LMFDB - Embedded newform 2842.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, 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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.73205 q^{10} -3.46410 q^{11} -2.00000 q^{12} +2.73205 q^{13} +5.46410 q^{15} +1.00000 q^{16} +6.19615 q^{17} +1.00000 q^{18} +3.46410 q^{19} -2.73205 q^{20} -3.46410 q^{22} +4.92820 q^{23} -2.00000 q^{24} +2.46410 q^{25} +2.73205 q^{26} +4.00000 q^{27} -1.00000 q^{29} +5.46410 q^{30} -8.19615 q^{31} +1.00000 q^{32} +6.92820 q^{33} +6.19615 q^{34} +1.00000 q^{36} -4.00000 q^{37} +3.46410 q^{38} -5.46410 q^{39} -2.73205 q^{40} -7.66025 q^{41} +10.9282 q^{43} -3.46410 q^{44} -2.73205 q^{45} +4.92820 q^{46} -9.66025 q^{47} -2.00000 q^{48} +2.46410 q^{50} -12.3923 q^{51} +2.73205 q^{52} -8.92820 q^{53} +4.00000 q^{54} +9.46410 q^{55} -6.92820 q^{57} -1.00000 q^{58} -7.26795 q^{59} +5.46410 q^{60} -4.00000 q^{61} -8.19615 q^{62} +1.00000 q^{64} -7.46410 q^{65} +6.92820 q^{66} +6.92820 q^{67} +6.19615 q^{68} -9.85641 q^{69} -4.92820 q^{71} +1.00000 q^{72} -8.73205 q^{73} -4.00000 q^{74} -4.92820 q^{75} +3.46410 q^{76} -5.46410 q^{78} -9.46410 q^{79} -2.73205 q^{80} -11.0000 q^{81} -7.66025 q^{82} +14.5885 q^{83} -16.9282 q^{85} +10.9282 q^{86} +2.00000 q^{87} -3.46410 q^{88} -5.80385 q^{89} -2.73205 q^{90} +4.92820 q^{92} +16.3923 q^{93} -9.66025 q^{94} -9.46410 q^{95} -2.00000 q^{96} +3.26795 q^{97} -3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 4 q^{23} - 4 q^{24} - 2 q^{25} + 2 q^{26} + 8 q^{27} - 2 q^{29} + 4 q^{30} - 6 q^{31} + 2 q^{32} + 2 q^{34} + 2 q^{36} - 8 q^{37} - 4 q^{39} - 2 q^{40} + 2 q^{41} + 8 q^{43} - 2 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 2 q^{50} - 4 q^{51} + 2 q^{52} - 4 q^{53} + 8 q^{54} + 12 q^{55} - 2 q^{58} - 18 q^{59} + 4 q^{60} - 8 q^{61} - 6 q^{62} + 2 q^{64} - 8 q^{65} + 2 q^{68} + 8 q^{69} + 4 q^{71} + 2 q^{72} - 14 q^{73} - 8 q^{74} + 4 q^{75} - 4 q^{78} - 12 q^{79} - 2 q^{80} - 22 q^{81} + 2 q^{82} - 2 q^{83} - 20 q^{85} + 8 q^{86} + 4 q^{87} - 22 q^{89} - 2 q^{90} - 4 q^{92} + 12 q^{93} - 2 q^{94} - 12 q^{95} - 4 q^{96} + 10 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^20 - 4 * q^23 - 4 * q^24 - 2 * q^25 + 2 * q^26 + 8 * q^27 - 2 * q^29 + 4 * q^30 - 6 * q^31 + 2 * q^32 + 2 * q^34 + 2 * q^36 - 8 * q^37 - 4 * q^39 - 2 * q^40 + 2 * q^41 + 8 * q^43 - 2 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 2 * q^50 - 4 * q^51 + 2 * q^52 - 4 * q^53 + 8 * q^54 + 12 * q^55 - 2 * q^58 - 18 * q^59 + 4 * q^60 - 8 * q^61 - 6 * q^62 + 2 * q^64 - 8 * q^65 + 2 * q^68 + 8 * q^69 + 4 * q^71 + 2 * q^72 - 14 * q^73 - 8 * q^74 + 4 * q^75 - 4 * q^78 - 12 * q^79 - 2 * q^80 - 22 * q^81 + 2 * q^82 - 2 * q^83 - 20 * q^85 + 8 * q^86 + 4 * q^87 - 22 * q^89 - 2 * q^90 - 4 * q^92 + 12 * q^93 - 2 * q^94 - 12 * q^95 - 4 * q^96 + 10 * q^97

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000	0.500000
$5$	−2.73205	−1.22181	−0.610905	−	0.791704i	$-0.709194\pi$
$5$	−2.73205	−1.22181	−0.610905	+	0.791704i	$0.709194\pi$
$6$	−2.00000	−0.816497
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.73205	−0.863950
$11$	−3.46410	−1.04447	−0.522233	−	0.852803i	$-0.674901\pi$
$11$	−3.46410	−1.04447	−0.522233	+	0.852803i	$0.674901\pi$
$12$	−2.00000	−0.577350
$13$	2.73205	0.757735	0.378867	−	0.925451i	$-0.376314\pi$
$13$	2.73205	0.757735	0.378867	+	0.925451i	$0.376314\pi$
$14$	0	0
$15$	5.46410	1.41082
$16$	1.00000	0.250000
$17$	6.19615	1.50279	0.751394	−	0.659854i	$-0.229382\pi$
$17$	6.19615	1.50279	0.751394	+	0.659854i	$0.229382\pi$
$18$	1.00000	0.235702
$19$	3.46410	0.794719	0.397360	−	0.917663i	$-0.369927\pi$
$19$	3.46410	0.794719	0.397360	+	0.917663i	$0.369927\pi$
$20$	−2.73205	−0.610905
$21$	0	0
$22$	−3.46410	−0.738549
$23$	4.92820	1.02760	0.513801	−	0.857910i	$-0.328237\pi$
$23$	4.92820	1.02760	0.513801	+	0.857910i	$0.328237\pi$
$24$	−2.00000	−0.408248
$25$	2.46410	0.492820
$26$	2.73205	0.535799
$27$	4.00000	0.769800
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	5.46410	0.997604
$31$	−8.19615	−1.47207	−0.736036	−	0.676942i	$-0.763305\pi$
$31$	−8.19615	−1.47207	−0.736036	+	0.676942i	$0.763305\pi$
$32$	1.00000	0.176777
$33$	6.92820	1.20605
$34$	6.19615	1.06263
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	3.46410	0.561951
$39$	−5.46410	−0.874957
$40$	−2.73205	−0.431975
$41$	−7.66025	−1.19633	−0.598165	−	0.801373i	$-0.704103\pi$
$41$	−7.66025	−1.19633	−0.598165	+	0.801373i	$0.704103\pi$
$42$	0	0
$43$	10.9282	1.66654	0.833268	−	0.552870i	$-0.186467\pi$
$43$	10.9282	1.66654	0.833268	+	0.552870i	$0.186467\pi$
$44$	−3.46410	−0.522233
$45$	−2.73205	−0.407270
$46$	4.92820	0.726624
$47$	−9.66025	−1.40909	−0.704546	−	0.709658i	$-0.748850\pi$
$47$	−9.66025	−1.40909	−0.704546	+	0.709658i	$0.748850\pi$
$48$	−2.00000	−0.288675
$49$	0	0
$50$	2.46410	0.348477
$51$	−12.3923	−1.73527
$52$	2.73205	0.378867
$53$	−8.92820	−1.22638	−0.613192	−	0.789934i	$-0.710115\pi$
$53$	−8.92820	−1.22638	−0.613192	+	0.789934i	$0.710115\pi$
$54$	4.00000	0.544331
$55$	9.46410	1.27614
$56$	0	0
$57$	−6.92820	−0.917663
$58$	−1.00000	−0.131306
$59$	−7.26795	−0.946206	−0.473103	−	0.881007i	$-0.656866\pi$
$59$	−7.26795	−0.946206	−0.473103	+	0.881007i	$0.656866\pi$
$60$	5.46410	0.705412
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	−8.19615	−1.04091
$63$	0	0
$64$	1.00000	0.125000
$65$	−7.46410	−0.925808
$66$	6.92820	0.852803
$67$	6.92820	0.846415	0.423207	−	0.906033i	$-0.360904\pi$
$67$	6.92820	0.846415	0.423207	+	0.906033i	$0.360904\pi$
$68$	6.19615	0.751394
$69$	−9.85641	−1.18657
$70$	0	0
$71$	−4.92820	−0.584870	−0.292435	−	0.956285i	$-0.594466\pi$
$71$	−4.92820	−0.584870	−0.292435	+	0.956285i	$0.594466\pi$
$72$	1.00000	0.117851
$73$	−8.73205	−1.02201	−0.511005	−	0.859578i	$-0.670727\pi$
$73$	−8.73205	−1.02201	−0.511005	+	0.859578i	$0.670727\pi$
$74$	−4.00000	−0.464991
$75$	−4.92820	−0.569060
$76$	3.46410	0.397360
$77$	0	0
$78$	−5.46410	−0.618688
$79$	−9.46410	−1.06479	−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410	−1.06479	−0.532397	+	0.846495i	$0.678709\pi$
$80$	−2.73205	−0.305453
$81$	−11.0000	−1.22222
$82$	−7.66025	−0.845934
$83$	14.5885	1.60129	0.800646	−	0.599138i	$-0.204490\pi$
$83$	14.5885	1.60129	0.800646	+	0.599138i	$0.204490\pi$
$84$	0	0
$85$	−16.9282	−1.83612
$86$	10.9282	1.17842
$87$	2.00000	0.214423
$88$	−3.46410	−0.369274
$89$	−5.80385	−0.615207	−0.307603	−	0.951515i	$-0.599527\pi$
$89$	−5.80385	−0.615207	−0.307603	+	0.951515i	$0.599527\pi$
$90$	−2.73205	−0.287983
$91$	0	0
$92$	4.92820	0.513801
$93$	16.3923	1.69980
$94$	−9.66025	−0.996379
$95$	−9.46410	−0.970996
$96$	−2.00000	−0.204124
$97$	3.26795	0.331810	0.165905	−	0.986142i	$-0.446945\pi$
$97$	3.26795	0.331810	0.165905	+	0.986142i	$0.446945\pi$
$98$	0	0
$99$	−3.46410	−0.348155
$100$	2.46410	0.246410
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	−12.3923	−1.22702
$103$	1.46410	0.144262	0.0721311	−	0.997395i	$-0.477020\pi$
$103$	1.46410	0.144262	0.0721311	+	0.997395i	$0.477020\pi$
$104$	2.73205	0.267900
$105$	0	0
$106$	−8.92820	−0.867184
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	4.00000	0.384900
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	9.46410	0.902367
$111$	8.00000	0.759326
$112$	0	0
$113$	3.46410	0.325875	0.162938	−	0.986636i	$-0.447903\pi$
$113$	3.46410	0.325875	0.162938	+	0.986636i	$0.447903\pi$
$114$	−6.92820	−0.648886
$115$	−13.4641	−1.25553
$116$	−1.00000	−0.0928477
$117$	2.73205	0.252578
$118$	−7.26795	−0.669069
$119$	0	0
$120$	5.46410	0.498802
$121$	1.00000	0.0909091
$122$	−4.00000	−0.362143
$123$	15.3205	1.38140
$124$	−8.19615	−0.736036
$125$	6.92820	0.619677
$126$	0	0
$127$	−13.4641	−1.19475	−0.597373	−	0.801964i	$-0.703789\pi$
$127$	−13.4641	−1.19475	−0.597373	+	0.801964i	$0.703789\pi$
$128$	1.00000	0.0883883
$129$	−21.8564	−1.92435
$130$	−7.46410	−0.654645
$131$	−15.4641	−1.35110	−0.675552	−	0.737312i	$-0.736095\pi$
$131$	−15.4641	−1.35110	−0.675552	+	0.737312i	$0.736095\pi$
$132$	6.92820	0.603023
$133$	0	0
$134$	6.92820	0.598506
$135$	−10.9282	−0.940550
$136$	6.19615	0.531316
$137$	−8.53590	−0.729271	−0.364636	−	0.931150i	$-0.618806\pi$
$137$	−8.53590	−0.729271	−0.364636	+	0.931150i	$0.618806\pi$
$138$	−9.85641	−0.839033
$139$	12.7321	1.07992	0.539959	−	0.841691i	$-0.318440\pi$
$139$	12.7321	1.07992	0.539959	+	0.841691i	$0.318440\pi$
$140$	0	0
$141$	19.3205	1.62708
$142$	−4.92820	−0.413566
$143$	−9.46410	−0.791428
$144$	1.00000	0.0833333
$145$	2.73205	0.226884
$146$	−8.73205	−0.722670
$147$	0	0
$148$	−4.00000	−0.328798
$149$	3.46410	0.283790	0.141895	−	0.989882i	$-0.454680\pi$
$149$	3.46410	0.283790	0.141895	+	0.989882i	$0.454680\pi$
$150$	−4.92820	−0.402386
$151$	−11.8564	−0.964861	−0.482430	−	0.875934i	$-0.660246\pi$
$151$	−11.8564	−0.964861	−0.482430	+	0.875934i	$0.660246\pi$
$152$	3.46410	0.280976
$153$	6.19615	0.500929
$154$	0	0
$155$	22.3923	1.79859
$156$	−5.46410	−0.437478
$157$	23.3205	1.86118	0.930590	−	0.366064i	$-0.119295\pi$
$157$	23.3205	1.86118	0.930590	+	0.366064i	$0.119295\pi$
$158$	−9.46410	−0.752923
$159$	17.8564	1.41611
$160$	−2.73205	−0.215988
$161$	0	0
$162$	−11.0000	−0.864242
$163$	8.53590	0.668583	0.334292	−	0.942470i	$-0.391503\pi$
$163$	8.53590	0.668583	0.334292	+	0.942470i	$0.391503\pi$
$164$	−7.66025	−0.598165
$165$	−18.9282	−1.47356
$166$	14.5885	1.13228
$167$	−10.9282	−0.845650	−0.422825	−	0.906211i	$-0.638961\pi$
$167$	−10.9282	−0.845650	−0.422825	+	0.906211i	$0.638961\pi$
$168$	0	0
$169$	−5.53590	−0.425838
$170$	−16.9282	−1.29833
$171$	3.46410	0.264906
$172$	10.9282	0.833268
$173$	−13.2679	−1.00874	−0.504372	−	0.863487i	$-0.668276\pi$
$173$	−13.2679	−1.00874	−0.504372	+	0.863487i	$0.668276\pi$
$174$	2.00000	0.151620
$175$	0	0
$176$	−3.46410	−0.261116
$177$	14.5359	1.09259
$178$	−5.80385	−0.435017
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	−2.73205	−0.203635
$181$	18.7321	1.39234	0.696171	−	0.717876i	$-0.254885\pi$
$181$	18.7321	1.39234	0.696171	+	0.717876i	$0.254885\pi$
$182$	0	0
$183$	8.00000	0.591377
$184$	4.92820	0.363312
$185$	10.9282	0.803457
$186$	16.3923	1.20194
$187$	−21.4641	−1.56961
$188$	−9.66025	−0.704546
$189$	0	0
$190$	−9.46410	−0.686598
$191$	20.3923	1.47554	0.737768	−	0.675055i	$-0.235880\pi$
$191$	20.3923	1.47554	0.737768	+	0.675055i	$0.235880\pi$
$192$	−2.00000	−0.144338
$193$	6.39230	0.460128	0.230064	−	0.973175i	$-0.426106\pi$
$193$	6.39230	0.460128	0.230064	+	0.973175i	$0.426106\pi$
$194$	3.26795	0.234625
$195$	14.9282	1.06903
$196$	0	0
$197$	−27.4641	−1.95674	−0.978368	−	0.206872i	$-0.933672\pi$
$197$	−27.4641	−1.95674	−0.978368	+	0.206872i	$0.933672\pi$
$198$	−3.46410	−0.246183
$199$	−10.5359	−0.746870	−0.373435	−	0.927656i	$-0.621820\pi$
$199$	−10.5359	−0.746870	−0.373435	+	0.927656i	$0.621820\pi$
$200$	2.46410	0.174238
$201$	−13.8564	−0.977356
$202$	−4.00000	−0.281439
$203$	0	0
$204$	−12.3923	−0.867635
$205$	20.9282	1.46169
$206$	1.46410	0.102009
$207$	4.92820	0.342534
$208$	2.73205	0.189434
$209$	−12.0000	−0.830057
$210$	0	0
$211$	−6.92820	−0.476957	−0.238479	−	0.971148i	$-0.576649\pi$
$211$	−6.92820	−0.476957	−0.238479	+	0.971148i	$0.576649\pi$
$212$	−8.92820	−0.613192
$213$	9.85641	0.675350
$214$	4.00000	0.273434
$215$	−29.8564	−2.03619
$216$	4.00000	0.272166
$217$	0	0
$218$	−10.0000	−0.677285
$219$	17.4641	1.18011
$220$	9.46410	0.638070
$221$	16.9282	1.13871
$222$	8.00000	0.536925
$223$	−20.3923	−1.36557	−0.682785	−	0.730619i	$-0.739231\pi$
$223$	−20.3923	−1.36557	−0.682785	+	0.730619i	$0.739231\pi$
$224$	0	0
$225$	2.46410	0.164273
$226$	3.46410	0.230429
$227$	−18.5885	−1.23376	−0.616880	−	0.787058i	$-0.711603\pi$
$227$	−18.5885	−1.23376	−0.616880	+	0.787058i	$0.711603\pi$
$228$	−6.92820	−0.458831
$229$	−8.39230	−0.554579	−0.277290	−	0.960786i	$-0.589436\pi$
$229$	−8.39230	−0.554579	−0.277290	+	0.960786i	$0.589436\pi$
$230$	−13.4641	−0.887797
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	0.143594	0.00940713	0.00470356	−	0.999989i	$-0.498503\pi$
$233$	0.143594	0.00940713	0.00470356	+	0.999989i	$0.498503\pi$
$234$	2.73205	0.178600
$235$	26.3923	1.72164
$236$	−7.26795	−0.473103
$237$	18.9282	1.22952
$238$	0	0
$239$	−27.7128	−1.79259	−0.896296	−	0.443455i	$-0.853752\pi$
$239$	−27.7128	−1.79259	−0.896296	+	0.443455i	$0.853752\pi$
$240$	5.46410	0.352706
$241$	3.07180	0.197872	0.0989359	−	0.995094i	$-0.468456\pi$
$241$	3.07180	0.197872	0.0989359	+	0.995094i	$0.468456\pi$
$242$	1.00000	0.0642824
$243$	10.0000	0.641500
$244$	−4.00000	−0.256074
$245$	0	0
$246$	15.3205	0.976800
$247$	9.46410	0.602186
$248$	−8.19615	−0.520456
$249$	−29.1769	−1.84901
$250$	6.92820	0.438178
$251$	−10.3923	−0.655956	−0.327978	−	0.944685i	$-0.606367\pi$
$251$	−10.3923	−0.655956	−0.327978	+	0.944685i	$0.606367\pi$
$252$	0	0
$253$	−17.0718	−1.07329
$254$	−13.4641	−0.844813
$255$	33.8564	2.12017
$256$	1.00000	0.0625000
$257$	−12.5359	−0.781968	−0.390984	−	0.920398i	$-0.627865\pi$
$257$	−12.5359	−0.781968	−0.390984	+	0.920398i	$0.627865\pi$
$258$	−21.8564	−1.36072
$259$	0	0
$260$	−7.46410	−0.462904
$261$	−1.00000	−0.0618984
$262$	−15.4641	−0.955375
$263$	−4.39230	−0.270841	−0.135421	−	0.990788i	$-0.543239\pi$
$263$	−4.39230	−0.270841	−0.135421	+	0.990788i	$0.543239\pi$
$264$	6.92820	0.426401
$265$	24.3923	1.49841
$266$	0	0
$267$	11.6077	0.710379
$268$	6.92820	0.423207
$269$	−25.8564	−1.57649	−0.788246	−	0.615360i	$-0.789011\pi$
$269$	−25.8564	−1.57649	−0.788246	+	0.615360i	$0.789011\pi$
$270$	−10.9282	−0.665069
$271$	16.5885	1.00768	0.503839	−	0.863798i	$-0.331921\pi$
$271$	16.5885	1.00768	0.503839	+	0.863798i	$0.331921\pi$
$272$	6.19615	0.375697
$273$	0	0
$274$	−8.53590	−0.515672
$275$	−8.53590	−0.514734
$276$	−9.85641	−0.593286
$277$	2.39230	0.143740	0.0718698	−	0.997414i	$-0.477103\pi$
$277$	2.39230	0.143740	0.0718698	+	0.997414i	$0.477103\pi$
$278$	12.7321	0.763618
$279$	−8.19615	−0.490691
$280$	0	0
$281$	−21.4641	−1.28044	−0.640220	−	0.768191i	$-0.721157\pi$
$281$	−21.4641	−1.28044	−0.640220	+	0.768191i	$0.721157\pi$
$282$	19.3205	1.15052
$283$	14.5885	0.867194	0.433597	−	0.901107i	$-0.357244\pi$
$283$	14.5885	0.867194	0.433597	+	0.901107i	$0.357244\pi$
$284$	−4.92820	−0.292435
$285$	18.9282	1.12121
$286$	−9.46410	−0.559624
$287$	0	0
$288$	1.00000	0.0589256
$289$	21.3923	1.25837
$290$	2.73205	0.160432
$291$	−6.53590	−0.383141
$292$	−8.73205	−0.511005
$293$	−24.3923	−1.42501	−0.712507	−	0.701665i	$-0.752440\pi$
$293$	−24.3923	−1.42501	−0.712507	+	0.701665i	$0.752440\pi$
$294$	0	0
$295$	19.8564	1.15608
$296$	−4.00000	−0.232495
$297$	−13.8564	−0.804030
$298$	3.46410	0.200670
$299$	13.4641	0.778649
$300$	−4.92820	−0.284530
$301$	0	0
$302$	−11.8564	−0.682260
$303$	8.00000	0.459588
$304$	3.46410	0.198680
$305$	10.9282	0.625747
$306$	6.19615	0.354210
$307$	16.9282	0.966144	0.483072	−	0.875581i	$-0.339521\pi$
$307$	16.9282	0.966144	0.483072	+	0.875581i	$0.339521\pi$
$308$	0	0
$309$	−2.92820	−0.166580
$310$	22.3923	1.27180
$311$	4.87564	0.276472	0.138236	−	0.990399i	$-0.455857\pi$
$311$	4.87564	0.276472	0.138236	+	0.990399i	$0.455857\pi$
$312$	−5.46410	−0.309344
$313$	−7.85641	−0.444070	−0.222035	−	0.975039i	$-0.571270\pi$
$313$	−7.85641	−0.444070	−0.222035	+	0.975039i	$0.571270\pi$
$314$	23.3205	1.31605
$315$	0	0
$316$	−9.46410	−0.532397
$317$	−12.9282	−0.726120	−0.363060	−	0.931766i	$-0.618268\pi$
$317$	−12.9282	−0.726120	−0.363060	+	0.931766i	$0.618268\pi$
$318$	17.8564	1.00134
$319$	3.46410	0.193952
$320$	−2.73205	−0.152726
$321$	−8.00000	−0.446516
$322$	0	0
$323$	21.4641	1.19429
$324$	−11.0000	−0.611111
$325$	6.73205	0.373427
$326$	8.53590	0.472760
$327$	20.0000	1.10600
$328$	−7.66025	−0.422967
$329$	0	0
$330$	−18.9282	−1.04196
$331$	−16.7846	−0.922566	−0.461283	−	0.887253i	$-0.652611\pi$
$331$	−16.7846	−0.922566	−0.461283	+	0.887253i	$0.652611\pi$
$332$	14.5885	0.800646
$333$	−4.00000	−0.219199
$334$	−10.9282	−0.597965
$335$	−18.9282	−1.03416
$336$	0	0
$337$	−14.0000	−0.762629	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000	−0.762629	−0.381314	+	0.924445i	$0.624528\pi$
$338$	−5.53590	−0.301113
$339$	−6.92820	−0.376288
$340$	−16.9282	−0.918061
$341$	28.3923	1.53753
$342$	3.46410	0.187317
$343$	0	0
$344$	10.9282	0.589209
$345$	26.9282	1.44977
$346$	−13.2679	−0.713289
$347$	−0.392305	−0.0210600	−0.0105300	−	0.999945i	$-0.503352\pi$
$347$	−0.392305	−0.0210600	−0.0105300	+	0.999945i	$0.503352\pi$
$348$	2.00000	0.107211
$349$	3.80385	0.203615	0.101808	−	0.994804i	$-0.467537\pi$
$349$	3.80385	0.203615	0.101808	+	0.994804i	$0.467537\pi$
$350$	0	0
$351$	10.9282	0.583304
$352$	−3.46410	−0.184637
$353$	15.8564	0.843951	0.421976	−	0.906607i	$-0.361337\pi$
$353$	15.8564	0.843951	0.421976	+	0.906607i	$0.361337\pi$
$354$	14.5359	0.772574
$355$	13.4641	0.714600
$356$	−5.80385	−0.307603
$357$	0	0
$358$	20.0000	1.05703
$359$	14.2487	0.752018	0.376009	−	0.926616i	$-0.377296\pi$
$359$	14.2487	0.752018	0.376009	+	0.926616i	$0.377296\pi$
$360$	−2.73205	−0.143992
$361$	−7.00000	−0.368421
$362$	18.7321	0.984535
$363$	−2.00000	−0.104973
$364$	0	0
$365$	23.8564	1.24870
$366$	8.00000	0.418167
$367$	13.6603	0.713059	0.356530	−	0.934284i	$-0.383960\pi$
$367$	13.6603	0.713059	0.356530	+	0.934284i	$0.383960\pi$
$368$	4.92820	0.256900
$369$	−7.66025	−0.398777
$370$	10.9282	0.568130
$371$	0	0
$372$	16.3923	0.849901
$373$	−3.46410	−0.179364	−0.0896822	−	0.995970i	$-0.528585\pi$
$373$	−3.46410	−0.179364	−0.0896822	+	0.995970i	$0.528585\pi$
$374$	−21.4641	−1.10988
$375$	−13.8564	−0.715542
$376$	−9.66025	−0.498190
$377$	−2.73205	−0.140708
$378$	0	0
$379$	16.7846	0.862167	0.431084	−	0.902312i	$-0.358131\pi$
$379$	16.7846	0.862167	0.431084	+	0.902312i	$0.358131\pi$
$380$	−9.46410	−0.485498
$381$	26.9282	1.37957
$382$	20.3923	1.04336
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	6.39230	0.325360
$387$	10.9282	0.555512
$388$	3.26795	0.165905
$389$	18.9282	0.959698	0.479849	−	0.877351i	$-0.340691\pi$
$389$	18.9282	0.959698	0.479849	+	0.877351i	$0.340691\pi$
$390$	14.9282	0.755919
$391$	30.5359	1.54427
$392$	0	0
$393$	30.9282	1.56012
$394$	−27.4641	−1.38362
$395$	25.8564	1.30098
$396$	−3.46410	−0.174078
$397$	23.1244	1.16058	0.580289	−	0.814411i	$-0.302940\pi$
$397$	23.1244	1.16058	0.580289	+	0.814411i	$0.302940\pi$
$398$	−10.5359	−0.528117
$399$	0	0
$400$	2.46410	0.123205
$401$	−19.8564	−0.991582	−0.495791	−	0.868442i	$-0.665122\pi$
$401$	−19.8564	−0.991582	−0.495791	+	0.868442i	$0.665122\pi$
$402$	−13.8564	−0.691095
$403$	−22.3923	−1.11544
$404$	−4.00000	−0.199007
$405$	30.0526	1.49332
$406$	0	0
$407$	13.8564	0.686837
$408$	−12.3923	−0.613511
$409$	9.12436	0.451170	0.225585	−	0.974223i	$-0.427571\pi$
$409$	9.12436	0.451170	0.225585	+	0.974223i	$0.427571\pi$
$410$	20.9282	1.03357
$411$	17.0718	0.842090
$412$	1.46410	0.0721311
$413$	0	0
$414$	4.92820	0.242208
$415$	−39.8564	−1.95647
$416$	2.73205	0.133950
$417$	−25.4641	−1.24698
$418$	−12.0000	−0.586939
$419$	−5.80385	−0.283537	−0.141768	−	0.989900i	$-0.545279\pi$
$419$	−5.80385	−0.283537	−0.141768	+	0.989900i	$0.545279\pi$
$420$	0	0
$421$	−36.7846	−1.79277	−0.896386	−	0.443274i	$-0.853817\pi$
$421$	−36.7846	−1.79277	−0.896386	+	0.443274i	$0.853817\pi$
$422$	−6.92820	−0.337260
$423$	−9.66025	−0.469698
$424$	−8.92820	−0.433592
$425$	15.2679	0.740604
$426$	9.85641	0.477544
$427$	0	0
$428$	4.00000	0.193347
$429$	18.9282	0.913862
$430$	−29.8564	−1.43980
$431$	35.7128	1.72023	0.860113	−	0.510104i	$-0.170393\pi$
$431$	35.7128	1.72023	0.860113	+	0.510104i	$0.170393\pi$
$432$	4.00000	0.192450
$433$	−12.7321	−0.611863	−0.305932	−	0.952053i	$-0.598968\pi$
$433$	−12.7321	−0.611863	−0.305932	+	0.952053i	$0.598968\pi$
$434$	0	0
$435$	−5.46410	−0.261984
$436$	−10.0000	−0.478913
$437$	17.0718	0.816655
$438$	17.4641	0.834467
$439$	−23.7128	−1.13175	−0.565875	−	0.824491i	$-0.691462\pi$
$439$	−23.7128	−1.13175	−0.565875	+	0.824491i	$0.691462\pi$
$440$	9.46410	0.451183
$441$	0	0
$442$	16.9282	0.805193
$443$	−35.4641	−1.68495	−0.842475	−	0.538735i	$-0.818902\pi$
$443$	−35.4641	−1.68495	−0.842475	+	0.538735i	$0.818902\pi$
$444$	8.00000	0.379663
$445$	15.8564	0.751666
$446$	−20.3923	−0.965604
$447$	−6.92820	−0.327693
$448$	0	0
$449$	−13.7128	−0.647148	−0.323574	−	0.946203i	$-0.604884\pi$
$449$	−13.7128	−0.647148	−0.323574	+	0.946203i	$0.604884\pi$
$450$	2.46410	0.116159
$451$	26.5359	1.24953
$452$	3.46410	0.162938
$453$	23.7128	1.11413
$454$	−18.5885	−0.872400
$455$	0	0
$456$	−6.92820	−0.324443
$457$	29.1769	1.36484	0.682419	−	0.730961i	$-0.260928\pi$
$457$	29.1769	1.36484	0.682419	+	0.730961i	$0.260928\pi$
$458$	−8.39230	−0.392147
$459$	24.7846	1.15685
$460$	−13.4641	−0.627767
$461$	17.8564	0.831656	0.415828	−	0.909443i	$-0.363492\pi$
$461$	17.8564	0.831656	0.415828	+	0.909443i	$0.363492\pi$
$462$	0	0
$463$	22.0000	1.02243	0.511213	−	0.859454i	$-0.329196\pi$
$463$	22.0000	1.02243	0.511213	+	0.859454i	$0.329196\pi$
$464$	−1.00000	−0.0464238
$465$	−44.7846	−2.07684
$466$	0.143594	0.00665184
$467$	17.3205	0.801498	0.400749	−	0.916188i	$-0.368750\pi$
$467$	17.3205	0.801498	0.400749	+	0.916188i	$0.368750\pi$
$468$	2.73205	0.126289
$469$	0	0
$470$	26.3923	1.21739
$471$	−46.6410	−2.14910
$472$	−7.26795	−0.334534
$473$	−37.8564	−1.74064
$474$	18.9282	0.869401
$475$	8.53590	0.391654
$476$	0	0
$477$	−8.92820	−0.408794
$478$	−27.7128	−1.26755
$479$	27.5167	1.25727	0.628634	−	0.777701i	$-0.283614\pi$
$479$	27.5167	1.25727	0.628634	+	0.777701i	$0.283614\pi$
$480$	5.46410	0.249401
$481$	−10.9282	−0.498283
$482$	3.07180	0.139917
$483$	0	0
$484$	1.00000	0.0454545
$485$	−8.92820	−0.405409
$486$	10.0000	0.453609
$487$	−10.9282	−0.495204	−0.247602	−	0.968862i	$-0.579643\pi$
$487$	−10.9282	−0.495204	−0.247602	+	0.968862i	$0.579643\pi$
$488$	−4.00000	−0.181071
$489$	−17.0718	−0.772013
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	15.3205	0.690702
$493$	−6.19615	−0.279061
$494$	9.46410	0.425810
$495$	9.46410	0.425380
$496$	−8.19615	−0.368018
$497$	0	0
$498$	−29.1769	−1.30745
$499$	24.7846	1.10951	0.554756	−	0.832013i	$-0.312812\pi$
$499$	24.7846	1.10951	0.554756	+	0.832013i	$0.312812\pi$
$500$	6.92820	0.309839
$501$	21.8564	0.976472
$502$	−10.3923	−0.463831
$503$	−24.1962	−1.07885	−0.539427	−	0.842033i	$-0.681359\pi$
$503$	−24.1962	−1.07885	−0.539427	+	0.842033i	$0.681359\pi$
$504$	0	0
$505$	10.9282	0.486299
$506$	−17.0718	−0.758934
$507$	11.0718	0.491716
$508$	−13.4641	−0.597373
$509$	−29.6603	−1.31467	−0.657334	−	0.753600i	$-0.728316\pi$
$509$	−29.6603	−1.31467	−0.657334	+	0.753600i	$0.728316\pi$
$510$	33.8564	1.49919
$511$	0	0
$512$	1.00000	0.0441942
$513$	13.8564	0.611775
$514$	−12.5359	−0.552935
$515$	−4.00000	−0.176261
$516$	−21.8564	−0.962175
$517$	33.4641	1.47175
$518$	0	0
$519$	26.5359	1.16480
$520$	−7.46410	−0.327323
$521$	−28.5359	−1.25018	−0.625090	−	0.780553i	$-0.714938\pi$
$521$	−28.5359	−1.25018	−0.625090	+	0.780553i	$0.714938\pi$
$522$	−1.00000	−0.0437688
$523$	40.7321	1.78109	0.890544	−	0.454897i	$-0.150324\pi$
$523$	40.7321	1.78109	0.890544	+	0.454897i	$0.150324\pi$
$524$	−15.4641	−0.675552
$525$	0	0
$526$	−4.39230	−0.191514
$527$	−50.7846	−2.21221
$528$	6.92820	0.301511
$529$	1.28719	0.0559647
$530$	24.3923	1.05953
$531$	−7.26795	−0.315402
$532$	0	0
$533$	−20.9282	−0.906501
$534$	11.6077	0.502314
$535$	−10.9282	−0.472467
$536$	6.92820	0.299253
$537$	−40.0000	−1.72613
$538$	−25.8564	−1.11475
$539$	0	0
$540$	−10.9282	−0.470275
$541$	4.92820	0.211880	0.105940	−	0.994373i	$-0.466215\pi$
$541$	4.92820	0.211880	0.105940	+	0.994373i	$0.466215\pi$
$542$	16.5885	0.712535
$543$	−37.4641	−1.60774
$544$	6.19615	0.265658
$545$	27.3205	1.17028
$546$	0	0
$547$	−10.2487	−0.438203	−0.219102	−	0.975702i	$-0.570313\pi$
$547$	−10.2487	−0.438203	−0.219102	+	0.975702i	$0.570313\pi$
$548$	−8.53590	−0.364636
$549$	−4.00000	−0.170716
$550$	−8.53590	−0.363972
$551$	−3.46410	−0.147576
$552$	−9.85641	−0.419517
$553$	0	0
$554$	2.39230	0.101639
$555$	−21.8564	−0.927753
$556$	12.7321	0.539959
$557$	23.8564	1.01083	0.505414	−	0.862877i	$-0.331340\pi$
$557$	23.8564	1.01083	0.505414	+	0.862877i	$0.331340\pi$
$558$	−8.19615	−0.346971
$559$	29.8564	1.26279
$560$	0	0
$561$	42.9282	1.81243
$562$	−21.4641	−0.905408
$563$	−42.1051	−1.77452	−0.887260	−	0.461270i	$-0.847394\pi$
$563$	−42.1051	−1.77452	−0.887260	+	0.461270i	$0.847394\pi$
$564$	19.3205	0.813540
$565$	−9.46410	−0.398158
$566$	14.5885	0.613199
$567$	0	0
$568$	−4.92820	−0.206783
$569$	26.7846	1.12287	0.561435	−	0.827521i	$-0.310250\pi$
$569$	26.7846	1.12287	0.561435	+	0.827521i	$0.310250\pi$
$570$	18.9282	0.792815
$571$	3.60770	0.150977	0.0754887	−	0.997147i	$-0.475948\pi$
$571$	3.60770	0.150977	0.0754887	+	0.997147i	$0.475948\pi$
$572$	−9.46410	−0.395714
$573$	−40.7846	−1.70380
$574$	0	0
$575$	12.1436	0.506423
$576$	1.00000	0.0416667
$577$	−33.5167	−1.39532	−0.697658	−	0.716431i	$-0.745775\pi$
$577$	−33.5167	−1.39532	−0.697658	+	0.716431i	$0.745775\pi$
$578$	21.3923	0.889803
$579$	−12.7846	−0.531310
$580$	2.73205	0.113442
$581$	0	0
$582$	−6.53590	−0.270922
$583$	30.9282	1.28092
$584$	−8.73205	−0.361335
$585$	−7.46410	−0.308603
$586$	−24.3923	−1.00764
$587$	−14.9808	−0.618322	−0.309161	−	0.951010i	$-0.600048\pi$
$587$	−14.9808	−0.618322	−0.309161	+	0.951010i	$0.600048\pi$
$588$	0	0
$589$	−28.3923	−1.16988
$590$	19.8564	0.817475
$591$	54.9282	2.25944
$592$	−4.00000	−0.164399
$593$	−12.9282	−0.530898	−0.265449	−	0.964125i	$-0.585520\pi$
$593$	−12.9282	−0.530898	−0.265449	+	0.964125i	$0.585520\pi$
$594$	−13.8564	−0.568535
$595$	0	0
$596$	3.46410	0.141895
$597$	21.0718	0.862411
$598$	13.4641	0.550588
$599$	4.67949	0.191199	0.0955994	−	0.995420i	$-0.469523\pi$
$599$	4.67949	0.191199	0.0955994	+	0.995420i	$0.469523\pi$
$600$	−4.92820	−0.201193
$601$	−36.0526	−1.47061	−0.735307	−	0.677734i	$-0.762962\pi$
$601$	−36.0526	−1.47061	−0.735307	+	0.677734i	$0.762962\pi$
$602$	0	0
$603$	6.92820	0.282138
$604$	−11.8564	−0.482430
$605$	−2.73205	−0.111074
$606$	8.00000	0.324978
$607$	−22.7321	−0.922665	−0.461333	−	0.887227i	$-0.652629\pi$
$607$	−22.7321	−0.922665	−0.461333	+	0.887227i	$0.652629\pi$
$608$	3.46410	0.140488
$609$	0	0
$610$	10.9282	0.442470
$611$	−26.3923	−1.06772
$612$	6.19615	0.250465
$613$	−28.2487	−1.14095	−0.570477	−	0.821313i	$-0.693242\pi$
$613$	−28.2487	−1.14095	−0.570477	+	0.821313i	$0.693242\pi$
$614$	16.9282	0.683167
$615$	−41.8564	−1.68781
$616$	0	0
$617$	21.7128	0.874125	0.437062	−	0.899431i	$-0.356019\pi$
$617$	21.7128	0.874125	0.437062	+	0.899431i	$0.356019\pi$
$618$	−2.92820	−0.117790
$619$	−31.4641	−1.26465	−0.632325	−	0.774704i	$-0.717899\pi$
$619$	−31.4641	−1.26465	−0.632325	+	0.774704i	$0.717899\pi$
$620$	22.3923	0.899297
$621$	19.7128	0.791048
$622$	4.87564	0.195496
$623$	0	0
$624$	−5.46410	−0.218739
$625$	−31.2487	−1.24995
$626$	−7.85641	−0.314005
$627$	24.0000	0.958468
$628$	23.3205	0.930590
$629$	−24.7846	−0.988227
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	−9.46410	−0.376462
$633$	13.8564	0.550743
$634$	−12.9282	−0.513445
$635$	36.7846	1.45975
$636$	17.8564	0.708053
$637$	0	0
$638$	3.46410	0.137145
$639$	−4.92820	−0.194957
$640$	−2.73205	−0.107994
$641$	20.1436	0.795624	0.397812	−	0.917467i	$-0.369770\pi$
$641$	20.1436	0.795624	0.397812	+	0.917467i	$0.369770\pi$
$642$	−8.00000	−0.315735
$643$	31.6603	1.24856	0.624279	−	0.781201i	$-0.285393\pi$
$643$	31.6603	1.24856	0.624279	+	0.781201i	$0.285393\pi$
$644$	0	0
$645$	59.7128	2.35119
$646$	21.4641	0.844494
$647$	15.6077	0.613602	0.306801	−	0.951774i	$-0.400741\pi$
$647$	15.6077	0.613602	0.306801	+	0.951774i	$0.400741\pi$
$648$	−11.0000	−0.432121
$649$	25.1769	0.988280
$650$	6.73205	0.264053
$651$	0	0
$652$	8.53590	0.334292
$653$	22.0000	0.860927	0.430463	−	0.902608i	$-0.358350\pi$
$653$	22.0000	0.860927	0.430463	+	0.902608i	$0.358350\pi$
$654$	20.0000	0.782062
$655$	42.2487	1.65079
$656$	−7.66025	−0.299083
$657$	−8.73205	−0.340670
$658$	0	0
$659$	−34.3923	−1.33973	−0.669867	−	0.742481i	$-0.733649\pi$
$659$	−34.3923	−1.33973	−0.669867	+	0.742481i	$0.733649\pi$
$660$	−18.9282	−0.736779
$661$	13.2679	0.516063	0.258032	−	0.966136i	$-0.416926\pi$
$661$	13.2679	0.516063	0.258032	+	0.966136i	$0.416926\pi$
$662$	−16.7846	−0.652352
$663$	−33.8564	−1.31487
$664$	14.5885	0.566142
$665$	0	0
$666$	−4.00000	−0.154997
$667$	−4.92820	−0.190821
$668$	−10.9282	−0.422825
$669$	40.7846	1.57682
$670$	−18.9282	−0.731260
$671$	13.8564	0.534921
$672$	0	0
$673$	45.4641	1.75251	0.876256	−	0.481846i	$-0.160033\pi$
$673$	45.4641	1.75251	0.876256	+	0.481846i	$0.160033\pi$
$674$	−14.0000	−0.539260
$675$	9.85641	0.379373
$676$	−5.53590	−0.212919
$677$	−33.1769	−1.27509	−0.637546	−	0.770412i	$-0.720050\pi$
$677$	−33.1769	−1.27509	−0.637546	+	0.770412i	$0.720050\pi$
$678$	−6.92820	−0.266076
$679$	0	0
$680$	−16.9282	−0.649167
$681$	37.1769	1.42462
$682$	28.3923	1.08720
$683$	−25.8564	−0.989368	−0.494684	−	0.869073i	$-0.664716\pi$
$683$	−25.8564	−0.989368	−0.494684	+	0.869073i	$0.664716\pi$
$684$	3.46410	0.132453
$685$	23.3205	0.891031
$686$	0	0
$687$	16.7846	0.640373
$688$	10.9282	0.416634
$689$	−24.3923	−0.929273
$690$	26.9282	1.02514
$691$	20.0526	0.762835	0.381418	−	0.924403i	$-0.375436\pi$
$691$	20.0526	0.762835	0.381418	+	0.924403i	$0.375436\pi$
$692$	−13.2679	−0.504372
$693$	0	0
$694$	−0.392305	−0.0148917
$695$	−34.7846	−1.31946
$696$	2.00000	0.0758098
$697$	−47.4641	−1.79783
$698$	3.80385	0.143978
$699$	−0.287187	−0.0108624
$700$	0	0
$701$	31.1769	1.17754	0.588768	−	0.808302i	$-0.299613\pi$
$701$	31.1769	1.17754	0.588768	+	0.808302i	$0.299613\pi$
$702$	10.9282	0.412458
$703$	−13.8564	−0.522604
$704$	−3.46410	−0.130558
$705$	−52.7846	−1.98798
$706$	15.8564	0.596764
$707$	0	0
$708$	14.5359	0.546293
$709$	−35.5692	−1.33583	−0.667915	−	0.744238i	$-0.732813\pi$
$709$	−35.5692	−1.33583	−0.667915	+	0.744238i	$0.732813\pi$
$710$	13.4641	0.505299
$711$	−9.46410	−0.354932
$712$	−5.80385	−0.217508
$713$	−40.3923	−1.51270
$714$	0	0
$715$	25.8564	0.966975
$716$	20.0000	0.747435
$717$	55.4256	2.06991
$718$	14.2487	0.531757
$719$	7.32051	0.273009	0.136504	−	0.990639i	$-0.456413\pi$
$719$	7.32051	0.273009	0.136504	+	0.990639i	$0.456413\pi$
$720$	−2.73205	−0.101818
$721$	0	0
$722$	−7.00000	−0.260513
$723$	−6.14359	−0.228483
$724$	18.7321	0.696171
$725$	−2.46410	−0.0915144
$726$	−2.00000	−0.0742270
$727$	27.9090	1.03509	0.517543	−	0.855657i	$-0.326847\pi$
$727$	27.9090	1.03509	0.517543	+	0.855657i	$0.326847\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	23.8564	0.882965
$731$	67.7128	2.50445
$732$	8.00000	0.295689
$733$	−15.7128	−0.580366	−0.290183	−	0.956971i	$-0.593716\pi$
$733$	−15.7128	−0.580366	−0.290183	+	0.956971i	$0.593716\pi$
$734$	13.6603	0.504209
$735$	0	0
$736$	4.92820	0.181656
$737$	−24.0000	−0.884051
$738$	−7.66025	−0.281978
$739$	48.7846	1.79457	0.897285	−	0.441451i	$-0.145536\pi$
$739$	48.7846	1.79457	0.897285	+	0.441451i	$0.145536\pi$
$740$	10.9282	0.401729
$741$	−18.9282	−0.695345
$742$	0	0
$743$	−34.9282	−1.28139	−0.640696	−	0.767795i	$-0.721354\pi$
$743$	−34.9282	−1.28139	−0.640696	+	0.767795i	$0.721354\pi$
$744$	16.3923	0.600971
$745$	−9.46410	−0.346738
$746$	−3.46410	−0.126830
$747$	14.5885	0.533764
$748$	−21.4641	−0.784805
$749$	0	0
$750$	−13.8564	−0.505964
$751$	49.5692	1.80881	0.904403	−	0.426679i	$-0.140316\pi$
$751$	49.5692	1.80881	0.904403	+	0.426679i	$0.140316\pi$
$752$	−9.66025	−0.352273
$753$	20.7846	0.757433
$754$	−2.73205	−0.0994954
$755$	32.3923	1.17888
$756$	0	0
$757$	−46.9282	−1.70563	−0.852817	−	0.522209i	$-0.825108\pi$
$757$	−46.9282	−1.70563	−0.852817	+	0.522209i	$0.825108\pi$
$758$	16.7846	0.609644
$759$	34.1436	1.23933
$760$	−9.46410	−0.343299
$761$	−33.7128	−1.22209	−0.611044	−	0.791596i	$-0.709250\pi$
$761$	−33.7128	−1.22209	−0.611044	+	0.791596i	$0.709250\pi$
$762$	26.9282	0.975506
$763$	0	0
$764$	20.3923	0.737768
$765$	−16.9282	−0.612040
$766$	16.0000	0.578103
$767$	−19.8564	−0.716973
$768$	−2.00000	−0.0721688
$769$	−53.5167	−1.92986	−0.964930	−	0.262507i	$-0.915451\pi$
$769$	−53.5167	−1.92986	−0.964930	+	0.262507i	$0.915451\pi$
$770$	0	0
$771$	25.0718	0.902939
$772$	6.39230	0.230064
$773$	44.3923	1.59668	0.798340	−	0.602207i	$-0.205712\pi$
$773$	44.3923	1.59668	0.798340	+	0.602207i	$0.205712\pi$
$774$	10.9282	0.392806
$775$	−20.1962	−0.725467
$776$	3.26795	0.117313
$777$	0	0
$778$	18.9282	0.678609
$779$	−26.5359	−0.950747
$780$	14.9282	0.534515
$781$	17.0718	0.610877
$782$	30.5359	1.09196
$783$	−4.00000	−0.142948
$784$	0	0
$785$	−63.7128	−2.27401
$786$	30.9282	1.10317
$787$	13.8038	0.492054	0.246027	−	0.969263i	$-0.420875\pi$
$787$	13.8038	0.492054	0.246027	+	0.969263i	$0.420875\pi$
$788$	−27.4641	−0.978368
$789$	8.78461	0.312740
$790$	25.8564	0.919930
$791$	0	0
$792$	−3.46410	−0.123091
$793$	−10.9282	−0.388072
$794$	23.1244	0.820653
$795$	−48.7846	−1.73021
$796$	−10.5359	−0.373435
$797$	36.3923	1.28908	0.644541	−	0.764570i	$-0.277049\pi$
$797$	36.3923	1.28908	0.644541	+	0.764570i	$0.277049\pi$
$798$	0	0
$799$	−59.8564	−2.11757
$800$	2.46410	0.0871191
$801$	−5.80385	−0.205069
$802$	−19.8564	−0.701154
$803$	30.2487	1.06745
$804$	−13.8564	−0.488678
$805$	0	0
$806$	−22.3923	−0.788735
$807$	51.7128	1.82038
$808$	−4.00000	−0.140720
$809$	24.2487	0.852539	0.426270	−	0.904596i	$-0.359827\pi$
$809$	24.2487	0.852539	0.426270	+	0.904596i	$0.359827\pi$
$810$	30.0526	1.05594
$811$	−24.8372	−0.872151	−0.436075	−	0.899910i	$-0.643632\pi$
$811$	−24.8372	−0.872151	−0.436075	+	0.899910i	$0.643632\pi$
$812$	0	0
$813$	−33.1769	−1.16357
$814$	13.8564	0.485667
$815$	−23.3205	−0.816882
$816$	−12.3923	−0.433817
$817$	37.8564	1.32443
$818$	9.12436	0.319026
$819$	0	0
$820$	20.9282	0.730845
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	17.0718	0.595447
$823$	−9.07180	−0.316223	−0.158111	−	0.987421i	$-0.550541\pi$
$823$	−9.07180	−0.316223	−0.158111	+	0.987421i	$0.550541\pi$
$824$	1.46410	0.0510044
$825$	17.0718	0.594364
$826$	0	0
$827$	−2.67949	−0.0931751	−0.0465875	−	0.998914i	$-0.514835\pi$
$827$	−2.67949	−0.0931751	−0.0465875	+	0.998914i	$0.514835\pi$
$828$	4.92820	0.171267
$829$	−9.07180	−0.315077	−0.157538	−	0.987513i	$-0.550356\pi$
$829$	−9.07180	−0.315077	−0.157538	+	0.987513i	$0.550356\pi$
$830$	−39.8564	−1.38344
$831$	−4.78461	−0.165976
$832$	2.73205	0.0947168
$833$	0	0
$834$	−25.4641	−0.881750
$835$	29.8564	1.03322
$836$	−12.0000	−0.415029
$837$	−32.7846	−1.13320
$838$	−5.80385	−0.200491
$839$	−34.7321	−1.19908	−0.599542	−	0.800343i	$-0.704650\pi$
$839$	−34.7321	−1.19908	−0.599542	+	0.800343i	$0.704650\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−36.7846	−1.26768
$843$	42.9282	1.47853
$844$	−6.92820	−0.238479
$845$	15.1244	0.520294
$846$	−9.66025	−0.332126
$847$	0	0
$848$	−8.92820	−0.306596
$849$	−29.1769	−1.00135
$850$	15.2679	0.523686
$851$	−19.7128	−0.675747
$852$	9.85641	0.337675
$853$	34.9282	1.19592	0.597959	−	0.801526i	$-0.295978\pi$
$853$	34.9282	1.19592	0.597959	+	0.801526i	$0.295978\pi$
$854$	0	0
$855$	−9.46410	−0.323665
$856$	4.00000	0.136717
$857$	43.8564	1.49811	0.749053	−	0.662510i	$-0.230509\pi$
$857$	43.8564	1.49811	0.749053	+	0.662510i	$0.230509\pi$
$858$	18.9282	0.646198
$859$	−50.4974	−1.72295	−0.861475	−	0.507800i	$-0.830459\pi$
$859$	−50.4974	−1.72295	−0.861475	+	0.507800i	$0.830459\pi$
$860$	−29.8564	−1.01810
$861$	0	0
$862$	35.7128	1.21638
$863$	−20.1436	−0.685696	−0.342848	−	0.939391i	$-0.611392\pi$
$863$	−20.1436	−0.685696	−0.342848	+	0.939391i	$0.611392\pi$
$864$	4.00000	0.136083
$865$	36.2487	1.23249
$866$	−12.7321	−0.432653
$867$	−42.7846	−1.45304
$868$	0	0
$869$	32.7846	1.11214
$870$	−5.46410	−0.185250
$871$	18.9282	0.641358
$872$	−10.0000	−0.338643
$873$	3.26795	0.110603
$874$	17.0718	0.577462
$875$	0	0
$876$	17.4641	0.590057
$877$	−39.1769	−1.32291	−0.661455	−	0.749985i	$-0.730061\pi$
$877$	−39.1769	−1.32291	−0.661455	+	0.749985i	$0.730061\pi$
$878$	−23.7128	−0.800269
$879$	48.7846	1.64546
$880$	9.46410	0.319035
$881$	−26.8756	−0.905463	−0.452732	−	0.891647i	$-0.649550\pi$
$881$	−26.8756	−0.905463	−0.452732	+	0.891647i	$0.649550\pi$
$882$	0	0
$883$	31.7128	1.06722	0.533611	−	0.845730i	$-0.320835\pi$
$883$	31.7128	1.06722	0.533611	+	0.845730i	$0.320835\pi$
$884$	16.9282	0.569357
$885$	−39.7128	−1.33493
$886$	−35.4641	−1.19144
$887$	28.9808	0.973079	0.486539	−	0.873659i	$-0.338259\pi$
$887$	28.9808	0.973079	0.486539	+	0.873659i	$0.338259\pi$
$888$	8.00000	0.268462
$889$	0	0
$890$	15.8564	0.531508
$891$	38.1051	1.27657
$892$	−20.3923	−0.682785
$893$	−33.4641	−1.11983
$894$	−6.92820	−0.231714
$895$	−54.6410	−1.82645
$896$	0	0
$897$	−26.9282	−0.899107
$898$	−13.7128	−0.457602
$899$	8.19615	0.273357
$900$	2.46410	0.0821367
$901$	−55.3205	−1.84299
$902$	26.5359	0.883549
$903$	0	0
$904$	3.46410	0.115214
$905$	−51.1769	−1.70118
$906$	23.7128	0.787805
$907$	−18.3923	−0.610706	−0.305353	−	0.952239i	$-0.598775\pi$
$907$	−18.3923	−0.610706	−0.305353	+	0.952239i	$0.598775\pi$
$908$	−18.5885	−0.616880
$909$	−4.00000	−0.132672
$910$	0	0
$911$	−58.2487	−1.92987	−0.964933	−	0.262496i	$-0.915454\pi$
$911$	−58.2487	−1.92987	−0.964933	+	0.262496i	$0.915454\pi$
$912$	−6.92820	−0.229416
$913$	−50.5359	−1.67249
$914$	29.1769	0.965087
$915$	−21.8564	−0.722551
$916$	−8.39230	−0.277290
$917$	0	0
$918$	24.7846	0.818014
$919$	−7.85641	−0.259159	−0.129579	−	0.991569i	$-0.541363\pi$
$919$	−7.85641	−0.259159	−0.129579	+	0.991569i	$0.541363\pi$
$920$	−13.4641	−0.443898
$921$	−33.8564	−1.11561
$922$	17.8564	0.588069
$923$	−13.4641	−0.443176
$924$	0	0
$925$	−9.85641	−0.324077
$926$	22.0000	0.722965
$927$	1.46410	0.0480874
$928$	−1.00000	−0.0328266
$929$	−2.78461	−0.0913601	−0.0456800	−	0.998956i	$-0.514545\pi$
$929$	−2.78461	−0.0913601	−0.0456800	+	0.998956i	$0.514545\pi$
$930$	−44.7846	−1.46855
$931$	0	0
$932$	0.143594	0.00470356
$933$	−9.75129	−0.319243
$934$	17.3205	0.566744
$935$	58.6410	1.91777
$936$	2.73205	0.0892999
$937$	43.5692	1.42334	0.711672	−	0.702512i	$-0.247938\pi$
$937$	43.5692	1.42334	0.711672	+	0.702512i	$0.247938\pi$
$938$	0	0
$939$	15.7128	0.512768
$940$	26.3923	0.860822
$941$	11.8038	0.384794	0.192397	−	0.981317i	$-0.438374\pi$
$941$	11.8038	0.384794	0.192397	+	0.981317i	$0.438374\pi$
$942$	−46.6410	−1.51965
$943$	−37.7513	−1.22935
$944$	−7.26795	−0.236552
$945$	0	0
$946$	−37.8564	−1.23082
$947$	8.78461	0.285461	0.142731	−	0.989762i	$-0.454412\pi$
$947$	8.78461	0.285461	0.142731	+	0.989762i	$0.454412\pi$
$948$	18.9282	0.614759
$949$	−23.8564	−0.774412
$950$	8.53590	0.276941
$951$	25.8564	0.838451
$952$	0	0
$953$	−32.3923	−1.04929	−0.524645	−	0.851321i	$-0.675802\pi$
$953$	−32.3923	−1.04929	−0.524645	+	0.851321i	$0.675802\pi$
$954$	−8.92820	−0.289061
$955$	−55.7128	−1.80282
$956$	−27.7128	−0.896296
$957$	−6.92820	−0.223957
$958$	27.5167	0.889023
$959$	0	0
$960$	5.46410	0.176353
$961$	36.1769	1.16700
$962$	−10.9282	−0.352339
$963$	4.00000	0.128898
$964$	3.07180	0.0989359
$965$	−17.4641	−0.562189
$966$	0	0
$967$	14.1436	0.454827	0.227414	−	0.973798i	$-0.426973\pi$
$967$	14.1436	0.454827	0.227414	+	0.973798i	$0.426973\pi$
$968$	1.00000	0.0321412
$969$	−42.9282	−1.37905
$970$	−8.92820	−0.286667
$971$	21.3205	0.684208	0.342104	−	0.939662i	$-0.388861\pi$
$971$	21.3205	0.684208	0.342104	+	0.939662i	$0.388861\pi$
$972$	10.0000	0.320750
$973$	0	0
$974$	−10.9282	−0.350162
$975$	−13.4641	−0.431196
$976$	−4.00000	−0.128037
$977$	−10.5359	−0.337073	−0.168537	−	0.985695i	$-0.553904\pi$
$977$	−10.5359	−0.337073	−0.168537	+	0.985695i	$0.553904\pi$
$978$	−17.0718	−0.545896
$979$	20.1051	0.642562
$980$	0	0
$981$	−10.0000	−0.319275
$982$	12.0000	0.382935
$983$	52.6936	1.68066	0.840332	−	0.542072i	$-0.182360\pi$
$983$	52.6936	1.68066	0.840332	+	0.542072i	$0.182360\pi$
$984$	15.3205	0.488400
$985$	75.0333	2.39076
$986$	−6.19615	−0.197326
$987$	0	0
$988$	9.46410	0.301093
$989$	53.8564	1.71253
$990$	9.46410	0.300789
$991$	−11.7128	−0.372070	−0.186035	−	0.982543i	$-0.559564\pi$
$991$	−11.7128	−0.372070	−0.186035	+	0.982543i	$0.559564\pi$
$992$	−8.19615	−0.260228
$993$	33.5692	1.06529
$994$	0	0
$995$	28.7846	0.912533
$996$	−29.1769	−0.924506
$997$	−11.7128	−0.370949	−0.185474	−	0.982649i	$-0.559382\pi$
$997$	−11.7128	−0.370949	−0.185474	+	0.982649i	$0.559382\pi$
$998$	24.7846	0.784543
$999$	−16.0000	−0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.i.1.1		2
7.6	odd	2		406.2.a.e.1.2	✓	2
21.20	even	2		3654.2.a.y.1.1		2
28.27	even	2		3248.2.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.a.e.1.2	✓	2	7.6	odd	2
2842.2.a.i.1.1		2	1.1	even	1	trivial
3248.2.a.o.1.2		2	28.27	even	2
3654.2.a.y.1.1		2	21.20	even	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} -2.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.73205 q^{10} -3.46410 q^{11} -2.00000 q^{12} +2.73205 q^{13} +5.46410 q^{15} +1.00000 q^{16} +6.19615 q^{17} +1.00000 q^{18} +3.46410 q^{19} -2.73205 q^{20} -3.46410 q^{22} +4.92820 q^{23} -2.00000 q^{24} +2.46410 q^{25} +2.73205 q^{26} +4.00000 q^{27} -1.00000 q^{29} +5.46410 q^{30} -8.19615 q^{31} +1.00000 q^{32} +6.92820 q^{33} +6.19615 q^{34} +1.00000 q^{36} -4.00000 q^{37} +3.46410 q^{38} -5.46410 q^{39} -2.73205 q^{40} -7.66025 q^{41} +10.9282 q^{43} -3.46410 q^{44} -2.73205 q^{45} +4.92820 q^{46} -9.66025 q^{47} -2.00000 q^{48} +2.46410 q^{50} -12.3923 q^{51} +2.73205 q^{52} -8.92820 q^{53} +4.00000 q^{54} +9.46410 q^{55} -6.92820 q^{57} -1.00000 q^{58} -7.26795 q^{59} +5.46410 q^{60} -4.00000 q^{61} -8.19615 q^{62} +1.00000 q^{64} -7.46410 q^{65} +6.92820 q^{66} +6.92820 q^{67} +6.19615 q^{68} -9.85641 q^{69} -4.92820 q^{71} +1.00000 q^{72} -8.73205 q^{73} -4.00000 q^{74} -4.92820 q^{75} +3.46410 q^{76} -5.46410 q^{78} -9.46410 q^{79} -2.73205 q^{80} -11.0000 q^{81} -7.66025 q^{82} +14.5885 q^{83} -16.9282 q^{85} +10.9282 q^{86} +2.00000 q^{87} -3.46410 q^{88} -5.80385 q^{89} -2.73205 q^{90} +4.92820 q^{92} +16.3923 q^{93} -9.66025 q^{94} -9.46410 q^{95} -2.00000 q^{96} +3.26795 q^{97} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} - 2 q^{5} - 4 q^{6} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 4 q^{23} - 4 q^{24} - 2 q^{25} + 2 q^{26} + 8 q^{27} - 2 q^{29} + 4 q^{30} - 6 q^{31} + 2 q^{32} + 2 q^{34} + 2 q^{36} - 8 q^{37} - 4 q^{39} - 2 q^{40} + 2 q^{41} + 8 q^{43} - 2 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 2 q^{50} - 4 q^{51} + 2 q^{52} - 4 q^{53} + 8 q^{54} + 12 q^{55} - 2 q^{58} - 18 q^{59} + 4 q^{60} - 8 q^{61} - 6 q^{62} + 2 q^{64} - 8 q^{65} + 2 q^{68} + 8 q^{69} + 4 q^{71} + 2 q^{72} - 14 q^{73} - 8 q^{74} + 4 q^{75} - 4 q^{78} - 12 q^{79} - 2 q^{80} - 22 q^{81} + 2 q^{82} - 2 q^{83} - 20 q^{85} + 8 q^{86} + 4 q^{87} - 22 q^{89} - 2 q^{90} - 4 q^{92} + 12 q^{93} - 2 q^{94} - 12 q^{95} - 4 q^{96} + 10 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 - 2 * q^5 - 4 * q^6 + 2 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 2 * q^20 - 4 * q^23 - 4 * q^24 - 2 * q^25 + 2 * q^26 + 8 * q^27 - 2 * q^29 + 4 * q^30 - 6 * q^31 + 2 * q^32 + 2 * q^34 + 2 * q^36 - 8 * q^37 - 4 * q^39 - 2 * q^40 + 2 * q^41 + 8 * q^43 - 2 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 2 * q^50 - 4 * q^51 + 2 * q^52 - 4 * q^53 + 8 * q^54 + 12 * q^55 - 2 * q^58 - 18 * q^59 + 4 * q^60 - 8 * q^61 - 6 * q^62 + 2 * q^64 - 8 * q^65 + 2 * q^68 + 8 * q^69 + 4 * q^71 + 2 * q^72 - 14 * q^73 - 8 * q^74 + 4 * q^75 - 4 * q^78 - 12 * q^79 - 2 * q^80 - 22 * q^81 + 2 * q^82 - 2 * q^83 - 20 * q^85 + 8 * q^86 + 4 * q^87 - 22 * q^89 - 2 * q^90 - 4 * q^92 + 12 * q^93 - 2 * q^94 - 12 * q^95 - 4 * q^96 + 10 * q^97

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