LMFDB - Embedded newform 503.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.257.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 3 $ x^3 - x^2 - 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.91223$ of defining polynomial
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.656620 q^{2} -1.91223 q^{3} -1.56885 q^{4} -1.25561 q^{6} -2.56885 q^{7} -2.34338 q^{8} +0.656620 q^{9} +O(q^{10})$	\(q+0.656620 q^{2} -1.91223 q^{3} -1.56885 q^{4} -1.25561 q^{6} -2.56885 q^{7} -2.34338 q^{8} +0.656620 q^{9} +5.91223 q^{11} +3.00000 q^{12} +3.25561 q^{13} -1.68676 q^{14} +1.59899 q^{16} +5.31324 q^{17} +0.431150 q^{18} +4.00000 q^{19} +4.91223 q^{21} +3.88209 q^{22} -4.00000 q^{23} +4.48108 q^{24} -5.00000 q^{25} +2.13770 q^{26} +4.48108 q^{27} +4.03014 q^{28} +2.51122 q^{29} -9.13770 q^{31} +5.73669 q^{32} -11.3055 q^{33} +3.48878 q^{34} -1.03014 q^{36} +9.64892 q^{37} +2.62648 q^{38} -6.22547 q^{39} -1.19798 q^{41} +3.22547 q^{42} -4.79432 q^{43} -9.27540 q^{44} -2.62648 q^{46} +10.1678 q^{47} -3.05763 q^{48} -0.401012 q^{49} -3.28310 q^{50} -10.1601 q^{51} -5.10756 q^{52} +12.3357 q^{53} +2.94237 q^{54} +6.01979 q^{56} -7.64892 q^{57} +1.64892 q^{58} +2.16784 q^{59} +2.00000 q^{61} -6.00000 q^{62} -1.68676 q^{63} +0.568850 q^{64} -7.42345 q^{66} +6.51892 q^{67} -8.33568 q^{68} +7.64892 q^{69} +2.68676 q^{71} -1.53871 q^{72} +15.2255 q^{73} +6.33568 q^{74} +9.56115 q^{75} -6.27540 q^{76} -15.1876 q^{77} -4.08777 q^{78} -11.5913 q^{79} -10.5387 q^{81} -0.786616 q^{82} +2.56885 q^{83} -7.70655 q^{84} -3.14805 q^{86} -4.80202 q^{87} -13.8546 q^{88} -6.33568 q^{89} -8.36317 q^{91} +6.27540 q^{92} +17.4734 q^{93} +6.67641 q^{94} -10.9699 q^{96} +5.53101 q^{97} -0.263312 q^{98} +3.88209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{3} + 4 q^{4} + q^{6} + q^{7} - 9 q^{8}+O(q^{10}) $ 3 * q + q^3 + 4 * q^4 + q^6 + q^7 - 9 * q^8	$ 3 q + q^{3} + 4 q^{4} + q^{6} + q^{7} - 9 q^{8} + 11 q^{11} + 9 q^{12} + 5 q^{13} - 9 q^{14} + 2 q^{16} + 12 q^{17} + 10 q^{18} + 12 q^{19} + 8 q^{21} - q^{22} - 12 q^{23} - 2 q^{24} - 15 q^{25} - 11 q^{26} - 2 q^{27} + 18 q^{28} - 2 q^{29} - 10 q^{31} - 3 q^{32} - 5 q^{33} + 20 q^{34} - 9 q^{36} + 2 q^{37} - 8 q^{39} + 2 q^{41} - q^{42} + 5 q^{43} + 7 q^{44} + 19 q^{47} - 10 q^{48} - 4 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{53} + 8 q^{54} - 12 q^{56} + 4 q^{57} - 22 q^{58} - 5 q^{59} + 6 q^{61} - 18 q^{62} - 9 q^{63} - 7 q^{64} - 6 q^{66} + 35 q^{67} - 2 q^{68} - 4 q^{69} + 12 q^{71} + 10 q^{72} + 35 q^{73} - 4 q^{74} - 5 q^{75} + 16 q^{76} - 4 q^{77} - 19 q^{78} - 7 q^{79} - 17 q^{81} + 42 q^{82} - q^{83} + 3 q^{84} - 28 q^{86} - 20 q^{87} - 34 q^{88} + 4 q^{89} + 3 q^{91} - 16 q^{92} + 12 q^{93} - 12 q^{94} - 27 q^{96} - 23 q^{97} - 21 q^{98} - q^{99}+O(q^{100}) $ 3 * q + q^3 + 4 * q^4 + q^6 + q^7 - 9 * q^8 + 11 * q^11 + 9 * q^12 + 5 * q^13 - 9 * q^14 + 2 * q^16 + 12 * q^17 + 10 * q^18 + 12 * q^19 + 8 * q^21 - q^22 - 12 * q^23 - 2 * q^24 - 15 * q^25 - 11 * q^26 - 2 * q^27 + 18 * q^28 - 2 * q^29 - 10 * q^31 - 3 * q^32 - 5 * q^33 + 20 * q^34 - 9 * q^36 + 2 * q^37 - 8 * q^39 + 2 * q^41 - q^42 + 5 * q^43 + 7 * q^44 + 19 * q^47 - 10 * q^48 - 4 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^53 + 8 * q^54 - 12 * q^56 + 4 * q^57 - 22 * q^58 - 5 * q^59 + 6 * q^61 - 18 * q^62 - 9 * q^63 - 7 * q^64 - 6 * q^66 + 35 * q^67 - 2 * q^68 - 4 * q^69 + 12 * q^71 + 10 * q^72 + 35 * q^73 - 4 * q^74 - 5 * q^75 + 16 * q^76 - 4 * q^77 - 19 * q^78 - 7 * q^79 - 17 * q^81 + 42 * q^82 - q^83 + 3 * q^84 - 28 * q^86 - 20 * q^87 - 34 * q^88 + 4 * q^89 + 3 * q^91 - 16 * q^92 + 12 * q^93 - 12 * q^94 - 27 * q^96 - 23 * q^97 - 21 * q^98 - 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 $

$2$	0.656620	0.464301	0.232150	−	0.972680i	$-0.425424\pi$
$2$	0.656620	0.464301	0.232150	+	0.972680i	$0.425424\pi$
$3$	−1.91223	−1.10403	−0.552013	−	0.833835i	$-0.686140\pi$
$3$	−1.91223	−1.10403	−0.552013	+	0.833835i	$0.686140\pi$
$4$	−1.56885	−0.784425
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	−1.25561	−0.512600
$7$	−2.56885	−0.970934	−0.485467	−	0.874255i	$-0.661350\pi$
$7$	−2.56885	−0.970934	−0.485467	+	0.874255i	$0.661350\pi$
$8$	−2.34338	−0.828510
$9$	0.656620	0.218873
$10$	0	0
$11$	5.91223	1.78260	0.891302	−	0.453410i	$-0.149793\pi$
$11$	5.91223	1.78260	0.891302	+	0.453410i	$0.149793\pi$
$12$	3.00000	0.866025
$13$	3.25561	0.902943	0.451472	−	0.892285i	$-0.350899\pi$
$13$	3.25561	0.902943	0.451472	+	0.892285i	$0.350899\pi$
$14$	−1.68676	−0.450805
$15$	0	0
$16$	1.59899	0.399747
$17$	5.31324	1.28865	0.644325	−	0.764752i	$-0.277138\pi$
$17$	5.31324	1.28865	0.644325	+	0.764752i	$0.277138\pi$
$18$	0.431150	0.101623
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	4.91223	1.07194
$22$	3.88209	0.827664
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	4.48108	0.914696
$25$	−5.00000	−1.00000
$26$	2.13770	0.419237
$27$	4.48108	0.862384
$28$	4.03014	0.761625
$29$	2.51122	0.466321	0.233161	−	0.972438i	$-0.425093\pi$
$29$	2.51122	0.466321	0.233161	+	0.972438i	$0.425093\pi$
$30$	0	0
$31$	−9.13770	−1.64118	−0.820590	−	0.571518i	$-0.806355\pi$
$31$	−9.13770	−1.64118	−0.820590	+	0.571518i	$0.806355\pi$
$32$	5.73669	1.01411
$33$	−11.3055	−1.96804
$34$	3.48878	0.598321
$35$	0	0
$36$	−1.03014	−0.171690
$37$	9.64892	1.58627	0.793136	−	0.609044i	$-0.208447\pi$
$37$	9.64892	1.58627	0.793136	+	0.609044i	$0.208447\pi$
$38$	2.62648	0.426072
$39$	−6.22547	−0.996873
$40$	0	0
$41$	−1.19798	−0.187093	−0.0935463	−	0.995615i	$-0.529820\pi$
$41$	−1.19798	−0.187093	−0.0935463	+	0.995615i	$0.529820\pi$
$42$	3.22547	0.497701
$43$	−4.79432	−0.731127	−0.365563	−	0.930786i	$-0.619124\pi$
$43$	−4.79432	−0.731127	−0.365563	+	0.930786i	$0.619124\pi$
$44$	−9.27540	−1.39832
$45$	0	0
$46$	−2.62648	−0.387254
$47$	10.1678	1.48313	0.741566	−	0.670880i	$-0.234084\pi$
$47$	10.1678	1.48313	0.741566	+	0.670880i	$0.234084\pi$
$48$	−3.05763	−0.441331
$49$	−0.401012	−0.0572874
$50$	−3.28310	−0.464301
$51$	−10.1601	−1.42270
$52$	−5.10756	−0.708291
$53$	12.3357	1.69444	0.847218	−	0.531246i	$-0.178276\pi$
$53$	12.3357	1.69444	0.847218	+	0.531246i	$0.178276\pi$
$54$	2.94237	0.400406
$55$	0	0
$56$	6.01979	0.804428
$57$	−7.64892	−1.01312
$58$	1.64892	0.216513
$59$	2.16784	0.282228	0.141114	−	0.989993i	$-0.454932\pi$
$59$	2.16784	0.282228	0.141114	+	0.989993i	$0.454932\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−6.00000	−0.762001
$63$	−1.68676	−0.212512
$64$	0.568850	0.0711062
$65$	0	0
$66$	−7.42345	−0.913763
$67$	6.51892	0.796413	0.398206	−	0.917296i	$-0.369633\pi$
$67$	6.51892	0.796413	0.398206	+	0.917296i	$0.369633\pi$
$68$	−8.33568	−1.01085
$69$	7.64892	0.920821
$70$	0	0
$71$	2.68676	0.318860	0.159430	−	0.987209i	$-0.449034\pi$
$71$	2.68676	0.318860	0.159430	+	0.987209i	$0.449034\pi$
$72$	−1.53871	−0.181339
$73$	15.2255	1.78201	0.891003	−	0.453997i	$-0.150002\pi$
$73$	15.2255	1.78201	0.891003	+	0.453997i	$0.150002\pi$
$74$	6.33568	0.736507
$75$	9.56115	1.10403
$76$	−6.27540	−0.719838
$77$	−15.1876	−1.73079
$78$	−4.08777	−0.462849
$79$	−11.5913	−1.30412	−0.652061	−	0.758167i	$-0.726095\pi$
$79$	−11.5913	−1.30412	−0.652061	+	0.758167i	$0.726095\pi$
$80$	0	0
$81$	−10.5387	−1.17097
$82$	−0.786616	−0.0868672
$83$	2.56885	0.281968	0.140984	−	0.990012i	$-0.454973\pi$
$83$	2.56885	0.281968	0.140984	+	0.990012i	$0.454973\pi$
$84$	−7.70655	−0.840853
$85$	0	0
$86$	−3.14805	−0.339463
$87$	−4.80202	−0.514831
$88$	−13.8546	−1.47691
$89$	−6.33568	−0.671580	−0.335790	−	0.941937i	$-0.609003\pi$
$89$	−6.33568	−0.671580	−0.335790	+	0.941937i	$0.609003\pi$
$90$	0	0
$91$	−8.36317	−0.876698
$92$	6.27540	0.654256
$93$	17.4734	1.81190
$94$	6.67641	0.688619
$95$	0	0
$96$	−10.9699	−1.11961
$97$	5.53101	0.561589	0.280794	−	0.959768i	$-0.409402\pi$
$97$	5.53101	0.561589	0.280794	+	0.959768i	$0.409402\pi$
$98$	−0.263312	−0.0265986
$99$	3.88209	0.390165
$100$	7.84425	0.784425
$101$	−16.9622	−1.68780	−0.843899	−	0.536502i	$-0.819745\pi$
$101$	−16.9622	−1.68780	−0.843899	+	0.536502i	$0.819745\pi$
$102$	−6.67135	−0.660562
$103$	−19.9243	−1.96320	−0.981601	−	0.190946i	$-0.938844\pi$
$103$	−19.9243	−1.96320	−0.981601	+	0.190946i	$0.938844\pi$
$104$	−7.62913	−0.748097
$105$	0	0
$106$	8.09986	0.786728
$107$	−11.6489	−1.12614	−0.563072	−	0.826408i	$-0.690380\pi$
$107$	−11.6489	−1.12614	−0.563072	+	0.826408i	$0.690380\pi$
$108$	−7.03014	−0.676475
$109$	4.11526	0.394171	0.197085	−	0.980386i	$-0.436852\pi$
$109$	4.11526	0.394171	0.197085	+	0.980386i	$0.436852\pi$
$110$	0	0
$111$	−18.4509	−1.75129
$112$	−4.10756	−0.388128
$113$	20.2677	1.90662	0.953312	−	0.301987i	$-0.0976498\pi$
$113$	20.2677	1.90662	0.953312	+	0.301987i	$0.0976498\pi$
$114$	−5.02243	−0.470394
$115$	0	0
$116$	−3.93972	−0.365794
$117$	2.13770	0.197630
$118$	1.42345	0.131039
$119$	−13.6489	−1.25119
$120$	0	0
$121$	23.9545	2.17768
$122$	1.31324	0.118895
$123$	2.29081	0.206555
$124$	14.3357	1.28738
$125$	0	0
$126$	−1.10756	−0.0986693
$127$	15.0774	1.33790	0.668952	−	0.743305i	$-0.266743\pi$
$127$	15.0774	1.33790	0.668952	+	0.743305i	$0.266743\pi$
$128$	−11.0999	−0.981098
$129$	9.16784	0.807183
$130$	0	0
$131$	4.79432	0.418882	0.209441	−	0.977821i	$-0.432836\pi$
$131$	4.79432	0.418882	0.209441	+	0.977821i	$0.432836\pi$
$132$	17.7367	1.54378
$133$	−10.2754	−0.890990
$134$	4.28046	0.369775
$135$	0	0
$136$	−12.4509	−1.06766
$137$	13.3132	1.13743	0.568713	−	0.822536i	$-0.307441\pi$
$137$	13.3132	1.13743	0.568713	+	0.822536i	$0.307441\pi$
$138$	5.02243	0.427538
$139$	19.2978	1.63682	0.818410	−	0.574634i	$-0.194856\pi$
$139$	19.2978	1.63682	0.818410	+	0.574634i	$0.194856\pi$
$140$	0	0
$141$	−19.4432	−1.63742
$142$	1.76418	0.148047
$143$	19.2479	1.60959
$144$	1.04993	0.0874940
$145$	0	0
$146$	9.99735	0.827387
$147$	0.766826	0.0632468
$148$	−15.1377	−1.24431
$149$	4.68676	0.383954	0.191977	−	0.981399i	$-0.438510\pi$
$149$	4.68676	0.383954	0.191977	+	0.981399i	$0.438510\pi$
$150$	6.27804	0.512600
$151$	19.7488	1.60713	0.803566	−	0.595215i	$-0.202933\pi$
$151$	19.7488	1.60713	0.803566	+	0.595215i	$0.202933\pi$
$152$	−9.37352	−0.760293
$153$	3.48878	0.282051
$154$	−9.97251	−0.803607
$155$	0	0
$156$	9.76683	0.781972
$157$	1.48878	0.118818	0.0594089	−	0.998234i	$-0.481078\pi$
$157$	1.48878	0.118818	0.0594089	+	0.998234i	$0.481078\pi$
$158$	−7.61107	−0.605505
$159$	−23.5886	−1.87070
$160$	0	0
$161$	10.2754	0.809815
$162$	−6.91993	−0.543681
$163$	−7.82446	−0.612859	−0.306429	−	0.951893i	$-0.599134\pi$
$163$	−7.82446	−0.612859	−0.306429	+	0.951893i	$0.599134\pi$
$164$	1.87945	0.146760
$165$	0	0
$166$	1.68676	0.130918
$167$	−13.6489	−1.05618	−0.528092	−	0.849187i	$-0.677093\pi$
$167$	−13.6489	−1.05618	−0.528092	+	0.849187i	$0.677093\pi$
$168$	−11.5112	−0.888110
$169$	−2.40101	−0.184693
$170$	0	0
$171$	2.62648	0.200852
$172$	7.52157	0.573514
$173$	−17.3253	−1.31722	−0.658610	−	0.752484i	$-0.728855\pi$
$173$	−17.3253	−1.31722	−0.658610	+	0.752484i	$0.728855\pi$
$174$	−3.15311	−0.239036
$175$	12.8442	0.970934
$176$	9.45359	0.712591
$177$	−4.14540	−0.311588
$178$	−4.16013	−0.311815
$179$	−10.8623	−0.811886	−0.405943	−	0.913898i	$-0.633057\pi$
$179$	−10.8623	−0.811886	−0.405943	+	0.913898i	$0.633057\pi$
$180$	0	0
$181$	9.70919	0.721679	0.360839	−	0.932628i	$-0.382490\pi$
$181$	9.70919	0.721679	0.360839	+	0.932628i	$0.382490\pi$
$182$	−5.49143	−0.407052
$183$	−3.82446	−0.282712
$184$	9.37352	0.691025
$185$	0	0
$186$	11.4734	0.841269
$187$	31.4131	2.29715
$188$	−15.9518	−1.16341
$189$	−11.5112	−0.837318
$190$	0	0
$191$	−9.19798	−0.665542	−0.332771	−	0.943008i	$-0.607984\pi$
$191$	−9.19798	−0.665542	−0.332771	+	0.943008i	$0.607984\pi$
$192$	−1.08777	−0.0785031
$193$	15.7092	1.13077	0.565386	−	0.824826i	$-0.308727\pi$
$193$	15.7092	1.13077	0.565386	+	0.824826i	$0.308727\pi$
$194$	3.63177	0.260746
$195$	0	0
$196$	0.629127	0.0449376
$197$	15.9243	1.13456	0.567280	−	0.823525i	$-0.307996\pi$
$197$	15.9243	1.13456	0.567280	+	0.823525i	$0.307996\pi$
$198$	2.54906	0.181154
$199$	−6.75912	−0.479141	−0.239571	−	0.970879i	$-0.577007\pi$
$199$	−6.75912	−0.479141	−0.239571	+	0.970879i	$0.577007\pi$
$200$	11.7169	0.828510
$201$	−12.4657	−0.879261
$202$	−11.1377	−0.783646
$203$	−6.45094	−0.452767
$204$	15.9397	1.11600
$205$	0	0
$206$	−13.0827	−0.911516
$207$	−2.62648	−0.182553
$208$	5.20568	0.360949
$209$	23.6489	1.63583
$210$	0	0
$211$	−16.3357	−1.12459	−0.562297	−	0.826935i	$-0.690082\pi$
$211$	−16.3357	−1.12459	−0.562297	+	0.826935i	$0.690082\pi$
$212$	−19.3528	−1.32916
$213$	−5.13770	−0.352029
$214$	−7.64892	−0.522869
$215$	0	0
$216$	−10.5009	−0.714494
$217$	23.4734	1.59348
$218$	2.70217	0.183014
$219$	−29.1146	−1.96738
$220$	0	0
$221$	17.2978	1.16358
$222$	−12.1153	−0.813123
$223$	−21.7367	−1.45560	−0.727798	−	0.685791i	$-0.759456\pi$
$223$	−21.7367	−1.45560	−0.727798	+	0.685791i	$0.759456\pi$
$224$	−14.7367	−0.984636
$225$	−3.28310	−0.218873
$226$	13.3082	0.885247
$227$	7.02243	0.466095	0.233048	−	0.972465i	$-0.425130\pi$
$227$	7.02243	0.466095	0.233048	+	0.972465i	$0.425130\pi$
$228$	12.0000	0.794719
$229$	6.90958	0.456598	0.228299	−	0.973591i	$-0.426684\pi$
$229$	6.90958	0.456598	0.228299	+	0.973591i	$0.426684\pi$
$230$	0	0
$231$	29.0422	1.91084
$232$	−5.88474	−0.386352
$233$	5.62142	0.368272	0.184136	−	0.982901i	$-0.441051\pi$
$233$	5.62142	0.368272	0.184136	+	0.982901i	$0.441051\pi$
$234$	1.40366	0.0917599
$235$	0	0
$236$	−3.40101	−0.221387
$237$	22.1652	1.43978
$238$	−8.96216	−0.580930
$239$	−3.54906	−0.229570	−0.114785	−	0.993390i	$-0.536618\pi$
$239$	−3.54906	−0.229570	−0.114785	+	0.993390i	$0.536618\pi$
$240$	0	0
$241$	−8.96216	−0.577303	−0.288652	−	0.957434i	$-0.593207\pi$
$241$	−8.96216	−0.577303	−0.288652	+	0.957434i	$0.593207\pi$
$242$	15.7290	1.01110
$243$	6.70919	0.430395
$244$	−3.13770	−0.200871
$245$	0	0
$246$	1.50419	0.0959036
$247$	13.0224	0.828598
$248$	21.4131	1.35973
$249$	−4.91223	−0.311300
$250$	0	0
$251$	−2.62648	−0.165782	−0.0828910	−	0.996559i	$-0.526415\pi$
$251$	−2.62648	−0.165782	−0.0828910	+	0.996559i	$0.526415\pi$
$252$	2.64627	0.166699
$253$	−23.6489	−1.48679
$254$	9.90014	0.621190
$255$	0	0
$256$	−8.42609	−0.526631
$257$	−15.9270	−0.993496	−0.496748	−	0.867895i	$-0.665473\pi$
$257$	−15.9270	−0.993496	−0.496748	+	0.867895i	$0.665473\pi$
$258$	6.01979	0.374776
$259$	−24.7866	−1.54017
$260$	0	0
$261$	1.64892	0.102065
$262$	3.14805	0.194487
$263$	−2.68411	−0.165510	−0.0827548	−	0.996570i	$-0.526372\pi$
$263$	−2.68411	−0.165510	−0.0827548	+	0.996570i	$0.526372\pi$
$264$	26.4932	1.63054
$265$	0	0
$266$	−6.74704	−0.413687
$267$	12.1153	0.741442
$268$	−10.2272	−0.624726
$269$	−23.9243	−1.45869	−0.729346	−	0.684145i	$-0.760175\pi$
$269$	−23.9243	−1.45869	−0.729346	+	0.684145i	$0.760175\pi$
$270$	0	0
$271$	14.3830	0.873703	0.436851	−	0.899534i	$-0.356094\pi$
$271$	14.3830	0.873703	0.436851	+	0.899534i	$0.356094\pi$
$272$	8.49581	0.515134
$273$	15.9923	0.967898
$274$	8.74175	0.528108
$275$	−29.5611	−1.78260
$276$	−12.0000	−0.722315
$277$	6.62648	0.398147	0.199073	−	0.979985i	$-0.436207\pi$
$277$	6.62648	0.398147	0.199073	+	0.979985i	$0.436207\pi$
$278$	12.6714	0.759977
$279$	−6.00000	−0.359211
$280$	0	0
$281$	−4.39595	−0.262241	−0.131120	−	0.991366i	$-0.541857\pi$
$281$	−4.39595	−0.262241	−0.131120	+	0.991366i	$0.541857\pi$
$282$	−12.7668	−0.760253
$283$	4.79432	0.284993	0.142496	−	0.989795i	$-0.454487\pi$
$283$	4.79432	0.284993	0.142496	+	0.989795i	$0.454487\pi$
$284$	−4.21512	−0.250121
$285$	0	0
$286$	12.6386	0.747334
$287$	3.07742	0.181654
$288$	3.76683	0.221962
$289$	11.2305	0.660619
$290$	0	0
$291$	−10.5766	−0.620009
$292$	−23.8865	−1.39785
$293$	−1.65662	−0.0967808	−0.0483904	−	0.998828i	$-0.515409\pi$
$293$	−1.65662	−0.0967808	−0.0483904	+	0.998828i	$0.515409\pi$
$294$	0.503514	0.0293655
$295$	0	0
$296$	−22.6111	−1.31424
$297$	26.4932	1.53729
$298$	3.07742	0.178270
$299$	−13.0224	−0.753107
$300$	−15.0000	−0.866025
$301$	12.3159	0.709876
$302$	12.9674	0.746193
$303$	32.4355	1.86337
$304$	6.39595	0.366833
$305$	0	0
$306$	2.29081	0.130957
$307$	19.0620	1.08793	0.543963	−	0.839109i	$-0.316923\pi$
$307$	19.0620	1.08793	0.543963	+	0.839109i	$0.316923\pi$
$308$	23.8271	1.35768
$309$	38.0999	2.16743
$310$	0	0
$311$	10.2358	0.580420	0.290210	−	0.956963i	$-0.406275\pi$
$311$	10.2358	0.580420	0.290210	+	0.956963i	$0.406275\pi$
$312$	14.5886	0.825919
$313$	−25.5886	−1.44636	−0.723178	−	0.690662i	$-0.757319\pi$
$313$	−25.5886	−1.44636	−0.723178	+	0.690662i	$0.757319\pi$
$314$	0.977565	0.0551672
$315$	0	0
$316$	18.1850	1.02299
$317$	−28.6188	−1.60739	−0.803695	−	0.595041i	$-0.797136\pi$
$317$	−28.6188	−1.60739	−0.803695	+	0.595041i	$0.797136\pi$
$318$	−15.4888	−0.868568
$319$	14.8469	0.831266
$320$	0	0
$321$	22.2754	1.24329
$322$	6.74704	0.375998
$323$	21.2530	1.18255
$324$	16.5337	0.918536
$325$	−16.2780	−0.902943
$326$	−5.13770	−0.284551
$327$	−7.86933	−0.435175
$328$	2.80731	0.155008
$329$	−26.1196	−1.44002
$330$	0	0
$331$	8.62648	0.474154	0.237077	−	0.971491i	$-0.423811\pi$
$331$	8.62648	0.474154	0.237077	+	0.971491i	$0.423811\pi$
$332$	−4.03014	−0.221183
$333$	6.33568	0.347193
$334$	−8.96216	−0.490387
$335$	0	0
$336$	7.85460	0.428503
$337$	26.8416	1.46216	0.731078	−	0.682294i	$-0.239018\pi$
$337$	26.8416	1.46216	0.731078	+	0.682294i	$0.239018\pi$
$338$	−1.57655	−0.0857532
$339$	−38.7565	−2.10496
$340$	0	0
$341$	−54.0242	−2.92557
$342$	1.72460	0.0932558
$343$	19.0121	1.02656
$344$	11.2349	0.605746
$345$	0	0
$346$	−11.3762	−0.611586
$347$	−25.2978	−1.35806	−0.679029	−	0.734111i	$-0.737599\pi$
$347$	−25.2978	−1.35806	−0.679029	+	0.734111i	$0.737599\pi$
$348$	7.53365	0.403846
$349$	6.09986	0.326518	0.163259	−	0.986583i	$-0.447799\pi$
$349$	6.09986	0.326518	0.163259	+	0.986583i	$0.447799\pi$
$350$	8.43380	0.450805
$351$	14.5886	0.778684
$352$	33.9166	1.80776
$353$	−7.31324	−0.389245	−0.194622	−	0.980878i	$-0.562348\pi$
$353$	−7.31324	−0.389245	−0.194622	+	0.980878i	$0.562348\pi$
$354$	−2.72196	−0.144670
$355$	0	0
$356$	9.93972	0.526804
$357$	26.0999	1.38135
$358$	−7.13241	−0.376960
$359$	8.09986	0.427494	0.213747	−	0.976889i	$-0.431433\pi$
$359$	8.09986	0.427494	0.213747	+	0.976889i	$0.431433\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	6.37526	0.335076
$363$	−45.8064	−2.40421
$364$	13.1206	0.687704
$365$	0	0
$366$	−2.51122	−0.131263
$367$	−20.1876	−1.05379	−0.526893	−	0.849932i	$-0.676643\pi$
$367$	−20.1876	−1.05379	−0.526893	+	0.849932i	$0.676643\pi$
$368$	−6.39595	−0.333412
$369$	−0.786616	−0.0409496
$370$	0	0
$371$	−31.6885	−1.64518
$372$	−27.4131	−1.42130
$373$	25.6764	1.32947	0.664737	−	0.747077i	$-0.268544\pi$
$373$	25.6764	1.32947	0.664737	+	0.747077i	$0.268544\pi$
$374$	20.6265	1.06657
$375$	0	0
$376$	−23.8271	−1.22879
$377$	8.17554	0.421062
$378$	−7.55850	−0.388767
$379$	29.1953	1.49966	0.749832	−	0.661629i	$-0.230134\pi$
$379$	29.1953	1.49966	0.749832	+	0.661629i	$0.230134\pi$
$380$	0	0
$381$	−28.8315	−1.47708
$382$	−6.03958	−0.309012
$383$	−28.6738	−1.46516	−0.732580	−	0.680680i	$-0.761684\pi$
$383$	−28.6738	−1.46516	−0.732580	+	0.680680i	$0.761684\pi$
$384$	21.2255	1.08316
$385$	0	0
$386$	10.3150	0.525019
$387$	−3.14805	−0.160024
$388$	−8.67732	−0.440524
$389$	−13.8821	−0.703850	−0.351925	−	0.936028i	$-0.614473\pi$
$389$	−13.8821	−0.703850	−0.351925	+	0.936028i	$0.614473\pi$
$390$	0	0
$391$	−21.2530	−1.07481
$392$	0.939723	0.0474632
$393$	−9.16784	−0.462456
$394$	10.4562	0.526777
$395$	0	0
$396$	−6.09042	−0.306055
$397$	2.57391	0.129181	0.0645904	−	0.997912i	$-0.479426\pi$
$397$	2.57391	0.129181	0.0645904	+	0.997912i	$0.479426\pi$
$398$	−4.43818	−0.222466
$399$	19.6489	0.983676
$400$	−7.99494	−0.399747
$401$	31.9270	1.59436	0.797178	−	0.603744i	$-0.206325\pi$
$401$	31.9270	1.59436	0.797178	+	0.603744i	$0.206325\pi$
$402$	−8.18521	−0.408241
$403$	−29.7488	−1.48189
$404$	26.6111	1.32395
$405$	0	0
$406$	−4.23582	−0.210220
$407$	57.0466	2.82770
$408$	23.8091	1.17872
$409$	−8.03958	−0.397532	−0.198766	−	0.980047i	$-0.563693\pi$
$409$	−8.03958	−0.397532	−0.198766	+	0.980047i	$0.563693\pi$
$410$	0	0
$411$	−25.4580	−1.25575
$412$	31.2583	1.53998
$413$	−5.56885	−0.274025
$414$	−1.72460	−0.0847595
$415$	0	0
$416$	18.6764	0.915686
$417$	−36.9019	−1.80709
$418$	15.5284	0.759517
$419$	28.8865	1.41120	0.705598	−	0.708612i	$-0.250678\pi$
$419$	28.8865	1.41120	0.705598	+	0.708612i	$0.250678\pi$
$420$	0	0
$421$	29.9923	1.46174	0.730868	−	0.682519i	$-0.239116\pi$
$421$	29.9923	1.46174	0.730868	+	0.682519i	$0.239116\pi$
$422$	−10.7263	−0.522150
$423$	6.67641	0.324618
$424$	−28.9072	−1.40386
$425$	−26.5662	−1.28865
$426$	−3.37352	−0.163447
$427$	−5.13770	−0.248631
$428$	18.2754	0.883375
$429$	−36.8064	−1.77703
$430$	0	0
$431$	9.18257	0.442309	0.221154	−	0.975239i	$-0.429018\pi$
$431$	9.18257	0.442309	0.221154	+	0.975239i	$0.429018\pi$
$432$	7.16519	0.344735
$433$	−33.1696	−1.59403	−0.797014	−	0.603961i	$-0.793588\pi$
$433$	−33.1696	−1.59403	−0.797014	+	0.603961i	$0.793588\pi$
$434$	15.4131	0.739852
$435$	0	0
$436$	−6.45623	−0.309197
$437$	−16.0000	−0.765384
$438$	−19.1172	−0.913457
$439$	−3.07742	−0.146877	−0.0734387	−	0.997300i	$-0.523397\pi$
$439$	−3.07742	−0.146877	−0.0734387	+	0.997300i	$0.523397\pi$
$440$	0	0
$441$	−0.263312	−0.0125387
$442$	11.3581	0.540250
$443$	8.37790	0.398046	0.199023	−	0.979995i	$-0.436223\pi$
$443$	8.37790	0.398046	0.199023	+	0.979995i	$0.436223\pi$
$444$	28.9468	1.37375
$445$	0	0
$446$	−14.2728	−0.675834
$447$	−8.96216	−0.423896
$448$	−1.46129	−0.0690394
$449$	−23.4734	−1.10778	−0.553889	−	0.832591i	$-0.686857\pi$
$449$	−23.4734	−1.10778	−0.553889	+	0.832591i	$0.686857\pi$
$450$	−2.15575	−0.101623
$451$	−7.08271	−0.333512
$452$	−31.7970	−1.49560
$453$	−37.7642	−1.77432
$454$	4.61107	0.216408
$455$	0	0
$456$	17.9243	0.839383
$457$	−2.90188	−0.135744	−0.0678721	−	0.997694i	$-0.521621\pi$
$457$	−2.90188	−0.135744	−0.0678721	+	0.997694i	$0.521621\pi$
$458$	4.53697	0.211999
$459$	23.8091	1.11131
$460$	0	0
$461$	−8.86230	−0.412758	−0.206379	−	0.978472i	$-0.566168\pi$
$461$	−8.86230	−0.412758	−0.206379	+	0.978472i	$0.566168\pi$
$462$	19.0697	0.887204
$463$	−4.67135	−0.217096	−0.108548	−	0.994091i	$-0.534620\pi$
$463$	−4.67135	−0.217096	−0.108548	+	0.994091i	$0.534620\pi$
$464$	4.01541	0.186411
$465$	0	0
$466$	3.69114	0.170989
$467$	17.4734	0.808571	0.404286	−	0.914633i	$-0.367520\pi$
$467$	17.4734	0.808571	0.404286	+	0.914633i	$0.367520\pi$
$468$	−3.35373	−0.155026
$469$	−16.7461	−0.773264
$470$	0	0
$471$	−2.84689	−0.131178
$472$	−5.08007	−0.233829
$473$	−28.3451	−1.30331
$474$	14.5541	0.668493
$475$	−20.0000	−0.917663
$476$	21.4131	0.981468
$477$	8.09986	0.370867
$478$	−2.33039	−0.106589
$479$	−5.83987	−0.266830	−0.133415	−	0.991060i	$-0.542594\pi$
$479$	−5.83987	−0.266830	−0.133415	+	0.991060i	$0.542594\pi$
$480$	0	0
$481$	31.4131	1.43231
$482$	−5.88474	−0.268042
$483$	−19.6489	−0.894057
$484$	−37.5809	−1.70822
$485$	0	0
$486$	4.40539	0.199833
$487$	−33.2530	−1.50684	−0.753418	−	0.657542i	$-0.771596\pi$
$487$	−33.2530	−1.50684	−0.753418	+	0.657542i	$0.771596\pi$
$488$	−4.68676	−0.212160
$489$	14.9622	0.676612
$490$	0	0
$491$	−24.7109	−1.11519	−0.557594	−	0.830114i	$-0.688276\pi$
$491$	−24.7109	−1.11519	−0.557594	+	0.830114i	$0.688276\pi$
$492$	−3.59393	−0.162027
$493$	13.3427	0.600925
$494$	8.55080	0.384719
$495$	0	0
$496$	−14.6111	−0.656057
$497$	−6.90188	−0.309592
$498$	−3.22547	−0.144537
$499$	−2.23053	−0.0998522	−0.0499261	−	0.998753i	$-0.515899\pi$
$499$	−2.23053	−0.0998522	−0.0499261	+	0.998753i	$0.515899\pi$
$500$	0	0
$501$	26.0999	1.16606
$502$	−1.72460	−0.0769727
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	3.95272	0.176068
$505$	0	0
$506$	−15.5284	−0.690320
$507$	4.59128	0.203906
$508$	−23.6542	−1.04949
$509$	−23.4252	−1.03830	−0.519152	−	0.854682i	$-0.673752\pi$
$509$	−23.4252	−1.03830	−0.519152	+	0.854682i	$0.673752\pi$
$510$	0	0
$511$	−39.1119	−1.73021
$512$	16.6670	0.736583
$513$	17.9243	0.791378
$514$	−10.4580	−0.461281
$515$	0	0
$516$	−14.3830	−0.633174
$517$	60.1146	2.64384
$518$	−16.2754	−0.715100
$519$	33.1300	1.45425
$520$	0	0
$521$	−12.6291	−0.553292	−0.276646	−	0.960972i	$-0.589223\pi$
$521$	−12.6291	−0.553292	−0.276646	+	0.960972i	$0.589223\pi$
$522$	1.08271	0.0473890
$523$	9.52836	0.416646	0.208323	−	0.978060i	$-0.433199\pi$
$523$	9.52836	0.416646	0.208323	+	0.978060i	$0.433199\pi$
$524$	−7.52157	−0.328581
$525$	−24.5611	−1.07194
$526$	−1.76244	−0.0768462
$527$	−48.5508	−2.11491
$528$	−18.0774	−0.786719
$529$	−7.00000	−0.304348
$530$	0	0
$531$	1.42345	0.0617723
$532$	16.1206	0.698915
$533$	−3.90014	−0.168934
$534$	7.95513	0.344252
$535$	0	0
$536$	−15.2763	−0.659836
$537$	20.7712	0.896344
$538$	−15.7092	−0.677271
$539$	−2.37087	−0.102121
$540$	0	0
$541$	−6.39595	−0.274984	−0.137492	−	0.990503i	$-0.543904\pi$
$541$	−6.39595	−0.274984	−0.137492	+	0.990503i	$0.543904\pi$
$542$	9.44414	0.405661
$543$	−18.5662	−0.796752
$544$	30.4804	1.30684
$545$	0	0
$546$	10.5009	0.449396
$547$	11.5259	0.492814	0.246407	−	0.969166i	$-0.420750\pi$
$547$	11.5259	0.492814	0.246407	+	0.969166i	$0.420750\pi$
$548$	−20.8865	−0.892226
$549$	1.31324	0.0560478
$550$	−19.4105	−0.827664
$551$	10.0449	0.427926
$552$	−17.9243	−0.762910
$553$	29.7763	1.26622
$554$	4.35108	0.184860
$555$	0	0
$556$	−30.2754	−1.28396
$557$	34.3478	1.45536	0.727681	−	0.685916i	$-0.240598\pi$
$557$	34.3478	1.45536	0.727681	+	0.685916i	$0.240598\pi$
$558$	−3.93972	−0.166782
$559$	−15.6084	−0.660166
$560$	0	0
$561$	−60.0690	−2.53612
$562$	−2.88647	−0.121759
$563$	29.6335	1.24890	0.624452	−	0.781063i	$-0.285322\pi$
$563$	29.6335	1.24890	0.624452	+	0.781063i	$0.285322\pi$
$564$	30.5035	1.28443
$565$	0	0
$566$	3.14805	0.132322
$567$	27.0724	1.13693
$568$	−6.29610	−0.264178
$569$	41.6764	1.74717	0.873583	−	0.486675i	$-0.161790\pi$
$569$	41.6764	1.74717	0.873583	+	0.486675i	$0.161790\pi$
$570$	0	0
$571$	−20.4355	−0.855200	−0.427600	−	0.903968i	$-0.640641\pi$
$571$	−20.4355	−0.855200	−0.427600	+	0.903968i	$0.640641\pi$
$572$	−30.1971	−1.26260
$573$	17.5886	0.734776
$574$	2.02070	0.0843423
$575$	20.0000	0.834058
$576$	0.373518	0.0155633
$577$	−27.3581	−1.13893	−0.569467	−	0.822015i	$-0.692850\pi$
$577$	−27.3581	−1.13893	−0.569467	+	0.822015i	$0.692850\pi$
$578$	7.37419	0.306726
$579$	−30.0396	−1.24840
$580$	0	0
$581$	−6.59899	−0.273772
$582$	−6.94478	−0.287870
$583$	72.9313	3.02051
$584$	−35.6791	−1.47641
$585$	0	0
$586$	−1.08777	−0.0449354
$587$	19.9571	0.823718	0.411859	−	0.911248i	$-0.364880\pi$
$587$	19.9571	0.823718	0.411859	+	0.911248i	$0.364880\pi$
$588$	−1.20304	−0.0496123
$589$	−36.5508	−1.50605
$590$	0	0
$591$	−30.4509	−1.25258
$592$	15.4285	0.634108
$593$	−17.1980	−0.706236	−0.353118	−	0.935579i	$-0.614879\pi$
$593$	−17.1980	−0.706236	−0.353118	+	0.935579i	$0.614879\pi$
$594$	17.3960	0.713765
$595$	0	0
$596$	−7.35282	−0.301183
$597$	12.9250	0.528985
$598$	−8.55080	−0.349668
$599$	−32.3779	−1.32293	−0.661463	−	0.749978i	$-0.730064\pi$
$599$	−32.3779	−1.32293	−0.661463	+	0.749978i	$0.730064\pi$
$600$	−22.4054	−0.914696
$601$	−7.58094	−0.309233	−0.154616	−	0.987975i	$-0.549414\pi$
$601$	−7.58094	−0.309233	−0.154616	+	0.987975i	$0.549414\pi$
$602$	8.08686	0.329596
$603$	4.28046	0.174314
$604$	−30.9829	−1.26067
$605$	0	0
$606$	21.2978	0.865165
$607$	−19.1558	−0.777508	−0.388754	−	0.921342i	$-0.627094\pi$
$607$	−19.1558	−0.777508	−0.388754	+	0.921342i	$0.627094\pi$
$608$	22.9468	0.930614
$609$	12.3357	0.499867
$610$	0	0
$611$	33.1025	1.33918
$612$	−5.47338	−0.221248
$613$	−1.65421	−0.0668128	−0.0334064	−	0.999442i	$-0.510636\pi$
$613$	−1.65421	−0.0668128	−0.0334064	+	0.999442i	$0.510636\pi$
$614$	12.5165	0.505125
$615$	0	0
$616$	35.5904	1.43398
$617$	−30.3960	−1.22370	−0.611848	−	0.790976i	$-0.709573\pi$
$617$	−30.3960	−1.22370	−0.611848	+	0.790976i	$0.709573\pi$
$618$	25.0171	1.00634
$619$	−3.08271	−0.123905	−0.0619523	−	0.998079i	$-0.519733\pi$
$619$	−3.08271	−0.123905	−0.0619523	+	0.998079i	$0.519733\pi$
$620$	0	0
$621$	−17.9243	−0.719278
$622$	6.72105	0.269489
$623$	16.2754	0.652060
$624$	−9.95445	−0.398497
$625$	25.0000	1.00000
$626$	−16.8020	−0.671544
$627$	−45.2221	−1.80600
$628$	−2.33568	−0.0932036
$629$	51.2670	2.04415
$630$	0	0
$631$	13.4657	0.536060	0.268030	−	0.963411i	$-0.413627\pi$
$631$	13.4657	0.536060	0.268030	+	0.963411i	$0.413627\pi$
$632$	27.1628	1.08048
$633$	31.2376	1.24158
$634$	−18.7917	−0.746313
$635$	0	0
$636$	37.0070	1.46742
$637$	−1.30554	−0.0517273
$638$	9.74877	0.385958
$639$	1.76418	0.0697899
$640$	0	0
$641$	15.7169	0.620780	0.310390	−	0.950609i	$-0.399540\pi$
$641$	15.7169	0.620780	0.310390	+	0.950609i	$0.399540\pi$
$642$	14.6265	0.577261
$643$	48.5354	1.91405	0.957024	−	0.290007i	$-0.0936577\pi$
$643$	48.5354	1.91405	0.957024	+	0.290007i	$0.0936577\pi$
$644$	−16.1206	−0.635239
$645$	0	0
$646$	13.9551	0.549057
$647$	−4.79191	−0.188389	−0.0941946	−	0.995554i	$-0.530028\pi$
$647$	−4.79191	−0.188389	−0.0941946	+	0.995554i	$0.530028\pi$
$648$	24.6962	0.970158
$649$	12.8168	0.503102
$650$	−10.6885	−0.419237
$651$	−44.8865	−1.75924
$652$	12.2754	0.480742
$653$	−48.2419	−1.88785	−0.943926	−	0.330156i	$-0.892899\pi$
$653$	−48.2419	−1.88785	−0.943926	+	0.330156i	$0.892899\pi$
$654$	−5.16716	−0.202052
$655$	0	0
$656$	−1.91555	−0.0747897
$657$	9.99735	0.390034
$658$	−17.1507	−0.668604
$659$	−32.7237	−1.27473	−0.637367	−	0.770560i	$-0.719976\pi$
$659$	−32.7237	−1.27473	−0.637367	+	0.770560i	$0.719976\pi$
$660$	0	0
$661$	13.4105	0.521606	0.260803	−	0.965392i	$-0.416013\pi$
$661$	13.4105	0.521606	0.260803	+	0.965392i	$0.416013\pi$
$662$	5.66432	0.220150
$663$	−33.0774	−1.28462
$664$	−6.01979	−0.233613
$665$	0	0
$666$	4.16013	0.161202
$667$	−10.0449	−0.388939
$668$	21.4131	0.828498
$669$	41.5655	1.60702
$670$	0	0
$671$	11.8245	0.456478
$672$	28.1799	1.08706
$673$	25.4107	0.979510	0.489755	−	0.871860i	$-0.337086\pi$
$673$	25.4107	0.979510	0.489755	+	0.871860i	$0.337086\pi$
$674$	17.6247	0.678880
$675$	−22.4054	−0.862384
$676$	3.76683	0.144878
$677$	−40.6111	−1.56081	−0.780405	−	0.625274i	$-0.784987\pi$
$677$	−40.6111	−1.56081	−0.780405	+	0.625274i	$0.784987\pi$
$678$	−25.4483	−0.977336
$679$	−14.2083	−0.545265
$680$	0	0
$681$	−13.4285	−0.514581
$682$	−35.4734	−1.35835
$683$	33.8693	1.29597	0.647987	−	0.761651i	$-0.275611\pi$
$683$	33.8693	1.29597	0.647987	+	0.761651i	$0.275611\pi$
$684$	−4.12055	−0.157553
$685$	0	0
$686$	12.4837	0.476631
$687$	−13.2127	−0.504096
$688$	−7.66606	−0.292266
$689$	40.1601	1.52998
$690$	0	0
$691$	4.72898	0.179899	0.0899495	−	0.995946i	$-0.471329\pi$
$691$	4.72898	0.179899	0.0899495	+	0.995946i	$0.471329\pi$
$692$	27.1808	1.03326
$693$	−9.97251	−0.378824
$694$	−16.6111	−0.630548
$695$	0	0
$696$	11.2530	0.426542
$697$	−6.36514	−0.241097
$698$	4.00529	0.151602
$699$	−10.7494	−0.406582
$700$	−20.1507	−0.761625
$701$	31.7213	1.19810	0.599048	−	0.800713i	$-0.295546\pi$
$701$	31.7213	1.19810	0.599048	+	0.800713i	$0.295546\pi$
$702$	9.57920	0.361544
$703$	38.5957	1.45566
$704$	3.36317	0.126754
$705$	0	0
$706$	−4.80202	−0.180727
$707$	43.5732	1.63874
$708$	6.50351	0.244417
$709$	14.4355	0.542138	0.271069	−	0.962560i	$-0.412623\pi$
$709$	14.4355	0.542138	0.271069	+	0.962560i	$0.412623\pi$
$710$	0	0
$711$	−7.61107	−0.285438
$712$	14.8469	0.556411
$713$	36.5508	1.36884
$714$	17.1377	0.641362
$715$	0	0
$716$	17.0413	0.636864
$717$	6.78662	0.253451
$718$	5.31853	0.198486
$719$	−2.20833	−0.0823566	−0.0411783	−	0.999152i	$-0.513111\pi$
$719$	−2.20833	−0.0823566	−0.0411783	+	0.999152i	$0.513111\pi$
$720$	0	0
$721$	51.1826	1.90614
$722$	−1.96986	−0.0733106
$723$	17.1377	0.637358
$724$	−15.2323	−0.566103
$725$	−12.5561	−0.466321
$726$	−30.0774	−1.11628
$727$	19.1102	0.708758	0.354379	−	0.935102i	$-0.384692\pi$
$727$	19.1102	0.708758	0.354379	+	0.935102i	$0.384692\pi$
$728$	19.5981	0.726353
$729$	18.7866	0.695801
$730$	0	0
$731$	−25.4734	−0.942167
$732$	6.00000	0.221766
$733$	−14.2600	−0.526705	−0.263352	−	0.964700i	$-0.584828\pi$
$733$	−14.2600	−0.526705	−0.263352	+	0.964700i	$0.584828\pi$
$734$	−13.2556	−0.489273
$735$	0	0
$736$	−22.9468	−0.845828
$737$	38.5414	1.41969
$738$	−0.516508	−0.0190129
$739$	−33.2101	−1.22165	−0.610826	−	0.791765i	$-0.709162\pi$
$739$	−33.2101	−1.22165	−0.610826	+	0.791765i	$0.709162\pi$
$740$	0	0
$741$	−24.9019	−0.914793
$742$	−20.8073	−0.763861
$743$	16.3203	0.598733	0.299366	−	0.954138i	$-0.403225\pi$
$743$	16.3203	0.598733	0.299366	+	0.954138i	$0.403225\pi$
$744$	−40.9468	−1.50118
$745$	0	0
$746$	16.8597	0.617276
$747$	1.68676	0.0617153
$748$	−49.2824	−1.80194
$749$	29.9243	1.09341
$750$	0	0
$751$	−18.2151	−0.664679	−0.332340	−	0.943160i	$-0.607838\pi$
$751$	−18.2151	−0.664679	−0.332340	+	0.943160i	$0.607838\pi$
$752$	16.2583	0.592878
$753$	5.02243	0.183028
$754$	5.36823	0.195499
$755$	0	0
$756$	18.0594	0.656813
$757$	4.81743	0.175093	0.0875463	−	0.996160i	$-0.472097\pi$
$757$	4.81743	0.175093	0.0875463	+	0.996160i	$0.472097\pi$
$758$	19.1703	0.696295
$759$	45.2221	1.64146
$760$	0	0
$761$	−53.6456	−1.94465	−0.972326	−	0.233630i	$-0.924940\pi$
$761$	−53.6456	−1.94465	−0.972326	+	0.233630i	$0.924940\pi$
$762$	−18.9313	−0.685810
$763$	−10.5715	−0.382714
$764$	14.4302	0.522068
$765$	0	0
$766$	−18.8278	−0.680275
$767$	7.05763	0.254836
$768$	16.1126	0.581414
$769$	−18.9019	−0.681619	−0.340810	−	0.940132i	$-0.610701\pi$
$769$	−18.9019	−0.681619	−0.340810	+	0.940132i	$0.610701\pi$
$770$	0	0
$771$	30.4560	1.09685
$772$	−24.6454	−0.887006
$773$	8.27540	0.297645	0.148823	−	0.988864i	$-0.452452\pi$
$773$	8.27540	0.297645	0.148823	+	0.988864i	$0.452452\pi$
$774$	−2.06707	−0.0742994
$775$	45.6885	1.64118
$776$	−12.9612	−0.465282
$777$	47.3977	1.70038
$778$	−9.11526	−0.326798
$779$	−4.79191	−0.171688
$780$	0	0
$781$	15.8847	0.568401
$782$	−13.9551	−0.499034
$783$	11.2530	0.402148
$784$	−0.641213	−0.0229005
$785$	0	0
$786$	−6.01979	−0.214719
$787$	1.74877	0.0623370	0.0311685	−	0.999514i	$-0.490077\pi$
$787$	1.74877	0.0623370	0.0311685	+	0.999514i	$0.490077\pi$
$788$	−24.9829	−0.889977
$789$	5.13264	0.182727
$790$	0	0
$791$	−52.0647	−1.85121
$792$	−9.09721	−0.323255
$793$	6.51122	0.231220
$794$	1.69008	0.0599787
$795$	0	0
$796$	10.6040	0.375850
$797$	−27.5457	−0.975720	−0.487860	−	0.872922i	$-0.662222\pi$
$797$	−27.5457	−0.975720	−0.487860	+	0.872922i	$0.662222\pi$
$798$	12.9019	0.456722
$799$	54.0242	1.91124
$800$	−28.6834	−1.01411
$801$	−4.16013	−0.146991
$802$	20.9639	0.740261
$803$	90.0165	3.17661
$804$	19.5568	0.689714
$805$	0	0
$806$	−19.5337	−0.688044
$807$	45.7488	1.61043
$808$	39.7488	1.39836
$809$	7.41310	0.260631	0.130315	−	0.991473i	$-0.458401\pi$
$809$	7.41310	0.260631	0.130315	+	0.991473i	$0.458401\pi$
$810$	0	0
$811$	6.04487	0.212264	0.106132	−	0.994352i	$-0.466153\pi$
$811$	6.04487	0.212264	0.106132	+	0.994352i	$0.466153\pi$
$812$	10.1206	0.355162
$813$	−27.5035	−0.964590
$814$	37.4580	1.31290
$815$	0	0
$816$	−16.2459	−0.568722
$817$	−19.1773	−0.670928
$818$	−5.27895	−0.184574
$819$	−5.49143	−0.191886
$820$	0	0
$821$	−2.25123	−0.0785683	−0.0392842	−	0.999228i	$-0.512508\pi$
$821$	−2.25123	−0.0785683	−0.0392842	+	0.999228i	$0.512508\pi$
$822$	−16.7162	−0.583045
$823$	−41.4030	−1.44322	−0.721609	−	0.692301i	$-0.756597\pi$
$823$	−41.4030	−1.44322	−0.721609	+	0.692301i	$0.756597\pi$
$824$	46.6902	1.62653
$825$	56.5277	1.96804
$826$	−3.65662	−0.127230
$827$	2.07568	0.0721786	0.0360893	−	0.999349i	$-0.488510\pi$
$827$	2.07568	0.0721786	0.0360893	+	0.999349i	$0.488510\pi$
$828$	4.12055	0.143199
$829$	−11.2530	−0.390832	−0.195416	−	0.980720i	$-0.562606\pi$
$829$	−11.2530	−0.390832	−0.195416	+	0.980720i	$0.562606\pi$
$830$	0	0
$831$	−12.6714	−0.439564
$832$	1.85195	0.0642049
$833$	−2.13067	−0.0738234
$834$	−24.2305	−0.839035
$835$	0	0
$836$	−37.1016	−1.28319
$837$	−40.9468	−1.41533
$838$	18.9674	0.655220
$839$	16.6445	0.574633	0.287317	−	0.957836i	$-0.407237\pi$
$839$	16.6445	0.574633	0.287317	+	0.957836i	$0.407237\pi$
$840$	0	0
$841$	−22.6938	−0.782544
$842$	19.6936	0.678685
$843$	8.40607	0.289520
$844$	25.6282	0.882160
$845$	0	0
$846$	4.38387	0.150720
$847$	−61.5354	−2.11438
$848$	19.7246	0.677346
$849$	−9.16784	−0.314639
$850$	−17.4439	−0.598321
$851$	−38.5957	−1.32304
$852$	8.06028	0.276141
$853$	−0.744391	−0.0254875	−0.0127437	−	0.999919i	$-0.504057\pi$
$853$	−0.744391	−0.0254875	−0.0127437	+	0.999919i	$0.504057\pi$
$854$	−3.37352	−0.115439
$855$	0	0
$856$	27.2978	0.933021
$857$	2.72966	0.0932434	0.0466217	−	0.998913i	$-0.485154\pi$
$857$	2.72966	0.0932434	0.0466217	+	0.998913i	$0.485154\pi$
$858$	−24.1678	−0.825076
$859$	−39.6335	−1.35228	−0.676139	−	0.736774i	$-0.736348\pi$
$859$	−39.6335	−1.35228	−0.676139	+	0.736774i	$0.736348\pi$
$860$	0	0
$861$	−5.88474	−0.200551
$862$	6.02946	0.205364
$863$	17.8486	0.607574	0.303787	−	0.952740i	$-0.401749\pi$
$863$	17.8486	0.607574	0.303787	+	0.952740i	$0.401749\pi$
$864$	25.7065	0.874555
$865$	0	0
$866$	−21.7798	−0.740108
$867$	−21.4753	−0.729341
$868$	−36.8262	−1.24996
$869$	−68.5303	−2.32473
$870$	0	0
$871$	21.2231	0.719116
$872$	−9.64363	−0.326574
$873$	3.63177	0.122917
$874$	−10.5059	−0.355368
$875$	0	0
$876$	45.6764	1.54326
$877$	−35.5578	−1.20070	−0.600351	−	0.799736i	$-0.704973\pi$
$877$	−35.5578	−1.20070	−0.600351	+	0.799736i	$0.704973\pi$
$878$	−2.02070	−0.0681953
$879$	3.16784	0.106849
$880$	0	0
$881$	8.73933	0.294436	0.147218	−	0.989104i	$-0.452968\pi$
$881$	8.73933	0.294436	0.147218	+	0.989104i	$0.452968\pi$
$882$	−0.172896	−0.00582172
$883$	−17.9364	−0.603608	−0.301804	−	0.953370i	$-0.597589\pi$
$883$	−17.9364	−0.603608	−0.301804	+	0.953370i	$0.597589\pi$
$884$	−27.1377	−0.912740
$885$	0	0
$886$	5.50110	0.184813
$887$	35.2694	1.18423	0.592116	−	0.805853i	$-0.298293\pi$
$887$	35.2694	1.18423	0.592116	+	0.805853i	$0.298293\pi$
$888$	43.2376	1.45096
$889$	−38.7316	−1.29902
$890$	0	0
$891$	−62.3073	−2.08737
$892$	34.1016	1.14181
$893$	40.6714	1.36101
$894$	−5.88474	−0.196815
$895$	0	0
$896$	28.5139	0.952581
$897$	24.9019	0.831450
$898$	−15.4131	−0.514342
$899$	−22.9468	−0.765317
$900$	5.15069	0.171690
$901$	65.5424	2.18353
$902$	−4.65065	−0.154850
$903$	−23.5508	−0.783721
$904$	−47.4949	−1.57966
$905$	0	0
$906$	−24.7967	−0.823816
$907$	30.3960	1.00928	0.504641	−	0.863330i	$-0.331625\pi$
$907$	30.3960	1.00928	0.504641	+	0.863330i	$0.331625\pi$
$908$	−11.0171	−0.365617
$909$	−11.1377	−0.369414
$910$	0	0
$911$	22.0550	0.730714	0.365357	−	0.930867i	$-0.380947\pi$
$911$	22.0550	0.730714	0.365357	+	0.930867i	$0.380947\pi$
$912$	−12.2305	−0.404993
$913$	15.1876	0.502637
$914$	−1.90543	−0.0630261
$915$	0	0
$916$	−10.8401	−0.358167
$917$	−12.3159	−0.406706
$918$	15.6335	0.515983
$919$	−7.35547	−0.242634	−0.121317	−	0.992614i	$-0.538712\pi$
$919$	−7.35547	−0.242634	−0.121317	+	0.992614i	$0.538712\pi$
$920$	0	0
$921$	−36.4509	−1.20110
$922$	−5.81917	−0.191644
$923$	8.74704	0.287912
$924$	−45.5629	−1.49891
$925$	−48.2446	−1.58627
$926$	−3.06730	−0.100798
$927$	−13.0827	−0.429693
$928$	14.4061	0.472902
$929$	−15.3735	−0.504389	−0.252194	−	0.967677i	$-0.581152\pi$
$929$	−15.3735	−0.504389	−0.252194	+	0.967677i	$0.581152\pi$
$930$	0	0
$931$	−1.60405	−0.0525705
$932$	−8.81917	−0.288881
$933$	−19.5732	−0.640799
$934$	11.4734	0.375420
$935$	0	0
$936$	−5.00944	−0.163739
$937$	−23.6335	−0.772073	−0.386037	−	0.922483i	$-0.626156\pi$
$937$	−23.6335	−0.772073	−0.386037	+	0.922483i	$0.626156\pi$
$938$	−10.9958	−0.359027
$939$	48.9313	1.59681
$940$	0	0
$941$	26.9045	0.877062	0.438531	−	0.898716i	$-0.355499\pi$
$941$	26.9045	0.877062	0.438531	+	0.898716i	$0.355499\pi$
$942$	−1.86933	−0.0609060
$943$	4.79191	0.156046
$944$	3.46635	0.112820
$945$	0	0
$946$	−18.6120	−0.605128
$947$	−0.611074	−0.0198572	−0.00992862	−	0.999951i	$-0.503160\pi$
$947$	−0.611074	−0.0198572	−0.00992862	+	0.999951i	$0.503160\pi$
$948$	−34.7739	−1.12940
$949$	49.5682	1.60905
$950$	−13.1324	−0.426072
$951$	54.7257	1.77460
$952$	31.9846	1.03663
$953$	35.2453	1.14171	0.570853	−	0.821052i	$-0.306613\pi$
$953$	35.2453	1.14171	0.570853	+	0.821052i	$0.306613\pi$
$954$	5.31853	0.172194
$955$	0	0
$956$	5.56794	0.180080
$957$	−28.3907	−0.917740
$958$	−3.83458	−0.123890
$959$	−34.1997	−1.10437
$960$	0	0
$961$	52.4975	1.69347
$962$	20.6265	0.665024
$963$	−7.64892	−0.246483
$964$	14.0603	0.452851
$965$	0	0
$966$	−12.9019	−0.415111
$967$	−4.81743	−0.154918	−0.0774591	−	0.996996i	$-0.524681\pi$
$967$	−4.81743	−0.154918	−0.0774591	+	0.996996i	$0.524681\pi$
$968$	−56.1344	−1.80423
$969$	−40.6405	−1.30556
$970$	0	0
$971$	−42.2754	−1.35668	−0.678341	−	0.734747i	$-0.737301\pi$
$971$	−42.2754	−1.35668	−0.678341	+	0.734747i	$0.737301\pi$
$972$	−10.5257	−0.337613
$973$	−49.5732	−1.58924
$974$	−21.8346	−0.699625
$975$	31.1274	0.996873
$976$	3.19798	0.102365
$977$	−2.45335	−0.0784897	−0.0392449	−	0.999230i	$-0.512495\pi$
$977$	−2.45335	−0.0784897	−0.0392449	+	0.999230i	$0.512495\pi$
$978$	9.82446	0.314152
$979$	−37.4580	−1.19716
$980$	0	0
$981$	2.70217	0.0862735
$982$	−16.2257	−0.517783
$983$	−6.39066	−0.203830	−0.101915	−	0.994793i	$-0.532497\pi$
$983$	−6.39066	−0.203830	−0.101915	+	0.994793i	$0.532497\pi$
$984$	−5.36823	−0.171133
$985$	0	0
$986$	8.76109	0.279010
$987$	49.9468	1.58982
$988$	−20.4302	−0.649973
$989$	19.1773	0.609802
$990$	0	0
$991$	12.7143	0.403882	0.201941	−	0.979398i	$-0.435275\pi$
$991$	12.7143	0.403882	0.201941	+	0.979398i	$0.435275\pi$
$992$	−52.4201	−1.66434
$993$	−16.4958	−0.523479
$994$	−4.53192	−0.143744
$995$	0	0
$996$	7.70655	0.244191
$997$	42.3651	1.34172	0.670859	−	0.741585i	$-0.265926\pi$
$997$	42.3651	1.34172	0.670859	+	0.741585i	$0.265926\pi$
$998$	−1.46461	−0.0463614
$999$	43.2376	1.36798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.d.1.2	✓	3
3.2	odd	2		4527.2.a.j.1.2		3
4.3	odd	2		8048.2.a.m.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.d.1.2	✓	3	1.1	even	1	trivial
4527.2.a.j.1.2		3	3.2	odd	2
8048.2.a.m.1.3		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q+0.656620 q^{2} -1.91223 q^{3} -1.56885 q^{4} -1.25561 q^{6} -2.56885 q^{7} -2.34338 q^{8} +0.656620 q^{9} +O(q^{10})\)	\(q+0.656620 q^{2} -1.91223 q^{3} -1.56885 q^{4} -1.25561 q^{6} -2.56885 q^{7} -2.34338 q^{8} +0.656620 q^{9} +5.91223 q^{11} +3.00000 q^{12} +3.25561 q^{13} -1.68676 q^{14} +1.59899 q^{16} +5.31324 q^{17} +0.431150 q^{18} +4.00000 q^{19} +4.91223 q^{21} +3.88209 q^{22} -4.00000 q^{23} +4.48108 q^{24} -5.00000 q^{25} +2.13770 q^{26} +4.48108 q^{27} +4.03014 q^{28} +2.51122 q^{29} -9.13770 q^{31} +5.73669 q^{32} -11.3055 q^{33} +3.48878 q^{34} -1.03014 q^{36} +9.64892 q^{37} +2.62648 q^{38} -6.22547 q^{39} -1.19798 q^{41} +3.22547 q^{42} -4.79432 q^{43} -9.27540 q^{44} -2.62648 q^{46} +10.1678 q^{47} -3.05763 q^{48} -0.401012 q^{49} -3.28310 q^{50} -10.1601 q^{51} -5.10756 q^{52} +12.3357 q^{53} +2.94237 q^{54} +6.01979 q^{56} -7.64892 q^{57} +1.64892 q^{58} +2.16784 q^{59} +2.00000 q^{61} -6.00000 q^{62} -1.68676 q^{63} +0.568850 q^{64} -7.42345 q^{66} +6.51892 q^{67} -8.33568 q^{68} +7.64892 q^{69} +2.68676 q^{71} -1.53871 q^{72} +15.2255 q^{73} +6.33568 q^{74} +9.56115 q^{75} -6.27540 q^{76} -15.1876 q^{77} -4.08777 q^{78} -11.5913 q^{79} -10.5387 q^{81} -0.786616 q^{82} +2.56885 q^{83} -7.70655 q^{84} -3.14805 q^{86} -4.80202 q^{87} -13.8546 q^{88} -6.33568 q^{89} -8.36317 q^{91} +6.27540 q^{92} +17.4734 q^{93} +6.67641 q^{94} -10.9699 q^{96} +5.53101 q^{97} -0.263312 q^{98} +3.88209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{3} + 4 q^{4} + q^{6} + q^{7} - 9 q^{8}+O(q^{10}) \) 3 * q + q^3 + 4 * q^4 + q^6 + q^7 - 9 * q^8	\( 3 q + q^{3} + 4 q^{4} + q^{6} + q^{7} - 9 q^{8} + 11 q^{11} + 9 q^{12} + 5 q^{13} - 9 q^{14} + 2 q^{16} + 12 q^{17} + 10 q^{18} + 12 q^{19} + 8 q^{21} - q^{22} - 12 q^{23} - 2 q^{24} - 15 q^{25} - 11 q^{26} - 2 q^{27} + 18 q^{28} - 2 q^{29} - 10 q^{31} - 3 q^{32} - 5 q^{33} + 20 q^{34} - 9 q^{36} + 2 q^{37} - 8 q^{39} + 2 q^{41} - q^{42} + 5 q^{43} + 7 q^{44} + 19 q^{47} - 10 q^{48} - 4 q^{49} + 6 q^{51} + 8 q^{52} + 14 q^{53} + 8 q^{54} - 12 q^{56} + 4 q^{57} - 22 q^{58} - 5 q^{59} + 6 q^{61} - 18 q^{62} - 9 q^{63} - 7 q^{64} - 6 q^{66} + 35 q^{67} - 2 q^{68} - 4 q^{69} + 12 q^{71} + 10 q^{72} + 35 q^{73} - 4 q^{74} - 5 q^{75} + 16 q^{76} - 4 q^{77} - 19 q^{78} - 7 q^{79} - 17 q^{81} + 42 q^{82} - q^{83} + 3 q^{84} - 28 q^{86} - 20 q^{87} - 34 q^{88} + 4 q^{89} + 3 q^{91} - 16 q^{92} + 12 q^{93} - 12 q^{94} - 27 q^{96} - 23 q^{97} - 21 q^{98} - q^{99}+O(q^{100}) \) 3 * q + q^3 + 4 * q^4 + q^6 + q^7 - 9 * q^8 + 11 * q^11 + 9 * q^12 + 5 * q^13 - 9 * q^14 + 2 * q^16 + 12 * q^17 + 10 * q^18 + 12 * q^19 + 8 * q^21 - q^22 - 12 * q^23 - 2 * q^24 - 15 * q^25 - 11 * q^26 - 2 * q^27 + 18 * q^28 - 2 * q^29 - 10 * q^31 - 3 * q^32 - 5 * q^33 + 20 * q^34 - 9 * q^36 + 2 * q^37 - 8 * q^39 + 2 * q^41 - q^42 + 5 * q^43 + 7 * q^44 + 19 * q^47 - 10 * q^48 - 4 * q^49 + 6 * q^51 + 8 * q^52 + 14 * q^53 + 8 * q^54 - 12 * q^56 + 4 * q^57 - 22 * q^58 - 5 * q^59 + 6 * q^61 - 18 * q^62 - 9 * q^63 - 7 * q^64 - 6 * q^66 + 35 * q^67 - 2 * q^68 - 4 * q^69 + 12 * q^71 + 10 * q^72 + 35 * q^73 - 4 * q^74 - 5 * q^75 + 16 * q^76 - 4 * q^77 - 19 * q^78 - 7 * q^79 - 17 * q^81 + 42 * q^82 - q^83 + 3 * q^84 - 28 * q^86 - 20 * q^87 - 34 * q^88 + 4 * q^89 + 3 * q^91 - 16 * q^92 + 12 * q^93 - 12 * q^94 - 27 * q^96 - 23 * q^97 - 21 * q^98 - q^99

Introduction

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