LMFDB - Embedded newform 6223.2.a.p.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6223,2,Mod(1,6223)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6223, 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("6223.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6223 = 7^{2} \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6223.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:	$49.6909051778$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	no (minimal twist has level 889)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08520 q^{2} -2.29235 q^{3} +2.34805 q^{4} -0.933672 q^{5} +4.78000 q^{6} -0.725759 q^{8} +2.25486 q^{9} +O(q^{10})$	\(q-2.08520 q^{2} -2.29235 q^{3} +2.34805 q^{4} -0.933672 q^{5} +4.78000 q^{6} -0.725759 q^{8} +2.25486 q^{9} +1.94689 q^{10} +2.78681 q^{11} -5.38255 q^{12} +0.193825 q^{13} +2.14030 q^{15} -3.18275 q^{16} +2.51616 q^{17} -4.70182 q^{18} +7.64841 q^{19} -2.19231 q^{20} -5.81105 q^{22} -5.15083 q^{23} +1.66369 q^{24} -4.12826 q^{25} -0.404165 q^{26} +1.70813 q^{27} +5.69651 q^{29} -4.46295 q^{30} -0.00490923 q^{31} +8.08819 q^{32} -6.38833 q^{33} -5.24670 q^{34} +5.29452 q^{36} +6.30470 q^{37} -15.9485 q^{38} -0.444315 q^{39} +0.677621 q^{40} -0.548648 q^{41} +1.75331 q^{43} +6.54357 q^{44} -2.10530 q^{45} +10.7405 q^{46} +11.3206 q^{47} +7.29598 q^{48} +8.60823 q^{50} -5.76792 q^{51} +0.455112 q^{52} +12.5271 q^{53} -3.56179 q^{54} -2.60197 q^{55} -17.5328 q^{57} -11.8784 q^{58} +5.48337 q^{59} +5.02554 q^{60} +9.56485 q^{61} +0.0102367 q^{62} -10.5000 q^{64} -0.180970 q^{65} +13.3209 q^{66} +14.4966 q^{67} +5.90809 q^{68} +11.8075 q^{69} -15.3167 q^{71} -1.63648 q^{72} +6.92829 q^{73} -13.1466 q^{74} +9.46340 q^{75} +17.9589 q^{76} +0.926486 q^{78} -9.73689 q^{79} +2.97165 q^{80} -10.6802 q^{81} +1.14404 q^{82} +0.0567325 q^{83} -2.34927 q^{85} -3.65600 q^{86} -13.0584 q^{87} -2.02255 q^{88} -2.59339 q^{89} +4.38996 q^{90} -12.0944 q^{92} +0.0112537 q^{93} -23.6057 q^{94} -7.14111 q^{95} -18.5409 q^{96} +8.05520 q^{97} +6.28385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 2 q^{2} + 11 q^{3} + 38 q^{4} + 16 q^{5} + 11 q^{6} + 47 q^{9}+O(q^{10}) $ 38 * q - 2 * q^2 + 11 * q^3 + 38 * q^4 + 16 * q^5 + 11 * q^6 + 47 * q^9	$ 38 q - 2 q^{2} + 11 q^{3} + 38 q^{4} + 16 q^{5} + 11 q^{6} + 47 q^{9} + 12 q^{10} - 2 q^{11} + 30 q^{12} + 21 q^{13} + 7 q^{15} + 46 q^{16} + 58 q^{17} - 13 q^{18} + 17 q^{19} + 44 q^{20} + 21 q^{22} + 7 q^{23} + 21 q^{24} + 52 q^{25} + 49 q^{26} + 35 q^{27} - 2 q^{29} + 6 q^{30} + 2 q^{31} - 22 q^{32} + 29 q^{33} + 37 q^{34} + 25 q^{36} + 11 q^{37} + 40 q^{38} + 2 q^{39} - 8 q^{40} + 68 q^{41} - 38 q^{43} + 43 q^{44} + 60 q^{45} - 28 q^{46} + 35 q^{47} + 66 q^{48} - 25 q^{50} - 3 q^{51} + 32 q^{52} - 18 q^{53} - 68 q^{54} + 19 q^{55} - 31 q^{57} + 55 q^{58} + 21 q^{59} - 11 q^{60} + 5 q^{61} + 38 q^{62} + 18 q^{64} - 9 q^{65} + 20 q^{66} + 6 q^{67} + 74 q^{68} + 53 q^{69} - 26 q^{71} + 24 q^{72} + 22 q^{73} - 2 q^{74} + 38 q^{75} + 39 q^{76} - 114 q^{78} - 14 q^{79} + 140 q^{80} + 58 q^{81} - 8 q^{82} + 46 q^{83} - 11 q^{85} + 51 q^{86} + 59 q^{87} - 4 q^{88} + 74 q^{89} + q^{90} - 81 q^{92} + 92 q^{93} - 36 q^{94} + 20 q^{95} - 108 q^{96} + 66 q^{97} + 16 q^{99}+O(q^{100}) $ 38 * q - 2 * q^2 + 11 * q^3 + 38 * q^4 + 16 * q^5 + 11 * q^6 + 47 * q^9 + 12 * q^10 - 2 * q^11 + 30 * q^12 + 21 * q^13 + 7 * q^15 + 46 * q^16 + 58 * q^17 - 13 * q^18 + 17 * q^19 + 44 * q^20 + 21 * q^22 + 7 * q^23 + 21 * q^24 + 52 * q^25 + 49 * q^26 + 35 * q^27 - 2 * q^29 + 6 * q^30 + 2 * q^31 - 22 * q^32 + 29 * q^33 + 37 * q^34 + 25 * q^36 + 11 * q^37 + 40 * q^38 + 2 * q^39 - 8 * q^40 + 68 * q^41 - 38 * q^43 + 43 * q^44 + 60 * q^45 - 28 * q^46 + 35 * q^47 + 66 * q^48 - 25 * q^50 - 3 * q^51 + 32 * q^52 - 18 * q^53 - 68 * q^54 + 19 * q^55 - 31 * q^57 + 55 * q^58 + 21 * q^59 - 11 * q^60 + 5 * q^61 + 38 * q^62 + 18 * q^64 - 9 * q^65 + 20 * q^66 + 6 * q^67 + 74 * q^68 + 53 * q^69 - 26 * q^71 + 24 * q^72 + 22 * q^73 - 2 * q^74 + 38 * q^75 + 39 * q^76 - 114 * q^78 - 14 * q^79 + 140 * q^80 + 58 * q^81 - 8 * q^82 + 46 * q^83 - 11 * q^85 + 51 * q^86 + 59 * q^87 - 4 * q^88 + 74 * q^89 + q^90 - 81 * q^92 + 92 * q^93 - 36 * q^94 + 20 * q^95 - 108 * q^96 + 66 * q^97 + 16 * 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 $

$2$	−2.08520	−1.47446	−0.737229	−	0.675643i	$-0.763866\pi$
$2$	−2.08520	−1.47446	−0.737229	+	0.675643i	$0.763866\pi$
$3$	−2.29235	−1.32349	−0.661744	−	0.749730i	$-0.730183\pi$
$3$	−2.29235	−1.32349	−0.661744	+	0.749730i	$0.730183\pi$
$4$	2.34805	1.17403
$5$	−0.933672	−0.417551	−0.208776	−	0.977964i	$-0.566948\pi$
$5$	−0.933672	−0.417551	−0.208776	+	0.977964i	$0.566948\pi$
$6$	4.78000	1.95143
$7$	0	0
$7$	0	0
$8$	−0.725759	−0.256594
$9$	2.25486	0.751619
$10$	1.94689	0.615661
$11$	2.78681	0.840255	0.420127	−	0.907465i	$-0.361985\pi$
$11$	2.78681	0.840255	0.420127	+	0.907465i	$0.361985\pi$
$12$	−5.38255	−1.55381
$13$	0.193825	0.0537575	0.0268788	−	0.999639i	$-0.491443\pi$
$13$	0.193825	0.0537575	0.0268788	+	0.999639i	$0.491443\pi$
$14$	0	0
$15$	2.14030	0.552623
$16$	−3.18275	−0.795689
$17$	2.51616	0.610259	0.305130	−	0.952311i	$-0.401300\pi$
$17$	2.51616	0.610259	0.305130	+	0.952311i	$0.401300\pi$
$18$	−4.70182	−1.10823
$19$	7.64841	1.75467	0.877333	−	0.479881i	$-0.159320\pi$
$19$	7.64841	1.75467	0.877333	+	0.479881i	$0.159320\pi$
$20$	−2.19231	−0.490216
$21$	0	0
$22$	−5.81105	−1.23892
$23$	−5.15083	−1.07402	−0.537012	−	0.843575i	$-0.680447\pi$
$23$	−5.15083	−1.07402	−0.537012	+	0.843575i	$0.680447\pi$
$24$	1.66369	0.339599
$25$	−4.12826	−0.825651
$26$	−0.404165	−0.0792632
$27$	1.70813	0.328729
$28$	0	0
$29$	5.69651	1.05782	0.528908	−	0.848679i	$-0.322602\pi$
$29$	5.69651	1.05782	0.528908	+	0.848679i	$0.322602\pi$
$30$	−4.46295	−0.814820
$31$	−0.00490923	−0.000881724 0	−0.000440862	−	1.00000i	$-0.500140\pi$
$31$	−0.00490923	−0.000881724 0	−0.000440862		1.00000i	$0.500140\pi$
$32$	8.08819	1.42980
$33$	−6.38833	−1.11207
$34$	−5.24670	−0.899802
$35$	0	0
$36$	5.29452	0.882420
$37$	6.30470	1.03649	0.518244	−	0.855233i	$-0.326586\pi$
$37$	6.30470	1.03649	0.518244	+	0.855233i	$0.326586\pi$
$38$	−15.9485	−2.58718
$39$	−0.444315	−0.0711474
$40$	0.677621	0.107141
$41$	−0.548648	−0.0856845	−0.0428422	−	0.999082i	$-0.513641\pi$
$41$	−0.548648	−0.0856845	−0.0428422	+	0.999082i	$0.513641\pi$
$42$	0	0
$43$	1.75331	0.267377	0.133689	−	0.991023i	$-0.457318\pi$
$43$	1.75331	0.267377	0.133689	+	0.991023i	$0.457318\pi$
$44$	6.54357	0.986481
$45$	−2.10530	−0.313839
$46$	10.7405	1.58360
$47$	11.3206	1.65128	0.825639	−	0.564199i	$-0.190815\pi$
$47$	11.3206	1.65128	0.825639	+	0.564199i	$0.190815\pi$
$48$	7.29598	1.05308
$49$	0	0
$50$	8.60823	1.21739
$51$	−5.76792	−0.807671
$52$	0.455112	0.0631127
$53$	12.5271	1.72074	0.860368	−	0.509673i	$-0.170234\pi$
$53$	12.5271	1.72074	0.860368	+	0.509673i	$0.170234\pi$
$54$	−3.56179	−0.484698
$55$	−2.60197	−0.350849
$56$	0	0
$57$	−17.5328	−2.32228
$58$	−11.8784	−1.55970
$59$	5.48337	0.713874	0.356937	−	0.934128i	$-0.383821\pi$
$59$	5.48337	0.713874	0.356937	+	0.934128i	$0.383821\pi$
$60$	5.02554	0.648794
$61$	9.56485	1.22465	0.612327	−	0.790605i	$-0.290234\pi$
$61$	9.56485	1.22465	0.612327	+	0.790605i	$0.290234\pi$
$62$	0.0102367	0.00130007
$63$	0	0
$64$	−10.5000	−1.31250
$65$	−0.180970	−0.0224465
$66$	13.3209	1.63969
$67$	14.4966	1.77104	0.885519	−	0.464604i	$-0.153803\pi$
$67$	14.4966	1.77104	0.885519	+	0.464604i	$0.153803\pi$
$68$	5.90809	0.716461
$69$	11.8075	1.42146
$70$	0	0
$71$	−15.3167	−1.81776	−0.908879	−	0.417059i	$-0.863061\pi$
$71$	−15.3167	−1.81776	−0.908879	+	0.417059i	$0.863061\pi$
$72$	−1.63648	−0.192861
$73$	6.92829	0.810895	0.405447	−	0.914118i	$-0.367116\pi$
$73$	6.92829	0.810895	0.405447	+	0.914118i	$0.367116\pi$
$74$	−13.1466	−1.52826
$75$	9.46340	1.09274
$76$	17.9589	2.06002
$77$	0	0
$78$	0.926486	0.104904
$79$	−9.73689	−1.09549	−0.547743	−	0.836647i	$-0.684513\pi$
$79$	−9.73689	−1.09549	−0.547743	+	0.836647i	$0.684513\pi$
$80$	2.97165	0.332241
$81$	−10.6802	−1.18669
$82$	1.14404	0.126338
$83$	0.0567325	0.00622720	0.00311360	−	0.999995i	$-0.499009\pi$
$83$	0.0567325	0.00622720	0.00311360	+	0.999995i	$0.499009\pi$
$84$	0	0
$85$	−2.34927	−0.254814
$86$	−3.65600	−0.394237
$87$	−13.0584	−1.40001
$88$	−2.02255	−0.215605
$89$	−2.59339	−0.274899	−0.137449	−	0.990509i	$-0.543890\pi$
$89$	−2.59339	−0.274899	−0.137449	+	0.990509i	$0.543890\pi$
$90$	4.38996	0.462743
$91$	0	0
$92$	−12.0944	−1.26093
$93$	0.0112537	0.00116695
$94$	−23.6057	−2.43474
$95$	−7.14111	−0.732663
$96$	−18.5409	−1.89233
$97$	8.05520	0.817881	0.408941	−	0.912561i	$-0.365898\pi$
$97$	8.05520	0.817881	0.408941	+	0.912561i	$0.365898\pi$
$98$	0	0
$99$	6.28385	0.631551
$100$	−9.69336	−0.969336
$101$	6.45591	0.642387	0.321194	−	0.947014i	$-0.395916\pi$
$101$	6.45591	0.642387	0.321194	+	0.947014i	$0.395916\pi$
$102$	12.0273	1.19088
$103$	12.6560	1.24704	0.623518	−	0.781809i	$-0.285703\pi$
$103$	12.6560	1.24704	0.623518	+	0.781809i	$0.285703\pi$
$104$	−0.140671	−0.0137939
$105$	0	0
$106$	−26.1216	−2.53715
$107$	13.9590	1.34946	0.674732	−	0.738063i	$-0.264259\pi$
$107$	13.9590	1.34946	0.674732	+	0.738063i	$0.264259\pi$
$108$	4.01077	0.385937
$109$	−16.2293	−1.55448	−0.777241	−	0.629203i	$-0.783382\pi$
$109$	−16.2293	−1.55448	−0.777241	+	0.629203i	$0.783382\pi$
$110$	5.42562	0.517312
$111$	−14.4526	−1.37178
$112$	0	0
$113$	0.0544202	0.00511942	0.00255971	−	0.999997i	$-0.499185\pi$
$113$	0.0544202	0.00511942	0.00255971	+	0.999997i	$0.499185\pi$
$114$	36.5594	3.42410
$115$	4.80919	0.448460
$116$	13.3757	1.24190
$117$	0.437049	0.0404052
$118$	−11.4339	−1.05258
$119$	0	0
$120$	−1.55334	−0.141800
$121$	−3.23369	−0.293972
$122$	−19.9446	−1.80570
$123$	1.25769	0.113402
$124$	−0.0115271	−0.00103517
$125$	8.52280	0.762302
$126$	0	0
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	5.71815	0.505418
$129$	−4.01920	−0.353871
$130$	0.377357	0.0330964
$131$	−5.77731	−0.504766	−0.252383	−	0.967627i	$-0.581214\pi$
$131$	−5.77731	−0.504766	−0.252383	+	0.967627i	$0.581214\pi$
$132$	−15.0001	−1.30560
$133$	0	0
$134$	−30.2282	−2.61132
$135$	−1.59483	−0.137261
$136$	−1.82613	−0.156589
$137$	−8.77617	−0.749799	−0.374899	−	0.927065i	$-0.622323\pi$
$137$	−8.77617	−0.749799	−0.374899	+	0.927065i	$0.622323\pi$
$138$	−24.6210	−2.09588
$139$	−11.7256	−0.994555	−0.497277	−	0.867592i	$-0.665667\pi$
$139$	−11.7256	−0.994555	−0.497277	+	0.867592i	$0.665667\pi$
$140$	0	0
$141$	−25.9507	−2.18544
$142$	31.9384	2.68021
$143$	0.540155	0.0451700
$144$	−7.17665	−0.598054
$145$	−5.31867	−0.441692
$146$	−14.4469	−1.19563
$147$	0	0
$148$	14.8038	1.21686
$149$	11.2603	0.922479	0.461239	−	0.887276i	$-0.347405\pi$
$149$	11.2603	0.922479	0.461239	+	0.887276i	$0.347405\pi$
$150$	−19.7331	−1.61120
$151$	12.8444	1.04526	0.522630	−	0.852559i	$-0.324951\pi$
$151$	12.8444	1.04526	0.522630	+	0.852559i	$0.324951\pi$
$152$	−5.55090	−0.450238
$153$	5.67359	0.458682
$154$	0	0
$155$	0.00458361	0.000368165 0
$156$	−1.04328	−0.0835289
$157$	9.37504	0.748210	0.374105	−	0.927386i	$-0.377950\pi$
$157$	9.37504	0.748210	0.374105	+	0.927386i	$0.377950\pi$
$158$	20.3033	1.61525
$159$	−28.7166	−2.27737
$160$	−7.55172	−0.597016
$161$	0	0
$162$	22.2703	1.74972
$163$	7.37682	0.577798	0.288899	−	0.957360i	$-0.406711\pi$
$163$	7.37682	0.577798	0.288899	+	0.957360i	$0.406711\pi$
$164$	−1.28826	−0.100596
$165$	5.96461	0.464344
$166$	−0.118299	−0.00918175
$167$	2.44535	0.189227	0.0946133	−	0.995514i	$-0.469839\pi$
$167$	2.44535	0.189227	0.0946133	+	0.995514i	$0.469839\pi$
$168$	0	0
$169$	−12.9624	−0.997110
$170$	4.89870	0.375713
$171$	17.2461	1.31884
$172$	4.11686	0.313908
$173$	2.71740	0.206600	0.103300	−	0.994650i	$-0.467060\pi$
$173$	2.71740	0.206600	0.103300	+	0.994650i	$0.467060\pi$
$174$	27.2293	2.06425
$175$	0	0
$176$	−8.86973	−0.668581
$177$	−12.5698	−0.944803
$178$	5.40773	0.405326
$179$	4.73487	0.353901	0.176950	−	0.984220i	$-0.443377\pi$
$179$	4.73487	0.353901	0.176950	+	0.984220i	$0.443377\pi$
$180$	−4.94335	−0.368455
$181$	9.91117	0.736691	0.368346	−	0.929689i	$-0.379924\pi$
$181$	9.91117	0.736691	0.368346	+	0.929689i	$0.379924\pi$
$182$	0	0
$183$	−21.9260	−1.62081
$184$	3.73826	0.275588
$185$	−5.88653	−0.432786
$186$	−0.0234661	−0.00172062
$187$	7.01207	0.512773
$188$	26.5813	1.93864
$189$	0	0
$190$	14.8906	1.08028
$191$	7.35311	0.532052	0.266026	−	0.963966i	$-0.414289\pi$
$191$	7.35311	0.532052	0.266026	+	0.963966i	$0.414289\pi$
$192$	24.0696	1.73707
$193$	−22.0783	−1.58923	−0.794616	−	0.607112i	$-0.792328\pi$
$193$	−22.0783	−1.58923	−0.794616	+	0.607112i	$0.792328\pi$
$194$	−16.7967	−1.20593
$195$	0.414845	0.0297077
$196$	0	0
$197$	−15.5041	−1.10462	−0.552310	−	0.833639i	$-0.686253\pi$
$197$	−15.5041	−1.10462	−0.552310	+	0.833639i	$0.686253\pi$
$198$	−13.1031	−0.931196
$199$	−21.9047	−1.55278	−0.776392	−	0.630250i	$-0.782952\pi$
$199$	−21.9047	−1.55278	−0.776392	+	0.630250i	$0.782952\pi$
$200$	2.99612	0.211857
$201$	−33.2312	−2.34395
$202$	−13.4619	−0.947173
$203$	0	0
$204$	−13.5434	−0.948226
$205$	0.512258	0.0357776
$206$	−26.3903	−1.83870
$207$	−11.6144	−0.807256
$208$	−0.616899	−0.0427742
$209$	21.3147	1.47437
$210$	0	0
$211$	−24.5809	−1.69222	−0.846109	−	0.533010i	$-0.821061\pi$
$211$	−24.5809	−1.69222	−0.846109	+	0.533010i	$0.821061\pi$
$212$	29.4144	2.02019
$213$	35.1112	2.40578
$214$	−29.1072	−1.98973
$215$	−1.63702	−0.111644
$216$	−1.23969	−0.0843501
$217$	0	0
$218$	33.8413	2.29202
$219$	−15.8820	−1.07321
$220$	−6.10955	−0.411906
$221$	0.487697	0.0328060
$222$	30.1365	2.02263
$223$	−21.2711	−1.42442	−0.712210	−	0.701967i	$-0.752306\pi$
$223$	−21.2711	−1.42442	−0.712210	+	0.701967i	$0.752306\pi$
$224$	0	0
$225$	−9.30862	−0.620575
$226$	−0.113477	−0.00754837
$227$	18.9942	1.26069	0.630346	−	0.776314i	$-0.282913\pi$
$227$	18.9942	1.26069	0.630346	+	0.776314i	$0.282913\pi$
$228$	−41.1680	−2.72642
$229$	−19.5367	−1.29102	−0.645509	−	0.763753i	$-0.723355\pi$
$229$	−19.5367	−1.29102	−0.645509	+	0.763753i	$0.723355\pi$
$230$	−10.0281	−0.661235
$231$	0	0
$232$	−4.13429	−0.271429
$233$	−12.2178	−0.800415	−0.400208	−	0.916425i	$-0.631062\pi$
$233$	−12.2178	−0.800415	−0.400208	+	0.916425i	$0.631062\pi$
$234$	−0.911333	−0.0595757
$235$	−10.5697	−0.689492
$236$	12.8752	0.838107
$237$	22.3203	1.44986
$238$	0	0
$239$	13.3637	0.864424	0.432212	−	0.901772i	$-0.357733\pi$
$239$	13.3637	0.864424	0.432212	+	0.901772i	$0.357733\pi$
$240$	−6.81205	−0.439716
$241$	−4.66456	−0.300471	−0.150235	−	0.988650i	$-0.548003\pi$
$241$	−4.66456	−0.300471	−0.150235	+	0.988650i	$0.548003\pi$
$242$	6.74290	0.433450
$243$	19.3583	1.24184
$244$	22.4588	1.43778
$245$	0	0
$246$	−2.62254	−0.167207
$247$	1.48246	0.0943265
$248$	0.00356292	0.000226245 0
$249$	−0.130051	−0.00824163
$250$	−17.7717	−1.12398
$251$	5.22865	0.330030	0.165015	−	0.986291i	$-0.447233\pi$
$251$	5.22865	0.330030	0.165015	+	0.986291i	$0.447233\pi$
$252$	0	0
$253$	−14.3544	−0.902453
$254$	−2.08520	−0.130837
$255$	5.38535	0.337244
$256$	9.07647	0.567280
$257$	6.58612	0.410831	0.205416	−	0.978675i	$-0.434145\pi$
$257$	6.58612	0.410831	0.205416	+	0.978675i	$0.434145\pi$
$258$	8.38082	0.521767
$259$	0	0
$260$	−0.424926	−0.0263528
$261$	12.8448	0.795074
$262$	12.0468	0.744256
$263$	−13.5267	−0.834092	−0.417046	−	0.908885i	$-0.636935\pi$
$263$	−13.5267	−0.834092	−0.417046	+	0.908885i	$0.636935\pi$
$264$	4.63639	0.285350
$265$	−11.6963	−0.718495
$266$	0	0
$267$	5.94495	0.363825
$268$	34.0387	2.07924
$269$	2.96880	0.181011	0.0905054	−	0.995896i	$-0.471152\pi$
$269$	2.96880	0.181011	0.0905054	+	0.995896i	$0.471152\pi$
$270$	3.32554	0.202386
$271$	−15.0827	−0.916211	−0.458105	−	0.888898i	$-0.651472\pi$
$271$	−15.0827	−0.916211	−0.458105	+	0.888898i	$0.651472\pi$
$272$	−8.00833	−0.485576
$273$	0	0
$274$	18.3001	1.10555
$275$	−11.5047	−0.693757
$276$	27.7246	1.66883
$277$	7.56049	0.454266	0.227133	−	0.973864i	$-0.427065\pi$
$277$	7.56049	0.454266	0.227133	+	0.973864i	$0.427065\pi$
$278$	24.4503	1.46643
$279$	−0.0110696	−0.000662720 0
$280$	0	0
$281$	30.5712	1.82373	0.911864	−	0.410493i	$-0.134643\pi$
$281$	30.5712	1.82373	0.911864	+	0.410493i	$0.134643\pi$
$282$	54.1124	3.22235
$283$	−28.7658	−1.70995	−0.854975	−	0.518669i	$-0.826428\pi$
$283$	−28.7658	−1.70995	−0.854975	+	0.518669i	$0.826428\pi$
$284$	−35.9644	−2.13410
$285$	16.3699	0.969670
$286$	−1.12633	−0.0666013
$287$	0	0
$288$	18.2377	1.07467
$289$	−10.6689	−0.627583
$290$	11.0905	0.651256
$291$	−18.4653	−1.08246
$292$	16.2680	0.952011
$293$	10.6589	0.622697	0.311349	−	0.950296i	$-0.399219\pi$
$293$	10.6589	0.622697	0.311349	+	0.950296i	$0.399219\pi$
$294$	0	0
$295$	−5.11967	−0.298079
$296$	−4.57569	−0.265957
$297$	4.76023	0.276216
$298$	−23.4799	−1.36016
$299$	−0.998363	−0.0577368
$300$	22.2206	1.28290
$301$	0	0
$302$	−26.7831	−1.54119
$303$	−14.7992	−0.850191
$304$	−24.3430	−1.39617
$305$	−8.93044	−0.511356
$306$	−11.8306	−0.676308
$307$	12.1106	0.691191	0.345595	−	0.938384i	$-0.387677\pi$
$307$	12.1106	0.691191	0.345595	+	0.938384i	$0.387677\pi$
$308$	0	0
$309$	−29.0120	−1.65044
$310$	−0.00955775	−0.000542843 0
$311$	18.2756	1.03631	0.518156	−	0.855286i	$-0.326619\pi$
$311$	18.2756	1.03631	0.518156	+	0.855286i	$0.326619\pi$
$312$	0.322466	0.0182560
$313$	−25.3365	−1.43210	−0.716052	−	0.698047i	$-0.754053\pi$
$313$	−25.3365	−1.43210	−0.716052	+	0.698047i	$0.754053\pi$
$314$	−19.5488	−1.10320
$315$	0	0
$316$	−22.8627	−1.28613
$317$	−25.7654	−1.44713	−0.723566	−	0.690255i	$-0.757498\pi$
$317$	−25.7654	−1.44713	−0.723566	+	0.690255i	$0.757498\pi$
$318$	59.8797	3.35789
$319$	15.8751	0.888834
$320$	9.80354	0.548034
$321$	−31.9988	−1.78600
$322$	0	0
$323$	19.2447	1.07080
$324$	−25.0777	−1.39320
$325$	−0.800161	−0.0443850
$326$	−15.3821	−0.851938
$327$	37.2031	2.05734
$328$	0.398186	0.0219862
$329$	0	0
$330$	−12.4374	−0.684656
$331$	−13.1557	−0.723104	−0.361552	−	0.932352i	$-0.617753\pi$
$331$	−13.1557	−0.723104	−0.361552	+	0.932352i	$0.617753\pi$
$332$	0.133211	0.00731090
$333$	14.2162	0.779043
$334$	−5.09904	−0.279007
$335$	−13.5350	−0.739498
$336$	0	0
$337$	24.3915	1.32869	0.664346	−	0.747426i	$-0.268710\pi$
$337$	24.3915	1.32869	0.664346	+	0.747426i	$0.268710\pi$
$338$	27.0292	1.47020
$339$	−0.124750	−0.00677549
$340$	−5.51622	−0.299159
$341$	−0.0136811	−0.000740873 0
$342$	−35.9615	−1.94457
$343$	0	0
$344$	−1.27248	−0.0686075
$345$	−11.0243	−0.593530
$346$	−5.66632	−0.304623
$347$	−3.88385	−0.208496	−0.104248	−	0.994551i	$-0.533244\pi$
$347$	−3.88385	−0.208496	−0.104248	+	0.994551i	$0.533244\pi$
$348$	−30.6618	−1.64364
$349$	−6.73196	−0.360353	−0.180177	−	0.983634i	$-0.557667\pi$
$349$	−6.73196	−0.360353	−0.180177	+	0.983634i	$0.557667\pi$
$350$	0	0
$351$	0.331079	0.0176717
$352$	22.5402	1.20140
$353$	−13.2967	−0.707711	−0.353855	−	0.935300i	$-0.615130\pi$
$353$	−13.2967	−0.707711	−0.353855	+	0.935300i	$0.615130\pi$
$354$	26.2105	1.39307
$355$	14.3008	0.759007
$356$	−6.08941	−0.322738
$357$	0	0
$358$	−9.87314	−0.521811
$359$	6.68500	0.352821	0.176410	−	0.984317i	$-0.443551\pi$
$359$	6.68500	0.352821	0.176410	+	0.984317i	$0.443551\pi$
$360$	1.52794	0.0805294
$361$	39.4983	2.07886
$362$	−20.6668	−1.08622
$363$	7.41275	0.389069
$364$	0	0
$365$	−6.46875	−0.338590
$366$	45.7200	2.38982
$367$	−11.2531	−0.587405	−0.293702	−	0.955897i	$-0.594887\pi$
$367$	−11.2531	−0.587405	−0.293702	+	0.955897i	$0.594887\pi$
$368$	16.3938	0.854588
$369$	−1.23712	−0.0644021
$370$	12.2746	0.638125
$371$	0	0
$372$	0.0264242	0.00137003
$373$	2.79234	0.144582	0.0722910	−	0.997384i	$-0.476969\pi$
$373$	2.79234	0.144582	0.0722910	+	0.997384i	$0.476969\pi$
$374$	−14.6216	−0.756063
$375$	−19.5372	−1.00890
$376$	−8.21601	−0.423708
$377$	1.10413	0.0568655
$378$	0	0
$379$	16.7969	0.862797	0.431399	−	0.902161i	$-0.358020\pi$
$379$	16.7969	0.862797	0.431399	+	0.902161i	$0.358020\pi$
$380$	−16.7677	−0.860165
$381$	−2.29235	−0.117441
$382$	−15.3327	−0.784489
$383$	−3.42162	−0.174836	−0.0874182	−	0.996172i	$-0.527862\pi$
$383$	−3.42162	−0.174836	−0.0874182	+	0.996172i	$0.527862\pi$
$384$	−13.1080	−0.668914
$385$	0	0
$386$	46.0377	2.34326
$387$	3.95346	0.200966
$388$	18.9140	0.960214
$389$	−8.81296	−0.446835	−0.223417	−	0.974723i	$-0.571721\pi$
$389$	−8.81296	−0.446835	−0.223417	+	0.974723i	$0.571721\pi$
$390$	−0.865034	−0.0438027
$391$	−12.9603	−0.655433
$392$	0	0
$393$	13.2436	0.668051
$394$	32.3291	1.62872
$395$	9.09106	0.457421
$396$	14.7548	0.741458
$397$	10.5507	0.529522	0.264761	−	0.964314i	$-0.414707\pi$
$397$	10.5507	0.529522	0.264761	+	0.964314i	$0.414707\pi$
$398$	45.6757	2.28952
$399$	0	0
$400$	13.1392	0.656961
$401$	−18.2483	−0.911277	−0.455639	−	0.890165i	$-0.650589\pi$
$401$	−18.2483	−0.911277	−0.455639	+	0.890165i	$0.650589\pi$
$402$	69.2936	3.45605
$403$	−0.000951534 0	−4.73993e−5 0
$404$	15.1588	0.754179
$405$	9.97180	0.495503
$406$	0	0
$407$	17.5700	0.870913
$408$	4.18612	0.207244
$409$	31.0961	1.53760	0.768801	−	0.639488i	$-0.220854\pi$
$409$	31.0961	1.53760	0.768801	+	0.639488i	$0.220854\pi$
$410$	−1.06816	−0.0527526
$411$	20.1180	0.992349
$412$	29.7170	1.46405
$413$	0	0
$414$	24.2183	1.19027
$415$	−0.0529696	−0.00260018
$416$	1.56770	0.0768627
$417$	26.8792	1.31628
$418$	−44.4453	−2.17389
$419$	25.8715	1.26390	0.631952	−	0.775007i	$-0.282254\pi$
$419$	25.8715	1.26390	0.631952	+	0.775007i	$0.282254\pi$
$420$	0	0
$421$	−2.01873	−0.0983869	−0.0491934	−	0.998789i	$-0.515665\pi$
$421$	−2.01873	−0.0983869	−0.0491934	+	0.998789i	$0.515665\pi$
$422$	51.2560	2.49510
$423$	25.5263	1.24113
$424$	−9.09168	−0.441531
$425$	−10.3874	−0.503861
$426$	−73.2138	−3.54722
$427$	0	0
$428$	32.7764	1.58431
$429$	−1.23822	−0.0597819
$430$	3.41351	0.164614
$431$	16.6506	0.802031	0.401016	−	0.916071i	$-0.368657\pi$
$431$	16.6506	0.802031	0.401016	+	0.916071i	$0.368657\pi$
$432$	−5.43655	−0.261566
$433$	−1.22543	−0.0588905	−0.0294452	−	0.999566i	$-0.509374\pi$
$433$	−1.22543	−0.0588905	−0.0294452	+	0.999566i	$0.509374\pi$
$434$	0	0
$435$	12.1922	0.584574
$436$	−38.1072	−1.82500
$437$	−39.3957	−1.88455
$438$	33.1172	1.58240
$439$	−20.5160	−0.979177	−0.489589	−	0.871953i	$-0.662853\pi$
$439$	−20.5160	−0.979177	−0.489589	+	0.871953i	$0.662853\pi$
$440$	1.88840	0.0900259
$441$	0	0
$442$	−1.01694	−0.0483711
$443$	−27.2725	−1.29576	−0.647878	−	0.761744i	$-0.724344\pi$
$443$	−27.2725	−1.29576	−0.647878	+	0.761744i	$0.724344\pi$
$444$	−33.9354	−1.61050
$445$	2.42138	0.114784
$446$	44.3545	2.10025
$447$	−25.8125	−1.22089
$448$	0	0
$449$	5.50357	0.259730	0.129865	−	0.991532i	$-0.458546\pi$
$449$	5.50357	0.259730	0.129865	+	0.991532i	$0.458546\pi$
$450$	19.4103	0.915012
$451$	−1.52898	−0.0719968
$452$	0.127782	0.00601034
$453$	−29.4438	−1.38339
$454$	−39.6068	−1.85884
$455$	0	0
$456$	12.7246	0.595884
$457$	10.1859	0.476475	0.238237	−	0.971207i	$-0.423430\pi$
$457$	10.1859	0.476475	0.238237	+	0.971207i	$0.423430\pi$
$458$	40.7378	1.90355
$459$	4.29793	0.200610
$460$	11.2922	0.526503
$461$	26.3546	1.22746	0.613728	−	0.789518i	$-0.289669\pi$
$461$	26.3546	1.22746	0.613728	+	0.789518i	$0.289669\pi$
$462$	0	0
$463$	−11.3537	−0.527652	−0.263826	−	0.964570i	$-0.584985\pi$
$463$	−11.3537	−0.527652	−0.263826	+	0.964570i	$0.584985\pi$
$464$	−18.1306	−0.841692
$465$	−0.0105072	−0.000487261 0
$466$	25.4766	1.18018
$467$	29.9352	1.38523	0.692617	−	0.721305i	$-0.256458\pi$
$467$	29.9352	1.38523	0.692617	+	0.721305i	$0.256458\pi$
$468$	1.02621	0.0474367
$469$	0	0
$470$	22.0400	1.01663
$471$	−21.4909	−0.990246
$472$	−3.97960	−0.183176
$473$	4.88614	0.224665
$474$	−46.5423	−2.13776
$475$	−31.5746	−1.44874
$476$	0	0
$477$	28.2469	1.29334
$478$	−27.8659	−1.27456
$479$	12.7527	0.582685	0.291342	−	0.956619i	$-0.405898\pi$
$479$	12.7527	0.582685	0.291342	+	0.956619i	$0.405898\pi$
$480$	17.3112	0.790143
$481$	1.22201	0.0557190
$482$	9.72654	0.443032
$483$	0	0
$484$	−7.59289	−0.345131
$485$	−7.52092	−0.341507
$486$	−40.3659	−1.83104
$487$	18.2165	0.825467	0.412734	−	0.910852i	$-0.364574\pi$
$487$	18.2165	0.825467	0.412734	+	0.910852i	$0.364574\pi$
$488$	−6.94177	−0.314239
$489$	−16.9102	−0.764708
$490$	0	0
$491$	−16.9535	−0.765100	−0.382550	−	0.923935i	$-0.624954\pi$
$491$	−16.9535	−0.765100	−0.382550	+	0.923935i	$0.624954\pi$
$492$	2.95313	0.133137
$493$	14.3334	0.645542
$494$	−3.09122	−0.139080
$495$	−5.86706	−0.263705
$496$	0.0156249	0.000701578 0
$497$	0	0
$498$	0.271181	0.0121519
$499$	21.9257	0.981529	0.490764	−	0.871292i	$-0.336718\pi$
$499$	21.9257	0.981529	0.490764	+	0.871292i	$0.336718\pi$
$500$	20.0120	0.894963
$501$	−5.60559	−0.250439
$502$	−10.9028	−0.486615
$503$	26.9633	1.20223	0.601117	−	0.799161i	$-0.294723\pi$
$503$	26.9633	1.20223	0.601117	+	0.799161i	$0.294723\pi$
$504$	0	0
$505$	−6.02771	−0.268229
$506$	29.9318	1.33063
$507$	29.7144	1.31966
$508$	2.34805	0.104178
$509$	21.5261	0.954128	0.477064	−	0.878869i	$-0.341701\pi$
$509$	21.5261	0.954128	0.477064	+	0.878869i	$0.341701\pi$
$510$	−11.2295	−0.497252
$511$	0	0
$512$	−30.3626	−1.34185
$513$	13.0645	0.576811
$514$	−13.7334	−0.605753
$515$	−11.8166	−0.520701
$516$	−9.43728	−0.415453
$517$	31.5483	1.38749
$518$	0	0
$519$	−6.22923	−0.273433
$520$	0.131340	0.00575965
$521$	−12.9036	−0.565316	−0.282658	−	0.959221i	$-0.591216\pi$
$521$	−12.9036	−0.565316	−0.282658	+	0.959221i	$0.591216\pi$
$522$	−26.7840	−1.17230
$523$	−21.6556	−0.946931	−0.473466	−	0.880812i	$-0.656997\pi$
$523$	−21.6556	−0.946931	−0.473466	+	0.880812i	$0.656997\pi$
$524$	−13.5654	−0.592608
$525$	0	0
$526$	28.2058	1.22983
$527$	−0.0123524	−0.000538080 0
$528$	20.3325	0.884858
$529$	3.53110	0.153526
$530$	24.3890	1.05939
$531$	12.3642	0.536561
$532$	0	0
$533$	−0.106342	−0.00460618
$534$	−12.3964	−0.536444
$535$	−13.0331	−0.563470
$536$	−10.5210	−0.454438
$537$	−10.8540	−0.468383
$538$	−6.19053	−0.266893
$539$	0	0
$540$	−3.74475	−0.161148
$541$	−3.63466	−0.156266	−0.0781330	−	0.996943i	$-0.524896\pi$
$541$	−3.63466	−0.156266	−0.0781330	+	0.996943i	$0.524896\pi$
$542$	31.4505	1.35091
$543$	−22.7198	−0.975002
$544$	20.3512	0.872551
$545$	15.1528	0.649076
$546$	0	0
$547$	−10.3932	−0.444381	−0.222191	−	0.975003i	$-0.571321\pi$
$547$	−10.3932	−0.444381	−0.222191	+	0.975003i	$0.571321\pi$
$548$	−20.6069	−0.880284
$549$	21.5674	0.920473
$550$	23.9895	1.02292
$551$	43.5693	1.85611
$552$	−8.56940	−0.364738
$553$	0	0
$554$	−15.7651	−0.669796
$555$	13.4940	0.572787
$556$	−27.5324	−1.16763
$557$	22.4511	0.951284	0.475642	−	0.879639i	$-0.342216\pi$
$557$	22.4511	0.951284	0.475642	+	0.879639i	$0.342216\pi$
$558$	0.0230823	0.000977153 0
$559$	0.339836	0.0143735
$560$	0	0
$561$	−16.0741	−0.678649
$562$	−63.7471	−2.68901
$563$	−30.2139	−1.27336	−0.636682	−	0.771127i	$-0.719693\pi$
$563$	−30.2139	−1.27336	−0.636682	+	0.771127i	$0.719693\pi$
$564$	−60.9336	−2.56577
$565$	−0.0508107	−0.00213762
$566$	59.9824	2.52125
$567$	0	0
$568$	11.1162	0.466427
$569$	47.0362	1.97186	0.985931	−	0.167155i	$-0.0534582\pi$
$569$	47.0362	1.97186	0.985931	+	0.167155i	$0.0534582\pi$
$570$	−34.1345	−1.42974
$571$	−27.5118	−1.15133	−0.575666	−	0.817685i	$-0.695257\pi$
$571$	−27.5118	−1.15133	−0.575666	+	0.817685i	$0.695257\pi$
$572$	1.26831	0.0530308
$573$	−16.8559	−0.704165
$574$	0	0
$575$	21.2640	0.886769
$576$	−23.6759	−0.986497
$577$	16.8224	0.700327	0.350164	−	0.936689i	$-0.386126\pi$
$577$	16.8224	0.700327	0.350164	+	0.936689i	$0.386126\pi$
$578$	22.2468	0.925345
$579$	50.6112	2.10333
$580$	−12.4885	−0.518558
$581$	0	0
$582$	38.5038	1.59604
$583$	34.9108	1.44586
$584$	−5.02826	−0.208071
$585$	−0.408060	−0.0168712
$586$	−22.2258	−0.918141
$587$	8.96942	0.370208	0.185104	−	0.982719i	$-0.440738\pi$
$587$	8.96942	0.370208	0.185104	+	0.982719i	$0.440738\pi$
$588$	0	0
$589$	−0.0375478	−0.00154713
$590$	10.6755	0.439505
$591$	35.5407	1.46195
$592$	−20.0663	−0.824721
$593$	39.7027	1.63040	0.815198	−	0.579182i	$-0.196628\pi$
$593$	39.7027	1.63040	0.815198	+	0.579182i	$0.196628\pi$
$594$	−9.92602	−0.407269
$595$	0	0
$596$	26.4397	1.08301
$597$	50.2132	2.05509
$598$	2.08179	0.0851305
$599$	−47.1062	−1.92471	−0.962354	−	0.271799i	$-0.912381\pi$
$599$	−47.1062	−1.92471	−0.962354	+	0.271799i	$0.912381\pi$
$600$	−6.86814	−0.280391
$601$	13.9775	0.570154	0.285077	−	0.958505i	$-0.407981\pi$
$601$	13.9775	0.570154	0.285077	+	0.958505i	$0.407981\pi$
$602$	0	0
$603$	32.6877	1.33114
$604$	30.1593	1.22716
$605$	3.01921	0.122748
$606$	30.8593	1.25357
$607$	−22.5493	−0.915249	−0.457625	−	0.889146i	$-0.651300\pi$
$607$	−22.5493	−0.915249	−0.457625	+	0.889146i	$0.651300\pi$
$608$	61.8618	2.50883
$609$	0	0
$610$	18.6217	0.753972
$611$	2.19422	0.0887686
$612$	13.3219	0.538505
$613$	43.6758	1.76405	0.882025	−	0.471202i	$-0.156180\pi$
$613$	43.6758	1.76405	0.882025	+	0.471202i	$0.156180\pi$
$614$	−25.2531	−1.01913
$615$	−1.17427	−0.0473513
$616$	0	0
$617$	2.20142	0.0886258	0.0443129	−	0.999018i	$-0.485890\pi$
$617$	2.20142	0.0886258	0.0443129	+	0.999018i	$0.485890\pi$
$618$	60.4958	2.43350
$619$	−42.2248	−1.69716	−0.848580	−	0.529068i	$-0.822542\pi$
$619$	−42.2248	−1.69716	−0.848580	+	0.529068i	$0.822542\pi$
$620$	0.0107626	0.000432235 0
$621$	−8.79829	−0.353063
$622$	−38.1082	−1.52800
$623$	0	0
$624$	1.41415	0.0566112
$625$	12.6838	0.507351
$626$	52.8316	2.11158
$627$	−48.8606	−1.95131
$628$	22.0131	0.878418
$629$	15.8637	0.632526
$630$	0	0
$631$	30.8546	1.22830	0.614152	−	0.789188i	$-0.289498\pi$
$631$	30.8546	1.22830	0.614152	+	0.789188i	$0.289498\pi$
$632$	7.06663	0.281095
$633$	56.3479	2.23963
$634$	53.7261	2.13373
$635$	−0.933672	−0.0370517
$636$	−67.4280	−2.67369
$637$	0	0
$638$	−33.1027	−1.31055
$639$	−34.5370	−1.36626
$640$	−5.33888	−0.211038
$641$	−35.0810	−1.38562	−0.692808	−	0.721122i	$-0.743626\pi$
$641$	−35.0810	−1.38562	−0.692808	+	0.721122i	$0.743626\pi$
$642$	66.7239	2.63338
$643$	−3.80378	−0.150007	−0.0750033	−	0.997183i	$-0.523897\pi$
$643$	−3.80378	−0.150007	−0.0750033	+	0.997183i	$0.523897\pi$
$644$	0	0
$645$	3.75261	0.147759
$646$	−40.1289	−1.57885
$647$	−25.7342	−1.01172	−0.505858	−	0.862617i	$-0.668824\pi$
$647$	−25.7342	−1.01172	−0.505858	+	0.862617i	$0.668824\pi$
$648$	7.75124	0.304497
$649$	15.2811	0.599836
$650$	1.66849	0.0654437
$651$	0	0
$652$	17.3212	0.678349
$653$	0.517721	0.0202600	0.0101300	−	0.999949i	$-0.496775\pi$
$653$	0.517721	0.0202600	0.0101300	+	0.999949i	$0.496775\pi$
$654$	−77.5759	−3.03346
$655$	5.39412	0.210766
$656$	1.74621	0.0681782
$657$	15.6223	0.609484
$658$	0	0
$659$	1.28916	0.0502187	0.0251093	−	0.999685i	$-0.492007\pi$
$659$	1.28916	0.0502187	0.0251093	+	0.999685i	$0.492007\pi$
$660$	14.0052	0.545153
$661$	9.00670	0.350320	0.175160	−	0.984540i	$-0.443956\pi$
$661$	9.00670	0.350320	0.175160	+	0.984540i	$0.443956\pi$
$662$	27.4323	1.06619
$663$	−1.11797	−0.0434184
$664$	−0.0411741	−0.00159787
$665$	0	0
$666$	−29.6436	−1.14867
$667$	−29.3418	−1.13612
$668$	5.74180	0.222157
$669$	48.7608	1.88520
$670$	28.2233	1.09036
$671$	26.6554	1.02902
$672$	0	0
$673$	22.2110	0.856173	0.428086	−	0.903738i	$-0.359188\pi$
$673$	22.2110	0.856173	0.428086	+	0.903738i	$0.359188\pi$
$674$	−50.8612	−1.95910
$675$	−7.05159	−0.271416
$676$	−30.4365	−1.17063
$677$	−42.3852	−1.62900	−0.814499	−	0.580166i	$-0.802988\pi$
$677$	−42.3852	−1.62900	−0.814499	+	0.580166i	$0.802988\pi$
$678$	0.260129	0.00999018
$679$	0	0
$680$	1.70500	0.0653840
$681$	−43.5414	−1.66851
$682$	0.0285278	0.00109239
$683$	18.2898	0.699839	0.349920	−	0.936780i	$-0.386209\pi$
$683$	18.2898	0.699839	0.349920	+	0.936780i	$0.386209\pi$
$684$	40.4947	1.54835
$685$	8.19407	0.313079
$686$	0	0
$687$	44.7848	1.70865
$688$	−5.58036	−0.212749
$689$	2.42808	0.0925025
$690$	22.9879	0.875136
$691$	31.8326	1.21097	0.605484	−	0.795858i	$-0.292980\pi$
$691$	31.8326	1.21097	0.605484	+	0.795858i	$0.292980\pi$
$692$	6.38060	0.242554
$693$	0	0
$694$	8.09860	0.307419
$695$	10.9479	0.415277
$696$	9.47723	0.359233
$697$	−1.38049	−0.0522898
$698$	14.0375	0.531326
$699$	28.0075	1.05934
$700$	0	0
$701$	22.4553	0.848127	0.424063	−	0.905633i	$-0.360603\pi$
$701$	22.4553	0.848127	0.424063	+	0.905633i	$0.360603\pi$
$702$	−0.690365	−0.0260561
$703$	48.2210	1.81869
$704$	−29.2614	−1.10283
$705$	24.2295	0.912534
$706$	27.7262	1.04349
$707$	0	0
$708$	−29.5145	−1.10922
$709$	−23.9767	−0.900465	−0.450233	−	0.892911i	$-0.648659\pi$
$709$	−23.9767	−0.900465	−0.450233	+	0.892911i	$0.648659\pi$
$710$	−29.8200	−1.11912
$711$	−21.9553	−0.823387
$712$	1.88217	0.0705374
$713$	0.0252866	0.000946992 0
$714$	0	0
$715$	−0.504327	−0.0188608
$716$	11.1177	0.415489
$717$	−30.6342	−1.14405
$718$	−13.9396	−0.520220
$719$	32.0616	1.19570	0.597848	−	0.801609i	$-0.296022\pi$
$719$	32.0616	1.19570	0.597848	+	0.801609i	$0.296022\pi$
$720$	6.70064	0.249718
$721$	0	0
$722$	−82.3617	−3.06518
$723$	10.6928	0.397669
$724$	23.2719	0.864895
$725$	−23.5166	−0.873386
$726$	−15.4571	−0.573665
$727$	−15.4885	−0.574438	−0.287219	−	0.957865i	$-0.592731\pi$
$727$	−15.4885	−0.574438	−0.287219	+	0.957865i	$0.592731\pi$
$728$	0	0
$729$	−12.3354	−0.456868
$730$	13.4886	0.499236
$731$	4.41162	0.163170
$732$	−51.4833	−1.90288
$733$	45.9771	1.69820	0.849101	−	0.528230i	$-0.177144\pi$
$733$	45.9771	1.69820	0.849101	+	0.528230i	$0.177144\pi$
$734$	23.4648	0.866103
$735$	0	0
$736$	−41.6609	−1.53564
$737$	40.3992	1.48812
$738$	2.57965	0.0949581
$739$	15.5562	0.572245	0.286122	−	0.958193i	$-0.407634\pi$
$739$	15.5562	0.572245	0.286122	+	0.958193i	$0.407634\pi$
$740$	−13.8219	−0.508102
$741$	−3.39831	−0.124840
$742$	0	0
$743$	7.57725	0.277982	0.138991	−	0.990294i	$-0.455614\pi$
$743$	7.57725	0.277982	0.138991	+	0.990294i	$0.455614\pi$
$744$	−0.00816744	−0.000299433 0
$745$	−10.5134	−0.385182
$746$	−5.82259	−0.213180
$747$	0.127924	0.00468048
$748$	16.4647	0.602009
$749$	0	0
$750$	40.7390	1.48758
$751$	−46.6503	−1.70229	−0.851146	−	0.524928i	$-0.824092\pi$
$751$	−46.6503	−1.70229	−0.851146	+	0.524928i	$0.824092\pi$
$752$	−36.0306	−1.31390
$753$	−11.9859	−0.436790
$754$	−2.30233	−0.0838458
$755$	−11.9924	−0.436450
$756$	0	0
$757$	13.7608	0.500145	0.250073	−	0.968227i	$-0.419545\pi$
$757$	13.7608	0.500145	0.250073	+	0.968227i	$0.419545\pi$
$758$	−35.0248	−1.27216
$759$	32.9053	1.19439
$760$	5.18272	0.187997
$761$	0.805405	0.0291959	0.0145980	−	0.999893i	$-0.495353\pi$
$761$	0.805405	0.0291959	0.0145980	+	0.999893i	$0.495353\pi$
$762$	4.78000	0.173161
$763$	0	0
$764$	17.2655	0.624644
$765$	−5.29727	−0.191523
$766$	7.13475	0.257789
$767$	1.06282	0.0383761
$768$	−20.8064	−0.750787
$769$	−48.5248	−1.74985	−0.874925	−	0.484258i	$-0.839089\pi$
$769$	−48.5248	−1.74985	−0.874925	+	0.484258i	$0.839089\pi$
$770$	0	0
$771$	−15.0977	−0.543730
$772$	−51.8411	−1.86580
$773$	18.6869	0.672121	0.336060	−	0.941840i	$-0.390905\pi$
$773$	18.6869	0.672121	0.336060	+	0.941840i	$0.390905\pi$
$774$	−8.24375	−0.296316
$775$	0.0202666	0.000727996 0
$776$	−5.84613	−0.209864
$777$	0	0
$778$	18.3768	0.658839
$779$	−4.19629	−0.150348
$780$	0.974078	0.0348776
$781$	−42.6847	−1.52738
$782$	27.0249	0.966408
$783$	9.73037	0.347735
$784$	0	0
$785$	−8.75322	−0.312416
$786$	−27.6155	−0.985014
$787$	6.71735	0.239448	0.119724	−	0.992807i	$-0.461799\pi$
$787$	6.71735	0.239448	0.119724	+	0.992807i	$0.461799\pi$
$788$	−36.4044	−1.29685
$789$	31.0079	1.10391
$790$	−18.9567	−0.674448
$791$	0	0
$792$	−4.56056	−0.162052
$793$	1.85391	0.0658344
$794$	−22.0002	−0.780758
$795$	26.8119	0.950919
$796$	−51.4334	−1.82301
$797$	23.0778	0.817459	0.408730	−	0.912655i	$-0.365972\pi$
$797$	23.0778	0.817459	0.408730	+	0.912655i	$0.365972\pi$
$798$	0	0
$799$	28.4844	1.00771
$800$	−33.3901	−1.18052
$801$	−5.84772	−0.206619
$802$	38.0513	1.34364
$803$	19.3078	0.681358
$804$	−78.0285	−2.75185
$805$	0	0
$806$	0.00198414	6.98883e−5 0
$807$	−6.80552	−0.239566
$808$	−4.68543	−0.164833
$809$	53.9924	1.89827	0.949135	−	0.314869i	$-0.101961\pi$
$809$	53.9924	1.89827	0.949135	+	0.314869i	$0.101961\pi$
$810$	−20.7932	−0.730598
$811$	27.2849	0.958103	0.479051	−	0.877787i	$-0.340981\pi$
$811$	27.2849	0.958103	0.479051	+	0.877787i	$0.340981\pi$
$812$	0	0
$813$	34.5749	1.21259
$814$	−36.6370	−1.28412
$815$	−6.88754	−0.241260
$816$	18.3579	0.642654
$817$	13.4100	0.469158
$818$	−64.8415	−2.26713
$819$	0	0
$820$	1.20281	0.0420039
$821$	−0.485767	−0.0169534	−0.00847669	−	0.999964i	$-0.502698\pi$
$821$	−0.485767	−0.0169534	−0.00847669	+	0.999964i	$0.502698\pi$
$822$	−41.9501	−1.46318
$823$	−19.5296	−0.680760	−0.340380	−	0.940288i	$-0.610556\pi$
$823$	−19.5296	−0.680760	−0.340380	+	0.940288i	$0.610556\pi$
$824$	−9.18522	−0.319982
$825$	26.3727	0.918179
$826$	0	0
$827$	−33.0521	−1.14933	−0.574667	−	0.818387i	$-0.694868\pi$
$827$	−33.0521	−1.14933	−0.574667	+	0.818387i	$0.694868\pi$
$828$	−27.2712	−0.947740
$829$	1.53452	0.0532959	0.0266480	−	0.999645i	$-0.491517\pi$
$829$	1.53452	0.0532959	0.0266480	+	0.999645i	$0.491517\pi$
$830$	0.110452	0.00383385
$831$	−17.3313	−0.601215
$832$	−2.03516	−0.0705566
$833$	0	0
$834$	−56.0485	−1.94080
$835$	−2.28315	−0.0790118
$836$	50.0480	1.73095
$837$	−0.00838560	−0.000289849 0
$838$	−53.9472	−1.86357
$839$	3.69432	0.127542	0.0637710	−	0.997965i	$-0.479687\pi$
$839$	3.69432	0.127542	0.0637710	+	0.997965i	$0.479687\pi$
$840$	0	0
$841$	3.45022	0.118973
$842$	4.20945	0.145067
$843$	−70.0799	−2.41368
$844$	−57.7172	−1.98671
$845$	12.1027	0.416344
$846$	−53.2274	−1.83000
$847$	0	0
$848$	−39.8708	−1.36917
$849$	65.9412	2.26310
$850$	21.6597	0.742922
$851$	−32.4745	−1.11321
$852$	82.4430	2.82445
$853$	13.0036	0.445235	0.222618	−	0.974906i	$-0.428540\pi$
$853$	13.0036	0.445235	0.222618	+	0.974906i	$0.428540\pi$
$854$	0	0
$855$	−16.1022	−0.550683
$856$	−10.1308	−0.346265
$857$	−8.79211	−0.300333	−0.150166	−	0.988661i	$-0.547981\pi$
$857$	−8.79211	−0.300333	−0.150166	+	0.988661i	$0.547981\pi$
$858$	2.58194	0.0881459
$859$	−28.3314	−0.966655	−0.483328	−	0.875440i	$-0.660572\pi$
$859$	−28.3314	−0.966655	−0.483328	+	0.875440i	$0.660572\pi$
$860$	−3.84380	−0.131073
$861$	0	0
$862$	−34.7198	−1.18256
$863$	−17.6452	−0.600648	−0.300324	−	0.953837i	$-0.597095\pi$
$863$	−17.6452	−0.600648	−0.300324	+	0.953837i	$0.597095\pi$
$864$	13.8157	0.470019
$865$	−2.53716	−0.0862662
$866$	2.55527	0.0868315
$867$	24.4569	0.830599
$868$	0	0
$869$	−27.1348	−0.920487
$870$	−25.4233	−0.861929
$871$	2.80980	0.0952066
$872$	11.7785	0.398872
$873$	18.1633	0.614735
$874$	82.1479	2.77869
$875$	0	0
$876$	−37.2919	−1.25998
$877$	−12.6152	−0.425986	−0.212993	−	0.977054i	$-0.568321\pi$
$877$	−12.6152	−0.425986	−0.212993	+	0.977054i	$0.568321\pi$
$878$	42.7800	1.44376
$879$	−24.4338	−0.824132
$880$	8.28142	0.279167
$881$	−34.6918	−1.16880	−0.584398	−	0.811467i	$-0.698669\pi$
$881$	−34.6918	−1.16880	−0.584398	+	0.811467i	$0.698669\pi$
$882$	0	0
$883$	−1.63980	−0.0551838	−0.0275919	−	0.999619i	$-0.508784\pi$
$883$	−1.63980	−0.0551838	−0.0275919	+	0.999619i	$0.508784\pi$
$884$	1.14514	0.0385151
$885$	11.7361	0.394504
$886$	56.8686	1.91054
$887$	−46.9777	−1.57736	−0.788679	−	0.614806i	$-0.789234\pi$
$887$	−46.9777	−1.57736	−0.788679	+	0.614806i	$0.789234\pi$
$888$	10.4891	0.351990
$889$	0	0
$890$	−5.04905	−0.169244
$891$	−29.7637	−0.997120
$892$	−49.9457	−1.67231
$893$	86.5845	2.89744
$894$	53.8242	1.80015
$895$	−4.42081	−0.147772
$896$	0	0
$897$	2.28859	0.0764140
$898$	−11.4760	−0.382961
$899$	−0.0279655	−0.000932701 0
$900$	−21.8571	−0.728571
$901$	31.5204	1.05010
$902$	3.18822	0.106156
$903$	0	0
$904$	−0.0394959	−0.00131362
$905$	−9.25379	−0.307606
$906$	61.3961	2.03975
$907$	−17.9824	−0.597096	−0.298548	−	0.954395i	$-0.596502\pi$
$907$	−17.9824	−0.597096	−0.298548	+	0.954395i	$0.596502\pi$
$908$	44.5995	1.48009
$909$	14.5572	0.482830
$910$	0	0
$911$	−5.69883	−0.188811	−0.0944053	−	0.995534i	$-0.530095\pi$
$911$	−5.69883	−0.188811	−0.0944053	+	0.995534i	$0.530095\pi$
$912$	55.8027	1.84781
$913$	0.158103	0.00523244
$914$	−21.2396	−0.702542
$915$	20.4717	0.676773
$916$	−45.8731	−1.51569
$917$	0	0
$918$	−8.96204	−0.295791
$919$	30.9677	1.02153	0.510765	−	0.859720i	$-0.329362\pi$
$919$	30.9677	1.02153	0.510765	+	0.859720i	$0.329362\pi$
$920$	−3.49031	−0.115072
$921$	−27.7618	−0.914783
$922$	−54.9545	−1.80983
$923$	−2.96877	−0.0977182
$924$	0	0
$925$	−26.0274	−0.855777
$926$	23.6748	0.778001
$927$	28.5375	0.937295
$928$	46.0745	1.51247
$929$	9.62268	0.315710	0.157855	−	0.987462i	$-0.449542\pi$
$929$	9.62268	0.315710	0.157855	+	0.987462i	$0.449542\pi$
$930$	0.0219097	0.000718446 0
$931$	0	0
$932$	−28.6881	−0.939708
$933$	−41.8939	−1.37155
$934$	−62.4208	−2.04247
$935$	−6.54698	−0.214109
$936$	−0.317192	−0.0103677
$937$	27.5737	0.900795	0.450397	−	0.892828i	$-0.351282\pi$
$937$	27.5737	0.900795	0.450397	+	0.892828i	$0.351282\pi$
$938$	0	0
$939$	58.0801	1.89537
$940$	−24.8183	−0.809482
$941$	48.4998	1.58105	0.790524	−	0.612431i	$-0.209808\pi$
$941$	48.4998	1.58105	0.790524	+	0.612431i	$0.209808\pi$
$942$	44.8127	1.46008
$943$	2.82600	0.0920271
$944$	−17.4522	−0.568021
$945$	0	0
$946$	−10.1886	−0.331259
$947$	27.5695	0.895889	0.447945	−	0.894061i	$-0.352156\pi$
$947$	27.5695	0.895889	0.447945	+	0.894061i	$0.352156\pi$
$948$	52.4093	1.70217
$949$	1.34288	0.0435917
$950$	65.8393	2.13611
$951$	59.0634	1.91526
$952$	0	0
$953$	−6.77555	−0.219482	−0.109741	−	0.993960i	$-0.535002\pi$
$953$	−6.77555	−0.219482	−0.109741	+	0.993960i	$0.535002\pi$
$954$	−58.9004	−1.90697
$955$	−6.86540	−0.222159
$956$	31.3786	1.01486
$957$	−36.3912	−1.17636
$958$	−26.5919	−0.859145
$959$	0	0
$960$	−22.4731	−0.725317
$961$	−31.0000	−0.999999
$962$	−2.54814	−0.0821553
$963$	31.4755	1.01428
$964$	−10.9526	−0.352761
$965$	20.6139	0.663586
$966$	0	0
$967$	21.4389	0.689430	0.344715	−	0.938707i	$-0.387976\pi$
$967$	21.4389	0.689430	0.344715	+	0.938707i	$0.387976\pi$
$968$	2.34688	0.0754316
$969$	−44.1155	−1.41719
$970$	15.6826	0.503538
$971$	−12.5837	−0.403829	−0.201915	−	0.979403i	$-0.564716\pi$
$971$	−12.5837	−0.403829	−0.201915	+	0.979403i	$0.564716\pi$
$972$	45.4544	1.45795
$973$	0	0
$974$	−37.9850	−1.21712
$975$	1.83425	0.0587429
$976$	−30.4426	−0.974443
$977$	−16.0849	−0.514601	−0.257301	−	0.966331i	$-0.582833\pi$
$977$	−16.0849	−0.514601	−0.257301	+	0.966331i	$0.582833\pi$
$978$	35.2612	1.12753
$979$	−7.22728	−0.230985
$980$	0	0
$981$	−36.5947	−1.16838
$982$	35.3514	1.12811
$983$	48.8867	1.55924	0.779621	−	0.626251i	$-0.215412\pi$
$983$	48.8867	1.55924	0.779621	+	0.626251i	$0.215412\pi$
$984$	−0.912781	−0.0290984
$985$	14.4757	0.461235
$986$	−29.8879	−0.951824
$987$	0	0
$988$	3.48089	0.110742
$989$	−9.03101	−0.287169
$990$	12.2340	0.388822
$991$	−41.3328	−1.31298	−0.656490	−	0.754335i	$-0.727960\pi$
$991$	−41.3328	−1.31298	−0.656490	+	0.754335i	$0.727960\pi$
$992$	−0.0397068	−0.00126069
$993$	30.1575	0.957019
$994$	0	0
$995$	20.4518	0.648367
$996$	−0.305366	−0.00967589
$997$	32.7780	1.03809	0.519045	−	0.854747i	$-0.326288\pi$
$997$	32.7780	1.03809	0.519045	+	0.854747i	$0.326288\pi$
$998$	−45.7194	−1.44722
$999$	10.7692	0.340724

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6223.2.a.p.1.7		38
7.2	even	3		889.2.f.c.382.32	yes	76
7.4	even	3		889.2.f.c.128.32	✓	76
7.6	odd	2		6223.2.a.o.1.7		38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.f.c.128.32	✓	76	7.4	even	3
889.2.f.c.382.32	yes	76	7.2	even	3
6223.2.a.o.1.7		38	7.6	odd	2
6223.2.a.p.1.7		38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6223 = 7^{2} \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6223.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08520 q^{2} -2.29235 q^{3} +2.34805 q^{4} -0.933672 q^{5} +4.78000 q^{6} -0.725759 q^{8} +2.25486 q^{9} +O(q^{10})\)	\(q-2.08520 q^{2} -2.29235 q^{3} +2.34805 q^{4} -0.933672 q^{5} +4.78000 q^{6} -0.725759 q^{8} +2.25486 q^{9} +1.94689 q^{10} +2.78681 q^{11} -5.38255 q^{12} +0.193825 q^{13} +2.14030 q^{15} -3.18275 q^{16} +2.51616 q^{17} -4.70182 q^{18} +7.64841 q^{19} -2.19231 q^{20} -5.81105 q^{22} -5.15083 q^{23} +1.66369 q^{24} -4.12826 q^{25} -0.404165 q^{26} +1.70813 q^{27} +5.69651 q^{29} -4.46295 q^{30} -0.00490923 q^{31} +8.08819 q^{32} -6.38833 q^{33} -5.24670 q^{34} +5.29452 q^{36} +6.30470 q^{37} -15.9485 q^{38} -0.444315 q^{39} +0.677621 q^{40} -0.548648 q^{41} +1.75331 q^{43} +6.54357 q^{44} -2.10530 q^{45} +10.7405 q^{46} +11.3206 q^{47} +7.29598 q^{48} +8.60823 q^{50} -5.76792 q^{51} +0.455112 q^{52} +12.5271 q^{53} -3.56179 q^{54} -2.60197 q^{55} -17.5328 q^{57} -11.8784 q^{58} +5.48337 q^{59} +5.02554 q^{60} +9.56485 q^{61} +0.0102367 q^{62} -10.5000 q^{64} -0.180970 q^{65} +13.3209 q^{66} +14.4966 q^{67} +5.90809 q^{68} +11.8075 q^{69} -15.3167 q^{71} -1.63648 q^{72} +6.92829 q^{73} -13.1466 q^{74} +9.46340 q^{75} +17.9589 q^{76} +0.926486 q^{78} -9.73689 q^{79} +2.97165 q^{80} -10.6802 q^{81} +1.14404 q^{82} +0.0567325 q^{83} -2.34927 q^{85} -3.65600 q^{86} -13.0584 q^{87} -2.02255 q^{88} -2.59339 q^{89} +4.38996 q^{90} -12.0944 q^{92} +0.0112537 q^{93} -23.6057 q^{94} -7.14111 q^{95} -18.5409 q^{96} +8.05520 q^{97} +6.28385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 2 q^{2} + 11 q^{3} + 38 q^{4} + 16 q^{5} + 11 q^{6} + 47 q^{9}+O(q^{10}) \) 38 * q - 2 * q^2 + 11 * q^3 + 38 * q^4 + 16 * q^5 + 11 * q^6 + 47 * q^9	\( 38 q - 2 q^{2} + 11 q^{3} + 38 q^{4} + 16 q^{5} + 11 q^{6} + 47 q^{9} + 12 q^{10} - 2 q^{11} + 30 q^{12} + 21 q^{13} + 7 q^{15} + 46 q^{16} + 58 q^{17} - 13 q^{18} + 17 q^{19} + 44 q^{20} + 21 q^{22} + 7 q^{23} + 21 q^{24} + 52 q^{25} + 49 q^{26} + 35 q^{27} - 2 q^{29} + 6 q^{30} + 2 q^{31} - 22 q^{32} + 29 q^{33} + 37 q^{34} + 25 q^{36} + 11 q^{37} + 40 q^{38} + 2 q^{39} - 8 q^{40} + 68 q^{41} - 38 q^{43} + 43 q^{44} + 60 q^{45} - 28 q^{46} + 35 q^{47} + 66 q^{48} - 25 q^{50} - 3 q^{51} + 32 q^{52} - 18 q^{53} - 68 q^{54} + 19 q^{55} - 31 q^{57} + 55 q^{58} + 21 q^{59} - 11 q^{60} + 5 q^{61} + 38 q^{62} + 18 q^{64} - 9 q^{65} + 20 q^{66} + 6 q^{67} + 74 q^{68} + 53 q^{69} - 26 q^{71} + 24 q^{72} + 22 q^{73} - 2 q^{74} + 38 q^{75} + 39 q^{76} - 114 q^{78} - 14 q^{79} + 140 q^{80} + 58 q^{81} - 8 q^{82} + 46 q^{83} - 11 q^{85} + 51 q^{86} + 59 q^{87} - 4 q^{88} + 74 q^{89} + q^{90} - 81 q^{92} + 92 q^{93} - 36 q^{94} + 20 q^{95} - 108 q^{96} + 66 q^{97} + 16 q^{99}+O(q^{100}) \) 38 * q - 2 * q^2 + 11 * q^3 + 38 * q^4 + 16 * q^5 + 11 * q^6 + 47 * q^9 + 12 * q^10 - 2 * q^11 + 30 * q^12 + 21 * q^13 + 7 * q^15 + 46 * q^16 + 58 * q^17 - 13 * q^18 + 17 * q^19 + 44 * q^20 + 21 * q^22 + 7 * q^23 + 21 * q^24 + 52 * q^25 + 49 * q^26 + 35 * q^27 - 2 * q^29 + 6 * q^30 + 2 * q^31 - 22 * q^32 + 29 * q^33 + 37 * q^34 + 25 * q^36 + 11 * q^37 + 40 * q^38 + 2 * q^39 - 8 * q^40 + 68 * q^41 - 38 * q^43 + 43 * q^44 + 60 * q^45 - 28 * q^46 + 35 * q^47 + 66 * q^48 - 25 * q^50 - 3 * q^51 + 32 * q^52 - 18 * q^53 - 68 * q^54 + 19 * q^55 - 31 * q^57 + 55 * q^58 + 21 * q^59 - 11 * q^60 + 5 * q^61 + 38 * q^62 + 18 * q^64 - 9 * q^65 + 20 * q^66 + 6 * q^67 + 74 * q^68 + 53 * q^69 - 26 * q^71 + 24 * q^72 + 22 * q^73 - 2 * q^74 + 38 * q^75 + 39 * q^76 - 114 * q^78 - 14 * q^79 + 140 * q^80 + 58 * q^81 - 8 * q^82 + 46 * q^83 - 11 * q^85 + 51 * q^86 + 59 * q^87 - 4 * q^88 + 74 * q^89 + q^90 - 81 * q^92 + 92 * q^93 - 36 * q^94 + 20 * q^95 - 108 * q^96 + 66 * q^97 + 16 * q^99

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