LMFDB - Embedded newform 731.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.03648 q^{2} -3.27527 q^{3} +2.14723 q^{4} -3.88495 q^{5} -6.67000 q^{6} -1.33230 q^{7} +0.299836 q^{8} +7.72736 q^{9} +O(q^{10})$	\(q+2.03648 q^{2} -3.27527 q^{3} +2.14723 q^{4} -3.88495 q^{5} -6.67000 q^{6} -1.33230 q^{7} +0.299836 q^{8} +7.72736 q^{9} -7.91160 q^{10} +5.68000 q^{11} -7.03276 q^{12} +3.75535 q^{13} -2.71319 q^{14} +12.7242 q^{15} -3.68386 q^{16} -1.00000 q^{17} +15.7366 q^{18} +2.06005 q^{19} -8.34189 q^{20} +4.36363 q^{21} +11.5672 q^{22} -2.95120 q^{23} -0.982041 q^{24} +10.0928 q^{25} +7.64769 q^{26} -15.4834 q^{27} -2.86076 q^{28} +2.93976 q^{29} +25.9126 q^{30} +7.74005 q^{31} -8.10176 q^{32} -18.6035 q^{33} -2.03648 q^{34} +5.17591 q^{35} +16.5924 q^{36} +5.80622 q^{37} +4.19524 q^{38} -12.2998 q^{39} -1.16485 q^{40} -3.09112 q^{41} +8.88643 q^{42} +1.00000 q^{43} +12.1963 q^{44} -30.0204 q^{45} -6.01004 q^{46} +0.610436 q^{47} +12.0656 q^{48} -5.22498 q^{49} +20.5538 q^{50} +3.27527 q^{51} +8.06362 q^{52} +6.93704 q^{53} -31.5315 q^{54} -22.0665 q^{55} -0.399471 q^{56} -6.74721 q^{57} +5.98675 q^{58} +1.87452 q^{59} +27.3219 q^{60} +12.3075 q^{61} +15.7624 q^{62} -10.2952 q^{63} -9.13131 q^{64} -14.5894 q^{65} -37.8856 q^{66} -2.20987 q^{67} -2.14723 q^{68} +9.66595 q^{69} +10.5406 q^{70} +7.86429 q^{71} +2.31694 q^{72} +2.39700 q^{73} +11.8242 q^{74} -33.0567 q^{75} +4.42341 q^{76} -7.56746 q^{77} -25.0482 q^{78} -14.1968 q^{79} +14.3116 q^{80} +27.5301 q^{81} -6.29500 q^{82} -6.95948 q^{83} +9.36973 q^{84} +3.88495 q^{85} +2.03648 q^{86} -9.62849 q^{87} +1.70307 q^{88} +4.87968 q^{89} -61.1358 q^{90} -5.00325 q^{91} -6.33690 q^{92} -25.3507 q^{93} +1.24314 q^{94} -8.00319 q^{95} +26.5354 q^{96} +16.3109 q^{97} -10.6405 q^{98} +43.8914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * 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 $

$2$	2.03648	1.44001	0.720003	−	0.693971i	$-0.244140\pi$
$2$	2.03648	1.44001	0.720003	+	0.693971i	$0.244140\pi$
$3$	−3.27527	−1.89098	−0.945488	−	0.325658i	$-0.894414\pi$
$3$	−3.27527	−1.89098	−0.945488	+	0.325658i	$0.894414\pi$
$4$	2.14723	1.07362
$5$	−3.88495	−1.73740	−0.868701	−	0.495337i	$-0.835044\pi$
$5$	−3.88495	−1.73740	−0.868701	+	0.495337i	$0.835044\pi$
$6$	−6.67000	−2.72302
$7$	−1.33230	−0.503562	−0.251781	−	0.967784i	$-0.581016\pi$
$7$	−1.33230	−0.503562	−0.251781	+	0.967784i	$0.581016\pi$
$8$	0.299836	0.106008
$9$	7.72736	2.57579
$10$	−7.91160	−2.50187
$11$	5.68000	1.71258	0.856292	−	0.516491i	$-0.172762\pi$
$11$	5.68000	1.71258	0.856292	+	0.516491i	$0.172762\pi$
$12$	−7.03276	−2.03018
$13$	3.75535	1.04155	0.520774	−	0.853695i	$-0.325643\pi$
$13$	3.75535	1.04155	0.520774	+	0.853695i	$0.325643\pi$
$14$	−2.71319	−0.725132
$15$	12.7242	3.28538
$16$	−3.68386	−0.920964
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	15.7366	3.70915
$19$	2.06005	0.472608	0.236304	−	0.971679i	$-0.424064\pi$
$19$	2.06005	0.472608	0.236304	+	0.971679i	$0.424064\pi$
$20$	−8.34189	−1.86530
$21$	4.36363	0.952223
$22$	11.5672	2.46613
$23$	−2.95120	−0.615367	−0.307683	−	0.951489i	$-0.599554\pi$
$23$	−2.95120	−0.615367	−0.307683	+	0.951489i	$0.599554\pi$
$24$	−0.982041	−0.200458
$25$	10.0928	2.01856
$26$	7.64769	1.49983
$27$	−15.4834	−2.97978
$28$	−2.86076	−0.540632
$29$	2.93976	0.545900	0.272950	−	0.962028i	$-0.412001\pi$
$29$	2.93976	0.545900	0.272950	+	0.962028i	$0.412001\pi$
$30$	25.9126	4.73097
$31$	7.74005	1.39015	0.695077	−	0.718935i	$-0.255370\pi$
$31$	7.74005	1.39015	0.695077	+	0.718935i	$0.255370\pi$
$32$	−8.10176	−1.43220
$33$	−18.6035	−3.23846
$34$	−2.03648	−0.349253
$35$	5.17591	0.874889
$36$	16.5924	2.76541
$37$	5.80622	0.954537	0.477269	−	0.878757i	$-0.341627\pi$
$37$	5.80622	0.954537	0.477269	+	0.878757i	$0.341627\pi$
$38$	4.19524	0.680558
$39$	−12.2998	−1.96954
$40$	−1.16485	−0.184178
$41$	−3.09112	−0.482752	−0.241376	−	0.970432i	$-0.577599\pi$
$41$	−3.09112	−0.482752	−0.241376	+	0.970432i	$0.577599\pi$
$42$	8.88643	1.37121
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	12.1963	1.83866
$45$	−30.0204	−4.47518
$46$	−6.01004	−0.886132
$47$	0.610436	0.0890413	0.0445207	−	0.999008i	$-0.485824\pi$
$47$	0.610436	0.0890413	0.0445207	+	0.999008i	$0.485824\pi$
$48$	12.0656	1.74152
$49$	−5.22498	−0.746426
$50$	20.5538	2.90674
$51$	3.27527	0.458629
$52$	8.06362	1.11822
$53$	6.93704	0.952876	0.476438	−	0.879208i	$-0.341928\pi$
$53$	6.93704	0.952876	0.476438	+	0.879208i	$0.341928\pi$
$54$	−31.5315	−4.29089
$55$	−22.0665	−2.97545
$56$	−0.399471	−0.0533815
$57$	−6.74721	−0.893690
$58$	5.98675	0.786099
$59$	1.87452	0.244041	0.122021	−	0.992528i	$-0.461063\pi$
$59$	1.87452	0.244041	0.122021	+	0.992528i	$0.461063\pi$
$60$	27.3219	3.52724
$61$	12.3075	1.57581	0.787907	−	0.615795i	$-0.211165\pi$
$61$	12.3075	1.57581	0.787907	+	0.615795i	$0.211165\pi$
$62$	15.7624	2.00183
$63$	−10.2952	−1.29707
$64$	−9.13131	−1.14141
$65$	−14.5894	−1.80959
$66$	−37.8856	−4.66339
$67$	−2.20987	−0.269978	−0.134989	−	0.990847i	$-0.543100\pi$
$67$	−2.20987	−0.269978	−0.134989	+	0.990847i	$0.543100\pi$
$68$	−2.14723	−0.260390
$69$	9.66595	1.16364
$70$	10.5406	1.25984
$71$	7.86429	0.933319	0.466660	−	0.884437i	$-0.345457\pi$
$71$	7.86429	0.933319	0.466660	+	0.884437i	$0.345457\pi$
$72$	2.31694	0.273054
$73$	2.39700	0.280548	0.140274	−	0.990113i	$-0.455202\pi$
$73$	2.39700	0.280548	0.140274	+	0.990113i	$0.455202\pi$
$74$	11.8242	1.37454
$75$	−33.0567	−3.81705
$76$	4.42341	0.507400
$77$	−7.56746	−0.862392
$78$	−25.0482	−2.83615
$79$	−14.1968	−1.59726	−0.798632	−	0.601819i	$-0.794443\pi$
$79$	−14.1968	−1.59726	−0.798632	+	0.601819i	$0.794443\pi$
$80$	14.3116	1.60008
$81$	27.5301	3.05889
$82$	−6.29500	−0.695166
$83$	−6.95948	−0.763903	−0.381951	−	0.924182i	$-0.624748\pi$
$83$	−6.95948	−0.763903	−0.381951	+	0.924182i	$0.624748\pi$
$84$	9.36973	1.02232
$85$	3.88495	0.421382
$86$	2.03648	0.219599
$87$	−9.62849	−1.03228
$88$	1.70307	0.181547
$89$	4.87968	0.517245	0.258623	−	0.965978i	$-0.416731\pi$
$89$	4.87968	0.517245	0.258623	+	0.965978i	$0.416731\pi$
$90$	−61.1358	−6.44428
$91$	−5.00325	−0.524483
$92$	−6.33690	−0.660668
$93$	−25.3507	−2.62875
$94$	1.24314	0.128220
$95$	−8.00319	−0.821110
$96$	26.5354	2.70826
$97$	16.3109	1.65612	0.828059	−	0.560641i	$-0.189445\pi$
$97$	16.3109	1.65612	0.828059	+	0.560641i	$0.189445\pi$
$98$	−10.6405	−1.07486
$99$	43.8914	4.41126
$100$	21.6716	2.16716
$101$	5.46545	0.543833	0.271916	−	0.962321i	$-0.412343\pi$
$101$	5.46545	0.543833	0.271916	+	0.962321i	$0.412343\pi$
$102$	6.67000	0.660428
$103$	−9.93634	−0.979057	−0.489528	−	0.871987i	$-0.662831\pi$
$103$	−9.93634	−0.979057	−0.489528	+	0.871987i	$0.662831\pi$
$104$	1.12599	0.110412
$105$	−16.9525	−1.65439
$106$	14.1271	1.37215
$107$	8.89727	0.860131	0.430066	−	0.902798i	$-0.358490\pi$
$107$	8.89727	0.860131	0.430066	+	0.902798i	$0.358490\pi$
$108$	−33.2464	−3.19914
$109$	18.0158	1.72560	0.862801	−	0.505544i	$-0.168708\pi$
$109$	18.0158	1.72560	0.862801	+	0.505544i	$0.168708\pi$
$110$	−44.9379	−4.28466
$111$	−19.0169	−1.80501
$112$	4.90800	0.463762
$113$	−9.48676	−0.892439	−0.446220	−	0.894923i	$-0.647230\pi$
$113$	−9.48676	−0.892439	−0.446220	+	0.894923i	$0.647230\pi$
$114$	−13.7405	−1.28692
$115$	11.4652	1.06914
$116$	6.31235	0.586087
$117$	29.0190	2.68281
$118$	3.81741	0.351421
$119$	1.33230	0.122132
$120$	3.81518	0.348276
$121$	21.2624	1.93295
$122$	25.0639	2.26918
$123$	10.1242	0.912873
$124$	16.6197	1.49249
$125$	−19.7853	−1.76965
$126$	−20.9658	−1.86778
$127$	17.0113	1.50951	0.754755	−	0.656007i	$-0.227756\pi$
$127$	17.0113	1.50951	0.754755	+	0.656007i	$0.227756\pi$
$128$	−2.39218	−0.211441
$129$	−3.27527	−0.288371
$130$	−29.7109	−2.60581
$131$	14.2616	1.24604	0.623020	−	0.782206i	$-0.285905\pi$
$131$	14.2616	1.24604	0.623020	+	0.782206i	$0.285905\pi$
$132$	−39.9461	−3.47686
$133$	−2.74460	−0.237987
$134$	−4.50034	−0.388770
$135$	60.1521	5.17707
$136$	−0.299836	−0.0257107
$137$	−6.00094	−0.512695	−0.256347	−	0.966585i	$-0.582519\pi$
$137$	−6.00094	−0.512695	−0.256347	+	0.966585i	$0.582519\pi$
$138$	19.6845	1.67565
$139$	−16.6073	−1.40861	−0.704305	−	0.709898i	$-0.748741\pi$
$139$	−16.6073	−1.40861	−0.704305	+	0.709898i	$0.748741\pi$
$140$	11.1139	0.939295
$141$	−1.99934	−0.168375
$142$	16.0154	1.34398
$143$	21.3304	1.78374
$144$	−28.4665	−2.37221
$145$	−11.4208	−0.948447
$146$	4.88143	0.403990
$147$	17.1132	1.41147
$148$	12.4673	1.02481
$149$	8.04840	0.659351	0.329675	−	0.944094i	$-0.393061\pi$
$149$	8.04840	0.659351	0.329675	+	0.944094i	$0.393061\pi$
$150$	−67.3191	−5.49658
$151$	−0.0486290	−0.00395737	−0.00197869	−	0.999998i	$-0.500630\pi$
$151$	−0.0486290	−0.00395737	−0.00197869	+	0.999998i	$0.500630\pi$
$152$	0.617676	0.0501002
$153$	−7.72736	−0.624720
$154$	−15.4109	−1.24185
$155$	−30.0697	−2.41526
$156$	−26.4105	−2.11453
$157$	4.80237	0.383271	0.191636	−	0.981466i	$-0.438621\pi$
$157$	4.80237	0.383271	0.191636	+	0.981466i	$0.438621\pi$
$158$	−28.9114	−2.30007
$159$	−22.7207	−1.80187
$160$	31.4749	2.48831
$161$	3.93187	0.309875
$162$	56.0643	4.40483
$163$	15.1062	1.18321	0.591605	−	0.806228i	$-0.298495\pi$
$163$	15.1062	1.18321	0.591605	+	0.806228i	$0.298495\pi$
$164$	−6.63736	−0.518291
$165$	72.2737	5.62650
$166$	−14.1728	−1.10002
$167$	−18.7930	−1.45424	−0.727121	−	0.686509i	$-0.759142\pi$
$167$	−18.7930	−1.45424	−0.727121	+	0.686509i	$0.759142\pi$
$168$	1.30837	0.100943
$169$	1.10268	0.0848218
$170$	7.91160	0.606792
$171$	15.9188	1.21734
$172$	2.14723	0.163725
$173$	−13.9844	−1.06321	−0.531605	−	0.846992i	$-0.678411\pi$
$173$	−13.9844	−1.06321	−0.531605	+	0.846992i	$0.678411\pi$
$174$	−19.6082	−1.48649
$175$	−13.4466	−1.01647
$176$	−20.9243	−1.57723
$177$	−6.13954	−0.461476
$178$	9.93735	0.744836
$179$	−15.6906	−1.17277	−0.586384	−	0.810033i	$-0.699449\pi$
$179$	−15.6906	−1.17277	−0.586384	+	0.810033i	$0.699449\pi$
$180$	−64.4608	−4.80462
$181$	−5.82957	−0.433308	−0.216654	−	0.976248i	$-0.569514\pi$
$181$	−5.82957	−0.433308	−0.216654	+	0.976248i	$0.569514\pi$
$182$	−10.1890	−0.755259
$183$	−40.3103	−2.97982
$184$	−0.884873	−0.0652337
$185$	−22.5569	−1.65841
$186$	−51.6261	−3.78541
$187$	−5.68000	−0.415363
$188$	1.31075	0.0955962
$189$	20.6285	1.50050
$190$	−16.2983	−1.18240
$191$	−8.95845	−0.648210	−0.324105	−	0.946021i	$-0.605063\pi$
$191$	−8.95845	−0.648210	−0.324105	+	0.946021i	$0.605063\pi$
$192$	29.9075	2.15839
$193$	−5.40004	−0.388703	−0.194352	−	0.980932i	$-0.562260\pi$
$193$	−5.40004	−0.388703	−0.194352	+	0.980932i	$0.562260\pi$
$194$	33.2167	2.38482
$195$	47.7840	3.42188
$196$	−11.2192	−0.801375
$197$	7.38861	0.526417	0.263208	−	0.964739i	$-0.415219\pi$
$197$	7.38861	0.526417	0.263208	+	0.964739i	$0.415219\pi$
$198$	89.3838	6.35223
$199$	1.86234	0.132018	0.0660090	−	0.997819i	$-0.478973\pi$
$199$	1.86234	0.132018	0.0660090	+	0.997819i	$0.478973\pi$
$200$	3.02619	0.213984
$201$	7.23790	0.510522
$202$	11.1303	0.783122
$203$	−3.91664	−0.274894
$204$	7.03276	0.492391
$205$	12.0088	0.838734
$206$	−20.2351	−1.40985
$207$	−22.8050	−1.58505
$208$	−13.8342	−0.959228
$209$	11.7011	0.809381
$210$	−34.5233	−2.38234
$211$	−7.65659	−0.527101	−0.263551	−	0.964646i	$-0.584894\pi$
$211$	−7.65659	−0.527101	−0.263551	+	0.964646i	$0.584894\pi$
$212$	14.8954	1.02302
$213$	−25.7576	−1.76488
$214$	18.1191	1.23859
$215$	−3.88495	−0.264951
$216$	−4.64246	−0.315880
$217$	−10.3121	−0.700028
$218$	36.6888	2.48488
$219$	−7.85081	−0.530509
$220$	−47.3819	−3.19449
$221$	−3.75535	−0.252612
$222$	−38.7275	−2.59922
$223$	0.374850	0.0251018	0.0125509	−	0.999921i	$-0.496005\pi$
$223$	0.374850	0.0251018	0.0125509	+	0.999921i	$0.496005\pi$
$224$	10.7940	0.721202
$225$	77.9909	5.19939
$226$	−19.3196	−1.28512
$227$	−9.85035	−0.653791	−0.326895	−	0.945061i	$-0.606002\pi$
$227$	−9.85035	−0.653791	−0.326895	+	0.945061i	$0.606002\pi$
$228$	−14.4878	−0.959480
$229$	26.2278	1.73319	0.866593	−	0.499016i	$-0.166305\pi$
$229$	26.2278	1.73319	0.866593	+	0.499016i	$0.166305\pi$
$230$	23.3487	1.53957
$231$	24.7854	1.63076
$232$	0.881445	0.0578697
$233$	7.02910	0.460492	0.230246	−	0.973132i	$-0.426047\pi$
$233$	7.02910	0.460492	0.230246	+	0.973132i	$0.426047\pi$
$234$	59.0965	3.86326
$235$	−2.37151	−0.154700
$236$	4.02502	0.262007
$237$	46.4983	3.02039
$238$	2.71319	0.175870
$239$	−25.2185	−1.63125	−0.815625	−	0.578580i	$-0.803607\pi$
$239$	−25.2185	−1.63125	−0.815625	+	0.578580i	$0.803607\pi$
$240$	−46.8743	−3.02572
$241$	−13.2951	−0.856412	−0.428206	−	0.903681i	$-0.640854\pi$
$241$	−13.2951	−0.856412	−0.428206	+	0.903681i	$0.640854\pi$
$242$	43.3004	2.78345
$243$	−43.7181	−2.80452
$244$	26.4271	1.69182
$245$	20.2988	1.29684
$246$	20.6178	1.31454
$247$	7.73622	0.492244
$248$	2.32074	0.147367
$249$	22.7942	1.44452
$250$	−40.2923	−2.54831
$251$	21.0524	1.32882	0.664408	−	0.747370i	$-0.268684\pi$
$251$	21.0524	1.32882	0.664408	+	0.747370i	$0.268684\pi$
$252$	−22.1061	−1.39255
$253$	−16.7628	−1.05387
$254$	34.6431	2.17370
$255$	−12.7242	−0.796822
$256$	13.3910	0.836938
$257$	29.3904	1.83332	0.916662	−	0.399663i	$-0.130873\pi$
$257$	29.3904	1.83332	0.916662	+	0.399663i	$0.130873\pi$
$258$	−6.67000	−0.415256
$259$	−7.73563	−0.480668
$260$	−31.3267	−1.94280
$261$	22.7166	1.40612
$262$	29.0434	1.79431
$263$	−15.8425	−0.976887	−0.488444	−	0.872595i	$-0.662435\pi$
$263$	−15.8425	−0.976887	−0.488444	+	0.872595i	$0.662435\pi$
$264$	−5.57799	−0.343302
$265$	−26.9501	−1.65553
$266$	−5.58932	−0.342703
$267$	−15.9823	−0.978098
$268$	−4.74510	−0.289853
$269$	16.8688	1.02851	0.514254	−	0.857638i	$-0.328069\pi$
$269$	16.8688	1.02851	0.514254	+	0.857638i	$0.328069\pi$
$270$	122.498	7.45501
$271$	18.9025	1.14824	0.574121	−	0.818770i	$-0.305344\pi$
$271$	18.9025	1.14824	0.574121	+	0.818770i	$0.305344\pi$
$272$	3.68386	0.223367
$273$	16.3870	0.991785
$274$	−12.2208	−0.738283
$275$	57.3272	3.45696
$276$	20.7550	1.24931
$277$	−5.45484	−0.327750	−0.163875	−	0.986481i	$-0.552399\pi$
$277$	−5.45484	−0.327750	−0.163875	+	0.986481i	$0.552399\pi$
$278$	−33.8203	−2.02841
$279$	59.8102	3.58074
$280$	1.55192	0.0927451
$281$	−32.5694	−1.94293	−0.971464	−	0.237185i	$-0.923775\pi$
$281$	−32.5694	−1.94293	−0.971464	+	0.237185i	$0.923775\pi$
$282$	−4.07161	−0.242461
$283$	−1.97936	−0.117661	−0.0588305	−	0.998268i	$-0.518737\pi$
$283$	−1.97936	−0.117661	−0.0588305	+	0.998268i	$0.518737\pi$
$284$	16.8865	1.00203
$285$	26.2126	1.55270
$286$	43.4389	2.56859
$287$	4.11830	0.243095
$288$	−62.6052	−3.68905
$289$	1.00000	0.0588235
$290$	−23.2582	−1.36577
$291$	−53.4224	−3.13168
$292$	5.14692	0.301201
$293$	−4.59389	−0.268378	−0.134189	−	0.990956i	$-0.542843\pi$
$293$	−4.59389	−0.268378	−0.134189	+	0.990956i	$0.542843\pi$
$294$	34.8506	2.03253
$295$	−7.28240	−0.423998
$296$	1.74091	0.101188
$297$	−87.9456	−5.10312
$298$	16.3904	0.949469
$299$	−11.0828	−0.640934
$300$	−70.9803	−4.09805
$301$	−1.33230	−0.0767924
$302$	−0.0990318	−0.00569864
$303$	−17.9008	−1.02837
$304$	−7.58893	−0.435255
$305$	−47.8140	−2.73782
$306$	−15.7366	−0.899601
$307$	9.24910	0.527874	0.263937	−	0.964540i	$-0.414979\pi$
$307$	9.24910	0.527874	0.263937	+	0.964540i	$0.414979\pi$
$308$	−16.2491	−0.925878
$309$	32.5442	1.85137
$310$	−61.2362	−3.47798
$311$	−2.60427	−0.147674	−0.0738372	−	0.997270i	$-0.523525\pi$
$311$	−2.60427	−0.147674	−0.0738372	+	0.997270i	$0.523525\pi$
$312$	−3.68791	−0.208787
$313$	8.65474	0.489195	0.244597	−	0.969625i	$-0.421344\pi$
$313$	8.65474	0.489195	0.244597	+	0.969625i	$0.421344\pi$
$314$	9.77992	0.551913
$315$	39.9961	2.25353
$316$	−30.4838	−1.71485
$317$	−3.60434	−0.202440	−0.101220	−	0.994864i	$-0.532275\pi$
$317$	−3.60434	−0.202440	−0.101220	+	0.994864i	$0.532275\pi$
$318$	−46.2701	−2.59470
$319$	16.6978	0.934900
$320$	35.4747	1.98309
$321$	−29.1409	−1.62649
$322$	8.00717	0.446222
$323$	−2.06005	−0.114624
$324$	59.1134	3.28408
$325$	37.9021	2.10243
$326$	30.7634	1.70383
$327$	−59.0066	−3.26307
$328$	−0.926828	−0.0511755
$329$	−0.813284	−0.0448378
$330$	147.184	8.10219
$331$	−9.88950	−0.543576	−0.271788	−	0.962357i	$-0.587615\pi$
$331$	−9.88950	−0.543576	−0.271788	+	0.962357i	$0.587615\pi$
$332$	−14.9436	−0.820138
$333$	44.8668	2.45869
$334$	−38.2714	−2.09412
$335$	8.58522	0.469060
$336$	−16.0750	−0.876963
$337$	−16.3536	−0.890835	−0.445417	−	0.895323i	$-0.646945\pi$
$337$	−16.3536	−0.890835	−0.445417	+	0.895323i	$0.646945\pi$
$338$	2.24559	0.122144
$339$	31.0717	1.68758
$340$	8.34189	0.452402
$341$	43.9635	2.38076
$342$	32.4182	1.75297
$343$	16.2873	0.879433
$344$	0.299836	0.0161660
$345$	−37.5517	−2.02172
$346$	−28.4788	−1.53103
$347$	−2.44822	−0.131427	−0.0657137	−	0.997839i	$-0.520932\pi$
$347$	−2.44822	−0.131427	−0.0657137	+	0.997839i	$0.520932\pi$
$348$	−20.6746	−1.10828
$349$	8.13357	0.435380	0.217690	−	0.976018i	$-0.430148\pi$
$349$	8.13357	0.435380	0.217690	+	0.976018i	$0.430148\pi$
$350$	−27.3838	−1.46372
$351$	−58.1455	−3.10358
$352$	−46.0180	−2.45277
$353$	16.6944	0.888551	0.444275	−	0.895890i	$-0.353461\pi$
$353$	16.6944	0.888551	0.444275	+	0.895890i	$0.353461\pi$
$354$	−12.5030	−0.664528
$355$	−30.5523	−1.62155
$356$	10.4778	0.555323
$357$	−4.36363	−0.230948
$358$	−31.9535	−1.68879
$359$	29.4781	1.55579	0.777896	−	0.628393i	$-0.216287\pi$
$359$	29.4781	1.55579	0.777896	+	0.628393i	$0.216287\pi$
$360$	−9.00118	−0.474404
$361$	−14.7562	−0.776642
$362$	−11.8718	−0.623966
$363$	−69.6401	−3.65515
$364$	−10.7431	−0.563094
$365$	−9.31222	−0.487424
$366$	−82.0910	−4.29096
$367$	−16.5197	−0.862320	−0.431160	−	0.902275i	$-0.641896\pi$
$367$	−16.5197	−0.862320	−0.431160	+	0.902275i	$0.641896\pi$
$368$	10.8718	0.566731
$369$	−23.8862	−1.24347
$370$	−45.9365	−2.38813
$371$	−9.24222	−0.479832
$372$	−54.4339	−2.82227
$373$	13.5847	0.703388	0.351694	−	0.936115i	$-0.385606\pi$
$373$	13.5847	0.703388	0.351694	+	0.936115i	$0.385606\pi$
$374$	−11.5672	−0.598125
$375$	64.8022	3.34637
$376$	0.183031	0.00943908
$377$	11.0398	0.568581
$378$	42.0094	2.16073
$379$	−17.1210	−0.879445	−0.439723	−	0.898134i	$-0.644923\pi$
$379$	−17.1210	−0.879445	−0.439723	+	0.898134i	$0.644923\pi$
$380$	−17.1847	−0.881557
$381$	−55.7166	−2.85445
$382$	−18.2437	−0.933427
$383$	−25.6811	−1.31224	−0.656121	−	0.754655i	$-0.727804\pi$
$383$	−25.6811	−1.31224	−0.656121	+	0.754655i	$0.727804\pi$
$384$	7.83504	0.399830
$385$	29.3992	1.49832
$386$	−10.9970	−0.559735
$387$	7.72736	0.392804
$388$	35.0232	1.77803
$389$	−10.0682	−0.510477	−0.255239	−	0.966878i	$-0.582154\pi$
$389$	−10.0682	−0.510477	−0.255239	+	0.966878i	$0.582154\pi$
$390$	97.3110	4.92753
$391$	2.95120	0.149248
$392$	−1.56663	−0.0791270
$393$	−46.7105	−2.35623
$394$	15.0467	0.758043
$395$	55.1538	2.77509
$396$	94.2451	4.73600
$397$	3.31217	0.166233	0.0831165	−	0.996540i	$-0.473513\pi$
$397$	3.31217	0.166233	0.0831165	+	0.996540i	$0.473513\pi$
$398$	3.79262	0.190107
$399$	8.98930	0.450028
$400$	−37.1805	−1.85903
$401$	10.9610	0.547366	0.273683	−	0.961820i	$-0.411758\pi$
$401$	10.9610	0.547366	0.273683	+	0.961820i	$0.411758\pi$
$402$	14.7398	0.735155
$403$	29.0666	1.44791
$404$	11.7356	0.583868
$405$	−106.953	−5.31453
$406$	−7.97614	−0.395849
$407$	32.9794	1.63473
$408$	0.982041	0.0486183
$409$	10.4714	0.517779	0.258889	−	0.965907i	$-0.416643\pi$
$409$	10.4714	0.517779	0.258889	+	0.965907i	$0.416643\pi$
$410$	24.4557	1.20778
$411$	19.6547	0.969493
$412$	−21.3356	−1.05113
$413$	−2.49742	−0.122890
$414$	−46.4417	−2.28249
$415$	27.0372	1.32721
$416$	−30.4250	−1.49171
$417$	54.3932	2.66365
$418$	23.8290	1.16551
$419$	−37.5568	−1.83477	−0.917386	−	0.397999i	$-0.869705\pi$
$419$	−37.5568	−1.83477	−0.917386	+	0.397999i	$0.869705\pi$
$420$	−36.4009	−1.77618
$421$	13.7531	0.670284	0.335142	−	0.942168i	$-0.391216\pi$
$421$	13.7531	0.670284	0.335142	+	0.942168i	$0.391216\pi$
$422$	−15.5925	−0.759029
$423$	4.71706	0.229352
$424$	2.07997	0.101012
$425$	−10.0928	−0.489574
$426$	−52.4548	−2.54144
$427$	−16.3973	−0.793519
$428$	19.1045	0.923451
$429$	−69.8628	−3.37301
$430$	−7.91160	−0.381531
$431$	17.7828	0.856569	0.428285	−	0.903644i	$-0.359118\pi$
$431$	17.7828	0.856569	0.428285	+	0.903644i	$0.359118\pi$
$432$	57.0385	2.74427
$433$	24.4893	1.17688	0.588440	−	0.808541i	$-0.299742\pi$
$433$	24.4893	1.17688	0.588440	+	0.808541i	$0.299742\pi$
$434$	−21.0003	−1.00804
$435$	37.4062	1.79349
$436$	38.6841	1.85263
$437$	−6.07961	−0.290827
$438$	−15.9880	−0.763936
$439$	34.2193	1.63320	0.816600	−	0.577204i	$-0.195856\pi$
$439$	34.2193	1.63320	0.816600	+	0.577204i	$0.195856\pi$
$440$	−6.61632	−0.315421
$441$	−40.3753	−1.92263
$442$	−7.64769	−0.363763
$443$	−5.64373	−0.268142	−0.134071	−	0.990972i	$-0.542805\pi$
$443$	−5.64373	−0.268142	−0.134071	+	0.990972i	$0.542805\pi$
$444$	−40.8338	−1.93788
$445$	−18.9573	−0.898663
$446$	0.763374	0.0361468
$447$	−26.3607	−1.24682
$448$	12.1656	0.574772
$449$	−13.3272	−0.628949	−0.314475	−	0.949266i	$-0.601828\pi$
$449$	−13.3272	−0.628949	−0.314475	+	0.949266i	$0.601828\pi$
$450$	158.826	7.48715
$451$	−17.5576	−0.826754
$452$	−20.3703	−0.958137
$453$	0.159273	0.00748329
$454$	−20.0600	−0.941462
$455$	19.4374	0.911238
$456$	−2.02305	−0.0947382
$457$	16.3777	0.766118	0.383059	−	0.923724i	$-0.374871\pi$
$457$	16.3777	0.766118	0.383059	+	0.923724i	$0.374871\pi$
$458$	53.4124	2.49580
$459$	15.4834	0.722702
$460$	24.6185	1.14785
$461$	−8.81456	−0.410535	−0.205268	−	0.978706i	$-0.565806\pi$
$461$	−8.81456	−0.410535	−0.205268	+	0.978706i	$0.565806\pi$
$462$	50.4749	2.34831
$463$	19.7941	0.919910	0.459955	−	0.887942i	$-0.347866\pi$
$463$	19.7941	0.919910	0.459955	+	0.887942i	$0.347866\pi$
$464$	−10.8297	−0.502754
$465$	98.4862	4.56719
$466$	14.3146	0.663111
$467$	3.49294	0.161634	0.0808169	−	0.996729i	$-0.474247\pi$
$467$	3.49294	0.161634	0.0808169	+	0.996729i	$0.474247\pi$
$468$	62.3105	2.88030
$469$	2.94420	0.135951
$470$	−4.82953	−0.222770
$471$	−15.7291	−0.724756
$472$	0.562047	0.0258703
$473$	5.68000	0.261167
$474$	94.6926	4.34938
$475$	20.7917	0.953989
$476$	2.86076	0.131123
$477$	53.6051	2.45441
$478$	−51.3569	−2.34901
$479$	19.0622	0.870972	0.435486	−	0.900196i	$-0.356577\pi$
$479$	19.0622	0.870972	0.435486	+	0.900196i	$0.356577\pi$
$480$	−103.089	−4.70533
$481$	21.8044	0.994196
$482$	−27.0751	−1.23324
$483$	−12.8779	−0.585966
$484$	45.6553	2.07524
$485$	−63.3669	−2.87734
$486$	−89.0309	−4.03852
$487$	−22.2845	−1.00981	−0.504903	−	0.863176i	$-0.668472\pi$
$487$	−22.2845	−1.00981	−0.504903	+	0.863176i	$0.668472\pi$
$488$	3.69022	0.167049
$489$	−49.4768	−2.23742
$490$	41.3380	1.86746
$491$	−28.9478	−1.30640	−0.653199	−	0.757186i	$-0.726574\pi$
$491$	−28.9478	−1.30640	−0.653199	+	0.757186i	$0.726574\pi$
$492$	21.7391	0.980075
$493$	−2.93976	−0.132400
$494$	15.7546	0.708834
$495$	−170.516	−7.66412
$496$	−28.5132	−1.28028
$497$	−10.4776	−0.469984
$498$	46.4197	2.08012
$499$	−22.3750	−1.00164	−0.500822	−	0.865550i	$-0.666969\pi$
$499$	−22.3750	−1.00164	−0.500822	+	0.865550i	$0.666969\pi$
$500$	−42.4837	−1.89993
$501$	61.5519	2.74994
$502$	42.8727	1.91350
$503$	3.15373	0.140618	0.0703089	−	0.997525i	$-0.477601\pi$
$503$	3.15373	0.140618	0.0703089	+	0.997525i	$0.477601\pi$
$504$	−3.08685	−0.137499
$505$	−21.2330	−0.944856
$506$	−34.1370	−1.51758
$507$	−3.61158	−0.160396
$508$	36.5272	1.62063
$509$	−25.8404	−1.14536	−0.572678	−	0.819781i	$-0.694095\pi$
$509$	−25.8404	−1.14536	−0.572678	+	0.819781i	$0.694095\pi$
$510$	−25.9126	−1.14743
$511$	−3.19352	−0.141273
$512$	32.0548	1.41664
$513$	−31.8965	−1.40827
$514$	59.8529	2.64000
$515$	38.6022	1.70101
$516$	−7.03276	−0.309600
$517$	3.46728	0.152491
$518$	−15.7534	−0.692165
$519$	45.8025	2.01051
$520$	−4.37441	−0.191830
$521$	−2.70552	−0.118531	−0.0592654	−	0.998242i	$-0.518876\pi$
$521$	−2.70552	−0.118531	−0.0592654	+	0.998242i	$0.518876\pi$
$522$	46.2618	2.02482
$523$	−21.7049	−0.949088	−0.474544	−	0.880232i	$-0.657387\pi$
$523$	−21.7049	−0.949088	−0.474544	+	0.880232i	$0.657387\pi$
$524$	30.6229	1.33777
$525$	44.0413	1.92212
$526$	−32.2628	−1.40672
$527$	−7.74005	−0.337162
$528$	68.5327	2.98250
$529$	−14.2904	−0.621324
$530$	−54.8831	−2.38397
$531$	14.4851	0.628599
$532$	−5.89330	−0.255507
$533$	−11.6083	−0.502810
$534$	−32.5475	−1.40847
$535$	−34.5654	−1.49439
$536$	−0.662596	−0.0286198
$537$	51.3908	2.21768
$538$	34.3529	1.48106
$539$	−29.6779	−1.27832
$540$	129.161	5.55818
$541$	31.7746	1.36609	0.683047	−	0.730374i	$-0.260654\pi$
$541$	31.7746	1.36609	0.683047	+	0.730374i	$0.260654\pi$
$542$	38.4944	1.65348
$543$	19.0934	0.819375
$544$	8.10176	0.347360
$545$	−69.9905	−2.99806
$546$	33.3717	1.42818
$547$	0.398520	0.0170395	0.00851974	−	0.999964i	$-0.497288\pi$
$547$	0.398520	0.0170395	0.00851974	+	0.999964i	$0.497288\pi$
$548$	−12.8854	−0.550437
$549$	95.1045	4.05896
$550$	116.745	4.97804
$551$	6.05606	0.257997
$552$	2.89819	0.123355
$553$	18.9144	0.804321
$554$	−11.1086	−0.471961
$555$	73.8798	3.13602
$556$	−35.6597	−1.51231
$557$	41.4141	1.75477	0.877386	−	0.479786i	$-0.159286\pi$
$557$	41.4141	1.75477	0.877386	+	0.479786i	$0.159286\pi$
$558$	121.802	5.15629
$559$	3.75535	0.158835
$560$	−19.0673	−0.805741
$561$	18.6035	0.785441
$562$	−66.3268	−2.79783
$563$	−21.1517	−0.891439	−0.445719	−	0.895173i	$-0.647052\pi$
$563$	−21.1517	−0.891439	−0.445719	+	0.895173i	$0.647052\pi$
$564$	−4.29305	−0.180770
$565$	36.8556	1.55053
$566$	−4.03092	−0.169432
$567$	−36.6783	−1.54034
$568$	2.35799	0.0989392
$569$	−16.2209	−0.680017	−0.340008	−	0.940422i	$-0.610430\pi$
$569$	−16.2209	−0.680017	−0.340008	+	0.940422i	$0.610430\pi$
$570$	53.3813	2.23589
$571$	31.1384	1.30310	0.651551	−	0.758605i	$-0.274119\pi$
$571$	31.1384	1.30310	0.651551	+	0.758605i	$0.274119\pi$
$572$	45.8014	1.91505
$573$	29.3413	1.22575
$574$	8.38681	0.350059
$575$	−29.7859	−1.24216
$576$	−70.5610	−2.94004
$577$	−10.0419	−0.418048	−0.209024	−	0.977910i	$-0.567029\pi$
$577$	−10.0419	−0.418048	−0.209024	+	0.977910i	$0.567029\pi$
$578$	2.03648	0.0847062
$579$	17.6866	0.735028
$580$	−24.5231	−1.01827
$581$	9.27211	0.384672
$582$	−108.793	−4.50963
$583$	39.4024	1.63188
$584$	0.718706	0.0297403
$585$	−112.737	−4.66111
$586$	−9.35534	−0.386466
$587$	−13.8173	−0.570300	−0.285150	−	0.958483i	$-0.592043\pi$
$587$	−13.8173	−0.570300	−0.285150	+	0.958483i	$0.592043\pi$
$588$	36.7460	1.51538
$589$	15.9449	0.656998
$590$	−14.8304	−0.610559
$591$	−24.1997	−0.995441
$592$	−21.3893	−0.879095
$593$	−26.7554	−1.09871	−0.549356	−	0.835589i	$-0.685127\pi$
$593$	−26.7554	−1.09871	−0.549356	+	0.835589i	$0.685127\pi$
$594$	−179.099	−7.34852
$595$	−5.17591	−0.212192
$596$	17.2818	0.707890
$597$	−6.09967	−0.249643
$598$	−22.5698	−0.922948
$599$	34.0507	1.39128	0.695638	−	0.718393i	$-0.255122\pi$
$599$	34.0507	1.39128	0.695638	+	0.718393i	$0.255122\pi$
$600$	−9.91156	−0.404638
$601$	12.4143	0.506391	0.253196	−	0.967415i	$-0.418518\pi$
$601$	12.4143	0.506391	0.253196	+	0.967415i	$0.418518\pi$
$602$	−2.71319	−0.110582
$603$	−17.0764	−0.695406
$604$	−0.104418	−0.00424870
$605$	−82.6034	−3.35830
$606$	−36.4546	−1.48086
$607$	23.0125	0.934049	0.467024	−	0.884244i	$-0.345326\pi$
$607$	23.0125	0.934049	0.467024	+	0.884244i	$0.345326\pi$
$608$	−16.6900	−0.676870
$609$	12.8280	0.519818
$610$	−97.3720	−3.94248
$611$	2.29241	0.0927408
$612$	−16.5924	−0.670710
$613$	6.08575	0.245801	0.122901	−	0.992419i	$-0.460780\pi$
$613$	6.08575	0.245801	0.122901	+	0.992419i	$0.460780\pi$
$614$	18.8356	0.760142
$615$	−39.3322	−1.58603
$616$	−2.26899	−0.0914203
$617$	−9.06158	−0.364805	−0.182403	−	0.983224i	$-0.558387\pi$
$617$	−9.06158	−0.364805	−0.182403	+	0.983224i	$0.558387\pi$
$618$	66.2754	2.66599
$619$	4.39857	0.176793	0.0883967	−	0.996085i	$-0.471826\pi$
$619$	4.39857	0.176793	0.0883967	+	0.996085i	$0.471826\pi$
$620$	−64.5666	−2.59306
$621$	45.6945	1.83366
$622$	−5.30353	−0.212652
$623$	−6.50119	−0.260465
$624$	45.3106	1.81388
$625$	26.4009	1.05604
$626$	17.6252	0.704443
$627$	−38.3242	−1.53052
$628$	10.3118	0.411486
$629$	−5.80622	−0.231509
$630$	81.4512	3.24509
$631$	−19.6990	−0.784203	−0.392102	−	0.919922i	$-0.628252\pi$
$631$	−19.6990	−0.784203	−0.392102	+	0.919922i	$0.628252\pi$
$632$	−4.25670	−0.169323
$633$	25.0774	0.996736
$634$	−7.34016	−0.291515
$635$	−66.0881	−2.62262
$636$	−48.7865	−1.93451
$637$	−19.6216	−0.777438
$638$	34.0047	1.34626
$639$	60.7702	2.40403
$640$	9.29351	0.367358
$641$	8.68198	0.342917	0.171459	−	0.985191i	$-0.445152\pi$
$641$	8.68198	0.342917	0.171459	+	0.985191i	$0.445152\pi$
$642$	−59.3447	−2.34215
$643$	36.2258	1.42861	0.714303	−	0.699837i	$-0.246744\pi$
$643$	36.2258	1.42861	0.714303	+	0.699837i	$0.246744\pi$
$644$	8.44265	0.332687
$645$	12.7242	0.501016
$646$	−4.19524	−0.165060
$647$	31.9590	1.25644	0.628219	−	0.778036i	$-0.283784\pi$
$647$	31.9590	1.25644	0.628219	+	0.778036i	$0.283784\pi$
$648$	8.25449	0.324267
$649$	10.6473	0.417941
$650$	77.1867	3.02751
$651$	33.7747	1.32374
$652$	32.4365	1.27031
$653$	−32.8915	−1.28714	−0.643571	−	0.765386i	$-0.722548\pi$
$653$	−32.8915	−1.28714	−0.643571	+	0.765386i	$0.722548\pi$
$654$	−120.165	−4.69884
$655$	−55.4055	−2.16487
$656$	11.3873	0.444598
$657$	18.5225	0.722631
$658$	−1.65623	−0.0645667
$659$	−35.6087	−1.38712	−0.693560	−	0.720399i	$-0.743959\pi$
$659$	−35.6087	−1.38712	−0.693560	+	0.720399i	$0.743959\pi$
$660$	155.188	6.04070
$661$	−32.6602	−1.27034	−0.635168	−	0.772374i	$-0.719069\pi$
$661$	−32.6602	−1.27034	−0.635168	+	0.772374i	$0.719069\pi$
$662$	−20.1397	−0.782753
$663$	12.2998	0.477684
$664$	−2.08670	−0.0809797
$665$	10.6626	0.413479
$666$	91.3702	3.54052
$667$	−8.67581	−0.335929
$668$	−40.3528	−1.56130
$669$	−1.22773	−0.0474670
$670$	17.4836	0.675450
$671$	69.9066	2.69871
$672$	−35.3531	−1.36377
$673$	−32.2886	−1.24463	−0.622316	−	0.782766i	$-0.713808\pi$
$673$	−32.2886	−1.24463	−0.622316	+	0.782766i	$0.713808\pi$
$674$	−33.3036	−1.28281
$675$	−156.271	−6.01487
$676$	2.36772	0.0910660
$677$	21.7101	0.834389	0.417194	−	0.908817i	$-0.363013\pi$
$677$	21.7101	0.834389	0.417194	+	0.908817i	$0.363013\pi$
$678$	63.2767	2.43013
$679$	−21.7309	−0.833957
$680$	1.16485	0.0446698
$681$	32.2625	1.23630
$682$	89.5306	3.42830
$683$	−49.3407	−1.88797	−0.943984	−	0.329991i	$-0.892954\pi$
$683$	−49.3407	−1.88797	−0.943984	+	0.329991i	$0.892954\pi$
$684$	34.1813	1.30695
$685$	23.3133	0.890757
$686$	33.1687	1.26639
$687$	−85.9032	−3.27741
$688$	−3.68386	−0.140446
$689$	26.0511	0.992466
$690$	−76.4731	−2.91128
$691$	21.5772	0.820835	0.410418	−	0.911898i	$-0.365383\pi$
$691$	21.5772	0.820835	0.410418	+	0.911898i	$0.365383\pi$
$692$	−30.0277	−1.14148
$693$	−58.4765	−2.22134
$694$	−4.98574	−0.189256
$695$	64.5183	2.44732
$696$	−2.88696	−0.109430
$697$	3.09112	0.117085
$698$	16.5638	0.626949
$699$	−23.0222	−0.870779
$700$	−28.8731	−1.09130
$701$	−14.1779	−0.535491	−0.267745	−	0.963490i	$-0.586279\pi$
$701$	−14.1779	−0.535491	−0.267745	+	0.963490i	$0.586279\pi$
$702$	−118.412	−4.46917
$703$	11.9611	0.451122
$704$	−51.8659	−1.95477
$705$	7.76734	0.292535
$706$	33.9976	1.27952
$707$	−7.28162	−0.273853
$708$	−13.1830	−0.495448
$709$	8.47300	0.318210	0.159105	−	0.987262i	$-0.449139\pi$
$709$	8.47300	0.318210	0.159105	+	0.987262i	$0.449139\pi$
$710$	−62.2191	−2.33504
$711$	−109.704	−4.11421
$712$	1.46310	0.0548321
$713$	−22.8424	−0.855455
$714$	−8.88643	−0.332566
$715$	−82.8675	−3.09907
$716$	−33.6913	−1.25910
$717$	82.5974	3.08465
$718$	60.0314	2.24035
$719$	−36.7304	−1.36981	−0.684907	−	0.728630i	$-0.740157\pi$
$719$	−36.7304	−1.36981	−0.684907	+	0.728630i	$0.740157\pi$
$720$	110.591	4.12148
$721$	13.2382	0.493015
$722$	−30.0506	−1.11837
$723$	43.5450	1.61945
$724$	−12.5174	−0.465207
$725$	29.6705	1.10193
$726$	−141.820	−5.26344
$727$	−48.7945	−1.80969	−0.904843	−	0.425745i	$-0.860012\pi$
$727$	−48.7945	−1.80969	−0.904843	+	0.425745i	$0.860012\pi$
$728$	−1.50015	−0.0555994
$729$	60.5983	2.24438
$730$	−18.9641	−0.701893
$731$	−1.00000	−0.0369863
$732$	−86.5556	−3.19919
$733$	15.4395	0.570269	0.285135	−	0.958487i	$-0.407962\pi$
$733$	15.4395	0.570269	0.285135	+	0.958487i	$0.407962\pi$
$734$	−33.6419	−1.24175
$735$	−66.4839	−2.45229
$736$	23.9099	0.881329
$737$	−12.5520	−0.462360
$738$	−48.6437	−1.79060
$739$	16.8451	0.619655	0.309828	−	0.950793i	$-0.399729\pi$
$739$	16.8451	0.619655	0.309828	+	0.950793i	$0.399729\pi$
$740$	−48.4349	−1.78050
$741$	−25.3382	−0.930821
$742$	−18.8215	−0.690961
$743$	26.9803	0.989813	0.494906	−	0.868946i	$-0.335202\pi$
$743$	26.9803	0.989813	0.494906	+	0.868946i	$0.335202\pi$
$744$	−7.60105	−0.278668
$745$	−31.2676	−1.14556
$746$	27.6649	1.01288
$747$	−53.7785	−1.96765
$748$	−12.1963	−0.445940
$749$	−11.8538	−0.433129
$750$	131.968	4.81879
$751$	−7.28216	−0.265730	−0.132865	−	0.991134i	$-0.542418\pi$
$751$	−7.28216	−0.265730	−0.132865	+	0.991134i	$0.542418\pi$
$752$	−2.24876	−0.0820039
$753$	−68.9522	−2.51276
$754$	22.4824	0.818759
$755$	0.188921	0.00687554
$756$	44.2941	1.61096
$757$	29.2939	1.06471	0.532353	−	0.846522i	$-0.321308\pi$
$757$	29.2939	1.06471	0.532353	+	0.846522i	$0.321308\pi$
$758$	−34.8664	−1.26641
$759$	54.9026	1.99284
$760$	−2.39964	−0.0870441
$761$	−29.5824	−1.07236	−0.536181	−	0.844103i	$-0.680134\pi$
$761$	−29.5824	−1.07236	−0.536181	+	0.844103i	$0.680134\pi$
$762$	−113.465	−4.11042
$763$	−24.0024	−0.868947
$764$	−19.2359	−0.695929
$765$	30.0204	1.08539
$766$	−52.2989	−1.88964
$767$	7.03947	0.254181
$768$	−43.8591	−1.58263
$769$	22.7460	0.820240	0.410120	−	0.912032i	$-0.365487\pi$
$769$	22.7460	0.820240	0.410120	+	0.912032i	$0.365487\pi$
$770$	59.8707	2.15759
$771$	−96.2614	−3.46677
$772$	−11.5951	−0.417318
$773$	−0.653462	−0.0235034	−0.0117517	−	0.999931i	$-0.503741\pi$
$773$	−0.653462	−0.0235034	−0.0117517	+	0.999931i	$0.503741\pi$
$774$	15.7366	0.565640
$775$	78.1189	2.80612
$776$	4.89058	0.175561
$777$	25.3362	0.908932
$778$	−20.5036	−0.735090
$779$	−6.36787	−0.228153
$780$	102.603	3.67379
$781$	44.6692	1.59839
$782$	6.01004	0.214919
$783$	−45.5174	−1.62666
$784$	19.2481	0.687431
$785$	−18.6570	−0.665896
$786$	−95.1248	−3.39299
$787$	19.3157	0.688532	0.344266	−	0.938872i	$-0.388128\pi$
$787$	19.3157	0.688532	0.344266	+	0.938872i	$0.388128\pi$
$788$	15.8651	0.565170
$789$	51.8882	1.84727
$790$	112.319	3.99614
$791$	12.6392	0.449398
$792$	13.1602	0.467628
$793$	46.2190	1.64128
$794$	6.74515	0.239376
$795$	88.2686	3.13056
$796$	3.99889	0.141737
$797$	28.8060	1.02036	0.510180	−	0.860068i	$-0.329579\pi$
$797$	28.8060	1.02036	0.510180	+	0.860068i	$0.329579\pi$
$798$	18.3065	0.648043
$799$	−0.610436	−0.0215957
$800$	−81.7696	−2.89099
$801$	37.7071	1.33231
$802$	22.3218	0.788210
$803$	13.6150	0.480462
$804$	15.5415	0.548105
$805$	−15.2751	−0.538377
$806$	59.1935	2.08500
$807$	−55.2498	−1.94488
$808$	1.63874	0.0576506
$809$	−6.45279	−0.226868	−0.113434	−	0.993546i	$-0.536185\pi$
$809$	−6.45279	−0.226868	−0.113434	+	0.993546i	$0.536185\pi$
$810$	−217.807	−7.65295
$811$	−39.5619	−1.38921	−0.694603	−	0.719393i	$-0.744420\pi$
$811$	−39.5619	−1.38921	−0.694603	+	0.719393i	$0.744420\pi$
$812$	−8.40993	−0.295131
$813$	−61.9105	−2.17130
$814$	67.1617	2.35402
$815$	−58.6868	−2.05571
$816$	−12.0656	−0.422381
$817$	2.06005	0.0720721
$818$	21.3248	0.745605
$819$	−38.6620	−1.35096
$820$	25.7858	0.900479
$821$	50.3636	1.75770	0.878851	−	0.477097i	$-0.158311\pi$
$821$	50.3636	1.75770	0.878851	+	0.477097i	$0.158311\pi$
$822$	40.0262	1.39608
$823$	−40.1402	−1.39920	−0.699601	−	0.714534i	$-0.746639\pi$
$823$	−40.1402	−1.39920	−0.699601	+	0.714534i	$0.746639\pi$
$824$	−2.97927	−0.103788
$825$	−187.762	−6.53703
$826$	−5.08593	−0.176962
$827$	6.45257	0.224378	0.112189	−	0.993687i	$-0.464214\pi$
$827$	6.45257	0.224378	0.112189	+	0.993687i	$0.464214\pi$
$828$	−48.9676	−1.70174
$829$	−51.3902	−1.78486	−0.892428	−	0.451189i	$-0.851000\pi$
$829$	−51.3902	−1.78486	−0.892428	+	0.451189i	$0.851000\pi$
$830$	55.0607	1.91118
$831$	17.8660	0.619766
$832$	−34.2913	−1.18884
$833$	5.22498	0.181035
$834$	110.770	3.83567
$835$	73.0096	2.52660
$836$	25.1250	0.868965
$837$	−119.842	−4.14235
$838$	−76.4836	−2.64208
$839$	23.3504	0.806147	0.403073	−	0.915168i	$-0.367942\pi$
$839$	23.3504	0.806147	0.403073	+	0.915168i	$0.367942\pi$
$840$	−5.08296	−0.175379
$841$	−20.3578	−0.701993
$842$	28.0078	0.965213
$843$	106.673	3.67403
$844$	−16.4405	−0.565905
$845$	−4.28387	−0.147369
$846$	9.60619	0.330267
$847$	−28.3279	−0.973358
$848$	−25.5551	−0.877565
$849$	6.48294	0.222494
$850$	−20.5538	−0.704989
$851$	−17.1353	−0.587391
$852$	−55.3076	−1.89481
$853$	−9.76031	−0.334186	−0.167093	−	0.985941i	$-0.553438\pi$
$853$	−9.76031	−0.334186	−0.167093	+	0.985941i	$0.553438\pi$
$854$	−33.3926	−1.14267
$855$	−61.8436	−2.11500
$856$	2.66772	0.0911807
$857$	16.5488	0.565297	0.282648	−	0.959224i	$-0.408787\pi$
$857$	16.5488	0.565297	0.282648	+	0.959224i	$0.408787\pi$
$858$	−142.274	−4.85715
$859$	44.9073	1.53222	0.766108	−	0.642712i	$-0.222191\pi$
$859$	44.9073	1.53222	0.766108	+	0.642712i	$0.222191\pi$
$860$	−8.34189	−0.284456
$861$	−13.4885	−0.459688
$862$	36.2143	1.23346
$863$	−5.51119	−0.187603	−0.0938015	−	0.995591i	$-0.529902\pi$
$863$	−5.51119	−0.187603	−0.0938015	+	0.995591i	$0.529902\pi$
$864$	125.442	4.26764
$865$	54.3285	1.84722
$866$	49.8718	1.69471
$867$	−3.27527	−0.111234
$868$	−22.1424	−0.751562
$869$	−80.6378	−2.73545
$870$	76.1768	2.58264
$871$	−8.29883	−0.281195
$872$	5.40178	0.182927
$873$	126.040	4.26581
$874$	−12.3810	−0.418793
$875$	26.3600	0.891130
$876$	−16.8575	−0.569563
$877$	4.81358	0.162543	0.0812716	−	0.996692i	$-0.474102\pi$
$877$	4.81358	0.162543	0.0812716	+	0.996692i	$0.474102\pi$
$878$	69.6868	2.35182
$879$	15.0462	0.507496
$880$	81.2899	2.74028
$881$	−43.4195	−1.46284	−0.731420	−	0.681927i	$-0.761142\pi$
$881$	−43.4195	−1.46284	−0.731420	+	0.681927i	$0.761142\pi$
$882$	−82.2233	−2.76860
$883$	20.0534	0.674850	0.337425	−	0.941352i	$-0.390444\pi$
$883$	20.0534	0.674850	0.337425	+	0.941352i	$0.390444\pi$
$884$	−8.06362	−0.271209
$885$	23.8518	0.801769
$886$	−11.4933	−0.386126
$887$	−20.9931	−0.704879	−0.352439	−	0.935835i	$-0.614648\pi$
$887$	−20.9931	−0.704879	−0.352439	+	0.935835i	$0.614648\pi$
$888$	−5.70195	−0.191345
$889$	−22.6642	−0.760131
$890$	−38.6061	−1.29408
$891$	156.371	5.23862
$892$	0.804891	0.0269497
$893$	1.25753	0.0420816
$894$	−53.6828	−1.79542
$895$	60.9570	2.03757
$896$	3.18710	0.106474
$897$	36.2991	1.21199
$898$	−27.1405	−0.905691
$899$	22.7539	0.758885
$900$	167.465	5.58215
$901$	−6.93704	−0.231106
$902$	−35.7556	−1.19053
$903$	4.36363	0.145213
$904$	−2.84447	−0.0946056
$905$	22.6476	0.752830
$906$	0.324355	0.0107760
$907$	7.82454	0.259810	0.129905	−	0.991526i	$-0.458533\pi$
$907$	7.82454	0.259810	0.129905	+	0.991526i	$0.458533\pi$
$908$	−21.1510	−0.701920
$909$	42.2335	1.40080
$910$	39.5837	1.31219
$911$	22.6272	0.749674	0.374837	−	0.927091i	$-0.377699\pi$
$911$	22.6272	0.749674	0.374837	+	0.927091i	$0.377699\pi$
$912$	24.8558	0.823057
$913$	−39.5299	−1.30825
$914$	33.3529	1.10321
$915$	156.603	5.17715
$916$	56.3173	1.86078
$917$	−19.0007	−0.627458
$918$	31.5315	1.04069
$919$	−3.97162	−0.131012	−0.0655058	−	0.997852i	$-0.520866\pi$
$919$	−3.97162	−0.131012	−0.0655058	+	0.997852i	$0.520866\pi$
$920$	3.43769	0.113337
$921$	−30.2933	−0.998197
$922$	−17.9506	−0.591173
$923$	29.5332	0.972097
$924$	53.2201	1.75081
$925$	58.6012	1.92679
$926$	40.3102	1.32468
$927$	−76.7817	−2.52184
$928$	−23.8172	−0.781839
$929$	−35.7603	−1.17326	−0.586628	−	0.809856i	$-0.699545\pi$
$929$	−35.7603	−1.17326	−0.586628	+	0.809856i	$0.699545\pi$
$930$	200.565	6.57678
$931$	−10.7637	−0.352767
$932$	15.0931	0.494392
$933$	8.52967	0.279249
$934$	7.11328	0.232754
$935$	22.0665	0.721652
$936$	8.70092	0.284399
$937$	32.0456	1.04688	0.523442	−	0.852061i	$-0.324648\pi$
$937$	32.0456	1.04688	0.523442	+	0.852061i	$0.324648\pi$
$938$	5.99580	0.195770
$939$	−28.3466	−0.925055
$940$	−5.09219	−0.166089
$941$	−13.0283	−0.424709	−0.212355	−	0.977193i	$-0.568113\pi$
$941$	−13.0283	−0.424709	−0.212355	+	0.977193i	$0.568113\pi$
$942$	−32.0318	−1.04365
$943$	9.12251	0.297070
$944$	−6.90545	−0.224753
$945$	−80.1405	−2.60697
$946$	11.5672	0.376082
$947$	42.2695	1.37357	0.686787	−	0.726859i	$-0.259021\pi$
$947$	42.2695	1.37357	0.686787	+	0.726859i	$0.259021\pi$
$948$	99.8426	3.24274
$949$	9.00158	0.292204
$950$	42.3418	1.37375
$951$	11.8052	0.382809
$952$	0.399471	0.0129469
$953$	−9.27686	−0.300507	−0.150253	−	0.988648i	$-0.548009\pi$
$953$	−9.27686	−0.300507	−0.150253	+	0.988648i	$0.548009\pi$
$954$	109.165	3.53436
$955$	34.8031	1.12620
$956$	−54.1500	−1.75134
$957$	−54.6899	−1.76787
$958$	38.8196	1.25420
$959$	7.99504	0.258173
$960$	−116.189	−3.74998
$961$	28.9084	0.932529
$962$	44.4042	1.43165
$963$	68.7524	2.21552
$964$	−28.5477	−0.919458
$965$	20.9789	0.675334
$966$	−26.2256	−0.843795
$967$	−23.7769	−0.764615	−0.382308	−	0.924035i	$-0.624870\pi$
$967$	−23.7769	−0.764615	−0.382308	+	0.924035i	$0.624870\pi$
$968$	6.37523	0.204908
$969$	6.74721	0.216752
$970$	−129.045	−4.14339
$971$	24.3361	0.780983	0.390491	−	0.920607i	$-0.372305\pi$
$971$	24.3361	0.780983	0.390491	+	0.920607i	$0.372305\pi$
$972$	−93.8730	−3.01098
$973$	22.1258	0.709322
$974$	−45.3818	−1.45413
$975$	−124.139	−3.97564
$976$	−45.3391	−1.45127
$977$	35.4514	1.13419	0.567095	−	0.823652i	$-0.308067\pi$
$977$	35.4514	1.13419	0.567095	+	0.823652i	$0.308067\pi$
$978$	−100.758	−3.22190
$979$	27.7166	0.885826
$980$	43.5862	1.39231
$981$	139.215	4.44478
$982$	−58.9516	−1.88122
$983$	56.5872	1.80485	0.902425	−	0.430847i	$-0.141785\pi$
$983$	56.5872	1.80485	0.902425	+	0.430847i	$0.141785\pi$
$984$	3.03561	0.0967717
$985$	−28.7044	−0.914597
$986$	−5.98675	−0.190657
$987$	2.66372	0.0847871
$988$	16.6115	0.528481
$989$	−2.95120	−0.0938426
$990$	−347.251	−11.0364
$991$	45.5000	1.44535	0.722677	−	0.691186i	$-0.242911\pi$
$991$	45.5000	1.44535	0.722677	+	0.691186i	$0.242911\pi$
$992$	−62.7080	−1.99098
$993$	32.3907	1.02789
$994$	−21.3373	−0.676779
$995$	−7.23511	−0.229368
$996$	48.9444	1.55086
$997$	−19.9770	−0.632678	−0.316339	−	0.948646i	$-0.602454\pi$
$997$	−19.9770	−0.632678	−0.316339	+	0.948646i	$0.602454\pi$
$998$	−45.5662	−1.44237
$999$	−89.8999	−2.84431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.17	✓	21
3.2	odd	2		6579.2.a.u.1.5		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.17	✓	21	1.1	even	1	trivial
6579.2.a.u.1.5		21	3.2	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+2.03648 q^{2} -3.27527 q^{3} +2.14723 q^{4} -3.88495 q^{5} -6.67000 q^{6} -1.33230 q^{7} +0.299836 q^{8} +7.72736 q^{9} +O(q^{10})\)	\(q+2.03648 q^{2} -3.27527 q^{3} +2.14723 q^{4} -3.88495 q^{5} -6.67000 q^{6} -1.33230 q^{7} +0.299836 q^{8} +7.72736 q^{9} -7.91160 q^{10} +5.68000 q^{11} -7.03276 q^{12} +3.75535 q^{13} -2.71319 q^{14} +12.7242 q^{15} -3.68386 q^{16} -1.00000 q^{17} +15.7366 q^{18} +2.06005 q^{19} -8.34189 q^{20} +4.36363 q^{21} +11.5672 q^{22} -2.95120 q^{23} -0.982041 q^{24} +10.0928 q^{25} +7.64769 q^{26} -15.4834 q^{27} -2.86076 q^{28} +2.93976 q^{29} +25.9126 q^{30} +7.74005 q^{31} -8.10176 q^{32} -18.6035 q^{33} -2.03648 q^{34} +5.17591 q^{35} +16.5924 q^{36} +5.80622 q^{37} +4.19524 q^{38} -12.2998 q^{39} -1.16485 q^{40} -3.09112 q^{41} +8.88643 q^{42} +1.00000 q^{43} +12.1963 q^{44} -30.0204 q^{45} -6.01004 q^{46} +0.610436 q^{47} +12.0656 q^{48} -5.22498 q^{49} +20.5538 q^{50} +3.27527 q^{51} +8.06362 q^{52} +6.93704 q^{53} -31.5315 q^{54} -22.0665 q^{55} -0.399471 q^{56} -6.74721 q^{57} +5.98675 q^{58} +1.87452 q^{59} +27.3219 q^{60} +12.3075 q^{61} +15.7624 q^{62} -10.2952 q^{63} -9.13131 q^{64} -14.5894 q^{65} -37.8856 q^{66} -2.20987 q^{67} -2.14723 q^{68} +9.66595 q^{69} +10.5406 q^{70} +7.86429 q^{71} +2.31694 q^{72} +2.39700 q^{73} +11.8242 q^{74} -33.0567 q^{75} +4.42341 q^{76} -7.56746 q^{77} -25.0482 q^{78} -14.1968 q^{79} +14.3116 q^{80} +27.5301 q^{81} -6.29500 q^{82} -6.95948 q^{83} +9.36973 q^{84} +3.88495 q^{85} +2.03648 q^{86} -9.62849 q^{87} +1.70307 q^{88} +4.87968 q^{89} -61.1358 q^{90} -5.00325 q^{91} -6.33690 q^{92} -25.3507 q^{93} +1.24314 q^{94} -8.00319 q^{95} +26.5354 q^{96} +16.3109 q^{97} -10.6405 q^{98} +43.8914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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