LMFDB - Embedded newform 1205.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, 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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.05446 q^{2} +2.79403 q^{3} -0.888118 q^{4} +1.00000 q^{5} +2.94619 q^{6} -1.63707 q^{7} -3.04540 q^{8} +4.80663 q^{9} +O(q^{10})$	\(q+1.05446 q^{2} +2.79403 q^{3} -0.888118 q^{4} +1.00000 q^{5} +2.94619 q^{6} -1.63707 q^{7} -3.04540 q^{8} +4.80663 q^{9} +1.05446 q^{10} +3.48187 q^{11} -2.48143 q^{12} +1.54127 q^{13} -1.72622 q^{14} +2.79403 q^{15} -1.43501 q^{16} +5.66858 q^{17} +5.06839 q^{18} +8.06291 q^{19} -0.888118 q^{20} -4.57402 q^{21} +3.67149 q^{22} -9.08730 q^{23} -8.50895 q^{24} +1.00000 q^{25} +1.62521 q^{26} +5.04778 q^{27} +1.45391 q^{28} -5.83770 q^{29} +2.94619 q^{30} -0.515390 q^{31} +4.57764 q^{32} +9.72848 q^{33} +5.97728 q^{34} -1.63707 q^{35} -4.26885 q^{36} +8.17318 q^{37} +8.50200 q^{38} +4.30637 q^{39} -3.04540 q^{40} -2.50706 q^{41} -4.82311 q^{42} -2.34062 q^{43} -3.09232 q^{44} +4.80663 q^{45} -9.58218 q^{46} +7.36336 q^{47} -4.00947 q^{48} -4.32002 q^{49} +1.05446 q^{50} +15.8382 q^{51} -1.36883 q^{52} -6.12837 q^{53} +5.32267 q^{54} +3.48187 q^{55} +4.98552 q^{56} +22.5281 q^{57} -6.15561 q^{58} +1.35442 q^{59} -2.48143 q^{60} -11.6587 q^{61} -0.543457 q^{62} -7.86876 q^{63} +7.69695 q^{64} +1.54127 q^{65} +10.2583 q^{66} +1.12494 q^{67} -5.03437 q^{68} -25.3902 q^{69} -1.72622 q^{70} -6.10631 q^{71} -14.6381 q^{72} +5.57776 q^{73} +8.61827 q^{74} +2.79403 q^{75} -7.16082 q^{76} -5.70006 q^{77} +4.54089 q^{78} -9.29499 q^{79} -1.43501 q^{80} -0.316215 q^{81} -2.64359 q^{82} -4.55159 q^{83} +4.06227 q^{84} +5.66858 q^{85} -2.46809 q^{86} -16.3107 q^{87} -10.6037 q^{88} -2.59790 q^{89} +5.06839 q^{90} -2.52316 q^{91} +8.07060 q^{92} -1.44002 q^{93} +7.76435 q^{94} +8.06291 q^{95} +12.7901 q^{96} -12.3273 q^{97} -4.55528 q^{98} +16.7361 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.05446	0.745614	0.372807	−	0.927909i	$-0.378395\pi$
$2$	1.05446	0.745614	0.372807	+	0.927909i	$0.378395\pi$
$3$	2.79403	1.61314	0.806568	−	0.591141i	$-0.201322\pi$
$3$	2.79403	1.61314	0.806568	+	0.591141i	$0.201322\pi$
$4$	−0.888118	−0.444059
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.94619	1.20278
$7$	−1.63707	−0.618752	−0.309376	−	0.950940i	$-0.600120\pi$
$7$	−1.63707	−0.618752	−0.309376	+	0.950940i	$0.600120\pi$
$8$	−3.04540	−1.07671
$9$	4.80663	1.60221
$10$	1.05446	0.333449
$11$	3.48187	1.04982	0.524912	−	0.851156i	$-0.324098\pi$
$11$	3.48187	1.04982	0.524912	+	0.851156i	$0.324098\pi$
$12$	−2.48143	−0.716328
$13$	1.54127	0.427472	0.213736	−	0.976891i	$-0.431437\pi$
$13$	1.54127	0.427472	0.213736	+	0.976891i	$0.431437\pi$
$14$	−1.72622	−0.461351
$15$	2.79403	0.721417
$16$	−1.43501	−0.358752
$17$	5.66858	1.37483	0.687416	−	0.726264i	$-0.258745\pi$
$17$	5.66858	1.37483	0.687416	+	0.726264i	$0.258745\pi$
$18$	5.06839	1.19463
$19$	8.06291	1.84976	0.924879	−	0.380260i	$-0.124166\pi$
$19$	8.06291	1.84976	0.924879	+	0.380260i	$0.124166\pi$
$20$	−0.888118	−0.198589
$21$	−4.57402	−0.998132
$22$	3.67149	0.782765
$23$	−9.08730	−1.89483	−0.947417	−	0.320002i	$-0.896316\pi$
$23$	−9.08730	−1.89483	−0.947417	+	0.320002i	$0.896316\pi$
$24$	−8.50895	−1.73688
$25$	1.00000	0.200000
$26$	1.62521	0.318729
$27$	5.04778	0.971446
$28$	1.45391	0.274763
$29$	−5.83770	−1.08403	−0.542017	−	0.840367i	$-0.682339\pi$
$29$	−5.83770	−1.08403	−0.542017	+	0.840367i	$0.682339\pi$
$30$	2.94619	0.537899
$31$	−0.515390	−0.0925668	−0.0462834	−	0.998928i	$-0.514738\pi$
$31$	−0.515390	−0.0925668	−0.0462834	+	0.998928i	$0.514738\pi$
$32$	4.57764	0.809220
$33$	9.72848	1.69351
$34$	5.97728	1.02509
$35$	−1.63707	−0.276715
$36$	−4.26885	−0.711476
$37$	8.17318	1.34366	0.671831	−	0.740704i	$-0.265508\pi$
$37$	8.17318	1.34366	0.671831	+	0.740704i	$0.265508\pi$
$38$	8.50200	1.37921
$39$	4.30637	0.689571
$40$	−3.04540	−0.481520
$41$	−2.50706	−0.391537	−0.195768	−	0.980650i	$-0.562720\pi$
$41$	−2.50706	−0.391537	−0.195768	+	0.980650i	$0.562720\pi$
$42$	−4.82311	−0.744222
$43$	−2.34062	−0.356942	−0.178471	−	0.983945i	$-0.557115\pi$
$43$	−2.34062	−0.356942	−0.178471	+	0.983945i	$0.557115\pi$
$44$	−3.09232	−0.466184
$45$	4.80663	0.716530
$46$	−9.58218	−1.41282
$47$	7.36336	1.07406	0.537028	−	0.843564i	$-0.319547\pi$
$47$	7.36336	1.07406	0.537028	+	0.843564i	$0.319547\pi$
$48$	−4.00947	−0.578717
$49$	−4.32002	−0.617145
$50$	1.05446	0.149123
$51$	15.8382	2.21779
$52$	−1.36883	−0.189823
$53$	−6.12837	−0.841796	−0.420898	−	0.907108i	$-0.638285\pi$
$53$	−6.12837	−0.841796	−0.420898	+	0.907108i	$0.638285\pi$
$54$	5.32267	0.724324
$55$	3.48187	0.469496
$56$	4.98552	0.666218
$57$	22.5281	2.98391
$58$	−6.15561	−0.808272
$59$	1.35442	0.176330	0.0881652	−	0.996106i	$-0.471900\pi$
$59$	1.35442	0.176330	0.0881652	+	0.996106i	$0.471900\pi$
$60$	−2.48143	−0.320352
$61$	−11.6587	−1.49274	−0.746370	−	0.665531i	$-0.768205\pi$
$61$	−11.6587	−1.49274	−0.746370	+	0.665531i	$0.768205\pi$
$62$	−0.543457	−0.0690191
$63$	−7.86876	−0.991371
$64$	7.69695	0.962119
$65$	1.54127	0.191171
$66$	10.2583	1.26271
$67$	1.12494	0.137433	0.0687164	−	0.997636i	$-0.478110\pi$
$67$	1.12494	0.137433	0.0687164	+	0.997636i	$0.478110\pi$
$68$	−5.03437	−0.610506
$69$	−25.3902	−3.05663
$70$	−1.72622	−0.206322
$71$	−6.10631	−0.724686	−0.362343	−	0.932045i	$-0.618023\pi$
$71$	−6.10631	−0.724686	−0.362343	+	0.932045i	$0.618023\pi$
$72$	−14.6381	−1.72512
$73$	5.57776	0.652828	0.326414	−	0.945227i	$-0.394160\pi$
$73$	5.57776	0.652828	0.326414	+	0.945227i	$0.394160\pi$
$74$	8.61827	1.00185
$75$	2.79403	0.322627
$76$	−7.16082	−0.821402
$77$	−5.70006	−0.649582
$78$	4.54089	0.514154
$79$	−9.29499	−1.04577	−0.522884	−	0.852404i	$-0.675144\pi$
$79$	−9.29499	−1.04577	−0.522884	+	0.852404i	$0.675144\pi$
$80$	−1.43501	−0.160439
$81$	−0.316215	−0.0351350
$82$	−2.64359	−0.291936
$83$	−4.55159	−0.499601	−0.249801	−	0.968297i	$-0.580365\pi$
$83$	−4.55159	−0.499601	−0.249801	+	0.968297i	$0.580365\pi$
$84$	4.06227	0.443230
$85$	5.66858	0.614843
$86$	−2.46809	−0.266141
$87$	−16.3107	−1.74869
$88$	−10.6037	−1.13036
$89$	−2.59790	−0.275376	−0.137688	−	0.990476i	$-0.543967\pi$
$89$	−2.59790	−0.275376	−0.137688	+	0.990476i	$0.543967\pi$
$90$	5.06839	0.534255
$91$	−2.52316	−0.264499
$92$	8.07060	0.841418
$93$	−1.44002	−0.149323
$94$	7.76435	0.800832
$95$	8.06291	0.827237
$96$	12.7901	1.30538
$97$	−12.3273	−1.25165	−0.625824	−	0.779965i	$-0.715237\pi$
$97$	−12.3273	−1.25165	−0.625824	+	0.779965i	$0.715237\pi$
$98$	−4.55528	−0.460153
$99$	16.7361	1.68204
$100$	−0.888118	−0.0888118
$101$	5.94499	0.591549	0.295774	−	0.955258i	$-0.404422\pi$
$101$	5.94499	0.591549	0.295774	+	0.955258i	$0.404422\pi$
$102$	16.7007	1.65362
$103$	−14.0762	−1.38697	−0.693487	−	0.720469i	$-0.743926\pi$
$103$	−14.0762	−1.38697	−0.693487	+	0.720469i	$0.743926\pi$
$104$	−4.69379	−0.460264
$105$	−4.57402	−0.446378
$106$	−6.46211	−0.627655
$107$	15.7771	1.52523	0.762613	−	0.646855i	$-0.223916\pi$
$107$	15.7771	1.52523	0.762613	+	0.646855i	$0.223916\pi$
$108$	−4.48302	−0.431379
$109$	5.72700	0.548547	0.274274	−	0.961652i	$-0.411563\pi$
$109$	5.72700	0.548547	0.274274	+	0.961652i	$0.411563\pi$
$110$	3.67149	0.350063
$111$	22.8361	2.16751
$112$	2.34920	0.221979
$113$	−8.94457	−0.841435	−0.420717	−	0.907192i	$-0.638222\pi$
$113$	−8.94457	−0.841435	−0.420717	+	0.907192i	$0.638222\pi$
$114$	23.7549	2.22485
$115$	−9.08730	−0.847395
$116$	5.18457	0.481375
$117$	7.40832	0.684900
$118$	1.42818	0.131475
$119$	−9.27983	−0.850680
$120$	−8.50895	−0.776757
$121$	1.12345	0.102132
$122$	−12.2936	−1.11301
$123$	−7.00481	−0.631602
$124$	0.457727	0.0411051
$125$	1.00000	0.0894427
$126$	−8.29728	−0.739180
$127$	−12.8828	−1.14316	−0.571580	−	0.820547i	$-0.693669\pi$
$127$	−12.8828	−1.14316	−0.571580	+	0.820547i	$0.693669\pi$
$128$	−1.03917	−0.0918506
$129$	−6.53978	−0.575796
$130$	1.62521	0.142540
$131$	−8.85544	−0.773703	−0.386852	−	0.922142i	$-0.626437\pi$
$131$	−8.85544	−0.773703	−0.386852	+	0.922142i	$0.626437\pi$
$132$	−8.64004	−0.752019
$133$	−13.1995	−1.14454
$134$	1.18620	0.102472
$135$	5.04778	0.434444
$136$	−17.2631	−1.48030
$137$	9.38215	0.801571	0.400785	−	0.916172i	$-0.368737\pi$
$137$	9.38215	0.801571	0.400785	+	0.916172i	$0.368737\pi$
$138$	−26.7729	−2.27906
$139$	−2.58528	−0.219281	−0.109640	−	0.993971i	$-0.534970\pi$
$139$	−2.58528	−0.219281	−0.109640	+	0.993971i	$0.534970\pi$
$140$	1.45391	0.122878
$141$	20.5735	1.73260
$142$	−6.43885	−0.540336
$143$	5.36652	0.448771
$144$	−6.89756	−0.574796
$145$	−5.83770	−0.484795
$146$	5.88152	0.486758
$147$	−12.0703	−0.995540
$148$	−7.25875	−0.596665
$149$	−12.3891	−1.01495	−0.507476	−	0.861666i	$-0.669421\pi$
$149$	−12.3891	−1.01495	−0.507476	+	0.861666i	$0.669421\pi$
$150$	2.94619	0.240556
$151$	19.3470	1.57444	0.787219	−	0.616673i	$-0.211520\pi$
$151$	19.3470	1.57444	0.787219	+	0.616673i	$0.211520\pi$
$152$	−24.5548	−1.99166
$153$	27.2467	2.20277
$154$	−6.01047	−0.484337
$155$	−0.515390	−0.0413971
$156$	−3.82456	−0.306210
$157$	−6.87800	−0.548925	−0.274462	−	0.961598i	$-0.588500\pi$
$157$	−6.87800	−0.548925	−0.274462	+	0.961598i	$0.588500\pi$
$158$	−9.80117	−0.779740
$159$	−17.1229	−1.35793
$160$	4.57764	0.361894
$161$	14.8765	1.17243
$162$	−0.333435	−0.0261972
$163$	21.9432	1.71872	0.859361	−	0.511369i	$-0.170862\pi$
$163$	21.9432	1.71872	0.859361	+	0.511369i	$0.170862\pi$
$164$	2.22656	0.173865
$165$	9.72848	0.757361
$166$	−4.79946	−0.372510
$167$	4.56559	0.353296	0.176648	−	0.984274i	$-0.443475\pi$
$167$	4.56559	0.353296	0.176648	+	0.984274i	$0.443475\pi$
$168$	13.9297	1.07470
$169$	−10.6245	−0.817268
$170$	5.97728	0.458436
$171$	38.7554	2.96370
$172$	2.07875	0.158503
$173$	−5.76678	−0.438440	−0.219220	−	0.975675i	$-0.570351\pi$
$173$	−5.76678	−0.438440	−0.219220	+	0.975675i	$0.570351\pi$
$174$	−17.1990	−1.30385
$175$	−1.63707	−0.123750
$176$	−4.99652	−0.376627
$177$	3.78430	0.284445
$178$	−2.73937	−0.205325
$179$	9.76703	0.730022	0.365011	−	0.931003i	$-0.381065\pi$
$179$	9.76703	0.730022	0.365011	+	0.931003i	$0.381065\pi$
$180$	−4.26885	−0.318182
$181$	−13.2947	−0.988187	−0.494093	−	0.869409i	$-0.664500\pi$
$181$	−13.2947	−0.988187	−0.494093	+	0.869409i	$0.664500\pi$
$182$	−2.66057	−0.197215
$183$	−32.5747	−2.40799
$184$	27.6745	2.04019
$185$	8.17318	0.600904
$186$	−1.51844	−0.111337
$187$	19.7373	1.44333
$188$	−6.53953	−0.476944
$189$	−8.26354	−0.601084
$190$	8.50200	0.616800
$191$	−7.08002	−0.512292	−0.256146	−	0.966638i	$-0.582453\pi$
$191$	−7.08002	−0.512292	−0.256146	+	0.966638i	$0.582453\pi$
$192$	21.5055	1.55203
$193$	6.95584	0.500693	0.250346	−	0.968156i	$-0.419456\pi$
$193$	6.95584	0.500693	0.250346	+	0.968156i	$0.419456\pi$
$194$	−12.9986	−0.933246
$195$	4.30637	0.308385
$196$	3.83669	0.274049
$197$	−0.690805	−0.0492178	−0.0246089	−	0.999697i	$-0.507834\pi$
$197$	−0.690805	−0.0492178	−0.0246089	+	0.999697i	$0.507834\pi$
$198$	17.6475	1.25415
$199$	22.4460	1.59116	0.795579	−	0.605850i	$-0.207167\pi$
$199$	22.4460	1.59116	0.795579	+	0.605850i	$0.207167\pi$
$200$	−3.04540	−0.215342
$201$	3.14311	0.221698
$202$	6.26874	0.441067
$203$	9.55670	0.670749
$204$	−14.0662	−0.984830
$205$	−2.50706	−0.175101
$206$	−14.8428	−1.03415
$207$	−43.6793	−3.03592
$208$	−2.21174	−0.153357
$209$	28.0741	1.94192
$210$	−4.82311	−0.332826
$211$	−17.6232	−1.21323	−0.606614	−	0.794996i	$-0.707473\pi$
$211$	−17.6232	−1.21323	−0.606614	+	0.794996i	$0.707473\pi$
$212$	5.44271	0.373807
$213$	−17.0612	−1.16902
$214$	16.6363	1.13723
$215$	−2.34062	−0.159629
$216$	−15.3725	−1.04597
$217$	0.843727	0.0572759
$218$	6.03889	0.409005
$219$	15.5845	1.05310
$220$	−3.09232	−0.208484
$221$	8.73682	0.587702
$222$	24.0798	1.61613
$223$	19.7302	1.32123	0.660615	−	0.750725i	$-0.270296\pi$
$223$	19.7302	1.32123	0.660615	+	0.750725i	$0.270296\pi$
$224$	−7.49390	−0.500707
$225$	4.80663	0.320442
$226$	−9.43168	−0.627386
$227$	−26.9603	−1.78942	−0.894708	−	0.446652i	$-0.852616\pi$
$227$	−26.9603	−1.78942	−0.894708	+	0.446652i	$0.852616\pi$
$228$	−20.0076	−1.32503
$229$	22.0051	1.45414	0.727069	−	0.686565i	$-0.240882\pi$
$229$	22.0051	1.45414	0.727069	+	0.686565i	$0.240882\pi$
$230$	−9.58218	−0.631830
$231$	−15.9262	−1.04786
$232$	17.7781	1.16719
$233$	22.4590	1.47134	0.735669	−	0.677341i	$-0.236868\pi$
$233$	22.4590	1.47134	0.735669	+	0.677341i	$0.236868\pi$
$234$	7.81177	0.510671
$235$	7.36336	0.480332
$236$	−1.20288	−0.0783011
$237$	−25.9705	−1.68697
$238$	−9.78519	−0.634280
$239$	−8.19022	−0.529781	−0.264891	−	0.964278i	$-0.585336\pi$
$239$	−8.19022	−0.529781	−0.264891	+	0.964278i	$0.585336\pi$
$240$	−4.00947	−0.258810
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	1.18463	0.0761512
$243$	−16.0269	−1.02812
$244$	10.3543	0.662865
$245$	−4.32002	−0.275996
$246$	−7.38628	−0.470932
$247$	12.4271	0.790720
$248$	1.56957	0.0996677
$249$	−12.7173	−0.805925
$250$	1.05446	0.0666898
$251$	26.4262	1.66801	0.834003	−	0.551761i	$-0.186044\pi$
$251$	26.4262	1.66801	0.834003	+	0.551761i	$0.186044\pi$
$252$	6.98839	0.440227
$253$	−31.6409	−1.98924
$254$	−13.5843	−0.852356
$255$	15.8382	0.991826
$256$	−16.4897	−1.03060
$257$	−7.70531	−0.480644	−0.240322	−	0.970693i	$-0.577253\pi$
$257$	−7.70531	−0.480644	−0.240322	+	0.970693i	$0.577253\pi$
$258$	−6.89593	−0.429322
$259$	−13.3800	−0.831394
$260$	−1.36883	−0.0848914
$261$	−28.0597	−1.73685
$262$	−9.33769	−0.576884
$263$	−2.81855	−0.173800	−0.0868998	−	0.996217i	$-0.527696\pi$
$263$	−2.81855	−0.173800	−0.0868998	+	0.996217i	$0.527696\pi$
$264$	−29.6271	−1.82342
$265$	−6.12837	−0.376463
$266$	−13.9183	−0.853388
$267$	−7.25861	−0.444220
$268$	−0.999076	−0.0610283
$269$	−14.8449	−0.905110	−0.452555	−	0.891737i	$-0.649487\pi$
$269$	−14.8449	−0.905110	−0.452555	+	0.891737i	$0.649487\pi$
$270$	5.32267	0.323927
$271$	24.6495	1.49735	0.748675	−	0.662938i	$-0.230691\pi$
$271$	24.6495	1.49735	0.748675	+	0.662938i	$0.230691\pi$
$272$	−8.13446	−0.493224
$273$	−7.04981	−0.426674
$274$	9.89308	0.597663
$275$	3.48187	0.209965
$276$	22.5495	1.35732
$277$	9.81233	0.589566	0.294783	−	0.955564i	$-0.404753\pi$
$277$	9.81233	0.589566	0.294783	+	0.955564i	$0.404753\pi$
$278$	−2.72607	−0.163499
$279$	−2.47729	−0.148311
$280$	4.98552	0.297942
$281$	−20.3307	−1.21283	−0.606414	−	0.795149i	$-0.707393\pi$
$281$	−20.3307	−1.21283	−0.606414	+	0.795149i	$0.707393\pi$
$282$	21.6939	1.29185
$283$	1.04410	0.0620654	0.0310327	−	0.999518i	$-0.490120\pi$
$283$	1.04410	0.0620654	0.0310327	+	0.999518i	$0.490120\pi$
$284$	5.42313	0.321803
$285$	22.5281	1.33445
$286$	5.65877	0.334610
$287$	4.10422	0.242264
$288$	22.0030	1.29654
$289$	15.1328	0.890162
$290$	−6.15561	−0.361470
$291$	−34.4429	−2.01908
$292$	−4.95371	−0.289894
$293$	11.4411	0.668396	0.334198	−	0.942503i	$-0.391535\pi$
$293$	11.4411	0.668396	0.334198	+	0.942503i	$0.391535\pi$
$294$	−12.7276	−0.742289
$295$	1.35442	0.0788574
$296$	−24.8906	−1.44674
$297$	17.5757	1.01985
$298$	−13.0638	−0.756763
$299$	−14.0060	−0.809989
$300$	−2.48143	−0.143266
$301$	3.83175	0.220859
$302$	20.4006	1.17392
$303$	16.6105	0.954249
$304$	−11.5704	−0.663606
$305$	−11.6587	−0.667574
$306$	28.7305	1.64242
$307$	−13.5057	−0.770810	−0.385405	−	0.922747i	$-0.625938\pi$
$307$	−13.5057	−0.770810	−0.385405	+	0.922747i	$0.625938\pi$
$308$	5.06232	0.288453
$309$	−39.3295	−2.23738
$310$	−0.543457	−0.0308663
$311$	13.9235	0.789529	0.394765	−	0.918782i	$-0.370826\pi$
$311$	13.9235	0.789529	0.394765	+	0.918782i	$0.370826\pi$
$312$	−13.1146	−0.742469
$313$	3.11900	0.176296	0.0881482	−	0.996107i	$-0.471905\pi$
$313$	3.11900	0.176296	0.0881482	+	0.996107i	$0.471905\pi$
$314$	−7.25257	−0.409286
$315$	−7.86876	−0.443355
$316$	8.25505	0.464383
$317$	27.7341	1.55770	0.778852	−	0.627208i	$-0.215802\pi$
$317$	27.7341	1.55770	0.778852	+	0.627208i	$0.215802\pi$
$318$	−18.0553	−1.01249
$319$	−20.3262	−1.13805
$320$	7.69695	0.430273
$321$	44.0817	2.46040
$322$	15.6867	0.874183
$323$	45.7052	2.54311
$324$	0.280836	0.0156020
$325$	1.54127	0.0854944
$326$	23.1382	1.28150
$327$	16.0014	0.884882
$328$	7.63500	0.421572
$329$	−12.0543	−0.664575
$330$	10.2583	0.564699
$331$	−22.3339	−1.22758	−0.613790	−	0.789469i	$-0.710356\pi$
$331$	−22.3339	−1.22758	−0.613790	+	0.789469i	$0.710356\pi$
$332$	4.04235	0.221853
$333$	39.2854	2.15283
$334$	4.81423	0.263423
$335$	1.12494	0.0614618
$336$	6.56376	0.358082
$337$	4.07474	0.221965	0.110983	−	0.993822i	$-0.464600\pi$
$337$	4.07474	0.221965	0.110983	+	0.993822i	$0.464600\pi$
$338$	−11.2031	−0.609367
$339$	−24.9914	−1.35735
$340$	−5.03437	−0.273027
$341$	−1.79452	−0.0971789
$342$	40.8660	2.20978
$343$	18.5316	1.00061
$344$	7.12813	0.384323
$345$	−25.3902	−1.36696
$346$	−6.08082	−0.326907
$347$	11.5031	0.617517	0.308758	−	0.951140i	$-0.400087\pi$
$347$	11.5031	0.617517	0.308758	+	0.951140i	$0.400087\pi$
$348$	14.4859	0.776524
$349$	−36.4019	−1.94855	−0.974275	−	0.225364i	$-0.927643\pi$
$349$	−36.4019	−1.94855	−0.974275	+	0.225364i	$0.927643\pi$
$350$	−1.72622	−0.0922702
$351$	7.78000	0.415266
$352$	15.9388	0.849540
$353$	−8.31570	−0.442600	−0.221300	−	0.975206i	$-0.571030\pi$
$353$	−8.31570	−0.442600	−0.221300	+	0.975206i	$0.571030\pi$
$354$	3.99038	0.212086
$355$	−6.10631	−0.324089
$356$	2.30724	0.122283
$357$	−25.9282	−1.37226
$358$	10.2989	0.544315
$359$	−6.85192	−0.361631	−0.180815	−	0.983517i	$-0.557874\pi$
$359$	−6.85192	−0.361631	−0.180815	+	0.983517i	$0.557874\pi$
$360$	−14.6381	−0.771496
$361$	46.0106	2.42161
$362$	−14.0187	−0.736806
$363$	3.13897	0.164753
$364$	2.24087	0.117453
$365$	5.57776	0.291953
$366$	−34.3487	−1.79544
$367$	23.7426	1.23935	0.619677	−	0.784857i	$-0.287263\pi$
$367$	23.7426	1.23935	0.619677	+	0.784857i	$0.287263\pi$
$368$	13.0404	0.679776
$369$	−12.0505	−0.627324
$370$	8.61827	0.448043
$371$	10.0325	0.520863
$372$	1.27891	0.0663082
$373$	6.28408	0.325377	0.162689	−	0.986677i	$-0.447983\pi$
$373$	6.28408	0.325377	0.162689	+	0.986677i	$0.447983\pi$
$374$	20.8121	1.07617
$375$	2.79403	0.144283
$376$	−22.4244	−1.15645
$377$	−8.99749	−0.463394
$378$	−8.71356	−0.448177
$379$	−32.3509	−1.66175	−0.830877	−	0.556457i	$-0.812161\pi$
$379$	−32.3509	−1.66175	−0.830877	+	0.556457i	$0.812161\pi$
$380$	−7.16082	−0.367342
$381$	−35.9949	−1.84407
$382$	−7.46559	−0.381973
$383$	−21.9938	−1.12383	−0.561914	−	0.827195i	$-0.689935\pi$
$383$	−21.9938	−1.12383	−0.561914	+	0.827195i	$0.689935\pi$
$384$	−2.90348	−0.148168
$385$	−5.70006	−0.290502
$386$	7.33464	0.373324
$387$	−11.2505	−0.571895
$388$	10.9481	0.555805
$389$	16.2176	0.822264	0.411132	−	0.911576i	$-0.365134\pi$
$389$	16.2176	0.822264	0.411132	+	0.911576i	$0.365134\pi$
$390$	4.54089	0.229937
$391$	−51.5121	−2.60508
$392$	13.1562	0.664487
$393$	−24.7424	−1.24809
$394$	−0.728425	−0.0366975
$395$	−9.29499	−0.467682
$396$	−14.8636	−0.746925
$397$	17.7440	0.890547	0.445273	−	0.895395i	$-0.353106\pi$
$397$	17.7440	0.890547	0.445273	+	0.895395i	$0.353106\pi$
$398$	23.6684	1.18639
$399$	−36.8799	−1.84630
$400$	−1.43501	−0.0717505
$401$	−13.6586	−0.682079	−0.341039	−	0.940049i	$-0.610779\pi$
$401$	−13.6586	−0.682079	−0.341039	+	0.940049i	$0.610779\pi$
$402$	3.31428	0.165301
$403$	−0.794357	−0.0395697
$404$	−5.27985	−0.262683
$405$	−0.316215	−0.0157128
$406$	10.0771	0.500120
$407$	28.4580	1.41061
$408$	−48.2336	−2.38792
$409$	4.73162	0.233963	0.116982	−	0.993134i	$-0.462678\pi$
$409$	4.73162	0.233963	0.116982	+	0.993134i	$0.462678\pi$
$410$	−2.64359	−0.130558
$411$	26.2140	1.29304
$412$	12.5014	0.615898
$413$	−2.21727	−0.109105
$414$	−46.0580	−2.26363
$415$	−4.55159	−0.223429
$416$	7.05539	0.345919
$417$	−7.22337	−0.353730
$418$	29.6029	1.44793
$419$	−17.9594	−0.877373	−0.438686	−	0.898640i	$-0.644556\pi$
$419$	−17.9594	−0.877373	−0.438686	+	0.898640i	$0.644556\pi$
$420$	4.06227	0.198218
$421$	25.1465	1.22557	0.612783	−	0.790251i	$-0.290050\pi$
$421$	25.1465	1.22557	0.612783	+	0.790251i	$0.290050\pi$
$422$	−18.5829	−0.904600
$423$	35.3929	1.72086
$424$	18.6633	0.906371
$425$	5.66858	0.274966
$426$	−17.9904	−0.871636
$427$	19.0860	0.923637
$428$	−14.0119	−0.677291
$429$	14.9942	0.723929
$430$	−2.46809	−0.119022
$431$	1.28313	0.0618060	0.0309030	−	0.999522i	$-0.490162\pi$
$431$	1.28313	0.0618060	0.0309030	+	0.999522i	$0.490162\pi$
$432$	−7.24361	−0.348508
$433$	−27.0984	−1.30226	−0.651132	−	0.758965i	$-0.725706\pi$
$433$	−27.0984	−1.30226	−0.651132	+	0.758965i	$0.725706\pi$
$434$	0.889675	0.0427058
$435$	−16.3107	−0.782040
$436$	−5.08626	−0.243587
$437$	−73.2701	−3.50499
$438$	16.4332	0.785207
$439$	−11.1696	−0.533097	−0.266549	−	0.963822i	$-0.585883\pi$
$439$	−11.1696	−0.533097	−0.266549	+	0.963822i	$0.585883\pi$
$440$	−10.6037	−0.505512
$441$	−20.7647	−0.988796
$442$	9.21261	0.438199
$443$	15.0784	0.716395	0.358198	−	0.933646i	$-0.383391\pi$
$443$	15.0784	0.716395	0.358198	+	0.933646i	$0.383391\pi$
$444$	−20.2812	−0.962503
$445$	−2.59790	−0.123152
$446$	20.8046	0.985128
$447$	−34.6155	−1.63726
$448$	−12.6004	−0.595313
$449$	−30.3624	−1.43289	−0.716446	−	0.697643i	$-0.754232\pi$
$449$	−30.3624	−1.43289	−0.716446	+	0.697643i	$0.754232\pi$
$450$	5.06839	0.238926
$451$	−8.72927	−0.411045
$452$	7.94384	0.373647
$453$	54.0563	2.53978
$454$	−28.4285	−1.33421
$455$	−2.52316	−0.118288
$456$	−68.6069	−3.21281
$457$	36.8679	1.72461	0.862305	−	0.506390i	$-0.169020\pi$
$457$	36.8679	1.72461	0.862305	+	0.506390i	$0.169020\pi$
$458$	23.2034	1.08423
$459$	28.6137	1.33557
$460$	8.07060	0.376294
$461$	9.47241	0.441174	0.220587	−	0.975367i	$-0.429203\pi$
$461$	9.47241	0.441174	0.220587	+	0.975367i	$0.429203\pi$
$462$	−16.7935	−0.781302
$463$	26.8175	1.24631	0.623156	−	0.782097i	$-0.285850\pi$
$463$	26.8175	1.24631	0.623156	+	0.782097i	$0.285850\pi$
$464$	8.37716	0.388900
$465$	−1.44002	−0.0667792
$466$	23.6821	1.09705
$467$	−9.85314	−0.455949	−0.227975	−	0.973667i	$-0.573210\pi$
$467$	−9.85314	−0.455949	−0.227975	+	0.973667i	$0.573210\pi$
$468$	−6.57947	−0.304136
$469$	−1.84159	−0.0850369
$470$	7.76435	0.358143
$471$	−19.2174	−0.885490
$472$	−4.12475	−0.189857
$473$	−8.14976	−0.374726
$474$	−27.3848	−1.25783
$475$	8.06291	0.369952
$476$	8.24158	0.377752
$477$	−29.4568	−1.34873
$478$	−8.63624	−0.395012
$479$	−11.9289	−0.545043	−0.272522	−	0.962150i	$-0.587858\pi$
$479$	−11.9289	−0.545043	−0.272522	+	0.962150i	$0.587858\pi$
$480$	12.7901	0.583785
$481$	12.5971	0.574378
$482$	−1.05446	−0.0480292
$483$	41.5655	1.89129
$484$	−0.997759	−0.0453527
$485$	−12.3273	−0.559754
$486$	−16.8996	−0.766583
$487$	−10.8850	−0.493246	−0.246623	−	0.969112i	$-0.579321\pi$
$487$	−10.8850	−0.493246	−0.246623	+	0.969112i	$0.579321\pi$
$488$	35.5053	1.60725
$489$	61.3100	2.77253
$490$	−4.55528	−0.205786
$491$	31.9444	1.44163	0.720815	−	0.693128i	$-0.243768\pi$
$491$	31.9444	1.44163	0.720815	+	0.693128i	$0.243768\pi$
$492$	6.22110	0.280469
$493$	−33.0915	−1.49036
$494$	13.1039	0.589573
$495$	16.7361	0.752231
$496$	0.739590	0.0332086
$497$	9.99643	0.448401
$498$	−13.4098	−0.600910
$499$	−30.8274	−1.38003	−0.690013	−	0.723797i	$-0.742395\pi$
$499$	−30.8274	−1.38003	−0.690013	+	0.723797i	$0.742395\pi$
$500$	−0.888118	−0.0397179
$501$	12.7564	0.569915
$502$	27.8653	1.24369
$503$	−5.52996	−0.246569	−0.123284	−	0.992371i	$-0.539343\pi$
$503$	−5.52996	−0.246569	−0.123284	+	0.992371i	$0.539343\pi$
$504$	23.9635	1.06742
$505$	5.94499	0.264549
$506$	−33.3640	−1.48321
$507$	−29.6852	−1.31836
$508$	11.4414	0.507630
$509$	9.57644	0.424468	0.212234	−	0.977219i	$-0.431926\pi$
$509$	9.57644	0.424468	0.212234	+	0.977219i	$0.431926\pi$
$510$	16.7007	0.739520
$511$	−9.13116	−0.403939
$512$	−15.3093	−0.676583
$513$	40.6998	1.79694
$514$	−8.12492	−0.358375
$515$	−14.0762	−0.620273
$516$	5.80810	0.255687
$517$	25.6383	1.12757
$518$	−14.1087	−0.619900
$519$	−16.1126	−0.707263
$520$	−4.69379	−0.205836
$521$	−35.5269	−1.55646	−0.778230	−	0.627979i	$-0.783882\pi$
$521$	−35.5269	−1.55646	−0.778230	+	0.627979i	$0.783882\pi$
$522$	−29.5877	−1.29502
$523$	−30.2099	−1.32099	−0.660493	−	0.750832i	$-0.729653\pi$
$523$	−30.2099	−1.32099	−0.660493	+	0.750832i	$0.729653\pi$
$524$	7.86467	0.343570
$525$	−4.57402	−0.199626
$526$	−2.97205	−0.129587
$527$	−2.92153	−0.127264
$528$	−13.9605	−0.607551
$529$	59.5791	2.59040
$530$	−6.46211	−0.280696
$531$	6.51019	0.282518
$532$	11.7227	0.508245
$533$	−3.86406	−0.167371
$534$	−7.65390	−0.331217
$535$	15.7771	0.682102
$536$	−3.42588	−0.147975
$537$	27.2894	1.17763
$538$	−15.6533	−0.674863
$539$	−15.0418	−0.647895
$540$	−4.48302	−0.192919
$541$	−4.21274	−0.181120	−0.0905600	−	0.995891i	$-0.528866\pi$
$541$	−4.21274	−0.181120	−0.0905600	+	0.995891i	$0.528866\pi$
$542$	25.9918	1.11645
$543$	−37.1458	−1.59408
$544$	25.9487	1.11254
$545$	5.72700	0.245318
$546$	−7.43373	−0.318134
$547$	−25.6016	−1.09464	−0.547322	−	0.836922i	$-0.684353\pi$
$547$	−25.6016	−1.09464	−0.547322	+	0.836922i	$0.684353\pi$
$548$	−8.33246	−0.355945
$549$	−56.0389	−2.39168
$550$	3.67149	0.156553
$551$	−47.0689	−2.00520
$552$	77.3234	3.29110
$553$	15.2165	0.647071
$554$	10.3467	0.439589
$555$	22.8361	0.969340
$556$	2.29604	0.0973737
$557$	8.44569	0.357855	0.178928	−	0.983862i	$-0.442737\pi$
$557$	8.44569	0.357855	0.178928	+	0.983862i	$0.442737\pi$
$558$	−2.61220	−0.110583
$559$	−3.60754	−0.152583
$560$	2.34920	0.0992720
$561$	55.1466	2.32829
$562$	−21.4379	−0.904302
$563$	−4.02353	−0.169572	−0.0847858	−	0.996399i	$-0.527021\pi$
$563$	−4.02353	−0.169572	−0.0847858	+	0.996399i	$0.527021\pi$
$564$	−18.2717	−0.769376
$565$	−8.94457	−0.376301
$566$	1.10096	0.0462769
$567$	0.517664	0.0217399
$568$	18.5962	0.780278
$569$	21.4219	0.898054	0.449027	−	0.893518i	$-0.351771\pi$
$569$	21.4219	0.898054	0.449027	+	0.893518i	$0.351771\pi$
$570$	23.7549	0.994983
$571$	31.0188	1.29810	0.649048	−	0.760747i	$-0.275167\pi$
$571$	31.0188	1.29810	0.649048	+	0.760747i	$0.275167\pi$
$572$	−4.76610	−0.199281
$573$	−19.7818	−0.826398
$574$	4.32773	0.180636
$575$	−9.08730	−0.378967
$576$	36.9964	1.54152
$577$	9.10433	0.379018	0.189509	−	0.981879i	$-0.439310\pi$
$577$	9.10433	0.379018	0.189509	+	0.981879i	$0.439310\pi$
$578$	15.9569	0.663718
$579$	19.4349	0.807685
$580$	5.18457	0.215278
$581$	7.45124	0.309130
$582$	−36.3186	−1.50545
$583$	−21.3382	−0.883738
$584$	−16.9865	−0.702907
$585$	7.40832	0.306297
$586$	12.0642	0.498366
$587$	−23.2720	−0.960540	−0.480270	−	0.877121i	$-0.659461\pi$
$587$	−23.2720	−0.960540	−0.480270	+	0.877121i	$0.659461\pi$
$588$	10.7198	0.442078
$589$	−4.15555	−0.171226
$590$	1.42818	0.0587972
$591$	−1.93013	−0.0793951
$592$	−11.7286	−0.482042
$593$	5.45489	0.224005	0.112003	−	0.993708i	$-0.464273\pi$
$593$	5.45489	0.224005	0.112003	+	0.993708i	$0.464273\pi$
$594$	18.5329	0.760413
$595$	−9.27983	−0.380436
$596$	11.0030	0.450699
$597$	62.7150	2.56675
$598$	−14.7688	−0.603939
$599$	35.7616	1.46118	0.730590	−	0.682817i	$-0.239245\pi$
$599$	35.7616	1.46118	0.730590	+	0.682817i	$0.239245\pi$
$600$	−8.50895	−0.347376
$601$	15.8192	0.645277	0.322639	−	0.946522i	$-0.395430\pi$
$601$	15.8192	0.645277	0.322639	+	0.946522i	$0.395430\pi$
$602$	4.04042	0.164675
$603$	5.40715	0.220196
$604$	−17.1824	−0.699144
$605$	1.12345	0.0456749
$606$	17.5151	0.711502
$607$	38.5787	1.56586	0.782931	−	0.622109i	$-0.213724\pi$
$607$	38.5787	1.56586	0.782931	+	0.622109i	$0.213724\pi$
$608$	36.9091	1.49686
$609$	26.7017	1.08201
$610$	−12.2936	−0.497753
$611$	11.3489	0.459129
$612$	−24.1983	−0.978159
$613$	11.8347	0.477999	0.239000	−	0.971020i	$-0.423180\pi$
$613$	11.8347	0.477999	0.239000	+	0.971020i	$0.423180\pi$
$614$	−14.2412	−0.574727
$615$	−7.00481	−0.282461
$616$	17.3589	0.699412
$617$	39.6717	1.59712	0.798562	−	0.601913i	$-0.205595\pi$
$617$	39.6717	1.59712	0.798562	+	0.601913i	$0.205595\pi$
$618$	−41.4713	−1.66822
$619$	8.91772	0.358433	0.179217	−	0.983810i	$-0.442644\pi$
$619$	8.91772	0.358433	0.179217	+	0.983810i	$0.442644\pi$
$620$	0.457727	0.0183828
$621$	−45.8707	−1.84073
$622$	14.6817	0.588684
$623$	4.25292	0.170390
$624$	−6.17968	−0.247385
$625$	1.00000	0.0400000
$626$	3.28886	0.131449
$627$	78.4399	3.13259
$628$	6.10848	0.243755
$629$	46.3303	1.84731
$630$	−8.29728	−0.330572
$631$	4.50997	0.179539	0.0897696	−	0.995963i	$-0.471387\pi$
$631$	4.50997	0.179539	0.0897696	+	0.995963i	$0.471387\pi$
$632$	28.3069	1.12599
$633$	−49.2397	−1.95710
$634$	29.2445	1.16145
$635$	−12.8828	−0.511236
$636$	15.2071	0.603002
$637$	−6.65833	−0.263812
$638$	−21.4331	−0.848544
$639$	−29.3508	−1.16110
$640$	−1.03917	−0.0410768
$641$	8.51496	0.336321	0.168160	−	0.985760i	$-0.446217\pi$
$641$	8.51496	0.336321	0.168160	+	0.985760i	$0.446217\pi$
$642$	46.4823	1.83451
$643$	37.8001	1.49069	0.745345	−	0.666679i	$-0.232285\pi$
$643$	37.8001	1.49069	0.745345	+	0.666679i	$0.232285\pi$
$644$	−13.2121	−0.520630
$645$	−6.53978	−0.257504
$646$	48.1943	1.89618
$647$	16.2259	0.637906	0.318953	−	0.947771i	$-0.396669\pi$
$647$	16.2259	0.637906	0.318953	+	0.947771i	$0.396669\pi$
$648$	0.963001	0.0378302
$649$	4.71592	0.185116
$650$	1.62521	0.0637459
$651$	2.35740	0.0923939
$652$	−19.4881	−0.763214
$653$	−41.0192	−1.60520	−0.802602	−	0.596515i	$-0.796552\pi$
$653$	−41.0192	−1.60520	−0.802602	+	0.596515i	$0.796552\pi$
$654$	16.8729	0.659781
$655$	−8.85544	−0.346011
$656$	3.59765	0.140465
$657$	26.8102	1.04597
$658$	−12.7107	−0.495517
$659$	10.6147	0.413490	0.206745	−	0.978395i	$-0.433713\pi$
$659$	10.6147	0.413490	0.206745	+	0.978395i	$0.433713\pi$
$660$	−8.64004	−0.336313
$661$	28.9677	1.12671	0.563356	−	0.826214i	$-0.309510\pi$
$661$	28.9677	1.12671	0.563356	+	0.826214i	$0.309510\pi$
$662$	−23.5501	−0.915302
$663$	24.4110	0.948044
$664$	13.8614	0.537927
$665$	−13.1995	−0.511855
$666$	41.4248	1.60518
$667$	53.0490	2.05406
$668$	−4.05479	−0.156884
$669$	55.1268	2.13132
$670$	1.18620	0.0458268
$671$	−40.5941	−1.56712
$672$	−20.9382	−0.807709
$673$	−46.5073	−1.79272	−0.896362	−	0.443323i	$-0.853799\pi$
$673$	−46.5073	−1.79272	−0.896362	+	0.443323i	$0.853799\pi$
$674$	4.29665	0.165501
$675$	5.04778	0.194289
$676$	9.43579	0.362915
$677$	−29.8062	−1.14555	−0.572773	−	0.819714i	$-0.694132\pi$
$677$	−29.8062	−1.14555	−0.572773	+	0.819714i	$0.694132\pi$
$678$	−26.3524	−1.01206
$679$	20.1806	0.774460
$680$	−17.2631	−0.662009
$681$	−75.3279	−2.88657
$682$	−1.89225	−0.0724580
$683$	35.8028	1.36996	0.684978	−	0.728564i	$-0.259812\pi$
$683$	35.8028	1.36996	0.684978	+	0.728564i	$0.259812\pi$
$684$	−34.4194	−1.31606
$685$	9.38215	0.358473
$686$	19.5408	0.746071
$687$	61.4830	2.34572
$688$	3.35882	0.128054
$689$	−9.44549	−0.359844
$690$	−26.7729	−1.01923
$691$	32.5225	1.23721	0.618607	−	0.785700i	$-0.287697\pi$
$691$	32.5225	1.23721	0.618607	+	0.785700i	$0.287697\pi$
$692$	5.12158	0.194693
$693$	−27.3980	−1.04077
$694$	12.1295	0.460430
$695$	−2.58528	−0.0980654
$696$	49.6727	1.88284
$697$	−14.2115	−0.538297
$698$	−38.3843	−1.45287
$699$	62.7512	2.37347
$700$	1.45391	0.0549525
$701$	−14.1055	−0.532757	−0.266379	−	0.963868i	$-0.585827\pi$
$701$	−14.1055	−0.532757	−0.266379	+	0.963868i	$0.585827\pi$
$702$	8.20369	0.309628
$703$	65.8996	2.48545
$704$	26.7998	1.01006
$705$	20.5735	0.774842
$706$	−8.76856	−0.330009
$707$	−9.73233	−0.366022
$708$	−3.36090	−0.126310
$709$	19.9520	0.749315	0.374657	−	0.927163i	$-0.377760\pi$
$709$	19.9520	0.749315	0.374657	+	0.927163i	$0.377760\pi$
$710$	−6.43885	−0.241646
$711$	−44.6775	−1.67554
$712$	7.91163	0.296501
$713$	4.68351	0.175399
$714$	−27.3402	−1.02318
$715$	5.36652	0.200696
$716$	−8.67428	−0.324173
$717$	−22.8837	−0.854609
$718$	−7.22507	−0.269637
$719$	−47.2522	−1.76221	−0.881105	−	0.472921i	$-0.843200\pi$
$719$	−47.2522	−1.76221	−0.881105	+	0.472921i	$0.843200\pi$
$720$	−6.89756	−0.257057
$721$	23.0437	0.858193
$722$	48.5162	1.80559
$723$	−2.79403	−0.103911
$724$	11.8073	0.438813
$725$	−5.83770	−0.216807
$726$	3.30991	0.122842
$727$	−42.3566	−1.57092	−0.785460	−	0.618912i	$-0.787574\pi$
$727$	−42.3566	−1.57092	−0.785460	+	0.618912i	$0.787574\pi$
$728$	7.68404	0.284790
$729$	−43.8309	−1.62337
$730$	5.88152	0.217685
$731$	−13.2680	−0.490735
$732$	28.9302	1.06929
$733$	−26.4674	−0.977597	−0.488799	−	0.872397i	$-0.662565\pi$
$733$	−26.4674	−0.977597	−0.488799	+	0.872397i	$0.662565\pi$
$734$	25.0356	0.924081
$735$	−12.0703	−0.445219
$736$	−41.5984	−1.53334
$737$	3.91689	0.144280
$738$	−12.7067	−0.467742
$739$	−25.6941	−0.945171	−0.472586	−	0.881285i	$-0.656679\pi$
$739$	−25.6941	−0.945171	−0.472586	+	0.881285i	$0.656679\pi$
$740$	−7.25875	−0.266837
$741$	34.7219	1.27554
$742$	10.5789	0.388363
$743$	17.9250	0.657605	0.328803	−	0.944399i	$-0.393355\pi$
$743$	17.9250	0.657605	0.328803	+	0.944399i	$0.393355\pi$
$744$	4.38543	0.160778
$745$	−12.3891	−0.453900
$746$	6.62630	0.242606
$747$	−21.8778	−0.800466
$748$	−17.5290	−0.640925
$749$	−25.8281	−0.943738
$750$	2.94619	0.107580
$751$	41.8868	1.52847	0.764236	−	0.644936i	$-0.223116\pi$
$751$	41.8868	1.52847	0.764236	+	0.644936i	$0.223116\pi$
$752$	−10.5665	−0.385320
$753$	73.8356	2.69072
$754$	−9.48748	−0.345514
$755$	19.3470	0.704110
$756$	7.33900	0.266917
$757$	−2.42982	−0.0883133	−0.0441566	−	0.999025i	$-0.514060\pi$
$757$	−2.42982	−0.0883133	−0.0441566	+	0.999025i	$0.514060\pi$
$758$	−34.1127	−1.23903
$759$	−88.4056	−3.20892
$760$	−24.5548	−0.890696
$761$	−39.7501	−1.44094	−0.720470	−	0.693486i	$-0.756074\pi$
$761$	−39.7501	−1.44094	−0.720470	+	0.693486i	$0.756074\pi$
$762$	−37.9551	−1.37497
$763$	−9.37548	−0.339415
$764$	6.28790	0.227488
$765$	27.2467	0.985108
$766$	−23.1915	−0.837943
$767$	2.08753	0.0753763
$768$	−46.0727	−1.66250
$769$	23.8206	0.858993	0.429497	−	0.903069i	$-0.358691\pi$
$769$	23.8206	0.858993	0.429497	+	0.903069i	$0.358691\pi$
$770$	−6.01047	−0.216602
$771$	−21.5289	−0.775344
$772$	−6.17761	−0.222337
$773$	23.2106	0.834829	0.417414	−	0.908716i	$-0.362936\pi$
$773$	23.2106	0.834829	0.417414	+	0.908716i	$0.362936\pi$
$774$	−11.8632	−0.426413
$775$	−0.515390	−0.0185134
$776$	37.5415	1.34766
$777$	−37.3842	−1.34115
$778$	17.1008	0.613092
$779$	−20.2142	−0.724249
$780$	−3.82456	−0.136941
$781$	−21.2614	−0.760793
$782$	−54.3173	−1.94238
$783$	−29.4674	−1.05308
$784$	6.19927	0.221402
$785$	−6.87800	−0.245487
$786$	−26.0898	−0.930593
$787$	28.9293	1.03122	0.515609	−	0.856824i	$-0.327566\pi$
$787$	28.9293	1.03122	0.515609	+	0.856824i	$0.327566\pi$
$788$	0.613517	0.0218556
$789$	−7.87514	−0.280362
$790$	−9.80117	−0.348710
$791$	14.6429	0.520640
$792$	−50.9680	−1.81107
$793$	−17.9692	−0.638105
$794$	18.7103	0.664005
$795$	−17.1229	−0.607286
$796$	−19.9347	−0.706568
$797$	14.6683	0.519578	0.259789	−	0.965665i	$-0.416347\pi$
$797$	14.6683	0.519578	0.259789	+	0.965665i	$0.416347\pi$
$798$	−38.8883	−1.37663
$799$	41.7398	1.47665
$800$	4.57764	0.161844
$801$	−12.4871	−0.441211
$802$	−14.4024	−0.508568
$803$	19.4211	0.685355
$804$	−2.79145	−0.0984469
$805$	14.8765	0.524328
$806$	−0.837616	−0.0295038
$807$	−41.4772	−1.46007
$808$	−18.1049	−0.636927
$809$	5.88041	0.206744	0.103372	−	0.994643i	$-0.467037\pi$
$809$	5.88041	0.206744	0.103372	+	0.994643i	$0.467037\pi$
$810$	−0.333435	−0.0117157
$811$	54.6211	1.91801	0.959004	−	0.283393i	$-0.0914600\pi$
$811$	54.6211	1.91801	0.959004	+	0.283393i	$0.0914600\pi$
$812$	−8.48748	−0.297852
$813$	68.8715	2.41543
$814$	30.0078	1.05177
$815$	21.9432	0.768636
$816$	−22.7280	−0.795638
$817$	−18.8722	−0.660256
$818$	4.98929	0.174447
$819$	−12.1279	−0.423783
$820$	2.22656	0.0777550
$821$	−39.3076	−1.37185	−0.685923	−	0.727674i	$-0.740601\pi$
$821$	−39.3076	−1.37185	−0.685923	+	0.727674i	$0.740601\pi$
$822$	27.6416	0.964112
$823$	43.0976	1.50229	0.751145	−	0.660138i	$-0.229502\pi$
$823$	43.0976	1.50229	0.751145	+	0.660138i	$0.229502\pi$
$824$	42.8678	1.49337
$825$	9.72848	0.338702
$826$	−2.33802	−0.0813502
$827$	−28.9347	−1.00616	−0.503079	−	0.864241i	$-0.667799\pi$
$827$	−28.9347	−1.00616	−0.503079	+	0.864241i	$0.667799\pi$
$828$	38.7924	1.34813
$829$	37.3545	1.29737	0.648687	−	0.761055i	$-0.275318\pi$
$829$	37.3545	1.29737	0.648687	+	0.761055i	$0.275318\pi$
$830$	−4.79946	−0.166592
$831$	27.4160	0.951050
$832$	11.8631	0.411279
$833$	−24.4883	−0.848471
$834$	−7.61674	−0.263746
$835$	4.56559	0.157999
$836$	−24.9331	−0.862328
$837$	−2.60158	−0.0899236
$838$	−18.9374	−0.654182
$839$	21.6809	0.748507	0.374254	−	0.927326i	$-0.377899\pi$
$839$	21.6809	0.748507	0.374254	+	0.927326i	$0.377899\pi$
$840$	13.9297	0.480621
$841$	5.07877	0.175130
$842$	26.5159	0.913800
$843$	−56.8047	−1.95646
$844$	15.6514	0.538745
$845$	−10.6245	−0.365493
$846$	37.3203	1.28310
$847$	−1.83917	−0.0631945
$848$	8.79427	0.301996
$849$	2.91726	0.100120
$850$	5.97728	0.205019
$851$	−74.2722	−2.54602
$852$	15.1524	0.519113
$853$	−32.7846	−1.12252	−0.561262	−	0.827638i	$-0.689684\pi$
$853$	−32.7846	−1.12252	−0.561262	+	0.827638i	$0.689684\pi$
$854$	20.1254	0.688677
$855$	38.7554	1.32541
$856$	−48.0475	−1.64223
$857$	−10.2792	−0.351131	−0.175566	−	0.984468i	$-0.556175\pi$
$857$	−10.2792	−0.351131	−0.175566	+	0.984468i	$0.556175\pi$
$858$	15.8108	0.539772
$859$	28.3672	0.967875	0.483938	−	0.875102i	$-0.339206\pi$
$859$	28.3672	0.967875	0.483938	+	0.875102i	$0.339206\pi$
$860$	2.07875	0.0708848
$861$	11.4673	0.390806
$862$	1.35300	0.0460835
$863$	40.9311	1.39331	0.696656	−	0.717405i	$-0.254670\pi$
$863$	40.9311	1.39331	0.696656	+	0.717405i	$0.254670\pi$
$864$	23.1069	0.786113
$865$	−5.76678	−0.196076
$866$	−28.5741	−0.970987
$867$	42.2814	1.43595
$868$	−0.749329	−0.0254339
$869$	−32.3640	−1.09787
$870$	−17.1990	−0.583100
$871$	1.73383	0.0587487
$872$	−17.4410	−0.590627
$873$	−59.2527	−2.00540
$874$	−77.2603	−2.61337
$875$	−1.63707	−0.0553429
$876$	−13.8408	−0.467639
$877$	17.1968	0.580695	0.290348	−	0.956921i	$-0.406229\pi$
$877$	17.1968	0.580695	0.290348	+	0.956921i	$0.406229\pi$
$878$	−11.7779	−0.397485
$879$	31.9668	1.07821
$880$	−4.99652	−0.168433
$881$	−46.3133	−1.56034	−0.780168	−	0.625571i	$-0.784866\pi$
$881$	−46.3133	−1.56034	−0.780168	+	0.625571i	$0.784866\pi$
$882$	−21.8955	−0.737261
$883$	22.7174	0.764501	0.382251	−	0.924059i	$-0.375149\pi$
$883$	22.7174	0.764501	0.382251	+	0.924059i	$0.375149\pi$
$884$	−7.75933	−0.260975
$885$	3.78430	0.127208
$886$	15.8995	0.534155
$887$	26.3777	0.885677	0.442838	−	0.896602i	$-0.353972\pi$
$887$	26.3777	0.885677	0.442838	+	0.896602i	$0.353972\pi$
$888$	−69.5452	−2.33378
$889$	21.0899	0.707333
$890$	−2.73937	−0.0918240
$891$	−1.10102	−0.0368856
$892$	−17.5227	−0.586704
$893$	59.3701	1.98674
$894$	−36.5006	−1.22076
$895$	9.76703	0.326476
$896$	1.70119	0.0568328
$897$	−39.1333	−1.30662
$898$	−32.0159	−1.06838
$899$	3.00869	0.100346
$900$	−4.26885	−0.142295
$901$	−34.7391	−1.15733
$902$	−9.20465	−0.306481
$903$	10.7061	0.356275
$904$	27.2398	0.905982
$905$	−13.2947	−0.441930
$906$	57.0001	1.89370
$907$	−28.2859	−0.939218	−0.469609	−	0.882875i	$-0.655605\pi$
$907$	−28.2859	−0.939218	−0.469609	+	0.882875i	$0.655605\pi$
$908$	23.9439	0.794606
$909$	28.5753	0.947785
$910$	−2.66057	−0.0881971
$911$	−16.8558	−0.558458	−0.279229	−	0.960224i	$-0.590079\pi$
$911$	−16.8558	−0.558458	−0.279229	+	0.960224i	$0.590079\pi$
$912$	−32.3280	−1.07049
$913$	−15.8481	−0.524494
$914$	38.8757	1.28589
$915$	−32.5747	−1.07689
$916$	−19.5431	−0.645723
$917$	14.4969	0.478731
$918$	30.1720	0.995823
$919$	−1.29982	−0.0428770	−0.0214385	−	0.999770i	$-0.506825\pi$
$919$	−1.29982	−0.0428770	−0.0214385	+	0.999770i	$0.506825\pi$
$920$	27.6745	0.912400
$921$	−37.7354	−1.24342
$922$	9.98826	0.328946
$923$	−9.41150	−0.309783
$924$	14.1443	0.465313
$925$	8.17318	0.268732
$926$	28.2779	0.929269
$927$	−67.6593	−2.22222
$928$	−26.7229	−0.877222
$929$	−39.6792	−1.30183	−0.650916	−	0.759150i	$-0.725615\pi$
$929$	−39.6792	−1.30183	−0.650916	+	0.759150i	$0.725615\pi$
$930$	−1.51844	−0.0497916
$931$	−34.8319	−1.14157
$932$	−19.9462	−0.653361
$933$	38.9027	1.27362
$934$	−10.3897	−0.339962
$935$	19.7373	0.645478
$936$	−22.5613	−0.737439
$937$	20.9516	0.684460	0.342230	−	0.939616i	$-0.388818\pi$
$937$	20.9516	0.684460	0.342230	+	0.939616i	$0.388818\pi$
$938$	−1.94188	−0.0634047
$939$	8.71460	0.284390
$940$	−6.53953	−0.213296
$941$	−53.5965	−1.74720	−0.873598	−	0.486648i	$-0.838219\pi$
$941$	−53.5965	−1.74720	−0.873598	+	0.486648i	$0.838219\pi$
$942$	−20.2639	−0.660234
$943$	22.7824	0.741897
$944$	−1.94361	−0.0632590
$945$	−8.26354	−0.268813
$946$	−8.59358	−0.279401
$947$	−29.3031	−0.952222	−0.476111	−	0.879385i	$-0.657954\pi$
$947$	−29.3031	−0.952222	−0.476111	+	0.879385i	$0.657954\pi$
$948$	23.0649	0.749113
$949$	8.59685	0.279066
$950$	8.50200	0.275841
$951$	77.4901	2.51279
$952$	28.2608	0.915937
$953$	−5.54779	−0.179711	−0.0898553	−	0.995955i	$-0.528640\pi$
$953$	−5.54779	−0.179711	−0.0898553	+	0.995955i	$0.528640\pi$
$954$	−31.0609	−1.00564
$955$	−7.08002	−0.229104
$956$	7.27388	0.235254
$957$	−56.7920	−1.83582
$958$	−12.5785	−0.406392
$959$	−15.3592	−0.495974
$960$	21.5055	0.694088
$961$	−30.7344	−0.991431
$962$	13.2831	0.428265
$963$	75.8345	2.44373
$964$	0.888118	0.0286044
$965$	6.95584	0.223917
$966$	43.8290	1.41018
$967$	37.2637	1.19832	0.599160	−	0.800629i	$-0.295501\pi$
$967$	37.2637	1.19832	0.599160	+	0.800629i	$0.295501\pi$
$968$	−3.42136	−0.109967
$969$	127.702	4.10238
$970$	−12.9986	−0.417360
$971$	−43.1081	−1.38341	−0.691703	−	0.722183i	$-0.743139\pi$
$971$	−43.1081	−1.38341	−0.691703	+	0.722183i	$0.743139\pi$
$972$	14.2337	0.456547
$973$	4.23228	0.135681
$974$	−11.4778	−0.367771
$975$	4.30637	0.137914
$976$	16.7303	0.535524
$977$	41.1995	1.31809	0.659045	−	0.752104i	$-0.270961\pi$
$977$	41.1995	1.31809	0.659045	+	0.752104i	$0.270961\pi$
$978$	64.6488	2.06724
$979$	−9.04555	−0.289097
$980$	3.83669	0.122558
$981$	27.5276	0.878888
$982$	33.6840	1.07490
$983$	13.6061	0.433967	0.216984	−	0.976175i	$-0.430378\pi$
$983$	13.6061	0.433967	0.216984	+	0.976175i	$0.430378\pi$
$984$	21.3324	0.680053
$985$	−0.690805	−0.0220109
$986$	−34.8936	−1.11124
$987$	−33.6801	−1.07205
$988$	−11.0368	−0.351127
$989$	21.2700	0.676345
$990$	17.6475	0.560874
$991$	47.5600	1.51079	0.755396	−	0.655268i	$-0.227444\pi$
$991$	47.5600	1.51079	0.755396	+	0.655268i	$0.227444\pi$
$992$	−2.35927	−0.0749069
$993$	−62.4016	−1.98025
$994$	10.5408	0.334334
$995$	22.4460	0.711587
$996$	11.2945	0.357878
$997$	−61.0129	−1.93230	−0.966149	−	0.257986i	$-0.916941\pi$
$997$	−61.0129	−1.93230	−0.966149	+	0.257986i	$0.916941\pi$
$998$	−32.5062	−1.02897
$999$	41.2564	1.30529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.e.1.16	✓	25
5.4	even	2		6025.2.a.j.1.10		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.16	✓	25	1.1	even	1	trivial
6025.2.a.j.1.10		25	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q+1.05446 q^{2} +2.79403 q^{3} -0.888118 q^{4} +1.00000 q^{5} +2.94619 q^{6} -1.63707 q^{7} -3.04540 q^{8} +4.80663 q^{9} +O(q^{10})\)	\(q+1.05446 q^{2} +2.79403 q^{3} -0.888118 q^{4} +1.00000 q^{5} +2.94619 q^{6} -1.63707 q^{7} -3.04540 q^{8} +4.80663 q^{9} +1.05446 q^{10} +3.48187 q^{11} -2.48143 q^{12} +1.54127 q^{13} -1.72622 q^{14} +2.79403 q^{15} -1.43501 q^{16} +5.66858 q^{17} +5.06839 q^{18} +8.06291 q^{19} -0.888118 q^{20} -4.57402 q^{21} +3.67149 q^{22} -9.08730 q^{23} -8.50895 q^{24} +1.00000 q^{25} +1.62521 q^{26} +5.04778 q^{27} +1.45391 q^{28} -5.83770 q^{29} +2.94619 q^{30} -0.515390 q^{31} +4.57764 q^{32} +9.72848 q^{33} +5.97728 q^{34} -1.63707 q^{35} -4.26885 q^{36} +8.17318 q^{37} +8.50200 q^{38} +4.30637 q^{39} -3.04540 q^{40} -2.50706 q^{41} -4.82311 q^{42} -2.34062 q^{43} -3.09232 q^{44} +4.80663 q^{45} -9.58218 q^{46} +7.36336 q^{47} -4.00947 q^{48} -4.32002 q^{49} +1.05446 q^{50} +15.8382 q^{51} -1.36883 q^{52} -6.12837 q^{53} +5.32267 q^{54} +3.48187 q^{55} +4.98552 q^{56} +22.5281 q^{57} -6.15561 q^{58} +1.35442 q^{59} -2.48143 q^{60} -11.6587 q^{61} -0.543457 q^{62} -7.86876 q^{63} +7.69695 q^{64} +1.54127 q^{65} +10.2583 q^{66} +1.12494 q^{67} -5.03437 q^{68} -25.3902 q^{69} -1.72622 q^{70} -6.10631 q^{71} -14.6381 q^{72} +5.57776 q^{73} +8.61827 q^{74} +2.79403 q^{75} -7.16082 q^{76} -5.70006 q^{77} +4.54089 q^{78} -9.29499 q^{79} -1.43501 q^{80} -0.316215 q^{81} -2.64359 q^{82} -4.55159 q^{83} +4.06227 q^{84} +5.66858 q^{85} -2.46809 q^{86} -16.3107 q^{87} -10.6037 q^{88} -2.59790 q^{89} +5.06839 q^{90} -2.52316 q^{91} +8.07060 q^{92} -1.44002 q^{93} +7.76435 q^{94} +8.06291 q^{95} +12.7901 q^{96} -12.3273 q^{97} -4.55528 q^{98} +16.7361 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

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