LMFDB - Embedded newform 6019.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.75200 q^{2} +0.205353 q^{3} +5.57349 q^{4} -1.15382 q^{5} -0.565131 q^{6} +4.79173 q^{7} -9.83422 q^{8} -2.95783 q^{9} +O(q^{10})$	\(q-2.75200 q^{2} +0.205353 q^{3} +5.57349 q^{4} -1.15382 q^{5} -0.565131 q^{6} +4.79173 q^{7} -9.83422 q^{8} -2.95783 q^{9} +3.17530 q^{10} +1.52722 q^{11} +1.14453 q^{12} +1.00000 q^{13} -13.1868 q^{14} -0.236939 q^{15} +15.9168 q^{16} -0.141785 q^{17} +8.13994 q^{18} -3.31104 q^{19} -6.43077 q^{20} +0.983996 q^{21} -4.20290 q^{22} -1.71610 q^{23} -2.01949 q^{24} -3.66871 q^{25} -2.75200 q^{26} -1.22346 q^{27} +26.7066 q^{28} +3.25041 q^{29} +0.652056 q^{30} -0.673687 q^{31} -24.1345 q^{32} +0.313619 q^{33} +0.390191 q^{34} -5.52877 q^{35} -16.4854 q^{36} +4.67789 q^{37} +9.11197 q^{38} +0.205353 q^{39} +11.3469 q^{40} -4.41872 q^{41} -2.70795 q^{42} +10.6815 q^{43} +8.51194 q^{44} +3.41279 q^{45} +4.72270 q^{46} -6.19782 q^{47} +3.26856 q^{48} +15.9607 q^{49} +10.0963 q^{50} -0.0291159 q^{51} +5.57349 q^{52} -13.4826 q^{53} +3.36695 q^{54} -1.76213 q^{55} -47.1229 q^{56} -0.679932 q^{57} -8.94513 q^{58} -6.63760 q^{59} -1.32058 q^{60} -10.5081 q^{61} +1.85399 q^{62} -14.1731 q^{63} +34.5844 q^{64} -1.15382 q^{65} -0.863079 q^{66} +4.99335 q^{67} -0.790234 q^{68} -0.352406 q^{69} +15.2152 q^{70} +6.18190 q^{71} +29.0880 q^{72} -10.4445 q^{73} -12.8735 q^{74} -0.753380 q^{75} -18.4540 q^{76} +7.31803 q^{77} -0.565131 q^{78} +10.0883 q^{79} -18.3650 q^{80} +8.62225 q^{81} +12.1603 q^{82} +2.07969 q^{83} +5.48429 q^{84} +0.163593 q^{85} -29.3956 q^{86} +0.667482 q^{87} -15.0190 q^{88} +15.2276 q^{89} -9.39199 q^{90} +4.79173 q^{91} -9.56466 q^{92} -0.138344 q^{93} +17.0564 q^{94} +3.82033 q^{95} -4.95608 q^{96} -16.4525 q^{97} -43.9237 q^{98} -4.51726 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.75200	−1.94596	−0.972978	−	0.230899i	$-0.925833\pi$
$2$	−2.75200	−1.94596	−0.972978	+	0.230899i	$0.925833\pi$
$3$	0.205353	0.118561	0.0592803	−	0.998241i	$-0.481119\pi$
$3$	0.205353	0.118561	0.0592803	+	0.998241i	$0.481119\pi$
$4$	5.57349	2.78674
$5$	−1.15382	−0.516002	−0.258001	−	0.966145i	$-0.583064\pi$
$5$	−1.15382	−0.516002	−0.258001	+	0.966145i	$0.583064\pi$
$6$	−0.565131	−0.230714
$7$	4.79173	1.81110	0.905552	−	0.424236i	$-0.139457\pi$
$7$	4.79173	1.81110	0.905552	+	0.424236i	$0.139457\pi$
$8$	−9.83422	−3.47692
$9$	−2.95783	−0.985943
$10$	3.17530	1.00412
$11$	1.52722	0.460474	0.230237	−	0.973135i	$-0.426050\pi$
$11$	1.52722	0.460474	0.230237	+	0.973135i	$0.426050\pi$
$12$	1.14453	0.330398
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−13.1868	−3.52433
$15$	−0.236939	−0.0611775
$16$	15.9168	3.97919
$17$	−0.141785	−0.0343878	−0.0171939	−	0.999852i	$-0.505473\pi$
$17$	−0.141785	−0.0343878	−0.0171939	+	0.999852i	$0.505473\pi$
$18$	8.13994	1.91860
$19$	−3.31104	−0.759604	−0.379802	−	0.925068i	$-0.624008\pi$
$19$	−3.31104	−0.759604	−0.379802	+	0.925068i	$0.624008\pi$
$20$	−6.43077	−1.43796
$21$	0.983996	0.214725
$22$	−4.20290	−0.896062
$23$	−1.71610	−0.357832	−0.178916	−	0.983864i	$-0.557259\pi$
$23$	−1.71610	−0.357832	−0.178916	+	0.983864i	$0.557259\pi$
$24$	−2.01949	−0.412226
$25$	−3.66871	−0.733742
$26$	−2.75200	−0.539711
$27$	−1.22346	−0.235455
$28$	26.7066	5.04708
$29$	3.25041	0.603587	0.301793	−	0.953373i	$-0.402415\pi$
$29$	3.25041	0.603587	0.301793	+	0.953373i	$0.402415\pi$
$30$	0.652056	0.119049
$31$	−0.673687	−0.120998	−0.0604989	−	0.998168i	$-0.519269\pi$
$31$	−0.673687	−0.120998	−0.0604989	+	0.998168i	$0.519269\pi$
$32$	−24.1345	−4.26641
$33$	0.313619	0.0545941
$34$	0.390191	0.0669172
$35$	−5.52877	−0.934533
$36$	−16.4854	−2.74757
$37$	4.67789	0.769040	0.384520	−	0.923117i	$-0.374367\pi$
$37$	4.67789	0.769040	0.384520	+	0.923117i	$0.374367\pi$
$38$	9.11197	1.47816
$39$	0.205353	0.0328828
$40$	11.3469	1.79410
$41$	−4.41872	−0.690088	−0.345044	−	0.938587i	$-0.612136\pi$
$41$	−4.41872	−0.690088	−0.345044	+	0.938587i	$0.612136\pi$
$42$	−2.70795	−0.417846
$43$	10.6815	1.62892	0.814460	−	0.580219i	$-0.197033\pi$
$43$	10.6815	1.62892	0.814460	+	0.580219i	$0.197033\pi$
$44$	8.51194	1.28322
$45$	3.41279	0.508749
$46$	4.72270	0.696324
$47$	−6.19782	−0.904045	−0.452022	−	0.892007i	$-0.649297\pi$
$47$	−6.19782	−0.904045	−0.452022	+	0.892007i	$0.649297\pi$
$48$	3.26856	0.471776
$49$	15.9607	2.28010
$50$	10.0963	1.42783
$51$	−0.0291159	−0.00407704
$52$	5.57349	0.772903
$53$	−13.4826	−1.85198	−0.925992	−	0.377543i	$-0.876769\pi$
$53$	−13.4826	−1.85198	−0.925992	+	0.377543i	$0.876769\pi$
$54$	3.36695	0.458184
$55$	−1.76213	−0.237606
$56$	−47.1229	−6.29707
$57$	−0.679932	−0.0900591
$58$	−8.94513	−1.17455
$59$	−6.63760	−0.864142	−0.432071	−	0.901839i	$-0.642217\pi$
$59$	−6.63760	−0.864142	−0.432071	+	0.901839i	$0.642217\pi$
$60$	−1.32058	−0.170486
$61$	−10.5081	−1.34542	−0.672710	−	0.739906i	$-0.734870\pi$
$61$	−10.5081	−1.34542	−0.672710	+	0.739906i	$0.734870\pi$
$62$	1.85399	0.235456
$63$	−14.1731	−1.78565
$64$	34.5844	4.32305
$65$	−1.15382	−0.143113
$66$	−0.863079	−0.106238
$67$	4.99335	0.610035	0.305018	−	0.952347i	$-0.401338\pi$
$67$	4.99335	0.610035	0.305018	+	0.952347i	$0.401338\pi$
$68$	−0.790234	−0.0958300
$69$	−0.352406	−0.0424247
$70$	15.2152	1.81856
$71$	6.18190	0.733656	0.366828	−	0.930289i	$-0.380444\pi$
$71$	6.18190	0.733656	0.366828	+	0.930289i	$0.380444\pi$
$72$	29.0880	3.42805
$73$	−10.4445	−1.22243	−0.611215	−	0.791464i	$-0.709319\pi$
$73$	−10.4445	−1.22243	−0.611215	+	0.791464i	$0.709319\pi$
$74$	−12.8735	−1.49652
$75$	−0.753380	−0.0869929
$76$	−18.4540	−2.11682
$77$	7.31803	0.833966
$78$	−0.565131	−0.0639884
$79$	10.0883	1.13503	0.567513	−	0.823364i	$-0.307905\pi$
$79$	10.0883	1.13503	0.567513	+	0.823364i	$0.307905\pi$
$80$	−18.3650	−2.05327
$81$	8.62225	0.958028
$82$	12.1603	1.34288
$83$	2.07969	0.228276	0.114138	−	0.993465i	$-0.463589\pi$
$83$	2.07969	0.228276	0.114138	+	0.993465i	$0.463589\pi$
$84$	5.48429	0.598385
$85$	0.163593	0.0177442
$86$	−29.3956	−3.16981
$87$	0.667482	0.0715616
$88$	−15.0190	−1.60103
$89$	15.2276	1.61413	0.807063	−	0.590465i	$-0.201056\pi$
$89$	15.2276	1.61413	0.807063	+	0.590465i	$0.201056\pi$
$90$	−9.39199	−0.990002
$91$	4.79173	0.502310
$92$	−9.56466	−0.997185
$93$	−0.138344	−0.0143456
$94$	17.0564	1.75923
$95$	3.82033	0.391957
$96$	−4.95608	−0.505828
$97$	−16.4525	−1.67050	−0.835249	−	0.549871i	$-0.814677\pi$
$97$	−16.4525	−1.67050	−0.835249	+	0.549871i	$0.814677\pi$
$98$	−43.9237	−4.43697
$99$	−4.51726	−0.454001
$100$	−20.4475	−2.04475
$101$	−0.373807	−0.0371952	−0.0185976	−	0.999827i	$-0.505920\pi$
$101$	−0.373807	−0.0371952	−0.0185976	+	0.999827i	$0.505920\pi$
$102$	0.0801268	0.00793374
$103$	−0.568829	−0.0560483	−0.0280242	−	0.999607i	$-0.508922\pi$
$103$	−0.568829	−0.0560483	−0.0280242	+	0.999607i	$0.508922\pi$
$104$	−9.83422	−0.964325
$105$	−1.13535	−0.110799
$106$	37.1042	3.60388
$107$	−4.12073	−0.398366	−0.199183	−	0.979962i	$-0.563829\pi$
$107$	−4.12073	−0.398366	−0.199183	+	0.979962i	$0.563829\pi$
$108$	−6.81893	−0.656151
$109$	0.406028	0.0388904	0.0194452	−	0.999811i	$-0.493810\pi$
$109$	0.406028	0.0388904	0.0194452	+	0.999811i	$0.493810\pi$
$110$	4.84938	0.462370
$111$	0.960618	0.0911778
$112$	76.2689	7.20673
$113$	−9.29084	−0.874009	−0.437004	−	0.899459i	$-0.643961\pi$
$113$	−9.29084	−0.874009	−0.437004	+	0.899459i	$0.643961\pi$
$114$	1.87117	0.175251
$115$	1.98006	0.184642
$116$	18.1161	1.68204
$117$	−2.95783	−0.273451
$118$	18.2667	1.68158
$119$	−0.679394	−0.0622799
$120$	2.33011	0.212709
$121$	−8.66760	−0.787964
$122$	28.9182	2.61813
$123$	−0.907396	−0.0818172
$124$	−3.75479	−0.337190
$125$	10.0021	0.894614
$126$	39.0044	3.47479
$127$	−16.7861	−1.48952	−0.744762	−	0.667330i	$-0.767437\pi$
$127$	−16.7861	−1.48952	−0.744762	+	0.667330i	$0.767437\pi$
$128$	−46.9073	−4.14606
$129$	2.19349	0.193126
$130$	3.17530	0.278492
$131$	−4.47736	−0.391189	−0.195594	−	0.980685i	$-0.562664\pi$
$131$	−4.47736	−0.391189	−0.195594	+	0.980685i	$0.562664\pi$
$132$	1.74795	0.152140
$133$	−15.8656	−1.37572
$134$	−13.7417	−1.18710
$135$	1.41164	0.121495
$136$	1.39434	0.119564
$137$	7.72326	0.659842	0.329921	−	0.944008i	$-0.392978\pi$
$137$	7.72326	0.659842	0.329921	+	0.944008i	$0.392978\pi$
$138$	0.969821	0.0825566
$139$	−21.8994	−1.85748	−0.928742	−	0.370728i	$-0.879108\pi$
$139$	−21.8994	−1.85748	−0.928742	+	0.370728i	$0.879108\pi$
$140$	−30.8145	−2.60430
$141$	−1.27274	−0.107184
$142$	−17.0126	−1.42766
$143$	1.52722	0.127713
$144$	−47.0791	−3.92326
$145$	−3.75038	−0.311452
$146$	28.7431	2.37880
$147$	3.27757	0.270330
$148$	26.0721	2.14312
$149$	−2.16761	−0.177578	−0.0887890	−	0.996050i	$-0.528300\pi$
$149$	−2.16761	−0.177578	−0.0887890	+	0.996050i	$0.528300\pi$
$150$	2.07330	0.169284
$151$	4.86204	0.395667	0.197833	−	0.980236i	$-0.436609\pi$
$151$	4.86204	0.395667	0.197833	+	0.980236i	$0.436609\pi$
$152$	32.5615	2.64109
$153$	0.419375	0.0339044
$154$	−20.1392	−1.62286
$155$	0.777311	0.0624351
$156$	1.14453	0.0916359
$157$	−14.7169	−1.17454	−0.587269	−	0.809392i	$-0.699797\pi$
$157$	−14.7169	−1.17454	−0.587269	+	0.809392i	$0.699797\pi$
$158$	−27.7631	−2.20871
$159$	−2.76870	−0.219572
$160$	27.8467	2.20148
$161$	−8.22309	−0.648070
$162$	−23.7284	−1.86428
$163$	2.35323	0.184319	0.0921597	−	0.995744i	$-0.470623\pi$
$163$	2.35323	0.184319	0.0921597	+	0.995744i	$0.470623\pi$
$164$	−24.6277	−1.92310
$165$	−0.361859	−0.0281706
$166$	−5.72331	−0.444215
$167$	−9.75573	−0.754921	−0.377461	−	0.926026i	$-0.623203\pi$
$167$	−9.75573	−0.754921	−0.377461	+	0.926026i	$0.623203\pi$
$168$	−9.67683	−0.746584
$169$	1.00000	0.0769231
$170$	−0.450208	−0.0345294
$171$	9.79349	0.748927
$172$	59.5335	4.53938
$173$	11.1886	0.850656	0.425328	−	0.905039i	$-0.360159\pi$
$173$	11.1886	0.850656	0.425328	+	0.905039i	$0.360159\pi$
$174$	−1.83691	−0.139256
$175$	−17.5795	−1.32888
$176$	24.3084	1.83232
$177$	−1.36305	−0.102453
$178$	−41.9064	−3.14102
$179$	−19.5042	−1.45781	−0.728905	−	0.684615i	$-0.759970\pi$
$179$	−19.5042	−1.45781	−0.728905	+	0.684615i	$0.759970\pi$
$180$	19.0211	1.41775
$181$	−10.2751	−0.763745	−0.381872	−	0.924215i	$-0.624721\pi$
$181$	−10.2751	−0.763745	−0.381872	+	0.924215i	$0.624721\pi$
$182$	−13.1868	−0.977473
$183$	−2.15786	−0.159514
$184$	16.8765	1.24415
$185$	−5.39742	−0.396826
$186$	0.380721	0.0279158
$187$	−0.216536	−0.0158347
$188$	−34.5435	−2.51934
$189$	−5.86248	−0.426433
$190$	−10.5135	−0.762732
$191$	−0.0633950	−0.00458710	−0.00229355	−	0.999997i	$-0.500730\pi$
$191$	−0.0633950	−0.00458710	−0.00229355	+	0.999997i	$0.500730\pi$
$192$	7.10202	0.512544
$193$	7.16572	0.515800	0.257900	−	0.966172i	$-0.416970\pi$
$193$	7.16572	0.515800	0.257900	+	0.966172i	$0.416970\pi$
$194$	45.2772	3.25072
$195$	−0.236939	−0.0169676
$196$	88.9566	6.35404
$197$	5.57075	0.396900	0.198450	−	0.980111i	$-0.436409\pi$
$197$	5.57075	0.396900	0.198450	+	0.980111i	$0.436409\pi$
$198$	12.4315	0.883467
$199$	0.453531	0.0321500	0.0160750	−	0.999871i	$-0.494883\pi$
$199$	0.453531	0.0321500	0.0160750	+	0.999871i	$0.494883\pi$
$200$	36.0789	2.55116
$201$	1.02540	0.0723261
$202$	1.02872	0.0723802
$203$	15.5751	1.09316
$204$	−0.162277	−0.0113617
$205$	5.09838	0.356087
$206$	1.56541	0.109068
$207$	5.07593	0.352802
$208$	15.9168	1.10363
$209$	−5.05668	−0.349778
$210$	3.12448	0.215610
$211$	−19.8140	−1.36405	−0.682025	−	0.731329i	$-0.738900\pi$
$211$	−19.8140	−1.36405	−0.682025	+	0.731329i	$0.738900\pi$
$212$	−75.1454	−5.16100
$213$	1.26947	0.0869827
$214$	11.3402	0.775202
$215$	−12.3245	−0.840526
$216$	12.0318	0.818657
$217$	−3.22813	−0.219140
$218$	−1.11739	−0.0756790
$219$	−2.14480	−0.144932
$220$	−9.82121	−0.662146
$221$	−0.141785	−0.00953746
$222$	−2.64362	−0.177428
$223$	23.5472	1.57684	0.788418	−	0.615140i	$-0.210900\pi$
$223$	23.5472	1.57684	0.788418	+	0.615140i	$0.210900\pi$
$224$	−115.646	−7.72691
$225$	10.8514	0.723428
$226$	25.5684	1.70078
$227$	−1.55547	−0.103240	−0.0516202	−	0.998667i	$-0.516439\pi$
$227$	−1.55547	−0.103240	−0.0516202	+	0.998667i	$0.516439\pi$
$228$	−3.78959	−0.250972
$229$	−6.93662	−0.458385	−0.229193	−	0.973381i	$-0.573609\pi$
$229$	−6.93662	−0.458385	−0.229193	+	0.973381i	$0.573609\pi$
$230$	−5.44913	−0.359305
$231$	1.50278	0.0988755
$232$	−31.9653	−2.09862
$233$	11.9640	0.783785	0.391893	−	0.920011i	$-0.371820\pi$
$233$	11.9640	0.783785	0.391893	+	0.920011i	$0.371820\pi$
$234$	8.13994	0.532124
$235$	7.15114	0.466489
$236$	−36.9946	−2.40814
$237$	2.07167	0.134569
$238$	1.86969	0.121194
$239$	−26.5601	−1.71803	−0.859016	−	0.511948i	$-0.828924\pi$
$239$	−26.5601	−1.71803	−0.859016	+	0.511948i	$0.828924\pi$
$240$	−3.77131	−0.243437
$241$	−19.5186	−1.25731	−0.628653	−	0.777686i	$-0.716393\pi$
$241$	−19.5186	−1.25731	−0.628653	+	0.777686i	$0.716393\pi$
$242$	23.8532	1.53334
$243$	5.44098	0.349039
$244$	−58.5666	−3.74934
$245$	−18.4157	−1.17653
$246$	2.49715	0.159213
$247$	−3.31104	−0.210676
$248$	6.62519	0.420700
$249$	0.427071	0.0270645
$250$	−27.5257	−1.74088
$251$	16.8171	1.06149	0.530744	−	0.847532i	$-0.321913\pi$
$251$	16.8171	1.06149	0.530744	+	0.847532i	$0.321913\pi$
$252$	−78.9937	−4.97614
$253$	−2.62086	−0.164772
$254$	46.1953	2.89855
$255$	0.0335944	0.00210376
$256$	59.9199	3.74499
$257$	21.3539	1.33202	0.666011	−	0.745942i	$-0.268001\pi$
$257$	21.3539	1.33202	0.666011	+	0.745942i	$0.268001\pi$
$258$	−6.03647	−0.375814
$259$	22.4152	1.39281
$260$	−6.43077	−0.398820
$261$	−9.61417	−0.595102
$262$	12.3217	0.761236
$263$	−25.1571	−1.55125	−0.775626	−	0.631193i	$-0.782566\pi$
$263$	−25.1571	−1.55125	−0.775626	+	0.631193i	$0.782566\pi$
$264$	−3.08420	−0.189819
$265$	15.5565	0.955628
$266$	43.6621	2.67709
$267$	3.12704	0.191372
$268$	27.8304	1.70001
$269$	18.6948	1.13984	0.569921	−	0.821700i	$-0.306974\pi$
$269$	18.6948	1.13984	0.569921	+	0.821700i	$0.306974\pi$
$270$	−3.88484	−0.236424
$271$	26.9885	1.63943	0.819716	−	0.572770i	$-0.194131\pi$
$271$	26.9885	1.63943	0.819716	+	0.572770i	$0.194131\pi$
$272$	−2.25675	−0.136836
$273$	0.983996	0.0595541
$274$	−21.2544	−1.28402
$275$	−5.60293	−0.337869
$276$	−1.96413	−0.118227
$277$	−11.4022	−0.685091	−0.342545	−	0.939501i	$-0.611289\pi$
$277$	−11.4022	−0.685091	−0.342545	+	0.939501i	$0.611289\pi$
$278$	60.2671	3.61458
$279$	1.99265	0.119297
$280$	54.3712	3.24930
$281$	−13.7879	−0.822516	−0.411258	−	0.911519i	$-0.634911\pi$
$281$	−13.7879	−0.822516	−0.411258	+	0.911519i	$0.634911\pi$
$282$	3.50258	0.208575
$283$	−3.18479	−0.189316	−0.0946582	−	0.995510i	$-0.530176\pi$
$283$	−3.18479	−0.189316	−0.0946582	+	0.995510i	$0.530176\pi$
$284$	34.4547	2.04451
$285$	0.784516	0.0464707
$286$	−4.20290	−0.248523
$287$	−21.1733	−1.24982
$288$	71.3857	4.20644
$289$	−16.9799	−0.998817
$290$	10.3210	0.606072
$291$	−3.37857	−0.198055
$292$	−58.2120	−3.40660
$293$	17.6067	1.02860	0.514298	−	0.857611i	$-0.328052\pi$
$293$	17.6067	1.02860	0.514298	+	0.857611i	$0.328052\pi$
$294$	−9.01987	−0.526049
$295$	7.65857	0.445899
$296$	−46.0034	−2.67389
$297$	−1.86849	−0.108421
$298$	5.96527	0.345559
$299$	−1.71610	−0.0992446
$300$	−4.19895	−0.242427
$301$	51.1831	2.95014
$302$	−13.3803	−0.769950
$303$	−0.0767624	−0.00440989
$304$	−52.7011	−3.02261
$305$	12.1244	0.694239
$306$	−1.15412	−0.0659765
$307$	11.2508	0.642120	0.321060	−	0.947059i	$-0.395961\pi$
$307$	11.2508	0.642120	0.321060	+	0.947059i	$0.395961\pi$
$308$	40.7869	2.32405
$309$	−0.116811	−0.00664512
$310$	−2.13916	−0.121496
$311$	3.64845	0.206885	0.103442	−	0.994635i	$-0.467014\pi$
$311$	3.64845	0.206885	0.103442	+	0.994635i	$0.467014\pi$
$312$	−2.01949	−0.114331
$313$	22.7005	1.28311	0.641555	−	0.767077i	$-0.278290\pi$
$313$	22.7005	1.28311	0.641555	+	0.767077i	$0.278290\pi$
$314$	40.5009	2.28560
$315$	16.3532	0.921397
$316$	56.2272	3.16303
$317$	19.8621	1.11557	0.557784	−	0.829986i	$-0.311652\pi$
$317$	19.8621	1.11557	0.557784	+	0.829986i	$0.311652\pi$
$318$	7.61946	0.427278
$319$	4.96410	0.277936
$320$	−39.9041	−2.23070
$321$	−0.846204	−0.0472305
$322$	22.6299	1.26112
$323$	0.469454	0.0261211
$324$	48.0560	2.66978
$325$	−3.66871	−0.203503
$326$	−6.47609	−0.358677
$327$	0.0833790	0.00461087
$328$	43.4546	2.39938
$329$	−29.6983	−1.63732
$330$	0.995834	0.0548188
$331$	29.6133	1.62769	0.813846	−	0.581081i	$-0.197370\pi$
$331$	29.6133	1.62769	0.813846	+	0.581081i	$0.197370\pi$
$332$	11.5911	0.636146
$333$	−13.8364	−0.758230
$334$	26.8478	1.46904
$335$	−5.76141	−0.314779
$336$	15.6620	0.854434
$337$	9.66369	0.526414	0.263207	−	0.964739i	$-0.415220\pi$
$337$	9.66369	0.526414	0.263207	+	0.964739i	$0.415220\pi$
$338$	−2.75200	−0.149689
$339$	−1.90790	−0.103623
$340$	0.911785	0.0494485
$341$	−1.02887	−0.0557164
$342$	−26.9517	−1.45738
$343$	42.9371	2.31839
$344$	−105.045	−5.66363
$345$	0.406612	0.0218912
$346$	−30.7911	−1.65534
$347$	−15.3461	−0.823821	−0.411910	−	0.911224i	$-0.635138\pi$
$347$	−15.3461	−0.823821	−0.411910	+	0.911224i	$0.635138\pi$
$348$	3.72020	0.199424
$349$	3.27772	0.175452	0.0877261	−	0.996145i	$-0.472040\pi$
$349$	3.27772	0.175452	0.0877261	+	0.996145i	$0.472040\pi$
$350$	48.3786	2.58595
$351$	−1.22346	−0.0653034
$352$	−36.8586	−1.96457
$353$	14.4516	0.769183	0.384592	−	0.923087i	$-0.374342\pi$
$353$	14.4516	0.769183	0.384592	+	0.923087i	$0.374342\pi$
$354$	3.75111	0.199369
$355$	−7.13277	−0.378568
$356$	84.8710	4.49816
$357$	−0.139515	−0.00738394
$358$	53.6754	2.83683
$359$	−8.03755	−0.424205	−0.212103	−	0.977247i	$-0.568031\pi$
$359$	−8.03755	−0.424205	−0.212103	+	0.977247i	$0.568031\pi$
$360$	−33.5621	−1.76888
$361$	−8.03702	−0.423001
$362$	28.2771	1.48621
$363$	−1.77992	−0.0934214
$364$	26.7066	1.39981
$365$	12.0510	0.630777
$366$	5.93843	0.310407
$367$	−34.0246	−1.77607	−0.888036	−	0.459774i	$-0.847930\pi$
$367$	−34.0246	−1.77607	−0.888036	+	0.459774i	$0.847930\pi$
$368$	−27.3148	−1.42388
$369$	13.0698	0.680387
$370$	14.8537	0.772206
$371$	−64.6052	−3.35414
$372$	−0.771057	−0.0399774
$373$	15.5844	0.806929	0.403465	−	0.914995i	$-0.367806\pi$
$373$	15.5844	0.806929	0.403465	+	0.914995i	$0.367806\pi$
$374$	0.595907	0.0308136
$375$	2.05396	0.106066
$376$	60.9507	3.14329
$377$	3.25041	0.167405
$378$	16.1335	0.829819
$379$	8.98168	0.461358	0.230679	−	0.973030i	$-0.425905\pi$
$379$	8.98168	0.461358	0.230679	+	0.973030i	$0.425905\pi$
$380$	21.2925	1.09228
$381$	−3.44707	−0.176599
$382$	0.174463	0.00892629
$383$	−13.2760	−0.678371	−0.339185	−	0.940720i	$-0.610151\pi$
$383$	−13.2760	−0.678371	−0.339185	+	0.940720i	$0.610151\pi$
$384$	−9.63255	−0.491559
$385$	−8.44365	−0.430328
$386$	−19.7200	−1.00372
$387$	−31.5942	−1.60602
$388$	−91.6978	−4.65525
$389$	−34.8117	−1.76502	−0.882512	−	0.470289i	$-0.844150\pi$
$389$	−34.8117	−1.76502	−0.882512	+	0.470289i	$0.844150\pi$
$390$	0.652056	0.0330182
$391$	0.243317	0.0123050
$392$	−156.961	−7.92772
$393$	−0.919439	−0.0463796
$394$	−15.3307	−0.772349
$395$	−11.6401	−0.585676
$396$	−25.1769	−1.26519
$397$	1.70020	0.0853308	0.0426654	−	0.999089i	$-0.486415\pi$
$397$	1.70020	0.0853308	0.0426654	+	0.999089i	$0.486415\pi$
$398$	−1.24812	−0.0625624
$399$	−3.25805	−0.163106
$400$	−58.3940	−2.91970
$401$	−5.32925	−0.266130	−0.133065	−	0.991107i	$-0.542482\pi$
$401$	−5.32925	−0.266130	−0.133065	+	0.991107i	$0.542482\pi$
$402$	−2.82190	−0.140743
$403$	−0.673687	−0.0335588
$404$	−2.08341	−0.103653
$405$	−9.94849	−0.494344
$406$	−42.8626	−2.12724
$407$	7.14416	0.354123
$408$	0.286332	0.0141755
$409$	16.3368	0.807800	0.403900	−	0.914803i	$-0.367654\pi$
$409$	16.3368	0.807800	0.403900	+	0.914803i	$0.367654\pi$
$410$	−14.0307	−0.692929
$411$	1.58599	0.0782313
$412$	−3.17036	−0.156192
$413$	−31.8056	−1.56505
$414$	−13.9689	−0.686536
$415$	−2.39958	−0.117791
$416$	−24.1345	−1.18329
$417$	−4.49711	−0.220224
$418$	13.9160	0.680653
$419$	−27.2314	−1.33034	−0.665169	−	0.746693i	$-0.731641\pi$
$419$	−27.2314	−1.33034	−0.665169	+	0.746693i	$0.731641\pi$
$420$	−6.32786	−0.308768
$421$	−19.2636	−0.938849	−0.469425	−	0.882973i	$-0.655539\pi$
$421$	−19.2636	−0.938849	−0.469425	+	0.882973i	$0.655539\pi$
$422$	54.5280	2.65438
$423$	18.3321	0.891337
$424$	132.591	6.43921
$425$	0.520167	0.0252318
$426$	−3.49358	−0.169264
$427$	−50.3518	−2.43670
$428$	−22.9668	−1.11014
$429$	0.313619	0.0151417
$430$	33.9171	1.63563
$431$	12.8607	0.619480	0.309740	−	0.950821i	$-0.399758\pi$
$431$	12.8607	0.619480	0.309740	+	0.950821i	$0.399758\pi$
$432$	−19.4735	−0.936919
$433$	1.27368	0.0612092	0.0306046	−	0.999532i	$-0.490257\pi$
$433$	1.27368	0.0612092	0.0306046	+	0.999532i	$0.490257\pi$
$434$	8.88380	0.426436
$435$	−0.770151	−0.0369259
$436$	2.26299	0.108378
$437$	5.68207	0.271810
$438$	5.90248	0.282031
$439$	27.8920	1.33121	0.665606	−	0.746303i	$-0.268173\pi$
$439$	27.8920	1.33121	0.665606	+	0.746303i	$0.268173\pi$
$440$	17.3292	0.826136
$441$	−47.2090	−2.24805
$442$	0.390191	0.0185595
$443$	21.6477	1.02851	0.514256	−	0.857637i	$-0.328068\pi$
$443$	21.6477	1.02851	0.514256	+	0.857637i	$0.328068\pi$
$444$	5.35399	0.254089
$445$	−17.5699	−0.832893
$446$	−64.8018	−3.06845
$447$	−0.445126	−0.0210537
$448$	165.719	7.82950
$449$	−21.5071	−1.01498	−0.507491	−	0.861657i	$-0.669427\pi$
$449$	−21.5071	−1.01498	−0.507491	+	0.861657i	$0.669427\pi$
$450$	−29.8631	−1.40776
$451$	−6.74835	−0.317767
$452$	−51.7824	−2.43564
$453$	0.998433	0.0469105
$454$	4.28066	0.200901
$455$	−5.52877	−0.259193
$456$	6.68660	0.313129
$457$	−11.9444	−0.558734	−0.279367	−	0.960184i	$-0.590125\pi$
$457$	−11.9444	−0.558734	−0.279367	+	0.960184i	$0.590125\pi$
$458$	19.0896	0.891997
$459$	0.173467	0.00809677
$460$	11.0359	0.514549
$461$	33.0743	1.54043	0.770213	−	0.637787i	$-0.220150\pi$
$461$	33.0743	1.54043	0.770213	+	0.637787i	$0.220150\pi$
$462$	−4.13564	−0.192407
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	51.7361	2.40179
$465$	0.159623	0.00740234
$466$	−32.9248	−1.52521
$467$	−2.75668	−0.127564	−0.0637820	−	0.997964i	$-0.520316\pi$
$467$	−2.75668	−0.127564	−0.0637820	+	0.997964i	$0.520316\pi$
$468$	−16.4854	−0.762039
$469$	23.9268	1.10484
$470$	−19.6799	−0.907767
$471$	−3.02216	−0.139254
$472$	65.2757	3.00456
$473$	16.3131	0.750076
$474$	−5.70123	−0.261866
$475$	12.1472	0.557354
$476$	−3.78659	−0.173558
$477$	39.8794	1.82595
$478$	73.0934	3.34321
$479$	−24.7911	−1.13273	−0.566367	−	0.824153i	$-0.691651\pi$
$479$	−24.7911	−1.13273	−0.566367	+	0.824153i	$0.691651\pi$
$480$	5.71841	0.261008
$481$	4.67789	0.213293
$482$	53.7152	2.44666
$483$	−1.68864	−0.0768356
$484$	−48.3087	−2.19585
$485$	18.9832	0.861981
$486$	−14.9736	−0.679214
$487$	1.42250	0.0644598	0.0322299	−	0.999480i	$-0.489739\pi$
$487$	1.42250	0.0644598	0.0322299	+	0.999480i	$0.489739\pi$
$488$	103.339	4.67792
$489$	0.483243	0.0218530
$490$	50.6799	2.28948
$491$	−29.4194	−1.32768	−0.663840	−	0.747875i	$-0.731074\pi$
$491$	−29.4194	−1.32768	−0.663840	+	0.747875i	$0.731074\pi$
$492$	−5.05736	−0.228003
$493$	−0.460859	−0.0207560
$494$	9.11197	0.409967
$495$	5.21208	0.234266
$496$	−10.7229	−0.481474
$497$	29.6220	1.32873
$498$	−1.17530	−0.0526663
$499$	−37.0492	−1.65855	−0.829274	−	0.558842i	$-0.811246\pi$
$499$	−37.0492	−1.65855	−0.829274	+	0.558842i	$0.811246\pi$
$500$	55.7465	2.49306
$501$	−2.00337	−0.0895039
$502$	−46.2807	−2.06561
$503$	18.5319	0.826296	0.413148	−	0.910664i	$-0.364429\pi$
$503$	18.5319	0.826296	0.413148	+	0.910664i	$0.364429\pi$
$504$	139.382	6.20855
$505$	0.431305	0.0191928
$506$	7.21260	0.320639
$507$	0.205353	0.00912004
$508$	−93.5570	−4.15092
$509$	0.114733	0.00508545	0.00254272	−	0.999997i	$-0.499191\pi$
$509$	0.114733	0.00508545	0.00254272	+	0.999997i	$0.499191\pi$
$510$	−0.0924516	−0.00409382
$511$	−50.0470	−2.21395
$512$	−71.0847	−3.14153
$513$	4.05092	0.178852
$514$	−58.7659	−2.59205
$515$	0.656323	0.0289211
$516$	12.2254	0.538192
$517$	−9.46543	−0.416289
$518$	−61.6865	−2.71035
$519$	2.29762	0.100854
$520$	11.3469	0.497594
$521$	11.6194	0.509054	0.254527	−	0.967066i	$-0.418080\pi$
$521$	11.6194	0.509054	0.254527	+	0.967066i	$0.418080\pi$
$522$	26.4582	1.15804
$523$	7.38198	0.322792	0.161396	−	0.986890i	$-0.448400\pi$
$523$	7.38198	0.322792	0.161396	+	0.986890i	$0.448400\pi$
$524$	−24.9545	−1.09014
$525$	−3.61000	−0.157553
$526$	69.2322	3.01867
$527$	0.0955185	0.00416085
$528$	4.99180	0.217240
$529$	−20.0550	−0.871957
$530$	−42.8114	−1.85961
$531$	19.6329	0.851995
$532$	−88.4267	−3.83379
$533$	−4.41872	−0.191396
$534$	−8.60561	−0.372401
$535$	4.75456	0.205558
$536$	−49.1058	−2.12105
$537$	−4.00524	−0.172839
$538$	−51.4480	−2.21808
$539$	24.3755	1.04993
$540$	7.86778	0.338575
$541$	15.0710	0.647953	0.323976	−	0.946065i	$-0.394980\pi$
$541$	15.0710	0.647953	0.323976	+	0.946065i	$0.394980\pi$
$542$	−74.2721	−3.19026
$543$	−2.11003	−0.0905500
$544$	3.42190	0.146713
$545$	−0.468481	−0.0200675
$546$	−2.70795	−0.115890
$547$	−8.61014	−0.368143	−0.184071	−	0.982913i	$-0.558928\pi$
$547$	−8.61014	−0.368143	−0.184071	+	0.982913i	$0.558928\pi$
$548$	43.0455	1.83881
$549$	31.0811	1.32651
$550$	15.4192	0.657478
$551$	−10.7622	−0.458487
$552$	3.46564	0.147507
$553$	48.3406	2.05565
$554$	31.3788	1.33316
$555$	−1.10838	−0.0470479
$556$	−122.056	−5.17633
$557$	−30.2364	−1.28116	−0.640579	−	0.767892i	$-0.721306\pi$
$557$	−30.2364	−1.28116	−0.640579	+	0.767892i	$0.721306\pi$
$558$	−5.48377	−0.232147
$559$	10.6815	0.451781
$560$	−88.0002	−3.71869
$561$	−0.0444664	−0.00187737
$562$	37.9442	1.60058
$563$	4.75793	0.200523	0.100261	−	0.994961i	$-0.468032\pi$
$563$	4.75793	0.200523	0.100261	+	0.994961i	$0.468032\pi$
$564$	−7.09360	−0.298694
$565$	10.7199	0.450990
$566$	8.76454	0.368401
$567$	41.3155	1.73509
$568$	−60.7942	−2.55087
$569$	−17.4780	−0.732717	−0.366358	−	0.930474i	$-0.619396\pi$
$569$	−17.4780	−0.732717	−0.366358	+	0.930474i	$0.619396\pi$
$570$	−2.15898	−0.0904299
$571$	−44.2055	−1.84994	−0.924972	−	0.380035i	$-0.875912\pi$
$571$	−44.2055	−1.84994	−0.924972	+	0.380035i	$0.875912\pi$
$572$	8.51194	0.355902
$573$	−0.0130183	−0.000543849 0
$574$	58.2688	2.43209
$575$	6.29587	0.262556
$576$	−102.295	−4.26229
$577$	16.8497	0.701463	0.350731	−	0.936476i	$-0.385933\pi$
$577$	16.8497	0.701463	0.350731	+	0.936476i	$0.385933\pi$
$578$	46.7286	1.94365
$579$	1.47150	0.0611535
$580$	−20.9027	−0.867937
$581$	9.96532	0.413431
$582$	9.29781	0.385407
$583$	−20.5910	−0.852791
$584$	102.713	4.25030
$585$	3.41279	0.141102
$586$	−48.4537	−2.00160
$587$	−17.0232	−0.702624	−0.351312	−	0.936258i	$-0.614264\pi$
$587$	−17.0232	−0.702624	−0.351312	+	0.936258i	$0.614264\pi$
$588$	18.2675	0.753339
$589$	2.23061	0.0919105
$590$	−21.0764	−0.867700
$591$	1.14397	0.0470567
$592$	74.4569	3.06016
$593$	−23.0605	−0.946981	−0.473490	−	0.880799i	$-0.657006\pi$
$593$	−23.0605	−0.946981	−0.473490	+	0.880799i	$0.657006\pi$
$594$	5.14208	0.210982
$595$	0.783895	0.0321366
$596$	−12.0812	−0.494864
$597$	0.0931340	0.00381172
$598$	4.72270	0.193126
$599$	−13.4063	−0.547768	−0.273884	−	0.961763i	$-0.588308\pi$
$599$	−13.4063	−0.547768	−0.273884	+	0.961763i	$0.588308\pi$
$600$	7.40891	0.302467
$601$	30.0904	1.22741	0.613707	−	0.789534i	$-0.289677\pi$
$601$	30.0904	1.22741	0.613707	+	0.789534i	$0.289677\pi$
$602$	−140.856	−5.74085
$603$	−14.7695	−0.601460
$604$	27.0985	1.10262
$605$	10.0008	0.406591
$606$	0.211250	0.00858144
$607$	−6.21168	−0.252124	−0.126062	−	0.992022i	$-0.540234\pi$
$607$	−6.21168	−0.252124	−0.126062	+	0.992022i	$0.540234\pi$
$608$	79.9102	3.24079
$609$	3.19839	0.129605
$610$	−33.3662	−1.35096
$611$	−6.19782	−0.250737
$612$	2.33738	0.0944830
$613$	−6.76878	−0.273389	−0.136694	−	0.990613i	$-0.543648\pi$
$613$	−6.76878	−0.273389	−0.136694	+	0.990613i	$0.543648\pi$
$614$	−30.9623	−1.24954
$615$	1.04697	0.0422178
$616$	−71.9671	−2.89964
$617$	33.6852	1.35612	0.678058	−	0.735008i	$-0.262822\pi$
$617$	33.6852	1.35612	0.678058	+	0.735008i	$0.262822\pi$
$618$	0.321462	0.0129311
$619$	6.71903	0.270061	0.135030	−	0.990841i	$-0.456887\pi$
$619$	6.71903	0.270061	0.135030	+	0.990841i	$0.456887\pi$
$620$	4.33233	0.173991
$621$	2.09958	0.0842531
$622$	−10.0405	−0.402589
$623$	72.9667	2.92335
$624$	3.26856	0.130847
$625$	6.80298	0.272119
$626$	−62.4718	−2.49687
$627$	−1.03841	−0.0414699
$628$	−82.0246	−3.27314
$629$	−0.663252	−0.0264456
$630$	−45.0039	−1.79300
$631$	−36.5841	−1.45639	−0.728195	−	0.685370i	$-0.759641\pi$
$631$	−36.5841	−1.45639	−0.728195	+	0.685370i	$0.759641\pi$
$632$	−99.2110	−3.94640
$633$	−4.06885	−0.161722
$634$	−54.6605	−2.17085
$635$	19.3680	0.768597
$636$	−15.4313	−0.611892
$637$	15.9607	0.632385
$638$	−13.6612	−0.540851
$639$	−18.2850	−0.723344
$640$	54.1224	2.13938
$641$	−48.8676	−1.93015	−0.965076	−	0.261970i	$-0.915628\pi$
$641$	−48.8676	−1.93015	−0.965076	+	0.261970i	$0.915628\pi$
$642$	2.32875	0.0919084
$643$	33.0459	1.30320	0.651602	−	0.758561i	$-0.274097\pi$
$643$	33.0459	1.30320	0.651602	+	0.758561i	$0.274097\pi$
$644$	−45.8313	−1.80600
$645$	−2.53088	−0.0996533
$646$	−1.29194	−0.0508306
$647$	−29.6039	−1.16385	−0.581924	−	0.813243i	$-0.697700\pi$
$647$	−29.6039	−1.16385	−0.581924	+	0.813243i	$0.697700\pi$
$648$	−84.7931	−3.33099
$649$	−10.1371	−0.397915
$650$	10.0963	0.396009
$651$	−0.662906	−0.0259813
$652$	13.1157	0.513651
$653$	6.32656	0.247577	0.123789	−	0.992309i	$-0.460495\pi$
$653$	6.32656	0.247577	0.123789	+	0.992309i	$0.460495\pi$
$654$	−0.229459	−0.00897255
$655$	5.16605	0.201854
$656$	−70.3317	−2.74599
$657$	30.8929	1.20525
$658$	81.7296	3.18615
$659$	−42.6616	−1.66186	−0.830929	−	0.556378i	$-0.812191\pi$
$659$	−42.6616	−1.66186	−0.830929	+	0.556378i	$0.812191\pi$
$660$	−2.01681	−0.0785044
$661$	33.1401	1.28900	0.644500	−	0.764604i	$-0.277065\pi$
$661$	33.1401	1.28900	0.644500	+	0.764604i	$0.277065\pi$
$662$	−81.4956	−3.16742
$663$	−0.0291159	−0.00113077
$664$	−20.4522	−0.793698
$665$	18.3060	0.709876
$666$	38.0777	1.47548
$667$	−5.57804	−0.215982
$668$	−54.3735	−2.10377
$669$	4.83548	0.186951
$670$	15.8554	0.612547
$671$	−16.0481	−0.619531
$672$	−23.7482	−0.916107
$673$	−34.4580	−1.32826	−0.664129	−	0.747618i	$-0.731197\pi$
$673$	−34.4580	−1.32826	−0.664129	+	0.747618i	$0.731197\pi$
$674$	−26.5944	−1.02438
$675$	4.48851	0.172763
$676$	5.57349	0.214365
$677$	−23.5894	−0.906613	−0.453307	−	0.891355i	$-0.649756\pi$
$677$	−23.5894	−0.906613	−0.453307	+	0.891355i	$0.649756\pi$
$678$	5.25054	0.201646
$679$	−78.8360	−3.02545
$680$	−1.60881	−0.0616951
$681$	−0.319421	−0.0122402
$682$	2.83144	0.108422
$683$	9.40360	0.359819	0.179909	−	0.983683i	$-0.442420\pi$
$683$	9.40360	0.359819	0.179909	+	0.983683i	$0.442420\pi$
$684$	54.5839	2.08707
$685$	−8.91121	−0.340480
$686$	−118.163	−4.51148
$687$	−1.42446	−0.0543464
$688$	170.016	6.48179
$689$	−13.4826	−0.513648
$690$	−1.11899	−0.0425994
$691$	−11.3695	−0.432516	−0.216258	−	0.976336i	$-0.569385\pi$
$691$	−11.3695	−0.432516	−0.216258	+	0.976336i	$0.569385\pi$
$692$	62.3597	2.37056
$693$	−21.6455	−0.822244
$694$	42.2324	1.60312
$695$	25.2679	0.958465
$696$	−6.56417	−0.248814
$697$	0.626506	0.0237306
$698$	−9.02026	−0.341422
$699$	2.45683	0.0929260
$700$	−97.9789	−3.70325
$701$	−18.5596	−0.700986	−0.350493	−	0.936565i	$-0.613986\pi$
$701$	−18.5596	−0.700986	−0.350493	+	0.936565i	$0.613986\pi$
$702$	3.36695	0.127077
$703$	−15.4887	−0.584166
$704$	52.8180	1.99065
$705$	1.46851	0.0553072
$706$	−39.7709	−1.49680
$707$	−1.79118	−0.0673644
$708$	−7.59695	−0.285511
$709$	−5.66889	−0.212900	−0.106450	−	0.994318i	$-0.533948\pi$
$709$	−5.66889	−0.212900	−0.106450	+	0.994318i	$0.533948\pi$
$710$	19.6294	0.736677
$711$	−29.8396	−1.11907
$712$	−149.752	−5.61219
$713$	1.15611	0.0432968
$714$	0.383946	0.0143688
$715$	−1.76213	−0.0658999
$716$	−108.706	−4.06254
$717$	−5.45420	−0.203691
$718$	22.1193	0.825485
$719$	29.0275	1.08254	0.541272	−	0.840848i	$-0.317943\pi$
$719$	29.0275	1.08254	0.541272	+	0.840848i	$0.317943\pi$
$720$	54.3206	2.02441
$721$	−2.72567	−0.101509
$722$	22.1179	0.823141
$723$	−4.00821	−0.149067
$724$	−57.2683	−2.12836
$725$	−11.9248	−0.442877
$726$	4.89833	0.181794
$727$	−49.9742	−1.85344	−0.926721	−	0.375750i	$-0.877385\pi$
$727$	−49.9742	−1.85344	−0.926721	+	0.375750i	$0.877385\pi$
$728$	−47.1229	−1.74649
$729$	−24.7494	−0.916646
$730$	−33.1642	−1.22746
$731$	−1.51448	−0.0560150
$732$	−12.0268	−0.444524
$733$	−28.6224	−1.05719	−0.528595	−	0.848874i	$-0.677281\pi$
$733$	−28.6224	−1.05719	−0.528595	+	0.848874i	$0.677281\pi$
$734$	93.6357	3.45616
$735$	−3.78171	−0.139491
$736$	41.4172	1.52666
$737$	7.62595	0.280905
$738$	−35.9681	−1.32400
$739$	−38.1615	−1.40379	−0.701896	−	0.712279i	$-0.747663\pi$
$739$	−38.1615	−1.40379	−0.701896	+	0.712279i	$0.747663\pi$
$740$	−30.0824	−1.10585
$741$	−0.679932	−0.0249779
$742$	177.793	6.52700
$743$	22.8513	0.838334	0.419167	−	0.907909i	$-0.362322\pi$
$743$	22.8513	0.838334	0.419167	+	0.907909i	$0.362322\pi$
$744$	1.36050	0.0498784
$745$	2.50103	0.0916306
$746$	−42.8882	−1.57025
$747$	−6.15138	−0.225067
$748$	−1.20686	−0.0441272
$749$	−19.7454	−0.721482
$750$	−5.65249	−0.206400
$751$	−36.9554	−1.34852	−0.674261	−	0.738493i	$-0.735538\pi$
$751$	−36.9554	−1.34852	−0.674261	+	0.738493i	$0.735538\pi$
$752$	−98.6493	−3.59737
$753$	3.45344	0.125851
$754$	−8.94513	−0.325762
$755$	−5.60989	−0.204165
$756$	−32.6745	−1.18836
$757$	24.6940	0.897518	0.448759	−	0.893653i	$-0.351866\pi$
$757$	24.6940	0.897518	0.448759	+	0.893653i	$0.351866\pi$
$758$	−24.7175	−0.897782
$759$	−0.538202	−0.0195355
$760$	−37.5700	−1.36281
$761$	9.95249	0.360777	0.180389	−	0.983595i	$-0.442264\pi$
$761$	9.95249	0.360777	0.180389	+	0.983595i	$0.442264\pi$
$762$	9.48633	0.343654
$763$	1.94558	0.0704346
$764$	−0.353331	−0.0127831
$765$	−0.483881	−0.0174948
$766$	36.5354	1.32008
$767$	−6.63760	−0.239670
$768$	12.3047	0.444009
$769$	−34.2506	−1.23511	−0.617555	−	0.786528i	$-0.711877\pi$
$769$	−34.2506	−1.23511	−0.617555	+	0.786528i	$0.711877\pi$
$770$	23.2369	0.837400
$771$	4.38509	0.157925
$772$	39.9380	1.43740
$773$	12.8648	0.462716	0.231358	−	0.972869i	$-0.425683\pi$
$773$	12.8648	0.462716	0.231358	+	0.972869i	$0.425683\pi$
$774$	86.9472	3.12525
$775$	2.47156	0.0887812
$776$	161.798	5.80819
$777$	4.60302	0.165132
$778$	95.8018	3.43466
$779$	14.6305	0.524194
$780$	−1.32058	−0.0472843
$781$	9.44112	0.337830
$782$	−0.669606	−0.0239451
$783$	−3.97674	−0.142117
$784$	254.043	9.07295
$785$	16.9806	0.606064
$786$	2.53029	0.0902526
$787$	−25.9718	−0.925794	−0.462897	−	0.886412i	$-0.653190\pi$
$787$	−25.9718	−0.925794	−0.462897	+	0.886412i	$0.653190\pi$
$788$	31.0485	1.10606
$789$	−5.16608	−0.183917
$790$	32.0335	1.13970
$791$	−44.5192	−1.58292
$792$	44.4237	1.57853
$793$	−10.5081	−0.373152
$794$	−4.67896	−0.166050
$795$	3.19457	0.113300
$796$	2.52775	0.0895937
$797$	18.1609	0.643294	0.321647	−	0.946860i	$-0.395764\pi$
$797$	18.1609	0.643294	0.321647	+	0.946860i	$0.395764\pi$
$798$	8.96614	0.317398
$799$	0.878755	0.0310881
$800$	88.5424	3.13045
$801$	−45.0408	−1.59144
$802$	14.6661	0.517877
$803$	−15.9510	−0.562898
$804$	5.71505	0.201554
$805$	9.48793	0.334405
$806$	1.85399	0.0653039
$807$	3.83903	0.135140
$808$	3.67610	0.129325
$809$	−20.4160	−0.717787	−0.358893	−	0.933379i	$-0.616846\pi$
$809$	−20.4160	−0.717787	−0.358893	+	0.933379i	$0.616846\pi$
$810$	27.3782	0.961972
$811$	29.2597	1.02745	0.513724	−	0.857955i	$-0.328265\pi$
$811$	29.2597	1.02745	0.513724	+	0.857955i	$0.328265\pi$
$812$	86.8076	3.04635
$813$	5.54216	0.194372
$814$	−19.6607	−0.689107
$815$	−2.71520	−0.0951092
$816$	−0.463431	−0.0162233
$817$	−35.3670	−1.23734
$818$	−44.9587	−1.57194
$819$	−14.1731	−0.495249
$820$	28.4158	0.992322
$821$	14.2056	0.495778	0.247889	−	0.968788i	$-0.420263\pi$
$821$	14.2056	0.495778	0.247889	+	0.968788i	$0.420263\pi$
$822$	−4.36465	−0.152235
$823$	−47.3646	−1.65103	−0.825514	−	0.564382i	$-0.809114\pi$
$823$	−47.3646	−1.65103	−0.825514	+	0.564382i	$0.809114\pi$
$824$	5.59399	0.194876
$825$	−1.15058	−0.0400580
$826$	87.5289	3.04552
$827$	47.1545	1.63972	0.819862	−	0.572561i	$-0.194050\pi$
$827$	47.1545	1.63972	0.819862	+	0.572561i	$0.194050\pi$
$828$	28.2906	0.983168
$829$	22.1434	0.769073	0.384536	−	0.923110i	$-0.374361\pi$
$829$	22.1434	0.769073	0.384536	+	0.923110i	$0.374361\pi$
$830$	6.60364	0.229216
$831$	−2.34147	−0.0812248
$832$	34.5844	1.19900
$833$	−2.26298	−0.0784075
$834$	12.3760	0.428547
$835$	11.2563	0.389541
$836$	−28.1834	−0.974742
$837$	0.824228	0.0284895
$838$	74.9406	2.58878
$839$	−41.6518	−1.43798	−0.718990	−	0.695020i	$-0.755395\pi$
$839$	−41.6518	−1.43798	−0.718990	+	0.695020i	$0.755395\pi$
$840$	11.1653	0.385239
$841$	−18.4348	−0.635683
$842$	53.0133	1.82696
$843$	−2.83138	−0.0975180
$844$	−110.433	−3.80125
$845$	−1.15382	−0.0396925
$846$	−50.4499	−1.73450
$847$	−41.5328	−1.42708
$848$	−214.600	−7.36940
$849$	−0.654007	−0.0224455
$850$	−1.43150	−0.0490999
$851$	−8.02772	−0.275187
$852$	7.07538	0.242398
$853$	−20.5128	−0.702346	−0.351173	−	0.936311i	$-0.614217\pi$
$853$	−20.5128	−0.702346	−0.351173	+	0.936311i	$0.614217\pi$
$854$	138.568	4.74170
$855$	−11.2999	−0.386448
$856$	40.5242	1.38509
$857$	−43.2887	−1.47871	−0.739357	−	0.673313i	$-0.764871\pi$
$857$	−43.2887	−1.47871	−0.739357	+	0.673313i	$0.764871\pi$
$858$	−0.863079	−0.0294650
$859$	−12.2698	−0.418641	−0.209320	−	0.977847i	$-0.567125\pi$
$859$	−12.2698	−0.418641	−0.209320	+	0.977847i	$0.567125\pi$
$860$	−68.6906	−2.34233
$861$	−4.34800	−0.148179
$862$	−35.3927	−1.20548
$863$	−41.5933	−1.41585	−0.707926	−	0.706287i	$-0.750369\pi$
$863$	−41.5933	−1.41585	−0.707926	+	0.706287i	$0.750369\pi$
$864$	29.5275	1.00455
$865$	−12.9096	−0.438940
$866$	−3.50517	−0.119110
$867$	−3.48687	−0.118420
$868$	−17.9919	−0.610686
$869$	15.4071	0.522650
$870$	2.11945	0.0718562
$871$	4.99335	0.169193
$872$	−3.99297	−0.135219
$873$	48.6637	1.64702
$874$	−15.6370	−0.528931
$875$	47.9273	1.62024
$876$	−11.9540	−0.403888
$877$	−12.1558	−0.410471	−0.205236	−	0.978713i	$-0.565796\pi$
$877$	−12.1558	−0.410471	−0.205236	+	0.978713i	$0.565796\pi$
$878$	−76.7587	−2.59048
$879$	3.61560	0.121951
$880$	−28.0474	−0.945479
$881$	55.5800	1.87254	0.936269	−	0.351284i	$-0.114255\pi$
$881$	55.5800	1.87254	0.936269	+	0.351284i	$0.114255\pi$
$882$	129.919	4.37460
$883$	39.9560	1.34463	0.672314	−	0.740266i	$-0.265300\pi$
$883$	39.9560	1.34463	0.672314	+	0.740266i	$0.265300\pi$
$884$	−0.790234	−0.0265785
$885$	1.57271	0.0528661
$886$	−59.5743	−2.00144
$887$	0.329602	0.0110669	0.00553347	−	0.999985i	$-0.498239\pi$
$887$	0.329602	0.0110669	0.00553347	+	0.999985i	$0.498239\pi$
$888$	−9.44693	−0.317018
$889$	−80.4344	−2.69768
$890$	48.3523	1.62077
$891$	13.1681	0.441147
$892$	131.240	4.39424
$893$	20.5212	0.686717
$894$	1.22499	0.0409696
$895$	22.5042	0.752233
$896$	−224.767	−7.50894
$897$	−0.352406	−0.0117665
$898$	59.1875	1.97511
$899$	−2.18976	−0.0730327
$900$	60.4802	2.01601
$901$	1.91163	0.0636857
$902$	18.5714	0.618361
$903$	10.5106	0.349771
$904$	91.3682	3.03886
$905$	11.8556	0.394094
$906$	−2.74768	−0.0912857
$907$	−28.5390	−0.947622	−0.473811	−	0.880627i	$-0.657122\pi$
$907$	−28.5390	−0.947622	−0.473811	+	0.880627i	$0.657122\pi$
$908$	−8.66941	−0.287705
$909$	1.10566	0.0366724
$910$	15.2152	0.504378
$911$	35.1480	1.16450	0.582252	−	0.813008i	$-0.302172\pi$
$911$	35.1480	1.16450	0.582252	+	0.813008i	$0.302172\pi$
$912$	−10.8223	−0.358363
$913$	3.17615	0.105115
$914$	32.8708	1.08727
$915$	2.48978	0.0823094
$916$	−38.6612	−1.27740
$917$	−21.4543	−0.708483
$918$	−0.477382	−0.0157560
$919$	19.9683	0.658692	0.329346	−	0.944209i	$-0.393172\pi$
$919$	19.9683	0.658692	0.329346	+	0.944209i	$0.393172\pi$
$920$	−19.4724	−0.641985
$921$	2.31039	0.0761301
$922$	−91.0205	−2.99760
$923$	6.18190	0.203480
$924$	8.37571	0.275541
$925$	−17.1618	−0.564277
$926$	−2.75200	−0.0904362
$927$	1.68250	0.0552605
$928$	−78.4470	−2.57515
$929$	−20.0142	−0.656643	−0.328322	−	0.944566i	$-0.606483\pi$
$929$	−20.0142	−0.656643	−0.328322	+	0.944566i	$0.606483\pi$
$930$	−0.439282	−0.0144046
$931$	−52.8464	−1.73197
$932$	66.6810	2.18421
$933$	0.749220	0.0245284
$934$	7.58638	0.248234
$935$	0.249843	0.00817074
$936$	29.0880	0.950770
$937$	45.7677	1.49517	0.747583	−	0.664169i	$-0.231214\pi$
$937$	45.7677	1.49517	0.747583	+	0.664169i	$0.231214\pi$
$938$	−65.8465	−2.14996
$939$	4.66162	0.152126
$940$	39.8568	1.29998
$941$	−17.0906	−0.557137	−0.278569	−	0.960416i	$-0.589860\pi$
$941$	−17.0906	−0.557137	−0.278569	+	0.960416i	$0.589860\pi$
$942$	8.31698	0.270982
$943$	7.58296	0.246935
$944$	−105.649	−3.43859
$945$	6.76422	0.220040
$946$	−44.8935	−1.45961
$947$	27.4001	0.890383	0.445192	−	0.895435i	$-0.353136\pi$
$947$	27.4001	0.890383	0.445192	+	0.895435i	$0.353136\pi$
$948$	11.5464	0.375010
$949$	−10.4445	−0.339041
$950$	−33.4292	−1.08459
$951$	4.07875	0.132262
$952$	6.68131	0.216542
$953$	10.0806	0.326543	0.163272	−	0.986581i	$-0.447795\pi$
$953$	10.0806	0.326543	0.163272	+	0.986581i	$0.447795\pi$
$954$	−109.748	−3.55322
$955$	0.0731461	0.00236695
$956$	−148.033	−4.78772
$957$	1.01939	0.0329523
$958$	68.2250	2.20425
$959$	37.0078	1.19504
$960$	−8.19442	−0.264474
$961$	−30.5461	−0.985360
$962$	−12.8735	−0.415059
$963$	12.1884	0.392766
$964$	−108.787	−3.50379
$965$	−8.26792	−0.266154
$966$	4.64712	0.149519
$967$	−21.2207	−0.682413	−0.341207	−	0.939988i	$-0.610836\pi$
$967$	−21.2207	−0.682413	−0.341207	+	0.939988i	$0.610836\pi$
$968$	85.2391	2.73969
$969$	0.0964038	0.00309694
$970$	−52.2416	−1.67738
$971$	−54.2817	−1.74198	−0.870992	−	0.491297i	$-0.836523\pi$
$971$	−54.2817	−1.74198	−0.870992	+	0.491297i	$0.836523\pi$
$972$	30.3252	0.972682
$973$	−104.936	−3.36410
$974$	−3.91473	−0.125436
$975$	−0.753380	−0.0241275
$976$	−167.255	−5.35369
$977$	58.8851	1.88390	0.941950	−	0.335753i	$-0.108991\pi$
$977$	58.8851	1.88390	0.941950	+	0.335753i	$0.108991\pi$
$978$	−1.32988	−0.0425250
$979$	23.2560	0.743263
$980$	−102.640	−3.27870
$981$	−1.20096	−0.0383438
$982$	80.9621	2.58361
$983$	−25.9952	−0.829117	−0.414559	−	0.910023i	$-0.636064\pi$
$983$	−25.9952	−0.829117	−0.414559	+	0.910023i	$0.636064\pi$
$984$	8.92354	0.284472
$985$	−6.42762	−0.204801
$986$	1.26828	0.0403903
$987$	−6.09863	−0.194121
$988$	−18.4540	−0.587101
$989$	−18.3306	−0.582879
$990$	−14.3436	−0.455870
$991$	13.3336	0.423555	0.211778	−	0.977318i	$-0.432075\pi$
$991$	13.3336	0.423555	0.211778	+	0.977318i	$0.432075\pi$
$992$	16.2591	0.516227
$993$	6.08117	0.192980
$994$	−81.5196	−2.58565
$995$	−0.523291	−0.0165895
$996$	2.38027	0.0754219
$997$	49.7275	1.57489	0.787443	−	0.616388i	$-0.211405\pi$
$997$	49.7275	1.57489	0.787443	+	0.616388i	$0.211405\pi$
$998$	101.959	3.22746
$999$	−5.72320	−0.181074

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.2	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.2	✓	101	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)

\(f(q)\)	\(=\)	\(q-2.75200 q^{2} +0.205353 q^{3} +5.57349 q^{4} -1.15382 q^{5} -0.565131 q^{6} +4.79173 q^{7} -9.83422 q^{8} -2.95783 q^{9} +O(q^{10})\)	\(q-2.75200 q^{2} +0.205353 q^{3} +5.57349 q^{4} -1.15382 q^{5} -0.565131 q^{6} +4.79173 q^{7} -9.83422 q^{8} -2.95783 q^{9} +3.17530 q^{10} +1.52722 q^{11} +1.14453 q^{12} +1.00000 q^{13} -13.1868 q^{14} -0.236939 q^{15} +15.9168 q^{16} -0.141785 q^{17} +8.13994 q^{18} -3.31104 q^{19} -6.43077 q^{20} +0.983996 q^{21} -4.20290 q^{22} -1.71610 q^{23} -2.01949 q^{24} -3.66871 q^{25} -2.75200 q^{26} -1.22346 q^{27} +26.7066 q^{28} +3.25041 q^{29} +0.652056 q^{30} -0.673687 q^{31} -24.1345 q^{32} +0.313619 q^{33} +0.390191 q^{34} -5.52877 q^{35} -16.4854 q^{36} +4.67789 q^{37} +9.11197 q^{38} +0.205353 q^{39} +11.3469 q^{40} -4.41872 q^{41} -2.70795 q^{42} +10.6815 q^{43} +8.51194 q^{44} +3.41279 q^{45} +4.72270 q^{46} -6.19782 q^{47} +3.26856 q^{48} +15.9607 q^{49} +10.0963 q^{50} -0.0291159 q^{51} +5.57349 q^{52} -13.4826 q^{53} +3.36695 q^{54} -1.76213 q^{55} -47.1229 q^{56} -0.679932 q^{57} -8.94513 q^{58} -6.63760 q^{59} -1.32058 q^{60} -10.5081 q^{61} +1.85399 q^{62} -14.1731 q^{63} +34.5844 q^{64} -1.15382 q^{65} -0.863079 q^{66} +4.99335 q^{67} -0.790234 q^{68} -0.352406 q^{69} +15.2152 q^{70} +6.18190 q^{71} +29.0880 q^{72} -10.4445 q^{73} -12.8735 q^{74} -0.753380 q^{75} -18.4540 q^{76} +7.31803 q^{77} -0.565131 q^{78} +10.0883 q^{79} -18.3650 q^{80} +8.62225 q^{81} +12.1603 q^{82} +2.07969 q^{83} +5.48429 q^{84} +0.163593 q^{85} -29.3956 q^{86} +0.667482 q^{87} -15.0190 q^{88} +15.2276 q^{89} -9.39199 q^{90} +4.79173 q^{91} -9.56466 q^{92} -0.138344 q^{93} +17.0564 q^{94} +3.82033 q^{95} -4.95608 q^{96} -16.4525 q^{97} -43.9237 q^{98} -4.51726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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