LMFDB - Embedded newform 7203.2.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7203,2,Mod(1,7203)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7203, 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("7203.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7203 = 3 \cdot 7^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7203.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:	$57.5162445759$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 147)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	7203.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.544156 q^{2} -1.00000 q^{3} -1.70389 q^{4} +1.49980 q^{5} -0.544156 q^{6} -2.01550 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.544156 q^{2} -1.00000 q^{3} -1.70389 q^{4} +1.49980 q^{5} -0.544156 q^{6} -2.01550 q^{8} +1.00000 q^{9} +0.816125 q^{10} +2.07645 q^{11} +1.70389 q^{12} +1.32003 q^{13} -1.49980 q^{15} +2.31105 q^{16} +2.93373 q^{17} +0.544156 q^{18} -3.32463 q^{19} -2.55550 q^{20} +1.12991 q^{22} +4.03146 q^{23} +2.01550 q^{24} -2.75060 q^{25} +0.718302 q^{26} -1.00000 q^{27} -8.46165 q^{29} -0.816125 q^{30} -7.52264 q^{31} +5.28856 q^{32} -2.07645 q^{33} +1.59641 q^{34} -1.70389 q^{36} -7.09374 q^{37} -1.80912 q^{38} -1.32003 q^{39} -3.02284 q^{40} -8.04091 q^{41} -2.47227 q^{43} -3.53806 q^{44} +1.49980 q^{45} +2.19374 q^{46} +8.99217 q^{47} -2.31105 q^{48} -1.49675 q^{50} -2.93373 q^{51} -2.24919 q^{52} +5.93975 q^{53} -0.544156 q^{54} +3.11427 q^{55} +3.32463 q^{57} -4.60445 q^{58} +0.751758 q^{59} +2.55550 q^{60} -4.60531 q^{61} -4.09349 q^{62} -1.74429 q^{64} +1.97978 q^{65} -1.12991 q^{66} +1.60390 q^{67} -4.99877 q^{68} -4.03146 q^{69} +13.0422 q^{71} -2.01550 q^{72} +14.8852 q^{73} -3.86010 q^{74} +2.75060 q^{75} +5.66482 q^{76} -0.718302 q^{78} -5.92634 q^{79} +3.46611 q^{80} +1.00000 q^{81} -4.37551 q^{82} -5.27216 q^{83} +4.40001 q^{85} -1.34530 q^{86} +8.46165 q^{87} -4.18508 q^{88} +14.7319 q^{89} +0.816125 q^{90} -6.86918 q^{92} +7.52264 q^{93} +4.89314 q^{94} -4.98628 q^{95} -5.28856 q^{96} -8.41896 q^{97} +2.07645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} - 24 q^{3} + 18 q^{4} + 6 q^{6} - 18 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 - 24 * q^3 + 18 * q^4 + 6 * q^6 - 18 * q^8 + 24 * q^9	$ 24 q - 6 q^{2} - 24 q^{3} + 18 q^{4} + 6 q^{6} - 18 q^{8} + 24 q^{9} + 12 q^{10} - 12 q^{11} - 18 q^{12} + 14 q^{13} + 6 q^{16} - 2 q^{17} - 6 q^{18} + 26 q^{19} - 6 q^{20} - 24 q^{22} - 24 q^{23} + 18 q^{24} + 13 q^{26} - 24 q^{27} - 36 q^{29} - 12 q^{30} + 36 q^{31} - 42 q^{32} + 12 q^{33} + 4 q^{34} + 18 q^{36} - 50 q^{37} - 38 q^{38} - 14 q^{39} + 28 q^{40} - 25 q^{41} - 36 q^{43} - 30 q^{44} - 30 q^{46} - 6 q^{47} - 6 q^{48} - 6 q^{50} + 2 q^{51} + 41 q^{52} - 63 q^{53} + 6 q^{54} + 44 q^{55} - 26 q^{57} - 3 q^{58} + 41 q^{59} + 6 q^{60} + 38 q^{61} - 22 q^{62} - 6 q^{64} - 14 q^{65} + 24 q^{66} - 34 q^{67} - 22 q^{68} + 24 q^{69} - 32 q^{71} - 18 q^{72} + 13 q^{73} - 43 q^{74} + 105 q^{76} - 13 q^{78} - 34 q^{79} - 55 q^{80} + 24 q^{81} - 28 q^{82} - 42 q^{83} - 92 q^{85} + 40 q^{86} + 36 q^{87} - 10 q^{88} - 32 q^{89} + 12 q^{90} - 14 q^{92} - 36 q^{93} + 64 q^{94} - 38 q^{95} + 42 q^{96} + 62 q^{97} - 12 q^{99}+O(q^{100}) $ 24 * q - 6 * q^2 - 24 * q^3 + 18 * q^4 + 6 * q^6 - 18 * q^8 + 24 * q^9 + 12 * q^10 - 12 * q^11 - 18 * q^12 + 14 * q^13 + 6 * q^16 - 2 * q^17 - 6 * q^18 + 26 * q^19 - 6 * q^20 - 24 * q^22 - 24 * q^23 + 18 * q^24 + 13 * q^26 - 24 * q^27 - 36 * q^29 - 12 * q^30 + 36 * q^31 - 42 * q^32 + 12 * q^33 + 4 * q^34 + 18 * q^36 - 50 * q^37 - 38 * q^38 - 14 * q^39 + 28 * q^40 - 25 * q^41 - 36 * q^43 - 30 * q^44 - 30 * q^46 - 6 * q^47 - 6 * q^48 - 6 * q^50 + 2 * q^51 + 41 * q^52 - 63 * q^53 + 6 * q^54 + 44 * q^55 - 26 * q^57 - 3 * q^58 + 41 * q^59 + 6 * q^60 + 38 * q^61 - 22 * q^62 - 6 * q^64 - 14 * q^65 + 24 * q^66 - 34 * q^67 - 22 * q^68 + 24 * q^69 - 32 * q^71 - 18 * q^72 + 13 * q^73 - 43 * q^74 + 105 * q^76 - 13 * q^78 - 34 * q^79 - 55 * q^80 + 24 * q^81 - 28 * q^82 - 42 * q^83 - 92 * q^85 + 40 * q^86 + 36 * q^87 - 10 * q^88 - 32 * q^89 + 12 * q^90 - 14 * q^92 - 36 * q^93 + 64 * q^94 - 38 * q^95 + 42 * q^96 + 62 * q^97 - 12 * 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 $

$2$	0.544156	0.384776	0.192388	−	0.981319i	$-0.438377\pi$
$2$	0.544156	0.384776	0.192388	+	0.981319i	$0.438377\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.70389	−0.851947
$5$	1.49980	0.670731	0.335366	−	0.942088i	$-0.391140\pi$
$5$	1.49980	0.670731	0.335366	+	0.942088i	$0.391140\pi$
$6$	−0.544156	−0.222151
$7$	0	0
$7$	0	0
$8$	−2.01550	−0.712585
$9$	1.00000	0.333333
$10$	0.816125	0.258081
$11$	2.07645	0.626074	0.313037	−	0.949741i	$-0.398654\pi$
$11$	2.07645	0.626074	0.313037	+	0.949741i	$0.398654\pi$
$12$	1.70389	0.491872
$13$	1.32003	0.366110	0.183055	−	0.983103i	$-0.441401\pi$
$13$	1.32003	0.366110	0.183055	+	0.983103i	$0.441401\pi$
$14$	0	0
$15$	−1.49980	−0.387247
$16$	2.31105	0.577761
$17$	2.93373	0.711535	0.355767	−	0.934575i	$-0.384220\pi$
$17$	2.93373	0.711535	0.355767	+	0.934575i	$0.384220\pi$
$18$	0.544156	0.128259
$19$	−3.32463	−0.762722	−0.381361	−	0.924426i	$-0.624545\pi$
$19$	−3.32463	−0.762722	−0.381361	+	0.924426i	$0.624545\pi$
$20$	−2.55550	−0.571428
$21$	0	0
$22$	1.12991	0.240898
$23$	4.03146	0.840617	0.420309	−	0.907381i	$-0.361922\pi$
$23$	4.03146	0.840617	0.420309	+	0.907381i	$0.361922\pi$
$24$	2.01550	0.411411
$25$	−2.75060	−0.550119
$26$	0.718302	0.140871
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.46165	−1.57129	−0.785644	−	0.618678i	$-0.787668\pi$
$29$	−8.46165	−1.57129	−0.785644	+	0.618678i	$0.787668\pi$
$30$	−0.816125	−0.149003
$31$	−7.52264	−1.35111	−0.675553	−	0.737312i	$-0.736095\pi$
$31$	−7.52264	−1.35111	−0.675553	+	0.737312i	$0.736095\pi$
$32$	5.28856	0.934894
$33$	−2.07645	−0.361464
$34$	1.59641	0.273782
$35$	0	0
$36$	−1.70389	−0.283982
$37$	−7.09374	−1.16620	−0.583102	−	0.812399i	$-0.698161\pi$
$37$	−7.09374	−1.16620	−0.583102	+	0.812399i	$0.698161\pi$
$38$	−1.80912	−0.293477
$39$	−1.32003	−0.211374
$40$	−3.02284	−0.477953
$41$	−8.04091	−1.25578	−0.627890	−	0.778302i	$-0.716081\pi$
$41$	−8.04091	−1.25578	−0.627890	+	0.778302i	$0.716081\pi$
$42$	0	0
$43$	−2.47227	−0.377018	−0.188509	−	0.982071i	$-0.560365\pi$
$43$	−2.47227	−0.377018	−0.188509	+	0.982071i	$0.560365\pi$
$44$	−3.53806	−0.533382
$45$	1.49980	0.223577
$46$	2.19374	0.323450
$47$	8.99217	1.31164	0.655822	−	0.754916i	$-0.272322\pi$
$47$	8.99217	1.31164	0.655822	+	0.754916i	$0.272322\pi$
$48$	−2.31105	−0.333571
$49$	0	0
$50$	−1.49675	−0.211673
$51$	−2.93373	−0.410805
$52$	−2.24919	−0.311907
$53$	5.93975	0.815888	0.407944	−	0.913007i	$-0.366246\pi$
$53$	5.93975	0.815888	0.407944	+	0.913007i	$0.366246\pi$
$54$	−0.544156	−0.0740502
$55$	3.11427	0.419927
$56$	0	0
$57$	3.32463	0.440358
$58$	−4.60445	−0.604594
$59$	0.751758	0.0978706	0.0489353	−	0.998802i	$-0.484417\pi$
$59$	0.751758	0.0978706	0.0489353	+	0.998802i	$0.484417\pi$
$60$	2.55550	0.329914
$61$	−4.60531	−0.589649	−0.294825	−	0.955551i	$-0.595261\pi$
$61$	−4.60531	−0.589649	−0.294825	+	0.955551i	$0.595261\pi$
$62$	−4.09349	−0.519873
$63$	0	0
$64$	−1.74429	−0.218036
$65$	1.97978	0.245562
$66$	−1.12991	−0.139083
$67$	1.60390	0.195947	0.0979737	−	0.995189i	$-0.468764\pi$
$67$	1.60390	0.195947	0.0979737	+	0.995189i	$0.468764\pi$
$68$	−4.99877	−0.606190
$69$	−4.03146	−0.485331
$70$	0	0
$71$	13.0422	1.54783	0.773915	−	0.633290i	$-0.218296\pi$
$71$	13.0422	1.54783	0.773915	+	0.633290i	$0.218296\pi$
$72$	−2.01550	−0.237528
$73$	14.8852	1.74218	0.871089	−	0.491125i	$-0.163414\pi$
$73$	14.8852	1.74218	0.871089	+	0.491125i	$0.163414\pi$
$74$	−3.86010	−0.448728
$75$	2.75060	0.317612
$76$	5.66482	0.649799
$77$	0	0
$78$	−0.718302	−0.0813317
$79$	−5.92634	−0.666766	−0.333383	−	0.942792i	$-0.608190\pi$
$79$	−5.92634	−0.666766	−0.333383	+	0.942792i	$0.608190\pi$
$80$	3.46611	0.387523
$81$	1.00000	0.111111
$82$	−4.37551	−0.483194
$83$	−5.27216	−0.578695	−0.289347	−	0.957224i	$-0.593438\pi$
$83$	−5.27216	−0.578695	−0.289347	+	0.957224i	$0.593438\pi$
$84$	0	0
$85$	4.40001	0.477249
$86$	−1.34530	−0.145068
$87$	8.46165	0.907184
$88$	−4.18508	−0.446131
$89$	14.7319	1.56158	0.780788	−	0.624796i	$-0.214818\pi$
$89$	14.7319	1.56158	0.780788	+	0.624796i	$0.214818\pi$
$90$	0.816125	0.0860272
$91$	0	0
$92$	−6.86918	−0.716162
$93$	7.52264	0.780061
$94$	4.89314	0.504689
$95$	−4.98628	−0.511582
$96$	−5.28856	−0.539761
$97$	−8.41896	−0.854816	−0.427408	−	0.904059i	$-0.640573\pi$
$97$	−8.41896	−0.854816	−0.427408	+	0.904059i	$0.640573\pi$
$98$	0	0
$99$	2.07645	0.208691
$100$	4.68673	0.468673
$101$	2.12002	0.210950	0.105475	−	0.994422i	$-0.466364\pi$
$101$	2.12002	0.210950	0.105475	+	0.994422i	$0.466364\pi$
$102$	−1.59641	−0.158068
$103$	4.61816	0.455041	0.227521	−	0.973773i	$-0.426938\pi$
$103$	4.61816	0.455041	0.227521	+	0.973773i	$0.426938\pi$
$104$	−2.66051	−0.260885
$105$	0	0
$106$	3.23215	0.313934
$107$	−10.5677	−1.02162	−0.510811	−	0.859693i	$-0.670655\pi$
$107$	−10.5677	−1.02162	−0.510811	+	0.859693i	$0.670655\pi$
$108$	1.70389	0.163957
$109$	13.8542	1.32699	0.663495	−	0.748181i	$-0.269072\pi$
$109$	13.8542	1.32699	0.663495	+	0.748181i	$0.269072\pi$
$110$	1.69465	0.161578
$111$	7.09374	0.673308
$112$	0	0
$113$	3.33338	0.313578	0.156789	−	0.987632i	$-0.449886\pi$
$113$	3.33338	0.313578	0.156789	+	0.987632i	$0.449886\pi$
$114$	1.80912	0.169439
$115$	6.04639	0.563828
$116$	14.4178	1.33866
$117$	1.32003	0.122037
$118$	0.409074	0.0376583
$119$	0	0
$120$	3.02284	0.275946
$121$	−6.68835	−0.608031
$122$	−2.50601	−0.226883
$123$	8.04091	0.725025
$124$	12.8178	1.15107
$125$	−11.6244	−1.03971
$126$	0	0
$127$	−18.3184	−1.62550	−0.812748	−	0.582616i	$-0.802029\pi$
$127$	−18.3184	−1.62550	−0.812748	+	0.582616i	$0.802029\pi$
$128$	−11.5263	−1.01879
$129$	2.47227	0.217671
$130$	1.07731	0.0944863
$131$	−14.9098	−1.30267	−0.651337	−	0.758789i	$-0.725791\pi$
$131$	−14.9098	−1.30267	−0.651337	+	0.758789i	$0.725791\pi$
$132$	3.53806	0.307948
$133$	0	0
$134$	0.872771	0.0753959
$135$	−1.49980	−0.129082
$136$	−5.91292	−0.507029
$137$	9.24353	0.789728	0.394864	−	0.918740i	$-0.370792\pi$
$137$	9.24353	0.789728	0.394864	+	0.918740i	$0.370792\pi$
$138$	−2.19374	−0.186744
$139$	8.97523	0.761269	0.380634	−	0.924726i	$-0.375706\pi$
$139$	8.97523	0.761269	0.380634	+	0.924726i	$0.375706\pi$
$140$	0	0
$141$	−8.99217	−0.757278
$142$	7.09701	0.595568
$143$	2.74098	0.229212
$144$	2.31105	0.192587
$145$	−12.6908	−1.05391
$146$	8.09985	0.670349
$147$	0	0
$148$	12.0870	0.993544
$149$	−23.1750	−1.89857	−0.949287	−	0.314411i	$-0.898193\pi$
$149$	−23.1750	−1.89857	−0.949287	+	0.314411i	$0.898193\pi$
$150$	1.49675	0.122209
$151$	−5.50106	−0.447670	−0.223835	−	0.974627i	$-0.571858\pi$
$151$	−5.50106	−0.447670	−0.223835	+	0.974627i	$0.571858\pi$
$152$	6.70077	0.543504
$153$	2.93373	0.237178
$154$	0	0
$155$	−11.2825	−0.906229
$156$	2.24919	0.180079
$157$	−9.47605	−0.756271	−0.378135	−	0.925750i	$-0.623435\pi$
$157$	−9.47605	−0.756271	−0.378135	+	0.925750i	$0.623435\pi$
$158$	−3.22485	−0.256556
$159$	−5.93975	−0.471053
$160$	7.93179	0.627063
$161$	0	0
$162$	0.544156	0.0427529
$163$	−16.4552	−1.28887	−0.644436	−	0.764659i	$-0.722908\pi$
$163$	−16.4552	−1.28887	−0.644436	+	0.764659i	$0.722908\pi$
$164$	13.7009	1.06986
$165$	−3.11427	−0.242445
$166$	−2.86888	−0.222668
$167$	21.8664	1.69208	0.846038	−	0.533123i	$-0.178982\pi$
$167$	21.8664	1.69208	0.846038	+	0.533123i	$0.178982\pi$
$168$	0	0
$169$	−11.2575	−0.865963
$170$	2.39429	0.183634
$171$	−3.32463	−0.254241
$172$	4.21249	0.321199
$173$	21.1185	1.60561	0.802806	−	0.596240i	$-0.203339\pi$
$173$	21.1185	1.60561	0.802806	+	0.596240i	$0.203339\pi$
$174$	4.60445	0.349063
$175$	0	0
$176$	4.79878	0.361721
$177$	−0.751758	−0.0565056
$178$	8.01644	0.600857
$179$	−3.66849	−0.274196	−0.137098	−	0.990558i	$-0.543777\pi$
$179$	−3.66849	−0.274196	−0.137098	+	0.990558i	$0.543777\pi$
$180$	−2.55550	−0.190476
$181$	−12.2809	−0.912830	−0.456415	−	0.889767i	$-0.650867\pi$
$181$	−12.2809	−0.912830	−0.456415	+	0.889767i	$0.650867\pi$
$182$	0	0
$183$	4.60531	0.340434
$184$	−8.12539	−0.599011
$185$	−10.6392	−0.782210
$186$	4.09349	0.300149
$187$	6.09175	0.445473
$188$	−15.3217	−1.11745
$189$	0	0
$190$	−2.71331	−0.196844
$191$	−20.4761	−1.48160	−0.740798	−	0.671728i	$-0.765552\pi$
$191$	−20.4761	−1.48160	−0.740798	+	0.671728i	$0.765552\pi$
$192$	1.74429	0.125883
$193$	−19.9065	−1.43290	−0.716451	−	0.697637i	$-0.754235\pi$
$193$	−19.9065	−1.43290	−0.716451	+	0.697637i	$0.754235\pi$
$194$	−4.58123	−0.328913
$195$	−1.97978	−0.141775
$196$	0	0
$197$	−14.0362	−1.00003	−0.500017	−	0.866015i	$-0.666673\pi$
$197$	−14.0362	−1.00003	−0.500017	+	0.866015i	$0.666673\pi$
$198$	1.12991	0.0802994
$199$	−2.34570	−0.166282	−0.0831412	−	0.996538i	$-0.526495\pi$
$199$	−2.34570	−0.166282	−0.0831412	+	0.996538i	$0.526495\pi$
$200$	5.54382	0.392007
$201$	−1.60390	−0.113130
$202$	1.15362	0.0811686
$203$	0	0
$204$	4.99877	0.349984
$205$	−12.0598	−0.842291
$206$	2.51300	0.175089
$207$	4.03146	0.280206
$208$	3.05065	0.211525
$209$	−6.90343	−0.477520
$210$	0	0
$211$	−23.5209	−1.61924	−0.809622	−	0.586951i	$-0.800328\pi$
$211$	−23.5209	−1.61924	−0.809622	+	0.586951i	$0.800328\pi$
$212$	−10.1207	−0.695094
$213$	−13.0422	−0.893640
$214$	−5.75050	−0.393096
$215$	−3.70792	−0.252878
$216$	2.01550	0.137137
$217$	0	0
$218$	7.53883	0.510594
$219$	−14.8852	−1.00585
$220$	−5.30638	−0.357756
$221$	3.87261	0.260500
$222$	3.86010	0.259073
$223$	2.84754	0.190686	0.0953428	−	0.995444i	$-0.469605\pi$
$223$	2.84754	0.190686	0.0953428	+	0.995444i	$0.469605\pi$
$224$	0	0
$225$	−2.75060	−0.183373
$226$	1.81388	0.120657
$227$	−3.82551	−0.253908	−0.126954	−	0.991909i	$-0.540520\pi$
$227$	−3.82551	−0.253908	−0.126954	+	0.991909i	$0.540520\pi$
$228$	−5.66482	−0.375162
$229$	−15.3467	−1.01414	−0.507068	−	0.861906i	$-0.669271\pi$
$229$	−15.3467	−1.01414	−0.507068	+	0.861906i	$0.669271\pi$
$230$	3.29018	0.216948
$231$	0	0
$232$	17.0544	1.11968
$233$	12.1109	0.793411	0.396705	−	0.917946i	$-0.370153\pi$
$233$	12.1109	0.793411	0.396705	+	0.917946i	$0.370153\pi$
$234$	0.718302	0.0469569
$235$	13.4865	0.879760
$236$	−1.28092	−0.0833806
$237$	5.92634	0.384957
$238$	0	0
$239$	−14.1414	−0.914733	−0.457367	−	0.889278i	$-0.651207\pi$
$239$	−14.1414	−0.914733	−0.457367	+	0.889278i	$0.651207\pi$
$240$	−3.46611	−0.223736
$241$	−3.55401	−0.228934	−0.114467	−	0.993427i	$-0.536516\pi$
$241$	−3.55401	−0.228934	−0.114467	+	0.993427i	$0.536516\pi$
$242$	−3.63950	−0.233956
$243$	−1.00000	−0.0641500
$244$	7.84696	0.502350
$245$	0	0
$246$	4.37551	0.278972
$247$	−4.38861	−0.279241
$248$	15.1618	0.962778
$249$	5.27216	0.334110
$250$	−6.32546	−0.400057
$251$	−12.8036	−0.808158	−0.404079	−	0.914724i	$-0.632408\pi$
$251$	−12.8036	−0.808158	−0.404079	+	0.914724i	$0.632408\pi$
$252$	0	0
$253$	8.37113	0.526289
$254$	−9.96806	−0.625452
$255$	−4.40001	−0.275540
$256$	−2.78351	−0.173969
$257$	4.96308	0.309589	0.154794	−	0.987947i	$-0.450529\pi$
$257$	4.96308	0.309589	0.154794	+	0.987947i	$0.450529\pi$
$258$	1.34530	0.0837548
$259$	0	0
$260$	−3.37334	−0.209206
$261$	−8.46165	−0.523763
$262$	−8.11324	−0.501238
$263$	−6.86664	−0.423415	−0.211708	−	0.977333i	$-0.567902\pi$
$263$	−6.86664	−0.423415	−0.211708	+	0.977333i	$0.567902\pi$
$264$	4.18508	0.257574
$265$	8.90845	0.547242
$266$	0	0
$267$	−14.7319	−0.901577
$268$	−2.73288	−0.166937
$269$	−15.5252	−0.946586	−0.473293	−	0.880905i	$-0.656935\pi$
$269$	−15.5252	−0.946586	−0.473293	+	0.880905i	$0.656935\pi$
$270$	−0.816125	−0.0496678
$271$	16.7480	1.01737	0.508683	−	0.860954i	$-0.330132\pi$
$271$	16.7480	1.01737	0.508683	+	0.860954i	$0.330132\pi$
$272$	6.77999	0.411097
$273$	0	0
$274$	5.02992	0.303868
$275$	−5.71148	−0.344415
$276$	6.86918	0.413476
$277$	−7.47049	−0.448858	−0.224429	−	0.974490i	$-0.572052\pi$
$277$	−7.47049	−0.448858	−0.224429	+	0.974490i	$0.572052\pi$
$278$	4.88392	0.292918
$279$	−7.52264	−0.450368
$280$	0	0
$281$	32.2499	1.92387	0.961934	−	0.273282i	$-0.0881091\pi$
$281$	32.2499	1.92387	0.961934	+	0.273282i	$0.0881091\pi$
$282$	−4.89314	−0.291382
$283$	11.3385	0.674005	0.337002	−	0.941504i	$-0.390587\pi$
$283$	11.3385	0.674005	0.337002	+	0.941504i	$0.390587\pi$
$284$	−22.2226	−1.31867
$285$	4.98628	0.295362
$286$	1.49152	0.0881954
$287$	0	0
$288$	5.28856	0.311631
$289$	−8.39322	−0.493719
$290$	−6.90577	−0.405520
$291$	8.41896	0.493528
$292$	−25.3628	−1.48424
$293$	−7.69626	−0.449620	−0.224810	−	0.974403i	$-0.572176\pi$
$293$	−7.69626	−0.449620	−0.224810	+	0.974403i	$0.572176\pi$
$294$	0	0
$295$	1.12749	0.0656449
$296$	14.2974	0.831020
$297$	−2.07645	−0.120488
$298$	−12.6108	−0.730526
$299$	5.32165	0.307759
$300$	−4.68673	−0.270588
$301$	0	0
$302$	−2.99344	−0.172253
$303$	−2.12002	−0.121792
$304$	−7.68337	−0.440671
$305$	−6.90705	−0.395496
$306$	1.59641	0.0912605
$307$	14.8120	0.845366	0.422683	−	0.906277i	$-0.361088\pi$
$307$	14.8120	0.845366	0.422683	+	0.906277i	$0.361088\pi$
$308$	0	0
$309$	−4.61816	−0.262718
$310$	−6.13941	−0.348695
$311$	11.8680	0.672975	0.336487	−	0.941688i	$-0.390761\pi$
$311$	11.8680	0.672975	0.336487	+	0.941688i	$0.390761\pi$
$312$	2.66051	0.150622
$313$	−20.9236	−1.18267	−0.591335	−	0.806426i	$-0.701399\pi$
$313$	−20.9236	−1.18267	−0.591335	+	0.806426i	$0.701399\pi$
$314$	−5.15644	−0.290995
$315$	0	0
$316$	10.0979	0.568049
$317$	−12.8244	−0.720288	−0.360144	−	0.932897i	$-0.617272\pi$
$317$	−12.8244	−0.720288	−0.360144	+	0.932897i	$0.617272\pi$
$318$	−3.23215	−0.181250
$319$	−17.5702	−0.983743
$320$	−2.61609	−0.146244
$321$	10.5677	0.589834
$322$	0	0
$323$	−9.75357	−0.542703
$324$	−1.70389	−0.0946608
$325$	−3.63087	−0.201404
$326$	−8.95419	−0.495927
$327$	−13.8542	−0.766138
$328$	16.2064	0.894850
$329$	0	0
$330$	−1.69465	−0.0932871
$331$	−9.29944	−0.511143	−0.255572	−	0.966790i	$-0.582264\pi$
$331$	−9.29944	−0.511143	−0.255572	+	0.966790i	$0.582264\pi$
$332$	8.98321	0.493018
$333$	−7.09374	−0.388735
$334$	11.8987	0.651070
$335$	2.40553	0.131428
$336$	0	0
$337$	−18.0634	−0.983978	−0.491989	−	0.870601i	$-0.663730\pi$
$337$	−18.0634	−0.983978	−0.491989	+	0.870601i	$0.663730\pi$
$338$	−6.12584	−0.333202
$339$	−3.33338	−0.181045
$340$	−7.49716	−0.406591
$341$	−15.6204	−0.845892
$342$	−1.80912	−0.0978258
$343$	0	0
$344$	4.98285	0.268657
$345$	−6.04639	−0.325527
$346$	11.4918	0.617801
$347$	−6.14485	−0.329873	−0.164936	−	0.986304i	$-0.552742\pi$
$347$	−6.14485	−0.329873	−0.164936	+	0.986304i	$0.552742\pi$
$348$	−14.4178	−0.772873
$349$	15.3338	0.820798	0.410399	−	0.911906i	$-0.365389\pi$
$349$	15.3338	0.820798	0.410399	+	0.911906i	$0.365389\pi$
$350$	0	0
$351$	−1.32003	−0.0704580
$352$	10.9814	0.585313
$353$	29.6700	1.57918	0.789588	−	0.613637i	$-0.210294\pi$
$353$	29.6700	1.57918	0.789588	+	0.613637i	$0.210294\pi$
$354$	−0.409074	−0.0217420
$355$	19.5608	1.03818
$356$	−25.1016	−1.33038
$357$	0	0
$358$	−1.99623	−0.105504
$359$	−7.16260	−0.378028	−0.189014	−	0.981974i	$-0.560529\pi$
$359$	−7.16260	−0.378028	−0.189014	+	0.981974i	$0.560529\pi$
$360$	−3.02284	−0.159318
$361$	−7.94685	−0.418255
$362$	−6.68271	−0.351235
$363$	6.68835	0.351047
$364$	0	0
$365$	22.3248	1.16853
$366$	2.50601	0.130991
$367$	−28.2510	−1.47469	−0.737345	−	0.675517i	$-0.763921\pi$
$367$	−28.2510	−1.47469	−0.737345	+	0.675517i	$0.763921\pi$
$368$	9.31689	0.485676
$369$	−8.04091	−0.418593
$370$	−5.78938	−0.300976
$371$	0	0
$372$	−12.8178	−0.664571
$373$	15.2562	0.789935	0.394967	−	0.918695i	$-0.370756\pi$
$373$	15.2562	0.789935	0.394967	+	0.918695i	$0.370756\pi$
$374$	3.31486	0.171407
$375$	11.6244	0.600279
$376$	−18.1237	−0.934658
$377$	−11.1696	−0.575265
$378$	0	0
$379$	0.0492134	0.00252792	0.00126396	−	0.999999i	$-0.499598\pi$
$379$	0.0492134	0.00252792	0.00126396	+	0.999999i	$0.499598\pi$
$380$	8.49610	0.435841
$381$	18.3184	0.938480
$382$	−11.1422	−0.570083
$383$	36.4561	1.86282	0.931409	−	0.363974i	$-0.118580\pi$
$383$	36.4561	1.86282	0.931409	+	0.363974i	$0.118580\pi$
$384$	11.5263	0.588198
$385$	0	0
$386$	−10.8322	−0.551347
$387$	−2.47227	−0.125673
$388$	14.3450	0.728258
$389$	12.8170	0.649848	0.324924	−	0.945740i	$-0.394661\pi$
$389$	12.8170	0.649848	0.324924	+	0.945740i	$0.394661\pi$
$390$	−1.07731	−0.0545517
$391$	11.8272	0.598128
$392$	0	0
$393$	14.9098	0.752099
$394$	−7.63785	−0.384790
$395$	−8.88834	−0.447221
$396$	−3.53806	−0.177794
$397$	10.0426	0.504024	0.252012	−	0.967724i	$-0.418908\pi$
$397$	10.0426	0.504024	0.252012	+	0.967724i	$0.418908\pi$
$398$	−1.27643	−0.0639815
$399$	0	0
$400$	−6.35676	−0.317838
$401$	21.0914	1.05326	0.526628	−	0.850096i	$-0.323456\pi$
$401$	21.0914	1.05326	0.526628	+	0.850096i	$0.323456\pi$
$402$	−0.872771	−0.0435299
$403$	−9.93011	−0.494654
$404$	−3.61230	−0.179718
$405$	1.49980	0.0745257
$406$	0	0
$407$	−14.7298	−0.730130
$408$	5.91292	0.292733
$409$	−35.3687	−1.74887	−0.874434	−	0.485144i	$-0.838767\pi$
$409$	−35.3687	−1.74887	−0.874434	+	0.485144i	$0.838767\pi$
$410$	−6.56239	−0.324093
$411$	−9.24353	−0.455950
$412$	−7.86886	−0.387671
$413$	0	0
$414$	2.19374	0.107817
$415$	−7.90719	−0.388149
$416$	6.98106	0.342275
$417$	−8.97523	−0.439519
$418$	−3.75654	−0.183738
$419$	−29.1398	−1.42357	−0.711787	−	0.702395i	$-0.752114\pi$
$419$	−29.1398	−1.42357	−0.711787	+	0.702395i	$0.752114\pi$
$420$	0	0
$421$	−31.5787	−1.53905	−0.769526	−	0.638616i	$-0.779507\pi$
$421$	−31.5787	−1.53905	−0.769526	+	0.638616i	$0.779507\pi$
$422$	−12.7990	−0.623047
$423$	8.99217	0.437214
$424$	−11.9715	−0.581390
$425$	−8.06951	−0.391429
$426$	−7.09701	−0.343851
$427$	0	0
$428$	18.0063	0.870368
$429$	−2.74098	−0.132336
$430$	−2.01768	−0.0973013
$431$	−3.52732	−0.169905	−0.0849525	−	0.996385i	$-0.527074\pi$
$431$	−3.52732	−0.169905	−0.0849525	+	0.996385i	$0.527074\pi$
$432$	−2.31105	−0.111190
$433$	−9.35205	−0.449431	−0.224715	−	0.974424i	$-0.572145\pi$
$433$	−9.35205	−0.449431	−0.224715	+	0.974424i	$0.572145\pi$
$434$	0	0
$435$	12.6908	0.608477
$436$	−23.6061	−1.13053
$437$	−13.4031	−0.641157
$438$	−8.09985	−0.387026
$439$	24.9501	1.19080	0.595402	−	0.803428i	$-0.296993\pi$
$439$	24.9501	1.19080	0.595402	+	0.803428i	$0.296993\pi$
$440$	−6.27679	−0.299234
$441$	0	0
$442$	2.10731	0.100234
$443$	12.5777	0.597584	0.298792	−	0.954318i	$-0.403416\pi$
$443$	12.5777	0.597584	0.298792	+	0.954318i	$0.403416\pi$
$444$	−12.0870	−0.573623
$445$	22.0949	1.04740
$446$	1.54951	0.0733713
$447$	23.1750	1.09614
$448$	0	0
$449$	−23.4982	−1.10895	−0.554474	−	0.832201i	$-0.687080\pi$
$449$	−23.4982	−1.10895	−0.554474	+	0.832201i	$0.687080\pi$
$450$	−1.49675	−0.0705576
$451$	−16.6966	−0.786211
$452$	−5.67973	−0.267152
$453$	5.50106	0.258463
$454$	−2.08167	−0.0976976
$455$	0	0
$456$	−6.70077	−0.313792
$457$	−12.1405	−0.567907	−0.283954	−	0.958838i	$-0.591646\pi$
$457$	−12.1405	−0.567907	−0.283954	+	0.958838i	$0.591646\pi$
$458$	−8.35098	−0.390216
$459$	−2.93373	−0.136935
$460$	−10.3024	−0.480352
$461$	−30.3603	−1.41402	−0.707010	−	0.707203i	$-0.749957\pi$
$461$	−30.3603	−1.41402	−0.707010	+	0.707203i	$0.749957\pi$
$462$	0	0
$463$	33.7127	1.56676	0.783381	−	0.621542i	$-0.213493\pi$
$463$	33.7127	1.56676	0.783381	+	0.621542i	$0.213493\pi$
$464$	−19.5553	−0.907830
$465$	11.2825	0.523211
$466$	6.59021	0.305286
$467$	1.63286	0.0755597	0.0377798	−	0.999286i	$-0.487971\pi$
$467$	1.63286	0.0755597	0.0377798	+	0.999286i	$0.487971\pi$
$468$	−2.24919	−0.103969
$469$	0	0
$470$	7.33874	0.338511
$471$	9.47605	0.436633
$472$	−1.51517	−0.0697411
$473$	−5.13355	−0.236041
$474$	3.22485	0.148122
$475$	9.14471	0.419588
$476$	0	0
$477$	5.93975	0.271963
$478$	−7.69514	−0.351968
$479$	−32.6150	−1.49022	−0.745109	−	0.666942i	$-0.767603\pi$
$479$	−32.6150	−1.49022	−0.745109	+	0.666942i	$0.767603\pi$
$480$	−7.93179	−0.362035
$481$	−9.36395	−0.426960
$482$	−1.93394	−0.0880884
$483$	0	0
$484$	11.3962	0.518011
$485$	−12.6268	−0.573352
$486$	−0.544156	−0.0246834
$487$	29.5500	1.33904	0.669519	−	0.742795i	$-0.266500\pi$
$487$	29.5500	1.33904	0.669519	+	0.742795i	$0.266500\pi$
$488$	9.28198	0.420175
$489$	16.4552	0.744130
$490$	0	0
$491$	−17.6456	−0.796334	−0.398167	−	0.917313i	$-0.630353\pi$
$491$	−17.6456	−0.796334	−0.398167	+	0.917313i	$0.630353\pi$
$492$	−13.7009	−0.617683
$493$	−24.8242	−1.11803
$494$	−2.38809	−0.107445
$495$	3.11427	0.139976
$496$	−17.3852	−0.780617
$497$	0	0
$498$	2.86888	0.128557
$499$	5.45939	0.244396	0.122198	−	0.992506i	$-0.461006\pi$
$499$	5.45939	0.244396	0.122198	+	0.992506i	$0.461006\pi$
$500$	19.8067	0.885781
$501$	−21.8664	−0.976920
$502$	−6.96716	−0.310960
$503$	23.4835	1.04708	0.523539	−	0.852002i	$-0.324612\pi$
$503$	23.4835	1.04708	0.523539	+	0.852002i	$0.324612\pi$
$504$	0	0
$505$	3.17961	0.141491
$506$	4.55520	0.202503
$507$	11.2575	0.499964
$508$	31.2126	1.38484
$509$	21.5256	0.954107	0.477053	−	0.878874i	$-0.341705\pi$
$509$	21.5256	0.954107	0.477053	+	0.878874i	$0.341705\pi$
$510$	−2.39429	−0.106021
$511$	0	0
$512$	21.5379	0.951850
$513$	3.32463	0.146786
$514$	2.70069	0.119122
$515$	6.92633	0.305210
$516$	−4.21249	−0.185445
$517$	18.6718	0.821186
$518$	0	0
$519$	−21.1185	−0.927001
$520$	−3.99024	−0.174984
$521$	−29.8877	−1.30940	−0.654702	−	0.755887i	$-0.727206\pi$
$521$	−29.8877	−1.30940	−0.654702	+	0.755887i	$0.727206\pi$
$522$	−4.60445	−0.201531
$523$	29.3434	1.28310	0.641550	−	0.767081i	$-0.278292\pi$
$523$	29.3434	1.28310	0.641550	+	0.767081i	$0.278292\pi$
$524$	25.4047	1.10981
$525$	0	0
$526$	−3.73652	−0.162920
$527$	−22.0694	−0.961358
$528$	−4.79878	−0.208840
$529$	−6.74734	−0.293362
$530$	4.84758	0.210566
$531$	0.751758	0.0326235
$532$	0	0
$533$	−10.6142	−0.459754
$534$	−8.01644	−0.346905
$535$	−15.8495	−0.685234
$536$	−3.23265	−0.139629
$537$	3.66849	0.158307
$538$	−8.44811	−0.364224
$539$	0	0
$540$	2.55550	0.109971
$541$	−32.1485	−1.38217	−0.691086	−	0.722773i	$-0.742867\pi$
$541$	−32.1485	−1.38217	−0.691086	+	0.722773i	$0.742867\pi$
$542$	9.11350	0.391458
$543$	12.2809	0.527023
$544$	15.5152	0.665209
$545$	20.7785	0.890054
$546$	0	0
$547$	1.02869	0.0439836	0.0219918	−	0.999758i	$-0.492999\pi$
$547$	1.02869	0.0439836	0.0219918	+	0.999758i	$0.492999\pi$
$548$	−15.7500	−0.672807
$549$	−4.60531	−0.196550
$550$	−3.10794	−0.132523
$551$	28.1318	1.19846
$552$	8.12539	0.345839
$553$	0	0
$554$	−4.06511	−0.172710
$555$	10.6392	0.451609
$556$	−15.2928	−0.648561
$557$	−5.49995	−0.233040	−0.116520	−	0.993188i	$-0.537174\pi$
$557$	−5.49995	−0.233040	−0.116520	+	0.993188i	$0.537174\pi$
$558$	−4.09349	−0.173291
$559$	−3.26347	−0.138030
$560$	0	0
$561$	−6.09175	−0.257194
$562$	17.5490	0.740259
$563$	31.2833	1.31843	0.659217	−	0.751952i	$-0.270888\pi$
$563$	31.2833	1.31843	0.659217	+	0.751952i	$0.270888\pi$
$564$	15.3217	0.645161
$565$	4.99941	0.210327
$566$	6.16992	0.259341
$567$	0	0
$568$	−26.2866	−1.10296
$569$	5.94226	0.249112	0.124556	−	0.992213i	$-0.460249\pi$
$569$	5.94226	0.249112	0.124556	+	0.992213i	$0.460249\pi$
$570$	2.71331	0.113648
$571$	21.0492	0.880883	0.440442	−	0.897781i	$-0.354822\pi$
$571$	21.0492	0.880883	0.440442	+	0.897781i	$0.354822\pi$
$572$	−4.67034	−0.195277
$573$	20.4761	0.855400
$574$	0	0
$575$	−11.0889	−0.462440
$576$	−1.74429	−0.0726788
$577$	9.23182	0.384326	0.192163	−	0.981363i	$-0.438450\pi$
$577$	9.23182	0.384326	0.192163	+	0.981363i	$0.438450\pi$
$578$	−4.56722	−0.189971
$579$	19.9065	0.827286
$580$	21.6238	0.897878
$581$	0	0
$582$	4.58123	0.189898
$583$	12.3336	0.510806
$584$	−30.0010	−1.24145
$585$	1.97978	0.0818539
$586$	−4.18796	−0.173003
$587$	−28.4418	−1.17392	−0.586960	−	0.809616i	$-0.699675\pi$
$587$	−28.4418	−1.17392	−0.586960	+	0.809616i	$0.699675\pi$
$588$	0	0
$589$	25.0100	1.03052
$590$	0.613529	0.0252586
$591$	14.0362	0.577370
$592$	−16.3940	−0.673788
$593$	−37.4947	−1.53972	−0.769861	−	0.638212i	$-0.779674\pi$
$593$	−37.4947	−1.53972	−0.769861	+	0.638212i	$0.779674\pi$
$594$	−1.12991	−0.0463609
$595$	0	0
$596$	39.4878	1.61748
$597$	2.34570	0.0960032
$598$	2.89580	0.118418
$599$	15.1402	0.618613	0.309306	−	0.950962i	$-0.399903\pi$
$599$	15.1402	0.618613	0.309306	+	0.950962i	$0.399903\pi$
$600$	−5.54382	−0.226325
$601$	−18.1516	−0.740419	−0.370209	−	0.928948i	$-0.620714\pi$
$601$	−18.1516	−0.740419	−0.370209	+	0.928948i	$0.620714\pi$
$602$	0	0
$603$	1.60390	0.0653158
$604$	9.37323	0.381392
$605$	−10.0312	−0.407826
$606$	−1.15362	−0.0468627
$607$	−10.5543	−0.428388	−0.214194	−	0.976791i	$-0.568712\pi$
$607$	−10.5543	−0.428388	−0.214194	+	0.976791i	$0.568712\pi$
$608$	−17.5825	−0.713064
$609$	0	0
$610$	−3.75851	−0.152178
$611$	11.8699	0.480206
$612$	−4.99877	−0.202063
$613$	−31.4795	−1.27144	−0.635722	−	0.771918i	$-0.719297\pi$
$613$	−31.4795	−1.27144	−0.635722	+	0.771918i	$0.719297\pi$
$614$	8.06004	0.325277
$615$	12.0598	0.486297
$616$	0	0
$617$	26.7487	1.07686	0.538431	−	0.842670i	$-0.319017\pi$
$617$	26.7487	1.07686	0.538431	+	0.842670i	$0.319017\pi$
$618$	−2.51300	−0.101088
$619$	27.8682	1.12012	0.560059	−	0.828453i	$-0.310779\pi$
$619$	27.8682	1.12012	0.560059	+	0.828453i	$0.310779\pi$
$620$	19.2241	0.772059
$621$	−4.03146	−0.161777
$622$	6.45806	0.258945
$623$	0	0
$624$	−3.05065	−0.122124
$625$	−3.68123	−0.147249
$626$	−11.3857	−0.455063
$627$	6.90343	0.275697
$628$	16.1462	0.644303
$629$	−20.8111	−0.829794
$630$	0	0
$631$	2.96274	0.117945	0.0589725	−	0.998260i	$-0.481218\pi$
$631$	2.96274	0.117945	0.0589725	+	0.998260i	$0.481218\pi$
$632$	11.9445	0.475127
$633$	23.5209	0.934871
$634$	−6.97845	−0.277150
$635$	−27.4740	−1.09027
$636$	10.1207	0.401312
$637$	0	0
$638$	−9.56093	−0.378521
$639$	13.0422	0.515943
$640$	−17.2871	−0.683334
$641$	−24.5454	−0.969484	−0.484742	−	0.874657i	$-0.661087\pi$
$641$	−24.5454	−0.969484	−0.484742	+	0.874657i	$0.661087\pi$
$642$	5.75050	0.226954
$643$	0.165870	0.00654126	0.00327063	−	0.999995i	$-0.498959\pi$
$643$	0.165870	0.00654126	0.00327063	+	0.999995i	$0.498959\pi$
$644$	0	0
$645$	3.70792	0.145999
$646$	−5.30746	−0.208819
$647$	29.0337	1.14143	0.570716	−	0.821148i	$-0.306666\pi$
$647$	29.0337	1.14143	0.570716	+	0.821148i	$0.306666\pi$
$648$	−2.01550	−0.0791761
$649$	1.56099	0.0612742
$650$	−1.97576	−0.0774956
$651$	0	0
$652$	28.0379	1.09805
$653$	−1.34558	−0.0526565	−0.0263283	−	0.999653i	$-0.508382\pi$
$653$	−1.34558	−0.0526565	−0.0263283	+	0.999653i	$0.508382\pi$
$654$	−7.53883	−0.294792
$655$	−22.3617	−0.873744
$656$	−18.5829	−0.725541
$657$	14.8852	0.580726
$658$	0	0
$659$	18.3937	0.716518	0.358259	−	0.933622i	$-0.383370\pi$
$659$	18.3937	0.716518	0.358259	+	0.933622i	$0.383370\pi$
$660$	5.30638	0.206551
$661$	5.77591	0.224657	0.112328	−	0.993671i	$-0.464169\pi$
$661$	5.77591	0.224657	0.112328	+	0.993671i	$0.464169\pi$
$662$	−5.06034	−0.196676
$663$	−3.87261	−0.150400
$664$	10.6260	0.412369
$665$	0	0
$666$	−3.86010	−0.149576
$667$	−34.1128	−1.32085
$668$	−37.2581	−1.44156
$669$	−2.84754	−0.110092
$670$	1.30898	0.0505704
$671$	−9.56271	−0.369164
$672$	0	0
$673$	−3.63349	−0.140061	−0.0700304	−	0.997545i	$-0.522310\pi$
$673$	−3.63349	−0.140061	−0.0700304	+	0.997545i	$0.522310\pi$
$674$	−9.82932	−0.378611
$675$	2.75060	0.105871
$676$	19.1816	0.737755
$677$	−16.3393	−0.627969	−0.313984	−	0.949428i	$-0.601664\pi$
$677$	−16.3393	−0.627969	−0.313984	+	0.949428i	$0.601664\pi$
$678$	−1.81388	−0.0696616
$679$	0	0
$680$	−8.86821	−0.340080
$681$	3.82551	0.146594
$682$	−8.49993	−0.325479
$683$	37.3755	1.43013	0.715066	−	0.699057i	$-0.246396\pi$
$683$	37.3755	1.43013	0.715066	+	0.699057i	$0.246396\pi$
$684$	5.66482	0.216600
$685$	13.8635	0.529695
$686$	0	0
$687$	15.3467	0.585512
$688$	−5.71353	−0.217826
$689$	7.84066	0.298705
$690$	−3.29018	−0.125255
$691$	18.9750	0.721845	0.360922	−	0.932596i	$-0.382462\pi$
$691$	18.9750	0.721845	0.360922	+	0.932596i	$0.382462\pi$
$692$	−35.9838	−1.36790
$693$	0	0
$694$	−3.34375	−0.126927
$695$	13.4611	0.510607
$696$	−17.0544	−0.646446
$697$	−23.5899	−0.893531
$698$	8.34396	0.315824
$699$	−12.1109	−0.458076
$700$	0	0
$701$	2.68843	0.101541	0.0507703	−	0.998710i	$-0.483832\pi$
$701$	2.68843	0.101541	0.0507703	+	0.998710i	$0.483832\pi$
$702$	−0.718302	−0.0271106
$703$	23.5841	0.889489
$704$	−3.62194	−0.136507
$705$	−13.4865	−0.507930
$706$	16.1451	0.607630
$707$	0	0
$708$	1.28092	0.0481398
$709$	−31.7483	−1.19233	−0.596166	−	0.802861i	$-0.703310\pi$
$709$	−31.7483	−1.19233	−0.596166	+	0.802861i	$0.703310\pi$
$710$	10.6441	0.399466
$711$	−5.92634	−0.222255
$712$	−29.6920	−1.11276
$713$	−30.3272	−1.13576
$714$	0	0
$715$	4.11092	0.153740
$716$	6.25072	0.233600
$717$	14.1414	0.528121
$718$	−3.89757	−0.145456
$719$	−39.3202	−1.46639	−0.733197	−	0.680016i	$-0.761973\pi$
$719$	−39.3202	−1.46639	−0.733197	+	0.680016i	$0.761973\pi$
$720$	3.46611	0.129174
$721$	0	0
$722$	−4.32432	−0.160935
$723$	3.55401	0.132175
$724$	20.9253	0.777683
$725$	23.2746	0.864396
$726$	3.63950	0.135075
$727$	−23.5355	−0.872884	−0.436442	−	0.899732i	$-0.643762\pi$
$727$	−23.5355	−0.872884	−0.436442	+	0.899732i	$0.643762\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.1482	0.449624
$731$	−7.25298	−0.268261
$732$	−7.84696	−0.290032
$733$	−8.36693	−0.309040	−0.154520	−	0.987990i	$-0.549383\pi$
$733$	−8.36693	−0.309040	−0.154520	+	0.987990i	$0.549383\pi$
$734$	−15.3729	−0.567425
$735$	0	0
$736$	21.3206	0.785888
$737$	3.33042	0.122678
$738$	−4.37551	−0.161065
$739$	−2.41594	−0.0888717	−0.0444358	−	0.999012i	$-0.514149\pi$
$739$	−2.41594	−0.0888717	−0.0444358	+	0.999012i	$0.514149\pi$
$740$	18.1281	0.666401
$741$	4.38861	0.161220
$742$	0	0
$743$	−32.2364	−1.18264	−0.591319	−	0.806437i	$-0.701393\pi$
$743$	−32.2364	−1.18264	−0.591319	+	0.806437i	$0.701393\pi$
$744$	−15.1618	−0.555860
$745$	−34.7580	−1.27343
$746$	8.30173	0.303948
$747$	−5.27216	−0.192898
$748$	−10.3797	−0.379520
$749$	0	0
$750$	6.32546	0.230973
$751$	38.1440	1.39190	0.695948	−	0.718092i	$-0.254984\pi$
$751$	38.1440	1.39190	0.695948	+	0.718092i	$0.254984\pi$
$752$	20.7813	0.757817
$753$	12.8036	0.466590
$754$	−6.07802	−0.221348
$755$	−8.25050	−0.300267
$756$	0	0
$757$	−36.5240	−1.32749	−0.663744	−	0.747959i	$-0.731034\pi$
$757$	−36.5240	−1.32749	−0.663744	+	0.747959i	$0.731034\pi$
$758$	0.0267798	0.000972685 0
$759$	−8.37113	−0.303853
$760$	10.0498	0.364545
$761$	9.33868	0.338527	0.169264	−	0.985571i	$-0.445861\pi$
$761$	9.33868	0.338527	0.169264	+	0.985571i	$0.445861\pi$
$762$	9.96806	0.361105
$763$	0	0
$764$	34.8891	1.26224
$765$	4.40001	0.159083
$766$	19.8378	0.716768
$767$	0.992344	0.0358314
$768$	2.78351	0.100441
$769$	−50.8397	−1.83333	−0.916664	−	0.399659i	$-0.869128\pi$
$769$	−50.8397	−1.83333	−0.916664	+	0.399659i	$0.869128\pi$
$770$	0	0
$771$	−4.96308	−0.178741
$772$	33.9186	1.22076
$773$	−30.7449	−1.10582	−0.552909	−	0.833242i	$-0.686482\pi$
$773$	−30.7449	−1.10582	−0.552909	+	0.833242i	$0.686482\pi$
$774$	−1.34530	−0.0483558
$775$	20.6917	0.743269
$776$	16.9684	0.609129
$777$	0	0
$778$	6.97445	0.250046
$779$	26.7330	0.957811
$780$	3.37334	0.120785
$781$	27.0816	0.969056
$782$	6.43585	0.230146
$783$	8.46165	0.302395
$784$	0	0
$785$	−14.2122	−0.507255
$786$	8.11324	0.289390
$787$	−0.618568	−0.0220496	−0.0110248	−	0.999939i	$-0.503509\pi$
$787$	−0.618568	−0.0220496	−0.0110248	+	0.999939i	$0.503509\pi$
$788$	23.9161	0.851977
$789$	6.86664	0.244459
$790$	−4.83664	−0.172080
$791$	0	0
$792$	−4.18508	−0.148710
$793$	−6.07915	−0.215877
$794$	5.46474	0.193936
$795$	−8.90845	−0.315950
$796$	3.99683	0.141664
$797$	−13.3217	−0.471880	−0.235940	−	0.971768i	$-0.575817\pi$
$797$	−13.3217	−0.471880	−0.235940	+	0.971768i	$0.575817\pi$
$798$	0	0
$799$	26.3806	0.933280
$800$	−14.5467	−0.514303
$801$	14.7319	0.520526
$802$	11.4770	0.405268
$803$	30.9084	1.09073
$804$	2.73288	0.0963811
$805$	0	0
$806$	−5.40352	−0.190331
$807$	15.5252	0.546512
$808$	−4.27290	−0.150320
$809$	9.74839	0.342735	0.171368	−	0.985207i	$-0.445181\pi$
$809$	9.74839	0.342735	0.171368	+	0.985207i	$0.445181\pi$
$810$	0.816125	0.0286757
$811$	−13.4503	−0.472302	−0.236151	−	0.971716i	$-0.575886\pi$
$811$	−13.4503	−0.472302	−0.236151	+	0.971716i	$0.575886\pi$
$812$	0	0
$813$	−16.7480	−0.587377
$814$	−8.01531	−0.280937
$815$	−24.6795	−0.864486
$816$	−6.77999	−0.237347
$817$	8.21938	0.287560
$818$	−19.2461	−0.672923
$819$	0	0
$820$	20.5486	0.717587
$821$	−22.9344	−0.800415	−0.400207	−	0.916425i	$-0.631062\pi$
$821$	−22.9344	−0.800415	−0.400207	+	0.916425i	$0.631062\pi$
$822$	−5.02992	−0.175439
$823$	32.9785	1.14956	0.574779	−	0.818309i	$-0.305088\pi$
$823$	32.9785	1.14956	0.574779	+	0.818309i	$0.305088\pi$
$824$	−9.30789	−0.324256
$825$	5.71148	0.198848
$826$	0	0
$827$	−50.0947	−1.74196	−0.870982	−	0.491316i	$-0.836516\pi$
$827$	−50.0947	−1.74196	−0.870982	+	0.491316i	$0.836516\pi$
$828$	−6.86918	−0.238721
$829$	25.6020	0.889194	0.444597	−	0.895731i	$-0.353347\pi$
$829$	25.6020	0.889194	0.444597	+	0.895731i	$0.353347\pi$
$830$	−4.30274	−0.149350
$831$	7.47049	0.259148
$832$	−2.30252	−0.0798254
$833$	0	0
$834$	−4.88392	−0.169116
$835$	32.7953	1.13493
$836$	11.7627	0.406822
$837$	7.52264	0.260020
$838$	−15.8566	−0.547757
$839$	−17.6478	−0.609269	−0.304634	−	0.952469i	$-0.598534\pi$
$839$	−17.6478	−0.609269	−0.304634	+	0.952469i	$0.598534\pi$
$840$	0	0
$841$	42.5995	1.46895
$842$	−17.1837	−0.592190
$843$	−32.2499	−1.11075
$844$	40.0771	1.37951
$845$	−16.8840	−0.580829
$846$	4.89314	0.168230
$847$	0	0
$848$	13.7270	0.471389
$849$	−11.3385	−0.389137
$850$	−4.39107	−0.150613
$851$	−28.5981	−0.980331
$852$	22.2226	0.761334
$853$	−26.6907	−0.913873	−0.456936	−	0.889499i	$-0.651053\pi$
$853$	−26.6907	−0.913873	−0.456936	+	0.889499i	$0.651053\pi$
$854$	0	0
$855$	−4.98628	−0.170527
$856$	21.2992	0.727993
$857$	−3.64280	−0.124436	−0.0622178	−	0.998063i	$-0.519817\pi$
$857$	−3.64280	−0.124436	−0.0622178	+	0.998063i	$0.519817\pi$
$858$	−1.49152	−0.0509196
$859$	10.5055	0.358444	0.179222	−	0.983809i	$-0.442642\pi$
$859$	10.5055	0.358444	0.179222	+	0.983809i	$0.442642\pi$
$860$	6.31790	0.215438
$861$	0	0
$862$	−1.91941	−0.0653754
$863$	−9.66704	−0.329070	−0.164535	−	0.986371i	$-0.552612\pi$
$863$	−9.66704	−0.329070	−0.164535	+	0.986371i	$0.552612\pi$
$864$	−5.28856	−0.179920
$865$	31.6736	1.07693
$866$	−5.08897	−0.172930
$867$	8.39322	0.285049
$868$	0	0
$869$	−12.3058	−0.417445
$870$	6.90577	0.234127
$871$	2.11720	0.0717384
$872$	−27.9230	−0.945593
$873$	−8.41896	−0.284939
$874$	−7.29337	−0.246702
$875$	0	0
$876$	25.3628	0.856929
$877$	−42.2581	−1.42696	−0.713478	−	0.700678i	$-0.752881\pi$
$877$	−42.2581	−1.42696	−0.713478	+	0.700678i	$0.752881\pi$
$878$	13.5767	0.458193
$879$	7.69626	0.259588
$880$	7.19721	0.242618
$881$	1.78601	0.0601721	0.0300860	−	0.999547i	$-0.490422\pi$
$881$	1.78601	0.0601721	0.0300860	+	0.999547i	$0.490422\pi$
$882$	0	0
$883$	−16.8203	−0.566048	−0.283024	−	0.959113i	$-0.591338\pi$
$883$	−16.8203	−0.566048	−0.283024	+	0.959113i	$0.591338\pi$
$884$	−6.59853	−0.221932
$885$	−1.12749	−0.0379001
$886$	6.84422	0.229936
$887$	−16.4762	−0.553215	−0.276608	−	0.960983i	$-0.589210\pi$
$887$	−16.4762	−0.553215	−0.276608	+	0.960983i	$0.589210\pi$
$888$	−14.2974	−0.479789
$889$	0	0
$890$	12.0231	0.403014
$891$	2.07645	0.0695638
$892$	−4.85191	−0.162454
$893$	−29.8956	−1.00042
$894$	12.6108	0.421769
$895$	−5.50200	−0.183912
$896$	0	0
$897$	−5.32165	−0.177685
$898$	−12.7867	−0.426696
$899$	63.6539	2.12298
$900$	4.68673	0.156224
$901$	17.4256	0.580533
$902$	−9.08553	−0.302515
$903$	0	0
$904$	−6.71842	−0.223451
$905$	−18.4189	−0.612264
$906$	2.99344	0.0994502
$907$	54.3255	1.80385	0.901924	−	0.431895i	$-0.142155\pi$
$907$	54.3255	1.80385	0.901924	+	0.431895i	$0.142155\pi$
$908$	6.51826	0.216316
$909$	2.12002	0.0703167
$910$	0	0
$911$	54.5129	1.80609	0.903047	−	0.429542i	$-0.141325\pi$
$911$	54.5129	1.80609	0.903047	+	0.429542i	$0.141325\pi$
$912$	7.68337	0.254422
$913$	−10.9474	−0.362306
$914$	−6.60630	−0.218517
$915$	6.90705	0.228340
$916$	26.1491	0.863991
$917$	0	0
$918$	−1.59641	−0.0526893
$919$	5.92200	0.195349	0.0976744	−	0.995218i	$-0.468860\pi$
$919$	5.92200	0.195349	0.0976744	+	0.995218i	$0.468860\pi$
$920$	−12.1865	−0.401776
$921$	−14.8120	−0.488073
$922$	−16.5207	−0.544082
$923$	17.2162	0.566676
$924$	0	0
$925$	19.5120	0.641551
$926$	18.3450	0.602853
$927$	4.61816	0.151680
$928$	−44.7499	−1.46899
$929$	−35.1114	−1.15197	−0.575983	−	0.817461i	$-0.695381\pi$
$929$	−35.1114	−1.15197	−0.575983	+	0.817461i	$0.695381\pi$
$930$	6.13941	0.201319
$931$	0	0
$932$	−20.6357	−0.675944
$933$	−11.8680	−0.388542
$934$	0.888529	0.0290736
$935$	9.13642	0.298793
$936$	−2.66051	−0.0869616
$937$	23.7251	0.775066	0.387533	−	0.921856i	$-0.373327\pi$
$937$	23.7251	0.775066	0.387533	+	0.921856i	$0.373327\pi$
$938$	0	0
$939$	20.9236	0.682815
$940$	−22.9795	−0.749510
$941$	6.41717	0.209194	0.104597	−	0.994515i	$-0.466645\pi$
$941$	6.41717	0.209194	0.104597	+	0.994515i	$0.466645\pi$
$942$	5.15644	0.168006
$943$	−32.4166	−1.05563
$944$	1.73735	0.0565459
$945$	0	0
$946$	−2.79345	−0.0908230
$947$	−8.35040	−0.271351	−0.135676	−	0.990753i	$-0.543321\pi$
$947$	−8.35040	−0.271351	−0.135676	+	0.990753i	$0.543321\pi$
$948$	−10.0979	−0.327963
$949$	19.6489	0.637830
$950$	4.97615	0.161448
$951$	12.8244	0.415858
$952$	0	0
$953$	−3.45651	−0.111967	−0.0559836	−	0.998432i	$-0.517829\pi$
$953$	−3.45651	−0.111967	−0.0559836	+	0.998432i	$0.517829\pi$
$954$	3.23215	0.104645
$955$	−30.7100	−0.993753
$956$	24.0955	0.779304
$957$	17.5702	0.567964
$958$	−17.7477	−0.573401
$959$	0	0
$960$	2.61609	0.0844340
$961$	25.5901	0.825486
$962$	−5.09545	−0.164284
$963$	−10.5677	−0.340541
$964$	6.05567	0.195040
$965$	−29.8558	−0.961092
$966$	0	0
$967$	−45.9988	−1.47922	−0.739610	−	0.673035i	$-0.764990\pi$
$967$	−45.9988	−1.47922	−0.739610	+	0.673035i	$0.764990\pi$
$968$	13.4803	0.433274
$969$	9.75357	0.313330
$970$	−6.87093	−0.220612
$971$	−50.7728	−1.62938	−0.814689	−	0.579899i	$-0.803092\pi$
$971$	−50.7728	−1.62938	−0.814689	+	0.579899i	$0.803092\pi$
$972$	1.70389	0.0546524
$973$	0	0
$974$	16.0798	0.515230
$975$	3.63087	0.116281
$976$	−10.6431	−0.340677
$977$	−7.71371	−0.246783	−0.123392	−	0.992358i	$-0.539377\pi$
$977$	−7.71371	−0.246783	−0.123392	+	0.992358i	$0.539377\pi$
$978$	8.95419	0.286324
$979$	30.5901	0.977662
$980$	0	0
$981$	13.8542	0.442330
$982$	−9.60194	−0.306410
$983$	−24.2536	−0.773569	−0.386784	−	0.922170i	$-0.626414\pi$
$983$	−24.2536	−0.773569	−0.386784	+	0.922170i	$0.626414\pi$
$984$	−16.2064	−0.516642
$985$	−21.0514	−0.670755
$986$	−13.5082	−0.430190
$987$	0	0
$988$	7.47773	0.237898
$989$	−9.96686	−0.316928
$990$	1.69465	0.0538594
$991$	12.7716	0.405703	0.202852	−	0.979209i	$-0.434979\pi$
$991$	12.7716	0.405703	0.202852	+	0.979209i	$0.434979\pi$
$992$	−39.7839	−1.26314
$993$	9.29944	0.295109
$994$	0	0
$995$	−3.51809	−0.111531
$996$	−8.98321	−0.284644
$997$	1.24950	0.0395722	0.0197861	−	0.999804i	$-0.493701\pi$
$997$	1.24950	0.0395722	0.0197861	+	0.999804i	$0.493701\pi$
$998$	2.97076	0.0940377
$999$	7.09374	0.224436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7203.2.a.i.1.15		24
7.6	odd	2		7203.2.a.k.1.15		24
49.2	even	21		147.2.m.a.4.3	✓	48
49.25	even	21		147.2.m.a.37.3	yes	48
147.2	odd	42		441.2.bb.c.298.2		48
147.74	odd	42		441.2.bb.c.37.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.m.a.4.3	✓	48	49.2	even	21
147.2.m.a.37.3	yes	48	49.25	even	21
441.2.bb.c.37.2		48	147.74	odd	42
441.2.bb.c.298.2		48	147.2	odd	42
7203.2.a.i.1.15		24	1.1	even	1	trivial
7203.2.a.k.1.15		24	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7203 = 3 \cdot 7^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7203.a (trivial)

\(f(q)\)	\(=\)	\(q+0.544156 q^{2} -1.00000 q^{3} -1.70389 q^{4} +1.49980 q^{5} -0.544156 q^{6} -2.01550 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.544156 q^{2} -1.00000 q^{3} -1.70389 q^{4} +1.49980 q^{5} -0.544156 q^{6} -2.01550 q^{8} +1.00000 q^{9} +0.816125 q^{10} +2.07645 q^{11} +1.70389 q^{12} +1.32003 q^{13} -1.49980 q^{15} +2.31105 q^{16} +2.93373 q^{17} +0.544156 q^{18} -3.32463 q^{19} -2.55550 q^{20} +1.12991 q^{22} +4.03146 q^{23} +2.01550 q^{24} -2.75060 q^{25} +0.718302 q^{26} -1.00000 q^{27} -8.46165 q^{29} -0.816125 q^{30} -7.52264 q^{31} +5.28856 q^{32} -2.07645 q^{33} +1.59641 q^{34} -1.70389 q^{36} -7.09374 q^{37} -1.80912 q^{38} -1.32003 q^{39} -3.02284 q^{40} -8.04091 q^{41} -2.47227 q^{43} -3.53806 q^{44} +1.49980 q^{45} +2.19374 q^{46} +8.99217 q^{47} -2.31105 q^{48} -1.49675 q^{50} -2.93373 q^{51} -2.24919 q^{52} +5.93975 q^{53} -0.544156 q^{54} +3.11427 q^{55} +3.32463 q^{57} -4.60445 q^{58} +0.751758 q^{59} +2.55550 q^{60} -4.60531 q^{61} -4.09349 q^{62} -1.74429 q^{64} +1.97978 q^{65} -1.12991 q^{66} +1.60390 q^{67} -4.99877 q^{68} -4.03146 q^{69} +13.0422 q^{71} -2.01550 q^{72} +14.8852 q^{73} -3.86010 q^{74} +2.75060 q^{75} +5.66482 q^{76} -0.718302 q^{78} -5.92634 q^{79} +3.46611 q^{80} +1.00000 q^{81} -4.37551 q^{82} -5.27216 q^{83} +4.40001 q^{85} -1.34530 q^{86} +8.46165 q^{87} -4.18508 q^{88} +14.7319 q^{89} +0.816125 q^{90} -6.86918 q^{92} +7.52264 q^{93} +4.89314 q^{94} -4.98628 q^{95} -5.28856 q^{96} -8.41896 q^{97} +2.07645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} - 24 q^{3} + 18 q^{4} + 6 q^{6} - 18 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 - 24 * q^3 + 18 * q^4 + 6 * q^6 - 18 * q^8 + 24 * q^9	\( 24 q - 6 q^{2} - 24 q^{3} + 18 q^{4} + 6 q^{6} - 18 q^{8} + 24 q^{9} + 12 q^{10} - 12 q^{11} - 18 q^{12} + 14 q^{13} + 6 q^{16} - 2 q^{17} - 6 q^{18} + 26 q^{19} - 6 q^{20} - 24 q^{22} - 24 q^{23} + 18 q^{24} + 13 q^{26} - 24 q^{27} - 36 q^{29} - 12 q^{30} + 36 q^{31} - 42 q^{32} + 12 q^{33} + 4 q^{34} + 18 q^{36} - 50 q^{37} - 38 q^{38} - 14 q^{39} + 28 q^{40} - 25 q^{41} - 36 q^{43} - 30 q^{44} - 30 q^{46} - 6 q^{47} - 6 q^{48} - 6 q^{50} + 2 q^{51} + 41 q^{52} - 63 q^{53} + 6 q^{54} + 44 q^{55} - 26 q^{57} - 3 q^{58} + 41 q^{59} + 6 q^{60} + 38 q^{61} - 22 q^{62} - 6 q^{64} - 14 q^{65} + 24 q^{66} - 34 q^{67} - 22 q^{68} + 24 q^{69} - 32 q^{71} - 18 q^{72} + 13 q^{73} - 43 q^{74} + 105 q^{76} - 13 q^{78} - 34 q^{79} - 55 q^{80} + 24 q^{81} - 28 q^{82} - 42 q^{83} - 92 q^{85} + 40 q^{86} + 36 q^{87} - 10 q^{88} - 32 q^{89} + 12 q^{90} - 14 q^{92} - 36 q^{93} + 64 q^{94} - 38 q^{95} + 42 q^{96} + 62 q^{97} - 12 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 - 24 * q^3 + 18 * q^4 + 6 * q^6 - 18 * q^8 + 24 * q^9 + 12 * q^10 - 12 * q^11 - 18 * q^12 + 14 * q^13 + 6 * q^16 - 2 * q^17 - 6 * q^18 + 26 * q^19 - 6 * q^20 - 24 * q^22 - 24 * q^23 + 18 * q^24 + 13 * q^26 - 24 * q^27 - 36 * q^29 - 12 * q^30 + 36 * q^31 - 42 * q^32 + 12 * q^33 + 4 * q^34 + 18 * q^36 - 50 * q^37 - 38 * q^38 - 14 * q^39 + 28 * q^40 - 25 * q^41 - 36 * q^43 - 30 * q^44 - 30 * q^46 - 6 * q^47 - 6 * q^48 - 6 * q^50 + 2 * q^51 + 41 * q^52 - 63 * q^53 + 6 * q^54 + 44 * q^55 - 26 * q^57 - 3 * q^58 + 41 * q^59 + 6 * q^60 + 38 * q^61 - 22 * q^62 - 6 * q^64 - 14 * q^65 + 24 * q^66 - 34 * q^67 - 22 * q^68 + 24 * q^69 - 32 * q^71 - 18 * q^72 + 13 * q^73 - 43 * q^74 + 105 * q^76 - 13 * q^78 - 34 * q^79 - 55 * q^80 + 24 * q^81 - 28 * q^82 - 42 * q^83 - 92 * q^85 + 40 * q^86 + 36 * q^87 - 10 * q^88 - 32 * q^89 + 12 * q^90 - 14 * q^92 - 36 * q^93 + 64 * q^94 - 38 * q^95 + 42 * q^96 + 62 * q^97 - 12 * q^99

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