LMFDB - Embedded newform 2842.2.a.s.1.5

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:	$5$
Coefficient field:	5.5.369849.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 6x^3 + 3x^2 + 3*x - 1
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			1.5
Root			$0.299252$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.04241 q^{3} +1.00000 q^{4} -0.868034 q^{5} -2.04241 q^{6} -1.00000 q^{8} +1.17146 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.04241 q^{3} +1.00000 q^{4} -0.868034 q^{5} -2.04241 q^{6} -1.00000 q^{8} +1.17146 q^{9} +0.868034 q^{10} -4.52582 q^{11} +2.04241 q^{12} +4.81113 q^{13} -1.77288 q^{15} +1.00000 q^{16} -0.259761 q^{17} -1.17146 q^{18} +1.04241 q^{19} -0.868034 q^{20} +4.52582 q^{22} -7.24235 q^{23} -2.04241 q^{24} -4.24652 q^{25} -4.81113 q^{26} -3.73464 q^{27} +1.00000 q^{29} +1.77288 q^{30} -2.40963 q^{31} -1.00000 q^{32} -9.24359 q^{33} +0.259761 q^{34} +1.17146 q^{36} -7.46202 q^{37} -1.04241 q^{38} +9.82632 q^{39} +0.868034 q^{40} +5.52999 q^{41} +6.24794 q^{43} -4.52582 q^{44} -1.01686 q^{45} +7.24235 q^{46} -12.0092 q^{47} +2.04241 q^{48} +4.24652 q^{50} -0.530539 q^{51} +4.81113 q^{52} +5.23942 q^{53} +3.73464 q^{54} +3.92856 q^{55} +2.12904 q^{57} -1.00000 q^{58} -10.8814 q^{59} -1.77288 q^{60} +14.4456 q^{61} +2.40963 q^{62} +1.00000 q^{64} -4.17622 q^{65} +9.24359 q^{66} +6.20553 q^{67} -0.259761 q^{68} -14.7919 q^{69} -9.47016 q^{71} -1.17146 q^{72} -10.6617 q^{73} +7.46202 q^{74} -8.67315 q^{75} +1.04241 q^{76} -9.82632 q^{78} -13.8798 q^{79} -0.868034 q^{80} -11.1421 q^{81} -5.52999 q^{82} -6.90833 q^{83} +0.225481 q^{85} -6.24794 q^{86} +2.04241 q^{87} +4.52582 q^{88} -1.73757 q^{89} +1.01686 q^{90} -7.24235 q^{92} -4.92147 q^{93} +12.0092 q^{94} -0.904851 q^{95} -2.04241 q^{96} +5.00070 q^{97} -5.30180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^8 + 4 * q^9	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{8} + 4 q^{9} + 5 q^{10} + 4 q^{11} - 3 q^{12} - 2 q^{13} + 6 q^{15} + 5 q^{16} - 2 q^{17} - 4 q^{18} - 8 q^{19} - 5 q^{20} - 4 q^{22} - 9 q^{23} + 3 q^{24} + 8 q^{25} + 2 q^{26} - 15 q^{27} + 5 q^{29} - 6 q^{30} + 15 q^{31} - 5 q^{32} - 29 q^{33} + 2 q^{34} + 4 q^{36} - 22 q^{37} + 8 q^{38} + 32 q^{39} + 5 q^{40} - q^{41} + 7 q^{43} + 4 q^{44} + 8 q^{45} + 9 q^{46} - 20 q^{47} - 3 q^{48} - 8 q^{50} - 15 q^{51} - 2 q^{52} + 11 q^{53} + 15 q^{54} + 4 q^{55} + 22 q^{57} - 5 q^{58} - 13 q^{59} + 6 q^{60} + 15 q^{61} - 15 q^{62} + 5 q^{64} - 7 q^{65} + 29 q^{66} + 20 q^{67} - 2 q^{68} - 20 q^{69} - 4 q^{71} - 4 q^{72} + 22 q^{74} - 20 q^{75} - 8 q^{76} - 32 q^{78} + q^{79} - 5 q^{80} + 21 q^{81} + q^{82} - 48 q^{83} - 13 q^{85} - 7 q^{86} - 3 q^{87} - 4 q^{88} + 7 q^{89} - 8 q^{90} - 9 q^{92} - 23 q^{93} + 20 q^{94} + 11 q^{95} + 3 q^{96} - 6 q^{97} + 32 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^8 + 4 * q^9 + 5 * q^10 + 4 * q^11 - 3 * q^12 - 2 * q^13 + 6 * q^15 + 5 * q^16 - 2 * q^17 - 4 * q^18 - 8 * q^19 - 5 * q^20 - 4 * q^22 - 9 * q^23 + 3 * q^24 + 8 * q^25 + 2 * q^26 - 15 * q^27 + 5 * q^29 - 6 * q^30 + 15 * q^31 - 5 * q^32 - 29 * q^33 + 2 * q^34 + 4 * q^36 - 22 * q^37 + 8 * q^38 + 32 * q^39 + 5 * q^40 - q^41 + 7 * q^43 + 4 * q^44 + 8 * q^45 + 9 * q^46 - 20 * q^47 - 3 * q^48 - 8 * q^50 - 15 * q^51 - 2 * q^52 + 11 * q^53 + 15 * q^54 + 4 * q^55 + 22 * q^57 - 5 * q^58 - 13 * q^59 + 6 * q^60 + 15 * q^61 - 15 * q^62 + 5 * q^64 - 7 * q^65 + 29 * q^66 + 20 * q^67 - 2 * q^68 - 20 * q^69 - 4 * q^71 - 4 * q^72 + 22 * q^74 - 20 * q^75 - 8 * q^76 - 32 * q^78 + q^79 - 5 * q^80 + 21 * q^81 + q^82 - 48 * q^83 - 13 * q^85 - 7 * q^86 - 3 * q^87 - 4 * q^88 + 7 * q^89 - 8 * q^90 - 9 * q^92 - 23 * q^93 + 20 * q^94 + 11 * q^95 + 3 * q^96 - 6 * q^97 + 32 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.04241	1.17919	0.589594	−	0.807700i	$-0.299288\pi$
$3$	2.04241	1.17919	0.589594	+	0.807700i	$0.299288\pi$
$4$	1.00000	0.500000
$5$	−0.868034	−0.388196	−0.194098	−	0.980982i	$-0.562178\pi$
$5$	−0.868034	−0.388196	−0.194098	+	0.980982i	$0.562178\pi$
$6$	−2.04241	−0.833812
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.17146	0.390486
$10$	0.868034	0.274496
$11$	−4.52582	−1.36459	−0.682293	−	0.731079i	$-0.739017\pi$
$11$	−4.52582	−1.36459	−0.682293	+	0.731079i	$0.739017\pi$
$12$	2.04241	0.589594
$13$	4.81113	1.33437	0.667183	−	0.744894i	$-0.267500\pi$
$13$	4.81113	1.33437	0.667183	+	0.744894i	$0.267500\pi$
$14$	0	0
$15$	−1.77288	−0.457757
$16$	1.00000	0.250000
$17$	−0.259761	−0.0630012	−0.0315006	−	0.999504i	$-0.510029\pi$
$17$	−0.259761	−0.0630012	−0.0315006	+	0.999504i	$0.510029\pi$
$18$	−1.17146	−0.276115
$19$	1.04241	0.239146	0.119573	−	0.992825i	$-0.461847\pi$
$19$	1.04241	0.239146	0.119573	+	0.992825i	$0.461847\pi$
$20$	−0.868034	−0.194098
$21$	0	0
$22$	4.52582	0.964907
$23$	−7.24235	−1.51013	−0.755067	−	0.655648i	$-0.772396\pi$
$23$	−7.24235	−1.51013	−0.755067	+	0.655648i	$0.772396\pi$
$24$	−2.04241	−0.416906
$25$	−4.24652	−0.849304
$26$	−4.81113	−0.943540
$27$	−3.73464	−0.718732
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.77288	0.323683
$31$	−2.40963	−0.432783	−0.216391	−	0.976307i	$-0.569429\pi$
$31$	−2.40963	−0.432783	−0.216391	+	0.976307i	$0.569429\pi$
$32$	−1.00000	−0.176777
$33$	−9.24359	−1.60910
$34$	0.259761	0.0445486
$35$	0	0
$36$	1.17146	0.195243
$37$	−7.46202	−1.22675	−0.613375	−	0.789792i	$-0.710188\pi$
$37$	−7.46202	−1.22675	−0.613375	+	0.789792i	$0.710188\pi$
$38$	−1.04241	−0.169102
$39$	9.82632	1.57347
$40$	0.868034	0.137248
$41$	5.52999	0.863639	0.431820	−	0.901960i	$-0.357872\pi$
$41$	5.52999	0.863639	0.431820	+	0.901960i	$0.357872\pi$
$42$	0	0
$43$	6.24794	0.952802	0.476401	−	0.879228i	$-0.341941\pi$
$43$	6.24794	0.952802	0.476401	+	0.879228i	$0.341941\pi$
$44$	−4.52582	−0.682293
$45$	−1.01686	−0.151585
$46$	7.24235	1.06783
$47$	−12.0092	−1.75172	−0.875862	−	0.482561i	$-0.839707\pi$
$47$	−12.0092	−1.75172	−0.875862	+	0.482561i	$0.839707\pi$
$48$	2.04241	0.294797
$49$	0	0
$50$	4.24652	0.600548
$51$	−0.530539	−0.0742903
$52$	4.81113	0.667183
$53$	5.23942	0.719690	0.359845	−	0.933012i	$-0.382830\pi$
$53$	5.23942	0.719690	0.359845	+	0.933012i	$0.382830\pi$
$54$	3.73464	0.508220
$55$	3.92856	0.529727
$56$	0	0
$57$	2.12904	0.281999
$58$	−1.00000	−0.131306
$59$	−10.8814	−1.41664	−0.708320	−	0.705891i	$-0.750547\pi$
$59$	−10.8814	−1.41664	−0.708320	+	0.705891i	$0.750547\pi$
$60$	−1.77288	−0.228878
$61$	14.4456	1.84958	0.924788	−	0.380483i	$-0.124242\pi$
$61$	14.4456	1.84958	0.924788	+	0.380483i	$0.124242\pi$
$62$	2.40963	0.306023
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.17622	−0.517996
$66$	9.24359	1.13781
$67$	6.20553	0.758126	0.379063	−	0.925371i	$-0.376246\pi$
$67$	6.20553	0.758126	0.379063	+	0.925371i	$0.376246\pi$
$68$	−0.259761	−0.0315006
$69$	−14.7919	−1.78073
$70$	0	0
$71$	−9.47016	−1.12390	−0.561951	−	0.827171i	$-0.689949\pi$
$71$	−9.47016	−1.12390	−0.561951	+	0.827171i	$0.689949\pi$
$72$	−1.17146	−0.138058
$73$	−10.6617	−1.24786	−0.623931	−	0.781479i	$-0.714466\pi$
$73$	−10.6617	−1.24786	−0.623931	+	0.781479i	$0.714466\pi$
$74$	7.46202	0.867443
$75$	−8.67315	−1.00149
$76$	1.04241	0.119573
$77$	0	0
$78$	−9.82632	−1.11261
$79$	−13.8798	−1.56160	−0.780799	−	0.624782i	$-0.785188\pi$
$79$	−13.8798	−1.56160	−0.780799	+	0.624782i	$0.785188\pi$
$80$	−0.868034	−0.0970491
$81$	−11.1421	−1.23801
$82$	−5.52999	−0.610685
$83$	−6.90833	−0.758287	−0.379144	−	0.925338i	$-0.623781\pi$
$83$	−6.90833	−0.758287	−0.379144	+	0.925338i	$0.623781\pi$
$84$	0	0
$85$	0.225481	0.0244569
$86$	−6.24794	−0.673733
$87$	2.04241	0.218970
$88$	4.52582	0.482454
$89$	−1.73757	−0.184182	−0.0920908	−	0.995751i	$-0.529355\pi$
$89$	−1.73757	−0.184182	−0.0920908	+	0.995751i	$0.529355\pi$
$90$	1.01686	0.107187
$91$	0	0
$92$	−7.24235	−0.755067
$93$	−4.92147	−0.510332
$94$	12.0092	1.23866
$95$	−0.904851	−0.0928358
$96$	−2.04241	−0.208453
$97$	5.00070	0.507744	0.253872	−	0.967238i	$-0.418296\pi$
$97$	5.00070	0.507744	0.253872	+	0.967238i	$0.418296\pi$
$98$	0	0
$99$	−5.30180	−0.532851
$100$	−4.24652	−0.424652
$101$	9.18777	0.914217	0.457109	−	0.889411i	$-0.348885\pi$
$101$	9.18777	0.914217	0.457109	+	0.889411i	$0.348885\pi$
$102$	0.530539	0.0525312
$103$	−1.83455	−0.180764	−0.0903820	−	0.995907i	$-0.528809\pi$
$103$	−1.83455	−0.180764	−0.0903820	+	0.995907i	$0.528809\pi$
$104$	−4.81113	−0.471770
$105$	0	0
$106$	−5.23942	−0.508898
$107$	8.27836	0.800300	0.400150	−	0.916450i	$-0.368958\pi$
$107$	8.27836	0.800300	0.400150	+	0.916450i	$0.368958\pi$
$108$	−3.73464	−0.359366
$109$	−2.21154	−0.211827	−0.105914	−	0.994375i	$-0.533777\pi$
$109$	−2.21154	−0.211827	−0.105914	+	0.994375i	$0.533777\pi$
$110$	−3.92856	−0.374574
$111$	−15.2405	−1.44657
$112$	0	0
$113$	1.22861	0.115578	0.0577891	−	0.998329i	$-0.481595\pi$
$113$	1.22861	0.115578	0.0577891	+	0.998329i	$0.481595\pi$
$114$	−2.12904	−0.199403
$115$	6.28660	0.586228
$116$	1.00000	0.0928477
$117$	5.63603	0.521051
$118$	10.8814	1.00172
$119$	0	0
$120$	1.77288	0.161841
$121$	9.48302	0.862092
$122$	−14.4456	−1.30785
$123$	11.2945	1.01839
$124$	−2.40963	−0.216391
$125$	8.02629	0.717893
$126$	0	0
$127$	−16.7966	−1.49046	−0.745230	−	0.666807i	$-0.767660\pi$
$127$	−16.7966	−1.49046	−0.745230	+	0.666807i	$0.767660\pi$
$128$	−1.00000	−0.0883883
$129$	12.7609	1.12353
$130$	4.17622	0.366279
$131$	−5.41544	−0.473149	−0.236574	−	0.971613i	$-0.576025\pi$
$131$	−5.41544	−0.473149	−0.236574	+	0.971613i	$0.576025\pi$
$132$	−9.24359	−0.804552
$133$	0	0
$134$	−6.20553	−0.536076
$135$	3.24180	0.279009
$136$	0.259761	0.0222743
$137$	−13.2042	−1.12811	−0.564055	−	0.825738i	$-0.690759\pi$
$137$	−13.2042	−1.12811	−0.564055	+	0.825738i	$0.690759\pi$
$138$	14.7919	1.25917
$139$	−13.8810	−1.17737	−0.588687	−	0.808361i	$-0.700355\pi$
$139$	−13.8810	−1.17737	−0.588687	+	0.808361i	$0.700355\pi$
$140$	0	0
$141$	−24.5278	−2.06561
$142$	9.47016	0.794718
$143$	−21.7743	−1.82086
$144$	1.17146	0.0976215
$145$	−0.868034	−0.0720863
$146$	10.6617	0.882372
$147$	0	0
$148$	−7.46202	−0.613375
$149$	0.148831	0.0121927	0.00609635	−	0.999981i	$-0.498059\pi$
$149$	0.148831	0.0121927	0.00609635	+	0.999981i	$0.498059\pi$
$150$	8.67315	0.708160
$151$	11.4143	0.928886	0.464443	−	0.885603i	$-0.346255\pi$
$151$	11.4143	0.928886	0.464443	+	0.885603i	$0.346255\pi$
$152$	−1.04241	−0.0845510
$153$	−0.304299	−0.0246011
$154$	0	0
$155$	2.09164	0.168005
$156$	9.82632	0.786735
$157$	10.0814	0.804580	0.402290	−	0.915512i	$-0.368214\pi$
$157$	10.0814	0.804580	0.402290	+	0.915512i	$0.368214\pi$
$158$	13.8798	1.10422
$159$	10.7011	0.848650
$160$	0.868034	0.0686241
$161$	0	0
$162$	11.1421	0.875403
$163$	3.25834	0.255213	0.127606	−	0.991825i	$-0.459271\pi$
$163$	3.25834	0.255213	0.127606	+	0.991825i	$0.459271\pi$
$164$	5.52999	0.431820
$165$	8.02375	0.624648
$166$	6.90833	0.536190
$167$	−13.2848	−1.02801	−0.514003	−	0.857789i	$-0.671838\pi$
$167$	−13.2848	−1.02801	−0.514003	+	0.857789i	$0.671838\pi$
$168$	0	0
$169$	10.1469	0.780534
$170$	−0.225481	−0.0172936
$171$	1.22114	0.0933832
$172$	6.24794	0.476401
$173$	−13.3968	−1.01854	−0.509269	−	0.860607i	$-0.670084\pi$
$173$	−13.3968	−1.01854	−0.509269	+	0.860607i	$0.670084\pi$
$174$	−2.04241	−0.154835
$175$	0	0
$176$	−4.52582	−0.341146
$177$	−22.2244	−1.67049
$178$	1.73757	0.130236
$179$	−6.33944	−0.473832	−0.236916	−	0.971530i	$-0.576137\pi$
$179$	−6.33944	−0.473832	−0.236916	+	0.971530i	$0.576137\pi$
$180$	−1.01686	−0.0757926
$181$	−20.7120	−1.53951	−0.769754	−	0.638341i	$-0.779621\pi$
$181$	−20.7120	−1.53951	−0.769754	+	0.638341i	$0.779621\pi$
$182$	0	0
$183$	29.5040	2.18100
$184$	7.24235	0.533913
$185$	6.47729	0.476220
$186$	4.92147	0.360859
$187$	1.17563	0.0859705
$188$	−12.0092	−0.875862
$189$	0	0
$190$	0.904851	0.0656448
$191$	13.2608	0.959517	0.479758	−	0.877401i	$-0.340724\pi$
$191$	13.2608	0.959517	0.479758	+	0.877401i	$0.340724\pi$
$192$	2.04241	0.147399
$193$	1.55926	0.112238	0.0561191	−	0.998424i	$-0.482127\pi$
$193$	1.55926	0.112238	0.0561191	+	0.998424i	$0.482127\pi$
$194$	−5.00070	−0.359029
$195$	−8.52957	−0.610815
$196$	0	0
$197$	22.2602	1.58597	0.792986	−	0.609239i	$-0.208525\pi$
$197$	22.2602	1.58597	0.792986	+	0.609239i	$0.208525\pi$
$198$	5.30180	0.376783
$199$	−5.13225	−0.363816	−0.181908	−	0.983316i	$-0.558227\pi$
$199$	−5.13225	−0.363816	−0.181908	+	0.983316i	$0.558227\pi$
$200$	4.24652	0.300274
$201$	12.6743	0.893973
$202$	−9.18777	−0.646449
$203$	0	0
$204$	−0.530539	−0.0371452
$205$	−4.80022	−0.335262
$206$	1.83455	0.127819
$207$	−8.48410	−0.589686
$208$	4.81113	0.333592
$209$	−4.71778	−0.326335
$210$	0	0
$211$	24.7400	1.70317	0.851586	−	0.524214i	$-0.175641\pi$
$211$	24.7400	1.70317	0.851586	+	0.524214i	$0.175641\pi$
$212$	5.23942	0.359845
$213$	−19.3420	−1.32529
$214$	−8.27836	−0.565897
$215$	−5.42342	−0.369875
$216$	3.73464	0.254110
$217$	0	0
$218$	2.21154	0.149784
$219$	−21.7757	−1.47147
$220$	3.92856	0.264864
$221$	−1.24974	−0.0840667
$222$	15.2405	1.02288
$223$	8.31616	0.556891	0.278446	−	0.960452i	$-0.410181\pi$
$223$	8.31616	0.556891	0.278446	+	0.960452i	$0.410181\pi$
$224$	0	0
$225$	−4.97461	−0.331641
$226$	−1.22861	−0.0817261
$227$	−1.88729	−0.125264	−0.0626319	−	0.998037i	$-0.519949\pi$
$227$	−1.88729	−0.125264	−0.0626319	+	0.998037i	$0.519949\pi$
$228$	2.12904	0.140999
$229$	1.27985	0.0845748	0.0422874	−	0.999105i	$-0.486535\pi$
$229$	1.27985	0.0845748	0.0422874	+	0.999105i	$0.486535\pi$
$230$	−6.28660	−0.414526
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	25.2784	1.65604	0.828022	−	0.560696i	$-0.189466\pi$
$233$	25.2784	1.65604	0.828022	+	0.560696i	$0.189466\pi$
$234$	−5.63603	−0.368439
$235$	10.4244	0.680013
$236$	−10.8814	−0.708320
$237$	−28.3483	−1.84142
$238$	0	0
$239$	−25.9113	−1.67606	−0.838031	−	0.545622i	$-0.816293\pi$
$239$	−25.9113	−1.67606	−0.838031	+	0.545622i	$0.816293\pi$
$240$	−1.77288	−0.114439
$241$	−4.46734	−0.287767	−0.143883	−	0.989595i	$-0.545959\pi$
$241$	−4.46734	−0.287767	−0.143883	+	0.989595i	$0.545959\pi$
$242$	−9.48302	−0.609591
$243$	−11.5528	−0.741111
$244$	14.4456	0.924788
$245$	0	0
$246$	−11.2945	−0.720113
$247$	5.01519	0.319109
$248$	2.40963	0.153012
$249$	−14.1097	−0.894164
$250$	−8.02629	−0.507627
$251$	3.34504	0.211137	0.105568	−	0.994412i	$-0.466334\pi$
$251$	3.34504	0.211137	0.105568	+	0.994412i	$0.466334\pi$
$252$	0	0
$253$	32.7775	2.06071
$254$	16.7966	1.05391
$255$	0.460526	0.0288392
$256$	1.00000	0.0625000
$257$	−21.8611	−1.36366	−0.681829	−	0.731512i	$-0.738815\pi$
$257$	−21.8611	−1.36366	−0.681829	+	0.731512i	$0.738815\pi$
$258$	−12.7609	−0.794458
$259$	0	0
$260$	−4.17622	−0.258998
$261$	1.17146	0.0725114
$262$	5.41544	0.334567
$263$	22.4538	1.38456	0.692280	−	0.721629i	$-0.256606\pi$
$263$	22.4538	1.38456	0.692280	+	0.721629i	$0.256606\pi$
$264$	9.24359	0.568904
$265$	−4.54799	−0.279381
$266$	0	0
$267$	−3.54883	−0.217185
$268$	6.20553	0.379063
$269$	−14.9206	−0.909726	−0.454863	−	0.890561i	$-0.650312\pi$
$269$	−14.9206	−0.909726	−0.454863	+	0.890561i	$0.650312\pi$
$270$	−3.24180	−0.197289
$271$	14.5421	0.883369	0.441684	−	0.897170i	$-0.354381\pi$
$271$	14.5421	0.883369	0.441684	+	0.897170i	$0.354381\pi$
$272$	−0.259761	−0.0157503
$273$	0	0
$274$	13.2042	0.797694
$275$	19.2190	1.15895
$276$	−14.7919	−0.890366
$277$	8.12828	0.488381	0.244191	−	0.969727i	$-0.421478\pi$
$277$	8.12828	0.488381	0.244191	+	0.969727i	$0.421478\pi$
$278$	13.8810	0.832529
$279$	−2.82278	−0.168995
$280$	0	0
$281$	7.24131	0.431980	0.215990	−	0.976396i	$-0.430702\pi$
$281$	7.24131	0.431980	0.215990	+	0.976396i	$0.430702\pi$
$282$	24.5278	1.46061
$283$	−3.71191	−0.220650	−0.110325	−	0.993896i	$-0.535189\pi$
$283$	−3.71191	−0.220650	−0.110325	+	0.993896i	$0.535189\pi$
$284$	−9.47016	−0.561951
$285$	−1.84808	−0.109471
$286$	21.7743	1.28754
$287$	0	0
$288$	−1.17146	−0.0690288
$289$	−16.9325	−0.996031
$290$	0.868034	0.0509727
$291$	10.2135	0.598726
$292$	−10.6617	−0.623931
$293$	22.7486	1.32899	0.664494	−	0.747294i	$-0.268647\pi$
$293$	22.7486	1.32899	0.664494	+	0.747294i	$0.268647\pi$
$294$	0	0
$295$	9.44544	0.549935
$296$	7.46202	0.433721
$297$	16.9023	0.980771
$298$	−0.148831	−0.00862154
$299$	−34.8438	−2.01507
$300$	−8.67315	−0.500745
$301$	0	0
$302$	−11.4143	−0.656821
$303$	18.7652	1.07803
$304$	1.04241	0.0597866
$305$	−12.5393	−0.717999
$306$	0.304299	0.0173956
$307$	4.92960	0.281347	0.140674	−	0.990056i	$-0.455073\pi$
$307$	4.92960	0.281347	0.140674	+	0.990056i	$0.455073\pi$
$308$	0	0
$309$	−3.74692	−0.213155
$310$	−2.09164	−0.118797
$311$	9.61384	0.545151	0.272575	−	0.962134i	$-0.412125\pi$
$311$	9.61384	0.545151	0.272575	+	0.962134i	$0.412125\pi$
$312$	−9.82632	−0.556306
$313$	−31.8007	−1.79748	−0.898742	−	0.438477i	$-0.855518\pi$
$313$	−31.8007	−1.79748	−0.898742	+	0.438477i	$0.855518\pi$
$314$	−10.0814	−0.568924
$315$	0	0
$316$	−13.8798	−0.780799
$317$	−9.64071	−0.541476	−0.270738	−	0.962653i	$-0.587268\pi$
$317$	−9.64071	−0.541476	−0.270738	+	0.962653i	$0.587268\pi$
$318$	−10.7011	−0.600086
$319$	−4.52582	−0.253397
$320$	−0.868034	−0.0485246
$321$	16.9078	0.943704
$322$	0	0
$323$	−0.270778	−0.0150665
$324$	−11.1421	−0.619003
$325$	−20.4305	−1.13328
$326$	−3.25834	−0.180463
$327$	−4.51688	−0.249784
$328$	−5.52999	−0.305343
$329$	0	0
$330$	−8.02375	−0.441693
$331$	−3.55713	−0.195517	−0.0977587	−	0.995210i	$-0.531167\pi$
$331$	−3.55713	−0.195517	−0.0977587	+	0.995210i	$0.531167\pi$
$332$	−6.90833	−0.379144
$333$	−8.74144	−0.479028
$334$	13.2848	0.726910
$335$	−5.38661	−0.294302
$336$	0	0
$337$	−29.9327	−1.63054	−0.815269	−	0.579082i	$-0.803411\pi$
$337$	−29.9327	−1.63054	−0.815269	+	0.579082i	$0.803411\pi$
$338$	−10.1469	−0.551921
$339$	2.50934	0.136289
$340$	0.225481	0.0122284
$341$	10.9055	0.590569
$342$	−1.22114	−0.0660319
$343$	0	0
$344$	−6.24794	−0.336867
$345$	12.8398	0.691274
$346$	13.3968	0.720215
$347$	22.7359	1.22053	0.610264	−	0.792198i	$-0.291063\pi$
$347$	22.7359	1.22053	0.610264	+	0.792198i	$0.291063\pi$
$348$	2.04241	0.109485
$349$	−4.50926	−0.241375	−0.120688	−	0.992691i	$-0.538510\pi$
$349$	−4.50926	−0.241375	−0.120688	+	0.992691i	$0.538510\pi$
$350$	0	0
$351$	−17.9678	−0.959052
$352$	4.52582	0.241227
$353$	5.88890	0.313435	0.156717	−	0.987644i	$-0.449909\pi$
$353$	5.88890	0.313435	0.156717	+	0.987644i	$0.449909\pi$
$354$	22.2244	1.18121
$355$	8.22042	0.436294
$356$	−1.73757	−0.0920908
$357$	0	0
$358$	6.33944	0.335050
$359$	−18.8561	−0.995188	−0.497594	−	0.867410i	$-0.665783\pi$
$359$	−18.8561	−0.995188	−0.497594	+	0.867410i	$0.665783\pi$
$360$	1.01686	0.0535935
$361$	−17.9134	−0.942809
$362$	20.7120	1.08860
$363$	19.3683	1.01657
$364$	0	0
$365$	9.25475	0.484416
$366$	−29.5040	−1.54220
$367$	34.3704	1.79412	0.897060	−	0.441909i	$-0.145699\pi$
$367$	34.3704	1.79412	0.897060	+	0.441909i	$0.145699\pi$
$368$	−7.24235	−0.377533
$369$	6.47815	0.337239
$370$	−6.47729	−0.336738
$371$	0	0
$372$	−4.92147	−0.255166
$373$	8.60633	0.445619	0.222809	−	0.974862i	$-0.428477\pi$
$373$	8.60633	0.445619	0.222809	+	0.974862i	$0.428477\pi$
$374$	−1.17563	−0.0607903
$375$	16.3930	0.846531
$376$	12.0092	0.619328
$377$	4.81113	0.247786
$378$	0	0
$379$	−3.16987	−0.162825	−0.0814126	−	0.996680i	$-0.525943\pi$
$379$	−3.16987	−0.162825	−0.0814126	+	0.996680i	$0.525943\pi$
$380$	−0.904851	−0.0464179
$381$	−34.3057	−1.75753
$382$	−13.2608	−0.678481
$383$	1.48444	0.0758514	0.0379257	−	0.999281i	$-0.487925\pi$
$383$	1.48444	0.0758514	0.0379257	+	0.999281i	$0.487925\pi$
$384$	−2.04241	−0.104227
$385$	0	0
$386$	−1.55926	−0.0793644
$387$	7.31920	0.372056
$388$	5.00070	0.253872
$389$	4.47816	0.227052	0.113526	−	0.993535i	$-0.463785\pi$
$389$	4.47816	0.227052	0.113526	+	0.993535i	$0.463785\pi$
$390$	8.52957	0.431912
$391$	1.88128	0.0951403
$392$	0	0
$393$	−11.0606	−0.557932
$394$	−22.2602	−1.12145
$395$	12.0481	0.606207
$396$	−5.30180	−0.266426
$397$	−11.8046	−0.592458	−0.296229	−	0.955117i	$-0.595729\pi$
$397$	−11.8046	−0.592458	−0.296229	+	0.955117i	$0.595729\pi$
$398$	5.13225	0.257256
$399$	0	0
$400$	−4.24652	−0.212326
$401$	−19.0594	−0.951782	−0.475891	−	0.879504i	$-0.657874\pi$
$401$	−19.0594	−0.951782	−0.475891	+	0.879504i	$0.657874\pi$
$402$	−12.6743	−0.632135
$403$	−11.5930	−0.577491
$404$	9.18777	0.457109
$405$	9.67168	0.480590
$406$	0	0
$407$	33.7718	1.67400
$408$	0.530539	0.0262656
$409$	−20.5188	−1.01459	−0.507294	−	0.861773i	$-0.669354\pi$
$409$	−20.5188	−1.01459	−0.507294	+	0.861773i	$0.669354\pi$
$410$	4.80022	0.237066
$411$	−26.9684	−1.33025
$412$	−1.83455	−0.0903820
$413$	0	0
$414$	8.48410	0.416971
$415$	5.99666	0.294364
$416$	−4.81113	−0.235885
$417$	−28.3508	−1.38835
$418$	4.71778	0.230754
$419$	−13.1307	−0.641475	−0.320737	−	0.947168i	$-0.603931\pi$
$419$	−13.1307	−0.641475	−0.320737	+	0.947168i	$0.603931\pi$
$420$	0	0
$421$	−18.0216	−0.878321	−0.439160	−	0.898409i	$-0.644724\pi$
$421$	−18.0216	−0.878321	−0.439160	+	0.898409i	$0.644724\pi$
$422$	−24.7400	−1.20432
$423$	−14.0683	−0.684024
$424$	−5.23942	−0.254449
$425$	1.10308	0.0535072
$426$	19.3420	0.937123
$427$	0	0
$428$	8.27836	0.400150
$429$	−44.4721	−2.14713
$430$	5.42342	0.261541
$431$	28.0392	1.35060	0.675300	−	0.737543i	$-0.264014\pi$
$431$	28.0392	1.35060	0.675300	+	0.737543i	$0.264014\pi$
$432$	−3.73464	−0.179683
$433$	16.0875	0.773118	0.386559	−	0.922265i	$-0.373664\pi$
$433$	16.0875	0.773118	0.386559	+	0.922265i	$0.373664\pi$
$434$	0	0
$435$	−1.77288	−0.0850033
$436$	−2.21154	−0.105914
$437$	−7.54953	−0.361143
$438$	21.7757	1.04048
$439$	28.4144	1.35615	0.678074	−	0.734994i	$-0.262815\pi$
$439$	28.4144	1.35615	0.678074	+	0.734994i	$0.262815\pi$
$440$	−3.92856	−0.187287
$441$	0	0
$442$	1.24974	0.0594442
$443$	29.2378	1.38913	0.694565	−	0.719430i	$-0.255597\pi$
$443$	29.2378	1.38913	0.694565	+	0.719430i	$0.255597\pi$
$444$	−15.2405	−0.723284
$445$	1.50827	0.0714986
$446$	−8.31616	−0.393781
$447$	0.303974	0.0143775
$448$	0	0
$449$	13.3895	0.631890	0.315945	−	0.948778i	$-0.397679\pi$
$449$	13.3895	0.631890	0.315945	+	0.948778i	$0.397679\pi$
$450$	4.97461	0.234506
$451$	−25.0277	−1.17851
$452$	1.22861	0.0577891
$453$	23.3128	1.09533
$454$	1.88729	0.0885748
$455$	0	0
$456$	−2.12904	−0.0997016
$457$	17.7237	0.829081	0.414541	−	0.910031i	$-0.363942\pi$
$457$	17.7237	0.829081	0.414541	+	0.910031i	$0.363942\pi$
$458$	−1.27985	−0.0598034
$459$	0.970113	0.0452810
$460$	6.28660	0.293114
$461$	40.2149	1.87299	0.936497	−	0.350675i	$-0.114048\pi$
$461$	40.2149	1.87299	0.936497	+	0.350675i	$0.114048\pi$
$462$	0	0
$463$	−33.6300	−1.56292	−0.781460	−	0.623955i	$-0.785525\pi$
$463$	−33.6300	−1.56292	−0.781460	+	0.623955i	$0.785525\pi$
$464$	1.00000	0.0464238
$465$	4.27200	0.198109
$466$	−25.2784	−1.17100
$467$	−17.1603	−0.794084	−0.397042	−	0.917800i	$-0.629963\pi$
$467$	−17.1603	−0.794084	−0.397042	+	0.917800i	$0.629963\pi$
$468$	5.63603	0.260526
$469$	0	0
$470$	−10.4244	−0.480842
$471$	20.5903	0.948751
$472$	10.8814	0.500858
$473$	−28.2770	−1.30018
$474$	28.3483	1.30208
$475$	−4.42663	−0.203108
$476$	0	0
$477$	6.13776	0.281029
$478$	25.9113	1.18515
$479$	−43.1048	−1.96951	−0.984755	−	0.173948i	$-0.944348\pi$
$479$	−43.1048	−1.96951	−0.984755	+	0.173948i	$0.944348\pi$
$480$	1.77288	0.0809207
$481$	−35.9007	−1.63693
$482$	4.46734	0.203482
$483$	0	0
$484$	9.48302	0.431046
$485$	−4.34077	−0.197104
$486$	11.5528	0.524045
$487$	−30.7365	−1.39280	−0.696401	−	0.717653i	$-0.745216\pi$
$487$	−30.7365	−1.39280	−0.696401	+	0.717653i	$0.745216\pi$
$488$	−14.4456	−0.653924
$489$	6.65487	0.300944
$490$	0	0
$491$	12.2771	0.554058	0.277029	−	0.960861i	$-0.410650\pi$
$491$	12.2771	0.554058	0.277029	+	0.960861i	$0.410650\pi$
$492$	11.2945	0.509197
$493$	−0.259761	−0.0116990
$494$	−5.01519	−0.225644
$495$	4.60214	0.206851
$496$	−2.40963	−0.108196
$497$	0	0
$498$	14.1097	0.632269
$499$	1.36698	0.0611943	0.0305972	−	0.999532i	$-0.490259\pi$
$499$	1.36698	0.0611943	0.0305972	+	0.999532i	$0.490259\pi$
$500$	8.02629	0.358947
$501$	−27.1330	−1.21221
$502$	−3.34504	−0.149296
$503$	−23.5002	−1.04782	−0.523912	−	0.851773i	$-0.675528\pi$
$503$	−23.5002	−1.04782	−0.523912	+	0.851773i	$0.675528\pi$
$504$	0	0
$505$	−7.97530	−0.354896
$506$	−32.7775	−1.45714
$507$	20.7243	0.920397
$508$	−16.7966	−0.745230
$509$	−13.3589	−0.592124	−0.296062	−	0.955169i	$-0.595673\pi$
$509$	−13.3589	−0.592124	−0.296062	+	0.955169i	$0.595673\pi$
$510$	−0.460526	−0.0203924
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−3.89305	−0.171882
$514$	21.8611	0.964251
$515$	1.59245	0.0701719
$516$	12.7609	0.561767
$517$	54.3515	2.39038
$518$	0	0
$519$	−27.3618	−1.20105
$520$	4.17622	0.183139
$521$	22.8211	0.999810	0.499905	−	0.866080i	$-0.333368\pi$
$521$	22.8211	0.999810	0.499905	+	0.866080i	$0.333368\pi$
$522$	−1.17146	−0.0512733
$523$	23.1709	1.01319	0.506597	−	0.862183i	$-0.330903\pi$
$523$	23.1709	1.01319	0.506597	+	0.862183i	$0.330903\pi$
$524$	−5.41544	−0.236574
$525$	0	0
$526$	−22.4538	−0.979031
$527$	0.625928	0.0272658
$528$	−9.24359	−0.402276
$529$	29.4516	1.28050
$530$	4.54799	0.197552
$531$	−12.7471	−0.553178
$532$	0	0
$533$	26.6055	1.15241
$534$	3.54883	0.153573
$535$	−7.18590	−0.310673
$536$	−6.20553	−0.268038
$537$	−12.9478	−0.558737
$538$	14.9206	0.643273
$539$	0	0
$540$	3.24180	0.139505
$541$	31.9244	1.37254	0.686269	−	0.727348i	$-0.259247\pi$
$541$	31.9244	1.37254	0.686269	+	0.727348i	$0.259247\pi$
$542$	−14.5421	−0.624636
$543$	−42.3024	−1.81537
$544$	0.259761	0.0111371
$545$	1.91969	0.0822305
$546$	0	0
$547$	38.1123	1.62956	0.814781	−	0.579768i	$-0.196857\pi$
$547$	38.1123	1.62956	0.814781	+	0.579768i	$0.196857\pi$
$548$	−13.2042	−0.564055
$549$	16.9225	0.722233
$550$	−19.2190	−0.819499
$551$	1.04241	0.0444084
$552$	14.7919	0.629584
$553$	0	0
$554$	−8.12828	−0.345338
$555$	13.2293	0.561553
$556$	−13.8810	−0.588687
$557$	−0.0241543	−0.00102345	−0.000511725	−	1.00000i	$-0.500163\pi$
$557$	−0.0241543	−0.00102345	−0.000511725		1.00000i	$0.500163\pi$
$558$	2.82278	0.119498
$559$	30.0596	1.27139
$560$	0	0
$561$	2.40112	0.101375
$562$	−7.24131	−0.305456
$563$	−14.5356	−0.612604	−0.306302	−	0.951934i	$-0.599092\pi$
$563$	−14.5356	−0.612604	−0.306302	+	0.951934i	$0.599092\pi$
$564$	−24.5278	−1.03281
$565$	−1.06648	−0.0448671
$566$	3.71191	0.156023
$567$	0	0
$568$	9.47016	0.397359
$569$	14.1911	0.594922	0.297461	−	0.954734i	$-0.403860\pi$
$569$	14.1911	0.594922	0.297461	+	0.954734i	$0.403860\pi$
$570$	1.84808	0.0774076
$571$	−23.7143	−0.992415	−0.496207	−	0.868204i	$-0.665274\pi$
$571$	−23.7143	−0.992415	−0.496207	+	0.868204i	$0.665274\pi$
$572$	−21.7743	−0.910428
$573$	27.0840	1.13145
$574$	0	0
$575$	30.7547	1.28256
$576$	1.17146	0.0488107
$577$	−14.1396	−0.588640	−0.294320	−	0.955707i	$-0.595093\pi$
$577$	−14.1396	−0.588640	−0.294320	+	0.955707i	$0.595093\pi$
$578$	16.9325	0.704300
$579$	3.18466	0.132350
$580$	−0.868034	−0.0360431
$581$	0	0
$582$	−10.2135	−0.423363
$583$	−23.7127	−0.982078
$584$	10.6617	0.441186
$585$	−4.89226	−0.202270
$586$	−22.7486	−0.939736
$587$	11.6325	0.480124	0.240062	−	0.970758i	$-0.422832\pi$
$587$	11.6325	0.480124	0.240062	+	0.970758i	$0.422832\pi$
$588$	0	0
$589$	−2.51183	−0.103498
$590$	−9.44544	−0.388863
$591$	45.4645	1.87016
$592$	−7.46202	−0.306687
$593$	13.0595	0.536288	0.268144	−	0.963379i	$-0.413590\pi$
$593$	13.0595	0.536288	0.268144	+	0.963379i	$0.413590\pi$
$594$	−16.9023	−0.693510
$595$	0	0
$596$	0.148831	0.00609635
$597$	−10.4822	−0.429007
$598$	34.8438	1.42487
$599$	45.5493	1.86109	0.930546	−	0.366174i	$-0.119333\pi$
$599$	45.5493	1.86109	0.930546	+	0.366174i	$0.119333\pi$
$600$	8.67315	0.354080
$601$	32.3140	1.31812	0.659058	−	0.752092i	$-0.270955\pi$
$601$	32.3140	1.31812	0.659058	+	0.752092i	$0.270955\pi$
$602$	0	0
$603$	7.26951	0.296037
$604$	11.4143	0.464443
$605$	−8.23158	−0.334661
$606$	−18.7652	−0.762286
$607$	−4.77660	−0.193876	−0.0969381	−	0.995290i	$-0.530905\pi$
$607$	−4.77660	−0.193876	−0.0969381	+	0.995290i	$0.530905\pi$
$608$	−1.04241	−0.0422755
$609$	0	0
$610$	12.5393	0.507702
$611$	−57.7779	−2.33744
$612$	−0.304299	−0.0123005
$613$	−2.02485	−0.0817830	−0.0408915	−	0.999164i	$-0.513020\pi$
$613$	−2.02485	−0.0817830	−0.0408915	+	0.999164i	$0.513020\pi$
$614$	−4.92960	−0.198943
$615$	−9.80403	−0.395337
$616$	0	0
$617$	19.2876	0.776491	0.388246	−	0.921556i	$-0.373081\pi$
$617$	19.2876	0.776491	0.388246	+	0.921556i	$0.373081\pi$
$618$	3.74692	0.150723
$619$	−8.99043	−0.361356	−0.180678	−	0.983542i	$-0.557829\pi$
$619$	−8.99043	−0.361356	−0.180678	+	0.983542i	$0.557829\pi$
$620$	2.09164	0.0840023
$621$	27.0476	1.08538
$622$	−9.61384	−0.385480
$623$	0	0
$624$	9.82632	0.393367
$625$	14.2655	0.570620
$626$	31.8007	1.27101
$627$	−9.63566	−0.384811
$628$	10.0814	0.402290
$629$	1.93834	0.0772867
$630$	0	0
$631$	35.4821	1.41252	0.706259	−	0.707953i	$-0.250381\pi$
$631$	35.4821	1.41252	0.706259	+	0.707953i	$0.250381\pi$
$632$	13.8798	0.552108
$633$	50.5294	2.00836
$634$	9.64071	0.382881
$635$	14.5800	0.578591
$636$	10.7011	0.424325
$637$	0	0
$638$	4.52582	0.179179
$639$	−11.0939	−0.438867
$640$	0.868034	0.0343120
$641$	−31.7682	−1.25477	−0.627384	−	0.778710i	$-0.715874\pi$
$641$	−31.7682	−1.25477	−0.627384	+	0.778710i	$0.715874\pi$
$642$	−16.9078	−0.667300
$643$	−44.8753	−1.76971	−0.884855	−	0.465866i	$-0.845743\pi$
$643$	−44.8753	−1.76971	−0.884855	+	0.465866i	$0.845743\pi$
$644$	0	0
$645$	−11.0769	−0.436152
$646$	0.270778	0.0106536
$647$	36.1562	1.42145	0.710724	−	0.703471i	$-0.248368\pi$
$647$	36.1562	1.42145	0.710724	+	0.703471i	$0.248368\pi$
$648$	11.1421	0.437701
$649$	49.2473	1.93313
$650$	20.4305	0.801352
$651$	0	0
$652$	3.25834	0.127606
$653$	−30.9296	−1.21037	−0.605185	−	0.796085i	$-0.706901\pi$
$653$	−30.9296	−1.21037	−0.605185	+	0.796085i	$0.706901\pi$
$654$	4.51688	0.176624
$655$	4.70078	0.183675
$656$	5.52999	0.215910
$657$	−12.4898	−0.487273
$658$	0	0
$659$	−42.2313	−1.64510	−0.822550	−	0.568693i	$-0.807449\pi$
$659$	−42.2313	−1.64510	−0.822550	+	0.568693i	$0.807449\pi$
$660$	8.02375	0.312324
$661$	20.5109	0.797780	0.398890	−	0.916999i	$-0.369395\pi$
$661$	20.5109	0.797780	0.398890	+	0.916999i	$0.369395\pi$
$662$	3.55713	0.138252
$663$	−2.55249	−0.0991305
$664$	6.90833	0.268095
$665$	0	0
$666$	8.74144	0.338724
$667$	−7.24235	−0.280425
$668$	−13.2848	−0.514003
$669$	16.9850	0.656680
$670$	5.38661	0.208103
$671$	−65.3784	−2.52390
$672$	0	0
$673$	−2.41486	−0.0930861	−0.0465431	−	0.998916i	$-0.514820\pi$
$673$	−2.41486	−0.0930861	−0.0465431	+	0.998916i	$0.514820\pi$
$674$	29.9327	1.15297
$675$	15.8592	0.610422
$676$	10.1469	0.390267
$677$	−26.0598	−1.00156	−0.500780	−	0.865575i	$-0.666953\pi$
$677$	−26.0598	−1.00156	−0.500780	+	0.865575i	$0.666953\pi$
$678$	−2.50934	−0.0963705
$679$	0	0
$680$	−0.225481	−0.00864680
$681$	−3.85463	−0.147710
$682$	−10.9055	−0.417595
$683$	−30.3162	−1.16002	−0.580008	−	0.814611i	$-0.696950\pi$
$683$	−30.3162	−1.16002	−0.580008	+	0.814611i	$0.696950\pi$
$684$	1.22114	0.0466916
$685$	11.4617	0.437928
$686$	0	0
$687$	2.61398	0.0997297
$688$	6.24794	0.238201
$689$	25.2075	0.960330
$690$	−12.8398	−0.488804
$691$	28.0275	1.06622	0.533108	−	0.846047i	$-0.321024\pi$
$691$	28.0275	1.06622	0.533108	+	0.846047i	$0.321024\pi$
$692$	−13.3968	−0.509269
$693$	0	0
$694$	−22.7359	−0.863043
$695$	12.0492	0.457053
$696$	−2.04241	−0.0774175
$697$	−1.43647	−0.0544103
$698$	4.50926	0.170678
$699$	51.6290	1.95279
$700$	0	0
$701$	9.56961	0.361439	0.180720	−	0.983535i	$-0.442157\pi$
$701$	9.56961	0.361439	0.180720	+	0.983535i	$0.442157\pi$
$702$	17.9678	0.678152
$703$	−7.77852	−0.293373
$704$	−4.52582	−0.170573
$705$	21.2910	0.801864
$706$	−5.88890	−0.221632
$707$	0	0
$708$	−22.2244	−0.835243
$709$	35.2632	1.32434	0.662169	−	0.749355i	$-0.269636\pi$
$709$	35.2632	1.32434	0.662169	+	0.749355i	$0.269636\pi$
$710$	−8.22042	−0.308507
$711$	−16.2596	−0.609782
$712$	1.73757	0.0651180
$713$	17.4514	0.653559
$714$	0	0
$715$	18.9008	0.706850
$716$	−6.33944	−0.236916
$717$	−52.9216	−1.97639
$718$	18.8561	0.703704
$719$	−3.29912	−0.123036	−0.0615181	−	0.998106i	$-0.519594\pi$
$719$	−3.29912	−0.123036	−0.0615181	+	0.998106i	$0.519594\pi$
$720$	−1.01686	−0.0378963
$721$	0	0
$722$	17.9134	0.666667
$723$	−9.12416	−0.339331
$724$	−20.7120	−0.769754
$725$	−4.24652	−0.157712
$726$	−19.3683	−0.718823
$727$	18.2413	0.676532	0.338266	−	0.941051i	$-0.390160\pi$
$727$	18.2413	0.676532	0.338266	+	0.941051i	$0.390160\pi$
$728$	0	0
$729$	9.83061	0.364097
$730$	−9.25475	−0.342534
$731$	−1.62297	−0.0600277
$732$	29.5040	1.09050
$733$	44.8721	1.65739	0.828694	−	0.559703i	$-0.189085\pi$
$733$	44.8721	1.65739	0.828694	+	0.559703i	$0.189085\pi$
$734$	−34.3704	−1.26863
$735$	0	0
$736$	7.24235	0.266956
$737$	−28.0851	−1.03453
$738$	−6.47815	−0.238464
$739$	0.811066	0.0298355	0.0149178	−	0.999889i	$-0.495251\pi$
$739$	0.811066	0.0298355	0.0149178	+	0.999889i	$0.495251\pi$
$740$	6.47729	0.238110
$741$	10.2431	0.376290
$742$	0	0
$743$	29.9370	1.09828	0.549142	−	0.835729i	$-0.314955\pi$
$743$	29.9370	1.09828	0.549142	+	0.835729i	$0.314955\pi$
$744$	4.92147	0.180430
$745$	−0.129190	−0.00473316
$746$	−8.60633	−0.315100
$747$	−8.09281	−0.296100
$748$	1.17563	0.0429853
$749$	0	0
$750$	−16.3930	−0.598588
$751$	13.5353	0.493910	0.246955	−	0.969027i	$-0.420570\pi$
$751$	13.5353	0.493910	0.246955	+	0.969027i	$0.420570\pi$
$752$	−12.0092	−0.437931
$753$	6.83196	0.248970
$754$	−4.81113	−0.175211
$755$	−9.90803	−0.360590
$756$	0	0
$757$	−32.4918	−1.18094	−0.590468	−	0.807061i	$-0.701057\pi$
$757$	−32.4918	−1.18094	−0.590468	+	0.807061i	$0.701057\pi$
$758$	3.16987	0.115135
$759$	66.9453	2.42996
$760$	0.904851	0.0328224
$761$	−10.7653	−0.390243	−0.195121	−	0.980779i	$-0.562510\pi$
$761$	−10.7653	−0.390243	−0.195121	+	0.980779i	$0.562510\pi$
$762$	34.3057	1.24276
$763$	0	0
$764$	13.2608	0.479758
$765$	0.264141	0.00955005
$766$	−1.48444	−0.0536351
$767$	−52.3519	−1.89032
$768$	2.04241	0.0736993
$769$	53.4576	1.92773	0.963866	−	0.266389i	$-0.0858304\pi$
$769$	53.4576	1.92773	0.963866	+	0.266389i	$0.0858304\pi$
$770$	0	0
$771$	−44.6494	−1.60801
$772$	1.55926	0.0561191
$773$	−21.5547	−0.775269	−0.387635	−	0.921813i	$-0.626708\pi$
$773$	−21.5547	−0.775269	−0.387635	+	0.921813i	$0.626708\pi$
$774$	−7.31920	−0.263083
$775$	10.2325	0.367564
$776$	−5.00070	−0.179515
$777$	0	0
$778$	−4.47816	−0.160550
$779$	5.76454	0.206536
$780$	−8.52957	−0.305408
$781$	42.8602	1.53366
$782$	−1.88128	−0.0672743
$783$	−3.73464	−0.133465
$784$	0	0
$785$	−8.75096	−0.312335
$786$	11.0606	0.394517
$787$	−12.7403	−0.454141	−0.227071	−	0.973878i	$-0.572915\pi$
$787$	−12.7403	−0.454141	−0.227071	+	0.973878i	$0.572915\pi$
$788$	22.2602	0.792986
$789$	45.8599	1.63266
$790$	−12.0481	−0.428653
$791$	0	0
$792$	5.30180	0.188391
$793$	69.4999	2.46801
$794$	11.8046	0.418931
$795$	−9.28889	−0.329443
$796$	−5.13225	−0.181908
$797$	−14.5075	−0.513884	−0.256942	−	0.966427i	$-0.582715\pi$
$797$	−14.5075	−0.513884	−0.256942	+	0.966427i	$0.582715\pi$
$798$	0	0
$799$	3.11952	0.110361
$800$	4.24652	0.150137
$801$	−2.03548	−0.0719203
$802$	19.0594	0.673012
$803$	48.2531	1.70282
$804$	12.6743	0.446987
$805$	0	0
$806$	11.5930	0.408348
$807$	−30.4741	−1.07274
$808$	−9.18777	−0.323225
$809$	18.1617	0.638532	0.319266	−	0.947665i	$-0.396564\pi$
$809$	18.1617	0.638532	0.319266	+	0.947665i	$0.396564\pi$
$810$	−9.67168	−0.339828
$811$	−4.45962	−0.156598	−0.0782992	−	0.996930i	$-0.524949\pi$
$811$	−4.45962	−0.156598	−0.0782992	+	0.996930i	$0.524949\pi$
$812$	0	0
$813$	29.7010	1.04166
$814$	−33.7718	−1.18370
$815$	−2.82834	−0.0990726
$816$	−0.530539	−0.0185726
$817$	6.51295	0.227859
$818$	20.5188	0.717422
$819$	0	0
$820$	−4.80022	−0.167631
$821$	−19.6618	−0.686202	−0.343101	−	0.939298i	$-0.611477\pi$
$821$	−19.6618	−0.686202	−0.343101	+	0.939298i	$0.611477\pi$
$822$	26.9684	0.940631
$823$	34.0102	1.18552	0.592760	−	0.805379i	$-0.298038\pi$
$823$	34.0102	1.18552	0.592760	+	0.805379i	$0.298038\pi$
$824$	1.83455	0.0639097
$825$	39.2531	1.36662
$826$	0	0
$827$	−9.94008	−0.345650	−0.172825	−	0.984953i	$-0.555290\pi$
$827$	−9.94008	−0.345650	−0.172825	+	0.984953i	$0.555290\pi$
$828$	−8.48410	−0.294843
$829$	−0.831125	−0.0288662	−0.0144331	−	0.999896i	$-0.504594\pi$
$829$	−0.831125	−0.0288662	−0.0144331	+	0.999896i	$0.504594\pi$
$830$	−5.99666	−0.208147
$831$	16.6013	0.575894
$832$	4.81113	0.166796
$833$	0	0
$834$	28.3508	0.981709
$835$	11.5316	0.399068
$836$	−4.71778	−0.163168
$837$	8.99911	0.311055
$838$	13.1307	0.453591
$839$	20.4554	0.706199	0.353100	−	0.935586i	$-0.385128\pi$
$839$	20.4554	0.706199	0.353100	+	0.935586i	$0.385128\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	18.0216	0.621066
$843$	14.7897	0.509386
$844$	24.7400	0.851586
$845$	−8.80789	−0.303001
$846$	14.0683	0.483678
$847$	0	0
$848$	5.23942	0.179922
$849$	−7.58126	−0.260188
$850$	−1.10308	−0.0378353
$851$	54.0426	1.85255
$852$	−19.3420	−0.662646
$853$	12.6286	0.432394	0.216197	−	0.976350i	$-0.430635\pi$
$853$	12.6286	0.432394	0.216197	+	0.976350i	$0.430635\pi$
$854$	0	0
$855$	−1.05999	−0.0362510
$856$	−8.27836	−0.282949
$857$	−35.0864	−1.19853	−0.599265	−	0.800551i	$-0.704540\pi$
$857$	−35.0864	−1.19853	−0.599265	+	0.800551i	$0.704540\pi$
$858$	44.4721	1.51825
$859$	18.8935	0.644637	0.322318	−	0.946631i	$-0.395538\pi$
$859$	18.8935	0.644637	0.322318	+	0.946631i	$0.395538\pi$
$860$	−5.42342	−0.184937
$861$	0	0
$862$	−28.0392	−0.955018
$863$	42.0411	1.43110	0.715548	−	0.698564i	$-0.246177\pi$
$863$	42.0411	1.43110	0.715548	+	0.698564i	$0.246177\pi$
$864$	3.73464	0.127055
$865$	11.6289	0.395393
$866$	−16.0875	−0.546677
$867$	−34.5832	−1.17451
$868$	0	0
$869$	62.8174	2.13093
$870$	1.77288	0.0601064
$871$	29.8556	1.01162
$872$	2.21154	0.0748922
$873$	5.85810	0.198267
$874$	7.54953	0.255367
$875$	0	0
$876$	−21.7757	−0.735733
$877$	52.8075	1.78318	0.891592	−	0.452840i	$-0.149589\pi$
$877$	52.8075	1.78318	0.891592	+	0.452840i	$0.149589\pi$
$878$	−28.4144	−0.958941
$879$	46.4621	1.56713
$880$	3.92856	0.132432
$881$	−27.6107	−0.930229	−0.465114	−	0.885251i	$-0.653987\pi$
$881$	−27.6107	−0.930229	−0.465114	+	0.885251i	$0.653987\pi$
$882$	0	0
$883$	5.24316	0.176446	0.0882232	−	0.996101i	$-0.471881\pi$
$883$	5.24316	0.176446	0.0882232	+	0.996101i	$0.471881\pi$
$884$	−1.24974	−0.0420334
$885$	19.2915	0.648477
$886$	−29.2378	−0.982264
$887$	−26.5924	−0.892887	−0.446444	−	0.894812i	$-0.647310\pi$
$887$	−26.5924	−0.892887	−0.446444	+	0.894812i	$0.647310\pi$
$888$	15.2405	0.511439
$889$	0	0
$890$	−1.50827	−0.0505572
$891$	50.4269	1.68937
$892$	8.31616	0.278446
$893$	−12.5186	−0.418918
$894$	−0.303974	−0.0101664
$895$	5.50285	0.183940
$896$	0	0
$897$	−71.1656	−2.37615
$898$	−13.3895	−0.446813
$899$	−2.40963	−0.0803657
$900$	−4.97461	−0.165820
$901$	−1.36100	−0.0453414
$902$	25.0277	0.833332
$903$	0	0
$904$	−1.22861	−0.0408631
$905$	17.9787	0.597631
$906$	−23.3128	−0.774516
$907$	39.9778	1.32744	0.663721	−	0.747980i	$-0.268976\pi$
$907$	39.9778	1.32744	0.663721	+	0.747980i	$0.268976\pi$
$908$	−1.88729	−0.0626319
$909$	10.7631	0.356989
$910$	0	0
$911$	44.5464	1.47589	0.737944	−	0.674862i	$-0.235797\pi$
$911$	44.5464	1.47589	0.737944	+	0.674862i	$0.235797\pi$
$912$	2.12904	0.0704997
$913$	31.2658	1.03475
$914$	−17.7237	−0.586249
$915$	−25.6105	−0.846656
$916$	1.27985	0.0422874
$917$	0	0
$918$	−0.970113	−0.0320185
$919$	−52.9806	−1.74767	−0.873835	−	0.486223i	$-0.838374\pi$
$919$	−52.9806	−1.74767	−0.873835	+	0.486223i	$0.838374\pi$
$920$	−6.28660	−0.207263
$921$	10.0683	0.331761
$922$	−40.2149	−1.32441
$923$	−45.5621	−1.49970
$924$	0	0
$925$	31.6876	1.04188
$926$	33.6300	1.10515
$927$	−2.14910	−0.0705858
$928$	−1.00000	−0.0328266
$929$	44.6379	1.46452	0.732261	−	0.681024i	$-0.238465\pi$
$929$	44.6379	1.46452	0.732261	+	0.681024i	$0.238465\pi$
$930$	−4.27200	−0.140084
$931$	0	0
$932$	25.2784	0.828022
$933$	19.6354	0.642836
$934$	17.1603	0.561502
$935$	−1.02049	−0.0333735
$936$	−5.63603	−0.184219
$937$	−39.7696	−1.29921	−0.649607	−	0.760270i	$-0.725067\pi$
$937$	−39.7696	−1.29921	−0.649607	+	0.760270i	$0.725067\pi$
$938$	0	0
$939$	−64.9503	−2.11957
$940$	10.4244	0.340007
$941$	−7.66901	−0.250002	−0.125001	−	0.992157i	$-0.539893\pi$
$941$	−7.66901	−0.250002	−0.125001	+	0.992157i	$0.539893\pi$
$942$	−20.5903	−0.670868
$943$	−40.0501	−1.30421
$944$	−10.8814	−0.354160
$945$	0	0
$946$	28.2770	0.919366
$947$	−39.8309	−1.29433	−0.647165	−	0.762350i	$-0.724046\pi$
$947$	−39.8309	−1.29433	−0.647165	+	0.762350i	$0.724046\pi$
$948$	−28.3483	−0.920710
$949$	−51.2950	−1.66511
$950$	4.42663	0.143619
$951$	−19.6903	−0.638503
$952$	0	0
$953$	−5.43327	−0.176001	−0.0880004	−	0.996120i	$-0.528048\pi$
$953$	−5.43327	−0.176001	−0.0880004	+	0.996120i	$0.528048\pi$
$954$	−6.13776	−0.198717
$955$	−11.5108	−0.372481
$956$	−25.9113	−0.838031
$957$	−9.24359	−0.298803
$958$	43.1048	1.39265
$959$	0	0
$960$	−1.77288	−0.0572196
$961$	−25.1937	−0.812699
$962$	35.9007	1.15749
$963$	9.69775	0.312506
$964$	−4.46734	−0.143883
$965$	−1.35349	−0.0435705
$966$	0	0
$967$	−42.8343	−1.37746	−0.688729	−	0.725019i	$-0.741831\pi$
$967$	−42.8343	−1.37746	−0.688729	+	0.725019i	$0.741831\pi$
$968$	−9.48302	−0.304796
$969$	−0.553042	−0.0177663
$970$	4.34077	0.139374
$971$	−22.8379	−0.732903	−0.366452	−	0.930437i	$-0.619427\pi$
$971$	−22.8379	−0.732903	−0.366452	+	0.930437i	$0.619427\pi$
$972$	−11.5528	−0.370556
$973$	0	0
$974$	30.7365	0.984860
$975$	−41.7276	−1.33635
$976$	14.4456	0.462394
$977$	−21.1921	−0.677996	−0.338998	−	0.940787i	$-0.610088\pi$
$977$	−21.1921	−0.677996	−0.338998	+	0.940787i	$0.610088\pi$
$978$	−6.65487	−0.212799
$979$	7.86390	0.251331
$980$	0	0
$981$	−2.59073	−0.0827155
$982$	−12.2771	−0.391778
$983$	29.4370	0.938895	0.469447	−	0.882960i	$-0.344453\pi$
$983$	29.4370	0.938895	0.469447	+	0.882960i	$0.344453\pi$
$984$	−11.2945	−0.360056
$985$	−19.3226	−0.615669
$986$	0.259761	0.00827247
$987$	0	0
$988$	5.01519	0.159554
$989$	−45.2498	−1.43886
$990$	−4.60214	−0.146266
$991$	−21.8055	−0.692674	−0.346337	−	0.938110i	$-0.612575\pi$
$991$	−21.8055	−0.692674	−0.346337	+	0.938110i	$0.612575\pi$
$992$	2.40963	0.0765059
$993$	−7.26513	−0.230552
$994$	0	0
$995$	4.45497	0.141232
$996$	−14.1097	−0.447082
$997$	4.80466	0.152165	0.0760825	−	0.997102i	$-0.475759\pi$
$997$	4.80466	0.152165	0.0760825	+	0.997102i	$0.475759\pi$
$998$	−1.36698	−0.0432709
$999$	27.8680	0.881704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.s.1.5		5
7.3	odd	6		406.2.e.c.233.5	✓	10
7.5	odd	6		406.2.e.c.291.5	yes	10
7.6	odd	2		2842.2.a.v.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.c.233.5	✓	10	7.3	odd	6
406.2.e.c.291.5	yes	10	7.5	odd	6
2842.2.a.s.1.5		5	1.1	even	1	trivial
2842.2.a.v.1.1		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.04241 q^{3} +1.00000 q^{4} -0.868034 q^{5} -2.04241 q^{6} -1.00000 q^{8} +1.17146 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.04241 q^{3} +1.00000 q^{4} -0.868034 q^{5} -2.04241 q^{6} -1.00000 q^{8} +1.17146 q^{9} +0.868034 q^{10} -4.52582 q^{11} +2.04241 q^{12} +4.81113 q^{13} -1.77288 q^{15} +1.00000 q^{16} -0.259761 q^{17} -1.17146 q^{18} +1.04241 q^{19} -0.868034 q^{20} +4.52582 q^{22} -7.24235 q^{23} -2.04241 q^{24} -4.24652 q^{25} -4.81113 q^{26} -3.73464 q^{27} +1.00000 q^{29} +1.77288 q^{30} -2.40963 q^{31} -1.00000 q^{32} -9.24359 q^{33} +0.259761 q^{34} +1.17146 q^{36} -7.46202 q^{37} -1.04241 q^{38} +9.82632 q^{39} +0.868034 q^{40} +5.52999 q^{41} +6.24794 q^{43} -4.52582 q^{44} -1.01686 q^{45} +7.24235 q^{46} -12.0092 q^{47} +2.04241 q^{48} +4.24652 q^{50} -0.530539 q^{51} +4.81113 q^{52} +5.23942 q^{53} +3.73464 q^{54} +3.92856 q^{55} +2.12904 q^{57} -1.00000 q^{58} -10.8814 q^{59} -1.77288 q^{60} +14.4456 q^{61} +2.40963 q^{62} +1.00000 q^{64} -4.17622 q^{65} +9.24359 q^{66} +6.20553 q^{67} -0.259761 q^{68} -14.7919 q^{69} -9.47016 q^{71} -1.17146 q^{72} -10.6617 q^{73} +7.46202 q^{74} -8.67315 q^{75} +1.04241 q^{76} -9.82632 q^{78} -13.8798 q^{79} -0.868034 q^{80} -11.1421 q^{81} -5.52999 q^{82} -6.90833 q^{83} +0.225481 q^{85} -6.24794 q^{86} +2.04241 q^{87} +4.52582 q^{88} -1.73757 q^{89} +1.01686 q^{90} -7.24235 q^{92} -4.92147 q^{93} +12.0092 q^{94} -0.904851 q^{95} -2.04241 q^{96} +5.00070 q^{97} -5.30180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^8 + 4 * q^9	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{8} + 4 q^{9} + 5 q^{10} + 4 q^{11} - 3 q^{12} - 2 q^{13} + 6 q^{15} + 5 q^{16} - 2 q^{17} - 4 q^{18} - 8 q^{19} - 5 q^{20} - 4 q^{22} - 9 q^{23} + 3 q^{24} + 8 q^{25} + 2 q^{26} - 15 q^{27} + 5 q^{29} - 6 q^{30} + 15 q^{31} - 5 q^{32} - 29 q^{33} + 2 q^{34} + 4 q^{36} - 22 q^{37} + 8 q^{38} + 32 q^{39} + 5 q^{40} - q^{41} + 7 q^{43} + 4 q^{44} + 8 q^{45} + 9 q^{46} - 20 q^{47} - 3 q^{48} - 8 q^{50} - 15 q^{51} - 2 q^{52} + 11 q^{53} + 15 q^{54} + 4 q^{55} + 22 q^{57} - 5 q^{58} - 13 q^{59} + 6 q^{60} + 15 q^{61} - 15 q^{62} + 5 q^{64} - 7 q^{65} + 29 q^{66} + 20 q^{67} - 2 q^{68} - 20 q^{69} - 4 q^{71} - 4 q^{72} + 22 q^{74} - 20 q^{75} - 8 q^{76} - 32 q^{78} + q^{79} - 5 q^{80} + 21 q^{81} + q^{82} - 48 q^{83} - 13 q^{85} - 7 q^{86} - 3 q^{87} - 4 q^{88} + 7 q^{89} - 8 q^{90} - 9 q^{92} - 23 q^{93} + 20 q^{94} + 11 q^{95} + 3 q^{96} - 6 q^{97} + 32 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^8 + 4 * q^9 + 5 * q^10 + 4 * q^11 - 3 * q^12 - 2 * q^13 + 6 * q^15 + 5 * q^16 - 2 * q^17 - 4 * q^18 - 8 * q^19 - 5 * q^20 - 4 * q^22 - 9 * q^23 + 3 * q^24 + 8 * q^25 + 2 * q^26 - 15 * q^27 + 5 * q^29 - 6 * q^30 + 15 * q^31 - 5 * q^32 - 29 * q^33 + 2 * q^34 + 4 * q^36 - 22 * q^37 + 8 * q^38 + 32 * q^39 + 5 * q^40 - q^41 + 7 * q^43 + 4 * q^44 + 8 * q^45 + 9 * q^46 - 20 * q^47 - 3 * q^48 - 8 * q^50 - 15 * q^51 - 2 * q^52 + 11 * q^53 + 15 * q^54 + 4 * q^55 + 22 * q^57 - 5 * q^58 - 13 * q^59 + 6 * q^60 + 15 * q^61 - 15 * q^62 + 5 * q^64 - 7 * q^65 + 29 * q^66 + 20 * q^67 - 2 * q^68 - 20 * q^69 - 4 * q^71 - 4 * q^72 + 22 * q^74 - 20 * q^75 - 8 * q^76 - 32 * q^78 + q^79 - 5 * q^80 + 21 * q^81 + q^82 - 48 * q^83 - 13 * q^85 - 7 * q^86 - 3 * q^87 - 4 * q^88 + 7 * q^89 - 8 * q^90 - 9 * q^92 - 23 * q^93 + 20 * q^94 + 11 * q^95 + 3 * q^96 - 6 * q^97 + 32 * q^99

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