LMFDB - Embedded newform 6019.2.a.c.1.18

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:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-2.18373 q^{2} +2.09330 q^{3} +2.76866 q^{4} +2.17810 q^{5} -4.57119 q^{6} -2.34745 q^{7} -1.67854 q^{8} +1.38190 q^{9} +O(q^{10})$	\(q-2.18373 q^{2} +2.09330 q^{3} +2.76866 q^{4} +2.17810 q^{5} -4.57119 q^{6} -2.34745 q^{7} -1.67854 q^{8} +1.38190 q^{9} -4.75637 q^{10} -3.00332 q^{11} +5.79563 q^{12} -1.00000 q^{13} +5.12619 q^{14} +4.55941 q^{15} -1.87184 q^{16} +3.33571 q^{17} -3.01768 q^{18} -3.57317 q^{19} +6.03042 q^{20} -4.91391 q^{21} +6.55844 q^{22} +4.76590 q^{23} -3.51369 q^{24} -0.255882 q^{25} +2.18373 q^{26} -3.38717 q^{27} -6.49929 q^{28} +2.11920 q^{29} -9.95651 q^{30} +5.73883 q^{31} +7.44468 q^{32} -6.28685 q^{33} -7.28428 q^{34} -5.11298 q^{35} +3.82600 q^{36} -9.29779 q^{37} +7.80283 q^{38} -2.09330 q^{39} -3.65603 q^{40} +2.20335 q^{41} +10.7306 q^{42} -10.4981 q^{43} -8.31518 q^{44} +3.00991 q^{45} -10.4074 q^{46} +5.22842 q^{47} -3.91833 q^{48} -1.48948 q^{49} +0.558776 q^{50} +6.98263 q^{51} -2.76866 q^{52} +8.52718 q^{53} +7.39666 q^{54} -6.54154 q^{55} +3.94029 q^{56} -7.47972 q^{57} -4.62775 q^{58} -6.83343 q^{59} +12.6235 q^{60} +10.1192 q^{61} -12.5320 q^{62} -3.24393 q^{63} -12.5134 q^{64} -2.17810 q^{65} +13.7288 q^{66} -4.03486 q^{67} +9.23544 q^{68} +9.97644 q^{69} +11.1653 q^{70} +5.45532 q^{71} -2.31957 q^{72} +5.46706 q^{73} +20.3038 q^{74} -0.535637 q^{75} -9.89290 q^{76} +7.05015 q^{77} +4.57119 q^{78} +5.08897 q^{79} -4.07706 q^{80} -11.2361 q^{81} -4.81151 q^{82} -7.60495 q^{83} -13.6049 q^{84} +7.26551 q^{85} +22.9251 q^{86} +4.43612 q^{87} +5.04120 q^{88} -10.7414 q^{89} -6.57281 q^{90} +2.34745 q^{91} +13.1951 q^{92} +12.0131 q^{93} -11.4174 q^{94} -7.78273 q^{95} +15.5839 q^{96} -19.4503 q^{97} +3.25262 q^{98} -4.15028 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.18373	−1.54413	−0.772064	−	0.635545i	$-0.780775\pi$
$2$	−2.18373	−1.54413	−0.772064	+	0.635545i	$0.780775\pi$
$3$	2.09330	1.20857	0.604283	−	0.796770i	$-0.293460\pi$
$3$	2.09330	1.20857	0.604283	+	0.796770i	$0.293460\pi$
$4$	2.76866	1.38433
$5$	2.17810	0.974076	0.487038	−	0.873381i	$-0.338077\pi$
$5$	2.17810	0.974076	0.487038	+	0.873381i	$0.338077\pi$
$6$	−4.57119	−1.86618
$7$	−2.34745	−0.887252	−0.443626	−	0.896212i	$-0.646308\pi$
$7$	−2.34745	−0.887252	−0.443626	+	0.896212i	$0.646308\pi$
$8$	−1.67854	−0.593454
$9$	1.38190	0.460632
$10$	−4.75637	−1.50410
$11$	−3.00332	−0.905536	−0.452768	−	0.891628i	$-0.649563\pi$
$11$	−3.00332	−0.905536	−0.452768	+	0.891628i	$0.649563\pi$
$12$	5.79563	1.67305
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	5.12619	1.37003
$15$	4.55941	1.17723
$16$	−1.87184	−0.467961
$17$	3.33571	0.809028	0.404514	−	0.914532i	$-0.367441\pi$
$17$	3.33571	0.809028	0.404514	+	0.914532i	$0.367441\pi$
$18$	−3.01768	−0.711275
$19$	−3.57317	−0.819742	−0.409871	−	0.912143i	$-0.634426\pi$
$19$	−3.57317	−0.819742	−0.409871	+	0.912143i	$0.634426\pi$
$20$	6.03042	1.34844
$21$	−4.91391	−1.07230
$22$	6.55844	1.39826
$23$	4.76590	0.993758	0.496879	−	0.867820i	$-0.334479\pi$
$23$	4.76590	0.993758	0.496879	+	0.867820i	$0.334479\pi$
$24$	−3.51369	−0.717229
$25$	−0.255882	−0.0511764
$26$	2.18373	0.428264
$27$	−3.38717	−0.651862
$28$	−6.49929	−1.22825
$29$	2.11920	0.393526	0.196763	−	0.980451i	$-0.436957\pi$
$29$	2.11920	0.393526	0.196763	+	0.980451i	$0.436957\pi$
$30$	−9.95651	−1.81780
$31$	5.73883	1.03072	0.515362	−	0.856973i	$-0.327658\pi$
$31$	5.73883	1.03072	0.515362	+	0.856973i	$0.327658\pi$
$32$	7.44468	1.31605
$33$	−6.28685	−1.09440
$34$	−7.28428	−1.24924
$35$	−5.11298	−0.864251
$36$	3.82600	0.637667
$37$	−9.29779	−1.52855	−0.764274	−	0.644892i	$-0.776902\pi$
$37$	−9.29779	−1.52855	−0.764274	+	0.644892i	$0.776902\pi$
$38$	7.80283	1.26579
$39$	−2.09330	−0.335196
$40$	−3.65603	−0.578069
$41$	2.20335	0.344105	0.172053	−	0.985088i	$-0.444960\pi$
$41$	2.20335	0.344105	0.172053	+	0.985088i	$0.444960\pi$
$42$	10.7306	1.65577
$43$	−10.4981	−1.60095	−0.800475	−	0.599366i	$-0.795420\pi$
$43$	−10.4981	−1.60095	−0.800475	+	0.599366i	$0.795420\pi$
$44$	−8.31518	−1.25356
$45$	3.00991	0.448691
$46$	−10.4074	−1.53449
$47$	5.22842	0.762643	0.381322	−	0.924442i	$-0.375469\pi$
$47$	5.22842	0.762643	0.381322	+	0.924442i	$0.375469\pi$
$48$	−3.91833	−0.565562
$49$	−1.48948	−0.212783
$50$	0.558776	0.0790228
$51$	6.98263	0.977764
$52$	−2.76866	−0.383944
$53$	8.52718	1.17130	0.585649	−	0.810565i	$-0.300840\pi$
$53$	8.52718	1.17130	0.585649	+	0.810565i	$0.300840\pi$
$54$	7.39666	1.00656
$55$	−6.54154	−0.882061
$56$	3.94029	0.526544
$57$	−7.47972	−0.990713
$58$	−4.62775	−0.607654
$59$	−6.83343	−0.889637	−0.444818	−	0.895621i	$-0.646732\pi$
$59$	−6.83343	−0.889637	−0.444818	+	0.895621i	$0.646732\pi$
$60$	12.6235	1.62968
$61$	10.1192	1.29563	0.647813	−	0.761799i	$-0.275684\pi$
$61$	10.1192	1.29563	0.647813	+	0.761799i	$0.275684\pi$
$62$	−12.5320	−1.59157
$63$	−3.24393	−0.408697
$64$	−12.5134	−1.56418
$65$	−2.17810	−0.270160
$66$	13.7288	1.68989
$67$	−4.03486	−0.492937	−0.246469	−	0.969151i	$-0.579270\pi$
$67$	−4.03486	−0.492937	−0.246469	+	0.969151i	$0.579270\pi$
$68$	9.23544	1.11996
$69$	9.97644	1.20102
$70$	11.1653	1.33451
$71$	5.45532	0.647428	0.323714	−	0.946155i	$-0.395069\pi$
$71$	5.45532	0.647428	0.323714	+	0.946155i	$0.395069\pi$
$72$	−2.31957	−0.273364
$73$	5.46706	0.639871	0.319935	−	0.947439i	$-0.396339\pi$
$73$	5.46706	0.639871	0.319935	+	0.947439i	$0.396339\pi$
$74$	20.3038	2.36027
$75$	−0.535637	−0.0618500
$76$	−9.89290	−1.13479
$77$	7.05015	0.803439
$78$	4.57119	0.517585
$79$	5.08897	0.572553	0.286277	−	0.958147i	$-0.407582\pi$
$79$	5.08897	0.572553	0.286277	+	0.958147i	$0.407582\pi$
$80$	−4.07706	−0.455829
$81$	−11.2361	−1.24845
$82$	−4.81151	−0.531342
$83$	−7.60495	−0.834752	−0.417376	−	0.908734i	$-0.637050\pi$
$83$	−7.60495	−0.834752	−0.417376	+	0.908734i	$0.637050\pi$
$84$	−13.6049	−1.48442
$85$	7.26551	0.788055
$86$	22.9251	2.47207
$87$	4.43612	0.475602
$88$	5.04120	0.537394
$89$	−10.7414	−1.13859	−0.569295	−	0.822133i	$-0.692784\pi$
$89$	−10.7414	−1.13859	−0.569295	+	0.822133i	$0.692784\pi$
$90$	−6.57281	−0.692835
$91$	2.34745	0.246080
$92$	13.1951	1.37569
$93$	12.0131	1.24570
$94$	−11.4174	−1.17762
$95$	−7.78273	−0.798491
$96$	15.5839	1.59053
$97$	−19.4503	−1.97488	−0.987438	−	0.158009i	$-0.949492\pi$
$97$	−19.4503	−1.97488	−0.987438	+	0.158009i	$0.949492\pi$
$98$	3.25262	0.328565
$99$	−4.15028	−0.417119
$100$	−0.708450	−0.0708450
$101$	−14.2729	−1.42020	−0.710102	−	0.704099i	$-0.751351\pi$
$101$	−14.2729	−1.42020	−0.710102	+	0.704099i	$0.751351\pi$
$102$	−15.2482	−1.50979
$103$	3.35740	0.330814	0.165407	−	0.986225i	$-0.447106\pi$
$103$	3.35740	0.330814	0.165407	+	0.986225i	$0.447106\pi$
$104$	1.67854	0.164595
$105$	−10.7030	−1.04450
$106$	−18.6210	−1.80863
$107$	19.7245	1.90684	0.953421	−	0.301643i	$-0.0975349\pi$
$107$	19.7245	1.90684	0.953421	+	0.301643i	$0.0975349\pi$
$108$	−9.37793	−0.902392
$109$	6.59222	0.631420	0.315710	−	0.948856i	$-0.397757\pi$
$109$	6.59222	0.631420	0.315710	+	0.948856i	$0.397757\pi$
$110$	14.2849	1.36201
$111$	−19.4630	−1.84735
$112$	4.39406	0.415199
$113$	−8.62881	−0.811730	−0.405865	−	0.913933i	$-0.633030\pi$
$113$	−8.62881	−0.811730	−0.405865	+	0.913933i	$0.633030\pi$
$114$	16.3337	1.52979
$115$	10.3806	0.967995
$116$	5.86735	0.544769
$117$	−1.38190	−0.127756
$118$	14.9223	1.37371
$119$	−7.83041	−0.717812
$120$	−7.65316	−0.698635
$121$	−1.98005	−0.180005
$122$	−22.0975	−2.00061
$123$	4.61226	0.415874
$124$	15.8889	1.42686
$125$	−11.4478	−1.02393
$126$	7.08386	0.631080
$127$	5.80001	0.514668	0.257334	−	0.966323i	$-0.417156\pi$
$127$	5.80001	0.514668	0.257334	+	0.966323i	$0.417156\pi$
$128$	12.4366	1.09925
$129$	−21.9757	−1.93485
$130$	4.75637	0.417162
$131$	−3.79863	−0.331888	−0.165944	−	0.986135i	$-0.553067\pi$
$131$	−3.79863	−0.331888	−0.165944	+	0.986135i	$0.553067\pi$
$132$	−17.4061	−1.51501
$133$	8.38784	0.727318
$134$	8.81104	0.761158
$135$	−7.37760	−0.634963
$136$	−5.59913	−0.480121
$137$	−17.8462	−1.52470	−0.762352	−	0.647162i	$-0.775956\pi$
$137$	−17.8462	−1.52470	−0.762352	+	0.647162i	$0.775956\pi$
$138$	−21.7858	−1.85453
$139$	6.28181	0.532817	0.266408	−	0.963860i	$-0.414163\pi$
$139$	6.28181	0.532817	0.266408	+	0.963860i	$0.414163\pi$
$140$	−14.1561	−1.19641
$141$	10.9446	0.921705
$142$	−11.9129	−0.999711
$143$	3.00332	0.251151
$144$	−2.58669	−0.215558
$145$	4.61583	0.383324
$146$	−11.9386	−0.988042
$147$	−3.11793	−0.257163
$148$	−25.7424	−2.11601
$149$	−3.21520	−0.263400	−0.131700	−	0.991290i	$-0.542044\pi$
$149$	−3.21520	−0.263400	−0.131700	+	0.991290i	$0.542044\pi$
$150$	1.16968	0.0955043
$151$	−16.0929	−1.30962	−0.654812	−	0.755792i	$-0.727252\pi$
$151$	−16.0929	−1.30962	−0.654812	+	0.755792i	$0.727252\pi$
$152$	5.99772	0.486479
$153$	4.60960	0.372664
$154$	−15.3956	−1.24061
$155$	12.4997	1.00400
$156$	−5.79563	−0.464022
$157$	−8.74228	−0.697710	−0.348855	−	0.937177i	$-0.613429\pi$
$157$	−8.74228	−0.697710	−0.348855	+	0.937177i	$0.613429\pi$
$158$	−11.1129	−0.884096
$159$	17.8499	1.41559
$160$	16.2152	1.28193
$161$	−11.1877	−0.881714
$162$	24.5365	1.92777
$163$	−20.2942	−1.58956	−0.794782	−	0.606895i	$-0.792415\pi$
$163$	−20.2942	−1.58956	−0.794782	+	0.606895i	$0.792415\pi$
$164$	6.10032	0.476355
$165$	−13.6934	−1.06603
$166$	16.6071	1.28896
$167$	7.88128	0.609872	0.304936	−	0.952373i	$-0.401365\pi$
$167$	7.88128	0.609872	0.304936	+	0.952373i	$0.401365\pi$
$168$	8.24820	0.636363
$169$	1.00000	0.0769231
$170$	−15.8659	−1.21686
$171$	−4.93775	−0.377600
$172$	−29.0658	−2.21624
$173$	0.615966	0.0468310	0.0234155	−	0.999726i	$-0.492546\pi$
$173$	0.615966	0.0468310	0.0234155	+	0.999726i	$0.492546\pi$
$174$	−9.68727	−0.734390
$175$	0.600670	0.0454063
$176$	5.62175	0.423755
$177$	−14.3044	−1.07519
$178$	23.4564	1.75813
$179$	−2.26361	−0.169190	−0.0845952	−	0.996415i	$-0.526960\pi$
$179$	−2.26361	−0.169190	−0.0845952	+	0.996415i	$0.526960\pi$
$180$	8.33341	0.621136
$181$	−15.7833	−1.17316	−0.586581	−	0.809891i	$-0.699526\pi$
$181$	−15.7833	−1.17316	−0.586581	+	0.809891i	$0.699526\pi$
$182$	−5.12619	−0.379978
$183$	21.1824	1.56585
$184$	−7.99975	−0.589750
$185$	−20.2515	−1.48892
$186$	−26.2333	−1.92352
$187$	−10.0182	−0.732604
$188$	14.4757	1.05575
$189$	7.95122	0.578366
$190$	16.9953	1.23297
$191$	−2.48808	−0.180031	−0.0900157	−	0.995940i	$-0.528692\pi$
$191$	−2.48808	−0.180031	−0.0900157	+	0.995940i	$0.528692\pi$
$192$	−26.1944	−1.89042
$193$	−10.1355	−0.729572	−0.364786	−	0.931091i	$-0.618858\pi$
$193$	−10.1355	−0.729572	−0.364786	+	0.931091i	$0.618858\pi$
$194$	42.4741	3.04946
$195$	−4.55941	−0.326506
$196$	−4.12387	−0.294562
$197$	8.26887	0.589133	0.294566	−	0.955631i	$-0.404825\pi$
$197$	8.26887	0.589133	0.294566	+	0.955631i	$0.404825\pi$
$198$	9.06308	0.644085
$199$	7.54357	0.534750	0.267375	−	0.963593i	$-0.413844\pi$
$199$	7.54357	0.534750	0.267375	+	0.963593i	$0.413844\pi$
$200$	0.429508	0.0303708
$201$	−8.44617	−0.595747
$202$	31.1681	2.19298
$203$	−4.97472	−0.349157
$204$	19.3325	1.35355
$205$	4.79911	0.335184
$206$	−7.33163	−0.510819
$207$	6.58597	0.457757
$208$	1.87184	0.129789
$209$	10.7314	0.742306
$210$	23.3724	1.61285
$211$	−27.8060	−1.91424	−0.957120	−	0.289690i	$-0.906448\pi$
$211$	−27.8060	−1.91424	−0.957120	+	0.289690i	$0.906448\pi$
$212$	23.6088	1.62146
$213$	11.4196	0.782459
$214$	−43.0730	−2.94441
$215$	−22.8660	−1.55945
$216$	5.68551	0.386850
$217$	−13.4716	−0.914512
$218$	−14.3956	−0.974993
$219$	11.4442	0.773326
$220$	−18.1113	−1.22106
$221$	−3.33571	−0.224384
$222$	42.5020	2.85254
$223$	−29.0789	−1.94726	−0.973632	−	0.228123i	$-0.926741\pi$
$223$	−29.0789	−1.94726	−0.973632	+	0.228123i	$0.926741\pi$
$224$	−17.4760	−1.16766
$225$	−0.353602	−0.0235735
$226$	18.8430	1.25341
$227$	−5.05251	−0.335347	−0.167673	−	0.985843i	$-0.553625\pi$
$227$	−5.05251	−0.335347	−0.167673	+	0.985843i	$0.553625\pi$
$228$	−20.7088	−1.37147
$229$	−16.0092	−1.05792	−0.528958	−	0.848648i	$-0.677417\pi$
$229$	−16.0092	−1.05792	−0.528958	+	0.848648i	$0.677417\pi$
$230$	−22.6684	−1.49471
$231$	14.7581	0.971009
$232$	−3.55717	−0.233539
$233$	−28.3613	−1.85801	−0.929005	−	0.370068i	$-0.879334\pi$
$233$	−28.3613	−1.85801	−0.929005	+	0.370068i	$0.879334\pi$
$234$	3.01768	0.197272
$235$	11.3880	0.742872
$236$	−18.9194	−1.23155
$237$	10.6527	0.691969
$238$	17.0995	1.10839
$239$	−6.83617	−0.442195	−0.221098	−	0.975252i	$-0.570964\pi$
$239$	−6.83617	−0.442195	−0.221098	+	0.975252i	$0.570964\pi$
$240$	−8.53450	−0.550900
$241$	−4.25768	−0.274261	−0.137130	−	0.990553i	$-0.543788\pi$
$241$	−4.25768	−0.274261	−0.137130	+	0.990553i	$0.543788\pi$
$242$	4.32389	0.277950
$243$	−13.3589	−0.856973
$244$	28.0165	1.79357
$245$	−3.24424	−0.207267
$246$	−10.0719	−0.642162
$247$	3.57317	0.227356
$248$	−9.63286	−0.611687
$249$	−15.9194	−1.00885
$250$	24.9989	1.58107
$251$	−18.6978	−1.18019	−0.590097	−	0.807332i	$-0.700911\pi$
$251$	−18.6978	−1.18019	−0.590097	+	0.807332i	$0.700911\pi$
$252$	−8.98134	−0.565771
$253$	−14.3135	−0.899884
$254$	−12.6656	−0.794713
$255$	15.2089	0.952416
$256$	−2.13121	−0.133200
$257$	13.2574	0.826977	0.413488	−	0.910509i	$-0.364310\pi$
$257$	13.2574	0.826977	0.413488	+	0.910509i	$0.364310\pi$
$258$	47.9890	2.98766
$259$	21.8261	1.35621
$260$	−6.03042	−0.373991
$261$	2.92852	0.181271
$262$	8.29516	0.512477
$263$	−25.9900	−1.60261	−0.801307	−	0.598254i	$-0.795861\pi$
$263$	−25.9900	−1.60261	−0.801307	+	0.598254i	$0.795861\pi$
$264$	10.5527	0.649476
$265$	18.5730	1.14093
$266$	−18.3167	−1.12307
$267$	−22.4850	−1.37606
$268$	−11.1712	−0.682387
$269$	0.968877	0.0590735	0.0295367	−	0.999564i	$-0.490597\pi$
$269$	0.968877	0.0590735	0.0295367	+	0.999564i	$0.490597\pi$
$270$	16.1107	0.980464
$271$	7.99952	0.485936	0.242968	−	0.970034i	$-0.421879\pi$
$271$	7.99952	0.485936	0.242968	+	0.970034i	$0.421879\pi$
$272$	−6.24393	−0.378594
$273$	4.91391	0.297403
$274$	38.9712	2.35434
$275$	0.768496	0.0463420
$276$	27.6214	1.66261
$277$	23.0850	1.38704	0.693521	−	0.720437i	$-0.256059\pi$
$277$	23.0850	1.38704	0.693521	+	0.720437i	$0.256059\pi$
$278$	−13.7178	−0.822737
$279$	7.93046	0.474784
$280$	8.58235	0.512893
$281$	−12.9659	−0.773480	−0.386740	−	0.922189i	$-0.626399\pi$
$281$	−12.9659	−0.773480	−0.386740	+	0.922189i	$0.626399\pi$
$282$	−23.9001	−1.42323
$283$	22.3983	1.33144	0.665721	−	0.746201i	$-0.268124\pi$
$283$	22.3983	1.33144	0.665721	+	0.746201i	$0.268124\pi$
$284$	15.1039	0.896253
$285$	−16.2916	−0.965029
$286$	−6.55844	−0.387808
$287$	−5.17225	−0.305308
$288$	10.2878	0.606213
$289$	−5.87304	−0.345473
$290$	−10.0797	−0.591901
$291$	−40.7152	−2.38677
$292$	15.1364	0.885792
$293$	6.87255	0.401498	0.200749	−	0.979643i	$-0.435662\pi$
$293$	6.87255	0.401498	0.200749	+	0.979643i	$0.435662\pi$
$294$	6.80871	0.397092
$295$	−14.8839	−0.866574
$296$	15.6067	0.907123
$297$	10.1728	0.590284
$298$	7.02113	0.406723
$299$	−4.76590	−0.275619
$300$	−1.48300	−0.0856208
$301$	24.6438	1.42045
$302$	35.1425	2.02223
$303$	−29.8774	−1.71641
$304$	6.68842	0.383607
$305$	22.0406	1.26204
$306$	−10.0661	−0.575441
$307$	0.130484	0.00744713	0.00372357	−	0.999993i	$-0.498815\pi$
$307$	0.130484	0.00744713	0.00372357	+	0.999993i	$0.498815\pi$
$308$	19.5195	1.11222
$309$	7.02803	0.399811
$310$	−27.2960	−1.55031
$311$	34.7139	1.96845	0.984223	−	0.176932i	$-0.0566173\pi$
$311$	34.7139	1.96845	0.984223	+	0.176932i	$0.0566173\pi$
$312$	3.51369	0.198923
$313$	6.24031	0.352723	0.176362	−	0.984325i	$-0.443567\pi$
$313$	6.24031	0.352723	0.176362	+	0.984325i	$0.443567\pi$
$314$	19.0908	1.07735
$315$	−7.06560	−0.398102
$316$	14.0896	0.792603
$317$	−8.42010	−0.472920	−0.236460	−	0.971641i	$-0.575987\pi$
$317$	−8.42010	−0.472920	−0.236460	+	0.971641i	$0.575987\pi$
$318$	−38.9793	−2.18585
$319$	−6.36465	−0.356352
$320$	−27.2555	−1.52363
$321$	41.2893	2.30454
$322$	24.4309	1.36148
$323$	−11.9191	−0.663195
$324$	−31.1088	−1.72827
$325$	0.255882	0.0141938
$326$	44.3170	2.45449
$327$	13.7995	0.763112
$328$	−3.69841	−0.204211
$329$	−12.2734	−0.676657
$330$	29.9026	1.64608
$331$	28.6634	1.57548	0.787742	−	0.616005i	$-0.211250\pi$
$331$	28.6634	1.57548	0.787742	+	0.616005i	$0.211250\pi$
$332$	−21.0555	−1.15557
$333$	−12.8486	−0.704098
$334$	−17.2106	−0.941720
$335$	−8.78834	−0.480158
$336$	9.19807	0.501796
$337$	13.8780	0.755984	0.377992	−	0.925809i	$-0.376615\pi$
$337$	13.8780	0.755984	0.377992	+	0.925809i	$0.376615\pi$
$338$	−2.18373	−0.118779
$339$	−18.0627	−0.981029
$340$	20.1157	1.09093
$341$	−17.2355	−0.933357
$342$	10.7827	0.583062
$343$	19.9286	1.07604
$344$	17.6216	0.950091
$345$	21.7297	1.16989
$346$	−1.34510	−0.0723131
$347$	6.07364	0.326050	0.163025	−	0.986622i	$-0.447875\pi$
$347$	6.07364	0.326050	0.163025	+	0.986622i	$0.447875\pi$
$348$	12.2821	0.658390
$349$	25.6713	1.37415	0.687077	−	0.726585i	$-0.258894\pi$
$349$	25.6713	1.37415	0.687077	+	0.726585i	$0.258894\pi$
$350$	−1.31170	−0.0701132
$351$	3.38717	0.180794
$352$	−22.3588	−1.19173
$353$	−23.4828	−1.24986	−0.624932	−	0.780679i	$-0.714873\pi$
$353$	−23.4828	−1.24986	−0.624932	+	0.780679i	$0.714873\pi$
$354$	31.2369	1.66022
$355$	11.8822	0.630643
$356$	−29.7394	−1.57618
$357$	−16.3914	−0.867524
$358$	4.94311	0.261252
$359$	15.9297	0.840738	0.420369	−	0.907353i	$-0.361901\pi$
$359$	15.9297	0.840738	0.420369	+	0.907353i	$0.361901\pi$
$360$	−5.05226	−0.266277
$361$	−6.23243	−0.328023
$362$	34.4664	1.81151
$363$	−4.14483	−0.217547
$364$	6.49929	0.340655
$365$	11.9078	0.623282
$366$	−46.2566	−2.41787
$367$	2.39775	0.125162	0.0625808	−	0.998040i	$-0.480067\pi$
$367$	2.39775	0.125162	0.0625808	+	0.998040i	$0.480067\pi$
$368$	−8.92101	−0.465040
$369$	3.04480	0.158506
$370$	44.2238	2.29908
$371$	−20.0171	−1.03924
$372$	33.2601	1.72446
$373$	−5.88945	−0.304944	−0.152472	−	0.988308i	$-0.548723\pi$
$373$	−5.88945	−0.304944	−0.152472	+	0.988308i	$0.548723\pi$
$374$	21.8770	1.13123
$375$	−23.9637	−1.23748
$376$	−8.77612	−0.452594
$377$	−2.11920	−0.109144
$378$	−17.3633	−0.893071
$379$	−5.47100	−0.281026	−0.140513	−	0.990079i	$-0.544875\pi$
$379$	−5.47100	−0.281026	−0.140513	+	0.990079i	$0.544875\pi$
$380$	−21.5477	−1.10537
$381$	12.1412	0.622010
$382$	5.43330	0.277992
$383$	−6.70387	−0.342552	−0.171276	−	0.985223i	$-0.554789\pi$
$383$	−6.70387	−0.342552	−0.171276	+	0.985223i	$0.554789\pi$
$384$	26.0335	1.32852
$385$	15.3559	0.782610
$386$	22.1333	1.12655
$387$	−14.5073	−0.737449
$388$	−53.8512	−2.73388
$389$	3.63301	0.184201	0.0921006	−	0.995750i	$-0.470642\pi$
$389$	3.63301	0.184201	0.0921006	+	0.995750i	$0.470642\pi$
$390$	9.95651	0.504167
$391$	15.8976	0.803978
$392$	2.50016	0.126277
$393$	−7.95166	−0.401108
$394$	−18.0570	−0.909696
$395$	11.0843	0.557710
$396$	−11.4907	−0.577430
$397$	−15.2955	−0.767659	−0.383830	−	0.923404i	$-0.625395\pi$
$397$	−15.2955	−0.767659	−0.383830	+	0.923404i	$0.625395\pi$
$398$	−16.4731	−0.825722
$399$	17.5583	0.879012
$400$	0.478971	0.0239485
$401$	−4.08771	−0.204130	−0.102065	−	0.994778i	$-0.532545\pi$
$401$	−4.08771	−0.204130	−0.102065	+	0.994778i	$0.532545\pi$
$402$	18.4441	0.919909
$403$	−5.73883	−0.285871
$404$	−39.5167	−1.96603
$405$	−24.4732	−1.21609
$406$	10.8634	0.539142
$407$	27.9243	1.38415
$408$	−11.7206	−0.580258
$409$	30.0340	1.48508	0.742542	−	0.669800i	$-0.233620\pi$
$409$	30.0340	1.48508	0.742542	+	0.669800i	$0.233620\pi$
$410$	−10.4799	−0.517567
$411$	−37.3574	−1.84271
$412$	9.29548	0.457956
$413$	16.0411	0.789332
$414$	−14.3820	−0.706835
$415$	−16.5643	−0.813112
$416$	−7.44468	−0.365005
$417$	13.1497	0.643944
$418$	−23.4344	−1.14622
$419$	11.2123	0.547755	0.273877	−	0.961765i	$-0.411694\pi$
$419$	11.2123	0.547755	0.273877	+	0.961765i	$0.411694\pi$
$420$	−29.6329	−1.44594
$421$	18.5660	0.904850	0.452425	−	0.891803i	$-0.350559\pi$
$421$	18.5660	0.904850	0.452425	+	0.891803i	$0.350559\pi$
$422$	60.7206	2.95583
$423$	7.22513	0.351298
$424$	−14.3132	−0.695111
$425$	−0.853547	−0.0414031
$426$	−24.9373	−1.20822
$427$	−23.7542	−1.14955
$428$	54.6105	2.63970
$429$	6.28685	0.303532
$430$	49.9331	2.40799
$431$	6.08107	0.292915	0.146457	−	0.989217i	$-0.453213\pi$
$431$	6.08107	0.292915	0.146457	+	0.989217i	$0.453213\pi$
$432$	6.34026	0.305046
$433$	−34.4568	−1.65589	−0.827944	−	0.560811i	$-0.810489\pi$
$433$	−34.4568	−1.65589	−0.827944	+	0.560811i	$0.810489\pi$
$434$	29.4183	1.41212
$435$	9.66231	0.463272
$436$	18.2516	0.874093
$437$	−17.0294	−0.814625
$438$	−24.9910	−1.19411
$439$	8.01169	0.382377	0.191189	−	0.981553i	$-0.438766\pi$
$439$	8.01169	0.382377	0.191189	+	0.981553i	$0.438766\pi$
$440$	10.9802	0.523463
$441$	−2.05831	−0.0980148
$442$	7.28428	0.346478
$443$	23.0945	1.09725	0.548626	−	0.836068i	$-0.315151\pi$
$443$	23.0945	1.09725	0.548626	+	0.836068i	$0.315151\pi$
$444$	−53.8865	−2.55734
$445$	−23.3959	−1.10907
$446$	63.5003	3.00683
$447$	−6.73038	−0.318336
$448$	29.3747	1.38782
$449$	−12.1921	−0.575381	−0.287690	−	0.957723i	$-0.592887\pi$
$449$	−12.1921	−0.575381	−0.287690	+	0.957723i	$0.592887\pi$
$450$	0.772170	0.0364004
$451$	−6.61736	−0.311600
$452$	−23.8902	−1.12370
$453$	−33.6873	−1.58277
$454$	11.0333	0.517818
$455$	5.11298	0.239700
$456$	12.5550	0.587943
$457$	−29.6083	−1.38502	−0.692508	−	0.721410i	$-0.743494\pi$
$457$	−29.6083	−1.38502	−0.692508	+	0.721410i	$0.743494\pi$
$458$	34.9597	1.63356
$459$	−11.2986	−0.527375
$460$	28.7403	1.34002
$461$	33.4297	1.55698	0.778489	−	0.627658i	$-0.215987\pi$
$461$	33.4297	1.55698	0.778489	+	0.627658i	$0.215987\pi$
$462$	−32.2276	−1.49936
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−3.96681	−0.184155
$465$	26.1657	1.21340
$466$	61.9333	2.86900
$467$	28.7629	1.33099	0.665494	−	0.746403i	$-0.268221\pi$
$467$	28.7629	1.33099	0.665494	+	0.746403i	$0.268221\pi$
$468$	−3.82600	−0.176857
$469$	9.47164	0.437360
$470$	−24.8683	−1.14709
$471$	−18.3002	−0.843229
$472$	11.4702	0.527959
$473$	31.5293	1.44972
$474$	−23.2626	−1.06849
$475$	0.914310	0.0419514
$476$	−21.6797	−0.993689
$477$	11.7837	0.539537
$478$	14.9283	0.682806
$479$	25.7355	1.17589	0.587943	−	0.808902i	$-0.299938\pi$
$479$	25.7355	1.17589	0.587943	+	0.808902i	$0.299938\pi$
$480$	33.9433	1.54929
$481$	9.29779	0.423943
$482$	9.29760	0.423494
$483$	−23.4192	−1.06561
$484$	−5.48208	−0.249186
$485$	−42.3646	−1.92368
$486$	29.1721	1.32328
$487$	2.73349	0.123866	0.0619331	−	0.998080i	$-0.480273\pi$
$487$	2.73349	0.123866	0.0619331	+	0.998080i	$0.480273\pi$
$488$	−16.9854	−0.768895
$489$	−42.4818	−1.92109
$490$	7.08454	0.320047
$491$	27.4268	1.23776	0.618878	−	0.785487i	$-0.287588\pi$
$491$	27.4268	1.23776	0.618878	+	0.785487i	$0.287588\pi$
$492$	12.7698	0.575706
$493$	7.06904	0.318373
$494$	−7.80283	−0.351066
$495$	−9.03973	−0.406305
$496$	−10.7422	−0.482338
$497$	−12.8061	−0.574432
$498$	34.7637	1.55780
$499$	−10.1759	−0.455536	−0.227768	−	0.973715i	$-0.573143\pi$
$499$	−10.1759	−0.455536	−0.227768	+	0.973715i	$0.573143\pi$
$500$	−31.6952	−1.41745
$501$	16.4979	0.737070
$502$	40.8309	1.82237
$503$	−37.3694	−1.66622	−0.833109	−	0.553110i	$-0.813441\pi$
$503$	−37.3694	−1.66622	−0.833109	+	0.553110i	$0.813441\pi$
$504$	5.44507	0.242543
$505$	−31.0877	−1.38339
$506$	31.2568	1.38953
$507$	2.09330	0.0929666
$508$	16.0583	0.712470
$509$	−29.7009	−1.31647	−0.658235	−	0.752813i	$-0.728696\pi$
$509$	−29.7009	−1.31647	−0.658235	+	0.752813i	$0.728696\pi$
$510$	−33.2120	−1.47065
$511$	−12.8336	−0.567727
$512$	−20.2192	−0.893571
$513$	12.1030	0.534359
$514$	−28.9506	−1.27696
$515$	7.31274	0.322238
$516$	−60.8433	−2.67848
$517$	−15.7026	−0.690601
$518$	−47.6622	−2.09416
$519$	1.28940	0.0565984
$520$	3.65603	0.160328
$521$	−4.20101	−0.184050	−0.0920248	−	0.995757i	$-0.529334\pi$
$521$	−4.20101	−0.184050	−0.0920248	+	0.995757i	$0.529334\pi$
$522$	−6.39508	−0.279905
$523$	−24.2796	−1.06167	−0.530836	−	0.847475i	$-0.678122\pi$
$523$	−24.2796	−1.06167	−0.530836	+	0.847475i	$0.678122\pi$
$524$	−10.5171	−0.459442
$525$	1.25738	0.0548766
$526$	56.7551	2.47464
$527$	19.1431	0.833885
$528$	11.7680	0.512136
$529$	−0.286242	−0.0124453
$530$	−40.5584	−1.76175
$531$	−9.44309	−0.409795
$532$	23.2231	1.00685
$533$	−2.20335	−0.0954376
$534$	49.1012	2.12481
$535$	42.9620	1.85741
$536$	6.77269	0.292536
$537$	−4.73842	−0.204478
$538$	−2.11576	−0.0912170
$539$	4.47340	0.192683
$540$	−20.4261	−0.878998
$541$	2.14389	0.0921730	0.0460865	−	0.998937i	$-0.485325\pi$
$541$	2.14389	0.0921730	0.0460865	+	0.998937i	$0.485325\pi$
$542$	−17.4688	−0.750348
$543$	−33.0391	−1.41784
$544$	24.8333	1.06472
$545$	14.3585	0.615051
$546$	−10.7306	−0.459229
$547$	31.5265	1.34798	0.673988	−	0.738743i	$-0.264580\pi$
$547$	31.5265	1.34798	0.673988	+	0.738743i	$0.264580\pi$
$548$	−49.4101	−2.11069
$549$	13.9836	0.596807
$550$	−1.67818	−0.0715580
$551$	−7.57227	−0.322590
$552$	−16.7459	−0.712752
$553$	−11.9461	−0.507999
$554$	−50.4113	−2.14177
$555$	−42.3925	−1.79946
$556$	17.3922	0.737594
$557$	−35.7375	−1.51425	−0.757123	−	0.653273i	$-0.773395\pi$
$557$	−35.7375	−1.51425	−0.757123	+	0.653273i	$0.773395\pi$
$558$	−17.3180	−0.733127
$559$	10.4981	0.444024
$560$	9.57069	0.404436
$561$	−20.9711	−0.885401
$562$	28.3139	1.19435
$563$	−41.2103	−1.73681	−0.868404	−	0.495857i	$-0.834854\pi$
$563$	−41.2103	−1.73681	−0.868404	+	0.495857i	$0.834854\pi$
$564$	30.3020	1.27594
$565$	−18.7944	−0.790687
$566$	−48.9118	−2.05592
$567$	26.3761	1.10769
$568$	−9.15699	−0.384219
$569$	−6.87590	−0.288253	−0.144126	−	0.989559i	$-0.546037\pi$
$569$	−6.87590	−0.288253	−0.144126	+	0.989559i	$0.546037\pi$
$570$	35.5763	1.49013
$571$	33.8843	1.41801	0.709007	−	0.705202i	$-0.249144\pi$
$571$	33.8843	1.41801	0.709007	+	0.705202i	$0.249144\pi$
$572$	8.31518	0.347675
$573$	−5.20830	−0.217580
$574$	11.2948	0.471435
$575$	−1.21951	−0.0508569
$576$	−17.2923	−0.720512
$577$	27.1688	1.13105	0.565526	−	0.824730i	$-0.308673\pi$
$577$	27.1688	1.13105	0.565526	+	0.824730i	$0.308673\pi$
$578$	12.8251	0.533455
$579$	−21.2167	−0.881736
$580$	12.7797	0.530647
$581$	17.8522	0.740636
$582$	88.9108	3.68547
$583$	−25.6099	−1.06065
$584$	−9.17668	−0.379734
$585$	−3.00991	−0.124444
$586$	−15.0078	−0.619965
$587$	3.11809	0.128697	0.0643486	−	0.997927i	$-0.479503\pi$
$587$	3.11809	0.128697	0.0643486	+	0.997927i	$0.479503\pi$
$588$	−8.63249	−0.355998
$589$	−20.5058	−0.844928
$590$	32.5023	1.33810
$591$	17.3092	0.712006
$592$	17.4040	0.715300
$593$	30.9213	1.26979	0.634893	−	0.772600i	$-0.281044\pi$
$593$	30.9213	1.26979	0.634893	+	0.772600i	$0.281044\pi$
$594$	−22.2146	−0.911474
$595$	−17.0554	−0.699204
$596$	−8.90181	−0.364632
$597$	15.7909	0.646280
$598$	10.4074	0.425591
$599$	27.0857	1.10669	0.553345	−	0.832952i	$-0.313351\pi$
$599$	27.0857	1.10669	0.553345	+	0.832952i	$0.313351\pi$
$600$	0.899089	0.0367052
$601$	−10.6669	−0.435110	−0.217555	−	0.976048i	$-0.569808\pi$
$601$	−10.6669	−0.435110	−0.217555	+	0.976048i	$0.569808\pi$
$602$	−53.8154	−2.19335
$603$	−5.57576	−0.227063
$604$	−44.5558	−1.81295
$605$	−4.31275	−0.175338
$606$	65.2440	2.65036
$607$	17.6255	0.715397	0.357699	−	0.933837i	$-0.383561\pi$
$607$	17.6255	0.715397	0.357699	+	0.933837i	$0.383561\pi$
$608$	−26.6011	−1.07882
$609$	−10.4136	−0.421979
$610$	−48.1305	−1.94875
$611$	−5.22842	−0.211519
$612$	12.7624	0.515890
$613$	−0.351865	−0.0142117	−0.00710585	−	0.999975i	$-0.502262\pi$
$613$	−0.351865	−0.0142117	−0.00710585	+	0.999975i	$0.502262\pi$
$614$	−0.284942	−0.0114993
$615$	10.0460	0.405093
$616$	−11.8340	−0.476804
$617$	43.7378	1.76082	0.880410	−	0.474214i	$-0.157268\pi$
$617$	43.7378	1.76082	0.880410	+	0.474214i	$0.157268\pi$
$618$	−15.3473	−0.617359
$619$	−19.1649	−0.770302	−0.385151	−	0.922854i	$-0.625851\pi$
$619$	−19.1649	−0.770302	−0.385151	+	0.922854i	$0.625851\pi$
$620$	34.6075	1.38987
$621$	−16.1429	−0.647793
$622$	−75.8057	−3.03953
$623$	25.2150	1.01022
$624$	3.91833	0.156859
$625$	−23.6551	−0.946205
$626$	−13.6271	−0.544650
$627$	22.4640	0.897126
$628$	−24.2044	−0.965861
$629$	−31.0147	−1.23664
$630$	15.4293	0.614720
$631$	−24.4022	−0.971437	−0.485719	−	0.874115i	$-0.661442\pi$
$631$	−24.4022	−0.971437	−0.485719	+	0.874115i	$0.661442\pi$
$632$	−8.54204	−0.339784
$633$	−58.2061	−2.31349
$634$	18.3872	0.730249
$635$	12.6330	0.501326
$636$	49.4203	1.95964
$637$	1.48948	0.0590155
$638$	13.8986	0.550253
$639$	7.53869	0.298226
$640$	27.0881	1.07075
$641$	−8.63890	−0.341216	−0.170608	−	0.985339i	$-0.554573\pi$
$641$	−8.63890	−0.341216	−0.170608	+	0.985339i	$0.554573\pi$
$642$	−90.1646	−3.55851
$643$	47.7235	1.88203	0.941015	−	0.338366i	$-0.109874\pi$
$643$	47.7235	1.88203	0.941015	+	0.338366i	$0.109874\pi$
$644$	−30.9749	−1.22058
$645$	−47.8653	−1.88470
$646$	26.0280	1.02406
$647$	−8.96305	−0.352374	−0.176187	−	0.984357i	$-0.556376\pi$
$647$	−8.96305	−0.352374	−0.176187	+	0.984357i	$0.556376\pi$
$648$	18.8602	0.740898
$649$	20.5230	0.805598
$650$	−0.558776	−0.0219170
$651$	−28.2001	−1.10525
$652$	−56.1877	−2.20048
$653$	−11.5514	−0.452041	−0.226020	−	0.974123i	$-0.572572\pi$
$653$	−11.5514	−0.452041	−0.226020	+	0.974123i	$0.572572\pi$
$654$	−30.1343	−1.17834
$655$	−8.27379	−0.323284
$656$	−4.12432	−0.161028
$657$	7.55490	0.294745
$658$	26.8018	1.04484
$659$	1.60792	0.0626355	0.0313177	−	0.999509i	$-0.490030\pi$
$659$	1.60792	0.0626355	0.0313177	+	0.999509i	$0.490030\pi$
$660$	−37.9123	−1.47574
$661$	−38.0373	−1.47948	−0.739740	−	0.672893i	$-0.765052\pi$
$661$	−38.0373	−1.47948	−0.739740	+	0.672893i	$0.765052\pi$
$662$	−62.5931	−2.43275
$663$	−6.98263	−0.271183
$664$	12.7652	0.495387
$665$	18.2696	0.708463
$666$	28.0578	1.08722
$667$	10.0999	0.391069
$668$	21.8206	0.844263
$669$	−60.8707	−2.35340
$670$	19.1913	0.741425
$671$	−30.3911	−1.17324
$672$	−36.5825	−1.41120
$673$	8.60104	0.331546	0.165773	−	0.986164i	$-0.446988\pi$
$673$	8.60104	0.331546	0.165773	+	0.986164i	$0.446988\pi$
$674$	−30.3058	−1.16733
$675$	0.866716	0.0333599
$676$	2.76866	0.106487
$677$	−0.585977	−0.0225209	−0.0112605	−	0.999937i	$-0.503584\pi$
$677$	−0.585977	−0.0225209	−0.0112605	+	0.999937i	$0.503584\pi$
$678$	39.4439	1.51483
$679$	45.6585	1.75221
$680$	−12.1955	−0.467674
$681$	−10.5764	−0.405289
$682$	37.6377	1.44122
$683$	−27.6086	−1.05641	−0.528206	−	0.849116i	$-0.677135\pi$
$683$	−27.6086	−1.05641	−0.528206	+	0.849116i	$0.677135\pi$
$684$	−13.6710	−0.522722
$685$	−38.8708	−1.48518
$686$	−43.5187	−1.66155
$687$	−33.5120	−1.27856
$688$	19.6509	0.749182
$689$	−8.52718	−0.324860
$690$	−47.4517	−1.80645
$691$	−3.95559	−0.150478	−0.0752389	−	0.997166i	$-0.523972\pi$
$691$	−3.95559	−0.150478	−0.0752389	+	0.997166i	$0.523972\pi$
$692$	1.70540	0.0648296
$693$	9.74257	0.370090
$694$	−13.2632	−0.503463
$695$	13.6824	0.519004
$696$	−7.44621	−0.282248
$697$	7.34973	0.278391
$698$	−56.0591	−2.12187
$699$	−59.3686	−2.24553
$700$	1.66305	0.0628574
$701$	−16.6680	−0.629541	−0.314770	−	0.949168i	$-0.601928\pi$
$701$	−16.6680	−0.629541	−0.314770	+	0.949168i	$0.601928\pi$
$702$	−7.39666	−0.279169
$703$	33.2226	1.25301
$704$	37.5819	1.41642
$705$	23.8385	0.897810
$706$	51.2801	1.92995
$707$	33.5048	1.26008
$708$	−39.6040	−1.48841
$709$	26.4805	0.994496	0.497248	−	0.867609i	$-0.334344\pi$
$709$	26.4805	0.994496	0.497248	+	0.867609i	$0.334344\pi$
$710$	−25.9475	−0.973794
$711$	7.03242	0.263736
$712$	18.0300	0.675701
$713$	27.3506	1.02429
$714$	35.7943	1.33957
$715$	6.54154	0.244640
$716$	−6.26717	−0.234215
$717$	−14.3101	−0.534422
$718$	−34.7861	−1.29821
$719$	−15.1419	−0.564699	−0.282349	−	0.959312i	$-0.591114\pi$
$719$	−15.1419	−0.564699	−0.282349	+	0.959312i	$0.591114\pi$
$720$	−5.63408	−0.209970
$721$	−7.88131	−0.293515
$722$	13.6099	0.506509
$723$	−8.91258	−0.331462
$724$	−43.6985	−1.62404
$725$	−0.542265	−0.0201392
$726$	9.05118	0.335921
$727$	39.9807	1.48280	0.741402	−	0.671062i	$-0.234161\pi$
$727$	39.9807	1.48280	0.741402	+	0.671062i	$0.234161\pi$
$728$	−3.94029	−0.146037
$729$	5.74403	0.212742
$730$	−26.0034	−0.962428
$731$	−35.0187	−1.29521
$732$	58.6470	2.16765
$733$	−31.4396	−1.16125	−0.580623	−	0.814172i	$-0.697191\pi$
$733$	−31.4396	−1.16125	−0.580623	+	0.814172i	$0.697191\pi$
$734$	−5.23603	−0.193266
$735$	−6.79117	−0.250496
$736$	35.4806	1.30783
$737$	12.1180	0.446372
$738$	−6.64900	−0.244753
$739$	2.18516	0.0803823	0.0401911	−	0.999192i	$-0.487203\pi$
$739$	2.18516	0.0803823	0.0401911	+	0.999192i	$0.487203\pi$
$740$	−56.0695	−2.06116
$741$	7.47972	0.274774
$742$	43.7119	1.60471
$743$	22.7250	0.833699	0.416850	−	0.908975i	$-0.363134\pi$
$743$	22.7250	0.833699	0.416850	+	0.908975i	$0.363134\pi$
$744$	−20.1644	−0.739264
$745$	−7.00304	−0.256571
$746$	12.8609	0.470873
$747$	−10.5093	−0.384513
$748$	−27.7370	−1.01417
$749$	−46.3023	−1.69185
$750$	52.3302	1.91083
$751$	28.6412	1.04513	0.522566	−	0.852599i	$-0.324975\pi$
$751$	28.6412	1.04513	0.522566	+	0.852599i	$0.324975\pi$
$752$	−9.78678	−0.356887
$753$	−39.1401	−1.42634
$754$	4.62775	0.168533
$755$	−35.0520	−1.27567
$756$	22.0142	0.800649
$757$	20.2347	0.735441	0.367721	−	0.929936i	$-0.380138\pi$
$757$	20.2347	0.735441	0.367721	+	0.929936i	$0.380138\pi$
$758$	11.9472	0.433941
$759$	−29.9625	−1.08757
$760$	13.0636	0.473868
$761$	24.1931	0.877001	0.438500	−	0.898731i	$-0.355510\pi$
$761$	24.1931	0.877001	0.438500	+	0.898731i	$0.355510\pi$
$762$	−26.5130	−0.960463
$763$	−15.4749	−0.560229
$764$	−6.88866	−0.249223
$765$	10.0402	0.363003
$766$	14.6394	0.528944
$767$	6.83343	0.246741
$768$	−4.46125	−0.160982
$769$	−32.8115	−1.18321	−0.591606	−	0.806227i	$-0.701506\pi$
$769$	−32.8115	−1.18321	−0.591606	+	0.806227i	$0.701506\pi$
$770$	−33.5331	−1.20845
$771$	27.7518	0.999456
$772$	−28.0619	−1.00997
$773$	7.68910	0.276558	0.138279	−	0.990393i	$-0.455843\pi$
$773$	7.68910	0.276558	0.138279	+	0.990393i	$0.455843\pi$
$774$	31.6800	1.13872
$775$	−1.46846	−0.0527487
$776$	32.6481	1.17200
$777$	45.6885	1.63907
$778$	−7.93351	−0.284430
$779$	−7.87294	−0.282077
$780$	−12.6235	−0.451992
$781$	−16.3841	−0.586269
$782$	−34.7161	−1.24145
$783$	−7.17810	−0.256524
$784$	2.78808	0.0995743
$785$	−19.0416	−0.679623
$786$	17.3642	0.619362
$787$	−51.2261	−1.82601	−0.913006	−	0.407945i	$-0.866245\pi$
$787$	−51.2261	−1.82601	−0.913006	+	0.407945i	$0.866245\pi$
$788$	22.8937	0.815554
$789$	−54.4049	−1.93686
$790$	−24.2050	−0.861176
$791$	20.2557	0.720209
$792$	6.96642	0.247541
$793$	−10.1192	−0.359342
$794$	33.4012	1.18536
$795$	38.8789	1.37889
$796$	20.8856	0.740270
$797$	17.8258	0.631423	0.315712	−	0.948855i	$-0.397757\pi$
$797$	17.8258	0.631423	0.315712	+	0.948855i	$0.397757\pi$
$798$	−38.3424	−1.35731
$799$	17.4405	0.617000
$800$	−1.90496	−0.0673504
$801$	−14.8436	−0.524471
$802$	8.92644	0.315203
$803$	−16.4193	−0.579426
$804$	−23.3846	−0.824710
$805$	−24.3679	−0.858856
$806$	12.5320	0.441422
$807$	2.02815	0.0713942
$808$	23.9576	0.842826
$809$	−11.3384	−0.398637	−0.199319	−	0.979935i	$-0.563873\pi$
$809$	−11.3384	−0.398637	−0.199319	+	0.979935i	$0.563873\pi$
$810$	53.4429	1.87779
$811$	−43.0631	−1.51215	−0.756075	−	0.654485i	$-0.772885\pi$
$811$	−43.0631	−1.51215	−0.756075	+	0.654485i	$0.772885\pi$
$812$	−13.7733	−0.483348
$813$	16.7454	0.587286
$814$	−60.9790	−2.13731
$815$	−44.2028	−1.54836
$816$	−13.0704	−0.457555
$817$	37.5117	1.31237
$818$	−65.5859	−2.29316
$819$	3.24393	0.113352
$820$	13.2871	0.464006
$821$	−28.4867	−0.994192	−0.497096	−	0.867695i	$-0.665600\pi$
$821$	−28.4867	−0.994192	−0.497096	+	0.867695i	$0.665600\pi$
$822$	81.5784	2.84537
$823$	28.4013	0.990008	0.495004	−	0.868891i	$-0.335167\pi$
$823$	28.4013	0.990008	0.495004	+	0.868891i	$0.335167\pi$
$824$	−5.63553	−0.196323
$825$	1.60869	0.0560074
$826$	−35.0294	−1.21883
$827$	−41.1758	−1.43182	−0.715912	−	0.698191i	$-0.753989\pi$
$827$	−41.1758	−1.43182	−0.715912	+	0.698191i	$0.753989\pi$
$828$	18.2343	0.633686
$829$	10.4542	0.363090	0.181545	−	0.983383i	$-0.441890\pi$
$829$	10.4542	0.363090	0.181545	+	0.983383i	$0.441890\pi$
$830$	36.1720	1.25555
$831$	48.3237	1.67633
$832$	12.5134	0.433826
$833$	−4.96848	−0.172148
$834$	−28.7154	−0.994332
$835$	17.1662	0.594061
$836$	29.7116	1.02760
$837$	−19.4384	−0.671889
$838$	−24.4845	−0.845803
$839$	5.27533	0.182125	0.0910623	−	0.995845i	$-0.470974\pi$
$839$	5.27533	0.182125	0.0910623	+	0.995845i	$0.470974\pi$
$840$	17.9654	0.619866
$841$	−24.5090	−0.845137
$842$	−40.5430	−1.39720
$843$	−27.1415	−0.934802
$844$	−76.9852	−2.64994
$845$	2.17810	0.0749289
$846$	−15.7777	−0.542449
$847$	4.64807	0.159709
$848$	−15.9615	−0.548121
$849$	46.8864	1.60914
$850$	1.86391	0.0639317
$851$	−44.3123	−1.51901
$852$	31.6170	1.08318
$853$	−27.6990	−0.948395	−0.474197	−	0.880419i	$-0.657262\pi$
$853$	−27.6990	−0.948395	−0.474197	+	0.880419i	$0.657262\pi$
$854$	51.8727	1.77505
$855$	−10.7549	−0.367811
$856$	−33.1084	−1.13162
$857$	−2.25488	−0.0770252	−0.0385126	−	0.999258i	$-0.512262\pi$
$857$	−2.25488	−0.0770252	−0.0385126	+	0.999258i	$0.512262\pi$
$858$	−13.7288	−0.468692
$859$	−20.7032	−0.706384	−0.353192	−	0.935551i	$-0.614904\pi$
$859$	−20.7032	−0.706384	−0.353192	+	0.935551i	$0.614904\pi$
$860$	−63.3081	−2.15879
$861$	−10.8271	−0.368985
$862$	−13.2794	−0.452298
$863$	13.0053	0.442706	0.221353	−	0.975194i	$-0.428953\pi$
$863$	13.0053	0.442706	0.221353	+	0.975194i	$0.428953\pi$
$864$	−25.2164	−0.857880
$865$	1.34164	0.0456170
$866$	75.2442	2.55690
$867$	−12.2940	−0.417527
$868$	−37.2983	−1.26599
$869$	−15.2838	−0.518468
$870$	−21.0998	−0.715351
$871$	4.03486	0.136716
$872$	−11.0653	−0.374719
$873$	−26.8782	−0.909691
$874$	37.1875	1.25789
$875$	26.8732	0.908480
$876$	31.6850	1.07054
$877$	−31.5819	−1.06644	−0.533222	−	0.845975i	$-0.679019\pi$
$877$	−31.5819	−1.06644	−0.533222	+	0.845975i	$0.679019\pi$
$878$	−17.4953	−0.590439
$879$	14.3863	0.485237
$880$	12.2447	0.412770
$881$	−42.8466	−1.44354	−0.721770	−	0.692133i	$-0.756671\pi$
$881$	−42.8466	−1.44354	−0.721770	+	0.692133i	$0.756671\pi$
$882$	4.49479	0.151347
$883$	−19.2358	−0.647335	−0.323667	−	0.946171i	$-0.604916\pi$
$883$	−19.2358	−0.647335	−0.323667	+	0.946171i	$0.604916\pi$
$884$	−9.23544	−0.310622
$885$	−31.1564	−1.04731
$886$	−50.4321	−1.69430
$887$	43.0616	1.44587	0.722934	−	0.690917i	$-0.242793\pi$
$887$	43.0616	1.44587	0.722934	+	0.690917i	$0.242793\pi$
$888$	32.6695	1.09632
$889$	−13.6152	−0.456640
$890$	51.0903	1.71255
$891$	33.7455	1.13052
$892$	−80.5095	−2.69566
$893$	−18.6820	−0.625171
$894$	14.6973	0.491552
$895$	−4.93038	−0.164804
$896$	−29.1943	−0.975312
$897$	−9.97644	−0.333104
$898$	26.6242	0.888461
$899$	12.1617	0.405616
$900$	−0.979004	−0.0326335
$901$	28.4442	0.947613
$902$	14.4505	0.481149
$903$	51.5869	1.71670
$904$	14.4838	0.481725
$905$	−34.3775	−1.14275
$906$	73.5638	2.44399
$907$	40.9436	1.35951	0.679755	−	0.733439i	$-0.262086\pi$
$907$	40.9436	1.35951	0.679755	+	0.733439i	$0.262086\pi$
$908$	−13.9887	−0.464230
$909$	−19.7236	−0.654192
$910$	−11.1653	−0.370128
$911$	13.5368	0.448494	0.224247	−	0.974532i	$-0.428008\pi$
$911$	13.5368	0.448494	0.224247	+	0.974532i	$0.428008\pi$
$912$	14.0009	0.463615
$913$	22.8401	0.755898
$914$	64.6563	2.13864
$915$	46.1375	1.52526
$916$	−44.3240	−1.46451
$917$	8.91708	0.294468
$918$	24.6731	0.814334
$919$	−46.9114	−1.54747	−0.773733	−	0.633512i	$-0.781613\pi$
$919$	−46.9114	−1.54747	−0.773733	+	0.633512i	$0.781613\pi$
$920$	−17.4243	−0.574461
$921$	0.273143	0.00900035
$922$	−73.0014	−2.40417
$923$	−5.45532	−0.179564
$924$	40.8600	1.34420
$925$	2.37914	0.0782255
$926$	2.18373	0.0717617
$927$	4.63957	0.152384
$928$	15.7768	0.517898
$929$	−18.8745	−0.619253	−0.309626	−	0.950858i	$-0.600204\pi$
$929$	−18.8745	−0.619253	−0.309626	+	0.950858i	$0.600204\pi$
$930$	−57.1387	−1.87365
$931$	5.32218	0.174427
$932$	−78.5227	−2.57210
$933$	72.6666	2.37900
$934$	−62.8103	−2.05521
$935$	−21.8207	−0.713612
$936$	2.31957	0.0758175
$937$	49.9205	1.63083	0.815415	−	0.578876i	$-0.196509\pi$
$937$	49.9205	1.63083	0.815415	+	0.578876i	$0.196509\pi$
$938$	−20.6835	−0.675339
$939$	13.0628	0.426289
$940$	31.5295	1.02838
$941$	−8.74673	−0.285135	−0.142568	−	0.989785i	$-0.545536\pi$
$941$	−8.74673	−0.285135	−0.142568	+	0.989785i	$0.545536\pi$
$942$	39.9626	1.30205
$943$	10.5009	0.341957
$944$	12.7911	0.416315
$945$	17.3185	0.563372
$946$	−68.8513	−2.23855
$947$	37.0510	1.20400	0.601998	−	0.798498i	$-0.294371\pi$
$947$	37.0510	1.20400	0.601998	+	0.798498i	$0.294371\pi$
$948$	29.4938	0.957913
$949$	−5.46706	−0.177468
$950$	−1.99660	−0.0647783
$951$	−17.6258	−0.571555
$952$	13.1437	0.425989
$953$	0.596845	0.0193337	0.00966685	−	0.999953i	$-0.496923\pi$
$953$	0.596845	0.0193337	0.00966685	+	0.999953i	$0.496923\pi$
$954$	−25.7323	−0.833114
$955$	−5.41930	−0.175364
$956$	−18.9270	−0.612144
$957$	−13.3231	−0.430675
$958$	−56.1993	−1.81572
$959$	41.8931	1.35280
$960$	−57.0540	−1.84141
$961$	1.93412	0.0623910
$962$	−20.3038	−0.654622
$963$	27.2572	0.878353
$964$	−11.7881	−0.379668
$965$	−22.0762	−0.710659
$966$	51.1411	1.64544
$967$	40.5001	1.30239	0.651197	−	0.758909i	$-0.274267\pi$
$967$	40.5001	1.30239	0.651197	+	0.758909i	$0.274267\pi$
$968$	3.32360	0.106824
$969$	−24.9502	−0.801515
$970$	92.5127	2.97040
$971$	55.5060	1.78127	0.890636	−	0.454716i	$-0.150259\pi$
$971$	55.5060	1.78127	0.890636	+	0.454716i	$0.150259\pi$
$972$	−36.9862	−1.18633
$973$	−14.7462	−0.472743
$974$	−5.96919	−0.191265
$975$	0.535637	0.0171541
$976$	−18.9415	−0.606303
$977$	35.1795	1.12549	0.562746	−	0.826630i	$-0.309745\pi$
$977$	35.1795	1.12549	0.562746	+	0.826630i	$0.309745\pi$
$978$	92.7686	2.96641
$979$	32.2600	1.03103
$980$	−8.98221	−0.286926
$981$	9.10976	0.290852
$982$	−59.8927	−1.91125
$983$	−24.2502	−0.773462	−0.386731	−	0.922193i	$-0.626396\pi$
$983$	−24.2502	−0.773462	−0.386731	+	0.922193i	$0.626396\pi$
$984$	−7.74188	−0.246802
$985$	18.0104	0.573860
$986$	−15.4368	−0.491609
$987$	−25.6920	−0.817784
$988$	9.89290	0.314735
$989$	−50.0330	−1.59096
$990$	19.7403	0.627387
$991$	−22.2492	−0.706768	−0.353384	−	0.935478i	$-0.614969\pi$
$991$	−22.2492	−0.706768	−0.353384	+	0.935478i	$0.614969\pi$
$992$	42.7237	1.35648
$993$	60.0011	1.90408
$994$	27.9650	0.886996
$995$	16.4307	0.520887
$996$	−44.0755	−1.39659
$997$	−14.6775	−0.464841	−0.232420	−	0.972615i	$-0.574665\pi$
$997$	−14.6775	−0.464841	−0.232420	+	0.972615i	$0.574665\pi$
$998$	22.2214	0.703406
$999$	31.4932	0.996402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.18	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.18	✓	108	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)

\(f(q)\)	\(=\)	\(q-2.18373 q^{2} +2.09330 q^{3} +2.76866 q^{4} +2.17810 q^{5} -4.57119 q^{6} -2.34745 q^{7} -1.67854 q^{8} +1.38190 q^{9} +O(q^{10})\)	\(q-2.18373 q^{2} +2.09330 q^{3} +2.76866 q^{4} +2.17810 q^{5} -4.57119 q^{6} -2.34745 q^{7} -1.67854 q^{8} +1.38190 q^{9} -4.75637 q^{10} -3.00332 q^{11} +5.79563 q^{12} -1.00000 q^{13} +5.12619 q^{14} +4.55941 q^{15} -1.87184 q^{16} +3.33571 q^{17} -3.01768 q^{18} -3.57317 q^{19} +6.03042 q^{20} -4.91391 q^{21} +6.55844 q^{22} +4.76590 q^{23} -3.51369 q^{24} -0.255882 q^{25} +2.18373 q^{26} -3.38717 q^{27} -6.49929 q^{28} +2.11920 q^{29} -9.95651 q^{30} +5.73883 q^{31} +7.44468 q^{32} -6.28685 q^{33} -7.28428 q^{34} -5.11298 q^{35} +3.82600 q^{36} -9.29779 q^{37} +7.80283 q^{38} -2.09330 q^{39} -3.65603 q^{40} +2.20335 q^{41} +10.7306 q^{42} -10.4981 q^{43} -8.31518 q^{44} +3.00991 q^{45} -10.4074 q^{46} +5.22842 q^{47} -3.91833 q^{48} -1.48948 q^{49} +0.558776 q^{50} +6.98263 q^{51} -2.76866 q^{52} +8.52718 q^{53} +7.39666 q^{54} -6.54154 q^{55} +3.94029 q^{56} -7.47972 q^{57} -4.62775 q^{58} -6.83343 q^{59} +12.6235 q^{60} +10.1192 q^{61} -12.5320 q^{62} -3.24393 q^{63} -12.5134 q^{64} -2.17810 q^{65} +13.7288 q^{66} -4.03486 q^{67} +9.23544 q^{68} +9.97644 q^{69} +11.1653 q^{70} +5.45532 q^{71} -2.31957 q^{72} +5.46706 q^{73} +20.3038 q^{74} -0.535637 q^{75} -9.89290 q^{76} +7.05015 q^{77} +4.57119 q^{78} +5.08897 q^{79} -4.07706 q^{80} -11.2361 q^{81} -4.81151 q^{82} -7.60495 q^{83} -13.6049 q^{84} +7.26551 q^{85} +22.9251 q^{86} +4.43612 q^{87} +5.04120 q^{88} -10.7414 q^{89} -6.57281 q^{90} +2.34745 q^{91} +13.1951 q^{92} +12.0131 q^{93} -11.4174 q^{94} -7.78273 q^{95} +15.5839 q^{96} -19.4503 q^{97} +3.25262 q^{98} -4.15028 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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