LMFDB - Embedded newform 1441.2.a.f.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68410 q^{2} -1.38946 q^{3} +0.836201 q^{4} -3.96942 q^{5} -2.33999 q^{6} +0.750944 q^{7} -1.95996 q^{8} -1.06941 q^{9} +O(q^{10})$	\(q+1.68410 q^{2} -1.38946 q^{3} +0.836201 q^{4} -3.96942 q^{5} -2.33999 q^{6} +0.750944 q^{7} -1.95996 q^{8} -1.06941 q^{9} -6.68491 q^{10} -1.00000 q^{11} -1.16187 q^{12} -0.0294758 q^{13} +1.26467 q^{14} +5.51534 q^{15} -4.97317 q^{16} +7.46608 q^{17} -1.80099 q^{18} +2.54485 q^{19} -3.31924 q^{20} -1.04340 q^{21} -1.68410 q^{22} +8.13090 q^{23} +2.72328 q^{24} +10.7563 q^{25} -0.0496403 q^{26} +5.65427 q^{27} +0.627940 q^{28} -7.66958 q^{29} +9.28840 q^{30} -6.50793 q^{31} -4.45542 q^{32} +1.38946 q^{33} +12.5736 q^{34} -2.98081 q^{35} -0.894241 q^{36} +2.24610 q^{37} +4.28579 q^{38} +0.0409554 q^{39} +7.77989 q^{40} +11.9653 q^{41} -1.75720 q^{42} -3.54647 q^{43} -0.836201 q^{44} +4.24493 q^{45} +13.6933 q^{46} +4.31867 q^{47} +6.91001 q^{48} -6.43608 q^{49} +18.1147 q^{50} -10.3738 q^{51} -0.0246477 q^{52} +5.31436 q^{53} +9.52237 q^{54} +3.96942 q^{55} -1.47182 q^{56} -3.53597 q^{57} -12.9164 q^{58} -12.8940 q^{59} +4.61194 q^{60} +1.65139 q^{61} -10.9600 q^{62} -0.803065 q^{63} +2.44296 q^{64} +0.117002 q^{65} +2.33999 q^{66} +12.0344 q^{67} +6.24314 q^{68} -11.2975 q^{69} -5.01999 q^{70} +11.3791 q^{71} +2.09599 q^{72} -4.85423 q^{73} +3.78266 q^{74} -14.9454 q^{75} +2.12801 q^{76} -0.750944 q^{77} +0.0689731 q^{78} -6.42517 q^{79} +19.7406 q^{80} -4.64814 q^{81} +20.1509 q^{82} -8.46038 q^{83} -0.872496 q^{84} -29.6360 q^{85} -5.97263 q^{86} +10.6565 q^{87} +1.95996 q^{88} -11.3047 q^{89} +7.14890 q^{90} -0.0221347 q^{91} +6.79907 q^{92} +9.04249 q^{93} +7.27309 q^{94} -10.1016 q^{95} +6.19061 q^{96} +8.93829 q^{97} -10.8390 q^{98} +1.06941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.68410	1.19084	0.595420	−	0.803414i	$-0.296986\pi$
$2$	1.68410	1.19084	0.595420	+	0.803414i	$0.296986\pi$
$3$	−1.38946	−0.802204	−0.401102	−	0.916033i	$-0.631373\pi$
$3$	−1.38946	−0.802204	−0.401102	+	0.916033i	$0.631373\pi$
$4$	0.836201	0.418101
$5$	−3.96942	−1.77518	−0.887590	−	0.460635i	$-0.847622\pi$
$5$	−3.96942	−1.77518	−0.887590	+	0.460635i	$0.847622\pi$
$6$	−2.33999	−0.955296
$7$	0.750944	0.283830	0.141915	−	0.989879i	$-0.454674\pi$
$7$	0.750944	0.283830	0.141915	+	0.989879i	$0.454674\pi$
$8$	−1.95996	−0.692949
$9$	−1.06941	−0.356469
$10$	−6.68491	−2.11396
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.16187	−0.335402
$13$	−0.0294758	−0.00817512	−0.00408756	−	0.999992i	$-0.501301\pi$
$13$	−0.0294758	−0.00817512	−0.00408756	+	0.999992i	$0.501301\pi$
$14$	1.26467	0.337996
$15$	5.51534	1.42406
$16$	−4.97317	−1.24329
$17$	7.46608	1.81079	0.905395	−	0.424571i	$-0.139575\pi$
$17$	7.46608	1.81079	0.905395	+	0.424571i	$0.139575\pi$
$18$	−1.80099	−0.424498
$19$	2.54485	0.583829	0.291915	−	0.956444i	$-0.405708\pi$
$19$	2.54485	0.583829	0.291915	+	0.956444i	$0.405708\pi$
$20$	−3.31924	−0.742204
$21$	−1.04340	−0.227689
$22$	−1.68410	−0.359052
$23$	8.13090	1.69541	0.847705	−	0.530468i	$-0.177984\pi$
$23$	8.13090	1.69541	0.847705	+	0.530468i	$0.177984\pi$
$24$	2.72328	0.555886
$25$	10.7563	2.15126
$26$	−0.0496403	−0.00973526
$27$	5.65427	1.08816
$28$	0.627940	0.118670
$29$	−7.66958	−1.42420	−0.712102	−	0.702076i	$-0.752257\pi$
$29$	−7.66958	−1.42420	−0.712102	+	0.702076i	$0.752257\pi$
$30$	9.28840	1.69582
$31$	−6.50793	−1.16886	−0.584429	−	0.811445i	$-0.698682\pi$
$31$	−6.50793	−1.16886	−0.584429	+	0.811445i	$0.698682\pi$
$32$	−4.45542	−0.787614
$33$	1.38946	0.241873
$34$	12.5736	2.15636
$35$	−2.98081	−0.503849
$36$	−0.894241	−0.149040
$37$	2.24610	0.369256	0.184628	−	0.982808i	$-0.440892\pi$
$37$	2.24610	0.369256	0.184628	+	0.982808i	$0.440892\pi$
$38$	4.28579	0.695248
$39$	0.0409554	0.00655811
$40$	7.77989	1.23011
$41$	11.9653	1.86867	0.934337	−	0.356392i	$-0.115993\pi$
$41$	11.9653	1.86867	0.934337	+	0.356392i	$0.115993\pi$
$42$	−1.75720	−0.271142
$43$	−3.54647	−0.540832	−0.270416	−	0.962744i	$-0.587161\pi$
$43$	−3.54647	−0.540832	−0.270416	+	0.962744i	$0.587161\pi$
$44$	−0.836201	−0.126062
$45$	4.24493	0.632797
$46$	13.6933	2.01896
$47$	4.31867	0.629943	0.314972	−	0.949101i	$-0.398005\pi$
$47$	4.31867	0.629943	0.314972	+	0.949101i	$0.398005\pi$
$48$	6.91001	0.997374
$49$	−6.43608	−0.919441
$50$	18.1147	2.56181
$51$	−10.3738	−1.45262
$52$	−0.0246477	−0.00341802
$53$	5.31436	0.729984	0.364992	−	0.931011i	$-0.381072\pi$
$53$	5.31436	0.729984	0.364992	+	0.931011i	$0.381072\pi$
$54$	9.52237	1.29583
$55$	3.96942	0.535237
$56$	−1.47182	−0.196680
$57$	−3.53597	−0.468350
$58$	−12.9164	−1.69600
$59$	−12.8940	−1.67865	−0.839325	−	0.543630i	$-0.817050\pi$
$59$	−12.8940	−1.67865	−0.839325	+	0.543630i	$0.817050\pi$
$60$	4.61194	0.595398
$61$	1.65139	0.211438	0.105719	−	0.994396i	$-0.466286\pi$
$61$	1.65139	0.211438	0.105719	+	0.994396i	$0.466286\pi$
$62$	−10.9600	−1.39192
$63$	−0.803065	−0.101177
$64$	2.44296	0.305370
$65$	0.117002	0.0145123
$66$	2.33999	0.288033
$67$	12.0344	1.47023	0.735117	−	0.677940i	$-0.237127\pi$
$67$	12.0344	1.47023	0.735117	+	0.677940i	$0.237127\pi$
$68$	6.24314	0.757092
$69$	−11.2975	−1.36006
$70$	−5.01999	−0.600004
$71$	11.3791	1.35045	0.675226	−	0.737611i	$-0.264046\pi$
$71$	11.3791	1.35045	0.675226	+	0.737611i	$0.264046\pi$
$72$	2.09599	0.247015
$73$	−4.85423	−0.568145	−0.284073	−	0.958803i	$-0.591686\pi$
$73$	−4.85423	−0.568145	−0.284073	+	0.958803i	$0.591686\pi$
$74$	3.78266	0.439725
$75$	−14.9454	−1.72575
$76$	2.12801	0.244100
$77$	−0.750944	−0.0855780
$78$	0.0689731	0.00780966
$79$	−6.42517	−0.722889	−0.361444	−	0.932394i	$-0.617716\pi$
$79$	−6.42517	−0.722889	−0.361444	+	0.932394i	$0.617716\pi$
$80$	19.7406	2.20707
$81$	−4.64814	−0.516460
$82$	20.1509	2.22529
$83$	−8.46038	−0.928648	−0.464324	−	0.885666i	$-0.653703\pi$
$83$	−8.46038	−0.928648	−0.464324	+	0.885666i	$0.653703\pi$
$84$	−0.872496	−0.0951971
$85$	−29.6360	−3.21448
$86$	−5.97263	−0.644045
$87$	10.6565	1.14250
$88$	1.95996	0.208932
$89$	−11.3047	−1.19830	−0.599148	−	0.800638i	$-0.704494\pi$
$89$	−11.3047	−1.19830	−0.599148	+	0.800638i	$0.704494\pi$
$90$	7.14890	0.753560
$91$	−0.0221347	−0.00232034
$92$	6.79907	0.708852
$93$	9.04249	0.937663
$94$	7.27309	0.750162
$95$	−10.1016	−1.03640
$96$	6.19061	0.631827
$97$	8.93829	0.907546	0.453773	−	0.891117i	$-0.350078\pi$
$97$	8.93829	0.907546	0.453773	+	0.891117i	$0.350078\pi$
$98$	−10.8390	−1.09491
$99$	1.06941	0.107480
$100$	8.99444	0.899444
$101$	−0.712744	−0.0709207	−0.0354604	−	0.999371i	$-0.511290\pi$
$101$	−0.712744	−0.0709207	−0.0354604	+	0.999371i	$0.511290\pi$
$102$	−17.4705	−1.72984
$103$	10.4450	1.02918	0.514588	−	0.857438i	$-0.327945\pi$
$103$	10.4450	1.02918	0.514588	+	0.857438i	$0.327945\pi$
$104$	0.0577713	0.00566494
$105$	4.14171	0.404190
$106$	8.94993	0.869294
$107$	6.65339	0.643208	0.321604	−	0.946874i	$-0.395778\pi$
$107$	6.65339	0.643208	0.321604	+	0.946874i	$0.395778\pi$
$108$	4.72811	0.454962
$109$	16.5299	1.58328	0.791640	−	0.610988i	$-0.209227\pi$
$109$	16.5299	1.58328	0.791640	+	0.610988i	$0.209227\pi$
$110$	6.68491	0.637381
$111$	−3.12086	−0.296219
$112$	−3.73457	−0.352884
$113$	1.38984	0.130745	0.0653724	−	0.997861i	$-0.479176\pi$
$113$	1.38984	0.130745	0.0653724	+	0.997861i	$0.479176\pi$
$114$	−5.95493	−0.557730
$115$	−32.2750	−3.00966
$116$	−6.41331	−0.595461
$117$	0.0315217	0.00291418
$118$	−21.7147	−1.99900
$119$	5.60660	0.513956
$120$	−10.8098	−0.986798
$121$	1.00000	0.0909091
$122$	2.78111	0.251789
$123$	−16.6253	−1.49906
$124$	−5.44194	−0.488701
$125$	−22.8492	−2.04370
$126$	−1.35244	−0.120485
$127$	8.71106	0.772981	0.386491	−	0.922293i	$-0.373687\pi$
$127$	8.71106	0.772981	0.386491	+	0.922293i	$0.373687\pi$
$128$	13.0250	1.15126
$129$	4.92767	0.433858
$130$	0.197043	0.0172818
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.16187	0.101127
$133$	1.91104	0.165708
$134$	20.2671	1.75081
$135$	−22.4442	−1.93169
$136$	−14.6332	−1.25478
$137$	23.3695	1.99660	0.998298	−	0.0583272i	$-0.0185767\pi$
$137$	23.3695	1.99660	0.998298	+	0.0583272i	$0.0185767\pi$
$138$	−19.0262	−1.61962
$139$	−6.74418	−0.572034	−0.286017	−	0.958225i	$-0.592331\pi$
$139$	−6.74418	−0.572034	−0.286017	+	0.958225i	$0.592331\pi$
$140$	−2.49256	−0.210660
$141$	−6.00061	−0.505343
$142$	19.1636	1.60817
$143$	0.0294758	0.00246489
$144$	5.31835	0.443196
$145$	30.4438	2.52822
$146$	−8.17503	−0.676570
$147$	8.94266	0.737578
$148$	1.87819	0.154386
$149$	24.0474	1.97004	0.985018	−	0.172450i	$-0.0551685\pi$
$149$	24.0474	1.97004	0.985018	+	0.172450i	$0.0551685\pi$
$150$	−25.1696	−2.05509
$151$	−5.67072	−0.461477	−0.230738	−	0.973016i	$-0.574114\pi$
$151$	−5.67072	−0.461477	−0.230738	+	0.973016i	$0.574114\pi$
$152$	−4.98780	−0.404564
$153$	−7.98428	−0.645491
$154$	−1.26467	−0.101910
$155$	25.8327	2.07493
$156$	0.0342469	0.00274195
$157$	3.43287	0.273973	0.136986	−	0.990573i	$-0.456258\pi$
$157$	3.43287	0.273973	0.136986	+	0.990573i	$0.456258\pi$
$158$	−10.8207	−0.860845
$159$	−7.38408	−0.585595
$160$	17.6854	1.39816
$161$	6.10585	0.481208
$162$	−7.82795	−0.615022
$163$	−2.47129	−0.193566	−0.0967832	−	0.995305i	$-0.530855\pi$
$163$	−2.47129	−0.193566	−0.0967832	+	0.995305i	$0.530855\pi$
$164$	10.0054	0.781294
$165$	−5.51534	−0.429369
$166$	−14.2482	−1.10587
$167$	4.98485	0.385739	0.192870	−	0.981224i	$-0.438221\pi$
$167$	4.98485	0.385739	0.192870	+	0.981224i	$0.438221\pi$
$168$	2.04503	0.157777
$169$	−12.9991	−0.999933
$170$	−49.9101	−3.82793
$171$	−2.72149	−0.208117
$172$	−2.96557	−0.226122
$173$	9.39973	0.714648	0.357324	−	0.933980i	$-0.383689\pi$
$173$	9.39973	0.714648	0.357324	+	0.933980i	$0.383689\pi$
$174$	17.9467	1.36054
$175$	8.07738	0.610593
$176$	4.97317	0.374867
$177$	17.9156	1.34662
$178$	−19.0383	−1.42698
$179$	−13.4941	−1.00860	−0.504298	−	0.863530i	$-0.668249\pi$
$179$	−13.4941	−1.00860	−0.504298	+	0.863530i	$0.668249\pi$
$180$	3.54962	0.264573
$181$	−5.09207	−0.378491	−0.189245	−	0.981930i	$-0.560604\pi$
$181$	−5.09207	−0.378491	−0.189245	+	0.981930i	$0.560604\pi$
$182$	−0.0372771	−0.00276316
$183$	−2.29453	−0.169617
$184$	−15.9362	−1.17483
$185$	−8.91571	−0.655496
$186$	15.2285	1.11661
$187$	−7.46608	−0.545974
$188$	3.61128	0.263380
$189$	4.24604	0.308854
$190$	−17.0121	−1.23419
$191$	17.0064	1.23054	0.615270	−	0.788316i	$-0.289047\pi$
$191$	17.0064	1.23054	0.615270	+	0.788316i	$0.289047\pi$
$192$	−3.39439	−0.244969
$193$	2.74492	0.197583	0.0987917	−	0.995108i	$-0.468502\pi$
$193$	2.74492	0.197583	0.0987917	+	0.995108i	$0.468502\pi$
$194$	15.0530	1.08074
$195$	−0.162569	−0.0116418
$196$	−5.38186	−0.384419
$197$	17.8287	1.27025	0.635123	−	0.772411i	$-0.280950\pi$
$197$	17.8287	1.27025	0.635123	+	0.772411i	$0.280950\pi$
$198$	1.80099	0.127991
$199$	−20.2305	−1.43410	−0.717051	−	0.697020i	$-0.754509\pi$
$199$	−20.2305	−1.43410	−0.717051	+	0.697020i	$0.754509\pi$
$200$	−21.0819	−1.49071
$201$	−16.7213	−1.17943
$202$	−1.20033	−0.0844552
$203$	−5.75942	−0.404232
$204$	−8.67458	−0.607342
$205$	−47.4955	−3.31723
$206$	17.5904	1.22558
$207$	−8.69525	−0.604362
$208$	0.146588	0.0101641
$209$	−2.54485	−0.176031
$210$	6.97507	0.481325
$211$	−6.30293	−0.433912	−0.216956	−	0.976181i	$-0.569613\pi$
$211$	−6.30293	−0.433912	−0.216956	+	0.976181i	$0.569613\pi$
$212$	4.44388	0.305207
$213$	−15.8108	−1.08334
$214$	11.2050	0.765958
$215$	14.0775	0.960074
$216$	−11.0821	−0.754043
$217$	−4.88709	−0.331757
$218$	27.8381	1.88543
$219$	6.74475	0.455768
$220$	3.31924	0.223783
$221$	−0.220069	−0.0148034
$222$	−5.25585	−0.352749
$223$	12.3818	0.829148	0.414574	−	0.910016i	$-0.363931\pi$
$223$	12.3818	0.829148	0.414574	+	0.910016i	$0.363931\pi$
$224$	−3.34577	−0.223548
$225$	−11.5029	−0.766859
$226$	2.34063	0.155696
$227$	−17.8125	−1.18226	−0.591129	−	0.806577i	$-0.701318\pi$
$227$	−17.8125	−1.18226	−0.591129	+	0.806577i	$0.701318\pi$
$228$	−2.95678	−0.195817
$229$	−3.84669	−0.254197	−0.127098	−	0.991890i	$-0.540566\pi$
$229$	−3.84669	−0.254197	−0.127098	+	0.991890i	$0.540566\pi$
$230$	−54.3543	−3.58402
$231$	1.04340	0.0686510
$232$	15.0320	0.986901
$233$	−6.45088	−0.422611	−0.211305	−	0.977420i	$-0.567771\pi$
$233$	−6.45088	−0.422611	−0.211305	+	0.977420i	$0.567771\pi$
$234$	0.0530857	0.00347032
$235$	−17.1426	−1.11826
$236$	−10.7819	−0.701845
$237$	8.92751	0.579904
$238$	9.44209	0.612040
$239$	26.2440	1.69758	0.848792	−	0.528726i	$-0.177330\pi$
$239$	26.2440	1.69758	0.848792	+	0.528726i	$0.177330\pi$
$240$	−27.4287	−1.77052
$241$	−24.1023	−1.55256	−0.776282	−	0.630386i	$-0.782897\pi$
$241$	−24.1023	−1.55256	−0.776282	+	0.630386i	$0.782897\pi$
$242$	1.68410	0.108258
$243$	−10.5044	−0.673858
$244$	1.38089	0.0884026
$245$	25.5475	1.63217
$246$	−27.9988	−1.78514
$247$	−0.0750116	−0.00477287
$248$	12.7553	0.809960
$249$	11.7553	0.744964
$250$	−38.4804	−2.43372
$251$	28.2614	1.78384	0.891922	−	0.452189i	$-0.149357\pi$
$251$	28.2614	1.78384	0.891922	+	0.452189i	$0.149357\pi$
$252$	−0.671524	−0.0423021
$253$	−8.13090	−0.511185
$254$	14.6703	0.920497
$255$	41.1780	2.57866
$256$	17.0496	1.06560
$257$	0.418334	0.0260950	0.0130475	−	0.999915i	$-0.495847\pi$
$257$	0.418334	0.0260950	0.0130475	+	0.999915i	$0.495847\pi$
$258$	8.29871	0.516655
$259$	1.68669	0.104806
$260$	0.0978372	0.00606760
$261$	8.20191	0.507685
$262$	1.68410	0.104044
$263$	22.4236	1.38270	0.691348	−	0.722522i	$-0.257017\pi$
$263$	22.4236	1.38270	0.691348	+	0.722522i	$0.257017\pi$
$264$	−2.72328	−0.167606
$265$	−21.0949	−1.29585
$266$	3.21839	0.197332
$267$	15.7074	0.961278
$268$	10.0632	0.614706
$269$	−14.6533	−0.893429	−0.446714	−	0.894677i	$-0.647406\pi$
$269$	−14.6533	−0.893429	−0.446714	+	0.894677i	$0.647406\pi$
$270$	−37.7983	−2.30033
$271$	−22.0074	−1.33685	−0.668427	−	0.743778i	$-0.733032\pi$
$271$	−22.0074	−1.33685	−0.668427	+	0.743778i	$0.733032\pi$
$272$	−37.1301	−2.25134
$273$	0.0307552	0.00186139
$274$	39.3567	2.37763
$275$	−10.7563	−0.648630
$276$	−9.44702	−0.568644
$277$	6.13367	0.368537	0.184268	−	0.982876i	$-0.441008\pi$
$277$	6.13367	0.368537	0.184268	+	0.982876i	$0.441008\pi$
$278$	−11.3579	−0.681201
$279$	6.95963	0.416662
$280$	5.84226	0.349142
$281$	−5.24122	−0.312665	−0.156333	−	0.987704i	$-0.549967\pi$
$281$	−5.24122	−0.312665	−0.156333	+	0.987704i	$0.549967\pi$
$282$	−10.1056	−0.601782
$283$	16.2335	0.964982	0.482491	−	0.875901i	$-0.339732\pi$
$283$	16.2335	0.964982	0.482491	+	0.875901i	$0.339732\pi$
$284$	9.51523	0.564625
$285$	14.0357	0.831405
$286$	0.0496403	0.00293529
$287$	8.98530	0.530386
$288$	4.76466	0.280760
$289$	38.7423	2.27896
$290$	51.2704	3.01070
$291$	−12.4194	−0.728037
$292$	−4.05912	−0.237542
$293$	19.3483	1.13034	0.565170	−	0.824974i	$-0.308811\pi$
$293$	19.3483	1.13034	0.565170	+	0.824974i	$0.308811\pi$
$294$	15.0604	0.878338
$295$	51.1816	2.97991
$296$	−4.40225	−0.255876
$297$	−5.65427	−0.328094
$298$	40.4982	2.34600
$299$	−0.239665	−0.0138602
$300$	−12.4974	−0.721537
$301$	−2.66320	−0.153504
$302$	−9.55008	−0.549545
$303$	0.990328	0.0568928
$304$	−12.6560	−0.725871
$305$	−6.55505	−0.375341
$306$	−13.4464	−0.768677
$307$	11.1521	0.636484	0.318242	−	0.948010i	$-0.396908\pi$
$307$	11.1521	0.636484	0.318242	+	0.948010i	$0.396908\pi$
$308$	−0.627940	−0.0357802
$309$	−14.5129	−0.825608
$310$	43.5049	2.47091
$311$	23.9162	1.35616	0.678082	−	0.734986i	$-0.262812\pi$
$311$	23.9162	1.35616	0.678082	+	0.734986i	$0.262812\pi$
$312$	−0.0802707	−0.00454444
$313$	−29.7319	−1.68055	−0.840274	−	0.542162i	$-0.817606\pi$
$313$	−29.7319	−1.68055	−0.840274	+	0.542162i	$0.817606\pi$
$314$	5.78131	0.326258
$315$	3.18771	0.179607
$316$	−5.37274	−0.302240
$317$	−24.3255	−1.36626	−0.683128	−	0.730299i	$-0.739381\pi$
$317$	−24.3255	−1.36626	−0.683128	+	0.730299i	$0.739381\pi$
$318$	−12.4355	−0.697351
$319$	7.66958	0.429414
$320$	−9.69715	−0.542087
$321$	−9.24460	−0.515983
$322$	10.2829	0.573042
$323$	19.0001	1.05719
$324$	−3.88678	−0.215932
$325$	−0.317051	−0.0175868
$326$	−4.16191	−0.230507
$327$	−22.9676	−1.27011
$328$	−23.4516	−1.29490
$329$	3.24308	0.178797
$330$	−9.28840	−0.511310
$331$	−5.93545	−0.326242	−0.163121	−	0.986606i	$-0.552156\pi$
$331$	−5.93545	−0.326242	−0.163121	+	0.986606i	$0.552156\pi$
$332$	−7.07458	−0.388268
$333$	−2.40200	−0.131629
$334$	8.39499	0.459354
$335$	−47.7695	−2.60993
$336$	5.18903	0.283085
$337$	13.6444	0.743259	0.371629	−	0.928381i	$-0.378799\pi$
$337$	13.6444	0.743259	0.371629	+	0.928381i	$0.378799\pi$
$338$	−21.8919	−1.19076
$339$	−1.93112	−0.104884
$340$	−24.7817	−1.34397
$341$	6.50793	0.352424
$342$	−4.58326	−0.247835
$343$	−10.0897	−0.544795
$344$	6.95093	0.374769
$345$	44.8447	2.41436
$346$	15.8301	0.851032
$347$	−19.0425	−1.02226	−0.511128	−	0.859504i	$-0.670772\pi$
$347$	−19.0425	−1.02226	−0.511128	+	0.859504i	$0.670772\pi$
$348$	8.91102	0.477681
$349$	−9.46006	−0.506385	−0.253193	−	0.967416i	$-0.581481\pi$
$349$	−9.46006	−0.506385	−0.253193	+	0.967416i	$0.581481\pi$
$350$	13.6031	0.727118
$351$	−0.166664	−0.00889587
$352$	4.45542	0.237474
$353$	−29.5916	−1.57500	−0.787502	−	0.616312i	$-0.788626\pi$
$353$	−29.5916	−1.57500	−0.787502	+	0.616312i	$0.788626\pi$
$354$	30.1717	1.60361
$355$	−45.1685	−2.39730
$356$	−9.45301	−0.501009
$357$	−7.79014	−0.412298
$358$	−22.7254	−1.20108
$359$	17.5193	0.924631	0.462316	−	0.886715i	$-0.347019\pi$
$359$	17.5193	0.924631	0.462316	+	0.886715i	$0.347019\pi$
$360$	−8.31988	−0.438496
$361$	−12.5237	−0.659143
$362$	−8.57557	−0.450722
$363$	−1.38946	−0.0729276
$364$	−0.0185090	−0.000970138 0
$365$	19.2685	1.00856
$366$	−3.86423	−0.201986
$367$	6.00731	0.313579	0.156789	−	0.987632i	$-0.449886\pi$
$367$	6.00731	0.313579	0.156789	+	0.987632i	$0.449886\pi$
$368$	−40.4363	−2.10789
$369$	−12.7958	−0.666125
$370$	−15.0150	−0.780591
$371$	3.99079	0.207191
$372$	7.56134	0.392037
$373$	20.3979	1.05616	0.528081	−	0.849194i	$-0.322912\pi$
$373$	20.3979	1.05616	0.528081	+	0.849194i	$0.322912\pi$
$374$	−12.5736	−0.650167
$375$	31.7480	1.63946
$376$	−8.46441	−0.436519
$377$	0.226067	0.0116430
$378$	7.15076	0.367796
$379$	−15.8943	−0.816437	−0.408218	−	0.912884i	$-0.633850\pi$
$379$	−15.8943	−0.816437	−0.408218	+	0.912884i	$0.633850\pi$
$380$	−8.44697	−0.433320
$381$	−12.1036	−0.620088
$382$	28.6405	1.46538
$383$	10.6404	0.543698	0.271849	−	0.962340i	$-0.412365\pi$
$383$	10.6404	0.543698	0.271849	+	0.962340i	$0.412365\pi$
$384$	−18.0977	−0.923546
$385$	2.98081	0.151916
$386$	4.62272	0.235290
$387$	3.79263	0.192790
$388$	7.47421	0.379446
$389$	−26.3363	−1.33530	−0.667652	−	0.744473i	$-0.732701\pi$
$389$	−26.3363	−1.33530	−0.667652	+	0.744473i	$0.732701\pi$
$390$	−0.273783	−0.0138635
$391$	60.7059	3.07003
$392$	12.6144	0.637125
$393$	−1.38946	−0.0700889
$394$	30.0254	1.51266
$395$	25.5042	1.28326
$396$	0.894241	0.0449373
$397$	−8.11689	−0.407375	−0.203688	−	0.979036i	$-0.565293\pi$
$397$	−8.11689	−0.407375	−0.203688	+	0.979036i	$0.565293\pi$
$398$	−34.0702	−1.70779
$399$	−2.65531	−0.132932
$400$	−53.4929	−2.67465
$401$	−3.38988	−0.169282	−0.0846412	−	0.996411i	$-0.526974\pi$
$401$	−3.38988	−0.169282	−0.0846412	+	0.996411i	$0.526974\pi$
$402$	−28.1603	−1.40451
$403$	0.191826	0.00955556
$404$	−0.595998	−0.0296520
$405$	18.4504	0.916809
$406$	−9.69945	−0.481376
$407$	−2.24610	−0.111335
$408$	20.3322	1.00659
$409$	17.3518	0.857992	0.428996	−	0.903306i	$-0.358868\pi$
$409$	17.3518	0.857992	0.428996	+	0.903306i	$0.358868\pi$
$410$	−79.9873	−3.95029
$411$	−32.4710	−1.60168
$412$	8.73412	0.430299
$413$	−9.68264	−0.476451
$414$	−14.6437	−0.719698
$415$	33.5828	1.64852
$416$	0.131327	0.00643884
$417$	9.37075	0.458888
$418$	−4.28579	−0.209625
$419$	35.5236	1.73544	0.867722	−	0.497050i	$-0.165583\pi$
$419$	35.5236	1.73544	0.867722	+	0.497050i	$0.165583\pi$
$420$	3.46331	0.168992
$421$	35.7239	1.74108	0.870539	−	0.492099i	$-0.163770\pi$
$421$	35.7239	1.74108	0.870539	+	0.492099i	$0.163770\pi$
$422$	−10.6148	−0.516720
$423$	−4.61842	−0.224555
$424$	−10.4159	−0.505841
$425$	80.3074	3.89548
$426$	−26.6270	−1.29008
$427$	1.24010	0.0600126
$428$	5.56358	0.268926
$429$	−0.0409554	−0.00197734
$430$	23.7079	1.14330
$431$	31.7617	1.52991	0.764954	−	0.644085i	$-0.222762\pi$
$431$	31.7617	1.52991	0.764954	+	0.644085i	$0.222762\pi$
$432$	−28.1196	−1.35291
$433$	1.53647	0.0738378	0.0369189	−	0.999318i	$-0.488246\pi$
$433$	1.53647	0.0738378	0.0369189	+	0.999318i	$0.488246\pi$
$434$	−8.23036	−0.395070
$435$	−42.3003	−2.02815
$436$	13.8224	0.661971
$437$	20.6919	0.989830
$438$	11.3589	0.542747
$439$	−20.9248	−0.998688	−0.499344	−	0.866404i	$-0.666426\pi$
$439$	−20.9248	−0.998688	−0.499344	+	0.866404i	$0.666426\pi$
$440$	−7.77989	−0.370892
$441$	6.88280	0.327752
$442$	−0.370618	−0.0176285
$443$	−15.2540	−0.724739	−0.362370	−	0.932034i	$-0.618032\pi$
$443$	−15.2540	−0.724739	−0.362370	+	0.932034i	$0.618032\pi$
$444$	−2.60967	−0.123849
$445$	44.8731	2.12719
$446$	20.8522	0.987382
$447$	−33.4128	−1.58037
$448$	1.83453	0.0866733
$449$	−5.26826	−0.248625	−0.124312	−	0.992243i	$-0.539672\pi$
$449$	−5.26826	−0.248625	−0.124312	+	0.992243i	$0.539672\pi$
$450$	−19.3720	−0.913207
$451$	−11.9653	−0.563426
$452$	1.16218	0.0546645
$453$	7.87922	0.370198
$454$	−29.9981	−1.40788
$455$	0.0878618	0.00411903
$456$	6.93034	0.324543
$457$	−0.359880	−0.0168345	−0.00841724	−	0.999965i	$-0.502679\pi$
$457$	−0.359880	−0.0168345	−0.00841724	+	0.999965i	$0.502679\pi$
$458$	−6.47823	−0.302708
$459$	42.2152	1.97044
$460$	−26.9884	−1.25834
$461$	−12.9497	−0.603128	−0.301564	−	0.953446i	$-0.597509\pi$
$461$	−12.9497	−0.603128	−0.301564	+	0.953446i	$0.597509\pi$
$462$	1.75720	0.0817523
$463$	−3.01804	−0.140260	−0.0701302	−	0.997538i	$-0.522341\pi$
$463$	−3.01804	−0.140260	−0.0701302	+	0.997538i	$0.522341\pi$
$464$	38.1421	1.77070
$465$	−35.8935	−1.66452
$466$	−10.8639	−0.503262
$467$	−13.7770	−0.637523	−0.318761	−	0.947835i	$-0.603267\pi$
$467$	−13.7770	−0.637523	−0.318761	+	0.947835i	$0.603267\pi$
$468$	0.0263585	0.00121842
$469$	9.03715	0.417297
$470$	−28.8699	−1.33167
$471$	−4.76983	−0.219782
$472$	25.2716	1.16322
$473$	3.54647	0.163067
$474$	15.0348	0.690573
$475$	27.3732	1.25597
$476$	4.68825	0.214886
$477$	−5.68322	−0.260217
$478$	44.1976	2.02155
$479$	25.5154	1.16583	0.582915	−	0.812533i	$-0.301912\pi$
$479$	25.5154	1.16583	0.582915	+	0.812533i	$0.301912\pi$
$480$	−24.5731	−1.12161
$481$	−0.0662056	−0.00301871
$482$	−40.5907	−1.84885
$483$	−8.48381	−0.386027
$484$	0.836201	0.0380092
$485$	−35.4799	−1.61106
$486$	−17.6905	−0.802458
$487$	8.51570	0.385883	0.192942	−	0.981210i	$-0.438197\pi$
$487$	8.51570	0.385883	0.192942	+	0.981210i	$0.438197\pi$
$488$	−3.23665	−0.146516
$489$	3.43375	0.155280
$490$	43.0247	1.94366
$491$	−2.41685	−0.109071	−0.0545355	−	0.998512i	$-0.517368\pi$
$491$	−2.41685	−0.109071	−0.0545355	+	0.998512i	$0.517368\pi$
$492$	−13.9021	−0.626757
$493$	−57.2616	−2.57893
$494$	−0.126327	−0.00568373
$495$	−4.24493	−0.190796
$496$	32.3650	1.45323
$497$	8.54508	0.383299
$498$	19.7972	0.887134
$499$	20.9033	0.935758	0.467879	−	0.883793i	$-0.345018\pi$
$499$	20.9033	0.935758	0.467879	+	0.883793i	$0.345018\pi$
$500$	−19.1065	−0.854471
$501$	−6.92623	−0.309441
$502$	47.5951	2.12427
$503$	14.4845	0.645834	0.322917	−	0.946427i	$-0.395337\pi$
$503$	14.4845	0.645834	0.322917	+	0.946427i	$0.395337\pi$
$504$	1.57397	0.0701103
$505$	2.82918	0.125897
$506$	−13.6933	−0.608740
$507$	18.0617	0.802150
$508$	7.28420	0.323184
$509$	−7.52897	−0.333716	−0.166858	−	0.985981i	$-0.553362\pi$
$509$	−7.52897	−0.333716	−0.166858	+	0.985981i	$0.553362\pi$
$510$	69.3479	3.07078
$511$	−3.64526	−0.161257
$512$	2.66315	0.117696
$513$	14.3893	0.635303
$514$	0.704517	0.0310749
$515$	−41.4606	−1.82697
$516$	4.12053	0.181396
$517$	−4.31867	−0.189935
$518$	2.84057	0.124807
$519$	−13.0605	−0.573293
$520$	−0.229319	−0.0100563
$521$	12.3773	0.542261	0.271130	−	0.962543i	$-0.412603\pi$
$521$	12.3773	0.542261	0.271130	+	0.962543i	$0.412603\pi$
$522$	13.8129	0.604572
$523$	25.6190	1.12024	0.560120	−	0.828412i	$-0.310755\pi$
$523$	25.6190	1.12024	0.560120	+	0.828412i	$0.310755\pi$
$524$	0.836201	0.0365296
$525$	−11.2232	−0.489820
$526$	37.7636	1.64657
$527$	−48.5887	−2.11656
$528$	−6.91001	−0.300719
$529$	43.1115	1.87441
$530$	−35.5260	−1.54315
$531$	13.7889	0.598388
$532$	1.59802	0.0692828
$533$	−0.352688	−0.0152766
$534$	26.4529	1.14473
$535$	−26.4101	−1.14181
$536$	−23.5869	−1.01880
$537$	18.7495	0.809099
$538$	−24.6777	−1.06393
$539$	6.43608	0.277222
$540$	−18.7679	−0.807640
$541$	−9.78657	−0.420757	−0.210379	−	0.977620i	$-0.567470\pi$
$541$	−9.78657	−0.420757	−0.210379	+	0.977620i	$0.567470\pi$
$542$	−37.0627	−1.59198
$543$	7.07522	0.303627
$544$	−33.2645	−1.42620
$545$	−65.6143	−2.81061
$546$	0.0517949	0.00221662
$547$	−5.64359	−0.241302	−0.120651	−	0.992695i	$-0.538498\pi$
$547$	−5.64359	−0.241302	−0.120651	+	0.992695i	$0.538498\pi$
$548$	19.5416	0.834778
$549$	−1.76601	−0.0753714
$550$	−18.1147	−0.772414
$551$	−19.5179	−0.831492
$552$	22.1427	0.942455
$553$	−4.82494	−0.205177
$554$	10.3297	0.438868
$555$	12.3880	0.525841
$556$	−5.63949	−0.239168
$557$	26.8857	1.13918	0.569591	−	0.821928i	$-0.307102\pi$
$557$	26.8857	1.13918	0.569591	+	0.821928i	$0.307102\pi$
$558$	11.7207	0.496178
$559$	0.104535	0.00442137
$560$	14.8241	0.626432
$561$	10.3738	0.437982
$562$	−8.82676	−0.372334
$563$	41.7127	1.75798	0.878990	−	0.476840i	$-0.158218\pi$
$563$	41.7127	1.75798	0.878990	+	0.476840i	$0.158218\pi$
$564$	−5.01772	−0.211284
$565$	−5.51685	−0.232096
$566$	27.3389	1.14914
$567$	−3.49049	−0.146587
$568$	−22.3026	−0.935795
$569$	−26.8781	−1.12679	−0.563394	−	0.826188i	$-0.690505\pi$
$569$	−26.8781	−1.12679	−0.563394	+	0.826188i	$0.690505\pi$
$570$	23.6376	0.990071
$571$	3.49729	0.146357	0.0731784	−	0.997319i	$-0.476686\pi$
$571$	3.49729	0.146357	0.0731784	+	0.997319i	$0.476686\pi$
$572$	0.0246477	0.00103057
$573$	−23.6297	−0.987144
$574$	15.1322	0.631605
$575$	87.4584	3.64727
$576$	−2.61252	−0.108855
$577$	−24.6575	−1.02651	−0.513254	−	0.858237i	$-0.671560\pi$
$577$	−24.6575	−1.02651	−0.513254	+	0.858237i	$0.671560\pi$
$578$	65.2460	2.71388
$579$	−3.81394	−0.158502
$580$	25.4571	1.05705
$581$	−6.35327	−0.263578
$582$	−20.9155	−0.866976
$583$	−5.31436	−0.220098
$584$	9.51409	0.393696
$585$	−0.125123	−0.00517319
$586$	32.5845	1.34605
$587$	17.1469	0.707728	0.353864	−	0.935297i	$-0.384868\pi$
$587$	17.1469	0.707728	0.353864	+	0.935297i	$0.384868\pi$
$588$	7.47787	0.308382
$589$	−16.5617	−0.682414
$590$	86.1950	3.54859
$591$	−24.7723	−1.01900
$592$	−11.1702	−0.459094
$593$	39.0316	1.60284	0.801419	−	0.598104i	$-0.204079\pi$
$593$	39.0316	1.60284	0.801419	+	0.598104i	$0.204079\pi$
$594$	−9.52237	−0.390708
$595$	−22.2550	−0.912365
$596$	20.1084	0.823674
$597$	28.1094	1.15044
$598$	−0.403620	−0.0165053
$599$	6.34578	0.259282	0.129641	−	0.991561i	$-0.458618\pi$
$599$	6.34578	0.259282	0.129641	+	0.991561i	$0.458618\pi$
$600$	29.2924	1.19586
$601$	−6.14397	−0.250618	−0.125309	−	0.992118i	$-0.539992\pi$
$601$	−6.14397	−0.250618	−0.125309	+	0.992118i	$0.539992\pi$
$602$	−4.48511	−0.182799
$603$	−12.8697	−0.524094
$604$	−4.74187	−0.192944
$605$	−3.96942	−0.161380
$606$	1.66781	0.0677503
$607$	−10.7443	−0.436096	−0.218048	−	0.975938i	$-0.569969\pi$
$607$	−10.7443	−0.436096	−0.218048	+	0.975938i	$0.569969\pi$
$608$	−11.3384	−0.459832
$609$	8.00247	0.324276
$610$	−11.0394	−0.446971
$611$	−0.127296	−0.00514986
$612$	−6.67647	−0.269880
$613$	−28.9450	−1.16908	−0.584538	−	0.811366i	$-0.698724\pi$
$613$	−28.9450	−1.16908	−0.584538	+	0.811366i	$0.698724\pi$
$614$	18.7813	0.757951
$615$	65.9930	2.66109
$616$	1.47182	0.0593012
$617$	−24.8291	−0.999583	−0.499791	−	0.866146i	$-0.666590\pi$
$617$	−24.8291	−0.999583	−0.499791	+	0.866146i	$0.666590\pi$
$618$	−24.4412	−0.983168
$619$	17.0455	0.685116	0.342558	−	0.939497i	$-0.388707\pi$
$619$	17.0455	0.685116	0.342558	+	0.939497i	$0.388707\pi$
$620$	21.6014	0.867531
$621$	45.9743	1.84488
$622$	40.2773	1.61497
$623$	−8.48920	−0.340113
$624$	−0.203678	−0.00815365
$625$	36.9166	1.47666
$626$	−50.0716	−2.00126
$627$	3.53597	0.141213
$628$	2.87057	0.114548
$629$	16.7695	0.668645
$630$	5.36842	0.213883
$631$	−14.2640	−0.567841	−0.283921	−	0.958848i	$-0.591635\pi$
$631$	−14.2640	−0.567841	−0.283921	+	0.958848i	$0.591635\pi$
$632$	12.5931	0.500925
$633$	8.75765	0.348086
$634$	−40.9666	−1.62699
$635$	−34.5779	−1.37218
$636$	−6.17458	−0.244838
$637$	0.189709	0.00751653
$638$	12.9164	0.511363
$639$	−12.1689	−0.481395
$640$	−51.7018	−2.04369
$641$	−33.1107	−1.30780	−0.653898	−	0.756583i	$-0.726867\pi$
$641$	−33.1107	−1.30780	−0.653898	+	0.756583i	$0.726867\pi$
$642$	−15.5689	−0.614454
$643$	−0.605314	−0.0238712	−0.0119356	−	0.999929i	$-0.503799\pi$
$643$	−0.605314	−0.0238712	−0.0119356	+	0.999929i	$0.503799\pi$
$644$	5.10572	0.201193
$645$	−19.5600	−0.770175
$646$	31.9981	1.25895
$647$	5.95333	0.234050	0.117025	−	0.993129i	$-0.462664\pi$
$647$	5.95333	0.234050	0.117025	+	0.993129i	$0.462664\pi$
$648$	9.11015	0.357881
$649$	12.8940	0.506132
$650$	−0.533946	−0.0209431
$651$	6.79040	0.266137
$652$	−2.06650	−0.0809302
$653$	−28.0011	−1.09577	−0.547884	−	0.836555i	$-0.684566\pi$
$653$	−28.0011	−1.09577	−0.547884	+	0.836555i	$0.684566\pi$
$654$	−38.6799	−1.51250
$655$	−3.96942	−0.155098
$656$	−59.5057	−2.32331
$657$	5.19116	0.202526
$658$	5.46168	0.212918
$659$	31.3738	1.22215	0.611074	−	0.791573i	$-0.290738\pi$
$659$	31.3738	1.22215	0.611074	+	0.791573i	$0.290738\pi$
$660$	−4.61194	−0.179519
$661$	−48.2922	−1.87835	−0.939174	−	0.343441i	$-0.888407\pi$
$661$	−48.2922	−1.87835	−0.939174	+	0.343441i	$0.888407\pi$
$662$	−9.99591	−0.388502
$663$	0.305776	0.0118754
$664$	16.5820	0.643505
$665$	−7.58573	−0.294162
$666$	−4.04521	−0.156749
$667$	−62.3605	−2.41461
$668$	4.16834	0.161278
$669$	−17.2040	−0.665145
$670$	−80.4488	−3.10801
$671$	−1.65139	−0.0637511
$672$	4.64880	0.179331
$673$	−10.2210	−0.393991	−0.196996	−	0.980404i	$-0.563118\pi$
$673$	−10.2210	−0.393991	−0.196996	+	0.980404i	$0.563118\pi$
$674$	22.9786	0.885103
$675$	60.8191	2.34093
$676$	−10.8699	−0.418073
$677$	18.0630	0.694217	0.347109	−	0.937825i	$-0.387164\pi$
$677$	18.0630	0.694217	0.347109	+	0.937825i	$0.387164\pi$
$678$	−3.25220	−0.124900
$679$	6.71215	0.257589
$680$	58.0853	2.22747
$681$	24.7497	0.948411
$682$	10.9600	0.419681
$683$	26.7346	1.02297	0.511485	−	0.859292i	$-0.329096\pi$
$683$	26.7346	1.02297	0.511485	+	0.859292i	$0.329096\pi$
$684$	−2.27571	−0.0870140
$685$	−92.7636	−3.54431
$686$	−16.9922	−0.648764
$687$	5.34482	0.203918
$688$	17.6372	0.672413
$689$	−0.156645	−0.00596770
$690$	75.5230	2.87511
$691$	15.4869	0.589151	0.294576	−	0.955628i	$-0.404822\pi$
$691$	15.4869	0.589151	0.294576	+	0.955628i	$0.404822\pi$
$692$	7.86007	0.298795
$693$	0.803065	0.0305059
$694$	−32.0696	−1.21734
$695$	26.7705	1.01546
$696$	−20.8864	−0.791696
$697$	89.3342	3.38377
$698$	−15.9317	−0.603024
$699$	8.96322	0.339020
$700$	6.75432	0.255289
$701$	18.7885	0.709632	0.354816	−	0.934936i	$-0.384544\pi$
$701$	18.7885	0.709632	0.354816	+	0.934936i	$0.384544\pi$
$702$	−0.280680	−0.0105936
$703$	5.71599	0.215583
$704$	−2.44296	−0.0920726
$705$	23.8190	0.897074
$706$	−49.8353	−1.87558
$707$	−0.535231	−0.0201294
$708$	14.9811	0.563023
$709$	−19.7231	−0.740716	−0.370358	−	0.928889i	$-0.620765\pi$
$709$	−19.7231	−0.740716	−0.370358	+	0.928889i	$0.620765\pi$
$710$	−76.0684	−2.85480
$711$	6.87113	0.257688
$712$	22.1567	0.830359
$713$	−52.9153	−1.98169
$714$	−13.1194	−0.490981
$715$	−0.117002	−0.00437562
$716$	−11.2838	−0.421695
$717$	−36.4650	−1.36181
$718$	29.5042	1.10109
$719$	−13.5035	−0.503596	−0.251798	−	0.967780i	$-0.581022\pi$
$719$	−13.5035	−0.503596	−0.251798	+	0.967780i	$0.581022\pi$
$720$	−21.1108	−0.786752
$721$	7.84360	0.292111
$722$	−21.0912	−0.784934
$723$	33.4891	1.24547
$724$	−4.25800	−0.158247
$725$	−82.4963	−3.06384
$726$	−2.33999	−0.0868451
$727$	27.3178	1.01316	0.506580	−	0.862193i	$-0.330909\pi$
$727$	27.3178	1.01316	0.506580	+	0.862193i	$0.330909\pi$
$728$	0.0433830	0.00160788
$729$	28.5399	1.05703
$730$	32.4501	1.20103
$731$	−26.4782	−0.979333
$732$	−1.91869	−0.0709169
$733$	8.51583	0.314539	0.157270	−	0.987556i	$-0.449731\pi$
$733$	8.51583	0.314539	0.157270	+	0.987556i	$0.449731\pi$
$734$	10.1169	0.373422
$735$	−35.4972	−1.30933
$736$	−36.2265	−1.33533
$737$	−12.0344	−0.443292
$738$	−21.5495	−0.793248
$739$	−33.5192	−1.23302	−0.616512	−	0.787345i	$-0.711455\pi$
$739$	−33.5192	−1.23302	−0.616512	+	0.787345i	$0.711455\pi$
$740$	−7.45533	−0.274063
$741$	0.104225	0.00382882
$742$	6.72089	0.246732
$743$	−8.49214	−0.311546	−0.155773	−	0.987793i	$-0.549787\pi$
$743$	−8.49214	−0.311546	−0.155773	+	0.987793i	$0.549787\pi$
$744$	−17.7229	−0.649752
$745$	−95.4541	−3.49717
$746$	34.3521	1.25772
$747$	9.04760	0.331034
$748$	−6.24314	−0.228272
$749$	4.99632	0.182562
$750$	53.4669	1.95234
$751$	−6.45090	−0.235397	−0.117698	−	0.993049i	$-0.537552\pi$
$751$	−6.45090	−0.235397	−0.117698	+	0.993049i	$0.537552\pi$
$752$	−21.4775	−0.783204
$753$	−39.2680	−1.43101
$754$	0.380720	0.0138650
$755$	22.5095	0.819204
$756$	3.55054	0.129132
$757$	38.4773	1.39848	0.699241	−	0.714886i	$-0.253522\pi$
$757$	38.4773	1.39848	0.699241	+	0.714886i	$0.253522\pi$
$758$	−26.7677	−0.972246
$759$	11.2975	0.410075
$760$	19.7987	0.718174
$761$	−42.7987	−1.55145	−0.775725	−	0.631071i	$-0.782616\pi$
$761$	−42.7987	−1.55145	−0.775725	+	0.631071i	$0.782616\pi$
$762$	−20.3838	−0.738426
$763$	12.4130	0.449383
$764$	14.2208	0.514490
$765$	31.6930	1.14586
$766$	17.9195	0.647457
$767$	0.380060	0.0137232
$768$	−23.6896	−0.854826
$769$	48.0925	1.73426	0.867129	−	0.498083i	$-0.165963\pi$
$769$	48.0925	1.73426	0.867129	+	0.498083i	$0.165963\pi$
$770$	5.01999	0.180908
$771$	−0.581257	−0.0209335
$772$	2.29530	0.0826098
$773$	−2.02099	−0.0726900	−0.0363450	−	0.999339i	$-0.511572\pi$
$773$	−2.02099	−0.0726900	−0.0363450	+	0.999339i	$0.511572\pi$
$774$	6.38718	0.229582
$775$	−70.0013	−2.51452
$776$	−17.5187	−0.628883
$777$	−2.34359	−0.0840758
$778$	−44.3531	−1.59013
$779$	30.4501	1.09099
$780$	−0.135941	−0.00486745
$781$	−11.3791	−0.407177
$782$	102.235	3.65592
$783$	−43.3658	−1.54977
$784$	32.0077	1.14313
$785$	−13.6265	−0.486351
$786$	−2.33999	−0.0834646
$787$	−2.87767	−0.102578	−0.0512889	−	0.998684i	$-0.516333\pi$
$787$	−2.87767	−0.102578	−0.0512889	+	0.998684i	$0.516333\pi$
$788$	14.9084	0.531090
$789$	−31.1566	−1.10920
$790$	42.9517	1.52815
$791$	1.04369	0.0371093
$792$	−2.09599	−0.0744779
$793$	−0.0486760	−0.00172853
$794$	−13.6697	−0.485119
$795$	29.3105	1.03954
$796$	−16.9168	−0.599599
$797$	−16.1321	−0.571429	−0.285714	−	0.958315i	$-0.592231\pi$
$797$	−16.1321	−0.571429	−0.285714	+	0.958315i	$0.592231\pi$
$798$	−4.47182	−0.158301
$799$	32.2435	1.14069
$800$	−47.9238	−1.69436
$801$	12.0893	0.427156
$802$	−5.70890	−0.201588
$803$	4.85423	0.171302
$804$	−13.9823	−0.493119
$805$	−24.2367	−0.854231
$806$	0.323055	0.0113791
$807$	20.3602	0.716712
$808$	1.39695	0.0491444
$809$	−5.28791	−0.185913	−0.0929564	−	0.995670i	$-0.529632\pi$
$809$	−5.28791	−0.185913	−0.0929564	+	0.995670i	$0.529632\pi$
$810$	31.0724	1.09177
$811$	−22.9535	−0.806006	−0.403003	−	0.915199i	$-0.632034\pi$
$811$	−22.9535	−0.806006	−0.403003	+	0.915199i	$0.632034\pi$
$812$	−4.81603	−0.169010
$813$	30.5783	1.07243
$814$	−3.78266	−0.132582
$815$	9.80959	0.343615
$816$	51.5906	1.80603
$817$	−9.02526	−0.315754
$818$	29.2222	1.02173
$819$	0.0236710	0.000827132 0
$820$	−39.7158	−1.38694
$821$	8.07760	0.281910	0.140955	−	0.990016i	$-0.454983\pi$
$821$	8.07760	0.281910	0.140955	+	0.990016i	$0.454983\pi$
$822$	−54.6845	−1.90734
$823$	0.109631	0.00382151	0.00191076	−	0.999998i	$-0.499392\pi$
$823$	0.109631	0.00382151	0.00191076	+	0.999998i	$0.499392\pi$
$824$	−20.4717	−0.713166
$825$	14.9454	0.520333
$826$	−16.3066	−0.567378
$827$	−22.2669	−0.774298	−0.387149	−	0.922017i	$-0.626540\pi$
$827$	−22.2669	−0.774298	−0.387149	+	0.922017i	$0.626540\pi$
$828$	−7.27098	−0.252684
$829$	36.9782	1.28430	0.642152	−	0.766577i	$-0.278042\pi$
$829$	36.9782	1.28430	0.642152	+	0.766577i	$0.278042\pi$
$830$	56.5569	1.96312
$831$	−8.52247	−0.295641
$832$	−0.0720083	−0.00249644
$833$	−48.0523	−1.66491
$834$	15.7813	0.546462
$835$	−19.7870	−0.684756
$836$	−2.12801	−0.0735988
$837$	−36.7976	−1.27191
$838$	59.8255	2.06664
$839$	2.88260	0.0995185	0.0497592	−	0.998761i	$-0.484155\pi$
$839$	2.88260	0.0995185	0.0497592	+	0.998761i	$0.484155\pi$
$840$	−8.11757	−0.280083
$841$	29.8224	1.02836
$842$	60.1628	2.07335
$843$	7.28246	0.250821
$844$	−5.27052	−0.181419
$845$	51.5990	1.77506
$846$	−7.77790	−0.267410
$847$	0.750944	0.0258027
$848$	−26.4292	−0.907583
$849$	−22.5558	−0.774112
$850$	135.246	4.63890
$851$	18.2628	0.626041
$852$	−13.2210	−0.452944
$853$	9.59044	0.328371	0.164185	−	0.986430i	$-0.447501\pi$
$853$	9.59044	0.328371	0.164185	+	0.986430i	$0.447501\pi$
$854$	2.08845	0.0714654
$855$	10.8027	0.369446
$856$	−13.0404	−0.445710
$857$	21.2609	0.726257	0.363129	−	0.931739i	$-0.381709\pi$
$857$	21.2609	0.726257	0.363129	+	0.931739i	$0.381709\pi$
$858$	−0.0689731	−0.00235470
$859$	10.5033	0.358368	0.179184	−	0.983816i	$-0.442654\pi$
$859$	10.5033	0.358368	0.179184	+	0.983816i	$0.442654\pi$
$860$	11.7716	0.401408
$861$	−12.4847	−0.425477
$862$	53.4900	1.82188
$863$	31.0289	1.05624	0.528118	−	0.849171i	$-0.322898\pi$
$863$	31.0289	1.05624	0.528118	+	0.849171i	$0.322898\pi$
$864$	−25.1921	−0.857053
$865$	−37.3115	−1.26863
$866$	2.58757	0.0879291
$867$	−53.8308	−1.82819
$868$	−4.08659	−0.138708
$869$	6.42517	0.217959
$870$	−71.2381	−2.41520
$871$	−0.354723	−0.0120193
$872$	−32.3979	−1.09713
$873$	−9.55868	−0.323512
$874$	34.8474	1.17873
$875$	−17.1585	−0.580062
$876$	5.63997	0.190557
$877$	−15.7643	−0.532323	−0.266161	−	0.963928i	$-0.585755\pi$
$877$	−15.7643	−0.532323	−0.266161	+	0.963928i	$0.585755\pi$
$878$	−35.2396	−1.18928
$879$	−26.8836	−0.906763
$880$	−19.7406	−0.665456
$881$	−51.4818	−1.73446	−0.867232	−	0.497904i	$-0.834103\pi$
$881$	−51.4818	−1.73446	−0.867232	+	0.497904i	$0.834103\pi$
$882$	11.5913	0.390301
$883$	19.6902	0.662629	0.331315	−	0.943520i	$-0.392508\pi$
$883$	19.6902	0.662629	0.331315	+	0.943520i	$0.392508\pi$
$884$	−0.184022	−0.00618932
$885$	−71.1146	−2.39049
$886$	−25.6893	−0.863049
$887$	−52.2487	−1.75434	−0.877170	−	0.480180i	$-0.840571\pi$
$887$	−52.2487	−1.75434	−0.877170	+	0.480180i	$0.840571\pi$
$888$	6.11675	0.205265
$889$	6.54151	0.219395
$890$	75.5710	2.53315
$891$	4.64814	0.155719
$892$	10.3537	0.346667
$893$	10.9904	0.367779
$894$	−56.2705	−1.88197
$895$	53.5637	1.79044
$896$	9.78107	0.326762
$897$	0.333004	0.0111187
$898$	−8.87229	−0.296072
$899$	49.9131	1.66469
$900$	−9.61873	−0.320624
$901$	39.6774	1.32185
$902$	−20.1509	−0.670951
$903$	3.70041	0.123142
$904$	−2.72402	−0.0905995
$905$	20.2126	0.671889
$906$	13.2694	0.440847
$907$	−7.95009	−0.263978	−0.131989	−	0.991251i	$-0.542136\pi$
$907$	−7.95009	−0.263978	−0.131989	+	0.991251i	$0.542136\pi$
$908$	−14.8948	−0.494303
$909$	0.762215	0.0252811
$910$	0.147968	0.00490510
$911$	3.64911	0.120900	0.0604502	−	0.998171i	$-0.480746\pi$
$911$	3.64911	0.120900	0.0604502	+	0.998171i	$0.480746\pi$
$912$	17.5850	0.582296
$913$	8.46038	0.279998
$914$	−0.606075	−0.0200472
$915$	9.10797	0.301100
$916$	−3.21661	−0.106280
$917$	0.750944	0.0247983
$918$	71.0947	2.34648
$919$	−48.5324	−1.60093	−0.800467	−	0.599376i	$-0.795415\pi$
$919$	−48.5324	−1.60093	−0.800467	+	0.599376i	$0.795415\pi$
$920$	63.2575	2.08554
$921$	−15.4954	−0.510590
$922$	−21.8086	−0.718229
$923$	−0.335409	−0.0110401
$924$	0.872496	0.0287030
$925$	24.1597	0.794367
$926$	−5.08270	−0.167028
$927$	−11.1700	−0.366870
$928$	34.1711	1.12172
$929$	−55.1697	−1.81006	−0.905030	−	0.425348i	$-0.860152\pi$
$929$	−55.1697	−1.81006	−0.905030	+	0.425348i	$0.860152\pi$
$930$	−60.4483	−1.98218
$931$	−16.3789	−0.536796
$932$	−5.39423	−0.176694
$933$	−33.2305	−1.08792
$934$	−23.2018	−0.759188
$935$	29.6360	0.969201
$936$	−0.0617811	−0.00201938
$937$	−21.2649	−0.694693	−0.347347	−	0.937737i	$-0.612917\pi$
$937$	−21.2649	−0.694693	−0.347347	+	0.937737i	$0.612917\pi$
$938$	15.2195	0.496934
$939$	41.3113	1.34814
$940$	−14.3347	−0.467546
$941$	41.4316	1.35063	0.675317	−	0.737528i	$-0.264007\pi$
$941$	41.4316	1.35063	0.675317	+	0.737528i	$0.264007\pi$
$942$	−8.03288	−0.261725
$943$	97.2890	3.16817
$944$	64.1238	2.08705
$945$	−16.8543	−0.548271
$946$	5.97263	0.194187
$947$	28.4166	0.923417	0.461708	−	0.887032i	$-0.347237\pi$
$947$	28.4166	0.923417	0.461708	+	0.887032i	$0.347237\pi$
$948$	7.46519	0.242458
$949$	0.143082	0.00464465
$950$	46.0993	1.49566
$951$	33.7992	1.09602
$952$	−10.9887	−0.356146
$953$	−39.6929	−1.28578	−0.642889	−	0.765960i	$-0.722264\pi$
$953$	−39.6929	−1.28578	−0.642889	+	0.765960i	$0.722264\pi$
$954$	−9.57113	−0.309877
$955$	−67.5056	−2.18443
$956$	21.9453	0.709762
$957$	−10.6565	−0.344477
$958$	42.9706	1.38832
$959$	17.5492	0.566694
$960$	13.4738	0.434864
$961$	11.3531	0.366230
$962$	−0.111497	−0.00359481
$963$	−7.11519	−0.229284
$964$	−20.1543	−0.649128
$965$	−10.8957	−0.350746
$966$	−14.2876	−0.459696
$967$	29.6134	0.952303	0.476152	−	0.879363i	$-0.342031\pi$
$967$	29.6134	0.952303	0.476152	+	0.879363i	$0.342031\pi$
$968$	−1.95996	−0.0629954
$969$	−26.3998	−0.848083
$970$	−59.7517	−1.91851
$971$	31.9257	1.02454	0.512272	−	0.858823i	$-0.328804\pi$
$971$	31.9257	1.02454	0.512272	+	0.858823i	$0.328804\pi$
$972$	−8.78381	−0.281741
$973$	−5.06450	−0.162360
$974$	14.3413	0.459525
$975$	0.440529	0.0141082
$976$	−8.21263	−0.262880
$977$	32.4837	1.03925	0.519623	−	0.854396i	$-0.326072\pi$
$977$	32.4837	1.03925	0.519623	+	0.854396i	$0.326072\pi$
$978$	5.78279	0.184913
$979$	11.3047	0.361300
$980$	21.3629	0.682412
$981$	−17.6772	−0.564391
$982$	−4.07023	−0.129886
$983$	−39.2093	−1.25058	−0.625291	−	0.780391i	$-0.715020\pi$
$983$	−39.2093	−1.25058	−0.625291	+	0.780391i	$0.715020\pi$
$984$	32.5849	1.03877
$985$	−70.7698	−2.25491
$986$	−96.4345	−3.07110
$987$	−4.50612	−0.143431
$988$	−0.0627248	−0.00199554
$989$	−28.8360	−0.916932
$990$	−7.14890	−0.227207
$991$	2.50141	0.0794598	0.0397299	−	0.999210i	$-0.487350\pi$
$991$	2.50141	0.0794598	0.0397299	+	0.999210i	$0.487350\pi$
$992$	28.9955	0.920609
$993$	8.24705	0.261712
$994$	14.3908	0.456448
$995$	80.3034	2.54579
$996$	9.82983	0.311470
$997$	−35.8062	−1.13400	−0.566998	−	0.823720i	$-0.691895\pi$
$997$	−35.8062	−1.13400	−0.566998	+	0.823720i	$0.691895\pi$
$998$	35.2032	1.11434
$999$	12.7000	0.401812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.23	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.23	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+1.68410 q^{2} -1.38946 q^{3} +0.836201 q^{4} -3.96942 q^{5} -2.33999 q^{6} +0.750944 q^{7} -1.95996 q^{8} -1.06941 q^{9} +O(q^{10})\)	\(q+1.68410 q^{2} -1.38946 q^{3} +0.836201 q^{4} -3.96942 q^{5} -2.33999 q^{6} +0.750944 q^{7} -1.95996 q^{8} -1.06941 q^{9} -6.68491 q^{10} -1.00000 q^{11} -1.16187 q^{12} -0.0294758 q^{13} +1.26467 q^{14} +5.51534 q^{15} -4.97317 q^{16} +7.46608 q^{17} -1.80099 q^{18} +2.54485 q^{19} -3.31924 q^{20} -1.04340 q^{21} -1.68410 q^{22} +8.13090 q^{23} +2.72328 q^{24} +10.7563 q^{25} -0.0496403 q^{26} +5.65427 q^{27} +0.627940 q^{28} -7.66958 q^{29} +9.28840 q^{30} -6.50793 q^{31} -4.45542 q^{32} +1.38946 q^{33} +12.5736 q^{34} -2.98081 q^{35} -0.894241 q^{36} +2.24610 q^{37} +4.28579 q^{38} +0.0409554 q^{39} +7.77989 q^{40} +11.9653 q^{41} -1.75720 q^{42} -3.54647 q^{43} -0.836201 q^{44} +4.24493 q^{45} +13.6933 q^{46} +4.31867 q^{47} +6.91001 q^{48} -6.43608 q^{49} +18.1147 q^{50} -10.3738 q^{51} -0.0246477 q^{52} +5.31436 q^{53} +9.52237 q^{54} +3.96942 q^{55} -1.47182 q^{56} -3.53597 q^{57} -12.9164 q^{58} -12.8940 q^{59} +4.61194 q^{60} +1.65139 q^{61} -10.9600 q^{62} -0.803065 q^{63} +2.44296 q^{64} +0.117002 q^{65} +2.33999 q^{66} +12.0344 q^{67} +6.24314 q^{68} -11.2975 q^{69} -5.01999 q^{70} +11.3791 q^{71} +2.09599 q^{72} -4.85423 q^{73} +3.78266 q^{74} -14.9454 q^{75} +2.12801 q^{76} -0.750944 q^{77} +0.0689731 q^{78} -6.42517 q^{79} +19.7406 q^{80} -4.64814 q^{81} +20.1509 q^{82} -8.46038 q^{83} -0.872496 q^{84} -29.6360 q^{85} -5.97263 q^{86} +10.6565 q^{87} +1.95996 q^{88} -11.3047 q^{89} +7.14890 q^{90} -0.0221347 q^{91} +6.79907 q^{92} +9.04249 q^{93} +7.27309 q^{94} -10.1016 q^{95} +6.19061 q^{96} +8.93829 q^{97} -10.8390 q^{98} +1.06941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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