LMFDB - Embedded newform 9282.2.a.bs.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9282,2,Mod(1,9282)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9282, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9282.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9282.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:	$74.1171431562$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.1462249.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 7x^{2} + 15x + 2 $ x^5 - 2x^4 - 7x^3 + 7x^2 + 15x + 2
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			1.1
Root			$2.96233$ of defining polynomial
Character	$\chi$	$=$	9282.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.96233 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.96233 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.96233 q^{10} -2.25524 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +3.96233 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -6.47112 q^{19} -3.96233 q^{20} -1.00000 q^{21} -2.25524 q^{22} +2.91330 q^{23} -1.00000 q^{24} +10.7000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.33320 q^{29} +3.96233 q^{30} -3.76015 q^{31} +1.00000 q^{32} +2.25524 q^{33} +1.00000 q^{34} -3.96233 q^{35} +1.00000 q^{36} +1.35548 q^{37} -6.47112 q^{38} -1.00000 q^{39} -3.96233 q^{40} -2.43487 q^{41} -1.00000 q^{42} +8.09908 q^{43} -2.25524 q^{44} -3.96233 q^{45} +2.91330 q^{46} +5.82098 q^{47} -1.00000 q^{48} +1.00000 q^{49} +10.7000 q^{50} -1.00000 q^{51} +1.00000 q^{52} -0.0455926 q^{53} -1.00000 q^{54} +8.93601 q^{55} +1.00000 q^{56} +6.47112 q^{57} +5.33320 q^{58} +5.64151 q^{59} +3.96233 q^{60} -5.96980 q^{61} -3.76015 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.96233 q^{65} +2.25524 q^{66} +2.70305 q^{67} +1.00000 q^{68} -2.91330 q^{69} -3.96233 q^{70} -7.94981 q^{71} +1.00000 q^{72} +4.01539 q^{73} +1.35548 q^{74} -10.7000 q^{75} -6.47112 q^{76} -2.25524 q^{77} -1.00000 q^{78} +3.56513 q^{79} -3.96233 q^{80} +1.00000 q^{81} -2.43487 q^{82} -6.96074 q^{83} -1.00000 q^{84} -3.96233 q^{85} +8.09908 q^{86} -5.33320 q^{87} -2.25524 q^{88} -9.63174 q^{89} -3.96233 q^{90} +1.00000 q^{91} +2.91330 q^{92} +3.76015 q^{93} +5.82098 q^{94} +25.6407 q^{95} -1.00000 q^{96} +3.25743 q^{97} +1.00000 q^{98} -2.25524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9} - 7 q^{10} - 9 q^{11} - 5 q^{12} + 5 q^{13} + 5 q^{14} + 7 q^{15} + 5 q^{16} + 5 q^{17} + 5 q^{18} - q^{19} - 7 q^{20} - 5 q^{21} - 9 q^{22} - 6 q^{23} - 5 q^{24} + 2 q^{25} + 5 q^{26} - 5 q^{27} + 5 q^{28} - 10 q^{29} + 7 q^{30} - 7 q^{31} + 5 q^{32} + 9 q^{33} + 5 q^{34} - 7 q^{35} + 5 q^{36} - 3 q^{37} - q^{38} - 5 q^{39} - 7 q^{40} - 19 q^{41} - 5 q^{42} - 3 q^{43} - 9 q^{44} - 7 q^{45} - 6 q^{46} - 2 q^{47} - 5 q^{48} + 5 q^{49} + 2 q^{50} - 5 q^{51} + 5 q^{52} + 5 q^{53} - 5 q^{54} + 14 q^{55} + 5 q^{56} + q^{57} - 10 q^{58} - 12 q^{59} + 7 q^{60} - 21 q^{61} - 7 q^{62} + 5 q^{63} + 5 q^{64} - 7 q^{65} + 9 q^{66} + 12 q^{67} + 5 q^{68} + 6 q^{69} - 7 q^{70} + 4 q^{71} + 5 q^{72} + 6 q^{73} - 3 q^{74} - 2 q^{75} - q^{76} - 9 q^{77} - 5 q^{78} + 11 q^{79} - 7 q^{80} + 5 q^{81} - 19 q^{82} - 23 q^{83} - 5 q^{84} - 7 q^{85} - 3 q^{86} + 10 q^{87} - 9 q^{88} - 12 q^{89} - 7 q^{90} + 5 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} + 15 q^{95} - 5 q^{96} - 9 q^{97} + 5 q^{98} - 9 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9 - 7 * q^10 - 9 * q^11 - 5 * q^12 + 5 * q^13 + 5 * q^14 + 7 * q^15 + 5 * q^16 + 5 * q^17 + 5 * q^18 - q^19 - 7 * q^20 - 5 * q^21 - 9 * q^22 - 6 * q^23 - 5 * q^24 + 2 * q^25 + 5 * q^26 - 5 * q^27 + 5 * q^28 - 10 * q^29 + 7 * q^30 - 7 * q^31 + 5 * q^32 + 9 * q^33 + 5 * q^34 - 7 * q^35 + 5 * q^36 - 3 * q^37 - q^38 - 5 * q^39 - 7 * q^40 - 19 * q^41 - 5 * q^42 - 3 * q^43 - 9 * q^44 - 7 * q^45 - 6 * q^46 - 2 * q^47 - 5 * q^48 + 5 * q^49 + 2 * q^50 - 5 * q^51 + 5 * q^52 + 5 * q^53 - 5 * q^54 + 14 * q^55 + 5 * q^56 + q^57 - 10 * q^58 - 12 * q^59 + 7 * q^60 - 21 * q^61 - 7 * q^62 + 5 * q^63 + 5 * q^64 - 7 * q^65 + 9 * q^66 + 12 * q^67 + 5 * q^68 + 6 * q^69 - 7 * q^70 + 4 * q^71 + 5 * q^72 + 6 * q^73 - 3 * q^74 - 2 * q^75 - q^76 - 9 * q^77 - 5 * q^78 + 11 * q^79 - 7 * q^80 + 5 * q^81 - 19 * q^82 - 23 * q^83 - 5 * q^84 - 7 * q^85 - 3 * q^86 + 10 * q^87 - 9 * q^88 - 12 * q^89 - 7 * q^90 + 5 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 + 15 * q^95 - 5 * q^96 - 9 * q^97 + 5 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.96233	−1.77201	−0.886003	−	0.463679i	$-0.846529\pi$
$5$	−3.96233	−1.77201	−0.886003	+	0.463679i	$0.846529\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.96233	−1.25300
$11$	−2.25524	−0.679981	−0.339991	−	0.940429i	$-0.610424\pi$
$11$	−2.25524	−0.679981	−0.339991	+	0.940429i	$0.610424\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.00000	0.267261
$15$	3.96233	1.02307
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−6.47112	−1.48458	−0.742288	−	0.670081i	$-0.766259\pi$
$19$	−6.47112	−1.48458	−0.742288	+	0.670081i	$0.766259\pi$
$20$	−3.96233	−0.886003
$21$	−1.00000	−0.218218
$22$	−2.25524	−0.480819
$23$	2.91330	0.607465	0.303733	−	0.952757i	$-0.401767\pi$
$23$	2.91330	0.607465	0.303733	+	0.952757i	$0.401767\pi$
$24$	−1.00000	−0.204124
$25$	10.7000	2.14001
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	5.33320	0.990351	0.495176	−	0.868793i	$-0.335104\pi$
$29$	5.33320	0.990351	0.495176	+	0.868793i	$0.335104\pi$
$30$	3.96233	0.723419
$31$	−3.76015	−0.675343	−0.337671	−	0.941264i	$-0.609639\pi$
$31$	−3.76015	−0.675343	−0.337671	+	0.941264i	$0.609639\pi$
$32$	1.00000	0.176777
$33$	2.25524	0.392587
$34$	1.00000	0.171499
$35$	−3.96233	−0.669756
$36$	1.00000	0.166667
$37$	1.35548	0.222840	0.111420	−	0.993773i	$-0.464460\pi$
$37$	1.35548	0.222840	0.111420	+	0.993773i	$0.464460\pi$
$38$	−6.47112	−1.04975
$39$	−1.00000	−0.160128
$40$	−3.96233	−0.626499
$41$	−2.43487	−0.380262	−0.190131	−	0.981759i	$-0.560891\pi$
$41$	−2.43487	−0.380262	−0.190131	+	0.981759i	$0.560891\pi$
$42$	−1.00000	−0.154303
$43$	8.09908	1.23510	0.617549	−	0.786532i	$-0.288126\pi$
$43$	8.09908	1.23510	0.617549	+	0.786532i	$0.288126\pi$
$44$	−2.25524	−0.339991
$45$	−3.96233	−0.590669
$46$	2.91330	0.429543
$47$	5.82098	0.849077	0.424539	−	0.905410i	$-0.360436\pi$
$47$	5.82098	0.849077	0.424539	+	0.905410i	$0.360436\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	10.7000	1.51321
$51$	−1.00000	−0.140028
$52$	1.00000	0.138675
$53$	−0.0455926	−0.00626263	−0.00313132	−	0.999995i	$-0.500997\pi$
$53$	−0.0455926	−0.00626263	−0.00313132	+	0.999995i	$0.500997\pi$
$54$	−1.00000	−0.136083
$55$	8.93601	1.20493
$56$	1.00000	0.133631
$57$	6.47112	0.857121
$58$	5.33320	0.700284
$59$	5.64151	0.734462	0.367231	−	0.930130i	$-0.380306\pi$
$59$	5.64151	0.734462	0.367231	+	0.930130i	$0.380306\pi$
$60$	3.96233	0.511534
$61$	−5.96980	−0.764354	−0.382177	−	0.924089i	$-0.624826\pi$
$61$	−5.96980	−0.764354	−0.382177	+	0.924089i	$0.624826\pi$
$62$	−3.76015	−0.477539
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−3.96233	−0.491466
$66$	2.25524	0.277601
$67$	2.70305	0.330230	0.165115	−	0.986274i	$-0.447200\pi$
$67$	2.70305	0.330230	0.165115	+	0.986274i	$0.447200\pi$
$68$	1.00000	0.121268
$69$	−2.91330	−0.350720
$70$	−3.96233	−0.473589
$71$	−7.94981	−0.943469	−0.471735	−	0.881741i	$-0.656372\pi$
$71$	−7.94981	−0.943469	−0.471735	+	0.881741i	$0.656372\pi$
$72$	1.00000	0.117851
$73$	4.01539	0.469966	0.234983	−	0.971999i	$-0.424497\pi$
$73$	4.01539	0.469966	0.234983	+	0.971999i	$0.424497\pi$
$74$	1.35548	0.157572
$75$	−10.7000	−1.23553
$76$	−6.47112	−0.742288
$77$	−2.25524	−0.257009
$78$	−1.00000	−0.113228
$79$	3.56513	0.401109	0.200554	−	0.979683i	$-0.435726\pi$
$79$	3.56513	0.401109	0.200554	+	0.979683i	$0.435726\pi$
$80$	−3.96233	−0.443002
$81$	1.00000	0.111111
$82$	−2.43487	−0.268886
$83$	−6.96074	−0.764041	−0.382020	−	0.924154i	$-0.624772\pi$
$83$	−6.96074	−0.764041	−0.382020	+	0.924154i	$0.624772\pi$
$84$	−1.00000	−0.109109
$85$	−3.96233	−0.429775
$86$	8.09908	0.873347
$87$	−5.33320	−0.571779
$88$	−2.25524	−0.240410
$89$	−9.63174	−1.02096	−0.510481	−	0.859889i	$-0.670533\pi$
$89$	−9.63174	−1.02096	−0.510481	+	0.859889i	$0.670533\pi$
$90$	−3.96233	−0.417666
$91$	1.00000	0.104828
$92$	2.91330	0.303733
$93$	3.76015	0.389909
$94$	5.82098	0.600388
$95$	25.6407	2.63068
$96$	−1.00000	−0.102062
$97$	3.25743	0.330742	0.165371	−	0.986231i	$-0.447118\pi$
$97$	3.25743	0.330742	0.165371	+	0.986231i	$0.447118\pi$
$98$	1.00000	0.101015
$99$	−2.25524	−0.226660
$100$	10.7000	1.07000
$101$	4.79481	0.477102	0.238551	−	0.971130i	$-0.423328\pi$
$101$	4.79481	0.477102	0.238551	+	0.971130i	$0.423328\pi$
$102$	−1.00000	−0.0990148
$103$	−3.51999	−0.346835	−0.173418	−	0.984848i	$-0.555481\pi$
$103$	−3.51999	−0.346835	−0.173418	+	0.984848i	$0.555481\pi$
$104$	1.00000	0.0980581
$105$	3.96233	0.386684
$106$	−0.0455926	−0.00442835
$107$	−16.4738	−1.59259	−0.796293	−	0.604911i	$-0.793209\pi$
$107$	−16.4738	−1.59259	−0.796293	+	0.604911i	$0.793209\pi$
$108$	−1.00000	−0.0962250
$109$	−12.9743	−1.24271	−0.621356	−	0.783529i	$-0.713418\pi$
$109$	−12.9743	−1.24271	−0.621356	+	0.783529i	$0.713418\pi$
$110$	8.93601	0.852015
$111$	−1.35548	−0.128657
$112$	1.00000	0.0944911
$113$	−14.7472	−1.38730	−0.693651	−	0.720311i	$-0.743999\pi$
$113$	−14.7472	−1.38730	−0.693651	+	0.720311i	$0.743999\pi$
$114$	6.47112	0.606076
$115$	−11.5435	−1.07643
$116$	5.33320	0.495176
$117$	1.00000	0.0924500
$118$	5.64151	0.519343
$119$	1.00000	0.0916698
$120$	3.96233	0.361709
$121$	−5.91388	−0.537626
$122$	−5.96980	−0.540480
$123$	2.43487	0.219544
$124$	−3.76015	−0.337671
$125$	−22.5854	−2.02010
$126$	1.00000	0.0890871
$127$	17.7837	1.57805	0.789026	−	0.614360i	$-0.210586\pi$
$127$	17.7837	1.57805	0.789026	+	0.614360i	$0.210586\pi$
$128$	1.00000	0.0883883
$129$	−8.09908	−0.713085
$130$	−3.96233	−0.347519
$131$	11.5643	1.01038	0.505190	−	0.863008i	$-0.331423\pi$
$131$	11.5643	1.01038	0.505190	+	0.863008i	$0.331423\pi$
$132$	2.25524	0.196294
$133$	−6.47112	−0.561117
$134$	2.70305	0.233508
$135$	3.96233	0.341023
$136$	1.00000	0.0857493
$137$	10.0135	0.855515	0.427757	−	0.903894i	$-0.359304\pi$
$137$	10.0135	0.855515	0.427757	+	0.903894i	$0.359304\pi$
$138$	−2.91330	−0.247997
$139$	−1.04156	−0.0883437	−0.0441718	−	0.999024i	$-0.514065\pi$
$139$	−1.04156	−0.0883437	−0.0441718	+	0.999024i	$0.514065\pi$
$140$	−3.96233	−0.334878
$141$	−5.82098	−0.490215
$142$	−7.94981	−0.667134
$143$	−2.25524	−0.188593
$144$	1.00000	0.0833333
$145$	−21.1319	−1.75491
$146$	4.01539	0.332316
$147$	−1.00000	−0.0824786
$148$	1.35548	0.111420
$149$	−17.9534	−1.47080	−0.735401	−	0.677632i	$-0.763006\pi$
$149$	−17.9534	−1.47080	−0.735401	+	0.677632i	$0.763006\pi$
$150$	−10.7000	−0.873655
$151$	2.69011	0.218918	0.109459	−	0.993991i	$-0.465088\pi$
$151$	2.69011	0.218918	0.109459	+	0.993991i	$0.465088\pi$
$152$	−6.47112	−0.524877
$153$	1.00000	0.0808452
$154$	−2.25524	−0.181733
$155$	14.8989	1.19671
$156$	−1.00000	−0.0800641
$157$	22.3962	1.78741	0.893706	−	0.448654i	$-0.148096\pi$
$157$	22.3962	1.78741	0.893706	+	0.448654i	$0.148096\pi$
$158$	3.56513	0.283627
$159$	0.0455926	0.00361573
$160$	−3.96233	−0.313250
$161$	2.91330	0.229600
$162$	1.00000	0.0785674
$163$	17.0961	1.33907	0.669534	−	0.742781i	$-0.266494\pi$
$163$	17.0961	1.33907	0.669534	+	0.742781i	$0.266494\pi$
$164$	−2.43487	−0.190131
$165$	−8.93601	−0.695667
$166$	−6.96074	−0.540258
$167$	10.8236	0.837555	0.418778	−	0.908089i	$-0.362459\pi$
$167$	10.8236	0.837555	0.418778	+	0.908089i	$0.362459\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	−3.96233	−0.303897
$171$	−6.47112	−0.494859
$172$	8.09908	0.617549
$173$	−11.3536	−0.863201	−0.431601	−	0.902065i	$-0.642051\pi$
$173$	−11.3536	−0.863201	−0.431601	+	0.902065i	$0.642051\pi$
$174$	−5.33320	−0.404309
$175$	10.7000	0.808847
$176$	−2.25524	−0.169995
$177$	−5.64151	−0.424042
$178$	−9.63174	−0.721930
$179$	−3.83577	−0.286699	−0.143349	−	0.989672i	$-0.545787\pi$
$179$	−3.83577	−0.286699	−0.143349	+	0.989672i	$0.545787\pi$
$180$	−3.96233	−0.295334
$181$	−22.2565	−1.65432	−0.827158	−	0.561969i	$-0.810044\pi$
$181$	−22.2565	−1.65432	−0.827158	+	0.561969i	$0.810044\pi$
$182$	1.00000	0.0741249
$183$	5.96980	0.441300
$184$	2.91330	0.214771
$185$	−5.37088	−0.394875
$186$	3.76015	0.275707
$187$	−2.25524	−0.164920
$188$	5.82098	0.424539
$189$	−1.00000	−0.0727393
$190$	25.6407	1.86017
$191$	−10.8837	−0.787517	−0.393759	−	0.919214i	$-0.628825\pi$
$191$	−10.8837	−0.787517	−0.393759	+	0.919214i	$0.628825\pi$
$192$	−1.00000	−0.0721688
$193$	24.6673	1.77559	0.887795	−	0.460239i	$-0.152236\pi$
$193$	24.6673	1.77559	0.887795	+	0.460239i	$0.152236\pi$
$194$	3.25743	0.233870
$195$	3.96233	0.283748
$196$	1.00000	0.0714286
$197$	−12.6432	−0.900794	−0.450397	−	0.892828i	$-0.648718\pi$
$197$	−12.6432	−0.900794	−0.450397	+	0.892828i	$0.648718\pi$
$198$	−2.25524	−0.160273
$199$	−10.4260	−0.739078	−0.369539	−	0.929215i	$-0.620484\pi$
$199$	−10.4260	−0.739078	−0.369539	+	0.929215i	$0.620484\pi$
$200$	10.7000	0.756607
$201$	−2.70305	−0.190658
$202$	4.79481	0.337362
$203$	5.33320	0.374318
$204$	−1.00000	−0.0700140
$205$	9.64773	0.673827
$206$	−3.51999	−0.245250
$207$	2.91330	0.202488
$208$	1.00000	0.0693375
$209$	14.5939	1.00948
$210$	3.96233	0.273427
$211$	−3.27222	−0.225269	−0.112634	−	0.993636i	$-0.535929\pi$
$211$	−3.27222	−0.225269	−0.112634	+	0.993636i	$0.535929\pi$
$212$	−0.0455926	−0.00313132
$213$	7.94981	0.544712
$214$	−16.4738	−1.12613
$215$	−32.0912	−2.18860
$216$	−1.00000	−0.0680414
$217$	−3.76015	−0.255256
$218$	−12.9743	−0.878729
$219$	−4.01539	−0.271335
$220$	8.93601	0.602466
$221$	1.00000	0.0672673
$222$	−1.35548	−0.0909742
$223$	−17.0179	−1.13960	−0.569800	−	0.821783i	$-0.692979\pi$
$223$	−17.0179	−1.13960	−0.569800	+	0.821783i	$0.692979\pi$
$224$	1.00000	0.0668153
$225$	10.7000	0.713336
$226$	−14.7472	−0.980971
$227$	−22.1254	−1.46852	−0.734258	−	0.678871i	$-0.762470\pi$
$227$	−22.1254	−1.46852	−0.734258	+	0.678871i	$0.762470\pi$
$228$	6.47112	0.428560
$229$	−4.86224	−0.321306	−0.160653	−	0.987011i	$-0.551360\pi$
$229$	−4.86224	−0.321306	−0.160653	+	0.987011i	$0.551360\pi$
$230$	−11.5435	−0.761153
$231$	2.25524	0.148384
$232$	5.33320	0.350142
$233$	2.89117	0.189407	0.0947035	−	0.995506i	$-0.469810\pi$
$233$	2.89117	0.189407	0.0947035	+	0.995506i	$0.469810\pi$
$234$	1.00000	0.0653720
$235$	−23.0646	−1.50457
$236$	5.64151	0.367231
$237$	−3.56513	−0.231580
$238$	1.00000	0.0648204
$239$	−26.9063	−1.74042	−0.870211	−	0.492680i	$-0.836017\pi$
$239$	−26.9063	−1.74042	−0.870211	+	0.492680i	$0.836017\pi$
$240$	3.96233	0.255767
$241$	−7.93947	−0.511426	−0.255713	−	0.966753i	$-0.582310\pi$
$241$	−7.93947	−0.511426	−0.255713	+	0.966753i	$0.582310\pi$
$242$	−5.91388	−0.380159
$243$	−1.00000	−0.0641500
$244$	−5.96980	−0.382177
$245$	−3.96233	−0.253144
$246$	2.43487	0.155241
$247$	−6.47112	−0.411747
$248$	−3.76015	−0.238770
$249$	6.96074	0.441119
$250$	−22.5854	−1.42843
$251$	−0.943053	−0.0595250	−0.0297625	−	0.999557i	$-0.509475\pi$
$251$	−0.943053	−0.0595250	−0.0297625	+	0.999557i	$0.509475\pi$
$252$	1.00000	0.0629941
$253$	−6.57020	−0.413065
$254$	17.7837	1.11585
$255$	3.96233	0.248131
$256$	1.00000	0.0625000
$257$	−23.5309	−1.46782	−0.733910	−	0.679247i	$-0.762307\pi$
$257$	−23.5309	−1.46782	−0.733910	+	0.679247i	$0.762307\pi$
$258$	−8.09908	−0.504227
$259$	1.35548	0.0842257
$260$	−3.96233	−0.245733
$261$	5.33320	0.330117
$262$	11.5643	0.714446
$263$	15.2745	0.941867	0.470934	−	0.882169i	$-0.343917\pi$
$263$	15.2745	0.941867	0.470934	+	0.882169i	$0.343917\pi$
$264$	2.25524	0.138801
$265$	0.180653	0.0110974
$266$	−6.47112	−0.396770
$267$	9.63174	0.589453
$268$	2.70305	0.165115
$269$	−21.9309	−1.33715	−0.668575	−	0.743645i	$-0.733095\pi$
$269$	−21.9309	−1.33715	−0.668575	+	0.743645i	$0.733095\pi$
$270$	3.96233	0.241140
$271$	27.0643	1.64404	0.822020	−	0.569458i	$-0.192847\pi$
$271$	27.0643	1.64404	0.822020	+	0.569458i	$0.192847\pi$
$272$	1.00000	0.0606339
$273$	−1.00000	−0.0605228
$274$	10.0135	0.604940
$275$	−24.1312	−1.45517
$276$	−2.91330	−0.175360
$277$	−0.0429912	−0.00258309	−0.00129154	−	0.999999i	$-0.500411\pi$
$277$	−0.0429912	−0.00258309	−0.00129154	+	0.999999i	$0.500411\pi$
$278$	−1.04156	−0.0624684
$279$	−3.76015	−0.225114
$280$	−3.96233	−0.236794
$281$	−18.5037	−1.10384	−0.551920	−	0.833897i	$-0.686105\pi$
$281$	−18.5037	−1.10384	−0.551920	+	0.833897i	$0.686105\pi$
$282$	−5.82098	−0.346634
$283$	5.73772	0.341072	0.170536	−	0.985351i	$-0.445450\pi$
$283$	5.73772	0.341072	0.170536	+	0.985351i	$0.445450\pi$
$284$	−7.94981	−0.471735
$285$	−25.6407	−1.51882
$286$	−2.25524	−0.133355
$287$	−2.43487	−0.143726
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−21.1319	−1.24091
$291$	−3.25743	−0.190954
$292$	4.01539	0.234983
$293$	−10.7157	−0.626018	−0.313009	−	0.949750i	$-0.601337\pi$
$293$	−10.7157	−0.626018	−0.313009	+	0.949750i	$0.601337\pi$
$294$	−1.00000	−0.0583212
$295$	−22.3535	−1.30147
$296$	1.35548	0.0787860
$297$	2.25524	0.130862
$298$	−17.9534	−1.04001
$299$	2.91330	0.168481
$300$	−10.7000	−0.617767
$301$	8.09908	0.466823
$302$	2.69011	0.154798
$303$	−4.79481	−0.275455
$304$	−6.47112	−0.371144
$305$	23.6543	1.35444
$306$	1.00000	0.0571662
$307$	−12.4597	−0.711112	−0.355556	−	0.934655i	$-0.615709\pi$
$307$	−12.4597	−0.711112	−0.355556	+	0.934655i	$0.615709\pi$
$308$	−2.25524	−0.128504
$309$	3.51999	0.200245
$310$	14.8989	0.846203
$311$	1.66772	0.0945676	0.0472838	−	0.998881i	$-0.484943\pi$
$311$	1.66772	0.0945676	0.0472838	+	0.998881i	$0.484943\pi$
$312$	−1.00000	−0.0566139
$313$	24.8826	1.40645	0.703223	−	0.710969i	$-0.251743\pi$
$313$	24.8826	1.40645	0.703223	+	0.710969i	$0.251743\pi$
$314$	22.3962	1.26389
$315$	−3.96233	−0.223252
$316$	3.56513	0.200554
$317$	−22.9947	−1.29151	−0.645755	−	0.763544i	$-0.723457\pi$
$317$	−22.9947	−1.29151	−0.645755	+	0.763544i	$0.723457\pi$
$318$	0.0455926	0.00255671
$319$	−12.0277	−0.673420
$320$	−3.96233	−0.221501
$321$	16.4738	0.919480
$322$	2.91330	0.162352
$323$	−6.47112	−0.360063
$324$	1.00000	0.0555556
$325$	10.7000	0.593532
$326$	17.0961	0.946864
$327$	12.9743	0.717480
$328$	−2.43487	−0.134443
$329$	5.82098	0.320921
$330$	−8.93601	−0.491911
$331$	−5.22783	−0.287348	−0.143674	−	0.989625i	$-0.545892\pi$
$331$	−5.22783	−0.287348	−0.143674	+	0.989625i	$0.545892\pi$
$332$	−6.96074	−0.382020
$333$	1.35548	0.0742801
$334$	10.8236	0.592241
$335$	−10.7104	−0.585170
$336$	−1.00000	−0.0545545
$337$	15.8199	0.861763	0.430881	−	0.902409i	$-0.358203\pi$
$337$	15.8199	0.861763	0.430881	+	0.902409i	$0.358203\pi$
$338$	1.00000	0.0543928
$339$	14.7472	0.800959
$340$	−3.96233	−0.214887
$341$	8.48005	0.459220
$342$	−6.47112	−0.349918
$343$	1.00000	0.0539949
$344$	8.09908	0.436673
$345$	11.5435	0.621479
$346$	−11.3536	−0.610375
$347$	−6.67789	−0.358488	−0.179244	−	0.983805i	$-0.557365\pi$
$347$	−6.67789	−0.358488	−0.179244	+	0.983805i	$0.557365\pi$
$348$	−5.33320	−0.285890
$349$	10.9660	0.586995	0.293498	−	0.955960i	$-0.405181\pi$
$349$	10.9660	0.586995	0.293498	+	0.955960i	$0.405181\pi$
$350$	10.7000	0.571941
$351$	−1.00000	−0.0533761
$352$	−2.25524	−0.120205
$353$	−1.66394	−0.0885627	−0.0442814	−	0.999019i	$-0.514100\pi$
$353$	−1.66394	−0.0885627	−0.0442814	+	0.999019i	$0.514100\pi$
$354$	−5.64151	−0.299843
$355$	31.4998	1.67183
$356$	−9.63174	−0.510481
$357$	−1.00000	−0.0529256
$358$	−3.83577	−0.202727
$359$	−1.12052	−0.0591390	−0.0295695	−	0.999563i	$-0.509414\pi$
$359$	−1.12052	−0.0591390	−0.0295695	+	0.999563i	$0.509414\pi$
$360$	−3.96233	−0.208833
$361$	22.8754	1.20397
$362$	−22.2565	−1.16978
$363$	5.91388	0.310398
$364$	1.00000	0.0524142
$365$	−15.9103	−0.832783
$366$	5.96980	0.312046
$367$	−30.0476	−1.56847	−0.784237	−	0.620462i	$-0.786945\pi$
$367$	−30.0476	−1.56847	−0.784237	+	0.620462i	$0.786945\pi$
$368$	2.91330	0.151866
$369$	−2.43487	−0.126754
$370$	−5.37088	−0.279219
$371$	−0.0455926	−0.00236705
$372$	3.76015	0.194955
$373$	−7.17816	−0.371671	−0.185836	−	0.982581i	$-0.559499\pi$
$373$	−7.17816	−0.371671	−0.185836	+	0.982581i	$0.559499\pi$
$374$	−2.25524	−0.116616
$375$	22.5854	1.16631
$376$	5.82098	0.300194
$377$	5.33320	0.274674
$378$	−1.00000	−0.0514344
$379$	−19.4853	−1.00090	−0.500448	−	0.865767i	$-0.666831\pi$
$379$	−19.4853	−1.00090	−0.500448	+	0.865767i	$0.666831\pi$
$380$	25.6407	1.31534
$381$	−17.7837	−0.911088
$382$	−10.8837	−0.556859
$383$	11.2639	0.575556	0.287778	−	0.957697i	$-0.407083\pi$
$383$	11.2639	0.575556	0.287778	+	0.957697i	$0.407083\pi$
$384$	−1.00000	−0.0510310
$385$	8.93601	0.455421
$386$	24.6673	1.25553
$387$	8.09908	0.411700
$388$	3.25743	0.165371
$389$	−1.44305	−0.0731653	−0.0365827	−	0.999331i	$-0.511647\pi$
$389$	−1.44305	−0.0731653	−0.0365827	+	0.999331i	$0.511647\pi$
$390$	3.96233	0.200640
$391$	2.91330	0.147332
$392$	1.00000	0.0505076
$393$	−11.5643	−0.583343
$394$	−12.6432	−0.636958
$395$	−14.1262	−0.710768
$396$	−2.25524	−0.113330
$397$	−28.6415	−1.43748	−0.718739	−	0.695280i	$-0.755280\pi$
$397$	−28.6415	−1.43748	−0.718739	+	0.695280i	$0.755280\pi$
$398$	−10.4260	−0.522607
$399$	6.47112	0.323961
$400$	10.7000	0.535002
$401$	−37.4132	−1.86833	−0.934163	−	0.356848i	$-0.883851\pi$
$401$	−37.4132	−1.86833	−0.934163	+	0.356848i	$0.883851\pi$
$402$	−2.70305	−0.134816
$403$	−3.76015	−0.187306
$404$	4.79481	0.238551
$405$	−3.96233	−0.196890
$406$	5.33320	0.264682
$407$	−3.05695	−0.151527
$408$	−1.00000	−0.0495074
$409$	−21.7871	−1.07730	−0.538650	−	0.842529i	$-0.681066\pi$
$409$	−21.7871	−1.07730	−0.538650	+	0.842529i	$0.681066\pi$
$410$	9.64773	0.476468
$411$	−10.0135	−0.493932
$412$	−3.51999	−0.173418
$413$	5.64151	0.277601
$414$	2.91330	0.143181
$415$	27.5807	1.35389
$416$	1.00000	0.0490290
$417$	1.04156	0.0510052
$418$	14.5939	0.713813
$419$	15.8604	0.774832	0.387416	−	0.921905i	$-0.373368\pi$
$419$	15.8604	0.774832	0.387416	+	0.921905i	$0.373368\pi$
$420$	3.96233	0.193342
$421$	27.5318	1.34182	0.670909	−	0.741539i	$-0.265904\pi$
$421$	27.5318	1.34182	0.670909	+	0.741539i	$0.265904\pi$
$422$	−3.27222	−0.159289
$423$	5.82098	0.283026
$424$	−0.0455926	−0.00221417
$425$	10.7000	0.519028
$426$	7.94981	0.385170
$427$	−5.96980	−0.288899
$428$	−16.4738	−0.796293
$429$	2.25524	0.108884
$430$	−32.0912	−1.54758
$431$	−20.1039	−0.968370	−0.484185	−	0.874966i	$-0.660884\pi$
$431$	−20.1039	−0.968370	−0.484185	+	0.874966i	$0.660884\pi$
$432$	−1.00000	−0.0481125
$433$	20.2747	0.974340	0.487170	−	0.873307i	$-0.338029\pi$
$433$	20.2747	0.974340	0.487170	+	0.873307i	$0.338029\pi$
$434$	−3.76015	−0.180493
$435$	21.1319	1.01320
$436$	−12.9743	−0.621356
$437$	−18.8523	−0.901829
$438$	−4.01539	−0.191863
$439$	−0.905252	−0.0432053	−0.0216026	−	0.999767i	$-0.506877\pi$
$439$	−0.905252	−0.0432053	−0.0216026	+	0.999767i	$0.506877\pi$
$440$	8.93601	0.426008
$441$	1.00000	0.0476190
$442$	1.00000	0.0475651
$443$	−22.1783	−1.05372	−0.526862	−	0.849951i	$-0.676632\pi$
$443$	−22.1783	−1.05372	−0.526862	+	0.849951i	$0.676632\pi$
$444$	−1.35548	−0.0643285
$445$	38.1641	1.80915
$446$	−17.0179	−0.805819
$447$	17.9534	0.849169
$448$	1.00000	0.0472456
$449$	−8.31393	−0.392359	−0.196179	−	0.980568i	$-0.562853\pi$
$449$	−8.31393	−0.392359	−0.196179	+	0.980568i	$0.562853\pi$
$450$	10.7000	0.504405
$451$	5.49121	0.258571
$452$	−14.7472	−0.693651
$453$	−2.69011	−0.126392
$454$	−22.1254	−1.03840
$455$	−3.96233	−0.185757
$456$	6.47112	0.303038
$457$	−9.61257	−0.449657	−0.224829	−	0.974398i	$-0.572182\pi$
$457$	−9.61257	−0.449657	−0.224829	+	0.974398i	$0.572182\pi$
$458$	−4.86224	−0.227197
$459$	−1.00000	−0.0466760
$460$	−11.5435	−0.538216
$461$	−21.9450	−1.02208	−0.511040	−	0.859557i	$-0.670740\pi$
$461$	−21.9450	−1.02208	−0.511040	+	0.859557i	$0.670740\pi$
$462$	2.25524	0.104923
$463$	2.93470	0.136387	0.0681936	−	0.997672i	$-0.478276\pi$
$463$	2.93470	0.136387	0.0681936	+	0.997672i	$0.478276\pi$
$464$	5.33320	0.247588
$465$	−14.8989	−0.690922
$466$	2.89117	0.133931
$467$	−17.2636	−0.798864	−0.399432	−	0.916763i	$-0.630793\pi$
$467$	−17.2636	−0.798864	−0.399432	+	0.916763i	$0.630793\pi$
$468$	1.00000	0.0462250
$469$	2.70305	0.124815
$470$	−23.0646	−1.06389
$471$	−22.3962	−1.03196
$472$	5.64151	0.259672
$473$	−18.2654	−0.839844
$474$	−3.56513	−0.163752
$475$	−69.2412	−3.17701
$476$	1.00000	0.0458349
$477$	−0.0455926	−0.00208754
$478$	−26.9063	−1.23066
$479$	−27.4509	−1.25426	−0.627131	−	0.778914i	$-0.715771\pi$
$479$	−27.4509	−1.25426	−0.627131	+	0.778914i	$0.715771\pi$
$480$	3.96233	0.180855
$481$	1.35548	0.0618048
$482$	−7.93947	−0.361633
$483$	−2.91330	−0.132560
$484$	−5.91388	−0.268813
$485$	−12.9070	−0.586077
$486$	−1.00000	−0.0453609
$487$	18.2194	0.825601	0.412800	−	0.910822i	$-0.364551\pi$
$487$	18.2194	0.825601	0.412800	+	0.910822i	$0.364551\pi$
$488$	−5.96980	−0.270240
$489$	−17.0961	−0.773111
$490$	−3.96233	−0.179000
$491$	−31.3391	−1.41431	−0.707157	−	0.707057i	$-0.750023\pi$
$491$	−31.3391	−1.41431	−0.707157	+	0.707057i	$0.750023\pi$
$492$	2.43487	0.109772
$493$	5.33320	0.240195
$494$	−6.47112	−0.291149
$495$	8.93601	0.401644
$496$	−3.76015	−0.168836
$497$	−7.94981	−0.356598
$498$	6.96074	0.311918
$499$	−23.3004	−1.04307	−0.521535	−	0.853230i	$-0.674640\pi$
$499$	−23.3004	−1.04307	−0.521535	+	0.853230i	$0.674640\pi$
$500$	−22.5854	−1.01005
$501$	−10.8236	−0.483563
$502$	−0.943053	−0.0420905
$503$	5.68835	0.253631	0.126815	−	0.991926i	$-0.459524\pi$
$503$	5.68835	0.253631	0.126815	+	0.991926i	$0.459524\pi$
$504$	1.00000	0.0445435
$505$	−18.9986	−0.845428
$506$	−6.57020	−0.292081
$507$	−1.00000	−0.0444116
$508$	17.7837	0.789026
$509$	−17.1876	−0.761825	−0.380913	−	0.924611i	$-0.624390\pi$
$509$	−17.1876	−0.761825	−0.380913	+	0.924611i	$0.624390\pi$
$510$	3.96233	0.175455
$511$	4.01539	0.177630
$512$	1.00000	0.0441942
$513$	6.47112	0.285707
$514$	−23.5309	−1.03791
$515$	13.9474	0.614594
$516$	−8.09908	−0.356542
$517$	−13.1277	−0.577357
$518$	1.35548	0.0595566
$519$	11.3536	0.498369
$520$	−3.96233	−0.173760
$521$	−2.74662	−0.120332	−0.0601658	−	0.998188i	$-0.519163\pi$
$521$	−2.74662	−0.120332	−0.0601658	+	0.998188i	$0.519163\pi$
$522$	5.33320	0.233428
$523$	−44.0703	−1.92706	−0.963529	−	0.267603i	$-0.913768\pi$
$523$	−44.0703	−1.92706	−0.963529	+	0.267603i	$0.913768\pi$
$524$	11.5643	0.505190
$525$	−10.7000	−0.466988
$526$	15.2745	0.666001
$527$	−3.76015	−0.163795
$528$	2.25524	0.0981468
$529$	−14.5127	−0.630986
$530$	0.180653	0.00784707
$531$	5.64151	0.244821
$532$	−6.47112	−0.280559
$533$	−2.43487	−0.105466
$534$	9.63174	0.416806
$535$	65.2748	2.82207
$536$	2.70305	0.116754
$537$	3.83577	0.165526
$538$	−21.9309	−0.945507
$539$	−2.25524	−0.0971402
$540$	3.96233	0.170511
$541$	−18.3942	−0.790829	−0.395414	−	0.918503i	$-0.629399\pi$
$541$	−18.3942	−0.790829	−0.395414	+	0.918503i	$0.629399\pi$
$542$	27.0643	1.16251
$543$	22.2565	0.955120
$544$	1.00000	0.0428746
$545$	51.4084	2.20209
$546$	−1.00000	−0.0427960
$547$	24.1730	1.03356	0.516782	−	0.856117i	$-0.327130\pi$
$547$	24.1730	1.03356	0.516782	+	0.856117i	$0.327130\pi$
$548$	10.0135	0.427757
$549$	−5.96980	−0.254785
$550$	−24.1312	−1.02896
$551$	−34.5118	−1.47025
$552$	−2.91330	−0.123998
$553$	3.56513	0.151605
$554$	−0.0429912	−0.00182652
$555$	5.37088	0.227981
$556$	−1.04156	−0.0441718
$557$	−0.281728	−0.0119372	−0.00596859	−	0.999982i	$-0.501900\pi$
$557$	−0.281728	−0.0119372	−0.00596859	+	0.999982i	$0.501900\pi$
$558$	−3.76015	−0.159180
$559$	8.09908	0.342555
$560$	−3.96233	−0.167439
$561$	2.25524	0.0952164
$562$	−18.5037	−0.780533
$563$	27.9089	1.17622	0.588110	−	0.808781i	$-0.299872\pi$
$563$	27.9089	1.17622	0.588110	+	0.808781i	$0.299872\pi$
$564$	−5.82098	−0.245107
$565$	58.4333	2.45831
$566$	5.73772	0.241174
$567$	1.00000	0.0419961
$568$	−7.94981	−0.333567
$569$	−25.5115	−1.06950	−0.534750	−	0.845011i	$-0.679594\pi$
$569$	−25.5115	−1.06950	−0.534750	+	0.845011i	$0.679594\pi$
$570$	−25.6407	−1.07397
$571$	14.1627	0.592689	0.296344	−	0.955081i	$-0.404232\pi$
$571$	14.1627	0.592689	0.296344	+	0.955081i	$0.404232\pi$
$572$	−2.25524	−0.0942964
$573$	10.8837	0.454673
$574$	−2.43487	−0.101629
$575$	31.1725	1.29998
$576$	1.00000	0.0416667
$577$	−43.9480	−1.82958	−0.914790	−	0.403930i	$-0.867644\pi$
$577$	−43.9480	−1.82958	−0.914790	+	0.403930i	$0.867644\pi$
$578$	1.00000	0.0415945
$579$	−24.6673	−1.02514
$580$	−21.1319	−0.877454
$581$	−6.96074	−0.288780
$582$	−3.25743	−0.135025
$583$	0.102822	0.00425847
$584$	4.01539	0.166158
$585$	−3.96233	−0.163822
$586$	−10.7157	−0.442661
$587$	2.30712	0.0952252	0.0476126	−	0.998866i	$-0.484839\pi$
$587$	2.30712	0.0952252	0.0476126	+	0.998866i	$0.484839\pi$
$588$	−1.00000	−0.0412393
$589$	24.3324	1.00260
$590$	−22.3535	−0.920279
$591$	12.6432	0.520074
$592$	1.35548	0.0557101
$593$	30.2710	1.24308	0.621540	−	0.783383i	$-0.286507\pi$
$593$	30.2710	1.24308	0.621540	+	0.783383i	$0.286507\pi$
$594$	2.25524	0.0925337
$595$	−3.96233	−0.162440
$596$	−17.9534	−0.735401
$597$	10.4260	0.426707
$598$	2.91330	0.119134
$599$	29.8523	1.21973	0.609867	−	0.792504i	$-0.291223\pi$
$599$	29.8523	1.21973	0.609867	+	0.792504i	$0.291223\pi$
$600$	−10.7000	−0.436827
$601$	3.18799	0.130041	0.0650203	−	0.997884i	$-0.479289\pi$
$601$	3.18799	0.130041	0.0650203	+	0.997884i	$0.479289\pi$
$602$	8.09908	0.330094
$603$	2.70305	0.110077
$604$	2.69011	0.109459
$605$	23.4327	0.952676
$606$	−4.79481	−0.194776
$607$	43.9007	1.78187	0.890937	−	0.454127i	$-0.150049\pi$
$607$	43.9007	1.78187	0.890937	+	0.454127i	$0.150049\pi$
$608$	−6.47112	−0.262438
$609$	−5.33320	−0.216112
$610$	23.6543	0.957735
$611$	5.82098	0.235492
$612$	1.00000	0.0404226
$613$	29.0206	1.17213	0.586066	−	0.810264i	$-0.300676\pi$
$613$	29.0206	1.17213	0.586066	+	0.810264i	$0.300676\pi$
$614$	−12.4597	−0.502832
$615$	−9.64773	−0.389034
$616$	−2.25524	−0.0908663
$617$	23.9539	0.964346	0.482173	−	0.876076i	$-0.339848\pi$
$617$	23.9539	0.964346	0.482173	+	0.876076i	$0.339848\pi$
$618$	3.51999	0.141595
$619$	−12.2500	−0.492370	−0.246185	−	0.969223i	$-0.579177\pi$
$619$	−12.2500	−0.492370	−0.246185	+	0.969223i	$0.579177\pi$
$620$	14.8989	0.598356
$621$	−2.91330	−0.116907
$622$	1.66772	0.0668694
$623$	−9.63174	−0.385888
$624$	−1.00000	−0.0400320
$625$	35.9907	1.43963
$626$	24.8826	0.994508
$627$	−14.5939	−0.582826
$628$	22.3962	0.893706
$629$	1.35548	0.0540467
$630$	−3.96233	−0.157863
$631$	−41.2936	−1.64387	−0.821936	−	0.569580i	$-0.807106\pi$
$631$	−41.2936	−1.64387	−0.821936	+	0.569580i	$0.807106\pi$
$632$	3.56513	0.141813
$633$	3.27222	0.130059
$634$	−22.9947	−0.913236
$635$	−70.4650	−2.79632
$636$	0.0455926	0.00180787
$637$	1.00000	0.0396214
$638$	−12.0277	−0.476180
$639$	−7.94981	−0.314490
$640$	−3.96233	−0.156625
$641$	−19.3860	−0.765700	−0.382850	−	0.923811i	$-0.625057\pi$
$641$	−19.3860	−0.765700	−0.382850	+	0.923811i	$0.625057\pi$
$642$	16.4738	0.650171
$643$	30.5857	1.20618	0.603092	−	0.797672i	$-0.293935\pi$
$643$	30.5857	1.20618	0.603092	+	0.797672i	$0.293935\pi$
$644$	2.91330	0.114800
$645$	32.0912	1.26359
$646$	−6.47112	−0.254603
$647$	−3.29605	−0.129581	−0.0647906	−	0.997899i	$-0.520638\pi$
$647$	−3.29605	−0.129581	−0.0647906	+	0.997899i	$0.520638\pi$
$648$	1.00000	0.0392837
$649$	−12.7230	−0.499420
$650$	10.7000	0.419690
$651$	3.76015	0.147372
$652$	17.0961	0.669534
$653$	−49.0959	−1.92127	−0.960635	−	0.277815i	$-0.910390\pi$
$653$	−49.0959	−1.92127	−0.960635	+	0.277815i	$0.910390\pi$
$654$	12.9743	0.507335
$655$	−45.8216	−1.79040
$656$	−2.43487	−0.0950655
$657$	4.01539	0.156655
$658$	5.82098	0.226925
$659$	3.55050	0.138308	0.0691539	−	0.997606i	$-0.477970\pi$
$659$	3.55050	0.138308	0.0691539	+	0.997606i	$0.477970\pi$
$660$	−8.93601	−0.347834
$661$	33.2229	1.29222	0.646110	−	0.763244i	$-0.276395\pi$
$661$	33.2229	1.29222	0.646110	+	0.763244i	$0.276395\pi$
$662$	−5.22783	−0.203185
$663$	−1.00000	−0.0388368
$664$	−6.96074	−0.270129
$665$	25.6407	0.994303
$666$	1.35548	0.0525240
$667$	15.5372	0.601604
$668$	10.8236	0.418778
$669$	17.0179	0.657948
$670$	−10.7104	−0.413778
$671$	13.4633	0.519747
$672$	−1.00000	−0.0385758
$673$	48.8004	1.88112	0.940560	−	0.339629i	$-0.110301\pi$
$673$	48.8004	1.88112	0.940560	+	0.339629i	$0.110301\pi$
$674$	15.8199	0.609358
$675$	−10.7000	−0.411845
$676$	1.00000	0.0384615
$677$	22.2408	0.854783	0.427392	−	0.904067i	$-0.359433\pi$
$677$	22.2408	0.854783	0.427392	+	0.904067i	$0.359433\pi$
$678$	14.7472	0.566364
$679$	3.25743	0.125009
$680$	−3.96233	−0.151948
$681$	22.1254	0.847848
$682$	8.48005	0.324718
$683$	7.58771	0.290336	0.145168	−	0.989407i	$-0.453628\pi$
$683$	7.58771	0.290336	0.145168	+	0.989407i	$0.453628\pi$
$684$	−6.47112	−0.247429
$685$	−39.6769	−1.51598
$686$	1.00000	0.0381802
$687$	4.86224	0.185506
$688$	8.09908	0.308775
$689$	−0.0455926	−0.00173694
$690$	11.5435	0.439452
$691$	−29.1776	−1.10997	−0.554984	−	0.831861i	$-0.687276\pi$
$691$	−29.1776	−1.10997	−0.554984	+	0.831861i	$0.687276\pi$
$692$	−11.3536	−0.431601
$693$	−2.25524	−0.0856696
$694$	−6.67789	−0.253489
$695$	4.12699	0.156546
$696$	−5.33320	−0.202155
$697$	−2.43487	−0.0922271
$698$	10.9660	0.415068
$699$	−2.89117	−0.109354
$700$	10.7000	0.404424
$701$	2.53477	0.0957368	0.0478684	−	0.998854i	$-0.484757\pi$
$701$	2.53477	0.0957368	0.0478684	+	0.998854i	$0.484757\pi$
$702$	−1.00000	−0.0377426
$703$	−8.77150	−0.330823
$704$	−2.25524	−0.0849976
$705$	23.0646	0.868664
$706$	−1.66394	−0.0626233
$707$	4.79481	0.180328
$708$	−5.64151	−0.212021
$709$	14.3259	0.538021	0.269010	−	0.963137i	$-0.413303\pi$
$709$	14.3259	0.538021	0.269010	+	0.963137i	$0.413303\pi$
$710$	31.4998	1.18217
$711$	3.56513	0.133703
$712$	−9.63174	−0.360965
$713$	−10.9544	−0.410247
$714$	−1.00000	−0.0374241
$715$	8.93601	0.334188
$716$	−3.83577	−0.143349
$717$	26.9063	1.00483
$718$	−1.12052	−0.0418176
$719$	−16.4280	−0.612659	−0.306330	−	0.951925i	$-0.599101\pi$
$719$	−16.4280	−0.612659	−0.306330	+	0.951925i	$0.599101\pi$
$720$	−3.96233	−0.147667
$721$	−3.51999	−0.131091
$722$	22.8754	0.851333
$723$	7.93947	0.295272
$724$	−22.2565	−0.827158
$725$	57.0655	2.11936
$726$	5.91388	0.219485
$727$	−10.6432	−0.394736	−0.197368	−	0.980329i	$-0.563239\pi$
$727$	−10.6432	−0.394736	−0.197368	+	0.980329i	$0.563239\pi$
$728$	1.00000	0.0370625
$729$	1.00000	0.0370370
$730$	−15.9103	−0.588866
$731$	8.09908	0.299555
$732$	5.96980	0.220650
$733$	−29.5099	−1.08997	−0.544987	−	0.838445i	$-0.683465\pi$
$733$	−29.5099	−1.08997	−0.544987	+	0.838445i	$0.683465\pi$
$734$	−30.0476	−1.10908
$735$	3.96233	0.146153
$736$	2.91330	0.107386
$737$	−6.09603	−0.224550
$738$	−2.43487	−0.0896286
$739$	24.0124	0.883310	0.441655	−	0.897185i	$-0.354391\pi$
$739$	24.0124	0.883310	0.441655	+	0.897185i	$0.354391\pi$
$740$	−5.37088	−0.197437
$741$	6.47112	0.237722
$742$	−0.0455926	−0.00167376
$743$	−12.7196	−0.466639	−0.233319	−	0.972400i	$-0.574959\pi$
$743$	−12.7196	−0.466639	−0.233319	+	0.972400i	$0.574959\pi$
$744$	3.76015	0.137854
$745$	71.1374	2.60627
$746$	−7.17816	−0.262811
$747$	−6.96074	−0.254680
$748$	−2.25524	−0.0824598
$749$	−16.4738	−0.601941
$750$	22.5854	0.824704
$751$	−45.3554	−1.65504	−0.827522	−	0.561434i	$-0.810250\pi$
$751$	−45.3554	−1.65504	−0.827522	+	0.561434i	$0.810250\pi$
$752$	5.82098	0.212269
$753$	0.943053	0.0343668
$754$	5.33320	0.194224
$755$	−10.6591	−0.387924
$756$	−1.00000	−0.0363696
$757$	10.4868	0.381150	0.190575	−	0.981673i	$-0.438965\pi$
$757$	10.4868	0.381150	0.190575	+	0.981673i	$0.438965\pi$
$758$	−19.4853	−0.707740
$759$	6.57020	0.238483
$760$	25.6407	0.930086
$761$	50.3268	1.82435	0.912173	−	0.409806i	$-0.134403\pi$
$761$	50.3268	1.82435	0.912173	+	0.409806i	$0.134403\pi$
$762$	−17.7837	−0.644237
$763$	−12.9743	−0.469701
$764$	−10.8837	−0.393759
$765$	−3.96233	−0.143258
$766$	11.2639	0.406979
$767$	5.64151	0.203703
$768$	−1.00000	−0.0360844
$769$	32.6466	1.17727	0.588634	−	0.808400i	$-0.299666\pi$
$769$	32.6466	1.17727	0.588634	+	0.808400i	$0.299666\pi$
$770$	8.93601	0.322031
$771$	23.5309	0.847446
$772$	24.6673	0.887795
$773$	21.1763	0.761659	0.380830	−	0.924645i	$-0.375638\pi$
$773$	21.1763	0.761659	0.380830	+	0.924645i	$0.375638\pi$
$774$	8.09908	0.291116
$775$	−40.2337	−1.44524
$776$	3.25743	0.116935
$777$	−1.35548	−0.0486277
$778$	−1.44305	−0.0517357
$779$	15.7563	0.564528
$780$	3.96233	0.141874
$781$	17.9288	0.641541
$782$	2.91330	0.104179
$783$	−5.33320	−0.190593
$784$	1.00000	0.0357143
$785$	−88.7411	−3.16731
$786$	−11.5643	−0.412486
$787$	−17.8030	−0.634607	−0.317304	−	0.948324i	$-0.602777\pi$
$787$	−17.8030	−0.634607	−0.317304	+	0.948324i	$0.602777\pi$
$788$	−12.6432	−0.450397
$789$	−15.2745	−0.543787
$790$	−14.1262	−0.502589
$791$	−14.7472	−0.524351
$792$	−2.25524	−0.0801366
$793$	−5.96980	−0.211994
$794$	−28.6415	−1.01645
$795$	−0.180653	−0.00640710
$796$	−10.4260	−0.369539
$797$	3.84554	0.136216	0.0681079	−	0.997678i	$-0.478304\pi$
$797$	3.84554	0.136216	0.0681079	+	0.997678i	$0.478304\pi$
$798$	6.47112	0.229075
$799$	5.82098	0.205931
$800$	10.7000	0.378304
$801$	−9.63174	−0.340321
$802$	−37.4132	−1.32111
$803$	−9.05568	−0.319568
$804$	−2.70305	−0.0953292
$805$	−11.5435	−0.406853
$806$	−3.76015	−0.132446
$807$	21.9309	0.772004
$808$	4.79481	0.168681
$809$	0.580938	0.0204247	0.0102123	−	0.999948i	$-0.496749\pi$
$809$	0.580938	0.0204247	0.0102123	+	0.999948i	$0.496749\pi$
$810$	−3.96233	−0.139222
$811$	−12.3281	−0.432899	−0.216450	−	0.976294i	$-0.569448\pi$
$811$	−12.3281	−0.432899	−0.216450	+	0.976294i	$0.569448\pi$
$812$	5.33320	0.187159
$813$	−27.0643	−0.949187
$814$	−3.05695	−0.107146
$815$	−67.7403	−2.37284
$816$	−1.00000	−0.0350070
$817$	−52.4101	−1.83360
$818$	−21.7871	−0.761767
$819$	1.00000	0.0349428
$820$	9.64773	0.336914
$821$	−9.36051	−0.326684	−0.163342	−	0.986570i	$-0.552227\pi$
$821$	−9.36051	−0.326684	−0.163342	+	0.986570i	$0.552227\pi$
$822$	−10.0135	−0.349262
$823$	22.4636	0.783031	0.391515	−	0.920172i	$-0.371951\pi$
$823$	22.4636	0.783031	0.391515	+	0.920172i	$0.371951\pi$
$824$	−3.51999	−0.122625
$825$	24.1312	0.840140
$826$	5.64151	0.196293
$827$	3.44363	0.119747	0.0598733	−	0.998206i	$-0.480930\pi$
$827$	3.44363	0.119747	0.0598733	+	0.998206i	$0.480930\pi$
$828$	2.91330	0.101244
$829$	56.1659	1.95072	0.975361	−	0.220616i	$-0.0708068\pi$
$829$	56.1659	1.95072	0.975361	+	0.220616i	$0.0708068\pi$
$830$	27.5807	0.957341
$831$	0.0429912	0.00149135
$832$	1.00000	0.0346688
$833$	1.00000	0.0346479
$834$	1.04156	0.0360661
$835$	−42.8866	−1.48415
$836$	14.5939	0.504742
$837$	3.76015	0.129970
$838$	15.8604	0.547889
$839$	48.3749	1.67009	0.835043	−	0.550185i	$-0.185443\pi$
$839$	48.3749	1.67009	0.835043	+	0.550185i	$0.185443\pi$
$840$	3.96233	0.136713
$841$	−0.556938	−0.0192048
$842$	27.5318	0.948809
$843$	18.5037	0.637303
$844$	−3.27222	−0.112634
$845$	−3.96233	−0.136308
$846$	5.82098	0.200129
$847$	−5.91388	−0.203203
$848$	−0.0455926	−0.00156566
$849$	−5.73772	−0.196918
$850$	10.7000	0.367008
$851$	3.94894	0.135368
$852$	7.94981	0.272356
$853$	5.72571	0.196045	0.0980223	−	0.995184i	$-0.468748\pi$
$853$	5.72571	0.196045	0.0980223	+	0.995184i	$0.468748\pi$
$854$	−5.96980	−0.204282
$855$	25.6407	0.876893
$856$	−16.4738	−0.563064
$857$	31.7321	1.08395	0.541974	−	0.840395i	$-0.317677\pi$
$857$	31.7321	1.08395	0.541974	+	0.840395i	$0.317677\pi$
$858$	2.25524	0.0769927
$859$	−34.8157	−1.18790	−0.593948	−	0.804503i	$-0.702432\pi$
$859$	−34.8157	−1.18790	−0.593948	+	0.804503i	$0.702432\pi$
$860$	−32.0912	−1.09430
$861$	2.43487	0.0829800
$862$	−20.1039	−0.684741
$863$	39.3860	1.34071	0.670357	−	0.742039i	$-0.266141\pi$
$863$	39.3860	1.34071	0.670357	+	0.742039i	$0.266141\pi$
$864$	−1.00000	−0.0340207
$865$	44.9868	1.52960
$866$	20.2747	0.688963
$867$	−1.00000	−0.0339618
$868$	−3.76015	−0.127628
$869$	−8.04024	−0.272747
$870$	21.1319	0.716439
$871$	2.70305	0.0915893
$872$	−12.9743	−0.439365
$873$	3.25743	0.110247
$874$	−18.8523	−0.637689
$875$	−22.5854	−0.763527
$876$	−4.01539	−0.135667
$877$	−8.50864	−0.287316	−0.143658	−	0.989627i	$-0.545887\pi$
$877$	−8.50864	−0.287316	−0.143658	+	0.989627i	$0.545887\pi$
$878$	−0.905252	−0.0305508
$879$	10.7157	0.361431
$880$	8.93601	0.301233
$881$	18.2487	0.614813	0.307406	−	0.951578i	$-0.400539\pi$
$881$	18.2487	0.614813	0.307406	+	0.951578i	$0.400539\pi$
$882$	1.00000	0.0336718
$883$	−15.7368	−0.529584	−0.264792	−	0.964306i	$-0.585303\pi$
$883$	−15.7368	−0.529584	−0.264792	+	0.964306i	$0.585303\pi$
$884$	1.00000	0.0336336
$885$	22.3535	0.751405
$886$	−22.1783	−0.745096
$887$	30.3980	1.02066	0.510332	−	0.859977i	$-0.329522\pi$
$887$	30.3980	1.02066	0.510332	+	0.859977i	$0.329522\pi$
$888$	−1.35548	−0.0454871
$889$	17.7837	0.596447
$890$	38.1641	1.27926
$891$	−2.25524	−0.0755535
$892$	−17.0179	−0.569800
$893$	−37.6682	−1.26052
$894$	17.9534	0.600453
$895$	15.1986	0.508032
$896$	1.00000	0.0334077
$897$	−2.91330	−0.0972723
$898$	−8.31393	−0.277439
$899$	−20.0536	−0.668826
$900$	10.7000	0.356668
$901$	−0.0455926	−0.00151891
$902$	5.49121	0.182837
$903$	−8.09908	−0.269521
$904$	−14.7472	−0.490485
$905$	88.1877	2.93146
$906$	−2.69011	−0.0893728
$907$	−15.5325	−0.515748	−0.257874	−	0.966179i	$-0.583022\pi$
$907$	−15.5325	−0.515748	−0.257874	+	0.966179i	$0.583022\pi$
$908$	−22.1254	−0.734258
$909$	4.79481	0.159034
$910$	−3.96233	−0.131350
$911$	7.09187	0.234964	0.117482	−	0.993075i	$-0.462518\pi$
$911$	7.09187	0.234964	0.117482	+	0.993075i	$0.462518\pi$
$912$	6.47112	0.214280
$913$	15.6982	0.519533
$914$	−9.61257	−0.317956
$915$	−23.6543	−0.781987
$916$	−4.86224	−0.160653
$917$	11.5643	0.381887
$918$	−1.00000	−0.0330049
$919$	30.4597	1.00477	0.502386	−	0.864644i	$-0.332456\pi$
$919$	30.4597	1.00477	0.502386	+	0.864644i	$0.332456\pi$
$920$	−11.5435	−0.380576
$921$	12.4597	0.410561
$922$	−21.9450	−0.722720
$923$	−7.94981	−0.261671
$924$	2.25524	0.0741920
$925$	14.5037	0.476880
$926$	2.93470	0.0964404
$927$	−3.51999	−0.115612
$928$	5.33320	0.175071
$929$	7.78430	0.255395	0.127697	−	0.991813i	$-0.459241\pi$
$929$	7.78430	0.255395	0.127697	+	0.991813i	$0.459241\pi$
$930$	−14.8989	−0.488556
$931$	−6.47112	−0.212082
$932$	2.89117	0.0947035
$933$	−1.66772	−0.0545987
$934$	−17.2636	−0.564882
$935$	8.93601	0.292239
$936$	1.00000	0.0326860
$937$	−14.6695	−0.479233	−0.239617	−	0.970868i	$-0.577022\pi$
$937$	−14.6695	−0.479233	−0.239617	+	0.970868i	$0.577022\pi$
$938$	2.70305	0.0882577
$939$	−24.8826	−0.812012
$940$	−23.0646	−0.752285
$941$	−48.0686	−1.56699	−0.783495	−	0.621398i	$-0.786565\pi$
$941$	−48.0686	−1.56699	−0.783495	+	0.621398i	$0.786565\pi$
$942$	−22.3962	−0.729708
$943$	−7.09350	−0.230996
$944$	5.64151	0.183615
$945$	3.96233	0.128895
$946$	−18.2654	−0.593859
$947$	54.5368	1.77221	0.886104	−	0.463487i	$-0.153402\pi$
$947$	54.5368	1.77221	0.886104	+	0.463487i	$0.153402\pi$
$948$	−3.56513	−0.115790
$949$	4.01539	0.130345
$950$	−69.2412	−2.24648
$951$	22.9947	0.745654
$952$	1.00000	0.0324102
$953$	11.5535	0.374255	0.187127	−	0.982336i	$-0.440082\pi$
$953$	11.5535	0.374255	0.187127	+	0.982336i	$0.440082\pi$
$954$	−0.0455926	−0.00147612
$955$	43.1248	1.39549
$956$	−26.9063	−0.870211
$957$	12.0277	0.388799
$958$	−27.4509	−0.886897
$959$	10.0135	0.323354
$960$	3.96233	0.127884
$961$	−16.8613	−0.543912
$962$	1.35548	0.0437026
$963$	−16.4738	−0.530862
$964$	−7.93947	−0.255713
$965$	−97.7399	−3.14636
$966$	−2.91330	−0.0937339
$967$	−33.3746	−1.07326	−0.536628	−	0.843819i	$-0.680302\pi$
$967$	−33.3746	−1.07326	−0.536628	+	0.843819i	$0.680302\pi$
$968$	−5.91388	−0.190079
$969$	6.47112	0.207882
$970$	−12.9070	−0.414419
$971$	22.0560	0.707810	0.353905	−	0.935281i	$-0.384854\pi$
$971$	22.0560	0.707810	0.353905	+	0.935281i	$0.384854\pi$
$972$	−1.00000	−0.0320750
$973$	−1.04156	−0.0333908
$974$	18.2194	0.583788
$975$	−10.7000	−0.342676
$976$	−5.96980	−0.191089
$977$	43.1076	1.37913	0.689567	−	0.724222i	$-0.257801\pi$
$977$	43.1076	1.37913	0.689567	+	0.724222i	$0.257801\pi$
$978$	−17.0961	−0.546672
$979$	21.7219	0.694235
$980$	−3.96233	−0.126572
$981$	−12.9743	−0.414237
$982$	−31.3391	−1.00007
$983$	−25.5654	−0.815409	−0.407705	−	0.913114i	$-0.633671\pi$
$983$	−25.5654	−0.815409	−0.407705	+	0.913114i	$0.633671\pi$
$984$	2.43487	0.0776207
$985$	50.0967	1.59621
$986$	5.33320	0.169844
$987$	−5.82098	−0.185284
$988$	−6.47112	−0.205874
$989$	23.5951	0.750280
$990$	8.93601	0.284005
$991$	9.41683	0.299136	0.149568	−	0.988751i	$-0.452212\pi$
$991$	9.41683	0.299136	0.149568	+	0.988751i	$0.452212\pi$
$992$	−3.76015	−0.119385
$993$	5.22783	0.165900
$994$	−7.94981	−0.252153
$995$	41.3111	1.30965
$996$	6.96074	0.220560
$997$	−28.6032	−0.905873	−0.452936	−	0.891543i	$-0.649624\pi$
$997$	−28.6032	−0.905873	−0.452936	+	0.891543i	$0.649624\pi$
$998$	−23.3004	−0.737562
$999$	−1.35548	−0.0428856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.bs.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.bs.1.1	✓	5	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:	\( N \)	\(=\)	\( 9282 = 2 \cdot 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9282.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.96233 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.96233 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.96233 q^{10} -2.25524 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{14} +3.96233 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -6.47112 q^{19} -3.96233 q^{20} -1.00000 q^{21} -2.25524 q^{22} +2.91330 q^{23} -1.00000 q^{24} +10.7000 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.33320 q^{29} +3.96233 q^{30} -3.76015 q^{31} +1.00000 q^{32} +2.25524 q^{33} +1.00000 q^{34} -3.96233 q^{35} +1.00000 q^{36} +1.35548 q^{37} -6.47112 q^{38} -1.00000 q^{39} -3.96233 q^{40} -2.43487 q^{41} -1.00000 q^{42} +8.09908 q^{43} -2.25524 q^{44} -3.96233 q^{45} +2.91330 q^{46} +5.82098 q^{47} -1.00000 q^{48} +1.00000 q^{49} +10.7000 q^{50} -1.00000 q^{51} +1.00000 q^{52} -0.0455926 q^{53} -1.00000 q^{54} +8.93601 q^{55} +1.00000 q^{56} +6.47112 q^{57} +5.33320 q^{58} +5.64151 q^{59} +3.96233 q^{60} -5.96980 q^{61} -3.76015 q^{62} +1.00000 q^{63} +1.00000 q^{64} -3.96233 q^{65} +2.25524 q^{66} +2.70305 q^{67} +1.00000 q^{68} -2.91330 q^{69} -3.96233 q^{70} -7.94981 q^{71} +1.00000 q^{72} +4.01539 q^{73} +1.35548 q^{74} -10.7000 q^{75} -6.47112 q^{76} -2.25524 q^{77} -1.00000 q^{78} +3.56513 q^{79} -3.96233 q^{80} +1.00000 q^{81} -2.43487 q^{82} -6.96074 q^{83} -1.00000 q^{84} -3.96233 q^{85} +8.09908 q^{86} -5.33320 q^{87} -2.25524 q^{88} -9.63174 q^{89} -3.96233 q^{90} +1.00000 q^{91} +2.91330 q^{92} +3.76015 q^{93} +5.82098 q^{94} +25.6407 q^{95} -1.00000 q^{96} +3.25743 q^{97} +1.00000 q^{98} -2.25524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 5 q^{7} + 5 q^{8} + 5 q^{9} - 7 q^{10} - 9 q^{11} - 5 q^{12} + 5 q^{13} + 5 q^{14} + 7 q^{15} + 5 q^{16} + 5 q^{17} + 5 q^{18} - q^{19} - 7 q^{20} - 5 q^{21} - 9 q^{22} - 6 q^{23} - 5 q^{24} + 2 q^{25} + 5 q^{26} - 5 q^{27} + 5 q^{28} - 10 q^{29} + 7 q^{30} - 7 q^{31} + 5 q^{32} + 9 q^{33} + 5 q^{34} - 7 q^{35} + 5 q^{36} - 3 q^{37} - q^{38} - 5 q^{39} - 7 q^{40} - 19 q^{41} - 5 q^{42} - 3 q^{43} - 9 q^{44} - 7 q^{45} - 6 q^{46} - 2 q^{47} - 5 q^{48} + 5 q^{49} + 2 q^{50} - 5 q^{51} + 5 q^{52} + 5 q^{53} - 5 q^{54} + 14 q^{55} + 5 q^{56} + q^{57} - 10 q^{58} - 12 q^{59} + 7 q^{60} - 21 q^{61} - 7 q^{62} + 5 q^{63} + 5 q^{64} - 7 q^{65} + 9 q^{66} + 12 q^{67} + 5 q^{68} + 6 q^{69} - 7 q^{70} + 4 q^{71} + 5 q^{72} + 6 q^{73} - 3 q^{74} - 2 q^{75} - q^{76} - 9 q^{77} - 5 q^{78} + 11 q^{79} - 7 q^{80} + 5 q^{81} - 19 q^{82} - 23 q^{83} - 5 q^{84} - 7 q^{85} - 3 q^{86} + 10 q^{87} - 9 q^{88} - 12 q^{89} - 7 q^{90} + 5 q^{91} - 6 q^{92} + 7 q^{93} - 2 q^{94} + 15 q^{95} - 5 q^{96} - 9 q^{97} + 5 q^{98} - 9 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 5 * q^7 + 5 * q^8 + 5 * q^9 - 7 * q^10 - 9 * q^11 - 5 * q^12 + 5 * q^13 + 5 * q^14 + 7 * q^15 + 5 * q^16 + 5 * q^17 + 5 * q^18 - q^19 - 7 * q^20 - 5 * q^21 - 9 * q^22 - 6 * q^23 - 5 * q^24 + 2 * q^25 + 5 * q^26 - 5 * q^27 + 5 * q^28 - 10 * q^29 + 7 * q^30 - 7 * q^31 + 5 * q^32 + 9 * q^33 + 5 * q^34 - 7 * q^35 + 5 * q^36 - 3 * q^37 - q^38 - 5 * q^39 - 7 * q^40 - 19 * q^41 - 5 * q^42 - 3 * q^43 - 9 * q^44 - 7 * q^45 - 6 * q^46 - 2 * q^47 - 5 * q^48 + 5 * q^49 + 2 * q^50 - 5 * q^51 + 5 * q^52 + 5 * q^53 - 5 * q^54 + 14 * q^55 + 5 * q^56 + q^57 - 10 * q^58 - 12 * q^59 + 7 * q^60 - 21 * q^61 - 7 * q^62 + 5 * q^63 + 5 * q^64 - 7 * q^65 + 9 * q^66 + 12 * q^67 + 5 * q^68 + 6 * q^69 - 7 * q^70 + 4 * q^71 + 5 * q^72 + 6 * q^73 - 3 * q^74 - 2 * q^75 - q^76 - 9 * q^77 - 5 * q^78 + 11 * q^79 - 7 * q^80 + 5 * q^81 - 19 * q^82 - 23 * q^83 - 5 * q^84 - 7 * q^85 - 3 * q^86 + 10 * q^87 - 9 * q^88 - 12 * q^89 - 7 * q^90 + 5 * q^91 - 6 * q^92 + 7 * q^93 - 2 * q^94 + 15 * q^95 - 5 * q^96 - 9 * q^97 + 5 * q^98 - 9 * q^99

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