910$	7.22461	0.239494
$911$	−2.06437	−0.0683955	−0.0341977	−	0.999415i	$-0.510888\pi$
$911$	−2.06437	−0.0683955	−0.0341977	+	0.999415i	$0.510888\pi$
$912$	3.01625	0.0998779
$913$	−2.39944	−0.0794099
$914$	26.0219	0.860727
$915$	−7.54882	−0.249556
$916$	−21.5774	−0.712936
$917$	−15.0588	−0.497285
$918$	9.79388	0.323246
$919$	38.7581	1.27851	0.639256	−	0.768994i	$-0.279242\pi$
$919$	38.7581	1.27851	0.639256	+	0.768994i	$0.279242\pi$
$920$	18.5939	0.613022
$921$	2.83682	0.0934764
$922$	22.1268	0.728708
$923$	−6.33550	−0.208536
$924$	−0.809661	−0.0266359
$925$	−0.0314774	−0.00103497
$926$	18.9937	0.624171
$927$	2.56796	0.0843430
$928$	−10.1950	−0.334667
$929$	−22.1175	−0.725653	−0.362826	−	0.931857i	$-0.618188\pi$
$929$	−22.1175	−0.725653	−0.362826	+	0.931857i	$0.618188\pi$
$930$	−2.59861	−0.0852119
$931$	23.2793	0.762947
$932$	22.8480	0.748412
$933$	5.29073	0.173211
$934$	−20.0636	−0.656502
$935$	9.07128	0.296663
$936$	4.67393	0.152772
$937$	36.0675	1.17828	0.589138	−	0.808033i	$-0.299468\pi$
$937$	36.0675	1.17828	0.589138	+	0.808033i	$0.299468\pi$
$938$	22.3857	0.730920
$939$	1.19736	0.0390742
$940$	17.3724	0.566624
$941$	−45.9104	−1.49664	−0.748319	−	0.663339i	$-0.769139\pi$
$941$	−45.9104	−1.49664	−0.748319	+	0.663339i	$0.769139\pi$
$942$	0.885907	0.0288644
$943$	47.1595	1.53573
$944$	7.99838	0.260325
$945$	−10.5897	−0.344482
$946$	−7.31501	−0.237831
$947$	−29.7380	−0.966356	−0.483178	−	0.875522i	$-0.660518\pi$
$947$	−29.7380	−0.966356	−0.483178	+	0.875522i	$0.660518\pi$
$948$	5.77875	0.187685
$949$	0.703787	0.0228459
$950$	0.275997	0.00895451
$951$	−0.521381	−0.0169069
$952$	7.86812	0.255007
$953$	−17.7427	−0.574741	−0.287370	−	0.957820i	$-0.592781\pi$
$953$	−17.7427	−0.574741	−0.287370	+	0.957820i	$0.592781\pi$
$954$	−21.9074	−0.709277
$955$	−18.8456	−0.609829
$956$	15.0535	0.486866
$957$	−4.23991	−0.137057
$958$	30.9779	1.00085
$959$	2.50351	0.0808424
$960$	0.933471	0.0301276
$961$	−23.2503	−0.750011
$962$	1.36755	0.0440915
$963$	−40.1188	−1.29281
$964$	−5.12265	−0.164989
$965$	48.0699	1.54742
$966$	6.70720	0.215801
$967$	56.9254	1.83060	0.915299	−	0.402774i	$-0.131954\pi$
$967$	56.9254	1.83060	0.915299	+	0.402774i	$0.131954\pi$
$968$	−1.00000	−0.0321412
$969$	−12.1900	−0.391599
$970$	29.8887	0.959668
$971$	−14.3546	−0.460662	−0.230331	−	0.973112i	$-0.573981\pi$
$971$	−14.3546	−0.460662	−0.230331	+	0.973112i	$0.573981\pi$
$972$	−10.3781	−0.332877
$973$	−30.2810	−0.970763
$974$	40.2405	1.28939
$975$	−0.0261653	−0.000837960 0
$976$	−8.08683	−0.258853
$977$	−9.26264	−0.296338	−0.148169	−	0.988962i	$-0.547338\pi$
$977$	−9.26264	−0.296338	−0.148169	+	0.988962i	$0.547338\pi$
$978$	8.51668	0.272333
$979$	10.9318	0.349383
$980$	7.20449	0.230139
$981$	−11.9738	−0.382293
$982$	−23.9956	−0.765731
$983$	−25.0803	−0.799938	−0.399969	−	0.916529i	$-0.630979\pi$
$983$	−25.0803	−0.799938	−0.399969	+	0.916529i	$0.630979\pi$
$984$	2.36756	0.0754750
$985$	−2.24456	−0.0715177
$986$	41.2025	1.31216
$987$	6.26658	0.199467
$988$	−11.9908	−0.381477
$989$	60.5973	1.92688
$990$	−6.34547	−0.201672
$991$	−22.6092	−0.718206	−0.359103	−	0.933298i	$-0.616917\pi$
$991$	−22.6092	−0.718206	−0.359103	+	0.933298i	$0.616917\pi$
$992$	−2.78382	−0.0883864
$993$	12.4810	0.396073
$994$	7.46045	0.236631
$995$	−5.34092	−0.169318
$996$	0.997882	0.0316191
$997$	−15.6951	−0.497070	−0.248535	−	0.968623i	$-0.579949\pi$
$997$	−15.6951	−0.497070	−0.248535	+	0.968623i	$0.579949\pi$
$998$	−10.6271	−0.336394
$999$	−2.00452	−0.0634202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.7	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.7	✓	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.415881 q^{3} +1.00000 q^{4} -2.24456 q^{5} +0.415881 q^{6} +1.94686 q^{7} -1.00000 q^{8} -2.82704 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.415881 q^{3} +1.00000 q^{4} -2.24456 q^{5} +0.415881 q^{6} +1.94686 q^{7} -1.00000 q^{8} -2.82704 q^{9} +2.24456 q^{10} +1.00000 q^{11} -0.415881 q^{12} +1.65329 q^{13} -1.94686 q^{14} +0.933471 q^{15} +1.00000 q^{16} -4.04145 q^{17} +2.82704 q^{18} -7.25266 q^{19} -2.24456 q^{20} -0.809661 q^{21} -1.00000 q^{22} +8.28397 q^{23} +0.415881 q^{24} +0.0380545 q^{25} -1.65329 q^{26} +2.42336 q^{27} +1.94686 q^{28} +10.1950 q^{29} -0.933471 q^{30} +2.78382 q^{31} -1.00000 q^{32} -0.415881 q^{33} +4.04145 q^{34} -4.36984 q^{35} -2.82704 q^{36} -0.827167 q^{37} +7.25266 q^{38} -0.687573 q^{39} +2.24456 q^{40} +5.69287 q^{41} +0.809661 q^{42} +7.31501 q^{43} +1.00000 q^{44} +6.34547 q^{45} -8.28397 q^{46} -7.73976 q^{47} -0.415881 q^{48} -3.20976 q^{49} -0.0380545 q^{50} +1.68076 q^{51} +1.65329 q^{52} -7.74921 q^{53} -2.42336 q^{54} -2.24456 q^{55} -1.94686 q^{56} +3.01625 q^{57} -10.1950 q^{58} +7.99838 q^{59} +0.933471 q^{60} -8.08683 q^{61} -2.78382 q^{62} -5.50384 q^{63} +1.00000 q^{64} -3.71092 q^{65} +0.415881 q^{66} -11.4984 q^{67} -4.04145 q^{68} -3.44515 q^{69} +4.36984 q^{70} -3.83205 q^{71} +2.82704 q^{72} +0.425688 q^{73} +0.827167 q^{74} -0.0158262 q^{75} -7.25266 q^{76} +1.94686 q^{77} +0.687573 q^{78} -13.8952 q^{79} -2.24456 q^{80} +7.47330 q^{81} -5.69287 q^{82} -2.39944 q^{83} -0.809661 q^{84} +9.07128 q^{85} -7.31501 q^{86} -4.23991 q^{87} -1.00000 q^{88} +10.9318 q^{89} -6.34547 q^{90} +3.21872 q^{91} +8.28397 q^{92} -1.15774 q^{93} +7.73976 q^{94} +16.2790 q^{95} +0.415881 q^{96} +13.3160 q^{97} +3.20976 q^{98} -2.82704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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