LMFDB - Embedded newform 6019.2.a.d.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.60439 q^{2} -3.42443 q^{3} +4.78284 q^{4} -1.92258 q^{5} +8.91854 q^{6} -3.26289 q^{7} -7.24759 q^{8} +8.72671 q^{9} +O(q^{10})$	\(q-2.60439 q^{2} -3.42443 q^{3} +4.78284 q^{4} -1.92258 q^{5} +8.91854 q^{6} -3.26289 q^{7} -7.24759 q^{8} +8.72671 q^{9} +5.00714 q^{10} +2.91679 q^{11} -16.3785 q^{12} -1.00000 q^{13} +8.49784 q^{14} +6.58372 q^{15} +9.30987 q^{16} -0.154769 q^{17} -22.7277 q^{18} +2.03344 q^{19} -9.19537 q^{20} +11.1735 q^{21} -7.59645 q^{22} +1.20403 q^{23} +24.8189 q^{24} -1.30370 q^{25} +2.60439 q^{26} -19.6107 q^{27} -15.6059 q^{28} +2.48804 q^{29} -17.1466 q^{30} +3.90008 q^{31} -9.75133 q^{32} -9.98833 q^{33} +0.403078 q^{34} +6.27316 q^{35} +41.7384 q^{36} +5.08361 q^{37} -5.29586 q^{38} +3.42443 q^{39} +13.9341 q^{40} +8.47932 q^{41} -29.1003 q^{42} +8.73442 q^{43} +13.9505 q^{44} -16.7778 q^{45} -3.13576 q^{46} +12.0214 q^{47} -31.8810 q^{48} +3.64648 q^{49} +3.39534 q^{50} +0.529994 q^{51} -4.78284 q^{52} +6.76794 q^{53} +51.0739 q^{54} -5.60775 q^{55} +23.6481 q^{56} -6.96335 q^{57} -6.47981 q^{58} -1.93850 q^{59} +31.4889 q^{60} +0.599857 q^{61} -10.1573 q^{62} -28.4743 q^{63} +6.77651 q^{64} +1.92258 q^{65} +26.0135 q^{66} +10.4205 q^{67} -0.740234 q^{68} -4.12311 q^{69} -16.3378 q^{70} -4.20840 q^{71} -63.2476 q^{72} +14.1033 q^{73} -13.2397 q^{74} +4.46443 q^{75} +9.72559 q^{76} -9.51717 q^{77} -8.91854 q^{78} +9.99960 q^{79} -17.8989 q^{80} +40.9753 q^{81} -22.0834 q^{82} +6.70204 q^{83} +53.4413 q^{84} +0.297555 q^{85} -22.7478 q^{86} -8.52010 q^{87} -21.1397 q^{88} -2.40563 q^{89} +43.6958 q^{90} +3.26289 q^{91} +5.75867 q^{92} -13.3556 q^{93} -31.3084 q^{94} -3.90944 q^{95} +33.3927 q^{96} -0.564527 q^{97} -9.49685 q^{98} +25.4540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60439	−1.84158	−0.920790	−	0.390058i	$-0.872455\pi$
$2$	−2.60439	−1.84158	−0.920790	+	0.390058i	$0.872455\pi$
$3$	−3.42443	−1.97709	−0.988547	−	0.150912i	$-0.951779\pi$
$3$	−3.42443	−1.97709	−0.988547	+	0.150912i	$0.951779\pi$
$4$	4.78284	2.39142
$5$	−1.92258	−0.859802	−0.429901	−	0.902876i	$-0.641452\pi$
$5$	−1.92258	−0.859802	−0.429901	+	0.902876i	$0.641452\pi$
$6$	8.91854	3.64098
$7$	−3.26289	−1.23326	−0.616629	−	0.787254i	$-0.711502\pi$
$7$	−3.26289	−1.23326	−0.616629	+	0.787254i	$0.711502\pi$
$8$	−7.24759	−2.56241
$9$	8.72671	2.90890
$10$	5.00714	1.58340
$11$	2.91679	0.879445	0.439722	−	0.898134i	$-0.355077\pi$
$11$	2.91679	0.879445	0.439722	+	0.898134i	$0.355077\pi$
$12$	−16.3785	−4.72806
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	8.49784	2.27114
$15$	6.58372	1.69991
$16$	9.30987	2.32747
$17$	−0.154769	−0.0375369	−0.0187685	−	0.999824i	$-0.505975\pi$
$17$	−0.154769	−0.0375369	−0.0187685	+	0.999824i	$0.505975\pi$
$18$	−22.7277	−5.35698
$19$	2.03344	0.466502	0.233251	−	0.972417i	$-0.425064\pi$
$19$	2.03344	0.466502	0.233251	+	0.972417i	$0.425064\pi$
$20$	−9.19537	−2.05615
$21$	11.1735	2.43827
$22$	−7.59645	−1.61957
$23$	1.20403	0.251057	0.125529	−	0.992090i	$-0.459937\pi$
$23$	1.20403	0.251057	0.125529	+	0.992090i	$0.459937\pi$
$24$	24.8189	5.06613
$25$	−1.30370	−0.260740
$26$	2.60439	0.510763
$27$	−19.6107	−3.77408
$28$	−15.6059	−2.94924
$29$	2.48804	0.462017	0.231008	−	0.972952i	$-0.425798\pi$
$29$	2.48804	0.462017	0.231008	+	0.972952i	$0.425798\pi$
$30$	−17.1466	−3.13052
$31$	3.90008	0.700476	0.350238	−	0.936661i	$-0.386101\pi$
$31$	3.90008	0.700476	0.350238	+	0.936661i	$0.386101\pi$
$32$	−9.75133	−1.72381
$33$	−9.98833	−1.73875
$34$	0.403078	0.0691273
$35$	6.27316	1.06036
$36$	41.7384	6.95641
$37$	5.08361	0.835740	0.417870	−	0.908507i	$-0.362777\pi$
$37$	5.08361	0.835740	0.417870	+	0.908507i	$0.362777\pi$
$38$	−5.29586	−0.859101
$39$	3.42443	0.548347
$40$	13.9341	2.20317
$41$	8.47932	1.32425	0.662124	−	0.749394i	$-0.269655\pi$
$41$	8.47932	1.32425	0.662124	+	0.749394i	$0.269655\pi$
$42$	−29.1003	−4.49027
$43$	8.73442	1.33199	0.665993	−	0.745958i	$-0.268008\pi$
$43$	8.73442	1.33199	0.665993	+	0.745958i	$0.268008\pi$
$44$	13.9505	2.10312
$45$	−16.7778	−2.50108
$46$	−3.13576	−0.462342
$47$	12.0214	1.75350	0.876750	−	0.480947i	$-0.159707\pi$
$47$	12.0214	1.75350	0.876750	+	0.480947i	$0.159707\pi$
$48$	−31.8810	−4.60162
$49$	3.64648	0.520926
$50$	3.39534	0.480174
$51$	0.529994	0.0742141
$52$	−4.78284	−0.663260
$53$	6.76794	0.929649	0.464824	−	0.885403i	$-0.346117\pi$
$53$	6.76794	0.929649	0.464824	+	0.885403i	$0.346117\pi$
$54$	51.0739	6.95027
$55$	−5.60775	−0.756149
$56$	23.6481	3.16011
$57$	−6.96335	−0.922319
$58$	−6.47981	−0.850841
$59$	−1.93850	−0.252371	−0.126185	−	0.992007i	$-0.540273\pi$
$59$	−1.93850	−0.252371	−0.126185	+	0.992007i	$0.540273\pi$
$60$	31.4889	4.06520
$61$	0.599857	0.0768038	0.0384019	−	0.999262i	$-0.487773\pi$
$61$	0.599857	0.0768038	0.0384019	+	0.999262i	$0.487773\pi$
$62$	−10.1573	−1.28998
$63$	−28.4743	−3.58743
$64$	6.77651	0.847064
$65$	1.92258	0.238466
$66$	26.0135	3.20204
$67$	10.4205	1.27307	0.636533	−	0.771250i	$-0.280368\pi$
$67$	10.4205	1.27307	0.636533	+	0.771250i	$0.280368\pi$
$68$	−0.740234	−0.0897665
$69$	−4.12311	−0.496364
$70$	−16.3378	−1.95274
$71$	−4.20840	−0.499445	−0.249723	−	0.968317i	$-0.580339\pi$
$71$	−4.20840	−0.499445	−0.249723	+	0.968317i	$0.580339\pi$
$72$	−63.2476	−7.45380
$73$	14.1033	1.65067	0.825335	−	0.564643i	$-0.190986\pi$
$73$	14.1033	1.65067	0.825335	+	0.564643i	$0.190986\pi$
$74$	−13.2397	−1.53908
$75$	4.46443	0.515508
$76$	9.72559	1.11560
$77$	−9.51717	−1.08458
$78$	−8.91854	−1.00983
$79$	9.99960	1.12504	0.562521	−	0.826783i	$-0.309831\pi$
$79$	9.99960	1.12504	0.562521	+	0.826783i	$0.309831\pi$
$80$	−17.8989	−2.00116
$81$	40.9753	4.55281
$82$	−22.0834	−2.43871
$83$	6.70204	0.735644	0.367822	−	0.929896i	$-0.380104\pi$
$83$	6.70204	0.735644	0.367822	+	0.929896i	$0.380104\pi$
$84$	53.4413	5.83092
$85$	0.297555	0.0322743
$86$	−22.7478	−2.45296
$87$	−8.52010	−0.913451
$88$	−21.1397	−2.25350
$89$	−2.40563	−0.254997	−0.127498	−	0.991839i	$-0.540695\pi$
$89$	−2.40563	−0.254997	−0.127498	+	0.991839i	$0.540695\pi$
$90$	43.6958	4.60594
$91$	3.26289	0.342044
$92$	5.75867	0.600383
$93$	−13.3556	−1.38491
$94$	−31.3084	−3.22921
$95$	−3.90944	−0.401100
$96$	33.3927	3.40813
$97$	−0.564527	−0.0573191	−0.0286595	−	0.999589i	$-0.509124\pi$
$97$	−0.564527	−0.0573191	−0.0286595	+	0.999589i	$0.509124\pi$
$98$	−9.49685	−0.959327
$99$	25.4540	2.55822
$100$	−6.23539	−0.623539
$101$	6.61925	0.658640	0.329320	−	0.944218i	$-0.393180\pi$
$101$	6.61925	0.658640	0.329320	+	0.944218i	$0.393180\pi$
$102$	−1.38031	−0.136671
$103$	−18.6030	−1.83301	−0.916504	−	0.400026i	$-0.869001\pi$
$103$	−18.6030	−1.83301	−0.916504	+	0.400026i	$0.869001\pi$
$104$	7.24759	0.710685
$105$	−21.4820	−2.09643
$106$	−17.6264	−1.71202
$107$	5.74762	0.555643	0.277822	−	0.960633i	$-0.410388\pi$
$107$	5.74762	0.555643	0.277822	+	0.960633i	$0.410388\pi$
$108$	−93.7948	−9.02541
$109$	6.41783	0.614717	0.307358	−	0.951594i	$-0.400555\pi$
$109$	6.41783	0.614717	0.307358	+	0.951594i	$0.400555\pi$
$110$	14.6048	1.39251
$111$	−17.4084	−1.65234
$112$	−30.3771	−2.87037
$113$	17.7326	1.66814	0.834071	−	0.551657i	$-0.186004\pi$
$113$	17.7326	1.66814	0.834071	+	0.551657i	$0.186004\pi$
$114$	18.1353	1.69852
$115$	−2.31484	−0.215860
$116$	11.8999	1.10488
$117$	−8.72671	−0.806784
$118$	5.04860	0.464761
$119$	0.504994	0.0462927
$120$	−47.7162	−4.35587
$121$	−2.49235	−0.226577
$122$	−1.56226	−0.141440
$123$	−29.0368	−2.61816
$124$	18.6535	1.67513
$125$	12.1193	1.08399
$126$	74.1582	6.60654
$127$	−1.97141	−0.174934	−0.0874672	−	0.996167i	$-0.527877\pi$
$127$	−1.97141	−0.174934	−0.0874672	+	0.996167i	$0.527877\pi$
$128$	1.85400	0.163872
$129$	−29.9104	−2.63346
$130$	−5.00714	−0.439155
$131$	4.96193	0.433525	0.216763	−	0.976224i	$-0.430450\pi$
$131$	4.96193	0.433525	0.216763	+	0.976224i	$0.430450\pi$
$132$	−47.7726	−4.15807
$133$	−6.63489	−0.575318
$134$	−27.1390	−2.34445
$135$	37.7031	3.24496
$136$	1.12170	0.0961850
$137$	10.0989	0.862805	0.431402	−	0.902160i	$-0.358019\pi$
$137$	10.0989	0.862805	0.431402	+	0.902160i	$0.358019\pi$
$138$	10.7382	0.914094
$139$	14.4161	1.22275	0.611377	−	0.791339i	$-0.290616\pi$
$139$	14.4161	1.22275	0.611377	+	0.791339i	$0.290616\pi$
$140$	30.0035	2.53576
$141$	−41.1664	−3.46683
$142$	10.9603	0.919768
$143$	−2.91679	−0.243914
$144$	81.2445	6.77038
$145$	−4.78344	−0.397243
$146$	−36.7306	−3.03984
$147$	−12.4871	−1.02992
$148$	24.3141	1.99860
$149$	0.719691	0.0589594	0.0294797	−	0.999565i	$-0.490615\pi$
$149$	0.719691	0.0589594	0.0294797	+	0.999565i	$0.490615\pi$
$150$	−11.6271	−0.949349
$151$	−13.5465	−1.10240	−0.551198	−	0.834374i	$-0.685829\pi$
$151$	−13.5465	−1.10240	−0.551198	+	0.834374i	$0.685829\pi$
$152$	−14.7375	−1.19537
$153$	−1.35062	−0.109191
$154$	24.7864	1.99735
$155$	−7.49821	−0.602271
$156$	16.3785	1.31133
$157$	6.17655	0.492942	0.246471	−	0.969150i	$-0.420729\pi$
$157$	6.17655	0.492942	0.246471	+	0.969150i	$0.420729\pi$
$158$	−26.0428	−2.07186
$159$	−23.1763	−1.83800
$160$	18.7477	1.48213
$161$	−3.92862	−0.309618
$162$	−106.716	−8.38437
$163$	−22.6607	−1.77492	−0.887460	−	0.460884i	$-0.847532\pi$
$163$	−22.6607	−1.77492	−0.887460	+	0.460884i	$0.847532\pi$
$164$	40.5552	3.16683
$165$	19.2033	1.49498
$166$	−17.4547	−1.35475
$167$	9.47324	0.733061	0.366530	−	0.930406i	$-0.380546\pi$
$167$	9.47324	0.733061	0.366530	+	0.930406i	$0.380546\pi$
$168$	−80.9813	−6.24784
$169$	1.00000	0.0769231
$170$	−0.774948	−0.0594358
$171$	17.7452	1.35701
$172$	41.7753	3.18534
$173$	−14.3036	−1.08748	−0.543742	−	0.839253i	$-0.682993\pi$
$173$	−14.3036	−1.08748	−0.543742	+	0.839253i	$0.682993\pi$
$174$	22.1897	1.68219
$175$	4.25384	0.321560
$176$	27.1549	2.04688
$177$	6.63825	0.498961
$178$	6.26521	0.469597
$179$	−10.1224	−0.756580	−0.378290	−	0.925687i	$-0.623488\pi$
$179$	−10.1224	−0.756580	−0.378290	+	0.925687i	$0.623488\pi$
$180$	−80.2453	−5.98113
$181$	−6.55275	−0.487062	−0.243531	−	0.969893i	$-0.578306\pi$
$181$	−6.55275	−0.487062	−0.243531	+	0.969893i	$0.578306\pi$
$182$	−8.49784	−0.629902
$183$	−2.05417	−0.151848
$184$	−8.72631	−0.643312
$185$	−9.77362	−0.718571
$186$	34.7831	2.55042
$187$	−0.451428	−0.0330117
$188$	57.4964	4.19335
$189$	63.9876	4.65442
$190$	10.1817	0.738657
$191$	17.1821	1.24326	0.621628	−	0.783313i	$-0.286472\pi$
$191$	17.1821	1.24326	0.621628	+	0.783313i	$0.286472\pi$
$192$	−23.2057	−1.67472
$193$	17.6729	1.27213	0.636063	−	0.771637i	$-0.280562\pi$
$193$	17.6729	1.27213	0.636063	+	0.771637i	$0.280562\pi$
$194$	1.47025	0.105558
$195$	−6.58372	−0.471470
$196$	17.4405	1.24575
$197$	13.5305	0.964005	0.482003	−	0.876170i	$-0.339910\pi$
$197$	13.5305	0.964005	0.482003	+	0.876170i	$0.339910\pi$
$198$	−66.2920	−4.71117
$199$	−9.42684	−0.668251	−0.334126	−	0.942529i	$-0.608441\pi$
$199$	−9.42684	−0.668251	−0.334126	+	0.942529i	$0.608441\pi$
$200$	9.44869	0.668123
$201$	−35.6842	−2.51697
$202$	−17.2391	−1.21294
$203$	−8.11820	−0.569786
$204$	2.53488	0.177477
$205$	−16.3021	−1.13859
$206$	48.4494	3.37563
$207$	10.5072	0.730301
$208$	−9.30987	−0.645523
$209$	5.93110	0.410263
$210$	55.9475	3.86074
$211$	−24.8803	−1.71283	−0.856414	−	0.516289i	$-0.827313\pi$
$211$	−24.8803	−1.71283	−0.856414	+	0.516289i	$0.827313\pi$
$212$	32.3700	2.22318
$213$	14.4114	0.987450
$214$	−14.9690	−1.02326
$215$	−16.7926	−1.14524
$216$	142.130	9.67074
$217$	−12.7256	−0.863868
$218$	−16.7145	−1.13205
$219$	−48.2959	−3.26353
$220$	−26.8210	−1.80827
$221$	0.154769	0.0104109
$222$	45.3384	3.04291
$223$	2.02347	0.135502	0.0677508	−	0.997702i	$-0.478418\pi$
$223$	2.02347	0.135502	0.0677508	+	0.997702i	$0.478418\pi$
$224$	31.8176	2.12590
$225$	−11.3770	−0.758467
$226$	−46.1826	−3.07202
$227$	−3.88967	−0.258166	−0.129083	−	0.991634i	$-0.541203\pi$
$227$	−3.88967	−0.258166	−0.129083	+	0.991634i	$0.541203\pi$
$228$	−33.3046	−2.20565
$229$	19.2120	1.26957	0.634783	−	0.772691i	$-0.281090\pi$
$229$	19.2120	1.26957	0.634783	+	0.772691i	$0.281090\pi$
$230$	6.02873	0.397523
$231$	32.5909	2.14432
$232$	−18.0323	−1.18388
$233$	26.6050	1.74295	0.871476	−	0.490439i	$-0.163163\pi$
$233$	26.6050	1.74295	0.871476	+	0.490439i	$0.163163\pi$
$234$	22.7277	1.48576
$235$	−23.1120	−1.50766
$236$	−9.27152	−0.603525
$237$	−34.2429	−2.22432
$238$	−1.31520	−0.0852518
$239$	−22.6082	−1.46240	−0.731201	−	0.682162i	$-0.761040\pi$
$239$	−22.6082	−1.46240	−0.731201	+	0.682162i	$0.761040\pi$
$240$	61.2936	3.95649
$241$	−18.6665	−1.20241	−0.601207	−	0.799093i	$-0.705313\pi$
$241$	−18.6665	−1.20241	−0.601207	+	0.799093i	$0.705313\pi$
$242$	6.49104	0.417260
$243$	−81.4849	−5.22726
$244$	2.86902	0.183670
$245$	−7.01064	−0.447893
$246$	75.6232	4.82156
$247$	−2.03344	−0.129384
$248$	−28.2662	−1.79491
$249$	−22.9506	−1.45444
$250$	−31.5635	−1.99625
$251$	15.6111	0.985366	0.492683	−	0.870209i	$-0.336016\pi$
$251$	15.6111	0.985366	0.492683	+	0.870209i	$0.336016\pi$
$252$	−136.188	−8.57904
$253$	3.51190	0.220791
$254$	5.13432	0.322156
$255$	−1.01895	−0.0638094
$256$	−18.3815	−1.14885
$257$	−20.8338	−1.29958	−0.649789	−	0.760114i	$-0.725143\pi$
$257$	−20.8338	−1.29958	−0.649789	+	0.760114i	$0.725143\pi$
$258$	77.8982	4.84973
$259$	−16.5873	−1.03068
$260$	9.19537	0.570273
$261$	21.7124	1.34396
$262$	−12.9228	−0.798372
$263$	12.3520	0.761656	0.380828	−	0.924646i	$-0.375639\pi$
$263$	12.3520	0.761656	0.380828	+	0.924646i	$0.375639\pi$
$264$	72.3914	4.45538
$265$	−13.0119	−0.799314
$266$	17.2798	1.05949
$267$	8.23792	0.504153
$268$	49.8395	3.04443
$269$	5.74614	0.350348	0.175174	−	0.984537i	$-0.443951\pi$
$269$	5.74614	0.350348	0.175174	+	0.984537i	$0.443951\pi$
$270$	−98.1934	−5.97586
$271$	−28.2514	−1.71615	−0.858074	−	0.513526i	$-0.828339\pi$
$271$	−28.2514	−1.71615	−0.858074	+	0.513526i	$0.828339\pi$
$272$	−1.44088	−0.0873660
$273$	−11.1735	−0.676254
$274$	−26.3014	−1.58892
$275$	−3.80262	−0.229306
$276$	−19.7202	−1.18701
$277$	−7.42667	−0.446225	−0.223113	−	0.974793i	$-0.571622\pi$
$277$	−7.42667	−0.446225	−0.223113	+	0.974793i	$0.571622\pi$
$278$	−37.5450	−2.25180
$279$	34.0349	2.03762
$280$	−45.4653	−2.71707
$281$	−5.17023	−0.308430	−0.154215	−	0.988037i	$-0.549285\pi$
$281$	−5.17023	−0.308430	−0.154215	+	0.988037i	$0.549285\pi$
$282$	107.213	6.38446
$283$	−22.2374	−1.32188	−0.660938	−	0.750441i	$-0.729841\pi$
$283$	−22.2374	−1.32188	−0.660938	+	0.750441i	$0.729841\pi$
$284$	−20.1281	−1.19438
$285$	13.3876	0.793012
$286$	7.59645	0.449187
$287$	−27.6671	−1.63314
$288$	−85.0970	−5.01439
$289$	−16.9760	−0.998591
$290$	12.4579	0.731555
$291$	1.93318	0.113325
$292$	67.4540	3.94745
$293$	28.0017	1.63587	0.817937	−	0.575307i	$-0.195118\pi$
$293$	28.0017	1.63587	0.817937	+	0.575307i	$0.195118\pi$
$294$	32.5213	1.89668
$295$	3.72691	0.216989
$296$	−36.8439	−2.14151
$297$	−57.2002	−3.31909
$298$	−1.87435	−0.108578
$299$	−1.20403	−0.0696308
$300$	21.3526	1.23279
$301$	−28.4995	−1.64268
$302$	35.2803	2.03015
$303$	−22.6672	−1.30219
$304$	18.9310	1.08577
$305$	−1.15327	−0.0660361
$306$	3.51754	0.201085
$307$	−15.2525	−0.870509	−0.435254	−	0.900308i	$-0.643342\pi$
$307$	−15.2525	−0.870509	−0.435254	+	0.900308i	$0.643342\pi$
$308$	−45.5191	−2.59369
$309$	63.7046	3.62403
$310$	19.5283	1.10913
$311$	7.31859	0.414999	0.207500	−	0.978235i	$-0.433467\pi$
$311$	7.31859	0.414999	0.207500	+	0.978235i	$0.433467\pi$
$312$	−24.8189	−1.40509
$313$	−26.7131	−1.50991	−0.754957	−	0.655774i	$-0.772342\pi$
$313$	−26.7131	−1.50991	−0.754957	+	0.655774i	$0.772342\pi$
$314$	−16.0861	−0.907792
$315$	54.7441	3.08448
$316$	47.8265	2.69045
$317$	11.8568	0.665947	0.332973	−	0.942936i	$-0.391948\pi$
$317$	11.8568	0.665947	0.332973	+	0.942936i	$0.391948\pi$
$318$	60.3602	3.38483
$319$	7.25708	0.406318
$320$	−13.0284	−0.728307
$321$	−19.6823	−1.09856
$322$	10.2316	0.570187
$323$	−0.314712	−0.0175111
$324$	195.978	10.8877
$325$	1.30370	0.0723163
$326$	59.0172	3.26866
$327$	−21.9774	−1.21535
$328$	−61.4547	−3.39327
$329$	−39.2245	−2.16252
$330$	−50.0129	−2.75312
$331$	23.0548	1.26721	0.633604	−	0.773658i	$-0.281575\pi$
$331$	23.0548	1.26721	0.633604	+	0.773658i	$0.281575\pi$
$332$	32.0548	1.75923
$333$	44.3632	2.43109
$334$	−24.6720	−1.34999
$335$	−20.0342	−1.09458
$336$	104.024	5.67499
$337$	−2.00359	−0.109142	−0.0545712	−	0.998510i	$-0.517379\pi$
$337$	−2.00359	−0.109142	−0.0545712	+	0.998510i	$0.517379\pi$
$338$	−2.60439	−0.141660
$339$	−60.7240	−3.29807
$340$	1.42316	0.0771815
$341$	11.3757	0.616030
$342$	−46.2154	−2.49904
$343$	10.9422	0.590822
$344$	−63.3035	−3.41310
$345$	7.92699	0.426775
$346$	37.2522	2.00269
$347$	−6.84634	−0.367531	−0.183765	−	0.982970i	$-0.558829\pi$
$347$	−6.84634	−0.367531	−0.183765	+	0.982970i	$0.558829\pi$
$348$	−40.7503	−2.18444
$349$	10.8588	0.581257	0.290629	−	0.956836i	$-0.406136\pi$
$349$	10.8588	0.581257	0.290629	+	0.956836i	$0.406136\pi$
$350$	−11.0786	−0.592178
$351$	19.6107	1.04674
$352$	−28.4426	−1.51599
$353$	−15.8966	−0.846091	−0.423045	−	0.906109i	$-0.639039\pi$
$353$	−15.8966	−0.846091	−0.423045	+	0.906109i	$0.639039\pi$
$354$	−17.2886	−0.918877
$355$	8.09097	0.429424
$356$	−11.5058	−0.609804
$357$	−1.72932	−0.0915251
$358$	26.3625	1.39330
$359$	27.3272	1.44227	0.721136	−	0.692793i	$-0.243620\pi$
$359$	27.3272	1.44227	0.721136	+	0.692793i	$0.243620\pi$
$360$	121.598	6.40880
$361$	−14.8651	−0.782376
$362$	17.0659	0.896965
$363$	8.53486	0.447964
$364$	15.6059	0.817971
$365$	−27.1147	−1.41925
$366$	5.34985	0.279641
$367$	−4.61321	−0.240807	−0.120404	−	0.992725i	$-0.538419\pi$
$367$	−4.61321	−0.240807	−0.120404	+	0.992725i	$0.538419\pi$
$368$	11.2093	0.584328
$369$	73.9966	3.85211
$370$	25.4543	1.32331
$371$	−22.0831	−1.14650
$372$	−63.8775	−3.31189
$373$	−0.434919	−0.0225192	−0.0112596	−	0.999937i	$-0.503584\pi$
$373$	−0.434919	−0.0225192	−0.0112596	+	0.999937i	$0.503584\pi$
$374$	1.17569	0.0607936
$375$	−41.5018	−2.14314
$376$	−87.1261	−4.49319
$377$	−2.48804	−0.128140
$378$	−166.649	−8.57148
$379$	−30.0325	−1.54267	−0.771334	−	0.636431i	$-0.780410\pi$
$379$	−30.0325	−1.54267	−0.771334	+	0.636431i	$0.780410\pi$
$380$	−18.6982	−0.959197
$381$	6.75096	0.345862
$382$	−44.7489	−2.28956
$383$	−13.3513	−0.682221	−0.341111	−	0.940023i	$-0.610803\pi$
$383$	−13.3513	−0.682221	−0.341111	+	0.940023i	$0.610803\pi$
$384$	−6.34888	−0.323990
$385$	18.2975	0.932527
$386$	−46.0272	−2.34272
$387$	76.2227	3.87462
$388$	−2.70004	−0.137074
$389$	5.45355	0.276506	0.138253	−	0.990397i	$-0.455851\pi$
$389$	5.45355	0.276506	0.138253	+	0.990397i	$0.455851\pi$
$390$	17.1466	0.868251
$391$	−0.186346	−0.00942392
$392$	−26.4282	−1.33483
$393$	−16.9918	−0.857121
$394$	−35.2386	−1.77529
$395$	−19.2250	−0.967314
$396$	121.742	6.11777
$397$	26.3398	1.32196	0.660978	−	0.750405i	$-0.270142\pi$
$397$	26.3398	1.32196	0.660978	+	0.750405i	$0.270142\pi$
$398$	24.5512	1.23064
$399$	22.7207	1.13746
$400$	−12.1373	−0.606864
$401$	27.7989	1.38821	0.694106	−	0.719873i	$-0.255800\pi$
$401$	27.7989	1.38821	0.694106	+	0.719873i	$0.255800\pi$
$402$	92.9356	4.63521
$403$	−3.90008	−0.194277
$404$	31.6588	1.57509
$405$	−78.7781	−3.91452
$406$	21.1430	1.04931
$407$	14.8278	0.734987
$408$	−3.84118	−0.190167
$409$	24.2600	1.19958	0.599791	−	0.800157i	$-0.295250\pi$
$409$	24.2600	1.19958	0.599791	+	0.800157i	$0.295250\pi$
$410$	42.4571	2.09681
$411$	−34.5829	−1.70585
$412$	−88.9751	−4.38349
$413$	6.32511	0.311239
$414$	−27.3648	−1.34491
$415$	−12.8852	−0.632508
$416$	9.75133	0.478098
$417$	−49.3668	−2.41750
$418$	−15.4469	−0.755532
$419$	−23.5573	−1.15085	−0.575424	−	0.817855i	$-0.695163\pi$
$419$	−23.5573	−1.15085	−0.575424	+	0.817855i	$0.695163\pi$
$420$	−102.745	−5.01344
$421$	16.0375	0.781619	0.390809	−	0.920472i	$-0.372195\pi$
$421$	16.0375	0.781619	0.390809	+	0.920472i	$0.372195\pi$
$422$	64.7979	3.15431
$423$	104.907	5.10076
$424$	−49.0513	−2.38214
$425$	0.201772	0.00978738
$426$	−37.5328	−1.81847
$427$	−1.95727	−0.0947189
$428$	27.4899	1.32878
$429$	9.98833	0.482241
$430$	43.7344	2.10906
$431$	1.73794	0.0837136	0.0418568	−	0.999124i	$-0.486673\pi$
$431$	1.73794	0.0837136	0.0418568	+	0.999124i	$0.486673\pi$
$432$	−182.573	−8.78405
$433$	4.28940	0.206136	0.103068	−	0.994674i	$-0.467134\pi$
$433$	4.28940	0.206136	0.103068	+	0.994674i	$0.467134\pi$
$434$	33.1423	1.59088
$435$	16.3806	0.785387
$436$	30.6954	1.47005
$437$	2.44831	0.117119
$438$	125.781	6.01006
$439$	13.3426	0.636809	0.318405	−	0.947955i	$-0.396853\pi$
$439$	13.3426	0.636809	0.318405	+	0.947955i	$0.396853\pi$
$440$	40.6427	1.93756
$441$	31.8218	1.51532
$442$	−0.403078	−0.0191725
$443$	20.3897	0.968742	0.484371	−	0.874863i	$-0.339049\pi$
$443$	20.3897	0.968742	0.484371	+	0.874863i	$0.339049\pi$
$444$	−83.2618	−3.95143
$445$	4.62502	0.219247
$446$	−5.26991	−0.249537
$447$	−2.46453	−0.116568
$448$	−22.1110	−1.04465
$449$	−5.79517	−0.273491	−0.136745	−	0.990606i	$-0.543664\pi$
$449$	−5.79517	−0.273491	−0.136745	+	0.990606i	$0.543664\pi$
$450$	29.6301	1.39678
$451$	24.7324	1.16460
$452$	84.8121	3.98923
$453$	46.3889	2.17954
$454$	10.1302	0.475434
$455$	−6.27316	−0.294090
$456$	50.4675	2.36336
$457$	6.77969	0.317140	0.158570	−	0.987348i	$-0.449312\pi$
$457$	6.77969	0.317140	0.158570	+	0.987348i	$0.449312\pi$
$458$	−50.0355	−2.33801
$459$	3.03512	0.141667
$460$	−11.0715	−0.516211
$461$	21.3393	0.993872	0.496936	−	0.867787i	$-0.334458\pi$
$461$	21.3393	0.993872	0.496936	+	0.867787i	$0.334458\pi$
$462$	−84.8793	−3.94894
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	23.1633	1.07533
$465$	25.6771	1.19075
$466$	−69.2897	−3.20979
$467$	12.1963	0.564376	0.282188	−	0.959359i	$-0.408940\pi$
$467$	12.1963	0.564376	0.282188	+	0.959359i	$0.408940\pi$
$468$	−41.7384	−1.92936
$469$	−34.0010	−1.57002
$470$	60.1927	2.77648
$471$	−21.1511	−0.974593
$472$	14.0494	0.646678
$473$	25.4764	1.17141
$474$	89.1818	4.09626
$475$	−2.65099	−0.121636
$476$	2.41531	0.110705
$477$	59.0619	2.70426
$478$	58.8805	2.69313
$479$	−10.0922	−0.461126	−0.230563	−	0.973057i	$-0.574057\pi$
$479$	−10.0922	−0.461126	−0.230563	+	0.973057i	$0.574057\pi$
$480$	−64.2001	−2.93032
$481$	−5.08361	−0.231793
$482$	48.6148	2.21434
$483$	13.4533	0.612145
$484$	−11.9205	−0.541841
$485$	1.08535	0.0492831
$486$	212.218	9.62641
$487$	28.6451	1.29803	0.649016	−	0.760775i	$-0.275181\pi$
$487$	28.6451	1.29803	0.649016	+	0.760775i	$0.275181\pi$
$488$	−4.34752	−0.196803
$489$	77.5998	3.50919
$490$	18.2584	0.824832
$491$	−10.2983	−0.464757	−0.232378	−	0.972625i	$-0.574651\pi$
$491$	−10.2983	−0.464757	−0.232378	+	0.972625i	$0.574651\pi$
$492$	−138.878	−6.26112
$493$	−0.385070	−0.0173427
$494$	5.29586	0.238272
$495$	−48.9372	−2.19956
$496$	36.3093	1.63033
$497$	13.7316	0.615945
$498$	59.7724	2.67846
$499$	32.2143	1.44211	0.721055	−	0.692877i	$-0.243657\pi$
$499$	32.2143	1.44211	0.721055	+	0.692877i	$0.243657\pi$
$500$	57.9649	2.59227
$501$	−32.4404	−1.44933
$502$	−40.6574	−1.81463
$503$	−19.2792	−0.859617	−0.429808	−	0.902920i	$-0.641419\pi$
$503$	−19.2792	−0.859617	−0.429808	+	0.902920i	$0.641419\pi$
$504$	206.370	9.19246
$505$	−12.7260	−0.566301
$506$	−9.14634	−0.406604
$507$	−3.42443	−0.152084
$508$	−9.42894	−0.418342
$509$	41.8350	1.85430	0.927151	−	0.374688i	$-0.122250\pi$
$509$	41.8350	1.85430	0.927151	+	0.374688i	$0.122250\pi$
$510$	2.65375	0.117510
$511$	−46.0177	−2.03570
$512$	44.1647	1.95182
$513$	−39.8771	−1.76062
$514$	54.2594	2.39328
$515$	35.7657	1.57602
$516$	−143.057	−6.29771
$517$	35.0638	1.54211
$518$	43.1997	1.89809
$519$	48.9817	2.15006
$520$	−13.9341	−0.611049
$521$	31.3690	1.37430	0.687151	−	0.726515i	$-0.258861\pi$
$521$	31.3690	1.37430	0.687151	+	0.726515i	$0.258861\pi$
$522$	−56.5474	−2.47501
$523$	8.09553	0.353993	0.176996	−	0.984212i	$-0.443362\pi$
$523$	8.09553	0.353993	0.176996	+	0.984212i	$0.443362\pi$
$524$	23.7321	1.03674
$525$	−14.5670	−0.635754
$526$	−32.1694	−1.40265
$527$	−0.603611	−0.0262937
$528$	−92.9901	−4.04687
$529$	−21.5503	−0.936970
$530$	33.8880	1.47200
$531$	−16.9167	−0.734122
$532$	−31.7336	−1.37583
$533$	−8.47932	−0.367280
$534$	−21.4547	−0.928438
$535$	−11.0502	−0.477744
$536$	−75.5235	−3.26212
$537$	34.6633	1.49583
$538$	−14.9652	−0.645194
$539$	10.6360	0.458126
$540$	180.328	7.76007
$541$	−32.8630	−1.41289	−0.706445	−	0.707768i	$-0.749702\pi$
$541$	−32.8630	−1.41289	−0.706445	+	0.707768i	$0.749702\pi$
$542$	73.5775	3.16043
$543$	22.4394	0.962968
$544$	1.50920	0.0647065
$545$	−12.3388	−0.528535
$546$	29.1003	1.24538
$547$	6.96287	0.297711	0.148855	−	0.988859i	$-0.452441\pi$
$547$	6.96287	0.297711	0.148855	+	0.988859i	$0.452441\pi$
$548$	48.3013	2.06333
$549$	5.23477	0.223415
$550$	9.90349	0.422286
$551$	5.05926	0.215532
$552$	29.8826	1.27189
$553$	−32.6276	−1.38747
$554$	19.3419	0.821760
$555$	33.4691	1.42068
$556$	68.9497	2.92412
$557$	11.6975	0.495639	0.247819	−	0.968806i	$-0.420286\pi$
$557$	11.6975	0.495639	0.247819	+	0.968806i	$0.420286\pi$
$558$	−88.6401	−3.75243
$559$	−8.73442	−0.369426
$560$	58.4023	2.46795
$561$	1.54588	0.0652672
$562$	13.4653	0.567998
$563$	−27.8396	−1.17330	−0.586649	−	0.809842i	$-0.699553\pi$
$563$	−27.8396	−1.17330	−0.586649	+	0.809842i	$0.699553\pi$
$564$	−196.892	−8.29066
$565$	−34.0923	−1.43427
$566$	57.9148	2.43434
$567$	−133.698	−5.61479
$568$	30.5008	1.27978
$569$	−24.4202	−1.02375	−0.511875	−	0.859060i	$-0.671049\pi$
$569$	−24.4202	−1.02375	−0.511875	+	0.859060i	$0.671049\pi$
$570$	−34.8665	−1.46040
$571$	21.4247	0.896595	0.448297	−	0.893884i	$-0.352031\pi$
$571$	21.4247	0.896595	0.448297	+	0.893884i	$0.352031\pi$
$572$	−13.9505	−0.583301
$573$	−58.8390	−2.45803
$574$	72.0560	3.00756
$575$	−1.56969	−0.0654607
$576$	59.1366	2.46403
$577$	0.856639	0.0356624	0.0178312	−	0.999841i	$-0.494324\pi$
$577$	0.856639	0.0356624	0.0178312	+	0.999841i	$0.494324\pi$
$578$	44.2122	1.83899
$579$	−60.5197	−2.51511
$580$	−22.8784	−0.949975
$581$	−21.8680	−0.907239
$582$	−5.03476	−0.208698
$583$	19.7407	0.817575
$584$	−102.215	−4.22970
$585$	16.7778	0.693675
$586$	−72.9272	−3.01260
$587$	−41.7546	−1.72340	−0.861699	−	0.507421i	$-0.830599\pi$
$587$	−41.7546	−1.72340	−0.861699	+	0.507421i	$0.830599\pi$
$588$	−59.7238	−2.46297
$589$	7.93057	0.326773
$590$	−9.70632	−0.399603
$591$	−46.3341	−1.90593
$592$	47.3277	1.94516
$593$	16.2801	0.668543	0.334271	−	0.942477i	$-0.391510\pi$
$593$	16.2801	0.668543	0.334271	+	0.942477i	$0.391510\pi$
$594$	148.972	6.11238
$595$	−0.970890	−0.0398026
$596$	3.44217	0.140997
$597$	32.2815	1.32120
$598$	3.13576	0.128231
$599$	8.40918	0.343590	0.171795	−	0.985133i	$-0.445043\pi$
$599$	8.40918	0.343590	0.171795	+	0.985133i	$0.445043\pi$
$600$	−32.3563	−1.32094
$601$	0.986605	0.0402445	0.0201222	−	0.999798i	$-0.493594\pi$
$601$	0.986605	0.0402445	0.0201222	+	0.999798i	$0.493594\pi$
$602$	74.2237	3.02513
$603$	90.9366	3.70322
$604$	−64.7906	−2.63629
$605$	4.79173	0.194811
$606$	59.0341	2.39810
$607$	−27.3519	−1.11018	−0.555090	−	0.831790i	$-0.687316\pi$
$607$	−27.3519	−1.11018	−0.555090	+	0.831790i	$0.687316\pi$
$608$	−19.8287	−0.804160
$609$	27.8002	1.12652
$610$	3.00356	0.121611
$611$	−12.0214	−0.486333
$612$	−6.45980	−0.261122
$613$	32.4709	1.31149	0.655743	−	0.754984i	$-0.272355\pi$
$613$	32.4709	1.31149	0.655743	+	0.754984i	$0.272355\pi$
$614$	39.7235	1.60311
$615$	55.8255	2.25110
$616$	68.9766	2.77915
$617$	−11.3620	−0.457416	−0.228708	−	0.973495i	$-0.573450\pi$
$617$	−11.3620	−0.457416	−0.228708	+	0.973495i	$0.573450\pi$
$618$	−165.912	−6.67394
$619$	−45.6899	−1.83643	−0.918216	−	0.396081i	$-0.870370\pi$
$619$	−45.6899	−1.83643	−0.918216	+	0.396081i	$0.870370\pi$
$620$	−35.8627	−1.44028
$621$	−23.6118	−0.947510
$622$	−19.0604	−0.764254
$623$	7.84933	0.314477
$624$	31.8810	1.27626
$625$	−16.7819	−0.671275
$626$	69.5713	2.78063
$627$	−20.3106	−0.811128
$628$	29.5414	1.17883
$629$	−0.786784	−0.0313711
$630$	−142.575	−5.68032
$631$	28.4939	1.13432	0.567162	−	0.823606i	$-0.308041\pi$
$631$	28.4939	1.13432	0.567162	+	0.823606i	$0.308041\pi$
$632$	−72.4730	−2.88282
$633$	85.2007	3.38642
$634$	−30.8798	−1.22639
$635$	3.79019	0.150409
$636$	−110.849	−4.39544
$637$	−3.64648	−0.144479
$638$	−18.9002	−0.748268
$639$	−36.7255	−1.45284
$640$	−3.56445	−0.140897
$641$	−26.3963	−1.04259	−0.521295	−	0.853377i	$-0.674551\pi$
$641$	−26.3963	−1.04259	−0.521295	+	0.853377i	$0.674551\pi$
$642$	51.2604	2.02309
$643$	−30.1401	−1.18861	−0.594304	−	0.804241i	$-0.702572\pi$
$643$	−30.1401	−1.18861	−0.594304	+	0.804241i	$0.702572\pi$
$644$	−18.7899	−0.740428
$645$	57.5050	2.26426
$646$	0.819633	0.0322480
$647$	−33.5367	−1.31846	−0.659231	−	0.751940i	$-0.729118\pi$
$647$	−33.5367	−1.31846	−0.659231	+	0.751940i	$0.729118\pi$
$648$	−296.972	−11.6662
$649$	−5.65419	−0.221946
$650$	−3.39534	−0.133176
$651$	43.5778	1.70795
$652$	−108.382	−4.24458
$653$	17.7021	0.692738	0.346369	−	0.938098i	$-0.387415\pi$
$653$	17.7021	0.692738	0.346369	+	0.938098i	$0.387415\pi$
$654$	57.2377	2.23817
$655$	−9.53968	−0.372746
$656$	78.9414	3.08214
$657$	123.076	4.80164
$658$	102.156	3.98245
$659$	−27.3286	−1.06457	−0.532286	−	0.846564i	$-0.678667\pi$
$659$	−27.3286	−1.06457	−0.532286	+	0.846564i	$0.678667\pi$
$660$	91.8464	3.57512
$661$	0.982327	0.0382081	0.0191040	−	0.999818i	$-0.493919\pi$
$661$	0.982327	0.0382081	0.0191040	+	0.999818i	$0.493919\pi$
$662$	−60.0437	−2.33366
$663$	−0.529994	−0.0205833
$664$	−48.5736	−1.88502
$665$	12.7561	0.494659
$666$	−115.539	−4.47704
$667$	2.99567	0.115993
$668$	45.3090	1.75306
$669$	−6.92923	−0.267900
$670$	52.1768	2.01577
$671$	1.74965	0.0675447
$672$	−108.957	−4.20311
$673$	26.3662	1.01634	0.508171	−	0.861256i	$-0.330322\pi$
$673$	26.3662	1.01634	0.508171	+	0.861256i	$0.330322\pi$
$674$	5.21812	0.200994
$675$	25.5665	0.984054
$676$	4.78284	0.183955
$677$	−26.9082	−1.03417	−0.517084	−	0.855935i	$-0.672983\pi$
$677$	−26.9082	−1.03417	−0.517084	+	0.855935i	$0.672983\pi$
$678$	158.149	6.07367
$679$	1.84199	0.0706892
$680$	−2.15656	−0.0827001
$681$	13.3199	0.510419
$682$	−29.6268	−1.13447
$683$	17.8927	0.684646	0.342323	−	0.939582i	$-0.388786\pi$
$683$	17.8927	0.684646	0.342323	+	0.939582i	$0.388786\pi$
$684$	84.8724	3.24518
$685$	−19.4159	−0.741842
$686$	−28.4977	−1.08805
$687$	−65.7902	−2.51005
$688$	81.3163	3.10015
$689$	−6.76794	−0.257838
$690$	−20.6450	−0.785940
$691$	39.1050	1.48763	0.743813	−	0.668388i	$-0.233015\pi$
$691$	39.1050	1.48763	0.743813	+	0.668388i	$0.233015\pi$
$692$	−68.4119	−2.60063
$693$	−83.0536	−3.15494
$694$	17.8305	0.676838
$695$	−27.7160	−1.05133
$696$	61.7502	2.34064
$697$	−1.31233	−0.0497082
$698$	−28.2805	−1.07043
$699$	−91.1069	−3.44598
$700$	20.3454	0.768984
$701$	11.3005	0.426813	0.213407	−	0.976963i	$-0.431544\pi$
$701$	11.3005	0.426813	0.213407	+	0.976963i	$0.431544\pi$
$702$	−51.0739	−1.92766
$703$	10.3372	0.389874
$704$	19.7656	0.744946
$705$	79.1455	2.98079
$706$	41.4009	1.55814
$707$	−21.5979	−0.812274
$708$	31.7497	1.19323
$709$	33.0059	1.23956	0.619781	−	0.784775i	$-0.287221\pi$
$709$	33.0059	1.23956	0.619781	+	0.784775i	$0.287221\pi$
$710$	−21.0720	−0.790819
$711$	87.2636	3.27264
$712$	17.4351	0.653406
$713$	4.69581	0.175860
$714$	4.50381	0.168551
$715$	5.60775	0.209718
$716$	−48.4136	−1.80930
$717$	77.4201	2.89131
$718$	−71.1706	−2.65606
$719$	34.1292	1.27280	0.636402	−	0.771358i	$-0.280422\pi$
$719$	34.1292	1.27280	0.636402	+	0.771358i	$0.280422\pi$
$720$	−156.199	−5.82118
$721$	60.6996	2.26057
$722$	38.7146	1.44081
$723$	63.9220	2.37729
$724$	−31.3408	−1.16477
$725$	−3.24365	−0.120466
$726$	−22.2281	−0.824962
$727$	9.14126	0.339031	0.169515	−	0.985528i	$-0.445780\pi$
$727$	9.14126	0.339031	0.169515	+	0.985528i	$0.445780\pi$
$728$	−23.6481	−0.876458
$729$	156.113	5.78197
$730$	70.6173	2.61366
$731$	−1.35181	−0.0499987
$732$	−9.82475	−0.363133
$733$	36.8924	1.36265	0.681325	−	0.731981i	$-0.261404\pi$
$733$	36.8924	1.36265	0.681325	+	0.731981i	$0.261404\pi$
$734$	12.0146	0.443466
$735$	24.0074	0.885527
$736$	−11.7409	−0.432774
$737$	30.3944	1.11959
$738$	−192.716	−7.09397
$739$	49.8239	1.83280	0.916400	−	0.400263i	$-0.131081\pi$
$739$	49.8239	1.83280	0.916400	+	0.400263i	$0.131081\pi$
$740$	−46.7457	−1.71841
$741$	6.96335	0.255805
$742$	57.5129	2.11137
$743$	−4.44173	−0.162951	−0.0814757	−	0.996675i	$-0.525963\pi$
$743$	−4.44173	−0.162951	−0.0814757	+	0.996675i	$0.525963\pi$
$744$	96.7957	3.54870
$745$	−1.38366	−0.0506934
$746$	1.13270	0.0414710
$747$	58.4867	2.13992
$748$	−2.15911	−0.0789447
$749$	−18.7539	−0.685252
$750$	108.087	3.94677
$751$	25.7331	0.939016	0.469508	−	0.882928i	$-0.344431\pi$
$751$	25.7331	0.939016	0.469508	+	0.882928i	$0.344431\pi$
$752$	111.918	4.08121
$753$	−53.4592	−1.94816
$754$	6.47981	0.235981
$755$	26.0441	0.947843
$756$	306.043	11.1307
$757$	38.6590	1.40509	0.702543	−	0.711641i	$-0.252048\pi$
$757$	38.6590	1.40509	0.702543	+	0.711641i	$0.252048\pi$
$758$	78.2164	2.84095
$759$	−12.0262	−0.436525
$760$	28.3340	1.02778
$761$	2.47473	0.0897089	0.0448545	−	0.998994i	$-0.485718\pi$
$761$	2.47473	0.0897089	0.0448545	+	0.998994i	$0.485718\pi$
$762$	−17.5821	−0.636933
$763$	−20.9407	−0.758104
$764$	82.1794	2.97315
$765$	2.59667	0.0938829
$766$	34.7721	1.25637
$767$	1.93850	0.0699951
$768$	62.9463	2.27138
$769$	−14.5799	−0.525765	−0.262883	−	0.964828i	$-0.584673\pi$
$769$	−14.5799	−0.525765	−0.262883	+	0.964828i	$0.584673\pi$
$770$	−47.6538	−1.71732
$771$	71.3440	2.56939
$772$	84.5268	3.04219
$773$	−6.14603	−0.221057	−0.110529	−	0.993873i	$-0.535254\pi$
$773$	−6.14603	−0.221057	−0.110529	+	0.993873i	$0.535254\pi$
$774$	−198.513	−7.13542
$775$	−5.08454	−0.182642
$776$	4.09146	0.146875
$777$	56.8019	2.03776
$778$	−14.2032	−0.509208
$779$	17.2422	0.617764
$780$	−31.4889	−1.12748
$781$	−12.2750	−0.439234
$782$	0.485317	0.0173549
$783$	−48.7921	−1.74369
$784$	33.9483	1.21244
$785$	−11.8749	−0.423833
$786$	44.2531	1.57846
$787$	−46.7840	−1.66767	−0.833835	−	0.552014i	$-0.813860\pi$
$787$	−46.7840	−1.66767	−0.833835	+	0.552014i	$0.813860\pi$
$788$	64.7140	2.30534
$789$	−42.2985	−1.50587
$790$	50.0694	1.78139
$791$	−57.8596	−2.05725
$792$	−184.480	−6.55521
$793$	−0.599857	−0.0213015
$794$	−68.5990	−2.43449
$795$	44.5583	1.58032
$796$	−45.0871	−1.59807
$797$	−6.63880	−0.235158	−0.117579	−	0.993064i	$-0.537513\pi$
$797$	−6.63880	−0.235158	−0.117579	+	0.993064i	$0.537513\pi$
$798$	−59.1735	−2.09472
$799$	−1.86054	−0.0658210
$800$	12.7128	0.449466
$801$	−20.9933	−0.741761
$802$	−72.3992	−2.55650
$803$	41.1364	1.45167
$804$	−170.672	−6.01913
$805$	7.55307	0.266211
$806$	10.1573	0.357777
$807$	−19.6772	−0.692671
$808$	−47.9737	−1.68771
$809$	−0.740306	−0.0260278	−0.0130139	−	0.999915i	$-0.504143\pi$
$809$	−0.740306	−0.0260278	−0.0130139	+	0.999915i	$0.504143\pi$
$810$	205.169	7.20890
$811$	−6.67958	−0.234552	−0.117276	−	0.993099i	$-0.537416\pi$
$811$	−6.67958	−0.234552	−0.117276	+	0.993099i	$0.537416\pi$
$812$	−38.8281	−1.36260
$813$	96.7448	3.39299
$814$	−38.6174	−1.35354
$815$	43.5669	1.52608
$816$	4.93418	0.172731
$817$	17.7609	0.621374
$818$	−63.1826	−2.20913
$819$	28.4743	0.994973
$820$	−77.9705	−2.72285
$821$	−44.7967	−1.56341	−0.781707	−	0.623646i	$-0.785651\pi$
$821$	−44.7967	−1.56341	−0.781707	+	0.623646i	$0.785651\pi$
$822$	90.0672	3.14145
$823$	−31.1819	−1.08693	−0.543467	−	0.839431i	$-0.682889\pi$
$823$	−31.1819	−1.08693	−0.543467	+	0.839431i	$0.682889\pi$
$824$	134.827	4.69692
$825$	13.0218	0.453360
$826$	−16.4731	−0.573171
$827$	−14.5036	−0.504339	−0.252170	−	0.967683i	$-0.581144\pi$
$827$	−14.5036	−0.504339	−0.252170	+	0.967683i	$0.581144\pi$
$828$	50.2543	1.74646
$829$	43.8711	1.52370	0.761852	−	0.647751i	$-0.224290\pi$
$829$	43.8711	1.52370	0.761852	+	0.647751i	$0.224290\pi$
$830$	33.5580	1.16482
$831$	25.4321	0.882230
$832$	−6.77651	−0.234933
$833$	−0.564361	−0.0195540
$834$	128.570	4.45202
$835$	−18.2130	−0.630288
$836$	28.3675	0.981110
$837$	−76.4834	−2.64365
$838$	61.3523	2.11938
$839$	−28.6421	−0.988835	−0.494417	−	0.869225i	$-0.664619\pi$
$839$	−28.6421	−0.988835	−0.494417	+	0.869225i	$0.664619\pi$
$840$	155.693	5.37191
$841$	−22.8097	−0.786540
$842$	−41.7678	−1.43941
$843$	17.7051	0.609795
$844$	−118.998	−4.09609
$845$	−1.92258	−0.0661386
$846$	−273.219	−9.39346
$847$	8.13227	0.279428
$848$	63.0087	2.16373
$849$	76.1503	2.61347
$850$	−0.525493	−0.0180242
$851$	6.12081	0.209819
$852$	68.9272	2.36141
$853$	−4.49285	−0.153832	−0.0769162	−	0.997038i	$-0.524507\pi$
$853$	−4.49285	−0.153832	−0.0769162	+	0.997038i	$0.524507\pi$
$854$	5.09749	0.174432
$855$	−34.1165	−1.16676
$856$	−41.6564	−1.42379
$857$	−41.0957	−1.40380	−0.701901	−	0.712275i	$-0.747665\pi$
$857$	−41.0957	−1.40380	−0.701901	+	0.712275i	$0.747665\pi$
$858$	−26.0135	−0.888086
$859$	30.6028	1.04415	0.522077	−	0.852899i	$-0.325158\pi$
$859$	30.6028	1.04415	0.522077	+	0.852899i	$0.325158\pi$
$860$	−80.3162	−2.73876
$861$	94.7441	3.22887
$862$	−4.52627	−0.154165
$863$	26.2671	0.894142	0.447071	−	0.894498i	$-0.352467\pi$
$863$	26.2671	0.894142	0.447071	+	0.894498i	$0.352467\pi$
$864$	191.230	6.50579
$865$	27.4998	0.935021
$866$	−11.1713	−0.379615
$867$	58.1332	1.97431
$868$	−60.8643	−2.06587
$869$	29.1667	0.989413
$870$	−42.6613	−1.44635
$871$	−10.4205	−0.353085
$872$	−46.5138	−1.57516
$873$	−4.92647	−0.166736
$874$	−6.37636	−0.215684
$875$	−39.5441	−1.33684
$876$	−230.991	−7.80447
$877$	46.7468	1.57853	0.789264	−	0.614054i	$-0.210462\pi$
$877$	46.7468	1.57853	0.789264	+	0.614054i	$0.210462\pi$
$878$	−34.7494	−1.17274
$879$	−95.8897	−3.23428
$880$	−52.2074	−1.75991
$881$	25.0392	0.843593	0.421796	−	0.906691i	$-0.361400\pi$
$881$	25.0392	0.843593	0.421796	+	0.906691i	$0.361400\pi$
$882$	−82.8763	−2.79059
$883$	−3.53046	−0.118810	−0.0594048	−	0.998234i	$-0.518920\pi$
$883$	−3.53046	−0.118810	−0.0594048	+	0.998234i	$0.518920\pi$
$884$	0.740234	0.0248968
$885$	−12.7625	−0.429008
$886$	−53.1026	−1.78402
$887$	36.5454	1.22707	0.613537	−	0.789666i	$-0.289746\pi$
$887$	36.5454	1.22707	0.613537	+	0.789666i	$0.289746\pi$
$888$	126.169	4.23397
$889$	6.43251	0.215739
$890$	−12.0453	−0.403761
$891$	119.516	4.00395
$892$	9.67794	0.324041
$893$	24.4447	0.818011
$894$	6.41859	0.214670
$895$	19.4610	0.650510
$896$	−6.04939	−0.202096
$897$	4.12311	0.137667
$898$	15.0929	0.503656
$899$	9.70355	0.323632
$900$	−54.4144	−1.81381
$901$	−1.04747	−0.0348962
$902$	−64.4127	−2.14471
$903$	97.5944	3.24774
$904$	−128.519	−4.27446
$905$	12.5982	0.418777
$906$	−120.815	−4.01380
$907$	27.2141	0.903630	0.451815	−	0.892112i	$-0.350777\pi$
$907$	27.2141	0.903630	0.451815	+	0.892112i	$0.350777\pi$
$908$	−18.6037	−0.617384
$909$	57.7643	1.91592
$910$	16.3378	0.541591
$911$	−2.78258	−0.0921910	−0.0460955	−	0.998937i	$-0.514678\pi$
$911$	−2.78258	−0.0921910	−0.0460955	+	0.998937i	$0.514678\pi$
$912$	−64.8279	−2.14667
$913$	19.5484	0.646958
$914$	−17.6569	−0.584040
$915$	3.94929	0.130560
$916$	91.8880	3.03606
$917$	−16.1902	−0.534649
$918$	−7.90464	−0.260892
$919$	6.77451	0.223471	0.111735	−	0.993738i	$-0.464359\pi$
$919$	6.77451	0.223471	0.111735	+	0.993738i	$0.464359\pi$
$920$	16.7770	0.553121
$921$	52.2312	1.72108
$922$	−55.5759	−1.83030
$923$	4.20840	0.138521
$924$	155.877	5.12797
$925$	−6.62750	−0.217911
$926$	−2.60439	−0.0855855
$927$	−162.343	−5.33204
$928$	−24.2617	−0.796428
$929$	−56.6019	−1.85705	−0.928524	−	0.371271i	$-0.878922\pi$
$929$	−56.6019	−1.85705	−0.928524	+	0.371271i	$0.878922\pi$
$930$	−66.8731	−2.19286
$931$	7.41488	0.243013
$932$	127.247	4.16813
$933$	−25.0620	−0.820492
$934$	−31.7638	−1.03934
$935$	0.867904	0.0283835
$936$	63.2476	2.06731
$937$	−0.861969	−0.0281593	−0.0140796	−	0.999901i	$-0.504482\pi$
$937$	−0.861969	−0.0281593	−0.0140796	+	0.999901i	$0.504482\pi$
$938$	88.5517	2.89132
$939$	91.4771	2.98524
$940$	−110.541	−3.60545
$941$	−8.80940	−0.287178	−0.143589	−	0.989637i	$-0.545864\pi$
$941$	−8.80940	−0.287178	−0.143589	+	0.989637i	$0.545864\pi$
$942$	55.0858	1.79479
$943$	10.2093	0.332462
$944$	−18.0472	−0.587385
$945$	−123.021	−4.00188
$946$	−66.3505	−2.15724
$947$	−38.5479	−1.25264	−0.626320	−	0.779566i	$-0.715440\pi$
$947$	−38.5479	−1.25264	−0.626320	+	0.779566i	$0.715440\pi$
$948$	−163.778	−5.31927
$949$	−14.1033	−0.457814
$950$	6.90421	0.224002
$951$	−40.6029	−1.31664
$952$	−3.65999	−0.118621
$953$	−5.52996	−0.179133	−0.0895664	−	0.995981i	$-0.528548\pi$
$953$	−5.52996	−0.179133	−0.0895664	+	0.995981i	$0.528548\pi$
$954$	−153.820	−4.98011
$955$	−33.0340	−1.06895
$956$	−108.131	−3.49722
$957$	−24.8513	−0.803330
$958$	26.2841	0.849200
$959$	−32.9516	−1.06406
$960$	44.6147	1.43993
$961$	−15.7893	−0.509334
$962$	13.2397	0.426865
$963$	50.1578	1.61631
$964$	−89.2788	−2.87548
$965$	−33.9776	−1.09378
$966$	−35.0375	−1.12731
$967$	25.2698	0.812621	0.406310	−	0.913735i	$-0.366815\pi$
$967$	25.2698	0.812621	0.406310	+	0.913735i	$0.366815\pi$
$968$	18.0635	0.580583
$969$	1.07771	0.0346210
$970$	−2.82667	−0.0907588
$971$	26.1304	0.838563	0.419282	−	0.907856i	$-0.362282\pi$
$971$	26.1304	0.838563	0.419282	+	0.907856i	$0.362282\pi$
$972$	−389.729	−12.5006
$973$	−47.0381	−1.50797
$974$	−74.6029	−2.39043
$975$	−4.46443	−0.142976
$976$	5.58459	0.178758
$977$	7.32903	0.234477	0.117238	−	0.993104i	$-0.462596\pi$
$977$	7.32903	0.234477	0.117238	+	0.993104i	$0.462596\pi$
$978$	−202.100	−6.46245
$979$	−7.01672	−0.224255
$980$	−33.5308	−1.07110
$981$	56.0065	1.78815
$982$	26.8208	0.855887
$983$	−61.2233	−1.95272	−0.976361	−	0.216147i	$-0.930651\pi$
$983$	−61.2233	−1.95272	−0.976361	+	0.216147i	$0.930651\pi$
$984$	210.447	6.70881
$985$	−26.0133	−0.828854
$986$	1.00287	0.0319380
$987$	134.322	4.27550
$988$	−9.72559	−0.309412
$989$	10.5165	0.334405
$990$	127.451	4.05067
$991$	−9.99518	−0.317507	−0.158754	−	0.987318i	$-0.550748\pi$
$991$	−9.99518	−0.317507	−0.158754	+	0.987318i	$0.550748\pi$
$992$	−38.0310	−1.20749
$993$	−78.9496	−2.50539
$994$	−35.7623	−1.13431
$995$	18.1238	0.574564
$996$	−109.769	−3.47817
$997$	−29.7458	−0.942058	−0.471029	−	0.882118i	$-0.656117\pi$
$997$	−29.7458	−0.942058	−0.471029	+	0.882118i	$0.656117\pi$
$998$	−83.8986	−2.65576
$999$	−99.6931	−3.15415

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.7	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.60439 q^{2} -3.42443 q^{3} +4.78284 q^{4} -1.92258 q^{5} +8.91854 q^{6} -3.26289 q^{7} -7.24759 q^{8} +8.72671 q^{9} +O(q^{10})\)	\(q-2.60439 q^{2} -3.42443 q^{3} +4.78284 q^{4} -1.92258 q^{5} +8.91854 q^{6} -3.26289 q^{7} -7.24759 q^{8} +8.72671 q^{9} +5.00714 q^{10} +2.91679 q^{11} -16.3785 q^{12} -1.00000 q^{13} +8.49784 q^{14} +6.58372 q^{15} +9.30987 q^{16} -0.154769 q^{17} -22.7277 q^{18} +2.03344 q^{19} -9.19537 q^{20} +11.1735 q^{21} -7.59645 q^{22} +1.20403 q^{23} +24.8189 q^{24} -1.30370 q^{25} +2.60439 q^{26} -19.6107 q^{27} -15.6059 q^{28} +2.48804 q^{29} -17.1466 q^{30} +3.90008 q^{31} -9.75133 q^{32} -9.98833 q^{33} +0.403078 q^{34} +6.27316 q^{35} +41.7384 q^{36} +5.08361 q^{37} -5.29586 q^{38} +3.42443 q^{39} +13.9341 q^{40} +8.47932 q^{41} -29.1003 q^{42} +8.73442 q^{43} +13.9505 q^{44} -16.7778 q^{45} -3.13576 q^{46} +12.0214 q^{47} -31.8810 q^{48} +3.64648 q^{49} +3.39534 q^{50} +0.529994 q^{51} -4.78284 q^{52} +6.76794 q^{53} +51.0739 q^{54} -5.60775 q^{55} +23.6481 q^{56} -6.96335 q^{57} -6.47981 q^{58} -1.93850 q^{59} +31.4889 q^{60} +0.599857 q^{61} -10.1573 q^{62} -28.4743 q^{63} +6.77651 q^{64} +1.92258 q^{65} +26.0135 q^{66} +10.4205 q^{67} -0.740234 q^{68} -4.12311 q^{69} -16.3378 q^{70} -4.20840 q^{71} -63.2476 q^{72} +14.1033 q^{73} -13.2397 q^{74} +4.46443 q^{75} +9.72559 q^{76} -9.51717 q^{77} -8.91854 q^{78} +9.99960 q^{79} -17.8989 q^{80} +40.9753 q^{81} -22.0834 q^{82} +6.70204 q^{83} +53.4413 q^{84} +0.297555 q^{85} -22.7478 q^{86} -8.52010 q^{87} -21.1397 q^{88} -2.40563 q^{89} +43.6958 q^{90} +3.26289 q^{91} +5.75867 q^{92} -13.3556 q^{93} -31.3084 q^{94} -3.90944 q^{95} +33.3927 q^{96} -0.564527 q^{97} -9.49685 q^{98} +25.4540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 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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