LMFDB - Embedded newform 1183.2.a.r.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(1,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} + \cdots + 29 $ x^12 - 3x^11 - 15x^10 + 46x^9 + 80x^8 - 246x^7 - 199x^6 + 562x^5 + 262x^4 - 542x^3 - 157x^2 + 183*x + 29
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.23724$ of defining polynomial
Character	$\chi$	$=$	1183.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.23724 q^{2} +3.02592 q^{3} +3.00523 q^{4} -3.28547 q^{5} +6.76971 q^{6} +1.00000 q^{7} +2.24893 q^{8} +6.15622 q^{9} +O(q^{10})$	\(q+2.23724 q^{2} +3.02592 q^{3} +3.00523 q^{4} -3.28547 q^{5} +6.76971 q^{6} +1.00000 q^{7} +2.24893 q^{8} +6.15622 q^{9} -7.35037 q^{10} +3.69978 q^{11} +9.09359 q^{12} +2.23724 q^{14} -9.94158 q^{15} -0.979066 q^{16} +0.705252 q^{17} +13.7729 q^{18} +0.911595 q^{19} -9.87358 q^{20} +3.02592 q^{21} +8.27729 q^{22} -3.01033 q^{23} +6.80509 q^{24} +5.79431 q^{25} +9.55048 q^{27} +3.00523 q^{28} +6.55076 q^{29} -22.2417 q^{30} -9.55811 q^{31} -6.68826 q^{32} +11.1953 q^{33} +1.57782 q^{34} -3.28547 q^{35} +18.5008 q^{36} -7.26452 q^{37} +2.03945 q^{38} -7.38879 q^{40} +0.884807 q^{41} +6.76971 q^{42} +0.536043 q^{43} +11.1187 q^{44} -20.2261 q^{45} -6.73483 q^{46} -11.4085 q^{47} -2.96258 q^{48} +1.00000 q^{49} +12.9633 q^{50} +2.13404 q^{51} +3.77189 q^{53} +21.3667 q^{54} -12.1555 q^{55} +2.24893 q^{56} +2.75842 q^{57} +14.6556 q^{58} -7.40281 q^{59} -29.8767 q^{60} -1.81991 q^{61} -21.3838 q^{62} +6.15622 q^{63} -13.0051 q^{64} +25.0465 q^{66} +6.41024 q^{67} +2.11944 q^{68} -9.10904 q^{69} -7.35037 q^{70} +10.7248 q^{71} +13.8449 q^{72} +9.72504 q^{73} -16.2524 q^{74} +17.5332 q^{75} +2.73955 q^{76} +3.69978 q^{77} -7.00757 q^{79} +3.21669 q^{80} +10.4304 q^{81} +1.97952 q^{82} -2.31514 q^{83} +9.09359 q^{84} -2.31709 q^{85} +1.19925 q^{86} +19.8221 q^{87} +8.32055 q^{88} -2.23203 q^{89} -45.2505 q^{90} -9.04673 q^{92} -28.9221 q^{93} -25.5235 q^{94} -2.99502 q^{95} -20.2382 q^{96} +8.79590 q^{97} +2.23724 q^{98} +22.7767 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * 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 $

$2$	2.23724	1.58197	0.790983	−	0.611839i	$-0.209570\pi$
$2$	2.23724	1.58197	0.790983	+	0.611839i	$0.209570\pi$
$3$	3.02592	1.74702	0.873509	−	0.486808i	$-0.161839\pi$
$3$	3.02592	1.74702	0.873509	+	0.486808i	$0.161839\pi$
$4$	3.00523	1.50261
$5$	−3.28547	−1.46931	−0.734653	−	0.678443i	$-0.762655\pi$
$5$	−3.28547	−1.46931	−0.734653	+	0.678443i	$0.762655\pi$
$6$	6.76971	2.76372
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.24893	0.795117
$9$	6.15622	2.05207
$10$	−7.35037	−2.32439
$11$	3.69978	1.11553	0.557763	−	0.830000i	$-0.311660\pi$
$11$	3.69978	1.11553	0.557763	+	0.830000i	$0.311660\pi$
$12$	9.09359	2.62509
$13$	0	0
$13$	0	0
$14$	2.23724	0.597927
$15$	−9.94158	−2.56691
$16$	−0.979066	−0.244766
$17$	0.705252	0.171049	0.0855244	−	0.996336i	$-0.472743\pi$
$17$	0.705252	0.171049	0.0855244	+	0.996336i	$0.472743\pi$
$18$	13.7729	3.24631
$19$	0.911595	0.209134	0.104567	−	0.994518i	$-0.466654\pi$
$19$	0.911595	0.209134	0.104567	+	0.994518i	$0.466654\pi$
$20$	−9.87358	−2.20780
$21$	3.02592	0.660311
$22$	8.27729	1.76472
$23$	−3.01033	−0.627698	−0.313849	−	0.949473i	$-0.601619\pi$
$23$	−3.01033	−0.627698	−0.313849	+	0.949473i	$0.601619\pi$
$24$	6.80509	1.38908
$25$	5.79431	1.15886
$26$	0	0
$27$	9.55048	1.83799
$28$	3.00523	0.567934
$29$	6.55076	1.21645	0.608223	−	0.793767i	$-0.291883\pi$
$29$	6.55076	1.21645	0.608223	+	0.793767i	$0.291883\pi$
$30$	−22.2417	−4.06076
$31$	−9.55811	−1.71669	−0.858344	−	0.513075i	$-0.828506\pi$
$31$	−9.55811	−1.71669	−0.858344	+	0.513075i	$0.828506\pi$
$32$	−6.68826	−1.18233
$33$	11.1953	1.94885
$34$	1.57782	0.270593
$35$	−3.28547	−0.555346
$36$	18.5008	3.08347
$37$	−7.26452	−1.19428	−0.597140	−	0.802137i	$-0.703696\pi$
$37$	−7.26452	−1.19428	−0.597140	+	0.802137i	$0.703696\pi$
$38$	2.03945	0.330843
$39$	0	0
$40$	−7.38879	−1.16827
$41$	0.884807	0.138184	0.0690918	−	0.997610i	$-0.477990\pi$
$41$	0.884807	0.138184	0.0690918	+	0.997610i	$0.477990\pi$
$42$	6.76971	1.04459
$43$	0.536043	0.0817458	0.0408729	−	0.999164i	$-0.486986\pi$
$43$	0.536043	0.0817458	0.0408729	+	0.999164i	$0.486986\pi$
$44$	11.1187	1.67621
$45$	−20.2261	−3.01512
$46$	−6.73483	−0.992996
$47$	−11.4085	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$47$	−11.4085	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$48$	−2.96258	−0.427611
$49$	1.00000	0.142857
$50$	12.9633	1.83328
$51$	2.13404	0.298825
$52$	0	0
$53$	3.77189	0.518109	0.259054	−	0.965863i	$-0.416589\pi$
$53$	3.77189	0.518109	0.259054	+	0.965863i	$0.416589\pi$
$54$	21.3667	2.90764
$55$	−12.1555	−1.63905
$56$	2.24893	0.300526
$57$	2.75842	0.365361
$58$	14.6556	1.92437
$59$	−7.40281	−0.963764	−0.481882	−	0.876236i	$-0.660047\pi$
$59$	−7.40281	−0.963764	−0.481882	+	0.876236i	$0.660047\pi$
$60$	−29.8767	−3.85707
$61$	−1.81991	−0.233015	−0.116508	−	0.993190i	$-0.537170\pi$
$61$	−1.81991	−0.233015	−0.116508	+	0.993190i	$0.537170\pi$
$62$	−21.3838	−2.71574
$63$	6.15622	0.775611
$64$	−13.0051	−1.62564
$65$	0	0
$66$	25.0465	3.08301
$67$	6.41024	0.783135	0.391568	−	0.920149i	$-0.371933\pi$
$67$	6.41024	0.783135	0.391568	+	0.920149i	$0.371933\pi$
$68$	2.11944	0.257020
$69$	−9.10904	−1.09660
$70$	−7.35037	−0.878538
$71$	10.7248	1.27280	0.636402	−	0.771357i	$-0.280422\pi$
$71$	10.7248	1.27280	0.636402	+	0.771357i	$0.280422\pi$
$72$	13.8449	1.63164
$73$	9.72504	1.13823	0.569115	−	0.822258i	$-0.307286\pi$
$73$	9.72504	1.13823	0.569115	+	0.822258i	$0.307286\pi$
$74$	−16.2524	−1.88931
$75$	17.5332	2.02455
$76$	2.73955	0.314248
$77$	3.69978	0.421630
$78$	0	0
$79$	−7.00757	−0.788414	−0.394207	−	0.919022i	$-0.628981\pi$
$79$	−7.00757	−0.788414	−0.394207	+	0.919022i	$0.628981\pi$
$80$	3.21669	0.359637
$81$	10.4304	1.15893
$82$	1.97952	0.218602
$83$	−2.31514	−0.254120	−0.127060	−	0.991895i	$-0.540554\pi$
$83$	−2.31514	−0.254120	−0.127060	+	0.991895i	$0.540554\pi$
$84$	9.09359	0.992192
$85$	−2.31709	−0.251323
$86$	1.19925	0.129319
$87$	19.8221	2.12515
$88$	8.32055	0.886974
$89$	−2.23203	−0.236595	−0.118297	−	0.992978i	$-0.537744\pi$
$89$	−2.23203	−0.236595	−0.118297	+	0.992978i	$0.537744\pi$
$90$	−45.2505	−4.76982
$91$	0	0
$92$	−9.04673	−0.943187
$93$	−28.9221	−2.99908
$94$	−25.5235	−2.63255
$95$	−2.99502	−0.307283
$96$	−20.2382	−2.06555
$97$	8.79590	0.893088	0.446544	−	0.894762i	$-0.352655\pi$
$97$	8.79590	0.893088	0.446544	+	0.894762i	$0.352655\pi$
$98$	2.23724	0.225995
$99$	22.7767	2.28914
$100$	17.4132	1.74132
$101$	8.54632	0.850391	0.425195	−	0.905102i	$-0.360205\pi$
$101$	8.54632	0.850391	0.425195	+	0.905102i	$0.360205\pi$
$102$	4.77435	0.472731
$103$	−13.7298	−1.35284	−0.676420	−	0.736516i	$-0.736469\pi$
$103$	−13.7298	−1.35284	−0.676420	+	0.736516i	$0.736469\pi$
$104$	0	0
$105$	−9.94158	−0.970199
$106$	8.43860	0.819630
$107$	−17.4965	−1.69145	−0.845725	−	0.533620i	$-0.820831\pi$
$107$	−17.4965	−1.69145	−0.845725	+	0.533620i	$0.820831\pi$
$108$	28.7013	2.76179
$109$	6.94941	0.665633	0.332816	−	0.942992i	$-0.392001\pi$
$109$	6.94941	0.665633	0.332816	+	0.942992i	$0.392001\pi$
$110$	−27.1948	−2.59292
$111$	−21.9819	−2.08643
$112$	−0.979066	−0.0925130
$113$	−2.83036	−0.266258	−0.133129	−	0.991099i	$-0.542502\pi$
$113$	−2.83036	−0.266258	−0.133129	+	0.991099i	$0.542502\pi$
$114$	6.17123	0.577989
$115$	9.89036	0.922281
$116$	19.6865	1.82785
$117$	0	0
$118$	−16.5618	−1.52464
$119$	0.705252	0.0646504
$120$	−22.3579	−2.04099
$121$	2.68840	0.244400
$122$	−4.07156	−0.368622
$123$	2.67736	0.241409
$124$	−28.7243	−2.57952
$125$	−2.60969	−0.233418
$126$	13.7729	1.22699
$127$	3.59346	0.318868	0.159434	−	0.987209i	$-0.449033\pi$
$127$	3.59346	0.318868	0.159434	+	0.987209i	$0.449033\pi$
$128$	−15.7189	−1.38937
$129$	1.62202	0.142811
$130$	0	0
$131$	1.05865	0.0924943	0.0462471	−	0.998930i	$-0.485274\pi$
$131$	1.05865	0.0924943	0.0462471	+	0.998930i	$0.485274\pi$
$132$	33.6443	2.92836
$133$	0.911595	0.0790454
$134$	14.3412	1.23889
$135$	−31.3778	−2.70057
$136$	1.58606	0.136004
$137$	−8.29848	−0.708987	−0.354494	−	0.935058i	$-0.615347\pi$
$137$	−8.29848	−0.708987	−0.354494	+	0.935058i	$0.615347\pi$
$138$	−20.3791	−1.73478
$139$	−7.02640	−0.595971	−0.297986	−	0.954570i	$-0.596315\pi$
$139$	−7.02640	−0.595971	−0.297986	+	0.954570i	$0.596315\pi$
$140$	−9.87358	−0.834470
$141$	−34.5213	−2.90721
$142$	23.9940	2.01353
$143$	0	0
$144$	−6.02734	−0.502278
$145$	−21.5223	−1.78733
$146$	21.7572	1.80064
$147$	3.02592	0.249574
$148$	−21.8315	−1.79454
$149$	−7.93264	−0.649867	−0.324934	−	0.945737i	$-0.605342\pi$
$149$	−7.93264	−0.649867	−0.324934	+	0.945737i	$0.605342\pi$
$150$	39.2258	3.20277
$151$	21.1019	1.71725	0.858625	−	0.512604i	$-0.171319\pi$
$151$	21.1019	1.71725	0.858625	+	0.512604i	$0.171319\pi$
$152$	2.05011	0.166286
$153$	4.34169	0.351005
$154$	8.27729	0.667003
$155$	31.4029	2.52234
$156$	0	0
$157$	4.49489	0.358732	0.179366	−	0.983782i	$-0.442595\pi$
$157$	4.49489	0.358732	0.179366	+	0.983782i	$0.442595\pi$
$158$	−15.6776	−1.24724
$159$	11.4134	0.905145
$160$	21.9741	1.73720
$161$	−3.01033	−0.237247
$162$	23.3352	1.83339
$163$	2.10111	0.164572	0.0822860	−	0.996609i	$-0.473778\pi$
$163$	2.10111	0.164572	0.0822860	+	0.996609i	$0.473778\pi$
$164$	2.65904	0.207637
$165$	−36.7817	−2.86345
$166$	−5.17951	−0.402008
$167$	12.6092	0.975727	0.487863	−	0.872920i	$-0.337776\pi$
$167$	12.6092	0.975727	0.487863	+	0.872920i	$0.337776\pi$
$168$	6.80509	0.525024
$169$	0	0
$170$	−5.18387	−0.397584
$171$	5.61198	0.429159
$172$	1.61093	0.122832
$173$	3.96895	0.301754	0.150877	−	0.988553i	$-0.451790\pi$
$173$	3.96895	0.301754	0.150877	+	0.988553i	$0.451790\pi$
$174$	44.3467	3.36192
$175$	5.79431	0.438009
$176$	−3.62233	−0.273044
$177$	−22.4003	−1.68371
$178$	−4.99357	−0.374284
$179$	23.6790	1.76985	0.884926	−	0.465731i	$-0.154209\pi$
$179$	23.6790	1.76985	0.884926	+	0.465731i	$0.154209\pi$
$180$	−60.7839	−4.53057
$181$	−24.6397	−1.83145	−0.915727	−	0.401801i	$-0.868384\pi$
$181$	−24.6397	−1.83145	−0.915727	+	0.401801i	$0.868384\pi$
$182$	0	0
$183$	−5.50690	−0.407082
$184$	−6.77003	−0.499093
$185$	23.8674	1.75476
$186$	−64.7056	−4.74445
$187$	2.60928	0.190810
$188$	−34.2851	−2.50050
$189$	9.55048	0.694695
$190$	−6.70057	−0.486110
$191$	2.98048	0.215660	0.107830	−	0.994169i	$-0.465610\pi$
$191$	2.98048	0.215660	0.107830	+	0.994169i	$0.465610\pi$
$192$	−39.3524	−2.84002
$193$	−17.5119	−1.26053	−0.630266	−	0.776379i	$-0.717054\pi$
$193$	−17.5119	−1.26053	−0.630266	+	0.776379i	$0.717054\pi$
$194$	19.6785	1.41283
$195$	0	0
$196$	3.00523	0.214659
$197$	19.6212	1.39795	0.698976	−	0.715145i	$-0.253639\pi$
$197$	19.6212	1.39795	0.698976	+	0.715145i	$0.253639\pi$
$198$	50.9568	3.62134
$199$	−24.8307	−1.76020	−0.880102	−	0.474784i	$-0.842526\pi$
$199$	−24.8307	−1.76020	−0.880102	+	0.474784i	$0.842526\pi$
$200$	13.0310	0.921431
$201$	19.3969	1.36815
$202$	19.1201	1.34529
$203$	6.55076	0.459773
$204$	6.41327	0.449019
$205$	−2.90701	−0.203034
$206$	−30.7169	−2.14014
$207$	−18.5323	−1.28808
$208$	0	0
$209$	3.37271	0.233295
$210$	−22.2417	−1.53482
$211$	−1.39982	−0.0963674	−0.0481837	−	0.998838i	$-0.515343\pi$
$211$	−1.39982	−0.0963674	−0.0481837	+	0.998838i	$0.515343\pi$
$212$	11.3354	0.778517
$213$	32.4526	2.22361
$214$	−39.1438	−2.67581
$215$	−1.76115	−0.120110
$216$	21.4783	1.46142
$217$	−9.55811	−0.648847
$218$	15.5475	1.05301
$219$	29.4272	1.98851
$220$	−36.5301	−2.46286
$221$	0	0
$222$	−49.1787	−3.30066
$223$	9.68552	0.648591	0.324295	−	0.945956i	$-0.394873\pi$
$223$	9.68552	0.648591	0.324295	+	0.945956i	$0.394873\pi$
$224$	−6.68826	−0.446878
$225$	35.6711	2.37807
$226$	−6.33219	−0.421211
$227$	23.2669	1.54428	0.772139	−	0.635454i	$-0.219187\pi$
$227$	23.2669	1.54428	0.772139	+	0.635454i	$0.219187\pi$
$228$	8.28967	0.548997
$229$	20.5801	1.35997	0.679987	−	0.733224i	$-0.261985\pi$
$229$	20.5801	1.35997	0.679987	+	0.733224i	$0.261985\pi$
$230$	22.1271	1.45902
$231$	11.1953	0.736594
$232$	14.7322	0.967216
$233$	27.2955	1.78819	0.894094	−	0.447880i	$-0.147821\pi$
$233$	27.2955	1.78819	0.894094	+	0.447880i	$0.147821\pi$
$234$	0	0
$235$	37.4823	2.44507
$236$	−22.2471	−1.44816
$237$	−21.2044	−1.37737
$238$	1.57782	0.102275
$239$	22.9752	1.48614	0.743070	−	0.669214i	$-0.233369\pi$
$239$	22.9752	1.48614	0.743070	+	0.669214i	$0.233369\pi$
$240$	9.73346	0.628292
$241$	−10.7263	−0.690939	−0.345469	−	0.938430i	$-0.612280\pi$
$241$	−10.7263	−0.690939	−0.345469	+	0.938430i	$0.612280\pi$
$242$	6.01459	0.386633
$243$	2.91006	0.186680
$244$	−5.46923	−0.350132
$245$	−3.28547	−0.209901
$246$	5.98988	0.381901
$247$	0	0
$248$	−21.4955	−1.36497
$249$	−7.00544	−0.443951
$250$	−5.83850	−0.369259
$251$	7.34076	0.463345	0.231672	−	0.972794i	$-0.425580\pi$
$251$	7.34076	0.463345	0.231672	+	0.972794i	$0.425580\pi$
$252$	18.5008	1.16544
$253$	−11.1376	−0.700214
$254$	8.03942	0.504438
$255$	−7.01132	−0.439066
$256$	−9.15680	−0.572300
$257$	14.9907	0.935092	0.467546	−	0.883969i	$-0.345138\pi$
$257$	14.9907	0.935092	0.467546	+	0.883969i	$0.345138\pi$
$258$	3.62885	0.225923
$259$	−7.26452	−0.451395
$260$	0	0
$261$	40.3279	2.49623
$262$	2.36844	0.146323
$263$	8.05245	0.496535	0.248268	−	0.968692i	$-0.420139\pi$
$263$	8.05245	0.496535	0.248268	+	0.968692i	$0.420139\pi$
$264$	25.1774	1.54956
$265$	−12.3924	−0.761261
$266$	2.03945	0.125047
$267$	−6.75395	−0.413335
$268$	19.2642	1.17675
$269$	−2.52431	−0.153910	−0.0769549	−	0.997035i	$-0.524520\pi$
$269$	−2.52431	−0.153910	−0.0769549	+	0.997035i	$0.524520\pi$
$270$	−70.1996	−4.27221
$271$	−0.785036	−0.0476875	−0.0238438	−	0.999716i	$-0.507590\pi$
$271$	−0.785036	−0.0476875	−0.0238438	+	0.999716i	$0.507590\pi$
$272$	−0.690488	−0.0418670
$273$	0	0
$274$	−18.5657	−1.12159
$275$	21.4377	1.29274
$276$	−27.3747	−1.64777
$277$	21.4193	1.28696	0.643482	−	0.765462i	$-0.277489\pi$
$277$	21.4193	1.28696	0.643482	+	0.765462i	$0.277489\pi$
$278$	−15.7197	−0.942806
$279$	−58.8418	−3.52277
$280$	−7.38879	−0.441565
$281$	22.3710	1.33454	0.667270	−	0.744816i	$-0.267463\pi$
$281$	22.3710	1.33454	0.667270	+	0.744816i	$0.267463\pi$
$282$	−77.2322	−4.59911
$283$	−24.8797	−1.47895	−0.739473	−	0.673186i	$-0.764925\pi$
$283$	−24.8797	−1.47895	−0.739473	+	0.673186i	$0.764925\pi$
$284$	32.2306	1.91253
$285$	−9.06270	−0.536828
$286$	0	0
$287$	0.884807	0.0522285
$288$	−41.1744	−2.42622
$289$	−16.5026	−0.970742
$290$	−48.1505	−2.82750
$291$	26.6157	1.56024
$292$	29.2259	1.71032
$293$	11.7686	0.687528	0.343764	−	0.939056i	$-0.388298\pi$
$293$	11.7686	0.687528	0.343764	+	0.939056i	$0.388298\pi$
$294$	6.76971	0.394817
$295$	24.3217	1.41607
$296$	−16.3374	−0.949591
$297$	35.3347	2.05033
$298$	−17.7472	−1.02807
$299$	0	0
$300$	52.6911	3.04212
$301$	0.536043	0.0308970
$302$	47.2100	2.71663
$303$	25.8605	1.48565
$304$	−0.892512	−0.0511891
$305$	5.97925	0.342371
$306$	9.71338	0.555277
$307$	20.3861	1.16350	0.581749	−	0.813368i	$-0.302369\pi$
$307$	20.3861	1.16350	0.581749	+	0.813368i	$0.302369\pi$
$308$	11.1187	0.633546
$309$	−41.5454	−2.36344
$310$	70.2557	3.99026
$311$	−11.6036	−0.657979	−0.328990	−	0.944334i	$-0.606708\pi$
$311$	−11.6036	−0.657979	−0.328990	+	0.944334i	$0.606708\pi$
$312$	0	0
$313$	6.91958	0.391118	0.195559	−	0.980692i	$-0.437348\pi$
$313$	6.91958	0.391118	0.195559	+	0.980692i	$0.437348\pi$
$314$	10.0561	0.567501
$315$	−20.2261	−1.13961
$316$	−21.0593	−1.18468
$317$	21.6606	1.21658	0.608290	−	0.793715i	$-0.291856\pi$
$317$	21.6606	1.21658	0.608290	+	0.793715i	$0.291856\pi$
$318$	25.5346	1.43191
$319$	24.2364	1.35698
$320$	42.7278	2.38856
$321$	−52.9430	−2.95499
$322$	−6.73483	−0.375317
$323$	0.642905	0.0357722
$324$	31.3456	1.74142
$325$	0	0
$326$	4.70069	0.260347
$327$	21.0284	1.16287
$328$	1.98987	0.109872
$329$	−11.4085	−0.628971
$330$	−82.2894	−4.52988
$331$	−23.6068	−1.29755	−0.648774	−	0.760981i	$-0.724718\pi$
$331$	−23.6068	−1.29755	−0.648774	+	0.760981i	$0.724718\pi$
$332$	−6.95752	−0.381843
$333$	−44.7219	−2.45075
$334$	28.2097	1.54357
$335$	−21.0607	−1.15067
$336$	−2.96258	−0.161622
$337$	−3.99359	−0.217544	−0.108772	−	0.994067i	$-0.534692\pi$
$337$	−3.99359	−0.217544	−0.108772	+	0.994067i	$0.534692\pi$
$338$	0	0
$339$	−8.56446	−0.465158
$340$	−6.96337	−0.377642
$341$	−35.3630	−1.91501
$342$	12.5553	0.678914
$343$	1.00000	0.0539949
$344$	1.20552	0.0649974
$345$	29.9275	1.61124
$346$	8.87948	0.477364
$347$	28.5043	1.53019	0.765095	−	0.643917i	$-0.222692\pi$
$347$	28.5043	1.53019	0.765095	+	0.643917i	$0.222692\pi$
$348$	59.5699	3.19328
$349$	−3.99439	−0.213815	−0.106907	−	0.994269i	$-0.534095\pi$
$349$	−3.99439	−0.213815	−0.106907	+	0.994269i	$0.534095\pi$
$350$	12.9633	0.692915
$351$	0	0
$352$	−24.7451	−1.31892
$353$	−24.1725	−1.28657	−0.643285	−	0.765627i	$-0.722429\pi$
$353$	−24.1725	−1.28657	−0.643285	+	0.765627i	$0.722429\pi$
$354$	−50.1149	−2.66358
$355$	−35.2361	−1.87014
$356$	−6.70775	−0.355510
$357$	2.13404	0.112945
$358$	52.9755	2.79984
$359$	−13.5039	−0.712709	−0.356355	−	0.934351i	$-0.615981\pi$
$359$	−13.5039	−0.712709	−0.356355	+	0.934351i	$0.615981\pi$
$360$	−45.4870	−2.39738
$361$	−18.1690	−0.956263
$362$	−55.1248	−2.89730
$363$	8.13490	0.426972
$364$	0	0
$365$	−31.9513	−1.67241
$366$	−12.3202	−0.643989
$367$	15.9888	0.834611	0.417306	−	0.908766i	$-0.362975\pi$
$367$	15.9888	0.834611	0.417306	+	0.908766i	$0.362975\pi$
$368$	2.94731	0.153639
$369$	5.44706	0.283563
$370$	53.3969	2.77597
$371$	3.77189	0.195827
$372$	−86.9176	−4.50647
$373$	24.5970	1.27358	0.636791	−	0.771036i	$-0.280261\pi$
$373$	24.5970	1.27358	0.636791	+	0.771036i	$0.280261\pi$
$374$	5.83758	0.301854
$375$	−7.89674	−0.407786
$376$	−25.6569	−1.32315
$377$	0	0
$378$	21.3667	1.09898
$379$	−8.07743	−0.414910	−0.207455	−	0.978245i	$-0.566518\pi$
$379$	−8.07743	−0.414910	−0.207455	+	0.978245i	$0.566518\pi$
$380$	−9.00071	−0.461727
$381$	10.8735	0.557068
$382$	6.66804	0.341167
$383$	3.45536	0.176561	0.0882803	−	0.996096i	$-0.471863\pi$
$383$	3.45536	0.176561	0.0882803	+	0.996096i	$0.471863\pi$
$384$	−47.5643	−2.42726
$385$	−12.1555	−0.619503
$386$	−39.1782	−1.99412
$387$	3.30000	0.167748
$388$	26.4337	1.34197
$389$	−23.6133	−1.19724	−0.598620	−	0.801033i	$-0.704284\pi$
$389$	−23.6133	−1.19724	−0.598620	+	0.801033i	$0.704284\pi$
$390$	0	0
$391$	−2.12304	−0.107367
$392$	2.24893	0.113588
$393$	3.20338	0.161589
$394$	43.8972	2.21151
$395$	23.0232	1.15842
$396$	68.4491	3.43970
$397$	−5.84404	−0.293304	−0.146652	−	0.989188i	$-0.546850\pi$
$397$	−5.84404	−0.293304	−0.146652	+	0.989188i	$0.546850\pi$
$398$	−55.5522	−2.78458
$399$	2.75842	0.138094
$400$	−5.67301	−0.283651
$401$	−25.0841	−1.25264	−0.626320	−	0.779566i	$-0.715440\pi$
$401$	−25.0841	−1.25264	−0.626320	+	0.779566i	$0.715440\pi$
$402$	43.3955	2.16437
$403$	0	0
$404$	25.6836	1.27781
$405$	−34.2686	−1.70282
$406$	14.6556	0.727345
$407$	−26.8771	−1.33225
$408$	4.79931	0.237601
$409$	0.157493	0.00778752	0.00389376	−	0.999992i	$-0.498761\pi$
$409$	0.157493	0.00778752	0.00389376	+	0.999992i	$0.498761\pi$
$410$	−6.50366	−0.321193
$411$	−25.1106	−1.23861
$412$	−41.2612	−2.03279
$413$	−7.40281	−0.364269
$414$	−41.4611	−2.03770
$415$	7.60632	0.373380
$416$	0	0
$417$	−21.2614	−1.04117
$418$	7.54554	0.369064
$419$	−6.94332	−0.339203	−0.169602	−	0.985513i	$-0.554248\pi$
$419$	−6.94332	−0.339203	−0.169602	+	0.985513i	$0.554248\pi$
$420$	−29.8767	−1.45783
$421$	−18.2428	−0.889100	−0.444550	−	0.895754i	$-0.646636\pi$
$421$	−18.2428	−0.889100	−0.444550	+	0.895754i	$0.646636\pi$
$422$	−3.13172	−0.152450
$423$	−70.2332	−3.41486
$424$	8.48271	0.411957
$425$	4.08645	0.198222
$426$	72.6040	3.51768
$427$	−1.81991	−0.0880715
$428$	−52.5809	−2.54159
$429$	0	0
$430$	−3.94011	−0.190009
$431$	−24.6803	−1.18881	−0.594404	−	0.804167i	$-0.702612\pi$
$431$	−24.6803	−1.18881	−0.594404	+	0.804167i	$0.702612\pi$
$432$	−9.35054	−0.449878
$433$	−8.18788	−0.393485	−0.196742	−	0.980455i	$-0.563036\pi$
$433$	−8.18788	−0.393485	−0.196742	+	0.980455i	$0.563036\pi$
$434$	−21.3838	−1.02645
$435$	−65.1249	−3.12250
$436$	20.8846	1.00019
$437$	−2.74421	−0.131273
$438$	65.8357	3.14575
$439$	28.8065	1.37486	0.687429	−	0.726252i	$-0.258739\pi$
$439$	28.8065	1.37486	0.687429	+	0.726252i	$0.258739\pi$
$440$	−27.3369	−1.30324
$441$	6.15622	0.293153
$442$	0	0
$443$	15.6483	0.743472	0.371736	−	0.928338i	$-0.378763\pi$
$443$	15.6483	0.743472	0.371736	+	0.928338i	$0.378763\pi$
$444$	−66.0605	−3.13509
$445$	7.33326	0.347630
$446$	21.6688	1.02605
$447$	−24.0036	−1.13533
$448$	−13.0051	−0.614433
$449$	18.0140	0.850131	0.425066	−	0.905163i	$-0.360251\pi$
$449$	18.0140	0.850131	0.425066	+	0.905163i	$0.360251\pi$
$450$	79.8046	3.76202
$451$	3.27359	0.154148
$452$	−8.50588	−0.400083
$453$	63.8528	3.00007
$454$	52.0535	2.44299
$455$	0	0
$456$	6.20349	0.290505
$457$	9.21009	0.430830	0.215415	−	0.976523i	$-0.430890\pi$
$457$	9.21009	0.430830	0.215415	+	0.976523i	$0.430890\pi$
$458$	46.0426	2.15143
$459$	6.73549	0.314386
$460$	29.7228	1.38583
$461$	−17.2980	−0.805648	−0.402824	−	0.915278i	$-0.631971\pi$
$461$	−17.2980	−0.805648	−0.402824	+	0.915278i	$0.631971\pi$
$462$	25.0465	1.16527
$463$	−17.9458	−0.834011	−0.417005	−	0.908904i	$-0.636920\pi$
$463$	−17.9458	−0.834011	−0.417005	+	0.908904i	$0.636920\pi$
$464$	−6.41362	−0.297745
$465$	95.0228	4.40658
$466$	61.0665	2.82885
$467$	14.8415	0.686783	0.343391	−	0.939192i	$-0.388424\pi$
$467$	14.8415	0.686783	0.343391	+	0.939192i	$0.388424\pi$
$468$	0	0
$469$	6.41024	0.295997
$470$	83.8567	3.86802
$471$	13.6012	0.626711
$472$	−16.6484	−0.766305
$473$	1.98324	0.0911896
$474$	−47.4392	−2.17896
$475$	5.28207	0.242358
$476$	2.11944	0.0971445
$477$	23.2206	1.06320
$478$	51.4009	2.35102
$479$	4.23377	0.193446	0.0967229	−	0.995311i	$-0.469164\pi$
$479$	4.23377	0.193446	0.0967229	+	0.995311i	$0.469164\pi$
$480$	66.4919	3.03493
$481$	0	0
$482$	−23.9972	−1.09304
$483$	−9.10904	−0.414476
$484$	8.07926	0.367239
$485$	−28.8987	−1.31222
$486$	6.51049	0.295322
$487$	2.98273	0.135160	0.0675802	−	0.997714i	$-0.478472\pi$
$487$	2.98273	0.135160	0.0675802	+	0.997714i	$0.478472\pi$
$488$	−4.09284	−0.185274
$489$	6.35781	0.287510
$490$	−7.35037	−0.332056
$491$	−7.33211	−0.330894	−0.165447	−	0.986219i	$-0.552907\pi$
$491$	−7.33211	−0.330894	−0.165447	+	0.986219i	$0.552907\pi$
$492$	8.04607	0.362745
$493$	4.61994	0.208071
$494$	0	0
$495$	−74.8321	−3.36345
$496$	9.35802	0.420188
$497$	10.7248	0.481075
$498$	−15.6728	−0.702316
$499$	−15.6355	−0.699939	−0.349970	−	0.936761i	$-0.613808\pi$
$499$	−15.6355	−0.699939	−0.349970	+	0.936761i	$0.613808\pi$
$500$	−7.84272	−0.350737
$501$	38.1544	1.70461
$502$	16.4230	0.732995
$503$	27.1014	1.20839	0.604196	−	0.796836i	$-0.293494\pi$
$503$	27.1014	1.20839	0.604196	+	0.796836i	$0.293494\pi$
$504$	13.8449	0.616701
$505$	−28.0787	−1.24949
$506$	−24.9174	−1.10771
$507$	0	0
$508$	10.7992	0.479135
$509$	44.3319	1.96498	0.982489	−	0.186321i	$-0.0596564\pi$
$509$	44.3319	1.96498	0.982489	+	0.186321i	$0.0596564\pi$
$510$	−15.6860	−0.694587
$511$	9.72504	0.430210
$512$	10.9519	0.484012
$513$	8.70617	0.384387
$514$	33.5376	1.47928
$515$	45.1089	1.98774
$516$	4.87455	0.214590
$517$	−42.2090	−1.85635
$518$	−16.2524	−0.714091
$519$	12.0097	0.527169
$520$	0	0
$521$	−2.24230	−0.0982371	−0.0491186	−	0.998793i	$-0.515641\pi$
$521$	−2.24230	−0.0982371	−0.0491186	+	0.998793i	$0.515641\pi$
$522$	90.2230	3.94895
$523$	−41.8877	−1.83162	−0.915810	−	0.401612i	$-0.868450\pi$
$523$	−41.8877	−1.83162	−0.915810	+	0.401612i	$0.868450\pi$
$524$	3.18147	0.138983
$525$	17.5332	0.765210
$526$	18.0152	0.785501
$527$	−6.74088	−0.293637
$528$	−10.9609	−0.477012
$529$	−13.9379	−0.605995
$530$	−27.7248	−1.20429
$531$	−45.5733	−1.97771
$532$	2.73955	0.118775
$533$	0	0
$534$	−15.1102	−0.653881
$535$	57.4842	2.48526
$536$	14.4162	0.622684
$537$	71.6509	3.09196
$538$	−5.64747	−0.243480
$539$	3.69978	0.159361
$540$	−94.2974	−4.05791
$541$	−13.4214	−0.577032	−0.288516	−	0.957475i	$-0.593162\pi$
$541$	−13.4214	−0.577032	−0.288516	+	0.957475i	$0.593162\pi$
$542$	−1.75631	−0.0754400
$543$	−74.5579	−3.19958
$544$	−4.71691	−0.202236
$545$	−22.8321	−0.978019
$546$	0	0
$547$	29.3951	1.25684	0.628422	−	0.777873i	$-0.283701\pi$
$547$	29.3951	1.25684	0.628422	+	0.777873i	$0.283701\pi$
$548$	−24.9388	−1.06533
$549$	−11.2037	−0.478164
$550$	47.9612	2.04507
$551$	5.97164	0.254400
$552$	−20.4856	−0.871925
$553$	−7.00757	−0.297992
$554$	47.9201	2.03593
$555$	72.2208	3.06560
$556$	−21.1159	−0.895515
$557$	−38.9882	−1.65198	−0.825991	−	0.563683i	$-0.809384\pi$
$557$	−38.9882	−1.65198	−0.825991	+	0.563683i	$0.809384\pi$
$558$	−131.643	−5.57290
$559$	0	0
$560$	3.21669	0.135930
$561$	7.89549	0.333348
$562$	50.0492	2.11120
$563$	−3.99187	−0.168237	−0.0841186	−	0.996456i	$-0.526807\pi$
$563$	−3.99187	−0.168237	−0.0841186	+	0.996456i	$0.526807\pi$
$564$	−103.744	−4.36842
$565$	9.29907	0.391215
$566$	−55.6618	−2.33964
$567$	10.4304	0.438034
$568$	24.1194	1.01203
$569$	18.8465	0.790087	0.395043	−	0.918663i	$-0.370730\pi$
$569$	18.8465	0.790087	0.395043	+	0.918663i	$0.370730\pi$
$570$	−20.2754	−0.849243
$571$	12.1859	0.509965	0.254983	−	0.966946i	$-0.417930\pi$
$571$	12.1859	0.509965	0.254983	+	0.966946i	$0.417930\pi$
$572$	0	0
$573$	9.01871	0.376762
$574$	1.97952	0.0826236
$575$	−17.4428	−0.727416
$576$	−80.0622	−3.33592
$577$	−23.1257	−0.962736	−0.481368	−	0.876519i	$-0.659860\pi$
$577$	−23.1257	−0.962736	−0.481368	+	0.876519i	$0.659860\pi$
$578$	−36.9203	−1.53568
$579$	−52.9896	−2.20217
$580$	−64.6794	−2.68567
$581$	−2.31514	−0.0960482
$582$	59.5456	2.46825
$583$	13.9552	0.577964
$584$	21.8709	0.905026
$585$	0	0
$586$	26.3291	1.08765
$587$	−42.2460	−1.74368	−0.871840	−	0.489790i	$-0.837073\pi$
$587$	−42.2460	−1.74368	−0.871840	+	0.489790i	$0.837073\pi$
$588$	9.09359	0.375013
$589$	−8.71313	−0.359018
$590$	54.4134	2.24017
$591$	59.3722	2.44225
$592$	7.11244	0.292319
$593$	−12.3223	−0.506017	−0.253008	−	0.967464i	$-0.581420\pi$
$593$	−12.3223	−0.506017	−0.253008	+	0.967464i	$0.581420\pi$
$594$	79.0521	3.24355
$595$	−2.31709	−0.0949912
$596$	−23.8394	−0.976499
$597$	−75.1359	−3.07511
$598$	0	0
$599$	−13.3578	−0.545785	−0.272893	−	0.962045i	$-0.587980\pi$
$599$	−13.3578	−0.545785	−0.272893	+	0.962045i	$0.587980\pi$
$600$	39.4308	1.60976
$601$	−15.9766	−0.651700	−0.325850	−	0.945421i	$-0.605651\pi$
$601$	−15.9766	−0.651700	−0.325850	+	0.945421i	$0.605651\pi$
$602$	1.19925	0.0488780
$603$	39.4628	1.60705
$604$	63.4161	2.58036
$605$	−8.83266	−0.359099
$606$	57.8561	2.35024
$607$	−27.4273	−1.11324	−0.556619	−	0.830768i	$-0.687902\pi$
$607$	−27.4273	−1.11324	−0.556619	+	0.830768i	$0.687902\pi$
$608$	−6.09699	−0.247266
$609$	19.8221	0.803232
$610$	13.3770	0.541619
$611$	0	0
$612$	13.0478	0.527424
$613$	−18.2538	−0.737262	−0.368631	−	0.929576i	$-0.620173\pi$
$613$	−18.2538	−0.737262	−0.368631	+	0.929576i	$0.620173\pi$
$614$	45.6086	1.84061
$615$	−8.79638	−0.354704
$616$	8.32055	0.335245
$617$	27.9970	1.12712	0.563558	−	0.826076i	$-0.309432\pi$
$617$	27.9970	1.12712	0.563558	+	0.826076i	$0.309432\pi$
$618$	−92.9469	−3.73887
$619$	4.93459	0.198338	0.0991689	−	0.995071i	$-0.468382\pi$
$619$	4.93459	0.198338	0.0991689	+	0.995071i	$0.468382\pi$
$620$	94.3728	3.79010
$621$	−28.7501	−1.15370
$622$	−25.9600	−1.04090
$623$	−2.23203	−0.0894243
$624$	0	0
$625$	−20.3975	−0.815900
$626$	15.4807	0.618735
$627$	10.2056	0.407571
$628$	13.5082	0.539035
$629$	−5.12332	−0.204280
$630$	−45.2505	−1.80282
$631$	24.1702	0.962199	0.481100	−	0.876666i	$-0.340237\pi$
$631$	24.1702	0.962199	0.481100	+	0.876666i	$0.340237\pi$
$632$	−15.7595	−0.626881
$633$	−4.23574	−0.168356
$634$	48.4599	1.92459
$635$	−11.8062	−0.468515
$636$	34.3000	1.36008
$637$	0	0
$638$	54.2225	2.14669
$639$	66.0245	2.61189
$640$	51.6441	2.04141
$641$	23.0926	0.912103	0.456052	−	0.889953i	$-0.349263\pi$
$641$	23.0926	0.912103	0.456052	+	0.889953i	$0.349263\pi$
$642$	−118.446	−4.67469
$643$	−3.73802	−0.147413	−0.0737065	−	0.997280i	$-0.523483\pi$
$643$	−3.73802	−0.147413	−0.0737065	+	0.997280i	$0.523483\pi$
$644$	−9.04673	−0.356491
$645$	−5.32911	−0.209834
$646$	1.43833	0.0565903
$647$	−21.3102	−0.837789	−0.418895	−	0.908035i	$-0.637582\pi$
$647$	−21.3102	−0.837789	−0.418895	+	0.908035i	$0.637582\pi$
$648$	23.4572	0.921484
$649$	−27.3888	−1.07510
$650$	0	0
$651$	−28.9221	−1.13355
$652$	6.31432	0.247288
$653$	−13.2897	−0.520067	−0.260034	−	0.965600i	$-0.583734\pi$
$653$	−13.2897	−0.520067	−0.260034	+	0.965600i	$0.583734\pi$
$654$	47.0455	1.83962
$655$	−3.47815	−0.135902
$656$	−0.866284	−0.0338227
$657$	59.8695	2.33573
$658$	−25.5235	−0.995010
$659$	−47.9835	−1.86917	−0.934586	−	0.355737i	$-0.884230\pi$
$659$	−47.9835	−1.86917	−0.934586	+	0.355737i	$0.884230\pi$
$660$	−110.537	−4.30266
$661$	−34.2025	−1.33032	−0.665161	−	0.746700i	$-0.731637\pi$
$661$	−34.2025	−1.33032	−0.665161	+	0.746700i	$0.731637\pi$
$662$	−52.8141	−2.05268
$663$	0	0
$664$	−5.20659	−0.202055
$665$	−2.99502	−0.116142
$666$	−100.054	−3.87700
$667$	−19.7200	−0.763560
$668$	37.8934	1.46614
$669$	29.3077	1.13310
$670$	−47.1177	−1.82031
$671$	−6.73326	−0.259935
$672$	−20.2382	−0.780704
$673$	19.0820	0.735556	0.367778	−	0.929914i	$-0.380119\pi$
$673$	19.0820	0.735556	0.367778	+	0.929914i	$0.380119\pi$
$674$	−8.93459	−0.344148
$675$	55.3385	2.12998
$676$	0	0
$677$	36.3983	1.39890	0.699451	−	0.714681i	$-0.253428\pi$
$677$	36.3983	1.39890	0.699451	+	0.714681i	$0.253428\pi$
$678$	−19.1607	−0.735863
$679$	8.79590	0.337555
$680$	−5.21096	−0.199831
$681$	70.4039	2.69788
$682$	−79.1153	−3.02948
$683$	−38.5512	−1.47512	−0.737560	−	0.675282i	$-0.764022\pi$
$683$	−38.5512	−1.47512	−0.737560	+	0.675282i	$0.764022\pi$
$684$	16.8653	0.644860
$685$	27.2644	1.04172
$686$	2.23724	0.0854181
$687$	62.2739	2.37590
$688$	−0.524821	−0.0200086
$689$	0	0
$690$	66.9548	2.54893
$691$	−25.7213	−0.978483	−0.489241	−	0.872148i	$-0.662726\pi$
$691$	−25.7213	−0.978483	−0.489241	+	0.872148i	$0.662726\pi$
$692$	11.9276	0.453419
$693$	22.7767	0.865214
$694$	63.7708	2.42071
$695$	23.0850	0.875665
$696$	44.5785	1.68974
$697$	0.624012	0.0236361
$698$	−8.93639	−0.338247
$699$	82.5941	3.12400
$700$	17.4132	0.658158
$701$	−20.7378	−0.783255	−0.391627	−	0.920124i	$-0.628088\pi$
$701$	−20.7378	−0.783255	−0.391627	+	0.920124i	$0.628088\pi$
$702$	0	0
$703$	−6.62230	−0.249765
$704$	−48.1160	−1.81344
$705$	113.419	4.27159
$706$	−54.0795	−2.03531
$707$	8.54632	0.321418
$708$	−67.3181	−2.52997
$709$	19.1426	0.718915	0.359458	−	0.933161i	$-0.382962\pi$
$709$	19.1426	0.718915	0.359458	+	0.933161i	$0.382962\pi$
$710$	−78.8316	−2.95850
$711$	−43.1401	−1.61788
$712$	−5.01968	−0.188120
$713$	28.7731	1.07756
$714$	4.77435	0.178676
$715$	0	0
$716$	71.1608	2.65940
$717$	69.5211	2.59631
$718$	−30.2115	−1.12748
$719$	24.2544	0.904538	0.452269	−	0.891882i	$-0.350615\pi$
$719$	24.2544	0.904538	0.452269	+	0.891882i	$0.350615\pi$
$720$	19.8027	0.738001
$721$	−13.7298	−0.511325
$722$	−40.6483	−1.51277
$723$	−32.4568	−1.20708
$724$	−74.0479	−2.75197
$725$	37.9571	1.40969
$726$	18.1997	0.675454
$727$	45.3677	1.68260	0.841298	−	0.540572i	$-0.181792\pi$
$727$	45.3677	1.68260	0.841298	+	0.540572i	$0.181792\pi$
$728$	0	0
$729$	−22.4855	−0.832795
$730$	−71.4827	−2.64569
$731$	0.378045	0.0139825
$732$	−16.5495	−0.611687
$733$	1.81036	0.0668671	0.0334336	−	0.999441i	$-0.489356\pi$
$733$	1.81036	0.0668671	0.0334336	+	0.999441i	$0.489356\pi$
$734$	35.7708	1.32033
$735$	−9.94158	−0.366701
$736$	20.1339	0.742145
$737$	23.7165	0.873609
$738$	12.1864	0.448586
$739$	41.5849	1.52973	0.764863	−	0.644193i	$-0.222807\pi$
$739$	41.5849	1.52973	0.764863	+	0.644193i	$0.222807\pi$
$740$	71.7268	2.63673
$741$	0	0
$742$	8.43860	0.309791
$743$	−15.0289	−0.551357	−0.275678	−	0.961250i	$-0.588902\pi$
$743$	−15.0289	−0.551357	−0.275678	+	0.961250i	$0.588902\pi$
$744$	−65.0438	−2.38462
$745$	26.0625	0.954854
$746$	55.0292	2.01476
$747$	−14.2525	−0.521472
$748$	7.84148	0.286713
$749$	−17.4965	−0.639308
$750$	−17.6669	−0.645103
$751$	−20.1839	−0.736522	−0.368261	−	0.929723i	$-0.620047\pi$
$751$	−20.1839	−0.736522	−0.368261	+	0.929723i	$0.620047\pi$
$752$	11.1697	0.407316
$753$	22.2126	0.809472
$754$	0	0
$755$	−69.3297	−2.52317
$756$	28.7013	1.04386
$757$	−17.7415	−0.644824	−0.322412	−	0.946599i	$-0.604494\pi$
$757$	−17.7415	−0.644824	−0.322412	+	0.946599i	$0.604494\pi$
$758$	−18.0711	−0.656373
$759$	−33.7015	−1.22329
$760$	−6.73559	−0.244325
$761$	29.2075	1.05877	0.529386	−	0.848381i	$-0.322422\pi$
$761$	29.2075	1.05877	0.529386	+	0.848381i	$0.322422\pi$
$762$	24.3267	0.881262
$763$	6.94941	0.251586
$764$	8.95703	0.324054
$765$	−14.2645	−0.515733
$766$	7.73045	0.279313
$767$	0	0
$768$	−27.7078	−0.999819
$769$	−12.5419	−0.452271	−0.226136	−	0.974096i	$-0.572609\pi$
$769$	−12.5419	−0.452271	−0.226136	+	0.974096i	$0.572609\pi$
$770$	−27.1948	−0.980032
$771$	45.3606	1.63362
$772$	−52.6272	−1.89409
$773$	34.4451	1.23891	0.619453	−	0.785034i	$-0.287355\pi$
$773$	34.4451	1.23891	0.619453	+	0.785034i	$0.287355\pi$
$774$	7.38287	0.265372
$775$	−55.3827	−1.98941
$776$	19.7814	0.710109
$777$	−21.9819	−0.788595
$778$	−52.8285	−1.89399
$779$	0.806586	0.0288989
$780$	0	0
$781$	39.6796	1.41985
$782$	−4.74975	−0.169851
$783$	62.5628	2.23581
$784$	−0.979066	−0.0349666
$785$	−14.7678	−0.527087
$786$	7.16672	0.255628
$787$	−0.728879	−0.0259817	−0.0129909	−	0.999916i	$-0.504135\pi$
$787$	−0.728879	−0.0259817	−0.0129909	+	0.999916i	$0.504135\pi$
$788$	58.9661	2.10058
$789$	24.3661	0.867456
$790$	51.5083	1.83258
$791$	−2.83036	−0.100636
$792$	51.2231	1.82014
$793$	0	0
$794$	−13.0745	−0.463997
$795$	−37.4985	−1.32994
$796$	−74.6220	−2.64491
$797$	−26.0339	−0.922167	−0.461084	−	0.887357i	$-0.652539\pi$
$797$	−26.0339	−0.922167	−0.461084	+	0.887357i	$0.652539\pi$
$798$	6.17123	0.218459
$799$	−8.04587	−0.284642
$800$	−38.7539	−1.37016
$801$	−13.7409	−0.485509
$802$	−56.1190	−1.98163
$803$	35.9805	1.26973
$804$	58.2921	2.05580
$805$	9.89036	0.348589
$806$	0	0
$807$	−7.63836	−0.268883
$808$	19.2201	0.676160
$809$	15.0861	0.530398	0.265199	−	0.964194i	$-0.414562\pi$
$809$	15.0861	0.530398	0.265199	+	0.964194i	$0.414562\pi$
$810$	−76.6671	−2.69381
$811$	−6.89347	−0.242062	−0.121031	−	0.992649i	$-0.538620\pi$
$811$	−6.89347	−0.242062	−0.121031	+	0.992649i	$0.538620\pi$
$812$	19.6865	0.690861
$813$	−2.37546	−0.0833110
$814$	−60.1305	−2.10757
$815$	−6.90315	−0.241807
$816$	−2.08937	−0.0731424
$817$	0.488654	0.0170958
$818$	0.352349	0.0123196
$819$	0	0
$820$	−8.73621	−0.305082
$821$	−14.8223	−0.517301	−0.258650	−	0.965971i	$-0.583278\pi$
$821$	−14.8223	−0.517301	−0.258650	+	0.965971i	$0.583278\pi$
$822$	−56.1783	−1.95944
$823$	−7.29232	−0.254194	−0.127097	−	0.991890i	$-0.540566\pi$
$823$	−7.29232	−0.254194	−0.127097	+	0.991890i	$0.540566\pi$
$824$	−30.8774	−1.07567
$825$	64.8689	2.25844
$826$	−16.5618	−0.576260
$827$	−20.3151	−0.706424	−0.353212	−	0.935543i	$-0.614911\pi$
$827$	−20.3151	−0.706424	−0.353212	+	0.935543i	$0.614911\pi$
$828$	−55.6937	−1.93549
$829$	16.4470	0.571227	0.285614	−	0.958345i	$-0.407803\pi$
$829$	16.4470	0.571227	0.285614	+	0.958345i	$0.407803\pi$
$830$	17.0171	0.590673
$831$	64.8133	2.24835
$832$	0	0
$833$	0.705252	0.0244355
$834$	−47.5667	−1.64710
$835$	−41.4271	−1.43364
$836$	10.1357	0.350552
$837$	−91.2845	−3.15525
$838$	−15.5338	−0.536608
$839$	24.0612	0.830687	0.415343	−	0.909665i	$-0.363661\pi$
$839$	24.0612	0.830687	0.415343	+	0.909665i	$0.363661\pi$
$840$	−22.3579	−0.771422
$841$	13.9124	0.479739
$842$	−40.8135	−1.40653
$843$	67.6929	2.33147
$844$	−4.20677	−0.144803
$845$	0	0
$846$	−157.128	−5.40218
$847$	2.68840	0.0923746
$848$	−3.69293	−0.126816
$849$	−75.2842	−2.58375
$850$	9.14236	0.313580
$851$	21.8686	0.749646
$852$	97.5273	3.34123
$853$	20.1772	0.690854	0.345427	−	0.938446i	$-0.387734\pi$
$853$	20.1772	0.690854	0.345427	+	0.938446i	$0.387734\pi$
$854$	−4.07156	−0.139326
$855$	−18.4380	−0.630566
$856$	−39.3484	−1.34490
$857$	35.6705	1.21848	0.609241	−	0.792985i	$-0.291474\pi$
$857$	35.6705	1.21848	0.609241	+	0.792985i	$0.291474\pi$
$858$	0	0
$859$	18.8085	0.641738	0.320869	−	0.947124i	$-0.396025\pi$
$859$	18.8085	0.641738	0.320869	+	0.947124i	$0.396025\pi$
$860$	−5.29266	−0.180478
$861$	2.67736	0.0912441
$862$	−55.2157	−1.88065
$863$	−19.3191	−0.657631	−0.328815	−	0.944394i	$-0.606649\pi$
$863$	−19.3191	−0.657631	−0.328815	+	0.944394i	$0.606649\pi$
$864$	−63.8761	−2.17311
$865$	−13.0399	−0.443369
$866$	−18.3182	−0.622479
$867$	−49.9357	−1.69590
$868$	−28.7243	−0.974966
$869$	−25.9265	−0.879497
$870$	−145.700	−4.93969
$871$	0	0
$872$	15.6287	0.529256
$873$	54.1494	1.83268
$874$	−6.13944	−0.207670
$875$	−2.60969	−0.0882238
$876$	88.4355	2.98796
$877$	−45.9401	−1.55129	−0.775644	−	0.631171i	$-0.782575\pi$
$877$	−45.9401	−1.55129	−0.775644	+	0.631171i	$0.782575\pi$
$878$	64.4469	2.17498
$879$	35.6108	1.20112
$880$	11.9011	0.401185
$881$	−36.3751	−1.22551	−0.612755	−	0.790273i	$-0.709939\pi$
$881$	−36.3751	−1.22551	−0.612755	+	0.790273i	$0.709939\pi$
$882$	13.7729	0.463758
$883$	−33.5090	−1.12767	−0.563834	−	0.825888i	$-0.690674\pi$
$883$	−33.5090	−1.12767	−0.563834	+	0.825888i	$0.690674\pi$
$884$	0	0
$885$	73.5957	2.47389
$886$	35.0089	1.17615
$887$	0.246789	0.00828635	0.00414318	−	0.999991i	$-0.498681\pi$
$887$	0.246789	0.00828635	0.00414318	+	0.999991i	$0.498681\pi$
$888$	−49.4357	−1.65895
$889$	3.59346	0.120521
$890$	16.4062	0.549938
$891$	38.5901	1.29282
$892$	29.1072	0.974581
$893$	−10.3999	−0.348021
$894$	−53.7017	−1.79605
$895$	−77.7967	−2.60046
$896$	−15.7189	−0.525133
$897$	0	0
$898$	40.3015	1.34488
$899$	−62.6129	−2.08826
$900$	107.200	3.57332
$901$	2.66013	0.0886218
$902$	7.32380	0.243856
$903$	1.62202	0.0539776
$904$	−6.36529	−0.211706
$905$	80.9530	2.69097
$906$	142.854	4.74600
$907$	45.4657	1.50966	0.754831	−	0.655919i	$-0.227719\pi$
$907$	45.4657	1.50966	0.754831	+	0.655919i	$0.227719\pi$
$908$	69.9223	2.32045
$909$	52.6130	1.74506
$910$	0	0
$911$	−41.7848	−1.38439	−0.692195	−	0.721710i	$-0.743356\pi$
$911$	−41.7848	−1.38439	−0.692195	+	0.721710i	$0.743356\pi$
$912$	−2.70067	−0.0894282
$913$	−8.56552	−0.283477
$914$	20.6051	0.681558
$915$	18.0928	0.598128
$916$	61.8480	2.04351
$917$	1.05865	0.0349595
$918$	15.0689	0.497348
$919$	−31.3491	−1.03411	−0.517056	−	0.855951i	$-0.672972\pi$
$919$	−31.3491	−1.03411	−0.517056	+	0.855951i	$0.672972\pi$
$920$	22.2427	0.733321
$921$	61.6869	2.03265
$922$	−38.6997	−1.27451
$923$	0	0
$924$	33.6443	1.10682
$925$	−42.0929	−1.38401
$926$	−40.1489	−1.31938
$927$	−84.5238	−2.77612
$928$	−43.8132	−1.43824
$929$	46.7428	1.53358	0.766791	−	0.641896i	$-0.221852\pi$
$929$	46.7428	1.53358	0.766791	+	0.641896i	$0.221852\pi$
$930$	212.588	6.97105
$931$	0.911595	0.0298763
$932$	82.0292	2.68695
$933$	−35.1116	−1.14950
$934$	33.2039	1.08647
$935$	−8.57271	−0.280358
$936$	0	0
$937$	46.2840	1.51203	0.756016	−	0.654553i	$-0.227143\pi$
$937$	46.2840	1.51203	0.756016	+	0.654553i	$0.227143\pi$
$938$	14.3412	0.468257
$939$	20.9381	0.683290
$940$	112.643	3.67400
$941$	−12.0118	−0.391574	−0.195787	−	0.980646i	$-0.562726\pi$
$941$	−12.0118	−0.391574	−0.195787	+	0.980646i	$0.562726\pi$
$942$	30.4291	0.991434
$943$	−2.66356	−0.0867375
$944$	7.24784	0.235897
$945$	−31.3778	−1.02072
$946$	4.43698	0.144259
$947$	−22.5259	−0.731993	−0.365997	−	0.930616i	$-0.619272\pi$
$947$	−22.5259	−0.731993	−0.365997	+	0.930616i	$0.619272\pi$
$948$	−63.7240	−2.06966
$949$	0	0
$950$	11.8172	0.383402
$951$	65.5433	2.12539
$952$	1.58606	0.0514046
$953$	46.1823	1.49599	0.747995	−	0.663704i	$-0.231017\pi$
$953$	46.1823	1.49599	0.747995	+	0.663704i	$0.231017\pi$
$954$	51.9499	1.68194
$955$	−9.79229	−0.316871
$956$	69.0456	2.23309
$957$	73.3375	2.37066
$958$	9.47194	0.306024
$959$	−8.29848	−0.267972
$960$	129.291	4.17286
$961$	60.3575	1.94702
$962$	0	0
$963$	−107.712	−3.47098
$964$	−32.2348	−1.03821
$965$	57.5348	1.85211
$966$	−20.3791	−0.655686
$967$	−1.04412	−0.0335765	−0.0167882	−	0.999859i	$-0.505344\pi$
$967$	−1.04412	−0.0335765	−0.0167882	+	0.999859i	$0.505344\pi$
$968$	6.04603	0.194327
$969$	1.94538	0.0624946
$970$	−64.6531	−2.07589
$971$	−6.88771	−0.221037	−0.110519	−	0.993874i	$-0.535251\pi$
$971$	−6.88771	−0.221037	−0.110519	+	0.993874i	$0.535251\pi$
$972$	8.74539	0.280508
$973$	−7.02640	−0.225256
$974$	6.67308	0.213819
$975$	0	0
$976$	1.78181	0.0570343
$977$	14.2731	0.456637	0.228319	−	0.973586i	$-0.426677\pi$
$977$	14.2731	0.456637	0.228319	+	0.973586i	$0.426677\pi$
$978$	14.2239	0.454831
$979$	−8.25802	−0.263928
$980$	−9.87358	−0.315400
$981$	42.7821	1.36593
$982$	−16.4037	−0.523462
$983$	−8.84698	−0.282175	−0.141087	−	0.989997i	$-0.545060\pi$
$983$	−8.84698	−0.282175	−0.141087	+	0.989997i	$0.545060\pi$
$984$	6.02119	0.191949
$985$	−64.4648	−2.05402
$986$	10.3359	0.329162
$987$	−34.5213	−1.09882
$988$	0	0
$989$	−1.61367	−0.0513116
$990$	−167.417	−5.32086
$991$	−35.7187	−1.13464	−0.567321	−	0.823497i	$-0.692020\pi$
$991$	−35.7187	−1.13464	−0.567321	+	0.823497i	$0.692020\pi$
$992$	63.9272	2.02969
$993$	−71.4325	−2.26684
$994$	23.9940	0.761044
$995$	81.5806	2.58628
$996$	−21.0529	−0.667087
$997$	43.5743	1.38001	0.690006	−	0.723804i	$-0.257608\pi$
$997$	43.5743	1.38001	0.690006	+	0.723804i	$0.257608\pi$
$998$	−34.9802	−1.10728
$999$	−69.3796	−2.19507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.a.r.1.10	yes	12
7.6	odd	2		8281.2.a.cq.1.10		12
13.5	odd	4		1183.2.c.j.337.4		24
13.8	odd	4		1183.2.c.j.337.21		24
13.12	even	2		1183.2.a.q.1.3	✓	12
91.90	odd	2		8281.2.a.cn.1.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.3	✓	12	13.12	even	2
1183.2.a.r.1.10	yes	12	1.1	even	1	trivial
1183.2.c.j.337.4		24	13.5	odd	4
1183.2.c.j.337.21		24	13.8	odd	4
8281.2.a.cn.1.3		12	91.90	odd	2
8281.2.a.cq.1.10		12	7.6	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.a (trivial)

\(f(q)\)	\(=\)	\(q+2.23724 q^{2} +3.02592 q^{3} +3.00523 q^{4} -3.28547 q^{5} +6.76971 q^{6} +1.00000 q^{7} +2.24893 q^{8} +6.15622 q^{9} +O(q^{10})\)	\(q+2.23724 q^{2} +3.02592 q^{3} +3.00523 q^{4} -3.28547 q^{5} +6.76971 q^{6} +1.00000 q^{7} +2.24893 q^{8} +6.15622 q^{9} -7.35037 q^{10} +3.69978 q^{11} +9.09359 q^{12} +2.23724 q^{14} -9.94158 q^{15} -0.979066 q^{16} +0.705252 q^{17} +13.7729 q^{18} +0.911595 q^{19} -9.87358 q^{20} +3.02592 q^{21} +8.27729 q^{22} -3.01033 q^{23} +6.80509 q^{24} +5.79431 q^{25} +9.55048 q^{27} +3.00523 q^{28} +6.55076 q^{29} -22.2417 q^{30} -9.55811 q^{31} -6.68826 q^{32} +11.1953 q^{33} +1.57782 q^{34} -3.28547 q^{35} +18.5008 q^{36} -7.26452 q^{37} +2.03945 q^{38} -7.38879 q^{40} +0.884807 q^{41} +6.76971 q^{42} +0.536043 q^{43} +11.1187 q^{44} -20.2261 q^{45} -6.73483 q^{46} -11.4085 q^{47} -2.96258 q^{48} +1.00000 q^{49} +12.9633 q^{50} +2.13404 q^{51} +3.77189 q^{53} +21.3667 q^{54} -12.1555 q^{55} +2.24893 q^{56} +2.75842 q^{57} +14.6556 q^{58} -7.40281 q^{59} -29.8767 q^{60} -1.81991 q^{61} -21.3838 q^{62} +6.15622 q^{63} -13.0051 q^{64} +25.0465 q^{66} +6.41024 q^{67} +2.11944 q^{68} -9.10904 q^{69} -7.35037 q^{70} +10.7248 q^{71} +13.8449 q^{72} +9.72504 q^{73} -16.2524 q^{74} +17.5332 q^{75} +2.73955 q^{76} +3.69978 q^{77} -7.00757 q^{79} +3.21669 q^{80} +10.4304 q^{81} +1.97952 q^{82} -2.31514 q^{83} +9.09359 q^{84} -2.31709 q^{85} +1.19925 q^{86} +19.8221 q^{87} +8.32055 q^{88} -2.23203 q^{89} -45.2505 q^{90} -9.04673 q^{92} -28.9221 q^{93} -25.5235 q^{94} -2.99502 q^{95} -20.2382 q^{96} +8.79590 q^{97} +2.23724 q^{98} +22.7767 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9	\( 12 q + 3 q^{2} + 8 q^{3} + 15 q^{4} - 4 q^{5} + 2 q^{6} + 12 q^{7} + 12 q^{8} + 26 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} + 3 q^{14} + 11 q^{15} + 13 q^{16} + 31 q^{17} - 29 q^{18} - 3 q^{19} - 18 q^{20} + 8 q^{21} - 4 q^{22} + 18 q^{23} - 6 q^{24} + 32 q^{25} + 32 q^{27} + 15 q^{28} + 15 q^{29} - 10 q^{30} - 21 q^{31} - 3 q^{32} - 29 q^{33} + 3 q^{34} - 4 q^{35} + 49 q^{36} + 5 q^{37} + 45 q^{38} - 20 q^{40} - 16 q^{41} + 2 q^{42} - 22 q^{43} + 35 q^{44} + 5 q^{45} + 2 q^{46} - 4 q^{47} + 11 q^{48} + 12 q^{49} + 13 q^{50} + 18 q^{51} + 53 q^{53} - 5 q^{54} - 26 q^{55} + 12 q^{56} - 8 q^{57} + 32 q^{58} - 26 q^{59} + 38 q^{60} + 22 q^{61} + 19 q^{62} + 26 q^{63} + 2 q^{64} - 34 q^{66} + 12 q^{67} + 34 q^{68} + 3 q^{69} - 6 q^{70} + 21 q^{71} - 4 q^{72} - 15 q^{73} - 40 q^{74} + 15 q^{75} + 43 q^{76} + 12 q^{77} + 2 q^{79} + 13 q^{80} + 36 q^{81} - 32 q^{82} - 9 q^{83} + 13 q^{84} - 39 q^{85} + 44 q^{86} + 27 q^{87} - 48 q^{88} - 22 q^{89} - 26 q^{90} + 52 q^{92} - 53 q^{93} - 44 q^{94} + 29 q^{95} - 114 q^{96} + 9 q^{97} + 3 q^{98} + 37 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 8 * q^3 + 15 * q^4 - 4 * q^5 + 2 * q^6 + 12 * q^7 + 12 * q^8 + 26 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 + 3 * q^14 + 11 * q^15 + 13 * q^16 + 31 * q^17 - 29 * q^18 - 3 * q^19 - 18 * q^20 + 8 * q^21 - 4 * q^22 + 18 * q^23 - 6 * q^24 + 32 * q^25 + 32 * q^27 + 15 * q^28 + 15 * q^29 - 10 * q^30 - 21 * q^31 - 3 * q^32 - 29 * q^33 + 3 * q^34 - 4 * q^35 + 49 * q^36 + 5 * q^37 + 45 * q^38 - 20 * q^40 - 16 * q^41 + 2 * q^42 - 22 * q^43 + 35 * q^44 + 5 * q^45 + 2 * q^46 - 4 * q^47 + 11 * q^48 + 12 * q^49 + 13 * q^50 + 18 * q^51 + 53 * q^53 - 5 * q^54 - 26 * q^55 + 12 * q^56 - 8 * q^57 + 32 * q^58 - 26 * q^59 + 38 * q^60 + 22 * q^61 + 19 * q^62 + 26 * q^63 + 2 * q^64 - 34 * q^66 + 12 * q^67 + 34 * q^68 + 3 * q^69 - 6 * q^70 + 21 * q^71 - 4 * q^72 - 15 * q^73 - 40 * q^74 + 15 * q^75 + 43 * q^76 + 12 * q^77 + 2 * q^79 + 13 * q^80 + 36 * q^81 - 32 * q^82 - 9 * q^83 + 13 * q^84 - 39 * q^85 + 44 * q^86 + 27 * q^87 - 48 * q^88 - 22 * q^89 - 26 * q^90 + 52 * q^92 - 53 * q^93 - 44 * q^94 + 29 * q^95 - 114 * q^96 + 9 * q^97 + 3 * q^98 + 37 * q^99

Introduction

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