LMFDB - Embedded newform 547.4.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,4,Mod(1,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("547.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	547.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:	$32.2740447731$
Analytic rank:	$1$
Dimension:	$65$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.93855 q^{2} +1.10159 q^{3} +7.51219 q^{4} +5.92954 q^{5} -4.33869 q^{6} -15.7024 q^{7} +1.92127 q^{8} -25.7865 q^{9} +O(q^{10})$	\(q-3.93855 q^{2} +1.10159 q^{3} +7.51219 q^{4} +5.92954 q^{5} -4.33869 q^{6} -15.7024 q^{7} +1.92127 q^{8} -25.7865 q^{9} -23.3538 q^{10} -2.04404 q^{11} +8.27539 q^{12} +69.6715 q^{13} +61.8448 q^{14} +6.53195 q^{15} -67.6645 q^{16} +94.3749 q^{17} +101.561 q^{18} -109.145 q^{19} +44.5438 q^{20} -17.2977 q^{21} +8.05055 q^{22} +56.8024 q^{23} +2.11646 q^{24} -89.8405 q^{25} -274.405 q^{26} -58.1493 q^{27} -117.959 q^{28} -178.929 q^{29} -25.7264 q^{30} -18.7078 q^{31} +251.130 q^{32} -2.25170 q^{33} -371.700 q^{34} -93.1081 q^{35} -193.713 q^{36} +262.622 q^{37} +429.872 q^{38} +76.7498 q^{39} +11.3922 q^{40} +63.2007 q^{41} +68.1279 q^{42} +275.224 q^{43} -15.3552 q^{44} -152.902 q^{45} -223.719 q^{46} +398.283 q^{47} -74.5389 q^{48} -96.4343 q^{49} +353.842 q^{50} +103.963 q^{51} +523.386 q^{52} -193.903 q^{53} +229.024 q^{54} -12.1202 q^{55} -30.1685 q^{56} -120.233 q^{57} +704.720 q^{58} -549.698 q^{59} +49.0693 q^{60} -610.914 q^{61} +73.6818 q^{62} +404.910 q^{63} -447.773 q^{64} +413.120 q^{65} +8.86844 q^{66} -34.9807 q^{67} +708.962 q^{68} +62.5732 q^{69} +366.711 q^{70} +862.125 q^{71} -49.5427 q^{72} -933.523 q^{73} -1034.35 q^{74} -98.9679 q^{75} -819.915 q^{76} +32.0963 q^{77} -302.283 q^{78} +990.518 q^{79} -401.220 q^{80} +632.178 q^{81} -248.919 q^{82} -579.469 q^{83} -129.944 q^{84} +559.600 q^{85} -1083.98 q^{86} -197.107 q^{87} -3.92714 q^{88} -1665.66 q^{89} +602.213 q^{90} -1094.01 q^{91} +426.710 q^{92} -20.6085 q^{93} -1568.66 q^{94} -647.178 q^{95} +276.644 q^{96} -1621.05 q^{97} +379.811 q^{98} +52.7086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) $ 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * 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 $

$2$	−3.93855	−1.39249	−0.696244	−	0.717805i	$-0.745147\pi$
$2$	−3.93855	−1.39249	−0.696244	+	0.717805i	$0.745147\pi$
$3$	1.10159	0.212002	0.106001	−	0.994366i	$-0.466195\pi$
$3$	1.10159	0.212002	0.106001	+	0.994366i	$0.466195\pi$
$4$	7.51219	0.939024
$5$	5.92954	0.530354	0.265177	−	0.964200i	$-0.414570\pi$
$5$	5.92954	0.530354	0.265177	+	0.964200i	$0.414570\pi$
$6$	−4.33869	−0.295210
$7$	−15.7024	−0.847851	−0.423925	−	0.905697i	$-0.639348\pi$
$7$	−15.7024	−0.847851	−0.423925	+	0.905697i	$0.639348\pi$
$8$	1.92127	0.0849088
$9$	−25.7865	−0.955055
$10$	−23.3538	−0.738512
$11$	−2.04404	−0.0560273	−0.0280137	−	0.999608i	$-0.508918\pi$
$11$	−2.04404	−0.0560273	−0.0280137	+	0.999608i	$0.508918\pi$
$12$	8.27539	0.199075
$13$	69.6715	1.48642	0.743208	−	0.669061i	$-0.233303\pi$
$13$	69.6715	1.48642	0.743208	+	0.669061i	$0.233303\pi$
$14$	61.8448	1.18062
$15$	6.53195	0.112436
$16$	−67.6645	−1.05726
$17$	94.3749	1.34643	0.673214	−	0.739448i	$-0.264913\pi$
$17$	94.3749	1.34643	0.673214	+	0.739448i	$0.264913\pi$
$18$	101.561	1.32990
$19$	−109.145	−1.31787	−0.658934	−	0.752200i	$-0.728992\pi$
$19$	−109.145	−1.31787	−0.658934	+	0.752200i	$0.728992\pi$
$20$	44.5438	0.498015
$21$	−17.2977	−0.179746
$22$	8.05055	0.0780174
$23$	56.8024	0.514962	0.257481	−	0.966283i	$-0.417108\pi$
$23$	56.8024	0.514962	0.257481	+	0.966283i	$0.417108\pi$
$24$	2.11646	0.0180008
$25$	−89.8405	−0.718724
$26$	−274.405	−2.06982
$27$	−58.1493	−0.414476
$28$	−117.959	−0.796152
$29$	−178.929	−1.14573	−0.572866	−	0.819649i	$-0.694168\pi$
$29$	−178.929	−1.14573	−0.572866	+	0.819649i	$0.694168\pi$
$30$	−25.7264	−0.156566
$31$	−18.7078	−0.108388	−0.0541940	−	0.998530i	$-0.517259\pi$
$31$	−18.7078	−0.108388	−0.0541940	+	0.998530i	$0.517259\pi$
$32$	251.130	1.38731
$33$	−2.25170	−0.0118779
$34$	−371.700	−1.87488
$35$	−93.1081	−0.449661
$36$	−193.713	−0.896819
$37$	262.622	1.16689	0.583444	−	0.812153i	$-0.301705\pi$
$37$	262.622	1.16689	0.583444	+	0.812153i	$0.301705\pi$
$38$	429.872	1.83512
$39$	76.7498	0.315123
$40$	11.3922	0.0450317
$41$	63.2007	0.240739	0.120369	−	0.992729i	$-0.461592\pi$
$41$	63.2007	0.240739	0.120369	+	0.992729i	$0.461592\pi$
$42$	68.1279	0.250294
$43$	275.224	0.976075	0.488038	−	0.872823i	$-0.337713\pi$
$43$	275.224	0.976075	0.488038	+	0.872823i	$0.337713\pi$
$44$	−15.3552	−0.0526110
$45$	−152.902	−0.506518
$46$	−223.719	−0.717078
$47$	398.283	1.23607	0.618037	−	0.786149i	$-0.287928\pi$
$47$	398.283	1.23607	0.618037	+	0.786149i	$0.287928\pi$
$48$	−74.5389	−0.224141
$49$	−96.4343	−0.281150
$50$	353.842	1.00082
$51$	103.963	0.285445
$52$	523.386	1.39578
$53$	−193.903	−0.502541	−0.251270	−	0.967917i	$-0.580848\pi$
$53$	−193.903	−0.502541	−0.251270	+	0.967917i	$0.580848\pi$
$54$	229.024	0.577152
$55$	−12.1202	−0.0297143
$56$	−30.1685	−0.0719900
$57$	−120.233	−0.279391
$58$	704.720	1.59542
$59$	−549.698	−1.21296	−0.606480	−	0.795099i	$-0.707419\pi$
$59$	−549.698	−1.21296	−0.606480	+	0.795099i	$0.707419\pi$
$60$	49.0693	0.105580
$61$	−610.914	−1.28229	−0.641144	−	0.767421i	$-0.721540\pi$
$61$	−610.914	−1.28229	−0.641144	+	0.767421i	$0.721540\pi$
$62$	73.6818	0.150929
$63$	404.910	0.809744
$64$	−447.773	−0.874556
$65$	413.120	0.788327
$66$	8.86844	0.0165398
$67$	−34.9807	−0.0637846	−0.0318923	−	0.999491i	$-0.510153\pi$
$67$	−34.9807	−0.0637846	−0.0318923	+	0.999491i	$0.510153\pi$
$68$	708.962	1.26433
$69$	62.5732	0.109173
$70$	366.711	0.626148
$71$	862.125	1.44106	0.720531	−	0.693422i	$-0.243898\pi$
$71$	862.125	1.44106	0.720531	+	0.693422i	$0.243898\pi$
$72$	−49.5427	−0.0810926
$73$	−933.523	−1.49672	−0.748360	−	0.663292i	$-0.769159\pi$
$73$	−933.523	−1.49672	−0.748360	+	0.663292i	$0.769159\pi$
$74$	−1034.35	−1.62488
$75$	−98.9679	−0.152371
$76$	−819.915	−1.23751
$77$	32.0963	0.0475028
$78$	−302.283	−0.438805
$79$	990.518	1.41066	0.705329	−	0.708880i	$-0.250799\pi$
$79$	990.518	1.41066	0.705329	+	0.708880i	$0.250799\pi$
$80$	−401.220	−0.560721
$81$	632.178	0.867185
$82$	−248.919	−0.335226
$83$	−579.469	−0.766326	−0.383163	−	0.923681i	$-0.625165\pi$
$83$	−579.469	−0.766326	−0.383163	+	0.923681i	$0.625165\pi$
$84$	−129.944	−0.168786
$85$	559.600	0.714083
$86$	−1083.98	−1.35917
$87$	−197.107	−0.242897
$88$	−3.92714	−0.00475721
$89$	−1665.66	−1.98382	−0.991910	−	0.126943i	$-0.959483\pi$
$89$	−1665.66	−1.98382	−0.991910	+	0.126943i	$0.959483\pi$
$90$	602.213	0.705320
$91$	−1094.01	−1.26026
$92$	426.710	0.483561
$93$	−20.6085	−0.0229785
$94$	−1568.66	−1.72122
$95$	−647.178	−0.698937
$96$	276.644	0.294113
$97$	−1621.05	−1.69684	−0.848418	−	0.529327i	$-0.822444\pi$
$97$	−1621.05	−1.69684	−0.848418	+	0.529327i	$0.822444\pi$
$98$	379.811	0.391497
$99$	52.7086	0.0535092
$100$	−674.899	−0.674899
$101$	−1145.68	−1.12870	−0.564352	−	0.825534i	$-0.690874\pi$
$101$	−1145.68	−1.12870	−0.564352	+	0.825534i	$0.690874\pi$
$102$	−409.463	−0.397479
$103$	1233.93	1.18042	0.590209	−	0.807250i	$-0.299045\pi$
$103$	1233.93	1.18042	0.590209	+	0.807250i	$0.299045\pi$
$104$	133.858	0.126210
$105$	−102.567	−0.0953291
$106$	763.698	0.699782
$107$	−1687.99	−1.52508	−0.762541	−	0.646940i	$-0.776048\pi$
$107$	−1687.99	−1.52508	−0.762541	+	0.646940i	$0.776048\pi$
$108$	−436.829	−0.389202
$109$	−774.557	−0.680634	−0.340317	−	0.940311i	$-0.610534\pi$
$109$	−774.557	−0.680634	−0.340317	+	0.940311i	$0.610534\pi$
$110$	47.7361	0.0413769
$111$	289.303	0.247383
$112$	1062.50	0.896397
$113$	432.103	0.359724	0.179862	−	0.983692i	$-0.442435\pi$
$113$	432.103	0.359724	0.179862	+	0.983692i	$0.442435\pi$
$114$	473.545	0.389048
$115$	336.812	0.273112
$116$	−1344.15	−1.07587
$117$	−1796.58	−1.41961
$118$	2165.01	1.68903
$119$	−1481.91	−1.14157
$120$	12.5496	0.00954682
$121$	−1326.82	−0.996861
$122$	2406.12	1.78557
$123$	69.6215	0.0510371
$124$	−140.537	−0.101779
$125$	−1273.91	−0.911533
$126$	−1594.76	−1.12756
$127$	322.714	0.225482	0.112741	−	0.993624i	$-0.464037\pi$
$127$	322.714	0.225482	0.112741	+	0.993624i	$0.464037\pi$
$128$	−245.465	−0.169502
$129$	303.185	0.206930
$130$	−1627.10	−1.09774
$131$	−1619.94	−1.08042	−0.540211	−	0.841530i	$-0.681655\pi$
$131$	−1619.94	−1.08042	−0.540211	+	0.841530i	$0.681655\pi$
$132$	−16.9152	−0.0111536
$133$	1713.83	1.11736
$134$	137.773	0.0888193
$135$	−344.799	−0.219819
$136$	181.319	0.114324
$137$	1320.83	0.823695	0.411847	−	0.911253i	$-0.364884\pi$
$137$	1320.83	0.823695	0.411847	+	0.911253i	$0.364884\pi$
$138$	−246.448	−0.152022
$139$	487.375	0.297400	0.148700	−	0.988882i	$-0.452491\pi$
$139$	487.375	0.297400	0.148700	+	0.988882i	$0.452491\pi$
$140$	−699.446	−0.422242
$141$	438.746	0.262050
$142$	−3395.53	−2.00666
$143$	−142.411	−0.0832799
$144$	1744.83	1.00974
$145$	−1060.96	−0.607643
$146$	3676.73	2.08417
$147$	−106.232	−0.0596043
$148$	1972.87	1.09574
$149$	−1063.28	−0.584614	−0.292307	−	0.956325i	$-0.594423\pi$
$149$	−1063.28	−0.584614	−0.292307	+	0.956325i	$0.594423\pi$
$150$	389.790	0.212175
$151$	−940.766	−0.507009	−0.253505	−	0.967334i	$-0.581583\pi$
$151$	−940.766	−0.507009	−0.253505	+	0.967334i	$0.581583\pi$
$152$	−209.696	−0.111899
$153$	−2433.60	−1.28591
$154$	−126.413	−0.0661471
$155$	−110.929	−0.0574840
$156$	576.559	0.295908
$157$	−2208.86	−1.12284	−0.561421	−	0.827530i	$-0.689745\pi$
$157$	−2208.86	−1.12284	−0.561421	+	0.827530i	$0.689745\pi$
$158$	−3901.20	−1.96432
$159$	−213.603	−0.106540
$160$	1489.09	0.735766
$161$	−891.935	−0.436610
$162$	−2489.87	−1.20755
$163$	−1028.98	−0.494452	−0.247226	−	0.968958i	$-0.579519\pi$
$163$	−1028.98	−0.494452	−0.247226	+	0.968958i	$0.579519\pi$
$164$	474.776	0.226059
$165$	−13.3516	−0.00629950
$166$	2282.27	1.06710
$167$	−3146.59	−1.45803	−0.729014	−	0.684499i	$-0.760021\pi$
$167$	−3146.59	−1.45803	−0.729014	+	0.684499i	$0.760021\pi$
$168$	−33.2335	−0.0152620
$169$	2657.12	1.20943
$170$	−2204.01	−0.994353
$171$	2814.46	1.25864
$172$	2067.53	0.916558
$173$	−2668.79	−1.17286	−0.586428	−	0.810001i	$-0.699466\pi$
$173$	−2668.79	−1.17286	−0.586428	+	0.810001i	$0.699466\pi$
$174$	776.315	0.338232
$175$	1410.71	0.609371
$176$	138.309	0.0592354
$177$	−605.545	−0.257150
$178$	6560.30	2.76245
$179$	−237.971	−0.0993676	−0.0496838	−	0.998765i	$-0.515821\pi$
$179$	−237.971	−0.0993676	−0.0496838	+	0.998765i	$0.515821\pi$
$180$	−1148.63	−0.475632
$181$	2188.76	0.898836	0.449418	−	0.893322i	$-0.351631\pi$
$181$	2188.76	0.898836	0.449418	+	0.893322i	$0.351631\pi$
$182$	4308.82	1.75490
$183$	−672.980	−0.271847
$184$	109.133	0.0437248
$185$	1557.23	0.618864
$186$	81.1675	0.0319972
$187$	−192.906	−0.0754367
$188$	2991.97	1.16070
$189$	913.085	0.351413
$190$	2548.94	0.973262
$191$	−501.787	−0.190095	−0.0950473	−	0.995473i	$-0.530300\pi$
$191$	−501.787	−0.190095	−0.0950473	+	0.995473i	$0.530300\pi$
$192$	−493.264	−0.185408
$193$	−191.710	−0.0715004	−0.0357502	−	0.999361i	$-0.511382\pi$
$193$	−191.710	−0.0715004	−0.0357502	+	0.999361i	$0.511382\pi$
$194$	6384.60	2.36282
$195$	455.091	0.167127
$196$	−724.433	−0.264006
$197$	−1535.48	−0.555321	−0.277660	−	0.960679i	$-0.589559\pi$
$197$	−1535.48	−0.555321	−0.277660	+	0.960679i	$0.589559\pi$
$198$	−207.595	−0.0745109
$199$	−3493.57	−1.24449	−0.622243	−	0.782824i	$-0.713779\pi$
$199$	−3493.57	−1.24449	−0.622243	+	0.782824i	$0.713779\pi$
$200$	−172.608	−0.0610260
$201$	−38.5345	−0.0135225
$202$	4512.31	1.57171
$203$	2809.61	0.971409
$204$	780.989	0.268040
$205$	374.751	0.127677
$206$	−4859.91	−1.64372
$207$	−1464.73	−0.491817
$208$	−4714.29	−1.57153
$209$	223.096	0.0738367
$210$	403.967	0.132745
$211$	2231.15	0.727958	0.363979	−	0.931407i	$-0.381418\pi$
$211$	2231.15	0.727958	0.363979	+	0.931407i	$0.381418\pi$
$212$	−1456.64	−0.471898
$213$	949.713	0.305508
$214$	6648.22	2.12366
$215$	1631.95	0.517666
$216$	−111.720	−0.0351926
$217$	293.758	0.0918968
$218$	3050.63	0.947775
$219$	−1028.36	−0.317308
$220$	−91.0493	−0.0279025
$221$	6575.24	2.00135
$222$	−1139.44	−0.344477
$223$	5963.47	1.79078	0.895389	−	0.445286i	$-0.146898\pi$
$223$	5963.47	1.79078	0.895389	+	0.445286i	$0.146898\pi$
$224$	−3943.35	−1.17623
$225$	2316.67	0.686421
$226$	−1701.86	−0.500912
$227$	−2485.67	−0.726784	−0.363392	−	0.931636i	$-0.618381\pi$
$227$	−2485.67	−0.726784	−0.363392	+	0.931636i	$0.618381\pi$
$228$	−903.215	−0.262355
$229$	−3517.68	−1.01509	−0.507543	−	0.861627i	$-0.669446\pi$
$229$	−3517.68	−1.01509	−0.507543	+	0.861627i	$0.669446\pi$
$230$	−1326.55	−0.380305
$231$	35.3571	0.0100707
$232$	−343.770	−0.0972827
$233$	−966.104	−0.271638	−0.135819	−	0.990734i	$-0.543367\pi$
$233$	−966.104	−0.271638	−0.135819	+	0.990734i	$0.543367\pi$
$234$	7075.94	1.97679
$235$	2361.63	0.655557
$236$	−4129.44	−1.13900
$237$	1091.15	0.299062
$238$	5836.59	1.58962
$239$	4186.37	1.13303	0.566514	−	0.824052i	$-0.308292\pi$
$239$	4186.37	1.13303	0.566514	+	0.824052i	$0.308292\pi$
$240$	−441.981	−0.118874
$241$	2705.69	0.723190	0.361595	−	0.932335i	$-0.382232\pi$
$241$	2705.69	0.723190	0.361595	+	0.932335i	$0.382232\pi$
$242$	5225.76	1.38812
$243$	2266.44	0.598321
$244$	−4589.30	−1.20410
$245$	−571.811	−0.149109
$246$	−274.208	−0.0710686
$247$	−7604.28	−1.95890
$248$	−35.9428	−0.00920309
$249$	−638.341	−0.162463
$250$	5017.34	1.26930
$251$	109.402	0.0275116	0.0137558	−	0.999905i	$-0.495621\pi$
$251$	109.402	0.0275116	0.0137558	+	0.999905i	$0.495621\pi$
$252$	3041.76	0.760369
$253$	−116.106	−0.0288519
$254$	−1271.03	−0.313981
$255$	616.452	0.151387
$256$	4548.96	1.11059
$257$	−4161.18	−1.00999	−0.504994	−	0.863123i	$-0.668505\pi$
$257$	−4161.18	−1.00999	−0.504994	+	0.863123i	$0.668505\pi$
$258$	−1194.11	−0.288148
$259$	−4123.80	−0.989346
$260$	3103.44	0.740258
$261$	4613.94	1.09424
$262$	6380.23	1.50447
$263$	5618.53	1.31731	0.658657	−	0.752444i	$-0.271125\pi$
$263$	5618.53	1.31731	0.658657	+	0.752444i	$0.271125\pi$
$264$	−4.32612	−0.00100854
$265$	−1149.76	−0.266525
$266$	−6750.03	−1.55590
$267$	−1834.89	−0.420574
$268$	−262.781	−0.0598952
$269$	−5662.05	−1.28335	−0.641675	−	0.766977i	$-0.721760\pi$
$269$	−5662.05	−1.28335	−0.641675	+	0.766977i	$0.721760\pi$
$270$	1358.01	0.306095
$271$	2268.20	0.508426	0.254213	−	0.967148i	$-0.418184\pi$
$271$	2268.20	0.508426	0.254213	+	0.967148i	$0.418184\pi$
$272$	−6385.83	−1.42352
$273$	−1205.16	−0.267177
$274$	−5202.16	−1.14699
$275$	183.638	0.0402682
$276$	470.062	0.102516
$277$	1916.40	0.415687	0.207844	−	0.978162i	$-0.433355\pi$
$277$	1916.40	0.415687	0.207844	+	0.978162i	$0.433355\pi$
$278$	−1919.55	−0.414126
$279$	482.409	0.103516
$280$	−178.885	−0.0381802
$281$	−3474.53	−0.737626	−0.368813	−	0.929504i	$-0.620236\pi$
$281$	−3474.53	−0.737626	−0.368813	+	0.929504i	$0.620236\pi$
$282$	−1728.02	−0.364902
$283$	−6360.19	−1.33595	−0.667975	−	0.744183i	$-0.732839\pi$
$283$	−6360.19	−1.33595	−0.667975	+	0.744183i	$0.732839\pi$
$284$	6476.45	1.35319
$285$	−712.928	−0.148176
$286$	560.894	0.115966
$287$	−992.403	−0.204110
$288$	−6475.76	−1.32496
$289$	3993.61	0.812867
$290$	4178.66	0.846136
$291$	−1785.74	−0.359733
$292$	−7012.80	−1.40546
$293$	8228.55	1.64067	0.820336	−	0.571882i	$-0.193786\pi$
$293$	8228.55	1.64067	0.820336	+	0.571882i	$0.193786\pi$
$294$	418.398	0.0829982
$295$	−3259.46	−0.643298
$296$	504.568	0.0990790
$297$	118.859	0.0232220
$298$	4187.79	0.814068
$299$	3957.51	0.765447
$300$	−743.465	−0.143080
$301$	−4321.68	−0.827566
$302$	3705.25	0.706005
$303$	−1262.07	−0.239288
$304$	7385.22	1.39333
$305$	−3622.44	−0.680066
$306$	9584.84	1.79062
$307$	2966.26	0.551445	0.275723	−	0.961237i	$-0.411083\pi$
$307$	2966.26	0.551445	0.275723	+	0.961237i	$0.411083\pi$
$308$	241.114	0.0446063
$309$	1359.29	0.250251
$310$	436.899	0.0800458
$311$	−1134.04	−0.206770	−0.103385	−	0.994641i	$-0.532967\pi$
$311$	−1134.04	−0.206770	−0.103385	+	0.994641i	$0.532967\pi$
$312$	147.457	0.0267567
$313$	8713.71	1.57357	0.786786	−	0.617226i	$-0.211744\pi$
$313$	8713.71	1.57357	0.786786	+	0.617226i	$0.211744\pi$
$314$	8699.71	1.56354
$315$	2400.93	0.429451
$316$	7440.96	1.32464
$317$	10150.4	1.79843	0.899217	−	0.437503i	$-0.144137\pi$
$317$	10150.4	1.79843	0.899217	+	0.437503i	$0.144137\pi$
$318$	841.286	0.148355
$319$	365.737	0.0641923
$320$	−2655.09	−0.463824
$321$	−1859.48	−0.323320
$322$	3512.93	0.607975
$323$	−10300.5	−1.77441
$324$	4749.04	0.814308
$325$	−6259.33	−1.06832
$326$	4052.68	0.688519
$327$	−853.248	−0.144296
$328$	121.425	0.0204408
$329$	−6254.00	−1.04801
$330$	52.5858	0.00877198
$331$	−7788.08	−1.29327	−0.646634	−	0.762801i	$-0.723824\pi$
$331$	−7788.08	−1.29327	−0.646634	+	0.762801i	$0.723824\pi$
$332$	−4353.08	−0.719598
$333$	−6772.11	−1.11444
$334$	12393.0	2.03029
$335$	−207.419	−0.0338284
$336$	1170.44	0.190038
$337$	−1881.16	−0.304076	−0.152038	−	0.988375i	$-0.548584\pi$
$337$	−1881.16	−0.304076	−0.152038	+	0.988375i	$0.548584\pi$
$338$	−10465.2	−1.68412
$339$	476.003	0.0762623
$340$	4203.82	0.670541
$341$	38.2395	0.00607269
$342$	−11084.9	−1.75264
$343$	6900.18	1.08622
$344$	528.778	0.0828774
$345$	371.030	0.0579003
$346$	10511.2	1.63319
$347$	−2329.24	−0.360346	−0.180173	−	0.983635i	$-0.557666\pi$
$347$	−2329.24	−0.360346	−0.180173	+	0.983635i	$0.557666\pi$
$348$	−1480.70	−0.228086
$349$	11091.6	1.70121	0.850605	−	0.525805i	$-0.176236\pi$
$349$	11091.6	1.70121	0.850605	+	0.525805i	$0.176236\pi$
$350$	−5556.17	−0.848542
$351$	−4051.35	−0.616083
$352$	−513.319	−0.0777273
$353$	−12791.5	−1.92868	−0.964339	−	0.264670i	$-0.914737\pi$
$353$	−12791.5	−1.92868	−0.964339	+	0.264670i	$0.914737\pi$
$354$	2384.97	0.358078
$355$	5112.01	0.764274
$356$	−12512.8	−1.86285
$357$	−1632.47	−0.242015
$358$	937.262	0.138368
$359$	−10224.0	−1.50307	−0.751533	−	0.659695i	$-0.770685\pi$
$359$	−10224.0	−1.50307	−0.751533	+	0.659695i	$0.770685\pi$
$360$	−293.766	−0.0430078
$361$	5053.56	0.736778
$362$	−8620.54	−1.25162
$363$	−1461.62	−0.211337
$364$	−8218.42	−1.18341
$365$	−5535.36	−0.793792
$366$	2650.57	0.378544
$367$	10129.0	1.44068	0.720342	−	0.693619i	$-0.243985\pi$
$367$	10129.0	1.44068	0.720342	+	0.693619i	$0.243985\pi$
$368$	−3843.51	−0.544447
$369$	−1629.72	−0.229919
$370$	−6133.23	−0.861761
$371$	3044.75	0.426079
$372$	−154.815	−0.0215773
$373$	7105.52	0.986353	0.493177	−	0.869929i	$-0.335836\pi$
$373$	7105.52	0.986353	0.493177	+	0.869929i	$0.335836\pi$
$374$	759.769	0.105045
$375$	−1403.33	−0.193247
$376$	765.207	0.104954
$377$	−12466.2	−1.70303
$378$	−3596.23	−0.489339
$379$	−5391.75	−0.730753	−0.365377	−	0.930860i	$-0.619060\pi$
$379$	−5391.75	−0.730753	−0.365377	+	0.930860i	$0.619060\pi$
$380$	−4861.72	−0.656319
$381$	355.500	0.0478027
$382$	1976.32	0.264705
$383$	−1408.01	−0.187849	−0.0939245	−	0.995579i	$-0.529941\pi$
$383$	−1408.01	−0.187849	−0.0939245	+	0.995579i	$0.529941\pi$
$384$	−270.403	−0.0359347
$385$	190.316	0.0251933
$386$	755.060	0.0995635
$387$	−7097.06	−0.932206
$388$	−12177.7	−1.59337
$389$	−7696.11	−1.00311	−0.501553	−	0.865127i	$-0.667238\pi$
$389$	−7696.11	−1.00311	−0.501553	+	0.865127i	$0.667238\pi$
$390$	−1792.40	−0.232722
$391$	5360.72	0.693358
$392$	−185.276	−0.0238721
$393$	−1784.52	−0.229051
$394$	6047.56	0.773278
$395$	5873.31	0.748148
$396$	395.957	0.0502464
$397$	−2577.21	−0.325810	−0.162905	−	0.986642i	$-0.552086\pi$
$397$	−2577.21	−0.325810	−0.162905	+	0.986642i	$0.552086\pi$
$398$	13759.6	1.73293
$399$	1887.95	0.236882
$400$	6079.02	0.759877
$401$	−8976.34	−1.11785	−0.558924	−	0.829219i	$-0.688786\pi$
$401$	−8976.34	−1.11785	−0.558924	+	0.829219i	$0.688786\pi$
$402$	151.770	0.0188299
$403$	−1303.40	−0.161110
$404$	−8606.54	−1.05988
$405$	3748.53	0.459915
$406$	−11065.8	−1.35268
$407$	−536.810	−0.0653776
$408$	199.740	0.0242368
$409$	−3113.28	−0.376385	−0.188193	−	0.982132i	$-0.560263\pi$
$409$	−3113.28	−0.376385	−0.188193	+	0.982132i	$0.560263\pi$
$410$	−1475.98	−0.177788
$411$	1455.02	0.174625
$412$	9269.54	1.10844
$413$	8631.59	1.02841
$414$	5768.93	0.684849
$415$	−3435.99	−0.406424
$416$	17496.6	2.06212
$417$	536.889	0.0630494
$418$	−878.675	−0.102817
$419$	337.975	0.0394061	0.0197031	−	0.999806i	$-0.493728\pi$
$419$	337.975	0.0394061	0.0197031	+	0.999806i	$0.493728\pi$
$420$	−770.506	−0.0895162
$421$	−3892.42	−0.450606	−0.225303	−	0.974289i	$-0.572337\pi$
$421$	−3892.42	−0.450606	−0.225303	+	0.974289i	$0.572337\pi$
$422$	−8787.52	−1.01367
$423$	−10270.3	−1.18052
$424$	−372.540	−0.0426701
$425$	−8478.69	−0.967710
$426$	−3740.49	−0.425417
$427$	9592.82	1.08719
$428$	−12680.5	−1.43209
$429$	−156.879	−0.0176555
$430$	−6427.52	−0.720843
$431$	8745.07	0.977344	0.488672	−	0.872468i	$-0.337482\pi$
$431$	8745.07	0.977344	0.488672	+	0.872468i	$0.337482\pi$
$432$	3934.65	0.438208
$433$	2985.46	0.331345	0.165672	−	0.986181i	$-0.447021\pi$
$433$	2985.46	0.331345	0.165672	+	0.986181i	$0.447021\pi$
$434$	−1156.98	−0.127965
$435$	−1168.75	−0.128822
$436$	−5818.62	−0.639131
$437$	−6199.68	−0.678652
$438$	4050.27	0.441847
$439$	7796.53	0.847627	0.423814	−	0.905749i	$-0.360691\pi$
$439$	7796.53	0.847627	0.423814	+	0.905749i	$0.360691\pi$
$440$	−23.2862	−0.00252301
$441$	2486.70	0.268513
$442$	−25896.9	−2.78686
$443$	10900.6	1.16908	0.584540	−	0.811365i	$-0.301275\pi$
$443$	10900.6	1.16908	0.584540	+	0.811365i	$0.301275\pi$
$444$	2173.30	0.232298
$445$	−9876.62	−1.05213
$446$	−23487.4	−2.49364
$447$	−1171.31	−0.123939
$448$	7031.11	0.741493
$449$	−13990.7	−1.47052	−0.735261	−	0.677784i	$-0.762940\pi$
$449$	−13990.7	−1.47052	−0.735261	+	0.677784i	$0.762940\pi$
$450$	−9124.33	−0.955834
$451$	−129.185	−0.0134880
$452$	3246.04	0.337790
$453$	−1036.34	−0.107487
$454$	9789.95	1.01204
$455$	−6486.98	−0.668383
$456$	−231.000	−0.0237227
$457$	14475.3	1.48168	0.740839	−	0.671683i	$-0.234428\pi$
$457$	14475.3	1.48168	0.740839	+	0.671683i	$0.234428\pi$
$458$	13854.6	1.41349
$459$	−5487.83	−0.558061
$460$	2530.20	0.256459
$461$	10844.6	1.09562	0.547811	−	0.836602i	$-0.315461\pi$
$461$	10844.6	1.09562	0.547811	+	0.836602i	$0.315461\pi$
$462$	−139.256	−0.0140233
$463$	10971.3	1.10125	0.550627	−	0.834751i	$-0.314389\pi$
$463$	10971.3	1.10125	0.550627	+	0.834751i	$0.314389\pi$
$464$	12107.1	1.21133
$465$	−122.199	−0.0121867
$466$	3805.05	0.378252
$467$	702.094	0.0695697	0.0347849	−	0.999395i	$-0.488925\pi$
$467$	702.094	0.0695697	0.0347849	+	0.999395i	$0.488925\pi$
$468$	−13496.3	−1.33305
$469$	549.281	0.0540798
$470$	−9301.41	−0.912856
$471$	−2433.27	−0.238045
$472$	−1056.12	−0.102991
$473$	−562.568	−0.0546869
$474$	−4297.55	−0.416441
$475$	9805.62	0.947184
$476$	−11132.4	−1.07196
$477$	5000.08	0.479954
$478$	−16488.2	−1.57773
$479$	7355.12	0.701595	0.350797	−	0.936451i	$-0.385911\pi$
$479$	7355.12	0.701595	0.350797	+	0.936451i	$0.385911\pi$
$480$	1640.37	0.155984
$481$	18297.3	1.73448
$482$	−10656.5	−1.00703
$483$	−982.550	−0.0925623
$484$	−9967.34	−0.936076
$485$	−9612.10	−0.899924
$486$	−8926.47	−0.833155
$487$	−9805.27	−0.912360	−0.456180	−	0.889888i	$-0.650783\pi$
$487$	−9805.27	−0.912360	−0.456180	+	0.889888i	$0.650783\pi$
$488$	−1173.73	−0.108877
$489$	−1133.52	−0.104825
$490$	2252.11	0.207632
$491$	−3228.08	−0.296703	−0.148351	−	0.988935i	$-0.547397\pi$
$491$	−3228.08	−0.296703	−0.148351	+	0.988935i	$0.547397\pi$
$492$	523.010	0.0479250
$493$	−16886.4	−1.54264
$494$	29949.8	2.72775
$495$	312.538	0.0283788
$496$	1265.86	0.114594
$497$	−13537.4	−1.22181
$498$	2514.14	0.226227
$499$	−4086.32	−0.366591	−0.183295	−	0.983058i	$-0.558676\pi$
$499$	−4086.32	−0.366591	−0.183295	+	0.983058i	$0.558676\pi$
$500$	−9569.82	−0.855951
$501$	−3466.27	−0.309105
$502$	−430.886	−0.0383095
$503$	−3651.39	−0.323673	−0.161836	−	0.986818i	$-0.551742\pi$
$503$	−3651.39	−0.323673	−0.161836	+	0.986818i	$0.551742\pi$
$504$	777.940	0.0687544
$505$	−6793.34	−0.598613
$506$	457.290	0.0401760
$507$	2927.07	0.256402
$508$	2424.29	0.211733
$509$	4282.26	0.372903	0.186452	−	0.982464i	$-0.440301\pi$
$509$	4282.26	0.372903	0.186452	+	0.982464i	$0.440301\pi$
$510$	−2427.93	−0.210805
$511$	14658.6	1.26900
$512$	−15952.6	−1.37698
$513$	6346.69	0.546224
$514$	16389.0	1.40640
$515$	7316.66	0.626040
$516$	2277.58	0.194312
$517$	−814.105	−0.0692539
$518$	16241.8	1.37765
$519$	−2939.92	−0.248648
$520$	793.714	0.0669359
$521$	1770.95	0.148919	0.0744595	−	0.997224i	$-0.476277\pi$
$521$	1770.95	0.148919	0.0744595	+	0.997224i	$0.476277\pi$
$522$	−18172.2	−1.52371
$523$	−11143.1	−0.931650	−0.465825	−	0.884877i	$-0.654242\pi$
$523$	−11143.1	−0.931650	−0.465825	+	0.884877i	$0.654242\pi$
$524$	−12169.3	−1.01454
$525$	1554.03	0.129188
$526$	−22128.9	−1.83434
$527$	−1765.55	−0.145937
$528$	152.360	0.0125580
$529$	−8940.49	−0.734815
$530$	4528.38	0.371132
$531$	14174.8	1.15844
$532$	12874.6	1.04922
$533$	4403.29	0.357838
$534$	7226.79	0.585644
$535$	−10009.0	−0.808833
$536$	−67.2072	−0.00541587
$537$	−262.148	−0.0210661
$538$	22300.3	1.78705
$539$	197.115	0.0157521
$540$	−2590.19	−0.206415
$541$	−3486.37	−0.277063	−0.138531	−	0.990358i	$-0.544238\pi$
$541$	−3486.37	−0.277063	−0.138531	+	0.990358i	$0.544238\pi$
$542$	−8933.43	−0.707977
$543$	2411.13	0.190555
$544$	23700.4	1.86791
$545$	−4592.77	−0.360977
$546$	4746.57	0.372041
$547$	547.000	0.0427569
$547$	547.000	0.0427569
$548$	9922.33	0.773469
$549$	15753.3	1.22466
$550$	−723.266	−0.0560730
$551$	19529.1	1.50992
$552$	120.220	0.00926974
$553$	−15553.5	−1.19603
$554$	−7547.84	−0.578840
$555$	1715.44	0.131200
$556$	3661.25	0.279266
$557$	−27.6172	−0.00210086	−0.00105043	−	0.999999i	$-0.500334\pi$
$557$	−27.6172	−0.00210086	−0.00105043	+	0.999999i	$0.500334\pi$
$558$	−1899.99	−0.144145
$559$	19175.3	1.45085
$560$	6300.11	0.475408
$561$	−212.504	−0.0159927
$562$	13684.6	1.02714
$563$	6983.45	0.522766	0.261383	−	0.965235i	$-0.415821\pi$
$563$	6983.45	0.522766	0.261383	+	0.965235i	$0.415821\pi$
$564$	3295.94	0.246071
$565$	2562.17	0.190781
$566$	25049.9	1.86030
$567$	−9926.72	−0.735244
$568$	1656.37	0.122359
$569$	−26528.3	−1.95453	−0.977263	−	0.212030i	$-0.931993\pi$
$569$	−26528.3	−1.95453	−0.977263	+	0.212030i	$0.931993\pi$
$570$	2807.90	0.206333
$571$	25717.1	1.88481	0.942406	−	0.334472i	$-0.108558\pi$
$571$	25717.1	1.88481	0.942406	+	0.334472i	$0.108558\pi$
$572$	−1069.82	−0.0782018
$573$	−552.766	−0.0403004
$574$	3908.63	0.284221
$575$	−5103.16	−0.370115
$576$	11546.5	0.835249
$577$	3163.28	0.228231	0.114115	−	0.993467i	$-0.463597\pi$
$577$	3163.28	0.228231	0.114115	+	0.993467i	$0.463597\pi$
$578$	−15729.1	−1.13191
$579$	−211.187	−0.0151582
$580$	−7970.17	−0.570592
$581$	9099.07	0.649730
$582$	7033.25	0.500923
$583$	396.346	0.0281560
$584$	−1793.55	−0.127085
$585$	−10652.9	−0.752896
$586$	−32408.6	−2.28462
$587$	7244.57	0.509396	0.254698	−	0.967021i	$-0.418024\pi$
$587$	7244.57	0.509396	0.254698	+	0.967021i	$0.418024\pi$
$588$	−798.031	−0.0559698
$589$	2041.86	0.142841
$590$	12837.5	0.895785
$591$	−1691.47	−0.117729
$592$	−17770.2	−1.23370
$593$	25168.0	1.74288	0.871438	−	0.490505i	$-0.163188\pi$
$593$	25168.0	1.74288	0.871438	+	0.490505i	$0.163188\pi$
$594$	−468.134	−0.0323363
$595$	−8787.06	−0.605436
$596$	−7987.58	−0.548966
$597$	−3848.50	−0.263834
$598$	−15586.9	−1.06588
$599$	13803.0	0.941527	0.470764	−	0.882259i	$-0.343978\pi$
$599$	13803.0	0.941527	0.470764	+	0.882259i	$0.343978\pi$
$600$	−190.144	−0.0129376
$601$	−7008.67	−0.475690	−0.237845	−	0.971303i	$-0.576441\pi$
$601$	−7008.67	−0.475690	−0.237845	+	0.971303i	$0.576441\pi$
$602$	17021.2	1.15238
$603$	902.028	0.0609178
$604$	−7067.21	−0.476094
$605$	−7867.44	−0.528689
$606$	4970.73	0.333205
$607$	−21659.1	−1.44830	−0.724148	−	0.689644i	$-0.757767\pi$
$607$	−21659.1	−1.44830	−0.724148	+	0.689644i	$0.757767\pi$
$608$	−27409.5	−1.82829
$609$	3095.05	0.205941
$610$	14267.2	0.946985
$611$	27749.0	1.83732
$612$	−18281.6	−1.20750
$613$	−9765.36	−0.643424	−0.321712	−	0.946837i	$-0.604258\pi$
$613$	−9765.36	−0.643424	−0.321712	+	0.946837i	$0.604258\pi$
$614$	−11682.8	−0.767881
$615$	412.824	0.0270677
$616$	61.6656	0.00403341
$617$	4959.79	0.323620	0.161810	−	0.986822i	$-0.448267\pi$
$617$	4959.79	0.323620	0.161810	+	0.986822i	$0.448267\pi$
$618$	−5353.65	−0.348472
$619$	−7135.88	−0.463352	−0.231676	−	0.972793i	$-0.574421\pi$
$619$	−7135.88	−0.463352	−0.231676	+	0.972793i	$0.574421\pi$
$620$	−833.319	−0.0539789
$621$	−3303.02	−0.213439
$622$	4466.47	0.287925
$623$	26154.9	1.68198
$624$	−5193.24	−0.333167
$625$	3676.39	0.235289
$626$	−34319.4	−2.19118
$627$	245.761	0.0156535
$628$	−16593.4	−1.05437
$629$	24784.9	1.57113
$630$	−9456.19	−0.598006
$631$	−21377.8	−1.34871	−0.674356	−	0.738406i	$-0.735579\pi$
$631$	−21377.8	−1.34871	−0.674356	+	0.738406i	$0.735579\pi$
$632$	1903.05	0.119777
$633$	2457.83	0.154328
$634$	−39977.9	−2.50430
$635$	1913.55	0.119585
$636$	−1604.62	−0.100043
$637$	−6718.72	−0.417905
$638$	−1440.47	−0.0893870
$639$	−22231.2	−1.37629
$640$	−1455.49	−0.0898961
$641$	25688.0	1.58286	0.791431	−	0.611259i	$-0.209336\pi$
$641$	25688.0	1.58286	0.791431	+	0.611259i	$0.209336\pi$
$642$	7323.64	0.450220
$643$	31621.2	1.93937	0.969687	−	0.244351i	$-0.0785748\pi$
$643$	31621.2	1.93937	0.969687	+	0.244351i	$0.0785748\pi$
$644$	−6700.38	−0.409988
$645$	1797.75	0.109746
$646$	40569.1	2.47085
$647$	6182.40	0.375665	0.187832	−	0.982201i	$-0.439854\pi$
$647$	6182.40	0.375665	0.187832	+	0.982201i	$0.439854\pi$
$648$	1214.58	0.0736317
$649$	1123.60	0.0679589
$650$	24652.7	1.48763
$651$	323.602	0.0194823
$652$	−7729.87	−0.464302
$653$	18466.2	1.10664	0.553322	−	0.832967i	$-0.313360\pi$
$653$	18466.2	1.10664	0.553322	+	0.832967i	$0.313360\pi$
$654$	3360.56	0.200930
$655$	−9605.53	−0.573006
$656$	−4276.44	−0.254523
$657$	24072.3	1.42945
$658$	24631.7	1.45934
$659$	−15339.2	−0.906726	−0.453363	−	0.891326i	$-0.649776\pi$
$659$	−15339.2	−0.906726	−0.453363	+	0.891326i	$0.649776\pi$
$660$	−100.299	−0.00591538
$661$	−8518.30	−0.501246	−0.250623	−	0.968085i	$-0.580635\pi$
$661$	−8518.30	−0.501246	−0.250623	+	0.968085i	$0.580635\pi$
$662$	30673.7	1.80086
$663$	7243.25	0.424290
$664$	−1113.32	−0.0650678
$665$	10162.3	0.592594
$666$	26672.3	1.55185
$667$	−10163.6	−0.590008
$668$	−23637.8	−1.36912
$669$	6569.32	0.379648
$670$	816.931	0.0471057
$671$	1248.73	0.0718431
$672$	−4343.97	−0.249364
$673$	28363.1	1.62454	0.812271	−	0.583281i	$-0.198231\pi$
$673$	28363.1	1.62454	0.812271	+	0.583281i	$0.198231\pi$
$674$	7409.06	0.423422
$675$	5224.17	0.297894
$676$	19960.8	1.13569
$677$	−23147.2	−1.31406	−0.657029	−	0.753865i	$-0.728187\pi$
$677$	−23147.2	−1.31406	−0.657029	+	0.753865i	$0.728187\pi$
$678$	−1874.76	−0.106194
$679$	25454.5	1.43866
$680$	1075.14	0.0606320
$681$	−2738.20	−0.154080
$682$	−150.608	−0.00845615
$683$	356.178	0.0199543	0.00997714	−	0.999950i	$-0.496824\pi$
$683$	356.178	0.0199543	0.00997714	+	0.999950i	$0.496824\pi$
$684$	21142.7	1.18189
$685$	7831.92	0.436850
$686$	−27176.7	−1.51255
$687$	−3875.05	−0.215200
$688$	−18622.9	−1.03196
$689$	−13509.5	−0.746984
$690$	−1461.32	−0.0806255
$691$	−28208.0	−1.55294	−0.776472	−	0.630152i	$-0.782993\pi$
$691$	−28208.0	−1.55294	−0.776472	+	0.630152i	$0.782993\pi$
$692$	−20048.4	−1.10134
$693$	−827.652	−0.0453678
$694$	9173.83	0.501778
$695$	2889.91	0.157727
$696$	−378.695	−0.0206241
$697$	5964.56	0.324137
$698$	−43685.0	−2.36892
$699$	−1064.26	−0.0575877
$700$	10597.5	0.572214
$701$	24941.8	1.34385	0.671924	−	0.740620i	$-0.265468\pi$
$701$	24941.8	1.34385	0.671924	+	0.740620i	$0.265468\pi$
$702$	15956.5	0.857889
$703$	−28663.8	−1.53780
$704$	915.264	0.0489990
$705$	2601.56	0.138979
$706$	50380.0	2.68566
$707$	17989.9	0.956972
$708$	−4548.97	−0.241470
$709$	20194.5	1.06970	0.534852	−	0.844946i	$-0.320367\pi$
$709$	20194.5	1.06970	0.534852	+	0.844946i	$0.320367\pi$
$710$	−20133.9	−1.06424
$711$	−25542.0	−1.34726
$712$	−3200.18	−0.168444
$713$	−1062.65	−0.0558156
$714$	6429.56	0.337003
$715$	−844.433	−0.0441679
$716$	−1787.68	−0.0933085
$717$	4611.68	0.240204
$718$	40267.7	2.09300
$719$	−21239.7	−1.10168	−0.550841	−	0.834610i	$-0.685693\pi$
$719$	−21239.7	−1.10168	−0.550841	+	0.834610i	$0.685693\pi$
$720$	10346.0	0.535520
$721$	−19375.7	−1.00082
$722$	−19903.7	−1.02595
$723$	2980.57	0.153318
$724$	16442.4	0.844028
$725$	16075.0	0.823465
$726$	5756.67	0.294284
$727$	−25640.7	−1.30806	−0.654030	−	0.756469i	$-0.726923\pi$
$727$	−25640.7	−1.30806	−0.654030	+	0.756469i	$0.726923\pi$
$728$	−2101.89	−0.107007
$729$	−14572.1	−0.740340
$730$	21801.3	1.10535
$731$	25974.2	1.31421
$732$	−5055.55	−0.255271
$733$	38416.3	1.93579	0.967897	−	0.251348i	$-0.0808739\pi$
$733$	38416.3	1.93579	0.967897	+	0.251348i	$0.0808739\pi$
$734$	−39893.7	−2.00614
$735$	−629.904	−0.0316114
$736$	14264.8	0.714412
$737$	71.5018	0.00357368
$738$	6418.75	0.320159
$739$	13783.7	0.686116	0.343058	−	0.939314i	$-0.388537\pi$
$739$	13783.7	0.686116	0.343058	+	0.939314i	$0.388537\pi$
$740$	11698.2	0.581128
$741$	−8376.83	−0.415291
$742$	−11991.9	−0.593311
$743$	−7073.69	−0.349271	−0.174636	−	0.984633i	$-0.555875\pi$
$743$	−7073.69	−0.349271	−0.174636	+	0.984633i	$0.555875\pi$
$744$	−39.5943	−0.00195107
$745$	−6304.78	−0.310053
$746$	−27985.4	−1.37349
$747$	14942.5	0.731883
$748$	−1449.14	−0.0708369
$749$	26505.4	1.29304
$750$	5527.08	0.269094
$751$	−36526.5	−1.77480	−0.887398	−	0.461003i	$-0.847490\pi$
$751$	−36526.5	−1.77480	−0.887398	+	0.461003i	$0.847490\pi$
$752$	−26949.6	−1.30685
$753$	120.517	0.00583251
$754$	49098.9	2.37145
$755$	−5578.31	−0.268895
$756$	6859.26	0.329985
$757$	4774.10	0.229218	0.114609	−	0.993411i	$-0.463439\pi$
$757$	4774.10	0.229218	0.114609	+	0.993411i	$0.463439\pi$
$758$	21235.7	1.01757
$759$	−127.902	−0.00611667
$760$	−1243.40	−0.0593459
$761$	−8485.35	−0.404197	−0.202098	−	0.979365i	$-0.564776\pi$
$761$	−8485.35	−0.404197	−0.202098	+	0.979365i	$0.564776\pi$
$762$	−1400.16	−0.0665647
$763$	12162.4	0.577076
$764$	−3769.52	−0.178503
$765$	−14430.1	−0.681989
$766$	5545.53	0.261577
$767$	−38298.3	−1.80296
$768$	5011.11	0.235446
$769$	−16542.5	−0.775731	−0.387865	−	0.921716i	$-0.626787\pi$
$769$	−16542.5	−0.775731	−0.387865	+	0.921716i	$0.626787\pi$
$770$	−749.571	−0.0350814
$771$	−4583.93	−0.214120
$772$	−1440.16	−0.0671406
$773$	−26389.5	−1.22790	−0.613948	−	0.789347i	$-0.710419\pi$
$773$	−26389.5	−1.22790	−0.613948	+	0.789347i	$0.710419\pi$
$774$	27952.1	1.29809
$775$	1680.72	0.0779011
$776$	−3114.48	−0.144076
$777$	−4542.76	−0.209743
$778$	30311.5	1.39681
$779$	−6898.02	−0.317262
$780$	3418.73	0.156936
$781$	−1762.22	−0.0807389
$782$	−21113.5	−0.965493
$783$	10404.6	0.474878
$784$	6525.18	0.297248
$785$	−13097.5	−0.595504
$786$	7028.43	0.318952
$787$	−39467.8	−1.78764	−0.893821	−	0.448424i	$-0.851985\pi$
$787$	−39467.8	−1.78764	−0.893821	+	0.448424i	$0.851985\pi$
$788$	−11534.8	−0.521459
$789$	6189.34	0.279273
$790$	−23132.3	−1.04179
$791$	−6785.06	−0.304992
$792$	101.267	0.00454340
$793$	−42563.3	−1.90601
$794$	10150.5	0.453687
$795$	−1266.57	−0.0565037
$796$	−26244.4	−1.16860
$797$	26516.7	1.17851	0.589253	−	0.807949i	$-0.299422\pi$
$797$	26516.7	1.17851	0.589253	+	0.807949i	$0.299422\pi$
$798$	−7435.79	−0.329855
$799$	37587.9	1.66428
$800$	−22561.7	−0.997094
$801$	42951.6	1.89466
$802$	35353.8	1.55659
$803$	1908.16	0.0838573
$804$	−289.478	−0.0126979
$805$	−5288.76	−0.231558
$806$	5133.52	0.224343
$807$	−6237.28	−0.272073
$808$	−2201.15	−0.0958369
$809$	−14045.3	−0.610393	−0.305196	−	0.952289i	$-0.598722\pi$
$809$	−14045.3	−0.610393	−0.305196	+	0.952289i	$0.598722\pi$
$810$	−14763.8	−0.640427
$811$	−42882.0	−1.85671	−0.928355	−	0.371695i	$-0.878777\pi$
$811$	−42882.0	−1.85671	−0.928355	+	0.371695i	$0.878777\pi$
$812$	21106.3	0.912176
$813$	2498.64	0.107787
$814$	2114.25	0.0910376
$815$	−6101.36	−0.262235
$816$	−7034.60	−0.301789
$817$	−30039.2	−1.28634
$818$	12261.8	0.524112
$819$	28210.7	1.20362
$820$	2815.20	0.119892
$821$	−10379.2	−0.441216	−0.220608	−	0.975363i	$-0.570804\pi$
$821$	−10379.2	−0.441216	−0.220608	+	0.975363i	$0.570804\pi$
$822$	−5730.67	−0.243163
$823$	−20224.4	−0.856595	−0.428298	−	0.903638i	$-0.640886\pi$
$823$	−20224.4	−0.856595	−0.428298	+	0.903638i	$0.640886\pi$
$824$	2370.72	0.100228
$825$	202.294	0.00853694
$826$	−33995.9	−1.43205
$827$	−25184.5	−1.05895	−0.529476	−	0.848325i	$-0.677611\pi$
$827$	−25184.5	−1.05895	−0.529476	+	0.848325i	$0.677611\pi$
$828$	−11003.4	−0.461828
$829$	−41231.1	−1.72740	−0.863701	−	0.504004i	$-0.831860\pi$
$829$	−41231.1	−1.72740	−0.863701	+	0.504004i	$0.831860\pi$
$830$	13532.8	0.565941
$831$	2111.10	0.0881265
$832$	−31197.0	−1.29995
$833$	−9100.97	−0.378547
$834$	−2114.57	−0.0877955
$835$	−18657.8	−0.773271
$836$	1675.94	0.0693344
$837$	1087.85	0.0449242
$838$	−1331.13	−0.0548726
$839$	−28247.1	−1.16233	−0.581167	−	0.813784i	$-0.697404\pi$
$839$	−28247.1	−1.16233	−0.581167	+	0.813784i	$0.697404\pi$
$840$	−197.059	−0.00809428
$841$	7626.45	0.312700
$842$	15330.5	0.627464
$843$	−3827.52	−0.156378
$844$	16760.9	0.683569
$845$	15755.5	0.641427
$846$	40450.1	1.64386
$847$	20834.3	0.845189
$848$	13120.4	0.531315
$849$	−7006.35	−0.283224
$850$	33393.8	1.34753
$851$	14917.6	0.600902
$852$	7134.42	0.286879
$853$	24616.7	0.988111	0.494055	−	0.869430i	$-0.335514\pi$
$853$	24616.7	0.988111	0.494055	+	0.869430i	$0.335514\pi$
$854$	−37781.8	−1.51390
$855$	16688.4	0.667524
$856$	−3243.07	−0.129493
$857$	−10926.9	−0.435536	−0.217768	−	0.976001i	$-0.569878\pi$
$857$	−10926.9	−0.435536	−0.217768	+	0.976001i	$0.569878\pi$
$858$	617.878	0.0245851
$859$	13608.1	0.540514	0.270257	−	0.962788i	$-0.412891\pi$
$859$	13608.1	0.540514	0.270257	+	0.962788i	$0.412891\pi$
$860$	12259.5	0.486100
$861$	−1093.23	−0.0432718
$862$	−34442.9	−1.36094
$863$	30754.1	1.21307	0.606537	−	0.795055i	$-0.292558\pi$
$863$	30754.1	1.21307	0.606537	+	0.795055i	$0.292558\pi$
$864$	−14603.0	−0.575007
$865$	−15824.7	−0.622029
$866$	−11758.4	−0.461394
$867$	4399.34	0.172329
$868$	2206.77	0.0862933
$869$	−2024.66	−0.0790354
$870$	4603.19	0.179383
$871$	−2437.16	−0.0948104
$872$	−1488.13	−0.0577918
$873$	41801.3	1.62057
$874$	24417.8	0.945015
$875$	20003.4	0.772843
$876$	−7725.27	−0.297960
$877$	33224.5	1.27926	0.639631	−	0.768682i	$-0.279087\pi$
$877$	33224.5	1.27926	0.639631	+	0.768682i	$0.279087\pi$
$878$	−30707.1	−1.18031
$879$	9064.53	0.347826
$880$	820.108	0.0314157
$881$	−40368.3	−1.54375	−0.771874	−	0.635775i	$-0.780681\pi$
$881$	−40368.3	−1.54375	−0.771874	+	0.635775i	$0.780681\pi$
$882$	−9794.00	−0.373902
$883$	44664.6	1.70225	0.851123	−	0.524967i	$-0.175922\pi$
$883$	44664.6	1.70225	0.851123	+	0.524967i	$0.175922\pi$
$884$	49394.5	1.87932
$885$	−3590.60	−0.136380
$886$	−42932.5	−1.62793
$887$	35260.2	1.33475	0.667374	−	0.744722i	$-0.267418\pi$
$887$	35260.2	1.33475	0.667374	+	0.744722i	$0.267418\pi$
$888$	555.829	0.0210050
$889$	−5067.39	−0.191175
$890$	38899.6	1.46507
$891$	−1292.20	−0.0485861
$892$	44798.7	1.68158
$893$	−43470.4	−1.62898
$894$	4613.25	0.172584
$895$	−1411.06	−0.0527000
$896$	3854.39	0.143712
$897$	4359.57	0.162276
$898$	55103.3	2.04768
$899$	3347.37	0.124183
$900$	17403.3	0.644566
$901$	−18299.6	−0.676634
$902$	508.800	0.0187818
$903$	−4760.74	−0.175446
$904$	830.186	0.0305438
$905$	12978.3	0.476701
$906$	4081.69	0.149674
$907$	−8646.86	−0.316554	−0.158277	−	0.987395i	$-0.550594\pi$
$907$	−8646.86	−0.316554	−0.158277	+	0.987395i	$0.550594\pi$
$908$	−18672.8	−0.682467
$909$	29543.0	1.07797
$910$	25549.3	0.930716
$911$	10416.0	0.378811	0.189406	−	0.981899i	$-0.439344\pi$
$911$	10416.0	0.378811	0.189406	+	0.981899i	$0.439344\pi$
$912$	8135.52	0.295388
$913$	1184.46	0.0429352
$914$	−57011.8	−2.06322
$915$	−3990.46	−0.144175
$916$	−26425.5	−0.953190
$917$	25437.0	0.916036
$918$	21614.1	0.777094
$919$	−17160.1	−0.615953	−0.307977	−	0.951394i	$-0.599652\pi$
$919$	−17160.1	−0.615953	−0.307977	+	0.951394i	$0.599652\pi$
$920$	647.106	0.0231896
$921$	3267.62	0.116907
$922$	−42711.9	−1.52564
$923$	60065.6	2.14202
$924$	265.610	0.00945662
$925$	−23594.1	−0.838671
$926$	−43211.2	−1.53348
$927$	−31818.8	−1.12736
$928$	−44934.4	−1.58949
$929$	−33512.3	−1.18353	−0.591767	−	0.806109i	$-0.701569\pi$
$929$	−33512.3	−1.18353	−0.591767	+	0.806109i	$0.701569\pi$
$930$	481.286	0.0169699
$931$	10525.3	0.370518
$932$	−7257.56	−0.255074
$933$	−1249.25	−0.0438356
$934$	−2765.23	−0.0968750
$935$	−1143.84	−0.0400082
$936$	−3451.72	−0.120537
$937$	−19078.2	−0.665161	−0.332581	−	0.943075i	$-0.607919\pi$
$937$	−19078.2	−0.665161	−0.332581	+	0.943075i	$0.607919\pi$
$938$	−2163.37	−0.0753055
$939$	9598.98	0.333600
$940$	17741.0	0.615584
$941$	45072.4	1.56144	0.780722	−	0.624878i	$-0.214851\pi$
$941$	45072.4	1.56144	0.780722	+	0.624878i	$0.214851\pi$
$942$	9583.55	0.331474
$943$	3589.95	0.123971
$944$	37195.1	1.28241
$945$	5414.17	0.186374
$946$	2215.70	0.0761509
$947$	−27048.3	−0.928142	−0.464071	−	0.885798i	$-0.653612\pi$
$947$	−27048.3	−0.928142	−0.464071	+	0.885798i	$0.653612\pi$
$948$	8196.92	0.280826
$949$	−65040.0	−2.22475
$950$	−38619.9	−1.31894
$951$	11181.6	0.381272
$952$	−2847.15	−0.0969293
$953$	−48610.7	−1.65231	−0.826157	−	0.563439i	$-0.809478\pi$
$953$	−48610.7	−1.65231	−0.826157	+	0.563439i	$0.809478\pi$
$954$	−19693.1	−0.668330
$955$	−2975.37	−0.100817
$956$	31448.8	1.06394
$957$	402.894	0.0136089
$958$	−28968.5	−0.976963
$959$	−20740.2	−0.698370
$960$	−2924.83	−0.0983317
$961$	−29441.0	−0.988252
$962$	−72064.9	−2.41524
$963$	43527.2	1.45654
$964$	20325.6	0.679092
$965$	−1136.75	−0.0379206
$966$	3869.83	0.128892
$967$	20268.4	0.674032	0.337016	−	0.941499i	$-0.390582\pi$
$967$	20268.4	0.674032	0.337016	+	0.941499i	$0.390582\pi$
$968$	−2549.18	−0.0846423
$969$	−11347.0	−0.376179
$970$	37857.8	1.25313
$971$	35826.0	1.18405	0.592025	−	0.805920i	$-0.298329\pi$
$971$	35826.0	1.18405	0.592025	+	0.805920i	$0.298329\pi$
$972$	17025.9	0.561837
$973$	−7652.96	−0.252151
$974$	38618.6	1.27045
$975$	−6895.24	−0.226487
$976$	41337.2	1.35571
$977$	30211.8	0.989316	0.494658	−	0.869088i	$-0.335293\pi$
$977$	30211.8	0.989316	0.494658	+	0.869088i	$0.335293\pi$
$978$	4464.41	0.145967
$979$	3404.68	0.111148
$980$	−4295.55	−0.140017
$981$	19973.1	0.650043
$982$	12714.0	0.413155
$983$	2020.37	0.0655541	0.0327771	−	0.999463i	$-0.489565\pi$
$983$	2020.37	0.0655541	0.0327771	+	0.999463i	$0.489565\pi$
$984$	133.762	0.00433350
$985$	−9104.67	−0.294517
$986$	66507.8	2.14811
$987$	−6889.37	−0.222179
$988$	−57124.8	−1.83945
$989$	15633.4	0.502641
$990$	−1230.95	−0.0395172
$991$	33668.7	1.07923	0.539617	−	0.841911i	$-0.318569\pi$
$991$	33668.7	1.07923	0.539617	+	0.841911i	$0.318569\pi$
$992$	−4698.10	−0.150368
$993$	−8579.31	−0.274175
$994$	53317.9	1.70135
$995$	−20715.3	−0.660019
$996$	−4795.34	−0.152556
$997$	59598.9	1.89319	0.946597	−	0.322419i	$-0.104496\pi$
$997$	59598.9	1.89319	0.946597	+	0.322419i	$0.104496\pi$
$998$	16094.2	0.510473
$999$	−15271.3	−0.483647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.4.a.a.1.12	✓	65

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.4.a.a.1.12	✓	65	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:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	547.a (trivial)

\(f(q)\)	\(=\)	\(q-3.93855 q^{2} +1.10159 q^{3} +7.51219 q^{4} +5.92954 q^{5} -4.33869 q^{6} -15.7024 q^{7} +1.92127 q^{8} -25.7865 q^{9} +O(q^{10})\)	\(q-3.93855 q^{2} +1.10159 q^{3} +7.51219 q^{4} +5.92954 q^{5} -4.33869 q^{6} -15.7024 q^{7} +1.92127 q^{8} -25.7865 q^{9} -23.3538 q^{10} -2.04404 q^{11} +8.27539 q^{12} +69.6715 q^{13} +61.8448 q^{14} +6.53195 q^{15} -67.6645 q^{16} +94.3749 q^{17} +101.561 q^{18} -109.145 q^{19} +44.5438 q^{20} -17.2977 q^{21} +8.05055 q^{22} +56.8024 q^{23} +2.11646 q^{24} -89.8405 q^{25} -274.405 q^{26} -58.1493 q^{27} -117.959 q^{28} -178.929 q^{29} -25.7264 q^{30} -18.7078 q^{31} +251.130 q^{32} -2.25170 q^{33} -371.700 q^{34} -93.1081 q^{35} -193.713 q^{36} +262.622 q^{37} +429.872 q^{38} +76.7498 q^{39} +11.3922 q^{40} +63.2007 q^{41} +68.1279 q^{42} +275.224 q^{43} -15.3552 q^{44} -152.902 q^{45} -223.719 q^{46} +398.283 q^{47} -74.5389 q^{48} -96.4343 q^{49} +353.842 q^{50} +103.963 q^{51} +523.386 q^{52} -193.903 q^{53} +229.024 q^{54} -12.1202 q^{55} -30.1685 q^{56} -120.233 q^{57} +704.720 q^{58} -549.698 q^{59} +49.0693 q^{60} -610.914 q^{61} +73.6818 q^{62} +404.910 q^{63} -447.773 q^{64} +413.120 q^{65} +8.86844 q^{66} -34.9807 q^{67} +708.962 q^{68} +62.5732 q^{69} +366.711 q^{70} +862.125 q^{71} -49.5427 q^{72} -933.523 q^{73} -1034.35 q^{74} -98.9679 q^{75} -819.915 q^{76} +32.0963 q^{77} -302.283 q^{78} +990.518 q^{79} -401.220 q^{80} +632.178 q^{81} -248.919 q^{82} -579.469 q^{83} -129.944 q^{84} +559.600 q^{85} -1083.98 q^{86} -197.107 q^{87} -3.92714 q^{88} -1665.66 q^{89} +602.213 q^{90} -1094.01 q^{91} +426.710 q^{92} -20.6085 q^{93} -1568.66 q^{94} -647.178 q^{95} +276.644 q^{96} -1621.05 q^{97} +379.811 q^{98} +52.7086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9	\( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 65 * q - 12 * q^2 - 35 * q^3 + 234 * q^4 - 151 * q^5 - 60 * q^6 - 74 * q^7 - 144 * q^8 + 468 * q^9 - 60 * q^10 - 191 * q^11 - 483 * q^12 - 333 * q^13 - 377 * q^14 - 166 * q^15 + 818 * q^16 - 858 * q^17 - 279 * q^18 - 185 * q^19 - 1188 * q^20 - 406 * q^21 - 356 * q^22 - 836 * q^23 - 505 * q^24 + 1156 * q^25 - 696 * q^26 - 1094 * q^27 - 1096 * q^28 - 1209 * q^29 - 1054 * q^30 - 286 * q^31 - 1484 * q^32 - 1296 * q^33 - 763 * q^34 - 1374 * q^35 + 296 * q^36 - 1705 * q^37 - 2535 * q^38 - 622 * q^39 - 888 * q^40 - 1348 * q^41 - 1716 * q^42 - 973 * q^43 - 2568 * q^44 - 4529 * q^45 - 322 * q^46 - 2498 * q^47 - 5358 * q^48 + 2081 * q^49 - 2002 * q^50 - 1108 * q^51 - 3290 * q^52 - 5947 * q^53 - 2783 * q^54 - 1344 * q^55 - 5111 * q^56 - 3134 * q^57 - 1676 * q^58 - 1625 * q^59 - 2902 * q^60 - 3103 * q^61 - 5242 * q^62 - 3106 * q^63 + 1722 * q^64 - 3160 * q^65 - 3672 * q^66 - 2395 * q^67 - 8447 * q^68 - 4944 * q^69 - 597 * q^70 - 2654 * q^71 - 3929 * q^72 - 2116 * q^73 - 3969 * q^74 - 3759 * q^75 - 1844 * q^76 - 9938 * q^77 - 3935 * q^78 - 1206 * q^79 - 11619 * q^80 + 1889 * q^81 - 7674 * q^82 - 4337 * q^83 - 1873 * q^84 - 2624 * q^85 - 3543 * q^86 - 3066 * q^87 - 3689 * q^88 - 5774 * q^89 - 3149 * q^90 - 3148 * q^91 - 8942 * q^92 - 7118 * q^93 - 5137 * q^94 - 2742 * q^95 - 6558 * q^96 - 6378 * q^97 - 7250 * q^98 - 3941 * q^99

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