LMFDB - Embedded newform 401.2.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [401,2,Mod(1,401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(401, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("401.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	401.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:	$3.20200112105$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.47194 q^{2} +3.10691 q^{3} +0.166608 q^{4} +0.927390 q^{5} -4.57319 q^{6} +2.05052 q^{7} +2.69864 q^{8} +6.65291 q^{9} +O(q^{10})$	\(q-1.47194 q^{2} +3.10691 q^{3} +0.166608 q^{4} +0.927390 q^{5} -4.57319 q^{6} +2.05052 q^{7} +2.69864 q^{8} +6.65291 q^{9} -1.36506 q^{10} -4.08964 q^{11} +0.517637 q^{12} -1.13028 q^{13} -3.01824 q^{14} +2.88132 q^{15} -4.30546 q^{16} +4.27241 q^{17} -9.79269 q^{18} +2.51473 q^{19} +0.154511 q^{20} +6.37079 q^{21} +6.01971 q^{22} -3.31378 q^{23} +8.38445 q^{24} -4.13995 q^{25} +1.66371 q^{26} +11.3493 q^{27} +0.341633 q^{28} -5.02240 q^{29} -4.24113 q^{30} +4.52623 q^{31} +0.940089 q^{32} -12.7062 q^{33} -6.28873 q^{34} +1.90163 q^{35} +1.10843 q^{36} +5.63769 q^{37} -3.70153 q^{38} -3.51169 q^{39} +2.50270 q^{40} -10.1879 q^{41} -9.37742 q^{42} +4.76419 q^{43} -0.681367 q^{44} +6.16985 q^{45} +4.87769 q^{46} +9.09242 q^{47} -13.3767 q^{48} -2.79537 q^{49} +6.09376 q^{50} +13.2740 q^{51} -0.188314 q^{52} +6.04906 q^{53} -16.7055 q^{54} -3.79269 q^{55} +5.53362 q^{56} +7.81305 q^{57} +7.39267 q^{58} -11.8425 q^{59} +0.480051 q^{60} +5.17264 q^{61} -6.66233 q^{62} +13.6419 q^{63} +7.22716 q^{64} -1.04821 q^{65} +18.7027 q^{66} -5.82578 q^{67} +0.711817 q^{68} -10.2956 q^{69} -2.79909 q^{70} -8.08992 q^{71} +17.9538 q^{72} +15.1979 q^{73} -8.29835 q^{74} -12.8625 q^{75} +0.418974 q^{76} -8.38589 q^{77} +5.16899 q^{78} -5.28702 q^{79} -3.99284 q^{80} +15.3025 q^{81} +14.9960 q^{82} +5.68704 q^{83} +1.06142 q^{84} +3.96219 q^{85} -7.01260 q^{86} -15.6042 q^{87} -11.0365 q^{88} -11.2267 q^{89} -9.08164 q^{90} -2.31766 q^{91} -0.552103 q^{92} +14.0626 q^{93} -13.3835 q^{94} +2.33214 q^{95} +2.92078 q^{96} -10.4335 q^{97} +4.11461 q^{98} -27.2080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9	\( 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9} + 7 q^{10} + q^{11} - 7 q^{12} + 9 q^{13} - 11 q^{14} + q^{15} + 30 q^{16} - q^{17} - 10 q^{18} + 38 q^{19} + q^{20} + q^{21} - q^{22} + 3 q^{23} + 21 q^{24} + 26 q^{25} - 2 q^{26} + 6 q^{27} + 25 q^{28} - 4 q^{29} - 21 q^{30} + 70 q^{31} - 10 q^{32} - 8 q^{33} + 13 q^{34} + 12 q^{35} + 15 q^{36} + 3 q^{37} - 13 q^{38} + 36 q^{39} - 7 q^{40} - 2 q^{41} - 21 q^{42} + 10 q^{43} - 26 q^{44} - 21 q^{45} - 4 q^{46} + 9 q^{47} - 34 q^{48} + 39 q^{49} - 24 q^{50} - 16 q^{51} - q^{52} - 17 q^{53} + 5 q^{54} + 45 q^{55} - 65 q^{56} - 21 q^{57} - 27 q^{58} + 7 q^{59} - 66 q^{60} + 32 q^{61} - 9 q^{62} + 41 q^{63} + 22 q^{64} - 39 q^{65} - 66 q^{66} + 6 q^{67} - 46 q^{68} - 7 q^{69} - 33 q^{70} + 15 q^{71} - 73 q^{72} + 18 q^{73} - 39 q^{74} - 9 q^{75} + 48 q^{76} - 26 q^{77} - 76 q^{78} + 49 q^{79} - 51 q^{80} - 39 q^{81} - 26 q^{82} - 3 q^{83} - 81 q^{84} - q^{85} - 64 q^{86} + 15 q^{87} - 46 q^{88} - 35 q^{89} - 68 q^{90} + 34 q^{91} - 54 q^{92} - 40 q^{93} - 4 q^{94} - 6 q^{95} - 14 q^{96} - 6 q^{97} - 90 q^{98} - 36 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9 + 7 * q^10 + q^11 - 7 * q^12 + 9 * q^13 - 11 * q^14 + q^15 + 30 * q^16 - q^17 - 10 * q^18 + 38 * q^19 + q^20 + q^21 - q^22 + 3 * q^23 + 21 * q^24 + 26 * q^25 - 2 * q^26 + 6 * q^27 + 25 * q^28 - 4 * q^29 - 21 * q^30 + 70 * q^31 - 10 * q^32 - 8 * q^33 + 13 * q^34 + 12 * q^35 + 15 * q^36 + 3 * q^37 - 13 * q^38 + 36 * q^39 - 7 * q^40 - 2 * q^41 - 21 * q^42 + 10 * q^43 - 26 * q^44 - 21 * q^45 - 4 * q^46 + 9 * q^47 - 34 * q^48 + 39 * q^49 - 24 * q^50 - 16 * q^51 - q^52 - 17 * q^53 + 5 * q^54 + 45 * q^55 - 65 * q^56 - 21 * q^57 - 27 * q^58 + 7 * q^59 - 66 * q^60 + 32 * q^61 - 9 * q^62 + 41 * q^63 + 22 * q^64 - 39 * q^65 - 66 * q^66 + 6 * q^67 - 46 * q^68 - 7 * q^69 - 33 * q^70 + 15 * q^71 - 73 * q^72 + 18 * q^73 - 39 * q^74 - 9 * q^75 + 48 * q^76 - 26 * q^77 - 76 * q^78 + 49 * q^79 - 51 * q^80 - 39 * q^81 - 26 * q^82 - 3 * q^83 - 81 * q^84 - q^85 - 64 * q^86 + 15 * q^87 - 46 * q^88 - 35 * q^89 - 68 * q^90 + 34 * q^91 - 54 * q^92 - 40 * q^93 - 4 * q^94 - 6 * q^95 - 14 * q^96 - 6 * q^97 - 90 * q^98 - 36 * 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 $

$2$	−1.47194	−1.04082	−0.520409	−	0.853917i	$-0.674221\pi$
$2$	−1.47194	−1.04082	−0.520409	+	0.853917i	$0.674221\pi$
$3$	3.10691	1.79378	0.896889	−	0.442256i	$-0.145822\pi$
$3$	3.10691	1.79378	0.896889	+	0.442256i	$0.145822\pi$
$4$	0.166608	0.0833040
$5$	0.927390	0.414742	0.207371	−	0.978262i	$-0.433509\pi$
$5$	0.927390	0.414742	0.207371	+	0.978262i	$0.433509\pi$
$6$	−4.57319	−1.86700
$7$	2.05052	0.775024	0.387512	−	0.921865i	$-0.373335\pi$
$7$	2.05052	0.775024	0.387512	+	0.921865i	$0.373335\pi$
$8$	2.69864	0.954115
$9$	6.65291	2.21764
$10$	−1.36506	−0.431671
$11$	−4.08964	−1.23307	−0.616537	−	0.787326i	$-0.711465\pi$
$11$	−4.08964	−1.23307	−0.616537	+	0.787326i	$0.711465\pi$
$12$	0.517637	0.149429
$13$	−1.13028	−0.313484	−0.156742	−	0.987640i	$-0.550099\pi$
$13$	−1.13028	−0.313484	−0.156742	+	0.987640i	$0.550099\pi$
$14$	−3.01824	−0.806659
$15$	2.88132	0.743954
$16$	−4.30546	−1.07636
$17$	4.27241	1.03621	0.518106	−	0.855317i	$-0.326637\pi$
$17$	4.27241	1.03621	0.518106	+	0.855317i	$0.326637\pi$
$18$	−9.79269	−2.30816
$19$	2.51473	0.576919	0.288459	−	0.957492i	$-0.406857\pi$
$19$	2.51473	0.576919	0.288459	+	0.957492i	$0.406857\pi$
$20$	0.154511	0.0345496
$21$	6.37079	1.39022
$22$	6.01971	1.28341
$23$	−3.31378	−0.690971	−0.345486	−	0.938424i	$-0.612286\pi$
$23$	−3.31378	−0.690971	−0.345486	+	0.938424i	$0.612286\pi$
$24$	8.38445	1.71147
$25$	−4.13995	−0.827989
$26$	1.66371	0.326280
$27$	11.3493	2.18417
$28$	0.341633	0.0645626
$29$	−5.02240	−0.932636	−0.466318	−	0.884617i	$-0.654420\pi$
$29$	−5.02240	−0.932636	−0.466318	+	0.884617i	$0.654420\pi$
$30$	−4.24113	−0.774321
$31$	4.52623	0.812934	0.406467	−	0.913665i	$-0.366761\pi$
$31$	4.52623	0.812934	0.406467	+	0.913665i	$0.366761\pi$
$32$	0.940089	0.166186
$33$	−12.7062	−2.21186
$34$	−6.28873	−1.07851
$35$	1.90163	0.321435
$36$	1.10843	0.184738
$37$	5.63769	0.926831	0.463416	−	0.886141i	$-0.346624\pi$
$37$	5.63769	0.926831	0.463416	+	0.886141i	$0.346624\pi$
$38$	−3.70153	−0.600468
$39$	−3.51169	−0.562320
$40$	2.50270	0.395711
$41$	−10.1879	−1.59108	−0.795542	−	0.605899i	$-0.792814\pi$
$41$	−10.1879	−1.59108	−0.795542	+	0.605899i	$0.792814\pi$
$42$	−9.37742	−1.44697
$43$	4.76419	0.726532	0.363266	−	0.931686i	$-0.381662\pi$
$43$	4.76419	0.726532	0.363266	+	0.931686i	$0.381662\pi$
$44$	−0.681367	−0.102720
$45$	6.16985	0.919746
$46$	4.87769	0.719176
$47$	9.09242	1.32627	0.663133	−	0.748502i	$-0.269227\pi$
$47$	9.09242	1.32627	0.663133	+	0.748502i	$0.269227\pi$
$48$	−13.3767	−1.93076
$49$	−2.79537	−0.399338
$50$	6.09376	0.861787
$51$	13.2740	1.85873
$52$	−0.188314	−0.0261144
$53$	6.04906	0.830902	0.415451	−	0.909616i	$-0.363624\pi$
$53$	6.04906	0.830902	0.415451	+	0.909616i	$0.363624\pi$
$54$	−16.7055	−2.27333
$55$	−3.79269	−0.511407
$56$	5.53362	0.739461
$57$	7.81305	1.03486
$58$	7.39267	0.970705
$59$	−11.8425	−1.54176	−0.770879	−	0.636982i	$-0.780183\pi$
$59$	−11.8425	−1.54176	−0.770879	+	0.636982i	$0.780183\pi$
$60$	0.480051	0.0619743
$61$	5.17264	0.662289	0.331144	−	0.943580i	$-0.392565\pi$
$61$	5.17264	0.662289	0.331144	+	0.943580i	$0.392565\pi$
$62$	−6.66233	−0.846117
$63$	13.6419	1.71872
$64$	7.22716	0.903395
$65$	−1.04821	−0.130015
$66$	18.7027	2.30215
$67$	−5.82578	−0.711732	−0.355866	−	0.934537i	$-0.615814\pi$
$67$	−5.82578	−0.711732	−0.355866	+	0.934537i	$0.615814\pi$
$68$	0.711817	0.0863205
$69$	−10.2956	−1.23945
$70$	−2.79909	−0.334555
$71$	−8.08992	−0.960097	−0.480048	−	0.877242i	$-0.659381\pi$
$71$	−8.08992	−0.960097	−0.480048	+	0.877242i	$0.659381\pi$
$72$	17.9538	2.11588
$73$	15.1979	1.77878	0.889391	−	0.457148i	$-0.151129\pi$
$73$	15.1979	1.77878	0.889391	+	0.457148i	$0.151129\pi$
$74$	−8.29835	−0.964664
$75$	−12.8625	−1.48523
$76$	0.418974	0.0480596
$77$	−8.38589	−0.955661
$78$	5.16899	0.585273
$79$	−5.28702	−0.594836	−0.297418	−	0.954747i	$-0.596126\pi$
$79$	−5.28702	−0.594836	−0.297418	+	0.954747i	$0.596126\pi$
$80$	−3.99284	−0.446413
$81$	15.3025	1.70028
$82$	14.9960	1.65603
$83$	5.68704	0.624233	0.312117	−	0.950044i	$-0.398962\pi$
$83$	5.68704	0.624233	0.312117	+	0.950044i	$0.398962\pi$
$84$	1.06142	0.115811
$85$	3.96219	0.429760
$86$	−7.01260	−0.756188
$87$	−15.6042	−1.67294
$88$	−11.0365	−1.17649
$89$	−11.2267	−1.19002	−0.595012	−	0.803717i	$-0.702853\pi$
$89$	−11.2267	−1.19002	−0.595012	+	0.803717i	$0.702853\pi$
$90$	−9.08164	−0.957289
$91$	−2.31766	−0.242957
$92$	−0.552103	−0.0575607
$93$	14.0626	1.45822
$94$	−13.3835	−1.38040
$95$	2.33214	0.239272
$96$	2.92078	0.298101
$97$	−10.4335	−1.05936	−0.529679	−	0.848198i	$-0.677688\pi$
$97$	−10.4335	−1.05936	−0.529679	+	0.848198i	$0.677688\pi$
$98$	4.11461	0.415639
$99$	−27.2080	−2.73451
$100$	−0.689748	−0.0689748
$101$	−13.5428	−1.34756	−0.673781	−	0.738931i	$-0.735331\pi$
$101$	−13.5428	−1.34756	−0.673781	+	0.738931i	$0.735331\pi$
$102$	−19.5385	−1.93460
$103$	−17.0193	−1.67696	−0.838480	−	0.544932i	$-0.816555\pi$
$103$	−17.0193	−1.67696	−0.838480	+	0.544932i	$0.816555\pi$
$104$	−3.05023	−0.299099
$105$	5.90821	0.576582
$106$	−8.90385	−0.864818
$107$	−11.7503	−1.13594	−0.567970	−	0.823049i	$-0.692271\pi$
$107$	−11.7503	−1.13594	−0.567970	+	0.823049i	$0.692271\pi$
$108$	1.89088	0.181950
$109$	−2.80403	−0.268578	−0.134289	−	0.990942i	$-0.542875\pi$
$109$	−2.80403	−0.268578	−0.134289	+	0.990942i	$0.542875\pi$
$110$	5.58262	0.532282
$111$	17.5158	1.66253
$112$	−8.82843	−0.834208
$113$	−3.49109	−0.328414	−0.164207	−	0.986426i	$-0.552507\pi$
$113$	−3.49109	−0.328414	−0.164207	+	0.986426i	$0.552507\pi$
$114$	−11.5003	−1.07711
$115$	−3.07317	−0.286575
$116$	−0.836772	−0.0776923
$117$	−7.51966	−0.695193
$118$	17.4314	1.60469
$119$	8.76066	0.803088
$120$	7.77566	0.709817
$121$	5.72518	0.520471
$122$	−7.61382	−0.689323
$123$	−31.6529	−2.85405
$124$	0.754105	0.0677207
$125$	−8.47630	−0.758143
$126$	−20.0801	−1.78888
$127$	8.03492	0.712984	0.356492	−	0.934298i	$-0.383973\pi$
$127$	8.03492	0.712984	0.356492	+	0.934298i	$0.383973\pi$
$128$	−12.5181	−1.10646
$129$	14.8019	1.30324
$130$	1.54291	0.135322
$131$	4.70525	0.411100	0.205550	−	0.978647i	$-0.434102\pi$
$131$	4.70525	0.411100	0.205550	+	0.978647i	$0.434102\pi$
$132$	−2.11695	−0.184257
$133$	5.15651	0.447126
$134$	8.57519	0.740784
$135$	10.5252	0.905866
$136$	11.5297	0.988664
$137$	7.44801	0.636326	0.318163	−	0.948036i	$-0.396934\pi$
$137$	7.44801	0.636326	0.318163	+	0.948036i	$0.396934\pi$
$138$	15.1546	1.29004
$139$	8.39161	0.711767	0.355883	−	0.934530i	$-0.384180\pi$
$139$	8.39161	0.711767	0.355883	+	0.934530i	$0.384180\pi$
$140$	0.316827	0.0267768
$141$	28.2494	2.37902
$142$	11.9079	0.999287
$143$	4.62245	0.386548
$144$	−28.6438	−2.38699
$145$	−4.65772	−0.386803
$146$	−22.3704	−1.85139
$147$	−8.68497	−0.716324
$148$	0.939285	0.0772087
$149$	−11.4652	−0.939264	−0.469632	−	0.882862i	$-0.655613\pi$
$149$	−11.4652	−0.939264	−0.469632	+	0.882862i	$0.655613\pi$
$150$	18.9328	1.54585
$151$	19.4533	1.58308	0.791542	−	0.611115i	$-0.209279\pi$
$151$	19.4533	1.58308	0.791542	+	0.611115i	$0.209279\pi$
$152$	6.78636	0.550447
$153$	28.4240	2.29794
$154$	12.3435	0.994670
$155$	4.19758	0.337158
$156$	−0.585075	−0.0468435
$157$	4.67586	0.373174	0.186587	−	0.982438i	$-0.440257\pi$
$157$	4.67586	0.373174	0.186587	+	0.982438i	$0.440257\pi$
$158$	7.78218	0.619117
$159$	18.7939	1.49045
$160$	0.871830	0.0689242
$161$	−6.79498	−0.535519
$162$	−22.5244	−1.76968
$163$	−15.4622	−1.21109	−0.605546	−	0.795810i	$-0.707045\pi$
$163$	−15.4622	−1.21109	−0.605546	+	0.795810i	$0.707045\pi$
$164$	−1.69739	−0.132544
$165$	−11.7836	−0.917350
$166$	−8.37098	−0.649714
$167$	4.81157	0.372330	0.186165	−	0.982518i	$-0.440394\pi$
$167$	4.81157	0.372330	0.186165	+	0.982518i	$0.440394\pi$
$168$	17.1925	1.32643
$169$	−11.7225	−0.901728
$170$	−5.83211	−0.447302
$171$	16.7303	1.27940
$172$	0.793751	0.0605230
$173$	−23.4562	−1.78334	−0.891672	−	0.452682i	$-0.850467\pi$
$173$	−23.4562	−1.78334	−0.891672	+	0.452682i	$0.850467\pi$
$174$	22.9684	1.74123
$175$	−8.48905	−0.641712
$176$	17.6078	1.32724
$177$	−36.7935	−2.76557
$178$	16.5250	1.23860
$179$	−18.8856	−1.41158	−0.705789	−	0.708422i	$-0.749407\pi$
$179$	−18.8856	−1.41158	−0.705789	+	0.708422i	$0.749407\pi$
$180$	1.02795	0.0766185
$181$	8.69552	0.646333	0.323167	−	0.946342i	$-0.395253\pi$
$181$	8.69552	0.646333	0.323167	+	0.946342i	$0.395253\pi$
$182$	3.41146	0.252875
$183$	16.0709	1.18800
$184$	−8.94272	−0.659266
$185$	5.22834	0.384395
$186$	−20.6993	−1.51775
$187$	−17.4726	−1.27772
$188$	1.51487	0.110483
$189$	23.2719	1.69278
$190$	−3.43277	−0.249039
$191$	8.58300	0.621044	0.310522	−	0.950566i	$-0.399496\pi$
$191$	8.58300	0.621044	0.310522	+	0.950566i	$0.399496\pi$
$192$	22.4542	1.62049
$193$	21.5933	1.55432	0.777160	−	0.629303i	$-0.216660\pi$
$193$	21.5933	1.55432	0.777160	+	0.629303i	$0.216660\pi$
$194$	15.3574	1.10260
$195$	−3.25670	−0.233217
$196$	−0.465731	−0.0332665
$197$	19.3951	1.38184	0.690922	−	0.722930i	$-0.257205\pi$
$197$	19.3951	1.38184	0.690922	+	0.722930i	$0.257205\pi$
$198$	40.0486	2.84613
$199$	0.846591	0.0600133	0.0300066	−	0.999550i	$-0.490447\pi$
$199$	0.846591	0.0600133	0.0300066	+	0.999550i	$0.490447\pi$
$200$	−11.1722	−0.789997
$201$	−18.1002	−1.27669
$202$	19.9342	1.40257
$203$	−10.2985	−0.722815
$204$	2.21155	0.154840
$205$	−9.44816	−0.659888
$206$	25.0514	1.74541
$207$	−22.0463	−1.53232
$208$	4.86638	0.337423
$209$	−10.2844	−0.711383
$210$	−8.69653	−0.600117
$211$	−14.0435	−0.966796	−0.483398	−	0.875401i	$-0.660598\pi$
$211$	−14.0435	−0.966796	−0.483398	+	0.875401i	$0.660598\pi$
$212$	1.00782	0.0692174
$213$	−25.1347	−1.72220
$214$	17.2957	1.18231
$215$	4.41826	0.301323
$216$	30.6277	2.08395
$217$	9.28112	0.630043
$218$	4.12737	0.279541
$219$	47.2186	3.19074
$220$	−0.631893	−0.0426022
$221$	−4.82902	−0.324835
$222$	−25.7823	−1.73039
$223$	22.0389	1.47584	0.737918	−	0.674890i	$-0.235809\pi$
$223$	22.0389	1.47584	0.737918	+	0.674890i	$0.235809\pi$
$224$	1.92767	0.128798
$225$	−27.5427	−1.83618
$226$	5.13868	0.341820
$227$	17.7452	1.17779	0.588896	−	0.808209i	$-0.299563\pi$
$227$	17.7452	1.17779	0.588896	+	0.808209i	$0.299563\pi$
$228$	1.30172	0.0862083
$229$	11.3853	0.752364	0.376182	−	0.926546i	$-0.377237\pi$
$229$	11.3853	0.752364	0.376182	+	0.926546i	$0.377237\pi$
$230$	4.52352	0.298272
$231$	−26.0543	−1.71424
$232$	−13.5537	−0.889841
$233$	−9.27555	−0.607661	−0.303831	−	0.952726i	$-0.598266\pi$
$233$	−9.27555	−0.607661	−0.303831	+	0.952726i	$0.598266\pi$
$234$	11.0685	0.723570
$235$	8.43222	0.550057
$236$	−1.97305	−0.128435
$237$	−16.4263	−1.06700
$238$	−12.8952	−0.835869
$239$	11.7902	0.762642	0.381321	−	0.924443i	$-0.375469\pi$
$239$	11.7902	0.762642	0.381321	+	0.924443i	$0.375469\pi$
$240$	−12.4054	−0.800766
$241$	15.5813	1.00368	0.501841	−	0.864960i	$-0.332656\pi$
$241$	15.5813	1.00368	0.501841	+	0.864960i	$0.332656\pi$
$242$	−8.42712	−0.541716
$243$	13.4957	0.865750
$244$	0.861803	0.0551713
$245$	−2.59240	−0.165622
$246$	46.5912	2.97055
$247$	−2.84235	−0.180855
$248$	12.2147	0.775632
$249$	17.6691	1.11974
$250$	12.4766	0.789090
$251$	−0.246411	−0.0155533	−0.00777665	−	0.999970i	$-0.502475\pi$
$251$	−0.246411	−0.0155533	−0.00777665	+	0.999970i	$0.502475\pi$
$252$	2.27285	0.143176
$253$	13.5522	0.852019
$254$	−11.8269	−0.742087
$255$	12.3102	0.770893
$256$	3.97161	0.248226
$257$	10.0259	0.625399	0.312700	−	0.949852i	$-0.398767\pi$
$257$	10.0259	0.625399	0.312700	+	0.949852i	$0.398767\pi$
$258$	−21.7875	−1.35643
$259$	11.5602	0.718316
$260$	−0.174640	−0.0108307
$261$	−33.4136	−2.06825
$262$	−6.92585	−0.427881
$263$	24.9911	1.54102	0.770510	−	0.637428i	$-0.220002\pi$
$263$	24.9911	1.54102	0.770510	+	0.637428i	$0.220002\pi$
$264$	−34.2894	−2.11037
$265$	5.60984	0.344609
$266$	−7.59007	−0.465377
$267$	−34.8803	−2.13464
$268$	−0.970621	−0.0592901
$269$	−10.8100	−0.659097	−0.329548	−	0.944139i	$-0.606896\pi$
$269$	−10.8100	−0.659097	−0.329548	+	0.944139i	$0.606896\pi$
$270$	−15.4925	−0.942843
$271$	−1.88024	−0.114216	−0.0571082	−	0.998368i	$-0.518188\pi$
$271$	−1.88024	−0.114216	−0.0571082	+	0.998368i	$0.518188\pi$
$272$	−18.3947	−1.11534
$273$	−7.20078	−0.435811
$274$	−10.9630	−0.662300
$275$	16.9309	1.02097
$276$	−1.71534	−0.103251
$277$	5.12906	0.308175	0.154088	−	0.988057i	$-0.450756\pi$
$277$	5.12906	0.308175	0.154088	+	0.988057i	$0.450756\pi$
$278$	−12.3519	−0.740820
$279$	30.1126	1.80279
$280$	5.13183	0.306685
$281$	18.7444	1.11820	0.559100	−	0.829100i	$-0.311147\pi$
$281$	18.7444	1.11820	0.559100	+	0.829100i	$0.311147\pi$
$282$	−41.5814	−2.47613
$283$	−13.2277	−0.786304	−0.393152	−	0.919474i	$-0.628615\pi$
$283$	−13.2277	−0.786304	−0.393152	+	0.919474i	$0.628615\pi$
$284$	−1.34785	−0.0799799
$285$	7.24575	0.429201
$286$	−6.80397	−0.402327
$287$	−20.8905	−1.23313
$288$	6.25433	0.368540
$289$	1.25347	0.0737337
$290$	6.85589	0.402592
$291$	−32.4159	−1.90025
$292$	2.53209	0.148180
$293$	25.4385	1.48614	0.743068	−	0.669216i	$-0.233370\pi$
$293$	25.4385	1.48614	0.743068	+	0.669216i	$0.233370\pi$
$294$	12.7837	0.745563
$295$	−10.9826	−0.639431
$296$	15.2141	0.884303
$297$	−46.4145	−2.69324
$298$	16.8761	0.977603
$299$	3.74551	0.216608
$300$	−2.14299	−0.123725
$301$	9.76906	0.563079
$302$	−28.6340	−1.64770
$303$	−42.0764	−2.41723
$304$	−10.8271	−0.620975
$305$	4.79706	0.274679
$306$	−41.8384	−2.39174
$307$	4.38569	0.250305	0.125152	−	0.992138i	$-0.460058\pi$
$307$	4.38569	0.250305	0.125152	+	0.992138i	$0.460058\pi$
$308$	−1.39716	−0.0796104
$309$	−52.8775	−3.00809
$310$	−6.17858	−0.350920
$311$	14.8923	0.844467	0.422233	−	0.906487i	$-0.361246\pi$
$311$	14.8923	0.844467	0.422233	+	0.906487i	$0.361246\pi$
$312$	−9.47679	−0.536518
$313$	−16.0710	−0.908385	−0.454192	−	0.890904i	$-0.650072\pi$
$313$	−16.0710	−0.908385	−0.454192	+	0.890904i	$0.650072\pi$
$314$	−6.88259	−0.388407
$315$	12.6514	0.712825
$316$	−0.880860	−0.0495522
$317$	7.21073	0.404995	0.202497	−	0.979283i	$-0.435094\pi$
$317$	7.21073	0.404995	0.202497	+	0.979283i	$0.435094\pi$
$318$	−27.6635	−1.55129
$319$	20.5398	1.15001
$320$	6.70240	0.374675
$321$	−36.5070	−2.03762
$322$	10.0018	0.557379
$323$	10.7440	0.597810
$324$	2.54952	0.141640
$325$	4.67931	0.259561
$326$	22.7594	1.26053
$327$	−8.71189	−0.481769
$328$	−27.4935	−1.51808
$329$	18.6442	1.02789
$330$	17.3447	0.954795
$331$	29.3442	1.61290	0.806451	−	0.591301i	$-0.201385\pi$
$331$	29.3442	1.61290	0.806451	+	0.591301i	$0.201385\pi$
$332$	0.947506	0.0520011
$333$	37.5071	2.05538
$334$	−7.08234	−0.387528
$335$	−5.40277	−0.295185
$336$	−27.4292	−1.49638
$337$	−24.9819	−1.36085	−0.680425	−	0.732818i	$-0.738205\pi$
$337$	−24.9819	−1.36085	−0.680425	+	0.732818i	$0.738205\pi$
$338$	17.2548	0.938536
$339$	−10.8465	−0.589102
$340$	0.660132	0.0358007
$341$	−18.5106	−1.00241
$342$	−24.6260	−1.33162
$343$	−20.0856	−1.08452
$344$	12.8568	0.693194
$345$	−9.54807	−0.514051
$346$	34.5262	1.85614
$347$	31.7171	1.70266	0.851331	−	0.524629i	$-0.175796\pi$
$347$	31.7171	1.70266	0.851331	+	0.524629i	$0.175796\pi$
$348$	−2.59978	−0.139363
$349$	−28.2234	−1.51077	−0.755383	−	0.655284i	$-0.772549\pi$
$349$	−28.2234	−1.51077	−0.755383	+	0.655284i	$0.772549\pi$
$350$	12.4954	0.667905
$351$	−12.8279	−0.684702
$352$	−3.84463	−0.204919
$353$	−19.1905	−1.02141	−0.510705	−	0.859756i	$-0.670615\pi$
$353$	−19.1905	−1.02141	−0.510705	+	0.859756i	$0.670615\pi$
$354$	54.1578	2.87846
$355$	−7.50251	−0.398192
$356$	−1.87045	−0.0991337
$357$	27.2186	1.44056
$358$	27.7985	1.46920
$359$	26.9116	1.42034	0.710170	−	0.704030i	$-0.248618\pi$
$359$	26.9116	1.42034	0.710170	+	0.704030i	$0.248618\pi$
$360$	16.6502	0.877543
$361$	−12.6761	−0.667165
$362$	−12.7993	−0.672716
$363$	17.7876	0.933609
$364$	−0.386141	−0.0202393
$365$	14.0944	0.737734
$366$	−23.6555	−1.23649
$367$	0.219152	0.0114397	0.00571983	−	0.999984i	$-0.498179\pi$
$367$	0.219152	0.0114397	0.00571983	+	0.999984i	$0.498179\pi$
$368$	14.2674	0.743737
$369$	−67.7792	−3.52845
$370$	−7.69581	−0.400086
$371$	12.4037	0.643969
$372$	2.34294	0.121476
$373$	−16.0466	−0.830863	−0.415432	−	0.909624i	$-0.636369\pi$
$373$	−16.0466	−0.830863	−0.415432	+	0.909624i	$0.636369\pi$
$374$	25.7187	1.32988
$375$	−26.3351	−1.35994
$376$	24.5372	1.26541
$377$	5.67672	0.292366
$378$	−34.2549	−1.76188
$379$	15.9938	0.821545	0.410773	−	0.911738i	$-0.365259\pi$
$379$	15.9938	0.821545	0.410773	+	0.911738i	$0.365259\pi$
$380$	0.388553	0.0199323
$381$	24.9638	1.27893
$382$	−12.6337	−0.646395
$383$	−33.8895	−1.73167	−0.865837	−	0.500326i	$-0.833213\pi$
$383$	−33.8895	−1.73167	−0.865837	+	0.500326i	$0.833213\pi$
$384$	−38.8927	−1.98474
$385$	−7.77700	−0.396352
$386$	−31.7840	−1.61776
$387$	31.6957	1.61118
$388$	−1.73830	−0.0882488
$389$	37.5984	1.90632	0.953158	−	0.302473i	$-0.0978123\pi$
$389$	37.5984	1.90632	0.953158	+	0.302473i	$0.0978123\pi$
$390$	4.79367	0.242737
$391$	−14.1578	−0.715992
$392$	−7.54370	−0.381014
$393$	14.6188	0.737422
$394$	−28.5484	−1.43825
$395$	−4.90313	−0.246703
$396$	−4.53308	−0.227796
$397$	−23.0638	−1.15754	−0.578769	−	0.815492i	$-0.696467\pi$
$397$	−23.0638	−1.15754	−0.578769	+	0.815492i	$0.696467\pi$
$398$	−1.24613	−0.0624629
$399$	16.0208	0.802044
$400$	17.8244	0.891218
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	26.6424	1.32880
$403$	−5.11591	−0.254842
$404$	−2.25634	−0.112257
$405$	14.1914	0.705176
$406$	15.1588	0.752319
$407$	−23.0562	−1.14285
$408$	35.8218	1.77344
$409$	0.531940	0.0263027	0.0131514	−	0.999914i	$-0.495814\pi$
$409$	0.531940	0.0263027	0.0131514	+	0.999914i	$0.495814\pi$
$410$	13.9071	0.686824
$411$	23.1403	1.14143
$412$	−2.83555	−0.139697
$413$	−24.2832	−1.19490
$414$	32.4508	1.59487
$415$	5.27410	0.258895
$416$	−1.06257	−0.0520966
$417$	26.0720	1.27675
$418$	15.1379	0.740421
$419$	5.45265	0.266379	0.133190	−	0.991091i	$-0.457478\pi$
$419$	5.45265	0.266379	0.133190	+	0.991091i	$0.457478\pi$
$420$	0.984354	0.0480316
$421$	16.3488	0.796793	0.398397	−	0.917213i	$-0.369567\pi$
$421$	16.3488	0.796793	0.398397	+	0.917213i	$0.369567\pi$
$422$	20.6712	1.00626
$423$	60.4911	2.94118
$424$	16.3242	0.792775
$425$	−17.6875	−0.857972
$426$	36.9967	1.79250
$427$	10.6066	0.513290
$428$	−1.95769	−0.0946283
$429$	14.3615	0.693382
$430$	−6.50341	−0.313622
$431$	33.4717	1.61227	0.806137	−	0.591729i	$-0.201555\pi$
$431$	33.4717	1.61227	0.806137	+	0.591729i	$0.201555\pi$
$432$	−48.8639	−2.35096
$433$	−4.60044	−0.221083	−0.110542	−	0.993871i	$-0.535259\pi$
$433$	−4.60044	−0.221083	−0.110542	+	0.993871i	$0.535259\pi$
$434$	−13.6613	−0.655761
$435$	−14.4711	−0.693838
$436$	−0.467174	−0.0223736
$437$	−8.33327	−0.398634
$438$	−69.5030	−3.32098
$439$	−3.01525	−0.143910	−0.0719549	−	0.997408i	$-0.522924\pi$
$439$	−3.01525	−0.143910	−0.0719549	+	0.997408i	$0.522924\pi$
$440$	−10.2351	−0.487941
$441$	−18.5973	−0.885587
$442$	7.10803	0.338095
$443$	1.77532	0.0843480	0.0421740	−	0.999110i	$-0.486572\pi$
$443$	1.77532	0.0843480	0.0421740	+	0.999110i	$0.486572\pi$
$444$	2.91828	0.138495
$445$	−10.4115	−0.493552
$446$	−32.4400	−1.53608
$447$	−35.6213	−1.68483
$448$	14.8194	0.700153
$449$	−31.8489	−1.50304	−0.751521	−	0.659710i	$-0.770679\pi$
$449$	−31.8489	−1.50304	−0.751521	+	0.659710i	$0.770679\pi$
$450$	40.5412	1.91113
$451$	41.6649	1.96192
$452$	−0.581643	−0.0273582
$453$	60.4396	2.83970
$454$	−26.1199	−1.22587
$455$	−2.14938	−0.100764
$456$	21.0846	0.987379
$457$	−36.5721	−1.71077	−0.855386	−	0.517991i	$-0.826680\pi$
$457$	−36.5721	−1.71077	−0.855386	+	0.517991i	$0.826680\pi$
$458$	−16.7585	−0.783075
$459$	48.4888	2.26326
$460$	−0.512015	−0.0238728
$461$	−39.1828	−1.82492	−0.912462	−	0.409163i	$-0.865821\pi$
$461$	−39.1828	−1.82492	−0.912462	+	0.409163i	$0.865821\pi$
$462$	38.3503	1.78422
$463$	29.3247	1.36283	0.681416	−	0.731896i	$-0.261364\pi$
$463$	29.3247	1.36283	0.681416	+	0.731896i	$0.261364\pi$
$464$	21.6237	1.00386
$465$	13.0415	0.604786
$466$	13.6531	0.632465
$467$	5.86015	0.271175	0.135588	−	0.990765i	$-0.456708\pi$
$467$	5.86015	0.271175	0.135588	+	0.990765i	$0.456708\pi$
$468$	−1.25284	−0.0579124
$469$	−11.9459	−0.551609
$470$	−12.4117	−0.572510
$471$	14.5275	0.669392
$472$	−31.9586	−1.47101
$473$	−19.4838	−0.895867
$474$	24.1786	1.11056
$475$	−10.4109	−0.477683
$476$	1.45960	0.0669005
$477$	40.2438	1.84264
$478$	−17.3544	−0.793773
$479$	20.7665	0.948847	0.474424	−	0.880297i	$-0.342656\pi$
$479$	20.7665	0.948847	0.474424	+	0.880297i	$0.342656\pi$
$480$	2.70870	0.123635
$481$	−6.37218	−0.290546
$482$	−22.9348	−1.04465
$483$	−21.1114	−0.960602
$484$	0.953860	0.0433573
$485$	−9.67590	−0.439360
$486$	−19.8649	−0.901089
$487$	−0.970333	−0.0439700	−0.0219850	−	0.999758i	$-0.506999\pi$
$487$	−0.970333	−0.0439700	−0.0219850	+	0.999758i	$0.506999\pi$
$488$	13.9591	0.631899
$489$	−48.0397	−2.17243
$490$	3.81585	0.172383
$491$	12.4328	0.561083	0.280541	−	0.959842i	$-0.409486\pi$
$491$	12.4328	0.561083	0.280541	+	0.959842i	$0.409486\pi$
$492$	−5.27363	−0.237754
$493$	−21.4577	−0.966408
$494$	4.18377	0.188237
$495$	−25.2325	−1.13411
$496$	−19.4875	−0.875013
$497$	−16.5885	−0.744098
$498$	−26.0079	−1.16544
$499$	−22.0439	−0.986821	−0.493410	−	0.869797i	$-0.664250\pi$
$499$	−22.0439	−0.986821	−0.493410	+	0.869797i	$0.664250\pi$
$500$	−1.41222	−0.0631563
$501$	14.9491	0.667878
$502$	0.362702	0.0161882
$503$	42.9352	1.91439	0.957194	−	0.289448i	$-0.0934718\pi$
$503$	42.9352	1.91439	0.957194	+	0.289448i	$0.0934718\pi$
$504$	36.8147	1.63986
$505$	−12.5595	−0.558890
$506$	−19.9480	−0.886797
$507$	−36.4207	−1.61750
$508$	1.33868	0.0593944
$509$	−18.4564	−0.818064	−0.409032	−	0.912520i	$-0.634133\pi$
$509$	−18.4564	−0.818064	−0.409032	+	0.912520i	$0.634133\pi$
$510$	−18.1199	−0.802360
$511$	31.1636	1.37860
$512$	19.1903	0.848098
$513$	28.5404	1.26009
$514$	−14.7575	−0.650927
$515$	−15.7835	−0.695505
$516$	2.46612	0.108565
$517$	−37.1847	−1.63538
$518$	−17.0159	−0.747637
$519$	−72.8765	−3.19892
$520$	−2.82875	−0.124049
$521$	18.0675	0.791551	0.395775	−	0.918347i	$-0.370476\pi$
$521$	18.0675	0.791551	0.395775	+	0.918347i	$0.370476\pi$
$522$	49.1828	2.15267
$523$	9.18654	0.401699	0.200850	−	0.979622i	$-0.435630\pi$
$523$	9.18654	0.401699	0.200850	+	0.979622i	$0.435630\pi$
$524$	0.783933	0.0342463
$525$	−26.3747	−1.15109
$526$	−36.7855	−1.60392
$527$	19.3379	0.842372
$528$	54.7059	2.38077
$529$	−12.0188	−0.522558
$530$	−8.25734	−0.358676
$531$	−78.7869	−3.41906
$532$	0.859115	0.0372474
$533$	11.5152	0.498779
$534$	51.3416	2.22177
$535$	−10.8971	−0.471121
$536$	−15.7217	−0.679074
$537$	−58.6760	−2.53206
$538$	15.9117	0.686000
$539$	11.4321	0.492413
$540$	1.75358	0.0754623
$541$	30.3806	1.30616	0.653082	−	0.757287i	$-0.273476\pi$
$541$	30.3806	1.30616	0.653082	+	0.757287i	$0.273476\pi$
$542$	2.76760	0.118878
$543$	27.0162	1.15938
$544$	4.01645	0.172204
$545$	−2.60043	−0.111390
$546$	10.5991	0.453601
$547$	−9.13164	−0.390441	−0.195220	−	0.980759i	$-0.562542\pi$
$547$	−9.13164	−0.390441	−0.195220	+	0.980759i	$0.562542\pi$
$548$	1.24090	0.0530085
$549$	34.4131	1.46872
$550$	−24.9213	−1.06265
$551$	−12.6300	−0.538055
$552$	−27.7843	−1.18258
$553$	−10.8411	−0.461012
$554$	−7.54967	−0.320755
$555$	16.2440	0.689520
$556$	1.39811	0.0592930
$557$	42.2364	1.78961	0.894807	−	0.446452i	$-0.147313\pi$
$557$	42.2364	1.78961	0.894807	+	0.446452i	$0.147313\pi$
$558$	−44.3239	−1.87638
$559$	−5.38487	−0.227756
$560$	−8.18740	−0.345981
$561$	−54.2859	−2.29195
$562$	−27.5907	−1.16384
$563$	−40.2677	−1.69708	−0.848541	−	0.529130i	$-0.822518\pi$
$563$	−40.2677	−1.69708	−0.848541	+	0.529130i	$0.822518\pi$
$564$	4.70657	0.198182
$565$	−3.23760	−0.136207
$566$	19.4704	0.818400
$567$	31.3781	1.31776
$568$	−21.8318	−0.916042
$569$	5.00703	0.209906	0.104953	−	0.994477i	$-0.466531\pi$
$569$	5.00703	0.209906	0.104953	+	0.994477i	$0.466531\pi$
$570$	−10.6653	−0.446721
$571$	−4.94807	−0.207070	−0.103535	−	0.994626i	$-0.533015\pi$
$571$	−4.94807	−0.207070	−0.103535	+	0.994626i	$0.533015\pi$
$572$	0.770137	0.0322010
$573$	26.6666	1.11402
$574$	30.7496	1.28346
$575$	13.7189	0.572117
$576$	48.0817	2.00340
$577$	37.8859	1.57721	0.788605	−	0.614900i	$-0.210803\pi$
$577$	37.8859	1.57721	0.788605	+	0.614900i	$0.210803\pi$
$578$	−1.84504	−0.0767435
$579$	67.0885	2.78810
$580$	−0.776014	−0.0322222
$581$	11.6614	0.483796
$582$	47.7143	1.97782
$583$	−24.7385	−1.02456
$584$	41.0138	1.69716
$585$	−6.97366	−0.288325
$586$	−37.4440	−1.54680
$587$	21.2828	0.878434	0.439217	−	0.898381i	$-0.355256\pi$
$587$	21.2828	0.878434	0.439217	+	0.898381i	$0.355256\pi$
$588$	−1.44698	−0.0596726
$589$	11.3822	0.468997
$590$	16.1657	0.665532
$591$	60.2589	2.47872
$592$	−24.2729	−0.997608
$593$	−8.30150	−0.340902	−0.170451	−	0.985366i	$-0.554522\pi$
$593$	−8.30150	−0.340902	−0.170451	+	0.985366i	$0.554522\pi$
$594$	68.3194	2.80318
$595$	8.12455	0.333074
$596$	−1.91019	−0.0782444
$597$	2.63029	0.107650
$598$	−5.51316	−0.225450
$599$	−20.5248	−0.838621	−0.419311	−	0.907843i	$-0.637728\pi$
$599$	−20.5248	−0.838621	−0.419311	+	0.907843i	$0.637728\pi$
$600$	−34.7112	−1.41708
$601$	42.2075	1.72168	0.860840	−	0.508875i	$-0.169938\pi$
$601$	42.2075	1.72168	0.860840	+	0.508875i	$0.169938\pi$
$602$	−14.3795	−0.586064
$603$	−38.7584	−1.57836
$604$	3.24107	0.131877
$605$	5.30947	0.215861
$606$	61.9339	2.51589
$607$	26.7238	1.08469	0.542344	−	0.840157i	$-0.317537\pi$
$607$	26.7238	1.08469	0.542344	+	0.840157i	$0.317537\pi$
$608$	2.36407	0.0958758
$609$	−31.9966	−1.29657
$610$	−7.06098	−0.285891
$611$	−10.2770	−0.415762
$612$	4.73566	0.191428
$613$	−14.5199	−0.586452	−0.293226	−	0.956043i	$-0.594729\pi$
$613$	−14.5199	−0.586452	−0.293226	+	0.956043i	$0.594729\pi$
$614$	−6.45548	−0.260522
$615$	−29.3546	−1.18369
$616$	−22.6305	−0.911810
$617$	32.3609	1.30280	0.651401	−	0.758734i	$-0.274182\pi$
$617$	32.3609	1.30280	0.651401	+	0.758734i	$0.274182\pi$
$618$	77.8325	3.13088
$619$	7.09727	0.285263	0.142632	−	0.989776i	$-0.454444\pi$
$619$	7.09727	0.285263	0.142632	+	0.989776i	$0.454444\pi$
$620$	0.699350	0.0280866
$621$	−37.6091	−1.50920
$622$	−21.9206	−0.878937
$623$	−23.0205	−0.922296
$624$	15.1194	0.605261
$625$	12.8389	0.513556
$626$	23.6555	0.945464
$627$	−31.9526	−1.27606
$628$	0.779036	0.0310869
$629$	24.0865	0.960393
$630$	−18.6221	−0.741922
$631$	46.0506	1.83324	0.916622	−	0.399755i	$-0.130905\pi$
$631$	46.0506	1.83324	0.916622	+	0.399755i	$0.130905\pi$
$632$	−14.2678	−0.567542
$633$	−43.6320	−1.73422
$634$	−10.6138	−0.421526
$635$	7.45150	0.295704
$636$	3.13121	0.124161
$637$	3.15955	0.125186
$638$	−30.2334	−1.19695
$639$	−53.8215	−2.12915
$640$	−11.6092	−0.458893
$641$	4.76637	0.188260	0.0941301	−	0.995560i	$-0.469993\pi$
$641$	4.76637	0.188260	0.0941301	+	0.995560i	$0.469993\pi$
$642$	53.7362	2.12080
$643$	−14.1073	−0.556336	−0.278168	−	0.960532i	$-0.589727\pi$
$643$	−14.1073	−0.556336	−0.278168	+	0.960532i	$0.589727\pi$
$644$	−1.13210	−0.0446109
$645$	13.7272	0.540506
$646$	−15.8145	−0.622212
$647$	−31.1578	−1.22494	−0.612470	−	0.790494i	$-0.709824\pi$
$647$	−31.1578	−1.22494	−0.612470	+	0.790494i	$0.709824\pi$
$648$	41.2960	1.62226
$649$	48.4314	1.90110
$650$	−6.88766	−0.270156
$651$	28.8356	1.13016
$652$	−2.57612	−0.100889
$653$	−6.03426	−0.236139	−0.118069	−	0.993005i	$-0.537671\pi$
$653$	−6.03426	−0.236139	−0.118069	+	0.993005i	$0.537671\pi$
$654$	12.8234	0.501434
$655$	4.36361	0.170500
$656$	43.8636	1.71259
$657$	101.110	3.94469
$658$	−27.4431	−1.06984
$659$	−2.19024	−0.0853198	−0.0426599	−	0.999090i	$-0.513583\pi$
$659$	−2.19024	−0.0853198	−0.0426599	+	0.999090i	$0.513583\pi$
$660$	−1.96324	−0.0764189
$661$	−11.6395	−0.452726	−0.226363	−	0.974043i	$-0.572684\pi$
$661$	−11.6395	−0.452726	−0.226363	+	0.974043i	$0.572684\pi$
$662$	−43.1929	−1.67874
$663$	−15.0034	−0.582682
$664$	15.3473	0.595590
$665$	4.78209	0.185442
$666$	−55.2082	−2.13927
$667$	16.6431	0.644425
$668$	0.801645	0.0310166
$669$	68.4731	2.64732
$670$	7.95255	0.307234
$671$	−21.1543	−0.816651
$672$	5.98911	0.231035
$673$	−1.99411	−0.0768675	−0.0384337	−	0.999261i	$-0.512237\pi$
$673$	−1.99411	−0.0768675	−0.0384337	+	0.999261i	$0.512237\pi$
$674$	36.7719	1.41640
$675$	−46.9854	−1.80847
$676$	−1.95306	−0.0751175
$677$	−4.81720	−0.185140	−0.0925700	−	0.995706i	$-0.529508\pi$
$677$	−4.81720	−0.185140	−0.0925700	+	0.995706i	$0.529508\pi$
$678$	15.9654	0.613148
$679$	−21.3940	−0.821028
$680$	10.6925	0.410040
$681$	55.1329	2.11270
$682$	27.2466	1.04332
$683$	−43.7981	−1.67589	−0.837944	−	0.545756i	$-0.816243\pi$
$683$	−43.7981	−1.67589	−0.837944	+	0.545756i	$0.816243\pi$
$684$	2.78740	0.106579
$685$	6.90721	0.263911
$686$	29.5648	1.12879
$687$	35.3732	1.34957
$688$	−20.5120	−0.782013
$689$	−6.83713	−0.260474
$690$	14.0542	0.535034
$691$	−51.5320	−1.96037	−0.980184	−	0.198088i	$-0.936527\pi$
$691$	−51.5320	−1.96037	−0.980184	+	0.198088i	$0.936527\pi$
$692$	−3.90799	−0.148560
$693$	−55.7906	−2.11931
$694$	−46.6856	−1.77216
$695$	7.78229	0.295199
$696$	−42.1101	−1.59618
$697$	−43.5269	−1.64870
$698$	41.5432	1.57243
$699$	−28.8183	−1.09001
$700$	−1.41434	−0.0534571
$701$	−31.0627	−1.17322	−0.586611	−	0.809869i	$-0.699538\pi$
$701$	−31.0627	−1.17322	−0.586611	+	0.809869i	$0.699538\pi$
$702$	18.8819	0.712650
$703$	14.1773	0.534706
$704$	−29.5565	−1.11395
$705$	26.1982	0.986680
$706$	28.2473	1.06310
$707$	−27.7698	−1.04439
$708$	−6.13009	−0.230383
$709$	−28.2091	−1.05942	−0.529708	−	0.848180i	$-0.677698\pi$
$709$	−28.2091	−1.05942	−0.529708	+	0.848180i	$0.677698\pi$
$710$	11.0432	0.414446
$711$	−35.1741	−1.31913
$712$	−30.2967	−1.13542
$713$	−14.9989	−0.561714
$714$	−40.0642	−1.49936
$715$	4.28681	0.160318
$716$	−3.14650	−0.117590
$717$	36.6310	1.36801
$718$	−39.6123	−1.47832
$719$	27.3168	1.01874	0.509372	−	0.860546i	$-0.329878\pi$
$719$	27.3168	1.01874	0.509372	+	0.860546i	$0.329878\pi$
$720$	−26.5640	−0.989982
$721$	−34.8984	−1.29968
$722$	18.6585	0.694398
$723$	48.4099	1.80038
$724$	1.44874	0.0538421
$725$	20.7925	0.772213
$726$	−26.1823	−0.971717
$727$	−28.6593	−1.06291	−0.531457	−	0.847085i	$-0.678355\pi$
$727$	−28.6593	−1.06291	−0.531457	+	0.847085i	$0.678355\pi$
$728$	−6.25455	−0.231809
$729$	−3.97750	−0.147315
$730$	−20.7461	−0.767848
$731$	20.3546	0.752840
$732$	2.67755	0.0989650
$733$	−0.0495397	−0.00182979	−0.000914896	−	1.00000i	$-0.500291\pi$
$733$	−0.0495397	−0.00182979	−0.000914896		1.00000i	$0.500291\pi$
$734$	−0.322579	−0.0119066
$735$	−8.05435	−0.297089
$736$	−3.11525	−0.114830
$737$	23.8253	0.877618
$738$	99.7670	3.67247
$739$	2.24524	0.0825926	0.0412963	−	0.999147i	$-0.486851\pi$
$739$	2.24524	0.0825926	0.0412963	+	0.999147i	$0.486851\pi$
$740$	0.871084	0.0320217
$741$	−8.83095	−0.324413
$742$	−18.2575	−0.670255
$743$	−7.55385	−0.277124	−0.138562	−	0.990354i	$-0.544248\pi$
$743$	−7.55385	−0.277124	−0.138562	+	0.990354i	$0.544248\pi$
$744$	37.9499	1.39131
$745$	−10.6327	−0.389552
$746$	23.6197	0.864778
$747$	37.8354	1.38432
$748$	−2.91108	−0.106440
$749$	−24.0941	−0.880380
$750$	38.7637	1.41545
$751$	26.2001	0.956055	0.478028	−	0.878345i	$-0.341352\pi$
$751$	26.2001	0.956055	0.478028	+	0.878345i	$0.341352\pi$
$752$	−39.1470	−1.42754
$753$	−0.765576	−0.0278991
$754$	−8.35580	−0.304300
$755$	18.0408	0.656570
$756$	3.87729	0.141016
$757$	23.4434	0.852064	0.426032	−	0.904708i	$-0.359911\pi$
$757$	23.4434	0.852064	0.426032	+	0.904708i	$0.359911\pi$
$758$	−23.5419	−0.855080
$759$	42.1055	1.52833
$760$	6.29361	0.228293
$761$	12.4394	0.450927	0.225464	−	0.974252i	$-0.427610\pi$
$761$	12.4394	0.450927	0.225464	+	0.974252i	$0.427610\pi$
$762$	−36.7452	−1.33114
$763$	−5.74973	−0.208154
$764$	1.43000	0.0517355
$765$	26.3601	0.953051
$766$	49.8834	1.80236
$767$	13.3853	0.483316
$768$	12.3395	0.445262
$769$	7.20942	0.259978	0.129989	−	0.991515i	$-0.458506\pi$
$769$	7.20942	0.259978	0.129989	+	0.991515i	$0.458506\pi$
$770$	11.4473	0.412531
$771$	31.1496	1.12183
$772$	3.59762	0.129481
$773$	28.6569	1.03072	0.515358	−	0.856975i	$-0.327659\pi$
$773$	28.6569	1.03072	0.515358	+	0.856975i	$0.327659\pi$
$774$	−46.6542	−1.67695
$775$	−18.7383	−0.673101
$776$	−28.1562	−1.01075
$777$	35.9166	1.28850
$778$	−55.3426	−1.98413
$779$	−25.6198	−0.917926
$780$	−0.542593	−0.0194279
$781$	33.0849	1.18387
$782$	20.8395	0.745218
$783$	−57.0006	−2.03704
$784$	12.0353	0.429833
$785$	4.33635	0.154771
$786$	−21.5180	−0.767522
$787$	41.9222	1.49437	0.747183	−	0.664618i	$-0.231406\pi$
$787$	41.9222	1.49437	0.747183	+	0.664618i	$0.231406\pi$
$788$	3.23138	0.115113
$789$	77.6453	2.76425
$790$	7.21712	0.256773
$791$	−7.15855	−0.254529
$792$	−73.4248	−2.60904
$793$	−5.84654	−0.207617
$794$	33.9485	1.20479
$795$	17.4293	0.618153
$796$	0.141049	0.00499934
$797$	−10.5423	−0.373426	−0.186713	−	0.982414i	$-0.559784\pi$
$797$	−10.5423	−0.373426	−0.186713	+	0.982414i	$0.559784\pi$
$798$	−23.5817	−0.834783
$799$	38.8465	1.37429
$800$	−3.89192	−0.137600
$801$	−74.6900	−2.63904
$802$	−1.47194	−0.0519760
$803$	−62.1540	−2.19337
$804$	−3.01563	−0.106353
$805$	−6.30160	−0.222102
$806$	7.53031	0.265244
$807$	−33.5857	−1.18227
$808$	−36.5473	−1.28573
$809$	0.534741	0.0188005	0.00940024	−	0.999956i	$-0.497008\pi$
$809$	0.534741	0.0188005	0.00940024	+	0.999956i	$0.497008\pi$
$810$	−20.8889	−0.733960
$811$	38.5091	1.35224	0.676119	−	0.736793i	$-0.263661\pi$
$811$	38.5091	1.35224	0.676119	+	0.736793i	$0.263661\pi$
$812$	−1.71582	−0.0602134
$813$	−5.84174	−0.204879
$814$	33.9373	1.18950
$815$	−14.3395	−0.502290
$816$	−57.1507	−2.00067
$817$	11.9806	0.419150
$818$	−0.782983	−0.0273764
$819$	−15.4192	−0.538791
$820$	−1.57414	−0.0549713
$821$	−1.39706	−0.0487577	−0.0243789	−	0.999703i	$-0.507761\pi$
$821$	−1.39706	−0.0487577	−0.0243789	+	0.999703i	$0.507761\pi$
$822$	−34.0612	−1.18802
$823$	45.5221	1.58680	0.793400	−	0.608701i	$-0.208309\pi$
$823$	45.5221	1.58680	0.793400	+	0.608701i	$0.208309\pi$
$824$	−45.9290	−1.60001
$825$	52.6029	1.83140
$826$	35.7434	1.24367
$827$	41.0398	1.42709	0.713547	−	0.700607i	$-0.247087\pi$
$827$	41.0398	1.42709	0.713547	+	0.700607i	$0.247087\pi$
$828$	−3.67309	−0.127649
$829$	−15.7574	−0.547276	−0.273638	−	0.961833i	$-0.588227\pi$
$829$	−15.7574	−0.547276	−0.273638	+	0.961833i	$0.588227\pi$
$830$	−7.76316	−0.269463
$831$	15.9356	0.552798
$832$	−8.16872	−0.283200
$833$	−11.9430	−0.413799
$834$	−38.3764	−1.32887
$835$	4.46220	0.154421
$836$	−1.71345	−0.0592611
$837$	51.3694	1.77559
$838$	−8.02597	−0.277253
$839$	34.4466	1.18923	0.594614	−	0.804011i	$-0.297305\pi$
$839$	34.4466	1.18923	0.594614	+	0.804011i	$0.297305\pi$
$840$	15.9441	0.550125
$841$	−3.77552	−0.130190
$842$	−24.0645	−0.829318
$843$	58.2374	2.00580
$844$	−2.33976	−0.0805379
$845$	−10.8713	−0.373984
$846$	−89.0392	−3.06123
$847$	11.7396	0.403377
$848$	−26.0440	−0.894353
$849$	−41.0973	−1.41045
$850$	26.0350	0.892993
$851$	−18.6821	−0.640414
$852$	−4.18764	−0.143466
$853$	−20.2690	−0.693998	−0.346999	−	0.937865i	$-0.612799\pi$
$853$	−20.2690	−0.693998	−0.346999	+	0.937865i	$0.612799\pi$
$854$	−15.6123	−0.534241
$855$	15.5155	0.530619
$856$	−31.7097	−1.08382
$857$	−17.8230	−0.608823	−0.304411	−	0.952541i	$-0.598460\pi$
$857$	−17.8230	−0.608823	−0.304411	+	0.952541i	$0.598460\pi$
$858$	−21.1393	−0.721685
$859$	27.1323	0.925742	0.462871	−	0.886426i	$-0.346819\pi$
$859$	27.1323	0.925742	0.462871	+	0.886426i	$0.346819\pi$
$860$	0.736117	0.0251014
$861$	−64.9050	−2.21196
$862$	−49.2683	−1.67808
$863$	8.58386	0.292198	0.146099	−	0.989270i	$-0.453328\pi$
$863$	8.58386	0.292198	0.146099	+	0.989270i	$0.453328\pi$
$864$	10.6693	0.362978
$865$	−21.7531	−0.739627
$866$	6.77158	0.230108
$867$	3.89443	0.132262
$868$	1.54631	0.0524851
$869$	21.6220	0.733477
$870$	21.3007	0.722160
$871$	6.58477	0.223116
$872$	−7.56709	−0.256254
$873$	−69.4130	−2.34927
$874$	12.2661	0.414906
$875$	−17.3808	−0.587579
$876$	7.86700	0.265801
$877$	20.6684	0.697922	0.348961	−	0.937137i	$-0.386535\pi$
$877$	20.6684	0.697922	0.348961	+	0.937137i	$0.386535\pi$
$878$	4.43826	0.149784
$879$	79.0353	2.66580
$880$	16.3293	0.550460
$881$	−25.7661	−0.868081	−0.434040	−	0.900893i	$-0.642913\pi$
$881$	−25.7661	−0.868081	−0.434040	+	0.900893i	$0.642913\pi$
$882$	27.3742	0.921736
$883$	12.7305	0.428415	0.214208	−	0.976788i	$-0.431283\pi$
$883$	12.7305	0.428415	0.214208	+	0.976788i	$0.431283\pi$
$884$	−0.804554	−0.0270601
$885$	−34.1219	−1.14700
$886$	−2.61317	−0.0877910
$887$	12.7757	0.428965	0.214482	−	0.976728i	$-0.431194\pi$
$887$	12.7757	0.428965	0.214482	+	0.976728i	$0.431194\pi$
$888$	47.2690	1.58624
$889$	16.4758	0.552579
$890$	15.3251	0.513698
$891$	−62.5818	−2.09657
$892$	3.67186	0.122943
$893$	22.8650	0.765147
$894$	52.4324	1.75360
$895$	−17.5143	−0.585440
$896$	−25.6687	−0.857530
$897$	11.6370	0.388547
$898$	46.8796	1.56439
$899$	−22.7325	−0.758172
$900$	−4.58883	−0.152961
$901$	25.8440	0.860990
$902$	−61.3282	−2.04201
$903$	30.3516	1.01004
$904$	−9.42121	−0.313345
$905$	8.06414	0.268061
$906$	−88.9635	−2.95561
$907$	51.3680	1.70565	0.852823	−	0.522201i	$-0.174889\pi$
$907$	51.3680	1.70565	0.852823	+	0.522201i	$0.174889\pi$
$908$	2.95650	0.0981148
$909$	−90.0992	−2.98840
$910$	3.16376	0.104878
$911$	−29.0945	−0.963944	−0.481972	−	0.876187i	$-0.660079\pi$
$911$	−29.0945	−0.963944	−0.481972	+	0.876187i	$0.660079\pi$
$912$	−33.6388	−1.11389
$913$	−23.2579	−0.769726
$914$	53.8320	1.78060
$915$	14.9040	0.492712
$916$	1.89689	0.0626749
$917$	9.64822	0.318612
$918$	−71.3726	−2.35565
$919$	−20.6239	−0.680318	−0.340159	−	0.940368i	$-0.610481\pi$
$919$	−20.6239	−0.680318	−0.340159	+	0.940368i	$0.610481\pi$
$920$	−8.29339	−0.273425
$921$	13.6260	0.448991
$922$	57.6747	1.89941
$923$	9.14388	0.300975
$924$	−4.34085	−0.142803
$925$	−23.3398	−0.767407
$926$	−43.1641	−1.41846
$927$	−113.228	−3.71889
$928$	−4.72150	−0.154991
$929$	−16.4463	−0.539587	−0.269794	−	0.962918i	$-0.586955\pi$
$929$	−16.4463	−0.539587	−0.269794	+	0.962918i	$0.586955\pi$
$930$	−19.1963	−0.629472
$931$	−7.02960	−0.230386
$932$	−1.54538	−0.0506206
$933$	46.2692	1.51478
$934$	−8.62579	−0.282244
$935$	−16.2039	−0.529926
$936$	−20.2929	−0.663294
$937$	−31.2975	−1.02244	−0.511222	−	0.859449i	$-0.670807\pi$
$937$	−31.2975	−1.02244	−0.511222	+	0.859449i	$0.670807\pi$
$938$	17.5836	0.574125
$939$	−49.9311	−1.62944
$940$	1.40487	0.0458220
$941$	−39.1049	−1.27478	−0.637392	−	0.770540i	$-0.719987\pi$
$941$	−39.1049	−1.27478	−0.637392	+	0.770540i	$0.719987\pi$
$942$	−21.3836	−0.696716
$943$	33.7605	1.09939
$944$	50.9872	1.65949
$945$	21.5822	0.702068
$946$	28.6790	0.932435
$947$	−5.97403	−0.194130	−0.0970650	−	0.995278i	$-0.530945\pi$
$947$	−5.97403	−0.194130	−0.0970650	+	0.995278i	$0.530945\pi$
$948$	−2.73676	−0.0888857
$949$	−17.1779	−0.557619
$950$	15.3242	0.497181
$951$	22.4031	0.726471
$952$	23.6419	0.766238
$953$	−3.72918	−0.120800	−0.0604000	−	0.998174i	$-0.519238\pi$
$953$	−3.72918	−0.120800	−0.0604000	+	0.998174i	$0.519238\pi$
$954$	−59.2365	−1.91785
$955$	7.95979	0.257573
$956$	1.96434	0.0635312
$957$	63.8154	2.06286
$958$	−30.5671	−0.987578
$959$	15.2723	0.493168
$960$	20.8238	0.672084
$961$	−10.5133	−0.339138
$962$	9.37947	0.302406
$963$	−78.1734	−2.51910
$964$	2.59598	0.0836107
$965$	20.0254	0.644641
$966$	31.0747	0.999813
$967$	−30.9432	−0.995066	−0.497533	−	0.867445i	$-0.665761\pi$
$967$	−30.9432	−0.995066	−0.497533	+	0.867445i	$0.665761\pi$
$968$	15.4502	0.496589
$969$	33.3805	1.07234
$970$	14.2423	0.457294
$971$	−58.5371	−1.87855	−0.939273	−	0.343170i	$-0.888499\pi$
$971$	−58.5371	−1.87855	−0.939273	+	0.343170i	$0.888499\pi$
$972$	2.24849	0.0721205
$973$	17.2072	0.551636
$974$	1.42827	0.0457648
$975$	14.5382	0.465595
$976$	−22.2706	−0.712864
$977$	19.1115	0.611433	0.305716	−	0.952123i	$-0.401104\pi$
$977$	19.1115	0.611433	0.305716	+	0.952123i	$0.401104\pi$
$978$	70.7116	2.26111
$979$	45.9130	1.46739
$980$	−0.431914	−0.0137970
$981$	−18.6550	−0.595608
$982$	−18.3003	−0.583986
$983$	11.8405	0.377653	0.188826	−	0.982010i	$-0.439532\pi$
$983$	11.8405	0.377653	0.188826	+	0.982010i	$0.439532\pi$
$984$	−85.4200	−2.72309
$985$	17.9868	0.573108
$986$	31.5845	1.00586
$987$	57.9259	1.84380
$988$	−0.473559	−0.0150659
$989$	−15.7875	−0.502013
$990$	37.1407	1.18041
$991$	16.2699	0.516829	0.258415	−	0.966034i	$-0.416800\pi$
$991$	16.2699	0.516829	0.258415	+	0.966034i	$0.416800\pi$
$992$	4.25506	0.135098
$993$	91.1698	2.89319
$994$	24.4173	0.774471
$995$	0.785120	0.0248900
$996$	2.94382	0.0932784
$997$	−21.7322	−0.688267	−0.344134	−	0.938921i	$-0.611827\pi$
$997$	−21.7322	−0.688267	−0.344134	+	0.938921i	$0.611827\pi$
$998$	32.4473	1.02710
$999$	63.9838	2.02436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	401.2.a.b.1.7	✓	21
3.2	odd	2		3609.2.a.g.1.15		21
4.3	odd	2		6416.2.a.m.1.1		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
401.2.a.b.1.7	✓	21	1.1	even	1	trivial
3609.2.a.g.1.15		21	3.2	odd	2
6416.2.a.m.1.1		21	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	401.a (trivial)

\(f(q)\)	\(=\)	\(q-1.47194 q^{2} +3.10691 q^{3} +0.166608 q^{4} +0.927390 q^{5} -4.57319 q^{6} +2.05052 q^{7} +2.69864 q^{8} +6.65291 q^{9} +O(q^{10})\)	\(q-1.47194 q^{2} +3.10691 q^{3} +0.166608 q^{4} +0.927390 q^{5} -4.57319 q^{6} +2.05052 q^{7} +2.69864 q^{8} +6.65291 q^{9} -1.36506 q^{10} -4.08964 q^{11} +0.517637 q^{12} -1.13028 q^{13} -3.01824 q^{14} +2.88132 q^{15} -4.30546 q^{16} +4.27241 q^{17} -9.79269 q^{18} +2.51473 q^{19} +0.154511 q^{20} +6.37079 q^{21} +6.01971 q^{22} -3.31378 q^{23} +8.38445 q^{24} -4.13995 q^{25} +1.66371 q^{26} +11.3493 q^{27} +0.341633 q^{28} -5.02240 q^{29} -4.24113 q^{30} +4.52623 q^{31} +0.940089 q^{32} -12.7062 q^{33} -6.28873 q^{34} +1.90163 q^{35} +1.10843 q^{36} +5.63769 q^{37} -3.70153 q^{38} -3.51169 q^{39} +2.50270 q^{40} -10.1879 q^{41} -9.37742 q^{42} +4.76419 q^{43} -0.681367 q^{44} +6.16985 q^{45} +4.87769 q^{46} +9.09242 q^{47} -13.3767 q^{48} -2.79537 q^{49} +6.09376 q^{50} +13.2740 q^{51} -0.188314 q^{52} +6.04906 q^{53} -16.7055 q^{54} -3.79269 q^{55} +5.53362 q^{56} +7.81305 q^{57} +7.39267 q^{58} -11.8425 q^{59} +0.480051 q^{60} +5.17264 q^{61} -6.66233 q^{62} +13.6419 q^{63} +7.22716 q^{64} -1.04821 q^{65} +18.7027 q^{66} -5.82578 q^{67} +0.711817 q^{68} -10.2956 q^{69} -2.79909 q^{70} -8.08992 q^{71} +17.9538 q^{72} +15.1979 q^{73} -8.29835 q^{74} -12.8625 q^{75} +0.418974 q^{76} -8.38589 q^{77} +5.16899 q^{78} -5.28702 q^{79} -3.99284 q^{80} +15.3025 q^{81} +14.9960 q^{82} +5.68704 q^{83} +1.06142 q^{84} +3.96219 q^{85} -7.01260 q^{86} -15.6042 q^{87} -11.0365 q^{88} -11.2267 q^{89} -9.08164 q^{90} -2.31766 q^{91} -0.552103 q^{92} +14.0626 q^{93} -13.3835 q^{94} +2.33214 q^{95} +2.92078 q^{96} -10.4335 q^{97} +4.11461 q^{98} -27.2080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9	\( 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9} + 7 q^{10} + q^{11} - 7 q^{12} + 9 q^{13} - 11 q^{14} + q^{15} + 30 q^{16} - q^{17} - 10 q^{18} + 38 q^{19} + q^{20} + q^{21} - q^{22} + 3 q^{23} + 21 q^{24} + 26 q^{25} - 2 q^{26} + 6 q^{27} + 25 q^{28} - 4 q^{29} - 21 q^{30} + 70 q^{31} - 10 q^{32} - 8 q^{33} + 13 q^{34} + 12 q^{35} + 15 q^{36} + 3 q^{37} - 13 q^{38} + 36 q^{39} - 7 q^{40} - 2 q^{41} - 21 q^{42} + 10 q^{43} - 26 q^{44} - 21 q^{45} - 4 q^{46} + 9 q^{47} - 34 q^{48} + 39 q^{49} - 24 q^{50} - 16 q^{51} - q^{52} - 17 q^{53} + 5 q^{54} + 45 q^{55} - 65 q^{56} - 21 q^{57} - 27 q^{58} + 7 q^{59} - 66 q^{60} + 32 q^{61} - 9 q^{62} + 41 q^{63} + 22 q^{64} - 39 q^{65} - 66 q^{66} + 6 q^{67} - 46 q^{68} - 7 q^{69} - 33 q^{70} + 15 q^{71} - 73 q^{72} + 18 q^{73} - 39 q^{74} - 9 q^{75} + 48 q^{76} - 26 q^{77} - 76 q^{78} + 49 q^{79} - 51 q^{80} - 39 q^{81} - 26 q^{82} - 3 q^{83} - 81 q^{84} - q^{85} - 64 q^{86} + 15 q^{87} - 46 q^{88} - 35 q^{89} - 68 q^{90} + 34 q^{91} - 54 q^{92} - 40 q^{93} - 4 q^{94} - 6 q^{95} - 14 q^{96} - 6 q^{97} - 90 q^{98} - 36 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9 + 7 * q^10 + q^11 - 7 * q^12 + 9 * q^13 - 11 * q^14 + q^15 + 30 * q^16 - q^17 - 10 * q^18 + 38 * q^19 + q^20 + q^21 - q^22 + 3 * q^23 + 21 * q^24 + 26 * q^25 - 2 * q^26 + 6 * q^27 + 25 * q^28 - 4 * q^29 - 21 * q^30 + 70 * q^31 - 10 * q^32 - 8 * q^33 + 13 * q^34 + 12 * q^35 + 15 * q^36 + 3 * q^37 - 13 * q^38 + 36 * q^39 - 7 * q^40 - 2 * q^41 - 21 * q^42 + 10 * q^43 - 26 * q^44 - 21 * q^45 - 4 * q^46 + 9 * q^47 - 34 * q^48 + 39 * q^49 - 24 * q^50 - 16 * q^51 - q^52 - 17 * q^53 + 5 * q^54 + 45 * q^55 - 65 * q^56 - 21 * q^57 - 27 * q^58 + 7 * q^59 - 66 * q^60 + 32 * q^61 - 9 * q^62 + 41 * q^63 + 22 * q^64 - 39 * q^65 - 66 * q^66 + 6 * q^67 - 46 * q^68 - 7 * q^69 - 33 * q^70 + 15 * q^71 - 73 * q^72 + 18 * q^73 - 39 * q^74 - 9 * q^75 + 48 * q^76 - 26 * q^77 - 76 * q^78 + 49 * q^79 - 51 * q^80 - 39 * q^81 - 26 * q^82 - 3 * q^83 - 81 * q^84 - q^85 - 64 * q^86 + 15 * q^87 - 46 * q^88 - 35 * q^89 - 68 * q^90 + 34 * q^91 - 54 * q^92 - 40 * q^93 - 4 * q^94 - 6 * q^95 - 14 * q^96 - 6 * q^97 - 90 * q^98 - 36 * q^99

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