LMFDB - Embedded newform 6029.2.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$0$
Dimension:	$268$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66122 q^{2} +1.83704 q^{3} +5.08208 q^{4} -0.683386 q^{5} -4.88877 q^{6} +2.95312 q^{7} -8.20207 q^{8} +0.374729 q^{9} +O(q^{10})$	\(q-2.66122 q^{2} +1.83704 q^{3} +5.08208 q^{4} -0.683386 q^{5} -4.88877 q^{6} +2.95312 q^{7} -8.20207 q^{8} +0.374729 q^{9} +1.81864 q^{10} -0.152491 q^{11} +9.33600 q^{12} -3.53230 q^{13} -7.85888 q^{14} -1.25541 q^{15} +11.6633 q^{16} +3.13556 q^{17} -0.997236 q^{18} -5.88432 q^{19} -3.47302 q^{20} +5.42500 q^{21} +0.405811 q^{22} +6.09868 q^{23} -15.0676 q^{24} -4.53298 q^{25} +9.40021 q^{26} -4.82274 q^{27} +15.0080 q^{28} -4.89414 q^{29} +3.34092 q^{30} +6.32960 q^{31} -14.6346 q^{32} -0.280132 q^{33} -8.34441 q^{34} -2.01812 q^{35} +1.90440 q^{36} +7.93284 q^{37} +15.6594 q^{38} -6.48898 q^{39} +5.60518 q^{40} -7.45170 q^{41} -14.4371 q^{42} +8.25434 q^{43} -0.774969 q^{44} -0.256085 q^{45} -16.2299 q^{46} -3.13130 q^{47} +21.4261 q^{48} +1.72089 q^{49} +12.0633 q^{50} +5.76016 q^{51} -17.9514 q^{52} +11.2808 q^{53} +12.8343 q^{54} +0.104210 q^{55} -24.2217 q^{56} -10.8097 q^{57} +13.0244 q^{58} -3.65612 q^{59} -6.38009 q^{60} +0.380585 q^{61} -16.8444 q^{62} +1.10662 q^{63} +15.6190 q^{64} +2.41392 q^{65} +0.745492 q^{66} +3.26632 q^{67} +15.9352 q^{68} +11.2035 q^{69} +5.37065 q^{70} -12.2928 q^{71} -3.07356 q^{72} +16.3590 q^{73} -21.1110 q^{74} -8.32729 q^{75} -29.9045 q^{76} -0.450323 q^{77} +17.2686 q^{78} +16.4614 q^{79} -7.97057 q^{80} -9.98377 q^{81} +19.8306 q^{82} +1.49968 q^{83} +27.5703 q^{84} -2.14280 q^{85} -21.9666 q^{86} -8.99074 q^{87} +1.25074 q^{88} -12.2053 q^{89} +0.681497 q^{90} -10.4313 q^{91} +30.9940 q^{92} +11.6277 q^{93} +8.33306 q^{94} +4.02126 q^{95} -26.8843 q^{96} -5.13998 q^{97} -4.57967 q^{98} -0.0571427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) $ 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.66122	−1.88176	−0.940882	−	0.338734i	$-0.890001\pi$
$2$	−2.66122	−1.88176	−0.940882	+	0.338734i	$0.890001\pi$
$3$	1.83704	1.06062	0.530309	−	0.847805i	$-0.322076\pi$
$3$	1.83704	1.06062	0.530309	+	0.847805i	$0.322076\pi$
$4$	5.08208	2.54104
$5$	−0.683386	−0.305620	−0.152810	−	0.988256i	$-0.548832\pi$
$5$	−0.683386	−0.305620	−0.152810	+	0.988256i	$0.548832\pi$
$6$	−4.88877	−1.99583
$7$	2.95312	1.11617	0.558086	−	0.829783i	$-0.311536\pi$
$7$	2.95312	1.11617	0.558086	+	0.829783i	$0.311536\pi$
$8$	−8.20207	−2.89987
$9$	0.374729	0.124910
$10$	1.81864	0.575104
$11$	−0.152491	−0.0459777	−0.0229888	−	0.999736i	$-0.507318\pi$
$11$	−0.152491	−0.0459777	−0.0229888	+	0.999736i	$0.507318\pi$
$12$	9.33600	2.69507
$13$	−3.53230	−0.979683	−0.489842	−	0.871811i	$-0.662945\pi$
$13$	−3.53230	−0.979683	−0.489842	+	0.871811i	$0.662945\pi$
$14$	−7.85888	−2.10037
$15$	−1.25541	−0.324146
$16$	11.6633	2.91584
$17$	3.13556	0.760485	0.380243	−	0.924887i	$-0.375840\pi$
$17$	3.13556	0.760485	0.380243	+	0.924887i	$0.375840\pi$
$18$	−0.997236	−0.235051
$19$	−5.88432	−1.34995	−0.674977	−	0.737838i	$-0.735847\pi$
$19$	−5.88432	−1.34995	−0.674977	+	0.737838i	$0.735847\pi$
$20$	−3.47302	−0.776591
$21$	5.42500	1.18383
$22$	0.405811	0.0865192
$23$	6.09868	1.27166	0.635832	−	0.771828i	$-0.280657\pi$
$23$	6.09868	1.27166	0.635832	+	0.771828i	$0.280657\pi$
$24$	−15.0676	−3.07565
$25$	−4.53298	−0.906597
$26$	9.40021	1.84353
$27$	−4.82274	−0.928136
$28$	15.0080	2.83624
$29$	−4.89414	−0.908818	−0.454409	−	0.890793i	$-0.650150\pi$
$29$	−4.89414	−0.908818	−0.454409	+	0.890793i	$0.650150\pi$
$30$	3.34092	0.609966
$31$	6.32960	1.13683	0.568415	−	0.822742i	$-0.307557\pi$
$31$	6.32960	1.13683	0.568415	+	0.822742i	$0.307557\pi$
$32$	−14.6346	−2.58705
$33$	−0.280132	−0.0487647
$34$	−8.34441	−1.43105
$35$	−2.01812	−0.341124
$36$	1.90440	0.317400
$37$	7.93284	1.30415	0.652075	−	0.758154i	$-0.273899\pi$
$37$	7.93284	1.30415	0.652075	+	0.758154i	$0.273899\pi$
$38$	15.6594	2.54030
$39$	−6.48898	−1.03907
$40$	5.60518	0.886258
$41$	−7.45170	−1.16376	−0.581880	−	0.813274i	$-0.697683\pi$
$41$	−7.45170	−1.16376	−0.581880	+	0.813274i	$0.697683\pi$
$42$	−14.4371	−2.22769
$43$	8.25434	1.25877	0.629387	−	0.777092i	$-0.283306\pi$
$43$	8.25434	1.25877	0.629387	+	0.777092i	$0.283306\pi$
$44$	−0.774969	−0.116831
$45$	−0.256085	−0.0381749
$46$	−16.2299	−2.39297
$47$	−3.13130	−0.456747	−0.228373	−	0.973574i	$-0.573341\pi$
$47$	−3.13130	−0.456747	−0.228373	+	0.973574i	$0.573341\pi$
$48$	21.4261	3.09259
$49$	1.72089	0.245842
$50$	12.0633	1.70600
$51$	5.76016	0.806584
$52$	−17.9514	−2.48941
$53$	11.2808	1.54954	0.774770	−	0.632244i	$-0.217866\pi$
$53$	11.2808	1.54954	0.774770	+	0.632244i	$0.217866\pi$
$54$	12.8343	1.74653
$55$	0.104210	0.0140517
$56$	−24.2217	−3.23676
$57$	−10.8097	−1.43179
$58$	13.0244	1.71018
$59$	−3.65612	−0.475987	−0.237993	−	0.971267i	$-0.576490\pi$
$59$	−3.65612	−0.475987	−0.237993	+	0.971267i	$0.576490\pi$
$60$	−6.38009	−0.823666
$61$	0.380585	0.0487289	0.0243644	−	0.999703i	$-0.492244\pi$
$61$	0.380585	0.0487289	0.0243644	+	0.999703i	$0.492244\pi$
$62$	−16.8444	−2.13925
$63$	1.10662	0.139421
$64$	15.6190	1.95238
$65$	2.41392	0.299410
$66$	0.745492	0.0917638
$67$	3.26632	0.399045	0.199523	−	0.979893i	$-0.436061\pi$
$67$	3.26632	0.399045	0.199523	+	0.979893i	$0.436061\pi$
$68$	15.9352	1.93242
$69$	11.2035	1.34875
$70$	5.37065	0.641916
$71$	−12.2928	−1.45889	−0.729444	−	0.684041i	$-0.760221\pi$
$71$	−12.2928	−1.45889	−0.729444	+	0.684041i	$0.760221\pi$
$72$	−3.07356	−0.362222
$73$	16.3590	1.91468	0.957340	−	0.288965i	$-0.0933112\pi$
$73$	16.3590	1.91468	0.957340	+	0.288965i	$0.0933112\pi$
$74$	−21.1110	−2.45410
$75$	−8.32729	−0.961552
$76$	−29.9045	−3.43029
$77$	−0.450323	−0.0513190
$78$	17.2686	1.95528
$79$	16.4614	1.85206	0.926028	−	0.377454i	$-0.123200\pi$
$79$	16.4614	1.85206	0.926028	+	0.377454i	$0.123200\pi$
$80$	−7.97057	−0.891137
$81$	−9.98377	−1.10931
$82$	19.8306	2.18992
$83$	1.49968	0.164611	0.0823054	−	0.996607i	$-0.473772\pi$
$83$	1.49968	0.164611	0.0823054	+	0.996607i	$0.473772\pi$
$84$	27.5703	3.00816
$85$	−2.14280	−0.232419
$86$	−21.9666	−2.36872
$87$	−8.99074	−0.963909
$88$	1.25074	0.133329
$89$	−12.2053	−1.29376	−0.646881	−	0.762591i	$-0.723927\pi$
$89$	−12.2053	−1.29376	−0.646881	+	0.762591i	$0.723927\pi$
$90$	0.681497	0.0718361
$91$	−10.4313	−1.09350
$92$	30.9940	3.23135
$93$	11.6277	1.20574
$94$	8.33306	0.859489
$95$	4.02126	0.412573
$96$	−26.8843	−2.74387
$97$	−5.13998	−0.521886	−0.260943	−	0.965354i	$-0.584033\pi$
$97$	−5.13998	−0.521886	−0.260943	+	0.965354i	$0.584033\pi$
$98$	−4.57967	−0.462617
$99$	−0.0571427	−0.00574306
$100$	−23.0370	−2.30370
$101$	13.0099	1.29454	0.647268	−	0.762263i	$-0.275911\pi$
$101$	13.0099	1.29454	0.647268	+	0.762263i	$0.275911\pi$
$102$	−15.3290	−1.51780
$103$	17.3100	1.70560	0.852801	−	0.522236i	$-0.174902\pi$
$103$	17.3100	1.70560	0.852801	+	0.522236i	$0.174902\pi$
$104$	28.9722	2.84095
$105$	−3.70737	−0.361802
$106$	−30.0207	−2.91587
$107$	6.19480	0.598874	0.299437	−	0.954116i	$-0.403201\pi$
$107$	6.19480	0.598874	0.299437	+	0.954116i	$0.403201\pi$
$108$	−24.5095	−2.35843
$109$	12.0829	1.15733	0.578666	−	0.815565i	$-0.303574\pi$
$109$	12.0829	1.15733	0.578666	+	0.815565i	$0.303574\pi$
$110$	−0.277326	−0.0264420
$111$	14.5730	1.38320
$112$	34.4432	3.25458
$113$	−11.2433	−1.05768	−0.528839	−	0.848722i	$-0.677372\pi$
$113$	−11.2433	−1.05768	−0.528839	+	0.848722i	$0.677372\pi$
$114$	28.7671	2.69428
$115$	−4.16776	−0.388645
$116$	−24.8724	−2.30934
$117$	−1.32366	−0.122372
$118$	9.72974	0.895695
$119$	9.25968	0.848833
$120$	10.2970	0.939980
$121$	−10.9767	−0.997886
$122$	−1.01282	−0.0916963
$123$	−13.6891	−1.23431
$124$	32.1675	2.88873
$125$	6.51471	0.582693
$126$	−2.94495	−0.262357
$127$	10.6446	0.944554	0.472277	−	0.881450i	$-0.343432\pi$
$127$	10.6446	0.944554	0.472277	+	0.881450i	$0.343432\pi$
$128$	−12.2965	−1.08687
$129$	15.1636	1.33508
$130$	−6.42397	−0.563420
$131$	−5.28092	−0.461396	−0.230698	−	0.973025i	$-0.574101\pi$
$131$	−5.28092	−0.461396	−0.230698	+	0.973025i	$0.574101\pi$
$132$	−1.42365	−0.123913
$133$	−17.3771	−1.50678
$134$	−8.69240	−0.750909
$135$	3.29579	0.283657
$136$	−25.7181	−2.20531
$137$	−5.40403	−0.461698	−0.230849	−	0.972990i	$-0.574150\pi$
$137$	−5.40403	−0.461698	−0.230849	+	0.972990i	$0.574150\pi$
$138$	−29.8151	−2.53803
$139$	1.93120	0.163802	0.0819012	−	0.996640i	$-0.473901\pi$
$139$	1.93120	0.163802	0.0819012	+	0.996640i	$0.473901\pi$
$140$	−10.2562	−0.866810
$141$	−5.75233	−0.484433
$142$	32.7138	2.74528
$143$	0.538643	0.0450435
$144$	4.37060	0.364216
$145$	3.34459	0.277753
$146$	−43.5349	−3.60298
$147$	3.16136	0.260744
$148$	40.3153	3.31390
$149$	12.6361	1.03519	0.517595	−	0.855626i	$-0.326828\pi$
$149$	12.6361	1.03519	0.517595	+	0.855626i	$0.326828\pi$
$150$	22.1607	1.80942
$151$	8.08761	0.658160	0.329080	−	0.944302i	$-0.393261\pi$
$151$	8.08761	0.658160	0.329080	+	0.944302i	$0.393261\pi$
$152$	48.2636	3.91469
$153$	1.17499	0.0949920
$154$	1.19841	0.0965703
$155$	−4.32556	−0.347437
$156$	−32.9775	−2.64031
$157$	11.9193	0.951263	0.475631	−	0.879645i	$-0.342220\pi$
$157$	11.9193	0.951263	0.475631	+	0.879645i	$0.342220\pi$
$158$	−43.8075	−3.48513
$159$	20.7234	1.64347
$160$	10.0011	0.790652
$161$	18.0101	1.41940
$162$	26.5690	2.08746
$163$	−7.48098	−0.585956	−0.292978	−	0.956119i	$-0.594646\pi$
$163$	−7.48098	−0.585956	−0.292978	+	0.956119i	$0.594646\pi$
$164$	−37.8701	−2.95716
$165$	0.191438	0.0149035
$166$	−3.99096	−0.309759
$167$	9.71360	0.751661	0.375831	−	0.926688i	$-0.377357\pi$
$167$	9.71360	0.751661	0.375831	+	0.926688i	$0.377357\pi$
$168$	−44.4963	−3.43296
$169$	−0.522874	−0.0402211
$170$	5.70245	0.437358
$171$	−2.20503	−0.168623
$172$	41.9492	3.19859
$173$	17.8408	1.35641	0.678207	−	0.734871i	$-0.262757\pi$
$173$	17.8408	1.35641	0.678207	+	0.734871i	$0.262757\pi$
$174$	23.9263	1.81385
$175$	−13.3864	−1.01192
$176$	−1.77855	−0.134063
$177$	−6.71646	−0.504840
$178$	32.4810	2.43456
$179$	2.69970	0.201785	0.100892	−	0.994897i	$-0.467830\pi$
$179$	2.69970	0.201785	0.100892	+	0.994897i	$0.467830\pi$
$180$	−1.30144	−0.0970038
$181$	13.8499	1.02945	0.514726	−	0.857355i	$-0.327894\pi$
$181$	13.8499	1.02945	0.514726	+	0.857355i	$0.327894\pi$
$182$	27.7599	2.05770
$183$	0.699151	0.0516827
$184$	−50.0219	−3.68766
$185$	−5.42119	−0.398574
$186$	−30.9440	−2.26892
$187$	−0.478144	−0.0349653
$188$	−15.9135	−1.16061
$189$	−14.2421	−1.03596
$190$	−10.7014	−0.776365
$191$	24.6440	1.78318	0.891588	−	0.452848i	$-0.149592\pi$
$191$	24.6440	1.78318	0.891588	+	0.452848i	$0.149592\pi$
$192$	28.6928	2.07073
$193$	9.34097	0.672377	0.336189	−	0.941795i	$-0.390862\pi$
$193$	9.34097	0.672377	0.336189	+	0.941795i	$0.390862\pi$
$194$	13.6786	0.982067
$195$	4.43448	0.317560
$196$	8.74571	0.624694
$197$	−19.5376	−1.39200	−0.695998	−	0.718044i	$-0.745038\pi$
$197$	−19.5376	−1.39200	−0.695998	+	0.718044i	$0.745038\pi$
$198$	0.152069	0.0108071
$199$	−2.62320	−0.185954	−0.0929770	−	0.995668i	$-0.529638\pi$
$199$	−2.62320	−0.185954	−0.0929770	+	0.995668i	$0.529638\pi$
$200$	37.1799	2.62901
$201$	6.00038	0.423234
$202$	−34.6222	−2.43601
$203$	−14.4530	−1.01440
$204$	29.2736	2.04956
$205$	5.09239	0.355668
$206$	−46.0656	−3.20954
$207$	2.28536	0.158843
$208$	−41.1984	−2.85660
$209$	0.897303	0.0620678
$210$	9.86612	0.680827
$211$	20.5950	1.41782	0.708909	−	0.705300i	$-0.249188\pi$
$211$	20.5950	1.41782	0.708909	+	0.705300i	$0.249188\pi$
$212$	57.3300	3.93744
$213$	−22.5824	−1.54732
$214$	−16.4857	−1.12694
$215$	−5.64090	−0.384706
$216$	39.5564	2.69148
$217$	18.6920	1.26890
$218$	−32.1552	−2.17782
$219$	30.0522	2.03074
$220$	0.529603	0.0357059
$221$	−11.0757	−0.745035
$222$	−38.7818	−2.60287
$223$	−14.2717	−0.955706	−0.477853	−	0.878440i	$-0.658585\pi$
$223$	−14.2717	−0.955706	−0.477853	+	0.878440i	$0.658585\pi$
$224$	−43.2175	−2.88759
$225$	−1.69864	−0.113243
$226$	29.9208	1.99030
$227$	−2.50009	−0.165937	−0.0829684	−	0.996552i	$-0.526440\pi$
$227$	−2.50009	−0.165937	−0.0829684	+	0.996552i	$0.526440\pi$
$228$	−54.9360	−3.63822
$229$	24.8887	1.64469	0.822345	−	0.568989i	$-0.192665\pi$
$229$	24.8887	1.64469	0.822345	+	0.568989i	$0.192665\pi$
$230$	11.0913	0.731339
$231$	−0.827262	−0.0544299
$232$	40.1421	2.63546
$233$	−0.0563915	−0.00369433	−0.00184717	−	0.999998i	$-0.500588\pi$
$233$	−0.0563915	−0.00369433	−0.00184717	+	0.999998i	$0.500588\pi$
$234$	3.52253	0.230275
$235$	2.13988	0.139591
$236$	−18.5807	−1.20950
$237$	30.2404	1.96432
$238$	−24.6420	−1.59730
$239$	28.1999	1.82410	0.912050	−	0.410078i	$-0.134499\pi$
$239$	28.1999	1.82410	0.912050	+	0.410078i	$0.134499\pi$
$240$	−14.6423	−0.945156
$241$	28.9136	1.86249	0.931245	−	0.364393i	$-0.118724\pi$
$241$	28.9136	1.86249	0.931245	+	0.364393i	$0.118724\pi$
$242$	29.2115	1.87779
$243$	−3.87240	−0.248415
$244$	1.93416	0.123822
$245$	−1.17604	−0.0751341
$246$	36.4297	2.32267
$247$	20.7852	1.32253
$248$	−51.9158	−3.29666
$249$	2.75497	0.174589
$250$	−17.3371	−1.09649
$251$	−13.6546	−0.861868	−0.430934	−	0.902384i	$-0.641816\pi$
$251$	−13.6546	−0.861868	−0.430934	+	0.902384i	$0.641816\pi$
$252$	5.62392	0.354274
$253$	−0.929993	−0.0584681
$254$	−28.3275	−1.77743
$255$	−3.93642	−0.246508
$256$	1.48563	0.0928517
$257$	−22.9383	−1.43085	−0.715426	−	0.698689i	$-0.753767\pi$
$257$	−22.9383	−1.43085	−0.715426	+	0.698689i	$0.753767\pi$
$258$	−40.3536	−2.51230
$259$	23.4266	1.45566
$260$	12.2677	0.760813
$261$	−1.83398	−0.113520
$262$	14.0537	0.868239
$263$	−6.13372	−0.378221	−0.189111	−	0.981956i	$-0.560560\pi$
$263$	−6.13372	−0.378221	−0.189111	+	0.981956i	$0.560560\pi$
$264$	2.29766	0.141411
$265$	−7.70915	−0.473570
$266$	46.2442	2.83541
$267$	−22.4217	−1.37219
$268$	16.5997	1.01399
$269$	13.5955	0.828929	0.414465	−	0.910065i	$-0.363969\pi$
$269$	13.5955	0.828929	0.414465	+	0.910065i	$0.363969\pi$
$270$	−8.77082	−0.533775
$271$	−26.8148	−1.62888	−0.814441	−	0.580246i	$-0.802957\pi$
$271$	−26.8148	−1.62888	−0.814441	+	0.580246i	$0.802957\pi$
$272$	36.5711	2.21745
$273$	−19.1627	−1.15978
$274$	14.3813	0.868807
$275$	0.691238	0.0416832
$276$	56.9373	3.42722
$277$	−18.4714	−1.10984	−0.554920	−	0.831904i	$-0.687251\pi$
$277$	−18.4714	−1.10984	−0.554920	+	0.831904i	$0.687251\pi$
$278$	−5.13935	−0.308238
$279$	2.37189	0.142001
$280$	16.5528	0.989217
$281$	26.4525	1.57803	0.789013	−	0.614377i	$-0.210592\pi$
$281$	26.4525	1.57803	0.789013	+	0.614377i	$0.210592\pi$
$282$	15.3082	0.911590
$283$	26.4094	1.56988	0.784938	−	0.619574i	$-0.212695\pi$
$283$	26.4094	1.56988	0.784938	+	0.619574i	$0.212695\pi$
$284$	−62.4730	−3.70709
$285$	7.38723	0.437582
$286$	−1.43344	−0.0847614
$287$	−22.0057	−1.29896
$288$	−5.48399	−0.323147
$289$	−7.16825	−0.421662
$290$	−8.90067	−0.522665
$291$	−9.44237	−0.553522
$292$	83.1378	4.86527
$293$	−13.1869	−0.770385	−0.385193	−	0.922836i	$-0.625865\pi$
$293$	−13.1869	−0.770385	−0.385193	+	0.922836i	$0.625865\pi$
$294$	−8.41306	−0.490660
$295$	2.49854	0.145471
$296$	−65.0657	−3.78187
$297$	0.735423	0.0426735
$298$	−33.6274	−1.94798
$299$	−21.5424	−1.24583
$300$	−42.3199	−2.44334
$301$	24.3760	1.40501
$302$	−21.5229	−1.23850
$303$	23.8998	1.37301
$304$	−68.6308	−3.93625
$305$	−0.260086	−0.0148925
$306$	−3.12689	−0.178753
$307$	−9.26072	−0.528537	−0.264269	−	0.964449i	$-0.585131\pi$
$307$	−9.26072	−0.528537	−0.264269	+	0.964449i	$0.585131\pi$
$308$	−2.28857	−0.130404
$309$	31.7992	1.80899
$310$	11.5113	0.653795
$311$	−31.3491	−1.77765	−0.888824	−	0.458250i	$-0.848477\pi$
$311$	−31.3491	−1.77765	−0.888824	+	0.458250i	$0.848477\pi$
$312$	53.2231	3.01317
$313$	13.0099	0.735362	0.367681	−	0.929952i	$-0.380152\pi$
$313$	13.0099	0.735362	0.367681	+	0.929952i	$0.380152\pi$
$314$	−31.7198	−1.79005
$315$	−0.756248	−0.0426098
$316$	83.6583	4.70615
$317$	21.8258	1.22586	0.612929	−	0.790138i	$-0.289991\pi$
$317$	21.8258	1.22586	0.612929	+	0.790138i	$0.289991\pi$
$318$	−55.1493	−3.09262
$319$	0.746310	0.0417854
$320$	−10.6738	−0.596685
$321$	11.3801	0.635176
$322$	−47.9288	−2.67097
$323$	−18.4506	−1.02662
$324$	−50.7383	−2.81879
$325$	16.0118	0.888177
$326$	19.9085	1.10263
$327$	22.1968	1.22749
$328$	61.1194	3.37476
$329$	−9.24708	−0.509808
$330$	−0.509459	−0.0280448
$331$	3.34345	0.183773	0.0918864	−	0.995769i	$-0.470710\pi$
$331$	3.34345	0.183773	0.0918864	+	0.995769i	$0.470710\pi$
$332$	7.62147	0.418282
$333$	2.97267	0.162901
$334$	−25.8500	−1.41445
$335$	−2.23216	−0.121956
$336$	63.2737	3.45186
$337$	−1.18625	−0.0646192	−0.0323096	−	0.999478i	$-0.510286\pi$
$337$	−1.18625	−0.0646192	−0.0323096	+	0.999478i	$0.510286\pi$
$338$	1.39148	0.0756866
$339$	−20.6544	−1.12179
$340$	−10.8899	−0.590586
$341$	−0.965205	−0.0522688
$342$	5.86805	0.317308
$343$	−15.5898	−0.841771
$344$	−67.7027	−3.65028
$345$	−7.65635	−0.412204
$346$	−47.4784	−2.55245
$347$	−17.3281	−0.930219	−0.465109	−	0.885253i	$-0.653985\pi$
$347$	−17.3281	−0.930219	−0.465109	+	0.885253i	$0.653985\pi$
$348$	−45.6916	−2.44933
$349$	−6.76699	−0.362229	−0.181114	−	0.983462i	$-0.557970\pi$
$349$	−6.76699	−0.362229	−0.181114	+	0.983462i	$0.557970\pi$
$350$	35.6242	1.90419
$351$	17.0353	0.909279
$352$	2.23163	0.118946
$353$	−5.20827	−0.277208	−0.138604	−	0.990348i	$-0.544262\pi$
$353$	−5.20827	−0.277208	−0.138604	+	0.990348i	$0.544262\pi$
$354$	17.8740	0.949990
$355$	8.40073	0.445864
$356$	−62.0284	−3.28750
$357$	17.0104	0.900287
$358$	−7.18448	−0.379712
$359$	5.15561	0.272103	0.136051	−	0.990702i	$-0.456559\pi$
$359$	5.15561	0.272103	0.136051	+	0.990702i	$0.456559\pi$
$360$	2.10043	0.110702
$361$	15.6252	0.822378
$362$	−36.8575	−1.93719
$363$	−20.1648	−1.05838
$364$	−53.0126	−2.77861
$365$	−11.1795	−0.585164
$366$	−1.86059	−0.0972547
$367$	−21.8341	−1.13973	−0.569866	−	0.821737i	$-0.693005\pi$
$367$	−21.8341	−1.13973	−0.569866	+	0.821737i	$0.693005\pi$
$368$	71.1311	3.70796
$369$	−2.79237	−0.145365
$370$	14.4270	0.750022
$371$	33.3136	1.72955
$372$	59.0931	3.06383
$373$	7.91452	0.409798	0.204899	−	0.978783i	$-0.434313\pi$
$373$	7.91452	0.409798	0.204899	+	0.978783i	$0.434313\pi$
$374$	1.27244	0.0657966
$375$	11.9678	0.618015
$376$	25.6831	1.32451
$377$	17.2875	0.890354
$378$	37.9013	1.94943
$379$	−5.24827	−0.269586	−0.134793	−	0.990874i	$-0.543037\pi$
$379$	−5.24827	−0.269586	−0.134793	+	0.990874i	$0.543037\pi$
$380$	20.4364	1.04836
$381$	19.5546	1.00181
$382$	−65.5830	−3.35552
$383$	28.1143	1.43657	0.718286	−	0.695748i	$-0.244927\pi$
$383$	28.1143	1.43657	0.718286	+	0.695748i	$0.244927\pi$
$384$	−22.5892	−1.15275
$385$	0.307744	0.0156841
$386$	−24.8583	−1.26526
$387$	3.09314	0.157233
$388$	−26.1218	−1.32613
$389$	−16.8490	−0.854277	−0.427139	−	0.904186i	$-0.640478\pi$
$389$	−16.8490	−0.854277	−0.427139	+	0.904186i	$0.640478\pi$
$390$	−11.8011	−0.597573
$391$	19.1228	0.967081
$392$	−14.1149	−0.712910
$393$	−9.70128	−0.489365
$394$	51.9938	2.61941
$395$	−11.2495	−0.566025
$396$	−0.290404	−0.0145933
$397$	−6.78833	−0.340697	−0.170348	−	0.985384i	$-0.554489\pi$
$397$	−6.78833	−0.340697	−0.170348	+	0.985384i	$0.554489\pi$
$398$	6.98091	0.349922
$399$	−31.9224	−1.59812
$400$	−52.8698	−2.64349
$401$	−15.9178	−0.794895	−0.397447	−	0.917625i	$-0.630104\pi$
$401$	−15.9178	−0.794895	−0.397447	+	0.917625i	$0.630104\pi$
$402$	−15.9683	−0.796427
$403$	−22.3580	−1.11373
$404$	66.1174	3.28947
$405$	6.82277	0.339026
$406$	38.4624	1.90886
$407$	−1.20968	−0.0599618
$408$	−47.2453	−2.33899
$409$	21.7027	1.07313	0.536566	−	0.843859i	$-0.319721\pi$
$409$	21.7027	1.07313	0.536566	+	0.843859i	$0.319721\pi$
$410$	−13.5520	−0.669284
$411$	−9.92745	−0.489685
$412$	87.9706	4.33400
$413$	−10.7970	−0.531284
$414$	−6.08183	−0.298905
$415$	−1.02486	−0.0503083
$416$	51.6936	2.53449
$417$	3.54770	0.173732
$418$	−2.38792	−0.116797
$419$	13.8890	0.678520	0.339260	−	0.940693i	$-0.389823\pi$
$419$	13.8890	0.678520	0.339260	+	0.940693i	$0.389823\pi$
$420$	−18.8411	−0.919354
$421$	−22.4155	−1.09247	−0.546233	−	0.837633i	$-0.683939\pi$
$421$	−22.4155	−1.09247	−0.546233	+	0.837633i	$0.683939\pi$
$422$	−54.8078	−2.66800
$423$	−1.17339	−0.0570521
$424$	−92.5261	−4.49346
$425$	−14.2134	−0.689453
$426$	60.0967	2.91169
$427$	1.12391	0.0543898
$428$	31.4825	1.52176
$429$	0.989510	0.0477740
$430$	15.0117	0.723927
$431$	−15.9690	−0.769200	−0.384600	−	0.923083i	$-0.625661\pi$
$431$	−15.9690	−0.769200	−0.384600	+	0.923083i	$0.625661\pi$
$432$	−56.2493	−2.70629
$433$	−1.37672	−0.0661610	−0.0330805	−	0.999453i	$-0.510532\pi$
$433$	−1.37672	−0.0661610	−0.0330805	+	0.999453i	$0.510532\pi$
$434$	−49.7436	−2.38777
$435$	6.14415	0.294589
$436$	61.4062	2.94082
$437$	−35.8866	−1.71669
$438$	−79.9755	−3.82138
$439$	−32.2197	−1.53776	−0.768882	−	0.639390i	$-0.779187\pi$
$439$	−32.2197	−1.53776	−0.768882	+	0.639390i	$0.779187\pi$
$440$	−0.854739	−0.0407481
$441$	0.644869	0.0307081
$442$	29.4749	1.40198
$443$	−15.8622	−0.753634	−0.376817	−	0.926288i	$-0.622981\pi$
$443$	−15.8622	−0.753634	−0.376817	+	0.926288i	$0.622981\pi$
$444$	74.0609	3.51478
$445$	8.34096	0.395399
$446$	37.9802	1.79841
$447$	23.2131	1.09794
$448$	46.1248	2.17919
$449$	−5.95821	−0.281185	−0.140593	−	0.990068i	$-0.544901\pi$
$449$	−5.95821	−0.281185	−0.140593	+	0.990068i	$0.544901\pi$
$450$	4.52045	0.213096
$451$	1.13632	0.0535070
$452$	−57.1391	−2.68760
$453$	14.8573	0.698056
$454$	6.65328	0.312254
$455$	7.12860	0.334194
$456$	88.6623	4.15199
$457$	−4.86062	−0.227370	−0.113685	−	0.993517i	$-0.536265\pi$
$457$	−4.86062	−0.227370	−0.113685	+	0.993517i	$0.536265\pi$
$458$	−66.2342	−3.09492
$459$	−15.1220	−0.705834
$460$	−21.1809	−0.987563
$461$	−27.7079	−1.29049	−0.645244	−	0.763977i	$-0.723244\pi$
$461$	−27.7079	−1.29049	−0.645244	+	0.763977i	$0.723244\pi$
$462$	2.20153	0.102424
$463$	−21.9254	−1.01896	−0.509480	−	0.860483i	$-0.670162\pi$
$463$	−21.9254	−1.01896	−0.509480	+	0.860483i	$0.670162\pi$
$464$	−57.0820	−2.64997
$465$	−7.94624	−0.368498
$466$	0.150070	0.00695186
$467$	18.6344	0.862299	0.431149	−	0.902281i	$-0.358108\pi$
$467$	18.6344	0.862299	0.431149	+	0.902281i	$0.358108\pi$
$468$	−6.72692	−0.310952
$469$	9.64583	0.445403
$470$	−5.69470	−0.262677
$471$	21.8963	1.00893
$472$	29.9878	1.38030
$473$	−1.25871	−0.0578755
$474$	−80.4762	−3.69640
$475$	26.6735	1.22386
$476$	47.0584	2.15692
$477$	4.22725	0.193553
$478$	−75.0461	−3.43253
$479$	9.23657	0.422030	0.211015	−	0.977483i	$-0.432323\pi$
$479$	9.23657	0.422030	0.211015	+	0.977483i	$0.432323\pi$
$480$	18.3724	0.838580
$481$	−28.0211	−1.27765
$482$	−76.9454	−3.50477
$483$	33.0854	1.50544
$484$	−55.7847	−2.53567
$485$	3.51259	0.159499
$486$	10.3053	0.467458
$487$	−10.6949	−0.484630	−0.242315	−	0.970198i	$-0.577907\pi$
$487$	−10.6949	−0.484630	−0.242315	+	0.970198i	$0.577907\pi$
$488$	−3.12158	−0.141307
$489$	−13.7429	−0.621475
$490$	3.12969	0.141385
$491$	−29.9064	−1.34965	−0.674827	−	0.737976i	$-0.735782\pi$
$491$	−29.9064	−1.34965	−0.674827	+	0.737976i	$0.735782\pi$
$492$	−69.5691	−3.13642
$493$	−15.3459	−0.691143
$494$	−55.3138	−2.48869
$495$	0.0390506	0.00175519
$496$	73.8243	3.31481
$497$	−36.3021	−1.62837
$498$	−7.33157	−0.328536
$499$	18.0398	0.807571	0.403785	−	0.914854i	$-0.367694\pi$
$499$	18.0398	0.807571	0.403785	+	0.914854i	$0.367694\pi$
$500$	33.1083	1.48065
$501$	17.8443	0.797225
$502$	36.3377	1.62183
$503$	12.9041	0.575367	0.287684	−	0.957725i	$-0.407115\pi$
$503$	12.9041	0.575367	0.287684	+	0.957725i	$0.407115\pi$
$504$	−9.07657	−0.404303
$505$	−8.89080	−0.395636
$506$	2.47491	0.110023
$507$	−0.960543	−0.0426592
$508$	54.0966	2.40015
$509$	16.0152	0.709860	0.354930	−	0.934893i	$-0.384505\pi$
$509$	16.0152	0.709860	0.354930	+	0.934893i	$0.384505\pi$
$510$	10.4757	0.463870
$511$	48.3101	2.13711
$512$	20.6394	0.912143
$513$	28.3785	1.25294
$514$	61.0438	2.69252
$515$	−11.8294	−0.521265
$516$	77.0625	3.39249
$517$	0.477494	0.0210001
$518$	−62.3432	−2.73920
$519$	32.7744	1.43864
$520$	−19.7992	−0.868251
$521$	1.45764	0.0638605	0.0319302	−	0.999490i	$-0.489835\pi$
$521$	1.45764	0.0638605	0.0319302	+	0.999490i	$0.489835\pi$
$522$	4.88061	0.213618
$523$	4.66912	0.204166	0.102083	−	0.994776i	$-0.467449\pi$
$523$	4.66912	0.204166	0.102083	+	0.994776i	$0.467449\pi$
$524$	−26.8380	−1.17242
$525$	−24.5914	−1.07326
$526$	16.3232	0.711723
$527$	19.8468	0.864542
$528$	−3.26728	−0.142190
$529$	14.1939	0.617128
$530$	20.5157	0.891146
$531$	−1.37006	−0.0594554
$532$	−88.3116	−3.82879
$533$	26.3216	1.14012
$534$	59.6691	2.58213
$535$	−4.23344	−0.183028
$536$	−26.7906	−1.15718
$537$	4.95946	0.214017
$538$	−36.1804	−1.55985
$539$	−0.262420	−0.0113032
$540$	16.7495	0.720782
$541$	−28.7282	−1.23512	−0.617560	−	0.786524i	$-0.711879\pi$
$541$	−28.7282	−1.23512	−0.617560	+	0.786524i	$0.711879\pi$
$542$	71.3600	3.06517
$543$	25.4428	1.09185
$544$	−45.8875	−1.96741
$545$	−8.25728	−0.353703
$546$	50.9962	2.18243
$547$	27.2258	1.16409	0.582046	−	0.813156i	$-0.302252\pi$
$547$	27.2258	1.16409	0.582046	+	0.813156i	$0.302252\pi$
$548$	−27.4637	−1.17319
$549$	0.142616	0.00608671
$550$	−1.83953	−0.0784380
$551$	28.7986	1.22686
$552$	−91.8923	−3.91120
$553$	48.6125	2.06722
$554$	49.1564	2.08846
$555$	−9.95896	−0.422735
$556$	9.81452	0.416228
$557$	25.1286	1.06473	0.532367	−	0.846514i	$-0.321303\pi$
$557$	25.1286	1.06473	0.532367	+	0.846514i	$0.321303\pi$
$558$	−6.31210	−0.267213
$559$	−29.1568	−1.23320
$560$	−23.5380	−0.994663
$561$	−0.878371	−0.0370849
$562$	−70.3959	−2.96947
$563$	−31.1219	−1.31163	−0.655816	−	0.754921i	$-0.727675\pi$
$563$	−31.1219	−1.31163	−0.655816	+	0.754921i	$0.727675\pi$
$564$	−29.2338	−1.23096
$565$	7.68349	0.323247
$566$	−70.2812	−2.95414
$567$	−29.4832	−1.23818
$568$	100.826	4.23058
$569$	5.54739	0.232559	0.116279	−	0.993217i	$-0.462903\pi$
$569$	5.54739	0.232559	0.116279	+	0.993217i	$0.462903\pi$
$570$	−19.6590	−0.823426
$571$	−34.6104	−1.44840	−0.724200	−	0.689590i	$-0.757791\pi$
$571$	−34.6104	−1.44840	−0.724200	+	0.689590i	$0.757791\pi$
$572$	2.73742	0.114457
$573$	45.2721	1.89127
$574$	58.5621	2.44433
$575$	−27.6452	−1.15289
$576$	5.85290	0.243871
$577$	39.5516	1.64655	0.823277	−	0.567640i	$-0.192144\pi$
$577$	39.5516	1.64655	0.823277	+	0.567640i	$0.192144\pi$
$578$	19.0763	0.793469
$579$	17.1598	0.713135
$580$	16.9974	0.705780
$581$	4.42872	0.183734
$582$	25.1282	1.04160
$583$	−1.72022	−0.0712442
$584$	−134.178	−5.55232
$585$	0.904568	0.0373993
$586$	35.0931	1.44968
$587$	−21.9205	−0.904756	−0.452378	−	0.891826i	$-0.649424\pi$
$587$	−21.9205	−0.904756	−0.452378	+	0.891826i	$0.649424\pi$
$588$	16.0663	0.662561
$589$	−37.2454	−1.53467
$590$	−6.64917	−0.273742
$591$	−35.8914	−1.47637
$592$	92.5234	3.80269
$593$	31.2643	1.28387	0.641935	−	0.766759i	$-0.278132\pi$
$593$	31.2643	1.28387	0.641935	+	0.766759i	$0.278132\pi$
$594$	−1.95712	−0.0803016
$595$	−6.32794	−0.259420
$596$	64.2176	2.63046
$597$	−4.81894	−0.197226
$598$	57.3289	2.34435
$599$	26.5745	1.08581	0.542903	−	0.839795i	$-0.317325\pi$
$599$	26.5745	1.08581	0.542903	+	0.839795i	$0.317325\pi$
$600$	68.3010	2.78838
$601$	45.8709	1.87111	0.935556	−	0.353177i	$-0.114899\pi$
$601$	45.8709	1.87111	0.935556	+	0.353177i	$0.114899\pi$
$602$	−64.8699	−2.64390
$603$	1.22399	0.0498446
$604$	41.1018	1.67241
$605$	7.50136	0.304974
$606$	−63.6026	−2.58368
$607$	5.85697	0.237727	0.118864	−	0.992911i	$-0.462075\pi$
$607$	5.85697	0.237727	0.118864	+	0.992911i	$0.462075\pi$
$608$	86.1143	3.49240
$609$	−26.5507	−1.07589
$610$	0.692146	0.0280242
$611$	11.0607	0.447467
$612$	5.97137	0.241378
$613$	15.5194	0.626821	0.313410	−	0.949618i	$-0.398528\pi$
$613$	15.5194	0.626821	0.313410	+	0.949618i	$0.398528\pi$
$614$	24.6448	0.994583
$615$	9.35495	0.377228
$616$	3.69358	0.148819
$617$	10.2176	0.411344	0.205672	−	0.978621i	$-0.434062\pi$
$617$	10.2176	0.411344	0.205672	+	0.978621i	$0.434062\pi$
$618$	−84.6245	−3.40410
$619$	−23.4614	−0.942991	−0.471496	−	0.881868i	$-0.656286\pi$
$619$	−23.4614	−0.942991	−0.471496	+	0.881868i	$0.656286\pi$
$620$	−21.9828	−0.882852
$621$	−29.4123	−1.18028
$622$	83.4269	3.34511
$623$	−36.0438	−1.44406
$624$	−75.6833	−3.02976
$625$	18.2129	0.728514
$626$	−34.6221	−1.38378
$627$	1.64839	0.0658302
$628$	60.5747	2.41719
$629$	24.8739	0.991787
$630$	2.01254	0.0801815
$631$	−8.07584	−0.321494	−0.160747	−	0.986996i	$-0.551390\pi$
$631$	−8.07584	−0.321494	−0.160747	+	0.986996i	$0.551390\pi$
$632$	−135.018	−5.37073
$633$	37.8339	1.50376
$634$	−58.0831	−2.30678
$635$	−7.27436	−0.288674
$636$	105.318	4.17612
$637$	−6.07871	−0.240847
$638$	−1.98609	−0.0786302
$639$	−4.60647	−0.182229
$640$	8.40326	0.332168
$641$	9.09809	0.359353	0.179677	−	0.983726i	$-0.442495\pi$
$641$	9.09809	0.359353	0.179677	+	0.983726i	$0.442495\pi$
$642$	−30.2850	−1.19525
$643$	−26.9354	−1.06223	−0.531114	−	0.847300i	$-0.678226\pi$
$643$	−26.9354	−1.06223	−0.531114	+	0.847300i	$0.678226\pi$
$644$	91.5288	3.60674
$645$	−10.3626	−0.408026
$646$	49.1011	1.93186
$647$	3.63714	0.142991	0.0714955	−	0.997441i	$-0.477223\pi$
$647$	3.63714	0.142991	0.0714955	+	0.997441i	$0.477223\pi$
$648$	81.8876	3.21685
$649$	0.557525	0.0218848
$650$	−42.6110	−1.67134
$651$	34.3381	1.34582
$652$	−38.0189	−1.48894
$653$	40.5071	1.58516	0.792582	−	0.609765i	$-0.208736\pi$
$653$	40.5071	1.58516	0.792582	+	0.609765i	$0.208736\pi$
$654$	−59.0705	−2.30984
$655$	3.60891	0.141012
$656$	−86.9118	−3.39334
$657$	6.13021	0.239162
$658$	24.6085	0.959339
$659$	−2.13536	−0.0831817	−0.0415909	−	0.999135i	$-0.513243\pi$
$659$	−2.13536	−0.0831817	−0.0415909	+	0.999135i	$0.513243\pi$
$660$	0.972905	0.0378703
$661$	−30.1213	−1.17158	−0.585791	−	0.810462i	$-0.699216\pi$
$661$	−30.1213	−1.17158	−0.585791	+	0.810462i	$0.699216\pi$
$662$	−8.89766	−0.345817
$663$	−20.3466	−0.790197
$664$	−12.3005	−0.477350
$665$	11.8752	0.460502
$666$	−7.91091	−0.306542
$667$	−29.8478	−1.15571
$668$	49.3653	1.91000
$669$	−26.2178	−1.01364
$670$	5.94027	0.229492
$671$	−0.0580356	−0.00224044
$672$	−79.3925	−3.06263
$673$	−44.1377	−1.70138	−0.850691	−	0.525666i	$-0.823816\pi$
$673$	−44.1377	−1.70138	−0.850691	+	0.525666i	$0.823816\pi$
$674$	3.15687	0.121598
$675$	21.8614	0.841445
$676$	−2.65729	−0.102203
$677$	40.9331	1.57319	0.786593	−	0.617471i	$-0.211843\pi$
$677$	40.9331	1.57319	0.786593	+	0.617471i	$0.211843\pi$
$678$	54.9657	2.11095
$679$	−15.1790	−0.582515
$680$	17.5754	0.673986
$681$	−4.59277	−0.175995
$682$	2.56862	0.0983575
$683$	46.0681	1.76275	0.881373	−	0.472420i	$-0.156619\pi$
$683$	46.0681	1.76275	0.881373	+	0.472420i	$0.156619\pi$
$684$	−11.2061	−0.428476
$685$	3.69304	0.141104
$686$	41.4879	1.58401
$687$	45.7216	1.74439
$688$	96.2732	3.67038
$689$	−39.8472	−1.51806
$690$	20.3752	0.775671
$691$	29.2123	1.11129	0.555644	−	0.831420i	$-0.312472\pi$
$691$	29.2123	1.11129	0.555644	+	0.831420i	$0.312472\pi$
$692$	90.6685	3.44670
$693$	−0.168749	−0.00641025
$694$	46.1137	1.75045
$695$	−1.31976	−0.0500612
$696$	73.7427	2.79521
$697$	−23.3653	−0.885023
$698$	18.0084	0.681629
$699$	−0.103594	−0.00391827
$700$	−68.0308	−2.57132
$701$	20.2033	0.763068	0.381534	−	0.924355i	$-0.375396\pi$
$701$	20.2033	0.763068	0.381534	+	0.924355i	$0.375396\pi$
$702$	−45.3347	−1.71105
$703$	−46.6793	−1.76054
$704$	−2.38176	−0.0897658
$705$	3.93106	0.148052
$706$	13.8603	0.521641
$707$	38.4198	1.44493
$708$	−34.1336	−1.28282
$709$	−28.3759	−1.06568	−0.532840	−	0.846216i	$-0.678875\pi$
$709$	−28.3759	−1.06568	−0.532840	+	0.846216i	$0.678875\pi$
$710$	−22.3562	−0.839012
$711$	6.16858	0.231340
$712$	100.109	3.75175
$713$	38.6022	1.44566
$714$	−45.2684	−1.69413
$715$	−0.368101	−0.0137662
$716$	13.7201	0.512743
$717$	51.8045	1.93467
$718$	−13.7202	−0.512033
$719$	17.3101	0.645558	0.322779	−	0.946474i	$-0.395383\pi$
$719$	17.3101	0.645558	0.322779	+	0.946474i	$0.395383\pi$
$720$	−2.98681	−0.111312
$721$	51.1184	1.90375
$722$	−41.5820	−1.54752
$723$	53.1156	1.97539
$724$	70.3860	2.61588
$725$	22.1850	0.823932
$726$	53.6628	1.99161
$727$	50.8090	1.88440	0.942201	−	0.335049i	$-0.108753\pi$
$727$	50.8090	1.88440	0.942201	+	0.335049i	$0.108753\pi$
$728$	85.5582	3.17100
$729$	22.8375	0.845834
$730$	29.7512	1.10114
$731$	25.8820	0.957280
$732$	3.55314	0.131328
$733$	15.7916	0.583277	0.291638	−	0.956529i	$-0.405800\pi$
$733$	15.7916	0.583277	0.291638	+	0.956529i	$0.405800\pi$
$734$	58.1054	2.14471
$735$	−2.16043	−0.0796886
$736$	−89.2515	−3.28985
$737$	−0.498084	−0.0183472
$738$	7.43111	0.273543
$739$	13.1800	0.484835	0.242417	−	0.970172i	$-0.422060\pi$
$739$	13.1800	0.484835	0.242417	+	0.970172i	$0.422060\pi$
$740$	−27.5509	−1.01279
$741$	38.1832	1.40270
$742$	−88.6546	−3.25461
$743$	31.0633	1.13960	0.569800	−	0.821783i	$-0.307021\pi$
$743$	31.0633	1.13960	0.569800	+	0.821783i	$0.307021\pi$
$744$	−95.3716	−3.49649
$745$	−8.63533	−0.316374
$746$	−21.0623	−0.771144
$747$	0.561972	0.0205615
$748$	−2.42996	−0.0888483
$749$	18.2940	0.668447
$750$	−31.8489	−1.16296
$751$	−0.844484	−0.0308157	−0.0154078	−	0.999881i	$-0.504905\pi$
$751$	−0.844484	−0.0308157	−0.0154078	+	0.999881i	$0.504905\pi$
$752$	−36.5214	−1.33180
$753$	−25.0840	−0.914112
$754$	−46.0059	−1.67544
$755$	−5.52696	−0.201147
$756$	−72.3794	−2.63241
$757$	−41.7701	−1.51816	−0.759080	−	0.650998i	$-0.774351\pi$
$757$	−41.7701	−1.51816	−0.759080	+	0.650998i	$0.774351\pi$
$758$	13.9668	0.507297
$759$	−1.70844	−0.0620123
$760$	−32.9827	−1.19641
$761$	−25.6012	−0.928042	−0.464021	−	0.885824i	$-0.653594\pi$
$761$	−25.6012	−0.928042	−0.464021	+	0.885824i	$0.653594\pi$
$762$	−52.0389	−1.88517
$763$	35.6822	1.29178
$764$	125.243	4.53112
$765$	−0.802970	−0.0290314
$766$	−74.8181	−2.70329
$767$	12.9145	0.466316
$768$	2.72916	0.0984802
$769$	−13.4234	−0.484059	−0.242029	−	0.970269i	$-0.577813\pi$
$769$	−13.4234	−0.484059	−0.242029	+	0.970269i	$0.577813\pi$
$770$	−0.818975	−0.0295138
$771$	−42.1386	−1.51759
$772$	47.4715	1.70854
$773$	−29.4411	−1.05892	−0.529461	−	0.848334i	$-0.677606\pi$
$773$	−29.4411	−1.05892	−0.529461	+	0.848334i	$0.677606\pi$
$774$	−8.23152	−0.295876
$775$	−28.6920	−1.03065
$776$	42.1585	1.51340
$777$	43.0357	1.54390
$778$	44.8388	1.60755
$779$	43.8482	1.57102
$780$	22.5364	0.806932
$781$	1.87454	0.0670762
$782$	−50.8899	−1.81982
$783$	23.6031	0.843507
$784$	20.0714	0.716835
$785$	−8.14548	−0.290725
$786$	25.8172	0.920869
$787$	−32.4326	−1.15610	−0.578048	−	0.816003i	$-0.696185\pi$
$787$	−32.4326	−1.15610	−0.578048	+	0.816003i	$0.696185\pi$
$788$	−99.2915	−3.53711
$789$	−11.2679	−0.401148
$790$	29.9374	1.06513
$791$	−33.2027	−1.18055
$792$	0.468689	0.0166541
$793$	−1.34434	−0.0477389
$794$	18.0652	0.641111
$795$	−14.1621	−0.502276
$796$	−13.3313	−0.472516
$797$	−49.9646	−1.76984	−0.884918	−	0.465747i	$-0.845786\pi$
$797$	−49.9646	−1.76984	−0.884918	+	0.465747i	$0.845786\pi$
$798$	84.9525	3.00729
$799$	−9.81837	−0.347349
$800$	66.3382	2.34541
$801$	−4.57370	−0.161604
$802$	42.3606	1.49580
$803$	−2.49460	−0.0880325
$804$	30.4944	1.07545
$805$	−12.3079	−0.433795
$806$	59.4995	2.09578
$807$	24.9754	0.879177
$808$	−106.708	−3.75399
$809$	44.1041	1.55062	0.775308	−	0.631583i	$-0.217594\pi$
$809$	44.1041	1.55062	0.775308	+	0.631583i	$0.217594\pi$
$810$	−18.1569	−0.637967
$811$	49.9012	1.75227	0.876135	−	0.482067i	$-0.160114\pi$
$811$	49.9012	1.75227	0.876135	+	0.482067i	$0.160114\pi$
$812$	−73.4510	−2.57762
$813$	−49.2600	−1.72762
$814$	3.21923	0.112834
$815$	5.11240	0.179080
$816$	67.1828	2.35187
$817$	−48.5711	−1.69929
$818$	−57.7557	−2.01938
$819$	−3.90891	−0.136588
$820$	25.8799	0.903766
$821$	−2.45987	−0.0858501	−0.0429251	−	0.999078i	$-0.513668\pi$
$821$	−2.45987	−0.0858501	−0.0429251	+	0.999078i	$0.513668\pi$
$822$	26.4191	0.921472
$823$	−51.1669	−1.78357	−0.891783	−	0.452462i	$-0.850546\pi$
$823$	−51.1669	−1.78357	−0.891783	+	0.452462i	$0.850546\pi$
$824$	−141.978	−4.94603
$825$	1.26983	0.0442099
$826$	28.7331	0.999751
$827$	42.2431	1.46894	0.734468	−	0.678643i	$-0.237432\pi$
$827$	42.2431	1.46894	0.734468	+	0.678643i	$0.237432\pi$
$828$	11.6144	0.403627
$829$	48.0879	1.67016	0.835082	−	0.550126i	$-0.185420\pi$
$829$	48.0879	1.67016	0.835082	+	0.550126i	$0.185420\pi$
$830$	2.72737	0.0946684
$831$	−33.9328	−1.17712
$832$	−55.1710	−1.91271
$833$	5.39597	0.186959
$834$	−9.44121	−0.326922
$835$	−6.63814	−0.229722
$836$	4.56016	0.157717
$837$	−30.5260	−1.05513
$838$	−36.9615	−1.27682
$839$	19.1779	0.662095	0.331047	−	0.943614i	$-0.392598\pi$
$839$	19.1779	0.662095	0.331047	+	0.943614i	$0.392598\pi$
$840$	30.4081	1.04918
$841$	−5.04743	−0.174049
$842$	59.6526	2.05577
$843$	48.5945	1.67368
$844$	104.665	3.60273
$845$	0.357325	0.0122924
$846$	3.12264	0.107359
$847$	−32.4156	−1.11381
$848$	131.572	4.51820
$849$	48.5153	1.66504
$850$	37.8251	1.29739
$851$	48.3799	1.65844
$852$	−114.766	−3.93180
$853$	6.89532	0.236091	0.118046	−	0.993008i	$-0.462337\pi$
$853$	6.89532	0.236091	0.118046	+	0.993008i	$0.462337\pi$
$854$	−2.99097	−0.102349
$855$	1.50688	0.0515344
$856$	−50.8102	−1.73666
$857$	26.4121	0.902221	0.451110	−	0.892468i	$-0.351028\pi$
$857$	26.4121	0.902221	0.451110	+	0.892468i	$0.351028\pi$
$858$	−2.63330	−0.0898994
$859$	−30.7017	−1.04753	−0.523764	−	0.851863i	$-0.675473\pi$
$859$	−30.7017	−1.04753	−0.523764	+	0.851863i	$0.675473\pi$
$860$	−28.6675	−0.977553
$861$	−40.4255	−1.37770
$862$	42.4970	1.44745
$863$	−4.70732	−0.160239	−0.0801195	−	0.996785i	$-0.525530\pi$
$863$	−4.70732	−0.160239	−0.0801195	+	0.996785i	$0.525530\pi$
$864$	70.5786	2.40113
$865$	−12.1922	−0.414547
$866$	3.66375	0.124499
$867$	−13.1684	−0.447222
$868$	94.9944	3.22432
$869$	−2.51022	−0.0851533
$870$	−16.3509	−0.554348
$871$	−11.5376	−0.390938
$872$	−99.1048	−3.35611
$873$	−1.92610	−0.0651887
$874$	95.5020	3.23040
$875$	19.2387	0.650387
$876$	152.728	5.16019
$877$	44.7751	1.51195	0.755974	−	0.654602i	$-0.227164\pi$
$877$	44.7751	1.51195	0.755974	+	0.654602i	$0.227164\pi$
$878$	85.7437	2.89371
$879$	−24.2249	−0.817084
$880$	1.21544	0.0409724
$881$	7.01158	0.236226	0.118113	−	0.993000i	$-0.462315\pi$
$881$	7.01158	0.236226	0.118113	+	0.993000i	$0.462315\pi$
$882$	−1.71614	−0.0577854
$883$	20.5843	0.692716	0.346358	−	0.938102i	$-0.387418\pi$
$883$	20.5843	0.692716	0.346358	+	0.938102i	$0.387418\pi$
$884$	−56.2877	−1.89316
$885$	4.58994	0.154289
$886$	42.2127	1.41816
$887$	31.7956	1.06759	0.533797	−	0.845613i	$-0.320765\pi$
$887$	31.7956	1.06759	0.533797	+	0.845613i	$0.320765\pi$
$888$	−119.529	−4.01112
$889$	31.4347	1.05429
$890$	−22.1971	−0.744048
$891$	1.52243	0.0510034
$892$	−72.5300	−2.42849
$893$	18.4255	0.616587
$894$	−61.7750	−2.06606
$895$	−1.84494	−0.0616694
$896$	−36.3130	−1.21313
$897$	−39.5743	−1.32135
$898$	15.8561	0.529125
$899$	−30.9779	−1.03317
$900$	−8.63263	−0.287754
$901$	35.3717	1.17840
$902$	−3.02398	−0.100688
$903$	44.7798	1.49018
$904$	92.2181	3.06713
$905$	−9.46480	−0.314621
$906$	−39.5385	−1.31358
$907$	5.26219	0.174728	0.0873640	−	0.996176i	$-0.472156\pi$
$907$	5.26219	0.174728	0.0873640	+	0.996176i	$0.472156\pi$
$908$	−12.7056	−0.421652
$909$	4.87520	0.161700
$910$	−18.9707	−0.628874
$911$	12.4307	0.411848	0.205924	−	0.978568i	$-0.433980\pi$
$911$	12.4307	0.411848	0.205924	+	0.978568i	$0.433980\pi$
$912$	−126.078	−4.17485
$913$	−0.228687	−0.00756842
$914$	12.9352	0.427857
$915$	−0.477790	−0.0157952
$916$	126.486	4.17922
$917$	−15.5952	−0.514998
$918$	40.2429	1.32821
$919$	−28.6276	−0.944336	−0.472168	−	0.881509i	$-0.656528\pi$
$919$	−28.6276	−0.944336	−0.472168	+	0.881509i	$0.656528\pi$
$920$	34.1842	1.12702
$921$	−17.0123	−0.560576
$922$	73.7368	2.42839
$923$	43.4218	1.42925
$924$	−4.20421	−0.138308
$925$	−35.9594	−1.18234
$926$	58.3483	1.91744
$927$	6.48655	0.213046
$928$	71.6235	2.35116
$929$	55.1002	1.80778	0.903889	−	0.427767i	$-0.140699\pi$
$929$	55.1002	1.80778	0.903889	+	0.427767i	$0.140699\pi$
$930$	21.1467	0.693427
$931$	−10.1263	−0.331876
$932$	−0.286586	−0.00938743
$933$	−57.5898	−1.88540
$934$	−49.5903	−1.62264
$935$	0.326757	0.0106861
$936$	10.8567	0.354863
$937$	−8.81420	−0.287947	−0.143974	−	0.989582i	$-0.545988\pi$
$937$	−8.81420	−0.287947	−0.143974	+	0.989582i	$0.545988\pi$
$938$	−25.6697	−0.838144
$939$	23.8997	0.779938
$940$	10.8751	0.354705
$941$	37.8522	1.23395	0.616973	−	0.786985i	$-0.288359\pi$
$941$	37.8522	1.23395	0.616973	+	0.786985i	$0.288359\pi$
$942$	−58.2707	−1.89856
$943$	−45.4456	−1.47991
$944$	−42.6426	−1.38790
$945$	9.73286	0.316610
$946$	3.34970	0.108908
$947$	−57.0976	−1.85542	−0.927712	−	0.373297i	$-0.878227\pi$
$947$	−57.0976	−1.85542	−0.927712	+	0.373297i	$0.878227\pi$
$948$	153.684	4.99142
$949$	−57.7849	−1.87578
$950$	−70.9840	−2.30302
$951$	40.0949	1.30017
$952$	−75.9486	−2.46151
$953$	−56.5475	−1.83175	−0.915876	−	0.401461i	$-0.868503\pi$
$953$	−56.5475	−1.83175	−0.915876	+	0.401461i	$0.868503\pi$
$954$	−11.2496	−0.364220
$955$	−16.8414	−0.544973
$956$	143.314	4.63511
$957$	1.37100	0.0443183
$958$	−24.5805	−0.794160
$959$	−15.9587	−0.515335
$960$	−19.6083	−0.632855
$961$	9.06380	0.292381
$962$	74.5703	2.40424
$963$	2.32137	0.0748052
$964$	146.941	4.73266
$965$	−6.38349	−0.205492
$966$	−88.0474	−2.83288
$967$	−5.54389	−0.178279	−0.0891397	−	0.996019i	$-0.528412\pi$
$967$	−5.54389	−0.178279	−0.0891397	+	0.996019i	$0.528412\pi$
$968$	90.0321	2.89374
$969$	−33.8946	−1.08885
$970$	−9.34777	−0.300139
$971$	−19.2618	−0.618140	−0.309070	−	0.951039i	$-0.600018\pi$
$971$	−19.2618	−0.618140	−0.309070	+	0.951039i	$0.600018\pi$
$972$	−19.6798	−0.631231
$973$	5.70306	0.182832
$974$	28.4613	0.911960
$975$	29.4145	0.942017
$976$	4.43889	0.142085
$977$	−3.24011	−0.103660	−0.0518301	−	0.998656i	$-0.516505\pi$
$977$	−3.24011	−0.103660	−0.0518301	+	0.998656i	$0.516505\pi$
$978$	36.5728	1.16947
$979$	1.86120	0.0594842
$980$	−5.97670	−0.190919
$981$	4.52781	0.144562
$982$	79.5873	2.53973
$983$	0.174291	0.00555901	0.00277951	−	0.999996i	$-0.499115\pi$
$983$	0.174291	0.00555901	0.00277951	+	0.999996i	$0.499115\pi$
$984$	112.279	3.57933
$985$	13.3517	0.425421
$986$	40.8387	1.30057
$987$	−16.9873	−0.540711
$988$	105.632	3.36059
$989$	50.3406	1.60074
$990$	−0.103922	−0.00330286
$991$	32.7984	1.04188	0.520938	−	0.853594i	$-0.325582\pi$
$991$	32.7984	1.04188	0.520938	+	0.853594i	$0.325582\pi$
$992$	−92.6308	−2.94103
$993$	6.14207	0.194913
$994$	96.6077	3.06421
$995$	1.79266	0.0568312
$996$	14.0010	0.443638
$997$	28.7977	0.912031	0.456016	−	0.889972i	$-0.349276\pi$
$997$	28.7977	0.912031	0.456016	+	0.889972i	$0.349276\pi$
$998$	−48.0077	−1.51966
$999$	−38.2580	−1.21043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.b.1.12	✓	268

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.b.1.12	✓	268	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66122 q^{2} +1.83704 q^{3} +5.08208 q^{4} -0.683386 q^{5} -4.88877 q^{6} +2.95312 q^{7} -8.20207 q^{8} +0.374729 q^{9} +O(q^{10})\)	\(q-2.66122 q^{2} +1.83704 q^{3} +5.08208 q^{4} -0.683386 q^{5} -4.88877 q^{6} +2.95312 q^{7} -8.20207 q^{8} +0.374729 q^{9} +1.81864 q^{10} -0.152491 q^{11} +9.33600 q^{12} -3.53230 q^{13} -7.85888 q^{14} -1.25541 q^{15} +11.6633 q^{16} +3.13556 q^{17} -0.997236 q^{18} -5.88432 q^{19} -3.47302 q^{20} +5.42500 q^{21} +0.405811 q^{22} +6.09868 q^{23} -15.0676 q^{24} -4.53298 q^{25} +9.40021 q^{26} -4.82274 q^{27} +15.0080 q^{28} -4.89414 q^{29} +3.34092 q^{30} +6.32960 q^{31} -14.6346 q^{32} -0.280132 q^{33} -8.34441 q^{34} -2.01812 q^{35} +1.90440 q^{36} +7.93284 q^{37} +15.6594 q^{38} -6.48898 q^{39} +5.60518 q^{40} -7.45170 q^{41} -14.4371 q^{42} +8.25434 q^{43} -0.774969 q^{44} -0.256085 q^{45} -16.2299 q^{46} -3.13130 q^{47} +21.4261 q^{48} +1.72089 q^{49} +12.0633 q^{50} +5.76016 q^{51} -17.9514 q^{52} +11.2808 q^{53} +12.8343 q^{54} +0.104210 q^{55} -24.2217 q^{56} -10.8097 q^{57} +13.0244 q^{58} -3.65612 q^{59} -6.38009 q^{60} +0.380585 q^{61} -16.8444 q^{62} +1.10662 q^{63} +15.6190 q^{64} +2.41392 q^{65} +0.745492 q^{66} +3.26632 q^{67} +15.9352 q^{68} +11.2035 q^{69} +5.37065 q^{70} -12.2928 q^{71} -3.07356 q^{72} +16.3590 q^{73} -21.1110 q^{74} -8.32729 q^{75} -29.9045 q^{76} -0.450323 q^{77} +17.2686 q^{78} +16.4614 q^{79} -7.97057 q^{80} -9.98377 q^{81} +19.8306 q^{82} +1.49968 q^{83} +27.5703 q^{84} -2.14280 q^{85} -21.9666 q^{86} -8.99074 q^{87} +1.25074 q^{88} -12.2053 q^{89} +0.681497 q^{90} -10.4313 q^{91} +30.9940 q^{92} +11.6277 q^{93} +8.33306 q^{94} +4.02126 q^{95} -26.8843 q^{96} -5.13998 q^{97} -4.57967 q^{98} -0.0571427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * q^99

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