LMFDB - Embedded newform 6007.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$0$
Dimension:	$261$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46886 q^{2} -1.31806 q^{3} +4.09526 q^{4} +2.84222 q^{5} +3.25411 q^{6} -1.17521 q^{7} -5.17289 q^{8} -1.26271 q^{9} +O(q^{10})$	\(q-2.46886 q^{2} -1.31806 q^{3} +4.09526 q^{4} +2.84222 q^{5} +3.25411 q^{6} -1.17521 q^{7} -5.17289 q^{8} -1.26271 q^{9} -7.01703 q^{10} -4.95188 q^{11} -5.39780 q^{12} -3.11020 q^{13} +2.90141 q^{14} -3.74622 q^{15} +4.58061 q^{16} +1.94721 q^{17} +3.11746 q^{18} +3.98598 q^{19} +11.6396 q^{20} +1.54899 q^{21} +12.2255 q^{22} -2.66581 q^{23} +6.81819 q^{24} +3.07821 q^{25} +7.67863 q^{26} +5.61852 q^{27} -4.81277 q^{28} -7.87103 q^{29} +9.24888 q^{30} +5.37804 q^{31} -0.963101 q^{32} +6.52689 q^{33} -4.80739 q^{34} -3.34019 q^{35} -5.17113 q^{36} -2.52412 q^{37} -9.84081 q^{38} +4.09943 q^{39} -14.7025 q^{40} +8.52497 q^{41} -3.82424 q^{42} -9.40632 q^{43} -20.2792 q^{44} -3.58891 q^{45} +6.58150 q^{46} +5.37021 q^{47} -6.03753 q^{48} -5.61889 q^{49} -7.59965 q^{50} -2.56655 q^{51} -12.7370 q^{52} +8.27608 q^{53} -13.8713 q^{54} -14.0743 q^{55} +6.07921 q^{56} -5.25377 q^{57} +19.4325 q^{58} -12.4914 q^{59} -15.3417 q^{60} -6.62529 q^{61} -13.2776 q^{62} +1.48395 q^{63} -6.78347 q^{64} -8.83986 q^{65} -16.1139 q^{66} +0.668405 q^{67} +7.97434 q^{68} +3.51370 q^{69} +8.24645 q^{70} -10.1879 q^{71} +6.53187 q^{72} -10.6949 q^{73} +6.23169 q^{74} -4.05727 q^{75} +16.3236 q^{76} +5.81948 q^{77} -10.1209 q^{78} +6.63907 q^{79} +13.0191 q^{80} -3.61742 q^{81} -21.0469 q^{82} +9.54303 q^{83} +6.34352 q^{84} +5.53441 q^{85} +23.2229 q^{86} +10.3745 q^{87} +25.6155 q^{88} -1.43873 q^{89} +8.86050 q^{90} +3.65512 q^{91} -10.9172 q^{92} -7.08859 q^{93} -13.2583 q^{94} +11.3290 q^{95} +1.26943 q^{96} +7.44079 q^{97} +13.8722 q^{98} +6.25280 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) $ 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9 + 35 * q^10 + 32 * q^11 + 51 * q^12 + 60 * q^13 + 55 * q^14 + 16 * q^15 + 288 * q^16 + 270 * q^17 + 45 * q^18 + 34 * q^19 + 157 * q^20 + 27 * q^21 + 38 * q^22 + 116 * q^23 + 48 * q^24 + 335 * q^25 + 46 * q^26 + 73 * q^27 + 70 * q^28 + 99 * q^29 + 33 * q^30 + 33 * q^31 + 150 * q^32 + 172 * q^33 + 24 * q^34 + 114 * q^35 + 339 * q^36 + 36 * q^37 + 112 * q^38 + 30 * q^39 + 106 * q^40 + 209 * q^41 + 64 * q^42 + 64 * q^43 + 65 * q^44 + 153 * q^45 + 135 * q^47 + 87 * q^48 + 332 * q^49 + 82 * q^50 + 52 * q^51 + 102 * q^52 + 163 * q^53 + 52 * q^54 + 56 * q^55 + 134 * q^56 + 181 * q^57 + q^58 + 89 * q^59 - 43 * q^60 + 112 * q^61 + 228 * q^62 + 130 * q^63 + 268 * q^64 + 248 * q^65 + 5 * q^66 + 42 * q^67 + 453 * q^68 + 51 * q^69 - 22 * q^70 + 98 * q^71 + 113 * q^72 + 206 * q^73 + 81 * q^74 + 29 * q^75 + 62 * q^76 + 185 * q^77 - 25 * q^78 + 29 * q^79 + 258 * q^80 + 393 * q^81 + 79 * q^82 + 265 * q^83 - 25 * q^84 + 84 * q^85 + 36 * q^86 + 131 * q^87 + 24 * q^88 + 195 * q^89 + 89 * q^90 - 18 * q^91 + 261 * q^92 + 52 * q^93 + 3 * q^94 + 104 * q^95 + 92 * q^96 + 213 * q^97 + 156 * q^98 + 47 * 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 $

$2$	−2.46886	−1.74575	−0.872873	−	0.487948i	$-0.837746\pi$
$2$	−2.46886	−1.74575	−0.872873	+	0.487948i	$0.837746\pi$
$3$	−1.31806	−0.760983	−0.380492	−	0.924784i	$-0.624245\pi$
$3$	−1.31806	−0.760983	−0.380492	+	0.924784i	$0.624245\pi$
$4$	4.09526	2.04763
$5$	2.84222	1.27108	0.635539	−	0.772068i	$-0.280778\pi$
$5$	2.84222	1.27108	0.635539	+	0.772068i	$0.280778\pi$
$6$	3.25411	1.32848
$7$	−1.17521	−0.444186	−0.222093	−	0.975026i	$-0.571289\pi$
$7$	−1.17521	−0.444186	−0.222093	+	0.975026i	$0.571289\pi$
$8$	−5.17289	−1.82889
$9$	−1.26271	−0.420904
$10$	−7.01703	−2.21898
$11$	−4.95188	−1.49305	−0.746524	−	0.665358i	$-0.768279\pi$
$11$	−4.95188	−1.49305	−0.746524	+	0.665358i	$0.768279\pi$
$12$	−5.39780	−1.55821
$13$	−3.11020	−0.862613	−0.431307	−	0.902205i	$-0.641947\pi$
$13$	−3.11020	−0.862613	−0.431307	+	0.902205i	$0.641947\pi$
$14$	2.90141	0.775436
$15$	−3.74622	−0.967270
$16$	4.58061	1.14515
$17$	1.94721	0.472269	0.236134	−	0.971720i	$-0.424119\pi$
$17$	1.94721	0.472269	0.236134	+	0.971720i	$0.424119\pi$
$18$	3.11746	0.734792
$19$	3.98598	0.914446	0.457223	−	0.889352i	$-0.348844\pi$
$19$	3.98598	0.914446	0.457223	+	0.889352i	$0.348844\pi$
$20$	11.6396	2.60270
$21$	1.54899	0.338018
$22$	12.2255	2.60648
$23$	−2.66581	−0.555859	−0.277930	−	0.960601i	$-0.589648\pi$
$23$	−2.66581	−0.555859	−0.277930	+	0.960601i	$0.589648\pi$
$24$	6.81819	1.39176
$25$	3.07821	0.615641
$26$	7.67863	1.50590
$27$	5.61852	1.08128
$28$	−4.81277	−0.909527
$29$	−7.87103	−1.46161	−0.730807	−	0.682584i	$-0.760856\pi$
$29$	−7.87103	−1.46161	−0.730807	+	0.682584i	$0.760856\pi$
$30$	9.24888	1.68861
$31$	5.37804	0.965925	0.482962	−	0.875641i	$-0.339561\pi$
$31$	5.37804	0.965925	0.482962	+	0.875641i	$0.339561\pi$
$32$	−0.963101	−0.170254
$33$	6.52689	1.13618
$34$	−4.80739	−0.824461
$35$	−3.34019	−0.564595
$36$	−5.17113	−0.861855
$37$	−2.52412	−0.414962	−0.207481	−	0.978239i	$-0.566527\pi$
$37$	−2.52412	−0.414962	−0.207481	+	0.978239i	$0.566527\pi$
$38$	−9.84081	−1.59639
$39$	4.09943	0.656434
$40$	−14.7025	−2.32467
$41$	8.52497	1.33138	0.665688	−	0.746230i	$-0.268138\pi$
$41$	8.52497	1.33138	0.665688	+	0.746230i	$0.268138\pi$
$42$	−3.82424	−0.590094
$43$	−9.40632	−1.43445	−0.717225	−	0.696841i	$-0.754588\pi$
$43$	−9.40632	−1.43445	−0.717225	+	0.696841i	$0.754588\pi$
$44$	−20.2792	−3.05721
$45$	−3.58891	−0.535002
$46$	6.58150	0.970389
$47$	5.37021	0.783326	0.391663	−	0.920109i	$-0.371900\pi$
$47$	5.37021	0.783326	0.391663	+	0.920109i	$0.371900\pi$
$48$	−6.03753	−0.871443
$49$	−5.61889	−0.802699
$50$	−7.59965	−1.07475
$51$	−2.56655	−0.359389
$52$	−12.7370	−1.76631
$53$	8.27608	1.13681	0.568404	−	0.822750i	$-0.307561\pi$
$53$	8.27608	1.13681	0.568404	+	0.822750i	$0.307561\pi$
$54$	−13.8713	−1.88765
$55$	−14.0743	−1.89778
$56$	6.07921	0.812368
$57$	−5.25377	−0.695878
$58$	19.4325	2.55161
$59$	−12.4914	−1.62624	−0.813119	−	0.582098i	$-0.802232\pi$
$59$	−12.4914	−1.62624	−0.813119	+	0.582098i	$0.802232\pi$
$60$	−15.3417	−1.98061
$61$	−6.62529	−0.848282	−0.424141	−	0.905596i	$-0.639424\pi$
$61$	−6.62529	−0.848282	−0.424141	+	0.905596i	$0.639424\pi$
$62$	−13.2776	−1.68626
$63$	1.48395	0.186960
$64$	−6.78347	−0.847933
$65$	−8.83986	−1.09645
$66$	−16.1139	−1.98349
$67$	0.668405	0.0816587	0.0408293	−	0.999166i	$-0.487000\pi$
$67$	0.668405	0.0816587	0.0408293	+	0.999166i	$0.487000\pi$
$68$	7.97434	0.967031
$69$	3.51370	0.423000
$70$	8.24645	0.985640
$71$	−10.1879	−1.20908	−0.604539	−	0.796576i	$-0.706643\pi$
$71$	−10.1879	−1.20908	−0.604539	+	0.796576i	$0.706643\pi$
$72$	6.53187	0.769789
$73$	−10.6949	−1.25175	−0.625874	−	0.779924i	$-0.715257\pi$
$73$	−10.6949	−1.25175	−0.625874	+	0.779924i	$0.715257\pi$
$74$	6.23169	0.724419
$75$	−4.05727	−0.468493
$76$	16.3236	1.87245
$77$	5.81948	0.663191
$78$	−10.1209	−1.14597
$79$	6.63907	0.746954	0.373477	−	0.927639i	$-0.378165\pi$
$79$	6.63907	0.746954	0.373477	+	0.927639i	$0.378165\pi$
$80$	13.0191	1.45558
$81$	−3.61742	−0.401935
$82$	−21.0469	−2.32424
$83$	9.54303	1.04748	0.523742	−	0.851877i	$-0.324536\pi$
$83$	9.54303	1.04748	0.523742	+	0.851877i	$0.324536\pi$
$84$	6.34352	0.692135
$85$	5.53441	0.600291
$86$	23.2229	2.50419
$87$	10.3745	1.11226
$88$	25.6155	2.73062
$89$	−1.43873	−0.152505	−0.0762525	−	0.997089i	$-0.524296\pi$
$89$	−1.43873	−0.152505	−0.0762525	+	0.997089i	$0.524296\pi$
$90$	8.86050	0.933978
$91$	3.65512	0.383160
$92$	−10.9172	−1.13819
$93$	−7.08859	−0.735053
$94$	−13.2583	−1.36749
$95$	11.3290	1.16233
$96$	1.26943	0.129560
$97$	7.44079	0.755498	0.377749	−	0.925908i	$-0.376698\pi$
$97$	7.44079	0.755498	0.377749	+	0.925908i	$0.376698\pi$
$98$	13.8722	1.40131
$99$	6.25280	0.628430
$100$	12.6060	1.26060
$101$	14.2117	1.41412	0.707058	−	0.707156i	$-0.250022\pi$
$101$	14.2117	1.41412	0.707058	+	0.707156i	$0.250022\pi$
$102$	6.33644	0.627401
$103$	−12.0665	−1.18895	−0.594475	−	0.804114i	$-0.702640\pi$
$103$	−12.0665	−1.18895	−0.594475	+	0.804114i	$0.702640\pi$
$104$	16.0887	1.57763
$105$	4.40258	0.429648
$106$	−20.4325	−1.98458
$107$	−19.7653	−1.91078	−0.955391	−	0.295344i	$-0.904566\pi$
$107$	−19.7653	−1.91078	−0.955391	+	0.295344i	$0.904566\pi$
$108$	23.0093	2.21407
$109$	−11.0478	−1.05818	−0.529092	−	0.848564i	$-0.677467\pi$
$109$	−11.0478	−1.05818	−0.529092	+	0.848564i	$0.677467\pi$
$110$	34.7475	3.31304
$111$	3.32694	0.315780
$112$	−5.38316	−0.508661
$113$	−2.69830	−0.253835	−0.126917	−	0.991913i	$-0.540508\pi$
$113$	−2.69830	−0.253835	−0.126917	+	0.991913i	$0.540508\pi$
$114$	12.9708	1.21483
$115$	−7.57681	−0.706541
$116$	−32.2339	−2.99284
$117$	3.92728	0.363077
$118$	30.8394	2.83900
$119$	−2.28838	−0.209775
$120$	19.3788	1.76903
$121$	13.5211	1.22919
$122$	16.3569	1.48088
$123$	−11.2364	−1.01316
$124$	22.0245	1.97785
$125$	−5.46216	−0.488550
$126$	−3.66365	−0.326384
$127$	21.0176	1.86501	0.932505	−	0.361157i	$-0.117618\pi$
$127$	21.0176	1.86501	0.932505	+	0.361157i	$0.117618\pi$
$128$	18.6736	1.65053
$129$	12.3981	1.09159
$130$	21.8243	1.91412
$131$	4.96503	0.433796	0.216898	−	0.976194i	$-0.430406\pi$
$131$	4.96503	0.433796	0.216898	+	0.976194i	$0.430406\pi$
$132$	26.7293	2.32648
$133$	−4.68434	−0.406184
$134$	−1.65020	−0.142555
$135$	15.9691	1.37440
$136$	−10.0727	−0.863729
$137$	5.97184	0.510209	0.255105	−	0.966913i	$-0.417890\pi$
$137$	5.97184	0.510209	0.255105	+	0.966913i	$0.417890\pi$
$138$	−8.67483	−0.738450
$139$	−6.55230	−0.555759	−0.277879	−	0.960616i	$-0.589632\pi$
$139$	−6.55230	−0.555759	−0.277879	+	0.960616i	$0.589632\pi$
$140$	−13.6789	−1.15608
$141$	−7.07827	−0.596098
$142$	25.1524	2.11074
$143$	15.4013	1.28792
$144$	−5.78400	−0.482000
$145$	−22.3712	−1.85783
$146$	26.4043	2.18523
$147$	7.40605	0.610841
$148$	−10.3369	−0.849689
$149$	−4.11209	−0.336876	−0.168438	−	0.985712i	$-0.553872\pi$
$149$	−4.11209	−0.336876	−0.168438	+	0.985712i	$0.553872\pi$
$150$	10.0168	0.817870
$151$	13.5084	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$151$	13.5084	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$152$	−20.6190	−1.67242
$153$	−2.45877	−0.198780
$154$	−14.3675	−1.15776
$155$	15.2856	1.22777
$156$	16.7882	1.34413
$157$	9.88063	0.788560	0.394280	−	0.918990i	$-0.370994\pi$
$157$	9.88063	0.788560	0.394280	+	0.918990i	$0.370994\pi$
$158$	−16.3909	−1.30399
$159$	−10.9084	−0.865092
$160$	−2.73734	−0.216406
$161$	3.13287	0.246905
$162$	8.93089	0.701677
$163$	−18.9621	−1.48522	−0.742612	−	0.669722i	$-0.766413\pi$
$163$	−18.9621	−1.48522	−0.742612	+	0.669722i	$0.766413\pi$
$164$	34.9119	2.72616
$165$	18.5508	1.44418
$166$	−23.5604	−1.82864
$167$	3.59943	0.278532	0.139266	−	0.990255i	$-0.455526\pi$
$167$	3.59943	0.278532	0.139266	+	0.990255i	$0.455526\pi$
$168$	−8.01277	−0.618199
$169$	−3.32668	−0.255899
$170$	−13.6637	−1.04796
$171$	−5.03315	−0.384894
$172$	−38.5213	−2.93722
$173$	20.4481	1.55464	0.777320	−	0.629105i	$-0.216579\pi$
$173$	20.4481	1.55464	0.777320	+	0.629105i	$0.216579\pi$
$174$	−25.6132	−1.94173
$175$	−3.61753	−0.273459
$176$	−22.6826	−1.70977
$177$	16.4644	1.23754
$178$	3.55202	0.266235
$179$	−18.7071	−1.39823	−0.699117	−	0.715008i	$-0.746423\pi$
$179$	−18.7071	−1.39823	−0.699117	+	0.715008i	$0.746423\pi$
$180$	−14.6975	−1.09549
$181$	20.2561	1.50562	0.752811	−	0.658237i	$-0.228697\pi$
$181$	20.2561	1.50562	0.752811	+	0.658237i	$0.228697\pi$
$182$	−9.02397	−0.668901
$183$	8.73255	0.645529
$184$	13.7899	1.01661
$185$	−7.17409	−0.527450
$186$	17.5007	1.28322
$187$	−9.64237	−0.705120
$188$	21.9924	1.60396
$189$	−6.60291	−0.480291
$190$	−27.9697	−2.02914
$191$	−1.24630	−0.0901788	−0.0450894	−	0.998983i	$-0.514357\pi$
$191$	−1.24630	−0.0901788	−0.0450894	+	0.998983i	$0.514357\pi$
$192$	8.94103	0.645263
$193$	9.93658	0.715250	0.357625	−	0.933865i	$-0.383587\pi$
$193$	9.93658	0.715250	0.357625	+	0.933865i	$0.383587\pi$
$194$	−18.3702	−1.31891
$195$	11.6515	0.834380
$196$	−23.0108	−1.64363
$197$	6.41131	0.456787	0.228393	−	0.973569i	$-0.426653\pi$
$197$	6.41131	0.456787	0.228393	+	0.973569i	$0.426653\pi$
$198$	−15.4373	−1.09708
$199$	5.96913	0.423140	0.211570	−	0.977363i	$-0.432142\pi$
$199$	5.96913	0.423140	0.211570	+	0.977363i	$0.432142\pi$
$200$	−15.9232	−1.12594
$201$	−0.880999	−0.0621409
$202$	−35.0866	−2.46869
$203$	9.25008	0.649228
$204$	−10.5107	−0.735894
$205$	24.2298	1.69228
$206$	29.7906	2.07561
$207$	3.36615	0.233964
$208$	−14.2466	−0.987824
$209$	−19.7381	−1.36531
$210$	−10.8693	−0.750055
$211$	−10.2294	−0.704218	−0.352109	−	0.935959i	$-0.614535\pi$
$211$	−10.2294	−0.704218	−0.352109	+	0.935959i	$0.614535\pi$
$212$	33.8927	2.32776
$213$	13.4282	0.920088
$214$	48.7977	3.33574
$215$	−26.7348	−1.82330
$216$	−29.0640	−1.97755
$217$	−6.32030	−0.429050
$218$	27.2754	1.84732
$219$	14.0966	0.952559
$220$	−57.6380	−3.88595
$221$	−6.05622	−0.407385
$222$	−8.21375	−0.551271
$223$	−5.04768	−0.338018	−0.169009	−	0.985615i	$-0.554057\pi$
$223$	−5.04768	−0.338018	−0.169009	+	0.985615i	$0.554057\pi$
$224$	1.13184	0.0756243
$225$	−3.88689	−0.259126
$226$	6.66171	0.443131
$227$	−26.0218	−1.72713	−0.863563	−	0.504242i	$-0.831772\pi$
$227$	−26.0218	−1.72713	−0.863563	+	0.504242i	$0.831772\pi$
$228$	−21.5155	−1.42490
$229$	23.5364	1.55533	0.777666	−	0.628678i	$-0.216404\pi$
$229$	23.5364	1.55533	0.777666	+	0.628678i	$0.216404\pi$
$230$	18.7061	1.23344
$231$	−7.67043	−0.504677
$232$	40.7160	2.67313
$233$	3.94490	0.258439	0.129220	−	0.991616i	$-0.458753\pi$
$233$	3.94490	0.258439	0.129220	+	0.991616i	$0.458753\pi$
$234$	−9.69590	−0.633841
$235$	15.2633	0.995669
$236$	−51.1554	−3.32993
$237$	−8.75071	−0.568420
$238$	5.64967	0.366214
$239$	−19.2028	−1.24212	−0.621062	−	0.783761i	$-0.713299\pi$
$239$	−19.2028	−1.24212	−0.621062	+	0.783761i	$0.713299\pi$
$240$	−17.1600	−1.10767
$241$	14.7896	0.952680	0.476340	−	0.879261i	$-0.341963\pi$
$241$	14.7896	0.952680	0.476340	+	0.879261i	$0.341963\pi$
$242$	−33.3817	−2.14586
$243$	−12.0876	−0.775418
$244$	−27.1323	−1.73697
$245$	−15.9701	−1.02029
$246$	27.7412	1.76871
$247$	−12.3972	−0.788813
$248$	−27.8200	−1.76657
$249$	−12.5783	−0.797117
$250$	13.4853	0.852884
$251$	3.48984	0.220277	0.110138	−	0.993916i	$-0.464871\pi$
$251$	3.48984	0.220277	0.110138	+	0.993916i	$0.464871\pi$
$252$	6.07714	0.382824
$253$	13.2008	0.829925
$254$	−51.8894	−3.25583
$255$	−7.29469	−0.456811
$256$	−32.5356	−2.03347
$257$	20.4131	1.27333	0.636667	−	0.771139i	$-0.280313\pi$
$257$	20.4131	1.27333	0.636667	+	0.771139i	$0.280313\pi$
$258$	−30.6092	−1.90564
$259$	2.96636	0.184320
$260$	−36.2015	−2.24512
$261$	9.93885	0.615199
$262$	−12.2579	−0.757298
$263$	17.1172	1.05549	0.527747	−	0.849402i	$-0.323037\pi$
$263$	17.1172	1.05549	0.527747	+	0.849402i	$0.323037\pi$
$264$	−33.7629	−2.07796
$265$	23.5224	1.44497
$266$	11.5650	0.709094
$267$	1.89634	0.116054
$268$	2.73729	0.167207
$269$	−17.8223	−1.08664	−0.543321	−	0.839525i	$-0.682833\pi$
$269$	−17.8223	−1.08664	−0.543321	+	0.839525i	$0.682833\pi$
$270$	−39.4253	−2.39935
$271$	−27.4219	−1.66576	−0.832880	−	0.553454i	$-0.813309\pi$
$271$	−27.4219	−1.66576	−0.832880	+	0.553454i	$0.813309\pi$
$272$	8.91943	0.540820
$273$	−4.81767	−0.291579
$274$	−14.7436	−0.890695
$275$	−15.2429	−0.919182
$276$	14.3895	0.866146
$277$	−31.8190	−1.91182	−0.955908	−	0.293666i	$-0.905125\pi$
$277$	−31.8190	−1.91182	−0.955908	+	0.293666i	$0.905125\pi$
$278$	16.1767	0.970213
$279$	−6.79092	−0.406562
$280$	17.2784	1.03258
$281$	26.7259	1.59433	0.797166	−	0.603760i	$-0.206332\pi$
$281$	26.7259	1.59433	0.797166	+	0.603760i	$0.206332\pi$
$282$	17.4752	1.04064
$283$	2.13232	0.126753	0.0633766	−	0.997990i	$-0.479813\pi$
$283$	2.13232	0.126753	0.0633766	+	0.997990i	$0.479813\pi$
$284$	−41.7219	−2.47574
$285$	−14.9324	−0.884516
$286$	−38.0237	−2.24839
$287$	−10.0186	−0.591378
$288$	1.21612	0.0716606
$289$	−13.2084	−0.776962
$290$	55.2313	3.24329
$291$	−9.80742	−0.574921
$292$	−43.7985	−2.56311
$293$	28.0083	1.63626	0.818130	−	0.575033i	$-0.195011\pi$
$293$	28.0083	1.63626	0.818130	+	0.575033i	$0.195011\pi$
$294$	−18.2845	−1.06637
$295$	−35.5032	−2.06708
$296$	13.0570	0.758922
$297$	−27.8222	−1.61441
$298$	10.1522	0.588099
$299$	8.29119	0.479492
$300$	−16.6156	−0.959299
$301$	11.0544	0.637163
$302$	−33.3504	−1.91910
$303$	−18.7319	−1.07612
$304$	18.2582	1.04718
$305$	−18.8305	−1.07823
$306$	6.07036	0.347019
$307$	−1.92895	−0.110091	−0.0550456	−	0.998484i	$-0.517530\pi$
$307$	−1.92895	−0.110091	−0.0550456	+	0.998484i	$0.517530\pi$
$308$	23.8322	1.35797
$309$	15.9044	0.904772
$310$	−37.7379	−2.14337
$311$	−1.22357	−0.0693824	−0.0346912	−	0.999398i	$-0.511045\pi$
$311$	−1.22357	−0.0693824	−0.0346912	+	0.999398i	$0.511045\pi$
$312$	−21.2059	−1.20055
$313$	−13.3563	−0.754942	−0.377471	−	0.926021i	$-0.623206\pi$
$313$	−13.3563	−0.754942	−0.377471	+	0.926021i	$0.623206\pi$
$314$	−24.3939	−1.37662
$315$	4.21770	0.237641
$316$	27.1887	1.52948
$317$	−5.59941	−0.314494	−0.157247	−	0.987559i	$-0.550262\pi$
$317$	−5.59941	−0.314494	−0.157247	+	0.987559i	$0.550262\pi$
$318$	26.9313	1.51023
$319$	38.9764	2.18226
$320$	−19.2801	−1.07779
$321$	26.0519	1.45407
$322$	−7.73461	−0.431033
$323$	7.76155	0.431864
$324$	−14.8143	−0.823014
$325$	−9.57383	−0.531060
$326$	46.8146	2.59282
$327$	14.5616	0.805261
$328$	−44.0987	−2.43494
$329$	−6.31110	−0.347942
$330$	−45.7994	−2.52117
$331$	−9.91718	−0.545098	−0.272549	−	0.962142i	$-0.587867\pi$
$331$	−9.91718	−0.545098	−0.272549	+	0.962142i	$0.587867\pi$
$332$	39.0811	2.14486
$333$	3.18724	0.174659
$334$	−8.88649	−0.486247
$335$	1.89975	0.103795
$336$	7.09534	0.387082
$337$	18.8075	1.02451	0.512254	−	0.858834i	$-0.328811\pi$
$337$	18.8075	1.02451	0.512254	+	0.858834i	$0.328811\pi$
$338$	8.21311	0.446734
$339$	3.55652	0.193164
$340$	22.6648	1.22917
$341$	−26.6314	−1.44217
$342$	12.4261	0.671927
$343$	14.8298	0.800733
$344$	48.6579	2.62346
$345$	9.98671	0.537666
$346$	−50.4834	−2.71401
$347$	26.7807	1.43766	0.718832	−	0.695183i	$-0.244677\pi$
$347$	26.7807	1.43766	0.718832	+	0.695183i	$0.244677\pi$
$348$	42.4863	2.27750
$349$	−24.6970	−1.32200	−0.660999	−	0.750387i	$-0.729867\pi$
$349$	−24.6970	−1.32200	−0.660999	+	0.750387i	$0.729867\pi$
$350$	8.93115	0.477390
$351$	−17.4747	−0.932730
$352$	4.76916	0.254197
$353$	33.4940	1.78271	0.891354	−	0.453308i	$-0.149756\pi$
$353$	33.4940	1.78271	0.891354	+	0.453308i	$0.149756\pi$
$354$	−40.6482	−2.16043
$355$	−28.9562	−1.53683
$356$	−5.89197	−0.312274
$357$	3.01622	0.159635
$358$	46.1851	2.44096
$359$	28.7463	1.51717	0.758585	−	0.651574i	$-0.225891\pi$
$359$	28.7463	1.51717	0.758585	+	0.651574i	$0.225891\pi$
$360$	18.5650	0.978462
$361$	−3.11198	−0.163788
$362$	−50.0094	−2.62843
$363$	−17.8217	−0.935395
$364$	14.9686	0.784570
$365$	−30.3973	−1.59107
$366$	−21.5594	−1.12693
$367$	20.9874	1.09553	0.547767	−	0.836631i	$-0.315478\pi$
$367$	20.9874	1.09553	0.547767	+	0.836631i	$0.315478\pi$
$368$	−12.2110	−0.636544
$369$	−10.7646	−0.560382
$370$	17.7118	0.920793
$371$	−9.72610	−0.504954
$372$	−29.0296	−1.50511
$373$	26.0032	1.34639	0.673196	−	0.739464i	$-0.264921\pi$
$373$	26.0032	1.34639	0.673196	+	0.739464i	$0.264921\pi$
$374$	23.8056	1.23096
$375$	7.19946	0.371778
$376$	−27.7795	−1.43262
$377$	24.4804	1.26081
$378$	16.3017	0.838466
$379$	18.9866	0.975276	0.487638	−	0.873046i	$-0.337859\pi$
$379$	18.9866	0.975276	0.487638	+	0.873046i	$0.337859\pi$
$380$	46.3952	2.38003
$381$	−27.7025	−1.41924
$382$	3.07693	0.157429
$383$	27.4894	1.40464	0.702322	−	0.711860i	$-0.252147\pi$
$383$	27.4894	1.40464	0.702322	+	0.711860i	$0.252147\pi$
$384$	−24.6130	−1.25603
$385$	16.5402	0.842968
$386$	−24.5320	−1.24865
$387$	11.8775	0.603766
$388$	30.4719	1.54698
$389$	3.48938	0.176919	0.0884593	−	0.996080i	$-0.471806\pi$
$389$	3.48938	0.176919	0.0884593	+	0.996080i	$0.471806\pi$
$390$	−28.7658	−1.45661
$391$	−5.19090	−0.262515
$392$	29.0659	1.46805
$393$	−6.54421	−0.330112
$394$	−15.8286	−0.797434
$395$	18.8697	0.949438
$396$	25.6068	1.28679
$397$	33.4628	1.67945	0.839725	−	0.543011i	$-0.182716\pi$
$397$	33.4628	1.67945	0.839725	+	0.543011i	$0.182716\pi$
$398$	−14.7369	−0.738696
$399$	6.17425	0.309099
$400$	14.1001	0.705004
$401$	14.8662	0.742380	0.371190	−	0.928557i	$-0.378950\pi$
$401$	14.8662	0.742380	0.371190	+	0.928557i	$0.378950\pi$
$402$	2.17506	0.108482
$403$	−16.7268	−0.833219
$404$	58.2005	2.89558
$405$	−10.2815	−0.510892
$406$	−22.8371	−1.13339
$407$	12.4991	0.619559
$408$	13.2765	0.657283
$409$	−2.74158	−0.135562	−0.0677812	−	0.997700i	$-0.521592\pi$
$409$	−2.74158	−0.135562	−0.0677812	+	0.997700i	$0.521592\pi$
$410$	−59.8200	−2.95430
$411$	−7.87126	−0.388261
$412$	−49.4156	−2.43453
$413$	14.6799	0.722352
$414$	−8.31054	−0.408441
$415$	27.1234	1.33143
$416$	2.99543	0.146863
$417$	8.63633	0.422923
$418$	48.7305	2.38349
$419$	0.0403985	0.00197360	0.000986798	−	1.00000i	$-0.499686\pi$
$419$	0.0403985	0.00197360	0.000986798		1.00000i	$0.499686\pi$
$420$	18.0297	0.879759
$421$	4.01771	0.195811	0.0979056	−	0.995196i	$-0.468786\pi$
$421$	4.01771	0.195811	0.0979056	+	0.995196i	$0.468786\pi$
$422$	25.2548	1.22938
$423$	−6.78104	−0.329705
$424$	−42.8113	−2.07910
$425$	5.99393	0.290748
$426$	−33.1524	−1.60624
$427$	7.78608	0.376795
$428$	−80.9439	−3.91257
$429$	−20.2999	−0.980088
$430$	66.0045	3.18302
$431$	−0.0322375	−0.00155282	−0.000776412	−	1.00000i	$-0.500247\pi$
$431$	−0.0322375	−0.00155282	−0.000776412		1.00000i	$0.500247\pi$
$432$	25.7363	1.23824
$433$	−16.4309	−0.789618	−0.394809	−	0.918763i	$-0.629189\pi$
$433$	−16.4309	−0.789618	−0.394809	+	0.918763i	$0.629189\pi$
$434$	15.6039	0.749012
$435$	29.4866	1.41377
$436$	−45.2435	−2.16677
$437$	−10.6259	−0.508304
$438$	−34.8025	−1.66293
$439$	−15.6923	−0.748950	−0.374475	−	0.927237i	$-0.622177\pi$
$439$	−15.6923	−0.748950	−0.374475	+	0.927237i	$0.622177\pi$
$440$	72.8049	3.47084
$441$	7.09505	0.337859
$442$	14.9519	0.711191
$443$	36.1593	1.71798	0.858991	−	0.511991i	$-0.171092\pi$
$443$	36.1593	1.71798	0.858991	+	0.511991i	$0.171092\pi$
$444$	13.6247	0.646599
$445$	−4.08919	−0.193846
$446$	12.4620	0.590093
$447$	5.41999	0.256357
$448$	7.97197	0.376640
$449$	−5.54211	−0.261549	−0.130774	−	0.991412i	$-0.541746\pi$
$449$	−5.54211	−0.261549	−0.130774	+	0.991412i	$0.541746\pi$
$450$	9.59618	0.452368
$451$	−42.2146	−1.98781
$452$	−11.0502	−0.519759
$453$	−17.8049	−0.836549
$454$	64.2440	3.01512
$455$	10.3886	0.487027
$456$	27.1772	1.27269
$457$	33.7092	1.57685	0.788426	−	0.615130i	$-0.210896\pi$
$457$	33.7092	1.57685	0.788426	+	0.615130i	$0.210896\pi$
$458$	−58.1081	−2.71521
$459$	10.9405	0.510657
$460$	−31.0290	−1.44673
$461$	−4.50543	−0.209839	−0.104919	−	0.994481i	$-0.533458\pi$
$461$	−4.50543	−0.209839	−0.104919	+	0.994481i	$0.533458\pi$
$462$	18.9372	0.881038
$463$	10.0273	0.466007	0.233003	−	0.972476i	$-0.425145\pi$
$463$	10.0273	0.466007	0.233003	+	0.972476i	$0.425145\pi$
$464$	−36.0541	−1.67377
$465$	−20.1473	−0.934310
$466$	−9.73940	−0.451169
$467$	−19.6393	−0.908799	−0.454400	−	0.890798i	$-0.650146\pi$
$467$	−19.6393	−0.908799	−0.454400	+	0.890798i	$0.650146\pi$
$468$	16.0832	0.743448
$469$	−0.785513	−0.0362716
$470$	−37.6830	−1.73819
$471$	−13.0233	−0.600081
$472$	64.6165	2.97421
$473$	46.5790	2.14170
$474$	21.6043	0.992316
$475$	12.2697	0.562971
$476$	−9.37149	−0.429541
$477$	−10.4503	−0.478487
$478$	47.4089	2.16843
$479$	29.7970	1.36146	0.680731	−	0.732534i	$-0.261662\pi$
$479$	29.7970	1.36146	0.680731	+	0.732534i	$0.261662\pi$
$480$	3.60799	0.164681
$481$	7.85050	0.357952
$482$	−36.5133	−1.66314
$483$	−4.12932	−0.187891
$484$	55.3725	2.51693
$485$	21.1484	0.960297
$486$	29.8425	1.35368
$487$	−11.1410	−0.504847	−0.252423	−	0.967617i	$-0.581228\pi$
$487$	−11.1410	−0.504847	−0.252423	+	0.967617i	$0.581228\pi$
$488$	34.2719	1.55142
$489$	24.9932	1.13023
$490$	39.4280	1.78117
$491$	−14.6083	−0.659265	−0.329632	−	0.944109i	$-0.606925\pi$
$491$	−14.6083	−0.659265	−0.329632	+	0.944109i	$0.606925\pi$
$492$	−46.0161	−2.07457
$493$	−15.3266	−0.690274
$494$	30.6068	1.37707
$495$	17.7718	0.798784
$496$	24.6347	1.10613
$497$	11.9728	0.537055
$498$	31.0540	1.39156
$499$	−35.4073	−1.58505	−0.792524	−	0.609841i	$-0.791233\pi$
$499$	−35.4073	−1.58505	−0.792524	+	0.609841i	$0.791233\pi$
$500$	−22.3689	−1.00037
$501$	−4.74427	−0.211959
$502$	−8.61592	−0.384547
$503$	39.8110	1.77508	0.887541	−	0.460728i	$-0.152412\pi$
$503$	39.8110	1.77508	0.887541	+	0.460728i	$0.152412\pi$
$504$	−7.67629	−0.341929
$505$	40.3927	1.79745
$506$	−32.5908	−1.44884
$507$	4.38477	0.194735
$508$	86.0725	3.81885
$509$	38.2117	1.69370	0.846852	−	0.531829i	$-0.178495\pi$
$509$	38.2117	1.69370	0.846852	+	0.531829i	$0.178495\pi$
$510$	18.0096	0.797476
$511$	12.5687	0.556009
$512$	42.9784	1.89940
$513$	22.3953	0.988776
$514$	−50.3970	−2.22292
$515$	−34.2957	−1.51125
$516$	50.7735	2.23518
$517$	−26.5927	−1.16954
$518$	−7.32351	−0.321777
$519$	−26.9519	−1.18306
$520$	45.7276	2.00529
$521$	8.94592	0.391928	0.195964	−	0.980611i	$-0.437216\pi$
$521$	8.94592	0.391928	0.195964	+	0.980611i	$0.437216\pi$
$522$	−24.5376	−1.07398
$523$	−28.3908	−1.24144	−0.620721	−	0.784032i	$-0.713160\pi$
$523$	−28.3908	−1.24144	−0.620721	+	0.784032i	$0.713160\pi$
$524$	20.3331	0.888254
$525$	4.76812	0.208098
$526$	−42.2600	−1.84262
$527$	10.4722	0.456176
$528$	29.8971	1.30111
$529$	−15.8935	−0.691020
$530$	−58.0736	−2.52255
$531$	15.7730	0.684490
$532$	−19.1836	−0.831714
$533$	−26.5143	−1.14846
$534$	−4.68178	−0.202600
$535$	−56.1773	−2.42875
$536$	−3.45759	−0.149345
$537$	24.6571	1.06403
$538$	44.0006	1.89700
$539$	27.8241	1.19847
$540$	65.3974	2.81426
$541$	31.3807	1.34916	0.674580	−	0.738201i	$-0.264325\pi$
$541$	31.3807	1.34916	0.674580	+	0.738201i	$0.264325\pi$
$542$	67.7007	2.90799
$543$	−26.6988	−1.14575
$544$	−1.87536	−0.0804056
$545$	−31.4002	−1.34504
$546$	11.8941	0.509022
$547$	12.5677	0.537354	0.268677	−	0.963230i	$-0.413414\pi$
$547$	12.5677	0.537354	0.268677	+	0.963230i	$0.413414\pi$
$548$	24.4562	1.04472
$549$	8.36584	0.357045
$550$	37.6326	1.60466
$551$	−31.3738	−1.33657
$552$	−18.1760	−0.773621
$553$	−7.80227	−0.331786
$554$	78.5565	3.33755
$555$	9.45590	0.401381
$556$	−26.8333	−1.13799
$557$	25.6401	1.08640	0.543202	−	0.839602i	$-0.317212\pi$
$557$	25.6401	1.08640	0.543202	+	0.839602i	$0.317212\pi$
$558$	16.7658	0.709754
$559$	29.2555	1.23738
$560$	−15.3001	−0.646548
$561$	12.7092	0.536585
$562$	−65.9824	−2.78330
$563$	−13.0810	−0.551297	−0.275649	−	0.961258i	$-0.588893\pi$
$563$	−13.0810	−0.551297	−0.275649	+	0.961258i	$0.588893\pi$
$564$	−28.9873	−1.22059
$565$	−7.66915	−0.322644
$566$	−5.26439	−0.221279
$567$	4.25121	0.178534
$568$	52.7007	2.21127
$569$	−31.6319	−1.32608	−0.663039	−	0.748585i	$-0.730734\pi$
$569$	−31.6319	−1.32608	−0.663039	+	0.748585i	$0.730734\pi$
$570$	36.8658	1.54414
$571$	−19.0959	−0.799138	−0.399569	−	0.916703i	$-0.630840\pi$
$571$	−19.0959	−0.799138	−0.399569	+	0.916703i	$0.630840\pi$
$572$	63.0723	2.63719
$573$	1.64270	0.0686246
$574$	24.7345	1.03240
$575$	−8.20591	−0.342210
$576$	8.56557	0.356899
$577$	−13.0583	−0.543626	−0.271813	−	0.962350i	$-0.587623\pi$
$577$	−13.0583	−0.543626	−0.271813	+	0.962350i	$0.587623\pi$
$578$	32.6096	1.35638
$579$	−13.0970	−0.544294
$580$	−91.6158	−3.80414
$581$	−11.2150	−0.465277
$582$	24.2131	1.00367
$583$	−40.9822	−1.69731
$584$	55.3237	2.28931
$585$	11.1622	0.461500
$586$	−69.1484	−2.85649
$587$	2.05359	0.0847609	0.0423805	−	0.999102i	$-0.486506\pi$
$587$	2.05359	0.0847609	0.0423805	+	0.999102i	$0.486506\pi$
$588$	30.3297	1.25077
$589$	21.4368	0.883286
$590$	87.6523	3.60859
$591$	−8.45050	−0.347607
$592$	−11.5620	−0.475196
$593$	38.0287	1.56165	0.780826	−	0.624749i	$-0.214799\pi$
$593$	38.0287	1.56165	0.780826	+	0.624749i	$0.214799\pi$
$594$	68.6891	2.81835
$595$	−6.50406	−0.266641
$596$	−16.8401	−0.689796
$597$	−7.86768	−0.322003
$598$	−20.4698	−0.837070
$599$	−37.4792	−1.53136	−0.765680	−	0.643222i	$-0.777597\pi$
$599$	−37.4792	−1.53136	−0.765680	+	0.643222i	$0.777597\pi$
$600$	20.9878	0.856823
$601$	32.1378	1.31093	0.655463	−	0.755227i	$-0.272473\pi$
$601$	32.1378	1.31093	0.655463	+	0.755227i	$0.272473\pi$
$602$	−27.2916	−1.11232
$603$	−0.844004	−0.0343705
$604$	55.3204	2.25096
$605$	38.4300	1.56240
$606$	46.2463	1.87863
$607$	−14.3486	−0.582392	−0.291196	−	0.956663i	$-0.594053\pi$
$607$	−14.3486	−0.582392	−0.291196	+	0.956663i	$0.594053\pi$
$608$	−3.83890	−0.155688
$609$	−12.1922	−0.494052
$610$	46.4899	1.88232
$611$	−16.7024	−0.675707
$612$	−10.0693	−0.407027
$613$	−39.3487	−1.58928	−0.794639	−	0.607082i	$-0.792340\pi$
$613$	−39.3487	−1.58928	−0.794639	+	0.607082i	$0.792340\pi$
$614$	4.76231	0.192191
$615$	−31.9364	−1.28780
$616$	−30.1035	−1.21290
$617$	30.4985	1.22782	0.613911	−	0.789375i	$-0.289595\pi$
$617$	30.4985	1.22782	0.613911	+	0.789375i	$0.289595\pi$
$618$	−39.2658	−1.57950
$619$	18.0125	0.723984	0.361992	−	0.932181i	$-0.382097\pi$
$619$	18.0125	0.723984	0.361992	+	0.932181i	$0.382097\pi$
$620$	62.5983	2.51401
$621$	−14.9779	−0.601042
$622$	3.02082	0.121124
$623$	1.69080	0.0677406
$624$	18.7779	0.751718
$625$	−30.9157	−1.23663
$626$	32.9748	1.31794
$627$	26.0160	1.03898
$628$	40.4637	1.61468
$629$	−4.91500	−0.195974
$630$	−10.4129	−0.414860
$631$	−17.6349	−0.702033	−0.351017	−	0.936369i	$-0.614164\pi$
$631$	−17.6349	−0.702033	−0.351017	+	0.936369i	$0.614164\pi$
$632$	−34.3432	−1.36610
$633$	13.4829	0.535898
$634$	13.8241	0.549027
$635$	59.7366	2.37057
$636$	−44.6727	−1.77139
$637$	17.4759	0.692419
$638$	−96.2272	−3.80967
$639$	12.8644	0.508906
$640$	53.0745	2.09795
$641$	−15.3953	−0.608076	−0.304038	−	0.952660i	$-0.598335\pi$
$641$	−15.3953	−0.608076	−0.304038	+	0.952660i	$0.598335\pi$
$642$	−64.3184	−2.53844
$643$	−15.8981	−0.626961	−0.313481	−	0.949595i	$-0.601495\pi$
$643$	−15.8981	−0.626961	−0.313481	+	0.949595i	$0.601495\pi$
$644$	12.8299	0.505569
$645$	35.2382	1.38750
$646$	−19.1622	−0.753925
$647$	33.7772	1.32792	0.663960	−	0.747768i	$-0.268875\pi$
$647$	33.7772	1.32792	0.663960	+	0.747768i	$0.268875\pi$
$648$	18.7125	0.735097
$649$	61.8558	2.42805
$650$	23.6364	0.927096
$651$	8.33055	0.326500
$652$	−77.6545	−3.04119
$653$	−6.97695	−0.273029	−0.136515	−	0.990638i	$-0.543590\pi$
$653$	−6.97695	−0.273029	−0.136515	+	0.990638i	$0.543590\pi$
$654$	−35.9506	−1.40578
$655$	14.1117	0.551390
$656$	39.0496	1.52463
$657$	13.5046	0.526866
$658$	15.5812	0.607419
$659$	−21.9173	−0.853777	−0.426889	−	0.904304i	$-0.640390\pi$
$659$	−21.9173	−0.853777	−0.426889	+	0.904304i	$0.640390\pi$
$660$	75.9704	2.95715
$661$	−32.2115	−1.25288	−0.626441	−	0.779469i	$-0.715489\pi$
$661$	−32.2115	−1.25288	−0.626441	+	0.779469i	$0.715489\pi$
$662$	24.4841	0.951602
$663$	7.98247	0.310013
$664$	−49.3650	−1.91573
$665$	−13.3139	−0.516292
$666$	−7.86883	−0.304911
$667$	20.9827	0.812452
$668$	14.7406	0.570331
$669$	6.65316	0.257226
$670$	−4.69022	−0.181199
$671$	32.8077	1.26653
$672$	−1.49184	−0.0575489
$673$	1.18695	0.0457537	0.0228769	−	0.999738i	$-0.492717\pi$
$673$	1.18695	0.0457537	0.0228769	+	0.999738i	$0.492717\pi$
$674$	−46.4330	−1.78853
$675$	17.2950	0.665684
$676$	−13.6236	−0.523985
$677$	6.42904	0.247088	0.123544	−	0.992339i	$-0.460574\pi$
$677$	6.42904	0.247088	0.123544	+	0.992339i	$0.460574\pi$
$678$	−8.78055	−0.337215
$679$	−8.74446	−0.335581
$680$	−28.6289	−1.09787
$681$	34.2983	1.31431
$682$	65.7492	2.51767
$683$	35.9215	1.37450	0.687250	−	0.726421i	$-0.258818\pi$
$683$	35.9215	1.37450	0.687250	+	0.726421i	$0.258818\pi$
$684$	−20.6120	−0.788120
$685$	16.9733	0.648516
$686$	−36.6126	−1.39788
$687$	−31.0225	−1.18358
$688$	−43.0867	−1.64267
$689$	−25.7402	−0.980625
$690$	−24.6558	−0.938628
$691$	37.0374	1.40897	0.704484	−	0.709720i	$-0.251178\pi$
$691$	37.0374	1.40897	0.704484	+	0.709720i	$0.251178\pi$
$692$	83.7402	3.18333
$693$	−7.34833	−0.279140
$694$	−66.1178	−2.50980
$695$	−18.6231	−0.706413
$696$	−53.6662	−2.03421
$697$	16.5999	0.628767
$698$	60.9733	2.30787
$699$	−5.19963	−0.196668
$700$	−14.8147	−0.559943
$701$	45.4206	1.71551	0.857756	−	0.514056i	$-0.171858\pi$
$701$	45.4206	1.71551	0.857756	+	0.514056i	$0.171858\pi$
$702$	43.1425	1.62831
$703$	−10.0611	−0.379461
$704$	33.5909	1.26601
$705$	−20.1180	−0.757688
$706$	−82.6920	−3.11215
$707$	−16.7016	−0.628130
$708$	67.4259	2.53402
$709$	19.3890	0.728168	0.364084	−	0.931366i	$-0.381382\pi$
$709$	19.3890	0.728168	0.364084	+	0.931366i	$0.381382\pi$
$710$	71.4886	2.68292
$711$	−8.38324	−0.314396
$712$	7.44239	0.278915
$713$	−14.3368	−0.536918
$714$	−7.44662	−0.278683
$715$	43.7739	1.63705
$716$	−76.6103	−2.86306
$717$	25.3105	0.945236
$718$	−70.9704	−2.64859
$719$	1.97065	0.0734928	0.0367464	−	0.999325i	$-0.488301\pi$
$719$	1.97065	0.0734928	0.0367464	+	0.999325i	$0.488301\pi$
$720$	−16.4394	−0.612660
$721$	14.1807	0.528115
$722$	7.68303	0.285933
$723$	−19.4936	−0.724974
$724$	82.9538	3.08295
$725$	−24.2287	−0.899830
$726$	43.9992	1.63296
$727$	−53.2162	−1.97368	−0.986839	−	0.161705i	$-0.948301\pi$
$727$	−53.2162	−1.97368	−0.986839	+	0.161705i	$0.948301\pi$
$728$	−18.9075	−0.700759
$729$	26.7844	0.992016
$730$	75.0467	2.77760
$731$	−18.3161	−0.677446
$732$	35.7620	1.32180
$733$	−32.7090	−1.20813	−0.604067	−	0.796934i	$-0.706454\pi$
$733$	−32.7090	−1.20813	−0.604067	+	0.796934i	$0.706454\pi$
$734$	−51.8149	−1.91252
$735$	21.0496	0.776427
$736$	2.56744	0.0946372
$737$	−3.30986	−0.121920
$738$	26.5762	0.978284
$739$	−36.7246	−1.35094	−0.675468	−	0.737389i	$-0.736059\pi$
$739$	−36.7246	−1.35094	−0.675468	+	0.737389i	$0.736059\pi$
$740$	−29.3798	−1.08002
$741$	16.3402	0.600274
$742$	24.0123	0.881521
$743$	2.02331	0.0742281	0.0371140	−	0.999311i	$-0.488184\pi$
$743$	2.02331	0.0742281	0.0371140	+	0.999311i	$0.488184\pi$
$744$	36.6685	1.34433
$745$	−11.6875	−0.428196
$746$	−64.1981	−2.35046
$747$	−12.0501	−0.440890
$748$	−39.4880	−1.44382
$749$	23.2283	0.848742
$750$	−17.7744	−0.649031
$751$	−29.0332	−1.05944	−0.529718	−	0.848174i	$-0.677702\pi$
$751$	−29.0332	−1.05944	−0.529718	+	0.848174i	$0.677702\pi$
$752$	24.5989	0.897029
$753$	−4.59982	−0.167627
$754$	−60.4387	−2.20105
$755$	38.3939	1.39730
$756$	−27.0406	−0.983458
$757$	−50.2522	−1.82645	−0.913224	−	0.407457i	$-0.866415\pi$
$757$	−50.2522	−1.82645	−0.913224	+	0.407457i	$0.866415\pi$
$758$	−46.8752	−1.70258
$759$	−17.3994	−0.631559
$760$	−58.6038	−2.12578
$761$	−30.3914	−1.10169	−0.550844	−	0.834608i	$-0.685694\pi$
$761$	−30.3914	−1.10169	−0.550844	+	0.834608i	$0.685694\pi$
$762$	68.3935	2.47764
$763$	12.9834	0.470031
$764$	−5.10390	−0.184653
$765$	−6.98837	−0.252665
$766$	−67.8674	−2.45215
$767$	38.8506	1.40281
$768$	42.8839	1.54744
$769$	52.3089	1.88631	0.943154	−	0.332355i	$-0.107843\pi$
$769$	52.3089	1.88631	0.943154	+	0.332355i	$0.107843\pi$
$770$	−40.8355	−1.47161
$771$	−26.9057	−0.968985
$772$	40.6928	1.46457
$773$	−31.1026	−1.11868	−0.559341	−	0.828938i	$-0.688946\pi$
$773$	−31.1026	−1.11868	−0.559341	+	0.828938i	$0.688946\pi$
$774$	−29.3238	−1.05402
$775$	16.5547	0.594663
$776$	−38.4904	−1.38172
$777$	−3.90984	−0.140265
$778$	−8.61478	−0.308855
$779$	33.9803	1.21747
$780$	47.7158	1.70850
$781$	50.4491	1.80521
$782$	12.8156	0.458284
$783$	−44.2235	−1.58042
$784$	−25.7380	−0.919213
$785$	28.0829	1.00232
$786$	16.1567	0.576291
$787$	35.1879	1.25431	0.627157	−	0.778893i	$-0.284218\pi$
$787$	35.1879	1.25431	0.627157	+	0.778893i	$0.284218\pi$
$788$	26.2560	0.935330
$789$	−22.5616	−0.803213
$790$	−46.5866	−1.65748
$791$	3.17105	0.112750
$792$	−32.3451	−1.14933
$793$	20.6060	0.731739
$794$	−82.6149	−2.93189
$795$	−31.0040	−1.09960
$796$	24.4451	0.866434
$797$	37.2923	1.32096	0.660481	−	0.750843i	$-0.270353\pi$
$797$	37.2923	1.32096	0.660481	+	0.750843i	$0.270353\pi$
$798$	−15.2434	−0.539609
$799$	10.4570	0.369940
$800$	−2.96462	−0.104815
$801$	1.81670	0.0641900
$802$	−36.7024	−1.29601
$803$	52.9600	1.86892
$804$	−3.60792	−0.127241
$805$	8.90431	0.313836
$806$	41.2960	1.45459
$807$	23.4908	0.826917
$808$	−73.5155	−2.58626
$809$	8.98970	0.316061	0.158031	−	0.987434i	$-0.449486\pi$
$809$	8.98970	0.316061	0.158031	+	0.987434i	$0.449486\pi$
$810$	25.3835	0.891887
$811$	−13.6723	−0.480100	−0.240050	−	0.970761i	$-0.577164\pi$
$811$	−13.6723	−0.480100	−0.240050	+	0.970761i	$0.577164\pi$
$812$	37.8814	1.32938
$813$	36.1437	1.26762
$814$	−30.8586	−1.08159
$815$	−53.8943	−1.88784
$816$	−11.7564	−0.411555
$817$	−37.4934	−1.31173
$818$	6.76857	0.236658
$819$	−4.61536	−0.161274
$820$	99.2273	3.46517
$821$	38.3880	1.33975	0.669875	−	0.742474i	$-0.266348\pi$
$821$	38.3880	1.33975	0.669875	+	0.742474i	$0.266348\pi$
$822$	19.4330	0.677804
$823$	48.0594	1.67524	0.837622	−	0.546250i	$-0.183945\pi$
$823$	48.0594	1.67524	0.837622	+	0.546250i	$0.183945\pi$
$824$	62.4189	2.17446
$825$	20.0911	0.699482
$826$	−36.2426	−1.26104
$827$	15.5578	0.540998	0.270499	−	0.962720i	$-0.412811\pi$
$827$	15.5578	0.540998	0.270499	+	0.962720i	$0.412811\pi$
$828$	13.7852	0.479070
$829$	−45.8552	−1.59262	−0.796309	−	0.604890i	$-0.793217\pi$
$829$	−45.8552	−1.59262	−0.796309	+	0.604890i	$0.793217\pi$
$830$	−66.9637	−2.32434
$831$	41.9394	1.45486
$832$	21.0979	0.731438
$833$	−10.9412	−0.379090
$834$	−21.3219	−0.738316
$835$	10.2304	0.354037
$836$	−80.8325	−2.79565
$837$	30.2166	1.04444
$838$	−0.0997381	−0.00344540
$839$	15.5601	0.537193	0.268597	−	0.963253i	$-0.413440\pi$
$839$	15.5601	0.537193	0.268597	+	0.963253i	$0.413440\pi$
$840$	−22.7740	−0.785779
$841$	32.9531	1.13631
$842$	−9.91915	−0.341837
$843$	−35.2264	−1.21326
$844$	−41.8918	−1.44198
$845$	−9.45516	−0.325267
$846$	16.7414	0.575582
$847$	−15.8901	−0.545990
$848$	37.9095	1.30182
$849$	−2.81053	−0.0964570
$850$	−14.7982	−0.507572
$851$	6.72881	0.230661
$852$	54.9921	1.88400
$853$	40.1019	1.37306	0.686531	−	0.727101i	$-0.259133\pi$
$853$	40.1019	1.37306	0.686531	+	0.727101i	$0.259133\pi$
$854$	−19.2227	−0.657788
$855$	−14.3053	−0.489231
$856$	102.244	3.49462
$857$	−15.2815	−0.522007	−0.261004	−	0.965338i	$-0.584053\pi$
$857$	−15.2815	−0.522007	−0.261004	+	0.965338i	$0.584053\pi$
$858$	50.1175	1.71098
$859$	−29.4284	−1.00408	−0.502042	−	0.864843i	$-0.667418\pi$
$859$	−29.4284	−1.00408	−0.502042	+	0.864843i	$0.667418\pi$
$860$	−109.486	−3.73344
$861$	13.2051	0.450029
$862$	0.0795897	0.00271084
$863$	11.0503	0.376156	0.188078	−	0.982154i	$-0.439774\pi$
$863$	11.0503	0.376156	0.188078	+	0.982154i	$0.439774\pi$
$864$	−5.41120	−0.184093
$865$	58.1180	1.97607
$866$	40.5655	1.37847
$867$	17.4094	0.591255
$868$	−25.8833	−0.878535
$869$	−32.8759	−1.11524
$870$	−72.7982	−2.46809
$871$	−2.07887	−0.0704398
$872$	57.1489	1.93531
$873$	−9.39558	−0.317992
$874$	26.2337	0.887369
$875$	6.41915	0.217007
$876$	57.7291	1.95049
$877$	51.5573	1.74097	0.870483	−	0.492199i	$-0.163807\pi$
$877$	51.5573	1.74097	0.870483	+	0.492199i	$0.163807\pi$
$878$	38.7419	1.30748
$879$	−36.9166	−1.24517
$880$	−64.4690	−2.17325
$881$	3.32750	0.112106	0.0560531	−	0.998428i	$-0.482148\pi$
$881$	3.32750	0.112106	0.0560531	+	0.998428i	$0.482148\pi$
$882$	−17.5167	−0.589817
$883$	33.5648	1.12954	0.564772	−	0.825247i	$-0.308964\pi$
$883$	33.5648	1.12954	0.564772	+	0.825247i	$0.308964\pi$
$884$	−24.8018	−0.834173
$885$	46.7954	1.57301
$886$	−89.2722	−2.99916
$887$	−36.4843	−1.22502	−0.612512	−	0.790462i	$-0.709841\pi$
$887$	−36.4843	−1.22502	−0.612512	+	0.790462i	$0.709841\pi$
$888$	−17.2099	−0.577527
$889$	−24.7000	−0.828411
$890$	10.0956	0.338406
$891$	17.9130	0.600109
$892$	−20.6716	−0.692135
$893$	21.4056	0.716310
$894$	−13.3812	−0.447534
$895$	−53.1696	−1.77726
$896$	−21.9453	−0.733142
$897$	−10.9283	−0.364885
$898$	13.6827	0.456597
$899$	−42.3307	−1.41181
$900$	−15.9178	−0.530594
$901$	16.1153	0.536879
$902$	104.222	3.47021
$903$	−14.5703	−0.484870
$904$	13.9580	0.464236
$905$	57.5722	1.91376
$906$	43.9578	1.46040
$907$	−29.5720	−0.981923	−0.490961	−	0.871181i	$-0.663354\pi$
$907$	−29.5720	−0.981923	−0.490961	+	0.871181i	$0.663354\pi$
$908$	−106.566	−3.53651
$909$	−17.9453	−0.595207
$910$	−25.6481	−0.850226
$911$	−15.3658	−0.509091	−0.254546	−	0.967061i	$-0.581926\pi$
$911$	−15.3658	−0.509091	−0.254546	+	0.967061i	$0.581926\pi$
$912$	−24.0655	−0.796887
$913$	−47.2559	−1.56394
$914$	−83.2233	−2.75278
$915$	24.8198	0.820518
$916$	96.3877	3.18474
$917$	−5.83493	−0.192686
$918$	−27.0104	−0.891477
$919$	42.4273	1.39955	0.699774	−	0.714364i	$-0.253284\pi$
$919$	42.4273	1.39955	0.699774	+	0.714364i	$0.253284\pi$
$920$	39.1940	1.29219
$921$	2.54248	0.0837775
$922$	11.1233	0.366325
$923$	31.6863	1.04297
$924$	−31.4124	−1.03339
$925$	−7.76976	−0.255468
$926$	−24.7559	−0.813529
$927$	15.2366	0.500435
$928$	7.58060	0.248845
$929$	17.5344	0.575284	0.287642	−	0.957738i	$-0.407129\pi$
$929$	17.5344	0.575284	0.287642	+	0.957738i	$0.407129\pi$
$930$	49.7409	1.63107
$931$	−22.3968	−0.734025
$932$	16.1554	0.529187
$933$	1.61274	0.0527988
$934$	48.4867	1.58653
$935$	−27.4057	−0.896263
$936$	−20.3154	−0.664030
$937$	16.7573	0.547438	0.273719	−	0.961810i	$-0.411746\pi$
$937$	16.7573	0.547438	0.273719	+	0.961810i	$0.411746\pi$
$938$	1.93932	0.0633210
$939$	17.6044	0.574499
$940$	62.5072	2.03876
$941$	6.34587	0.206869	0.103435	−	0.994636i	$-0.467017\pi$
$941$	6.34587	0.206869	0.103435	+	0.994636i	$0.467017\pi$
$942$	32.1526	1.04759
$943$	−22.7259	−0.740058
$944$	−57.2181	−1.86229
$945$	−18.7669	−0.610488
$946$	−114.997	−3.73887
$947$	−4.28925	−0.139382	−0.0696909	−	0.997569i	$-0.522201\pi$
$947$	−4.28925	−0.139382	−0.0696909	+	0.997569i	$0.522201\pi$
$948$	−35.8364	−1.16391
$949$	33.2633	1.07977
$950$	−30.2921	−0.982804
$951$	7.38037	0.239325
$952$	11.8375	0.383656
$953$	−39.5273	−1.28041	−0.640207	−	0.768202i	$-0.721152\pi$
$953$	−39.5273	−1.28041	−0.640207	+	0.768202i	$0.721152\pi$
$954$	25.8003	0.835317
$955$	−3.54225	−0.114624
$956$	−78.6403	−2.54341
$957$	−51.3733	−1.66066
$958$	−73.5646	−2.37676
$959$	−7.01814	−0.226628
$960$	25.4124	0.820180
$961$	−2.07667	−0.0669894
$962$	−19.3818	−0.624893
$963$	24.9579	0.804256
$964$	60.5671	1.95073
$965$	28.2419	0.909140
$966$	10.1947	0.328009
$967$	−29.2176	−0.939574	−0.469787	−	0.882780i	$-0.655669\pi$
$967$	−29.2176	−0.939574	−0.469787	+	0.882780i	$0.655669\pi$
$968$	−69.9433	−2.24806
$969$	−10.2302	−0.328642
$970$	−52.2123	−1.67643
$971$	14.7718	0.474051	0.237025	−	0.971503i	$-0.423828\pi$
$971$	14.7718	0.474051	0.237025	+	0.971503i	$0.423828\pi$
$972$	−49.5017	−1.58777
$973$	7.70029	0.246860
$974$	27.5055	0.881334
$975$	12.6189	0.404128
$976$	−30.3479	−0.971413
$977$	−13.4211	−0.429379	−0.214689	−	0.976682i	$-0.568874\pi$
$977$	−13.4211	−0.429379	−0.214689	+	0.976682i	$0.568874\pi$
$978$	−61.7046	−1.97309
$979$	7.12442	0.227697
$980$	−65.4017	−2.08918
$981$	13.9502	0.445394
$982$	36.0659	1.15091
$983$	−37.1177	−1.18387	−0.591935	−	0.805986i	$-0.701636\pi$
$983$	−37.1177	−1.18387	−0.591935	+	0.805986i	$0.701636\pi$
$984$	58.1248	1.85295
$985$	18.2223	0.580612
$986$	37.8391	1.20504
$987$	8.31843	0.264778
$988$	−50.7696	−1.61520
$989$	25.0755	0.797353
$990$	−43.8761	−1.39447
$991$	35.5265	1.12854	0.564268	−	0.825592i	$-0.309159\pi$
$991$	35.5265	1.12854	0.564268	+	0.825592i	$0.309159\pi$
$992$	−5.17960	−0.164452
$993$	13.0715	0.414810
$994$	−29.5592	−0.937562
$995$	16.9656	0.537845
$996$	−51.5114	−1.63220
$997$	5.11729	0.162066	0.0810331	−	0.996711i	$-0.474178\pi$
$997$	5.11729	0.162066	0.0810331	+	0.996711i	$0.474178\pi$
$998$	87.4155	2.76709
$999$	−14.1818	−0.448692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.c.1.20	✓	261

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.c.1.20	✓	261	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46886 q^{2} -1.31806 q^{3} +4.09526 q^{4} +2.84222 q^{5} +3.25411 q^{6} -1.17521 q^{7} -5.17289 q^{8} -1.26271 q^{9} +O(q^{10})\)	\(q-2.46886 q^{2} -1.31806 q^{3} +4.09526 q^{4} +2.84222 q^{5} +3.25411 q^{6} -1.17521 q^{7} -5.17289 q^{8} -1.26271 q^{9} -7.01703 q^{10} -4.95188 q^{11} -5.39780 q^{12} -3.11020 q^{13} +2.90141 q^{14} -3.74622 q^{15} +4.58061 q^{16} +1.94721 q^{17} +3.11746 q^{18} +3.98598 q^{19} +11.6396 q^{20} +1.54899 q^{21} +12.2255 q^{22} -2.66581 q^{23} +6.81819 q^{24} +3.07821 q^{25} +7.67863 q^{26} +5.61852 q^{27} -4.81277 q^{28} -7.87103 q^{29} +9.24888 q^{30} +5.37804 q^{31} -0.963101 q^{32} +6.52689 q^{33} -4.80739 q^{34} -3.34019 q^{35} -5.17113 q^{36} -2.52412 q^{37} -9.84081 q^{38} +4.09943 q^{39} -14.7025 q^{40} +8.52497 q^{41} -3.82424 q^{42} -9.40632 q^{43} -20.2792 q^{44} -3.58891 q^{45} +6.58150 q^{46} +5.37021 q^{47} -6.03753 q^{48} -5.61889 q^{49} -7.59965 q^{50} -2.56655 q^{51} -12.7370 q^{52} +8.27608 q^{53} -13.8713 q^{54} -14.0743 q^{55} +6.07921 q^{56} -5.25377 q^{57} +19.4325 q^{58} -12.4914 q^{59} -15.3417 q^{60} -6.62529 q^{61} -13.2776 q^{62} +1.48395 q^{63} -6.78347 q^{64} -8.83986 q^{65} -16.1139 q^{66} +0.668405 q^{67} +7.97434 q^{68} +3.51370 q^{69} +8.24645 q^{70} -10.1879 q^{71} +6.53187 q^{72} -10.6949 q^{73} +6.23169 q^{74} -4.05727 q^{75} +16.3236 q^{76} +5.81948 q^{77} -10.1209 q^{78} +6.63907 q^{79} +13.0191 q^{80} -3.61742 q^{81} -21.0469 q^{82} +9.54303 q^{83} +6.34352 q^{84} +5.53441 q^{85} +23.2229 q^{86} +10.3745 q^{87} +25.6155 q^{88} -1.43873 q^{89} +8.86050 q^{90} +3.65512 q^{91} -10.9172 q^{92} -7.08859 q^{93} -13.2583 q^{94} +11.3290 q^{95} +1.26943 q^{96} +7.44079 q^{97} +13.8722 q^{98} +6.25280 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9 + 35 * q^10 + 32 * q^11 + 51 * q^12 + 60 * q^13 + 55 * q^14 + 16 * q^15 + 288 * q^16 + 270 * q^17 + 45 * q^18 + 34 * q^19 + 157 * q^20 + 27 * q^21 + 38 * q^22 + 116 * q^23 + 48 * q^24 + 335 * q^25 + 46 * q^26 + 73 * q^27 + 70 * q^28 + 99 * q^29 + 33 * q^30 + 33 * q^31 + 150 * q^32 + 172 * q^33 + 24 * q^34 + 114 * q^35 + 339 * q^36 + 36 * q^37 + 112 * q^38 + 30 * q^39 + 106 * q^40 + 209 * q^41 + 64 * q^42 + 64 * q^43 + 65 * q^44 + 153 * q^45 + 135 * q^47 + 87 * q^48 + 332 * q^49 + 82 * q^50 + 52 * q^51 + 102 * q^52 + 163 * q^53 + 52 * q^54 + 56 * q^55 + 134 * q^56 + 181 * q^57 + q^58 + 89 * q^59 - 43 * q^60 + 112 * q^61 + 228 * q^62 + 130 * q^63 + 268 * q^64 + 248 * q^65 + 5 * q^66 + 42 * q^67 + 453 * q^68 + 51 * q^69 - 22 * q^70 + 98 * q^71 + 113 * q^72 + 206 * q^73 + 81 * q^74 + 29 * q^75 + 62 * q^76 + 185 * q^77 - 25 * q^78 + 29 * q^79 + 258 * q^80 + 393 * q^81 + 79 * q^82 + 265 * q^83 - 25 * q^84 + 84 * q^85 + 36 * q^86 + 131 * q^87 + 24 * q^88 + 195 * q^89 + 89 * q^90 - 18 * q^91 + 261 * q^92 + 52 * q^93 + 3 * q^94 + 104 * q^95 + 92 * q^96 + 213 * q^97 + 156 * q^98 + 47 * q^99

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