LMFDB - Embedded newform 1003.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.02992 q^{2} -1.59232 q^{3} +2.12059 q^{4} -2.38274 q^{5} +3.23228 q^{6} -2.16746 q^{7} -0.244779 q^{8} -0.464532 q^{9} +O(q^{10})$	\(q-2.02992 q^{2} -1.59232 q^{3} +2.12059 q^{4} -2.38274 q^{5} +3.23228 q^{6} -2.16746 q^{7} -0.244779 q^{8} -0.464532 q^{9} +4.83678 q^{10} -0.350805 q^{11} -3.37664 q^{12} -1.38151 q^{13} +4.39978 q^{14} +3.79408 q^{15} -3.74429 q^{16} -1.00000 q^{17} +0.942965 q^{18} -7.93030 q^{19} -5.05281 q^{20} +3.45128 q^{21} +0.712108 q^{22} -7.04636 q^{23} +0.389765 q^{24} +0.677467 q^{25} +2.80436 q^{26} +5.51663 q^{27} -4.59629 q^{28} -1.13030 q^{29} -7.70169 q^{30} -5.69511 q^{31} +8.09017 q^{32} +0.558593 q^{33} +2.02992 q^{34} +5.16451 q^{35} -0.985081 q^{36} -1.95172 q^{37} +16.0979 q^{38} +2.19980 q^{39} +0.583245 q^{40} -7.56103 q^{41} -7.00584 q^{42} -8.31197 q^{43} -0.743913 q^{44} +1.10686 q^{45} +14.3036 q^{46} +8.74689 q^{47} +5.96209 q^{48} -2.30211 q^{49} -1.37521 q^{50} +1.59232 q^{51} -2.92961 q^{52} +7.45871 q^{53} -11.1983 q^{54} +0.835879 q^{55} +0.530549 q^{56} +12.6275 q^{57} +2.29441 q^{58} +1.00000 q^{59} +8.04567 q^{60} -13.2114 q^{61} +11.5606 q^{62} +1.00686 q^{63} -8.93385 q^{64} +3.29178 q^{65} -1.13390 q^{66} +4.38461 q^{67} -2.12059 q^{68} +11.2200 q^{69} -10.4835 q^{70} -14.0683 q^{71} +0.113708 q^{72} +10.0601 q^{73} +3.96185 q^{74} -1.07874 q^{75} -16.8169 q^{76} +0.760357 q^{77} -4.46542 q^{78} +4.06484 q^{79} +8.92168 q^{80} -7.39061 q^{81} +15.3483 q^{82} +0.755594 q^{83} +7.31874 q^{84} +2.38274 q^{85} +16.8726 q^{86} +1.79979 q^{87} +0.0858697 q^{88} +11.0402 q^{89} -2.24684 q^{90} +2.99437 q^{91} -14.9424 q^{92} +9.06841 q^{93} -17.7555 q^{94} +18.8959 q^{95} -12.8821 q^{96} -0.193133 q^{97} +4.67310 q^{98} +0.162960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * 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 $

$2$	−2.02992	−1.43537	−0.717686	−	0.696367i	$-0.754799\pi$
$2$	−2.02992	−1.43537	−0.717686	+	0.696367i	$0.754799\pi$
$3$	−1.59232	−0.919324	−0.459662	−	0.888094i	$-0.652029\pi$
$3$	−1.59232	−0.919324	−0.459662	+	0.888094i	$0.652029\pi$
$4$	2.12059	1.06029
$5$	−2.38274	−1.06560	−0.532798	−	0.846243i	$-0.678859\pi$
$5$	−2.38274	−1.06560	−0.532798	+	0.846243i	$0.678859\pi$
$6$	3.23228	1.31957
$7$	−2.16746	−0.819224	−0.409612	−	0.912260i	$-0.634336\pi$
$7$	−2.16746	−0.819224	−0.409612	+	0.912260i	$0.634336\pi$
$8$	−0.244779	−0.0865424
$9$	−0.464532	−0.154844
$10$	4.83678	1.52953
$11$	−0.350805	−0.105772	−0.0528859	−	0.998601i	$-0.516842\pi$
$11$	−0.350805	−0.105772	−0.0528859	+	0.998601i	$0.516842\pi$
$12$	−3.37664	−0.974752
$13$	−1.38151	−0.383162	−0.191581	−	0.981477i	$-0.561361\pi$
$13$	−1.38151	−0.383162	−0.191581	+	0.981477i	$0.561361\pi$
$14$	4.39978	1.17589
$15$	3.79408	0.979627
$16$	−3.74429	−0.936072
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.942965	0.222259
$19$	−7.93030	−1.81933	−0.909667	−	0.415338i	$-0.863663\pi$
$19$	−7.93030	−1.81933	−0.909667	+	0.415338i	$0.863663\pi$
$20$	−5.05281	−1.12984
$21$	3.45128	0.753131
$22$	0.712108	0.151822
$23$	−7.04636	−1.46927	−0.734634	−	0.678464i	$-0.762646\pi$
$23$	−7.04636	−1.46927	−0.734634	+	0.678464i	$0.762646\pi$
$24$	0.389765	0.0795604
$25$	0.677467	0.135493
$26$	2.80436	0.549980
$27$	5.51663	1.06168
$28$	−4.59629	−0.868617
$29$	−1.13030	−0.209891	−0.104945	−	0.994478i	$-0.533467\pi$
$29$	−1.13030	−0.209891	−0.104945	+	0.994478i	$0.533467\pi$
$30$	−7.70169	−1.40613
$31$	−5.69511	−1.02287	−0.511436	−	0.859322i	$-0.670886\pi$
$31$	−5.69511	−1.02287	−0.511436	+	0.859322i	$0.670886\pi$
$32$	8.09017	1.43015
$33$	0.558593	0.0972385
$34$	2.02992	0.348129
$35$	5.16451	0.872961
$36$	−0.985081	−0.164180
$37$	−1.95172	−0.320861	−0.160431	−	0.987047i	$-0.551288\pi$
$37$	−1.95172	−0.320861	−0.160431	+	0.987047i	$0.551288\pi$
$38$	16.0979	2.61142
$39$	2.19980	0.352250
$40$	0.583245	0.0922191
$41$	−7.56103	−1.18083	−0.590417	−	0.807098i	$-0.701037\pi$
$41$	−7.56103	−1.18083	−0.590417	+	0.807098i	$0.701037\pi$
$42$	−7.00584	−1.08102
$43$	−8.31197	−1.26756	−0.633782	−	0.773512i	$-0.718498\pi$
$43$	−8.31197	−1.26756	−0.633782	+	0.773512i	$0.718498\pi$
$44$	−0.743913	−0.112149
$45$	1.10686	0.165001
$46$	14.3036	2.10894
$47$	8.74689	1.27586	0.637932	−	0.770092i	$-0.279790\pi$
$47$	8.74689	1.27586	0.637932	+	0.770092i	$0.279790\pi$
$48$	5.96209	0.860553
$49$	−2.30211	−0.328873
$50$	−1.37521	−0.194483
$51$	1.59232	0.222969
$52$	−2.92961	−0.406264
$53$	7.45871	1.02453	0.512267	−	0.858827i	$-0.328806\pi$
$53$	7.45871	1.02453	0.512267	+	0.858827i	$0.328806\pi$
$54$	−11.1983	−1.52390
$55$	0.835879	0.112710
$56$	0.530549	0.0708975
$57$	12.6275	1.67256
$58$	2.29441	0.301271
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	8.04567	1.03869
$61$	−13.2114	−1.69154	−0.845772	−	0.533544i	$-0.820860\pi$
$61$	−13.2114	−1.69154	−0.845772	+	0.533544i	$0.820860\pi$
$62$	11.5606	1.46820
$63$	1.00686	0.126852
$64$	−8.93385	−1.11673
$65$	3.29178	0.408296
$66$	−1.13390	−0.139573
$67$	4.38461	0.535665	0.267832	−	0.963465i	$-0.413693\pi$
$67$	4.38461	0.535665	0.267832	+	0.963465i	$0.413693\pi$
$68$	−2.12059	−0.257159
$69$	11.2200	1.35073
$70$	−10.4835	−1.25302
$71$	−14.0683	−1.66960	−0.834798	−	0.550556i	$-0.814416\pi$
$71$	−14.0683	−1.66960	−0.834798	+	0.550556i	$0.814416\pi$
$72$	0.113708	0.0134006
$73$	10.0601	1.17744	0.588722	−	0.808336i	$-0.299631\pi$
$73$	10.0601	1.17744	0.588722	+	0.808336i	$0.299631\pi$
$74$	3.96185	0.460555
$75$	−1.07874	−0.124562
$76$	−16.8169	−1.92903
$77$	0.760357	0.0866507
$78$	−4.46542	−0.505609
$79$	4.06484	0.457330	0.228665	−	0.973505i	$-0.426564\pi$
$79$	4.06484	0.457330	0.228665	+	0.973505i	$0.426564\pi$
$80$	8.92168	0.997474
$81$	−7.39061	−0.821179
$82$	15.3483	1.69494
$83$	0.755594	0.0829372	0.0414686	−	0.999140i	$-0.486796\pi$
$83$	0.755594	0.0829372	0.0414686	+	0.999140i	$0.486796\pi$
$84$	7.31874	0.798540
$85$	2.38274	0.258445
$86$	16.8726	1.81942
$87$	1.79979	0.192958
$88$	0.0858697	0.00915374
$89$	11.0402	1.17026	0.585128	−	0.810941i	$-0.301044\pi$
$89$	11.0402	1.17026	0.585128	+	0.810941i	$0.301044\pi$
$90$	−2.24684	−0.236838
$91$	2.99437	0.313895
$92$	−14.9424	−1.55785
$93$	9.06841	0.940350
$94$	−17.7555	−1.83134
$95$	18.8959	1.93867
$96$	−12.8821	−1.31477
$97$	−0.193133	−0.0196097	−0.00980483	−	0.999952i	$-0.503121\pi$
$97$	−0.193133	−0.0196097	−0.00980483	+	0.999952i	$0.503121\pi$
$98$	4.67310	0.472055
$99$	0.162960	0.0163781
$100$	1.43663	0.143663
$101$	15.2819	1.52061	0.760304	−	0.649567i	$-0.225050\pi$
$101$	15.2819	1.52061	0.760304	+	0.649567i	$0.225050\pi$
$102$	−3.23228	−0.320043
$103$	6.44986	0.635524	0.317762	−	0.948171i	$-0.397069\pi$
$103$	6.44986	0.635524	0.317762	+	0.948171i	$0.397069\pi$
$104$	0.338164	0.0331597
$105$	−8.22352	−0.802533
$106$	−15.1406	−1.47059
$107$	−9.79758	−0.947168	−0.473584	−	0.880749i	$-0.657040\pi$
$107$	−9.79758	−0.947168	−0.473584	+	0.880749i	$0.657040\pi$
$108$	11.6985	1.12569
$109$	5.56891	0.533405	0.266703	−	0.963779i	$-0.414066\pi$
$109$	5.56891	0.533405	0.266703	+	0.963779i	$0.414066\pi$
$110$	−1.69677	−0.161781
$111$	3.10776	0.294975
$112$	8.11560	0.766852
$113$	18.4141	1.73225	0.866126	−	0.499825i	$-0.166602\pi$
$113$	18.4141	1.73225	0.866126	+	0.499825i	$0.166602\pi$
$114$	−25.6329	−2.40074
$115$	16.7897	1.56564
$116$	−2.39689	−0.222546
$117$	0.641756	0.0593304
$118$	−2.02992	−0.186870
$119$	2.16746	0.198691
$120$	−0.928710	−0.0847792
$121$	−10.8769	−0.988812
$122$	26.8181	2.42800
$123$	12.0395	1.08557
$124$	−12.0770	−1.08454
$125$	10.2995	0.921214
$126$	−2.04384	−0.182080
$127$	−2.55395	−0.226626	−0.113313	−	0.993559i	$-0.536146\pi$
$127$	−2.55395	−0.226626	−0.113313	+	0.993559i	$0.536146\pi$
$128$	1.95467	0.172770
$129$	13.2353	1.16530
$130$	−6.68207	−0.586056
$131$	3.17732	0.277604	0.138802	−	0.990320i	$-0.455675\pi$
$131$	3.17732	0.277604	0.138802	+	0.990320i	$0.455675\pi$
$132$	1.18454	0.103101
$133$	17.1886	1.49044
$134$	−8.90041	−0.768879
$135$	−13.1447	−1.13132
$136$	0.244779	0.0209896
$137$	−21.2658	−1.81686	−0.908431	−	0.418034i	$-0.862719\pi$
$137$	−21.2658	−1.81686	−0.908431	+	0.418034i	$0.862719\pi$
$138$	−22.7758	−1.93880
$139$	−4.15550	−0.352465	−0.176232	−	0.984349i	$-0.556391\pi$
$139$	−4.15550	−0.352465	−0.176232	+	0.984349i	$0.556391\pi$
$140$	10.9518	0.925594
$141$	−13.9278	−1.17293
$142$	28.5575	2.39649
$143$	0.484641	0.0405277
$144$	1.73934	0.144945
$145$	2.69321	0.223659
$146$	−20.4212	−1.69007
$147$	3.66568	0.302341
$148$	−4.13880	−0.340207
$149$	7.60381	0.622928	0.311464	−	0.950258i	$-0.399181\pi$
$149$	7.60381	0.622928	0.311464	+	0.950258i	$0.399181\pi$
$150$	2.18976	0.178793
$151$	−0.395854	−0.0322142	−0.0161071	−	0.999870i	$-0.505127\pi$
$151$	−0.395854	−0.0322142	−0.0161071	+	0.999870i	$0.505127\pi$
$152$	1.94117	0.157450
$153$	0.464532	0.0375552
$154$	−1.54347	−0.124376
$155$	13.5700	1.08997
$156$	4.66486	0.373488
$157$	−15.9694	−1.27450	−0.637249	−	0.770658i	$-0.719928\pi$
$157$	−15.9694	−1.27450	−0.637249	+	0.770658i	$0.719928\pi$
$158$	−8.25131	−0.656439
$159$	−11.8766	−0.941877
$160$	−19.2768	−1.52397
$161$	15.2727	1.20366
$162$	15.0024	1.17870
$163$	−0.183914	−0.0144053	−0.00720265	−	0.999974i	$-0.502293\pi$
$163$	−0.183914	−0.0144053	−0.00720265	+	0.999974i	$0.502293\pi$
$164$	−16.0338	−1.25203
$165$	−1.33098	−0.103617
$166$	−1.53380	−0.119046
$167$	−19.4177	−1.50259	−0.751295	−	0.659967i	$-0.770570\pi$
$167$	−19.4177	−1.50259	−0.751295	+	0.659967i	$0.770570\pi$
$168$	−0.844801	−0.0651778
$169$	−11.0914	−0.853187
$170$	−4.83678	−0.370964
$171$	3.68388	0.281713
$172$	−17.6262	−1.34399
$173$	15.8416	1.20442	0.602208	−	0.798339i	$-0.294288\pi$
$173$	15.8416	1.20442	0.602208	+	0.798339i	$0.294288\pi$
$174$	−3.65343	−0.276966
$175$	−1.46838	−0.110999
$176$	1.31352	0.0990100
$177$	−1.59232	−0.119686
$178$	−22.4107	−1.67975
$179$	9.94725	0.743493	0.371746	−	0.928334i	$-0.378759\pi$
$179$	9.94725	0.743493	0.371746	+	0.928334i	$0.378759\pi$
$180$	2.34719	0.174950
$181$	3.07573	0.228617	0.114309	−	0.993445i	$-0.463535\pi$
$181$	3.07573	0.228617	0.114309	+	0.993445i	$0.463535\pi$
$182$	−6.07834	−0.450556
$183$	21.0367	1.55508
$184$	1.72480	0.127154
$185$	4.65046	0.341908
$186$	−18.4082	−1.34975
$187$	0.350805	0.0256534
$188$	18.5485	1.35279
$189$	−11.9571	−0.869749
$190$	−38.3571	−2.78272
$191$	2.89829	0.209713	0.104856	−	0.994487i	$-0.466562\pi$
$191$	2.89829	0.209713	0.104856	+	0.994487i	$0.466562\pi$
$192$	14.2255	1.02664
$193$	2.21563	0.159485	0.0797424	−	0.996816i	$-0.474590\pi$
$193$	2.21563	0.159485	0.0797424	+	0.996816i	$0.474590\pi$
$194$	0.392045	0.0281472
$195$	−5.24156	−0.375356
$196$	−4.88182	−0.348701
$197$	−21.1203	−1.50476	−0.752379	−	0.658730i	$-0.771094\pi$
$197$	−21.1203	−1.50476	−0.752379	+	0.658730i	$0.771094\pi$
$198$	−0.330797	−0.0235087
$199$	3.86869	0.274244	0.137122	−	0.990554i	$-0.456215\pi$
$199$	3.86869	0.274244	0.137122	+	0.990554i	$0.456215\pi$
$200$	−0.165829	−0.0117259
$201$	−6.98168	−0.492449
$202$	−31.0211	−2.18264
$203$	2.44987	0.171947
$204$	3.37664	0.236412
$205$	18.0160	1.25829
$206$	−13.0927	−0.912213
$207$	3.27326	0.227507
$208$	5.17277	0.358667
$209$	2.78199	0.192434
$210$	16.6931	1.15193
$211$	−8.07983	−0.556238	−0.278119	−	0.960547i	$-0.589711\pi$
$211$	−8.07983	−0.556238	−0.278119	+	0.960547i	$0.589711\pi$
$212$	15.8168	1.08630
$213$	22.4011	1.53490
$214$	19.8883	1.35954
$215$	19.8053	1.35071
$216$	−1.35035	−0.0918799
$217$	12.3439	0.837960
$218$	−11.3045	−0.765635
$219$	−16.0188	−1.08245
$220$	1.77255	0.119506
$221$	1.38151	0.0929304
$222$	−6.30851	−0.423399
$223$	7.82111	0.523741	0.261870	−	0.965103i	$-0.415661\pi$
$223$	7.82111	0.523741	0.261870	+	0.965103i	$0.415661\pi$
$224$	−17.5351	−1.17162
$225$	−0.314705	−0.0209804
$226$	−37.3792	−2.48643
$227$	3.50729	0.232787	0.116394	−	0.993203i	$-0.462867\pi$
$227$	3.50729	0.232787	0.116394	+	0.993203i	$0.462867\pi$
$228$	26.7778	1.77340
$229$	−27.6767	−1.82892	−0.914462	−	0.404671i	$-0.867386\pi$
$229$	−27.6767	−1.82892	−0.914462	+	0.404671i	$0.867386\pi$
$230$	−34.0817	−2.24728
$231$	−1.21073	−0.0796601
$232$	0.276673	0.0181644
$233$	−21.9300	−1.43668	−0.718340	−	0.695692i	$-0.755098\pi$
$233$	−21.9300	−1.43668	−0.718340	+	0.695692i	$0.755098\pi$
$234$	−1.30272	−0.0851612
$235$	−20.8416	−1.35956
$236$	2.12059	0.138038
$237$	−6.47250	−0.420434
$238$	−4.39978	−0.285195
$239$	−9.40768	−0.608532	−0.304266	−	0.952587i	$-0.598411\pi$
$239$	−9.40768	−0.608532	−0.304266	+	0.952587i	$0.598411\pi$
$240$	−14.2061	−0.917001
$241$	−1.82870	−0.117797	−0.0588986	−	0.998264i	$-0.518759\pi$
$241$	−1.82870	−0.117797	−0.0588986	+	0.998264i	$0.518759\pi$
$242$	22.0793	1.41931
$243$	−4.78170	−0.306746
$244$	−28.0159	−1.79353
$245$	5.48534	0.350445
$246$	−24.4393	−1.55819
$247$	10.9558	0.697100
$248$	1.39404	0.0885217
$249$	−1.20314	−0.0762461
$250$	−20.9072	−1.32229
$251$	−21.7374	−1.37205	−0.686026	−	0.727577i	$-0.740646\pi$
$251$	−21.7374	−1.37205	−0.686026	+	0.727577i	$0.740646\pi$
$252$	2.13512	0.134500
$253$	2.47190	0.155407
$254$	5.18431	0.325293
$255$	−3.79408	−0.237594
$256$	13.8999	0.868741
$257$	−3.34767	−0.208822	−0.104411	−	0.994534i	$-0.533296\pi$
$257$	−3.34767	−0.208822	−0.104411	+	0.994534i	$0.533296\pi$
$258$	−26.8666	−1.67264
$259$	4.23029	0.262857
$260$	6.98051	0.432913
$261$	0.525059	0.0325003
$262$	−6.44971	−0.398464
$263$	−23.8007	−1.46761	−0.733806	−	0.679359i	$-0.762258\pi$
$263$	−23.8007	−1.46761	−0.733806	+	0.679359i	$0.762258\pi$
$264$	−0.136732	−0.00841525
$265$	−17.7722	−1.09174
$266$	−34.8915	−2.13934
$267$	−17.5794	−1.07584
$268$	9.29793	0.567962
$269$	16.3926	0.999472	0.499736	−	0.866178i	$-0.333430\pi$
$269$	16.3926	0.999472	0.499736	+	0.866178i	$0.333430\pi$
$270$	26.6827	1.62386
$271$	−4.66083	−0.283125	−0.141563	−	0.989929i	$-0.545213\pi$
$271$	−4.66083	−0.283125	−0.141563	+	0.989929i	$0.545213\pi$
$272$	3.74429	0.227031
$273$	−4.76798	−0.288571
$274$	43.1680	2.60787
$275$	−0.237659	−0.0143314
$276$	23.7930	1.43217
$277$	−23.0648	−1.38583	−0.692914	−	0.721020i	$-0.743674\pi$
$277$	−23.0648	−1.38583	−0.692914	+	0.721020i	$0.743674\pi$
$278$	8.43534	0.505918
$279$	2.64556	0.158386
$280$	−1.26416	−0.0755481
$281$	25.8430	1.54166	0.770831	−	0.637040i	$-0.219841\pi$
$281$	25.8430	1.54166	0.770831	+	0.637040i	$0.219841\pi$
$282$	28.2724	1.68359
$283$	−8.95352	−0.532232	−0.266116	−	0.963941i	$-0.585740\pi$
$283$	−8.95352	−0.532232	−0.266116	+	0.963941i	$0.585740\pi$
$284$	−29.8330	−1.77026
$285$	−30.0882	−1.78227
$286$	−0.983784	−0.0581724
$287$	16.3882	0.967367
$288$	−3.75815	−0.221451
$289$	1.00000	0.0588235
$290$	−5.46700	−0.321033
$291$	0.307528	0.0180276
$292$	21.3333	1.24843
$293$	33.7799	1.97344	0.986721	−	0.162424i	$-0.0519312\pi$
$293$	33.7799	1.97344	0.986721	+	0.162424i	$0.0519312\pi$
$294$	−7.44106	−0.433971
$295$	−2.38274	−0.138729
$296$	0.477740	0.0277681
$297$	−1.93526	−0.112295
$298$	−15.4351	−0.894134
$299$	9.73461	0.562967
$300$	−2.28756	−0.132072
$301$	18.0159	1.03842
$302$	0.803554	0.0462393
$303$	−24.3336	−1.39793
$304$	29.6933	1.70303
$305$	31.4793	1.80250
$306$	−0.942965	−0.0539057
$307$	30.4230	1.73633	0.868166	−	0.496273i	$-0.165299\pi$
$307$	30.4230	1.73633	0.868166	+	0.496273i	$0.165299\pi$
$308$	1.61240	0.0918751
$309$	−10.2702	−0.584252
$310$	−27.5460	−1.56451
$311$	−31.9166	−1.80983	−0.904913	−	0.425596i	$-0.860064\pi$
$311$	−31.9166	−1.80983	−0.904913	+	0.425596i	$0.860064\pi$
$312$	−0.538464	−0.0304845
$313$	−0.425419	−0.0240461	−0.0120230	−	0.999928i	$-0.503827\pi$
$313$	−0.425419	−0.0240461	−0.0120230	+	0.999928i	$0.503827\pi$
$314$	32.4167	1.82938
$315$	−2.39908	−0.135173
$316$	8.61984	0.484904
$317$	17.2091	0.966560	0.483280	−	0.875466i	$-0.339445\pi$
$317$	17.2091	0.966560	0.483280	+	0.875466i	$0.339445\pi$
$318$	24.1086	1.35194
$319$	0.396514	0.0222005
$320$	21.2871	1.18998
$321$	15.6008	0.870754
$322$	−31.0024	−1.72770
$323$	7.93030	0.441253
$324$	−15.6724	−0.870690
$325$	−0.935927	−0.0519159
$326$	0.373332	0.0206769
$327$	−8.86746	−0.490372
$328$	1.85078	0.102192
$329$	−18.9585	−1.04522
$330$	2.70179	0.148729
$331$	−33.1659	−1.82296	−0.911480	−	0.411343i	$-0.865060\pi$
$331$	−33.1659	−1.82296	−0.911480	+	0.411343i	$0.865060\pi$
$332$	1.60230	0.0879377
$333$	0.906639	0.0496835
$334$	39.4165	2.15678
$335$	−10.4474	−0.570802
$336$	−12.9226	−0.704985
$337$	−18.4199	−1.00340	−0.501699	−	0.865042i	$-0.667292\pi$
$337$	−18.4199	−1.00340	−0.501699	+	0.865042i	$0.667292\pi$
$338$	22.5147	1.22464
$339$	−29.3210	−1.59250
$340$	5.05281	0.274027
$341$	1.99787	0.108191
$342$	−7.47799	−0.404363
$343$	20.1620	1.08864
$344$	2.03459	0.109698
$345$	−26.7344	−1.43933
$346$	−32.1572	−1.72878
$347$	−22.9176	−1.23028	−0.615141	−	0.788417i	$-0.710901\pi$
$347$	−22.9176	−1.23028	−0.615141	+	0.788417i	$0.710901\pi$
$348$	3.81660	0.204591
$349$	25.4345	1.36148	0.680739	−	0.732526i	$-0.261659\pi$
$349$	25.4345	1.36148	0.680739	+	0.732526i	$0.261659\pi$
$350$	2.98070	0.159325
$351$	−7.62128	−0.406794
$352$	−2.83808	−0.151270
$353$	24.1948	1.28776	0.643880	−	0.765126i	$-0.277323\pi$
$353$	24.1948	1.28776	0.643880	+	0.765126i	$0.277323\pi$
$354$	3.23228	0.171794
$355$	33.5211	1.77911
$356$	23.4116	1.24081
$357$	−3.45128	−0.182661
$358$	−20.1922	−1.06719
$359$	−31.9543	−1.68648	−0.843242	−	0.537535i	$-0.819356\pi$
$359$	−31.9543	−1.68648	−0.843242	+	0.537535i	$0.819356\pi$
$360$	−0.270936	−0.0142796
$361$	43.8896	2.30998
$362$	−6.24349	−0.328150
$363$	17.3195	0.909038
$364$	6.34982	0.332821
$365$	−23.9706	−1.25468
$366$	−42.7028	−2.23211
$367$	−5.65852	−0.295372	−0.147686	−	0.989034i	$-0.547183\pi$
$367$	−5.65852	−0.295372	−0.147686	+	0.989034i	$0.547183\pi$
$368$	26.3836	1.37534
$369$	3.51234	0.182845
$370$	−9.44006	−0.490766
$371$	−16.1665	−0.839322
$372$	19.2303	0.997046
$373$	37.0596	1.91887	0.959436	−	0.281925i	$-0.0909730\pi$
$373$	37.0596	1.91887	0.959436	+	0.281925i	$0.0909730\pi$
$374$	−0.712108	−0.0368222
$375$	−16.4000	−0.846894
$376$	−2.14105	−0.110416
$377$	1.56152	0.0804221
$378$	24.2719	1.24841
$379$	23.8664	1.22594	0.612968	−	0.790107i	$-0.289975\pi$
$379$	23.8664	1.22594	0.612968	+	0.790107i	$0.289975\pi$
$380$	40.0703	2.05556
$381$	4.06669	0.208343
$382$	−5.88330	−0.301016
$383$	−18.4659	−0.943565	−0.471783	−	0.881715i	$-0.656389\pi$
$383$	−18.4659	−0.943565	−0.471783	+	0.881715i	$0.656389\pi$
$384$	−3.11245	−0.158832
$385$	−1.81174	−0.0923346
$386$	−4.49756	−0.228920
$387$	3.86118	0.196275
$388$	−0.409555	−0.0207920
$389$	16.8470	0.854179	0.427090	−	0.904209i	$-0.359539\pi$
$389$	16.8470	0.854179	0.427090	+	0.904209i	$0.359539\pi$
$390$	10.6400	0.538775
$391$	7.04636	0.356350
$392$	0.563508	0.0284614
$393$	−5.05929	−0.255208
$394$	42.8726	2.15989
$395$	−9.68547	−0.487329
$396$	0.345572	0.0173656
$397$	21.5510	1.08161	0.540806	−	0.841147i	$-0.318119\pi$
$397$	21.5510	1.08161	0.540806	+	0.841147i	$0.318119\pi$
$398$	−7.85313	−0.393642
$399$	−27.3697	−1.37020
$400$	−2.53663	−0.126832
$401$	−19.4346	−0.970517	−0.485259	−	0.874371i	$-0.661275\pi$
$401$	−19.4346	−0.970517	−0.485259	+	0.874371i	$0.661275\pi$
$402$	14.1723	0.706848
$403$	7.86785	0.391925
$404$	32.4066	1.61229
$405$	17.6099	0.875045
$406$	−4.97305	−0.246809
$407$	0.684675	0.0339381
$408$	−0.389765	−0.0192962
$409$	−33.8482	−1.67368	−0.836842	−	0.547444i	$-0.815601\pi$
$409$	−33.8482	−1.67368	−0.836842	+	0.547444i	$0.815601\pi$
$410$	−36.5711	−1.80612
$411$	33.8619	1.67028
$412$	13.6775	0.673841
$413$	−2.16746	−0.106654
$414$	−6.64447	−0.326558
$415$	−1.80039	−0.0883775
$416$	−11.1767	−0.547981
$417$	6.61686	0.324029
$418$	−5.64722	−0.276215
$419$	−14.3313	−0.700130	−0.350065	−	0.936725i	$-0.613841\pi$
$419$	−14.3313	−0.700130	−0.350065	+	0.936725i	$0.613841\pi$
$420$	−17.4387	−0.850920
$421$	−19.0264	−0.927289	−0.463644	−	0.886021i	$-0.653459\pi$
$421$	−19.0264	−0.927289	−0.463644	+	0.886021i	$0.653459\pi$
$422$	16.4014	0.798409
$423$	−4.06321	−0.197560
$424$	−1.82573	−0.0886655
$425$	−0.677467	−0.0328620
$426$	−45.4725	−2.20315
$427$	28.6352	1.38575
$428$	−20.7766	−1.00428
$429$	−0.771701	−0.0372581
$430$	−40.2032	−1.93877
$431$	4.38106	0.211028	0.105514	−	0.994418i	$-0.466351\pi$
$431$	4.38106	0.211028	0.105514	+	0.994418i	$0.466351\pi$
$432$	−20.6558	−0.993805
$433$	14.5339	0.698455	0.349227	−	0.937038i	$-0.386444\pi$
$433$	14.5339	0.698455	0.349227	+	0.937038i	$0.386444\pi$
$434$	−25.0572	−1.20278
$435$	−4.28843	−0.205615
$436$	11.8094	0.565566
$437$	55.8797	2.67309
$438$	32.5170	1.55372
$439$	−11.5376	−0.550659	−0.275330	−	0.961350i	$-0.588787\pi$
$439$	−11.5376	−0.550659	−0.275330	+	0.961350i	$0.588787\pi$
$440$	−0.204606	−0.00975419
$441$	1.06940	0.0509240
$442$	−2.80436	−0.133390
$443$	−18.6535	−0.886254	−0.443127	−	0.896459i	$-0.646131\pi$
$443$	−18.6535	−0.886254	−0.443127	+	0.896459i	$0.646131\pi$
$444$	6.59027	0.312760
$445$	−26.3059	−1.24702
$446$	−15.8763	−0.751763
$447$	−12.1077	−0.572673
$448$	19.3638	0.914852
$449$	−5.36826	−0.253344	−0.126672	−	0.991945i	$-0.540430\pi$
$449$	−5.36826	−0.253344	−0.126672	+	0.991945i	$0.540430\pi$
$450$	0.638827	0.0301146
$451$	2.65245	0.124899
$452$	39.0487	1.83669
$453$	0.630325	0.0296153
$454$	−7.11953	−0.334136
$455$	−7.13482	−0.334485
$456$	−3.09095	−0.144747
$457$	37.0724	1.73418	0.867088	−	0.498156i	$-0.165989\pi$
$457$	37.0724	1.73418	0.867088	+	0.498156i	$0.165989\pi$
$458$	56.1815	2.62519
$459$	−5.51663	−0.257494
$460$	35.6039	1.66004
$461$	15.3901	0.716789	0.358394	−	0.933570i	$-0.383324\pi$
$461$	15.3901	0.716789	0.358394	+	0.933570i	$0.383324\pi$
$462$	2.45768	0.114342
$463$	0.645558	0.0300016	0.0150008	−	0.999887i	$-0.495225\pi$
$463$	0.645558	0.0300016	0.0150008	+	0.999887i	$0.495225\pi$
$464$	4.23216	0.196473
$465$	−21.6077	−1.00203
$466$	44.5162	2.06217
$467$	17.8050	0.823915	0.411958	−	0.911203i	$-0.364845\pi$
$467$	17.8050	0.823915	0.411958	+	0.911203i	$0.364845\pi$
$468$	1.36090	0.0629076
$469$	−9.50347	−0.438829
$470$	42.3068	1.95147
$471$	25.4283	1.17168
$472$	−0.244779	−0.0112669
$473$	2.91588	0.134072
$474$	13.1387	0.603480
$475$	−5.37251	−0.246508
$476$	4.59629	0.210670
$477$	−3.46481	−0.158643
$478$	19.0969	0.873470
$479$	−12.7713	−0.583536	−0.291768	−	0.956489i	$-0.594244\pi$
$479$	−12.7713	−0.583536	−0.291768	+	0.956489i	$0.594244\pi$
$480$	30.6948	1.40102
$481$	2.69633	0.122942
$482$	3.71213	0.169083
$483$	−24.3190	−1.10655
$484$	−23.0655	−1.04843
$485$	0.460186	0.0208960
$486$	9.70648	0.440295
$487$	−12.2179	−0.553648	−0.276824	−	0.960921i	$-0.589282\pi$
$487$	−12.2179	−0.553648	−0.276824	+	0.960921i	$0.589282\pi$
$488$	3.23387	0.146390
$489$	0.292850	0.0132431
$490$	−11.1348	−0.503019
$491$	17.2703	0.779396	0.389698	−	0.920943i	$-0.372579\pi$
$491$	17.2703	0.779396	0.389698	+	0.920943i	$0.372579\pi$
$492$	25.5309	1.15102
$493$	1.13030	0.0509060
$494$	−22.2394	−1.00060
$495$	−0.388293	−0.0174525
$496$	21.3241	0.957482
$497$	30.4924	1.36777
$498$	2.44229	0.109442
$499$	1.66766	0.0746545	0.0373273	−	0.999303i	$-0.488116\pi$
$499$	1.66766	0.0746545	0.0373273	+	0.999303i	$0.488116\pi$
$500$	21.8409	0.976757
$501$	30.9192	1.38137
$502$	44.1252	1.96940
$503$	18.8247	0.839353	0.419677	−	0.907674i	$-0.362143\pi$
$503$	18.8247	0.839353	0.419677	+	0.907674i	$0.362143\pi$
$504$	−0.246457	−0.0109781
$505$	−36.4129	−1.62035
$506$	−5.01777	−0.223067
$507$	17.6611	0.784355
$508$	−5.41586	−0.240290
$509$	6.97154	0.309008	0.154504	−	0.987992i	$-0.450622\pi$
$509$	6.97154	0.309008	0.154504	+	0.987992i	$0.450622\pi$
$510$	7.70169	0.341036
$511$	−21.8048	−0.964590
$512$	−32.1250	−1.41974
$513$	−43.7485	−1.93154
$514$	6.79550	0.299737
$515$	−15.3684	−0.677211
$516$	28.0665	1.23556
$517$	−3.06846	−0.134951
$518$	−8.58715	−0.377298
$519$	−25.2248	−1.10725
$520$	−0.805759	−0.0353349
$521$	−29.9862	−1.31372	−0.656859	−	0.754014i	$-0.728115\pi$
$521$	−29.9862	−1.31372	−0.656859	+	0.754014i	$0.728115\pi$
$522$	−1.06583	−0.0466501
$523$	1.10210	0.0481914	0.0240957	−	0.999710i	$-0.492329\pi$
$523$	1.10210	0.0481914	0.0240957	+	0.999710i	$0.492329\pi$
$524$	6.73778	0.294341
$525$	2.33813	0.102044
$526$	48.3135	2.10657
$527$	5.69511	0.248083
$528$	−2.09153	−0.0910223
$529$	26.6511	1.15875
$530$	36.0762	1.56705
$531$	−0.464532	−0.0201590
$532$	36.4499	1.58030
$533$	10.4456	0.452451
$534$	35.6849	1.54424
$535$	23.3451	1.00930
$536$	−1.07326	−0.0463577
$537$	−15.8392	−0.683510
$538$	−33.2756	−1.43461
$539$	0.807593	0.0347855
$540$	−27.8745	−1.19953
$541$	1.60725	0.0691012	0.0345506	−	0.999403i	$-0.489000\pi$
$541$	1.60725	0.0691012	0.0345506	+	0.999403i	$0.489000\pi$
$542$	9.46113	0.406390
$543$	−4.89753	−0.210173
$544$	−8.09017	−0.346863
$545$	−13.2693	−0.568394
$546$	9.67863	0.414207
$547$	−15.8855	−0.679216	−0.339608	−	0.940567i	$-0.610294\pi$
$547$	−15.8855	−0.679216	−0.339608	+	0.940567i	$0.610294\pi$
$548$	−45.0960	−1.92641
$549$	6.13712	0.261926
$550$	0.482429	0.0205709
$551$	8.96358	0.381861
$552$	−2.74642	−0.116896
$553$	−8.81038	−0.374656
$554$	46.8197	1.98918
$555$	−7.40499	−0.314324
$556$	−8.81209	−0.373716
$557$	27.6798	1.17283	0.586415	−	0.810010i	$-0.300539\pi$
$557$	27.6798	1.17283	0.586415	+	0.810010i	$0.300539\pi$
$558$	−5.37029	−0.227342
$559$	11.4831	0.485682
$560$	−19.3374	−0.817154
$561$	−0.558593	−0.0235838
$562$	−52.4592	−2.21286
$563$	14.0046	0.590223	0.295112	−	0.955463i	$-0.404643\pi$
$563$	14.0046	0.590223	0.295112	+	0.955463i	$0.404643\pi$
$564$	−29.5351	−1.24365
$565$	−43.8761	−1.84588
$566$	18.1750	0.763950
$567$	16.0189	0.672729
$568$	3.44361	0.144491
$569$	−14.5196	−0.608695	−0.304347	−	0.952561i	$-0.598438\pi$
$569$	−14.5196	−0.608695	−0.304347	+	0.952561i	$0.598438\pi$
$570$	61.0766	2.55822
$571$	−28.2712	−1.18311	−0.591557	−	0.806263i	$-0.701487\pi$
$571$	−28.2712	−1.18311	−0.591557	+	0.806263i	$0.701487\pi$
$572$	1.02772	0.0429713
$573$	−4.61499	−0.192794
$574$	−33.2668	−1.38853
$575$	−4.77367	−0.199076
$576$	4.15006	0.172919
$577$	−17.3030	−0.720332	−0.360166	−	0.932888i	$-0.617280\pi$
$577$	−17.3030	−0.720332	−0.360166	+	0.932888i	$0.617280\pi$
$578$	−2.02992	−0.0844336
$579$	−3.52799	−0.146618
$580$	5.71117	0.237144
$581$	−1.63772	−0.0679441
$582$	−0.624259	−0.0258764
$583$	−2.61656	−0.108367
$584$	−2.46250	−0.101899
$585$	−1.52914	−0.0632222
$586$	−68.5706	−2.83262
$587$	12.3675	0.510463	0.255231	−	0.966880i	$-0.417848\pi$
$587$	12.3675	0.510463	0.255231	+	0.966880i	$0.417848\pi$
$588$	7.77340	0.320569
$589$	45.1639	1.86095
$590$	4.83678	0.199127
$591$	33.6302	1.38336
$592$	7.30781	0.300349
$593$	19.0153	0.780865	0.390432	−	0.920632i	$-0.372326\pi$
$593$	19.0153	0.780865	0.390432	+	0.920632i	$0.372326\pi$
$594$	3.92843	0.161186
$595$	−5.16451	−0.211724
$596$	16.1245	0.660486
$597$	−6.16017	−0.252119
$598$	−19.7605	−0.808067
$599$	28.2373	1.15374	0.576872	−	0.816835i	$-0.304273\pi$
$599$	28.2373	1.15374	0.576872	+	0.816835i	$0.304273\pi$
$600$	0.264053	0.0107799
$601$	19.9123	0.812241	0.406120	−	0.913820i	$-0.366881\pi$
$601$	19.9123	0.812241	0.406120	+	0.913820i	$0.366881\pi$
$602$	−36.5708	−1.49052
$603$	−2.03679	−0.0829446
$604$	−0.839443	−0.0341565
$605$	25.9169	1.05367
$606$	49.3954	2.00655
$607$	−42.1172	−1.70948	−0.854742	−	0.519054i	$-0.826284\pi$
$607$	−42.1172	−1.70948	−0.854742	+	0.519054i	$0.826284\pi$
$608$	−64.1575	−2.60193
$609$	−3.90097	−0.158075
$610$	−63.9006	−2.58726
$611$	−12.0839	−0.488863
$612$	0.985081	0.0398195
$613$	1.70826	0.0689961	0.0344980	−	0.999405i	$-0.489017\pi$
$613$	1.70826	0.0689961	0.0344980	+	0.999405i	$0.489017\pi$
$614$	−61.7563	−2.49228
$615$	−28.6871	−1.15678
$616$	−0.186119	−0.00749896
$617$	−46.8393	−1.88568	−0.942839	−	0.333247i	$-0.891856\pi$
$617$	−46.8393	−1.88568	−0.942839	+	0.333247i	$0.891856\pi$
$618$	20.8477	0.838619
$619$	−0.905371	−0.0363900	−0.0181950	−	0.999834i	$-0.505792\pi$
$619$	−0.905371	−0.0363900	−0.0181950	+	0.999834i	$0.505792\pi$
$620$	28.7763	1.15568
$621$	−38.8721	−1.55988
$622$	64.7883	2.59777
$623$	−23.9292	−0.958702
$624$	−8.23668	−0.329731
$625$	−27.9284	−1.11713
$626$	0.863567	0.0345151
$627$	−4.42981	−0.176909
$628$	−33.8645	−1.35134
$629$	1.95172	0.0778203
$630$	4.86995	0.194023
$631$	13.0627	0.520019	0.260009	−	0.965606i	$-0.416274\pi$
$631$	13.0627	0.520019	0.260009	+	0.965606i	$0.416274\pi$
$632$	−0.994986	−0.0395784
$633$	12.8656	0.511363
$634$	−34.9332	−1.38737
$635$	6.08540	0.241492
$636$	−25.1854	−0.998666
$637$	3.18039	0.126012
$638$	−0.804893	−0.0318660
$639$	6.53517	0.258527
$640$	−4.65748	−0.184103
$641$	−4.32576	−0.170857	−0.0854287	−	0.996344i	$-0.527226\pi$
$641$	−4.32576	−0.170857	−0.0854287	+	0.996344i	$0.527226\pi$
$642$	−31.6685	−1.24986
$643$	−40.0963	−1.58124	−0.790622	−	0.612305i	$-0.790242\pi$
$643$	−40.0963	−1.58124	−0.790622	+	0.612305i	$0.790242\pi$
$644$	32.3871	1.27623
$645$	−31.5363	−1.24174
$646$	−16.0979	−0.633363
$647$	−9.00784	−0.354135	−0.177067	−	0.984199i	$-0.556661\pi$
$647$	−9.00784	−0.354135	−0.177067	+	0.984199i	$0.556661\pi$
$648$	1.80907	0.0710668
$649$	−0.350805	−0.0137703
$650$	1.89986	0.0745186
$651$	−19.6554	−0.770357
$652$	−0.390006	−0.0152738
$653$	11.1999	0.438288	0.219144	−	0.975693i	$-0.429674\pi$
$653$	11.1999	0.438288	0.219144	+	0.975693i	$0.429674\pi$
$654$	18.0003	0.703866
$655$	−7.57074	−0.295813
$656$	28.3107	1.10535
$657$	−4.67324	−0.182320
$658$	38.4844	1.50028
$659$	−25.8735	−1.00789	−0.503944	−	0.863737i	$-0.668118\pi$
$659$	−25.8735	−1.00789	−0.503944	+	0.863737i	$0.668118\pi$
$660$	−2.82246	−0.109864
$661$	−18.0006	−0.700142	−0.350071	−	0.936723i	$-0.613843\pi$
$661$	−18.0006	−0.700142	−0.350071	+	0.936723i	$0.613843\pi$
$662$	67.3241	2.61663
$663$	−2.19980	−0.0854331
$664$	−0.184953	−0.00717758
$665$	−40.9561	−1.58821
$666$	−1.84041	−0.0713143
$667$	7.96447	0.308386
$668$	−41.1770	−1.59318
$669$	−12.4537	−0.481487
$670$	21.2074	0.819313
$671$	4.63463	0.178918
$672$	27.9215	1.07709
$673$	−39.6024	−1.52656	−0.763279	−	0.646069i	$-0.776412\pi$
$673$	−39.6024	−1.52656	−0.763279	+	0.646069i	$0.776412\pi$
$674$	37.3911	1.44025
$675$	3.73733	0.143850
$676$	−23.5203	−0.904628
$677$	−20.5751	−0.790764	−0.395382	−	0.918517i	$-0.629388\pi$
$677$	−20.5751	−0.790764	−0.395382	+	0.918517i	$0.629388\pi$
$678$	59.5194	2.28583
$679$	0.418608	0.0160647
$680$	−0.583245	−0.0223664
$681$	−5.58472	−0.214007
$682$	−4.05553	−0.155294
$683$	28.3843	1.08609	0.543047	−	0.839702i	$-0.317271\pi$
$683$	28.3843	1.08609	0.543047	+	0.839702i	$0.317271\pi$
$684$	7.81198	0.298699
$685$	50.6710	1.93604
$686$	−40.9272	−1.56261
$687$	44.0700	1.68137
$688$	31.1224	1.18653
$689$	−10.3043	−0.392562
$690$	54.2688	2.06598
$691$	−17.1338	−0.651801	−0.325901	−	0.945404i	$-0.605667\pi$
$691$	−17.1338	−0.651801	−0.325901	+	0.945404i	$0.605667\pi$
$692$	33.5935	1.27703
$693$	−0.353211	−0.0134174
$694$	46.5210	1.76591
$695$	9.90148	0.375585
$696$	−0.440550	−0.0166990
$697$	7.56103	0.286394
$698$	−51.6301	−1.95423
$699$	34.9194	1.32077
$700$	−3.11383	−0.117692
$701$	1.69086	0.0638630	0.0319315	−	0.999490i	$-0.489834\pi$
$701$	1.69086	0.0638630	0.0319315	+	0.999490i	$0.489834\pi$
$702$	15.4706	0.583900
$703$	15.4777	0.583754
$704$	3.13404	0.118119
$705$	33.1864	1.24987
$706$	−49.1136	−1.84842
$707$	−33.1230	−1.24572
$708$	−3.37664	−0.126902
$709$	47.5219	1.78472	0.892362	−	0.451321i	$-0.149047\pi$
$709$	47.5219	1.78472	0.892362	+	0.451321i	$0.149047\pi$
$710$	−68.0452	−2.55369
$711$	−1.88825	−0.0708149
$712$	−2.70240	−0.101277
$713$	40.1298	1.50287
$714$	7.00584	0.262187
$715$	−1.15478	−0.0431862
$716$	21.0940	0.788320
$717$	14.9800	0.559438
$718$	64.8648	2.42073
$719$	−36.5370	−1.36260	−0.681301	−	0.732003i	$-0.738586\pi$
$719$	−36.5370	−1.36260	−0.681301	+	0.732003i	$0.738586\pi$
$720$	−4.14441	−0.154453
$721$	−13.9798	−0.520636
$722$	−89.0925	−3.31568
$723$	2.91187	0.108294
$724$	6.52234	0.242401
$725$	−0.765738	−0.0284388
$726$	−35.1573	−1.30481
$727$	−9.77715	−0.362614	−0.181307	−	0.983427i	$-0.558033\pi$
$727$	−9.77715	−0.362614	−0.181307	+	0.983427i	$0.558033\pi$
$728$	−0.732958	−0.0271652
$729$	29.7858	1.10318
$730$	48.6585	1.80093
$731$	8.31197	0.307429
$732$	44.6101	1.64884
$733$	6.85288	0.253117	0.126558	−	0.991959i	$-0.459607\pi$
$733$	6.85288	0.253117	0.126558	+	0.991959i	$0.459607\pi$
$734$	11.4864	0.423969
$735$	−8.73439	−0.322173
$736$	−57.0063	−2.10128
$737$	−1.53814	−0.0566583
$738$	−7.12978	−0.262451
$739$	0.531567	0.0195540	0.00977700	−	0.999952i	$-0.496888\pi$
$739$	0.531567	0.0195540	0.00977700	+	0.999952i	$0.496888\pi$
$740$	9.86169	0.362523
$741$	−17.4451	−0.640860
$742$	32.8167	1.20474
$743$	37.7610	1.38532	0.692659	−	0.721265i	$-0.256439\pi$
$743$	37.7610	1.38532	0.692659	+	0.721265i	$0.256439\pi$
$744$	−2.21975	−0.0813801
$745$	−18.1179	−0.663789
$746$	−75.2281	−2.75430
$747$	−0.350998	−0.0128423
$748$	0.743913	0.0272001
$749$	21.2359	0.775942
$750$	33.2908	1.21561
$751$	32.0664	1.17012	0.585059	−	0.810990i	$-0.301071\pi$
$751$	32.0664	1.17012	0.585059	+	0.810990i	$0.301071\pi$
$752$	−32.7509	−1.19430
$753$	34.6128	1.26136
$754$	−3.16976	−0.115436
$755$	0.943220	0.0343273
$756$	−25.3560	−0.922189
$757$	−25.0664	−0.911052	−0.455526	−	0.890222i	$-0.650549\pi$
$757$	−25.0664	−0.911052	−0.455526	+	0.890222i	$0.650549\pi$
$758$	−48.4470	−1.75968
$759$	−3.93604	−0.142869
$760$	−4.62531	−0.167777
$761$	−41.2631	−1.49579	−0.747894	−	0.663818i	$-0.768935\pi$
$761$	−41.2631	−1.49579	−0.747894	+	0.663818i	$0.768935\pi$
$762$	−8.25506	−0.299049
$763$	−12.0704	−0.436978
$764$	6.14607	0.222357
$765$	−1.10686	−0.0400187
$766$	37.4844	1.35437
$767$	−1.38151	−0.0498834
$768$	−22.1330	−0.798655
$769$	3.75144	0.135280	0.0676401	−	0.997710i	$-0.478453\pi$
$769$	3.75144	0.135280	0.0676401	+	0.997710i	$0.478453\pi$
$770$	3.67768	0.132535
$771$	5.33054	0.191975
$772$	4.69844	0.169101
$773$	4.03698	0.145200	0.0726000	−	0.997361i	$-0.476870\pi$
$773$	4.03698	0.145200	0.0726000	+	0.997361i	$0.476870\pi$
$774$	−7.83789	−0.281727
$775$	−3.85825	−0.138592
$776$	0.0472748	0.00169707
$777$	−6.73595	−0.241651
$778$	−34.1982	−1.22607
$779$	59.9612	2.14833
$780$	−11.1152	−0.397987
$781$	4.93522	0.176596
$782$	−14.3036	−0.511494
$783$	−6.23542	−0.222836
$784$	8.61976	0.307849
$785$	38.0510	1.35810
$786$	10.2700	0.366318
$787$	−8.67565	−0.309254	−0.154627	−	0.987973i	$-0.549418\pi$
$787$	−8.67565	−0.309254	−0.154627	+	0.987973i	$0.549418\pi$
$788$	−44.7874	−1.59548
$789$	37.8982	1.34921
$790$	19.6607	0.699498
$791$	−39.9118	−1.41910
$792$	−0.0398893	−0.00141740
$793$	18.2517	0.648136
$794$	−43.7468	−1.55252
$795$	28.2989	1.00366
$796$	8.20388	0.290779
$797$	−12.0254	−0.425962	−0.212981	−	0.977056i	$-0.568317\pi$
$797$	−12.0254	−0.425962	−0.212981	+	0.977056i	$0.568317\pi$
$798$	55.5583	1.96674
$799$	−8.74689	−0.309443
$800$	5.48082	0.193776
$801$	−5.12852	−0.181207
$802$	39.4507	1.39305
$803$	−3.52913	−0.124540
$804$	−14.8052	−0.522141
$805$	−36.3909	−1.28261
$806$	−15.9711	−0.562559
$807$	−26.1021	−0.918838
$808$	−3.74069	−0.131597
$809$	−34.9742	−1.22963	−0.614814	−	0.788672i	$-0.710769\pi$
$809$	−34.9742	−1.22963	−0.614814	+	0.788672i	$0.710769\pi$
$810$	−35.7468	−1.25601
$811$	17.8275	0.626008	0.313004	−	0.949752i	$-0.398665\pi$
$811$	17.8275	0.626008	0.313004	+	0.949752i	$0.398665\pi$
$812$	5.19517	0.182315
$813$	7.42151	0.260284
$814$	−1.38984	−0.0487138
$815$	0.438221	0.0153502
$816$	−5.96209	−0.208715
$817$	65.9164	2.30612
$818$	68.7092	2.40236
$819$	−1.39098	−0.0486048
$820$	38.2044	1.33416
$821$	−7.48783	−0.261327	−0.130663	−	0.991427i	$-0.541711\pi$
$821$	−7.48783	−0.261327	−0.130663	+	0.991427i	$0.541711\pi$
$822$	−68.7370	−2.39748
$823$	−16.3566	−0.570155	−0.285078	−	0.958504i	$-0.592019\pi$
$823$	−16.3566	−0.570155	−0.285078	+	0.958504i	$0.592019\pi$
$824$	−1.57879	−0.0549998
$825$	0.378428	0.0131752
$826$	4.39978	0.153088
$827$	−21.6756	−0.753734	−0.376867	−	0.926267i	$-0.622999\pi$
$827$	−21.6756	−0.753734	−0.376867	+	0.926267i	$0.622999\pi$
$828$	6.94123	0.241224
$829$	33.3807	1.15936	0.579680	−	0.814845i	$-0.303178\pi$
$829$	33.3807	1.15936	0.579680	+	0.814845i	$0.303178\pi$
$830$	3.65465	0.126855
$831$	36.7264	1.27402
$832$	12.3422	0.427889
$833$	2.30211	0.0797634
$834$	−13.4317	−0.465102
$835$	46.2675	1.60115
$836$	5.89945	0.204037
$837$	−31.4178	−1.08596
$838$	29.0915	1.00495
$839$	3.07791	0.106261	0.0531306	−	0.998588i	$-0.483080\pi$
$839$	3.07791	0.106261	0.0531306	+	0.998588i	$0.483080\pi$
$840$	2.01294	0.0694531
$841$	−27.7224	−0.955946
$842$	38.6221	1.33100
$843$	−41.1501	−1.41729
$844$	−17.1340	−0.589775
$845$	26.4280	0.909152
$846$	8.24801	0.283572
$847$	23.5753	0.810058
$848$	−27.9276	−0.959037
$849$	14.2568	0.489293
$850$	1.37521	0.0471691
$851$	13.7525	0.471431
$852$	47.5035	1.62744
$853$	−5.94748	−0.203638	−0.101819	−	0.994803i	$-0.532466\pi$
$853$	−5.94748	−0.203638	−0.101819	+	0.994803i	$0.532466\pi$
$854$	−58.1272	−1.98907
$855$	−8.77774	−0.300192
$856$	2.39824	0.0819702
$857$	−1.39483	−0.0476465	−0.0238233	−	0.999716i	$-0.507584\pi$
$857$	−1.39483	−0.0476465	−0.0238233	+	0.999716i	$0.507584\pi$
$858$	1.56649	0.0534792
$859$	9.15249	0.312279	0.156140	−	0.987735i	$-0.450095\pi$
$859$	9.15249	0.312279	0.156140	+	0.987735i	$0.450095\pi$
$860$	41.9988	1.43215
$861$	−26.0952	−0.889323
$862$	−8.89322	−0.302904
$863$	11.3103	0.385008	0.192504	−	0.981296i	$-0.438339\pi$
$863$	11.3103	0.385008	0.192504	+	0.981296i	$0.438339\pi$
$864$	44.6305	1.51836
$865$	−37.7465	−1.28342
$866$	−29.5027	−1.00254
$867$	−1.59232	−0.0540779
$868$	26.1764	0.888483
$869$	−1.42597	−0.0483726
$870$	8.70519	0.295133
$871$	−6.05738	−0.205246
$872$	−1.36315	−0.0461621
$873$	0.0897165	0.00303644
$874$	−113.431	−3.83688
$875$	−22.3237	−0.754680
$876$	−33.9693	−1.14772
$877$	−22.6374	−0.764411	−0.382205	−	0.924077i	$-0.624835\pi$
$877$	−22.6374	−0.764411	−0.382205	+	0.924077i	$0.624835\pi$
$878$	23.4204	0.790401
$879$	−53.7882	−1.81423
$880$	−3.12977	−0.105505
$881$	21.0211	0.708219	0.354110	−	0.935204i	$-0.384784\pi$
$881$	21.0211	0.708219	0.354110	+	0.935204i	$0.384784\pi$
$882$	−2.17081	−0.0730949
$883$	−21.7658	−0.732477	−0.366238	−	0.930521i	$-0.619355\pi$
$883$	−21.7658	−0.732477	−0.366238	+	0.930521i	$0.619355\pi$
$884$	2.92961	0.0985334
$885$	3.79408	0.127537
$886$	37.8651	1.27210
$887$	−10.1223	−0.339875	−0.169937	−	0.985455i	$-0.554357\pi$
$887$	−10.1223	−0.339875	−0.169937	+	0.985455i	$0.554357\pi$
$888$	−0.760713	−0.0255279
$889$	5.53558	0.185657
$890$	53.3990	1.78994
$891$	2.59267	0.0868576
$892$	16.5853	0.555318
$893$	−69.3654	−2.32123
$894$	24.5776	0.821998
$895$	−23.7018	−0.792262
$896$	−4.23667	−0.141537
$897$	−15.5006	−0.517549
$898$	10.8972	0.363643
$899$	6.43716	0.214691
$900$	−0.667359	−0.0222453
$901$	−7.45871	−0.248486
$902$	−5.38426	−0.179276
$903$	−28.6869	−0.954642
$904$	−4.50738	−0.149913
$905$	−7.32867	−0.243613
$906$	−1.27951	−0.0425089
$907$	−18.9505	−0.629242	−0.314621	−	0.949217i	$-0.601877\pi$
$907$	−18.9505	−0.629242	−0.314621	+	0.949217i	$0.601877\pi$
$908$	7.43751	0.246823
$909$	−7.09895	−0.235457
$910$	14.4831	0.480111
$911$	−19.5839	−0.648843	−0.324422	−	0.945913i	$-0.605170\pi$
$911$	−19.5839	−0.648843	−0.324422	+	0.945913i	$0.605170\pi$
$912$	−47.2811	−1.56563
$913$	−0.265066	−0.00877242
$914$	−75.2542	−2.48919
$915$	−50.1250	−1.65708
$916$	−58.6907	−1.93920
$917$	−6.88672	−0.227419
$918$	11.1983	0.369600
$919$	−53.5348	−1.76595	−0.882975	−	0.469421i	$-0.844463\pi$
$919$	−53.5348	−1.76595	−0.882975	+	0.469421i	$0.844463\pi$
$920$	−4.10975	−0.135495
$921$	−48.4430	−1.59625
$922$	−31.2407	−1.02886
$923$	19.4355	0.639726
$924$	−2.56745	−0.0844630
$925$	−1.32223	−0.0434746
$926$	−1.31043	−0.0430635
$927$	−2.99617	−0.0984072
$928$	−9.14429	−0.300176
$929$	−19.8396	−0.650917	−0.325458	−	0.945556i	$-0.605519\pi$
$929$	−19.8396	−0.650917	−0.325458	+	0.945556i	$0.605519\pi$
$930$	43.8619	1.43829
$931$	18.2564	0.598330
$932$	−46.5044	−1.52330
$933$	50.8213	1.66382
$934$	−36.1427	−1.18262
$935$	−0.835879	−0.0273362
$936$	−0.157088	−0.00513459
$937$	26.5441	0.867157	0.433578	−	0.901116i	$-0.357251\pi$
$937$	26.5441	0.867157	0.433578	+	0.901116i	$0.357251\pi$
$938$	19.2913	0.629883
$939$	0.677401	0.0221061
$940$	−44.1964	−1.44153
$941$	3.68996	0.120289	0.0601446	−	0.998190i	$-0.480844\pi$
$941$	3.68996	0.120289	0.0601446	+	0.998190i	$0.480844\pi$
$942$	−51.6176	−1.68179
$943$	53.2777	1.73496
$944$	−3.74429	−0.121866
$945$	28.4907	0.926801
$946$	−5.91902	−0.192444
$947$	−6.12594	−0.199066	−0.0995332	−	0.995034i	$-0.531735\pi$
$947$	−6.12594	−0.199066	−0.0995332	+	0.995034i	$0.531735\pi$
$948$	−13.7255	−0.445783
$949$	−13.8981	−0.451152
$950$	10.9058	0.353830
$951$	−27.4023	−0.888582
$952$	−0.530549	−0.0171952
$953$	−34.5161	−1.11809	−0.559043	−	0.829139i	$-0.688831\pi$
$953$	−34.5161	−1.11809	−0.559043	+	0.829139i	$0.688831\pi$
$954$	7.03330	0.227712
$955$	−6.90588	−0.223469
$956$	−19.9498	−0.645222
$957$	−0.631375	−0.0204095
$958$	25.9248	0.837591
$959$	46.0929	1.48842
$960$	−33.8957	−1.09398
$961$	1.43425	0.0462661
$962$	−5.47333	−0.176467
$963$	4.55129	0.146663
$964$	−3.87792	−0.124899
$965$	−5.27929	−0.169946
$966$	49.3656	1.58831
$967$	−36.0074	−1.15792	−0.578960	−	0.815356i	$-0.696541\pi$
$967$	−36.0074	−1.15792	−0.578960	+	0.815356i	$0.696541\pi$
$968$	2.66244	0.0855742
$969$	−12.6275	−0.405655
$970$	−0.934142	−0.0299935
$971$	−24.4959	−0.786111	−0.393056	−	0.919515i	$-0.628582\pi$
$971$	−24.4959	−0.786111	−0.393056	+	0.919515i	$0.628582\pi$
$972$	−10.1400	−0.325241
$973$	9.00688	0.288747
$974$	24.8015	0.794690
$975$	1.49029	0.0477275
$976$	49.4672	1.58341
$977$	−14.3090	−0.457784	−0.228892	−	0.973452i	$-0.573510\pi$
$977$	−14.3090	−0.457784	−0.228892	+	0.973452i	$0.573510\pi$
$978$	−0.594462	−0.0190088
$979$	−3.87295	−0.123780
$980$	11.6321	0.371575
$981$	−2.58694	−0.0825947
$982$	−35.0573	−1.11872
$983$	−11.3054	−0.360586	−0.180293	−	0.983613i	$-0.557705\pi$
$983$	−11.3054	−0.360586	−0.180293	+	0.983613i	$0.557705\pi$
$984$	−2.94702	−0.0939477
$985$	50.3243	1.60346
$986$	−2.29441	−0.0730690
$987$	30.1880	0.960894
$988$	23.2327	0.739130
$989$	58.5691	1.86239
$990$	0.788205	0.0250508
$991$	30.1991	0.959305	0.479653	−	0.877458i	$-0.340763\pi$
$991$	30.1991	0.959305	0.479653	+	0.877458i	$0.340763\pi$
$992$	−46.0744	−1.46286
$993$	52.8105	1.67589
$994$	−61.8973	−1.96326
$995$	−9.21809	−0.292233
$996$	−2.55137	−0.0808432
$997$	14.8817	0.471308	0.235654	−	0.971837i	$-0.424277\pi$
$997$	14.8817	0.471308	0.235654	+	0.971837i	$0.424277\pi$
$998$	−3.38521	−0.107157
$999$	−10.7669	−0.340651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.4	✓	22
3.2	odd	2		9027.2.a.s.1.19		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.4	✓	22	1.1	even	1	trivial
9027.2.a.s.1.19		22	3.2	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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.02992 q^{2} -1.59232 q^{3} +2.12059 q^{4} -2.38274 q^{5} +3.23228 q^{6} -2.16746 q^{7} -0.244779 q^{8} -0.464532 q^{9} +O(q^{10})\)	\(q-2.02992 q^{2} -1.59232 q^{3} +2.12059 q^{4} -2.38274 q^{5} +3.23228 q^{6} -2.16746 q^{7} -0.244779 q^{8} -0.464532 q^{9} +4.83678 q^{10} -0.350805 q^{11} -3.37664 q^{12} -1.38151 q^{13} +4.39978 q^{14} +3.79408 q^{15} -3.74429 q^{16} -1.00000 q^{17} +0.942965 q^{18} -7.93030 q^{19} -5.05281 q^{20} +3.45128 q^{21} +0.712108 q^{22} -7.04636 q^{23} +0.389765 q^{24} +0.677467 q^{25} +2.80436 q^{26} +5.51663 q^{27} -4.59629 q^{28} -1.13030 q^{29} -7.70169 q^{30} -5.69511 q^{31} +8.09017 q^{32} +0.558593 q^{33} +2.02992 q^{34} +5.16451 q^{35} -0.985081 q^{36} -1.95172 q^{37} +16.0979 q^{38} +2.19980 q^{39} +0.583245 q^{40} -7.56103 q^{41} -7.00584 q^{42} -8.31197 q^{43} -0.743913 q^{44} +1.10686 q^{45} +14.3036 q^{46} +8.74689 q^{47} +5.96209 q^{48} -2.30211 q^{49} -1.37521 q^{50} +1.59232 q^{51} -2.92961 q^{52} +7.45871 q^{53} -11.1983 q^{54} +0.835879 q^{55} +0.530549 q^{56} +12.6275 q^{57} +2.29441 q^{58} +1.00000 q^{59} +8.04567 q^{60} -13.2114 q^{61} +11.5606 q^{62} +1.00686 q^{63} -8.93385 q^{64} +3.29178 q^{65} -1.13390 q^{66} +4.38461 q^{67} -2.12059 q^{68} +11.2200 q^{69} -10.4835 q^{70} -14.0683 q^{71} +0.113708 q^{72} +10.0601 q^{73} +3.96185 q^{74} -1.07874 q^{75} -16.8169 q^{76} +0.760357 q^{77} -4.46542 q^{78} +4.06484 q^{79} +8.92168 q^{80} -7.39061 q^{81} +15.3483 q^{82} +0.755594 q^{83} +7.31874 q^{84} +2.38274 q^{85} +16.8726 q^{86} +1.79979 q^{87} +0.0858697 q^{88} +11.0402 q^{89} -2.24684 q^{90} +2.99437 q^{91} -14.9424 q^{92} +9.06841 q^{93} -17.7555 q^{94} +18.8959 q^{95} -12.8821 q^{96} -0.193133 q^{97} +4.67310 q^{98} +0.162960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

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