LMFDB - Embedded newform 6047.2.a.b.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.58121 q^{2} +2.05935 q^{3} +4.66263 q^{4} -2.01171 q^{5} -5.31560 q^{6} -0.352944 q^{7} -6.87281 q^{8} +1.24091 q^{9} +O(q^{10})$	\(q-2.58121 q^{2} +2.05935 q^{3} +4.66263 q^{4} -2.01171 q^{5} -5.31560 q^{6} -0.352944 q^{7} -6.87281 q^{8} +1.24091 q^{9} +5.19265 q^{10} -6.09554 q^{11} +9.60198 q^{12} +6.44647 q^{13} +0.911021 q^{14} -4.14281 q^{15} +8.41489 q^{16} +4.71560 q^{17} -3.20305 q^{18} +1.24882 q^{19} -9.37988 q^{20} -0.726833 q^{21} +15.7339 q^{22} -9.09118 q^{23} -14.1535 q^{24} -0.953015 q^{25} -16.6397 q^{26} -3.62257 q^{27} -1.64565 q^{28} -2.93437 q^{29} +10.6935 q^{30} -4.54028 q^{31} -7.97496 q^{32} -12.5528 q^{33} -12.1719 q^{34} +0.710021 q^{35} +5.78592 q^{36} +6.38811 q^{37} -3.22346 q^{38} +13.2755 q^{39} +13.8261 q^{40} +10.3564 q^{41} +1.87611 q^{42} -1.14497 q^{43} -28.4213 q^{44} -2.49636 q^{45} +23.4662 q^{46} -4.58186 q^{47} +17.3292 q^{48} -6.87543 q^{49} +2.45993 q^{50} +9.71106 q^{51} +30.0575 q^{52} -3.02120 q^{53} +9.35061 q^{54} +12.2625 q^{55} +2.42572 q^{56} +2.57175 q^{57} +7.57421 q^{58} +9.66534 q^{59} -19.3164 q^{60} -0.163747 q^{61} +11.7194 q^{62} -0.437972 q^{63} +3.75524 q^{64} -12.9684 q^{65} +32.4015 q^{66} +10.4811 q^{67} +21.9871 q^{68} -18.7219 q^{69} -1.83271 q^{70} +6.01369 q^{71} -8.52856 q^{72} +11.2145 q^{73} -16.4890 q^{74} -1.96259 q^{75} +5.82278 q^{76} +2.15138 q^{77} -34.2669 q^{78} +2.36568 q^{79} -16.9283 q^{80} -11.1829 q^{81} -26.7320 q^{82} -11.1472 q^{83} -3.38896 q^{84} -9.48643 q^{85} +2.95540 q^{86} -6.04288 q^{87} +41.8935 q^{88} +1.38550 q^{89} +6.44362 q^{90} -2.27524 q^{91} -42.3888 q^{92} -9.35002 q^{93} +11.8267 q^{94} -2.51226 q^{95} -16.4232 q^{96} -7.21764 q^{97} +17.7469 q^{98} -7.56403 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58121	−1.82519	−0.912595	−	0.408865i	$-0.865925\pi$
$2$	−2.58121	−1.82519	−0.912595	+	0.408865i	$0.865925\pi$
$3$	2.05935	1.18896	0.594482	−	0.804109i	$-0.297357\pi$
$3$	2.05935	1.18896	0.594482	+	0.804109i	$0.297357\pi$
$4$	4.66263	2.33132
$5$	−2.01171	−0.899665	−0.449832	−	0.893113i	$-0.648516\pi$
$5$	−2.01171	−0.899665	−0.449832	+	0.893113i	$0.648516\pi$
$6$	−5.31560	−2.17009
$7$	−0.352944	−0.133400	−0.0667001	−	0.997773i	$-0.521247\pi$
$7$	−0.352944	−0.133400	−0.0667001	+	0.997773i	$0.521247\pi$
$8$	−6.87281	−2.42991
$9$	1.24091	0.413637
$10$	5.19265	1.64206
$11$	−6.09554	−1.83788	−0.918938	−	0.394403i	$-0.870951\pi$
$11$	−6.09554	−1.83788	−0.918938	+	0.394403i	$0.870951\pi$
$12$	9.60198	2.77185
$13$	6.44647	1.78793	0.893965	−	0.448137i	$-0.147912\pi$
$13$	6.44647	1.78793	0.893965	+	0.448137i	$0.147912\pi$
$14$	0.911021	0.243481
$15$	−4.14281	−1.06967
$16$	8.41489	2.10372
$17$	4.71560	1.14370	0.571850	−	0.820358i	$-0.306226\pi$
$17$	4.71560	1.14370	0.571850	+	0.820358i	$0.306226\pi$
$18$	−3.20305	−0.754967
$19$	1.24882	0.286499	0.143249	−	0.989687i	$-0.454245\pi$
$19$	1.24882	0.286499	0.143249	+	0.989687i	$0.454245\pi$
$20$	−9.37988	−2.09740
$21$	−0.726833	−0.158608
$22$	15.7339	3.35447
$23$	−9.09118	−1.89564	−0.947821	−	0.318804i	$-0.896719\pi$
$23$	−9.09118	−1.89564	−0.947821	+	0.318804i	$0.896719\pi$
$24$	−14.1535	−2.88907
$25$	−0.953015	−0.190603
$26$	−16.6397	−3.26331
$27$	−3.62257	−0.697164
$28$	−1.64565	−0.310998
$29$	−2.93437	−0.544898	−0.272449	−	0.962170i	$-0.587834\pi$
$29$	−2.93437	−0.544898	−0.272449	+	0.962170i	$0.587834\pi$
$30$	10.6935	1.95235
$31$	−4.54028	−0.815459	−0.407729	−	0.913103i	$-0.633679\pi$
$31$	−4.54028	−0.815459	−0.407729	+	0.913103i	$0.633679\pi$
$32$	−7.97496	−1.40979
$33$	−12.5528	−2.18517
$34$	−12.1719	−2.08747
$35$	0.710021	0.120015
$36$	5.78592	0.964320
$37$	6.38811	1.05020	0.525099	−	0.851041i	$-0.324028\pi$
$37$	6.38811	1.05020	0.525099	+	0.851041i	$0.324028\pi$
$38$	−3.22346	−0.522914
$39$	13.2755	2.12579
$40$	13.8261	2.18610
$41$	10.3564	1.61740	0.808698	−	0.588225i	$-0.200173\pi$
$41$	10.3564	1.61740	0.808698	+	0.588225i	$0.200173\pi$
$42$	1.87611	0.289490
$43$	−1.14497	−0.174606	−0.0873030	−	0.996182i	$-0.527825\pi$
$43$	−1.14497	−0.174606	−0.0873030	+	0.996182i	$0.527825\pi$
$44$	−28.4213	−4.28467
$45$	−2.49636	−0.372135
$46$	23.4662	3.45991
$47$	−4.58186	−0.668333	−0.334166	−	0.942514i	$-0.608455\pi$
$47$	−4.58186	−0.668333	−0.334166	+	0.942514i	$0.608455\pi$
$48$	17.3292	2.50125
$49$	−6.87543	−0.982204
$50$	2.45993	0.347887
$51$	9.71106	1.35982
$52$	30.0575	4.16823
$53$	−3.02120	−0.414994	−0.207497	−	0.978236i	$-0.566532\pi$
$53$	−3.02120	−0.414994	−0.207497	+	0.978236i	$0.566532\pi$
$54$	9.35061	1.27246
$55$	12.2625	1.65347
$56$	2.42572	0.324150
$57$	2.57175	0.340637
$58$	7.57421	0.994543
$59$	9.66534	1.25832	0.629160	−	0.777276i	$-0.283399\pi$
$59$	9.66534	1.25832	0.629160	+	0.777276i	$0.283399\pi$
$60$	−19.3164	−2.49374
$61$	−0.163747	−0.0209656	−0.0104828	−	0.999945i	$-0.503337\pi$
$61$	−0.163747	−0.0209656	−0.0104828	+	0.999945i	$0.503337\pi$
$62$	11.7194	1.48837
$63$	−0.437972	−0.0551793
$64$	3.75524	0.469405
$65$	−12.9684	−1.60854
$66$	32.4015	3.98835
$67$	10.4811	1.28048	0.640238	−	0.768177i	$-0.278836\pi$
$67$	10.4811	1.28048	0.640238	+	0.768177i	$0.278836\pi$
$68$	21.9871	2.66633
$69$	−18.7219	−2.25385
$70$	−1.83271	−0.219051
$71$	6.01369	0.713694	0.356847	−	0.934163i	$-0.383852\pi$
$71$	6.01369	0.713694	0.356847	+	0.934163i	$0.383852\pi$
$72$	−8.52856	−1.00510
$73$	11.2145	1.31256	0.656278	−	0.754519i	$-0.272130\pi$
$73$	11.2145	1.31256	0.656278	+	0.754519i	$0.272130\pi$
$74$	−16.4890	−1.91681
$75$	−1.96259	−0.226620
$76$	5.82278	0.667919
$77$	2.15138	0.245173
$78$	−34.2669	−3.87996
$79$	2.36568	0.266160	0.133080	−	0.991105i	$-0.457513\pi$
$79$	2.36568	0.266160	0.133080	+	0.991105i	$0.457513\pi$
$80$	−16.9283	−1.89265
$81$	−11.1829	−1.24254
$82$	−26.7320	−2.95205
$83$	−11.1472	−1.22356	−0.611782	−	0.791027i	$-0.709547\pi$
$83$	−11.1472	−1.22356	−0.611782	+	0.791027i	$0.709547\pi$
$84$	−3.38896	−0.369766
$85$	−9.48643	−1.02895
$86$	2.95540	0.318689
$87$	−6.04288	−0.647865
$88$	41.8935	4.46586
$89$	1.38550	0.146863	0.0734315	−	0.997300i	$-0.476605\pi$
$89$	1.38550	0.146863	0.0734315	+	0.997300i	$0.476605\pi$
$90$	6.44362	0.679217
$91$	−2.27524	−0.238510
$92$	−42.3888	−4.41934
$93$	−9.35002	−0.969552
$94$	11.8267	1.21983
$95$	−2.51226	−0.257753
$96$	−16.4232	−1.67619
$97$	−7.21764	−0.732840	−0.366420	−	0.930449i	$-0.619417\pi$
$97$	−7.21764	−0.732840	−0.366420	+	0.930449i	$0.619417\pi$
$98$	17.7469	1.79271
$99$	−7.56403	−0.760214
$100$	−4.44356	−0.444356
$101$	15.5840	1.55066	0.775332	−	0.631554i	$-0.217583\pi$
$101$	15.5840	1.55066	0.775332	+	0.631554i	$0.217583\pi$
$102$	−25.0663	−2.48193
$103$	−12.9650	−1.27748	−0.638739	−	0.769423i	$-0.720544\pi$
$103$	−12.9650	−1.27748	−0.638739	+	0.769423i	$0.720544\pi$
$104$	−44.3054	−4.34450
$105$	1.46218	0.142694
$106$	7.79835	0.757443
$107$	−10.8054	−1.04460	−0.522301	−	0.852761i	$-0.674926\pi$
$107$	−10.8054	−1.04460	−0.522301	+	0.852761i	$0.674926\pi$
$108$	−16.8907	−1.62531
$109$	1.36652	0.130889	0.0654444	−	0.997856i	$-0.479153\pi$
$109$	1.36652	0.130889	0.0654444	+	0.997856i	$0.479153\pi$
$110$	−31.6520	−3.01790
$111$	13.1553	1.24865
$112$	−2.96998	−0.280637
$113$	10.5426	0.991764	0.495882	−	0.868390i	$-0.334845\pi$
$113$	10.5426	0.991764	0.495882	+	0.868390i	$0.334845\pi$
$114$	−6.63822	−0.621727
$115$	18.2888	1.70544
$116$	−13.6819	−1.27033
$117$	7.99951	0.739555
$118$	−24.9483	−2.29667
$119$	−1.66434	−0.152570
$120$	28.4728	2.59920
$121$	26.1556	2.37779
$122$	0.422664	0.0382662
$123$	21.3274	1.92303
$124$	−21.1697	−1.90109
$125$	11.9758	1.07114
$126$	1.13050	0.100713
$127$	4.11486	0.365135	0.182567	−	0.983193i	$-0.441559\pi$
$127$	4.11486	0.365135	0.182567	+	0.983193i	$0.441559\pi$
$128$	6.25686	0.553033
$129$	−2.35789	−0.207600
$130$	33.4742	2.93589
$131$	−6.75716	−0.590375	−0.295188	−	0.955439i	$-0.595382\pi$
$131$	−6.75716	−0.590375	−0.295188	+	0.955439i	$0.595382\pi$
$132$	−58.5293	−5.09432
$133$	−0.440762	−0.0382189
$134$	−27.0540	−2.33711
$135$	7.28757	0.627214
$136$	−32.4094	−2.77909
$137$	−11.8858	−1.01548	−0.507738	−	0.861511i	$-0.669518\pi$
$137$	−11.8858	−1.01548	−0.507738	+	0.861511i	$0.669518\pi$
$138$	48.3251	4.11371
$139$	11.1417	0.945026	0.472513	−	0.881324i	$-0.343347\pi$
$139$	11.1417	0.945026	0.472513	+	0.881324i	$0.343347\pi$
$140$	3.31057	0.279794
$141$	−9.43564	−0.794624
$142$	−15.5226	−1.30263
$143$	−39.2947	−3.28599
$144$	10.4421	0.870179
$145$	5.90310	0.490226
$146$	−28.9469	−2.39566
$147$	−14.1589	−1.16781
$148$	29.7854	2.44835
$149$	11.2806	0.924145	0.462073	−	0.886842i	$-0.347106\pi$
$149$	11.2806	0.924145	0.462073	+	0.886842i	$0.347106\pi$
$150$	5.06585	0.413625
$151$	19.7375	1.60621	0.803107	−	0.595835i	$-0.203179\pi$
$151$	19.7375	1.60621	0.803107	+	0.595835i	$0.203179\pi$
$152$	−8.58290	−0.696165
$153$	5.85165	0.473078
$154$	−5.55317	−0.447487
$155$	9.13374	0.733640
$156$	61.8989	4.95588
$157$	−21.1538	−1.68826	−0.844128	−	0.536141i	$-0.819881\pi$
$157$	−21.1538	−1.68826	−0.844128	+	0.536141i	$0.819881\pi$
$158$	−6.10631	−0.485792
$159$	−6.22171	−0.493413
$160$	16.0433	1.26834
$161$	3.20867	0.252879
$162$	28.8653	2.26787
$163$	7.08183	0.554692	0.277346	−	0.960770i	$-0.410545\pi$
$163$	7.08183	0.554692	0.277346	+	0.960770i	$0.410545\pi$
$164$	48.2880	3.77066
$165$	25.2527	1.96592
$166$	28.7732	2.23323
$167$	12.7180	0.984147	0.492073	−	0.870554i	$-0.336239\pi$
$167$	12.7180	0.984147	0.492073	+	0.870554i	$0.336239\pi$
$168$	4.99539	0.385403
$169$	28.5570	2.19669
$170$	24.4864	1.87802
$171$	1.54967	0.118507
$172$	−5.33857	−0.407062
$173$	7.77715	0.591286	0.295643	−	0.955299i	$-0.404466\pi$
$173$	7.77715	0.591286	0.295643	+	0.955299i	$0.404466\pi$
$174$	15.5979	1.18248
$175$	0.336361	0.0254265
$176$	−51.2933	−3.86638
$177$	19.9043	1.49610
$178$	−3.57627	−0.268053
$179$	9.77398	0.730541	0.365271	−	0.930901i	$-0.380976\pi$
$179$	9.77398	0.730541	0.365271	+	0.930901i	$0.380976\pi$
$180$	−11.6396	−0.867565
$181$	−15.0176	−1.11625	−0.558125	−	0.829757i	$-0.688479\pi$
$181$	−15.0176	−1.11625	−0.558125	+	0.829757i	$0.688479\pi$
$182$	5.87287	0.435326
$183$	−0.337211	−0.0249274
$184$	62.4820	4.60623
$185$	−12.8510	−0.944826
$186$	24.1343	1.76962
$187$	−28.7441	−2.10198
$188$	−21.3635	−1.55810
$189$	1.27856	0.0930018
$190$	6.48467	0.470448
$191$	−8.02614	−0.580751	−0.290376	−	0.956913i	$-0.593780\pi$
$191$	−8.02614	−0.580751	−0.290376	+	0.956913i	$0.593780\pi$
$192$	7.73335	0.558106
$193$	−13.3470	−0.960734	−0.480367	−	0.877067i	$-0.659497\pi$
$193$	−13.3470	−0.960734	−0.480367	+	0.877067i	$0.659497\pi$
$194$	18.6302	1.33757
$195$	−26.7065	−1.91249
$196$	−32.0576	−2.28983
$197$	−7.33395	−0.522522	−0.261261	−	0.965268i	$-0.584138\pi$
$197$	−7.33395	−0.522522	−0.261261	+	0.965268i	$0.584138\pi$
$198$	19.5243	1.38753
$199$	−19.0883	−1.35313	−0.676567	−	0.736381i	$-0.736533\pi$
$199$	−19.0883	−1.35313	−0.676567	+	0.736381i	$0.736533\pi$
$200$	6.54990	0.463148
$201$	21.5843	1.52244
$202$	−40.2255	−2.83026
$203$	1.03567	0.0726895
$204$	45.2791	3.17017
$205$	−20.8341	−1.45511
$206$	33.4653	2.33164
$207$	−11.2814	−0.784108
$208$	54.2464	3.76131
$209$	−7.61223	−0.526549
$210$	−3.77419	−0.260444
$211$	12.5315	0.862704	0.431352	−	0.902184i	$-0.358037\pi$
$211$	12.5315	0.862704	0.431352	+	0.902184i	$0.358037\pi$
$212$	−14.0868	−0.967483
$213$	12.3843	0.848557
$214$	27.8911	1.90660
$215$	2.30335	0.157087
$216$	24.8973	1.69404
$217$	1.60246	0.108782
$218$	−3.52727	−0.238897
$219$	23.0945	1.56058
$220$	57.1754	3.85477
$221$	30.3990	2.04486
$222$	−33.9566	−2.27902
$223$	21.1393	1.41559	0.707796	−	0.706417i	$-0.249690\pi$
$223$	21.1393	1.41559	0.707796	+	0.706417i	$0.249690\pi$
$224$	2.81471	0.188066
$225$	−1.18261	−0.0788406
$226$	−27.2126	−1.81016
$227$	−13.2052	−0.876462	−0.438231	−	0.898862i	$-0.644395\pi$
$227$	−13.2052	−0.876462	−0.438231	+	0.898862i	$0.644395\pi$
$228$	11.9911	0.794132
$229$	−21.3603	−1.41153	−0.705763	−	0.708448i	$-0.749396\pi$
$229$	−21.3603	−1.41153	−0.705763	+	0.708448i	$0.749396\pi$
$230$	−47.2073	−3.11276
$231$	4.43044	0.291502
$232$	20.1674	1.32405
$233$	14.8917	0.975589	0.487795	−	0.872958i	$-0.337801\pi$
$233$	14.8917	0.975589	0.487795	+	0.872958i	$0.337801\pi$
$234$	−20.6484	−1.34983
$235$	9.21738	0.601276
$236$	45.0660	2.93354
$237$	4.87176	0.316455
$238$	4.29601	0.278469
$239$	9.72610	0.629129	0.314565	−	0.949236i	$-0.398141\pi$
$239$	9.72610	0.629129	0.314565	+	0.949236i	$0.398141\pi$
$240$	−34.8613	−2.25029
$241$	15.5418	1.00114	0.500569	−	0.865697i	$-0.333124\pi$
$241$	15.5418	1.00114	0.500569	+	0.865697i	$0.333124\pi$
$242$	−67.5131	−4.33991
$243$	−12.1617	−0.780174
$244$	−0.763491	−0.0488775
$245$	13.8314	0.883655
$246$	−55.0504	−3.50989
$247$	8.05047	0.512239
$248$	31.2045	1.98149
$249$	−22.9559	−1.45477
$250$	−30.9119	−1.95504
$251$	−13.2305	−0.835104	−0.417552	−	0.908653i	$-0.637112\pi$
$251$	−13.2305	−0.835104	−0.417552	+	0.908653i	$0.637112\pi$
$252$	−2.04210	−0.128640
$253$	55.4157	3.48395
$254$	−10.6213	−0.666441
$255$	−19.5358	−1.22338
$256$	−23.6607	−1.47880
$257$	15.7668	0.983506	0.491753	−	0.870735i	$-0.336356\pi$
$257$	15.7668	0.983506	0.491753	+	0.870735i	$0.336356\pi$
$258$	6.08620	0.378910
$259$	−2.25464	−0.140097
$260$	−60.4671	−3.75001
$261$	−3.64129	−0.225390
$262$	17.4416	1.07755
$263$	10.7173	0.660860	0.330430	−	0.943831i	$-0.392806\pi$
$263$	10.7173	0.660860	0.330430	+	0.943831i	$0.392806\pi$
$264$	86.2733	5.30976
$265$	6.07779	0.373356
$266$	1.13770	0.0697568
$267$	2.85323	0.174615
$268$	48.8697	2.98519
$269$	28.7451	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$269$	28.7451	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$270$	−18.8107	−1.14479
$271$	−18.4227	−1.11910	−0.559550	−	0.828796i	$-0.689026\pi$
$271$	−18.4227	−1.11910	−0.559550	+	0.828796i	$0.689026\pi$
$272$	39.6813	2.40603
$273$	−4.68551	−0.283580
$274$	30.6798	1.85344
$275$	5.80915	0.350305
$276$	−87.2933	−5.25444
$277$	28.2619	1.69809	0.849047	−	0.528317i	$-0.177177\pi$
$277$	28.2619	1.69809	0.849047	+	0.528317i	$0.177177\pi$
$278$	−28.7590	−1.72485
$279$	−5.63409	−0.337304
$280$	−4.87984	−0.291626
$281$	−1.58808	−0.0947367	−0.0473683	−	0.998877i	$-0.515083\pi$
$281$	−1.58808	−0.0947367	−0.0473683	+	0.998877i	$0.515083\pi$
$282$	24.3553	1.45034
$283$	0.0755594	0.00449154	0.00224577	−	0.999997i	$-0.499285\pi$
$283$	0.0755594	0.00449154	0.00224577	+	0.999997i	$0.499285\pi$
$284$	28.0397	1.66385
$285$	−5.17362	−0.306459
$286$	101.428	5.99756
$287$	−3.65522	−0.215761
$288$	−9.89622	−0.583141
$289$	5.23688	0.308051
$290$	−15.2371	−0.894755
$291$	−14.8636	−0.871322
$292$	52.2890	3.05998
$293$	26.4573	1.54565	0.772827	−	0.634616i	$-0.218842\pi$
$293$	26.4573	1.54565	0.772827	+	0.634616i	$0.218842\pi$
$294$	36.5471	2.13147
$295$	−19.4439	−1.13207
$296$	−43.9043	−2.55188
$297$	22.0815	1.28130
$298$	−29.1177	−1.68674
$299$	−58.6060	−3.38927
$300$	−9.15084	−0.528324
$301$	0.404109	0.0232925
$302$	−50.9465	−2.93164
$303$	32.0928	1.84368
$304$	10.5087	0.602714
$305$	0.329411	0.0188620
$306$	−15.1043	−0.863456
$307$	−7.63804	−0.435926	−0.217963	−	0.975957i	$-0.569941\pi$
$307$	−7.63804	−0.435926	−0.217963	+	0.975957i	$0.569941\pi$
$308$	10.0311	0.571576
$309$	−26.6994	−1.51888
$310$	−23.5761	−1.33903
$311$	7.65129	0.433865	0.216932	−	0.976187i	$-0.430395\pi$
$311$	7.65129	0.433865	0.216932	+	0.976187i	$0.430395\pi$
$312$	−91.2402	−5.16546
$313$	17.3225	0.979123	0.489561	−	0.871969i	$-0.337157\pi$
$313$	17.3225	0.979123	0.489561	+	0.871969i	$0.337157\pi$
$314$	54.6023	3.08139
$315$	0.881074	0.0496429
$316$	11.0303	0.620503
$317$	10.8533	0.609582	0.304791	−	0.952419i	$-0.401413\pi$
$317$	10.8533	0.609582	0.304791	+	0.952419i	$0.401413\pi$
$318$	16.0595	0.900573
$319$	17.8866	1.00145
$320$	−7.55446	−0.422307
$321$	−22.2522	−1.24200
$322$	−8.28225	−0.461552
$323$	5.88893	0.327669
$324$	−52.1417	−2.89676
$325$	−6.14359	−0.340785
$326$	−18.2797	−1.01242
$327$	2.81414	0.155622
$328$	−71.1775	−3.93012
$329$	1.61714	0.0891557
$330$	−65.1825	−3.58818
$331$	20.3490	1.11848	0.559242	−	0.829004i	$-0.311092\pi$
$331$	20.3490	1.11848	0.559242	+	0.829004i	$0.311092\pi$
$332$	−51.9753	−2.85251
$333$	7.92708	0.434401
$334$	−32.8278	−1.79625
$335$	−21.0850	−1.15200
$336$	−6.11622	−0.333667
$337$	10.1235	0.551463	0.275731	−	0.961235i	$-0.411080\pi$
$337$	10.1235	0.551463	0.275731	+	0.961235i	$0.411080\pi$
$338$	−73.7115	−4.00938
$339$	21.7109	1.17917
$340$	−44.2317	−2.39880
$341$	27.6755	1.49871
$342$	−4.00003	−0.216297
$343$	4.89724	0.264426
$344$	7.86915	0.424276
$345$	37.6631	2.02771
$346$	−20.0744	−1.07921
$347$	30.9631	1.66219	0.831094	−	0.556132i	$-0.187715\pi$
$347$	30.9631	1.66219	0.831094	+	0.556132i	$0.187715\pi$
$348$	−28.1757	−1.51038
$349$	36.5075	1.95420	0.977100	−	0.212781i	$-0.0682520\pi$
$349$	36.5075	1.95420	0.977100	+	0.212781i	$0.0682520\pi$
$350$	−0.868217	−0.0464081
$351$	−23.3528	−1.24648
$352$	48.6117	2.59101
$353$	9.48373	0.504768	0.252384	−	0.967627i	$-0.418785\pi$
$353$	9.48373	0.504768	0.252384	+	0.967627i	$0.418785\pi$
$354$	−51.3771	−2.73066
$355$	−12.0978	−0.642086
$356$	6.46009	0.342384
$357$	−3.42746	−0.181400
$358$	−25.2287	−1.33338
$359$	−25.7848	−1.36087	−0.680435	−	0.732809i	$-0.738209\pi$
$359$	−25.7848	−1.36087	−0.680435	+	0.732809i	$0.738209\pi$
$360$	17.1570	0.904253
$361$	−17.4405	−0.917919
$362$	38.7636	2.03737
$363$	53.8635	2.82710
$364$	−10.6086	−0.556042
$365$	−22.5603	−1.18086
$366$	0.870412	0.0454972
$367$	3.13849	0.163828	0.0819139	−	0.996639i	$-0.473897\pi$
$367$	3.13849	0.163828	0.0819139	+	0.996639i	$0.473897\pi$
$368$	−76.5013	−3.98790
$369$	12.8514	0.669015
$370$	33.1712	1.72449
$371$	1.06631	0.0553603
$372$	−43.5957	−2.26033
$373$	−15.3914	−0.796935	−0.398468	−	0.917182i	$-0.630458\pi$
$373$	−15.3914	−0.796935	−0.398468	+	0.917182i	$0.630458\pi$
$374$	74.1946	3.83651
$375$	24.6622	1.27355
$376$	31.4903	1.62399
$377$	−18.9163	−0.974240
$378$	−3.30024	−0.169746
$379$	−12.4094	−0.637426	−0.318713	−	0.947851i	$-0.603251\pi$
$379$	−12.4094	−0.637426	−0.318713	+	0.947851i	$0.603251\pi$
$380$	−11.7138	−0.600903
$381$	8.47393	0.434133
$382$	20.7171	1.05998
$383$	−13.9477	−0.712695	−0.356347	−	0.934354i	$-0.615978\pi$
$383$	−13.9477	−0.712695	−0.356347	+	0.934354i	$0.615978\pi$
$384$	12.8850	0.657537
$385$	−4.32796	−0.220573
$386$	34.4513	1.75352
$387$	−1.42081	−0.0722236
$388$	−33.6532	−1.70848
$389$	−20.9977	−1.06463	−0.532314	−	0.846547i	$-0.678677\pi$
$389$	−20.9977	−1.06463	−0.532314	+	0.846547i	$0.678677\pi$
$390$	68.9351	3.49066
$391$	−42.8703	−2.16805
$392$	47.2536	2.38666
$393$	−13.9153	−0.701936
$394$	18.9304	0.953702
$395$	−4.75907	−0.239455
$396$	−35.2683	−1.77230
$397$	−34.9798	−1.75558	−0.877792	−	0.479042i	$-0.840984\pi$
$397$	−34.9798	−1.75558	−0.877792	+	0.479042i	$0.840984\pi$
$398$	49.2709	2.46973
$399$	−0.907683	−0.0454410
$400$	−8.01952	−0.400976
$401$	31.6291	1.57948	0.789741	−	0.613440i	$-0.210215\pi$
$401$	31.6291	1.57948	0.789741	+	0.613440i	$0.210215\pi$
$402$	−55.7136	−2.77874
$403$	−29.2688	−1.45798
$404$	72.6624	3.61509
$405$	22.4967	1.11787
$406$	−2.67327	−0.132672
$407$	−38.9390	−1.93013
$408$	−66.7423	−3.30424
$409$	24.7353	1.22308	0.611541	−	0.791213i	$-0.290550\pi$
$409$	24.7353	1.22308	0.611541	+	0.791213i	$0.290550\pi$
$410$	53.7770	2.65586
$411$	−24.4771	−1.20737
$412$	−60.4510	−2.97821
$413$	−3.41132	−0.167860
$414$	29.1195	1.43115
$415$	22.4249	1.10080
$416$	−51.4103	−2.52060
$417$	22.9446	1.12360
$418$	19.6487	0.961051
$419$	−7.51631	−0.367196	−0.183598	−	0.983001i	$-0.558774\pi$
$419$	−7.51631	−0.367196	−0.183598	+	0.983001i	$0.558774\pi$
$420$	6.81761	0.332665
$421$	22.0206	1.07322	0.536610	−	0.843831i	$-0.319705\pi$
$421$	22.0206	1.07322	0.536610	+	0.843831i	$0.319705\pi$
$422$	−32.3464	−1.57460
$423$	−5.68569	−0.276447
$424$	20.7642	1.00840
$425$	−4.49404	−0.217993
$426$	−31.9664	−1.54878
$427$	0.0577933	0.00279682
$428$	−50.3818	−2.43530
$429$	−80.9215	−3.90693
$430$	−5.94542	−0.286713
$431$	−28.0800	−1.35257	−0.676283	−	0.736642i	$-0.736410\pi$
$431$	−28.0800	−1.35257	−0.676283	+	0.736642i	$0.736410\pi$
$432$	−30.4836	−1.46664
$433$	−1.01096	−0.0485837	−0.0242918	−	0.999705i	$-0.507733\pi$
$433$	−1.01096	−0.0485837	−0.0242918	+	0.999705i	$0.507733\pi$
$434$	−4.13629	−0.198548
$435$	12.1565	0.582861
$436$	6.37158	0.305143
$437$	−11.3532	−0.543099
$438$	−59.6117	−2.84836
$439$	−14.0909	−0.672522	−0.336261	−	0.941769i	$-0.609162\pi$
$439$	−14.0909	−0.672522	−0.336261	+	0.941769i	$0.609162\pi$
$440$	−84.2777	−4.01778
$441$	−8.53181	−0.406277
$442$	−78.4661	−3.73225
$443$	−27.6521	−1.31379	−0.656894	−	0.753983i	$-0.728130\pi$
$443$	−27.6521	−1.31379	−0.656894	+	0.753983i	$0.728130\pi$
$444$	61.3385	2.91100
$445$	−2.78723	−0.132128
$446$	−54.5649	−2.58372
$447$	23.2307	1.09878
$448$	−1.32539	−0.0626187
$449$	14.6692	0.692281	0.346140	−	0.938183i	$-0.387492\pi$
$449$	14.6692	0.692281	0.346140	+	0.938183i	$0.387492\pi$
$450$	3.05256	0.143899
$451$	−63.1278	−2.97257
$452$	49.1563	2.31212
$453$	40.6463	1.90973
$454$	34.0854	1.59971
$455$	4.57713	0.214579
$456$	−17.6752	−0.827715
$457$	−19.4828	−0.911368	−0.455684	−	0.890141i	$-0.650605\pi$
$457$	−19.4828	−0.911368	−0.455684	+	0.890141i	$0.650605\pi$
$458$	55.1353	2.57630
$459$	−17.0826	−0.797348
$460$	85.2741	3.97593
$461$	30.0109	1.39775	0.698874	−	0.715245i	$-0.253685\pi$
$461$	30.0109	1.39775	0.698874	+	0.715245i	$0.253685\pi$
$462$	−11.4359	−0.532046
$463$	−11.1914	−0.520111	−0.260055	−	0.965594i	$-0.583741\pi$
$463$	−11.1914	−0.520111	−0.260055	+	0.965594i	$0.583741\pi$
$464$	−24.6924	−1.14631
$465$	18.8095	0.872272
$466$	−38.4386	−1.78064
$467$	29.5558	1.36768	0.683841	−	0.729632i	$-0.260308\pi$
$467$	29.5558	1.36768	0.683841	+	0.729632i	$0.260308\pi$
$468$	37.2988	1.72414
$469$	−3.69925	−0.170816
$470$	−23.7920	−1.09744
$471$	−43.5630	−2.00728
$472$	−66.4281	−3.05760
$473$	6.97920	0.320904
$474$	−12.5750	−0.577590
$475$	−1.19014	−0.0546075
$476$	−7.76021	−0.355689
$477$	−3.74905	−0.171657
$478$	−25.1051	−1.14828
$479$	−21.4831	−0.981590	−0.490795	−	0.871275i	$-0.663294\pi$
$479$	−21.4831	−0.981590	−0.490795	+	0.871275i	$0.663294\pi$
$480$	33.0388	1.50801
$481$	41.1807	1.87768
$482$	−40.1167	−1.82727
$483$	6.60777	0.300664
$484$	121.954	5.54337
$485$	14.5198	0.659311
$486$	31.3919	1.42397
$487$	30.9622	1.40303	0.701516	−	0.712654i	$-0.252507\pi$
$487$	30.9622	1.40303	0.701516	+	0.712654i	$0.252507\pi$
$488$	1.12540	0.0509445
$489$	14.5840	0.659509
$490$	−35.7017	−1.61284
$491$	26.6640	1.20333	0.601665	−	0.798749i	$-0.294504\pi$
$491$	26.6640	1.20333	0.601665	+	0.798749i	$0.294504\pi$
$492$	99.4418	4.48318
$493$	−13.8373	−0.623201
$494$	−20.7799	−0.934934
$495$	15.2167	0.683938
$496$	−38.2060	−1.71550
$497$	−2.12249	−0.0952069
$498$	59.2541	2.65524
$499$	−6.89821	−0.308806	−0.154403	−	0.988008i	$-0.549345\pi$
$499$	−6.89821	−0.308806	−0.154403	+	0.988008i	$0.549345\pi$
$500$	55.8386	2.49718
$501$	26.1907	1.17012
$502$	34.1508	1.52422
$503$	34.3204	1.53027	0.765136	−	0.643868i	$-0.222672\pi$
$503$	34.3204	1.53027	0.765136	+	0.643868i	$0.222672\pi$
$504$	3.01010	0.134081
$505$	−31.3505	−1.39508
$506$	−143.039	−6.35887
$507$	58.8088	2.61179
$508$	19.1861	0.851245
$509$	20.6896	0.917050	0.458525	−	0.888681i	$-0.348378\pi$
$509$	20.6896	0.917050	0.458525	+	0.888681i	$0.348378\pi$
$510$	50.4261	2.23290
$511$	−3.95808	−0.175095
$512$	48.5596	2.14605
$513$	−4.52394	−0.199737
$514$	−40.6974	−1.79508
$515$	26.0818	1.14930
$516$	−10.9940	−0.483983
$517$	27.9289	1.22831
$518$	5.81970	0.255703
$519$	16.0159	0.703018
$520$	89.1297	3.90860
$521$	−21.0063	−0.920305	−0.460152	−	0.887840i	$-0.652205\pi$
$521$	−21.0063	−0.920305	−0.460152	+	0.887840i	$0.652205\pi$
$522$	9.39893	0.411380
$523$	36.5816	1.59960	0.799800	−	0.600266i	$-0.204939\pi$
$523$	36.5816	1.59960	0.799800	+	0.600266i	$0.204939\pi$
$524$	−31.5061	−1.37635
$525$	0.692683	0.0302312
$526$	−27.6637	−1.20619
$527$	−21.4101	−0.932641
$528$	−105.631	−4.59699
$529$	59.6495	2.59346
$530$	−15.6880	−0.681445
$531$	11.9938	0.520488
$532$	−2.05511	−0.0891005
$533$	66.7621	2.89179
$534$	−7.36479	−0.318705
$535$	21.7374	0.939792
$536$	−72.0349	−3.11143
$537$	20.1280	0.868588
$538$	−74.1970	−3.19886
$539$	41.9095	1.80517
$540$	33.9793	1.46224
$541$	−7.07094	−0.304004	−0.152002	−	0.988380i	$-0.548572\pi$
$541$	−7.07094	−0.304004	−0.152002	+	0.988380i	$0.548572\pi$
$542$	47.5529	2.04257
$543$	−30.9265	−1.32718
$544$	−37.6067	−1.61237
$545$	−2.74904	−0.117756
$546$	12.0943	0.517587
$547$	−31.6230	−1.35210	−0.676051	−	0.736854i	$-0.736310\pi$
$547$	−31.6230	−1.35210	−0.676051	+	0.736854i	$0.736310\pi$
$548$	−55.4193	−2.36740
$549$	−0.203195	−0.00867216
$550$	−14.9946	−0.639372
$551$	−3.66449	−0.156113
$552$	128.672	5.47665
$553$	−0.834952	−0.0355058
$554$	−72.9499	−3.09935
$555$	−26.4647	−1.12337
$556$	51.9496	2.20316
$557$	7.73131	0.327586	0.163793	−	0.986495i	$-0.447627\pi$
$557$	7.73131	0.327586	0.163793	+	0.986495i	$0.447627\pi$
$558$	14.5428	0.615644
$559$	−7.38101	−0.312183
$560$	5.97475	0.252479
$561$	−59.1942	−2.49918
$562$	4.09916	0.172912
$563$	30.0285	1.26555	0.632776	−	0.774335i	$-0.281915\pi$
$563$	30.0285	1.26555	0.632776	+	0.774335i	$0.281915\pi$
$564$	−43.9949	−1.85252
$565$	−21.2087	−0.892255
$566$	−0.195035	−0.00819791
$567$	3.94692	0.165755
$568$	−41.3310	−1.73421
$569$	−0.264178	−0.0110749	−0.00553747	−	0.999985i	$-0.501763\pi$
$569$	−0.264178	−0.0110749	−0.00553747	+	0.999985i	$0.501763\pi$
$570$	13.3542	0.559346
$571$	−18.9016	−0.791008	−0.395504	−	0.918464i	$-0.629430\pi$
$571$	−18.9016	−0.791008	−0.395504	+	0.918464i	$0.629430\pi$
$572$	−183.217	−7.66069
$573$	−16.5286	−0.690493
$574$	9.43488	0.393804
$575$	8.66403	0.361315
$576$	4.65992	0.194164
$577$	6.21698	0.258816	0.129408	−	0.991591i	$-0.458692\pi$
$577$	6.21698	0.258816	0.129408	+	0.991591i	$0.458692\pi$
$578$	−13.5175	−0.562252
$579$	−27.4860	−1.14228
$580$	27.5240	1.14287
$581$	3.93433	0.163223
$582$	38.3661	1.59033
$583$	18.4159	0.762707
$584$	−77.0750	−3.18939
$585$	−16.0927	−0.665351
$586$	−68.2919	−2.82111
$587$	38.4060	1.58519	0.792593	−	0.609751i	$-0.208730\pi$
$587$	38.4060	1.58519	0.792593	+	0.609751i	$0.208730\pi$
$588$	−66.0178	−2.72253
$589$	−5.66999	−0.233628
$590$	50.1887	2.06624
$591$	−15.1031	−0.621261
$592$	53.7552	2.20933
$593$	0.834337	0.0342621	0.0171311	−	0.999853i	$-0.494547\pi$
$593$	0.834337	0.0342621	0.0171311	+	0.999853i	$0.494547\pi$
$594$	−56.9971	−2.33862
$595$	3.34817	0.137262
$596$	52.5975	2.15448
$597$	−39.3094	−1.60883
$598$	151.274	6.18607
$599$	−19.4049	−0.792864	−0.396432	−	0.918064i	$-0.629752\pi$
$599$	−19.4049	−0.792864	−0.396432	+	0.918064i	$0.629752\pi$
$600$	13.4885	0.550666
$601$	26.9263	1.09835	0.549173	−	0.835709i	$-0.314943\pi$
$601$	26.9263	1.09835	0.549173	+	0.835709i	$0.314943\pi$
$602$	−1.04309	−0.0425132
$603$	13.0062	0.529653
$604$	92.0287	3.74459
$605$	−52.6176	−2.13921
$606$	−82.8383	−3.36507
$607$	0.788407	0.0320005	0.0160002	−	0.999872i	$-0.494907\pi$
$607$	0.788407	0.0320005	0.0160002	+	0.999872i	$0.494907\pi$
$608$	−9.95927	−0.403902
$609$	2.13280	0.0864253
$610$	−0.850278	−0.0344268
$611$	−29.5368	−1.19493
$612$	27.2841	1.10289
$613$	−27.8046	−1.12302	−0.561509	−	0.827471i	$-0.689779\pi$
$613$	−27.8046	−1.12302	−0.561509	+	0.827471i	$0.689779\pi$
$614$	19.7154	0.795647
$615$	−42.9046	−1.73008
$616$	−14.7860	−0.595747
$617$	19.4327	0.782330	0.391165	−	0.920321i	$-0.372072\pi$
$617$	19.4327	0.782330	0.391165	+	0.920321i	$0.372072\pi$
$618$	68.9168	2.77224
$619$	15.8900	0.638674	0.319337	−	0.947641i	$-0.396540\pi$
$619$	15.8900	0.638674	0.319337	+	0.947641i	$0.396540\pi$
$620$	42.5873	1.71035
$621$	32.9334	1.32157
$622$	−19.7496	−0.791886
$623$	−0.489004	−0.0195915
$624$	111.712	4.47206
$625$	−19.3267	−0.773067
$626$	−44.7129	−1.78709
$627$	−15.6762	−0.626048
$628$	−98.6324	−3.93586
$629$	30.1237	1.20111
$630$	−2.27423	−0.0906077
$631$	25.4766	1.01421	0.507104	−	0.861885i	$-0.330716\pi$
$631$	25.4766	1.01421	0.507104	+	0.861885i	$0.330716\pi$
$632$	−16.2589	−0.646744
$633$	25.8067	1.02572
$634$	−28.0146	−1.11260
$635$	−8.27792	−0.328499
$636$	−29.0095	−1.15030
$637$	−44.3223	−1.75611
$638$	−46.1689	−1.82785
$639$	7.46247	0.295211
$640$	−12.5870	−0.497545
$641$	7.78770	0.307596	0.153798	−	0.988102i	$-0.450850\pi$
$641$	7.78770	0.307596	0.153798	+	0.988102i	$0.450850\pi$
$642$	57.4375	2.26688
$643$	−3.39238	−0.133782	−0.0668912	−	0.997760i	$-0.521308\pi$
$643$	−3.39238	−0.133782	−0.0668912	+	0.997760i	$0.521308\pi$
$644$	14.9609	0.589541
$645$	4.74339	0.186771
$646$	−15.2005	−0.598057
$647$	23.9006	0.939632	0.469816	−	0.882764i	$-0.344320\pi$
$647$	23.9006	0.939632	0.469816	+	0.882764i	$0.344320\pi$
$648$	76.8578	3.01926
$649$	−58.9155	−2.31264
$650$	15.8579	0.621997
$651$	3.30003	0.129338
$652$	33.0200	1.29316
$653$	10.9502	0.428513	0.214256	−	0.976777i	$-0.431267\pi$
$653$	10.9502	0.428513	0.214256	+	0.976777i	$0.431267\pi$
$654$	−7.26388	−0.284040
$655$	13.5934	0.531140
$656$	87.1478	3.40255
$657$	13.9162	0.542922
$658$	−4.17417	−0.162726
$659$	−25.2579	−0.983907	−0.491953	−	0.870622i	$-0.663717\pi$
$659$	−25.2579	−0.983907	−0.491953	+	0.870622i	$0.663717\pi$
$660$	117.744	4.58318
$661$	33.8691	1.31735	0.658677	−	0.752426i	$-0.271116\pi$
$661$	33.8691	1.31735	0.658677	+	0.752426i	$0.271116\pi$
$662$	−52.5251	−2.04145
$663$	62.6021	2.43126
$664$	76.6126	2.97314
$665$	0.886687	0.0343842
$666$	−20.4614	−0.792865
$667$	26.6768	1.03293
$668$	59.2993	2.29436
$669$	43.5332	1.68309
$670$	54.4249	2.10262
$671$	0.998125	0.0385322
$672$	5.79647	0.223604
$673$	−20.2675	−0.781253	−0.390627	−	0.920549i	$-0.627742\pi$
$673$	−20.2675	−0.781253	−0.390627	+	0.920549i	$0.627742\pi$
$674$	−26.1309	−1.00652
$675$	3.45237	0.132882
$676$	133.151	5.12119
$677$	0.395318	0.0151933	0.00759666	−	0.999971i	$-0.497582\pi$
$677$	0.395318	0.0151933	0.00759666	+	0.999971i	$0.497582\pi$
$678$	−56.0403	−2.15221
$679$	2.54742	0.0977610
$680$	65.1984	2.50025
$681$	−27.1942	−1.04208
$682$	−71.4362	−2.73543
$683$	−24.6628	−0.943695	−0.471848	−	0.881680i	$-0.656413\pi$
$683$	−24.6628	−0.943695	−0.471848	+	0.881680i	$0.656413\pi$
$684$	7.22556	0.276276
$685$	23.9109	0.913588
$686$	−12.6408	−0.482628
$687$	−43.9882	−1.67826
$688$	−9.63478	−0.367323
$689$	−19.4761	−0.741980
$690$	−97.2162	−3.70096
$691$	2.07973	0.0791167	0.0395584	−	0.999217i	$-0.487405\pi$
$691$	2.07973	0.0791167	0.0395584	+	0.999217i	$0.487405\pi$
$692$	36.2620	1.37847
$693$	2.66968	0.101413
$694$	−79.9223	−3.03381
$695$	−22.4139	−0.850207
$696$	41.5316	1.57425
$697$	48.8365	1.84982
$698$	−94.2334	−3.56679
$699$	30.6672	1.15994
$700$	1.56833	0.0592772
$701$	4.43680	0.167576	0.0837878	−	0.996484i	$-0.473298\pi$
$701$	4.43680	0.167576	0.0837878	+	0.996484i	$0.473298\pi$
$702$	60.2785	2.27506
$703$	7.97758	0.300880
$704$	−22.8902	−0.862708
$705$	18.9818	0.714896
$706$	−24.4795	−0.921297
$707$	−5.50026	−0.206859
$708$	92.8065	3.48788
$709$	17.0496	0.640310	0.320155	−	0.947365i	$-0.396265\pi$
$709$	17.0496	0.640310	0.320155	+	0.947365i	$0.396265\pi$
$710$	31.2270	1.17193
$711$	2.93560	0.110094
$712$	−9.52230	−0.356863
$713$	41.2765	1.54582
$714$	8.84697	0.331090
$715$	79.0497	2.95629
$716$	45.5725	1.70312
$717$	20.0294	0.748013
$718$	66.5559	2.48385
$719$	4.86194	0.181320	0.0906599	−	0.995882i	$-0.471102\pi$
$719$	4.86194	0.181320	0.0906599	+	0.995882i	$0.471102\pi$
$720$	−21.0066	−0.782869
$721$	4.57591	0.170416
$722$	45.0174	1.67538
$723$	32.0061	1.19032
$724$	−70.0216	−2.60233
$725$	2.79650	0.103859
$726$	−139.033	−5.16000
$727$	−27.5040	−1.02007	−0.510034	−	0.860154i	$-0.670367\pi$
$727$	−27.5040	−1.02007	−0.510034	+	0.860154i	$0.670367\pi$
$728$	15.6373	0.579557
$729$	8.50344	0.314942
$730$	58.2328	2.15529
$731$	−5.39921	−0.199697
$732$	−1.57229	−0.0581136
$733$	−9.99882	−0.369315	−0.184657	−	0.982803i	$-0.559118\pi$
$733$	−9.99882	−0.369315	−0.184657	+	0.982803i	$0.559118\pi$
$734$	−8.10109	−0.299017
$735$	28.4836	1.05063
$736$	72.5017	2.67245
$737$	−63.8882	−2.35335
$738$	−33.1720	−1.22108
$739$	−10.1396	−0.372991	−0.186495	−	0.982456i	$-0.559713\pi$
$739$	−10.1396	−0.372991	−0.186495	+	0.982456i	$0.559713\pi$
$740$	−59.9197	−2.20269
$741$	16.5787	0.609034
$742$	−2.75238	−0.101043
$743$	30.5809	1.12190	0.560952	−	0.827848i	$-0.310435\pi$
$743$	30.5809	1.12190	0.560952	+	0.827848i	$0.310435\pi$
$744$	64.2609	2.35592
$745$	−22.6934	−0.831421
$746$	39.7283	1.45456
$747$	−13.8327	−0.506112
$748$	−134.023	−4.90038
$749$	3.81371	0.139350
$750$	−63.6584	−2.32447
$751$	39.2192	1.43113	0.715564	−	0.698547i	$-0.246170\pi$
$751$	39.2192	1.43113	0.715564	+	0.698547i	$0.246170\pi$
$752$	−38.5558	−1.40599
$753$	−27.2463	−0.992909
$754$	48.8269	1.77817
$755$	−39.7061	−1.44505
$756$	5.96148	0.216817
$757$	15.3298	0.557173	0.278586	−	0.960411i	$-0.410134\pi$
$757$	15.3298	0.557173	0.278586	+	0.960411i	$0.410134\pi$
$758$	32.0311	1.16342
$759$	114.120	4.14230
$760$	17.2663	0.626315
$761$	−43.7136	−1.58462	−0.792308	−	0.610121i	$-0.791121\pi$
$761$	−43.7136	−1.58462	−0.792308	+	0.610121i	$0.791121\pi$
$762$	−21.8730	−0.792374
$763$	−0.482304	−0.0174606
$764$	−37.4230	−1.35392
$765$	−11.7718	−0.425611
$766$	36.0019	1.30080
$767$	62.3073	2.24979
$768$	−48.7257	−1.75824
$769$	−23.6420	−0.852553	−0.426277	−	0.904593i	$-0.640175\pi$
$769$	−23.6420	−0.852553	−0.426277	+	0.904593i	$0.640175\pi$
$770$	11.1714	0.402588
$771$	32.4693	1.16935
$772$	−62.2319	−2.23978
$773$	27.3096	0.982258	0.491129	−	0.871087i	$-0.336584\pi$
$773$	27.3096	0.982258	0.491129	+	0.871087i	$0.336584\pi$
$774$	3.66739	0.131822
$775$	4.32696	0.155429
$776$	49.6055	1.78073
$777$	−4.64309	−0.166570
$778$	54.1995	1.94315
$779$	12.9332	0.463381
$780$	−124.523	−4.45863
$781$	−36.6567	−1.31168
$782$	110.657	3.95710
$783$	10.6300	0.379884
$784$	−57.8560	−2.06629
$785$	42.5553	1.51887
$786$	35.9184	1.28117
$787$	38.6132	1.37641	0.688206	−	0.725516i	$-0.258399\pi$
$787$	38.6132	1.37641	0.688206	+	0.725516i	$0.258399\pi$
$788$	−34.1955	−1.21816
$789$	22.0707	0.785739
$790$	12.2841	0.437050
$791$	−3.72094	−0.132301
$792$	51.9862	1.84725
$793$	−1.05559	−0.0374850
$794$	90.2901	3.20427
$795$	12.5163	0.443907
$796$	−89.0018	−3.15458
$797$	0.192565	0.00682101	0.00341051	−	0.999994i	$-0.498914\pi$
$797$	0.192565	0.00682101	0.00341051	+	0.999994i	$0.498914\pi$
$798$	2.34292	0.0829384
$799$	−21.6062	−0.764373
$800$	7.60026	0.268710
$801$	1.71929	0.0607481
$802$	−81.6413	−2.88286
$803$	−68.3583	−2.41231
$804$	100.640	3.54929
$805$	−6.45492	−0.227506
$806$	75.5489	2.66109
$807$	59.1961	2.08380
$808$	−107.106	−3.76797
$809$	−6.60266	−0.232137	−0.116069	−	0.993241i	$-0.537029\pi$
$809$	−6.60266	−0.232137	−0.116069	+	0.993241i	$0.537029\pi$
$810$	−58.0687	−2.04033
$811$	7.60106	0.266909	0.133455	−	0.991055i	$-0.457393\pi$
$811$	7.60106	0.266909	0.133455	+	0.991055i	$0.457393\pi$
$812$	4.82893	0.169462
$813$	−37.9388	−1.33057
$814$	100.510	3.52286
$815$	−14.2466	−0.499037
$816$	81.7175	2.86068
$817$	−1.42986	−0.0500244
$818$	−63.8470	−2.23236
$819$	−2.82337	−0.0986567
$820$	−97.1416	−3.39233
$821$	−28.4524	−0.992996	−0.496498	−	0.868038i	$-0.665381\pi$
$821$	−28.4524	−0.992996	−0.496498	+	0.868038i	$0.665381\pi$
$822$	63.1804	2.20367
$823$	26.8875	0.937239	0.468620	−	0.883400i	$-0.344752\pi$
$823$	26.8875	0.937239	0.468620	+	0.883400i	$0.344752\pi$
$824$	89.1059	3.10415
$825$	11.9631	0.416500
$826$	8.80533	0.306376
$827$	−9.64628	−0.335434	−0.167717	−	0.985835i	$-0.553639\pi$
$827$	−9.64628	−0.335434	−0.167717	+	0.985835i	$0.553639\pi$
$828$	−52.6008	−1.82801
$829$	10.1534	0.352641	0.176321	−	0.984333i	$-0.443580\pi$
$829$	10.1534	0.352641	0.176321	+	0.984333i	$0.443580\pi$
$830$	−57.8834	−2.00916
$831$	58.2011	2.01898
$832$	24.2081	0.839263
$833$	−32.4218	−1.12335
$834$	−59.2248	−2.05079
$835$	−25.5849	−0.885402
$836$	−35.4930	−1.22755
$837$	16.4475	0.568509
$838$	19.4012	0.670202
$839$	−31.5849	−1.09043	−0.545216	−	0.838296i	$-0.683552\pi$
$839$	−31.5849	−1.09043	−0.545216	+	0.838296i	$0.683552\pi$
$840$	−10.0493	−0.346733
$841$	−20.3895	−0.703086
$842$	−56.8398	−1.95883
$843$	−3.27040	−0.112639
$844$	58.4298	2.01124
$845$	−57.4484	−1.97629
$846$	14.6759	0.504569
$847$	−9.23146	−0.317197
$848$	−25.4231	−0.873032
$849$	0.155603	0.00534028
$850$	11.6000	0.397878
$851$	−58.0754	−1.99080
$852$	57.7434	1.97826
$853$	29.8459	1.02191	0.510953	−	0.859609i	$-0.329293\pi$
$853$	29.8459	1.02191	0.510953	+	0.859609i	$0.329293\pi$
$854$	−0.149177	−0.00510472
$855$	−3.11750	−0.106616
$856$	74.2638	2.53828
$857$	−47.8939	−1.63602	−0.818012	−	0.575202i	$-0.804924\pi$
$857$	−47.8939	−1.63602	−0.818012	+	0.575202i	$0.804924\pi$
$858$	208.875	7.13088
$859$	2.36211	0.0805942	0.0402971	−	0.999188i	$-0.487170\pi$
$859$	2.36211	0.0805942	0.0402971	+	0.999188i	$0.487170\pi$
$860$	10.7397	0.366219
$861$	−7.52737	−0.256532
$862$	72.4803	2.46869
$863$	4.49659	0.153066	0.0765329	−	0.997067i	$-0.475615\pi$
$863$	4.49659	0.153066	0.0765329	+	0.997067i	$0.475615\pi$
$864$	28.8899	0.982853
$865$	−15.6454	−0.531959
$866$	2.60950	0.0886744
$867$	10.7845	0.366262
$868$	7.47170	0.253606
$869$	−14.4201	−0.489169
$870$	−31.3785	−1.06383
$871$	67.5664	2.28940
$872$	−9.39184	−0.318048
$873$	−8.95646	−0.303130
$874$	29.3050	0.991258
$875$	−4.22676	−0.142891
$876$	107.681	3.63821
$877$	−27.7536	−0.937174	−0.468587	−	0.883417i	$-0.655237\pi$
$877$	−27.7536	−0.937174	−0.468587	+	0.883417i	$0.655237\pi$
$878$	36.3715	1.22748
$879$	54.4849	1.83773
$880$	103.187	3.47845
$881$	13.6021	0.458266	0.229133	−	0.973395i	$-0.426411\pi$
$881$	13.6021	0.458266	0.229133	+	0.973395i	$0.426411\pi$
$882$	22.0224	0.741532
$883$	10.6253	0.357571	0.178786	−	0.983888i	$-0.442783\pi$
$883$	10.6253	0.357571	0.178786	+	0.983888i	$0.442783\pi$
$884$	141.739	4.76721
$885$	−40.0417	−1.34599
$886$	71.3757	2.39791
$887$	42.7175	1.43431	0.717156	−	0.696913i	$-0.245443\pi$
$887$	42.7175	1.43431	0.717156	+	0.696913i	$0.245443\pi$
$888$	−90.4141	−3.03410
$889$	−1.45231	−0.0487091
$890$	7.19443	0.241158
$891$	68.1657	2.28364
$892$	98.5648	3.30019
$893$	−5.72191	−0.191476
$894$	−59.9634	−2.00547
$895$	−19.6624	−0.657242
$896$	−2.20832	−0.0737747
$897$	−120.690	−4.02973
$898$	−37.8642	−1.26354
$899$	13.3229	0.444342
$900$	−5.51407	−0.183802
$901$	−14.2468	−0.474629
$902$	162.946	5.42550
$903$	0.832201	0.0276939
$904$	−72.4573	−2.40989
$905$	30.2111	1.00425
$906$	−104.917	−3.48562
$907$	29.0579	0.964851	0.482425	−	0.875937i	$-0.339756\pi$
$907$	29.0579	0.964851	0.482425	+	0.875937i	$0.339756\pi$
$908$	−61.5712	−2.04331
$909$	19.3384	0.641413
$910$	−11.8145	−0.391648
$911$	−44.0440	−1.45924	−0.729622	−	0.683851i	$-0.760304\pi$
$911$	−44.0440	−1.45924	−0.729622	+	0.683851i	$0.760304\pi$
$912$	21.6410	0.716605
$913$	67.9482	2.24876
$914$	50.2892	1.66342
$915$	0.678372	0.0224263
$916$	−99.5951	−3.29072
$917$	2.38489	0.0787562
$918$	44.0937	1.45531
$919$	10.7300	0.353948	0.176974	−	0.984215i	$-0.443369\pi$
$919$	10.7300	0.353948	0.176974	+	0.984215i	$0.443369\pi$
$920$	−125.696	−4.14406
$921$	−15.7294	−0.518300
$922$	−77.4644	−2.55115
$923$	38.7671	1.27603
$924$	20.6575	0.679583
$925$	−6.08796	−0.200171
$926$	28.8875	0.949301
$927$	−16.0884	−0.528413
$928$	23.4014	0.768190
$929$	−46.9434	−1.54016	−0.770082	−	0.637945i	$-0.779785\pi$
$929$	−46.9434	−1.54016	−0.770082	+	0.637945i	$0.779785\pi$
$930$	−48.5513	−1.59206
$931$	−8.58616	−0.281400
$932$	69.4347	2.27441
$933$	15.7567	0.515850
$934$	−76.2898	−2.49628
$935$	57.8249	1.89108
$936$	−54.9791	−1.79705
$937$	50.2987	1.64319	0.821594	−	0.570073i	$-0.193085\pi$
$937$	50.2987	1.64319	0.821594	+	0.570073i	$0.193085\pi$
$938$	9.54854	0.311771
$939$	35.6730	1.16414
$940$	42.9773	1.40176
$941$	9.27133	0.302237	0.151118	−	0.988516i	$-0.451713\pi$
$941$	9.27133	0.302237	0.151118	+	0.988516i	$0.451713\pi$
$942$	112.445	3.66366
$943$	−94.1517	−3.06600
$944$	81.3328	2.64716
$945$	−2.57210	−0.0836705
$946$	−18.0148	−0.585711
$947$	12.3814	0.402341	0.201171	−	0.979556i	$-0.435525\pi$
$947$	12.3814	0.402341	0.201171	+	0.979556i	$0.435525\pi$
$948$	22.7152	0.737756
$949$	72.2938	2.34676
$950$	3.07201	0.0996691
$951$	22.3507	0.724772
$952$	11.4387	0.370730
$953$	7.17067	0.232281	0.116140	−	0.993233i	$-0.462948\pi$
$953$	7.17067	0.232281	0.116140	+	0.993233i	$0.462948\pi$
$954$	9.67707	0.313307
$955$	16.1463	0.522482
$956$	45.3493	1.46670
$957$	36.8346	1.19069
$958$	55.4525	1.79159
$959$	4.19503	0.135465
$960$	−15.5573	−0.502109
$961$	−10.3858	−0.335027
$962$	−106.296	−3.42712
$963$	−13.4086	−0.432087
$964$	72.4659	2.33397
$965$	26.8502	0.864339
$966$	−17.0560	−0.548769
$967$	3.32373	0.106884	0.0534419	−	0.998571i	$-0.482981\pi$
$967$	3.32373	0.106884	0.0534419	+	0.998571i	$0.482981\pi$
$968$	−179.763	−5.77780
$969$	12.1273	0.389587
$970$	−37.4787	−1.20337
$971$	−2.91546	−0.0935615	−0.0467807	−	0.998905i	$-0.514896\pi$
$971$	−2.91546	−0.0935615	−0.0467807	+	0.998905i	$0.514896\pi$
$972$	−56.7056	−1.81883
$973$	−3.93239	−0.126067
$974$	−79.9199	−2.56080
$975$	−12.6518	−0.405181
$976$	−1.37791	−0.0441058
$977$	−12.5160	−0.400423	−0.200211	−	0.979753i	$-0.564163\pi$
$977$	−12.5160	−0.400423	−0.200211	+	0.979753i	$0.564163\pi$
$978$	−37.6442	−1.20373
$979$	−8.44539	−0.269916
$980$	64.4907	2.06008
$981$	1.69573	0.0541405
$982$	−68.8254	−2.19631
$983$	21.7947	0.695143	0.347571	−	0.937654i	$-0.387006\pi$
$983$	21.7947	0.695143	0.347571	+	0.937654i	$0.387006\pi$
$984$	−146.579	−4.67277
$985$	14.7538	0.470095
$986$	35.7169	1.13746
$987$	3.33025	0.106003
$988$	37.5364	1.19419
$989$	10.4091	0.330990
$990$	−39.2774	−1.24832
$991$	−45.8651	−1.45695	−0.728476	−	0.685071i	$-0.759771\pi$
$991$	−45.8651	−1.45695	−0.728476	+	0.685071i	$0.759771\pi$
$992$	36.2086	1.14962
$993$	41.9058	1.32984
$994$	5.47860	0.173771
$995$	38.4002	1.21737
$996$	−107.035	−3.39154
$997$	26.6778	0.844894	0.422447	−	0.906388i	$-0.361171\pi$
$997$	26.6778	0.844894	0.422447	+	0.906388i	$0.361171\pi$
$998$	17.8057	0.563630
$999$	−23.1414	−0.732161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.17	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.58121 q^{2} +2.05935 q^{3} +4.66263 q^{4} -2.01171 q^{5} -5.31560 q^{6} -0.352944 q^{7} -6.87281 q^{8} +1.24091 q^{9} +O(q^{10})\)	\(q-2.58121 q^{2} +2.05935 q^{3} +4.66263 q^{4} -2.01171 q^{5} -5.31560 q^{6} -0.352944 q^{7} -6.87281 q^{8} +1.24091 q^{9} +5.19265 q^{10} -6.09554 q^{11} +9.60198 q^{12} +6.44647 q^{13} +0.911021 q^{14} -4.14281 q^{15} +8.41489 q^{16} +4.71560 q^{17} -3.20305 q^{18} +1.24882 q^{19} -9.37988 q^{20} -0.726833 q^{21} +15.7339 q^{22} -9.09118 q^{23} -14.1535 q^{24} -0.953015 q^{25} -16.6397 q^{26} -3.62257 q^{27} -1.64565 q^{28} -2.93437 q^{29} +10.6935 q^{30} -4.54028 q^{31} -7.97496 q^{32} -12.5528 q^{33} -12.1719 q^{34} +0.710021 q^{35} +5.78592 q^{36} +6.38811 q^{37} -3.22346 q^{38} +13.2755 q^{39} +13.8261 q^{40} +10.3564 q^{41} +1.87611 q^{42} -1.14497 q^{43} -28.4213 q^{44} -2.49636 q^{45} +23.4662 q^{46} -4.58186 q^{47} +17.3292 q^{48} -6.87543 q^{49} +2.45993 q^{50} +9.71106 q^{51} +30.0575 q^{52} -3.02120 q^{53} +9.35061 q^{54} +12.2625 q^{55} +2.42572 q^{56} +2.57175 q^{57} +7.57421 q^{58} +9.66534 q^{59} -19.3164 q^{60} -0.163747 q^{61} +11.7194 q^{62} -0.437972 q^{63} +3.75524 q^{64} -12.9684 q^{65} +32.4015 q^{66} +10.4811 q^{67} +21.9871 q^{68} -18.7219 q^{69} -1.83271 q^{70} +6.01369 q^{71} -8.52856 q^{72} +11.2145 q^{73} -16.4890 q^{74} -1.96259 q^{75} +5.82278 q^{76} +2.15138 q^{77} -34.2669 q^{78} +2.36568 q^{79} -16.9283 q^{80} -11.1829 q^{81} -26.7320 q^{82} -11.1472 q^{83} -3.38896 q^{84} -9.48643 q^{85} +2.95540 q^{86} -6.04288 q^{87} +41.8935 q^{88} +1.38550 q^{89} +6.44362 q^{90} -2.27524 q^{91} -42.3888 q^{92} -9.35002 q^{93} +11.8267 q^{94} -2.51226 q^{95} -16.4232 q^{96} -7.21764 q^{97} +17.7469 q^{98} -7.56403 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 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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