LMFDB - Embedded newform 2842.2.a.y.1.2

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:	$0$
Dimension:	$5$
Coefficient field:	5.5.345065.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 8x^{2} + 14x - 3 $ x^5 - 2x^4 - 7x^3 + 8x^2 + 14x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.2
Root			$2.04534$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.04534 q^{3} +1.00000 q^{4} -0.635591 q^{5} -1.04534 q^{6} +1.00000 q^{8} -1.90726 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.04534 q^{3} +1.00000 q^{4} -0.635591 q^{5} -1.04534 q^{6} +1.00000 q^{8} -1.90726 q^{9} -0.635591 q^{10} -6.16435 q^{11} -1.04534 q^{12} +3.50826 q^{13} +0.664410 q^{15} +1.00000 q^{16} +4.49417 q^{17} -1.90726 q^{18} -2.66684 q^{19} -0.635591 q^{20} -6.16435 q^{22} +0.452171 q^{23} -1.04534 q^{24} -4.59602 q^{25} +3.50826 q^{26} +5.12976 q^{27} +1.00000 q^{29} +0.664410 q^{30} +8.57744 q^{31} +1.00000 q^{32} +6.44385 q^{33} +4.49417 q^{34} -1.90726 q^{36} +3.80826 q^{37} -2.66684 q^{38} -3.66733 q^{39} -0.635591 q^{40} +7.48968 q^{41} +2.90726 q^{43} -6.16435 q^{44} +1.21224 q^{45} +0.452171 q^{46} -5.21018 q^{47} -1.04534 q^{48} -4.59602 q^{50} -4.69794 q^{51} +3.50826 q^{52} +14.4482 q^{53} +5.12976 q^{54} +3.91801 q^{55} +2.78776 q^{57} +1.00000 q^{58} +5.00626 q^{59} +0.664410 q^{60} +2.07416 q^{61} +8.57744 q^{62} +1.00000 q^{64} -2.22982 q^{65} +6.44385 q^{66} -4.11658 q^{67} +4.49417 q^{68} -0.472673 q^{69} +2.69502 q^{71} -1.90726 q^{72} -8.43154 q^{73} +3.80826 q^{74} +4.80441 q^{75} -2.66684 q^{76} -3.66733 q^{78} -0.108600 q^{79} -0.635591 q^{80} +0.359432 q^{81} +7.48968 q^{82} +0.985249 q^{83} -2.85646 q^{85} +2.90726 q^{86} -1.04534 q^{87} -6.16435 q^{88} +17.7911 q^{89} +1.21224 q^{90} +0.452171 q^{92} -8.96636 q^{93} -5.21018 q^{94} +1.69502 q^{95} -1.04534 q^{96} -2.64094 q^{97} +11.7570 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 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 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9} + 7 q^{10} + 3 q^{12} + 8 q^{13} + 4 q^{15} + 5 q^{16} + 16 q^{17} + 4 q^{18} + 2 q^{19} + 7 q^{20} - 5 q^{23} + 3 q^{24} + 4 q^{25} + 8 q^{26} + 9 q^{27} + 5 q^{29} + 4 q^{30} + 5 q^{31} + 5 q^{32} + 3 q^{33} + 16 q^{34} + 4 q^{36} + 2 q^{38} - 20 q^{39} + 7 q^{40} + 17 q^{41} + q^{43} + 14 q^{45} - 5 q^{46} - 4 q^{47} + 3 q^{48} + 4 q^{50} - 3 q^{51} + 8 q^{52} + 5 q^{53} + 9 q^{54} + 12 q^{55} + 6 q^{57} + 5 q^{58} + 17 q^{59} + 4 q^{60} + 13 q^{61} + 5 q^{62} + 5 q^{64} - 7 q^{65} + 3 q^{66} - 14 q^{67} + 16 q^{68} + 16 q^{69} - 8 q^{71} + 4 q^{72} + 6 q^{73} + 8 q^{75} + 2 q^{76} - 20 q^{78} + 11 q^{79} + 7 q^{80} - 19 q^{81} + 17 q^{82} + 2 q^{83} + 39 q^{85} + q^{86} + 3 q^{87} + 9 q^{89} + 14 q^{90} - 5 q^{92} - 3 q^{93} - 4 q^{94} - 13 q^{95} + 3 q^{96} + 12 q^{97} + 10 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9 + 7 * q^10 + 3 * q^12 + 8 * q^13 + 4 * q^15 + 5 * q^16 + 16 * q^17 + 4 * q^18 + 2 * q^19 + 7 * q^20 - 5 * q^23 + 3 * q^24 + 4 * q^25 + 8 * q^26 + 9 * q^27 + 5 * q^29 + 4 * q^30 + 5 * q^31 + 5 * q^32 + 3 * q^33 + 16 * q^34 + 4 * q^36 + 2 * q^38 - 20 * q^39 + 7 * q^40 + 17 * q^41 + q^43 + 14 * q^45 - 5 * q^46 - 4 * q^47 + 3 * q^48 + 4 * q^50 - 3 * q^51 + 8 * q^52 + 5 * q^53 + 9 * q^54 + 12 * q^55 + 6 * q^57 + 5 * q^58 + 17 * q^59 + 4 * q^60 + 13 * q^61 + 5 * q^62 + 5 * q^64 - 7 * q^65 + 3 * q^66 - 14 * q^67 + 16 * q^68 + 16 * q^69 - 8 * q^71 + 4 * q^72 + 6 * q^73 + 8 * q^75 + 2 * q^76 - 20 * q^78 + 11 * q^79 + 7 * q^80 - 19 * q^81 + 17 * q^82 + 2 * q^83 + 39 * q^85 + q^86 + 3 * q^87 + 9 * q^89 + 14 * q^90 - 5 * q^92 - 3 * q^93 - 4 * q^94 - 13 * q^95 + 3 * q^96 + 12 * q^97 + 10 * 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
$3$	−1.04534	−0.603528	−0.301764	−	0.953383i	$-0.597575\pi$
$3$	−1.04534	−0.603528	−0.301764	+	0.953383i	$0.597575\pi$
$4$	1.00000	0.500000
$5$	−0.635591	−0.284245	−0.142123	−	0.989849i	$-0.545393\pi$
$5$	−0.635591	−0.284245	−0.142123	+	0.989849i	$0.545393\pi$
$6$	−1.04534	−0.426759
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−1.90726	−0.635754
$10$	−0.635591	−0.200992
$11$	−6.16435	−1.85862	−0.929311	−	0.369297i	$-0.879599\pi$
$11$	−6.16435	−1.85862	−0.929311	+	0.369297i	$0.879599\pi$
$12$	−1.04534	−0.301764
$13$	3.50826	0.973017	0.486508	−	0.873676i	$-0.338270\pi$
$13$	3.50826	0.973017	0.486508	+	0.873676i	$0.338270\pi$
$14$	0	0
$15$	0.664410	0.171550
$16$	1.00000	0.250000
$17$	4.49417	1.09000	0.544998	−	0.838437i	$-0.316530\pi$
$17$	4.49417	1.09000	0.544998	+	0.838437i	$0.316530\pi$
$18$	−1.90726	−0.449546
$19$	−2.66684	−0.611816	−0.305908	−	0.952061i	$-0.598960\pi$
$19$	−2.66684	−0.611816	−0.305908	+	0.952061i	$0.598960\pi$
$20$	−0.635591	−0.142123
$21$	0	0
$22$	−6.16435	−1.31424
$23$	0.452171	0.0942841	0.0471421	−	0.998888i	$-0.484989\pi$
$23$	0.452171	0.0942841	0.0471421	+	0.998888i	$0.484989\pi$
$24$	−1.04534	−0.213379
$25$	−4.59602	−0.919205
$26$	3.50826	0.688027
$27$	5.12976	0.987223
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.664410	0.121304
$31$	8.57744	1.54055	0.770277	−	0.637709i	$-0.220118\pi$
$31$	8.57744	1.54055	0.770277	+	0.637709i	$0.220118\pi$
$32$	1.00000	0.176777
$33$	6.44385	1.12173
$34$	4.49417	0.770744
$35$	0	0
$36$	−1.90726	−0.317877
$37$	3.80826	0.626075	0.313037	−	0.949741i	$-0.398654\pi$
$37$	3.80826	0.626075	0.313037	+	0.949741i	$0.398654\pi$
$38$	−2.66684	−0.432619
$39$	−3.66733	−0.587243
$40$	−0.635591	−0.100496
$41$	7.48968	1.16969	0.584846	−	0.811144i	$-0.301155\pi$
$41$	7.48968	1.16969	0.584846	+	0.811144i	$0.301155\pi$
$42$	0	0
$43$	2.90726	0.443353	0.221677	−	0.975120i	$-0.428847\pi$
$43$	2.90726	0.443353	0.221677	+	0.975120i	$0.428847\pi$
$44$	−6.16435	−0.929311
$45$	1.21224	0.180710
$46$	0.452171	0.0666689
$47$	−5.21018	−0.759983	−0.379992	−	0.924990i	$-0.624073\pi$
$47$	−5.21018	−0.759983	−0.379992	+	0.924990i	$0.624073\pi$
$48$	−1.04534	−0.150882
$49$	0	0
$50$	−4.59602	−0.649976
$51$	−4.69794	−0.657844
$52$	3.50826	0.486508
$53$	14.4482	1.98461	0.992307	−	0.123800i	$-0.0395082\pi$
$53$	14.4482	1.98461	0.992307	+	0.123800i	$0.0395082\pi$
$54$	5.12976	0.698072
$55$	3.91801	0.528305
$56$	0	0
$57$	2.78776	0.369248
$58$	1.00000	0.131306
$59$	5.00626	0.651760	0.325880	−	0.945411i	$-0.394340\pi$
$59$	5.00626	0.651760	0.325880	+	0.945411i	$0.394340\pi$
$60$	0.664410	0.0857750
$61$	2.07416	0.265569	0.132784	−	0.991145i	$-0.457608\pi$
$61$	2.07416	0.265569	0.132784	+	0.991145i	$0.457608\pi$
$62$	8.57744	1.08934
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.22982	−0.276575
$66$	6.44385	0.793184
$67$	−4.11658	−0.502920	−0.251460	−	0.967868i	$-0.580911\pi$
$67$	−4.11658	−0.502920	−0.251460	+	0.967868i	$0.580911\pi$
$68$	4.49417	0.544998
$69$	−0.472673	−0.0569031
$70$	0	0
$71$	2.69502	0.319840	0.159920	−	0.987130i	$-0.448876\pi$
$71$	2.69502	0.319840	0.159920	+	0.987130i	$0.448876\pi$
$72$	−1.90726	−0.224773
$73$	−8.43154	−0.986837	−0.493418	−	0.869792i	$-0.664253\pi$
$73$	−8.43154	−0.986837	−0.493418	+	0.869792i	$0.664253\pi$
$74$	3.80826	0.442702
$75$	4.80441	0.554766
$76$	−2.66684	−0.305908
$77$	0	0
$78$	−3.66733	−0.415243
$79$	−0.108600	−0.0122185	−0.00610923	−	0.999981i	$-0.501945\pi$
$79$	−0.108600	−0.0122185	−0.00610923	+	0.999981i	$0.501945\pi$
$80$	−0.635591	−0.0710613
$81$	0.359432	0.0399369
$82$	7.48968	0.827097
$83$	0.985249	0.108145	0.0540726	−	0.998537i	$-0.482780\pi$
$83$	0.985249	0.108145	0.0540726	+	0.998537i	$0.482780\pi$
$84$	0	0
$85$	−2.85646	−0.309826
$86$	2.90726	0.313498
$87$	−1.04534	−0.112072
$88$	−6.16435	−0.657122
$89$	17.7911	1.88586	0.942929	−	0.332995i	$-0.108059\pi$
$89$	17.7911	1.88586	0.942929	+	0.332995i	$0.108059\pi$
$90$	1.21224	0.127781
$91$	0	0
$92$	0.452171	0.0471421
$93$	−8.96636	−0.929768
$94$	−5.21018	−0.537389
$95$	1.69502	0.173906
$96$	−1.04534	−0.106690
$97$	−2.64094	−0.268147	−0.134074	−	0.990971i	$-0.542806\pi$
$97$	−2.64094	−0.268147	−0.134074	+	0.990971i	$0.542806\pi$
$98$	0	0
$99$	11.7570	1.18163
$100$	−4.59602	−0.459602
$101$	1.78442	0.177556	0.0887782	−	0.996051i	$-0.471704\pi$
$101$	1.78442	0.177556	0.0887782	+	0.996051i	$0.471704\pi$
$102$	−4.69794	−0.465166
$103$	−11.6741	−1.15028	−0.575139	−	0.818056i	$-0.695052\pi$
$103$	−11.6741	−1.15028	−0.575139	+	0.818056i	$0.695052\pi$
$104$	3.50826	0.344013
$105$	0	0
$106$	14.4482	1.40333
$107$	−10.8464	−1.04856	−0.524282	−	0.851545i	$-0.675666\pi$
$107$	−10.8464	−1.04856	−0.524282	+	0.851545i	$0.675666\pi$
$108$	5.12976	0.493612
$109$	−12.0238	−1.15168	−0.575838	−	0.817564i	$-0.695324\pi$
$109$	−12.0238	−1.15168	−0.575838	+	0.817564i	$0.695324\pi$
$110$	3.91801	0.373568
$111$	−3.98093	−0.377854
$112$	0	0
$113$	20.4936	1.92787	0.963937	−	0.266132i	$-0.0857457\pi$
$113$	20.4936	1.92787	0.963937	+	0.266132i	$0.0857457\pi$
$114$	2.78776	0.261098
$115$	−0.287396	−0.0267998
$116$	1.00000	0.0928477
$117$	−6.69117	−0.618599
$118$	5.00626	0.460864
$119$	0	0
$120$	0.664410	0.0606521
$121$	26.9993	2.45448
$122$	2.07416	0.187786
$123$	−7.82927	−0.705942
$124$	8.57744	0.770277
$125$	6.09915	0.545525
$126$	0	0
$127$	8.47893	0.752384	0.376192	−	0.926542i	$-0.377233\pi$
$127$	8.47893	0.752384	0.376192	+	0.926542i	$0.377233\pi$
$128$	1.00000	0.0883883
$129$	−3.03908	−0.267576
$130$	−2.22982	−0.195568
$131$	−0.635591	−0.0555319	−0.0277659	−	0.999614i	$-0.508839\pi$
$131$	−0.635591	−0.0555319	−0.0277659	+	0.999614i	$0.508839\pi$
$132$	6.44385	0.560866
$133$	0	0
$134$	−4.11658	−0.355618
$135$	−3.26043	−0.280613
$136$	4.49417	0.385372
$137$	2.85938	0.244293	0.122147	−	0.992512i	$-0.461022\pi$
$137$	2.85938	0.244293	0.122147	+	0.992512i	$0.461022\pi$
$138$	−0.472673	−0.0402366
$139$	21.2565	1.80295	0.901476	−	0.432829i	$-0.142484\pi$
$139$	21.2565	1.80295	0.901476	+	0.432829i	$0.142484\pi$
$140$	0	0
$141$	5.44642	0.458671
$142$	2.69502	0.226161
$143$	−21.6262	−1.80847
$144$	−1.90726	−0.158938
$145$	−0.635591	−0.0527830
$146$	−8.43154	−0.697799
$147$	0	0
$148$	3.80826	0.313037
$149$	8.48185	0.694861	0.347430	−	0.937706i	$-0.387054\pi$
$149$	8.48185	0.694861	0.347430	+	0.937706i	$0.387054\pi$
$150$	4.80441	0.392279
$151$	11.4003	0.927745	0.463873	−	0.885902i	$-0.346460\pi$
$151$	11.4003	0.927745	0.463873	+	0.885902i	$0.346460\pi$
$152$	−2.66684	−0.216310
$153$	−8.57156	−0.692970
$154$	0	0
$155$	−5.45175	−0.437895
$156$	−3.66733	−0.293621
$157$	−15.3723	−1.22684	−0.613421	−	0.789756i	$-0.710207\pi$
$157$	−15.3723	−1.22684	−0.613421	+	0.789756i	$0.710207\pi$
$158$	−0.108600	−0.00863976
$159$	−15.1033	−1.19777
$160$	−0.635591	−0.0502479
$161$	0	0
$162$	0.359432	0.0282397
$163$	14.9818	1.17347	0.586733	−	0.809781i	$-0.300414\pi$
$163$	14.9818	1.17347	0.586733	+	0.809781i	$0.300414\pi$
$164$	7.48968	0.584846
$165$	−4.09566	−0.318847
$166$	0.985249	0.0764702
$167$	10.8187	0.837174	0.418587	−	0.908177i	$-0.362525\pi$
$167$	10.8187	0.837174	0.418587	+	0.908177i	$0.362525\pi$
$168$	0	0
$169$	−0.692102	−0.0532386
$170$	−2.85646	−0.219080
$171$	5.08637	0.388964
$172$	2.90726	0.221677
$173$	8.59512	0.653475	0.326737	−	0.945115i	$-0.394051\pi$
$173$	8.59512	0.653475	0.326737	+	0.945115i	$0.394051\pi$
$174$	−1.04534	−0.0792471
$175$	0	0
$176$	−6.16435	−0.464656
$177$	−5.23325	−0.393355
$178$	17.7911	1.33350
$179$	−10.4823	−0.783482	−0.391741	−	0.920076i	$-0.628127\pi$
$179$	−10.4823	−0.783482	−0.391741	+	0.920076i	$0.628127\pi$
$180$	1.21224	0.0903550
$181$	−8.98480	−0.667835	−0.333918	−	0.942602i	$-0.608371\pi$
$181$	−8.98480	−0.667835	−0.333918	+	0.942602i	$0.608371\pi$
$182$	0	0
$183$	−2.16820	−0.160278
$184$	0.452171	0.0333345
$185$	−2.42050	−0.177959
$186$	−8.96636	−0.657445
$187$	−27.7037	−2.02589
$188$	−5.21018	−0.379992
$189$	0	0
$190$	1.69502	0.122970
$191$	−4.17699	−0.302236	−0.151118	−	0.988516i	$-0.548287\pi$
$191$	−4.17699	−0.302236	−0.151118	+	0.988516i	$0.548287\pi$
$192$	−1.04534	−0.0754410
$193$	−22.9970	−1.65536	−0.827679	−	0.561202i	$-0.810339\pi$
$193$	−22.9970	−1.65536	−0.827679	+	0.561202i	$0.810339\pi$
$194$	−2.64094	−0.189609
$195$	2.33092	0.166921
$196$	0	0
$197$	−26.1448	−1.86274	−0.931371	−	0.364070i	$-0.881387\pi$
$197$	−26.1448	−1.86274	−0.931371	+	0.364070i	$0.881387\pi$
$198$	11.7570	0.835536
$199$	−14.5540	−1.03171	−0.515854	−	0.856677i	$-0.672525\pi$
$199$	−14.5540	−1.03171	−0.515854	+	0.856677i	$0.672525\pi$
$200$	−4.59602	−0.324988
$201$	4.30323	0.303527
$202$	1.78442	0.125551
$203$	0	0
$204$	−4.69794	−0.328922
$205$	−4.76038	−0.332479
$206$	−11.6741	−0.813370
$207$	−0.862408	−0.0599415
$208$	3.50826	0.243254
$209$	16.4394	1.13713
$210$	0	0
$211$	−14.7774	−1.01732	−0.508660	−	0.860967i	$-0.669859\pi$
$211$	−14.7774	−1.01732	−0.508660	+	0.860967i	$0.669859\pi$
$212$	14.4482	0.992307
$213$	−2.81722	−0.193033
$214$	−10.8464	−0.741447
$215$	−1.84783	−0.126021
$216$	5.12976	0.349036
$217$	0	0
$218$	−12.0238	−0.814357
$219$	8.81383	0.595584
$220$	3.91801	0.264152
$221$	15.7667	1.06058
$222$	−3.98093	−0.267183
$223$	−12.1276	−0.812127	−0.406063	−	0.913845i	$-0.633099\pi$
$223$	−12.1276	−0.812127	−0.406063	+	0.913845i	$0.633099\pi$
$224$	0	0
$225$	8.76582	0.584388
$226$	20.4936	1.36321
$227$	25.7246	1.70740	0.853701	−	0.520764i	$-0.174353\pi$
$227$	25.7246	1.70740	0.853701	+	0.520764i	$0.174353\pi$
$228$	2.78776	0.184624
$229$	7.39225	0.488494	0.244247	−	0.969713i	$-0.421459\pi$
$229$	7.39225	0.488494	0.244247	+	0.969713i	$0.421459\pi$
$230$	−0.287396	−0.0189503
$231$	0	0
$232$	1.00000	0.0656532
$233$	1.24860	0.0817987	0.0408994	−	0.999163i	$-0.486978\pi$
$233$	1.24860	0.0817987	0.0408994	+	0.999163i	$0.486978\pi$
$234$	−6.69117	−0.437416
$235$	3.31155	0.216022
$236$	5.00626	0.325880
$237$	0.113524	0.00737418
$238$	0	0
$239$	22.6217	1.46328	0.731640	−	0.681692i	$-0.238755\pi$
$239$	22.6217	1.46328	0.731640	+	0.681692i	$0.238755\pi$
$240$	0.664410	0.0428875
$241$	29.9759	1.93092	0.965458	−	0.260560i	$-0.0839072\pi$
$241$	29.9759	1.93092	0.965458	+	0.260560i	$0.0839072\pi$
$242$	26.9993	1.73558
$243$	−15.7650	−1.01133
$244$	2.07416	0.132784
$245$	0	0
$246$	−7.82927	−0.499176
$247$	−9.35598	−0.595307
$248$	8.57744	0.544668
$249$	−1.02992	−0.0652686
$250$	6.09915	0.385744
$251$	−6.13268	−0.387092	−0.193546	−	0.981091i	$-0.561999\pi$
$251$	−6.13268	−0.387092	−0.193546	+	0.981091i	$0.561999\pi$
$252$	0	0
$253$	−2.78734	−0.175239
$254$	8.47893	0.532016
$255$	2.98597	0.186989
$256$	1.00000	0.0625000
$257$	28.8072	1.79694	0.898472	−	0.439031i	$-0.144678\pi$
$257$	28.8072	1.79694	0.898472	+	0.439031i	$0.144678\pi$
$258$	−3.03908	−0.189205
$259$	0	0
$260$	−2.22982	−0.138288
$261$	−1.90726	−0.118057
$262$	−0.635591	−0.0392670
$263$	−12.6525	−0.780185	−0.390092	−	0.920776i	$-0.627557\pi$
$263$	−12.6525	−0.780185	−0.390092	+	0.920776i	$0.627557\pi$
$264$	6.44385	0.396592
$265$	−9.18316	−0.564117
$266$	0	0
$267$	−18.5978	−1.13817
$268$	−4.11658	−0.251460
$269$	25.5822	1.55977	0.779886	−	0.625921i	$-0.215277\pi$
$269$	25.5822	1.55977	0.779886	+	0.625921i	$0.215277\pi$
$270$	−3.26043	−0.198424
$271$	9.13120	0.554681	0.277340	−	0.960772i	$-0.410547\pi$
$271$	9.13120	0.554681	0.277340	+	0.960772i	$0.410547\pi$
$272$	4.49417	0.272499
$273$	0	0
$274$	2.85938	0.172741
$275$	28.3315	1.70845
$276$	−0.472673	−0.0284516
$277$	−7.53642	−0.452820	−0.226410	−	0.974032i	$-0.572699\pi$
$277$	−7.53642	−0.452820	−0.226410	+	0.974032i	$0.572699\pi$
$278$	21.2565	1.27488
$279$	−16.3594	−0.979414
$280$	0	0
$281$	4.16607	0.248527	0.124264	−	0.992249i	$-0.460343\pi$
$281$	4.16607	0.248527	0.124264	+	0.992249i	$0.460343\pi$
$282$	5.44642	0.324330
$283$	2.62137	0.155824	0.0779121	−	0.996960i	$-0.475175\pi$
$283$	2.62137	0.155824	0.0779121	+	0.996960i	$0.475175\pi$
$284$	2.69502	0.159920
$285$	−1.77188	−0.104957
$286$	−21.6262	−1.27878
$287$	0	0
$288$	−1.90726	−0.112386
$289$	3.19758	0.188093
$290$	−0.635591	−0.0373232
$291$	2.76069	0.161834
$292$	−8.43154	−0.493418
$293$	15.0423	0.878780	0.439390	−	0.898296i	$-0.355195\pi$
$293$	15.0423	0.878780	0.439390	+	0.898296i	$0.355195\pi$
$294$	0	0
$295$	−3.18194	−0.185260
$296$	3.80826	0.221351
$297$	−31.6217	−1.83488
$298$	8.48185	0.491341
$299$	1.58633	0.0917400
$300$	4.80441	0.277383
$301$	0	0
$302$	11.4003	0.656015
$303$	−1.86533	−0.107160
$304$	−2.66684	−0.152954
$305$	−1.31832	−0.0754867
$306$	−8.57156	−0.490004
$307$	−2.56941	−0.146644	−0.0733221	−	0.997308i	$-0.523360\pi$
$307$	−2.56941	−0.146644	−0.0733221	+	0.997308i	$0.523360\pi$
$308$	0	0
$309$	12.2034	0.694225
$310$	−5.45175	−0.309639
$311$	−8.70307	−0.493506	−0.246753	−	0.969078i	$-0.579364\pi$
$311$	−8.70307	−0.493506	−0.246753	+	0.969078i	$0.579364\pi$
$312$	−3.66733	−0.207622
$313$	17.5432	0.991601	0.495800	−	0.868437i	$-0.334875\pi$
$313$	17.5432	0.991601	0.495800	+	0.868437i	$0.334875\pi$
$314$	−15.3723	−0.867508
$315$	0	0
$316$	−0.108600	−0.00610923
$317$	−13.6648	−0.767492	−0.383746	−	0.923439i	$-0.625366\pi$
$317$	−13.6648	−0.767492	−0.383746	+	0.923439i	$0.625366\pi$
$318$	−15.1033	−0.846952
$319$	−6.16435	−0.345138
$320$	−0.635591	−0.0355306
$321$	11.3382	0.632838
$322$	0	0
$323$	−11.9852	−0.666877
$324$	0.359432	0.0199685
$325$	−16.1241	−0.894401
$326$	14.9818	0.829765
$327$	12.5690	0.695068
$328$	7.48968	0.413549
$329$	0	0
$330$	−4.09566	−0.225459
$331$	−30.2232	−1.66122	−0.830609	−	0.556855i	$-0.812008\pi$
$331$	−30.2232	−1.66122	−0.830609	+	0.556855i	$0.812008\pi$
$332$	0.985249	0.0540726
$333$	−7.26335	−0.398029
$334$	10.8187	0.591972
$335$	2.61646	0.142953
$336$	0	0
$337$	25.4947	1.38878	0.694392	−	0.719597i	$-0.255673\pi$
$337$	25.4947	1.38878	0.694392	+	0.719597i	$0.255673\pi$
$338$	−0.692102	−0.0376454
$339$	−21.4228	−1.16353
$340$	−2.85646	−0.154913
$341$	−52.8744	−2.86331
$342$	5.08637	0.275039
$343$	0	0
$344$	2.90726	0.156749
$345$	0.300427	0.0161744
$346$	8.59512	0.462076
$347$	13.5955	0.729845	0.364923	−	0.931038i	$-0.381095\pi$
$347$	13.5955	0.729845	0.364923	+	0.931038i	$0.381095\pi$
$348$	−1.04534	−0.0560362
$349$	−10.7077	−0.573171	−0.286585	−	0.958055i	$-0.592520\pi$
$349$	−10.7077	−0.573171	−0.286585	+	0.958055i	$0.592520\pi$
$350$	0	0
$351$	17.9965	0.960585
$352$	−6.16435	−0.328561
$353$	−2.57148	−0.136866	−0.0684330	−	0.997656i	$-0.521800\pi$
$353$	−2.57148	−0.136866	−0.0684330	+	0.997656i	$0.521800\pi$
$354$	−5.23325	−0.278144
$355$	−1.71293	−0.0909131
$356$	17.7911	0.942929
$357$	0	0
$358$	−10.4823	−0.554005
$359$	3.91909	0.206842	0.103421	−	0.994638i	$-0.467021\pi$
$359$	3.91909	0.206842	0.103421	+	0.994638i	$0.467021\pi$
$360$	1.21224	0.0638906
$361$	−11.8879	−0.625682
$362$	−8.98480	−0.472231
$363$	−28.2234	−1.48135
$364$	0	0
$365$	5.35901	0.280504
$366$	−2.16820	−0.113334
$367$	−3.16192	−0.165051	−0.0825255	−	0.996589i	$-0.526299\pi$
$367$	−3.16192	−0.165051	−0.0825255	+	0.996589i	$0.526299\pi$
$368$	0.452171	0.0235710
$369$	−14.2848	−0.743636
$370$	−2.42050	−0.125836
$371$	0	0
$372$	−8.96636	−0.464884
$373$	1.74384	0.0902924	0.0451462	−	0.998980i	$-0.485625\pi$
$373$	1.74384	0.0902924	0.0451462	+	0.998980i	$0.485625\pi$
$374$	−27.7037	−1.43252
$375$	−6.37569	−0.329239
$376$	−5.21018	−0.268695
$377$	3.50826	0.180685
$378$	0	0
$379$	16.9277	0.869515	0.434758	−	0.900548i	$-0.356834\pi$
$379$	16.9277	0.869515	0.434758	+	0.900548i	$0.356834\pi$
$380$	1.69502	0.0869528
$381$	−8.86338	−0.454085
$382$	−4.17699	−0.213713
$383$	35.6648	1.82239	0.911194	−	0.411978i	$-0.135162\pi$
$383$	35.6648	1.82239	0.911194	+	0.411978i	$0.135162\pi$
$384$	−1.04534	−0.0533448
$385$	0	0
$386$	−22.9970	−1.17051
$387$	−5.54491	−0.281864
$388$	−2.64094	−0.134074
$389$	7.20134	0.365122	0.182561	−	0.983194i	$-0.441561\pi$
$389$	7.20134	0.365122	0.182561	+	0.983194i	$0.441561\pi$
$390$	2.33092	0.118031
$391$	2.03213	0.102769
$392$	0	0
$393$	0.664410	0.0335150
$394$	−26.1448	−1.31716
$395$	0.0690253	0.00347304
$396$	11.7570	0.590813
$397$	−29.7904	−1.49514	−0.747568	−	0.664185i	$-0.768779\pi$
$397$	−29.7904	−1.49514	−0.747568	+	0.664185i	$0.768779\pi$
$398$	−14.5540	−0.729527
$399$	0	0
$400$	−4.59602	−0.229801
$401$	−33.3827	−1.66705	−0.833525	−	0.552482i	$-0.813681\pi$
$401$	−33.3827	−1.66705	−0.833525	+	0.552482i	$0.813681\pi$
$402$	4.30323	0.214626
$403$	30.0919	1.49899
$404$	1.78442	0.0887782
$405$	−0.228452	−0.0113519
$406$	0	0
$407$	−23.4755	−1.16364
$408$	−4.69794	−0.232583
$409$	−10.8266	−0.535342	−0.267671	−	0.963510i	$-0.586254\pi$
$409$	−10.8266	−0.535342	−0.267671	+	0.963510i	$0.586254\pi$
$410$	−4.76038	−0.235098
$411$	−2.98902	−0.147438
$412$	−11.6741	−0.575139
$413$	0	0
$414$	−0.862408	−0.0423850
$415$	−0.626216	−0.0307397
$416$	3.50826	0.172007
$417$	−22.2203	−1.08813
$418$	16.4394	0.804076
$419$	−14.9526	−0.730485	−0.365242	−	0.930912i	$-0.619014\pi$
$419$	−14.9526	−0.730485	−0.365242	+	0.930912i	$0.619014\pi$
$420$	0	0
$421$	−25.2610	−1.23115	−0.615573	−	0.788080i	$-0.711075\pi$
$421$	−25.2610	−1.23115	−0.615573	+	0.788080i	$0.711075\pi$
$422$	−14.7774	−0.719354
$423$	9.93718	0.483162
$424$	14.4482	0.701667
$425$	−20.6553	−1.00193
$426$	−2.81722	−0.136495
$427$	0	0
$428$	−10.8464	−0.524282
$429$	22.6067	1.09146
$430$	−1.84783	−0.0891103
$431$	19.1672	0.923251	0.461625	−	0.887075i	$-0.347266\pi$
$431$	19.1672	0.923251	0.461625	+	0.887075i	$0.347266\pi$
$432$	5.12976	0.246806
$433$	−3.89446	−0.187156	−0.0935778	−	0.995612i	$-0.529830\pi$
$433$	−3.89446	−0.187156	−0.0935778	+	0.995612i	$0.529830\pi$
$434$	0	0
$435$	0.664410	0.0318560
$436$	−12.0238	−0.575838
$437$	−1.20587	−0.0576845
$438$	8.81383	0.421141
$439$	29.6761	1.41637	0.708183	−	0.706029i	$-0.249515\pi$
$439$	29.6761	1.41637	0.708183	+	0.706029i	$0.249515\pi$
$440$	3.91801	0.186784
$441$	0	0
$442$	15.7667	0.749947
$443$	−16.1588	−0.767727	−0.383864	−	0.923390i	$-0.625407\pi$
$443$	−16.1588	−0.767727	−0.383864	+	0.923390i	$0.625407\pi$
$444$	−3.98093	−0.188927
$445$	−11.3079	−0.536046
$446$	−12.1276	−0.574260
$447$	−8.86643	−0.419368
$448$	0	0
$449$	7.30425	0.344709	0.172354	−	0.985035i	$-0.444863\pi$
$449$	7.30425	0.344709	0.172354	+	0.985035i	$0.444863\pi$
$450$	8.76582	0.413225
$451$	−46.1691	−2.17402
$452$	20.4936	0.963937
$453$	−11.9172	−0.559920
$454$	25.7246	1.20732
$455$	0	0
$456$	2.78776	0.130549
$457$	30.1311	1.40947	0.704737	−	0.709469i	$-0.251065\pi$
$457$	30.1311	1.40947	0.704737	+	0.709469i	$0.251065\pi$
$458$	7.39225	0.345417
$459$	23.0540	1.07607
$460$	−0.287396	−0.0133999
$461$	−41.2596	−1.92165	−0.960825	−	0.277156i	$-0.910608\pi$
$461$	−41.2596	−1.92165	−0.960825	+	0.277156i	$0.910608\pi$
$462$	0	0
$463$	−11.3019	−0.525246	−0.262623	−	0.964899i	$-0.584588\pi$
$463$	−11.3019	−0.525246	−0.262623	+	0.964899i	$0.584588\pi$
$464$	1.00000	0.0464238
$465$	5.69894	0.264282
$466$	1.24860	0.0578404
$467$	−17.3358	−0.802205	−0.401102	−	0.916033i	$-0.631373\pi$
$467$	−17.3358	−0.802205	−0.401102	+	0.916033i	$0.631373\pi$
$468$	−6.69117	−0.309300
$469$	0	0
$470$	3.31155	0.152750
$471$	16.0693	0.740433
$472$	5.00626	0.230432
$473$	−17.9214	−0.824027
$474$	0.113524	0.00521434
$475$	12.2569	0.562384
$476$	0	0
$477$	−27.5565	−1.26173
$478$	22.6217	1.03469
$479$	0.254037	0.0116072	0.00580361	−	0.999983i	$-0.498153\pi$
$479$	0.254037	0.0116072	0.00580361	+	0.999983i	$0.498153\pi$
$480$	0.664410	0.0303260
$481$	13.3604	0.609181
$482$	29.9759	1.36536
$483$	0	0
$484$	26.9993	1.22724
$485$	1.67856	0.0762196
$486$	−15.7650	−0.715116
$487$	−22.7370	−1.03031	−0.515157	−	0.857096i	$-0.672266\pi$
$487$	−22.7370	−1.03031	−0.515157	+	0.857096i	$0.672266\pi$
$488$	2.07416	0.0938928
$489$	−15.6611	−0.708219
$490$	0	0
$491$	−9.39496	−0.423988	−0.211994	−	0.977271i	$-0.567996\pi$
$491$	−9.39496	−0.423988	−0.211994	+	0.977271i	$0.567996\pi$
$492$	−7.82927	−0.352971
$493$	4.49417	0.202407
$494$	−9.35598	−0.420946
$495$	−7.47267	−0.335872
$496$	8.57744	0.385139
$497$	0	0
$498$	−1.02992	−0.0461519
$499$	15.1235	0.677022	0.338511	−	0.940962i	$-0.390077\pi$
$499$	15.1235	0.677022	0.338511	+	0.940962i	$0.390077\pi$
$500$	6.09915	0.272762
$501$	−11.3092	−0.505258
$502$	−6.13268	−0.273715
$503$	−25.8775	−1.15382	−0.576910	−	0.816808i	$-0.695742\pi$
$503$	−25.8775	−1.15382	−0.576910	+	0.816808i	$0.695742\pi$
$504$	0	0
$505$	−1.13416	−0.0504696
$506$	−2.78734	−0.123912
$507$	0.723483	0.0321310
$508$	8.47893	0.376192
$509$	13.1819	0.584278	0.292139	−	0.956376i	$-0.405633\pi$
$509$	13.1819	0.584278	0.292139	+	0.956376i	$0.405633\pi$
$510$	2.98597	0.132221
$511$	0	0
$512$	1.00000	0.0441942
$513$	−13.6803	−0.603999
$514$	28.8072	1.27063
$515$	7.41993	0.326961
$516$	−3.03908	−0.133788
$517$	32.1174	1.41252
$518$	0	0
$519$	−8.98483	−0.394390
$520$	−2.22982	−0.0977841
$521$	27.9223	1.22330	0.611648	−	0.791130i	$-0.290507\pi$
$521$	27.9223	1.22330	0.611648	+	0.791130i	$0.290507\pi$
$522$	−1.90726	−0.0834786
$523$	−30.4241	−1.33035	−0.665177	−	0.746686i	$-0.731644\pi$
$523$	−30.4241	−1.33035	−0.665177	+	0.746686i	$0.731644\pi$
$524$	−0.635591	−0.0277659
$525$	0	0
$526$	−12.6525	−0.551674
$527$	38.5485	1.67920
$528$	6.44385	0.280433
$529$	−22.7955	−0.991111
$530$	−9.18316	−0.398891
$531$	−9.54825	−0.414359
$532$	0	0
$533$	26.2758	1.13813
$534$	−18.5978	−0.804806
$535$	6.89390	0.298049
$536$	−4.11658	−0.177809
$537$	10.9576	0.472853
$538$	25.5822	1.10293
$539$	0	0
$540$	−3.26043	−0.140307
$541$	−17.9943	−0.773636	−0.386818	−	0.922156i	$-0.626426\pi$
$541$	−17.9943	−0.773636	−0.386818	+	0.922156i	$0.626426\pi$
$542$	9.13120	0.392219
$543$	9.39218	0.403057
$544$	4.49417	0.192686
$545$	7.64225	0.327358
$546$	0	0
$547$	0.298717	0.0127722	0.00638610	−	0.999980i	$-0.497967\pi$
$547$	0.298717	0.0127722	0.00638610	+	0.999980i	$0.497967\pi$
$548$	2.85938	0.122147
$549$	−3.95597	−0.168836
$550$	28.3315	1.20806
$551$	−2.66684	−0.113611
$552$	−0.472673	−0.0201183
$553$	0	0
$554$	−7.53642	−0.320192
$555$	2.53025	0.107403
$556$	21.2565	0.901476
$557$	6.32568	0.268028	0.134014	−	0.990979i	$-0.457213\pi$
$557$	6.32568	0.268028	0.134014	+	0.990979i	$0.457213\pi$
$558$	−16.3594	−0.692550
$559$	10.1994	0.431390
$560$	0	0
$561$	28.9598	1.22268
$562$	4.16607	0.175735
$563$	−32.1866	−1.35650	−0.678251	−	0.734830i	$-0.737262\pi$
$563$	−32.1866	−1.35650	−0.678251	+	0.734830i	$0.737262\pi$
$564$	5.44642	0.229336
$565$	−13.0255	−0.547989
$566$	2.62137	0.110184
$567$	0	0
$568$	2.69502	0.113081
$569$	−5.75826	−0.241399	−0.120699	−	0.992689i	$-0.538514\pi$
$569$	−5.75826	−0.241399	−0.120699	+	0.992689i	$0.538514\pi$
$570$	−1.77188	−0.0742158
$571$	10.5601	0.441926	0.220963	−	0.975282i	$-0.429080\pi$
$571$	10.5601	0.441926	0.220963	+	0.975282i	$0.429080\pi$
$572$	−21.6262	−0.904235
$573$	4.36638	0.182408
$574$	0	0
$575$	−2.07819	−0.0866664
$576$	−1.90726	−0.0794692
$577$	−7.50762	−0.312546	−0.156273	−	0.987714i	$-0.549948\pi$
$577$	−7.50762	−0.312546	−0.156273	+	0.987714i	$0.549948\pi$
$578$	3.19758	0.133002
$579$	24.0397	0.999055
$580$	−0.635591	−0.0263915
$581$	0	0
$582$	2.76069	0.114434
$583$	−89.0639	−3.68865
$584$	−8.43154	−0.348899
$585$	4.25285	0.175834
$586$	15.0423	0.621391
$587$	−39.3707	−1.62500	−0.812502	−	0.582958i	$-0.801895\pi$
$587$	−39.3707	−1.62500	−0.812502	+	0.582958i	$0.801895\pi$
$588$	0	0
$589$	−22.8747	−0.942535
$590$	−3.18194	−0.130998
$591$	27.3303	1.12422
$592$	3.80826	0.156519
$593$	6.32018	0.259539	0.129769	−	0.991544i	$-0.458576\pi$
$593$	6.32018	0.259539	0.129769	+	0.991544i	$0.458576\pi$
$594$	−31.6217	−1.29745
$595$	0	0
$596$	8.48185	0.347430
$597$	15.2139	0.622664
$598$	1.58633	0.0648700
$599$	8.59138	0.351034	0.175517	−	0.984476i	$-0.443840\pi$
$599$	8.59138	0.351034	0.175517	+	0.984476i	$0.443840\pi$
$600$	4.80441	0.196139
$601$	−8.77356	−0.357881	−0.178941	−	0.983860i	$-0.557267\pi$
$601$	−8.77356	−0.357881	−0.178941	+	0.983860i	$0.557267\pi$
$602$	0	0
$603$	7.85140	0.319734
$604$	11.4003	0.463873
$605$	−17.1605	−0.697674
$606$	−1.86533	−0.0757738
$607$	−41.5762	−1.68753	−0.843763	−	0.536716i	$-0.819664\pi$
$607$	−41.5762	−1.68753	−0.843763	+	0.536716i	$0.819664\pi$
$608$	−2.66684	−0.108155
$609$	0	0
$610$	−1.31832	−0.0533771
$611$	−18.2787	−0.739476
$612$	−8.57156	−0.346485
$613$	32.3946	1.30841	0.654204	−	0.756318i	$-0.273004\pi$
$613$	32.3946	1.30841	0.654204	+	0.756318i	$0.273004\pi$
$614$	−2.56941	−0.103693
$615$	4.97622	0.200661
$616$	0	0
$617$	−15.8684	−0.638840	−0.319420	−	0.947613i	$-0.603488\pi$
$617$	−15.8684	−0.638840	−0.319420	+	0.947613i	$0.603488\pi$
$618$	12.2034	0.490891
$619$	33.3284	1.33958	0.669790	−	0.742551i	$-0.266384\pi$
$619$	33.3284	1.33958	0.669790	+	0.742551i	$0.266384\pi$
$620$	−5.45175	−0.218948
$621$	2.31953	0.0930795
$622$	−8.70307	−0.348961
$623$	0	0
$624$	−3.66733	−0.146811
$625$	19.1035	0.764142
$626$	17.5432	0.701168
$627$	−17.1847	−0.686293
$628$	−15.3723	−0.613421
$629$	17.1150	0.682419
$630$	0	0
$631$	14.0390	0.558884	0.279442	−	0.960163i	$-0.409850\pi$
$631$	14.0390	0.558884	0.279442	+	0.960163i	$0.409850\pi$
$632$	−0.108600	−0.00431988
$633$	15.4475	0.613981
$634$	−13.6648	−0.542699
$635$	−5.38914	−0.213861
$636$	−15.1033	−0.598885
$637$	0	0
$638$	−6.16435	−0.244049
$639$	−5.14011	−0.203340
$640$	−0.635591	−0.0251240
$641$	27.5077	1.08649	0.543245	−	0.839574i	$-0.317196\pi$
$641$	27.5077	1.08649	0.543245	+	0.839574i	$0.317196\pi$
$642$	11.3382	0.447484
$643$	9.62486	0.379568	0.189784	−	0.981826i	$-0.439221\pi$
$643$	9.62486	0.379568	0.189784	+	0.981826i	$0.439221\pi$
$644$	0	0
$645$	1.93161	0.0760572
$646$	−11.9852	−0.471553
$647$	−6.83452	−0.268693	−0.134346	−	0.990934i	$-0.542893\pi$
$647$	−6.83452	−0.268693	−0.134346	+	0.990934i	$0.542893\pi$
$648$	0.359432	0.0141198
$649$	−30.8604	−1.21138
$650$	−16.1241	−0.632437
$651$	0	0
$652$	14.9818	0.586733
$653$	−10.6600	−0.417159	−0.208580	−	0.978005i	$-0.566884\pi$
$653$	−10.6600	−0.417159	−0.208580	+	0.978005i	$0.566884\pi$
$654$	12.5690	0.491488
$655$	0.403976	0.0157847
$656$	7.48968	0.292423
$657$	16.0811	0.627385
$658$	0	0
$659$	−35.7780	−1.39371	−0.696857	−	0.717210i	$-0.745419\pi$
$659$	−35.7780	−1.39371	−0.696857	+	0.717210i	$0.745419\pi$
$660$	−4.09566	−0.159423
$661$	20.8487	0.810920	0.405460	−	0.914113i	$-0.367111\pi$
$661$	20.8487	0.810920	0.405460	+	0.914113i	$0.367111\pi$
$662$	−30.2232	−1.17466
$663$	−16.4816	−0.640093
$664$	0.985249	0.0382351
$665$	0	0
$666$	−7.26335	−0.281449
$667$	0.452171	0.0175081
$668$	10.8187	0.418587
$669$	12.6775	0.490141
$670$	2.61646	0.101083
$671$	−12.7859	−0.493593
$672$	0	0
$673$	34.7639	1.34005	0.670024	−	0.742339i	$-0.266284\pi$
$673$	34.7639	1.34005	0.670024	+	0.742339i	$0.266284\pi$
$674$	25.4947	0.982019
$675$	−23.5765	−0.907460
$676$	−0.692102	−0.0266193
$677$	−2.27679	−0.0875043	−0.0437521	−	0.999042i	$-0.513931\pi$
$677$	−2.27679	−0.0875043	−0.0437521	+	0.999042i	$0.513931\pi$
$678$	−21.4228	−0.822737
$679$	0	0
$680$	−2.85646	−0.109540
$681$	−26.8910	−1.03046
$682$	−52.8744	−2.02467
$683$	−17.2288	−0.659240	−0.329620	−	0.944114i	$-0.606921\pi$
$683$	−17.2288	−0.659240	−0.329620	+	0.944114i	$0.606921\pi$
$684$	5.08637	0.194482
$685$	−1.81740	−0.0694391
$686$	0	0
$687$	−7.72743	−0.294820
$688$	2.90726	0.110838
$689$	50.6881	1.93106
$690$	0.300427	0.0114370
$691$	30.8224	1.17254	0.586269	−	0.810116i	$-0.300596\pi$
$691$	30.8224	1.17254	0.586269	+	0.810116i	$0.300596\pi$
$692$	8.59512	0.326737
$693$	0	0
$694$	13.5955	0.516079
$695$	−13.5104	−0.512480
$696$	−1.04534	−0.0396236
$697$	33.6599	1.27496
$698$	−10.7077	−0.405293
$699$	−1.30522	−0.0493678
$700$	0	0
$701$	−40.7823	−1.54033	−0.770163	−	0.637848i	$-0.779825\pi$
$701$	−40.7823	−1.54033	−0.770163	+	0.637848i	$0.779825\pi$
$702$	17.9965	0.679236
$703$	−10.1560	−0.383042
$704$	−6.16435	−0.232328
$705$	−3.46170	−0.130375
$706$	−2.57148	−0.0967788
$707$	0	0
$708$	−5.23325	−0.196678
$709$	26.9991	1.01397	0.506986	−	0.861954i	$-0.330760\pi$
$709$	26.9991	1.01397	0.506986	+	0.861954i	$0.330760\pi$
$710$	−1.71293	−0.0642852
$711$	0.207129	0.00776793
$712$	17.7911	0.666751
$713$	3.87847	0.145250
$714$	0	0
$715$	13.7454	0.514049
$716$	−10.4823	−0.391741
$717$	−23.6474	−0.883130
$718$	3.91909	0.146259
$719$	−35.4494	−1.32204	−0.661020	−	0.750368i	$-0.729876\pi$
$719$	−35.4494	−1.32204	−0.661020	+	0.750368i	$0.729876\pi$
$720$	1.21224	0.0451775
$721$	0	0
$722$	−11.8879	−0.442424
$723$	−31.3350	−1.16536
$724$	−8.98480	−0.333918
$725$	−4.59602	−0.170692
$726$	−28.2234	−1.04747
$727$	22.5096	0.834834	0.417417	−	0.908715i	$-0.362936\pi$
$727$	22.5096	0.834834	0.417417	+	0.908715i	$0.362936\pi$
$728$	0	0
$729$	15.4015	0.570427
$730$	5.35901	0.198346
$731$	13.0657	0.483254
$732$	−2.16820	−0.0801392
$733$	−7.77593	−0.287211	−0.143605	−	0.989635i	$-0.545870\pi$
$733$	−7.77593	−0.287211	−0.143605	+	0.989635i	$0.545870\pi$
$734$	−3.16192	−0.116709
$735$	0	0
$736$	0.452171	0.0166672
$737$	25.3761	0.934739
$738$	−14.2848	−0.525830
$739$	36.7027	1.35013	0.675065	−	0.737758i	$-0.264116\pi$
$739$	36.7027	1.35013	0.675065	+	0.737758i	$0.264116\pi$
$740$	−2.42050	−0.0889793
$741$	9.78019	0.359284
$742$	0	0
$743$	11.3936	0.417992	0.208996	−	0.977916i	$-0.432980\pi$
$743$	11.3936	0.417992	0.208996	+	0.977916i	$0.432980\pi$
$744$	−8.96636	−0.328723
$745$	−5.39099	−0.197511
$746$	1.74384	0.0638464
$747$	−1.87913	−0.0687537
$748$	−27.7037	−1.01295
$749$	0	0
$750$	−6.37569	−0.232807
$751$	−50.6364	−1.84775	−0.923874	−	0.382697i	$-0.874995\pi$
$751$	−50.6364	−1.84775	−0.923874	+	0.382697i	$0.874995\pi$
$752$	−5.21018	−0.189996
$753$	6.41075	0.233621
$754$	3.50826	0.127763
$755$	−7.24595	−0.263707
$756$	0	0
$757$	37.8232	1.37471	0.687354	−	0.726323i	$-0.258772\pi$
$757$	37.8232	1.37471	0.687354	+	0.726323i	$0.258772\pi$
$758$	16.9277	0.614840
$759$	2.91372	0.105761
$760$	1.69502	0.0614849
$761$	16.1435	0.585200	0.292600	−	0.956235i	$-0.405479\pi$
$761$	16.1435	0.585200	0.292600	+	0.956235i	$0.405479\pi$
$762$	−8.86338	−0.321086
$763$	0	0
$764$	−4.17699	−0.151118
$765$	5.44801	0.196973
$766$	35.6648	1.28862
$767$	17.5633	0.634173
$768$	−1.04534	−0.0377205
$769$	14.3761	0.518414	0.259207	−	0.965822i	$-0.416539\pi$
$769$	14.3761	0.518414	0.259207	+	0.965822i	$0.416539\pi$
$770$	0	0
$771$	−30.1134	−1.08451
$772$	−22.9970	−0.827679
$773$	26.5183	0.953799	0.476899	−	0.878958i	$-0.341761\pi$
$773$	26.5183	0.953799	0.476899	+	0.878958i	$0.341761\pi$
$774$	−5.54491	−0.199308
$775$	−39.4221	−1.41609
$776$	−2.64094	−0.0948044
$777$	0	0
$778$	7.20134	0.258180
$779$	−19.9738	−0.715636
$780$	2.33092	0.0834605
$781$	−16.6131	−0.594463
$782$	2.03213	0.0726689
$783$	5.12976	0.183323
$784$	0	0
$785$	9.77049	0.348724
$786$	0.664410	0.0236987
$787$	−21.1678	−0.754550	−0.377275	−	0.926101i	$-0.623139\pi$
$787$	−21.1678	−0.754550	−0.377275	+	0.926101i	$0.623139\pi$
$788$	−26.1448	−0.931371
$789$	13.2261	0.470863
$790$	0.0690253	0.00245581
$791$	0	0
$792$	11.7570	0.417768
$793$	7.27669	0.258403
$794$	−29.7904	−1.05722
$795$	9.59953	0.340460
$796$	−14.5540	−0.515854
$797$	−16.3454	−0.578983	−0.289491	−	0.957181i	$-0.593486\pi$
$797$	−16.3454	−0.578983	−0.289491	+	0.957181i	$0.593486\pi$
$798$	0	0
$799$	−23.4155	−0.828379
$800$	−4.59602	−0.162494
$801$	−33.9324	−1.19894
$802$	−33.3827	−1.17878
$803$	51.9750	1.83416
$804$	4.30323	0.151763
$805$	0	0
$806$	30.0919	1.05994
$807$	−26.7421	−0.941367
$808$	1.78442	0.0627757
$809$	1.26689	0.0445416	0.0222708	−	0.999752i	$-0.492910\pi$
$809$	1.26689	0.0445416	0.0222708	+	0.999752i	$0.492910\pi$
$810$	−0.228452	−0.00802699
$811$	−8.85737	−0.311024	−0.155512	−	0.987834i	$-0.549703\pi$
$811$	−8.85737	−0.311024	−0.155512	+	0.987834i	$0.549703\pi$
$812$	0	0
$813$	−9.54522	−0.334765
$814$	−23.4755	−0.822815
$815$	−9.52230	−0.333552
$816$	−4.69794	−0.164461
$817$	−7.75321	−0.271250
$818$	−10.8266	−0.378544
$819$	0	0
$820$	−4.76038	−0.166240
$821$	18.6382	0.650476	0.325238	−	0.945632i	$-0.394556\pi$
$821$	18.6382	0.650476	0.325238	+	0.945632i	$0.394556\pi$
$822$	−2.98902	−0.104254
$823$	34.2281	1.19312	0.596559	−	0.802569i	$-0.296534\pi$
$823$	34.2281	1.19312	0.596559	+	0.802569i	$0.296534\pi$
$824$	−11.6741	−0.406685
$825$	−29.6161	−1.03110
$826$	0	0
$827$	23.0340	0.800971	0.400486	−	0.916303i	$-0.368841\pi$
$827$	23.0340	0.800971	0.400486	+	0.916303i	$0.368841\pi$
$828$	−0.862408	−0.0299707
$829$	9.14291	0.317546	0.158773	−	0.987315i	$-0.449246\pi$
$829$	9.14291	0.317546	0.158773	+	0.987315i	$0.449246\pi$
$830$	−0.626216	−0.0217363
$831$	7.87813	0.273289
$832$	3.50826	0.121627
$833$	0	0
$834$	−22.2203	−0.769426
$835$	−6.87626	−0.237963
$836$	16.4394	0.568567
$837$	44.0003	1.52087
$838$	−14.9526	−0.516531
$839$	−38.9599	−1.34505	−0.672523	−	0.740076i	$-0.734789\pi$
$839$	−38.9599	−1.34505	−0.672523	+	0.740076i	$0.734789\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−25.2610	−0.870552
$843$	−4.35497	−0.149993
$844$	−14.7774	−0.508660
$845$	0.439894	0.0151328
$846$	9.93718	0.341647
$847$	0	0
$848$	14.4482	0.496154
$849$	−2.74023	−0.0940443
$850$	−20.6553	−0.708472
$851$	1.72198	0.0590289
$852$	−2.81722	−0.0965163
$853$	−2.41528	−0.0826975	−0.0413487	−	0.999145i	$-0.513165\pi$
$853$	−2.41528	−0.0826975	−0.0413487	+	0.999145i	$0.513165\pi$
$854$	0	0
$855$	−3.23285	−0.110561
$856$	−10.8464	−0.370724
$857$	52.7601	1.80225	0.901125	−	0.433560i	$-0.142743\pi$
$857$	52.7601	1.80225	0.901125	+	0.433560i	$0.142743\pi$
$858$	22.6067	0.771781
$859$	−35.0323	−1.19529	−0.597643	−	0.801762i	$-0.703896\pi$
$859$	−35.0323	−1.19529	−0.597643	+	0.801762i	$0.703896\pi$
$860$	−1.84783	−0.0630105
$861$	0	0
$862$	19.1672	0.652837
$863$	−0.337360	−0.0114839	−0.00574193	−	0.999984i	$-0.501828\pi$
$863$	−0.337360	−0.0114839	−0.00574193	+	0.999984i	$0.501828\pi$
$864$	5.12976	0.174518
$865$	−5.46298	−0.185747
$866$	−3.89446	−0.132339
$867$	−3.34256	−0.113519
$868$	0	0
$869$	0.669449	0.0227095
$870$	0.664410	0.0225256
$871$	−14.4420	−0.489350
$872$	−12.0238	−0.407179
$873$	5.03697	0.170476
$874$	−1.20587	−0.0407891
$875$	0	0
$876$	8.81383	0.297792
$877$	20.1477	0.680340	0.340170	−	0.940364i	$-0.389515\pi$
$877$	20.1477	0.680340	0.340170	+	0.940364i	$0.389515\pi$
$878$	29.6761	1.00152
$879$	−15.7243	−0.530368
$880$	3.91801	0.132076
$881$	43.0268	1.44961	0.724805	−	0.688954i	$-0.241930\pi$
$881$	43.0268	1.44961	0.724805	+	0.688954i	$0.241930\pi$
$882$	0	0
$883$	17.9078	0.602647	0.301323	−	0.953522i	$-0.402572\pi$
$883$	17.9078	0.602647	0.301323	+	0.953522i	$0.402572\pi$
$884$	15.7667	0.530292
$885$	3.32621	0.111809
$886$	−16.1588	−0.542865
$887$	1.24843	0.0419183	0.0209591	−	0.999780i	$-0.493328\pi$
$887$	1.24843	0.0419183	0.0209591	+	0.999780i	$0.493328\pi$
$888$	−3.98093	−0.133591
$889$	0	0
$890$	−11.3079	−0.379042
$891$	−2.21567	−0.0742277
$892$	−12.1276	−0.406063
$893$	13.8947	0.464970
$894$	−8.86643	−0.296538
$895$	6.66244	0.222701
$896$	0	0
$897$	−1.65826	−0.0553677
$898$	7.30425	0.243746
$899$	8.57744	0.286074
$900$	8.76582	0.292194
$901$	64.9327	2.16322
$902$	−46.1691	−1.53726
$903$	0	0
$904$	20.4936	0.681606
$905$	5.71066	0.189829
$906$	−11.9172	−0.395923
$907$	20.6827	0.686757	0.343379	−	0.939197i	$-0.388429\pi$
$907$	20.6827	0.686757	0.343379	+	0.939197i	$0.388429\pi$
$908$	25.7246	0.853701
$909$	−3.40336	−0.112882
$910$	0	0
$911$	−34.2033	−1.13320	−0.566602	−	0.823991i	$-0.691742\pi$
$911$	−34.2033	−1.13320	−0.566602	+	0.823991i	$0.691742\pi$
$912$	2.78776	0.0923120
$913$	−6.07343	−0.201001
$914$	30.1311	0.996649
$915$	1.37809	0.0455583
$916$	7.39225	0.244247
$917$	0	0
$918$	23.0540	0.760897
$919$	23.5515	0.776892	0.388446	−	0.921472i	$-0.373012\pi$
$919$	23.5515	0.776892	0.388446	+	0.921472i	$0.373012\pi$
$920$	−0.287396	−0.00947516
$921$	2.68591	0.0885038
$922$	−41.2596	−1.35881
$923$	9.45484	0.311210
$924$	0	0
$925$	−17.5029	−0.575491
$926$	−11.3019	−0.371405
$927$	22.2655	0.731294
$928$	1.00000	0.0328266
$929$	40.4148	1.32597	0.662983	−	0.748635i	$-0.269290\pi$
$929$	40.4148	1.32597	0.662983	+	0.748635i	$0.269290\pi$
$930$	5.69894	0.186876
$931$	0	0
$932$	1.24860	0.0408994
$933$	9.09768	0.297845
$934$	−17.3358	−0.567244
$935$	17.6082	0.575850
$936$	−6.69117	−0.218708
$937$	8.61562	0.281460	0.140730	−	0.990048i	$-0.455055\pi$
$937$	8.61562	0.281460	0.140730	+	0.990048i	$0.455055\pi$
$938$	0	0
$939$	−18.3386	−0.598459
$940$	3.31155	0.108011
$941$	14.4716	0.471761	0.235880	−	0.971782i	$-0.424203\pi$
$941$	14.4716	0.471761	0.235880	+	0.971782i	$0.424203\pi$
$942$	16.0693	0.523565
$943$	3.38662	0.110283
$944$	5.00626	0.162940
$945$	0	0
$946$	−17.9214	−0.582675
$947$	17.9649	0.583782	0.291891	−	0.956452i	$-0.405715\pi$
$947$	17.9649	0.583782	0.291891	+	0.956452i	$0.405715\pi$
$948$	0.113524	0.00368709
$949$	−29.5800	−0.960209
$950$	12.2569	0.397665
$951$	14.2844	0.463203
$952$	0	0
$953$	−16.4336	−0.532336	−0.266168	−	0.963927i	$-0.585758\pi$
$953$	−16.4336	−0.532336	−0.266168	+	0.963927i	$0.585758\pi$
$954$	−27.5565	−0.892175
$955$	2.65486	0.0859092
$956$	22.6217	0.731640
$957$	6.44385	0.208300
$958$	0.254037	0.00820755
$959$	0	0
$960$	0.664410	0.0214437
$961$	42.5726	1.37331
$962$	13.3604	0.430756
$963$	20.6870	0.666629
$964$	29.9759	0.965458
$965$	14.6167	0.470527
$966$	0	0
$967$	−30.2292	−0.972105	−0.486052	−	0.873930i	$-0.661564\pi$
$967$	−30.2292	−0.972105	−0.486052	+	0.873930i	$0.661564\pi$
$968$	26.9993	0.867789
$969$	12.5287	0.402479
$970$	1.67856	0.0538954
$971$	46.4281	1.48995	0.744974	−	0.667093i	$-0.232462\pi$
$971$	46.4281	1.48995	0.744974	+	0.667093i	$0.232462\pi$
$972$	−15.7650	−0.505663
$973$	0	0
$974$	−22.7370	−0.728541
$975$	16.8551	0.539796
$976$	2.07416	0.0663922
$977$	9.28266	0.296978	0.148489	−	0.988914i	$-0.452559\pi$
$977$	9.28266	0.296978	0.148489	+	0.988914i	$0.452559\pi$
$978$	−15.6611	−0.500786
$979$	−109.671	−3.50510
$980$	0	0
$981$	22.9326	0.732182
$982$	−9.39496	−0.299805
$983$	27.4369	0.875100	0.437550	−	0.899194i	$-0.355846\pi$
$983$	27.4369	0.875100	0.437550	+	0.899194i	$0.355846\pi$
$984$	−7.82927	−0.249588
$985$	16.6174	0.529476
$986$	4.49417	0.143124
$987$	0	0
$988$	−9.35598	−0.297653
$989$	1.31458	0.0418012
$990$	−7.47267	−0.237497
$991$	2.03251	0.0645649	0.0322825	−	0.999479i	$-0.489722\pi$
$991$	2.03251	0.0645649	0.0322825	+	0.999479i	$0.489722\pi$
$992$	8.57744	0.272334
$993$	31.5936	1.00259
$994$	0	0
$995$	9.25041	0.293258
$996$	−1.02992	−0.0326343
$997$	−6.56303	−0.207853	−0.103927	−	0.994585i	$-0.533141\pi$
$997$	−6.56303	−0.207853	−0.103927	+	0.994585i	$0.533141\pi$
$998$	15.1235	0.478727
$999$	19.5355	0.618075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.y.1.2		5
7.3	odd	6		406.2.e.b.233.2	✓	10
7.5	odd	6		406.2.e.b.291.2	yes	10
7.6	odd	2		2842.2.a.w.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.b.233.2	✓	10	7.3	odd	6
406.2.e.b.291.2	yes	10	7.5	odd	6
2842.2.a.w.1.4		5	7.6	odd	2
2842.2.a.y.1.2		5	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.04534 q^{3} +1.00000 q^{4} -0.635591 q^{5} -1.04534 q^{6} +1.00000 q^{8} -1.90726 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.04534 q^{3} +1.00000 q^{4} -0.635591 q^{5} -1.04534 q^{6} +1.00000 q^{8} -1.90726 q^{9} -0.635591 q^{10} -6.16435 q^{11} -1.04534 q^{12} +3.50826 q^{13} +0.664410 q^{15} +1.00000 q^{16} +4.49417 q^{17} -1.90726 q^{18} -2.66684 q^{19} -0.635591 q^{20} -6.16435 q^{22} +0.452171 q^{23} -1.04534 q^{24} -4.59602 q^{25} +3.50826 q^{26} +5.12976 q^{27} +1.00000 q^{29} +0.664410 q^{30} +8.57744 q^{31} +1.00000 q^{32} +6.44385 q^{33} +4.49417 q^{34} -1.90726 q^{36} +3.80826 q^{37} -2.66684 q^{38} -3.66733 q^{39} -0.635591 q^{40} +7.48968 q^{41} +2.90726 q^{43} -6.16435 q^{44} +1.21224 q^{45} +0.452171 q^{46} -5.21018 q^{47} -1.04534 q^{48} -4.59602 q^{50} -4.69794 q^{51} +3.50826 q^{52} +14.4482 q^{53} +5.12976 q^{54} +3.91801 q^{55} +2.78776 q^{57} +1.00000 q^{58} +5.00626 q^{59} +0.664410 q^{60} +2.07416 q^{61} +8.57744 q^{62} +1.00000 q^{64} -2.22982 q^{65} +6.44385 q^{66} -4.11658 q^{67} +4.49417 q^{68} -0.472673 q^{69} +2.69502 q^{71} -1.90726 q^{72} -8.43154 q^{73} +3.80826 q^{74} +4.80441 q^{75} -2.66684 q^{76} -3.66733 q^{78} -0.108600 q^{79} -0.635591 q^{80} +0.359432 q^{81} +7.48968 q^{82} +0.985249 q^{83} -2.85646 q^{85} +2.90726 q^{86} -1.04534 q^{87} -6.16435 q^{88} +17.7911 q^{89} +1.21224 q^{90} +0.452171 q^{92} -8.96636 q^{93} -5.21018 q^{94} +1.69502 q^{95} -1.04534 q^{96} -2.64094 q^{97} +11.7570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9} + 7 q^{10} + 3 q^{12} + 8 q^{13} + 4 q^{15} + 5 q^{16} + 16 q^{17} + 4 q^{18} + 2 q^{19} + 7 q^{20} - 5 q^{23} + 3 q^{24} + 4 q^{25} + 8 q^{26} + 9 q^{27} + 5 q^{29} + 4 q^{30} + 5 q^{31} + 5 q^{32} + 3 q^{33} + 16 q^{34} + 4 q^{36} + 2 q^{38} - 20 q^{39} + 7 q^{40} + 17 q^{41} + q^{43} + 14 q^{45} - 5 q^{46} - 4 q^{47} + 3 q^{48} + 4 q^{50} - 3 q^{51} + 8 q^{52} + 5 q^{53} + 9 q^{54} + 12 q^{55} + 6 q^{57} + 5 q^{58} + 17 q^{59} + 4 q^{60} + 13 q^{61} + 5 q^{62} + 5 q^{64} - 7 q^{65} + 3 q^{66} - 14 q^{67} + 16 q^{68} + 16 q^{69} - 8 q^{71} + 4 q^{72} + 6 q^{73} + 8 q^{75} + 2 q^{76} - 20 q^{78} + 11 q^{79} + 7 q^{80} - 19 q^{81} + 17 q^{82} + 2 q^{83} + 39 q^{85} + q^{86} + 3 q^{87} + 9 q^{89} + 14 q^{90} - 5 q^{92} - 3 q^{93} - 4 q^{94} - 13 q^{95} + 3 q^{96} + 12 q^{97} + 10 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9 + 7 * q^10 + 3 * q^12 + 8 * q^13 + 4 * q^15 + 5 * q^16 + 16 * q^17 + 4 * q^18 + 2 * q^19 + 7 * q^20 - 5 * q^23 + 3 * q^24 + 4 * q^25 + 8 * q^26 + 9 * q^27 + 5 * q^29 + 4 * q^30 + 5 * q^31 + 5 * q^32 + 3 * q^33 + 16 * q^34 + 4 * q^36 + 2 * q^38 - 20 * q^39 + 7 * q^40 + 17 * q^41 + q^43 + 14 * q^45 - 5 * q^46 - 4 * q^47 + 3 * q^48 + 4 * q^50 - 3 * q^51 + 8 * q^52 + 5 * q^53 + 9 * q^54 + 12 * q^55 + 6 * q^57 + 5 * q^58 + 17 * q^59 + 4 * q^60 + 13 * q^61 + 5 * q^62 + 5 * q^64 - 7 * q^65 + 3 * q^66 - 14 * q^67 + 16 * q^68 + 16 * q^69 - 8 * q^71 + 4 * q^72 + 6 * q^73 + 8 * q^75 + 2 * q^76 - 20 * q^78 + 11 * q^79 + 7 * q^80 - 19 * q^81 + 17 * q^82 + 2 * q^83 + 39 * q^85 + q^86 + 3 * q^87 + 9 * q^89 + 14 * q^90 - 5 * q^92 - 3 * q^93 - 4 * q^94 - 13 * q^95 + 3 * q^96 + 12 * q^97 + 10 * q^99

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