LMFDB - Embedded newform 381.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [381,2,Mod(1,381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(381, 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("381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 381 = 3 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	381.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:	$3.04230031701$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 14x^{7} + 26x^{6} + 59x^{5} - 99x^{4} - 66x^{3} + 102x^{2} - 24x + 1 $ x^9 - 2x^8 - 14x^7 + 26x^6 + 59x^5 - 99x^4 - 66x^3 + 102x^2 - 24x + 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			1.2
Root			$2.55353$ of defining polynomial
Character	$\chi$	$=$	381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55353 q^{2} +1.00000 q^{3} +4.52051 q^{4} +2.44899 q^{5} -2.55353 q^{6} +3.89705 q^{7} -6.43620 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.55353 q^{2} +1.00000 q^{3} +4.52051 q^{4} +2.44899 q^{5} -2.55353 q^{6} +3.89705 q^{7} -6.43620 q^{8} +1.00000 q^{9} -6.25358 q^{10} +3.82323 q^{11} +4.52051 q^{12} +4.41381 q^{13} -9.95122 q^{14} +2.44899 q^{15} +7.39400 q^{16} -7.77710 q^{17} -2.55353 q^{18} -5.77710 q^{19} +11.0707 q^{20} +3.89705 q^{21} -9.76272 q^{22} -4.71830 q^{23} -6.43620 q^{24} +0.997574 q^{25} -11.2708 q^{26} +1.00000 q^{27} +17.6166 q^{28} -1.05007 q^{29} -6.25358 q^{30} -0.879109 q^{31} -6.00840 q^{32} +3.82323 q^{33} +19.8590 q^{34} +9.54384 q^{35} +4.52051 q^{36} +2.79920 q^{37} +14.7520 q^{38} +4.41381 q^{39} -15.7622 q^{40} +0.154217 q^{41} -9.95122 q^{42} -12.0189 q^{43} +17.2829 q^{44} +2.44899 q^{45} +12.0483 q^{46} +5.65025 q^{47} +7.39400 q^{48} +8.18697 q^{49} -2.54734 q^{50} -7.77710 q^{51} +19.9527 q^{52} -5.76838 q^{53} -2.55353 q^{54} +9.36306 q^{55} -25.0822 q^{56} -5.77710 q^{57} +2.68139 q^{58} +4.10330 q^{59} +11.0707 q^{60} +4.94156 q^{61} +2.24483 q^{62} +3.89705 q^{63} +0.554626 q^{64} +10.8094 q^{65} -9.76272 q^{66} -11.4692 q^{67} -35.1565 q^{68} -4.71830 q^{69} -24.3705 q^{70} +14.7531 q^{71} -6.43620 q^{72} -12.0563 q^{73} -7.14784 q^{74} +0.997574 q^{75} -26.1154 q^{76} +14.8993 q^{77} -11.2708 q^{78} +6.49805 q^{79} +18.1079 q^{80} +1.00000 q^{81} -0.393799 q^{82} -14.3278 q^{83} +17.6166 q^{84} -19.0461 q^{85} +30.6907 q^{86} -1.05007 q^{87} -24.6071 q^{88} +2.55754 q^{89} -6.25358 q^{90} +17.2008 q^{91} -21.3292 q^{92} -0.879109 q^{93} -14.4281 q^{94} -14.1481 q^{95} -6.00840 q^{96} -2.23970 q^{97} -20.9057 q^{98} +3.82323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9} - 4 q^{10} + 8 q^{11} + 14 q^{12} + 14 q^{13} + 4 q^{14} - 4 q^{15} + 32 q^{16} - 6 q^{17} - 2 q^{18} + 12 q^{19} - 28 q^{20} + 10 q^{21} - 18 q^{22} - 4 q^{23} - 6 q^{24} + 21 q^{25} - 14 q^{26} + 9 q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 29 q^{32} + 8 q^{33} - 3 q^{34} + 6 q^{35} + 14 q^{36} + 22 q^{37} - 7 q^{38} + 14 q^{39} - 2 q^{41} + 4 q^{42} + 6 q^{43} + 17 q^{44} - 4 q^{45} - 10 q^{46} - 2 q^{47} + 32 q^{48} + 23 q^{49} - 20 q^{50} - 6 q^{51} - 9 q^{52} - 12 q^{53} - 2 q^{54} - 22 q^{55} + 18 q^{56} + 12 q^{57} - 28 q^{58} - 6 q^{59} - 28 q^{60} + 2 q^{61} - 15 q^{62} + 10 q^{63} + 24 q^{64} + 4 q^{65} - 18 q^{66} + 18 q^{67} - 24 q^{68} - 4 q^{69} - 72 q^{70} + 24 q^{71} - 6 q^{72} + 14 q^{73} + 3 q^{74} + 21 q^{75} + 4 q^{76} - 18 q^{77} - 14 q^{78} + 12 q^{79} - 86 q^{80} + 9 q^{81} + 4 q^{82} - 20 q^{83} - 24 q^{85} + 16 q^{86} - 8 q^{87} - 55 q^{88} - 30 q^{89} - 4 q^{90} + 14 q^{91} - 46 q^{92} + 4 q^{93} - 66 q^{94} - 32 q^{95} - 29 q^{96} + 12 q^{97} - 62 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9 - 4 * q^10 + 8 * q^11 + 14 * q^12 + 14 * q^13 + 4 * q^14 - 4 * q^15 + 32 * q^16 - 6 * q^17 - 2 * q^18 + 12 * q^19 - 28 * q^20 + 10 * q^21 - 18 * q^22 - 4 * q^23 - 6 * q^24 + 21 * q^25 - 14 * q^26 + 9 * q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 29 * q^32 + 8 * q^33 - 3 * q^34 + 6 * q^35 + 14 * q^36 + 22 * q^37 - 7 * q^38 + 14 * q^39 - 2 * q^41 + 4 * q^42 + 6 * q^43 + 17 * q^44 - 4 * q^45 - 10 * q^46 - 2 * q^47 + 32 * q^48 + 23 * q^49 - 20 * q^50 - 6 * q^51 - 9 * q^52 - 12 * q^53 - 2 * q^54 - 22 * q^55 + 18 * q^56 + 12 * q^57 - 28 * q^58 - 6 * q^59 - 28 * q^60 + 2 * q^61 - 15 * q^62 + 10 * q^63 + 24 * q^64 + 4 * q^65 - 18 * q^66 + 18 * q^67 - 24 * q^68 - 4 * q^69 - 72 * q^70 + 24 * q^71 - 6 * q^72 + 14 * q^73 + 3 * q^74 + 21 * q^75 + 4 * q^76 - 18 * q^77 - 14 * q^78 + 12 * q^79 - 86 * q^80 + 9 * q^81 + 4 * q^82 - 20 * q^83 - 24 * q^85 + 16 * q^86 - 8 * q^87 - 55 * q^88 - 30 * q^89 - 4 * q^90 + 14 * q^91 - 46 * q^92 + 4 * q^93 - 66 * q^94 - 32 * q^95 - 29 * q^96 + 12 * q^97 - 62 * q^98 + 8 * 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 $

$2$	−2.55353	−1.80562	−0.902809	−	0.430042i	$-0.858499\pi$
$2$	−2.55353	−1.80562	−0.902809	+	0.430042i	$0.858499\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.52051	2.26026
$5$	2.44899	1.09522	0.547612	−	0.836733i	$-0.315537\pi$
$5$	2.44899	1.09522	0.547612	+	0.836733i	$0.315537\pi$
$6$	−2.55353	−1.04247
$7$	3.89705	1.47294	0.736472	−	0.676468i	$-0.236490\pi$
$7$	3.89705	1.47294	0.736472	+	0.676468i	$0.236490\pi$
$8$	−6.43620	−2.27554
$9$	1.00000	0.333333
$10$	−6.25358	−1.97756
$11$	3.82323	1.15275	0.576373	−	0.817187i	$-0.304467\pi$
$11$	3.82323	1.15275	0.576373	+	0.817187i	$0.304467\pi$
$12$	4.52051	1.30496
$13$	4.41381	1.22417	0.612085	−	0.790792i	$-0.290331\pi$
$13$	4.41381	1.22417	0.612085	+	0.790792i	$0.290331\pi$
$14$	−9.95122	−2.65958
$15$	2.44899	0.632328
$16$	7.39400	1.84850
$17$	−7.77710	−1.88622	−0.943112	−	0.332476i	$-0.892116\pi$
$17$	−7.77710	−1.88622	−0.943112	+	0.332476i	$0.892116\pi$
$18$	−2.55353	−0.601873
$19$	−5.77710	−1.32536	−0.662679	−	0.748904i	$-0.730580\pi$
$19$	−5.77710	−1.32536	−0.662679	+	0.748904i	$0.730580\pi$
$20$	11.0707	2.47549
$21$	3.89705	0.850405
$22$	−9.76272	−2.08142
$23$	−4.71830	−0.983835	−0.491917	−	0.870642i	$-0.663704\pi$
$23$	−4.71830	−0.983835	−0.491917	+	0.870642i	$0.663704\pi$
$24$	−6.43620	−1.31378
$25$	0.997574	0.199515
$26$	−11.2708	−2.21038
$27$	1.00000	0.192450
$28$	17.6166	3.32923
$29$	−1.05007	−0.194993	−0.0974966	−	0.995236i	$-0.531084\pi$
$29$	−1.05007	−0.194993	−0.0974966	+	0.995236i	$0.531084\pi$
$30$	−6.25358	−1.14174
$31$	−0.879109	−0.157893	−0.0789463	−	0.996879i	$-0.525156\pi$
$31$	−0.879109	−0.157893	−0.0789463	+	0.996879i	$0.525156\pi$
$32$	−6.00840	−1.06215
$33$	3.82323	0.665539
$34$	19.8590	3.40580
$35$	9.54384	1.61320
$36$	4.52051	0.753419
$37$	2.79920	0.460186	0.230093	−	0.973169i	$-0.426097\pi$
$37$	2.79920	0.460186	0.230093	+	0.973169i	$0.426097\pi$
$38$	14.7520	2.39309
$39$	4.41381	0.706775
$40$	−15.7622	−2.49223
$41$	0.154217	0.0240847	0.0120424	−	0.999927i	$-0.496167\pi$
$41$	0.154217	0.0240847	0.0120424	+	0.999927i	$0.496167\pi$
$42$	−9.95122	−1.53551
$43$	−12.0189	−1.83287	−0.916434	−	0.400185i	$-0.868946\pi$
$43$	−12.0189	−1.83287	−0.916434	+	0.400185i	$0.868946\pi$
$44$	17.2829	2.60550
$45$	2.44899	0.365075
$46$	12.0483	1.77643
$47$	5.65025	0.824174	0.412087	−	0.911145i	$-0.364800\pi$
$47$	5.65025	0.824174	0.412087	+	0.911145i	$0.364800\pi$
$48$	7.39400	1.06723
$49$	8.18697	1.16957
$50$	−2.54734	−0.360248
$51$	−7.77710	−1.08901
$52$	19.9527	2.76694
$53$	−5.76838	−0.792347	−0.396174	−	0.918176i	$-0.629662\pi$
$53$	−5.76838	−0.792347	−0.396174	+	0.918176i	$0.629662\pi$
$54$	−2.55353	−0.347491
$55$	9.36306	1.26252
$56$	−25.0822	−3.35175
$57$	−5.77710	−0.765195
$58$	2.68139	0.352083
$59$	4.10330	0.534205	0.267102	−	0.963668i	$-0.413934\pi$
$59$	4.10330	0.534205	0.267102	+	0.963668i	$0.413934\pi$
$60$	11.0707	1.42922
$61$	4.94156	0.632701	0.316351	−	0.948642i	$-0.397542\pi$
$61$	4.94156	0.632701	0.316351	+	0.948642i	$0.397542\pi$
$62$	2.24483	0.285094
$63$	3.89705	0.490982
$64$	0.554626	0.0693283
$65$	10.8094	1.34074
$66$	−9.76272	−1.20171
$67$	−11.4692	−1.40118	−0.700592	−	0.713562i	$-0.747080\pi$
$67$	−11.4692	−1.40118	−0.700592	+	0.713562i	$0.747080\pi$
$68$	−35.1565	−4.26335
$69$	−4.71830	−0.568017
$70$	−24.3705	−2.91283
$71$	14.7531	1.75087	0.875433	−	0.483339i	$-0.160576\pi$
$71$	14.7531	1.75087	0.875433	+	0.483339i	$0.160576\pi$
$72$	−6.43620	−0.758514
$73$	−12.0563	−1.41108	−0.705542	−	0.708668i	$-0.749296\pi$
$73$	−12.0563	−1.41108	−0.705542	+	0.708668i	$0.749296\pi$
$74$	−7.14784	−0.830919
$75$	0.997574	0.115190
$76$	−26.1154	−2.99565
$77$	14.8993	1.69793
$78$	−11.2708	−1.27617
$79$	6.49805	0.731088	0.365544	−	0.930794i	$-0.380883\pi$
$79$	6.49805	0.731088	0.365544	+	0.930794i	$0.380883\pi$
$80$	18.1079	2.02452
$81$	1.00000	0.111111
$82$	−0.393799	−0.0434878
$83$	−14.3278	−1.57268	−0.786338	−	0.617796i	$-0.788026\pi$
$83$	−14.3278	−1.57268	−0.786338	+	0.617796i	$0.788026\pi$
$84$	17.6166	1.92213
$85$	−19.0461	−2.06584
$86$	30.6907	3.30946
$87$	−1.05007	−0.112579
$88$	−24.6071	−2.62312
$89$	2.55754	0.271098	0.135549	−	0.990771i	$-0.456720\pi$
$89$	2.55754	0.271098	0.135549	+	0.990771i	$0.456720\pi$
$90$	−6.25358	−0.659185
$91$	17.2008	1.80314
$92$	−21.3292	−2.22372
$93$	−0.879109	−0.0911594
$94$	−14.4281	−1.48814
$95$	−14.1481	−1.45156
$96$	−6.00840	−0.613230
$97$	−2.23970	−0.227408	−0.113704	−	0.993515i	$-0.536271\pi$
$97$	−2.23970	−0.227408	−0.113704	+	0.993515i	$0.536271\pi$
$98$	−20.9057	−2.11179
$99$	3.82323	0.384249
$100$	4.50955	0.450955
$101$	−6.82762	−0.679374	−0.339687	−	0.940539i	$-0.610321\pi$
$101$	−6.82762	−0.679374	−0.339687	+	0.940539i	$0.610321\pi$
$102$	19.8590	1.96634
$103$	12.4296	1.22472	0.612361	−	0.790578i	$-0.290220\pi$
$103$	12.4296	1.22472	0.612361	+	0.790578i	$0.290220\pi$
$104$	−28.4082	−2.78565
$105$	9.54384	0.931384
$106$	14.7297	1.43068
$107$	15.4762	1.49614	0.748070	−	0.663620i	$-0.230981\pi$
$107$	15.4762	1.49614	0.748070	+	0.663620i	$0.230981\pi$
$108$	4.52051	0.434986
$109$	−11.3499	−1.08713	−0.543563	−	0.839368i	$-0.682925\pi$
$109$	−11.3499	−1.08713	−0.543563	+	0.839368i	$0.682925\pi$
$110$	−23.9089	−2.27962
$111$	2.79920	0.265688
$112$	28.8148	2.72274
$113$	2.22852	0.209642	0.104821	−	0.994491i	$-0.466573\pi$
$113$	2.22852	0.209642	0.104821	+	0.994491i	$0.466573\pi$
$114$	14.7520	1.38165
$115$	−11.5551	−1.07752
$116$	−4.74686	−0.440735
$117$	4.41381	0.408057
$118$	−10.4779	−0.964569
$119$	−30.3077	−2.77830
$120$	−15.7622	−1.43889
$121$	3.61707	0.328825
$122$	−12.6184	−1.14242
$123$	0.154217	0.0139053
$124$	−3.97402	−0.356878
$125$	−9.80192	−0.876710
$126$	−9.95122	−0.886525
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	10.6006	0.936965
$129$	−12.0189	−1.05821
$130$	−27.6021	−2.42087
$131$	−0.0851636	−0.00744078	−0.00372039	−	0.999993i	$-0.501184\pi$
$131$	−0.0851636	−0.00744078	−0.00372039	+	0.999993i	$0.501184\pi$
$132$	17.2829	1.50429
$133$	−22.5136	−1.95218
$134$	29.2869	2.53000
$135$	2.44899	0.210776
$136$	50.0550	4.29218
$137$	0.378848	0.0323672	0.0161836	−	0.999869i	$-0.494848\pi$
$137$	0.378848	0.0323672	0.0161836	+	0.999869i	$0.494848\pi$
$138$	12.0483	1.02562
$139$	−3.02979	−0.256983	−0.128492	−	0.991711i	$-0.541014\pi$
$139$	−3.02979	−0.256983	−0.128492	+	0.991711i	$0.541014\pi$
$140$	43.1431	3.64625
$141$	5.65025	0.475837
$142$	−37.6724	−3.16140
$143$	16.8750	1.41116
$144$	7.39400	0.616167
$145$	−2.57162	−0.213561
$146$	30.7861	2.54788
$147$	8.18697	0.675250
$148$	12.6538	1.04014
$149$	7.96111	0.652200	0.326100	−	0.945335i	$-0.394265\pi$
$149$	7.96111	0.652200	0.326100	+	0.945335i	$0.394265\pi$
$150$	−2.54734	−0.207989
$151$	20.9642	1.70605	0.853023	−	0.521874i	$-0.174767\pi$
$151$	20.9642	1.70605	0.853023	+	0.521874i	$0.174767\pi$
$152$	37.1826	3.01590
$153$	−7.77710	−0.628741
$154$	−38.0458	−3.06582
$155$	−2.15293	−0.172928
$156$	19.9527	1.59749
$157$	3.36423	0.268495	0.134247	−	0.990948i	$-0.457138\pi$
$157$	3.36423	0.268495	0.134247	+	0.990948i	$0.457138\pi$
$158$	−16.5930	−1.32007
$159$	−5.76838	−0.457462
$160$	−14.7145	−1.16329
$161$	−18.3875	−1.44913
$162$	−2.55353	−0.200624
$163$	4.23778	0.331928	0.165964	−	0.986132i	$-0.446926\pi$
$163$	4.23778	0.331928	0.165964	+	0.986132i	$0.446926\pi$
$164$	0.697142	0.0544376
$165$	9.36306	0.728914
$166$	36.5864	2.83965
$167$	12.5341	0.969918	0.484959	−	0.874537i	$-0.338835\pi$
$167$	12.5341	0.969918	0.484959	+	0.874537i	$0.338835\pi$
$168$	−25.0822	−1.93513
$169$	6.48173	0.498594
$170$	48.6347	3.73011
$171$	−5.77710	−0.441786
$172$	−54.3317	−4.14275
$173$	−9.15129	−0.695760	−0.347880	−	0.937539i	$-0.613098\pi$
$173$	−9.15129	−0.695760	−0.347880	+	0.937539i	$0.613098\pi$
$174$	2.68139	0.203275
$175$	3.88759	0.293874
$176$	28.2690	2.13085
$177$	4.10330	0.308423
$178$	−6.53074	−0.489500
$179$	17.5670	1.31302	0.656511	−	0.754317i	$-0.272032\pi$
$179$	17.5670	1.31302	0.656511	+	0.754317i	$0.272032\pi$
$180$	11.0707	0.825162
$181$	6.77582	0.503643	0.251822	−	0.967774i	$-0.418970\pi$
$181$	6.77582	0.503643	0.251822	+	0.967774i	$0.418970\pi$
$182$	−43.9228	−3.25578
$183$	4.94156	0.365290
$184$	30.3680	2.23876
$185$	6.85522	0.504006
$186$	2.24483	0.164599
$187$	−29.7336	−2.17434
$188$	25.5420	1.86284
$189$	3.89705	0.283468
$190$	36.1275	2.62097
$191$	1.65216	0.119546	0.0597730	−	0.998212i	$-0.480962\pi$
$191$	1.65216	0.119546	0.0597730	+	0.998212i	$0.480962\pi$
$192$	0.554626	0.0400267
$193$	−22.2545	−1.60192	−0.800959	−	0.598720i	$-0.795676\pi$
$193$	−22.2545	−1.60192	−0.800959	+	0.598720i	$0.795676\pi$
$194$	5.71915	0.410611
$195$	10.8094	0.774077
$196$	37.0093	2.64352
$197$	14.8955	1.06126	0.530630	−	0.847603i	$-0.321955\pi$
$197$	14.8955	1.06126	0.530630	+	0.847603i	$0.321955\pi$
$198$	−9.76272	−0.693807
$199$	−7.89145	−0.559410	−0.279705	−	0.960086i	$-0.590237\pi$
$199$	−7.89145	−0.559410	−0.279705	+	0.960086i	$0.590237\pi$
$200$	−6.42059	−0.454004
$201$	−11.4692	−0.808974
$202$	17.4345	1.22669
$203$	−4.09217	−0.287214
$204$	−35.1565	−2.46144
$205$	0.377678	0.0263781
$206$	−31.7393	−2.21138
$207$	−4.71830	−0.327945
$208$	32.6357	2.26288
$209$	−22.0872	−1.52780
$210$	−24.3705	−1.68172
$211$	10.3296	0.711117	0.355558	−	0.934654i	$-0.384291\pi$
$211$	10.3296	0.711117	0.355558	+	0.934654i	$0.384291\pi$
$212$	−26.0760	−1.79091
$213$	14.7531	1.01086
$214$	−39.5189	−2.70146
$215$	−29.4343	−2.00740
$216$	−6.43620	−0.437928
$217$	−3.42593	−0.232567
$218$	28.9824	1.96293
$219$	−12.0563	−0.814690
$220$	42.3258	2.85361
$221$	−34.3266	−2.30906
$222$	−7.14784	−0.479732
$223$	9.21433	0.617037	0.308518	−	0.951218i	$-0.400167\pi$
$223$	9.21433	0.617037	0.308518	+	0.951218i	$0.400167\pi$
$224$	−23.4150	−1.56448
$225$	0.997574	0.0665050
$226$	−5.69060	−0.378533
$227$	−6.19616	−0.411254	−0.205627	−	0.978630i	$-0.565923\pi$
$227$	−6.19616	−0.411254	−0.205627	+	0.978630i	$0.565923\pi$
$228$	−26.1154	−1.72954
$229$	10.3639	0.684864	0.342432	−	0.939543i	$-0.388749\pi$
$229$	10.3639	0.684864	0.342432	+	0.939543i	$0.388749\pi$
$230$	29.5063	1.94559
$231$	14.8993	0.980302
$232$	6.75847	0.443715
$233$	−7.72395	−0.506012	−0.253006	−	0.967465i	$-0.581419\pi$
$233$	−7.72395	−0.506012	−0.253006	+	0.967465i	$0.581419\pi$
$234$	−11.2708	−0.736795
$235$	13.8374	0.902654
$236$	18.5490	1.20744
$237$	6.49805	0.422094
$238$	77.3916	5.01655
$239$	−12.5030	−0.808753	−0.404377	−	0.914593i	$-0.632512\pi$
$239$	−12.5030	−0.808753	−0.404377	+	0.914593i	$0.632512\pi$
$240$	18.1079	1.16886
$241$	−1.33181	−0.0857894	−0.0428947	−	0.999080i	$-0.513658\pi$
$241$	−1.33181	−0.0857894	−0.0428947	+	0.999080i	$0.513658\pi$
$242$	−9.23629	−0.593731
$243$	1.00000	0.0641500
$244$	22.3384	1.43007
$245$	20.0498	1.28094
$246$	−0.393799	−0.0251077
$247$	−25.4990	−1.62246
$248$	5.65812	0.359291
$249$	−14.3278	−0.907985
$250$	25.0295	1.58300
$251$	5.84067	0.368660	0.184330	−	0.982864i	$-0.440988\pi$
$251$	5.84067	0.368660	0.184330	+	0.982864i	$0.440988\pi$
$252$	17.6166	1.10974
$253$	−18.0392	−1.13411
$254$	2.55353	0.160223
$255$	−19.0461	−1.19271
$256$	−28.1781	−1.76113
$257$	−25.3594	−1.58188	−0.790938	−	0.611896i	$-0.790407\pi$
$257$	−25.3594	−1.58188	−0.790938	+	0.611896i	$0.790407\pi$
$258$	30.6907	1.91072
$259$	10.9086	0.677828
$260$	48.8640	3.03042
$261$	−1.05007	−0.0649977
$262$	0.217468	0.0134352
$263$	−21.5029	−1.32593	−0.662963	−	0.748652i	$-0.730701\pi$
$263$	−21.5029	−1.32593	−0.662963	+	0.748652i	$0.730701\pi$
$264$	−24.6071	−1.51446
$265$	−14.1267	−0.867798
$266$	57.4892	3.52489
$267$	2.55754	0.156519
$268$	−51.8466	−3.16703
$269$	12.4571	0.759522	0.379761	−	0.925085i	$-0.376006\pi$
$269$	12.4571	0.759522	0.379761	+	0.925085i	$0.376006\pi$
$270$	−6.25358	−0.380581
$271$	24.6211	1.49563	0.747814	−	0.663909i	$-0.231104\pi$
$271$	24.6211	1.49563	0.747814	+	0.663909i	$0.231104\pi$
$272$	−57.5039	−3.48669
$273$	17.2008	1.04104
$274$	−0.967399	−0.0584427
$275$	3.81395	0.229990
$276$	−21.3292	−1.28386
$277$	8.66539	0.520653	0.260326	−	0.965521i	$-0.416170\pi$
$277$	8.66539	0.520653	0.260326	+	0.965521i	$0.416170\pi$
$278$	7.73665	0.464014
$279$	−0.879109	−0.0526309
$280$	−61.4261	−3.67091
$281$	−9.51624	−0.567691	−0.283846	−	0.958870i	$-0.591610\pi$
$281$	−9.51624	−0.567691	−0.283846	+	0.958870i	$0.591610\pi$
$282$	−14.4281	−0.859180
$283$	3.00430	0.178587	0.0892934	−	0.996005i	$-0.471539\pi$
$283$	3.00430	0.178587	0.0892934	+	0.996005i	$0.471539\pi$
$284$	66.6914	3.95741
$285$	−14.1481	−0.838060
$286$	−43.0908	−2.54801
$287$	0.600992	0.0354755
$288$	−6.00840	−0.354049
$289$	43.4833	2.55784
$290$	6.56670	0.385610
$291$	−2.23970	−0.131294
$292$	−54.5007	−3.18941
$293$	12.7522	0.744993	0.372497	−	0.928034i	$-0.378502\pi$
$293$	12.7522	0.744993	0.372497	+	0.928034i	$0.378502\pi$
$294$	−20.9057	−1.21924
$295$	10.0490	0.585073
$296$	−18.0162	−1.04717
$297$	3.82323	0.221846
$298$	−20.3289	−1.17762
$299$	−20.8257	−1.20438
$300$	4.50955	0.260359
$301$	−46.8383	−2.69971
$302$	−53.5328	−3.08047
$303$	−6.82762	−0.392237
$304$	−42.7159	−2.44992
$305$	12.1018	0.692949
$306$	19.8590	1.13527
$307$	−23.4460	−1.33813	−0.669067	−	0.743202i	$-0.733306\pi$
$307$	−23.4460	−1.33813	−0.669067	+	0.743202i	$0.733306\pi$
$308$	67.3524	3.83776
$309$	12.4296	0.707094
$310$	5.49758	0.312242
$311$	−11.9555	−0.677933	−0.338967	−	0.940798i	$-0.610077\pi$
$311$	−11.9555	−0.677933	−0.338967	+	0.940798i	$0.610077\pi$
$312$	−28.4082	−1.60830
$313$	23.0054	1.30034	0.650172	−	0.759787i	$-0.274697\pi$
$313$	23.0054	1.30034	0.650172	+	0.759787i	$0.274697\pi$
$314$	−8.59066	−0.484799
$315$	9.54384	0.537735
$316$	29.3745	1.65245
$317$	−9.24711	−0.519369	−0.259685	−	0.965693i	$-0.583619\pi$
$317$	−9.24711	−0.519369	−0.259685	+	0.965693i	$0.583619\pi$
$318$	14.7297	0.826001
$319$	−4.01466	−0.224778
$320$	1.35828	0.0759300
$321$	15.4762	0.863796
$322$	46.9529	2.61658
$323$	44.9291	2.49992
$324$	4.52051	0.251140
$325$	4.40310	0.244240
$326$	−10.8213	−0.599335
$327$	−11.3499	−0.627652
$328$	−0.992574	−0.0548057
$329$	22.0193	1.21396
$330$	−23.9089	−1.31614
$331$	31.5913	1.73641	0.868206	−	0.496204i	$-0.165273\pi$
$331$	31.5913	1.73641	0.868206	+	0.496204i	$0.165273\pi$
$332$	−64.7688	−3.55465
$333$	2.79920	0.153395
$334$	−32.0062	−1.75130
$335$	−28.0880	−1.53461
$336$	28.8148	1.57197
$337$	−15.7777	−0.859465	−0.429733	−	0.902956i	$-0.641392\pi$
$337$	−15.7777	−0.859465	−0.429733	+	0.902956i	$0.641392\pi$
$338$	−16.5513	−0.900271
$339$	2.22852	0.121037
$340$	−86.0980	−4.66932
$341$	−3.36103	−0.182010
$342$	14.7520	0.797696
$343$	4.62567	0.249763
$344$	77.3562	4.17077
$345$	−11.5551	−0.622106
$346$	23.3681	1.25628
$347$	21.3471	1.14597	0.572987	−	0.819564i	$-0.305785\pi$
$347$	21.3471	1.14597	0.572987	+	0.819564i	$0.305785\pi$
$348$	−4.74686	−0.254458
$349$	−2.19003	−0.117230	−0.0586148	−	0.998281i	$-0.518668\pi$
$349$	−2.19003	−0.117230	−0.0586148	+	0.998281i	$0.518668\pi$
$350$	−9.92708	−0.530625
$351$	4.41381	0.235592
$352$	−22.9715	−1.22438
$353$	−0.825057	−0.0439133	−0.0219567	−	0.999759i	$-0.506990\pi$
$353$	−0.825057	−0.0439133	−0.0219567	+	0.999759i	$0.506990\pi$
$354$	−10.4779	−0.556894
$355$	36.1302	1.91759
$356$	11.5614	0.612751
$357$	−30.3077	−1.60405
$358$	−44.8579	−2.37082
$359$	−22.3795	−1.18115	−0.590574	−	0.806984i	$-0.701098\pi$
$359$	−22.3795	−1.18115	−0.590574	+	0.806984i	$0.701098\pi$
$360$	−15.7622	−0.830742
$361$	14.3749	0.756572
$362$	−17.3023	−0.909387
$363$	3.61707	0.189847
$364$	77.7565	4.07555
$365$	−29.5258	−1.54545
$366$	−12.6184	−0.659575
$367$	29.0135	1.51449	0.757246	−	0.653130i	$-0.226545\pi$
$367$	29.0135	1.51449	0.757246	+	0.653130i	$0.226545\pi$
$368$	−34.8872	−1.81862
$369$	0.154217	0.00802824
$370$	−17.5050	−0.910043
$371$	−22.4796	−1.16708
$372$	−3.97402	−0.206044
$373$	2.32666	0.120470	0.0602348	−	0.998184i	$-0.480815\pi$
$373$	2.32666	0.120470	0.0602348	+	0.998184i	$0.480815\pi$
$374$	75.9257	3.92602
$375$	−9.80192	−0.506169
$376$	−36.3661	−1.87544
$377$	−4.63481	−0.238705
$378$	−9.95122	−0.511836
$379$	14.5711	0.748466	0.374233	−	0.927335i	$-0.377906\pi$
$379$	14.5711	0.748466	0.374233	+	0.927335i	$0.377906\pi$
$380$	−63.9566	−3.28090
$381$	−1.00000	−0.0512316
$382$	−4.21884	−0.215854
$383$	9.95839	0.508850	0.254425	−	0.967093i	$-0.418114\pi$
$383$	9.95839	0.508850	0.254425	+	0.967093i	$0.418114\pi$
$384$	10.6006	0.540957
$385$	36.4883	1.85962
$386$	56.8276	2.89245
$387$	−12.0189	−0.610956
$388$	−10.1246	−0.513999
$389$	−30.7848	−1.56085	−0.780426	−	0.625248i	$-0.784998\pi$
$389$	−30.7848	−1.56085	−0.780426	+	0.625248i	$0.784998\pi$
$390$	−27.6021	−1.39769
$391$	36.6947	1.85573
$392$	−52.6930	−2.66140
$393$	−0.0851636	−0.00429594
$394$	−38.0361	−1.91623
$395$	15.9137	0.800705
$396$	17.2829	0.868501
$397$	−21.9196	−1.10011	−0.550057	−	0.835127i	$-0.685394\pi$
$397$	−21.9196	−1.10011	−0.550057	+	0.835127i	$0.685394\pi$
$398$	20.1511	1.01008
$399$	−22.5136	−1.12709
$400$	7.37607	0.368803
$401$	−2.34919	−0.117313	−0.0586566	−	0.998278i	$-0.518682\pi$
$401$	−2.34919	−0.117313	−0.0586566	+	0.998278i	$0.518682\pi$
$402$	29.2869	1.46070
$403$	−3.88022	−0.193288
$404$	−30.8643	−1.53556
$405$	2.44899	0.121692
$406$	10.4495	0.518599
$407$	10.7020	0.530477
$408$	50.0550	2.47809
$409$	−38.2148	−1.88960	−0.944800	−	0.327648i	$-0.893744\pi$
$409$	−38.2148	−1.88960	−0.944800	+	0.327648i	$0.893744\pi$
$410$	−0.964411	−0.0476288
$411$	0.378848	0.0186872
$412$	56.1880	2.76819
$413$	15.9908	0.786854
$414$	12.0483	0.592143
$415$	−35.0886	−1.72243
$416$	−26.5200	−1.30025
$417$	−3.02979	−0.148369
$418$	56.4002	2.75862
$419$	34.8133	1.70074	0.850371	−	0.526184i	$-0.176378\pi$
$419$	34.8133	1.70074	0.850371	+	0.526184i	$0.176378\pi$
$420$	43.1431	2.10517
$421$	1.27040	0.0619155	0.0309577	−	0.999521i	$-0.490144\pi$
$421$	1.27040	0.0619155	0.0309577	+	0.999521i	$0.490144\pi$
$422$	−26.3769	−1.28401
$423$	5.65025	0.274725
$424$	37.1264	1.80302
$425$	−7.75823	−0.376330
$426$	−37.6724	−1.82523
$427$	19.2575	0.931934
$428$	69.9603	3.38166
$429$	16.8750	0.814733
$430$	75.1613	3.62460
$431$	19.7115	0.949472	0.474736	−	0.880128i	$-0.342544\pi$
$431$	19.7115	0.949472	0.474736	+	0.880128i	$0.342544\pi$
$432$	7.39400	0.355744
$433$	26.3026	1.26402	0.632011	−	0.774960i	$-0.282230\pi$
$433$	26.3026	1.26402	0.632011	+	0.774960i	$0.282230\pi$
$434$	8.74821	0.419928
$435$	−2.57162	−0.123300
$436$	−51.3075	−2.45718
$437$	27.2581	1.30393
$438$	30.7861	1.47102
$439$	−6.21716	−0.296729	−0.148364	−	0.988933i	$-0.547401\pi$
$439$	−6.21716	−0.296729	−0.148364	+	0.988933i	$0.547401\pi$
$440$	−60.2626	−2.87290
$441$	8.18697	0.389856
$442$	87.6541	4.16928
$443$	17.0352	0.809365	0.404682	−	0.914457i	$-0.367382\pi$
$443$	17.0352	0.809365	0.404682	+	0.914457i	$0.367382\pi$
$444$	12.6538	0.600523
$445$	6.26339	0.296913
$446$	−23.5291	−1.11413
$447$	7.96111	0.376548
$448$	2.16140	0.102117
$449$	−31.8463	−1.50292	−0.751461	−	0.659778i	$-0.770650\pi$
$449$	−31.8463	−1.50292	−0.751461	+	0.659778i	$0.770650\pi$
$450$	−2.54734	−0.120083
$451$	0.589608	0.0277636
$452$	10.0741	0.473844
$453$	20.9642	0.984986
$454$	15.8221	0.742567
$455$	42.1247	1.97484
$456$	37.1826	1.74123
$457$	35.9612	1.68220	0.841098	−	0.540883i	$-0.181910\pi$
$457$	35.9612	1.68220	0.841098	+	0.540883i	$0.181910\pi$
$458$	−26.4644	−1.23660
$459$	−7.77710	−0.363004
$460$	−52.2350	−2.43547
$461$	−19.4444	−0.905617	−0.452809	−	0.891608i	$-0.649578\pi$
$461$	−19.4444	−0.905617	−0.452809	+	0.891608i	$0.649578\pi$
$462$	−38.0458	−1.77005
$463$	−26.9817	−1.25395	−0.626973	−	0.779041i	$-0.715706\pi$
$463$	−26.9817	−1.25395	−0.626973	+	0.779041i	$0.715706\pi$
$464$	−7.76423	−0.360445
$465$	−2.15293	−0.0998399
$466$	19.7233	0.913665
$467$	−34.8369	−1.61206	−0.806029	−	0.591876i	$-0.798387\pi$
$467$	−34.8369	−1.61206	−0.806029	+	0.591876i	$0.798387\pi$
$468$	19.9527	0.922313
$469$	−44.6959	−2.06387
$470$	−35.3343	−1.62985
$471$	3.36423	0.155016
$472$	−26.4097	−1.21560
$473$	−45.9511	−2.11283
$474$	−16.5930	−0.762140
$475$	−5.76308	−0.264428
$476$	−137.006	−6.27968
$477$	−5.76838	−0.264116
$478$	31.9268	1.46030
$479$	−6.86253	−0.313557	−0.156779	−	0.987634i	$-0.550111\pi$
$479$	−6.86253	−0.313557	−0.156779	+	0.987634i	$0.550111\pi$
$480$	−14.7145	−0.671624
$481$	12.3551	0.563346
$482$	3.40082	0.154903
$483$	−18.3875	−0.836658
$484$	16.3510	0.743228
$485$	−5.48502	−0.249062
$486$	−2.55353	−0.115830
$487$	−16.9608	−0.768565	−0.384283	−	0.923216i	$-0.625551\pi$
$487$	−16.9608	−0.768565	−0.384283	+	0.923216i	$0.625551\pi$
$488$	−31.8048	−1.43974
$489$	4.23778	0.191639
$490$	−51.1979	−2.31288
$491$	−1.90424	−0.0859372	−0.0429686	−	0.999076i	$-0.513682\pi$
$491$	−1.90424	−0.0859372	−0.0429686	+	0.999076i	$0.513682\pi$
$492$	0.697142	0.0314296
$493$	8.16650	0.367801
$494$	65.1125	2.92955
$495$	9.36306	0.420838
$496$	−6.50014	−0.291865
$497$	57.4934	2.57893
$498$	36.5864	1.63947
$499$	−36.4821	−1.63316	−0.816582	−	0.577229i	$-0.804134\pi$
$499$	−36.4821	−1.63316	−0.816582	+	0.577229i	$0.804134\pi$
$500$	−44.3097	−1.98159
$501$	12.5341	0.559982
$502$	−14.9143	−0.665659
$503$	36.6800	1.63548	0.817741	−	0.575586i	$-0.195226\pi$
$503$	36.6800	1.63548	0.817741	+	0.575586i	$0.195226\pi$
$504$	−25.0822	−1.11725
$505$	−16.7208	−0.744066
$506$	46.0635	2.04777
$507$	6.48173	0.287864
$508$	−4.52051	−0.200565
$509$	−31.3055	−1.38759	−0.693797	−	0.720171i	$-0.744063\pi$
$509$	−31.3055	−1.38759	−0.693797	+	0.720171i	$0.744063\pi$
$510$	48.6347	2.15358
$511$	−46.9840	−2.07845
$512$	50.7524	2.24296
$513$	−5.77710	−0.255065
$514$	64.7560	2.85627
$515$	30.4400	1.34134
$516$	−54.3317	−2.39182
$517$	21.6022	0.950063
$518$	−27.8555	−1.22390
$519$	−9.15129	−0.401697
$520$	−69.5715	−3.05091
$521$	−4.68368	−0.205196	−0.102598	−	0.994723i	$-0.532716\pi$
$521$	−4.68368	−0.205196	−0.102598	+	0.994723i	$0.532716\pi$
$522$	2.68139	0.117361
$523$	9.51110	0.415891	0.207946	−	0.978140i	$-0.433322\pi$
$523$	9.51110	0.415891	0.207946	+	0.978140i	$0.433322\pi$
$524$	−0.384983	−0.0168181
$525$	3.88759	0.169668
$526$	54.9083	2.39412
$527$	6.83692	0.297821
$528$	28.2690	1.23025
$529$	−0.737598	−0.0320695
$530$	36.0730	1.56691
$531$	4.10330	0.178068
$532$	−101.773	−4.41242
$533$	0.680686	0.0294838
$534$	−6.53074	−0.282613
$535$	37.9011	1.63861
$536$	73.8179	3.18845
$537$	17.5670	0.758073
$538$	−31.8095	−1.37141
$539$	31.3006	1.34821
$540$	11.0707	0.476407
$541$	12.9800	0.558055	0.279028	−	0.960283i	$-0.409988\pi$
$541$	12.9800	0.558055	0.279028	+	0.960283i	$0.409988\pi$
$542$	−62.8708	−2.70053
$543$	6.77582	0.290778
$544$	46.7279	2.00344
$545$	−27.7959	−1.19065
$546$	−43.9228	−1.87972
$547$	−17.8217	−0.762002	−0.381001	−	0.924575i	$-0.624421\pi$
$547$	−17.8217	−0.762002	−0.381001	+	0.924575i	$0.624421\pi$
$548$	1.71259	0.0731581
$549$	4.94156	0.210900
$550$	−9.73904	−0.415274
$551$	6.06636	0.258436
$552$	30.3680	1.29255
$553$	25.3232	1.07685
$554$	−22.1273	−0.940100
$555$	6.85522	0.290988
$556$	−13.6962	−0.580848
$557$	7.06935	0.299538	0.149769	−	0.988721i	$-0.452147\pi$
$557$	7.06935	0.299538	0.149769	+	0.988721i	$0.452147\pi$
$558$	2.24483	0.0950313
$559$	−53.0493	−2.24374
$560$	70.5672	2.98201
$561$	−29.7336	−1.25535
$562$	24.3000	1.02503
$563$	−29.7344	−1.25316	−0.626579	−	0.779358i	$-0.715545\pi$
$563$	−29.7344	−1.25316	−0.626579	+	0.779358i	$0.715545\pi$
$564$	25.5420	1.07551
$565$	5.45764	0.229605
$566$	−7.67156	−0.322460
$567$	3.89705	0.163661
$568$	−94.9537	−3.98417
$569$	19.0302	0.797786	0.398893	−	0.916997i	$-0.369394\pi$
$569$	19.0302	0.797786	0.398893	+	0.916997i	$0.369394\pi$
$570$	36.1275	1.51322
$571$	31.1583	1.30393	0.651966	−	0.758248i	$-0.273944\pi$
$571$	31.1583	1.30393	0.651966	+	0.758248i	$0.273944\pi$
$572$	76.2837	3.18958
$573$	1.65216	0.0690199
$574$	−1.53465	−0.0640551
$575$	−4.70686	−0.196290
$576$	0.554626	0.0231094
$577$	−5.26050	−0.218998	−0.109499	−	0.993987i	$-0.534925\pi$
$577$	−5.26050	−0.218998	−0.109499	+	0.993987i	$0.534925\pi$
$578$	−111.036	−4.61848
$579$	−22.2545	−0.924867
$580$	−11.6250	−0.482703
$581$	−55.8360	−2.31647
$582$	5.71915	0.237066
$583$	−22.0538	−0.913376
$584$	77.5968	3.21098
$585$	10.8094	0.446914
$586$	−32.5632	−1.34517
$587$	17.7687	0.733391	0.366696	−	0.930341i	$-0.380489\pi$
$587$	17.7687	0.733391	0.366696	+	0.930341i	$0.380489\pi$
$588$	37.0093	1.52624
$589$	5.07870	0.209264
$590$	−25.6603	−1.05642
$591$	14.8955	0.612719
$592$	20.6973	0.850653
$593$	−11.9800	−0.491961	−0.245981	−	0.969275i	$-0.579110\pi$
$593$	−11.9800	−0.491961	−0.245981	+	0.969275i	$0.579110\pi$
$594$	−9.76272	−0.400569
$595$	−74.2234	−3.04286
$596$	35.9883	1.47414
$597$	−7.89145	−0.322976
$598$	53.1791	2.17465
$599$	−37.2111	−1.52041	−0.760203	−	0.649686i	$-0.774900\pi$
$599$	−37.2111	−1.52041	−0.760203	+	0.649686i	$0.774900\pi$
$600$	−6.42059	−0.262119
$601$	−25.5961	−1.04409	−0.522044	−	0.852919i	$-0.674830\pi$
$601$	−25.5961	−1.04409	−0.522044	+	0.852919i	$0.674830\pi$
$602$	119.603	4.87465
$603$	−11.4692	−0.467061
$604$	94.7691	3.85610
$605$	8.85818	0.360136
$606$	17.4345	0.708229
$607$	−4.02451	−0.163350	−0.0816748	−	0.996659i	$-0.526027\pi$
$607$	−4.02451	−0.163350	−0.0816748	+	0.996659i	$0.526027\pi$
$608$	34.7111	1.40772
$609$	−4.09217	−0.165823
$610$	−30.9024	−1.25120
$611$	24.9391	1.00893
$612$	−35.1565	−1.42112
$613$	24.6810	0.996857	0.498429	−	0.866931i	$-0.333911\pi$
$613$	24.6810	0.996857	0.498429	+	0.866931i	$0.333911\pi$
$614$	59.8701	2.41616
$615$	0.377678	0.0152294
$616$	−95.8948	−3.86371
$617$	23.2530	0.936132	0.468066	−	0.883693i	$-0.344951\pi$
$617$	23.2530	0.936132	0.468066	+	0.883693i	$0.344951\pi$
$618$	−31.7393	−1.27674
$619$	3.14807	0.126532	0.0632658	−	0.997997i	$-0.479848\pi$
$619$	3.14807	0.126532	0.0632658	+	0.997997i	$0.479848\pi$
$620$	−9.73236	−0.390861
$621$	−4.71830	−0.189339
$622$	30.5287	1.22409
$623$	9.96684	0.399313
$624$	32.6357	1.30647
$625$	−28.9927	−1.15971
$626$	−58.7450	−2.34792
$627$	−22.0872	−0.882076
$628$	15.2080	0.606867
$629$	−21.7697	−0.868013
$630$	−24.3705	−0.970943
$631$	−14.8108	−0.589610	−0.294805	−	0.955557i	$-0.595255\pi$
$631$	−14.8108	−0.589610	−0.294805	+	0.955557i	$0.595255\pi$
$632$	−41.8228	−1.66362
$633$	10.3296	0.410564
$634$	23.6128	0.937782
$635$	−2.44899	−0.0971854
$636$	−26.0760	−1.03398
$637$	36.1357	1.43175
$638$	10.2515	0.405863
$639$	14.7531	0.583622
$640$	25.9607	1.02619
$641$	4.47852	0.176891	0.0884454	−	0.996081i	$-0.471810\pi$
$641$	4.47852	0.176891	0.0884454	+	0.996081i	$0.471810\pi$
$642$	−39.5189	−1.55969
$643$	30.8163	1.21528	0.607639	−	0.794213i	$-0.292117\pi$
$643$	30.8163	1.21528	0.607639	+	0.794213i	$0.292117\pi$
$644$	−83.1207	−3.27541
$645$	−29.4343	−1.15897
$646$	−114.728	−4.51390
$647$	−4.58862	−0.180397	−0.0901987	−	0.995924i	$-0.528750\pi$
$647$	−4.58862	−0.180397	−0.0901987	+	0.995924i	$0.528750\pi$
$648$	−6.43620	−0.252838
$649$	15.6879	0.615802
$650$	−11.2435	−0.441005
$651$	−3.42593	−0.134273
$652$	19.1569	0.750243
$653$	1.41093	0.0552139	0.0276069	−	0.999619i	$-0.491211\pi$
$653$	1.41093	0.0552139	0.0276069	+	0.999619i	$0.491211\pi$
$654$	28.9824	1.13330
$655$	−0.208565	−0.00814932
$656$	1.14028	0.0445206
$657$	−12.0563	−0.470361
$658$	−56.2269	−2.19195
$659$	37.3998	1.45689	0.728444	−	0.685105i	$-0.240244\pi$
$659$	37.3998	1.45689	0.728444	+	0.685105i	$0.240244\pi$
$660$	42.3258	1.64753
$661$	−27.1575	−1.05630	−0.528152	−	0.849150i	$-0.677115\pi$
$661$	−27.1575	−1.05630	−0.528152	+	0.849150i	$0.677115\pi$
$662$	−80.6692	−3.13530
$663$	−34.3266	−1.33314
$664$	92.2164	3.57869
$665$	−55.1357	−2.13807
$666$	−7.14784	−0.276973
$667$	4.95455	0.191841
$668$	56.6605	2.19226
$669$	9.21433	0.356246
$670$	71.7234	2.77092
$671$	18.8927	0.729344
$672$	−23.4150	−0.903254
$673$	−0.583317	−0.0224852	−0.0112426	−	0.999937i	$-0.503579\pi$
$673$	−0.583317	−0.0224852	−0.0112426	+	0.999937i	$0.503579\pi$
$674$	40.2888	1.55187
$675$	0.997574	0.0383967
$676$	29.3007	1.12695
$677$	−6.45528	−0.248097	−0.124048	−	0.992276i	$-0.539588\pi$
$677$	−6.45528	−0.248097	−0.124048	+	0.992276i	$0.539588\pi$
$678$	−5.69060	−0.218546
$679$	−8.72823	−0.334959
$680$	122.584	4.70089
$681$	−6.19616	−0.237438
$682$	8.58250	0.328641
$683$	4.93815	0.188953	0.0944765	−	0.995527i	$-0.469882\pi$
$683$	4.93815	0.188953	0.0944765	+	0.995527i	$0.469882\pi$
$684$	−26.1154	−0.998549
$685$	0.927797	0.0354493
$686$	−11.8118	−0.450976
$687$	10.3639	0.395406
$688$	−88.8680	−3.38806
$689$	−25.4605	−0.969969
$690$	29.5063	1.12329
$691$	23.1086	0.879091	0.439546	−	0.898220i	$-0.355139\pi$
$691$	23.1086	0.879091	0.439546	+	0.898220i	$0.355139\pi$
$692$	−41.3685	−1.57260
$693$	14.8993	0.565977
$694$	−54.5105	−2.06919
$695$	−7.41994	−0.281454
$696$	6.75847	0.256179
$697$	−1.19936	−0.0454291
$698$	5.59231	0.211672
$699$	−7.72395	−0.292146
$700$	17.5739	0.664231
$701$	−16.0358	−0.605664	−0.302832	−	0.953044i	$-0.597932\pi$
$701$	−16.0358	−0.605664	−0.302832	+	0.953044i	$0.597932\pi$
$702$	−11.2708	−0.425389
$703$	−16.1713	−0.609910
$704$	2.12046	0.0799179
$705$	13.8374	0.521148
$706$	2.10681	0.0792907
$707$	−26.6076	−1.00068
$708$	18.5490	0.697115
$709$	−13.3502	−0.501376	−0.250688	−	0.968068i	$-0.580657\pi$
$709$	−13.3502	−0.501376	−0.250688	+	0.968068i	$0.580657\pi$
$710$	−92.2594	−3.46243
$711$	6.49805	0.243696
$712$	−16.4608	−0.616895
$713$	4.14791	0.155340
$714$	77.3916	2.89631
$715$	41.3268	1.54553
$716$	79.4120	2.96776
$717$	−12.5030	−0.466934
$718$	57.1468	2.13270
$719$	34.9098	1.30192	0.650959	−	0.759113i	$-0.274367\pi$
$719$	34.9098	1.30192	0.650959	+	0.759113i	$0.274367\pi$
$720$	18.1079	0.674841
$721$	48.4386	1.80395
$722$	−36.7066	−1.36608
$723$	−1.33181	−0.0495305
$724$	30.6302	1.13836
$725$	−1.04752	−0.0389040
$726$	−9.23629	−0.342791
$727$	51.1378	1.89659	0.948297	−	0.317383i	$-0.102804\pi$
$727$	51.1378	1.89659	0.948297	+	0.317383i	$0.102804\pi$
$728$	−110.708	−4.10311
$729$	1.00000	0.0370370
$730$	75.3951	2.79050
$731$	93.4723	3.45720
$732$	22.3384	0.825650
$733$	0.278165	0.0102743	0.00513713	−	0.999987i	$-0.498365\pi$
$733$	0.278165	0.0102743	0.00513713	+	0.999987i	$0.498365\pi$
$734$	−74.0868	−2.73459
$735$	20.0498	0.739549
$736$	28.3495	1.04498
$737$	−43.8493	−1.61521
$738$	−0.393799	−0.0144959
$739$	−7.90691	−0.290860	−0.145430	−	0.989369i	$-0.546457\pi$
$739$	−7.90691	−0.290860	−0.145430	+	0.989369i	$0.546457\pi$
$740$	30.9891	1.13918
$741$	−25.4990	−0.936730
$742$	57.4024	2.10731
$743$	20.1569	0.739487	0.369743	−	0.929134i	$-0.379446\pi$
$743$	20.1569	0.739487	0.369743	+	0.929134i	$0.379446\pi$
$744$	5.65812	0.207437
$745$	19.4967	0.714305
$746$	−5.94118	−0.217522
$747$	−14.3278	−0.524226
$748$	−134.411	−4.91456
$749$	60.3114	2.20373
$750$	25.0295	0.913948
$751$	18.2248	0.665031	0.332515	−	0.943098i	$-0.392103\pi$
$751$	18.2248	0.665031	0.332515	+	0.943098i	$0.392103\pi$
$752$	41.7780	1.52349
$753$	5.84067	0.212846
$754$	11.8351	0.431010
$755$	51.3413	1.86850
$756$	17.6166	0.640711
$757$	17.3018	0.628843	0.314422	−	0.949283i	$-0.398189\pi$
$757$	17.3018	0.628843	0.314422	+	0.949283i	$0.398189\pi$
$758$	−37.2077	−1.35144
$759$	−18.0392	−0.654780
$760$	91.0599	3.30309
$761$	−2.44843	−0.0887556	−0.0443778	−	0.999015i	$-0.514131\pi$
$761$	−2.44843	−0.0887556	−0.0443778	+	0.999015i	$0.514131\pi$
$762$	2.55353	0.0925046
$763$	−44.2312	−1.60128
$764$	7.46860	0.270205
$765$	−19.0461	−0.688612
$766$	−25.4290	−0.918788
$767$	18.1112	0.653958
$768$	−28.1781	−1.01679
$769$	31.3994	1.13229	0.566146	−	0.824305i	$-0.308434\pi$
$769$	31.3994	1.13229	0.566146	+	0.824305i	$0.308434\pi$
$770$	−93.1739	−3.35775
$771$	−25.3594	−0.913297
$772$	−100.602	−3.62074
$773$	7.09070	0.255035	0.127517	−	0.991836i	$-0.459299\pi$
$773$	7.09070	0.255035	0.127517	+	0.991836i	$0.459299\pi$
$774$	30.6907	1.10315
$775$	−0.876977	−0.0315019
$776$	14.4152	0.517475
$777$	10.9086	0.391344
$778$	78.6100	2.81830
$779$	−0.890929	−0.0319208
$780$	48.8640	1.74961
$781$	56.4043	2.01830
$782$	−93.7010	−3.35074
$783$	−1.05007	−0.0375265
$784$	60.5345	2.16195
$785$	8.23898	0.294062
$786$	0.217468	0.00775682
$787$	11.6900	0.416702	0.208351	−	0.978054i	$-0.433190\pi$
$787$	11.6900	0.416702	0.208351	+	0.978054i	$0.433190\pi$
$788$	67.3353	2.39872
$789$	−21.5029	−0.765524
$790$	−40.6361	−1.44577
$791$	8.68465	0.308791
$792$	−24.6071	−0.874374
$793$	21.8111	0.774535
$794$	55.9724	1.98638
$795$	−14.1267	−0.501023
$796$	−35.6734	−1.26441
$797$	−46.9377	−1.66262	−0.831310	−	0.555809i	$-0.812409\pi$
$797$	−46.9377	−1.66262	−0.831310	+	0.555809i	$0.812409\pi$
$798$	57.4892	2.03510
$799$	−43.9425	−1.55458
$800$	−5.99383	−0.211914
$801$	2.55754	0.0903661
$802$	5.99874	0.211823
$803$	−46.0940	−1.62662
$804$	−51.8466	−1.82849
$805$	−45.0308	−1.58713
$806$	9.90826	0.349004
$807$	12.4571	0.438510
$808$	43.9439	1.54594
$809$	−23.0704	−0.811113	−0.405556	−	0.914070i	$-0.632922\pi$
$809$	−23.0704	−0.811113	−0.405556	+	0.914070i	$0.632922\pi$
$810$	−6.25358	−0.219728
$811$	−5.97647	−0.209862	−0.104931	−	0.994480i	$-0.533462\pi$
$811$	−5.97647	−0.209862	−0.104931	+	0.994480i	$0.533462\pi$
$812$	−18.4987	−0.649178
$813$	24.6211	0.863501
$814$	−27.3278	−0.957839
$815$	10.3783	0.363536
$816$	−57.5039	−2.01304
$817$	69.4345	2.42921
$818$	97.5826	3.41190
$819$	17.2008	0.601045
$820$	1.70730	0.0596214
$821$	39.5214	1.37931	0.689653	−	0.724140i	$-0.257763\pi$
$821$	39.5214	1.37931	0.689653	+	0.724140i	$0.257763\pi$
$822$	−0.967399	−0.0337419
$823$	−41.1393	−1.43403	−0.717013	−	0.697060i	$-0.754491\pi$
$823$	−41.1393	−1.43403	−0.717013	+	0.697060i	$0.754491\pi$
$824$	−79.9992	−2.78690
$825$	3.81395	0.132785
$826$	−40.8329	−1.42076
$827$	38.8786	1.35194	0.675971	−	0.736928i	$-0.263725\pi$
$827$	38.8786	1.35194	0.675971	+	0.736928i	$0.263725\pi$
$828$	−21.3292	−0.741239
$829$	5.18917	0.180227	0.0901136	−	0.995931i	$-0.471277\pi$
$829$	5.18917	0.180227	0.0901136	+	0.995931i	$0.471277\pi$
$830$	89.5998	3.11006
$831$	8.66539	0.300599
$832$	2.44801	0.0848696
$833$	−63.6709	−2.20606
$834$	7.73665	0.267898
$835$	30.6959	1.06228
$836$	−99.8453	−3.45322
$837$	−0.879109	−0.0303865
$838$	−88.8968	−3.07089
$839$	−11.6267	−0.401399	−0.200699	−	0.979653i	$-0.564321\pi$
$839$	−11.6267	−0.401399	−0.200699	+	0.979653i	$0.564321\pi$
$840$	−61.4261	−2.11940
$841$	−27.8974	−0.961978
$842$	−3.24400	−0.111796
$843$	−9.51624	−0.327757
$844$	46.6949	1.60731
$845$	15.8737	0.546072
$846$	−14.4281	−0.496048
$847$	14.0959	0.484340
$848$	−42.6514	−1.46465
$849$	3.00430	0.103107
$850$	19.8109	0.679507
$851$	−13.2075	−0.452747
$852$	66.6914	2.28481
$853$	−2.04861	−0.0701432	−0.0350716	−	0.999385i	$-0.511166\pi$
$853$	−2.04861	−0.0701432	−0.0350716	+	0.999385i	$0.511166\pi$
$854$	−49.1745	−1.68272
$855$	−14.1481	−0.483854
$856$	−99.6078	−3.40453
$857$	3.08215	0.105284	0.0526421	−	0.998613i	$-0.483236\pi$
$857$	3.08215	0.105284	0.0526421	+	0.998613i	$0.483236\pi$
$858$	−43.0908	−1.47110
$859$	−49.3371	−1.68336	−0.841680	−	0.539976i	$-0.818433\pi$
$859$	−49.3371	−1.68336	−0.841680	+	0.539976i	$0.818433\pi$
$860$	−133.058	−4.53724
$861$	0.600992	0.0204818
$862$	−50.3340	−1.71438
$863$	−7.72911	−0.263102	−0.131551	−	0.991309i	$-0.541996\pi$
$863$	−7.72911	−0.263102	−0.131551	+	0.991309i	$0.541996\pi$
$864$	−6.00840	−0.204410
$865$	−22.4115	−0.762013
$866$	−67.1644	−2.28234
$867$	43.4833	1.47677
$868$	−15.4870	−0.525661
$869$	24.8435	0.842759
$870$	6.56670	0.222632
$871$	−50.6228	−1.71529
$872$	73.0504	2.47380
$873$	−2.23970	−0.0758025
$874$	−69.6044	−2.35440
$875$	−38.1985	−1.29135
$876$	−54.5007	−1.84141
$877$	29.1830	0.985439	0.492720	−	0.870188i	$-0.336003\pi$
$877$	29.1830	0.985439	0.492720	+	0.870188i	$0.336003\pi$
$878$	15.8757	0.535779
$879$	12.7522	0.430122
$880$	69.2305	2.33376
$881$	−17.3481	−0.584473	−0.292237	−	0.956346i	$-0.594399\pi$
$881$	−17.3481	−0.584473	−0.292237	+	0.956346i	$0.594399\pi$
$882$	−20.9057	−0.703930
$883$	2.60337	0.0876104	0.0438052	−	0.999040i	$-0.486052\pi$
$883$	2.60337	0.0876104	0.0438052	+	0.999040i	$0.486052\pi$
$884$	−155.174	−5.21907
$885$	10.0490	0.337792
$886$	−43.4998	−1.46140
$887$	−51.0504	−1.71411	−0.857053	−	0.515229i	$-0.827707\pi$
$887$	−51.0504	−1.71411	−0.857053	+	0.515229i	$0.827707\pi$
$888$	−18.0162	−0.604584
$889$	−3.89705	−0.130703
$890$	−15.9938	−0.536112
$891$	3.82323	0.128083
$892$	41.6535	1.39466
$893$	−32.6420	−1.09232
$894$	−20.3289	−0.679901
$895$	43.0216	1.43805
$896$	41.3108	1.38010
$897$	−20.8257	−0.695350
$898$	81.3206	2.71370
$899$	0.923127	0.0307880
$900$	4.50955	0.150318
$901$	44.8612	1.49454
$902$	−1.50558	−0.0501304
$903$	−46.8383	−1.55868
$904$	−14.3432	−0.477048
$905$	16.5940	0.551602
$906$	−53.5328	−1.77851
$907$	−14.0974	−0.468098	−0.234049	−	0.972225i	$-0.575198\pi$
$907$	−14.0974	−0.468098	−0.234049	+	0.972225i	$0.575198\pi$
$908$	−28.0098	−0.929539
$909$	−6.82762	−0.226458
$910$	−107.567	−3.56580
$911$	46.1625	1.52943	0.764716	−	0.644368i	$-0.222879\pi$
$911$	46.1625	1.52943	0.764716	+	0.644368i	$0.222879\pi$
$912$	−42.7159	−1.41446
$913$	−54.7783	−1.81290
$914$	−91.8281	−3.03740
$915$	12.1018	0.400075
$916$	46.8500	1.54797
$917$	−0.331887	−0.0109599
$918$	19.8590	0.655446
$919$	25.0206	0.825354	0.412677	−	0.910877i	$-0.364594\pi$
$919$	25.0206	0.825354	0.412677	+	0.910877i	$0.364594\pi$
$920$	74.3710	2.45194
$921$	−23.4460	−0.772572
$922$	49.6519	1.63520
$923$	65.1172	2.14336
$924$	67.3524	2.21573
$925$	2.79241	0.0918139
$926$	68.8985	2.26415
$927$	12.4296	0.408241
$928$	6.30925	0.207111
$929$	−21.4236	−0.702884	−0.351442	−	0.936210i	$-0.614309\pi$
$929$	−21.4236	−0.702884	−0.351442	+	0.936210i	$0.614309\pi$
$930$	5.49758	0.180273
$931$	−47.2969	−1.55009
$932$	−34.9162	−1.14372
$933$	−11.9555	−0.391405
$934$	88.9569	2.91076
$935$	−72.8175	−2.38139
$936$	−28.4082	−0.928550
$937$	15.0693	0.492293	0.246147	−	0.969233i	$-0.420835\pi$
$937$	15.0693	0.492293	0.246147	+	0.969233i	$0.420835\pi$
$938$	114.132	3.72655
$939$	23.0054	0.750754
$940$	62.5523	2.04023
$941$	27.3929	0.892983	0.446492	−	0.894788i	$-0.352673\pi$
$941$	27.3929	0.892983	0.446492	+	0.894788i	$0.352673\pi$
$942$	−8.59066	−0.279899
$943$	−0.727645	−0.0236954
$944$	30.3398	0.987478
$945$	9.54384	0.310461
$946$	117.337	3.81497
$947$	−32.9494	−1.07071	−0.535356	−	0.844627i	$-0.679823\pi$
$947$	−32.9494	−1.07071	−0.535356	+	0.844627i	$0.679823\pi$
$948$	29.3745	0.954040
$949$	−53.2143	−1.72741
$950$	14.7162	0.477457
$951$	−9.24711	−0.299858
$952$	195.067	6.32214
$953$	35.6548	1.15497	0.577487	−	0.816400i	$-0.304034\pi$
$953$	35.6548	1.15497	0.577487	+	0.816400i	$0.304034\pi$
$954$	14.7297	0.476892
$955$	4.04613	0.130930
$956$	−56.5201	−1.82799
$957$	−4.01466	−0.129775
$958$	17.5237	0.566164
$959$	1.47639	0.0476751
$960$	1.35828	0.0438382
$961$	−30.2272	−0.975070
$962$	−31.5492	−1.01719
$963$	15.4762	0.498713
$964$	−6.02046	−0.193906
$965$	−54.5013	−1.75446
$966$	46.9529	1.51068
$967$	49.3265	1.58623	0.793117	−	0.609069i	$-0.208457\pi$
$967$	49.3265	1.58623	0.793117	+	0.609069i	$0.208457\pi$
$968$	−23.2802	−0.748254
$969$	44.9291	1.44333
$970$	14.0062	0.449711
$971$	−18.4196	−0.591113	−0.295556	−	0.955325i	$-0.595505\pi$
$971$	−18.4196	−0.591113	−0.295556	+	0.955325i	$0.595505\pi$
$972$	4.52051	0.144995
$973$	−11.8072	−0.378522
$974$	43.3098	1.38773
$975$	4.40310	0.141012
$976$	36.5379	1.16955
$977$	28.6577	0.916840	0.458420	−	0.888736i	$-0.348416\pi$
$977$	28.6577	0.916840	0.458420	+	0.888736i	$0.348416\pi$
$978$	−10.8213	−0.346026
$979$	9.77804	0.312508
$980$	90.6355	2.89525
$981$	−11.3499	−0.362375
$982$	4.86254	0.155170
$983$	11.3897	0.363275	0.181638	−	0.983366i	$-0.441860\pi$
$983$	11.3897	0.363275	0.181638	+	0.983366i	$0.441860\pi$
$984$	−0.992574	−0.0316421
$985$	36.4790	1.16232
$986$	−20.8534	−0.664108
$987$	22.0193	0.700882
$988$	−115.269	−3.66718
$989$	56.7089	1.80324
$990$	−23.9089	−0.759873
$991$	−22.5603	−0.716650	−0.358325	−	0.933597i	$-0.616652\pi$
$991$	−22.5603	−0.716650	−0.358325	+	0.933597i	$0.616652\pi$
$992$	5.28204	0.167705
$993$	31.5913	1.00252
$994$	−146.811	−4.65656
$995$	−19.3261	−0.612679
$996$	−64.7688	−2.05228
$997$	−30.4430	−0.964139	−0.482069	−	0.876133i	$-0.660115\pi$
$997$	−30.4430	−0.964139	−0.482069	+	0.876133i	$0.660115\pi$
$998$	93.1582	2.94887
$999$	2.79920	0.0885628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	381.2.a.e.1.2	✓	9
3.2	odd	2		1143.2.a.j.1.8		9
4.3	odd	2		6096.2.a.bk.1.8		9
5.4	even	2		9525.2.a.p.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
381.2.a.e.1.2	✓	9	1.1	even	1	trivial
1143.2.a.j.1.8		9	3.2	odd	2
6096.2.a.bk.1.8		9	4.3	odd	2
9525.2.a.p.1.8		9	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 381 = 3 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55353 q^{2} +1.00000 q^{3} +4.52051 q^{4} +2.44899 q^{5} -2.55353 q^{6} +3.89705 q^{7} -6.43620 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.55353 q^{2} +1.00000 q^{3} +4.52051 q^{4} +2.44899 q^{5} -2.55353 q^{6} +3.89705 q^{7} -6.43620 q^{8} +1.00000 q^{9} -6.25358 q^{10} +3.82323 q^{11} +4.52051 q^{12} +4.41381 q^{13} -9.95122 q^{14} +2.44899 q^{15} +7.39400 q^{16} -7.77710 q^{17} -2.55353 q^{18} -5.77710 q^{19} +11.0707 q^{20} +3.89705 q^{21} -9.76272 q^{22} -4.71830 q^{23} -6.43620 q^{24} +0.997574 q^{25} -11.2708 q^{26} +1.00000 q^{27} +17.6166 q^{28} -1.05007 q^{29} -6.25358 q^{30} -0.879109 q^{31} -6.00840 q^{32} +3.82323 q^{33} +19.8590 q^{34} +9.54384 q^{35} +4.52051 q^{36} +2.79920 q^{37} +14.7520 q^{38} +4.41381 q^{39} -15.7622 q^{40} +0.154217 q^{41} -9.95122 q^{42} -12.0189 q^{43} +17.2829 q^{44} +2.44899 q^{45} +12.0483 q^{46} +5.65025 q^{47} +7.39400 q^{48} +8.18697 q^{49} -2.54734 q^{50} -7.77710 q^{51} +19.9527 q^{52} -5.76838 q^{53} -2.55353 q^{54} +9.36306 q^{55} -25.0822 q^{56} -5.77710 q^{57} +2.68139 q^{58} +4.10330 q^{59} +11.0707 q^{60} +4.94156 q^{61} +2.24483 q^{62} +3.89705 q^{63} +0.554626 q^{64} +10.8094 q^{65} -9.76272 q^{66} -11.4692 q^{67} -35.1565 q^{68} -4.71830 q^{69} -24.3705 q^{70} +14.7531 q^{71} -6.43620 q^{72} -12.0563 q^{73} -7.14784 q^{74} +0.997574 q^{75} -26.1154 q^{76} +14.8993 q^{77} -11.2708 q^{78} +6.49805 q^{79} +18.1079 q^{80} +1.00000 q^{81} -0.393799 q^{82} -14.3278 q^{83} +17.6166 q^{84} -19.0461 q^{85} +30.6907 q^{86} -1.05007 q^{87} -24.6071 q^{88} +2.55754 q^{89} -6.25358 q^{90} +17.2008 q^{91} -21.3292 q^{92} -0.879109 q^{93} -14.4281 q^{94} -14.1481 q^{95} -6.00840 q^{96} -2.23970 q^{97} -20.9057 q^{98} +3.82323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9	\( 9 q - 2 q^{2} + 9 q^{3} + 14 q^{4} - 4 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 9 q^{9} - 4 q^{10} + 8 q^{11} + 14 q^{12} + 14 q^{13} + 4 q^{14} - 4 q^{15} + 32 q^{16} - 6 q^{17} - 2 q^{18} + 12 q^{19} - 28 q^{20} + 10 q^{21} - 18 q^{22} - 4 q^{23} - 6 q^{24} + 21 q^{25} - 14 q^{26} + 9 q^{27} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 29 q^{32} + 8 q^{33} - 3 q^{34} + 6 q^{35} + 14 q^{36} + 22 q^{37} - 7 q^{38} + 14 q^{39} - 2 q^{41} + 4 q^{42} + 6 q^{43} + 17 q^{44} - 4 q^{45} - 10 q^{46} - 2 q^{47} + 32 q^{48} + 23 q^{49} - 20 q^{50} - 6 q^{51} - 9 q^{52} - 12 q^{53} - 2 q^{54} - 22 q^{55} + 18 q^{56} + 12 q^{57} - 28 q^{58} - 6 q^{59} - 28 q^{60} + 2 q^{61} - 15 q^{62} + 10 q^{63} + 24 q^{64} + 4 q^{65} - 18 q^{66} + 18 q^{67} - 24 q^{68} - 4 q^{69} - 72 q^{70} + 24 q^{71} - 6 q^{72} + 14 q^{73} + 3 q^{74} + 21 q^{75} + 4 q^{76} - 18 q^{77} - 14 q^{78} + 12 q^{79} - 86 q^{80} + 9 q^{81} + 4 q^{82} - 20 q^{83} - 24 q^{85} + 16 q^{86} - 8 q^{87} - 55 q^{88} - 30 q^{89} - 4 q^{90} + 14 q^{91} - 46 q^{92} + 4 q^{93} - 66 q^{94} - 32 q^{95} - 29 q^{96} + 12 q^{97} - 62 q^{98} + 8 q^{99}+O(q^{100}) \) 9 * q - 2 * q^2 + 9 * q^3 + 14 * q^4 - 4 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 9 * q^9 - 4 * q^10 + 8 * q^11 + 14 * q^12 + 14 * q^13 + 4 * q^14 - 4 * q^15 + 32 * q^16 - 6 * q^17 - 2 * q^18 + 12 * q^19 - 28 * q^20 + 10 * q^21 - 18 * q^22 - 4 * q^23 - 6 * q^24 + 21 * q^25 - 14 * q^26 + 9 * q^27 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 29 * q^32 + 8 * q^33 - 3 * q^34 + 6 * q^35 + 14 * q^36 + 22 * q^37 - 7 * q^38 + 14 * q^39 - 2 * q^41 + 4 * q^42 + 6 * q^43 + 17 * q^44 - 4 * q^45 - 10 * q^46 - 2 * q^47 + 32 * q^48 + 23 * q^49 - 20 * q^50 - 6 * q^51 - 9 * q^52 - 12 * q^53 - 2 * q^54 - 22 * q^55 + 18 * q^56 + 12 * q^57 - 28 * q^58 - 6 * q^59 - 28 * q^60 + 2 * q^61 - 15 * q^62 + 10 * q^63 + 24 * q^64 + 4 * q^65 - 18 * q^66 + 18 * q^67 - 24 * q^68 - 4 * q^69 - 72 * q^70 + 24 * q^71 - 6 * q^72 + 14 * q^73 + 3 * q^74 + 21 * q^75 + 4 * q^76 - 18 * q^77 - 14 * q^78 + 12 * q^79 - 86 * q^80 + 9 * q^81 + 4 * q^82 - 20 * q^83 - 24 * q^85 + 16 * q^86 - 8 * q^87 - 55 * q^88 - 30 * q^89 - 4 * q^90 + 14 * q^91 - 46 * q^92 + 4 * q^93 - 66 * q^94 - 32 * q^95 - 29 * q^96 + 12 * q^97 - 62 * q^98 + 8 * q^99

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