LMFDB - Embedded newform 1441.2.a.c.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5064429313$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.28535 q^{2} +0.625999 q^{3} +3.22283 q^{4} -3.41400 q^{5} +1.43063 q^{6} -3.04305 q^{7} +2.79459 q^{8} -2.60812 q^{9} +O(q^{10})$	\(q+2.28535 q^{2} +0.625999 q^{3} +3.22283 q^{4} -3.41400 q^{5} +1.43063 q^{6} -3.04305 q^{7} +2.79459 q^{8} -2.60812 q^{9} -7.80220 q^{10} +1.00000 q^{11} +2.01749 q^{12} -0.0108256 q^{13} -6.95444 q^{14} -2.13716 q^{15} -0.0590304 q^{16} +4.75014 q^{17} -5.96048 q^{18} -6.00532 q^{19} -11.0028 q^{20} -1.90495 q^{21} +2.28535 q^{22} -6.25975 q^{23} +1.74941 q^{24} +6.65543 q^{25} -0.0247403 q^{26} -3.51068 q^{27} -9.80723 q^{28} +6.23221 q^{29} -4.88417 q^{30} -4.73298 q^{31} -5.72409 q^{32} +0.625999 q^{33} +10.8557 q^{34} +10.3890 q^{35} -8.40554 q^{36} -7.75151 q^{37} -13.7243 q^{38} -0.00677683 q^{39} -9.54076 q^{40} +7.20698 q^{41} -4.35347 q^{42} +2.12700 q^{43} +3.22283 q^{44} +8.90415 q^{45} -14.3057 q^{46} -5.17378 q^{47} -0.0369530 q^{48} +2.26016 q^{49} +15.2100 q^{50} +2.97358 q^{51} -0.0348891 q^{52} +0.876970 q^{53} -8.02314 q^{54} -3.41400 q^{55} -8.50409 q^{56} -3.75932 q^{57} +14.2428 q^{58} -2.17407 q^{59} -6.88772 q^{60} +10.2203 q^{61} -10.8165 q^{62} +7.93666 q^{63} -12.9635 q^{64} +0.0369587 q^{65} +1.43063 q^{66} -0.594405 q^{67} +15.3089 q^{68} -3.91860 q^{69} +23.7425 q^{70} -9.32442 q^{71} -7.28865 q^{72} +6.92029 q^{73} -17.7149 q^{74} +4.16629 q^{75} -19.3541 q^{76} -3.04305 q^{77} -0.0154874 q^{78} -8.92707 q^{79} +0.201530 q^{80} +5.62669 q^{81} +16.4705 q^{82} +5.23145 q^{83} -6.13932 q^{84} -16.2170 q^{85} +4.86095 q^{86} +3.90136 q^{87} +2.79459 q^{88} +12.8067 q^{89} +20.3491 q^{90} +0.0329429 q^{91} -20.1741 q^{92} -2.96284 q^{93} -11.8239 q^{94} +20.5022 q^{95} -3.58328 q^{96} +5.22347 q^{97} +5.16526 q^{98} -2.60812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.28535	1.61599	0.807994	−	0.589191i	$-0.200554\pi$
$2$	2.28535	1.61599	0.807994	+	0.589191i	$0.200554\pi$
$3$	0.625999	0.361421	0.180710	−	0.983536i	$-0.442160\pi$
$3$	0.625999	0.361421	0.180710	+	0.983536i	$0.442160\pi$
$4$	3.22283	1.61141
$5$	−3.41400	−1.52679	−0.763395	−	0.645932i	$-0.776469\pi$
$5$	−3.41400	−1.52679	−0.763395	+	0.645932i	$0.776469\pi$
$6$	1.43063	0.584051
$7$	−3.04305	−1.15017	−0.575083	−	0.818095i	$-0.695030\pi$
$7$	−3.04305	−1.15017	−0.575083	+	0.818095i	$0.695030\pi$
$8$	2.79459	0.988038
$9$	−2.60812	−0.869375
$10$	−7.80220	−2.46727
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.01749	0.582399
$13$	−0.0108256	−0.00300249	−0.00150124	−	0.999999i	$-0.500478\pi$
$13$	−0.0108256	−0.00300249	−0.00150124	+	0.999999i	$0.500478\pi$
$14$	−6.95444	−1.85865
$15$	−2.13716	−0.551813
$16$	−0.0590304	−0.0147576
$17$	4.75014	1.15208	0.576039	−	0.817422i	$-0.304598\pi$
$17$	4.75014	1.15208	0.576039	+	0.817422i	$0.304598\pi$
$18$	−5.96048	−1.40490
$19$	−6.00532	−1.37771	−0.688857	−	0.724897i	$-0.741887\pi$
$19$	−6.00532	−1.37771	−0.688857	+	0.724897i	$0.741887\pi$
$20$	−11.0028	−2.46029
$21$	−1.90495	−0.415694
$22$	2.28535	0.487238
$23$	−6.25975	−1.30525	−0.652624	−	0.757682i	$-0.726332\pi$
$23$	−6.25975	−1.30525	−0.652624	+	0.757682i	$0.726332\pi$
$24$	1.74941	0.357098
$25$	6.65543	1.33109
$26$	−0.0247403	−0.00485198
$27$	−3.51068	−0.675631
$28$	−9.80723	−1.85339
$29$	6.23221	1.15729	0.578646	−	0.815579i	$-0.303581\pi$
$29$	6.23221	1.15729	0.578646	+	0.815579i	$0.303581\pi$
$30$	−4.88417	−0.891723
$31$	−4.73298	−0.850068	−0.425034	−	0.905177i	$-0.639738\pi$
$31$	−4.73298	−0.850068	−0.425034	+	0.905177i	$0.639738\pi$
$32$	−5.72409	−1.01189
$33$	0.625999	0.108972
$34$	10.8557	1.86174
$35$	10.3890	1.75606
$36$	−8.40554	−1.40092
$37$	−7.75151	−1.27434	−0.637171	−	0.770723i	$-0.719895\pi$
$37$	−7.75151	−1.27434	−0.637171	+	0.770723i	$0.719895\pi$
$38$	−13.7243	−2.22637
$39$	−0.00677683	−0.00108516
$40$	−9.54076	−1.50853
$41$	7.20698	1.12554	0.562771	−	0.826613i	$-0.309735\pi$
$41$	7.20698	1.12554	0.562771	+	0.826613i	$0.309735\pi$
$42$	−4.35347	−0.671756
$43$	2.12700	0.324365	0.162183	−	0.986761i	$-0.448147\pi$
$43$	2.12700	0.324365	0.162183	+	0.986761i	$0.448147\pi$
$44$	3.22283	0.485860
$45$	8.90415	1.32735
$46$	−14.3057	−2.10926
$47$	−5.17378	−0.754673	−0.377336	−	0.926076i	$-0.623160\pi$
$47$	−5.17378	−0.754673	−0.377336	+	0.926076i	$0.623160\pi$
$48$	−0.0369530	−0.00533371
$49$	2.26016	0.322880
$50$	15.2100	2.15102
$51$	2.97358	0.416385
$52$	−0.0348891	−0.00483825
$53$	0.876970	0.120461	0.0602306	−	0.998184i	$-0.480816\pi$
$53$	0.876970	0.120461	0.0602306	+	0.998184i	$0.480816\pi$
$54$	−8.02314	−1.09181
$55$	−3.41400	−0.460344
$56$	−8.50409	−1.13641
$57$	−3.75932	−0.497935
$58$	14.2428	1.87017
$59$	−2.17407	−0.283039	−0.141520	−	0.989935i	$-0.545199\pi$
$59$	−2.17407	−0.283039	−0.141520	+	0.989935i	$0.545199\pi$
$60$	−6.88772	−0.889200
$61$	10.2203	1.30857	0.654287	−	0.756246i	$-0.272969\pi$
$61$	10.2203	1.30857	0.654287	+	0.756246i	$0.272969\pi$
$62$	−10.8165	−1.37370
$63$	7.93666	0.999925
$64$	−12.9635	−1.62044
$65$	0.0369587	0.00458416
$66$	1.43063	0.176098
$67$	−0.594405	−0.0726181	−0.0363090	−	0.999341i	$-0.511560\pi$
$67$	−0.594405	−0.0726181	−0.0363090	+	0.999341i	$0.511560\pi$
$68$	15.3089	1.85648
$69$	−3.91860	−0.471744
$70$	23.7425	2.83777
$71$	−9.32442	−1.10660	−0.553302	−	0.832980i	$-0.686633\pi$
$71$	−9.32442	−1.10660	−0.553302	+	0.832980i	$0.686633\pi$
$72$	−7.28865	−0.858976
$73$	6.92029	0.809959	0.404979	−	0.914326i	$-0.367279\pi$
$73$	6.92029	0.809959	0.404979	+	0.914326i	$0.367279\pi$
$74$	−17.7149	−2.05932
$75$	4.16629	0.481082
$76$	−19.3541	−2.22007
$77$	−3.04305	−0.346788
$78$	−0.0154874	−0.00175361
$79$	−8.92707	−1.00437	−0.502187	−	0.864759i	$-0.667471\pi$
$79$	−8.92707	−1.00437	−0.502187	+	0.864759i	$0.667471\pi$
$80$	0.201530	0.0225318
$81$	5.62669	0.625188
$82$	16.4705	1.81886
$83$	5.23145	0.574226	0.287113	−	0.957897i	$-0.407304\pi$
$83$	5.23145	0.574226	0.287113	+	0.957897i	$0.407304\pi$
$84$	−6.13932	−0.669855
$85$	−16.2170	−1.75898
$86$	4.86095	0.524170
$87$	3.90136	0.418269
$88$	2.79459	0.297905
$89$	12.8067	1.35751	0.678755	−	0.734365i	$-0.262520\pi$
$89$	12.8067	1.35751	0.678755	+	0.734365i	$0.262520\pi$
$90$	20.3491	2.14498
$91$	0.0329429	0.00345336
$92$	−20.1741	−2.10329
$93$	−2.96284	−0.307232
$94$	−11.8239	−1.21954
$95$	20.5022	2.10348
$96$	−3.58328	−0.365717
$97$	5.22347	0.530364	0.265182	−	0.964198i	$-0.414568\pi$
$97$	5.22347	0.530364	0.265182	+	0.964198i	$0.414568\pi$
$98$	5.16526	0.521770
$99$	−2.60812	−0.262126
$100$	21.4493	2.14493
$101$	−9.00194	−0.895726	−0.447863	−	0.894102i	$-0.647815\pi$
$101$	−9.00194	−0.895726	−0.447863	+	0.894102i	$0.647815\pi$
$102$	6.79568	0.672873
$103$	4.57925	0.451207	0.225604	−	0.974219i	$-0.427565\pi$
$103$	4.57925	0.451207	0.225604	+	0.974219i	$0.427565\pi$
$104$	−0.0302532	−0.00296657
$105$	6.50350	0.634677
$106$	2.00419	0.194664
$107$	14.6031	1.41174	0.705870	−	0.708342i	$-0.250556\pi$
$107$	14.6031	1.41174	0.705870	+	0.708342i	$0.250556\pi$
$108$	−11.3143	−1.08872
$109$	1.45475	0.139340	0.0696699	−	0.997570i	$-0.477805\pi$
$109$	1.45475	0.139340	0.0696699	+	0.997570i	$0.477805\pi$
$110$	−7.80220	−0.743910
$111$	−4.85244	−0.460573
$112$	0.179633	0.0169737
$113$	−6.71325	−0.631529	−0.315765	−	0.948838i	$-0.602261\pi$
$113$	−6.71325	−0.631529	−0.315765	+	0.948838i	$0.602261\pi$
$114$	−8.59137	−0.804656
$115$	21.3708	1.99284
$116$	20.0853	1.86488
$117$	0.0282346	0.00261029
$118$	−4.96851	−0.457388
$119$	−14.4549	−1.32508
$120$	−5.97251	−0.545213
$121$	1.00000	0.0909091
$122$	23.3570	2.11464
$123$	4.51156	0.406794
$124$	−15.2536	−1.36981
$125$	−5.65164	−0.505498
$126$	18.1380	1.61587
$127$	10.1962	0.904765	0.452382	−	0.891824i	$-0.350574\pi$
$127$	10.1962	0.904765	0.452382	+	0.891824i	$0.350574\pi$
$128$	−18.1780	−1.60672
$129$	1.33150	0.117232
$130$	0.0844636	0.00740795
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	2.01749	0.175600
$133$	18.2745	1.58460
$134$	−1.35842	−0.117350
$135$	11.9855	1.03155
$136$	13.2747	1.13830
$137$	4.34957	0.371609	0.185804	−	0.982587i	$-0.440511\pi$
$137$	4.34957	0.371609	0.185804	+	0.982587i	$0.440511\pi$
$138$	−8.95537	−0.762332
$139$	−14.7670	−1.25252	−0.626262	−	0.779612i	$-0.715416\pi$
$139$	−14.7670	−1.25252	−0.626262	+	0.779612i	$0.715416\pi$
$140$	33.4819	2.82974
$141$	−3.23878	−0.272755
$142$	−21.3096	−1.78826
$143$	−0.0108256	−0.000905284 0
$144$	0.153959	0.0128299
$145$	−21.2768	−1.76694
$146$	15.8153	1.30888
$147$	1.41486	0.116696
$148$	−24.9818	−2.05349
$149$	−18.9955	−1.55617	−0.778085	−	0.628159i	$-0.783809\pi$
$149$	−18.9955	−1.55617	−0.778085	+	0.628159i	$0.783809\pi$
$150$	9.52144	0.777422
$151$	5.01177	0.407852	0.203926	−	0.978986i	$-0.434630\pi$
$151$	5.01177	0.407852	0.203926	+	0.978986i	$0.434630\pi$
$152$	−16.7824	−1.36123
$153$	−12.3890	−1.00159
$154$	−6.95444	−0.560405
$155$	16.1584	1.29788
$156$	−0.0218406	−0.00174864
$157$	−13.8980	−1.10918	−0.554589	−	0.832124i	$-0.687125\pi$
$157$	−13.8980	−1.10918	−0.554589	+	0.832124i	$0.687125\pi$
$158$	−20.4015	−1.62305
$159$	0.548983	0.0435372
$160$	19.5421	1.54494
$161$	19.0487	1.50125
$162$	12.8590	1.01030
$163$	−12.6704	−0.992420	−0.496210	−	0.868202i	$-0.665275\pi$
$163$	−12.6704	−0.992420	−0.496210	+	0.868202i	$0.665275\pi$
$164$	23.2269	1.81371
$165$	−2.13716	−0.166378
$166$	11.9557	0.927942
$167$	−7.40610	−0.573101	−0.286551	−	0.958065i	$-0.592509\pi$
$167$	−7.40610	−0.573101	−0.286551	+	0.958065i	$0.592509\pi$
$168$	−5.32356	−0.410721
$169$	−12.9999	−0.999991
$170$	−37.0615	−2.84249
$171$	15.6626	1.19775
$172$	6.85497	0.522687
$173$	11.2227	0.853247	0.426623	−	0.904429i	$-0.359703\pi$
$173$	11.2227	0.853247	0.426623	+	0.904429i	$0.359703\pi$
$174$	8.91597	0.675918
$175$	−20.2528	−1.53097
$176$	−0.0590304	−0.00444959
$177$	−1.36096	−0.102296
$178$	29.2678	2.19372
$179$	−22.4696	−1.67946	−0.839730	−	0.543004i	$-0.817287\pi$
$179$	−22.4696	−1.67946	−0.839730	+	0.543004i	$0.817287\pi$
$180$	28.6966	2.13891
$181$	3.35621	0.249465	0.124732	−	0.992190i	$-0.460193\pi$
$181$	3.35621	0.249465	0.124732	+	0.992190i	$0.460193\pi$
$182$	0.0752861	0.00558058
$183$	6.39790	0.472946
$184$	−17.4935	−1.28963
$185$	26.4637	1.94565
$186$	−6.77114	−0.496484
$187$	4.75014	0.347365
$188$	−16.6742	−1.21609
$189$	10.6832	0.777087
$190$	46.8547	3.39920
$191$	−19.8650	−1.43738	−0.718692	−	0.695329i	$-0.755259\pi$
$191$	−19.8650	−1.43738	−0.718692	+	0.695329i	$0.755259\pi$
$192$	−8.11514	−0.585660
$193$	−21.0622	−1.51609	−0.758045	−	0.652203i	$-0.773845\pi$
$193$	−21.0622	−1.51609	−0.758045	+	0.652203i	$0.773845\pi$
$194$	11.9375	0.857061
$195$	0.0231361	0.00165681
$196$	7.28411	0.520294
$197$	−7.23662	−0.515588	−0.257794	−	0.966200i	$-0.582996\pi$
$197$	−7.23662	−0.515588	−0.257794	+	0.966200i	$0.582996\pi$
$198$	−5.96048	−0.423593
$199$	15.1954	1.07717	0.538586	−	0.842571i	$-0.318959\pi$
$199$	15.1954	1.07717	0.538586	+	0.842571i	$0.318959\pi$
$200$	18.5992	1.31516
$201$	−0.372097	−0.0262457
$202$	−20.5726	−1.44748
$203$	−18.9649	−1.33108
$204$	9.58335	0.670969
$205$	−24.6047	−1.71846
$206$	10.4652	0.729145
$207$	16.3262	1.13475
$208$	0.000639041 0	4.43095e−5 0
$209$	−6.00532	−0.415396
$210$	14.8628	1.02563
$211$	6.22681	0.428671	0.214336	−	0.976760i	$-0.431241\pi$
$211$	6.22681	0.428671	0.214336	+	0.976760i	$0.431241\pi$
$212$	2.82633	0.194113
$213$	−5.83708	−0.399950
$214$	33.3733	2.28135
$215$	−7.26160	−0.495237
$216$	−9.81093	−0.667549
$217$	14.4027	0.977719
$218$	3.32461	0.225171
$219$	4.33210	0.292736
$220$	−11.0028	−0.741805
$221$	−0.0514232	−0.00345910
$222$	−11.0895	−0.744281
$223$	5.43047	0.363651	0.181826	−	0.983331i	$-0.441799\pi$
$223$	5.43047	0.363651	0.181826	+	0.983331i	$0.441799\pi$
$224$	17.4187	1.16384
$225$	−17.3582	−1.15721
$226$	−15.3421	−1.02054
$227$	−27.0783	−1.79725	−0.898626	−	0.438715i	$-0.855434\pi$
$227$	−27.0783	−1.79725	−0.898626	+	0.438715i	$0.855434\pi$
$228$	−12.1157	−0.802379
$229$	−10.6788	−0.705672	−0.352836	−	0.935685i	$-0.614783\pi$
$229$	−10.6788	−0.705672	−0.352836	+	0.935685i	$0.614783\pi$
$230$	48.8398	3.22040
$231$	−1.90495	−0.125336
$232$	17.4165	1.14345
$233$	−20.3700	−1.33448	−0.667240	−	0.744843i	$-0.732524\pi$
$233$	−20.3700	−1.33448	−0.667240	+	0.744843i	$0.732524\pi$
$234$	0.0645259	0.00421819
$235$	17.6633	1.15223
$236$	−7.00665	−0.456094
$237$	−5.58834	−0.363001
$238$	−33.0346	−2.14131
$239$	−11.7567	−0.760476	−0.380238	−	0.924889i	$-0.624158\pi$
$239$	−11.7567	−0.760476	−0.380238	+	0.924889i	$0.624158\pi$
$240$	0.126158	0.00814345
$241$	28.9606	1.86552	0.932759	−	0.360501i	$-0.117394\pi$
$241$	28.9606	1.86552	0.932759	+	0.360501i	$0.117394\pi$
$242$	2.28535	0.146908
$243$	14.0544	0.901587
$244$	32.9383	2.10866
$245$	−7.71620	−0.492970
$246$	10.3105	0.657374
$247$	0.0650113	0.00413657
$248$	−13.2268	−0.839900
$249$	3.27488	0.207537
$250$	−12.9160	−0.816878
$251$	−20.1552	−1.27219	−0.636093	−	0.771612i	$-0.719451\pi$
$251$	−20.1552	−1.27219	−0.636093	+	0.771612i	$0.719451\pi$
$252$	25.5785	1.61129
$253$	−6.25975	−0.393547
$254$	23.3018	1.46209
$255$	−10.1518	−0.635732
$256$	−15.6160	−0.976002
$257$	−25.3621	−1.58205	−0.791023	−	0.611786i	$-0.790451\pi$
$257$	−25.3621	−1.58205	−0.791023	+	0.611786i	$0.790451\pi$
$258$	3.04295	0.189446
$259$	23.5883	1.46570
$260$	0.119112	0.00738699
$261$	−16.2544	−1.00612
$262$	2.28535	0.141189
$263$	25.5828	1.57750	0.788751	−	0.614712i	$-0.210728\pi$
$263$	25.5828	1.57750	0.788751	+	0.614712i	$0.210728\pi$
$264$	1.74941	0.107669
$265$	−2.99398	−0.183919
$266$	41.7636	2.56069
$267$	8.01699	0.490632
$268$	−1.91566	−0.117018
$269$	9.25347	0.564194	0.282097	−	0.959386i	$-0.408970\pi$
$269$	9.25347	0.564194	0.282097	+	0.959386i	$0.408970\pi$
$270$	27.3910	1.66697
$271$	−30.6090	−1.85936	−0.929681	−	0.368365i	$-0.879918\pi$
$271$	−30.6090	−1.85936	−0.929681	+	0.368365i	$0.879918\pi$
$272$	−0.280403	−0.0170019
$273$	0.0206222	0.00124811
$274$	9.94029	0.600515
$275$	6.65543	0.401337
$276$	−12.6290	−0.760175
$277$	−24.8681	−1.49418	−0.747089	−	0.664724i	$-0.768549\pi$
$277$	−24.8681	−1.49418	−0.747089	+	0.664724i	$0.768549\pi$
$278$	−33.7479	−2.02406
$279$	12.3442	0.739028
$280$	29.0330	1.73505
$281$	−14.1455	−0.843852	−0.421926	−	0.906630i	$-0.638646\pi$
$281$	−14.1455	−0.843852	−0.421926	+	0.906630i	$0.638646\pi$
$282$	−7.40175	−0.440768
$283$	4.59348	0.273054	0.136527	−	0.990636i	$-0.456406\pi$
$283$	4.59348	0.273054	0.136527	+	0.990636i	$0.456406\pi$
$284$	−30.0510	−1.78320
$285$	12.8343	0.760241
$286$	−0.0247403	−0.00146293
$287$	−21.9312	−1.29456
$288$	14.9291	0.879709
$289$	5.56383	0.327284
$290$	−48.6249	−2.85535
$291$	3.26989	0.191684
$292$	22.3029	1.30518
$293$	−13.2730	−0.775418	−0.387709	−	0.921782i	$-0.626733\pi$
$293$	−13.2730	−0.775418	−0.387709	+	0.921782i	$0.626733\pi$
$294$	3.23345	0.188579
$295$	7.42227	0.432142
$296$	−21.6623	−1.25910
$297$	−3.51068	−0.203710
$298$	−43.4113	−2.51475
$299$	0.0677656	0.00391899
$300$	13.4272	0.775223
$301$	−6.47258	−0.373074
$302$	11.4536	0.659083
$303$	−5.63521	−0.323734
$304$	0.354496	0.0203318
$305$	−34.8921	−1.99792
$306$	−28.3131	−1.61855
$307$	8.29178	0.473237	0.236618	−	0.971603i	$-0.423961\pi$
$307$	8.29178	0.473237	0.236618	+	0.971603i	$0.423961\pi$
$308$	−9.80723	−0.558819
$309$	2.86661	0.163076
$310$	36.9277	2.09735
$311$	−1.09869	−0.0623011	−0.0311506	−	0.999515i	$-0.509917\pi$
$311$	−1.09869	−0.0623011	−0.0311506	+	0.999515i	$0.509917\pi$
$312$	−0.0189385	−0.00107218
$313$	−3.83734	−0.216899	−0.108450	−	0.994102i	$-0.534589\pi$
$313$	−3.83734	−0.216899	−0.108450	+	0.994102i	$0.534589\pi$
$314$	−31.7617	−1.79242
$315$	−27.0958	−1.52667
$316$	−28.7704	−1.61846
$317$	6.23095	0.349965	0.174982	−	0.984572i	$-0.444013\pi$
$317$	6.23095	0.349965	0.174982	+	0.984572i	$0.444013\pi$
$318$	1.25462	0.0703555
$319$	6.23221	0.348936
$320$	44.2575	2.47407
$321$	9.14156	0.510232
$322$	43.5330	2.42600
$323$	−28.5261	−1.58723
$324$	18.1339	1.00744
$325$	−0.0720491	−0.00399657
$326$	−28.9563	−1.60374
$327$	0.910672	0.0503603
$328$	20.1406	1.11208
$329$	15.7441	0.867999
$330$	−4.88417	−0.268865
$331$	26.8560	1.47614	0.738070	−	0.674724i	$-0.235737\pi$
$331$	26.8560	1.47614	0.738070	+	0.674724i	$0.235737\pi$
$332$	16.8601	0.925316
$333$	20.2169	1.10788
$334$	−16.9255	−0.926124
$335$	2.02930	0.110873
$336$	0.112450	0.00613464
$337$	1.26112	0.0686974	0.0343487	−	0.999410i	$-0.489064\pi$
$337$	1.26112	0.0686974	0.0343487	+	0.999410i	$0.489064\pi$
$338$	−29.7093	−1.61597
$339$	−4.20249	−0.228248
$340$	−52.2646	−2.83445
$341$	−4.73298	−0.256305
$342$	35.7946	1.93555
$343$	14.4236	0.778800
$344$	5.94411	0.320485
$345$	13.3781	0.720253
$346$	25.6478	1.37884
$347$	18.2177	0.977977	0.488989	−	0.872290i	$-0.337366\pi$
$347$	18.2177	0.977977	0.488989	+	0.872290i	$0.337366\pi$
$348$	12.5734	0.674005
$349$	23.6341	1.26510	0.632552	−	0.774518i	$-0.282007\pi$
$349$	23.6341	1.26510	0.632552	+	0.774518i	$0.282007\pi$
$350$	−46.2848	−2.47403
$351$	0.0380053	0.00202857
$352$	−5.72409	−0.305095
$353$	−17.2990	−0.920735	−0.460367	−	0.887728i	$-0.652282\pi$
$353$	−17.2990	−0.920735	−0.460367	+	0.887728i	$0.652282\pi$
$354$	−3.11028	−0.165310
$355$	31.8336	1.68955
$356$	41.2739	2.18751
$357$	−9.04877	−0.478912
$358$	−51.3510	−2.71399
$359$	−14.8987	−0.786321	−0.393160	−	0.919470i	$-0.628618\pi$
$359$	−14.8987	−0.786321	−0.393160	+	0.919470i	$0.628618\pi$
$360$	24.8835	1.31147
$361$	17.0638	0.898096
$362$	7.67011	0.403132
$363$	0.625999	0.0328564
$364$	0.106169	0.00556479
$365$	−23.6259	−1.23664
$366$	14.6214	0.764275
$367$	−3.06626	−0.160057	−0.0800287	−	0.996793i	$-0.525501\pi$
$367$	−3.06626	−0.160057	−0.0800287	+	0.996793i	$0.525501\pi$
$368$	0.369516	0.0192623
$369$	−18.7967	−0.978517
$370$	60.4789	3.14415
$371$	−2.66867	−0.138550
$372$	−9.54874	−0.495079
$373$	32.0797	1.66102	0.830511	−	0.557002i	$-0.188048\pi$
$373$	32.0797	1.66102	0.830511	+	0.557002i	$0.188048\pi$
$374$	10.8557	0.561337
$375$	−3.53792	−0.182697
$376$	−14.4586	−0.745646
$377$	−0.0674675	−0.00347475
$378$	24.4148	1.25576
$379$	3.81803	0.196119	0.0980594	−	0.995181i	$-0.468736\pi$
$379$	3.81803	0.196119	0.0980594	+	0.995181i	$0.468736\pi$
$380$	66.0750	3.38958
$381$	6.38280	0.327001
$382$	−45.3986	−2.32279
$383$	1.48384	0.0758204	0.0379102	−	0.999281i	$-0.487930\pi$
$383$	1.48384	0.0758204	0.0379102	+	0.999281i	$0.487930\pi$
$384$	−11.3794	−0.580702
$385$	10.3890	0.529472
$386$	−48.1345	−2.44998
$387$	−5.54749	−0.281995
$388$	16.8344	0.854636
$389$	18.3270	0.929215	0.464607	−	0.885517i	$-0.346195\pi$
$389$	18.3270	0.929215	0.464607	+	0.885517i	$0.346195\pi$
$390$	0.0528742	0.00267739
$391$	−29.7347	−1.50375
$392$	6.31623	0.319018
$393$	0.625999	0.0315775
$394$	−16.5382	−0.833183
$395$	30.4770	1.53347
$396$	−8.40554	−0.422394
$397$	5.86500	0.294356	0.147178	−	0.989110i	$-0.452981\pi$
$397$	5.86500	0.294356	0.147178	+	0.989110i	$0.452981\pi$
$398$	34.7267	1.74069
$399$	11.4398	0.572707
$400$	−0.392873	−0.0196436
$401$	4.60085	0.229756	0.114878	−	0.993380i	$-0.463352\pi$
$401$	4.60085	0.229756	0.114878	+	0.993380i	$0.463352\pi$
$402$	−0.850372	−0.0424127
$403$	0.0512374	0.00255232
$404$	−29.0117	−1.44339
$405$	−19.2095	−0.954530
$406$	−43.3415	−2.15100
$407$	−7.75151	−0.384228
$408$	8.30996	0.411404
$409$	21.9050	1.08313	0.541567	−	0.840658i	$-0.317831\pi$
$409$	21.9050	1.08313	0.541567	+	0.840658i	$0.317831\pi$
$410$	−56.2303	−2.77702
$411$	2.72283	0.134307
$412$	14.7582	0.727082
$413$	6.61580	0.325542
$414$	37.3111	1.83374
$415$	−17.8602	−0.876722
$416$	0.0619668	0.00303817
$417$	−9.24416	−0.452689
$418$	−13.7243	−0.671275
$419$	−26.4611	−1.29271	−0.646355	−	0.763037i	$-0.723707\pi$
$419$	−26.4611	−1.29271	−0.646355	+	0.763037i	$0.723707\pi$
$420$	20.9597	1.02273
$421$	−24.2536	−1.18205	−0.591024	−	0.806654i	$-0.701276\pi$
$421$	−24.2536	−1.18205	−0.591024	+	0.806654i	$0.701276\pi$
$422$	14.2304	0.692727
$423$	13.4939	0.656094
$424$	2.45078	0.119020
$425$	31.6142	1.53351
$426$	−13.3398	−0.646314
$427$	−31.1009	−1.50508
$428$	47.0634	2.27490
$429$	−0.00677683	−0.000327188 0
$430$	−16.5953	−0.800297
$431$	14.6517	0.705748	0.352874	−	0.935671i	$-0.385204\pi$
$431$	14.6517	0.705748	0.352874	+	0.935671i	$0.385204\pi$
$432$	0.207237	0.00997070
$433$	14.1500	0.680008	0.340004	−	0.940424i	$-0.389572\pi$
$433$	14.1500	0.680008	0.340004	+	0.940424i	$0.389572\pi$
$434$	32.9152	1.57998
$435$	−13.3192	−0.638609
$436$	4.68841	0.224534
$437$	37.5918	1.79826
$438$	9.90036	0.473058
$439$	10.7900	0.514981	0.257490	−	0.966281i	$-0.417104\pi$
$439$	10.7900	0.514981	0.257490	+	0.966281i	$0.417104\pi$
$440$	−9.54076	−0.454838
$441$	−5.89478	−0.280704
$442$	−0.117520	−0.00558986
$443$	7.07636	0.336208	0.168104	−	0.985769i	$-0.446236\pi$
$443$	7.07636	0.336208	0.168104	+	0.985769i	$0.446236\pi$
$444$	−15.6386	−0.742175
$445$	−43.7222	−2.07263
$446$	12.4105	0.587656
$447$	−11.8911	−0.562432
$448$	39.4486	1.86377
$449$	−29.7176	−1.40246	−0.701231	−	0.712934i	$-0.747366\pi$
$449$	−29.7176	−1.40246	−0.701231	+	0.712934i	$0.747366\pi$
$450$	−39.6695	−1.87004
$451$	7.20698	0.339363
$452$	−21.6357	−1.01766
$453$	3.13736	0.147406
$454$	−61.8835	−2.90434
$455$	−0.112467	−0.00527255
$456$	−10.5058	−0.491978
$457$	−8.23787	−0.385351	−0.192676	−	0.981263i	$-0.561717\pi$
$457$	−8.23787	−0.385351	−0.192676	+	0.981263i	$0.561717\pi$
$458$	−24.4047	−1.14036
$459$	−16.6762	−0.778380
$460$	68.8745	3.21129
$461$	−3.65351	−0.170161	−0.0850804	−	0.996374i	$-0.527115\pi$
$461$	−3.65351	−0.170161	−0.0850804	+	0.996374i	$0.527115\pi$
$462$	−4.35347	−0.202542
$463$	−14.9695	−0.695693	−0.347847	−	0.937551i	$-0.613087\pi$
$463$	−14.9695	−0.695693	−0.347847	+	0.937551i	$0.613087\pi$
$464$	−0.367890	−0.0170789
$465$	10.1152	0.469079
$466$	−46.5525	−2.15650
$467$	−5.87790	−0.271997	−0.135998	−	0.990709i	$-0.543424\pi$
$467$	−5.87790	−0.271997	−0.135998	+	0.990709i	$0.543424\pi$
$468$	0.0909952	0.00420625
$469$	1.80880	0.0835228
$470$	40.3668	1.86198
$471$	−8.70012	−0.400880
$472$	−6.07563	−0.279654
$473$	2.12700	0.0977998
$474$	−12.7713	−0.586606
$475$	−39.9679	−1.83386
$476$	−46.5857	−2.13525
$477$	−2.28725	−0.104726
$478$	−26.8681	−1.22892
$479$	−18.2741	−0.834965	−0.417482	−	0.908685i	$-0.637087\pi$
$479$	−18.2741	−0.834965	−0.417482	+	0.908685i	$0.637087\pi$
$480$	12.2333	0.558372
$481$	0.0839149	0.00382619
$482$	66.1852	3.01465
$483$	11.9245	0.542583
$484$	3.22283	0.146492
$485$	−17.8330	−0.809753
$486$	32.1191	1.45695
$487$	17.7520	0.804420	0.402210	−	0.915547i	$-0.368242\pi$
$487$	17.7520	0.804420	0.402210	+	0.915547i	$0.368242\pi$
$488$	28.5616	1.29292
$489$	−7.93165	−0.358681
$490$	−17.6342	−0.796633
$491$	27.2756	1.23093	0.615466	−	0.788163i	$-0.288968\pi$
$491$	27.2756	1.23093	0.615466	+	0.788163i	$0.288968\pi$
$492$	14.5400	0.655514
$493$	29.6038	1.33329
$494$	0.148574	0.00668464
$495$	8.90415	0.400212
$496$	0.279390	0.0125450
$497$	28.3747	1.27278
$498$	7.48426	0.335378
$499$	41.4776	1.85679	0.928396	−	0.371591i	$-0.121188\pi$
$499$	41.4776	1.85679	0.928396	+	0.371591i	$0.121188\pi$
$500$	−18.2143	−0.814566
$501$	−4.63621	−0.207131
$502$	−46.0618	−2.05584
$503$	17.6695	0.787846	0.393923	−	0.919143i	$-0.371118\pi$
$503$	17.6695	0.787846	0.393923	+	0.919143i	$0.371118\pi$
$504$	22.1797	0.987964
$505$	30.7327	1.36759
$506$	−14.3057	−0.635967
$507$	−8.13792	−0.361418
$508$	32.8605	1.45795
$509$	36.0967	1.59996	0.799978	−	0.600029i	$-0.204844\pi$
$509$	36.0967	1.59996	0.799978	+	0.600029i	$0.204844\pi$
$510$	−23.2005	−1.02734
$511$	−21.0588	−0.931586
$512$	0.667828	0.0295141
$513$	21.0828	0.930826
$514$	−57.9614	−2.55657
$515$	−15.6336	−0.688899
$516$	4.29121	0.188910
$517$	−5.17378	−0.227542
$518$	53.9074	2.36856
$519$	7.02541	0.308381
$520$	0.103285	0.00452933
$521$	35.8947	1.57258	0.786289	−	0.617859i	$-0.212000\pi$
$521$	35.8947	1.57258	0.786289	+	0.617859i	$0.212000\pi$
$522$	−37.1469	−1.62588
$523$	23.6971	1.03620	0.518102	−	0.855319i	$-0.326639\pi$
$523$	23.6971	1.03620	0.518102	+	0.855319i	$0.326639\pi$
$524$	3.22283	0.140790
$525$	−12.6782	−0.553324
$526$	58.4657	2.54922
$527$	−22.4823	−0.979345
$528$	−0.0369530	−0.00160817
$529$	16.1844	0.703671
$530$	−6.84230	−0.297210
$531$	5.67024	0.246067
$532$	58.8955	2.55345
$533$	−0.0780200	−0.00337942
$534$	18.3216	0.792855
$535$	−49.8552	−2.15543
$536$	−1.66112	−0.0717494
$537$	−14.0660	−0.606992
$538$	21.1474	0.911730
$539$	2.26016	0.0973520
$540$	38.6272	1.66225
$541$	4.98153	0.214173	0.107086	−	0.994250i	$-0.465848\pi$
$541$	4.98153	0.214173	0.107086	+	0.994250i	$0.465848\pi$
$542$	−69.9522	−3.00471
$543$	2.10098	0.0901618
$544$	−27.1902	−1.16577
$545$	−4.96652	−0.212742
$546$	0.0471291	0.00201694
$547$	−27.2658	−1.16580	−0.582901	−	0.812543i	$-0.698082\pi$
$547$	−27.2658	−1.16580	−0.582901	+	0.812543i	$0.698082\pi$
$548$	14.0179	0.598816
$549$	−26.6558	−1.13764
$550$	15.2100	0.648556
$551$	−37.4264	−1.59442
$552$	−10.9509	−0.466101
$553$	27.1655	1.15520
$554$	−56.8323	−2.41457
$555$	16.5663	0.703199
$556$	−47.5917	−2.01834
$557$	21.9279	0.929113	0.464557	−	0.885543i	$-0.346214\pi$
$557$	21.9279	0.929113	0.464557	+	0.885543i	$0.346214\pi$
$558$	28.2108	1.19426
$559$	−0.0230261	−0.000973902 0
$560$	−0.613266	−0.0259152
$561$	2.97358	0.125545
$562$	−32.3275	−1.36365
$563$	2.12941	0.0897441	0.0448720	−	0.998993i	$-0.485712\pi$
$563$	2.12941	0.0897441	0.0448720	+	0.998993i	$0.485712\pi$
$564$	−10.4380	−0.439521
$565$	22.9191	0.964212
$566$	10.4977	0.441252
$567$	−17.1223	−0.719069
$568$	−26.0580	−1.09337
$569$	−16.8097	−0.704700	−0.352350	−	0.935868i	$-0.614617\pi$
$569$	−16.8097	−0.704700	−0.352350	+	0.935868i	$0.614617\pi$
$570$	29.3310	1.22854
$571$	5.64611	0.236282	0.118141	−	0.992997i	$-0.462306\pi$
$571$	5.64611	0.236282	0.118141	+	0.992997i	$0.462306\pi$
$572$	−0.0348891	−0.00145879
$573$	−12.4355	−0.519500
$574$	−50.1205	−2.09199
$575$	−41.6613	−1.73740
$576$	33.8104	1.40877
$577$	−24.3326	−1.01298	−0.506490	−	0.862246i	$-0.669057\pi$
$577$	−24.3326	−1.01298	−0.506490	+	0.862246i	$0.669057\pi$
$578$	12.7153	0.528887
$579$	−13.1849	−0.547946
$580$	−68.5714	−2.84727
$581$	−15.9196	−0.660455
$582$	7.47285	0.309760
$583$	0.876970	0.0363204
$584$	19.3394	0.800270
$585$	−0.0963929	−0.00398536
$586$	−30.3335	−1.25307
$587$	2.64036	0.108979	0.0544896	−	0.998514i	$-0.482647\pi$
$587$	2.64036	0.108979	0.0544896	+	0.998514i	$0.482647\pi$
$588$	4.55985	0.188045
$589$	28.4230	1.17115
$590$	16.9625	0.698335
$591$	−4.53012	−0.186344
$592$	0.457575	0.0188062
$593$	−28.0305	−1.15107	−0.575536	−	0.817776i	$-0.695207\pi$
$593$	−28.0305	−1.15107	−0.575536	+	0.817776i	$0.695207\pi$
$594$	−8.02314	−0.329193
$595$	49.3492	2.02312
$596$	−61.2191	−2.50763
$597$	9.51229	0.389312
$598$	0.154868	0.00633303
$599$	−44.6393	−1.82391	−0.911955	−	0.410289i	$-0.865428\pi$
$599$	−44.6393	−1.82391	−0.911955	+	0.410289i	$0.865428\pi$
$600$	11.6431	0.475327
$601$	27.5586	1.12414	0.562070	−	0.827090i	$-0.310005\pi$
$601$	27.5586	1.12414	0.562070	+	0.827090i	$0.310005\pi$
$602$	−14.7921	−0.602882
$603$	1.55028	0.0631323
$604$	16.1521	0.657218
$605$	−3.41400	−0.138799
$606$	−12.8784	−0.523150
$607$	−27.1488	−1.10194	−0.550968	−	0.834527i	$-0.685741\pi$
$607$	−27.1488	−1.10194	−0.550968	+	0.834527i	$0.685741\pi$
$608$	34.3750	1.39409
$609$	−11.8720	−0.481079
$610$	−79.7408	−3.22861
$611$	0.0560093	0.00226589
$612$	−39.9275	−1.61397
$613$	10.6730	0.431080	0.215540	−	0.976495i	$-0.430849\pi$
$613$	10.6730	0.431080	0.215540	+	0.976495i	$0.430849\pi$
$614$	18.9496	0.764744
$615$	−15.4025	−0.621089
$616$	−8.50409	−0.342640
$617$	19.5305	0.786270	0.393135	−	0.919481i	$-0.371391\pi$
$617$	19.5305	0.786270	0.393135	+	0.919481i	$0.371391\pi$
$618$	6.55121	0.263528
$619$	−15.0138	−0.603454	−0.301727	−	0.953394i	$-0.597563\pi$
$619$	−15.0138	−0.603454	−0.301727	+	0.953394i	$0.597563\pi$
$620$	52.0758	2.09142
$621$	21.9760	0.881866
$622$	−2.51090	−0.100678
$623$	−38.9715	−1.56136
$624$	0.000400039 0	1.60144e−5 0
$625$	−13.9824	−0.559297
$626$	−8.76967	−0.350507
$627$	−3.75932	−0.150133
$628$	−44.7908	−1.78735
$629$	−36.8208	−1.46814
$630$	−61.9234	−2.46709
$631$	−37.4169	−1.48954	−0.744772	−	0.667319i	$-0.767442\pi$
$631$	−37.4169	−1.48954	−0.744772	+	0.667319i	$0.767442\pi$
$632$	−24.9475	−0.992359
$633$	3.89798	0.154931
$634$	14.2399	0.565539
$635$	−34.8098	−1.38138
$636$	1.76928	0.0701564
$637$	−0.0244676	−0.000969443 0
$638$	14.2428	0.563877
$639$	24.3192	0.962054
$640$	62.0597	2.45312
$641$	4.24496	0.167666	0.0838328	−	0.996480i	$-0.473284\pi$
$641$	4.24496	0.167666	0.0838328	+	0.996480i	$0.473284\pi$
$642$	20.8917	0.824528
$643$	6.83059	0.269372	0.134686	−	0.990888i	$-0.456997\pi$
$643$	6.83059	0.269372	0.134686	+	0.990888i	$0.456997\pi$
$644$	61.3908	2.41914
$645$	−4.54576	−0.178989
$646$	−65.1921	−2.56495
$647$	18.5599	0.729663	0.364832	−	0.931073i	$-0.381127\pi$
$647$	18.5599	0.729663	0.364832	+	0.931073i	$0.381127\pi$
$648$	15.7243	0.617709
$649$	−2.17407	−0.0853396
$650$	−0.164658	−0.00645840
$651$	9.01608	0.353368
$652$	−40.8345	−1.59920
$653$	30.8751	1.20824	0.604118	−	0.796895i	$-0.293526\pi$
$653$	30.8751	1.20824	0.604118	+	0.796895i	$0.293526\pi$
$654$	2.08121	0.0813816
$655$	−3.41400	−0.133396
$656$	−0.425431	−0.0166103
$657$	−18.0490	−0.704158
$658$	35.9807	1.40267
$659$	−19.0248	−0.741100	−0.370550	−	0.928813i	$-0.620831\pi$
$659$	−19.0248	−0.741100	−0.370550	+	0.928813i	$0.620831\pi$
$660$	−6.88772	−0.268104
$661$	46.7520	1.81844	0.909221	−	0.416315i	$-0.136679\pi$
$661$	46.7520	1.81844	0.909221	+	0.416315i	$0.136679\pi$
$662$	61.3754	2.38542
$663$	−0.0321909	−0.00125019
$664$	14.6198	0.567357
$665$	−62.3892	−2.41935
$666$	46.2028	1.79032
$667$	−39.0120	−1.51055
$668$	−23.8686	−0.923504
$669$	3.39947	0.131431
$670$	4.63766	0.179169
$671$	10.2203	0.394550
$672$	10.9041	0.420635
$673$	10.7149	0.413030	0.206515	−	0.978443i	$-0.433788\pi$
$673$	10.7149	0.413030	0.206515	+	0.978443i	$0.433788\pi$
$674$	2.88209	0.111014
$675$	−23.3651	−0.899323
$676$	−41.8964	−1.61140
$677$	24.8883	0.956536	0.478268	−	0.878214i	$-0.341265\pi$
$677$	24.8883	0.956536	0.478268	+	0.878214i	$0.341265\pi$
$678$	−9.60416	−0.368846
$679$	−15.8953	−0.610006
$680$	−45.3199	−1.73794
$681$	−16.9510	−0.649564
$682$	−10.8165	−0.414186
$683$	12.1928	0.466546	0.233273	−	0.972411i	$-0.425056\pi$
$683$	12.1928	0.466546	0.233273	+	0.972411i	$0.425056\pi$
$684$	50.4779	1.93007
$685$	−14.8495	−0.567368
$686$	32.9629	1.25853
$687$	−6.68490	−0.255045
$688$	−0.125558	−0.00478685
$689$	−0.00949375	−0.000361683 0
$690$	30.5737	1.16392
$691$	3.79018	0.144185	0.0720927	−	0.997398i	$-0.477032\pi$
$691$	3.79018	0.144185	0.0720927	+	0.997398i	$0.477032\pi$
$692$	36.1689	1.37493
$693$	7.93666	0.301489
$694$	41.6338	1.58040
$695$	50.4148	1.91234
$696$	10.9027	0.413266
$697$	34.2342	1.29671
$698$	54.0122	2.04439
$699$	−12.7516	−0.482309
$700$	−65.2713	−2.46702
$701$	8.87579	0.335234	0.167617	−	0.985852i	$-0.446393\pi$
$701$	8.87579	0.335234	0.167617	+	0.985852i	$0.446393\pi$
$702$	0.0868555	0.00327815
$703$	46.5503	1.75568
$704$	−12.9635	−0.488580
$705$	11.0572	0.416439
$706$	−39.5344	−1.48790
$707$	27.3934	1.03023
$708$	−4.38616	−0.164842
$709$	1.80043	0.0676164	0.0338082	−	0.999428i	$-0.489236\pi$
$709$	1.80043	0.0676164	0.0338082	+	0.999428i	$0.489236\pi$
$710$	72.7510	2.73029
$711$	23.2829	0.873177
$712$	35.7896	1.34127
$713$	29.6273	1.10955
$714$	−20.6796	−0.773915
$715$	0.0369587	0.00138218
$716$	−72.4158	−2.70631
$717$	−7.35967	−0.274852
$718$	−34.0487	−1.27068
$719$	9.82920	0.366567	0.183284	−	0.983060i	$-0.441327\pi$
$719$	9.82920	0.366567	0.183284	+	0.983060i	$0.441327\pi$
$720$	−0.525616	−0.0195885
$721$	−13.9349	−0.518963
$722$	38.9968	1.45131
$723$	18.1293	0.674237
$724$	10.8165	0.401991
$725$	41.4780	1.54045
$726$	1.43063	0.0530956
$727$	52.5736	1.94985	0.974923	−	0.222542i	$-0.0714355\pi$
$727$	52.5736	1.94985	0.974923	+	0.222542i	$0.0714355\pi$
$728$	0.0920621	0.00341205
$729$	−8.08206	−0.299335
$730$	−53.9935	−1.99839
$731$	10.1036	0.373694
$732$	20.6193	0.762112
$733$	−10.3010	−0.380476	−0.190238	−	0.981738i	$-0.560926\pi$
$733$	−10.3010	−0.380476	−0.190238	+	0.981738i	$0.560926\pi$
$734$	−7.00748	−0.258651
$735$	−4.83033	−0.178170
$736$	35.8314	1.32076
$737$	−0.594405	−0.0218952
$738$	−42.9571	−1.58127
$739$	−24.8784	−0.915167	−0.457584	−	0.889167i	$-0.651285\pi$
$739$	−24.8784	−0.915167	−0.457584	+	0.889167i	$0.651285\pi$
$740$	85.2880	3.13525
$741$	0.0406970	0.00149504
$742$	−6.09884	−0.223895
$743$	−51.7388	−1.89811	−0.949056	−	0.315107i	$-0.897960\pi$
$743$	−51.7388	−1.89811	−0.949056	+	0.315107i	$0.897960\pi$
$744$	−8.27994	−0.303557
$745$	64.8506	2.37594
$746$	73.3133	2.68419
$747$	−13.6443	−0.499218
$748$	15.3089	0.559748
$749$	−44.4381	−1.62373
$750$	−8.08539	−0.295237
$751$	48.1833	1.75823	0.879117	−	0.476606i	$-0.158133\pi$
$751$	48.1833	1.75823	0.879117	+	0.476606i	$0.158133\pi$
$752$	0.305410	0.0111372
$753$	−12.6172	−0.459795
$754$	−0.154187	−0.00561515
$755$	−17.1102	−0.622704
$756$	34.4301	1.25221
$757$	−46.0196	−1.67261	−0.836305	−	0.548264i	$-0.815289\pi$
$757$	−46.0196	−1.67261	−0.836305	+	0.548264i	$0.815289\pi$
$758$	8.72553	0.316926
$759$	−3.91860	−0.142236
$760$	57.2953	2.07832
$761$	−9.71343	−0.352112	−0.176056	−	0.984380i	$-0.556334\pi$
$761$	−9.71343	−0.352112	−0.176056	+	0.984380i	$0.556334\pi$
$762$	14.5869	0.528429
$763$	−4.42688	−0.160264
$764$	−64.0216	−2.31622
$765$	42.2960	1.52921
$766$	3.39108	0.122525
$767$	0.0235356	0.000849822 0
$768$	−9.77562	−0.352747
$769$	7.91813	0.285535	0.142768	−	0.989756i	$-0.454400\pi$
$769$	7.91813	0.285535	0.142768	+	0.989756i	$0.454400\pi$
$770$	23.7425	0.855620
$771$	−15.8767	−0.571785
$772$	−67.8798	−2.44305
$773$	−29.6612	−1.06684	−0.533420	−	0.845850i	$-0.679094\pi$
$773$	−29.6612	−1.06684	−0.533420	+	0.845850i	$0.679094\pi$
$774$	−12.6780	−0.455700
$775$	−31.5000	−1.13151
$776$	14.5975	0.524019
$777$	14.7662	0.529736
$778$	41.8836	1.50160
$779$	−43.2802	−1.55067
$780$	0.0745638	0.00266981
$781$	−9.32442	−0.333654
$782$	−67.9542	−2.43004
$783$	−21.8793	−0.781902
$784$	−0.133418	−0.00476494
$785$	47.4477	1.69348
$786$	1.43063	0.0510288
$787$	40.3453	1.43816	0.719078	−	0.694930i	$-0.244565\pi$
$787$	40.3453	1.43816	0.719078	+	0.694930i	$0.244565\pi$
$788$	−23.3224	−0.830825
$789$	16.0148	0.570142
$790$	69.6507	2.47806
$791$	20.4288	0.726363
$792$	−7.28865	−0.258991
$793$	−0.110641	−0.00392898
$794$	13.4036	0.475675
$795$	−1.87423	−0.0664721
$796$	48.9721	1.73577
$797$	45.5958	1.61509	0.807543	−	0.589809i	$-0.200797\pi$
$797$	45.5958	1.61509	0.807543	+	0.589809i	$0.200797\pi$
$798$	26.1440	0.925487
$799$	−24.5762	−0.869442
$800$	−38.0963	−1.34691
$801$	−33.4015	−1.18018
$802$	10.5146	0.371282
$803$	6.92029	0.244212
$804$	−1.19920	−0.0422927
$805$	−65.0325	−2.29209
$806$	0.117096	0.00412451
$807$	5.79267	0.203911
$808$	−25.1568	−0.885012
$809$	47.0220	1.65321	0.826603	−	0.562786i	$-0.190270\pi$
$809$	47.0220	1.65321	0.826603	+	0.562786i	$0.190270\pi$
$810$	−43.9006	−1.54251
$811$	46.8094	1.64370	0.821850	−	0.569704i	$-0.192942\pi$
$811$	46.8094	1.64370	0.821850	+	0.569704i	$0.192942\pi$
$812$	−61.1207	−2.14492
$813$	−19.1612	−0.672012
$814$	−17.7149	−0.620908
$815$	43.2567	1.51522
$816$	−0.175532	−0.00614485
$817$	−12.7733	−0.446882
$818$	50.0607	1.75033
$819$	−0.0859192	−0.00300226
$820$	−79.2966	−2.76916
$821$	9.86244	0.344202	0.172101	−	0.985079i	$-0.444945\pi$
$821$	9.86244	0.344202	0.172101	+	0.985079i	$0.444945\pi$
$822$	6.22262	0.217039
$823$	−6.40260	−0.223181	−0.111590	−	0.993754i	$-0.535594\pi$
$823$	−6.40260	−0.223181	−0.111590	+	0.993754i	$0.535594\pi$
$824$	12.7972	0.445810
$825$	4.16629	0.145052
$826$	15.1194	0.526072
$827$	24.0935	0.837812	0.418906	−	0.908030i	$-0.362414\pi$
$827$	24.0935	0.837812	0.418906	+	0.908030i	$0.362414\pi$
$828$	52.6166	1.82855
$829$	−24.2924	−0.843711	−0.421856	−	0.906663i	$-0.638621\pi$
$829$	−24.2924	−0.843711	−0.421856	+	0.906663i	$0.638621\pi$
$830$	−40.8168	−1.41677
$831$	−15.5674	−0.540027
$832$	0.140338	0.00486534
$833$	10.7361	0.371983
$834$	−21.1262	−0.731539
$835$	25.2845	0.875005
$836$	−19.3541	−0.669376
$837$	16.6160	0.574333
$838$	−60.4729	−2.08900
$839$	34.1622	1.17941	0.589706	−	0.807618i	$-0.299244\pi$
$839$	34.1622	1.17941	0.589706	+	0.807618i	$0.299244\pi$
$840$	18.1746	0.627085
$841$	9.84038	0.339323
$842$	−55.4280	−1.91017
$843$	−8.85509	−0.304986
$844$	20.0679	0.690767
$845$	44.3817	1.52678
$846$	30.8382	1.06024
$847$	−3.04305	−0.104560
$848$	−0.0517679	−0.00177772
$849$	2.87551	0.0986874
$850$	72.2496	2.47814
$851$	48.5225	1.66333
$852$	−18.8119	−0.644485
$853$	−52.2081	−1.78757	−0.893786	−	0.448494i	$-0.851960\pi$
$853$	−52.2081	−1.78757	−0.893786	+	0.448494i	$0.851960\pi$
$854$	−71.0764	−2.43219
$855$	−53.4722	−1.82871
$856$	40.8099	1.39485
$857$	53.9409	1.84259	0.921293	−	0.388869i	$-0.127134\pi$
$857$	53.9409	1.84259	0.921293	+	0.388869i	$0.127134\pi$
$858$	−0.0154874	−0.000528732 0
$859$	−55.6501	−1.89876	−0.949379	−	0.314134i	$-0.898286\pi$
$859$	−55.6501	−1.89876	−0.949379	+	0.314134i	$0.898286\pi$
$860$	−23.4029	−0.798033
$861$	−13.7289	−0.467880
$862$	33.4843	1.14048
$863$	6.83176	0.232556	0.116278	−	0.993217i	$-0.462904\pi$
$863$	6.83176	0.232556	0.116278	+	0.993217i	$0.462904\pi$
$864$	20.0955	0.683662
$865$	−38.3144	−1.30273
$866$	32.3378	1.09888
$867$	3.48295	0.118287
$868$	46.4175	1.57551
$869$	−8.92707	−0.302830
$870$	−30.4392	−1.03198
$871$	0.00643480	0.000218035 0
$872$	4.06543	0.137673
$873$	−13.6235	−0.461085
$874$	85.9104	2.90596
$875$	17.1982	0.581406
$876$	13.9616	0.471719
$877$	−54.9463	−1.85541	−0.927703	−	0.373320i	$-0.878220\pi$
$877$	−54.9463	−1.85541	−0.927703	+	0.373320i	$0.878220\pi$
$878$	24.6590	0.832202
$879$	−8.30890	−0.280252
$880$	0.201530	0.00679358
$881$	44.6060	1.50281	0.751407	−	0.659839i	$-0.229376\pi$
$881$	44.6060	1.50281	0.751407	+	0.659839i	$0.229376\pi$
$882$	−13.4716	−0.453614
$883$	−46.0754	−1.55056	−0.775280	−	0.631617i	$-0.782391\pi$
$883$	−46.0754	−1.55056	−0.775280	+	0.631617i	$0.782391\pi$
$884$	−0.165728	−0.00557404
$885$	4.64634	0.156185
$886$	16.1720	0.543308
$887$	−20.4964	−0.688201	−0.344101	−	0.938933i	$-0.611816\pi$
$887$	−20.4964	−0.688201	−0.344101	+	0.938933i	$0.611816\pi$
$888$	−13.5606	−0.455064
$889$	−31.0275	−1.04063
$890$	−99.9205	−3.34934
$891$	5.62669	0.188501
$892$	17.5015	0.585993
$893$	31.0702	1.03972
$894$	−27.1754	−0.908883
$895$	76.7115	2.56418
$896$	55.3165	1.84799
$897$	0.0424212	0.00141640
$898$	−67.9152	−2.26636
$899$	−29.4969	−0.983777
$900$	−55.9425	−1.86475
$901$	4.16573	0.138781
$902$	16.4705	0.548407
$903$	−4.05183	−0.134837
$904$	−18.7608	−0.623975
$905$	−11.4581	−0.380880
$906$	7.16997	0.238206
$907$	−49.7031	−1.65037	−0.825183	−	0.564866i	$-0.808928\pi$
$907$	−49.7031	−1.65037	−0.825183	+	0.564866i	$0.808928\pi$
$908$	−87.2688	−2.89612
$909$	23.4782	0.778722
$910$	−0.257027	−0.00852037
$911$	−14.7006	−0.487051	−0.243526	−	0.969894i	$-0.578304\pi$
$911$	−14.7006	−0.487051	−0.243526	+	0.969894i	$0.578304\pi$
$912$	0.221914	0.00734832
$913$	5.23145	0.173136
$914$	−18.8264	−0.622723
$915$	−21.8424	−0.722089
$916$	−34.4158	−1.13713
$917$	−3.04305	−0.100490
$918$	−38.1110	−1.25785
$919$	5.44729	0.179690	0.0898448	−	0.995956i	$-0.471363\pi$
$919$	5.44729	0.179690	0.0898448	+	0.995956i	$0.471363\pi$
$920$	59.7227	1.96900
$921$	5.19065	0.171038
$922$	−8.34954	−0.274978
$923$	0.100943	0.00332257
$924$	−6.13932	−0.201969
$925$	−51.5896	−1.69626
$926$	−34.2107	−1.12423
$927$	−11.9433	−0.392268
$928$	−35.6737	−1.17105
$929$	−32.8599	−1.07810	−0.539050	−	0.842274i	$-0.681217\pi$
$929$	−32.8599	−1.07810	−0.539050	+	0.842274i	$0.681217\pi$
$930$	23.1167	0.758026
$931$	−13.5730	−0.444836
$932$	−65.6489	−2.15040
$933$	−0.687781	−0.0225169
$934$	−13.4331	−0.439544
$935$	−16.2170	−0.530353
$936$	0.0789041	0.00257906
$937$	−26.2894	−0.858838	−0.429419	−	0.903105i	$-0.641282\pi$
$937$	−26.2894	−0.858838	−0.429419	+	0.903105i	$0.641282\pi$
$938$	4.13375	0.134972
$939$	−2.40217	−0.0783919
$940$	56.9258	1.85671
$941$	−47.9330	−1.56257	−0.781286	−	0.624173i	$-0.785436\pi$
$941$	−47.9330	−1.56257	−0.781286	+	0.624173i	$0.785436\pi$
$942$	−19.8828	−0.647817
$943$	−45.1139	−1.46911
$944$	0.128336	0.00417698
$945$	−36.4724	−1.18645
$946$	4.86095	0.158043
$947$	−38.2861	−1.24413	−0.622066	−	0.782965i	$-0.713706\pi$
$947$	−38.2861	−1.24413	−0.622066	+	0.782965i	$0.713706\pi$
$948$	−18.0103	−0.584946
$949$	−0.0749164	−0.00243189
$950$	−91.3408	−2.96349
$951$	3.90057	0.126485
$952$	−40.3956	−1.30923
$953$	−19.5592	−0.633584	−0.316792	−	0.948495i	$-0.602606\pi$
$953$	−19.5592	−0.633584	−0.316792	+	0.948495i	$0.602606\pi$
$954$	−5.22716	−0.169236
$955$	67.8193	2.19458
$956$	−37.8897	−1.22544
$957$	3.90136	0.126113
$958$	−41.7627	−1.34929
$959$	−13.2360	−0.427412
$960$	27.7051	0.894179
$961$	−8.59889	−0.277384
$962$	0.191775	0.00618308
$963$	−38.0868	−1.22733
$964$	93.3351	3.00612
$965$	71.9064	2.31475
$966$	27.2517	0.876807
$967$	−35.6743	−1.14721	−0.573603	−	0.819133i	$-0.694455\pi$
$967$	−35.6743	−1.14721	−0.573603	+	0.819133i	$0.694455\pi$
$968$	2.79459	0.0898216
$969$	−17.8573	−0.573660
$970$	−40.7546	−1.30855
$971$	−35.8202	−1.14952	−0.574762	−	0.818321i	$-0.694905\pi$
$971$	−35.8202	−1.14952	−0.574762	+	0.818321i	$0.694905\pi$
$972$	45.2948	1.45283
$973$	44.9369	1.44061
$974$	40.5696	1.29993
$975$	−0.0451027	−0.00144444
$976$	−0.603308	−0.0193114
$977$	−36.7316	−1.17515	−0.587574	−	0.809170i	$-0.699917\pi$
$977$	−36.7316	−1.17515	−0.587574	+	0.809170i	$0.699917\pi$
$978$	−18.1266	−0.579625
$979$	12.8067	0.409304
$980$	−24.8680	−0.794379
$981$	−3.79417	−0.121138
$982$	62.3344	1.98917
$983$	−3.29456	−0.105080	−0.0525401	−	0.998619i	$-0.516732\pi$
$983$	−3.29456	−0.105080	−0.0525401	+	0.998619i	$0.516732\pi$
$984$	12.6080	0.401928
$985$	24.7058	0.787194
$986$	67.6552	2.15458
$987$	9.85577	0.313713
$988$	0.209520	0.00666572
$989$	−13.3145	−0.423377
$990$	20.3491	0.646737
$991$	−15.2335	−0.483907	−0.241954	−	0.970288i	$-0.577788\pi$
$991$	−15.2335	−0.483907	−0.241954	+	0.970288i	$0.577788\pi$
$992$	27.0920	0.860173
$993$	16.8119	0.533508
$994$	64.8461	2.05679
$995$	−51.8771	−1.64461
$996$	10.5544	0.334429
$997$	46.2050	1.46333	0.731664	−	0.681665i	$-0.238744\pi$
$997$	46.2050	1.46333	0.731664	+	0.681665i	$0.238744\pi$
$998$	94.7909	3.00055
$999$	27.2131	0.860984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.23	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.23	✓	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)

\(f(q)\)	\(=\)	\(q+2.28535 q^{2} +0.625999 q^{3} +3.22283 q^{4} -3.41400 q^{5} +1.43063 q^{6} -3.04305 q^{7} +2.79459 q^{8} -2.60812 q^{9} +O(q^{10})\)	\(q+2.28535 q^{2} +0.625999 q^{3} +3.22283 q^{4} -3.41400 q^{5} +1.43063 q^{6} -3.04305 q^{7} +2.79459 q^{8} -2.60812 q^{9} -7.80220 q^{10} +1.00000 q^{11} +2.01749 q^{12} -0.0108256 q^{13} -6.95444 q^{14} -2.13716 q^{15} -0.0590304 q^{16} +4.75014 q^{17} -5.96048 q^{18} -6.00532 q^{19} -11.0028 q^{20} -1.90495 q^{21} +2.28535 q^{22} -6.25975 q^{23} +1.74941 q^{24} +6.65543 q^{25} -0.0247403 q^{26} -3.51068 q^{27} -9.80723 q^{28} +6.23221 q^{29} -4.88417 q^{30} -4.73298 q^{31} -5.72409 q^{32} +0.625999 q^{33} +10.8557 q^{34} +10.3890 q^{35} -8.40554 q^{36} -7.75151 q^{37} -13.7243 q^{38} -0.00677683 q^{39} -9.54076 q^{40} +7.20698 q^{41} -4.35347 q^{42} +2.12700 q^{43} +3.22283 q^{44} +8.90415 q^{45} -14.3057 q^{46} -5.17378 q^{47} -0.0369530 q^{48} +2.26016 q^{49} +15.2100 q^{50} +2.97358 q^{51} -0.0348891 q^{52} +0.876970 q^{53} -8.02314 q^{54} -3.41400 q^{55} -8.50409 q^{56} -3.75932 q^{57} +14.2428 q^{58} -2.17407 q^{59} -6.88772 q^{60} +10.2203 q^{61} -10.8165 q^{62} +7.93666 q^{63} -12.9635 q^{64} +0.0369587 q^{65} +1.43063 q^{66} -0.594405 q^{67} +15.3089 q^{68} -3.91860 q^{69} +23.7425 q^{70} -9.32442 q^{71} -7.28865 q^{72} +6.92029 q^{73} -17.7149 q^{74} +4.16629 q^{75} -19.3541 q^{76} -3.04305 q^{77} -0.0154874 q^{78} -8.92707 q^{79} +0.201530 q^{80} +5.62669 q^{81} +16.4705 q^{82} +5.23145 q^{83} -6.13932 q^{84} -16.2170 q^{85} +4.86095 q^{86} +3.90136 q^{87} +2.79459 q^{88} +12.8067 q^{89} +20.3491 q^{90} +0.0329429 q^{91} -20.1741 q^{92} -2.96284 q^{93} -11.8239 q^{94} +20.5022 q^{95} -3.58328 q^{96} +5.22347 q^{97} +5.16526 q^{98} -2.60812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 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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