LMFDB - Embedded newform 2793.2.a.be.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,2,Mod(1,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2793.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2793 = 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2793.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:	$22.3022172845$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1240016.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 2x^{2} + 16x + 6 $ x^5 - x^4 - 8x^3 + 2x^2 + 16*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.36162$ of defining polynomial
Character	$\chi$	$=$	2793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.215612 q^{2} -1.00000 q^{3} -1.95351 q^{4} -1.06804 q^{5} -0.215612 q^{6} -0.852423 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.215612 q^{2} -1.00000 q^{3} -1.95351 q^{4} -1.06804 q^{5} -0.215612 q^{6} -0.852423 q^{8} +1.00000 q^{9} -0.230281 q^{10} +2.72323 q^{11} +1.95351 q^{12} -1.56878 q^{13} +1.06804 q^{15} +3.72323 q^{16} -4.83899 q^{17} +0.215612 q^{18} -1.00000 q^{19} +2.08642 q^{20} +0.587160 q^{22} -2.72323 q^{23} +0.852423 q^{24} -3.85930 q^{25} -0.338247 q^{26} -1.00000 q^{27} -1.65520 q^{29} +0.230281 q^{30} -4.72323 q^{31} +2.50762 q^{32} -2.72323 q^{33} -1.04334 q^{34} -1.95351 q^{36} +10.0431 q^{37} -0.215612 q^{38} +1.56878 q^{39} +0.910418 q^{40} +6.33825 q^{41} -8.76632 q^{43} -5.31986 q^{44} -1.06804 q^{45} -0.587160 q^{46} +9.79127 q^{47} -3.72323 q^{48} -0.832110 q^{50} +4.83899 q^{51} +3.06462 q^{52} -10.5607 q^{53} -0.215612 q^{54} -2.90851 q^{55} +1.00000 q^{57} -0.356880 q^{58} -5.44646 q^{59} -2.08642 q^{60} +1.77095 q^{61} -1.01838 q^{62} -6.90579 q^{64} +1.67551 q^{65} -0.587160 q^{66} +8.92541 q^{67} +9.45302 q^{68} +2.72323 q^{69} -9.26707 q^{71} -0.852423 q^{72} -8.76947 q^{73} +2.16541 q^{74} +3.85930 q^{75} +1.95351 q^{76} +0.338247 q^{78} +3.01838 q^{79} -3.97654 q^{80} +1.00000 q^{81} +1.36660 q^{82} +8.97820 q^{83} +5.16821 q^{85} -1.89012 q^{86} +1.65520 q^{87} -2.32135 q^{88} +10.6104 q^{89} -0.230281 q^{90} +5.31986 q^{92} +4.72323 q^{93} +2.11111 q^{94} +1.06804 q^{95} -2.50762 q^{96} +5.83145 q^{97} +2.72323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 7 q^{12} - 8 q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 2 q^{23} - 3 q^{24} + 11 q^{25} + 32 q^{26} - 5 q^{27} - 8 q^{31} - 3 q^{32} + 2 q^{33} + 8 q^{34} + 7 q^{36} + 2 q^{37} - q^{38} + 8 q^{39} + 36 q^{40} - 2 q^{41} + 20 q^{43} + 6 q^{44} + 2 q^{45} - 2 q^{46} + 26 q^{47} - 3 q^{48} - q^{50} - 2 q^{51} - 4 q^{52} + 4 q^{53} - q^{54} + 4 q^{55} + 5 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} - 10 q^{61} - 4 q^{62} - 21 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} + 58 q^{68} - 2 q^{69} + 10 q^{71} + 3 q^{72} - 10 q^{73} - 6 q^{74} - 11 q^{75} - 7 q^{76} - 32 q^{78} + 14 q^{79} + 6 q^{80} + 5 q^{81} + 26 q^{82} + 34 q^{83} - 36 q^{85} + 8 q^{86} + 6 q^{88} - 10 q^{89} - 6 q^{92} + 8 q^{93} + 8 q^{94} - 2 q^{95} + 3 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 7 * q^12 - 8 * q^13 - 2 * q^15 + 3 * q^16 + 2 * q^17 + q^18 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 2 * q^23 - 3 * q^24 + 11 * q^25 + 32 * q^26 - 5 * q^27 - 8 * q^31 - 3 * q^32 + 2 * q^33 + 8 * q^34 + 7 * q^36 + 2 * q^37 - q^38 + 8 * q^39 + 36 * q^40 - 2 * q^41 + 20 * q^43 + 6 * q^44 + 2 * q^45 - 2 * q^46 + 26 * q^47 - 3 * q^48 - q^50 - 2 * q^51 - 4 * q^52 + 4 * q^53 - q^54 + 4 * q^55 + 5 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 - 10 * q^61 - 4 * q^62 - 21 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 + 58 * q^68 - 2 * q^69 + 10 * q^71 + 3 * q^72 - 10 * q^73 - 6 * q^74 - 11 * q^75 - 7 * q^76 - 32 * q^78 + 14 * q^79 + 6 * q^80 + 5 * q^81 + 26 * q^82 + 34 * q^83 - 36 * q^85 + 8 * q^86 + 6 * q^88 - 10 * q^89 - 6 * q^92 + 8 * q^93 + 8 * q^94 - 2 * q^95 + 3 * q^96 + 16 * q^97 - 2 * 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 $

$2$	0.215612	0.152461	0.0762303	−	0.997090i	$-0.475712\pi$
$2$	0.215612	0.152461	0.0762303	+	0.997090i	$0.475712\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.95351	−0.976756
$5$	−1.06804	−0.477640	−0.238820	−	0.971064i	$-0.576761\pi$
$5$	−1.06804	−0.477640	−0.238820	+	0.971064i	$0.576761\pi$
$6$	−0.215612	−0.0880231
$7$	0	0
$7$	0	0
$8$	−0.852423	−0.301377
$9$	1.00000	0.333333
$10$	−0.230281	−0.0728212
$11$	2.72323	0.821085	0.410542	−	0.911841i	$-0.365339\pi$
$11$	2.72323	0.821085	0.410542	+	0.911841i	$0.365339\pi$
$12$	1.95351	0.563930
$13$	−1.56878	−0.435100	−0.217550	−	0.976049i	$-0.569807\pi$
$13$	−1.56878	−0.435100	−0.217550	+	0.976049i	$0.569807\pi$
$14$	0	0
$15$	1.06804	0.275765
$16$	3.72323	0.930808
$17$	−4.83899	−1.17363	−0.586813	−	0.809722i	$-0.699618\pi$
$17$	−4.83899	−1.17363	−0.586813	+	0.809722i	$0.699618\pi$
$18$	0.215612	0.0508202
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.08642	0.466537
$21$	0	0
$22$	0.587160	0.125183
$23$	−2.72323	−0.567833	−0.283916	−	0.958849i	$-0.591634\pi$
$23$	−2.72323	−0.567833	−0.283916	+	0.958849i	$0.591634\pi$
$24$	0.852423	0.174000
$25$	−3.85930	−0.771860
$26$	−0.338247	−0.0663356
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.65520	−0.307362	−0.153681	−	0.988121i	$-0.549113\pi$
$29$	−1.65520	−0.307362	−0.153681	+	0.988121i	$0.549113\pi$
$30$	0.230281	0.0420433
$31$	−4.72323	−0.848317	−0.424159	−	0.905588i	$-0.639430\pi$
$31$	−4.72323	−0.848317	−0.424159	+	0.905588i	$0.639430\pi$
$32$	2.50762	0.443289
$33$	−2.72323	−0.474054
$34$	−1.04334	−0.178932
$35$	0	0
$36$	−1.95351	−0.325585
$37$	10.0431	1.65107	0.825537	−	0.564348i	$-0.190872\pi$
$37$	10.0431	1.65107	0.825537	+	0.564348i	$0.190872\pi$
$38$	−0.215612	−0.0349768
$39$	1.56878	0.251205
$40$	0.910418	0.143950
$41$	6.33825	0.989868	0.494934	−	0.868931i	$-0.335192\pi$
$41$	6.33825	0.989868	0.494934	+	0.868931i	$0.335192\pi$
$42$	0	0
$43$	−8.76632	−1.33685	−0.668426	−	0.743779i	$-0.733032\pi$
$43$	−8.76632	−1.33685	−0.668426	+	0.743779i	$0.733032\pi$
$44$	−5.31986	−0.801999
$45$	−1.06804	−0.159213
$46$	−0.587160	−0.0865721
$47$	9.79127	1.42820	0.714101	−	0.700042i	$-0.246836\pi$
$47$	9.79127	1.42820	0.714101	+	0.700042i	$0.246836\pi$
$48$	−3.72323	−0.537402
$49$	0	0
$50$	−0.832110	−0.117678
$51$	4.83899	0.677594
$52$	3.06462	0.424987
$53$	−10.5607	−1.45063	−0.725314	−	0.688418i	$-0.758306\pi$
$53$	−10.5607	−1.45063	−0.725314	+	0.688418i	$0.758306\pi$
$54$	−0.215612	−0.0293410
$55$	−2.90851	−0.392183
$56$	0	0
$57$	1.00000	0.132453
$58$	−0.356880	−0.0468606
$59$	−5.44646	−0.709069	−0.354534	−	0.935043i	$-0.615361\pi$
$59$	−5.44646	−0.709069	−0.354534	+	0.935043i	$0.615361\pi$
$60$	−2.08642	−0.269356
$61$	1.77095	0.226747	0.113374	−	0.993552i	$-0.463834\pi$
$61$	1.77095	0.226747	0.113374	+	0.993552i	$0.463834\pi$
$62$	−1.01838	−0.129335
$63$	0	0
$64$	−6.90579	−0.863224
$65$	1.67551	0.207821
$66$	−0.587160	−0.0722745
$67$	8.92541	1.09041	0.545206	−	0.838302i	$-0.316451\pi$
$67$	8.92541	1.09041	0.545206	+	0.838302i	$0.316451\pi$
$68$	9.45302	1.14635
$69$	2.72323	0.327838
$70$	0	0
$71$	−9.26707	−1.09980	−0.549899	−	0.835231i	$-0.685334\pi$
$71$	−9.26707	−1.09980	−0.549899	+	0.835231i	$0.685334\pi$
$72$	−0.852423	−0.100459
$73$	−8.76947	−1.02639	−0.513194	−	0.858272i	$-0.671538\pi$
$73$	−8.76947	−1.02639	−0.513194	+	0.858272i	$0.671538\pi$
$74$	2.16541	0.251724
$75$	3.85930	0.445634
$76$	1.95351	0.224083
$77$	0	0
$78$	0.338247	0.0382989
$79$	3.01838	0.339595	0.169797	−	0.985479i	$-0.445689\pi$
$79$	3.01838	0.339595	0.169797	+	0.985479i	$0.445689\pi$
$80$	−3.97654	−0.444591
$81$	1.00000	0.111111
$82$	1.36660	0.150916
$83$	8.97820	0.985486	0.492743	−	0.870175i	$-0.335994\pi$
$83$	8.97820	0.985486	0.492743	+	0.870175i	$0.335994\pi$
$84$	0	0
$85$	5.16821	0.560571
$86$	−1.89012	−0.203817
$87$	1.65520	0.177456
$88$	−2.32135	−0.247456
$89$	10.6104	1.12470	0.562349	−	0.826900i	$-0.309898\pi$
$89$	10.6104	1.12470	0.562349	+	0.826900i	$0.309898\pi$
$90$	−0.230281	−0.0242737
$91$	0	0
$92$	5.31986	0.554634
$93$	4.72323	0.489776
$94$	2.11111	0.217745
$95$	1.06804	0.109578
$96$	−2.50762	−0.255933
$97$	5.83145	0.592094	0.296047	−	0.955173i	$-0.404332\pi$
$97$	5.83145	0.592094	0.296047	+	0.955173i	$0.404332\pi$
$98$	0	0
$99$	2.72323	0.273695
$100$	7.53919	0.753919
$101$	10.2854	1.02344	0.511720	−	0.859152i	$-0.329008\pi$
$101$	10.2854	1.02344	0.511720	+	0.859152i	$0.329008\pi$
$102$	1.04334	0.103306
$103$	14.9516	1.47322	0.736612	−	0.676315i	$-0.236424\pi$
$103$	14.9516	1.47322	0.736612	+	0.676315i	$0.236424\pi$
$104$	1.33726	0.131129
$105$	0	0
$106$	−2.27702	−0.221164
$107$	−8.80650	−0.851357	−0.425678	−	0.904875i	$-0.639965\pi$
$107$	−8.80650	−0.851357	−0.425678	+	0.904875i	$0.639965\pi$
$108$	1.95351	0.187977
$109$	9.58253	0.917840	0.458920	−	0.888478i	$-0.348236\pi$
$109$	9.58253	0.917840	0.458920	+	0.888478i	$0.348236\pi$
$110$	−0.627108	−0.0597924
$111$	−10.0431	−0.953248
$112$	0	0
$113$	16.4678	1.54916	0.774578	−	0.632478i	$-0.217962\pi$
$113$	16.4678	1.54916	0.774578	+	0.632478i	$0.217962\pi$
$114$	0.215612	0.0201939
$115$	2.90851	0.271220
$116$	3.23344	0.300218
$117$	−1.56878	−0.145033
$118$	−1.17432	−0.108105
$119$	0	0
$120$	−0.910418	−0.0831094
$121$	−3.58401	−0.325820
$122$	0.381838	0.0345700
$123$	−6.33825	−0.571500
$124$	9.22689	0.828599
$125$	9.46204	0.846311
$126$	0	0
$127$	6.88864	0.611268	0.305634	−	0.952149i	$-0.401132\pi$
$127$	6.88864	0.611268	0.305634	+	0.952149i	$0.401132\pi$
$128$	−6.50421	−0.574896
$129$	8.76632	0.771832
$130$	0.361259	0.0316845
$131$	−1.56222	−0.136492	−0.0682458	−	0.997669i	$-0.521740\pi$
$131$	−1.56222	−0.136492	−0.0682458	+	0.997669i	$0.521740\pi$
$132$	5.31986	0.463035
$133$	0	0
$134$	1.92442	0.166245
$135$	1.06804	0.0919218
$136$	4.12487	0.353704
$137$	22.3981	1.91360	0.956798	−	0.290754i	$-0.0939062\pi$
$137$	22.3981	1.91360	0.956798	+	0.290754i	$0.0939062\pi$
$138$	0.587160	0.0499824
$139$	10.7695	0.913455	0.456727	−	0.889607i	$-0.349022\pi$
$139$	10.7695	0.913455	0.456727	+	0.889607i	$0.349022\pi$
$140$	0	0
$141$	−9.79127	−0.824573
$142$	−1.99809	−0.167676
$143$	−4.27214	−0.357254
$144$	3.72323	0.310269
$145$	1.76781	0.146808
$146$	−1.89080	−0.156484
$147$	0	0
$148$	−19.6193	−1.61270
$149$	−1.58253	−0.129646	−0.0648230	−	0.997897i	$-0.520648\pi$
$149$	−1.58253	−0.129646	−0.0648230	+	0.997897i	$0.520648\pi$
$150$	0.832110	0.0679415
$151$	0.570440	0.0464217	0.0232109	−	0.999731i	$-0.492611\pi$
$151$	0.570440	0.0464217	0.0232109	+	0.999731i	$0.492611\pi$
$152$	0.852423	0.0691407
$153$	−4.83899	−0.391209
$154$	0	0
$155$	5.04458	0.405190
$156$	−3.06462	−0.245366
$157$	5.18065	0.413461	0.206730	−	0.978398i	$-0.433718\pi$
$157$	5.18065	0.413461	0.206730	+	0.978398i	$0.433718\pi$
$158$	0.650799	0.0517748
$159$	10.5607	0.837521
$160$	−2.67823	−0.211732
$161$	0	0
$162$	0.215612	0.0169401
$163$	9.35663	0.732868	0.366434	−	0.930444i	$-0.380579\pi$
$163$	9.35663	0.732868	0.366434	+	0.930444i	$0.380579\pi$
$164$	−12.3818	−0.966859
$165$	2.90851	0.226427
$166$	1.93581	0.150248
$167$	13.2736	1.02714	0.513572	−	0.858047i	$-0.328322\pi$
$167$	13.2736	1.02714	0.513572	+	0.858047i	$0.328322\pi$
$168$	0	0
$169$	−10.5389	−0.810688
$170$	1.11433	0.0854649
$171$	−1.00000	−0.0764719
$172$	17.1251	1.30578
$173$	0.891785	0.0678012	0.0339006	−	0.999425i	$-0.489207\pi$
$173$	0.891785	0.0678012	0.0339006	+	0.999425i	$0.489207\pi$
$174$	0.356880	0.0270550
$175$	0	0
$176$	10.1392	0.764272
$177$	5.44646	0.409381
$178$	2.28772	0.171472
$179$	9.72763	0.727077	0.363539	−	0.931579i	$-0.381569\pi$
$179$	9.72763	0.727077	0.363539	+	0.931579i	$0.381569\pi$
$180$	2.08642	0.155512
$181$	−15.0247	−1.11678	−0.558389	−	0.829579i	$-0.688580\pi$
$181$	−15.0247	−1.11678	−0.558389	+	0.829579i	$0.688580\pi$
$182$	0	0
$183$	−1.77095	−0.130913
$184$	2.32135	0.171132
$185$	−10.7264	−0.788619
$186$	1.01838	0.0746715
$187$	−13.1777	−0.963647
$188$	−19.1274	−1.39501
$189$	0	0
$190$	0.230281	0.0167063
$191$	−2.41136	−0.174480	−0.0872398	−	0.996187i	$-0.527805\pi$
$191$	−2.41136	−0.174480	−0.0872398	+	0.996187i	$0.527805\pi$
$192$	6.90579	0.498382
$193$	4.59663	0.330873	0.165436	−	0.986220i	$-0.447097\pi$
$193$	4.59663	0.330873	0.165436	+	0.986220i	$0.447097\pi$
$194$	1.25733	0.0902709
$195$	−1.67551	−0.119986
$196$	0	0
$197$	21.5356	1.53435	0.767174	−	0.641438i	$-0.221662\pi$
$197$	21.5356	1.53435	0.767174	+	0.641438i	$0.221662\pi$
$198$	0.587160	0.0417277
$199$	7.31039	0.518220	0.259110	−	0.965848i	$-0.416571\pi$
$199$	7.31039	0.518220	0.259110	+	0.965848i	$0.416571\pi$
$200$	3.28976	0.232621
$201$	−8.92541	−0.629550
$202$	2.21766	0.156034
$203$	0	0
$204$	−9.45302	−0.661844
$205$	−6.76947	−0.472800
$206$	3.22374	0.224609
$207$	−2.72323	−0.189278
$208$	−5.84092	−0.404995
$209$	−2.72323	−0.188370
$210$	0	0
$211$	8.10359	0.557874	0.278937	−	0.960309i	$-0.410018\pi$
$211$	8.10359	0.557874	0.278937	+	0.960309i	$0.410018\pi$
$212$	20.6305	1.41691
$213$	9.26707	0.634969
$214$	−1.89879	−0.129798
$215$	9.36274	0.638534
$216$	0.852423	0.0580001
$217$	0	0
$218$	2.06611	0.139934
$219$	8.76947	0.592586
$220$	5.68180	0.383067
$221$	7.59129	0.510645
$222$	−2.16541	−0.145333
$223$	−0.265137	−0.0177549	−0.00887743	−	0.999961i	$-0.502826\pi$
$223$	−0.265137	−0.0177549	−0.00887743	+	0.999961i	$0.502826\pi$
$224$	0	0
$225$	−3.85930	−0.257287
$226$	3.55064	0.236185
$227$	−4.23151	−0.280855	−0.140428	−	0.990091i	$-0.544848\pi$
$227$	−4.23151	−0.280855	−0.140428	+	0.990091i	$0.544848\pi$
$228$	−1.95351	−0.129374
$229$	−12.5404	−0.828694	−0.414347	−	0.910119i	$-0.635990\pi$
$229$	−12.5404	−0.828694	−0.414347	+	0.910119i	$0.635990\pi$
$230$	0.627108	0.0413503
$231$	0	0
$232$	1.41093	0.0926319
$233$	21.6750	1.41998	0.709989	−	0.704213i	$-0.248700\pi$
$233$	21.6750	1.41998	0.709989	+	0.704213i	$0.248700\pi$
$234$	−0.338247	−0.0221119
$235$	−10.4574	−0.682167
$236$	10.6397	0.692587
$237$	−3.01838	−0.196065
$238$	0	0
$239$	−21.2574	−1.37502	−0.687512	−	0.726173i	$-0.741297\pi$
$239$	−21.2574	−1.37502	−0.687512	+	0.726173i	$0.741297\pi$
$240$	3.97654	0.256685
$241$	−27.9544	−1.80070	−0.900351	−	0.435165i	$-0.856690\pi$
$241$	−27.9544	−1.80070	−0.900351	+	0.435165i	$0.856690\pi$
$242$	−0.772756	−0.0496746
$243$	−1.00000	−0.0641500
$244$	−3.45958	−0.221477
$245$	0	0
$246$	−1.36660	−0.0871312
$247$	1.56878	0.0998189
$248$	4.02619	0.255663
$249$	−8.97820	−0.568971
$250$	2.04013	0.129029
$251$	15.2964	0.965500	0.482750	−	0.875758i	$-0.339638\pi$
$251$	15.2964	0.965500	0.482750	+	0.875758i	$0.339638\pi$
$252$	0	0
$253$	−7.41599	−0.466239
$254$	1.48527	0.0931942
$255$	−5.16821	−0.323646
$256$	12.4092	0.775575
$257$	−3.52568	−0.219926	−0.109963	−	0.993936i	$-0.535073\pi$
$257$	−3.52568	−0.219926	−0.109963	+	0.993936i	$0.535073\pi$
$258$	1.89012	0.117674
$259$	0	0
$260$	−3.27313	−0.202991
$261$	−1.65520	−0.102454
$262$	−0.336833	−0.0208096
$263$	−6.95475	−0.428848	−0.214424	−	0.976741i	$-0.568787\pi$
$263$	−6.95475	−0.428848	−0.214424	+	0.976741i	$0.568787\pi$
$264$	2.32135	0.142869
$265$	11.2792	0.692878
$266$	0	0
$267$	−10.6104	−0.649345
$268$	−17.4359	−1.06507
$269$	−20.2884	−1.23700	−0.618502	−	0.785783i	$-0.712260\pi$
$269$	−20.2884	−1.23700	−0.618502	+	0.785783i	$0.712260\pi$
$270$	0.230281	0.0140144
$271$	−17.8939	−1.08698	−0.543489	−	0.839416i	$-0.682897\pi$
$271$	−17.8939	−1.08698	−0.543489	+	0.839416i	$0.682897\pi$
$272$	−18.0167	−1.09242
$273$	0	0
$274$	4.82928	0.291748
$275$	−10.5098	−0.633763
$276$	−5.31986	−0.320218
$277$	−20.9852	−1.26088	−0.630440	−	0.776238i	$-0.717125\pi$
$277$	−20.9852	−1.26088	−0.630440	+	0.776238i	$0.717125\pi$
$278$	2.32202	0.139266
$279$	−4.72323	−0.282772
$280$	0	0
$281$	0.165641	0.00988130	0.00494065	−	0.999988i	$-0.498427\pi$
$281$	0.165641	0.00988130	0.00494065	+	0.999988i	$0.498427\pi$
$282$	−2.11111	−0.125715
$283$	28.8430	1.71454	0.857270	−	0.514867i	$-0.172159\pi$
$283$	28.8430	1.71454	0.857270	+	0.514867i	$0.172159\pi$
$284$	18.1033	1.07423
$285$	−1.06804	−0.0632649
$286$	−0.921124	−0.0544672
$287$	0	0
$288$	2.50762	0.147763
$289$	6.41581	0.377400
$290$	0.381160	0.0223825
$291$	−5.83145	−0.341845
$292$	17.1313	1.00253
$293$	33.8152	1.97550	0.987752	−	0.156032i	$-0.0498702\pi$
$293$	33.8152	1.97550	0.987752	+	0.156032i	$0.0498702\pi$
$294$	0	0
$295$	5.81701	0.338680
$296$	−8.56097	−0.497596
$297$	−2.72323	−0.158018
$298$	−0.341212	−0.0197659
$299$	4.27214	0.247064
$300$	−7.53919	−0.435275
$301$	0	0
$302$	0.122993	0.00707748
$303$	−10.2854	−0.590884
$304$	−3.72323	−0.213542
$305$	−1.89144	−0.108304
$306$	−1.04334	−0.0596439
$307$	−6.44812	−0.368014	−0.184007	−	0.982925i	$-0.558907\pi$
$307$	−6.44812	−0.368014	−0.184007	+	0.982925i	$0.558907\pi$
$308$	0	0
$309$	−14.9516	−0.850567
$310$	1.08767	0.0617755
$311$	−6.69681	−0.379741	−0.189871	−	0.981809i	$-0.560807\pi$
$311$	−6.69681	−0.379741	−0.189871	+	0.981809i	$0.560807\pi$
$312$	−1.33726	−0.0757075
$313$	−0.324492	−0.0183413	−0.00917067	−	0.999958i	$-0.502919\pi$
$313$	−0.324492	−0.0183413	−0.00917067	+	0.999958i	$0.502919\pi$
$314$	1.11701	0.0630364
$315$	0	0
$316$	−5.89645	−0.331701
$317$	2.06637	0.116059	0.0580295	−	0.998315i	$-0.481518\pi$
$317$	2.06637	0.116059	0.0580295	+	0.998315i	$0.481518\pi$
$318$	2.27702	0.127689
$319$	−4.50748	−0.252370
$320$	7.37563	0.412310
$321$	8.80650	0.491531
$322$	0	0
$323$	4.83899	0.269248
$324$	−1.95351	−0.108528
$325$	6.05438	0.335837
$326$	2.01740	0.111733
$327$	−9.58253	−0.529915
$328$	−5.40287	−0.298324
$329$	0	0
$330$	0.627108	0.0345212
$331$	−21.5588	−1.18498	−0.592490	−	0.805578i	$-0.701855\pi$
$331$	−21.5588	−1.18498	−0.592490	+	0.805578i	$0.701855\pi$
$332$	−17.5390	−0.962579
$333$	10.0431	0.550358
$334$	2.86195	0.156599
$335$	−9.53265	−0.520824
$336$	0	0
$337$	−35.5195	−1.93487	−0.967436	−	0.253115i	$-0.918545\pi$
$337$	−35.5195	−1.93487	−0.967436	+	0.253115i	$0.918545\pi$
$338$	−2.27232	−0.123598
$339$	−16.4678	−0.894406
$340$	−10.0962	−0.547541
$341$	−12.8624	−0.696541
$342$	−0.215612	−0.0116589
$343$	0	0
$344$	7.47262	0.402897
$345$	−2.90851	−0.156589
$346$	0.192279	0.0103370
$347$	8.58087	0.460645	0.230323	−	0.973114i	$-0.426022\pi$
$347$	8.58087	0.460645	0.230323	+	0.973114i	$0.426022\pi$
$348$	−3.23344	−0.173331
$349$	18.4044	0.985162	0.492581	−	0.870266i	$-0.336053\pi$
$349$	18.4044	0.985162	0.492581	+	0.870266i	$0.336053\pi$
$350$	0	0
$351$	1.56878	0.0837351
$352$	6.82883	0.363978
$353$	30.3872	1.61735	0.808674	−	0.588257i	$-0.200186\pi$
$353$	30.3872	1.61735	0.808674	+	0.588257i	$0.200186\pi$
$354$	1.17432	0.0624145
$355$	9.89755	0.525307
$356$	−20.7275	−1.09856
$357$	0	0
$358$	2.09739	0.110851
$359$	7.98374	0.421366	0.210683	−	0.977554i	$-0.432431\pi$
$359$	7.98374	0.421366	0.210683	+	0.977554i	$0.432431\pi$
$360$	0.910418	0.0479832
$361$	1.00000	0.0526316
$362$	−3.23950	−0.170265
$363$	3.58401	0.188112
$364$	0	0
$365$	9.36610	0.490244
$366$	−0.381838	−0.0199590
$367$	18.1361	0.946695	0.473348	−	0.880876i	$-0.343045\pi$
$367$	18.1361	0.946695	0.473348	+	0.880876i	$0.343045\pi$
$368$	−10.1392	−0.528543
$369$	6.33825	0.329956
$370$	−2.31273	−0.120233
$371$	0	0
$372$	−9.22689	−0.478392
$373$	19.2018	0.994233	0.497117	−	0.867684i	$-0.334392\pi$
$373$	19.2018	0.994233	0.497117	+	0.867684i	$0.334392\pi$
$374$	−2.84126	−0.146918
$375$	−9.46204	−0.488618
$376$	−8.34630	−0.430428
$377$	2.59663	0.133733
$378$	0	0
$379$	−7.46336	−0.383367	−0.191684	−	0.981457i	$-0.561395\pi$
$379$	−7.46336	−0.383367	−0.191684	+	0.981457i	$0.561395\pi$
$380$	−2.08642	−0.107031
$381$	−6.88864	−0.352916
$382$	−0.519917	−0.0266013
$383$	13.2736	0.678250	0.339125	−	0.940741i	$-0.389869\pi$
$383$	13.2736	0.678250	0.339125	+	0.940741i	$0.389869\pi$
$384$	6.50421	0.331916
$385$	0	0
$386$	0.991088	0.0504450
$387$	−8.76632	−0.445617
$388$	−11.3918	−0.578331
$389$	−5.64750	−0.286340	−0.143170	−	0.989698i	$-0.545730\pi$
$389$	−5.64750	−0.286340	−0.143170	+	0.989698i	$0.545730\pi$
$390$	−0.361259	−0.0182931
$391$	13.1777	0.666424
$392$	0	0
$393$	1.56222	0.0788035
$394$	4.64333	0.233928
$395$	−3.22374	−0.162204
$396$	−5.31986	−0.267333
$397$	−10.8562	−0.544855	−0.272427	−	0.962176i	$-0.587826\pi$
$397$	−10.8562	−0.544855	−0.272427	+	0.962176i	$0.587826\pi$
$398$	1.57621	0.0790081
$399$	0	0
$400$	−14.3691	−0.718453
$401$	7.43630	0.371351	0.185676	−	0.982611i	$-0.440553\pi$
$401$	7.43630	0.371351	0.185676	+	0.982611i	$0.440553\pi$
$402$	−1.92442	−0.0959815
$403$	7.40969	0.369103
$404$	−20.0927	−0.999651
$405$	−1.06804	−0.0530711
$406$	0	0
$407$	27.3497	1.35567
$408$	−4.12487	−0.204211
$409$	−13.6947	−0.677159	−0.338580	−	0.940938i	$-0.609946\pi$
$409$	−13.6947	−0.677159	−0.338580	+	0.940938i	$0.609946\pi$
$410$	−1.45958	−0.0720834
$411$	−22.3981	−1.10481
$412$	−29.2081	−1.43898
$413$	0	0
$414$	−0.587160	−0.0288574
$415$	−9.58904	−0.470707
$416$	−3.93389	−0.192875
$417$	−10.7695	−0.527383
$418$	−0.587160	−0.0287190
$419$	12.9757	0.633906	0.316953	−	0.948441i	$-0.397340\pi$
$419$	12.9757	0.633906	0.316953	+	0.948441i	$0.397340\pi$
$420$	0	0
$421$	14.0300	0.683779	0.341890	−	0.939740i	$-0.388933\pi$
$421$	14.0300	0.683779	0.341890	+	0.939740i	$0.388933\pi$
$422$	1.74723	0.0850537
$423$	9.79127	0.476068
$424$	9.00222	0.437186
$425$	18.6751	0.905876
$426$	1.99809	0.0968077
$427$	0	0
$428$	17.2036	0.831568
$429$	4.27214	0.206261
$430$	2.01872	0.0973512
$431$	−19.3063	−0.929952	−0.464976	−	0.885323i	$-0.653937\pi$
$431$	−19.3063	−0.929952	−0.464976	+	0.885323i	$0.653937\pi$
$432$	−3.72323	−0.179134
$433$	−25.0552	−1.20408	−0.602038	−	0.798468i	$-0.705644\pi$
$433$	−25.0552	−1.20408	−0.602038	+	0.798468i	$0.705644\pi$
$434$	0	0
$435$	−1.76781	−0.0847599
$436$	−18.7196	−0.896506
$437$	2.72323	0.130270
$438$	1.89080	0.0903459
$439$	9.12758	0.435636	0.217818	−	0.975989i	$-0.430106\pi$
$439$	9.12758	0.435636	0.217818	+	0.975989i	$0.430106\pi$
$440$	2.47928	0.118195
$441$	0	0
$442$	1.63677	0.0778533
$443$	−38.5779	−1.83289	−0.916446	−	0.400159i	$-0.868955\pi$
$443$	−38.5779	−1.83289	−0.916446	+	0.400159i	$0.868955\pi$
$444$	19.6193	0.931091
$445$	−11.3323	−0.537201
$446$	−0.0571665	−0.00270691
$447$	1.58253	0.0748512
$448$	0	0
$449$	22.9719	1.08411	0.542056	−	0.840343i	$-0.317646\pi$
$449$	22.9719	1.08411	0.542056	+	0.840343i	$0.317646\pi$
$450$	−0.832110	−0.0392261
$451$	17.2605	0.812766
$452$	−32.1700	−1.51315
$453$	−0.570440	−0.0268016
$454$	−0.912364	−0.0428194
$455$	0	0
$456$	−0.852423	−0.0399184
$457$	11.1344	0.520846	0.260423	−	0.965495i	$-0.416138\pi$
$457$	11.1344	0.520846	0.260423	+	0.965495i	$0.416138\pi$
$458$	−2.70386	−0.126343
$459$	4.83899	0.225865
$460$	−5.68180	−0.264915
$461$	−25.1567	−1.17166	−0.585832	−	0.810433i	$-0.699232\pi$
$461$	−25.1567	−1.17166	−0.585832	+	0.810433i	$0.699232\pi$
$462$	0	0
$463$	−3.81405	−0.177254	−0.0886269	−	0.996065i	$-0.528248\pi$
$463$	−3.81405	−0.177254	−0.0886269	+	0.996065i	$0.528248\pi$
$464$	−6.16267	−0.286095
$465$	−5.04458	−0.233937
$466$	4.67339	0.216490
$467$	23.2402	1.07543	0.537714	−	0.843127i	$-0.319288\pi$
$467$	23.2402	1.07543	0.537714	+	0.843127i	$0.319288\pi$
$468$	3.06462	0.141662
$469$	0	0
$470$	−2.25474	−0.104003
$471$	−5.18065	−0.238712
$472$	4.64269	0.213697
$473$	−23.8727	−1.09767
$474$	−0.650799	−0.0298922
$475$	3.85930	0.177077
$476$	0	0
$477$	−10.5607	−0.483543
$478$	−4.58334	−0.209637
$479$	−7.36994	−0.336741	−0.168371	−	0.985724i	$-0.553851\pi$
$479$	−7.36994	−0.336741	−0.168371	+	0.985724i	$0.553851\pi$
$480$	2.67823	0.122244
$481$	−15.7554	−0.718383
$482$	−6.02730	−0.274536
$483$	0	0
$484$	7.00141	0.318246
$485$	−6.22819	−0.282807
$486$	−0.215612	−0.00978035
$487$	−32.5603	−1.47545	−0.737725	−	0.675102i	$-0.764100\pi$
$487$	−32.5603	−1.47545	−0.737725	+	0.675102i	$0.764100\pi$
$488$	−1.50960	−0.0683365
$489$	−9.35663	−0.423121
$490$	0	0
$491$	21.1987	0.956683	0.478342	−	0.878174i	$-0.341238\pi$
$491$	21.1987	0.956683	0.478342	+	0.878174i	$0.341238\pi$
$492$	12.3818	0.558216
$493$	8.00947	0.360728
$494$	0.338247	0.0152184
$495$	−2.90851	−0.130728
$496$	−17.5857	−0.789620
$497$	0	0
$498$	−1.93581	−0.0867455
$499$	0.642691	0.0287708	0.0143854	−	0.999897i	$-0.495421\pi$
$499$	0.642691	0.0287708	0.0143854	+	0.999897i	$0.495421\pi$
$500$	−18.4842	−0.826639
$501$	−13.2736	−0.593022
$502$	3.29808	0.147201
$503$	27.1477	1.21046	0.605228	−	0.796052i	$-0.293082\pi$
$503$	27.1477	1.21046	0.605228	+	0.796052i	$0.293082\pi$
$504$	0	0
$505$	−10.9852	−0.488836
$506$	−1.59897	−0.0710830
$507$	10.5389	0.468051
$508$	−13.4570	−0.597059
$509$	−8.47432	−0.375617	−0.187809	−	0.982206i	$-0.560139\pi$
$509$	−8.47432	−0.375617	−0.187809	+	0.982206i	$0.560139\pi$
$510$	−1.11433	−0.0493432
$511$	0	0
$512$	15.6840	0.693141
$513$	1.00000	0.0441511
$514$	−0.760179	−0.0335300
$515$	−15.9688	−0.703671
$516$	−17.1251	−0.753891
$517$	26.6639	1.17268
$518$	0	0
$519$	−0.891785	−0.0391450
$520$	−1.42824	−0.0626326
$521$	−2.10673	−0.0922976	−0.0461488	−	0.998935i	$-0.514695\pi$
$521$	−2.10673	−0.0922976	−0.0461488	+	0.998935i	$0.514695\pi$
$522$	−0.356880	−0.0156202
$523$	−25.9499	−1.13471	−0.567356	−	0.823473i	$-0.692034\pi$
$523$	−25.9499	−1.13471	−0.567356	+	0.823473i	$0.692034\pi$
$524$	3.05181	0.133319
$525$	0	0
$526$	−1.49952	−0.0653824
$527$	22.8557	0.995608
$528$	−10.1392	−0.441253
$529$	−15.5840	−0.677566
$530$	2.43194	0.105637
$531$	−5.44646	−0.236356
$532$	0	0
$533$	−9.94329	−0.430692
$534$	−2.28772	−0.0989995
$535$	9.40566	0.406642
$536$	−7.60823	−0.328625
$537$	−9.72763	−0.419778
$538$	−4.37441	−0.188594
$539$	0	0
$540$	−2.08642	−0.0897852
$541$	16.4601	0.707673	0.353837	−	0.935307i	$-0.384877\pi$
$541$	16.4601	0.707673	0.353837	+	0.935307i	$0.384877\pi$
$542$	−3.85814	−0.165721
$543$	15.0247	0.644772
$544$	−12.1343	−0.520255
$545$	−10.2345	−0.438397
$546$	0	0
$547$	32.8295	1.40369	0.701843	−	0.712331i	$-0.252361\pi$
$547$	32.8295	1.40369	0.701843	+	0.712331i	$0.252361\pi$
$548$	−43.7549	−1.86912
$549$	1.77095	0.0755824
$550$	−2.26603	−0.0966238
$551$	1.65520	0.0705137
$552$	−2.32135	−0.0988030
$553$	0	0
$554$	−4.52466	−0.192234
$555$	10.7264	0.455309
$556$	−21.0383	−0.892222
$557$	−20.1947	−0.855679	−0.427839	−	0.903855i	$-0.640725\pi$
$557$	−20.1947	−0.855679	−0.427839	+	0.903855i	$0.640725\pi$
$558$	−1.01838	−0.0431116
$559$	13.7524	0.581665
$560$	0	0
$561$	13.1777	0.556362
$562$	0.0357141	0.00150651
$563$	32.4436	1.36734	0.683668	−	0.729793i	$-0.260384\pi$
$563$	32.4436	1.36734	0.683668	+	0.729793i	$0.260384\pi$
$564$	19.1274	0.805407
$565$	−17.5881	−0.739939
$566$	6.21890	0.261400
$567$	0	0
$568$	7.89946	0.331454
$569$	41.3801	1.73475	0.867373	−	0.497659i	$-0.165807\pi$
$569$	41.3801	1.73475	0.867373	+	0.497659i	$0.165807\pi$
$570$	−0.230281	−0.00964540
$571$	36.7627	1.53847	0.769235	−	0.638966i	$-0.220637\pi$
$571$	36.7627	1.53847	0.769235	+	0.638966i	$0.220637\pi$
$572$	8.34568	0.348950
$573$	2.41136	0.100736
$574$	0	0
$575$	10.5098	0.438288
$576$	−6.90579	−0.287741
$577$	−21.4866	−0.894498	−0.447249	−	0.894409i	$-0.647596\pi$
$577$	−21.4866	−0.894498	−0.447249	+	0.894409i	$0.647596\pi$
$578$	1.38332	0.0575386
$579$	−4.59663	−0.191030
$580$	−3.45343	−0.143396
$581$	0	0
$582$	−1.25733	−0.0521179
$583$	−28.7593	−1.19109
$584$	7.47530	0.309330
$585$	1.67551	0.0692738
$586$	7.29095	0.301186
$587$	45.4194	1.87466	0.937329	−	0.348446i	$-0.113291\pi$
$587$	45.4194	1.87466	0.937329	+	0.348446i	$0.113291\pi$
$588$	0	0
$589$	4.72323	0.194617
$590$	1.25422	0.0516353
$591$	−21.5356	−0.885857
$592$	37.3928	1.53683
$593$	−40.5977	−1.66715	−0.833574	−	0.552407i	$-0.813709\pi$
$593$	−40.5977	−1.66715	−0.833574	+	0.552407i	$0.813709\pi$
$594$	−0.587160	−0.0240915
$595$	0	0
$596$	3.09149	0.126633
$597$	−7.31039	−0.299194
$598$	0.921124	0.0376675
$599$	31.4462	1.28486	0.642429	−	0.766345i	$-0.277927\pi$
$599$	31.4462	1.28486	0.642429	+	0.766345i	$0.277927\pi$
$600$	−3.28976	−0.134304
$601$	−37.2799	−1.52068	−0.760339	−	0.649527i	$-0.774967\pi$
$601$	−37.2799	−1.52068	−0.760339	+	0.649527i	$0.774967\pi$
$602$	0	0
$603$	8.92541	0.363471
$604$	−1.11436	−0.0453427
$605$	3.82785	0.155624
$606$	−2.21766	−0.0900864
$607$	−13.4465	−0.545775	−0.272888	−	0.962046i	$-0.587979\pi$
$607$	−13.4465	−0.545775	−0.272888	+	0.962046i	$0.587979\pi$
$608$	−2.50762	−0.101697
$609$	0	0
$610$	−0.407817	−0.0165120
$611$	−15.3603	−0.621412
$612$	9.45302	0.382116
$613$	−32.9793	−1.33202	−0.666010	−	0.745942i	$-0.731999\pi$
$613$	−32.9793	−1.33202	−0.666010	+	0.745942i	$0.731999\pi$
$614$	−1.39029	−0.0561076
$615$	6.76947	0.272971
$616$	0	0
$617$	14.2184	0.572411	0.286206	−	0.958168i	$-0.407606\pi$
$617$	14.2184	0.572411	0.286206	+	0.958168i	$0.407606\pi$
$618$	−3.22374	−0.129678
$619$	−16.9322	−0.680561	−0.340280	−	0.940324i	$-0.610522\pi$
$619$	−16.9322	−0.680561	−0.340280	+	0.940324i	$0.610522\pi$
$620$	−9.85464	−0.395772
$621$	2.72323	0.109279
$622$	−1.44391	−0.0578955
$623$	0	0
$624$	5.84092	0.233824
$625$	9.19071	0.367628
$626$	−0.0699642	−0.00279633
$627$	2.72323	0.108755
$628$	−10.1205	−0.403850
$629$	−48.5984	−1.93775
$630$	0	0
$631$	37.8074	1.50509	0.752545	−	0.658541i	$-0.228826\pi$
$631$	37.8074	1.50509	0.752545	+	0.658541i	$0.228826\pi$
$632$	−2.57294	−0.102346
$633$	−8.10359	−0.322089
$634$	0.445534	0.0176944
$635$	−7.35731	−0.291966
$636$	−20.6305	−0.818053
$637$	0	0
$638$	−0.971865	−0.0384765
$639$	−9.26707	−0.366599
$640$	6.94672	0.274593
$641$	38.0198	1.50169	0.750846	−	0.660477i	$-0.229646\pi$
$641$	38.0198	1.50169	0.750846	+	0.660477i	$0.229646\pi$
$642$	1.89879	0.0749391
$643$	−24.6833	−0.973415	−0.486708	−	0.873565i	$-0.661802\pi$
$643$	−24.6833	−0.973415	−0.486708	+	0.873565i	$0.661802\pi$
$644$	0	0
$645$	−9.36274	−0.368658
$646$	1.04334	0.0410498
$647$	45.1075	1.77336	0.886679	−	0.462385i	$-0.153006\pi$
$647$	45.1075	1.77336	0.886679	+	0.462385i	$0.153006\pi$
$648$	−0.852423	−0.0334864
$649$	−14.8320	−0.582206
$650$	1.30540	0.0512018
$651$	0	0
$652$	−18.2783	−0.715833
$653$	−10.0862	−0.394703	−0.197351	−	0.980333i	$-0.563234\pi$
$653$	−10.0862	−0.394703	−0.197351	+	0.980333i	$0.563234\pi$
$654$	−2.06611	−0.0807911
$655$	1.66850	0.0651939
$656$	23.5988	0.921377
$657$	−8.76947	−0.342130
$658$	0	0
$659$	14.9983	0.584249	0.292124	−	0.956380i	$-0.405638\pi$
$659$	14.9983	0.584249	0.292124	+	0.956380i	$0.405638\pi$
$660$	−5.68180	−0.221164
$661$	26.9493	1.04821	0.524103	−	0.851655i	$-0.324401\pi$
$661$	26.9493	1.04821	0.524103	+	0.851655i	$0.324401\pi$
$662$	−4.64833	−0.180663
$663$	−7.59129	−0.294821
$664$	−7.65323	−0.297003
$665$	0	0
$666$	2.16541	0.0839079
$667$	4.50748	0.174530
$668$	−25.9302	−1.00327
$669$	0.265137	0.0102508
$670$	−2.05535	−0.0794051
$671$	4.82271	0.186179
$672$	0	0
$673$	12.2645	0.472760	0.236380	−	0.971661i	$-0.424039\pi$
$673$	12.2645	0.472760	0.236380	+	0.971661i	$0.424039\pi$
$674$	−7.65843	−0.294992
$675$	3.85930	0.148545
$676$	20.5879	0.791844
$677$	5.92707	0.227796	0.113898	−	0.993492i	$-0.463666\pi$
$677$	5.92707	0.227796	0.113898	+	0.993492i	$0.463666\pi$
$678$	−3.55064	−0.136362
$679$	0	0
$680$	−4.40550	−0.168943
$681$	4.23151	0.162152
$682$	−2.77329	−0.106195
$683$	19.4923	0.745850	0.372925	−	0.927861i	$-0.378355\pi$
$683$	19.4923	0.745850	0.372925	+	0.927861i	$0.378355\pi$
$684$	1.95351	0.0746944
$685$	−23.9219	−0.914009
$686$	0	0
$687$	12.5404	0.478447
$688$	−32.6390	−1.24435
$689$	16.5674	0.631169
$690$	−0.627108	−0.0238736
$691$	−23.9781	−0.912171	−0.456085	−	0.889936i	$-0.650749\pi$
$691$	−23.9781	−0.912171	−0.456085	+	0.889936i	$0.650749\pi$
$692$	−1.74211	−0.0662252
$693$	0	0
$694$	1.85014	0.0702302
$695$	−11.5022	−0.436302
$696$	−1.41093	−0.0534811
$697$	−30.6707	−1.16174
$698$	3.96819	0.150198
$699$	−21.6750	−0.819824
$700$	0	0
$701$	−26.4842	−1.00030	−0.500148	−	0.865940i	$-0.666721\pi$
$701$	−26.4842	−1.00030	−0.500148	+	0.865940i	$0.666721\pi$
$702$	0.338247	0.0127663
$703$	−10.0431	−0.378782
$704$	−18.8061	−0.708780
$705$	10.4574	0.393849
$706$	6.55184	0.246582
$707$	0	0
$708$	−10.6397	−0.399865
$709$	−39.6587	−1.48942	−0.744708	−	0.667391i	$-0.767411\pi$
$709$	−39.6587	−1.48942	−0.744708	+	0.667391i	$0.767411\pi$
$710$	2.13403	0.0800886
$711$	3.01838	0.113198
$712$	−9.04454	−0.338959
$713$	12.8624	0.481702
$714$	0	0
$715$	4.56280	0.170639
$716$	−19.0030	−0.710177
$717$	21.2574	0.793871
$718$	1.72139	0.0642416
$719$	37.0915	1.38328	0.691641	−	0.722242i	$-0.256888\pi$
$719$	37.0915	1.38328	0.691641	+	0.722242i	$0.256888\pi$
$720$	−3.97654	−0.148197
$721$	0	0
$722$	0.215612	0.00802424
$723$	27.9544	1.03964
$724$	29.3509	1.09082
$725$	6.38790	0.237241
$726$	0.772756	0.0286796
$727$	24.9055	0.923695	0.461848	−	0.886959i	$-0.347187\pi$
$727$	24.9055	0.923695	0.461848	+	0.886959i	$0.347187\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.01944	0.0747429
$731$	42.4201	1.56897
$732$	3.45958	0.127870
$733$	−30.3608	−1.12140	−0.560701	−	0.828019i	$-0.689468\pi$
$733$	−30.3608	−1.12140	−0.560701	+	0.828019i	$0.689468\pi$
$734$	3.91035	0.144334
$735$	0	0
$736$	−6.82883	−0.251714
$737$	24.3059	0.895321
$738$	1.36660	0.0503052
$739$	−14.8681	−0.546930	−0.273465	−	0.961882i	$-0.588170\pi$
$739$	−14.8681	−0.546930	−0.273465	+	0.961882i	$0.588170\pi$
$740$	20.9541	0.770288
$741$	−1.56878	−0.0576304
$742$	0	0
$743$	30.1726	1.10693	0.553463	−	0.832874i	$-0.313306\pi$
$743$	30.1726	1.10693	0.553463	+	0.832874i	$0.313306\pi$
$744$	−4.02619	−0.147607
$745$	1.69020	0.0619241
$746$	4.14014	0.151581
$747$	8.97820	0.328495
$748$	25.7428	0.941248
$749$	0	0
$750$	−2.04013	−0.0744949
$751$	18.7806	0.685313	0.342657	−	0.939461i	$-0.388673\pi$
$751$	18.7806	0.685313	0.342657	+	0.939461i	$0.388673\pi$
$752$	36.4551	1.32938
$753$	−15.2964	−0.557432
$754$	0.559864	0.0203891
$755$	−0.609250	−0.0221729
$756$	0	0
$757$	14.3119	0.520174	0.260087	−	0.965585i	$-0.416249\pi$
$757$	14.3119	0.520174	0.260087	+	0.965585i	$0.416249\pi$
$758$	−1.60919	−0.0584484
$759$	7.41599	0.269183
$760$	−0.910418	−0.0330243
$761$	−45.7382	−1.65801	−0.829005	−	0.559241i	$-0.811093\pi$
$761$	−45.7382	−1.65801	−0.829005	+	0.559241i	$0.811093\pi$
$762$	−1.48527	−0.0538057
$763$	0	0
$764$	4.71061	0.170424
$765$	5.16821	0.186857
$766$	2.86195	0.103406
$767$	8.54428	0.308516
$768$	−12.4092	−0.447778
$769$	41.1147	1.48263	0.741317	−	0.671155i	$-0.234202\pi$
$769$	41.1147	1.48263	0.741317	+	0.671155i	$0.234202\pi$
$770$	0	0
$771$	3.52568	0.126974
$772$	−8.97957	−0.323182
$773$	−20.1891	−0.726150	−0.363075	−	0.931760i	$-0.618273\pi$
$773$	−20.1891	−0.726150	−0.363075	+	0.931760i	$0.618273\pi$
$774$	−1.89012	−0.0679390
$775$	18.2284	0.654782
$776$	−4.97086	−0.178443
$777$	0	0
$778$	−1.21767	−0.0436555
$779$	−6.33825	−0.227091
$780$	3.27313	0.117197
$781$	−25.2364	−0.903028
$782$	2.84126	0.101603
$783$	1.65520	0.0591519
$784$	0	0
$785$	−5.53311	−0.197485
$786$	0.336833	0.0120144
$787$	2.50680	0.0893578	0.0446789	−	0.999001i	$-0.485774\pi$
$787$	2.50680	0.0893578	0.0446789	+	0.999001i	$0.485774\pi$
$788$	−42.0701	−1.49868
$789$	6.95475	0.247595
$790$	−0.695076	−0.0247297
$791$	0	0
$792$	−2.32135	−0.0824854
$793$	−2.77823	−0.0986578
$794$	−2.34071	−0.0830688
$795$	−11.2792	−0.400033
$796$	−14.2809	−0.506174
$797$	51.3144	1.81765	0.908824	−	0.417179i	$-0.136981\pi$
$797$	51.3144	1.81765	0.908824	+	0.417179i	$0.136981\pi$
$798$	0	0
$799$	−47.3798	−1.67618
$800$	−9.67766	−0.342157
$801$	10.6104	0.374900
$802$	1.60335	0.0566164
$803$	−23.8813	−0.842752
$804$	17.4359	0.614916
$805$	0	0
$806$	1.59762	0.0562737
$807$	20.2884	0.714184
$808$	−8.76756	−0.308442
$809$	43.8635	1.54216	0.771079	−	0.636740i	$-0.219717\pi$
$809$	43.8635	1.54216	0.771079	+	0.636740i	$0.219717\pi$
$810$	−0.230281	−0.00809125
$811$	−51.7206	−1.81615	−0.908077	−	0.418802i	$-0.862450\pi$
$811$	−51.7206	−1.81615	−0.908077	+	0.418802i	$0.862450\pi$
$812$	0	0
$813$	17.8939	0.627567
$814$	5.89691	0.206686
$815$	−9.99321	−0.350047
$816$	18.0167	0.630710
$817$	8.76632	0.306695
$818$	−2.95274	−0.103240
$819$	0	0
$820$	13.2242	0.461810
$821$	12.9060	0.450424	0.225212	−	0.974310i	$-0.427693\pi$
$821$	12.9060	0.450424	0.225212	+	0.974310i	$0.427693\pi$
$822$	−4.82928	−0.168441
$823$	21.3165	0.743048	0.371524	−	0.928423i	$-0.378835\pi$
$823$	21.3165	0.743048	0.371524	+	0.928423i	$0.378835\pi$
$824$	−12.7451	−0.443996
$825$	10.5098	0.365903
$826$	0	0
$827$	15.4767	0.538177	0.269088	−	0.963116i	$-0.413278\pi$
$827$	15.4767	0.538177	0.269088	+	0.963116i	$0.413278\pi$
$828$	5.31986	0.184878
$829$	7.98557	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$829$	7.98557	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$830$	−2.06751	−0.0717643
$831$	20.9852	0.727969
$832$	10.8336	0.375589
$833$	0	0
$834$	−2.32202	−0.0804051
$835$	−14.1767	−0.490605
$836$	5.31986	0.183991
$837$	4.72323	0.163259
$838$	2.79772	0.0966457
$839$	12.3706	0.427079	0.213539	−	0.976934i	$-0.431501\pi$
$839$	12.3706	0.427079	0.213539	+	0.976934i	$0.431501\pi$
$840$	0	0
$841$	−26.2603	−0.905529
$842$	3.02503	0.104249
$843$	−0.165641	−0.00570497
$844$	−15.8304	−0.544907
$845$	11.2560	0.387217
$846$	2.11111	0.0725815
$847$	0	0
$848$	−39.3201	−1.35026
$849$	−28.8430	−0.989891
$850$	4.02657	0.138110
$851$	−27.3497	−0.937534
$852$	−18.1033	−0.620210
$853$	−7.07455	−0.242228	−0.121114	−	0.992639i	$-0.538647\pi$
$853$	−7.07455	−0.242228	−0.121114	+	0.992639i	$0.538647\pi$
$854$	0	0
$855$	1.06804	0.0365260
$856$	7.50687	0.256580
$857$	−27.0144	−0.922794	−0.461397	−	0.887194i	$-0.652652\pi$
$857$	−27.0144	−0.922794	−0.461397	+	0.887194i	$0.652652\pi$
$858$	0.921124	0.0314466
$859$	2.63973	0.0900663	0.0450331	−	0.998985i	$-0.485661\pi$
$859$	2.63973	0.0900663	0.0450331	+	0.998985i	$0.485661\pi$
$860$	−18.2902	−0.623692
$861$	0	0
$862$	−4.16266	−0.141781
$863$	−22.2588	−0.757698	−0.378849	−	0.925458i	$-0.623680\pi$
$863$	−22.2588	−0.757698	−0.378849	+	0.925458i	$0.623680\pi$
$864$	−2.50762	−0.0853109
$865$	−0.952458	−0.0323845
$866$	−5.40219	−0.183574
$867$	−6.41581	−0.217892
$868$	0	0
$869$	8.21976	0.278836
$870$	−0.381160	−0.0129225
$871$	−14.0020	−0.474439
$872$	−8.16837	−0.276616
$873$	5.83145	0.197365
$874$	0.587160	0.0198610
$875$	0	0
$876$	−17.1313	−0.578812
$877$	−10.6237	−0.358738	−0.179369	−	0.983782i	$-0.557406\pi$
$877$	−10.6237	−0.358738	−0.179369	+	0.983782i	$0.557406\pi$
$878$	1.96801	0.0664173
$879$	−33.8152	−1.14056
$880$	−10.8290	−0.365047
$881$	−26.7063	−0.899757	−0.449879	−	0.893090i	$-0.648533\pi$
$881$	−26.7063	−0.899757	−0.449879	+	0.893090i	$0.648533\pi$
$882$	0	0
$883$	5.28674	0.177913	0.0889565	−	0.996036i	$-0.471647\pi$
$883$	5.28674	0.177913	0.0889565	+	0.996036i	$0.471647\pi$
$884$	−14.8297	−0.498776
$885$	−5.81701	−0.195537
$886$	−8.31785	−0.279444
$887$	−16.5646	−0.556185	−0.278093	−	0.960554i	$-0.589702\pi$
$887$	−16.5646	−0.556185	−0.278093	+	0.960554i	$0.589702\pi$
$888$	8.56097	0.287287
$889$	0	0
$890$	−2.44337	−0.0819019
$891$	2.72323	0.0912317
$892$	0.517947	0.0173422
$893$	−9.79127	−0.327652
$894$	0.341212	0.0114118
$895$	−10.3894	−0.347281
$896$	0	0
$897$	−4.27214	−0.142643
$898$	4.95301	0.165284
$899$	7.81787	0.260741
$900$	7.53919	0.251306
$901$	51.1033	1.70250
$902$	3.72157	0.123915
$903$	0	0
$904$	−14.0375	−0.466880
$905$	16.0469	0.533418
$906$	−0.122993	−0.00408618
$907$	−1.30314	−0.0432701	−0.0216351	−	0.999766i	$-0.506887\pi$
$907$	−1.30314	−0.0432701	−0.0216351	+	0.999766i	$0.506887\pi$
$908$	8.26631	0.274327
$909$	10.2854	0.341147
$910$	0	0
$911$	39.0195	1.29277	0.646386	−	0.763010i	$-0.276279\pi$
$911$	39.0195	1.29277	0.646386	+	0.763010i	$0.276279\pi$
$912$	3.72323	0.123288
$913$	24.4497	0.809168
$914$	2.40071	0.0794084
$915$	1.89144	0.0625291
$916$	24.4979	0.809432
$917$	0	0
$918$	1.04334	0.0344354
$919$	51.0653	1.68449	0.842244	−	0.539096i	$-0.181234\pi$
$919$	51.0653	1.68449	0.842244	+	0.539096i	$0.181234\pi$
$920$	−2.47928	−0.0817394
$921$	6.44812	0.212473
$922$	−5.42408	−0.178632
$923$	14.5380	0.478523
$924$	0	0
$925$	−38.7593	−1.27440
$926$	−0.822353	−0.0270242
$927$	14.9516	0.491075
$928$	−4.15060	−0.136250
$929$	−50.6776	−1.66268	−0.831339	−	0.555766i	$-0.812425\pi$
$929$	−50.6776	−1.66268	−0.831339	+	0.555766i	$0.812425\pi$
$930$	−1.08767	−0.0356661
$931$	0	0
$932$	−42.3424	−1.38697
$933$	6.69681	0.219244
$934$	5.01086	0.163960
$935$	14.0742	0.460276
$936$	1.33726	0.0437098
$937$	5.41599	0.176933	0.0884663	−	0.996079i	$-0.471803\pi$
$937$	5.41599	0.176933	0.0884663	+	0.996079i	$0.471803\pi$
$938$	0	0
$939$	0.324492	0.0105894
$940$	20.4287	0.666310
$941$	16.6941	0.544211	0.272106	−	0.962267i	$-0.412280\pi$
$941$	16.6941	0.544211	0.272106	+	0.962267i	$0.412280\pi$
$942$	−1.11701	−0.0363941
$943$	−17.2605	−0.562079
$944$	−20.2784	−0.660007
$945$	0	0
$946$	−5.14724	−0.167351
$947$	15.3010	0.497214	0.248607	−	0.968604i	$-0.420027\pi$
$947$	15.3010	0.497214	0.248607	+	0.968604i	$0.420027\pi$
$948$	5.89645	0.191508
$949$	13.7573	0.446582
$950$	0.832110	0.0269972
$951$	−2.06637	−0.0670067
$952$	0	0
$953$	−61.1007	−1.97925	−0.989623	−	0.143690i	$-0.954103\pi$
$953$	−61.1007	−1.97925	−0.989623	+	0.143690i	$0.954103\pi$
$954$	−2.27702	−0.0737212
$955$	2.57541	0.0833384
$956$	41.5265	1.34306
$957$	4.50748	0.145706
$958$	−1.58905	−0.0513397
$959$	0	0
$960$	−7.37563	−0.238047
$961$	−8.69109	−0.280358
$962$	−3.39704	−0.109525
$963$	−8.80650	−0.283786
$964$	54.6092	1.75885
$965$	−4.90936	−0.158038
$966$	0	0
$967$	42.5373	1.36791	0.683954	−	0.729525i	$-0.260259\pi$
$967$	42.5373	1.36791	0.683954	+	0.729525i	$0.260259\pi$
$968$	3.05510	0.0981946
$969$	−4.83899	−0.155451
$970$	−1.34287	−0.0431170
$971$	−24.4233	−0.783781	−0.391890	−	0.920012i	$-0.628179\pi$
$971$	−24.4233	−0.783781	−0.391890	+	0.920012i	$0.628179\pi$
$972$	1.95351	0.0626589
$973$	0	0
$974$	−7.02039	−0.224948
$975$	−6.05438	−0.193895
$976$	6.59367	0.211058
$977$	−23.8150	−0.761908	−0.380954	−	0.924594i	$-0.624404\pi$
$977$	−23.8150	−0.761908	−0.380954	+	0.924594i	$0.624404\pi$
$978$	−2.01740	−0.0645093
$979$	28.8945	0.923473
$980$	0	0
$981$	9.58253	0.305947
$982$	4.57068	0.145856
$983$	−49.3070	−1.57265	−0.786324	−	0.617814i	$-0.788018\pi$
$983$	−49.3070	−1.57265	−0.786324	+	0.617814i	$0.788018\pi$
$984$	5.40287	0.172237
$985$	−23.0008	−0.732866
$986$	1.72694	0.0549968
$987$	0	0
$988$	−3.06462	−0.0974987
$989$	23.8727	0.759108
$990$	−0.627108	−0.0199308
$991$	−7.43203	−0.236086	−0.118043	−	0.993008i	$-0.537662\pi$
$991$	−7.43203	−0.236086	−0.118043	+	0.993008i	$0.537662\pi$
$992$	−11.8441	−0.376049
$993$	21.5588	0.684148
$994$	0	0
$995$	−7.80775	−0.247522
$996$	17.5390	0.555745
$997$	−25.2668	−0.800209	−0.400104	−	0.916470i	$-0.631026\pi$
$997$	−25.2668	−0.800209	−0.400104	+	0.916470i	$0.631026\pi$
$998$	0.138572	0.00438641
$999$	−10.0431	−0.317749

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2793.2.a.be.1.3		5
3.2	odd	2		8379.2.a.ce.1.3		5
7.6	odd	2		399.2.a.f.1.3	✓	5
21.20	even	2		1197.2.a.p.1.3		5
28.27	even	2		6384.2.a.cc.1.3		5
35.34	odd	2		9975.2.a.bq.1.3		5
133.132	even	2		7581.2.a.x.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.a.f.1.3	✓	5	7.6	odd	2
1197.2.a.p.1.3		5	21.20	even	2
2793.2.a.be.1.3		5	1.1	even	1	trivial
6384.2.a.cc.1.3		5	28.27	even	2
7581.2.a.x.1.3		5	133.132	even	2
8379.2.a.ce.1.3		5	3.2	odd	2
9975.2.a.bq.1.3		5	35.34	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:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2793.a (trivial)

\(f(q)\)	\(=\)	\(q+0.215612 q^{2} -1.00000 q^{3} -1.95351 q^{4} -1.06804 q^{5} -0.215612 q^{6} -0.852423 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.215612 q^{2} -1.00000 q^{3} -1.95351 q^{4} -1.06804 q^{5} -0.215612 q^{6} -0.852423 q^{8} +1.00000 q^{9} -0.230281 q^{10} +2.72323 q^{11} +1.95351 q^{12} -1.56878 q^{13} +1.06804 q^{15} +3.72323 q^{16} -4.83899 q^{17} +0.215612 q^{18} -1.00000 q^{19} +2.08642 q^{20} +0.587160 q^{22} -2.72323 q^{23} +0.852423 q^{24} -3.85930 q^{25} -0.338247 q^{26} -1.00000 q^{27} -1.65520 q^{29} +0.230281 q^{30} -4.72323 q^{31} +2.50762 q^{32} -2.72323 q^{33} -1.04334 q^{34} -1.95351 q^{36} +10.0431 q^{37} -0.215612 q^{38} +1.56878 q^{39} +0.910418 q^{40} +6.33825 q^{41} -8.76632 q^{43} -5.31986 q^{44} -1.06804 q^{45} -0.587160 q^{46} +9.79127 q^{47} -3.72323 q^{48} -0.832110 q^{50} +4.83899 q^{51} +3.06462 q^{52} -10.5607 q^{53} -0.215612 q^{54} -2.90851 q^{55} +1.00000 q^{57} -0.356880 q^{58} -5.44646 q^{59} -2.08642 q^{60} +1.77095 q^{61} -1.01838 q^{62} -6.90579 q^{64} +1.67551 q^{65} -0.587160 q^{66} +8.92541 q^{67} +9.45302 q^{68} +2.72323 q^{69} -9.26707 q^{71} -0.852423 q^{72} -8.76947 q^{73} +2.16541 q^{74} +3.85930 q^{75} +1.95351 q^{76} +0.338247 q^{78} +3.01838 q^{79} -3.97654 q^{80} +1.00000 q^{81} +1.36660 q^{82} +8.97820 q^{83} +5.16821 q^{85} -1.89012 q^{86} +1.65520 q^{87} -2.32135 q^{88} +10.6104 q^{89} -0.230281 q^{90} +5.31986 q^{92} +4.72323 q^{93} +2.11111 q^{94} +1.06804 q^{95} -2.50762 q^{96} +5.83145 q^{97} +2.72323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 7 q^{12} - 8 q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 2 q^{23} - 3 q^{24} + 11 q^{25} + 32 q^{26} - 5 q^{27} - 8 q^{31} - 3 q^{32} + 2 q^{33} + 8 q^{34} + 7 q^{36} + 2 q^{37} - q^{38} + 8 q^{39} + 36 q^{40} - 2 q^{41} + 20 q^{43} + 6 q^{44} + 2 q^{45} - 2 q^{46} + 26 q^{47} - 3 q^{48} - q^{50} - 2 q^{51} - 4 q^{52} + 4 q^{53} - q^{54} + 4 q^{55} + 5 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} - 10 q^{61} - 4 q^{62} - 21 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} + 58 q^{68} - 2 q^{69} + 10 q^{71} + 3 q^{72} - 10 q^{73} - 6 q^{74} - 11 q^{75} - 7 q^{76} - 32 q^{78} + 14 q^{79} + 6 q^{80} + 5 q^{81} + 26 q^{82} + 34 q^{83} - 36 q^{85} + 8 q^{86} + 6 q^{88} - 10 q^{89} - 6 q^{92} + 8 q^{93} + 8 q^{94} - 2 q^{95} + 3 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 7 * q^12 - 8 * q^13 - 2 * q^15 + 3 * q^16 + 2 * q^17 + q^18 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 2 * q^23 - 3 * q^24 + 11 * q^25 + 32 * q^26 - 5 * q^27 - 8 * q^31 - 3 * q^32 + 2 * q^33 + 8 * q^34 + 7 * q^36 + 2 * q^37 - q^38 + 8 * q^39 + 36 * q^40 - 2 * q^41 + 20 * q^43 + 6 * q^44 + 2 * q^45 - 2 * q^46 + 26 * q^47 - 3 * q^48 - q^50 - 2 * q^51 - 4 * q^52 + 4 * q^53 - q^54 + 4 * q^55 + 5 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 - 10 * q^61 - 4 * q^62 - 21 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 + 58 * q^68 - 2 * q^69 + 10 * q^71 + 3 * q^72 - 10 * q^73 - 6 * q^74 - 11 * q^75 - 7 * q^76 - 32 * q^78 + 14 * q^79 + 6 * q^80 + 5 * q^81 + 26 * q^82 + 34 * q^83 - 36 * q^85 + 8 * q^86 + 6 * q^88 - 10 * q^89 - 6 * q^92 + 8 * q^93 + 8 * q^94 - 2 * q^95 + 3 * q^96 + 16 * q^97 - 2 * q^99

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