LMFDB - Embedded newform 6047.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56224 q^{2} +3.46263 q^{3} +4.56507 q^{4} -4.38158 q^{5} -8.87209 q^{6} +2.36597 q^{7} -6.57231 q^{8} +8.98983 q^{9} +O(q^{10})$	\(q-2.56224 q^{2} +3.46263 q^{3} +4.56507 q^{4} -4.38158 q^{5} -8.87209 q^{6} +2.36597 q^{7} -6.57231 q^{8} +8.98983 q^{9} +11.2266 q^{10} +1.32306 q^{11} +15.8071 q^{12} -1.37551 q^{13} -6.06219 q^{14} -15.1718 q^{15} +7.70970 q^{16} -2.61790 q^{17} -23.0341 q^{18} +7.91786 q^{19} -20.0022 q^{20} +8.19250 q^{21} -3.39000 q^{22} -5.32918 q^{23} -22.7575 q^{24} +14.1982 q^{25} +3.52440 q^{26} +20.7406 q^{27} +10.8008 q^{28} -6.30611 q^{29} +38.8737 q^{30} -5.35609 q^{31} -6.60947 q^{32} +4.58128 q^{33} +6.70769 q^{34} -10.3667 q^{35} +41.0392 q^{36} +6.43913 q^{37} -20.2875 q^{38} -4.76290 q^{39} +28.7971 q^{40} -3.57356 q^{41} -20.9911 q^{42} -6.58681 q^{43} +6.03987 q^{44} -39.3896 q^{45} +13.6546 q^{46} +10.8031 q^{47} +26.6959 q^{48} -1.40216 q^{49} -36.3792 q^{50} -9.06483 q^{51} -6.27931 q^{52} +0.0571206 q^{53} -53.1423 q^{54} -5.79710 q^{55} -15.5499 q^{56} +27.4167 q^{57} +16.1577 q^{58} +11.9462 q^{59} -69.2602 q^{60} +6.01684 q^{61} +13.7236 q^{62} +21.2697 q^{63} +1.51563 q^{64} +6.02692 q^{65} -11.7383 q^{66} -2.39266 q^{67} -11.9509 q^{68} -18.4530 q^{69} +26.5620 q^{70} +5.70967 q^{71} -59.0839 q^{72} -6.72493 q^{73} -16.4986 q^{74} +49.1632 q^{75} +36.1456 q^{76} +3.13033 q^{77} +12.2037 q^{78} +7.46714 q^{79} -33.7806 q^{80} +44.8475 q^{81} +9.15631 q^{82} +11.0220 q^{83} +37.3993 q^{84} +11.4705 q^{85} +16.8770 q^{86} -21.8357 q^{87} -8.69558 q^{88} +11.1516 q^{89} +100.926 q^{90} -3.25443 q^{91} -24.3281 q^{92} -18.5462 q^{93} -27.6802 q^{94} -34.6927 q^{95} -22.8862 q^{96} +3.06939 q^{97} +3.59268 q^{98} +11.8941 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.56224	−1.81178	−0.905888	−	0.423517i	$-0.860795\pi$
$2$	−2.56224	−1.81178	−0.905888	+	0.423517i	$0.860795\pi$
$3$	3.46263	1.99915	0.999576	−	0.0291184i	$-0.00927000\pi$
$3$	3.46263	1.99915	0.999576	+	0.0291184i	$0.00927000\pi$
$4$	4.56507	2.28253
$5$	−4.38158	−1.95950	−0.979750	−	0.200224i	$-0.935833\pi$
$5$	−4.38158	−1.95950	−0.979750	+	0.200224i	$0.935833\pi$
$6$	−8.87209	−3.62202
$7$	2.36597	0.894254	0.447127	−	0.894470i	$-0.352447\pi$
$7$	2.36597	0.894254	0.447127	+	0.894470i	$0.352447\pi$
$8$	−6.57231	−2.32366
$9$	8.98983	2.99661
$10$	11.2266	3.55018
$11$	1.32306	0.398919	0.199459	−	0.979906i	$-0.436081\pi$
$11$	1.32306	0.398919	0.199459	+	0.979906i	$0.436081\pi$
$12$	15.8071	4.56313
$13$	−1.37551	−0.381499	−0.190750	−	0.981639i	$-0.561092\pi$
$13$	−1.37551	−0.381499	−0.190750	+	0.981639i	$0.561092\pi$
$14$	−6.06219	−1.62019
$15$	−15.1718	−3.91734
$16$	7.70970	1.92743
$17$	−2.61790	−0.634934	−0.317467	−	0.948269i	$-0.602832\pi$
$17$	−2.61790	−0.634934	−0.317467	+	0.948269i	$0.602832\pi$
$18$	−23.0341	−5.42918
$19$	7.91786	1.81648	0.908241	−	0.418447i	$-0.137425\pi$
$19$	7.91786	1.81648	0.908241	+	0.418447i	$0.137425\pi$
$20$	−20.0022	−4.47262
$21$	8.19250	1.78775
$22$	−3.39000	−0.722751
$23$	−5.32918	−1.11121	−0.555605	−	0.831446i	$-0.687513\pi$
$23$	−5.32918	−1.11121	−0.555605	+	0.831446i	$0.687513\pi$
$24$	−22.7575	−4.64536
$25$	14.1982	2.83964
$26$	3.52440	0.691191
$27$	20.7406	3.99152
$28$	10.8008	2.04117
$29$	−6.30611	−1.17101	−0.585507	−	0.810667i	$-0.699105\pi$
$29$	−6.30611	−1.17101	−0.585507	+	0.810667i	$0.699105\pi$
$30$	38.8737	7.09734
$31$	−5.35609	−0.961982	−0.480991	−	0.876725i	$-0.659723\pi$
$31$	−5.35609	−0.961982	−0.480991	+	0.876725i	$0.659723\pi$
$32$	−6.60947	−1.16840
$33$	4.58128	0.797499
$34$	6.70769	1.15036
$35$	−10.3667	−1.75229
$36$	41.0392	6.83986
$37$	6.43913	1.05859	0.529293	−	0.848439i	$-0.322457\pi$
$37$	6.43913	1.05859	0.529293	+	0.848439i	$0.322457\pi$
$38$	−20.2875	−3.29106
$39$	−4.76290	−0.762675
$40$	28.7971	4.55322
$41$	−3.57356	−0.558096	−0.279048	−	0.960277i	$-0.590019\pi$
$41$	−3.57356	−0.558096	−0.279048	+	0.960277i	$0.590019\pi$
$42$	−20.9911	−3.23900
$43$	−6.58681	−1.00448	−0.502239	−	0.864729i	$-0.667490\pi$
$43$	−6.58681	−1.00448	−0.502239	+	0.864729i	$0.667490\pi$
$44$	6.03987	0.910545
$45$	−39.3896	−5.87185
$46$	13.6546	2.01326
$47$	10.8031	1.57580	0.787901	−	0.615803i	$-0.211168\pi$
$47$	10.8031	1.57580	0.787901	+	0.615803i	$0.211168\pi$
$48$	26.6959	3.85322
$49$	−1.40216	−0.200309
$50$	−36.3792	−5.14479
$51$	−9.06483	−1.26933
$52$	−6.27931	−0.870784
$53$	0.0571206	0.00784611	0.00392306	−	0.999992i	$-0.498751\pi$
$53$	0.0571206	0.00784611	0.00392306	+	0.999992i	$0.498751\pi$
$54$	−53.1423	−7.23175
$55$	−5.79710	−0.781681
$56$	−15.5499	−2.07795
$57$	27.4167	3.63142
$58$	16.1577	2.12162
$59$	11.9462	1.55526	0.777631	−	0.628721i	$-0.216421\pi$
$59$	11.9462	1.55526	0.777631	+	0.628721i	$0.216421\pi$
$60$	−69.2602	−8.94146
$61$	6.01684	0.770378	0.385189	−	0.922838i	$-0.374136\pi$
$61$	6.01684	0.770378	0.385189	+	0.922838i	$0.374136\pi$
$62$	13.7236	1.74290
$63$	21.2697	2.67973
$64$	1.51563	0.189454
$65$	6.02692	0.747547
$66$	−11.7383	−1.44489
$67$	−2.39266	−0.292310	−0.146155	−	0.989262i	$-0.546690\pi$
$67$	−2.39266	−0.292310	−0.146155	+	0.989262i	$0.546690\pi$
$68$	−11.9509	−1.44926
$69$	−18.4530	−2.22148
$70$	26.5620	3.17476
$71$	5.70967	0.677613	0.338807	−	0.940856i	$-0.389977\pi$
$71$	5.70967	0.677613	0.338807	+	0.940856i	$0.389977\pi$
$72$	−59.0839	−6.96311
$73$	−6.72493	−0.787093	−0.393547	−	0.919305i	$-0.628752\pi$
$73$	−6.72493	−0.787093	−0.393547	+	0.919305i	$0.628752\pi$
$74$	−16.4986	−1.91792
$75$	49.1632	5.67687
$76$	36.1456	4.14618
$77$	3.13033	0.356735
$78$	12.2037	1.38180
$79$	7.46714	0.840119	0.420059	−	0.907497i	$-0.362009\pi$
$79$	7.46714	0.840119	0.420059	+	0.907497i	$0.362009\pi$
$80$	−33.7806	−3.77679
$81$	44.8475	4.98305
$82$	9.15631	1.01115
$83$	11.0220	1.20982	0.604908	−	0.796295i	$-0.293210\pi$
$83$	11.0220	1.20982	0.604908	+	0.796295i	$0.293210\pi$
$84$	37.3993	4.08060
$85$	11.4705	1.24415
$86$	16.8770	1.81989
$87$	−21.8357	−2.34104
$88$	−8.69558	−0.926952
$89$	11.1516	1.18206	0.591032	−	0.806648i	$-0.298721\pi$
$89$	11.1516	1.18206	0.591032	+	0.806648i	$0.298721\pi$
$90$	100.926	10.6385
$91$	−3.25443	−0.341157
$92$	−24.3281	−2.53637
$93$	−18.5462	−1.92315
$94$	−27.6802	−2.85500
$95$	−34.6927	−3.55940
$96$	−22.8862	−2.33581
$97$	3.06939	0.311649	0.155825	−	0.987785i	$-0.450197\pi$
$97$	3.06939	0.311649	0.155825	+	0.987785i	$0.450197\pi$
$98$	3.59268	0.362915
$99$	11.8941	1.19540
$100$	64.8157	6.48157
$101$	3.96857	0.394887	0.197444	−	0.980314i	$-0.436736\pi$
$101$	3.96857	0.394887	0.197444	+	0.980314i	$0.436736\pi$
$102$	23.2263	2.29974
$103$	−7.35362	−0.724574	−0.362287	−	0.932067i	$-0.618004\pi$
$103$	−7.35362	−0.724574	−0.362287	+	0.932067i	$0.618004\pi$
$104$	9.04031	0.886475
$105$	−35.8961	−3.50310
$106$	−0.146357	−0.0142154
$107$	6.08782	0.588532	0.294266	−	0.955724i	$-0.404925\pi$
$107$	6.08782	0.588532	0.294266	+	0.955724i	$0.404925\pi$
$108$	94.6821	9.11079
$109$	7.12008	0.681980	0.340990	−	0.940067i	$-0.389238\pi$
$109$	7.12008	0.681980	0.340990	+	0.940067i	$0.389238\pi$
$110$	14.8536	1.41623
$111$	22.2963	2.11627
$112$	18.2410	1.72361
$113$	4.87776	0.458861	0.229431	−	0.973325i	$-0.426314\pi$
$113$	4.87776	0.458861	0.229431	+	0.973325i	$0.426314\pi$
$114$	−70.2480	−6.57933
$115$	23.3502	2.17742
$116$	−28.7878	−2.67288
$117$	−12.3656	−1.14320
$118$	−30.6090	−2.81779
$119$	−6.19389	−0.567793
$120$	99.7137	9.10258
$121$	−9.24950	−0.840864
$122$	−15.4166	−1.39575
$123$	−12.3739	−1.11572
$124$	−24.4509	−2.19576
$125$	−40.3026	−3.60478
$126$	−54.4981	−4.85507
$127$	3.28747	0.291715	0.145858	−	0.989306i	$-0.453406\pi$
$127$	3.28747	0.291715	0.145858	+	0.989306i	$0.453406\pi$
$128$	9.33553	0.825152
$129$	−22.8077	−2.00811
$130$	−15.4424	−1.35439
$131$	−14.8484	−1.29731	−0.648655	−	0.761082i	$-0.724668\pi$
$131$	−14.8484	−1.29731	−0.648655	+	0.761082i	$0.724668\pi$
$132$	20.9139	1.82032
$133$	18.7335	1.62440
$134$	6.13058	0.529601
$135$	−90.8764	−7.82139
$136$	17.2057	1.47537
$137$	8.50403	0.726549	0.363274	−	0.931682i	$-0.381659\pi$
$137$	8.50403	0.726549	0.363274	+	0.931682i	$0.381659\pi$
$138$	47.2809	4.02482
$139$	−12.3798	−1.05004	−0.525019	−	0.851091i	$-0.675942\pi$
$139$	−12.3798	−1.05004	−0.525019	+	0.851091i	$0.675942\pi$
$140$	−47.3247	−3.99966
$141$	37.4073	3.15027
$142$	−14.6295	−1.22768
$143$	−1.81989	−0.152187
$144$	69.3089	5.77574
$145$	27.6307	2.29460
$146$	17.2309	1.42604
$147$	−4.85517	−0.400448
$148$	29.3951	2.41626
$149$	−11.4284	−0.936249	−0.468125	−	0.883663i	$-0.655070\pi$
$149$	−11.4284	−0.936249	−0.468125	+	0.883663i	$0.655070\pi$
$150$	−125.968	−10.2852
$151$	−15.1448	−1.23247	−0.616234	−	0.787563i	$-0.711342\pi$
$151$	−15.1448	−1.23247	−0.616234	+	0.787563i	$0.711342\pi$
$152$	−52.0387	−4.22089
$153$	−23.5345	−1.90265
$154$	−8.02066	−0.646323
$155$	23.4681	1.88500
$156$	−21.7430	−1.74083
$157$	4.20776	0.335816	0.167908	−	0.985803i	$-0.446299\pi$
$157$	4.20776	0.335816	0.167908	+	0.985803i	$0.446299\pi$
$158$	−19.1326	−1.52211
$159$	0.197788	0.0156856
$160$	28.9599	2.28948
$161$	−12.6087	−0.993705
$162$	−114.910	−9.02818
$163$	6.18417	0.484382	0.242191	−	0.970229i	$-0.422134\pi$
$163$	6.18417	0.484382	0.242191	+	0.970229i	$0.422134\pi$
$164$	−16.3135	−1.27387
$165$	−20.0732	−1.56270
$166$	−28.2409	−2.19192
$167$	6.43197	0.497721	0.248860	−	0.968539i	$-0.419944\pi$
$167$	6.43197	0.497721	0.248860	+	0.968539i	$0.419944\pi$
$168$	−53.8437	−4.15413
$169$	−11.1080	−0.854458
$170$	−29.3902	−2.25413
$171$	71.1802	5.44329
$172$	−30.0692	−2.29276
$173$	13.6603	1.03857	0.519286	−	0.854601i	$-0.326198\pi$
$173$	13.6603	1.03857	0.519286	+	0.854601i	$0.326198\pi$
$174$	55.9483	4.24143
$175$	33.5926	2.53936
$176$	10.2004	0.768886
$177$	41.3653	3.10920
$178$	−28.5730	−2.14164
$179$	−20.2324	−1.51224	−0.756119	−	0.654434i	$-0.772907\pi$
$179$	−20.2324	−1.51224	−0.756119	+	0.654434i	$0.772907\pi$
$180$	−179.816	−13.4027
$181$	3.01369	0.224006	0.112003	−	0.993708i	$-0.464273\pi$
$181$	3.01369	0.224006	0.112003	+	0.993708i	$0.464273\pi$
$182$	8.33863	0.618101
$183$	20.8341	1.54010
$184$	35.0250	2.58208
$185$	−28.2135	−2.07430
$186$	47.5197	3.48432
$187$	−3.46365	−0.253287
$188$	49.3171	3.59682
$189$	49.0717	3.56944
$190$	88.8910	6.44883
$191$	9.22794	0.667710	0.333855	−	0.942624i	$-0.391650\pi$
$191$	9.22794	0.667710	0.333855	+	0.942624i	$0.391650\pi$
$192$	5.24807	0.378747
$193$	14.4682	1.04144	0.520721	−	0.853727i	$-0.325663\pi$
$193$	14.4682	1.04144	0.520721	+	0.853727i	$0.325663\pi$
$194$	−7.86451	−0.564639
$195$	20.8690	1.49446
$196$	−6.40097	−0.457212
$197$	8.78335	0.625788	0.312894	−	0.949788i	$-0.398702\pi$
$197$	8.78335	0.625788	0.312894	+	0.949788i	$0.398702\pi$
$198$	−30.4755	−2.16580
$199$	−20.2844	−1.43793	−0.718963	−	0.695049i	$-0.755383\pi$
$199$	−20.2844	−1.43793	−0.718963	+	0.695049i	$0.755383\pi$
$200$	−93.3150	−6.59837
$201$	−8.28492	−0.584373
$202$	−10.1684	−0.715447
$203$	−14.9201	−1.04718
$204$	−41.3815	−2.89729
$205$	15.6578	1.09359
$206$	18.8417	1.31277
$207$	−47.9084	−3.32986
$208$	−10.6048	−0.735311
$209$	10.4758	0.724629
$210$	91.9743	6.34683
$211$	21.2173	1.46066	0.730330	−	0.683094i	$-0.239366\pi$
$211$	21.2173	1.46066	0.730330	+	0.683094i	$0.239366\pi$
$212$	0.260759	0.0179090
$213$	19.7705	1.35465
$214$	−15.5984	−1.06629
$215$	28.8606	1.96828
$216$	−136.313	−9.27496
$217$	−12.6724	−0.860257
$218$	−18.2433	−1.23559
$219$	−23.2860	−1.57352
$220$	−26.4642	−1.78421
$221$	3.60096	0.242227
$222$	−57.1285	−3.83422
$223$	−12.7862	−0.856227	−0.428113	−	0.903725i	$-0.640822\pi$
$223$	−12.7862	−0.856227	−0.428113	+	0.903725i	$0.640822\pi$
$224$	−15.6378	−1.04485
$225$	127.639	8.50929
$226$	−12.4980	−0.831354
$227$	10.7255	0.711877	0.355939	−	0.934509i	$-0.384161\pi$
$227$	10.7255	0.711877	0.355939	+	0.934509i	$0.384161\pi$
$228$	125.159	8.28885
$229$	20.2229	1.33637	0.668183	−	0.743997i	$-0.267073\pi$
$229$	20.2229	1.33637	0.668183	+	0.743997i	$0.267073\pi$
$230$	−59.8288	−3.94499
$231$	10.8392	0.713167
$232$	41.4457	2.72104
$233$	−17.4914	−1.14590	−0.572950	−	0.819590i	$-0.694201\pi$
$233$	−17.4914	−1.14590	−0.572950	+	0.819590i	$0.694201\pi$
$234$	31.6837	2.07123
$235$	−47.3348	−3.08778
$236$	54.5352	3.54994
$237$	25.8560	1.67952
$238$	15.8702	1.02871
$239$	−13.6578	−0.883451	−0.441725	−	0.897150i	$-0.645633\pi$
$239$	−13.6578	−0.883451	−0.441725	+	0.897150i	$0.645633\pi$
$240$	−116.970	−7.55038
$241$	0.164735	0.0106115	0.00530577	−	0.999986i	$-0.498311\pi$
$241$	0.164735	0.0106115	0.00530577	+	0.999986i	$0.498311\pi$
$242$	23.6994	1.52346
$243$	93.0687	5.97036
$244$	27.4673	1.75841
$245$	6.14368	0.392505
$246$	31.7049	2.02143
$247$	−10.8911	−0.692986
$248$	35.2019	2.23532
$249$	38.1650	2.41861
$250$	103.265	6.53105
$251$	29.0490	1.83356	0.916778	−	0.399398i	$-0.130781\pi$
$251$	29.0490	1.83356	0.916778	+	0.399398i	$0.130781\pi$
$252$	97.0976	6.11657
$253$	−7.05084	−0.443282
$254$	−8.42327	−0.528523
$255$	39.7182	2.48725
$256$	−26.9511	−1.68444
$257$	−5.27321	−0.328934	−0.164467	−	0.986383i	$-0.552590\pi$
$257$	−5.27321	−0.328934	−0.164467	+	0.986383i	$0.552590\pi$
$258$	58.4388	3.63824
$259$	15.2348	0.946646
$260$	27.5133	1.70630
$261$	−56.6908	−3.50907
$262$	38.0451	2.35044
$263$	10.5665	0.651560	0.325780	−	0.945446i	$-0.394373\pi$
$263$	10.5665	0.651560	0.325780	+	0.945446i	$0.394373\pi$
$264$	−30.1096	−1.85312
$265$	−0.250278	−0.0153745
$266$	−47.9996	−2.94305
$267$	38.6138	2.36313
$268$	−10.9227	−0.667208
$269$	−5.72052	−0.348786	−0.174393	−	0.984676i	$-0.555796\pi$
$269$	−5.72052	−0.348786	−0.174393	+	0.984676i	$0.555796\pi$
$270$	232.847	14.1706
$271$	−4.37604	−0.265825	−0.132913	−	0.991128i	$-0.542433\pi$
$271$	−4.37604	−0.265825	−0.132913	+	0.991128i	$0.542433\pi$
$272$	−20.1832	−1.22379
$273$	−11.2689	−0.682025
$274$	−21.7894	−1.31634
$275$	18.7851	1.13279
$276$	−84.2391	−5.07060
$277$	16.9420	1.01794	0.508972	−	0.860783i	$-0.330026\pi$
$277$	16.9420	1.01794	0.508972	+	0.860783i	$0.330026\pi$
$278$	31.7199	1.90243
$279$	−48.1503	−2.88268
$280$	68.1332	4.07174
$281$	−3.67995	−0.219527	−0.109764	−	0.993958i	$-0.535009\pi$
$281$	−3.67995	−0.219527	−0.109764	+	0.993958i	$0.535009\pi$
$282$	−95.8465	−5.70758
$283$	6.39902	0.380382	0.190191	−	0.981747i	$-0.439089\pi$
$283$	6.39902	0.380382	0.190191	+	0.981747i	$0.439089\pi$
$284$	26.0650	1.54667
$285$	−120.128	−7.11578
$286$	4.66300	0.275729
$287$	−8.45495	−0.499080
$288$	−59.4180	−3.50124
$289$	−10.1466	−0.596859
$290$	−70.7964	−4.15731
$291$	10.6282	0.623034
$292$	−30.6997	−1.79657
$293$	16.5622	0.967576	0.483788	−	0.875185i	$-0.339261\pi$
$293$	16.5622	0.967576	0.483788	+	0.875185i	$0.339261\pi$
$294$	12.4401	0.725522
$295$	−52.3431	−3.04754
$296$	−42.3200	−2.45980
$297$	27.4411	1.59229
$298$	29.2822	1.69627
$299$	7.33036	0.423926
$300$	224.433	12.9577
$301$	−15.5842	−0.898260
$302$	38.8046	2.23296
$303$	13.7417	0.789439
$304$	61.0444	3.50113
$305$	−26.3633	−1.50956
$306$	60.3009	3.44717
$307$	−26.7967	−1.52937	−0.764685	−	0.644404i	$-0.777105\pi$
$307$	−26.7967	−1.52937	−0.764685	+	0.644404i	$0.777105\pi$
$308$	14.2902	0.814259
$309$	−25.4629	−1.44853
$310$	−60.1309	−3.41521
$311$	17.4217	0.987891	0.493946	−	0.869493i	$-0.335554\pi$
$311$	17.4217	0.987891	0.493946	+	0.869493i	$0.335554\pi$
$312$	31.3033	1.77220
$313$	19.5526	1.10518	0.552589	−	0.833454i	$-0.313640\pi$
$313$	19.5526	1.10518	0.552589	+	0.833454i	$0.313640\pi$
$314$	−10.7813	−0.608423
$315$	−93.1948	−5.25093
$316$	34.0880	1.91760
$317$	−4.34503	−0.244041	−0.122021	−	0.992528i	$-0.538937\pi$
$317$	−4.34503	−0.244041	−0.122021	+	0.992528i	$0.538937\pi$
$318$	−0.506779	−0.0284187
$319$	−8.34338	−0.467139
$320$	−6.64085	−0.371235
$321$	21.0799	1.17656
$322$	32.3065	1.80037
$323$	−20.7282	−1.15335
$324$	204.732	11.3740
$325$	−19.5298	−1.08332
$326$	−15.8453	−0.877591
$327$	24.6542	1.36338
$328$	23.4865	1.29683
$329$	25.5600	1.40917
$330$	51.4324	2.83126
$331$	−23.4022	−1.28630	−0.643151	−	0.765739i	$-0.722373\pi$
$331$	−23.4022	−1.28630	−0.643151	+	0.765739i	$0.722373\pi$
$332$	50.3159	2.76145
$333$	57.8866	3.17217
$334$	−16.4802	−0.901759
$335$	10.4836	0.572782
$336$	63.1617	3.44576
$337$	17.2667	0.940579	0.470290	−	0.882512i	$-0.344149\pi$
$337$	17.2667	0.940579	0.470290	+	0.882512i	$0.344149\pi$
$338$	28.4612	1.54809
$339$	16.8899	0.917333
$340$	52.3637	2.83982
$341$	−7.08645	−0.383753
$342$	−182.381	−9.86202
$343$	−19.8793	−1.07338
$344$	43.2906	2.33407
$345$	80.8531	4.35299
$346$	−35.0009	−1.88166
$347$	20.5442	1.10287	0.551435	−	0.834218i	$-0.314080\pi$
$347$	20.5442	1.10287	0.551435	+	0.834218i	$0.314080\pi$
$348$	−99.6816	−5.34349
$349$	12.1958	0.652829	0.326414	−	0.945227i	$-0.394160\pi$
$349$	12.1958	0.652829	0.326414	+	0.945227i	$0.394160\pi$
$350$	−86.0722	−4.60076
$351$	−28.5289	−1.52276
$352$	−8.74474	−0.466096
$353$	21.1620	1.12634	0.563170	−	0.826341i	$-0.309582\pi$
$353$	21.1620	1.12634	0.563170	+	0.826341i	$0.309582\pi$
$354$	−105.988	−5.63318
$355$	−25.0173	−1.32778
$356$	50.9077	2.69810
$357$	−21.4472	−1.13510
$358$	51.8402	2.73984
$359$	8.02764	0.423683	0.211841	−	0.977304i	$-0.432054\pi$
$359$	8.02764	0.423683	0.211841	+	0.977304i	$0.432054\pi$
$360$	258.881	13.6442
$361$	43.6926	2.29961
$362$	−7.72179	−0.405848
$363$	−32.0276	−1.68101
$364$	−14.8567	−0.778703
$365$	29.4658	1.54231
$366$	−53.3820	−2.79032
$367$	7.70861	0.402386	0.201193	−	0.979552i	$-0.435518\pi$
$367$	7.70861	0.402386	0.201193	+	0.979552i	$0.435518\pi$
$368$	−41.0864	−2.14177
$369$	−32.1257	−1.67240
$370$	72.2898	3.75817
$371$	0.135146	0.00701642
$372$	−84.6645	−4.38965
$373$	−2.29114	−0.118631	−0.0593155	−	0.998239i	$-0.518892\pi$
$373$	−2.29114	−0.118631	−0.0593155	+	0.998239i	$0.518892\pi$
$374$	8.87469	0.458899
$375$	−139.553	−7.20650
$376$	−71.0017	−3.66163
$377$	8.67414	0.446741
$378$	−125.733	−6.46702
$379$	−9.56171	−0.491152	−0.245576	−	0.969377i	$-0.578977\pi$
$379$	−9.56171	−0.491152	−0.245576	+	0.969377i	$0.578977\pi$
$380$	−158.375	−8.12444
$381$	11.3833	0.583184
$382$	−23.6442	−1.20974
$383$	29.5660	1.51075	0.755377	−	0.655290i	$-0.227454\pi$
$383$	29.5660	1.51075	0.755377	+	0.655290i	$0.227454\pi$
$384$	32.3255	1.64960
$385$	−13.7158	−0.699022
$386$	−37.0709	−1.88686
$387$	−59.2143	−3.01003
$388$	14.0120	0.711350
$389$	−30.3472	−1.53866	−0.769331	−	0.638851i	$-0.779410\pi$
$389$	−30.3472	−1.53866	−0.769331	+	0.638851i	$0.779410\pi$
$390$	−53.4714	−2.70763
$391$	13.9513	0.705545
$392$	9.21545	0.465451
$393$	−51.4146	−2.59352
$394$	−22.5050	−1.13379
$395$	−32.7178	−1.64621
$396$	54.2974	2.72855
$397$	13.7105	0.688111	0.344056	−	0.938949i	$-0.388199\pi$
$397$	13.7105	0.688111	0.344056	+	0.938949i	$0.388199\pi$
$398$	51.9736	2.60520
$399$	64.8671	3.24742
$400$	109.464	5.47320
$401$	20.7479	1.03610	0.518051	−	0.855350i	$-0.326658\pi$
$401$	20.7479	1.03610	0.518051	+	0.855350i	$0.326658\pi$
$402$	21.2279	1.05875
$403$	7.36738	0.366995
$404$	18.1168	0.901343
$405$	−196.503	−9.76429
$406$	38.2288	1.89726
$407$	8.51937	0.422290
$408$	59.5769	2.94950
$409$	10.6525	0.526731	0.263366	−	0.964696i	$-0.415167\pi$
$409$	10.6525	0.526731	0.263366	+	0.964696i	$0.415167\pi$
$410$	−40.1191	−1.98134
$411$	29.4463	1.45248
$412$	−33.5698	−1.65386
$413$	28.2644	1.39080
$414$	122.753	6.03297
$415$	−48.2935	−2.37064
$416$	9.09142	0.445743
$417$	−42.8666	−2.09918
$418$	−26.8416	−1.31286
$419$	9.07363	0.443276	0.221638	−	0.975129i	$-0.428860\pi$
$419$	9.07363	0.443276	0.221638	+	0.975129i	$0.428860\pi$
$420$	−163.868	−7.99594
$421$	5.33294	0.259912	0.129956	−	0.991520i	$-0.458516\pi$
$421$	5.33294	0.259912	0.129956	+	0.991520i	$0.458516\pi$
$422$	−54.3638	−2.64639
$423$	97.1184	4.72206
$424$	−0.375414	−0.0182317
$425$	−37.1695	−1.80299
$426$	−50.6567	−2.45433
$427$	14.2357	0.688914
$428$	27.7913	1.34334
$429$	−6.30162	−0.304245
$430$	−73.9477	−3.56608
$431$	−14.0858	−0.678487	−0.339244	−	0.940699i	$-0.610171\pi$
$431$	−14.0858	−0.678487	−0.339244	+	0.940699i	$0.610171\pi$
$432$	159.904	7.69336
$433$	−24.6893	−1.18649	−0.593245	−	0.805022i	$-0.702154\pi$
$433$	−24.6893	−1.18649	−0.593245	+	0.805022i	$0.702154\pi$
$434$	32.4697	1.55859
$435$	95.6749	4.58726
$436$	32.5036	1.55664
$437$	−42.1957	−2.01849
$438$	59.6642	2.85086
$439$	−26.5227	−1.26586	−0.632930	−	0.774209i	$-0.718148\pi$
$439$	−26.5227	−1.26586	−0.632930	+	0.774209i	$0.718148\pi$
$440$	38.1004	1.81636
$441$	−12.6052	−0.600247
$442$	−9.22652	−0.438861
$443$	16.6443	0.790793	0.395396	−	0.918511i	$-0.370607\pi$
$443$	16.6443	0.790793	0.395396	+	0.918511i	$0.370607\pi$
$444$	101.784	4.83047
$445$	−48.8615	−2.31626
$446$	32.7613	1.55129
$447$	−39.5723	−1.87170
$448$	3.58594	0.169420
$449$	26.9240	1.27062	0.635310	−	0.772257i	$-0.280872\pi$
$449$	26.9240	1.27062	0.635310	+	0.772257i	$0.280872\pi$
$450$	−327.043	−15.4169
$451$	−4.72804	−0.222635
$452$	22.2673	1.04737
$453$	−52.4409	−2.46389
$454$	−27.4813	−1.28976
$455$	14.2595	0.668498
$456$	−180.191	−8.43821
$457$	15.1849	0.710322	0.355161	−	0.934805i	$-0.384426\pi$
$457$	15.1849	0.710322	0.355161	+	0.934805i	$0.384426\pi$
$458$	−51.8158	−2.42119
$459$	−54.2967	−2.53435
$460$	106.595	4.97003
$461$	28.1090	1.30917	0.654583	−	0.755990i	$-0.272844\pi$
$461$	28.1090	1.30917	0.654583	+	0.755990i	$0.272844\pi$
$462$	−27.7726	−1.29210
$463$	0.327779	0.0152332	0.00761660	−	0.999971i	$-0.497576\pi$
$463$	0.327779	0.0152332	0.00761660	+	0.999971i	$0.497576\pi$
$464$	−48.6182	−2.25704
$465$	81.2615	3.76841
$466$	44.8171	2.07611
$467$	−5.73910	−0.265574	−0.132787	−	0.991145i	$-0.542393\pi$
$467$	−5.73910	−0.265574	−0.132787	+	0.991145i	$0.542393\pi$
$468$	−56.4499	−2.60940
$469$	−5.66098	−0.261400
$470$	121.283	5.59437
$471$	14.5699	0.671347
$472$	−78.5141	−3.61390
$473$	−8.71476	−0.400705
$474$	−66.2491	−3.04292
$475$	112.419	5.15816
$476$	−28.2755	−1.29601
$477$	0.513504	0.0235117
$478$	34.9946	1.60062
$479$	−6.23778	−0.285012	−0.142506	−	0.989794i	$-0.545516\pi$
$479$	−6.23778	−0.285012	−0.142506	+	0.989794i	$0.545516\pi$
$480$	100.277	4.57702
$481$	−8.85711	−0.403850
$482$	−0.422091	−0.0192257
$483$	−43.6593	−1.98657
$484$	−42.2246	−1.91930
$485$	−13.4488	−0.610677
$486$	−238.464	−10.8170
$487$	30.1815	1.36765	0.683827	−	0.729644i	$-0.260314\pi$
$487$	30.1815	1.36765	0.683827	+	0.729644i	$0.260314\pi$
$488$	−39.5446	−1.79010
$489$	21.4135	0.968352
$490$	−15.7416	−0.711132
$491$	−37.8267	−1.70710	−0.853548	−	0.521015i	$-0.825554\pi$
$491$	−37.8267	−1.70710	−0.853548	+	0.521015i	$0.825554\pi$
$492$	−56.4878	−2.54667
$493$	16.5088	0.743517
$494$	27.9057	1.25554
$495$	−52.1149	−2.34239
$496$	−41.2939	−1.85415
$497$	13.5089	0.605959
$498$	−97.7878	−4.38197
$499$	24.3939	1.09202	0.546010	−	0.837778i	$-0.316146\pi$
$499$	24.3939	1.09202	0.546010	+	0.837778i	$0.316146\pi$
$500$	−183.984	−8.22802
$501$	22.2716	0.995020
$502$	−74.4304	−3.32199
$503$	−3.56402	−0.158912	−0.0794559	−	0.996838i	$-0.525318\pi$
$503$	−3.56402	−0.158912	−0.0794559	+	0.996838i	$0.525318\pi$
$504$	−139.791	−6.22679
$505$	−17.3886	−0.773781
$506$	18.0659	0.803129
$507$	−38.4628	−1.70819
$508$	15.0075	0.665850
$509$	−20.1047	−0.891125	−0.445562	−	0.895251i	$-0.646996\pi$
$509$	−20.1047	−0.891125	−0.445562	+	0.895251i	$0.646996\pi$
$510$	−101.768	−4.50634
$511$	−15.9110	−0.703862
$512$	50.3841	2.22668
$513$	164.221	7.25053
$514$	13.5112	0.595955
$515$	32.2204	1.41980
$516$	−104.119	−4.58357
$517$	14.2932	0.628616
$518$	−39.0352	−1.71511
$519$	47.3005	2.07626
$520$	−39.6108	−1.73705
$521$	35.7275	1.56525	0.782625	−	0.622494i	$-0.213880\pi$
$521$	35.7275	1.56525	0.782625	+	0.622494i	$0.213880\pi$
$522$	145.255	6.35765
$523$	16.5164	0.722212	0.361106	−	0.932525i	$-0.382399\pi$
$523$	16.5164	0.722212	0.361106	+	0.932525i	$0.382399\pi$
$524$	−67.7839	−2.96115
$525$	116.319	5.07657
$526$	−27.0740	−1.18048
$527$	14.0217	0.610795
$528$	35.3203	1.53712
$529$	5.40013	0.234788
$530$	0.641272	0.0278551
$531$	107.394	4.66051
$532$	85.5195	3.70774
$533$	4.91548	0.212913
$534$	−98.9378	−4.28146
$535$	−26.6742	−1.15323
$536$	15.7253	0.679231
$537$	−70.0573	−3.02320
$538$	14.6573	0.631923
$539$	−1.85515	−0.0799070
$540$	−414.857	−17.8526
$541$	−2.21410	−0.0951914	−0.0475957	−	0.998867i	$-0.515156\pi$
$541$	−2.21410	−0.0951914	−0.0475957	+	0.998867i	$0.515156\pi$
$542$	11.2125	0.481616
$543$	10.4353	0.447822
$544$	17.3029	0.741857
$545$	−31.1971	−1.33634
$546$	28.8736	1.23568
$547$	29.7131	1.27044	0.635220	−	0.772331i	$-0.280909\pi$
$547$	29.7131	1.27044	0.635220	+	0.772331i	$0.280909\pi$
$548$	38.8215	1.65837
$549$	54.0904	2.30852
$550$	−48.1320	−2.05235
$551$	−49.9309	−2.12713
$552$	121.279	5.16197
$553$	17.6671	0.751280
$554$	−43.4093	−1.84429
$555$	−97.6931	−4.14684
$556$	−56.5144	−2.39675
$557$	−1.16593	−0.0494021	−0.0247010	−	0.999695i	$-0.507863\pi$
$557$	−1.16593	−0.0494021	−0.0247010	+	0.999695i	$0.507863\pi$
$558$	123.373	5.22278
$559$	9.06025	0.383208
$560$	−79.9241	−3.37741
$561$	−11.9933	−0.506359
$562$	9.42890	0.397734
$563$	−45.8182	−1.93101	−0.965504	−	0.260388i	$-0.916149\pi$
$563$	−45.8182	−1.93101	−0.965504	+	0.260388i	$0.916149\pi$
$564$	170.767	7.19059
$565$	−21.3723	−0.899139
$566$	−16.3958	−0.689168
$567$	106.108	4.45612
$568$	−37.5257	−1.57454
$569$	22.4787	0.942358	0.471179	−	0.882038i	$-0.343829\pi$
$569$	22.4787	0.942358	0.471179	+	0.882038i	$0.343829\pi$
$570$	307.797	12.8922
$571$	−20.6810	−0.865472	−0.432736	−	0.901521i	$-0.642452\pi$
$571$	−20.6810	−0.865472	−0.432736	+	0.901521i	$0.642452\pi$
$572$	−8.30793	−0.347372
$573$	31.9530	1.33485
$574$	21.6636	0.904221
$575$	−75.6647	−3.15544
$576$	13.6253	0.567719
$577$	−9.01600	−0.375341	−0.187670	−	0.982232i	$-0.560094\pi$
$577$	−9.01600	−0.375341	−0.187670	+	0.982232i	$0.560094\pi$
$578$	25.9980	1.08137
$579$	50.0980	2.08200
$580$	126.136	5.23751
$581$	26.0777	1.08188
$582$	−27.2319	−1.12880
$583$	0.0755741	0.00312996
$584$	44.1983	1.82894
$585$	54.1810	2.24011
$586$	−42.4364	−1.75303
$587$	33.7976	1.39498	0.697488	−	0.716597i	$-0.254301\pi$
$587$	33.7976	1.39498	0.697488	+	0.716597i	$0.254301\pi$
$588$	−22.1642	−0.914036
$589$	−42.4088	−1.74742
$590$	134.116	5.52145
$591$	30.4135	1.25105
$592$	49.6438	2.04035
$593$	22.6849	0.931558	0.465779	−	0.884901i	$-0.345774\pi$
$593$	22.6849	0.931558	0.465779	+	0.884901i	$0.345774\pi$
$594$	−70.3106	−2.88488
$595$	27.1390	1.11259
$596$	−52.1713	−2.13702
$597$	−70.2375	−2.87463
$598$	−18.7821	−0.768058
$599$	−29.4337	−1.20263	−0.601315	−	0.799012i	$-0.705356\pi$
$599$	−29.4337	−1.20263	−0.601315	+	0.799012i	$0.705356\pi$
$600$	−323.116	−13.1911
$601$	8.58499	0.350189	0.175094	−	0.984552i	$-0.443977\pi$
$601$	8.58499	0.350189	0.175094	+	0.984552i	$0.443977\pi$
$602$	39.9305	1.62745
$603$	−21.5096	−0.875940
$604$	−69.1371	−2.81315
$605$	40.5274	1.64767
$606$	−35.2095	−1.43029
$607$	−23.9672	−0.972799	−0.486399	−	0.873737i	$-0.661690\pi$
$607$	−23.9672	−0.972799	−0.486399	+	0.873737i	$0.661690\pi$
$608$	−52.3329	−2.12238
$609$	−51.6628	−2.09348
$610$	67.5489	2.73498
$611$	−14.8599	−0.601167
$612$	−107.436	−4.34286
$613$	27.9853	1.13032	0.565159	−	0.824982i	$-0.308815\pi$
$613$	27.9853	1.13032	0.565159	+	0.824982i	$0.308815\pi$
$614$	68.6596	2.77088
$615$	54.2173	2.18625
$616$	−20.5735	−0.828931
$617$	17.0602	0.686819	0.343409	−	0.939186i	$-0.388418\pi$
$617$	17.0602	0.686819	0.343409	+	0.939186i	$0.388418\pi$
$618$	65.2420	2.62442
$619$	2.99800	0.120500	0.0602500	−	0.998183i	$-0.480810\pi$
$619$	2.99800	0.120500	0.0602500	+	0.998183i	$0.480810\pi$
$620$	107.134	4.30259
$621$	−110.530	−4.43542
$622$	−44.6384	−1.78984
$623$	26.3844	1.05707
$624$	−36.7205	−1.47000
$625$	105.598	4.22392
$626$	−50.0984	−2.00234
$627$	36.2740	1.44864
$628$	19.2087	0.766511
$629$	−16.8570	−0.672133
$630$	238.787	9.51351
$631$	6.24018	0.248418	0.124209	−	0.992256i	$-0.460361\pi$
$631$	6.24018	0.248418	0.124209	+	0.992256i	$0.460361\pi$
$632$	−49.0764	−1.95215
$633$	73.4678	2.92008
$634$	11.1330	0.442148
$635$	−14.4043	−0.571616
$636$	0.902913	0.0358028
$637$	1.92869	0.0764177
$638$	21.3777	0.846352
$639$	51.3289	2.03054
$640$	−40.9043	−1.61689
$641$	−14.1090	−0.557272	−0.278636	−	0.960397i	$-0.589882\pi$
$641$	−14.1090	−0.557272	−0.278636	+	0.960397i	$0.589882\pi$
$642$	−54.0117	−2.13167
$643$	−27.3864	−1.08001	−0.540007	−	0.841661i	$-0.681578\pi$
$643$	−27.3864	−1.08001	−0.540007	+	0.841661i	$0.681578\pi$
$644$	−57.5596	−2.26816
$645$	99.9337	3.93488
$646$	53.1106	2.08961
$647$	5.55142	0.218249	0.109124	−	0.994028i	$-0.465195\pi$
$647$	5.55142	0.218249	0.109124	+	0.994028i	$0.465195\pi$
$648$	−294.752	−11.5789
$649$	15.8056	0.620423
$650$	50.0401	1.96273
$651$	−43.8798	−1.71978
$652$	28.2311	1.10562
$653$	−6.27734	−0.245651	−0.122826	−	0.992428i	$-0.539196\pi$
$653$	−6.27734	−0.245651	−0.122826	+	0.992428i	$0.539196\pi$
$654$	−63.1700	−2.47014
$655$	65.0594	2.54208
$656$	−27.5511	−1.07569
$657$	−60.4559	−2.35861
$658$	−65.4908	−2.55310
$659$	4.58597	0.178644	0.0893221	−	0.996003i	$-0.471530\pi$
$659$	4.58597	0.178644	0.0893221	+	0.996003i	$0.471530\pi$
$660$	−91.6356	−3.56691
$661$	−35.9063	−1.39659	−0.698296	−	0.715809i	$-0.746058\pi$
$661$	−35.9063	−1.39659	−0.698296	+	0.715809i	$0.746058\pi$
$662$	59.9621	2.33049
$663$	12.4688	0.484248
$664$	−72.4397	−2.81121
$665$	−82.0821	−3.18301
$666$	−148.319	−5.74726
$667$	33.6064	1.30124
$668$	29.3624	1.13606
$669$	−44.2739	−1.71173
$670$	−26.8616	−1.03775
$671$	7.96066	0.307318
$672$	−54.1481	−2.08881
$673$	−4.95613	−0.191045	−0.0955224	−	0.995427i	$-0.530452\pi$
$673$	−4.95613	−0.191045	−0.0955224	+	0.995427i	$0.530452\pi$
$674$	−44.2415	−1.70412
$675$	294.479	11.3345
$676$	−50.7086	−1.95033
$677$	−44.7719	−1.72072	−0.860362	−	0.509683i	$-0.829763\pi$
$677$	−44.7719	−1.72072	−0.860362	+	0.509683i	$0.829763\pi$
$678$	−43.2759	−1.66200
$679$	7.26210	0.278694
$680$	−75.3879	−2.89099
$681$	37.1385	1.42315
$682$	18.1572	0.695274
$683$	−1.37254	−0.0525189	−0.0262594	−	0.999655i	$-0.508360\pi$
$683$	−1.37254	−0.0525189	−0.0262594	+	0.999655i	$0.508360\pi$
$684$	324.942	12.4245
$685$	−37.2611	−1.42367
$686$	50.9355	1.94473
$687$	70.0244	2.67160
$688$	−50.7823	−1.93606
$689$	−0.0785702	−0.00299328
$690$	−207.165	−7.88664
$691$	10.0675	0.382985	0.191493	−	0.981494i	$-0.438667\pi$
$691$	10.0675	0.382985	0.191493	+	0.981494i	$0.438667\pi$
$692$	62.3601	2.37057
$693$	28.1412	1.06899
$694$	−52.6391	−1.99815
$695$	54.2428	2.05755
$696$	143.511	5.43978
$697$	9.35522	0.354354
$698$	−31.2487	−1.18278
$699$	−60.5663	−2.29083
$700$	153.352	5.79618
$701$	−7.50404	−0.283424	−0.141712	−	0.989908i	$-0.545261\pi$
$701$	−7.50404	−0.283424	−0.141712	+	0.989908i	$0.545261\pi$
$702$	73.0980	2.75890
$703$	50.9842	1.92290
$704$	2.00527	0.0755766
$705$	−163.903	−6.17295
$706$	−54.2221	−2.04068
$707$	9.38953	0.353129
$708$	188.835	7.09686
$709$	4.70478	0.176692	0.0883458	−	0.996090i	$-0.471842\pi$
$709$	4.70478	0.176692	0.0883458	+	0.996090i	$0.471842\pi$
$710$	64.1004	2.40565
$711$	67.1283	2.51751
$712$	−73.2917	−2.74672
$713$	28.5436	1.06896
$714$	54.9527	2.05655
$715$	7.97400	0.298211
$716$	−92.3622	−3.45174
$717$	−47.2920	−1.76615
$718$	−20.5687	−0.767618
$719$	−0.662966	−0.0247244	−0.0123622	−	0.999924i	$-0.503935\pi$
$719$	−0.662966	−0.0247244	−0.0123622	+	0.999924i	$0.503935\pi$
$720$	−303.682	−11.3176
$721$	−17.3985	−0.647953
$722$	−111.951	−4.16638
$723$	0.570418	0.0212141
$724$	13.7577	0.511301
$725$	−89.5354	−3.32526
$726$	82.0624	3.04562
$727$	12.3694	0.458756	0.229378	−	0.973337i	$-0.426331\pi$
$727$	12.3694	0.458756	0.229378	+	0.973337i	$0.426331\pi$
$728$	21.3891	0.792735
$729$	187.720	6.95260
$730$	−75.4984	−2.79432
$731$	17.2436	0.637778
$732$	95.1091	3.51533
$733$	−24.8622	−0.918306	−0.459153	−	0.888357i	$-0.651847\pi$
$733$	−24.8622	−0.918306	−0.459153	+	0.888357i	$0.651847\pi$
$734$	−19.7513	−0.729033
$735$	21.2733	0.784678
$736$	35.2230	1.29834
$737$	−3.16564	−0.116608
$738$	82.3136	3.03001
$739$	32.4080	1.19215	0.596074	−	0.802929i	$-0.296726\pi$
$739$	32.4080	1.19215	0.596074	+	0.802929i	$0.296726\pi$
$740$	−128.797	−4.73466
$741$	−37.7120	−1.38539
$742$	−0.346276	−0.0127122
$743$	−6.70784	−0.246087	−0.123043	−	0.992401i	$-0.539265\pi$
$743$	−6.70784	−0.246087	−0.123043	+	0.992401i	$0.539265\pi$
$744$	121.891	4.46875
$745$	50.0743	1.83458
$746$	5.87046	0.214933
$747$	99.0854	3.62535
$748$	−15.8118	−0.578136
$749$	14.4036	0.526297
$750$	357.569	13.0566
$751$	−0.118946	−0.00434040	−0.00217020	−	0.999998i	$-0.500691\pi$
$751$	−0.118946	−0.00434040	−0.00217020	+	0.999998i	$0.500691\pi$
$752$	83.2890	3.03724
$753$	100.586	3.66556
$754$	−22.2252	−0.809395
$755$	66.3582	2.41502
$756$	224.015	8.14736
$757$	−8.40446	−0.305465	−0.152733	−	0.988268i	$-0.548807\pi$
$757$	−8.40446	−0.305465	−0.152733	+	0.988268i	$0.548807\pi$
$758$	24.4994	0.889858
$759$	−24.4145	−0.886189
$760$	228.011	8.27084
$761$	−53.6916	−1.94632	−0.973159	−	0.230134i	$-0.926083\pi$
$761$	−53.6916	−1.94632	−0.973159	+	0.230134i	$0.926083\pi$
$762$	−29.1667	−1.05660
$763$	16.8459	0.609863
$764$	42.1261	1.52407
$765$	103.118	3.72824
$766$	−75.7553	−2.73715
$767$	−16.4322	−0.593331
$768$	−93.3218	−3.36746
$769$	−15.4530	−0.557249	−0.278624	−	0.960400i	$-0.589878\pi$
$769$	−15.4530	−0.557249	−0.278624	+	0.960400i	$0.589878\pi$
$770$	35.1431	1.26647
$771$	−18.2592	−0.657589
$772$	66.0482	2.37713
$773$	−46.6362	−1.67739	−0.838693	−	0.544604i	$-0.816680\pi$
$773$	−46.6362	−1.67739	−0.838693	+	0.544604i	$0.816680\pi$
$774$	151.721	5.45350
$775$	−76.0469	−2.73168
$776$	−20.1730	−0.724168
$777$	52.7526	1.89249
$778$	77.7566	2.78771
$779$	−28.2949	−1.01377
$780$	95.2684	3.41116
$781$	7.55425	0.270312
$782$	−35.7465	−1.27829
$783$	−130.792	−4.67413
$784$	−10.8103	−0.386081
$785$	−18.4366	−0.658031
$786$	131.736	4.69888
$787$	−7.62751	−0.271891	−0.135946	−	0.990716i	$-0.543407\pi$
$787$	−7.62751	−0.271891	−0.135946	+	0.990716i	$0.543407\pi$
$788$	40.0966	1.42838
$789$	36.5880	1.30257
$790$	83.8309	2.98257
$791$	11.5407	0.410339
$792$	−78.1718	−2.77771
$793$	−8.27625	−0.293898
$794$	−35.1296	−1.24670
$795$	−0.866621	−0.0307359
$796$	−92.5998	−3.28211
$797$	−22.0834	−0.782235	−0.391117	−	0.920341i	$-0.627911\pi$
$797$	−22.0834	−0.782235	−0.391117	+	0.920341i	$0.627911\pi$
$798$	−166.205	−5.88359
$799$	−28.2816	−1.00053
$800$	−93.8426	−3.31784
$801$	100.251	3.54219
$802$	−53.1611	−1.87718
$803$	−8.89751	−0.313986
$804$	−37.8212	−1.33385
$805$	55.2460	1.94716
$806$	−18.8770	−0.664913
$807$	−19.8081	−0.697277
$808$	−26.0827	−0.917585
$809$	−1.78083	−0.0626108	−0.0313054	−	0.999510i	$-0.509966\pi$
$809$	−1.78083	−0.0626108	−0.0313054	+	0.999510i	$0.509966\pi$
$810$	503.487	17.6907
$811$	5.94095	0.208615	0.104308	−	0.994545i	$-0.466737\pi$
$811$	5.94095	0.208615	0.104308	+	0.994545i	$0.466737\pi$
$812$	−68.1112	−2.39023
$813$	−15.1526	−0.531425
$814$	−21.8287	−0.765094
$815$	−27.0964	−0.949146
$816$	−69.8871	−2.44654
$817$	−52.1535	−1.82462
$818$	−27.2942	−0.954320
$819$	−29.2568	−1.02231
$820$	71.4790	2.49615
$821$	−22.0133	−0.768268	−0.384134	−	0.923277i	$-0.625500\pi$
$821$	−22.0133	−0.768268	−0.384134	+	0.923277i	$0.625500\pi$
$822$	−75.4486	−2.63157
$823$	14.5591	0.507498	0.253749	−	0.967270i	$-0.418336\pi$
$823$	14.5591	0.507498	0.253749	+	0.967270i	$0.418336\pi$
$824$	48.3303	1.68367
$825$	65.0460	2.26461
$826$	−72.4201	−2.51982
$827$	−48.5830	−1.68940	−0.844699	−	0.535242i	$-0.820220\pi$
$827$	−48.5830	−1.68940	−0.844699	+	0.535242i	$0.820220\pi$
$828$	−218.705	−7.60052
$829$	−26.3991	−0.916880	−0.458440	−	0.888725i	$-0.651592\pi$
$829$	−26.3991	−0.916880	−0.458440	+	0.888725i	$0.651592\pi$
$830$	123.739	4.29506
$831$	58.6638	2.03502
$832$	−2.08477	−0.0722764
$833$	3.67072	0.127183
$834$	109.834	3.80325
$835$	−28.1822	−0.975284
$836$	47.8229	1.65399
$837$	−111.088	−3.83978
$838$	−23.2488	−0.803117
$839$	−20.5242	−0.708574	−0.354287	−	0.935137i	$-0.615276\pi$
$839$	−20.5242	−0.708574	−0.354287	+	0.935137i	$0.615276\pi$
$840$	235.920	8.14002
$841$	10.7670	0.371275
$842$	−13.6643	−0.470902
$843$	−12.7423	−0.438868
$844$	96.8585	3.33401
$845$	48.6704	1.67431
$846$	−248.841	−8.55531
$847$	−21.8841	−0.751946
$848$	0.440382	0.0151228
$849$	22.1575	0.760442
$850$	95.2371	3.26661
$851$	−34.3153	−1.17631
$852$	90.2536	3.09204
$853$	6.48475	0.222034	0.111017	−	0.993819i	$-0.464589\pi$
$853$	6.48475	0.222034	0.111017	+	0.993819i	$0.464589\pi$
$854$	−36.4753	−1.24816
$855$	−311.882	−10.6661
$856$	−40.0111	−1.36755
$857$	37.0241	1.26472	0.632360	−	0.774675i	$-0.282087\pi$
$857$	37.0241	1.26472	0.632360	+	0.774675i	$0.282087\pi$
$858$	16.1463	0.551224
$859$	28.7500	0.980938	0.490469	−	0.871459i	$-0.336826\pi$
$859$	28.7500	0.980938	0.490469	+	0.871459i	$0.336826\pi$
$860$	131.751	4.49266
$861$	−29.2764	−0.997736
$862$	36.0911	1.22927
$863$	−45.7522	−1.55742	−0.778711	−	0.627382i	$-0.784126\pi$
$863$	−45.7522	−1.55742	−0.778711	+	0.627382i	$0.784126\pi$
$864$	−137.084	−4.66370
$865$	−59.8535	−2.03508
$866$	63.2598	2.14966
$867$	−35.1339	−1.19321
$868$	−57.8502	−1.96357
$869$	9.87949	0.335139
$870$	−245.142	−8.31109
$871$	3.29114	0.111516
$872$	−46.7954	−1.58469
$873$	27.5933	0.933891
$874$	108.115	3.65706
$875$	−95.3550	−3.22359
$876$	−106.302	−3.59161
$877$	22.7356	0.767726	0.383863	−	0.923390i	$-0.374593\pi$
$877$	22.7356	0.767726	0.383863	+	0.923390i	$0.374593\pi$
$878$	67.9575	2.29345
$879$	57.3489	1.93433
$880$	−44.6939	−1.50663
$881$	19.8434	0.668542	0.334271	−	0.942477i	$-0.391510\pi$
$881$	19.8434	0.668542	0.334271	+	0.942477i	$0.391510\pi$
$882$	32.2975	1.08751
$883$	−35.4754	−1.19384	−0.596921	−	0.802300i	$-0.703610\pi$
$883$	−35.4754	−1.19384	−0.596921	+	0.802300i	$0.703610\pi$
$884$	16.4386	0.552891
$885$	−181.245	−6.09249
$886$	−42.6466	−1.43274
$887$	−0.594051	−0.0199463	−0.00997314	−	0.999950i	$-0.503175\pi$
$887$	−0.594051	−0.0199463	−0.00997314	+	0.999950i	$0.503175\pi$
$888$	−146.539	−4.91751
$889$	7.77806	0.260868
$890$	125.195	4.19654
$891$	59.3361	1.98783
$892$	−58.3698	−1.95437
$893$	85.5379	2.86242
$894$	101.394	3.39111
$895$	88.6497	2.96323
$896$	22.0876	0.737896
$897$	25.3823	0.847492
$898$	−68.9856	−2.30208
$899$	33.7761	1.12650
$900$	582.682	19.4227
$901$	−0.149536	−0.00498177
$902$	12.1144	0.403364
$903$	−53.9624	−1.79576
$904$	−32.0582	−1.06624
$905$	−13.2047	−0.438939
$906$	134.366	4.46402
$907$	52.6614	1.74859	0.874296	−	0.485393i	$-0.161323\pi$
$907$	52.6614	1.74859	0.874296	+	0.485393i	$0.161323\pi$
$908$	48.9627	1.62488
$909$	35.6767	1.18332
$910$	−36.5363	−1.21117
$911$	31.4520	1.04205	0.521026	−	0.853541i	$-0.325549\pi$
$911$	31.4520	1.04205	0.521026	+	0.853541i	$0.325549\pi$
$912$	211.374	6.99930
$913$	14.5827	0.482618
$914$	−38.9074	−1.28694
$915$	−91.2863	−3.01783
$916$	92.3188	3.05030
$917$	−35.1309	−1.16013
$918$	139.121	4.59168
$919$	52.0410	1.71667	0.858337	−	0.513086i	$-0.171498\pi$
$919$	52.0410	1.71667	0.858337	+	0.513086i	$0.171498\pi$
$920$	−153.465	−5.05958
$921$	−92.7872	−3.05744
$922$	−72.0219	−2.37192
$923$	−7.85373	−0.258509
$924$	49.4817	1.62783
$925$	91.4241	3.00600
$926$	−0.839849	−0.0275991
$927$	−66.1078	−2.17126
$928$	41.6800	1.36821
$929$	−4.08132	−0.133904	−0.0669520	−	0.997756i	$-0.521327\pi$
$929$	−4.08132	−0.133904	−0.0669520	+	0.997756i	$0.521327\pi$
$930$	−208.211	−6.82752
$931$	−11.1021	−0.363858
$932$	−79.8494	−2.61555
$933$	60.3248	1.97495
$934$	14.7049	0.481160
$935$	15.1762	0.496316
$936$	81.2708	2.65642
$937$	14.5703	0.475991	0.237996	−	0.971266i	$-0.423510\pi$
$937$	14.5703	0.475991	0.237996	+	0.971266i	$0.423510\pi$
$938$	14.5048	0.473598
$939$	67.7035	2.20942
$940$	−216.087	−7.04797
$941$	−20.0808	−0.654617	−0.327308	−	0.944918i	$-0.606142\pi$
$941$	−20.0808	−0.654617	−0.327308	+	0.944918i	$0.606142\pi$
$942$	−37.3316	−1.21633
$943$	19.0441	0.620162
$944$	92.1016	2.99765
$945$	−215.011	−6.99431
$946$	22.3293	0.725988
$947$	−9.41814	−0.306048	−0.153024	−	0.988222i	$-0.548901\pi$
$947$	−9.41814	−0.306048	−0.153024	+	0.988222i	$0.548901\pi$
$948$	118.034	3.83357
$949$	9.25024	0.300275
$950$	−288.045	−9.34543
$951$	−15.0453	−0.487876
$952$	40.7082	1.31936
$953$	−55.6882	−1.80392	−0.901958	−	0.431824i	$-0.857870\pi$
$953$	−55.6882	−1.80392	−0.901958	+	0.431824i	$0.857870\pi$
$954$	−1.31572	−0.0425980
$955$	−40.4329	−1.30838
$956$	−62.3488	−2.01651
$957$	−28.8900	−0.933883
$958$	15.9827	0.516377
$959$	20.1203	0.649719
$960$	−22.9948	−0.742155
$961$	−2.31229	−0.0745900
$962$	22.6940	0.731685
$963$	54.7284	1.76360
$964$	0.752028	0.0242212
$965$	−63.3934	−2.04071
$966$	111.866	3.59921
$967$	33.6991	1.08369	0.541846	−	0.840478i	$-0.317726\pi$
$967$	33.6991	1.08369	0.541846	+	0.840478i	$0.317726\pi$
$968$	60.7906	1.95389
$969$	−71.7741	−2.30572
$970$	34.4589	1.10641
$971$	20.4133	0.655095	0.327548	−	0.944835i	$-0.393778\pi$
$971$	20.4133	0.655095	0.327548	+	0.944835i	$0.393778\pi$
$972$	424.865	13.6275
$973$	−29.2902	−0.939001
$974$	−77.3322	−2.47788
$975$	−67.6246	−2.16572
$976$	46.3881	1.48485
$977$	13.7951	0.441345	0.220672	−	0.975348i	$-0.429175\pi$
$977$	13.7951	0.441345	0.220672	+	0.975348i	$0.429175\pi$
$978$	−54.8665	−1.75444
$979$	14.7542	0.471548
$980$	28.0463	0.895907
$981$	64.0082	2.04363
$982$	96.9210	3.09287
$983$	−16.8083	−0.536102	−0.268051	−	0.963405i	$-0.586380\pi$
$983$	−16.8083	−0.536102	−0.268051	+	0.963405i	$0.586380\pi$
$984$	81.3253	2.59255
$985$	−38.4849	−1.22623
$986$	−42.2994	−1.34709
$987$	88.5048	2.81714
$988$	−49.7188	−1.58176
$989$	35.1023	1.11619
$990$	133.531	4.24389
$991$	4.94826	0.157187	0.0785933	−	0.996907i	$-0.474957\pi$
$991$	4.94826	0.157187	0.0785933	+	0.996907i	$0.474957\pi$
$992$	35.4009	1.12398
$993$	−81.0333	−2.57151
$994$	−34.6131	−1.09786
$995$	88.8778	2.81761
$996$	174.226	5.52055
$997$	0.894892	0.0283415	0.0141708	−	0.999900i	$-0.495489\pi$
$997$	0.894892	0.0283415	0.0141708	+	0.999900i	$0.495489\pi$
$998$	−62.5030	−1.97850
$999$	133.551	4.22537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.18	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.18	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56224 q^{2} +3.46263 q^{3} +4.56507 q^{4} -4.38158 q^{5} -8.87209 q^{6} +2.36597 q^{7} -6.57231 q^{8} +8.98983 q^{9} +O(q^{10})\)	\(q-2.56224 q^{2} +3.46263 q^{3} +4.56507 q^{4} -4.38158 q^{5} -8.87209 q^{6} +2.36597 q^{7} -6.57231 q^{8} +8.98983 q^{9} +11.2266 q^{10} +1.32306 q^{11} +15.8071 q^{12} -1.37551 q^{13} -6.06219 q^{14} -15.1718 q^{15} +7.70970 q^{16} -2.61790 q^{17} -23.0341 q^{18} +7.91786 q^{19} -20.0022 q^{20} +8.19250 q^{21} -3.39000 q^{22} -5.32918 q^{23} -22.7575 q^{24} +14.1982 q^{25} +3.52440 q^{26} +20.7406 q^{27} +10.8008 q^{28} -6.30611 q^{29} +38.8737 q^{30} -5.35609 q^{31} -6.60947 q^{32} +4.58128 q^{33} +6.70769 q^{34} -10.3667 q^{35} +41.0392 q^{36} +6.43913 q^{37} -20.2875 q^{38} -4.76290 q^{39} +28.7971 q^{40} -3.57356 q^{41} -20.9911 q^{42} -6.58681 q^{43} +6.03987 q^{44} -39.3896 q^{45} +13.6546 q^{46} +10.8031 q^{47} +26.6959 q^{48} -1.40216 q^{49} -36.3792 q^{50} -9.06483 q^{51} -6.27931 q^{52} +0.0571206 q^{53} -53.1423 q^{54} -5.79710 q^{55} -15.5499 q^{56} +27.4167 q^{57} +16.1577 q^{58} +11.9462 q^{59} -69.2602 q^{60} +6.01684 q^{61} +13.7236 q^{62} +21.2697 q^{63} +1.51563 q^{64} +6.02692 q^{65} -11.7383 q^{66} -2.39266 q^{67} -11.9509 q^{68} -18.4530 q^{69} +26.5620 q^{70} +5.70967 q^{71} -59.0839 q^{72} -6.72493 q^{73} -16.4986 q^{74} +49.1632 q^{75} +36.1456 q^{76} +3.13033 q^{77} +12.2037 q^{78} +7.46714 q^{79} -33.7806 q^{80} +44.8475 q^{81} +9.15631 q^{82} +11.0220 q^{83} +37.3993 q^{84} +11.4705 q^{85} +16.8770 q^{86} -21.8357 q^{87} -8.69558 q^{88} +11.1516 q^{89} +100.926 q^{90} -3.25443 q^{91} -24.3281 q^{92} -18.5462 q^{93} -27.6802 q^{94} -34.6927 q^{95} -22.8862 q^{96} +3.06939 q^{97} +3.59268 q^{98} +11.8941 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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