LMFDB - Embedded newform 4031.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.40700 q^{2} +1.38079 q^{3} -0.0203573 q^{4} +0.687727 q^{5} -1.94276 q^{6} -3.68772 q^{7} +2.84264 q^{8} -1.09343 q^{9} +O(q^{10})$	\(q-1.40700 q^{2} +1.38079 q^{3} -0.0203573 q^{4} +0.687727 q^{5} -1.94276 q^{6} -3.68772 q^{7} +2.84264 q^{8} -1.09343 q^{9} -0.967630 q^{10} +1.60109 q^{11} -0.0281091 q^{12} +3.78693 q^{13} +5.18862 q^{14} +0.949604 q^{15} -3.95887 q^{16} +1.87797 q^{17} +1.53845 q^{18} -3.16856 q^{19} -0.0140002 q^{20} -5.09196 q^{21} -2.25274 q^{22} +4.14449 q^{23} +3.92508 q^{24} -4.52703 q^{25} -5.32820 q^{26} -5.65215 q^{27} +0.0750720 q^{28} +1.00000 q^{29} -1.33609 q^{30} +1.12520 q^{31} -0.115154 q^{32} +2.21077 q^{33} -2.64230 q^{34} -2.53615 q^{35} +0.0222592 q^{36} -4.88332 q^{37} +4.45816 q^{38} +5.22894 q^{39} +1.95496 q^{40} -5.80635 q^{41} +7.16438 q^{42} +12.3349 q^{43} -0.0325939 q^{44} -0.751981 q^{45} -5.83129 q^{46} -11.2953 q^{47} -5.46635 q^{48} +6.59931 q^{49} +6.36952 q^{50} +2.59307 q^{51} -0.0770915 q^{52} -5.34065 q^{53} +7.95256 q^{54} +1.10112 q^{55} -10.4829 q^{56} -4.37510 q^{57} -1.40700 q^{58} -15.2129 q^{59} -0.0193314 q^{60} +12.6713 q^{61} -1.58316 q^{62} +4.03227 q^{63} +8.07976 q^{64} +2.60437 q^{65} -3.11055 q^{66} +8.93358 q^{67} -0.0382303 q^{68} +5.72266 q^{69} +3.56835 q^{70} +14.1575 q^{71} -3.10822 q^{72} -1.43161 q^{73} +6.87083 q^{74} -6.25086 q^{75} +0.0645032 q^{76} -5.90440 q^{77} -7.35710 q^{78} -2.48162 q^{79} -2.72262 q^{80} -4.52412 q^{81} +8.16953 q^{82} +2.38962 q^{83} +0.103658 q^{84} +1.29153 q^{85} -17.3552 q^{86} +1.38079 q^{87} +4.55133 q^{88} +8.69691 q^{89} +1.05804 q^{90} -13.9651 q^{91} -0.0843706 q^{92} +1.55367 q^{93} +15.8925 q^{94} -2.17910 q^{95} -0.159003 q^{96} +0.0753954 q^{97} -9.28522 q^{98} -1.75068 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * 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 $

$2$	−1.40700	−0.994898	−0.497449	−	0.867493i	$-0.665730\pi$
$2$	−1.40700	−0.994898	−0.497449	+	0.867493i	$0.665730\pi$
$3$	1.38079	0.797197	0.398599	−	0.917125i	$-0.369497\pi$
$3$	1.38079	0.797197	0.398599	+	0.917125i	$0.369497\pi$
$4$	−0.0203573	−0.0101786
$5$	0.687727	0.307561	0.153780	−	0.988105i	$-0.450855\pi$
$5$	0.687727	0.307561	0.153780	+	0.988105i	$0.450855\pi$
$6$	−1.94276	−0.793130
$7$	−3.68772	−1.39383	−0.696914	−	0.717154i	$-0.745444\pi$
$7$	−3.68772	−1.39383	−0.696914	+	0.717154i	$0.745444\pi$
$8$	2.84264	1.00502
$9$	−1.09343	−0.364476
$10$	−0.967630	−0.305992
$11$	1.60109	0.482748	0.241374	−	0.970432i	$-0.422402\pi$
$11$	1.60109	0.482748	0.241374	+	0.970432i	$0.422402\pi$
$12$	−0.0281091	−0.00811438
$13$	3.78693	1.05030	0.525152	−	0.851008i	$-0.324008\pi$
$13$	3.78693	1.05030	0.525152	+	0.851008i	$0.324008\pi$
$14$	5.18862	1.38672
$15$	0.949604	0.245187
$16$	−3.95887	−0.989718
$17$	1.87797	0.455474	0.227737	−	0.973723i	$-0.426867\pi$
$17$	1.87797	0.455474	0.227737	+	0.973723i	$0.426867\pi$
$18$	1.53845	0.362617
$19$	−3.16856	−0.726917	−0.363459	−	0.931610i	$-0.618404\pi$
$19$	−3.16856	−0.726917	−0.363459	+	0.931610i	$0.618404\pi$
$20$	−0.0140002	−0.00313055
$21$	−5.09196	−1.11116
$22$	−2.25274	−0.480285
$23$	4.14449	0.864187	0.432093	−	0.901829i	$-0.357775\pi$
$23$	4.14449	0.864187	0.432093	+	0.901829i	$0.357775\pi$
$24$	3.92508	0.801203
$25$	−4.52703	−0.905406
$26$	−5.32820	−1.04495
$27$	−5.65215	−1.08776
$28$	0.0750720	0.0141873
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.33609	−0.243936
$31$	1.12520	0.202093	0.101046	−	0.994882i	$-0.467781\pi$
$31$	1.12520	0.202093	0.101046	+	0.994882i	$0.467781\pi$
$32$	−0.115154	−0.0203565
$33$	2.21077	0.384846
$34$	−2.64230	−0.453150
$35$	−2.53615	−0.428687
$36$	0.0222592	0.00370987
$37$	−4.88332	−0.802814	−0.401407	−	0.915900i	$-0.631479\pi$
$37$	−4.88332	−0.802814	−0.401407	+	0.915900i	$0.631479\pi$
$38$	4.45816	0.723208
$39$	5.22894	0.837300
$40$	1.95496	0.309106
$41$	−5.80635	−0.906800	−0.453400	−	0.891307i	$-0.649789\pi$
$41$	−5.80635	−0.906800	−0.453400	+	0.891307i	$0.649789\pi$
$42$	7.16438	1.10549
$43$	12.3349	1.88106	0.940530	−	0.339711i	$-0.110329\pi$
$43$	12.3349	1.88106	0.940530	+	0.339711i	$0.110329\pi$
$44$	−0.0325939	−0.00491372
$45$	−0.751981	−0.112099
$46$	−5.83129	−0.859777
$47$	−11.2953	−1.64760	−0.823798	−	0.566884i	$-0.808149\pi$
$47$	−11.2953	−1.64760	−0.823798	+	0.566884i	$0.808149\pi$
$48$	−5.46635	−0.789000
$49$	6.59931	0.942759
$50$	6.36952	0.900787
$51$	2.59307	0.363103
$52$	−0.0770915	−0.0106907
$53$	−5.34065	−0.733595	−0.366798	−	0.930301i	$-0.619546\pi$
$53$	−5.34065	−0.733595	−0.366798	+	0.930301i	$0.619546\pi$
$54$	7.95256	1.08221
$55$	1.10112	0.148474
$56$	−10.4829	−1.40083
$57$	−4.37510	−0.579497
$58$	−1.40700	−0.184748
$59$	−15.2129	−1.98055	−0.990273	−	0.139139i	$-0.955567\pi$
$59$	−15.2129	−1.98055	−0.990273	+	0.139139i	$0.955567\pi$
$60$	−0.0193314	−0.00249567
$61$	12.6713	1.62240	0.811198	−	0.584772i	$-0.198816\pi$
$61$	12.6713	1.62240	0.811198	+	0.584772i	$0.198816\pi$
$62$	−1.58316	−0.201062
$63$	4.03227	0.508018
$64$	8.07976	1.00997
$65$	2.60437	0.323033
$66$	−3.11055	−0.382882
$67$	8.93358	1.09141	0.545705	−	0.837977i	$-0.316262\pi$
$67$	8.93358	1.09141	0.545705	+	0.837977i	$0.316262\pi$
$68$	−0.0382303	−0.00463611
$69$	5.72266	0.688927
$70$	3.56835	0.426500
$71$	14.1575	1.68019	0.840093	−	0.542442i	$-0.182500\pi$
$71$	14.1575	1.68019	0.840093	+	0.542442i	$0.182500\pi$
$72$	−3.10822	−0.366308
$73$	−1.43161	−0.167557	−0.0837785	−	0.996484i	$-0.526699\pi$
$73$	−1.43161	−0.167557	−0.0837785	+	0.996484i	$0.526699\pi$
$74$	6.87083	0.798717
$75$	−6.25086	−0.721788
$76$	0.0645032	0.00739903
$77$	−5.90440	−0.672868
$78$	−7.35710	−0.833028
$79$	−2.48162	−0.279204	−0.139602	−	0.990208i	$-0.544582\pi$
$79$	−2.48162	−0.279204	−0.139602	+	0.990208i	$0.544582\pi$
$80$	−2.72262	−0.304398
$81$	−4.52412	−0.502681
$82$	8.16953	0.902173
$83$	2.38962	0.262294	0.131147	−	0.991363i	$-0.458134\pi$
$83$	2.38962	0.262294	0.131147	+	0.991363i	$0.458134\pi$
$84$	0.103658	0.0113101
$85$	1.29153	0.140086
$86$	−17.3552	−1.87146
$87$	1.38079	0.148036
$88$	4.55133	0.485174
$89$	8.69691	0.921871	0.460935	−	0.887434i	$-0.347514\pi$
$89$	8.69691	0.921871	0.460935	+	0.887434i	$0.347514\pi$
$90$	1.05804	0.111527
$91$	−13.9651	−1.46394
$92$	−0.0843706	−0.00879624
$93$	1.55367	0.161108
$94$	15.8925	1.63919
$95$	−2.17910	−0.223571
$96$	−0.159003	−0.0162281
$97$	0.0753954	0.00765524	0.00382762	−	0.999993i	$-0.498782\pi$
$97$	0.0753954	0.00765524	0.00382762	+	0.999993i	$0.498782\pi$
$98$	−9.28522	−0.937948
$99$	−1.75068	−0.175950
$100$	0.0921580	0.00921580
$101$	−7.03895	−0.700401	−0.350201	−	0.936675i	$-0.613887\pi$
$101$	−7.03895	−0.700401	−0.350201	+	0.936675i	$0.613887\pi$
$102$	−3.64845	−0.361250
$103$	−6.90949	−0.680812	−0.340406	−	0.940279i	$-0.610565\pi$
$103$	−6.90949	−0.680812	−0.340406	+	0.940279i	$0.610565\pi$
$104$	10.7649	1.05558
$105$	−3.50188	−0.341748
$106$	7.51429	0.729852
$107$	9.36196	0.905055	0.452527	−	0.891751i	$-0.350522\pi$
$107$	9.36196	0.905055	0.452527	+	0.891751i	$0.350522\pi$
$108$	0.115062	0.0110719
$109$	4.95622	0.474720	0.237360	−	0.971422i	$-0.423718\pi$
$109$	4.95622	0.474720	0.237360	+	0.971422i	$0.423718\pi$
$110$	−1.54927	−0.147717
$111$	−6.74283	−0.640001
$112$	14.5992	1.37950
$113$	−20.3745	−1.91667	−0.958334	−	0.285649i	$-0.907791\pi$
$113$	−20.3745	−1.91667	−0.958334	+	0.285649i	$0.907791\pi$
$114$	6.15576	0.576540
$115$	2.85028	0.265790
$116$	−0.0203573	−0.00189013
$117$	−4.14074	−0.382811
$118$	21.4045	1.97044
$119$	−6.92543	−0.634853
$120$	2.69938	0.246419
$121$	−8.43650	−0.766954
$122$	−17.8285	−1.61412
$123$	−8.01733	−0.722898
$124$	−0.0229061	−0.00205703
$125$	−6.55200	−0.586028
$126$	−5.67339	−0.505426
$127$	−18.7960	−1.66787	−0.833936	−	0.551861i	$-0.813918\pi$
$127$	−18.7960	−1.66787	−0.833936	+	0.551861i	$0.813918\pi$
$128$	−11.1379	−0.984461
$129$	17.0319	1.49958
$130$	−3.66435	−0.321384
$131$	−12.0946	−1.05671	−0.528354	−	0.849024i	$-0.677191\pi$
$131$	−12.0946	−1.05671	−0.528354	+	0.849024i	$0.677191\pi$
$132$	−0.0450053	−0.00391721
$133$	11.6848	1.01320
$134$	−12.5695	−1.08584
$135$	−3.88714	−0.334551
$136$	5.33839	0.457763
$137$	21.5190	1.83850	0.919248	−	0.393680i	$-0.128798\pi$
$137$	21.5190	1.83850	0.919248	+	0.393680i	$0.128798\pi$
$138$	−8.05177	−0.685412
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	0.0516291	0.00436345
$141$	−15.5965	−1.31346
$142$	−19.9196	−1.67161
$143$	6.06323	0.507033
$144$	4.32875	0.360729
$145$	0.687727	0.0571126
$146$	2.01427	0.166702
$147$	9.11224	0.751565
$148$	0.0994112	0.00817155
$149$	−3.43244	−0.281196	−0.140598	−	0.990067i	$-0.544903\pi$
$149$	−3.43244	−0.281196	−0.140598	+	0.990067i	$0.544903\pi$
$150$	8.79495	0.718105
$151$	−0.764509	−0.0622148	−0.0311074	−	0.999516i	$-0.509903\pi$
$151$	−0.764509	−0.0622148	−0.0311074	+	0.999516i	$0.509903\pi$
$152$	−9.00707	−0.730570
$153$	−2.05343	−0.166010
$154$	8.30747	0.669435
$155$	0.773833	0.0621558
$156$	−0.106447	−0.00852258
$157$	−17.3054	−1.38112	−0.690562	−	0.723274i	$-0.742637\pi$
$157$	−17.3054	−1.38112	−0.690562	+	0.723274i	$0.742637\pi$
$158$	3.49163	0.277779
$159$	−7.37430	−0.584820
$160$	−0.0791943	−0.00626086
$161$	−15.2837	−1.20453
$162$	6.36543	0.500116
$163$	−16.8957	−1.32337	−0.661687	−	0.749780i	$-0.730159\pi$
$163$	−16.8957	−1.32337	−0.661687	+	0.749780i	$0.730159\pi$
$164$	0.118202	0.00922999
$165$	1.52041	0.118363
$166$	−3.36218	−0.260956
$167$	−17.0722	−1.32109	−0.660545	−	0.750786i	$-0.729675\pi$
$167$	−17.0722	−1.32109	−0.660545	+	0.750786i	$0.729675\pi$
$168$	−14.4746	−1.11674
$169$	1.34082	0.103140
$170$	−1.81718	−0.139371
$171$	3.46460	0.264944
$172$	−0.251106	−0.0191466
$173$	−10.2412	−0.778621	−0.389311	−	0.921106i	$-0.627287\pi$
$173$	−10.2412	−0.778621	−0.389311	+	0.921106i	$0.627287\pi$
$174$	−1.94276	−0.147280
$175$	16.6944	1.26198
$176$	−6.33853	−0.477785
$177$	−21.0057	−1.57889
$178$	−12.2365	−0.917167
$179$	−10.2816	−0.768485	−0.384243	−	0.923232i	$-0.625537\pi$
$179$	−10.2816	−0.768485	−0.384243	+	0.923232i	$0.625537\pi$
$180$	0.0153083	0.00114101
$181$	−21.0769	−1.56663	−0.783316	−	0.621624i	$-0.786473\pi$
$181$	−21.0769	−1.56663	−0.783316	+	0.621624i	$0.786473\pi$
$182$	19.6489	1.45648
$183$	17.4964	1.29337
$184$	11.7813	0.868529
$185$	−3.35839	−0.246914
$186$	−2.18601	−0.160286
$187$	3.00681	0.219879
$188$	0.229943	0.0167703
$189$	20.8436	1.51615
$190$	3.06599	0.222431
$191$	−15.7659	−1.14078	−0.570389	−	0.821375i	$-0.693208\pi$
$191$	−15.7659	−1.14078	−0.570389	+	0.821375i	$0.693208\pi$
$192$	11.1564	0.805146
$193$	−8.79023	−0.632735	−0.316367	−	0.948637i	$-0.602463\pi$
$193$	−8.79023	−0.632735	−0.316367	+	0.948637i	$0.602463\pi$
$194$	−0.106081	−0.00761618
$195$	3.59608	0.257521
$196$	−0.134344	−0.00959600
$197$	−6.04326	−0.430565	−0.215282	−	0.976552i	$-0.569067\pi$
$197$	−6.04326	−0.430565	−0.215282	+	0.976552i	$0.569067\pi$
$198$	2.46321	0.175053
$199$	−1.99037	−0.141094	−0.0705468	−	0.997508i	$-0.522474\pi$
$199$	−1.99037	−0.141094	−0.0705468	+	0.997508i	$0.522474\pi$
$200$	−12.8687	−0.909955
$201$	12.3354	0.870069
$202$	9.90378	0.696828
$203$	−3.68772	−0.258828
$204$	−0.0527879	−0.00369589
$205$	−3.99318	−0.278896
$206$	9.72163	0.677338
$207$	−4.53171	−0.314976
$208$	−14.9920	−1.03951
$209$	−5.07316	−0.350918
$210$	4.92713	0.340005
$211$	17.3578	1.19496	0.597481	−	0.801883i	$-0.296168\pi$
$211$	17.3578	1.19496	0.597481	+	0.801883i	$0.296168\pi$
$212$	0.108721	0.00746700
$213$	19.5485	1.33944
$214$	−13.1723	−0.900437
$215$	8.48307	0.578540
$216$	−16.0670	−1.09322
$217$	−4.14944	−0.281683
$218$	−6.97340	−0.472298
$219$	−1.97674	−0.133576
$220$	−0.0224157	−0.00151127
$221$	7.11173	0.478387
$222$	9.48714	0.636735
$223$	−11.4138	−0.764322	−0.382161	−	0.924096i	$-0.624820\pi$
$223$	−11.4138	−0.764322	−0.382161	+	0.924096i	$0.624820\pi$
$224$	0.424655	0.0283735
$225$	4.94999	0.329999
$226$	28.6668	1.90689
$227$	2.52336	0.167482	0.0837408	−	0.996488i	$-0.473313\pi$
$227$	2.52336	0.167482	0.0837408	+	0.996488i	$0.473313\pi$
$228$	0.0890652	0.00589849
$229$	8.37895	0.553696	0.276848	−	0.960914i	$-0.410710\pi$
$229$	8.37895	0.553696	0.276848	+	0.960914i	$0.410710\pi$
$230$	−4.01034	−0.264434
$231$	−8.15271	−0.536409
$232$	2.84264	0.186628
$233$	2.19411	0.143741	0.0718706	−	0.997414i	$-0.477103\pi$
$233$	2.19411	0.143741	0.0718706	+	0.997414i	$0.477103\pi$
$234$	5.82601	0.380858
$235$	−7.76812	−0.506736
$236$	0.309692	0.0201593
$237$	−3.42659	−0.222581
$238$	9.74407	0.631614
$239$	21.8645	1.41430	0.707149	−	0.707064i	$-0.249981\pi$
$239$	21.8645	1.41430	0.707149	+	0.707064i	$0.249981\pi$
$240$	−3.75936	−0.242666
$241$	2.25576	0.145306	0.0726530	−	0.997357i	$-0.476853\pi$
$241$	2.25576	0.145306	0.0726530	+	0.997357i	$0.476853\pi$
$242$	11.8701	0.763041
$243$	10.7096	0.687021
$244$	−0.257953	−0.0165138
$245$	4.53852	0.289956
$246$	11.2804	0.719210
$247$	−11.9991	−0.763485
$248$	3.19855	0.203108
$249$	3.29955	0.209100
$250$	9.21864	0.583038
$251$	23.7768	1.50078	0.750389	−	0.660996i	$-0.229866\pi$
$251$	23.7768	1.50078	0.750389	+	0.660996i	$0.229866\pi$
$252$	−0.0820860	−0.00517093
$253$	6.63573	0.417185
$254$	26.4459	1.65936
$255$	1.78333	0.111676
$256$	−0.488524	−0.0305327
$257$	4.62725	0.288640	0.144320	−	0.989531i	$-0.453901\pi$
$257$	4.62725	0.288640	0.144320	+	0.989531i	$0.453901\pi$
$258$	−23.9639	−1.49192
$259$	18.0084	1.11898
$260$	−0.0530179	−0.00328803
$261$	−1.09343	−0.0676816
$262$	17.0171	1.05132
$263$	−23.9203	−1.47499	−0.737495	−	0.675352i	$-0.763992\pi$
$263$	−23.9203	−1.47499	−0.737495	+	0.675352i	$0.763992\pi$
$264$	6.28442	0.386779
$265$	−3.67291	−0.225625
$266$	−16.4404	−1.00803
$267$	12.0086	0.734913
$268$	−0.181863	−0.0111091
$269$	0.931853	0.0568161	0.0284080	−	0.999596i	$-0.490956\pi$
$269$	0.931853	0.0568161	0.0284080	+	0.999596i	$0.490956\pi$
$270$	5.46919	0.332844
$271$	5.50588	0.334458	0.167229	−	0.985918i	$-0.446518\pi$
$271$	5.50588	0.334458	0.167229	+	0.985918i	$0.446518\pi$
$272$	−7.43464	−0.450791
$273$	−19.2829	−1.16705
$274$	−30.2772	−1.82911
$275$	−7.24821	−0.437083
$276$	−0.116498	−0.00701234
$277$	−14.2617	−0.856903	−0.428452	−	0.903565i	$-0.640941\pi$
$277$	−14.2617	−0.856903	−0.428452	+	0.903565i	$0.640941\pi$
$278$	−1.40700	−0.0843861
$279$	−1.23033	−0.0736580
$280$	−7.20935	−0.430841
$281$	−24.5009	−1.46160	−0.730802	−	0.682590i	$-0.760854\pi$
$281$	−24.5009	−1.46160	−0.730802	+	0.682590i	$0.760854\pi$
$282$	21.9442	1.30676
$283$	5.66625	0.336823	0.168412	−	0.985717i	$-0.446136\pi$
$283$	5.66625	0.336823	0.168412	+	0.985717i	$0.446136\pi$
$284$	−0.288208	−0.0171020
$285$	−3.00888	−0.178230
$286$	−8.53095	−0.504446
$287$	21.4122	1.26392
$288$	0.125912	0.00741946
$289$	−13.4732	−0.792543
$290$	−0.967630	−0.0568212
$291$	0.104105	0.00610274
$292$	0.0291436	0.00170550
$293$	10.2582	0.599288	0.299644	−	0.954051i	$-0.403132\pi$
$293$	10.2582	0.599288	0.299644	+	0.954051i	$0.403132\pi$
$294$	−12.8209	−0.747730
$295$	−10.4623	−0.609138
$296$	−13.8815	−0.806847
$297$	−9.04963	−0.525113
$298$	4.82943	0.279762
$299$	15.6949	0.907659
$300$	0.127251	0.00734682
$301$	−45.4878	−2.62188
$302$	1.07566	0.0618974
$303$	−9.71928	−0.558358
$304$	12.5439	0.719443
$305$	8.71440	0.498985
$306$	2.88917	0.165163
$307$	−3.01607	−0.172136	−0.0860680	−	0.996289i	$-0.527430\pi$
$307$	−3.01607	−0.172136	−0.0860680	+	0.996289i	$0.527430\pi$
$308$	0.120197	0.00684889
$309$	−9.54053	−0.542742
$310$	−1.08878	−0.0618387
$311$	−8.64442	−0.490180	−0.245090	−	0.969500i	$-0.578818\pi$
$311$	−8.64442	−0.490180	−0.245090	+	0.969500i	$0.578818\pi$
$312$	14.8640	0.841507
$313$	0.918430	0.0519127	0.0259564	−	0.999663i	$-0.491737\pi$
$313$	0.918430	0.0519127	0.0259564	+	0.999663i	$0.491737\pi$
$314$	24.3487	1.37408
$315$	2.77310	0.156246
$316$	0.0505190	0.00284192
$317$	−13.5407	−0.760520	−0.380260	−	0.924880i	$-0.624165\pi$
$317$	−13.5407	−0.760520	−0.380260	+	0.924880i	$0.624165\pi$
$318$	10.3756	0.581836
$319$	1.60109	0.0896441
$320$	5.55667	0.310627
$321$	12.9269	0.721507
$322$	21.5042	1.19838
$323$	−5.95045	−0.331092
$324$	0.0920989	0.00511660
$325$	−17.1435	−0.950952
$326$	23.7722	1.31662
$327$	6.84349	0.378446
$328$	−16.5054	−0.911356
$329$	41.6541	2.29647
$330$	−2.13921	−0.117760
$331$	−21.0574	−1.15742	−0.578709	−	0.815534i	$-0.696443\pi$
$331$	−21.0574	−1.15742	−0.578709	+	0.815534i	$0.696443\pi$
$332$	−0.0486461	−0.00266980
$333$	5.33957	0.292607
$334$	24.0206	1.31435
$335$	6.14386	0.335675
$336$	20.1584	1.09973
$337$	−8.86591	−0.482957	−0.241479	−	0.970406i	$-0.577632\pi$
$337$	−8.86591	−0.482957	−0.241479	+	0.970406i	$0.577632\pi$
$338$	−1.88652	−0.102613
$339$	−28.1328	−1.52796
$340$	−0.0262920	−0.00142589
$341$	1.80156	0.0975599
$342$	−4.87468	−0.263592
$343$	1.47763	0.0797845
$344$	35.0638	1.89051
$345$	3.93563	0.211887
$346$	14.4093	0.774649
$347$	−11.2654	−0.604756	−0.302378	−	0.953188i	$-0.597780\pi$
$347$	−11.2654	−0.604756	−0.302378	+	0.953188i	$0.597780\pi$
$348$	−0.0281091	−0.00150680
$349$	−3.77759	−0.202210	−0.101105	−	0.994876i	$-0.532238\pi$
$349$	−3.77759	−0.202210	−0.101105	+	0.994876i	$0.532238\pi$
$350$	−23.4890	−1.25554
$351$	−21.4043	−1.14248
$352$	−0.184372	−0.00982706
$353$	5.85264	0.311504	0.155752	−	0.987796i	$-0.450220\pi$
$353$	5.85264	0.311504	0.155752	+	0.987796i	$0.450220\pi$
$354$	29.5550	1.57083
$355$	9.73649	0.516759
$356$	−0.177045	−0.00938339
$357$	−9.56254	−0.506103
$358$	14.4662	0.764564
$359$	3.56564	0.188187	0.0940936	−	0.995563i	$-0.470005\pi$
$359$	3.56564	0.188187	0.0940936	+	0.995563i	$0.470005\pi$
$360$	−2.13761	−0.112662
$361$	−8.96023	−0.471591
$362$	29.6551	1.55864
$363$	−11.6490	−0.611414
$364$	0.284292	0.0149010
$365$	−0.984555	−0.0515340
$366$	−24.6174	−1.28677
$367$	12.4065	0.647616	0.323808	−	0.946123i	$-0.395037\pi$
$367$	12.4065	0.647616	0.323808	+	0.946123i	$0.395037\pi$
$368$	−16.4075	−0.855301
$369$	6.34884	0.330507
$370$	4.72525	0.245654
$371$	19.6949	1.02251
$372$	−0.0316284	−0.00163986
$373$	6.08497	0.315068	0.157534	−	0.987514i	$-0.449646\pi$
$373$	6.08497	0.315068	0.157534	+	0.987514i	$0.449646\pi$
$374$	−4.23057	−0.218758
$375$	−9.04691	−0.467180
$376$	−32.1086	−1.65587
$377$	3.78693	0.195037
$378$	−29.3269	−1.50841
$379$	27.5861	1.41700	0.708500	−	0.705710i	$-0.249372\pi$
$379$	27.5861	1.41700	0.708500	+	0.705710i	$0.249372\pi$
$380$	0.0443606	0.00227565
$381$	−25.9532	−1.32962
$382$	22.1825	1.13496
$383$	−8.73937	−0.446561	−0.223280	−	0.974754i	$-0.571677\pi$
$383$	−8.73937	−0.446561	−0.223280	+	0.974754i	$0.571677\pi$
$384$	−15.3791	−0.784809
$385$	−4.06061	−0.206948
$386$	12.3678	0.629506
$387$	−13.4874	−0.685602
$388$	−0.00153484	−7.79199e−5 0
$389$	−15.7801	−0.800081	−0.400040	−	0.916497i	$-0.631004\pi$
$389$	−15.7801	−0.800081	−0.400040	+	0.916497i	$0.631004\pi$
$390$	−5.05968	−0.256207
$391$	7.78323	0.393615
$392$	18.7595	0.947496
$393$	−16.7000	−0.842405
$394$	8.50286	0.428368
$395$	−1.70668	−0.0858722
$396$	0.0356392	0.00179094
$397$	−28.8779	−1.44934	−0.724671	−	0.689095i	$-0.758008\pi$
$397$	−28.8779	−1.44934	−0.724671	+	0.689095i	$0.758008\pi$
$398$	2.80045	0.140374
$399$	16.1342	0.807719
$400$	17.9219	0.896097
$401$	−25.1487	−1.25587	−0.627933	−	0.778267i	$-0.716099\pi$
$401$	−25.1487	−1.25587	−0.627933	+	0.778267i	$0.716099\pi$
$402$	−17.3558	−0.865630
$403$	4.26107	0.212259
$404$	0.143294	0.00712913
$405$	−3.11136	−0.154605
$406$	5.18862	0.257507
$407$	−7.81866	−0.387557
$408$	7.37117	0.364927
$409$	−33.9296	−1.67771	−0.838855	−	0.544354i	$-0.816775\pi$
$409$	−33.9296	−1.67771	−0.838855	+	0.544354i	$0.816775\pi$
$410$	5.61840	0.277473
$411$	29.7132	1.46564
$412$	0.140658	0.00692974
$413$	56.1008	2.76054
$414$	6.37611	0.313369
$415$	1.64340	0.0806715
$416$	−0.436079	−0.0213805
$417$	1.38079	0.0676174
$418$	7.13793	0.349128
$419$	2.51018	0.122630	0.0613152	−	0.998118i	$-0.480471\pi$
$419$	2.51018	0.122630	0.0613152	+	0.998118i	$0.480471\pi$
$420$	0.0712887	0.00347853
$421$	−6.32541	−0.308281	−0.154141	−	0.988049i	$-0.549261\pi$
$421$	−6.32541	−0.308281	−0.154141	+	0.988049i	$0.549261\pi$
$422$	−24.4224	−1.18886
$423$	12.3507	0.600510
$424$	−15.1815	−0.737281
$425$	−8.50162	−0.412389
$426$	−27.5047	−1.33261
$427$	−46.7283	−2.26134
$428$	−0.190584	−0.00921223
$429$	8.37202	0.404205
$430$	−11.9357	−0.575588
$431$	3.07210	0.147978	0.0739890	−	0.997259i	$-0.476427\pi$
$431$	3.07210	0.147978	0.0739890	+	0.997259i	$0.476427\pi$
$432$	22.3761	1.07657
$433$	14.7930	0.710907	0.355454	−	0.934694i	$-0.384326\pi$
$433$	14.7930	0.710907	0.355454	+	0.934694i	$0.384326\pi$
$434$	5.83826	0.280245
$435$	0.949604	0.0455300
$436$	−0.100895	−0.00483201
$437$	−13.1321	−0.628192
$438$	2.78128	0.132894
$439$	−16.9558	−0.809255	−0.404628	−	0.914482i	$-0.632599\pi$
$439$	−16.9558	−0.809255	−0.404628	+	0.914482i	$0.632599\pi$
$440$	3.13007	0.149220
$441$	−7.21588	−0.343613
$442$	−10.0062	−0.475946
$443$	−14.7575	−0.701149	−0.350575	−	0.936535i	$-0.614014\pi$
$443$	−14.7575	−0.701149	−0.350575	+	0.936535i	$0.614014\pi$
$444$	0.137266	0.00651434
$445$	5.98110	0.283531
$446$	16.0591	0.760422
$447$	−4.73947	−0.224169
$448$	−29.7959	−1.40773
$449$	14.8531	0.700963	0.350481	−	0.936570i	$-0.386018\pi$
$449$	14.8531	0.700963	0.350481	+	0.936570i	$0.386018\pi$
$450$	−6.96462	−0.328315
$451$	−9.29652	−0.437756
$452$	0.414769	0.0195091
$453$	−1.05562	−0.0495975
$454$	−3.55037	−0.166627
$455$	−9.60420	−0.450252
$456$	−12.4368	−0.582408
$457$	−21.6718	−1.01377	−0.506883	−	0.862015i	$-0.669202\pi$
$457$	−21.6718	−1.01377	−0.506883	+	0.862015i	$0.669202\pi$
$458$	−11.7892	−0.550871
$459$	−10.6146	−0.495445
$460$	−0.0580239	−0.00270538
$461$	41.5155	1.93357	0.966784	−	0.255596i	$-0.0822716\pi$
$461$	41.5155	1.93357	0.966784	+	0.255596i	$0.0822716\pi$
$462$	11.4708	0.533672
$463$	2.89583	0.134580	0.0672902	−	0.997733i	$-0.478565\pi$
$463$	2.89583	0.134580	0.0672902	+	0.997733i	$0.478565\pi$
$464$	−3.95887	−0.183786
$465$	1.06850	0.0495504
$466$	−3.08711	−0.143008
$467$	13.4240	0.621190	0.310595	−	0.950542i	$-0.399472\pi$
$467$	13.4240	0.621190	0.310595	+	0.950542i	$0.399472\pi$
$468$	0.0842941	0.00389650
$469$	−32.9446	−1.52124
$470$	10.9297	0.504150
$471$	−23.8951	−1.10103
$472$	−43.2447	−1.99050
$473$	19.7494	0.908078
$474$	4.82120	0.221445
$475$	14.3442	0.658156
$476$	0.140983	0.00646194
$477$	5.83963	0.267378
$478$	−30.7633	−1.40708
$479$	3.53655	0.161589	0.0807944	−	0.996731i	$-0.474254\pi$
$479$	3.53655	0.161589	0.0807944	+	0.996731i	$0.474254\pi$
$480$	−0.109350	−0.00499114
$481$	−18.4928	−0.843199
$482$	−3.17385	−0.144565
$483$	−21.1036	−0.960247
$484$	0.171744	0.00780655
$485$	0.0518514	0.00235445
$486$	−15.0684	−0.683516
$487$	42.1140	1.90837	0.954183	−	0.299225i	$-0.0967281\pi$
$487$	42.1140	1.90837	0.954183	+	0.299225i	$0.0967281\pi$
$488$	36.0200	1.63055
$489$	−23.3294	−1.05499
$490$	−6.38569	−0.288476
$491$	−8.06600	−0.364013	−0.182007	−	0.983297i	$-0.558259\pi$
$491$	−8.06600	−0.364013	−0.182007	+	0.983297i	$0.558259\pi$
$492$	0.163211	0.00735812
$493$	1.87797	0.0845794
$494$	16.8827	0.759589
$495$	−1.20399	−0.0541154
$496$	−4.45454	−0.200015
$497$	−52.2090	−2.34189
$498$	−4.64246	−0.208033
$499$	0.0442007	0.00197869	0.000989347	−	1.00000i	$-0.499685\pi$
$499$	0.0442007	0.00197869	0.000989347		1.00000i	$0.499685\pi$
$500$	0.133381	0.00596497
$501$	−23.5731	−1.05317
$502$	−33.4539	−1.49312
$503$	12.9548	0.577626	0.288813	−	0.957386i	$-0.406739\pi$
$503$	12.9548	0.577626	0.288813	+	0.957386i	$0.406739\pi$
$504$	11.4623	0.510570
$505$	−4.84087	−0.215416
$506$	−9.33645	−0.415056
$507$	1.85138	0.0822227
$508$	0.382635	0.0169767
$509$	20.3130	0.900357	0.450178	−	0.892939i	$-0.351360\pi$
$509$	20.3130	0.900357	0.450178	+	0.892939i	$0.351360\pi$
$510$	−2.50914	−0.111106
$511$	5.27938	0.233546
$512$	22.9632	1.01484
$513$	17.9092	0.790709
$514$	−6.51053	−0.287167
$515$	−4.75184	−0.209391
$516$	−0.346723	−0.0152636
$517$	−18.0849	−0.795374
$518$	−25.3377	−1.11328
$519$	−14.1409	−0.620715
$520$	7.40329	0.324656
$521$	15.3136	0.670903	0.335451	−	0.942058i	$-0.391111\pi$
$521$	15.3136	0.670903	0.335451	+	0.942058i	$0.391111\pi$
$522$	1.53845	0.0673362
$523$	−4.65837	−0.203696	−0.101848	−	0.994800i	$-0.532476\pi$
$523$	−4.65837	−0.203696	−0.101848	+	0.994800i	$0.532476\pi$
$524$	0.246213	0.0107559
$525$	23.0515	1.00605
$526$	33.6558	1.46746
$527$	2.11310	0.0920480
$528$	−8.75215	−0.380889
$529$	−5.82318	−0.253182
$530$	5.16778	0.224474
$531$	16.6342	0.721862
$532$	−0.237870	−0.0103130
$533$	−21.9882	−0.952416
$534$	−16.8960	−0.731163
$535$	6.43847	0.278359
$536$	25.3949	1.09689
$537$	−14.1967	−0.612634
$538$	−1.31112	−0.0565262
$539$	10.5661	0.455115
$540$	0.0791315	0.00340528
$541$	11.2437	0.483405	0.241703	−	0.970350i	$-0.422294\pi$
$541$	11.2437	0.483405	0.241703	+	0.970350i	$0.422294\pi$
$542$	−7.74676	−0.332752
$543$	−29.1027	−1.24891
$544$	−0.216255	−0.00927186
$545$	3.40853	0.146005
$546$	27.1310	1.16110
$547$	−12.8466	−0.549279	−0.274640	−	0.961547i	$-0.588559\pi$
$547$	−12.8466	−0.549279	−0.274640	+	0.961547i	$0.588559\pi$
$548$	−0.438069	−0.0187134
$549$	−13.8552	−0.591325
$550$	10.1982	0.434853
$551$	−3.16856	−0.134985
$552$	16.2674	0.692389
$553$	9.15153	0.389163
$554$	20.0662	0.852531
$555$	−4.63722	−0.196839
$556$	−0.0203573	−0.000863341 0
$557$	−10.5747	−0.448062	−0.224031	−	0.974582i	$-0.571922\pi$
$557$	−10.5747	−0.448062	−0.224031	+	0.974582i	$0.571922\pi$
$558$	1.73107	0.0732822
$559$	46.7115	1.97569
$560$	10.0403	0.424279
$561$	4.15176	0.175287
$562$	34.4728	1.45415
$563$	19.6880	0.829752	0.414876	−	0.909878i	$-0.363825\pi$
$563$	19.6880	0.829752	0.414876	+	0.909878i	$0.363825\pi$
$564$	0.317502	0.0133692
$565$	−14.0121	−0.589492
$566$	−7.97240	−0.335105
$567$	16.6837	0.700651
$568$	40.2447	1.68863
$569$	−46.5794	−1.95271	−0.976354	−	0.216177i	$-0.930641\pi$
$569$	−46.5794	−1.95271	−0.976354	+	0.216177i	$0.930641\pi$
$570$	4.23348	0.177321
$571$	−31.6206	−1.32328	−0.661640	−	0.749822i	$-0.730139\pi$
$571$	−31.6206	−1.32328	−0.661640	+	0.749822i	$0.730139\pi$
$572$	−0.123431	−0.00516090
$573$	−21.7693	−0.909425
$574$	−30.1270	−1.25747
$575$	−18.7623	−0.782440
$576$	−8.83465	−0.368110
$577$	31.7889	1.32339	0.661695	−	0.749773i	$-0.269837\pi$
$577$	31.7889	1.32339	0.661695	+	0.749773i	$0.269837\pi$
$578$	18.9568	0.788499
$579$	−12.1374	−0.504414
$580$	−0.0140002	−0.000581329 0
$581$	−8.81224	−0.365593
$582$	−0.146475	−0.00607160
$583$	−8.55089	−0.354142
$584$	−4.06954	−0.168399
$585$	−2.84770	−0.117738
$586$	−14.4332	−0.596230
$587$	−16.0264	−0.661480	−0.330740	−	0.943722i	$-0.607298\pi$
$587$	−16.0264	−0.661480	−0.330740	+	0.943722i	$0.607298\pi$
$588$	−0.185500	−0.00764991
$589$	−3.56528	−0.146905
$590$	14.7204	0.606030
$591$	−8.34445	−0.343245
$592$	19.3324	0.794559
$593$	13.6669	0.561233	0.280617	−	0.959820i	$-0.409461\pi$
$593$	13.6669	0.561233	0.280617	+	0.959820i	$0.409461\pi$
$594$	12.7328	0.522433
$595$	−4.76280	−0.195256
$596$	0.0698751	0.00286220
$597$	−2.74828	−0.112479
$598$	−22.0827	−0.903028
$599$	−3.38547	−0.138327	−0.0691633	−	0.997605i	$-0.522033\pi$
$599$	−3.38547	−0.138327	−0.0691633	+	0.997605i	$0.522033\pi$
$600$	−17.7689	−0.725414
$601$	−2.52992	−0.103198	−0.0515988	−	0.998668i	$-0.516432\pi$
$601$	−2.52992	−0.103198	−0.0515988	+	0.998668i	$0.516432\pi$
$602$	64.0013	2.60850
$603$	−9.76824	−0.397793
$604$	0.0155633	0.000633262 0
$605$	−5.80200	−0.235885
$606$	13.6750	0.555509
$607$	−13.8993	−0.564153	−0.282077	−	0.959392i	$-0.591023\pi$
$607$	−13.8993	−0.564153	−0.282077	+	0.959392i	$0.591023\pi$
$608$	0.364871	0.0147975
$609$	−5.09196	−0.206337
$610$	−12.2611	−0.496439
$611$	−42.7747	−1.73048
$612$	0.0418022	0.00168975
$613$	42.5924	1.72029	0.860146	−	0.510048i	$-0.170372\pi$
$613$	42.5924	1.72029	0.860146	+	0.510048i	$0.170372\pi$
$614$	4.24360	0.171258
$615$	−5.51374	−0.222335
$616$	−16.7841	−0.676249
$617$	−39.8241	−1.60326	−0.801629	−	0.597822i	$-0.796033\pi$
$617$	−39.8241	−1.60326	−0.801629	+	0.597822i	$0.796033\pi$
$618$	13.4235	0.539972
$619$	37.6500	1.51328	0.756640	−	0.653832i	$-0.226840\pi$
$619$	37.6500	1.51328	0.756640	+	0.653832i	$0.226840\pi$
$620$	−0.0157531	−0.000632661 0
$621$	−23.4253	−0.940025
$622$	12.1627	0.487679
$623$	−32.0718	−1.28493
$624$	−20.7007	−0.828691
$625$	18.1292	0.725167
$626$	−1.29223	−0.0516478
$627$	−7.00496	−0.279751
$628$	0.352291	0.0140580
$629$	−9.17073	−0.365661
$630$	−3.90174	−0.155449
$631$	8.69800	0.346262	0.173131	−	0.984899i	$-0.444612\pi$
$631$	8.69800	0.346262	0.173131	+	0.984899i	$0.444612\pi$
$632$	−7.05435	−0.280607
$633$	23.9674	0.952620
$634$	19.0517	0.756640
$635$	−12.9265	−0.512972
$636$	0.150121	0.00595267
$637$	24.9911	0.990184
$638$	−2.25274	−0.0891867
$639$	−15.4802	−0.612388
$640$	−7.65983	−0.302782
$641$	12.5478	0.495608	0.247804	−	0.968810i	$-0.420291\pi$
$641$	12.5478	0.495608	0.247804	+	0.968810i	$0.420291\pi$
$642$	−18.1881	−0.717826
$643$	−39.2767	−1.54892	−0.774460	−	0.632623i	$-0.781978\pi$
$643$	−39.2767	−1.54892	−0.774460	+	0.632623i	$0.781978\pi$
$644$	0.311136	0.0122605
$645$	11.7133	0.461211
$646$	8.37228	0.329403
$647$	21.7202	0.853910	0.426955	−	0.904273i	$-0.359586\pi$
$647$	21.7202	0.853910	0.426955	+	0.904273i	$0.359586\pi$
$648$	−12.8604	−0.505206
$649$	−24.3572	−0.956105
$650$	24.1209	0.946100
$651$	−5.72950	−0.224557
$652$	0.343951	0.0134702
$653$	−18.2519	−0.714253	−0.357127	−	0.934056i	$-0.616244\pi$
$653$	−18.2519	−0.714253	−0.357127	+	0.934056i	$0.616244\pi$
$654$	−9.62877	−0.376515
$655$	−8.31777	−0.325002
$656$	22.9866	0.897476
$657$	1.56536	0.0610706
$658$	−58.6073	−2.28475
$659$	35.4722	1.38180	0.690900	−	0.722950i	$-0.257214\pi$
$659$	35.4722	1.38180	0.690900	+	0.722950i	$0.257214\pi$
$660$	−0.0309513	−0.00120478
$661$	−9.99591	−0.388796	−0.194398	−	0.980923i	$-0.562275\pi$
$661$	−9.99591	−0.388796	−0.194398	+	0.980923i	$0.562275\pi$
$662$	29.6277	1.15151
$663$	9.81978	0.381369
$664$	6.79281	0.263612
$665$	8.03593	0.311620
$666$	−7.51276	−0.291114
$667$	4.14449	0.160475
$668$	0.347545	0.0134469
$669$	−15.7600	−0.609316
$670$	−8.64440	−0.333962
$671$	20.2880	0.783209
$672$	0.586358	0.0226192
$673$	20.9494	0.807540	0.403770	−	0.914861i	$-0.367700\pi$
$673$	20.9494	0.807540	0.403770	+	0.914861i	$0.367700\pi$
$674$	12.4743	0.480493
$675$	25.5875	0.984862
$676$	−0.0272954	−0.00104982
$677$	18.7169	0.719347	0.359673	−	0.933078i	$-0.382888\pi$
$677$	18.7169	0.719347	0.359673	+	0.933078i	$0.382888\pi$
$678$	39.5828	1.52017
$679$	−0.278037	−0.0106701
$680$	3.67135	0.140790
$681$	3.48423	0.133516
$682$	−2.53479	−0.0970621
$683$	10.9621	0.419453	0.209726	−	0.977760i	$-0.432743\pi$
$683$	10.9621	0.419453	0.209726	+	0.977760i	$0.432743\pi$
$684$	−0.0705297	−0.00269677
$685$	14.7992	0.565449
$686$	−2.07902	−0.0793774
$687$	11.5695	0.441405
$688$	−48.8324	−1.86172
$689$	−20.2247	−0.770499
$690$	−5.53742	−0.210806
$691$	−1.33373	−0.0507375	−0.0253688	−	0.999678i	$-0.508076\pi$
$691$	−1.33373	−0.0507375	−0.0253688	+	0.999678i	$0.508076\pi$
$692$	0.208482	0.00792531
$693$	6.45604	0.245245
$694$	15.8503	0.601670
$695$	0.687727	0.0260870
$696$	3.92508	0.148780
$697$	−10.9041	−0.413024
$698$	5.31505	0.201178
$699$	3.02960	0.114590
$700$	−0.339853	−0.0128453
$701$	−1.17791	−0.0444892	−0.0222446	−	0.999753i	$-0.507081\pi$
$701$	−1.17791	−0.0444892	−0.0222446	+	0.999753i	$0.507081\pi$
$702$	30.1158	1.13665
$703$	15.4731	0.583579
$704$	12.9365	0.487561
$705$	−10.7261	−0.403969
$706$	−8.23465	−0.309915
$707$	25.9577	0.976239
$708$	0.427619	0.0160709
$709$	−6.80606	−0.255607	−0.127804	−	0.991800i	$-0.540793\pi$
$709$	−6.80606	−0.255607	−0.127804	+	0.991800i	$0.540793\pi$
$710$	−13.6992	−0.514123
$711$	2.71348	0.101763
$712$	24.7222	0.926503
$713$	4.66340	0.174646
$714$	13.4545	0.503521
$715$	4.16985	0.155943
$716$	0.209306	0.00782213
$717$	30.1902	1.12747
$718$	−5.01684	−0.187227
$719$	−43.0437	−1.60526	−0.802629	−	0.596479i	$-0.796566\pi$
$719$	−43.0437	−1.60526	−0.802629	+	0.596479i	$0.796566\pi$
$720$	2.97699	0.110946
$721$	25.4803	0.948935
$722$	12.6070	0.469185
$723$	3.11472	0.115838
$724$	0.429068	0.0159462
$725$	−4.52703	−0.168130
$726$	16.3901	0.608294
$727$	37.6870	1.39773	0.698867	−	0.715251i	$-0.253688\pi$
$727$	37.6870	1.39773	0.698867	+	0.715251i	$0.253688\pi$
$728$	−39.6978	−1.47130
$729$	28.3600	1.05037
$730$	1.38527	0.0512710
$731$	23.1646	0.856774
$732$	−0.356179	−0.0131647
$733$	7.20472	0.266112	0.133056	−	0.991108i	$-0.457521\pi$
$733$	7.20472	0.266112	0.133056	+	0.991108i	$0.457521\pi$
$734$	−17.4560	−0.644312
$735$	6.26673	0.231152
$736$	−0.477254	−0.0175918
$737$	14.3035	0.526876
$738$	−8.93280	−0.328821
$739$	−22.7473	−0.836772	−0.418386	−	0.908269i	$-0.637404\pi$
$739$	−22.7473	−0.836772	−0.418386	+	0.908269i	$0.637404\pi$
$740$	0.0683678	0.00251325
$741$	−16.5682	−0.608648
$742$	−27.7106	−1.01729
$743$	26.5097	0.972545	0.486272	−	0.873807i	$-0.338356\pi$
$743$	26.5097	0.972545	0.486272	+	0.873807i	$0.338356\pi$
$744$	4.41651	0.161917
$745$	−2.36058	−0.0864850
$746$	−8.56154	−0.313460
$747$	−2.61288	−0.0956001
$748$	−0.0612104	−0.00223807
$749$	−34.5243	−1.26149
$750$	12.7290	0.464797
$751$	11.5903	0.422935	0.211467	−	0.977385i	$-0.432176\pi$
$751$	11.5903	0.422935	0.211467	+	0.977385i	$0.432176\pi$
$752$	44.7168	1.63065
$753$	32.8307	1.19642
$754$	−5.32820	−0.194042
$755$	−0.525773	−0.0191348
$756$	−0.424318	−0.0154323
$757$	−12.2917	−0.446751	−0.223375	−	0.974732i	$-0.571708\pi$
$757$	−12.2917	−0.446751	−0.223375	+	0.974732i	$0.571708\pi$
$758$	−38.8135	−1.40977
$759$	9.16252	0.332578
$760$	−6.19440	−0.224695
$761$	−29.5037	−1.06951	−0.534754	−	0.845008i	$-0.679596\pi$
$761$	−29.5037	−1.06951	−0.534754	+	0.845008i	$0.679596\pi$
$762$	36.5161	1.32284
$763$	−18.2772	−0.661679
$764$	0.320950	0.0116116
$765$	−1.41220	−0.0510581
$766$	12.2963	0.444282
$767$	−57.6100	−2.08018
$768$	−0.674547	−0.0243406
$769$	−2.90638	−0.104807	−0.0524033	−	0.998626i	$-0.516688\pi$
$769$	−2.90638	−0.104807	−0.0524033	+	0.998626i	$0.516688\pi$
$770$	5.71327	0.205892
$771$	6.38925	0.230103
$772$	0.178945	0.00644038
$773$	−7.42921	−0.267210	−0.133605	−	0.991035i	$-0.542655\pi$
$773$	−7.42921	−0.267210	−0.133605	+	0.991035i	$0.542655\pi$
$774$	18.9767	0.682104
$775$	−5.09384	−0.182976
$776$	0.214322	0.00769370
$777$	24.8657	0.892052
$778$	22.2025	0.795999
$779$	18.3978	0.659169
$780$	−0.0732064	−0.00262121
$781$	22.6675	0.811107
$782$	−10.9510	−0.391606
$783$	−5.65215	−0.201991
$784$	−26.1258	−0.933065
$785$	−11.9014	−0.424779
$786$	23.4969	0.838107
$787$	1.75972	0.0627271	0.0313636	−	0.999508i	$-0.490015\pi$
$787$	1.75972	0.0627271	0.0313636	+	0.999508i	$0.490015\pi$
$788$	0.123024	0.00438256
$789$	−33.0289	−1.17586
$790$	2.40129	0.0854341
$791$	75.1354	2.67151
$792$	−4.97656	−0.176834
$793$	47.9853	1.70401
$794$	40.6312	1.44195
$795$	−5.07151	−0.179868
$796$	0.0405185	0.00143614
$797$	−26.7126	−0.946210	−0.473105	−	0.881006i	$-0.656867\pi$
$797$	−26.7126	−0.946210	−0.473105	+	0.881006i	$0.656867\pi$
$798$	−22.7007	−0.803598
$799$	−21.2123	−0.750438
$800$	0.521304	0.0184309
$801$	−9.50946	−0.336000
$802$	35.3842	1.24946
$803$	−2.29214	−0.0808879
$804$	−0.251114	−0.00885612
$805$	−10.5110	−0.370466
$806$	−5.99531	−0.211176
$807$	1.28669	0.0452936
$808$	−20.0092	−0.703920
$809$	2.64982	0.0931625	0.0465813	−	0.998915i	$-0.485167\pi$
$809$	2.64982	0.0931625	0.0465813	+	0.998915i	$0.485167\pi$
$810$	4.37768	0.153816
$811$	−25.1136	−0.881857	−0.440929	−	0.897542i	$-0.645351\pi$
$811$	−25.1136	−0.881857	−0.440929	+	0.897542i	$0.645351\pi$
$812$	0.0750720	0.00263451
$813$	7.60244	0.266629
$814$	11.0008	0.385579
$815$	−11.6196	−0.407018
$816$	−10.2656	−0.359369
$817$	−39.0840	−1.36738
$818$	47.7389	1.66915
$819$	15.2699	0.533573
$820$	0.0812904	0.00283878
$821$	−29.7680	−1.03891	−0.519455	−	0.854498i	$-0.673865\pi$
$821$	−29.7680	−1.03891	−0.519455	+	0.854498i	$0.673865\pi$
$822$	−41.8064	−1.45817
$823$	−10.9727	−0.382484	−0.191242	−	0.981543i	$-0.561251\pi$
$823$	−10.9727	−0.382484	−0.191242	+	0.981543i	$0.561251\pi$
$824$	−19.6412	−0.684233
$825$	−10.0082	−0.348442
$826$	−78.9338	−2.74646
$827$	−0.760936	−0.0264603	−0.0132302	−	0.999912i	$-0.504211\pi$
$827$	−0.760936	−0.0264603	−0.0132302	+	0.999912i	$0.504211\pi$
$828$	0.0922533	0.00320602
$829$	4.14082	0.143817	0.0719083	−	0.997411i	$-0.477091\pi$
$829$	4.14082	0.143817	0.0719083	+	0.997411i	$0.477091\pi$
$830$	−2.31226	−0.0802599
$831$	−19.6924	−0.683121
$832$	30.5975	1.06078
$833$	12.3933	0.429402
$834$	−1.94276	−0.0672724
$835$	−11.7410	−0.406316
$836$	0.103276	0.00357187
$837$	−6.35983	−0.219828
$838$	−3.53182	−0.122005
$839$	34.9057	1.20508	0.602539	−	0.798089i	$-0.294156\pi$
$839$	34.9057	1.20508	0.602539	+	0.798089i	$0.294156\pi$
$840$	−9.95457	−0.343465
$841$	1.00000	0.0344828
$842$	8.89983	0.306708
$843$	−33.8306	−1.16519
$844$	−0.353358	−0.0121631
$845$	0.922115	0.0317217
$846$	−17.3774	−0.597446
$847$	31.1115	1.06900
$848$	21.1430	0.726052
$849$	7.82388	0.268515
$850$	11.9618	0.410285
$851$	−20.2389	−0.693781
$852$	−0.397954	−0.0136337
$853$	−17.2183	−0.589543	−0.294771	−	0.955568i	$-0.595243\pi$
$853$	−17.2183	−0.589543	−0.294771	+	0.955568i	$0.595243\pi$
$854$	65.7466	2.24980
$855$	2.38270	0.0814865
$856$	26.6127	0.909602
$857$	−19.4620	−0.664808	−0.332404	−	0.943137i	$-0.607860\pi$
$857$	−19.4620	−0.664808	−0.332404	+	0.943137i	$0.607860\pi$
$858$	−11.7794	−0.402143
$859$	−45.8701	−1.56507	−0.782533	−	0.622609i	$-0.786073\pi$
$859$	−45.8701	−1.56507	−0.782533	+	0.622609i	$0.786073\pi$
$860$	−0.172692	−0.00588875
$861$	29.5657	1.00760
$862$	−4.32244	−0.147223
$863$	3.86135	0.131442	0.0657209	−	0.997838i	$-0.479065\pi$
$863$	3.86135	0.131442	0.0657209	+	0.997838i	$0.479065\pi$
$864$	0.650866	0.0221429
$865$	−7.04313	−0.239473
$866$	−20.8137	−0.707280
$867$	−18.6037	−0.631813
$868$	0.0844714	0.00286715
$869$	−3.97331	−0.134785
$870$	−1.33609	−0.0452977
$871$	33.8308	1.14631
$872$	14.0888	0.477105
$873$	−0.0824395	−0.00279015
$874$	18.4768	0.624987
$875$	24.1620	0.816823
$876$	0.0402411	0.00135962
$877$	21.1168	0.713065	0.356532	−	0.934283i	$-0.383959\pi$
$877$	21.1168	0.713065	0.356532	+	0.934283i	$0.383959\pi$
$878$	23.8567	0.805126
$879$	14.1643	0.477751
$880$	−4.35918	−0.146948
$881$	−14.5456	−0.490055	−0.245027	−	0.969516i	$-0.578797\pi$
$881$	−14.5456	−0.490055	−0.245027	+	0.969516i	$0.578797\pi$
$882$	10.1527	0.341860
$883$	47.0542	1.58350	0.791749	−	0.610846i	$-0.209171\pi$
$883$	47.0542	1.58350	0.791749	+	0.610846i	$0.209171\pi$
$884$	−0.144775	−0.00486933
$885$	−14.4462	−0.485603
$886$	20.7637	0.697572
$887$	41.8614	1.40557	0.702783	−	0.711404i	$-0.251940\pi$
$887$	41.8614	1.40557	0.702783	+	0.711404i	$0.251940\pi$
$888$	−19.1674	−0.643216
$889$	69.3143	2.32473
$890$	−8.41540	−0.282085
$891$	−7.24355	−0.242668
$892$	0.232353	0.00777976
$893$	35.7900	1.19767
$894$	6.66842	0.223025
$895$	−7.07096	−0.236356
$896$	41.0735	1.37217
$897$	21.6713	0.723583
$898$	−20.8983	−0.697386
$899$	1.12520	0.0375277
$900$	−0.100768	−0.00335894
$901$	−10.0296	−0.334134
$902$	13.0802	0.435523
$903$	−62.8090	−2.09015
$904$	−57.9172	−1.92630
$905$	−14.4951	−0.481835
$906$	1.48526	0.0493444
$907$	3.58575	0.119063	0.0595315	−	0.998226i	$-0.481039\pi$
$907$	3.58575	0.119063	0.0595315	+	0.998226i	$0.481039\pi$
$908$	−0.0513688	−0.00170473
$909$	7.69659	0.255280
$910$	13.5131	0.447955
$911$	20.5661	0.681385	0.340693	−	0.940175i	$-0.389338\pi$
$911$	20.5661	0.681385	0.340693	+	0.940175i	$0.389338\pi$
$912$	17.3205	0.573538
$913$	3.82600	0.126622
$914$	30.4922	1.00859
$915$	12.0327	0.397790
$916$	−0.170573	−0.00563588
$917$	44.6015	1.47287
$918$	14.9347	0.492917
$919$	50.4343	1.66367	0.831837	−	0.555021i	$-0.187290\pi$
$919$	50.4343	1.66367	0.831837	+	0.555021i	$0.187290\pi$
$920$	8.10231	0.267125
$921$	−4.16454	−0.137226
$922$	−58.4122	−1.92370
$923$	53.6134	1.76471
$924$	0.165967	0.00545991
$925$	22.1070	0.726872
$926$	−4.07442	−0.133894
$927$	7.55504	0.248140
$928$	−0.115154	−0.00378010
$929$	−52.2434	−1.71405	−0.857025	−	0.515275i	$-0.827690\pi$
$929$	−52.2434	−1.71405	−0.857025	+	0.515275i	$0.827690\pi$
$930$	−1.50338	−0.0492976
$931$	−20.9103	−0.685308
$932$	−0.0446662	−0.00146309
$933$	−11.9361	−0.390770
$934$	−18.8876	−0.618021
$935$	2.06786	0.0676263
$936$	−11.7706	−0.384735
$937$	−31.0416	−1.01408	−0.507042	−	0.861921i	$-0.669261\pi$
$937$	−31.0416	−1.01408	−0.507042	+	0.861921i	$0.669261\pi$
$938$	46.3529	1.51348
$939$	1.26816	0.0413847
$940$	0.158138	0.00515788
$941$	42.8611	1.39723	0.698616	−	0.715497i	$-0.253800\pi$
$941$	42.8611	1.39723	0.698616	+	0.715497i	$0.253800\pi$
$942$	33.6203	1.09541
$943$	−24.0644	−0.783644
$944$	60.2258	1.96018
$945$	14.3347	0.466307
$946$	−27.7874	−0.903445
$947$	49.8327	1.61934	0.809672	−	0.586883i	$-0.199645\pi$
$947$	49.8327	1.61934	0.809672	+	0.586883i	$0.199645\pi$
$948$	0.0697560	0.00226557
$949$	−5.42140	−0.175986
$950$	−20.1822	−0.654797
$951$	−18.6968	−0.606285
$952$	−19.6865	−0.638043
$953$	60.4329	1.95761	0.978807	−	0.204786i	$-0.0656499\pi$
$953$	60.4329	1.95761	0.978807	+	0.204786i	$0.0656499\pi$
$954$	−8.21634	−0.266014
$955$	−10.8426	−0.350859
$956$	−0.445102	−0.0143956
$957$	2.21077	0.0714640
$958$	−4.97591	−0.160764
$959$	−79.3563	−2.56255
$960$	7.67257	0.247631
$961$	−29.7339	−0.959159
$962$	26.0193	0.838896
$963$	−10.2366	−0.329871
$964$	−0.0459211	−0.00147902
$965$	−6.04528	−0.194604
$966$	29.6927	0.955347
$967$	25.3210	0.814270	0.407135	−	0.913368i	$-0.366528\pi$
$967$	25.3210	0.814270	0.407135	+	0.913368i	$0.366528\pi$
$968$	−23.9819	−0.770808
$969$	−8.21631	−0.263946
$970$	−0.0729548	−0.00234244
$971$	43.0928	1.38292	0.691458	−	0.722417i	$-0.256969\pi$
$971$	43.0928	1.38292	0.691458	+	0.722417i	$0.256969\pi$
$972$	−0.218018	−0.00699294
$973$	−3.68772	−0.118223
$974$	−59.2542	−1.89863
$975$	−23.6716	−0.758097
$976$	−50.1641	−1.60571
$977$	18.4348	0.589783	0.294891	−	0.955531i	$-0.404717\pi$
$977$	18.4348	0.589783	0.294891	+	0.955531i	$0.404717\pi$
$978$	32.8244	1.04961
$979$	13.9246	0.445032
$980$	−0.0923920	−0.00295135
$981$	−5.41928	−0.173024
$982$	11.3488	0.362156
$983$	−21.3604	−0.681293	−0.340646	−	0.940192i	$-0.610646\pi$
$983$	−21.3604	−0.681293	−0.340646	+	0.940192i	$0.610646\pi$
$984$	−22.7904	−0.726531
$985$	−4.15611	−0.132425
$986$	−2.64230	−0.0841479
$987$	57.5155	1.83074
$988$	0.244269	0.00777123
$989$	51.1221	1.62559
$990$	1.69401	0.0538393
$991$	−1.92917	−0.0612822	−0.0306411	−	0.999530i	$-0.509755\pi$
$991$	−1.92917	−0.0612822	−0.0306411	+	0.999530i	$0.509755\pi$
$992$	−0.129571	−0.00411390
$993$	−29.0758	−0.922691
$994$	73.4579	2.32994
$995$	−1.36883	−0.0433949
$996$	−0.0671698	−0.00212836
$997$	2.94729	0.0933417	0.0466709	−	0.998910i	$-0.485139\pi$
$997$	2.94729	0.0933417	0.0466709	+	0.998910i	$0.485139\pi$
$998$	−0.0621903	−0.00196860
$999$	27.6013	0.873266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.b.1.17	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.b.1.17	✓	59	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.40700 q^{2} +1.38079 q^{3} -0.0203573 q^{4} +0.687727 q^{5} -1.94276 q^{6} -3.68772 q^{7} +2.84264 q^{8} -1.09343 q^{9} +O(q^{10})\)	\(q-1.40700 q^{2} +1.38079 q^{3} -0.0203573 q^{4} +0.687727 q^{5} -1.94276 q^{6} -3.68772 q^{7} +2.84264 q^{8} -1.09343 q^{9} -0.967630 q^{10} +1.60109 q^{11} -0.0281091 q^{12} +3.78693 q^{13} +5.18862 q^{14} +0.949604 q^{15} -3.95887 q^{16} +1.87797 q^{17} +1.53845 q^{18} -3.16856 q^{19} -0.0140002 q^{20} -5.09196 q^{21} -2.25274 q^{22} +4.14449 q^{23} +3.92508 q^{24} -4.52703 q^{25} -5.32820 q^{26} -5.65215 q^{27} +0.0750720 q^{28} +1.00000 q^{29} -1.33609 q^{30} +1.12520 q^{31} -0.115154 q^{32} +2.21077 q^{33} -2.64230 q^{34} -2.53615 q^{35} +0.0222592 q^{36} -4.88332 q^{37} +4.45816 q^{38} +5.22894 q^{39} +1.95496 q^{40} -5.80635 q^{41} +7.16438 q^{42} +12.3349 q^{43} -0.0325939 q^{44} -0.751981 q^{45} -5.83129 q^{46} -11.2953 q^{47} -5.46635 q^{48} +6.59931 q^{49} +6.36952 q^{50} +2.59307 q^{51} -0.0770915 q^{52} -5.34065 q^{53} +7.95256 q^{54} +1.10112 q^{55} -10.4829 q^{56} -4.37510 q^{57} -1.40700 q^{58} -15.2129 q^{59} -0.0193314 q^{60} +12.6713 q^{61} -1.58316 q^{62} +4.03227 q^{63} +8.07976 q^{64} +2.60437 q^{65} -3.11055 q^{66} +8.93358 q^{67} -0.0382303 q^{68} +5.72266 q^{69} +3.56835 q^{70} +14.1575 q^{71} -3.10822 q^{72} -1.43161 q^{73} +6.87083 q^{74} -6.25086 q^{75} +0.0645032 q^{76} -5.90440 q^{77} -7.35710 q^{78} -2.48162 q^{79} -2.72262 q^{80} -4.52412 q^{81} +8.16953 q^{82} +2.38962 q^{83} +0.103658 q^{84} +1.29153 q^{85} -17.3552 q^{86} +1.38079 q^{87} +4.55133 q^{88} +8.69691 q^{89} +1.05804 q^{90} -13.9651 q^{91} -0.0843706 q^{92} +1.55367 q^{93} +15.8925 q^{94} -2.17910 q^{95} -0.159003 q^{96} +0.0753954 q^{97} -9.28522 q^{98} -1.75068 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * q^99

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