LMFDB - Embedded newform 123.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [123,2,Mod(1,123)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(123, 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("123.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 123 = 3 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	123.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:	$0.982159944862$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	123.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +1.00000 q^{3} +0.585786 q^{5} +1.41421 q^{6} -0.585786 q^{7} -2.82843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +1.00000 q^{3} +0.585786 q^{5} +1.41421 q^{6} -0.585786 q^{7} -2.82843 q^{8} +1.00000 q^{9} +0.828427 q^{10} -0.414214 q^{11} -2.24264 q^{13} -0.828427 q^{14} +0.585786 q^{15} -4.00000 q^{16} +2.41421 q^{17} +1.41421 q^{18} -2.58579 q^{19} -0.585786 q^{21} -0.585786 q^{22} +1.41421 q^{23} -2.82843 q^{24} -4.65685 q^{25} -3.17157 q^{26} +1.00000 q^{27} +8.07107 q^{29} +0.828427 q^{30} -3.00000 q^{31} -0.414214 q^{33} +3.41421 q^{34} -0.343146 q^{35} +7.48528 q^{37} -3.65685 q^{38} -2.24264 q^{39} -1.65685 q^{40} -1.00000 q^{41} -0.828427 q^{42} -5.00000 q^{43} +0.585786 q^{45} +2.00000 q^{46} +7.58579 q^{47} -4.00000 q^{48} -6.65685 q^{49} -6.58579 q^{50} +2.41421 q^{51} +1.17157 q^{53} +1.41421 q^{54} -0.242641 q^{55} +1.65685 q^{56} -2.58579 q^{57} +11.4142 q^{58} +8.48528 q^{59} +6.65685 q^{61} -4.24264 q^{62} -0.585786 q^{63} +8.00000 q^{64} -1.31371 q^{65} -0.585786 q^{66} -6.48528 q^{67} +1.41421 q^{69} -0.485281 q^{70} -4.07107 q^{71} -2.82843 q^{72} +12.3137 q^{73} +10.5858 q^{74} -4.65685 q^{75} +0.242641 q^{77} -3.17157 q^{78} +3.65685 q^{79} -2.34315 q^{80} +1.00000 q^{81} -1.41421 q^{82} -13.0711 q^{83} +1.41421 q^{85} -7.07107 q^{86} +8.07107 q^{87} +1.17157 q^{88} -0.343146 q^{89} +0.828427 q^{90} +1.31371 q^{91} -3.00000 q^{93} +10.7279 q^{94} -1.51472 q^{95} +16.2426 q^{97} -9.41421 q^{98} -0.414214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9	$ 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9} - 4 q^{10} + 2 q^{11} + 4 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} + 2 q^{17} - 8 q^{19} - 4 q^{21} - 4 q^{22} + 2 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{29} - 4 q^{30} - 6 q^{31} + 2 q^{33} + 4 q^{34} - 12 q^{35} - 2 q^{37} + 4 q^{38} + 4 q^{39} + 8 q^{40} - 2 q^{41} + 4 q^{42} - 10 q^{43} + 4 q^{45} + 4 q^{46} + 18 q^{47} - 8 q^{48} - 2 q^{49} - 16 q^{50} + 2 q^{51} + 8 q^{53} + 8 q^{55} - 8 q^{56} - 8 q^{57} + 20 q^{58} + 2 q^{61} - 4 q^{63} + 16 q^{64} + 20 q^{65} - 4 q^{66} + 4 q^{67} + 16 q^{70} + 6 q^{71} + 2 q^{73} + 24 q^{74} + 2 q^{75} - 8 q^{77} - 12 q^{78} - 4 q^{79} - 16 q^{80} + 2 q^{81} - 12 q^{83} + 2 q^{87} + 8 q^{88} - 12 q^{89} - 4 q^{90} - 20 q^{91} - 6 q^{93} - 4 q^{94} - 20 q^{95} + 24 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9 - 4 * q^10 + 2 * q^11 + 4 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 + 2 * q^17 - 8 * q^19 - 4 * q^21 - 4 * q^22 + 2 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^29 - 4 * q^30 - 6 * q^31 + 2 * q^33 + 4 * q^34 - 12 * q^35 - 2 * q^37 + 4 * q^38 + 4 * q^39 + 8 * q^40 - 2 * q^41 + 4 * q^42 - 10 * q^43 + 4 * q^45 + 4 * q^46 + 18 * q^47 - 8 * q^48 - 2 * q^49 - 16 * q^50 + 2 * q^51 + 8 * q^53 + 8 * q^55 - 8 * q^56 - 8 * q^57 + 20 * q^58 + 2 * q^61 - 4 * q^63 + 16 * q^64 + 20 * q^65 - 4 * q^66 + 4 * q^67 + 16 * q^70 + 6 * q^71 + 2 * q^73 + 24 * q^74 + 2 * q^75 - 8 * q^77 - 12 * q^78 - 4 * q^79 - 16 * q^80 + 2 * q^81 - 12 * q^83 + 2 * q^87 + 8 * q^88 - 12 * q^89 - 4 * q^90 - 20 * q^91 - 6 * q^93 - 4 * q^94 - 20 * q^95 + 24 * q^97 - 16 * q^98 + 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 $

$2$	1.41421	1.00000	0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.41421	1.00000	0.500000	+	0.866025i	$0.333333\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0	0
$5$	0.585786	0.261972	0.130986	−	0.991384i	$-0.458186\pi$
$5$	0.585786	0.261972	0.130986	+	0.991384i	$0.458186\pi$
$6$	1.41421	0.577350
$7$	−0.585786	−0.221406	−0.110703	−	0.993854i	$-0.535310\pi$
$7$	−0.585786	−0.221406	−0.110703	+	0.993854i	$0.535310\pi$
$8$	−2.82843	−1.00000
$9$	1.00000	0.333333
$10$	0.828427	0.261972
$11$	−0.414214	−0.124890	−0.0624450	−	0.998048i	$-0.519890\pi$
$11$	−0.414214	−0.124890	−0.0624450	+	0.998048i	$0.519890\pi$
$12$	0	0
$13$	−2.24264	−0.621997	−0.310998	−	0.950410i	$-0.600663\pi$
$13$	−2.24264	−0.621997	−0.310998	+	0.950410i	$0.600663\pi$
$14$	−0.828427	−0.221406
$15$	0.585786	0.151249
$16$	−4.00000	−1.00000
$17$	2.41421	0.585533	0.292766	−	0.956184i	$-0.405424\pi$
$17$	2.41421	0.585533	0.292766	+	0.956184i	$0.405424\pi$
$18$	1.41421	0.333333
$19$	−2.58579	−0.593220	−0.296610	−	0.954999i	$-0.595856\pi$
$19$	−2.58579	−0.593220	−0.296610	+	0.954999i	$0.595856\pi$
$20$	0	0
$21$	−0.585786	−0.127829
$22$	−0.585786	−0.124890
$23$	1.41421	0.294884	0.147442	−	0.989071i	$-0.452896\pi$
$23$	1.41421	0.294884	0.147442	+	0.989071i	$0.452896\pi$
$24$	−2.82843	−0.577350
$25$	−4.65685	−0.931371
$26$	−3.17157	−0.621997
$27$	1.00000	0.192450
$28$	0	0
$29$	8.07107	1.49876	0.749380	−	0.662140i	$-0.230352\pi$
$29$	8.07107	1.49876	0.749380	+	0.662140i	$0.230352\pi$
$30$	0.828427	0.151249
$31$	−3.00000	−0.538816	−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000	−0.538816	−0.269408	+	0.963026i	$0.586828\pi$
$32$	0	0
$33$	−0.414214	−0.0721053
$34$	3.41421	0.585533
$35$	−0.343146	−0.0580022
$36$	0	0
$37$	7.48528	1.23057	0.615286	−	0.788304i	$-0.289040\pi$
$37$	7.48528	1.23057	0.615286	+	0.788304i	$0.289040\pi$
$38$	−3.65685	−0.593220
$39$	−2.24264	−0.359110
$40$	−1.65685	−0.261972
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	−0.828427	−0.127829
$43$	−5.00000	−0.762493	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000	−0.762493	−0.381246	+	0.924473i	$0.624505\pi$
$44$	0	0
$45$	0.585786	0.0873239
$46$	2.00000	0.294884
$47$	7.58579	1.10650	0.553250	−	0.833015i	$-0.313387\pi$
$47$	7.58579	1.10650	0.553250	+	0.833015i	$0.313387\pi$
$48$	−4.00000	−0.577350
$49$	−6.65685	−0.950979
$50$	−6.58579	−0.931371
$51$	2.41421	0.338058
$52$	0	0
$53$	1.17157	0.160928	0.0804640	−	0.996758i	$-0.474360\pi$
$53$	1.17157	0.160928	0.0804640	+	0.996758i	$0.474360\pi$
$54$	1.41421	0.192450
$55$	−0.242641	−0.0327177
$56$	1.65685	0.221406
$57$	−2.58579	−0.342496
$58$	11.4142	1.49876
$59$	8.48528	1.10469	0.552345	−	0.833616i	$-0.313733\pi$
$59$	8.48528	1.10469	0.552345	+	0.833616i	$0.313733\pi$
$60$	0	0
$61$	6.65685	0.852323	0.426161	−	0.904647i	$-0.359866\pi$
$61$	6.65685	0.852323	0.426161	+	0.904647i	$0.359866\pi$
$62$	−4.24264	−0.538816
$63$	−0.585786	−0.0738022
$64$	8.00000	1.00000
$65$	−1.31371	−0.162945
$66$	−0.585786	−0.0721053
$67$	−6.48528	−0.792303	−0.396152	−	0.918185i	$-0.629655\pi$
$67$	−6.48528	−0.792303	−0.396152	+	0.918185i	$0.629655\pi$
$68$	0	0
$69$	1.41421	0.170251
$70$	−0.485281	−0.0580022
$71$	−4.07107	−0.483147	−0.241573	−	0.970383i	$-0.577663\pi$
$71$	−4.07107	−0.483147	−0.241573	+	0.970383i	$0.577663\pi$
$72$	−2.82843	−0.333333
$73$	12.3137	1.44121	0.720605	−	0.693346i	$-0.243864\pi$
$73$	12.3137	1.44121	0.720605	+	0.693346i	$0.243864\pi$
$74$	10.5858	1.23057
$75$	−4.65685	−0.537727
$76$	0	0
$77$	0.242641	0.0276515
$78$	−3.17157	−0.359110
$79$	3.65685	0.411428	0.205714	−	0.978612i	$-0.434048\pi$
$79$	3.65685	0.411428	0.205714	+	0.978612i	$0.434048\pi$
$80$	−2.34315	−0.261972
$81$	1.00000	0.111111
$82$	−1.41421	−0.156174
$83$	−13.0711	−1.43474	−0.717368	−	0.696694i	$-0.754653\pi$
$83$	−13.0711	−1.43474	−0.717368	+	0.696694i	$0.754653\pi$
$84$	0	0
$85$	1.41421	0.153393
$86$	−7.07107	−0.762493
$87$	8.07107	0.865309
$88$	1.17157	0.124890
$89$	−0.343146	−0.0363734	−0.0181867	−	0.999835i	$-0.505789\pi$
$89$	−0.343146	−0.0363734	−0.0181867	+	0.999835i	$0.505789\pi$
$90$	0.828427	0.0873239
$91$	1.31371	0.137714
$92$	0	0
$93$	−3.00000	−0.311086
$94$	10.7279	1.10650
$95$	−1.51472	−0.155407
$96$	0	0
$97$	16.2426	1.64919	0.824595	−	0.565723i	$-0.191403\pi$
$97$	16.2426	1.64919	0.824595	+	0.565723i	$0.191403\pi$
$98$	−9.41421	−0.950979
$99$	−0.414214	−0.0416300
$100$	0	0
$101$	2.41421	0.240223	0.120112	−	0.992760i	$-0.461675\pi$
$101$	2.41421	0.240223	0.120112	+	0.992760i	$0.461675\pi$
$102$	3.41421	0.338058
$103$	−16.3137	−1.60744	−0.803719	−	0.595009i	$-0.797148\pi$
$103$	−16.3137	−1.60744	−0.803719	+	0.595009i	$0.797148\pi$
$104$	6.34315	0.621997
$105$	−0.343146	−0.0334876
$106$	1.65685	0.160928
$107$	−11.6569	−1.12691	−0.563455	−	0.826147i	$-0.690528\pi$
$107$	−11.6569	−1.12691	−0.563455	+	0.826147i	$0.690528\pi$
$108$	0	0
$109$	−11.8995	−1.13976	−0.569882	−	0.821726i	$-0.693011\pi$
$109$	−11.8995	−1.13976	−0.569882	+	0.821726i	$0.693011\pi$
$110$	−0.343146	−0.0327177
$111$	7.48528	0.710471
$112$	2.34315	0.221406
$113$	−18.7279	−1.76177	−0.880887	−	0.473326i	$-0.843053\pi$
$113$	−18.7279	−1.76177	−0.880887	+	0.473326i	$0.843053\pi$
$114$	−3.65685	−0.342496
$115$	0.828427	0.0772512
$116$	0	0
$117$	−2.24264	−0.207332
$118$	12.0000	1.10469
$119$	−1.41421	−0.129641
$120$	−1.65685	−0.151249
$121$	−10.8284	−0.984402
$122$	9.41421	0.852323
$123$	−1.00000	−0.0901670
$124$	0	0
$125$	−5.65685	−0.505964
$126$	−0.828427	−0.0738022
$127$	−13.3137	−1.18140	−0.590700	−	0.806891i	$-0.701148\pi$
$127$	−13.3137	−1.18140	−0.590700	+	0.806891i	$0.701148\pi$
$128$	11.3137	1.00000
$129$	−5.00000	−0.440225
$130$	−1.85786	−0.162945
$131$	−13.4142	−1.17201	−0.586003	−	0.810309i	$-0.699299\pi$
$131$	−13.4142	−1.17201	−0.586003	+	0.810309i	$0.699299\pi$
$132$	0	0
$133$	1.51472	0.131343
$134$	−9.17157	−0.792303
$135$	0.585786	0.0504165
$136$	−6.82843	−0.585533
$137$	18.0711	1.54392	0.771958	−	0.635674i	$-0.219278\pi$
$137$	18.0711	1.54392	0.771958	+	0.635674i	$0.219278\pi$
$138$	2.00000	0.170251
$139$	−7.65685	−0.649446	−0.324723	−	0.945809i	$-0.605271\pi$
$139$	−7.65685	−0.649446	−0.324723	+	0.945809i	$0.605271\pi$
$140$	0	0
$141$	7.58579	0.638838
$142$	−5.75736	−0.483147
$143$	0.928932	0.0776812
$144$	−4.00000	−0.333333
$145$	4.72792	0.392633
$146$	17.4142	1.44121
$147$	−6.65685	−0.549048
$148$	0	0
$149$	−5.31371	−0.435316	−0.217658	−	0.976025i	$-0.569842\pi$
$149$	−5.31371	−0.435316	−0.217658	+	0.976025i	$0.569842\pi$
$150$	−6.58579	−0.537727
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	7.31371	0.593220
$153$	2.41421	0.195178
$154$	0.343146	0.0276515
$155$	−1.75736	−0.141154
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	5.17157	0.411428
$159$	1.17157	0.0929118
$160$	0	0
$161$	−0.828427	−0.0652892
$162$	1.41421	0.111111
$163$	7.48528	0.586292	0.293146	−	0.956068i	$-0.405298\pi$
$163$	7.48528	0.586292	0.293146	+	0.956068i	$0.405298\pi$
$164$	0	0
$165$	−0.242641	−0.0188896
$166$	−18.4853	−1.43474
$167$	7.65685	0.592505	0.296253	−	0.955110i	$-0.404263\pi$
$167$	7.65685	0.592505	0.296253	+	0.955110i	$0.404263\pi$
$168$	1.65685	0.127829
$169$	−7.97056	−0.613120
$170$	2.00000	0.153393
$171$	−2.58579	−0.197740
$172$	0	0
$173$	5.07107	0.385546	0.192773	−	0.981243i	$-0.438252\pi$
$173$	5.07107	0.385546	0.192773	+	0.981243i	$0.438252\pi$
$174$	11.4142	0.865309
$175$	2.72792	0.206212
$176$	1.65685	0.124890
$177$	8.48528	0.637793
$178$	−0.485281	−0.0363734
$179$	14.8995	1.11364	0.556820	−	0.830633i	$-0.312021\pi$
$179$	14.8995	1.11364	0.556820	+	0.830633i	$0.312021\pi$
$180$	0	0
$181$	15.3137	1.13826	0.569129	−	0.822248i	$-0.307280\pi$
$181$	15.3137	1.13826	0.569129	+	0.822248i	$0.307280\pi$
$182$	1.85786	0.137714
$183$	6.65685	0.492089
$184$	−4.00000	−0.294884
$185$	4.38478	0.322375
$186$	−4.24264	−0.311086
$187$	−1.00000	−0.0731272
$188$	0	0
$189$	−0.585786	−0.0426097
$190$	−2.14214	−0.155407
$191$	13.1716	0.953062	0.476531	−	0.879158i	$-0.341894\pi$
$191$	13.1716	0.953062	0.476531	+	0.879158i	$0.341894\pi$
$192$	8.00000	0.577350
$193$	3.41421	0.245760	0.122880	−	0.992422i	$-0.460787\pi$
$193$	3.41421	0.245760	0.122880	+	0.992422i	$0.460787\pi$
$194$	22.9706	1.64919
$195$	−1.31371	−0.0940766
$196$	0	0
$197$	13.7574	0.980171	0.490086	−	0.871674i	$-0.336965\pi$
$197$	13.7574	0.980171	0.490086	+	0.871674i	$0.336965\pi$
$198$	−0.585786	−0.0416300
$199$	−7.75736	−0.549905	−0.274952	−	0.961458i	$-0.588662\pi$
$199$	−7.75736	−0.549905	−0.274952	+	0.961458i	$0.588662\pi$
$200$	13.1716	0.931371
$201$	−6.48528	−0.457436
$202$	3.41421	0.240223
$203$	−4.72792	−0.331835
$204$	0	0
$205$	−0.585786	−0.0409131
$206$	−23.0711	−1.60744
$207$	1.41421	0.0982946
$208$	8.97056	0.621997
$209$	1.07107	0.0740873
$210$	−0.485281	−0.0334876
$211$	−7.51472	−0.517335	−0.258667	−	0.965966i	$-0.583283\pi$
$211$	−7.51472	−0.517335	−0.258667	+	0.965966i	$0.583283\pi$
$212$	0	0
$213$	−4.07107	−0.278945
$214$	−16.4853	−1.12691
$215$	−2.92893	−0.199752
$216$	−2.82843	−0.192450
$217$	1.75736	0.119297
$218$	−16.8284	−1.13976
$219$	12.3137	0.832083
$220$	0	0
$221$	−5.41421	−0.364199
$222$	10.5858	0.710471
$223$	21.6569	1.45025	0.725125	−	0.688617i	$-0.241782\pi$
$223$	21.6569	1.45025	0.725125	+	0.688617i	$0.241782\pi$
$224$	0	0
$225$	−4.65685	−0.310457
$226$	−26.4853	−1.76177
$227$	20.8995	1.38715	0.693574	−	0.720385i	$-0.256035\pi$
$227$	20.8995	1.38715	0.693574	+	0.720385i	$0.256035\pi$
$228$	0	0
$229$	8.24264	0.544689	0.272345	−	0.962200i	$-0.412201\pi$
$229$	8.24264	0.544689	0.272345	+	0.962200i	$0.412201\pi$
$230$	1.17157	0.0772512
$231$	0.242641	0.0159646
$232$	−22.8284	−1.49876
$233$	−18.0000	−1.17922	−0.589610	−	0.807688i	$-0.700718\pi$
$233$	−18.0000	−1.17922	−0.589610	+	0.807688i	$0.700718\pi$
$234$	−3.17157	−0.207332
$235$	4.44365	0.289872
$236$	0	0
$237$	3.65685	0.237538
$238$	−2.00000	−0.129641
$239$	−10.1421	−0.656040	−0.328020	−	0.944671i	$-0.606381\pi$
$239$	−10.1421	−0.656040	−0.328020	+	0.944671i	$0.606381\pi$
$240$	−2.34315	−0.151249
$241$	−7.48528	−0.482169	−0.241085	−	0.970504i	$-0.577503\pi$
$241$	−7.48528	−0.482169	−0.241085	+	0.970504i	$0.577503\pi$
$242$	−15.3137	−0.984402
$243$	1.00000	0.0641500
$244$	0	0
$245$	−3.89949	−0.249130
$246$	−1.41421	−0.0901670
$247$	5.79899	0.368981
$248$	8.48528	0.538816
$249$	−13.0711	−0.828345
$250$	−8.00000	−0.505964
$251$	3.17157	0.200188	0.100094	−	0.994978i	$-0.468086\pi$
$251$	3.17157	0.200188	0.100094	+	0.994978i	$0.468086\pi$
$252$	0	0
$253$	−0.585786	−0.0368281
$254$	−18.8284	−1.18140
$255$	1.41421	0.0885615
$256$	0	0
$257$	−24.8995	−1.55319	−0.776594	−	0.630002i	$-0.783054\pi$
$257$	−24.8995	−1.55319	−0.776594	+	0.630002i	$0.783054\pi$
$258$	−7.07107	−0.440225
$259$	−4.38478	−0.272457
$260$	0	0
$261$	8.07107	0.499587
$262$	−18.9706	−1.17201
$263$	−0.414214	−0.0255415	−0.0127708	−	0.999918i	$-0.504065\pi$
$263$	−0.414214	−0.0255415	−0.0127708	+	0.999918i	$0.504065\pi$
$264$	1.17157	0.0721053
$265$	0.686292	0.0421586
$266$	2.14214	0.131343
$267$	−0.343146	−0.0210002
$268$	0	0
$269$	8.48528	0.517357	0.258678	−	0.965964i	$-0.416713\pi$
$269$	8.48528	0.517357	0.258678	+	0.965964i	$0.416713\pi$
$270$	0.828427	0.0504165
$271$	−20.7990	−1.26345	−0.631724	−	0.775193i	$-0.717653\pi$
$271$	−20.7990	−1.26345	−0.631724	+	0.775193i	$0.717653\pi$
$272$	−9.65685	−0.585533
$273$	1.31371	0.0795093
$274$	25.5563	1.54392
$275$	1.92893	0.116319
$276$	0	0
$277$	29.2843	1.75952	0.879761	−	0.475417i	$-0.157703\pi$
$277$	29.2843	1.75952	0.879761	+	0.475417i	$0.157703\pi$
$278$	−10.8284	−0.649446
$279$	−3.00000	−0.179605
$280$	0.970563	0.0580022
$281$	−19.3848	−1.15640	−0.578199	−	0.815895i	$-0.696244\pi$
$281$	−19.3848	−1.15640	−0.578199	+	0.815895i	$0.696244\pi$
$282$	10.7279	0.638838
$283$	21.8284	1.29757	0.648783	−	0.760974i	$-0.275278\pi$
$283$	21.8284	1.29757	0.648783	+	0.760974i	$0.275278\pi$
$284$	0	0
$285$	−1.51472	−0.0897242
$286$	1.31371	0.0776812
$287$	0.585786	0.0345779
$288$	0	0
$289$	−11.1716	−0.657151
$290$	6.68629	0.392633
$291$	16.2426	0.952160
$292$	0	0
$293$	12.4142	0.725246	0.362623	−	0.931936i	$-0.381881\pi$
$293$	12.4142	0.725246	0.362623	+	0.931936i	$0.381881\pi$
$294$	−9.41421	−0.549048
$295$	4.97056	0.289397
$296$	−21.1716	−1.23057
$297$	−0.414214	−0.0240351
$298$	−7.51472	−0.435316
$299$	−3.17157	−0.183417
$300$	0	0
$301$	2.92893	0.168821
$302$	−22.6274	−1.30206
$303$	2.41421	0.138693
$304$	10.3431	0.593220
$305$	3.89949	0.223284
$306$	3.41421	0.195178
$307$	22.3137	1.27351	0.636755	−	0.771066i	$-0.280276\pi$
$307$	22.3137	1.27351	0.636755	+	0.771066i	$0.280276\pi$
$308$	0	0
$309$	−16.3137	−0.928054
$310$	−2.48528	−0.141154
$311$	21.1716	1.20053	0.600265	−	0.799801i	$-0.295062\pi$
$311$	21.1716	1.20053	0.600265	+	0.799801i	$0.295062\pi$
$312$	6.34315	0.359110
$313$	24.8701	1.40574	0.702869	−	0.711319i	$-0.251902\pi$
$313$	24.8701	1.40574	0.702869	+	0.711319i	$0.251902\pi$
$314$	25.4558	1.43656
$315$	−0.343146	−0.0193341
$316$	0	0
$317$	2.07107	0.116323	0.0581614	−	0.998307i	$-0.481476\pi$
$317$	2.07107	0.116323	0.0581614	+	0.998307i	$0.481476\pi$
$318$	1.65685	0.0929118
$319$	−3.34315	−0.187180
$320$	4.68629	0.261972
$321$	−11.6569	−0.650622
$322$	−1.17157	−0.0652892
$323$	−6.24264	−0.347350
$324$	0	0
$325$	10.4437	0.579310
$326$	10.5858	0.586292
$327$	−11.8995	−0.658044
$328$	2.82843	0.156174
$329$	−4.44365	−0.244986
$330$	−0.343146	−0.0188896
$331$	7.75736	0.426383	0.213192	−	0.977010i	$-0.431614\pi$
$331$	7.75736	0.426383	0.213192	+	0.977010i	$0.431614\pi$
$332$	0	0
$333$	7.48528	0.410191
$334$	10.8284	0.592505
$335$	−3.79899	−0.207561
$336$	2.34315	0.127829
$337$	−13.9706	−0.761025	−0.380513	−	0.924776i	$-0.624252\pi$
$337$	−13.9706	−0.761025	−0.380513	+	0.924776i	$0.624252\pi$
$338$	−11.2721	−0.613120
$339$	−18.7279	−1.01716
$340$	0	0
$341$	1.24264	0.0672928
$342$	−3.65685	−0.197740
$343$	8.00000	0.431959
$344$	14.1421	0.762493
$345$	0.828427	0.0446010
$346$	7.17157	0.385546
$347$	−18.8995	−1.01458	−0.507289	−	0.861776i	$-0.669352\pi$
$347$	−18.8995	−1.01458	−0.507289	+	0.861776i	$0.669352\pi$
$348$	0	0
$349$	−19.1421	−1.02466	−0.512328	−	0.858790i	$-0.671217\pi$
$349$	−19.1421	−1.02466	−0.512328	+	0.858790i	$0.671217\pi$
$350$	3.85786	0.206212
$351$	−2.24264	−0.119703
$352$	0	0
$353$	−1.02944	−0.0547914	−0.0273957	−	0.999625i	$-0.508721\pi$
$353$	−1.02944	−0.0547914	−0.0273957	+	0.999625i	$0.508721\pi$
$354$	12.0000	0.637793
$355$	−2.38478	−0.126571
$356$	0	0
$357$	−1.41421	−0.0748481
$358$	21.0711	1.11364
$359$	7.75736	0.409418	0.204709	−	0.978823i	$-0.434375\pi$
$359$	7.75736	0.409418	0.204709	+	0.978823i	$0.434375\pi$
$360$	−1.65685	−0.0873239
$361$	−12.3137	−0.648090
$362$	21.6569	1.13826
$363$	−10.8284	−0.568345
$364$	0	0
$365$	7.21320	0.377556
$366$	9.41421	0.492089
$367$	4.65685	0.243086	0.121543	−	0.992586i	$-0.461216\pi$
$367$	4.65685	0.243086	0.121543	+	0.992586i	$0.461216\pi$
$368$	−5.65685	−0.294884
$369$	−1.00000	−0.0520579
$370$	6.20101	0.322375
$371$	−0.686292	−0.0356305
$372$	0	0
$373$	4.85786	0.251531	0.125765	−	0.992060i	$-0.459861\pi$
$373$	4.85786	0.251531	0.125765	+	0.992060i	$0.459861\pi$
$374$	−1.41421	−0.0731272
$375$	−5.65685	−0.292119
$376$	−21.4558	−1.10650
$377$	−18.1005	−0.932223
$378$	−0.828427	−0.0426097
$379$	−6.97056	−0.358054	−0.179027	−	0.983844i	$-0.557295\pi$
$379$	−6.97056	−0.358054	−0.179027	+	0.983844i	$0.557295\pi$
$380$	0	0
$381$	−13.3137	−0.682082
$382$	18.6274	0.953062
$383$	36.8995	1.88548	0.942738	−	0.333534i	$-0.108241\pi$
$383$	36.8995	1.88548	0.942738	+	0.333534i	$0.108241\pi$
$384$	11.3137	0.577350
$385$	0.142136	0.00724390
$386$	4.82843	0.245760
$387$	−5.00000	−0.254164
$388$	0	0
$389$	−13.7574	−0.697526	−0.348763	−	0.937211i	$-0.613398\pi$
$389$	−13.7574	−0.697526	−0.348763	+	0.937211i	$0.613398\pi$
$390$	−1.85786	−0.0940766
$391$	3.41421	0.172664
$392$	18.8284	0.950979
$393$	−13.4142	−0.676658
$394$	19.4558	0.980171
$395$	2.14214	0.107783
$396$	0	0
$397$	−34.5269	−1.73286	−0.866428	−	0.499302i	$-0.833590\pi$
$397$	−34.5269	−1.73286	−0.866428	+	0.499302i	$0.833590\pi$
$398$	−10.9706	−0.549905
$399$	1.51472	0.0758308
$400$	18.6274	0.931371
$401$	−34.6274	−1.72921	−0.864605	−	0.502452i	$-0.832432\pi$
$401$	−34.6274	−1.72921	−0.864605	+	0.502452i	$0.832432\pi$
$402$	−9.17157	−0.457436
$403$	6.72792	0.335142
$404$	0	0
$405$	0.585786	0.0291080
$406$	−6.68629	−0.331835
$407$	−3.10051	−0.153686
$408$	−6.82843	−0.338058
$409$	21.8284	1.07935	0.539673	−	0.841875i	$-0.318548\pi$
$409$	21.8284	1.07935	0.539673	+	0.841875i	$0.318548\pi$
$410$	−0.828427	−0.0409131
$411$	18.0711	0.891380
$412$	0	0
$413$	−4.97056	−0.244585
$414$	2.00000	0.0982946
$415$	−7.65685	−0.375860
$416$	0	0
$417$	−7.65685	−0.374958
$418$	1.51472	0.0740873
$419$	0.928932	0.0453813	0.0226907	−	0.999743i	$-0.492777\pi$
$419$	0.928932	0.0453813	0.0226907	+	0.999743i	$0.492777\pi$
$420$	0	0
$421$	24.9706	1.21699	0.608495	−	0.793557i	$-0.291773\pi$
$421$	24.9706	1.21699	0.608495	+	0.793557i	$0.291773\pi$
$422$	−10.6274	−0.517335
$423$	7.58579	0.368834
$424$	−3.31371	−0.160928
$425$	−11.2426	−0.545348
$426$	−5.75736	−0.278945
$427$	−3.89949	−0.188710
$428$	0	0
$429$	0.928932	0.0448493
$430$	−4.14214	−0.199752
$431$	39.0711	1.88199	0.940994	−	0.338424i	$-0.109894\pi$
$431$	39.0711	1.88199	0.940994	+	0.338424i	$0.109894\pi$
$432$	−4.00000	−0.192450
$433$	−11.4853	−0.551947	−0.275974	−	0.961165i	$-0.589000\pi$
$433$	−11.4853	−0.551947	−0.275974	+	0.961165i	$0.589000\pi$
$434$	2.48528	0.119297
$435$	4.72792	0.226687
$436$	0	0
$437$	−3.65685	−0.174931
$438$	17.4142	0.832083
$439$	−30.9706	−1.47814	−0.739072	−	0.673626i	$-0.764736\pi$
$439$	−30.9706	−1.47814	−0.739072	+	0.673626i	$0.764736\pi$
$440$	0.686292	0.0327177
$441$	−6.65685	−0.316993
$442$	−7.65685	−0.364199
$443$	20.2843	0.963735	0.481867	−	0.876244i	$-0.339959\pi$
$443$	20.2843	0.963735	0.481867	+	0.876244i	$0.339959\pi$
$444$	0	0
$445$	−0.201010	−0.00952879
$446$	30.6274	1.45025
$447$	−5.31371	−0.251330
$448$	−4.68629	−0.221406
$449$	20.4853	0.966760	0.483380	−	0.875411i	$-0.339409\pi$
$449$	20.4853	0.966760	0.483380	+	0.875411i	$0.339409\pi$
$450$	−6.58579	−0.310457
$451$	0.414214	0.0195046
$452$	0	0
$453$	−16.0000	−0.751746
$454$	29.5563	1.38715
$455$	0.769553	0.0360772
$456$	7.31371	0.342496
$457$	−4.00000	−0.187112	−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000	−0.187112	−0.0935561	+	0.995614i	$0.529823\pi$
$458$	11.6569	0.544689
$459$	2.41421	0.112686
$460$	0	0
$461$	−16.6274	−0.774416	−0.387208	−	0.921992i	$-0.626560\pi$
$461$	−16.6274	−0.774416	−0.387208	+	0.921992i	$0.626560\pi$
$462$	0.343146	0.0159646
$463$	5.55635	0.258225	0.129113	−	0.991630i	$-0.458787\pi$
$463$	5.55635	0.258225	0.129113	+	0.991630i	$0.458787\pi$
$464$	−32.2843	−1.49876
$465$	−1.75736	−0.0814956
$466$	−25.4558	−1.17922
$467$	21.3137	0.986281	0.493140	−	0.869950i	$-0.335849\pi$
$467$	21.3137	0.986281	0.493140	+	0.869950i	$0.335849\pi$
$468$	0	0
$469$	3.79899	0.175421
$470$	6.28427	0.289872
$471$	18.0000	0.829396
$472$	−24.0000	−1.10469
$473$	2.07107	0.0952278
$474$	5.17157	0.237538
$475$	12.0416	0.552508
$476$	0	0
$477$	1.17157	0.0536426
$478$	−14.3431	−0.656040
$479$	−12.8995	−0.589393	−0.294696	−	0.955591i	$-0.595219\pi$
$479$	−12.8995	−0.589393	−0.294696	+	0.955591i	$0.595219\pi$
$480$	0	0
$481$	−16.7868	−0.765412
$482$	−10.5858	−0.482169
$483$	−0.828427	−0.0376947
$484$	0	0
$485$	9.51472	0.432041
$486$	1.41421	0.0641500
$487$	−31.9706	−1.44872	−0.724362	−	0.689420i	$-0.757866\pi$
$487$	−31.9706	−1.44872	−0.724362	+	0.689420i	$0.757866\pi$
$488$	−18.8284	−0.852323
$489$	7.48528	0.338496
$490$	−5.51472	−0.249130
$491$	1.07107	0.0483366	0.0241683	−	0.999708i	$-0.492306\pi$
$491$	1.07107	0.0483366	0.0241683	+	0.999708i	$0.492306\pi$
$492$	0	0
$493$	19.4853	0.877573
$494$	8.20101	0.368981
$495$	−0.242641	−0.0109059
$496$	12.0000	0.538816
$497$	2.38478	0.106972
$498$	−18.4853	−0.828345
$499$	−36.4853	−1.63331	−0.816653	−	0.577129i	$-0.804173\pi$
$499$	−36.4853	−1.63331	−0.816653	+	0.577129i	$0.804173\pi$
$500$	0	0
$501$	7.65685	0.342083
$502$	4.48528	0.200188
$503$	−35.3848	−1.57773	−0.788865	−	0.614567i	$-0.789331\pi$
$503$	−35.3848	−1.57773	−0.788865	+	0.614567i	$0.789331\pi$
$504$	1.65685	0.0738022
$505$	1.41421	0.0629317
$506$	−0.828427	−0.0368281
$507$	−7.97056	−0.353985
$508$	0	0
$509$	−33.8701	−1.50126	−0.750632	−	0.660721i	$-0.770251\pi$
$509$	−33.8701	−1.50126	−0.750632	+	0.660721i	$0.770251\pi$
$510$	2.00000	0.0885615
$511$	−7.21320	−0.319093
$512$	−22.6274	−1.00000
$513$	−2.58579	−0.114165
$514$	−35.2132	−1.55319
$515$	−9.55635	−0.421103
$516$	0	0
$517$	−3.14214	−0.138191
$518$	−6.20101	−0.272457
$519$	5.07107	0.222595
$520$	3.71573	0.162945
$521$	22.7574	0.997018	0.498509	−	0.866885i	$-0.333881\pi$
$521$	22.7574	0.997018	0.498509	+	0.866885i	$0.333881\pi$
$522$	11.4142	0.499587
$523$	34.0000	1.48672	0.743358	−	0.668894i	$-0.233232\pi$
$523$	34.0000	1.48672	0.743358	+	0.668894i	$0.233232\pi$
$524$	0	0
$525$	2.72792	0.119056
$526$	−0.585786	−0.0255415
$527$	−7.24264	−0.315494
$528$	1.65685	0.0721053
$529$	−21.0000	−0.913043
$530$	0.970563	0.0421586
$531$	8.48528	0.368230
$532$	0	0
$533$	2.24264	0.0971396
$534$	−0.485281	−0.0210002
$535$	−6.82843	−0.295219
$536$	18.3431	0.792303
$537$	14.8995	0.642961
$538$	12.0000	0.517357
$539$	2.75736	0.118768
$540$	0	0
$541$	18.9706	0.815608	0.407804	−	0.913069i	$-0.366295\pi$
$541$	18.9706	0.815608	0.407804	+	0.913069i	$0.366295\pi$
$542$	−29.4142	−1.26345
$543$	15.3137	0.657174
$544$	0	0
$545$	−6.97056	−0.298586
$546$	1.85786	0.0795093
$547$	−7.51472	−0.321306	−0.160653	−	0.987011i	$-0.551360\pi$
$547$	−7.51472	−0.321306	−0.160653	+	0.987011i	$0.551360\pi$
$548$	0	0
$549$	6.65685	0.284108
$550$	2.72792	0.116319
$551$	−20.8701	−0.889094
$552$	−4.00000	−0.170251
$553$	−2.14214	−0.0910929
$554$	41.4142	1.75952
$555$	4.38478	0.186123
$556$	0	0
$557$	39.7279	1.68333	0.841663	−	0.540003i	$-0.181577\pi$
$557$	39.7279	1.68333	0.841663	+	0.540003i	$0.181577\pi$
$558$	−4.24264	−0.179605
$559$	11.2132	0.474268
$560$	1.37258	0.0580022
$561$	−1.00000	−0.0422200
$562$	−27.4142	−1.15640
$563$	−12.8995	−0.543649	−0.271824	−	0.962347i	$-0.587627\pi$
$563$	−12.8995	−0.543649	−0.271824	+	0.962347i	$0.587627\pi$
$564$	0	0
$565$	−10.9706	−0.461535
$566$	30.8701	1.29757
$567$	−0.585786	−0.0246007
$568$	11.5147	0.483147
$569$	−35.5563	−1.49060	−0.745300	−	0.666729i	$-0.767694\pi$
$569$	−35.5563	−1.49060	−0.745300	+	0.666729i	$0.767694\pi$
$570$	−2.14214	−0.0897242
$571$	42.6274	1.78390	0.891951	−	0.452132i	$-0.149336\pi$
$571$	42.6274	1.78390	0.891951	+	0.452132i	$0.149336\pi$
$572$	0	0
$573$	13.1716	0.550250
$574$	0.828427	0.0345779
$575$	−6.58579	−0.274646
$576$	8.00000	0.333333
$577$	−19.5147	−0.812408	−0.406204	−	0.913782i	$-0.633148\pi$
$577$	−19.5147	−0.812408	−0.406204	+	0.913782i	$0.633148\pi$
$578$	−15.7990	−0.657151
$579$	3.41421	0.141890
$580$	0	0
$581$	7.65685	0.317660
$582$	22.9706	0.952160
$583$	−0.485281	−0.0200983
$584$	−34.8284	−1.44121
$585$	−1.31371	−0.0543152
$586$	17.5563	0.725246
$587$	7.38478	0.304802	0.152401	−	0.988319i	$-0.451299\pi$
$587$	7.38478	0.304802	0.152401	+	0.988319i	$0.451299\pi$
$588$	0	0
$589$	7.75736	0.319636
$590$	7.02944	0.289397
$591$	13.7574	0.565902
$592$	−29.9411	−1.23057
$593$	4.41421	0.181270	0.0906350	−	0.995884i	$-0.471110\pi$
$593$	4.41421	0.181270	0.0906350	+	0.995884i	$0.471110\pi$
$594$	−0.585786	−0.0240351
$595$	−0.828427	−0.0339622
$596$	0	0
$597$	−7.75736	−0.317488
$598$	−4.48528	−0.183417
$599$	35.3553	1.44458	0.722290	−	0.691590i	$-0.243090\pi$
$599$	35.3553	1.44458	0.722290	+	0.691590i	$0.243090\pi$
$600$	13.1716	0.537727
$601$	−9.51472	−0.388113	−0.194057	−	0.980990i	$-0.562165\pi$
$601$	−9.51472	−0.388113	−0.194057	+	0.980990i	$0.562165\pi$
$602$	4.14214	0.168821
$603$	−6.48528	−0.264101
$604$	0	0
$605$	−6.34315	−0.257886
$606$	3.41421	0.138693
$607$	−17.5147	−0.710900	−0.355450	−	0.934695i	$-0.615672\pi$
$607$	−17.5147	−0.710900	−0.355450	+	0.934695i	$0.615672\pi$
$608$	0	0
$609$	−4.72792	−0.191585
$610$	5.51472	0.223284
$611$	−17.0122	−0.688240
$612$	0	0
$613$	−3.31371	−0.133839	−0.0669197	−	0.997758i	$-0.521317\pi$
$613$	−3.31371	−0.133839	−0.0669197	+	0.997758i	$0.521317\pi$
$614$	31.5563	1.27351
$615$	−0.585786	−0.0236212
$616$	−0.686292	−0.0276515
$617$	27.2132	1.09556	0.547781	−	0.836622i	$-0.315473\pi$
$617$	27.2132	1.09556	0.547781	+	0.836622i	$0.315473\pi$
$618$	−23.0711	−0.928054
$619$	12.3137	0.494930	0.247465	−	0.968897i	$-0.420403\pi$
$619$	12.3137	0.494930	0.247465	+	0.968897i	$0.420403\pi$
$620$	0	0
$621$	1.41421	0.0567504
$622$	29.9411	1.20053
$623$	0.201010	0.00805330
$624$	8.97056	0.359110
$625$	19.9706	0.798823
$626$	35.1716	1.40574
$627$	1.07107	0.0427743
$628$	0	0
$629$	18.0711	0.720541
$630$	−0.485281	−0.0193341
$631$	22.4558	0.893953	0.446977	−	0.894546i	$-0.352501\pi$
$631$	22.4558	0.893953	0.446977	+	0.894546i	$0.352501\pi$
$632$	−10.3431	−0.411428
$633$	−7.51472	−0.298683
$634$	2.92893	0.116323
$635$	−7.79899	−0.309493
$636$	0	0
$637$	14.9289	0.591506
$638$	−4.72792	−0.187180
$639$	−4.07107	−0.161049
$640$	6.62742	0.261972
$641$	22.5563	0.890922	0.445461	−	0.895301i	$-0.353040\pi$
$641$	22.5563	0.890922	0.445461	+	0.895301i	$0.353040\pi$
$642$	−16.4853	−0.650622
$643$	−13.4558	−0.530647	−0.265323	−	0.964159i	$-0.585479\pi$
$643$	−13.4558	−0.530647	−0.265323	+	0.964159i	$0.585479\pi$
$644$	0	0
$645$	−2.92893	−0.115327
$646$	−8.82843	−0.347350
$647$	7.55635	0.297071	0.148535	−	0.988907i	$-0.452544\pi$
$647$	7.55635	0.297071	0.148535	+	0.988907i	$0.452544\pi$
$648$	−2.82843	−0.111111
$649$	−3.51472	−0.137965
$650$	14.7696	0.579310
$651$	1.75736	0.0688763
$652$	0	0
$653$	12.8995	0.504796	0.252398	−	0.967623i	$-0.418781\pi$
$653$	12.8995	0.504796	0.252398	+	0.967623i	$0.418781\pi$
$654$	−16.8284	−0.658044
$655$	−7.85786	−0.307032
$656$	4.00000	0.156174
$657$	12.3137	0.480404
$658$	−6.28427	−0.244986
$659$	−29.1716	−1.13636	−0.568182	−	0.822903i	$-0.692353\pi$
$659$	−29.1716	−1.13636	−0.568182	+	0.822903i	$0.692353\pi$
$660$	0	0
$661$	−37.4558	−1.45686	−0.728432	−	0.685118i	$-0.759750\pi$
$661$	−37.4558	−1.45686	−0.728432	+	0.685118i	$0.759750\pi$
$662$	10.9706	0.426383
$663$	−5.41421	−0.210271
$664$	36.9706	1.43474
$665$	0.887302	0.0344081
$666$	10.5858	0.410191
$667$	11.4142	0.441960
$668$	0	0
$669$	21.6569	0.837302
$670$	−5.37258	−0.207561
$671$	−2.75736	−0.106447
$672$	0	0
$673$	−17.7990	−0.686101	−0.343050	−	0.939317i	$-0.611460\pi$
$673$	−17.7990	−0.686101	−0.343050	+	0.939317i	$0.611460\pi$
$674$	−19.7574	−0.761025
$675$	−4.65685	−0.179242
$676$	0	0
$677$	2.44365	0.0939171	0.0469586	−	0.998897i	$-0.485047\pi$
$677$	2.44365	0.0939171	0.0469586	+	0.998897i	$0.485047\pi$
$678$	−26.4853	−1.01716
$679$	−9.51472	−0.365141
$680$	−4.00000	−0.153393
$681$	20.8995	0.800870
$682$	1.75736	0.0672928
$683$	50.2843	1.92407	0.962037	−	0.272919i	$-0.0879890\pi$
$683$	50.2843	1.92407	0.962037	+	0.272919i	$0.0879890\pi$
$684$	0	0
$685$	10.5858	0.404462
$686$	11.3137	0.431959
$687$	8.24264	0.314476
$688$	20.0000	0.762493
$689$	−2.62742	−0.100097
$690$	1.17157	0.0446010
$691$	−14.7279	−0.560277	−0.280138	−	0.959960i	$-0.590380\pi$
$691$	−14.7279	−0.560277	−0.280138	+	0.959960i	$0.590380\pi$
$692$	0	0
$693$	0.242641	0.00921716
$694$	−26.7279	−1.01458
$695$	−4.48528	−0.170136
$696$	−22.8284	−0.865309
$697$	−2.41421	−0.0914449
$698$	−27.0711	−1.02466
$699$	−18.0000	−0.680823
$700$	0	0
$701$	−6.20101	−0.234209	−0.117104	−	0.993120i	$-0.537361\pi$
$701$	−6.20101	−0.234209	−0.117104	+	0.993120i	$0.537361\pi$
$702$	−3.17157	−0.119703
$703$	−19.3553	−0.730000
$704$	−3.31371	−0.124890
$705$	4.44365	0.167358
$706$	−1.45584	−0.0547914
$707$	−1.41421	−0.0531870
$708$	0	0
$709$	−13.5147	−0.507556	−0.253778	−	0.967263i	$-0.581673\pi$
$709$	−13.5147	−0.507556	−0.253778	+	0.967263i	$0.581673\pi$
$710$	−3.37258	−0.126571
$711$	3.65685	0.137143
$712$	0.970563	0.0363734
$713$	−4.24264	−0.158888
$714$	−2.00000	−0.0748481
$715$	0.544156	0.0203503
$716$	0	0
$717$	−10.1421	−0.378765
$718$	10.9706	0.409418
$719$	9.44365	0.352189	0.176094	−	0.984373i	$-0.443654\pi$
$719$	9.44365	0.352189	0.176094	+	0.984373i	$0.443654\pi$
$720$	−2.34315	−0.0873239
$721$	9.55635	0.355897
$722$	−17.4142	−0.648090
$723$	−7.48528	−0.278381
$724$	0	0
$725$	−37.5858	−1.39590
$726$	−15.3137	−0.568345
$727$	−7.27208	−0.269706	−0.134853	−	0.990866i	$-0.543056\pi$
$727$	−7.27208	−0.269706	−0.134853	+	0.990866i	$0.543056\pi$
$728$	−3.71573	−0.137714
$729$	1.00000	0.0370370
$730$	10.2010	0.377556
$731$	−12.0711	−0.446465
$732$	0	0
$733$	−2.85786	−0.105558	−0.0527788	−	0.998606i	$-0.516808\pi$
$733$	−2.85786	−0.105558	−0.0527788	+	0.998606i	$0.516808\pi$
$734$	6.58579	0.243086
$735$	−3.89949	−0.143835
$736$	0	0
$737$	2.68629	0.0989508
$738$	−1.41421	−0.0520579
$739$	11.3431	0.417264	0.208632	−	0.977994i	$-0.433099\pi$
$739$	11.3431	0.417264	0.208632	+	0.977994i	$0.433099\pi$
$740$	0	0
$741$	5.79899	0.213031
$742$	−0.970563	−0.0356305
$743$	−28.6274	−1.05024	−0.525119	−	0.851029i	$-0.675979\pi$
$743$	−28.6274	−1.05024	−0.525119	+	0.851029i	$0.675979\pi$
$744$	8.48528	0.311086
$745$	−3.11270	−0.114040
$746$	6.87006	0.251531
$747$	−13.0711	−0.478245
$748$	0	0
$749$	6.82843	0.249505
$750$	−8.00000	−0.292119
$751$	1.02944	0.0375647	0.0187823	−	0.999824i	$-0.494021\pi$
$751$	1.02944	0.0375647	0.0187823	+	0.999824i	$0.494021\pi$
$752$	−30.3431	−1.10650
$753$	3.17157	0.115579
$754$	−25.5980	−0.932223
$755$	−9.37258	−0.341103
$756$	0	0
$757$	−0.242641	−0.00881893	−0.00440946	−	0.999990i	$-0.501404\pi$
$757$	−0.242641	−0.00881893	−0.00440946	+	0.999990i	$0.501404\pi$
$758$	−9.85786	−0.358054
$759$	−0.585786	−0.0212627
$760$	4.28427	0.155407
$761$	9.17157	0.332469	0.166235	−	0.986086i	$-0.446839\pi$
$761$	9.17157	0.332469	0.166235	+	0.986086i	$0.446839\pi$
$762$	−18.8284	−0.682082
$763$	6.97056	0.252351
$764$	0	0
$765$	1.41421	0.0511310
$766$	52.1838	1.88548
$767$	−19.0294	−0.687113
$768$	0	0
$769$	−16.5147	−0.595536	−0.297768	−	0.954638i	$-0.596242\pi$
$769$	−16.5147	−0.595536	−0.297768	+	0.954638i	$0.596242\pi$
$770$	0.201010	0.00724390
$771$	−24.8995	−0.896733
$772$	0	0
$773$	47.5858	1.71154	0.855771	−	0.517355i	$-0.173083\pi$
$773$	47.5858	1.71154	0.855771	+	0.517355i	$0.173083\pi$
$774$	−7.07107	−0.254164
$775$	13.9706	0.501837
$776$	−45.9411	−1.64919
$777$	−4.38478	−0.157303
$778$	−19.4558	−0.697526
$779$	2.58579	0.0926454
$780$	0	0
$781$	1.68629	0.0603403
$782$	4.82843	0.172664
$783$	8.07107	0.288436
$784$	26.6274	0.950979
$785$	10.5442	0.376337
$786$	−18.9706	−0.676658
$787$	19.9706	0.711874	0.355937	−	0.934510i	$-0.384162\pi$
$787$	19.9706	0.711874	0.355937	+	0.934510i	$0.384162\pi$
$788$	0	0
$789$	−0.414214	−0.0147464
$790$	3.02944	0.107783
$791$	10.9706	0.390068
$792$	1.17157	0.0416300
$793$	−14.9289	−0.530142
$794$	−48.8284	−1.73286
$795$	0.686292	0.0243403
$796$	0	0
$797$	−15.8579	−0.561714	−0.280857	−	0.959750i	$-0.590619\pi$
$797$	−15.8579	−0.561714	−0.280857	+	0.959750i	$0.590619\pi$
$798$	2.14214	0.0758308
$799$	18.3137	0.647892
$800$	0	0
$801$	−0.343146	−0.0121245
$802$	−48.9706	−1.72921
$803$	−5.10051	−0.179993
$804$	0	0
$805$	−0.485281	−0.0171039
$806$	9.51472	0.335142
$807$	8.48528	0.298696
$808$	−6.82843	−0.240223
$809$	−37.1127	−1.30481	−0.652406	−	0.757869i	$-0.726240\pi$
$809$	−37.1127	−1.30481	−0.652406	+	0.757869i	$0.726240\pi$
$810$	0.828427	0.0291080
$811$	15.9706	0.560802	0.280401	−	0.959883i	$-0.409533\pi$
$811$	15.9706	0.560802	0.280401	+	0.959883i	$0.409533\pi$
$812$	0	0
$813$	−20.7990	−0.729452
$814$	−4.38478	−0.153686
$815$	4.38478	0.153592
$816$	−9.65685	−0.338058
$817$	12.9289	0.452326
$818$	30.8701	1.07935
$819$	1.31371	0.0459047
$820$	0	0
$821$	14.8701	0.518969	0.259484	−	0.965747i	$-0.416447\pi$
$821$	14.8701	0.518969	0.259484	+	0.965747i	$0.416447\pi$
$822$	25.5563	0.891380
$823$	−52.4264	−1.82747	−0.913735	−	0.406311i	$-0.866815\pi$
$823$	−52.4264	−1.82747	−0.913735	+	0.406311i	$0.866815\pi$
$824$	46.1421	1.60744
$825$	1.92893	0.0671568
$826$	−7.02944	−0.244585
$827$	22.0711	0.767486	0.383743	−	0.923440i	$-0.374635\pi$
$827$	22.0711	0.767486	0.383743	+	0.923440i	$0.374635\pi$
$828$	0	0
$829$	42.9411	1.49141	0.745703	−	0.666278i	$-0.232114\pi$
$829$	42.9411	1.49141	0.745703	+	0.666278i	$0.232114\pi$
$830$	−10.8284	−0.375860
$831$	29.2843	1.01586
$832$	−17.9411	−0.621997
$833$	−16.0711	−0.556829
$834$	−10.8284	−0.374958
$835$	4.48528	0.155220
$836$	0	0
$837$	−3.00000	−0.103695
$838$	1.31371	0.0453813
$839$	−17.1716	−0.592829	−0.296414	−	0.955059i	$-0.595791\pi$
$839$	−17.1716	−0.592829	−0.296414	+	0.955059i	$0.595791\pi$
$840$	0.970563	0.0334876
$841$	36.1421	1.24628
$842$	35.3137	1.21699
$843$	−19.3848	−0.667647
$844$	0	0
$845$	−4.66905	−0.160620
$846$	10.7279	0.368834
$847$	6.34315	0.217953
$848$	−4.68629	−0.160928
$849$	21.8284	0.749150
$850$	−15.8995	−0.545348
$851$	10.5858	0.362876
$852$	0	0
$853$	0	0		−	1.00000i	$-0.5\pi$
$853$	0	0			1.00000i	$0.5\pi$
$854$	−5.51472	−0.188710
$855$	−1.51472	−0.0518023
$856$	32.9706	1.12691
$857$	12.2010	0.416779	0.208389	−	0.978046i	$-0.433178\pi$
$857$	12.2010	0.416779	0.208389	+	0.978046i	$0.433178\pi$
$858$	1.31371	0.0448493
$859$	5.34315	0.182306	0.0911529	−	0.995837i	$-0.470945\pi$
$859$	5.34315	0.182306	0.0911529	+	0.995837i	$0.470945\pi$
$860$	0	0
$861$	0.585786	0.0199635
$862$	55.2548	1.88199
$863$	10.9289	0.372025	0.186013	−	0.982547i	$-0.440443\pi$
$863$	10.9289	0.372025	0.186013	+	0.982547i	$0.440443\pi$
$864$	0	0
$865$	2.97056	0.101002
$866$	−16.2426	−0.551947
$867$	−11.1716	−0.379407
$868$	0	0
$869$	−1.51472	−0.0513833
$870$	6.68629	0.226687
$871$	14.5442	0.492810
$872$	33.6569	1.13976
$873$	16.2426	0.549730
$874$	−5.17157	−0.174931
$875$	3.31371	0.112024
$876$	0	0
$877$	1.14214	0.0385672	0.0192836	−	0.999814i	$-0.493861\pi$
$877$	1.14214	0.0385672	0.0192836	+	0.999814i	$0.493861\pi$
$878$	−43.7990	−1.47814
$879$	12.4142	0.418721
$880$	0.970563	0.0327177
$881$	2.62742	0.0885199	0.0442600	−	0.999020i	$-0.485907\pi$
$881$	2.62742	0.0885199	0.0442600	+	0.999020i	$0.485907\pi$
$882$	−9.41421	−0.316993
$883$	−6.58579	−0.221629	−0.110815	−	0.993841i	$-0.535346\pi$
$883$	−6.58579	−0.221629	−0.110815	+	0.993841i	$0.535346\pi$
$884$	0	0
$885$	4.97056	0.167084
$886$	28.6863	0.963735
$887$	−46.0122	−1.54494	−0.772469	−	0.635052i	$-0.780979\pi$
$887$	−46.0122	−1.54494	−0.772469	+	0.635052i	$0.780979\pi$
$888$	−21.1716	−0.710471
$889$	7.79899	0.261570
$890$	−0.284271	−0.00952879
$891$	−0.414214	−0.0138767
$892$	0	0
$893$	−19.6152	−0.656398
$894$	−7.51472	−0.251330
$895$	8.72792	0.291742
$896$	−6.62742	−0.221406
$897$	−3.17157	−0.105896
$898$	28.9706	0.966760
$899$	−24.2132	−0.807556
$900$	0	0
$901$	2.82843	0.0942286
$902$	0.585786	0.0195046
$903$	2.92893	0.0974688
$904$	52.9706	1.76177
$905$	8.97056	0.298192
$906$	−22.6274	−0.751746
$907$	4.34315	0.144212	0.0721059	−	0.997397i	$-0.477028\pi$
$907$	4.34315	0.144212	0.0721059	+	0.997397i	$0.477028\pi$
$908$	0	0
$909$	2.41421	0.0800744
$910$	1.08831	0.0360772
$911$	53.8995	1.78577	0.892885	−	0.450285i	$-0.148678\pi$
$911$	53.8995	1.78577	0.892885	+	0.450285i	$0.148678\pi$
$912$	10.3431	0.342496
$913$	5.41421	0.179184
$914$	−5.65685	−0.187112
$915$	3.89949	0.128913
$916$	0	0
$917$	7.85786	0.259490
$918$	3.41421	0.112686
$919$	−12.5858	−0.415167	−0.207583	−	0.978217i	$-0.566560\pi$
$919$	−12.5858	−0.415167	−0.207583	+	0.978217i	$0.566560\pi$
$920$	−2.34315	−0.0772512
$921$	22.3137	0.735262
$922$	−23.5147	−0.774416
$923$	9.12994	0.300516
$924$	0	0
$925$	−34.8579	−1.14612
$926$	7.85786	0.258225
$927$	−16.3137	−0.535812
$928$	0	0
$929$	45.8701	1.50495	0.752474	−	0.658622i	$-0.228860\pi$
$929$	45.8701	1.50495	0.752474	+	0.658622i	$0.228860\pi$
$930$	−2.48528	−0.0814956
$931$	17.2132	0.564140
$932$	0	0
$933$	21.1716	0.693126
$934$	30.1421	0.986281
$935$	−0.585786	−0.0191573
$936$	6.34315	0.207332
$937$	19.0294	0.621665	0.310832	−	0.950465i	$-0.399392\pi$
$937$	19.0294	0.621665	0.310832	+	0.950465i	$0.399392\pi$
$938$	5.37258	0.175421
$939$	24.8701	0.811604
$940$	0	0
$941$	−7.37258	−0.240339	−0.120170	−	0.992753i	$-0.538344\pi$
$941$	−7.37258	−0.240339	−0.120170	+	0.992753i	$0.538344\pi$
$942$	25.4558	0.829396
$943$	−1.41421	−0.0460531
$944$	−33.9411	−1.10469
$945$	−0.343146	−0.0111625
$946$	2.92893	0.0952278
$947$	−57.5980	−1.87168	−0.935841	−	0.352421i	$-0.885358\pi$
$947$	−57.5980	−1.87168	−0.935841	+	0.352421i	$0.885358\pi$
$948$	0	0
$949$	−27.6152	−0.896428
$950$	17.0294	0.552508
$951$	2.07107	0.0671590
$952$	4.00000	0.129641
$953$	17.6985	0.573310	0.286655	−	0.958034i	$-0.407457\pi$
$953$	17.6985	0.573310	0.286655	+	0.958034i	$0.407457\pi$
$954$	1.65685	0.0536426
$955$	7.71573	0.249675
$956$	0	0
$957$	−3.34315	−0.108069
$958$	−18.2426	−0.589393
$959$	−10.5858	−0.341833
$960$	4.68629	0.151249
$961$	−22.0000	−0.709677
$962$	−23.7401	−0.765412
$963$	−11.6569	−0.375637
$964$	0	0
$965$	2.00000	0.0643823
$966$	−1.17157	−0.0376947
$967$	−34.9706	−1.12458	−0.562289	−	0.826941i	$-0.690079\pi$
$967$	−34.9706	−1.12458	−0.562289	+	0.826941i	$0.690079\pi$
$968$	30.6274	0.984402
$969$	−6.24264	−0.200543
$970$	13.4558	0.432041
$971$	9.44365	0.303061	0.151531	−	0.988453i	$-0.451580\pi$
$971$	9.44365	0.303061	0.151531	+	0.988453i	$0.451580\pi$
$972$	0	0
$973$	4.48528	0.143792
$974$	−45.2132	−1.44872
$975$	10.4437	0.334465
$976$	−26.6274	−0.852323
$977$	10.4142	0.333180	0.166590	−	0.986026i	$-0.446724\pi$
$977$	10.4142	0.333180	0.166590	+	0.986026i	$0.446724\pi$
$978$	10.5858	0.338496
$979$	0.142136	0.00454267
$980$	0	0
$981$	−11.8995	−0.379922
$982$	1.51472	0.0483366
$983$	−37.0711	−1.18238	−0.591192	−	0.806531i	$-0.701342\pi$
$983$	−37.0711	−1.18238	−0.591192	+	0.806531i	$0.701342\pi$
$984$	2.82843	0.0901670
$985$	8.05887	0.256777
$986$	27.5563	0.877573
$987$	−4.44365	−0.141443
$988$	0	0
$989$	−7.07107	−0.224847
$990$	−0.343146	−0.0109059
$991$	−11.5147	−0.365777	−0.182889	−	0.983134i	$-0.558545\pi$
$991$	−11.5147	−0.365777	−0.182889	+	0.983134i	$0.558545\pi$
$992$	0	0
$993$	7.75736	0.246172
$994$	3.37258	0.106972
$995$	−4.54416	−0.144059
$996$	0	0
$997$	12.5858	0.398596	0.199298	−	0.979939i	$-0.436134\pi$
$997$	12.5858	0.398596	0.199298	+	0.979939i	$0.436134\pi$
$998$	−51.5980	−1.63331
$999$	7.48528	0.236824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	123.2.a.c.1.2	✓	2
3.2	odd	2		369.2.a.c.1.1		2
4.3	odd	2		1968.2.a.r.1.1		2
5.4	even	2		3075.2.a.p.1.1		2
7.6	odd	2		6027.2.a.m.1.2		2
8.3	odd	2		7872.2.a.bo.1.2		2
8.5	even	2		7872.2.a.bk.1.2		2
12.11	even	2		5904.2.a.w.1.2		2
15.14	odd	2		9225.2.a.bm.1.2		2
41.40	even	2		5043.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
123.2.a.c.1.2	✓	2	1.1	even	1	trivial
369.2.a.c.1.1		2	3.2	odd	2
1968.2.a.r.1.1		2	4.3	odd	2
3075.2.a.p.1.1		2	5.4	even	2
5043.2.a.e.1.2		2	41.40	even	2
5904.2.a.w.1.2		2	12.11	even	2
6027.2.a.m.1.2		2	7.6	odd	2
7872.2.a.bk.1.2		2	8.5	even	2
7872.2.a.bo.1.2		2	8.3	odd	2
9225.2.a.bm.1.2		2	15.14	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:	\( N \)	\(=\)	\( 123 = 3 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	123.a (trivial)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +1.00000 q^{3} +0.585786 q^{5} +1.41421 q^{6} -0.585786 q^{7} -2.82843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +1.00000 q^{3} +0.585786 q^{5} +1.41421 q^{6} -0.585786 q^{7} -2.82843 q^{8} +1.00000 q^{9} +0.828427 q^{10} -0.414214 q^{11} -2.24264 q^{13} -0.828427 q^{14} +0.585786 q^{15} -4.00000 q^{16} +2.41421 q^{17} +1.41421 q^{18} -2.58579 q^{19} -0.585786 q^{21} -0.585786 q^{22} +1.41421 q^{23} -2.82843 q^{24} -4.65685 q^{25} -3.17157 q^{26} +1.00000 q^{27} +8.07107 q^{29} +0.828427 q^{30} -3.00000 q^{31} -0.414214 q^{33} +3.41421 q^{34} -0.343146 q^{35} +7.48528 q^{37} -3.65685 q^{38} -2.24264 q^{39} -1.65685 q^{40} -1.00000 q^{41} -0.828427 q^{42} -5.00000 q^{43} +0.585786 q^{45} +2.00000 q^{46} +7.58579 q^{47} -4.00000 q^{48} -6.65685 q^{49} -6.58579 q^{50} +2.41421 q^{51} +1.17157 q^{53} +1.41421 q^{54} -0.242641 q^{55} +1.65685 q^{56} -2.58579 q^{57} +11.4142 q^{58} +8.48528 q^{59} +6.65685 q^{61} -4.24264 q^{62} -0.585786 q^{63} +8.00000 q^{64} -1.31371 q^{65} -0.585786 q^{66} -6.48528 q^{67} +1.41421 q^{69} -0.485281 q^{70} -4.07107 q^{71} -2.82843 q^{72} +12.3137 q^{73} +10.5858 q^{74} -4.65685 q^{75} +0.242641 q^{77} -3.17157 q^{78} +3.65685 q^{79} -2.34315 q^{80} +1.00000 q^{81} -1.41421 q^{82} -13.0711 q^{83} +1.41421 q^{85} -7.07107 q^{86} +8.07107 q^{87} +1.17157 q^{88} -0.343146 q^{89} +0.828427 q^{90} +1.31371 q^{91} -3.00000 q^{93} +10.7279 q^{94} -1.51472 q^{95} +16.2426 q^{97} -9.41421 q^{98} -0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9	\( 2 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9} - 4 q^{10} + 2 q^{11} + 4 q^{13} + 4 q^{14} + 4 q^{15} - 8 q^{16} + 2 q^{17} - 8 q^{19} - 4 q^{21} - 4 q^{22} + 2 q^{25} - 12 q^{26} + 2 q^{27} + 2 q^{29} - 4 q^{30} - 6 q^{31} + 2 q^{33} + 4 q^{34} - 12 q^{35} - 2 q^{37} + 4 q^{38} + 4 q^{39} + 8 q^{40} - 2 q^{41} + 4 q^{42} - 10 q^{43} + 4 q^{45} + 4 q^{46} + 18 q^{47} - 8 q^{48} - 2 q^{49} - 16 q^{50} + 2 q^{51} + 8 q^{53} + 8 q^{55} - 8 q^{56} - 8 q^{57} + 20 q^{58} + 2 q^{61} - 4 q^{63} + 16 q^{64} + 20 q^{65} - 4 q^{66} + 4 q^{67} + 16 q^{70} + 6 q^{71} + 2 q^{73} + 24 q^{74} + 2 q^{75} - 8 q^{77} - 12 q^{78} - 4 q^{79} - 16 q^{80} + 2 q^{81} - 12 q^{83} + 2 q^{87} + 8 q^{88} - 12 q^{89} - 4 q^{90} - 20 q^{91} - 6 q^{93} - 4 q^{94} - 20 q^{95} + 24 q^{97} - 16 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 2 * q^9 - 4 * q^10 + 2 * q^11 + 4 * q^13 + 4 * q^14 + 4 * q^15 - 8 * q^16 + 2 * q^17 - 8 * q^19 - 4 * q^21 - 4 * q^22 + 2 * q^25 - 12 * q^26 + 2 * q^27 + 2 * q^29 - 4 * q^30 - 6 * q^31 + 2 * q^33 + 4 * q^34 - 12 * q^35 - 2 * q^37 + 4 * q^38 + 4 * q^39 + 8 * q^40 - 2 * q^41 + 4 * q^42 - 10 * q^43 + 4 * q^45 + 4 * q^46 + 18 * q^47 - 8 * q^48 - 2 * q^49 - 16 * q^50 + 2 * q^51 + 8 * q^53 + 8 * q^55 - 8 * q^56 - 8 * q^57 + 20 * q^58 + 2 * q^61 - 4 * q^63 + 16 * q^64 + 20 * q^65 - 4 * q^66 + 4 * q^67 + 16 * q^70 + 6 * q^71 + 2 * q^73 + 24 * q^74 + 2 * q^75 - 8 * q^77 - 12 * q^78 - 4 * q^79 - 16 * q^80 + 2 * q^81 - 12 * q^83 + 2 * q^87 + 8 * q^88 - 12 * q^89 - 4 * q^90 - 20 * q^91 - 6 * q^93 - 4 * q^94 - 20 * q^95 + 24 * q^97 - 16 * q^98 + 2 * q^99

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