LMFDB - Embedded newform 6033.2.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.47475 q^{2} -1.00000 q^{3} +4.12439 q^{4} +0.484092 q^{5} +2.47475 q^{6} -1.35174 q^{7} -5.25735 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.47475 q^{2} -1.00000 q^{3} +4.12439 q^{4} +0.484092 q^{5} +2.47475 q^{6} -1.35174 q^{7} -5.25735 q^{8} +1.00000 q^{9} -1.19801 q^{10} -6.00442 q^{11} -4.12439 q^{12} -0.350564 q^{13} +3.34522 q^{14} -0.484092 q^{15} +4.76184 q^{16} -5.65624 q^{17} -2.47475 q^{18} -5.60148 q^{19} +1.99659 q^{20} +1.35174 q^{21} +14.8594 q^{22} +8.85668 q^{23} +5.25735 q^{24} -4.76565 q^{25} +0.867558 q^{26} -1.00000 q^{27} -5.57511 q^{28} +5.60574 q^{29} +1.19801 q^{30} -7.46605 q^{31} -1.26967 q^{32} +6.00442 q^{33} +13.9978 q^{34} -0.654367 q^{35} +4.12439 q^{36} -8.16535 q^{37} +13.8623 q^{38} +0.350564 q^{39} -2.54504 q^{40} -2.63774 q^{41} -3.34522 q^{42} -12.1657 q^{43} -24.7646 q^{44} +0.484092 q^{45} -21.9181 q^{46} -7.92097 q^{47} -4.76184 q^{48} -5.17280 q^{49} +11.7938 q^{50} +5.65624 q^{51} -1.44586 q^{52} +4.10016 q^{53} +2.47475 q^{54} -2.90669 q^{55} +7.10656 q^{56} +5.60148 q^{57} -13.8728 q^{58} +1.78166 q^{59} -1.99659 q^{60} -3.18886 q^{61} +18.4766 q^{62} -1.35174 q^{63} -6.38156 q^{64} -0.169705 q^{65} -14.8594 q^{66} -1.53185 q^{67} -23.3286 q^{68} -8.85668 q^{69} +1.61939 q^{70} +7.30174 q^{71} -5.25735 q^{72} -14.8695 q^{73} +20.2072 q^{74} +4.76565 q^{75} -23.1027 q^{76} +8.11641 q^{77} -0.867558 q^{78} +15.0000 q^{79} +2.30517 q^{80} +1.00000 q^{81} +6.52775 q^{82} -5.71995 q^{83} +5.57511 q^{84} -2.73814 q^{85} +30.1070 q^{86} -5.60574 q^{87} +31.5673 q^{88} -15.0000 q^{89} -1.19801 q^{90} +0.473871 q^{91} +36.5284 q^{92} +7.46605 q^{93} +19.6024 q^{94} -2.71163 q^{95} +1.26967 q^{96} +11.4478 q^{97} +12.8014 q^{98} -6.00442 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.47475	−1.74991	−0.874957	−	0.484201i	$-0.839110\pi$
$2$	−2.47475	−1.74991	−0.874957	+	0.484201i	$0.839110\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.12439	2.06220
$5$	0.484092	0.216493	0.108246	−	0.994124i	$-0.465476\pi$
$5$	0.484092	0.216493	0.108246	+	0.994124i	$0.465476\pi$
$6$	2.47475	1.01031
$7$	−1.35174	−0.510910	−0.255455	−	0.966821i	$-0.582225\pi$
$7$	−1.35174	−0.510910	−0.255455	+	0.966821i	$0.582225\pi$
$8$	−5.25735	−1.85875
$9$	1.00000	0.333333
$10$	−1.19801	−0.378843
$11$	−6.00442	−1.81040	−0.905200	−	0.424986i	$-0.860279\pi$
$11$	−6.00442	−1.81040	−0.905200	+	0.424986i	$0.860279\pi$
$12$	−4.12439	−1.19061
$13$	−0.350564	−0.0972289	−0.0486145	−	0.998818i	$-0.515481\pi$
$13$	−0.350564	−0.0972289	−0.0486145	+	0.998818i	$0.515481\pi$
$14$	3.34522	0.894048
$15$	−0.484092	−0.124992
$16$	4.76184	1.19046
$17$	−5.65624	−1.37184	−0.685920	−	0.727677i	$-0.740600\pi$
$17$	−5.65624	−1.37184	−0.685920	+	0.727677i	$0.740600\pi$
$18$	−2.47475	−0.583304
$19$	−5.60148	−1.28507	−0.642534	−	0.766257i	$-0.722117\pi$
$19$	−5.60148	−1.28507	−0.642534	+	0.766257i	$0.722117\pi$
$20$	1.99659	0.446450
$21$	1.35174	0.294974
$22$	14.8594	3.16804
$23$	8.85668	1.84675	0.923373	−	0.383905i	$-0.125421\pi$
$23$	8.85668	1.84675	0.923373	+	0.383905i	$0.125421\pi$
$24$	5.25735	1.07315
$25$	−4.76565	−0.953131
$26$	0.867558	0.170142
$27$	−1.00000	−0.192450
$28$	−5.57511	−1.05360
$29$	5.60574	1.04096	0.520480	−	0.853874i	$-0.325753\pi$
$29$	5.60574	1.04096	0.520480	+	0.853874i	$0.325753\pi$
$30$	1.19801	0.218725
$31$	−7.46605	−1.34094	−0.670471	−	0.741935i	$-0.733908\pi$
$31$	−7.46605	−1.34094	−0.670471	+	0.741935i	$0.733908\pi$
$32$	−1.26967	−0.224448
$33$	6.00442	1.04523
$34$	13.9978	2.40060
$35$	−0.654367	−0.110608
$36$	4.12439	0.687399
$37$	−8.16535	−1.34237	−0.671187	−	0.741288i	$-0.734215\pi$
$37$	−8.16535	−1.34237	−0.671187	+	0.741288i	$0.734215\pi$
$38$	13.8623	2.24876
$39$	0.350564	0.0561351
$40$	−2.54504	−0.402406
$41$	−2.63774	−0.411946	−0.205973	−	0.978558i	$-0.566036\pi$
$41$	−2.63774	−0.411946	−0.205973	+	0.978558i	$0.566036\pi$
$42$	−3.34522	−0.516179
$43$	−12.1657	−1.85525	−0.927624	−	0.373517i	$-0.878152\pi$
$43$	−12.1657	−1.85525	−0.927624	+	0.373517i	$0.878152\pi$
$44$	−24.7646	−3.73340
$45$	0.484092	0.0721642
$46$	−21.9181	−3.23164
$47$	−7.92097	−1.15539	−0.577696	−	0.816252i	$-0.696048\pi$
$47$	−7.92097	−1.15539	−0.577696	+	0.816252i	$0.696048\pi$
$48$	−4.76184	−0.687312
$49$	−5.17280	−0.738971
$50$	11.7938	1.66790
$51$	5.65624	0.792032
$52$	−1.44586	−0.200505
$53$	4.10016	0.563200	0.281600	−	0.959532i	$-0.409135\pi$
$53$	4.10016	0.563200	0.281600	+	0.959532i	$0.409135\pi$
$54$	2.47475	0.336771
$55$	−2.90669	−0.391938
$56$	7.10656	0.949655
$57$	5.60148	0.741934
$58$	−13.8728	−1.82159
$59$	1.78166	0.231952	0.115976	−	0.993252i	$-0.463000\pi$
$59$	1.78166	0.231952	0.115976	+	0.993252i	$0.463000\pi$
$60$	−1.99659	−0.257758
$61$	−3.18886	−0.408292	−0.204146	−	0.978940i	$-0.565442\pi$
$61$	−3.18886	−0.408292	−0.204146	+	0.978940i	$0.565442\pi$
$62$	18.4766	2.34653
$63$	−1.35174	−0.170303
$64$	−6.38156	−0.797695
$65$	−0.169705	−0.0210493
$66$	−14.8594	−1.82907
$67$	−1.53185	−0.187145	−0.0935727	−	0.995612i	$-0.529829\pi$
$67$	−1.53185	−0.187145	−0.0935727	+	0.995612i	$0.529829\pi$
$68$	−23.3286	−2.82900
$69$	−8.85668	−1.06622
$70$	1.61939	0.193555
$71$	7.30174	0.866557	0.433278	−	0.901260i	$-0.357357\pi$
$71$	7.30174	0.866557	0.433278	+	0.901260i	$0.357357\pi$
$72$	−5.25735	−0.619584
$73$	−14.8695	−1.74035	−0.870173	−	0.492746i	$-0.835993\pi$
$73$	−14.8695	−1.74035	−0.870173	+	0.492746i	$0.835993\pi$
$74$	20.2072	2.34904
$75$	4.76565	0.550290
$76$	−23.1027	−2.65006
$77$	8.11641	0.924950
$78$	−0.867558	−0.0982316
$79$	15.0000	1.68763	0.843815	−	0.536634i	$-0.180305\pi$
$79$	15.0000	1.68763	0.843815	+	0.536634i	$0.180305\pi$
$80$	2.30517	0.257726
$81$	1.00000	0.111111
$82$	6.52775	0.720870
$83$	−5.71995	−0.627846	−0.313923	−	0.949448i	$-0.601643\pi$
$83$	−5.71995	−0.627846	−0.313923	+	0.949448i	$0.601643\pi$
$84$	5.57511	0.608294
$85$	−2.73814	−0.296993
$86$	30.1070	3.24652
$87$	−5.60574	−0.600999
$88$	31.5673	3.36508
$89$	−15.0000	−1.59000	−0.794999	−	0.606611i	$-0.792529\pi$
$89$	−15.0000	−1.59000	−0.794999	+	0.606611i	$0.792529\pi$
$90$	−1.19801	−0.126281
$91$	0.473871	0.0496752
$92$	36.5284	3.80835
$93$	7.46605	0.774194
$94$	19.6024	2.02184
$95$	−2.71163	−0.278208
$96$	1.26967	0.129585
$97$	11.4478	1.16235	0.581176	−	0.813778i	$-0.302593\pi$
$97$	11.4478	1.16235	0.581176	+	0.813778i	$0.302593\pi$
$98$	12.8014	1.29314
$99$	−6.00442	−0.603466
$100$	−19.6554	−1.96554
$101$	−17.4283	−1.73418	−0.867092	−	0.498148i	$-0.834014\pi$
$101$	−17.4283	−1.73418	−0.867092	+	0.498148i	$0.834014\pi$
$102$	−13.9978	−1.38599
$103$	6.24699	0.615534	0.307767	−	0.951462i	$-0.400418\pi$
$103$	6.24699	0.615534	0.307767	+	0.951462i	$0.400418\pi$
$104$	1.84304	0.180725
$105$	0.654367	0.0638596
$106$	−10.1469	−0.985551
$107$	6.49908	0.628290	0.314145	−	0.949375i	$-0.398282\pi$
$107$	6.49908	0.628290	0.314145	+	0.949375i	$0.398282\pi$
$108$	−4.12439	−0.396870
$109$	−9.74698	−0.933592	−0.466796	−	0.884365i	$-0.654592\pi$
$109$	−9.74698	−0.933592	−0.466796	+	0.884365i	$0.654592\pi$
$110$	7.19333	0.685858
$111$	8.16535	0.775020
$112$	−6.43676	−0.608217
$113$	−1.74282	−0.163951	−0.0819756	−	0.996634i	$-0.526123\pi$
$113$	−1.74282	−0.163951	−0.0819756	+	0.996634i	$0.526123\pi$
$114$	−13.8623	−1.29832
$115$	4.28745	0.399807
$116$	23.1203	2.14666
$117$	−0.350564	−0.0324096
$118$	−4.40916	−0.405896
$119$	7.64577	0.700886
$120$	2.54504	0.232329
$121$	25.0530	2.27755
$122$	7.89164	0.714476
$123$	2.63774	0.237837
$124$	−30.7929	−2.76529
$125$	−4.72748	−0.422838
$126$	3.34522	0.298016
$127$	14.3366	1.27217	0.636086	−	0.771618i	$-0.280552\pi$
$127$	14.3366	1.27217	0.636086	+	0.771618i	$0.280552\pi$
$128$	18.3321	1.62034
$129$	12.1657	1.07113
$130$	0.419978	0.0368345
$131$	21.4388	1.87312	0.936558	−	0.350514i	$-0.113993\pi$
$131$	21.4388	1.87312	0.936558	+	0.350514i	$0.113993\pi$
$132$	24.7646	2.15548
$133$	7.57174	0.656553
$134$	3.79095	0.327488
$135$	−0.484092	−0.0416640
$136$	29.7368	2.54991
$137$	−19.4972	−1.66576	−0.832879	−	0.553455i	$-0.813309\pi$
$137$	−19.4972	−1.66576	−0.832879	+	0.553455i	$0.813309\pi$
$138$	21.9181	1.86579
$139$	−17.3550	−1.47203	−0.736015	−	0.676966i	$-0.763295\pi$
$139$	−17.3550	−1.47203	−0.736015	+	0.676966i	$0.763295\pi$
$140$	−2.69887	−0.228096
$141$	7.92097	0.667066
$142$	−18.0700	−1.51640
$143$	2.10493	0.176023
$144$	4.76184	0.396820
$145$	2.71370	0.225360
$146$	36.7984	3.04546
$147$	5.17280	0.426645
$148$	−33.6771	−2.76824
$149$	3.20431	0.262507	0.131254	−	0.991349i	$-0.458100\pi$
$149$	3.20431	0.262507	0.131254	+	0.991349i	$0.458100\pi$
$150$	−11.7938	−0.962961
$151$	10.0652	0.819092	0.409546	−	0.912289i	$-0.365687\pi$
$151$	10.0652	0.819092	0.409546	+	0.912289i	$0.365687\pi$
$152$	29.4489	2.38862
$153$	−5.65624	−0.457280
$154$	−20.0861	−1.61858
$155$	−3.61426	−0.290304
$156$	1.44586	0.115762
$157$	−10.0046	−0.798455	−0.399227	−	0.916852i	$-0.630722\pi$
$157$	−10.0046	−0.798455	−0.399227	+	0.916852i	$0.630722\pi$
$158$	−37.1212	−2.95321
$159$	−4.10016	−0.325164
$160$	−0.614637	−0.0485913
$161$	−11.9719	−0.943520
$162$	−2.47475	−0.194435
$163$	8.18801	0.641334	0.320667	−	0.947192i	$-0.396093\pi$
$163$	8.18801	0.641334	0.320667	+	0.947192i	$0.396093\pi$
$164$	−10.8791	−0.849514
$165$	2.90669	0.226285
$166$	14.1554	1.09868
$167$	0.176247	0.0136384	0.00681920	−	0.999977i	$-0.497829\pi$
$167$	0.176247	0.0136384	0.00681920	+	0.999977i	$0.497829\pi$
$168$	−7.10656	−0.548283
$169$	−12.8771	−0.990547
$170$	6.77622	0.519712
$171$	−5.60148	−0.428356
$172$	−50.1760	−3.82588
$173$	17.9602	1.36549	0.682743	−	0.730658i	$-0.260787\pi$
$173$	17.9602	1.36549	0.682743	+	0.730658i	$0.260787\pi$
$174$	13.8728	1.05170
$175$	6.44193	0.486964
$176$	−28.5920	−2.15521
$177$	−1.78166	−0.133917
$178$	37.1213	2.78236
$179$	−16.6372	−1.24352	−0.621761	−	0.783207i	$-0.713582\pi$
$179$	−16.6372	−1.24352	−0.621761	+	0.783207i	$0.713582\pi$
$180$	1.99659	0.148817
$181$	−17.5301	−1.30300	−0.651502	−	0.758647i	$-0.725861\pi$
$181$	−17.5301	−1.30300	−0.651502	+	0.758647i	$0.725861\pi$
$182$	−1.17271	−0.0869273
$183$	3.18886	0.235728
$184$	−46.5626	−3.43264
$185$	−3.95278	−0.290614
$186$	−18.4766	−1.35477
$187$	33.9624	2.48358
$188$	−32.6692	−2.38265
$189$	1.35174	0.0983246
$190$	6.71061	0.486839
$191$	−14.0412	−1.01598	−0.507992	−	0.861362i	$-0.669612\pi$
$191$	−14.0412	−1.01598	−0.507992	+	0.861362i	$0.669612\pi$
$192$	6.38156	0.460549
$193$	13.3953	0.964217	0.482109	−	0.876111i	$-0.339871\pi$
$193$	13.3953	0.964217	0.482109	+	0.876111i	$0.339871\pi$
$194$	−28.3305	−2.03401
$195$	0.169705	0.0121528
$196$	−21.3347	−1.52390
$197$	−14.0101	−0.998178	−0.499089	−	0.866551i	$-0.666332\pi$
$197$	−14.0101	−0.998178	−0.499089	+	0.866551i	$0.666332\pi$
$198$	14.8594	1.05601
$199$	−17.8994	−1.26886	−0.634429	−	0.772981i	$-0.718765\pi$
$199$	−17.8994	−1.26886	−0.634429	+	0.772981i	$0.718765\pi$
$200$	25.0547	1.77163
$201$	1.53185	0.108048
$202$	43.1308	3.03467
$203$	−7.57750	−0.531837
$204$	23.3286	1.63333
$205$	−1.27691	−0.0891832
$206$	−15.4597	−1.07713
$207$	8.85668	0.615582
$208$	−1.66933	−0.115747
$209$	33.6336	2.32649
$210$	−1.61939	−0.111749
$211$	19.5450	1.34554	0.672768	−	0.739853i	$-0.265105\pi$
$211$	19.5450	1.34554	0.672768	+	0.739853i	$0.265105\pi$
$212$	16.9107	1.16143
$213$	−7.30174	−0.500307
$214$	−16.0836	−1.09945
$215$	−5.88930	−0.401647
$216$	5.25735	0.357717
$217$	10.0922	0.685100
$218$	24.1214	1.63370
$219$	14.8695	1.00479
$220$	−11.9883	−0.808253
$221$	1.98287	0.133383
$222$	−20.2072	−1.35622
$223$	−2.95718	−0.198028	−0.0990138	−	0.995086i	$-0.531569\pi$
$223$	−2.95718	−0.198028	−0.0990138	+	0.995086i	$0.531569\pi$
$224$	1.71626	0.114673
$225$	−4.76565	−0.317710
$226$	4.31306	0.286900
$227$	−0.161264	−0.0107034	−0.00535172	−	0.999986i	$-0.501704\pi$
$227$	−0.161264	−0.0107034	−0.00535172	+	0.999986i	$0.501704\pi$
$228$	23.1027	1.53001
$229$	−20.1721	−1.33301	−0.666506	−	0.745500i	$-0.732211\pi$
$229$	−20.1721	−1.33301	−0.666506	+	0.745500i	$0.732211\pi$
$230$	−10.6104	−0.699627
$231$	−8.11641	−0.534020
$232$	−29.4713	−1.93489
$233$	14.6703	0.961084	0.480542	−	0.876972i	$-0.340440\pi$
$233$	14.6703	0.961084	0.480542	+	0.876972i	$0.340440\pi$
$234$	0.867558	0.0567141
$235$	−3.83448	−0.250134
$236$	7.34825	0.478330
$237$	−15.0000	−0.974354
$238$	−18.9214	−1.22649
$239$	−5.54915	−0.358944	−0.179472	−	0.983763i	$-0.557439\pi$
$239$	−5.54915	−0.358944	−0.179472	+	0.983763i	$0.557439\pi$
$240$	−2.30517	−0.148798
$241$	12.7906	0.823917	0.411958	−	0.911203i	$-0.364845\pi$
$241$	12.7906	0.823917	0.411958	+	0.911203i	$0.364845\pi$
$242$	−62.0000	−3.98551
$243$	−1.00000	−0.0641500
$244$	−13.1521	−0.841979
$245$	−2.50411	−0.159982
$246$	−6.52775	−0.416194
$247$	1.96368	0.124946
$248$	39.2516	2.49248
$249$	5.71995	0.362487
$250$	11.6993	0.739930
$251$	8.78855	0.554728	0.277364	−	0.960765i	$-0.410539\pi$
$251$	8.78855	0.554728	0.277364	+	0.960765i	$0.410539\pi$
$252$	−5.57511	−0.351199
$253$	−53.1792	−3.34335
$254$	−35.4796	−2.22619
$255$	2.73814	0.171469
$256$	−32.6043	−2.03777
$257$	−9.23711	−0.576195	−0.288098	−	0.957601i	$-0.593023\pi$
$257$	−9.23711	−0.576195	−0.288098	+	0.957601i	$0.593023\pi$
$258$	−30.1070	−1.87438
$259$	11.0374	0.685832
$260$	−0.699931	−0.0434079
$261$	5.60574	0.346987
$262$	−53.0557	−3.27779
$263$	24.5274	1.51242	0.756211	−	0.654328i	$-0.227048\pi$
$263$	24.5274	1.51242	0.756211	+	0.654328i	$0.227048\pi$
$264$	−31.5673	−1.94283
$265$	1.98485	0.121929
$266$	−18.7382	−1.14891
$267$	15.0000	0.917986
$268$	−6.31796	−0.385931
$269$	−6.62280	−0.403799	−0.201899	−	0.979406i	$-0.564711\pi$
$269$	−6.62280	−0.403799	−0.201899	+	0.979406i	$0.564711\pi$
$270$	1.19801	0.0729084
$271$	5.57875	0.338885	0.169443	−	0.985540i	$-0.445803\pi$
$271$	5.57875	0.338885	0.169443	+	0.985540i	$0.445803\pi$
$272$	−26.9341	−1.63312
$273$	−0.473871	−0.0286800
$274$	48.2507	2.91493
$275$	28.6150	1.72555
$276$	−36.5284	−2.19875
$277$	2.14437	0.128843	0.0644215	−	0.997923i	$-0.479480\pi$
$277$	2.14437	0.128843	0.0644215	+	0.997923i	$0.479480\pi$
$278$	42.9492	2.57592
$279$	−7.46605	−0.446981
$280$	3.44023	0.205593
$281$	−21.5108	−1.28323	−0.641614	−	0.767028i	$-0.721735\pi$
$281$	−21.5108	−1.28323	−0.641614	+	0.767028i	$0.721735\pi$
$282$	−19.6024	−1.16731
$283$	9.48309	0.563711	0.281856	−	0.959457i	$-0.409050\pi$
$283$	9.48309	0.563711	0.281856	+	0.959457i	$0.409050\pi$
$284$	30.1152	1.78701
$285$	2.71163	0.160623
$286$	−5.20918	−0.308025
$287$	3.56554	0.210467
$288$	−1.26967	−0.0748159
$289$	14.9931	0.881945
$290$	−6.71572	−0.394361
$291$	−11.4478	−0.671084
$292$	−61.3278	−3.58894
$293$	−0.379526	−0.0221721	−0.0110861	−	0.999939i	$-0.503529\pi$
$293$	−0.379526	−0.0221721	−0.0110861	+	0.999939i	$0.503529\pi$
$294$	−12.8014	−0.746592
$295$	0.862486	0.0502158
$296$	42.9280	2.49514
$297$	6.00442	0.348412
$298$	−7.92986	−0.459365
$299$	−3.10483	−0.179557
$300$	19.6554	1.13481
$301$	16.4448	0.947864
$302$	−24.9088	−1.43334
$303$	17.4283	1.00123
$304$	−26.6733	−1.52982
$305$	−1.54370	−0.0883922
$306$	13.9978	0.800200
$307$	1.18886	0.0678520	0.0339260	−	0.999424i	$-0.489199\pi$
$307$	1.18886	0.0678520	0.0339260	+	0.999424i	$0.489199\pi$
$308$	33.4753	1.90743
$309$	−6.24699	−0.355379
$310$	8.94439	0.508007
$311$	−21.9275	−1.24339	−0.621696	−	0.783259i	$-0.713556\pi$
$311$	−21.9275	−1.24339	−0.621696	+	0.783259i	$0.713556\pi$
$312$	−1.84304	−0.104341
$313$	−12.8059	−0.723834	−0.361917	−	0.932210i	$-0.617878\pi$
$313$	−12.8059	−0.723834	−0.361917	+	0.932210i	$0.617878\pi$
$314$	24.7589	1.39723
$315$	−0.654367	−0.0368694
$316$	61.8658	3.48023
$317$	14.8765	0.835550	0.417775	−	0.908551i	$-0.362810\pi$
$317$	14.8765	0.835550	0.417775	+	0.908551i	$0.362810\pi$
$318$	10.1469	0.569008
$319$	−33.6592	−1.88455
$320$	−3.08926	−0.172695
$321$	−6.49908	−0.362743
$322$	29.6275	1.65108
$323$	31.6833	1.76291
$324$	4.12439	0.229133
$325$	1.67067	0.0926719
$326$	−20.2633	−1.12228
$327$	9.74698	0.539009
$328$	13.8675	0.765706
$329$	10.7071	0.590301
$330$	−7.19333	−0.395980
$331$	8.87383	0.487750	0.243875	−	0.969807i	$-0.421581\pi$
$331$	8.87383	0.487750	0.243875	+	0.969807i	$0.421581\pi$
$332$	−23.5913	−1.29474
$333$	−8.16535	−0.447458
$334$	−0.436167	−0.0238660
$335$	−0.741557	−0.0405156
$336$	6.43676	0.351154
$337$	−14.7067	−0.801126	−0.400563	−	0.916269i	$-0.631185\pi$
$337$	−14.7067	−0.801126	−0.400563	+	0.916269i	$0.631185\pi$
$338$	31.8676	1.73337
$339$	1.74282	0.0946573
$340$	−11.2932	−0.612458
$341$	44.8293	2.42764
$342$	13.8623	0.749586
$343$	16.4545	0.888457
$344$	63.9591	3.44845
$345$	−4.28745	−0.230828
$346$	−44.4470	−2.38948
$347$	4.85296	0.260521	0.130260	−	0.991480i	$-0.458419\pi$
$347$	4.85296	0.260521	0.130260	+	0.991480i	$0.458419\pi$
$348$	−23.1203	−1.23938
$349$	−27.5486	−1.47464	−0.737322	−	0.675542i	$-0.763910\pi$
$349$	−27.5486	−1.47464	−0.737322	+	0.675542i	$0.763910\pi$
$350$	−15.9422	−0.852144
$351$	0.350564	0.0187117
$352$	7.62362	0.406340
$353$	−1.97098	−0.104905	−0.0524524	−	0.998623i	$-0.516704\pi$
$353$	−1.97098	−0.104905	−0.0524524	+	0.998623i	$0.516704\pi$
$354$	4.40916	0.234344
$355$	3.53471	0.187603
$356$	−61.8660	−3.27889
$357$	−7.64577	−0.404657
$358$	41.1729	2.17605
$359$	−0.760303	−0.0401273	−0.0200636	−	0.999799i	$-0.506387\pi$
$359$	−0.760303	−0.0401273	−0.0200636	+	0.999799i	$0.506387\pi$
$360$	−2.54504	−0.134135
$361$	12.3766	0.651398
$362$	43.3827	2.28015
$363$	−25.0530	−1.31494
$364$	1.95443	0.102440
$365$	−7.19822	−0.376772
$366$	−7.89164	−0.412503
$367$	6.80594	0.355267	0.177634	−	0.984097i	$-0.443156\pi$
$367$	6.80594	0.355267	0.177634	+	0.984097i	$0.443156\pi$
$368$	42.1741	2.19847
$369$	−2.63774	−0.137315
$370$	9.78214	0.508549
$371$	−5.54235	−0.287744
$372$	30.7929	1.59654
$373$	−4.45474	−0.230658	−0.115329	−	0.993327i	$-0.536792\pi$
$373$	−4.45474	−0.230658	−0.115329	+	0.993327i	$0.536792\pi$
$374$	−84.0486	−4.34605
$375$	4.72748	0.244126
$376$	41.6433	2.14759
$377$	−1.96517	−0.101211
$378$	−3.34522	−0.172060
$379$	−29.1430	−1.49698	−0.748489	−	0.663148i	$-0.769220\pi$
$379$	−29.1430	−1.49698	−0.748489	+	0.663148i	$0.769220\pi$
$380$	−11.1838	−0.573719
$381$	−14.3366	−0.734489
$382$	34.7484	1.77789
$383$	−27.0731	−1.38337	−0.691685	−	0.722199i	$-0.743131\pi$
$383$	−27.0731	−1.38337	−0.691685	+	0.722199i	$0.743131\pi$
$384$	−18.3321	−0.935507
$385$	3.92909	0.200245
$386$	−33.1501	−1.68730
$387$	−12.1657	−0.618416
$388$	47.2154	2.39700
$389$	−19.3507	−0.981120	−0.490560	−	0.871408i	$-0.663208\pi$
$389$	−19.3507	−0.981120	−0.490560	+	0.871408i	$0.663208\pi$
$390$	−0.419978	−0.0212664
$391$	−50.0955	−2.53344
$392$	27.1952	1.37356
$393$	−21.4388	−1.08144
$394$	34.6715	1.74673
$395$	7.26137	0.365359
$396$	−24.7646	−1.24447
$397$	−5.78785	−0.290484	−0.145242	−	0.989396i	$-0.546396\pi$
$397$	−5.78785	−0.290484	−0.145242	+	0.989396i	$0.546396\pi$
$398$	44.2967	2.22039
$399$	−7.57174	−0.379061
$400$	−22.6933	−1.13466
$401$	8.00276	0.399639	0.199819	−	0.979833i	$-0.435964\pi$
$401$	8.00276	0.399639	0.199819	+	0.979833i	$0.435964\pi$
$402$	−3.79095	−0.189075
$403$	2.61733	0.130378
$404$	−71.8813	−3.57623
$405$	0.484092	0.0240547
$406$	18.7524	0.930668
$407$	49.0281	2.43023
$408$	−29.7368	−1.47219
$409$	−13.7359	−0.679197	−0.339599	−	0.940570i	$-0.610291\pi$
$409$	−13.7359	−0.679197	−0.339599	+	0.940570i	$0.610291\pi$
$410$	3.16003	0.156063
$411$	19.4972	0.961726
$412$	25.7650	1.26935
$413$	−2.40834	−0.118506
$414$	−21.9181	−1.07721
$415$	−2.76898	−0.135924
$416$	0.445100	0.0218228
$417$	17.3550	0.849877
$418$	−83.2348	−4.07115
$419$	−17.9045	−0.874693	−0.437347	−	0.899293i	$-0.644082\pi$
$419$	−17.9045	−0.874693	−0.437347	+	0.899293i	$0.644082\pi$
$420$	2.69887	0.131691
$421$	14.3223	0.698026	0.349013	−	0.937118i	$-0.386517\pi$
$421$	14.3223	0.698026	0.349013	+	0.937118i	$0.386517\pi$
$422$	−48.3691	−2.35457
$423$	−7.92097	−0.385131
$424$	−21.5560	−1.04685
$425$	26.9557	1.30754
$426$	18.0700	0.875494
$427$	4.31051	0.208600
$428$	26.8048	1.29566
$429$	−2.10493	−0.101627
$430$	14.5746	0.702848
$431$	−20.6980	−0.996989	−0.498494	−	0.866893i	$-0.666114\pi$
$431$	−20.6980	−0.996989	−0.498494	+	0.866893i	$0.666114\pi$
$432$	−4.76184	−0.229104
$433$	−17.2633	−0.829624	−0.414812	−	0.909907i	$-0.636153\pi$
$433$	−17.2633	−0.829624	−0.414812	+	0.909907i	$0.636153\pi$
$434$	−24.9756	−1.19887
$435$	−2.71370	−0.130112
$436$	−40.2004	−1.92525
$437$	−49.6105	−2.37319
$438$	−36.7984	−1.75829
$439$	−13.6076	−0.649453	−0.324727	−	0.945808i	$-0.605272\pi$
$439$	−13.6076	−0.649453	−0.324727	+	0.945808i	$0.605272\pi$
$440$	15.2815	0.728516
$441$	−5.17280	−0.246324
$442$	−4.90712	−0.233408
$443$	23.3562	1.10969	0.554843	−	0.831955i	$-0.312778\pi$
$443$	23.3562	1.10969	0.554843	+	0.831955i	$0.312778\pi$
$444$	33.6771	1.59824
$445$	−7.26139	−0.344223
$446$	7.31829	0.346531
$447$	−3.20431	−0.151559
$448$	8.62621	0.407550
$449$	15.1906	0.716887	0.358444	−	0.933551i	$-0.383307\pi$
$449$	15.1906	0.716887	0.358444	+	0.933551i	$0.383307\pi$
$450$	11.7938	0.555966
$451$	15.8381	0.745787
$452$	−7.18810	−0.338100
$453$	−10.0652	−0.472903
$454$	0.399087	0.0187301
$455$	0.229397	0.0107543
$456$	−29.4489	−1.37907
$457$	24.0073	1.12301	0.561507	−	0.827472i	$-0.310222\pi$
$457$	24.0073	1.12301	0.561507	+	0.827472i	$0.310222\pi$
$458$	49.9210	2.33266
$459$	5.65624	0.264011
$460$	17.6831	0.824480
$461$	−12.6875	−0.590918	−0.295459	−	0.955355i	$-0.595472\pi$
$461$	−12.6875	−0.590918	−0.295459	+	0.955355i	$0.595472\pi$
$462$	20.0861	0.934489
$463$	15.5755	0.723856	0.361928	−	0.932206i	$-0.382119\pi$
$463$	15.5755	0.723856	0.361928	+	0.932206i	$0.382119\pi$
$464$	26.6936	1.23922
$465$	3.61426	0.167607
$466$	−36.3054	−1.68181
$467$	−41.4323	−1.91726	−0.958629	−	0.284660i	$-0.908119\pi$
$467$	−41.4323	−1.91726	−0.958629	+	0.284660i	$0.908119\pi$
$468$	−1.44586	−0.0668351
$469$	2.07066	0.0956144
$470$	9.48938	0.437713
$471$	10.0046	0.460988
$472$	−9.36678	−0.431141
$473$	73.0477	3.35874
$474$	37.1212	1.70503
$475$	26.6947	1.22484
$476$	31.5342	1.44537
$477$	4.10016	0.187733
$478$	13.7328	0.628122
$479$	5.83866	0.266775	0.133388	−	0.991064i	$-0.457414\pi$
$479$	5.83866	0.266775	0.133388	+	0.991064i	$0.457414\pi$
$480$	0.614637	0.0280542
$481$	2.86248	0.130518
$482$	−31.6536	−1.44178
$483$	11.9719	0.544742
$484$	103.328	4.69675
$485$	5.54180	0.251640
$486$	2.47475	0.112257
$487$	22.9726	1.04099	0.520494	−	0.853865i	$-0.325748\pi$
$487$	22.9726	1.04099	0.520494	+	0.853865i	$0.325748\pi$
$488$	16.7650	0.758914
$489$	−8.18801	−0.370275
$490$	6.19705	0.279954
$491$	34.2021	1.54352	0.771759	−	0.635915i	$-0.219377\pi$
$491$	34.2021	1.54352	0.771759	+	0.635915i	$0.219377\pi$
$492$	10.8791	0.490467
$493$	−31.7074	−1.42803
$494$	−4.85961	−0.218644
$495$	−2.90669	−0.130646
$496$	−35.5521	−1.59634
$497$	−9.87005	−0.442732
$498$	−14.1554	−0.634321
$499$	−16.5934	−0.742823	−0.371412	−	0.928468i	$-0.621126\pi$
$499$	−16.5934	−0.742823	−0.371412	+	0.928468i	$0.621126\pi$
$500$	−19.4980	−0.871976
$501$	−0.176247	−0.00787413
$502$	−21.7495	−0.970726
$503$	38.8525	1.73235	0.866174	−	0.499743i	$-0.166572\pi$
$503$	38.8525	1.73235	0.866174	+	0.499743i	$0.166572\pi$
$504$	7.10656	0.316552
$505$	−8.43692	−0.375438
$506$	131.605	5.85057
$507$	12.8771	0.571892
$508$	59.1300	2.62347
$509$	19.4615	0.862617	0.431308	−	0.902205i	$-0.358052\pi$
$509$	19.4615	0.862617	0.431308	+	0.902205i	$0.358052\pi$
$510$	−6.77622	−0.300056
$511$	20.0997	0.889160
$512$	44.0233	1.94557
$513$	5.60148	0.247311
$514$	22.8596	1.00829
$515$	3.02412	0.133259
$516$	50.1760	2.20888
$517$	47.5608	2.09172
$518$	−27.3149	−1.20015
$519$	−17.9602	−0.788364
$520$	0.892199	0.0391255
$521$	3.04247	0.133293	0.0666466	−	0.997777i	$-0.478770\pi$
$521$	3.04247	0.133293	0.0666466	+	0.997777i	$0.478770\pi$
$522$	−13.8728	−0.607197
$523$	18.9301	0.827757	0.413878	−	0.910332i	$-0.364174\pi$
$523$	18.9301	0.827757	0.413878	+	0.910332i	$0.364174\pi$
$524$	88.4220	3.86273
$525$	−6.44193	−0.281149
$526$	−60.6991	−2.64661
$527$	42.2298	1.83956
$528$	28.5920	1.24431
$529$	55.4408	2.41047
$530$	−4.91202	−0.213365
$531$	1.78166	0.0773173
$532$	31.2288	1.35394
$533$	0.924697	0.0400531
$534$	−37.1213	−1.60640
$535$	3.14615	0.136020
$536$	8.05347	0.347857
$537$	16.6372	0.717947
$538$	16.3898	0.706613
$539$	31.0596	1.33783
$540$	−1.99659	−0.0859194
$541$	−2.84827	−0.122457	−0.0612284	−	0.998124i	$-0.519502\pi$
$541$	−2.84827	−0.122457	−0.0612284	+	0.998124i	$0.519502\pi$
$542$	−13.8060	−0.593020
$543$	17.5301	0.752290
$544$	7.18155	0.307907
$545$	−4.71844	−0.202116
$546$	1.17271	0.0501875
$547$	−8.62714	−0.368870	−0.184435	−	0.982845i	$-0.559045\pi$
$547$	−8.62714	−0.368870	−0.184435	+	0.982845i	$0.559045\pi$
$548$	−80.4141	−3.43512
$549$	−3.18886	−0.136097
$550$	−70.8149	−3.01956
$551$	−31.4004	−1.33770
$552$	46.5626	1.98184
$553$	−20.2761	−0.862226
$554$	−5.30679	−0.225464
$555$	3.95278	0.167786
$556$	−71.5787	−3.03561
$557$	39.4741	1.67257	0.836285	−	0.548295i	$-0.184723\pi$
$557$	39.4741	1.67257	0.836285	+	0.548295i	$0.184723\pi$
$558$	18.4766	0.782178
$559$	4.26484	0.180384
$560$	−3.11599	−0.131674
$561$	−33.9624	−1.43389
$562$	53.2339	2.24554
$563$	11.5526	0.486884	0.243442	−	0.969915i	$-0.421723\pi$
$563$	11.5526	0.486884	0.243442	+	0.969915i	$0.421723\pi$
$564$	32.6692	1.37562
$565$	−0.843688	−0.0354942
$566$	−23.4683	−0.986446
$567$	−1.35174	−0.0567677
$568$	−38.3878	−1.61071
$569$	−20.7485	−0.869821	−0.434910	−	0.900474i	$-0.643220\pi$
$569$	−20.7485	−0.869821	−0.434910	+	0.900474i	$0.643220\pi$
$570$	−6.71061	−0.281077
$571$	14.7115	0.615658	0.307829	−	0.951442i	$-0.400397\pi$
$571$	14.7115	0.615658	0.307829	+	0.951442i	$0.400397\pi$
$572$	8.68157	0.362994
$573$	14.0412	0.586579
$574$	−8.82382	−0.368299
$575$	−42.2079	−1.76019
$576$	−6.38156	−0.265898
$577$	36.8330	1.53338	0.766690	−	0.642018i	$-0.221902\pi$
$577$	36.8330	1.53338	0.766690	+	0.642018i	$0.221902\pi$
$578$	−37.1041	−1.54333
$579$	−13.3953	−0.556691
$580$	11.1923	0.464737
$581$	7.73188	0.320772
$582$	28.3305	1.17434
$583$	−24.6191	−1.01962
$584$	78.1743	3.23487
$585$	−0.169705	−0.00701645
$586$	0.939232	0.0387993
$587$	−1.94716	−0.0803680	−0.0401840	−	0.999192i	$-0.512794\pi$
$587$	−1.94716	−0.0803680	−0.0401840	+	0.999192i	$0.512794\pi$
$588$	21.3347	0.879827
$589$	41.8209	1.72320
$590$	−2.13444	−0.0878734
$591$	14.0101	0.576298
$592$	−38.8820	−1.59804
$593$	−25.4065	−1.04332	−0.521660	−	0.853154i	$-0.674687\pi$
$593$	−25.4065	−1.04332	−0.521660	+	0.853154i	$0.674687\pi$
$594$	−14.8594	−0.609690
$595$	3.70126	0.151737
$596$	13.2158	0.541341
$597$	17.8994	0.732575
$598$	7.68369	0.314209
$599$	−1.62062	−0.0662167	−0.0331084	−	0.999452i	$-0.510541\pi$
$599$	−1.62062	−0.0662167	−0.0331084	+	0.999452i	$0.510541\pi$
$600$	−25.0547	−1.02285
$601$	14.3891	0.586943	0.293472	−	0.955968i	$-0.405189\pi$
$601$	14.3891	0.586943	0.293472	+	0.955968i	$0.405189\pi$
$602$	−40.6968	−1.65868
$603$	−1.53185	−0.0623818
$604$	41.5127	1.68913
$605$	12.1280	0.493072
$606$	−43.1308	−1.75207
$607$	3.05826	0.124131	0.0620654	−	0.998072i	$-0.480231\pi$
$607$	3.05826	0.124131	0.0620654	+	0.998072i	$0.480231\pi$
$608$	7.11202	0.288431
$609$	7.57750	0.307056
$610$	3.82028	0.154679
$611$	2.77681	0.112338
$612$	−23.3286	−0.943001
$613$	−30.3704	−1.22665	−0.613325	−	0.789830i	$-0.710169\pi$
$613$	−30.3704	−1.22665	−0.613325	+	0.789830i	$0.710169\pi$
$614$	−2.94214	−0.118735
$615$	1.27691	0.0514900
$616$	−42.6708	−1.71925
$617$	16.5253	0.665282	0.332641	−	0.943054i	$-0.392060\pi$
$617$	16.5253	0.665282	0.332641	+	0.943054i	$0.392060\pi$
$618$	15.4597	0.621882
$619$	0.263661	0.0105974	0.00529871	−	0.999986i	$-0.498313\pi$
$619$	0.263661	0.0105974	0.00529871	+	0.999986i	$0.498313\pi$
$620$	−14.9066	−0.598664
$621$	−8.85668	−0.355406
$622$	54.2650	2.17583
$623$	20.2761	0.812345
$624$	1.66933	0.0668266
$625$	21.5397	0.861590
$626$	31.6915	1.26665
$627$	−33.6336	−1.34320
$628$	−41.2630	−1.64657
$629$	46.1852	1.84152
$630$	1.61939	0.0645182
$631$	−14.2837	−0.568625	−0.284312	−	0.958732i	$-0.591765\pi$
$631$	−14.2837	−0.568625	−0.284312	+	0.958732i	$0.591765\pi$
$632$	−78.8601	−3.13689
$633$	−19.5450	−0.776846
$634$	−36.8157	−1.46214
$635$	6.94026	0.275416
$636$	−16.9107	−0.670552
$637$	1.81340	0.0718494
$638$	83.2982	3.29781
$639$	7.30174	0.288852
$640$	8.87443	0.350793
$641$	10.2844	0.406208	0.203104	−	0.979157i	$-0.434897\pi$
$641$	10.2844	0.406208	0.203104	+	0.979157i	$0.434897\pi$
$642$	16.0836	0.634769
$643$	−20.4344	−0.805853	−0.402926	−	0.915232i	$-0.632007\pi$
$643$	−20.4344	−0.805853	−0.402926	+	0.915232i	$0.632007\pi$
$644$	−49.3769	−1.94572
$645$	5.88930	0.231891
$646$	−78.4083	−3.08493
$647$	−3.50035	−0.137613	−0.0688064	−	0.997630i	$-0.521919\pi$
$647$	−3.50035	−0.137613	−0.0688064	+	0.997630i	$0.521919\pi$
$648$	−5.25735	−0.206528
$649$	−10.6978	−0.419925
$650$	−4.13448	−0.162168
$651$	−10.0922	−0.395543
$652$	33.7706	1.32256
$653$	4.13908	0.161975	0.0809874	−	0.996715i	$-0.474193\pi$
$653$	4.13908	0.161975	0.0809874	+	0.996715i	$0.474193\pi$
$654$	−24.1214	−0.943220
$655$	10.3783	0.405515
$656$	−12.5605	−0.490405
$657$	−14.8695	−0.580116
$658$	−26.4974	−1.03298
$659$	14.7283	0.573733	0.286867	−	0.957971i	$-0.407386\pi$
$659$	14.7283	0.573733	0.286867	+	0.957971i	$0.407386\pi$
$660$	11.9883	0.466645
$661$	21.6958	0.843871	0.421935	−	0.906626i	$-0.361351\pi$
$661$	21.6958	0.843871	0.421935	+	0.906626i	$0.361351\pi$
$662$	−21.9605	−0.853520
$663$	−1.98287	−0.0770084
$664$	30.0717	1.16701
$665$	3.66542	0.142139
$666$	20.2072	0.783013
$667$	49.6483	1.92239
$668$	0.726912	0.0281251
$669$	2.95718	0.114331
$670$	1.83517	0.0708988
$671$	19.1473	0.739172
$672$	−1.71626	−0.0662062
$673$	41.5559	1.60186	0.800932	−	0.598756i	$-0.204338\pi$
$673$	41.5559	1.60186	0.800932	+	0.598756i	$0.204338\pi$
$674$	36.3955	1.40190
$675$	4.76565	0.183430
$676$	−53.1103	−2.04270
$677$	28.3027	1.08776	0.543880	−	0.839163i	$-0.316955\pi$
$677$	28.3027	1.08776	0.543880	+	0.839163i	$0.316955\pi$
$678$	−4.31306	−0.165642
$679$	−15.4745	−0.593856
$680$	14.3954	0.552037
$681$	0.161264	0.00617964
$682$	−110.941	−4.24816
$683$	−5.66311	−0.216693	−0.108346	−	0.994113i	$-0.534556\pi$
$683$	−5.66311	−0.216693	−0.108346	+	0.994113i	$0.534556\pi$
$684$	−23.1027	−0.883354
$685$	−9.43844	−0.360624
$686$	−40.7207	−1.55472
$687$	20.1721	0.769615
$688$	−57.9309	−2.20860
$689$	−1.43737	−0.0547593
$690$	10.6104	0.403930
$691$	−22.2058	−0.844747	−0.422373	−	0.906422i	$-0.638803\pi$
$691$	−22.2058	−0.844747	−0.422373	+	0.906422i	$0.638803\pi$
$692$	74.0748	2.81590
$693$	8.11641	0.308317
$694$	−12.0099	−0.455889
$695$	−8.40140	−0.318683
$696$	29.4713	1.11711
$697$	14.9197	0.565124
$698$	68.1760	2.58050
$699$	−14.6703	−0.554882
$700$	26.5690	1.00422
$701$	28.8511	1.08969	0.544846	−	0.838536i	$-0.316588\pi$
$701$	28.8511	1.08969	0.544846	+	0.838536i	$0.316588\pi$
$702$	−0.867558	−0.0327439
$703$	45.7380	1.72504
$704$	38.3175	1.44415
$705$	3.83448	0.144415
$706$	4.87769	0.183574
$707$	23.5586	0.886012
$708$	−7.34825	−0.276164
$709$	−44.7985	−1.68244	−0.841222	−	0.540690i	$-0.818163\pi$
$709$	−44.7985	−1.68244	−0.841222	+	0.540690i	$0.818163\pi$
$710$	−8.74753	−0.328289
$711$	15.0000	0.562543
$712$	78.8603	2.95541
$713$	−66.1244	−2.47638
$714$	18.9214	0.708115
$715$	1.01898	0.0381077
$716$	−68.6183	−2.56439
$717$	5.54915	0.207237
$718$	1.88156	0.0702192
$719$	17.0690	0.636566	0.318283	−	0.947996i	$-0.396894\pi$
$719$	17.0690	0.636566	0.318283	+	0.947996i	$0.396894\pi$
$720$	2.30517	0.0859085
$721$	−8.44430	−0.314482
$722$	−30.6289	−1.13989
$723$	−12.7906	−0.475689
$724$	−72.3012	−2.68705
$725$	−26.7150	−0.992171
$726$	62.0000	2.30103
$727$	−11.2812	−0.418396	−0.209198	−	0.977873i	$-0.567085\pi$
$727$	−11.2812	−0.418396	−0.209198	+	0.977873i	$0.567085\pi$
$728$	−2.49130	−0.0923339
$729$	1.00000	0.0370370
$730$	17.8138	0.659319
$731$	68.8120	2.54510
$732$	13.1521	0.486117
$733$	−32.7894	−1.21110	−0.605552	−	0.795806i	$-0.707048\pi$
$733$	−32.7894	−1.21110	−0.605552	+	0.795806i	$0.707048\pi$
$734$	−16.8430	−0.621687
$735$	2.50411	0.0923655
$736$	−11.2450	−0.414498
$737$	9.19787	0.338808
$738$	6.52775	0.240290
$739$	−22.8644	−0.841082	−0.420541	−	0.907273i	$-0.638160\pi$
$739$	−22.8644	−0.841082	−0.420541	+	0.907273i	$0.638160\pi$
$740$	−16.3028	−0.599303
$741$	−1.96368	−0.0721375
$742$	13.7159	0.503528
$743$	−3.50506	−0.128588	−0.0642942	−	0.997931i	$-0.520480\pi$
$743$	−3.50506	−0.128588	−0.0642942	+	0.997931i	$0.520480\pi$
$744$	−39.2516	−1.43903
$745$	1.55118	0.0568308
$746$	11.0244	0.403631
$747$	−5.71995	−0.209282
$748$	140.074	5.12163
$749$	−8.78506	−0.320999
$750$	−11.6993	−0.427199
$751$	−4.55135	−0.166081	−0.0830405	−	0.996546i	$-0.526463\pi$
$751$	−4.55135	−0.166081	−0.0830405	+	0.996546i	$0.526463\pi$
$752$	−37.7184	−1.37545
$753$	−8.78855	−0.320272
$754$	4.86331	0.177111
$755$	4.87247	0.177327
$756$	5.57511	0.202765
$757$	−7.53331	−0.273803	−0.136901	−	0.990585i	$-0.543714\pi$
$757$	−7.53331	−0.273803	−0.136901	+	0.990585i	$0.543714\pi$
$758$	72.1218	2.61958
$759$	53.1792	1.93028
$760$	14.2560	0.517119
$761$	20.8982	0.757559	0.378779	−	0.925487i	$-0.376344\pi$
$761$	20.8982	0.757559	0.378779	+	0.925487i	$0.376344\pi$
$762$	35.4796	1.28529
$763$	13.1754	0.476981
$764$	−57.9114	−2.09516
$765$	−2.73814	−0.0989977
$766$	66.9992	2.42078
$767$	−0.624584	−0.0225524
$768$	32.6043	1.17651
$769$	−7.64726	−0.275767	−0.137884	−	0.990448i	$-0.544030\pi$
$769$	−7.64726	−0.275767	−0.137884	+	0.990448i	$0.544030\pi$
$770$	−9.72352	−0.350411
$771$	9.23711	0.332667
$772$	55.2476	1.98841
$773$	31.0711	1.11755	0.558775	−	0.829319i	$-0.311271\pi$
$773$	31.0711	1.11755	0.558775	+	0.829319i	$0.311271\pi$
$774$	30.1070	1.08217
$775$	35.5806	1.27809
$776$	−60.1852	−2.16052
$777$	−11.0374	−0.395965
$778$	47.8882	1.71687
$779$	14.7753	0.529378
$780$	0.699931	0.0250616
$781$	−43.8427	−1.56881
$782$	123.974	4.43330
$783$	−5.60574	−0.200333
$784$	−24.6320	−0.879715
$785$	−4.84315	−0.172860
$786$	53.0557	1.89243
$787$	14.8797	0.530404	0.265202	−	0.964193i	$-0.414561\pi$
$787$	14.8797	0.530404	0.265202	+	0.964193i	$0.414561\pi$
$788$	−57.7832	−2.05844
$789$	−24.5274	−0.873198
$790$	−17.9701	−0.639347
$791$	2.35585	0.0837642
$792$	31.5673	1.12169
$793$	1.11790	0.0396978
$794$	14.3235	0.508322
$795$	−1.98485	−0.0703955
$796$	−73.8243	−2.61663
$797$	1.72185	0.0609911	0.0304955	−	0.999535i	$-0.490291\pi$
$797$	1.72185	0.0609911	0.0304955	+	0.999535i	$0.490291\pi$
$798$	18.7382	0.663324
$799$	44.8029	1.58501
$800$	6.05080	0.213928
$801$	−15.0000	−0.529999
$802$	−19.8048	−0.699333
$803$	89.2828	3.15072
$804$	6.31796	0.222817
$805$	−5.79551	−0.204265
$806$	−6.47724	−0.228151
$807$	6.62280	0.233133
$808$	91.6268	3.22342
$809$	−28.5570	−1.00401	−0.502006	−	0.864864i	$-0.667404\pi$
$809$	−28.5570	−1.00401	−0.502006	+	0.864864i	$0.667404\pi$
$810$	−1.19801	−0.0420937
$811$	24.1112	0.846658	0.423329	−	0.905976i	$-0.360861\pi$
$811$	24.1112	0.846658	0.423329	+	0.905976i	$0.360861\pi$
$812$	−31.2526	−1.09675
$813$	−5.57875	−0.195655
$814$	−121.332	−4.25270
$815$	3.96375	0.138844
$816$	26.9341	0.942882
$817$	68.1457	2.38412
$818$	33.9930	1.18854
$819$	0.473871	0.0165584
$820$	−5.26648	−0.183913
$821$	3.68103	0.128469	0.0642345	−	0.997935i	$-0.479539\pi$
$821$	3.68103	0.128469	0.0642345	+	0.997935i	$0.479539\pi$
$822$	−48.2507	−1.68294
$823$	56.7945	1.97973	0.989866	−	0.142005i	$-0.0453548\pi$
$823$	56.7945	1.97973	0.989866	+	0.142005i	$0.0453548\pi$
$824$	−32.8426	−1.14413
$825$	−28.6150	−0.996245
$826$	5.96003	0.207376
$827$	47.9916	1.66883	0.834416	−	0.551135i	$-0.185805\pi$
$827$	47.9916	1.66883	0.834416	+	0.551135i	$0.185805\pi$
$828$	36.5284	1.26945
$829$	−21.3145	−0.740284	−0.370142	−	0.928975i	$-0.620691\pi$
$829$	−21.3145	−0.740284	−0.370142	+	0.928975i	$0.620691\pi$
$830$	6.85254	0.237855
$831$	−2.14437	−0.0743875
$832$	2.23714	0.0775590
$833$	29.2586	1.01375
$834$	−42.9492	−1.48721
$835$	0.0853197	0.00295261
$836$	138.718	4.79767
$837$	7.46605	0.258065
$838$	44.3092	1.53064
$839$	−47.7904	−1.64991	−0.824954	−	0.565200i	$-0.808799\pi$
$839$	−47.7904	−1.64991	−0.824954	+	0.565200i	$0.808799\pi$
$840$	−3.44023	−0.118699
$841$	2.42434	0.0835981
$842$	−35.4441	−1.22148
$843$	21.5108	0.740872
$844$	80.6115	2.77476
$845$	−6.23370	−0.214446
$846$	19.6024	0.673946
$847$	−33.8651	−1.16362
$848$	19.5243	0.670467
$849$	−9.48309	−0.325459
$850$	−66.7086	−2.28809
$851$	−72.3179	−2.47902
$852$	−30.1152	−1.03173
$853$	−19.8046	−0.678096	−0.339048	−	0.940769i	$-0.610105\pi$
$853$	−19.8046	−0.678096	−0.339048	+	0.940769i	$0.610105\pi$
$854$	−10.6674	−0.365033
$855$	−2.71163	−0.0927358
$856$	−34.1679	−1.16784
$857$	−46.7331	−1.59637	−0.798186	−	0.602411i	$-0.794207\pi$
$857$	−46.7331	−1.59637	−0.798186	+	0.602411i	$0.794207\pi$
$858$	5.20918	0.177839
$859$	−17.8659	−0.609578	−0.304789	−	0.952420i	$-0.598586\pi$
$859$	−17.8659	−0.609578	−0.304789	+	0.952420i	$0.598586\pi$
$860$	−24.2898	−0.828276
$861$	−3.56554	−0.121513
$862$	51.2225	1.74464
$863$	−29.8304	−1.01544	−0.507719	−	0.861523i	$-0.669511\pi$
$863$	−29.8304	−1.01544	−0.507719	+	0.861523i	$0.669511\pi$
$864$	1.26967	0.0431950
$865$	8.69438	0.295618
$866$	42.7225	1.45177
$867$	−14.9931	−0.509191
$868$	41.6240	1.41281
$869$	−90.0661	−3.05528
$870$	6.71572	0.227684
$871$	0.537012	0.0181959
$872$	51.2433	1.73532
$873$	11.4478	0.387450
$874$	122.774	4.15288
$875$	6.39032	0.216032
$876$	61.3278	2.07207
$877$	42.5927	1.43825	0.719126	−	0.694880i	$-0.244542\pi$
$877$	42.5927	1.43825	0.719126	+	0.694880i	$0.244542\pi$
$878$	33.6753	1.13649
$879$	0.379526	0.0128011
$880$	−13.8412	−0.466586
$881$	49.1193	1.65487	0.827435	−	0.561562i	$-0.189799\pi$
$881$	49.1193	1.65487	0.827435	+	0.561562i	$0.189799\pi$
$882$	12.8014	0.431045
$883$	12.1089	0.407495	0.203748	−	0.979023i	$-0.434688\pi$
$883$	12.1089	0.407495	0.203748	+	0.979023i	$0.434688\pi$
$884$	8.17815	0.275061
$885$	−0.862486	−0.0289921
$886$	−57.8007	−1.94185
$887$	−22.1549	−0.743888	−0.371944	−	0.928255i	$-0.621309\pi$
$887$	−22.1549	−0.743888	−0.371944	+	0.928255i	$0.621309\pi$
$888$	−42.9280	−1.44057
$889$	−19.3794	−0.649965
$890$	17.9701	0.602360
$891$	−6.00442	−0.201155
$892$	−12.1966	−0.408372
$893$	44.3692	1.48476
$894$	7.92986	0.265214
$895$	−8.05393	−0.269213
$896$	−24.7802	−0.827850
$897$	3.10483	0.103667
$898$	−37.5929	−1.25449
$899$	−41.8528	−1.39587
$900$	−19.6554	−0.655181
$901$	−23.1915	−0.772621
$902$	−39.1953	−1.30506
$903$	−16.4448	−0.547249
$904$	9.16263	0.304745
$905$	−8.48620	−0.282091
$906$	24.9088	0.827540
$907$	−59.4929	−1.97543	−0.987714	−	0.156270i	$-0.950053\pi$
$907$	−59.4929	−1.97543	−0.987714	+	0.156270i	$0.950053\pi$
$908$	−0.665115	−0.0220726
$909$	−17.4283	−0.578061
$910$	−0.567701	−0.0188191
$911$	−0.376071	−0.0124598	−0.00622989	−	0.999981i	$-0.501983\pi$
$911$	−0.376071	−0.0124598	−0.00622989	+	0.999981i	$0.501983\pi$
$912$	26.6733	0.883242
$913$	34.3449	1.13665
$914$	−59.4121	−1.96518
$915$	1.54370	0.0510333
$916$	−83.1978	−2.74893
$917$	−28.9797	−0.956993
$918$	−13.9978	−0.461996
$919$	−36.4679	−1.20296	−0.601482	−	0.798886i	$-0.705423\pi$
$919$	−36.4679	−1.20296	−0.601482	+	0.798886i	$0.705423\pi$
$920$	−22.5406	−0.743142
$921$	−1.18886	−0.0391744
$922$	31.3985	1.03405
$923$	−2.55973	−0.0842544
$924$	−33.4753	−1.10126
$925$	38.9132	1.27946
$926$	−38.5456	−1.26669
$927$	6.24699	0.205178
$928$	−7.11744	−0.233641
$929$	27.7516	0.910501	0.455251	−	0.890363i	$-0.349550\pi$
$929$	27.7516	0.910501	0.455251	+	0.890363i	$0.349550\pi$
$930$	−8.94439	−0.293298
$931$	28.9753	0.949628
$932$	60.5061	1.98194
$933$	21.9275	0.717873
$934$	102.535	3.35503
$935$	16.4409	0.537676
$936$	1.84304	0.0602415
$937$	−26.8960	−0.878655	−0.439327	−	0.898327i	$-0.644783\pi$
$937$	−26.8960	−0.878655	−0.439327	+	0.898327i	$0.644783\pi$
$938$	−5.12438	−0.167317
$939$	12.8059	0.417906
$940$	−15.8149	−0.515825
$941$	36.9826	1.20560	0.602800	−	0.797892i	$-0.294052\pi$
$941$	36.9826	1.20560	0.602800	+	0.797892i	$0.294052\pi$
$942$	−24.7589	−0.806689
$943$	−23.3616	−0.760759
$944$	8.48395	0.276129
$945$	0.654367	0.0212865
$946$	−180.775	−5.87750
$947$	−32.5380	−1.05734	−0.528672	−	0.848826i	$-0.677310\pi$
$947$	−32.5380	−1.05734	−0.528672	+	0.848826i	$0.677310\pi$
$948$	−61.8658	−2.00931
$949$	5.21272	0.169212
$950$	−66.0628	−2.14336
$951$	−14.8765	−0.482405
$952$	−40.1964	−1.30277
$953$	−54.3405	−1.76026	−0.880131	−	0.474730i	$-0.842546\pi$
$953$	−54.3405	−1.76026	−0.880131	+	0.474730i	$0.842546\pi$
$954$	−10.1469	−0.328517
$955$	−6.79723	−0.219953
$956$	−22.8869	−0.740214
$957$	33.6592	1.08805
$958$	−14.4492	−0.466834
$959$	26.3551	0.851052
$960$	3.08926	0.0997055
$961$	24.7419	0.798127
$962$	−7.08391	−0.228395
$963$	6.49908	0.209430
$964$	52.7536	1.69908
$965$	6.48457	0.208746
$966$	−29.6275	−0.953250
$967$	40.5558	1.30419	0.652094	−	0.758138i	$-0.273891\pi$
$967$	40.5558	1.30419	0.652094	+	0.758138i	$0.273891\pi$
$968$	−131.712	−4.23339
$969$	−31.6833	−1.01781
$970$	−13.7146	−0.440349
$971$	28.1791	0.904310	0.452155	−	0.891939i	$-0.350655\pi$
$971$	28.1791	0.904310	0.452155	+	0.891939i	$0.350655\pi$
$972$	−4.12439	−0.132290
$973$	23.4594	0.752074
$974$	−56.8515	−1.82164
$975$	−1.67067	−0.0535041
$976$	−15.1848	−0.486055
$977$	60.4702	1.93461	0.967307	−	0.253610i	$-0.0816179\pi$
$977$	60.4702	1.93461	0.967307	+	0.253610i	$0.0816179\pi$
$978$	20.2633	0.647948
$979$	90.0663	2.87853
$980$	−10.3279	−0.329914
$981$	−9.74698	−0.311197
$982$	−84.6416	−2.70102
$983$	59.7441	1.90554	0.952771	−	0.303690i	$-0.0982187\pi$
$983$	59.7441	1.90554	0.952771	+	0.303690i	$0.0982187\pi$
$984$	−13.8675	−0.442080
$985$	−6.78218	−0.216098
$986$	78.4680	2.49893
$987$	−10.7071	−0.340811
$988$	8.09897	0.257663
$989$	−107.747	−3.42617
$990$	7.19333	0.228619
$991$	27.7977	0.883023	0.441512	−	0.897256i	$-0.354442\pi$
$991$	27.7977	0.883023	0.441512	+	0.897256i	$0.354442\pi$
$992$	9.47941	0.300972
$993$	−8.87383	−0.281602
$994$	24.4259	0.774743
$995$	−8.66498	−0.274698
$996$	23.5913	0.747519
$997$	20.4625	0.648053	0.324026	−	0.946048i	$-0.394963\pi$
$997$	20.4625	0.648053	0.324026	+	0.946048i	$0.394963\pi$
$998$	41.0646	1.29988
$999$	8.16535	0.258340

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.6	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.47475 q^{2} -1.00000 q^{3} +4.12439 q^{4} +0.484092 q^{5} +2.47475 q^{6} -1.35174 q^{7} -5.25735 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.47475 q^{2} -1.00000 q^{3} +4.12439 q^{4} +0.484092 q^{5} +2.47475 q^{6} -1.35174 q^{7} -5.25735 q^{8} +1.00000 q^{9} -1.19801 q^{10} -6.00442 q^{11} -4.12439 q^{12} -0.350564 q^{13} +3.34522 q^{14} -0.484092 q^{15} +4.76184 q^{16} -5.65624 q^{17} -2.47475 q^{18} -5.60148 q^{19} +1.99659 q^{20} +1.35174 q^{21} +14.8594 q^{22} +8.85668 q^{23} +5.25735 q^{24} -4.76565 q^{25} +0.867558 q^{26} -1.00000 q^{27} -5.57511 q^{28} +5.60574 q^{29} +1.19801 q^{30} -7.46605 q^{31} -1.26967 q^{32} +6.00442 q^{33} +13.9978 q^{34} -0.654367 q^{35} +4.12439 q^{36} -8.16535 q^{37} +13.8623 q^{38} +0.350564 q^{39} -2.54504 q^{40} -2.63774 q^{41} -3.34522 q^{42} -12.1657 q^{43} -24.7646 q^{44} +0.484092 q^{45} -21.9181 q^{46} -7.92097 q^{47} -4.76184 q^{48} -5.17280 q^{49} +11.7938 q^{50} +5.65624 q^{51} -1.44586 q^{52} +4.10016 q^{53} +2.47475 q^{54} -2.90669 q^{55} +7.10656 q^{56} +5.60148 q^{57} -13.8728 q^{58} +1.78166 q^{59} -1.99659 q^{60} -3.18886 q^{61} +18.4766 q^{62} -1.35174 q^{63} -6.38156 q^{64} -0.169705 q^{65} -14.8594 q^{66} -1.53185 q^{67} -23.3286 q^{68} -8.85668 q^{69} +1.61939 q^{70} +7.30174 q^{71} -5.25735 q^{72} -14.8695 q^{73} +20.2072 q^{74} +4.76565 q^{75} -23.1027 q^{76} +8.11641 q^{77} -0.867558 q^{78} +15.0000 q^{79} +2.30517 q^{80} +1.00000 q^{81} +6.52775 q^{82} -5.71995 q^{83} +5.57511 q^{84} -2.73814 q^{85} +30.1070 q^{86} -5.60574 q^{87} +31.5673 q^{88} -15.0000 q^{89} -1.19801 q^{90} +0.473871 q^{91} +36.5284 q^{92} +7.46605 q^{93} +19.6024 q^{94} -2.71163 q^{95} +1.26967 q^{96} +11.4478 q^{97} +12.8014 q^{98} -6.00442 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 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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