LMFDB - Embedded newform 6019.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.33535 q^{2} -1.90450 q^{3} +3.45386 q^{4} -1.81837 q^{5} +4.44767 q^{6} +2.51906 q^{7} -3.39528 q^{8} +0.627108 q^{9} +O(q^{10})$	\(q-2.33535 q^{2} -1.90450 q^{3} +3.45386 q^{4} -1.81837 q^{5} +4.44767 q^{6} +2.51906 q^{7} -3.39528 q^{8} +0.627108 q^{9} +4.24653 q^{10} +3.56949 q^{11} -6.57787 q^{12} +1.00000 q^{13} -5.88290 q^{14} +3.46307 q^{15} +1.02144 q^{16} +6.66281 q^{17} -1.46452 q^{18} -5.56778 q^{19} -6.28039 q^{20} -4.79755 q^{21} -8.33601 q^{22} -5.39935 q^{23} +6.46630 q^{24} -1.69354 q^{25} -2.33535 q^{26} +4.51917 q^{27} +8.70050 q^{28} -9.17154 q^{29} -8.08749 q^{30} +6.39662 q^{31} +4.40513 q^{32} -6.79808 q^{33} -15.5600 q^{34} -4.58058 q^{35} +2.16595 q^{36} +4.50512 q^{37} +13.0027 q^{38} -1.90450 q^{39} +6.17387 q^{40} +6.58635 q^{41} +11.2040 q^{42} -2.59754 q^{43} +12.3285 q^{44} -1.14031 q^{45} +12.6094 q^{46} +0.401509 q^{47} -1.94534 q^{48} -0.654322 q^{49} +3.95501 q^{50} -12.6893 q^{51} +3.45386 q^{52} +12.0446 q^{53} -10.5538 q^{54} -6.49065 q^{55} -8.55292 q^{56} +10.6038 q^{57} +21.4188 q^{58} +8.60083 q^{59} +11.9610 q^{60} +8.40005 q^{61} -14.9384 q^{62} +1.57972 q^{63} -12.3304 q^{64} -1.81837 q^{65} +15.8759 q^{66} +1.71282 q^{67} +23.0124 q^{68} +10.2830 q^{69} +10.6973 q^{70} +7.47139 q^{71} -2.12921 q^{72} -10.7382 q^{73} -10.5210 q^{74} +3.22534 q^{75} -19.2304 q^{76} +8.99177 q^{77} +4.44767 q^{78} +6.50693 q^{79} -1.85736 q^{80} -10.4881 q^{81} -15.3814 q^{82} -7.37508 q^{83} -16.5701 q^{84} -12.1154 q^{85} +6.06618 q^{86} +17.4672 q^{87} -12.1194 q^{88} +10.5981 q^{89} +2.66303 q^{90} +2.51906 q^{91} -18.6486 q^{92} -12.1823 q^{93} -0.937664 q^{94} +10.1243 q^{95} -8.38956 q^{96} -14.8977 q^{97} +1.52807 q^{98} +2.23846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.33535	−1.65134	−0.825671	−	0.564152i	$-0.809203\pi$
$2$	−2.33535	−1.65134	−0.825671	+	0.564152i	$0.809203\pi$
$3$	−1.90450	−1.09956	−0.549781	−	0.835309i	$-0.685289\pi$
$3$	−1.90450	−1.09956	−0.549781	+	0.835309i	$0.685289\pi$
$4$	3.45386	1.72693
$5$	−1.81837	−0.813199	−0.406599	−	0.913607i	$-0.633285\pi$
$5$	−1.81837	−0.813199	−0.406599	+	0.913607i	$0.633285\pi$
$6$	4.44767	1.81575
$7$	2.51906	0.952116	0.476058	−	0.879414i	$-0.342065\pi$
$7$	2.51906	0.952116	0.476058	+	0.879414i	$0.342065\pi$
$8$	−3.39528	−1.20041
$9$	0.627108	0.209036
$10$	4.24653	1.34287
$11$	3.56949	1.07624	0.538121	−	0.842868i	$-0.319134\pi$
$11$	3.56949	1.07624	0.538121	+	0.842868i	$0.319134\pi$
$12$	−6.57787	−1.89887
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−5.88290	−1.57227
$15$	3.46307	0.894162
$16$	1.02144	0.255361
$17$	6.66281	1.61597	0.807984	−	0.589204i	$-0.200559\pi$
$17$	6.66281	1.61597	0.807984	+	0.589204i	$0.200559\pi$
$18$	−1.46452	−0.345190
$19$	−5.56778	−1.27734	−0.638668	−	0.769482i	$-0.720514\pi$
$19$	−5.56778	−1.27734	−0.638668	+	0.769482i	$0.720514\pi$
$20$	−6.28039	−1.40434
$21$	−4.79755	−1.04691
$22$	−8.33601	−1.77724
$23$	−5.39935	−1.12584	−0.562921	−	0.826510i	$-0.690323\pi$
$23$	−5.39935	−1.12584	−0.562921	+	0.826510i	$0.690323\pi$
$24$	6.46630	1.31993
$25$	−1.69354	−0.338708
$26$	−2.33535	−0.458000
$27$	4.51917	0.869714
$28$	8.70050	1.64424
$29$	−9.17154	−1.70311	−0.851556	−	0.524264i	$-0.824340\pi$
$29$	−9.17154	−1.70311	−0.851556	+	0.524264i	$0.824340\pi$
$30$	−8.08749	−1.47657
$31$	6.39662	1.14887	0.574434	−	0.818551i	$-0.305222\pi$
$31$	6.39662	1.14887	0.574434	+	0.818551i	$0.305222\pi$
$32$	4.40513	0.778724
$33$	−6.79808	−1.18339
$34$	−15.5600	−2.66852
$35$	−4.58058	−0.774260
$36$	2.16595	0.360991
$37$	4.50512	0.740637	0.370319	−	0.928905i	$-0.379249\pi$
$37$	4.50512	0.740637	0.370319	+	0.928905i	$0.379249\pi$
$38$	13.0027	2.10932
$39$	−1.90450	−0.304964
$40$	6.17387	0.976174
$41$	6.58635	1.02861	0.514307	−	0.857606i	$-0.328049\pi$
$41$	6.58635	1.02861	0.514307	+	0.857606i	$0.328049\pi$
$42$	11.2040	1.72881
$43$	−2.59754	−0.396122	−0.198061	−	0.980190i	$-0.563464\pi$
$43$	−2.59754	−0.396122	−0.198061	+	0.980190i	$0.563464\pi$
$44$	12.3285	1.85860
$45$	−1.14031	−0.169988
$46$	12.6094	1.85915
$47$	0.401509	0.0585661	0.0292830	−	0.999571i	$-0.490678\pi$
$47$	0.401509	0.0585661	0.0292830	+	0.999571i	$0.490678\pi$
$48$	−1.94534	−0.280785
$49$	−0.654322	−0.0934746
$50$	3.95501	0.559323
$51$	−12.6893	−1.77686
$52$	3.45386	0.478965
$53$	12.0446	1.65446	0.827229	−	0.561865i	$-0.189916\pi$
$53$	12.0446	1.65446	0.827229	+	0.561865i	$0.189916\pi$
$54$	−10.5538	−1.43620
$55$	−6.49065	−0.875198
$56$	−8.55292	−1.14293
$57$	10.6038	1.40451
$58$	21.4188	2.81242
$59$	8.60083	1.11973	0.559867	−	0.828583i	$-0.310852\pi$
$59$	8.60083	1.11973	0.559867	+	0.828583i	$0.310852\pi$
$60$	11.9610	1.54416
$61$	8.40005	1.07552	0.537758	−	0.843099i	$-0.319271\pi$
$61$	8.40005	1.07552	0.537758	+	0.843099i	$0.319271\pi$
$62$	−14.9384	−1.89717
$63$	1.57972	0.199027
$64$	−12.3304	−1.54130
$65$	−1.81837	−0.225541
$66$	15.8759	1.95419
$67$	1.71282	0.209254	0.104627	−	0.994512i	$-0.466635\pi$
$67$	1.71282	0.209254	0.104627	+	0.994512i	$0.466635\pi$
$68$	23.0124	2.79067
$69$	10.2830	1.23793
$70$	10.6973	1.27857
$71$	7.47139	0.886691	0.443345	−	0.896351i	$-0.353792\pi$
$71$	7.47139	0.886691	0.443345	+	0.896351i	$0.353792\pi$
$72$	−2.12921	−0.250930
$73$	−10.7382	−1.25681	−0.628404	−	0.777888i	$-0.716291\pi$
$73$	−10.7382	−1.25681	−0.628404	+	0.777888i	$0.716291\pi$
$74$	−10.5210	−1.22305
$75$	3.22534	0.372430
$76$	−19.2304	−2.20587
$77$	8.99177	1.02471
$78$	4.44767	0.503599
$79$	6.50693	0.732086	0.366043	−	0.930598i	$-0.380712\pi$
$79$	6.50693	0.732086	0.366043	+	0.930598i	$0.380712\pi$
$80$	−1.85736	−0.207659
$81$	−10.4881	−1.16534
$82$	−15.3814	−1.69859
$83$	−7.37508	−0.809520	−0.404760	−	0.914423i	$-0.632645\pi$
$83$	−7.37508	−0.809520	−0.404760	+	0.914423i	$0.632645\pi$
$84$	−16.5701	−1.80794
$85$	−12.1154	−1.31410
$86$	6.06618	0.654133
$87$	17.4672	1.87268
$88$	−12.1194	−1.29193
$89$	10.5981	1.12340	0.561698	−	0.827342i	$-0.310148\pi$
$89$	10.5981	1.12340	0.561698	+	0.827342i	$0.310148\pi$
$90$	2.66303	0.280708
$91$	2.51906	0.264070
$92$	−18.6486	−1.94425
$93$	−12.1823	−1.26325
$94$	−0.937664	−0.0967126
$95$	10.1243	1.03873
$96$	−8.38956	−0.856255
$97$	−14.8977	−1.51263	−0.756314	−	0.654208i	$-0.773002\pi$
$97$	−14.8977	−1.51263	−0.756314	+	0.654208i	$0.773002\pi$
$98$	1.52807	0.154359
$99$	2.23846	0.224973
$100$	−5.84926	−0.584926
$101$	7.67153	0.763345	0.381673	−	0.924298i	$-0.375348\pi$
$101$	7.67153	0.763345	0.381673	+	0.924298i	$0.375348\pi$
$102$	29.6340	2.93420
$103$	−17.7267	−1.74666	−0.873331	−	0.487128i	$-0.838045\pi$
$103$	−17.7267	−1.74666	−0.873331	+	0.487128i	$0.838045\pi$
$104$	−3.39528	−0.332935
$105$	8.72370	0.851346
$106$	−28.1285	−2.73208
$107$	16.0552	1.55212	0.776059	−	0.630660i	$-0.217216\pi$
$107$	16.0552	1.55212	0.776059	+	0.630660i	$0.217216\pi$
$108$	15.6086	1.50194
$109$	−5.05951	−0.484613	−0.242307	−	0.970200i	$-0.577904\pi$
$109$	−5.05951	−0.484613	−0.242307	+	0.970200i	$0.577904\pi$
$110$	15.1579	1.44525
$111$	−8.57999	−0.814376
$112$	2.57308	0.243133
$113$	2.85436	0.268515	0.134258	−	0.990946i	$-0.457135\pi$
$113$	2.85436	0.268515	0.134258	+	0.990946i	$0.457135\pi$
$114$	−24.7636	−2.31933
$115$	9.81801	0.915534
$116$	−31.6772	−2.94116
$117$	0.627108	0.0579762
$118$	−20.0860	−1.84906
$119$	16.7840	1.53859
$120$	−11.7581	−1.07336
$121$	1.74126	0.158297
$122$	−19.6171	−1.77604
$123$	−12.5437	−1.13103
$124$	22.0931	1.98402
$125$	12.1713	1.08864
$126$	−3.68921	−0.328661
$127$	−11.6072	−1.02997	−0.514985	−	0.857199i	$-0.672203\pi$
$127$	−11.6072	−1.02997	−0.514985	+	0.857199i	$0.672203\pi$
$128$	19.9856	1.76649
$129$	4.94702	0.435560
$130$	4.24653	0.372445
$131$	−17.7447	−1.55036	−0.775181	−	0.631739i	$-0.782341\pi$
$131$	−17.7447	−1.55036	−0.775181	+	0.631739i	$0.782341\pi$
$132$	−23.4797	−2.04364
$133$	−14.0256	−1.21617
$134$	−4.00003	−0.345550
$135$	−8.21750	−0.707250
$136$	−22.6221	−1.93983
$137$	15.0217	1.28339	0.641697	−	0.766959i	$-0.278231\pi$
$137$	15.0217	1.28339	0.641697	+	0.766959i	$0.278231\pi$
$138$	−24.0145	−2.04425
$139$	19.6651	1.66798	0.833988	−	0.551783i	$-0.186052\pi$
$139$	19.6651	1.66798	0.833988	+	0.551783i	$0.186052\pi$
$140$	−15.8207	−1.33709
$141$	−0.764672	−0.0643970
$142$	−17.4483	−1.46423
$143$	3.56949	0.298496
$144$	0.640556	0.0533797
$145$	16.6772	1.38497
$146$	25.0774	2.07542
$147$	1.24615	0.102781
$148$	15.5601	1.27903
$149$	−10.0579	−0.823975	−0.411988	−	0.911189i	$-0.635165\pi$
$149$	−10.0579	−0.823975	−0.411988	+	0.911189i	$0.635165\pi$
$150$	−7.53230	−0.615010
$151$	−13.2589	−1.07900	−0.539498	−	0.841987i	$-0.681386\pi$
$151$	−13.2589	−1.07900	−0.539498	+	0.841987i	$0.681386\pi$
$152$	18.9042	1.53333
$153$	4.17830	0.337795
$154$	−20.9989	−1.69214
$155$	−11.6314	−0.934258
$156$	−6.57787	−0.526651
$157$	7.90092	0.630562	0.315281	−	0.948998i	$-0.397901\pi$
$157$	7.90092	0.630562	0.315281	+	0.948998i	$0.397901\pi$
$158$	−15.1960	−1.20893
$159$	−22.9390	−1.81918
$160$	−8.01014	−0.633258
$161$	−13.6013	−1.07193
$162$	24.4933	1.92438
$163$	15.2603	1.19528	0.597639	−	0.801765i	$-0.296105\pi$
$163$	15.2603	1.19528	0.597639	+	0.801765i	$0.296105\pi$
$164$	22.7483	1.77635
$165$	12.3614	0.962335
$166$	17.2234	1.33680
$167$	19.6730	1.52234	0.761172	−	0.648550i	$-0.224624\pi$
$167$	19.6730	1.52234	0.761172	+	0.648550i	$0.224624\pi$
$168$	16.2890	1.25673
$169$	1.00000	0.0769231
$170$	28.2938	2.17003
$171$	−3.49160	−0.267009
$172$	−8.97156	−0.684075
$173$	−22.7680	−1.73102	−0.865509	−	0.500894i	$-0.833005\pi$
$173$	−22.7680	−1.73102	−0.865509	+	0.500894i	$0.833005\pi$
$174$	−40.7919	−3.09243
$175$	−4.26613	−0.322489
$176$	3.64604	0.274830
$177$	−16.3803	−1.23122
$178$	−24.7503	−1.85511
$179$	−13.4276	−1.00363	−0.501815	−	0.864975i	$-0.667334\pi$
$179$	−13.4276	−1.00363	−0.501815	+	0.864975i	$0.667334\pi$
$180$	−3.93848	−0.293557
$181$	20.9386	1.55636	0.778179	−	0.628043i	$-0.216144\pi$
$181$	20.9386	1.55636	0.778179	+	0.628043i	$0.216144\pi$
$182$	−5.88290	−0.436069
$183$	−15.9979	−1.18260
$184$	18.3323	1.35148
$185$	−8.19196	−0.602285
$186$	28.4501	2.08606
$187$	23.7828	1.73917
$188$	1.38676	0.101140
$189$	11.3841	0.828069
$190$	−23.6437	−1.71530
$191$	−4.43016	−0.320555	−0.160278	−	0.987072i	$-0.551239\pi$
$191$	−4.43016	−0.320555	−0.160278	+	0.987072i	$0.551239\pi$
$192$	23.4832	1.69476
$193$	−1.26388	−0.0909759	−0.0454879	−	0.998965i	$-0.514484\pi$
$193$	−1.26388	−0.0909759	−0.0454879	+	0.998965i	$0.514484\pi$
$194$	34.7913	2.49787
$195$	3.46307	0.247996
$196$	−2.25994	−0.161424
$197$	−9.60215	−0.684125	−0.342062	−	0.939677i	$-0.611125\pi$
$197$	−9.60215	−0.684125	−0.342062	+	0.939677i	$0.611125\pi$
$198$	−5.22758	−0.371508
$199$	−3.53220	−0.250391	−0.125195	−	0.992132i	$-0.539956\pi$
$199$	−3.53220	−0.250391	−0.125195	+	0.992132i	$0.539956\pi$
$200$	5.75004	0.406589
$201$	−3.26206	−0.230088
$202$	−17.9157	−1.26054
$203$	−23.1037	−1.62156
$204$	−43.8271	−3.06851
$205$	−11.9764	−0.836468
$206$	41.3980	2.88434
$207$	−3.38598	−0.235342
$208$	1.02144	0.0708244
$209$	−19.8741	−1.37472
$210$	−20.3729	−1.40586
$211$	−11.3359	−0.780395	−0.390197	−	0.920731i	$-0.627593\pi$
$211$	−11.3359	−0.780395	−0.390197	+	0.920731i	$0.627593\pi$
$212$	41.6005	2.85714
$213$	−14.2292	−0.974971
$214$	−37.4946	−2.56308
$215$	4.72329	0.322126
$216$	−15.3438	−1.04402
$217$	16.1135	1.09386
$218$	11.8157	0.800262
$219$	20.4508	1.38194
$220$	−22.4178	−1.51141
$221$	6.66281	0.448189
$222$	20.0373	1.34481
$223$	−17.5784	−1.17713	−0.588567	−	0.808448i	$-0.700308\pi$
$223$	−17.5784	−1.17713	−0.588567	+	0.808448i	$0.700308\pi$
$224$	11.0968	0.741436
$225$	−1.06203	−0.0708022
$226$	−6.66593	−0.443411
$227$	2.99115	0.198529	0.0992647	−	0.995061i	$-0.468351\pi$
$227$	2.99115	0.198529	0.0992647	+	0.995061i	$0.468351\pi$
$228$	36.6241	2.42549
$229$	3.65295	0.241394	0.120697	−	0.992689i	$-0.461487\pi$
$229$	3.65295	0.241394	0.120697	+	0.992689i	$0.461487\pi$
$230$	−22.9285	−1.51186
$231$	−17.1248	−1.12673
$232$	31.1399	2.04444
$233$	−19.5185	−1.27870	−0.639351	−	0.768915i	$-0.720797\pi$
$233$	−19.5185	−1.27870	−0.639351	+	0.768915i	$0.720797\pi$
$234$	−1.46452	−0.0957385
$235$	−0.730091	−0.0476259
$236$	29.7061	1.93370
$237$	−12.3924	−0.804974
$238$	−39.1966	−2.54074
$239$	−4.20923	−0.272272	−0.136136	−	0.990690i	$-0.543468\pi$
$239$	−4.20923	−0.272272	−0.136136	+	0.990690i	$0.543468\pi$
$240$	3.53734	0.228334
$241$	−7.80043	−0.502470	−0.251235	−	0.967926i	$-0.580837\pi$
$241$	−7.80043	−0.502470	−0.251235	+	0.967926i	$0.580837\pi$
$242$	−4.06646	−0.261402
$243$	6.41698	0.411649
$244$	29.0126	1.85734
$245$	1.18980	0.0760134
$246$	29.2939	1.86771
$247$	−5.56778	−0.354269
$248$	−21.7183	−1.37912
$249$	14.0458	0.890118
$250$	−28.4243	−1.79771
$251$	13.6154	0.859393	0.429697	−	0.902973i	$-0.358620\pi$
$251$	13.6154	0.859393	0.429697	+	0.902973i	$0.358620\pi$
$252$	5.45615	0.343705
$253$	−19.2729	−1.21168
$254$	27.1068	1.70083
$255$	23.0738	1.44494
$256$	−22.0125	−1.37578
$257$	0.987730	0.0616129	0.0308064	−	0.999525i	$-0.490192\pi$
$257$	0.987730	0.0616129	0.0308064	+	0.999525i	$0.490192\pi$
$258$	−11.5530	−0.719259
$259$	11.3487	0.705173
$260$	−6.28039	−0.389493
$261$	−5.75154	−0.356012
$262$	41.4401	2.56018
$263$	17.2559	1.06404	0.532021	−	0.846731i	$-0.321433\pi$
$263$	17.2559	1.06404	0.532021	+	0.846731i	$0.321433\pi$
$264$	23.0814	1.42056
$265$	−21.9016	−1.34540
$266$	32.7547	2.00832
$267$	−20.1840	−1.23524
$268$	5.91584	0.361368
$269$	16.2442	0.990423	0.495212	−	0.868772i	$-0.335090\pi$
$269$	16.2442	0.990423	0.495212	+	0.868772i	$0.335090\pi$
$270$	19.1908	1.16791
$271$	22.5760	1.37139	0.685697	−	0.727888i	$-0.259498\pi$
$271$	22.5760	1.37139	0.685697	+	0.727888i	$0.259498\pi$
$272$	6.80569	0.412655
$273$	−4.79755	−0.290361
$274$	−35.0810	−2.11932
$275$	−6.04508	−0.364532
$276$	35.5162	2.13783
$277$	−2.82704	−0.169860	−0.0849302	−	0.996387i	$-0.527067\pi$
$277$	−2.82704	−0.169860	−0.0849302	+	0.996387i	$0.527067\pi$
$278$	−45.9250	−2.75440
$279$	4.01137	0.240155
$280$	15.5524	0.929431
$281$	−30.0635	−1.79344	−0.896720	−	0.442598i	$-0.854057\pi$
$281$	−30.0635	−1.79344	−0.896720	+	0.442598i	$0.854057\pi$
$282$	1.78578	0.106342
$283$	22.1132	1.31449	0.657247	−	0.753675i	$-0.271721\pi$
$283$	22.1132	1.31449	0.657247	+	0.753675i	$0.271721\pi$
$284$	25.8052	1.53125
$285$	−19.2816	−1.14215
$286$	−8.33601	−0.492919
$287$	16.5914	0.979361
$288$	2.76249	0.162781
$289$	27.3930	1.61135
$290$	−38.9472	−2.28706
$291$	28.3726	1.66323
$292$	−37.0882	−2.17042
$293$	−4.32437	−0.252633	−0.126316	−	0.991990i	$-0.540315\pi$
$293$	−4.32437	−0.252633	−0.126316	+	0.991990i	$0.540315\pi$
$294$	−2.91021	−0.169727
$295$	−15.6395	−0.910565
$296$	−15.2961	−0.889070
$297$	16.1311	0.936022
$298$	23.4887	1.36067
$299$	−5.39935	−0.312253
$300$	11.1399	0.643162
$301$	−6.54338	−0.377154
$302$	30.9642	1.78179
$303$	−14.6104	−0.839345
$304$	−5.68718	−0.326182
$305$	−15.2744	−0.874608
$306$	−9.75779	−0.557816
$307$	−30.4909	−1.74020	−0.870102	−	0.492871i	$-0.835948\pi$
$307$	−30.4909	−1.74020	−0.870102	+	0.492871i	$0.835948\pi$
$308$	31.0563	1.76960
$309$	33.7604	1.92056
$310$	27.1634	1.54278
$311$	9.71507	0.550891	0.275446	−	0.961317i	$-0.411175\pi$
$311$	9.71507	0.550891	0.275446	+	0.961317i	$0.411175\pi$
$312$	6.46630	0.366082
$313$	3.75098	0.212018	0.106009	−	0.994365i	$-0.466193\pi$
$313$	3.75098	0.212018	0.106009	+	0.994365i	$0.466193\pi$
$314$	−18.4514	−1.04127
$315$	−2.87252	−0.161848
$316$	22.4740	1.26426
$317$	5.50271	0.309063	0.154531	−	0.987988i	$-0.450613\pi$
$317$	5.50271	0.309063	0.154531	+	0.987988i	$0.450613\pi$
$318$	53.5706	3.00409
$319$	−32.7377	−1.83296
$320$	22.4212	1.25338
$321$	−30.5771	−1.70665
$322$	31.7638	1.77013
$323$	−37.0970	−2.06413
$324$	−36.2243	−2.01246
$325$	−1.69354	−0.0939407
$326$	−35.6381	−1.97381
$327$	9.63582	0.532862
$328$	−22.3625	−1.23476
$329$	1.01143	0.0557617
$330$	−28.8682	−1.58914
$331$	1.66101	0.0912975	0.0456488	−	0.998958i	$-0.485464\pi$
$331$	1.66101	0.0912975	0.0456488	+	0.998958i	$0.485464\pi$
$332$	−25.4725	−1.39799
$333$	2.82520	0.154820
$334$	−45.9434	−2.51391
$335$	−3.11453	−0.170165
$336$	−4.90043	−0.267340
$337$	15.2802	0.832364	0.416182	−	0.909281i	$-0.363368\pi$
$337$	15.2802	0.832364	0.416182	+	0.909281i	$0.363368\pi$
$338$	−2.33535	−0.127026
$339$	−5.43612	−0.295249
$340$	−41.8450	−2.26937
$341$	22.8327	1.23646
$342$	8.15411	0.440924
$343$	−19.2817	−1.04111
$344$	8.81939	0.475510
$345$	−18.6984	−1.00669
$346$	53.1712	2.85850
$347$	−13.6808	−0.734422	−0.367211	−	0.930138i	$-0.619687\pi$
$347$	−13.6808	−0.734422	−0.367211	+	0.930138i	$0.619687\pi$
$348$	60.3292	3.23398
$349$	−13.2245	−0.707893	−0.353947	−	0.935266i	$-0.615161\pi$
$349$	−13.2245	−0.707893	−0.353947	+	0.935266i	$0.615161\pi$
$350$	9.96292	0.532540
$351$	4.51917	0.241215
$352$	15.7241	0.838096
$353$	−18.4548	−0.982247	−0.491124	−	0.871090i	$-0.663414\pi$
$353$	−18.4548	−0.982247	−0.491124	+	0.871090i	$0.663414\pi$
$354$	38.2536	2.03316
$355$	−13.5857	−0.721056
$356$	36.6044	1.94003
$357$	−31.9651	−1.69177
$358$	31.3583	1.65734
$359$	−21.2946	−1.12389	−0.561943	−	0.827176i	$-0.689946\pi$
$359$	−21.2946	−1.12389	−0.561943	+	0.827176i	$0.689946\pi$
$360$	3.87168	0.204056
$361$	12.0002	0.631588
$362$	−48.8991	−2.57008
$363$	−3.31623	−0.174057
$364$	8.70050	0.456030
$365$	19.5259	1.02203
$366$	37.3606	1.95287
$367$	−12.9955	−0.678360	−0.339180	−	0.940722i	$-0.610150\pi$
$367$	−12.9955	−0.678360	−0.339180	+	0.940722i	$0.610150\pi$
$368$	−5.51514	−0.287496
$369$	4.13035	0.215017
$370$	19.1311	0.994579
$371$	30.3412	1.57524
$372$	−42.0762	−2.18155
$373$	−30.8173	−1.59566	−0.797830	−	0.602882i	$-0.794019\pi$
$373$	−30.8173	−1.59566	−0.797830	+	0.602882i	$0.794019\pi$
$374$	−55.5412	−2.87197
$375$	−23.1802	−1.19702
$376$	−1.36323	−0.0703035
$377$	−9.17154	−0.472358
$378$	−26.5858	−1.36742
$379$	26.9707	1.38539	0.692695	−	0.721230i	$-0.256423\pi$
$379$	26.9707	1.38539	0.692695	+	0.721230i	$0.256423\pi$
$380$	34.9678	1.79381
$381$	22.1058	1.13252
$382$	10.3460	0.529347
$383$	−19.1042	−0.976178	−0.488089	−	0.872794i	$-0.662306\pi$
$383$	−19.1042	−0.976178	−0.488089	+	0.872794i	$0.662306\pi$
$384$	−38.0625	−1.94237
$385$	−16.3503	−0.833291
$386$	2.95160	0.150232
$387$	−1.62894	−0.0828037
$388$	−51.4545	−2.61221
$389$	7.90435	0.400767	0.200383	−	0.979718i	$-0.435781\pi$
$389$	7.90435	0.400767	0.200383	+	0.979718i	$0.435781\pi$
$390$	−8.08749	−0.409526
$391$	−35.9748	−1.81933
$392$	2.22161	0.112208
$393$	33.7947	1.70472
$394$	22.4244	1.12972
$395$	−11.8320	−0.595332
$396$	7.73132	0.388514
$397$	35.1006	1.76165	0.880825	−	0.473441i	$-0.156988\pi$
$397$	35.1006	1.76165	0.880825	+	0.473441i	$0.156988\pi$
$398$	8.24892	0.413481
$399$	26.7117	1.33726
$400$	−1.72986	−0.0864928
$401$	27.8052	1.38853	0.694263	−	0.719722i	$-0.255731\pi$
$401$	27.8052	1.38853	0.694263	+	0.719722i	$0.255731\pi$
$402$	7.61805	0.379954
$403$	6.39662	0.318639
$404$	26.4964	1.31825
$405$	19.0711	0.947653
$406$	53.9552	2.67775
$407$	16.0810	0.797105
$408$	43.0837	2.13296
$409$	14.3369	0.708912	0.354456	−	0.935073i	$-0.384666\pi$
$409$	14.3369	0.708912	0.354456	+	0.935073i	$0.384666\pi$
$410$	27.9691	1.38129
$411$	−28.6088	−1.41117
$412$	−61.2255	−3.01636
$413$	21.6660	1.06612
$414$	7.90744	0.388630
$415$	13.4106	0.658301
$416$	4.40513	0.215979
$417$	−37.4522	−1.83404
$418$	46.4131	2.27014
$419$	29.7875	1.45521	0.727607	−	0.685994i	$-0.240632\pi$
$419$	29.7875	1.45521	0.727607	+	0.685994i	$0.240632\pi$
$420$	30.1305	1.47022
$421$	3.74341	0.182443	0.0912213	−	0.995831i	$-0.470923\pi$
$421$	3.74341	0.182443	0.0912213	+	0.995831i	$0.470923\pi$
$422$	26.4733	1.28870
$423$	0.251789	0.0122424
$424$	−40.8949	−1.98603
$425$	−11.2837	−0.547341
$426$	33.2303	1.61001
$427$	21.1602	1.02402
$428$	55.4526	2.68040
$429$	−6.79808	−0.328215
$430$	−11.0305	−0.531940
$431$	14.1323	0.680731	0.340366	−	0.940293i	$-0.389449\pi$
$431$	14.1323	0.680731	0.340366	+	0.940293i	$0.389449\pi$
$432$	4.61608	0.222091
$433$	7.68924	0.369521	0.184761	−	0.982784i	$-0.440849\pi$
$433$	7.68924	0.369521	0.184761	+	0.982784i	$0.440849\pi$
$434$	−37.6307	−1.80633
$435$	−31.7617	−1.52286
$436$	−17.4749	−0.836894
$437$	30.0624	1.43808
$438$	−47.7598	−2.28205
$439$	−16.5993	−0.792244	−0.396122	−	0.918198i	$-0.629644\pi$
$439$	−16.5993	−0.792244	−0.396122	+	0.918198i	$0.629644\pi$
$440$	22.0376	1.05060
$441$	−0.410331	−0.0195396
$442$	−15.5600	−0.740113
$443$	12.6876	0.602808	0.301404	−	0.953497i	$-0.402545\pi$
$443$	12.6876	0.602808	0.301404	+	0.953497i	$0.402545\pi$
$444$	−29.6341	−1.40637
$445$	−19.2712	−0.913544
$446$	41.0517	1.94385
$447$	19.1552	0.906012
$448$	−31.0611	−1.46750
$449$	−7.45279	−0.351719	−0.175859	−	0.984415i	$-0.556270\pi$
$449$	−7.45279	−0.351719	−0.175859	+	0.984415i	$0.556270\pi$
$450$	2.48022	0.116919
$451$	23.5099	1.10704
$452$	9.85856	0.463708
$453$	25.2516	1.18642
$454$	−6.98538	−0.327840
$455$	−4.58058	−0.214741
$456$	−36.0029	−1.68599
$457$	−1.00665	−0.0470889	−0.0235445	−	0.999723i	$-0.507495\pi$
$457$	−1.00665	−0.0470889	−0.0235445	+	0.999723i	$0.507495\pi$
$458$	−8.53093	−0.398624
$459$	30.1103	1.40543
$460$	33.9100	1.58106
$461$	−6.14344	−0.286129	−0.143064	−	0.989713i	$-0.545696\pi$
$461$	−6.14344	−0.286129	−0.143064	+	0.989713i	$0.545696\pi$
$462$	39.9924	1.86062
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−9.36821	−0.434908
$465$	22.1520	1.02727
$466$	45.5827	2.11158
$467$	−8.93000	−0.413231	−0.206616	−	0.978422i	$-0.566245\pi$
$467$	−8.93000	−0.413231	−0.206616	+	0.978422i	$0.566245\pi$
$468$	2.16595	0.100121
$469$	4.31470	0.199234
$470$	1.70502	0.0786466
$471$	−15.0473	−0.693342
$472$	−29.2022	−1.34414
$473$	−9.27191	−0.426323
$474$	28.9407	1.32929
$475$	9.42926	0.432644
$476$	57.9697	2.65704
$477$	7.55329	0.345841
$478$	9.83002	0.449615
$479$	29.7555	1.35956	0.679781	−	0.733415i	$-0.262075\pi$
$479$	29.7555	1.35956	0.679781	+	0.733415i	$0.262075\pi$
$480$	15.2553	0.696306
$481$	4.50512	0.205416
$482$	18.2167	0.829750
$483$	25.9036	1.17866
$484$	6.01409	0.273368
$485$	27.0894	1.23007
$486$	−14.9859	−0.679774
$487$	10.0993	0.457642	0.228821	−	0.973468i	$-0.426513\pi$
$487$	10.0993	0.457642	0.228821	+	0.973468i	$0.426513\pi$
$488$	−28.5205	−1.29106
$489$	−29.0632	−1.31428
$490$	−2.77860	−0.125524
$491$	25.2044	1.13746	0.568729	−	0.822525i	$-0.307435\pi$
$491$	25.2044	1.13746	0.568729	+	0.822525i	$0.307435\pi$
$492$	−43.3241	−1.95320
$493$	−61.1082	−2.75217
$494$	13.0027	0.585020
$495$	−4.07034	−0.182948
$496$	6.53379	0.293376
$497$	18.8209	0.844233
$498$	−32.8019	−1.46989
$499$	15.5288	0.695163	0.347582	−	0.937650i	$-0.387003\pi$
$499$	15.5288	0.695163	0.347582	+	0.937650i	$0.387003\pi$
$500$	42.0381	1.88000
$501$	−37.4672	−1.67391
$502$	−31.7966	−1.41915
$503$	3.01400	0.134388	0.0671938	−	0.997740i	$-0.478595\pi$
$503$	3.01400	0.134388	0.0671938	+	0.997740i	$0.478595\pi$
$504$	−5.36361	−0.238914
$505$	−13.9497	−0.620751
$506$	45.0091	2.00090
$507$	−1.90450	−0.0845817
$508$	−40.0896	−1.77869
$509$	−13.7612	−0.609953	−0.304977	−	0.952360i	$-0.598649\pi$
$509$	−13.7612	−0.609953	−0.304977	+	0.952360i	$0.598649\pi$
$510$	−53.8854	−2.38609
$511$	−27.0501	−1.19663
$512$	11.4358	0.505395
$513$	−25.1617	−1.11092
$514$	−2.30670	−0.101744
$515$	32.2336	1.42038
$516$	17.0863	0.752183
$517$	1.43318	0.0630313
$518$	−26.5031	−1.16448
$519$	43.3615	1.90336
$520$	6.17387	0.270742
$521$	−13.8024	−0.604693	−0.302346	−	0.953198i	$-0.597770\pi$
$521$	−13.8024	−0.604693	−0.302346	+	0.953198i	$0.597770\pi$
$522$	13.4319	0.587897
$523$	−0.999640	−0.0437112	−0.0218556	−	0.999761i	$-0.506957\pi$
$523$	−0.999640	−0.0437112	−0.0218556	+	0.999761i	$0.506957\pi$
$524$	−61.2878	−2.67737
$525$	8.12484	0.354597
$526$	−40.2985	−1.75710
$527$	42.6195	1.85653
$528$	−6.94386	−0.302193
$529$	6.15300	0.267522
$530$	51.1479	2.22172
$531$	5.39365	0.234065
$532$	−48.4425	−2.10025
$533$	6.58635	0.285286
$534$	47.1368	2.03981
$535$	−29.1943	−1.26218
$536$	−5.81550	−0.251191
$537$	25.5729	1.10355
$538$	−37.9358	−1.63553
$539$	−2.33560	−0.100601
$540$	−28.3821	−1.22137
$541$	−17.0483	−0.732964	−0.366482	−	0.930425i	$-0.619438\pi$
$541$	−17.0483	−0.732964	−0.366482	+	0.930425i	$0.619438\pi$
$542$	−52.7228	−2.26464
$543$	−39.8776	−1.71131
$544$	29.3505	1.25839
$545$	9.20005	0.394087
$546$	11.2040	0.479485
$547$	−5.50332	−0.235305	−0.117652	−	0.993055i	$-0.537537\pi$
$547$	−5.50332	−0.235305	−0.117652	+	0.993055i	$0.537537\pi$
$548$	51.8830	2.21633
$549$	5.26774	0.224821
$550$	14.1174	0.601967
$551$	51.0651	2.17545
$552$	−34.9138	−1.48603
$553$	16.3914	0.697031
$554$	6.60213	0.280498
$555$	15.6016	0.662250
$556$	67.9207	2.88048
$557$	−11.0658	−0.468872	−0.234436	−	0.972132i	$-0.575324\pi$
$557$	−11.0658	−0.468872	−0.234436	+	0.972132i	$0.575324\pi$
$558$	−9.36797	−0.396578
$559$	−2.59754	−0.109864
$560$	−4.67881	−0.197716
$561$	−45.2943	−1.91233
$562$	70.2089	2.96158
$563$	21.3211	0.898577	0.449288	−	0.893387i	$-0.351678\pi$
$563$	21.3211	0.898577	0.449288	+	0.893387i	$0.351678\pi$
$564$	−2.64107	−0.111209
$565$	−5.19027	−0.218356
$566$	−51.6421	−2.17068
$567$	−26.4201	−1.10954
$568$	−25.3675	−1.06439
$569$	37.8893	1.58840	0.794200	−	0.607656i	$-0.207890\pi$
$569$	37.8893	1.58840	0.794200	+	0.607656i	$0.207890\pi$
$570$	45.0294	1.88607
$571$	18.9971	0.795006	0.397503	−	0.917601i	$-0.369877\pi$
$571$	18.9971	0.795006	0.397503	+	0.917601i	$0.369877\pi$
$572$	12.3285	0.515482
$573$	8.43723	0.352470
$574$	−38.7468	−1.61726
$575$	9.14402	0.381332
$576$	−7.73250	−0.322188
$577$	−15.6954	−0.653406	−0.326703	−	0.945127i	$-0.605938\pi$
$577$	−15.6954	−0.653406	−0.326703	+	0.945127i	$0.605938\pi$
$578$	−63.9722	−2.66089
$579$	2.40705	0.100034
$580$	57.6008	2.39174
$581$	−18.5783	−0.770758
$582$	−66.2599	−2.74656
$583$	42.9932	1.78060
$584$	36.4591	1.50869
$585$	−1.14031	−0.0471461
$586$	10.0989	0.417183
$587$	0.0806513	0.00332884	0.00166442	−	0.999999i	$-0.499470\pi$
$587$	0.0806513	0.00332884	0.00166442	+	0.999999i	$0.499470\pi$
$588$	4.30405	0.177496
$589$	−35.6150	−1.46749
$590$	36.5237	1.50366
$591$	18.2873	0.752237
$592$	4.60173	0.189130
$593$	28.0642	1.15246	0.576230	−	0.817288i	$-0.304523\pi$
$593$	28.0642	1.15246	0.576230	+	0.817288i	$0.304523\pi$
$594$	−37.6718	−1.54569
$595$	−30.5195	−1.25118
$596$	−34.7386	−1.42295
$597$	6.72706	0.275320
$598$	12.6094	0.515636
$599$	33.6628	1.37542	0.687712	−	0.725984i	$-0.258615\pi$
$599$	33.6628	1.37542	0.687712	+	0.725984i	$0.258615\pi$
$600$	−10.9509	−0.447070
$601$	23.3860	0.953935	0.476968	−	0.878921i	$-0.341736\pi$
$601$	23.3860	0.953935	0.476968	+	0.878921i	$0.341736\pi$
$602$	15.2811	0.622810
$603$	1.07412	0.0437416
$604$	−45.7945	−1.86335
$605$	−3.16626	−0.128727
$606$	34.1204	1.38605
$607$	14.6563	0.594882	0.297441	−	0.954740i	$-0.403867\pi$
$607$	14.6563	0.594882	0.297441	+	0.954740i	$0.403867\pi$
$608$	−24.5268	−0.994693
$609$	44.0009	1.78301
$610$	35.6710	1.44428
$611$	0.401509	0.0162433
$612$	14.4313	0.583350
$613$	−41.1260	−1.66106	−0.830531	−	0.556972i	$-0.811963\pi$
$613$	−41.1260	−1.66106	−0.830531	+	0.556972i	$0.811963\pi$
$614$	71.2068	2.87367
$615$	22.8090	0.919748
$616$	−30.5296	−1.23007
$617$	−28.3348	−1.14072	−0.570359	−	0.821396i	$-0.693196\pi$
$617$	−28.3348	−1.14072	−0.570359	+	0.821396i	$0.693196\pi$
$618$	−78.8424	−3.17151
$619$	27.5108	1.10575	0.552875	−	0.833264i	$-0.313531\pi$
$619$	27.5108	1.10575	0.552875	+	0.833264i	$0.313531\pi$
$620$	−40.1733	−1.61340
$621$	−24.4006	−0.979161
$622$	−22.6881	−0.909710
$623$	26.6973	1.06960
$624$	−1.94534	−0.0778758
$625$	−13.6642	−0.546569
$626$	−8.75985	−0.350114
$627$	37.8502	1.51159
$628$	27.2887	1.08894
$629$	30.0167	1.19685
$630$	6.70834	0.267267
$631$	−30.4033	−1.21034	−0.605169	−	0.796097i	$-0.706894\pi$
$631$	−30.4033	−1.21034	−0.605169	+	0.796097i	$0.706894\pi$
$632$	−22.0928	−0.878806
$633$	21.5892	0.858092
$634$	−12.8508	−0.510369
$635$	21.1061	0.837571
$636$	−79.2281	−3.14160
$637$	−0.654322	−0.0259252
$638$	76.4540	3.02684
$639$	4.68537	0.185350
$640$	−36.3411	−1.43651
$641$	14.6106	0.577085	0.288543	−	0.957467i	$-0.406829\pi$
$641$	14.6106	0.577085	0.288543	+	0.957467i	$0.406829\pi$
$642$	71.4084	2.81826
$643$	−0.0190412	−0.000750911 0	−0.000375456	−	1.00000i	$-0.500120\pi$
$643$	−0.0190412	−0.000750911 0	−0.000375456		1.00000i	$0.500120\pi$
$644$	−46.9771	−1.85116
$645$	−8.99549	−0.354197
$646$	86.6346	3.40859
$647$	−28.6383	−1.12589	−0.562944	−	0.826495i	$-0.690331\pi$
$647$	−28.6383	−1.12589	−0.562944	+	0.826495i	$0.690331\pi$
$648$	35.6099	1.39889
$649$	30.7006	1.20510
$650$	3.95501	0.155128
$651$	−30.6881	−1.20276
$652$	52.7070	2.06416
$653$	39.6071	1.54995	0.774974	−	0.631993i	$-0.217763\pi$
$653$	39.6071	1.54995	0.774974	+	0.631993i	$0.217763\pi$
$654$	−22.5030	−0.879938
$655$	32.2664	1.26075
$656$	6.72759	0.262668
$657$	−6.73399	−0.262718
$658$	−2.36203	−0.0920817
$659$	47.2191	1.83940	0.919698	−	0.392627i	$-0.128434\pi$
$659$	47.2191	1.83940	0.919698	+	0.392627i	$0.128434\pi$
$660$	42.6946	1.66189
$661$	35.0301	1.36251	0.681256	−	0.732045i	$-0.261434\pi$
$661$	35.0301	1.36251	0.681256	+	0.732045i	$0.261434\pi$
$662$	−3.87905	−0.150763
$663$	−12.6893	−0.492811
$664$	25.0405	0.971759
$665$	25.5037	0.988990
$666$	−6.59783	−0.255661
$667$	49.5204	1.91744
$668$	67.9479	2.62898
$669$	33.4779	1.29433
$670$	7.27353	0.281001
$671$	29.9839	1.15751
$672$	−21.1338	−0.815255
$673$	−27.2484	−1.05035	−0.525174	−	0.850995i	$-0.676000\pi$
$673$	−27.2484	−1.05035	−0.525174	+	0.850995i	$0.676000\pi$
$674$	−35.6846	−1.37452
$675$	−7.65339	−0.294579
$676$	3.45386	0.132841
$677$	19.4291	0.746723	0.373361	−	0.927686i	$-0.378205\pi$
$677$	19.4291	0.746723	0.373361	+	0.927686i	$0.378205\pi$
$678$	12.6952	0.487558
$679$	−37.5282	−1.44020
$680$	41.1353	1.57747
$681$	−5.69663	−0.218295
$682$	−53.3223	−2.04182
$683$	6.31463	0.241623	0.120811	−	0.992675i	$-0.461450\pi$
$683$	6.31463	0.241623	0.120811	+	0.992675i	$0.461450\pi$
$684$	−12.0595	−0.461107
$685$	−27.3150	−1.04365
$686$	45.0296	1.71924
$687$	−6.95704	−0.265428
$688$	−2.65325	−0.101154
$689$	12.0446	0.458864
$690$	43.6672	1.66238
$691$	2.73155	0.103913	0.0519566	−	0.998649i	$-0.483454\pi$
$691$	2.73155	0.103913	0.0519566	+	0.998649i	$0.483454\pi$
$692$	−78.6375	−2.98935
$693$	5.63881	0.214201
$694$	31.9494	1.21278
$695$	−35.7585	−1.35640
$696$	−59.3059	−2.24798
$697$	43.8836	1.66221
$698$	30.8839	1.16897
$699$	37.1730	1.40601
$700$	−14.7346	−0.556917
$701$	43.9735	1.66086	0.830429	−	0.557125i	$-0.188096\pi$
$701$	43.9735	1.66086	0.830429	+	0.557125i	$0.188096\pi$
$702$	−10.5538	−0.398329
$703$	−25.0835	−0.946043
$704$	−44.0133	−1.65881
$705$	1.39046	0.0523676
$706$	43.0983	1.62203
$707$	19.3251	0.726793
$708$	−56.5752	−2.12623
$709$	17.7112	0.665159	0.332579	−	0.943075i	$-0.392081\pi$
$709$	17.7112	0.665159	0.332579	+	0.943075i	$0.392081\pi$
$710$	31.7274	1.19071
$711$	4.08055	0.153032
$712$	−35.9835	−1.34854
$713$	−34.5376	−1.29344
$714$	74.6498	2.79370
$715$	−6.49065	−0.242736
$716$	−46.3772	−1.73320
$717$	8.01646	0.299380
$718$	49.7303	1.85592
$719$	−49.2621	−1.83717	−0.918583	−	0.395228i	$-0.870666\pi$
$719$	−49.2621	−1.83717	−0.918583	+	0.395228i	$0.870666\pi$
$720$	−1.16477	−0.0434083
$721$	−44.6546	−1.66302
$722$	−28.0246	−1.04297
$723$	14.8559	0.552497
$724$	72.3192	2.68772
$725$	15.5324	0.576857
$726$	7.74456	0.287428
$727$	−48.9188	−1.81430	−0.907149	−	0.420810i	$-0.861746\pi$
$727$	−48.9188	−1.81430	−0.907149	+	0.420810i	$0.861746\pi$
$728$	−8.55292	−0.316992
$729$	19.2431	0.712706
$730$	−45.5999	−1.68773
$731$	−17.3069	−0.640120
$732$	−55.2544	−2.04226
$733$	16.7313	0.617984	0.308992	−	0.951065i	$-0.400008\pi$
$733$	16.7313	0.617984	0.308992	+	0.951065i	$0.400008\pi$
$734$	30.3491	1.12020
$735$	−2.26597	−0.0835814
$736$	−23.7848	−0.876721
$737$	6.11389	0.225208
$738$	−9.64582	−0.355067
$739$	−34.3170	−1.26237	−0.631186	−	0.775631i	$-0.717432\pi$
$739$	−34.3170	−1.26237	−0.631186	+	0.775631i	$0.717432\pi$
$740$	−28.2939	−1.04011
$741$	10.6038	0.389541
$742$	−70.8573	−2.60126
$743$	−6.94980	−0.254963	−0.127482	−	0.991841i	$-0.540689\pi$
$743$	−6.94980	−0.254963	−0.127482	+	0.991841i	$0.540689\pi$
$744$	41.3625	1.51642
$745$	18.2890	0.670056
$746$	71.9692	2.63498
$747$	−4.62497	−0.169219
$748$	82.1426	3.00343
$749$	40.4441	1.47780
$750$	54.1340	1.97669
$751$	20.8347	0.760269	0.380135	−	0.924931i	$-0.375878\pi$
$751$	20.8347	0.760269	0.380135	+	0.924931i	$0.375878\pi$
$752$	0.410119	0.0149555
$753$	−25.9304	−0.944956
$754$	21.4188	0.780025
$755$	24.1096	0.877437
$756$	39.3190	1.43002
$757$	47.5959	1.72990	0.864951	−	0.501856i	$-0.167349\pi$
$757$	47.5959	1.72990	0.864951	+	0.501856i	$0.167349\pi$
$758$	−62.9860	−2.28775
$759$	36.7052	1.33232
$760$	−34.3747	−1.24690
$761$	−19.9569	−0.723436	−0.361718	−	0.932288i	$-0.617810\pi$
$761$	−19.9569	−0.723436	−0.361718	+	0.932288i	$0.617810\pi$
$762$	−51.6249	−1.87017
$763$	−12.7452	−0.461408
$764$	−15.3012	−0.553577
$765$	−7.59768	−0.274695
$766$	44.6150	1.61200
$767$	8.60083	0.310558
$768$	41.9228	1.51276
$769$	14.9493	0.539085	0.269543	−	0.962988i	$-0.413127\pi$
$769$	14.9493	0.539085	0.269543	+	0.962988i	$0.413127\pi$
$770$	38.1838	1.37605
$771$	−1.88113	−0.0677472
$772$	−4.36526	−0.157109
$773$	23.6141	0.849339	0.424670	−	0.905348i	$-0.360390\pi$
$773$	23.6141	0.849339	0.424670	+	0.905348i	$0.360390\pi$
$774$	3.80415	0.136737
$775$	−10.8329	−0.389131
$776$	50.5818	1.81578
$777$	−21.6135	−0.775381
$778$	−18.4594	−0.661803
$779$	−36.6713	−1.31389
$780$	11.9610	0.428272
$781$	26.6691	0.954294
$782$	84.0139	3.00433
$783$	−41.4477	−1.48122
$784$	−0.668354	−0.0238698
$785$	−14.3668	−0.512772
$786$	−78.9225	−2.81507
$787$	−20.2728	−0.722649	−0.361324	−	0.932440i	$-0.617675\pi$
$787$	−20.2728	−0.722649	−0.361324	+	0.932440i	$0.617675\pi$
$788$	−33.1645	−1.18144
$789$	−32.8638	−1.16998
$790$	27.6318	0.983097
$791$	7.19031	0.255658
$792$	−7.60019	−0.270061
$793$	8.40005	0.298294
$794$	−81.9723	−2.90909
$795$	41.7115	1.47935
$796$	−12.1997	−0.432408
$797$	−36.3904	−1.28901	−0.644507	−	0.764599i	$-0.722937\pi$
$797$	−36.3904	−1.28901	−0.644507	+	0.764599i	$0.722937\pi$
$798$	−62.3812	−2.20827
$799$	2.67518	0.0946409
$800$	−7.46026	−0.263760
$801$	6.64615	0.234830
$802$	−64.9349	−2.29293
$803$	−38.3298	−1.35263
$804$	−11.2667	−0.397346
$805$	24.7322	0.871695
$806$	−14.9384	−0.526181
$807$	−30.9369	−1.08903
$808$	−26.0470	−0.916330
$809$	17.2323	0.605854	0.302927	−	0.953014i	$-0.402036\pi$
$809$	17.2323	0.605854	0.302927	+	0.953014i	$0.402036\pi$
$810$	−44.5378	−1.56490
$811$	−21.5554	−0.756912	−0.378456	−	0.925619i	$-0.623545\pi$
$811$	−21.5554	−0.756912	−0.378456	+	0.925619i	$0.623545\pi$
$812$	−79.7969	−2.80032
$813$	−42.9959	−1.50793
$814$	−37.5547	−1.31629
$815$	−27.7488	−0.971999
$816$	−12.9614	−0.453740
$817$	14.4626	0.505981
$818$	−33.4816	−1.17066
$819$	1.57972	0.0552000
$820$	−41.3648	−1.44452
$821$	17.7315	0.618834	0.309417	−	0.950926i	$-0.399866\pi$
$821$	17.7315	0.618834	0.309417	+	0.950926i	$0.399866\pi$
$822$	66.8117	2.33033
$823$	25.5237	0.889699	0.444849	−	0.895605i	$-0.353257\pi$
$823$	25.5237	0.889699	0.444849	+	0.895605i	$0.353257\pi$
$824$	60.1870	2.09671
$825$	11.5128	0.400825
$826$	−50.5978	−1.76052
$827$	10.0923	0.350944	0.175472	−	0.984484i	$-0.443855\pi$
$827$	10.0923	0.350944	0.175472	+	0.984484i	$0.443855\pi$
$828$	−11.6947	−0.406419
$829$	−2.45537	−0.0852784	−0.0426392	−	0.999091i	$-0.513577\pi$
$829$	−2.45537	−0.0852784	−0.0426392	+	0.999091i	$0.513577\pi$
$830$	−31.3185	−1.08708
$831$	5.38409	0.186772
$832$	−12.3304	−0.427480
$833$	−4.35962	−0.151052
$834$	87.4640	3.02863
$835$	−35.7728	−1.23797
$836$	−68.6426	−2.37405
$837$	28.9074	0.999186
$838$	−69.5643	−2.40306
$839$	38.6462	1.33421	0.667107	−	0.744962i	$-0.267532\pi$
$839$	38.6462	1.33421	0.667107	+	0.744962i	$0.267532\pi$
$840$	−29.6194	−1.02197
$841$	55.1171	1.90059
$842$	−8.74217	−0.301275
$843$	57.2559	1.97200
$844$	−39.1526	−1.34769
$845$	−1.81837	−0.0625537
$846$	−0.588017	−0.0202164
$847$	4.38635	0.150717
$848$	12.3029	0.422484
$849$	−42.1146	−1.44537
$850$	26.3515	0.903848
$851$	−24.3247	−0.833841
$852$	−49.1458	−1.68371
$853$	54.2767	1.85840	0.929200	−	0.369578i	$-0.120498\pi$
$853$	54.2767	1.85840	0.929200	+	0.369578i	$0.120498\pi$
$854$	−49.4166	−1.69100
$855$	6.34901	0.217132
$856$	−54.5120	−1.86318
$857$	−34.4120	−1.17549	−0.587746	−	0.809046i	$-0.699985\pi$
$857$	−34.4120	−1.17549	−0.587746	+	0.809046i	$0.699985\pi$
$858$	15.8759	0.541995
$859$	26.8179	0.915016	0.457508	−	0.889205i	$-0.348742\pi$
$859$	26.8179	0.915016	0.457508	+	0.889205i	$0.348742\pi$
$860$	16.3136	0.556289
$861$	−31.5983	−1.07687
$862$	−33.0040	−1.12412
$863$	24.8999	0.847603	0.423801	−	0.905755i	$-0.360695\pi$
$863$	24.8999	0.847603	0.423801	+	0.905755i	$0.360695\pi$
$864$	19.9075	0.677267
$865$	41.4005	1.40766
$866$	−17.9571	−0.610206
$867$	−52.1699	−1.77178
$868$	55.6538	1.88901
$869$	23.2264	0.787902
$870$	74.1747	2.51476
$871$	1.71282	0.0580366
$872$	17.1785	0.581736
$873$	−9.34245	−0.316194
$874$	−70.2063	−2.37476
$875$	30.6603	1.03651
$876$	70.6343	2.38651
$877$	−7.50843	−0.253542	−0.126771	−	0.991932i	$-0.540461\pi$
$877$	−7.50843	−0.253542	−0.126771	+	0.991932i	$0.540461\pi$
$878$	38.7653	1.30827
$879$	8.23576	0.277785
$880$	−6.62983	−0.223492
$881$	25.8015	0.869273	0.434637	−	0.900606i	$-0.356877\pi$
$881$	25.8015	0.869273	0.434637	+	0.900606i	$0.356877\pi$
$882$	0.958266	0.0322665
$883$	−22.8282	−0.768230	−0.384115	−	0.923285i	$-0.625493\pi$
$883$	−22.8282	−0.768230	−0.384115	+	0.923285i	$0.625493\pi$
$884$	23.0124	0.773992
$885$	29.7853	1.00122
$886$	−29.6301	−0.995442
$887$	−26.1273	−0.877268	−0.438634	−	0.898666i	$-0.644538\pi$
$887$	−26.1273	−0.877268	−0.438634	+	0.898666i	$0.644538\pi$
$888$	29.1315	0.977588
$889$	−29.2392	−0.980652
$890$	45.0051	1.50857
$891$	−37.4370	−1.25419
$892$	−60.7133	−2.03283
$893$	−2.23551	−0.0748086
$894$	−44.7342	−1.49614
$895$	24.4164	0.816150
$896$	50.3449	1.68191
$897$	10.2830	0.343341
$898$	17.4049	0.580808
$899$	−58.6669	−1.95665
$900$	−3.66811	−0.122270
$901$	80.2511	2.67355
$902$	−54.9039	−1.82810
$903$	12.4618	0.414704
$904$	−9.69135	−0.322329
$905$	−38.0741	−1.26563
$906$	−58.9712	−1.95919
$907$	−35.7554	−1.18724	−0.593619	−	0.804746i	$-0.702301\pi$
$907$	−35.7554	−1.18724	−0.593619	+	0.804746i	$0.702301\pi$
$908$	10.3310	0.342847
$909$	4.81088	0.159567
$910$	10.6973	0.354611
$911$	32.7612	1.08543	0.542714	−	0.839918i	$-0.317397\pi$
$911$	32.7612	1.08543	0.542714	+	0.839918i	$0.317397\pi$
$912$	10.8312	0.358657
$913$	−26.3253	−0.871240
$914$	2.35087	0.0777599
$915$	29.0900	0.961685
$916$	12.6168	0.416871
$917$	−44.7000	−1.47612
$918$	−70.3182	−2.32085
$919$	−33.5648	−1.10720	−0.553600	−	0.832783i	$-0.686746\pi$
$919$	−33.5648	−1.10720	−0.553600	+	0.832783i	$0.686746\pi$
$920$	−33.3349	−1.09902
$921$	58.0697	1.91346
$922$	14.3471	0.472496
$923$	7.47139	0.245924
$924$	−59.1467	−1.94578
$925$	−7.62960	−0.250860
$926$	2.33535	0.0767444
$927$	−11.1165	−0.365115
$928$	−40.4018	−1.32625
$929$	56.1500	1.84222	0.921111	−	0.389300i	$-0.127283\pi$
$929$	56.1500	1.84222	0.921111	+	0.389300i	$0.127283\pi$
$930$	−51.7327	−1.69638
$931$	3.64312	0.119398
$932$	−67.4144	−2.20823
$933$	−18.5023	−0.605739
$934$	20.8547	0.682386
$935$	−43.2459	−1.41429
$936$	−2.12921	−0.0695953
$937$	−18.3816	−0.600502	−0.300251	−	0.953860i	$-0.597070\pi$
$937$	−18.3816	−0.600502	−0.300251	+	0.953860i	$0.597070\pi$
$938$	−10.0763	−0.329004
$939$	−7.14372	−0.233127
$940$	−2.52163	−0.0822466
$941$	−45.7359	−1.49095	−0.745474	−	0.666535i	$-0.767777\pi$
$941$	−45.7359	−1.49095	−0.745474	+	0.666535i	$0.767777\pi$
$942$	35.1407	1.14494
$943$	−35.5620	−1.15806
$944$	8.78527	0.285936
$945$	−20.7004	−0.673384
$946$	21.6532	0.704005
$947$	−38.7822	−1.26025	−0.630126	−	0.776493i	$-0.716997\pi$
$947$	−38.7822	−1.26025	−0.630126	+	0.776493i	$0.716997\pi$
$948$	−42.8017	−1.39014
$949$	−10.7382	−0.348576
$950$	−22.0206	−0.714443
$951$	−10.4799	−0.339834
$952$	−56.9865	−1.84694
$953$	9.42787	0.305399	0.152699	−	0.988273i	$-0.451203\pi$
$953$	9.42787	0.305399	0.152699	+	0.988273i	$0.451203\pi$
$954$	−17.6396	−0.571103
$955$	8.05566	0.260675
$956$	−14.5381	−0.470196
$957$	62.3489	2.01545
$958$	−69.4895	−2.24510
$959$	37.8407	1.22194
$960$	−42.7011	−1.37817
$961$	9.91680	0.319897
$962$	−10.5210	−0.339212
$963$	10.0684	0.324449
$964$	−26.9416	−0.867731
$965$	2.29819	0.0739815
$966$	−60.4941	−1.94637
$967$	60.3688	1.94133	0.970665	−	0.240438i	$-0.0772910\pi$
$967$	60.3688	1.94133	0.970665	+	0.240438i	$0.0772910\pi$
$968$	−5.91208	−0.190021
$969$	70.6512	2.26964
$970$	−63.2633	−2.03126
$971$	13.1409	0.421712	0.210856	−	0.977517i	$-0.432375\pi$
$971$	13.1409	0.421712	0.210856	+	0.977517i	$0.432375\pi$
$972$	22.1634	0.710891
$973$	49.5377	1.58811
$974$	−23.5854	−0.755724
$975$	3.22534	0.103294
$976$	8.58018	0.274645
$977$	−51.0106	−1.63197	−0.815987	−	0.578070i	$-0.803806\pi$
$977$	−51.0106	−1.63197	−0.815987	+	0.578070i	$0.803806\pi$
$978$	67.8727	2.17033
$979$	37.8298	1.20905
$980$	4.10940	0.131270
$981$	−3.17286	−0.101302
$982$	−58.8611	−1.87833
$983$	13.4683	0.429572	0.214786	−	0.976661i	$-0.431095\pi$
$983$	13.4683	0.429572	0.214786	+	0.976661i	$0.431095\pi$
$984$	42.5893	1.35770
$985$	17.4602	0.556329
$986$	142.709	4.54478
$987$	−1.92626	−0.0613135
$988$	−19.2304	−0.611799
$989$	14.0251	0.445971
$990$	9.50566	0.302110
$991$	−41.4450	−1.31654	−0.658272	−	0.752780i	$-0.728712\pi$
$991$	−41.4450	−1.31654	−0.658272	+	0.752780i	$0.728712\pi$
$992$	28.1780	0.894651
$993$	−3.16339	−0.100387
$994$	−43.9534	−1.39412
$995$	6.42283	0.203617
$996$	48.5123	1.53717
$997$	59.0937	1.87152	0.935759	−	0.352641i	$-0.114716\pi$
$997$	59.0937	1.87152	0.935759	+	0.352641i	$0.114716\pi$
$998$	−36.2651	−1.14795
$999$	20.3594	0.644142

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.17	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.17	✓	130	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)

\(f(q)\)	\(=\)	\(q-2.33535 q^{2} -1.90450 q^{3} +3.45386 q^{4} -1.81837 q^{5} +4.44767 q^{6} +2.51906 q^{7} -3.39528 q^{8} +0.627108 q^{9} +O(q^{10})\)	\(q-2.33535 q^{2} -1.90450 q^{3} +3.45386 q^{4} -1.81837 q^{5} +4.44767 q^{6} +2.51906 q^{7} -3.39528 q^{8} +0.627108 q^{9} +4.24653 q^{10} +3.56949 q^{11} -6.57787 q^{12} +1.00000 q^{13} -5.88290 q^{14} +3.46307 q^{15} +1.02144 q^{16} +6.66281 q^{17} -1.46452 q^{18} -5.56778 q^{19} -6.28039 q^{20} -4.79755 q^{21} -8.33601 q^{22} -5.39935 q^{23} +6.46630 q^{24} -1.69354 q^{25} -2.33535 q^{26} +4.51917 q^{27} +8.70050 q^{28} -9.17154 q^{29} -8.08749 q^{30} +6.39662 q^{31} +4.40513 q^{32} -6.79808 q^{33} -15.5600 q^{34} -4.58058 q^{35} +2.16595 q^{36} +4.50512 q^{37} +13.0027 q^{38} -1.90450 q^{39} +6.17387 q^{40} +6.58635 q^{41} +11.2040 q^{42} -2.59754 q^{43} +12.3285 q^{44} -1.14031 q^{45} +12.6094 q^{46} +0.401509 q^{47} -1.94534 q^{48} -0.654322 q^{49} +3.95501 q^{50} -12.6893 q^{51} +3.45386 q^{52} +12.0446 q^{53} -10.5538 q^{54} -6.49065 q^{55} -8.55292 q^{56} +10.6038 q^{57} +21.4188 q^{58} +8.60083 q^{59} +11.9610 q^{60} +8.40005 q^{61} -14.9384 q^{62} +1.57972 q^{63} -12.3304 q^{64} -1.81837 q^{65} +15.8759 q^{66} +1.71282 q^{67} +23.0124 q^{68} +10.2830 q^{69} +10.6973 q^{70} +7.47139 q^{71} -2.12921 q^{72} -10.7382 q^{73} -10.5210 q^{74} +3.22534 q^{75} -19.2304 q^{76} +8.99177 q^{77} +4.44767 q^{78} +6.50693 q^{79} -1.85736 q^{80} -10.4881 q^{81} -15.3814 q^{82} -7.37508 q^{83} -16.5701 q^{84} -12.1154 q^{85} +6.06618 q^{86} +17.4672 q^{87} -12.1194 q^{88} +10.5981 q^{89} +2.66303 q^{90} +2.51906 q^{91} -18.6486 q^{92} -12.1823 q^{93} -0.937664 q^{94} +10.1243 q^{95} -8.38956 q^{96} -14.8977 q^{97} +1.52807 q^{98} +2.23846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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