LMFDB - Embedded newform 6033.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05866 q^{2} -1.00000 q^{3} +2.23808 q^{4} -1.30769 q^{5} +2.05866 q^{6} +4.57045 q^{7} -0.490135 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.05866 q^{2} -1.00000 q^{3} +2.23808 q^{4} -1.30769 q^{5} +2.05866 q^{6} +4.57045 q^{7} -0.490135 q^{8} +1.00000 q^{9} +2.69208 q^{10} -0.918607 q^{11} -2.23808 q^{12} -2.76605 q^{13} -9.40900 q^{14} +1.30769 q^{15} -3.46715 q^{16} +8.09044 q^{17} -2.05866 q^{18} -7.36397 q^{19} -2.92671 q^{20} -4.57045 q^{21} +1.89110 q^{22} -2.57296 q^{23} +0.490135 q^{24} -3.28996 q^{25} +5.69436 q^{26} -1.00000 q^{27} +10.2290 q^{28} +0.768395 q^{29} -2.69208 q^{30} +2.52172 q^{31} +8.11795 q^{32} +0.918607 q^{33} -16.6555 q^{34} -5.97671 q^{35} +2.23808 q^{36} -5.29874 q^{37} +15.1599 q^{38} +2.76605 q^{39} +0.640942 q^{40} +0.984105 q^{41} +9.40900 q^{42} -9.30764 q^{43} -2.05592 q^{44} -1.30769 q^{45} +5.29685 q^{46} +2.09739 q^{47} +3.46715 q^{48} +13.8890 q^{49} +6.77290 q^{50} -8.09044 q^{51} -6.19065 q^{52} -8.93207 q^{53} +2.05866 q^{54} +1.20125 q^{55} -2.24013 q^{56} +7.36397 q^{57} -1.58186 q^{58} +5.92594 q^{59} +2.92671 q^{60} -1.31796 q^{61} -5.19137 q^{62} +4.57045 q^{63} -9.77781 q^{64} +3.61713 q^{65} -1.89110 q^{66} +13.4320 q^{67} +18.1071 q^{68} +2.57296 q^{69} +12.3040 q^{70} +1.27527 q^{71} -0.490135 q^{72} -3.49431 q^{73} +10.9083 q^{74} +3.28996 q^{75} -16.4812 q^{76} -4.19844 q^{77} -5.69436 q^{78} +2.31819 q^{79} +4.53394 q^{80} +1.00000 q^{81} -2.02594 q^{82} -1.29838 q^{83} -10.2290 q^{84} -10.5798 q^{85} +19.1613 q^{86} -0.768395 q^{87} +0.450241 q^{88} +17.6098 q^{89} +2.69208 q^{90} -12.6421 q^{91} -5.75850 q^{92} -2.52172 q^{93} -4.31781 q^{94} +9.62977 q^{95} -8.11795 q^{96} +10.2317 q^{97} -28.5927 q^{98} -0.918607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * 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 $

$2$	−2.05866	−1.45569	−0.727847	−	0.685740i	$-0.759479\pi$
$2$	−2.05866	−1.45569	−0.727847	+	0.685740i	$0.759479\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.23808	1.11904
$5$	−1.30769	−0.584815	−0.292408	−	0.956294i	$-0.594456\pi$
$5$	−1.30769	−0.584815	−0.292408	+	0.956294i	$0.594456\pi$
$6$	2.05866	0.840445
$7$	4.57045	1.72747	0.863733	−	0.503949i	$-0.168120\pi$
$7$	4.57045	1.72747	0.863733	+	0.503949i	$0.168120\pi$
$8$	−0.490135	−0.173289
$9$	1.00000	0.333333
$10$	2.69208	0.851311
$11$	−0.918607	−0.276970	−0.138485	−	0.990365i	$-0.544223\pi$
$11$	−0.918607	−0.276970	−0.138485	+	0.990365i	$0.544223\pi$
$12$	−2.23808	−0.646079
$13$	−2.76605	−0.767164	−0.383582	−	0.923507i	$-0.625310\pi$
$13$	−2.76605	−0.767164	−0.383582	+	0.923507i	$0.625310\pi$
$14$	−9.40900	−2.51466
$15$	1.30769	0.337643
$16$	−3.46715	−0.866787
$17$	8.09044	1.96222	0.981109	−	0.193454i	$-0.0619690\pi$
$17$	8.09044	1.96222	0.981109	+	0.193454i	$0.0619690\pi$
$18$	−2.05866	−0.485231
$19$	−7.36397	−1.68941	−0.844706	−	0.535231i	$-0.820224\pi$
$19$	−7.36397	−1.68941	−0.844706	+	0.535231i	$0.820224\pi$
$20$	−2.92671	−0.654433
$21$	−4.57045	−0.997353
$22$	1.89110	0.403184
$23$	−2.57296	−0.536499	−0.268250	−	0.963349i	$-0.586445\pi$
$23$	−2.57296	−0.536499	−0.268250	+	0.963349i	$0.586445\pi$
$24$	0.490135	0.100048
$25$	−3.28996	−0.657991
$26$	5.69436	1.11676
$27$	−1.00000	−0.192450
$28$	10.2290	1.93311
$29$	0.768395	0.142687	0.0713437	−	0.997452i	$-0.477271\pi$
$29$	0.768395	0.142687	0.0713437	+	0.997452i	$0.477271\pi$
$30$	−2.69208	−0.491505
$31$	2.52172	0.452915	0.226457	−	0.974021i	$-0.427286\pi$
$31$	2.52172	0.452915	0.226457	+	0.974021i	$0.427286\pi$
$32$	8.11795	1.43506
$33$	0.918607	0.159909
$34$	−16.6555	−2.85639
$35$	−5.97671	−1.01025
$36$	2.23808	0.373014
$37$	−5.29874	−0.871108	−0.435554	−	0.900163i	$-0.643448\pi$
$37$	−5.29874	−0.871108	−0.435554	+	0.900163i	$0.643448\pi$
$38$	15.1599	2.45926
$39$	2.76605	0.442923
$40$	0.640942	0.101342
$41$	0.984105	0.153691	0.0768457	−	0.997043i	$-0.475515\pi$
$41$	0.984105	0.153691	0.0768457	+	0.997043i	$0.475515\pi$
$42$	9.40900	1.45184
$43$	−9.30764	−1.41940	−0.709701	−	0.704503i	$-0.751170\pi$
$43$	−9.30764	−1.41940	−0.709701	+	0.704503i	$0.751170\pi$
$44$	−2.05592	−0.309941
$45$	−1.30769	−0.194938
$46$	5.29685	0.780978
$47$	2.09739	0.305935	0.152968	−	0.988231i	$-0.451117\pi$
$47$	2.09739	0.305935	0.152968	+	0.988231i	$0.451117\pi$
$48$	3.46715	0.500440
$49$	13.8890	1.98414
$50$	6.77290	0.957833
$51$	−8.09044	−1.13289
$52$	−6.19065	−0.858489
$53$	−8.93207	−1.22691	−0.613457	−	0.789728i	$-0.710222\pi$
$53$	−8.93207	−1.22691	−0.613457	+	0.789728i	$0.710222\pi$
$54$	2.05866	0.280148
$55$	1.20125	0.161976
$56$	−2.24013	−0.299351
$57$	7.36397	0.975382
$58$	−1.58186	−0.207709
$59$	5.92594	0.771492	0.385746	−	0.922605i	$-0.373944\pi$
$59$	5.92594	0.771492	0.385746	+	0.922605i	$0.373944\pi$
$60$	2.92671	0.377837
$61$	−1.31796	−0.168747	−0.0843737	−	0.996434i	$-0.526889\pi$
$61$	−1.31796	−0.168747	−0.0843737	+	0.996434i	$0.526889\pi$
$62$	−5.19137	−0.659305
$63$	4.57045	0.575822
$64$	−9.77781	−1.22223
$65$	3.61713	0.448649
$66$	−1.89110	−0.232778
$67$	13.4320	1.64098	0.820492	−	0.571659i	$-0.193700\pi$
$67$	13.4320	1.64098	0.820492	+	0.571659i	$0.193700\pi$
$68$	18.1071	2.19581
$69$	2.57296	0.309748
$70$	12.3040	1.47061
$71$	1.27527	0.151346	0.0756732	−	0.997133i	$-0.475889\pi$
$71$	1.27527	0.151346	0.0756732	+	0.997133i	$0.475889\pi$
$72$	−0.490135	−0.0577629
$73$	−3.49431	−0.408978	−0.204489	−	0.978869i	$-0.565553\pi$
$73$	−3.49431	−0.408978	−0.204489	+	0.978869i	$0.565553\pi$
$74$	10.9083	1.26807
$75$	3.28996	0.379891
$76$	−16.4812	−1.89052
$77$	−4.19844	−0.478457
$78$	−5.69436	−0.644759
$79$	2.31819	0.260817	0.130408	−	0.991460i	$-0.458371\pi$
$79$	2.31819	0.260817	0.130408	+	0.991460i	$0.458371\pi$
$80$	4.53394	0.506910
$81$	1.00000	0.111111
$82$	−2.02594	−0.223727
$83$	−1.29838	−0.142515	−0.0712576	−	0.997458i	$-0.522701\pi$
$83$	−1.29838	−0.142515	−0.0712576	+	0.997458i	$0.522701\pi$
$84$	−10.2290	−1.11608
$85$	−10.5798	−1.14754
$86$	19.1613	2.06621
$87$	−0.768395	−0.0823806
$88$	0.450241	0.0479958
$89$	17.6098	1.86663	0.933317	−	0.359054i	$-0.116901\pi$
$89$	17.6098	1.86663	0.933317	+	0.359054i	$0.116901\pi$
$90$	2.69208	0.283770
$91$	−12.6421	−1.32525
$92$	−5.75850	−0.600365
$93$	−2.52172	−0.261490
$94$	−4.31781	−0.445348
$95$	9.62977	0.987993
$96$	−8.11795	−0.828535
$97$	10.2317	1.03887	0.519437	−	0.854509i	$-0.326142\pi$
$97$	10.2317	1.03887	0.519437	+	0.854509i	$0.326142\pi$
$98$	−28.5927	−2.88830
$99$	−0.918607	−0.0923234
$100$	−7.36320	−0.736320
$101$	17.8289	1.77404	0.887021	−	0.461730i	$-0.152771\pi$
$101$	17.8289	1.77404	0.887021	+	0.461730i	$0.152771\pi$
$102$	16.6555	1.64914
$103$	−10.2418	−1.00915	−0.504577	−	0.863367i	$-0.668351\pi$
$103$	−10.2418	−1.00915	−0.504577	+	0.863367i	$0.668351\pi$
$104$	1.35574	0.132941
$105$	5.97671	0.583267
$106$	18.3881	1.78601
$107$	10.3412	0.999718	0.499859	−	0.866107i	$-0.333385\pi$
$107$	10.3412	0.999718	0.499859	+	0.866107i	$0.333385\pi$
$108$	−2.23808	−0.215360
$109$	9.51513	0.911384	0.455692	−	0.890137i	$-0.349392\pi$
$109$	9.51513	0.911384	0.455692	+	0.890137i	$0.349392\pi$
$110$	−2.47296	−0.235788
$111$	5.29874	0.502935
$112$	−15.8464	−1.49735
$113$	−15.1869	−1.42866	−0.714330	−	0.699809i	$-0.753268\pi$
$113$	−15.1869	−1.42866	−0.714330	+	0.699809i	$0.753268\pi$
$114$	−15.1599	−1.41986
$115$	3.36463	0.313753
$116$	1.71973	0.159673
$117$	−2.76605	−0.255721
$118$	−12.1995	−1.12306
$119$	36.9769	3.38967
$120$	−0.640942	−0.0585098
$121$	−10.1562	−0.923287
$122$	2.71323	0.245644
$123$	−0.984105	−0.0887337
$124$	5.64383	0.506831
$125$	10.8407	0.969618
$126$	−9.40900	−0.838220
$127$	−0.708075	−0.0628315	−0.0314157	−	0.999506i	$-0.510002\pi$
$127$	−0.708075	−0.0628315	−0.0314157	+	0.999506i	$0.510002\pi$
$128$	3.89329	0.344122
$129$	9.30764	0.819492
$130$	−7.44644	−0.653096
$131$	12.5842	1.09949	0.549744	−	0.835333i	$-0.314725\pi$
$131$	12.5842	1.09949	0.549744	+	0.835333i	$0.314725\pi$
$132$	2.05592	0.178945
$133$	−33.6566	−2.91840
$134$	−27.6520	−2.38877
$135$	1.30769	0.112548
$136$	−3.96540	−0.340031
$137$	−6.20267	−0.529930	−0.264965	−	0.964258i	$-0.585360\pi$
$137$	−6.20267	−0.529930	−0.264965	+	0.964258i	$0.585360\pi$
$138$	−5.29685	−0.450898
$139$	−3.85746	−0.327186	−0.163593	−	0.986528i	$-0.552308\pi$
$139$	−3.85746	−0.327186	−0.163593	+	0.986528i	$0.552308\pi$
$140$	−13.3764	−1.13051
$141$	−2.09739	−0.176632
$142$	−2.62534	−0.220314
$143$	2.54091	0.212482
$144$	−3.46715	−0.288929
$145$	−1.00482	−0.0834457
$146$	7.19360	0.595347
$147$	−13.8890	−1.14554
$148$	−11.8590	−0.974807
$149$	−0.503725	−0.0412667	−0.0206334	−	0.999787i	$-0.506568\pi$
$149$	−0.503725	−0.0412667	−0.0206334	+	0.999787i	$0.506568\pi$
$150$	−6.77290	−0.553005
$151$	15.6004	1.26954	0.634772	−	0.772699i	$-0.281094\pi$
$151$	15.6004	1.26954	0.634772	+	0.772699i	$0.281094\pi$
$152$	3.60934	0.292756
$153$	8.09044	0.654073
$154$	8.64317	0.696486
$155$	−3.29762	−0.264871
$156$	6.19065	0.495649
$157$	−18.8930	−1.50783	−0.753914	−	0.656973i	$-0.771837\pi$
$157$	−18.8930	−1.50783	−0.753914	+	0.656973i	$0.771837\pi$
$158$	−4.77237	−0.379669
$159$	8.93207	0.708359
$160$	−10.6157	−0.839247
$161$	−11.7596	−0.926785
$162$	−2.05866	−0.161744
$163$	25.3076	1.98225	0.991123	−	0.132949i	$-0.0424446\pi$
$163$	25.3076	1.98225	0.991123	+	0.132949i	$0.0424446\pi$
$164$	2.20251	0.171987
$165$	−1.20125	−0.0935171
$166$	2.67291	0.207458
$167$	25.1869	1.94902	0.974511	−	0.224341i	$-0.0720229\pi$
$167$	25.1869	1.94902	0.974511	+	0.224341i	$0.0720229\pi$
$168$	2.24013	0.172830
$169$	−5.34896	−0.411459
$170$	21.7801	1.67046
$171$	−7.36397	−0.563137
$172$	−20.8313	−1.58837
$173$	0.103255	0.00785036	0.00392518	−	0.999992i	$-0.498751\pi$
$173$	0.103255	0.00785036	0.00392518	+	0.999992i	$0.498751\pi$
$174$	1.58186	0.119921
$175$	−15.0366	−1.13666
$176$	3.18494	0.240074
$177$	−5.92594	−0.445421
$178$	−36.2526	−2.71725
$179$	−4.84058	−0.361802	−0.180901	−	0.983501i	$-0.557901\pi$
$179$	−4.84058	−0.361802	−0.180901	+	0.983501i	$0.557901\pi$
$180$	−2.92671	−0.218144
$181$	−13.7694	−1.02347	−0.511737	−	0.859142i	$-0.670998\pi$
$181$	−13.7694	−1.02347	−0.511737	+	0.859142i	$0.670998\pi$
$182$	26.0258	1.92916
$183$	1.31796	0.0974263
$184$	1.26110	0.0929693
$185$	6.92909	0.509437
$186$	5.19137	0.380650
$187$	−7.43193	−0.543476
$188$	4.69413	0.342355
$189$	−4.57045	−0.332451
$190$	−19.8244	−1.43821
$191$	−24.6216	−1.78155	−0.890776	−	0.454442i	$-0.849839\pi$
$191$	−24.6216	−1.78155	−0.890776	+	0.454442i	$0.849839\pi$
$192$	9.77781	0.705653
$193$	−10.9530	−0.788414	−0.394207	−	0.919022i	$-0.628981\pi$
$193$	−10.9530	−0.788414	−0.394207	+	0.919022i	$0.628981\pi$
$194$	−21.0637	−1.51228
$195$	−3.61713	−0.259028
$196$	31.0847	2.22034
$197$	−8.03654	−0.572580	−0.286290	−	0.958143i	$-0.592422\pi$
$197$	−8.03654	−0.572580	−0.286290	+	0.958143i	$0.592422\pi$
$198$	1.89110	0.134395
$199$	2.84538	0.201704	0.100852	−	0.994901i	$-0.467843\pi$
$199$	2.84538	0.201704	0.100852	+	0.994901i	$0.467843\pi$
$200$	1.61252	0.114023
$201$	−13.4320	−0.947422
$202$	−36.7036	−2.58246
$203$	3.51191	0.246488
$204$	−18.1071	−1.26775
$205$	−1.28690	−0.0898810
$206$	21.0844	1.46902
$207$	−2.57296	−0.178833
$208$	9.59031	0.664968
$209$	6.76459	0.467917
$210$	−12.3040	−0.849058
$211$	−26.2907	−1.80993	−0.904965	−	0.425486i	$-0.860103\pi$
$211$	−26.2907	−1.80993	−0.904965	+	0.425486i	$0.860103\pi$
$212$	−19.9907	−1.37297
$213$	−1.27527	−0.0873798
$214$	−21.2889	−1.45528
$215$	12.1715	0.830088
$216$	0.490135	0.0333494
$217$	11.5254	0.782395
$218$	−19.5884	−1.32670
$219$	3.49431	0.236124
$220$	2.68850	0.181258
$221$	−22.3786	−1.50534
$222$	−10.9083	−0.732118
$223$	3.87781	0.259677	0.129839	−	0.991535i	$-0.458554\pi$
$223$	3.87781	0.259677	0.129839	+	0.991535i	$0.458554\pi$
$224$	37.1027	2.47903
$225$	−3.28996	−0.219330
$226$	31.2646	2.07969
$227$	−17.9875	−1.19387	−0.596937	−	0.802288i	$-0.703616\pi$
$227$	−17.9875	−1.19387	−0.596937	+	0.802288i	$0.703616\pi$
$228$	16.4812	1.09149
$229$	30.2165	1.99676	0.998382	−	0.0568643i	$-0.0181103\pi$
$229$	30.2165	1.99676	0.998382	+	0.0568643i	$0.0181103\pi$
$230$	−6.92662	−0.456728
$231$	4.19844	0.276237
$232$	−0.376617	−0.0247261
$233$	−0.934311	−0.0612088	−0.0306044	−	0.999532i	$-0.509743\pi$
$233$	−0.934311	−0.0612088	−0.0306044	+	0.999532i	$0.509743\pi$
$234$	5.69436	0.372252
$235$	−2.74273	−0.178916
$236$	13.2628	0.863332
$237$	−2.31819	−0.150583
$238$	−76.1229	−4.93432
$239$	−15.2437	−0.986030	−0.493015	−	0.870021i	$-0.664105\pi$
$239$	−15.2437	−0.986030	−0.493015	+	0.870021i	$0.664105\pi$
$240$	−4.53394	−0.292665
$241$	10.1209	0.651944	0.325972	−	0.945379i	$-0.394308\pi$
$241$	10.1209	0.651944	0.325972	+	0.945379i	$0.394308\pi$
$242$	20.9081	1.34402
$243$	−1.00000	−0.0641500
$244$	−2.94970	−0.188835
$245$	−18.1624	−1.16036
$246$	2.02594	0.129169
$247$	20.3691	1.29606
$248$	−1.23598	−0.0784850
$249$	1.29838	0.0822812
$250$	−22.3172	−1.41147
$251$	−12.9253	−0.815840	−0.407920	−	0.913018i	$-0.633746\pi$
$251$	−12.9253	−0.815840	−0.407920	+	0.913018i	$0.633746\pi$
$252$	10.2290	0.644369
$253$	2.36354	0.148594
$254$	1.45769	0.0914633
$255$	10.5798	0.662530
$256$	11.5406	0.721290
$257$	−7.94744	−0.495748	−0.247874	−	0.968792i	$-0.579732\pi$
$257$	−7.94744	−0.495748	−0.247874	+	0.968792i	$0.579732\pi$
$258$	−19.1613	−1.19293
$259$	−24.2176	−1.50481
$260$	8.09543	0.502058
$261$	0.768395	0.0475625
$262$	−25.9066	−1.60052
$263$	29.7439	1.83409	0.917043	−	0.398788i	$-0.130569\pi$
$263$	29.7439	1.83409	0.917043	+	0.398788i	$0.130569\pi$
$264$	−0.450241	−0.0277104
$265$	11.6803	0.717518
$266$	69.2876	4.24830
$267$	−17.6098	−1.07770
$268$	30.0620	1.83633
$269$	3.67792	0.224247	0.112124	−	0.993694i	$-0.464235\pi$
$269$	3.67792	0.224247	0.112124	+	0.993694i	$0.464235\pi$
$270$	−2.69208	−0.163835
$271$	6.41698	0.389804	0.194902	−	0.980823i	$-0.437561\pi$
$271$	6.41698	0.389804	0.194902	+	0.980823i	$0.437561\pi$
$272$	−28.0507	−1.70083
$273$	12.6421	0.765134
$274$	12.7692	0.771415
$275$	3.02218	0.182244
$276$	5.75850	0.346621
$277$	5.46465	0.328339	0.164170	−	0.986432i	$-0.447506\pi$
$277$	5.46465	0.328339	0.164170	+	0.986432i	$0.447506\pi$
$278$	7.94121	0.476282
$279$	2.52172	0.150972
$280$	2.92939	0.175065
$281$	−1.98093	−0.118172	−0.0590861	−	0.998253i	$-0.518819\pi$
$281$	−1.98093	−0.118172	−0.0590861	+	0.998253i	$0.518819\pi$
$282$	4.31781	0.257122
$283$	7.98568	0.474699	0.237350	−	0.971424i	$-0.423721\pi$
$283$	7.98568	0.474699	0.237350	+	0.971424i	$0.423721\pi$
$284$	2.85415	0.169363
$285$	−9.62977	−0.570418
$286$	−5.23088	−0.309308
$287$	4.49780	0.265497
$288$	8.11795	0.478355
$289$	48.4551	2.85030
$290$	2.06858	0.121471
$291$	−10.2317	−0.599795
$292$	−7.82056	−0.457664
$293$	20.4363	1.19390	0.596951	−	0.802277i	$-0.296378\pi$
$293$	20.4363	1.19390	0.596951	+	0.802277i	$0.296378\pi$
$294$	28.5927	1.66756
$295$	−7.74927	−0.451180
$296$	2.59710	0.150953
$297$	0.918607	0.0533030
$298$	1.03700	0.0600717
$299$	7.11694	0.411583
$300$	7.36320	0.425115
$301$	−42.5401	−2.45197
$302$	−32.1160	−1.84807
$303$	−17.8289	−1.02424
$304$	25.5320	1.46436
$305$	1.72348	0.0986860
$306$	−16.6555	−0.952129
$307$	20.0372	1.14359	0.571793	−	0.820398i	$-0.306248\pi$
$307$	20.0372	1.14359	0.571793	+	0.820398i	$0.306248\pi$
$308$	−9.39647	−0.535414
$309$	10.2418	0.582635
$310$	6.78868	0.385571
$311$	−11.8306	−0.670851	−0.335426	−	0.942067i	$-0.608880\pi$
$311$	−11.8306	−0.670851	−0.335426	+	0.942067i	$0.608880\pi$
$312$	−1.35574	−0.0767535
$313$	8.93334	0.504942	0.252471	−	0.967604i	$-0.418757\pi$
$313$	8.93334	0.504942	0.252471	+	0.967604i	$0.418757\pi$
$314$	38.8943	2.19493
$315$	−5.97671	−0.336750
$316$	5.18831	0.291865
$317$	12.1983	0.685124	0.342562	−	0.939495i	$-0.388705\pi$
$317$	12.1983	0.685124	0.342562	+	0.939495i	$0.388705\pi$
$318$	−18.3881	−1.03115
$319$	−0.705853	−0.0395202
$320$	12.7863	0.714776
$321$	−10.3412	−0.577188
$322$	24.2090	1.34911
$323$	−59.5777	−3.31499
$324$	2.23808	0.124338
$325$	9.10019	0.504788
$326$	−52.0998	−2.88554
$327$	−9.51513	−0.526188
$328$	−0.482344	−0.0266330
$329$	9.58600	0.528493
$330$	2.47296	0.136132
$331$	−5.02661	−0.276288	−0.138144	−	0.990412i	$-0.544114\pi$
$331$	−5.02661	−0.276288	−0.138144	+	0.990412i	$0.544114\pi$
$332$	−2.90587	−0.159481
$333$	−5.29874	−0.290369
$334$	−51.8513	−2.83718
$335$	−17.5649	−0.959672
$336$	15.8464	0.864493
$337$	14.9354	0.813581	0.406791	−	0.913521i	$-0.366648\pi$
$337$	14.9354	0.813581	0.406791	+	0.913521i	$0.366648\pi$
$338$	11.0117	0.598957
$339$	15.1869	0.824837
$340$	−23.6784	−1.28414
$341$	−2.31647	−0.125444
$342$	15.1599	0.819755
$343$	31.4858	1.70007
$344$	4.56200	0.245966
$345$	−3.36463	−0.181145
$346$	−0.212568	−0.0114277
$347$	17.6268	0.946255	0.473127	−	0.880994i	$-0.343125\pi$
$347$	17.6268	0.946255	0.473127	+	0.880994i	$0.343125\pi$
$348$	−1.71973	−0.0921874
$349$	20.8482	1.11598	0.557988	−	0.829849i	$-0.311573\pi$
$349$	20.8482	1.11598	0.557988	+	0.829849i	$0.311573\pi$
$350$	30.9552	1.65463
$351$	2.76605	0.147641
$352$	−7.45720	−0.397470
$353$	−12.6378	−0.672640	−0.336320	−	0.941748i	$-0.609182\pi$
$353$	−12.6378	−0.672640	−0.336320	+	0.941748i	$0.609182\pi$
$354$	12.1995	0.648396
$355$	−1.66765	−0.0885096
$356$	39.4122	2.08884
$357$	−36.9769	−1.95703
$358$	9.96512	0.526673
$359$	−4.34767	−0.229461	−0.114731	−	0.993397i	$-0.536600\pi$
$359$	−4.34767	−0.229461	−0.114731	+	0.993397i	$0.536600\pi$
$360$	0.640942	0.0337806
$361$	35.2281	1.85411
$362$	28.3466	1.48986
$363$	10.1562	0.533060
$364$	−28.2941	−1.48301
$365$	4.56946	0.239177
$366$	−2.71323	−0.141823
$367$	19.5724	1.02167	0.510836	−	0.859678i	$-0.329336\pi$
$367$	19.5724	1.02167	0.510836	+	0.859678i	$0.329336\pi$
$368$	8.92083	0.465031
$369$	0.984105	0.0512305
$370$	−14.2647	−0.741584
$371$	−40.8235	−2.11945
$372$	−5.64383	−0.292619
$373$	7.97016	0.412679	0.206340	−	0.978480i	$-0.433845\pi$
$373$	7.97016	0.412679	0.206340	+	0.978480i	$0.433845\pi$
$374$	15.2998	0.791135
$375$	−10.8407	−0.559809
$376$	−1.02800	−0.0530152
$377$	−2.12542	−0.109465
$378$	9.40900	0.483947
$379$	8.82125	0.453117	0.226559	−	0.973998i	$-0.427253\pi$
$379$	8.82125	0.453117	0.226559	+	0.973998i	$0.427253\pi$
$380$	21.5522	1.10561
$381$	0.708075	0.0362758
$382$	50.6874	2.59339
$383$	13.9233	0.711448	0.355724	−	0.934591i	$-0.384234\pi$
$383$	13.9233	0.711448	0.355724	+	0.934591i	$0.384234\pi$
$384$	−3.89329	−0.198679
$385$	5.49025	0.279809
$386$	22.5485	1.14769
$387$	−9.30764	−0.473134
$388$	22.8995	1.16254
$389$	19.9379	1.01089	0.505446	−	0.862858i	$-0.331328\pi$
$389$	19.9379	1.01089	0.505446	+	0.862858i	$0.331328\pi$
$390$	7.44644	0.377065
$391$	−20.8164	−1.05273
$392$	−6.80748	−0.343829
$393$	−12.5842	−0.634789
$394$	16.5445	0.833500
$395$	−3.03147	−0.152530
$396$	−2.05592	−0.103314
$397$	4.75621	0.238707	0.119354	−	0.992852i	$-0.461918\pi$
$397$	4.75621	0.238707	0.119354	+	0.992852i	$0.461918\pi$
$398$	−5.85767	−0.293618
$399$	33.6566	1.68494
$400$	11.4068	0.570338
$401$	18.3981	0.918760	0.459380	−	0.888240i	$-0.348072\pi$
$401$	18.3981	0.918760	0.459380	+	0.888240i	$0.348072\pi$
$402$	27.6520	1.37916
$403$	−6.97521	−0.347460
$404$	39.9026	1.98523
$405$	−1.30769	−0.0649795
$406$	−7.22983	−0.358810
$407$	4.86746	0.241271
$408$	3.96540	0.196317
$409$	−12.4959	−0.617882	−0.308941	−	0.951081i	$-0.599975\pi$
$409$	−12.4959	−0.617882	−0.308941	+	0.951081i	$0.599975\pi$
$410$	2.64929	0.130839
$411$	6.20267	0.305955
$412$	−22.9220	−1.12929
$413$	27.0842	1.33273
$414$	5.29685	0.260326
$415$	1.69787	0.0833450
$416$	−22.4547	−1.10093
$417$	3.85746	0.188901
$418$	−13.9260	−0.681143
$419$	14.0663	0.687182	0.343591	−	0.939119i	$-0.388357\pi$
$419$	14.0663	0.687182	0.343591	+	0.939119i	$0.388357\pi$
$420$	13.3764	0.652701
$421$	−14.8262	−0.722584	−0.361292	−	0.932453i	$-0.617664\pi$
$421$	−14.8262	−0.722584	−0.361292	+	0.932453i	$0.617664\pi$
$422$	54.1237	2.63470
$423$	2.09739	0.101978
$424$	4.37792	0.212610
$425$	−26.6172	−1.29112
$426$	2.62534	0.127198
$427$	−6.02366	−0.291505
$428$	23.1444	1.11873
$429$	−2.54091	−0.122676
$430$	−25.0569	−1.20835
$431$	8.14128	0.392152	0.196076	−	0.980589i	$-0.437180\pi$
$431$	8.14128	0.392152	0.196076	+	0.980589i	$0.437180\pi$
$432$	3.46715	0.166813
$433$	−19.0089	−0.913511	−0.456756	−	0.889592i	$-0.650989\pi$
$433$	−19.0089	−0.913511	−0.456756	+	0.889592i	$0.650989\pi$
$434$	−23.7269	−1.13893
$435$	1.00482	0.0481774
$436$	21.2957	1.01988
$437$	18.9472	0.906368
$438$	−7.19360	−0.343724
$439$	−34.1757	−1.63112	−0.815559	−	0.578674i	$-0.803570\pi$
$439$	−34.1757	−1.63112	−0.815559	+	0.578674i	$0.803570\pi$
$440$	−0.588774	−0.0280687
$441$	13.8890	0.661380
$442$	46.0699	2.19132
$443$	−4.17730	−0.198469	−0.0992347	−	0.995064i	$-0.531639\pi$
$443$	−4.17730	−0.198469	−0.0992347	+	0.995064i	$0.531639\pi$
$444$	11.8590	0.562805
$445$	−23.0281	−1.09164
$446$	−7.98309	−0.378010
$447$	0.503725	0.0238254
$448$	−44.6890	−2.11136
$449$	14.1970	0.669999	0.334999	−	0.942218i	$-0.391264\pi$
$449$	14.1970	0.669999	0.334999	+	0.942218i	$0.391264\pi$
$450$	6.77290	0.319278
$451$	−0.904005	−0.0425679
$452$	−33.9895	−1.59873
$453$	−15.6004	−0.732972
$454$	37.0302	1.73791
$455$	16.5319	0.775027
$456$	−3.60934	−0.169023
$457$	23.7143	1.10931	0.554654	−	0.832081i	$-0.312851\pi$
$457$	23.7143	1.10931	0.554654	+	0.832081i	$0.312851\pi$
$458$	−62.2056	−2.90668
$459$	−8.09044	−0.377629
$460$	7.53032	0.351103
$461$	−22.8085	−1.06230	−0.531149	−	0.847279i	$-0.678240\pi$
$461$	−22.8085	−1.06230	−0.531149	+	0.847279i	$0.678240\pi$
$462$	−8.64317	−0.402117
$463$	−18.8214	−0.874704	−0.437352	−	0.899290i	$-0.644084\pi$
$463$	−18.8214	−0.874704	−0.437352	+	0.899290i	$0.644084\pi$
$464$	−2.66414	−0.123680
$465$	3.29762	0.152924
$466$	1.92343	0.0891012
$467$	33.8786	1.56771	0.783857	−	0.620941i	$-0.213250\pi$
$467$	33.8786	1.56771	0.783857	+	0.620941i	$0.213250\pi$
$468$	−6.19065	−0.286163
$469$	61.3904	2.83474
$470$	5.64634	0.260446
$471$	18.8930	0.870545
$472$	−2.90451	−0.133691
$473$	8.55006	0.393132
$474$	4.77237	0.219202
$475$	24.2271	1.11162
$476$	82.7574	3.79318
$477$	−8.93207	−0.408971
$478$	31.3815	1.43536
$479$	−21.0401	−0.961348	−0.480674	−	0.876899i	$-0.659608\pi$
$479$	−21.0401	−0.961348	−0.480674	+	0.876899i	$0.659608\pi$
$480$	10.6157	0.484540
$481$	14.6566	0.668283
$482$	−20.8355	−0.949030
$483$	11.7596	0.535080
$484$	−22.7303	−1.03320
$485$	−13.3799	−0.607550
$486$	2.05866	0.0933827
$487$	−11.3560	−0.514587	−0.257294	−	0.966333i	$-0.582831\pi$
$487$	−11.3560	−0.514587	−0.257294	+	0.966333i	$0.582831\pi$
$488$	0.645977	0.0292420
$489$	−25.3076	−1.14445
$490$	37.3903	1.68912
$491$	1.43605	0.0648082	0.0324041	−	0.999475i	$-0.489684\pi$
$491$	1.43605	0.0648082	0.0324041	+	0.999475i	$0.489684\pi$
$492$	−2.20251	−0.0992968
$493$	6.21665	0.279984
$494$	−41.9331	−1.88666
$495$	1.20125	0.0539921
$496$	−8.74318	−0.392581
$497$	5.82854	0.261446
$498$	−2.67291	−0.119776
$499$	−5.32086	−0.238194	−0.119097	−	0.992883i	$-0.538000\pi$
$499$	−5.32086	−0.238194	−0.119097	+	0.992883i	$0.538000\pi$
$500$	24.2623	1.08504
$501$	−25.1869	−1.12527
$502$	26.6089	1.18761
$503$	30.7386	1.37057	0.685283	−	0.728277i	$-0.259678\pi$
$503$	30.7386	1.37057	0.685283	+	0.728277i	$0.259678\pi$
$504$	−2.24013	−0.0997835
$505$	−23.3146	−1.03749
$506$	−4.86572	−0.216308
$507$	5.34896	0.237556
$508$	−1.58473	−0.0703111
$509$	0.602871	0.0267218	0.0133609	−	0.999911i	$-0.495747\pi$
$509$	0.602871	0.0267218	0.0133609	+	0.999911i	$0.495747\pi$
$510$	−21.7801	−0.964440
$511$	−15.9706	−0.706496
$512$	−31.5449	−1.39410
$513$	7.36397	0.325127
$514$	16.3611	0.721657
$515$	13.3930	0.590168
$516$	20.8313	0.917046
$517$	−1.92667	−0.0847350
$518$	49.8559	2.19054
$519$	−0.103255	−0.00453241
$520$	−1.77288	−0.0777459
$521$	−22.9929	−1.00734	−0.503668	−	0.863897i	$-0.668017\pi$
$521$	−22.9929	−1.00734	−0.503668	+	0.863897i	$0.668017\pi$
$522$	−1.58186	−0.0692363
$523$	−19.8923	−0.869828	−0.434914	−	0.900472i	$-0.643221\pi$
$523$	−19.8923	−0.869828	−0.434914	+	0.900472i	$0.643221\pi$
$524$	28.1645	1.23037
$525$	15.0366	0.656250
$526$	−61.2326	−2.66987
$527$	20.4018	0.888718
$528$	−3.18494	−0.138607
$529$	−16.3799	−0.712168
$530$	−24.0459	−1.04449
$531$	5.92594	0.257164
$532$	−75.3264	−3.26581
$533$	−2.72208	−0.117907
$534$	36.2526	1.56880
$535$	−13.5230	−0.584650
$536$	−6.58350	−0.284364
$537$	4.84058	0.208887
$538$	−7.57160	−0.326435
$539$	−12.7585	−0.549548
$540$	2.92671	0.125946
$541$	13.4010	0.576156	0.288078	−	0.957607i	$-0.406984\pi$
$541$	13.4010	0.576156	0.288078	+	0.957607i	$0.406984\pi$
$542$	−13.2104	−0.567435
$543$	13.7694	0.590903
$544$	65.6777	2.81591
$545$	−12.4428	−0.532991
$546$	−26.0258	−1.11380
$547$	−21.5692	−0.922233	−0.461117	−	0.887339i	$-0.652551\pi$
$547$	−21.5692	−0.922233	−0.461117	+	0.887339i	$0.652551\pi$
$548$	−13.8821	−0.593014
$549$	−1.31796	−0.0562491
$550$	−6.22163	−0.265291
$551$	−5.65844	−0.241058
$552$	−1.26110	−0.0536759
$553$	10.5952	0.450552
$554$	−11.2499	−0.477961
$555$	−6.92909	−0.294124
$556$	−8.63333	−0.366135
$557$	27.3453	1.15866	0.579329	−	0.815094i	$-0.303315\pi$
$557$	27.3453	1.15866	0.579329	+	0.815094i	$0.303315\pi$
$558$	−5.19137	−0.219768
$559$	25.7454	1.08891
$560$	20.7221	0.875670
$561$	7.43193	0.313776
$562$	4.07806	0.172022
$563$	39.9668	1.68440	0.842200	−	0.539165i	$-0.181260\pi$
$563$	39.9668	1.68440	0.842200	+	0.539165i	$0.181260\pi$
$564$	−4.69413	−0.197659
$565$	19.8596	0.835502
$566$	−16.4398	−0.691016
$567$	4.57045	0.191941
$568$	−0.625053	−0.0262266
$569$	−4.70878	−0.197402	−0.0987011	−	0.995117i	$-0.531469\pi$
$569$	−4.70878	−0.197402	−0.0987011	+	0.995117i	$0.531469\pi$
$570$	19.8244	0.830354
$571$	18.2039	0.761809	0.380905	−	0.924614i	$-0.375613\pi$
$571$	18.2039	0.761809	0.380905	+	0.924614i	$0.375613\pi$
$572$	5.68678	0.237776
$573$	24.6216	1.02858
$574$	−9.25944	−0.386482
$575$	8.46493	0.353012
$576$	−9.77781	−0.407409
$577$	23.1345	0.963104	0.481552	−	0.876418i	$-0.340073\pi$
$577$	23.1345	0.963104	0.481552	+	0.876418i	$0.340073\pi$
$578$	−99.7527	−4.14917
$579$	10.9530	0.455191
$580$	−2.24887	−0.0933793
$581$	−5.93416	−0.246190
$582$	21.0637	0.873117
$583$	8.20505	0.339819
$584$	1.71268	0.0708713
$585$	3.61713	0.149550
$586$	−42.0715	−1.73796
$587$	24.7217	1.02037	0.510187	−	0.860064i	$-0.329576\pi$
$587$	24.7217	1.02037	0.510187	+	0.860064i	$0.329576\pi$
$588$	−31.0847	−1.28191
$589$	−18.5699	−0.765159
$590$	15.9531	0.656780
$591$	8.03654	0.330579
$592$	18.3715	0.755065
$593$	9.84188	0.404157	0.202079	−	0.979369i	$-0.435230\pi$
$593$	9.84188	0.404157	0.202079	+	0.979369i	$0.435230\pi$
$594$	−1.89110	−0.0775927
$595$	−48.3542	−1.98233
$596$	−1.12738	−0.0461792
$597$	−2.84538	−0.116454
$598$	−14.6514	−0.599139
$599$	0.826523	0.0337708	0.0168854	−	0.999857i	$-0.494625\pi$
$599$	0.826523	0.0337708	0.0168854	+	0.999857i	$0.494625\pi$
$600$	−1.61252	−0.0658309
$601$	13.5602	0.553133	0.276567	−	0.960995i	$-0.410803\pi$
$601$	13.5602	0.553133	0.276567	+	0.960995i	$0.410803\pi$
$602$	87.5756	3.56931
$603$	13.4320	0.546994
$604$	34.9151	1.42067
$605$	13.2811	0.539952
$606$	36.7036	1.49098
$607$	0.381423	0.0154815	0.00774073	−	0.999970i	$-0.497536\pi$
$607$	0.381423	0.0154815	0.00774073	+	0.999970i	$0.497536\pi$
$608$	−59.7804	−2.42441
$609$	−3.51191	−0.142310
$610$	−3.54805	−0.143657
$611$	−5.80148	−0.234703
$612$	18.1071	0.731935
$613$	−1.03537	−0.0418183	−0.0209091	−	0.999781i	$-0.506656\pi$
$613$	−1.03537	−0.0418183	−0.0209091	+	0.999781i	$0.506656\pi$
$614$	−41.2499	−1.66471
$615$	1.28690	0.0518928
$616$	2.05780	0.0829112
$617$	31.2149	1.25667	0.628333	−	0.777945i	$-0.283738\pi$
$617$	31.2149	1.25667	0.628333	+	0.777945i	$0.283738\pi$
$618$	−21.0844	−0.848138
$619$	−45.4979	−1.82872	−0.914358	−	0.404906i	$-0.867304\pi$
$619$	−45.4979	−1.82872	−0.914358	+	0.404906i	$0.867304\pi$
$620$	−7.38036	−0.296402
$621$	2.57296	0.103249
$622$	24.3552	0.976554
$623$	80.4846	3.22455
$624$	−9.59031	−0.383920
$625$	2.27360	0.0909438
$626$	−18.3907	−0.735041
$627$	−6.76459	−0.270152
$628$	−42.2842	−1.68732
$629$	−42.8691	−1.70930
$630$	12.3040	0.490204
$631$	36.2113	1.44155	0.720774	−	0.693170i	$-0.243786\pi$
$631$	36.2113	1.44155	0.720774	+	0.693170i	$0.243786\pi$
$632$	−1.13623	−0.0451966
$633$	26.2907	1.04496
$634$	−25.1121	−0.997330
$635$	0.925940	0.0367448
$636$	19.9907	0.792683
$637$	−38.4176	−1.52216
$638$	1.45311	0.0575292
$639$	1.27527	0.0504488
$640$	−5.09121	−0.201248
$641$	19.7363	0.779539	0.389769	−	0.920913i	$-0.372555\pi$
$641$	19.7363	0.779539	0.389769	+	0.920913i	$0.372555\pi$
$642$	21.2889	0.840208
$643$	−29.2664	−1.15416	−0.577078	−	0.816689i	$-0.695807\pi$
$643$	−29.2664	−1.15416	−0.577078	+	0.816689i	$0.695807\pi$
$644$	−26.3189	−1.03711
$645$	−12.1715	−0.479251
$646$	122.650	4.82561
$647$	37.0532	1.45671	0.728355	−	0.685199i	$-0.240285\pi$
$647$	37.0532	1.45671	0.728355	+	0.685199i	$0.240285\pi$
$648$	−0.490135	−0.0192543
$649$	−5.44361	−0.213680
$650$	−18.7342	−0.734816
$651$	−11.5254	−0.451716
$652$	56.6406	2.21822
$653$	−27.7963	−1.08775	−0.543877	−	0.839165i	$-0.683044\pi$
$653$	−27.7963	−1.08775	−0.543877	+	0.839165i	$0.683044\pi$
$654$	19.5884	0.765968
$655$	−16.4562	−0.642997
$656$	−3.41204	−0.133218
$657$	−3.49431	−0.136326
$658$	−19.7343	−0.769324
$659$	−42.3761	−1.65074	−0.825370	−	0.564592i	$-0.809034\pi$
$659$	−42.3761	−1.65074	−0.825370	+	0.564592i	$0.809034\pi$
$660$	−2.68850	−0.104650
$661$	46.7817	1.81960	0.909798	−	0.415052i	$-0.136237\pi$
$661$	46.7817	1.81960	0.909798	+	0.415052i	$0.136237\pi$
$662$	10.3481	0.402190
$663$	22.3786	0.869111
$664$	0.636379	0.0246963
$665$	44.0123	1.70673
$666$	10.9083	0.422689
$667$	−1.97705	−0.0765517
$668$	56.3704	2.18104
$669$	−3.87781	−0.149925
$670$	36.1601	1.39699
$671$	1.21069	0.0467380
$672$	−37.1027	−1.43127
$673$	12.6268	0.486726	0.243363	−	0.969935i	$-0.421749\pi$
$673$	12.6268	0.486726	0.243363	+	0.969935i	$0.421749\pi$
$674$	−30.7469	−1.18432
$675$	3.28996	0.126630
$676$	−11.9714	−0.460440
$677$	−25.4414	−0.977791	−0.488896	−	0.872342i	$-0.662600\pi$
$677$	−25.4414	−0.977791	−0.488896	+	0.872342i	$0.662600\pi$
$678$	−31.2646	−1.20071
$679$	46.7636	1.79462
$680$	5.18550	0.198855
$681$	17.9875	0.689283
$682$	4.76883	0.182608
$683$	7.25195	0.277488	0.138744	−	0.990328i	$-0.455693\pi$
$683$	7.25195	0.277488	0.138744	+	0.990328i	$0.455693\pi$
$684$	−16.4812	−0.630174
$685$	8.11115	0.309911
$686$	−64.8185	−2.47478
$687$	−30.2165	−1.15283
$688$	32.2710	1.23032
$689$	24.7065	0.941245
$690$	6.92662	0.263692
$691$	12.9723	0.493489	0.246745	−	0.969081i	$-0.420639\pi$
$691$	12.9723	0.493489	0.246745	+	0.969081i	$0.420639\pi$
$692$	0.231094	0.00878489
$693$	−4.19844	−0.159486
$694$	−36.2875	−1.37746
$695$	5.04435	0.191343
$696$	0.376617	0.0142756
$697$	7.96184	0.301576
$698$	−42.9193	−1.62452
$699$	0.934311	0.0353389
$700$	−33.6531	−1.27197
$701$	36.8307	1.39108	0.695538	−	0.718489i	$-0.255166\pi$
$701$	36.8307	1.39108	0.695538	+	0.718489i	$0.255166\pi$
$702$	−5.69436	−0.214920
$703$	39.0198	1.47166
$704$	8.98196	0.338520
$705$	2.74273	0.103297
$706$	26.0169	0.979158
$707$	81.4860	3.06460
$708$	−13.2628	−0.498445
$709$	18.5658	0.697253	0.348627	−	0.937262i	$-0.386648\pi$
$709$	18.5658	0.697253	0.348627	+	0.937262i	$0.386648\pi$
$710$	3.43312	0.128843
$711$	2.31819	0.0869390
$712$	−8.63117	−0.323467
$713$	−6.48829	−0.242988
$714$	76.1229	2.84883
$715$	−3.32272	−0.124263
$716$	−10.8336	−0.404872
$717$	15.2437	0.569285
$718$	8.95038	0.334025
$719$	−17.4201	−0.649659	−0.324830	−	0.945773i	$-0.605307\pi$
$719$	−17.4201	−0.649659	−0.324830	+	0.945773i	$0.605307\pi$
$720$	4.53394	0.168970
$721$	−46.8096	−1.74328
$722$	−72.5227	−2.69902
$723$	−10.1209	−0.376400
$724$	−30.8172	−1.14531
$725$	−2.52799	−0.0938871
$726$	−20.9081	−0.775972
$727$	38.8655	1.44144	0.720721	−	0.693225i	$-0.243811\pi$
$727$	38.8655	1.44144	0.720721	+	0.693225i	$0.243811\pi$
$728$	6.19633	0.229651
$729$	1.00000	0.0370370
$730$	−9.40697	−0.348168
$731$	−75.3029	−2.78518
$732$	2.94970	0.109024
$733$	−22.5046	−0.831226	−0.415613	−	0.909542i	$-0.636433\pi$
$733$	−22.5046	−0.831226	−0.415613	+	0.909542i	$0.636433\pi$
$734$	−40.2930	−1.48724
$735$	18.1624	0.669932
$736$	−20.8872	−0.769911
$737$	−12.3387	−0.454504
$738$	−2.02594	−0.0745758
$739$	−33.6968	−1.23956	−0.619778	−	0.784777i	$-0.712777\pi$
$739$	−33.6968	−1.23956	−0.619778	+	0.784777i	$0.712777\pi$
$740$	15.5079	0.570082
$741$	−20.3691	−0.748278
$742$	84.0418	3.08527
$743$	−7.24403	−0.265758	−0.132879	−	0.991132i	$-0.542422\pi$
$743$	−7.24403	−0.265758	−0.132879	+	0.991132i	$0.542422\pi$
$744$	1.23598	0.0453134
$745$	0.658714	0.0241334
$746$	−16.4079	−0.600735
$747$	−1.29838	−0.0475051
$748$	−16.6333	−0.608173
$749$	47.2637	1.72698
$750$	22.3172	0.814911
$751$	41.8949	1.52877	0.764384	−	0.644761i	$-0.223043\pi$
$751$	41.8949	1.52877	0.764384	+	0.644761i	$0.223043\pi$
$752$	−7.27195	−0.265181
$753$	12.9253	0.471025
$754$	4.37552	0.159347
$755$	−20.4005	−0.742449
$756$	−10.2290	−0.372027
$757$	1.30512	0.0474354	0.0237177	−	0.999719i	$-0.492450\pi$
$757$	1.30512	0.0474354	0.0237177	+	0.999719i	$0.492450\pi$
$758$	−18.1600	−0.659600
$759$	−2.36354	−0.0857910
$760$	−4.71988	−0.171208
$761$	2.45401	0.0889579	0.0444789	−	0.999010i	$-0.485837\pi$
$761$	2.45401	0.0889579	0.0444789	+	0.999010i	$0.485837\pi$
$762$	−1.45769	−0.0528064
$763$	43.4884	1.57439
$764$	−55.1051	−1.99363
$765$	−10.5798	−0.382512
$766$	−28.6634	−1.03565
$767$	−16.3915	−0.591861
$768$	−11.5406	−0.416437
$769$	3.58245	0.129186	0.0645932	−	0.997912i	$-0.479425\pi$
$769$	3.58245	0.129186	0.0645932	+	0.997912i	$0.479425\pi$
$770$	−11.3026	−0.407316
$771$	7.94744	0.286220
$772$	−24.5137	−0.882268
$773$	12.6657	0.455554	0.227777	−	0.973713i	$-0.426854\pi$
$773$	12.6657	0.455554	0.227777	+	0.973713i	$0.426854\pi$
$774$	19.1613	0.688738
$775$	−8.29636	−0.298014
$776$	−5.01492	−0.180025
$777$	24.2176	0.868803
$778$	−41.0454	−1.47155
$779$	−7.24692	−0.259648
$780$	−8.09543	−0.289863
$781$	−1.17147	−0.0419184
$782$	42.8539	1.53245
$783$	−0.768395	−0.0274602
$784$	−48.1552	−1.71983
$785$	24.7062	0.881801
$786$	25.9066	0.924059
$787$	7.96377	0.283878	0.141939	−	0.989875i	$-0.454666\pi$
$787$	7.96377	0.283878	0.141939	+	0.989875i	$0.454666\pi$
$788$	−17.9864	−0.640741
$789$	−29.7439	−1.05891
$790$	6.24076	0.222036
$791$	−69.4107	−2.46796
$792$	0.450241	0.0159986
$793$	3.64554	0.129457
$794$	−9.79142	−0.347484
$795$	−11.6803	−0.414259
$796$	6.36820	0.225715
$797$	−55.5697	−1.96838	−0.984189	−	0.177121i	$-0.943322\pi$
$797$	−55.5697	−1.96838	−0.984189	+	0.177121i	$0.943322\pi$
$798$	−69.2876	−2.45276
$799$	16.9688	0.600312
$800$	−26.7077	−0.944260
$801$	17.6098	0.622211
$802$	−37.8755	−1.33743
$803$	3.20990	0.113275
$804$	−30.0620	−1.06021
$805$	15.3778	0.541998
$806$	14.3596	0.505795
$807$	−3.67792	−0.129469
$808$	−8.73856	−0.307421
$809$	−44.1167	−1.55106	−0.775529	−	0.631311i	$-0.782517\pi$
$809$	−44.1167	−1.55106	−0.775529	+	0.631311i	$0.782517\pi$
$810$	2.69208	0.0945901
$811$	−39.4278	−1.38450	−0.692249	−	0.721659i	$-0.743380\pi$
$811$	−39.4278	−1.38450	−0.692249	+	0.721659i	$0.743380\pi$
$812$	7.85995	0.275830
$813$	−6.41698	−0.225053
$814$	−10.0205	−0.351217
$815$	−33.0944	−1.15925
$816$	28.0507	0.981972
$817$	68.5412	2.39795
$818$	25.7248	0.899447
$819$	−12.6421	−0.441750
$820$	−2.88019	−0.100581
$821$	−36.8785	−1.28707	−0.643534	−	0.765417i	$-0.722533\pi$
$821$	−36.8785	−1.28707	−0.643534	+	0.765417i	$0.722533\pi$
$822$	−12.7692	−0.445377
$823$	23.8121	0.830039	0.415020	−	0.909813i	$-0.363775\pi$
$823$	23.8121	0.830039	0.415020	+	0.909813i	$0.363775\pi$
$824$	5.01986	0.174875
$825$	−3.02218	−0.105219
$826$	−55.7572	−1.94004
$827$	14.0870	0.489854	0.244927	−	0.969542i	$-0.421236\pi$
$827$	14.0870	0.489854	0.244927	+	0.969542i	$0.421236\pi$
$828$	−5.75850	−0.200122
$829$	−10.3678	−0.360087	−0.180044	−	0.983659i	$-0.557624\pi$
$829$	−10.3678	−0.360087	−0.180044	+	0.983659i	$0.557624\pi$
$830$	−3.49533	−0.121325
$831$	−5.46465	−0.189567
$832$	27.0459	0.937649
$833$	112.368	3.89332
$834$	−7.94121	−0.274982
$835$	−32.9366	−1.13982
$836$	15.1397	0.523619
$837$	−2.52172	−0.0871635
$838$	−28.9577	−1.00033
$839$	54.1742	1.87030	0.935150	−	0.354253i	$-0.115265\pi$
$839$	54.1742	1.87030	0.935150	+	0.354253i	$0.115265\pi$
$840$	−2.92939	−0.101074
$841$	−28.4096	−0.979640
$842$	30.5221	1.05186
$843$	1.98093	0.0682268
$844$	−58.8409	−2.02539
$845$	6.99476	0.240627
$846$	−4.31781	−0.148449
$847$	−46.4182	−1.59495
$848$	30.9688	1.06347
$849$	−7.98568	−0.274068
$850$	54.7957	1.87948
$851$	13.6335	0.467349
$852$	−2.85415	−0.0977817
$853$	−3.80636	−0.130327	−0.0651637	−	0.997875i	$-0.520757\pi$
$853$	−3.80636	−0.130327	−0.0651637	+	0.997875i	$0.520757\pi$
$854$	12.4007	0.424342
$855$	9.62977	0.329331
$856$	−5.06856	−0.173240
$857$	−28.7673	−0.982672	−0.491336	−	0.870970i	$-0.663491\pi$
$857$	−28.7673	−0.982672	−0.491336	+	0.870970i	$0.663491\pi$
$858$	5.23088	0.178579
$859$	−9.12311	−0.311276	−0.155638	−	0.987814i	$-0.549743\pi$
$859$	−9.12311	−0.311276	−0.155638	+	0.987814i	$0.549743\pi$
$860$	27.2408	0.928903
$861$	−4.49780	−0.153285
$862$	−16.7601	−0.570852
$863$	−31.6936	−1.07886	−0.539431	−	0.842030i	$-0.681361\pi$
$863$	−31.6936	−1.07886	−0.539431	+	0.842030i	$0.681361\pi$
$864$	−8.11795	−0.276178
$865$	−0.135026	−0.00459101
$866$	39.1330	1.32979
$867$	−48.4551	−1.64562
$868$	25.7948	0.875533
$869$	−2.12951	−0.0722385
$870$	−2.06858	−0.0701315
$871$	−37.1537	−1.25890
$872$	−4.66370	−0.157933
$873$	10.2317	0.346292
$874$	−39.0059	−1.31939
$875$	49.5467	1.67498
$876$	7.82056	0.264232
$877$	−43.6458	−1.47381	−0.736907	−	0.675994i	$-0.763714\pi$
$877$	−43.6458	−1.47381	−0.736907	+	0.675994i	$0.763714\pi$
$878$	70.3562	2.37441
$879$	−20.4363	−0.689300
$880$	−4.16491	−0.140399
$881$	46.5937	1.56978	0.784891	−	0.619634i	$-0.212719\pi$
$881$	46.5937	1.56978	0.784891	+	0.619634i	$0.212719\pi$
$882$	−28.5927	−0.962767
$883$	45.6099	1.53489	0.767447	−	0.641113i	$-0.221527\pi$
$883$	45.6099	1.53489	0.767447	+	0.641113i	$0.221527\pi$
$884$	−50.0851	−1.68454
$885$	7.74927	0.260489
$886$	8.59964	0.288911
$887$	13.1230	0.440628	0.220314	−	0.975429i	$-0.429292\pi$
$887$	13.1230	0.440628	0.220314	+	0.975429i	$0.429292\pi$
$888$	−2.59710	−0.0871529
$889$	−3.23622	−0.108539
$890$	47.4070	1.58909
$891$	−0.918607	−0.0307745
$892$	8.67886	0.290590
$893$	−15.4451	−0.516851
$894$	−1.03700	−0.0346824
$895$	6.32997	0.211587
$896$	17.7941	0.594459
$897$	−7.11694	−0.237628
$898$	−29.2268	−0.975313
$899$	1.93768	0.0646252
$900$	−7.36320	−0.245440
$901$	−72.2643	−2.40747
$902$	1.86104	0.0619659
$903$	42.5401	1.41565
$904$	7.44361	0.247571
$905$	18.0061	0.598543
$906$	32.1160	1.06698
$907$	17.4016	0.577812	0.288906	−	0.957357i	$-0.406708\pi$
$907$	17.4016	0.577812	0.288906	+	0.957357i	$0.406708\pi$
$908$	−40.2576	−1.33600
$909$	17.8289	0.591347
$910$	−34.0335	−1.12820
$911$	53.0873	1.75886	0.879430	−	0.476027i	$-0.157924\pi$
$911$	53.0873	1.75886	0.879430	+	0.476027i	$0.157924\pi$
$912$	−25.5320	−0.845448
$913$	1.19270	0.0394725
$914$	−48.8197	−1.61481
$915$	−1.72348	−0.0569764
$916$	67.6271	2.23446
$917$	57.5155	1.89933
$918$	16.6555	0.549712
$919$	3.10598	0.102457	0.0512284	−	0.998687i	$-0.483686\pi$
$919$	3.10598	0.102457	0.0512284	+	0.998687i	$0.483686\pi$
$920$	−1.64912	−0.0543699
$921$	−20.0372	−0.660249
$922$	46.9550	1.54638
$923$	−3.52745	−0.116108
$924$	9.39647	0.309121
$925$	17.4326	0.573182
$926$	38.7468	1.27330
$927$	−10.2418	−0.336385
$928$	6.23779	0.204766
$929$	14.3277	0.470078	0.235039	−	0.971986i	$-0.424478\pi$
$929$	14.3277	0.470078	0.235039	+	0.971986i	$0.424478\pi$
$930$	−6.78868	−0.222610
$931$	−102.278	−3.35203
$932$	−2.09107	−0.0684952
$933$	11.8306	0.387316
$934$	−69.7445	−2.28211
$935$	9.71863	0.317833
$936$	1.35574	0.0443137
$937$	22.5807	0.737678	0.368839	−	0.929493i	$-0.379755\pi$
$937$	22.5807	0.737678	0.368839	+	0.929493i	$0.379755\pi$
$938$	−126.382	−4.12652
$939$	−8.93334	−0.291529
$940$	−6.13845	−0.200214
$941$	−45.2967	−1.47663	−0.738315	−	0.674456i	$-0.764378\pi$
$941$	−45.2967	−1.47663	−0.738315	+	0.674456i	$0.764378\pi$
$942$	−38.8943	−1.26725
$943$	−2.53206	−0.0824553
$944$	−20.5461	−0.668719
$945$	5.97671	0.194422
$946$	−17.6017	−0.572280
$947$	44.6180	1.44989	0.724944	−	0.688807i	$-0.241865\pi$
$947$	44.6180	1.44989	0.724944	+	0.688807i	$0.241865\pi$
$948$	−5.18831	−0.168508
$949$	9.66544	0.313754
$950$	−49.8755	−1.61817
$951$	−12.1983	−0.395557
$952$	−18.1237	−0.587391
$953$	44.2331	1.43285	0.716426	−	0.697663i	$-0.245777\pi$
$953$	44.2331	1.43285	0.716426	+	0.697663i	$0.245777\pi$
$954$	18.3881	0.595337
$955$	32.1973	1.04188
$956$	−34.1166	−1.10341
$957$	0.705853	0.0228170
$958$	43.3145	1.39943
$959$	−28.3490	−0.915436
$960$	−12.7863	−0.412676
$961$	−24.6409	−0.794868
$962$	−30.1730	−0.972815
$963$	10.3412	0.333239
$964$	22.6514	0.729553
$965$	14.3231	0.461076
$966$	−24.2090	−0.778911
$967$	−49.2481	−1.58371	−0.791856	−	0.610707i	$-0.790885\pi$
$967$	−49.2481	−1.58371	−0.791856	+	0.610707i	$0.790885\pi$
$968$	4.97789	0.159995
$969$	59.5777	1.91391
$970$	27.5447	0.884406
$971$	48.6674	1.56181	0.780905	−	0.624650i	$-0.214758\pi$
$971$	48.6674	1.56181	0.780905	+	0.624650i	$0.214758\pi$
$972$	−2.23808	−0.0717866
$973$	−17.6303	−0.565202
$974$	23.3781	0.749081
$975$	−9.10019	−0.291439
$976$	4.56956	0.146268
$977$	−18.2388	−0.583512	−0.291756	−	0.956493i	$-0.594240\pi$
$977$	−18.2388	−0.583512	−0.291756	+	0.956493i	$0.594240\pi$
$978$	52.0998	1.66597
$979$	−16.1765	−0.517002
$980$	−40.6491	−1.29849
$981$	9.51513	0.303795
$982$	−2.95635	−0.0943409
$983$	−17.3628	−0.553787	−0.276894	−	0.960901i	$-0.589305\pi$
$983$	−17.3628	−0.553787	−0.276894	+	0.960901i	$0.589305\pi$
$984$	0.482344	0.0153766
$985$	10.5093	0.334853
$986$	−12.7980	−0.407571
$987$	−9.58600	−0.305126
$988$	45.5878	1.45034
$989$	23.9482	0.761508
$990$	−2.47296	−0.0785960
$991$	3.94289	0.125250	0.0626249	−	0.998037i	$-0.480053\pi$
$991$	3.94289	0.125250	0.0626249	+	0.998037i	$0.480053\pi$
$992$	20.4712	0.649962
$993$	5.02661	0.159515
$994$	−11.9990	−0.380585
$995$	−3.72086	−0.117959
$996$	2.90587	0.0920761
$997$	15.4115	0.488087	0.244043	−	0.969764i	$-0.421526\pi$
$997$	15.4115	0.488087	0.244043	+	0.969764i	$0.421526\pi$
$998$	10.9538	0.346738
$999$	5.29874	0.167645

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.12	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.12	✓	82	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05866 q^{2} -1.00000 q^{3} +2.23808 q^{4} -1.30769 q^{5} +2.05866 q^{6} +4.57045 q^{7} -0.490135 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.05866 q^{2} -1.00000 q^{3} +2.23808 q^{4} -1.30769 q^{5} +2.05866 q^{6} +4.57045 q^{7} -0.490135 q^{8} +1.00000 q^{9} +2.69208 q^{10} -0.918607 q^{11} -2.23808 q^{12} -2.76605 q^{13} -9.40900 q^{14} +1.30769 q^{15} -3.46715 q^{16} +8.09044 q^{17} -2.05866 q^{18} -7.36397 q^{19} -2.92671 q^{20} -4.57045 q^{21} +1.89110 q^{22} -2.57296 q^{23} +0.490135 q^{24} -3.28996 q^{25} +5.69436 q^{26} -1.00000 q^{27} +10.2290 q^{28} +0.768395 q^{29} -2.69208 q^{30} +2.52172 q^{31} +8.11795 q^{32} +0.918607 q^{33} -16.6555 q^{34} -5.97671 q^{35} +2.23808 q^{36} -5.29874 q^{37} +15.1599 q^{38} +2.76605 q^{39} +0.640942 q^{40} +0.984105 q^{41} +9.40900 q^{42} -9.30764 q^{43} -2.05592 q^{44} -1.30769 q^{45} +5.29685 q^{46} +2.09739 q^{47} +3.46715 q^{48} +13.8890 q^{49} +6.77290 q^{50} -8.09044 q^{51} -6.19065 q^{52} -8.93207 q^{53} +2.05866 q^{54} +1.20125 q^{55} -2.24013 q^{56} +7.36397 q^{57} -1.58186 q^{58} +5.92594 q^{59} +2.92671 q^{60} -1.31796 q^{61} -5.19137 q^{62} +4.57045 q^{63} -9.77781 q^{64} +3.61713 q^{65} -1.89110 q^{66} +13.4320 q^{67} +18.1071 q^{68} +2.57296 q^{69} +12.3040 q^{70} +1.27527 q^{71} -0.490135 q^{72} -3.49431 q^{73} +10.9083 q^{74} +3.28996 q^{75} -16.4812 q^{76} -4.19844 q^{77} -5.69436 q^{78} +2.31819 q^{79} +4.53394 q^{80} +1.00000 q^{81} -2.02594 q^{82} -1.29838 q^{83} -10.2290 q^{84} -10.5798 q^{85} +19.1613 q^{86} -0.768395 q^{87} +0.450241 q^{88} +17.6098 q^{89} +2.69208 q^{90} -12.6421 q^{91} -5.75850 q^{92} -2.52172 q^{93} -4.31781 q^{94} +9.62977 q^{95} -8.11795 q^{96} +10.2317 q^{97} -28.5927 q^{98} -0.918607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

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