LMFDB - Embedded newform 799.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [799,2,Mod(1,799)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(799, 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("799.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 799 = 17 \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	799.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:	$6.38004712150$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} - 24 x^{18} + 108 x^{17} + 221 x^{16} - 1200 x^{15} - 931 x^{14} + 7128 x^{13} + \cdots + 63 $ x^20 - 4x^19 - 24x^18 + 108x^17 + 221x^16 - 1200x^15 - 931x^14 + 7128x^13 + 1280x^12 - 24559x^11 + 3411x^10 + 49829x^9 - 15132x^8 - 58070x^7 + 20659x^6 + 36738x^5 - 11129x^4 - 11299x^3 + 1589x^2 + 1289*x + 63
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Root			$2.64443$ of defining polynomial
Character	$\chi$	$=$	799.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.64443 q^{2} +2.73641 q^{3} +4.99303 q^{4} -3.13323 q^{5} +7.23626 q^{6} -1.81022 q^{7} +7.91488 q^{8} +4.48794 q^{9} +O(q^{10})$	\(q+2.64443 q^{2} +2.73641 q^{3} +4.99303 q^{4} -3.13323 q^{5} +7.23626 q^{6} -1.81022 q^{7} +7.91488 q^{8} +4.48794 q^{9} -8.28563 q^{10} -0.553008 q^{11} +13.6630 q^{12} +0.601061 q^{13} -4.78700 q^{14} -8.57381 q^{15} +10.9443 q^{16} -1.00000 q^{17} +11.8681 q^{18} +4.50744 q^{19} -15.6443 q^{20} -4.95349 q^{21} -1.46239 q^{22} -7.28680 q^{23} +21.6584 q^{24} +4.81714 q^{25} +1.58947 q^{26} +4.07162 q^{27} -9.03847 q^{28} +2.50389 q^{29} -22.6729 q^{30} -9.60133 q^{31} +13.1118 q^{32} -1.51326 q^{33} -2.64443 q^{34} +5.67183 q^{35} +22.4085 q^{36} -4.56133 q^{37} +11.9196 q^{38} +1.64475 q^{39} -24.7992 q^{40} +10.8389 q^{41} -13.0992 q^{42} -4.59190 q^{43} -2.76119 q^{44} -14.0618 q^{45} -19.2695 q^{46} +1.00000 q^{47} +29.9482 q^{48} -3.72312 q^{49} +12.7386 q^{50} -2.73641 q^{51} +3.00112 q^{52} +0.0565505 q^{53} +10.7671 q^{54} +1.73270 q^{55} -14.3276 q^{56} +12.3342 q^{57} +6.62137 q^{58} +11.9547 q^{59} -42.8093 q^{60} +8.36297 q^{61} -25.3901 q^{62} -8.12415 q^{63} +12.7846 q^{64} -1.88326 q^{65} -4.00171 q^{66} -15.7774 q^{67} -4.99303 q^{68} -19.9397 q^{69} +14.9988 q^{70} +4.84854 q^{71} +35.5215 q^{72} +3.41250 q^{73} -12.0621 q^{74} +13.1817 q^{75} +22.5058 q^{76} +1.00106 q^{77} +4.34944 q^{78} +3.47942 q^{79} -34.2911 q^{80} -2.32220 q^{81} +28.6628 q^{82} -6.02539 q^{83} -24.7330 q^{84} +3.13323 q^{85} -12.1430 q^{86} +6.85167 q^{87} -4.37700 q^{88} +16.2853 q^{89} -37.1854 q^{90} -1.08805 q^{91} -36.3833 q^{92} -26.2732 q^{93} +2.64443 q^{94} -14.1228 q^{95} +35.8792 q^{96} +2.05567 q^{97} -9.84554 q^{98} -2.48187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) $ 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * 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 $

$2$	2.64443	1.86990	0.934949	−	0.354783i	$-0.115445\pi$
$2$	2.64443	1.86990	0.934949	+	0.354783i	$0.115445\pi$
$3$	2.73641	1.57987	0.789934	−	0.613192i	$-0.210115\pi$
$3$	2.73641	1.57987	0.789934	+	0.613192i	$0.210115\pi$
$4$	4.99303	2.49652
$5$	−3.13323	−1.40122	−0.700612	−	0.713543i	$-0.747090\pi$
$5$	−3.13323	−1.40122	−0.700612	+	0.713543i	$0.747090\pi$
$6$	7.23626	2.95419
$7$	−1.81022	−0.684197	−0.342099	−	0.939664i	$-0.611138\pi$
$7$	−1.81022	−0.684197	−0.342099	+	0.939664i	$0.611138\pi$
$8$	7.91488	2.79833
$9$	4.48794	1.49598
$10$	−8.28563	−2.62015
$11$	−0.553008	−0.166738	−0.0833691	−	0.996519i	$-0.526568\pi$
$11$	−0.553008	−0.166738	−0.0833691	+	0.996519i	$0.526568\pi$
$12$	13.6630	3.94417
$13$	0.601061	0.166704	0.0833522	−	0.996520i	$-0.473437\pi$
$13$	0.601061	0.166704	0.0833522	+	0.996520i	$0.473437\pi$
$14$	−4.78700	−1.27938
$15$	−8.57381	−2.21375
$16$	10.9443	2.73608
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	11.8681	2.79733
$19$	4.50744	1.03408	0.517038	−	0.855962i	$-0.327034\pi$
$19$	4.50744	1.03408	0.517038	+	0.855962i	$0.327034\pi$
$20$	−15.6443	−3.49818
$21$	−4.95349	−1.08094
$22$	−1.46239	−0.311783
$23$	−7.28680	−1.51940	−0.759702	−	0.650272i	$-0.774655\pi$
$23$	−7.28680	−1.51940	−0.759702	+	0.650272i	$0.774655\pi$
$24$	21.6584	4.42100
$25$	4.81714	0.963428
$26$	1.58947	0.311720
$27$	4.07162	0.783584
$28$	−9.03847	−1.70811
$29$	2.50389	0.464960	0.232480	−	0.972601i	$-0.425316\pi$
$29$	2.50389	0.464960	0.232480	+	0.972601i	$0.425316\pi$
$30$	−22.6729	−4.13948
$31$	−9.60133	−1.72445	−0.862225	−	0.506526i	$-0.830930\pi$
$31$	−9.60133	−1.72445	−0.862225	+	0.506526i	$0.830930\pi$
$32$	13.1118	2.31786
$33$	−1.51326	−0.263424
$34$	−2.64443	−0.453517
$35$	5.67183	0.958714
$36$	22.4085	3.73474
$37$	−4.56133	−0.749878	−0.374939	−	0.927049i	$-0.622336\pi$
$37$	−4.56133	−0.749878	−0.374939	+	0.927049i	$0.622336\pi$
$38$	11.9196	1.93362
$39$	1.64475	0.263371
$40$	−24.7992	−3.92109
$41$	10.8389	1.69276	0.846378	−	0.532583i	$-0.178778\pi$
$41$	10.8389	1.69276	0.846378	+	0.532583i	$0.178778\pi$
$42$	−13.0992	−2.02125
$43$	−4.59190	−0.700259	−0.350129	−	0.936701i	$-0.613862\pi$
$43$	−4.59190	−0.700259	−0.350129	+	0.936701i	$0.613862\pi$
$44$	−2.76119	−0.416265
$45$	−14.0618	−2.09620
$46$	−19.2695	−2.84113
$47$	1.00000	0.145865
$47$	1.00000	0.145865
$48$	29.9482	4.32264
$49$	−3.72312	−0.531874
$50$	12.7386	1.80151
$51$	−2.73641	−0.383174
$52$	3.00112	0.416180
$53$	0.0565505	0.00776781	0.00388390	−	0.999992i	$-0.498764\pi$
$53$	0.0565505	0.00776781	0.00388390	+	0.999992i	$0.498764\pi$
$54$	10.7671	1.46522
$55$	1.73270	0.233638
$56$	−14.3276	−1.91461
$57$	12.3342	1.63370
$58$	6.62137	0.869428
$59$	11.9547	1.55637	0.778184	−	0.628036i	$-0.216141\pi$
$59$	11.9547	1.55637	0.778184	+	0.628036i	$0.216141\pi$
$60$	−42.8093	−5.52666
$61$	8.36297	1.07077	0.535384	−	0.844608i	$-0.320167\pi$
$61$	8.36297	1.07077	0.535384	+	0.844608i	$0.320167\pi$
$62$	−25.3901	−3.22454
$63$	−8.12415	−1.02355
$64$	12.7846	1.59807
$65$	−1.88326	−0.233590
$66$	−4.00171	−0.492577
$67$	−15.7774	−1.92752	−0.963760	−	0.266772i	$-0.914043\pi$
$67$	−15.7774	−1.92752	−0.963760	+	0.266772i	$0.914043\pi$
$68$	−4.99303	−0.605494
$69$	−19.9397	−2.40046
$70$	14.9988	1.79270
$71$	4.84854	0.575416	0.287708	−	0.957718i	$-0.407107\pi$
$71$	4.84854	0.575416	0.287708	+	0.957718i	$0.407107\pi$
$72$	35.5215	4.18625
$73$	3.41250	0.399403	0.199702	−	0.979857i	$-0.436003\pi$
$73$	3.41250	0.399403	0.199702	+	0.979857i	$0.436003\pi$
$74$	−12.0621	−1.40220
$75$	13.1817	1.52209
$76$	22.5058	2.58159
$77$	1.00106	0.114082
$78$	4.34944	0.492477
$79$	3.47942	0.391465	0.195733	−	0.980657i	$-0.437292\pi$
$79$	3.47942	0.391465	0.195733	+	0.980657i	$0.437292\pi$
$80$	−34.2911	−3.83386
$81$	−2.32220	−0.258022
$82$	28.6628	3.16528
$83$	−6.02539	−0.661373	−0.330686	−	0.943741i	$-0.607280\pi$
$83$	−6.02539	−0.661373	−0.330686	+	0.943741i	$0.607280\pi$
$84$	−24.7330	−2.69859
$85$	3.13323	0.339847
$86$	−12.1430	−1.30941
$87$	6.85167	0.734576
$88$	−4.37700	−0.466589
$89$	16.2853	1.72623	0.863117	−	0.505004i	$-0.168509\pi$
$89$	16.2853	1.72623	0.863117	+	0.505004i	$0.168509\pi$
$90$	−37.1854	−3.91969
$91$	−1.08805	−0.114059
$92$	−36.3833	−3.79322
$93$	−26.2732	−2.72440
$94$	2.64443	0.272753
$95$	−14.1228	−1.44897
$96$	35.8792	3.66191
$97$	2.05567	0.208722	0.104361	−	0.994539i	$-0.466720\pi$
$97$	2.05567	0.208722	0.104361	+	0.994539i	$0.466720\pi$
$98$	−9.84554	−0.994550
$99$	−2.48187	−0.249437
$100$	24.0522	2.40522
$101$	10.9779	1.09235	0.546173	−	0.837672i	$-0.316084\pi$
$101$	10.9779	1.09235	0.546173	+	0.837672i	$0.316084\pi$
$102$	−7.23626	−0.716496
$103$	−9.96147	−0.981533	−0.490766	−	0.871291i	$-0.663283\pi$
$103$	−9.96147	−0.981533	−0.490766	+	0.871291i	$0.663283\pi$
$104$	4.75733	0.466495
$105$	15.5204	1.51464
$106$	0.149544	0.0145250
$107$	13.6857	1.32304	0.661522	−	0.749926i	$-0.269911\pi$
$107$	13.6857	1.32304	0.661522	+	0.749926i	$0.269911\pi$
$108$	20.3298	1.95623
$109$	−0.302525	−0.0289766	−0.0144883	−	0.999895i	$-0.504612\pi$
$109$	−0.302525	−0.0289766	−0.0144883	+	0.999895i	$0.504612\pi$
$110$	4.58202	0.436878
$111$	−12.4817	−1.18471
$112$	−19.8116	−1.87202
$113$	−16.2192	−1.52577	−0.762885	−	0.646534i	$-0.776218\pi$
$113$	−16.2192	−1.52577	−0.762885	+	0.646534i	$0.776218\pi$
$114$	32.6170	3.05486
$115$	22.8312	2.12902
$116$	12.5020	1.16078
$117$	2.69753	0.249387
$118$	31.6134	2.91025
$119$	1.81022	0.165942
$120$	−67.8607	−6.19481
$121$	−10.6942	−0.972198
$122$	22.1153	2.00223
$123$	29.6598	2.67433
$124$	−47.9398	−4.30512
$125$	0.572939	0.0512452
$126$	−21.4838	−1.91393
$127$	8.81457	0.782166	0.391083	−	0.920355i	$-0.372100\pi$
$127$	8.81457	0.782166	0.391083	+	0.920355i	$0.372100\pi$
$128$	7.58447	0.670379
$129$	−12.5653	−1.10632
$130$	−4.98017	−0.436790
$131$	−5.13376	−0.448539	−0.224269	−	0.974527i	$-0.572000\pi$
$131$	−5.13376	−0.448539	−0.224269	+	0.974527i	$0.572000\pi$
$132$	−7.55575	−0.657643
$133$	−8.15943	−0.707513
$134$	−41.7224	−3.60426
$135$	−12.7573	−1.09798
$136$	−7.91488	−0.678696
$137$	18.2819	1.56193	0.780963	−	0.624578i	$-0.214729\pi$
$137$	18.2819	1.56193	0.780963	+	0.624578i	$0.214729\pi$
$138$	−52.7292	−4.48861
$139$	12.3582	1.04821	0.524105	−	0.851654i	$-0.324400\pi$
$139$	12.3582	1.04821	0.524105	+	0.851654i	$0.324400\pi$
$140$	28.3196	2.39344
$141$	2.73641	0.230447
$142$	12.8217	1.07597
$143$	−0.332392	−0.0277960
$144$	49.1175	4.09312
$145$	−7.84526	−0.651514
$146$	9.02414	0.746843
$147$	−10.1880	−0.840290
$148$	−22.7749	−1.87208
$149$	18.1494	1.48686	0.743430	−	0.668814i	$-0.233198\pi$
$149$	18.1494	1.48686	0.743430	+	0.668814i	$0.233198\pi$
$150$	34.8581	2.84615
$151$	13.5427	1.10209	0.551046	−	0.834475i	$-0.314229\pi$
$151$	13.5427	1.10209	0.551046	+	0.834475i	$0.314229\pi$
$152$	35.6758	2.89369
$153$	−4.48794	−0.362829
$154$	2.64725	0.213321
$155$	30.0832	2.41634
$156$	8.21230	0.657510
$157$	−5.66275	−0.451937	−0.225968	−	0.974135i	$-0.572555\pi$
$157$	−5.66275	−0.451937	−0.225968	+	0.974135i	$0.572555\pi$
$158$	9.20109	0.732000
$159$	0.154745	0.0122721
$160$	−41.0822	−3.24784
$161$	13.1907	1.03957
$162$	−6.14090	−0.482474
$163$	22.7374	1.78093	0.890467	−	0.455049i	$-0.150378\pi$
$163$	22.7374	1.78093	0.890467	+	0.455049i	$0.150378\pi$
$164$	54.1191	4.22599
$165$	4.74139	0.369116
$166$	−15.9338	−1.23670
$167$	2.77813	0.214978	0.107489	−	0.994206i	$-0.465719\pi$
$167$	2.77813	0.214978	0.107489	+	0.994206i	$0.465719\pi$
$168$	−39.2063	−3.02483
$169$	−12.6387	−0.972210
$170$	8.28563	0.635479
$171$	20.2291	1.54696
$172$	−22.9275	−1.74821
$173$	17.9802	1.36701	0.683506	−	0.729945i	$-0.260454\pi$
$173$	17.9802	1.36701	0.683506	+	0.729945i	$0.260454\pi$
$174$	18.1188	1.37358
$175$	−8.72007	−0.659175
$176$	−6.05230	−0.456209
$177$	32.7130	2.45886
$178$	43.0653	3.22788
$179$	−4.10372	−0.306726	−0.153363	−	0.988170i	$-0.549010\pi$
$179$	−4.10372	−0.306726	−0.153363	+	0.988170i	$0.549010\pi$
$180$	−70.2109	−5.23321
$181$	10.0366	0.746014	0.373007	−	0.927828i	$-0.378327\pi$
$181$	10.0366	0.746014	0.373007	+	0.927828i	$0.378327\pi$
$182$	−2.87728	−0.213278
$183$	22.8845	1.69167
$184$	−57.6742	−4.25180
$185$	14.2917	1.05075
$186$	−69.4777	−5.09435
$187$	0.553008	0.0404400
$188$	4.99303	0.364154
$189$	−7.37052	−0.536126
$190$	−37.3469	−2.70943
$191$	−14.1847	−1.02637	−0.513183	−	0.858279i	$-0.671534\pi$
$191$	−14.1847	−1.02637	−0.513183	+	0.858279i	$0.671534\pi$
$192$	34.9839	2.52475
$193$	−11.4410	−0.823542	−0.411771	−	0.911287i	$-0.635090\pi$
$193$	−11.4410	−0.823542	−0.411771	+	0.911287i	$0.635090\pi$
$194$	5.43609	0.390288
$195$	−5.15338	−0.369042
$196$	−18.5897	−1.32783
$197$	−21.2895	−1.51681	−0.758406	−	0.651782i	$-0.774022\pi$
$197$	−21.2895	−1.51681	−0.758406	+	0.651782i	$0.774022\pi$
$198$	−6.56314	−0.466422
$199$	2.39273	0.169616	0.0848079	−	0.996397i	$-0.472972\pi$
$199$	2.39273	0.169616	0.0848079	+	0.996397i	$0.472972\pi$
$200$	38.1271	2.69599
$201$	−43.1735	−3.04522
$202$	29.0305	2.04258
$203$	−4.53258	−0.318125
$204$	−13.6630	−0.956601
$205$	−33.9609	−2.37193
$206$	−26.3425	−1.83537
$207$	−32.7028	−2.27300
$208$	6.57821	0.456117
$209$	−2.49265	−0.172420
$210$	41.0428	2.83222
$211$	9.04792	0.622885	0.311442	−	0.950265i	$-0.399188\pi$
$211$	9.04792	0.622885	0.311442	+	0.950265i	$0.399188\pi$
$212$	0.282358	0.0193925
$213$	13.2676	0.909082
$214$	36.1909	2.47396
$215$	14.3875	0.981219
$216$	32.2264	2.19273
$217$	17.3805	1.17986
$218$	−0.800006	−0.0541833
$219$	9.33801	0.631004
$220$	8.65145	0.583280
$221$	−0.601061	−0.0404318
$222$	−33.0070	−2.21528
$223$	−21.2470	−1.42281	−0.711403	−	0.702785i	$-0.751940\pi$
$223$	−21.2470	−1.42281	−0.711403	+	0.702785i	$0.751940\pi$
$224$	−23.7352	−1.58587
$225$	21.6191	1.44127
$226$	−42.8905	−2.85303
$227$	−6.39796	−0.424648	−0.212324	−	0.977199i	$-0.568103\pi$
$227$	−6.39796	−0.424648	−0.212324	+	0.977199i	$0.568103\pi$
$228$	61.5851	4.07857
$229$	−21.7587	−1.43786	−0.718929	−	0.695083i	$-0.755368\pi$
$229$	−21.7587	−1.43786	−0.718929	+	0.695083i	$0.755368\pi$
$230$	60.3757	3.98106
$231$	2.73932	0.180234
$232$	19.8180	1.30111
$233$	−23.4628	−1.53710	−0.768548	−	0.639792i	$-0.779020\pi$
$233$	−23.4628	−1.53710	−0.768548	+	0.639792i	$0.779020\pi$
$234$	7.13344	0.466327
$235$	−3.13323	−0.204390
$236$	59.6902	3.88550
$237$	9.52112	0.618463
$238$	4.78700	0.310295
$239$	22.3236	1.44399	0.721996	−	0.691897i	$-0.243225\pi$
$239$	22.3236	1.44399	0.721996	+	0.691897i	$0.243225\pi$
$240$	−93.8345	−6.05699
$241$	13.5938	0.875655	0.437828	−	0.899059i	$-0.355748\pi$
$241$	13.5938	0.875655	0.437828	+	0.899059i	$0.355748\pi$
$242$	−28.2801	−1.81791
$243$	−18.5694	−1.19122
$244$	41.7566	2.67319
$245$	11.6654	0.745275
$246$	78.4333	5.00072
$247$	2.70925	0.172385
$248$	−75.9934	−4.82559
$249$	−16.4879	−1.04488
$250$	1.51510	0.0958232
$251$	−3.09155	−0.195137	−0.0975684	−	0.995229i	$-0.531106\pi$
$251$	−3.09155	−0.195137	−0.0975684	+	0.995229i	$0.531106\pi$
$252$	−40.5641	−2.55530
$253$	4.02966	0.253343
$254$	23.3095	1.46257
$255$	8.57381	0.536913
$256$	−5.51256	−0.344535
$257$	−1.48432	−0.0925894	−0.0462947	−	0.998928i	$-0.514741\pi$
$257$	−1.48432	−0.0925894	−0.0462947	+	0.998928i	$0.514741\pi$
$258$	−33.2282	−2.06870
$259$	8.25700	0.513065
$260$	−9.40320	−0.583162
$261$	11.2373	0.695572
$262$	−13.5759	−0.838722
$263$	−31.1594	−1.92137	−0.960685	−	0.277641i	$-0.910447\pi$
$263$	−31.1594	−1.92137	−0.960685	+	0.277641i	$0.910447\pi$
$264$	−11.9773	−0.737149
$265$	−0.177186	−0.0108844
$266$	−21.5771	−1.32298
$267$	44.5632	2.72722
$268$	−78.7772	−4.81208
$269$	−6.20598	−0.378386	−0.189193	−	0.981940i	$-0.560587\pi$
$269$	−6.20598	−0.378386	−0.189193	+	0.981940i	$0.560587\pi$
$270$	−33.7359	−2.05310
$271$	−13.8384	−0.840624	−0.420312	−	0.907380i	$-0.638079\pi$
$271$	−13.8384	−0.840624	−0.420312	+	0.907380i	$0.638079\pi$
$272$	−10.9443	−0.663597
$273$	−2.97735	−0.180198
$274$	48.3452	2.92064
$275$	−2.66392	−0.160640
$276$	−99.5595	−5.99278
$277$	−22.3386	−1.34220	−0.671098	−	0.741369i	$-0.734177\pi$
$277$	−22.3386	−1.34220	−0.671098	+	0.741369i	$0.734177\pi$
$278$	32.6805	1.96005
$279$	−43.0902	−2.57974
$280$	44.8918	2.68280
$281$	−1.61186	−0.0961555	−0.0480777	−	0.998844i	$-0.515310\pi$
$281$	−1.61186	−0.0961555	−0.0480777	+	0.998844i	$0.515310\pi$
$282$	7.23626	0.430913
$283$	1.90278	0.113109	0.0565544	−	0.998400i	$-0.481989\pi$
$283$	1.90278	0.113109	0.0565544	+	0.998400i	$0.481989\pi$
$284$	24.2090	1.43654
$285$	−38.6459	−2.28919
$286$	−0.878988	−0.0519757
$287$	−19.6208	−1.15818
$288$	58.8449	3.46747
$289$	1.00000	0.0588235
$290$	−20.7463	−1.21826
$291$	5.62516	0.329753
$292$	17.0387	0.997117
$293$	−15.8029	−0.923218	−0.461609	−	0.887083i	$-0.652728\pi$
$293$	−15.8029	−0.923218	−0.461609	+	0.887083i	$0.652728\pi$
$294$	−26.9414	−1.57126
$295$	−37.4568	−2.18082
$296$	−36.1024	−2.09841
$297$	−2.25164	−0.130653
$298$	47.9950	2.78028
$299$	−4.37982	−0.253291
$300$	65.8166	3.79992
$301$	8.31233	0.479115
$302$	35.8129	2.06080
$303$	30.0402	1.72576
$304$	49.3308	2.82932
$305$	−26.2031	−1.50039
$306$	−11.8681	−0.678453
$307$	4.93239	0.281507	0.140753	−	0.990045i	$-0.455048\pi$
$307$	4.93239	0.281507	0.140753	+	0.990045i	$0.455048\pi$
$308$	4.99835	0.284807
$309$	−27.2587	−1.55069
$310$	79.5530	4.51831
$311$	31.9393	1.81111	0.905554	−	0.424230i	$-0.139455\pi$
$311$	31.9393	1.81111	0.905554	+	0.424230i	$0.139455\pi$
$312$	13.0180	0.737000
$313$	6.11717	0.345763	0.172882	−	0.984943i	$-0.444692\pi$
$313$	6.11717	0.345763	0.172882	+	0.984943i	$0.444692\pi$
$314$	−14.9748	−0.845076
$315$	25.4548	1.43422
$316$	17.3729	0.977299
$317$	4.30598	0.241848	0.120924	−	0.992662i	$-0.461414\pi$
$317$	4.30598	0.241848	0.120924	+	0.992662i	$0.461414\pi$
$318$	0.409214	0.0229476
$319$	−1.38467	−0.0775267
$320$	−40.0571	−2.23926
$321$	37.4496	2.09023
$322$	34.8819	1.94389
$323$	−4.50744	−0.250800
$324$	−11.5948	−0.644156
$325$	2.89540	0.160608
$326$	60.1276	3.33016
$327$	−0.827831	−0.0457792
$328$	85.7888	4.73690
$329$	−1.81022	−0.0998004
$330$	12.5383	0.690210
$331$	−3.63561	−0.199831	−0.0999157	−	0.994996i	$-0.531857\pi$
$331$	−3.63561	−0.199831	−0.0999157	+	0.994996i	$0.531857\pi$
$332$	−30.0850	−1.65113
$333$	−20.4710	−1.12180
$334$	7.34659	0.401987
$335$	49.4343	2.70089
$336$	−54.2126	−2.95754
$337$	−28.5515	−1.55530	−0.777648	−	0.628700i	$-0.783588\pi$
$337$	−28.5515	−1.55530	−0.777648	+	0.628700i	$0.783588\pi$
$338$	−33.4223	−1.81793
$339$	−44.3823	−2.41051
$340$	15.6443	0.848433
$341$	5.30961	0.287532
$342$	53.4946	2.89266
$343$	19.4112	1.04810
$344$	−36.3444	−1.95956
$345$	62.4757	3.36358
$346$	47.5476	2.55617
$347$	−11.4415	−0.614211	−0.307106	−	0.951675i	$-0.599361\pi$
$347$	−11.4415	−0.614211	−0.307106	+	0.951675i	$0.599361\pi$
$348$	34.2106	1.83388
$349$	1.80988	0.0968809	0.0484405	−	0.998826i	$-0.484575\pi$
$349$	1.80988	0.0968809	0.0484405	+	0.998826i	$0.484575\pi$
$350$	−23.0596	−1.23259
$351$	2.44730	0.130627
$352$	−7.25092	−0.386475
$353$	−6.62644	−0.352690	−0.176345	−	0.984328i	$-0.556427\pi$
$353$	−6.62644	−0.352690	−0.176345	+	0.984328i	$0.556427\pi$
$354$	86.5073	4.59781
$355$	−15.1916	−0.806287
$356$	81.3129	4.30957
$357$	4.95349	0.262167
$358$	−10.8520	−0.573547
$359$	0.741280	0.0391233	0.0195616	−	0.999809i	$-0.493773\pi$
$359$	0.741280	0.0391233	0.0195616	+	0.999809i	$0.493773\pi$
$360$	−111.297	−5.86588
$361$	1.31698	0.0693146
$362$	26.5411	1.39497
$363$	−29.2637	−1.53594
$364$	−5.43267	−0.284750
$365$	−10.6922	−0.559653
$366$	60.5166	3.16326
$367$	−7.02173	−0.366531	−0.183266	−	0.983063i	$-0.558667\pi$
$367$	−7.02173	−0.366531	−0.183266	+	0.983063i	$0.558667\pi$
$368$	−79.7491	−4.15721
$369$	48.6445	2.53233
$370$	37.7935	1.96479
$371$	−0.102369	−0.00531471
$372$	−131.183	−6.80152
$373$	14.0870	0.729398	0.364699	−	0.931125i	$-0.381172\pi$
$373$	14.0870	0.729398	0.364699	+	0.931125i	$0.381172\pi$
$374$	1.46239	0.0756186
$375$	1.56780	0.0809606
$376$	7.91488	0.408179
$377$	1.50499	0.0775110
$378$	−19.4909	−1.00250
$379$	−8.26406	−0.424496	−0.212248	−	0.977216i	$-0.568079\pi$
$379$	−8.26406	−0.424496	−0.212248	+	0.977216i	$0.568079\pi$
$380$	−70.5158	−3.61739
$381$	24.1203	1.23572
$382$	−37.5104	−1.91920
$383$	−5.36991	−0.274389	−0.137195	−	0.990544i	$-0.543809\pi$
$383$	−5.36991	−0.274389	−0.137195	+	0.990544i	$0.543809\pi$
$384$	20.7542	1.05911
$385$	−3.13657	−0.159854
$386$	−30.2550	−1.53994
$387$	−20.6082	−1.04757
$388$	10.2640	0.521078
$389$	5.39200	0.273385	0.136693	−	0.990614i	$-0.456353\pi$
$389$	5.39200	0.273385	0.136693	+	0.990614i	$0.456353\pi$
$390$	−13.6278	−0.690070
$391$	7.28680	0.368510
$392$	−29.4680	−1.48836
$393$	−14.0481	−0.708632
$394$	−56.2986	−2.83628
$395$	−10.9018	−0.548530
$396$	−12.3921	−0.622724
$397$	−14.7214	−0.738848	−0.369424	−	0.929261i	$-0.620445\pi$
$397$	−14.7214	−0.738848	−0.369424	+	0.929261i	$0.620445\pi$
$398$	6.32741	0.317164
$399$	−22.3276	−1.11778
$400$	52.7203	2.63602
$401$	16.3151	0.814738	0.407369	−	0.913264i	$-0.366446\pi$
$401$	16.3151	0.814738	0.407369	+	0.913264i	$0.366446\pi$
$402$	−114.170	−5.69426
$403$	−5.77099	−0.287473
$404$	54.8133	2.72706
$405$	7.27598	0.361546
$406$	−11.9861	−0.594861
$407$	2.52245	0.125033
$408$	−21.6584	−1.07225
$409$	−28.2570	−1.39722	−0.698609	−	0.715504i	$-0.746197\pi$
$409$	−28.2570	−1.39722	−0.698609	+	0.715504i	$0.746197\pi$
$410$	−89.8073	−4.43527
$411$	50.0267	2.46764
$412$	−49.7380	−2.45041
$413$	−21.6406	−1.06486
$414$	−86.4803	−4.25028
$415$	18.8790	0.926731
$416$	7.88098	0.386397
$417$	33.8172	1.65603
$418$	−6.59165	−0.322408
$419$	−14.9348	−0.729611	−0.364805	−	0.931084i	$-0.618864\pi$
$419$	−14.9348	−0.729611	−0.364805	+	0.931084i	$0.618864\pi$
$420$	77.4941	3.78133
$421$	18.1123	0.882738	0.441369	−	0.897326i	$-0.354493\pi$
$421$	18.1123	0.882738	0.441369	+	0.897326i	$0.354493\pi$
$422$	23.9266	1.16473
$423$	4.48794	0.218211
$424$	0.447590	0.0217369
$425$	−4.81714	−0.233666
$426$	35.0853	1.69989
$427$	−15.1388	−0.732617
$428$	68.3330	3.30300
$429$	−0.909561	−0.0439140
$430$	38.0468	1.83478
$431$	19.4432	0.936547	0.468273	−	0.883584i	$-0.344876\pi$
$431$	19.4432	0.936547	0.468273	+	0.883584i	$0.344876\pi$
$432$	44.5612	2.14395
$433$	3.50895	0.168629	0.0843147	−	0.996439i	$-0.473130\pi$
$433$	3.50895	0.168629	0.0843147	+	0.996439i	$0.473130\pi$
$434$	45.9615	2.20622
$435$	−21.4679	−1.02931
$436$	−1.51052	−0.0723406
$437$	−32.8448	−1.57118
$438$	24.6937	1.17991
$439$	−25.6234	−1.22294	−0.611470	−	0.791267i	$-0.709422\pi$
$439$	−25.6234	−1.22294	−0.611470	+	0.791267i	$0.709422\pi$
$440$	13.7141	0.653796
$441$	−16.7091	−0.795673
$442$	−1.58947	−0.0756033
$443$	−11.9297	−0.566795	−0.283398	−	0.959003i	$-0.591462\pi$
$443$	−11.9297	−0.566795	−0.283398	+	0.959003i	$0.591462\pi$
$444$	−62.3215	−2.95765
$445$	−51.0255	−2.41884
$446$	−56.1863	−2.66050
$447$	49.6643	2.34904
$448$	−23.1429	−1.09340
$449$	−28.2323	−1.33236	−0.666182	−	0.745789i	$-0.732073\pi$
$449$	−28.2323	−1.33236	−0.666182	+	0.745789i	$0.732073\pi$
$450$	57.1702	2.69503
$451$	−5.99402	−0.282247
$452$	−80.9828	−3.80911
$453$	37.0585	1.74116
$454$	−16.9190	−0.794048
$455$	3.40912	0.159822
$456$	97.6237	4.57165
$457$	36.4110	1.70323	0.851617	−	0.524165i	$-0.175623\pi$
$457$	36.4110	1.70323	0.851617	+	0.524165i	$0.175623\pi$
$458$	−57.5396	−2.68865
$459$	−4.07162	−0.190047
$460$	113.997	5.31515
$461$	−4.53770	−0.211342	−0.105671	−	0.994401i	$-0.533699\pi$
$461$	−4.53770	−0.211342	−0.105671	+	0.994401i	$0.533699\pi$
$462$	7.24396	0.337020
$463$	39.3894	1.83058	0.915290	−	0.402795i	$-0.131961\pi$
$463$	39.3894	1.83058	0.915290	+	0.402795i	$0.131961\pi$
$464$	27.4034	1.27217
$465$	82.3200	3.81750
$466$	−62.0457	−2.87421
$467$	−5.87990	−0.272089	−0.136045	−	0.990703i	$-0.543439\pi$
$467$	−5.87990	−0.272089	−0.136045	+	0.990703i	$0.543439\pi$
$468$	13.4689	0.622598
$469$	28.5605	1.31880
$470$	−8.28563	−0.382187
$471$	−15.4956	−0.714000
$472$	94.6200	4.35524
$473$	2.53936	0.116760
$474$	25.1780	1.15646
$475$	21.7130	0.996259
$476$	9.03847	0.414278
$477$	0.253795	0.0116205
$478$	59.0332	2.70012
$479$	−16.0596	−0.733780	−0.366890	−	0.930264i	$-0.619577\pi$
$479$	−16.0596	−0.733780	−0.366890	+	0.930264i	$0.619577\pi$
$480$	−112.418	−5.13115
$481$	−2.74164	−0.125008
$482$	35.9480	1.63739
$483$	36.0951	1.64239
$484$	−53.3964	−2.42711
$485$	−6.44089	−0.292466
$486$	−49.1054	−2.22747
$487$	−31.7392	−1.43824	−0.719121	−	0.694885i	$-0.755455\pi$
$487$	−31.7392	−1.43824	−0.719121	+	0.694885i	$0.755455\pi$
$488$	66.1920	2.99637
$489$	62.2189	2.81364
$490$	30.8484	1.39359
$491$	−17.6360	−0.795903	−0.397952	−	0.917406i	$-0.630279\pi$
$491$	−17.6360	−0.795903	−0.397952	+	0.917406i	$0.630279\pi$
$492$	148.092	6.67651
$493$	−2.50389	−0.112769
$494$	7.16442	0.322343
$495$	7.77627	0.349517
$496$	−105.080	−4.71823
$497$	−8.77691	−0.393698
$498$	−43.6013	−1.95382
$499$	−19.2620	−0.862284	−0.431142	−	0.902284i	$-0.641889\pi$
$499$	−19.2620	−0.862284	−0.431142	+	0.902284i	$0.641889\pi$
$500$	2.86070	0.127934
$501$	7.60211	0.339637
$502$	−8.17540	−0.364886
$503$	−1.16135	−0.0517820	−0.0258910	−	0.999665i	$-0.508242\pi$
$503$	−1.16135	−0.0517820	−0.0258910	+	0.999665i	$0.508242\pi$
$504$	−64.3017	−2.86422
$505$	−34.3965	−1.53062
$506$	10.6562	0.473725
$507$	−34.5847	−1.53596
$508$	44.0114	1.95269
$509$	36.4195	1.61427	0.807134	−	0.590368i	$-0.201018\pi$
$509$	36.4195	1.61427	0.807134	+	0.590368i	$0.201018\pi$
$510$	22.6729	1.00397
$511$	−6.17737	−0.273271
$512$	−29.7465	−1.31462
$513$	18.3526	0.810286
$514$	−3.92519	−0.173133
$515$	31.2116	1.37535
$516$	−62.7391	−2.76194
$517$	−0.553008	−0.0243213
$518$	21.8351	0.959379
$519$	49.2013	2.15970
$520$	−14.9058	−0.653663
$521$	−17.6202	−0.771955	−0.385977	−	0.922508i	$-0.626136\pi$
$521$	−17.6202	−0.771955	−0.385977	+	0.922508i	$0.626136\pi$
$522$	29.7163	1.30065
$523$	24.0011	1.04950	0.524748	−	0.851258i	$-0.324160\pi$
$523$	24.0011	1.04950	0.524748	+	0.851258i	$0.324160\pi$
$524$	−25.6330	−1.11978
$525$	−23.8617	−1.04141
$526$	−82.3989	−3.59276
$527$	9.60133	0.418240
$528$	−16.5616	−0.720750
$529$	30.0975	1.30859
$530$	−0.468556	−0.0203528
$531$	53.6520	2.32830
$532$	−40.7403	−1.76632
$533$	6.51486	0.282190
$534$	117.844	5.09962
$535$	−42.8804	−1.85388
$536$	−124.876	−5.39384
$537$	−11.2295	−0.484587
$538$	−16.4113	−0.707542
$539$	2.05891	0.0886837
$540$	−63.6978	−2.74112
$541$	29.8116	1.28170	0.640850	−	0.767666i	$-0.278582\pi$
$541$	29.8116	1.28170	0.640850	+	0.767666i	$0.278582\pi$
$542$	−36.5948	−1.57188
$543$	27.4642	1.17860
$544$	−13.1118	−0.562163
$545$	0.947880	0.0406027
$546$	−7.87342	−0.336951
$547$	−2.89547	−0.123801	−0.0619006	−	0.998082i	$-0.519716\pi$
$547$	−2.89547	−0.123801	−0.0619006	+	0.998082i	$0.519716\pi$
$548$	91.2820	3.89937
$549$	37.5325	1.60185
$550$	−7.04456	−0.300381
$551$	11.2861	0.480805
$552$	−157.820	−6.71728
$553$	−6.29850	−0.267839
$554$	−59.0729	−2.50977
$555$	39.1080	1.66004
$556$	61.7050	2.61687
$557$	28.2886	1.19863	0.599314	−	0.800514i	$-0.295440\pi$
$557$	28.2886	1.19863	0.599314	+	0.800514i	$0.295440\pi$
$558$	−113.949	−4.82386
$559$	−2.76001	−0.116736
$560$	62.0743	2.62312
$561$	1.51326	0.0638898
$562$	−4.26246	−0.179801
$563$	12.9456	0.545592	0.272796	−	0.962072i	$-0.412052\pi$
$563$	12.9456	0.545592	0.272796	+	0.962072i	$0.412052\pi$
$564$	13.6630	0.575316
$565$	50.8184	2.13795
$566$	5.03179	0.211502
$567$	4.20368	0.176538
$568$	38.3757	1.61021
$569$	32.7516	1.37302	0.686509	−	0.727121i	$-0.259142\pi$
$569$	32.7516	1.37302	0.686509	+	0.727121i	$0.259142\pi$
$570$	−102.197	−4.28054
$571$	−3.80076	−0.159057	−0.0795284	−	0.996833i	$-0.525341\pi$
$571$	−3.80076	−0.159057	−0.0795284	+	0.996833i	$0.525341\pi$
$572$	−1.65964	−0.0693932
$573$	−38.8151	−1.62152
$574$	−51.8859	−2.16568
$575$	−35.1016	−1.46384
$576$	57.3765	2.39069
$577$	35.8041	1.49054	0.745272	−	0.666761i	$-0.232320\pi$
$577$	35.8041	1.49054	0.745272	+	0.666761i	$0.232320\pi$
$578$	2.64443	0.109994
$579$	−31.3073	−1.30109
$580$	−39.1717	−1.62652
$581$	10.9073	0.452510
$582$	14.8754	0.616604
$583$	−0.0312729	−0.00129519
$584$	27.0096	1.11766
$585$	−8.45198	−0.349447
$586$	−41.7899	−1.72632
$587$	−11.7990	−0.486997	−0.243498	−	0.969901i	$-0.578295\pi$
$587$	−11.7990	−0.486997	−0.243498	+	0.969901i	$0.578295\pi$
$588$	−50.8689	−2.09780
$589$	−43.2774	−1.78321
$590$	−99.0522	−4.07791
$591$	−58.2568	−2.39636
$592$	−49.9207	−2.05173
$593$	25.3555	1.04123	0.520613	−	0.853793i	$-0.325704\pi$
$593$	25.3555	1.04123	0.520613	+	0.853793i	$0.325704\pi$
$594$	−5.95432	−0.244309
$595$	−5.67183	−0.232522
$596$	90.6207	3.71197
$597$	6.54748	0.267971
$598$	−11.5821	−0.473629
$599$	6.12955	0.250446	0.125223	−	0.992129i	$-0.460035\pi$
$599$	6.12955	0.250446	0.125223	+	0.992129i	$0.460035\pi$
$600$	104.331	4.25931
$601$	30.6272	1.24931	0.624654	−	0.780902i	$-0.285240\pi$
$601$	30.6272	1.24931	0.624654	+	0.780902i	$0.285240\pi$
$602$	21.9814	0.895896
$603$	−70.8082	−2.88353
$604$	67.6193	2.75139
$605$	33.5074	1.36227
$606$	79.4393	3.22700
$607$	−3.16682	−0.128537	−0.0642686	−	0.997933i	$-0.520471\pi$
$607$	−3.16682	−0.128537	−0.0642686	+	0.997933i	$0.520471\pi$
$608$	59.1005	2.39684
$609$	−12.4030	−0.502595
$610$	−69.2925	−2.80557
$611$	0.601061	0.0243163
$612$	−22.4085	−0.905808
$613$	−13.1859	−0.532574	−0.266287	−	0.963894i	$-0.585797\pi$
$613$	−13.1859	−0.532574	−0.266287	+	0.963894i	$0.585797\pi$
$614$	13.0434	0.526388
$615$	−92.9309	−3.74734
$616$	7.92331	0.319239
$617$	17.0538	0.686560	0.343280	−	0.939233i	$-0.388462\pi$
$617$	17.0538	0.686560	0.343280	+	0.939233i	$0.388462\pi$
$618$	−72.0838	−2.89963
$619$	−26.9188	−1.08196	−0.540979	−	0.841036i	$-0.681946\pi$
$619$	−26.9188	−1.08196	−0.540979	+	0.841036i	$0.681946\pi$
$620$	150.206	6.03243
$621$	−29.6691	−1.19058
$622$	84.4613	3.38659
$623$	−29.4798	−1.18108
$624$	18.0007	0.720604
$625$	−25.8809	−1.03523
$626$	16.1765	0.646542
$627$	−6.82091	−0.272401
$628$	−28.2743	−1.12827
$629$	4.56133	0.181872
$630$	67.3136	2.68184
$631$	12.3723	0.492534	0.246267	−	0.969202i	$-0.420796\pi$
$631$	12.3723	0.492534	0.246267	+	0.969202i	$0.420796\pi$
$632$	27.5392	1.09545
$633$	24.7588	0.984075
$634$	11.3869	0.452231
$635$	−27.6181	−1.09599
$636$	0.772649	0.0306375
$637$	−2.23782	−0.0886657
$638$	−3.66167	−0.144967
$639$	21.7600	0.860812
$640$	−23.7639	−0.939351
$641$	−6.86240	−0.271049	−0.135524	−	0.990774i	$-0.543272\pi$
$641$	−6.86240	−0.271049	−0.135524	+	0.990774i	$0.543272\pi$
$642$	99.0330	3.90852
$643$	22.8976	0.902995	0.451498	−	0.892272i	$-0.350890\pi$
$643$	22.8976	0.902995	0.451498	+	0.892272i	$0.350890\pi$
$644$	65.8616	2.59531
$645$	39.3701	1.55020
$646$	−11.9196	−0.468971
$647$	−49.5515	−1.94807	−0.974035	−	0.226397i	$-0.927305\pi$
$647$	−49.5515	−1.94807	−0.974035	+	0.226397i	$0.927305\pi$
$648$	−18.3799	−0.722031
$649$	−6.61105	−0.259506
$650$	7.65669	0.300320
$651$	47.5601	1.86403
$652$	113.529	4.44613
$653$	44.0053	1.72206	0.861029	−	0.508555i	$-0.169820\pi$
$653$	44.0053	1.72206	0.861029	+	0.508555i	$0.169820\pi$
$654$	−2.18915	−0.0856024
$655$	16.0853	0.628503
$656$	118.625	4.63152
$657$	15.3151	0.597500
$658$	−4.78700	−0.186617
$659$	−39.6406	−1.54418	−0.772089	−	0.635515i	$-0.780788\pi$
$659$	−39.6406	−1.54418	−0.772089	+	0.635515i	$0.780788\pi$
$660$	23.6739	0.921506
$661$	−8.97888	−0.349238	−0.174619	−	0.984636i	$-0.555869\pi$
$661$	−8.97888	−0.349238	−0.174619	+	0.984636i	$0.555869\pi$
$662$	−9.61415	−0.373664
$663$	−1.64475	−0.0638768
$664$	−47.6903	−1.85074
$665$	25.5654	0.991383
$666$	−54.1342	−2.09766
$667$	−18.2453	−0.706463
$668$	13.8713	0.536697
$669$	−58.1405	−2.24784
$670$	130.726	5.05038
$671$	−4.62479	−0.178538
$672$	−64.9491	−2.50547
$673$	11.7692	0.453669	0.226834	−	0.973933i	$-0.427162\pi$
$673$	11.7692	0.453669	0.226834	+	0.973933i	$0.427162\pi$
$674$	−75.5024	−2.90825
$675$	19.6136	0.754927
$676$	−63.1056	−2.42714
$677$	22.1849	0.852634	0.426317	−	0.904574i	$-0.359811\pi$
$677$	22.1849	0.852634	0.426317	+	0.904574i	$0.359811\pi$
$678$	−117.366	−4.50742
$679$	−3.72121	−0.142807
$680$	24.7992	0.951005
$681$	−17.5075	−0.670887
$682$	14.0409	0.537655
$683$	−1.17426	−0.0449318	−0.0224659	−	0.999748i	$-0.507152\pi$
$683$	−1.17426	−0.0449318	−0.0224659	+	0.999748i	$0.507152\pi$
$684$	101.005	3.86201
$685$	−57.2813	−2.18861
$686$	51.3315	1.95985
$687$	−59.5409	−2.27163
$688$	−50.2553	−1.91596
$689$	0.0339903	0.00129493
$690$	165.213	6.28954
$691$	−37.1299	−1.41249	−0.706244	−	0.707969i	$-0.749612\pi$
$691$	−37.1299	−1.41249	−0.706244	+	0.707969i	$0.749612\pi$
$692$	89.7759	3.41277
$693$	4.49272	0.170664
$694$	−30.2563	−1.14851
$695$	−38.7212	−1.46878
$696$	54.2301	2.05559
$697$	−10.8389	−0.410554
$698$	4.78612	0.181157
$699$	−64.2037	−2.42841
$700$	−43.5396	−1.64564
$701$	27.3371	1.03251	0.516255	−	0.856435i	$-0.327326\pi$
$701$	27.3371	1.03251	0.516255	+	0.856435i	$0.327326\pi$
$702$	6.47171	0.244259
$703$	−20.5599	−0.775432
$704$	−7.06999	−0.266460
$705$	−8.57381	−0.322908
$706$	−17.5232	−0.659494
$707$	−19.8725	−0.747381
$708$	163.337	6.13858
$709$	−13.0898	−0.491597	−0.245799	−	0.969321i	$-0.579050\pi$
$709$	−13.0898	−0.491597	−0.245799	+	0.969321i	$0.579050\pi$
$710$	−40.1732	−1.50767
$711$	15.6154	0.585624
$712$	128.896	4.83058
$713$	69.9630	2.62014
$714$	13.0992	0.490225
$715$	1.04146	0.0389484
$716$	−20.4900	−0.765748
$717$	61.0865	2.28132
$718$	1.96027	0.0731565
$719$	2.48890	0.0928204	0.0464102	−	0.998922i	$-0.485222\pi$
$719$	2.48890	0.0928204	0.0464102	+	0.998922i	$0.485222\pi$
$720$	−153.897	−5.73538
$721$	18.0324	0.671562
$722$	3.48266	0.129611
$723$	37.1983	1.38342
$724$	50.1131	1.86244
$725$	12.0616	0.447956
$726$	−77.3859	−2.87206
$727$	10.9052	0.404452	0.202226	−	0.979339i	$-0.435182\pi$
$727$	10.9052	0.404452	0.202226	+	0.979339i	$0.435182\pi$
$728$	−8.61180	−0.319174
$729$	−43.8468	−1.62395
$730$	−28.2747	−1.04649
$731$	4.59190	0.169838
$732$	114.263	4.22329
$733$	8.86060	0.327274	0.163637	−	0.986521i	$-0.447677\pi$
$733$	8.86060	0.327274	0.163637	+	0.986521i	$0.447677\pi$
$734$	−18.5685	−0.685376
$735$	31.9213	1.17743
$736$	−95.5430	−3.52176
$737$	8.72505	0.321391
$738$	128.637	4.73520
$739$	−45.8965	−1.68833	−0.844165	−	0.536084i	$-0.819903\pi$
$739$	−45.8965	−1.68833	−0.844165	+	0.536084i	$0.819903\pi$
$740$	71.3590	2.62321
$741$	7.41361	0.272346
$742$	−0.270707	−0.00993797
$743$	−26.0962	−0.957377	−0.478688	−	0.877985i	$-0.658888\pi$
$743$	−26.0962	−0.957377	−0.478688	+	0.877985i	$0.658888\pi$
$744$	−207.949	−7.62379
$745$	−56.8664	−2.08342
$746$	37.2522	1.36390
$747$	−27.0416	−0.989401
$748$	2.76119	0.100959
$749$	−24.7740	−0.905223
$750$	4.14593	0.151388
$751$	29.9043	1.09122	0.545611	−	0.838038i	$-0.316298\pi$
$751$	29.9043	1.09122	0.545611	+	0.838038i	$0.316298\pi$
$752$	10.9443	0.399098
$753$	−8.45975	−0.308290
$754$	3.97985	0.144938
$755$	−42.4325	−1.54428
$756$	−36.8012	−1.33845
$757$	−12.5101	−0.454687	−0.227344	−	0.973815i	$-0.573004\pi$
$757$	−12.5101	−0.454687	−0.227344	+	0.973815i	$0.573004\pi$
$758$	−21.8538	−0.793765
$759$	11.0268	0.400248
$760$	−111.781	−4.05471
$761$	11.5782	0.419708	0.209854	−	0.977733i	$-0.432701\pi$
$761$	11.5782	0.419708	0.209854	+	0.977733i	$0.432701\pi$
$762$	63.7845	2.31067
$763$	0.547635	0.0198257
$764$	−70.8246	−2.56234
$765$	14.0618	0.508404
$766$	−14.2004	−0.513080
$767$	7.18551	0.259454
$768$	−15.0846	−0.544319
$769$	4.10679	0.148095	0.0740473	−	0.997255i	$-0.476408\pi$
$769$	4.10679	0.148095	0.0740473	+	0.997255i	$0.476408\pi$
$770$	−8.29445	−0.298911
$771$	−4.06171	−0.146279
$772$	−57.1253	−2.05599
$773$	−2.29506	−0.0825477	−0.0412738	−	0.999148i	$-0.513142\pi$
$773$	−2.29506	−0.0825477	−0.0412738	+	0.999148i	$0.513142\pi$
$774$	−54.4970	−1.95886
$775$	−46.2510	−1.66138
$776$	16.2704	0.584073
$777$	22.5945	0.810574
$778$	14.2588	0.511202
$779$	48.8558	1.75044
$780$	−25.7310	−0.921319
$781$	−2.68129	−0.0959439
$782$	19.2695	0.689075
$783$	10.1949	0.364336
$784$	−40.7470	−1.45525
$785$	17.7427	0.633265
$786$	−37.1492	−1.32507
$787$	−14.0524	−0.500913	−0.250457	−	0.968128i	$-0.580581\pi$
$787$	−14.0524	−0.500913	−0.250457	+	0.968128i	$0.580581\pi$
$788$	−106.299	−3.78675
$789$	−85.2649	−3.03551
$790$	−28.8292	−1.02570
$791$	29.3602	1.04393
$792$	−19.6437	−0.698009
$793$	5.02666	0.178502
$794$	−38.9299	−1.38157
$795$	−0.484853	−0.0171960
$796$	11.9470	0.423449
$797$	−34.1633	−1.21013	−0.605063	−	0.796178i	$-0.706852\pi$
$797$	−34.1633	−1.21013	−0.605063	+	0.796178i	$0.706852\pi$
$798$	−59.0438	−2.09013
$799$	−1.00000	−0.0353775
$800$	63.1613	2.23309
$801$	73.0873	2.58241
$802$	43.1443	1.52348
$803$	−1.88714	−0.0665958
$804$	−215.567	−7.60246
$805$	−41.3295	−1.45667
$806$	−15.2610	−0.537546
$807$	−16.9821	−0.597799
$808$	86.8892	3.05675
$809$	−3.92390	−0.137957	−0.0689785	−	0.997618i	$-0.521974\pi$
$809$	−3.92390	−0.137957	−0.0689785	+	0.997618i	$0.521974\pi$
$810$	19.2408	0.676055
$811$	9.16119	0.321693	0.160847	−	0.986979i	$-0.448578\pi$
$811$	9.16119	0.321693	0.160847	+	0.986979i	$0.448578\pi$
$812$	−22.6313	−0.794204
$813$	−37.8676	−1.32807
$814$	6.67047	0.233800
$815$	−71.2416	−2.49549
$816$	−29.9482	−1.04840
$817$	−20.6977	−0.724121
$818$	−74.7237	−2.61265
$819$	−4.88311	−0.170630
$820$	−169.568	−5.92156
$821$	−34.7544	−1.21294	−0.606468	−	0.795108i	$-0.707414\pi$
$821$	−34.7544	−1.21294	−0.606468	+	0.795108i	$0.707414\pi$
$822$	132.292	4.61423
$823$	−38.2623	−1.33374	−0.666870	−	0.745174i	$-0.732366\pi$
$823$	−38.2623	−1.33374	−0.666870	+	0.745174i	$0.732366\pi$
$824$	−78.8439	−2.74666
$825$	−7.28958	−0.253790
$826$	−57.2271	−1.99119
$827$	35.6867	1.24095	0.620474	−	0.784227i	$-0.286940\pi$
$827$	35.6867	1.24095	0.620474	+	0.784227i	$0.286940\pi$
$828$	−163.286	−5.67458
$829$	−32.7275	−1.13667	−0.568336	−	0.822797i	$-0.692413\pi$
$829$	−32.7275	−1.13667	−0.568336	+	0.822797i	$0.692413\pi$
$830$	49.9242	1.73289
$831$	−61.1275	−2.12049
$832$	7.68433	0.266406
$833$	3.72312	0.128998
$834$	89.4273	3.09661
$835$	−8.70453	−0.301233
$836$	−12.4459	−0.430450
$837$	−39.0930	−1.35125
$838$	−39.4940	−1.36430
$839$	8.66003	0.298977	0.149489	−	0.988763i	$-0.452237\pi$
$839$	8.66003	0.298977	0.149489	+	0.988763i	$0.452237\pi$
$840$	122.843	4.23847
$841$	−22.7305	−0.783812
$842$	47.8967	1.65063
$843$	−4.41071	−0.151913
$844$	45.1766	1.55504
$845$	39.6001	1.36228
$846$	11.8681	0.408033
$847$	19.3588	0.665176
$848$	0.618907	0.0212533
$849$	5.20680	0.178697
$850$	−12.7386	−0.436931
$851$	33.2375	1.13937
$852$	66.2456	2.26954
$853$	47.6875	1.63279	0.816394	−	0.577495i	$-0.195970\pi$
$853$	47.6875	1.63279	0.816394	+	0.577495i	$0.195970\pi$
$854$	−40.0335	−1.36992
$855$	−63.3825	−2.16764
$856$	108.320	3.70232
$857$	−16.0804	−0.549296	−0.274648	−	0.961545i	$-0.588561\pi$
$857$	−16.0804	−0.549296	−0.274648	+	0.961545i	$0.588561\pi$
$858$	−2.40527	−0.0821147
$859$	−48.2924	−1.64772	−0.823858	−	0.566796i	$-0.808183\pi$
$859$	−48.2924	−1.64772	−0.823858	+	0.566796i	$0.808183\pi$
$860$	71.8373	2.44963
$861$	−53.6906	−1.82977
$862$	51.4163	1.75125
$863$	26.8559	0.914185	0.457092	−	0.889419i	$-0.348891\pi$
$863$	26.8559	0.914185	0.457092	+	0.889419i	$0.348891\pi$
$864$	53.3862	1.81624
$865$	−56.3363	−1.91549
$866$	9.27919	0.315320
$867$	2.73641	0.0929334
$868$	86.7813	2.94555
$869$	−1.92415	−0.0652722
$870$	−56.7704	−1.92470
$871$	−9.48320	−0.321326
$872$	−2.39445	−0.0810862
$873$	9.22574	0.312244
$874$	−86.8559	−2.93795
$875$	−1.03714	−0.0350618
$876$	46.6250	1.57531
$877$	14.0899	0.475783	0.237892	−	0.971292i	$-0.423544\pi$
$877$	14.0899	0.475783	0.237892	+	0.971292i	$0.423544\pi$
$878$	−67.7595	−2.28677
$879$	−43.2434	−1.45856
$880$	18.9633	0.639251
$881$	19.8027	0.667171	0.333585	−	0.942720i	$-0.391741\pi$
$881$	19.8027	0.667171	0.333585	+	0.942720i	$0.391741\pi$
$882$	−44.1862	−1.48783
$883$	27.7650	0.934365	0.467183	−	0.884161i	$-0.345269\pi$
$883$	27.7650	0.934365	0.467183	+	0.884161i	$0.345269\pi$
$884$	−3.00112	−0.100939
$885$	−102.497	−3.44541
$886$	−31.5472	−1.05985
$887$	48.2129	1.61883	0.809416	−	0.587236i	$-0.199784\pi$
$887$	48.2129	1.61883	0.809416	+	0.587236i	$0.199784\pi$
$888$	−98.7910	−3.31521
$889$	−15.9563	−0.535156
$890$	−134.934	−4.52298
$891$	1.28419	0.0430221
$892$	−106.087	−3.55206
$893$	4.50744	0.150836
$894$	131.334	4.39247
$895$	12.8579	0.429792
$896$	−13.7295	−0.458671
$897$	−11.9850	−0.400167
$898$	−74.6585	−2.49138
$899$	−24.0407	−0.801801
$900$	107.945	3.59816
$901$	−0.0565505	−0.00188397
$902$	−15.8508	−0.527773
$903$	22.7460	0.756938
$904$	−128.373	−4.26961
$905$	−31.4470	−1.04533
$906$	97.9987	3.25579
$907$	39.2276	1.30253	0.651266	−	0.758850i	$-0.274238\pi$
$907$	39.2276	1.30253	0.651266	+	0.758850i	$0.274238\pi$
$908$	−31.9453	−1.06014
$909$	49.2684	1.63413
$910$	9.01518	0.298850
$911$	−34.7576	−1.15157	−0.575785	−	0.817601i	$-0.695303\pi$
$911$	−34.7576	−1.15157	−0.575785	+	0.817601i	$0.695303\pi$
$912$	134.989	4.46995
$913$	3.33209	0.110276
$914$	96.2864	3.18487
$915$	−71.7025	−2.37041
$916$	−108.642	−3.58964
$917$	9.29322	0.306889
$918$	−10.7671	−0.355369
$919$	−14.9943	−0.494617	−0.247308	−	0.968937i	$-0.579546\pi$
$919$	−14.9943	−0.494617	−0.247308	+	0.968937i	$0.579546\pi$
$920$	180.707	5.95772
$921$	13.4971	0.444743
$922$	−11.9997	−0.395188
$923$	2.91427	0.0959245
$924$	13.6775	0.449958
$925$	−21.9726	−0.722454
$926$	104.163	3.42300
$927$	−44.7065	−1.46835
$928$	32.8304	1.07771
$929$	13.0823	0.429217	0.214608	−	0.976700i	$-0.431153\pi$
$929$	13.0823	0.429217	0.214608	+	0.976700i	$0.431153\pi$
$930$	217.690	7.13833
$931$	−16.7817	−0.549999
$932$	−117.150	−3.83739
$933$	87.3989	2.86131
$934$	−15.5490	−0.508779
$935$	−1.73270	−0.0566654
$936$	21.3506	0.697867
$937$	−34.2302	−1.11825	−0.559126	−	0.829083i	$-0.688863\pi$
$937$	−34.2302	−1.11825	−0.559126	+	0.829083i	$0.688863\pi$
$938$	75.5265	2.46603
$939$	16.7391	0.546260
$940$	−15.6443	−0.510262
$941$	−22.2717	−0.726037	−0.363018	−	0.931782i	$-0.618254\pi$
$941$	−22.2717	−0.726037	−0.363018	+	0.931782i	$0.618254\pi$
$942$	−40.9771	−1.33511
$943$	−78.9811	−2.57198
$944$	130.836	4.25835
$945$	23.0935	0.751233
$946$	6.71517	0.218329
$947$	35.0927	1.14036	0.570180	−	0.821520i	$-0.306873\pi$
$947$	35.0927	1.14036	0.570180	+	0.821520i	$0.306873\pi$
$948$	47.5393	1.54400
$949$	2.05112	0.0665823
$950$	57.4185	1.86290
$951$	11.7829	0.382088
$952$	14.3276	0.464362
$953$	33.2502	1.07708	0.538540	−	0.842600i	$-0.318976\pi$
$953$	33.2502	1.07708	0.538540	+	0.842600i	$0.318976\pi$
$954$	0.671145	0.0217291
$955$	44.4439	1.43817
$956$	111.462	3.60495
$957$	−3.78903	−0.122482
$958$	−42.4684	−1.37209
$959$	−33.0941	−1.06867
$960$	−109.613	−3.53773
$961$	61.1855	1.97373
$962$	−7.25009	−0.233752
$963$	61.4205	1.97925
$964$	67.8744	2.18609
$965$	35.8473	1.15397
$966$	95.4512	3.07109
$967$	50.2009	1.61435	0.807175	−	0.590312i	$-0.200995\pi$
$967$	50.2009	1.61435	0.807175	+	0.590312i	$0.200995\pi$
$968$	−84.6432	−2.72054
$969$	−12.3342	−0.396231
$970$	−17.0325	−0.546881
$971$	−31.6070	−1.01432	−0.507158	−	0.861853i	$-0.669304\pi$
$971$	−31.6070	−1.01432	−0.507158	+	0.861853i	$0.669304\pi$
$972$	−92.7174	−2.97391
$973$	−22.3710	−0.717183
$974$	−83.9323	−2.68936
$975$	7.92300	0.253739
$976$	91.5271	2.92971
$977$	21.8888	0.700285	0.350142	−	0.936696i	$-0.386133\pi$
$977$	21.8888	0.700285	0.350142	+	0.936696i	$0.386133\pi$
$978$	164.534	5.26122
$979$	−9.00588	−0.287829
$980$	58.2457	1.86059
$981$	−1.35771	−0.0433484
$982$	−46.6373	−1.48826
$983$	3.43164	0.109452	0.0547262	−	0.998501i	$-0.482571\pi$
$983$	3.43164	0.109452	0.0547262	+	0.998501i	$0.482571\pi$
$984$	234.754	7.48367
$985$	66.7049	2.12539
$986$	−6.62137	−0.210867
$987$	−4.95349	−0.157671
$988$	13.5274	0.430362
$989$	33.4603	1.06398
$990$	20.5638	0.653562
$991$	32.7586	1.04061	0.520305	−	0.853981i	$-0.325818\pi$
$991$	32.7586	1.04061	0.520305	+	0.853981i	$0.325818\pi$
$992$	−125.891	−3.99703
$993$	−9.94853	−0.315707
$994$	−23.2100	−0.736176
$995$	−7.49696	−0.237670
$996$	−82.3249	−2.60856
$997$	−31.7979	−1.00705	−0.503524	−	0.863981i	$-0.667964\pi$
$997$	−31.7979	−1.00705	−0.503524	+	0.863981i	$0.667964\pi$
$998$	−50.9370	−1.61238
$999$	−18.5720	−0.587593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	799.2.a.g.1.19	✓	20
3.2	odd	2		7191.2.a.bb.1.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
799.2.a.g.1.19	✓	20	1.1	even	1	trivial
7191.2.a.bb.1.2		20	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:	\( N \)	\(=\)	\( 799 = 17 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	799.a (trivial)

\(f(q)\)	\(=\)	\(q+2.64443 q^{2} +2.73641 q^{3} +4.99303 q^{4} -3.13323 q^{5} +7.23626 q^{6} -1.81022 q^{7} +7.91488 q^{8} +4.48794 q^{9} +O(q^{10})\)	\(q+2.64443 q^{2} +2.73641 q^{3} +4.99303 q^{4} -3.13323 q^{5} +7.23626 q^{6} -1.81022 q^{7} +7.91488 q^{8} +4.48794 q^{9} -8.28563 q^{10} -0.553008 q^{11} +13.6630 q^{12} +0.601061 q^{13} -4.78700 q^{14} -8.57381 q^{15} +10.9443 q^{16} -1.00000 q^{17} +11.8681 q^{18} +4.50744 q^{19} -15.6443 q^{20} -4.95349 q^{21} -1.46239 q^{22} -7.28680 q^{23} +21.6584 q^{24} +4.81714 q^{25} +1.58947 q^{26} +4.07162 q^{27} -9.03847 q^{28} +2.50389 q^{29} -22.6729 q^{30} -9.60133 q^{31} +13.1118 q^{32} -1.51326 q^{33} -2.64443 q^{34} +5.67183 q^{35} +22.4085 q^{36} -4.56133 q^{37} +11.9196 q^{38} +1.64475 q^{39} -24.7992 q^{40} +10.8389 q^{41} -13.0992 q^{42} -4.59190 q^{43} -2.76119 q^{44} -14.0618 q^{45} -19.2695 q^{46} +1.00000 q^{47} +29.9482 q^{48} -3.72312 q^{49} +12.7386 q^{50} -2.73641 q^{51} +3.00112 q^{52} +0.0565505 q^{53} +10.7671 q^{54} +1.73270 q^{55} -14.3276 q^{56} +12.3342 q^{57} +6.62137 q^{58} +11.9547 q^{59} -42.8093 q^{60} +8.36297 q^{61} -25.3901 q^{62} -8.12415 q^{63} +12.7846 q^{64} -1.88326 q^{65} -4.00171 q^{66} -15.7774 q^{67} -4.99303 q^{68} -19.9397 q^{69} +14.9988 q^{70} +4.84854 q^{71} +35.5215 q^{72} +3.41250 q^{73} -12.0621 q^{74} +13.1817 q^{75} +22.5058 q^{76} +1.00106 q^{77} +4.34944 q^{78} +3.47942 q^{79} -34.2911 q^{80} -2.32220 q^{81} +28.6628 q^{82} -6.02539 q^{83} -24.7330 q^{84} +3.13323 q^{85} -12.1430 q^{86} +6.85167 q^{87} -4.37700 q^{88} +16.2853 q^{89} -37.1854 q^{90} -1.08805 q^{91} -36.3833 q^{92} -26.2732 q^{93} +2.64443 q^{94} -14.1228 q^{95} +35.8792 q^{96} +2.05567 q^{97} -9.84554 q^{98} -2.48187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9}+O(q^{10}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9	\( 20 q + 4 q^{2} + 3 q^{3} + 24 q^{4} + 13 q^{5} + 11 q^{6} - 3 q^{7} + 12 q^{8} + 37 q^{9} - 2 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} + 13 q^{14} + q^{15} + 28 q^{16} - 20 q^{17} + 15 q^{18} + 5 q^{19} + 37 q^{20} + 6 q^{21} - 19 q^{22} + 4 q^{23} + 30 q^{24} + 41 q^{25} - 9 q^{26} + 6 q^{27} - 25 q^{28} + 26 q^{29} - 25 q^{30} + 6 q^{31} + 28 q^{32} + 29 q^{33} - 4 q^{34} + 21 q^{35} - 5 q^{36} - 8 q^{37} - 21 q^{38} - 19 q^{39} - 25 q^{40} + 69 q^{41} + 3 q^{42} - 7 q^{43} + 16 q^{44} + 39 q^{45} - 24 q^{46} + 20 q^{47} + 26 q^{48} + 53 q^{49} + 16 q^{50} - 3 q^{51} + 18 q^{52} + 29 q^{53} + 23 q^{54} + 5 q^{55} - 22 q^{56} - 36 q^{57} - q^{58} + 55 q^{59} - 103 q^{60} - 17 q^{61} - 7 q^{62} - 9 q^{63} + 58 q^{64} + 40 q^{65} + 50 q^{66} - 6 q^{67} - 24 q^{68} + 17 q^{69} - 15 q^{70} + 47 q^{71} + 7 q^{72} - 32 q^{73} - 67 q^{74} - 22 q^{75} - 5 q^{76} + 4 q^{77} - 60 q^{78} - 26 q^{79} + 108 q^{80} + 68 q^{81} + 25 q^{82} + 3 q^{83} + 24 q^{84} - 13 q^{85} + 8 q^{86} - 41 q^{87} - 47 q^{88} + 119 q^{89} - 54 q^{90} - 35 q^{91} - 15 q^{93} + 4 q^{94} - 48 q^{95} - 84 q^{96} - 13 q^{97} + q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 + 3 * q^3 + 24 * q^4 + 13 * q^5 + 11 * q^6 - 3 * q^7 + 12 * q^8 + 37 * q^9 - 2 * q^10 + 10 * q^11 + 8 * q^12 + q^13 + 13 * q^14 + q^15 + 28 * q^16 - 20 * q^17 + 15 * q^18 + 5 * q^19 + 37 * q^20 + 6 * q^21 - 19 * q^22 + 4 * q^23 + 30 * q^24 + 41 * q^25 - 9 * q^26 + 6 * q^27 - 25 * q^28 + 26 * q^29 - 25 * q^30 + 6 * q^31 + 28 * q^32 + 29 * q^33 - 4 * q^34 + 21 * q^35 - 5 * q^36 - 8 * q^37 - 21 * q^38 - 19 * q^39 - 25 * q^40 + 69 * q^41 + 3 * q^42 - 7 * q^43 + 16 * q^44 + 39 * q^45 - 24 * q^46 + 20 * q^47 + 26 * q^48 + 53 * q^49 + 16 * q^50 - 3 * q^51 + 18 * q^52 + 29 * q^53 + 23 * q^54 + 5 * q^55 - 22 * q^56 - 36 * q^57 - q^58 + 55 * q^59 - 103 * q^60 - 17 * q^61 - 7 * q^62 - 9 * q^63 + 58 * q^64 + 40 * q^65 + 50 * q^66 - 6 * q^67 - 24 * q^68 + 17 * q^69 - 15 * q^70 + 47 * q^71 + 7 * q^72 - 32 * q^73 - 67 * q^74 - 22 * q^75 - 5 * q^76 + 4 * q^77 - 60 * q^78 - 26 * q^79 + 108 * q^80 + 68 * q^81 + 25 * q^82 + 3 * q^83 + 24 * q^84 - 13 * q^85 + 8 * q^86 - 41 * q^87 - 47 * q^88 + 119 * q^89 - 54 * q^90 - 35 * q^91 - 15 * q^93 + 4 * q^94 - 48 * q^95 - 84 * q^96 - 13 * q^97 + q^98 - 5 * q^99

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