LMFDB - Embedded newform 1339.2.a.g.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.947942 q^{2} +3.31104 q^{3} -1.10141 q^{4} +4.30053 q^{5} +3.13867 q^{6} +1.61201 q^{7} -2.93995 q^{8} +7.96298 q^{9} +O(q^{10})$	\(q+0.947942 q^{2} +3.31104 q^{3} -1.10141 q^{4} +4.30053 q^{5} +3.13867 q^{6} +1.61201 q^{7} -2.93995 q^{8} +7.96298 q^{9} +4.07665 q^{10} -4.11384 q^{11} -3.64680 q^{12} -1.00000 q^{13} +1.52809 q^{14} +14.2392 q^{15} -0.584091 q^{16} -7.15332 q^{17} +7.54844 q^{18} -2.76598 q^{19} -4.73663 q^{20} +5.33743 q^{21} -3.89968 q^{22} +3.00016 q^{23} -9.73430 q^{24} +13.4945 q^{25} -0.947942 q^{26} +16.4326 q^{27} -1.77548 q^{28} +3.44689 q^{29} +13.4979 q^{30} -6.97691 q^{31} +5.32622 q^{32} -13.6211 q^{33} -6.78093 q^{34} +6.93249 q^{35} -8.77048 q^{36} -7.40550 q^{37} -2.62199 q^{38} -3.31104 q^{39} -12.6433 q^{40} -8.57012 q^{41} +5.05957 q^{42} +6.28809 q^{43} +4.53101 q^{44} +34.2450 q^{45} +2.84398 q^{46} +2.96090 q^{47} -1.93395 q^{48} -4.40142 q^{49} +12.7920 q^{50} -23.6849 q^{51} +1.10141 q^{52} -1.70867 q^{53} +15.5772 q^{54} -17.6917 q^{55} -4.73923 q^{56} -9.15826 q^{57} +3.26745 q^{58} -5.66552 q^{59} -15.6832 q^{60} -10.4501 q^{61} -6.61370 q^{62} +12.8364 q^{63} +6.21713 q^{64} -4.30053 q^{65} -12.9120 q^{66} +0.0391610 q^{67} +7.87871 q^{68} +9.93366 q^{69} +6.57160 q^{70} +5.28176 q^{71} -23.4108 q^{72} +8.49628 q^{73} -7.01998 q^{74} +44.6809 q^{75} +3.04647 q^{76} -6.63155 q^{77} -3.13867 q^{78} -5.97733 q^{79} -2.51190 q^{80} +30.5201 q^{81} -8.12398 q^{82} +6.37508 q^{83} -5.87868 q^{84} -30.7630 q^{85} +5.96074 q^{86} +11.4128 q^{87} +12.0945 q^{88} +2.38460 q^{89} +32.4623 q^{90} -1.61201 q^{91} -3.30440 q^{92} -23.1008 q^{93} +2.80676 q^{94} -11.8952 q^{95} +17.6353 q^{96} +18.0075 q^{97} -4.17229 q^{98} -32.7584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) $ 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.947942	0.670296	0.335148	−	0.942165i	$-0.391214\pi$
$2$	0.947942	0.670296	0.335148	+	0.942165i	$0.391214\pi$
$3$	3.31104	1.91163	0.955815	−	0.293970i	$-0.0949767\pi$
$3$	3.31104	1.91163	0.955815	+	0.293970i	$0.0949767\pi$
$4$	−1.10141	−0.550703
$5$	4.30053	1.92325	0.961627	−	0.274361i	$-0.0884664\pi$
$5$	4.30053	1.92325	0.961627	+	0.274361i	$0.0884664\pi$
$6$	3.13867	1.28136
$7$	1.61201	0.609283	0.304641	−	0.952467i	$-0.401463\pi$
$7$	1.61201	0.609283	0.304641	+	0.952467i	$0.401463\pi$
$8$	−2.93995	−1.03943
$9$	7.96298	2.65433
$10$	4.07665	1.28915
$11$	−4.11384	−1.24037	−0.620184	−	0.784456i	$-0.712942\pi$
$11$	−4.11384	−1.24037	−0.620184	+	0.784456i	$0.712942\pi$
$12$	−3.64680	−1.05274
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.52809	0.408400
$15$	14.2392	3.67655
$16$	−0.584091	−0.146023
$17$	−7.15332	−1.73493	−0.867467	−	0.497495i	$-0.834253\pi$
$17$	−7.15332	−1.73493	−0.867467	+	0.497495i	$0.834253\pi$
$18$	7.54844	1.77918
$19$	−2.76598	−0.634559	−0.317280	−	0.948332i	$-0.602769\pi$
$19$	−2.76598	−0.634559	−0.317280	+	0.948332i	$0.602769\pi$
$20$	−4.73663	−1.05914
$21$	5.33743	1.16472
$22$	−3.89968	−0.831414
$23$	3.00016	0.625578	0.312789	−	0.949823i	$-0.398737\pi$
$23$	3.00016	0.625578	0.312789	+	0.949823i	$0.398737\pi$
$24$	−9.73430	−1.98701
$25$	13.4945	2.69890
$26$	−0.947942	−0.185907
$27$	16.4326	3.16246
$28$	−1.77548	−0.335534
$29$	3.44689	0.640072	0.320036	−	0.947405i	$-0.396305\pi$
$29$	3.44689	0.640072	0.320036	+	0.947405i	$0.396305\pi$
$30$	13.4979	2.46438
$31$	−6.97691	−1.25309	−0.626545	−	0.779386i	$-0.715531\pi$
$31$	−6.97691	−1.25309	−0.626545	+	0.779386i	$0.715531\pi$
$32$	5.32622	0.941552
$33$	−13.6211	−2.37112
$34$	−6.78093	−1.16292
$35$	6.93249	1.17180
$36$	−8.77048	−1.46175
$37$	−7.40550	−1.21746	−0.608728	−	0.793379i	$-0.708320\pi$
$37$	−7.40550	−1.21746	−0.608728	+	0.793379i	$0.708320\pi$
$38$	−2.62199	−0.425343
$39$	−3.31104	−0.530191
$40$	−12.6433	−1.99909
$41$	−8.57012	−1.33843	−0.669214	−	0.743070i	$-0.733369\pi$
$41$	−8.57012	−1.33843	−0.669214	+	0.743070i	$0.733369\pi$
$42$	5.05957	0.780709
$43$	6.28809	0.958924	0.479462	−	0.877563i	$-0.340832\pi$
$43$	6.28809	0.958924	0.479462	+	0.877563i	$0.340832\pi$
$44$	4.53101	0.683075
$45$	34.2450	5.10494
$46$	2.84398	0.419322
$47$	2.96090	0.431891	0.215946	−	0.976405i	$-0.430717\pi$
$47$	2.96090	0.431891	0.215946	+	0.976405i	$0.430717\pi$
$48$	−1.93395	−0.279141
$49$	−4.40142	−0.628775
$50$	12.7920	1.80906
$51$	−23.6849	−3.31655
$52$	1.10141	0.152738
$53$	−1.70867	−0.234704	−0.117352	−	0.993090i	$-0.537441\pi$
$53$	−1.70867	−0.234704	−0.117352	+	0.993090i	$0.537441\pi$
$54$	15.5772	2.11978
$55$	−17.6917	−2.38554
$56$	−4.73923	−0.633307
$57$	−9.15826	−1.21304
$58$	3.26745	0.429038
$59$	−5.66552	−0.737588	−0.368794	−	0.929511i	$-0.620229\pi$
$59$	−5.66552	−0.737588	−0.368794	+	0.929511i	$0.620229\pi$
$60$	−15.6832	−2.02469
$61$	−10.4501	−1.33800	−0.669001	−	0.743262i	$-0.733278\pi$
$61$	−10.4501	−1.33800	−0.669001	+	0.743262i	$0.733278\pi$
$62$	−6.61370	−0.839941
$63$	12.8364	1.61723
$64$	6.21713	0.777141
$65$	−4.30053	−0.533415
$66$	−12.9120	−1.58936
$67$	0.0391610	0.00478428	0.00239214	−	0.999997i	$-0.499239\pi$
$67$	0.0391610	0.00478428	0.00239214	+	0.999997i	$0.499239\pi$
$68$	7.87871	0.955434
$69$	9.93366	1.19587
$70$	6.57160	0.785456
$71$	5.28176	0.626830	0.313415	−	0.949616i	$-0.398527\pi$
$71$	5.28176	0.626830	0.313415	+	0.949616i	$0.398527\pi$
$72$	−23.4108	−2.75899
$73$	8.49628	0.994415	0.497207	−	0.867632i	$-0.334359\pi$
$73$	8.49628	0.994415	0.497207	+	0.867632i	$0.334359\pi$
$74$	−7.01998	−0.816056
$75$	44.6809	5.15930
$76$	3.04647	0.349454
$77$	−6.63155	−0.755735
$78$	−3.13867	−0.355385
$79$	−5.97733	−0.672502	−0.336251	−	0.941772i	$-0.609159\pi$
$79$	−5.97733	−0.672502	−0.336251	+	0.941772i	$0.609159\pi$
$80$	−2.51190	−0.280839
$81$	30.5201	3.39112
$82$	−8.12398	−0.897143
$83$	6.37508	0.699756	0.349878	−	0.936795i	$-0.386223\pi$
$83$	6.37508	0.699756	0.349878	+	0.936795i	$0.386223\pi$
$84$	−5.87868	−0.641416
$85$	−30.7630	−3.33672
$86$	5.96074	0.642763
$87$	11.4128	1.22358
$88$	12.0945	1.28928
$89$	2.38460	0.252767	0.126383	−	0.991981i	$-0.459663\pi$
$89$	2.38460	0.252767	0.126383	+	0.991981i	$0.459663\pi$
$90$	32.4623	3.42182
$91$	−1.61201	−0.168985
$92$	−3.30440	−0.344508
$93$	−23.1008	−2.39544
$94$	2.80676	0.289495
$95$	−11.8952	−1.22042
$96$	17.6353	1.79990
$97$	18.0075	1.82839	0.914193	−	0.405278i	$-0.132825\pi$
$97$	18.0075	1.82839	0.914193	+	0.405278i	$0.132825\pi$
$98$	−4.17229	−0.421465
$99$	−32.7584	−3.29234
$100$	−14.8630	−1.48630
$101$	1.35254	0.134583	0.0672914	−	0.997733i	$-0.478564\pi$
$101$	1.35254	0.134583	0.0672914	+	0.997733i	$0.478564\pi$
$102$	−22.4519	−2.22307
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.93995	0.288286
$105$	22.9537	2.24006
$106$	−1.61972	−0.157321
$107$	10.8475	1.04866	0.524331	−	0.851514i	$-0.324315\pi$
$107$	10.8475	1.04866	0.524331	+	0.851514i	$0.324315\pi$
$108$	−18.0990	−1.74158
$109$	5.09333	0.487853	0.243926	−	0.969794i	$-0.421564\pi$
$109$	5.09333	0.487853	0.243926	+	0.969794i	$0.421564\pi$
$110$	−16.7707	−1.59902
$111$	−24.5199	−2.32732
$112$	−0.941561	−0.0889691
$113$	14.3797	1.35273	0.676364	−	0.736568i	$-0.263555\pi$
$113$	14.3797	1.35273	0.676364	+	0.736568i	$0.263555\pi$
$114$	−8.68150	−0.813097
$115$	12.9023	1.20314
$116$	−3.79643	−0.352490
$117$	−7.96298	−0.736178
$118$	−5.37058	−0.494402
$119$	−11.5312	−1.05706
$120$	−41.8626	−3.82151
$121$	5.92366	0.538514
$122$	−9.90611	−0.896857
$123$	−28.3760	−2.55858
$124$	7.68441	0.690080
$125$	36.5309	3.26742
$126$	12.1682	1.08403
$127$	−0.662829	−0.0588166	−0.0294083	−	0.999567i	$-0.509362\pi$
$127$	−0.662829	−0.0588166	−0.0294083	+	0.999567i	$0.509362\pi$
$128$	−4.75897	−0.420637
$129$	20.8201	1.83311
$130$	−4.07665	−0.357546
$131$	−0.717732	−0.0627086	−0.0313543	−	0.999508i	$-0.509982\pi$
$131$	−0.717732	−0.0627086	−0.0313543	+	0.999508i	$0.509982\pi$
$132$	15.0023	1.30579
$133$	−4.45879	−0.386626
$134$	0.0371224	0.00320689
$135$	70.6689	6.08221
$136$	21.0304	1.80334
$137$	1.94623	0.166277	0.0831387	−	0.996538i	$-0.473506\pi$
$137$	1.94623	0.166277	0.0831387	+	0.996538i	$0.473506\pi$
$138$	9.41653	0.801589
$139$	−1.39770	−0.118551	−0.0592757	−	0.998242i	$-0.518879\pi$
$139$	−1.39770	−0.118551	−0.0592757	+	0.998242i	$0.518879\pi$
$140$	−7.63549	−0.645317
$141$	9.80365	0.825616
$142$	5.00680	0.420161
$143$	4.11384	0.344016
$144$	−4.65110	−0.387592
$145$	14.8235	1.23102
$146$	8.05398	0.666552
$147$	−14.5733	−1.20198
$148$	8.15646	0.670457
$149$	−18.2519	−1.49526	−0.747628	−	0.664118i	$-0.768807\pi$
$149$	−18.2519	−1.49526	−0.747628	+	0.664118i	$0.768807\pi$
$150$	42.3549	3.45826
$151$	13.6893	1.11402	0.557008	−	0.830507i	$-0.311949\pi$
$151$	13.6893	1.11402	0.557008	+	0.830507i	$0.311949\pi$
$152$	8.13185	0.659580
$153$	−56.9617	−4.60508
$154$	−6.28632	−0.506566
$155$	−30.0044	−2.41001
$156$	3.64680	0.291978
$157$	7.78320	0.621167	0.310583	−	0.950546i	$-0.399476\pi$
$157$	7.78320	0.621167	0.310583	+	0.950546i	$0.399476\pi$
$158$	−5.66616	−0.450776
$159$	−5.65748	−0.448668
$160$	22.9055	1.81084
$161$	4.83630	0.381154
$162$	28.9313	2.27305
$163$	−7.56819	−0.592787	−0.296393	−	0.955066i	$-0.595784\pi$
$163$	−7.56819	−0.592787	−0.296393	+	0.955066i	$0.595784\pi$
$164$	9.43919	0.737077
$165$	−58.5778	−4.56027
$166$	6.04321	0.469044
$167$	−12.0035	−0.928861	−0.464431	−	0.885609i	$-0.653741\pi$
$167$	−12.0035	−0.928861	−0.464431	+	0.885609i	$0.653741\pi$
$168$	−15.6918	−1.21065
$169$	1.00000	0.0769231
$170$	−29.1615	−2.23659
$171$	−22.0254	−1.68433
$172$	−6.92574	−0.528083
$173$	6.81832	0.518387	0.259193	−	0.965825i	$-0.416543\pi$
$173$	6.81832	0.518387	0.259193	+	0.965825i	$0.416543\pi$
$174$	10.8187	0.820161
$175$	21.7533	1.64439
$176$	2.40286	0.181122
$177$	−18.7588	−1.40999
$178$	2.26046	0.169429
$179$	1.11339	0.0832184	0.0416092	−	0.999134i	$-0.486752\pi$
$179$	1.11339	0.0832184	0.0416092	+	0.999134i	$0.486752\pi$
$180$	−37.7177	−2.81131
$181$	−1.75856	−0.130713	−0.0653565	−	0.997862i	$-0.520818\pi$
$181$	−1.75856	−0.130713	−0.0653565	+	0.997862i	$0.520818\pi$
$182$	−1.52809	−0.113270
$183$	−34.6008	−2.55776
$184$	−8.82034	−0.650244
$185$	−31.8475	−2.34148
$186$	−21.8982	−1.60566
$187$	29.4276	2.15196
$188$	−3.26115	−0.237844
$189$	26.4895	1.92683
$190$	−11.2759	−0.818041
$191$	−19.0221	−1.37639	−0.688196	−	0.725525i	$-0.741597\pi$
$191$	−19.0221	−1.37639	−0.688196	+	0.725525i	$0.741597\pi$
$192$	20.5852	1.48561
$193$	−8.76901	−0.631207	−0.315603	−	0.948891i	$-0.602207\pi$
$193$	−8.76901	−0.631207	−0.315603	+	0.948891i	$0.602207\pi$
$194$	17.0701	1.22556
$195$	−14.2392	−1.01969
$196$	4.84776	0.346268
$197$	14.4635	1.03048	0.515240	−	0.857046i	$-0.327703\pi$
$197$	14.4635	1.03048	0.515240	+	0.857046i	$0.327703\pi$
$198$	−31.0531	−2.20684
$199$	−3.02114	−0.214163	−0.107081	−	0.994250i	$-0.534151\pi$
$199$	−3.02114	−0.214163	−0.107081	+	0.994250i	$0.534151\pi$
$200$	−39.6732	−2.80532
$201$	0.129664	0.00914577
$202$	1.28213	0.0902103
$203$	5.55643	0.389985
$204$	26.0867	1.82643
$205$	−36.8560	−2.57414
$206$	0.947942	0.0660462
$207$	23.8902	1.66049
$208$	0.584091	0.0404994
$209$	11.3788	0.787087
$210$	21.7588	1.50150
$211$	7.49776	0.516167	0.258084	−	0.966123i	$-0.416909\pi$
$211$	7.49776	0.516167	0.258084	+	0.966123i	$0.416909\pi$
$212$	1.88194	0.129252
$213$	17.4881	1.19827
$214$	10.2828	0.702914
$215$	27.0421	1.84425
$216$	−48.3111	−3.28715
$217$	−11.2468	−0.763485
$218$	4.82818	0.327006
$219$	28.1315	1.90095
$220$	19.4857	1.31373
$221$	7.15332	0.481184
$222$	−23.2434	−1.56000
$223$	−18.0044	−1.20566	−0.602832	−	0.797868i	$-0.705961\pi$
$223$	−18.0044	−1.20566	−0.602832	+	0.797868i	$0.705961\pi$
$224$	8.58592	0.573671
$225$	107.457	7.16377
$226$	13.6311	0.906728
$227$	−29.6335	−1.96684	−0.983421	−	0.181336i	$-0.941958\pi$
$227$	−29.6335	−1.96684	−0.983421	+	0.181336i	$0.941958\pi$
$228$	10.0870	0.668026
$229$	18.0647	1.19375	0.596873	−	0.802336i	$-0.296410\pi$
$229$	18.0647	1.19375	0.596873	+	0.802336i	$0.296410\pi$
$230$	12.2306	0.806463
$231$	−21.9573	−1.44468
$232$	−10.1337	−0.665310
$233$	10.5013	0.687964	0.343982	−	0.938976i	$-0.388224\pi$
$233$	10.5013	0.687964	0.343982	+	0.938976i	$0.388224\pi$
$234$	−7.54844	−0.493457
$235$	12.7334	0.830637
$236$	6.24004	0.406192
$237$	−19.7912	−1.28557
$238$	−10.9309	−0.708546
$239$	−23.0081	−1.48827	−0.744134	−	0.668030i	$-0.767138\pi$
$239$	−23.0081	−1.48827	−0.744134	+	0.668030i	$0.767138\pi$
$240$	−8.31699	−0.536860
$241$	−14.4881	−0.933259	−0.466630	−	0.884453i	$-0.654532\pi$
$241$	−14.4881	−0.933259	−0.466630	+	0.884453i	$0.654532\pi$
$242$	5.61528	0.360964
$243$	51.7553	3.32011
$244$	11.5098	0.736842
$245$	−18.9284	−1.20929
$246$	−26.8988	−1.71501
$247$	2.76598	0.175995
$248$	20.5118	1.30250
$249$	21.1081	1.33767
$250$	34.6292	2.19014
$251$	−16.8503	−1.06358	−0.531790	−	0.846876i	$-0.678480\pi$
$251$	−16.8503	−1.06358	−0.531790	+	0.846876i	$0.678480\pi$
$252$	−14.1381	−0.890616
$253$	−12.3422	−0.775947
$254$	−0.628324	−0.0394245
$255$	−101.858	−6.37857
$256$	−16.9455	−1.05909
$257$	17.8571	1.11390	0.556948	−	0.830547i	$-0.311972\pi$
$257$	17.8571	1.11390	0.556948	+	0.830547i	$0.311972\pi$
$258$	19.7362	1.22872
$259$	−11.9377	−0.741775
$260$	4.73663	0.293753
$261$	27.4475	1.69896
$262$	−0.680368	−0.0420333
$263$	−4.05740	−0.250190	−0.125095	−	0.992145i	$-0.539924\pi$
$263$	−4.05740	−0.250190	−0.125095	+	0.992145i	$0.539924\pi$
$264$	40.0453	2.46462
$265$	−7.34819	−0.451396
$266$	−4.22667	−0.259154
$267$	7.89550	0.483197
$268$	−0.0431322	−0.00263472
$269$	20.3623	1.24151	0.620755	−	0.784005i	$-0.286826\pi$
$269$	20.3623	1.24151	0.620755	+	0.784005i	$0.286826\pi$
$270$	66.9900	4.07688
$271$	3.93392	0.238969	0.119484	−	0.992836i	$-0.461876\pi$
$271$	3.93392	0.238969	0.119484	+	0.992836i	$0.461876\pi$
$272$	4.17819	0.253340
$273$	−5.33743	−0.323036
$274$	1.84491	0.111455
$275$	−55.5143	−3.34764
$276$	−10.9410	−0.658571
$277$	5.98154	0.359396	0.179698	−	0.983722i	$-0.442488\pi$
$277$	5.98154	0.359396	0.179698	+	0.983722i	$0.442488\pi$
$278$	−1.32494	−0.0794645
$279$	−55.5569	−3.32611
$280$	−20.3812	−1.21801
$281$	21.4991	1.28253	0.641265	−	0.767320i	$-0.278410\pi$
$281$	21.4991	1.28253	0.641265	+	0.767320i	$0.278410\pi$
$282$	9.29329	0.553407
$283$	−8.70106	−0.517224	−0.258612	−	0.965981i	$-0.583265\pi$
$283$	−8.70106	−0.517224	−0.258612	+	0.965981i	$0.583265\pi$
$284$	−5.81736	−0.345197
$285$	−39.3854	−2.33299
$286$	3.89968	0.230593
$287$	−13.8151	−0.815481
$288$	42.4126	2.49919
$289$	34.1699	2.01000
$290$	14.0518	0.825149
$291$	59.6236	3.49520
$292$	−9.35786	−0.547627
$293$	−2.74729	−0.160498	−0.0802492	−	0.996775i	$-0.525572\pi$
$293$	−2.74729	−0.160498	−0.0802492	+	0.996775i	$0.525572\pi$
$294$	−13.8146	−0.805685
$295$	−24.3647	−1.41857
$296$	21.7718	1.26546
$297$	−67.6011	−3.92261
$298$	−17.3018	−1.00226
$299$	−3.00016	−0.173504
$300$	−49.2118	−2.84124
$301$	10.1365	0.584256
$302$	12.9766	0.746721
$303$	4.47831	0.257272
$304$	1.61558	0.0926601
$305$	−44.9410	−2.57332
$306$	−53.9964	−3.08677
$307$	16.4026	0.936143	0.468072	−	0.883691i	$-0.344949\pi$
$307$	16.4026	0.936143	0.468072	+	0.883691i	$0.344949\pi$
$308$	7.30403	0.416186
$309$	3.31104	0.188358
$310$	−28.4424	−1.61542
$311$	4.67063	0.264847	0.132424	−	0.991193i	$-0.457724\pi$
$311$	4.67063	0.264847	0.132424	+	0.991193i	$0.457724\pi$
$312$	9.73430	0.551096
$313$	12.7632	0.721418	0.360709	−	0.932678i	$-0.382535\pi$
$313$	12.7632	0.721418	0.360709	+	0.932678i	$0.382535\pi$
$314$	7.37802	0.416366
$315$	55.2033	3.11035
$316$	6.58347	0.370349
$317$	25.7476	1.44613	0.723066	−	0.690779i	$-0.242732\pi$
$317$	25.7476	1.44613	0.723066	+	0.690779i	$0.242732\pi$
$318$	−5.36296	−0.300740
$319$	−14.1800	−0.793925
$320$	26.7369	1.49464
$321$	35.9163	2.00465
$322$	4.58453	0.255486
$323$	19.7859	1.10092
$324$	−33.6150	−1.86750
$325$	−13.4945	−0.748541
$326$	−7.17421	−0.397343
$327$	16.8642	0.932593
$328$	25.1958	1.39120
$329$	4.77300	0.263144
$330$	−55.5283	−3.05673
$331$	−28.0707	−1.54291	−0.771453	−	0.636286i	$-0.780470\pi$
$331$	−28.0707	−1.54291	−0.771453	+	0.636286i	$0.780470\pi$
$332$	−7.02156	−0.385358
$333$	−58.9698	−3.23153
$334$	−11.3787	−0.622612
$335$	0.168413	0.00920139
$336$	−3.11754	−0.170076
$337$	19.5571	1.06535	0.532673	−	0.846321i	$-0.321188\pi$
$337$	19.5571	1.06535	0.532673	+	0.846321i	$0.321188\pi$
$338$	0.947942	0.0515612
$339$	47.6117	2.58591
$340$	33.8826	1.83754
$341$	28.7019	1.55429
$342$	−20.8788	−1.12900
$343$	−18.3792	−0.992384
$344$	−18.4867	−0.996735
$345$	42.7200	2.29997
$346$	6.46337	0.347473
$347$	−21.6142	−1.16031	−0.580156	−	0.814505i	$-0.697009\pi$
$347$	−21.6142	−1.16031	−0.580156	+	0.814505i	$0.697009\pi$
$348$	−12.5701	−0.673830
$349$	28.4604	1.52345	0.761726	−	0.647900i	$-0.224352\pi$
$349$	28.4604	1.52345	0.761726	+	0.647900i	$0.224352\pi$
$350$	20.6209	1.10223
$351$	−16.4326	−0.877108
$352$	−21.9112	−1.16787
$353$	−18.3775	−0.978138	−0.489069	−	0.872245i	$-0.662663\pi$
$353$	−18.3775	−0.978138	−0.489069	+	0.872245i	$0.662663\pi$
$354$	−17.7822	−0.945114
$355$	22.7143	1.20555
$356$	−2.62641	−0.139200
$357$	−38.1803	−2.02072
$358$	1.05542	0.0557809
$359$	−3.01891	−0.159332	−0.0796660	−	0.996822i	$-0.525385\pi$
$359$	−3.01891	−0.159332	−0.0796660	+	0.996822i	$0.525385\pi$
$360$	−100.679	−5.30623
$361$	−11.3494	−0.597335
$362$	−1.66702	−0.0876165
$363$	19.6135	1.02944
$364$	1.77548	0.0930603
$365$	36.5385	1.91251
$366$	−32.7995	−1.71446
$367$	2.94029	0.153482	0.0767408	−	0.997051i	$-0.475549\pi$
$367$	2.94029	0.153482	0.0767408	+	0.997051i	$0.475549\pi$
$368$	−1.75237	−0.0913486
$369$	−68.2437	−3.55263
$370$	−30.1896	−1.56948
$371$	−2.75440	−0.143001
$372$	25.4434	1.31918
$373$	−2.99205	−0.154923	−0.0774613	−	0.996995i	$-0.524681\pi$
$373$	−2.99205	−0.154923	−0.0774613	+	0.996995i	$0.524681\pi$
$374$	27.8956	1.44245
$375$	120.955	6.24610
$376$	−8.70490	−0.448921
$377$	−3.44689	−0.177524
$378$	25.1105	1.29155
$379$	−10.6104	−0.545019	−0.272509	−	0.962153i	$-0.587854\pi$
$379$	−10.6104	−0.545019	−0.272509	+	0.962153i	$0.587854\pi$
$380$	13.1014	0.672088
$381$	−2.19465	−0.112436
$382$	−18.0319	−0.922590
$383$	26.7098	1.36481	0.682403	−	0.730976i	$-0.260935\pi$
$383$	26.7098	1.36481	0.682403	+	0.730976i	$0.260935\pi$
$384$	−15.7571	−0.804102
$385$	−28.5191	−1.45347
$386$	−8.31251	−0.423095
$387$	50.0719	2.54530
$388$	−19.8336	−1.00690
$389$	−12.9692	−0.657564	−0.328782	−	0.944406i	$-0.606638\pi$
$389$	−12.9692	−0.657564	−0.328782	+	0.944406i	$0.606638\pi$
$390$	−13.4979	−0.683495
$391$	−21.4611	−1.08534
$392$	12.9400	0.653568
$393$	−2.37644	−0.119875
$394$	13.7105	0.690727
$395$	−25.7057	−1.29339
$396$	36.0803	1.81310
$397$	13.4155	0.673304	0.336652	−	0.941629i	$-0.390705\pi$
$397$	13.4155	0.673304	0.336652	+	0.941629i	$0.390705\pi$
$398$	−2.86386	−0.143552
$399$	−14.7632	−0.739085
$400$	−7.88203	−0.394101
$401$	−4.14025	−0.206754	−0.103377	−	0.994642i	$-0.532965\pi$
$401$	−4.14025	−0.206754	−0.103377	+	0.994642i	$0.532965\pi$
$402$	0.122914	0.00613038
$403$	6.97691	0.347544
$404$	−1.48970	−0.0741152
$405$	131.252	6.52198
$406$	5.26717	0.261405
$407$	30.4650	1.51009
$408$	69.6325	3.44732
$409$	−18.0257	−0.891312	−0.445656	−	0.895204i	$-0.647030\pi$
$409$	−18.0257	−0.891312	−0.445656	+	0.895204i	$0.647030\pi$
$410$	−34.9374	−1.72543
$411$	6.44403	0.317861
$412$	−1.10141	−0.0542624
$413$	−9.13288	−0.449400
$414$	22.6466	1.11302
$415$	27.4162	1.34581
$416$	−5.32622	−0.261139
$417$	−4.62784	−0.226626
$418$	10.7864	0.527582
$419$	10.5788	0.516806	0.258403	−	0.966037i	$-0.416804\pi$
$419$	10.5788	0.516806	0.258403	+	0.966037i	$0.416804\pi$
$420$	−25.2814	−1.23361
$421$	−31.7094	−1.54542	−0.772712	−	0.634757i	$-0.781100\pi$
$421$	−31.7094	−1.54542	−0.772712	+	0.634757i	$0.781100\pi$
$422$	7.10744	0.345985
$423$	23.5776	1.14638
$424$	5.02342	0.243959
$425$	−96.5306	−4.68242
$426$	16.5777	0.803193
$427$	−16.8457	−0.815221
$428$	−11.9475	−0.577502
$429$	13.6211	0.657632
$430$	25.6343	1.23620
$431$	−13.9356	−0.671254	−0.335627	−	0.941995i	$-0.608948\pi$
$431$	−13.9356	−0.671254	−0.335627	+	0.941995i	$0.608948\pi$
$432$	−9.59814	−0.461791
$433$	−38.0862	−1.83031	−0.915154	−	0.403104i	$-0.867931\pi$
$433$	−38.0862	−1.83031	−0.915154	+	0.403104i	$0.867931\pi$
$434$	−10.6614	−0.511761
$435$	49.0810	2.35326
$436$	−5.60983	−0.268662
$437$	−8.29839	−0.396966
$438$	26.6670	1.27420
$439$	4.51899	0.215680	0.107840	−	0.994168i	$-0.465607\pi$
$439$	4.51899	0.215680	0.107840	+	0.994168i	$0.465607\pi$
$440$	52.0127	2.47961
$441$	−35.0484	−1.66897
$442$	6.78093	0.322536
$443$	−6.43634	−0.305800	−0.152900	−	0.988242i	$-0.548861\pi$
$443$	−6.43634	−0.305800	−0.152900	+	0.988242i	$0.548861\pi$
$444$	27.0064	1.28167
$445$	10.2550	0.486135
$446$	−17.0671	−0.808152
$447$	−60.4328	−2.85837
$448$	10.0221	0.473499
$449$	−40.8292	−1.92685	−0.963424	−	0.267982i	$-0.913643\pi$
$449$	−40.8292	−1.92685	−0.963424	+	0.267982i	$0.913643\pi$
$450$	101.863	4.80185
$451$	35.2561	1.66014
$452$	−15.8379	−0.744952
$453$	45.3257	2.12959
$454$	−28.0908	−1.31837
$455$	−6.93249	−0.325000
$456$	26.9249	1.26087
$457$	−5.54926	−0.259583	−0.129792	−	0.991541i	$-0.541431\pi$
$457$	−5.54926	−0.259583	−0.129792	+	0.991541i	$0.541431\pi$
$458$	17.1242	0.800163
$459$	−117.548	−5.48666
$460$	−14.2107	−0.662575
$461$	12.8611	0.599001	0.299500	−	0.954096i	$-0.403180\pi$
$461$	12.8611	0.599001	0.299500	+	0.954096i	$0.403180\pi$
$462$	−20.8143	−0.968367
$463$	−4.36466	−0.202843	−0.101422	−	0.994844i	$-0.532339\pi$
$463$	−4.36466	−0.202843	−0.101422	+	0.994844i	$0.532339\pi$
$464$	−2.01330	−0.0934651
$465$	−99.3456	−4.60704
$466$	9.95463	0.461139
$467$	22.4684	1.03971	0.519856	−	0.854254i	$-0.325985\pi$
$467$	22.4684	1.03971	0.519856	+	0.854254i	$0.325985\pi$
$468$	8.77048	0.405415
$469$	0.0631280	0.00291498
$470$	12.0705	0.556772
$471$	25.7705	1.18744
$472$	16.6564	0.766671
$473$	−25.8682	−1.18942
$474$	−18.7609	−0.861716
$475$	−37.3256	−1.71261
$476$	12.7006	0.582129
$477$	−13.6061	−0.622982
$478$	−21.8103	−0.997580
$479$	−8.51408	−0.389018	−0.194509	−	0.980901i	$-0.562311\pi$
$479$	−8.51408	−0.389018	−0.194509	+	0.980901i	$0.562311\pi$
$480$	75.8412	3.46166
$481$	7.40550	0.337662
$482$	−13.7339	−0.625560
$483$	16.0132	0.728624
$484$	−6.52435	−0.296562
$485$	77.4418	3.51645
$486$	49.0611	2.22545
$487$	20.7123	0.938565	0.469282	−	0.883048i	$-0.344513\pi$
$487$	20.7123	0.938565	0.469282	+	0.883048i	$0.344513\pi$
$488$	30.7229	1.39076
$489$	−25.0586	−1.13319
$490$	−17.9431	−0.810585
$491$	37.5392	1.69412	0.847060	−	0.531497i	$-0.178370\pi$
$491$	37.5392	1.69412	0.847060	+	0.531497i	$0.178370\pi$
$492$	31.2535	1.40902
$493$	−24.6567	−1.11048
$494$	2.62199	0.117969
$495$	−140.878	−6.33201
$496$	4.07515	0.182980
$497$	8.51425	0.381916
$498$	20.0093	0.896638
$499$	−9.46962	−0.423918	−0.211959	−	0.977279i	$-0.567984\pi$
$499$	−9.46962	−0.423918	−0.211959	+	0.977279i	$0.567984\pi$
$500$	−40.2354	−1.79938
$501$	−39.7442	−1.77564
$502$	−15.9731	−0.712914
$503$	20.3219	0.906110	0.453055	−	0.891483i	$-0.350334\pi$
$503$	20.3219	0.906110	0.453055	+	0.891483i	$0.350334\pi$
$504$	−37.7384	−1.68100
$505$	5.81663	0.258837
$506$	−11.6997	−0.520114
$507$	3.31104	0.147048
$508$	0.730045	0.0323905
$509$	3.97731	0.176291	0.0881456	−	0.996108i	$-0.471906\pi$
$509$	3.97731	0.176291	0.0881456	+	0.996108i	$0.471906\pi$
$510$	−96.5550	−4.27553
$511$	13.6961	0.605880
$512$	−6.54540	−0.289268
$513$	−45.4523	−2.00677
$514$	16.9275	0.746640
$515$	4.30053	0.189504
$516$	−22.9314	−1.00950
$517$	−12.1807	−0.535704
$518$	−11.3163	−0.497209
$519$	22.5757	0.990964
$520$	12.6433	0.554447
$521$	25.6859	1.12532	0.562660	−	0.826688i	$-0.309778\pi$
$521$	25.6859	1.12532	0.562660	+	0.826688i	$0.309778\pi$
$522$	26.0187	1.13881
$523$	−24.1565	−1.05629	−0.528145	−	0.849154i	$-0.677112\pi$
$523$	−24.1565	−1.05629	−0.528145	+	0.849154i	$0.677112\pi$
$524$	0.790515	0.0345338
$525$	72.0260	3.14347
$526$	−3.84618	−0.167701
$527$	49.9080	2.17403
$528$	7.95595	0.346238
$529$	−13.9990	−0.608653
$530$	−6.96566	−0.302569
$531$	−45.1144	−1.95780
$532$	4.91094	0.212916
$533$	8.57012	0.371213
$534$	7.48447	0.323885
$535$	46.6497	2.01684
$536$	−0.115132	−0.00497293
$537$	3.68646	0.159083
$538$	19.3022	0.832179
$539$	18.1067	0.779913
$540$	−77.8351	−3.34949
$541$	2.58865	0.111295	0.0556475	−	0.998450i	$-0.482278\pi$
$541$	2.58865	0.111295	0.0556475	+	0.998450i	$0.482278\pi$
$542$	3.72913	0.160180
$543$	−5.82268	−0.249875
$544$	−38.1001	−1.63353
$545$	21.9040	0.938264
$546$	−5.05957	−0.216530
$547$	33.2812	1.42300	0.711501	−	0.702685i	$-0.248016\pi$
$547$	33.2812	1.42300	0.711501	+	0.702685i	$0.248016\pi$
$548$	−2.14359	−0.0915694
$549$	−83.2141	−3.55149
$550$	−52.6243	−2.24391
$551$	−9.53404	−0.406164
$552$	−29.2045	−1.24303
$553$	−9.63552	−0.409744
$554$	5.67015	0.240901
$555$	−105.448	−4.47604
$556$	1.53944	0.0652866
$557$	−0.0999411	−0.00423464	−0.00211732	−	0.999998i	$-0.500674\pi$
$557$	−0.0999411	−0.00423464	−0.00211732	+	0.999998i	$0.500674\pi$
$558$	−52.6647	−2.22948
$559$	−6.28809	−0.265958
$560$	−4.04921	−0.171110
$561$	97.4358	4.11374
$562$	20.3799	0.859674
$563$	−0.876807	−0.0369530	−0.0184765	−	0.999829i	$-0.505882\pi$
$563$	−0.876807	−0.0369530	−0.0184765	+	0.999829i	$0.505882\pi$
$564$	−10.7978	−0.454669
$565$	61.8403	2.60164
$566$	−8.24809	−0.346693
$567$	49.1987	2.06615
$568$	−15.5281	−0.651546
$569$	−11.2458	−0.471447	−0.235724	−	0.971820i	$-0.575746\pi$
$569$	−11.2458	−0.471447	−0.235724	+	0.971820i	$0.575746\pi$
$570$	−37.3350	−1.56379
$571$	−19.1425	−0.801088	−0.400544	−	0.916278i	$-0.631179\pi$
$571$	−19.1425	−0.801088	−0.400544	+	0.916278i	$0.631179\pi$
$572$	−4.53101	−0.189451
$573$	−62.9830	−2.63115
$574$	−13.0959	−0.546614
$575$	40.4858	1.68837
$576$	49.5069	2.06279
$577$	17.2086	0.716402	0.358201	−	0.933645i	$-0.383390\pi$
$577$	17.2086	0.716402	0.358201	+	0.933645i	$0.383390\pi$
$578$	32.3911	1.34729
$579$	−29.0345	−1.20663
$580$	−16.3267	−0.677927
$581$	10.2767	0.426349
$582$	56.5197	2.34282
$583$	7.02920	0.291120
$584$	−24.9787	−1.03362
$585$	−34.2450	−1.41586
$586$	−2.60427	−0.107581
$587$	11.6077	0.479102	0.239551	−	0.970884i	$-0.423000\pi$
$587$	11.6077	0.479102	0.239551	+	0.970884i	$0.423000\pi$
$588$	16.0511	0.661937
$589$	19.2980	0.795159
$590$	−23.0963	−0.950861
$591$	47.8891	1.96990
$592$	4.32548	0.177776
$593$	−31.1979	−1.28114	−0.640571	−	0.767899i	$-0.721302\pi$
$593$	−31.1979	−1.28114	−0.640571	+	0.767899i	$0.721302\pi$
$594$	−64.0819	−2.62931
$595$	−49.5903	−2.03300
$596$	20.1028	0.823442
$597$	−10.0031	−0.409400
$598$	−2.84398	−0.116299
$599$	−22.5424	−0.921056	−0.460528	−	0.887645i	$-0.652340\pi$
$599$	−22.5424	−0.921056	−0.460528	+	0.887645i	$0.652340\pi$
$600$	−131.360	−5.36274
$601$	−17.3958	−0.709590	−0.354795	−	0.934944i	$-0.615449\pi$
$601$	−17.3958	−0.709590	−0.354795	+	0.934944i	$0.615449\pi$
$602$	9.60877	0.391624
$603$	0.311838	0.0126990
$604$	−15.0774	−0.613492
$605$	25.4748	1.03570
$606$	4.24518	0.172449
$607$	−33.5479	−1.36167	−0.680834	−	0.732438i	$-0.738382\pi$
$607$	−33.5479	−1.36167	−0.680834	+	0.732438i	$0.738382\pi$
$608$	−14.7322	−0.597470
$609$	18.3975	0.745506
$610$	−42.6015	−1.72488
$611$	−2.96090	−0.119785
$612$	62.7380	2.53603
$613$	−41.5641	−1.67876	−0.839378	−	0.543548i	$-0.817081\pi$
$613$	−41.5641	−1.67876	−0.839378	+	0.543548i	$0.817081\pi$
$614$	15.5487	0.627493
$615$	−122.032	−4.92080
$616$	19.4964	0.785534
$617$	22.8231	0.918822	0.459411	−	0.888224i	$-0.348060\pi$
$617$	22.8231	0.918822	0.459411	+	0.888224i	$0.348060\pi$
$618$	3.13867	0.126256
$619$	−30.0490	−1.20777	−0.603885	−	0.797071i	$-0.706381\pi$
$619$	−30.0490	−1.20777	−0.603885	+	0.797071i	$0.706381\pi$
$620$	33.0470	1.32720
$621$	49.3005	1.97836
$622$	4.42749	0.177526
$623$	3.84400	0.154006
$624$	1.93395	0.0774199
$625$	89.6295	3.58518
$626$	12.0988	0.483564
$627$	37.6756	1.50462
$628$	−8.57246	−0.342078
$629$	52.9739	2.11221
$630$	52.3295	2.08486
$631$	−2.89777	−0.115359	−0.0576793	−	0.998335i	$-0.518370\pi$
$631$	−2.89777	−0.115359	−0.0576793	+	0.998335i	$0.518370\pi$
$632$	17.5731	0.699019
$633$	24.8254	0.986720
$634$	24.4073	0.969336
$635$	−2.85051	−0.113119
$636$	6.23119	0.247083
$637$	4.40142	0.174391
$638$	−13.4418	−0.532165
$639$	42.0585	1.66381
$640$	−20.4661	−0.808992
$641$	−25.0028	−0.987550	−0.493775	−	0.869590i	$-0.664383\pi$
$641$	−25.0028	−0.987550	−0.493775	+	0.869590i	$0.664383\pi$
$642$	34.0466	1.34371
$643$	−14.4923	−0.571520	−0.285760	−	0.958301i	$-0.592246\pi$
$643$	−14.4923	−0.571520	−0.285760	+	0.958301i	$0.592246\pi$
$644$	−5.32673	−0.209902
$645$	89.5374	3.52553
$646$	18.7559	0.737941
$647$	15.9795	0.628220	0.314110	−	0.949387i	$-0.398294\pi$
$647$	15.9795	0.628220	0.314110	+	0.949387i	$0.398294\pi$
$648$	−89.7276	−3.52483
$649$	23.3070	0.914881
$650$	−12.7920	−0.501744
$651$	−37.2387	−1.45950
$652$	8.33566	0.326450
$653$	29.8702	1.16891	0.584455	−	0.811426i	$-0.301308\pi$
$653$	29.8702	1.16891	0.584455	+	0.811426i	$0.301308\pi$
$654$	15.9863	0.625114
$655$	−3.08663	−0.120604
$656$	5.00573	0.195441
$657$	67.6557	2.63950
$658$	4.52452	0.176384
$659$	40.5871	1.58105	0.790524	−	0.612431i	$-0.209808\pi$
$659$	40.5871	1.58105	0.790524	+	0.612431i	$0.209808\pi$
$660$	64.5179	2.51136
$661$	45.5257	1.77074	0.885372	−	0.464883i	$-0.153904\pi$
$661$	45.5257	1.77074	0.885372	+	0.464883i	$0.153904\pi$
$662$	−26.6094	−1.03420
$663$	23.6849	0.919845
$664$	−18.7424	−0.727348
$665$	−19.1751	−0.743579
$666$	−55.8999	−2.16608
$667$	10.3413	0.400415
$668$	13.2208	0.511527
$669$	−59.6133	−2.30478
$670$	0.159646	0.00616765
$671$	42.9901	1.65961
$672$	28.4283	1.09665
$673$	43.6940	1.68428	0.842141	−	0.539258i	$-0.181295\pi$
$673$	43.6940	1.68428	0.842141	+	0.539258i	$0.181295\pi$
$674$	18.5390	0.714097
$675$	221.750	8.53517
$676$	−1.10141	−0.0423618
$677$	27.5173	1.05758	0.528788	−	0.848754i	$-0.322647\pi$
$677$	27.5173	1.05758	0.528788	+	0.848754i	$0.322647\pi$
$678$	45.1331	1.73333
$679$	29.0283	1.11400
$680$	90.4418	3.46829
$681$	−98.1176	−3.75987
$682$	27.2077	1.04184
$683$	43.9033	1.67991	0.839957	−	0.542653i	$-0.182580\pi$
$683$	43.9033	1.67991	0.839957	+	0.542653i	$0.182580\pi$
$684$	24.2590	0.927564
$685$	8.36979	0.319793
$686$	−17.4224	−0.665191
$687$	59.8128	2.28200
$688$	−3.67281	−0.140025
$689$	1.70867	0.0650953
$690$	40.4960	1.54166
$691$	38.1922	1.45290	0.726450	−	0.687219i	$-0.241169\pi$
$691$	38.1922	1.45290	0.726450	+	0.687219i	$0.241169\pi$
$692$	−7.50974	−0.285477
$693$	−52.8069	−2.00597
$694$	−20.4890	−0.777753
$695$	−6.01084	−0.228004
$696$	−33.5531	−1.27183
$697$	61.3048	2.32208
$698$	26.9788	1.02116
$699$	34.7702	1.31513
$700$	−23.9592	−0.905574
$701$	15.1278	0.571370	0.285685	−	0.958324i	$-0.407779\pi$
$701$	15.1278	0.571370	0.285685	+	0.958324i	$0.407779\pi$
$702$	−15.5772	−0.587922
$703$	20.4835	0.772548
$704$	−25.5763	−0.963942
$705$	42.1608	1.58787
$706$	−17.4208	−0.655642
$707$	2.18031	0.0819989
$708$	20.6610	0.776489
$709$	−33.5400	−1.25962	−0.629811	−	0.776748i	$-0.716868\pi$
$709$	−33.5400	−1.25962	−0.629811	+	0.776748i	$0.716868\pi$
$710$	21.5319	0.808077
$711$	−47.5974	−1.78504
$712$	−7.01061	−0.262734
$713$	−20.9319	−0.783905
$714$	−36.1927	−1.35448
$715$	17.6917	0.661631
$716$	−1.22629	−0.0458286
$717$	−76.1806	−2.84502
$718$	−2.86175	−0.106800
$719$	21.4251	0.799023	0.399511	−	0.916728i	$-0.369180\pi$
$719$	21.4251	0.799023	0.399511	+	0.916728i	$0.369180\pi$
$720$	−20.0022	−0.745438
$721$	1.61201	0.0600344
$722$	−10.7585	−0.400391
$723$	−47.9706	−1.78405
$724$	1.93689	0.0719841
$725$	46.5142	1.72749
$726$	18.5924	0.690029
$727$	49.8397	1.84845	0.924227	−	0.381845i	$-0.124711\pi$
$727$	49.8397	1.84845	0.924227	+	0.381845i	$0.124711\pi$
$728$	4.73923	0.175648
$729$	79.8037	2.95569
$730$	34.6364	1.28195
$731$	−44.9807	−1.66367
$732$	38.1095	1.40857
$733$	−34.1517	−1.26142	−0.630711	−	0.776018i	$-0.717237\pi$
$733$	−34.1517	−1.26142	−0.630711	+	0.776018i	$0.717237\pi$
$734$	2.78722	0.102878
$735$	−62.6728	−2.31172
$736$	15.9795	0.589014
$737$	−0.161102	−0.00593427
$738$	−64.6911	−2.38131
$739$	−18.6211	−0.684989	−0.342495	−	0.939520i	$-0.611272\pi$
$739$	−18.6211	−0.684989	−0.342495	+	0.939520i	$0.611272\pi$
$740$	35.0771	1.28946
$741$	9.15826	0.336437
$742$	−2.61101	−0.0958532
$743$	−10.5862	−0.388370	−0.194185	−	0.980965i	$-0.562206\pi$
$743$	−10.5862	−0.388370	−0.194185	+	0.980965i	$0.562206\pi$
$744$	67.9153	2.48989
$745$	−78.4929	−2.87576
$746$	−2.83629	−0.103844
$747$	50.7646	1.85738
$748$	−32.4117	−1.18509
$749$	17.4862	0.638932
$750$	114.659	4.18674
$751$	−24.3473	−0.888445	−0.444222	−	0.895917i	$-0.646520\pi$
$751$	−24.3473	−0.888445	−0.444222	+	0.895917i	$0.646520\pi$
$752$	−1.72943	−0.0630660
$753$	−55.7919	−2.03317
$754$	−3.26745	−0.118994
$755$	58.8710	2.14254
$756$	−29.1757	−1.06111
$757$	0.410113	0.0149058	0.00745290	−	0.999972i	$-0.497628\pi$
$757$	0.410113	0.0149058	0.00745290	+	0.999972i	$0.497628\pi$
$758$	−10.0580	−0.365324
$759$	−40.8655	−1.48332
$760$	34.9712	1.26854
$761$	32.1461	1.16530	0.582648	−	0.812724i	$-0.302016\pi$
$761$	32.1461	1.16530	0.582648	+	0.812724i	$0.302016\pi$
$762$	−2.08040	−0.0753651
$763$	8.21050	0.297240
$764$	20.9511	0.757983
$765$	−244.965	−8.85674
$766$	25.3193	0.914824
$767$	5.66552	0.204570
$768$	−56.1071	−2.02459
$769$	33.8836	1.22187	0.610936	−	0.791680i	$-0.290793\pi$
$769$	33.8836	1.22187	0.610936	+	0.791680i	$0.290793\pi$
$770$	−27.0345	−0.974255
$771$	59.1256	2.12936
$772$	9.65824	0.347608
$773$	50.1697	1.80448	0.902239	−	0.431235i	$-0.141922\pi$
$773$	50.1697	1.80448	0.902239	+	0.431235i	$0.141922\pi$
$774$	47.4652	1.70610
$775$	−94.1500	−3.38197
$776$	−52.9413	−1.90048
$777$	−39.5263	−1.41800
$778$	−12.2940	−0.440763
$779$	23.7048	0.849312
$780$	15.6832	0.561547
$781$	−21.7283	−0.777500
$782$	−20.3439	−0.727496
$783$	56.6415	2.02420
$784$	2.57083	0.0918154
$785$	33.4718	1.19466
$786$	−2.25273	−0.0803521
$787$	−16.4099	−0.584951	−0.292476	−	0.956273i	$-0.594479\pi$
$787$	−16.4099	−0.584951	−0.292476	+	0.956273i	$0.594479\pi$
$788$	−15.9302	−0.567489
$789$	−13.4342	−0.478270
$790$	−24.3675	−0.866956
$791$	23.1802	0.824194
$792$	96.3081	3.42216
$793$	10.4501	0.371095
$794$	12.7171	0.451313
$795$	−24.3302	−0.862902
$796$	3.32750	0.117940
$797$	25.9760	0.920116	0.460058	−	0.887889i	$-0.347829\pi$
$797$	25.9760	0.920116	0.460058	+	0.887889i	$0.347829\pi$
$798$	−13.9947	−0.495406
$799$	−21.1802	−0.749303
$800$	71.8748	2.54116
$801$	18.9885	0.670926
$802$	−3.92472	−0.138587
$803$	−34.9523	−1.23344
$804$	−0.142812	−0.00503661
$805$	20.7986	0.733055
$806$	6.61370	0.232958
$807$	67.4203	2.37331
$808$	−3.97640	−0.139889
$809$	−4.76108	−0.167391	−0.0836954	−	0.996491i	$-0.526672\pi$
$809$	−4.76108	−0.167391	−0.0836954	+	0.996491i	$0.526672\pi$
$810$	124.420	4.37166
$811$	−42.0820	−1.47770	−0.738849	−	0.673871i	$-0.764630\pi$
$811$	−42.0820	−1.47770	−0.738849	+	0.673871i	$0.764630\pi$
$812$	−6.11989	−0.214766
$813$	13.0254	0.456819
$814$	28.8791	1.01221
$815$	−32.5472	−1.14008
$816$	13.8341	0.484292
$817$	−17.3927	−0.608494
$818$	−17.0873	−0.597443
$819$	−12.8364	−0.448540
$820$	40.5935	1.41759
$821$	−20.9132	−0.729875	−0.364938	−	0.931032i	$-0.618910\pi$
$821$	−20.9132	−0.729875	−0.364938	+	0.931032i	$0.618910\pi$
$822$	6.10856	0.213061
$823$	18.2455	0.635999	0.318000	−	0.948091i	$-0.396989\pi$
$823$	18.2455	0.635999	0.318000	+	0.948091i	$0.396989\pi$
$824$	−2.93995	−0.102418
$825$	−183.810	−6.39944
$826$	−8.65744	−0.301231
$827$	−26.7317	−0.929551	−0.464775	−	0.885429i	$-0.653865\pi$
$827$	−26.7317	−0.929551	−0.464775	+	0.885429i	$0.653865\pi$
$828$	−26.3129	−0.914436
$829$	18.1463	0.630248	0.315124	−	0.949050i	$-0.397954\pi$
$829$	18.1463	0.630248	0.315124	+	0.949050i	$0.397954\pi$
$830$	25.9890	0.902090
$831$	19.8051	0.687031
$832$	−6.21713	−0.215540
$833$	31.4848	1.09088
$834$	−4.38692	−0.151907
$835$	−51.6215	−1.78644
$836$	−12.5327	−0.433452
$837$	−114.649	−3.96284
$838$	10.0280	0.346413
$839$	6.52893	0.225404	0.112702	−	0.993629i	$-0.464050\pi$
$839$	6.52893	0.225404	0.112702	+	0.993629i	$0.464050\pi$
$840$	−67.4829	−2.32838
$841$	−17.1189	−0.590308
$842$	−30.0587	−1.03589
$843$	71.1844	2.45172
$844$	−8.25808	−0.284255
$845$	4.30053	0.147943
$846$	22.3502	0.768414
$847$	9.54900	0.328107
$848$	0.998021	0.0342722
$849$	−28.8095	−0.988741
$850$	−91.5053	−3.13861
$851$	−22.2177	−0.761613
$852$	−19.2615	−0.659889
$853$	−19.1930	−0.657157	−0.328579	−	0.944477i	$-0.606570\pi$
$853$	−19.1930	−0.657157	−0.328579	+	0.944477i	$0.606570\pi$
$854$	−15.9687	−0.546439
$855$	−94.7209	−3.23939
$856$	−31.8910	−1.09001
$857$	41.2284	1.40833	0.704167	−	0.710034i	$-0.251321\pi$
$857$	41.2284	1.40833	0.704167	+	0.710034i	$0.251321\pi$
$858$	12.9120	0.440808
$859$	−43.0206	−1.46784	−0.733922	−	0.679234i	$-0.762312\pi$
$859$	−43.0206	−1.46784	−0.733922	+	0.679234i	$0.762312\pi$
$860$	−29.7843	−1.01564
$861$	−45.7424	−1.55890
$862$	−13.2101	−0.449939
$863$	23.5308	0.800998	0.400499	−	0.916297i	$-0.368837\pi$
$863$	23.5308	0.800998	0.400499	+	0.916297i	$0.368837\pi$
$864$	87.5237	2.97762
$865$	29.3223	0.996990
$866$	−36.1035	−1.22685
$867$	113.138	3.84237
$868$	12.3873	0.420454
$869$	24.5898	0.834151
$870$	46.5260	1.57738
$871$	−0.0391610	−0.00132692
$872$	−14.9742	−0.507089
$873$	143.393	4.85313
$874$	−7.86639	−0.266085
$875$	58.8882	1.99078
$876$	−30.9842	−1.04686
$877$	12.8329	0.433337	0.216668	−	0.976245i	$-0.430481\pi$
$877$	12.8329	0.433337	0.216668	+	0.976245i	$0.430481\pi$
$878$	4.28374	0.144569
$879$	−9.09639	−0.306814
$880$	10.3335	0.348344
$881$	−19.7564	−0.665610	−0.332805	−	0.942996i	$-0.607995\pi$
$881$	−19.7564	−0.665610	−0.332805	+	0.942996i	$0.607995\pi$
$882$	−33.2239	−1.11871
$883$	−11.1023	−0.373621	−0.186811	−	0.982396i	$-0.559815\pi$
$883$	−11.1023	−0.373621	−0.186811	+	0.982396i	$0.559815\pi$
$884$	−7.87871	−0.264990
$885$	−80.6725	−2.71178
$886$	−6.10127	−0.204976
$887$	26.0511	0.874709	0.437355	−	0.899289i	$-0.355915\pi$
$887$	26.0511	0.874709	0.437355	+	0.899289i	$0.355915\pi$
$888$	72.0873	2.41909
$889$	−1.06849	−0.0358359
$890$	9.72117	0.325854
$891$	−125.555	−4.20624
$892$	19.8302	0.663963
$893$	−8.18978	−0.274061
$894$	−57.2868	−1.91596
$895$	4.78814	0.160050
$896$	−7.67150	−0.256287
$897$	−9.93366	−0.331675
$898$	−38.7037	−1.29156
$899$	−24.0487	−0.802068
$900$	−118.353	−3.94511
$901$	12.2227	0.407196
$902$	33.4207	1.11279
$903$	33.5622	1.11688
$904$	−42.2756	−1.40607
$905$	−7.56275	−0.251394
$906$	42.9661	1.42745
$907$	23.8772	0.792830	0.396415	−	0.918072i	$-0.370254\pi$
$907$	23.8772	0.792830	0.396415	+	0.918072i	$0.370254\pi$
$908$	32.6385	1.08315
$909$	10.7702	0.357227
$910$	−6.57160	−0.217846
$911$	−39.1909	−1.29845	−0.649226	−	0.760595i	$-0.724907\pi$
$911$	−39.1909	−1.29845	−0.649226	+	0.760595i	$0.724907\pi$
$912$	5.34926	0.177132
$913$	−26.2260	−0.867955
$914$	−5.26037	−0.173998
$915$	−148.801	−4.91922
$916$	−19.8965	−0.657400
$917$	−1.15699	−0.0382072
$918$	−111.428	−3.67768
$919$	26.2067	0.864481	0.432240	−	0.901758i	$-0.357723\pi$
$919$	26.2067	0.864481	0.432240	+	0.901758i	$0.357723\pi$
$920$	−37.9321	−1.25058
$921$	54.3095	1.78956
$922$	12.1916	0.401508
$923$	−5.28176	−0.173851
$924$	24.1839	0.795593
$925$	−99.9336	−3.28580
$926$	−4.13744	−0.135965
$927$	7.96298	0.261539
$928$	18.3589	0.602661
$929$	27.4020	0.899029	0.449515	−	0.893273i	$-0.351597\pi$
$929$	27.4020	0.899029	0.449515	+	0.893273i	$0.351597\pi$
$930$	−94.1738	−3.08808
$931$	12.1742	0.398995
$932$	−11.5662	−0.378864
$933$	15.4646	0.506290
$934$	21.2987	0.696915
$935$	126.554	4.13876
$936$	23.4108	0.765205
$937$	28.8057	0.941042	0.470521	−	0.882389i	$-0.344066\pi$
$937$	28.8057	0.941042	0.470521	+	0.882389i	$0.344066\pi$
$938$	0.0598417	0.00195390
$939$	42.2594	1.37908
$940$	−14.0247	−0.457434
$941$	−10.0079	−0.326248	−0.163124	−	0.986606i	$-0.552157\pi$
$941$	−10.0079	−0.326248	−0.163124	+	0.986606i	$0.552157\pi$
$942$	24.4289	0.795936
$943$	−25.7118	−0.837291
$944$	3.30918	0.107705
$945$	113.919	3.70578
$946$	−24.5215	−0.797263
$947$	−27.1732	−0.883011	−0.441506	−	0.897258i	$-0.645555\pi$
$947$	−27.1732	−0.883011	−0.441506	+	0.897258i	$0.645555\pi$
$948$	21.7981	0.707970
$949$	−8.49628	−0.275801
$950$	−35.3825	−1.14796
$951$	85.2514	2.76447
$952$	33.9012	1.09875
$953$	−9.64150	−0.312319	−0.156159	−	0.987732i	$-0.549911\pi$
$953$	−9.64150	−0.312319	−0.156159	+	0.987732i	$0.549911\pi$
$954$	−12.8978	−0.417582
$955$	−81.8051	−2.64715
$956$	25.3412	0.819594
$957$	−46.9504	−1.51769
$958$	−8.07085	−0.260757
$959$	3.13734	0.101310
$960$	88.5270	2.85720
$961$	17.6772	0.570233
$962$	7.01998	0.226333
$963$	86.3780	2.78349
$964$	15.9573	0.513949
$965$	−37.7113	−1.21397
$966$	15.1795	0.488394
$967$	14.6834	0.472185	0.236093	−	0.971731i	$-0.424133\pi$
$967$	14.6834	0.472185	0.236093	+	0.971731i	$0.424133\pi$
$968$	−17.4153	−0.559748
$969$	65.5120	2.10455
$970$	73.4103	2.35706
$971$	1.30020	0.0417254	0.0208627	−	0.999782i	$-0.493359\pi$
$971$	1.30020	0.0417254	0.0208627	+	0.999782i	$0.493359\pi$
$972$	−57.0037	−1.82839
$973$	−2.25311	−0.0722312
$974$	19.6341	0.629116
$975$	−44.6809	−1.43093
$976$	6.10382	0.195379
$977$	−15.8746	−0.507873	−0.253937	−	0.967221i	$-0.581725\pi$
$977$	−15.8746	−0.507873	−0.253937	+	0.967221i	$0.581725\pi$
$978$	−23.7541	−0.759572
$979$	−9.80985	−0.313524
$980$	20.8479	0.665962
$981$	40.5581	1.29492
$982$	35.5850	1.13556
$983$	−5.64251	−0.179968	−0.0899841	−	0.995943i	$-0.528682\pi$
$983$	−5.64251	−0.179968	−0.0899841	+	0.995943i	$0.528682\pi$
$984$	83.4241	2.65946
$985$	62.2006	1.98187
$986$	−23.3731	−0.744352
$987$	15.8036	0.503033
$988$	−3.04647	−0.0969210
$989$	18.8653	0.599882
$990$	−133.544	−4.24432
$991$	4.38588	0.139322	0.0696610	−	0.997571i	$-0.477808\pi$
$991$	4.38588	0.139322	0.0696610	+	0.997571i	$0.477808\pi$
$992$	−37.1605	−1.17985
$993$	−92.9432	−2.94946
$994$	8.07101	0.255997
$995$	−12.9925	−0.411889
$996$	−23.2486	−0.736661
$997$	10.3447	0.327619	0.163810	−	0.986492i	$-0.447622\pi$
$997$	10.3447	0.327619	0.163810	+	0.986492i	$0.447622\pi$
$998$	−8.97665	−0.284151
$999$	−121.692	−3.85015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.g.1.20	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.g.1.20	✓	30	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q+0.947942 q^{2} +3.31104 q^{3} -1.10141 q^{4} +4.30053 q^{5} +3.13867 q^{6} +1.61201 q^{7} -2.93995 q^{8} +7.96298 q^{9} +O(q^{10})\)	\(q+0.947942 q^{2} +3.31104 q^{3} -1.10141 q^{4} +4.30053 q^{5} +3.13867 q^{6} +1.61201 q^{7} -2.93995 q^{8} +7.96298 q^{9} +4.07665 q^{10} -4.11384 q^{11} -3.64680 q^{12} -1.00000 q^{13} +1.52809 q^{14} +14.2392 q^{15} -0.584091 q^{16} -7.15332 q^{17} +7.54844 q^{18} -2.76598 q^{19} -4.73663 q^{20} +5.33743 q^{21} -3.89968 q^{22} +3.00016 q^{23} -9.73430 q^{24} +13.4945 q^{25} -0.947942 q^{26} +16.4326 q^{27} -1.77548 q^{28} +3.44689 q^{29} +13.4979 q^{30} -6.97691 q^{31} +5.32622 q^{32} -13.6211 q^{33} -6.78093 q^{34} +6.93249 q^{35} -8.77048 q^{36} -7.40550 q^{37} -2.62199 q^{38} -3.31104 q^{39} -12.6433 q^{40} -8.57012 q^{41} +5.05957 q^{42} +6.28809 q^{43} +4.53101 q^{44} +34.2450 q^{45} +2.84398 q^{46} +2.96090 q^{47} -1.93395 q^{48} -4.40142 q^{49} +12.7920 q^{50} -23.6849 q^{51} +1.10141 q^{52} -1.70867 q^{53} +15.5772 q^{54} -17.6917 q^{55} -4.73923 q^{56} -9.15826 q^{57} +3.26745 q^{58} -5.66552 q^{59} -15.6832 q^{60} -10.4501 q^{61} -6.61370 q^{62} +12.8364 q^{63} +6.21713 q^{64} -4.30053 q^{65} -12.9120 q^{66} +0.0391610 q^{67} +7.87871 q^{68} +9.93366 q^{69} +6.57160 q^{70} +5.28176 q^{71} -23.4108 q^{72} +8.49628 q^{73} -7.01998 q^{74} +44.6809 q^{75} +3.04647 q^{76} -6.63155 q^{77} -3.13867 q^{78} -5.97733 q^{79} -2.51190 q^{80} +30.5201 q^{81} -8.12398 q^{82} +6.37508 q^{83} -5.87868 q^{84} -30.7630 q^{85} +5.96074 q^{86} +11.4128 q^{87} +12.0945 q^{88} +2.38460 q^{89} +32.4623 q^{90} -1.61201 q^{91} -3.30440 q^{92} -23.1008 q^{93} +2.80676 q^{94} -11.8952 q^{95} +17.6353 q^{96} +18.0075 q^{97} -4.17229 q^{98} -32.7584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9}+O(q^{10}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9	\( 30 q + 5 q^{3} + 34 q^{4} + 17 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 49 q^{9} + 5 q^{10} + q^{11} + 15 q^{12} - 30 q^{13} + 24 q^{14} + 6 q^{15} + 38 q^{16} + 17 q^{17} + 8 q^{18} + 9 q^{19} + 31 q^{20} + 27 q^{21} + 2 q^{22} + 14 q^{23} + 26 q^{24} + 47 q^{25} + 14 q^{27} - 6 q^{28} + 53 q^{29} + 25 q^{30} + 19 q^{31} - 4 q^{32} + q^{33} - 22 q^{34} + 9 q^{35} + 61 q^{36} + 46 q^{38} - 5 q^{39} - 35 q^{40} + 28 q^{41} - 7 q^{42} + 6 q^{43} - 12 q^{44} + 68 q^{45} + 7 q^{46} + 12 q^{47} + 13 q^{48} + 54 q^{49} - 18 q^{50} + 10 q^{51} - 34 q^{52} + 37 q^{53} + 22 q^{54} + 11 q^{55} + 67 q^{56} - 57 q^{57} - 5 q^{58} + 61 q^{59} - 102 q^{60} + 16 q^{61} - 2 q^{62} - 7 q^{63} + 29 q^{64} - 17 q^{65} - 83 q^{66} - 2 q^{67} + 57 q^{68} + 98 q^{69} - 10 q^{70} + 50 q^{71} - 8 q^{72} - 10 q^{73} - 13 q^{74} + 5 q^{75} - 19 q^{76} + 54 q^{77} - 3 q^{78} + 3 q^{79} + 76 q^{80} + 118 q^{81} + 7 q^{82} + 6 q^{83} + 44 q^{84} + 33 q^{85} - 29 q^{86} - 10 q^{87} - 13 q^{88} + 77 q^{89} + 38 q^{90} - 2 q^{91} - 3 q^{92} + 34 q^{93} - 25 q^{94} + 24 q^{95} - 28 q^{96} + 12 q^{97} - 14 q^{98} - 58 q^{99}+O(q^{100}) \) 30 * q + 5 * q^3 + 34 * q^4 + 17 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 49 * q^9 + 5 * q^10 + q^11 + 15 * q^12 - 30 * q^13 + 24 * q^14 + 6 * q^15 + 38 * q^16 + 17 * q^17 + 8 * q^18 + 9 * q^19 + 31 * q^20 + 27 * q^21 + 2 * q^22 + 14 * q^23 + 26 * q^24 + 47 * q^25 + 14 * q^27 - 6 * q^28 + 53 * q^29 + 25 * q^30 + 19 * q^31 - 4 * q^32 + q^33 - 22 * q^34 + 9 * q^35 + 61 * q^36 + 46 * q^38 - 5 * q^39 - 35 * q^40 + 28 * q^41 - 7 * q^42 + 6 * q^43 - 12 * q^44 + 68 * q^45 + 7 * q^46 + 12 * q^47 + 13 * q^48 + 54 * q^49 - 18 * q^50 + 10 * q^51 - 34 * q^52 + 37 * q^53 + 22 * q^54 + 11 * q^55 + 67 * q^56 - 57 * q^57 - 5 * q^58 + 61 * q^59 - 102 * q^60 + 16 * q^61 - 2 * q^62 - 7 * q^63 + 29 * q^64 - 17 * q^65 - 83 * q^66 - 2 * q^67 + 57 * q^68 + 98 * q^69 - 10 * q^70 + 50 * q^71 - 8 * q^72 - 10 * q^73 - 13 * q^74 + 5 * q^75 - 19 * q^76 + 54 * q^77 - 3 * q^78 + 3 * q^79 + 76 * q^80 + 118 * q^81 + 7 * q^82 + 6 * q^83 + 44 * q^84 + 33 * q^85 - 29 * q^86 - 10 * q^87 - 13 * q^88 + 77 * q^89 + 38 * q^90 - 2 * q^91 - 3 * q^92 + 34 * q^93 - 25 * q^94 + 24 * q^95 - 28 * q^96 + 12 * q^97 - 14 * q^98 - 58 * q^99

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