LMFDB - Embedded newform 1441.2.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.32496 q^{2} +0.816970 q^{3} -0.244480 q^{4} -1.13056 q^{5} +1.08245 q^{6} +0.353069 q^{7} -2.97385 q^{8} -2.33256 q^{9} +O(q^{10})$	\(q+1.32496 q^{2} +0.816970 q^{3} -0.244480 q^{4} -1.13056 q^{5} +1.08245 q^{6} +0.353069 q^{7} -2.97385 q^{8} -2.33256 q^{9} -1.49794 q^{10} +1.00000 q^{11} -0.199733 q^{12} +0.567908 q^{13} +0.467802 q^{14} -0.923632 q^{15} -3.45127 q^{16} -5.63645 q^{17} -3.09055 q^{18} +4.71220 q^{19} +0.276399 q^{20} +0.288447 q^{21} +1.32496 q^{22} -1.45083 q^{23} -2.42954 q^{24} -3.72184 q^{25} +0.752456 q^{26} -4.35654 q^{27} -0.0863183 q^{28} -3.70097 q^{29} -1.22378 q^{30} -6.22874 q^{31} +1.37490 q^{32} +0.816970 q^{33} -7.46808 q^{34} -0.399165 q^{35} +0.570264 q^{36} -5.83861 q^{37} +6.24348 q^{38} +0.463964 q^{39} +3.36211 q^{40} -1.85637 q^{41} +0.382181 q^{42} +3.51834 q^{43} -0.244480 q^{44} +2.63709 q^{45} -1.92230 q^{46} +3.12662 q^{47} -2.81958 q^{48} -6.87534 q^{49} -4.93129 q^{50} -4.60481 q^{51} -0.138842 q^{52} -12.7400 q^{53} -5.77225 q^{54} -1.13056 q^{55} -1.04997 q^{56} +3.84973 q^{57} -4.90363 q^{58} -4.57261 q^{59} +0.225810 q^{60} +2.35442 q^{61} -8.25284 q^{62} -0.823555 q^{63} +8.72423 q^{64} -0.642053 q^{65} +1.08245 q^{66} +11.9849 q^{67} +1.37800 q^{68} -1.18529 q^{69} -0.528878 q^{70} +8.13252 q^{71} +6.93668 q^{72} +1.48402 q^{73} -7.73593 q^{74} -3.04063 q^{75} -1.15204 q^{76} +0.353069 q^{77} +0.614734 q^{78} +7.57812 q^{79} +3.90186 q^{80} +3.43851 q^{81} -2.45962 q^{82} -9.80840 q^{83} -0.0705195 q^{84} +6.37234 q^{85} +4.66166 q^{86} -3.02358 q^{87} -2.97385 q^{88} +7.94786 q^{89} +3.49404 q^{90} +0.200511 q^{91} +0.354700 q^{92} -5.08870 q^{93} +4.14265 q^{94} -5.32741 q^{95} +1.12325 q^{96} -10.9689 q^{97} -9.10956 q^{98} -2.33256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.32496	0.936888	0.468444	−	0.883493i	$-0.344815\pi$
$2$	1.32496	0.936888	0.468444	+	0.883493i	$0.344815\pi$
$3$	0.816970	0.471678	0.235839	−	0.971792i	$-0.424216\pi$
$3$	0.816970	0.471678	0.235839	+	0.971792i	$0.424216\pi$
$4$	−0.244480	−0.122240
$5$	−1.13056	−0.505601	−0.252800	−	0.967518i	$-0.581352\pi$
$5$	−1.13056	−0.505601	−0.252800	+	0.967518i	$0.581352\pi$
$6$	1.08245	0.441910
$7$	0.353069	0.133448	0.0667238	−	0.997771i	$-0.478745\pi$
$7$	0.353069	0.133448	0.0667238	+	0.997771i	$0.478745\pi$
$8$	−2.97385	−1.05141
$9$	−2.33256	−0.777520
$10$	−1.49794	−0.473692
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.199733	−0.0576579
$13$	0.567908	0.157509	0.0787547	−	0.996894i	$-0.474906\pi$
$13$	0.567908	0.157509	0.0787547	+	0.996894i	$0.474906\pi$
$14$	0.467802	0.125025
$15$	−0.923632	−0.238481
$16$	−3.45127	−0.862817
$17$	−5.63645	−1.36704	−0.683520	−	0.729931i	$-0.739552\pi$
$17$	−5.63645	−1.36704	−0.683520	+	0.729931i	$0.739552\pi$
$18$	−3.09055	−0.728449
$19$	4.71220	1.08105	0.540526	−	0.841327i	$-0.318225\pi$
$19$	4.71220	1.08105	0.540526	+	0.841327i	$0.318225\pi$
$20$	0.276399	0.0618047
$21$	0.288447	0.0629443
$22$	1.32496	0.282482
$23$	−1.45083	−0.302520	−0.151260	−	0.988494i	$-0.548333\pi$
$23$	−1.45083	−0.302520	−0.151260	+	0.988494i	$0.548333\pi$
$24$	−2.42954	−0.495929
$25$	−3.72184	−0.744368
$26$	0.752456	0.147569
$27$	−4.35654	−0.838417
$28$	−0.0863183	−0.0163126
$29$	−3.70097	−0.687252	−0.343626	−	0.939107i	$-0.611655\pi$
$29$	−3.70097	−0.687252	−0.343626	+	0.939107i	$0.611655\pi$
$30$	−1.22378	−0.223430
$31$	−6.22874	−1.11872	−0.559358	−	0.828926i	$-0.688952\pi$
$31$	−6.22874	−1.11872	−0.559358	+	0.828926i	$0.688952\pi$
$32$	1.37490	0.243050
$33$	0.816970	0.142216
$34$	−7.46808	−1.28076
$35$	−0.399165	−0.0674712
$36$	0.570264	0.0950441
$37$	−5.83861	−0.959862	−0.479931	−	0.877306i	$-0.659338\pi$
$37$	−5.83861	−0.959862	−0.479931	+	0.877306i	$0.659338\pi$
$38$	6.24348	1.01283
$39$	0.463964	0.0742937
$40$	3.36211	0.531596
$41$	−1.85637	−0.289917	−0.144958	−	0.989438i	$-0.546305\pi$
$41$	−1.85637	−0.289917	−0.144958	+	0.989438i	$0.546305\pi$
$42$	0.382181	0.0589717
$43$	3.51834	0.536541	0.268271	−	0.963344i	$-0.413548\pi$
$43$	3.51834	0.536541	0.268271	+	0.963344i	$0.413548\pi$
$44$	−0.244480	−0.0368568
$45$	2.63709	0.393115
$46$	−1.92230	−0.283427
$47$	3.12662	0.456065	0.228032	−	0.973654i	$-0.426771\pi$
$47$	3.12662	0.456065	0.228032	+	0.973654i	$0.426771\pi$
$48$	−2.81958	−0.406972
$49$	−6.87534	−0.982192
$50$	−4.93129	−0.697390
$51$	−4.60481	−0.644803
$52$	−0.138842	−0.0192539
$53$	−12.7400	−1.74998	−0.874990	−	0.484141i	$-0.839132\pi$
$53$	−12.7400	−1.74998	−0.874990	+	0.484141i	$0.839132\pi$
$54$	−5.77225	−0.785503
$55$	−1.13056	−0.152444
$56$	−1.04997	−0.140309
$57$	3.84973	0.509909
$58$	−4.90363	−0.643879
$59$	−4.57261	−0.595303	−0.297652	−	0.954675i	$-0.596203\pi$
$59$	−4.57261	−0.595303	−0.297652	+	0.954675i	$0.596203\pi$
$60$	0.225810	0.0291519
$61$	2.35442	0.301453	0.150727	−	0.988575i	$-0.451839\pi$
$61$	2.35442	0.301453	0.150727	+	0.988575i	$0.451839\pi$
$62$	−8.25284	−1.04811
$63$	−0.823555	−0.103758
$64$	8.72423	1.09053
$65$	−0.642053	−0.0796369
$66$	1.08245	0.133241
$67$	11.9849	1.46419	0.732095	−	0.681202i	$-0.238542\pi$
$67$	11.9849	1.46419	0.732095	+	0.681202i	$0.238542\pi$
$68$	1.37800	0.167107
$69$	−1.18529	−0.142692
$70$	−0.528878	−0.0632130
$71$	8.13252	0.965153	0.482576	−	0.875854i	$-0.339701\pi$
$71$	8.13252	0.965153	0.482576	+	0.875854i	$0.339701\pi$
$72$	6.93668	0.817495
$73$	1.48402	0.173691	0.0868454	−	0.996222i	$-0.472321\pi$
$73$	1.48402	0.173691	0.0868454	+	0.996222i	$0.472321\pi$
$74$	−7.73593	−0.899283
$75$	−3.04063	−0.351102
$76$	−1.15204	−0.132148
$77$	0.353069	0.0402359
$78$	0.614734	0.0696049
$79$	7.57812	0.852605	0.426303	−	0.904581i	$-0.359816\pi$
$79$	7.57812	0.852605	0.426303	+	0.904581i	$0.359816\pi$
$80$	3.90186	0.436241
$81$	3.43851	0.382057
$82$	−2.45962	−0.271620
$83$	−9.80840	−1.07661	−0.538306	−	0.842750i	$-0.680935\pi$
$83$	−9.80840	−1.07661	−0.538306	+	0.842750i	$0.680935\pi$
$84$	−0.0705195	−0.00769431
$85$	6.37234	0.691177
$86$	4.66166	0.502679
$87$	−3.02358	−0.324162
$88$	−2.97385	−0.317013
$89$	7.94786	0.842472	0.421236	−	0.906951i	$-0.361596\pi$
$89$	7.94786	0.842472	0.421236	+	0.906951i	$0.361596\pi$
$90$	3.49404	0.368305
$91$	0.200511	0.0210192
$92$	0.354700	0.0369800
$93$	−5.08870	−0.527673
$94$	4.14265	0.427282
$95$	−5.32741	−0.546581
$96$	1.12325	0.114641
$97$	−10.9689	−1.11372	−0.556861	−	0.830605i	$-0.687995\pi$
$97$	−10.9689	−1.11372	−0.556861	+	0.830605i	$0.687995\pi$
$98$	−9.10956	−0.920204
$99$	−2.33256	−0.234431
$100$	0.909915	0.0909915
$101$	−0.342843	−0.0341142	−0.0170571	−	0.999855i	$-0.505430\pi$
$101$	−0.342843	−0.0341142	−0.0170571	+	0.999855i	$0.505430\pi$
$102$	−6.10120	−0.604109
$103$	16.9575	1.67088	0.835438	−	0.549585i	$-0.185214\pi$
$103$	16.9575	1.67088	0.835438	+	0.549585i	$0.185214\pi$
$104$	−1.68887	−0.165608
$105$	−0.326106	−0.0318247
$106$	−16.8801	−1.63954
$107$	3.94686	0.381557	0.190779	−	0.981633i	$-0.438899\pi$
$107$	3.94686	0.381557	0.190779	+	0.981633i	$0.438899\pi$
$108$	1.06509	0.102488
$109$	8.22252	0.787575	0.393787	−	0.919202i	$-0.371165\pi$
$109$	8.22252	0.787575	0.393787	+	0.919202i	$0.371165\pi$
$110$	−1.49794	−0.142823
$111$	−4.76997	−0.452746
$112$	−1.21854	−0.115141
$113$	−10.9013	−1.02551	−0.512753	−	0.858536i	$-0.671374\pi$
$113$	−10.9013	−1.02551	−0.512753	+	0.858536i	$0.671374\pi$
$114$	5.10073	0.477728
$115$	1.64025	0.152954
$116$	0.904813	0.0840097
$117$	−1.32468	−0.122467
$118$	−6.05853	−0.557733
$119$	−1.99006	−0.182428
$120$	2.74674	0.250742
$121$	1.00000	0.0909091
$122$	3.11952	0.282428
$123$	−1.51660	−0.136747
$124$	1.52280	0.136752
$125$	9.86054	0.881954
$126$	−1.09118	−0.0972098
$127$	14.3157	1.27031	0.635156	−	0.772384i	$-0.280936\pi$
$127$	14.3157	1.27031	0.635156	+	0.772384i	$0.280936\pi$
$128$	8.80945	0.778653
$129$	2.87438	0.253075
$130$	−0.850695	−0.0746109
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.199733	−0.0173845
$133$	1.66373	0.144264
$134$	15.8795	1.37178
$135$	4.92532	0.423904
$136$	16.7620	1.43733
$137$	7.72841	0.660282	0.330141	−	0.943932i	$-0.392904\pi$
$137$	7.72841	0.660282	0.330141	+	0.943932i	$0.392904\pi$
$138$	−1.57046	−0.133686
$139$	−8.89239	−0.754243	−0.377121	−	0.926164i	$-0.623086\pi$
$139$	−8.89239	−0.754243	−0.377121	+	0.926164i	$0.623086\pi$
$140$	0.0975879	0.00824768
$141$	2.55436	0.215116
$142$	10.7753	0.904241
$143$	0.567908	0.0474909
$144$	8.05029	0.670858
$145$	4.18416	0.347475
$146$	1.96626	0.162729
$147$	−5.61695	−0.463278
$148$	1.42742	0.117334
$149$	−21.5858	−1.76838	−0.884189	−	0.467129i	$-0.845288\pi$
$149$	−21.5858	−1.76838	−0.884189	+	0.467129i	$0.845288\pi$
$150$	−4.02872	−0.328943
$151$	−15.0394	−1.22389	−0.611943	−	0.790902i	$-0.709612\pi$
$151$	−15.0394	−1.22389	−0.611943	+	0.790902i	$0.709612\pi$
$152$	−14.0134	−1.13663
$153$	13.1474	1.06290
$154$	0.467802	0.0376966
$155$	7.04196	0.565624
$156$	−0.113430	−0.00908166
$157$	−9.06276	−0.723287	−0.361643	−	0.932317i	$-0.617784\pi$
$157$	−9.06276	−0.723287	−0.361643	+	0.932317i	$0.617784\pi$
$158$	10.0407	0.798796
$159$	−10.4082	−0.825427
$160$	−1.55440	−0.122886
$161$	−0.512244	−0.0403705
$162$	4.55590	0.357945
$163$	6.09907	0.477716	0.238858	−	0.971054i	$-0.423227\pi$
$163$	6.09907	0.477716	0.238858	+	0.971054i	$0.423227\pi$
$164$	0.453846	0.0354394
$165$	−0.923632	−0.0719047
$166$	−12.9957	−1.00867
$167$	18.8638	1.45972	0.729862	−	0.683594i	$-0.239584\pi$
$167$	18.8638	1.45972	0.729862	+	0.683594i	$0.239584\pi$
$168$	−0.857797	−0.0661805
$169$	−12.6775	−0.975191
$170$	8.44310	0.647556
$171$	−10.9915	−0.840540
$172$	−0.860163	−0.0655868
$173$	−3.88396	−0.295292	−0.147646	−	0.989040i	$-0.547170\pi$
$173$	−3.88396	−0.295292	−0.147646	+	0.989040i	$0.547170\pi$
$174$	−4.00612	−0.303703
$175$	−1.31407	−0.0993340
$176$	−3.45127	−0.260149
$177$	−3.73569	−0.280792
$178$	10.5306	0.789302
$179$	0.373747	0.0279351	0.0139676	−	0.999902i	$-0.495554\pi$
$179$	0.373747	0.0279351	0.0139676	+	0.999902i	$0.495554\pi$
$180$	−0.644717	−0.0480544
$181$	−11.8898	−0.883762	−0.441881	−	0.897074i	$-0.645689\pi$
$181$	−11.8898	−0.883762	−0.441881	+	0.897074i	$0.645689\pi$
$182$	0.265669	0.0196927
$183$	1.92349	0.142189
$184$	4.31456	0.318073
$185$	6.60089	0.485307
$186$	−6.74232	−0.494371
$187$	−5.63645	−0.412178
$188$	−0.764397	−0.0557494
$189$	−1.53816	−0.111885
$190$	−7.05861	−0.512086
$191$	18.4657	1.33613	0.668067	−	0.744101i	$-0.267122\pi$
$191$	18.4657	1.33613	0.668067	+	0.744101i	$0.267122\pi$
$192$	7.12743	0.514378
$193$	23.9288	1.72244	0.861218	−	0.508236i	$-0.169702\pi$
$193$	23.9288	1.72244	0.861218	+	0.508236i	$0.169702\pi$
$194$	−14.5334	−1.04343
$195$	−0.524538	−0.0375630
$196$	1.68088	0.120063
$197$	−17.2006	−1.22549	−0.612745	−	0.790281i	$-0.709935\pi$
$197$	−17.2006	−1.22549	−0.612745	+	0.790281i	$0.709935\pi$
$198$	−3.09055	−0.219636
$199$	−23.9808	−1.69995	−0.849977	−	0.526819i	$-0.823384\pi$
$199$	−23.9808	−1.69995	−0.849977	+	0.526819i	$0.823384\pi$
$200$	11.0682	0.782638
$201$	9.79132	0.690627
$202$	−0.454254	−0.0319612
$203$	−1.30670	−0.0917121
$204$	1.12579	0.0788207
$205$	2.09874	0.146582
$206$	22.4681	1.56542
$207$	3.38416	0.235215
$208$	−1.96000	−0.135902
$209$	4.71220	0.325950
$210$	−0.432077	−0.0298162
$211$	12.1342	0.835351	0.417675	−	0.908596i	$-0.362845\pi$
$211$	12.1342	0.835351	0.417675	+	0.908596i	$0.362845\pi$
$212$	3.11469	0.213918
$213$	6.64403	0.455241
$214$	5.22943	0.357477
$215$	−3.97768	−0.271276
$216$	12.9557	0.881523
$217$	−2.19918	−0.149290
$218$	10.8945	0.737870
$219$	1.21240	0.0819261
$220$	0.276399	0.0186348
$221$	−3.20099	−0.215322
$222$	−6.32002	−0.424172
$223$	−4.16564	−0.278952	−0.139476	−	0.990225i	$-0.544542\pi$
$223$	−4.16564	−0.278952	−0.139476	+	0.990225i	$0.544542\pi$
$224$	0.485434	0.0324344
$225$	8.68141	0.578761
$226$	−14.4438	−0.960784
$227$	22.0784	1.46540	0.732698	−	0.680554i	$-0.238261\pi$
$227$	22.0784	1.46540	0.732698	+	0.680554i	$0.238261\pi$
$228$	−0.941181	−0.0623312
$229$	−22.5611	−1.49088	−0.745439	−	0.666574i	$-0.767760\pi$
$229$	−22.5611	−1.49088	−0.745439	+	0.666574i	$0.767760\pi$
$230$	2.17327	0.143301
$231$	0.288447	0.0189784
$232$	11.0061	0.722586
$233$	−16.7389	−1.09660	−0.548302	−	0.836280i	$-0.684726\pi$
$233$	−16.7389	−1.09660	−0.548302	+	0.836280i	$0.684726\pi$
$234$	−1.75515	−0.114738
$235$	−3.53483	−0.230587
$236$	1.11791	0.0727699
$237$	6.19110	0.402155
$238$	−2.63675	−0.170915
$239$	−24.8151	−1.60516	−0.802578	−	0.596547i	$-0.796539\pi$
$239$	−24.8151	−1.60516	−0.802578	+	0.596547i	$0.796539\pi$
$240$	3.18770	0.205765
$241$	22.8503	1.47192	0.735958	−	0.677027i	$-0.236732\pi$
$241$	22.8503	1.47192	0.735958	+	0.677027i	$0.236732\pi$
$242$	1.32496	0.0851717
$243$	15.8788	1.01862
$244$	−0.575610	−0.0368496
$245$	7.77297	0.496597
$246$	−2.00944	−0.128117
$247$	2.67610	0.170276
$248$	18.5233	1.17623
$249$	−8.01317	−0.507814
$250$	13.0648	0.826292
$251$	−13.6950	−0.864421	−0.432211	−	0.901773i	$-0.642266\pi$
$251$	−13.6950	−0.864421	−0.432211	+	0.901773i	$0.642266\pi$
$252$	0.201343	0.0126834
$253$	−1.45083	−0.0912131
$254$	18.9677	1.19014
$255$	5.20601	0.326013
$256$	−5.77627	−0.361017
$257$	−5.49105	−0.342522	−0.171261	−	0.985226i	$-0.554784\pi$
$257$	−5.49105	−0.342522	−0.171261	+	0.985226i	$0.554784\pi$
$258$	3.80843	0.237103
$259$	−2.06143	−0.128091
$260$	0.156969	0.00973481
$261$	8.63273	0.534352
$262$	1.32496	0.0818563
$263$	−7.21750	−0.445050	−0.222525	−	0.974927i	$-0.571430\pi$
$263$	−7.21750	−0.445050	−0.222525	+	0.974927i	$0.571430\pi$
$264$	−2.42954	−0.149528
$265$	14.4034	0.884791
$266$	2.20438	0.135159
$267$	6.49317	0.397375
$268$	−2.93007	−0.178983
$269$	−8.07849	−0.492554	−0.246277	−	0.969199i	$-0.579207\pi$
$269$	−8.07849	−0.492554	−0.246277	+	0.969199i	$0.579207\pi$
$270$	6.52586	0.397151
$271$	16.9543	1.02990	0.514952	−	0.857219i	$-0.327810\pi$
$271$	16.9543	1.02990	0.514952	+	0.857219i	$0.327810\pi$
$272$	19.4529	1.17951
$273$	0.163811	0.00991431
$274$	10.2398	0.618611
$275$	−3.72184	−0.224435
$276$	0.289779	0.0174427
$277$	13.8143	0.830020	0.415010	−	0.909817i	$-0.363778\pi$
$277$	13.8143	0.830020	0.415010	+	0.909817i	$0.363778\pi$
$278$	−11.7821	−0.706641
$279$	14.5289	0.869824
$280$	1.18706	0.0709401
$281$	−1.10144	−0.0657061	−0.0328531	−	0.999460i	$-0.510459\pi$
$281$	−1.10144	−0.0657061	−0.0328531	+	0.999460i	$0.510459\pi$
$282$	3.38442	0.201539
$283$	−12.9968	−0.772581	−0.386291	−	0.922377i	$-0.626244\pi$
$283$	−12.9968	−0.772581	−0.386291	+	0.922377i	$0.626244\pi$
$284$	−1.98824	−0.117980
$285$	−4.35234	−0.257810
$286$	0.752456	0.0444936
$287$	−0.655428	−0.0386887
$288$	−3.20703	−0.188976
$289$	14.7696	0.868801
$290$	5.54384	0.325546
$291$	−8.96126	−0.525318
$292$	−0.362812	−0.0212320
$293$	−19.4555	−1.13660	−0.568300	−	0.822821i	$-0.692399\pi$
$293$	−19.4555	−1.13660	−0.568300	+	0.822821i	$0.692399\pi$
$294$	−7.44224	−0.434040
$295$	5.16960	0.300986
$296$	17.3631	1.00921
$297$	−4.35654	−0.252792
$298$	−28.6003	−1.65677
$299$	−0.823940	−0.0476497
$300$	0.743374	0.0429187
$301$	1.24222	0.0716001
$302$	−19.9266	−1.14665
$303$	−0.280093	−0.0160909
$304$	−16.2631	−0.932751
$305$	−2.66181	−0.152415
$306$	17.4197	0.995820
$307$	7.85757	0.448455	0.224228	−	0.974537i	$-0.428014\pi$
$307$	7.85757	0.448455	0.224228	+	0.974537i	$0.428014\pi$
$308$	−0.0863183	−0.00491844
$309$	13.8538	0.788115
$310$	9.33031	0.529926
$311$	−9.85437	−0.558790	−0.279395	−	0.960176i	$-0.590134\pi$
$311$	−9.85437	−0.558790	−0.279395	+	0.960176i	$0.590134\pi$
$312$	−1.37976	−0.0781134
$313$	−11.9184	−0.673667	−0.336834	−	0.941564i	$-0.609356\pi$
$313$	−11.9184	−0.673667	−0.336834	+	0.941564i	$0.609356\pi$
$314$	−12.0078	−0.677639
$315$	0.931076	0.0524602
$316$	−1.85270	−0.104222
$317$	13.8283	0.776675	0.388338	−	0.921517i	$-0.373049\pi$
$317$	13.8283	0.776675	0.388338	+	0.921517i	$0.373049\pi$
$318$	−13.7905	−0.773333
$319$	−3.70097	−0.207214
$320$	−9.86324	−0.551372
$321$	3.22447	0.179972
$322$	−0.678703	−0.0378227
$323$	−26.5601	−1.47784
$324$	−0.840648	−0.0467027
$325$	−2.11366	−0.117245
$326$	8.08103	0.447567
$327$	6.71755	0.371482
$328$	5.52057	0.304823
$329$	1.10391	0.0608607
$330$	−1.22378	−0.0673666
$331$	29.0450	1.59646	0.798229	−	0.602354i	$-0.205770\pi$
$331$	29.0450	1.59646	0.798229	+	0.602354i	$0.205770\pi$
$332$	2.39796	0.131605
$333$	13.6189	0.746312
$334$	24.9938	1.36760
$335$	−13.5496	−0.740296
$336$	−0.995508	−0.0543094
$337$	−33.6237	−1.83160	−0.915801	−	0.401633i	$-0.868443\pi$
$337$	−33.6237	−1.83160	−0.915801	+	0.401633i	$0.868443\pi$
$338$	−16.7972	−0.913645
$339$	−8.90601	−0.483708
$340$	−1.55791	−0.0844895
$341$	−6.22874	−0.337305
$342$	−14.5633	−0.787492
$343$	−4.89895	−0.264519
$344$	−10.4630	−0.564127
$345$	1.34004	0.0721451
$346$	−5.14610	−0.276656
$347$	−22.9925	−1.23430	−0.617152	−	0.786844i	$-0.711714\pi$
$347$	−22.9925	−1.23430	−0.617152	+	0.786844i	$0.711714\pi$
$348$	0.739205	0.0396255
$349$	−13.8803	−0.742993	−0.371497	−	0.928434i	$-0.621155\pi$
$349$	−13.8803	−0.742993	−0.371497	+	0.928434i	$0.621155\pi$
$350$	−1.74109	−0.0930649
$351$	−2.47412	−0.132059
$352$	1.37490	0.0732824
$353$	17.1640	0.913546	0.456773	−	0.889583i	$-0.349005\pi$
$353$	17.1640	0.913546	0.456773	+	0.889583i	$0.349005\pi$
$354$	−4.94964	−0.263070
$355$	−9.19429	−0.487982
$356$	−1.94309	−0.102984
$357$	−1.62582	−0.0860474
$358$	0.495200	0.0261721
$359$	−17.6863	−0.933448	−0.466724	−	0.884403i	$-0.654566\pi$
$359$	−17.6863	−0.933448	−0.466724	+	0.884403i	$0.654566\pi$
$360$	−7.84231	−0.413326
$361$	3.20482	0.168675
$362$	−15.7535	−0.827986
$363$	0.816970	0.0428798
$364$	−0.0490209	−0.00256939
$365$	−1.67777	−0.0878182
$366$	2.54855	0.133215
$367$	−15.9906	−0.834701	−0.417351	−	0.908745i	$-0.637041\pi$
$367$	−15.9906	−0.834701	−0.417351	+	0.908745i	$0.637041\pi$
$368$	5.00722	0.261019
$369$	4.33010	0.225416
$370$	8.74592	0.454679
$371$	−4.49811	−0.233530
$372$	1.24409	0.0645028
$373$	13.1988	0.683407	0.341704	−	0.939808i	$-0.388996\pi$
$373$	13.1988	0.683407	0.341704	+	0.939808i	$0.388996\pi$
$374$	−7.46808	−0.386165
$375$	8.05577	0.415998
$376$	−9.29810	−0.479513
$377$	−2.10181	−0.108249
$378$	−2.03800	−0.104823
$379$	−24.8970	−1.27887	−0.639437	−	0.768843i	$-0.720833\pi$
$379$	−24.8970	−1.27887	−0.639437	+	0.768843i	$0.720833\pi$
$380$	1.30245	0.0668141
$381$	11.6955	0.599178
$382$	24.4664	1.25181
$383$	12.2905	0.628014	0.314007	−	0.949421i	$-0.398328\pi$
$383$	12.2905	0.628014	0.314007	+	0.949421i	$0.398328\pi$
$384$	7.19706	0.367274
$385$	−0.399165	−0.0203433
$386$	31.7048	1.61373
$387$	−8.20673	−0.417172
$388$	2.68168	0.136141
$389$	−26.3703	−1.33703	−0.668514	−	0.743700i	$-0.733069\pi$
$389$	−26.3703	−1.33703	−0.668514	+	0.743700i	$0.733069\pi$
$390$	−0.694992	−0.0351923
$391$	8.17756	0.413557
$392$	20.4462	1.03269
$393$	0.816970	0.0412107
$394$	−22.7901	−1.14815
$395$	−8.56750	−0.431078
$396$	0.570264	0.0286569
$397$	4.16344	0.208957	0.104479	−	0.994527i	$-0.466683\pi$
$397$	4.16344	0.208957	0.104479	+	0.994527i	$0.466683\pi$
$398$	−31.7736	−1.59267
$399$	1.35922	0.0680461
$400$	12.8451	0.642253
$401$	3.26090	0.162842	0.0814209	−	0.996680i	$-0.474054\pi$
$401$	3.26090	0.162842	0.0814209	+	0.996680i	$0.474054\pi$
$402$	12.9731	0.647040
$403$	−3.53735	−0.176208
$404$	0.0838184	0.00417012
$405$	−3.88744	−0.193168
$406$	−1.73132	−0.0859240
$407$	−5.83861	−0.289409
$408$	13.6940	0.677955
$409$	13.4282	0.663983	0.331991	−	0.943282i	$-0.392280\pi$
$409$	13.4282	0.663983	0.331991	+	0.943282i	$0.392280\pi$
$410$	2.78074	0.137331
$411$	6.31388	0.311441
$412$	−4.14578	−0.204248
$413$	−1.61445	−0.0794418
$414$	4.48387	0.220370
$415$	11.0890	0.544336
$416$	0.780816	0.0382827
$417$	−7.26482	−0.355760
$418$	6.24348	0.305378
$419$	23.0541	1.12627	0.563133	−	0.826366i	$-0.309596\pi$
$419$	23.0541	1.12627	0.563133	+	0.826366i	$0.309596\pi$
$420$	0.0797264	0.00389025
$421$	−3.74427	−0.182484	−0.0912422	−	0.995829i	$-0.529084\pi$
$421$	−3.74427	−0.182484	−0.0912422	+	0.995829i	$0.529084\pi$
$422$	16.0773	0.782630
$423$	−7.29303	−0.354599
$424$	37.8869	1.83995
$425$	20.9780	1.01758
$426$	8.80307	0.426510
$427$	0.831274	0.0402282
$428$	−0.964928	−0.0466416
$429$	0.463964	0.0224004
$430$	−5.27027	−0.254155
$431$	28.1962	1.35816	0.679082	−	0.734063i	$-0.262378\pi$
$431$	28.1962	1.35816	0.679082	+	0.734063i	$0.262378\pi$
$432$	15.0356	0.723401
$433$	−5.68232	−0.273075	−0.136537	−	0.990635i	$-0.543597\pi$
$433$	−5.68232	−0.273075	−0.136537	+	0.990635i	$0.543597\pi$
$434$	−2.91382	−0.139868
$435$	3.41833	0.163896
$436$	−2.01024	−0.0962731
$437$	−6.83662	−0.327040
$438$	1.60638	0.0767557
$439$	−20.7453	−0.990117	−0.495058	−	0.868860i	$-0.664853\pi$
$439$	−20.7453	−0.990117	−0.495058	+	0.868860i	$0.664853\pi$
$440$	3.36211	0.160282
$441$	16.0371	0.763674
$442$	−4.24118	−0.201732
$443$	−8.28821	−0.393785	−0.196892	−	0.980425i	$-0.563085\pi$
$443$	−8.28821	−0.393785	−0.196892	+	0.980425i	$0.563085\pi$
$444$	1.16616	0.0553436
$445$	−8.98552	−0.425954
$446$	−5.51930	−0.261347
$447$	−17.6350	−0.834105
$448$	3.08025	0.145528
$449$	24.2012	1.14213	0.571063	−	0.820906i	$-0.306531\pi$
$449$	24.2012	1.14213	0.571063	+	0.820906i	$0.306531\pi$
$450$	11.5025	0.542234
$451$	−1.85637	−0.0874132
$452$	2.66514	0.125358
$453$	−12.2867	−0.577280
$454$	29.2530	1.37291
$455$	−0.226689	−0.0106273
$456$	−11.4485	−0.536125
$457$	−27.5128	−1.28699	−0.643497	−	0.765448i	$-0.722517\pi$
$457$	−27.5128	−1.28699	−0.643497	+	0.765448i	$0.722517\pi$
$458$	−29.8925	−1.39679
$459$	24.5555	1.14615
$460$	−0.401009	−0.0186971
$461$	38.5247	1.79428	0.897138	−	0.441750i	$-0.145642\pi$
$461$	38.5247	1.79428	0.897138	+	0.441750i	$0.145642\pi$
$462$	0.382181	0.0177807
$463$	16.3623	0.760423	0.380211	−	0.924900i	$-0.375851\pi$
$463$	16.3623	0.760423	0.380211	+	0.924900i	$0.375851\pi$
$464$	12.7730	0.592973
$465$	5.75307	0.266792
$466$	−22.1784	−1.02740
$467$	−38.6784	−1.78982	−0.894911	−	0.446244i	$-0.852761\pi$
$467$	−38.6784	−1.78982	−0.894911	+	0.446244i	$0.852761\pi$
$468$	0.323858	0.0149703
$469$	4.23150	0.195393
$470$	−4.68351	−0.216034
$471$	−7.40400	−0.341158
$472$	13.5983	0.625910
$473$	3.51834	0.161773
$474$	8.20296	0.376774
$475$	−17.5380	−0.804701
$476$	0.486529	0.0223000
$477$	29.7169	1.36064
$478$	−32.8791	−1.50385
$479$	−6.21669	−0.284048	−0.142024	−	0.989863i	$-0.545361\pi$
$479$	−6.21669	−0.284048	−0.142024	+	0.989863i	$0.545361\pi$
$480$	−1.26990	−0.0579628
$481$	−3.31579	−0.151187
$482$	30.2757	1.37902
$483$	−0.418488	−0.0190419
$484$	−0.244480	−0.0111127
$485$	12.4010	0.563099
$486$	21.0388	0.954338
$487$	36.7316	1.66447	0.832234	−	0.554424i	$-0.187061\pi$
$487$	36.7316	1.66447	0.832234	+	0.554424i	$0.187061\pi$
$488$	−7.00170	−0.316952
$489$	4.98276	0.225328
$490$	10.2989	0.465256
$491$	−21.3184	−0.962085	−0.481043	−	0.876697i	$-0.659742\pi$
$491$	−21.3184	−0.962085	−0.481043	+	0.876697i	$0.659742\pi$
$492$	0.370779	0.0167160
$493$	20.8603	0.939502
$494$	3.54572	0.159530
$495$	2.63709	0.118529
$496$	21.4971	0.965247
$497$	2.87134	0.128797
$498$	−10.6171	−0.475765
$499$	−36.5206	−1.63489	−0.817444	−	0.576008i	$-0.804610\pi$
$499$	−36.5206	−1.63489	−0.817444	+	0.576008i	$0.804610\pi$
$500$	−2.41071	−0.107810
$501$	15.4112	0.688520
$502$	−18.1453	−0.809866
$503$	4.94792	0.220617	0.110308	−	0.993897i	$-0.464816\pi$
$503$	4.94792	0.220617	0.110308	+	0.993897i	$0.464816\pi$
$504$	2.44913	0.109093
$505$	0.387604	0.0172482
$506$	−1.92230	−0.0854565
$507$	−10.3571	−0.459976
$508$	−3.49990	−0.155283
$509$	12.8344	0.568875	0.284438	−	0.958695i	$-0.408193\pi$
$509$	12.8344	0.568875	0.284438	+	0.958695i	$0.408193\pi$
$510$	6.89776	0.305438
$511$	0.523960	0.0231786
$512$	−25.2722	−1.11689
$513$	−20.5289	−0.906373
$514$	−7.27542	−0.320905
$515$	−19.1715	−0.844796
$516$	−0.702727	−0.0309359
$517$	3.12662	0.137509
$518$	−2.73132	−0.120007
$519$	−3.17308	−0.139283
$520$	1.90937	0.0837313
$521$	18.2773	0.800742	0.400371	−	0.916353i	$-0.368881\pi$
$521$	18.2773	0.800742	0.400371	+	0.916353i	$0.368881\pi$
$522$	11.4380	0.500629
$523$	−0.965625	−0.0422238	−0.0211119	−	0.999777i	$-0.506721\pi$
$523$	−0.965625	−0.0422238	−0.0211119	+	0.999777i	$0.506721\pi$
$524$	−0.244480	−0.0106802
$525$	−1.07355	−0.0468537
$526$	−9.56290	−0.416962
$527$	35.1080	1.52933
$528$	−2.81958	−0.122707
$529$	−20.8951	−0.908482
$530$	19.0839	0.828951
$531$	10.6659	0.462860
$532$	−0.406749	−0.0176348
$533$	−1.05425	−0.0456646
$534$	8.60319	0.372296
$535$	−4.46215	−0.192916
$536$	−35.6413	−1.53947
$537$	0.305340	0.0131764
$538$	−10.7037	−0.461468
$539$	−6.87534	−0.296142
$540$	−1.20414	−0.0518181
$541$	−30.3597	−1.30526	−0.652632	−	0.757675i	$-0.726335\pi$
$541$	−30.3597	−1.30526	−0.652632	+	0.757675i	$0.726335\pi$
$542$	22.4638	0.964904
$543$	−9.71361	−0.416851
$544$	−7.74956	−0.332259
$545$	−9.29604	−0.398198
$546$	0.217043	0.00928860
$547$	9.45301	0.404181	0.202091	−	0.979367i	$-0.435226\pi$
$547$	9.45301	0.404181	0.202091	+	0.979367i	$0.435226\pi$
$548$	−1.88944	−0.0807129
$549$	−5.49184	−0.234386
$550$	−4.93129	−0.210271
$551$	−17.4397	−0.742956
$552$	3.52486	0.150028
$553$	2.67560	0.113778
$554$	18.3034	0.777636
$555$	5.39273	0.228909
$556$	2.17401	0.0921986
$557$	−32.6157	−1.38197	−0.690986	−	0.722868i	$-0.742824\pi$
$557$	−32.6157	−1.38197	−0.690986	+	0.722868i	$0.742824\pi$
$558$	19.2502	0.814928
$559$	1.99809	0.0845103
$560$	1.37763	0.0582153
$561$	−4.60481	−0.194415
$562$	−1.45936	−0.0615593
$563$	−14.8633	−0.626413	−0.313206	−	0.949685i	$-0.601403\pi$
$563$	−14.8633	−0.626413	−0.313206	+	0.949685i	$0.601403\pi$
$564$	−0.624489	−0.0262957
$565$	12.3245	0.518496
$566$	−17.2203	−0.723822
$567$	1.21403	0.0509846
$568$	−24.1849	−1.01477
$569$	2.14758	0.0900312	0.0450156	−	0.998986i	$-0.485666\pi$
$569$	2.14758	0.0900312	0.0450156	+	0.998986i	$0.485666\pi$
$570$	−5.76668	−0.241539
$571$	40.6748	1.70219	0.851093	−	0.525014i	$-0.175940\pi$
$571$	40.6748	1.70219	0.851093	+	0.525014i	$0.175940\pi$
$572$	−0.138842	−0.00580528
$573$	15.0859	0.630225
$574$	−0.868416	−0.0362470
$575$	5.39977	0.225186
$576$	−20.3498	−0.847907
$577$	17.6505	0.734800	0.367400	−	0.930063i	$-0.380248\pi$
$577$	17.6505	0.734800	0.367400	+	0.930063i	$0.380248\pi$
$578$	19.5692	0.813970
$579$	19.5492	0.812435
$580$	−1.02294	−0.0424754
$581$	−3.46304	−0.143671
$582$	−11.8733	−0.492165
$583$	−12.7400	−0.527639
$584$	−4.41323	−0.182621
$585$	1.49763	0.0619193
$586$	−25.7777	−1.06487
$587$	21.5827	0.890815	0.445408	−	0.895328i	$-0.353059\pi$
$587$	21.5827	0.890815	0.445408	+	0.895328i	$0.353059\pi$
$588$	1.37323	0.0566311
$589$	−29.3511	−1.20939
$590$	6.84952	0.281990
$591$	−14.0523	−0.578036
$592$	20.1506	0.828185
$593$	7.97342	0.327429	0.163715	−	0.986508i	$-0.447652\pi$
$593$	7.97342	0.327429	0.163715	+	0.986508i	$0.447652\pi$
$594$	−5.77225	−0.236838
$595$	2.24987	0.0922359
$596$	5.27730	0.216167
$597$	−19.5916	−0.801831
$598$	−1.09169	−0.0446424
$599$	−10.1151	−0.413291	−0.206645	−	0.978416i	$-0.566255\pi$
$599$	−10.1151	−0.413291	−0.206645	+	0.978416i	$0.566255\pi$
$600$	9.04237	0.369153
$601$	−17.2278	−0.702735	−0.351367	−	0.936238i	$-0.614283\pi$
$601$	−17.2278	−0.702735	−0.351367	+	0.936238i	$0.614283\pi$
$602$	1.64589	0.0670813
$603$	−27.9555	−1.13844
$604$	3.67683	0.149608
$605$	−1.13056	−0.0459637
$606$	−0.371112	−0.0150754
$607$	−41.3546	−1.67853	−0.839266	−	0.543722i	$-0.817015\pi$
$607$	−41.3546	−1.67853	−0.839266	+	0.543722i	$0.817015\pi$
$608$	6.47880	0.262750
$609$	−1.06753	−0.0432586
$610$	−3.52680	−0.142796
$611$	1.77563	0.0718345
$612$	−3.21427	−0.129929
$613$	11.9734	0.483600	0.241800	−	0.970326i	$-0.422262\pi$
$613$	11.9734	0.483600	0.241800	+	0.970326i	$0.422262\pi$
$614$	10.4110	0.420153
$615$	1.71461	0.0691396
$616$	−1.04997	−0.0423046
$617$	4.34475	0.174913	0.0874565	−	0.996168i	$-0.472126\pi$
$617$	4.34475	0.174913	0.0874565	+	0.996168i	$0.472126\pi$
$618$	18.3557	0.738376
$619$	22.1688	0.891041	0.445520	−	0.895272i	$-0.353019\pi$
$619$	22.1688	0.891041	0.445520	+	0.895272i	$0.353019\pi$
$620$	−1.72162	−0.0691418
$621$	6.32062	0.253638
$622$	−13.0566	−0.523524
$623$	2.80614	0.112426
$624$	−1.60126	−0.0641019
$625$	7.46128	0.298451
$626$	−15.7914	−0.631151
$627$	3.84973	0.153743
$628$	2.21566	0.0884146
$629$	32.9091	1.31217
$630$	1.23364	0.0491494
$631$	45.5027	1.81144	0.905718	−	0.423882i	$-0.139333\pi$
$631$	45.5027	1.81144	0.905718	+	0.423882i	$0.139333\pi$
$632$	−22.5362	−0.896441
$633$	9.91325	0.394016
$634$	18.3220	0.727658
$635$	−16.1847	−0.642271
$636$	2.54461	0.100900
$637$	−3.90456	−0.154704
$638$	−4.90363	−0.194137
$639$	−18.9696	−0.750426
$640$	−9.95960	−0.393688
$641$	−13.7092	−0.541479	−0.270740	−	0.962653i	$-0.587268\pi$
$641$	−13.7092	−0.541479	−0.270740	+	0.962653i	$0.587268\pi$
$642$	4.27229	0.168614
$643$	26.3453	1.03896	0.519478	−	0.854484i	$-0.326127\pi$
$643$	26.3453	1.03896	0.519478	+	0.854484i	$0.326127\pi$
$644$	0.125233	0.00493489
$645$	−3.24965	−0.127955
$646$	−35.1911	−1.38457
$647$	−4.64873	−0.182760	−0.0913802	−	0.995816i	$-0.529128\pi$
$647$	−4.64873	−0.182760	−0.0913802	+	0.995816i	$0.529128\pi$
$648$	−10.2256	−0.401700
$649$	−4.57261	−0.179491
$650$	−2.80052	−0.109845
$651$	−1.79666	−0.0704167
$652$	−1.49110	−0.0583960
$653$	1.39299	0.0545118	0.0272559	−	0.999628i	$-0.491323\pi$
$653$	1.39299	0.0545118	0.0272559	+	0.999628i	$0.491323\pi$
$654$	8.90049	0.348037
$655$	−1.13056	−0.0441746
$656$	6.40685	0.250145
$657$	−3.46155	−0.135048
$658$	1.46264	0.0570197
$659$	−5.34689	−0.208285	−0.104143	−	0.994562i	$-0.533210\pi$
$659$	−5.34689	−0.208285	−0.104143	+	0.994562i	$0.533210\pi$
$660$	0.225810	0.00878963
$661$	4.09651	0.159336	0.0796680	−	0.996821i	$-0.474614\pi$
$661$	4.09651	0.159336	0.0796680	+	0.996821i	$0.474614\pi$
$662$	38.4835	1.49570
$663$	−2.61511	−0.101563
$664$	29.1687	1.13196
$665$	−1.88094	−0.0729399
$666$	18.0445	0.699211
$667$	5.36949	0.207907
$668$	−4.61182	−0.178437
$669$	−3.40320	−0.131575
$670$	−17.9527	−0.693575
$671$	2.35442	0.0908916
$672$	0.396585	0.0152986
$673$	−26.2802	−1.01303	−0.506514	−	0.862231i	$-0.669066\pi$
$673$	−26.2802	−1.01303	−0.506514	+	0.862231i	$0.669066\pi$
$674$	−44.5501	−1.71601
$675$	16.2143	0.624091
$676$	3.09939	0.119207
$677$	0.654150	0.0251410	0.0125705	−	0.999921i	$-0.495999\pi$
$677$	0.654150	0.0251410	0.0125705	+	0.999921i	$0.495999\pi$
$678$	−11.8001	−0.453181
$679$	−3.87278	−0.148624
$680$	−18.9504	−0.726713
$681$	18.0374	0.691195
$682$	−8.25284	−0.316018
$683$	−26.3731	−1.00914	−0.504570	−	0.863371i	$-0.668349\pi$
$683$	−26.3731	−1.00914	−0.504570	+	0.863371i	$0.668349\pi$
$684$	2.68720	0.102748
$685$	−8.73741	−0.333839
$686$	−6.49092	−0.247824
$687$	−18.4317	−0.703214
$688$	−12.1427	−0.462937
$689$	−7.23517	−0.275638
$690$	1.77549	0.0675919
$691$	47.3809	1.80246	0.901228	−	0.433346i	$-0.142667\pi$
$691$	47.3809	1.80246	0.901228	+	0.433346i	$0.142667\pi$
$692$	0.949551	0.0360965
$693$	−0.823555	−0.0312842
$694$	−30.4642	−1.15641
$695$	10.0534	0.381346
$696$	8.99166	0.340828
$697$	10.4634	0.396328
$698$	−18.3908	−0.696102
$699$	−13.6752	−0.517244
$700$	0.321263	0.0121426
$701$	−37.1967	−1.40490	−0.702449	−	0.711734i	$-0.747910\pi$
$701$	−37.1967	−1.40490	−0.702449	+	0.711734i	$0.747910\pi$
$702$	−3.27811	−0.123724
$703$	−27.5127	−1.03766
$704$	8.72423	0.328807
$705$	−2.88785	−0.108763
$706$	22.7416	0.855890
$707$	−0.121047	−0.00455246
$708$	0.913301	0.0343240
$709$	23.9449	0.899269	0.449635	−	0.893213i	$-0.351554\pi$
$709$	23.9449	0.899269	0.449635	+	0.893213i	$0.351554\pi$
$710$	−12.1821	−0.457185
$711$	−17.6764	−0.662917
$712$	−23.6357	−0.885786
$713$	9.03687	0.338433
$714$	−2.15414	−0.0806168
$715$	−0.642053	−0.0240114
$716$	−0.0913736	−0.00341479
$717$	−20.2732	−0.757117
$718$	−23.4337	−0.874537
$719$	−31.1065	−1.16008	−0.580039	−	0.814589i	$-0.696963\pi$
$719$	−31.1065	−1.16008	−0.580039	+	0.814589i	$0.696963\pi$
$720$	−9.10132	−0.339186
$721$	5.98718	0.222974
$722$	4.24626	0.158029
$723$	18.6680	0.694270
$724$	2.90682	0.108031
$725$	13.7744	0.511568
$726$	1.08245	0.0401736
$727$	−17.3848	−0.644765	−0.322383	−	0.946609i	$-0.604484\pi$
$727$	−17.3848	−0.644765	−0.322383	+	0.946609i	$0.604484\pi$
$728$	−0.596288	−0.0220999
$729$	2.65695	0.0984057
$730$	−2.22297	−0.0822759
$731$	−19.8309	−0.733474
$732$	−0.470256	−0.0173812
$733$	−26.7162	−0.986786	−0.493393	−	0.869807i	$-0.664243\pi$
$733$	−26.7162	−0.986786	−0.493393	+	0.869807i	$0.664243\pi$
$734$	−21.1869	−0.782022
$735$	6.35029	0.234234
$736$	−1.99475	−0.0735274
$737$	11.9849	0.441470
$738$	5.73721	0.211190
$739$	29.9806	1.10285	0.551427	−	0.834223i	$-0.314084\pi$
$739$	29.9806	1.10285	0.551427	+	0.834223i	$0.314084\pi$
$740$	−1.61379	−0.0593239
$741$	2.18629	0.0803154
$742$	−5.95982	−0.218792
$743$	−16.9536	−0.621967	−0.310984	−	0.950415i	$-0.600658\pi$
$743$	−16.9536	−0.621967	−0.310984	+	0.950415i	$0.600658\pi$
$744$	15.1330	0.554803
$745$	24.4040	0.894094
$746$	17.4879	0.640276
$747$	22.8787	0.837087
$748$	1.37800	0.0503847
$749$	1.39351	0.0509179
$750$	10.6736	0.389744
$751$	−25.9289	−0.946158	−0.473079	−	0.881020i	$-0.656857\pi$
$751$	−25.9289	−0.946158	−0.473079	+	0.881020i	$0.656857\pi$
$752$	−10.7908	−0.393501
$753$	−11.1884	−0.407728
$754$	−2.78481	−0.101417
$755$	17.0029	0.618798
$756$	0.376049	0.0136768
$757$	10.6084	0.385568	0.192784	−	0.981241i	$-0.438248\pi$
$757$	10.6084	0.385568	0.192784	+	0.981241i	$0.438248\pi$
$758$	−32.9876	−1.19816
$759$	−1.18529	−0.0430232
$760$	15.8429	0.574683
$761$	−11.9063	−0.431603	−0.215802	−	0.976437i	$-0.569236\pi$
$761$	−11.9063	−0.431603	−0.215802	+	0.976437i	$0.569236\pi$
$762$	15.4961	0.561363
$763$	2.90312	0.105100
$764$	−4.51450	−0.163329
$765$	−14.8639	−0.537404
$766$	16.2844	0.588379
$767$	−2.59682	−0.0937659
$768$	−4.71904	−0.170284
$769$	−42.4337	−1.53020	−0.765099	−	0.643912i	$-0.777310\pi$
$769$	−42.4337	−1.53020	−0.765099	+	0.643912i	$0.777310\pi$
$770$	−0.528878	−0.0190594
$771$	−4.48602	−0.161560
$772$	−5.85013	−0.210551
$773$	−0.285366	−0.0102639	−0.00513195	−	0.999987i	$-0.501634\pi$
$773$	−0.285366	−0.0102639	−0.00513195	+	0.999987i	$0.501634\pi$
$774$	−10.8736	−0.390843
$775$	23.1824	0.832736
$776$	32.6198	1.17098
$777$	−1.68413	−0.0604178
$778$	−34.9396	−1.25265
$779$	−8.74760	−0.313415
$780$	0.128239	0.00459170
$781$	8.13252	0.291005
$782$	10.8349	0.387457
$783$	16.1234	0.576204
$784$	23.7287	0.847452
$785$	10.2460	0.365694
$786$	1.08245	0.0386098
$787$	3.10167	0.110563	0.0552813	−	0.998471i	$-0.482394\pi$
$787$	3.10167	0.110563	0.0552813	+	0.998471i	$0.482394\pi$
$788$	4.20519	0.149804
$789$	−5.89648	−0.209920
$790$	−11.3516	−0.403872
$791$	−3.84890	−0.136851
$792$	6.93668	0.246484
$793$	1.33710	0.0474817
$794$	5.51639	0.195769
$795$	11.7671	0.417336
$796$	5.86283	0.207803
$797$	−15.1088	−0.535182	−0.267591	−	0.963533i	$-0.586228\pi$
$797$	−15.1088	−0.535182	−0.267591	+	0.963533i	$0.586228\pi$
$798$	1.80091	0.0637516
$799$	−17.6231	−0.623459
$800$	−5.11715	−0.180919
$801$	−18.5389	−0.655039
$802$	4.32057	0.152565
$803$	1.48402	0.0523698
$804$	−2.39378	−0.0844222
$805$	0.579122	0.0204114
$806$	−4.68685	−0.165087
$807$	−6.59988	−0.232327
$808$	1.01956	0.0358681
$809$	24.0748	0.846424	0.423212	−	0.906031i	$-0.360902\pi$
$809$	24.0748	0.846424	0.423212	+	0.906031i	$0.360902\pi$
$810$	−5.15070	−0.180977
$811$	−42.8940	−1.50621	−0.753107	−	0.657898i	$-0.771446\pi$
$811$	−42.8940	−1.50621	−0.753107	+	0.657898i	$0.771446\pi$
$812$	0.319461	0.0112109
$813$	13.8512	0.485783
$814$	−7.73593	−0.271144
$815$	−6.89535	−0.241534
$816$	15.8925	0.556347
$817$	16.5791	0.580029
$818$	17.7919	0.622078
$819$	−0.467703	−0.0163429
$820$	−0.513100	−0.0179182
$821$	−35.5513	−1.24075	−0.620375	−	0.784305i	$-0.713020\pi$
$821$	−35.5513	−1.24075	−0.620375	+	0.784305i	$0.713020\pi$
$822$	8.36564	0.291785
$823$	−22.2672	−0.776185	−0.388092	−	0.921620i	$-0.626866\pi$
$823$	−22.2672	−0.776185	−0.388092	+	0.921620i	$0.626866\pi$
$824$	−50.4291	−1.75678
$825$	−3.04063	−0.105861
$826$	−2.13908	−0.0744281
$827$	−6.43036	−0.223606	−0.111803	−	0.993730i	$-0.535663\pi$
$827$	−6.43036	−0.223606	−0.111803	+	0.993730i	$0.535663\pi$
$828$	−0.827358	−0.0287527
$829$	8.85710	0.307620	0.153810	−	0.988100i	$-0.450846\pi$
$829$	8.85710	0.307620	0.153810	+	0.988100i	$0.450846\pi$
$830$	14.6924	0.509982
$831$	11.2859	0.391502
$832$	4.95456	0.171768
$833$	38.7526	1.34270
$834$	−9.62559	−0.333307
$835$	−21.3266	−0.738038
$836$	−1.15204	−0.0398441
$837$	27.1358	0.937950
$838$	30.5458	1.05519
$839$	−43.8506	−1.51389	−0.756945	−	0.653479i	$-0.773309\pi$
$839$	−43.8506	−1.51389	−0.756945	+	0.653479i	$0.773309\pi$
$840$	0.969789	0.0334609
$841$	−15.3028	−0.527684
$842$	−4.96101	−0.170968
$843$	−0.899840	−0.0309921
$844$	−2.96656	−0.102113
$845$	14.3326	0.493057
$846$	−9.66298	−0.332220
$847$	0.353069	0.0121316
$848$	43.9693	1.50991
$849$	−10.6180	−0.364409
$850$	27.7950	0.953360
$851$	8.47085	0.290377
$852$	−1.62433	−0.0556487
$853$	56.8858	1.94773	0.973866	−	0.227125i	$-0.0729326\pi$
$853$	56.8858	1.94773	0.973866	+	0.227125i	$0.0729326\pi$
$854$	1.10141	0.0376893
$855$	12.4265	0.424978
$856$	−11.7374	−0.401175
$857$	−52.0275	−1.77723	−0.888614	−	0.458657i	$-0.848331\pi$
$857$	−52.0275	−1.77723	−0.888614	+	0.458657i	$0.848331\pi$
$858$	0.614734	0.0209867
$859$	−28.2083	−0.962456	−0.481228	−	0.876595i	$-0.659809\pi$
$859$	−28.2083	−0.962456	−0.481228	+	0.876595i	$0.659809\pi$
$860$	0.972464	0.0331608
$861$	−0.535465	−0.0182486
$862$	37.3589	1.27245
$863$	−50.1858	−1.70835	−0.854173	−	0.519989i	$-0.825936\pi$
$863$	−50.1858	−1.70835	−0.854173	+	0.519989i	$0.825936\pi$
$864$	−5.98981	−0.203777
$865$	4.39104	0.149300
$866$	−7.52885	−0.255841
$867$	12.0663	0.409794
$868$	0.537655	0.0182492
$869$	7.57812	0.257070
$870$	4.52915	0.153553
$871$	6.80633	0.230624
$872$	−24.4525	−0.828067
$873$	25.5856	0.865942
$874$	−9.05824	−0.306400
$875$	3.48145	0.117695
$876$	−0.296407	−0.0100147
$877$	12.8221	0.432972	0.216486	−	0.976286i	$-0.430540\pi$
$877$	12.8221	0.432972	0.216486	+	0.976286i	$0.430540\pi$
$878$	−27.4866	−0.927629
$879$	−15.8945	−0.536109
$880$	3.90186	0.131532
$881$	26.4485	0.891074	0.445537	−	0.895264i	$-0.353013\pi$
$881$	26.4485	0.891074	0.445537	+	0.895264i	$0.353013\pi$
$882$	21.2486	0.715477
$883$	23.9293	0.805284	0.402642	−	0.915358i	$-0.368092\pi$
$883$	23.9293	0.805284	0.402642	+	0.915358i	$0.368092\pi$
$884$	0.782578	0.0263209
$885$	4.22341	0.141968
$886$	−10.9816	−0.368932
$887$	−28.7223	−0.964402	−0.482201	−	0.876061i	$-0.660162\pi$
$887$	−28.7223	−0.964402	−0.482201	+	0.876061i	$0.660162\pi$
$888$	14.1852	0.476023
$889$	5.05443	0.169520
$890$	−11.9055	−0.399072
$891$	3.43851	0.115195
$892$	1.01842	0.0340991
$893$	14.7333	0.493030
$894$	−23.3656	−0.781463
$895$	−0.422542	−0.0141240
$896$	3.11035	0.103909
$897$	−0.673134	−0.0224753
$898$	32.0657	1.07004
$899$	23.0524	0.768840
$900$	−2.12243	−0.0707477
$901$	71.8087	2.39229
$902$	−2.45962	−0.0818964
$903$	1.01485	0.0337722
$904$	32.4187	1.07823
$905$	13.4421	0.446831
$906$	−16.2794	−0.540847
$907$	48.2491	1.60208	0.801042	−	0.598608i	$-0.204279\pi$
$907$	48.2491	1.60208	0.801042	+	0.598608i	$0.204279\pi$
$908$	−5.39773	−0.179130
$909$	0.799703	0.0265245
$910$	−0.300354	−0.00995664
$911$	34.4234	1.14050	0.570249	−	0.821472i	$-0.306847\pi$
$911$	34.4234	1.14050	0.570249	+	0.821472i	$0.306847\pi$
$912$	−13.2864	−0.439958
$913$	−9.80840	−0.324611
$914$	−36.4534	−1.20577
$915$	−2.17462	−0.0718908
$916$	5.51573	0.182245
$917$	0.353069	0.0116594
$918$	32.5350	1.07381
$919$	2.97546	0.0981515	0.0490758	−	0.998795i	$-0.484372\pi$
$919$	2.97546	0.0981515	0.0490758	+	0.998795i	$0.484372\pi$
$920$	−4.87786	−0.160818
$921$	6.41940	0.211527
$922$	51.0438	1.68104
$923$	4.61853	0.152021
$924$	−0.0705195	−0.00231992
$925$	21.7304	0.714490
$926$	21.6795	0.712431
$927$	−39.5545	−1.29914
$928$	−5.08846	−0.167037
$929$	−37.2443	−1.22195	−0.610974	−	0.791651i	$-0.709222\pi$
$929$	−37.2443	−1.22195	−0.610974	+	0.791651i	$0.709222\pi$
$930$	7.62259	0.249955
$931$	−32.3980	−1.06180
$932$	4.09234	0.134049
$933$	−8.05073	−0.263569
$934$	−51.2473	−1.67686
$935$	6.37234	0.208398
$936$	3.93939	0.128763
$937$	−16.0565	−0.524544	−0.262272	−	0.964994i	$-0.584472\pi$
$937$	−16.0565	−0.524544	−0.262272	+	0.964994i	$0.584472\pi$
$938$	5.60657	0.183061
$939$	−9.73697	−0.317754
$940$	0.864195	0.0281869
$941$	−41.0308	−1.33756	−0.668782	−	0.743458i	$-0.733184\pi$
$941$	−41.0308	−1.33756	−0.668782	+	0.743458i	$0.733184\pi$
$942$	−9.81001	−0.319627
$943$	2.69329	0.0877056
$944$	15.7813	0.513638
$945$	1.73898	0.0565690
$946$	4.66166	0.151564
$947$	−33.2447	−1.08031	−0.540154	−	0.841566i	$-0.681634\pi$
$947$	−33.2447	−1.08031	−0.540154	+	0.841566i	$0.681634\pi$
$948$	−1.51360	−0.0491594
$949$	0.842784	0.0273579
$950$	−23.2372	−0.753915
$951$	11.2973	0.366341
$952$	5.91813	0.191808
$953$	−57.0118	−1.84679	−0.923396	−	0.383848i	$-0.874599\pi$
$953$	−57.0118	−1.84679	−0.923396	+	0.383848i	$0.874599\pi$
$954$	39.3737	1.27477
$955$	−20.8766	−0.675550
$956$	6.06680	0.196214
$957$	−3.02358	−0.0977384
$958$	−8.23687	−0.266121
$959$	2.72866	0.0881130
$960$	−8.05797	−0.260070
$961$	7.79726	0.251525
$962$	−4.39330	−0.141646
$963$	−9.20629	−0.296668
$964$	−5.58644	−0.179927
$965$	−27.0529	−0.870865
$966$	−0.554480	−0.0178401
$967$	25.0159	0.804458	0.402229	−	0.915539i	$-0.368236\pi$
$967$	25.0159	0.804458	0.402229	+	0.915539i	$0.368236\pi$
$968$	−2.97385	−0.0955831
$969$	−21.6988	−0.697066
$970$	16.4308	0.527561
$971$	2.72160	0.0873404	0.0436702	−	0.999046i	$-0.486095\pi$
$971$	2.72160	0.0873404	0.0436702	+	0.999046i	$0.486095\pi$
$972$	−3.88205	−0.124517
$973$	−3.13963	−0.100652
$974$	48.6679	1.55942
$975$	−1.72680	−0.0553018
$976$	−8.12575	−0.260099
$977$	−29.5972	−0.946898	−0.473449	−	0.880821i	$-0.656991\pi$
$977$	−29.5972	−0.946898	−0.473449	+	0.880821i	$0.656991\pi$
$978$	6.60196	0.211107
$979$	7.94786	0.254015
$980$	−1.90034	−0.0607040
$981$	−19.1795	−0.612355
$982$	−28.2460	−0.901367
$983$	4.73749	0.151102	0.0755512	−	0.997142i	$-0.475928\pi$
$983$	4.73749	0.151102	0.0755512	+	0.997142i	$0.475928\pi$
$984$	4.51014	0.143778
$985$	19.4462	0.619608
$986$	27.6391	0.880209
$987$	0.901864	0.0287067
$988$	−0.654252	−0.0208145
$989$	−5.10452	−0.162314
$990$	3.49404	0.111048
$991$	−36.1994	−1.14991	−0.574955	−	0.818185i	$-0.694981\pi$
$991$	−36.1994	−1.14991	−0.574955	+	0.818185i	$0.694981\pi$
$992$	−8.56389	−0.271904
$993$	23.7289	0.753014
$994$	3.80441	0.120669
$995$	27.1117	0.859499
$996$	1.95906	0.0620752
$997$	−29.8803	−0.946319	−0.473160	−	0.880977i	$-0.656887\pi$
$997$	−29.8803	−0.946319	−0.473160	+	0.880977i	$0.656887\pi$
$998$	−48.3884	−1.53171
$999$	25.4362	0.804764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.c.1.18	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.c.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.32496 q^{2} +0.816970 q^{3} -0.244480 q^{4} -1.13056 q^{5} +1.08245 q^{6} +0.353069 q^{7} -2.97385 q^{8} -2.33256 q^{9} +O(q^{10})\)	\(q+1.32496 q^{2} +0.816970 q^{3} -0.244480 q^{4} -1.13056 q^{5} +1.08245 q^{6} +0.353069 q^{7} -2.97385 q^{8} -2.33256 q^{9} -1.49794 q^{10} +1.00000 q^{11} -0.199733 q^{12} +0.567908 q^{13} +0.467802 q^{14} -0.923632 q^{15} -3.45127 q^{16} -5.63645 q^{17} -3.09055 q^{18} +4.71220 q^{19} +0.276399 q^{20} +0.288447 q^{21} +1.32496 q^{22} -1.45083 q^{23} -2.42954 q^{24} -3.72184 q^{25} +0.752456 q^{26} -4.35654 q^{27} -0.0863183 q^{28} -3.70097 q^{29} -1.22378 q^{30} -6.22874 q^{31} +1.37490 q^{32} +0.816970 q^{33} -7.46808 q^{34} -0.399165 q^{35} +0.570264 q^{36} -5.83861 q^{37} +6.24348 q^{38} +0.463964 q^{39} +3.36211 q^{40} -1.85637 q^{41} +0.382181 q^{42} +3.51834 q^{43} -0.244480 q^{44} +2.63709 q^{45} -1.92230 q^{46} +3.12662 q^{47} -2.81958 q^{48} -6.87534 q^{49} -4.93129 q^{50} -4.60481 q^{51} -0.138842 q^{52} -12.7400 q^{53} -5.77225 q^{54} -1.13056 q^{55} -1.04997 q^{56} +3.84973 q^{57} -4.90363 q^{58} -4.57261 q^{59} +0.225810 q^{60} +2.35442 q^{61} -8.25284 q^{62} -0.823555 q^{63} +8.72423 q^{64} -0.642053 q^{65} +1.08245 q^{66} +11.9849 q^{67} +1.37800 q^{68} -1.18529 q^{69} -0.528878 q^{70} +8.13252 q^{71} +6.93668 q^{72} +1.48402 q^{73} -7.73593 q^{74} -3.04063 q^{75} -1.15204 q^{76} +0.353069 q^{77} +0.614734 q^{78} +7.57812 q^{79} +3.90186 q^{80} +3.43851 q^{81} -2.45962 q^{82} -9.80840 q^{83} -0.0705195 q^{84} +6.37234 q^{85} +4.66166 q^{86} -3.02358 q^{87} -2.97385 q^{88} +7.94786 q^{89} +3.49404 q^{90} +0.200511 q^{91} +0.354700 q^{92} -5.08870 q^{93} +4.14265 q^{94} -5.32741 q^{95} +1.12325 q^{96} -10.9689 q^{97} -9.10956 q^{98} -2.33256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 7 q^{2} - 3 q^{3} + 15 q^{4} - 9 q^{5} - 11 q^{6} - 12 q^{7} - 21 q^{8} + 12 q^{9}+O(q^{10}) \) 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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