LMFDB - Embedded newform 731.2.a.e.1.18

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			1.18
Root			$2.40179$ 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)

$f(q)$	$=$	$q+2.40179 q^{2} +2.16240 q^{3} +3.76858 q^{4} -1.65227 q^{5} +5.19362 q^{6} -1.91106 q^{7} +4.24776 q^{8} +1.67596 q^{9} +O(q^{10})$	\(q+2.40179 q^{2} +2.16240 q^{3} +3.76858 q^{4} -1.65227 q^{5} +5.19362 q^{6} -1.91106 q^{7} +4.24776 q^{8} +1.67596 q^{9} -3.96840 q^{10} +4.97761 q^{11} +8.14918 q^{12} +3.82594 q^{13} -4.58996 q^{14} -3.57286 q^{15} +2.66506 q^{16} +1.00000 q^{17} +4.02531 q^{18} -7.52266 q^{19} -6.22671 q^{20} -4.13247 q^{21} +11.9552 q^{22} -2.57401 q^{23} +9.18535 q^{24} -2.27001 q^{25} +9.18909 q^{26} -2.86309 q^{27} -7.20199 q^{28} +7.97242 q^{29} -8.58125 q^{30} -8.80832 q^{31} -2.09462 q^{32} +10.7636 q^{33} +2.40179 q^{34} +3.15758 q^{35} +6.31601 q^{36} +10.5970 q^{37} -18.0678 q^{38} +8.27320 q^{39} -7.01844 q^{40} -7.93834 q^{41} -9.92532 q^{42} -1.00000 q^{43} +18.7585 q^{44} -2.76914 q^{45} -6.18222 q^{46} +5.62851 q^{47} +5.76292 q^{48} -3.34785 q^{49} -5.45209 q^{50} +2.16240 q^{51} +14.4184 q^{52} +1.34197 q^{53} -6.87654 q^{54} -8.22434 q^{55} -8.11773 q^{56} -16.2670 q^{57} +19.1481 q^{58} -5.27708 q^{59} -13.4646 q^{60} -8.29292 q^{61} -21.1557 q^{62} -3.20287 q^{63} -10.3610 q^{64} -6.32147 q^{65} +25.8518 q^{66} -11.8970 q^{67} +3.76858 q^{68} -5.56603 q^{69} +7.58385 q^{70} +0.823141 q^{71} +7.11910 q^{72} +14.1286 q^{73} +25.4518 q^{74} -4.90867 q^{75} -28.3498 q^{76} -9.51251 q^{77} +19.8705 q^{78} +12.6088 q^{79} -4.40339 q^{80} -11.2190 q^{81} -19.0662 q^{82} +6.75367 q^{83} -15.5736 q^{84} -1.65227 q^{85} -2.40179 q^{86} +17.2395 q^{87} +21.1437 q^{88} +7.41281 q^{89} -6.65089 q^{90} -7.31160 q^{91} -9.70037 q^{92} -19.0471 q^{93} +13.5185 q^{94} +12.4295 q^{95} -4.52941 q^{96} +12.4514 q^{97} -8.04082 q^{98} +8.34229 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.40179	1.69832	0.849160	−	0.528135i	$-0.177109\pi$
$2$	2.40179	1.69832	0.849160	+	0.528135i	$0.177109\pi$
$3$	2.16240	1.24846	0.624230	−	0.781240i	$-0.285413\pi$
$3$	2.16240	1.24846	0.624230	+	0.781240i	$0.285413\pi$
$4$	3.76858	1.88429
$5$	−1.65227	−0.738917	−0.369458	−	0.929247i	$-0.620457\pi$
$5$	−1.65227	−0.738917	−0.369458	+	0.929247i	$0.620457\pi$
$6$	5.19362	2.12029
$7$	−1.91106	−0.722313	−0.361156	−	0.932505i	$-0.617618\pi$
$7$	−1.91106	−0.722313	−0.361156	+	0.932505i	$0.617618\pi$
$8$	4.24776	1.50181
$9$	1.67596	0.558654
$10$	−3.96840	−1.25492
$11$	4.97761	1.50081	0.750403	−	0.660981i	$-0.229860\pi$
$11$	4.97761	1.50081	0.750403	+	0.660981i	$0.229860\pi$
$12$	8.14918	2.35246
$13$	3.82594	1.06112	0.530562	−	0.847646i	$-0.321981\pi$
$13$	3.82594	1.06112	0.530562	+	0.847646i	$0.321981\pi$
$14$	−4.58996	−1.22672
$15$	−3.57286	−0.922508
$16$	2.66506	0.666265
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.02531	0.948774
$19$	−7.52266	−1.72582	−0.862909	−	0.505360i	$-0.831360\pi$
$19$	−7.52266	−1.72582	−0.862909	+	0.505360i	$0.831360\pi$
$20$	−6.22671	−1.39233
$21$	−4.13247	−0.901779
$22$	11.9552	2.54885
$23$	−2.57401	−0.536718	−0.268359	−	0.963319i	$-0.586481\pi$
$23$	−2.57401	−0.536718	−0.268359	+	0.963319i	$0.586481\pi$
$24$	9.18535	1.87495
$25$	−2.27001	−0.454002
$26$	9.18909	1.80213
$27$	−2.86309	−0.551003
$28$	−7.20199	−1.36105
$29$	7.97242	1.48044	0.740220	−	0.672364i	$-0.234721\pi$
$29$	7.97242	1.48044	0.740220	+	0.672364i	$0.234721\pi$
$30$	−8.58125	−1.56671
$31$	−8.80832	−1.58202	−0.791010	−	0.611803i	$-0.790445\pi$
$31$	−8.80832	−1.58202	−0.791010	+	0.611803i	$0.790445\pi$
$32$	−2.09462	−0.370281
$33$	10.7636	1.87370
$34$	2.40179	0.411903
$35$	3.15758	0.533729
$36$	6.31601	1.05267
$37$	10.5970	1.74214	0.871069	−	0.491161i	$-0.163427\pi$
$37$	10.5970	1.74214	0.871069	+	0.491161i	$0.163427\pi$
$38$	−18.0678	−2.93099
$39$	8.27320	1.32477
$40$	−7.01844	−1.10971
$41$	−7.93834	−1.23976	−0.619880	−	0.784696i	$-0.712819\pi$
$41$	−7.93834	−1.23976	−0.619880	+	0.784696i	$0.712819\pi$
$42$	−9.92532	−1.53151
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	18.7585	2.82796
$45$	−2.76914	−0.412799
$46$	−6.18222	−0.911519
$47$	5.62851	0.821003	0.410501	−	0.911860i	$-0.365354\pi$
$47$	5.62851	0.821003	0.410501	+	0.911860i	$0.365354\pi$
$48$	5.76292	0.831805
$49$	−3.34785	−0.478264
$50$	−5.45209	−0.771041
$51$	2.16240	0.302796
$52$	14.4184	1.99947
$53$	1.34197	0.184334	0.0921670	−	0.995744i	$-0.470621\pi$
$53$	1.34197	0.184334	0.0921670	+	0.995744i	$0.470621\pi$
$54$	−6.87654	−0.935779
$55$	−8.22434	−1.10897
$56$	−8.11773	−1.08478
$57$	−16.2670	−2.15461
$58$	19.1481	2.51426
$59$	−5.27708	−0.687017	−0.343508	−	0.939150i	$-0.611615\pi$
$59$	−5.27708	−0.687017	−0.343508	+	0.939150i	$0.611615\pi$
$60$	−13.4646	−1.73828
$61$	−8.29292	−1.06180	−0.530900	−	0.847434i	$-0.678146\pi$
$61$	−8.29292	−1.06180	−0.530900	+	0.847434i	$0.678146\pi$
$62$	−21.1557	−2.68678
$63$	−3.20287	−0.403523
$64$	−10.3610	−1.29512
$65$	−6.32147	−0.784082
$66$	25.8518	3.18214
$67$	−11.8970	−1.45345	−0.726726	−	0.686927i	$-0.758959\pi$
$67$	−11.8970	−1.45345	−0.726726	+	0.686927i	$0.758959\pi$
$68$	3.76858	0.457008
$69$	−5.56603	−0.670071
$70$	7.58385	0.906443
$71$	0.823141	0.0976889	0.0488445	−	0.998806i	$-0.484446\pi$
$71$	0.823141	0.0976889	0.0488445	+	0.998806i	$0.484446\pi$
$72$	7.11910	0.838993
$73$	14.1286	1.65363	0.826815	−	0.562473i	$-0.190150\pi$
$73$	14.1286	1.65363	0.826815	+	0.562473i	$0.190150\pi$
$74$	25.4518	2.95871
$75$	−4.90867	−0.566804
$76$	−28.3498	−3.25194
$77$	−9.51251	−1.08405
$78$	19.8705	2.24989
$79$	12.6088	1.41860	0.709299	−	0.704907i	$-0.249011\pi$
$79$	12.6088	1.41860	0.709299	+	0.704907i	$0.249011\pi$
$80$	−4.40339	−0.492314
$81$	−11.2190	−1.24656
$82$	−19.0662	−2.10551
$83$	6.75367	0.741311	0.370656	−	0.928770i	$-0.379133\pi$
$83$	6.75367	0.741311	0.370656	+	0.928770i	$0.379133\pi$
$84$	−15.5736	−1.69922
$85$	−1.65227	−0.179214
$86$	−2.40179	−0.258991
$87$	17.2395	1.84827
$88$	21.1437	2.25393
$89$	7.41281	0.785756	0.392878	−	0.919591i	$-0.371479\pi$
$89$	7.41281	0.785756	0.392878	+	0.919591i	$0.371479\pi$
$90$	−6.65089	−0.701065
$91$	−7.31160	−0.766464
$92$	−9.70037	−1.01133
$93$	−19.0471	−1.97509
$94$	13.5185	1.39433
$95$	12.4295	1.27523
$96$	−4.52941	−0.462281
$97$	12.4514	1.26425	0.632123	−	0.774868i	$-0.282184\pi$
$97$	12.4514	1.26425	0.632123	+	0.774868i	$0.282184\pi$
$98$	−8.04082	−0.812245
$99$	8.34229	0.838431
$100$	−8.55473	−0.855473
$101$	−11.6350	−1.15773	−0.578865	−	0.815424i	$-0.696504\pi$
$101$	−11.6350	−1.15773	−0.578865	+	0.815424i	$0.696504\pi$
$102$	5.19362	0.514245
$103$	13.5428	1.33441	0.667204	−	0.744875i	$-0.267491\pi$
$103$	13.5428	1.33441	0.667204	+	0.744875i	$0.267491\pi$
$104$	16.2517	1.59361
$105$	6.82795	0.666340
$106$	3.22313	0.313058
$107$	9.78399	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$107$	9.78399	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$108$	−10.7898	−1.03825
$109$	−3.97806	−0.381029	−0.190514	−	0.981684i	$-0.561016\pi$
$109$	−3.97806	−0.381029	−0.190514	+	0.981684i	$0.561016\pi$
$110$	−19.7531	−1.88339
$111$	22.9150	2.17499
$112$	−5.09309	−0.481252
$113$	12.9242	1.21581	0.607903	−	0.794011i	$-0.292011\pi$
$113$	12.9242	1.21581	0.607903	+	0.794011i	$0.292011\pi$
$114$	−39.0698	−3.65923
$115$	4.25295	0.396590
$116$	30.0447	2.78958
$117$	6.41213	0.592802
$118$	−12.6744	−1.16677
$119$	−1.91106	−0.175187
$120$	−15.1767	−1.38543
$121$	13.7766	1.25242
$122$	−19.9178	−1.80328
$123$	−17.1658	−1.54779
$124$	−33.1949	−2.98099
$125$	12.0120	1.07439
$126$	−7.69261	−0.685312
$127$	−3.37983	−0.299912	−0.149956	−	0.988693i	$-0.547913\pi$
$127$	−3.37983	−0.299912	−0.149956	+	0.988693i	$0.547913\pi$
$128$	−20.6956	−1.82925
$129$	−2.16240	−0.190388
$130$	−15.1828	−1.33162
$131$	−19.5896	−1.71155	−0.855776	−	0.517346i	$-0.826920\pi$
$131$	−19.5896	−1.71155	−0.855776	+	0.517346i	$0.826920\pi$
$132$	40.5634	3.53059
$133$	14.3763	1.24658
$134$	−28.5741	−2.46843
$135$	4.73060	0.407145
$136$	4.24776	0.364243
$137$	−3.03844	−0.259592	−0.129796	−	0.991541i	$-0.541432\pi$
$137$	−3.03844	−0.259592	−0.129796	+	0.991541i	$0.541432\pi$
$138$	−13.3684	−1.13800
$139$	14.0624	1.19276	0.596378	−	0.802704i	$-0.296606\pi$
$139$	14.0624	1.19276	0.596378	+	0.802704i	$0.296606\pi$
$140$	11.8996	1.00570
$141$	12.1711	1.02499
$142$	1.97701	0.165907
$143$	19.0440	1.59254
$144$	4.46654	0.372212
$145$	−13.1726	−1.09392
$146$	33.9340	2.80839
$147$	−7.23938	−0.597094
$148$	39.9357	3.28270
$149$	−7.70280	−0.631038	−0.315519	−	0.948919i	$-0.602179\pi$
$149$	−7.70280	−0.631038	−0.315519	+	0.948919i	$0.602179\pi$
$150$	−11.7896	−0.962615
$151$	4.55132	0.370381	0.185191	−	0.982703i	$-0.440710\pi$
$151$	4.55132	0.370381	0.185191	+	0.982703i	$0.440710\pi$
$152$	−31.9545	−2.59185
$153$	1.67596	0.135494
$154$	−22.8470	−1.84107
$155$	14.5537	1.16898
$156$	31.1783	2.49626
$157$	18.4945	1.47602	0.738010	−	0.674790i	$-0.235766\pi$
$157$	18.4945	1.47602	0.738010	+	0.674790i	$0.235766\pi$
$158$	30.2836	2.40924
$159$	2.90188	0.230134
$160$	3.46088	0.273606
$161$	4.91908	0.387678
$162$	−26.9457	−2.11706
$163$	2.26410	0.177338	0.0886690	−	0.996061i	$-0.471739\pi$
$163$	2.26410	0.177338	0.0886690	+	0.996061i	$0.471739\pi$
$164$	−29.9163	−2.33607
$165$	−17.7843	−1.38451
$166$	16.2209	1.25898
$167$	−4.05043	−0.313432	−0.156716	−	0.987644i	$-0.550091\pi$
$167$	−4.05043	−0.313432	−0.156716	+	0.987644i	$0.550091\pi$
$168$	−17.5538	−1.35430
$169$	1.63781	0.125985
$170$	−3.96840	−0.304362
$171$	−12.6077	−0.964135
$172$	−3.76858	−0.287352
$173$	−16.1293	−1.22629	−0.613145	−	0.789970i	$-0.710096\pi$
$173$	−16.1293	−1.22629	−0.613145	+	0.789970i	$0.710096\pi$
$174$	41.4057	3.13896
$175$	4.33813	0.327932
$176$	13.2656	0.999933
$177$	−11.4111	−0.857714
$178$	17.8040	1.33447
$179$	6.32615	0.472838	0.236419	−	0.971651i	$-0.424026\pi$
$179$	6.32615	0.472838	0.236419	+	0.971651i	$0.424026\pi$
$180$	−10.4357	−0.777834
$181$	17.9863	1.33691	0.668457	−	0.743751i	$-0.266955\pi$
$181$	17.9863	1.33691	0.668457	+	0.743751i	$0.266955\pi$
$182$	−17.5609	−1.30170
$183$	−17.9326	−1.32562
$184$	−10.9338	−0.806049
$185$	−17.5091	−1.28729
$186$	−45.7471	−3.35434
$187$	4.97761	0.363999
$188$	21.2115	1.54701
$189$	5.47155	0.397996
$190$	29.8529	2.16576
$191$	−4.77950	−0.345832	−0.172916	−	0.984937i	$-0.555319\pi$
$191$	−4.77950	−0.345832	−0.172916	+	0.984937i	$0.555319\pi$
$192$	−22.4045	−1.61691
$193$	−1.10315	−0.0794065	−0.0397033	−	0.999212i	$-0.512641\pi$
$193$	−1.10315	−0.0794065	−0.0397033	+	0.999212i	$0.512641\pi$
$194$	29.9056	2.14709
$195$	−13.6695	−0.978896
$196$	−12.6166	−0.901189
$197$	0.995534	0.0709289	0.0354644	−	0.999371i	$-0.488709\pi$
$197$	0.995534	0.0709289	0.0354644	+	0.999371i	$0.488709\pi$
$198$	20.0364	1.42393
$199$	15.2595	1.08172	0.540859	−	0.841113i	$-0.318099\pi$
$199$	15.2595	1.08172	0.540859	+	0.841113i	$0.318099\pi$
$200$	−9.64247	−0.681826
$201$	−25.7261	−1.81458
$202$	−27.9449	−1.96620
$203$	−15.2358	−1.06934
$204$	8.14918	0.570557
$205$	13.1163	0.916079
$206$	32.5268	2.26625
$207$	−4.31394	−0.299840
$208$	10.1963	0.706990
$209$	−37.4449	−2.59012
$210$	16.3993	1.13166
$211$	−4.52669	−0.311630	−0.155815	−	0.987786i	$-0.549800\pi$
$211$	−4.52669	−0.311630	−0.155815	+	0.987786i	$0.549800\pi$
$212$	5.05734	0.347339
$213$	1.77996	0.121961
$214$	23.4991	1.60636
$215$	1.65227	0.112684
$216$	−12.1617	−0.827502
$217$	16.8332	1.14271
$218$	−9.55445	−0.647109
$219$	30.5517	2.06449
$220$	−30.9941	−2.08962
$221$	3.82594	0.257360
$222$	55.0368	3.69383
$223$	−8.21013	−0.549791	−0.274895	−	0.961474i	$-0.588643\pi$
$223$	−8.21013	−0.549791	−0.274895	+	0.961474i	$0.588643\pi$
$224$	4.00295	0.267458
$225$	−3.80446	−0.253630
$226$	31.0412	2.06483
$227$	−22.7830	−1.51216	−0.756079	−	0.654480i	$-0.772887\pi$
$227$	−22.7830	−1.51216	−0.756079	+	0.654480i	$0.772887\pi$
$228$	−61.3035	−4.05992
$229$	2.59405	0.171420	0.0857099	−	0.996320i	$-0.472684\pi$
$229$	2.59405	0.171420	0.0857099	+	0.996320i	$0.472684\pi$
$230$	10.2147	0.673536
$231$	−20.5698	−1.35340
$232$	33.8649	2.22334
$233$	−5.47723	−0.358825	−0.179413	−	0.983774i	$-0.557420\pi$
$233$	−5.47723	−0.358825	−0.179413	+	0.983774i	$0.557420\pi$
$234$	15.4006	1.00677
$235$	−9.29981	−0.606653
$236$	−19.8871	−1.29454
$237$	27.2652	1.77107
$238$	−4.58996	−0.297523
$239$	18.4316	1.19224	0.596122	−	0.802894i	$-0.296708\pi$
$239$	18.4316	1.19224	0.596122	+	0.802894i	$0.296708\pi$
$240$	−9.52188	−0.614635
$241$	5.76669	0.371465	0.185733	−	0.982600i	$-0.440534\pi$
$241$	5.76669	0.371465	0.185733	+	0.982600i	$0.440534\pi$
$242$	33.0884	2.12700
$243$	−15.6707	−1.00528
$244$	−31.2526	−2.00074
$245$	5.53154	0.353397
$246$	−41.2287	−2.62865
$247$	−28.7812	−1.83131
$248$	−37.4157	−2.37590
$249$	14.6041	0.925498
$250$	28.8503	1.82465
$251$	−6.53005	−0.412173	−0.206086	−	0.978534i	$-0.566073\pi$
$251$	−6.53005	−0.412173	−0.206086	+	0.978534i	$0.566073\pi$
$252$	−12.0703	−0.760356
$253$	−12.8124	−0.805509
$254$	−8.11764	−0.509346
$255$	−3.57286	−0.223741
$256$	−28.9845	−1.81153
$257$	−11.4783	−0.715996	−0.357998	−	0.933722i	$-0.616541\pi$
$257$	−11.4783	−0.715996	−0.357998	+	0.933722i	$0.616541\pi$
$258$	−5.19362	−0.323341
$259$	−20.2515	−1.25837
$260$	−23.8230	−1.47744
$261$	13.3615	0.827055
$262$	−47.0501	−2.90676
$263$	20.3220	1.25311	0.626555	−	0.779377i	$-0.284464\pi$
$263$	20.3220	1.25311	0.626555	+	0.779377i	$0.284464\pi$
$264$	45.7211	2.81394
$265$	−2.21730	−0.136208
$266$	34.5287	2.11709
$267$	16.0294	0.980986
$268$	−44.8349	−2.73873
$269$	19.6991	1.20108	0.600538	−	0.799596i	$-0.294953\pi$
$269$	19.6991	1.20108	0.600538	+	0.799596i	$0.294953\pi$
$270$	11.3619	0.691463
$271$	−4.16002	−0.252703	−0.126352	−	0.991986i	$-0.540327\pi$
$271$	−4.16002	−0.252703	−0.126352	+	0.991986i	$0.540327\pi$
$272$	2.66506	0.161593
$273$	−15.8106	−0.956900
$274$	−7.29770	−0.440870
$275$	−11.2992	−0.681369
$276$	−20.9760	−1.26261
$277$	13.4853	0.810253	0.405126	−	0.914261i	$-0.367228\pi$
$277$	13.4853	0.810253	0.405126	+	0.914261i	$0.367228\pi$
$278$	33.7749	2.02568
$279$	−14.7624	−0.883803
$280$	13.4127	0.801560
$281$	7.94181	0.473769	0.236884	−	0.971538i	$-0.423874\pi$
$281$	7.94181	0.473769	0.236884	+	0.971538i	$0.423874\pi$
$282$	29.2324	1.74076
$283$	0.671905	0.0399406	0.0199703	−	0.999801i	$-0.493643\pi$
$283$	0.671905	0.0399406	0.0199703	+	0.999801i	$0.493643\pi$
$284$	3.10208	0.184074
$285$	26.8774	1.59208
$286$	45.7397	2.70464
$287$	15.1706	0.895495
$288$	−3.51051	−0.206859
$289$	1.00000	0.0588235
$290$	−31.6377	−1.85783
$291$	26.9248	1.57836
$292$	53.2449	3.11592
$293$	−12.4347	−0.726444	−0.363222	−	0.931703i	$-0.618323\pi$
$293$	−12.4347	−0.726444	−0.363222	+	0.931703i	$0.618323\pi$
$294$	−17.3874	−1.01406
$295$	8.71914	0.507648
$296$	45.0136	2.61636
$297$	−14.2514	−0.826948
$298$	−18.5005	−1.07170
$299$	−9.84800	−0.569524
$300$	−18.4987	−1.06802
$301$	1.91106	0.110152
$302$	10.9313	0.629026
$303$	−25.1596	−1.44538
$304$	−20.0483	−1.14985
$305$	13.7021	0.784582
$306$	4.02531	0.230112
$307$	−24.2341	−1.38311	−0.691556	−	0.722323i	$-0.743074\pi$
$307$	−24.2341	−1.38311	−0.691556	+	0.722323i	$0.743074\pi$
$308$	−35.8487	−2.04267
$309$	29.2848	1.66596
$310$	34.9549	1.98530
$311$	4.65629	0.264034	0.132017	−	0.991247i	$-0.457855\pi$
$311$	4.65629	0.264034	0.132017	+	0.991247i	$0.457855\pi$
$312$	35.1426	1.98956
$313$	−32.6685	−1.84653	−0.923266	−	0.384162i	$-0.874490\pi$
$313$	−32.6685	−1.84653	−0.923266	+	0.384162i	$0.874490\pi$
$314$	44.4198	2.50676
$315$	5.29199	0.298170
$316$	47.5173	2.67305
$317$	13.7553	0.772577	0.386289	−	0.922378i	$-0.373757\pi$
$317$	13.7553	0.772577	0.386289	+	0.922378i	$0.373757\pi$
$318$	6.96969	0.390841
$319$	39.6836	2.22185
$320$	17.1191	0.956985
$321$	21.1569	1.18086
$322$	11.8146	0.658402
$323$	−7.52266	−0.418572
$324$	−42.2799	−2.34888
$325$	−8.68492	−0.481753
$326$	5.43789	0.301177
$327$	−8.60214	−0.475700
$328$	−33.7202	−1.86189
$329$	−10.7564	−0.593021
$330$	−42.7141	−2.35133
$331$	−12.9455	−0.711546	−0.355773	−	0.934572i	$-0.615782\pi$
$331$	−12.9455	−0.711546	−0.355773	+	0.934572i	$0.615782\pi$
$332$	25.4518	1.39685
$333$	17.7602	0.973253
$334$	−9.72827	−0.532307
$335$	19.6571	1.07398
$336$	−11.0133	−0.600824
$337$	−23.4289	−1.27626	−0.638128	−	0.769930i	$-0.720291\pi$
$337$	−23.4289	−1.27626	−0.638128	+	0.769930i	$0.720291\pi$
$338$	3.93366	0.213963
$339$	27.9473	1.51789
$340$	−6.22671	−0.337691
$341$	−43.8443	−2.37430
$342$	−30.2810	−1.63741
$343$	19.7754	1.06777
$344$	−4.24776	−0.229024
$345$	9.19657	0.495127
$346$	−38.7392	−2.08263
$347$	4.45328	0.239065	0.119532	−	0.992830i	$-0.461860\pi$
$347$	4.45328	0.239065	0.119532	+	0.992830i	$0.461860\pi$
$348$	64.9686	3.48268
$349$	−5.40037	−0.289075	−0.144538	−	0.989499i	$-0.546169\pi$
$349$	−5.40037	−0.289075	−0.144538	+	0.989499i	$0.546169\pi$
$350$	10.4193	0.556933
$351$	−10.9540	−0.584682
$352$	−10.4262	−0.555719
$353$	−14.9976	−0.798240	−0.399120	−	0.916899i	$-0.630684\pi$
$353$	−14.9976	−0.798240	−0.399120	+	0.916899i	$0.630684\pi$
$354$	−27.4071	−1.45667
$355$	−1.36005	−0.0721840
$356$	27.9358	1.48059
$357$	−4.13247	−0.218714
$358$	15.1941	0.803031
$359$	−12.1906	−0.643397	−0.321698	−	0.946842i	$-0.604254\pi$
$359$	−12.1906	−0.643397	−0.321698	+	0.946842i	$0.604254\pi$
$360$	−11.7627	−0.619946
$361$	37.5904	1.97844
$362$	43.1994	2.27051
$363$	29.7904	1.56359
$364$	−27.5544	−1.44424
$365$	−23.3443	−1.22190
$366$	−43.0703	−2.25132
$367$	−26.6334	−1.39025	−0.695126	−	0.718887i	$-0.744652\pi$
$367$	−26.6334	−1.39025	−0.695126	+	0.718887i	$0.744652\pi$
$368$	−6.85988	−0.357596
$369$	−13.3044	−0.692598
$370$	−42.0531	−2.18624
$371$	−2.56459	−0.133147
$372$	−71.7805	−3.72165
$373$	−5.33822	−0.276402	−0.138201	−	0.990404i	$-0.544132\pi$
$373$	−5.33822	−0.276402	−0.138201	+	0.990404i	$0.544132\pi$
$374$	11.9552	0.618186
$375$	25.9747	1.34133
$376$	23.9086	1.23299
$377$	30.5020	1.57093
$378$	13.1415	0.675925
$379$	14.8782	0.764241	0.382120	−	0.924113i	$-0.375194\pi$
$379$	14.8782	0.764241	0.382120	+	0.924113i	$0.375194\pi$
$380$	46.8414	2.40291
$381$	−7.30854	−0.374428
$382$	−11.4793	−0.587334
$383$	−19.4798	−0.995373	−0.497687	−	0.867357i	$-0.665817\pi$
$383$	−19.4798	−0.995373	−0.497687	+	0.867357i	$0.665817\pi$
$384$	−44.7521	−2.28374
$385$	15.7172	0.801023
$386$	−2.64953	−0.134858
$387$	−1.67596	−0.0851940
$388$	46.9241	2.38221
$389$	0.110687	0.00561204	0.00280602	−	0.999996i	$-0.499107\pi$
$389$	0.110687	0.00561204	0.00280602	+	0.999996i	$0.499107\pi$
$390$	−32.8313	−1.66248
$391$	−2.57401	−0.130173
$392$	−14.2209	−0.718262
$393$	−42.3605	−2.13681
$394$	2.39106	0.120460
$395$	−20.8331	−1.04823
$396$	31.4386	1.57985
$397$	−9.68588	−0.486120	−0.243060	−	0.970011i	$-0.578151\pi$
$397$	−9.68588	−0.486120	−0.243060	+	0.970011i	$0.578151\pi$
$398$	36.6501	1.83710
$399$	31.0872	1.55631
$400$	−6.04971	−0.302486
$401$	−27.4278	−1.36968	−0.684839	−	0.728695i	$-0.740127\pi$
$401$	−27.4278	−1.36968	−0.684839	+	0.728695i	$0.740127\pi$
$402$	−61.7886	−3.08174
$403$	−33.7001	−1.67872
$404$	−43.8476	−2.18150
$405$	18.5369	0.921104
$406$	−36.5931	−1.81608
$407$	52.7478	2.61461
$408$	9.18535	0.454743
$409$	−22.3006	−1.10269	−0.551347	−	0.834276i	$-0.685886\pi$
$409$	−22.3006	−1.10269	−0.551347	+	0.834276i	$0.685886\pi$
$410$	31.5025	1.55580
$411$	−6.57032	−0.324090
$412$	51.0370	2.51441
$413$	10.0848	0.496241
$414$	−10.3612	−0.509224
$415$	−11.1589	−0.547767
$416$	−8.01390	−0.392914
$417$	30.4085	1.48911
$418$	−89.9346	−4.39885
$419$	−6.13302	−0.299618	−0.149809	−	0.988715i	$-0.547866\pi$
$419$	−6.13302	−0.299618	−0.149809	+	0.988715i	$0.547866\pi$
$420$	25.7317	1.25558
$421$	−16.9489	−0.826038	−0.413019	−	0.910722i	$-0.635526\pi$
$421$	−16.9489	−0.826038	−0.413019	+	0.910722i	$0.635526\pi$
$422$	−10.8722	−0.529248
$423$	9.43318	0.458657
$424$	5.70038	0.276835
$425$	−2.27001	−0.110112
$426$	4.27508	0.207128
$427$	15.8483	0.766952
$428$	36.8718	1.78226
$429$	41.1807	1.98823
$430$	3.96840	0.191373
$431$	21.2644	1.02427	0.512135	−	0.858905i	$-0.328855\pi$
$431$	21.2644	1.02427	0.512135	+	0.858905i	$0.328855\pi$
$432$	−7.63031	−0.367114
$433$	32.7816	1.57538	0.787692	−	0.616069i	$-0.211276\pi$
$433$	32.7816	1.57538	0.787692	+	0.616069i	$0.211276\pi$
$434$	40.4298	1.94069
$435$	−28.4843	−1.36572
$436$	−14.9916	−0.717970
$437$	19.3634	0.926277
$438$	73.3787	3.50617
$439$	18.1614	0.866797	0.433399	−	0.901202i	$-0.357314\pi$
$439$	18.1614	0.866797	0.433399	+	0.901202i	$0.357314\pi$
$440$	−34.9351	−1.66546
$441$	−5.61087	−0.267184
$442$	9.18909	0.437081
$443$	−0.170188	−0.00808586	−0.00404293	−	0.999992i	$-0.501287\pi$
$443$	−0.170188	−0.00808586	−0.00404293	+	0.999992i	$0.501287\pi$
$444$	86.3569	4.09832
$445$	−12.2479	−0.580608
$446$	−19.7190	−0.933721
$447$	−16.6565	−0.787826
$448$	19.8004	0.935482
$449$	25.8041	1.21777	0.608886	−	0.793258i	$-0.291617\pi$
$449$	25.8041	1.21777	0.608886	+	0.793258i	$0.291617\pi$
$450$	−9.13749	−0.430746
$451$	−39.5139	−1.86064
$452$	48.7059	2.29093
$453$	9.84176	0.462406
$454$	−54.7198	−2.56813
$455$	12.0807	0.566353
$456$	−69.0983	−3.23582
$457$	8.54457	0.399698	0.199849	−	0.979827i	$-0.435955\pi$
$457$	8.54457	0.399698	0.199849	+	0.979827i	$0.435955\pi$
$458$	6.23036	0.291126
$459$	−2.86309	−0.133638
$460$	16.0276	0.747291
$461$	30.2643	1.40955	0.704774	−	0.709432i	$-0.251048\pi$
$461$	30.2643	1.40955	0.704774	+	0.709432i	$0.251048\pi$
$462$	−49.4044	−2.29850
$463$	7.23741	0.336351	0.168176	−	0.985757i	$-0.446212\pi$
$463$	7.23741	0.336351	0.168176	+	0.985757i	$0.446212\pi$
$464$	21.2470	0.986365
$465$	31.4709	1.45943
$466$	−13.1551	−0.609400
$467$	−23.0303	−1.06572	−0.532859	−	0.846204i	$-0.678882\pi$
$467$	−23.0303	−1.06572	−0.532859	+	0.846204i	$0.678882\pi$
$468$	24.1647	1.11701
$469$	22.7359	1.04985
$470$	−22.3362	−1.03029
$471$	39.9924	1.84275
$472$	−22.4158	−1.03177
$473$	−4.97761	−0.228871
$474$	65.4852	3.00784
$475$	17.0765	0.783525
$476$	−7.20199	−0.330103
$477$	2.24910	0.102979
$478$	44.2689	2.02481
$479$	−25.3698	−1.15918	−0.579588	−	0.814909i	$-0.696787\pi$
$479$	−25.3698	−1.15918	−0.579588	+	0.814909i	$0.696787\pi$
$480$	7.48380	0.341587
$481$	40.5435	1.84863
$482$	13.8504	0.630867
$483$	10.6370	0.484001
$484$	51.9182	2.35992
$485$	−20.5730	−0.934172
$486$	−37.6378	−1.70728
$487$	−7.29733	−0.330673	−0.165337	−	0.986237i	$-0.552871\pi$
$487$	−7.29733	−0.330673	−0.165337	+	0.986237i	$0.552871\pi$
$488$	−35.2264	−1.59462
$489$	4.89588	0.221400
$490$	13.2856	0.600182
$491$	−27.4144	−1.23719	−0.618597	−	0.785709i	$-0.712298\pi$
$491$	−27.4144	−1.23719	−0.618597	+	0.785709i	$0.712298\pi$
$492$	−64.6909	−2.91649
$493$	7.97242	0.359060
$494$	−69.1264	−3.11015
$495$	−13.7837	−0.619531
$496$	−23.4747	−1.05404
$497$	−1.57307	−0.0705620
$498$	35.0760	1.57179
$499$	7.09369	0.317557	0.158779	−	0.987314i	$-0.449244\pi$
$499$	7.09369	0.317557	0.158779	+	0.987314i	$0.449244\pi$
$500$	45.2683	2.02446
$501$	−8.75864	−0.391307
$502$	−15.6838	−0.700002
$503$	−33.3840	−1.48852	−0.744260	−	0.667890i	$-0.767198\pi$
$503$	−33.3840	−1.48852	−0.744260	+	0.667890i	$0.767198\pi$
$504$	−13.6050	−0.606016
$505$	19.2242	0.855465
$506$	−30.7727	−1.36801
$507$	3.54159	0.157287
$508$	−12.7372	−0.565121
$509$	−26.2044	−1.16149	−0.580746	−	0.814085i	$-0.697239\pi$
$509$	−26.2044	−1.16149	−0.580746	+	0.814085i	$0.697239\pi$
$510$	−8.58125	−0.379984
$511$	−27.0007	−1.19444
$512$	−28.2234	−1.24731
$513$	21.5381	0.950930
$514$	−27.5684	−1.21599
$515$	−22.3763	−0.986016
$516$	−8.14918	−0.358748
$517$	28.0165	1.23217
$518$	−48.6399	−2.13711
$519$	−34.8780	−1.53098
$520$	−26.8521	−1.17754
$521$	32.9679	1.44435	0.722175	−	0.691710i	$-0.243142\pi$
$521$	32.9679	1.44435	0.722175	+	0.691710i	$0.243142\pi$
$522$	32.0914	1.40460
$523$	37.6834	1.64778	0.823890	−	0.566749i	$-0.191799\pi$
$523$	37.6834	1.64778	0.823890	+	0.566749i	$0.191799\pi$
$524$	−73.8251	−3.22507
$525$	9.38076	0.409410
$526$	48.8092	2.12818
$527$	−8.80832	−0.383696
$528$	28.6855	1.24838
$529$	−16.3745	−0.711934
$530$	−5.32548	−0.231324
$531$	−8.84419	−0.383805
$532$	54.1782	2.34892
$533$	−30.3716	−1.31554
$534$	38.4993	1.66603
$535$	−16.1658	−0.698907
$536$	−50.5357	−2.18281
$537$	13.6796	0.590320
$538$	47.3131	2.03981
$539$	−16.6643	−0.717781
$540$	17.8277	0.767180
$541$	13.2635	0.570242	0.285121	−	0.958492i	$-0.407966\pi$
$541$	13.2635	0.570242	0.285121	+	0.958492i	$0.407966\pi$
$542$	−9.99149	−0.429171
$543$	38.8936	1.66908
$544$	−2.09462	−0.0898062
$545$	6.57282	0.281549
$546$	−37.9737	−1.62512
$547$	−10.7318	−0.458861	−0.229430	−	0.973325i	$-0.573686\pi$
$547$	−10.7318	−0.458861	−0.229430	+	0.973325i	$0.573686\pi$
$548$	−11.4506	−0.489147
$549$	−13.8986	−0.593179
$550$	−27.1383	−1.15718
$551$	−59.9738	−2.55497
$552$	−23.6432	−1.00632
$553$	−24.0961	−1.02467
$554$	32.3888	1.37607
$555$	−37.8616	−1.60714
$556$	52.9953	2.24750
$557$	3.19657	0.135443	0.0677215	−	0.997704i	$-0.478427\pi$
$557$	3.19657	0.135443	0.0677215	+	0.997704i	$0.478427\pi$
$558$	−35.4562	−1.50098
$559$	−3.82594	−0.161820
$560$	8.41514	0.355605
$561$	10.7636	0.454438
$562$	19.0745	0.804611
$563$	25.4159	1.07115	0.535577	−	0.844487i	$-0.320094\pi$
$563$	25.4159	1.07115	0.535577	+	0.844487i	$0.320094\pi$
$564$	45.8677	1.93138
$565$	−21.3542	−0.898380
$566$	1.61377	0.0678319
$567$	21.4403	0.900406
$568$	3.49651	0.146710
$569$	−18.1656	−0.761543	−0.380771	−	0.924669i	$-0.624342\pi$
$569$	−18.1656	−0.761543	−0.380771	+	0.924669i	$0.624342\pi$
$570$	64.5538	2.70386
$571$	41.1463	1.72192	0.860960	−	0.508672i	$-0.169864\pi$
$571$	41.1463	1.72192	0.860960	+	0.508672i	$0.169864\pi$
$572$	71.7690	3.00081
$573$	−10.3352	−0.431758
$574$	36.4367	1.52084
$575$	5.84303	0.243671
$576$	−17.3646	−0.723524
$577$	17.8743	0.744117	0.372058	−	0.928209i	$-0.378652\pi$
$577$	17.8743	0.744117	0.372058	+	0.928209i	$0.378652\pi$
$578$	2.40179	0.0999012
$579$	−2.38545	−0.0991359
$580$	−49.6419	−2.06127
$581$	−12.9067	−0.535459
$582$	64.6677	2.68056
$583$	6.67981	0.276650
$584$	60.0151	2.48344
$585$	−10.5946	−0.438031
$586$	−29.8655	−1.23373
$587$	2.77183	0.114406	0.0572028	−	0.998363i	$-0.481782\pi$
$587$	2.77183	0.114406	0.0572028	+	0.998363i	$0.481782\pi$
$588$	−27.2822	−1.12510
$589$	66.2620	2.73028
$590$	20.9415	0.862149
$591$	2.15274	0.0885519
$592$	28.2417	1.16072
$593$	−24.7599	−1.01677	−0.508383	−	0.861131i	$-0.669757\pi$
$593$	−24.7599	−1.01677	−0.508383	+	0.861131i	$0.669757\pi$
$594$	−34.2287	−1.40442
$595$	3.15758	0.129448
$596$	−29.0286	−1.18906
$597$	32.9971	1.35048
$598$	−23.6528	−0.967235
$599$	37.6209	1.53715	0.768575	−	0.639760i	$-0.220966\pi$
$599$	37.6209	1.53715	0.768575	+	0.639760i	$0.220966\pi$
$600$	−20.8509	−0.851233
$601$	27.4906	1.12137	0.560683	−	0.828030i	$-0.310538\pi$
$601$	27.4906	1.12137	0.560683	+	0.828030i	$0.310538\pi$
$602$	4.58996	0.187073
$603$	−19.9390	−0.811978
$604$	17.1520	0.697906
$605$	−22.7626	−0.925431
$606$	−60.4280	−2.45472
$607$	−11.9689	−0.485804	−0.242902	−	0.970051i	$-0.578099\pi$
$607$	−11.9689	−0.485804	−0.242902	+	0.970051i	$0.578099\pi$
$608$	15.7571	0.639037
$609$	−32.9458	−1.33503
$610$	32.9096	1.33247
$611$	21.5343	0.871186
$612$	6.31601	0.255310
$613$	24.4464	0.987381	0.493690	−	0.869638i	$-0.335648\pi$
$613$	24.4464	0.987381	0.493690	+	0.869638i	$0.335648\pi$
$614$	−58.2051	−2.34897
$615$	28.3626	1.14369
$616$	−40.4069	−1.62804
$617$	16.9006	0.680394	0.340197	−	0.940354i	$-0.389506\pi$
$617$	16.9006	0.680394	0.340197	+	0.940354i	$0.389506\pi$
$618$	70.3360	2.82933
$619$	0.706173	0.0283835	0.0141917	−	0.999899i	$-0.495482\pi$
$619$	0.706173	0.0283835	0.0141917	+	0.999899i	$0.495482\pi$
$620$	54.8468	2.20270
$621$	7.36963	0.295733
$622$	11.1834	0.448414
$623$	−14.1663	−0.567562
$624$	22.0486	0.882649
$625$	−8.49699	−0.339880
$626$	−78.4627	−3.13600
$627$	−80.9707	−3.23366
$628$	69.6980	2.78125
$629$	10.5970	0.422530
$630$	12.7102	0.506388
$631$	−8.91140	−0.354757	−0.177379	−	0.984143i	$-0.556762\pi$
$631$	−8.91140	−0.354757	−0.177379	+	0.984143i	$0.556762\pi$
$632$	53.5591	2.13047
$633$	−9.78851	−0.389058
$634$	33.0374	1.31208
$635$	5.58439	0.221610
$636$	10.9360	0.433639
$637$	−12.8087	−0.507498
$638$	95.3115	3.77342
$639$	1.37955	0.0545743
$640$	34.1946	1.35166
$641$	−15.4500	−0.610236	−0.305118	−	0.952314i	$-0.598696\pi$
$641$	−15.4500	−0.610236	−0.305118	+	0.952314i	$0.598696\pi$
$642$	50.8143	2.00548
$643$	−43.2788	−1.70675	−0.853375	−	0.521298i	$-0.825448\pi$
$643$	−43.2788	−1.70675	−0.853375	+	0.521298i	$0.825448\pi$
$644$	18.5380	0.730499
$645$	3.57286	0.140681
$646$	−18.0678	−0.710870
$647$	7.36056	0.289373	0.144687	−	0.989478i	$-0.453783\pi$
$647$	7.36056	0.289373	0.144687	+	0.989478i	$0.453783\pi$
$648$	−47.6558	−1.87210
$649$	−26.2672	−1.03108
$650$	−20.8593	−0.818171
$651$	36.4001	1.42663
$652$	8.53245	0.334157
$653$	25.1601	0.984591	0.492295	−	0.870428i	$-0.336158\pi$
$653$	25.1601	0.984591	0.492295	+	0.870428i	$0.336158\pi$
$654$	−20.6605	−0.807890
$655$	32.3673	1.26469
$656$	−21.1561	−0.826008
$657$	23.6791	0.923808
$658$	−25.8347	−1.00714
$659$	−16.4021	−0.638935	−0.319468	−	0.947597i	$-0.603504\pi$
$659$	−16.4021	−0.638935	−0.319468	+	0.947597i	$0.603504\pi$
$660$	−67.0216	−2.60881
$661$	−35.8145	−1.39302	−0.696512	−	0.717546i	$-0.745265\pi$
$661$	−35.8145	−1.39302	−0.696512	+	0.717546i	$0.745265\pi$
$662$	−31.0922	−1.20843
$663$	8.27320	0.321304
$664$	28.6880	1.11331
$665$	−23.7534	−0.921119
$666$	42.6562	1.65290
$667$	−20.5211	−0.794579
$668$	−15.2644	−0.590597
$669$	−17.7536	−0.686392
$670$	47.2121	1.82396
$671$	−41.2789	−1.59356
$672$	8.65597	0.333911
$673$	17.5105	0.674979	0.337489	−	0.941329i	$-0.390422\pi$
$673$	17.5105	0.674979	0.337489	+	0.941329i	$0.390422\pi$
$674$	−56.2713	−2.16749
$675$	6.49926	0.250156
$676$	6.17221	0.237393
$677$	38.7196	1.48812	0.744058	−	0.668115i	$-0.232899\pi$
$677$	38.7196	1.48812	0.744058	+	0.668115i	$0.232899\pi$
$678$	67.1234	2.57786
$679$	−23.7953	−0.913181
$680$	−7.01844	−0.269145
$681$	−49.2658	−1.88787
$682$	−105.305	−4.03233
$683$	−49.9591	−1.91163	−0.955815	−	0.293969i	$-0.905024\pi$
$683$	−49.9591	−1.91163	−0.955815	+	0.293969i	$0.905024\pi$
$684$	−47.5132	−1.81671
$685$	5.02032	0.191817
$686$	47.4962	1.81341
$687$	5.60937	0.214011
$688$	−2.66506	−0.101604
$689$	5.13430	0.195601
$690$	22.0882	0.840884
$691$	−45.9602	−1.74841	−0.874204	−	0.485559i	$-0.838616\pi$
$691$	−45.9602	−1.74841	−0.874204	+	0.485559i	$0.838616\pi$
$692$	−60.7848	−2.31069
$693$	−15.9426	−0.605610
$694$	10.6958	0.406009
$695$	−23.2348	−0.881347
$696$	73.2295	2.77576
$697$	−7.93834	−0.300686
$698$	−12.9705	−0.490942
$699$	−11.8439	−0.447979
$700$	16.3486	0.617919
$701$	−14.3488	−0.541946	−0.270973	−	0.962587i	$-0.587345\pi$
$701$	−14.3488	−0.541946	−0.270973	+	0.962587i	$0.587345\pi$
$702$	−26.3092	−0.992978
$703$	−79.7177	−3.00661
$704$	−51.5728	−1.94372
$705$	−20.1099	−0.757382
$706$	−36.0210	−1.35567
$707$	22.2353	0.836243
$708$	−43.0038	−1.61618
$709$	9.79594	0.367894	0.183947	−	0.982936i	$-0.441112\pi$
$709$	9.79594	0.367894	0.183947	+	0.982936i	$0.441112\pi$
$710$	−3.26655	−0.122591
$711$	21.1319	0.792507
$712$	31.4879	1.18006
$713$	22.6727	0.849098
$714$	−9.92532	−0.371446
$715$	−31.4658	−1.17675
$716$	23.8406	0.890966
$717$	39.8565	1.48847
$718$	−29.2793	−1.09269
$719$	−21.7742	−0.812040	−0.406020	−	0.913864i	$-0.633084\pi$
$719$	−21.7742	−0.812040	−0.406020	+	0.913864i	$0.633084\pi$
$720$	−7.37992	−0.275033
$721$	−25.8810	−0.963860
$722$	90.2843	3.36003
$723$	12.4699	0.463760
$724$	67.7830	2.51914
$725$	−18.0975	−0.672123
$726$	71.5503	2.65548
$727$	−6.00070	−0.222554	−0.111277	−	0.993789i	$-0.535494\pi$
$727$	−6.00070	−0.222554	−0.111277	+	0.993789i	$0.535494\pi$
$728$	−31.0579	−1.15108
$729$	−0.229252	−0.00849083
$730$	−56.0680	−2.07517
$731$	−1.00000	−0.0369863
$732$	−67.5805	−2.49785
$733$	50.4371	1.86294	0.931469	−	0.363821i	$-0.118528\pi$
$733$	50.4371	1.86294	0.931469	+	0.363821i	$0.118528\pi$
$734$	−63.9678	−2.36109
$735$	11.9614	0.441203
$736$	5.39158	0.198736
$737$	−59.2187	−2.18135
$738$	−31.9543	−1.17625
$739$	2.44980	0.0901175	0.0450587	−	0.998984i	$-0.485653\pi$
$739$	2.44980	0.0901175	0.0450587	+	0.998984i	$0.485653\pi$
$740$	−65.9845	−2.42564
$741$	−62.2365	−2.28631
$742$	−6.15960	−0.226126
$743$	14.2353	0.522244	0.261122	−	0.965306i	$-0.415907\pi$
$743$	14.2353	0.522244	0.261122	+	0.965306i	$0.415907\pi$
$744$	−80.9075	−2.96621
$745$	12.7271	0.466284
$746$	−12.8213	−0.469420
$747$	11.3189	0.414137
$748$	18.7585	0.685880
$749$	−18.6978	−0.683202
$750$	62.3858	2.27801
$751$	−19.2275	−0.701623	−0.350812	−	0.936446i	$-0.614094\pi$
$751$	−19.2275	−0.701623	−0.350812	+	0.936446i	$0.614094\pi$
$752$	15.0003	0.547005
$753$	−14.1206	−0.514582
$754$	73.2593	2.66795
$755$	−7.52000	−0.273681
$756$	20.6200	0.749941
$757$	−14.4323	−0.524550	−0.262275	−	0.964993i	$-0.584473\pi$
$757$	−14.4323	−0.524550	−0.262275	+	0.964993i	$0.584473\pi$
$758$	35.7342	1.29793
$759$	−27.7055	−1.00565
$760$	52.7974	1.91516
$761$	−42.3871	−1.53653	−0.768266	−	0.640131i	$-0.778880\pi$
$761$	−42.3871	−1.53653	−0.768266	+	0.640131i	$0.778880\pi$
$762$	−17.5536	−0.635898
$763$	7.60231	0.275222
$764$	−18.0119	−0.651649
$765$	−2.76914	−0.100118
$766$	−46.7864	−1.69046
$767$	−20.1898	−0.729010
$768$	−62.6759	−2.26162
$769$	1.99889	0.0720820	0.0360410	−	0.999350i	$-0.488525\pi$
$769$	1.99889	0.0720820	0.0360410	+	0.999350i	$0.488525\pi$
$770$	37.7494	1.36039
$771$	−24.8206	−0.893893
$772$	−4.15732	−0.149625
$773$	3.42939	0.123347	0.0616733	−	0.998096i	$-0.480356\pi$
$773$	3.42939	0.123347	0.0616733	+	0.998096i	$0.480356\pi$
$774$	−4.02531	−0.144687
$775$	19.9950	0.718241
$776$	52.8905	1.89866
$777$	−43.7919	−1.57102
$778$	0.265846	0.00953103
$779$	59.7174	2.13960
$780$	−51.5148	−1.84453
$781$	4.09727	0.146612
$782$	−6.18222	−0.221076
$783$	−22.8258	−0.815727
$784$	−8.92221	−0.318650
$785$	−30.5578	−1.09066
$786$	−101.741	−3.62898
$787$	−45.5301	−1.62297	−0.811486	−	0.584371i	$-0.801341\pi$
$787$	−45.5301	−1.62297	−0.811486	+	0.584371i	$0.801341\pi$
$788$	3.75175	0.133651
$789$	43.9443	1.56446
$790$	−50.0366	−1.78022
$791$	−24.6989	−0.878193
$792$	35.4361	1.25917
$793$	−31.7282	−1.12670
$794$	−23.2634	−0.825588
$795$	−4.79468	−0.170050
$796$	57.5067	2.03827
$797$	−43.0585	−1.52521	−0.762605	−	0.646864i	$-0.776080\pi$
$797$	−43.0585	−1.52521	−0.762605	+	0.646864i	$0.776080\pi$
$798$	74.6648	2.64311
$799$	5.62851	0.199122
$800$	4.75482	0.168108
$801$	12.4236	0.438966
$802$	−65.8757	−2.32615
$803$	70.3268	2.48178
$804$	−96.9509	−3.41920
$805$	−8.12765	−0.286462
$806$	−80.9404	−2.85101
$807$	42.5973	1.49950
$808$	−49.4229	−1.73869
$809$	48.0876	1.69067	0.845336	−	0.534236i	$-0.179401\pi$
$809$	48.0876	1.69067	0.845336	+	0.534236i	$0.179401\pi$
$810$	44.5216	1.56433
$811$	42.4142	1.48936	0.744682	−	0.667420i	$-0.232601\pi$
$811$	42.4142	1.48936	0.744682	+	0.667420i	$0.232601\pi$
$812$	−57.4173	−2.01495
$813$	−8.99562	−0.315490
$814$	126.689	4.44044
$815$	−3.74090	−0.131038
$816$	5.76292	0.201742
$817$	7.52266	0.263185
$818$	−53.5613	−1.87273
$819$	−12.2540	−0.428188
$820$	49.4297	1.72616
$821$	−54.9569	−1.91801	−0.959005	−	0.283390i	$-0.908541\pi$
$821$	−54.9569	−1.91801	−0.959005	+	0.283390i	$0.908541\pi$
$822$	−15.7805	−0.550409
$823$	−4.52058	−0.157577	−0.0787887	−	0.996891i	$-0.525105\pi$
$823$	−4.52058	−0.157577	−0.0787887	+	0.996891i	$0.525105\pi$
$824$	57.5264	2.00403
$825$	−24.4334	−0.850662
$826$	24.2216	0.842777
$827$	−42.1241	−1.46480	−0.732399	−	0.680876i	$-0.761599\pi$
$827$	−42.1241	−1.46480	−0.732399	+	0.680876i	$0.761599\pi$
$828$	−16.2575	−0.564986
$829$	29.0415	1.00865	0.504327	−	0.863513i	$-0.331741\pi$
$829$	29.0415	1.00865	0.504327	+	0.863513i	$0.331741\pi$
$830$	−26.8012	−0.930284
$831$	29.1606	1.01157
$832$	−39.6404	−1.37428
$833$	−3.34785	−0.115996
$834$	73.0347	2.52898
$835$	6.69239	0.231600
$836$	−141.114	−4.88053
$837$	25.2190	0.871698
$838$	−14.7302	−0.508847
$839$	7.94665	0.274349	0.137174	−	0.990547i	$-0.456198\pi$
$839$	7.94665	0.274349	0.137174	+	0.990547i	$0.456198\pi$
$840$	29.0035	1.00072
$841$	34.5594	1.19170
$842$	−40.7076	−1.40288
$843$	17.1733	0.591481
$844$	−17.0592	−0.587203
$845$	−2.70609	−0.0930925
$846$	22.6565	0.778946
$847$	−26.3279	−0.904636
$848$	3.57643	0.122815
$849$	1.45293	0.0498643
$850$	−5.45209	−0.187005
$851$	−27.2768	−0.935036
$852$	6.70793	0.229810
$853$	21.1885	0.725482	0.362741	−	0.931890i	$-0.381841\pi$
$853$	21.1885	0.725482	0.362741	+	0.931890i	$0.381841\pi$
$854$	38.0642	1.30253
$855$	20.8313	0.712416
$856$	41.5601	1.42049
$857$	−13.3308	−0.455370	−0.227685	−	0.973735i	$-0.573116\pi$
$857$	−13.3308	−0.455370	−0.227685	+	0.973735i	$0.573116\pi$
$858$	98.9074	3.37664
$859$	45.4713	1.55146	0.775730	−	0.631065i	$-0.217382\pi$
$859$	45.4713	1.55146	0.775730	+	0.631065i	$0.217382\pi$
$860$	6.22671	0.212329
$861$	32.8050	1.11799
$862$	51.0726	1.73954
$863$	−38.8479	−1.32240	−0.661200	−	0.750210i	$-0.729952\pi$
$863$	−38.8479	−1.32240	−0.661200	+	0.750210i	$0.729952\pi$
$864$	5.99710	0.204026
$865$	26.6500	0.906126
$866$	78.7345	2.67551
$867$	2.16240	0.0734389
$868$	63.4374	2.15321
$869$	62.7616	2.12904
$870$	−68.4133	−2.31943
$871$	−45.5173	−1.54229
$872$	−16.8978	−0.572233
$873$	20.8681	0.706277
$874$	46.5068	1.57311
$875$	−22.9557	−0.776043
$876$	115.137	3.89011
$877$	−19.1014	−0.645009	−0.322504	−	0.946568i	$-0.604525\pi$
$877$	−19.1014	−0.645009	−0.322504	+	0.946568i	$0.604525\pi$
$878$	43.6199	1.47210
$879$	−26.8888	−0.906936
$880$	−21.9183	−0.738867
$881$	−3.37253	−0.113623	−0.0568117	−	0.998385i	$-0.518093\pi$
$881$	−3.37253	−0.113623	−0.0568117	+	0.998385i	$0.518093\pi$
$882$	−13.4761	−0.453764
$883$	17.3606	0.584231	0.292116	−	0.956383i	$-0.405641\pi$
$883$	17.3606	0.584231	0.292116	+	0.956383i	$0.405641\pi$
$884$	14.4184	0.484942
$885$	18.8543	0.633779
$886$	−0.408755	−0.0137324
$887$	11.9957	0.402775	0.201388	−	0.979512i	$-0.435455\pi$
$887$	11.9957	0.402775	0.201388	+	0.979512i	$0.435455\pi$
$888$	97.3373	3.26643
$889$	6.45906	0.216630
$890$	−29.4170	−0.986059
$891$	−55.8440	−1.87084
$892$	−30.9406	−1.03597
$893$	−42.3414	−1.41690
$894$	−40.0054	−1.33798
$895$	−10.4525	−0.349388
$896$	39.5505	1.32129
$897$	−21.2953	−0.711029
$898$	61.9760	2.06817
$899$	−70.2236	−2.34209
$900$	−14.3374	−0.477914
$901$	1.34197	0.0447076
$902$	−94.9041	−3.15996
$903$	4.13247	0.137520
$904$	54.8989	1.82591
$905$	−29.7183	−0.987868
$906$	23.6378	0.785314
$907$	−0.842221	−0.0279655	−0.0139827	−	0.999902i	$-0.504451\pi$
$907$	−0.842221	−0.0279655	−0.0139827	+	0.999902i	$0.504451\pi$
$908$	−85.8595	−2.84935
$909$	−19.4999	−0.646771
$910$	29.0153	0.961849
$911$	−0.123467	−0.00409064	−0.00204532	−	0.999998i	$-0.500651\pi$
$911$	−0.123467	−0.00409064	−0.00204532	+	0.999998i	$0.500651\pi$
$912$	−43.3525	−1.43554
$913$	33.6171	1.11256
$914$	20.5222	0.678815
$915$	29.6295	0.979520
$916$	9.77590	0.323005
$917$	37.4369	1.23628
$918$	−6.87654	−0.226960
$919$	12.7851	0.421742	0.210871	−	0.977514i	$-0.432370\pi$
$919$	12.7851	0.421742	0.210871	+	0.977514i	$0.432370\pi$
$920$	18.0655	0.595603
$921$	−52.4037	−1.72676
$922$	72.6884	2.39386
$923$	3.14929	0.103660
$924$	−77.5191	−2.55019
$925$	−24.0553	−0.790935
$926$	17.3827	0.571232
$927$	22.6972	0.745473
$928$	−16.6992	−0.548178
$929$	−23.8420	−0.782231	−0.391115	−	0.920342i	$-0.627911\pi$
$929$	−23.8420	−0.782231	−0.391115	+	0.920342i	$0.627911\pi$
$930$	75.5864	2.47858
$931$	25.1847	0.825396
$932$	−20.6414	−0.676131
$933$	10.0687	0.329636
$934$	−55.3140	−1.80993
$935$	−8.22434	−0.268965
$936$	27.2372	0.890276
$937$	16.5104	0.539371	0.269686	−	0.962948i	$-0.413080\pi$
$937$	16.5104	0.539371	0.269686	+	0.962948i	$0.413080\pi$
$938$	54.6069	1.78298
$939$	−70.6422	−2.30532
$940$	−35.0471	−1.14311
$941$	20.2020	0.658567	0.329283	−	0.944231i	$-0.393193\pi$
$941$	20.2020	0.658567	0.329283	+	0.944231i	$0.393193\pi$
$942$	96.0533	3.12959
$943$	20.4333	0.665401
$944$	−14.0637	−0.457735
$945$	−9.04046	−0.294086
$946$	−11.9552	−0.388696
$947$	31.7296	1.03107	0.515537	−	0.856868i	$-0.327593\pi$
$947$	31.7296	1.03107	0.515537	+	0.856868i	$0.327593\pi$
$948$	102.751	3.33720
$949$	54.0553	1.75471
$950$	41.0142	1.33068
$951$	29.7445	0.964532
$952$	−8.11773	−0.263097
$953$	13.9782	0.452798	0.226399	−	0.974035i	$-0.427305\pi$
$953$	13.9782	0.452798	0.226399	+	0.974035i	$0.427305\pi$
$954$	5.40185	0.174891
$955$	7.89701	0.255541
$956$	69.4612	2.24654
$957$	85.8116	2.77390
$958$	−60.9329	−1.96865
$959$	5.80665	0.187507
$960$	37.0182	1.19476
$961$	46.5865	1.50279
$962$	97.3769	3.13956
$963$	16.3976	0.528405
$964$	21.7323	0.699949
$965$	1.82270	0.0586748
$966$	25.5479	0.821989
$967$	−0.671262	−0.0215863	−0.0107932	−	0.999942i	$-0.503436\pi$
$967$	−0.671262	−0.0215863	−0.0107932	+	0.999942i	$0.503436\pi$
$968$	58.5196	1.88089
$969$	−16.2670	−0.522571
$970$	−49.4120	−1.58652
$971$	−48.4186	−1.55383	−0.776913	−	0.629608i	$-0.783215\pi$
$971$	−48.4186	−1.55383	−0.776913	+	0.629608i	$0.783215\pi$
$972$	−59.0565	−1.89424
$973$	−26.8741	−0.861543
$974$	−17.5266	−0.561589
$975$	−18.7803	−0.601450
$976$	−22.1011	−0.707440
$977$	−27.5991	−0.882972	−0.441486	−	0.897268i	$-0.645549\pi$
$977$	−27.5991	−0.882972	−0.441486	+	0.897268i	$0.645549\pi$
$978$	11.7589	0.376007
$979$	36.8981	1.17927
$980$	20.8461	0.665903
$981$	−6.66708	−0.212863
$982$	−65.8435	−2.10115
$983$	27.9769	0.892323	0.446162	−	0.894952i	$-0.352791\pi$
$983$	27.9769	0.892323	0.446162	+	0.894952i	$0.352791\pi$
$984$	−72.9165	−2.32449
$985$	−1.64489	−0.0524105
$986$	19.1481	0.609798
$987$	−23.2597	−0.740364
$988$	−108.465	−3.45072
$989$	2.57401	0.0818487
$990$	−33.1055	−1.05216
$991$	−38.9655	−1.23778	−0.618890	−	0.785478i	$-0.712417\pi$
$991$	−38.9655	−1.23778	−0.618890	+	0.785478i	$0.712417\pi$
$992$	18.4501	0.585792
$993$	−27.9932	−0.888338
$994$	−3.77819	−0.119837
$995$	−25.2128	−0.799299
$996$	55.0368	1.74391
$997$	40.2727	1.27545	0.637724	−	0.770265i	$-0.279876\pi$
$997$	40.2727	1.27545	0.637724	+	0.770265i	$0.279876\pi$
$998$	17.0375	0.539314
$999$	−30.3402	−0.959923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.18	✓	19
3.2	odd	2		6579.2.a.t.1.2		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.18	✓	19	1.1	even	1	trivial
6579.2.a.t.1.2		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)

\(f(q)\)	\(=\)	\(q+2.40179 q^{2} +2.16240 q^{3} +3.76858 q^{4} -1.65227 q^{5} +5.19362 q^{6} -1.91106 q^{7} +4.24776 q^{8} +1.67596 q^{9} +O(q^{10})\)	\(q+2.40179 q^{2} +2.16240 q^{3} +3.76858 q^{4} -1.65227 q^{5} +5.19362 q^{6} -1.91106 q^{7} +4.24776 q^{8} +1.67596 q^{9} -3.96840 q^{10} +4.97761 q^{11} +8.14918 q^{12} +3.82594 q^{13} -4.58996 q^{14} -3.57286 q^{15} +2.66506 q^{16} +1.00000 q^{17} +4.02531 q^{18} -7.52266 q^{19} -6.22671 q^{20} -4.13247 q^{21} +11.9552 q^{22} -2.57401 q^{23} +9.18535 q^{24} -2.27001 q^{25} +9.18909 q^{26} -2.86309 q^{27} -7.20199 q^{28} +7.97242 q^{29} -8.58125 q^{30} -8.80832 q^{31} -2.09462 q^{32} +10.7636 q^{33} +2.40179 q^{34} +3.15758 q^{35} +6.31601 q^{36} +10.5970 q^{37} -18.0678 q^{38} +8.27320 q^{39} -7.01844 q^{40} -7.93834 q^{41} -9.92532 q^{42} -1.00000 q^{43} +18.7585 q^{44} -2.76914 q^{45} -6.18222 q^{46} +5.62851 q^{47} +5.76292 q^{48} -3.34785 q^{49} -5.45209 q^{50} +2.16240 q^{51} +14.4184 q^{52} +1.34197 q^{53} -6.87654 q^{54} -8.22434 q^{55} -8.11773 q^{56} -16.2670 q^{57} +19.1481 q^{58} -5.27708 q^{59} -13.4646 q^{60} -8.29292 q^{61} -21.1557 q^{62} -3.20287 q^{63} -10.3610 q^{64} -6.32147 q^{65} +25.8518 q^{66} -11.8970 q^{67} +3.76858 q^{68} -5.56603 q^{69} +7.58385 q^{70} +0.823141 q^{71} +7.11910 q^{72} +14.1286 q^{73} +25.4518 q^{74} -4.90867 q^{75} -28.3498 q^{76} -9.51251 q^{77} +19.8705 q^{78} +12.6088 q^{79} -4.40339 q^{80} -11.2190 q^{81} -19.0662 q^{82} +6.75367 q^{83} -15.5736 q^{84} -1.65227 q^{85} -2.40179 q^{86} +17.2395 q^{87} +21.1437 q^{88} +7.41281 q^{89} -6.65089 q^{90} -7.31160 q^{91} -9.70037 q^{92} -19.0471 q^{93} +13.5185 q^{94} +12.4295 q^{95} -4.52941 q^{96} +12.4514 q^{97} -8.04082 q^{98} +8.34229 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 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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