LMFDB - Embedded newform 9282.2.a.bm.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:	$4$
Coefficient field:	4.4.45841.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 7x - 1 $ x^4 - 2x^3 - 7x^2 + 7*x - 1
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			$-2.34228$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.34228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.34228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.34228 q^{10} -2.40161 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +3.34228 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.08466 q^{19} -3.34228 q^{20} -1.00000 q^{21} -2.40161 q^{22} +8.19615 q^{23} -1.00000 q^{24} +6.17082 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -7.79454 q^{29} +3.34228 q^{30} +6.71855 q^{31} +1.00000 q^{32} +2.40161 q^{33} -1.00000 q^{34} -3.34228 q^{35} +1.00000 q^{36} +6.59990 q^{37} -2.08466 q^{38} +1.00000 q^{39} -3.34228 q^{40} +1.10999 q^{41} -1.00000 q^{42} +3.25762 q^{43} -2.40161 q^{44} -3.34228 q^{45} +8.19615 q^{46} -0.0868019 q^{47} -1.00000 q^{48} +1.00000 q^{49} +6.17082 q^{50} +1.00000 q^{51} -1.00000 q^{52} +1.42693 q^{53} -1.00000 q^{54} +8.02683 q^{55} +1.00000 q^{56} +2.08466 q^{57} -7.79454 q^{58} -11.0015 q^{59} +3.34228 q^{60} +0.940672 q^{61} +6.71855 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.34228 q^{65} +2.40161 q^{66} -0.938527 q^{67} -1.00000 q^{68} -8.19615 q^{69} -3.34228 q^{70} -4.99133 q^{71} +1.00000 q^{72} +1.00150 q^{73} +6.59990 q^{74} -6.17082 q^{75} -2.08466 q^{76} -2.40161 q^{77} +1.00000 q^{78} -0.0868019 q^{79} -3.34228 q^{80} +1.00000 q^{81} +1.10999 q^{82} -2.52241 q^{83} -1.00000 q^{84} +3.34228 q^{85} +3.25762 q^{86} +7.79454 q^{87} -2.40161 q^{88} -5.10999 q^{89} -3.34228 q^{90} -1.00000 q^{91} +8.19615 q^{92} -6.71855 q^{93} -0.0868019 q^{94} +6.96750 q^{95} -1.00000 q^{96} +12.1383 q^{97} +1.00000 q^{98} -2.40161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} - 3 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 11 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 4 q^{24} - 2 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 9 q^{29} + 2 q^{30} + 11 q^{31} + 4 q^{32} + 3 q^{33} - 4 q^{34} - 2 q^{35} + 4 q^{36} + q^{37} - 11 q^{38} + 4 q^{39} - 2 q^{40} + 5 q^{41} - 4 q^{42} - q^{43} - 3 q^{44} - 2 q^{45} + 4 q^{46} - 13 q^{47} - 4 q^{48} + 4 q^{49} - 2 q^{50} + 4 q^{51} - 4 q^{52} - 3 q^{53} - 4 q^{54} - 2 q^{55} + 4 q^{56} + 11 q^{57} - 9 q^{58} - 12 q^{59} + 2 q^{60} - q^{61} + 11 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} + 3 q^{66} + 11 q^{67} - 4 q^{68} - 4 q^{69} - 2 q^{70} - 11 q^{71} + 4 q^{72} - 28 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 3 q^{77} + 4 q^{78} - 13 q^{79} - 2 q^{80} + 4 q^{81} + 5 q^{82} - 23 q^{83} - 4 q^{84} + 2 q^{85} - q^{86} + 9 q^{87} - 3 q^{88} - 21 q^{89} - 2 q^{90} - 4 q^{91} + 4 q^{92} - 11 q^{93} - 13 q^{94} - 11 q^{95} - 4 q^{96} - 17 q^{97} + 4 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 - 3 * q^11 - 4 * q^12 - 4 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 11 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 4 * q^24 - 2 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 9 * q^29 + 2 * q^30 + 11 * q^31 + 4 * q^32 + 3 * q^33 - 4 * q^34 - 2 * q^35 + 4 * q^36 + q^37 - 11 * q^38 + 4 * q^39 - 2 * q^40 + 5 * q^41 - 4 * q^42 - q^43 - 3 * q^44 - 2 * q^45 + 4 * q^46 - 13 * q^47 - 4 * q^48 + 4 * q^49 - 2 * q^50 + 4 * q^51 - 4 * q^52 - 3 * q^53 - 4 * q^54 - 2 * q^55 + 4 * q^56 + 11 * q^57 - 9 * q^58 - 12 * q^59 + 2 * q^60 - q^61 + 11 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 + 3 * q^66 + 11 * q^67 - 4 * q^68 - 4 * q^69 - 2 * q^70 - 11 * q^71 + 4 * q^72 - 28 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 3 * q^77 + 4 * q^78 - 13 * q^79 - 2 * q^80 + 4 * q^81 + 5 * q^82 - 23 * q^83 - 4 * q^84 + 2 * q^85 - q^86 + 9 * q^87 - 3 * q^88 - 21 * q^89 - 2 * q^90 - 4 * q^91 + 4 * q^92 - 11 * q^93 - 13 * q^94 - 11 * q^95 - 4 * q^96 - 17 * q^97 + 4 * q^98 - 3 * 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
$5$	−3.34228	−1.49471	−0.747356	−	0.664424i	$-0.768677\pi$
$5$	−3.34228	−1.49471	−0.747356	+	0.664424i	$0.768677\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.34228	−1.05692
$11$	−2.40161	−0.724111	−0.362056	−	0.932156i	$-0.617925\pi$
$11$	−2.40161	−0.724111	−0.362056	+	0.932156i	$0.617925\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.00000	0.267261
$15$	3.34228	0.862972
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−2.08466	−0.478253	−0.239127	−	0.970988i	$-0.576861\pi$
$19$	−2.08466	−0.478253	−0.239127	+	0.970988i	$0.576861\pi$
$20$	−3.34228	−0.747356
$21$	−1.00000	−0.218218
$22$	−2.40161	−0.512024
$23$	8.19615	1.70901	0.854507	−	0.519439i	$-0.173859\pi$
$23$	8.19615	1.70901	0.854507	+	0.519439i	$0.173859\pi$
$24$	−1.00000	−0.204124
$25$	6.17082	1.23416
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−7.79454	−1.44741	−0.723705	−	0.690109i	$-0.757562\pi$
$29$	−7.79454	−1.44741	−0.723705	+	0.690109i	$0.757562\pi$
$30$	3.34228	0.610214
$31$	6.71855	1.20669	0.603344	−	0.797481i	$-0.293835\pi$
$31$	6.71855	1.20669	0.603344	+	0.797481i	$0.293835\pi$
$32$	1.00000	0.176777
$33$	2.40161	0.418066
$34$	−1.00000	−0.171499
$35$	−3.34228	−0.564948
$36$	1.00000	0.166667
$37$	6.59990	1.08502	0.542508	−	0.840051i	$-0.317475\pi$
$37$	6.59990	1.08502	0.542508	+	0.840051i	$0.317475\pi$
$38$	−2.08466	−0.338176
$39$	1.00000	0.160128
$40$	−3.34228	−0.528460
$41$	1.10999	0.173351	0.0866754	−	0.996237i	$-0.472376\pi$
$41$	1.10999	0.173351	0.0866754	+	0.996237i	$0.472376\pi$
$42$	−1.00000	−0.154303
$43$	3.25762	0.496782	0.248391	−	0.968660i	$-0.420098\pi$
$43$	3.25762	0.496782	0.248391	+	0.968660i	$0.420098\pi$
$44$	−2.40161	−0.362056
$45$	−3.34228	−0.498237
$46$	8.19615	1.20846
$47$	−0.0868019	−0.0126614	−0.00633068	−	0.999980i	$-0.502015\pi$
$47$	−0.0868019	−0.0126614	−0.00633068	+	0.999980i	$0.502015\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	6.17082	0.872685
$51$	1.00000	0.140028
$52$	−1.00000	−0.138675
$53$	1.42693	0.196005	0.0980023	−	0.995186i	$-0.468755\pi$
$53$	1.42693	0.196005	0.0980023	+	0.995186i	$0.468755\pi$
$54$	−1.00000	−0.136083
$55$	8.02683	1.08234
$56$	1.00000	0.133631
$57$	2.08466	0.276120
$58$	−7.79454	−1.02347
$59$	−11.0015	−1.43227	−0.716137	−	0.697960i	$-0.754091\pi$
$59$	−11.0015	−1.43227	−0.716137	+	0.697960i	$0.754091\pi$
$60$	3.34228	0.431486
$61$	0.940672	0.120441	0.0602203	−	0.998185i	$-0.480820\pi$
$61$	0.940672	0.120441	0.0602203	+	0.998185i	$0.480820\pi$
$62$	6.71855	0.853257
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	3.34228	0.414558
$66$	2.40161	0.295617
$67$	−0.938527	−0.114659	−0.0573297	−	0.998355i	$-0.518259\pi$
$67$	−0.938527	−0.114659	−0.0573297	+	0.998355i	$0.518259\pi$
$68$	−1.00000	−0.121268
$69$	−8.19615	−0.986700
$70$	−3.34228	−0.399479
$71$	−4.99133	−0.592362	−0.296181	−	0.955132i	$-0.595713\pi$
$71$	−4.99133	−0.592362	−0.296181	+	0.955132i	$0.595713\pi$
$72$	1.00000	0.117851
$73$	1.00150	0.117217	0.0586085	−	0.998281i	$-0.481334\pi$
$73$	1.00150	0.117217	0.0586085	+	0.998281i	$0.481334\pi$
$74$	6.59990	0.767222
$75$	−6.17082	−0.712545
$76$	−2.08466	−0.239127
$77$	−2.40161	−0.273688
$78$	1.00000	0.113228
$79$	−0.0868019	−0.00976598	−0.00488299	−	0.999988i	$-0.501554\pi$
$79$	−0.0868019	−0.00976598	−0.00488299	+	0.999988i	$0.501554\pi$
$80$	−3.34228	−0.373678
$81$	1.00000	0.111111
$82$	1.10999	0.122578
$83$	−2.52241	−0.276870	−0.138435	−	0.990372i	$-0.544207\pi$
$83$	−2.52241	−0.276870	−0.138435	+	0.990372i	$0.544207\pi$
$84$	−1.00000	−0.109109
$85$	3.34228	0.362521
$86$	3.25762	0.351278
$87$	7.79454	0.835663
$88$	−2.40161	−0.256012
$89$	−5.10999	−0.541658	−0.270829	−	0.962628i	$-0.587298\pi$
$89$	−5.10999	−0.541658	−0.270829	+	0.962628i	$0.587298\pi$
$90$	−3.34228	−0.352307
$91$	−1.00000	−0.104828
$92$	8.19615	0.854507
$93$	−6.71855	−0.696682
$94$	−0.0868019	−0.00895293
$95$	6.96750	0.714851
$96$	−1.00000	−0.102062
$97$	12.1383	1.23246	0.616230	−	0.787566i	$-0.288659\pi$
$97$	12.1383	1.23246	0.616230	+	0.787566i	$0.288659\pi$
$98$	1.00000	0.101015
$99$	−2.40161	−0.241370
$100$	6.17082	0.617082
$101$	−10.6824	−1.06294	−0.531470	−	0.847077i	$-0.678360\pi$
$101$	−10.6824	−1.06294	−0.531470	+	0.847077i	$0.678360\pi$
$102$	1.00000	0.0990148
$103$	5.60642	0.552417	0.276209	−	0.961098i	$-0.410922\pi$
$103$	5.60642	0.552417	0.276209	+	0.961098i	$0.410922\pi$
$104$	−1.00000	−0.0980581
$105$	3.34228	0.326173
$106$	1.42693	0.138596
$107$	−0.0339990	−0.00328680	−0.00164340	−	0.999999i	$-0.500523\pi$
$107$	−0.0339990	−0.00328680	−0.00164340	+	0.999999i	$0.500523\pi$
$108$	−1.00000	−0.0962250
$109$	5.13682	0.492018	0.246009	−	0.969268i	$-0.420881\pi$
$109$	5.13682	0.492018	0.246009	+	0.969268i	$0.420881\pi$
$110$	8.02683	0.765328
$111$	−6.59990	−0.626435
$112$	1.00000	0.0944911
$113$	13.1976	1.24153	0.620765	−	0.783997i	$-0.286822\pi$
$113$	13.1976	1.24153	0.620765	+	0.783997i	$0.286822\pi$
$114$	2.08466	0.195246
$115$	−27.3938	−2.55448
$116$	−7.79454	−0.723705
$117$	−1.00000	−0.0924500
$118$	−11.0015	−1.01277
$119$	−1.00000	−0.0916698
$120$	3.34228	0.305107
$121$	−5.23229	−0.475663
$122$	0.940672	0.0851644
$123$	−1.10999	−0.100084
$124$	6.71855	0.603344
$125$	−3.91320	−0.350007
$126$	1.00000	0.0890871
$127$	−10.9147	−0.968523	−0.484262	−	0.874923i	$-0.660912\pi$
$127$	−10.9147	−0.968523	−0.484262	+	0.874923i	$0.660912\pi$
$128$	1.00000	0.0883883
$129$	−3.25762	−0.286817
$130$	3.34228	0.293137
$131$	−22.2208	−1.94144	−0.970722	−	0.240207i	$-0.922785\pi$
$131$	−22.2208	−1.94144	−0.970722	+	0.240207i	$0.922785\pi$
$132$	2.40161	0.209033
$133$	−2.08466	−0.180763
$134$	−0.938527	−0.0810764
$135$	3.34228	0.287657
$136$	−1.00000	−0.0857493
$137$	13.8792	1.18578	0.592890	−	0.805283i	$-0.297987\pi$
$137$	13.8792	1.18578	0.592890	+	0.805283i	$0.297987\pi$
$138$	−8.19615	−0.697702
$139$	−13.6521	−1.15795	−0.578976	−	0.815344i	$-0.696548\pi$
$139$	−13.6521	−1.15795	−0.578976	+	0.815344i	$0.696548\pi$
$140$	−3.34228	−0.282474
$141$	0.0868019	0.00731004
$142$	−4.99133	−0.418863
$143$	2.40161	0.200832
$144$	1.00000	0.0833333
$145$	26.0515	2.16346
$146$	1.00150	0.0828850
$147$	−1.00000	−0.0824786
$148$	6.59990	0.542508
$149$	−8.17949	−0.670090	−0.335045	−	0.942202i	$-0.608751\pi$
$149$	−8.17949	−0.670090	−0.335045	+	0.942202i	$0.608751\pi$
$150$	−6.17082	−0.503845
$151$	−17.0530	−1.38776	−0.693878	−	0.720093i	$-0.744099\pi$
$151$	−17.0530	−1.38776	−0.693878	+	0.720093i	$0.744099\pi$
$152$	−2.08466	−0.169088
$153$	−1.00000	−0.0808452
$154$	−2.40161	−0.193527
$155$	−22.4553	−1.80365
$156$	1.00000	0.0800641
$157$	−17.7439	−1.41612	−0.708058	−	0.706154i	$-0.750428\pi$
$157$	−17.7439	−1.41612	−0.708058	+	0.706154i	$0.750428\pi$
$158$	−0.0868019	−0.00690559
$159$	−1.42693	−0.113163
$160$	−3.34228	−0.264230
$161$	8.19615	0.645947
$162$	1.00000	0.0785674
$163$	5.99786	0.469788	0.234894	−	0.972021i	$-0.424526\pi$
$163$	5.99786	0.469788	0.234894	+	0.972021i	$0.424526\pi$
$164$	1.10999	0.0866754
$165$	−8.02683	−0.624888
$166$	−2.52241	−0.195777
$167$	−4.28295	−0.331425	−0.165712	−	0.986174i	$-0.552992\pi$
$167$	−4.28295	−0.331425	−0.165712	+	0.986174i	$0.552992\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	3.34228	0.256341
$171$	−2.08466	−0.159418
$172$	3.25762	0.248391
$173$	5.42693	0.412602	0.206301	−	0.978489i	$-0.433857\pi$
$173$	5.42693	0.412602	0.206301	+	0.978489i	$0.433857\pi$
$174$	7.79454	0.590903
$175$	6.17082	0.466470
$176$	−2.40161	−0.181028
$177$	11.0015	0.826924
$178$	−5.10999	−0.383010
$179$	21.9502	1.64064	0.820318	−	0.571908i	$-0.193797\pi$
$179$	21.9502	1.64064	0.820318	+	0.571908i	$0.193797\pi$
$180$	−3.34228	−0.249119
$181$	−5.86468	−0.435919	−0.217959	−	0.975958i	$-0.569940\pi$
$181$	−5.86468	−0.435919	−0.217959	+	0.975958i	$0.569940\pi$
$182$	−1.00000	−0.0741249
$183$	−0.940672	−0.0695365
$184$	8.19615	0.604228
$185$	−22.0587	−1.62179
$186$	−6.71855	−0.492628
$187$	2.40161	0.175623
$188$	−0.0868019	−0.00633068
$189$	−1.00000	−0.0727393
$190$	6.96750	0.505476
$191$	−5.43711	−0.393415	−0.196708	−	0.980462i	$-0.563025\pi$
$191$	−5.43711	−0.393415	−0.196708	+	0.980462i	$0.563025\pi$
$192$	−1.00000	−0.0721688
$193$	7.27428	0.523614	0.261807	−	0.965120i	$-0.415682\pi$
$193$	7.27428	0.523614	0.261807	+	0.965120i	$0.415682\pi$
$194$	12.1383	0.871481
$195$	−3.34228	−0.239345
$196$	1.00000	0.0714286
$197$	−16.6586	−1.18687	−0.593437	−	0.804880i	$-0.702230\pi$
$197$	−16.6586	−1.18687	−0.593437	+	0.804880i	$0.702230\pi$
$198$	−2.40161	−0.170675
$199$	0.856014	0.0606812	0.0303406	−	0.999540i	$-0.490341\pi$
$199$	0.856014	0.0606812	0.0303406	+	0.999540i	$0.490341\pi$
$200$	6.17082	0.436343
$201$	0.938527	0.0661986
$202$	−10.6824	−0.751612
$203$	−7.79454	−0.547070
$204$	1.00000	0.0700140
$205$	−3.70988	−0.259110
$206$	5.60642	0.390618
$207$	8.19615	0.569672
$208$	−1.00000	−0.0693375
$209$	5.00653	0.346309
$210$	3.34228	0.230639
$211$	−24.1217	−1.66060	−0.830302	−	0.557314i	$-0.811832\pi$
$211$	−24.1217	−1.66060	−0.830302	+	0.557314i	$0.811832\pi$
$212$	1.42693	0.0980023
$213$	4.99133	0.342000
$214$	−0.0339990	−0.00232412
$215$	−10.8879	−0.742546
$216$	−1.00000	−0.0680414
$217$	6.71855	0.456085
$218$	5.13682	0.347909
$219$	−1.00150	−0.0676753
$220$	8.02683	0.541169
$221$	1.00000	0.0672673
$222$	−6.59990	−0.442956
$223$	−8.89001	−0.595319	−0.297660	−	0.954672i	$-0.596206\pi$
$223$	−8.89001	−0.595319	−0.297660	+	0.954672i	$0.596206\pi$
$224$	1.00000	0.0668153
$225$	6.17082	0.411388
$226$	13.1976	0.877895
$227$	20.3055	1.34772	0.673861	−	0.738858i	$-0.264634\pi$
$227$	20.3055	1.34772	0.673861	+	0.738858i	$0.264634\pi$
$228$	2.08466	0.138060
$229$	−5.57457	−0.368378	−0.184189	−	0.982891i	$-0.558966\pi$
$229$	−5.57457	−0.368378	−0.184189	+	0.982891i	$0.558966\pi$
$230$	−27.3938	−1.80629
$231$	2.40161	0.158014
$232$	−7.79454	−0.511737
$233$	−18.2107	−1.19302	−0.596510	−	0.802606i	$-0.703446\pi$
$233$	−18.2107	−1.19302	−0.596510	+	0.802606i	$0.703446\pi$
$234$	−1.00000	−0.0653720
$235$	0.290116	0.0189251
$236$	−11.0015	−0.716137
$237$	0.0868019	0.00563839
$238$	−1.00000	−0.0648204
$239$	16.2570	1.05158	0.525788	−	0.850615i	$-0.323770\pi$
$239$	16.2570	1.05158	0.525788	+	0.850615i	$0.323770\pi$
$240$	3.34228	0.215743
$241$	−4.21281	−0.271371	−0.135685	−	0.990752i	$-0.543324\pi$
$241$	−4.21281	−0.271371	−0.135685	+	0.990752i	$0.543324\pi$
$242$	−5.23229	−0.336344
$243$	−1.00000	−0.0641500
$244$	0.940672	0.0602203
$245$	−3.34228	−0.213530
$246$	−1.10999	−0.0707702
$247$	2.08466	0.132644
$248$	6.71855	0.426629
$249$	2.52241	0.159851
$250$	−3.91320	−0.247492
$251$	−14.7186	−0.929027	−0.464513	−	0.885566i	$-0.653771\pi$
$251$	−14.7186	−0.929027	−0.464513	+	0.885566i	$0.653771\pi$
$252$	1.00000	0.0629941
$253$	−19.6839	−1.23752
$254$	−10.9147	−0.684849
$255$	−3.34228	−0.209302
$256$	1.00000	0.0625000
$257$	0.887869	0.0553837	0.0276919	−	0.999617i	$-0.491184\pi$
$257$	0.887869	0.0553837	0.0276919	+	0.999617i	$0.491184\pi$
$258$	−3.25762	−0.202811
$259$	6.59990	0.410098
$260$	3.34228	0.207279
$261$	−7.79454	−0.482470
$262$	−22.2208	−1.37281
$263$	2.09917	0.129441	0.0647203	−	0.997903i	$-0.479384\pi$
$263$	2.09917	0.129441	0.0647203	+	0.997903i	$0.479384\pi$
$264$	2.40161	0.147809
$265$	−4.76921	−0.292970
$266$	−2.08466	−0.127819
$267$	5.10999	0.312726
$268$	−0.938527	−0.0573297
$269$	−14.9994	−0.914527	−0.457264	−	0.889331i	$-0.651170\pi$
$269$	−14.9994	−0.914527	−0.457264	+	0.889331i	$0.651170\pi$
$270$	3.34228	0.203405
$271$	−9.02533	−0.548250	−0.274125	−	0.961694i	$-0.588388\pi$
$271$	−9.02533	−0.548250	−0.274125	+	0.961694i	$0.588388\pi$
$272$	−1.00000	−0.0606339
$273$	1.00000	0.0605228
$274$	13.8792	0.838473
$275$	−14.8199	−0.893672
$276$	−8.19615	−0.493350
$277$	7.25548	0.435939	0.217970	−	0.975956i	$-0.430057\pi$
$277$	7.25548	0.435939	0.217970	+	0.975956i	$0.430057\pi$
$278$	−13.6521	−0.818796
$279$	6.71855	0.402229
$280$	−3.34228	−0.199739
$281$	−6.50078	−0.387804	−0.193902	−	0.981021i	$-0.562114\pi$
$281$	−6.50078	−0.387804	−0.193902	+	0.981021i	$0.562114\pi$
$282$	0.0868019	0.00516898
$283$	7.26994	0.432153	0.216076	−	0.976376i	$-0.430674\pi$
$283$	7.26994	0.432153	0.216076	+	0.976376i	$0.430674\pi$
$284$	−4.99133	−0.296181
$285$	−6.96750	−0.412719
$286$	2.40161	0.142010
$287$	1.10999	0.0655205
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	26.0515	1.52980
$291$	−12.1383	−0.711561
$292$	1.00150	0.0586085
$293$	−23.4776	−1.37158	−0.685788	−	0.727802i	$-0.740542\pi$
$293$	−23.4776	−1.37158	−0.685788	+	0.727802i	$0.740542\pi$
$294$	−1.00000	−0.0583212
$295$	36.7701	2.14084
$296$	6.59990	0.383611
$297$	2.40161	0.139355
$298$	−8.17949	−0.473825
$299$	−8.19615	−0.473995
$300$	−6.17082	−0.356272
$301$	3.25762	0.187766
$302$	−17.0530	−0.981291
$303$	10.6824	0.613688
$304$	−2.08466	−0.119563
$305$	−3.14399	−0.180024
$306$	−1.00000	−0.0571662
$307$	2.61007	0.148965	0.0744823	−	0.997222i	$-0.476270\pi$
$307$	2.61007	0.148965	0.0744823	+	0.997222i	$0.476270\pi$
$308$	−2.40161	−0.136844
$309$	−5.60642	−0.318938
$310$	−22.4553	−1.27537
$311$	−12.4451	−0.705697	−0.352848	−	0.935681i	$-0.614787\pi$
$311$	−12.4451	−0.705697	−0.352848	+	0.935681i	$0.614787\pi$
$312$	1.00000	0.0566139
$313$	−20.8735	−1.17984	−0.589921	−	0.807461i	$-0.700841\pi$
$313$	−20.8735	−1.17984	−0.589921	+	0.807461i	$0.700841\pi$
$314$	−17.7439	−1.00135
$315$	−3.34228	−0.188316
$316$	−0.0868019	−0.00488299
$317$	13.6499	0.766656	0.383328	−	0.923612i	$-0.374778\pi$
$317$	13.6499	0.766656	0.383328	+	0.923612i	$0.374778\pi$
$318$	−1.42693	−0.0800185
$319$	18.7194	1.04809
$320$	−3.34228	−0.186839
$321$	0.0339990	0.00189764
$322$	8.19615	0.456753
$323$	2.08466	0.115993
$324$	1.00000	0.0555556
$325$	−6.17082	−0.342295
$326$	5.99786	0.332191
$327$	−5.13682	−0.284067
$328$	1.10999	0.0612888
$329$	−0.0868019	−0.00478554
$330$	−8.02683	−0.441863
$331$	−8.50507	−0.467481	−0.233740	−	0.972299i	$-0.575097\pi$
$331$	−8.50507	−0.467481	−0.233740	+	0.972299i	$0.575097\pi$
$332$	−2.52241	−0.138435
$333$	6.59990	0.361672
$334$	−4.28295	−0.234353
$335$	3.13682	0.171383
$336$	−1.00000	−0.0545545
$337$	22.7238	1.23784	0.618921	−	0.785453i	$-0.287570\pi$
$337$	22.7238	1.23784	0.618921	+	0.785453i	$0.287570\pi$
$338$	1.00000	0.0543928
$339$	−13.1976	−0.716798
$340$	3.34228	0.181260
$341$	−16.1353	−0.873776
$342$	−2.08466	−0.112725
$343$	1.00000	0.0539949
$344$	3.25762	0.175639
$345$	27.3938	1.47483
$346$	5.42693	0.291754
$347$	17.7809	0.954528	0.477264	−	0.878760i	$-0.341629\pi$
$347$	17.7809	0.954528	0.477264	+	0.878760i	$0.341629\pi$
$348$	7.79454	0.417831
$349$	−11.0334	−0.590602	−0.295301	−	0.955404i	$-0.595420\pi$
$349$	−11.0334	−0.590602	−0.295301	+	0.955404i	$0.595420\pi$
$350$	6.17082	0.329844
$351$	1.00000	0.0533761
$352$	−2.40161	−0.128006
$353$	−7.31257	−0.389209	−0.194604	−	0.980882i	$-0.562342\pi$
$353$	−7.31257	−0.389209	−0.194604	+	0.980882i	$0.562342\pi$
$354$	11.0015	0.584723
$355$	16.6824	0.885410
$356$	−5.10999	−0.270829
$357$	1.00000	0.0529256
$358$	21.9502	1.16010
$359$	−29.7997	−1.57277	−0.786384	−	0.617738i	$-0.788049\pi$
$359$	−29.7997	−1.57277	−0.786384	+	0.617738i	$0.788049\pi$
$360$	−3.34228	−0.176153
$361$	−14.6542	−0.771274
$362$	−5.86468	−0.308241
$363$	5.23229	0.274624
$364$	−1.00000	−0.0524142
$365$	−3.34730	−0.175206
$366$	−0.940672	−0.0491697
$367$	−18.0370	−0.941524	−0.470762	−	0.882260i	$-0.656021\pi$
$367$	−18.0370	−0.941524	−0.470762	+	0.882260i	$0.656021\pi$
$368$	8.19615	0.427254
$369$	1.10999	0.0577836
$370$	−22.0587	−1.14678
$371$	1.42693	0.0740828
$372$	−6.71855	−0.348341
$373$	−25.8201	−1.33691	−0.668457	−	0.743751i	$-0.733045\pi$
$373$	−25.8201	−1.33691	−0.668457	+	0.743751i	$0.733045\pi$
$374$	2.40161	0.124184
$375$	3.91320	0.202077
$376$	−0.0868019	−0.00447647
$377$	7.79454	0.401439
$378$	−1.00000	−0.0514344
$379$	22.1949	1.14007	0.570037	−	0.821619i	$-0.306929\pi$
$379$	22.1949	1.14007	0.570037	+	0.821619i	$0.306929\pi$
$380$	6.96750	0.357425
$381$	10.9147	0.559177
$382$	−5.43711	−0.278187
$383$	−27.6434	−1.41251	−0.706257	−	0.707956i	$-0.749617\pi$
$383$	−27.6434	−1.41251	−0.706257	+	0.707956i	$0.749617\pi$
$384$	−1.00000	−0.0510310
$385$	8.02683	0.409085
$386$	7.27428	0.370251
$387$	3.25762	0.165594
$388$	12.1383	0.616230
$389$	−2.55787	−0.129689	−0.0648446	−	0.997895i	$-0.520655\pi$
$389$	−2.55787	−0.129689	−0.0648446	+	0.997895i	$0.520655\pi$
$390$	−3.34228	−0.169243
$391$	−8.19615	−0.414497
$392$	1.00000	0.0505076
$393$	22.2208	1.12089
$394$	−16.6586	−0.839247
$395$	0.290116	0.0145973
$396$	−2.40161	−0.120685
$397$	21.5103	1.07957	0.539786	−	0.841802i	$-0.318505\pi$
$397$	21.5103	1.07957	0.539786	+	0.841802i	$0.318505\pi$
$398$	0.856014	0.0429081
$399$	2.08466	0.104363
$400$	6.17082	0.308541
$401$	−9.60428	−0.479615	−0.239807	−	0.970820i	$-0.577084\pi$
$401$	−9.60428	−0.479615	−0.239807	+	0.970820i	$0.577084\pi$
$402$	0.938527	0.0468095
$403$	−6.71855	−0.334675
$404$	−10.6824	−0.531470
$405$	−3.34228	−0.166079
$406$	−7.79454	−0.386837
$407$	−15.8504	−0.785673
$408$	1.00000	0.0495074
$409$	23.3657	1.15536	0.577679	−	0.816264i	$-0.303958\pi$
$409$	23.3657	1.15536	0.577679	+	0.816264i	$0.303958\pi$
$410$	−3.70988	−0.183218
$411$	−13.8792	−0.684610
$412$	5.60642	0.276209
$413$	−11.0015	−0.541349
$414$	8.19615	0.402819
$415$	8.43058	0.413841
$416$	−1.00000	−0.0490290
$417$	13.6521	0.668544
$418$	5.00653	0.244877
$419$	15.1905	0.742104	0.371052	−	0.928612i	$-0.378997\pi$
$419$	15.1905	0.742104	0.371052	+	0.928612i	$0.378997\pi$
$420$	3.34228	0.163086
$421$	1.60054	0.0780055	0.0390027	−	0.999239i	$-0.487582\pi$
$421$	1.60054	0.0780055	0.0390027	+	0.999239i	$0.487582\pi$
$422$	−24.1217	−1.17422
$423$	−0.0868019	−0.00422045
$424$	1.42693	0.0692981
$425$	−6.17082	−0.299329
$426$	4.99133	0.241831
$427$	0.940672	0.0455223
$428$	−0.0339990	−0.00164340
$429$	−2.40161	−0.115951
$430$	−10.8879	−0.525060
$431$	−15.5971	−0.751286	−0.375643	−	0.926764i	$-0.622578\pi$
$431$	−15.5971	−0.751286	−0.375643	+	0.926764i	$0.622578\pi$
$432$	−1.00000	−0.0481125
$433$	−18.2237	−0.875773	−0.437887	−	0.899030i	$-0.644273\pi$
$433$	−18.2237	−0.875773	−0.437887	+	0.899030i	$0.644273\pi$
$434$	6.71855	0.322501
$435$	−26.0515	−1.24907
$436$	5.13682	0.246009
$437$	−17.0862	−0.817342
$438$	−1.00150	−0.0478537
$439$	3.12879	0.149329	0.0746645	−	0.997209i	$-0.476211\pi$
$439$	3.12879	0.149329	0.0746645	+	0.997209i	$0.476211\pi$
$440$	8.02683	0.382664
$441$	1.00000	0.0476190
$442$	1.00000	0.0475651
$443$	−28.9879	−1.37726	−0.688628	−	0.725114i	$-0.741787\pi$
$443$	−28.9879	−1.37726	−0.688628	+	0.725114i	$0.741787\pi$
$444$	−6.59990	−0.313217
$445$	17.0790	0.809622
$446$	−8.89001	−0.420954
$447$	8.17949	0.386876
$448$	1.00000	0.0472456
$449$	−27.7874	−1.31137	−0.655684	−	0.755036i	$-0.727619\pi$
$449$	−27.7874	−1.31137	−0.655684	+	0.755036i	$0.727619\pi$
$450$	6.17082	0.290895
$451$	−2.66575	−0.125525
$452$	13.1976	0.620765
$453$	17.0530	0.801221
$454$	20.3055	0.952984
$455$	3.34228	0.156688
$456$	2.08466	0.0976230
$457$	−14.6390	−0.684786	−0.342393	−	0.939557i	$-0.611237\pi$
$457$	−14.6390	−0.684786	−0.342393	+	0.939557i	$0.611237\pi$
$458$	−5.57457	−0.260482
$459$	1.00000	0.0466760
$460$	−27.3938	−1.27724
$461$	7.70057	0.358651	0.179326	−	0.983790i	$-0.442608\pi$
$461$	7.70057	0.358651	0.179326	+	0.983790i	$0.442608\pi$
$462$	2.40161	0.111733
$463$	14.7534	0.685649	0.342825	−	0.939399i	$-0.388616\pi$
$463$	14.7534	0.685649	0.342825	+	0.939399i	$0.388616\pi$
$464$	−7.79454	−0.361853
$465$	22.4553	1.04134
$466$	−18.2107	−0.843593
$467$	−11.4189	−0.528404	−0.264202	−	0.964467i	$-0.585109\pi$
$467$	−11.4189	−0.528404	−0.264202	+	0.964467i	$0.585109\pi$
$468$	−1.00000	−0.0462250
$469$	−0.938527	−0.0433372
$470$	0.290116	0.0133821
$471$	17.7439	0.817595
$472$	−11.0015	−0.506385
$473$	−7.82352	−0.359726
$474$	0.0868019	0.00398694
$475$	−12.8640	−0.590243
$476$	−1.00000	−0.0458349
$477$	1.42693	0.0653349
$478$	16.2570	0.743577
$479$	−10.3728	−0.473943	−0.236972	−	0.971517i	$-0.576155\pi$
$479$	−10.3728	−0.473943	−0.236972	+	0.971517i	$0.576155\pi$
$480$	3.34228	0.152553
$481$	−6.59990	−0.300929
$482$	−4.21281	−0.191888
$483$	−8.19615	−0.372938
$484$	−5.23229	−0.237831
$485$	−40.5696	−1.84217
$486$	−1.00000	−0.0453609
$487$	−38.6060	−1.74940	−0.874702	−	0.484662i	$-0.838943\pi$
$487$	−38.6060	−1.74940	−0.874702	+	0.484662i	$0.838943\pi$
$488$	0.940672	0.0425822
$489$	−5.99786	−0.271232
$490$	−3.34228	−0.150989
$491$	3.40096	0.153483	0.0767417	−	0.997051i	$-0.475548\pi$
$491$	3.40096	0.153483	0.0767417	+	0.997051i	$0.475548\pi$
$492$	−1.10999	−0.0500421
$493$	7.79454	0.351048
$494$	2.08466	0.0937932
$495$	8.02683	0.360779
$496$	6.71855	0.301672
$497$	−4.99133	−0.223892
$498$	2.52241	0.113032
$499$	37.5125	1.67929	0.839644	−	0.543137i	$-0.182764\pi$
$499$	37.5125	1.67929	0.839644	+	0.543137i	$0.182764\pi$
$500$	−3.91320	−0.175004
$501$	4.28295	0.191348
$502$	−14.7186	−0.656921
$503$	19.7107	0.878859	0.439429	−	0.898277i	$-0.355181\pi$
$503$	19.7107	0.878859	0.439429	+	0.898277i	$0.355181\pi$
$504$	1.00000	0.0445435
$505$	35.7036	1.58879
$506$	−19.6839	−0.875057
$507$	−1.00000	−0.0444116
$508$	−10.9147	−0.484262
$509$	−17.2359	−0.763969	−0.381985	−	0.924169i	$-0.624759\pi$
$509$	−17.2359	−0.763969	−0.381985	+	0.924169i	$0.624759\pi$
$510$	−3.34228	−0.147999
$511$	1.00150	0.0443039
$512$	1.00000	0.0441942
$513$	2.08466	0.0920399
$514$	0.887869	0.0391622
$515$	−18.7382	−0.825705
$516$	−3.25762	−0.143409
$517$	0.208464	0.00916823
$518$	6.59990	0.289983
$519$	−5.42693	−0.238216
$520$	3.34228	0.146569
$521$	6.60638	0.289431	0.144715	−	0.989473i	$-0.453773\pi$
$521$	6.60638	0.289431	0.144715	+	0.989473i	$0.453773\pi$
$522$	−7.79454	−0.341158
$523$	−1.76771	−0.0772965	−0.0386483	−	0.999253i	$-0.512305\pi$
$523$	−1.76771	−0.0772965	−0.0386483	+	0.999253i	$0.512305\pi$
$524$	−22.2208	−0.970722
$525$	−6.17082	−0.269317
$526$	2.09917	0.0915283
$527$	−6.71855	−0.292665
$528$	2.40161	0.104516
$529$	44.1768	1.92073
$530$	−4.76921	−0.207161
$531$	−11.0015	−0.477425
$532$	−2.08466	−0.0903814
$533$	−1.10999	−0.0480789
$534$	5.10999	0.221131
$535$	0.113634	0.00491282
$536$	−0.938527	−0.0405382
$537$	−21.9502	−0.947221
$538$	−14.9994	−0.646668
$539$	−2.40161	−0.103444
$540$	3.34228	0.143829
$541$	4.43560	0.190702	0.0953508	−	0.995444i	$-0.469603\pi$
$541$	4.43560	0.190702	0.0953508	+	0.995444i	$0.469603\pi$
$542$	−9.02533	−0.387671
$543$	5.86468	0.251678
$544$	−1.00000	−0.0428746
$545$	−17.1687	−0.735425
$546$	1.00000	0.0427960
$547$	−24.6688	−1.05476	−0.527380	−	0.849630i	$-0.676826\pi$
$547$	−24.6688	−1.05476	−0.527380	+	0.849630i	$0.676826\pi$
$548$	13.8792	0.592890
$549$	0.940672	0.0401469
$550$	−14.8199	−0.631921
$551$	16.2490	0.692229
$552$	−8.19615	−0.348851
$553$	−0.0868019	−0.00369119
$554$	7.25548	0.308256
$555$	22.0587	0.936339
$556$	−13.6521	−0.578976
$557$	36.0567	1.52777	0.763885	−	0.645352i	$-0.223289\pi$
$557$	36.0567	1.52777	0.763885	+	0.645352i	$0.223289\pi$
$558$	6.71855	0.284419
$559$	−3.25762	−0.137783
$560$	−3.34228	−0.141237
$561$	−2.40161	−0.101396
$562$	−6.50078	−0.274219
$563$	−14.1383	−0.595859	−0.297930	−	0.954588i	$-0.596296\pi$
$563$	−14.1383	−0.595859	−0.297930	+	0.954588i	$0.596296\pi$
$564$	0.0868019	0.00365502
$565$	−44.1102	−1.85573
$566$	7.26994	0.305578
$567$	1.00000	0.0419961
$568$	−4.99133	−0.209432
$569$	−35.2823	−1.47911	−0.739556	−	0.673095i	$-0.764964\pi$
$569$	−35.2823	−1.47911	−0.739556	+	0.673095i	$0.764964\pi$
$570$	−6.96750	−0.291837
$571$	21.2750	0.890329	0.445165	−	0.895449i	$-0.353145\pi$
$571$	21.2750	0.890329	0.445165	+	0.895449i	$0.353145\pi$
$572$	2.40161	0.100416
$573$	5.43711	0.227138
$574$	1.10999	0.0463300
$575$	50.5769	2.10920
$576$	1.00000	0.0416667
$577$	18.3169	0.762545	0.381272	−	0.924463i	$-0.375486\pi$
$577$	18.3169	0.762545	0.381272	+	0.924463i	$0.375486\pi$
$578$	1.00000	0.0415945
$579$	−7.27428	−0.302309
$580$	26.0515	1.08173
$581$	−2.52241	−0.104647
$582$	−12.1383	−0.503150
$583$	−3.42693	−0.141929
$584$	1.00150	0.0414425
$585$	3.34228	0.138186
$586$	−23.4776	−0.969850
$587$	29.7477	1.22782	0.613911	−	0.789376i	$-0.289596\pi$
$587$	29.7477	1.22782	0.613911	+	0.789376i	$0.289596\pi$
$588$	−1.00000	−0.0412393
$589$	−14.0059	−0.577102
$590$	36.7701	1.51380
$591$	16.6586	0.685243
$592$	6.59990	0.271254
$593$	−15.0904	−0.619690	−0.309845	−	0.950787i	$-0.600277\pi$
$593$	−15.0904	−0.619690	−0.309845	+	0.950787i	$0.600277\pi$
$594$	2.40161	0.0985391
$595$	3.34228	0.137020
$596$	−8.17949	−0.335045
$597$	−0.856014	−0.0350343
$598$	−8.19615	−0.335165
$599$	−17.2678	−0.705543	−0.352771	−	0.935710i	$-0.614761\pi$
$599$	−17.2678	−0.705543	−0.352771	+	0.935710i	$0.614761\pi$
$600$	−6.17082	−0.251923
$601$	43.8534	1.78882	0.894408	−	0.447252i	$-0.147597\pi$
$601$	43.8534	1.78882	0.894408	+	0.447252i	$0.147597\pi$
$602$	3.25762	0.132771
$603$	−0.938527	−0.0382198
$604$	−17.0530	−0.693878
$605$	17.4878	0.710979
$606$	10.6824	0.433943
$607$	−32.2319	−1.30825	−0.654126	−	0.756386i	$-0.726963\pi$
$607$	−32.2319	−1.30825	−0.654126	+	0.756386i	$0.726963\pi$
$608$	−2.08466	−0.0845440
$609$	7.79454	0.315851
$610$	−3.14399	−0.127296
$611$	0.0868019	0.00351163
$612$	−1.00000	−0.0404226
$613$	18.2230	0.736019	0.368010	−	0.929822i	$-0.380039\pi$
$613$	18.2230	0.736019	0.368010	+	0.929822i	$0.380039\pi$
$614$	2.61007	0.105334
$615$	3.70988	0.149597
$616$	−2.40161	−0.0967634
$617$	−33.9257	−1.36580	−0.682899	−	0.730513i	$-0.739281\pi$
$617$	−33.9257	−1.36580	−0.682899	+	0.730513i	$0.739281\pi$
$618$	−5.60642	−0.225523
$619$	4.49275	0.180579	0.0902894	−	0.995916i	$-0.471221\pi$
$619$	4.49275	0.180579	0.0902894	+	0.995916i	$0.471221\pi$
$620$	−22.4553	−0.901825
$621$	−8.19615	−0.328900
$622$	−12.4451	−0.499003
$623$	−5.10999	−0.204727
$624$	1.00000	0.0400320
$625$	−17.7751	−0.711004
$626$	−20.8735	−0.834274
$627$	−5.00653	−0.199941
$628$	−17.7439	−0.708058
$629$	−6.59990	−0.263155
$630$	−3.34228	−0.133160
$631$	22.5752	0.898705	0.449352	−	0.893355i	$-0.351655\pi$
$631$	22.5752	0.898705	0.449352	+	0.893355i	$0.351655\pi$
$632$	−0.0868019	−0.00345279
$633$	24.1217	0.958750
$634$	13.6499	0.542107
$635$	36.4800	1.44766
$636$	−1.42693	−0.0565817
$637$	−1.00000	−0.0396214
$638$	18.7194	0.741109
$639$	−4.99133	−0.197454
$640$	−3.34228	−0.132115
$641$	0.888548	0.0350956	0.0175478	−	0.999846i	$-0.494414\pi$
$641$	0.888548	0.0350956	0.0175478	+	0.999846i	$0.494414\pi$
$642$	0.0339990	0.00134183
$643$	−35.6962	−1.40772	−0.703861	−	0.710338i	$-0.748542\pi$
$643$	−35.6962	−1.40772	−0.703861	+	0.710338i	$0.748542\pi$
$644$	8.19615	0.322973
$645$	10.8879	0.428709
$646$	2.08466	0.0820198
$647$	−5.83571	−0.229425	−0.114713	−	0.993399i	$-0.536595\pi$
$647$	−5.83571	−0.229425	−0.114713	+	0.993399i	$0.536595\pi$
$648$	1.00000	0.0392837
$649$	26.4213	1.03713
$650$	−6.17082	−0.242039
$651$	−6.71855	−0.263321
$652$	5.99786	0.234894
$653$	19.7353	0.772300	0.386150	−	0.922436i	$-0.373805\pi$
$653$	19.7353	0.772300	0.386150	+	0.922436i	$0.373805\pi$
$654$	−5.13682	−0.200866
$655$	74.2682	2.90190
$656$	1.10999	0.0433377
$657$	1.00150	0.0390723
$658$	−0.0868019	−0.00338389
$659$	6.16649	0.240212	0.120106	−	0.992761i	$-0.461676\pi$
$659$	6.16649	0.240212	0.120106	+	0.992761i	$0.461676\pi$
$660$	−8.02683	−0.312444
$661$	42.8194	1.66548	0.832742	−	0.553662i	$-0.186770\pi$
$661$	42.8194	1.66548	0.832742	+	0.553662i	$0.186770\pi$
$662$	−8.50507	−0.330559
$663$	−1.00000	−0.0388368
$664$	−2.52241	−0.0978884
$665$	6.96750	0.270188
$666$	6.59990	0.255741
$667$	−63.8852	−2.47365
$668$	−4.28295	−0.165712
$669$	8.89001	0.343708
$670$	3.13682	0.121186
$671$	−2.25912	−0.0872125
$672$	−1.00000	−0.0385758
$673$	−24.4098	−0.940929	−0.470465	−	0.882419i	$-0.655914\pi$
$673$	−24.4098	−0.940929	−0.470465	+	0.882419i	$0.655914\pi$
$674$	22.7238	0.875286
$675$	−6.17082	−0.237515
$676$	1.00000	0.0384615
$677$	−10.4646	−0.402187	−0.201093	−	0.979572i	$-0.564449\pi$
$677$	−10.4646	−0.402187	−0.201093	+	0.979572i	$0.564449\pi$
$678$	−13.1976	−0.506853
$679$	12.1383	0.465826
$680$	3.34228	0.128170
$681$	−20.3055	−0.778108
$682$	−16.1353	−0.617853
$683$	4.42255	0.169224	0.0846122	−	0.996414i	$-0.473035\pi$
$683$	4.42255	0.169224	0.0846122	+	0.996414i	$0.473035\pi$
$684$	−2.08466	−0.0797089
$685$	−46.3881	−1.77240
$686$	1.00000	0.0381802
$687$	5.57457	0.212683
$688$	3.25762	0.124196
$689$	−1.42693	−0.0543619
$690$	27.3938	1.04286
$691$	0.426293	0.0162170	0.00810848	−	0.999967i	$-0.497419\pi$
$691$	0.426293	0.0162170	0.00810848	+	0.999967i	$0.497419\pi$
$692$	5.42693	0.206301
$693$	−2.40161	−0.0912295
$694$	17.7809	0.674953
$695$	45.6290	1.73081
$696$	7.79454	0.295451
$697$	−1.10999	−0.0420438
$698$	−11.0334	−0.417619
$699$	18.2107	0.688791
$700$	6.17082	0.233235
$701$	−21.7027	−0.819700	−0.409850	−	0.912153i	$-0.634419\pi$
$701$	−21.7027	−0.819700	−0.409850	+	0.912153i	$0.634419\pi$
$702$	1.00000	0.0377426
$703$	−13.7585	−0.518913
$704$	−2.40161	−0.0905139
$705$	−0.290116	−0.0109264
$706$	−7.31257	−0.275212
$707$	−10.6824	−0.401753
$708$	11.0015	0.413462
$709$	−34.7267	−1.30419	−0.652094	−	0.758138i	$-0.726109\pi$
$709$	−34.7267	−1.30419	−0.652094	+	0.758138i	$0.726109\pi$
$710$	16.6824	0.626080
$711$	−0.0868019	−0.00325533
$712$	−5.10999	−0.191505
$713$	55.0663	2.06225
$714$	1.00000	0.0374241
$715$	−8.02683	−0.300186
$716$	21.9502	0.820318
$717$	−16.2570	−0.607128
$718$	−29.7997	−1.11211
$719$	−42.4995	−1.58496	−0.792482	−	0.609895i	$-0.791211\pi$
$719$	−42.4995	−1.58496	−0.792482	+	0.609895i	$0.791211\pi$
$720$	−3.34228	−0.124559
$721$	5.60642	0.208794
$722$	−14.6542	−0.545373
$723$	4.21281	0.156676
$724$	−5.86468	−0.217959
$725$	−48.0987	−1.78634
$726$	5.23229	0.194189
$727$	−23.7714	−0.881632	−0.440816	−	0.897597i	$-0.645311\pi$
$727$	−23.7714	−0.881632	−0.440816	+	0.897597i	$0.645311\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	−3.34730	−0.123889
$731$	−3.25762	−0.120487
$732$	−0.940672	−0.0347682
$733$	11.2678	0.416185	0.208093	−	0.978109i	$-0.433274\pi$
$733$	11.2678	0.416185	0.208093	+	0.978109i	$0.433274\pi$
$734$	−18.0370	−0.665758
$735$	3.34228	0.123282
$736$	8.19615	0.302114
$737$	2.25397	0.0830262
$738$	1.10999	0.0408592
$739$	−31.8838	−1.17286	−0.586432	−	0.809998i	$-0.699468\pi$
$739$	−31.8838	−1.17286	−0.586432	+	0.809998i	$0.699468\pi$
$740$	−22.0587	−0.810893
$741$	−2.08466	−0.0765818
$742$	1.42693	0.0523844
$743$	−24.2990	−0.891444	−0.445722	−	0.895171i	$-0.647053\pi$
$743$	−24.2990	−0.891444	−0.445722	+	0.895171i	$0.647053\pi$
$744$	−6.71855	−0.246314
$745$	27.3381	1.00159
$746$	−25.8201	−0.945341
$747$	−2.52241	−0.0922900
$748$	2.40161	0.0878114
$749$	−0.0339990	−0.00124229
$750$	3.91320	0.142890
$751$	−41.0821	−1.49911	−0.749553	−	0.661945i	$-0.769731\pi$
$751$	−41.0821	−1.49911	−0.749553	+	0.661945i	$0.769731\pi$
$752$	−0.0868019	−0.00316534
$753$	14.7186	0.536374
$754$	7.79454	0.283860
$755$	56.9959	2.07429
$756$	−1.00000	−0.0363696
$757$	33.3121	1.21075	0.605375	−	0.795940i	$-0.293023\pi$
$757$	33.3121	1.21075	0.605375	+	0.795940i	$0.293023\pi$
$758$	22.1949	0.806154
$759$	19.6839	0.714481
$760$	6.96750	0.252738
$761$	−51.4258	−1.86419	−0.932093	−	0.362220i	$-0.882019\pi$
$761$	−51.4258	−1.86419	−0.932093	+	0.362220i	$0.882019\pi$
$762$	10.9147	0.395398
$763$	5.13682	0.185965
$764$	−5.43711	−0.196708
$765$	3.34228	0.120840
$766$	−27.6434	−0.998798
$767$	11.0015	0.397241
$768$	−1.00000	−0.0360844
$769$	−38.6305	−1.39305	−0.696525	−	0.717532i	$-0.745272\pi$
$769$	−38.6305	−1.39305	−0.696525	+	0.717532i	$0.745272\pi$
$770$	8.02683	0.289267
$771$	−0.887869	−0.0319758
$772$	7.27428	0.261807
$773$	20.0379	0.720712	0.360356	−	0.932815i	$-0.382655\pi$
$773$	20.0379	0.720712	0.360356	+	0.932815i	$0.382655\pi$
$774$	3.25762	0.117093
$775$	41.4590	1.48925
$776$	12.1383	0.435740
$777$	−6.59990	−0.236770
$778$	−2.55787	−0.0917041
$779$	−2.31394	−0.0829056
$780$	−3.34228	−0.119673
$781$	11.9872	0.428936
$782$	−8.19615	−0.293094
$783$	7.79454	0.278554
$784$	1.00000	0.0357143
$785$	59.3050	2.11669
$786$	22.2208	0.792591
$787$	34.8134	1.24096	0.620482	−	0.784221i	$-0.286937\pi$
$787$	34.8134	1.24096	0.620482	+	0.784221i	$0.286937\pi$
$788$	−16.6586	−0.593437
$789$	−2.09917	−0.0747325
$790$	0.290116	0.0103219
$791$	13.1976	0.469254
$792$	−2.40161	−0.0853373
$793$	−0.940672	−0.0334042
$794$	21.5103	0.763372
$795$	4.76921	0.169147
$796$	0.856014	0.0303406
$797$	−37.3555	−1.32320	−0.661600	−	0.749857i	$-0.730122\pi$
$797$	−37.3555	−1.32320	−0.661600	+	0.749857i	$0.730122\pi$
$798$	2.08466	0.0737961
$799$	0.0868019	0.00307083
$800$	6.17082	0.218171
$801$	−5.10999	−0.180553
$802$	−9.60428	−0.339139
$803$	−2.40521	−0.0848782
$804$	0.938527	0.0330993
$805$	−27.3938	−0.965504
$806$	−6.71855	−0.236651
$807$	14.9994	0.528002
$808$	−10.6824	−0.375806
$809$	0.0209483	0.000736503 0	0.000368251	−	1.00000i	$-0.499883\pi$
$809$	0.0209483	0.000736503 0	0.000368251		1.00000i	$0.499883\pi$
$810$	−3.34228	−0.117436
$811$	38.4408	1.34984	0.674919	−	0.737892i	$-0.264179\pi$
$811$	38.4408	1.34984	0.674919	+	0.737892i	$0.264179\pi$
$812$	−7.79454	−0.273535
$813$	9.02533	0.316532
$814$	−15.8504	−0.555554
$815$	−20.0465	−0.702198
$816$	1.00000	0.0350070
$817$	−6.79102	−0.237588
$818$	23.3657	0.816962
$819$	−1.00000	−0.0349428
$820$	−3.70988	−0.129555
$821$	−22.3561	−0.780233	−0.390117	−	0.920765i	$-0.627565\pi$
$821$	−22.3561	−0.780233	−0.390117	+	0.920765i	$0.627565\pi$
$822$	−13.8792	−0.484093
$823$	46.9727	1.63736	0.818682	−	0.574247i	$-0.194705\pi$
$823$	46.9727	1.63736	0.818682	+	0.574247i	$0.194705\pi$
$824$	5.60642	0.195309
$825$	14.8199	0.515962
$826$	−11.0015	−0.382791
$827$	−12.4711	−0.433662	−0.216831	−	0.976209i	$-0.569572\pi$
$827$	−12.4711	−0.433662	−0.216831	+	0.976209i	$0.569572\pi$
$828$	8.19615	0.284836
$829$	−26.9054	−0.934463	−0.467231	−	0.884135i	$-0.654749\pi$
$829$	−26.9054	−0.934463	−0.467231	+	0.884135i	$0.654749\pi$
$830$	8.43058	0.292630
$831$	−7.25548	−0.251690
$832$	−1.00000	−0.0346688
$833$	−1.00000	−0.0346479
$834$	13.6521	0.472732
$835$	14.3148	0.495384
$836$	5.00653	0.173154
$837$	−6.71855	−0.232227
$838$	15.1905	0.524747
$839$	11.8843	0.410293	0.205147	−	0.978731i	$-0.434233\pi$
$839$	11.8843	0.410293	0.205147	+	0.978731i	$0.434233\pi$
$840$	3.34228	0.115320
$841$	31.7549	1.09500
$842$	1.60054	0.0551582
$843$	6.50078	0.223899
$844$	−24.1217	−0.830302
$845$	−3.34228	−0.114978
$846$	−0.0868019	−0.00298431
$847$	−5.23229	−0.179784
$848$	1.42693	0.0490011
$849$	−7.26994	−0.249504
$850$	−6.17082	−0.211657
$851$	54.0937	1.85431
$852$	4.99133	0.171000
$853$	36.2940	1.24268	0.621341	−	0.783540i	$-0.286588\pi$
$853$	36.2940	1.24268	0.621341	+	0.783540i	$0.286588\pi$
$854$	0.940672	0.0321891
$855$	6.96750	0.238284
$856$	−0.0339990	−0.00116206
$857$	11.0058	0.375953	0.187976	−	0.982174i	$-0.439807\pi$
$857$	11.0058	0.375953	0.187976	+	0.982174i	$0.439807\pi$
$858$	−2.40161	−0.0819895
$859$	−18.3873	−0.627366	−0.313683	−	0.949528i	$-0.601563\pi$
$859$	−18.3873	−0.627366	−0.313683	+	0.949528i	$0.601563\pi$
$860$	−10.8879	−0.371273
$861$	−1.10999	−0.0378283
$862$	−15.5971	−0.531240
$863$	50.6977	1.72577	0.862885	−	0.505400i	$-0.168655\pi$
$863$	50.6977	1.72577	0.862885	+	0.505400i	$0.168655\pi$
$864$	−1.00000	−0.0340207
$865$	−18.1383	−0.616721
$866$	−18.2237	−0.619265
$867$	−1.00000	−0.0339618
$868$	6.71855	0.228043
$869$	0.208464	0.00707165
$870$	−26.0515	−0.883229
$871$	0.938527	0.0318008
$872$	5.13682	0.173955
$873$	12.1383	0.410820
$874$	−17.0862	−0.577948
$875$	−3.91320	−0.132290
$876$	−1.00150	−0.0338376
$877$	−15.2410	−0.514651	−0.257325	−	0.966325i	$-0.582841\pi$
$877$	−15.2410	−0.514651	−0.257325	+	0.966325i	$0.582841\pi$
$878$	3.12879	0.105592
$879$	23.4776	0.791880
$880$	8.02683	0.270584
$881$	−18.0805	−0.609147	−0.304574	−	0.952489i	$-0.598514\pi$
$881$	−18.0805	−0.609147	−0.304574	+	0.952489i	$0.598514\pi$
$882$	1.00000	0.0336718
$883$	2.58612	0.0870297	0.0435149	−	0.999053i	$-0.486144\pi$
$883$	2.58612	0.0870297	0.0435149	+	0.999053i	$0.486144\pi$
$884$	1.00000	0.0336336
$885$	−36.7701	−1.23601
$886$	−28.9879	−0.973868
$887$	35.8980	1.20534	0.602668	−	0.797992i	$-0.294104\pi$
$887$	35.8980	1.20534	0.602668	+	0.797992i	$0.294104\pi$
$888$	−6.59990	−0.221478
$889$	−10.9147	−0.366067
$890$	17.0790	0.572489
$891$	−2.40161	−0.0804568
$892$	−8.89001	−0.297660
$893$	0.180952	0.00605534
$894$	8.17949	0.273563
$895$	−73.3637	−2.45228
$896$	1.00000	0.0334077
$897$	8.19615	0.273661
$898$	−27.7874	−0.927277
$899$	−52.3680	−1.74657
$900$	6.17082	0.205694
$901$	−1.42693	−0.0475381
$902$	−2.66575	−0.0887598
$903$	−3.25762	−0.108407
$904$	13.1976	0.438947
$905$	19.6014	0.651573
$906$	17.0530	0.566549
$907$	4.20980	0.139784	0.0698921	−	0.997555i	$-0.477735\pi$
$907$	4.20980	0.139784	0.0698921	+	0.997555i	$0.477735\pi$
$908$	20.3055	0.673861
$909$	−10.6824	−0.354313
$910$	3.34228	0.110795
$911$	−25.6484	−0.849771	−0.424886	−	0.905247i	$-0.639686\pi$
$911$	−25.6484	−0.849771	−0.424886	+	0.905247i	$0.639686\pi$
$912$	2.08466	0.0690299
$913$	6.05783	0.200485
$914$	−14.6390	−0.484217
$915$	3.14399	0.103937
$916$	−5.57457	−0.184189
$917$	−22.2208	−0.733797
$918$	1.00000	0.0330049
$919$	20.9168	0.689983	0.344992	−	0.938606i	$-0.387882\pi$
$919$	20.9168	0.689983	0.344992	+	0.938606i	$0.387882\pi$
$920$	−27.3938	−0.903147
$921$	−2.61007	−0.0860047
$922$	7.70057	0.253605
$923$	4.99133	0.164292
$924$	2.40161	0.0790070
$925$	40.7268	1.33909
$926$	14.7534	0.484827
$927$	5.60642	0.184139
$928$	−7.79454	−0.255868
$929$	−53.6530	−1.76030	−0.880148	−	0.474698i	$-0.842557\pi$
$929$	−53.6530	−1.76030	−0.880148	+	0.474698i	$0.842557\pi$
$930$	22.4553	0.736337
$931$	−2.08466	−0.0683219
$932$	−18.2107	−0.596510
$933$	12.4451	0.407434
$934$	−11.4189	−0.373638
$935$	−8.02683	−0.262505
$936$	−1.00000	−0.0326860
$937$	4.92548	0.160908	0.0804542	−	0.996758i	$-0.474363\pi$
$937$	4.92548	0.160908	0.0804542	+	0.996758i	$0.474363\pi$
$938$	−0.938527	−0.0306440
$939$	20.8735	0.681182
$940$	0.290116	0.00946254
$941$	17.1657	0.559585	0.279792	−	0.960061i	$-0.409734\pi$
$941$	17.1657	0.559585	0.279792	+	0.960061i	$0.409734\pi$
$942$	17.7439	0.578127
$943$	9.09762	0.296259
$944$	−11.0015	−0.358068
$945$	3.34228	0.108724
$946$	−7.82352	−0.254365
$947$	−27.7926	−0.903137	−0.451569	−	0.892236i	$-0.649135\pi$
$947$	−27.7926	−0.903137	−0.451569	+	0.892236i	$0.649135\pi$
$948$	0.0868019	0.00281919
$949$	−1.00150	−0.0325102
$950$	−12.8640	−0.417365
$951$	−13.6499	−0.442629
$952$	−1.00000	−0.0324102
$953$	−46.4706	−1.50533	−0.752665	−	0.658404i	$-0.771232\pi$
$953$	−46.4706	−1.50533	−0.752665	+	0.658404i	$0.771232\pi$
$954$	1.42693	0.0461987
$955$	18.1723	0.588042
$956$	16.2570	0.525788
$957$	−18.7194	−0.605113
$958$	−10.3728	−0.335129
$959$	13.8792	0.448183
$960$	3.34228	0.107872
$961$	14.1390	0.456096
$962$	−6.59990	−0.212789
$963$	−0.0339990	−0.00109560
$964$	−4.21281	−0.135685
$965$	−24.3127	−0.782652
$966$	−8.19615	−0.263707
$967$	36.7672	1.18235	0.591177	−	0.806542i	$-0.298664\pi$
$967$	36.7672	1.18235	0.591177	+	0.806542i	$0.298664\pi$
$968$	−5.23229	−0.168172
$969$	−2.08466	−0.0669688
$970$	−40.5696	−1.30261
$971$	23.3706	0.749997	0.374999	−	0.927025i	$-0.377643\pi$
$971$	23.3706	0.749997	0.374999	+	0.927025i	$0.377643\pi$
$972$	−1.00000	−0.0320750
$973$	−13.6521	−0.437665
$974$	−38.6060	−1.23701
$975$	6.17082	0.197624
$976$	0.940672	0.0301102
$977$	50.5973	1.61875	0.809376	−	0.587291i	$-0.199805\pi$
$977$	50.5973	1.61875	0.809376	+	0.587291i	$0.199805\pi$
$978$	−5.99786	−0.191790
$979$	12.2722	0.392220
$980$	−3.34228	−0.106765
$981$	5.13682	0.164006
$982$	3.40096	0.108529
$983$	−24.5603	−0.783351	−0.391676	−	0.920103i	$-0.628104\pi$
$983$	−24.5603	−0.783351	−0.391676	+	0.920103i	$0.628104\pi$
$984$	−1.10999	−0.0353851
$985$	55.6776	1.77404
$986$	7.79454	0.248229
$987$	0.0868019	0.00276293
$988$	2.08466	0.0663218
$989$	26.6999	0.849008
$990$	8.02683	0.255109
$991$	31.7469	1.00847	0.504237	−	0.863565i	$-0.331774\pi$
$991$	31.7469	1.00847	0.504237	+	0.863565i	$0.331774\pi$
$992$	6.71855	0.213314
$993$	8.50507	0.269900
$994$	−4.99133	−0.158315
$995$	−2.86104	−0.0907010
$996$	2.52241	0.0799255
$997$	42.2044	1.33663	0.668313	−	0.743880i	$-0.267017\pi$
$997$	42.2044	1.33663	0.668313	+	0.743880i	$0.267017\pi$
$998$	37.5125	1.18744
$999$	−6.59990	−0.208812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9282.2.a.bm.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9282.2.a.bm.1.1	✓	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.34228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.34228 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.34228 q^{10} -2.40161 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +3.34228 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.08466 q^{19} -3.34228 q^{20} -1.00000 q^{21} -2.40161 q^{22} +8.19615 q^{23} -1.00000 q^{24} +6.17082 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -7.79454 q^{29} +3.34228 q^{30} +6.71855 q^{31} +1.00000 q^{32} +2.40161 q^{33} -1.00000 q^{34} -3.34228 q^{35} +1.00000 q^{36} +6.59990 q^{37} -2.08466 q^{38} +1.00000 q^{39} -3.34228 q^{40} +1.10999 q^{41} -1.00000 q^{42} +3.25762 q^{43} -2.40161 q^{44} -3.34228 q^{45} +8.19615 q^{46} -0.0868019 q^{47} -1.00000 q^{48} +1.00000 q^{49} +6.17082 q^{50} +1.00000 q^{51} -1.00000 q^{52} +1.42693 q^{53} -1.00000 q^{54} +8.02683 q^{55} +1.00000 q^{56} +2.08466 q^{57} -7.79454 q^{58} -11.0015 q^{59} +3.34228 q^{60} +0.940672 q^{61} +6.71855 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.34228 q^{65} +2.40161 q^{66} -0.938527 q^{67} -1.00000 q^{68} -8.19615 q^{69} -3.34228 q^{70} -4.99133 q^{71} +1.00000 q^{72} +1.00150 q^{73} +6.59990 q^{74} -6.17082 q^{75} -2.08466 q^{76} -2.40161 q^{77} +1.00000 q^{78} -0.0868019 q^{79} -3.34228 q^{80} +1.00000 q^{81} +1.10999 q^{82} -2.52241 q^{83} -1.00000 q^{84} +3.34228 q^{85} +3.25762 q^{86} +7.79454 q^{87} -2.40161 q^{88} -5.10999 q^{89} -3.34228 q^{90} -1.00000 q^{91} +8.19615 q^{92} -6.71855 q^{93} -0.0868019 q^{94} +6.96750 q^{95} -1.00000 q^{96} +12.1383 q^{97} +1.00000 q^{98} -2.40161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} - 3 q^{11} - 4 q^{12} - 4 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 11 q^{19} - 2 q^{20} - 4 q^{21} - 3 q^{22} + 4 q^{23} - 4 q^{24} - 2 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 9 q^{29} + 2 q^{30} + 11 q^{31} + 4 q^{32} + 3 q^{33} - 4 q^{34} - 2 q^{35} + 4 q^{36} + q^{37} - 11 q^{38} + 4 q^{39} - 2 q^{40} + 5 q^{41} - 4 q^{42} - q^{43} - 3 q^{44} - 2 q^{45} + 4 q^{46} - 13 q^{47} - 4 q^{48} + 4 q^{49} - 2 q^{50} + 4 q^{51} - 4 q^{52} - 3 q^{53} - 4 q^{54} - 2 q^{55} + 4 q^{56} + 11 q^{57} - 9 q^{58} - 12 q^{59} + 2 q^{60} - q^{61} + 11 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} + 3 q^{66} + 11 q^{67} - 4 q^{68} - 4 q^{69} - 2 q^{70} - 11 q^{71} + 4 q^{72} - 28 q^{73} + q^{74} + 2 q^{75} - 11 q^{76} - 3 q^{77} + 4 q^{78} - 13 q^{79} - 2 q^{80} + 4 q^{81} + 5 q^{82} - 23 q^{83} - 4 q^{84} + 2 q^{85} - q^{86} + 9 q^{87} - 3 q^{88} - 21 q^{89} - 2 q^{90} - 4 q^{91} + 4 q^{92} - 11 q^{93} - 13 q^{94} - 11 q^{95} - 4 q^{96} - 17 q^{97} + 4 q^{98} - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 - 3 * q^11 - 4 * q^12 - 4 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 11 * q^19 - 2 * q^20 - 4 * q^21 - 3 * q^22 + 4 * q^23 - 4 * q^24 - 2 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 9 * q^29 + 2 * q^30 + 11 * q^31 + 4 * q^32 + 3 * q^33 - 4 * q^34 - 2 * q^35 + 4 * q^36 + q^37 - 11 * q^38 + 4 * q^39 - 2 * q^40 + 5 * q^41 - 4 * q^42 - q^43 - 3 * q^44 - 2 * q^45 + 4 * q^46 - 13 * q^47 - 4 * q^48 + 4 * q^49 - 2 * q^50 + 4 * q^51 - 4 * q^52 - 3 * q^53 - 4 * q^54 - 2 * q^55 + 4 * q^56 + 11 * q^57 - 9 * q^58 - 12 * q^59 + 2 * q^60 - q^61 + 11 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 + 3 * q^66 + 11 * q^67 - 4 * q^68 - 4 * q^69 - 2 * q^70 - 11 * q^71 + 4 * q^72 - 28 * q^73 + q^74 + 2 * q^75 - 11 * q^76 - 3 * q^77 + 4 * q^78 - 13 * q^79 - 2 * q^80 + 4 * q^81 + 5 * q^82 - 23 * q^83 - 4 * q^84 + 2 * q^85 - q^86 + 9 * q^87 - 3 * q^88 - 21 * q^89 - 2 * q^90 - 4 * q^91 + 4 * q^92 - 11 * q^93 - 13 * q^94 - 11 * q^95 - 4 * q^96 - 17 * q^97 + 4 * q^98 - 3 * q^99

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