LMFDB - Embedded newform 6023.2.a.c.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.75960 q^{2} -3.30212 q^{3} +1.09619 q^{4} +2.64584 q^{5} +5.81041 q^{6} -0.291666 q^{7} +1.59034 q^{8} +7.90401 q^{9} +O(q^{10})$	\(q-1.75960 q^{2} -3.30212 q^{3} +1.09619 q^{4} +2.64584 q^{5} +5.81041 q^{6} -0.291666 q^{7} +1.59034 q^{8} +7.90401 q^{9} -4.65561 q^{10} -0.117911 q^{11} -3.61975 q^{12} +2.51403 q^{13} +0.513215 q^{14} -8.73688 q^{15} -4.99075 q^{16} -1.17762 q^{17} -13.9079 q^{18} +1.00000 q^{19} +2.90034 q^{20} +0.963115 q^{21} +0.207477 q^{22} -8.26455 q^{23} -5.25151 q^{24} +2.00045 q^{25} -4.42368 q^{26} -16.1936 q^{27} -0.319721 q^{28} -7.45560 q^{29} +15.3734 q^{30} -1.16803 q^{31} +5.60103 q^{32} +0.389358 q^{33} +2.07214 q^{34} -0.771700 q^{35} +8.66429 q^{36} +11.0343 q^{37} -1.75960 q^{38} -8.30162 q^{39} +4.20779 q^{40} -2.65101 q^{41} -1.69470 q^{42} +7.52853 q^{43} -0.129253 q^{44} +20.9127 q^{45} +14.5423 q^{46} -5.97907 q^{47} +16.4801 q^{48} -6.91493 q^{49} -3.52000 q^{50} +3.88864 q^{51} +2.75585 q^{52} +8.86838 q^{53} +28.4943 q^{54} -0.311975 q^{55} -0.463848 q^{56} -3.30212 q^{57} +13.1189 q^{58} -6.72984 q^{59} -9.57728 q^{60} -6.10529 q^{61} +2.05526 q^{62} -2.30533 q^{63} +0.125929 q^{64} +6.65171 q^{65} -0.685114 q^{66} +9.57047 q^{67} -1.29089 q^{68} +27.2905 q^{69} +1.35788 q^{70} +8.30387 q^{71} +12.5701 q^{72} -13.7617 q^{73} -19.4159 q^{74} -6.60574 q^{75} +1.09619 q^{76} +0.0343907 q^{77} +14.6075 q^{78} +3.41857 q^{79} -13.2047 q^{80} +29.7613 q^{81} +4.66472 q^{82} -4.38904 q^{83} +1.05576 q^{84} -3.11578 q^{85} -13.2472 q^{86} +24.6193 q^{87} -0.187520 q^{88} +11.5352 q^{89} -36.7980 q^{90} -0.733255 q^{91} -9.05951 q^{92} +3.85697 q^{93} +10.5208 q^{94} +2.64584 q^{95} -18.4953 q^{96} +7.34989 q^{97} +12.1675 q^{98} -0.931973 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.75960	−1.24422	−0.622112	−	0.782928i	$-0.713725\pi$
$2$	−1.75960	−1.24422	−0.622112	+	0.782928i	$0.713725\pi$
$3$	−3.30212	−1.90648	−0.953240	−	0.302213i	$-0.902275\pi$
$3$	−3.30212	−1.90648	−0.953240	+	0.302213i	$0.902275\pi$
$4$	1.09619	0.548095
$5$	2.64584	1.18325	0.591627	−	0.806212i	$-0.298486\pi$
$5$	2.64584	1.18325	0.591627	+	0.806212i	$0.298486\pi$
$6$	5.81041	2.37209
$7$	−0.291666	−0.110239	−0.0551196	−	0.998480i	$-0.517554\pi$
$7$	−0.291666	−0.110239	−0.0551196	+	0.998480i	$0.517554\pi$
$8$	1.59034	0.562271
$9$	7.90401	2.63467
$10$	−4.65561	−1.47223
$11$	−0.117911	−0.0355517	−0.0177758	−	0.999842i	$-0.505659\pi$
$11$	−0.117911	−0.0355517	−0.0177758	+	0.999842i	$0.505659\pi$
$12$	−3.61975	−1.04493
$13$	2.51403	0.697266	0.348633	−	0.937259i	$-0.386646\pi$
$13$	2.51403	0.697266	0.348633	+	0.937259i	$0.386646\pi$
$14$	0.513215	0.137162
$15$	−8.73688	−2.25585
$16$	−4.99075	−1.24769
$17$	−1.17762	−0.285614	−0.142807	−	0.989751i	$-0.545613\pi$
$17$	−1.17762	−0.285614	−0.142807	+	0.989751i	$0.545613\pi$
$18$	−13.9079	−3.27812
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.90034	0.648536
$21$	0.963115	0.210169
$22$	0.207477	0.0442342
$23$	−8.26455	−1.72328	−0.861638	−	0.507523i	$-0.830561\pi$
$23$	−8.26455	−1.72328	−0.861638	+	0.507523i	$0.830561\pi$
$24$	−5.25151	−1.07196
$25$	2.00045	0.400091
$26$	−4.42368	−0.867555
$27$	−16.1936	−3.11647
$28$	−0.319721	−0.0604216
$29$	−7.45560	−1.38447	−0.692235	−	0.721672i	$-0.743374\pi$
$29$	−7.45560	−1.38447	−0.692235	+	0.721672i	$0.743374\pi$
$30$	15.3734	2.80679
$31$	−1.16803	−0.209784	−0.104892	−	0.994484i	$-0.533450\pi$
$31$	−1.16803	−0.209784	−0.104892	+	0.994484i	$0.533450\pi$
$32$	5.60103	0.990131
$33$	0.389358	0.0677786
$34$	2.07214	0.355368
$35$	−0.771700	−0.130441
$36$	8.66429	1.44405
$37$	11.0343	1.81403	0.907013	−	0.421102i	$-0.138357\pi$
$37$	11.0343	1.81403	0.907013	+	0.421102i	$0.138357\pi$
$38$	−1.75960	−0.285445
$39$	−8.30162	−1.32932
$40$	4.20779	0.665310
$41$	−2.65101	−0.414018	−0.207009	−	0.978339i	$-0.566373\pi$
$41$	−2.65101	−0.414018	−0.207009	+	0.978339i	$0.566373\pi$
$42$	−1.69470	−0.261497
$43$	7.52853	1.14809	0.574045	−	0.818824i	$-0.305373\pi$
$43$	7.52853	1.14809	0.574045	+	0.818824i	$0.305373\pi$
$44$	−0.129253	−0.0194857
$45$	20.9127	3.11748
$46$	14.5423	2.14414
$47$	−5.97907	−0.872136	−0.436068	−	0.899914i	$-0.643629\pi$
$47$	−5.97907	−0.872136	−0.436068	+	0.899914i	$0.643629\pi$
$48$	16.4801	2.37869
$49$	−6.91493	−0.987847
$50$	−3.52000	−0.497803
$51$	3.88864	0.544518
$52$	2.75585	0.382168
$53$	8.86838	1.21817	0.609083	−	0.793106i	$-0.291538\pi$
$53$	8.86838	1.21817	0.609083	+	0.793106i	$0.291538\pi$
$54$	28.4943	3.87758
$55$	−0.311975	−0.0420666
$56$	−0.463848	−0.0619844
$57$	−3.30212	−0.437377
$58$	13.1189	1.72259
$59$	−6.72984	−0.876151	−0.438075	−	0.898938i	$-0.644340\pi$
$59$	−6.72984	−0.876151	−0.438075	+	0.898938i	$0.644340\pi$
$60$	−9.57728	−1.23642
$61$	−6.10529	−0.781703	−0.390851	−	0.920454i	$-0.627819\pi$
$61$	−6.10529	−0.781703	−0.390851	+	0.920454i	$0.627819\pi$
$62$	2.05526	0.261019
$63$	−2.30533	−0.290444
$64$	0.125929	0.0157411
$65$	6.65171	0.825043
$66$	−0.685114	−0.0843317
$67$	9.57047	1.16922	0.584610	−	0.811315i	$-0.301248\pi$
$67$	9.57047	1.16922	0.584610	+	0.811315i	$0.301248\pi$
$68$	−1.29089	−0.156544
$69$	27.2905	3.28539
$70$	1.35788	0.162298
$71$	8.30387	0.985488	0.492744	−	0.870174i	$-0.335994\pi$
$71$	8.30387	0.985488	0.492744	+	0.870174i	$0.335994\pi$
$72$	12.5701	1.48140
$73$	−13.7617	−1.61068	−0.805340	−	0.592813i	$-0.798017\pi$
$73$	−13.7617	−1.61068	−0.805340	+	0.592813i	$0.798017\pi$
$74$	−19.4159	−2.25706
$75$	−6.60574	−0.762766
$76$	1.09619	0.125742
$77$	0.0343907	0.00391919
$78$	14.6075	1.65398
$79$	3.41857	0.384619	0.192310	−	0.981334i	$-0.438402\pi$
$79$	3.41857	0.384619	0.192310	+	0.981334i	$0.438402\pi$
$80$	−13.2047	−1.47633
$81$	29.7613	3.30681
$82$	4.66472	0.515132
$83$	−4.38904	−0.481759	−0.240880	−	0.970555i	$-0.577436\pi$
$83$	−4.38904	−0.481759	−0.240880	+	0.970555i	$0.577436\pi$
$84$	1.05576	0.115193
$85$	−3.11578	−0.337954
$86$	−13.2472	−1.42848
$87$	24.6193	2.63946
$88$	−0.187520	−0.0199897
$89$	11.5352	1.22273	0.611365	−	0.791349i	$-0.290621\pi$
$89$	11.5352	1.22273	0.611365	+	0.791349i	$0.290621\pi$
$90$	−36.7980	−3.87885
$91$	−0.733255	−0.0768660
$92$	−9.05951	−0.944519
$93$	3.85697	0.399950
$94$	10.5208	1.08513
$95$	2.64584	0.271457
$96$	−18.4953	−1.88767
$97$	7.34989	0.746268	0.373134	−	0.927777i	$-0.378283\pi$
$97$	7.34989	0.746268	0.373134	+	0.927777i	$0.378283\pi$
$98$	12.1675	1.22910
$99$	−0.931973	−0.0936669
$100$	2.19288	0.219288
$101$	−0.980760	−0.0975892	−0.0487946	−	0.998809i	$-0.515538\pi$
$101$	−0.980760	−0.0975892	−0.0487946	+	0.998809i	$0.515538\pi$
$102$	−6.84244	−0.677503
$103$	−7.96823	−0.785133	−0.392567	−	0.919724i	$-0.628413\pi$
$103$	−7.96823	−0.785133	−0.392567	+	0.919724i	$0.628413\pi$
$104$	3.99817	0.392053
$105$	2.54825	0.248683
$106$	−15.6048	−1.51567
$107$	−6.71545	−0.649207	−0.324604	−	0.945850i	$-0.605231\pi$
$107$	−6.71545	−0.649207	−0.324604	+	0.945850i	$0.605231\pi$
$108$	−17.7513	−1.70812
$109$	13.6814	1.31044	0.655222	−	0.755436i	$-0.272575\pi$
$109$	13.6814	1.31044	0.655222	+	0.755436i	$0.272575\pi$
$110$	0.548950	0.0523404
$111$	−36.4366	−3.45841
$112$	1.45563	0.137544
$113$	20.6721	1.94467	0.972334	−	0.233595i	$-0.0750490\pi$
$113$	20.6721	1.94467	0.972334	+	0.233595i	$0.0750490\pi$
$114$	5.81041	0.544195
$115$	−21.8666	−2.03907
$116$	−8.17275	−0.758821
$117$	19.8709	1.83706
$118$	11.8418	1.09013
$119$	0.343471	0.0314859
$120$	−13.8946	−1.26840
$121$	−10.9861	−0.998736
$122$	10.7429	0.972614
$123$	8.75396	0.789318
$124$	−1.28038	−0.114982
$125$	−7.93631	−0.709845
$126$	4.05645	0.361377
$127$	−14.2624	−1.26558	−0.632792	−	0.774322i	$-0.718091\pi$
$127$	−14.2624	−1.26558	−0.632792	+	0.774322i	$0.718091\pi$
$128$	−11.4236	−1.00972
$129$	−24.8601	−2.18881
$130$	−11.7043	−1.02654
$131$	18.0937	1.58085	0.790426	−	0.612558i	$-0.209859\pi$
$131$	18.0937	1.58085	0.790426	+	0.612558i	$0.209859\pi$
$132$	0.426810	0.0371491
$133$	−0.291666	−0.0252906
$134$	−16.8402	−1.45477
$135$	−42.8457	−3.68757
$136$	−1.87282	−0.160593
$137$	10.7001	0.914168	0.457084	−	0.889424i	$-0.348894\pi$
$137$	10.7001	0.914168	0.457084	+	0.889424i	$0.348894\pi$
$138$	−48.0204	−4.08777
$139$	3.62769	0.307697	0.153848	−	0.988094i	$-0.450833\pi$
$139$	3.62769	0.307697	0.153848	+	0.988094i	$0.450833\pi$
$140$	−0.845929	−0.0714941
$141$	19.7436	1.66271
$142$	−14.6115	−1.22617
$143$	−0.296433	−0.0247889
$144$	−39.4469	−3.28724
$145$	−19.7263	−1.63818
$146$	24.2150	2.00405
$147$	22.8339	1.88331
$148$	12.0957	0.994259
$149$	−17.3135	−1.41837	−0.709187	−	0.705020i	$-0.750938\pi$
$149$	−17.3135	−1.41837	−0.709187	+	0.705020i	$0.750938\pi$
$150$	11.6235	0.949052
$151$	6.62753	0.539341	0.269670	−	0.962953i	$-0.413085\pi$
$151$	6.62753	0.539341	0.269670	+	0.962953i	$0.413085\pi$
$152$	1.59034	0.128994
$153$	−9.30790	−0.752499
$154$	−0.0605139	−0.00487635
$155$	−3.09041	−0.248228
$156$	−9.10016	−0.728596
$157$	11.8914	0.949039	0.474519	−	0.880245i	$-0.342622\pi$
$157$	11.8914	0.949039	0.474519	+	0.880245i	$0.342622\pi$
$158$	−6.01532	−0.478553
$159$	−29.2845	−2.32241
$160$	14.8194	1.17158
$161$	2.41048	0.189973
$162$	−52.3680	−4.11442
$163$	8.09863	0.634333	0.317167	−	0.948370i	$-0.397269\pi$
$163$	8.09863	0.634333	0.317167	+	0.948370i	$0.397269\pi$
$164$	−2.90601	−0.226921
$165$	1.03018	0.0801993
$166$	7.72295	0.599417
$167$	−23.2848	−1.80183	−0.900914	−	0.433998i	$-0.857103\pi$
$167$	−23.2848	−1.80183	−0.900914	+	0.433998i	$0.857103\pi$
$168$	1.53168	0.118172
$169$	−6.67967	−0.513821
$170$	5.48253	0.420491
$171$	7.90401	0.604435
$172$	8.25270	0.629262
$173$	15.1864	1.15460	0.577301	−	0.816532i	$-0.304106\pi$
$173$	15.1864	1.15460	0.577301	+	0.816532i	$0.304106\pi$
$174$	−43.3201	−3.28409
$175$	−0.583464	−0.0441057
$176$	0.588467	0.0443573
$177$	22.2228	1.67036
$178$	−20.2974	−1.52135
$179$	2.77732	0.207586	0.103793	−	0.994599i	$-0.466902\pi$
$179$	2.77732	0.207586	0.103793	+	0.994599i	$0.466902\pi$
$180$	22.9243	1.70868
$181$	−11.5969	−0.861988	−0.430994	−	0.902355i	$-0.641837\pi$
$181$	−11.5969	−0.861988	−0.430994	+	0.902355i	$0.641837\pi$
$182$	1.29024	0.0956386
$183$	20.1604	1.49030
$184$	−13.1435	−0.968949
$185$	29.1949	2.14645
$186$	−6.78673	−0.497627
$187$	0.138855	0.0101541
$188$	−6.55419	−0.478013
$189$	4.72313	0.343557
$190$	−4.65561	−0.337754
$191$	−18.4111	−1.33218	−0.666092	−	0.745870i	$-0.732034\pi$
$191$	−18.4111	−1.33218	−0.666092	+	0.745870i	$0.732034\pi$
$192$	−0.415832	−0.0300101
$193$	10.1869	0.733266	0.366633	−	0.930366i	$-0.380510\pi$
$193$	10.1869	0.733266	0.366633	+	0.930366i	$0.380510\pi$
$194$	−12.9329	−0.928526
$195$	−21.9647	−1.57293
$196$	−7.58008	−0.541434
$197$	16.9910	1.21056	0.605278	−	0.796014i	$-0.293062\pi$
$197$	16.9910	1.21056	0.605278	+	0.796014i	$0.293062\pi$
$198$	1.63990	0.116543
$199$	17.2825	1.22512	0.612560	−	0.790424i	$-0.290140\pi$
$199$	17.2825	1.22512	0.612560	+	0.790424i	$0.290140\pi$
$200$	3.18141	0.224960
$201$	−31.6029	−2.22909
$202$	1.72574	0.121423
$203$	2.17454	0.152623
$204$	4.26269	0.298448
$205$	−7.01414	−0.489889
$206$	14.0209	0.976882
$207$	−65.3230	−4.54027
$208$	−12.5469	−0.869969
$209$	−0.117911	−0.00815611
$210$	−4.48389	−0.309418
$211$	6.57365	0.452549	0.226275	−	0.974064i	$-0.427345\pi$
$211$	6.57365	0.452549	0.226275	+	0.974064i	$0.427345\pi$
$212$	9.72143	0.667671
$213$	−27.4204	−1.87881
$214$	11.8165	0.807759
$215$	19.9193	1.35848
$216$	−25.7534	−1.75230
$217$	0.340674	0.0231264
$218$	−24.0739	−1.63049
$219$	45.4427	3.07073
$220$	−0.341983	−0.0230565
$221$	−2.96056	−0.199149
$222$	64.1138	4.30304
$223$	12.6267	0.845545	0.422772	−	0.906236i	$-0.361057\pi$
$223$	12.6267	0.845545	0.422772	+	0.906236i	$0.361057\pi$
$224$	−1.63363	−0.109151
$225$	15.8116	1.05411
$226$	−36.3746	−2.41960
$227$	−5.12895	−0.340420	−0.170210	−	0.985408i	$-0.554445\pi$
$227$	−5.12895	−0.340420	−0.170210	+	0.985408i	$0.554445\pi$
$228$	−3.61975	−0.239724
$229$	1.60700	0.106193	0.0530967	−	0.998589i	$-0.483091\pi$
$229$	1.60700	0.106193	0.0530967	+	0.998589i	$0.483091\pi$
$230$	38.4765	2.53707
$231$	−0.113562	−0.00747185
$232$	−11.8570	−0.778448
$233$	16.1962	1.06105	0.530523	−	0.847670i	$-0.321995\pi$
$233$	16.1962	1.06105	0.530523	+	0.847670i	$0.321995\pi$
$234$	−34.9648	−2.28572
$235$	−15.8196	−1.03196
$236$	−7.37718	−0.480214
$237$	−11.2885	−0.733270
$238$	−0.604371	−0.0391755
$239$	0.318793	0.0206210	0.0103105	−	0.999947i	$-0.496718\pi$
$239$	0.318793	0.0206210	0.0103105	+	0.999947i	$0.496718\pi$
$240$	43.6035	2.81460
$241$	−7.68472	−0.495016	−0.247508	−	0.968886i	$-0.579612\pi$
$241$	−7.68472	−0.495016	−0.247508	+	0.968886i	$0.579612\pi$
$242$	19.3311	1.24265
$243$	−49.6946	−3.18791
$244$	−6.69256	−0.428447
$245$	−18.2958	−1.16887
$246$	−15.4035	−0.982089
$247$	2.51403	0.159964
$248$	−1.85757	−0.117956
$249$	14.4931	0.918465
$250$	13.9647	0.883207
$251$	−24.4056	−1.54047	−0.770235	−	0.637761i	$-0.779861\pi$
$251$	−24.4056	−1.54047	−0.770235	+	0.637761i	$0.779861\pi$
$252$	−2.52708	−0.159191
$253$	0.974485	0.0612653
$254$	25.0961	1.57467
$255$	10.2887	0.644303
$256$	19.8492	1.24057
$257$	17.9312	1.11852	0.559258	−	0.828994i	$-0.311086\pi$
$257$	17.9312	1.11852	0.559258	+	0.828994i	$0.311086\pi$
$258$	43.7438	2.72337
$259$	−3.21832	−0.199977
$260$	7.29153	0.452202
$261$	−58.9291	−3.64762
$262$	−31.8376	−1.96693
$263$	19.2130	1.18473	0.592364	−	0.805671i	$-0.298195\pi$
$263$	19.2130	1.18473	0.592364	+	0.805671i	$0.298195\pi$
$264$	0.619213	0.0381099
$265$	23.4643	1.44140
$266$	0.513215	0.0314672
$267$	−38.0907	−2.33111
$268$	10.4911	0.640843
$269$	6.03010	0.367662	0.183831	−	0.982958i	$-0.441150\pi$
$269$	6.03010	0.367662	0.183831	+	0.982958i	$0.441150\pi$
$270$	75.3913	4.58817
$271$	−7.63225	−0.463626	−0.231813	−	0.972760i	$-0.574466\pi$
$271$	−7.63225	−0.463626	−0.231813	+	0.972760i	$0.574466\pi$
$272$	5.87719	0.356357
$273$	2.42130	0.146544
$274$	−18.8278	−1.13743
$275$	−0.235877	−0.0142239
$276$	29.9156	1.80071
$277$	31.4541	1.88990	0.944948	−	0.327221i	$-0.106112\pi$
$277$	31.4541	1.88990	0.944948	+	0.327221i	$0.106112\pi$
$278$	−6.38328	−0.382844
$279$	−9.23211	−0.552712
$280$	−1.22727	−0.0733433
$281$	−32.0021	−1.90909	−0.954543	−	0.298074i	$-0.903656\pi$
$281$	−32.0021	−1.90909	−0.954543	+	0.298074i	$0.903656\pi$
$282$	−34.7408	−2.06879
$283$	−0.841341	−0.0500125	−0.0250063	−	0.999687i	$-0.507961\pi$
$283$	−0.841341	−0.0500125	−0.0250063	+	0.999687i	$0.507961\pi$
$284$	9.10261	0.540141
$285$	−8.73688	−0.517528
$286$	0.521603	0.0308430
$287$	0.773209	0.0456411
$288$	44.2706	2.60867
$289$	−15.6132	−0.918424
$290$	34.7104	2.03826
$291$	−24.2702	−1.42275
$292$	−15.0854	−0.882805
$293$	2.17545	0.127091	0.0635456	−	0.997979i	$-0.479759\pi$
$293$	2.17545	0.127091	0.0635456	+	0.997979i	$0.479759\pi$
$294$	−40.1786	−2.34326
$295$	−17.8061	−1.03671
$296$	17.5483	1.01998
$297$	1.90942	0.110796
$298$	30.4648	1.76478
$299$	−20.7773	−1.20158
$300$	−7.24115	−0.418068
$301$	−2.19581	−0.126565
$302$	−11.6618	−0.671061
$303$	3.23859	0.186052
$304$	−4.99075	−0.286239
$305$	−16.1536	−0.924953
$306$	16.3782	0.936278
$307$	−26.0711	−1.48795	−0.743977	−	0.668205i	$-0.767063\pi$
$307$	−26.0711	−1.48795	−0.743977	+	0.668205i	$0.767063\pi$
$308$	0.0376988	0.00214809
$309$	26.3121	1.49684
$310$	5.43789	0.308852
$311$	26.1109	1.48062	0.740308	−	0.672268i	$-0.234680\pi$
$311$	26.1109	1.48062	0.740308	+	0.672268i	$0.234680\pi$
$312$	−13.2024	−0.747441
$313$	−19.1095	−1.08013	−0.540067	−	0.841622i	$-0.681601\pi$
$313$	−19.1095	−1.08013	−0.540067	+	0.841622i	$0.681601\pi$
$314$	−20.9241	−1.18082
$315$	−6.09952	−0.343669
$316$	3.74740	0.210808
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	51.5290	2.88960
$319$	0.879100	0.0492202
$320$	0.333187	0.0186257
$321$	22.1752	1.23770
$322$	−4.24148	−0.236369
$323$	−1.17762	−0.0655244
$324$	32.6241	1.81245
$325$	5.02920	0.278970
$326$	−14.2503	−0.789253
$327$	−45.1778	−2.49834
$328$	−4.21602	−0.232791
$329$	1.74389	0.0961436
$330$	−1.81270	−0.0997859
$331$	21.9903	1.20870	0.604348	−	0.796720i	$-0.293434\pi$
$331$	21.9903	1.20870	0.604348	+	0.796720i	$0.293434\pi$
$332$	−4.81122	−0.264050
$333$	87.2152	4.77936
$334$	40.9718	2.24188
$335$	25.3219	1.38348
$336$	−4.80666	−0.262225
$337$	−6.92022	−0.376968	−0.188484	−	0.982076i	$-0.560357\pi$
$337$	−6.92022	−0.376968	−0.188484	+	0.982076i	$0.560357\pi$
$338$	11.7535	0.639308
$339$	−68.2618	−3.70747
$340$	−3.41549	−0.185231
$341$	0.137724	0.00745818
$342$	−13.9079	−0.752052
$343$	4.05851	0.219139
$344$	11.9729	0.645538
$345$	72.2063	3.88746
$346$	−26.7220	−1.43658
$347$	15.1131	0.811316	0.405658	−	0.914025i	$-0.367042\pi$
$347$	15.1131	0.811316	0.405658	+	0.914025i	$0.367042\pi$
$348$	26.9874	1.44668
$349$	−3.18935	−0.170722	−0.0853609	−	0.996350i	$-0.527204\pi$
$349$	−3.18935	−0.170722	−0.0853609	+	0.996350i	$0.527204\pi$
$350$	1.02666	0.0548774
$351$	−40.7112	−2.17301
$352$	−0.660426	−0.0352008
$353$	13.6920	0.728750	0.364375	−	0.931252i	$-0.381283\pi$
$353$	13.6920	0.728750	0.364375	+	0.931252i	$0.381283\pi$
$354$	−39.1031	−2.07831
$355$	21.9707	1.16608
$356$	12.6448	0.670172
$357$	−1.13418	−0.0600273
$358$	−4.88696	−0.258284
$359$	−20.4557	−1.07961	−0.539805	−	0.841790i	$-0.681502\pi$
$359$	−20.4557	−1.07961	−0.539805	+	0.841790i	$0.681502\pi$
$360$	33.2584	1.75287
$361$	1.00000	0.0526316
$362$	20.4058	1.07251
$363$	36.2774	1.90407
$364$	−0.803787	−0.0421299
$365$	−36.4111	−1.90584
$366$	−35.4743	−1.85427
$367$	25.4228	1.32706	0.663529	−	0.748150i	$-0.269058\pi$
$367$	25.4228	1.32706	0.663529	+	0.748150i	$0.269058\pi$
$368$	41.2463	2.15011
$369$	−20.9536	−1.09080
$370$	−51.3714	−2.67067
$371$	−2.58660	−0.134290
$372$	4.22798	0.219210
$373$	−0.847649	−0.0438896	−0.0219448	−	0.999759i	$-0.506986\pi$
$373$	−0.847649	−0.0438896	−0.0219448	+	0.999759i	$0.506986\pi$
$374$	−0.244329	−0.0126339
$375$	26.2067	1.35331
$376$	−9.50877	−0.490377
$377$	−18.7436	−0.965343
$378$	−8.31081	−0.427462
$379$	15.3667	0.789332	0.394666	−	0.918825i	$-0.370860\pi$
$379$	15.3667	0.789332	0.394666	+	0.918825i	$0.370860\pi$
$380$	2.90034	0.148784
$381$	47.0962	2.41281
$382$	32.3962	1.65754
$383$	3.43003	0.175266	0.0876332	−	0.996153i	$-0.472070\pi$
$383$	3.43003	0.175266	0.0876332	+	0.996153i	$0.472070\pi$
$384$	37.7223	1.92501
$385$	0.0909922	0.00463739
$386$	−17.9248	−0.912348
$387$	59.5056	3.02484
$388$	8.05688	0.409026
$389$	24.2545	1.22975	0.614875	−	0.788625i	$-0.289206\pi$
$389$	24.2545	1.22975	0.614875	+	0.788625i	$0.289206\pi$
$390$	38.6492	1.95708
$391$	9.73248	0.492192
$392$	−10.9971	−0.555438
$393$	−59.7475	−3.01386
$394$	−29.8973	−1.50620
$395$	9.04499	0.455103
$396$	−1.02162	−0.0513383
$397$	20.0695	1.00726	0.503628	−	0.863920i	$-0.331998\pi$
$397$	20.0695	1.00726	0.503628	+	0.863920i	$0.331998\pi$
$398$	−30.4102	−1.52433
$399$	0.963115	0.0482161
$400$	−9.98376	−0.499188
$401$	18.1072	0.904230	0.452115	−	0.891960i	$-0.350670\pi$
$401$	18.1072	0.904230	0.452115	+	0.891960i	$0.350670\pi$
$402$	55.6084	2.77349
$403$	−2.93646	−0.146275
$404$	−1.07510	−0.0534882
$405$	78.7436	3.91280
$406$	−3.82632	−0.189897
$407$	−1.30107	−0.0644916
$408$	6.18427	0.306167
$409$	−17.0583	−0.843480	−0.421740	−	0.906717i	$-0.638580\pi$
$409$	−17.0583	−0.843480	−0.421740	+	0.906717i	$0.638580\pi$
$410$	12.3421	0.609532
$411$	−35.3329	−1.74284
$412$	−8.73469	−0.430327
$413$	1.96286	0.0965861
$414$	114.942	5.64911
$415$	−11.6127	−0.570044
$416$	14.0811	0.690385
$417$	−11.9791	−0.586618
$418$	0.207477	0.0101480
$419$	−5.94519	−0.290442	−0.145221	−	0.989399i	$-0.546389\pi$
$419$	−5.94519	−0.290442	−0.145221	+	0.989399i	$0.546389\pi$
$420$	2.79336	0.136302
$421$	30.2205	1.47286	0.736429	−	0.676515i	$-0.236511\pi$
$421$	30.2205	1.47286	0.736429	+	0.676515i	$0.236511\pi$
$422$	−11.5670	−0.563073
$423$	−47.2586	−2.29779
$424$	14.1038	0.684940
$425$	−2.35577	−0.114272
$426$	48.2489	2.33767
$427$	1.78070	0.0861743
$428$	−7.36141	−0.355827
$429$	0.978857	0.0472597
$430$	−35.0499	−1.69026
$431$	−25.9092	−1.24800	−0.624000	−	0.781424i	$-0.714494\pi$
$431$	−25.9092	−1.24800	−0.624000	+	0.781424i	$0.714494\pi$
$432$	80.8183	3.88837
$433$	8.39215	0.403301	0.201651	−	0.979458i	$-0.435369\pi$
$433$	8.39215	0.403301	0.201651	+	0.979458i	$0.435369\pi$
$434$	−0.599450	−0.0287745
$435$	65.1386	3.12316
$436$	14.9975	0.718248
$437$	−8.26455	−0.395347
$438$	−79.9609	−3.82068
$439$	−12.4962	−0.596413	−0.298207	−	0.954501i	$-0.596388\pi$
$439$	−12.4962	−0.596413	−0.298207	+	0.954501i	$0.596388\pi$
$440$	−0.496147	−0.0236529
$441$	−54.6557	−2.60265
$442$	5.20941	0.247786
$443$	−34.4691	−1.63768	−0.818839	−	0.574023i	$-0.805382\pi$
$443$	−34.4691	−1.63768	−0.818839	+	0.574023i	$0.805382\pi$
$444$	−39.9414	−1.89554
$445$	30.5203	1.44680
$446$	−22.2179	−1.05205
$447$	57.1712	2.70410
$448$	−0.0367291	−0.00173528
$449$	−29.3780	−1.38643	−0.693216	−	0.720730i	$-0.743807\pi$
$449$	−29.3780	−1.38643	−0.693216	+	0.720730i	$0.743807\pi$
$450$	−27.8221	−1.31155
$451$	0.312585	0.0147190
$452$	22.6606	1.06586
$453$	−21.8849	−1.02824
$454$	9.02489	0.423559
$455$	−1.94007	−0.0909521
$456$	−5.25151	−0.245924
$457$	37.6836	1.76276	0.881382	−	0.472405i	$-0.156614\pi$
$457$	37.6836	1.76276	0.881382	+	0.472405i	$0.156614\pi$
$458$	−2.82767	−0.132128
$459$	19.0699	0.890107
$460$	−23.9700	−1.11761
$461$	9.51676	0.443240	0.221620	−	0.975133i	$-0.428866\pi$
$461$	9.51676	0.443240	0.221620	+	0.975133i	$0.428866\pi$
$462$	0.199824	0.00929667
$463$	−6.18844	−0.287601	−0.143801	−	0.989607i	$-0.545932\pi$
$463$	−6.18844	−0.287601	−0.143801	+	0.989607i	$0.545932\pi$
$464$	37.2090	1.72738
$465$	10.2049	0.473242
$466$	−28.4988	−1.32018
$467$	−9.15389	−0.423592	−0.211796	−	0.977314i	$-0.567931\pi$
$467$	−9.15389	−0.423592	−0.211796	+	0.977314i	$0.567931\pi$
$468$	21.7823	1.00689
$469$	−2.79138	−0.128894
$470$	27.8362	1.28399
$471$	−39.2669	−1.80932
$472$	−10.7028	−0.492634
$473$	−0.887700	−0.0408165
$474$	19.8633	0.912352
$475$	2.00045	0.0917871
$476$	0.376509	0.0172573
$477$	70.0958	3.20947
$478$	−0.560947	−0.0256571
$479$	−20.3249	−0.928668	−0.464334	−	0.885660i	$-0.653706\pi$
$479$	−20.3249	−0.928668	−0.464334	+	0.885660i	$0.653706\pi$
$480$	−48.9355	−2.23359
$481$	27.7405	1.26486
$482$	13.5220	0.615912
$483$	−7.95971	−0.362179
$484$	−12.0428	−0.547402
$485$	19.4466	0.883025
$486$	87.4426	3.96648
$487$	35.7226	1.61875	0.809373	−	0.587294i	$-0.199807\pi$
$487$	35.7226	1.61875	0.809373	+	0.587294i	$0.199807\pi$
$488$	−9.70952	−0.439529
$489$	−26.7427	−1.20934
$490$	32.1932	1.45434
$491$	34.0328	1.53588	0.767939	−	0.640523i	$-0.221282\pi$
$491$	34.0328	1.53588	0.767939	+	0.640523i	$0.221282\pi$
$492$	9.59601	0.432621
$493$	8.77984	0.395424
$494$	−4.42368	−0.199031
$495$	−2.46585	−0.110832
$496$	5.82934	0.261745
$497$	−2.42195	−0.108639
$498$	−25.5021	−1.14278
$499$	1.63944	0.0733912	0.0366956	−	0.999326i	$-0.488317\pi$
$499$	1.63944	0.0733912	0.0366956	+	0.999326i	$0.488317\pi$
$500$	−8.69970	−0.389063
$501$	76.8891	3.43515
$502$	42.9441	1.91669
$503$	−10.2047	−0.455004	−0.227502	−	0.973778i	$-0.573056\pi$
$503$	−10.2047	−0.455004	−0.227502	+	0.973778i	$0.573056\pi$
$504$	−3.66626	−0.163308
$505$	−2.59493	−0.115473
$506$	−1.71470	−0.0762279
$507$	22.0571	0.979589
$508$	−15.6343	−0.693660
$509$	11.2089	0.496827	0.248413	−	0.968654i	$-0.420091\pi$
$509$	11.2089	0.496827	0.248413	+	0.968654i	$0.420091\pi$
$510$	−18.1040	−0.801658
$511$	4.01380	0.177560
$512$	−12.0793	−0.533835
$513$	−16.1936	−0.714966
$514$	−31.5517	−1.39168
$515$	−21.0826	−0.929012
$516$	−27.2514	−1.19968
$517$	0.705001	0.0310059
$518$	5.66296	0.248816
$519$	−50.1474	−2.20122
$520$	10.5785	0.463898
$521$	8.54977	0.374572	0.187286	−	0.982305i	$-0.440031\pi$
$521$	8.54977	0.374572	0.187286	+	0.982305i	$0.440031\pi$
$522$	103.692	4.53846
$523$	20.1902	0.882855	0.441427	−	0.897297i	$-0.354472\pi$
$523$	20.1902	0.882855	0.441427	+	0.897297i	$0.354472\pi$
$524$	19.8341	0.866457
$525$	1.92667	0.0840867
$526$	−33.8073	−1.47407
$527$	1.37549	0.0599174
$528$	−1.94319	−0.0845664
$529$	45.3027	1.96968
$530$	−41.2878	−1.79343
$531$	−53.1927	−2.30837
$532$	−0.319721	−0.0138617
$533$	−6.66472	−0.288681
$534$	67.0243	2.90043
$535$	−17.7680	−0.768177
$536$	15.2203	0.657418
$537$	−9.17103	−0.395759
$538$	−10.6106	−0.457454
$539$	0.815350	0.0351196
$540$	−46.9670	−2.02114
$541$	−34.9876	−1.50424	−0.752118	−	0.659029i	$-0.770967\pi$
$541$	−34.9876	−1.50424	−0.752118	+	0.659029i	$0.770967\pi$
$542$	13.4297	0.576855
$543$	38.2942	1.64336
$544$	−6.59587	−0.282796
$545$	36.1989	1.55059
$546$	−4.26051	−0.182333
$547$	24.3610	1.04160	0.520801	−	0.853678i	$-0.325633\pi$
$547$	24.3610	1.04160	0.520801	+	0.853678i	$0.325633\pi$
$548$	11.7293	0.501051
$549$	−48.2563	−2.05953
$550$	0.415048	0.0176977
$551$	−7.45560	−0.317619
$552$	43.4013	1.84728
$553$	−0.997080	−0.0424001
$554$	−55.3467	−2.35145
$555$	−96.4053	−4.09218
$556$	3.97664	0.168647
$557$	30.2284	1.28082	0.640409	−	0.768034i	$-0.278765\pi$
$557$	30.2284	1.28082	0.640409	+	0.768034i	$0.278765\pi$
$558$	16.2448	0.687698
$559$	18.9269	0.800524
$560$	3.85136	0.162750
$561$	−0.458515	−0.0193585
$562$	56.3109	2.37533
$563$	17.9327	0.755771	0.377886	−	0.925852i	$-0.376651\pi$
$563$	17.9327	0.755771	0.377886	+	0.925852i	$0.376651\pi$
$564$	21.6427	0.911324
$565$	54.6950	2.30104
$566$	1.48042	0.0622268
$567$	−8.68035	−0.364541
$568$	13.2060	0.554111
$569$	23.2011	0.972639	0.486319	−	0.873781i	$-0.338339\pi$
$569$	23.2011	0.972639	0.486319	+	0.873781i	$0.338339\pi$
$570$	15.3734	0.643921
$571$	16.2942	0.681893	0.340946	−	0.940083i	$-0.389253\pi$
$571$	16.2942	0.681893	0.340946	+	0.940083i	$0.389253\pi$
$572$	−0.324947	−0.0135867
$573$	60.7958	2.53978
$574$	−1.36054	−0.0567877
$575$	−16.5328	−0.689467
$576$	0.995341	0.0414726
$577$	42.3922	1.76481	0.882406	−	0.470490i	$-0.155923\pi$
$577$	42.3922	1.76481	0.882406	+	0.470490i	$0.155923\pi$
$578$	27.4730	1.14273
$579$	−33.6382	−1.39796
$580$	−21.6238	−0.897878
$581$	1.28013	0.0531088
$582$	42.7059	1.77022
$583$	−1.04568	−0.0433078
$584$	−21.8858	−0.905639
$585$	52.5751	2.17371
$586$	−3.82792	−0.158130
$587$	−42.8189	−1.76733	−0.883663	−	0.468123i	$-0.844931\pi$
$587$	−42.8189	−1.76733	−0.883663	+	0.468123i	$0.844931\pi$
$588$	25.0303	1.03223
$589$	−1.16803	−0.0481278
$590$	31.3315	1.28990
$591$	−56.1062	−2.30790
$592$	−55.0694	−2.26334
$593$	39.2359	1.61123	0.805613	−	0.592442i	$-0.201836\pi$
$593$	39.2359	1.61123	0.805613	+	0.592442i	$0.201836\pi$
$594$	−3.35981	−0.137855
$595$	0.908767	0.0372558
$596$	−18.9789	−0.777404
$597$	−57.0688	−2.33567
$598$	36.5597	1.49504
$599$	−32.8611	−1.34267	−0.671334	−	0.741155i	$-0.734278\pi$
$599$	−32.8611	−1.34267	−0.671334	+	0.741155i	$0.734278\pi$
$600$	−10.5054	−0.428881
$601$	−36.0254	−1.46951	−0.734753	−	0.678335i	$-0.762702\pi$
$601$	−36.0254	−1.46951	−0.734753	+	0.678335i	$0.762702\pi$
$602$	3.86375	0.157475
$603$	75.6451	3.08051
$604$	7.26503	0.295610
$605$	−29.0674	−1.18176
$606$	−5.69862	−0.231490
$607$	23.1239	0.938571	0.469286	−	0.883046i	$-0.344512\pi$
$607$	23.1239	0.938571	0.469286	+	0.883046i	$0.344512\pi$
$608$	5.60103	0.227152
$609$	−7.18060	−0.290972
$610$	28.4239	1.15085
$611$	−15.0315	−0.608111
$612$	−10.2032	−0.412441
$613$	−41.9086	−1.69267	−0.846336	−	0.532650i	$-0.821196\pi$
$613$	−41.9086	−1.69267	−0.846336	+	0.532650i	$0.821196\pi$
$614$	45.8746	1.85135
$615$	23.1616	0.933964
$616$	0.0546931	0.00220365
$617$	−34.0177	−1.36950	−0.684750	−	0.728778i	$-0.740089\pi$
$617$	−34.0177	−1.36950	−0.684750	+	0.728778i	$0.740089\pi$
$618$	−46.2987	−1.86241
$619$	−31.9578	−1.28449	−0.642247	−	0.766498i	$-0.721998\pi$
$619$	−31.9578	−1.28449	−0.642247	+	0.766498i	$0.721998\pi$
$620$	−3.38768	−0.136053
$621$	133.833	5.37053
$622$	−45.9448	−1.84222
$623$	−3.36442	−0.134793
$624$	41.4313	1.65858
$625$	−31.0005	−1.24002
$626$	33.6251	1.34393
$627$	0.389358	0.0155495
$628$	13.0353	0.520163
$629$	−12.9942	−0.518112
$630$	10.7327	0.427601
$631$	41.0601	1.63458	0.817288	−	0.576229i	$-0.195476\pi$
$631$	41.0601	1.63458	0.817288	+	0.576229i	$0.195476\pi$
$632$	5.43670	0.216261
$633$	−21.7070	−0.862776
$634$	1.75960	0.0698826
$635$	−37.7360	−1.49751
$636$	−32.1014	−1.27290
$637$	−17.3843	−0.688792
$638$	−1.54686	−0.0612410
$639$	65.6338	2.59643
$640$	−30.2251	−1.19475
$641$	32.1380	1.26937	0.634687	−	0.772769i	$-0.281129\pi$
$641$	32.1380	1.26937	0.634687	+	0.772769i	$0.281129\pi$
$642$	−39.0195	−1.53998
$643$	11.2817	0.444909	0.222454	−	0.974943i	$-0.428593\pi$
$643$	11.2817	0.444909	0.222454	+	0.974943i	$0.428593\pi$
$644$	2.64235	0.104123
$645$	−65.7758	−2.58992
$646$	2.07214	0.0815271
$647$	30.8034	1.21101	0.605503	−	0.795843i	$-0.292972\pi$
$647$	30.8034	1.21101	0.605503	+	0.795843i	$0.292972\pi$
$648$	47.3307	1.85933
$649$	0.793525	0.0311486
$650$	−8.84937	−0.347101
$651$	−1.12495	−0.0440901
$652$	8.87763	0.347675
$653$	−39.6578	−1.55193	−0.775966	−	0.630775i	$-0.782737\pi$
$653$	−39.6578	−1.55193	−0.775966	+	0.630775i	$0.782737\pi$
$654$	79.4948	3.10849
$655$	47.8729	1.87055
$656$	13.2305	0.516565
$657$	−108.772	−4.24361
$658$	−3.06854	−0.119624
$659$	−28.3138	−1.10295	−0.551474	−	0.834192i	$-0.685934\pi$
$659$	−28.3138	−1.10295	−0.551474	+	0.834192i	$0.685934\pi$
$660$	1.12927	0.0439568
$661$	6.11004	0.237653	0.118827	−	0.992915i	$-0.462087\pi$
$661$	6.11004	0.237653	0.118827	+	0.992915i	$0.462087\pi$
$662$	−38.6941	−1.50389
$663$	9.77614	0.379674
$664$	−6.98008	−0.270880
$665$	−0.771700	−0.0299252
$666$	−153.464	−5.94660
$667$	61.6171	2.38582
$668$	−25.5245	−0.987573
$669$	−41.6948	−1.61202
$670$	−44.5564	−1.72136
$671$	0.719884	0.0277908
$672$	5.39444	0.208095
$673$	−32.0058	−1.23373	−0.616866	−	0.787068i	$-0.711598\pi$
$673$	−32.0058	−1.23373	−0.616866	+	0.787068i	$0.711598\pi$
$674$	12.1768	0.469033
$675$	−32.3946	−1.24687
$676$	−7.32218	−0.281622
$677$	−51.1099	−1.96431	−0.982157	−	0.188063i	$-0.939779\pi$
$677$	−51.1099	−1.96431	−0.982157	+	0.188063i	$0.939779\pi$
$678$	120.113	4.61293
$679$	−2.14371	−0.0822680
$680$	−4.95517	−0.190022
$681$	16.9364	0.649005
$682$	−0.242339	−0.00927965
$683$	27.5695	1.05492	0.527459	−	0.849580i	$-0.323145\pi$
$683$	27.5695	1.05492	0.527459	+	0.849580i	$0.323145\pi$
$684$	8.66429	0.331288
$685$	28.3106	1.08169
$686$	−7.14134	−0.272658
$687$	−5.30650	−0.202456
$688$	−37.5730	−1.43246
$689$	22.2954	0.849386
$690$	−127.054	−4.83687
$691$	5.63204	0.214253	0.107126	−	0.994245i	$-0.465835\pi$
$691$	5.63204	0.214253	0.107126	+	0.994245i	$0.465835\pi$
$692$	16.6472	0.632831
$693$	0.271825	0.0103258
$694$	−26.5931	−1.00946
$695$	9.59827	0.364083
$696$	39.1531	1.48410
$697$	3.12188	0.118250
$698$	5.61197	0.212416
$699$	−53.4817	−2.02286
$700$	−0.639587	−0.0241741
$701$	7.55722	0.285432	0.142716	−	0.989764i	$-0.454416\pi$
$701$	7.55722	0.285432	0.142716	+	0.989764i	$0.454416\pi$
$702$	71.6355	2.70371
$703$	11.0343	0.416166
$704$	−0.0148484	−0.000559622 0
$705$	52.2384	1.96741
$706$	−24.0924	−0.906728
$707$	0.286054	0.0107582
$708$	24.3604	0.915518
$709$	1.28138	0.0481233	0.0240616	−	0.999710i	$-0.492340\pi$
$709$	1.28138	0.0481233	0.0240616	+	0.999710i	$0.492340\pi$
$710$	−38.6596	−1.45087
$711$	27.0204	1.01335
$712$	18.3450	0.687506
$713$	9.65323	0.361516
$714$	1.99571	0.0746874
$715$	−0.784313	−0.0293316
$716$	3.04447	0.113777
$717$	−1.05269	−0.0393135
$718$	35.9938	1.34328
$719$	34.2686	1.27800	0.639002	−	0.769205i	$-0.279348\pi$
$719$	34.2686	1.27800	0.639002	+	0.769205i	$0.279348\pi$
$720$	−104.370	−3.88964
$721$	2.32406	0.0865525
$722$	−1.75960	−0.0654855
$723$	25.3759	0.943739
$724$	−12.7124	−0.472451
$725$	−14.9146	−0.553913
$726$	−63.8337	−2.36909
$727$	16.4701	0.610844	0.305422	−	0.952217i	$-0.401203\pi$
$727$	16.4701	0.610844	0.305422	+	0.952217i	$0.401203\pi$
$728$	−1.16613	−0.0432196
$729$	74.8137	2.77088
$730$	64.0689	2.37130
$731$	−8.86573	−0.327911
$732$	22.0997	0.816827
$733$	29.4870	1.08913	0.544563	−	0.838720i	$-0.316696\pi$
$733$	29.4870	1.08913	0.544563	+	0.838720i	$0.316696\pi$
$734$	−44.7339	−1.65116
$735$	60.4149	2.22844
$736$	−46.2900	−1.70627
$737$	−1.12847	−0.0415677
$738$	36.8700	1.35720
$739$	26.2651	0.966179	0.483090	−	0.875571i	$-0.339515\pi$
$739$	26.2651	0.966179	0.483090	+	0.875571i	$0.339515\pi$
$740$	32.0032	1.17646
$741$	−8.30162	−0.304968
$742$	4.55138	0.167087
$743$	−21.8436	−0.801363	−0.400681	−	0.916217i	$-0.631227\pi$
$743$	−21.8436	−0.801363	−0.400681	+	0.916217i	$0.631227\pi$
$744$	6.13392	0.224880
$745$	−45.8086	−1.67830
$746$	1.49152	0.0546085
$747$	−34.6910	−1.26928
$748$	0.152211	0.00556539
$749$	1.95867	0.0715681
$750$	−46.1132	−1.68382
$751$	−29.9177	−1.09171	−0.545856	−	0.837879i	$-0.683795\pi$
$751$	−29.9177	−1.09171	−0.545856	+	0.837879i	$0.683795\pi$
$752$	29.8400	1.08815
$753$	80.5903	2.93688
$754$	32.9812	1.20110
$755$	17.5354	0.638177
$756$	5.17744	0.188302
$757$	−29.5680	−1.07467	−0.537333	−	0.843370i	$-0.680568\pi$
$757$	−29.5680	−1.07467	−0.537333	+	0.843370i	$0.680568\pi$
$758$	−27.0392	−0.982106
$759$	−3.21787	−0.116801
$760$	4.20779	0.152633
$761$	42.4841	1.54005	0.770024	−	0.638015i	$-0.220244\pi$
$761$	42.4841	1.54005	0.770024	+	0.638015i	$0.220244\pi$
$762$	−82.8705	−3.00208
$763$	−3.99041	−0.144462
$764$	−20.1821	−0.730163
$765$	−24.6272	−0.890398
$766$	−6.03548	−0.218071
$767$	−16.9190	−0.610910
$768$	−65.5444	−2.36513
$769$	−4.58334	−0.165280	−0.0826398	−	0.996579i	$-0.526335\pi$
$769$	−4.58334	−0.165280	−0.0826398	+	0.996579i	$0.526335\pi$
$770$	−0.160110	−0.00576996
$771$	−59.2109	−2.13243
$772$	11.1667	0.401899
$773$	−38.1614	−1.37257	−0.686284	−	0.727333i	$-0.740759\pi$
$773$	−38.1614	−1.37257	−0.686284	+	0.727333i	$0.740759\pi$
$774$	−104.706	−3.76358
$775$	−2.33659	−0.0839327
$776$	11.6889	0.419605
$777$	10.6273	0.381252
$778$	−42.6781	−1.53009
$779$	−2.65101	−0.0949823
$780$	−24.0775	−0.862114
$781$	−0.979121	−0.0350357
$782$	−17.1253	−0.612398
$783$	120.733	4.31465
$784$	34.5107	1.23252
$785$	31.4628	1.12295
$786$	105.132	3.74992
$787$	−1.33006	−0.0474114	−0.0237057	−	0.999719i	$-0.507546\pi$
$787$	−1.33006	−0.0474114	−0.0237057	+	0.999719i	$0.507546\pi$
$788$	18.6253	0.663500
$789$	−63.4438	−2.25866
$790$	−15.9156	−0.566250
$791$	−6.02934	−0.214379
$792$	−1.48216	−0.0526662
$793$	−15.3489	−0.545055
$794$	−35.3142	−1.25325
$795$	−77.4820	−2.74800
$796$	18.9449	0.671483
$797$	−42.8120	−1.51648	−0.758240	−	0.651976i	$-0.773940\pi$
$797$	−42.8120	−1.51648	−0.758240	+	0.651976i	$0.773940\pi$
$798$	−1.69470	−0.0599916
$799$	7.04105	0.249095
$800$	11.2046	0.396142
$801$	91.1744	3.22149
$802$	−31.8614	−1.12506
$803$	1.62266	0.0572623
$804$	−34.6427	−1.22175
$805$	6.37775	0.224786
$806$	5.16699	0.181999
$807$	−19.9121	−0.700940
$808$	−1.55974	−0.0548716
$809$	−32.0686	−1.12747	−0.563735	−	0.825955i	$-0.690636\pi$
$809$	−32.0686	−1.12747	−0.563735	+	0.825955i	$0.690636\pi$
$810$	−138.557	−4.86840
$811$	32.7906	1.15143	0.575717	−	0.817649i	$-0.304723\pi$
$811$	32.7906	1.15143	0.575717	+	0.817649i	$0.304723\pi$
$812$	2.38371	0.0836518
$813$	25.2026	0.883895
$814$	2.28936	0.0802421
$815$	21.4276	0.750578
$816$	−19.4072	−0.679388
$817$	7.52853	0.263390
$818$	30.0158	1.04948
$819$	−5.79566	−0.202517
$820$	−7.68883	−0.268506
$821$	9.86679	0.344353	0.172177	−	0.985066i	$-0.444920\pi$
$821$	9.86679	0.344353	0.172177	+	0.985066i	$0.444920\pi$
$822$	62.1717	2.16849
$823$	19.0145	0.662805	0.331402	−	0.943490i	$-0.392478\pi$
$823$	19.0145	0.662805	0.331402	+	0.943490i	$0.392478\pi$
$824$	−12.6722	−0.441458
$825$	0.778893	0.0271176
$826$	−3.45385	−0.120175
$827$	1.35819	0.0472290	0.0236145	−	0.999721i	$-0.492483\pi$
$827$	1.35819	0.0472290	0.0236145	+	0.999721i	$0.492483\pi$
$828$	−71.6065	−2.48850
$829$	18.7950	0.652777	0.326388	−	0.945236i	$-0.394168\pi$
$829$	18.7950	0.652777	0.326388	+	0.945236i	$0.394168\pi$
$830$	20.4337	0.709263
$831$	−103.865	−3.60305
$832$	0.316588	0.0109757
$833$	8.14315	0.282143
$834$	21.0784	0.729884
$835$	−61.6077	−2.13202
$836$	−0.129253	−0.00447032
$837$	18.9146	0.653786
$838$	10.4612	0.361375
$839$	24.4560	0.844313	0.422157	−	0.906523i	$-0.361273\pi$
$839$	24.4560	0.844313	0.422157	+	0.906523i	$0.361273\pi$
$840$	4.05259	0.139828
$841$	26.5859	0.916755
$842$	−53.1760	−1.83257
$843$	105.675	3.63964
$844$	7.20597	0.248040
$845$	−17.6733	−0.607980
$846$	83.1562	2.85897
$847$	3.20427	0.110100
$848$	−44.2599	−1.51989
$849$	2.77821	0.0953479
$850$	4.14521	0.142180
$851$	−91.1934	−3.12607
$852$	−30.0579	−1.02977
$853$	23.7153	0.811996	0.405998	−	0.913874i	$-0.366924\pi$
$853$	23.7153	0.811996	0.405998	+	0.913874i	$0.366924\pi$
$854$	−3.13333	−0.107220
$855$	20.9127	0.715200
$856$	−10.6799	−0.365031
$857$	16.3381	0.558101	0.279050	−	0.960276i	$-0.409980\pi$
$857$	16.3381	0.558101	0.279050	+	0.960276i	$0.409980\pi$
$858$	−1.72240	−0.0588016
$859$	39.4131	1.34476	0.672379	−	0.740207i	$-0.265273\pi$
$859$	39.4131	1.34476	0.672379	+	0.740207i	$0.265273\pi$
$860$	21.8353	0.744577
$861$	−2.55323	−0.0870138
$862$	45.5898	1.55279
$863$	−3.35349	−0.114154	−0.0570770	−	0.998370i	$-0.518178\pi$
$863$	−3.35349	−0.114154	−0.0570770	+	0.998370i	$0.518178\pi$
$864$	−90.7010	−3.08571
$865$	40.1808	1.36619
$866$	−14.7668	−0.501797
$867$	51.5567	1.75096
$868$	0.373443	0.0126755
$869$	−0.403089	−0.0136739
$870$	−114.618	−3.88591
$871$	24.0604	0.815256
$872$	21.7582	0.736826
$873$	58.0936	1.96617
$874$	14.5423	0.491900
$875$	2.31475	0.0782528
$876$	49.8138	1.68305
$877$	34.2661	1.15708	0.578542	−	0.815653i	$-0.303622\pi$
$877$	34.2661	1.15708	0.578542	+	0.815653i	$0.303622\pi$
$878$	21.9884	0.742072
$879$	−7.18360	−0.242297
$880$	1.55699	0.0524860
$881$	5.95378	0.200588	0.100294	−	0.994958i	$-0.468022\pi$
$881$	5.95378	0.200588	0.100294	+	0.994958i	$0.468022\pi$
$882$	96.1721	3.23828
$883$	24.4289	0.822097	0.411049	−	0.911613i	$-0.365163\pi$
$883$	24.4289	0.822097	0.411049	+	0.911613i	$0.365163\pi$
$884$	−3.24534	−0.109153
$885$	58.7978	1.97647
$886$	60.6519	2.03764
$887$	45.1240	1.51512	0.757558	−	0.652768i	$-0.226392\pi$
$887$	45.1240	1.51512	0.757558	+	0.652768i	$0.226392\pi$
$888$	−57.9467	−1.94456
$889$	4.15985	0.139517
$890$	−53.7035	−1.80015
$891$	−3.50920	−0.117563
$892$	13.8412	0.463439
$893$	−5.97907	−0.200082
$894$	−100.598	−3.36451
$895$	7.34832	0.245627
$896$	3.33188	0.111310
$897$	68.6092	2.29079
$898$	51.6934	1.72503
$899$	8.70835	0.290440
$900$	17.3325	0.577751
$901$	−10.4436	−0.347926
$902$	−0.550024	−0.0183138
$903$	7.25084	0.241293
$904$	32.8757	1.09343
$905$	−30.6834	−1.01995
$906$	38.5087	1.27936
$907$	30.2882	1.00570	0.502852	−	0.864373i	$-0.332284\pi$
$907$	30.2882	1.00570	0.502852	+	0.864373i	$0.332284\pi$
$908$	−5.62230	−0.186583
$909$	−7.75193	−0.257115
$910$	3.41375	0.113165
$911$	−30.3604	−1.00589	−0.502943	−	0.864320i	$-0.667749\pi$
$911$	−30.3604	−1.00589	−0.502943	+	0.864320i	$0.667749\pi$
$912$	16.4801	0.545709
$913$	0.517518	0.0171273
$914$	−66.3080	−2.19327
$915$	53.3412	1.76341
$916$	1.76158	0.0582041
$917$	−5.27730	−0.174272
$918$	−33.5554	−1.10749
$919$	15.6783	0.517180	0.258590	−	0.965987i	$-0.416742\pi$
$919$	15.6783	0.517180	0.258590	+	0.965987i	$0.416742\pi$
$920$	−34.7755	−1.14651
$921$	86.0899	2.83676
$922$	−16.7457	−0.551490
$923$	20.8761	0.687147
$924$	−0.124486	−0.00409529
$925$	22.0736	0.725775
$926$	10.8892	0.357840
$927$	−62.9810	−2.06857
$928$	−41.7590	−1.37081
$929$	−44.8079	−1.47010	−0.735050	−	0.678013i	$-0.762841\pi$
$929$	−44.8079	−1.47010	−0.735050	+	0.678013i	$0.762841\pi$
$930$	−17.9566	−0.588820
$931$	−6.91493	−0.226628
$932$	17.7541	0.581554
$933$	−86.2215	−2.82276
$934$	16.1072	0.527043
$935$	0.367387	0.0120148
$936$	31.6016	1.03293
$937$	−30.8492	−1.00780	−0.503899	−	0.863763i	$-0.668102\pi$
$937$	−30.8492	−1.00780	−0.503899	+	0.863763i	$0.668102\pi$
$938$	4.91170	0.160373
$939$	63.1020	2.05926
$940$	−17.3413	−0.565612
$941$	46.9165	1.52944	0.764718	−	0.644366i	$-0.222878\pi$
$941$	46.9165	1.52944	0.764718	+	0.644366i	$0.222878\pi$
$942$	69.0941	2.25121
$943$	21.9094	0.713468
$944$	33.5869	1.09316
$945$	12.4966	0.406515
$946$	1.56200	0.0507849
$947$	−7.02068	−0.228142	−0.114071	−	0.993473i	$-0.536389\pi$
$947$	−7.02068	−0.228142	−0.114071	+	0.993473i	$0.536389\pi$
$948$	−12.3744	−0.401901
$949$	−34.5972	−1.12307
$950$	−3.52000	−0.114204
$951$	3.30212	0.107079
$952$	0.546236	0.0177036
$953$	31.8812	1.03273	0.516367	−	0.856367i	$-0.327284\pi$
$953$	31.8812	1.03273	0.516367	+	0.856367i	$0.327284\pi$
$954$	−123.341	−3.99330
$955$	−48.7129	−1.57631
$956$	0.349457	0.0113023
$957$	−2.90290	−0.0938373
$958$	35.7637	1.15547
$959$	−3.12084	−0.100777
$960$	−1.10022	−0.0355096
$961$	−29.6357	−0.955991
$962$	−48.8122	−1.57377
$963$	−53.0790	−1.71045
$964$	−8.42391	−0.271316
$965$	26.9528	0.867640
$966$	14.0059	0.450632
$967$	5.12064	0.164669	0.0823343	−	0.996605i	$-0.473762\pi$
$967$	5.12064	0.164669	0.0823343	+	0.996605i	$0.473762\pi$
$968$	−17.4717	−0.561561
$969$	3.88864	0.124921
$970$	−34.2183	−1.09868
$971$	−27.3000	−0.876100	−0.438050	−	0.898951i	$-0.644331\pi$
$971$	−27.3000	−0.876100	−0.438050	+	0.898951i	$0.644331\pi$
$972$	−54.4747	−1.74728
$973$	−1.05807	−0.0339202
$974$	−62.8575	−2.01408
$975$	−16.6070	−0.531850
$976$	30.4700	0.975320
$977$	16.4953	0.527732	0.263866	−	0.964559i	$-0.415002\pi$
$977$	16.4953	0.527732	0.263866	+	0.964559i	$0.415002\pi$
$978$	47.0564	1.50470
$979$	−1.36013	−0.0434701
$980$	−20.0557	−0.640654
$981$	108.138	3.45259
$982$	−59.8841	−1.91098
$983$	−43.7153	−1.39430	−0.697151	−	0.716924i	$-0.745549\pi$
$983$	−43.7153	−1.39430	−0.697151	+	0.716924i	$0.745549\pi$
$984$	13.9218	0.443811
$985$	44.9553	1.43240
$986$	−15.4490	−0.491997
$987$	−5.75853	−0.183296
$988$	2.75585	0.0876753
$989$	−62.2199	−1.97848
$990$	4.33891	0.137900
$991$	−6.14902	−0.195330	−0.0976650	−	0.995219i	$-0.531137\pi$
$991$	−6.14902	−0.195330	−0.0976650	+	0.995219i	$0.531137\pi$
$992$	−6.54216	−0.207714
$993$	−72.6147	−2.30436
$994$	4.26166	0.135172
$995$	45.7266	1.44963
$996$	15.8872	0.503406
$997$	−45.2612	−1.43344	−0.716719	−	0.697362i	$-0.754357\pi$
$997$	−45.2612	−1.43344	−0.716719	+	0.697362i	$0.754357\pi$
$998$	−2.88475	−0.0913152
$999$	−178.685	−5.65335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.29	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.29	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-1.75960 q^{2} -3.30212 q^{3} +1.09619 q^{4} +2.64584 q^{5} +5.81041 q^{6} -0.291666 q^{7} +1.59034 q^{8} +7.90401 q^{9} +O(q^{10})\)	\(q-1.75960 q^{2} -3.30212 q^{3} +1.09619 q^{4} +2.64584 q^{5} +5.81041 q^{6} -0.291666 q^{7} +1.59034 q^{8} +7.90401 q^{9} -4.65561 q^{10} -0.117911 q^{11} -3.61975 q^{12} +2.51403 q^{13} +0.513215 q^{14} -8.73688 q^{15} -4.99075 q^{16} -1.17762 q^{17} -13.9079 q^{18} +1.00000 q^{19} +2.90034 q^{20} +0.963115 q^{21} +0.207477 q^{22} -8.26455 q^{23} -5.25151 q^{24} +2.00045 q^{25} -4.42368 q^{26} -16.1936 q^{27} -0.319721 q^{28} -7.45560 q^{29} +15.3734 q^{30} -1.16803 q^{31} +5.60103 q^{32} +0.389358 q^{33} +2.07214 q^{34} -0.771700 q^{35} +8.66429 q^{36} +11.0343 q^{37} -1.75960 q^{38} -8.30162 q^{39} +4.20779 q^{40} -2.65101 q^{41} -1.69470 q^{42} +7.52853 q^{43} -0.129253 q^{44} +20.9127 q^{45} +14.5423 q^{46} -5.97907 q^{47} +16.4801 q^{48} -6.91493 q^{49} -3.52000 q^{50} +3.88864 q^{51} +2.75585 q^{52} +8.86838 q^{53} +28.4943 q^{54} -0.311975 q^{55} -0.463848 q^{56} -3.30212 q^{57} +13.1189 q^{58} -6.72984 q^{59} -9.57728 q^{60} -6.10529 q^{61} +2.05526 q^{62} -2.30533 q^{63} +0.125929 q^{64} +6.65171 q^{65} -0.685114 q^{66} +9.57047 q^{67} -1.29089 q^{68} +27.2905 q^{69} +1.35788 q^{70} +8.30387 q^{71} +12.5701 q^{72} -13.7617 q^{73} -19.4159 q^{74} -6.60574 q^{75} +1.09619 q^{76} +0.0343907 q^{77} +14.6075 q^{78} +3.41857 q^{79} -13.2047 q^{80} +29.7613 q^{81} +4.66472 q^{82} -4.38904 q^{83} +1.05576 q^{84} -3.11578 q^{85} -13.2472 q^{86} +24.6193 q^{87} -0.187520 q^{88} +11.5352 q^{89} -36.7980 q^{90} -0.733255 q^{91} -9.05951 q^{92} +3.85697 q^{93} +10.5208 q^{94} +2.64584 q^{95} -18.4953 q^{96} +7.34989 q^{97} +12.1675 q^{98} -0.931973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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