LMFDB - Embedded newform 9251.2.a.t.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 $ x^18 - 24x^16 - x^15 + 233x^14 + 24x^13 - 1184x^12 - 207x^11 + 3413x^10 + 820x^9 - 5661x^8 - 1595x^7 + 5262x^6 + 1498x^5 - 2567x^4 - 605x^3 + 583x^2 + 80*x - 41
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-0.901649$ of defining polynomial
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.901649 q^{2} -2.08118 q^{3} -1.18703 q^{4} -2.45917 q^{5} -1.87649 q^{6} -1.81835 q^{7} -2.87358 q^{8} +1.33130 q^{9} +O(q^{10})$	\(q+0.901649 q^{2} -2.08118 q^{3} -1.18703 q^{4} -2.45917 q^{5} -1.87649 q^{6} -1.81835 q^{7} -2.87358 q^{8} +1.33130 q^{9} -2.21731 q^{10} -1.00000 q^{11} +2.47042 q^{12} +2.28379 q^{13} -1.63952 q^{14} +5.11797 q^{15} -0.216906 q^{16} -0.0210826 q^{17} +1.20036 q^{18} -4.58773 q^{19} +2.91911 q^{20} +3.78432 q^{21} -0.901649 q^{22} -5.17045 q^{23} +5.98043 q^{24} +1.04752 q^{25} +2.05918 q^{26} +3.47286 q^{27} +2.15844 q^{28} +4.61461 q^{30} -7.35917 q^{31} +5.55159 q^{32} +2.08118 q^{33} -0.0190091 q^{34} +4.47164 q^{35} -1.58029 q^{36} +5.73905 q^{37} -4.13652 q^{38} -4.75297 q^{39} +7.06663 q^{40} +1.66279 q^{41} +3.41213 q^{42} +2.65816 q^{43} +1.18703 q^{44} -3.27389 q^{45} -4.66194 q^{46} +1.44724 q^{47} +0.451421 q^{48} -3.69359 q^{49} +0.944495 q^{50} +0.0438766 q^{51} -2.71093 q^{52} +1.86004 q^{53} +3.13131 q^{54} +2.45917 q^{55} +5.22519 q^{56} +9.54787 q^{57} +11.0269 q^{59} -6.07518 q^{60} -0.536034 q^{61} -6.63539 q^{62} -2.42077 q^{63} +5.43940 q^{64} -5.61623 q^{65} +1.87649 q^{66} -0.897625 q^{67} +0.0250256 q^{68} +10.7606 q^{69} +4.03185 q^{70} +14.9674 q^{71} -3.82559 q^{72} +3.36928 q^{73} +5.17461 q^{74} -2.18007 q^{75} +5.44576 q^{76} +1.81835 q^{77} -4.28552 q^{78} +9.45303 q^{79} +0.533410 q^{80} -11.2215 q^{81} +1.49925 q^{82} +9.84878 q^{83} -4.49209 q^{84} +0.0518457 q^{85} +2.39673 q^{86} +2.87358 q^{88} -10.5055 q^{89} -2.95190 q^{90} -4.15274 q^{91} +6.13748 q^{92} +15.3157 q^{93} +1.30490 q^{94} +11.2820 q^{95} -11.5538 q^{96} -1.40290 q^{97} -3.33032 q^{98} -1.33130 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * 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 $

$2$	0.901649	0.637562	0.318781	−	0.947828i	$-0.396726\pi$
$2$	0.901649	0.637562	0.318781	+	0.947828i	$0.396726\pi$
$3$	−2.08118	−1.20157	−0.600784	−	0.799411i	$-0.705145\pi$
$3$	−2.08118	−1.20157	−0.600784	+	0.799411i	$0.705145\pi$
$4$	−1.18703	−0.593514
$5$	−2.45917	−1.09977	−0.549887	−	0.835239i	$-0.685329\pi$
$5$	−2.45917	−1.09977	−0.549887	+	0.835239i	$0.685329\pi$
$6$	−1.87649	−0.766075
$7$	−1.81835	−0.687273	−0.343636	−	0.939103i	$-0.611659\pi$
$7$	−1.81835	−0.687273	−0.343636	+	0.939103i	$0.611659\pi$
$8$	−2.87358	−1.01596
$9$	1.33130	0.443766
$10$	−2.21731	−0.701175
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.47042	0.713148
$13$	2.28379	0.633410	0.316705	−	0.948524i	$-0.397424\pi$
$13$	2.28379	0.633410	0.316705	+	0.948524i	$0.397424\pi$
$14$	−1.63952	−0.438179
$15$	5.11797	1.32145
$16$	−0.216906	−0.0542266
$17$	−0.0210826	−0.00511328	−0.00255664	−	0.999997i	$-0.500814\pi$
$17$	−0.0210826	−0.00511328	−0.00255664	+	0.999997i	$0.500814\pi$
$18$	1.20036	0.282928
$19$	−4.58773	−1.05250	−0.526248	−	0.850331i	$-0.676402\pi$
$19$	−4.58773	−1.05250	−0.526248	+	0.850331i	$0.676402\pi$
$20$	2.91911	0.652732
$21$	3.78432	0.825805
$22$	−0.901649	−0.192232
$23$	−5.17045	−1.07811	−0.539057	−	0.842269i	$-0.681219\pi$
$23$	−5.17045	−1.07811	−0.539057	+	0.842269i	$0.681219\pi$
$24$	5.98043	1.22075
$25$	1.04752	0.209504
$26$	2.05918	0.403838
$27$	3.47286	0.668353
$28$	2.15844	0.407906
$29$	0	0
$29$	0	0
$30$	4.61461	0.842509
$31$	−7.35917	−1.32175	−0.660873	−	0.750497i	$-0.729814\pi$
$31$	−7.35917	−1.32175	−0.660873	+	0.750497i	$0.729814\pi$
$32$	5.55159	0.981392
$33$	2.08118	0.362286
$34$	−0.0190091	−0.00326003
$35$	4.47164	0.755845
$36$	−1.58029	−0.263381
$37$	5.73905	0.943493	0.471747	−	0.881734i	$-0.343624\pi$
$37$	5.73905	0.943493	0.471747	+	0.881734i	$0.343624\pi$
$38$	−4.13652	−0.671032
$39$	−4.75297	−0.761085
$40$	7.06663	1.11733
$41$	1.66279	0.259683	0.129842	−	0.991535i	$-0.458553\pi$
$41$	1.66279	0.259683	0.129842	+	0.991535i	$0.458553\pi$
$42$	3.41213	0.526502
$43$	2.65816	0.405365	0.202683	−	0.979244i	$-0.435034\pi$
$43$	2.65816	0.405365	0.202683	+	0.979244i	$0.435034\pi$
$44$	1.18703	0.178951
$45$	−3.27389	−0.488042
$46$	−4.66194	−0.687365
$47$	1.44724	0.211101	0.105550	−	0.994414i	$-0.466340\pi$
$47$	1.44724	0.211101	0.105550	+	0.994414i	$0.466340\pi$
$48$	0.451421	0.0651570
$49$	−3.69359	−0.527656
$50$	0.944495	0.133572
$51$	0.0438766	0.00614395
$52$	−2.71093	−0.375938
$53$	1.86004	0.255496	0.127748	−	0.991807i	$-0.459225\pi$
$53$	1.86004	0.255496	0.127748	+	0.991807i	$0.459225\pi$
$54$	3.13131	0.426117
$55$	2.45917	0.331594
$56$	5.22519	0.698245
$57$	9.54787	1.26465
$58$	0	0
$59$	11.0269	1.43558	0.717792	−	0.696258i	$-0.245153\pi$
$59$	11.0269	1.43558	0.717792	+	0.696258i	$0.245153\pi$
$60$	−6.07518	−0.784302
$61$	−0.536034	−0.0686322	−0.0343161	−	0.999411i	$-0.510925\pi$
$61$	−0.536034	−0.0686322	−0.0343161	+	0.999411i	$0.510925\pi$
$62$	−6.63539	−0.842696
$63$	−2.42077	−0.304988
$64$	5.43940	0.679925
$65$	−5.61623	−0.696608
$66$	1.87649	0.230980
$67$	−0.897625	−0.109662	−0.0548312	−	0.998496i	$-0.517462\pi$
$67$	−0.897625	−0.109662	−0.0548312	+	0.998496i	$0.517462\pi$
$68$	0.0250256	0.00303480
$69$	10.7606	1.29543
$70$	4.03185	0.481898
$71$	14.9674	1.77630	0.888151	−	0.459552i	$-0.151990\pi$
$71$	14.9674	1.77630	0.888151	+	0.459552i	$0.151990\pi$
$72$	−3.82559	−0.450851
$73$	3.36928	0.394344	0.197172	−	0.980369i	$-0.436824\pi$
$73$	3.36928	0.394344	0.197172	+	0.980369i	$0.436824\pi$
$74$	5.17461	0.601536
$75$	−2.18007	−0.251733
$76$	5.44576	0.624672
$77$	1.81835	0.207221
$78$	−4.28552	−0.485239
$79$	9.45303	1.06355	0.531774	−	0.846886i	$-0.321525\pi$
$79$	9.45303	1.06355	0.531774	+	0.846886i	$0.321525\pi$
$80$	0.533410	0.0596370
$81$	−11.2215	−1.24684
$82$	1.49925	0.165564
$83$	9.84878	1.08104	0.540522	−	0.841330i	$-0.318227\pi$
$83$	9.84878	1.08104	0.540522	+	0.841330i	$0.318227\pi$
$84$	−4.49209	−0.490127
$85$	0.0518457	0.00562345
$86$	2.39673	0.258446
$87$	0	0
$88$	2.87358	0.306325
$89$	−10.5055	−1.11358	−0.556792	−	0.830652i	$-0.687968\pi$
$89$	−10.5055	−1.11358	−0.556792	+	0.830652i	$0.687968\pi$
$90$	−2.95190	−0.311157
$91$	−4.15274	−0.435325
$92$	6.13748	0.639876
$93$	15.3157	1.58817
$94$	1.30490	0.134590
$95$	11.2820	1.15751
$96$	−11.5538	−1.17921
$97$	−1.40290	−0.142443	−0.0712213	−	0.997461i	$-0.522690\pi$
$97$	−1.40290	−0.142443	−0.0712213	+	0.997461i	$0.522690\pi$
$98$	−3.33032	−0.336414
$99$	−1.33130	−0.133800
$100$	−1.24344	−0.124344
$101$	9.58223	0.953468	0.476734	−	0.879048i	$-0.341820\pi$
$101$	9.58223	0.953468	0.476734	+	0.879048i	$0.341820\pi$
$102$	0.0395613	0.00391715
$103$	13.0187	1.28278	0.641388	−	0.767217i	$-0.278359\pi$
$103$	13.0187	1.28278	0.641388	+	0.767217i	$0.278359\pi$
$104$	−6.56266	−0.643522
$105$	−9.30628	−0.908200
$106$	1.67710	0.162895
$107$	−18.0084	−1.74093	−0.870467	−	0.492227i	$-0.836183\pi$
$107$	−18.0084	−1.74093	−0.870467	+	0.492227i	$0.836183\pi$
$108$	−4.12239	−0.396677
$109$	14.8368	1.42111	0.710556	−	0.703641i	$-0.248444\pi$
$109$	14.8368	1.42111	0.710556	+	0.703641i	$0.248444\pi$
$110$	2.21731	0.211412
$111$	−11.9440	−1.13367
$112$	0.394413	0.0372685
$113$	−4.39935	−0.413856	−0.206928	−	0.978356i	$-0.566347\pi$
$113$	−4.39935	−0.413856	−0.206928	+	0.978356i	$0.566347\pi$
$114$	8.60883	0.806291
$115$	12.7150	1.18568
$116$	0	0
$117$	3.04041	0.281086
$118$	9.94242	0.915274
$119$	0.0383356	0.00351422
$120$	−14.7069	−1.34255
$121$	1.00000	0.0909091
$122$	−0.483315	−0.0437573
$123$	−3.46055	−0.312027
$124$	8.73555	0.784475
$125$	9.71982	0.869367
$126$	−2.18269	−0.194449
$127$	4.41925	0.392145	0.196073	−	0.980589i	$-0.437181\pi$
$127$	4.41925	0.392145	0.196073	+	0.980589i	$0.437181\pi$
$128$	−6.19875	−0.547897
$129$	−5.53210	−0.487074
$130$	−5.06387	−0.444131
$131$	7.40811	0.647249	0.323625	−	0.946186i	$-0.395098\pi$
$131$	7.40811	0.647249	0.323625	+	0.946186i	$0.395098\pi$
$132$	−2.47042	−0.215022
$133$	8.34211	0.723352
$134$	−0.809343	−0.0699166
$135$	−8.54037	−0.735038
$136$	0.0605825	0.00519491
$137$	−8.65639	−0.739565	−0.369783	−	0.929118i	$-0.620568\pi$
$137$	−8.65639	−0.739565	−0.369783	+	0.929118i	$0.620568\pi$
$138$	9.70232	0.825916
$139$	−3.38014	−0.286700	−0.143350	−	0.989672i	$-0.545787\pi$
$139$	−3.38014	−0.286700	−0.143350	+	0.989672i	$0.545787\pi$
$140$	−5.30796	−0.448605
$141$	−3.01195	−0.253652
$142$	13.4953	1.13250
$143$	−2.28379	−0.190980
$144$	−0.288767	−0.0240639
$145$	0	0
$146$	3.03791	0.251419
$147$	7.68702	0.634014
$148$	−6.81241	−0.559977
$149$	5.71624	0.468293	0.234146	−	0.972201i	$-0.424771\pi$
$149$	5.71624	0.468293	0.234146	+	0.972201i	$0.424771\pi$
$150$	−1.96566	−0.160496
$151$	16.0161	1.30337	0.651684	−	0.758490i	$-0.274063\pi$
$151$	16.0161	1.30337	0.651684	+	0.758490i	$0.274063\pi$
$152$	13.1832	1.06930
$153$	−0.0280672	−0.00226910
$154$	1.63952	0.132116
$155$	18.0975	1.45362
$156$	5.64192	0.451715
$157$	−8.85393	−0.706621	−0.353310	−	0.935506i	$-0.614944\pi$
$157$	−8.85393	−0.706621	−0.353310	+	0.935506i	$0.614944\pi$
$158$	8.52332	0.678079
$159$	−3.87107	−0.306996
$160$	−13.6523	−1.07931
$161$	9.40171	0.740959
$162$	−10.1179	−0.794937
$163$	21.2602	1.66523	0.832615	−	0.553853i	$-0.186843\pi$
$163$	21.2602	1.66523	0.832615	+	0.553853i	$0.186843\pi$
$164$	−1.97377	−0.154126
$165$	−5.11797	−0.398433
$166$	8.88015	0.689233
$167$	−8.29303	−0.641734	−0.320867	−	0.947124i	$-0.603974\pi$
$167$	−8.29303	−0.641734	−0.320867	+	0.947124i	$0.603974\pi$
$168$	−10.8745	−0.838989
$169$	−7.78430	−0.598792
$170$	0.0467466	0.00358530
$171$	−6.10763	−0.467062
$172$	−3.15531	−0.240590
$173$	−17.8346	−1.35594	−0.677970	−	0.735089i	$-0.737140\pi$
$173$	−17.8346	−1.35594	−0.677970	+	0.735089i	$0.737140\pi$
$174$	0	0
$175$	−1.90476	−0.143986
$176$	0.216906	0.0163499
$177$	−22.9490	−1.72495
$178$	−9.47231	−0.709979
$179$	−24.7372	−1.84895	−0.924473	−	0.381248i	$-0.875495\pi$
$179$	−24.7372	−1.84895	−0.924473	+	0.381248i	$0.875495\pi$
$180$	3.88620	0.289660
$181$	−18.3145	−1.36130	−0.680652	−	0.732607i	$-0.738303\pi$
$181$	−18.3145	−1.36130	−0.680652	+	0.732607i	$0.738303\pi$
$182$	−3.74431	−0.277547
$183$	1.11558	0.0824662
$184$	14.8577	1.09533
$185$	−14.1133	−1.03763
$186$	13.8094	1.01256
$187$	0.0210826	0.00154171
$188$	−1.71791	−0.125291
$189$	−6.31490	−0.459341
$190$	10.1724	0.737984
$191$	−9.96806	−0.721263	−0.360632	−	0.932708i	$-0.617439\pi$
$191$	−9.96806	−0.721263	−0.360632	+	0.932708i	$0.617439\pi$
$192$	−11.3204	−0.816976
$193$	−23.0460	−1.65888	−0.829442	−	0.558593i	$-0.811341\pi$
$193$	−23.0460	−1.65888	−0.829442	+	0.558593i	$0.811341\pi$
$194$	−1.26492	−0.0908161
$195$	11.6884	0.837022
$196$	4.38440	0.313171
$197$	−17.5352	−1.24933	−0.624665	−	0.780893i	$-0.714765\pi$
$197$	−17.5352	−1.24933	−0.624665	+	0.780893i	$0.714765\pi$
$198$	−1.20036	−0.0853061
$199$	−20.5761	−1.45860	−0.729300	−	0.684194i	$-0.760154\pi$
$199$	−20.5761	−1.45860	−0.729300	+	0.684194i	$0.760154\pi$
$200$	−3.01013	−0.212849
$201$	1.86812	0.131767
$202$	8.63982	0.607895
$203$	0	0
$204$	−0.0520828	−0.00364652
$205$	−4.08907	−0.285593
$206$	11.7383	0.817849
$207$	−6.88341	−0.478430
$208$	−0.495369	−0.0343477
$209$	4.58773	0.317340
$210$	−8.39100	−0.579034
$211$	21.2644	1.46390	0.731951	−	0.681357i	$-0.238610\pi$
$211$	21.2644	1.46390	0.731951	+	0.681357i	$0.238610\pi$
$212$	−2.20792	−0.151641
$213$	−31.1498	−2.13435
$214$	−16.2372	−1.10995
$215$	−6.53687	−0.445811
$216$	−9.97956	−0.679023
$217$	13.3816	0.908401
$218$	13.3776	0.906047
$219$	−7.01206	−0.473831
$220$	−2.91911	−0.196806
$221$	−0.0481482	−0.00323880
$222$	−10.7693	−0.722786
$223$	5.09370	0.341099	0.170550	−	0.985349i	$-0.445446\pi$
$223$	5.09370	0.341099	0.170550	+	0.985349i	$0.445446\pi$
$224$	−10.0948	−0.674484
$225$	1.39456	0.0929707
$226$	−3.96667	−0.263859
$227$	3.27212	0.217178	0.108589	−	0.994087i	$-0.465367\pi$
$227$	3.27212	0.217178	0.108589	+	0.994087i	$0.465367\pi$
$228$	−11.3336	−0.750586
$229$	13.9590	0.922437	0.461218	−	0.887287i	$-0.347412\pi$
$229$	13.9590	0.922437	0.461218	+	0.887287i	$0.347412\pi$
$230$	11.4645	0.755947
$231$	−3.78432	−0.248990
$232$	0	0
$233$	26.5760	1.74105	0.870525	−	0.492125i	$-0.163780\pi$
$233$	26.5760	1.74105	0.870525	+	0.492125i	$0.163780\pi$
$234$	2.74138	0.179210
$235$	−3.55900	−0.232163
$236$	−13.0893	−0.852039
$237$	−19.6734	−1.27793
$238$	0.0345653	0.00224053
$239$	24.4328	1.58043	0.790213	−	0.612832i	$-0.209970\pi$
$239$	24.4328	1.58043	0.790213	+	0.612832i	$0.209970\pi$
$240$	−1.11012	−0.0716580
$241$	−9.83352	−0.633432	−0.316716	−	0.948520i	$-0.602580\pi$
$241$	−9.83352	−0.633432	−0.316716	+	0.948520i	$0.602580\pi$
$242$	0.901649	0.0579602
$243$	12.9354	0.829807
$244$	0.636288	0.0407342
$245$	9.08317	0.580302
$246$	−3.12020	−0.198937
$247$	−10.4774	−0.666662
$248$	21.1472	1.34285
$249$	−20.4971	−1.29895
$250$	8.76387	0.554276
$251$	−0.221224	−0.0139635	−0.00698175	−	0.999976i	$-0.502222\pi$
$251$	−0.221224	−0.0139635	−0.00698175	+	0.999976i	$0.502222\pi$
$252$	2.87352	0.181015
$253$	5.17045	0.325064
$254$	3.98462	0.250017
$255$	−0.107900	−0.00675696
$256$	−16.4679	−1.02924
$257$	−1.89343	−0.118109	−0.0590546	−	0.998255i	$-0.518809\pi$
$257$	−1.89343	−0.118109	−0.0590546	+	0.998255i	$0.518809\pi$
$258$	−4.98801	−0.310540
$259$	−10.4356	−0.648438
$260$	6.66663	0.413447
$261$	0	0
$262$	6.67952	0.412662
$263$	7.74569	0.477620	0.238810	−	0.971066i	$-0.423243\pi$
$263$	7.74569	0.477620	0.238810	+	0.971066i	$0.423243\pi$
$264$	−5.98043	−0.368070
$265$	−4.57415	−0.280988
$266$	7.52166	0.461182
$267$	21.8639	1.33805
$268$	1.06551	0.0650862
$269$	3.32237	0.202569	0.101284	−	0.994858i	$-0.467705\pi$
$269$	3.32237	0.202569	0.101284	+	0.994858i	$0.467705\pi$
$270$	−7.70042	−0.468632
$271$	24.4749	1.48674	0.743372	−	0.668878i	$-0.233225\pi$
$271$	24.4749	1.48674	0.743372	+	0.668878i	$0.233225\pi$
$272$	0.00457295	0.000277276 0
$273$	8.64259	0.523073
$274$	−7.80503	−0.471519
$275$	−1.04752	−0.0631678
$276$	−12.7732	−0.768855
$277$	−27.6125	−1.65907	−0.829537	−	0.558451i	$-0.811396\pi$
$277$	−27.6125	−1.65907	−0.829537	+	0.558451i	$0.811396\pi$
$278$	−3.04770	−0.182789
$279$	−9.79725	−0.586546
$280$	−12.8496	−0.767912
$281$	−23.3602	−1.39355	−0.696776	−	0.717289i	$-0.745383\pi$
$281$	−23.3602	−1.39355	−0.696776	+	0.717289i	$0.745383\pi$
$282$	−2.71572	−0.161719
$283$	−12.9834	−0.771786	−0.385893	−	0.922544i	$-0.626107\pi$
$283$	−12.9834	−0.771786	−0.385893	+	0.922544i	$0.626107\pi$
$284$	−17.7667	−1.05426
$285$	−23.4798	−1.39083
$286$	−2.05918	−0.121762
$287$	−3.02353	−0.178473
$288$	7.39082	0.435508
$289$	−16.9996	−0.999974
$290$	0	0
$291$	2.91968	0.171155
$292$	−3.99943	−0.234049
$293$	14.7483	0.861605	0.430803	−	0.902446i	$-0.358231\pi$
$293$	14.7483	0.861605	0.430803	+	0.902446i	$0.358231\pi$
$294$	6.93099	0.404224
$295$	−27.1171	−1.57882
$296$	−16.4916	−0.958556
$297$	−3.47286	−0.201516
$298$	5.15404	0.298566
$299$	−11.8082	−0.682888
$300$	2.58781	0.149407
$301$	−4.83347	−0.278597
$302$	14.4409	0.830979
$303$	−19.9423	−1.14566
$304$	0.995107	0.0570733
$305$	1.31820	0.0754799
$306$	−0.0253068	−0.00144669
$307$	−16.8992	−0.964490	−0.482245	−	0.876036i	$-0.660179\pi$
$307$	−16.8992	−0.964490	−0.482245	+	0.876036i	$0.660179\pi$
$308$	−2.15844	−0.122988
$309$	−27.0943	−1.54134
$310$	16.3176	0.926775
$311$	−15.3774	−0.871973	−0.435986	−	0.899953i	$-0.643600\pi$
$311$	−15.3774	−0.871973	−0.435986	+	0.899953i	$0.643600\pi$
$312$	13.6581	0.773235
$313$	12.5352	0.708533	0.354266	−	0.935145i	$-0.384731\pi$
$313$	12.5352	0.708533	0.354266	+	0.935145i	$0.384731\pi$
$314$	−7.98314	−0.450515
$315$	5.95309	0.335418
$316$	−11.2210	−0.631231
$317$	−11.2346	−0.630999	−0.315500	−	0.948926i	$-0.602172\pi$
$317$	−11.2346	−0.630999	−0.315500	+	0.948926i	$0.602172\pi$
$318$	−3.49035	−0.195729
$319$	0	0
$320$	−13.3764	−0.747764
$321$	37.4786	2.09185
$322$	8.47705	0.472407
$323$	0.0967211	0.00538171
$324$	13.3203	0.740016
$325$	2.39232	0.132702
$326$	19.1693	1.06169
$327$	−30.8781	−1.70756
$328$	−4.77815	−0.263829
$329$	−2.63158	−0.145084
$330$	−4.61461	−0.254026
$331$	27.2194	1.49611	0.748056	−	0.663635i	$-0.230987\pi$
$331$	27.2194	1.49611	0.748056	+	0.663635i	$0.230987\pi$
$332$	−11.6908	−0.641615
$333$	7.64038	0.418690
$334$	−7.47740	−0.409145
$335$	2.20741	0.120604
$336$	−0.820842	−0.0447806
$337$	−11.6060	−0.632219	−0.316110	−	0.948723i	$-0.602377\pi$
$337$	−11.6060	−0.632219	−0.316110	+	0.948723i	$0.602377\pi$
$338$	−7.01871	−0.381767
$339$	9.15582	0.497276
$340$	−0.0615423	−0.00333760
$341$	7.35917	0.398522
$342$	−5.50694	−0.297781
$343$	19.4447	1.04992
$344$	−7.63844	−0.411837
$345$	−26.4622	−1.42468
$346$	−16.0806	−0.864497
$347$	−1.51396	−0.0812735	−0.0406368	−	0.999174i	$-0.512939\pi$
$347$	−1.51396	−0.0812735	−0.0406368	+	0.999174i	$0.512939\pi$
$348$	0	0
$349$	10.8607	0.581362	0.290681	−	0.956820i	$-0.406118\pi$
$349$	10.8607	0.581362	0.290681	+	0.956820i	$0.406118\pi$
$350$	−1.71743	−0.0918003
$351$	7.93130	0.423341
$352$	−5.55159	−0.295901
$353$	0.806577	0.0429298	0.0214649	−	0.999770i	$-0.493167\pi$
$353$	0.806577	0.0429298	0.0214649	+	0.999770i	$0.493167\pi$
$354$	−20.6919	−1.09976
$355$	−36.8074	−1.95353
$356$	12.4704	0.660928
$357$	−0.0797831	−0.00422257
$358$	−22.3043	−1.17882
$359$	36.5214	1.92753	0.963764	−	0.266757i	$-0.0859520\pi$
$359$	36.5214	1.92753	0.963764	+	0.266757i	$0.0859520\pi$
$360$	9.40779	0.495834
$361$	2.04723	0.107749
$362$	−16.5132	−0.867916
$363$	−2.08118	−0.109233
$364$	4.92942	0.258372
$365$	−8.28563	−0.433690
$366$	1.00586	0.0525774
$367$	24.5364	1.28079	0.640395	−	0.768046i	$-0.278771\pi$
$367$	24.5364	1.28079	0.640395	+	0.768046i	$0.278771\pi$
$368$	1.12150	0.0584625
$369$	2.21366	0.115239
$370$	−12.7252	−0.661554
$371$	−3.38221	−0.175596
$372$	−18.1802	−0.942601
$373$	−16.2173	−0.839703	−0.419851	−	0.907593i	$-0.637918\pi$
$373$	−16.2173	−0.839703	−0.419851	+	0.907593i	$0.637918\pi$
$374$	0.0190091	0.000982937 0
$375$	−20.2287	−1.04460
$376$	−4.15875	−0.214471
$377$	0	0
$378$	−5.69382	−0.292859
$379$	3.35487	0.172328	0.0861641	−	0.996281i	$-0.472539\pi$
$379$	3.35487	0.172328	0.0861641	+	0.996281i	$0.472539\pi$
$380$	−13.3921	−0.686998
$381$	−9.19725	−0.471189
$382$	−8.98769	−0.459850
$383$	15.6896	0.801699	0.400849	−	0.916144i	$-0.368715\pi$
$383$	15.6896	0.801699	0.400849	+	0.916144i	$0.368715\pi$
$384$	12.9007	0.658336
$385$	−4.47164	−0.227896
$386$	−20.7794	−1.05764
$387$	3.53880	0.179887
$388$	1.66528	0.0845417
$389$	18.0973	0.917571	0.458786	−	0.888547i	$-0.348285\pi$
$389$	18.0973	0.917571	0.458786	+	0.888547i	$0.348285\pi$
$390$	10.5388	0.533654
$391$	0.109007	0.00551270
$392$	10.6138	0.536080
$393$	−15.4176	−0.777714
$394$	−15.8106	−0.796526
$395$	−23.2466	−1.16966
$396$	1.58029	0.0794125
$397$	−8.33186	−0.418164	−0.209082	−	0.977898i	$-0.567048\pi$
$397$	−8.33186	−0.418164	−0.209082	+	0.977898i	$0.567048\pi$
$398$	−18.5524	−0.929948
$399$	−17.3614	−0.869157
$400$	−0.227214	−0.0113607
$401$	−2.92717	−0.146176	−0.0730878	−	0.997326i	$-0.523285\pi$
$401$	−2.92717	−0.146176	−0.0730878	+	0.997326i	$0.523285\pi$
$402$	1.68439	0.0840096
$403$	−16.8068	−0.837207
$404$	−11.3744	−0.565897
$405$	27.5957	1.37124
$406$	0	0
$407$	−5.73905	−0.284474
$408$	−0.126083	−0.00624204
$409$	−16.7538	−0.828421	−0.414210	−	0.910181i	$-0.635942\pi$
$409$	−16.7538	−0.828421	−0.414210	+	0.910181i	$0.635942\pi$
$410$	−3.68691	−0.182084
$411$	18.0155	0.888638
$412$	−15.4536	−0.761345
$413$	−20.0508	−0.986638
$414$	−6.20643	−0.305029
$415$	−24.2198	−1.18890
$416$	12.6787	0.621623
$417$	7.03466	0.344489
$418$	4.13652	0.202324
$419$	−26.1432	−1.27718	−0.638591	−	0.769547i	$-0.720482\pi$
$419$	−26.1432	−1.27718	−0.638591	+	0.769547i	$0.720482\pi$
$420$	11.0468	0.539029
$421$	34.5703	1.68485	0.842426	−	0.538812i	$-0.181127\pi$
$421$	34.5703	1.68485	0.842426	+	0.538812i	$0.181127\pi$
$422$	19.1730	0.933329
$423$	1.92670	0.0936794
$424$	−5.34498	−0.259575
$425$	−0.0220844	−0.00107125
$426$	−28.0862	−1.36078
$427$	0.974700	0.0471690
$428$	21.3764	1.03327
$429$	4.75297	0.229476
$430$	−5.89396	−0.284232
$431$	−19.2983	−0.929567	−0.464783	−	0.885424i	$-0.653868\pi$
$431$	−19.2983	−0.929567	−0.464783	+	0.885424i	$0.653868\pi$
$432$	−0.753287	−0.0362425
$433$	−12.7137	−0.610980	−0.305490	−	0.952195i	$-0.598820\pi$
$433$	−12.7137	−0.610980	−0.305490	+	0.952195i	$0.598820\pi$
$434$	12.0655	0.579162
$435$	0	0
$436$	−17.6118	−0.843450
$437$	23.7206	1.13471
$438$	−6.32242	−0.302097
$439$	−37.7513	−1.80177	−0.900886	−	0.434057i	$-0.857082\pi$
$439$	−37.7513	−1.80177	−0.900886	+	0.434057i	$0.857082\pi$
$440$	−7.06663	−0.336888
$441$	−4.91727	−0.234156
$442$	−0.0434128	−0.00206494
$443$	−6.26361	−0.297593	−0.148796	−	0.988868i	$-0.547540\pi$
$443$	−6.26361	−0.297593	−0.148796	+	0.988868i	$0.547540\pi$
$444$	14.1778	0.672850
$445$	25.8349	1.22469
$446$	4.59273	0.217472
$447$	−11.8965	−0.562686
$448$	−9.89075	−0.467294
$449$	18.1463	0.856377	0.428188	−	0.903690i	$-0.359152\pi$
$449$	18.1463	0.856377	0.428188	+	0.903690i	$0.359152\pi$
$450$	1.25740	0.0592746
$451$	−1.66279	−0.0782975
$452$	5.22215	0.245629
$453$	−33.3322	−1.56609
$454$	2.95031	0.138465
$455$	10.2123	0.478760
$456$	−27.4366	−1.28484
$457$	−22.1440	−1.03585	−0.517926	−	0.855426i	$-0.673296\pi$
$457$	−22.1440	−1.03585	−0.517926	+	0.855426i	$0.673296\pi$
$458$	12.5861	0.588111
$459$	−0.0732170	−0.00341747
$460$	−15.0931	−0.703719
$461$	25.7062	1.19726	0.598628	−	0.801027i	$-0.295713\pi$
$461$	25.7062	1.19726	0.598628	+	0.801027i	$0.295713\pi$
$462$	−3.41213	−0.158746
$463$	−23.0322	−1.07040	−0.535199	−	0.844726i	$-0.679763\pi$
$463$	−23.0322	−1.07040	−0.535199	+	0.844726i	$0.679763\pi$
$464$	0	0
$465$	−37.6640	−1.74663
$466$	23.9622	1.11003
$467$	−4.28068	−0.198086	−0.0990431	−	0.995083i	$-0.531578\pi$
$467$	−4.28068	−0.198086	−0.0990431	+	0.995083i	$0.531578\pi$
$468$	−3.60905	−0.166828
$469$	1.63220	0.0753680
$470$	−3.20897	−0.148019
$471$	18.4266	0.849053
$472$	−31.6868	−1.45850
$473$	−2.65816	−0.122222
$474$	−17.7385	−0.814758
$475$	−4.80573	−0.220502
$476$	−0.0455054	−0.00208574
$477$	2.47627	0.113380
$478$	22.0298	1.00762
$479$	38.7121	1.76880	0.884401	−	0.466728i	$-0.154567\pi$
$479$	38.7121	1.76880	0.884401	+	0.466728i	$0.154567\pi$
$480$	28.4129	1.29686
$481$	13.1068	0.597618
$482$	−8.86638	−0.403853
$483$	−19.5666	−0.890312
$484$	−1.18703	−0.0539558
$485$	3.44996	0.156655
$486$	11.6632	0.529054
$487$	−6.28833	−0.284952	−0.142476	−	0.989798i	$-0.545506\pi$
$487$	−6.28833	−0.284952	−0.142476	+	0.989798i	$0.545506\pi$
$488$	1.54034	0.0697279
$489$	−44.2463	−2.00089
$490$	8.18983	0.369979
$491$	−10.6457	−0.480432	−0.240216	−	0.970719i	$-0.577218\pi$
$491$	−10.6457	−0.480432	−0.240216	+	0.970719i	$0.577218\pi$
$492$	4.10777	0.185193
$493$	0	0
$494$	−9.44695	−0.425038
$495$	3.27389	0.147150
$496$	1.59625	0.0716738
$497$	−27.2160	−1.22080
$498$	−18.4812	−0.828161
$499$	19.5840	0.876701	0.438350	−	0.898804i	$-0.355563\pi$
$499$	19.5840	0.876701	0.438350	+	0.898804i	$0.355563\pi$
$500$	−11.5377	−0.515982
$501$	17.2593	0.771087
$502$	−0.199466	−0.00890261
$503$	11.9087	0.530982	0.265491	−	0.964113i	$-0.414466\pi$
$503$	11.9087	0.530982	0.265491	+	0.964113i	$0.414466\pi$
$504$	6.95628	0.309857
$505$	−23.5643	−1.04860
$506$	4.66194	0.207248
$507$	16.2005	0.719490
$508$	−5.24578	−0.232744
$509$	−30.7745	−1.36406	−0.682028	−	0.731326i	$-0.738902\pi$
$509$	−30.7745	−1.36406	−0.682028	+	0.731326i	$0.738902\pi$
$510$	−0.0972880	−0.00430798
$511$	−6.12654	−0.271022
$512$	−2.45077	−0.108310
$513$	−15.9326	−0.703439
$514$	−1.70721	−0.0753020
$515$	−32.0153	−1.41076
$516$	6.56676	0.289085
$517$	−1.44724	−0.0636493
$518$	−9.40926	−0.413419
$519$	37.1170	1.62926
$520$	16.1387	0.707729
$521$	−18.7553	−0.821684	−0.410842	−	0.911706i	$-0.634765\pi$
$521$	−18.7553	−0.821684	−0.410842	+	0.911706i	$0.634765\pi$
$522$	0	0
$523$	−11.6470	−0.509287	−0.254644	−	0.967035i	$-0.581958\pi$
$523$	−11.6470	−0.509287	−0.254644	+	0.967035i	$0.581958\pi$
$524$	−8.79364	−0.384152
$525$	3.96414	0.173009
$526$	6.98390	0.304512
$527$	0.155150	0.00675846
$528$	−0.451421	−0.0196456
$529$	3.73360	0.162330
$530$	−4.12428	−0.179147
$531$	14.6801	0.637063
$532$	−9.90232	−0.429320
$533$	3.79746	0.164486
$534$	19.7135	0.853089
$535$	44.2856	1.91463
$536$	2.57940	0.111413
$537$	51.4825	2.22163
$538$	2.99562	0.129150
$539$	3.69359	0.159094
$540$	10.1377	0.436255
$541$	−11.1882	−0.481017	−0.240509	−	0.970647i	$-0.577314\pi$
$541$	−11.1882	−0.481017	−0.240509	+	0.970647i	$0.577314\pi$
$542$	22.0678	0.947892
$543$	38.1157	1.63570
$544$	−0.117042	−0.00501813
$545$	−36.4863	−1.56290
$546$	7.79258	0.333492
$547$	27.4682	1.17446	0.587228	−	0.809422i	$-0.300219\pi$
$547$	27.4682	1.17446	0.587228	+	0.809422i	$0.300219\pi$
$548$	10.2754	0.438943
$549$	−0.713621	−0.0304566
$550$	−0.944495	−0.0402734
$551$	0	0
$552$	−30.9216	−1.31611
$553$	−17.1889	−0.730948
$554$	−24.8968	−1.05776
$555$	29.3723	1.24678
$556$	4.01232	0.170160
$557$	−3.19180	−0.135241	−0.0676205	−	0.997711i	$-0.521541\pi$
$557$	−3.19180	−0.135241	−0.0676205	+	0.997711i	$0.521541\pi$
$558$	−8.83369	−0.373960
$559$	6.07068	0.256762
$560$	−0.969928	−0.0409869
$561$	−0.0438766	−0.00185247
$562$	−21.0627	−0.888476
$563$	−27.7349	−1.16888	−0.584442	−	0.811435i	$-0.698687\pi$
$563$	−27.7349	−1.16888	−0.584442	+	0.811435i	$0.698687\pi$
$564$	3.57527	0.150546
$565$	10.8187	0.455148
$566$	−11.7065	−0.492062
$567$	20.4047	0.856918
$568$	−43.0100	−1.80466
$569$	−35.8078	−1.50114	−0.750571	−	0.660789i	$-0.770222\pi$
$569$	−35.8078	−1.50114	−0.750571	+	0.660789i	$0.770222\pi$
$570$	−21.1706	−0.886738
$571$	41.1878	1.72365	0.861827	−	0.507202i	$-0.169320\pi$
$571$	41.1878	1.72365	0.861827	+	0.507202i	$0.169320\pi$
$572$	2.71093	0.113349
$573$	20.7453	0.866647
$574$	−2.72617	−0.113788
$575$	−5.41615	−0.225869
$576$	7.24146	0.301728
$577$	−2.52752	−0.105222	−0.0526111	−	0.998615i	$-0.516754\pi$
$577$	−2.52752	−0.105222	−0.0526111	+	0.998615i	$0.516754\pi$
$578$	−15.3276	−0.637546
$579$	47.9627	1.99326
$580$	0	0
$581$	−17.9086	−0.742972
$582$	2.63253	0.109122
$583$	−1.86004	−0.0770350
$584$	−9.68189	−0.400640
$585$	−7.47688	−0.309131
$586$	13.2978	0.549327
$587$	8.46814	0.349518	0.174759	−	0.984611i	$-0.444085\pi$
$587$	8.46814	0.349518	0.174759	+	0.984611i	$0.444085\pi$
$588$	−9.12471	−0.376297
$589$	33.7619	1.39113
$590$	−24.4501	−1.00659
$591$	36.4938	1.50116
$592$	−1.24484	−0.0511624
$593$	45.4203	1.86519	0.932595	−	0.360925i	$-0.117539\pi$
$593$	45.4203	1.86519	0.932595	+	0.360925i	$0.117539\pi$
$594$	−3.13131	−0.128479
$595$	−0.0942737	−0.00386485
$596$	−6.78534	−0.277938
$597$	42.8225	1.75261
$598$	−10.6469	−0.435384
$599$	38.7520	1.58336	0.791682	−	0.610934i	$-0.209206\pi$
$599$	38.7520	1.58336	0.791682	+	0.610934i	$0.209206\pi$
$600$	6.26462	0.255752
$601$	20.6885	0.843902	0.421951	−	0.906619i	$-0.361345\pi$
$601$	20.6885	0.843902	0.421951	+	0.906619i	$0.361345\pi$
$602$	−4.35810	−0.177623
$603$	−1.19501	−0.0486644
$604$	−19.0115	−0.773568
$605$	−2.45917	−0.0999795
$606$	−17.9810	−0.730428
$607$	−18.5557	−0.753153	−0.376576	−	0.926386i	$-0.622899\pi$
$607$	−18.5557	−0.753153	−0.376576	+	0.926386i	$0.622899\pi$
$608$	−25.4692	−1.03291
$609$	0	0
$610$	1.18855	0.0481231
$611$	3.30518	0.133713
$612$	0.0333166	0.00134674
$613$	14.8547	0.599975	0.299988	−	0.953943i	$-0.403017\pi$
$613$	14.8547	0.599975	0.299988	+	0.953943i	$0.403017\pi$
$614$	−15.2372	−0.614923
$615$	8.51009	0.343160
$616$	−5.22519	−0.210529
$617$	−5.74369	−0.231232	−0.115616	−	0.993294i	$-0.536884\pi$
$617$	−5.74369	−0.231232	−0.115616	+	0.993294i	$0.536884\pi$
$618$	−24.4296	−0.982702
$619$	−15.6813	−0.630283	−0.315142	−	0.949045i	$-0.602052\pi$
$619$	−15.6813	−0.630283	−0.315142	+	0.949045i	$0.602052\pi$
$620$	−21.4822	−0.862746
$621$	−17.9563	−0.720561
$622$	−13.8650	−0.555937
$623$	19.1028	0.765336
$624$	1.03095	0.0412711
$625$	−29.1403	−1.16561
$626$	11.3024	0.451734
$627$	−9.54787	−0.381305
$628$	10.5099	0.419389
$629$	−0.120994	−0.00482434
$630$	5.36760	0.213850
$631$	−47.3363	−1.88443	−0.942214	−	0.335011i	$-0.891260\pi$
$631$	−47.3363	−1.88443	−0.942214	+	0.335011i	$0.891260\pi$
$632$	−27.1640	−1.08053
$633$	−44.2550	−1.75898
$634$	−10.1297	−0.402301
$635$	−10.8677	−0.431272
$636$	4.59507	0.182206
$637$	−8.43539	−0.334222
$638$	0	0
$639$	19.9261	0.788262
$640$	15.2438	0.602563
$641$	23.5820	0.931433	0.465717	−	0.884934i	$-0.345797\pi$
$641$	23.5820	0.931433	0.465717	+	0.884934i	$0.345797\pi$
$642$	33.7925	1.33368
$643$	28.5033	1.12406	0.562030	−	0.827117i	$-0.310020\pi$
$643$	28.5033	1.12406	0.562030	+	0.827117i	$0.310020\pi$
$644$	−11.1601	−0.439770
$645$	13.6044	0.535672
$646$	0.0872085	0.00343117
$647$	20.3928	0.801722	0.400861	−	0.916139i	$-0.368711\pi$
$647$	20.3928	0.801722	0.400861	+	0.916139i	$0.368711\pi$
$648$	32.2460	1.26674
$649$	−11.0269	−0.432845
$650$	2.15703	0.0846057
$651$	−27.8494	−1.09151
$652$	−25.2365	−0.988337
$653$	34.3247	1.34323	0.671614	−	0.740901i	$-0.265601\pi$
$653$	34.3247	1.34323	0.671614	+	0.740901i	$0.265601\pi$
$654$	−27.8412	−1.08868
$655$	−18.2178	−0.711828
$656$	−0.360669	−0.0140818
$657$	4.48551	0.174996
$658$	−2.37277	−0.0925001
$659$	−10.1744	−0.396338	−0.198169	−	0.980168i	$-0.563500\pi$
$659$	−10.1744	−0.396338	−0.198169	+	0.980168i	$0.563500\pi$
$660$	6.07518	0.236476
$661$	−13.6903	−0.532493	−0.266246	−	0.963905i	$-0.585783\pi$
$661$	−13.6903	−0.532493	−0.266246	+	0.963905i	$0.585783\pi$
$662$	24.5423	0.953865
$663$	0.100205	0.00389164
$664$	−28.3013	−1.09830
$665$	−20.5147	−0.795525
$666$	6.88894	0.266941
$667$	0	0
$668$	9.84406	0.380878
$669$	−10.6009	−0.409854
$670$	1.99031	0.0768925
$671$	0.536034	0.0206934
$672$	21.0090	0.810439
$673$	26.8617	1.03544	0.517720	−	0.855550i	$-0.326781\pi$
$673$	26.8617	1.03544	0.517720	+	0.855550i	$0.326781\pi$
$674$	−10.4645	−0.403079
$675$	3.63789	0.140023
$676$	9.24018	0.355392
$677$	−11.8992	−0.457324	−0.228662	−	0.973506i	$-0.573435\pi$
$677$	−11.8992	−0.457324	−0.228662	+	0.973506i	$0.573435\pi$
$678$	8.25534	0.317044
$679$	2.55096	0.0978970
$680$	−0.148983	−0.00571323
$681$	−6.80986	−0.260955
$682$	6.63539	0.254082
$683$	41.0216	1.56965	0.784824	−	0.619719i	$-0.212754\pi$
$683$	41.0216	1.56965	0.784824	+	0.619719i	$0.212754\pi$
$684$	7.24993	0.277208
$685$	21.2875	0.813355
$686$	17.5323	0.669387
$687$	−29.0512	−1.10837
$688$	−0.576572	−0.0219816
$689$	4.24794	0.161834
$690$	−23.8596	−0.908321
$691$	45.0342	1.71318	0.856590	−	0.515998i	$-0.172579\pi$
$691$	45.0342	1.71318	0.856590	+	0.515998i	$0.172579\pi$
$692$	21.1702	0.804770
$693$	2.42077	0.0919574
$694$	−1.36506	−0.0518169
$695$	8.31233	0.315305
$696$	0	0
$697$	−0.0350558	−0.00132783
$698$	9.79257	0.370654
$699$	−55.3093	−2.09199
$700$	2.26100	0.0854579
$701$	11.0274	0.416500	0.208250	−	0.978076i	$-0.433223\pi$
$701$	11.0274	0.416500	0.208250	+	0.978076i	$0.433223\pi$
$702$	7.15125	0.269907
$703$	−26.3292	−0.993024
$704$	−5.43940	−0.205005
$705$	7.40690	0.278960
$706$	0.727250	0.0273704
$707$	−17.4239	−0.655293
$708$	27.2411	1.02378
$709$	13.3373	0.500893	0.250446	−	0.968131i	$-0.419423\pi$
$709$	13.3373	0.500893	0.250446	+	0.968131i	$0.419423\pi$
$710$	−33.1873	−1.24550
$711$	12.5848	0.471967
$712$	30.1885	1.13136
$713$	38.0503	1.42499
$714$	−0.0719364	−0.00269215
$715$	5.61623	0.210035
$716$	29.3638	1.09738
$717$	−50.8490	−1.89899
$718$	32.9295	1.22892
$719$	−7.08710	−0.264304	−0.132152	−	0.991229i	$-0.542189\pi$
$719$	−7.08710	−0.264304	−0.132152	+	0.991229i	$0.542189\pi$
$720$	0.710127	0.0264649
$721$	−23.6727	−0.881617
$722$	1.84589	0.0686968
$723$	20.4653	0.761112
$724$	21.7398	0.807954
$725$	0	0
$726$	−1.87649	−0.0696431
$727$	50.4912	1.87261	0.936307	−	0.351183i	$-0.114220\pi$
$727$	50.4912	1.87261	0.936307	+	0.351183i	$0.114220\pi$
$728$	11.9332	0.442275
$729$	6.74373	0.249768
$730$	−7.47073	−0.276504
$731$	−0.0560409	−0.00207275
$732$	−1.32423	−0.0489449
$733$	14.2665	0.526946	0.263473	−	0.964667i	$-0.415132\pi$
$733$	14.2665	0.526946	0.263473	+	0.964667i	$0.415132\pi$
$734$	22.1232	0.816584
$735$	−18.9037	−0.697273
$736$	−28.7042	−1.05805
$737$	0.897625	0.0330645
$738$	1.99595	0.0734718
$739$	0.512718	0.0188606	0.00943032	−	0.999956i	$-0.496998\pi$
$739$	0.512718	0.0188606	0.00943032	+	0.999956i	$0.496998\pi$
$740$	16.7529	0.615848
$741$	21.8053	0.801039
$742$	−3.04957	−0.111953
$743$	1.84211	0.0675804	0.0337902	−	0.999429i	$-0.489242\pi$
$743$	1.84211	0.0675804	0.0337902	+	0.999429i	$0.489242\pi$
$744$	−44.0110	−1.61352
$745$	−14.0572	−0.515016
$746$	−14.6224	−0.535363
$747$	13.1117	0.479731
$748$	−0.0250256	−0.000915028 0
$749$	32.7456	1.19650
$750$	−18.2392	−0.666000
$751$	33.5488	1.22421	0.612107	−	0.790775i	$-0.290322\pi$
$751$	33.5488	1.22421	0.612107	+	0.790775i	$0.290322\pi$
$752$	−0.313915	−0.0114473
$753$	0.460405	0.0167781
$754$	0	0
$755$	−39.3862	−1.43341
$756$	7.49596	0.272625
$757$	14.6323	0.531818	0.265909	−	0.963998i	$-0.414328\pi$
$757$	14.6323	0.531818	0.265909	+	0.963998i	$0.414328\pi$
$758$	3.02492	0.109870
$759$	−10.7606	−0.390586
$760$	−32.4198	−1.17599
$761$	42.0772	1.52530	0.762648	−	0.646813i	$-0.223899\pi$
$761$	42.0772	1.52530	0.762648	+	0.646813i	$0.223899\pi$
$762$	−8.29270	−0.300413
$763$	−26.9786	−0.976691
$764$	11.8324	0.428080
$765$	0.0690220	0.00249550
$766$	14.1465	0.511133
$767$	25.1832	0.909312
$768$	34.2726	1.23671
$769$	−25.0153	−0.902074	−0.451037	−	0.892505i	$-0.648946\pi$
$769$	−25.0153	−0.902074	−0.451037	+	0.892505i	$0.648946\pi$
$770$	−4.03185	−0.145298
$771$	3.94057	0.141916
$772$	27.3562	0.984571
$773$	6.14393	0.220982	0.110491	−	0.993877i	$-0.464758\pi$
$773$	6.14393	0.220982	0.110491	+	0.993877i	$0.464758\pi$
$774$	3.19076	0.114689
$775$	−7.70888	−0.276911
$776$	4.03134	0.144717
$777$	21.7184	0.779142
$778$	16.3174	0.585009
$779$	−7.62841	−0.273316
$780$	−13.8744	−0.496784
$781$	−14.9674	−0.535575
$782$	0.0982857	0.00351469
$783$	0	0
$784$	0.801164	0.0286130
$785$	21.7733	0.777123
$786$	−13.9013	−0.495841
$787$	3.24461	0.115658	0.0578290	−	0.998327i	$-0.481582\pi$
$787$	3.24461	0.115658	0.0578290	+	0.998327i	$0.481582\pi$
$788$	20.8148	0.741495
$789$	−16.1202	−0.573893
$790$	−20.9603	−0.745733
$791$	7.99957	0.284432
$792$	3.82559	0.135937
$793$	−1.22419	−0.0434723
$794$	−7.51242	−0.266606
$795$	9.51962	0.337626
$796$	24.4244	0.865700
$797$	−7.31467	−0.259099	−0.129549	−	0.991573i	$-0.541353\pi$
$797$	−7.31467	−0.259099	−0.129549	+	0.991573i	$0.541353\pi$
$798$	−15.6539	−0.554142
$799$	−0.0305115	−0.00107942
$800$	5.81540	0.205605
$801$	−13.9860	−0.494171
$802$	−2.63928	−0.0931961
$803$	−3.36928	−0.118899
$804$	−2.21751	−0.0782055
$805$	−23.1204	−0.814887
$806$	−15.1539	−0.533772
$807$	−6.91445	−0.243400
$808$	−27.5353	−0.968690
$809$	−13.6265	−0.479082	−0.239541	−	0.970886i	$-0.576997\pi$
$809$	−13.6265	−0.479082	−0.239541	+	0.970886i	$0.576997\pi$
$810$	24.8816	0.874251
$811$	8.22055	0.288663	0.144331	−	0.989529i	$-0.453897\pi$
$811$	8.22055	0.288663	0.144331	+	0.989529i	$0.453897\pi$
$812$	0	0
$813$	−50.9366	−1.78642
$814$	−5.17461	−0.181370
$815$	−52.2825	−1.83138
$816$	−0.00951711	−0.000333166 0
$817$	−12.1949	−0.426646
$818$	−15.1060	−0.528170
$819$	−5.52853	−0.193183
$820$	4.85385	0.169504
$821$	−32.0834	−1.11972	−0.559860	−	0.828587i	$-0.689145\pi$
$821$	−32.0834	−1.11972	−0.559860	+	0.828587i	$0.689145\pi$
$822$	16.2436	0.566562
$823$	−45.3128	−1.57950	−0.789752	−	0.613426i	$-0.789791\pi$
$823$	−45.3128	−1.57950	−0.789752	+	0.613426i	$0.789791\pi$
$824$	−37.4104	−1.30325
$825$	2.18007	0.0759004
$826$	−18.0788	−0.629043
$827$	18.3512	0.638135	0.319068	−	0.947732i	$-0.396630\pi$
$827$	18.3512	0.638135	0.319068	+	0.947732i	$0.396630\pi$
$828$	8.17081	0.283955
$829$	−39.2446	−1.36302	−0.681511	−	0.731808i	$-0.738677\pi$
$829$	−39.2446	−1.36302	−0.681511	+	0.731808i	$0.738677\pi$
$830$	−21.8378	−0.758001
$831$	57.4665	1.99349
$832$	12.4225	0.430671
$833$	0.0778704	0.00269805
$834$	6.34280	0.219633
$835$	20.3940	0.705762
$836$	−5.44576	−0.188346
$837$	−25.5574	−0.883393
$838$	−23.5720	−0.814283
$839$	49.0834	1.69455	0.847273	−	0.531158i	$-0.178243\pi$
$839$	49.0834	1.69455	0.847273	+	0.531158i	$0.178243\pi$
$840$	26.7423	0.922699
$841$	0	0
$842$	31.1703	1.07420
$843$	48.6167	1.67445
$844$	−25.2415	−0.868847
$845$	19.1429	0.658536
$846$	1.73721	0.0597265
$847$	−1.81835	−0.0624794
$848$	−0.403455	−0.0138547
$849$	27.0209	0.927353
$850$	−0.0199124	−0.000682990 0
$851$	−29.6735	−1.01719
$852$	36.9757	1.26677
$853$	−49.4071	−1.69167	−0.845833	−	0.533448i	$-0.820896\pi$
$853$	−49.4071	−1.69167	−0.845833	+	0.533448i	$0.820896\pi$
$854$	0.878837	0.0300732
$855$	15.0197	0.513663
$856$	51.7485	1.76873
$857$	29.4410	1.00569	0.502843	−	0.864378i	$-0.332287\pi$
$857$	29.4410	1.00569	0.502843	+	0.864378i	$0.332287\pi$
$858$	4.28552	0.146305
$859$	13.3959	0.457062	0.228531	−	0.973537i	$-0.426608\pi$
$859$	13.3959	0.457062	0.228531	+	0.973537i	$0.426608\pi$
$860$	7.75945	0.264595
$861$	6.29251	0.214448
$862$	−17.4003	−0.592657
$863$	−52.3124	−1.78074	−0.890368	−	0.455241i	$-0.849553\pi$
$863$	−52.3124	−1.78074	−0.890368	+	0.455241i	$0.849553\pi$
$864$	19.2799	0.655916
$865$	43.8584	1.49123
$866$	−11.4633	−0.389538
$867$	35.3791	1.20154
$868$	−15.8843	−0.539149
$869$	−9.45303	−0.320672
$870$	0	0
$871$	−2.04999	−0.0694612
$872$	−42.6349	−1.44380
$873$	−1.86767	−0.0632112
$874$	21.3877	0.723449
$875$	−17.6741	−0.597493
$876$	8.32352	0.281226
$877$	12.4119	0.419119	0.209559	−	0.977796i	$-0.432797\pi$
$877$	12.4119	0.419119	0.209559	+	0.977796i	$0.432797\pi$
$878$	−34.0384	−1.14874
$879$	−30.6938	−1.03528
$880$	−0.533410	−0.0179812
$881$	−5.27250	−0.177635	−0.0888176	−	0.996048i	$-0.528309\pi$
$881$	−5.27250	−0.177635	−0.0888176	+	0.996048i	$0.528309\pi$
$882$	−4.43365	−0.149289
$883$	−27.2906	−0.918403	−0.459201	−	0.888332i	$-0.651864\pi$
$883$	−27.2906	−0.918403	−0.459201	+	0.888332i	$0.651864\pi$
$884$	0.0571533	0.00192227
$885$	56.4355	1.89706
$886$	−5.64758	−0.189734
$887$	−58.2757	−1.95671	−0.978354	−	0.206939i	$-0.933650\pi$
$887$	−58.2757	−1.95671	−0.978354	+	0.206939i	$0.933650\pi$
$888$	34.3220	1.15177
$889$	−8.03577	−0.269511
$890$	23.2940	0.780817
$891$	11.2215	0.375936
$892$	−6.04636	−0.202447
$893$	−6.63952	−0.222183
$894$	−10.7265	−0.358747
$895$	60.8330	2.03342
$896$	11.2715	0.376555
$897$	24.5750	0.820536
$898$	16.3616	0.545993
$899$	0	0
$900$	−1.65538	−0.0551794
$901$	−0.0392144	−0.00130642
$902$	−1.49925	−0.0499196
$903$	10.0593	0.334753
$904$	12.6419	0.420463
$905$	45.0384	1.49713
$906$	−30.0540	−0.998477
$907$	−58.8165	−1.95297	−0.976485	−	0.215584i	$-0.930835\pi$
$907$	−58.8165	−1.95297	−0.976485	+	0.215584i	$0.930835\pi$
$908$	−3.88410	−0.128898
$909$	12.7568	0.423117
$910$	9.20791	0.305239
$911$	13.7340	0.455029	0.227514	−	0.973775i	$-0.426940\pi$
$911$	13.7340	0.455029	0.227514	+	0.973775i	$0.426940\pi$
$912$	−2.07099	−0.0685775
$913$	−9.84878	−0.325947
$914$	−19.9661	−0.660420
$915$	−2.74341	−0.0906942
$916$	−16.5697	−0.547479
$917$	−13.4706	−0.444837
$918$	−0.0660160	−0.00217885
$919$	−28.9429	−0.954739	−0.477369	−	0.878703i	$-0.658410\pi$
$919$	−28.9429	−0.954739	−0.477369	+	0.878703i	$0.658410\pi$
$920$	−36.5377	−1.20461
$921$	35.1703	1.15890
$922$	23.1780	0.763326
$923$	34.1824	1.12513
$924$	4.49209	0.147779
$925$	6.01176	0.197666
$926$	−20.7670	−0.682446
$927$	17.3318	0.569252
$928$	0	0
$929$	−13.6916	−0.449208	−0.224604	−	0.974450i	$-0.572109\pi$
$929$	−13.6916	−0.449208	−0.224604	+	0.974450i	$0.572109\pi$
$930$	−33.9597	−1.11358
$931$	16.9452	0.555356
$932$	−31.5464	−1.03334
$933$	32.0031	1.04773
$934$	−3.85967	−0.126292
$935$	−0.0518457	−0.00169553
$936$	−8.73686	−0.285573
$937$	−34.7912	−1.13658	−0.568290	−	0.822828i	$-0.692395\pi$
$937$	−34.7912	−1.13658	−0.568290	+	0.822828i	$0.692395\pi$
$938$	1.47167	0.0480518
$939$	−26.0880	−0.851350
$940$	4.22463	0.137792
$941$	−28.2582	−0.921190	−0.460595	−	0.887610i	$-0.652364\pi$
$941$	−28.2582	−0.921190	−0.460595	+	0.887610i	$0.652364\pi$
$942$	16.6143	0.541324
$943$	−8.59736	−0.279968
$944$	−2.39181	−0.0778468
$945$	15.5294	0.505172
$946$	−2.39673	−0.0779243
$947$	47.0564	1.52913	0.764564	−	0.644547i	$-0.222954\pi$
$947$	47.0564	1.52913	0.764564	+	0.644547i	$0.222954\pi$
$948$	23.3529	0.758467
$949$	7.69472	0.249781
$950$	−4.33309	−0.140584
$951$	23.3812	0.758189
$952$	−0.110160	−0.00357032
$953$	39.9258	1.29332	0.646661	−	0.762778i	$-0.276165\pi$
$953$	39.9258	1.29332	0.646661	+	0.762778i	$0.276165\pi$
$954$	2.23272	0.0722871
$955$	24.5132	0.793227
$956$	−29.0024	−0.938006
$957$	0	0
$958$	34.9048	1.12772
$959$	15.7404	0.508283
$960$	27.8387	0.898490
$961$	23.1574	0.747014
$962$	11.8177	0.381019
$963$	−23.9745	−0.772567
$964$	11.6727	0.375951
$965$	56.6739	1.82440
$966$	−17.6422	−0.567630
$967$	5.31593	0.170949	0.0854744	−	0.996340i	$-0.472759\pi$
$967$	5.31593	0.170949	0.0854744	+	0.996340i	$0.472759\pi$
$968$	−2.87358	−0.0923604
$969$	−0.201294	−0.00646649
$970$	3.11066	0.0998772
$971$	−59.1792	−1.89915	−0.949575	−	0.313539i	$-0.898485\pi$
$971$	−59.1792	−1.89915	−0.949575	+	0.313539i	$0.898485\pi$
$972$	−15.3547	−0.492502
$973$	6.14628	0.197041
$974$	−5.66987	−0.181674
$975$	−4.97883	−0.159450
$976$	0.116269	0.00372169
$977$	16.7658	0.536386	0.268193	−	0.963365i	$-0.413574\pi$
$977$	16.7658	0.536386	0.268193	+	0.963365i	$0.413574\pi$
$978$	−39.8946	−1.27569
$979$	10.5055	0.335758
$980$	−10.7820	−0.344418
$981$	19.7523	0.630641
$982$	−9.59865	−0.306305
$983$	−37.9846	−1.21152	−0.605761	−	0.795647i	$-0.707131\pi$
$983$	−37.9846	−1.21152	−0.605761	+	0.795647i	$0.707131\pi$
$984$	9.94418	0.317009
$985$	43.1220	1.37398
$986$	0	0
$987$	5.47679	0.174328
$988$	12.4370	0.395673
$989$	−13.7439	−0.437030
$990$	2.95190	0.0938175
$991$	−35.5302	−1.12865	−0.564326	−	0.825552i	$-0.690864\pi$
$991$	−35.5302	−1.12865	−0.564326	+	0.825552i	$0.690864\pi$
$992$	−40.8551	−1.29715
$993$	−56.6484	−1.79768
$994$	−24.5393	−0.778339
$995$	50.6001	1.60413
$996$	24.3306	0.770944
$997$	13.0432	0.413083	0.206541	−	0.978438i	$-0.433779\pi$
$997$	13.0432	0.413083	0.206541	+	0.978438i	$0.433779\pi$
$998$	17.6579	0.558952
$999$	19.9309	0.630587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.12	yes	18
29.28	even	2		9251.2.a.s.1.7	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.7	✓	18	29.28	even	2
9251.2.a.t.1.12	yes	18	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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q+0.901649 q^{2} -2.08118 q^{3} -1.18703 q^{4} -2.45917 q^{5} -1.87649 q^{6} -1.81835 q^{7} -2.87358 q^{8} +1.33130 q^{9} +O(q^{10})\)	\(q+0.901649 q^{2} -2.08118 q^{3} -1.18703 q^{4} -2.45917 q^{5} -1.87649 q^{6} -1.81835 q^{7} -2.87358 q^{8} +1.33130 q^{9} -2.21731 q^{10} -1.00000 q^{11} +2.47042 q^{12} +2.28379 q^{13} -1.63952 q^{14} +5.11797 q^{15} -0.216906 q^{16} -0.0210826 q^{17} +1.20036 q^{18} -4.58773 q^{19} +2.91911 q^{20} +3.78432 q^{21} -0.901649 q^{22} -5.17045 q^{23} +5.98043 q^{24} +1.04752 q^{25} +2.05918 q^{26} +3.47286 q^{27} +2.15844 q^{28} +4.61461 q^{30} -7.35917 q^{31} +5.55159 q^{32} +2.08118 q^{33} -0.0190091 q^{34} +4.47164 q^{35} -1.58029 q^{36} +5.73905 q^{37} -4.13652 q^{38} -4.75297 q^{39} +7.06663 q^{40} +1.66279 q^{41} +3.41213 q^{42} +2.65816 q^{43} +1.18703 q^{44} -3.27389 q^{45} -4.66194 q^{46} +1.44724 q^{47} +0.451421 q^{48} -3.69359 q^{49} +0.944495 q^{50} +0.0438766 q^{51} -2.71093 q^{52} +1.86004 q^{53} +3.13131 q^{54} +2.45917 q^{55} +5.22519 q^{56} +9.54787 q^{57} +11.0269 q^{59} -6.07518 q^{60} -0.536034 q^{61} -6.63539 q^{62} -2.42077 q^{63} +5.43940 q^{64} -5.61623 q^{65} +1.87649 q^{66} -0.897625 q^{67} +0.0250256 q^{68} +10.7606 q^{69} +4.03185 q^{70} +14.9674 q^{71} -3.82559 q^{72} +3.36928 q^{73} +5.17461 q^{74} -2.18007 q^{75} +5.44576 q^{76} +1.81835 q^{77} -4.28552 q^{78} +9.45303 q^{79} +0.533410 q^{80} -11.2215 q^{81} +1.49925 q^{82} +9.84878 q^{83} -4.49209 q^{84} +0.0518457 q^{85} +2.39673 q^{86} +2.87358 q^{88} -10.5055 q^{89} -2.95190 q^{90} -4.15274 q^{91} +6.13748 q^{92} +15.3157 q^{93} +1.30490 q^{94} +11.2820 q^{95} -11.5538 q^{96} -1.40290 q^{97} -3.33032 q^{98} -1.33130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

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