LMFDB - Embedded newform 1441.2.a.c.1.6

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:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-1.75710 q^{2} -2.59102 q^{3} +1.08739 q^{4} +2.84782 q^{5} +4.55267 q^{6} +2.84815 q^{7} +1.60354 q^{8} +3.71338 q^{9} +O(q^{10})$	\(q-1.75710 q^{2} -2.59102 q^{3} +1.08739 q^{4} +2.84782 q^{5} +4.55267 q^{6} +2.84815 q^{7} +1.60354 q^{8} +3.71338 q^{9} -5.00390 q^{10} +1.00000 q^{11} -2.81745 q^{12} -4.49259 q^{13} -5.00447 q^{14} -7.37876 q^{15} -4.99236 q^{16} -5.70698 q^{17} -6.52477 q^{18} +1.03517 q^{19} +3.09669 q^{20} -7.37960 q^{21} -1.75710 q^{22} +4.78540 q^{23} -4.15482 q^{24} +3.11008 q^{25} +7.89391 q^{26} -1.84838 q^{27} +3.09704 q^{28} -8.56994 q^{29} +12.9652 q^{30} -9.90144 q^{31} +5.56498 q^{32} -2.59102 q^{33} +10.0277 q^{34} +8.11101 q^{35} +4.03789 q^{36} +8.67521 q^{37} -1.81890 q^{38} +11.6404 q^{39} +4.56661 q^{40} +1.49162 q^{41} +12.9667 q^{42} -10.3017 q^{43} +1.08739 q^{44} +10.5750 q^{45} -8.40841 q^{46} -6.12149 q^{47} +12.9353 q^{48} +1.11194 q^{49} -5.46471 q^{50} +14.7869 q^{51} -4.88519 q^{52} +9.62982 q^{53} +3.24778 q^{54} +2.84782 q^{55} +4.56713 q^{56} -2.68215 q^{57} +15.0582 q^{58} -3.52083 q^{59} -8.02358 q^{60} +10.5743 q^{61} +17.3978 q^{62} +10.5762 q^{63} +0.206524 q^{64} -12.7941 q^{65} +4.55267 q^{66} -12.1204 q^{67} -6.20571 q^{68} -12.3991 q^{69} -14.2518 q^{70} -6.56643 q^{71} +5.95457 q^{72} +11.3669 q^{73} -15.2432 q^{74} -8.05828 q^{75} +1.12563 q^{76} +2.84815 q^{77} -20.4533 q^{78} -8.15707 q^{79} -14.2174 q^{80} -6.35095 q^{81} -2.62092 q^{82} -13.5464 q^{83} -8.02450 q^{84} -16.2525 q^{85} +18.1012 q^{86} +22.2049 q^{87} +1.60354 q^{88} -11.3243 q^{89} -18.5814 q^{90} -12.7956 q^{91} +5.20359 q^{92} +25.6548 q^{93} +10.7560 q^{94} +2.94798 q^{95} -14.4190 q^{96} +5.85850 q^{97} -1.95378 q^{98} +3.71338 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) $ 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * 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 $

$2$	−1.75710	−1.24246	−0.621228	−	0.783630i	$-0.713366\pi$
$2$	−1.75710	−1.24246	−0.621228	+	0.783630i	$0.713366\pi$
$3$	−2.59102	−1.49593	−0.747963	−	0.663741i	$-0.768968\pi$
$3$	−2.59102	−1.49593	−0.747963	+	0.663741i	$0.768968\pi$
$4$	1.08739	0.543695
$5$	2.84782	1.27358	0.636792	−	0.771036i	$-0.280261\pi$
$5$	2.84782	1.27358	0.636792	+	0.771036i	$0.280261\pi$
$6$	4.55267	1.85862
$7$	2.84815	1.07650	0.538249	−	0.842786i	$-0.319086\pi$
$7$	2.84815	1.07650	0.538249	+	0.842786i	$0.319086\pi$
$8$	1.60354	0.566939
$9$	3.71338	1.23779
$10$	−5.00390	−1.58237
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.81745	−0.813327
$13$	−4.49259	−1.24602	−0.623010	−	0.782214i	$-0.714090\pi$
$13$	−4.49259	−1.24602	−0.623010	+	0.782214i	$0.714090\pi$
$14$	−5.00447	−1.33750
$15$	−7.37876	−1.90519
$16$	−4.99236	−1.24809
$17$	−5.70698	−1.38415	−0.692073	−	0.721828i	$-0.743302\pi$
$17$	−5.70698	−1.38415	−0.692073	+	0.721828i	$0.743302\pi$
$18$	−6.52477	−1.53790
$19$	1.03517	0.237484	0.118742	−	0.992925i	$-0.462114\pi$
$19$	1.03517	0.237484	0.118742	+	0.992925i	$0.462114\pi$
$20$	3.09669	0.692441
$21$	−7.37960	−1.61036
$22$	−1.75710	−0.374614
$23$	4.78540	0.997825	0.498912	−	0.866652i	$-0.333733\pi$
$23$	4.78540	0.997825	0.498912	+	0.866652i	$0.333733\pi$
$24$	−4.15482	−0.848098
$25$	3.11008	0.622016
$26$	7.89391	1.54812
$27$	−1.84838	−0.355721
$28$	3.09704	0.585286
$29$	−8.56994	−1.59140	−0.795699	−	0.605693i	$-0.792896\pi$
$29$	−8.56994	−1.59140	−0.795699	+	0.605693i	$0.792896\pi$
$30$	12.9652	2.36711
$31$	−9.90144	−1.77835	−0.889176	−	0.457566i	$-0.848721\pi$
$31$	−9.90144	−1.77835	−0.889176	+	0.457566i	$0.848721\pi$
$32$	5.56498	0.983758
$33$	−2.59102	−0.451038
$34$	10.0277	1.71974
$35$	8.11101	1.37101
$36$	4.03789	0.672982
$37$	8.67521	1.42620	0.713098	−	0.701065i	$-0.247292\pi$
$37$	8.67521	1.42620	0.713098	+	0.701065i	$0.247292\pi$
$38$	−1.81890	−0.295064
$39$	11.6404	1.86395
$40$	4.56661	0.722044
$41$	1.49162	0.232952	0.116476	−	0.993193i	$-0.462840\pi$
$41$	1.49162	0.232952	0.116476	+	0.993193i	$0.462840\pi$
$42$	12.9667	2.00080
$43$	−10.3017	−1.57100	−0.785501	−	0.618861i	$-0.787595\pi$
$43$	−10.3017	−1.57100	−0.785501	+	0.618861i	$0.787595\pi$
$44$	1.08739	0.163930
$45$	10.5750	1.57643
$46$	−8.40841	−1.23975
$47$	−6.12149	−0.892911	−0.446455	−	0.894806i	$-0.647314\pi$
$47$	−6.12149	−0.892911	−0.446455	+	0.894806i	$0.647314\pi$
$48$	12.9353	1.86705
$49$	1.11194	0.158848
$50$	−5.46471	−0.772827
$51$	14.7869	2.07058
$52$	−4.88519	−0.677455
$53$	9.62982	1.32276	0.661378	−	0.750052i	$-0.269972\pi$
$53$	9.62982	1.32276	0.661378	+	0.750052i	$0.269972\pi$
$54$	3.24778	0.441967
$55$	2.84782	0.384000
$56$	4.56713	0.610308
$57$	−2.68215	−0.355259
$58$	15.0582	1.97724
$59$	−3.52083	−0.458373	−0.229187	−	0.973383i	$-0.573607\pi$
$59$	−3.52083	−0.458373	−0.229187	+	0.973383i	$0.573607\pi$
$60$	−8.02358	−1.03584
$61$	10.5743	1.35389	0.676947	−	0.736031i	$-0.263302\pi$
$61$	10.5743	1.35389	0.676947	+	0.736031i	$0.263302\pi$
$62$	17.3978	2.20952
$63$	10.5762	1.33248
$64$	0.206524	0.0258154
$65$	−12.7941	−1.58691
$66$	4.55267	0.560395
$67$	−12.1204	−1.48074	−0.740372	−	0.672197i	$-0.765351\pi$
$67$	−12.1204	−1.48074	−0.740372	+	0.672197i	$0.765351\pi$
$68$	−6.20571	−0.752553
$69$	−12.3991	−1.49267
$70$	−14.2518	−1.70342
$71$	−6.56643	−0.779292	−0.389646	−	0.920965i	$-0.627403\pi$
$71$	−6.56643	−0.779292	−0.389646	+	0.920965i	$0.627403\pi$
$72$	5.95457	0.701753
$73$	11.3669	1.33039	0.665195	−	0.746670i	$-0.268348\pi$
$73$	11.3669	1.33039	0.665195	+	0.746670i	$0.268348\pi$
$74$	−15.2432	−1.77198
$75$	−8.05828	−0.930490
$76$	1.12563	0.129119
$77$	2.84815	0.324576
$78$	−20.4533	−2.31588
$79$	−8.15707	−0.917742	−0.458871	−	0.888503i	$-0.651746\pi$
$79$	−8.15707	−0.917742	−0.458871	+	0.888503i	$0.651746\pi$
$80$	−14.2174	−1.58955
$81$	−6.35095	−0.705661
$82$	−2.62092	−0.289433
$83$	−13.5464	−1.48691	−0.743453	−	0.668788i	$-0.766813\pi$
$83$	−13.5464	−1.48691	−0.743453	+	0.668788i	$0.766813\pi$
$84$	−8.02450	−0.875545
$85$	−16.2525	−1.76283
$86$	18.1012	1.95190
$87$	22.2049	2.38061
$88$	1.60354	0.170938
$89$	−11.3243	−1.20037	−0.600185	−	0.799861i	$-0.704906\pi$
$89$	−11.3243	−1.20037	−0.600185	+	0.799861i	$0.704906\pi$
$90$	−18.5814	−1.95865
$91$	−12.7956	−1.34134
$92$	5.20359	0.542512
$93$	25.6548	2.66028
$94$	10.7560	1.10940
$95$	2.94798	0.302456
$96$	−14.4190	−1.47163
$97$	5.85850	0.594840	0.297420	−	0.954747i	$-0.403874\pi$
$97$	5.85850	0.594840	0.297420	+	0.954747i	$0.403874\pi$
$98$	−1.95378	−0.197362
$99$	3.71338	0.373209
$100$	3.38187	0.338187
$101$	8.87727	0.883321	0.441661	−	0.897182i	$-0.354389\pi$
$101$	8.87727	0.883321	0.441661	+	0.897182i	$0.354389\pi$
$102$	−25.9820	−2.57260
$103$	7.37385	0.726567	0.363284	−	0.931679i	$-0.381656\pi$
$103$	7.37385	0.726567	0.363284	+	0.931679i	$0.381656\pi$
$104$	−7.20407	−0.706417
$105$	−21.0158	−2.05093
$106$	−16.9205	−1.64347
$107$	−4.13384	−0.399633	−0.199817	−	0.979833i	$-0.564035\pi$
$107$	−4.13384	−0.399633	−0.199817	+	0.979833i	$0.564035\pi$
$108$	−2.00991	−0.193403
$109$	−17.7610	−1.70120	−0.850600	−	0.525814i	$-0.823761\pi$
$109$	−17.7610	−1.70120	−0.850600	+	0.525814i	$0.823761\pi$
$110$	−5.00390	−0.477103
$111$	−22.4776	−2.13348
$112$	−14.2190	−1.34357
$113$	−3.08055	−0.289794	−0.144897	−	0.989447i	$-0.546285\pi$
$113$	−3.08055	−0.289794	−0.144897	+	0.989447i	$0.546285\pi$
$114$	4.71279	0.441393
$115$	13.6280	1.27081
$116$	−9.31886	−0.865235
$117$	−16.6827	−1.54231
$118$	6.18644	0.569508
$119$	−16.2543	−1.49003
$120$	−11.8322	−1.08012
$121$	1.00000	0.0909091
$122$	−18.5800	−1.68215
$123$	−3.86482	−0.348479
$124$	−10.7667	−0.966880
$125$	−5.38215	−0.481394
$126$	−18.5835	−1.65555
$127$	14.6231	1.29759	0.648795	−	0.760963i	$-0.275273\pi$
$127$	14.6231	1.29759	0.648795	+	0.760963i	$0.275273\pi$
$128$	−11.4928	−1.01583
$129$	26.6920	2.35010
$130$	22.4805	1.97167
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−2.81745	−0.245227
$133$	2.94832	0.255652
$134$	21.2967	1.83976
$135$	−5.26385	−0.453040
$136$	−9.15140	−0.784726
$137$	16.0233	1.36896	0.684480	−	0.729031i	$-0.260029\pi$
$137$	16.0233	1.36896	0.684480	+	0.729031i	$0.260029\pi$
$138$	21.7863	1.85458
$139$	18.4500	1.56491	0.782455	−	0.622707i	$-0.213967\pi$
$139$	18.4500	1.56491	0.782455	+	0.622707i	$0.213967\pi$
$140$	8.81983	0.745411
$141$	15.8609	1.33573
$142$	11.5379	0.968236
$143$	−4.49259	−0.375689
$144$	−18.5385	−1.54488
$145$	−24.4056	−2.02678
$146$	−19.9727	−1.65295
$147$	−2.88105	−0.237625
$148$	9.43333	0.775415
$149$	4.04871	0.331683	0.165841	−	0.986152i	$-0.446966\pi$
$149$	4.04871	0.331683	0.165841	+	0.986152i	$0.446966\pi$
$150$	14.1592	1.15609
$151$	−18.3537	−1.49361	−0.746803	−	0.665045i	$-0.768412\pi$
$151$	−18.3537	−1.49361	−0.746803	+	0.665045i	$0.768412\pi$
$152$	1.65994	0.134639
$153$	−21.1922	−1.71329
$154$	−5.00447	−0.403272
$155$	−28.1975	−2.26488
$156$	12.6576	1.01342
$157$	6.86353	0.547770	0.273885	−	0.961762i	$-0.411691\pi$
$157$	6.86353	0.547770	0.273885	+	0.961762i	$0.411691\pi$
$158$	14.3328	1.14025
$159$	−24.9510	−1.97875
$160$	15.8481	1.25290
$161$	13.6295	1.07416
$162$	11.1592	0.876753
$163$	8.01406	0.627710	0.313855	−	0.949471i	$-0.398379\pi$
$163$	8.01406	0.627710	0.313855	+	0.949471i	$0.398379\pi$
$164$	1.62197	0.126655
$165$	−7.37876	−0.574435
$166$	23.8023	1.84741
$167$	−9.55549	−0.739426	−0.369713	−	0.929146i	$-0.620544\pi$
$167$	−9.55549	−0.739426	−0.369713	+	0.929146i	$0.620544\pi$
$168$	−11.8335	−0.912976
$169$	7.18336	0.552566
$170$	28.5571	2.19023
$171$	3.84398	0.293957
$172$	−11.2020	−0.854145
$173$	−9.12209	−0.693540	−0.346770	−	0.937950i	$-0.612722\pi$
$173$	−9.12209	−0.693540	−0.346770	+	0.937950i	$0.612722\pi$
$174$	−39.0161	−2.95780
$175$	8.85797	0.669599
$176$	−4.99236	−0.376314
$177$	9.12254	0.685692
$178$	19.8978	1.49141
$179$	−14.1968	−1.06112	−0.530560	−	0.847647i	$-0.678018\pi$
$179$	−14.1968	−1.06112	−0.530560	+	0.847647i	$0.678018\pi$
$180$	11.4992	0.857099
$181$	6.91621	0.514078	0.257039	−	0.966401i	$-0.417253\pi$
$181$	6.91621	0.514078	0.257039	+	0.966401i	$0.417253\pi$
$182$	22.4830	1.66655
$183$	−27.3981	−2.02533
$184$	7.67360	0.565705
$185$	24.7054	1.81638
$186$	−45.0780	−3.30528
$187$	−5.70698	−0.417336
$188$	−6.65644	−0.485471
$189$	−5.26445	−0.382933
$190$	−5.17989	−0.375789
$191$	−12.6048	−0.912053	−0.456027	−	0.889966i	$-0.650728\pi$
$191$	−12.6048	−0.912053	−0.456027	+	0.889966i	$0.650728\pi$
$192$	−0.535106	−0.0386180
$193$	−14.0338	−1.01018	−0.505088	−	0.863068i	$-0.668540\pi$
$193$	−14.0338	−1.01018	−0.505088	+	0.863068i	$0.668540\pi$
$194$	−10.2939	−0.739063
$195$	33.1497	2.37390
$196$	1.20911	0.0863650
$197$	−12.8222	−0.913545	−0.456772	−	0.889584i	$-0.650995\pi$
$197$	−12.8222	−0.913545	−0.456772	+	0.889584i	$0.650995\pi$
$198$	−6.52477	−0.463695
$199$	−6.23767	−0.442177	−0.221088	−	0.975254i	$-0.570961\pi$
$199$	−6.23767	−0.442177	−0.221088	+	0.975254i	$0.570961\pi$
$200$	4.98715	0.352645
$201$	31.4042	2.21508
$202$	−15.5982	−1.09749
$203$	−24.4084	−1.71314
$204$	16.0791	1.12576
$205$	4.24787	0.296684
$206$	−12.9566	−0.902728
$207$	17.7700	1.23510
$208$	22.4286	1.55515
$209$	1.03517	0.0716043
$210$	36.9268	2.54819
$211$	−4.92693	−0.339184	−0.169592	−	0.985514i	$-0.554245\pi$
$211$	−4.92693	−0.339184	−0.169592	+	0.985514i	$0.554245\pi$
$212$	10.4714	0.719176
$213$	17.0138	1.16576
$214$	7.26355	0.496526
$215$	−29.3375	−2.00080
$216$	−2.96396	−0.201672
$217$	−28.2007	−1.91439
$218$	31.2079	2.11366
$219$	−29.4517	−1.99016
$220$	3.09669	0.208779
$221$	25.6391	1.72467
$222$	39.4954	2.65076
$223$	9.94679	0.666086	0.333043	−	0.942912i	$-0.391925\pi$
$223$	9.94679	0.666086	0.333043	+	0.942912i	$0.391925\pi$
$224$	15.8499	1.05901
$225$	11.5489	0.769927
$226$	5.41282	0.360055
$227$	10.8544	0.720431	0.360216	−	0.932869i	$-0.382703\pi$
$227$	10.8544	0.720431	0.360216	+	0.932869i	$0.382703\pi$
$228$	−2.91654	−0.193153
$229$	−14.0008	−0.925196	−0.462598	−	0.886568i	$-0.653083\pi$
$229$	−14.0008	−0.925196	−0.462598	+	0.886568i	$0.653083\pi$
$230$	−23.9456	−1.57893
$231$	−7.37960	−0.485542
$232$	−13.7423	−0.902225
$233$	−8.77908	−0.575137	−0.287568	−	0.957760i	$-0.592847\pi$
$233$	−8.77908	−0.575137	−0.287568	+	0.957760i	$0.592847\pi$
$234$	29.3131	1.91626
$235$	−17.4329	−1.13720
$236$	−3.82851	−0.249215
$237$	21.1351	1.37287
$238$	28.5604	1.85130
$239$	−29.7656	−1.92538	−0.962688	−	0.270612i	$-0.912774\pi$
$239$	−29.7656	−1.92538	−0.962688	+	0.270612i	$0.912774\pi$
$240$	36.8374	2.37785
$241$	−4.18570	−0.269624	−0.134812	−	0.990871i	$-0.543043\pi$
$241$	−4.18570	−0.269624	−0.134812	+	0.990871i	$0.543043\pi$
$242$	−1.75710	−0.112950
$243$	22.0006	1.41134
$244$	11.4983	0.736106
$245$	3.16660	0.202307
$246$	6.79086	0.432970
$247$	−4.65060	−0.295910
$248$	−15.8774	−1.00822
$249$	35.0989	2.22430
$250$	9.45696	0.598111
$251$	8.97903	0.566751	0.283376	−	0.959009i	$-0.408546\pi$
$251$	8.97903	0.566751	0.283376	+	0.959009i	$0.408546\pi$
$252$	11.5005	0.724463
$253$	4.78540	0.300855
$254$	−25.6942	−1.61220
$255$	42.1104	2.63706
$256$	19.7810	1.23631
$257$	12.1185	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$257$	12.1185	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$258$	−46.9005	−2.91990
$259$	24.7083	1.53530
$260$	−13.9122	−0.862795
$261$	−31.8234	−1.96982
$262$	−1.75710	−0.108554
$263$	−32.2591	−1.98918	−0.994590	−	0.103879i	$-0.966874\pi$
$263$	−32.2591	−1.98918	−0.994590	+	0.103879i	$0.966874\pi$
$264$	−4.15482	−0.255711
$265$	27.4240	1.68464
$266$	−5.18048	−0.317636
$267$	29.3414	1.79566
$268$	−13.1796	−0.805073
$269$	10.7358	0.654572	0.327286	−	0.944925i	$-0.393866\pi$
$269$	10.7358	0.654572	0.327286	+	0.944925i	$0.393866\pi$
$270$	9.24909	0.562882
$271$	26.1073	1.58591	0.792953	−	0.609283i	$-0.208543\pi$
$271$	26.1073	1.58591	0.792953	+	0.609283i	$0.208543\pi$
$272$	28.4913	1.72754
$273$	33.1535	2.00654
$274$	−28.1545	−1.70087
$275$	3.11008	0.187545
$276$	−13.4826	−0.811558
$277$	30.3557	1.82390	0.911948	−	0.410306i	$-0.134578\pi$
$277$	30.3557	1.82390	0.911948	+	0.410306i	$0.134578\pi$
$278$	−32.4185	−1.94433
$279$	−36.7678	−2.20123
$280$	13.0064	0.777279
$281$	−16.5858	−0.989428	−0.494714	−	0.869056i	$-0.664727\pi$
$281$	−16.5858	−0.989428	−0.494714	+	0.869056i	$0.664727\pi$
$282$	−27.8691	−1.65958
$283$	−18.6677	−1.10968	−0.554840	−	0.831957i	$-0.687221\pi$
$283$	−18.6677	−1.10968	−0.554840	+	0.831957i	$0.687221\pi$
$284$	−7.14027	−0.423697
$285$	−7.63827	−0.452452
$286$	7.89391	0.466777
$287$	4.24836	0.250773
$288$	20.6649	1.21769
$289$	15.5696	0.915860
$290$	42.8831	2.51818
$291$	−15.1795	−0.889837
$292$	12.3602	0.723326
$293$	−0.272111	−0.0158969	−0.00794846	−	0.999968i	$-0.502530\pi$
$293$	−0.272111	−0.0158969	−0.00794846	+	0.999968i	$0.502530\pi$
$294$	5.06229	0.295239
$295$	−10.0267	−0.583777
$296$	13.9111	0.808566
$297$	−1.84838	−0.107254
$298$	−7.11397	−0.412101
$299$	−21.4988	−1.24331
$300$	−8.76249	−0.505903
$301$	−29.3409	−1.69118
$302$	32.2493	1.85574
$303$	−23.0012	−1.32138
$304$	−5.16795	−0.296402
$305$	30.1136	1.72430
$306$	37.2367	2.12868
$307$	8.94834	0.510709	0.255354	−	0.966848i	$-0.417808\pi$
$307$	8.94834	0.510709	0.255354	+	0.966848i	$0.417808\pi$
$308$	3.09704	0.176471
$309$	−19.1058	−1.08689
$310$	49.5458	2.81401
$311$	0.375622	0.0212995	0.0106498	−	0.999943i	$-0.496610\pi$
$311$	0.375622	0.0212995	0.0106498	+	0.999943i	$0.496610\pi$
$312$	18.6659	1.05675
$313$	−3.99540	−0.225833	−0.112917	−	0.993604i	$-0.536019\pi$
$313$	−3.99540	−0.225833	−0.112917	+	0.993604i	$0.536019\pi$
$314$	−12.0599	−0.680579
$315$	30.1193	1.69703
$316$	−8.86992	−0.498972
$317$	−21.0632	−1.18303	−0.591515	−	0.806294i	$-0.701470\pi$
$317$	−21.0632	−1.18303	−0.591515	+	0.806294i	$0.701470\pi$
$318$	43.8414	2.45850
$319$	−8.56994	−0.479824
$320$	0.588142	0.0328781
$321$	10.7109	0.597821
$322$	−23.9484	−1.33459
$323$	−5.90770	−0.328713
$324$	−6.90596	−0.383665
$325$	−13.9723	−0.775045
$326$	−14.0815	−0.779901
$327$	46.0192	2.54487
$328$	2.39188	0.132070
$329$	−17.4349	−0.961217
$330$	12.9652	0.713710
$331$	7.55820	0.415436	0.207718	−	0.978189i	$-0.433396\pi$
$331$	7.55820	0.415436	0.207718	+	0.978189i	$0.433396\pi$
$332$	−14.7302	−0.808423
$333$	32.2143	1.76533
$334$	16.7899	0.918704
$335$	−34.5168	−1.88585
$336$	36.8416	2.00988
$337$	16.0648	0.875105	0.437553	−	0.899193i	$-0.355845\pi$
$337$	16.0648	0.875105	0.437553	+	0.899193i	$0.355845\pi$
$338$	−12.6219	−0.686538
$339$	7.98176	0.433510
$340$	−17.6727	−0.958439
$341$	−9.90144	−0.536193
$342$	−6.75425	−0.365228
$343$	−16.7701	−0.905498
$344$	−16.5193	−0.890662
$345$	−35.3103	−1.90104
$346$	16.0284	0.861692
$347$	−33.1857	−1.78150	−0.890750	−	0.454494i	$-0.849820\pi$
$347$	−33.1857	−1.78150	−0.890750	+	0.454494i	$0.849820\pi$
$348$	24.1453	1.29433
$349$	2.02651	0.108477	0.0542384	−	0.998528i	$-0.482727\pi$
$349$	2.02651	0.108477	0.0542384	+	0.998528i	$0.482727\pi$
$350$	−15.5643	−0.831947
$351$	8.30400	0.443235
$352$	5.56498	0.296614
$353$	−8.56764	−0.456009	−0.228005	−	0.973660i	$-0.573220\pi$
$353$	−8.56764	−0.456009	−0.228005	+	0.973660i	$0.573220\pi$
$354$	−16.0292	−0.851941
$355$	−18.7000	−0.992494
$356$	−12.3139	−0.652635
$357$	42.1152	2.22897
$358$	24.9452	1.31839
$359$	−28.2201	−1.48940	−0.744701	−	0.667398i	$-0.767408\pi$
$359$	−28.2201	−1.48940	−0.744701	+	0.667398i	$0.767408\pi$
$360$	16.9575	0.893741
$361$	−17.9284	−0.943601
$362$	−12.1524	−0.638718
$363$	−2.59102	−0.135993
$364$	−13.9137	−0.729279
$365$	32.3708	1.69436
$366$	48.1411	2.51638
$367$	25.2010	1.31548	0.657740	−	0.753245i	$-0.271512\pi$
$367$	25.2010	1.31548	0.657740	+	0.753245i	$0.271512\pi$
$368$	−23.8904	−1.24538
$369$	5.53896	0.288347
$370$	−43.4099	−2.25677
$371$	27.4271	1.42395
$372$	27.8968	1.44638
$373$	1.68896	0.0874511	0.0437256	−	0.999044i	$-0.486077\pi$
$373$	1.68896	0.0874511	0.0437256	+	0.999044i	$0.486077\pi$
$374$	10.0277	0.518521
$375$	13.9453	0.720130
$376$	−9.81608	−0.506226
$377$	38.5012	1.98291
$378$	9.25015	0.475777
$379$	−23.6452	−1.21457	−0.607285	−	0.794484i	$-0.707742\pi$
$379$	−23.6452	−1.21457	−0.607285	+	0.794484i	$0.707742\pi$
$380$	3.20560	0.164444
$381$	−37.8887	−1.94110
$382$	22.1479	1.13319
$383$	12.3440	0.630751	0.315376	−	0.948967i	$-0.397870\pi$
$383$	12.3440	0.630751	0.315376	+	0.948967i	$0.397870\pi$
$384$	29.7782	1.51961
$385$	8.11101	0.413375
$386$	24.6588	1.25510
$387$	−38.2543	−1.94457
$388$	6.37047	0.323412
$389$	20.3325	1.03090	0.515450	−	0.856920i	$-0.327625\pi$
$389$	20.3325	1.03090	0.515450	+	0.856920i	$0.327625\pi$
$390$	−58.2473	−2.94947
$391$	−27.3102	−1.38113
$392$	1.78304	0.0900572
$393$	−2.59102	−0.130700
$394$	22.5299	1.13504
$395$	−23.2299	−1.16882
$396$	4.03789	0.202912
$397$	−0.976975	−0.0490330	−0.0245165	−	0.999699i	$-0.507805\pi$
$397$	−0.976975	−0.0490330	−0.0245165	+	0.999699i	$0.507805\pi$
$398$	10.9602	0.549385
$399$	−7.63915	−0.382436
$400$	−15.5267	−0.776333
$401$	−32.3962	−1.61779	−0.808894	−	0.587955i	$-0.799933\pi$
$401$	−32.3962	−1.61779	−0.808894	+	0.587955i	$0.799933\pi$
$402$	−55.1803	−2.75214
$403$	44.4831	2.21586
$404$	9.65305	0.480257
$405$	−18.0864	−0.898719
$406$	42.8880	2.12850
$407$	8.67521	0.430014
$408$	23.7114	1.17389
$409$	−2.73772	−0.135372	−0.0676858	−	0.997707i	$-0.521562\pi$
$409$	−2.73772	−0.135372	−0.0676858	+	0.997707i	$0.521562\pi$
$410$	−7.46392	−0.368617
$411$	−41.5166	−2.04786
$412$	8.01825	0.395031
$413$	−10.0278	−0.493438
$414$	−31.2236	−1.53456
$415$	−38.5776	−1.89370
$416$	−25.0012	−1.22578
$417$	−47.8043	−2.34099
$418$	−1.81890	−0.0889651
$419$	7.58532	0.370567	0.185283	−	0.982685i	$-0.440680\pi$
$419$	7.58532	0.370567	0.185283	+	0.982685i	$0.440680\pi$
$420$	−22.8523	−1.11508
$421$	−2.03402	−0.0991322	−0.0495661	−	0.998771i	$-0.515784\pi$
$421$	−2.03402	−0.0991322	−0.0495661	+	0.998771i	$0.515784\pi$
$422$	8.65709	0.421420
$423$	−22.7314	−1.10524
$424$	15.4418	0.749922
$425$	−17.7492	−0.860961
$426$	−29.8948	−1.44841
$427$	30.1170	1.45747
$428$	−4.49509	−0.217278
$429$	11.6404	0.562003
$430$	51.5489	2.48591
$431$	−13.7713	−0.663341	−0.331670	−	0.943395i	$-0.607612\pi$
$431$	−13.7713	−0.663341	−0.331670	+	0.943395i	$0.607612\pi$
$432$	9.22778	0.443972
$433$	39.9682	1.92075	0.960375	−	0.278711i	$-0.0899071\pi$
$433$	39.9682	1.92075	0.960375	+	0.278711i	$0.0899071\pi$
$434$	49.5514	2.37855
$435$	63.2355	3.03191
$436$	−19.3132	−0.924933
$437$	4.95370	0.236968
$438$	51.7496	2.47269
$439$	−5.80100	−0.276867	−0.138433	−	0.990372i	$-0.544207\pi$
$439$	−5.80100	−0.276867	−0.138433	+	0.990372i	$0.544207\pi$
$440$	4.56661	0.217704
$441$	4.12905	0.196621
$442$	−45.0504	−2.14283
$443$	7.52737	0.357636	0.178818	−	0.983882i	$-0.442773\pi$
$443$	7.52737	0.357636	0.178818	+	0.983882i	$0.442773\pi$
$444$	−24.4419	−1.15996
$445$	−32.2495	−1.52877
$446$	−17.4775	−0.827582
$447$	−10.4903	−0.496173
$448$	0.588209	0.0277903
$449$	5.79057	0.273274	0.136637	−	0.990621i	$-0.456371\pi$
$449$	5.79057	0.273274	0.136637	+	0.990621i	$0.456371\pi$
$450$	−20.2926	−0.956600
$451$	1.49162	0.0702377
$452$	−3.34976	−0.157559
$453$	47.5549	2.23432
$454$	−19.0722	−0.895104
$455$	−36.4394	−1.70831
$456$	−4.30094	−0.201410
$457$	−29.1621	−1.36414	−0.682072	−	0.731285i	$-0.738921\pi$
$457$	−29.1621	−1.36414	−0.682072	+	0.731285i	$0.738921\pi$
$458$	24.6007	1.14951
$459$	10.5487	0.492369
$460$	14.8189	0.690935
$461$	15.1624	0.706185	0.353093	−	0.935588i	$-0.385130\pi$
$461$	15.1624	0.706185	0.353093	+	0.935588i	$0.385130\pi$
$462$	12.9667	0.603264
$463$	−8.74032	−0.406197	−0.203099	−	0.979158i	$-0.565101\pi$
$463$	−8.74032	−0.406197	−0.203099	+	0.979158i	$0.565101\pi$
$464$	42.7842	1.98621
$465$	73.0603	3.38809
$466$	15.4257	0.714582
$467$	22.6015	1.04587	0.522937	−	0.852371i	$-0.324836\pi$
$467$	22.6015	1.04587	0.522937	+	0.852371i	$0.324836\pi$
$468$	−18.1406	−0.838549
$469$	−34.5207	−1.59402
$470$	30.6313	1.41292
$471$	−17.7835	−0.819423
$472$	−5.64581	−0.259869
$473$	−10.3017	−0.473675
$474$	−37.1365	−1.70573
$475$	3.21947	0.147719
$476$	−17.6748	−0.810122
$477$	35.7592	1.63730
$478$	52.3011	2.39219
$479$	7.08766	0.323844	0.161922	−	0.986804i	$-0.448231\pi$
$479$	7.08766	0.323844	0.161922	+	0.986804i	$0.448231\pi$
$480$	−41.0626	−1.87424
$481$	−38.9742	−1.77707
$482$	7.35467	0.334996
$483$	−35.3143	−1.60686
$484$	1.08739	0.0494268
$485$	16.6840	0.757579
$486$	−38.6571	−1.75352
$487$	11.3308	0.513447	0.256723	−	0.966485i	$-0.417357\pi$
$487$	11.3308	0.513447	0.256723	+	0.966485i	$0.417357\pi$
$488$	16.9563	0.767575
$489$	−20.7646	−0.939007
$490$	−5.56402	−0.251357
$491$	−26.6515	−1.20277	−0.601384	−	0.798960i	$-0.705384\pi$
$491$	−26.6515	−1.20277	−0.601384	+	0.798960i	$0.705384\pi$
$492$	−4.20257	−0.189466
$493$	48.9085	2.20273
$494$	8.17155	0.367655
$495$	10.5750	0.475313
$496$	49.4316	2.21954
$497$	−18.7022	−0.838907
$498$	−61.6721	−2.76359
$499$	32.7950	1.46810	0.734052	−	0.679093i	$-0.237627\pi$
$499$	32.7950	1.46810	0.734052	+	0.679093i	$0.237627\pi$
$500$	−5.85249	−0.261731
$501$	24.7585	1.10613
$502$	−15.7770	−0.704163
$503$	−25.3061	−1.12834	−0.564171	−	0.825658i	$-0.690804\pi$
$503$	−25.3061	−1.12834	−0.564171	+	0.825658i	$0.690804\pi$
$504$	16.9595	0.755436
$505$	25.2809	1.12498
$506$	−8.40841	−0.373799
$507$	−18.6122	−0.826597
$508$	15.9010	0.705493
$509$	−21.1163	−0.935962	−0.467981	−	0.883738i	$-0.655018\pi$
$509$	−21.1163	−0.935962	−0.467981	+	0.883738i	$0.655018\pi$
$510$	−73.9921	−3.27642
$511$	32.3745	1.43216
$512$	−11.7714	−0.520228
$513$	−1.91339	−0.0844781
$514$	−21.2933	−0.939207
$515$	20.9994	0.925345
$516$	29.0246	1.27774
$517$	−6.12149	−0.269223
$518$	−43.4148	−1.90754
$519$	23.6355	1.03748
$520$	−20.5159	−0.899681
$521$	−13.6039	−0.595996	−0.297998	−	0.954566i	$-0.596319\pi$
$521$	−13.6039	−0.595996	−0.297998	+	0.954566i	$0.596319\pi$
$522$	55.9168	2.44741
$523$	10.0234	0.438291	0.219145	−	0.975692i	$-0.429673\pi$
$523$	10.0234	0.438291	0.219145	+	0.975692i	$0.429673\pi$
$524$	1.08739	0.0475028
$525$	−22.9512	−1.00167
$526$	56.6823	2.47147
$527$	56.5073	2.46150
$528$	12.9353	0.562937
$529$	−0.0999622	−0.00434618
$530$	−48.1866	−2.09309
$531$	−13.0742	−0.567371
$532$	3.20597	0.138996
$533$	−6.70124	−0.290263
$534$	−51.5557	−2.23103
$535$	−11.7724	−0.508966
$536$	−19.4356	−0.839491
$537$	36.7842	1.58736
$538$	−18.8638	−0.813276
$539$	1.11194	0.0478945
$540$	−5.72386	−0.246316
$541$	23.3145	1.00237	0.501183	−	0.865341i	$-0.332898\pi$
$541$	23.3145	1.00237	0.501183	+	0.865341i	$0.332898\pi$
$542$	−45.8731	−1.97042
$543$	−17.9200	−0.769022
$544$	−31.7592	−1.36166
$545$	−50.5803	−2.16662
$546$	−58.2539	−2.49304
$547$	−9.53427	−0.407656	−0.203828	−	0.979007i	$-0.565338\pi$
$547$	−9.53427	−0.407656	−0.203828	+	0.979007i	$0.565338\pi$
$548$	17.4235	0.744297
$549$	39.2662	1.67584
$550$	−5.46471	−0.233016
$551$	−8.87135	−0.377932
$552$	−19.8824	−0.846253
$553$	−23.2325	−0.987948
$554$	−53.3379	−2.26611
$555$	−64.0123	−2.71717
$556$	20.0624	0.850833
$557$	39.7162	1.68283	0.841415	−	0.540390i	$-0.181723\pi$
$557$	39.7162	1.68283	0.841415	+	0.540390i	$0.181723\pi$
$558$	64.6046	2.73493
$559$	46.2815	1.95750
$560$	−40.4931	−1.71115
$561$	14.7869	0.624303
$562$	29.1429	1.22932
$563$	23.5725	0.993461	0.496730	−	0.867905i	$-0.334534\pi$
$563$	23.5725	0.993461	0.496730	+	0.867905i	$0.334534\pi$
$564$	17.2470	0.726228
$565$	−8.77285	−0.369076
$566$	32.8010	1.37873
$567$	−18.0884	−0.759643
$568$	−10.5296	−0.441811
$569$	−32.7431	−1.37266	−0.686332	−	0.727288i	$-0.740780\pi$
$569$	−32.7431	−1.37266	−0.686332	+	0.727288i	$0.740780\pi$
$570$	13.4212	0.562152
$571$	20.9599	0.877146	0.438573	−	0.898696i	$-0.355484\pi$
$571$	20.9599	0.877146	0.438573	+	0.898696i	$0.355484\pi$
$572$	−4.88519	−0.204260
$573$	32.6593	1.36436
$574$	−7.46477	−0.311574
$575$	14.8830	0.620663
$576$	0.766900	0.0319542
$577$	−28.7187	−1.19558	−0.597788	−	0.801654i	$-0.703954\pi$
$577$	−28.7187	−1.19558	−0.597788	+	0.801654i	$0.703954\pi$
$578$	−27.3573	−1.13791
$579$	36.3619	1.51115
$580$	−26.5384	−1.10195
$581$	−38.5820	−1.60065
$582$	26.6718	1.10558
$583$	9.62982	0.398826
$584$	18.2273	0.754250
$585$	−47.5093	−1.96427
$586$	0.478126	0.0197512
$587$	−0.360040	−0.0148605	−0.00743023	−	0.999972i	$-0.502365\pi$
$587$	−0.360040	−0.0148605	−0.00743023	+	0.999972i	$0.502365\pi$
$588$	−3.13283	−0.129196
$589$	−10.2497	−0.422331
$590$	17.6179	0.725316
$591$	33.2226	1.36659
$592$	−43.3098	−1.78002
$593$	−15.2715	−0.627125	−0.313562	−	0.949568i	$-0.601522\pi$
$593$	−15.2715	−0.627125	−0.313562	+	0.949568i	$0.601522\pi$
$594$	3.24778	0.133258
$595$	−46.2894	−1.89768
$596$	4.40252	0.180334
$597$	16.1619	0.661464
$598$	37.7755	1.54476
$599$	19.9639	0.815701	0.407850	−	0.913049i	$-0.366278\pi$
$599$	19.9639	0.815701	0.407850	+	0.913049i	$0.366278\pi$
$600$	−12.9218	−0.527531
$601$	−2.86189	−0.116739	−0.0583694	−	0.998295i	$-0.518590\pi$
$601$	−2.86189	−0.116739	−0.0583694	+	0.998295i	$0.518590\pi$
$602$	51.5548	2.10122
$603$	−45.0077	−1.83286
$604$	−19.9577	−0.812066
$605$	2.84782	0.115780
$606$	40.4153	1.64176
$607$	−11.9237	−0.483968	−0.241984	−	0.970280i	$-0.577798\pi$
$607$	−11.9237	−0.483968	−0.241984	+	0.970280i	$0.577798\pi$
$608$	5.76070	0.233627
$609$	63.2427	2.56272
$610$	−52.9125	−2.14236
$611$	27.5013	1.11258
$612$	−23.0442	−0.931505
$613$	19.6278	0.792760	0.396380	−	0.918087i	$-0.370266\pi$
$613$	19.6278	0.792760	0.396380	+	0.918087i	$0.370266\pi$
$614$	−15.7231	−0.634533
$615$	−11.0063	−0.443817
$616$	4.56713	0.184015
$617$	0.335093	0.0134903	0.00674517	−	0.999977i	$-0.497853\pi$
$617$	0.335093	0.0134903	0.00674517	+	0.999977i	$0.497853\pi$
$618$	33.5707	1.35041
$619$	−11.0293	−0.443304	−0.221652	−	0.975126i	$-0.571145\pi$
$619$	−11.0293	−0.443304	−0.221652	+	0.975126i	$0.571145\pi$
$620$	−30.6617	−1.23140
$621$	−8.84523	−0.354947
$622$	−0.660003	−0.0264637
$623$	−32.2532	−1.29220
$624$	−58.1130	−2.32638
$625$	−30.8778	−1.23511
$626$	7.02030	0.280587
$627$	−2.68215	−0.107115
$628$	7.46334	0.297820
$629$	−49.5092	−1.97406
$630$	−52.9224	−2.10848
$631$	3.97340	0.158179	0.0790894	−	0.996868i	$-0.474799\pi$
$631$	3.97340	0.158179	0.0790894	+	0.996868i	$0.474799\pi$
$632$	−13.0802	−0.520304
$633$	12.7658	0.507393
$634$	37.0101	1.46986
$635$	41.6440	1.65259
$636$	−27.1315	−1.07583
$637$	−4.99548	−0.197928
$638$	15.0582	0.596160
$639$	−24.3837	−0.964602
$640$	−32.7295	−1.29375
$641$	47.5752	1.87911	0.939553	−	0.342404i	$-0.111241\pi$
$641$	47.5752	1.87911	0.939553	+	0.342404i	$0.111241\pi$
$642$	−18.8200	−0.742766
$643$	−43.5662	−1.71808	−0.859042	−	0.511905i	$-0.828940\pi$
$643$	−43.5662	−1.71808	−0.859042	+	0.511905i	$0.828940\pi$
$644$	14.8206	0.584013
$645$	76.0141	2.99305
$646$	10.3804	0.408411
$647$	47.0518	1.84980	0.924899	−	0.380213i	$-0.124149\pi$
$647$	47.0518	1.84980	0.924899	+	0.380213i	$0.124149\pi$
$648$	−10.1840	−0.400067
$649$	−3.52083	−0.138205
$650$	24.5507	0.962958
$651$	73.0687	2.86379
$652$	8.71441	0.341283
$653$	8.27834	0.323956	0.161978	−	0.986794i	$-0.448213\pi$
$653$	8.27834	0.323956	0.161978	+	0.986794i	$0.448213\pi$
$654$	−80.8602	−3.16188
$655$	2.84782	0.111274
$656$	−7.44672	−0.290745
$657$	42.2094	1.64675
$658$	30.6348	1.19427
$659$	31.7765	1.23784	0.618919	−	0.785455i	$-0.287571\pi$
$659$	31.7765	1.23784	0.618919	+	0.785455i	$0.287571\pi$
$660$	−8.02358	−0.312318
$661$	−20.6805	−0.804378	−0.402189	−	0.915557i	$-0.631751\pi$
$661$	−20.6805	−0.804378	−0.402189	+	0.915557i	$0.631751\pi$
$662$	−13.2805	−0.516161
$663$	−66.4314	−2.57998
$664$	−21.7222	−0.842985
$665$	8.39628	0.325594
$666$	−56.6037	−2.19335
$667$	−41.0106	−1.58794
$668$	−10.3905	−0.402022
$669$	−25.7723	−0.996415
$670$	60.6493	2.34309
$671$	10.5743	0.408215
$672$	−41.0673	−1.58421
$673$	−0.949611	−0.0366048	−0.0183024	−	0.999832i	$-0.505826\pi$
$673$	−0.949611	−0.0366048	−0.0183024	+	0.999832i	$0.505826\pi$
$674$	−28.2274	−1.08728
$675$	−5.74861	−0.221264
$676$	7.81111	0.300427
$677$	7.73430	0.297253	0.148627	−	0.988893i	$-0.452515\pi$
$677$	7.73430	0.297253	0.148627	+	0.988893i	$0.452515\pi$
$678$	−14.0247	−0.538616
$679$	16.6859	0.640345
$680$	−26.0615	−0.999414
$681$	−28.1239	−1.07771
$682$	17.3978	0.666196
$683$	−34.2098	−1.30900	−0.654500	−	0.756062i	$-0.727121\pi$
$683$	−34.2098	−1.30900	−0.654500	+	0.756062i	$0.727121\pi$
$684$	4.17991	0.159823
$685$	45.6314	1.74349
$686$	29.4666	1.12504
$687$	36.2762	1.38402
$688$	51.4301	1.96075
$689$	−43.2628	−1.64818
$690$	62.0436	2.36196
$691$	−12.5419	−0.477117	−0.238558	−	0.971128i	$-0.576675\pi$
$691$	−12.5419	−0.477117	−0.238558	+	0.971128i	$0.576675\pi$
$692$	−9.91927	−0.377074
$693$	10.5762	0.401758
$694$	58.3104	2.21343
$695$	52.5423	1.99304
$696$	35.6065	1.34966
$697$	−8.51265	−0.322440
$698$	−3.56078	−0.134777
$699$	22.7468	0.860362
$700$	9.63206	0.364058
$701$	−8.49550	−0.320871	−0.160435	−	0.987046i	$-0.551290\pi$
$701$	−8.49550	−0.320871	−0.160435	+	0.987046i	$0.551290\pi$
$702$	−14.5909	−0.550700
$703$	8.98032	0.338699
$704$	0.206524	0.00778365
$705$	45.1690	1.70116
$706$	15.0542	0.566571
$707$	25.2838	0.950894
$708$	9.91975	0.372807
$709$	37.7907	1.41926	0.709630	−	0.704574i	$-0.248862\pi$
$709$	37.7907	1.41926	0.709630	+	0.704574i	$0.248862\pi$
$710$	32.8578	1.23313
$711$	−30.2903	−1.13597
$712$	−18.1590	−0.680536
$713$	−47.3823	−1.77448
$714$	−74.0005	−2.76940
$715$	−12.7941	−0.478472
$716$	−15.4375	−0.576925
$717$	77.1232	2.88022
$718$	49.5855	1.85052
$719$	−1.79384	−0.0668988	−0.0334494	−	0.999440i	$-0.510649\pi$
$719$	−1.79384	−0.0668988	−0.0334494	+	0.999440i	$0.510649\pi$
$720$	−52.7944	−1.96753
$721$	21.0018	0.782149
$722$	31.5020	1.17238
$723$	10.8452	0.403338
$724$	7.52061	0.279501
$725$	−26.6532	−0.989875
$726$	4.55267	0.168965
$727$	−33.1781	−1.23051	−0.615253	−	0.788330i	$-0.710946\pi$
$727$	−33.1781	−1.23051	−0.615253	+	0.788330i	$0.710946\pi$
$728$	−20.5182	−0.760457
$729$	−37.9510	−1.40559
$730$	−56.8786	−2.10517
$731$	58.7919	2.17450
$732$	−29.7924	−1.10116
$733$	−42.4401	−1.56756	−0.783780	−	0.621039i	$-0.786711\pi$
$733$	−42.4401	−1.56756	−0.783780	+	0.621039i	$0.786711\pi$
$734$	−44.2806	−1.63443
$735$	−8.20472	−0.302636
$736$	26.6306	0.981618
$737$	−12.1204	−0.446461
$738$	−9.73248	−0.358258
$739$	−42.1732	−1.55137	−0.775683	−	0.631123i	$-0.782594\pi$
$739$	−42.1732	−1.55137	−0.775683	+	0.631123i	$0.782594\pi$
$740$	26.8644	0.987556
$741$	12.0498	0.442660
$742$	−48.1921	−1.76919
$743$	20.5478	0.753827	0.376913	−	0.926249i	$-0.376985\pi$
$743$	20.5478	0.753827	0.376913	+	0.926249i	$0.376985\pi$
$744$	41.1386	1.50822
$745$	11.5300	0.422426
$746$	−2.96767	−0.108654
$747$	−50.3028	−1.84048
$748$	−6.20571	−0.226903
$749$	−11.7738	−0.430204
$750$	−24.5032	−0.894729
$751$	7.43795	0.271415	0.135707	−	0.990749i	$-0.456669\pi$
$751$	7.43795	0.271415	0.135707	+	0.990749i	$0.456669\pi$
$752$	30.5607	1.11443
$753$	−23.2648	−0.847818
$754$	−67.6504	−2.46368
$755$	−52.2682	−1.90223
$756$	−5.72451	−0.208198
$757$	0.0704045	0.00255890	0.00127945	−	0.999999i	$-0.499593\pi$
$757$	0.0704045	0.00255890	0.00127945	+	0.999999i	$0.499593\pi$
$758$	41.5469	1.50905
$759$	−12.3991	−0.450057
$760$	4.72722	0.171474
$761$	−21.5655	−0.781749	−0.390874	−	0.920444i	$-0.627827\pi$
$761$	−21.5655	−0.781749	−0.390874	+	0.920444i	$0.627827\pi$
$762$	66.5742	2.41173
$763$	−50.5860	−1.83134
$764$	−13.7064	−0.495879
$765$	−60.3515	−2.18201
$766$	−21.6897	−0.783680
$767$	15.8176	0.571142
$768$	−51.2529	−1.84943
$769$	−4.81710	−0.173709	−0.0868545	−	0.996221i	$-0.527682\pi$
$769$	−4.81710	−0.173709	−0.0868545	+	0.996221i	$0.527682\pi$
$770$	−14.2518	−0.513600
$771$	−31.3992	−1.13081
$772$	−15.2602	−0.549227
$773$	32.3123	1.16219	0.581097	−	0.813834i	$-0.302624\pi$
$773$	32.3123	1.16219	0.581097	+	0.813834i	$0.302624\pi$
$774$	67.2165	2.41605
$775$	−30.7943	−1.10616
$776$	9.39436	0.337238
$777$	−64.0196	−2.29669
$778$	−35.7262	−1.28085
$779$	1.54408	0.0553225
$780$	36.0467	1.29068
$781$	−6.56643	−0.234965
$782$	47.9866	1.71600
$783$	15.8405	0.566093
$784$	−5.55120	−0.198257
$785$	19.5461	0.697631
$786$	4.55267	0.162388
$787$	38.9154	1.38719	0.693593	−	0.720367i	$-0.256027\pi$
$787$	38.9154	1.38719	0.693593	+	0.720367i	$0.256027\pi$
$788$	−13.9427	−0.496690
$789$	83.5839	2.97566
$790$	40.8171	1.45221
$791$	−8.77385	−0.311962
$792$	5.95457	0.211586
$793$	−47.5058	−1.68698
$794$	1.71664	0.0609213
$795$	−71.0561	−2.52010
$796$	−6.78278	−0.240409
$797$	34.3711	1.21749	0.608743	−	0.793367i	$-0.291674\pi$
$797$	34.3711	1.21749	0.608743	+	0.793367i	$0.291674\pi$
$798$	13.4227	0.475159
$799$	34.9352	1.23592
$800$	17.3075	0.611914
$801$	−42.0513	−1.48581
$802$	56.9232	2.01003
$803$	11.3669	0.401128
$804$	34.1486	1.20433
$805$	38.8144	1.36803
$806$	−78.1611	−2.75311
$807$	−27.8166	−0.979190
$808$	14.2351	0.500789
$809$	−11.4665	−0.403139	−0.201570	−	0.979474i	$-0.564604\pi$
$809$	−11.4665	−0.403139	−0.201570	+	0.979474i	$0.564604\pi$
$810$	31.7795	1.11662
$811$	−17.2858	−0.606988	−0.303494	−	0.952833i	$-0.598153\pi$
$811$	−17.2858	−0.606988	−0.303494	+	0.952833i	$0.598153\pi$
$812$	−26.5415	−0.931423
$813$	−67.6445	−2.37240
$814$	−15.2432	−0.534273
$815$	22.8226	0.799441
$816$	−73.8215	−2.58427
$817$	−10.6641	−0.373088
$818$	4.81044	0.168193
$819$	−47.5147	−1.66030
$820$	4.61909	0.161306
$821$	20.1315	0.702596	0.351298	−	0.936264i	$-0.385740\pi$
$821$	20.1315	0.702596	0.351298	+	0.936264i	$0.385740\pi$
$822$	72.9487	2.54438
$823$	11.2512	0.392193	0.196096	−	0.980585i	$-0.437173\pi$
$823$	11.2512	0.392193	0.196096	+	0.980585i	$0.437173\pi$
$824$	11.8243	0.411919
$825$	−8.05828	−0.280553
$826$	17.6199	0.613074
$827$	−16.4545	−0.572180	−0.286090	−	0.958203i	$-0.592356\pi$
$827$	−16.4545	−0.572180	−0.286090	+	0.958203i	$0.592356\pi$
$828$	19.3229	0.671518
$829$	15.0407	0.522384	0.261192	−	0.965287i	$-0.415884\pi$
$829$	15.0407	0.522384	0.261192	+	0.965287i	$0.415884\pi$
$830$	67.7846	2.35284
$831$	−78.6521	−2.72841
$832$	−0.927826	−0.0321666
$833$	−6.34581	−0.219869
$834$	83.9969	2.90857
$835$	−27.2123	−0.941722
$836$	1.12563	0.0389309
$837$	18.3016	0.632596
$838$	−13.3281	−0.460413
$839$	5.52227	0.190650	0.0953250	−	0.995446i	$-0.469611\pi$
$839$	5.52227	0.190650	0.0953250	+	0.995446i	$0.469611\pi$
$840$	−33.6997	−1.16275
$841$	44.4438	1.53255
$842$	3.57398	0.123167
$843$	42.9742	1.48011
$844$	−5.35749	−0.184412
$845$	20.4569	0.703739
$846$	39.9413	1.37321
$847$	2.84815	0.0978635
$848$	−48.0755	−1.65092
$849$	48.3684	1.66000
$850$	31.1870	1.06971
$851$	41.5143	1.42309
$852$	18.5006	0.633819
$853$	6.99592	0.239536	0.119768	−	0.992802i	$-0.461785\pi$
$853$	6.99592	0.239536	0.119768	+	0.992802i	$0.461785\pi$
$854$	−52.9185	−1.81084
$855$	10.9470	0.374378
$856$	−6.62879	−0.226568
$857$	−19.9292	−0.680768	−0.340384	−	0.940287i	$-0.610557\pi$
$857$	−19.9292	−0.680768	−0.340384	+	0.940287i	$0.610557\pi$
$858$	−20.4533	−0.698264
$859$	1.88291	0.0642442	0.0321221	−	0.999484i	$-0.489773\pi$
$859$	1.88291	0.0642442	0.0321221	+	0.999484i	$0.489773\pi$
$860$	−31.9013	−1.08783
$861$	−11.0076	−0.375137
$862$	24.1975	0.824171
$863$	−56.1168	−1.91024	−0.955119	−	0.296223i	$-0.904273\pi$
$863$	−56.1168	−1.91024	−0.955119	+	0.296223i	$0.904273\pi$
$864$	−10.2862	−0.349943
$865$	−25.9781	−0.883281
$866$	−70.2280	−2.38645
$867$	−40.3412	−1.37006
$868$	−30.6652	−1.04084
$869$	−8.15707	−0.276710
$870$	−111.111	−3.76701
$871$	54.4520	1.84504
$872$	−28.4806	−0.964476
$873$	21.7548	0.736289
$874$	−8.70414	−0.294422
$875$	−15.3291	−0.518220
$876$	−32.0255	−1.08204
$877$	23.6365	0.798148	0.399074	−	0.916919i	$-0.369332\pi$
$877$	23.6365	0.798148	0.399074	+	0.916919i	$0.369332\pi$
$878$	10.1929	0.343994
$879$	0.705046	0.0237806
$880$	−14.2174	−0.479267
$881$	14.5623	0.490617	0.245309	−	0.969445i	$-0.421111\pi$
$881$	14.5623	0.490617	0.245309	+	0.969445i	$0.421111\pi$
$882$	−7.25513	−0.244293
$883$	30.4891	1.02604	0.513019	−	0.858377i	$-0.328527\pi$
$883$	30.4891	1.02604	0.513019	+	0.858377i	$0.328527\pi$
$884$	27.8797	0.937696
$885$	25.9793	0.873286
$886$	−13.2263	−0.444347
$887$	−34.3210	−1.15239	−0.576193	−	0.817314i	$-0.695462\pi$
$887$	−34.3210	−1.15239	−0.576193	+	0.817314i	$0.695462\pi$
$888$	−36.0439	−1.20955
$889$	41.6487	1.39685
$890$	56.6655	1.89943
$891$	−6.35095	−0.212765
$892$	10.8160	0.362148
$893$	−6.33679	−0.212052
$894$	18.4324	0.616473
$895$	−40.4300	−1.35143
$896$	−32.7333	−1.09354
$897$	55.7039	1.85990
$898$	−10.1746	−0.339530
$899$	84.8547	2.83006
$900$	12.5582	0.418606
$901$	−54.9572	−1.83089
$902$	−2.62092	−0.0872672
$903$	76.0228	2.52988
$904$	−4.93980	−0.164295
$905$	19.6961	0.654721
$906$	−83.5586	−2.77605
$907$	8.26727	0.274510	0.137255	−	0.990536i	$-0.456172\pi$
$907$	8.26727	0.274510	0.137255	+	0.990536i	$0.456172\pi$
$908$	11.8030	0.391695
$909$	32.9647	1.09337
$910$	64.0276	2.12249
$911$	−36.9337	−1.22367	−0.611835	−	0.790986i	$-0.709568\pi$
$911$	−36.9337	−1.22367	−0.611835	+	0.790986i	$0.709568\pi$
$912$	13.3903	0.443396
$913$	−13.5464	−0.448319
$914$	51.2406	1.69489
$915$	−78.0249	−2.57942
$916$	−15.2243	−0.503024
$917$	2.84815	0.0940541
$918$	−18.5350	−0.611747
$919$	35.4955	1.17089	0.585444	−	0.810713i	$-0.300920\pi$
$919$	35.4955	1.17089	0.585444	+	0.810713i	$0.300920\pi$
$920$	21.8530	0.720473
$921$	−23.1853	−0.763982
$922$	−26.6419	−0.877403
$923$	29.5003	0.971014
$924$	−8.02450	−0.263987
$925$	26.9806	0.887117
$926$	15.3576	0.504682
$927$	27.3819	0.899340
$928$	−47.6915	−1.56555
$929$	−9.81084	−0.321883	−0.160942	−	0.986964i	$-0.551453\pi$
$929$	−9.81084	−0.321883	−0.160942	+	0.986964i	$0.551453\pi$
$930$	−128.374	−4.20955
$931$	1.15105	0.0377240
$932$	−9.54628	−0.312699
$933$	−0.973243	−0.0318625
$934$	−39.7131	−1.29945
$935$	−16.2525	−0.531512
$936$	−26.7514	−0.874398
$937$	9.78650	0.319711	0.159856	−	0.987140i	$-0.448897\pi$
$937$	9.78650	0.319711	0.159856	+	0.987140i	$0.448897\pi$
$938$	60.6562	1.98050
$939$	10.3521	0.337829
$940$	−18.9564	−0.618288
$941$	38.3037	1.24867	0.624333	−	0.781158i	$-0.285371\pi$
$941$	38.3037	1.24867	0.624333	+	0.781158i	$0.285371\pi$
$942$	31.2474	1.01810
$943$	7.13800	0.232445
$944$	17.5773	0.572091
$945$	−14.9922	−0.487697
$946$	18.1012	0.588520
$947$	19.7912	0.643127	0.321564	−	0.946888i	$-0.395792\pi$
$947$	19.7912	0.643127	0.321564	+	0.946888i	$0.395792\pi$
$948$	22.9821	0.746424
$949$	−51.0666	−1.65769
$950$	−5.65691	−0.183534
$951$	54.5752	1.76972
$952$	−26.0645	−0.844756
$953$	9.09461	0.294603	0.147302	−	0.989092i	$-0.452941\pi$
$953$	9.09461	0.294603	0.147302	+	0.989092i	$0.452941\pi$
$954$	−62.8323	−2.03427
$955$	−35.8963	−1.16158
$956$	−32.3668	−1.04682
$957$	22.2049	0.717782
$958$	−12.4537	−0.402361
$959$	45.6366	1.47368
$960$	−1.52389	−0.0491832
$961$	67.0385	2.16253
$962$	68.4814	2.20793
$963$	−15.3505	−0.494663
$964$	−4.55148	−0.146593
$965$	−39.9658	−1.28654
$966$	62.0507	1.99645
$967$	46.7017	1.50183	0.750913	−	0.660401i	$-0.229614\pi$
$967$	46.7017	1.50183	0.750913	+	0.660401i	$0.229614\pi$
$968$	1.60354	0.0515399
$969$	15.3070	0.491730
$970$	−29.3153	−0.941258
$971$	46.7811	1.50128	0.750639	−	0.660713i	$-0.229746\pi$
$971$	46.7811	1.50128	0.750639	+	0.660713i	$0.229746\pi$
$972$	23.9232	0.767337
$973$	52.5483	1.68462
$974$	−19.9093	−0.637934
$975$	36.2025	1.15941
$976$	−52.7905	−1.68978
$977$	40.3140	1.28976	0.644880	−	0.764284i	$-0.276907\pi$
$977$	40.3140	1.28976	0.644880	+	0.764284i	$0.276907\pi$
$978$	36.4854	1.16667
$979$	−11.3243	−0.361925
$980$	3.44333	0.109993
$981$	−65.9535	−2.10573
$982$	46.8293	1.49438
$983$	−6.40442	−0.204269	−0.102135	−	0.994771i	$-0.532567\pi$
$983$	−6.40442	−0.204269	−0.102135	+	0.994771i	$0.532567\pi$
$984$	−6.19741	−0.197566
$985$	−36.5154	−1.16348
$986$	−85.9369	−2.73679
$987$	45.1741	1.43791
$988$	−5.05701	−0.160885
$989$	−49.2980	−1.56758
$990$	−18.5814	−0.590555
$991$	23.8654	0.758109	0.379055	−	0.925374i	$-0.376249\pi$
$991$	23.8654	0.758109	0.379055	+	0.925374i	$0.376249\pi$
$992$	−55.1013	−1.74947
$993$	−19.5834	−0.621462
$994$	32.8615	1.04230
$995$	−17.7638	−0.563149
$996$	38.1662	1.20934
$997$	−47.1224	−1.49238	−0.746191	−	0.665732i	$-0.768119\pi$
$997$	−47.1224	−1.49238	−0.746191	+	0.665732i	$0.768119\pi$
$998$	−57.6239	−1.82405
$999$	−16.0351	−0.507327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.6	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.6	✓	23	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)

\(f(q)\)	\(=\)	\(q-1.75710 q^{2} -2.59102 q^{3} +1.08739 q^{4} +2.84782 q^{5} +4.55267 q^{6} +2.84815 q^{7} +1.60354 q^{8} +3.71338 q^{9} +O(q^{10})\)	\(q-1.75710 q^{2} -2.59102 q^{3} +1.08739 q^{4} +2.84782 q^{5} +4.55267 q^{6} +2.84815 q^{7} +1.60354 q^{8} +3.71338 q^{9} -5.00390 q^{10} +1.00000 q^{11} -2.81745 q^{12} -4.49259 q^{13} -5.00447 q^{14} -7.37876 q^{15} -4.99236 q^{16} -5.70698 q^{17} -6.52477 q^{18} +1.03517 q^{19} +3.09669 q^{20} -7.37960 q^{21} -1.75710 q^{22} +4.78540 q^{23} -4.15482 q^{24} +3.11008 q^{25} +7.89391 q^{26} -1.84838 q^{27} +3.09704 q^{28} -8.56994 q^{29} +12.9652 q^{30} -9.90144 q^{31} +5.56498 q^{32} -2.59102 q^{33} +10.0277 q^{34} +8.11101 q^{35} +4.03789 q^{36} +8.67521 q^{37} -1.81890 q^{38} +11.6404 q^{39} +4.56661 q^{40} +1.49162 q^{41} +12.9667 q^{42} -10.3017 q^{43} +1.08739 q^{44} +10.5750 q^{45} -8.40841 q^{46} -6.12149 q^{47} +12.9353 q^{48} +1.11194 q^{49} -5.46471 q^{50} +14.7869 q^{51} -4.88519 q^{52} +9.62982 q^{53} +3.24778 q^{54} +2.84782 q^{55} +4.56713 q^{56} -2.68215 q^{57} +15.0582 q^{58} -3.52083 q^{59} -8.02358 q^{60} +10.5743 q^{61} +17.3978 q^{62} +10.5762 q^{63} +0.206524 q^{64} -12.7941 q^{65} +4.55267 q^{66} -12.1204 q^{67} -6.20571 q^{68} -12.3991 q^{69} -14.2518 q^{70} -6.56643 q^{71} +5.95457 q^{72} +11.3669 q^{73} -15.2432 q^{74} -8.05828 q^{75} +1.12563 q^{76} +2.84815 q^{77} -20.4533 q^{78} -8.15707 q^{79} -14.2174 q^{80} -6.35095 q^{81} -2.62092 q^{82} -13.5464 q^{83} -8.02450 q^{84} -16.2525 q^{85} +18.1012 q^{86} +22.2049 q^{87} +1.60354 q^{88} -11.3243 q^{89} -18.5814 q^{90} -12.7956 q^{91} +5.20359 q^{92} +25.6548 q^{93} +10.7560 q^{94} +2.94798 q^{95} -14.4190 q^{96} +5.85850 q^{97} -1.95378 q^{98} +3.71338 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9} - 2 q^{10} + 23 q^{11} + 8 q^{12} - 24 q^{13} - 13 q^{14} - 27 q^{15} + 7 q^{16} - 7 q^{17} - 14 q^{18} - 18 q^{19} - 4 q^{20} - 29 q^{21} - 7 q^{22} - 26 q^{23} - 4 q^{24} + 18 q^{25} + 8 q^{26} - 3 q^{27} - 11 q^{28} - 45 q^{29} + 19 q^{30} - 23 q^{31} - 34 q^{32} - 3 q^{33} - 2 q^{34} - 18 q^{35} - 6 q^{36} - 2 q^{37} - 8 q^{38} - 40 q^{39} - 24 q^{40} - 23 q^{41} + 59 q^{42} - 14 q^{43} + 15 q^{44} - 18 q^{45} - 12 q^{46} - 55 q^{47} + 10 q^{48} + 11 q^{49} - 41 q^{50} - 21 q^{51} - 37 q^{52} - 10 q^{53} - 68 q^{54} - 9 q^{55} + 2 q^{56} - 18 q^{57} + 27 q^{58} - 75 q^{59} - 63 q^{60} - 55 q^{61} + 14 q^{62} - 16 q^{63} + 19 q^{64} - 25 q^{65} - 11 q^{66} + 17 q^{67} + 41 q^{68} - 22 q^{69} + 27 q^{70} - 105 q^{71} - 11 q^{72} - 3 q^{73} - 39 q^{74} + 25 q^{75} - 30 q^{76} - 12 q^{77} + 25 q^{78} - 48 q^{79} - 37 q^{80} + 3 q^{81} + 36 q^{82} + 4 q^{83} - 111 q^{84} - 30 q^{85} + 22 q^{86} + 5 q^{87} - 21 q^{88} - 39 q^{89} + 100 q^{90} - 22 q^{91} - 30 q^{92} - 5 q^{93} + 11 q^{94} - 88 q^{95} + 13 q^{96} + 24 q^{97} - 91 q^{98} + 12 q^{99}+O(q^{100}) \) 23 * q - 7 * q^2 - 3 * q^3 + 15 * q^4 - 9 * q^5 - 11 * q^6 - 12 * q^7 - 21 * q^8 + 12 * q^9 - 2 * q^10 + 23 * q^11 + 8 * q^12 - 24 * q^13 - 13 * q^14 - 27 * q^15 + 7 * q^16 - 7 * q^17 - 14 * q^18 - 18 * q^19 - 4 * q^20 - 29 * q^21 - 7 * q^22 - 26 * q^23 - 4 * q^24 + 18 * q^25 + 8 * q^26 - 3 * q^27 - 11 * q^28 - 45 * q^29 + 19 * q^30 - 23 * q^31 - 34 * q^32 - 3 * q^33 - 2 * q^34 - 18 * q^35 - 6 * q^36 - 2 * q^37 - 8 * q^38 - 40 * q^39 - 24 * q^40 - 23 * q^41 + 59 * q^42 - 14 * q^43 + 15 * q^44 - 18 * q^45 - 12 * q^46 - 55 * q^47 + 10 * q^48 + 11 * q^49 - 41 * q^50 - 21 * q^51 - 37 * q^52 - 10 * q^53 - 68 * q^54 - 9 * q^55 + 2 * q^56 - 18 * q^57 + 27 * q^58 - 75 * q^59 - 63 * q^60 - 55 * q^61 + 14 * q^62 - 16 * q^63 + 19 * q^64 - 25 * q^65 - 11 * q^66 + 17 * q^67 + 41 * q^68 - 22 * q^69 + 27 * q^70 - 105 * q^71 - 11 * q^72 - 3 * q^73 - 39 * q^74 + 25 * q^75 - 30 * q^76 - 12 * q^77 + 25 * q^78 - 48 * q^79 - 37 * q^80 + 3 * q^81 + 36 * q^82 + 4 * q^83 - 111 * q^84 - 30 * q^85 + 22 * q^86 + 5 * q^87 - 21 * q^88 - 39 * q^89 + 100 * q^90 - 22 * q^91 - 30 * q^92 - 5 * q^93 + 11 * q^94 - 88 * q^95 + 13 * q^96 + 24 * q^97 - 91 * q^98 + 12 * q^99

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