LMFDB - Embedded newform 1931.2.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1931,2,Mod(1,1931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1931, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1931 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1931.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:	$15.4191126303$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	1931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75459 q^{2} +1.21931 q^{3} +5.58779 q^{4} -2.23120 q^{5} -3.35871 q^{6} +1.87951 q^{7} -9.88291 q^{8} -1.51327 q^{9} +O(q^{10})$	\(q-2.75459 q^{2} +1.21931 q^{3} +5.58779 q^{4} -2.23120 q^{5} -3.35871 q^{6} +1.87951 q^{7} -9.88291 q^{8} -1.51327 q^{9} +6.14605 q^{10} +0.0515300 q^{11} +6.81327 q^{12} +4.60264 q^{13} -5.17729 q^{14} -2.72053 q^{15} +16.0478 q^{16} +3.18322 q^{17} +4.16846 q^{18} +7.28569 q^{19} -12.4675 q^{20} +2.29171 q^{21} -0.141944 q^{22} -5.85589 q^{23} -12.0504 q^{24} -0.0217556 q^{25} -12.6784 q^{26} -5.50310 q^{27} +10.5023 q^{28} +7.41208 q^{29} +7.49396 q^{30} -6.32001 q^{31} -24.4394 q^{32} +0.0628312 q^{33} -8.76848 q^{34} -4.19356 q^{35} -8.45586 q^{36} -2.35397 q^{37} -20.0691 q^{38} +5.61206 q^{39} +22.0507 q^{40} +6.36674 q^{41} -6.31274 q^{42} +0.150994 q^{43} +0.287939 q^{44} +3.37641 q^{45} +16.1306 q^{46} +2.57146 q^{47} +19.5673 q^{48} -3.46743 q^{49} +0.0599280 q^{50} +3.88134 q^{51} +25.7186 q^{52} +7.83058 q^{53} +15.1588 q^{54} -0.114974 q^{55} -18.5750 q^{56} +8.88354 q^{57} -20.4173 q^{58} -12.6470 q^{59} -15.2018 q^{60} -13.3884 q^{61} +17.4091 q^{62} -2.84422 q^{63} +35.2251 q^{64} -10.2694 q^{65} -0.173074 q^{66} +4.49176 q^{67} +17.7872 q^{68} -7.14017 q^{69} +11.5516 q^{70} +11.3567 q^{71} +14.9556 q^{72} +14.7321 q^{73} +6.48422 q^{74} -0.0265270 q^{75} +40.7109 q^{76} +0.0968512 q^{77} -15.4589 q^{78} +10.8746 q^{79} -35.8059 q^{80} -2.17018 q^{81} -17.5378 q^{82} +0.112792 q^{83} +12.8056 q^{84} -7.10239 q^{85} -0.415927 q^{86} +9.03766 q^{87} -0.509266 q^{88} +11.7583 q^{89} -9.30065 q^{90} +8.65071 q^{91} -32.7215 q^{92} -7.70608 q^{93} -7.08334 q^{94} -16.2558 q^{95} -29.7993 q^{96} -3.05328 q^{97} +9.55137 q^{98} -0.0779790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9}+O(q^{10}) $ 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9} + 14 q^{10} + 29 q^{11} + 15 q^{12} + 41 q^{13} + 4 q^{14} + 22 q^{15} + 187 q^{16} + 9 q^{17} + 11 q^{18} + 34 q^{19} + 42 q^{20} + 72 q^{21} + 17 q^{22} + 19 q^{23} + 33 q^{24} + 172 q^{25} + 28 q^{26} + 36 q^{27} + 47 q^{28} + 68 q^{29} + q^{30} + 76 q^{31} + 9 q^{32} + 8 q^{33} + 50 q^{34} + 7 q^{35} + 198 q^{36} + 141 q^{37} - 13 q^{38} + 42 q^{39} + 32 q^{40} + 35 q^{41} - 46 q^{42} + 45 q^{43} + 67 q^{44} + 106 q^{45} + 86 q^{46} - 5 q^{47} + 7 q^{48} + 203 q^{49} + 4 q^{50} + 5 q^{51} + 30 q^{52} + 47 q^{53} + 20 q^{54} + 11 q^{55} - 4 q^{56} + 19 q^{57} + 92 q^{58} + 30 q^{59} + 35 q^{60} + 153 q^{61} - 20 q^{62} + 19 q^{63} + 276 q^{64} - 7 q^{65} - 18 q^{66} + 39 q^{67} - 7 q^{68} + 55 q^{69} - 8 q^{70} + 47 q^{71} - 4 q^{72} + 86 q^{73} + 9 q^{74} + 11 q^{75} + 50 q^{76} + 15 q^{77} - 15 q^{78} + 89 q^{79} + 26 q^{80} + 201 q^{81} - 9 q^{82} - 15 q^{83} + 60 q^{84} + 239 q^{85} + 13 q^{86} - 22 q^{87} + 5 q^{88} + 14 q^{89} - 85 q^{90} + 58 q^{91} - 4 q^{92} + 86 q^{93} + 21 q^{94} - 10 q^{95} + 6 q^{96} + 46 q^{97} - 68 q^{98} + 100 q^{99}+O(q^{100}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9 + 14 * q^10 + 29 * q^11 + 15 * q^12 + 41 * q^13 + 4 * q^14 + 22 * q^15 + 187 * q^16 + 9 * q^17 + 11 * q^18 + 34 * q^19 + 42 * q^20 + 72 * q^21 + 17 * q^22 + 19 * q^23 + 33 * q^24 + 172 * q^25 + 28 * q^26 + 36 * q^27 + 47 * q^28 + 68 * q^29 + q^30 + 76 * q^31 + 9 * q^32 + 8 * q^33 + 50 * q^34 + 7 * q^35 + 198 * q^36 + 141 * q^37 - 13 * q^38 + 42 * q^39 + 32 * q^40 + 35 * q^41 - 46 * q^42 + 45 * q^43 + 67 * q^44 + 106 * q^45 + 86 * q^46 - 5 * q^47 + 7 * q^48 + 203 * q^49 + 4 * q^50 + 5 * q^51 + 30 * q^52 + 47 * q^53 + 20 * q^54 + 11 * q^55 - 4 * q^56 + 19 * q^57 + 92 * q^58 + 30 * q^59 + 35 * q^60 + 153 * q^61 - 20 * q^62 + 19 * q^63 + 276 * q^64 - 7 * q^65 - 18 * q^66 + 39 * q^67 - 7 * q^68 + 55 * q^69 - 8 * q^70 + 47 * q^71 - 4 * q^72 + 86 * q^73 + 9 * q^74 + 11 * q^75 + 50 * q^76 + 15 * q^77 - 15 * q^78 + 89 * q^79 + 26 * q^80 + 201 * q^81 - 9 * q^82 - 15 * q^83 + 60 * q^84 + 239 * q^85 + 13 * q^86 - 22 * q^87 + 5 * q^88 + 14 * q^89 - 85 * q^90 + 58 * q^91 - 4 * q^92 + 86 * q^93 + 21 * q^94 - 10 * q^95 + 6 * q^96 + 46 * q^97 - 68 * q^98 + 100 * 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 $

$2$	−2.75459	−1.94779	−0.973896	−	0.226994i	$-0.927110\pi$
$2$	−2.75459	−1.94779	−0.973896	+	0.226994i	$0.927110\pi$
$3$	1.21931	0.703971	0.351985	−	0.936005i	$-0.385507\pi$
$3$	1.21931	0.703971	0.351985	+	0.936005i	$0.385507\pi$
$4$	5.58779	2.79390
$5$	−2.23120	−0.997822	−0.498911	−	0.866653i	$-0.666267\pi$
$5$	−2.23120	−0.997822	−0.498911	+	0.866653i	$0.666267\pi$
$6$	−3.35871	−1.37119
$7$	1.87951	0.710389	0.355194	−	0.934792i	$-0.384415\pi$
$7$	1.87951	0.710389	0.355194	+	0.934792i	$0.384415\pi$
$8$	−9.88291	−3.49414
$9$	−1.51327	−0.504425
$10$	6.14605	1.94355
$11$	0.0515300	0.0155369	0.00776843	−	0.999970i	$-0.497527\pi$
$11$	0.0515300	0.0155369	0.00776843	+	0.999970i	$0.497527\pi$
$12$	6.81327	1.96682
$13$	4.60264	1.27654	0.638271	−	0.769812i	$-0.279650\pi$
$13$	4.60264	1.27654	0.638271	+	0.769812i	$0.279650\pi$
$14$	−5.17729	−1.38369
$15$	−2.72053	−0.702438
$16$	16.0478	4.01196
$17$	3.18322	0.772044	0.386022	−	0.922490i	$-0.373849\pi$
$17$	3.18322	0.772044	0.386022	+	0.922490i	$0.373849\pi$
$18$	4.16846	0.982515
$19$	7.28569	1.67145	0.835726	−	0.549147i	$-0.185047\pi$
$19$	7.28569	1.67145	0.835726	+	0.549147i	$0.185047\pi$
$20$	−12.4675	−2.78781
$21$	2.29171	0.500093
$22$	−0.141944	−0.0302626
$23$	−5.85589	−1.22104	−0.610519	−	0.792001i	$-0.709039\pi$
$23$	−5.85589	−1.22104	−0.610519	+	0.792001i	$0.709039\pi$
$24$	−12.0504	−2.45977
$25$	−0.0217556	−0.00435113
$26$	−12.6784	−2.48644
$27$	−5.50310	−1.05907
$28$	10.5023	1.98475
$29$	7.41208	1.37639	0.688195	−	0.725526i	$-0.258403\pi$
$29$	7.41208	1.37639	0.688195	+	0.725526i	$0.258403\pi$
$30$	7.49396	1.36820
$31$	−6.32001	−1.13511	−0.567554	−	0.823336i	$-0.692110\pi$
$31$	−6.32001	−1.13511	−0.567554	+	0.823336i	$0.692110\pi$
$32$	−24.4394	−4.32032
$33$	0.0628312	0.0109375
$34$	−8.76848	−1.50378
$35$	−4.19356	−0.708842
$36$	−8.45586	−1.40931
$37$	−2.35397	−0.386989	−0.193495	−	0.981101i	$-0.561982\pi$
$37$	−2.35397	−0.386989	−0.193495	+	0.981101i	$0.561982\pi$
$38$	−20.0691	−3.25564
$39$	5.61206	0.898649
$40$	22.0507	3.48653
$41$	6.36674	0.994317	0.497159	−	0.867660i	$-0.334377\pi$
$41$	6.36674	0.994317	0.497159	+	0.867660i	$0.334377\pi$
$42$	−6.31274	−0.974078
$43$	0.150994	0.0230263	0.0115132	−	0.999934i	$-0.496335\pi$
$43$	0.150994	0.0230263	0.0115132	+	0.999934i	$0.496335\pi$
$44$	0.287939	0.0434084
$45$	3.37641	0.503326
$46$	16.1306	2.37833
$47$	2.57146	0.375086	0.187543	−	0.982256i	$-0.439948\pi$
$47$	2.57146	0.375086	0.187543	+	0.982256i	$0.439948\pi$
$48$	19.5673	2.82430
$49$	−3.46743	−0.495348
$50$	0.0599280	0.00847510
$51$	3.88134	0.543497
$52$	25.7186	3.56653
$53$	7.83058	1.07561	0.537806	−	0.843068i	$-0.319253\pi$
$53$	7.83058	1.07561	0.537806	+	0.843068i	$0.319253\pi$
$54$	15.1588	2.06285
$55$	−0.114974	−0.0155030
$56$	−18.5750	−2.48220
$57$	8.88354	1.17665
$58$	−20.4173	−2.68092
$59$	−12.6470	−1.64650	−0.823249	−	0.567681i	$-0.807841\pi$
$59$	−12.6470	−1.64650	−0.823249	+	0.567681i	$0.807841\pi$
$60$	−15.2018	−1.96254
$61$	−13.3884	−1.71421	−0.857104	−	0.515143i	$-0.827739\pi$
$61$	−13.3884	−1.71421	−0.857104	+	0.515143i	$0.827739\pi$
$62$	17.4091	2.21095
$63$	−2.84422	−0.358338
$64$	35.2251	4.40313
$65$	−10.2694	−1.27376
$66$	−0.173074	−0.0213040
$67$	4.49176	0.548756	0.274378	−	0.961622i	$-0.411528\pi$
$67$	4.49176	0.548756	0.274378	+	0.961622i	$0.411528\pi$
$68$	17.7872	2.15701
$69$	−7.14017	−0.859576
$70$	11.5516	1.38068
$71$	11.3567	1.34779	0.673895	−	0.738827i	$-0.264620\pi$
$71$	11.3567	1.34779	0.673895	+	0.738827i	$0.264620\pi$
$72$	14.9556	1.76253
$73$	14.7321	1.72426	0.862132	−	0.506683i	$-0.169129\pi$
$73$	14.7321	1.72426	0.862132	+	0.506683i	$0.169129\pi$
$74$	6.48422	0.753775
$75$	−0.0265270	−0.00306307
$76$	40.7109	4.66986
$77$	0.0968512	0.0110372
$78$	−15.4589	−1.75038
$79$	10.8746	1.22348	0.611742	−	0.791058i	$-0.290469\pi$
$79$	10.8746	1.22348	0.611742	+	0.791058i	$0.290469\pi$
$80$	−35.8059	−4.00322
$81$	−2.17018	−0.241131
$82$	−17.5378	−1.93672
$83$	0.112792	0.0123806	0.00619029	−	0.999981i	$-0.498030\pi$
$83$	0.112792	0.0123806	0.00619029	+	0.999981i	$0.498030\pi$
$84$	12.8056	1.39721
$85$	−7.10239	−0.770362
$86$	−0.415927	−0.0448505
$87$	9.03766	0.968938
$88$	−0.509266	−0.0542879
$89$	11.7583	1.24638	0.623191	−	0.782070i	$-0.285836\pi$
$89$	11.7583	1.24638	0.623191	+	0.782070i	$0.285836\pi$
$90$	−9.30065	−0.980375
$91$	8.65071	0.906841
$92$	−32.7215	−3.41145
$93$	−7.70608	−0.799083
$94$	−7.08334	−0.730590
$95$	−16.2558	−1.66781
$96$	−29.7993	−3.04138
$97$	−3.05328	−0.310013	−0.155007	−	0.987913i	$-0.549540\pi$
$97$	−3.05328	−0.310013	−0.155007	+	0.987913i	$0.549540\pi$
$98$	9.55137	0.964834
$99$	−0.0779790	−0.00783718
$100$	−0.121566	−0.0121566
$101$	12.7928	1.27293	0.636467	−	0.771304i	$-0.280395\pi$
$101$	12.7928	1.27293	0.636467	+	0.771304i	$0.280395\pi$
$102$	−10.6915	−1.05862
$103$	−13.7855	−1.35832	−0.679161	−	0.733989i	$-0.737656\pi$
$103$	−13.7855	−1.35832	−0.679161	+	0.733989i	$0.737656\pi$
$104$	−45.4875	−4.46041
$105$	−5.11327	−0.499004
$106$	−21.5701	−2.09507
$107$	−18.6604	−1.80397	−0.901986	−	0.431765i	$-0.857891\pi$
$107$	−18.6604	−1.80397	−0.901986	+	0.431765i	$0.857891\pi$
$108$	−30.7502	−2.95893
$109$	9.36808	0.897299	0.448650	−	0.893708i	$-0.351905\pi$
$109$	9.36808	0.897299	0.448650	+	0.893708i	$0.351905\pi$
$110$	0.316705	0.0301967
$111$	−2.87022	−0.272429
$112$	30.1621	2.85005
$113$	15.2053	1.43040	0.715199	−	0.698920i	$-0.246336\pi$
$113$	15.2053	1.43040	0.715199	+	0.698920i	$0.246336\pi$
$114$	−24.4705	−2.29188
$115$	13.0657	1.21838
$116$	41.4172	3.84549
$117$	−6.96505	−0.643920
$118$	34.8373	3.20703
$119$	5.98290	0.548451
$120$	26.8867	2.45441
$121$	−10.9973	−0.999759
$122$	36.8796	3.33892
$123$	7.76305	0.699970
$124$	−35.3149	−3.17137
$125$	11.2045	1.00216
$126$	7.83467	0.697968
$127$	−6.40030	−0.567934	−0.283967	−	0.958834i	$-0.591651\pi$
$127$	−6.40030	−0.567934	−0.283967	+	0.958834i	$0.591651\pi$
$128$	−48.1519	−4.25607
$129$	0.184109	0.0162099
$130$	28.2880	2.48102
$131$	−4.32179	−0.377596	−0.188798	−	0.982016i	$-0.560459\pi$
$131$	−4.32179	−0.377596	−0.188798	+	0.982016i	$0.560459\pi$
$132$	0.351087	0.0305582
$133$	13.6935	1.18738
$134$	−12.3730	−1.06886
$135$	12.2785	1.05676
$136$	−31.4595	−2.69763
$137$	7.05312	0.602588	0.301294	−	0.953531i	$-0.402581\pi$
$137$	7.05312	0.602588	0.301294	+	0.953531i	$0.402581\pi$
$138$	19.6683	1.67427
$139$	9.07477	0.769712	0.384856	−	0.922977i	$-0.374251\pi$
$139$	9.07477	0.769712	0.384856	+	0.922977i	$0.374251\pi$
$140$	−23.4328	−1.98043
$141$	3.13542	0.264050
$142$	−31.2830	−2.62521
$143$	0.237174	0.0198335
$144$	−24.2848	−2.02373
$145$	−16.5378	−1.37339
$146$	−40.5810	−3.35851
$147$	−4.22789	−0.348710
$148$	−13.1535	−1.08121
$149$	3.68015	0.301489	0.150745	−	0.988573i	$-0.451833\pi$
$149$	3.68015	0.301489	0.150745	+	0.988573i	$0.451833\pi$
$150$	0.0730710	0.00596622
$151$	13.5161	1.09993	0.549963	−	0.835189i	$-0.314642\pi$
$151$	13.5161	1.09993	0.549963	+	0.835189i	$0.314642\pi$
$152$	−72.0038	−5.84028
$153$	−4.81708	−0.389438
$154$	−0.266786	−0.0214982
$155$	14.1012	1.13264
$156$	31.3590	2.51073
$157$	1.46413	0.116850	0.0584250	−	0.998292i	$-0.481392\pi$
$157$	1.46413	0.116850	0.0584250	+	0.998292i	$0.481392\pi$
$158$	−29.9550	−2.38309
$159$	9.54793	0.757200
$160$	54.5292	4.31091
$161$	−11.0062	−0.867412
$162$	5.97796	0.469673
$163$	−10.9933	−0.861064	−0.430532	−	0.902575i	$-0.641674\pi$
$163$	−10.9933	−0.861064	−0.430532	+	0.902575i	$0.641674\pi$
$164$	35.5760	2.77802
$165$	−0.140189	−0.0109137
$166$	−0.310697	−0.0241148
$167$	22.5479	1.74481	0.872404	−	0.488786i	$-0.162560\pi$
$167$	22.5479	1.74481	0.872404	+	0.488786i	$0.162560\pi$
$168$	−22.6488	−1.74739
$169$	8.18428	0.629560
$170$	19.5642	1.50051
$171$	−11.0252	−0.843122
$172$	0.843722	0.0643332
$173$	21.4096	1.62774	0.813872	−	0.581045i	$-0.197356\pi$
$173$	21.4096	1.62774	0.813872	+	0.581045i	$0.197356\pi$
$174$	−24.8951	−1.88729
$175$	−0.0408900	−0.00309099
$176$	0.826944	0.0623332
$177$	−15.4206	−1.15909
$178$	−32.3895	−2.42769
$179$	10.4732	0.782803	0.391402	−	0.920220i	$-0.371990\pi$
$179$	10.4732	0.782803	0.391402	+	0.920220i	$0.371990\pi$
$180$	18.8667	1.40624
$181$	−5.21506	−0.387633	−0.193816	−	0.981038i	$-0.562087\pi$
$181$	−5.21506	−0.387633	−0.193816	+	0.981038i	$0.562087\pi$
$182$	−23.8292	−1.76634
$183$	−16.3247	−1.20675
$184$	57.8733	4.26647
$185$	5.25216	0.386147
$186$	21.2271	1.55645
$187$	0.164031	0.0119951
$188$	14.3688	1.04795
$189$	−10.3431	−0.752353
$190$	44.7782	3.24855
$191$	−6.77194	−0.490000	−0.245000	−	0.969523i	$-0.578788\pi$
$191$	−6.77194	−0.490000	−0.245000	+	0.969523i	$0.578788\pi$
$192$	42.9504	3.09968
$193$	−24.4917	−1.76295	−0.881477	−	0.472227i	$-0.843450\pi$
$193$	−24.4917	−1.76295	−0.881477	+	0.472227i	$0.843450\pi$
$194$	8.41054	0.603841
$195$	−12.5216	−0.896691
$196$	−19.3753	−1.38395
$197$	−9.84533	−0.701451	−0.350726	−	0.936478i	$-0.614065\pi$
$197$	−9.84533	−0.701451	−0.350726	+	0.936478i	$0.614065\pi$
$198$	0.214800	0.0152652
$199$	27.6661	1.96120	0.980598	−	0.196030i	$-0.0628049\pi$
$199$	27.6661	1.96120	0.980598	+	0.196030i	$0.0628049\pi$
$200$	0.215009	0.0152034
$201$	5.47686	0.386308
$202$	−35.2391	−2.47941
$203$	13.9311	0.977772
$204$	21.6881	1.51847
$205$	−14.2054	−0.992152
$206$	37.9734	2.64573
$207$	8.86158	0.615922
$208$	73.8623	5.12143
$209$	0.375431	0.0259691
$210$	14.0850	0.971956
$211$	14.3243	0.986123	0.493062	−	0.869994i	$-0.335878\pi$
$211$	14.3243	0.986123	0.493062	+	0.869994i	$0.335878\pi$
$212$	43.7556	3.00515
$213$	13.8474	0.948805
$214$	51.4019	3.51376
$215$	−0.336897	−0.0229762
$216$	54.3866	3.70054
$217$	−11.8785	−0.806368
$218$	−25.8053	−1.74775
$219$	17.9631	1.21383
$220$	−0.642448	−0.0433138
$221$	14.6512	0.985547
$222$	7.90630	0.530636
$223$	0.223857	0.0149906	0.00749528	−	0.999972i	$-0.497614\pi$
$223$	0.223857	0.0149906	0.00749528	+	0.999972i	$0.497614\pi$
$224$	−45.9342	−3.06911
$225$	0.0329223	0.00219482
$226$	−41.8846	−2.78612
$227$	13.6915	0.908734	0.454367	−	0.890815i	$-0.349866\pi$
$227$	13.6915	0.908734	0.454367	+	0.890815i	$0.349866\pi$
$228$	49.6393	3.28745
$229$	1.81430	0.119893	0.0599463	−	0.998202i	$-0.480907\pi$
$229$	1.81430	0.119893	0.0599463	+	0.998202i	$0.480907\pi$
$230$	−35.9906	−2.37315
$231$	0.118092	0.00776988
$232$	−73.2530	−4.80929
$233$	0.251627	0.0164846	0.00824232	−	0.999966i	$-0.497376\pi$
$233$	0.251627	0.0164846	0.00824232	+	0.999966i	$0.497376\pi$
$234$	19.1859	1.25422
$235$	−5.73744	−0.374269
$236$	−70.6687	−4.60014
$237$	13.2595	0.861297
$238$	−16.4805	−1.06827
$239$	23.0216	1.48915	0.744573	−	0.667541i	$-0.232653\pi$
$239$	23.0216	1.48915	0.744573	+	0.667541i	$0.232653\pi$
$240$	−43.6586	−2.81815
$241$	19.3087	1.24378	0.621892	−	0.783103i	$-0.286364\pi$
$241$	19.3087	1.24378	0.621892	+	0.783103i	$0.286364\pi$
$242$	30.2932	1.94732
$243$	13.8632	0.889322
$244$	−74.8116	−4.78932
$245$	7.73653	0.494269
$246$	−21.3840	−1.36340
$247$	33.5334	2.13368
$248$	62.4601	3.96622
$249$	0.137529	0.00871556
$250$	−30.8639	−1.95201
$251$	3.39726	0.214433	0.107216	−	0.994236i	$-0.465806\pi$
$251$	3.39726	0.214433	0.107216	+	0.994236i	$0.465806\pi$
$252$	−15.8929	−1.00116
$253$	−0.301754	−0.0189711
$254$	17.6302	1.10622
$255$	−8.66004	−0.542313
$256$	62.1889	3.88681
$257$	5.36778	0.334833	0.167417	−	0.985886i	$-0.446458\pi$
$257$	5.36778	0.334833	0.167417	+	0.985886i	$0.446458\pi$
$258$	−0.507145	−0.0315735
$259$	−4.42431	−0.274913
$260$	−57.3832	−3.55876
$261$	−11.2165	−0.694285
$262$	11.9048	0.735480
$263$	−7.83903	−0.483376	−0.241688	−	0.970354i	$-0.577701\pi$
$263$	−7.83903	−0.483376	−0.241688	+	0.970354i	$0.577701\pi$
$264$	−0.620955	−0.0382171
$265$	−17.4716	−1.07327
$266$	−37.7201	−2.31277
$267$	14.3371	0.877417
$268$	25.0990	1.53317
$269$	−13.6217	−0.830532	−0.415266	−	0.909700i	$-0.636311\pi$
$269$	−13.6217	−0.830532	−0.415266	+	0.909700i	$0.636311\pi$
$270$	−33.8223	−2.05836
$271$	23.6788	1.43838	0.719192	−	0.694811i	$-0.244512\pi$
$271$	23.6788	1.43838	0.719192	+	0.694811i	$0.244512\pi$
$272$	51.0837	3.09741
$273$	10.5479	0.638390
$274$	−19.4285	−1.17372
$275$	−0.00112107	−6.76029e−5 0
$276$	−39.8978	−2.40156
$277$	−3.96812	−0.238421	−0.119211	−	0.992869i	$-0.538036\pi$
$277$	−3.96812	−0.238421	−0.119211	+	0.992869i	$0.538036\pi$
$278$	−24.9973	−1.49924
$279$	9.56391	0.572576
$280$	41.4446	2.47679
$281$	9.16169	0.546541	0.273270	−	0.961937i	$-0.411895\pi$
$281$	9.16169	0.546541	0.273270	+	0.961937i	$0.411895\pi$
$282$	−8.63681	−0.514314
$283$	9.94082	0.590920	0.295460	−	0.955355i	$-0.404527\pi$
$283$	9.94082	0.590920	0.295460	+	0.955355i	$0.404527\pi$
$284$	63.4587	3.76558
$285$	−19.8209	−1.17409
$286$	−0.653317	−0.0386315
$287$	11.9664	0.706352
$288$	36.9836	2.17928
$289$	−6.86712	−0.403948
$290$	45.5550	2.67508
$291$	−3.72290	−0.218240
$292$	82.3200	4.81741
$293$	−19.9427	−1.16507	−0.582533	−	0.812807i	$-0.697938\pi$
$293$	−19.9427	−1.16507	−0.582533	+	0.812807i	$0.697938\pi$
$294$	11.6461	0.679215
$295$	28.2179	1.64291
$296$	23.2640	1.35219
$297$	−0.283574	−0.0164547
$298$	−10.1373	−0.587239
$299$	−26.9526	−1.55871
$300$	−0.148227	−0.00855789
$301$	0.283795	0.0163577
$302$	−37.2314	−2.14243
$303$	15.5985	0.896109
$304$	116.919	6.70579
$305$	29.8722	1.71048
$306$	13.2691	0.758545
$307$	−7.31223	−0.417331	−0.208665	−	0.977987i	$-0.566912\pi$
$307$	−7.31223	−0.417331	−0.208665	+	0.977987i	$0.566912\pi$
$308$	0.541184	0.0308368
$309$	−16.8088	−0.956220
$310$	−38.8431	−2.20614
$311$	−28.4615	−1.61390	−0.806952	−	0.590616i	$-0.798885\pi$
$311$	−28.4615	−1.61390	−0.806952	+	0.590616i	$0.798885\pi$
$312$	−55.4635	−3.14000
$313$	12.3495	0.698033	0.349016	−	0.937117i	$-0.386516\pi$
$313$	12.3495	0.698033	0.349016	+	0.937117i	$0.386516\pi$
$314$	−4.03307	−0.227599
$315$	6.34601	0.357557
$316$	60.7647	3.41828
$317$	−4.42405	−0.248479	−0.124240	−	0.992252i	$-0.539649\pi$
$317$	−4.42405	−0.248479	−0.124240	+	0.992252i	$0.539649\pi$
$318$	−26.3007	−1.47487
$319$	0.381944	0.0213848
$320$	−78.5941	−4.39354
$321$	−22.7529	−1.26994
$322$	30.3177	1.68954
$323$	23.1919	1.29043
$324$	−12.1265	−0.673694
$325$	−0.100133	−0.00555440
$326$	30.2822	1.67717
$327$	11.4226	0.631673
$328$	−62.9219	−3.47428
$329$	4.83309	0.266457
$330$	0.386163	0.0212576
$331$	6.93787	0.381340	0.190670	−	0.981654i	$-0.438934\pi$
$331$	6.93787	0.381340	0.190670	+	0.981654i	$0.438934\pi$
$332$	0.630260	0.0345900
$333$	3.56220	0.195207
$334$	−62.1103	−3.39852
$335$	−10.0220	−0.547561
$336$	36.7770	2.00635
$337$	24.2772	1.32246	0.661232	−	0.750182i	$-0.270034\pi$
$337$	24.2772	1.32246	0.661232	+	0.750182i	$0.270034\pi$
$338$	−22.5444	−1.22625
$339$	18.5401	1.00696
$340$	−39.6867	−2.15231
$341$	−0.325670	−0.0176360
$342$	30.3701	1.64223
$343$	−19.6737	−1.06228
$344$	−1.49226	−0.0804571
$345$	15.9311	0.857703
$346$	−58.9748	−3.17051
$347$	−14.3229	−0.768893	−0.384447	−	0.923147i	$-0.625608\pi$
$347$	−14.3229	−0.768893	−0.384447	+	0.923147i	$0.625608\pi$
$348$	50.5005	2.70711
$349$	−4.87469	−0.260936	−0.130468	−	0.991453i	$-0.541648\pi$
$349$	−4.87469	−0.260936	−0.130468	+	0.991453i	$0.541648\pi$
$350$	0.112635	0.00602061
$351$	−25.3288	−1.35195
$352$	−1.25936	−0.0671243
$353$	−22.2271	−1.18303	−0.591516	−	0.806293i	$-0.701470\pi$
$353$	−22.2271	−1.18303	−0.591516	+	0.806293i	$0.701470\pi$
$354$	42.4776	2.25766
$355$	−25.3390	−1.34485
$356$	65.7032	3.48226
$357$	7.29503	0.386094
$358$	−28.8494	−1.52474
$359$	14.7008	0.775880	0.387940	−	0.921685i	$-0.373187\pi$
$359$	14.7008	0.775880	0.387940	+	0.921685i	$0.373187\pi$
$360$	−33.3688	−1.75869
$361$	34.0812	1.79375
$362$	14.3654	0.755028
$363$	−13.4092	−0.703801
$364$	48.3384	2.53362
$365$	−32.8703	−1.72051
$366$	44.9678	2.35050
$367$	−1.05150	−0.0548879	−0.0274440	−	0.999623i	$-0.508737\pi$
$367$	−1.05150	−0.0548879	−0.0274440	+	0.999623i	$0.508737\pi$
$368$	−93.9744	−4.89875
$369$	−9.63462	−0.501558
$370$	−14.4676	−0.752134
$371$	14.7177	0.764103
$372$	−43.0599	−2.23255
$373$	−23.1764	−1.20003	−0.600015	−	0.799989i	$-0.704839\pi$
$373$	−23.1764	−1.20003	−0.600015	+	0.799989i	$0.704839\pi$
$374$	−0.451839	−0.0233641
$375$	13.6618	0.705494
$376$	−25.4135	−1.31060
$377$	34.1151	1.75702
$378$	28.4912	1.46543
$379$	−1.10049	−0.0565284	−0.0282642	−	0.999600i	$-0.508998\pi$
$379$	−1.10049	−0.0565284	−0.0282642	+	0.999600i	$0.508998\pi$
$380$	−90.8341	−4.65969
$381$	−7.80397	−0.399809
$382$	18.6539	0.954419
$383$	1.39478	0.0712701	0.0356351	−	0.999365i	$-0.488655\pi$
$383$	1.39478	0.0712701	0.0356351	+	0.999365i	$0.488655\pi$
$384$	−58.7123	−2.99615
$385$	−0.216094	−0.0110132
$386$	67.4648	3.43387
$387$	−0.228495	−0.0116151
$388$	−17.0611	−0.866144
$389$	−18.3253	−0.929129	−0.464564	−	0.885539i	$-0.653789\pi$
$389$	−18.3253	−0.929129	−0.464564	+	0.885539i	$0.653789\pi$
$390$	34.4920	1.74657
$391$	−18.6406	−0.942695
$392$	34.2683	1.73081
$393$	−5.26962	−0.265817
$394$	27.1199	1.36628
$395$	−24.2633	−1.22082
$396$	−0.435730	−0.0218963
$397$	12.5461	0.629673	0.314836	−	0.949146i	$-0.398050\pi$
$397$	12.5461	0.629673	0.314836	+	0.949146i	$0.398050\pi$
$398$	−76.2088	−3.82000
$399$	16.6967	0.835881
$400$	−0.349131	−0.0174565
$401$	−25.3899	−1.26791	−0.633957	−	0.773369i	$-0.718570\pi$
$401$	−25.3899	−1.26791	−0.633957	+	0.773369i	$0.718570\pi$
$402$	−15.0865	−0.752448
$403$	−29.0887	−1.44901
$404$	71.4837	3.55644
$405$	4.84209	0.240606
$406$	−38.3745	−1.90450
$407$	−0.121300	−0.00601260
$408$	−38.3589	−1.89905
$409$	17.1973	0.850350	0.425175	−	0.905111i	$-0.360212\pi$
$409$	17.1973	0.850350	0.425175	+	0.905111i	$0.360212\pi$
$410$	39.1302	1.93251
$411$	8.59996	0.424205
$412$	−77.0303	−3.79501
$413$	−23.7702	−1.16965
$414$	−24.4100	−1.19969
$415$	−0.251662	−0.0123536
$416$	−112.486	−5.51507
$417$	11.0650	0.541855
$418$	−1.03416	−0.0505824
$419$	31.1024	1.51945	0.759726	−	0.650243i	$-0.225333\pi$
$419$	31.1024	1.51945	0.759726	+	0.650243i	$0.225333\pi$
$420$	−28.5719	−1.39416
$421$	25.2948	1.23279	0.616397	−	0.787435i	$-0.288591\pi$
$421$	25.2948	1.23279	0.616397	+	0.787435i	$0.288591\pi$
$422$	−39.4576	−1.92076
$423$	−3.89133	−0.189203
$424$	−77.3889	−3.75834
$425$	−0.0692530	−0.00335926
$426$	−38.1438	−1.84808
$427$	−25.1637	−1.21775
$428$	−104.271	−5.04011
$429$	0.289189	0.0139622
$430$	0.928015	0.0447528
$431$	−18.2546	−0.879294	−0.439647	−	0.898171i	$-0.644897\pi$
$431$	−18.2546	−0.879294	−0.439647	+	0.898171i	$0.644897\pi$
$432$	−88.3127	−4.24895
$433$	−18.2301	−0.876080	−0.438040	−	0.898955i	$-0.644327\pi$
$433$	−18.2301	−0.876080	−0.438040	+	0.898955i	$0.644327\pi$
$434$	32.7206	1.57064
$435$	−20.1648	−0.966828
$436$	52.3469	2.50696
$437$	−42.6642	−2.04091
$438$	−49.4810	−2.36429
$439$	7.03885	0.335946	0.167973	−	0.985792i	$-0.446278\pi$
$439$	7.03885	0.335946	0.167973	+	0.985792i	$0.446278\pi$
$440$	1.13627	0.0541697
$441$	5.24718	0.249866
$442$	−40.3581	−1.91964
$443$	−9.54248	−0.453377	−0.226689	−	0.973967i	$-0.572790\pi$
$443$	−9.54248	−0.453377	−0.226689	+	0.973967i	$0.572790\pi$
$444$	−16.0382	−0.761139
$445$	−26.2352	−1.24367
$446$	−0.616635	−0.0291985
$447$	4.48725	0.212240
$448$	66.2060	3.12794
$449$	−9.38461	−0.442887	−0.221444	−	0.975173i	$-0.571077\pi$
$449$	−9.38461	−0.442887	−0.221444	+	0.975173i	$0.571077\pi$
$450$	−0.0906875	−0.00427505
$451$	0.328078	0.0154486
$452$	84.9643	3.99638
$453$	16.4804	0.774316
$454$	−37.7144	−1.77002
$455$	−19.3015	−0.904866
$456$	−87.7952	−4.11139
$457$	38.0938	1.78196	0.890978	−	0.454047i	$-0.150020\pi$
$457$	38.0938	1.78196	0.890978	+	0.454047i	$0.150020\pi$
$458$	−4.99767	−0.233526
$459$	−17.5176	−0.817650
$460$	73.0082	3.40402
$461$	28.6662	1.33512	0.667560	−	0.744556i	$-0.267339\pi$
$461$	28.6662	1.33512	0.667560	+	0.744556i	$0.267339\pi$
$462$	−0.325295	−0.0151341
$463$	−7.94153	−0.369074	−0.184537	−	0.982826i	$-0.559079\pi$
$463$	−7.94153	−0.369074	−0.184537	+	0.982826i	$0.559079\pi$
$464$	118.948	5.52201
$465$	17.1938	0.797343
$466$	−0.693130	−0.0321086
$467$	−36.5580	−1.69170	−0.845852	−	0.533418i	$-0.820907\pi$
$467$	−36.5580	−1.69170	−0.845852	+	0.533418i	$0.820907\pi$
$468$	−38.9193	−1.79904
$469$	8.44232	0.389830
$470$	15.8043	0.728999
$471$	1.78523	0.0822590
$472$	124.989	5.75309
$473$	0.00778070	0.000357757 0
$474$	−36.5245	−1.67763
$475$	−0.158505	−0.00727270
$476$	33.4312	1.53232
$477$	−11.8498	−0.542566
$478$	−63.4153	−2.90055
$479$	−12.3540	−0.564469	−0.282234	−	0.959345i	$-0.591076\pi$
$479$	−12.3540	−0.564469	−0.282234	+	0.959345i	$0.591076\pi$
$480$	66.4882	3.03476
$481$	−10.8344	−0.494008
$482$	−53.1877	−2.42263
$483$	−13.4200	−0.610633
$484$	−61.4509	−2.79322
$485$	6.81246	0.309338
$486$	−38.1874	−1.73222
$487$	21.7183	0.984151	0.492076	−	0.870552i	$-0.336238\pi$
$487$	21.7183	0.984151	0.492076	+	0.870552i	$0.336238\pi$
$488$	132.316	5.98968
$489$	−13.4043	−0.606164
$490$	−21.3110	−0.962733
$491$	12.8329	0.579141	0.289571	−	0.957157i	$-0.406487\pi$
$491$	12.8329	0.579141	0.289571	+	0.957157i	$0.406487\pi$
$492$	43.3783	1.95564
$493$	23.5943	1.06263
$494$	−92.3709	−4.15596
$495$	0.173987	0.00782011
$496$	−101.422	−4.55400
$497$	21.3450	0.957455
$498$	−0.378837	−0.0169761
$499$	−19.6832	−0.881139	−0.440570	−	0.897718i	$-0.645224\pi$
$499$	−19.6832	−0.881139	−0.440570	+	0.897718i	$0.645224\pi$
$500$	62.6086	2.79994
$501$	27.4929	1.22829
$502$	−9.35806	−0.417671
$503$	−28.7934	−1.28383	−0.641917	−	0.766774i	$-0.721861\pi$
$503$	−28.7934	−1.28383	−0.641917	+	0.766774i	$0.721861\pi$
$504$	28.1091	1.25208
$505$	−28.5433	−1.27016
$506$	0.831210	0.0369518
$507$	9.97920	0.443192
$508$	−35.7635	−1.58675
$509$	8.08074	0.358173	0.179086	−	0.983833i	$-0.442686\pi$
$509$	8.08074	0.358173	0.179086	+	0.983833i	$0.442686\pi$
$510$	23.8549	1.05631
$511$	27.6892	1.22490
$512$	−75.0014	−3.31462
$513$	−40.0938	−1.77019
$514$	−14.7861	−0.652185
$515$	30.7581	1.35536
$516$	1.02876	0.0452887
$517$	0.132507	0.00582767
$518$	12.1872	0.535474
$519$	26.1050	1.14588
$520$	101.492	4.45070
$521$	8.88158	0.389109	0.194554	−	0.980892i	$-0.437674\pi$
$521$	8.88158	0.389109	0.194554	+	0.980892i	$0.437674\pi$
$522$	30.8970	1.35232
$523$	−15.0021	−0.655994	−0.327997	−	0.944679i	$-0.606374\pi$
$523$	−15.0021	−0.655994	−0.327997	+	0.944679i	$0.606374\pi$
$524$	−24.1493	−1.05497
$525$	−0.0498577	−0.00217597
$526$	21.5934	0.941515
$527$	−20.1180	−0.876353
$528$	1.00830	0.0438808
$529$	11.2915	0.490935
$530$	48.1271	2.09051
$531$	19.1384	0.830534
$532$	76.5166	3.31742
$533$	29.3038	1.26929
$534$	−39.4929	−1.70903
$535$	41.6351	1.80004
$536$	−44.3917	−1.91743
$537$	12.7701	0.551071
$538$	37.5224	1.61770
$539$	−0.178677	−0.00769615
$540$	68.6097	2.95249
$541$	−4.90350	−0.210818	−0.105409	−	0.994429i	$-0.533615\pi$
$541$	−4.90350	−0.210818	−0.105409	+	0.994429i	$0.533615\pi$
$542$	−65.2255	−2.80167
$543$	−6.35880	−0.272882
$544$	−77.7961	−3.33548
$545$	−20.9020	−0.895345
$546$	−29.0553	−1.24345
$547$	−9.46585	−0.404730	−0.202365	−	0.979310i	$-0.564863\pi$
$547$	−9.46585	−0.404730	−0.202365	+	0.979310i	$0.564863\pi$
$548$	39.4113	1.68357
$549$	20.2603	0.864689
$550$	0.00308809	0.000131676 0
$551$	54.0021	2.30057
$552$	70.5657	3.00347
$553$	20.4389	0.869149
$554$	10.9306	0.464395
$555$	6.40403	0.271836
$556$	50.7079	2.15049
$557$	7.34752	0.311324	0.155662	−	0.987810i	$-0.450249\pi$
$557$	7.34752	0.311324	0.155662	+	0.987810i	$0.450249\pi$
$558$	−26.3447	−1.11526
$559$	0.694970	0.0293941
$560$	−67.2976	−2.84384
$561$	0.200005	0.00844423
$562$	−25.2367	−1.06455
$563$	−4.99490	−0.210510	−0.105255	−	0.994445i	$-0.533566\pi$
$563$	−4.99490	−0.210510	−0.105255	+	0.994445i	$0.533566\pi$
$564$	17.5201	0.737728
$565$	−33.9261	−1.42728
$566$	−27.3829	−1.15099
$567$	−4.07887	−0.171297
$568$	−112.237	−4.70936
$569$	−41.3350	−1.73285	−0.866426	−	0.499306i	$-0.833588\pi$
$569$	−41.3350	−1.73285	−0.866426	+	0.499306i	$0.833588\pi$
$570$	54.5986	2.28688
$571$	22.7685	0.952833	0.476417	−	0.879220i	$-0.341935\pi$
$571$	22.7685	0.952833	0.476417	+	0.879220i	$0.341935\pi$
$572$	1.32528	0.0554126
$573$	−8.25712	−0.344946
$574$	−32.9625	−1.37583
$575$	0.127399	0.00531290
$576$	−53.3052	−2.22105
$577$	−15.4586	−0.643550	−0.321775	−	0.946816i	$-0.604280\pi$
$577$	−15.4586	−0.643550	−0.321775	+	0.946816i	$0.604280\pi$
$578$	18.9161	0.786807
$579$	−29.8631	−1.24107
$580$	−92.4099	−3.83711
$581$	0.211995	0.00879502
$582$	10.2551	0.425087
$583$	0.403509	0.0167116
$584$	−145.596	−6.02481
$585$	15.5404	0.642517
$586$	54.9341	2.26931
$587$	−24.6419	−1.01708	−0.508539	−	0.861039i	$-0.669814\pi$
$587$	−24.6419	−1.01708	−0.508539	+	0.861039i	$0.669814\pi$
$588$	−23.6246	−0.974260
$589$	−46.0456	−1.89728
$590$	−77.7289	−3.20005
$591$	−12.0045	−0.493801
$592$	−37.7760	−1.55258
$593$	13.2160	0.542718	0.271359	−	0.962478i	$-0.412527\pi$
$593$	13.2160	0.542718	0.271359	+	0.962478i	$0.412527\pi$
$594$	0.781132	0.0320502
$595$	−13.3490	−0.547257
$596$	20.5639	0.842330
$597$	33.7336	1.38063
$598$	74.2434	3.03604
$599$	17.9481	0.733341	0.366670	−	0.930351i	$-0.380498\pi$
$599$	17.9481	0.733341	0.366670	+	0.930351i	$0.380498\pi$
$600$	0.262163	0.0107028
$601$	−8.85337	−0.361137	−0.180568	−	0.983562i	$-0.557794\pi$
$601$	−8.85337	−0.361137	−0.180568	+	0.983562i	$0.557794\pi$
$602$	−0.781739	−0.0318613
$603$	−6.79727	−0.276806
$604$	75.5252	3.07308
$605$	24.5373	0.997581
$606$	−42.9675	−1.74543
$607$	15.9699	0.648198	0.324099	−	0.946023i	$-0.394939\pi$
$607$	15.9699	0.648198	0.324099	+	0.946023i	$0.394939\pi$
$608$	−178.058	−7.22121
$609$	16.9864	0.688323
$610$	−82.2857	−3.33165
$611$	11.8355	0.478813
$612$	−26.9169	−1.08805
$613$	32.9665	1.33151	0.665753	−	0.746172i	$-0.268110\pi$
$613$	32.9665	1.33151	0.665753	+	0.746172i	$0.268110\pi$
$614$	20.1422	0.812874
$615$	−17.3209	−0.698446
$616$	−0.957171	−0.0385655
$617$	−32.2437	−1.29808	−0.649041	−	0.760753i	$-0.724830\pi$
$617$	−32.2437	−1.29808	−0.649041	+	0.760753i	$0.724830\pi$
$618$	46.3014	1.86252
$619$	32.9116	1.32283	0.661415	−	0.750020i	$-0.269956\pi$
$619$	32.9116	1.32283	0.661415	+	0.750020i	$0.269956\pi$
$620$	78.7945	3.16447
$621$	32.2256	1.29317
$622$	78.4000	3.14355
$623$	22.1000	0.885416
$624$	90.0613	3.60534
$625$	−24.8907	−0.995630
$626$	−34.0178	−1.35962
$627$	0.457768	0.0182815
$628$	8.18123	0.326467
$629$	−7.49319	−0.298773
$630$	−17.4807	−0.696448
$631$	−11.0718	−0.440761	−0.220381	−	0.975414i	$-0.570730\pi$
$631$	−11.0718	−0.440761	−0.220381	+	0.975414i	$0.570730\pi$
$632$	−107.472	−4.27502
$633$	17.4658	0.694202
$634$	12.1865	0.483986
$635$	14.2803	0.566698
$636$	53.3518	2.11554
$637$	−15.9593	−0.632332
$638$	−1.05210	−0.0416531
$639$	−17.1858	−0.679859
$640$	107.437	4.24680
$641$	0.422388	0.0166833	0.00834166	−	0.999965i	$-0.497345\pi$
$641$	0.422388	0.0166833	0.00834166	+	0.999965i	$0.497345\pi$
$642$	62.6751	2.47359
$643$	10.4941	0.413849	0.206924	−	0.978357i	$-0.433655\pi$
$643$	10.4941	0.413849	0.206924	+	0.978357i	$0.433655\pi$
$644$	−61.5005	−2.42346
$645$	−0.410783	−0.0161746
$646$	−63.8844	−2.51350
$647$	−25.4558	−1.00077	−0.500384	−	0.865803i	$-0.666808\pi$
$647$	−25.4558	−1.00077	−0.500384	+	0.865803i	$0.666808\pi$
$648$	21.4477	0.842544
$649$	−0.651699	−0.0255814
$650$	0.275827	0.0108188
$651$	−14.4837	−0.567660
$652$	−61.4284	−2.40572
$653$	24.5288	0.959888	0.479944	−	0.877299i	$-0.340657\pi$
$653$	24.5288	0.959888	0.479944	+	0.877299i	$0.340657\pi$
$654$	−31.4647	−1.23037
$655$	9.64277	0.376774
$656$	102.172	3.98916
$657$	−22.2937	−0.869762
$658$	−13.3132	−0.519003
$659$	1.16899	0.0455376	0.0227688	−	0.999741i	$-0.492752\pi$
$659$	1.16899	0.0455376	0.0227688	+	0.999741i	$0.492752\pi$
$660$	−0.783346	−0.0304917
$661$	10.2363	0.398144	0.199072	−	0.979985i	$-0.436207\pi$
$661$	10.2363	0.398144	0.199072	+	0.979985i	$0.436207\pi$
$662$	−19.1110	−0.742771
$663$	17.8644	0.693796
$664$	−1.11472	−0.0432594
$665$	−30.5530	−1.18479
$666$	−9.81240	−0.380223
$667$	−43.4044	−1.68062
$668$	125.993	4.87481
$669$	0.272952	0.0105529
$670$	27.6066	1.06653
$671$	−0.689904	−0.0266334
$672$	−56.0082	−2.16056
$673$	−11.7054	−0.451209	−0.225604	−	0.974219i	$-0.572436\pi$
$673$	−11.7054	−0.451209	−0.225604	+	0.974219i	$0.572436\pi$
$674$	−66.8739	−2.57589
$675$	0.119723	0.00460816
$676$	45.7320	1.75892
$677$	−11.3477	−0.436129	−0.218065	−	0.975934i	$-0.569974\pi$
$677$	−11.3477	−0.436129	−0.218065	+	0.975934i	$0.569974\pi$
$678$	−51.0704	−1.96135
$679$	−5.73867	−0.220230
$680$	70.1923	2.69175
$681$	16.6942	0.639722
$682$	0.897089	0.0343513
$683$	−5.30906	−0.203145	−0.101573	−	0.994828i	$-0.532387\pi$
$683$	−5.30906	−0.203145	−0.101573	+	0.994828i	$0.532387\pi$
$684$	−61.6068	−2.35559
$685$	−15.7369	−0.601276
$686$	54.1930	2.06910
$687$	2.21221	0.0844009
$688$	2.42312	0.0923806
$689$	36.0413	1.37306
$690$	−43.8838	−1.67063
$691$	−14.9871	−0.570135	−0.285068	−	0.958507i	$-0.592016\pi$
$691$	−14.9871	−0.570135	−0.285068	+	0.958507i	$0.592016\pi$
$692$	119.632	4.54774
$693$	−0.146562	−0.00556745
$694$	39.4538	1.49764
$695$	−20.2476	−0.768035
$696$	−89.3183	−3.38560
$697$	20.2667	0.767657
$698$	13.4278	0.508250
$699$	0.306812	0.0116047
$700$	−0.228485	−0.00863591
$701$	−18.0011	−0.679891	−0.339946	−	0.940445i	$-0.610409\pi$
$701$	−18.0011	−0.679891	−0.339946	+	0.940445i	$0.610409\pi$
$702$	69.7705	2.63332
$703$	−17.1503	−0.646834
$704$	1.81515	0.0684109
$705$	−6.99574	−0.263475
$706$	61.2268	2.30430
$707$	24.0443	0.904278
$708$	−86.1673	−3.23837
$709$	40.9731	1.53878	0.769389	−	0.638780i	$-0.220561\pi$
$709$	40.9731	1.53878	0.769389	+	0.638780i	$0.220561\pi$
$710$	69.7987	2.61950
$711$	−16.4562	−0.617155
$712$	−116.207	−4.35503
$713$	37.0093	1.38601
$714$	−20.0948	−0.752031
$715$	−0.529182	−0.0197903
$716$	58.5220	2.18707
$717$	28.0706	1.04832
$718$	−40.4948	−1.51125
$719$	4.97302	0.185462	0.0927312	−	0.995691i	$-0.470440\pi$
$719$	4.97302	0.185462	0.0927312	+	0.995691i	$0.470440\pi$
$720$	54.1841	2.01932
$721$	−25.9100	−0.964937
$722$	−93.8800	−3.49385
$723$	23.5434	0.875588
$724$	−29.1407	−1.08301
$725$	−0.161255	−0.00598885
$726$	36.9369	1.37086
$727$	40.9633	1.51924	0.759621	−	0.650365i	$-0.225384\pi$
$727$	40.9633	1.51924	0.759621	+	0.650365i	$0.225384\pi$
$728$	−85.4942	−3.16863
$729$	23.4141	0.867188
$730$	90.5443	3.35119
$731$	0.480646	0.0177773
$732$	−91.2188	−3.37154
$733$	−24.7843	−0.915429	−0.457714	−	0.889099i	$-0.651332\pi$
$733$	−24.7843	−0.915429	−0.457714	+	0.889099i	$0.651332\pi$
$734$	2.89646	0.106910
$735$	9.43326	0.347951
$736$	143.115	5.27528
$737$	0.231460	0.00852595
$738$	26.5395	0.976931
$739$	−23.4993	−0.864437	−0.432219	−	0.901769i	$-0.642269\pi$
$739$	−23.4993	−0.864437	−0.432219	+	0.901769i	$0.642269\pi$
$740$	29.3480	1.07885
$741$	40.8877	1.50205
$742$	−40.5412	−1.48831
$743$	−34.2648	−1.25705	−0.628526	−	0.777788i	$-0.716342\pi$
$743$	−34.2648	−1.25705	−0.628526	+	0.777788i	$0.716342\pi$
$744$	76.1585	2.79210
$745$	−8.21114	−0.300833
$746$	63.8417	2.33741
$747$	−0.170686	−0.00624507
$748$	0.916572	0.0335132
$749$	−35.0725	−1.28152
$750$	−37.6328	−1.37416
$751$	1.69026	0.0616783	0.0308391	−	0.999524i	$-0.490182\pi$
$751$	1.69026	0.0616783	0.0308391	+	0.999524i	$0.490182\pi$
$752$	41.2664	1.50483
$753$	4.14232	0.150955
$754$	−93.9734	−3.42231
$755$	−30.1571	−1.09753
$756$	−57.7953	−2.10199
$757$	−40.4623	−1.47063	−0.735314	−	0.677727i	$-0.762965\pi$
$757$	−40.4623	−1.47063	−0.735314	+	0.677727i	$0.762965\pi$
$758$	3.03140	0.110106
$759$	−0.367933	−0.0133551
$760$	160.655	5.82756
$761$	33.4217	1.21153	0.605767	−	0.795642i	$-0.292866\pi$
$761$	33.4217	1.21153	0.605767	+	0.795642i	$0.292866\pi$
$762$	21.4968	0.778746
$763$	17.6074	0.637431
$764$	−37.8402	−1.36901
$765$	10.7479	0.388590
$766$	−3.84206	−0.138819
$767$	−58.2095	−2.10182
$768$	75.8278	2.73620
$769$	−10.4799	−0.377914	−0.188957	−	0.981985i	$-0.560511\pi$
$769$	−10.4799	−0.377914	−0.188957	+	0.981985i	$0.560511\pi$
$770$	0.595252	0.0214514
$771$	6.54501	0.235713
$772$	−136.855	−4.92551
$773$	17.2813	0.621567	0.310783	−	0.950481i	$-0.399409\pi$
$773$	17.2813	0.621567	0.310783	+	0.950481i	$0.399409\pi$
$774$	0.629411	0.0226237
$775$	0.137496	0.00493900
$776$	30.1752	1.08323
$777$	−5.39462	−0.193531
$778$	50.4787	1.80975
$779$	46.3860	1.66195
$780$	−69.9682	−2.50526
$781$	0.585209	0.0209404
$782$	51.3473	1.83617
$783$	−40.7894	−1.45769
$784$	−55.6448	−1.98731
$785$	−3.26675	−0.116595
$786$	14.5157	0.517756
$787$	−17.1986	−0.613063	−0.306531	−	0.951861i	$-0.599168\pi$
$787$	−17.1986	−0.613063	−0.306531	+	0.951861i	$0.599168\pi$
$788$	−55.0137	−1.95978
$789$	−9.55824	−0.340282
$790$	66.8355	2.37790
$791$	28.5786	1.01614
$792$	0.770659	0.0273842
$793$	−61.6220	−2.18826
$794$	−34.5595	−1.22647
$795$	−21.3033	−0.755551
$796$	154.592	5.47938
$797$	5.68065	0.201219	0.100609	−	0.994926i	$-0.467921\pi$
$797$	5.68065	0.201219	0.100609	+	0.994926i	$0.467921\pi$
$798$	−45.9927	−1.62812
$799$	8.18553	0.289583
$800$	0.531696	0.0187983
$801$	−17.7936	−0.628706
$802$	69.9390	2.46963
$803$	0.759146	0.0267897
$804$	30.6036	1.07930
$805$	24.5571	0.865523
$806$	80.1276	2.82238
$807$	−16.6092	−0.584670
$808$	−126.430	−4.44780
$809$	−43.2137	−1.51931	−0.759657	−	0.650324i	$-0.774633\pi$
$809$	−43.2137	−1.51931	−0.759657	+	0.650324i	$0.774633\pi$
$810$	−13.3380	−0.468650
$811$	4.07332	0.143034	0.0715169	−	0.997439i	$-0.477216\pi$
$811$	4.07332	0.143034	0.0715169	+	0.997439i	$0.477216\pi$
$812$	77.8441	2.73179
$813$	28.8719	1.01258
$814$	0.334132	0.0117113
$815$	24.5283	0.859189
$816$	62.2871	2.18048
$817$	1.10009	0.0384874
$818$	−47.3715	−1.65631
$819$	−13.0909	−0.457433
$820$	−79.3771	−2.77197
$821$	−18.3536	−0.640545	−0.320272	−	0.947325i	$-0.603774\pi$
$821$	−18.3536	−0.640545	−0.320272	+	0.947325i	$0.603774\pi$
$822$	−23.6894	−0.826263
$823$	−35.2831	−1.22989	−0.614945	−	0.788570i	$-0.710822\pi$
$823$	−35.2831	−1.22989	−0.614945	+	0.788570i	$0.710822\pi$
$824$	136.241	4.74616
$825$	−0.00136693	−4.75905e−5 0
$826$	65.4772	2.27824
$827$	−16.0223	−0.557151	−0.278576	−	0.960414i	$-0.589862\pi$
$827$	−16.0223	−0.557151	−0.278576	+	0.960414i	$0.589862\pi$
$828$	49.5166	1.72082
$829$	−17.0105	−0.590799	−0.295399	−	0.955374i	$-0.595453\pi$
$829$	−17.0105	−0.590799	−0.295399	+	0.955374i	$0.595453\pi$
$830$	0.693227	0.0240623
$831$	−4.83838	−0.167841
$832$	162.128	5.62079
$833$	−11.0376	−0.382430
$834$	−30.4796	−1.05542
$835$	−50.3088	−1.74101
$836$	2.09783	0.0725550
$837$	34.7796	1.20216
$838$	−85.6746	−2.95958
$839$	−17.6451	−0.609178	−0.304589	−	0.952484i	$-0.598519\pi$
$839$	−17.6451	−0.609178	−0.304589	+	0.952484i	$0.598519\pi$
$840$	50.5340	1.74359
$841$	25.9390	0.894448
$842$	−69.6770	−2.40123
$843$	11.1710	0.384749
$844$	80.0410	2.75513
$845$	−18.2607	−0.628189
$846$	10.7190	0.368528
$847$	−20.6696	−0.710217
$848$	125.664	4.31531
$849$	12.1210	0.415991
$850$	0.190764	0.00654315
$851$	13.7846	0.472529
$852$	77.3761	2.65086
$853$	41.1059	1.40744	0.703719	−	0.710478i	$-0.251521\pi$
$853$	41.1059	1.40744	0.703719	+	0.710478i	$0.251521\pi$
$854$	69.3157	2.37193
$855$	24.5995	0.841285
$856$	184.419	6.30332
$857$	−28.7785	−0.983055	−0.491527	−	0.870862i	$-0.663561\pi$
$857$	−28.7785	−0.983055	−0.491527	+	0.870862i	$0.663561\pi$
$858$	−0.796599	−0.0271954
$859$	−49.4044	−1.68566	−0.842828	−	0.538183i	$-0.819111\pi$
$859$	−49.4044	−1.68566	−0.842828	+	0.538183i	$0.819111\pi$
$860$	−1.88251	−0.0641931
$861$	14.5907	0.497251
$862$	50.2841	1.71268
$863$	17.8102	0.606268	0.303134	−	0.952948i	$-0.401967\pi$
$863$	17.8102	0.606268	0.303134	+	0.952948i	$0.401967\pi$
$864$	134.493	4.57553
$865$	−47.7691	−1.62420
$866$	50.2164	1.70642
$867$	−8.37317	−0.284368
$868$	−66.3748	−2.25291
$869$	0.560365	0.0190091
$870$	55.5458	1.88318
$871$	20.6739	0.700510
$872$	−92.5839	−3.13529
$873$	4.62044	0.156378
$874$	117.523	3.97526
$875$	21.0591	0.711926
$876$	100.374	3.39132
$877$	40.6981	1.37428	0.687138	−	0.726527i	$-0.258867\pi$
$877$	40.6981	1.37428	0.687138	+	0.726527i	$0.258867\pi$
$878$	−19.3892	−0.654353
$879$	−24.3164	−0.820172
$880$	−1.84508	−0.0621975
$881$	35.1380	1.18383	0.591915	−	0.806000i	$-0.298372\pi$
$881$	35.1380	1.18383	0.591915	+	0.806000i	$0.298372\pi$
$882$	−14.4538	−0.486686
$883$	−36.9798	−1.24447	−0.622235	−	0.782831i	$-0.713775\pi$
$883$	−36.9798	−1.24447	−0.622235	+	0.782831i	$0.713775\pi$
$884$	81.8679	2.75351
$885$	34.4065	1.15656
$886$	26.2857	0.883084
$887$	−50.1088	−1.68249	−0.841244	−	0.540655i	$-0.818176\pi$
$887$	−50.1088	−1.68249	−0.841244	+	0.540655i	$0.818176\pi$
$888$	28.3661	0.951905
$889$	−12.0294	−0.403454
$890$	72.2673	2.42241
$891$	−0.111829	−0.00374642
$892$	1.25087	0.0418821
$893$	18.7349	0.626938
$894$	−12.3606	−0.413399
$895$	−23.3678	−0.781098
$896$	−90.5022	−3.02347
$897$	−32.8636	−1.09728
$898$	25.8508	0.862652
$899$	−46.8445	−1.56235
$900$	0.183963	0.00613209
$901$	24.9264	0.830420
$902$	−0.903721	−0.0300906
$903$	0.346035	0.0115153
$904$	−150.273	−4.99801
$905$	11.6358	0.386788
$906$	−45.3967	−1.50821
$907$	−38.0155	−1.26228	−0.631142	−	0.775667i	$-0.717413\pi$
$907$	−38.0155	−1.26228	−0.631142	+	0.775667i	$0.717413\pi$
$908$	76.5050	2.53891
$909$	−19.3591	−0.642100
$910$	53.1677	1.76249
$911$	−1.22417	−0.0405587	−0.0202793	−	0.999794i	$-0.506456\pi$
$911$	−1.22417	−0.0405587	−0.0202793	+	0.999794i	$0.506456\pi$
$912$	142.561	4.72068
$913$	0.00581219	0.000192355 0
$914$	−104.933	−3.47088
$915$	36.4235	1.20413
$916$	10.1380	0.334967
$917$	−8.12286	−0.268240
$918$	48.2538	1.59261
$919$	−7.52810	−0.248329	−0.124165	−	0.992262i	$-0.539625\pi$
$919$	−7.52810	−0.248329	−0.124165	+	0.992262i	$0.539625\pi$
$920$	−129.127	−4.25718
$921$	−8.91590	−0.293789
$922$	−78.9639	−2.60054
$923$	52.2707	1.72051
$924$	0.659873	0.0217082
$925$	0.0512120	0.00168384
$926$	21.8757	0.718880
$927$	20.8612	0.685172
$928$	−181.147	−5.94645
$929$	15.0961	0.495286	0.247643	−	0.968851i	$-0.420344\pi$
$929$	15.0961	0.495286	0.247643	+	0.968851i	$0.420344\pi$
$930$	−47.3619	−1.55306
$931$	−25.2626	−0.827949
$932$	1.40604	0.0460563
$933$	−34.7035	−1.13614
$934$	100.703	3.29509
$935$	−0.365986	−0.0119690
$936$	68.8350	2.24994
$937$	−10.8104	−0.353159	−0.176580	−	0.984286i	$-0.556503\pi$
$937$	−10.8104	−0.353159	−0.176580	+	0.984286i	$0.556503\pi$
$938$	−23.2552	−0.759308
$939$	15.0579	0.491395
$940$	−32.0596	−1.04567
$941$	46.1550	1.50461	0.752304	−	0.658816i	$-0.228942\pi$
$941$	46.1550	1.50461	0.752304	+	0.658816i	$0.228942\pi$
$942$	−4.91758	−0.160223
$943$	−37.2829	−1.21410
$944$	−202.957	−6.60568
$945$	23.0776	0.750714
$946$	−0.0214327	−0.000696837 0
$947$	−50.7981	−1.65072	−0.825358	−	0.564609i	$-0.809027\pi$
$947$	−50.7981	−1.65072	−0.825358	+	0.564609i	$0.809027\pi$
$948$	74.0913	2.40637
$949$	67.8066	2.20110
$950$	0.436616	0.0141657
$951$	−5.39430	−0.174922
$952$	−59.1284	−1.91636
$953$	−16.6789	−0.540283	−0.270142	−	0.962821i	$-0.587071\pi$
$953$	−16.6789	−0.540283	−0.270142	+	0.962821i	$0.587071\pi$
$954$	32.6414	1.05681
$955$	15.1095	0.488933
$956$	128.640	4.16052
$957$	0.465710	0.0150543
$958$	34.0303	1.09947
$959$	13.2564	0.428072
$960$	−95.8309	−3.09293
$961$	8.94255	0.288469
$962$	29.8445	0.962226
$963$	28.2384	0.909968
$964$	107.893	3.47500
$965$	54.6459	1.75911
$966$	36.9668	1.18939
$967$	−22.6676	−0.728940	−0.364470	−	0.931215i	$-0.618750\pi$
$967$	−22.6676	−0.728940	−0.364470	+	0.931215i	$0.618750\pi$
$968$	108.686	3.49329
$969$	28.2782	0.908428
$970$	−18.7656	−0.602526
$971$	57.7311	1.85268	0.926340	−	0.376688i	$-0.122937\pi$
$971$	57.7311	1.85268	0.926340	+	0.376688i	$0.122937\pi$
$972$	77.4645	2.48467
$973$	17.0561	0.546795
$974$	−59.8252	−1.91692
$975$	−0.122094	−0.00391014
$976$	−214.855	−6.87733
$977$	8.77804	0.280834	0.140417	−	0.990092i	$-0.455156\pi$
$977$	8.77804	0.280834	0.140417	+	0.990092i	$0.455156\pi$
$978$	36.9235	1.18068
$979$	0.605907	0.0193649
$980$	43.2301	1.38094
$981$	−14.1765	−0.452620
$982$	−35.3495	−1.12805
$983$	−50.3122	−1.60471	−0.802355	−	0.596848i	$-0.796420\pi$
$983$	−50.3122	−1.60471	−0.802355	+	0.596848i	$0.796420\pi$
$984$	−76.7215	−2.44579
$985$	21.9669	0.699923
$986$	−64.9927	−2.06979
$987$	5.89306	0.187578
$988$	187.378	5.96127
$989$	−0.884203	−0.0281160
$990$	−0.479262	−0.0152320
$991$	0.809047	0.0257002	0.0128501	−	0.999917i	$-0.495910\pi$
$991$	0.809047	0.0257002	0.0128501	+	0.999917i	$0.495910\pi$
$992$	154.458	4.90403
$993$	8.45944	0.268452
$994$	−58.7969	−1.86492
$995$	−61.7285	−1.95692
$996$	0.768485	0.0243504
$997$	48.0869	1.52293	0.761464	−	0.648208i	$-0.224481\pi$
$997$	48.0869	1.52293	0.761464	+	0.648208i	$0.224481\pi$
$998$	54.2191	1.71628
$999$	12.9541	0.409850

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1931.2.a.b.1.3	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1931.2.a.b.1.3	✓	101	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:	\( N \)	\(=\)	\( 1931 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1931.a (trivial)

\(f(q)\)	\(=\)	\(q-2.75459 q^{2} +1.21931 q^{3} +5.58779 q^{4} -2.23120 q^{5} -3.35871 q^{6} +1.87951 q^{7} -9.88291 q^{8} -1.51327 q^{9} +O(q^{10})\)	\(q-2.75459 q^{2} +1.21931 q^{3} +5.58779 q^{4} -2.23120 q^{5} -3.35871 q^{6} +1.87951 q^{7} -9.88291 q^{8} -1.51327 q^{9} +6.14605 q^{10} +0.0515300 q^{11} +6.81327 q^{12} +4.60264 q^{13} -5.17729 q^{14} -2.72053 q^{15} +16.0478 q^{16} +3.18322 q^{17} +4.16846 q^{18} +7.28569 q^{19} -12.4675 q^{20} +2.29171 q^{21} -0.141944 q^{22} -5.85589 q^{23} -12.0504 q^{24} -0.0217556 q^{25} -12.6784 q^{26} -5.50310 q^{27} +10.5023 q^{28} +7.41208 q^{29} +7.49396 q^{30} -6.32001 q^{31} -24.4394 q^{32} +0.0628312 q^{33} -8.76848 q^{34} -4.19356 q^{35} -8.45586 q^{36} -2.35397 q^{37} -20.0691 q^{38} +5.61206 q^{39} +22.0507 q^{40} +6.36674 q^{41} -6.31274 q^{42} +0.150994 q^{43} +0.287939 q^{44} +3.37641 q^{45} +16.1306 q^{46} +2.57146 q^{47} +19.5673 q^{48} -3.46743 q^{49} +0.0599280 q^{50} +3.88134 q^{51} +25.7186 q^{52} +7.83058 q^{53} +15.1588 q^{54} -0.114974 q^{55} -18.5750 q^{56} +8.88354 q^{57} -20.4173 q^{58} -12.6470 q^{59} -15.2018 q^{60} -13.3884 q^{61} +17.4091 q^{62} -2.84422 q^{63} +35.2251 q^{64} -10.2694 q^{65} -0.173074 q^{66} +4.49176 q^{67} +17.7872 q^{68} -7.14017 q^{69} +11.5516 q^{70} +11.3567 q^{71} +14.9556 q^{72} +14.7321 q^{73} +6.48422 q^{74} -0.0265270 q^{75} +40.7109 q^{76} +0.0968512 q^{77} -15.4589 q^{78} +10.8746 q^{79} -35.8059 q^{80} -2.17018 q^{81} -17.5378 q^{82} +0.112792 q^{83} +12.8056 q^{84} -7.10239 q^{85} -0.415927 q^{86} +9.03766 q^{87} -0.509266 q^{88} +11.7583 q^{89} -9.30065 q^{90} +8.65071 q^{91} -32.7215 q^{92} -7.70608 q^{93} -7.08334 q^{94} -16.2558 q^{95} -29.7993 q^{96} -3.05328 q^{97} +9.55137 q^{98} -0.0779790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9}+O(q^{10}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9	\( 101 q + 5 q^{2} + 9 q^{3} + 131 q^{4} + 25 q^{5} + 15 q^{6} + 20 q^{7} + 12 q^{8} + 138 q^{9} + 14 q^{10} + 29 q^{11} + 15 q^{12} + 41 q^{13} + 4 q^{14} + 22 q^{15} + 187 q^{16} + 9 q^{17} + 11 q^{18} + 34 q^{19} + 42 q^{20} + 72 q^{21} + 17 q^{22} + 19 q^{23} + 33 q^{24} + 172 q^{25} + 28 q^{26} + 36 q^{27} + 47 q^{28} + 68 q^{29} + q^{30} + 76 q^{31} + 9 q^{32} + 8 q^{33} + 50 q^{34} + 7 q^{35} + 198 q^{36} + 141 q^{37} - 13 q^{38} + 42 q^{39} + 32 q^{40} + 35 q^{41} - 46 q^{42} + 45 q^{43} + 67 q^{44} + 106 q^{45} + 86 q^{46} - 5 q^{47} + 7 q^{48} + 203 q^{49} + 4 q^{50} + 5 q^{51} + 30 q^{52} + 47 q^{53} + 20 q^{54} + 11 q^{55} - 4 q^{56} + 19 q^{57} + 92 q^{58} + 30 q^{59} + 35 q^{60} + 153 q^{61} - 20 q^{62} + 19 q^{63} + 276 q^{64} - 7 q^{65} - 18 q^{66} + 39 q^{67} - 7 q^{68} + 55 q^{69} - 8 q^{70} + 47 q^{71} - 4 q^{72} + 86 q^{73} + 9 q^{74} + 11 q^{75} + 50 q^{76} + 15 q^{77} - 15 q^{78} + 89 q^{79} + 26 q^{80} + 201 q^{81} - 9 q^{82} - 15 q^{83} + 60 q^{84} + 239 q^{85} + 13 q^{86} - 22 q^{87} + 5 q^{88} + 14 q^{89} - 85 q^{90} + 58 q^{91} - 4 q^{92} + 86 q^{93} + 21 q^{94} - 10 q^{95} + 6 q^{96} + 46 q^{97} - 68 q^{98} + 100 q^{99}+O(q^{100}) \) 101 * q + 5 * q^2 + 9 * q^3 + 131 * q^4 + 25 * q^5 + 15 * q^6 + 20 * q^7 + 12 * q^8 + 138 * q^9 + 14 * q^10 + 29 * q^11 + 15 * q^12 + 41 * q^13 + 4 * q^14 + 22 * q^15 + 187 * q^16 + 9 * q^17 + 11 * q^18 + 34 * q^19 + 42 * q^20 + 72 * q^21 + 17 * q^22 + 19 * q^23 + 33 * q^24 + 172 * q^25 + 28 * q^26 + 36 * q^27 + 47 * q^28 + 68 * q^29 + q^30 + 76 * q^31 + 9 * q^32 + 8 * q^33 + 50 * q^34 + 7 * q^35 + 198 * q^36 + 141 * q^37 - 13 * q^38 + 42 * q^39 + 32 * q^40 + 35 * q^41 - 46 * q^42 + 45 * q^43 + 67 * q^44 + 106 * q^45 + 86 * q^46 - 5 * q^47 + 7 * q^48 + 203 * q^49 + 4 * q^50 + 5 * q^51 + 30 * q^52 + 47 * q^53 + 20 * q^54 + 11 * q^55 - 4 * q^56 + 19 * q^57 + 92 * q^58 + 30 * q^59 + 35 * q^60 + 153 * q^61 - 20 * q^62 + 19 * q^63 + 276 * q^64 - 7 * q^65 - 18 * q^66 + 39 * q^67 - 7 * q^68 + 55 * q^69 - 8 * q^70 + 47 * q^71 - 4 * q^72 + 86 * q^73 + 9 * q^74 + 11 * q^75 + 50 * q^76 + 15 * q^77 - 15 * q^78 + 89 * q^79 + 26 * q^80 + 201 * q^81 - 9 * q^82 - 15 * q^83 + 60 * q^84 + 239 * q^85 + 13 * q^86 - 22 * q^87 + 5 * q^88 + 14 * q^89 - 85 * q^90 + 58 * q^91 - 4 * q^92 + 86 * q^93 + 21 * q^94 - 10 * q^95 + 6 * q^96 + 46 * q^97 - 68 * q^98 + 100 * q^99

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