LMFDB - Embedded newform 1573.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,2,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, 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("1573.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1573.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:	$12.5604682379$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -3.23607 q^{5} -2.76393 q^{6} +3.85410 q^{7} -2.23607 q^{8} -1.47214 q^{9} +O(q^{10})$	\(q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -3.23607 q^{5} -2.76393 q^{6} +3.85410 q^{7} -2.23607 q^{8} -1.47214 q^{9} +7.23607 q^{10} +3.70820 q^{12} -1.00000 q^{13} -8.61803 q^{14} -4.00000 q^{15} -1.00000 q^{16} +4.61803 q^{17} +3.29180 q^{18} -1.61803 q^{19} -9.70820 q^{20} +4.76393 q^{21} -8.00000 q^{23} -2.76393 q^{24} +5.47214 q^{25} +2.23607 q^{26} -5.52786 q^{27} +11.5623 q^{28} -5.61803 q^{29} +8.94427 q^{30} +5.61803 q^{31} +6.70820 q^{32} -10.3262 q^{34} -12.4721 q^{35} -4.41641 q^{36} +4.00000 q^{37} +3.61803 q^{38} -1.23607 q^{39} +7.23607 q^{40} -10.6525 q^{42} -4.00000 q^{43} +4.76393 q^{45} +17.8885 q^{46} +6.32624 q^{47} -1.23607 q^{48} +7.85410 q^{49} -12.2361 q^{50} +5.70820 q^{51} -3.00000 q^{52} +0.0901699 q^{53} +12.3607 q^{54} -8.61803 q^{56} -2.00000 q^{57} +12.5623 q^{58} -9.61803 q^{59} -12.0000 q^{60} -7.32624 q^{61} -12.5623 q^{62} -5.67376 q^{63} -13.0000 q^{64} +3.23607 q^{65} -1.52786 q^{67} +13.8541 q^{68} -9.88854 q^{69} +27.8885 q^{70} -11.5623 q^{71} +3.29180 q^{72} +5.70820 q^{73} -8.94427 q^{74} +6.76393 q^{75} -4.85410 q^{76} +2.76393 q^{78} -2.00000 q^{79} +3.23607 q^{80} -2.41641 q^{81} +8.09017 q^{83} +14.2918 q^{84} -14.9443 q^{85} +8.94427 q^{86} -6.94427 q^{87} -15.4164 q^{89} -10.6525 q^{90} -3.85410 q^{91} -24.0000 q^{92} +6.94427 q^{93} -14.1459 q^{94} +5.23607 q^{95} +8.29180 q^{96} -9.70820 q^{97} -17.5623 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 6 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 6 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 6 * q^9	$ 2 q - 2 q^{3} + 6 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 6 q^{9} + 10 q^{10} - 6 q^{12} - 2 q^{13} - 15 q^{14} - 8 q^{15} - 2 q^{16} + 7 q^{17} + 20 q^{18} - q^{19} - 6 q^{20} + 14 q^{21} - 16 q^{23} - 10 q^{24} + 2 q^{25} - 20 q^{27} + 3 q^{28} - 9 q^{29} + 9 q^{31} - 5 q^{34} - 16 q^{35} + 18 q^{36} + 8 q^{37} + 5 q^{38} + 2 q^{39} + 10 q^{40} + 10 q^{42} - 8 q^{43} + 14 q^{45} - 3 q^{47} + 2 q^{48} + 9 q^{49} - 20 q^{50} - 2 q^{51} - 6 q^{52} - 11 q^{53} - 20 q^{54} - 15 q^{56} - 4 q^{57} + 5 q^{58} - 17 q^{59} - 24 q^{60} + q^{61} - 5 q^{62} - 27 q^{63} - 26 q^{64} + 2 q^{65} - 12 q^{67} + 21 q^{68} + 16 q^{69} + 20 q^{70} - 3 q^{71} + 20 q^{72} - 2 q^{73} + 18 q^{75} - 3 q^{76} + 10 q^{78} - 4 q^{79} + 2 q^{80} + 22 q^{81} + 5 q^{83} + 42 q^{84} - 12 q^{85} + 4 q^{87} - 4 q^{89} + 10 q^{90} - q^{91} - 48 q^{92} - 4 q^{93} - 35 q^{94} + 6 q^{95} + 30 q^{96} - 6 q^{97} - 15 q^{98}+O(q^{100}) $ 2 * q - 2 * q^3 + 6 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 6 * q^9 + 10 * q^10 - 6 * q^12 - 2 * q^13 - 15 * q^14 - 8 * q^15 - 2 * q^16 + 7 * q^17 + 20 * q^18 - q^19 - 6 * q^20 + 14 * q^21 - 16 * q^23 - 10 * q^24 + 2 * q^25 - 20 * q^27 + 3 * q^28 - 9 * q^29 + 9 * q^31 - 5 * q^34 - 16 * q^35 + 18 * q^36 + 8 * q^37 + 5 * q^38 + 2 * q^39 + 10 * q^40 + 10 * q^42 - 8 * q^43 + 14 * q^45 - 3 * q^47 + 2 * q^48 + 9 * q^49 - 20 * q^50 - 2 * q^51 - 6 * q^52 - 11 * q^53 - 20 * q^54 - 15 * q^56 - 4 * q^57 + 5 * q^58 - 17 * q^59 - 24 * q^60 + q^61 - 5 * q^62 - 27 * q^63 - 26 * q^64 + 2 * q^65 - 12 * q^67 + 21 * q^68 + 16 * q^69 + 20 * q^70 - 3 * q^71 + 20 * q^72 - 2 * q^73 + 18 * q^75 - 3 * q^76 + 10 * q^78 - 4 * q^79 + 2 * q^80 + 22 * q^81 + 5 * q^83 + 42 * q^84 - 12 * q^85 + 4 * q^87 - 4 * q^89 + 10 * q^90 - q^91 - 48 * q^92 - 4 * q^93 - 35 * q^94 + 6 * q^95 + 30 * q^96 - 6 * q^97 - 15 * q^98

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 $

$2$	−2.23607	−1.58114	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−2.23607	−1.58114	−0.790569	+	0.612372i	$0.790215\pi$
$3$	1.23607	0.713644	0.356822	−	0.934172i	$-0.383860\pi$
$3$	1.23607	0.713644	0.356822	+	0.934172i	$0.383860\pi$
$4$	3.00000	1.50000
$5$	−3.23607	−1.44721	−0.723607	−	0.690212i	$-0.757517\pi$
$5$	−3.23607	−1.44721	−0.723607	+	0.690212i	$0.757517\pi$
$6$	−2.76393	−1.12837
$7$	3.85410	1.45671	0.728357	−	0.685198i	$-0.240284\pi$
$7$	3.85410	1.45671	0.728357	+	0.685198i	$0.240284\pi$
$8$	−2.23607	−0.790569
$9$	−1.47214	−0.490712
$10$	7.23607	2.28825
$11$	0	0
$11$	0	0
$12$	3.70820	1.07047
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−8.61803	−2.30327
$15$	−4.00000	−1.03280
$16$	−1.00000	−0.250000
$17$	4.61803	1.12004	0.560019	−	0.828480i	$-0.310794\pi$
$17$	4.61803	1.12004	0.560019	+	0.828480i	$0.310794\pi$
$18$	3.29180	0.775884
$19$	−1.61803	−0.371202	−0.185601	−	0.982625i	$-0.559423\pi$
$19$	−1.61803	−0.371202	−0.185601	+	0.982625i	$0.559423\pi$
$20$	−9.70820	−2.17082
$21$	4.76393	1.03958
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−2.76393	−0.564185
$25$	5.47214	1.09443
$26$	2.23607	0.438529
$27$	−5.52786	−1.06384
$28$	11.5623	2.18507
$29$	−5.61803	−1.04324	−0.521621	−	0.853177i	$-0.674673\pi$
$29$	−5.61803	−1.04324	−0.521621	+	0.853177i	$0.674673\pi$
$30$	8.94427	1.63299
$31$	5.61803	1.00903	0.504514	−	0.863403i	$-0.331672\pi$
$31$	5.61803	1.00903	0.504514	+	0.863403i	$0.331672\pi$
$32$	6.70820	1.18585
$33$	0	0
$34$	−10.3262	−1.77094
$35$	−12.4721	−2.10818
$36$	−4.41641	−0.736068
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	3.61803	0.586923
$39$	−1.23607	−0.197929
$40$	7.23607	1.14412
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	−10.6525	−1.64371
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	4.76393	0.710165
$46$	17.8885	2.63752
$47$	6.32624	0.922777	0.461388	−	0.887198i	$-0.347352\pi$
$47$	6.32624	0.922777	0.461388	+	0.887198i	$0.347352\pi$
$48$	−1.23607	−0.178411
$49$	7.85410	1.12201
$50$	−12.2361	−1.73044
$51$	5.70820	0.799308
$52$	−3.00000	−0.416025
$53$	0.0901699	0.0123858	0.00619290	−	0.999981i	$-0.498029\pi$
$53$	0.0901699	0.0123858	0.00619290	+	0.999981i	$0.498029\pi$
$54$	12.3607	1.68208
$55$	0	0
$56$	−8.61803	−1.15163
$57$	−2.00000	−0.264906
$58$	12.5623	1.64951
$59$	−9.61803	−1.25216	−0.626081	−	0.779758i	$-0.715342\pi$
$59$	−9.61803	−1.25216	−0.626081	+	0.779758i	$0.715342\pi$
$60$	−12.0000	−1.54919
$61$	−7.32624	−0.938029	−0.469014	−	0.883191i	$-0.655391\pi$
$61$	−7.32624	−0.938029	−0.469014	+	0.883191i	$0.655391\pi$
$62$	−12.5623	−1.59541
$63$	−5.67376	−0.714827
$64$	−13.0000	−1.62500
$65$	3.23607	0.401385
$66$	0	0
$67$	−1.52786	−0.186658	−0.0933292	−	0.995635i	$-0.529751\pi$
$67$	−1.52786	−0.186658	−0.0933292	+	0.995635i	$0.529751\pi$
$68$	13.8541	1.68006
$69$	−9.88854	−1.19044
$70$	27.8885	3.33332
$71$	−11.5623	−1.37219	−0.686097	−	0.727510i	$-0.740677\pi$
$71$	−11.5623	−1.37219	−0.686097	+	0.727510i	$0.740677\pi$
$72$	3.29180	0.387942
$73$	5.70820	0.668095	0.334047	−	0.942556i	$-0.391585\pi$
$73$	5.70820	0.668095	0.334047	+	0.942556i	$0.391585\pi$
$74$	−8.94427	−1.03975
$75$	6.76393	0.781032
$76$	−4.85410	−0.556804
$77$	0	0
$78$	2.76393	0.312954
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	3.23607	0.361803
$81$	−2.41641	−0.268490
$82$	0	0
$83$	8.09017	0.888012	0.444006	−	0.896024i	$-0.353557\pi$
$83$	8.09017	0.888012	0.444006	+	0.896024i	$0.353557\pi$
$84$	14.2918	1.55936
$85$	−14.9443	−1.62093
$86$	8.94427	0.964486
$87$	−6.94427	−0.744504
$88$	0	0
$89$	−15.4164	−1.63414	−0.817068	−	0.576541i	$-0.804402\pi$
$89$	−15.4164	−1.63414	−0.817068	+	0.576541i	$0.804402\pi$
$90$	−10.6525	−1.12287
$91$	−3.85410	−0.404020
$92$	−24.0000	−2.50217
$93$	6.94427	0.720087
$94$	−14.1459	−1.45904
$95$	5.23607	0.537209
$96$	8.29180	0.846278
$97$	−9.70820	−0.985719	−0.492859	−	0.870109i	$-0.664048\pi$
$97$	−9.70820	−0.985719	−0.492859	+	0.870109i	$0.664048\pi$
$98$	−17.5623	−1.77406
$99$	0	0
$100$	16.4164	1.64164
$101$	−3.38197	−0.336518	−0.168259	−	0.985743i	$-0.553815\pi$
$101$	−3.38197	−0.336518	−0.168259	+	0.985743i	$0.553815\pi$
$102$	−12.7639	−1.26382
$103$	−2.00000	−0.197066	−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000	−0.197066	−0.0985329	+	0.995134i	$0.531415\pi$
$104$	2.23607	0.219265
$105$	−15.4164	−1.50449
$106$	−0.201626	−0.0195837
$107$	6.29180	0.608251	0.304125	−	0.952632i	$-0.401636\pi$
$107$	6.29180	0.608251	0.304125	+	0.952632i	$0.401636\pi$
$108$	−16.5836	−1.59576
$109$	10.1803	0.975100	0.487550	−	0.873095i	$-0.337891\pi$
$109$	10.1803	0.975100	0.487550	+	0.873095i	$0.337891\pi$
$110$	0	0
$111$	4.94427	0.469290
$112$	−3.85410	−0.364178
$113$	1.85410	0.174419	0.0872096	−	0.996190i	$-0.472205\pi$
$113$	1.85410	0.174419	0.0872096	+	0.996190i	$0.472205\pi$
$114$	4.47214	0.418854
$115$	25.8885	2.41412
$116$	−16.8541	−1.56486
$117$	1.47214	0.136099
$118$	21.5066	1.97984
$119$	17.7984	1.63157
$120$	8.94427	0.816497
$121$	0	0
$122$	16.3820	1.48315
$123$	0	0
$124$	16.8541	1.51354
$125$	−1.52786	−0.136656
$126$	12.6869	1.13024
$127$	4.76393	0.422731	0.211365	−	0.977407i	$-0.432209\pi$
$127$	4.76393	0.422731	0.211365	+	0.977407i	$0.432209\pi$
$128$	15.6525	1.38350
$129$	−4.94427	−0.435319
$130$	−7.23607	−0.634645
$131$	−19.8885	−1.73767	−0.868835	−	0.495102i	$-0.835131\pi$
$131$	−19.8885	−1.73767	−0.868835	+	0.495102i	$0.835131\pi$
$132$	0	0
$133$	−6.23607	−0.540736
$134$	3.41641	0.295133
$135$	17.8885	1.53960
$136$	−10.3262	−0.885468
$137$	−13.7082	−1.17117	−0.585585	−	0.810611i	$-0.699135\pi$
$137$	−13.7082	−1.17117	−0.585585	+	0.810611i	$0.699135\pi$
$138$	22.1115	1.88225
$139$	−18.1803	−1.54204	−0.771018	−	0.636813i	$-0.780252\pi$
$139$	−18.1803	−1.54204	−0.771018	+	0.636813i	$0.780252\pi$
$140$	−37.4164	−3.16226
$141$	7.81966	0.658534
$142$	25.8541	2.16963
$143$	0	0
$144$	1.47214	0.122678
$145$	18.1803	1.50980
$146$	−12.7639	−1.05635
$147$	9.70820	0.800719
$148$	12.0000	0.986394
$149$	−7.70820	−0.631481	−0.315740	−	0.948846i	$-0.602253\pi$
$149$	−7.70820	−0.631481	−0.315740	+	0.948846i	$0.602253\pi$
$150$	−15.1246	−1.23492
$151$	12.0902	0.983884	0.491942	−	0.870628i	$-0.336287\pi$
$151$	12.0902	0.983884	0.491942	+	0.870628i	$0.336287\pi$
$152$	3.61803	0.293461
$153$	−6.79837	−0.549616
$154$	0	0
$155$	−18.1803	−1.46028
$156$	−3.70820	−0.296894
$157$	−14.7984	−1.18104	−0.590519	−	0.807023i	$-0.701077\pi$
$157$	−14.7984	−1.18104	−0.590519	+	0.807023i	$0.701077\pi$
$158$	4.47214	0.355784
$159$	0.111456	0.00883905
$160$	−21.7082	−1.71618
$161$	−30.8328	−2.42997
$162$	5.40325	0.424520
$163$	−5.38197	−0.421548	−0.210774	−	0.977535i	$-0.567598\pi$
$163$	−5.38197	−0.421548	−0.210774	+	0.977535i	$0.567598\pi$
$164$	0	0
$165$	0	0
$166$	−18.0902	−1.40407
$167$	3.14590	0.243437	0.121718	−	0.992565i	$-0.461160\pi$
$167$	3.14590	0.243437	0.121718	+	0.992565i	$0.461160\pi$
$168$	−10.6525	−0.821856
$169$	1.00000	0.0769231
$170$	33.4164	2.56292
$171$	2.38197	0.182153
$172$	−12.0000	−0.914991
$173$	−12.4721	−0.948239	−0.474119	−	0.880461i	$-0.657234\pi$
$173$	−12.4721	−0.948239	−0.474119	+	0.880461i	$0.657234\pi$
$174$	15.5279	1.17716
$175$	21.0902	1.59427
$176$	0	0
$177$	−11.8885	−0.893598
$178$	34.4721	2.58380
$179$	−21.7082	−1.62255	−0.811274	−	0.584667i	$-0.801225\pi$
$179$	−21.7082	−1.62255	−0.811274	+	0.584667i	$0.801225\pi$
$180$	14.2918	1.06525
$181$	3.38197	0.251380	0.125690	−	0.992070i	$-0.459886\pi$
$181$	3.38197	0.251380	0.125690	+	0.992070i	$0.459886\pi$
$182$	8.61803	0.638811
$183$	−9.05573	−0.669419
$184$	17.8885	1.31876
$185$	−12.9443	−0.951682
$186$	−15.5279	−1.13856
$187$	0	0
$188$	18.9787	1.38416
$189$	−21.3050	−1.54971
$190$	−11.7082	−0.849402
$191$	8.94427	0.647185	0.323592	−	0.946197i	$-0.395109\pi$
$191$	8.94427	0.647185	0.323592	+	0.946197i	$0.395109\pi$
$192$	−16.0689	−1.15967
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	21.7082	1.55856
$195$	4.00000	0.286446
$196$	23.5623	1.68302
$197$	−17.8885	−1.27451	−0.637253	−	0.770655i	$-0.719929\pi$
$197$	−17.8885	−1.27451	−0.637253	+	0.770655i	$0.719929\pi$
$198$	0	0
$199$	−12.9443	−0.917595	−0.458798	−	0.888541i	$-0.651720\pi$
$199$	−12.9443	−0.917595	−0.458798	+	0.888541i	$0.651720\pi$
$200$	−12.2361	−0.865221
$201$	−1.88854	−0.133208
$202$	7.56231	0.532082
$203$	−21.6525	−1.51971
$204$	17.1246	1.19896
$205$	0	0
$206$	4.47214	0.311588
$207$	11.7771	0.818564
$208$	1.00000	0.0693375
$209$	0	0
$210$	34.4721	2.37880
$211$	−9.52786	−0.655925	−0.327963	−	0.944691i	$-0.606362\pi$
$211$	−9.52786	−0.655925	−0.327963	+	0.944691i	$0.606362\pi$
$212$	0.270510	0.0185787
$213$	−14.2918	−0.979258
$214$	−14.0689	−0.961729
$215$	12.9443	0.882792
$216$	12.3607	0.841038
$217$	21.6525	1.46987
$218$	−22.7639	−1.54177
$219$	7.05573	0.476782
$220$	0	0
$221$	−4.61803	−0.310643
$222$	−11.0557	−0.742012
$223$	−8.94427	−0.598953	−0.299476	−	0.954104i	$-0.596812\pi$
$223$	−8.94427	−0.598953	−0.299476	+	0.954104i	$0.596812\pi$
$224$	25.8541	1.72745
$225$	−8.05573	−0.537049
$226$	−4.14590	−0.275781
$227$	4.14590	0.275173	0.137586	−	0.990490i	$-0.456066\pi$
$227$	4.14590	0.275173	0.137586	+	0.990490i	$0.456066\pi$
$228$	−6.00000	−0.397360
$229$	−17.7082	−1.17019	−0.585096	−	0.810964i	$-0.698943\pi$
$229$	−17.7082	−1.17019	−0.585096	+	0.810964i	$0.698943\pi$
$230$	−57.8885	−3.81706
$231$	0	0
$232$	12.5623	0.824756
$233$	8.67376	0.568237	0.284119	−	0.958789i	$-0.408299\pi$
$233$	8.67376	0.568237	0.284119	+	0.958789i	$0.408299\pi$
$234$	−3.29180	−0.215191
$235$	−20.4721	−1.33545
$236$	−28.8541	−1.87824
$237$	−2.47214	−0.160582
$238$	−39.7984	−2.57975
$239$	10.3262	0.667949	0.333974	−	0.942582i	$-0.391610\pi$
$239$	10.3262	0.667949	0.333974	+	0.942582i	$0.391610\pi$
$240$	4.00000	0.258199
$241$	−12.7639	−0.822197	−0.411099	−	0.911591i	$-0.634855\pi$
$241$	−12.7639	−0.822197	−0.411099	+	0.911591i	$0.634855\pi$
$242$	0	0
$243$	13.5967	0.872232
$244$	−21.9787	−1.40704
$245$	−25.4164	−1.62379
$246$	0	0
$247$	1.61803	0.102953
$248$	−12.5623	−0.797707
$249$	10.0000	0.633724
$250$	3.41641	0.216073
$251$	24.9443	1.57447	0.787234	−	0.616654i	$-0.211512\pi$
$251$	24.9443	1.57447	0.787234	+	0.616654i	$0.211512\pi$
$252$	−17.0213	−1.07224
$253$	0	0
$254$	−10.6525	−0.668396
$255$	−18.4721	−1.15677
$256$	−9.00000	−0.562500
$257$	−18.5066	−1.15441	−0.577204	−	0.816600i	$-0.695856\pi$
$257$	−18.5066	−1.15441	−0.577204	+	0.816600i	$0.695856\pi$
$258$	11.0557	0.688300
$259$	15.4164	0.957929
$260$	9.70820	0.602077
$261$	8.27051	0.511932
$262$	44.4721	2.74750
$263$	2.65248	0.163559	0.0817793	−	0.996650i	$-0.473940\pi$
$263$	2.65248	0.163559	0.0817793	+	0.996650i	$0.473940\pi$
$264$	0	0
$265$	−0.291796	−0.0179249
$266$	13.9443	0.854978
$267$	−19.0557	−1.16619
$268$	−4.58359	−0.279987
$269$	24.2705	1.47980	0.739900	−	0.672717i	$-0.234873\pi$
$269$	24.2705	1.47980	0.739900	+	0.672717i	$0.234873\pi$
$270$	−40.0000	−2.43432
$271$	−11.2705	−0.684635	−0.342317	−	0.939584i	$-0.611212\pi$
$271$	−11.2705	−0.684635	−0.342317	+	0.939584i	$0.611212\pi$
$272$	−4.61803	−0.280009
$273$	−4.76393	−0.288326
$274$	30.6525	1.85178
$275$	0	0
$276$	−29.6656	−1.78566
$277$	−22.2148	−1.33476	−0.667378	−	0.744719i	$-0.732584\pi$
$277$	−22.2148	−1.33476	−0.667378	+	0.744719i	$0.732584\pi$
$278$	40.6525	2.43817
$279$	−8.27051	−0.495142
$280$	27.8885	1.66666
$281$	30.3607	1.81117	0.905583	−	0.424169i	$-0.139434\pi$
$281$	30.3607	1.81117	0.905583	+	0.424169i	$0.139434\pi$
$282$	−17.4853	−1.04123
$283$	−7.88854	−0.468925	−0.234463	−	0.972125i	$-0.575333\pi$
$283$	−7.88854	−0.468925	−0.234463	+	0.972125i	$0.575333\pi$
$284$	−34.6869	−2.05829
$285$	6.47214	0.383376
$286$	0	0
$287$	0	0
$288$	−9.87539	−0.581913
$289$	4.32624	0.254485
$290$	−40.6525	−2.38720
$291$	−12.0000	−0.703452
$292$	17.1246	1.00214
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−21.7082	−1.26605
$295$	31.1246	1.81214
$296$	−8.94427	−0.519875
$297$	0	0
$298$	17.2361	0.998459
$299$	8.00000	0.462652
$300$	20.2918	1.17155
$301$	−15.4164	−0.888587
$302$	−27.0344	−1.55566
$303$	−4.18034	−0.240154
$304$	1.61803	0.0928006
$305$	23.7082	1.35753
$306$	15.2016	0.869019
$307$	4.79837	0.273858	0.136929	−	0.990581i	$-0.456277\pi$
$307$	4.79837	0.273858	0.136929	+	0.990581i	$0.456277\pi$
$308$	0	0
$309$	−2.47214	−0.140635
$310$	40.6525	2.30891
$311$	28.6525	1.62473	0.812366	−	0.583147i	$-0.198179\pi$
$311$	28.6525	1.62473	0.812366	+	0.583147i	$0.198179\pi$
$312$	2.76393	0.156477
$313$	−24.0344	−1.35851	−0.679253	−	0.733904i	$-0.737696\pi$
$313$	−24.0344	−1.35851	−0.679253	+	0.733904i	$0.737696\pi$
$314$	33.0902	1.86739
$315$	18.3607	1.03451
$316$	−6.00000	−0.337526
$317$	−4.29180	−0.241051	−0.120526	−	0.992710i	$-0.538458\pi$
$317$	−4.29180	−0.241051	−0.120526	+	0.992710i	$0.538458\pi$
$318$	−0.249224	−0.0139758
$319$	0	0
$320$	42.0689	2.35172
$321$	7.77709	0.434075
$322$	68.9443	3.84211
$323$	−7.47214	−0.415761
$324$	−7.24922	−0.402735
$325$	−5.47214	−0.303539
$326$	12.0344	0.666526
$327$	12.5836	0.695874
$328$	0	0
$329$	24.3820	1.34422
$330$	0	0
$331$	8.27051	0.454588	0.227294	−	0.973826i	$-0.427012\pi$
$331$	8.27051	0.454588	0.227294	+	0.973826i	$0.427012\pi$
$332$	24.2705	1.33202
$333$	−5.88854	−0.322690
$334$	−7.03444	−0.384908
$335$	4.94427	0.270134
$336$	−4.76393	−0.259894
$337$	29.7984	1.62322	0.811610	−	0.584199i	$-0.198591\pi$
$337$	29.7984	1.62322	0.811610	+	0.584199i	$0.198591\pi$
$338$	−2.23607	−0.121626
$339$	2.29180	0.124473
$340$	−44.8328	−2.43140
$341$	0	0
$342$	−5.32624	−0.288010
$343$	3.29180	0.177740
$344$	8.94427	0.482243
$345$	32.0000	1.72282
$346$	27.8885	1.49930
$347$	25.8885	1.38977	0.694885	−	0.719121i	$-0.255455\pi$
$347$	25.8885	1.38977	0.694885	+	0.719121i	$0.255455\pi$
$348$	−20.8328	−1.11676
$349$	12.1803	0.651999	0.325999	−	0.945370i	$-0.394299\pi$
$349$	12.1803	0.651999	0.325999	+	0.945370i	$0.394299\pi$
$350$	−47.1591	−2.52076
$351$	5.52786	0.295056
$352$	0	0
$353$	−5.52786	−0.294219	−0.147109	−	0.989120i	$-0.546997\pi$
$353$	−5.52786	−0.294219	−0.147109	+	0.989120i	$0.546997\pi$
$354$	26.5836	1.41290
$355$	37.4164	1.98586
$356$	−46.2492	−2.45120
$357$	22.0000	1.16436
$358$	48.5410	2.56547
$359$	30.7426	1.62253	0.811267	−	0.584675i	$-0.198778\pi$
$359$	30.7426	1.62253	0.811267	+	0.584675i	$0.198778\pi$
$360$	−10.6525	−0.561435
$361$	−16.3820	−0.862209
$362$	−7.56231	−0.397466
$363$	0	0
$364$	−11.5623	−0.606029
$365$	−18.4721	−0.966876
$366$	20.2492	1.05844
$367$	9.70820	0.506764	0.253382	−	0.967366i	$-0.418457\pi$
$367$	9.70820	0.506764	0.253382	+	0.967366i	$0.418457\pi$
$368$	8.00000	0.417029
$369$	0	0
$370$	28.9443	1.50474
$371$	0.347524	0.0180426
$372$	20.8328	1.08013
$373$	−9.85410	−0.510226	−0.255113	−	0.966911i	$-0.582113\pi$
$373$	−9.85410	−0.510226	−0.255113	+	0.966911i	$0.582113\pi$
$374$	0	0
$375$	−1.88854	−0.0975240
$376$	−14.1459	−0.729519
$377$	5.61803	0.289343
$378$	47.6393	2.45030
$379$	16.3607	0.840392	0.420196	−	0.907433i	$-0.361961\pi$
$379$	16.3607	0.840392	0.420196	+	0.907433i	$0.361961\pi$
$380$	15.7082	0.805814
$381$	5.88854	0.301679
$382$	−20.0000	−1.02329
$383$	−14.9787	−0.765377	−0.382688	−	0.923878i	$-0.625002\pi$
$383$	−14.9787	−0.765377	−0.382688	+	0.923878i	$0.625002\pi$
$384$	19.3475	0.987324
$385$	0	0
$386$	31.3050	1.59338
$387$	5.88854	0.299332
$388$	−29.1246	−1.47858
$389$	21.0344	1.06649	0.533244	−	0.845961i	$-0.320973\pi$
$389$	21.0344	1.06649	0.533244	+	0.845961i	$0.320973\pi$
$390$	−8.94427	−0.452911
$391$	−36.9443	−1.86835
$392$	−17.5623	−0.887030
$393$	−24.5836	−1.24008
$394$	40.0000	2.01517
$395$	6.47214	0.325649
$396$	0	0
$397$	18.1803	0.912445	0.456223	−	0.889866i	$-0.349202\pi$
$397$	18.1803	0.912445	0.456223	+	0.889866i	$0.349202\pi$
$398$	28.9443	1.45085
$399$	−7.70820	−0.385893
$400$	−5.47214	−0.273607
$401$	−35.8885	−1.79219	−0.896094	−	0.443864i	$-0.853607\pi$
$401$	−35.8885	−1.79219	−0.896094	+	0.443864i	$0.853607\pi$
$402$	4.22291	0.210620
$403$	−5.61803	−0.279854
$404$	−10.1459	−0.504777
$405$	7.81966	0.388562
$406$	48.4164	2.40287
$407$	0	0
$408$	−12.7639	−0.631909
$409$	−17.5967	−0.870103	−0.435052	−	0.900406i	$-0.643270\pi$
$409$	−17.5967	−0.870103	−0.435052	+	0.900406i	$0.643270\pi$
$410$	0	0
$411$	−16.9443	−0.835799
$412$	−6.00000	−0.295599
$413$	−37.0689	−1.82404
$414$	−26.3344	−1.29426
$415$	−26.1803	−1.28514
$416$	−6.70820	−0.328897
$417$	−22.4721	−1.10047
$418$	0	0
$419$	28.1803	1.37670	0.688350	−	0.725379i	$-0.258335\pi$
$419$	28.1803	1.37670	0.688350	+	0.725379i	$0.258335\pi$
$420$	−46.2492	−2.25673
$421$	−6.47214	−0.315433	−0.157716	−	0.987484i	$-0.550413\pi$
$421$	−6.47214	−0.315433	−0.157716	+	0.987484i	$0.550413\pi$
$422$	21.3050	1.03711
$423$	−9.31308	−0.452818
$424$	−0.201626	−0.00979183
$425$	25.2705	1.22580
$426$	31.9574	1.54834
$427$	−28.2361	−1.36644
$428$	18.8754	0.912376
$429$	0	0
$430$	−28.9443	−1.39582
$431$	6.90983	0.332835	0.166417	−	0.986055i	$-0.446780\pi$
$431$	6.90983	0.332835	0.166417	+	0.986055i	$0.446780\pi$
$432$	5.52786	0.265959
$433$	19.3820	0.931438	0.465719	−	0.884933i	$-0.345796\pi$
$433$	19.3820	0.931438	0.465719	+	0.884933i	$0.345796\pi$
$434$	−48.4164	−2.32406
$435$	22.4721	1.07746
$436$	30.5410	1.46265
$437$	12.9443	0.619208
$438$	−15.7771	−0.753858
$439$	10.4721	0.499808	0.249904	−	0.968271i	$-0.419601\pi$
$439$	10.4721	0.499808	0.249904	+	0.968271i	$0.419601\pi$
$440$	0	0
$441$	−11.5623	−0.550586
$442$	10.3262	0.491169
$443$	−20.7639	−0.986524	−0.493262	−	0.869881i	$-0.664196\pi$
$443$	−20.7639	−0.986524	−0.493262	+	0.869881i	$0.664196\pi$
$444$	14.8328	0.703934
$445$	49.8885	2.36494
$446$	20.0000	0.947027
$447$	−9.52786	−0.450653
$448$	−50.1033	−2.36716
$449$	31.1246	1.46886	0.734431	−	0.678684i	$-0.237449\pi$
$449$	31.1246	1.46886	0.734431	+	0.678684i	$0.237449\pi$
$450$	18.0132	0.849148
$451$	0	0
$452$	5.56231	0.261629
$453$	14.9443	0.702143
$454$	−9.27051	−0.435087
$455$	12.4721	0.584703
$456$	4.47214	0.209427
$457$	32.9443	1.54107	0.770534	−	0.637399i	$-0.219990\pi$
$457$	32.9443	1.54107	0.770534	+	0.637399i	$0.219990\pi$
$458$	39.5967	1.85023
$459$	−25.5279	−1.19154
$460$	77.6656	3.62118
$461$	−20.6525	−0.961882	−0.480941	−	0.876753i	$-0.659705\pi$
$461$	−20.6525	−0.961882	−0.480941	+	0.876753i	$0.659705\pi$
$462$	0	0
$463$	−4.85410	−0.225589	−0.112795	−	0.993618i	$-0.535980\pi$
$463$	−4.85410	−0.225589	−0.112795	+	0.993618i	$0.535980\pi$
$464$	5.61803	0.260811
$465$	−22.4721	−1.04212
$466$	−19.3951	−0.898462
$467$	−22.4721	−1.03989	−0.519943	−	0.854201i	$-0.674047\pi$
$467$	−22.4721	−1.03989	−0.519943	+	0.854201i	$0.674047\pi$
$468$	4.41641	0.204149
$469$	−5.88854	−0.271908
$470$	45.7771	2.11154
$471$	−18.2918	−0.842841
$472$	21.5066	0.989920
$473$	0	0
$474$	5.52786	0.253903
$475$	−8.85410	−0.406254
$476$	53.3951	2.44736
$477$	−0.132742	−0.00607786
$478$	−23.0902	−1.05612
$479$	27.9098	1.27523	0.637616	−	0.770354i	$-0.279921\pi$
$479$	27.9098	1.27523	0.637616	+	0.770354i	$0.279921\pi$
$480$	−26.8328	−1.22474
$481$	−4.00000	−0.182384
$482$	28.5410	1.30001
$483$	−38.1115	−1.73413
$484$	0	0
$485$	31.4164	1.42655
$486$	−30.4033	−1.37912
$487$	10.3262	0.467927	0.233963	−	0.972245i	$-0.424830\pi$
$487$	10.3262	0.467927	0.233963	+	0.972245i	$0.424830\pi$
$488$	16.3820	0.741577
$489$	−6.65248	−0.300835
$490$	56.8328	2.56744
$491$	16.4721	0.743377	0.371689	−	0.928357i	$-0.378779\pi$
$491$	16.4721	0.743377	0.371689	+	0.928357i	$0.378779\pi$
$492$	0	0
$493$	−25.9443	−1.16847
$494$	−3.61803	−0.162783
$495$	0	0
$496$	−5.61803	−0.252257
$497$	−44.5623	−1.99889
$498$	−22.3607	−1.00201
$499$	9.38197	0.419994	0.209997	−	0.977702i	$-0.432654\pi$
$499$	9.38197	0.419994	0.209997	+	0.977702i	$0.432654\pi$
$500$	−4.58359	−0.204984
$501$	3.88854	0.173727
$502$	−55.7771	−2.48945
$503$	−18.9443	−0.844683	−0.422342	−	0.906437i	$-0.638792\pi$
$503$	−18.9443	−0.844683	−0.422342	+	0.906437i	$0.638792\pi$
$504$	12.6869	0.565120
$505$	10.9443	0.487014
$506$	0	0
$507$	1.23607	0.0548957
$508$	14.2918	0.634096
$509$	29.7771	1.31985	0.659923	−	0.751333i	$-0.270589\pi$
$509$	29.7771	1.31985	0.659923	+	0.751333i	$0.270589\pi$
$510$	41.3050	1.82901
$511$	22.0000	0.973223
$512$	−11.1803	−0.494106
$513$	8.94427	0.394899
$514$	41.3820	1.82528
$515$	6.47214	0.285196
$516$	−14.8328	−0.652978
$517$	0	0
$518$	−34.4721	−1.51462
$519$	−15.4164	−0.676705
$520$	−7.23607	−0.317323
$521$	5.97871	0.261932	0.130966	−	0.991387i	$-0.458192\pi$
$521$	5.97871	0.261932	0.130966	+	0.991387i	$0.458192\pi$
$522$	−18.4934	−0.809435
$523$	−26.3607	−1.15267	−0.576336	−	0.817213i	$-0.695518\pi$
$523$	−26.3607	−1.15267	−0.576336	+	0.817213i	$0.695518\pi$
$524$	−59.6656	−2.60651
$525$	26.0689	1.13774
$526$	−5.93112	−0.258609
$527$	25.9443	1.13015
$528$	0	0
$529$	41.0000	1.78261
$530$	0.652476	0.0283417
$531$	14.1591	0.614451
$532$	−18.7082	−0.811104
$533$	0	0
$534$	42.6099	1.84391
$535$	−20.3607	−0.880269
$536$	3.41641	0.147566
$537$	−26.8328	−1.15792
$538$	−54.2705	−2.33977
$539$	0	0
$540$	53.6656	2.30940
$541$	36.1803	1.55551	0.777757	−	0.628565i	$-0.216357\pi$
$541$	36.1803	1.55551	0.777757	+	0.628565i	$0.216357\pi$
$542$	25.2016	1.08250
$543$	4.18034	0.179396
$544$	30.9787	1.32820
$545$	−32.9443	−1.41118
$546$	10.6525	0.455884
$547$	−13.7082	−0.586120	−0.293060	−	0.956094i	$-0.594674\pi$
$547$	−13.7082	−0.586120	−0.293060	+	0.956094i	$0.594674\pi$
$548$	−41.1246	−1.75676
$549$	10.7852	0.460302
$550$	0	0
$551$	9.09017	0.387254
$552$	22.1115	0.941126
$553$	−7.70820	−0.327786
$554$	49.6738	2.11044
$555$	−16.0000	−0.679162
$556$	−54.5410	−2.31305
$557$	34.3607	1.45591	0.727954	−	0.685626i	$-0.240471\pi$
$557$	34.3607	1.45591	0.727954	+	0.685626i	$0.240471\pi$
$558$	18.4934	0.782889
$559$	4.00000	0.169182
$560$	12.4721	0.527044
$561$	0	0
$562$	−67.8885	−2.86371
$563$	12.0689	0.508643	0.254321	−	0.967120i	$-0.418148\pi$
$563$	12.0689	0.508643	0.254321	+	0.967120i	$0.418148\pi$
$564$	23.4590	0.987801
$565$	−6.00000	−0.252422
$566$	17.6393	0.741436
$567$	−9.31308	−0.391113
$568$	25.8541	1.08481
$569$	22.7984	0.955758	0.477879	−	0.878426i	$-0.341406\pi$
$569$	22.7984	0.955758	0.477879	+	0.878426i	$0.341406\pi$
$570$	−14.4721	−0.606171
$571$	9.59675	0.401611	0.200806	−	0.979631i	$-0.435644\pi$
$571$	9.59675	0.401611	0.200806	+	0.979631i	$0.435644\pi$
$572$	0	0
$573$	11.0557	0.461860
$574$	0	0
$575$	−43.7771	−1.82563
$576$	19.1378	0.797407
$577$	−19.5279	−0.812956	−0.406478	−	0.913661i	$-0.633243\pi$
$577$	−19.5279	−0.812956	−0.406478	+	0.913661i	$0.633243\pi$
$578$	−9.67376	−0.402375
$579$	−17.3050	−0.719169
$580$	54.5410	2.26469
$581$	31.1803	1.29358
$582$	26.8328	1.11226
$583$	0	0
$584$	−12.7639	−0.528175
$585$	−4.76393	−0.196964
$586$	13.4164	0.554227
$587$	−17.5279	−0.723452	−0.361726	−	0.932284i	$-0.617812\pi$
$587$	−17.5279	−0.723452	−0.361726	+	0.932284i	$0.617812\pi$
$588$	29.1246	1.20108
$589$	−9.09017	−0.374554
$590$	−69.5967	−2.86525
$591$	−22.1115	−0.909544
$592$	−4.00000	−0.164399
$593$	20.8328	0.855501	0.427751	−	0.903897i	$-0.359306\pi$
$593$	20.8328	0.855501	0.427751	+	0.903897i	$0.359306\pi$
$594$	0	0
$595$	−57.5967	−2.36124
$596$	−23.1246	−0.947221
$597$	−16.0000	−0.654836
$598$	−17.8885	−0.731517
$599$	−13.2361	−0.540811	−0.270406	−	0.962747i	$-0.587158\pi$
$599$	−13.2361	−0.540811	−0.270406	+	0.962747i	$0.587158\pi$
$600$	−15.1246	−0.617460
$601$	19.3050	0.787465	0.393733	−	0.919225i	$-0.371184\pi$
$601$	19.3050	0.787465	0.393733	+	0.919225i	$0.371184\pi$
$602$	34.4721	1.40498
$603$	2.24922	0.0915955
$604$	36.2705	1.47583
$605$	0	0
$606$	9.34752	0.379717
$607$	13.1246	0.532712	0.266356	−	0.963875i	$-0.414180\pi$
$607$	13.1246	0.532712	0.266356	+	0.963875i	$0.414180\pi$
$608$	−10.8541	−0.440192
$609$	−26.7639	−1.08453
$610$	−53.0132	−2.14644
$611$	−6.32624	−0.255932
$612$	−20.3951	−0.824424
$613$	−5.81966	−0.235054	−0.117527	−	0.993070i	$-0.537497\pi$
$613$	−5.81966	−0.235054	−0.117527	+	0.993070i	$0.537497\pi$
$614$	−10.7295	−0.433007
$615$	0	0
$616$	0	0
$617$	15.4164	0.620641	0.310321	−	0.950632i	$-0.399564\pi$
$617$	15.4164	0.620641	0.310321	+	0.950632i	$0.399564\pi$
$618$	5.52786	0.222363
$619$	−33.3820	−1.34173	−0.670867	−	0.741577i	$-0.734078\pi$
$619$	−33.3820	−1.34173	−0.670867	+	0.741577i	$0.734078\pi$
$620$	−54.5410	−2.19042
$621$	44.2229	1.77460
$622$	−64.0689	−2.56893
$623$	−59.4164	−2.38047
$624$	1.23607	0.0494823
$625$	−22.4164	−0.896656
$626$	53.7426	2.14799
$627$	0	0
$628$	−44.3951	−1.77156
$629$	18.4721	0.736532
$630$	−41.0557	−1.63570
$631$	−17.4508	−0.694707	−0.347354	−	0.937734i	$-0.612920\pi$
$631$	−17.4508	−0.694707	−0.347354	+	0.937734i	$0.612920\pi$
$632$	4.47214	0.177892
$633$	−11.7771	−0.468097
$634$	9.59675	0.381136
$635$	−15.4164	−0.611781
$636$	0.334369	0.0132586
$637$	−7.85410	−0.311191
$638$	0	0
$639$	17.0213	0.673352
$640$	−50.6525	−2.00221
$641$	23.9098	0.944382	0.472191	−	0.881496i	$-0.343463\pi$
$641$	23.9098	0.944382	0.472191	+	0.881496i	$0.343463\pi$
$642$	−17.3901	−0.686332
$643$	16.4508	0.648758	0.324379	−	0.945927i	$-0.394845\pi$
$643$	16.4508	0.648758	0.324379	+	0.945927i	$0.394845\pi$
$644$	−92.4984	−3.64495
$645$	16.0000	0.629999
$646$	16.7082	0.657375
$647$	10.0000	0.393141	0.196570	−	0.980490i	$-0.437020\pi$
$647$	10.0000	0.393141	0.196570	+	0.980490i	$0.437020\pi$
$648$	5.40325	0.212260
$649$	0	0
$650$	12.2361	0.479938
$651$	26.7639	1.04896
$652$	−16.1459	−0.632322
$653$	−33.8541	−1.32481	−0.662407	−	0.749144i	$-0.730465\pi$
$653$	−33.8541	−1.32481	−0.662407	+	0.749144i	$0.730465\pi$
$654$	−28.1378	−1.10027
$655$	64.3607	2.51478
$656$	0	0
$657$	−8.40325	−0.327842
$658$	−54.5197	−2.12540
$659$	−37.4164	−1.45754	−0.728768	−	0.684761i	$-0.759907\pi$
$659$	−37.4164	−1.45754	−0.728768	+	0.684761i	$0.759907\pi$
$660$	0	0
$661$	21.1246	0.821652	0.410826	−	0.911714i	$-0.365240\pi$
$661$	21.1246	0.821652	0.410826	+	0.911714i	$0.365240\pi$
$662$	−18.4934	−0.718767
$663$	−5.70820	−0.221688
$664$	−18.0902	−0.702035
$665$	20.1803	0.782560
$666$	13.1672	0.510218
$667$	44.9443	1.74025
$668$	9.43769	0.365155
$669$	−11.0557	−0.427439
$670$	−11.0557	−0.427120
$671$	0	0
$672$	31.9574	1.23278
$673$	−25.3951	−0.978910	−0.489455	−	0.872029i	$-0.662804\pi$
$673$	−25.3951	−0.978910	−0.489455	+	0.872029i	$0.662804\pi$
$674$	−66.6312	−2.56654
$675$	−30.2492	−1.16429
$676$	3.00000	0.115385
$677$	13.0344	0.500954	0.250477	−	0.968123i	$-0.419413\pi$
$677$	13.0344	0.500954	0.250477	+	0.968123i	$0.419413\pi$
$678$	−5.12461	−0.196810
$679$	−37.4164	−1.43591
$680$	33.4164	1.28146
$681$	5.12461	0.196376
$682$	0	0
$683$	−29.9787	−1.14710	−0.573552	−	0.819169i	$-0.694435\pi$
$683$	−29.9787	−1.14710	−0.573552	+	0.819169i	$0.694435\pi$
$684$	7.14590	0.273230
$685$	44.3607	1.69493
$686$	−7.36068	−0.281032
$687$	−21.8885	−0.835100
$688$	4.00000	0.152499
$689$	−0.0901699	−0.00343520
$690$	−71.5542	−2.72402
$691$	−4.67376	−0.177798	−0.0888991	−	0.996041i	$-0.528335\pi$
$691$	−4.67376	−0.177798	−0.0888991	+	0.996041i	$0.528335\pi$
$692$	−37.4164	−1.42236
$693$	0	0
$694$	−57.8885	−2.19742
$695$	58.8328	2.23166
$696$	15.5279	0.588582
$697$	0	0
$698$	−27.2361	−1.03090
$699$	10.7214	0.405519
$700$	63.2705	2.39140
$701$	−12.0344	−0.454535	−0.227267	−	0.973832i	$-0.572979\pi$
$701$	−12.0344	−0.454535	−0.227267	+	0.973832i	$0.572979\pi$
$702$	−12.3607	−0.466524
$703$	−6.47214	−0.244101
$704$	0	0
$705$	−25.3050	−0.953040
$706$	12.3607	0.465200
$707$	−13.0344	−0.490211
$708$	−35.6656	−1.34040
$709$	14.4721	0.543512	0.271756	−	0.962366i	$-0.412396\pi$
$709$	14.4721	0.543512	0.271756	+	0.962366i	$0.412396\pi$
$710$	−83.6656	−3.13992
$711$	2.94427	0.110419
$712$	34.4721	1.29190
$713$	−44.9443	−1.68318
$714$	−49.1935	−1.84102
$715$	0	0
$716$	−65.1246	−2.43382
$717$	12.7639	0.476678
$718$	−68.7426	−2.56545
$719$	8.47214	0.315957	0.157979	−	0.987443i	$-0.449502\pi$
$719$	8.47214	0.315957	0.157979	+	0.987443i	$0.449502\pi$
$720$	−4.76393	−0.177541
$721$	−7.70820	−0.287069
$722$	36.6312	1.36327
$723$	−15.7771	−0.586756
$724$	10.1459	0.377069
$725$	−30.7426	−1.14175
$726$	0	0
$727$	−3.88854	−0.144218	−0.0721091	−	0.997397i	$-0.522973\pi$
$727$	−3.88854	−0.144218	−0.0721091	+	0.997397i	$0.522973\pi$
$728$	8.61803	0.319406
$729$	24.0557	0.890953
$730$	41.3050	1.52876
$731$	−18.4721	−0.683217
$732$	−27.1672	−1.00413
$733$	−32.1803	−1.18861	−0.594304	−	0.804240i	$-0.702572\pi$
$733$	−32.1803	−1.18861	−0.594304	+	0.804240i	$0.702572\pi$
$734$	−21.7082	−0.801264
$735$	−31.4164	−1.15881
$736$	−53.6656	−1.97814
$737$	0	0
$738$	0	0
$739$	−31.9230	−1.17431	−0.587153	−	0.809476i	$-0.699751\pi$
$739$	−31.9230	−1.17431	−0.587153	+	0.809476i	$0.699751\pi$
$740$	−38.8328	−1.42752
$741$	2.00000	0.0734718
$742$	−0.777088	−0.0285278
$743$	−19.5066	−0.715627	−0.357813	−	0.933793i	$-0.616478\pi$
$743$	−19.5066	−0.715627	−0.357813	+	0.933793i	$0.616478\pi$
$744$	−15.5279	−0.569279
$745$	24.9443	0.913887
$746$	22.0344	0.806738
$747$	−11.9098	−0.435758
$748$	0	0
$749$	24.2492	0.886047
$750$	4.22291	0.154199
$751$	−37.0132	−1.35063	−0.675315	−	0.737530i	$-0.735992\pi$
$751$	−37.0132	−1.35063	−0.675315	+	0.737530i	$0.735992\pi$
$752$	−6.32624	−0.230694
$753$	30.8328	1.12361
$754$	−12.5623	−0.457492
$755$	−39.1246	−1.42389
$756$	−63.9149	−2.32456
$757$	45.8541	1.66660	0.833298	−	0.552824i	$-0.186450\pi$
$757$	45.8541	1.66660	0.833298	+	0.552824i	$0.186450\pi$
$758$	−36.5836	−1.32878
$759$	0	0
$760$	−11.7082	−0.424701
$761$	−15.0557	−0.545770	−0.272885	−	0.962047i	$-0.587978\pi$
$761$	−15.0557	−0.545770	−0.272885	+	0.962047i	$0.587978\pi$
$762$	−13.1672	−0.476997
$763$	39.2361	1.42044
$764$	26.8328	0.970777
$765$	22.0000	0.795412
$766$	33.4934	1.21017
$767$	9.61803	0.347287
$768$	−11.1246	−0.401425
$769$	−51.3050	−1.85010	−0.925052	−	0.379841i	$-0.875979\pi$
$769$	−51.3050	−1.85010	−0.925052	+	0.379841i	$0.875979\pi$
$770$	0	0
$771$	−22.8754	−0.823837
$772$	−42.0000	−1.51161
$773$	11.0557	0.397647	0.198823	−	0.980035i	$-0.436288\pi$
$773$	11.0557	0.397647	0.198823	+	0.980035i	$0.436288\pi$
$774$	−13.1672	−0.473285
$775$	30.7426	1.10431
$776$	21.7082	0.779279
$777$	19.0557	0.683620
$778$	−47.0344	−1.68627
$779$	0	0
$780$	12.0000	0.429669
$781$	0	0
$782$	82.6099	2.95412
$783$	31.0557	1.10984
$784$	−7.85410	−0.280504
$785$	47.8885	1.70922
$786$	54.9706	1.96074
$787$	29.8885	1.06541	0.532706	−	0.846301i	$-0.321175\pi$
$787$	29.8885	1.06541	0.532706	+	0.846301i	$0.321175\pi$
$788$	−53.6656	−1.91176
$789$	3.27864	0.116723
$790$	−14.4721	−0.514895
$791$	7.14590	0.254079
$792$	0	0
$793$	7.32624	0.260162
$794$	−40.6525	−1.44270
$795$	−0.360680	−0.0127920
$796$	−38.8328	−1.37639
$797$	0.0901699	0.00319398	0.00159699	−	0.999999i	$-0.499492\pi$
$797$	0.0901699	0.00319398	0.00159699	+	0.999999i	$0.499492\pi$
$798$	17.2361	0.610150
$799$	29.2148	1.03354
$800$	36.7082	1.29783
$801$	22.6950	0.801890
$802$	80.2492	2.83370
$803$	0	0
$804$	−5.66563	−0.199811
$805$	99.7771	3.51668
$806$	12.5623	0.442488
$807$	30.0000	1.05605
$808$	7.56231	0.266041
$809$	−34.9443	−1.22858	−0.614288	−	0.789082i	$-0.710557\pi$
$809$	−34.9443	−1.22858	−0.614288	+	0.789082i	$0.710557\pi$
$810$	−17.4853	−0.614371
$811$	6.11146	0.214602	0.107301	−	0.994227i	$-0.465779\pi$
$811$	6.11146	0.214602	0.107301	+	0.994227i	$0.465779\pi$
$812$	−64.9574	−2.27956
$813$	−13.9311	−0.488586
$814$	0	0
$815$	17.4164	0.610070
$816$	−5.70820	−0.199827
$817$	6.47214	0.226431
$818$	39.3475	1.37575
$819$	5.67376	0.198257
$820$	0	0
$821$	28.2918	0.987390	0.493695	−	0.869635i	$-0.335646\pi$
$821$	28.2918	0.987390	0.493695	+	0.869635i	$0.335646\pi$
$822$	37.8885	1.32151
$823$	8.36068	0.291435	0.145717	−	0.989326i	$-0.453451\pi$
$823$	8.36068	0.291435	0.145717	+	0.989326i	$0.453451\pi$
$824$	4.47214	0.155794
$825$	0	0
$826$	82.8885	2.88406
$827$	−28.9443	−1.00649	−0.503245	−	0.864144i	$-0.667861\pi$
$827$	−28.9443	−1.00649	−0.503245	+	0.864144i	$0.667861\pi$
$828$	35.3313	1.22785
$829$	8.27051	0.287247	0.143623	−	0.989632i	$-0.454125\pi$
$829$	8.27051	0.287247	0.143623	+	0.989632i	$0.454125\pi$
$830$	58.5410	2.03199
$831$	−27.4590	−0.952541
$832$	13.0000	0.450694
$833$	36.2705	1.25670
$834$	50.2492	1.73999
$835$	−10.1803	−0.352305
$836$	0	0
$837$	−31.0557	−1.07344
$838$	−63.0132	−2.17675
$839$	6.74265	0.232782	0.116391	−	0.993203i	$-0.462867\pi$
$839$	6.74265	0.232782	0.116391	+	0.993203i	$0.462867\pi$
$840$	34.4721	1.18940
$841$	2.56231	0.0883554
$842$	14.4721	0.498743
$843$	37.5279	1.29253
$844$	−28.5836	−0.983888
$845$	−3.23607	−0.111324
$846$	20.8247	0.715967
$847$	0	0
$848$	−0.0901699	−0.00309645
$849$	−9.75078	−0.334646
$850$	−56.5066	−1.93816
$851$	−32.0000	−1.09695
$852$	−42.8754	−1.46889
$853$	−4.87539	−0.166930	−0.0834651	−	0.996511i	$-0.526599\pi$
$853$	−4.87539	−0.166930	−0.0834651	+	0.996511i	$0.526599\pi$
$854$	63.1378	2.16053
$855$	−7.70820	−0.263615
$856$	−14.0689	−0.480865
$857$	35.1591	1.20101	0.600505	−	0.799621i	$-0.294966\pi$
$857$	35.1591	1.20101	0.600505	+	0.799621i	$0.294966\pi$
$858$	0	0
$859$	2.87539	0.0981070	0.0490535	−	0.998796i	$-0.484380\pi$
$859$	2.87539	0.0981070	0.0490535	+	0.998796i	$0.484380\pi$
$860$	38.8328	1.32419
$861$	0	0
$862$	−15.4508	−0.526258
$863$	48.0000	1.63394	0.816970	−	0.576681i	$-0.195652\pi$
$863$	48.0000	1.63394	0.816970	+	0.576681i	$0.195652\pi$
$864$	−37.0820	−1.26156
$865$	40.3607	1.37230
$866$	−43.3394	−1.47273
$867$	5.34752	0.181611
$868$	64.9574	2.20480
$869$	0	0
$870$	−50.2492	−1.70361
$871$	1.52786	0.0517697
$872$	−22.7639	−0.770884
$873$	14.2918	0.483704
$874$	−28.9443	−0.979055
$875$	−5.88854	−0.199069
$876$	21.1672	0.715173
$877$	19.7082	0.665499	0.332749	−	0.943015i	$-0.392024\pi$
$877$	19.7082	0.665499	0.332749	+	0.943015i	$0.392024\pi$
$878$	−23.4164	−0.790265
$879$	−7.41641	−0.250149
$880$	0	0
$881$	27.1459	0.914569	0.457284	−	0.889321i	$-0.348822\pi$
$881$	27.1459	0.914569	0.457284	+	0.889321i	$0.348822\pi$
$882$	25.8541	0.870553
$883$	6.94427	0.233693	0.116847	−	0.993150i	$-0.462721\pi$
$883$	6.94427	0.233693	0.116847	+	0.993150i	$0.462721\pi$
$884$	−13.8541	−0.465964
$885$	38.4721	1.29323
$886$	46.4296	1.55983
$887$	−17.3475	−0.582473	−0.291236	−	0.956651i	$-0.594067\pi$
$887$	−17.3475	−0.582473	−0.291236	+	0.956651i	$0.594067\pi$
$888$	−11.0557	−0.371006
$889$	18.3607	0.615797
$890$	−111.554	−3.73930
$891$	0	0
$892$	−26.8328	−0.898429
$893$	−10.2361	−0.342537
$894$	21.3050	0.712544
$895$	70.2492	2.34817
$896$	60.3262	2.01536
$897$	9.88854	0.330169
$898$	−69.5967	−2.32247
$899$	−31.5623	−1.05266
$900$	−24.1672	−0.805573
$901$	0.416408	0.0138726
$902$	0	0
$903$	−19.0557	−0.634135
$904$	−4.14590	−0.137891
$905$	−10.9443	−0.363800
$906$	−33.4164	−1.11019
$907$	−28.6525	−0.951390	−0.475695	−	0.879610i	$-0.657803\pi$
$907$	−28.6525	−0.951390	−0.475695	+	0.879610i	$0.657803\pi$
$908$	12.4377	0.412759
$909$	4.97871	0.165134
$910$	−27.8885	−0.924496
$911$	−59.9574	−1.98648	−0.993239	−	0.116087i	$-0.962965\pi$
$911$	−59.9574	−1.98648	−0.993239	+	0.116087i	$0.962965\pi$
$912$	2.00000	0.0662266
$913$	0	0
$914$	−73.6656	−2.43664
$915$	29.3050	0.968792
$916$	−53.1246	−1.75529
$917$	−76.6525	−2.53129
$918$	57.0820	1.88399
$919$	21.0557	0.694564	0.347282	−	0.937761i	$-0.387105\pi$
$919$	21.0557	0.694564	0.347282	+	0.937761i	$0.387105\pi$
$920$	−57.8885	−1.90853
$921$	5.93112	0.195437
$922$	46.1803	1.52087
$923$	11.5623	0.380578
$924$	0	0
$925$	21.8885	0.719691
$926$	10.8541	0.356688
$927$	2.94427	0.0967026
$928$	−37.6869	−1.23713
$929$	5.63932	0.185020	0.0925100	−	0.995712i	$-0.470511\pi$
$929$	5.63932	0.185020	0.0925100	+	0.995712i	$0.470511\pi$
$930$	50.2492	1.64774
$931$	−12.7082	−0.416495
$932$	26.0213	0.852356
$933$	35.4164	1.15948
$934$	50.2492	1.64420
$935$	0	0
$936$	−3.29180	−0.107596
$937$	46.7426	1.52702	0.763508	−	0.645799i	$-0.223475\pi$
$937$	46.7426	1.52702	0.763508	+	0.645799i	$0.223475\pi$
$938$	13.1672	0.429924
$939$	−29.7082	−0.969491
$940$	−61.4164	−2.00318
$941$	−47.3050	−1.54210	−0.771049	−	0.636776i	$-0.780268\pi$
$941$	−47.3050	−1.54210	−0.771049	+	0.636776i	$0.780268\pi$
$942$	40.9017	1.33265
$943$	0	0
$944$	9.61803	0.313040
$945$	68.9443	2.24276
$946$	0	0
$947$	−40.5066	−1.31629	−0.658143	−	0.752893i	$-0.728658\pi$
$947$	−40.5066	−1.31629	−0.658143	+	0.752893i	$0.728658\pi$
$948$	−7.41641	−0.240874
$949$	−5.70820	−0.185296
$950$	19.7984	0.642344
$951$	−5.30495	−0.172025
$952$	−39.7984	−1.28987
$953$	−13.4164	−0.434600	−0.217300	−	0.976105i	$-0.569725\pi$
$953$	−13.4164	−0.434600	−0.217300	+	0.976105i	$0.569725\pi$
$954$	0.296821	0.00960994
$955$	−28.9443	−0.936615
$956$	30.9787	1.00192
$957$	0	0
$958$	−62.4083	−2.01632
$959$	−52.8328	−1.70606
$960$	52.0000	1.67829
$961$	0.562306	0.0181389
$962$	8.94427	0.288375
$963$	−9.26238	−0.298476
$964$	−38.2918	−1.23330
$965$	45.3050	1.45842
$966$	85.2198	2.74190
$967$	13.5279	0.435027	0.217513	−	0.976057i	$-0.430205\pi$
$967$	13.5279	0.435027	0.217513	+	0.976057i	$0.430205\pi$
$968$	0	0
$969$	−9.23607	−0.296705
$970$	−70.2492	−2.25557
$971$	−12.9443	−0.415401	−0.207701	−	0.978192i	$-0.566598\pi$
$971$	−12.9443	−0.415401	−0.207701	+	0.978192i	$0.566598\pi$
$972$	40.7902	1.30835
$973$	−70.0689	−2.24631
$974$	−23.0902	−0.739857
$975$	−6.76393	−0.216619
$976$	7.32624	0.234507
$977$	11.5279	0.368809	0.184405	−	0.982850i	$-0.440964\pi$
$977$	11.5279	0.368809	0.184405	+	0.982850i	$0.440964\pi$
$978$	14.8754	0.475662
$979$	0	0
$980$	−76.2492	−2.43569
$981$	−14.9868	−0.478493
$982$	−36.8328	−1.17538
$983$	8.67376	0.276650	0.138325	−	0.990387i	$-0.455828\pi$
$983$	8.67376	0.276650	0.138325	+	0.990387i	$0.455828\pi$
$984$	0	0
$985$	57.8885	1.84448
$986$	58.0132	1.84752
$987$	30.1378	0.959296
$988$	4.85410	0.154430
$989$	32.0000	1.01754
$990$	0	0
$991$	−7.34752	−0.233402	−0.116701	−	0.993167i	$-0.537232\pi$
$991$	−7.34752	−0.233402	−0.116701	+	0.993167i	$0.537232\pi$
$992$	37.6869	1.19656
$993$	10.2229	0.324414
$994$	99.6443	3.16053
$995$	41.8885	1.32796
$996$	30.0000	0.950586
$997$	−23.4508	−0.742696	−0.371348	−	0.928494i	$-0.621104\pi$
$997$	−23.4508	−0.742696	−0.371348	+	0.928494i	$0.621104\pi$
$998$	−20.9787	−0.664070
$999$	−22.1115	−0.699576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.2.a.d.1.1		2
11.3	even	5		143.2.h.a.53.1	yes	4
11.4	even	5		143.2.h.a.27.1	✓	4
11.10	odd	2		1573.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.a.27.1	✓	4	11.4	even	5
143.2.h.a.53.1	yes	4	11.3	even	5
1573.2.a.d.1.1		2	1.1	even	1	trivial
1573.2.a.e.1.2		2	11.10	odd	2

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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -3.23607 q^{5} -2.76393 q^{6} +3.85410 q^{7} -2.23607 q^{8} -1.47214 q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -3.23607 q^{5} -2.76393 q^{6} +3.85410 q^{7} -2.23607 q^{8} -1.47214 q^{9} +7.23607 q^{10} +3.70820 q^{12} -1.00000 q^{13} -8.61803 q^{14} -4.00000 q^{15} -1.00000 q^{16} +4.61803 q^{17} +3.29180 q^{18} -1.61803 q^{19} -9.70820 q^{20} +4.76393 q^{21} -8.00000 q^{23} -2.76393 q^{24} +5.47214 q^{25} +2.23607 q^{26} -5.52786 q^{27} +11.5623 q^{28} -5.61803 q^{29} +8.94427 q^{30} +5.61803 q^{31} +6.70820 q^{32} -10.3262 q^{34} -12.4721 q^{35} -4.41641 q^{36} +4.00000 q^{37} +3.61803 q^{38} -1.23607 q^{39} +7.23607 q^{40} -10.6525 q^{42} -4.00000 q^{43} +4.76393 q^{45} +17.8885 q^{46} +6.32624 q^{47} -1.23607 q^{48} +7.85410 q^{49} -12.2361 q^{50} +5.70820 q^{51} -3.00000 q^{52} +0.0901699 q^{53} +12.3607 q^{54} -8.61803 q^{56} -2.00000 q^{57} +12.5623 q^{58} -9.61803 q^{59} -12.0000 q^{60} -7.32624 q^{61} -12.5623 q^{62} -5.67376 q^{63} -13.0000 q^{64} +3.23607 q^{65} -1.52786 q^{67} +13.8541 q^{68} -9.88854 q^{69} +27.8885 q^{70} -11.5623 q^{71} +3.29180 q^{72} +5.70820 q^{73} -8.94427 q^{74} +6.76393 q^{75} -4.85410 q^{76} +2.76393 q^{78} -2.00000 q^{79} +3.23607 q^{80} -2.41641 q^{81} +8.09017 q^{83} +14.2918 q^{84} -14.9443 q^{85} +8.94427 q^{86} -6.94427 q^{87} -15.4164 q^{89} -10.6525 q^{90} -3.85410 q^{91} -24.0000 q^{92} +6.94427 q^{93} -14.1459 q^{94} +5.23607 q^{95} +8.29180 q^{96} -9.70820 q^{97} -17.5623 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 6 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 6 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 6 * q^9	\( 2 q - 2 q^{3} + 6 q^{4} - 2 q^{5} - 10 q^{6} + q^{7} + 6 q^{9} + 10 q^{10} - 6 q^{12} - 2 q^{13} - 15 q^{14} - 8 q^{15} - 2 q^{16} + 7 q^{17} + 20 q^{18} - q^{19} - 6 q^{20} + 14 q^{21} - 16 q^{23} - 10 q^{24} + 2 q^{25} - 20 q^{27} + 3 q^{28} - 9 q^{29} + 9 q^{31} - 5 q^{34} - 16 q^{35} + 18 q^{36} + 8 q^{37} + 5 q^{38} + 2 q^{39} + 10 q^{40} + 10 q^{42} - 8 q^{43} + 14 q^{45} - 3 q^{47} + 2 q^{48} + 9 q^{49} - 20 q^{50} - 2 q^{51} - 6 q^{52} - 11 q^{53} - 20 q^{54} - 15 q^{56} - 4 q^{57} + 5 q^{58} - 17 q^{59} - 24 q^{60} + q^{61} - 5 q^{62} - 27 q^{63} - 26 q^{64} + 2 q^{65} - 12 q^{67} + 21 q^{68} + 16 q^{69} + 20 q^{70} - 3 q^{71} + 20 q^{72} - 2 q^{73} + 18 q^{75} - 3 q^{76} + 10 q^{78} - 4 q^{79} + 2 q^{80} + 22 q^{81} + 5 q^{83} + 42 q^{84} - 12 q^{85} + 4 q^{87} - 4 q^{89} + 10 q^{90} - q^{91} - 48 q^{92} - 4 q^{93} - 35 q^{94} + 6 q^{95} + 30 q^{96} - 6 q^{97} - 15 q^{98}+O(q^{100}) \) 2 * q - 2 * q^3 + 6 * q^4 - 2 * q^5 - 10 * q^6 + q^7 + 6 * q^9 + 10 * q^10 - 6 * q^12 - 2 * q^13 - 15 * q^14 - 8 * q^15 - 2 * q^16 + 7 * q^17 + 20 * q^18 - q^19 - 6 * q^20 + 14 * q^21 - 16 * q^23 - 10 * q^24 + 2 * q^25 - 20 * q^27 + 3 * q^28 - 9 * q^29 + 9 * q^31 - 5 * q^34 - 16 * q^35 + 18 * q^36 + 8 * q^37 + 5 * q^38 + 2 * q^39 + 10 * q^40 + 10 * q^42 - 8 * q^43 + 14 * q^45 - 3 * q^47 + 2 * q^48 + 9 * q^49 - 20 * q^50 - 2 * q^51 - 6 * q^52 - 11 * q^53 - 20 * q^54 - 15 * q^56 - 4 * q^57 + 5 * q^58 - 17 * q^59 - 24 * q^60 + q^61 - 5 * q^62 - 27 * q^63 - 26 * q^64 + 2 * q^65 - 12 * q^67 + 21 * q^68 + 16 * q^69 + 20 * q^70 - 3 * q^71 + 20 * q^72 - 2 * q^73 + 18 * q^75 - 3 * q^76 + 10 * q^78 - 4 * q^79 + 2 * q^80 + 22 * q^81 + 5 * q^83 + 42 * q^84 - 12 * q^85 + 4 * q^87 - 4 * q^89 + 10 * q^90 - q^91 - 48 * q^92 - 4 * q^93 - 35 * q^94 + 6 * q^95 + 30 * q^96 - 6 * q^97 - 15 * q^98

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