LMFDB - Embedded newform 6010.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.88167 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.88167 q^{6} -3.66727 q^{7} +1.00000 q^{8} +0.540685 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.88167 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.88167 q^{6} -3.66727 q^{7} +1.00000 q^{8} +0.540685 q^{9} -1.00000 q^{10} -0.908393 q^{11} -1.88167 q^{12} +0.683603 q^{13} -3.66727 q^{14} +1.88167 q^{15} +1.00000 q^{16} +3.70546 q^{17} +0.540685 q^{18} -0.299224 q^{19} -1.00000 q^{20} +6.90060 q^{21} -0.908393 q^{22} +5.59466 q^{23} -1.88167 q^{24} +1.00000 q^{25} +0.683603 q^{26} +4.62762 q^{27} -3.66727 q^{28} +5.42437 q^{29} +1.88167 q^{30} -4.63702 q^{31} +1.00000 q^{32} +1.70930 q^{33} +3.70546 q^{34} +3.66727 q^{35} +0.540685 q^{36} -11.2720 q^{37} -0.299224 q^{38} -1.28632 q^{39} -1.00000 q^{40} +2.39519 q^{41} +6.90060 q^{42} -1.55228 q^{43} -0.908393 q^{44} -0.540685 q^{45} +5.59466 q^{46} +8.87308 q^{47} -1.88167 q^{48} +6.44888 q^{49} +1.00000 q^{50} -6.97246 q^{51} +0.683603 q^{52} -2.22493 q^{53} +4.62762 q^{54} +0.908393 q^{55} -3.66727 q^{56} +0.563041 q^{57} +5.42437 q^{58} -1.11605 q^{59} +1.88167 q^{60} -3.95524 q^{61} -4.63702 q^{62} -1.98284 q^{63} +1.00000 q^{64} -0.683603 q^{65} +1.70930 q^{66} +13.1300 q^{67} +3.70546 q^{68} -10.5273 q^{69} +3.66727 q^{70} +10.7072 q^{71} +0.540685 q^{72} -10.4880 q^{73} -11.2720 q^{74} -1.88167 q^{75} -0.299224 q^{76} +3.33132 q^{77} -1.28632 q^{78} +4.79574 q^{79} -1.00000 q^{80} -10.3297 q^{81} +2.39519 q^{82} +6.53173 q^{83} +6.90060 q^{84} -3.70546 q^{85} -1.55228 q^{86} -10.2069 q^{87} -0.908393 q^{88} -5.61781 q^{89} -0.540685 q^{90} -2.50696 q^{91} +5.59466 q^{92} +8.72535 q^{93} +8.87308 q^{94} +0.299224 q^{95} -1.88167 q^{96} -12.3322 q^{97} +6.44888 q^{98} -0.491155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.88167	−1.08638	−0.543192	−	0.839609i	$-0.682784\pi$
$3$	−1.88167	−1.08638	−0.543192	+	0.839609i	$0.682784\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.88167	−0.768189
$7$	−3.66727	−1.38610	−0.693049	−	0.720890i	$-0.743733\pi$
$7$	−3.66727	−1.38610	−0.693049	+	0.720890i	$0.743733\pi$
$8$	1.00000	0.353553
$9$	0.540685	0.180228
$10$	−1.00000	−0.316228
$11$	−0.908393	−0.273891	−0.136945	−	0.990579i	$-0.543728\pi$
$11$	−0.908393	−0.273891	−0.136945	+	0.990579i	$0.543728\pi$
$12$	−1.88167	−0.543192
$13$	0.683603	0.189597	0.0947986	−	0.995496i	$-0.469779\pi$
$13$	0.683603	0.189597	0.0947986	+	0.995496i	$0.469779\pi$
$14$	−3.66727	−0.980119
$15$	1.88167	0.485845
$16$	1.00000	0.250000
$17$	3.70546	0.898706	0.449353	−	0.893354i	$-0.351655\pi$
$17$	3.70546	0.898706	0.449353	+	0.893354i	$0.351655\pi$
$18$	0.540685	0.127441
$19$	−0.299224	−0.0686467	−0.0343233	−	0.999411i	$-0.510928\pi$
$19$	−0.299224	−0.0686467	−0.0343233	+	0.999411i	$0.510928\pi$
$20$	−1.00000	−0.223607
$21$	6.90060	1.50583
$22$	−0.908393	−0.193670
$23$	5.59466	1.16657	0.583283	−	0.812269i	$-0.301768\pi$
$23$	5.59466	1.16657	0.583283	+	0.812269i	$0.301768\pi$
$24$	−1.88167	−0.384094
$25$	1.00000	0.200000
$26$	0.683603	0.134066
$27$	4.62762	0.890586
$28$	−3.66727	−0.693049
$29$	5.42437	1.00728	0.503640	−	0.863913i	$-0.331994\pi$
$29$	5.42437	1.00728	0.503640	+	0.863913i	$0.331994\pi$
$30$	1.88167	0.343545
$31$	−4.63702	−0.832834	−0.416417	−	0.909174i	$-0.636714\pi$
$31$	−4.63702	−0.832834	−0.416417	+	0.909174i	$0.636714\pi$
$32$	1.00000	0.176777
$33$	1.70930	0.297550
$34$	3.70546	0.635481
$35$	3.66727	0.619882
$36$	0.540685	0.0901142
$37$	−11.2720	−1.85311	−0.926553	−	0.376164i	$-0.877243\pi$
$37$	−11.2720	−1.85311	−0.926553	+	0.376164i	$0.877243\pi$
$38$	−0.299224	−0.0485405
$39$	−1.28632	−0.205975
$40$	−1.00000	−0.158114
$41$	2.39519	0.374066	0.187033	−	0.982354i	$-0.440113\pi$
$41$	2.39519	0.374066	0.187033	+	0.982354i	$0.440113\pi$
$42$	6.90060	1.06479
$43$	−1.55228	−0.236720	−0.118360	−	0.992971i	$-0.537764\pi$
$43$	−1.55228	−0.236720	−0.118360	+	0.992971i	$0.537764\pi$
$44$	−0.908393	−0.136945
$45$	−0.540685	−0.0806006
$46$	5.59466	0.824887
$47$	8.87308	1.29427	0.647136	−	0.762375i	$-0.275967\pi$
$47$	8.87308	1.29427	0.647136	+	0.762375i	$0.275967\pi$
$48$	−1.88167	−0.271596
$49$	6.44888	0.921268
$50$	1.00000	0.141421
$51$	−6.97246	−0.976339
$52$	0.683603	0.0947986
$53$	−2.22493	−0.305617	−0.152809	−	0.988256i	$-0.548832\pi$
$53$	−2.22493	−0.305617	−0.152809	+	0.988256i	$0.548832\pi$
$54$	4.62762	0.629739
$55$	0.908393	0.122488
$56$	−3.66727	−0.490060
$57$	0.563041	0.0745766
$58$	5.42437	0.712255
$59$	−1.11605	−0.145298	−0.0726488	−	0.997358i	$-0.523145\pi$
$59$	−1.11605	−0.145298	−0.0726488	+	0.997358i	$0.523145\pi$
$60$	1.88167	0.242923
$61$	−3.95524	−0.506416	−0.253208	−	0.967412i	$-0.581486\pi$
$61$	−3.95524	−0.506416	−0.253208	+	0.967412i	$0.581486\pi$
$62$	−4.63702	−0.588902
$63$	−1.98284	−0.249814
$64$	1.00000	0.125000
$65$	−0.683603	−0.0847905
$66$	1.70930	0.210400
$67$	13.1300	1.60409	0.802044	−	0.597265i	$-0.203746\pi$
$67$	13.1300	1.60409	0.802044	+	0.597265i	$0.203746\pi$
$68$	3.70546	0.449353
$69$	−10.5273	−1.26734
$70$	3.66727	0.438323
$71$	10.7072	1.27072	0.635358	−	0.772218i	$-0.280853\pi$
$71$	10.7072	1.27072	0.635358	+	0.772218i	$0.280853\pi$
$72$	0.540685	0.0637204
$73$	−10.4880	−1.22753	−0.613764	−	0.789490i	$-0.710345\pi$
$73$	−10.4880	−1.22753	−0.613764	+	0.789490i	$0.710345\pi$
$74$	−11.2720	−1.31034
$75$	−1.88167	−0.217277
$76$	−0.299224	−0.0343233
$77$	3.33132	0.379639
$78$	−1.28632	−0.145647
$79$	4.79574	0.539563	0.269782	−	0.962922i	$-0.413049\pi$
$79$	4.79574	0.539563	0.269782	+	0.962922i	$0.413049\pi$
$80$	−1.00000	−0.111803
$81$	−10.3297	−1.14775
$82$	2.39519	0.264505
$83$	6.53173	0.716951	0.358475	−	0.933539i	$-0.383297\pi$
$83$	6.53173	0.716951	0.358475	+	0.933539i	$0.383297\pi$
$84$	6.90060	0.752917
$85$	−3.70546	−0.401914
$86$	−1.55228	−0.167386
$87$	−10.2069	−1.09429
$88$	−0.908393	−0.0968350
$89$	−5.61781	−0.595486	−0.297743	−	0.954646i	$-0.596234\pi$
$89$	−5.61781	−0.595486	−0.297743	+	0.954646i	$0.596234\pi$
$90$	−0.540685	−0.0569932
$91$	−2.50696	−0.262800
$92$	5.59466	0.583283
$93$	8.72535	0.904777
$94$	8.87308	0.915188
$95$	0.299224	0.0306997
$96$	−1.88167	−0.192047
$97$	−12.3322	−1.25215	−0.626074	−	0.779764i	$-0.715339\pi$
$97$	−12.3322	−1.25215	−0.626074	+	0.779764i	$0.715339\pi$
$98$	6.44888	0.651435
$99$	−0.491155	−0.0493629
$100$	1.00000	0.100000
$101$	−2.42825	−0.241620	−0.120810	−	0.992676i	$-0.538549\pi$
$101$	−2.42825	−0.241620	−0.120810	+	0.992676i	$0.538549\pi$
$102$	−6.97246	−0.690376
$103$	−9.21183	−0.907669	−0.453834	−	0.891086i	$-0.649944\pi$
$103$	−9.21183	−0.907669	−0.453834	+	0.891086i	$0.649944\pi$
$104$	0.683603	0.0670328
$105$	−6.90060	−0.673429
$106$	−2.22493	−0.216104
$107$	−17.0355	−1.64688	−0.823440	−	0.567403i	$-0.807948\pi$
$107$	−17.0355	−1.64688	−0.823440	+	0.567403i	$0.807948\pi$
$108$	4.62762	0.445293
$109$	8.22586	0.787894	0.393947	−	0.919133i	$-0.371109\pi$
$109$	8.22586	0.787894	0.393947	+	0.919133i	$0.371109\pi$
$110$	0.908393	0.0866119
$111$	21.2102	2.01318
$112$	−3.66727	−0.346525
$113$	−11.1109	−1.04522	−0.522612	−	0.852571i	$-0.675042\pi$
$113$	−11.1109	−1.04522	−0.522612	+	0.852571i	$0.675042\pi$
$114$	0.563041	0.0527336
$115$	−5.59466	−0.521704
$116$	5.42437	0.503640
$117$	0.369614	0.0341708
$118$	−1.11605	−0.102741
$119$	−13.5889	−1.24569
$120$	1.88167	0.171772
$121$	−10.1748	−0.924984
$122$	−3.95524	−0.358090
$123$	−4.50697	−0.406379
$124$	−4.63702	−0.416417
$125$	−1.00000	−0.0894427
$126$	−1.98284	−0.176645
$127$	−13.0073	−1.15421	−0.577105	−	0.816670i	$-0.695818\pi$
$127$	−13.0073	−1.15421	−0.577105	+	0.816670i	$0.695818\pi$
$128$	1.00000	0.0883883
$129$	2.92087	0.257168
$130$	−0.683603	−0.0599559
$131$	13.7686	1.20297	0.601486	−	0.798883i	$-0.294576\pi$
$131$	13.7686	1.20297	0.601486	+	0.798883i	$0.294576\pi$
$132$	1.70930	0.148775
$133$	1.09734	0.0951510
$134$	13.1300	1.13426
$135$	−4.62762	−0.398282
$136$	3.70546	0.317741
$137$	−12.9471	−1.10615	−0.553074	−	0.833132i	$-0.686545\pi$
$137$	−12.9471	−1.10615	−0.553074	+	0.833132i	$0.686545\pi$
$138$	−10.5273	−0.896144
$139$	1.58616	0.134536	0.0672681	−	0.997735i	$-0.478572\pi$
$139$	1.58616	0.134536	0.0672681	+	0.997735i	$0.478572\pi$
$140$	3.66727	0.309941
$141$	−16.6962	−1.40607
$142$	10.7072	0.898532
$143$	−0.620980	−0.0519289
$144$	0.540685	0.0450571
$145$	−5.42437	−0.450470
$146$	−10.4880	−0.867993
$147$	−12.1347	−1.00085
$148$	−11.2720	−0.926553
$149$	11.5198	0.943740	0.471870	−	0.881668i	$-0.343579\pi$
$149$	11.5198	0.943740	0.471870	+	0.881668i	$0.343579\pi$
$150$	−1.88167	−0.153638
$151$	−16.5340	−1.34551	−0.672757	−	0.739864i	$-0.734890\pi$
$151$	−16.5340	−1.34551	−0.672757	+	0.739864i	$0.734890\pi$
$152$	−0.299224	−0.0242703
$153$	2.00349	0.161972
$154$	3.33132	0.268446
$155$	4.63702	0.372455
$156$	−1.28632	−0.102988
$157$	−21.9216	−1.74953	−0.874767	−	0.484544i	$-0.838986\pi$
$157$	−21.9216	−1.74953	−0.874767	+	0.484544i	$0.838986\pi$
$158$	4.79574	0.381529
$159$	4.18658	0.332017
$160$	−1.00000	−0.0790569
$161$	−20.5171	−1.61698
$162$	−10.3297	−0.811579
$163$	−5.13559	−0.402250	−0.201125	−	0.979566i	$-0.564460\pi$
$163$	−5.13559	−0.402250	−0.201125	+	0.979566i	$0.564460\pi$
$164$	2.39519	0.187033
$165$	−1.70930	−0.133069
$166$	6.53173	0.506961
$167$	12.8131	0.991509	0.495754	−	0.868463i	$-0.334892\pi$
$167$	12.8131	0.991509	0.495754	+	0.868463i	$0.334892\pi$
$168$	6.90060	0.532393
$169$	−12.5327	−0.964053
$170$	−3.70546	−0.284196
$171$	−0.161786	−0.0123721
$172$	−1.55228	−0.118360
$173$	2.63769	0.200540	0.100270	−	0.994960i	$-0.468029\pi$
$173$	2.63769	0.200540	0.100270	+	0.994960i	$0.468029\pi$
$174$	−10.2069	−0.773782
$175$	−3.66727	−0.277220
$176$	−0.908393	−0.0684727
$177$	2.10004	0.157849
$178$	−5.61781	−0.421072
$179$	−13.2315	−0.988971	−0.494485	−	0.869186i	$-0.664643\pi$
$179$	−13.2315	−0.988971	−0.494485	+	0.869186i	$0.664643\pi$
$180$	−0.540685	−0.0403003
$181$	−15.1002	−1.12239	−0.561194	−	0.827684i	$-0.689658\pi$
$181$	−15.1002	−1.12239	−0.561194	+	0.827684i	$0.689658\pi$
$182$	−2.50696	−0.185828
$183$	7.44245	0.550162
$184$	5.59466	0.412444
$185$	11.2720	0.828734
$186$	8.72535	0.639774
$187$	−3.36601	−0.246147
$188$	8.87308	0.647136
$189$	−16.9707	−1.23444
$190$	0.299224	0.0217080
$191$	17.0009	1.23014	0.615071	−	0.788472i	$-0.289127\pi$
$191$	17.0009	1.23014	0.615071	+	0.788472i	$0.289127\pi$
$192$	−1.88167	−0.135798
$193$	−15.0627	−1.08424	−0.542120	−	0.840301i	$-0.682378\pi$
$193$	−15.0627	−1.08424	−0.542120	+	0.840301i	$0.682378\pi$
$194$	−12.3322	−0.885402
$195$	1.28632	0.0921150
$196$	6.44888	0.460634
$197$	7.18813	0.512133	0.256067	−	0.966659i	$-0.417573\pi$
$197$	7.18813	0.512133	0.256067	+	0.966659i	$0.417573\pi$
$198$	−0.491155	−0.0349048
$199$	21.3189	1.51125	0.755627	−	0.655002i	$-0.227332\pi$
$199$	21.3189	1.51125	0.755627	+	0.655002i	$0.227332\pi$
$200$	1.00000	0.0707107
$201$	−24.7064	−1.74265
$202$	−2.42825	−0.170851
$203$	−19.8926	−1.39619
$204$	−6.97246	−0.488170
$205$	−2.39519	−0.167288
$206$	−9.21183	−0.641819
$207$	3.02495	0.210248
$208$	0.683603	0.0473993
$209$	0.271813	0.0188017
$210$	−6.90060	−0.476186
$211$	13.7342	0.945505	0.472752	−	0.881195i	$-0.343261\pi$
$211$	13.7342	0.945505	0.472752	+	0.881195i	$0.343261\pi$
$212$	−2.22493	−0.152809
$213$	−20.1475	−1.38048
$214$	−17.0355	−1.16452
$215$	1.55228	0.105864
$216$	4.62762	0.314870
$217$	17.0052	1.15439
$218$	8.22586	0.557125
$219$	19.7350	1.33356
$220$	0.908393	0.0612438
$221$	2.53306	0.170392
$222$	21.2102	1.42354
$223$	−20.5419	−1.37559	−0.687795	−	0.725905i	$-0.741421\pi$
$223$	−20.5419	−1.37559	−0.687795	+	0.725905i	$0.741421\pi$
$224$	−3.66727	−0.245030
$225$	0.540685	0.0360457
$226$	−11.1109	−0.739085
$227$	24.1222	1.60105	0.800524	−	0.599301i	$-0.204555\pi$
$227$	24.1222	1.60105	0.800524	+	0.599301i	$0.204555\pi$
$228$	0.563041	0.0372883
$229$	−20.3007	−1.34151	−0.670753	−	0.741681i	$-0.734029\pi$
$229$	−20.3007	−1.34151	−0.670753	+	0.741681i	$0.734029\pi$
$230$	−5.59466	−0.368901
$231$	−6.26845	−0.412434
$232$	5.42437	0.356127
$233$	18.2611	1.19632	0.598161	−	0.801376i	$-0.295898\pi$
$233$	18.2611	1.19632	0.598161	+	0.801376i	$0.295898\pi$
$234$	0.369614	0.0241624
$235$	−8.87308	−0.578816
$236$	−1.11605	−0.0726488
$237$	−9.02401	−0.586172
$238$	−13.5889	−0.880839
$239$	−9.75380	−0.630921	−0.315461	−	0.948939i	$-0.602159\pi$
$239$	−9.75380	−0.630921	−0.315461	+	0.948939i	$0.602159\pi$
$240$	1.88167	0.121461
$241$	22.0999	1.42358	0.711791	−	0.702392i	$-0.247884\pi$
$241$	22.0999	1.42358	0.711791	+	0.702392i	$0.247884\pi$
$242$	−10.1748	−0.654062
$243$	5.55426	0.356306
$244$	−3.95524	−0.253208
$245$	−6.44888	−0.412004
$246$	−4.50697	−0.287354
$247$	−0.204550	−0.0130152
$248$	−4.63702	−0.294451
$249$	−12.2906	−0.778883
$250$	−1.00000	−0.0632456
$251$	−1.54938	−0.0977957	−0.0488979	−	0.998804i	$-0.515571\pi$
$251$	−1.54938	−0.0977957	−0.0488979	+	0.998804i	$0.515571\pi$
$252$	−1.98284	−0.124907
$253$	−5.08215	−0.319512
$254$	−13.0073	−0.816150
$255$	6.97246	0.436632
$256$	1.00000	0.0625000
$257$	−17.3285	−1.08092	−0.540462	−	0.841368i	$-0.681751\pi$
$257$	−17.3285	−1.08092	−0.540462	+	0.841368i	$0.681751\pi$
$258$	2.92087	0.181845
$259$	41.3375	2.56859
$260$	−0.683603	−0.0423952
$261$	2.93288	0.181541
$262$	13.7686	0.850630
$263$	−3.57425	−0.220398	−0.110199	−	0.993910i	$-0.535149\pi$
$263$	−3.57425	−0.220398	−0.110199	+	0.993910i	$0.535149\pi$
$264$	1.70930	0.105200
$265$	2.22493	0.136676
$266$	1.09734	0.0672819
$267$	10.5709	0.646926
$268$	13.1300	0.802044
$269$	−6.88237	−0.419625	−0.209813	−	0.977742i	$-0.567285\pi$
$269$	−6.88237	−0.419625	−0.209813	+	0.977742i	$0.567285\pi$
$270$	−4.62762	−0.281628
$271$	15.3896	0.934854	0.467427	−	0.884032i	$-0.345181\pi$
$271$	15.3896	0.934854	0.467427	+	0.884032i	$0.345181\pi$
$272$	3.70546	0.224676
$273$	4.71727	0.285502
$274$	−12.9471	−0.782165
$275$	−0.908393	−0.0547782
$276$	−10.5273	−0.633669
$277$	23.5907	1.41743	0.708714	−	0.705496i	$-0.249276\pi$
$277$	23.5907	1.41743	0.708714	+	0.705496i	$0.249276\pi$
$278$	1.58616	0.0951314
$279$	−2.50717	−0.150100
$280$	3.66727	0.219161
$281$	19.4394	1.15966	0.579829	−	0.814738i	$-0.303119\pi$
$281$	19.4394	1.15966	0.579829	+	0.814738i	$0.303119\pi$
$282$	−16.6962	−0.994245
$283$	−11.1270	−0.661432	−0.330716	−	0.943730i	$-0.607290\pi$
$283$	−11.1270	−0.661432	−0.330716	+	0.943730i	$0.607290\pi$
$284$	10.7072	0.635358
$285$	−0.563041	−0.0333517
$286$	−0.620980	−0.0367193
$287$	−8.78382	−0.518493
$288$	0.540685	0.0318602
$289$	−3.26957	−0.192328
$290$	−5.42437	−0.318530
$291$	23.2052	1.36031
$292$	−10.4880	−0.613764
$293$	−7.97232	−0.465748	−0.232874	−	0.972507i	$-0.574813\pi$
$293$	−7.97232	−0.465748	−0.232874	+	0.972507i	$0.574813\pi$
$294$	−12.1347	−0.707708
$295$	1.11605	0.0649790
$296$	−11.2720	−0.655172
$297$	−4.20370	−0.243923
$298$	11.5198	0.667325
$299$	3.82452	0.221178
$300$	−1.88167	−0.108638
$301$	5.69261	0.328117
$302$	−16.5340	−0.951422
$303$	4.56917	0.262492
$304$	−0.299224	−0.0171617
$305$	3.95524	0.226476
$306$	2.00349	0.114532
$307$	−24.2327	−1.38303	−0.691516	−	0.722361i	$-0.743057\pi$
$307$	−24.2327	−1.38303	−0.691516	+	0.722361i	$0.743057\pi$
$308$	3.33132	0.189820
$309$	17.3336	0.986076
$310$	4.63702	0.263365
$311$	−28.0411	−1.59006	−0.795031	−	0.606569i	$-0.792546\pi$
$311$	−28.0411	−1.59006	−0.795031	+	0.606569i	$0.792546\pi$
$312$	−1.28632	−0.0728233
$313$	4.41470	0.249534	0.124767	−	0.992186i	$-0.460182\pi$
$313$	4.41470	0.249534	0.124767	+	0.992186i	$0.460182\pi$
$314$	−21.9216	−1.23711
$315$	1.98284	0.111720
$316$	4.79574	0.269782
$317$	−1.32567	−0.0744571	−0.0372285	−	0.999307i	$-0.511853\pi$
$317$	−1.32567	−0.0744571	−0.0372285	+	0.999307i	$0.511853\pi$
$318$	4.18658	0.234772
$319$	−4.92746	−0.275885
$320$	−1.00000	−0.0559017
$321$	32.0551	1.78914
$322$	−20.5171	−1.14337
$323$	−1.10876	−0.0616932
$324$	−10.3297	−0.573873
$325$	0.683603	0.0379195
$326$	−5.13559	−0.284434
$327$	−15.4784	−0.855955
$328$	2.39519	0.132252
$329$	−32.5400	−1.79399
$330$	−1.70930	−0.0940937
$331$	16.4526	0.904319	0.452159	−	0.891937i	$-0.350654\pi$
$331$	16.4526	0.904319	0.452159	+	0.891937i	$0.350654\pi$
$332$	6.53173	0.358475
$333$	−6.09461	−0.333982
$334$	12.8131	0.701103
$335$	−13.1300	−0.717370
$336$	6.90060	0.376458
$337$	31.0875	1.69345	0.846723	−	0.532035i	$-0.178572\pi$
$337$	31.0875	1.69345	0.846723	+	0.532035i	$0.178572\pi$
$338$	−12.5327	−0.681688
$339$	20.9070	1.13551
$340$	−3.70546	−0.200957
$341$	4.21224	0.228106
$342$	−0.161786	−0.00874838
$343$	2.02112	0.109130
$344$	−1.55228	−0.0836931
$345$	10.5273	0.566771
$346$	2.63769	0.141803
$347$	−14.2470	−0.764822	−0.382411	−	0.923992i	$-0.624906\pi$
$347$	−14.2470	−0.764822	−0.382411	+	0.923992i	$0.624906\pi$
$348$	−10.2069	−0.547146
$349$	2.19421	0.117453	0.0587267	−	0.998274i	$-0.481296\pi$
$349$	2.19421	0.117453	0.0587267	+	0.998274i	$0.481296\pi$
$350$	−3.66727	−0.196024
$351$	3.16345	0.168853
$352$	−0.908393	−0.0484175
$353$	−36.6996	−1.95332	−0.976661	−	0.214789i	$-0.931094\pi$
$353$	−36.6996	−1.95332	−0.976661	+	0.214789i	$0.931094\pi$
$354$	2.10004	0.111616
$355$	−10.7072	−0.568281
$356$	−5.61781	−0.297743
$357$	25.5699	1.35330
$358$	−13.2315	−0.699308
$359$	25.6897	1.35585	0.677926	−	0.735130i	$-0.262879\pi$
$359$	25.6897	1.35585	0.677926	+	0.735130i	$0.262879\pi$
$360$	−0.540685	−0.0284966
$361$	−18.9105	−0.995288
$362$	−15.1002	−0.793648
$363$	19.1457	1.00489
$364$	−2.50696	−0.131400
$365$	10.4880	0.548967
$366$	7.44245	0.389023
$367$	−32.1657	−1.67904	−0.839518	−	0.543332i	$-0.817163\pi$
$367$	−32.1657	−1.67904	−0.839518	+	0.543332i	$0.817163\pi$
$368$	5.59466	0.291642
$369$	1.29505	0.0674174
$370$	11.2720	0.586004
$371$	8.15940	0.423615
$372$	8.72535	0.452388
$373$	−31.7781	−1.64541	−0.822705	−	0.568469i	$-0.807536\pi$
$373$	−31.7781	−1.64541	−0.822705	+	0.568469i	$0.807536\pi$
$374$	−3.36601	−0.174052
$375$	1.88167	0.0971691
$376$	8.87308	0.457594
$377$	3.70812	0.190978
$378$	−16.9707	−0.872881
$379$	−20.0949	−1.03221	−0.516104	−	0.856526i	$-0.672618\pi$
$379$	−20.0949	−1.03221	−0.516104	+	0.856526i	$0.672618\pi$
$380$	0.299224	0.0153499
$381$	24.4754	1.25391
$382$	17.0009	0.869842
$383$	−16.3876	−0.837365	−0.418683	−	0.908133i	$-0.637508\pi$
$383$	−16.3876	−0.837365	−0.418683	+	0.908133i	$0.637508\pi$
$384$	−1.88167	−0.0960236
$385$	−3.33132	−0.169780
$386$	−15.0627	−0.766674
$387$	−0.839292	−0.0426636
$388$	−12.3322	−0.626074
$389$	−23.9800	−1.21583	−0.607917	−	0.794001i	$-0.707995\pi$
$389$	−23.9800	−1.21583	−0.607917	+	0.794001i	$0.707995\pi$
$390$	1.28632	0.0651351
$391$	20.7308	1.04840
$392$	6.44888	0.325717
$393$	−25.9081	−1.30689
$394$	7.18813	0.362133
$395$	−4.79574	−0.241300
$396$	−0.491155	−0.0246815
$397$	−13.3852	−0.671784	−0.335892	−	0.941901i	$-0.609038\pi$
$397$	−13.3852	−0.671784	−0.335892	+	0.941901i	$0.609038\pi$
$398$	21.3189	1.06862
$399$	−2.06482	−0.103370
$400$	1.00000	0.0500000
$401$	32.0591	1.60096	0.800478	−	0.599363i	$-0.204579\pi$
$401$	32.0591	1.60096	0.800478	+	0.599363i	$0.204579\pi$
$402$	−24.7064	−1.23224
$403$	−3.16988	−0.157903
$404$	−2.42825	−0.120810
$405$	10.3297	0.513288
$406$	−19.8926	−0.987255
$407$	10.2394	0.507549
$408$	−6.97246	−0.345188
$409$	10.3950	0.514002	0.257001	−	0.966411i	$-0.417266\pi$
$409$	10.3950	0.514002	0.257001	+	0.966411i	$0.417266\pi$
$410$	−2.39519	−0.118290
$411$	24.3622	1.20170
$412$	−9.21183	−0.453834
$413$	4.09286	0.201397
$414$	3.02495	0.148668
$415$	−6.53173	−0.320630
$416$	0.683603	0.0335164
$417$	−2.98463	−0.146158
$418$	0.271813	0.0132948
$419$	8.60716	0.420487	0.210244	−	0.977649i	$-0.432574\pi$
$419$	8.60716	0.420487	0.210244	+	0.977649i	$0.432574\pi$
$420$	−6.90060	−0.336715
$421$	8.44059	0.411369	0.205684	−	0.978618i	$-0.434058\pi$
$421$	8.44059	0.411369	0.205684	+	0.978618i	$0.434058\pi$
$422$	13.7342	0.668573
$423$	4.79754	0.233265
$424$	−2.22493	−0.108052
$425$	3.70546	0.179741
$426$	−20.1475	−0.976150
$427$	14.5049	0.701943
$428$	−17.0355	−0.823440
$429$	1.16848	0.0564147
$430$	1.55228	0.0748574
$431$	−15.6568	−0.754160	−0.377080	−	0.926181i	$-0.623072\pi$
$431$	−15.6568	−0.754160	−0.377080	+	0.926181i	$0.623072\pi$
$432$	4.62762	0.222647
$433$	−28.8699	−1.38740	−0.693701	−	0.720263i	$-0.744021\pi$
$433$	−28.8699	−1.38740	−0.693701	+	0.720263i	$0.744021\pi$
$434$	17.0052	0.816277
$435$	10.2069	0.489383
$436$	8.22586	0.393947
$437$	−1.67406	−0.0800809
$438$	19.7350	0.942973
$439$	−15.9816	−0.762761	−0.381380	−	0.924418i	$-0.624551\pi$
$439$	−15.9816	−0.762761	−0.381380	+	0.924418i	$0.624551\pi$
$440$	0.908393	0.0433059
$441$	3.48681	0.166039
$442$	2.53306	0.120485
$443$	−10.2674	−0.487818	−0.243909	−	0.969798i	$-0.578430\pi$
$443$	−10.2674	−0.487818	−0.243909	+	0.969798i	$0.578430\pi$
$444$	21.2102	1.00659
$445$	5.61781	0.266310
$446$	−20.5419	−0.972689
$447$	−21.6765	−1.02526
$448$	−3.66727	−0.173262
$449$	−1.50828	−0.0711800	−0.0355900	−	0.999366i	$-0.511331\pi$
$449$	−1.50828	−0.0711800	−0.0355900	+	0.999366i	$0.511331\pi$
$450$	0.540685	0.0254882
$451$	−2.17578	−0.102453
$452$	−11.1109	−0.522612
$453$	31.1115	1.46174
$454$	24.1222	1.13211
$455$	2.50696	0.117528
$456$	0.563041	0.0263668
$457$	41.1766	1.92616	0.963079	−	0.269219i	$-0.0867655\pi$
$457$	41.1766	1.92616	0.963079	+	0.269219i	$0.0867655\pi$
$458$	−20.3007	−0.948588
$459$	17.1475	0.800375
$460$	−5.59466	−0.260852
$461$	−13.2143	−0.615453	−0.307727	−	0.951475i	$-0.599568\pi$
$461$	−13.2143	−0.615453	−0.307727	+	0.951475i	$0.599568\pi$
$462$	−6.26845	−0.291635
$463$	−15.5226	−0.721398	−0.360699	−	0.932682i	$-0.617462\pi$
$463$	−15.5226	−0.721398	−0.360699	+	0.932682i	$0.617462\pi$
$464$	5.42437	0.251820
$465$	−8.72535	−0.404628
$466$	18.2611	0.845928
$467$	−33.0771	−1.53063	−0.765314	−	0.643657i	$-0.777416\pi$
$467$	−33.0771	−1.53063	−0.765314	+	0.643657i	$0.777416\pi$
$468$	0.369614	0.0170854
$469$	−48.1514	−2.22342
$470$	−8.87308	−0.409285
$471$	41.2492	1.90066
$472$	−1.11605	−0.0513704
$473$	1.41008	0.0648354
$474$	−9.02401	−0.414486
$475$	−0.299224	−0.0137293
$476$	−13.5889	−0.622847
$477$	−1.20298	−0.0550809
$478$	−9.75380	−0.446129
$479$	−5.75113	−0.262776	−0.131388	−	0.991331i	$-0.541943\pi$
$479$	−5.75113	−0.262776	−0.131388	+	0.991331i	$0.541943\pi$
$480$	1.88167	0.0858861
$481$	−7.70557	−0.351344
$482$	22.0999	1.00662
$483$	38.6065	1.75666
$484$	−10.1748	−0.462492
$485$	12.3322	0.559978
$486$	5.55426	0.251946
$487$	−21.8663	−0.990856	−0.495428	−	0.868649i	$-0.664989\pi$
$487$	−21.8663	−0.990856	−0.495428	+	0.868649i	$0.664989\pi$
$488$	−3.95524	−0.179045
$489$	9.66349	0.436998
$490$	−6.44888	−0.291331
$491$	−2.75962	−0.124540	−0.0622700	−	0.998059i	$-0.519834\pi$
$491$	−2.75962	−0.124540	−0.0622700	+	0.998059i	$0.519834\pi$
$492$	−4.50697	−0.203190
$493$	20.0998	0.905249
$494$	−0.204550	−0.00920315
$495$	0.491155	0.0220758
$496$	−4.63702	−0.208208
$497$	−39.2664	−1.76134
$498$	−12.2906	−0.550754
$499$	41.5971	1.86214	0.931070	−	0.364840i	$-0.118876\pi$
$499$	41.5971	1.86214	0.931070	+	0.364840i	$0.118876\pi$
$500$	−1.00000	−0.0447214
$501$	−24.1101	−1.07716
$502$	−1.54938	−0.0691520
$503$	−10.3236	−0.460305	−0.230153	−	0.973155i	$-0.573923\pi$
$503$	−10.3236	−0.460305	−0.230153	+	0.973155i	$0.573923\pi$
$504$	−1.98284	−0.0883227
$505$	2.42825	0.108056
$506$	−5.08215	−0.225929
$507$	23.5824	1.04733
$508$	−13.0073	−0.577105
$509$	−0.467245	−0.0207103	−0.0103551	−	0.999946i	$-0.503296\pi$
$509$	−0.467245	−0.0207103	−0.0103551	+	0.999946i	$0.503296\pi$
$510$	6.97246	0.308746
$511$	38.4623	1.70147
$512$	1.00000	0.0441942
$513$	−1.38469	−0.0611358
$514$	−17.3285	−0.764329
$515$	9.21183	0.405922
$516$	2.92087	0.128584
$517$	−8.06024	−0.354489
$518$	41.3375	1.81627
$519$	−4.96327	−0.217863
$520$	−0.683603	−0.0299780
$521$	−34.1063	−1.49422	−0.747112	−	0.664698i	$-0.768560\pi$
$521$	−34.1063	−1.49422	−0.747112	+	0.664698i	$0.768560\pi$
$522$	2.93288	0.128369
$523$	7.23105	0.316192	0.158096	−	0.987424i	$-0.449465\pi$
$523$	7.23105	0.316192	0.158096	+	0.987424i	$0.449465\pi$
$524$	13.7686	0.601486
$525$	6.90060	0.301167
$526$	−3.57425	−0.155845
$527$	−17.1823	−0.748473
$528$	1.70930	0.0743876
$529$	8.30018	0.360878
$530$	2.22493	0.0966446
$531$	−0.603433	−0.0261867
$532$	1.09734	0.0475755
$533$	1.63736	0.0709220
$534$	10.5709	0.457446
$535$	17.0355	0.736507
$536$	13.1300	0.567131
$537$	24.8974	1.07440
$538$	−6.88237	−0.296720
$539$	−5.85811	−0.252327
$540$	−4.62762	−0.199141
$541$	24.7573	1.06440	0.532200	−	0.846619i	$-0.321366\pi$
$541$	24.7573	1.06440	0.532200	+	0.846619i	$0.321366\pi$
$542$	15.3896	0.661042
$543$	28.4136	1.21934
$544$	3.70546	0.158870
$545$	−8.22586	−0.352357
$546$	4.71727	0.201880
$547$	17.4586	0.746476	0.373238	−	0.927736i	$-0.378247\pi$
$547$	17.4586	0.746476	0.373238	+	0.927736i	$0.378247\pi$
$548$	−12.9471	−0.553074
$549$	−2.13854	−0.0912706
$550$	−0.908393	−0.0387340
$551$	−1.62310	−0.0691465
$552$	−10.5273	−0.448072
$553$	−17.5873	−0.747887
$554$	23.5907	1.00227
$555$	−21.2102	−0.900323
$556$	1.58616	0.0672681
$557$	31.1464	1.31971	0.659857	−	0.751391i	$-0.270617\pi$
$557$	31.1464	1.31971	0.659857	+	0.751391i	$0.270617\pi$
$558$	−2.50717	−0.106137
$559$	−1.06114	−0.0448814
$560$	3.66727	0.154970
$561$	6.33373	0.267410
$562$	19.4394	0.820002
$563$	−20.8278	−0.877785	−0.438893	−	0.898540i	$-0.644629\pi$
$563$	−20.8278	−0.877785	−0.438893	+	0.898540i	$0.644629\pi$
$564$	−16.6962	−0.703037
$565$	11.1109	0.467438
$566$	−11.1270	−0.467703
$567$	37.8819	1.59089
$568$	10.7072	0.449266
$569$	−17.5473	−0.735621	−0.367811	−	0.929901i	$-0.619893\pi$
$569$	−17.5473	−0.735621	−0.367811	+	0.929901i	$0.619893\pi$
$570$	−0.563041	−0.0235832
$571$	15.2528	0.638311	0.319155	−	0.947702i	$-0.396601\pi$
$571$	15.2528	0.638311	0.319155	+	0.947702i	$0.396601\pi$
$572$	−0.620980	−0.0259645
$573$	−31.9901	−1.33641
$574$	−8.78382	−0.366630
$575$	5.59466	0.233313
$576$	0.540685	0.0225286
$577$	0.906539	0.0377397	0.0188699	−	0.999822i	$-0.493993\pi$
$577$	0.906539	0.0377397	0.0188699	+	0.999822i	$0.493993\pi$
$578$	−3.26957	−0.135996
$579$	28.3431	1.17790
$580$	−5.42437	−0.225235
$581$	−23.9536	−0.993764
$582$	23.2052	0.961886
$583$	2.02111	0.0837057
$584$	−10.4880	−0.433996
$585$	−0.369614	−0.0152817
$586$	−7.97232	−0.329333
$587$	−14.5140	−0.599057	−0.299529	−	0.954087i	$-0.596829\pi$
$587$	−14.5140	−0.599057	−0.299529	+	0.954087i	$0.596829\pi$
$588$	−12.1347	−0.500425
$589$	1.38751	0.0571713
$590$	1.11605	0.0459471
$591$	−13.5257	−0.556373
$592$	−11.2720	−0.463277
$593$	−0.939146	−0.0385661	−0.0192831	−	0.999814i	$-0.506138\pi$
$593$	−0.939146	−0.0385661	−0.0192831	+	0.999814i	$0.506138\pi$
$594$	−4.20370	−0.172480
$595$	13.5889	0.557092
$596$	11.5198	0.471870
$597$	−40.1151	−1.64180
$598$	3.82452	0.156396
$599$	−37.7928	−1.54417	−0.772087	−	0.635517i	$-0.780787\pi$
$599$	−37.7928	−1.54417	−0.772087	+	0.635517i	$0.780787\pi$
$600$	−1.88167	−0.0768189
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	5.69261	0.232014
$603$	7.09921	0.289102
$604$	−16.5340	−0.672757
$605$	10.1748	0.413665
$606$	4.56917	0.185610
$607$	−19.9985	−0.811713	−0.405857	−	0.913937i	$-0.633027\pi$
$607$	−19.9985	−0.811713	−0.405857	+	0.913937i	$0.633027\pi$
$608$	−0.299224	−0.0121351
$609$	37.4314	1.51680
$610$	3.95524	0.160143
$611$	6.06566	0.245390
$612$	2.00349	0.0809862
$613$	−29.3408	−1.18506	−0.592531	−	0.805547i	$-0.701871\pi$
$613$	−29.3408	−1.18506	−0.592531	+	0.805547i	$0.701871\pi$
$614$	−24.2327	−0.977951
$615$	4.50697	0.181738
$616$	3.33132	0.134223
$617$	42.2628	1.70144	0.850718	−	0.525622i	$-0.176167\pi$
$617$	42.2628	1.70144	0.850718	+	0.525622i	$0.176167\pi$
$618$	17.3336	0.697261
$619$	29.4821	1.18499	0.592494	−	0.805575i	$-0.298143\pi$
$619$	29.4821	1.18499	0.592494	+	0.805575i	$0.298143\pi$
$620$	4.63702	0.186227
$621$	25.8900	1.03893
$622$	−28.0411	−1.12434
$623$	20.6020	0.825403
$624$	−1.28632	−0.0514938
$625$	1.00000	0.0400000
$626$	4.41470	0.176447
$627$	−0.511462	−0.0204258
$628$	−21.9216	−0.874767
$629$	−41.7680	−1.66540
$630$	1.98284	0.0789982
$631$	−18.6234	−0.741388	−0.370694	−	0.928755i	$-0.620880\pi$
$631$	−18.6234	−0.741388	−0.370694	+	0.928755i	$0.620880\pi$
$632$	4.79574	0.190764
$633$	−25.8433	−1.02718
$634$	−1.32567	−0.0526491
$635$	13.0073	0.516178
$636$	4.18658	0.166009
$637$	4.40847	0.174670
$638$	−4.92746	−0.195080
$639$	5.78925	0.229019
$640$	−1.00000	−0.0395285
$641$	26.1146	1.03147	0.515733	−	0.856749i	$-0.327520\pi$
$641$	26.1146	1.03147	0.515733	+	0.856749i	$0.327520\pi$
$642$	32.0551	1.26512
$643$	−7.23965	−0.285504	−0.142752	−	0.989758i	$-0.545595\pi$
$643$	−7.23965	−0.285504	−0.142752	+	0.989758i	$0.545595\pi$
$644$	−20.5171	−0.808488
$645$	−2.92087	−0.115009
$646$	−1.10876	−0.0436237
$647$	39.9308	1.56984	0.784921	−	0.619596i	$-0.212703\pi$
$647$	39.9308	1.56984	0.784921	+	0.619596i	$0.212703\pi$
$648$	−10.3297	−0.405790
$649$	1.01381	0.0397957
$650$	0.683603	0.0268131
$651$	−31.9982	−1.25411
$652$	−5.13559	−0.201125
$653$	−11.6502	−0.455909	−0.227954	−	0.973672i	$-0.573204\pi$
$653$	−11.6502	−0.455909	−0.227954	+	0.973672i	$0.573204\pi$
$654$	−15.4784	−0.605252
$655$	−13.7686	−0.537985
$656$	2.39519	0.0935166
$657$	−5.67071	−0.221235
$658$	−32.5400	−1.26854
$659$	−3.13655	−0.122183	−0.0610914	−	0.998132i	$-0.519458\pi$
$659$	−3.13655	−0.122183	−0.0610914	+	0.998132i	$0.519458\pi$
$660$	−1.70930	−0.0665343
$661$	16.7656	0.652108	0.326054	−	0.945351i	$-0.394281\pi$
$661$	16.7656	0.652108	0.326054	+	0.945351i	$0.394281\pi$
$662$	16.4526	0.639450
$663$	−4.76639	−0.185111
$664$	6.53173	0.253480
$665$	−1.09734	−0.0425528
$666$	−6.09461	−0.236161
$667$	30.3475	1.17506
$668$	12.8131	0.495754
$669$	38.6532	1.49442
$670$	−13.1300	−0.507257
$671$	3.59291	0.138703
$672$	6.90060	0.266196
$673$	−26.6501	−1.02729	−0.513643	−	0.858004i	$-0.671704\pi$
$673$	−26.6501	−1.02729	−0.513643	+	0.858004i	$0.671704\pi$
$674$	31.0875	1.19745
$675$	4.62762	0.178117
$676$	−12.5327	−0.482026
$677$	8.35449	0.321089	0.160545	−	0.987029i	$-0.448675\pi$
$677$	8.35449	0.321089	0.160545	+	0.987029i	$0.448675\pi$
$678$	20.9070	0.802929
$679$	45.2256	1.73560
$680$	−3.70546	−0.142098
$681$	−45.3901	−1.73935
$682$	4.21224	0.161295
$683$	−18.4773	−0.707016	−0.353508	−	0.935432i	$-0.615011\pi$
$683$	−18.4773	−0.707016	−0.353508	+	0.935432i	$0.615011\pi$
$684$	−0.161786	−0.00618604
$685$	12.9471	0.494685
$686$	2.02112	0.0771666
$687$	38.1992	1.45739
$688$	−1.55228	−0.0591799
$689$	−1.52096	−0.0579442
$690$	10.5273	0.400768
$691$	8.07465	0.307174	0.153587	−	0.988135i	$-0.450917\pi$
$691$	8.07465	0.307174	0.153587	+	0.988135i	$0.450917\pi$
$692$	2.63769	0.100270
$693$	1.80120	0.0684218
$694$	−14.2470	−0.540811
$695$	−1.58616	−0.0601664
$696$	−10.2069	−0.386891
$697$	8.87529	0.336176
$698$	2.19421	0.0830521
$699$	−34.3613	−1.29966
$700$	−3.66727	−0.138610
$701$	15.9334	0.601797	0.300898	−	0.953656i	$-0.402713\pi$
$701$	15.9334	0.601797	0.300898	+	0.953656i	$0.402713\pi$
$702$	3.16345	0.119397
$703$	3.37285	0.127210
$704$	−0.908393	−0.0342363
$705$	16.6962	0.628816
$706$	−36.6996	−1.38121
$707$	8.90506	0.334909
$708$	2.10004	0.0789244
$709$	−24.1436	−0.906730	−0.453365	−	0.891325i	$-0.649777\pi$
$709$	−24.1436	−0.906730	−0.453365	+	0.891325i	$0.649777\pi$
$710$	−10.7072	−0.401836
$711$	2.59299	0.0972446
$712$	−5.61781	−0.210536
$713$	−25.9426	−0.971556
$714$	25.5699	0.956929
$715$	0.620980	0.0232233
$716$	−13.2315	−0.494485
$717$	18.3534	0.685422
$718$	25.6897	0.958732
$719$	39.6951	1.48038	0.740189	−	0.672399i	$-0.234736\pi$
$719$	39.6951	1.48038	0.740189	+	0.672399i	$0.234736\pi$
$720$	−0.540685	−0.0201502
$721$	33.7823	1.25812
$722$	−18.9105	−0.703775
$723$	−41.5848	−1.54655
$724$	−15.1002	−0.561194
$725$	5.42437	0.201456
$726$	19.1457	0.710562
$727$	−8.79976	−0.326365	−0.163183	−	0.986596i	$-0.552176\pi$
$727$	−8.79976	−0.326365	−0.163183	+	0.986596i	$0.552176\pi$
$728$	−2.50696	−0.0929140
$729$	20.5379	0.760661
$730$	10.4880	0.388178
$731$	−5.75189	−0.212741
$732$	7.44245	0.275081
$733$	−37.5833	−1.38817	−0.694085	−	0.719893i	$-0.744191\pi$
$733$	−37.5833	−1.38817	−0.694085	+	0.719893i	$0.744191\pi$
$734$	−32.1657	−1.18726
$735$	12.1347	0.447594
$736$	5.59466	0.206222
$737$	−11.9272	−0.439345
$738$	1.29505	0.0476713
$739$	−5.96619	−0.219470	−0.109735	−	0.993961i	$-0.535000\pi$
$739$	−5.96619	−0.219470	−0.109735	+	0.993961i	$0.535000\pi$
$740$	11.2720	0.414367
$741$	0.384896	0.0141395
$742$	8.15940	0.299541
$743$	−7.33185	−0.268980	−0.134490	−	0.990915i	$-0.542940\pi$
$743$	−7.33185	−0.268980	−0.134490	+	0.990915i	$0.542940\pi$
$744$	8.72535	0.319887
$745$	−11.5198	−0.422053
$746$	−31.7781	−1.16348
$747$	3.53161	0.129215
$748$	−3.36601	−0.123074
$749$	62.4737	2.28274
$750$	1.88167	0.0687089
$751$	41.1174	1.50040	0.750198	−	0.661214i	$-0.229958\pi$
$751$	41.1174	1.50040	0.750198	+	0.661214i	$0.229958\pi$
$752$	8.87308	0.323568
$753$	2.91542	0.106244
$754$	3.70812	0.135042
$755$	16.5340	0.601732
$756$	−16.9707	−0.617220
$757$	47.0627	1.71052	0.855261	−	0.518197i	$-0.173397\pi$
$757$	47.0627	1.71052	0.855261	+	0.518197i	$0.173397\pi$
$758$	−20.0949	−0.729881
$759$	9.56293	0.347112
$760$	0.299224	0.0108540
$761$	−45.2718	−1.64110	−0.820551	−	0.571573i	$-0.806334\pi$
$761$	−45.2718	−1.64110	−0.820551	+	0.571573i	$0.806334\pi$
$762$	24.4754	0.886651
$763$	−30.1664	−1.09210
$764$	17.0009	0.615071
$765$	−2.00349	−0.0724362
$766$	−16.3876	−0.592107
$767$	−0.762936	−0.0275480
$768$	−1.88167	−0.0678989
$769$	9.14833	0.329897	0.164949	−	0.986302i	$-0.447254\pi$
$769$	9.14833	0.329897	0.164949	+	0.986302i	$0.447254\pi$
$770$	−3.33132	−0.120053
$771$	32.6066	1.17430
$772$	−15.0627	−0.542120
$773$	25.3246	0.910863	0.455431	−	0.890271i	$-0.349485\pi$
$773$	25.3246	0.910863	0.455431	+	0.890271i	$0.349485\pi$
$774$	−0.839292	−0.0301677
$775$	−4.63702	−0.166567
$776$	−12.3322	−0.442701
$777$	−77.7836	−2.79047
$778$	−23.9800	−0.859724
$779$	−0.716699	−0.0256784
$780$	1.28632	0.0460575
$781$	−9.72638	−0.348037
$782$	20.7308	0.741331
$783$	25.1019	0.897070
$784$	6.44888	0.230317
$785$	21.9216	0.782415
$786$	−25.9081	−0.924110
$787$	24.1051	0.859255	0.429628	−	0.903006i	$-0.358645\pi$
$787$	24.1051	0.859255	0.429628	+	0.903006i	$0.358645\pi$
$788$	7.18813	0.256067
$789$	6.72556	0.239436
$790$	−4.79574	−0.170625
$791$	40.7466	1.44878
$792$	−0.491155	−0.0174524
$793$	−2.70381	−0.0960151
$794$	−13.3852	−0.475023
$795$	−4.18658	−0.148483
$796$	21.3189	0.755627
$797$	41.4109	1.46685	0.733425	−	0.679771i	$-0.237921\pi$
$797$	41.4109	1.46685	0.733425	+	0.679771i	$0.237921\pi$
$798$	−2.06482	−0.0730940
$799$	32.8788	1.16317
$800$	1.00000	0.0353553
$801$	−3.03747	−0.107324
$802$	32.0591	1.13205
$803$	9.52722	0.336208
$804$	−24.7064	−0.871327
$805$	20.5171	0.723134
$806$	−3.16988	−0.111654
$807$	12.9503	0.455874
$808$	−2.42825	−0.0854257
$809$	47.1919	1.65918	0.829589	−	0.558374i	$-0.188575\pi$
$809$	47.1919	1.65918	0.829589	+	0.558374i	$0.188575\pi$
$810$	10.3297	0.362949
$811$	7.91536	0.277946	0.138973	−	0.990296i	$-0.455620\pi$
$811$	7.91536	0.277946	0.138973	+	0.990296i	$0.455620\pi$
$812$	−19.8926	−0.698095
$813$	−28.9582	−1.01561
$814$	10.2394	0.358891
$815$	5.13559	0.179892
$816$	−6.97246	−0.244085
$817$	0.464478	0.0162500
$818$	10.3950	0.363454
$819$	−1.35547	−0.0473641
$820$	−2.39519	−0.0836438
$821$	−22.4319	−0.782878	−0.391439	−	0.920204i	$-0.628023\pi$
$821$	−22.4319	−0.782878	−0.391439	+	0.920204i	$0.628023\pi$
$822$	24.3622	0.849731
$823$	−7.53343	−0.262599	−0.131299	−	0.991343i	$-0.541915\pi$
$823$	−7.53343	−0.262599	−0.131299	+	0.991343i	$0.541915\pi$
$824$	−9.21183	−0.320909
$825$	1.70930	0.0595101
$826$	4.09286	0.142409
$827$	48.4424	1.68451	0.842254	−	0.539080i	$-0.181228\pi$
$827$	48.4424	1.68451	0.842254	+	0.539080i	$0.181228\pi$
$828$	3.02495	0.105124
$829$	−31.5200	−1.09473	−0.547367	−	0.836892i	$-0.684370\pi$
$829$	−31.5200	−1.09473	−0.547367	+	0.836892i	$0.684370\pi$
$830$	−6.53173	−0.226720
$831$	−44.3900	−1.53987
$832$	0.683603	0.0236997
$833$	23.8961	0.827949
$834$	−2.98463	−0.103349
$835$	−12.8131	−0.443416
$836$	0.271813	0.00940085
$837$	−21.4584	−0.741710
$838$	8.60716	0.297329
$839$	39.4505	1.36198	0.680991	−	0.732292i	$-0.261549\pi$
$839$	39.4505	1.36198	0.680991	+	0.732292i	$0.261549\pi$
$840$	−6.90060	−0.238093
$841$	0.423806	0.0146140
$842$	8.44059	0.290882
$843$	−36.5786	−1.25983
$844$	13.7342	0.472752
$845$	12.5327	0.431138
$846$	4.79754	0.164943
$847$	37.3138	1.28212
$848$	−2.22493	−0.0764043
$849$	20.9374	0.718569
$850$	3.70546	0.127096
$851$	−63.0630	−2.16177
$852$	−20.1475	−0.690242
$853$	2.17779	0.0745662	0.0372831	−	0.999305i	$-0.488130\pi$
$853$	2.17779	0.0745662	0.0372831	+	0.999305i	$0.488130\pi$
$854$	14.5049	0.496348
$855$	0.161786	0.00553296
$856$	−17.0355	−0.582260
$857$	−27.4420	−0.937400	−0.468700	−	0.883357i	$-0.655278\pi$
$857$	−27.4420	−0.937400	−0.468700	+	0.883357i	$0.655278\pi$
$858$	1.16848	0.0398912
$859$	−28.6757	−0.978403	−0.489201	−	0.872171i	$-0.662712\pi$
$859$	−28.6757	−0.978403	−0.489201	+	0.872171i	$0.662712\pi$
$860$	1.55228	0.0529321
$861$	16.5283	0.563282
$862$	−15.6568	−0.533271
$863$	−15.0761	−0.513196	−0.256598	−	0.966518i	$-0.582602\pi$
$863$	−15.0761	−0.513196	−0.256598	+	0.966518i	$0.582602\pi$
$864$	4.62762	0.157435
$865$	−2.63769	−0.0896843
$866$	−28.8699	−0.981041
$867$	6.15225	0.208941
$868$	17.0052	0.577195
$869$	−4.35642	−0.147781
$870$	10.2069	0.346046
$871$	8.97572	0.304131
$872$	8.22586	0.278563
$873$	−6.66785	−0.225673
$874$	−1.67406	−0.0566258
$875$	3.66727	0.123976
$876$	19.7350	0.666782
$877$	−18.6086	−0.628367	−0.314183	−	0.949362i	$-0.601731\pi$
$877$	−18.6086	−0.628367	−0.314183	+	0.949362i	$0.601731\pi$
$878$	−15.9816	−0.539353
$879$	15.0013	0.505980
$880$	0.908393	0.0306219
$881$	53.5656	1.80467	0.902336	−	0.431033i	$-0.141851\pi$
$881$	53.5656	1.80467	0.902336	+	0.431033i	$0.141851\pi$
$882$	3.48681	0.117407
$883$	−46.7908	−1.57464	−0.787318	−	0.616547i	$-0.788531\pi$
$883$	−46.7908	−1.57464	−0.787318	+	0.616547i	$0.788531\pi$
$884$	2.53306	0.0851961
$885$	−2.10004	−0.0705921
$886$	−10.2674	−0.344939
$887$	−7.24843	−0.243378	−0.121689	−	0.992568i	$-0.538831\pi$
$887$	−7.24843	−0.243378	−0.121689	+	0.992568i	$0.538831\pi$
$888$	21.2102	0.711768
$889$	47.7012	1.59985
$890$	5.61781	0.188309
$891$	9.38344	0.314357
$892$	−20.5419	−0.687795
$893$	−2.65504	−0.0888474
$894$	−21.6765	−0.724971
$895$	13.2315	0.442281
$896$	−3.66727	−0.122515
$897$	−7.19649	−0.240284
$898$	−1.50828	−0.0503319
$899$	−25.1529	−0.838897
$900$	0.540685	0.0180228
$901$	−8.24437	−0.274660
$902$	−2.17578	−0.0724454
$903$	−10.7116	−0.356461
$904$	−11.1109	−0.369542
$905$	15.1002	0.501947
$906$	31.1115	1.03361
$907$	0.369768	0.0122779	0.00613896	−	0.999981i	$-0.498046\pi$
$907$	0.369768	0.0122779	0.00613896	+	0.999981i	$0.498046\pi$
$908$	24.1222	0.800524
$909$	−1.31292	−0.0435468
$910$	2.50696	0.0831048
$911$	−41.4773	−1.37420	−0.687101	−	0.726562i	$-0.741117\pi$
$911$	−41.4773	−1.37420	−0.687101	+	0.726562i	$0.741117\pi$
$912$	0.563041	0.0186441
$913$	−5.93338	−0.196366
$914$	41.1766	1.36200
$915$	−7.44245	−0.246040
$916$	−20.3007	−0.670753
$917$	−50.4933	−1.66744
$918$	17.1475	0.565951
$919$	−38.8897	−1.28285	−0.641427	−	0.767184i	$-0.721657\pi$
$919$	−38.8897	−1.28285	−0.641427	+	0.767184i	$0.721657\pi$
$920$	−5.59466	−0.184450
$921$	45.5979	1.50250
$922$	−13.2143	−0.435191
$923$	7.31950	0.240924
$924$	−6.26845	−0.206217
$925$	−11.2720	−0.370621
$926$	−15.5226	−0.510105
$927$	−4.98070	−0.163588
$928$	5.42437	0.178064
$929$	−26.4693	−0.868429	−0.434214	−	0.900810i	$-0.642974\pi$
$929$	−26.4693	−0.868429	−0.434214	+	0.900810i	$0.642974\pi$
$930$	−8.72535	−0.286116
$931$	−1.92966	−0.0632420
$932$	18.2611	0.598161
$933$	52.7640	1.72742
$934$	−33.0771	−1.08232
$935$	3.36601	0.110080
$936$	0.369614	0.0120812
$937$	11.8126	0.385901	0.192950	−	0.981209i	$-0.438194\pi$
$937$	11.8126	0.385901	0.192950	+	0.981209i	$0.438194\pi$
$938$	−48.1514	−1.57220
$939$	−8.30702	−0.271089
$940$	−8.87308	−0.289408
$941$	−59.2862	−1.93267	−0.966337	−	0.257280i	$-0.917174\pi$
$941$	−59.2862	−1.93267	−0.966337	+	0.257280i	$0.917174\pi$
$942$	41.2492	1.34397
$943$	13.4003	0.436373
$944$	−1.11605	−0.0363244
$945$	16.9707	0.552058
$946$	1.41008	0.0458455
$947$	4.82502	0.156792	0.0783960	−	0.996922i	$-0.475020\pi$
$947$	4.82502	0.156792	0.0783960	+	0.996922i	$0.475020\pi$
$948$	−9.02401	−0.293086
$949$	−7.16962	−0.232736
$950$	−0.299224	−0.00970811
$951$	2.49448	0.0808889
$952$	−13.5889	−0.440420
$953$	1.14160	0.0369800	0.0184900	−	0.999829i	$-0.494114\pi$
$953$	1.14160	0.0369800	0.0184900	+	0.999829i	$0.494114\pi$
$954$	−1.20298	−0.0389481
$955$	−17.0009	−0.550136
$956$	−9.75380	−0.315461
$957$	9.27186	0.299717
$958$	−5.75113	−0.185811
$959$	47.4807	1.53323
$960$	1.88167	0.0607307
$961$	−9.49802	−0.306388
$962$	−7.70557	−0.248438
$963$	−9.21083	−0.296815
$964$	22.0999	0.711791
$965$	15.0627	0.484887
$966$	38.6065	1.24214
$967$	18.1048	0.582211	0.291105	−	0.956691i	$-0.405977\pi$
$967$	18.1048	0.582211	0.291105	+	0.956691i	$0.405977\pi$
$968$	−10.1748	−0.327031
$969$	2.08633	0.0670224
$970$	12.3322	0.395964
$971$	47.2079	1.51497	0.757486	−	0.652851i	$-0.226427\pi$
$971$	47.2079	1.51497	0.757486	+	0.652851i	$0.226427\pi$
$972$	5.55426	0.178153
$973$	−5.81687	−0.186480
$974$	−21.8663	−0.700641
$975$	−1.28632	−0.0411951
$976$	−3.95524	−0.126604
$977$	28.0732	0.898142	0.449071	−	0.893496i	$-0.351755\pi$
$977$	28.0732	0.898142	0.449071	+	0.893496i	$0.351755\pi$
$978$	9.66349	0.309004
$979$	5.10318	0.163098
$980$	−6.44888	−0.206002
$981$	4.44760	0.142001
$982$	−2.75962	−0.0880630
$983$	−41.1529	−1.31257	−0.656287	−	0.754511i	$-0.727874\pi$
$983$	−41.1529	−1.31257	−0.656287	+	0.754511i	$0.727874\pi$
$984$	−4.50697	−0.143677
$985$	−7.18813	−0.229033
$986$	20.0998	0.640108
$987$	61.2295	1.94896
$988$	−0.204550	−0.00650761
$989$	−8.68445	−0.276149
$990$	0.491155	0.0156099
$991$	−20.8657	−0.662820	−0.331410	−	0.943487i	$-0.607524\pi$
$991$	−20.8657	−0.662820	−0.331410	+	0.943487i	$0.607524\pi$
$992$	−4.63702	−0.147226
$993$	−30.9585	−0.982437
$994$	−39.2664	−1.24545
$995$	−21.3189	−0.675853
$996$	−12.2906	−0.389442
$997$	−44.4899	−1.40901	−0.704505	−	0.709699i	$-0.748831\pi$
$997$	−44.4899	−1.40901	−0.704505	+	0.709699i	$0.748831\pi$
$998$	41.5971	1.31673
$999$	−52.1626	−1.65035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.6	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.88167 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.88167 q^{6} -3.66727 q^{7} +1.00000 q^{8} +0.540685 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.88167 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.88167 q^{6} -3.66727 q^{7} +1.00000 q^{8} +0.540685 q^{9} -1.00000 q^{10} -0.908393 q^{11} -1.88167 q^{12} +0.683603 q^{13} -3.66727 q^{14} +1.88167 q^{15} +1.00000 q^{16} +3.70546 q^{17} +0.540685 q^{18} -0.299224 q^{19} -1.00000 q^{20} +6.90060 q^{21} -0.908393 q^{22} +5.59466 q^{23} -1.88167 q^{24} +1.00000 q^{25} +0.683603 q^{26} +4.62762 q^{27} -3.66727 q^{28} +5.42437 q^{29} +1.88167 q^{30} -4.63702 q^{31} +1.00000 q^{32} +1.70930 q^{33} +3.70546 q^{34} +3.66727 q^{35} +0.540685 q^{36} -11.2720 q^{37} -0.299224 q^{38} -1.28632 q^{39} -1.00000 q^{40} +2.39519 q^{41} +6.90060 q^{42} -1.55228 q^{43} -0.908393 q^{44} -0.540685 q^{45} +5.59466 q^{46} +8.87308 q^{47} -1.88167 q^{48} +6.44888 q^{49} +1.00000 q^{50} -6.97246 q^{51} +0.683603 q^{52} -2.22493 q^{53} +4.62762 q^{54} +0.908393 q^{55} -3.66727 q^{56} +0.563041 q^{57} +5.42437 q^{58} -1.11605 q^{59} +1.88167 q^{60} -3.95524 q^{61} -4.63702 q^{62} -1.98284 q^{63} +1.00000 q^{64} -0.683603 q^{65} +1.70930 q^{66} +13.1300 q^{67} +3.70546 q^{68} -10.5273 q^{69} +3.66727 q^{70} +10.7072 q^{71} +0.540685 q^{72} -10.4880 q^{73} -11.2720 q^{74} -1.88167 q^{75} -0.299224 q^{76} +3.33132 q^{77} -1.28632 q^{78} +4.79574 q^{79} -1.00000 q^{80} -10.3297 q^{81} +2.39519 q^{82} +6.53173 q^{83} +6.90060 q^{84} -3.70546 q^{85} -1.55228 q^{86} -10.2069 q^{87} -0.908393 q^{88} -5.61781 q^{89} -0.540685 q^{90} -2.50696 q^{91} +5.59466 q^{92} +8.72535 q^{93} +8.87308 q^{94} +0.299224 q^{95} -1.88167 q^{96} -12.3322 q^{97} +6.44888 q^{98} -0.491155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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