LMFDB - Embedded newform 731.2.a.e.1.6

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:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + \cdots + 64 $ x^19 - 2x^18 - 30x^17 + 62x^16 + 365x^15 - 786x^14 - 2295x^13 + 5233x^12 + 7816x^11 - 19517x^10 - 13527x^9 + 40173x^8 + 8942x^7 - 41911x^6 + 1140x^5 + 18520x^4 - 1520x^3 - 2640x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.32959$ of defining polynomial
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)

$f(q)$	$=$	$q-1.32959 q^{2} -1.38064 q^{3} -0.232191 q^{4} -0.595657 q^{5} +1.83568 q^{6} -3.72326 q^{7} +2.96790 q^{8} -1.09384 q^{9} +O(q^{10})$	\(q-1.32959 q^{2} -1.38064 q^{3} -0.232191 q^{4} -0.595657 q^{5} +1.83568 q^{6} -3.72326 q^{7} +2.96790 q^{8} -1.09384 q^{9} +0.791980 q^{10} -4.08357 q^{11} +0.320572 q^{12} -0.436070 q^{13} +4.95040 q^{14} +0.822388 q^{15} -3.48171 q^{16} +1.00000 q^{17} +1.45435 q^{18} -4.36031 q^{19} +0.138306 q^{20} +5.14047 q^{21} +5.42948 q^{22} -3.77759 q^{23} -4.09760 q^{24} -4.64519 q^{25} +0.579794 q^{26} +5.65211 q^{27} +0.864507 q^{28} +0.0165787 q^{29} -1.09344 q^{30} +8.31824 q^{31} -1.30656 q^{32} +5.63794 q^{33} -1.32959 q^{34} +2.21778 q^{35} +0.253979 q^{36} -3.71176 q^{37} +5.79743 q^{38} +0.602055 q^{39} -1.76785 q^{40} +3.97399 q^{41} -6.83472 q^{42} -1.00000 q^{43} +0.948169 q^{44} +0.651551 q^{45} +5.02265 q^{46} -6.88951 q^{47} +4.80698 q^{48} +6.86263 q^{49} +6.17620 q^{50} -1.38064 q^{51} +0.101251 q^{52} +6.96855 q^{53} -7.51499 q^{54} +2.43241 q^{55} -11.0502 q^{56} +6.02002 q^{57} -0.0220428 q^{58} +7.32511 q^{59} -0.190951 q^{60} +11.7196 q^{61} -11.0598 q^{62} +4.07263 q^{63} +8.70060 q^{64} +0.259748 q^{65} -7.49615 q^{66} +0.915976 q^{67} -0.232191 q^{68} +5.21550 q^{69} -2.94874 q^{70} +0.304173 q^{71} -3.24639 q^{72} +15.7512 q^{73} +4.93512 q^{74} +6.41334 q^{75} +1.01243 q^{76} +15.2042 q^{77} -0.800486 q^{78} -5.42142 q^{79} +2.07390 q^{80} -4.52202 q^{81} -5.28378 q^{82} -13.1755 q^{83} -1.19357 q^{84} -0.595657 q^{85} +1.32959 q^{86} -0.0228892 q^{87} -12.1196 q^{88} -12.0956 q^{89} -0.866295 q^{90} +1.62360 q^{91} +0.877123 q^{92} -11.4845 q^{93} +9.16022 q^{94} +2.59725 q^{95} +1.80388 q^{96} +18.6764 q^{97} -9.12449 q^{98} +4.46676 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * 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 $

$2$	−1.32959	−0.940162	−0.470081	−	0.882623i	$-0.655775\pi$
$2$	−1.32959	−0.940162	−0.470081	+	0.882623i	$0.655775\pi$
$3$	−1.38064	−0.797112	−0.398556	−	0.917144i	$-0.630489\pi$
$3$	−1.38064	−0.797112	−0.398556	+	0.917144i	$0.630489\pi$
$4$	−0.232191	−0.116096
$5$	−0.595657	−0.266386	−0.133193	−	0.991090i	$-0.542523\pi$
$5$	−0.595657	−0.266386	−0.133193	+	0.991090i	$0.542523\pi$
$6$	1.83568	0.749415
$7$	−3.72326	−1.40726	−0.703629	−	0.710567i	$-0.748438\pi$
$7$	−3.72326	−1.40726	−0.703629	+	0.710567i	$0.748438\pi$
$8$	2.96790	1.04931
$9$	−1.09384	−0.364612
$10$	0.791980	0.250446
$11$	−4.08357	−1.23124	−0.615622	−	0.788042i	$-0.711095\pi$
$11$	−4.08357	−1.23124	−0.615622	+	0.788042i	$0.711095\pi$
$12$	0.320572	0.0925412
$13$	−0.436070	−0.120944	−0.0604720	−	0.998170i	$-0.519261\pi$
$13$	−0.436070	−0.120944	−0.0604720	+	0.998170i	$0.519261\pi$
$14$	4.95040	1.32305
$15$	0.822388	0.212340
$16$	−3.48171	−0.870426
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.45435	0.342794
$19$	−4.36031	−1.00032	−0.500162	−	0.865932i	$-0.666726\pi$
$19$	−4.36031	−1.00032	−0.500162	+	0.865932i	$0.666726\pi$
$20$	0.138306	0.0309262
$21$	5.14047	1.12174
$22$	5.42948	1.15757
$23$	−3.77759	−0.787683	−0.393841	−	0.919178i	$-0.628854\pi$
$23$	−3.77759	−0.787683	−0.393841	+	0.919178i	$0.628854\pi$
$24$	−4.09760	−0.836419
$25$	−4.64519	−0.929038
$26$	0.579794	0.113707
$27$	5.65211	1.08775
$28$	0.864507	0.163376
$29$	0.0165787	0.00307858	0.00153929	−	0.999999i	$-0.499510\pi$
$29$	0.0165787	0.00307858	0.00153929	+	0.999999i	$0.499510\pi$
$30$	−1.09344	−0.199634
$31$	8.31824	1.49400	0.747000	−	0.664824i	$-0.231494\pi$
$31$	8.31824	1.49400	0.747000	+	0.664824i	$0.231494\pi$
$32$	−1.30656	−0.230969
$33$	5.63794	0.981440
$34$	−1.32959	−0.228023
$35$	2.21778	0.374874
$36$	0.253979	0.0423298
$37$	−3.71176	−0.610210	−0.305105	−	0.952319i	$-0.598692\pi$
$37$	−3.71176	−0.610210	−0.305105	+	0.952319i	$0.598692\pi$
$38$	5.79743	0.940467
$39$	0.602055	0.0964059
$40$	−1.76785	−0.279522
$41$	3.97399	0.620633	0.310316	−	0.950633i	$-0.399565\pi$
$41$	3.97399	0.620633	0.310316	+	0.950633i	$0.399565\pi$
$42$	−6.83472	−1.05462
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.948169	0.142942
$45$	0.651551	0.0971274
$46$	5.02265	0.740549
$47$	−6.88951	−1.00494	−0.502469	−	0.864595i	$-0.667575\pi$
$47$	−6.88951	−1.00494	−0.502469	+	0.864595i	$0.667575\pi$
$48$	4.80698	0.693828
$49$	6.86263	0.980376
$50$	6.17620	0.873447
$51$	−1.38064	−0.193328
$52$	0.101251	0.0140410
$53$	6.96855	0.957204	0.478602	−	0.878032i	$-0.341144\pi$
$53$	6.96855	0.957204	0.478602	+	0.878032i	$0.341144\pi$
$54$	−7.51499	−1.02266
$55$	2.43241	0.327986
$56$	−11.0502	−1.47665
$57$	6.02002	0.797371
$58$	−0.0220428	−0.00289437
$59$	7.32511	0.953648	0.476824	−	0.878999i	$-0.341788\pi$
$59$	7.32511	0.953648	0.476824	+	0.878999i	$0.341788\pi$
$60$	−0.190951	−0.0246517
$61$	11.7196	1.50054	0.750269	−	0.661133i	$-0.229924\pi$
$61$	11.7196	1.50054	0.750269	+	0.661133i	$0.229924\pi$
$62$	−11.0598	−1.40460
$63$	4.07263	0.513103
$64$	8.70060	1.08757
$65$	0.259748	0.0322178
$66$	−7.49615	−0.922712
$67$	0.915976	0.111904	0.0559522	−	0.998433i	$-0.482181\pi$
$67$	0.915976	0.111904	0.0559522	+	0.998433i	$0.482181\pi$
$68$	−0.232191	−0.0281573
$69$	5.21550	0.627872
$70$	−2.94874	−0.352442
$71$	0.304173	0.0360988	0.0180494	−	0.999837i	$-0.494254\pi$
$71$	0.304173	0.0360988	0.0180494	+	0.999837i	$0.494254\pi$
$72$	−3.24639	−0.382591
$73$	15.7512	1.84354	0.921768	−	0.387741i	$-0.126745\pi$
$73$	15.7512	1.84354	0.921768	+	0.387741i	$0.126745\pi$
$74$	4.93512	0.573696
$75$	6.41334	0.740548
$76$	1.01243	0.116133
$77$	15.2042	1.73268
$78$	−0.800486	−0.0906372
$79$	−5.42142	−0.609957	−0.304978	−	0.952359i	$-0.598649\pi$
$79$	−5.42142	−0.609957	−0.304978	+	0.952359i	$0.598649\pi$
$80$	2.07390	0.231869
$81$	−4.52202	−0.502447
$82$	−5.28378	−0.583495
$83$	−13.1755	−1.44619	−0.723097	−	0.690746i	$-0.757282\pi$
$83$	−13.1755	−1.44619	−0.723097	+	0.690746i	$0.757282\pi$
$84$	−1.19357	−0.130229
$85$	−0.595657	−0.0646081
$86$	1.32959	0.143373
$87$	−0.0228892	−0.00245398
$88$	−12.1196	−1.29196
$89$	−12.0956	−1.28213	−0.641064	−	0.767488i	$-0.721507\pi$
$89$	−12.0956	−1.28213	−0.641064	+	0.767488i	$0.721507\pi$
$90$	−0.866295	−0.0913155
$91$	1.62360	0.170199
$92$	0.877123	0.0914464
$93$	−11.4845	−1.19089
$94$	9.16022	0.944805
$95$	2.59725	0.266472
$96$	1.80388	0.184108
$97$	18.6764	1.89631	0.948153	−	0.317816i	$-0.102949\pi$
$97$	18.6764	1.89631	0.948153	+	0.317816i	$0.102949\pi$
$98$	−9.12449	−0.921713
$99$	4.46676	0.448926
$100$	1.07857	0.107857
$101$	−1.28745	−0.128106	−0.0640531	−	0.997946i	$-0.520403\pi$
$101$	−1.28745	−0.128106	−0.0640531	+	0.997946i	$0.520403\pi$
$102$	1.83568	0.181760
$103$	−10.1709	−1.00217	−0.501083	−	0.865399i	$-0.667065\pi$
$103$	−10.1709	−1.00217	−0.501083	+	0.865399i	$0.667065\pi$
$104$	−1.29421	−0.126908
$105$	−3.06196	−0.298817
$106$	−9.26531	−0.899926
$107$	−1.40033	−0.135375	−0.0676877	−	0.997707i	$-0.521562\pi$
$107$	−1.40033	−0.135375	−0.0676877	+	0.997707i	$0.521562\pi$
$108$	−1.31237	−0.126283
$109$	1.34972	0.129280	0.0646400	−	0.997909i	$-0.479410\pi$
$109$	1.34972	0.129280	0.0646400	+	0.997909i	$0.479410\pi$
$110$	−3.23411	−0.308360
$111$	5.12460	0.486406
$112$	12.9633	1.22491
$113$	2.65405	0.249672	0.124836	−	0.992177i	$-0.460160\pi$
$113$	2.65405	0.249672	0.124836	+	0.992177i	$0.460160\pi$
$114$	−8.00415	−0.749658
$115$	2.25015	0.209828
$116$	−0.00384942	−0.000357410 0
$117$	0.476988	0.0440976
$118$	−9.73939	−0.896583
$119$	−3.72326	−0.341310
$120$	2.44076	0.222810
$121$	5.67557	0.515961
$122$	−15.5822	−1.41075
$123$	−5.48665	−0.494714
$124$	−1.93142	−0.173447
$125$	5.74523	0.513869
$126$	−5.41492	−0.482400
$127$	−18.7665	−1.66526	−0.832629	−	0.553831i	$-0.813165\pi$
$127$	−18.7665	−1.66526	−0.832629	+	0.553831i	$0.813165\pi$
$128$	−8.95511	−0.791527
$129$	1.38064	0.121559
$130$	−0.345358	−0.0302899
$131$	1.03888	0.0907675	0.0453838	−	0.998970i	$-0.485549\pi$
$131$	1.03888	0.0907675	0.0453838	+	0.998970i	$0.485549\pi$
$132$	−1.30908	−0.113941
$133$	16.2346	1.40771
$134$	−1.21787	−0.105208
$135$	−3.36672	−0.289761
$136$	2.96790	0.254495
$137$	−15.0939	−1.28956	−0.644778	−	0.764370i	$-0.723050\pi$
$137$	−15.0939	−1.28956	−0.644778	+	0.764370i	$0.723050\pi$
$138$	−6.93447	−0.590301
$139$	9.57241	0.811921	0.405961	−	0.913891i	$-0.366937\pi$
$139$	9.57241	0.811921	0.405961	+	0.913891i	$0.366937\pi$
$140$	−0.514950	−0.0435212
$141$	9.51193	0.801049
$142$	−0.404426	−0.0339387
$143$	1.78072	0.148911
$144$	3.80841	0.317368
$145$	−0.00987521	−0.000820091 0
$146$	−20.9426	−1.73322
$147$	−9.47482	−0.781470
$148$	0.861838	0.0708426
$149$	−6.75320	−0.553244	−0.276622	−	0.960979i	$-0.589215\pi$
$149$	−6.75320	−0.553244	−0.276622	+	0.960979i	$0.589215\pi$
$150$	−8.52711	−0.696235
$151$	19.4118	1.57971	0.789855	−	0.613294i	$-0.210156\pi$
$151$	19.4118	1.57971	0.789855	+	0.613294i	$0.210156\pi$
$152$	−12.9410	−1.04965
$153$	−1.09384	−0.0884313
$154$	−20.2153	−1.62900
$155$	−4.95482	−0.397981
$156$	−0.139792	−0.0111923
$157$	1.00029	0.0798317	0.0399159	−	0.999203i	$-0.487291\pi$
$157$	1.00029	0.0798317	0.0399159	+	0.999203i	$0.487291\pi$
$158$	7.20826	0.573458
$159$	−9.62105	−0.762999
$160$	0.778260	0.0615269
$161$	14.0650	1.10847
$162$	6.01243	0.472381
$163$	3.91439	0.306599	0.153299	−	0.988180i	$-0.451010\pi$
$163$	3.91439	0.306599	0.153299	+	0.988180i	$0.451010\pi$
$164$	−0.922725	−0.0720527
$165$	−3.35828	−0.261442
$166$	17.5180	1.35966
$167$	−19.5306	−1.51133	−0.755663	−	0.654960i	$-0.772685\pi$
$167$	−19.5306	−1.51133	−0.755663	+	0.654960i	$0.772685\pi$
$168$	15.2564	1.17706
$169$	−12.8098	−0.985373
$170$	0.791980	0.0607421
$171$	4.76946	0.364730
$172$	0.232191	0.0177044
$173$	−13.4894	−1.02558	−0.512792	−	0.858513i	$-0.671389\pi$
$173$	−13.4894	−1.02558	−0.512792	+	0.858513i	$0.671389\pi$
$174$	0.0304332	0.00230714
$175$	17.2952	1.30740
$176$	14.2178	1.07171
$177$	−10.1133	−0.760165
$178$	16.0821	1.20541
$179$	−3.03986	−0.227210	−0.113605	−	0.993526i	$-0.536240\pi$
$179$	−3.03986	−0.227210	−0.113605	+	0.993526i	$0.536240\pi$
$180$	−0.151284	−0.0112761
$181$	−10.0669	−0.748268	−0.374134	−	0.927375i	$-0.622060\pi$
$181$	−10.0669	−0.748268	−0.374134	+	0.927375i	$0.622060\pi$
$182$	−2.15872	−0.160015
$183$	−16.1805	−1.19610
$184$	−11.2115	−0.826524
$185$	2.21094	0.162551
$186$	15.2697	1.11963
$187$	−4.08357	−0.298620
$188$	1.59968	0.116669
$189$	−21.0443	−1.53074
$190$	−3.45328	−0.250527
$191$	1.61213	0.116649	0.0583247	−	0.998298i	$-0.481424\pi$
$191$	1.61213	0.116649	0.0583247	+	0.998298i	$0.481424\pi$
$192$	−12.0124	−0.866919
$193$	−13.4116	−0.965391	−0.482696	−	0.875788i	$-0.660342\pi$
$193$	−13.4116	−0.965391	−0.482696	+	0.875788i	$0.660342\pi$
$194$	−24.8320	−1.78283
$195$	−0.358618	−0.0256812
$196$	−1.59344	−0.113817
$197$	−15.7974	−1.12552	−0.562759	−	0.826621i	$-0.690260\pi$
$197$	−15.7974	−1.12552	−0.562759	+	0.826621i	$0.690260\pi$
$198$	−5.93895	−0.422063
$199$	21.9452	1.55565	0.777827	−	0.628478i	$-0.216322\pi$
$199$	21.9452	1.55565	0.777827	+	0.628478i	$0.216322\pi$
$200$	−13.7865	−0.974850
$201$	−1.26463	−0.0892003
$202$	1.71178	0.120441
$203$	−0.0617266	−0.00433236
$204$	0.320572	0.0224445
$205$	−2.36714	−0.165328
$206$	13.5231	0.942199
$207$	4.13206	0.287198
$208$	1.51827	0.105273
$209$	17.8057	1.23164
$210$	4.07115	0.280936
$211$	28.4621	1.95941	0.979706	−	0.200439i	$-0.0642369\pi$
$211$	28.4621	1.95941	0.979706	+	0.200439i	$0.0642369\pi$
$212$	−1.61803	−0.111127
$213$	−0.419954	−0.0287748
$214$	1.86187	0.127275
$215$	0.595657	0.0406235
$216$	16.7749	1.14139
$217$	−30.9709	−2.10244
$218$	−1.79458	−0.121544
$219$	−21.7467	−1.46951
$220$	−0.564784	−0.0380777
$221$	−0.436070	−0.0293332
$222$	−6.81362	−0.457300
$223$	−19.1124	−1.27986	−0.639930	−	0.768433i	$-0.721037\pi$
$223$	−19.1124	−1.27986	−0.639930	+	0.768433i	$0.721037\pi$
$224$	4.86465	0.325033
$225$	5.08107	0.338738
$226$	−3.52880	−0.234732
$227$	−18.3066	−1.21505	−0.607527	−	0.794299i	$-0.707838\pi$
$227$	−18.3066	−1.21505	−0.607527	+	0.794299i	$0.707838\pi$
$228$	−1.39779	−0.0925712
$229$	19.5461	1.29164	0.645822	−	0.763488i	$-0.276515\pi$
$229$	19.5461	1.29164	0.645822	+	0.763488i	$0.276515\pi$
$230$	−2.99178	−0.197272
$231$	−20.9915	−1.38114
$232$	0.0492038	0.00323039
$233$	18.9282	1.24003	0.620013	−	0.784591i	$-0.287127\pi$
$233$	18.9282	1.24003	0.620013	+	0.784591i	$0.287127\pi$
$234$	−0.634199	−0.0414589
$235$	4.10379	0.267701
$236$	−1.70082	−0.110714
$237$	7.48502	0.486204
$238$	4.95040	0.320887
$239$	5.52800	0.357576	0.178788	−	0.983888i	$-0.442782\pi$
$239$	5.52800	0.357576	0.178788	+	0.983888i	$0.442782\pi$
$240$	−2.86331	−0.184826
$241$	10.8982	0.702013	0.351007	−	0.936373i	$-0.385839\pi$
$241$	10.8982	0.702013	0.351007	+	0.936373i	$0.385839\pi$
$242$	−7.54618	−0.485087
$243$	−10.7131	−0.687243
$244$	−2.72118	−0.174206
$245$	−4.08778	−0.261159
$246$	7.29499	0.465112
$247$	1.90140	0.120983
$248$	24.6877	1.56767
$249$	18.1906	1.15278
$250$	−7.63880	−0.483120
$251$	−1.36270	−0.0860129	−0.0430065	−	0.999075i	$-0.513694\pi$
$251$	−1.36270	−0.0860129	−0.0430065	+	0.999075i	$0.513694\pi$
$252$	−0.945628	−0.0595689
$253$	15.4261	0.969830
$254$	24.9517	1.56561
$255$	0.822388	0.0514999
$256$	−5.49457	−0.343411
$257$	8.47650	0.528750	0.264375	−	0.964420i	$-0.414834\pi$
$257$	8.47650	0.528750	0.264375	+	0.964420i	$0.414834\pi$
$258$	−1.83568	−0.114285
$259$	13.8198	0.858723
$260$	−0.0603111	−0.00374034
$261$	−0.0181343	−0.00112249
$262$	−1.38129	−0.0853362
$263$	17.3449	1.06953	0.534766	−	0.845000i	$-0.320400\pi$
$263$	17.3449	1.06953	0.534766	+	0.845000i	$0.320400\pi$
$264$	16.7328	1.02984
$265$	−4.15087	−0.254986
$266$	−21.5853	−1.32348
$267$	16.6996	1.02200
$268$	−0.212681	−0.0129916
$269$	12.6754	0.772831	0.386415	−	0.922325i	$-0.373713\pi$
$269$	12.6754	0.772831	0.386415	+	0.922325i	$0.373713\pi$
$270$	4.47636	0.272422
$271$	14.6944	0.892620	0.446310	−	0.894878i	$-0.352738\pi$
$271$	14.6944	0.892620	0.446310	+	0.894878i	$0.352738\pi$
$272$	−3.48171	−0.211109
$273$	−2.24160	−0.135668
$274$	20.0686	1.21239
$275$	18.9690	1.14387
$276$	−1.21099	−0.0728931
$277$	1.44726	0.0869576	0.0434788	−	0.999054i	$-0.486156\pi$
$277$	1.44726	0.0869576	0.0434788	+	0.999054i	$0.486156\pi$
$278$	−12.7274	−0.763337
$279$	−9.09878	−0.544730
$280$	6.58216	0.393359
$281$	4.67199	0.278707	0.139354	−	0.990243i	$-0.455498\pi$
$281$	4.67199	0.278707	0.139354	+	0.990243i	$0.455498\pi$
$282$	−12.6470	−0.753116
$283$	−17.0842	−1.01555	−0.507775	−	0.861490i	$-0.669532\pi$
$283$	−17.0842	−1.01555	−0.507775	+	0.861490i	$0.669532\pi$
$284$	−0.0706264	−0.00419090
$285$	−3.58587	−0.212408
$286$	−2.36763	−0.140001
$287$	−14.7962	−0.873391
$288$	1.42916	0.0842139
$289$	1.00000	0.0588235
$290$	0.0131300	0.000771019 0
$291$	−25.7854	−1.51157
$292$	−3.65728	−0.214026
$293$	24.7410	1.44538	0.722692	−	0.691170i	$-0.242905\pi$
$293$	24.7410	1.44538	0.722692	+	0.691170i	$0.242905\pi$
$294$	12.5976	0.734709
$295$	−4.36325	−0.254038
$296$	−11.0161	−0.640300
$297$	−23.0808	−1.33928
$298$	8.97899	0.520139
$299$	1.64729	0.0952655
$300$	−1.48912	−0.0859743
$301$	3.72326	0.214605
$302$	−25.8097	−1.48518
$303$	1.77751	0.102115
$304$	15.1813	0.870708
$305$	−6.98085	−0.399722
$306$	1.45435	0.0831398
$307$	−2.04974	−0.116985	−0.0584925	−	0.998288i	$-0.518629\pi$
$307$	−2.04974	−0.116985	−0.0584925	+	0.998288i	$0.518629\pi$
$308$	−3.53028	−0.201156
$309$	14.0423	0.798840
$310$	6.58788	0.374166
$311$	−21.0331	−1.19268	−0.596339	−	0.802733i	$-0.703379\pi$
$311$	−21.0331	−1.19268	−0.596339	+	0.802733i	$0.703379\pi$
$312$	1.78684	0.101160
$313$	−15.4932	−0.875726	−0.437863	−	0.899042i	$-0.644265\pi$
$313$	−15.4932	−0.875726	−0.437863	+	0.899042i	$0.644265\pi$
$314$	−1.32997	−0.0750547
$315$	−2.42589	−0.136683
$316$	1.25880	0.0708133
$317$	−18.8681	−1.05974	−0.529869	−	0.848080i	$-0.677759\pi$
$317$	−18.8681	−1.05974	−0.529869	+	0.848080i	$0.677759\pi$
$318$	12.7921	0.717343
$319$	−0.0677002	−0.00379048
$320$	−5.18257	−0.289715
$321$	1.93336	0.107909
$322$	−18.7006	−1.04214
$323$	−4.36031	−0.242614
$324$	1.04997	0.0583318
$325$	2.02563	0.112362
$326$	−5.20453	−0.288252
$327$	−1.86348	−0.103051
$328$	11.7944	0.651237
$329$	25.6514	1.41421
$330$	4.46514	0.245798
$331$	27.0027	1.48421	0.742103	−	0.670286i	$-0.233829\pi$
$331$	27.0027	1.48421	0.742103	+	0.670286i	$0.233829\pi$
$332$	3.05922	0.167897
$333$	4.06005	0.222490
$334$	25.9677	1.42089
$335$	−0.545608	−0.0298097
$336$	−17.8976	−0.976395
$337$	27.5362	1.49999	0.749996	−	0.661442i	$-0.230055\pi$
$337$	27.5362	1.49999	0.749996	+	0.661442i	$0.230055\pi$
$338$	17.0318	0.926410
$339$	−3.66428	−0.199017
$340$	0.138306	0.00750071
$341$	−33.9681	−1.83948
$342$	−6.34143	−0.342905
$343$	0.511445	0.0276154
$344$	−2.96790	−0.160018
$345$	−3.10665	−0.167256
$346$	17.9354	0.964214
$347$	4.50435	0.241806	0.120903	−	0.992664i	$-0.461421\pi$
$347$	4.50435	0.241806	0.120903	+	0.992664i	$0.461421\pi$
$348$	0.00531466	0.000284896 0
$349$	7.12569	0.381429	0.190715	−	0.981646i	$-0.438919\pi$
$349$	7.12569	0.381429	0.190715	+	0.981646i	$0.438919\pi$
$350$	−22.9956	−1.22917
$351$	−2.46471	−0.131557
$352$	5.33542	0.284379
$353$	5.76791	0.306995	0.153498	−	0.988149i	$-0.450946\pi$
$353$	5.76791	0.306995	0.153498	+	0.988149i	$0.450946\pi$
$354$	13.4466	0.714678
$355$	−0.181183	−0.00961620
$356$	2.80848	0.148849
$357$	5.14047	0.272063
$358$	4.04177	0.213614
$359$	−7.33258	−0.386999	−0.193499	−	0.981100i	$-0.561984\pi$
$359$	−7.33258	−0.386999	−0.193499	+	0.981100i	$0.561984\pi$
$360$	1.93374	0.101917
$361$	0.0123142	0.000648114 0
$362$	13.3849	0.703493
$363$	−7.83592	−0.411279
$364$	−0.376985	−0.0197594
$365$	−9.38230	−0.491092
$366$	21.5134	1.12453
$367$	11.4556	0.597976	0.298988	−	0.954257i	$-0.403351\pi$
$367$	11.4556	0.597976	0.298988	+	0.954257i	$0.403351\pi$
$368$	13.1525	0.685620
$369$	−4.34689	−0.226290
$370$	−2.93964	−0.152825
$371$	−25.9457	−1.34703
$372$	2.66659	0.138257
$373$	33.0783	1.71273	0.856365	−	0.516371i	$-0.172717\pi$
$373$	33.0783	1.71273	0.856365	+	0.516371i	$0.172717\pi$
$374$	5.42948	0.280752
$375$	−7.93209	−0.409611
$376$	−20.4474	−1.05449
$377$	−0.00722945	−0.000372336 0
$378$	27.9802	1.43915
$379$	−10.5807	−0.543496	−0.271748	−	0.962368i	$-0.587602\pi$
$379$	−10.5807	−0.543496	−0.271748	+	0.962368i	$0.587602\pi$
$380$	−0.603058	−0.0309362
$381$	25.9098	1.32740
$382$	−2.14347	−0.109669
$383$	8.90575	0.455063	0.227531	−	0.973771i	$-0.426935\pi$
$383$	8.90575	0.455063	0.227531	+	0.973771i	$0.426935\pi$
$384$	12.3638	0.630936
$385$	−9.05648	−0.461561
$386$	17.8320	0.907624
$387$	1.09384	0.0556028
$388$	−4.33650	−0.220153
$389$	38.7707	1.96575	0.982877	−	0.184262i	$-0.0589895\pi$
$389$	38.7707	1.96575	0.982877	+	0.184262i	$0.0589895\pi$
$390$	0.476815	0.0241445
$391$	−3.77759	−0.191041
$392$	20.3676	1.02872
$393$	−1.43432	−0.0723519
$394$	21.0040	1.05817
$395$	3.22931	0.162484
$396$	−1.03714	−0.0521183
$397$	15.5618	0.781026	0.390513	−	0.920597i	$-0.372298\pi$
$397$	15.5618	0.781026	0.390513	+	0.920597i	$0.372298\pi$
$398$	−29.1781	−1.46257
$399$	−22.4141	−1.12211
$400$	16.1732	0.808660
$401$	15.7304	0.785541	0.392770	−	0.919637i	$-0.371517\pi$
$401$	15.7304	0.785541	0.392770	+	0.919637i	$0.371517\pi$
$402$	1.68144	0.0838628
$403$	−3.62733	−0.180690
$404$	0.298935	0.0148726
$405$	2.69357	0.133845
$406$	0.0820711	0.00407312
$407$	15.1572	0.751317
$408$	−4.09760	−0.202861
$409$	−22.8446	−1.12959	−0.564797	−	0.825230i	$-0.691045\pi$
$409$	−22.8446	−1.12959	−0.564797	+	0.825230i	$0.691045\pi$
$410$	3.14732	0.155435
$411$	20.8392	1.02792
$412$	2.36159	0.116347
$413$	−27.2733	−1.34203
$414$	−5.49395	−0.270013
$415$	7.84806	0.385246
$416$	0.569750	0.0279343
$417$	−13.2160	−0.647193
$418$	−23.6742	−1.15794
$419$	26.2326	1.28155	0.640773	−	0.767731i	$-0.278614\pi$
$419$	26.2326	1.28155	0.640773	+	0.767731i	$0.278614\pi$
$420$	0.710960	0.0346913
$421$	6.74947	0.328949	0.164474	−	0.986381i	$-0.447407\pi$
$421$	6.74947	0.328949	0.164474	+	0.986381i	$0.447407\pi$
$422$	−37.8429	−1.84216
$423$	7.53599	0.366412
$424$	20.6819	1.00440
$425$	−4.64519	−0.225325
$426$	0.558366	0.0270529
$427$	−43.6350	−2.11165
$428$	0.325145	0.0157165
$429$	−2.45853	−0.118699
$430$	−0.791980	−0.0381927
$431$	−4.77271	−0.229894	−0.114947	−	0.993372i	$-0.536670\pi$
$431$	−4.77271	−0.229894	−0.114947	+	0.993372i	$0.536670\pi$
$432$	−19.6790	−0.946805
$433$	34.8669	1.67560	0.837799	−	0.545979i	$-0.183842\pi$
$433$	34.8669	1.67560	0.837799	+	0.545979i	$0.183842\pi$
$434$	41.1786	1.97664
$435$	0.0136341	0.000653705 0
$436$	−0.313394	−0.0150088
$437$	16.4715	0.787938
$438$	28.9142	1.38157
$439$	−34.8396	−1.66280	−0.831402	−	0.555672i	$-0.812461\pi$
$439$	−34.8396	−1.66280	−0.831402	+	0.555672i	$0.812461\pi$
$440$	7.21915	0.344159
$441$	−7.50659	−0.357457
$442$	0.579794	0.0275780
$443$	14.3856	0.683480	0.341740	−	0.939794i	$-0.388984\pi$
$443$	14.3856	0.683480	0.341740	+	0.939794i	$0.388984\pi$
$444$	−1.18989	−0.0564695
$445$	7.20481	0.341541
$446$	25.4116	1.20328
$447$	9.32374	0.440998
$448$	−32.3945	−1.53050
$449$	−22.4760	−1.06071	−0.530353	−	0.847777i	$-0.677941\pi$
$449$	−22.4760	−1.06071	−0.530353	+	0.847777i	$0.677941\pi$
$450$	−6.75574	−0.318469
$451$	−16.2281	−0.764150
$452$	−0.616246	−0.0289858
$453$	−26.8007	−1.25921
$454$	24.3403	1.14235
$455$	−0.967108	−0.0453387
$456$	17.8668	0.836690
$457$	−6.66417	−0.311737	−0.155868	−	0.987778i	$-0.549818\pi$
$457$	−6.66417	−0.311737	−0.155868	+	0.987778i	$0.549818\pi$
$458$	−25.9883	−1.21435
$459$	5.65211	0.263818
$460$	−0.522465	−0.0243601
$461$	−10.8523	−0.505440	−0.252720	−	0.967539i	$-0.581325\pi$
$461$	−10.8523	−0.505440	−0.252720	+	0.967539i	$0.581325\pi$
$462$	27.9101	1.29849
$463$	9.29854	0.432140	0.216070	−	0.976378i	$-0.430676\pi$
$463$	9.29854	0.432140	0.216070	+	0.976378i	$0.430676\pi$
$464$	−0.0577221	−0.00267968
$465$	6.84082	0.317235
$466$	−25.1667	−1.16583
$467$	−9.28200	−0.429520	−0.214760	−	0.976667i	$-0.568897\pi$
$467$	−9.28200	−0.429520	−0.214760	+	0.976667i	$0.568897\pi$
$468$	−0.110752	−0.00511953
$469$	−3.41041	−0.157478
$470$	−5.45635	−0.251683
$471$	−1.38104	−0.0636349
$472$	21.7402	1.00067
$473$	4.08357	0.187763
$474$	−9.95201	−0.457111
$475$	20.2545	0.929340
$476$	0.864507	0.0396246
$477$	−7.62244	−0.349008
$478$	−7.34997	−0.336180
$479$	32.4949	1.48473	0.742365	−	0.669995i	$-0.233704\pi$
$479$	32.4949	1.48473	0.742365	+	0.669995i	$0.233704\pi$
$480$	−1.07450	−0.0490438
$481$	1.61859	0.0738012
$482$	−14.4901	−0.660006
$483$	−19.4186	−0.883578
$484$	−1.31782	−0.0599008
$485$	−11.1248	−0.505149
$486$	14.2440	0.646119
$487$	−23.4893	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$487$	−23.4893	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$488$	34.7825	1.57453
$489$	−5.40436	−0.244394
$490$	5.43507	0.245531
$491$	−38.5281	−1.73875	−0.869375	−	0.494152i	$-0.835478\pi$
$491$	−38.5281	−1.73875	−0.869375	+	0.494152i	$0.835478\pi$
$492$	1.27395	0.0574341
$493$	0.0165787	0.000746666 0
$494$	−2.52808	−0.113744
$495$	−2.66066	−0.119588
$496$	−28.9617	−1.30042
$497$	−1.13252	−0.0508003
$498$	−24.1860	−1.08380
$499$	21.2245	0.950137	0.475068	−	0.879949i	$-0.342423\pi$
$499$	21.2245	0.950137	0.475068	+	0.879949i	$0.342423\pi$
$500$	−1.33399	−0.0596579
$501$	26.9648	1.20470
$502$	1.81183	0.0808661
$503$	15.3854	0.686001	0.343001	−	0.939335i	$-0.388557\pi$
$503$	15.3854	0.686001	0.343001	+	0.939335i	$0.388557\pi$
$504$	12.0871	0.538404
$505$	0.766880	0.0341257
$506$	−20.5104	−0.911797
$507$	17.6858	0.785453
$508$	4.35741	0.193329
$509$	11.0546	0.489988	0.244994	−	0.969525i	$-0.421214\pi$
$509$	11.0546	0.489988	0.244994	+	0.969525i	$0.421214\pi$
$510$	−1.09344	−0.0484183
$511$	−58.6457	−2.59433
$512$	25.2157	1.11439
$513$	−24.6450	−1.08810
$514$	−11.2703	−0.497110
$515$	6.05836	0.266963
$516$	−0.320572	−0.0141124
$517$	28.1338	1.23732
$518$	−18.3747	−0.807339
$519$	18.6241	0.817505
$520$	0.770906	0.0338064
$521$	−4.86885	−0.213308	−0.106654	−	0.994296i	$-0.534014\pi$
$521$	−4.86885	−0.213308	−0.106654	+	0.994296i	$0.534014\pi$
$522$	0.0241112	0.00105532
$523$	−8.00026	−0.349827	−0.174913	−	0.984584i	$-0.555965\pi$
$523$	−8.00026	−0.349827	−0.174913	+	0.984584i	$0.555965\pi$
$524$	−0.241219	−0.0105377
$525$	−23.8785	−1.04214
$526$	−23.0616	−1.00553
$527$	8.31824	0.362348
$528$	−19.6297	−0.854271
$529$	−8.72978	−0.379556
$530$	5.51895	0.239728
$531$	−8.01246	−0.347711
$532$	−3.76952	−0.163429
$533$	−1.73294	−0.0750618
$534$	−22.2036	−0.960846
$535$	0.834119	0.0360621
$536$	2.71852	0.117422
$537$	4.19695	0.181112
$538$	−16.8530	−0.726586
$539$	−28.0241	−1.20708
$540$	0.781722	0.0336400
$541$	6.27967	0.269984	0.134992	−	0.990847i	$-0.456899\pi$
$541$	6.27967	0.269984	0.134992	+	0.990847i	$0.456899\pi$
$542$	−19.5375	−0.839208
$543$	13.8988	0.596454
$544$	−1.30656	−0.0560182
$545$	−0.803972	−0.0344384
$546$	2.98041	0.127550
$547$	−17.7129	−0.757349	−0.378674	−	0.925530i	$-0.623620\pi$
$547$	−17.7129	−0.757349	−0.378674	+	0.925530i	$0.623620\pi$
$548$	3.50466	0.149712
$549$	−12.8193	−0.547114
$550$	−25.2210	−1.07543
$551$	−0.0722882	−0.00307958
$552$	15.4791	0.658833
$553$	20.1853	0.858367
$554$	−1.92426	−0.0817542
$555$	−3.05251	−0.129572
$556$	−2.22263	−0.0942604
$557$	−26.9990	−1.14399	−0.571993	−	0.820259i	$-0.693829\pi$
$557$	−26.9990	−1.14399	−0.571993	+	0.820259i	$0.693829\pi$
$558$	12.0976	0.512134
$559$	0.436070	0.0184438
$560$	−7.72167	−0.326300
$561$	5.63794	0.238034
$562$	−6.21182	−0.262030
$563$	11.2333	0.473429	0.236714	−	0.971579i	$-0.423929\pi$
$563$	11.2333	0.473429	0.236714	+	0.971579i	$0.423929\pi$
$564$	−2.20858	−0.0929982
$565$	−1.58090	−0.0665091
$566$	22.7150	0.954782
$567$	16.8366	0.707072
$568$	0.902756	0.0378788
$569$	1.67312	0.0701408	0.0350704	−	0.999385i	$-0.488834\pi$
$569$	1.67312	0.0701408	0.0350704	+	0.999385i	$0.488834\pi$
$570$	4.76773	0.199698
$571$	−18.9323	−0.792292	−0.396146	−	0.918187i	$-0.629653\pi$
$571$	−18.9323	−0.792292	−0.396146	+	0.918187i	$0.629653\pi$
$572$	−0.413468	−0.0172880
$573$	−2.22577	−0.0929828
$574$	19.6729	0.821129
$575$	17.5477	0.731788
$576$	−9.51702	−0.396542
$577$	−39.0173	−1.62431	−0.812156	−	0.583441i	$-0.801706\pi$
$577$	−39.0173	−1.62431	−0.812156	+	0.583441i	$0.801706\pi$
$578$	−1.32959	−0.0553036
$579$	18.5166	0.769526
$580$	0.00229293	9.52089e−5 0
$581$	49.0556	2.03517
$582$	34.2840	1.42112
$583$	−28.4566	−1.17855
$584$	46.7479	1.93444
$585$	−0.284121	−0.0117470
$586$	−32.8954	−1.35889
$587$	28.3092	1.16845	0.584223	−	0.811594i	$-0.301400\pi$
$587$	28.3092	1.16845	0.584223	+	0.811594i	$0.301400\pi$
$588$	2.19997	0.0907252
$589$	−36.2701	−1.49448
$590$	5.80134	0.238837
$591$	21.8105	0.897164
$592$	12.9233	0.531143
$593$	−45.7519	−1.87880	−0.939402	−	0.342818i	$-0.888619\pi$
$593$	−45.7519	−1.87880	−0.939402	+	0.342818i	$0.888619\pi$
$594$	30.6880	1.25914
$595$	2.21778	0.0909203
$596$	1.56803	0.0642292
$597$	−30.2984	−1.24003
$598$	−2.19022	−0.0895650
$599$	−26.6948	−1.09072	−0.545361	−	0.838201i	$-0.683607\pi$
$599$	−26.6948	−1.09072	−0.545361	+	0.838201i	$0.683607\pi$
$600$	19.0341	0.777065
$601$	−16.3919	−0.668639	−0.334319	−	0.942460i	$-0.608506\pi$
$601$	−16.3919	−0.668639	−0.334319	+	0.942460i	$0.608506\pi$
$602$	−4.95040	−0.201763
$603$	−1.00193	−0.0408016
$604$	−4.50725	−0.183397
$605$	−3.38070	−0.137445
$606$	−2.36336	−0.0960048
$607$	−8.19321	−0.332552	−0.166276	−	0.986079i	$-0.553174\pi$
$607$	−8.19321	−0.332552	−0.166276	+	0.986079i	$0.553174\pi$
$608$	5.69700	0.231044
$609$	0.0852222	0.00345338
$610$	9.28167	0.375804
$611$	3.00431	0.121541
$612$	0.253979	0.0102665
$613$	15.4409	0.623653	0.311826	−	0.950139i	$-0.399059\pi$
$613$	15.4409	0.623653	0.311826	+	0.950139i	$0.399059\pi$
$614$	2.72532	0.109985
$615$	3.26816	0.131785
$616$	45.1245	1.81812
$617$	−30.0545	−1.20995	−0.604974	−	0.796245i	$-0.706816\pi$
$617$	−30.0545	−1.20995	−0.604974	+	0.796245i	$0.706816\pi$
$618$	−18.6705	−0.751039
$619$	−0.354790	−0.0142602	−0.00713012	−	0.999975i	$-0.502270\pi$
$619$	−0.354790	−0.0142602	−0.00713012	+	0.999975i	$0.502270\pi$
$620$	1.15046	0.0462038
$621$	−21.3514	−0.856801
$622$	27.9654	1.12131
$623$	45.0349	1.80429
$624$	−2.09618	−0.0839142
$625$	19.8038	0.792151
$626$	20.5996	0.823325
$627$	−24.5832	−0.981758
$628$	−0.232258	−0.00926810
$629$	−3.71176	−0.147998
$630$	3.22544	0.128505
$631$	−0.410511	−0.0163422	−0.00817109	−	0.999967i	$-0.502601\pi$
$631$	−0.410511	−0.0163422	−0.00817109	+	0.999967i	$0.502601\pi$
$632$	−16.0902	−0.640034
$633$	−39.2959	−1.56187
$634$	25.0868	0.996325
$635$	11.1784	0.443601
$636$	2.23392	0.0885808
$637$	−2.99259	−0.118571
$638$	0.0900135	0.00356367
$639$	−0.332716	−0.0131620
$640$	5.33418	0.210852
$641$	0.399559	0.0157816	0.00789081	−	0.999969i	$-0.497488\pi$
$641$	0.399559	0.0157816	0.00789081	+	0.999969i	$0.497488\pi$
$642$	−2.57057	−0.101452
$643$	−47.3102	−1.86573	−0.932867	−	0.360222i	$-0.882701\pi$
$643$	−47.3102	−1.86573	−0.932867	+	0.360222i	$0.882701\pi$
$644$	−3.26576	−0.128689
$645$	−0.822388	−0.0323815
$646$	5.79743	0.228097
$647$	−2.80859	−0.110417	−0.0552085	−	0.998475i	$-0.517582\pi$
$647$	−2.80859	−0.110417	−0.0552085	+	0.998475i	$0.517582\pi$
$648$	−13.4209	−0.527223
$649$	−29.9126	−1.17417
$650$	−2.69325	−0.105638
$651$	42.7597	1.67588
$652$	−0.908886	−0.0355947
$653$	43.1289	1.68777	0.843883	−	0.536528i	$-0.180264\pi$
$653$	43.1289	1.68777	0.843883	+	0.536528i	$0.180264\pi$
$654$	2.47767	0.0968844
$655$	−0.618817	−0.0241792
$656$	−13.8363	−0.540215
$657$	−17.2292	−0.672175
$658$	−34.1058	−1.32958
$659$	45.3085	1.76497	0.882484	−	0.470343i	$-0.155870\pi$
$659$	45.3085	1.76497	0.882484	+	0.470343i	$0.155870\pi$
$660$	0.779763	0.0303522
$661$	3.28179	0.127647	0.0638235	−	0.997961i	$-0.479671\pi$
$661$	3.28179	0.127647	0.0638235	+	0.997961i	$0.479671\pi$
$662$	−35.9026	−1.39539
$663$	0.602055	0.0233819
$664$	−39.1034	−1.51751
$665$	−9.67023	−0.374995
$666$	−5.39821	−0.209176
$667$	−0.0626275	−0.00242495
$668$	4.53484	0.175458
$669$	26.3873	1.02019
$670$	0.725435	0.0280260
$671$	−47.8578	−1.84753
$672$	−6.71632	−0.259088
$673$	−13.8178	−0.532638	−0.266319	−	0.963885i	$-0.585807\pi$
$673$	−13.8178	−0.532638	−0.266319	+	0.963885i	$0.585807\pi$
$674$	−36.6119	−1.41024
$675$	−26.2551	−1.01056
$676$	2.97433	0.114397
$677$	30.8435	1.18541	0.592706	−	0.805419i	$-0.298060\pi$
$677$	30.8435	1.18541	0.592706	+	0.805419i	$0.298060\pi$
$678$	4.87199	0.187108
$679$	−69.5372	−2.66859
$680$	−1.76785	−0.0677940
$681$	25.2748	0.968534
$682$	45.1637	1.72941
$683$	−33.9474	−1.29896	−0.649480	−	0.760378i	$-0.725013\pi$
$683$	−33.9474	−1.29896	−0.649480	+	0.760378i	$0.725013\pi$
$684$	−1.10743	−0.0423435
$685$	8.99076	0.343519
$686$	−0.680012	−0.0259630
$687$	−26.9862	−1.02959
$688$	3.48171	0.132739
$689$	−3.03877	−0.115768
$690$	4.13057	0.157248
$691$	−22.3706	−0.851017	−0.425509	−	0.904954i	$-0.639905\pi$
$691$	−22.3706	−0.851017	−0.425509	+	0.904954i	$0.639905\pi$
$692$	3.13213	0.119066
$693$	−16.6309	−0.631755
$694$	−5.98893	−0.227337
$695$	−5.70188	−0.216284
$696$	−0.0679327	−0.00257498
$697$	3.97399	0.150526
$698$	−9.47424	−0.358605
$699$	−26.1330	−0.988441
$700$	−4.01580	−0.151783
$701$	36.8969	1.39358	0.696788	−	0.717277i	$-0.254612\pi$
$701$	36.8969	1.39358	0.696788	+	0.717277i	$0.254612\pi$
$702$	3.27706	0.123685
$703$	16.1844	0.610408
$704$	−35.5295	−1.33907
$705$	−5.66585	−0.213388
$706$	−7.66896	−0.288625
$707$	4.79351	0.180279
$708$	2.34822	0.0882517
$709$	49.0466	1.84199	0.920993	−	0.389580i	$-0.127380\pi$
$709$	49.0466	1.84199	0.920993	+	0.389580i	$0.127380\pi$
$710$	0.240899	0.00904079
$711$	5.93014	0.222397
$712$	−35.8984	−1.34535
$713$	−31.4229	−1.17680
$714$	−6.83472	−0.255783
$715$	−1.06070	−0.0396679
$716$	0.705828	0.0263780
$717$	−7.63217	−0.285029
$718$	9.74932	0.363841
$719$	25.2207	0.940574	0.470287	−	0.882514i	$-0.344150\pi$
$719$	25.2207	0.940574	0.470287	+	0.882514i	$0.344150\pi$
$720$	−2.26851	−0.0845423
$721$	37.8688	1.41031
$722$	−0.0163728	−0.000609332 0
$723$	−15.0464	−0.559583
$724$	2.33745	0.0868705
$725$	−0.0770111	−0.00286012
$726$	10.4186	0.386669
$727$	−20.5474	−0.762060	−0.381030	−	0.924563i	$-0.624430\pi$
$727$	−20.5474	−0.762060	−0.381030	+	0.924563i	$0.624430\pi$
$728$	4.81868	0.178592
$729$	28.3569	1.05026
$730$	12.4746	0.461706
$731$	−1.00000	−0.0369863
$732$	3.75697	0.138862
$733$	45.7781	1.69085	0.845426	−	0.534093i	$-0.179347\pi$
$733$	45.7781	1.69085	0.845426	+	0.534093i	$0.179347\pi$
$734$	−15.2312	−0.562194
$735$	5.64375	0.208173
$736$	4.93564	0.181930
$737$	−3.74046	−0.137781
$738$	5.77958	0.212749
$739$	−8.08450	−0.297393	−0.148697	−	0.988883i	$-0.547508\pi$
$739$	−8.08450	−0.297393	−0.148697	+	0.988883i	$0.547508\pi$
$740$	−0.513360	−0.0188715
$741$	−2.62515	−0.0964371
$742$	34.4971	1.26643
$743$	19.5692	0.717923	0.358961	−	0.933352i	$-0.383131\pi$
$743$	19.5692	0.717923	0.358961	+	0.933352i	$0.383131\pi$
$744$	−34.0848	−1.24961
$745$	4.02259	0.147376
$746$	−43.9806	−1.61024
$747$	14.4118	0.527299
$748$	0.948169	0.0346685
$749$	5.21380	0.190508
$750$	10.5464	0.385101
$751$	47.4072	1.72991	0.864957	−	0.501846i	$-0.167345\pi$
$751$	47.4072	1.72991	0.864957	+	0.501846i	$0.167345\pi$
$752$	23.9872	0.874725
$753$	1.88140	0.0685620
$754$	0.00961221	0.000350056 0
$755$	−11.5628	−0.420813
$756$	4.88629	0.177713
$757$	5.51516	0.200452	0.100226	−	0.994965i	$-0.468043\pi$
$757$	5.51516	0.200452	0.100226	+	0.994965i	$0.468043\pi$
$758$	14.0680	0.510975
$759$	−21.2979	−0.773063
$760$	7.70838	0.279612
$761$	−21.2335	−0.769715	−0.384857	−	0.922976i	$-0.625749\pi$
$761$	−21.2335	−0.769715	−0.384857	+	0.922976i	$0.625749\pi$
$762$	−34.4494	−1.24797
$763$	−5.02536	−0.181930
$764$	−0.374322	−0.0135425
$765$	0.651551	0.0235569
$766$	−11.8410	−0.427833
$767$	−3.19426	−0.115338
$768$	7.58602	0.273737
$769$	14.6701	0.529018	0.264509	−	0.964383i	$-0.414790\pi$
$769$	14.6701	0.529018	0.264509	+	0.964383i	$0.414790\pi$
$770$	12.0414	0.433942
$771$	−11.7030	−0.421473
$772$	3.11406	0.112078
$773$	32.7860	1.17923	0.589615	−	0.807684i	$-0.299279\pi$
$773$	32.7860	1.17923	0.589615	+	0.807684i	$0.299279\pi$
$774$	−1.45435	−0.0522756
$775$	−38.6398	−1.38798
$776$	55.4298	1.98981
$777$	−19.0802	−0.684499
$778$	−51.5492	−1.84813
$779$	−17.3278	−0.620834
$780$	0.0832679	0.00298147
$781$	−1.24211	−0.0444464
$782$	5.02265	0.179610
$783$	0.0937045	0.00334872
$784$	−23.8937	−0.853345
$785$	−0.595829	−0.0212661
$786$	1.90706	0.0680225
$787$	17.3704	0.619189	0.309595	−	0.950869i	$-0.399807\pi$
$787$	17.3704	0.619189	0.309595	+	0.950869i	$0.399807\pi$
$788$	3.66801	0.130667
$789$	−23.9471	−0.852538
$790$	−4.29365	−0.152761
$791$	−9.88170	−0.351353
$792$	13.2569	0.471063
$793$	−5.11055	−0.181481
$794$	−20.6909	−0.734291
$795$	5.73085	0.203252
$796$	−5.09548	−0.180604
$797$	−25.9441	−0.918988	−0.459494	−	0.888181i	$-0.651969\pi$
$797$	−25.9441	−0.918988	−0.459494	+	0.888181i	$0.651969\pi$
$798$	29.8015	1.05496
$799$	−6.88951	−0.243733
$800$	6.06921	0.214579
$801$	13.2306	0.467479
$802$	−20.9150	−0.738535
$803$	−64.3211	−2.26984
$804$	0.293636	0.0103558
$805$	−8.37789	−0.295282
$806$	4.82286	0.169878
$807$	−17.5001	−0.616033
$808$	−3.82103	−0.134423
$809$	−24.8463	−0.873548	−0.436774	−	0.899571i	$-0.643879\pi$
$809$	−24.8463	−0.873548	−0.436774	+	0.899571i	$0.643879\pi$
$810$	−3.58135	−0.125836
$811$	37.0486	1.30095	0.650476	−	0.759527i	$-0.274570\pi$
$811$	37.0486	1.30095	0.650476	+	0.759527i	$0.274570\pi$
$812$	0.0143324	0.000502968 0
$813$	−20.2876	−0.711519
$814$	−20.1529	−0.706360
$815$	−2.33163	−0.0816736
$816$	4.80698	0.168278
$817$	4.36031	0.152548
$818$	30.3740	1.06200
$819$	−1.77595	−0.0620567
$820$	0.549628	0.0191938
$821$	−33.0536	−1.15358	−0.576790	−	0.816893i	$-0.695695\pi$
$821$	−33.0536	−1.15358	−0.576790	+	0.816893i	$0.695695\pi$
$822$	−27.7076	−0.966412
$823$	25.6024	0.892442	0.446221	−	0.894923i	$-0.352770\pi$
$823$	25.6024	0.892442	0.446221	+	0.894923i	$0.352770\pi$
$824$	−30.1861	−1.05158
$825$	−26.1893	−0.911795
$826$	36.2622	1.26172
$827$	20.1347	0.700154	0.350077	−	0.936721i	$-0.386155\pi$
$827$	20.1347	0.700154	0.350077	+	0.936721i	$0.386155\pi$
$828$	−0.959428	−0.0333424
$829$	9.24958	0.321251	0.160626	−	0.987015i	$-0.448649\pi$
$829$	9.24958	0.321251	0.160626	+	0.987015i	$0.448649\pi$
$830$	−10.4347	−0.362194
$831$	−1.99815	−0.0693150
$832$	−3.79406	−0.131536
$833$	6.86263	0.237776
$834$	17.5719	0.608466
$835$	11.6336	0.402596
$836$	−4.13431	−0.142988
$837$	47.0156	1.62510
$838$	−34.8786	−1.20486
$839$	−2.56897	−0.0886906	−0.0443453	−	0.999016i	$-0.514120\pi$
$839$	−2.56897	−0.0886906	−0.0443453	+	0.999016i	$0.514120\pi$
$840$	−9.08759	−0.313552
$841$	−28.9997	−0.999991
$842$	−8.97402	−0.309265
$843$	−6.45033	−0.222161
$844$	−6.60865	−0.227479
$845$	7.63028	0.262489
$846$	−10.0198	−0.344487
$847$	−21.1316	−0.726091
$848$	−24.2624	−0.833175
$849$	23.5871	0.809508
$850$	6.17620	0.211842
$851$	14.0215	0.480652
$852$	0.0975095	0.00334062
$853$	16.3157	0.558638	0.279319	−	0.960198i	$-0.409891\pi$
$853$	16.3157	0.558638	0.279319	+	0.960198i	$0.409891\pi$
$854$	58.0166	1.98529
$855$	−2.84096	−0.0971589
$856$	−4.15605	−0.142051
$857$	35.9324	1.22743	0.613714	−	0.789529i	$-0.289675\pi$
$857$	35.9324	1.22743	0.613714	+	0.789529i	$0.289675\pi$
$858$	3.26884	0.111596
$859$	2.87556	0.0981128	0.0490564	−	0.998796i	$-0.484379\pi$
$859$	2.87556	0.0981128	0.0490564	+	0.998796i	$0.484379\pi$
$860$	−0.138306	−0.00471620
$861$	20.4282	0.696191
$862$	6.34575	0.216137
$863$	−27.8513	−0.948070	−0.474035	−	0.880506i	$-0.657203\pi$
$863$	−27.8513	−0.948070	−0.474035	+	0.880506i	$0.657203\pi$
$864$	−7.38480	−0.251236
$865$	8.03508	0.273201
$866$	−46.3587	−1.57533
$867$	−1.38064	−0.0468890
$868$	7.19117	0.244084
$869$	22.1388	0.751006
$870$	−0.0181278	−0.000614589 0
$871$	−0.399429	−0.0135341
$872$	4.00584	0.135655
$873$	−20.4289	−0.691415
$874$	−21.9003	−0.740789
$875$	−21.3910	−0.723146
$876$	5.04939	0.170603
$877$	−47.3856	−1.60010	−0.800048	−	0.599936i	$-0.795193\pi$
$877$	−47.3856	−1.60010	−0.800048	+	0.599936i	$0.795193\pi$
$878$	46.3224	1.56330
$879$	−34.1584	−1.15213
$880$	−8.46893	−0.285488
$881$	32.3004	1.08823	0.544114	−	0.839011i	$-0.316866\pi$
$881$	32.3004	1.08823	0.544114	+	0.839011i	$0.316866\pi$
$882$	9.98069	0.336067
$883$	42.5758	1.43279	0.716394	−	0.697696i	$-0.245791\pi$
$883$	42.5758	1.43279	0.716394	+	0.697696i	$0.245791\pi$
$884$	0.101251	0.00340545
$885$	6.02408	0.202497
$886$	−19.1269	−0.642582
$887$	35.1595	1.18054	0.590270	−	0.807206i	$-0.299021\pi$
$887$	35.1595	1.18054	0.590270	+	0.807206i	$0.299021\pi$
$888$	15.2093	0.510391
$889$	69.8725	2.34345
$890$	−9.57945	−0.321104
$891$	18.4660	0.618634
$892$	4.43772	0.148586
$893$	30.0404	1.00526
$894$	−12.3967	−0.414609
$895$	1.81071	0.0605255
$896$	33.3422	1.11388
$897$	−2.27432	−0.0759373
$898$	29.8838	0.997235
$899$	0.137905	0.00459940
$900$	−1.17978	−0.0393260
$901$	6.96855	0.232156
$902$	21.5767	0.718425
$903$	−5.14047	−0.171064
$904$	7.87695	0.261983
$905$	5.99643	0.199328
$906$	35.6339	1.18386
$907$	28.9906	0.962617	0.481308	−	0.876551i	$-0.340162\pi$
$907$	28.9906	0.962617	0.481308	+	0.876551i	$0.340162\pi$
$908$	4.25063	0.141062
$909$	1.40826	0.0467091
$910$	1.28586	0.0426257
$911$	9.41314	0.311871	0.155936	−	0.987767i	$-0.450161\pi$
$911$	9.41314	0.311871	0.155936	+	0.987767i	$0.450161\pi$
$912$	−20.9599	−0.694052
$913$	53.8029	1.78062
$914$	8.86062	0.293083
$915$	9.63804	0.318624
$916$	−4.53844	−0.149954
$917$	−3.86802	−0.127733
$918$	−7.51499	−0.248032
$919$	28.4247	0.937643	0.468822	−	0.883293i	$-0.344679\pi$
$919$	28.4247	0.937643	0.468822	+	0.883293i	$0.344679\pi$
$920$	6.67822	0.220174
$921$	2.82995	0.0932502
$922$	14.4291	0.475196
$923$	−0.132641	−0.00436592
$924$	4.87404	0.160344
$925$	17.2418	0.566908
$926$	−12.3632	−0.406281
$927$	11.1253	0.365402
$928$	−0.0216610	−0.000711057 0
$929$	−37.9716	−1.24581	−0.622904	−	0.782299i	$-0.714047\pi$
$929$	−37.9716	−1.24581	−0.622904	+	0.782299i	$0.714047\pi$
$930$	−9.09548	−0.298253
$931$	−29.9232	−0.980694
$932$	−4.39496	−0.143962
$933$	29.0391	0.950698
$934$	12.3412	0.403818
$935$	2.43241	0.0795483
$936$	1.41565	0.0462720
$937$	24.6626	0.805692	0.402846	−	0.915268i	$-0.368021\pi$
$937$	24.6626	0.805692	0.402846	+	0.915268i	$0.368021\pi$
$938$	4.53445	0.148055
$939$	21.3905	0.698052
$940$	−0.952862	−0.0310789
$941$	−27.6043	−0.899874	−0.449937	−	0.893060i	$-0.648554\pi$
$941$	−27.6043	−0.899874	−0.449937	+	0.893060i	$0.648554\pi$
$942$	1.83621	0.0598271
$943$	−15.0121	−0.488862
$944$	−25.5039	−0.830080
$945$	12.5352	0.407769
$946$	−5.42948	−0.176528
$947$	44.2748	1.43874	0.719368	−	0.694629i	$-0.244431\pi$
$947$	44.2748	1.43874	0.719368	+	0.694629i	$0.244431\pi$
$948$	−1.73795	−0.0564461
$949$	−6.86861	−0.222965
$950$	−26.9302	−0.873730
$951$	26.0500	0.844730
$952$	−11.0502	−0.358141
$953$	11.3046	0.366191	0.183096	−	0.983095i	$-0.441388\pi$
$953$	11.3046	0.366191	0.183096	+	0.983095i	$0.441388\pi$
$954$	10.1347	0.328124
$955$	−0.960276	−0.0310738
$956$	−1.28355	−0.0415130
$957$	0.0934696	0.00302144
$958$	−43.2049	−1.39589
$959$	56.1983	1.81474
$960$	7.15526	0.230935
$961$	38.1931	1.23204
$962$	−2.15206	−0.0693851
$963$	1.53173	0.0493594
$964$	−2.53046	−0.0815006
$965$	7.98874	0.257167
$966$	25.8188	0.830706
$967$	40.5880	1.30522	0.652611	−	0.757693i	$-0.273674\pi$
$967$	40.5880	1.30522	0.652611	+	0.757693i	$0.273674\pi$
$968$	16.8445	0.541403
$969$	6.02002	0.193391
$970$	14.7914	0.474922
$971$	25.6945	0.824577	0.412289	−	0.911053i	$-0.364730\pi$
$971$	25.6945	0.824577	0.412289	+	0.911053i	$0.364730\pi$
$972$	2.48747	0.0797858
$973$	−35.6405	−1.14258
$974$	31.2311	1.00071
$975$	−2.79666	−0.0895648
$976$	−40.8041	−1.30611
$977$	−6.25279	−0.200044	−0.100022	−	0.994985i	$-0.531891\pi$
$977$	−6.25279	−0.200044	−0.100022	+	0.994985i	$0.531891\pi$
$978$	7.18558	0.229770
$979$	49.3931	1.57861
$980$	0.949145	0.0303193
$981$	−1.47637	−0.0471370
$982$	51.2266	1.63471
$983$	−28.6875	−0.914989	−0.457494	−	0.889213i	$-0.651253\pi$
$983$	−28.6875	−0.914989	−0.457494	+	0.889213i	$0.651253\pi$
$984$	−16.2838	−0.519109
$985$	9.40983	0.299822
$986$	−0.0220428	−0.000701987 0
$987$	−35.4153	−1.12728
$988$	−0.441488	−0.0140456
$989$	3.77759	0.120121
$990$	3.53758	0.112432
$991$	26.0584	0.827773	0.413886	−	0.910329i	$-0.364171\pi$
$991$	26.0584	0.827773	0.413886	+	0.910329i	$0.364171\pi$
$992$	−10.8683	−0.345067
$993$	−37.2811	−1.18308
$994$	1.50578	0.0477605
$995$	−13.0718	−0.414404
$996$	−4.22368	−0.133833
$997$	−45.4154	−1.43832	−0.719159	−	0.694845i	$-0.755473\pi$
$997$	−45.4154	−1.43832	−0.719159	+	0.694845i	$0.755473\pi$
$998$	−28.2198	−0.893283
$999$	−20.9793	−0.663755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.6	✓	19
3.2	odd	2		6579.2.a.t.1.14		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.6	✓	19	1.1	even	1	trivial
6579.2.a.t.1.14		19	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)

\(f(q)\)	\(=\)	\(q-1.32959 q^{2} -1.38064 q^{3} -0.232191 q^{4} -0.595657 q^{5} +1.83568 q^{6} -3.72326 q^{7} +2.96790 q^{8} -1.09384 q^{9} +O(q^{10})\)	\(q-1.32959 q^{2} -1.38064 q^{3} -0.232191 q^{4} -0.595657 q^{5} +1.83568 q^{6} -3.72326 q^{7} +2.96790 q^{8} -1.09384 q^{9} +0.791980 q^{10} -4.08357 q^{11} +0.320572 q^{12} -0.436070 q^{13} +4.95040 q^{14} +0.822388 q^{15} -3.48171 q^{16} +1.00000 q^{17} +1.45435 q^{18} -4.36031 q^{19} +0.138306 q^{20} +5.14047 q^{21} +5.42948 q^{22} -3.77759 q^{23} -4.09760 q^{24} -4.64519 q^{25} +0.579794 q^{26} +5.65211 q^{27} +0.864507 q^{28} +0.0165787 q^{29} -1.09344 q^{30} +8.31824 q^{31} -1.30656 q^{32} +5.63794 q^{33} -1.32959 q^{34} +2.21778 q^{35} +0.253979 q^{36} -3.71176 q^{37} +5.79743 q^{38} +0.602055 q^{39} -1.76785 q^{40} +3.97399 q^{41} -6.83472 q^{42} -1.00000 q^{43} +0.948169 q^{44} +0.651551 q^{45} +5.02265 q^{46} -6.88951 q^{47} +4.80698 q^{48} +6.86263 q^{49} +6.17620 q^{50} -1.38064 q^{51} +0.101251 q^{52} +6.96855 q^{53} -7.51499 q^{54} +2.43241 q^{55} -11.0502 q^{56} +6.02002 q^{57} -0.0220428 q^{58} +7.32511 q^{59} -0.190951 q^{60} +11.7196 q^{61} -11.0598 q^{62} +4.07263 q^{63} +8.70060 q^{64} +0.259748 q^{65} -7.49615 q^{66} +0.915976 q^{67} -0.232191 q^{68} +5.21550 q^{69} -2.94874 q^{70} +0.304173 q^{71} -3.24639 q^{72} +15.7512 q^{73} +4.93512 q^{74} +6.41334 q^{75} +1.01243 q^{76} +15.2042 q^{77} -0.800486 q^{78} -5.42142 q^{79} +2.07390 q^{80} -4.52202 q^{81} -5.28378 q^{82} -13.1755 q^{83} -1.19357 q^{84} -0.595657 q^{85} +1.32959 q^{86} -0.0228892 q^{87} -12.1196 q^{88} -12.0956 q^{89} -0.866295 q^{90} +1.62360 q^{91} +0.877123 q^{92} -11.4845 q^{93} +9.16022 q^{94} +2.59725 q^{95} +1.80388 q^{96} +18.6764 q^{97} -9.12449 q^{98} +4.46676 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

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