LMFDB - Embedded newform 4033.2.a.d.1.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.02880 q^{2} +1.40341 q^{3} -0.941581 q^{4} -3.68003 q^{5} -1.44382 q^{6} -1.52261 q^{7} +3.02628 q^{8} -1.03043 q^{9} +O(q^{10})$	\(q-1.02880 q^{2} +1.40341 q^{3} -0.941581 q^{4} -3.68003 q^{5} -1.44382 q^{6} -1.52261 q^{7} +3.02628 q^{8} -1.03043 q^{9} +3.78600 q^{10} -3.58258 q^{11} -1.32143 q^{12} +1.74641 q^{13} +1.56645 q^{14} -5.16460 q^{15} -1.23026 q^{16} +2.49376 q^{17} +1.06010 q^{18} +5.81181 q^{19} +3.46505 q^{20} -2.13684 q^{21} +3.68574 q^{22} +2.43252 q^{23} +4.24713 q^{24} +8.54264 q^{25} -1.79670 q^{26} -5.65636 q^{27} +1.43366 q^{28} -4.56833 q^{29} +5.31332 q^{30} +7.95024 q^{31} -4.78688 q^{32} -5.02784 q^{33} -2.56557 q^{34} +5.60324 q^{35} +0.970235 q^{36} -1.00000 q^{37} -5.97917 q^{38} +2.45093 q^{39} -11.1368 q^{40} +0.514064 q^{41} +2.19837 q^{42} +10.0374 q^{43} +3.37329 q^{44} +3.79202 q^{45} -2.50257 q^{46} +4.36490 q^{47} -1.72657 q^{48} -4.68167 q^{49} -8.78862 q^{50} +3.49978 q^{51} -1.64438 q^{52} -11.4533 q^{53} +5.81924 q^{54} +13.1840 q^{55} -4.60784 q^{56} +8.15638 q^{57} +4.69987 q^{58} +13.6805 q^{59} +4.86289 q^{60} +2.74270 q^{61} -8.17916 q^{62} +1.56894 q^{63} +7.38525 q^{64} -6.42684 q^{65} +5.17262 q^{66} -0.269055 q^{67} -2.34808 q^{68} +3.41383 q^{69} -5.76458 q^{70} -3.23405 q^{71} -3.11838 q^{72} -9.45394 q^{73} +1.02880 q^{74} +11.9888 q^{75} -5.47229 q^{76} +5.45486 q^{77} -2.52151 q^{78} +4.59433 q^{79} +4.52741 q^{80} -4.84691 q^{81} -0.528866 q^{82} -11.8111 q^{83} +2.01201 q^{84} -9.17713 q^{85} -10.3264 q^{86} -6.41125 q^{87} -10.8419 q^{88} -0.841795 q^{89} -3.90122 q^{90} -2.65909 q^{91} -2.29041 q^{92} +11.1575 q^{93} -4.49059 q^{94} -21.3877 q^{95} -6.71796 q^{96} -2.47963 q^{97} +4.81648 q^{98} +3.69161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−1.02880	−0.727468	−0.363734	−	0.931503i	$-0.618498\pi$
$2$	−1.02880	−0.727468	−0.363734	+	0.931503i	$0.618498\pi$
$3$	1.40341	0.810261	0.405130	−	0.914259i	$-0.367226\pi$
$3$	1.40341	0.810261	0.405130	+	0.914259i	$0.367226\pi$
$4$	−0.941581	−0.470790
$5$	−3.68003	−1.64576	−0.822880	−	0.568215i	$-0.807634\pi$
$5$	−3.68003	−1.64576	−0.822880	+	0.568215i	$0.807634\pi$
$6$	−1.44382	−0.589439
$7$	−1.52261	−0.575491	−0.287745	−	0.957707i	$-0.592906\pi$
$7$	−1.52261	−0.575491	−0.287745	+	0.957707i	$0.592906\pi$
$8$	3.02628	1.06995
$9$	−1.03043	−0.343477
$10$	3.78600	1.19724
$11$	−3.58258	−1.08019	−0.540094	−	0.841604i	$-0.681611\pi$
$11$	−3.58258	−1.08019	−0.540094	+	0.841604i	$0.681611\pi$
$12$	−1.32143	−0.381463
$13$	1.74641	0.484367	0.242183	−	0.970231i	$-0.422136\pi$
$13$	1.74641	0.484367	0.242183	+	0.970231i	$0.422136\pi$
$14$	1.56645	0.418651
$15$	−5.16460	−1.33350
$16$	−1.23026	−0.307566
$17$	2.49376	0.604827	0.302413	−	0.953177i	$-0.402208\pi$
$17$	2.49376	0.604827	0.302413	+	0.953177i	$0.402208\pi$
$18$	1.06010	0.249869
$19$	5.81181	1.33332	0.666661	−	0.745361i	$-0.267723\pi$
$19$	5.81181	1.33332	0.666661	+	0.745361i	$0.267723\pi$
$20$	3.46505	0.774808
$21$	−2.13684	−0.466298
$22$	3.68574	0.785803
$23$	2.43252	0.507216	0.253608	−	0.967307i	$-0.418383\pi$
$23$	2.43252	0.507216	0.253608	+	0.967307i	$0.418383\pi$
$24$	4.24713	0.866941
$25$	8.54264	1.70853
$26$	−1.79670	−0.352361
$27$	−5.65636	−1.08857
$28$	1.43366	0.270935
$29$	−4.56833	−0.848317	−0.424159	−	0.905588i	$-0.639430\pi$
$29$	−4.56833	−0.848317	−0.424159	+	0.905588i	$0.639430\pi$
$30$	5.31332	0.970075
$31$	7.95024	1.42790	0.713952	−	0.700194i	$-0.246903\pi$
$31$	7.95024	1.42790	0.713952	+	0.700194i	$0.246903\pi$
$32$	−4.78688	−0.846208
$33$	−5.02784	−0.875235
$34$	−2.56557	−0.439992
$35$	5.60324	0.947120
$36$	0.970235	0.161706
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−5.97917	−0.969949
$39$	2.45093	0.392463
$40$	−11.1368	−1.76089
$41$	0.514064	0.0802833	0.0401416	−	0.999194i	$-0.487219\pi$
$41$	0.514064	0.0802833	0.0401416	+	0.999194i	$0.487219\pi$
$42$	2.19837	0.339217
$43$	10.0374	1.53069	0.765346	−	0.643619i	$-0.222568\pi$
$43$	10.0374	1.53069	0.765346	+	0.643619i	$0.222568\pi$
$44$	3.37329	0.508542
$45$	3.79202	0.565282
$46$	−2.50257	−0.368983
$47$	4.36490	0.636686	0.318343	−	0.947976i	$-0.396874\pi$
$47$	4.36490	0.636686	0.318343	+	0.947976i	$0.396874\pi$
$48$	−1.72657	−0.249209
$49$	−4.68167	−0.668810
$50$	−8.78862	−1.24290
$51$	3.49978	0.490067
$52$	−1.64438	−0.228035
$53$	−11.4533	−1.57323	−0.786617	−	0.617441i	$-0.788169\pi$
$53$	−11.4533	−1.57323	−0.786617	+	0.617441i	$0.788169\pi$
$54$	5.81924	0.791898
$55$	13.1840	1.77773
$56$	−4.60784	−0.615748
$57$	8.15638	1.08034
$58$	4.69987	0.617124
$59$	13.6805	1.78104	0.890522	−	0.454941i	$-0.150340\pi$
$59$	13.6805	1.78104	0.890522	+	0.454941i	$0.150340\pi$
$60$	4.86289	0.627797
$61$	2.74270	0.351166	0.175583	−	0.984465i	$-0.443819\pi$
$61$	2.74270	0.351166	0.175583	+	0.984465i	$0.443819\pi$
$62$	−8.17916	−1.03875
$63$	1.56894	0.197668
$64$	7.38525	0.923156
$65$	−6.42684	−0.797151
$66$	5.17262	0.636705
$67$	−0.269055	−0.0328702	−0.0164351	−	0.999865i	$-0.505232\pi$
$67$	−0.269055	−0.0328702	−0.0164351	+	0.999865i	$0.505232\pi$
$68$	−2.34808	−0.284747
$69$	3.41383	0.410977
$70$	−5.76458	−0.688999
$71$	−3.23405	−0.383811	−0.191905	−	0.981413i	$-0.561467\pi$
$71$	−3.23405	−0.383811	−0.191905	+	0.981413i	$0.561467\pi$
$72$	−3.11838	−0.367505
$73$	−9.45394	−1.10650	−0.553250	−	0.833015i	$-0.686613\pi$
$73$	−9.45394	−1.10650	−0.553250	+	0.833015i	$0.686613\pi$
$74$	1.02880	0.119595
$75$	11.9888	1.38435
$76$	−5.47229	−0.627715
$77$	5.45486	0.621639
$78$	−2.52151	−0.285504
$79$	4.59433	0.516903	0.258451	−	0.966024i	$-0.416788\pi$
$79$	4.59433	0.516903	0.258451	+	0.966024i	$0.416788\pi$
$80$	4.52741	0.506180
$81$	−4.84691	−0.538546
$82$	−0.528866	−0.0584035
$83$	−11.8111	−1.29644	−0.648221	−	0.761453i	$-0.724487\pi$
$83$	−11.8111	−1.29644	−0.648221	+	0.761453i	$0.724487\pi$
$84$	2.01201	0.219528
$85$	−9.17713	−0.995400
$86$	−10.3264	−1.11353
$87$	−6.41125	−0.687358
$88$	−10.8419	−1.15575
$89$	−0.841795	−0.0892301	−0.0446150	−	0.999004i	$-0.514206\pi$
$89$	−0.841795	−0.0892301	−0.0446150	+	0.999004i	$0.514206\pi$
$90$	−3.90122	−0.411224
$91$	−2.65909	−0.278748
$92$	−2.29041	−0.238792
$93$	11.1575	1.15697
$94$	−4.49059	−0.463169
$95$	−21.3877	−2.19433
$96$	−6.71796	−0.685649
$97$	−2.47963	−0.251768	−0.125884	−	0.992045i	$-0.540177\pi$
$97$	−2.47963	−0.251768	−0.125884	+	0.992045i	$0.540177\pi$
$98$	4.81648	0.486538
$99$	3.69161	0.371021
$100$	−8.04358	−0.804358
$101$	−13.3575	−1.32912	−0.664561	−	0.747234i	$-0.731381\pi$
$101$	−13.3575	−1.32912	−0.664561	+	0.747234i	$0.731381\pi$
$102$	−3.60056	−0.356508
$103$	−4.95205	−0.487940	−0.243970	−	0.969783i	$-0.578450\pi$
$103$	−4.95205	−0.487940	−0.243970	+	0.969783i	$0.578450\pi$
$104$	5.28513	0.518249
$105$	7.86366	0.767414
$106$	11.7831	1.14448
$107$	12.3646	1.19533	0.597667	−	0.801745i	$-0.296095\pi$
$107$	12.3646	1.19533	0.597667	+	0.801745i	$0.296095\pi$
$108$	5.32592	0.512487
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−13.5636	−1.29324
$111$	−1.40341	−0.133206
$112$	1.87321	0.177002
$113$	−4.76956	−0.448682	−0.224341	−	0.974511i	$-0.572023\pi$
$113$	−4.76956	−0.448682	−0.224341	+	0.974511i	$0.572023\pi$
$114$	−8.39124	−0.785912
$115$	−8.95175	−0.834755
$116$	4.30145	0.399380
$117$	−1.79956	−0.166369
$118$	−14.0744	−1.29565
$119$	−3.79702	−0.348072
$120$	−15.6296	−1.42678
$121$	1.83489	0.166808
$122$	−2.82167	−0.255462
$123$	0.721444	0.0650504
$124$	−7.48579	−0.672244
$125$	−13.0370	−1.16607
$126$	−1.61412	−0.143797
$127$	10.7298	0.952113	0.476057	−	0.879415i	$-0.342066\pi$
$127$	10.7298	0.952113	0.476057	+	0.879415i	$0.342066\pi$
$128$	1.97585	0.174642
$129$	14.0866	1.24026
$130$	6.61190	0.579902
$131$	11.3794	0.994227	0.497114	−	0.867685i	$-0.334393\pi$
$131$	11.3794	0.994227	0.497114	+	0.867685i	$0.334393\pi$
$132$	4.73412	0.412052
$133$	−8.84910	−0.767314
$134$	0.276802	0.0239121
$135$	20.8156	1.79152
$136$	7.54684	0.647136
$137$	−6.73820	−0.575683	−0.287842	−	0.957678i	$-0.592938\pi$
$137$	−6.73820	−0.575683	−0.287842	+	0.957678i	$0.592938\pi$
$138$	−3.51213	−0.298973
$139$	7.05759	0.598617	0.299309	−	0.954156i	$-0.403244\pi$
$139$	7.05759	0.598617	0.299309	+	0.954156i	$0.403244\pi$
$140$	−5.27590	−0.445895
$141$	6.12576	0.515882
$142$	3.32717	0.279210
$143$	−6.25665	−0.523207
$144$	1.26770	0.105642
$145$	16.8116	1.39613
$146$	9.72617	0.804944
$147$	−6.57032	−0.541911
$148$	0.941581	0.0773974
$149$	−9.15845	−0.750289	−0.375145	−	0.926966i	$-0.622407\pi$
$149$	−9.15845	−0.750289	−0.375145	+	0.926966i	$0.622407\pi$
$150$	−12.3341	−1.00707
$151$	−11.1657	−0.908648	−0.454324	−	0.890836i	$-0.650119\pi$
$151$	−11.1657	−0.908648	−0.454324	+	0.890836i	$0.650119\pi$
$152$	17.5882	1.42659
$153$	−2.56966	−0.207744
$154$	−5.61193	−0.452222
$155$	−29.2571	−2.34999
$156$	−2.30775	−0.184768
$157$	12.3749	0.987621	0.493811	−	0.869569i	$-0.335604\pi$
$157$	12.3749	0.987621	0.493811	+	0.869569i	$0.335604\pi$
$158$	−4.72663	−0.376030
$159$	−16.0737	−1.27473
$160$	17.6159	1.39266
$161$	−3.70377	−0.291898
$162$	4.98648	0.391775
$163$	−13.5499	−1.06131	−0.530654	−	0.847589i	$-0.678053\pi$
$163$	−13.5499	−1.06131	−0.530654	+	0.847589i	$0.678053\pi$
$164$	−0.484032	−0.0377966
$165$	18.5026	1.44043
$166$	12.1512	0.943119
$167$	6.17640	0.477944	0.238972	−	0.971026i	$-0.423190\pi$
$167$	6.17640	0.477944	0.238972	+	0.971026i	$0.423190\pi$
$168$	−6.46670	−0.498916
$169$	−9.95006	−0.765389
$170$	9.44139	0.724122
$171$	−5.98868	−0.457966
$172$	−9.45104	−0.720635
$173$	−15.4669	−1.17593	−0.587964	−	0.808887i	$-0.700070\pi$
$173$	−15.4669	−1.17593	−0.587964	+	0.808887i	$0.700070\pi$
$174$	6.59586	0.500031
$175$	−13.0071	−0.983242
$176$	4.40752	0.332230
$177$	19.1993	1.44311
$178$	0.866034	0.0649120
$179$	1.10777	0.0827985	0.0413993	−	0.999143i	$-0.486818\pi$
$179$	1.10777	0.0827985	0.0413993	+	0.999143i	$0.486818\pi$
$180$	−3.57050	−0.266129
$181$	−14.7335	−1.09513	−0.547567	−	0.836762i	$-0.684446\pi$
$181$	−14.7335	−1.09513	−0.547567	+	0.836762i	$0.684446\pi$
$182$	2.73566	0.202781
$183$	3.84914	0.284536
$184$	7.36150	0.542697
$185$	3.68003	0.270561
$186$	−11.4787	−0.841662
$187$	−8.93411	−0.653327
$188$	−4.10990	−0.299746
$189$	8.61241	0.626460
$190$	22.0035	1.59630
$191$	−21.1045	−1.52707	−0.763533	−	0.645768i	$-0.776537\pi$
$191$	−21.1045	−1.52707	−0.763533	+	0.645768i	$0.776537\pi$
$192$	10.3645	0.747997
$193$	−10.8945	−0.784204	−0.392102	−	0.919922i	$-0.628252\pi$
$193$	−10.8945	−0.784204	−0.392102	+	0.919922i	$0.628252\pi$
$194$	2.55103	0.183153
$195$	−9.01951	−0.645900
$196$	4.40817	0.314869
$197$	2.54450	0.181288	0.0906440	−	0.995883i	$-0.471107\pi$
$197$	2.54450	0.181288	0.0906440	+	0.995883i	$0.471107\pi$
$198$	−3.79791	−0.269906
$199$	−22.3754	−1.58615	−0.793076	−	0.609122i	$-0.791522\pi$
$199$	−22.3754	−1.58615	−0.793076	+	0.609122i	$0.791522\pi$
$200$	25.8524	1.82804
$201$	−0.377595	−0.0266335
$202$	13.7421	0.966893
$203$	6.95576	0.488199
$204$	−3.29533	−0.230719
$205$	−1.89177	−0.132127
$206$	5.09465	0.354961
$207$	−2.50655	−0.174217
$208$	−2.14855	−0.148975
$209$	−20.8213	−1.44024
$210$	−8.09009	−0.558269
$211$	11.6907	0.804823	0.402412	−	0.915459i	$-0.368172\pi$
$211$	11.6907	0.804823	0.402412	+	0.915459i	$0.368172\pi$
$212$	10.7842	0.740663
$213$	−4.53870	−0.310987
$214$	−12.7207	−0.869567
$215$	−36.9380	−2.51915
$216$	−17.1178	−1.16472
$217$	−12.1051	−0.821746
$218$	1.02880	0.0696788
$219$	−13.2678	−0.896554
$220$	−12.4138	−0.836939
$221$	4.35513	0.292958
$222$	1.44382	0.0969031
$223$	21.6093	1.44707	0.723534	−	0.690289i	$-0.242517\pi$
$223$	21.6093	1.44707	0.723534	+	0.690289i	$0.242517\pi$
$224$	7.28853	0.486985
$225$	−8.80261	−0.586841
$226$	4.90690	0.326402
$227$	−4.12700	−0.273919	−0.136959	−	0.990577i	$-0.543733\pi$
$227$	−4.12700	−0.273919	−0.136959	+	0.990577i	$0.543733\pi$
$228$	−7.67988	−0.508613
$229$	−21.7668	−1.43839	−0.719197	−	0.694806i	$-0.755490\pi$
$229$	−21.7668	−1.43839	−0.719197	+	0.694806i	$0.755490\pi$
$230$	9.20952	0.607258
$231$	7.65542	0.503689
$232$	−13.8251	−0.907660
$233$	−9.02560	−0.591287	−0.295643	−	0.955298i	$-0.595534\pi$
$233$	−9.02560	−0.591287	−0.295643	+	0.955298i	$0.595534\pi$
$234$	1.85137	0.121028
$235$	−16.0630	−1.04783
$236$	−12.8812	−0.838498
$237$	6.44775	0.418826
$238$	3.90636	0.253211
$239$	13.2811	0.859086	0.429543	−	0.903046i	$-0.358675\pi$
$239$	13.2811	0.859086	0.429543	+	0.903046i	$0.358675\pi$
$240$	6.35383	0.410138
$241$	17.1131	1.10235	0.551176	−	0.834389i	$-0.314179\pi$
$241$	17.1131	1.10235	0.551176	+	0.834389i	$0.314179\pi$
$242$	−1.88772	−0.121347
$243$	10.1669	0.652205
$244$	−2.58247	−0.165326
$245$	17.2287	1.10070
$246$	−0.742218	−0.0473221
$247$	10.1498	0.645817
$248$	24.0597	1.52779
$249$	−16.5759	−1.05046
$250$	13.4124	0.848276
$251$	−4.37008	−0.275837	−0.137919	−	0.990444i	$-0.544041\pi$
$251$	−4.37008	−0.275837	−0.137919	+	0.990444i	$0.544041\pi$
$252$	−1.47729	−0.0930602
$253$	−8.71470	−0.547889
$254$	−11.0387	−0.692632
$255$	−12.8793	−0.806534
$256$	−16.8032	−1.05020
$257$	5.97230	0.372542	0.186271	−	0.982498i	$-0.440360\pi$
$257$	5.97230	0.372542	0.186271	+	0.982498i	$0.440360\pi$
$258$	−14.4923	−0.902249
$259$	1.52261	0.0946101
$260$	6.05139	0.375291
$261$	4.70735	0.291378
$262$	−11.7071	−0.723268
$263$	−2.68707	−0.165692	−0.0828459	−	0.996562i	$-0.526401\pi$
$263$	−2.68707	−0.165692	−0.0828459	+	0.996562i	$0.526401\pi$
$264$	−15.2157	−0.936460
$265$	42.1486	2.58917
$266$	9.10391	0.558197
$267$	−1.18139	−0.0722996
$268$	0.253337	0.0154750
$269$	17.6297	1.07490	0.537452	−	0.843294i	$-0.319387\pi$
$269$	17.6297	1.07490	0.537452	+	0.843294i	$0.319387\pi$
$270$	−21.4150	−1.30327
$271$	−8.33304	−0.506196	−0.253098	−	0.967441i	$-0.581449\pi$
$271$	−8.33304	−0.506196	−0.253098	+	0.967441i	$0.581449\pi$
$272$	−3.06799	−0.186024
$273$	−3.73180	−0.225859
$274$	6.93223	0.418791
$275$	−30.6047	−1.84553
$276$	−3.21440	−0.193484
$277$	5.20797	0.312917	0.156458	−	0.987685i	$-0.449992\pi$
$277$	5.20797	0.312917	0.156458	+	0.987685i	$0.449992\pi$
$278$	−7.26081	−0.435475
$279$	−8.19218	−0.490453
$280$	16.9570	1.01337
$281$	−0.495700	−0.0295710	−0.0147855	−	0.999891i	$-0.504707\pi$
$281$	−0.495700	−0.0295710	−0.0147855	+	0.999891i	$0.504707\pi$
$282$	−6.30215	−0.375287
$283$	9.00228	0.535130	0.267565	−	0.963540i	$-0.413781\pi$
$283$	9.00228	0.535130	0.267565	+	0.963540i	$0.413781\pi$
$284$	3.04511	0.180694
$285$	−30.0157	−1.77798
$286$	6.43681	0.380617
$287$	−0.782716	−0.0462023
$288$	4.93255	0.290653
$289$	−10.7811	−0.634185
$290$	−17.2957	−1.01564
$291$	−3.47994	−0.203998
$292$	8.90165	0.520930
$293$	13.7487	0.803208	0.401604	−	0.915813i	$-0.368453\pi$
$293$	13.7487	0.803208	0.401604	+	0.915813i	$0.368453\pi$
$294$	6.75951	0.394223
$295$	−50.3445	−2.93117
$296$	−3.02628	−0.175899
$297$	20.2644	1.17586
$298$	9.42217	0.545811
$299$	4.24817	0.245678
$300$	−11.2885	−0.651740
$301$	−15.2830	−0.880899
$302$	11.4872	0.661013
$303$	−18.7461	−1.07693
$304$	−7.15007	−0.410085
$305$	−10.0932	−0.577936
$306$	2.64365	0.151127
$307$	−25.2124	−1.43895	−0.719474	−	0.694520i	$-0.755617\pi$
$307$	−25.2124	−1.43895	−0.719474	+	0.694520i	$0.755617\pi$
$308$	−5.13619	−0.292661
$309$	−6.94977	−0.395359
$310$	30.0996	1.70954
$311$	7.50879	0.425785	0.212892	−	0.977076i	$-0.431712\pi$
$311$	7.50879	0.425785	0.212892	+	0.977076i	$0.431712\pi$
$312$	7.41722	0.419917
$313$	1.01410	0.0573205	0.0286602	−	0.999589i	$-0.490876\pi$
$313$	1.01410	0.0573205	0.0286602	+	0.999589i	$0.490876\pi$
$314$	−12.7312	−0.718463
$315$	−5.77376	−0.325314
$316$	−4.32593	−0.243353
$317$	−11.0099	−0.618380	−0.309190	−	0.951000i	$-0.600058\pi$
$317$	−11.0099	−0.618380	−0.309190	+	0.951000i	$0.600058\pi$
$318$	16.5366	0.927325
$319$	16.3664	0.916343
$320$	−27.1779	−1.51929
$321$	17.3527	0.968531
$322$	3.81042	0.212346
$323$	14.4933	0.806429
$324$	4.56376	0.253542
$325$	14.9189	0.827554
$326$	13.9400	0.772067
$327$	−1.40341	−0.0776089
$328$	1.55570	0.0858993
$329$	−6.64602	−0.366407
$330$	−19.0354	−1.04786
$331$	3.48903	0.191774	0.0958872	−	0.995392i	$-0.469431\pi$
$331$	3.48903	0.191774	0.0958872	+	0.995392i	$0.469431\pi$
$332$	11.1211	0.610352
$333$	1.03043	0.0564673
$334$	−6.35425	−0.347689
$335$	0.990129	0.0540965
$336$	2.62888	0.143417
$337$	24.9555	1.35941	0.679706	−	0.733485i	$-0.262107\pi$
$337$	24.9555	1.35941	0.679706	+	0.733485i	$0.262107\pi$
$338$	10.2366	0.556796
$339$	−6.69366	−0.363550
$340$	8.64101	0.468625
$341$	−28.4824	−1.54241
$342$	6.16113	0.333156
$343$	17.7866	0.960385
$344$	30.3761	1.63777
$345$	−12.5630	−0.676370
$346$	15.9123	0.855450
$347$	−8.42937	−0.452512	−0.226256	−	0.974068i	$-0.572649\pi$
$347$	−8.42937	−0.452512	−0.226256	+	0.974068i	$0.572649\pi$
$348$	6.03671	0.323602
$349$	5.07055	0.271420	0.135710	−	0.990749i	$-0.456668\pi$
$349$	5.07055	0.271420	0.135710	+	0.990749i	$0.456668\pi$
$350$	13.3816	0.715277
$351$	−9.87832	−0.527266
$352$	17.1494	0.914065
$353$	1.73050	0.0921051	0.0460525	−	0.998939i	$-0.485336\pi$
$353$	1.73050	0.0921051	0.0460525	+	0.998939i	$0.485336\pi$
$354$	−19.7522	−1.04982
$355$	11.9014	0.631660
$356$	0.792618	0.0420086
$357$	−5.32879	−0.282029
$358$	−1.13967	−0.0602333
$359$	−19.7681	−1.04332	−0.521661	−	0.853153i	$-0.674687\pi$
$359$	−19.7681	−1.04332	−0.521661	+	0.853153i	$0.674687\pi$
$360$	11.4757	0.604825
$361$	14.7772	0.777747
$362$	15.1578	0.796674
$363$	2.57510	0.135158
$364$	2.50375	0.131232
$365$	34.7908	1.82103
$366$	−3.95997	−0.206991
$367$	6.79896	0.354903	0.177452	−	0.984130i	$-0.443215\pi$
$367$	6.79896	0.354903	0.177452	+	0.984130i	$0.443215\pi$
$368$	−2.99264	−0.156002
$369$	−0.529708	−0.0275755
$370$	−3.78600	−0.196825
$371$	17.4389	0.905382
$372$	−10.5056	−0.544693
$373$	−20.9940	−1.08703	−0.543515	−	0.839400i	$-0.682907\pi$
$373$	−20.9940	−1.08703	−0.543515	+	0.839400i	$0.682907\pi$
$374$	9.19137	0.475275
$375$	−18.2963	−0.944818
$376$	13.2094	0.681224
$377$	−7.97817	−0.410897
$378$	−8.86040	−0.455730
$379$	20.9921	1.07829	0.539146	−	0.842212i	$-0.318747\pi$
$379$	20.9921	1.07829	0.539146	+	0.842212i	$0.318747\pi$
$380$	20.1382	1.03307
$381$	15.0583	0.771460
$382$	21.7122	1.11089
$383$	−11.0881	−0.566577	−0.283288	−	0.959035i	$-0.591425\pi$
$383$	−11.0881	−0.566577	−0.283288	+	0.959035i	$0.591425\pi$
$384$	2.77293	0.141506
$385$	−20.0741	−1.02307
$386$	11.2082	0.570484
$387$	−10.3429	−0.525758
$388$	2.33477	0.118530
$389$	−22.2534	−1.12829	−0.564147	−	0.825674i	$-0.690795\pi$
$389$	−22.2534	−1.12829	−0.564147	+	0.825674i	$0.690795\pi$
$390$	9.27923	0.469872
$391$	6.06613	0.306778
$392$	−14.1681	−0.715596
$393$	15.9701	0.805583
$394$	−2.61777	−0.131881
$395$	−16.9073	−0.850698
$396$	−3.47595	−0.174673
$397$	8.03490	0.403260	0.201630	−	0.979462i	$-0.435376\pi$
$397$	8.03490	0.403260	0.201630	+	0.979462i	$0.435376\pi$
$398$	23.0197	1.15388
$399$	−12.4189	−0.621725
$400$	−10.5097	−0.525485
$401$	−32.2243	−1.60921	−0.804603	−	0.593813i	$-0.797622\pi$
$401$	−32.2243	−1.60921	−0.804603	+	0.593813i	$0.797622\pi$
$402$	0.388467	0.0193750
$403$	13.8844	0.691629
$404$	12.5772	0.625737
$405$	17.8368	0.886317
$406$	−7.15605	−0.355149
$407$	3.58258	0.177582
$408$	10.5913	0.524349
$409$	26.0168	1.28645	0.643223	−	0.765679i	$-0.277597\pi$
$409$	26.0168	1.28645	0.643223	+	0.765679i	$0.277597\pi$
$410$	1.94624	0.0961182
$411$	−9.45648	−0.466454
$412$	4.66276	0.229717
$413$	−20.8299	−1.02497
$414$	2.57872	0.126737
$415$	43.4654	2.13363
$416$	−8.35984	−0.409875
$417$	9.90471	0.485036
$418$	21.4208	1.04773
$419$	40.2008	1.96394	0.981970	−	0.189038i	$-0.0605371\pi$
$419$	40.2008	1.96394	0.981970	+	0.189038i	$0.0605371\pi$
$420$	−7.40426	−0.361291
$421$	−17.8959	−0.872191	−0.436095	−	0.899901i	$-0.643639\pi$
$421$	−17.8959	−0.872191	−0.436095	+	0.899901i	$0.643639\pi$
$422$	−12.0274	−0.585483
$423$	−4.49773	−0.218687
$424$	−34.6610	−1.68329
$425$	21.3033	1.03336
$426$	4.66939	0.226233
$427$	−4.17605	−0.202093
$428$	−11.6423	−0.562751
$429$	−8.78066	−0.423934
$430$	38.0017	1.83260
$431$	−14.8429	−0.714956	−0.357478	−	0.933922i	$-0.616363\pi$
$431$	−14.8429	−0.714956	−0.357478	+	0.933922i	$0.616363\pi$
$432$	6.95882	0.334806
$433$	−25.7851	−1.23915	−0.619577	−	0.784936i	$-0.712696\pi$
$433$	−25.7851	−1.23915	−0.619577	+	0.784936i	$0.712696\pi$
$434$	12.4536	0.597794
$435$	23.5936	1.13123
$436$	0.941581	0.0450935
$437$	14.1374	0.676282
$438$	13.6498	0.652214
$439$	−29.8158	−1.42303	−0.711514	−	0.702672i	$-0.751990\pi$
$439$	−29.8158	−1.42303	−0.711514	+	0.702672i	$0.751990\pi$
$440$	39.8986	1.90209
$441$	4.82415	0.229721
$442$	−4.48054	−0.213117
$443$	−29.5344	−1.40322	−0.701612	−	0.712559i	$-0.747536\pi$
$443$	−29.5344	−1.40322	−0.701612	+	0.712559i	$0.747536\pi$
$444$	1.32143	0.0627121
$445$	3.09783	0.146851
$446$	−22.2316	−1.05270
$447$	−12.8531	−0.607930
$448$	−11.2448	−0.531268
$449$	27.3705	1.29169	0.645846	−	0.763468i	$-0.276505\pi$
$449$	27.3705	1.29169	0.645846	+	0.763468i	$0.276505\pi$
$450$	9.05608	0.426908
$451$	−1.84167	−0.0867211
$452$	4.49092	0.211235
$453$	−15.6700	−0.736242
$454$	4.24584	0.199267
$455$	9.78554	0.458753
$456$	24.6835	1.15591
$457$	3.76912	0.176312	0.0881560	−	0.996107i	$-0.471903\pi$
$457$	3.76912	0.176312	0.0881560	+	0.996107i	$0.471903\pi$
$458$	22.3936	1.04639
$459$	−14.1056	−0.658394
$460$	8.42880	0.392995
$461$	10.3851	0.483683	0.241842	−	0.970316i	$-0.422249\pi$
$461$	10.3851	0.483683	0.241842	+	0.970316i	$0.422249\pi$
$462$	−7.87586	−0.366418
$463$	12.2607	0.569804	0.284902	−	0.958557i	$-0.408039\pi$
$463$	12.2607	0.569804	0.284902	+	0.958557i	$0.408039\pi$
$464$	5.62025	0.260914
$465$	−41.0598	−1.90410
$466$	9.28549	0.430142
$467$	21.0845	0.975672	0.487836	−	0.872935i	$-0.337786\pi$
$467$	21.0845	0.975672	0.487836	+	0.872935i	$0.337786\pi$
$468$	1.69443	0.0783249
$469$	0.409664	0.0189165
$470$	16.5255	0.762265
$471$	17.3670	0.800231
$472$	41.4009	1.90563
$473$	−35.9599	−1.65344
$474$	−6.63341	−0.304683
$475$	49.6482	2.27802
$476$	3.57520	0.163869
$477$	11.8019	0.540370
$478$	−13.6636	−0.624957
$479$	−32.9620	−1.50607	−0.753036	−	0.657979i	$-0.771412\pi$
$479$	−32.9620	−1.50607	−0.753036	+	0.657979i	$0.771412\pi$
$480$	24.7223	1.12841
$481$	−1.74641	−0.0796294
$482$	−17.6059	−0.801925
$483$	−5.19792	−0.236513
$484$	−1.72769	−0.0785315
$485$	9.12512	0.414350
$486$	−10.4596	−0.474458
$487$	30.5782	1.38563	0.692816	−	0.721114i	$-0.256370\pi$
$487$	30.5782	1.38563	0.692816	+	0.721114i	$0.256370\pi$
$488$	8.30018	0.375732
$489$	−19.0161	−0.859936
$490$	−17.7248	−0.800725
$491$	−9.97992	−0.450388	−0.225194	−	0.974314i	$-0.572302\pi$
$491$	−9.97992	−0.450388	−0.225194	+	0.974314i	$0.572302\pi$
$492$	−0.679297	−0.0306251
$493$	−11.3923	−0.513085
$494$	−10.4421	−0.469811
$495$	−13.5852	−0.610611
$496$	−9.78090	−0.439175
$497$	4.92418	0.220879
$498$	17.0532	0.764173
$499$	−26.4904	−1.18587	−0.592936	−	0.805250i	$-0.702031\pi$
$499$	−26.4904	−1.18587	−0.592936	+	0.805250i	$0.702031\pi$
$500$	12.2754	0.548973
$501$	8.66804	0.387260
$502$	4.49592	0.200663
$503$	−38.7023	−1.72565	−0.862826	−	0.505501i	$-0.831308\pi$
$503$	−38.7023	−1.72565	−0.862826	+	0.505501i	$0.831308\pi$
$504$	4.74806	0.211496
$505$	49.1560	2.18742
$506$	8.96564	0.398571
$507$	−13.9640	−0.620165
$508$	−10.1029	−0.448246
$509$	15.4634	0.685402	0.342701	−	0.939445i	$-0.388658\pi$
$509$	15.4634	0.685402	0.342701	+	0.939445i	$0.388658\pi$
$510$	13.2502	0.586727
$511$	14.3946	0.636781
$512$	13.3354	0.589346
$513$	−32.8737	−1.45141
$514$	−6.14428	−0.271012
$515$	18.2237	0.803033
$516$	−13.2637	−0.583902
$517$	−15.6376	−0.687741
$518$	−1.56645	−0.0688258
$519$	−21.7065	−0.952808
$520$	−19.4494	−0.852914
$521$	−7.13207	−0.312462	−0.156231	−	0.987721i	$-0.549934\pi$
$521$	−7.13207	−0.312462	−0.156231	+	0.987721i	$0.549934\pi$
$522$	−4.84290	−0.211968
$523$	3.18367	0.139212	0.0696060	−	0.997575i	$-0.477826\pi$
$523$	3.18367	0.139212	0.0696060	+	0.997575i	$0.477826\pi$
$524$	−10.7147	−0.468072
$525$	−18.2543	−0.796682
$526$	2.76444	0.120535
$527$	19.8260	0.863635
$528$	6.18558	0.269193
$529$	−17.0828	−0.742732
$530$	−43.3623	−1.88354
$531$	−14.0968	−0.611748
$532$	8.33214	0.361244
$533$	0.897765	0.0388865
$534$	1.21540	0.0525957
$535$	−45.5022	−1.96723
$536$	−0.814235	−0.0351696
$537$	1.55466	0.0670884
$538$	−18.1374	−0.781959
$539$	16.7725	0.722441
$540$	−19.5996	−0.843431
$541$	−12.9773	−0.557938	−0.278969	−	0.960300i	$-0.589993\pi$
$541$	−12.9773	−0.557938	−0.278969	+	0.960300i	$0.589993\pi$
$542$	8.57299	0.368241
$543$	−20.6772	−0.887343
$544$	−11.9373	−0.511809
$545$	3.68003	0.157635
$546$	3.83926	0.164305
$547$	−17.6123	−0.753046	−0.376523	−	0.926407i	$-0.622880\pi$
$547$	−17.6123	−0.753046	−0.376523	+	0.926407i	$0.622880\pi$
$548$	6.34456	0.271026
$549$	−2.82616	−0.120618
$550$	31.4860	1.34257
$551$	−26.5503	−1.13108
$552$	10.3312	0.439726
$553$	−6.99536	−0.297473
$554$	−5.35794	−0.227637
$555$	5.16460	0.219225
$556$	−6.64529	−0.281823
$557$	−18.0975	−0.766816	−0.383408	−	0.923579i	$-0.625250\pi$
$557$	−18.0975	−0.766816	−0.383408	+	0.923579i	$0.625250\pi$
$558$	8.42807	0.356789
$559$	17.5294	0.741416
$560$	−6.89347	−0.291302
$561$	−12.5382	−0.529365
$562$	0.509973	0.0215119
$563$	19.1561	0.807334	0.403667	−	0.914906i	$-0.367736\pi$
$563$	19.1561	0.807334	0.403667	+	0.914906i	$0.367736\pi$
$564$	−5.76789	−0.242872
$565$	17.5521	0.738423
$566$	−9.26150	−0.389290
$567$	7.37993	0.309928
$568$	−9.78714	−0.410659
$569$	−31.3270	−1.31330	−0.656648	−	0.754198i	$-0.728026\pi$
$569$	−31.3270	−1.31330	−0.656648	+	0.754198i	$0.728026\pi$
$570$	30.8800	1.29342
$571$	−1.94705	−0.0814816	−0.0407408	−	0.999170i	$-0.512972\pi$
$571$	−1.94705	−0.0814816	−0.0407408	+	0.999170i	$0.512972\pi$
$572$	5.89114	0.246321
$573$	−29.6183	−1.23732
$574$	0.805255	0.0336107
$575$	20.7801	0.866592
$576$	−7.61000	−0.317083
$577$	−1.22937	−0.0511792	−0.0255896	−	0.999673i	$-0.508146\pi$
$577$	−1.22937	−0.0511792	−0.0255896	+	0.999673i	$0.508146\pi$
$578$	11.0916	0.461349
$579$	−15.2895	−0.635410
$580$	−15.8295	−0.657283
$581$	17.9837	0.746090
$582$	3.58015	0.148402
$583$	41.0324	1.69939
$584$	−28.6103	−1.18390
$585$	6.62242	0.273804
$586$	−14.1446	−0.584308
$587$	22.2036	0.916442	0.458221	−	0.888838i	$-0.348487\pi$
$587$	22.2036	0.916442	0.458221	+	0.888838i	$0.348487\pi$
$588$	6.18649	0.255126
$589$	46.2053	1.90386
$590$	51.7942	2.13233
$591$	3.57098	0.146891
$592$	1.23026	0.0505636
$593$	−44.6458	−1.83338	−0.916692	−	0.399595i	$-0.869151\pi$
$593$	−44.6458	−1.83338	−0.916692	+	0.399595i	$0.869151\pi$
$594$	−20.8479	−0.855399
$595$	13.9732	0.572843
$596$	8.62342	0.353229
$597$	−31.4020	−1.28520
$598$	−4.37050	−0.178723
$599$	13.5064	0.551856	0.275928	−	0.961178i	$-0.411015\pi$
$599$	13.5064	0.551856	0.275928	+	0.961178i	$0.411015\pi$
$600$	36.2817	1.48119
$601$	−15.0412	−0.613544	−0.306772	−	0.951783i	$-0.599249\pi$
$601$	−15.0412	−0.613544	−0.306772	+	0.951783i	$0.599249\pi$
$602$	15.7231	0.640826
$603$	0.277243	0.0112902
$604$	10.5134	0.427783
$605$	−6.75244	−0.274526
$606$	19.2859	0.783436
$607$	34.8825	1.41584	0.707919	−	0.706294i	$-0.249634\pi$
$607$	34.8825	1.41584	0.707919	+	0.706294i	$0.249634\pi$
$608$	−27.8204	−1.12827
$609$	9.76181	0.395568
$610$	10.3839	0.420430
$611$	7.62290	0.308389
$612$	2.41954	0.0978040
$613$	3.05329	0.123321	0.0616607	−	0.998097i	$-0.480360\pi$
$613$	3.05329	0.123321	0.0616607	+	0.998097i	$0.480360\pi$
$614$	25.9384	1.04679
$615$	−2.65494	−0.107057
$616$	16.5079	0.665124
$617$	2.62565	0.105705	0.0528523	−	0.998602i	$-0.483169\pi$
$617$	2.62565	0.105705	0.0528523	+	0.998602i	$0.483169\pi$
$618$	7.14989	0.287611
$619$	40.1347	1.61315	0.806574	−	0.591133i	$-0.201319\pi$
$619$	40.1347	1.61315	0.806574	+	0.591133i	$0.201319\pi$
$620$	27.5479	1.10635
$621$	−13.7592	−0.552138
$622$	−7.72501	−0.309745
$623$	1.28172	0.0513511
$624$	−3.01530	−0.120708
$625$	5.26346	0.210538
$626$	−1.04330	−0.0416988
$627$	−29.2209	−1.16697
$628$	−11.6519	−0.464963
$629$	−2.49376	−0.0994329
$630$	5.94001	0.236656
$631$	−36.8610	−1.46741	−0.733707	−	0.679466i	$-0.762211\pi$
$631$	−36.8610	−1.46741	−0.733707	+	0.679466i	$0.762211\pi$
$632$	13.9038	0.553062
$633$	16.4069	0.652117
$634$	11.3270	0.449851
$635$	−39.4859	−1.56695
$636$	15.1347	0.600130
$637$	−8.17611	−0.323949
$638$	−16.8377	−0.666610
$639$	3.33247	0.131830
$640$	−7.27119	−0.287419
$641$	−2.25909	−0.0892286	−0.0446143	−	0.999004i	$-0.514206\pi$
$641$	−2.25909	−0.0892286	−0.0446143	+	0.999004i	$0.514206\pi$
$642$	−17.8523	−0.704576
$643$	35.0468	1.38211	0.691055	−	0.722803i	$-0.257146\pi$
$643$	35.0468	1.38211	0.691055	+	0.722803i	$0.257146\pi$
$644$	3.48740	0.137423
$645$	−51.8393	−2.04117
$646$	−14.9106	−0.586651
$647$	3.20128	0.125855	0.0629277	−	0.998018i	$-0.479956\pi$
$647$	3.20128	0.125855	0.0629277	+	0.998018i	$0.479956\pi$
$648$	−14.6681	−0.576219
$649$	−49.0113	−1.92386
$650$	−15.3485	−0.602019
$651$	−16.9884	−0.665828
$652$	12.7583	0.499653
$653$	6.41614	0.251083	0.125541	−	0.992088i	$-0.459933\pi$
$653$	6.41614	0.251083	0.125541	+	0.992088i	$0.459933\pi$
$654$	1.44382	0.0564580
$655$	−41.8767	−1.63626
$656$	−0.632434	−0.0246924
$657$	9.74165	0.380058
$658$	6.83739	0.266549
$659$	−32.6045	−1.27009	−0.635045	−	0.772475i	$-0.719019\pi$
$659$	−32.6045	−1.27009	−0.635045	+	0.772475i	$0.719019\pi$
$660$	−17.4217	−0.678139
$661$	−0.619242	−0.0240857	−0.0120429	−	0.999927i	$-0.503833\pi$
$661$	−0.619242	−0.0240857	−0.0120429	+	0.999927i	$0.503833\pi$
$662$	−3.58950	−0.139510
$663$	6.11205	0.237372
$664$	−35.7439	−1.38713
$665$	32.5650	1.26282
$666$	−1.06010	−0.0410782
$667$	−11.1126	−0.430280
$668$	−5.81558	−0.225012
$669$	30.3268	1.17250
$670$	−1.01864	−0.0393535
$671$	−9.82594	−0.379326
$672$	10.2288	0.394585
$673$	−31.4894	−1.21383	−0.606913	−	0.794768i	$-0.707592\pi$
$673$	−31.4894	−1.21383	−0.606913	+	0.794768i	$0.707592\pi$
$674$	−25.6741	−0.988929
$675$	−48.3202	−1.85985
$676$	9.36878	0.360338
$677$	−33.6080	−1.29166	−0.645831	−	0.763481i	$-0.723489\pi$
$677$	−33.6080	−1.29166	−0.645831	+	0.763481i	$0.723489\pi$
$678$	6.88640	0.264471
$679$	3.77550	0.144890
$680$	−27.7726	−1.06503
$681$	−5.79189	−0.221946
$682$	29.3025	1.12205
$683$	−5.97281	−0.228543	−0.114272	−	0.993450i	$-0.536453\pi$
$683$	−5.97281	−0.228543	−0.114272	+	0.993450i	$0.536453\pi$
$684$	5.63883	0.215606
$685$	24.7968	0.947437
$686$	−18.2987	−0.698649
$687$	−30.5479	−1.16547
$688$	−12.3487	−0.470789
$689$	−20.0022	−0.762022
$690$	12.9248	0.492037
$691$	25.2145	0.959205	0.479602	−	0.877486i	$-0.340781\pi$
$691$	25.2145	0.959205	0.479602	+	0.877486i	$0.340781\pi$
$692$	14.5633	0.553615
$693$	−5.62086	−0.213519
$694$	8.67209	0.329188
$695$	−25.9722	−0.985180
$696$	−19.4023	−0.735441
$697$	1.28195	0.0485575
$698$	−5.21655	−0.197450
$699$	−12.6666	−0.479097
$700$	12.2472	0.462901
$701$	3.02804	0.114368	0.0571838	−	0.998364i	$-0.481788\pi$
$701$	3.02804	0.114368	0.0571838	+	0.998364i	$0.481788\pi$
$702$	10.1628	0.383569
$703$	−5.81181	−0.219197
$704$	−26.4582	−0.997182
$705$	−22.5430	−0.849018
$706$	−1.78033	−0.0670035
$707$	20.3382	0.764897
$708$	−18.0777	−0.679402
$709$	−12.8240	−0.481615	−0.240807	−	0.970573i	$-0.577412\pi$
$709$	−12.8240	−0.481615	−0.240807	+	0.970573i	$0.577412\pi$
$710$	−12.2441	−0.459513
$711$	−4.73415	−0.177544
$712$	−2.54751	−0.0954720
$713$	19.3391	0.724255
$714$	5.48223	0.205167
$715$	23.0247	0.861074
$716$	−1.04305	−0.0389807
$717$	18.6389	0.696084
$718$	20.3373	0.758983
$719$	33.6227	1.25392	0.626958	−	0.779053i	$-0.284300\pi$
$719$	33.6227	1.25392	0.626958	+	0.779053i	$0.284300\pi$
$720$	−4.66519	−0.173862
$721$	7.54002	0.280805
$722$	−15.2027	−0.565786
$723$	24.0167	0.893192
$724$	13.8728	0.515578
$725$	−39.0256	−1.44937
$726$	−2.64925	−0.0983230
$727$	9.01944	0.334513	0.167256	−	0.985913i	$-0.446509\pi$
$727$	9.01944	0.334513	0.167256	+	0.985913i	$0.446509\pi$
$728$	−8.04716	−0.298248
$729$	28.8090	1.06700
$730$	−35.7926	−1.32474
$731$	25.0310	0.925803
$732$	−3.62427	−0.133957
$733$	−21.0463	−0.777364	−0.388682	−	0.921372i	$-0.627069\pi$
$733$	−21.0463	−0.777364	−0.388682	+	0.921372i	$0.627069\pi$
$734$	−6.99474	−0.258181
$735$	24.1790	0.891855
$736$	−11.6442	−0.429210
$737$	0.963910	0.0355061
$738$	0.544961	0.0200603
$739$	−33.3480	−1.22673	−0.613363	−	0.789801i	$-0.710184\pi$
$739$	−33.3480	−1.22673	−0.613363	+	0.789801i	$0.710184\pi$
$740$	−3.46505	−0.127378
$741$	14.2444	0.523280
$742$	−17.9410	−0.658636
$743$	−15.4434	−0.566562	−0.283281	−	0.959037i	$-0.591423\pi$
$743$	−15.4434	−0.566562	−0.283281	+	0.959037i	$0.591423\pi$
$744$	33.7656	1.23791
$745$	33.7034	1.23480
$746$	21.5985	0.790779
$747$	12.1706	0.445298
$748$	8.41219	0.307580
$749$	−18.8264	−0.687903
$750$	18.8232	0.687325
$751$	−33.5823	−1.22544	−0.612719	−	0.790301i	$-0.709924\pi$
$751$	−33.5823	−1.22544	−0.612719	+	0.790301i	$0.709924\pi$
$752$	−5.36998	−0.195823
$753$	−6.13303	−0.223500
$754$	8.20790	0.298914
$755$	41.0900	1.49542
$756$	−8.10927	−0.294931
$757$	0.440230	0.0160004	0.00800021	−	0.999968i	$-0.497453\pi$
$757$	0.440230	0.0160004	0.00800021	+	0.999968i	$0.497453\pi$
$758$	−21.5966	−0.784423
$759$	−12.2303	−0.443933
$760$	−64.7251	−2.34783
$761$	−51.4032	−1.86336	−0.931682	−	0.363274i	$-0.881659\pi$
$761$	−51.4032	−1.86336	−0.931682	+	0.363274i	$0.881659\pi$
$762$	−15.4919	−0.561212
$763$	1.52261	0.0551220
$764$	19.8716	0.718928
$765$	9.45642	0.341897
$766$	11.4074	0.412166
$767$	23.8917	0.862678
$768$	−23.5819	−0.850938
$769$	−2.43789	−0.0879127	−0.0439563	−	0.999033i	$-0.513996\pi$
$769$	−2.43789	−0.0879127	−0.0439563	+	0.999033i	$0.513996\pi$
$770$	20.6521	0.744250
$771$	8.38161	0.301856
$772$	10.2581	0.369196
$773$	−2.59223	−0.0932359	−0.0466180	−	0.998913i	$-0.514844\pi$
$773$	−2.59223	−0.0932359	−0.0466180	+	0.998913i	$0.514844\pi$
$774$	10.6407	0.382472
$775$	67.9160	2.43961
$776$	−7.50406	−0.269380
$777$	2.13684	0.0766589
$778$	22.8942	0.820798
$779$	2.98764	0.107043
$780$	8.49259	0.304084
$781$	11.5862	0.414588
$782$	−6.24081	−0.223171
$783$	25.8401	0.923450
$784$	5.75970	0.205703
$785$	−45.5399	−1.62539
$786$	−16.4299	−0.586036
$787$	36.6075	1.30491	0.652457	−	0.757825i	$-0.273738\pi$
$787$	36.6075	1.30491	0.652457	+	0.757825i	$0.273738\pi$
$788$	−2.39585	−0.0853486
$789$	−3.77107	−0.134254
$790$	17.3941	0.618856
$791$	7.26215	0.258212
$792$	11.1719	0.396974
$793$	4.78987	0.170093
$794$	−8.26627	−0.293359
$795$	59.1519	2.09790
$796$	21.0683	0.746745
$797$	1.45782	0.0516385	0.0258193	−	0.999667i	$-0.491781\pi$
$797$	1.45782	0.0516385	0.0258193	+	0.999667i	$0.491781\pi$
$798$	12.7765	0.452285
$799$	10.8850	0.385085
$800$	−40.8926	−1.44577
$801$	0.867412	0.0306485
$802$	33.1522	1.17065
$803$	33.8695	1.19523
$804$	0.355536	0.0125388
$805$	13.6300	0.480394
$806$	−14.2842	−0.503138
$807$	24.7418	0.870953
$808$	−40.4236	−1.42210
$809$	−24.7234	−0.869230	−0.434615	−	0.900616i	$-0.643115\pi$
$809$	−24.7234	−0.869230	−0.434615	+	0.900616i	$0.643115\pi$
$810$	−18.3504	−0.644768
$811$	14.4798	0.508454	0.254227	−	0.967145i	$-0.418179\pi$
$811$	14.4798	0.508454	0.254227	+	0.967145i	$0.418179\pi$
$812$	−6.54941	−0.229839
$813$	−11.6947	−0.410151
$814$	−3.68574	−0.129185
$815$	49.8639	1.74666
$816$	−4.30566	−0.150728
$817$	58.3356	2.04090
$818$	−26.7659	−0.935849
$819$	2.74001	0.0957438
$820$	1.78125	0.0622041
$821$	−27.4271	−0.957212	−0.478606	−	0.878030i	$-0.658858\pi$
$821$	−27.4271	−0.957212	−0.478606	+	0.878030i	$0.658858\pi$
$822$	9.72878	0.339330
$823$	−44.5040	−1.55131	−0.775656	−	0.631156i	$-0.782581\pi$
$823$	−44.5040	−1.55131	−0.775656	+	0.631156i	$0.782581\pi$
$824$	−14.9863	−0.522073
$825$	−42.9510	−1.49536
$826$	21.4297	0.745636
$827$	32.8233	1.14138	0.570689	−	0.821167i	$-0.306676\pi$
$827$	32.8233	1.14138	0.570689	+	0.821167i	$0.306676\pi$
$828$	2.36012	0.0820197
$829$	33.7076	1.17071	0.585357	−	0.810776i	$-0.300954\pi$
$829$	33.7076	1.17071	0.585357	+	0.810776i	$0.300954\pi$
$830$	−44.7170	−1.55215
$831$	7.30893	0.253544
$832$	12.8977	0.447146
$833$	−11.6750	−0.404514
$834$	−10.1899	−0.352848
$835$	−22.7294	−0.786582
$836$	19.6049	0.678051
$837$	−44.9694	−1.55437
$838$	−41.3584	−1.42870
$839$	32.1958	1.11152	0.555762	−	0.831342i	$-0.312427\pi$
$839$	32.1958	1.11152	0.555762	+	0.831342i	$0.312427\pi$
$840$	23.7977	0.821097
$841$	−8.13037	−0.280358
$842$	18.4112	0.634491
$843$	−0.695671	−0.0239602
$844$	−11.0078	−0.378903
$845$	36.6165	1.25965
$846$	4.62725	0.159088
$847$	−2.79381	−0.0959964
$848$	14.0906	0.483874
$849$	12.6339	0.433595
$850$	−21.9168	−0.751739
$851$	−2.43252	−0.0833857
$852$	4.27355	0.146410
$853$	18.1501	0.621449	0.310724	−	0.950500i	$-0.399428\pi$
$853$	18.1501	0.621449	0.310724	+	0.950500i	$0.399428\pi$
$854$	4.29630	0.147016
$855$	22.0385	0.753702
$856$	37.4189	1.27895
$857$	−52.0977	−1.77962	−0.889812	−	0.456328i	$-0.849164\pi$
$857$	−52.0977	−1.77962	−0.889812	+	0.456328i	$0.849164\pi$
$858$	9.03350	0.308399
$859$	38.3797	1.30950	0.654750	−	0.755846i	$-0.272774\pi$
$859$	38.3797	1.30950	0.654750	+	0.755846i	$0.272774\pi$
$860$	34.7801	1.18599
$861$	−1.09847	−0.0374359
$862$	15.2703	0.520107
$863$	−14.5692	−0.495942	−0.247971	−	0.968767i	$-0.579764\pi$
$863$	−14.5692	−0.495942	−0.247971	+	0.968767i	$0.579764\pi$
$864$	27.0763	0.921155
$865$	56.9187	1.93529
$866$	26.5276	0.901444
$867$	−15.1304	−0.513855
$868$	11.3979	0.386870
$869$	−16.4596	−0.558353
$870$	−24.2730	−0.822931
$871$	−0.469879	−0.0159212
$872$	−3.02628	−0.102483
$873$	2.55509	0.0864767
$874$	−14.5444	−0.491973
$875$	19.8502	0.671060
$876$	12.4927	0.422089
$877$	−38.4272	−1.29759	−0.648797	−	0.760961i	$-0.724728\pi$
$877$	−38.4272	−1.29759	−0.648797	+	0.760961i	$0.724728\pi$
$878$	30.6743	1.03521
$879$	19.2951	0.650808
$880$	−16.2198	−0.546770
$881$	−31.1628	−1.04990	−0.524951	−	0.851133i	$-0.675916\pi$
$881$	−31.1628	−1.04990	−0.524951	+	0.851133i	$0.675916\pi$
$882$	−4.96306	−0.167115
$883$	30.6067	1.03000	0.514999	−	0.857191i	$-0.327792\pi$
$883$	30.6067	1.03000	0.514999	+	0.857191i	$0.327792\pi$
$884$	−4.10071	−0.137922
$885$	−70.6541	−2.37501
$886$	30.3849	1.02080
$887$	−36.6141	−1.22938	−0.614690	−	0.788769i	$-0.710719\pi$
$887$	−36.6141	−1.22938	−0.614690	+	0.788769i	$0.710719\pi$
$888$	−4.24713	−0.142524
$889$	−16.3372	−0.547932
$890$	−3.18703	−0.106830
$891$	17.3645	0.581731
$892$	−20.3469	−0.681265
$893$	25.3680	0.848907
$894$	13.2232	0.442250
$895$	−4.07662	−0.136267
$896$	−3.00844	−0.100505
$897$	5.96194	0.199063
$898$	−28.1586	−0.939664
$899$	−36.3193	−1.21132
$900$	8.28837	0.276279
$901$	−28.5619	−0.951534
$902$	1.89471	0.0630868
$903$	−21.4484	−0.713758
$904$	−14.4340	−0.480069
$905$	54.2198	1.80233
$906$	16.1213	0.535593
$907$	−6.32594	−0.210050	−0.105025	−	0.994470i	$-0.533492\pi$
$907$	−6.32594	−0.210050	−0.105025	+	0.994470i	$0.533492\pi$
$908$	3.88590	0.128958
$909$	13.7640	0.456523
$910$	−10.0673	−0.333728
$911$	24.6314	0.816076	0.408038	−	0.912965i	$-0.366213\pi$
$911$	24.6314	0.816076	0.408038	+	0.912965i	$0.366213\pi$
$912$	−10.0345	−0.332276
$913$	42.3144	1.40040
$914$	−3.87765	−0.128261
$915$	−14.1649	−0.468279
$916$	20.4952	0.677182
$917$	−17.3264	−0.572169
$918$	14.5118	0.478961
$919$	−0.272159	−0.00897770	−0.00448885	−	0.999990i	$-0.501429\pi$
$919$	−0.272159	−0.00897770	−0.00448885	+	0.999990i	$0.501429\pi$
$920$	−27.0905	−0.893149
$921$	−35.3834	−1.16592
$922$	−10.6842	−0.351864
$923$	−5.64797	−0.185905
$924$	−7.20819	−0.237132
$925$	−8.54264	−0.280880
$926$	−12.6138	−0.414514
$927$	5.10275	0.167596
$928$	21.8680	0.717853
$929$	21.0506	0.690647	0.345324	−	0.938484i	$-0.387769\pi$
$929$	21.0506	0.690647	0.345324	+	0.938484i	$0.387769\pi$
$930$	42.2421	1.38517
$931$	−27.2090	−0.891739
$932$	8.49833	0.278372
$933$	10.5379	0.344997
$934$	−21.6916	−0.709770
$935$	32.8778	1.07522
$936$	−5.44597	−0.178007
$937$	3.02862	0.0989406	0.0494703	−	0.998776i	$-0.484247\pi$
$937$	3.02862	0.0989406	0.0494703	+	0.998776i	$0.484247\pi$
$938$	−0.421460	−0.0137612
$939$	1.42321	0.0464445
$940$	15.1246	0.493309
$941$	−17.7348	−0.578139	−0.289070	−	0.957308i	$-0.593346\pi$
$941$	−17.7348	−0.578139	−0.289070	+	0.957308i	$0.593346\pi$
$942$	−17.8671	−0.582142
$943$	1.25047	0.0407209
$944$	−16.8306	−0.547789
$945$	−31.6939	−1.03100
$946$	36.9953	1.20282
$947$	7.70024	0.250224	0.125112	−	0.992143i	$-0.460071\pi$
$947$	7.70024	0.250224	0.125112	+	0.992143i	$0.460071\pi$
$948$	−6.07107	−0.197179
$949$	−16.5104	−0.535952
$950$	−51.0779	−1.65718
$951$	−15.4515	−0.501049
$952$	−11.4909	−0.372421
$953$	41.1888	1.33424	0.667118	−	0.744952i	$-0.267528\pi$
$953$	41.1888	1.33424	0.667118	+	0.744952i	$0.267528\pi$
$954$	−12.1417	−0.393102
$955$	77.6652	2.51319
$956$	−12.5053	−0.404449
$957$	22.9688	0.742477
$958$	33.9112	1.09562
$959$	10.2596	0.331300
$960$	−38.1419	−1.23102
$961$	32.2062	1.03891
$962$	1.79670	0.0579278
$963$	−12.7409	−0.410570
$964$	−16.1134	−0.518976
$965$	40.0922	1.29061
$966$	5.34759	0.172056
$967$	−30.7880	−0.990075	−0.495038	−	0.868872i	$-0.664846\pi$
$967$	−30.7880	−0.990075	−0.495038	+	0.868872i	$0.664846\pi$
$968$	5.55289	0.178477
$969$	20.3401	0.653418
$970$	−9.38788	−0.301427
$971$	−57.0379	−1.83043	−0.915217	−	0.402961i	$-0.867981\pi$
$971$	−57.0379	−1.83043	−0.915217	+	0.402961i	$0.867981\pi$
$972$	−9.57292	−0.307052
$973$	−10.7459	−0.344499
$974$	−31.4587	−1.00800
$975$	20.9374	0.670534
$976$	−3.37424	−0.108007
$977$	−0.777077	−0.0248609	−0.0124305	−	0.999923i	$-0.503957\pi$
$977$	−0.777077	−0.0248609	−0.0124305	+	0.999923i	$0.503957\pi$
$978$	19.5636	0.625576
$979$	3.01580	0.0963853
$980$	−16.2222	−0.518200
$981$	1.03043	0.0328992
$982$	10.2673	0.327643
$983$	−17.8992	−0.570896	−0.285448	−	0.958394i	$-0.592142\pi$
$983$	−17.8992	−0.570896	−0.285448	+	0.958394i	$0.592142\pi$
$984$	2.18329	0.0696008
$985$	−9.36384	−0.298357
$986$	11.7204	0.373253
$987$	−9.32711	−0.296885
$988$	−9.55686	−0.304044
$989$	24.4162	0.776391
$990$	13.9764	0.444200
$991$	−55.4921	−1.76276	−0.881382	−	0.472404i	$-0.843386\pi$
$991$	−55.4921	−1.76276	−0.881382	+	0.472404i	$0.843386\pi$
$992$	−38.0568	−1.20830
$993$	4.89655	0.155387
$994$	−5.06597	−0.160683
$995$	82.3423	2.61043
$996$	15.6076	0.494544
$997$	25.8445	0.818504	0.409252	−	0.912421i	$-0.365790\pi$
$997$	25.8445	0.818504	0.409252	+	0.912421i	$0.365790\pi$
$998$	27.2532	0.862684
$999$	5.65636	0.178959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.31	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.31	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.02880 q^{2} +1.40341 q^{3} -0.941581 q^{4} -3.68003 q^{5} -1.44382 q^{6} -1.52261 q^{7} +3.02628 q^{8} -1.03043 q^{9} +O(q^{10})\)	\(q-1.02880 q^{2} +1.40341 q^{3} -0.941581 q^{4} -3.68003 q^{5} -1.44382 q^{6} -1.52261 q^{7} +3.02628 q^{8} -1.03043 q^{9} +3.78600 q^{10} -3.58258 q^{11} -1.32143 q^{12} +1.74641 q^{13} +1.56645 q^{14} -5.16460 q^{15} -1.23026 q^{16} +2.49376 q^{17} +1.06010 q^{18} +5.81181 q^{19} +3.46505 q^{20} -2.13684 q^{21} +3.68574 q^{22} +2.43252 q^{23} +4.24713 q^{24} +8.54264 q^{25} -1.79670 q^{26} -5.65636 q^{27} +1.43366 q^{28} -4.56833 q^{29} +5.31332 q^{30} +7.95024 q^{31} -4.78688 q^{32} -5.02784 q^{33} -2.56557 q^{34} +5.60324 q^{35} +0.970235 q^{36} -1.00000 q^{37} -5.97917 q^{38} +2.45093 q^{39} -11.1368 q^{40} +0.514064 q^{41} +2.19837 q^{42} +10.0374 q^{43} +3.37329 q^{44} +3.79202 q^{45} -2.50257 q^{46} +4.36490 q^{47} -1.72657 q^{48} -4.68167 q^{49} -8.78862 q^{50} +3.49978 q^{51} -1.64438 q^{52} -11.4533 q^{53} +5.81924 q^{54} +13.1840 q^{55} -4.60784 q^{56} +8.15638 q^{57} +4.69987 q^{58} +13.6805 q^{59} +4.86289 q^{60} +2.74270 q^{61} -8.17916 q^{62} +1.56894 q^{63} +7.38525 q^{64} -6.42684 q^{65} +5.17262 q^{66} -0.269055 q^{67} -2.34808 q^{68} +3.41383 q^{69} -5.76458 q^{70} -3.23405 q^{71} -3.11838 q^{72} -9.45394 q^{73} +1.02880 q^{74} +11.9888 q^{75} -5.47229 q^{76} +5.45486 q^{77} -2.52151 q^{78} +4.59433 q^{79} +4.52741 q^{80} -4.84691 q^{81} -0.528866 q^{82} -11.8111 q^{83} +2.01201 q^{84} -9.17713 q^{85} -10.3264 q^{86} -6.41125 q^{87} -10.8419 q^{88} -0.841795 q^{89} -3.90122 q^{90} -2.65909 q^{91} -2.29041 q^{92} +11.1575 q^{93} -4.49059 q^{94} -21.3877 q^{95} -6.71796 q^{96} -2.47963 q^{97} +4.81648 q^{98} +3.69161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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