LMFDB - Embedded newform 8722.2.a.x.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8722,2,Mod(1,8722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8722, 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("8722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8722 = 2 \cdot 7^{2} \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8722.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:	$69.6455206430$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.135076.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 2 $ x^5 - x^4 - 5x^3 + 4x^2 + 4*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1246)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.15154$ of defining polynomial
Character	$\chi$	$=$	8722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.283134 q^{3} +1.00000 q^{4} +1.52242 q^{5} -0.283134 q^{6} +1.00000 q^{8} -2.91984 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.283134 q^{3} +1.00000 q^{4} +1.52242 q^{5} -0.283134 q^{6} +1.00000 q^{8} -2.91984 q^{9} +1.52242 q^{10} -2.81429 q^{11} -0.283134 q^{12} +6.32866 q^{13} -0.431050 q^{15} +1.00000 q^{16} +5.91984 q^{17} -2.91984 q^{18} -5.27817 q^{19} +1.52242 q^{20} -2.81429 q^{22} -2.94951 q^{23} -0.283134 q^{24} -2.68223 q^{25} +6.32866 q^{26} +1.67611 q^{27} -2.72807 q^{29} -0.431050 q^{30} -7.03015 q^{31} +1.00000 q^{32} +0.796822 q^{33} +5.91984 q^{34} -2.91984 q^{36} +2.35665 q^{37} -5.27817 q^{38} -1.79186 q^{39} +1.52242 q^{40} +7.62153 q^{41} +7.90614 q^{43} -2.81429 q^{44} -4.44522 q^{45} -2.94951 q^{46} +4.70713 q^{47} -0.283134 q^{48} -2.68223 q^{50} -1.67611 q^{51} +6.32866 q^{52} +9.16290 q^{53} +1.67611 q^{54} -4.28454 q^{55} +1.49443 q^{57} -2.72807 q^{58} +2.80724 q^{59} -0.431050 q^{60} +9.93978 q^{61} -7.03015 q^{62} +1.00000 q^{64} +9.63490 q^{65} +0.796822 q^{66} +11.9867 q^{67} +5.91984 q^{68} +0.835107 q^{69} +3.79891 q^{71} -2.91984 q^{72} +11.3403 q^{73} +2.35665 q^{74} +0.759431 q^{75} -5.27817 q^{76} -1.79186 q^{78} -6.17033 q^{79} +1.52242 q^{80} +8.28494 q^{81} +7.62153 q^{82} -1.89197 q^{83} +9.01249 q^{85} +7.90614 q^{86} +0.772411 q^{87} -2.81429 q^{88} +1.00000 q^{89} -4.44522 q^{90} -2.94951 q^{92} +1.99048 q^{93} +4.70713 q^{94} -8.03561 q^{95} -0.283134 q^{96} +6.86707 q^{97} +8.21726 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} + 6 q^{6} + 5 q^{8} + 7 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 + 6 * q^6 + 5 * q^8 + 7 * q^9	$ 5 q + 5 q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} + 6 q^{6} + 5 q^{8} + 7 q^{9} + 10 q^{10} - 8 q^{11} + 6 q^{12} + 8 q^{13} + 6 q^{15} + 5 q^{16} + 8 q^{17} + 7 q^{18} + 10 q^{19} + 10 q^{20} - 8 q^{22} - 2 q^{23} + 6 q^{24} + 17 q^{25} + 8 q^{26} + 24 q^{27} - 10 q^{29} + 6 q^{30} + 10 q^{31} + 5 q^{32} + 8 q^{34} + 7 q^{36} - 4 q^{37} + 10 q^{38} + 24 q^{39} + 10 q^{40} + 28 q^{41} - 10 q^{43} - 8 q^{44} + 12 q^{45} - 2 q^{46} + 10 q^{47} + 6 q^{48} + 17 q^{50} - 24 q^{51} + 8 q^{52} + 4 q^{53} + 24 q^{54} - 4 q^{55} + 2 q^{57} - 10 q^{58} + 10 q^{59} + 6 q^{60} + 16 q^{61} + 10 q^{62} + 5 q^{64} - 26 q^{65} + 8 q^{68} + 2 q^{69} - 16 q^{71} + 7 q^{72} - 10 q^{73} - 4 q^{74} + 10 q^{75} + 10 q^{76} + 24 q^{78} - 8 q^{79} + 10 q^{80} + 41 q^{81} + 28 q^{82} + 14 q^{83} + 18 q^{85} - 10 q^{86} - 22 q^{87} - 8 q^{88} + 5 q^{89} + 12 q^{90} - 2 q^{92} + 22 q^{93} + 10 q^{94} + 34 q^{95} + 6 q^{96} - 6 q^{97} - 8 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 + 6 * q^6 + 5 * q^8 + 7 * q^9 + 10 * q^10 - 8 * q^11 + 6 * q^12 + 8 * q^13 + 6 * q^15 + 5 * q^16 + 8 * q^17 + 7 * q^18 + 10 * q^19 + 10 * q^20 - 8 * q^22 - 2 * q^23 + 6 * q^24 + 17 * q^25 + 8 * q^26 + 24 * q^27 - 10 * q^29 + 6 * q^30 + 10 * q^31 + 5 * q^32 + 8 * q^34 + 7 * q^36 - 4 * q^37 + 10 * q^38 + 24 * q^39 + 10 * q^40 + 28 * q^41 - 10 * q^43 - 8 * q^44 + 12 * q^45 - 2 * q^46 + 10 * q^47 + 6 * q^48 + 17 * q^50 - 24 * q^51 + 8 * q^52 + 4 * q^53 + 24 * q^54 - 4 * q^55 + 2 * q^57 - 10 * q^58 + 10 * q^59 + 6 * q^60 + 16 * q^61 + 10 * q^62 + 5 * q^64 - 26 * q^65 + 8 * q^68 + 2 * q^69 - 16 * q^71 + 7 * q^72 - 10 * q^73 - 4 * q^74 + 10 * q^75 + 10 * q^76 + 24 * q^78 - 8 * q^79 + 10 * q^80 + 41 * q^81 + 28 * q^82 + 14 * q^83 + 18 * q^85 - 10 * q^86 - 22 * q^87 - 8 * q^88 + 5 * q^89 + 12 * q^90 - 2 * q^92 + 22 * q^93 + 10 * q^94 + 34 * q^95 + 6 * q^96 - 6 * q^97 - 8 * 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
$3$	−0.283134	−0.163468	−0.0817338	−	0.996654i	$-0.526046\pi$
$3$	−0.283134	−0.163468	−0.0817338	+	0.996654i	$0.526046\pi$
$4$	1.00000	0.500000
$5$	1.52242	0.680848	0.340424	−	0.940272i	$-0.389429\pi$
$5$	1.52242	0.680848	0.340424	+	0.940272i	$0.389429\pi$
$6$	−0.283134	−0.115589
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.91984	−0.973278
$10$	1.52242	0.481432
$11$	−2.81429	−0.848541	−0.424270	−	0.905536i	$-0.639469\pi$
$11$	−2.81429	−0.848541	−0.424270	+	0.905536i	$0.639469\pi$
$12$	−0.283134	−0.0817338
$13$	6.32866	1.75526	0.877628	−	0.479343i	$-0.159125\pi$
$13$	6.32866	1.75526	0.877628	+	0.479343i	$0.159125\pi$
$14$	0	0
$15$	−0.431050	−0.111297
$16$	1.00000	0.250000
$17$	5.91984	1.43577	0.717885	−	0.696161i	$-0.245110\pi$
$17$	5.91984	1.43577	0.717885	+	0.696161i	$0.245110\pi$
$18$	−2.91984	−0.688212
$19$	−5.27817	−1.21090	−0.605448	−	0.795885i	$-0.707006\pi$
$19$	−5.27817	−1.21090	−0.605448	+	0.795885i	$0.707006\pi$
$20$	1.52242	0.340424
$21$	0	0
$22$	−2.81429	−0.600009
$23$	−2.94951	−0.615015	−0.307508	−	0.951546i	$-0.599495\pi$
$23$	−2.94951	−0.615015	−0.307508	+	0.951546i	$0.599495\pi$
$24$	−0.283134	−0.0577945
$25$	−2.68223	−0.536446
$26$	6.32866	1.24115
$27$	1.67611	0.322567
$28$	0	0
$29$	−2.72807	−0.506590	−0.253295	−	0.967389i	$-0.581514\pi$
$29$	−2.72807	−0.506590	−0.253295	+	0.967389i	$0.581514\pi$
$30$	−0.431050	−0.0786986
$31$	−7.03015	−1.26265	−0.631326	−	0.775517i	$-0.717489\pi$
$31$	−7.03015	−1.26265	−0.631326	+	0.775517i	$0.717489\pi$
$32$	1.00000	0.176777
$33$	0.796822	0.138709
$34$	5.91984	1.01524
$35$	0	0
$36$	−2.91984	−0.486639
$37$	2.35665	0.387432	0.193716	−	0.981058i	$-0.437946\pi$
$37$	2.35665	0.387432	0.193716	+	0.981058i	$0.437946\pi$
$38$	−5.27817	−0.856233
$39$	−1.79186	−0.286927
$40$	1.52242	0.240716
$41$	7.62153	1.19028	0.595142	−	0.803621i	$-0.297096\pi$
$41$	7.62153	1.19028	0.595142	+	0.803621i	$0.297096\pi$
$42$	0	0
$43$	7.90614	1.20568	0.602838	−	0.797864i	$-0.294037\pi$
$43$	7.90614	1.20568	0.602838	+	0.797864i	$0.294037\pi$
$44$	−2.81429	−0.424270
$45$	−4.44522	−0.662655
$46$	−2.94951	−0.434881
$47$	4.70713	0.686606	0.343303	−	0.939225i	$-0.388454\pi$
$47$	4.70713	0.686606	0.343303	+	0.939225i	$0.388454\pi$
$48$	−0.283134	−0.0408669
$49$	0	0
$50$	−2.68223	−0.379325
$51$	−1.67611	−0.234702
$52$	6.32866	0.877628
$53$	9.16290	1.25862	0.629310	−	0.777154i	$-0.283337\pi$
$53$	9.16290	1.25862	0.629310	+	0.777154i	$0.283337\pi$
$54$	1.67611	0.228089
$55$	−4.28454	−0.577727
$56$	0	0
$57$	1.49443	0.197942
$58$	−2.72807	−0.358214
$59$	2.80724	0.365472	0.182736	−	0.983162i	$-0.441505\pi$
$59$	2.80724	0.365472	0.182736	+	0.983162i	$0.441505\pi$
$60$	−0.431050	−0.0556483
$61$	9.93978	1.27266	0.636329	−	0.771418i	$-0.280452\pi$
$61$	9.93978	1.27266	0.636329	+	0.771418i	$0.280452\pi$
$62$	−7.03015	−0.892830
$63$	0	0
$64$	1.00000	0.125000
$65$	9.63490	1.19506
$66$	0.796822	0.0980820
$67$	11.9867	1.46441	0.732205	−	0.681084i	$-0.238491\pi$
$67$	11.9867	1.46441	0.732205	+	0.681084i	$0.238491\pi$
$68$	5.91984	0.717885
$69$	0.835107	0.100535
$70$	0	0
$71$	3.79891	0.450848	0.225424	−	0.974261i	$-0.427623\pi$
$71$	3.79891	0.450848	0.225424	+	0.974261i	$0.427623\pi$
$72$	−2.91984	−0.344106
$73$	11.3403	1.32728	0.663640	−	0.748052i	$-0.269011\pi$
$73$	11.3403	1.32728	0.663640	+	0.748052i	$0.269011\pi$
$74$	2.35665	0.273956
$75$	0.759431	0.0876916
$76$	−5.27817	−0.605448
$77$	0	0
$78$	−1.79186	−0.202888
$79$	−6.17033	−0.694216	−0.347108	−	0.937825i	$-0.612836\pi$
$79$	−6.17033	−0.694216	−0.347108	+	0.937825i	$0.612836\pi$
$80$	1.52242	0.170212
$81$	8.28494	0.920549
$82$	7.62153	0.841657
$83$	−1.89197	−0.207670	−0.103835	−	0.994595i	$-0.533111\pi$
$83$	−1.89197	−0.207670	−0.103835	+	0.994595i	$0.533111\pi$
$84$	0	0
$85$	9.01249	0.977542
$86$	7.90614	0.852541
$87$	0.772411	0.0828111
$88$	−2.81429	−0.300004
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	−4.44522	−0.468568
$91$	0	0
$92$	−2.94951	−0.307508
$93$	1.99048	0.206403
$94$	4.70713	0.485504
$95$	−8.03561	−0.824436
$96$	−0.283134	−0.0288973
$97$	6.86707	0.697245	0.348622	−	0.937263i	$-0.386650\pi$
$97$	6.86707	0.697245	0.348622	+	0.937263i	$0.386650\pi$
$98$	0	0
$99$	8.21726	0.825866
$100$	−2.68223	−0.268223
$101$	3.95924	0.393959	0.196980	−	0.980408i	$-0.436887\pi$
$101$	3.95924	0.393959	0.196980	+	0.980408i	$0.436887\pi$
$102$	−1.67611	−0.165959
$103$	−5.97489	−0.588723	−0.294362	−	0.955694i	$-0.595107\pi$
$103$	−5.97489	−0.588723	−0.294362	+	0.955694i	$0.595107\pi$
$104$	6.32866	0.620577
$105$	0	0
$106$	9.16290	0.889979
$107$	−20.4155	−1.97364	−0.986820	−	0.161824i	$-0.948262\pi$
$107$	−20.4155	−1.97364	−0.986820	+	0.161824i	$0.948262\pi$
$108$	1.67611	0.161284
$109$	−13.4986	−1.29293	−0.646466	−	0.762943i	$-0.723754\pi$
$109$	−13.4986	−1.29293	−0.646466	+	0.762943i	$0.723754\pi$
$110$	−4.28454	−0.408515
$111$	−0.667250	−0.0633325
$112$	0	0
$113$	11.4204	1.07434	0.537172	−	0.843472i	$-0.319492\pi$
$113$	11.4204	1.07434	0.537172	+	0.843472i	$0.319492\pi$
$114$	1.49443	0.139966
$115$	−4.49040	−0.418732
$116$	−2.72807	−0.253295
$117$	−18.4787	−1.70835
$118$	2.80724	0.258427
$119$	0	0
$120$	−0.431050	−0.0393493
$121$	−3.07977	−0.279979
$122$	9.93978	0.899905
$123$	−2.15792	−0.194573
$124$	−7.03015	−0.631326
$125$	−11.6956	−1.04609
$126$	0	0
$127$	−7.02928	−0.623747	−0.311874	−	0.950124i	$-0.600957\pi$
$127$	−7.02928	−0.623747	−0.311874	+	0.950124i	$0.600957\pi$
$128$	1.00000	0.0883883
$129$	−2.23850	−0.197089
$130$	9.63490	0.845037
$131$	6.11905	0.534624	0.267312	−	0.963610i	$-0.413865\pi$
$131$	6.11905	0.534624	0.267312	+	0.963610i	$0.413865\pi$
$132$	0.796822	0.0693545
$133$	0	0
$134$	11.9867	1.03549
$135$	2.55174	0.219619
$136$	5.91984	0.507622
$137$	18.4828	1.57909	0.789544	−	0.613694i	$-0.210317\pi$
$137$	18.4828	1.57909	0.789544	+	0.613694i	$0.210317\pi$
$138$	0.835107	0.0710890
$139$	11.8710	1.00689	0.503444	−	0.864028i	$-0.332066\pi$
$139$	11.8710	1.00689	0.503444	+	0.864028i	$0.332066\pi$
$140$	0	0
$141$	−1.33275	−0.112238
$142$	3.79891	0.318798
$143$	−17.8107	−1.48941
$144$	−2.91984	−0.243320
$145$	−4.15328	−0.344911
$146$	11.3403	0.938528
$147$	0	0
$148$	2.35665	0.193716
$149$	−10.0751	−0.825382	−0.412691	−	0.910871i	$-0.635411\pi$
$149$	−10.0751	−0.825382	−0.412691	+	0.910871i	$0.635411\pi$
$150$	0.759431	0.0620073
$151$	18.7787	1.52819	0.764096	−	0.645103i	$-0.223186\pi$
$151$	18.7787	1.52819	0.764096	+	0.645103i	$0.223186\pi$
$152$	−5.27817	−0.428116
$153$	−17.2849	−1.39740
$154$	0	0
$155$	−10.7029	−0.859674
$156$	−1.79186	−0.143464
$157$	2.82282	0.225285	0.112643	−	0.993636i	$-0.464068\pi$
$157$	2.82282	0.225285	0.112643	+	0.993636i	$0.464068\pi$
$158$	−6.17033	−0.490885
$159$	−2.59433	−0.205744
$160$	1.52242	0.120358
$161$	0	0
$162$	8.28494	0.650926
$163$	11.7686	0.921791	0.460896	−	0.887454i	$-0.347528\pi$
$163$	11.7686	0.921791	0.460896	+	0.887454i	$0.347528\pi$
$164$	7.62153	0.595142
$165$	1.21310	0.0944397
$166$	−1.89197	−0.146845
$167$	−22.0583	−1.70692	−0.853461	−	0.521156i	$-0.825501\pi$
$167$	−22.0583	−1.70692	−0.853461	+	0.521156i	$0.825501\pi$
$168$	0	0
$169$	27.0520	2.08092
$170$	9.01249	0.691226
$171$	15.4114	1.17854
$172$	7.90614	0.602838
$173$	17.9857	1.36743	0.683714	−	0.729750i	$-0.260363\pi$
$173$	17.9857	1.36743	0.683714	+	0.729750i	$0.260363\pi$
$174$	0.772411	0.0585563
$175$	0	0
$176$	−2.81429	−0.212135
$177$	−0.794826	−0.0597428
$178$	1.00000	0.0749532
$179$	2.21109	0.165265	0.0826323	−	0.996580i	$-0.473667\pi$
$179$	2.21109	0.165265	0.0826323	+	0.996580i	$0.473667\pi$
$180$	−4.44522	−0.331327
$181$	−13.1317	−0.976069	−0.488034	−	0.872824i	$-0.662286\pi$
$181$	−13.1317	−0.976069	−0.488034	+	0.872824i	$0.662286\pi$
$182$	0	0
$183$	−2.81429	−0.208038
$184$	−2.94951	−0.217441
$185$	3.58782	0.263782
$186$	1.99048	0.145949
$187$	−16.6601	−1.21831
$188$	4.70713	0.343303
$189$	0	0
$190$	−8.03561	−0.582964
$191$	−2.80584	−0.203023	−0.101512	−	0.994834i	$-0.532368\pi$
$191$	−2.80584	−0.203023	−0.101512	+	0.994834i	$0.532368\pi$
$192$	−0.283134	−0.0204335
$193$	5.02738	0.361878	0.180939	−	0.983494i	$-0.442086\pi$
$193$	5.02738	0.361878	0.180939	+	0.983494i	$0.442086\pi$
$194$	6.86707	0.493027
$195$	−2.72797	−0.195354
$196$	0	0
$197$	−11.3342	−0.807530	−0.403765	−	0.914863i	$-0.632299\pi$
$197$	−11.3342	−0.807530	−0.403765	+	0.914863i	$0.632299\pi$
$198$	8.21726	0.583976
$199$	15.0694	1.06824	0.534122	−	0.845407i	$-0.320642\pi$
$199$	15.0694	1.06824	0.534122	+	0.845407i	$0.320642\pi$
$200$	−2.68223	−0.189662
$201$	−3.39385	−0.239384
$202$	3.95924	0.278571
$203$	0	0
$204$	−1.67611	−0.117351
$205$	11.6032	0.810402
$206$	−5.97489	−0.416290
$207$	8.61208	0.598581
$208$	6.32866	0.438814
$209$	14.8543	1.02749
$210$	0	0
$211$	−3.04632	−0.209717	−0.104859	−	0.994487i	$-0.533439\pi$
$211$	−3.04632	−0.209717	−0.104859	+	0.994487i	$0.533439\pi$
$212$	9.16290	0.629310
$213$	−1.07560	−0.0736990
$214$	−20.4155	−1.39557
$215$	12.0365	0.820881
$216$	1.67611	0.114045
$217$	0	0
$218$	−13.4986	−0.914241
$219$	−3.21082	−0.216967
$220$	−4.28454	−0.288864
$221$	37.4646	2.52014
$222$	−0.667250	−0.0447829
$223$	−0.865467	−0.0579559	−0.0289780	−	0.999580i	$-0.509225\pi$
$223$	−0.865467	−0.0579559	−0.0289780	+	0.999580i	$0.509225\pi$
$224$	0	0
$225$	7.83167	0.522111
$226$	11.4204	0.759677
$227$	−17.2417	−1.14437	−0.572185	−	0.820125i	$-0.693904\pi$
$227$	−17.2417	−1.14437	−0.572185	+	0.820125i	$0.693904\pi$
$228$	1.49443	0.0989711
$229$	22.3826	1.47909	0.739544	−	0.673109i	$-0.235041\pi$
$229$	22.3826	1.47909	0.739544	+	0.673109i	$0.235041\pi$
$230$	−4.49040	−0.296088
$231$	0	0
$232$	−2.72807	−0.179107
$233$	−6.70289	−0.439121	−0.219561	−	0.975599i	$-0.570462\pi$
$233$	−6.70289	−0.439121	−0.219561	+	0.975599i	$0.570462\pi$
$234$	−18.4787	−1.20799
$235$	7.16624	0.467474
$236$	2.80724	0.182736
$237$	1.74703	0.113482
$238$	0	0
$239$	−8.76876	−0.567204	−0.283602	−	0.958942i	$-0.591529\pi$
$239$	−8.76876	−0.567204	−0.283602	+	0.958942i	$0.591529\pi$
$240$	−0.431050	−0.0278241
$241$	−27.2361	−1.75443	−0.877215	−	0.480097i	$-0.840601\pi$
$241$	−27.2361	−1.75443	−0.877215	+	0.480097i	$0.840601\pi$
$242$	−3.07977	−0.197975
$243$	−7.37407	−0.473047
$244$	9.93978	0.636329
$245$	0	0
$246$	−2.15792	−0.137584
$247$	−33.4038	−2.12543
$248$	−7.03015	−0.446415
$249$	0.535681	0.0339474
$250$	−11.6956	−0.739695
$251$	24.9700	1.57609	0.788046	−	0.615616i	$-0.211093\pi$
$251$	24.9700	1.57609	0.788046	+	0.615616i	$0.211093\pi$
$252$	0	0
$253$	8.30078	0.521865
$254$	−7.02928	−0.441056
$255$	−2.55174	−0.159796
$256$	1.00000	0.0625000
$257$	10.9248	0.681470	0.340735	−	0.940159i	$-0.389324\pi$
$257$	10.9248	0.681470	0.340735	+	0.940159i	$0.389324\pi$
$258$	−2.23850	−0.139363
$259$	0	0
$260$	9.63490	0.597531
$261$	7.96552	0.493054
$262$	6.11905	0.378036
$263$	15.2838	0.942441	0.471220	−	0.882016i	$-0.343814\pi$
$263$	15.2838	0.942441	0.471220	+	0.882016i	$0.343814\pi$
$264$	0.796822	0.0490410
$265$	13.9498	0.856929
$266$	0	0
$267$	−0.283134	−0.0173275
$268$	11.9867	0.732205
$269$	−14.6450	−0.892924	−0.446462	−	0.894803i	$-0.647316\pi$
$269$	−14.6450	−0.892924	−0.446462	+	0.894803i	$0.647316\pi$
$270$	2.55174	0.155294
$271$	−12.0540	−0.732227	−0.366114	−	0.930570i	$-0.619312\pi$
$271$	−12.0540	−0.732227	−0.366114	+	0.930570i	$0.619312\pi$
$272$	5.91984	0.358943
$273$	0	0
$274$	18.4828	1.11658
$275$	7.54858	0.455196
$276$	0.835107	0.0502675
$277$	−22.9946	−1.38161	−0.690807	−	0.723039i	$-0.742745\pi$
$277$	−22.9946	−1.38161	−0.690807	+	0.723039i	$0.742745\pi$
$278$	11.8710	0.711977
$279$	20.5269	1.22891
$280$	0	0
$281$	−9.01251	−0.537641	−0.268821	−	0.963190i	$-0.586634\pi$
$281$	−9.01251	−0.537641	−0.268821	+	0.963190i	$0.586634\pi$
$282$	−1.33275	−0.0793641
$283$	13.7647	0.818225	0.409113	−	0.912484i	$-0.365838\pi$
$283$	13.7647	0.818225	0.409113	+	0.912484i	$0.365838\pi$
$284$	3.79891	0.225424
$285$	2.27516	0.134769
$286$	−17.8107	−1.05317
$287$	0	0
$288$	−2.91984	−0.172053
$289$	18.0444	1.06144
$290$	−4.15328	−0.243889
$291$	−1.94430	−0.113977
$292$	11.3403	0.663640
$293$	20.4051	1.19208	0.596038	−	0.802956i	$-0.296741\pi$
$293$	20.4051	1.19208	0.596038	+	0.802956i	$0.296741\pi$
$294$	0	0
$295$	4.27380	0.248831
$296$	2.35665	0.136978
$297$	−4.71705	−0.273711
$298$	−10.0751	−0.583633
$299$	−18.6665	−1.07951
$300$	0.759431	0.0438458
$301$	0	0
$302$	18.7787	1.08059
$303$	−1.12100	−0.0643996
$304$	−5.27817	−0.302724
$305$	15.1325	0.866487
$306$	−17.2849	−0.988114
$307$	15.8677	0.905615	0.452808	−	0.891608i	$-0.350422\pi$
$307$	15.8677	0.905615	0.452808	+	0.891608i	$0.350422\pi$
$308$	0	0
$309$	1.69170	0.0962372
$310$	−10.7029	−0.607881
$311$	20.5290	1.16409	0.582045	−	0.813156i	$-0.302253\pi$
$311$	20.5290	1.16409	0.582045	+	0.813156i	$0.302253\pi$
$312$	−1.79186	−0.101444
$313$	−2.67261	−0.151065	−0.0755325	−	0.997143i	$-0.524066\pi$
$313$	−2.67261	−0.151065	−0.0755325	+	0.997143i	$0.524066\pi$
$314$	2.82282	0.159301
$315$	0	0
$316$	−6.17033	−0.347108
$317$	−26.1210	−1.46710	−0.733551	−	0.679635i	$-0.762138\pi$
$317$	−26.1210	−1.46710	−0.733551	+	0.679635i	$0.762138\pi$
$318$	−2.59433	−0.145483
$319$	7.67759	0.429863
$320$	1.52242	0.0851060
$321$	5.78032	0.322626
$322$	0	0
$323$	−31.2459	−1.73857
$324$	8.28494	0.460275
$325$	−16.9749	−0.941600
$326$	11.7686	0.651805
$327$	3.82192	0.211353
$328$	7.62153	0.420829
$329$	0	0
$330$	1.21310	0.0667789
$331$	24.2456	1.33266	0.666330	−	0.745657i	$-0.267864\pi$
$331$	24.2456	1.33266	0.666330	+	0.745657i	$0.267864\pi$
$332$	−1.89197	−0.103835
$333$	−6.88104	−0.377079
$334$	−22.0583	−1.20698
$335$	18.2488	0.997040
$336$	0	0
$337$	34.9254	1.90251	0.951253	−	0.308413i	$-0.0997979\pi$
$337$	34.9254	1.90251	0.951253	+	0.308413i	$0.0997979\pi$
$338$	27.0520	1.47143
$339$	−3.23352	−0.175621
$340$	9.01249	0.488771
$341$	19.7849	1.07141
$342$	15.4114	0.833353
$343$	0	0
$344$	7.90614	0.426270
$345$	1.27139	0.0684491
$346$	17.9857	0.966918
$347$	−9.62659	−0.516782	−0.258391	−	0.966040i	$-0.583192\pi$
$347$	−9.62659	−0.516782	−0.258391	+	0.966040i	$0.583192\pi$
$348$	0.772411	0.0414056
$349$	0.529255	0.0283304	0.0141652	−	0.999900i	$-0.495491\pi$
$349$	0.529255	0.0283304	0.0141652	+	0.999900i	$0.495491\pi$
$350$	0	0
$351$	10.6075	0.566188
$352$	−2.81429	−0.150002
$353$	−20.1579	−1.07290	−0.536449	−	0.843933i	$-0.680235\pi$
$353$	−20.1579	−1.07290	−0.536449	+	0.843933i	$0.680235\pi$
$354$	−0.794826	−0.0422445
$355$	5.78355	0.306959
$356$	1.00000	0.0529999
$357$	0	0
$358$	2.21109	0.116860
$359$	17.0857	0.901748	0.450874	−	0.892588i	$-0.351112\pi$
$359$	17.0857	0.901748	0.450874	+	0.892588i	$0.351112\pi$
$360$	−4.44522	−0.234284
$361$	8.85912	0.466269
$362$	−13.1317	−0.690185
$363$	0.871987	0.0457675
$364$	0	0
$365$	17.2647	0.903675
$366$	−2.81429	−0.147105
$367$	−31.5635	−1.64760	−0.823800	−	0.566880i	$-0.808150\pi$
$367$	−31.5635	−1.64760	−0.823800	+	0.566880i	$0.808150\pi$
$368$	−2.94951	−0.153754
$369$	−22.2536	−1.15848
$370$	3.58782	0.186522
$371$	0	0
$372$	1.99048	0.103201
$373$	−8.84328	−0.457888	−0.228944	−	0.973440i	$-0.573527\pi$
$373$	−8.84328	−0.457888	−0.228944	+	0.973440i	$0.573527\pi$
$374$	−16.6601	−0.861475
$375$	3.31142	0.171001
$376$	4.70713	0.242752
$377$	−17.2651	−0.889196
$378$	0	0
$379$	13.4034	0.688486	0.344243	−	0.938881i	$-0.388136\pi$
$379$	13.4034	0.688486	0.344243	+	0.938881i	$0.388136\pi$
$380$	−8.03561	−0.412218
$381$	1.99023	0.101963
$382$	−2.80584	−0.143559
$383$	8.44442	0.431490	0.215745	−	0.976450i	$-0.430782\pi$
$383$	8.44442	0.431490	0.215745	+	0.976450i	$0.430782\pi$
$384$	−0.283134	−0.0144486
$385$	0	0
$386$	5.02738	0.255887
$387$	−23.0846	−1.17346
$388$	6.86707	0.348622
$389$	13.4954	0.684242	0.342121	−	0.939656i	$-0.388855\pi$
$389$	13.4954	0.684242	0.342121	+	0.939656i	$0.388855\pi$
$390$	−2.72797	−0.138136
$391$	−17.4606	−0.883021
$392$	0	0
$393$	−1.73251	−0.0873937
$394$	−11.3342	−0.571010
$395$	−9.39385	−0.472656
$396$	8.21726	0.412933
$397$	1.61816	0.0812133	0.0406067	−	0.999175i	$-0.487071\pi$
$397$	1.61816	0.0812133	0.0406067	+	0.999175i	$0.487071\pi$
$398$	15.0694	0.755363
$399$	0	0
$400$	−2.68223	−0.134112
$401$	1.80846	0.0903100	0.0451550	−	0.998980i	$-0.485622\pi$
$401$	1.80846	0.0903100	0.0451550	+	0.998980i	$0.485622\pi$
$402$	−3.39385	−0.169270
$403$	−44.4915	−2.21628
$404$	3.95924	0.196980
$405$	12.6132	0.626754
$406$	0	0
$407$	−6.63231	−0.328751
$408$	−1.67611	−0.0829797
$409$	22.1177	1.09365	0.546824	−	0.837248i	$-0.315837\pi$
$409$	22.1177	1.09365	0.546824	+	0.837248i	$0.315837\pi$
$410$	11.6032	0.573041
$411$	−5.23310	−0.258130
$412$	−5.97489	−0.294362
$413$	0	0
$414$	8.61208	0.423261
$415$	−2.88037	−0.141392
$416$	6.32866	0.310288
$417$	−3.36109	−0.164593
$418$	14.8543	0.726548
$419$	5.96489	0.291404	0.145702	−	0.989329i	$-0.453456\pi$
$419$	5.96489	0.291404	0.145702	+	0.989329i	$0.453456\pi$
$420$	0	0
$421$	6.54870	0.319164	0.159582	−	0.987185i	$-0.448985\pi$
$421$	6.54870	0.319164	0.159582	+	0.987185i	$0.448985\pi$
$422$	−3.04632	−0.148292
$423$	−13.7441	−0.668259
$424$	9.16290	0.444990
$425$	−15.8784	−0.770214
$426$	−1.07560	−0.0521131
$427$	0	0
$428$	−20.4155	−0.986820
$429$	5.04282	0.243470
$430$	12.0365	0.580451
$431$	−6.23620	−0.300387	−0.150194	−	0.988657i	$-0.547990\pi$
$431$	−6.23620	−0.300387	−0.150194	+	0.988657i	$0.547990\pi$
$432$	1.67611	0.0806418
$433$	33.0255	1.58710	0.793551	−	0.608504i	$-0.208230\pi$
$433$	33.0255	1.58710	0.793551	+	0.608504i	$0.208230\pi$
$434$	0	0
$435$	1.17594	0.0563818
$436$	−13.4986	−0.646466
$437$	15.5680	0.744720
$438$	−3.21082	−0.153419
$439$	23.2687	1.11055	0.555277	−	0.831665i	$-0.312612\pi$
$439$	23.2687	1.11055	0.555277	+	0.831665i	$0.312612\pi$
$440$	−4.28454	−0.204257
$441$	0	0
$442$	37.4646	1.78201
$443$	−22.3258	−1.06073	−0.530365	−	0.847769i	$-0.677945\pi$
$443$	−22.3258	−1.06073	−0.530365	+	0.847769i	$0.677945\pi$
$444$	−0.667250	−0.0316663
$445$	1.52242	0.0721697
$446$	−0.865467	−0.0409810
$447$	2.85260	0.134923
$448$	0	0
$449$	19.2679	0.909311	0.454655	−	0.890667i	$-0.349762\pi$
$449$	19.2679	0.909311	0.454655	+	0.890667i	$0.349762\pi$
$450$	7.83167	0.369189
$451$	−21.4492	−1.01000
$452$	11.4204	0.537172
$453$	−5.31690	−0.249810
$454$	−17.2417	−0.809191
$455$	0	0
$456$	1.49443	0.0699832
$457$	1.73774	0.0812878	0.0406439	−	0.999174i	$-0.487059\pi$
$457$	1.73774	0.0812878	0.0406439	+	0.999174i	$0.487059\pi$
$458$	22.3826	1.04587
$459$	9.92228	0.463132
$460$	−4.49040	−0.209366
$461$	25.7938	1.20134	0.600669	−	0.799498i	$-0.294901\pi$
$461$	25.7938	1.20134	0.600669	+	0.799498i	$0.294901\pi$
$462$	0	0
$463$	−12.4164	−0.577037	−0.288519	−	0.957474i	$-0.593163\pi$
$463$	−12.4164	−0.577037	−0.288519	+	0.957474i	$0.593163\pi$
$464$	−2.72807	−0.126648
$465$	3.03035	0.140529
$466$	−6.70289	−0.310505
$467$	−18.2629	−0.845105	−0.422552	−	0.906339i	$-0.638866\pi$
$467$	−18.2629	−0.845105	−0.422552	+	0.906339i	$0.638866\pi$
$468$	−18.4787	−0.854176
$469$	0	0
$470$	7.16624	0.330554
$471$	−0.799236	−0.0368268
$472$	2.80724	0.129214
$473$	−22.2502	−1.02306
$474$	1.74703	0.0802438
$475$	14.1573	0.649581
$476$	0	0
$477$	−26.7541	−1.22499
$478$	−8.76876	−0.401074
$479$	17.9655	0.820865	0.410432	−	0.911891i	$-0.365378\pi$
$479$	17.9655	0.820865	0.410432	+	0.911891i	$0.365378\pi$
$480$	−0.431050	−0.0196746
$481$	14.9145	0.680042
$482$	−27.2361	−1.24057
$483$	0	0
$484$	−3.07977	−0.139989
$485$	10.4546	0.474718
$486$	−7.37407	−0.334495
$487$	10.1077	0.458022	0.229011	−	0.973424i	$-0.426451\pi$
$487$	10.1077	0.458022	0.229011	+	0.973424i	$0.426451\pi$
$488$	9.93978	0.449953
$489$	−3.33211	−0.150683
$490$	0	0
$491$	−6.94899	−0.313603	−0.156802	−	0.987630i	$-0.550118\pi$
$491$	−6.94899	−0.313603	−0.156802	+	0.987630i	$0.550118\pi$
$492$	−2.15792	−0.0972864
$493$	−16.1497	−0.727348
$494$	−33.4038	−1.50291
$495$	12.5101	0.562289
$496$	−7.03015	−0.315663
$497$	0	0
$498$	0.535681	0.0240044
$499$	−32.3015	−1.44601	−0.723007	−	0.690841i	$-0.757240\pi$
$499$	−32.3015	−1.44601	−0.723007	+	0.690841i	$0.757240\pi$
$500$	−11.6956	−0.523043
$501$	6.24546	0.279027
$502$	24.9700	1.11447
$503$	−30.5663	−1.36289	−0.681443	−	0.731871i	$-0.738647\pi$
$503$	−30.5663	−1.36289	−0.681443	+	0.731871i	$0.738647\pi$
$504$	0	0
$505$	6.02764	0.268226
$506$	8.30078	0.369015
$507$	−7.65934	−0.340163
$508$	−7.02928	−0.311874
$509$	17.3284	0.768067	0.384034	−	0.923319i	$-0.374535\pi$
$509$	17.3284	0.768067	0.384034	+	0.923319i	$0.374535\pi$
$510$	−2.55174	−0.112993
$511$	0	0
$512$	1.00000	0.0441942
$513$	−8.84679	−0.390595
$514$	10.9248	0.481872
$515$	−9.09630	−0.400831
$516$	−2.23850	−0.0985444
$517$	−13.2472	−0.582613
$518$	0	0
$519$	−5.09237	−0.223530
$520$	9.63490	0.422518
$521$	6.49405	0.284509	0.142255	−	0.989830i	$-0.454565\pi$
$521$	6.49405	0.284509	0.142255	+	0.989830i	$0.454565\pi$
$522$	7.96552	0.348642
$523$	−0.554376	−0.0242411	−0.0121206	−	0.999927i	$-0.503858\pi$
$523$	−0.554376	−0.0242411	−0.0121206	+	0.999927i	$0.503858\pi$
$524$	6.11905	0.267312
$525$	0	0
$526$	15.2838	0.666406
$527$	−41.6173	−1.81288
$528$	0.796822	0.0346772
$529$	−14.3004	−0.621756
$530$	13.9498	0.605940
$531$	−8.19668	−0.355706
$532$	0	0
$533$	48.2341	2.08925
$534$	−0.283134	−0.0122524
$535$	−31.0810	−1.34375
$536$	11.9867	0.517747
$537$	−0.626035	−0.0270154
$538$	−14.6450	−0.631392
$539$	0	0
$540$	2.55174	0.109810
$541$	−41.1860	−1.77072	−0.885362	−	0.464902i	$-0.846090\pi$
$541$	−41.1860	−1.77072	−0.885362	+	0.464902i	$0.846090\pi$
$542$	−12.0540	−0.517763
$543$	3.71802	0.159556
$544$	5.91984	0.253811
$545$	−20.5506	−0.880290
$546$	0	0
$547$	−35.8790	−1.53408	−0.767038	−	0.641601i	$-0.778270\pi$
$547$	−35.8790	−1.53408	−0.767038	+	0.641601i	$0.778270\pi$
$548$	18.4828	0.789544
$549$	−29.0225	−1.23865
$550$	7.54858	0.321872
$551$	14.3992	0.613428
$552$	0.835107	0.0355445
$553$	0	0
$554$	−22.9946	−0.976949
$555$	−1.01584	−0.0431198
$556$	11.8710	0.503444
$557$	36.4641	1.54504	0.772518	−	0.634993i	$-0.218997\pi$
$557$	36.4641	1.54504	0.772518	+	0.634993i	$0.218997\pi$
$558$	20.5269	0.868972
$559$	50.0353	2.11627
$560$	0	0
$561$	4.71705	0.199154
$562$	−9.01251	−0.380170
$563$	20.9026	0.880939	0.440469	−	0.897768i	$-0.354812\pi$
$563$	20.9026	0.880939	0.440469	+	0.897768i	$0.354812\pi$
$564$	−1.33275	−0.0561189
$565$	17.3867	0.731465
$566$	13.7647	0.578573
$567$	0	0
$568$	3.79891	0.159399
$569$	−9.38887	−0.393602	−0.196801	−	0.980443i	$-0.563055\pi$
$569$	−9.38887	−0.393602	−0.196801	+	0.980443i	$0.563055\pi$
$570$	2.27516	0.0952958
$571$	−4.51926	−0.189125	−0.0945626	−	0.995519i	$-0.530145\pi$
$571$	−4.51926	−0.189125	−0.0945626	+	0.995519i	$0.530145\pi$
$572$	−17.8107	−0.744703
$573$	0.794428	0.0331877
$574$	0	0
$575$	7.91126	0.329923
$576$	−2.91984	−0.121660
$577$	−40.1679	−1.67221	−0.836106	−	0.548568i	$-0.815173\pi$
$577$	−40.1679	−1.67221	−0.836106	+	0.548568i	$0.815173\pi$
$578$	18.0444	0.750550
$579$	−1.42342	−0.0591554
$580$	−4.15328	−0.172456
$581$	0	0
$582$	−1.94430	−0.0805939
$583$	−25.7871	−1.06799
$584$	11.3403	0.469264
$585$	−28.1323	−1.16313
$586$	20.4051	0.842925
$587$	22.1777	0.915373	0.457687	−	0.889114i	$-0.348678\pi$
$587$	22.1777	0.915373	0.457687	+	0.889114i	$0.348678\pi$
$588$	0	0
$589$	37.1064	1.52894
$590$	4.27380	0.175950
$591$	3.20911	0.132005
$592$	2.35665	0.0968579
$593$	−18.8924	−0.775820	−0.387910	−	0.921697i	$-0.626803\pi$
$593$	−18.8924	−0.775820	−0.387910	+	0.921697i	$0.626803\pi$
$594$	−4.71705	−0.193543
$595$	0	0
$596$	−10.0751	−0.412691
$597$	−4.26667	−0.174623
$598$	−18.6665	−0.763328
$599$	−29.2882	−1.19668	−0.598341	−	0.801241i	$-0.704173\pi$
$599$	−29.2882	−1.19668	−0.598341	+	0.801241i	$0.704173\pi$
$600$	0.759431	0.0310037
$601$	−26.3732	−1.07579	−0.537893	−	0.843013i	$-0.680779\pi$
$601$	−26.3732	−1.07579	−0.537893	+	0.843013i	$0.680779\pi$
$602$	0	0
$603$	−34.9992	−1.42528
$604$	18.7787	0.764096
$605$	−4.68871	−0.190623
$606$	−1.12100	−0.0455374
$607$	18.5788	0.754089	0.377044	−	0.926195i	$-0.376940\pi$
$607$	18.5788	0.754089	0.377044	+	0.926195i	$0.376940\pi$
$608$	−5.27817	−0.214058
$609$	0	0
$610$	15.1325	0.612699
$611$	29.7899	1.20517
$612$	−17.2849	−0.698702
$613$	−42.7127	−1.72515	−0.862574	−	0.505931i	$-0.831149\pi$
$613$	−42.7127	−1.72515	−0.862574	+	0.505931i	$0.831149\pi$
$614$	15.8677	0.640367
$615$	−3.28526	−0.132474
$616$	0	0
$617$	5.36228	0.215877	0.107939	−	0.994158i	$-0.465575\pi$
$617$	5.36228	0.215877	0.107939	+	0.994158i	$0.465575\pi$
$618$	1.69170	0.0680500
$619$	−34.5682	−1.38941	−0.694707	−	0.719292i	$-0.744466\pi$
$619$	−34.5682	−1.38941	−0.694707	+	0.719292i	$0.744466\pi$
$620$	−10.7029	−0.429837
$621$	−4.94370	−0.198384
$622$	20.5290	0.823136
$623$	0	0
$624$	−1.79186	−0.0717319
$625$	−4.39449	−0.175779
$626$	−2.67261	−0.106819
$627$	−4.20576	−0.167962
$628$	2.82282	0.112643
$629$	13.9510	0.556263
$630$	0	0
$631$	3.28964	0.130959	0.0654793	−	0.997854i	$-0.479142\pi$
$631$	3.28964	0.130959	0.0654793	+	0.997854i	$0.479142\pi$
$632$	−6.17033	−0.245443
$633$	0.862517	0.0342820
$634$	−26.1210	−1.03740
$635$	−10.7015	−0.424677
$636$	−2.59433	−0.102872
$637$	0	0
$638$	7.67759	0.303959
$639$	−11.0922	−0.438801
$640$	1.52242	0.0601790
$641$	−33.5365	−1.32461	−0.662306	−	0.749233i	$-0.730422\pi$
$641$	−33.5365	−1.32461	−0.662306	+	0.749233i	$0.730422\pi$
$642$	5.78032	0.228131
$643$	40.3871	1.59271	0.796355	−	0.604829i	$-0.206759\pi$
$643$	40.3871	1.59271	0.796355	+	0.604829i	$0.206759\pi$
$644$	0	0
$645$	−3.40794	−0.134188
$646$	−31.2459	−1.22935
$647$	31.6134	1.24285	0.621425	−	0.783474i	$-0.286554\pi$
$647$	31.6134	1.24285	0.621425	+	0.783474i	$0.286554\pi$
$648$	8.28494	0.325463
$649$	−7.90039	−0.310117
$650$	−16.9749	−0.665812
$651$	0	0
$652$	11.7686	0.460896
$653$	−16.0273	−0.627195	−0.313598	−	0.949556i	$-0.601534\pi$
$653$	−16.0273	−0.627195	−0.313598	+	0.949556i	$0.601534\pi$
$654$	3.82192	0.149449
$655$	9.31578	0.363998
$656$	7.62153	0.297571
$657$	−33.1117	−1.29181
$658$	0	0
$659$	7.29424	0.284143	0.142072	−	0.989856i	$-0.454624\pi$
$659$	7.29424	0.284143	0.142072	+	0.989856i	$0.454624\pi$
$660$	1.21310	0.0472198
$661$	−37.5660	−1.46115	−0.730574	−	0.682834i	$-0.760747\pi$
$661$	−37.5660	−1.46115	−0.730574	+	0.682834i	$0.760747\pi$
$662$	24.2456	0.942332
$663$	−10.6075	−0.411962
$664$	−1.89197	−0.0734226
$665$	0	0
$666$	−6.88104	−0.266635
$667$	8.04648	0.311561
$668$	−22.0583	−0.853461
$669$	0.245043	0.00947392
$670$	18.2488	0.705014
$671$	−27.9734	−1.07990
$672$	0	0
$673$	44.1975	1.70369	0.851845	−	0.523794i	$-0.175484\pi$
$673$	44.1975	1.70369	0.851845	+	0.523794i	$0.175484\pi$
$674$	34.9254	1.34527
$675$	−4.49571	−0.173040
$676$	27.0520	1.04046
$677$	−13.0993	−0.503446	−0.251723	−	0.967799i	$-0.580997\pi$
$677$	−13.0993	−0.503446	−0.251723	+	0.967799i	$0.580997\pi$
$678$	−3.23352	−0.124183
$679$	0	0
$680$	9.01249	0.345613
$681$	4.88171	0.187067
$682$	19.7849	0.757603
$683$	38.9960	1.49214	0.746070	−	0.665867i	$-0.231938\pi$
$683$	38.9960	1.49214	0.746070	+	0.665867i	$0.231938\pi$
$684$	15.4114	0.589269
$685$	28.1386	1.07512
$686$	0	0
$687$	−6.33729	−0.241783
$688$	7.90614	0.301419
$689$	57.9889	2.20920
$690$	1.27139	0.0484008
$691$	−30.3793	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$691$	−30.3793	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$692$	17.9857	0.683714
$693$	0	0
$694$	−9.62659	−0.365420
$695$	18.0727	0.685537
$696$	0.772411	0.0292782
$697$	45.1182	1.70897
$698$	0.529255	0.0200326
$699$	1.89782	0.0717821
$700$	0	0
$701$	−23.7607	−0.897431	−0.448715	−	0.893675i	$-0.648118\pi$
$701$	−23.7607	−0.897431	−0.448715	+	0.893675i	$0.648118\pi$
$702$	10.6075	0.400355
$703$	−12.4388	−0.469139
$704$	−2.81429	−0.106068
$705$	−2.02901	−0.0764169
$706$	−20.1579	−0.758653
$707$	0	0
$708$	−0.794826	−0.0298714
$709$	−40.0967	−1.50586	−0.752932	−	0.658098i	$-0.771361\pi$
$709$	−40.0967	−1.50586	−0.752932	+	0.658098i	$0.771361\pi$
$710$	5.78355	0.217053
$711$	18.0163	0.675666
$712$	1.00000	0.0374766
$713$	20.7355	0.776550
$714$	0	0
$715$	−27.1154	−1.01406
$716$	2.21109	0.0826323
$717$	2.48274	0.0927195
$718$	17.0857	0.637632
$719$	36.7711	1.37133	0.685665	−	0.727917i	$-0.259511\pi$
$719$	36.7711	1.37133	0.685665	+	0.727917i	$0.259511\pi$
$720$	−4.44522	−0.165664
$721$	0	0
$722$	8.85912	0.329702
$723$	7.71147	0.286793
$724$	−13.1317	−0.488034
$725$	7.31732	0.271759
$726$	0.871987	0.0323625
$727$	4.85895	0.180208	0.0901042	−	0.995932i	$-0.471280\pi$
$727$	4.85895	0.180208	0.0901042	+	0.995932i	$0.471280\pi$
$728$	0	0
$729$	−22.7670	−0.843221
$730$	17.2647	0.638995
$731$	46.8030	1.73107
$732$	−2.81429	−0.104019
$733$	6.34626	0.234404	0.117202	−	0.993108i	$-0.462607\pi$
$733$	6.34626	0.234404	0.117202	+	0.993108i	$0.462607\pi$
$734$	−31.5635	−1.16503
$735$	0	0
$736$	−2.94951	−0.108720
$737$	−33.7341	−1.24261
$738$	−22.2536	−0.819167
$739$	−7.24937	−0.266672	−0.133336	−	0.991071i	$-0.542569\pi$
$739$	−7.24937	−0.266672	−0.133336	+	0.991071i	$0.542569\pi$
$740$	3.58782	0.131891
$741$	9.45775	0.347439
$742$	0	0
$743$	3.45805	0.126863	0.0634317	−	0.997986i	$-0.479795\pi$
$743$	3.45805	0.126863	0.0634317	+	0.997986i	$0.479795\pi$
$744$	1.99048	0.0729744
$745$	−15.3385	−0.561959
$746$	−8.84328	−0.323775
$747$	5.52423	0.202121
$748$	−16.6601	−0.609155
$749$	0	0
$750$	3.31142	0.120916
$751$	47.4680	1.73213	0.866066	−	0.499929i	$-0.166641\pi$
$751$	47.4680	1.73213	0.866066	+	0.499929i	$0.166641\pi$
$752$	4.70713	0.171651
$753$	−7.06986	−0.257640
$754$	−17.2651	−0.628756
$755$	28.5892	1.04047
$756$	0	0
$757$	−43.8444	−1.59355	−0.796776	−	0.604275i	$-0.793463\pi$
$757$	−43.8444	−1.59355	−0.796776	+	0.604275i	$0.793463\pi$
$758$	13.4034	0.486833
$759$	−2.35023	−0.0853081
$760$	−8.03561	−0.291482
$761$	24.8638	0.901313	0.450657	−	0.892697i	$-0.351190\pi$
$761$	24.8638	0.901313	0.450657	+	0.892697i	$0.351190\pi$
$762$	1.99023	0.0720984
$763$	0	0
$764$	−2.80584	−0.101512
$765$	−26.3150	−0.951420
$766$	8.44442	0.305109
$767$	17.7661	0.641496
$768$	−0.283134	−0.0102167
$769$	−21.4855	−0.774786	−0.387393	−	0.921915i	$-0.626624\pi$
$769$	−21.4855	−0.774786	−0.387393	+	0.921915i	$0.626624\pi$
$770$	0	0
$771$	−3.09318	−0.111398
$772$	5.02738	0.180939
$773$	−29.8108	−1.07222	−0.536110	−	0.844148i	$-0.680107\pi$
$773$	−29.8108	−1.07222	−0.536110	+	0.844148i	$0.680107\pi$
$774$	−23.0846	−0.829760
$775$	18.8565	0.677345
$776$	6.86707	0.246513
$777$	0	0
$778$	13.4954	0.483832
$779$	−40.2278	−1.44131
$780$	−2.72797	−0.0976770
$781$	−10.6912	−0.382563
$782$	−17.4606	−0.624390
$783$	−4.57254	−0.163409
$784$	0	0
$785$	4.29752	0.153385
$786$	−1.73251	−0.0617967
$787$	−37.3359	−1.33088	−0.665441	−	0.746451i	$-0.731756\pi$
$787$	−37.3359	−1.33088	−0.665441	+	0.746451i	$0.731756\pi$
$788$	−11.3342	−0.403765
$789$	−4.32737	−0.154059
$790$	−9.39385	−0.334218
$791$	0	0
$792$	8.21726	0.291988
$793$	62.9055	2.23384
$794$	1.61816	0.0574265
$795$	−3.94966	−0.140080
$796$	15.0694	0.534122
$797$	−16.5159	−0.585022	−0.292511	−	0.956262i	$-0.594491\pi$
$797$	−16.5159	−0.585022	−0.292511	+	0.956262i	$0.594491\pi$
$798$	0	0
$799$	27.8655	0.985809
$800$	−2.68223	−0.0948312
$801$	−2.91984	−0.103167
$802$	1.80846	0.0638588
$803$	−31.9148	−1.12625
$804$	−3.39385	−0.119692
$805$	0	0
$806$	−44.4915	−1.56714
$807$	4.14651	0.145964
$808$	3.95924	0.139286
$809$	−18.0395	−0.634237	−0.317118	−	0.948386i	$-0.602715\pi$
$809$	−18.0395	−0.634237	−0.317118	+	0.948386i	$0.602715\pi$
$810$	12.6132	0.443182
$811$	−42.1972	−1.48174	−0.740872	−	0.671646i	$-0.765588\pi$
$811$	−42.1972	−1.48174	−0.740872	+	0.671646i	$0.765588\pi$
$812$	0	0
$813$	3.41290	0.119695
$814$	−6.63231	−0.232462
$815$	17.9168	0.627600
$816$	−1.67611	−0.0586755
$817$	−41.7300	−1.45995
$818$	22.1177	0.773326
$819$	0	0
$820$	11.6032	0.405201
$821$	25.1379	0.877319	0.438660	−	0.898653i	$-0.355453\pi$
$821$	25.1379	0.877319	0.438660	+	0.898653i	$0.355453\pi$
$822$	−5.23310	−0.182525
$823$	−33.6549	−1.17314	−0.586569	−	0.809900i	$-0.699522\pi$
$823$	−33.6549	−1.17314	−0.586569	+	0.809900i	$0.699522\pi$
$824$	−5.97489	−0.208145
$825$	−2.13726	−0.0744099
$826$	0	0
$827$	−8.47416	−0.294675	−0.147338	−	0.989086i	$-0.547070\pi$
$827$	−8.47416	−0.294675	−0.147338	+	0.989086i	$0.547070\pi$
$828$	8.61208	0.299290
$829$	22.3732	0.777055	0.388527	−	0.921437i	$-0.372984\pi$
$829$	22.3732	0.777055	0.388527	+	0.921437i	$0.372984\pi$
$830$	−2.88037	−0.0999792
$831$	6.51057	0.225849
$832$	6.32866	0.219407
$833$	0	0
$834$	−3.36109	−0.116385
$835$	−33.5821	−1.16215
$836$	14.8543	0.513747
$837$	−11.7833	−0.407290
$838$	5.96489	0.206054
$839$	9.14804	0.315826	0.157913	−	0.987453i	$-0.449524\pi$
$839$	9.14804	0.315826	0.157913	+	0.987453i	$0.449524\pi$
$840$	0	0
$841$	−21.5576	−0.743366
$842$	6.54870	0.225683
$843$	2.55175	0.0878869
$844$	−3.04632	−0.104859
$845$	41.1845	1.41679
$846$	−13.7441	−0.472530
$847$	0	0
$848$	9.16290	0.314655
$849$	−3.89725	−0.133753
$850$	−15.8784	−0.544623
$851$	−6.95098	−0.238276
$852$	−1.07560	−0.0368495
$853$	33.6390	1.15178	0.575889	−	0.817528i	$-0.304656\pi$
$853$	33.6390	1.15178	0.575889	+	0.817528i	$0.304656\pi$
$854$	0	0
$855$	23.4627	0.802406
$856$	−20.4155	−0.697787
$857$	25.4442	0.869158	0.434579	−	0.900634i	$-0.356897\pi$
$857$	25.4442	0.869158	0.434579	+	0.900634i	$0.356897\pi$
$858$	5.04282	0.172159
$859$	8.14294	0.277834	0.138917	−	0.990304i	$-0.455638\pi$
$859$	8.14294	0.277834	0.138917	+	0.990304i	$0.455638\pi$
$860$	12.0365	0.410441
$861$	0	0
$862$	−6.23620	−0.212406
$863$	−3.67074	−0.124954	−0.0624768	−	0.998046i	$-0.519900\pi$
$863$	−3.67074	−0.124954	−0.0624768	+	0.998046i	$0.519900\pi$
$864$	1.67611	0.0570223
$865$	27.3818	0.931011
$866$	33.0255	1.12225
$867$	−5.10900	−0.173511
$868$	0	0
$869$	17.3651	0.589071
$870$	1.17594	0.0398679
$871$	75.8599	2.57041
$872$	−13.4986	−0.457121
$873$	−20.0507	−0.678613
$874$	15.5680	0.526596
$875$	0	0
$876$	−3.21082	−0.108484
$877$	4.24480	0.143337	0.0716683	−	0.997429i	$-0.477168\pi$
$877$	4.24480	0.143337	0.0716683	+	0.997429i	$0.477168\pi$
$878$	23.2687	0.785281
$879$	−5.77737	−0.194866
$880$	−4.28454	−0.144432
$881$	−8.10456	−0.273049	−0.136525	−	0.990637i	$-0.543593\pi$
$881$	−8.10456	−0.273049	−0.136525	+	0.990637i	$0.543593\pi$
$882$	0	0
$883$	16.6835	0.561444	0.280722	−	0.959789i	$-0.409426\pi$
$883$	16.6835	0.561444	0.280722	+	0.959789i	$0.409426\pi$
$884$	37.4646	1.26007
$885$	−1.21006	−0.0406757
$886$	−22.3258	−0.750050
$887$	48.8830	1.64133	0.820666	−	0.571408i	$-0.193603\pi$
$887$	48.8830	1.64133	0.820666	+	0.571408i	$0.193603\pi$
$888$	−0.667250	−0.0223914
$889$	0	0
$890$	1.52242	0.0510317
$891$	−23.3162	−0.781123
$892$	−0.865467	−0.0289780
$893$	−24.8451	−0.831408
$894$	2.85260	0.0954051
$895$	3.36621	0.112520
$896$	0	0
$897$	5.28511	0.176465
$898$	19.2679	0.642980
$899$	19.1788	0.639648
$900$	7.83167	0.261056
$901$	54.2428	1.80709
$902$	−21.4492	−0.714180
$903$	0	0
$904$	11.4204	0.379838
$905$	−19.9919	−0.664554
$906$	−5.31690	−0.176642
$907$	9.40259	0.312208	0.156104	−	0.987741i	$-0.450107\pi$
$907$	9.40259	0.312208	0.156104	+	0.987741i	$0.450107\pi$
$908$	−17.2417	−0.572185
$909$	−11.5603	−0.383432
$910$	0	0
$911$	21.6058	0.715832	0.357916	−	0.933754i	$-0.383487\pi$
$911$	21.6058	0.715832	0.357916	+	0.933754i	$0.383487\pi$
$912$	1.49443	0.0494856
$913$	5.32455	0.176217
$914$	1.73774	0.0574792
$915$	−4.28454	−0.141642
$916$	22.3826	0.739544
$917$	0	0
$918$	9.92228	0.327484
$919$	−25.7910	−0.850765	−0.425383	−	0.905014i	$-0.639860\pi$
$919$	−25.7910	−0.850765	−0.425383	+	0.905014i	$0.639860\pi$
$920$	−4.49040	−0.148044
$921$	−4.49268	−0.148039
$922$	25.7938	0.849475
$923$	24.0420	0.791353
$924$	0	0
$925$	−6.32109	−0.207836
$926$	−12.4164	−0.408027
$927$	17.4457	0.572992
$928$	−2.72807	−0.0895534
$929$	−5.68373	−0.186477	−0.0932386	−	0.995644i	$-0.529722\pi$
$929$	−5.68373	−0.186477	−0.0932386	+	0.995644i	$0.529722\pi$
$930$	3.03035	0.0993689
$931$	0	0
$932$	−6.70289	−0.219561
$933$	−5.81245	−0.190291
$934$	−18.2629	−0.597579
$935$	−25.3638	−0.829484
$936$	−18.4787	−0.603994
$937$	1.18573	0.0387361	0.0193680	−	0.999812i	$-0.493835\pi$
$937$	1.18573	0.0387361	0.0193680	+	0.999812i	$0.493835\pi$
$938$	0	0
$939$	0.756708	0.0246942
$940$	7.16624	0.233737
$941$	56.4467	1.84011	0.920055	−	0.391790i	$-0.128144\pi$
$941$	56.4467	1.84011	0.920055	+	0.391790i	$0.128144\pi$
$942$	−0.799236	−0.0260405
$943$	−22.4798	−0.732042
$944$	2.80724	0.0913679
$945$	0	0
$946$	−22.2502	−0.723416
$947$	59.4281	1.93115	0.965577	−	0.260116i	$-0.0837608\pi$
$947$	59.4281	1.93115	0.965577	+	0.260116i	$0.0837608\pi$
$948$	1.74703	0.0567409
$949$	71.7688	2.32971
$950$	14.1573	0.459323
$951$	7.39575	0.239824
$952$	0	0
$953$	−2.39444	−0.0775635	−0.0387817	−	0.999248i	$-0.512348\pi$
$953$	−2.39444	−0.0775635	−0.0387817	+	0.999248i	$0.512348\pi$
$954$	−26.7541	−0.866197
$955$	−4.27167	−0.138228
$956$	−8.76876	−0.283602
$957$	−2.17379	−0.0702686
$958$	17.9655	0.580439
$959$	0	0
$960$	−0.431050	−0.0139121
$961$	18.4230	0.594291
$962$	14.9145	0.480862
$963$	59.6098	1.92090
$964$	−27.2361	−0.877215
$965$	7.65379	0.246384
$966$	0	0
$967$	15.4892	0.498099	0.249049	−	0.968491i	$-0.419882\pi$
$967$	15.4892	0.498099	0.249049	+	0.968491i	$0.419882\pi$
$968$	−3.07977	−0.0989875
$969$	8.84679	0.284200
$970$	10.4546	0.335676
$971$	−19.1625	−0.614955	−0.307477	−	0.951555i	$-0.599485\pi$
$971$	−19.1625	−0.614955	−0.307477	+	0.951555i	$0.599485\pi$
$972$	−7.37407	−0.236524
$973$	0	0
$974$	10.1077	0.323870
$975$	4.80619	0.153921
$976$	9.93978	0.318165
$977$	−14.8874	−0.476290	−0.238145	−	0.971230i	$-0.576539\pi$
$977$	−14.8874	−0.476290	−0.238145	+	0.971230i	$0.576539\pi$
$978$	−3.33211	−0.106549
$979$	−2.81429	−0.0899451
$980$	0	0
$981$	39.4137	1.25838
$982$	−6.94899	−0.221751
$983$	−41.8849	−1.33592	−0.667961	−	0.744196i	$-0.732833\pi$
$983$	−41.8849	−1.33592	−0.667961	+	0.744196i	$0.732833\pi$
$984$	−2.15792	−0.0687919
$985$	−17.2555	−0.549805
$986$	−16.1497	−0.514313
$987$	0	0
$988$	−33.4038	−1.06272
$989$	−23.3192	−0.741509
$990$	12.5101	0.397599
$991$	25.4020	0.806922	0.403461	−	0.914997i	$-0.367807\pi$
$991$	25.4020	0.806922	0.403461	+	0.914997i	$0.367807\pi$
$992$	−7.03015	−0.223208
$993$	−6.86476	−0.217847
$994$	0	0
$995$	22.9421	0.727312
$996$	0.535681	0.0169737
$997$	−50.6555	−1.60428	−0.802138	−	0.597139i	$-0.796304\pi$
$997$	−50.6555	−1.60428	−0.802138	+	0.597139i	$0.796304\pi$
$998$	−32.3015	−1.02249
$999$	3.95001	0.124973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8722.2.a.x.1.2		5
7.6	odd	2		1246.2.a.n.1.4	✓	5
28.27	even	2		9968.2.a.z.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1246.2.a.n.1.4	✓	5	7.6	odd	2
8722.2.a.x.1.2		5	1.1	even	1	trivial
9968.2.a.z.1.2		5	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8722 = 2 \cdot 7^{2} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8722.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.283134 q^{3} +1.00000 q^{4} +1.52242 q^{5} -0.283134 q^{6} +1.00000 q^{8} -2.91984 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.283134 q^{3} +1.00000 q^{4} +1.52242 q^{5} -0.283134 q^{6} +1.00000 q^{8} -2.91984 q^{9} +1.52242 q^{10} -2.81429 q^{11} -0.283134 q^{12} +6.32866 q^{13} -0.431050 q^{15} +1.00000 q^{16} +5.91984 q^{17} -2.91984 q^{18} -5.27817 q^{19} +1.52242 q^{20} -2.81429 q^{22} -2.94951 q^{23} -0.283134 q^{24} -2.68223 q^{25} +6.32866 q^{26} +1.67611 q^{27} -2.72807 q^{29} -0.431050 q^{30} -7.03015 q^{31} +1.00000 q^{32} +0.796822 q^{33} +5.91984 q^{34} -2.91984 q^{36} +2.35665 q^{37} -5.27817 q^{38} -1.79186 q^{39} +1.52242 q^{40} +7.62153 q^{41} +7.90614 q^{43} -2.81429 q^{44} -4.44522 q^{45} -2.94951 q^{46} +4.70713 q^{47} -0.283134 q^{48} -2.68223 q^{50} -1.67611 q^{51} +6.32866 q^{52} +9.16290 q^{53} +1.67611 q^{54} -4.28454 q^{55} +1.49443 q^{57} -2.72807 q^{58} +2.80724 q^{59} -0.431050 q^{60} +9.93978 q^{61} -7.03015 q^{62} +1.00000 q^{64} +9.63490 q^{65} +0.796822 q^{66} +11.9867 q^{67} +5.91984 q^{68} +0.835107 q^{69} +3.79891 q^{71} -2.91984 q^{72} +11.3403 q^{73} +2.35665 q^{74} +0.759431 q^{75} -5.27817 q^{76} -1.79186 q^{78} -6.17033 q^{79} +1.52242 q^{80} +8.28494 q^{81} +7.62153 q^{82} -1.89197 q^{83} +9.01249 q^{85} +7.90614 q^{86} +0.772411 q^{87} -2.81429 q^{88} +1.00000 q^{89} -4.44522 q^{90} -2.94951 q^{92} +1.99048 q^{93} +4.70713 q^{94} -8.03561 q^{95} -0.283134 q^{96} +6.86707 q^{97} +8.21726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} + 6 q^{6} + 5 q^{8} + 7 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 + 6 * q^6 + 5 * q^8 + 7 * q^9	\( 5 q + 5 q^{2} + 6 q^{3} + 5 q^{4} + 10 q^{5} + 6 q^{6} + 5 q^{8} + 7 q^{9} + 10 q^{10} - 8 q^{11} + 6 q^{12} + 8 q^{13} + 6 q^{15} + 5 q^{16} + 8 q^{17} + 7 q^{18} + 10 q^{19} + 10 q^{20} - 8 q^{22} - 2 q^{23} + 6 q^{24} + 17 q^{25} + 8 q^{26} + 24 q^{27} - 10 q^{29} + 6 q^{30} + 10 q^{31} + 5 q^{32} + 8 q^{34} + 7 q^{36} - 4 q^{37} + 10 q^{38} + 24 q^{39} + 10 q^{40} + 28 q^{41} - 10 q^{43} - 8 q^{44} + 12 q^{45} - 2 q^{46} + 10 q^{47} + 6 q^{48} + 17 q^{50} - 24 q^{51} + 8 q^{52} + 4 q^{53} + 24 q^{54} - 4 q^{55} + 2 q^{57} - 10 q^{58} + 10 q^{59} + 6 q^{60} + 16 q^{61} + 10 q^{62} + 5 q^{64} - 26 q^{65} + 8 q^{68} + 2 q^{69} - 16 q^{71} + 7 q^{72} - 10 q^{73} - 4 q^{74} + 10 q^{75} + 10 q^{76} + 24 q^{78} - 8 q^{79} + 10 q^{80} + 41 q^{81} + 28 q^{82} + 14 q^{83} + 18 q^{85} - 10 q^{86} - 22 q^{87} - 8 q^{88} + 5 q^{89} + 12 q^{90} - 2 q^{92} + 22 q^{93} + 10 q^{94} + 34 q^{95} + 6 q^{96} - 6 q^{97} - 8 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 6 * q^3 + 5 * q^4 + 10 * q^5 + 6 * q^6 + 5 * q^8 + 7 * q^9 + 10 * q^10 - 8 * q^11 + 6 * q^12 + 8 * q^13 + 6 * q^15 + 5 * q^16 + 8 * q^17 + 7 * q^18 + 10 * q^19 + 10 * q^20 - 8 * q^22 - 2 * q^23 + 6 * q^24 + 17 * q^25 + 8 * q^26 + 24 * q^27 - 10 * q^29 + 6 * q^30 + 10 * q^31 + 5 * q^32 + 8 * q^34 + 7 * q^36 - 4 * q^37 + 10 * q^38 + 24 * q^39 + 10 * q^40 + 28 * q^41 - 10 * q^43 - 8 * q^44 + 12 * q^45 - 2 * q^46 + 10 * q^47 + 6 * q^48 + 17 * q^50 - 24 * q^51 + 8 * q^52 + 4 * q^53 + 24 * q^54 - 4 * q^55 + 2 * q^57 - 10 * q^58 + 10 * q^59 + 6 * q^60 + 16 * q^61 + 10 * q^62 + 5 * q^64 - 26 * q^65 + 8 * q^68 + 2 * q^69 - 16 * q^71 + 7 * q^72 - 10 * q^73 - 4 * q^74 + 10 * q^75 + 10 * q^76 + 24 * q^78 - 8 * q^79 + 10 * q^80 + 41 * q^81 + 28 * q^82 + 14 * q^83 + 18 * q^85 - 10 * q^86 - 22 * q^87 - 8 * q^88 + 5 * q^89 + 12 * q^90 - 2 * q^92 + 22 * q^93 + 10 * q^94 + 34 * q^95 + 6 * q^96 - 6 * q^97 - 8 * q^99

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