LMFDB - Embedded newform 6019.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74057 q^{2} -2.54852 q^{3} +5.51070 q^{4} -0.432732 q^{5} +6.98439 q^{6} +3.36424 q^{7} -9.62130 q^{8} +3.49496 q^{9} +O(q^{10})$	\(q-2.74057 q^{2} -2.54852 q^{3} +5.51070 q^{4} -0.432732 q^{5} +6.98439 q^{6} +3.36424 q^{7} -9.62130 q^{8} +3.49496 q^{9} +1.18593 q^{10} +5.41548 q^{11} -14.0441 q^{12} -1.00000 q^{13} -9.21993 q^{14} +1.10283 q^{15} +15.3464 q^{16} -0.578178 q^{17} -9.57816 q^{18} -3.17548 q^{19} -2.38466 q^{20} -8.57384 q^{21} -14.8415 q^{22} -2.22118 q^{23} +24.5201 q^{24} -4.81274 q^{25} +2.74057 q^{26} -1.26141 q^{27} +18.5393 q^{28} +1.70000 q^{29} -3.02237 q^{30} -10.8645 q^{31} -22.8152 q^{32} -13.8015 q^{33} +1.58453 q^{34} -1.45582 q^{35} +19.2597 q^{36} -10.8596 q^{37} +8.70261 q^{38} +2.54852 q^{39} +4.16345 q^{40} +10.3759 q^{41} +23.4972 q^{42} -10.5912 q^{43} +29.8431 q^{44} -1.51238 q^{45} +6.08728 q^{46} +5.09025 q^{47} -39.1106 q^{48} +4.31813 q^{49} +13.1896 q^{50} +1.47350 q^{51} -5.51070 q^{52} -8.58799 q^{53} +3.45697 q^{54} -2.34345 q^{55} -32.3684 q^{56} +8.09278 q^{57} -4.65897 q^{58} -8.62904 q^{59} +6.07735 q^{60} +13.7373 q^{61} +29.7750 q^{62} +11.7579 q^{63} +31.8338 q^{64} +0.432732 q^{65} +37.8238 q^{66} -2.58380 q^{67} -3.18616 q^{68} +5.66071 q^{69} +3.98976 q^{70} +6.28106 q^{71} -33.6260 q^{72} -4.96803 q^{73} +29.7615 q^{74} +12.2654 q^{75} -17.4991 q^{76} +18.2190 q^{77} -6.98439 q^{78} -6.72589 q^{79} -6.64088 q^{80} -7.27015 q^{81} -28.4358 q^{82} +10.1595 q^{83} -47.2479 q^{84} +0.250196 q^{85} +29.0258 q^{86} -4.33249 q^{87} -52.1040 q^{88} -11.7766 q^{89} +4.14478 q^{90} -3.36424 q^{91} -12.2402 q^{92} +27.6885 q^{93} -13.9502 q^{94} +1.37413 q^{95} +58.1451 q^{96} -5.95133 q^{97} -11.8341 q^{98} +18.9269 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.74057	−1.93787	−0.968936	−	0.247311i	$-0.920453\pi$
$2$	−2.74057	−1.93787	−0.968936	+	0.247311i	$0.920453\pi$
$3$	−2.54852	−1.47139	−0.735695	−	0.677313i	$-0.763144\pi$
$3$	−2.54852	−1.47139	−0.735695	+	0.677313i	$0.763144\pi$
$4$	5.51070	2.75535
$5$	−0.432732	−0.193524	−0.0967618	−	0.995308i	$-0.530849\pi$
$5$	−0.432732	−0.193524	−0.0967618	+	0.995308i	$0.530849\pi$
$6$	6.98439	2.85136
$7$	3.36424	1.27156	0.635782	−	0.771868i	$-0.280678\pi$
$7$	3.36424	1.27156	0.635782	+	0.771868i	$0.280678\pi$
$8$	−9.62130	−3.40164
$9$	3.49496	1.16499
$10$	1.18593	0.375024
$11$	5.41548	1.63283	0.816415	−	0.577466i	$-0.195958\pi$
$11$	5.41548	1.63283	0.816415	+	0.577466i	$0.195958\pi$
$12$	−14.0441	−4.05419
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−9.21993	−2.46413
$15$	1.10283	0.284749
$16$	15.3464	3.83660
$17$	−0.578178	−0.140229	−0.0701144	−	0.997539i	$-0.522336\pi$
$17$	−0.578178	−0.140229	−0.0701144	+	0.997539i	$0.522336\pi$
$18$	−9.57816	−2.25759
$19$	−3.17548	−0.728505	−0.364253	−	0.931300i	$-0.618675\pi$
$19$	−3.17548	−0.728505	−0.364253	+	0.931300i	$0.618675\pi$
$20$	−2.38466	−0.533225
$21$	−8.57384	−1.87097
$22$	−14.8415	−3.16421
$23$	−2.22118	−0.463147	−0.231574	−	0.972817i	$-0.574387\pi$
$23$	−2.22118	−0.463147	−0.231574	+	0.972817i	$0.574387\pi$
$24$	24.5201	5.00514
$25$	−4.81274	−0.962549
$26$	2.74057	0.537469
$27$	−1.26141	−0.242758
$28$	18.5393	3.50360
$29$	1.70000	0.315682	0.157841	−	0.987465i	$-0.449547\pi$
$29$	1.70000	0.315682	0.157841	+	0.987465i	$0.449547\pi$
$30$	−3.02237	−0.551807
$31$	−10.8645	−1.95133	−0.975664	−	0.219271i	$-0.929632\pi$
$31$	−10.8645	−1.95133	−0.975664	+	0.219271i	$0.929632\pi$
$32$	−22.8152	−4.03320
$33$	−13.8015	−2.40253
$34$	1.58453	0.271745
$35$	−1.45582	−0.246078
$36$	19.2597	3.20994
$37$	−10.8596	−1.78531	−0.892655	−	0.450740i	$-0.851160\pi$
$37$	−10.8596	−1.78531	−0.892655	+	0.450740i	$0.851160\pi$
$38$	8.70261	1.41175
$39$	2.54852	0.408090
$40$	4.16345	0.658299
$41$	10.3759	1.62044	0.810221	−	0.586124i	$-0.199347\pi$
$41$	10.3759	1.62044	0.810221	+	0.586124i	$0.199347\pi$
$42$	23.4972	3.62569
$43$	−10.5912	−1.61514	−0.807570	−	0.589772i	$-0.799218\pi$
$43$	−10.5912	−1.61514	−0.807570	+	0.589772i	$0.799218\pi$
$44$	29.8431	4.49902
$45$	−1.51238	−0.225452
$46$	6.08728	0.897521
$47$	5.09025	0.742489	0.371245	−	0.928535i	$-0.378931\pi$
$47$	5.09025	0.742489	0.371245	+	0.928535i	$0.378931\pi$
$48$	−39.1106	−5.64513
$49$	4.31813	0.616876
$50$	13.1896	1.86530
$51$	1.47350	0.206331
$52$	−5.51070	−0.764196
$53$	−8.58799	−1.17965	−0.589826	−	0.807531i	$-0.700804\pi$
$53$	−8.58799	−1.17965	−0.589826	+	0.807531i	$0.700804\pi$
$54$	3.45697	0.470435
$55$	−2.34345	−0.315991
$56$	−32.3684	−4.32541
$57$	8.09278	1.07191
$58$	−4.65897	−0.611752
$59$	−8.62904	−1.12341	−0.561703	−	0.827339i	$-0.689853\pi$
$59$	−8.62904	−1.12341	−0.561703	+	0.827339i	$0.689853\pi$
$60$	6.07735	0.784582
$61$	13.7373	1.75888	0.879439	−	0.476012i	$-0.157918\pi$
$61$	13.7373	1.75888	0.879439	+	0.476012i	$0.157918\pi$
$62$	29.7750	3.78142
$63$	11.7579	1.48135
$64$	31.8338	3.97923
$65$	0.432732	0.0536738
$66$	37.8238	4.65579
$67$	−2.58380	−0.315661	−0.157831	−	0.987466i	$-0.550450\pi$
$67$	−2.58380	−0.315661	−0.157831	+	0.987466i	$0.550450\pi$
$68$	−3.18616	−0.386379
$69$	5.66071	0.681470
$70$	3.98976	0.476867
$71$	6.28106	0.745424	0.372712	−	0.927947i	$-0.378428\pi$
$71$	6.28106	0.745424	0.372712	+	0.927947i	$0.378428\pi$
$72$	−33.6260	−3.96287
$73$	−4.96803	−0.581464	−0.290732	−	0.956804i	$-0.593899\pi$
$73$	−4.96803	−0.581464	−0.290732	+	0.956804i	$0.593899\pi$
$74$	29.7615	3.45970
$75$	12.2654	1.41628
$76$	−17.4991	−2.00729
$77$	18.2190	2.07625
$78$	−6.98439	−0.790826
$79$	−6.72589	−0.756722	−0.378361	−	0.925658i	$-0.623512\pi$
$79$	−6.72589	−0.756722	−0.378361	+	0.925658i	$0.623512\pi$
$80$	−6.64088	−0.742473
$81$	−7.27015	−0.807794
$82$	−28.4358	−3.14021
$83$	10.1595	1.11515	0.557576	−	0.830126i	$-0.311732\pi$
$83$	10.1595	1.11515	0.557576	+	0.830126i	$0.311732\pi$
$84$	−47.2479	−5.15517
$85$	0.250196	0.0271376
$86$	29.0258	3.12994
$87$	−4.33249	−0.464492
$88$	−52.1040	−5.55430
$89$	−11.7766	−1.24831	−0.624157	−	0.781299i	$-0.714557\pi$
$89$	−11.7766	−1.24831	−0.624157	+	0.781299i	$0.714557\pi$
$90$	4.14478	0.436898
$91$	−3.36424	−0.352669
$92$	−12.2402	−1.27613
$93$	27.6885	2.87116
$94$	−13.9502	−1.43885
$95$	1.37413	0.140983
$96$	58.1451	5.93441
$97$	−5.95133	−0.604266	−0.302133	−	0.953266i	$-0.597699\pi$
$97$	−5.95133	−0.604266	−0.302133	+	0.953266i	$0.597699\pi$
$98$	−11.8341	−1.19543
$99$	18.9269	1.90222
$100$	−26.5216	−2.65216
$101$	6.09371	0.606347	0.303174	−	0.952935i	$-0.401954\pi$
$101$	6.09371	0.606347	0.303174	+	0.952935i	$0.401954\pi$
$102$	−4.03822	−0.399843
$103$	18.4440	1.81734	0.908672	−	0.417510i	$-0.137097\pi$
$103$	18.4440	1.81734	0.908672	+	0.417510i	$0.137097\pi$
$104$	9.62130	0.943446
$105$	3.71018	0.362076
$106$	23.5360	2.28601
$107$	19.5647	1.89139	0.945697	−	0.325049i	$-0.105381\pi$
$107$	19.5647	1.89139	0.945697	+	0.325049i	$0.105381\pi$
$108$	−6.95125	−0.668884
$109$	6.10233	0.584497	0.292249	−	0.956342i	$-0.405597\pi$
$109$	6.10233	0.584497	0.292249	+	0.956342i	$0.405597\pi$
$110$	6.42239	0.612350
$111$	27.6760	2.62689
$112$	51.6290	4.87849
$113$	−13.3596	−1.25676	−0.628382	−	0.777905i	$-0.716283\pi$
$113$	−13.3596	−1.25676	−0.628382	+	0.777905i	$0.716283\pi$
$114$	−22.1788	−2.07723
$115$	0.961175	0.0896300
$116$	9.36820	0.869815
$117$	−3.49496	−0.323109
$118$	23.6484	2.17702
$119$	−1.94513	−0.178310
$120$	−10.6106	−0.968613
$121$	18.3274	1.66613
$122$	−37.6479	−3.40848
$123$	−26.4432	−2.38430
$124$	−59.8712	−5.37659
$125$	4.24629	0.379800
$126$	−32.2233	−2.87068
$127$	14.3149	1.27025	0.635123	−	0.772411i	$-0.280949\pi$
$127$	14.3149	1.27025	0.635123	+	0.772411i	$0.280949\pi$
$128$	−41.6122	−3.67803
$129$	26.9918	2.37650
$130$	−1.18593	−0.104013
$131$	−1.59654	−0.139490	−0.0697452	−	0.997565i	$-0.522219\pi$
$131$	−1.59654	−0.139490	−0.0697452	+	0.997565i	$0.522219\pi$
$132$	−76.0557	−6.61980
$133$	−10.6831	−0.926341
$134$	7.08107	0.611712
$135$	0.545852	0.0469795
$136$	5.56282	0.477008
$137$	9.22326	0.787996	0.393998	−	0.919111i	$-0.371092\pi$
$137$	9.22326	0.787996	0.393998	+	0.919111i	$0.371092\pi$
$138$	−15.5136	−1.32060
$139$	4.53709	0.384831	0.192416	−	0.981314i	$-0.438368\pi$
$139$	4.53709	0.384831	0.192416	+	0.981314i	$0.438368\pi$
$140$	−8.02256	−0.678030
$141$	−12.9726	−1.09249
$142$	−17.2136	−1.44454
$143$	−5.41548	−0.452865
$144$	53.6350	4.46959
$145$	−0.735645	−0.0610920
$146$	13.6152	1.12680
$147$	−11.0049	−0.907665
$148$	−59.8441	−4.91916
$149$	18.3163	1.50053	0.750266	−	0.661136i	$-0.229925\pi$
$149$	18.3163	1.50053	0.750266	+	0.661136i	$0.229925\pi$
$150$	−33.6141	−2.74458
$151$	9.68202	0.787912	0.393956	−	0.919129i	$-0.371106\pi$
$151$	9.68202	0.787912	0.393956	+	0.919129i	$0.371106\pi$
$152$	30.5522	2.47811
$153$	−2.02071	−0.163364
$154$	−49.9304	−4.02350
$155$	4.70143	0.377628
$156$	14.0441	1.12443
$157$	−2.80820	−0.224119	−0.112059	−	0.993702i	$-0.535745\pi$
$157$	−2.80820	−0.224119	−0.112059	+	0.993702i	$0.535745\pi$
$158$	18.4327	1.46643
$159$	21.8867	1.73573
$160$	9.87288	0.780520
$161$	−7.47258	−0.588922
$162$	19.9243	1.56540
$163$	10.6806	0.836567	0.418283	−	0.908317i	$-0.362632\pi$
$163$	10.6806	0.836567	0.418283	+	0.908317i	$0.362632\pi$
$164$	57.1784	4.46488
$165$	5.97234	0.464946
$166$	−27.8428	−2.16102
$167$	2.65784	0.205670	0.102835	−	0.994698i	$-0.467209\pi$
$167$	2.65784	0.205670	0.102835	+	0.994698i	$0.467209\pi$
$168$	82.4915	6.36436
$169$	1.00000	0.0769231
$170$	−0.685679	−0.0525892
$171$	−11.0982	−0.848698
$172$	−58.3648	−4.45028
$173$	−3.88930	−0.295698	−0.147849	−	0.989010i	$-0.547235\pi$
$173$	−3.88930	−0.295698	−0.147849	+	0.989010i	$0.547235\pi$
$174$	11.8735	0.900126
$175$	−16.1912	−1.22394
$176$	83.1082	6.26452
$177$	21.9913	1.65297
$178$	32.2744	2.41907
$179$	19.9606	1.49193	0.745963	−	0.665987i	$-0.231989\pi$
$179$	19.9606	1.49193	0.745963	+	0.665987i	$0.231989\pi$
$180$	−8.33427	−0.621200
$181$	−23.8400	−1.77202	−0.886008	−	0.463670i	$-0.846532\pi$
$181$	−23.8400	−1.77202	−0.886008	+	0.463670i	$0.846532\pi$
$182$	9.21993	0.683427
$183$	−35.0097	−2.58799
$184$	21.3706	1.57546
$185$	4.69931	0.345500
$186$	−75.8821	−5.56395
$187$	−3.13111	−0.228970
$188$	28.0508	2.04582
$189$	−4.24369	−0.308683
$190$	−3.76590	−0.273207
$191$	−6.01750	−0.435411	−0.217706	−	0.976014i	$-0.569857\pi$
$191$	−6.01750	−0.435411	−0.217706	+	0.976014i	$0.569857\pi$
$192$	−81.1292	−5.85499
$193$	−2.81803	−0.202846	−0.101423	−	0.994843i	$-0.532340\pi$
$193$	−2.81803	−0.202846	−0.101423	+	0.994843i	$0.532340\pi$
$194$	16.3100	1.17099
$195$	−1.10283	−0.0789751
$196$	23.7959	1.69971
$197$	−14.6417	−1.04318	−0.521589	−	0.853197i	$-0.674660\pi$
$197$	−14.6417	−1.04318	−0.521589	+	0.853197i	$0.674660\pi$
$198$	−51.8703	−3.68627
$199$	−10.0888	−0.715174	−0.357587	−	0.933880i	$-0.616400\pi$
$199$	−10.0888	−0.715174	−0.357587	+	0.933880i	$0.616400\pi$
$200$	46.3048	3.27425
$201$	6.58487	0.464461
$202$	−16.7002	−1.17502
$203$	5.71922	0.401411
$204$	8.12001	0.568514
$205$	−4.48998	−0.313594
$206$	−50.5471	−3.52178
$207$	−7.76292	−0.539560
$208$	−15.3464	−1.06408
$209$	−17.1968	−1.18952
$210$	−10.1680	−0.701658
$211$	17.6357	1.21409	0.607046	−	0.794667i	$-0.292354\pi$
$211$	17.6357	1.21409	0.607046	+	0.794667i	$0.292354\pi$
$212$	−47.3258	−3.25035
$213$	−16.0074	−1.09681
$214$	−53.6184	−3.66528
$215$	4.58314	0.312568
$216$	12.1364	0.825777
$217$	−36.5509	−2.48124
$218$	−16.7238	−1.13268
$219$	12.6611	0.855560
$220$	−12.9141	−0.870666
$221$	0.578178	0.0388925
$222$	−75.8478	−5.09057
$223$	−25.8864	−1.73348	−0.866742	−	0.498756i	$-0.833790\pi$
$223$	−25.8864	−1.73348	−0.866742	+	0.498756i	$0.833790\pi$
$224$	−76.7560	−5.12848
$225$	−16.8203	−1.12136
$226$	36.6128	2.43545
$227$	6.40869	0.425360	0.212680	−	0.977122i	$-0.431781\pi$
$227$	6.40869	0.425360	0.212680	+	0.977122i	$0.431781\pi$
$228$	44.5969	2.95350
$229$	12.3197	0.814111	0.407055	−	0.913403i	$-0.366556\pi$
$229$	12.3197	0.814111	0.407055	+	0.913403i	$0.366556\pi$
$230$	−2.63416	−0.173691
$231$	−46.4315	−3.05497
$232$	−16.3562	−1.07384
$233$	21.5276	1.41032	0.705159	−	0.709049i	$-0.250876\pi$
$233$	21.5276	1.41032	0.705159	+	0.709049i	$0.250876\pi$
$234$	9.57816	0.626144
$235$	−2.20271	−0.143689
$236$	−47.5520	−3.09537
$237$	17.1411	1.11343
$238$	5.33076	0.345542
$239$	−8.50064	−0.549861	−0.274930	−	0.961464i	$-0.588655\pi$
$239$	−8.50064	−0.549861	−0.274930	+	0.961464i	$0.588655\pi$
$240$	16.9244	1.09247
$241$	20.9922	1.35223	0.676114	−	0.736797i	$-0.263663\pi$
$241$	20.9922	1.35223	0.676114	+	0.736797i	$0.263663\pi$
$242$	−50.2276	−3.22875
$243$	22.3123	1.43134
$244$	75.7020	4.84632
$245$	−1.86859	−0.119380
$246$	72.4693	4.62047
$247$	3.17548	0.202051
$248$	104.531	6.63772
$249$	−25.8917	−1.64082
$250$	−11.6372	−0.736003
$251$	−11.5100	−0.726503	−0.363251	−	0.931691i	$-0.618333\pi$
$251$	−11.5100	−0.726503	−0.363251	+	0.931691i	$0.618333\pi$
$252$	64.7942	4.08165
$253$	−12.0287	−0.756241
$254$	−39.2311	−2.46158
$255$	−0.637630	−0.0399299
$256$	50.3734	3.14833
$257$	−19.9267	−1.24300	−0.621498	−	0.783416i	$-0.713476\pi$
$257$	−19.9267	−1.24300	−0.621498	+	0.783416i	$0.713476\pi$
$258$	−73.9729	−4.60535
$259$	−36.5344	−2.27014
$260$	2.38466	0.147890
$261$	5.94143	0.367766
$262$	4.37542	0.270315
$263$	4.86018	0.299692	0.149846	−	0.988709i	$-0.452122\pi$
$263$	4.86018	0.299692	0.149846	+	0.988709i	$0.452122\pi$
$264$	132.788	8.17254
$265$	3.71630	0.228291
$266$	29.2777	1.79513
$267$	30.0128	1.83675
$268$	−14.2385	−0.869758
$269$	2.01148	0.122642	0.0613209	−	0.998118i	$-0.480469\pi$
$269$	2.01148	0.122642	0.0613209	+	0.998118i	$0.480469\pi$
$270$	−1.49594	−0.0910402
$271$	−5.79847	−0.352232	−0.176116	−	0.984369i	$-0.556353\pi$
$271$	−5.79847	−0.352232	−0.176116	+	0.984369i	$0.556353\pi$
$272$	−8.87295	−0.538002
$273$	8.57384	0.518913
$274$	−25.2769	−1.52704
$275$	−26.0633	−1.57168
$276$	31.1945	1.87769
$277$	3.58137	0.215184	0.107592	−	0.994195i	$-0.465686\pi$
$277$	3.58137	0.215184	0.107592	+	0.994195i	$0.465686\pi$
$278$	−12.4342	−0.745754
$279$	−37.9711	−2.27327
$280$	14.0068	0.837069
$281$	17.7070	1.05631	0.528154	−	0.849149i	$-0.322884\pi$
$281$	17.7070	1.05631	0.528154	+	0.849149i	$0.322884\pi$
$282$	35.5523	2.11711
$283$	8.15745	0.484910	0.242455	−	0.970163i	$-0.422047\pi$
$283$	8.15745	0.484910	0.242455	+	0.970163i	$0.422047\pi$
$284$	34.6130	2.05390
$285$	−3.50200	−0.207441
$286$	14.8415	0.877595
$287$	34.9070	2.06050
$288$	−79.7383	−4.69862
$289$	−16.6657	−0.980336
$290$	2.01608	0.118389
$291$	15.1671	0.889110
$292$	−27.3773	−1.60214
$293$	6.40413	0.374133	0.187067	−	0.982347i	$-0.440102\pi$
$293$	6.40413	0.374133	0.187067	+	0.982347i	$0.440102\pi$
$294$	30.1595	1.75894
$295$	3.73406	0.217405
$296$	104.484	6.07299
$297$	−6.83114	−0.396383
$298$	−50.1971	−2.90784
$299$	2.22118	0.128454
$300$	67.5908	3.90236
$301$	−35.6313	−2.05375
$302$	−26.5342	−1.52687
$303$	−15.5300	−0.892172
$304$	−48.7322	−2.79498
$305$	−5.94456	−0.340385
$306$	5.53788	0.316580
$307$	−16.3837	−0.935067	−0.467533	−	0.883975i	$-0.654857\pi$
$307$	−16.3837	−0.935067	−0.467533	+	0.883975i	$0.654857\pi$
$308$	100.399	5.72079
$309$	−47.0050	−2.67402
$310$	−12.8846	−0.731795
$311$	1.30707	0.0741170	0.0370585	−	0.999313i	$-0.488201\pi$
$311$	1.30707	0.0741170	0.0370585	+	0.999313i	$0.488201\pi$
$312$	−24.5201	−1.38818
$313$	10.9201	0.617239	0.308620	−	0.951186i	$-0.400133\pi$
$313$	10.9201	0.617239	0.308620	+	0.951186i	$0.400133\pi$
$314$	7.69606	0.434314
$315$	−5.08802	−0.286677
$316$	−37.0644	−2.08503
$317$	15.2088	0.854210	0.427105	−	0.904202i	$-0.359533\pi$
$317$	15.2088	0.854210	0.427105	+	0.904202i	$0.359533\pi$
$318$	−59.9819	−3.36362
$319$	9.20633	0.515455
$320$	−13.7755	−0.770075
$321$	−49.8611	−2.78298
$322$	20.4791	1.14126
$323$	1.83599	0.102157
$324$	−40.0636	−2.22575
$325$	4.81274	0.266963
$326$	−29.2708	−1.62116
$327$	−15.5519	−0.860023
$328$	−99.8296	−5.51217
$329$	17.1248	0.944123
$330$	−16.3676	−0.901006
$331$	29.2123	1.60566	0.802828	−	0.596211i	$-0.203328\pi$
$331$	29.2123	1.60566	0.802828	+	0.596211i	$0.203328\pi$
$332$	55.9860	3.07263
$333$	−37.9539	−2.07986
$334$	−7.28398	−0.398562
$335$	1.11809	0.0610880
$336$	−131.578	−7.17815
$337$	26.6921	1.45401	0.727006	−	0.686631i	$-0.240911\pi$
$337$	26.6921	1.45401	0.727006	+	0.686631i	$0.240911\pi$
$338$	−2.74057	−0.149067
$339$	34.0472	1.84919
$340$	1.37876	0.0747735
$341$	−58.8367	−3.18619
$342$	30.4153	1.64467
$343$	−9.02245	−0.487167
$344$	101.901	5.49413
$345$	−2.44957	−0.131881
$346$	10.6589	0.573026
$347$	−3.67452	−0.197258	−0.0986292	−	0.995124i	$-0.531446\pi$
$347$	−3.67452	−0.197258	−0.0986292	+	0.995124i	$0.531446\pi$
$348$	−23.8750	−1.27984
$349$	−8.92683	−0.477842	−0.238921	−	0.971039i	$-0.576794\pi$
$349$	−8.92683	−0.477842	−0.238921	+	0.971039i	$0.576794\pi$
$350$	44.3731	2.37184
$351$	1.26141	0.0673290
$352$	−123.555	−6.58553
$353$	29.1745	1.55280	0.776402	−	0.630239i	$-0.217043\pi$
$353$	29.1745	1.55280	0.776402	+	0.630239i	$0.217043\pi$
$354$	−60.2685	−3.20324
$355$	−2.71801	−0.144257
$356$	−64.8971	−3.43954
$357$	4.95721	0.262363
$358$	−54.7034	−2.89116
$359$	−17.7812	−0.938454	−0.469227	−	0.883078i	$-0.655467\pi$
$359$	−17.7812	−0.938454	−0.469227	+	0.883078i	$0.655467\pi$
$360$	14.5511	0.766909
$361$	−8.91633	−0.469280
$362$	65.3352	3.43394
$363$	−46.7079	−2.45153
$364$	−18.5393	−0.971725
$365$	2.14983	0.112527
$366$	95.9465	5.01520
$367$	13.4597	0.702589	0.351295	−	0.936265i	$-0.385742\pi$
$367$	13.4597	0.702589	0.351295	+	0.936265i	$0.385742\pi$
$368$	−34.0871	−1.77691
$369$	36.2633	1.88779
$370$	−12.8788	−0.669535
$371$	−28.8921	−1.50000
$372$	152.583	7.91106
$373$	27.8148	1.44019	0.720097	−	0.693873i	$-0.244097\pi$
$373$	27.8148	1.44019	0.720097	+	0.693873i	$0.244097\pi$
$374$	8.58102	0.443714
$375$	−10.8218	−0.558833
$376$	−48.9748	−2.52568
$377$	−1.70000	−0.0875546
$378$	11.6301	0.598188
$379$	15.9001	0.816733	0.408367	−	0.912818i	$-0.366098\pi$
$379$	15.9001	0.816733	0.408367	+	0.912818i	$0.366098\pi$
$380$	7.57243	0.388457
$381$	−36.4819	−1.86903
$382$	16.4914	0.843771
$383$	0.693640	0.0354433	0.0177217	−	0.999843i	$-0.494359\pi$
$383$	0.693640	0.0354433	0.0177217	+	0.999843i	$0.494359\pi$
$384$	106.050	5.41182
$385$	−7.88395	−0.401803
$386$	7.72299	0.393090
$387$	−37.0157	−1.88162
$388$	−32.7960	−1.66496
$389$	10.6128	0.538091	0.269045	−	0.963128i	$-0.413292\pi$
$389$	10.6128	0.538091	0.269045	+	0.963128i	$0.413292\pi$
$390$	3.02237	0.153044
$391$	1.28424	0.0649466
$392$	−41.5461	−2.09839
$393$	4.06882	0.205245
$394$	40.1265	2.02154
$395$	2.91051	0.146444
$396$	104.300	5.24129
$397$	−17.5712	−0.881871	−0.440935	−	0.897539i	$-0.645353\pi$
$397$	−17.5712	−0.881871	−0.440935	+	0.897539i	$0.645353\pi$
$398$	27.6489	1.38592
$399$	27.2261	1.36301
$400$	−73.8583	−3.69292
$401$	10.2968	0.514196	0.257098	−	0.966385i	$-0.417234\pi$
$401$	10.2968	0.514196	0.257098	+	0.966385i	$0.417234\pi$
$402$	−18.0463	−0.900066
$403$	10.8645	0.541201
$404$	33.5806	1.67070
$405$	3.14603	0.156327
$406$	−15.6739	−0.777882
$407$	−58.8101	−2.91511
$408$	−14.1770	−0.701865
$409$	14.7847	0.731054	0.365527	−	0.930801i	$-0.380889\pi$
$409$	14.7847	0.731054	0.365527	+	0.930801i	$0.380889\pi$
$410$	12.3051	0.607705
$411$	−23.5057	−1.15945
$412$	101.640	5.00742
$413$	−29.0302	−1.42848
$414$	21.2748	1.04560
$415$	−4.39635	−0.215808
$416$	22.8152	1.11861
$417$	−11.5629	−0.566236
$418$	47.1288	2.30515
$419$	6.57416	0.321169	0.160584	−	0.987022i	$-0.448662\pi$
$419$	6.57416	0.321169	0.160584	+	0.987022i	$0.448662\pi$
$420$	20.4457	0.997647
$421$	19.5432	0.952477	0.476238	−	0.879316i	$-0.342000\pi$
$421$	19.5432	0.952477	0.476238	+	0.879316i	$0.342000\pi$
$422$	−48.3318	−2.35276
$423$	17.7902	0.864989
$424$	82.6277	4.01275
$425$	2.78262	0.134977
$426$	43.8693	2.12548
$427$	46.2155	2.23653
$428$	107.815	5.21145
$429$	13.8015	0.666341
$430$	−12.5604	−0.605717
$431$	−11.6147	−0.559462	−0.279731	−	0.960078i	$-0.590245\pi$
$431$	−11.6147	−0.559462	−0.279731	+	0.960078i	$0.590245\pi$
$432$	−19.3581	−0.931367
$433$	−16.0225	−0.769992	−0.384996	−	0.922918i	$-0.625797\pi$
$433$	−16.0225	−0.769992	−0.384996	+	0.922918i	$0.625797\pi$
$434$	100.170	4.80832
$435$	1.87481	0.0898901
$436$	33.6281	1.61049
$437$	7.05330	0.337405
$438$	−34.6987	−1.65797
$439$	36.9878	1.76533	0.882665	−	0.470003i	$-0.155747\pi$
$439$	36.9878	1.76533	0.882665	+	0.470003i	$0.155747\pi$
$440$	22.5471	1.07489
$441$	15.0917	0.718652
$442$	−1.58453	−0.0753686
$443$	−33.8364	−1.60762	−0.803809	−	0.594888i	$-0.797196\pi$
$443$	−33.8364	−1.60762	−0.803809	+	0.594888i	$0.797196\pi$
$444$	152.514	7.23799
$445$	5.09610	0.241578
$446$	70.9435	3.35927
$447$	−46.6796	−2.20787
$448$	107.097	5.05984
$449$	−40.1596	−1.89525	−0.947625	−	0.319385i	$-0.896524\pi$
$449$	−40.1596	−1.89525	−0.947625	+	0.319385i	$0.896524\pi$
$450$	46.0972	2.17304
$451$	56.1905	2.64591
$452$	−73.6207	−3.46283
$453$	−24.6748	−1.15932
$454$	−17.5634	−0.824293
$455$	1.45582	0.0682497
$456$	−77.8630	−3.64627
$457$	26.8917	1.25794	0.628971	−	0.777429i	$-0.283476\pi$
$457$	26.8917	1.25794	0.628971	+	0.777429i	$0.283476\pi$
$458$	−33.7630	−1.57764
$459$	0.729319	0.0340417
$460$	5.29674	0.246962
$461$	32.9832	1.53618	0.768091	−	0.640340i	$-0.221207\pi$
$461$	32.9832	1.53618	0.768091	+	0.640340i	$0.221207\pi$
$462$	127.249	5.92014
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	26.0889	1.21115
$465$	−11.9817	−0.555638
$466$	−58.9977	−2.73302
$467$	17.3700	0.803788	0.401894	−	0.915686i	$-0.368352\pi$
$467$	17.3700	0.803788	0.401894	+	0.915686i	$0.368352\pi$
$468$	−19.2597	−0.890278
$469$	−8.69253	−0.401384
$470$	6.03668	0.278451
$471$	7.15676	0.329766
$472$	83.0226	3.82142
$473$	−57.3564	−2.63725
$474$	−46.9762	−2.15769
$475$	15.2828	0.701221
$476$	−10.7190	−0.491306
$477$	−30.0147	−1.37428
$478$	23.2966	1.06556
$479$	37.4110	1.70935	0.854676	−	0.519161i	$-0.173756\pi$
$479$	37.4110	1.70935	0.854676	+	0.519161i	$0.173756\pi$
$480$	−25.1612	−1.14845
$481$	10.8596	0.495156
$482$	−57.5305	−2.62044
$483$	19.0440	0.866533
$484$	100.997	4.59077
$485$	2.57533	0.116940
$486$	−61.1484	−2.77375
$487$	36.3458	1.64699	0.823493	−	0.567327i	$-0.192022\pi$
$487$	36.3458	1.64699	0.823493	+	0.567327i	$0.192022\pi$
$488$	−132.170	−5.98308
$489$	−27.2196	−1.23091
$490$	5.12101	0.231344
$491$	5.54367	0.250182	0.125091	−	0.992145i	$-0.460078\pi$
$491$	5.54367	0.250182	0.125091	+	0.992145i	$0.460078\pi$
$492$	−145.720	−6.56958
$493$	−0.982903	−0.0442677
$494$	−8.70261	−0.391549
$495$	−8.19027	−0.368125
$496$	−166.732	−7.48647
$497$	21.1310	0.947855
$498$	70.9580	3.17970
$499$	−3.21572	−0.143955	−0.0719776	−	0.997406i	$-0.522931\pi$
$499$	−3.21572	−0.143955	−0.0719776	+	0.997406i	$0.522931\pi$
$500$	23.4000	1.04648
$501$	−6.77356	−0.302620
$502$	31.5438	1.40787
$503$	−40.4569	−1.80389	−0.901943	−	0.431855i	$-0.857859\pi$
$503$	−40.4569	−1.80389	−0.901943	+	0.431855i	$0.857859\pi$
$504$	−113.126	−5.03904
$505$	−2.63695	−0.117343
$506$	32.9656	1.46550
$507$	−2.54852	−0.113184
$508$	78.8854	3.49997
$509$	23.8723	1.05812	0.529062	−	0.848583i	$-0.322544\pi$
$509$	23.8723	1.05812	0.529062	+	0.848583i	$0.322544\pi$
$510$	1.74747	0.0773791
$511$	−16.7137	−0.739369
$512$	−54.8270	−2.42304
$513$	4.00558	0.176851
$514$	54.6105	2.40877
$515$	−7.98133	−0.351699
$516$	148.744	6.54809
$517$	27.5661	1.21236
$518$	100.125	4.39924
$519$	9.91197	0.435087
$520$	−4.16345	−0.182579
$521$	−10.1249	−0.443582	−0.221791	−	0.975094i	$-0.571190\pi$
$521$	−10.1249	−0.443582	−0.221791	+	0.975094i	$0.571190\pi$
$522$	−16.2829	−0.712683
$523$	−19.0198	−0.831678	−0.415839	−	0.909438i	$-0.636512\pi$
$523$	−19.0198	−0.831678	−0.415839	+	0.909438i	$0.636512\pi$
$524$	−8.79806	−0.384345
$525$	41.2637	1.80090
$526$	−13.3196	−0.580764
$527$	6.28163	0.273632
$528$	−211.803	−9.21754
$529$	−18.0664	−0.785495
$530$	−10.1848	−0.442398
$531$	−30.1581	−1.30875
$532$	−58.8713	−2.55239
$533$	−10.3759	−0.449430
$534$	−82.2521	−3.55940
$535$	−8.46629	−0.366030
$536$	24.8595	1.07377
$537$	−50.8700	−2.19520
$538$	−5.51258	−0.237664
$539$	23.3848	1.00725
$540$	3.00803	0.129445
$541$	12.9775	0.557946	0.278973	−	0.960299i	$-0.410006\pi$
$541$	12.9775	0.557946	0.278973	+	0.960299i	$0.410006\pi$
$542$	15.8911	0.682580
$543$	60.7568	2.60732
$544$	13.1913	0.565571
$545$	−2.64067	−0.113114
$546$	−23.4972	−1.00559
$547$	12.4789	0.533559	0.266779	−	0.963758i	$-0.414040\pi$
$547$	12.4789	0.533559	0.266779	+	0.963758i	$0.414040\pi$
$548$	50.8266	2.17120
$549$	48.0112	2.04907
$550$	71.4282	3.04571
$551$	−5.39832	−0.229976
$552$	−54.4634	−2.31812
$553$	−22.6275	−0.962220
$554$	−9.81498	−0.416999
$555$	−11.9763	−0.508365
$556$	25.0026	1.06034
$557$	13.2593	0.561813	0.280907	−	0.959735i	$-0.409365\pi$
$557$	13.2593	0.561813	0.280907	+	0.959735i	$0.409365\pi$
$558$	104.062	4.40531
$559$	10.5912	0.447959
$560$	−22.3415	−0.944103
$561$	7.97970	0.336903
$562$	−48.5271	−2.04699
$563$	−3.82403	−0.161163	−0.0805817	−	0.996748i	$-0.525678\pi$
$563$	−3.82403	−0.161163	−0.0805817	+	0.996748i	$0.525678\pi$
$564$	−71.4881	−3.01019
$565$	5.78112	0.243214
$566$	−22.3560	−0.939694
$567$	−24.4585	−1.02716
$568$	−60.4319	−2.53567
$569$	22.7664	0.954418	0.477209	−	0.878790i	$-0.341648\pi$
$569$	22.7664	0.954418	0.477209	+	0.878790i	$0.341648\pi$
$570$	9.59747	0.401994
$571$	12.7525	0.533675	0.266837	−	0.963742i	$-0.414021\pi$
$571$	12.7525	0.533675	0.266837	+	0.963742i	$0.414021\pi$
$572$	−29.8431	−1.24780
$573$	15.3357	0.640659
$574$	−95.6650	−3.99298
$575$	10.6900	0.445802
$576$	111.258	4.63574
$577$	38.8233	1.61623	0.808117	−	0.589021i	$-0.200487\pi$
$577$	38.8233	1.61623	0.808117	+	0.589021i	$0.200487\pi$
$578$	45.6735	1.89977
$579$	7.18180	0.298465
$580$	−4.05392	−0.168330
$581$	34.1791	1.41799
$582$	−41.5664	−1.72298
$583$	−46.5081	−1.92617
$584$	47.7989	1.97793
$585$	1.51238	0.0625292
$586$	−17.5509	−0.725022
$587$	−36.5133	−1.50707	−0.753533	−	0.657410i	$-0.771652\pi$
$587$	−36.5133	−1.50707	−0.753533	+	0.657410i	$0.771652\pi$
$588$	−60.6444	−2.50093
$589$	34.5001	1.42155
$590$	−10.2334	−0.421304
$591$	37.3147	1.53492
$592$	−166.656	−6.84953
$593$	−12.8413	−0.527328	−0.263664	−	0.964615i	$-0.584931\pi$
$593$	−12.8413	−0.527328	−0.263664	+	0.964615i	$0.584931\pi$
$594$	18.7212	0.768139
$595$	0.841721	0.0345072
$596$	100.936	4.13449
$597$	25.7114	1.05230
$598$	−6.08728	−0.248927
$599$	−4.32160	−0.176576	−0.0882878	−	0.996095i	$-0.528140\pi$
$599$	−4.32160	−0.176576	−0.0882878	+	0.996095i	$0.528140\pi$
$600$	−118.009	−4.81769
$601$	7.55623	0.308225	0.154112	−	0.988053i	$-0.450748\pi$
$601$	7.55623	0.308225	0.154112	+	0.988053i	$0.450748\pi$
$602$	97.6500	3.97992
$603$	−9.03027	−0.367741
$604$	53.3547	2.17097
$605$	−7.93087	−0.322436
$606$	42.5608	1.72892
$607$	3.04716	0.123681	0.0618403	−	0.998086i	$-0.480303\pi$
$607$	3.04716	0.123681	0.0618403	+	0.998086i	$0.480303\pi$
$608$	72.4493	2.93821
$609$	−14.5756	−0.590631
$610$	16.2915	0.659622
$611$	−5.09025	−0.205929
$612$	−11.1355	−0.450126
$613$	4.39791	0.177630	0.0888149	−	0.996048i	$-0.471692\pi$
$613$	4.39791	0.177630	0.0888149	+	0.996048i	$0.471692\pi$
$614$	44.9006	1.81204
$615$	11.4428	0.461419
$616$	−175.290	−7.06265
$617$	6.79310	0.273480	0.136740	−	0.990607i	$-0.456338\pi$
$617$	6.79310	0.273480	0.136740	+	0.990607i	$0.456338\pi$
$618$	128.820	5.18191
$619$	27.2665	1.09593	0.547966	−	0.836500i	$-0.315402\pi$
$619$	27.2665	1.09593	0.547966	+	0.836500i	$0.315402\pi$
$620$	25.9082	1.04050
$621$	2.80181	0.112433
$622$	−3.58210	−0.143629
$623$	−39.6192	−1.58731
$624$	39.1106	1.56568
$625$	22.2262	0.889048
$626$	−29.9272	−1.19613
$627$	43.8263	1.75025
$628$	−15.4752	−0.617526
$629$	6.27879	0.250352
$630$	13.9440	0.555544
$631$	−19.4304	−0.773511	−0.386755	−	0.922182i	$-0.626404\pi$
$631$	−19.4304	−0.773511	−0.386755	+	0.922182i	$0.626404\pi$
$632$	64.7118	2.57410
$633$	−44.9450	−1.78640
$634$	−41.6807	−1.65535
$635$	−6.19454	−0.245823
$636$	120.611	4.78253
$637$	−4.31813	−0.171091
$638$	−25.2305	−0.998887
$639$	21.9520	0.868409
$640$	18.0069	0.711787
$641$	7.79237	0.307780	0.153890	−	0.988088i	$-0.450820\pi$
$641$	7.79237	0.307780	0.153890	+	0.988088i	$0.450820\pi$
$642$	136.648	5.39305
$643$	−10.0431	−0.396062	−0.198031	−	0.980196i	$-0.563455\pi$
$643$	−10.0431	−0.396062	−0.198031	+	0.980196i	$0.563455\pi$
$644$	−41.1791	−1.62269
$645$	−11.6802	−0.459909
$646$	−5.03166	−0.197968
$647$	24.8285	0.976110	0.488055	−	0.872813i	$-0.337706\pi$
$647$	24.8285	0.976110	0.488055	+	0.872813i	$0.337706\pi$
$648$	69.9483	2.74783
$649$	−46.7304	−1.83433
$650$	−13.1896	−0.517340
$651$	93.1508	3.65087
$652$	58.8574	2.30503
$653$	12.3153	0.481934	0.240967	−	0.970533i	$-0.422535\pi$
$653$	12.3153	0.481934	0.240967	+	0.970533i	$0.422535\pi$
$654$	42.6210	1.66661
$655$	0.690875	0.0269947
$656$	159.233	6.21699
$657$	−17.3631	−0.677398
$658$	−46.9317	−1.82959
$659$	−31.9853	−1.24597	−0.622986	−	0.782233i	$-0.714081\pi$
$659$	−31.9853	−1.24597	−0.622986	+	0.782233i	$0.714081\pi$
$660$	32.9118	1.28109
$661$	−15.6751	−0.609689	−0.304845	−	0.952402i	$-0.598605\pi$
$661$	−15.6751	−0.609689	−0.304845	+	0.952402i	$0.598605\pi$
$662$	−80.0583	−3.11155
$663$	−1.47350	−0.0572259
$664$	−97.7477	−3.79335
$665$	4.62291	0.179269
$666$	104.015	4.03051
$667$	−3.77600	−0.146207
$668$	14.6466	0.566692
$669$	65.9721	2.55063
$670$	−3.06421	−0.118381
$671$	74.3940	2.87195
$672$	195.614	7.54598
$673$	−10.6369	−0.410023	−0.205011	−	0.978760i	$-0.565723\pi$
$673$	−10.6369	−0.410023	−0.205011	+	0.978760i	$0.565723\pi$
$674$	−73.1515	−2.81769
$675$	6.07084	0.233667
$676$	5.51070	0.211950
$677$	−39.8144	−1.53019	−0.765096	−	0.643917i	$-0.777308\pi$
$677$	−39.8144	−1.53019	−0.765096	+	0.643917i	$0.777308\pi$
$678$	−93.3086	−3.58349
$679$	−20.0217	−0.768363
$680$	−2.40721	−0.0923124
$681$	−16.3327	−0.625870
$682$	161.246	6.17442
$683$	30.1921	1.15527	0.577635	−	0.816295i	$-0.303976\pi$
$683$	30.1921	1.15527	0.577635	+	0.816295i	$0.303976\pi$
$684$	−61.1587	−2.33846
$685$	−3.99120	−0.152496
$686$	24.7266	0.944067
$687$	−31.3971	−1.19787
$688$	−162.537	−6.19665
$689$	8.58799	0.327176
$690$	6.71322	0.255568
$691$	18.9290	0.720095	0.360047	−	0.932934i	$-0.382761\pi$
$691$	18.9290	0.720095	0.360047	+	0.932934i	$0.382761\pi$
$692$	−21.4328	−0.814752
$693$	63.6746	2.41880
$694$	10.0703	0.382262
$695$	−1.96335	−0.0744740
$696$	41.6842	1.58004
$697$	−5.99911	−0.227233
$698$	24.4645	0.925997
$699$	−54.8634	−2.07513
$700$	−89.2250	−3.37239
$701$	51.6147	1.94946	0.974729	−	0.223389i	$-0.0717119\pi$
$701$	51.6147	1.94946	0.974729	+	0.223389i	$0.0717119\pi$
$702$	−3.45697	−0.130475
$703$	34.4845	1.30061
$704$	172.395	6.49740
$705$	5.61366	0.211423
$706$	−79.9547	−3.00913
$707$	20.5007	0.771009
$708$	121.187	4.55450
$709$	37.2458	1.39880	0.699398	−	0.714732i	$-0.253452\pi$
$709$	37.2458	1.39880	0.699398	+	0.714732i	$0.253452\pi$
$710$	7.44890	0.279552
$711$	−23.5067	−0.881570
$712$	113.306	4.24632
$713$	24.1320	0.903752
$714$	−13.5855	−0.508426
$715$	2.34345	0.0876402
$716$	109.997	4.11078
$717$	21.6641	0.809059
$718$	48.7305	1.81860
$719$	19.6728	0.733672	0.366836	−	0.930286i	$-0.380441\pi$
$719$	19.6728	0.733672	0.366836	+	0.930286i	$0.380441\pi$
$720$	−23.2096	−0.864971
$721$	62.0502	2.31087
$722$	24.4358	0.909406
$723$	−53.4991	−1.98965
$724$	−131.375	−4.88252
$725$	−8.18167	−0.303860
$726$	128.006	4.75075
$727$	8.95644	0.332176	0.166088	−	0.986111i	$-0.446886\pi$
$727$	8.95644	0.332176	0.166088	+	0.986111i	$0.446886\pi$
$728$	32.3684	1.19965
$729$	−35.0530	−1.29826
$730$	−5.89174	−0.218063
$731$	6.12359	0.226489
$732$	−192.928	−7.13083
$733$	40.5013	1.49595	0.747974	−	0.663728i	$-0.231027\pi$
$733$	40.5013	1.49595	0.747974	+	0.663728i	$0.231027\pi$
$734$	−36.8871	−1.36153
$735$	4.76215	0.175655
$736$	50.6767	1.86797
$737$	−13.9925	−0.515421
$738$	−99.3820	−3.65830
$739$	−39.5527	−1.45497	−0.727484	−	0.686125i	$-0.759310\pi$
$739$	−39.5527	−1.45497	−0.727484	+	0.686125i	$0.759310\pi$
$740$	25.8965	0.951973
$741$	−8.09278	−0.297296
$742$	79.1807	2.90681
$743$	1.20374	0.0441611	0.0220805	−	0.999756i	$-0.492971\pi$
$743$	1.20374	0.0441611	0.0220805	+	0.999756i	$0.492971\pi$
$744$	−266.399	−9.76667
$745$	−7.92607	−0.290389
$746$	−76.2282	−2.79091
$747$	35.5071	1.29914
$748$	−17.2546	−0.630891
$749$	65.8205	2.40503
$750$	29.6577	1.08295
$751$	−23.7603	−0.867025	−0.433513	−	0.901147i	$-0.642726\pi$
$751$	−23.7603	−0.867025	−0.433513	+	0.901147i	$0.642726\pi$
$752$	78.1170	2.84863
$753$	29.3334	1.06897
$754$	4.65897	0.169670
$755$	−4.18972	−0.152480
$756$	−23.3857	−0.850529
$757$	1.71984	0.0625088	0.0312544	−	0.999511i	$-0.490050\pi$
$757$	1.71984	0.0625088	0.0312544	+	0.999511i	$0.490050\pi$
$758$	−43.5753	−1.58273
$759$	30.6555	1.11272
$760$	−13.2209	−0.479574
$761$	1.86329	0.0675442	0.0337721	−	0.999430i	$-0.489248\pi$
$761$	1.86329	0.0675442	0.0337721	+	0.999430i	$0.489248\pi$
$762$	99.9812	3.62194
$763$	20.5297	0.743226
$764$	−33.1606	−1.19971
$765$	0.874425	0.0316149
$766$	−1.90097	−0.0686847
$767$	8.62904	0.311577
$768$	−128.378	−4.63243
$769$	−18.8264	−0.678898	−0.339449	−	0.940624i	$-0.610241\pi$
$769$	−18.8264	−0.678898	−0.339449	+	0.940624i	$0.610241\pi$
$770$	21.6065	0.778643
$771$	50.7837	1.82893
$772$	−15.5293	−0.558912
$773$	32.0552	1.15295	0.576473	−	0.817116i	$-0.304429\pi$
$773$	32.0552	1.15295	0.576473	+	0.817116i	$0.304429\pi$
$774$	101.444	3.64633
$775$	52.2882	1.87825
$776$	57.2595	2.05550
$777$	93.1087	3.34026
$778$	−29.0851	−1.04275
$779$	−32.9484	−1.18050
$780$	−6.07735	−0.217604
$781$	34.0149	1.21715
$782$	−3.51953	−0.125858
$783$	−2.14440	−0.0766345
$784$	66.2678	2.36671
$785$	1.21520	0.0433723
$786$	−11.1509	−0.397738
$787$	29.7868	1.06179	0.530893	−	0.847439i	$-0.321857\pi$
$787$	29.7868	1.06179	0.530893	+	0.847439i	$0.321857\pi$
$788$	−80.6860	−2.87432
$789$	−12.3863	−0.440963
$790$	−7.97644	−0.283789
$791$	−44.9449	−1.59806
$792$	−182.101	−6.47068
$793$	−13.7373	−0.487825
$794$	48.1549	1.70895
$795$	−9.47107	−0.335904
$796$	−55.5962	−1.97055
$797$	−0.925415	−0.0327799	−0.0163899	−	0.999866i	$-0.505217\pi$
$797$	−0.925415	−0.0327799	−0.0163899	+	0.999866i	$0.505217\pi$
$798$	−74.6148	−2.64134
$799$	−2.94307	−0.104118
$800$	109.804	3.88215
$801$	−41.1586	−1.45427
$802$	−28.2189	−0.996445
$803$	−26.9043	−0.949432
$804$	36.2872	1.27975
$805$	3.23362	0.113970
$806$	−29.7750	−1.04878
$807$	−5.12629	−0.180454
$808$	−58.6294	−2.06258
$809$	8.67280	0.304919	0.152460	−	0.988310i	$-0.451281\pi$
$809$	8.67280	0.304919	0.152460	+	0.988310i	$0.451281\pi$
$810$	−8.62189	−0.302942
$811$	−26.7418	−0.939030	−0.469515	−	0.882924i	$-0.655571\pi$
$811$	−26.7418	−0.939030	−0.469515	+	0.882924i	$0.655571\pi$
$812$	31.5169	1.10603
$813$	14.7775	0.518270
$814$	161.173	5.64911
$815$	−4.62182	−0.161895
$816$	22.6129	0.791610
$817$	33.6321	1.17664
$818$	−40.5183	−1.41669
$819$	−11.7579	−0.410854
$820$	−24.7429	−0.864061
$821$	46.5978	1.62627	0.813137	−	0.582072i	$-0.197758\pi$
$821$	46.5978	1.62627	0.813137	+	0.582072i	$0.197758\pi$
$822$	64.4188	2.24686
$823$	9.27725	0.323385	0.161692	−	0.986841i	$-0.448305\pi$
$823$	9.27725	0.323385	0.161692	+	0.986841i	$0.448305\pi$
$824$	−177.456	−6.18196
$825$	66.4229	2.31255
$826$	79.5591	2.76822
$827$	−9.06439	−0.315200	−0.157600	−	0.987503i	$-0.550376\pi$
$827$	−9.06439	−0.315200	−0.157600	+	0.987503i	$0.550376\pi$
$828$	−42.7791	−1.48668
$829$	−45.2918	−1.57305	−0.786525	−	0.617559i	$-0.788122\pi$
$829$	−45.2918	−1.57305	−0.786525	+	0.617559i	$0.788122\pi$
$830$	12.0485	0.418209
$831$	−9.12720	−0.316619
$832$	−31.8338	−1.10364
$833$	−2.49665	−0.0865038
$834$	31.6888	1.09729
$835$	−1.15013	−0.0398020
$836$	−94.7661	−3.27756
$837$	13.7046	0.473701
$838$	−18.0169	−0.622384
$839$	−53.7851	−1.85687	−0.928433	−	0.371499i	$-0.878844\pi$
$839$	−53.7851	−1.85687	−0.928433	+	0.371499i	$0.878844\pi$
$840$	−35.6967	−1.23165
$841$	−26.1100	−0.900345
$842$	−53.5594	−1.84578
$843$	−45.1265	−1.55424
$844$	97.1851	3.34525
$845$	−0.432732	−0.0148864
$846$	−48.7552	−1.67624
$847$	61.6580	2.11859
$848$	−131.795	−4.52585
$849$	−20.7894	−0.713491
$850$	−7.62596	−0.261568
$851$	24.1211	0.826862
$852$	−88.2120	−3.02209
$853$	−5.56296	−0.190472	−0.0952361	−	0.995455i	$-0.530361\pi$
$853$	−5.56296	−0.190472	−0.0952361	+	0.995455i	$0.530361\pi$
$854$	−126.657	−4.33410
$855$	4.80253	0.164243
$856$	−188.238	−6.43385
$857$	26.3933	0.901579	0.450789	−	0.892630i	$-0.351143\pi$
$857$	26.3933	0.901579	0.450789	+	0.892630i	$0.351143\pi$
$858$	−37.8238	−1.29128
$859$	−25.7116	−0.877267	−0.438633	−	0.898666i	$-0.644537\pi$
$859$	−25.7116	−0.877267	−0.438633	+	0.898666i	$0.644537\pi$
$860$	25.2563	0.861234
$861$	−88.9613	−3.03179
$862$	31.8309	1.08417
$863$	45.6426	1.55369	0.776845	−	0.629691i	$-0.216819\pi$
$863$	45.6426	1.55369	0.776845	+	0.629691i	$0.216819\pi$
$864$	28.7793	0.979093
$865$	1.68303	0.0572246
$866$	43.9107	1.49215
$867$	42.4729	1.44246
$868$	−201.421	−6.83668
$869$	−36.4239	−1.23560
$870$	−5.13803	−0.174196
$871$	2.58380	0.0875487
$872$	−58.7123	−1.98825
$873$	−20.7996	−0.703961
$874$	−19.3300	−0.653848
$875$	14.2855	0.482940
$876$	69.7717	2.35737
$877$	11.2687	0.380518	0.190259	−	0.981734i	$-0.439067\pi$
$877$	11.2687	0.380518	0.190259	+	0.981734i	$0.439067\pi$
$878$	−101.367	−3.42098
$879$	−16.3211	−0.550495
$880$	−35.9636	−1.21233
$881$	8.88699	0.299410	0.149705	−	0.988731i	$-0.452168\pi$
$881$	8.88699	0.299410	0.149705	+	0.988731i	$0.452168\pi$
$882$	−41.3598	−1.39266
$883$	−13.1720	−0.443272	−0.221636	−	0.975129i	$-0.571140\pi$
$883$	−13.1720	−0.443272	−0.221636	+	0.975129i	$0.571140\pi$
$884$	3.18616	0.107162
$885$	−9.51633	−0.319888
$886$	92.7310	3.11536
$887$	−29.9563	−1.00583	−0.502917	−	0.864335i	$-0.667740\pi$
$887$	−29.9563	−1.00583	−0.502917	+	0.864335i	$0.667740\pi$
$888$	−266.279	−8.93573
$889$	48.1590	1.61520
$890$	−13.9662	−0.468148
$891$	−39.3713	−1.31899
$892$	−142.652	−4.77636
$893$	−16.1640	−0.540907
$894$	127.928	4.27856
$895$	−8.63760	−0.288723
$896$	−139.994	−4.67686
$897$	−5.66071	−0.189006
$898$	110.060	3.67275
$899$	−18.4697	−0.616000
$900$	−92.6918	−3.08973
$901$	4.96539	0.165421
$902$	−153.994	−5.12743
$903$	90.8071	3.02187
$904$	128.537	4.27506
$905$	10.3163	0.342927
$906$	67.6230	2.24662
$907$	−46.7881	−1.55357	−0.776786	−	0.629765i	$-0.783151\pi$
$907$	−46.7881	−1.55357	−0.776786	+	0.629765i	$0.783151\pi$
$908$	35.3164	1.17202
$909$	21.2973	0.706386
$910$	−3.98976	−0.132259
$911$	21.1557	0.700918	0.350459	−	0.936578i	$-0.386026\pi$
$911$	21.1557	0.700918	0.350459	+	0.936578i	$0.386026\pi$
$912$	124.195	4.11251
$913$	55.0186	1.82085
$914$	−73.6986	−2.43773
$915$	15.1498	0.500838
$916$	67.8903	2.24316
$917$	−5.37115	−0.177371
$918$	−1.99875	−0.0659684
$919$	−37.7458	−1.24512	−0.622559	−	0.782573i	$-0.713907\pi$
$919$	−37.7458	−1.24512	−0.622559	+	0.782573i	$0.713907\pi$
$920$	−9.24775	−0.304889
$921$	41.7542	1.37585
$922$	−90.3927	−2.97693
$923$	−6.28106	−0.206743
$924$	−255.870	−8.41750
$925$	52.2646	1.71845
$926$	−2.74057	−0.0900606
$927$	64.4611	2.11718
$928$	−38.7859	−1.27321
$929$	31.7191	1.04067	0.520334	−	0.853963i	$-0.325807\pi$
$929$	31.7191	1.04067	0.520334	+	0.853963i	$0.325807\pi$
$930$	32.8366	1.07676
$931$	−13.7121	−0.449397
$932$	118.632	3.88592
$933$	−3.33109	−0.109055
$934$	−47.6036	−1.55764
$935$	1.35493	0.0443110
$936$	33.6260	1.09910
$937$	−44.6349	−1.45816	−0.729080	−	0.684429i	$-0.760052\pi$
$937$	−44.6349	−1.45816	−0.729080	+	0.684429i	$0.760052\pi$
$938$	23.8225	0.777831
$939$	−27.8300	−0.908199
$940$	−12.1385	−0.395914
$941$	28.5452	0.930549	0.465274	−	0.885167i	$-0.345956\pi$
$941$	28.5452	0.930549	0.465274	+	0.885167i	$0.345956\pi$
$942$	−19.6136	−0.639045
$943$	−23.0467	−0.750504
$944$	−132.425	−4.31006
$945$	1.83638	0.0597374
$946$	157.189	5.11065
$947$	21.1217	0.686365	0.343182	−	0.939269i	$-0.388495\pi$
$947$	21.1217	0.686365	0.343182	+	0.939269i	$0.388495\pi$
$948$	94.4593	3.06789
$949$	4.96803	0.161269
$950$	−41.8834	−1.35888
$951$	−38.7599	−1.25688
$952$	18.7147	0.606547
$953$	−45.4758	−1.47311	−0.736553	−	0.676379i	$-0.763548\pi$
$953$	−45.4758	−1.47311	−0.736553	+	0.676379i	$0.763548\pi$
$954$	82.2572	2.66317
$955$	2.60397	0.0842624
$956$	−46.8445	−1.51506
$957$	−23.4625	−0.758436
$958$	−102.527	−3.31251
$959$	31.0293	1.00199
$960$	35.1072	1.13308
$961$	87.0381	2.80768
$962$	−29.7615	−0.959549
$963$	68.3779	2.20345
$964$	115.682	3.72586
$965$	1.21945	0.0392555
$966$	−52.1914	−1.67923
$967$	−29.2303	−0.939984	−0.469992	−	0.882671i	$-0.655743\pi$
$967$	−29.2303	−0.939984	−0.469992	+	0.882671i	$0.655743\pi$
$968$	−176.334	−5.66758
$969$	−4.67906	−0.150313
$970$	−7.05786	−0.226614
$971$	−25.0932	−0.805278	−0.402639	−	0.915359i	$-0.631907\pi$
$971$	−25.0932	−0.805278	−0.402639	+	0.915359i	$0.631907\pi$
$972$	122.957	3.94383
$973$	15.2639	0.489338
$974$	−99.6080	−3.19165
$975$	−12.2654	−0.392806
$976$	210.818	6.74811
$977$	28.7445	0.919618	0.459809	−	0.888018i	$-0.347918\pi$
$977$	28.7445	0.919618	0.459809	+	0.888018i	$0.347918\pi$
$978$	74.5972	2.38536
$979$	−63.7758	−2.03828
$980$	−10.2973	−0.328934
$981$	21.3274	0.680931
$982$	−15.1928	−0.484821
$983$	−48.2666	−1.53947	−0.769733	−	0.638366i	$-0.779611\pi$
$983$	−48.2666	−1.53947	−0.769733	+	0.638366i	$0.779611\pi$
$984$	254.418	8.11054
$985$	6.33593	0.201880
$986$	2.69371	0.0857852
$987$	−43.6430	−1.38917
$988$	17.4991	0.556721
$989$	23.5249	0.748048
$990$	22.4460	0.713380
$991$	56.3049	1.78858	0.894292	−	0.447484i	$-0.147680\pi$
$991$	56.3049	1.78858	0.894292	+	0.447484i	$0.147680\pi$
$992$	247.877	7.87010
$993$	−74.4482	−2.36254
$994$	−57.9109	−1.83682
$995$	4.36573	0.138403
$996$	−142.681	−4.52104
$997$	42.4545	1.34455	0.672274	−	0.740302i	$-0.265318\pi$
$997$	42.4545	1.34455	0.672274	+	0.740302i	$0.265318\pi$
$998$	8.81288	0.278967
$999$	13.6984	0.433399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.2	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.2	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74057 q^{2} -2.54852 q^{3} +5.51070 q^{4} -0.432732 q^{5} +6.98439 q^{6} +3.36424 q^{7} -9.62130 q^{8} +3.49496 q^{9} +O(q^{10})\)	\(q-2.74057 q^{2} -2.54852 q^{3} +5.51070 q^{4} -0.432732 q^{5} +6.98439 q^{6} +3.36424 q^{7} -9.62130 q^{8} +3.49496 q^{9} +1.18593 q^{10} +5.41548 q^{11} -14.0441 q^{12} -1.00000 q^{13} -9.21993 q^{14} +1.10283 q^{15} +15.3464 q^{16} -0.578178 q^{17} -9.57816 q^{18} -3.17548 q^{19} -2.38466 q^{20} -8.57384 q^{21} -14.8415 q^{22} -2.22118 q^{23} +24.5201 q^{24} -4.81274 q^{25} +2.74057 q^{26} -1.26141 q^{27} +18.5393 q^{28} +1.70000 q^{29} -3.02237 q^{30} -10.8645 q^{31} -22.8152 q^{32} -13.8015 q^{33} +1.58453 q^{34} -1.45582 q^{35} +19.2597 q^{36} -10.8596 q^{37} +8.70261 q^{38} +2.54852 q^{39} +4.16345 q^{40} +10.3759 q^{41} +23.4972 q^{42} -10.5912 q^{43} +29.8431 q^{44} -1.51238 q^{45} +6.08728 q^{46} +5.09025 q^{47} -39.1106 q^{48} +4.31813 q^{49} +13.1896 q^{50} +1.47350 q^{51} -5.51070 q^{52} -8.58799 q^{53} +3.45697 q^{54} -2.34345 q^{55} -32.3684 q^{56} +8.09278 q^{57} -4.65897 q^{58} -8.62904 q^{59} +6.07735 q^{60} +13.7373 q^{61} +29.7750 q^{62} +11.7579 q^{63} +31.8338 q^{64} +0.432732 q^{65} +37.8238 q^{66} -2.58380 q^{67} -3.18616 q^{68} +5.66071 q^{69} +3.98976 q^{70} +6.28106 q^{71} -33.6260 q^{72} -4.96803 q^{73} +29.7615 q^{74} +12.2654 q^{75} -17.4991 q^{76} +18.2190 q^{77} -6.98439 q^{78} -6.72589 q^{79} -6.64088 q^{80} -7.27015 q^{81} -28.4358 q^{82} +10.1595 q^{83} -47.2479 q^{84} +0.250196 q^{85} +29.0258 q^{86} -4.33249 q^{87} -52.1040 q^{88} -11.7766 q^{89} +4.14478 q^{90} -3.36424 q^{91} -12.2402 q^{92} +27.6885 q^{93} -13.9502 q^{94} +1.37413 q^{95} +58.1451 q^{96} -5.95133 q^{97} -11.8341 q^{98} +18.9269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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