LMFDB - Embedded newform 5610.2.a.ck.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.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:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.19985813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 23x^{3} + 28x^{2} + 40x - 24 $ x^5 - 2x^4 - 23x^3 + 28x^2 + 40x - 24
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.29600$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.23070 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.23070 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.87255 q^{13} +1.23070 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -0.872548 q^{19} +1.00000 q^{20} +1.23070 q^{21} -1.00000 q^{22} +9.36130 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.87255 q^{26} +1.00000 q^{27} +1.23070 q^{28} +3.64185 q^{29} +1.00000 q^{30} +2.10662 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.23070 q^{35} +1.00000 q^{36} -10.3405 q^{37} -0.872548 q^{38} +4.87255 q^{39} +1.00000 q^{40} -8.59200 q^{41} +1.23070 q^{42} -0.979164 q^{43} -1.00000 q^{44} +1.00000 q^{45} +9.36130 q^{46} +8.59200 q^{47} +1.00000 q^{48} -5.48539 q^{49} +1.00000 q^{50} -1.00000 q^{51} +4.87255 q^{52} -7.92931 q^{53} +1.00000 q^{54} -1.00000 q^{55} +1.23070 q^{56} -0.872548 q^{57} +3.64185 q^{58} +9.46792 q^{59} +1.00000 q^{60} +0.00337115 q^{61} +2.10662 q^{62} +1.23070 q^{63} +1.00000 q^{64} +4.87255 q^{65} -1.00000 q^{66} -11.8791 q^{67} -1.00000 q^{68} +9.36130 q^{69} +1.23070 q^{70} -15.2130 q^{71} +1.00000 q^{72} +11.2547 q^{73} -10.3405 q^{74} +1.00000 q^{75} -0.872548 q^{76} -1.23070 q^{77} +4.87255 q^{78} +8.62102 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.59200 q^{82} -1.99663 q^{83} +1.23070 q^{84} -1.00000 q^{85} -0.979164 q^{86} +3.64185 q^{87} -1.00000 q^{88} +1.28370 q^{89} +1.00000 q^{90} +5.99663 q^{91} +9.36130 q^{92} +2.10662 q^{93} +8.59200 q^{94} -0.872548 q^{95} +1.00000 q^{96} +7.85171 q^{97} -5.48539 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} - 5 q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} + 11 q^{19} + 5 q^{20} + 2 q^{21} - 5 q^{22} + 4 q^{23} + 5 q^{24} + 5 q^{25} + 9 q^{26} + 5 q^{27} + 2 q^{28} + 7 q^{29} + 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + 7 q^{37} + 11 q^{38} + 9 q^{39} + 5 q^{40} + 4 q^{41} + 2 q^{42} + 11 q^{43} - 5 q^{44} + 5 q^{45} + 4 q^{46} - 4 q^{47} + 5 q^{48} + 19 q^{49} + 5 q^{50} - 5 q^{51} + 9 q^{52} + 12 q^{53} + 5 q^{54} - 5 q^{55} + 2 q^{56} + 11 q^{57} + 7 q^{58} + 4 q^{59} + 5 q^{60} + 19 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} - 5 q^{68} + 4 q^{69} + 2 q^{70} - 2 q^{71} + 5 q^{72} + 14 q^{73} + 7 q^{74} + 5 q^{75} + 11 q^{76} - 2 q^{77} + 9 q^{78} + 16 q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} + 9 q^{83} + 2 q^{84} - 5 q^{85} + 11 q^{86} + 7 q^{87} - 5 q^{88} - 16 q^{89} + 5 q^{90} + 11 q^{91} + 4 q^{92} + 10 q^{93} - 4 q^{94} + 11 q^{95} + 5 q^{96} + 8 q^{97} + 19 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9 + 5 * q^10 - 5 * q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 + 11 * q^19 + 5 * q^20 + 2 * q^21 - 5 * q^22 + 4 * q^23 + 5 * q^24 + 5 * q^25 + 9 * q^26 + 5 * q^27 + 2 * q^28 + 7 * q^29 + 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + 7 * q^37 + 11 * q^38 + 9 * q^39 + 5 * q^40 + 4 * q^41 + 2 * q^42 + 11 * q^43 - 5 * q^44 + 5 * q^45 + 4 * q^46 - 4 * q^47 + 5 * q^48 + 19 * q^49 + 5 * q^50 - 5 * q^51 + 9 * q^52 + 12 * q^53 + 5 * q^54 - 5 * q^55 + 2 * q^56 + 11 * q^57 + 7 * q^58 + 4 * q^59 + 5 * q^60 + 19 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 - 5 * q^68 + 4 * q^69 + 2 * q^70 - 2 * q^71 + 5 * q^72 + 14 * q^73 + 7 * q^74 + 5 * q^75 + 11 * q^76 - 2 * q^77 + 9 * q^78 + 16 * q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 + 9 * q^83 + 2 * q^84 - 5 * q^85 + 11 * q^86 + 7 * q^87 - 5 * q^88 - 16 * q^89 + 5 * q^90 + 11 * q^91 + 4 * q^92 + 10 * q^93 - 4 * q^94 + 11 * q^95 + 5 * q^96 + 8 * q^97 + 19 * q^98 - 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	1.23070	0.465160	0.232580	−	0.972577i	$-0.425283\pi$
$7$	1.23070	0.465160	0.232580	+	0.972577i	$0.425283\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	4.87255	1.35140	0.675701	−	0.737176i	$-0.263841\pi$
$13$	4.87255	1.35140	0.675701	+	0.737176i	$0.263841\pi$
$14$	1.23070	0.328918
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−0.872548	−0.200176	−0.100088	−	0.994979i	$-0.531912\pi$
$19$	−0.872548	−0.200176	−0.100088	+	0.994979i	$0.531912\pi$
$20$	1.00000	0.223607
$21$	1.23070	0.268560
$22$	−1.00000	−0.213201
$23$	9.36130	1.95197	0.975984	−	0.217844i	$-0.0699025\pi$
$23$	9.36130	1.95197	0.975984	+	0.217844i	$0.0699025\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.87255	0.955585
$27$	1.00000	0.192450
$28$	1.23070	0.232580
$29$	3.64185	0.676275	0.338137	−	0.941097i	$-0.390203\pi$
$29$	3.64185	0.676275	0.338137	+	0.941097i	$0.390203\pi$
$30$	1.00000	0.182574
$31$	2.10662	0.378359	0.189180	−	0.981942i	$-0.439417\pi$
$31$	2.10662	0.378359	0.189180	+	0.981942i	$0.439417\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	1.23070	0.208026
$36$	1.00000	0.166667
$37$	−10.3405	−1.69996	−0.849981	−	0.526813i	$-0.823387\pi$
$37$	−10.3405	−1.69996	−0.849981	+	0.526813i	$0.823387\pi$
$38$	−0.872548	−0.141546
$39$	4.87255	0.780232
$40$	1.00000	0.158114
$41$	−8.59200	−1.34185	−0.670923	−	0.741527i	$-0.734102\pi$
$41$	−8.59200	−1.34185	−0.670923	+	0.741527i	$0.734102\pi$
$42$	1.23070	0.189901
$43$	−0.979164	−0.149321	−0.0746606	−	0.997209i	$-0.523787\pi$
$43$	−0.979164	−0.149321	−0.0746606	+	0.997209i	$0.523787\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	9.36130	1.38025
$47$	8.59200	1.25327	0.626636	−	0.779312i	$-0.284431\pi$
$47$	8.59200	1.25327	0.626636	+	0.779312i	$0.284431\pi$
$48$	1.00000	0.144338
$49$	−5.48539	−0.783627
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	4.87255	0.675701
$53$	−7.92931	−1.08918	−0.544588	−	0.838704i	$-0.683314\pi$
$53$	−7.92931	−1.08918	−0.544588	+	0.838704i	$0.683314\pi$
$54$	1.00000	0.136083
$55$	−1.00000	−0.134840
$56$	1.23070	0.164459
$57$	−0.872548	−0.115572
$58$	3.64185	0.478199
$59$	9.46792	1.23262	0.616309	−	0.787504i	$-0.288627\pi$
$59$	9.46792	1.23262	0.616309	+	0.787504i	$0.288627\pi$
$60$	1.00000	0.129099
$61$	0.00337115	0.000431632 0	0.000215816	−	1.00000i	$-0.499931\pi$
$61$	0.00337115	0.000431632 0	0.000215816		1.00000i	$0.499931\pi$
$62$	2.10662	0.267540
$63$	1.23070	0.155053
$64$	1.00000	0.125000
$65$	4.87255	0.604365
$66$	−1.00000	−0.123091
$67$	−11.8791	−1.45126	−0.725630	−	0.688085i	$-0.758452\pi$
$67$	−11.8791	−1.45126	−0.725630	+	0.688085i	$0.758452\pi$
$68$	−1.00000	−0.121268
$69$	9.36130	1.12697
$70$	1.23070	0.147096
$71$	−15.2130	−1.80545	−0.902726	−	0.430215i	$-0.858438\pi$
$71$	−15.2130	−1.80545	−0.902726	+	0.430215i	$0.858438\pi$
$72$	1.00000	0.117851
$73$	11.2547	1.31726	0.658631	−	0.752466i	$-0.271136\pi$
$73$	11.2547	1.31726	0.658631	+	0.752466i	$0.271136\pi$
$74$	−10.3405	−1.20206
$75$	1.00000	0.115470
$76$	−0.872548	−0.100088
$77$	−1.23070	−0.140251
$78$	4.87255	0.551707
$79$	8.62102	0.969940	0.484970	−	0.874531i	$-0.338831\pi$
$79$	8.62102	0.969940	0.484970	+	0.874531i	$0.338831\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−8.59200	−0.948828
$83$	−1.99663	−0.219158	−0.109579	−	0.993978i	$-0.534950\pi$
$83$	−1.99663	−0.219158	−0.109579	+	0.993978i	$0.534950\pi$
$84$	1.23070	0.134280
$85$	−1.00000	−0.108465
$86$	−0.979164	−0.105586
$87$	3.64185	0.390447
$88$	−1.00000	−0.106600
$89$	1.28370	0.136072	0.0680361	−	0.997683i	$-0.478327\pi$
$89$	1.28370	0.136072	0.0680361	+	0.997683i	$0.478327\pi$
$90$	1.00000	0.105409
$91$	5.99663	0.628618
$92$	9.36130	0.975984
$93$	2.10662	0.218446
$94$	8.59200	0.886197
$95$	−0.872548	−0.0895215
$96$	1.00000	0.102062
$97$	7.85171	0.797221	0.398610	−	0.917120i	$-0.369493\pi$
$97$	7.85171	0.797221	0.398610	+	0.917120i	$0.369493\pi$
$98$	−5.48539	−0.554108
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−15.8757	−1.57969	−0.789846	−	0.613305i	$-0.789839\pi$
$101$	−15.8757	−1.57969	−0.789846	+	0.613305i	$0.789839\pi$
$102$	−1.00000	−0.0990148
$103$	16.4437	1.62025	0.810124	−	0.586259i	$-0.199400\pi$
$103$	16.4437	1.62025	0.810124	+	0.586259i	$0.199400\pi$
$104$	4.87255	0.477793
$105$	1.23070	0.120104
$106$	−7.92931	−0.770163
$107$	2.02736	0.195993	0.0979963	−	0.995187i	$-0.468757\pi$
$107$	2.02736	0.195993	0.0979963	+	0.995187i	$0.468757\pi$
$108$	1.00000	0.0962250
$109$	−0.209861	−0.0201010	−0.0100505	−	0.999949i	$-0.503199\pi$
$109$	−0.209861	−0.0201010	−0.0100505	+	0.999949i	$0.503199\pi$
$110$	−1.00000	−0.0953463
$111$	−10.3405	−0.981474
$112$	1.23070	0.116290
$113$	−0.875919	−0.0823996	−0.0411998	−	0.999151i	$-0.513118\pi$
$113$	−0.875919	−0.0823996	−0.0411998	+	0.999151i	$0.513118\pi$
$114$	−0.872548	−0.0817216
$115$	9.36130	0.872946
$116$	3.64185	0.338137
$117$	4.87255	0.450467
$118$	9.46792	0.871593
$119$	−1.23070	−0.112818
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	0.00337115	0.000305210 0
$123$	−8.59200	−0.774715
$124$	2.10662	0.189180
$125$	1.00000	0.0894427
$126$	1.23070	0.109639
$127$	6.13061	0.544004	0.272002	−	0.962297i	$-0.412314\pi$
$127$	6.13061	0.544004	0.272002	+	0.962297i	$0.412314\pi$
$128$	1.00000	0.0883883
$129$	−0.979164	−0.0862106
$130$	4.87255	0.427351
$131$	15.1874	1.32693	0.663464	−	0.748209i	$-0.269086\pi$
$131$	15.1874	1.32693	0.663464	+	0.748209i	$0.269086\pi$
$132$	−1.00000	−0.0870388
$133$	−1.07384	−0.0931139
$134$	−11.8791	−1.02620
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	14.4437	1.23401	0.617005	−	0.786959i	$-0.288346\pi$
$137$	14.4437	1.23401	0.617005	+	0.786959i	$0.288346\pi$
$138$	9.36130	0.796887
$139$	2.74366	0.232714	0.116357	−	0.993207i	$-0.462878\pi$
$139$	2.74366	0.232714	0.116357	+	0.993207i	$0.462878\pi$
$140$	1.23070	0.104013
$141$	8.59200	0.723577
$142$	−15.2130	−1.27665
$143$	−4.87255	−0.407463
$144$	1.00000	0.0833333
$145$	3.64185	0.302439
$146$	11.2547	0.931445
$147$	−5.48539	−0.452427
$148$	−10.3405	−0.849981
$149$	−12.3405	−1.01097	−0.505485	−	0.862835i	$-0.668687\pi$
$149$	−12.3405	−1.01097	−0.505485	+	0.862835i	$0.668687\pi$
$150$	1.00000	0.0816497
$151$	2.59537	0.211208	0.105604	−	0.994408i	$-0.466322\pi$
$151$	2.59537	0.211208	0.105604	+	0.994408i	$0.466322\pi$
$152$	−0.872548	−0.0707730
$153$	−1.00000	−0.0808452
$154$	−1.23070	−0.0991724
$155$	2.10662	0.169207
$156$	4.87255	0.390116
$157$	17.6208	1.40629	0.703146	−	0.711045i	$-0.251778\pi$
$157$	17.6208	1.40629	0.703146	+	0.711045i	$0.251778\pi$
$158$	8.62102	0.685851
$159$	−7.92931	−0.628836
$160$	1.00000	0.0790569
$161$	11.5209	0.907976
$162$	1.00000	0.0785674
$163$	2.79495	0.218917	0.109459	−	0.993991i	$-0.465088\pi$
$163$	2.79495	0.218917	0.109459	+	0.993991i	$0.465088\pi$
$164$	−8.59200	−0.670923
$165$	−1.00000	−0.0778499
$166$	−1.99663	−0.154968
$167$	−10.1306	−0.783930	−0.391965	−	0.919980i	$-0.628205\pi$
$167$	−10.1306	−0.783930	−0.391965	+	0.919980i	$0.628205\pi$
$168$	1.23070	0.0949503
$169$	10.7417	0.826287
$170$	−1.00000	−0.0766965
$171$	−0.872548	−0.0667254
$172$	−0.979164	−0.0746606
$173$	3.67259	0.279222	0.139611	−	0.990206i	$-0.455415\pi$
$173$	3.67259	0.279222	0.139611	+	0.990206i	$0.455415\pi$
$174$	3.64185	0.276088
$175$	1.23070	0.0930319
$176$	−1.00000	−0.0753778
$177$	9.46792	0.711653
$178$	1.28370	0.0962176
$179$	−11.4645	−0.856901	−0.428450	−	0.903565i	$-0.640940\pi$
$179$	−11.4645	−0.856901	−0.428450	+	0.903565i	$0.640940\pi$
$180$	1.00000	0.0745356
$181$	−7.85508	−0.583864	−0.291932	−	0.956439i	$-0.594298\pi$
$181$	−7.85508	−0.583864	−0.291932	+	0.956439i	$0.594298\pi$
$182$	5.99663	0.444500
$183$	0.00337115	0.000249203 0
$184$	9.36130	0.690125
$185$	−10.3405	−0.760246
$186$	2.10662	0.154465
$187$	1.00000	0.0731272
$188$	8.59200	0.626636
$189$	1.23070	0.0895200
$190$	−0.872548	−0.0633013
$191$	−9.64185	−0.697660	−0.348830	−	0.937186i	$-0.613421\pi$
$191$	−9.64185	−0.697660	−0.348830	+	0.937186i	$0.613421\pi$
$192$	1.00000	0.0721688
$193$	24.4967	1.76331	0.881656	−	0.471892i	$-0.156429\pi$
$193$	24.4967	1.76331	0.881656	+	0.471892i	$0.156429\pi$
$194$	7.85171	0.563720
$195$	4.87255	0.348930
$196$	−5.48539	−0.391813
$197$	−13.6242	−0.970682	−0.485341	−	0.874325i	$-0.661305\pi$
$197$	−13.6242	−0.970682	−0.485341	+	0.874325i	$0.661305\pi$
$198$	−1.00000	−0.0710669
$199$	−27.8307	−1.97286	−0.986432	−	0.164173i	$-0.947505\pi$
$199$	−27.8307	−1.97286	−0.986432	+	0.164173i	$0.947505\pi$
$200$	1.00000	0.0707107
$201$	−11.8791	−0.837885
$202$	−15.8757	−1.11701
$203$	4.48201	0.314576
$204$	−1.00000	−0.0700140
$205$	−8.59200	−0.600091
$206$	16.4437	1.14569
$207$	9.36130	0.650656
$208$	4.87255	0.337850
$209$	0.872548	0.0603554
$210$	1.23070	0.0849261
$211$	−11.9857	−0.825129	−0.412565	−	0.910928i	$-0.635367\pi$
$211$	−11.9857	−0.825129	−0.412565	+	0.910928i	$0.635367\pi$
$212$	−7.92931	−0.544588
$213$	−15.2130	−1.04238
$214$	2.02736	0.138588
$215$	−0.979164	−0.0667784
$216$	1.00000	0.0680414
$217$	2.59261	0.175998
$218$	−0.209861	−0.0142136
$219$	11.2547	0.760521
$220$	−1.00000	−0.0674200
$221$	−4.87255	−0.327763
$222$	−10.3405	−0.694007
$223$	−26.7466	−1.79108	−0.895542	−	0.444976i	$-0.853212\pi$
$223$	−26.7466	−1.79108	−0.895542	+	0.444976i	$0.853212\pi$
$224$	1.23070	0.0822294
$225$	1.00000	0.0666667
$226$	−0.875919	−0.0582653
$227$	−11.9277	−0.791667	−0.395833	−	0.918322i	$-0.629544\pi$
$227$	−11.9277	−0.791667	−0.395833	+	0.918322i	$0.629544\pi$
$228$	−0.872548	−0.0577859
$229$	−0.770954	−0.0509461	−0.0254730	−	0.999676i	$-0.508109\pi$
$229$	−0.770954	−0.0509461	−0.0254730	+	0.999676i	$0.508109\pi$
$230$	9.36130	0.617266
$231$	−1.23070	−0.0809739
$232$	3.64185	0.239099
$233$	5.00144	0.327655	0.163827	−	0.986489i	$-0.447616\pi$
$233$	5.00144	0.327655	0.163827	+	0.986489i	$0.447616\pi$
$234$	4.87255	0.318528
$235$	8.59200	0.560480
$236$	9.46792	0.616309
$237$	8.62102	0.559995
$238$	−1.23070	−0.0797742
$239$	−7.38418	−0.477643	−0.238821	−	0.971063i	$-0.576761\pi$
$239$	−7.38418	−0.477643	−0.238821	+	0.971063i	$0.576761\pi$
$240$	1.00000	0.0645497
$241$	24.6033	1.58484	0.792420	−	0.609976i	$-0.208821\pi$
$241$	24.6033	1.58484	0.792420	+	0.609976i	$0.208821\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	0.00337115	0.000215816 0
$245$	−5.48539	−0.350448
$246$	−8.59200	−0.547806
$247$	−4.25153	−0.270519
$248$	2.10662	0.133770
$249$	−1.99663	−0.126531
$250$	1.00000	0.0632456
$251$	4.23213	0.267130	0.133565	−	0.991040i	$-0.457358\pi$
$251$	4.23213	0.267130	0.133565	+	0.991040i	$0.457358\pi$
$252$	1.23070	0.0775266
$253$	−9.36130	−0.588540
$254$	6.13061	0.384669
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	15.4115	0.961346	0.480673	−	0.876900i	$-0.340392\pi$
$257$	15.4115	0.961346	0.480673	+	0.876900i	$0.340392\pi$
$258$	−0.979164	−0.0609601
$259$	−12.7260	−0.790754
$260$	4.87255	0.302183
$261$	3.64185	0.225425
$262$	15.1874	0.938279
$263$	−13.1600	−0.811481	−0.405741	−	0.913988i	$-0.632986\pi$
$263$	−13.1600	−0.811481	−0.405741	+	0.913988i	$0.632986\pi$
$264$	−1.00000	−0.0615457
$265$	−7.92931	−0.487094
$266$	−1.07384	−0.0658415
$267$	1.28370	0.0785613
$268$	−11.8791	−0.725630
$269$	−19.4355	−1.18501	−0.592503	−	0.805568i	$-0.701860\pi$
$269$	−19.4355	−1.18501	−0.592503	+	0.805568i	$0.701860\pi$
$270$	1.00000	0.0608581
$271$	4.31648	0.262207	0.131104	−	0.991369i	$-0.458148\pi$
$271$	4.31648	0.262207	0.131104	+	0.991369i	$0.458148\pi$
$272$	−1.00000	−0.0606339
$273$	5.99663	0.362932
$274$	14.4437	0.872577
$275$	−1.00000	−0.0603023
$276$	9.36130	0.563484
$277$	5.99326	0.360100	0.180050	−	0.983657i	$-0.442374\pi$
$277$	5.99326	0.360100	0.180050	+	0.983657i	$0.442374\pi$
$278$	2.74366	0.164554
$279$	2.10662	0.126120
$280$	1.23070	0.0735482
$281$	−8.07865	−0.481932	−0.240966	−	0.970534i	$-0.577464\pi$
$281$	−8.07865	−0.481932	−0.240966	+	0.970534i	$0.577464\pi$
$282$	8.59200	0.511646
$283$	−18.7294	−1.11334	−0.556672	−	0.830732i	$-0.687922\pi$
$283$	−18.7294	−1.11334	−0.556672	+	0.830732i	$0.687922\pi$
$284$	−15.2130	−0.902726
$285$	−0.872548	−0.0516853
$286$	−4.87255	−0.288120
$287$	−10.5741	−0.624172
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	3.64185	0.213857
$291$	7.85171	0.460276
$292$	11.2547	0.658631
$293$	−0.895423	−0.0523112	−0.0261556	−	0.999658i	$-0.508327\pi$
$293$	−0.895423	−0.0523112	−0.0261556	+	0.999658i	$0.508327\pi$
$294$	−5.48539	−0.319914
$295$	9.46792	0.551244
$296$	−10.3405	−0.601028
$297$	−1.00000	−0.0580259
$298$	−12.3405	−0.714864
$299$	45.6134	2.63789
$300$	1.00000	0.0577350
$301$	−1.20505	−0.0694582
$302$	2.59537	0.149347
$303$	−15.8757	−0.912035
$304$	−0.872548	−0.0500441
$305$	0.00337115	0.000193032 0
$306$	−1.00000	−0.0571662
$307$	20.3490	1.16138	0.580690	−	0.814124i	$-0.302783\pi$
$307$	20.3490	1.16138	0.580690	+	0.814124i	$0.302783\pi$
$308$	−1.23070	−0.0701255
$309$	16.4437	0.935450
$310$	2.10662	0.119648
$311$	21.1713	1.20052	0.600258	−	0.799806i	$-0.295064\pi$
$311$	21.1713	1.20052	0.600258	+	0.799806i	$0.295064\pi$
$312$	4.87255	0.275854
$313$	16.3262	0.922809	0.461405	−	0.887190i	$-0.347346\pi$
$313$	16.3262	0.922809	0.461405	+	0.887190i	$0.347346\pi$
$314$	17.6208	0.994399
$315$	1.23070	0.0693419
$316$	8.62102	0.484970
$317$	28.6536	1.60935	0.804673	−	0.593719i	$-0.202341\pi$
$317$	28.6536	1.60935	0.804673	+	0.593719i	$0.202341\pi$
$318$	−7.92931	−0.444654
$319$	−3.64185	−0.203905
$320$	1.00000	0.0559017
$321$	2.02736	0.113156
$322$	11.5209	0.642036
$323$	0.872548	0.0485499
$324$	1.00000	0.0555556
$325$	4.87255	0.270280
$326$	2.79495	0.154798
$327$	−0.209861	−0.0116053
$328$	−8.59200	−0.474414
$329$	10.5741	0.582972
$330$	−1.00000	−0.0550482
$331$	−26.6536	−1.46501	−0.732506	−	0.680760i	$-0.761650\pi$
$331$	−26.6536	−1.46501	−0.732506	+	0.680760i	$0.761650\pi$
$332$	−1.99663	−0.109579
$333$	−10.3405	−0.566654
$334$	−10.1306	−0.554322
$335$	−11.8791	−0.649023
$336$	1.23070	0.0671400
$337$	28.4387	1.54915	0.774577	−	0.632479i	$-0.217963\pi$
$337$	28.4387	1.54915	0.774577	+	0.632479i	$0.217963\pi$
$338$	10.7417	0.584273
$339$	−0.875919	−0.0475734
$340$	−1.00000	−0.0542326
$341$	−2.10662	−0.114080
$342$	−0.872548	−0.0471820
$343$	−15.3657	−0.829671
$344$	−0.979164	−0.0527930
$345$	9.36130	0.503996
$346$	3.67259	0.197439
$347$	−10.1135	−0.542923	−0.271461	−	0.962449i	$-0.587507\pi$
$347$	−10.1135	−0.542923	−0.271461	+	0.962449i	$0.587507\pi$
$348$	3.64185	0.195224
$349$	31.4742	1.68478	0.842389	−	0.538871i	$-0.181149\pi$
$349$	31.4742	1.68478	0.842389	+	0.538871i	$0.181149\pi$
$350$	1.23070	0.0657835
$351$	4.87255	0.260077
$352$	−1.00000	−0.0533002
$353$	−5.86879	−0.312364	−0.156182	−	0.987728i	$-0.549919\pi$
$353$	−5.86879	−0.312364	−0.156182	+	0.987728i	$0.549919\pi$
$354$	9.46792	0.503214
$355$	−15.2130	−0.807423
$356$	1.28370	0.0680361
$357$	−1.23070	−0.0651354
$358$	−11.4645	−0.605920
$359$	−1.96507	−0.103712	−0.0518562	−	0.998655i	$-0.516514\pi$
$359$	−1.96507	−0.103712	−0.0518562	+	0.998655i	$0.516514\pi$
$360$	1.00000	0.0527046
$361$	−18.2387	−0.959929
$362$	−7.85508	−0.412854
$363$	1.00000	0.0524864
$364$	5.99663	0.314309
$365$	11.2547	0.589097
$366$	0.00337115	0.000176213 0
$367$	−20.9291	−1.09249	−0.546245	−	0.837625i	$-0.683943\pi$
$367$	−20.9291	−1.09249	−0.546245	+	0.837625i	$0.683943\pi$
$368$	9.36130	0.487992
$369$	−8.59200	−0.447282
$370$	−10.3405	−0.537575
$371$	−9.75858	−0.506640
$372$	2.10662	0.109223
$373$	−32.1659	−1.66549	−0.832744	−	0.553657i	$-0.813232\pi$
$373$	−32.1659	−1.66549	−0.832744	+	0.553657i	$0.813232\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	8.59200	0.443099
$377$	17.7451	0.913919
$378$	1.23070	0.0633002
$379$	−27.6004	−1.41773	−0.708867	−	0.705342i	$-0.750794\pi$
$379$	−27.6004	−1.41773	−0.708867	+	0.705342i	$0.750794\pi$
$380$	−0.872548	−0.0447608
$381$	6.13061	0.314081
$382$	−9.64185	−0.493320
$383$	−11.6692	−0.596269	−0.298135	−	0.954524i	$-0.596364\pi$
$383$	−11.6692	−0.596269	−0.298135	+	0.954524i	$0.596364\pi$
$384$	1.00000	0.0510310
$385$	−1.23070	−0.0627221
$386$	24.4967	1.24685
$387$	−0.979164	−0.0497737
$388$	7.85171	0.398610
$389$	9.33057	0.473079	0.236539	−	0.971622i	$-0.423987\pi$
$389$	9.33057	0.473079	0.236539	+	0.971622i	$0.423987\pi$
$390$	4.87255	0.246731
$391$	−9.36130	−0.473422
$392$	−5.48539	−0.277054
$393$	15.1874	0.766102
$394$	−13.6242	−0.686376
$395$	8.62102	0.433770
$396$	−1.00000	−0.0502519
$397$	−20.5983	−1.03380	−0.516900	−	0.856046i	$-0.672914\pi$
$397$	−20.5983	−1.03380	−0.516900	+	0.856046i	$0.672914\pi$
$398$	−27.8307	−1.39503
$399$	−1.07384	−0.0537593
$400$	1.00000	0.0500000
$401$	1.53359	0.0765836	0.0382918	−	0.999267i	$-0.487808\pi$
$401$	1.53359	0.0765836	0.0382918	+	0.999267i	$0.487808\pi$
$402$	−11.8791	−0.592474
$403$	10.2646	0.511316
$404$	−15.8757	−0.789846
$405$	1.00000	0.0496904
$406$	4.48201	0.222439
$407$	10.3405	0.512558
$408$	−1.00000	−0.0495074
$409$	−10.9775	−0.542803	−0.271402	−	0.962466i	$-0.587487\pi$
$409$	−10.9775	−0.542803	−0.271402	+	0.962466i	$0.587487\pi$
$410$	−8.59200	−0.424329
$411$	14.4437	0.712456
$412$	16.4437	0.810124
$413$	11.6521	0.573364
$414$	9.36130	0.460083
$415$	−1.99663	−0.0980107
$416$	4.87255	0.238896
$417$	2.74366	0.134358
$418$	0.872548	0.0426777
$419$	−27.0562	−1.32178	−0.660890	−	0.750483i	$-0.729821\pi$
$419$	−27.0562	−1.32178	−0.660890	+	0.750483i	$0.729821\pi$
$420$	1.23070	0.0600518
$421$	27.5483	1.34262	0.671311	−	0.741176i	$-0.265732\pi$
$421$	27.5483	1.34262	0.671311	+	0.741176i	$0.265732\pi$
$422$	−11.9857	−0.583454
$423$	8.59200	0.417757
$424$	−7.92931	−0.385082
$425$	−1.00000	−0.0485071
$426$	−15.2130	−0.737073
$427$	0.00414887	0.000200778 0
$428$	2.02736	0.0979963
$429$	−4.87255	−0.235249
$430$	−0.979164	−0.0472195
$431$	3.62478	0.174599	0.0872996	−	0.996182i	$-0.472176\pi$
$431$	3.62478	0.174599	0.0872996	+	0.996182i	$0.472176\pi$
$432$	1.00000	0.0481125
$433$	−14.2065	−0.682720	−0.341360	−	0.939933i	$-0.610888\pi$
$433$	−14.2065	−0.682720	−0.341360	+	0.939933i	$0.610888\pi$
$434$	2.59261	0.124449
$435$	3.64185	0.174613
$436$	−0.209861	−0.0100505
$437$	−8.16819	−0.390737
$438$	11.2547	0.537770
$439$	10.2601	0.489688	0.244844	−	0.969563i	$-0.421263\pi$
$439$	10.2601	0.489688	0.244844	+	0.969563i	$0.421263\pi$
$440$	−1.00000	−0.0476731
$441$	−5.48539	−0.261209
$442$	−4.87255	−0.231763
$443$	−10.2287	−0.485978	−0.242989	−	0.970029i	$-0.578128\pi$
$443$	−10.2287	−0.485978	−0.242989	+	0.970029i	$0.578128\pi$
$444$	−10.3405	−0.490737
$445$	1.28370	0.0608534
$446$	−26.7466	−1.26649
$447$	−12.3405	−0.583684
$448$	1.23070	0.0581450
$449$	−16.7626	−0.791074	−0.395537	−	0.918450i	$-0.629442\pi$
$449$	−16.7626	−0.791074	−0.395537	+	0.918450i	$0.629442\pi$
$450$	1.00000	0.0471405
$451$	8.59200	0.404582
$452$	−0.875919	−0.0411998
$453$	2.59537	0.121941
$454$	−11.9277	−0.559793
$455$	5.99663	0.281126
$456$	−0.872548	−0.0408608
$457$	−4.41635	−0.206588	−0.103294	−	0.994651i	$-0.532938\pi$
$457$	−4.41635	−0.206588	−0.103294	+	0.994651i	$0.532938\pi$
$458$	−0.770954	−0.0360243
$459$	−1.00000	−0.0466760
$460$	9.36130	0.436473
$461$	−6.13735	−0.285845	−0.142922	−	0.989734i	$-0.545650\pi$
$461$	−6.13735	−0.285845	−0.142922	+	0.989734i	$0.545650\pi$
$462$	−1.23070	−0.0572572
$463$	21.3522	0.992321	0.496160	−	0.868231i	$-0.334743\pi$
$463$	21.3522	0.992321	0.496160	+	0.868231i	$0.334743\pi$
$464$	3.64185	0.169069
$465$	2.10662	0.0976920
$466$	5.00144	0.231687
$467$	−16.6143	−0.768817	−0.384408	−	0.923163i	$-0.625595\pi$
$467$	−16.6143	−0.768817	−0.384408	+	0.923163i	$0.625595\pi$
$468$	4.87255	0.225234
$469$	−14.6195	−0.675068
$470$	8.59200	0.396319
$471$	17.6208	0.811924
$472$	9.46792	0.435796
$473$	0.979164	0.0450220
$474$	8.62102	0.395976
$475$	−0.872548	−0.0400353
$476$	−1.23070	−0.0564089
$477$	−7.92931	−0.363058
$478$	−7.38418	−0.337745
$479$	14.7403	0.673501	0.336751	−	0.941594i	$-0.390672\pi$
$479$	14.7403	0.673501	0.336751	+	0.941594i	$0.390672\pi$
$480$	1.00000	0.0456435
$481$	−50.3844	−2.29733
$482$	24.6033	1.12065
$483$	11.5209	0.524220
$484$	1.00000	0.0454545
$485$	7.85171	0.356528
$486$	1.00000	0.0453609
$487$	4.51612	0.204645	0.102322	−	0.994751i	$-0.467373\pi$
$487$	4.51612	0.204645	0.102322	+	0.994751i	$0.467373\pi$
$488$	0.00337115	0.000152605 0
$489$	2.79495	0.126392
$490$	−5.48539	−0.247804
$491$	−34.6400	−1.56328	−0.781640	−	0.623729i	$-0.785617\pi$
$491$	−34.6400	−1.56328	−0.781640	+	0.623729i	$0.785617\pi$
$492$	−8.59200	−0.387357
$493$	−3.64185	−0.164021
$494$	−4.25153	−0.191285
$495$	−1.00000	−0.0449467
$496$	2.10662	0.0945898
$497$	−18.7226	−0.839824
$498$	−1.99663	−0.0894711
$499$	30.8778	1.38228	0.691140	−	0.722721i	$-0.257109\pi$
$499$	30.8778	1.38228	0.691140	+	0.722721i	$0.257109\pi$
$500$	1.00000	0.0447214
$501$	−10.1306	−0.452602
$502$	4.23213	0.188889
$503$	−27.6625	−1.23341	−0.616704	−	0.787195i	$-0.711533\pi$
$503$	−27.6625	−1.23341	−0.616704	+	0.787195i	$0.711533\pi$
$504$	1.23070	0.0548196
$505$	−15.8757	−0.706460
$506$	−9.36130	−0.416161
$507$	10.7417	0.477057
$508$	6.13061	0.272002
$509$	−6.15288	−0.272722	−0.136361	−	0.990659i	$-0.543541\pi$
$509$	−6.15288	−0.272722	−0.136361	+	0.990659i	$0.543541\pi$
$510$	−1.00000	−0.0442807
$511$	13.8511	0.612737
$512$	1.00000	0.0441942
$513$	−0.872548	−0.0385239
$514$	15.4115	0.679774
$515$	16.4437	0.724597
$516$	−0.979164	−0.0431053
$517$	−8.59200	−0.377876
$518$	−12.7260	−0.559148
$519$	3.67259	0.161209
$520$	4.87255	0.213675
$521$	−16.4870	−0.722310	−0.361155	−	0.932506i	$-0.617618\pi$
$521$	−16.4870	−0.722310	−0.361155	+	0.932506i	$0.617618\pi$
$522$	3.64185	0.159400
$523$	0.346211	0.0151387	0.00756937	−	0.999971i	$-0.497591\pi$
$523$	0.346211	0.0151387	0.00756937	+	0.999971i	$0.497591\pi$
$524$	15.1874	0.663464
$525$	1.23070	0.0537120
$526$	−13.1600	−0.573804
$527$	−2.10662	−0.0917656
$528$	−1.00000	−0.0435194
$529$	64.6340	2.81018
$530$	−7.92931	−0.344427
$531$	9.46792	0.410873
$532$	−1.07384	−0.0465570
$533$	−41.8649	−1.81337
$534$	1.28370	0.0555513
$535$	2.02736	0.0876506
$536$	−11.8791	−0.513098
$537$	−11.4645	−0.494732
$538$	−19.4355	−0.837925
$539$	5.48539	0.236272
$540$	1.00000	0.0430331
$541$	9.13194	0.392613	0.196306	−	0.980543i	$-0.437105\pi$
$541$	9.13194	0.392613	0.196306	+	0.980543i	$0.437105\pi$
$542$	4.31648	0.185409
$543$	−7.85508	−0.337094
$544$	−1.00000	−0.0428746
$545$	−0.209861	−0.00898945
$546$	5.99663	0.256632
$547$	−30.4130	−1.30037	−0.650184	−	0.759777i	$-0.725308\pi$
$547$	−30.4130	−1.30037	−0.650184	+	0.759777i	$0.725308\pi$
$548$	14.4437	0.617005
$549$	0.00337115	0.000143877 0
$550$	−1.00000	−0.0426401
$551$	−3.17769	−0.135374
$552$	9.36130	0.398444
$553$	10.6099	0.451177
$554$	5.99326	0.254629
$555$	−10.3405	−0.438928
$556$	2.74366	0.116357
$557$	7.04985	0.298712	0.149356	−	0.988784i	$-0.452280\pi$
$557$	7.04985	0.298712	0.149356	+	0.988784i	$0.452280\pi$
$558$	2.10662	0.0891802
$559$	−4.77102	−0.201793
$560$	1.23070	0.0520064
$561$	1.00000	0.0422200
$562$	−8.07865	−0.340777
$563$	−1.08058	−0.0455412	−0.0227706	−	0.999741i	$-0.507249\pi$
$563$	−1.08058	−0.0455412	−0.0227706	+	0.999741i	$0.507249\pi$
$564$	8.59200	0.361789
$565$	−0.875919	−0.0368502
$566$	−18.7294	−0.787253
$567$	1.23070	0.0516844
$568$	−15.2130	−0.638324
$569$	−25.0802	−1.05141	−0.525707	−	0.850665i	$-0.676199\pi$
$569$	−25.0802	−1.05141	−0.525707	+	0.850665i	$0.676199\pi$
$570$	−0.872548	−0.0365470
$571$	43.7447	1.83066	0.915329	−	0.402708i	$-0.131931\pi$
$571$	43.7447	1.83066	0.915329	+	0.402708i	$0.131931\pi$
$572$	−4.87255	−0.203731
$573$	−9.64185	−0.402794
$574$	−10.5741	−0.441356
$575$	9.36130	0.390393
$576$	1.00000	0.0416667
$577$	−3.69381	−0.153775	−0.0768877	−	0.997040i	$-0.524498\pi$
$577$	−3.69381	−0.153775	−0.0768877	+	0.997040i	$0.524498\pi$
$578$	1.00000	0.0415945
$579$	24.4967	1.01805
$580$	3.64185	0.151220
$581$	−2.45724	−0.101944
$582$	7.85171	0.325464
$583$	7.92931	0.328399
$584$	11.2547	0.465722
$585$	4.87255	0.201455
$586$	−0.895423	−0.0369896
$587$	11.4707	0.473446	0.236723	−	0.971577i	$-0.423927\pi$
$587$	11.4707	0.473446	0.236723	+	0.971577i	$0.423927\pi$
$588$	−5.48539	−0.226213
$589$	−1.83812	−0.0757386
$590$	9.46792	0.389788
$591$	−13.6242	−0.560424
$592$	−10.3405	−0.424991
$593$	9.85863	0.404845	0.202423	−	0.979298i	$-0.435119\pi$
$593$	9.85863	0.404845	0.202423	+	0.979298i	$0.435119\pi$
$594$	−1.00000	−0.0410305
$595$	−1.23070	−0.0504536
$596$	−12.3405	−0.505485
$597$	−27.8307	−1.13903
$598$	45.6134	1.86527
$599$	−9.28431	−0.379346	−0.189673	−	0.981847i	$-0.560743\pi$
$599$	−9.28431	−0.379346	−0.189673	+	0.981847i	$0.560743\pi$
$600$	1.00000	0.0408248
$601$	−4.98608	−0.203386	−0.101693	−	0.994816i	$-0.532426\pi$
$601$	−4.98608	−0.203386	−0.101693	+	0.994816i	$0.532426\pi$
$602$	−1.20505	−0.0491143
$603$	−11.8791	−0.483753
$604$	2.59537	0.105604
$605$	1.00000	0.0406558
$606$	−15.8757	−0.644906
$607$	13.3224	0.540740	0.270370	−	0.962757i	$-0.412854\pi$
$607$	13.3224	0.540740	0.270370	+	0.962757i	$0.412854\pi$
$608$	−0.872548	−0.0353865
$609$	4.48201	0.181620
$610$	0.00337115	0.000136494 0
$611$	41.8649	1.69367
$612$	−1.00000	−0.0404226
$613$	−6.10834	−0.246713	−0.123357	−	0.992362i	$-0.539366\pi$
$613$	−6.10834	−0.246713	−0.123357	+	0.992362i	$0.539366\pi$
$614$	20.3490	0.821220
$615$	−8.59200	−0.346463
$616$	−1.23070	−0.0495862
$617$	6.21169	0.250073	0.125037	−	0.992152i	$-0.460095\pi$
$617$	6.21169	0.250073	0.125037	+	0.992152i	$0.460095\pi$
$618$	16.4437	0.661463
$619$	21.7834	0.875549	0.437774	−	0.899085i	$-0.355767\pi$
$619$	21.7834	0.875549	0.437774	+	0.899085i	$0.355767\pi$
$620$	2.10662	0.0846037
$621$	9.36130	0.375656
$622$	21.1713	0.848894
$623$	1.57985	0.0632953
$624$	4.87255	0.195058
$625$	1.00000	0.0400000
$626$	16.3262	0.652525
$627$	0.872548	0.0348462
$628$	17.6208	0.703146
$629$	10.3405	0.412301
$630$	1.23070	0.0490321
$631$	2.51942	0.100297	0.0501483	−	0.998742i	$-0.484031\pi$
$631$	2.51942	0.100297	0.0501483	+	0.998742i	$0.484031\pi$
$632$	8.62102	0.342926
$633$	−11.9857	−0.476388
$634$	28.6536	1.13798
$635$	6.13061	0.243286
$636$	−7.92931	−0.314418
$637$	−26.7278	−1.05899
$638$	−3.64185	−0.144182
$639$	−15.2130	−0.601818
$640$	1.00000	0.0395285
$641$	−20.0012	−0.790001	−0.395000	−	0.918681i	$-0.629256\pi$
$641$	−20.0012	−0.790001	−0.395000	+	0.918681i	$0.629256\pi$
$642$	2.02736	0.0800137
$643$	−9.46957	−0.373443	−0.186722	−	0.982413i	$-0.559786\pi$
$643$	−9.46957	−0.373443	−0.186722	+	0.982413i	$0.559786\pi$
$644$	11.5209	0.453988
$645$	−0.979164	−0.0385545
$646$	0.872548	0.0343299
$647$	−31.7343	−1.24761	−0.623803	−	0.781582i	$-0.714413\pi$
$647$	−31.7343	−1.24761	−0.623803	+	0.781582i	$0.714413\pi$
$648$	1.00000	0.0392837
$649$	−9.46792	−0.371648
$650$	4.87255	0.191117
$651$	2.59261	0.101612
$652$	2.79495	0.109459
$653$	−11.7661	−0.460445	−0.230222	−	0.973138i	$-0.573945\pi$
$653$	−11.7661	−0.460445	−0.230222	+	0.973138i	$0.573945\pi$
$654$	−0.209861	−0.00820620
$655$	15.1874	0.593420
$656$	−8.59200	−0.335461
$657$	11.2547	0.439087
$658$	10.5741	0.412223
$659$	31.3385	1.22078	0.610388	−	0.792103i	$-0.291014\pi$
$659$	31.3385	1.22078	0.610388	+	0.792103i	$0.291014\pi$
$660$	−1.00000	−0.0389249
$661$	0.880407	0.0342439	0.0171219	−	0.999853i	$-0.494550\pi$
$661$	0.880407	0.0342439	0.0171219	+	0.999853i	$0.494550\pi$
$662$	−26.6536	−1.03592
$663$	−4.87255	−0.189234
$664$	−1.99663	−0.0774842
$665$	−1.07384	−0.0416418
$666$	−10.3405	−0.400685
$667$	34.0925	1.32007
$668$	−10.1306	−0.391965
$669$	−26.7466	−1.03408
$670$	−11.8791	−0.458929
$671$	−0.00337115	−0.000130142 0
$672$	1.23070	0.0474752
$673$	40.0416	1.54349	0.771746	−	0.635931i	$-0.219384\pi$
$673$	40.0416	1.54349	0.771746	+	0.635931i	$0.219384\pi$
$674$	28.4387	1.09542
$675$	1.00000	0.0384900
$676$	10.7417	0.413143
$677$	12.0759	0.464114	0.232057	−	0.972702i	$-0.425454\pi$
$677$	12.0759	0.464114	0.232057	+	0.972702i	$0.425454\pi$
$678$	−0.875919	−0.0336395
$679$	9.66308	0.370835
$680$	−1.00000	−0.0383482
$681$	−11.9277	−0.457069
$682$	−2.10662	−0.0806665
$683$	−50.0652	−1.91569	−0.957846	−	0.287284i	$-0.907248\pi$
$683$	−50.0652	−1.91569	−0.957846	+	0.287284i	$0.907248\pi$
$684$	−0.872548	−0.0333627
$685$	14.4437	0.551866
$686$	−15.3657	−0.586666
$687$	−0.770954	−0.0294137
$688$	−0.979164	−0.0373303
$689$	−38.6360	−1.47191
$690$	9.36130	0.356379
$691$	−0.302818	−0.0115197	−0.00575987	−	0.999983i	$-0.501833\pi$
$691$	−0.302818	−0.0115197	−0.00575987	+	0.999983i	$0.501833\pi$
$692$	3.67259	0.139611
$693$	−1.23070	−0.0467503
$694$	−10.1135	−0.383904
$695$	2.74366	0.104073
$696$	3.64185	0.138044
$697$	8.59200	0.325445
$698$	31.4742	1.19132
$699$	5.00144	0.189172
$700$	1.23070	0.0465160
$701$	−35.0467	−1.32369	−0.661847	−	0.749639i	$-0.730227\pi$
$701$	−35.0467	−1.32369	−0.661847	+	0.749639i	$0.730227\pi$
$702$	4.87255	0.183902
$703$	9.02256	0.340292
$704$	−1.00000	−0.0376889
$705$	8.59200	0.323594
$706$	−5.86879	−0.220875
$707$	−19.5382	−0.734809
$708$	9.46792	0.355826
$709$	16.1853	0.607853	0.303927	−	0.952695i	$-0.401702\pi$
$709$	16.1853	0.607853	0.303927	+	0.952695i	$0.401702\pi$
$710$	−15.2130	−0.570934
$711$	8.62102	0.323313
$712$	1.28370	0.0481088
$713$	19.7207	0.738545
$714$	−1.23070	−0.0460577
$715$	−4.87255	−0.182223
$716$	−11.4645	−0.428450
$717$	−7.38418	−0.275767
$718$	−1.96507	−0.0733358
$719$	−37.3778	−1.39396	−0.696979	−	0.717092i	$-0.745473\pi$
$719$	−37.3778	−1.39396	−0.696979	+	0.717092i	$0.745473\pi$
$720$	1.00000	0.0372678
$721$	20.2372	0.753674
$722$	−18.2387	−0.678773
$723$	24.6033	0.915008
$724$	−7.85508	−0.291932
$725$	3.64185	0.135255
$726$	1.00000	0.0371135
$727$	25.5108	0.946144	0.473072	−	0.881024i	$-0.343145\pi$
$727$	25.5108	0.946144	0.473072	+	0.881024i	$0.343145\pi$
$728$	5.99663	0.222250
$729$	1.00000	0.0370370
$730$	11.2547	0.416555
$731$	0.979164	0.0362157
$732$	0.00337115	0.000124601 0
$733$	−51.7116	−1.91001	−0.955005	−	0.296590i	$-0.904151\pi$
$733$	−51.7116	−1.91001	−0.955005	+	0.296590i	$0.904151\pi$
$734$	−20.9291	−0.772507
$735$	−5.48539	−0.202331
$736$	9.36130	0.345062
$737$	11.8791	0.437571
$738$	−8.59200	−0.316276
$739$	−9.43034	−0.346901	−0.173450	−	0.984843i	$-0.555492\pi$
$739$	−9.43034	−0.346901	−0.173450	+	0.984843i	$0.555492\pi$
$740$	−10.3405	−0.380123
$741$	−4.25153	−0.156184
$742$	−9.75858	−0.358249
$743$	5.02521	0.184357	0.0921785	−	0.995742i	$-0.470617\pi$
$743$	5.02521	0.184357	0.0921785	+	0.995742i	$0.470617\pi$
$744$	2.10662	0.0772323
$745$	−12.3405	−0.452120
$746$	−32.1659	−1.17768
$747$	−1.99663	−0.0730528
$748$	1.00000	0.0365636
$749$	2.49507	0.0911679
$750$	1.00000	0.0365148
$751$	−22.8806	−0.834924	−0.417462	−	0.908694i	$-0.637080\pi$
$751$	−22.8806	−0.834924	−0.417462	+	0.908694i	$0.637080\pi$
$752$	8.59200	0.313318
$753$	4.23213	0.154227
$754$	17.7451	0.646238
$755$	2.59537	0.0944553
$756$	1.23070	0.0447600
$757$	−26.3228	−0.956718	−0.478359	−	0.878164i	$-0.658768\pi$
$757$	−26.3228	−0.956718	−0.478359	+	0.878164i	$0.658768\pi$
$758$	−27.6004	−1.00249
$759$	−9.36130	−0.339794
$760$	−0.872548	−0.0316506
$761$	−48.1602	−1.74581	−0.872903	−	0.487894i	$-0.837765\pi$
$761$	−48.1602	−1.74581	−0.872903	+	0.487894i	$0.837765\pi$
$762$	6.13061	0.222089
$763$	−0.258275	−0.00935018
$764$	−9.64185	−0.348830
$765$	−1.00000	−0.0361551
$766$	−11.6692	−0.421626
$767$	46.1329	1.66576
$768$	1.00000	0.0360844
$769$	−18.3125	−0.660366	−0.330183	−	0.943917i	$-0.607110\pi$
$769$	−18.3125	−0.660366	−0.330183	+	0.943917i	$0.607110\pi$
$770$	−1.23070	−0.0443512
$771$	15.4115	0.555033
$772$	24.4967	0.881656
$773$	−6.03316	−0.216998	−0.108499	−	0.994097i	$-0.534604\pi$
$773$	−6.03316	−0.216998	−0.108499	+	0.994097i	$0.534604\pi$
$774$	−0.979164	−0.0351953
$775$	2.10662	0.0756719
$776$	7.85171	0.281860
$777$	−12.7260	−0.456542
$778$	9.33057	0.334517
$779$	7.49693	0.268606
$780$	4.87255	0.174465
$781$	15.2130	0.544365
$782$	−9.36130	−0.334760
$783$	3.64185	0.130149
$784$	−5.48539	−0.195907
$785$	17.6208	0.628913
$786$	15.1874	0.541716
$787$	−40.8744	−1.45702	−0.728508	−	0.685037i	$-0.759786\pi$
$787$	−40.8744	−1.45702	−0.728508	+	0.685037i	$0.759786\pi$
$788$	−13.6242	−0.485341
$789$	−13.1600	−0.468509
$790$	8.62102	0.306722
$791$	−1.07799	−0.0383289
$792$	−1.00000	−0.0355335
$793$	0.0164261	0.000583308 0
$794$	−20.5983	−0.731007
$795$	−7.92931	−0.281224
$796$	−27.8307	−0.986432
$797$	28.3520	1.00428	0.502139	−	0.864787i	$-0.332546\pi$
$797$	28.3520	1.00428	0.502139	+	0.864787i	$0.332546\pi$
$798$	−1.07384	−0.0380136
$799$	−8.59200	−0.303963
$800$	1.00000	0.0353553
$801$	1.28370	0.0453574
$802$	1.53359	0.0541528
$803$	−11.2547	−0.397169
$804$	−11.8791	−0.418943
$805$	11.5209	0.406059
$806$	10.2646	0.361555
$807$	−19.4355	−0.684163
$808$	−15.8757	−0.558505
$809$	−11.9337	−0.419568	−0.209784	−	0.977748i	$-0.567276\pi$
$809$	−11.9337	−0.419568	−0.209784	+	0.977748i	$0.567276\pi$
$810$	1.00000	0.0351364
$811$	10.9426	0.384246	0.192123	−	0.981371i	$-0.438463\pi$
$811$	10.9426	0.384246	0.192123	+	0.981371i	$0.438463\pi$
$812$	4.48201	0.157288
$813$	4.31648	0.151385
$814$	10.3405	0.362433
$815$	2.79495	0.0979027
$816$	−1.00000	−0.0350070
$817$	0.854368	0.0298905
$818$	−10.9775	−0.383820
$819$	5.99663	0.209539
$820$	−8.59200	−0.300046
$821$	24.8806	0.868338	0.434169	−	0.900831i	$-0.357042\pi$
$821$	24.8806	0.868338	0.434169	+	0.900831i	$0.357042\pi$
$822$	14.4437	0.503782
$823$	−27.1840	−0.947575	−0.473787	−	0.880639i	$-0.657113\pi$
$823$	−27.1840	−0.947575	−0.473787	+	0.880639i	$0.657113\pi$
$824$	16.4437	0.572844
$825$	−1.00000	−0.0348155
$826$	11.6521	0.405430
$827$	−2.68893	−0.0935034	−0.0467517	−	0.998907i	$-0.514887\pi$
$827$	−2.68893	−0.0935034	−0.0467517	+	0.998907i	$0.514887\pi$
$828$	9.36130	0.325328
$829$	20.9262	0.726796	0.363398	−	0.931634i	$-0.381617\pi$
$829$	20.9262	0.726796	0.363398	+	0.931634i	$0.381617\pi$
$830$	−1.99663	−0.0693040
$831$	5.99326	0.207904
$832$	4.87255	0.168925
$833$	5.48539	0.190057
$834$	2.74366	0.0950052
$835$	−10.1306	−0.350584
$836$	0.872548	0.0301777
$837$	2.10662	0.0728153
$838$	−27.0562	−0.934640
$839$	0.780241	0.0269369	0.0134684	−	0.999909i	$-0.495713\pi$
$839$	0.780241	0.0269369	0.0134684	+	0.999909i	$0.495713\pi$
$840$	1.23070	0.0424631
$841$	−15.7369	−0.542652
$842$	27.5483	0.949377
$843$	−8.07865	−0.278243
$844$	−11.9857	−0.412565
$845$	10.7417	0.369527
$846$	8.59200	0.295399
$847$	1.23070	0.0422872
$848$	−7.92931	−0.272294
$849$	−18.7294	−0.642790
$850$	−1.00000	−0.0342997
$851$	−96.8003	−3.31827
$852$	−15.2130	−0.521189
$853$	5.35274	0.183274	0.0916371	−	0.995792i	$-0.470790\pi$
$853$	5.35274	0.183274	0.0916371	+	0.995792i	$0.470790\pi$
$854$	0.00414887	0.000141971 0
$855$	−0.872548	−0.0298405
$856$	2.02736	0.0692939
$857$	−16.2468	−0.554981	−0.277491	−	0.960728i	$-0.589503\pi$
$857$	−16.2468	−0.554981	−0.277491	+	0.960728i	$0.589503\pi$
$858$	−4.87255	−0.166346
$859$	−4.22424	−0.144129	−0.0720646	−	0.997400i	$-0.522959\pi$
$859$	−4.22424	−0.144129	−0.0720646	+	0.997400i	$0.522959\pi$
$860$	−0.979164	−0.0333892
$861$	−10.5741	−0.360366
$862$	3.62478	0.123460
$863$	23.0248	0.783773	0.391886	−	0.920014i	$-0.371823\pi$
$863$	23.0248	0.783773	0.391886	+	0.920014i	$0.371823\pi$
$864$	1.00000	0.0340207
$865$	3.67259	0.124872
$866$	−14.2065	−0.482756
$867$	1.00000	0.0339618
$868$	2.59261	0.0879988
$869$	−8.62102	−0.292448
$870$	3.64185	0.123470
$871$	−57.8814	−1.96124
$872$	−0.209861	−0.00710678
$873$	7.85171	0.265740
$874$	−8.16819	−0.276293
$875$	1.23070	0.0416051
$876$	11.2547	0.380261
$877$	49.0208	1.65531	0.827657	−	0.561234i	$-0.189673\pi$
$877$	49.0208	1.65531	0.827657	+	0.561234i	$0.189673\pi$
$878$	10.2601	0.346262
$879$	−0.895423	−0.0302019
$880$	−1.00000	−0.0337100
$881$	−3.99878	−0.134722	−0.0673611	−	0.997729i	$-0.521458\pi$
$881$	−3.99878	−0.134722	−0.0673611	+	0.997729i	$0.521458\pi$
$882$	−5.48539	−0.184703
$883$	−9.04665	−0.304444	−0.152222	−	0.988346i	$-0.548643\pi$
$883$	−9.04665	−0.304444	−0.152222	+	0.988346i	$0.548643\pi$
$884$	−4.87255	−0.163882
$885$	9.46792	0.318261
$886$	−10.2287	−0.343638
$887$	−2.48886	−0.0835678	−0.0417839	−	0.999127i	$-0.513304\pi$
$887$	−2.48886	−0.0835678	−0.0417839	+	0.999127i	$0.513304\pi$
$888$	−10.3405	−0.347003
$889$	7.54492	0.253048
$890$	1.28370	0.0430298
$891$	−1.00000	−0.0335013
$892$	−26.7466	−0.895542
$893$	−7.49693	−0.250875
$894$	−12.3405	−0.412727
$895$	−11.4645	−0.383218
$896$	1.23070	0.0411147
$897$	45.6134	1.52299
$898$	−16.7626	−0.559374
$899$	7.67198	0.255875
$900$	1.00000	0.0333333
$901$	7.92931	0.264164
$902$	8.59200	0.286082
$903$	−1.20505	−0.0401017
$904$	−0.875919	−0.0291326
$905$	−7.85508	−0.261112
$906$	2.59537	0.0862255
$907$	25.3591	0.842033	0.421017	−	0.907053i	$-0.361673\pi$
$907$	25.3591	0.842033	0.421017	+	0.907053i	$0.361673\pi$
$908$	−11.9277	−0.395833
$909$	−15.8757	−0.526564
$910$	5.99663	0.198786
$911$	−21.7324	−0.720028	−0.360014	−	0.932947i	$-0.617228\pi$
$911$	−21.7324	−0.720028	−0.360014	+	0.932947i	$0.617228\pi$
$912$	−0.872548	−0.0288930
$913$	1.99663	0.0660788
$914$	−4.41635	−0.146080
$915$	0.00337115	0.000111447 0
$916$	−0.770954	−0.0254730
$917$	18.6911	0.617233
$918$	−1.00000	−0.0330049
$919$	29.3870	0.969388	0.484694	−	0.874684i	$-0.338931\pi$
$919$	29.3870	0.969388	0.484694	+	0.874684i	$0.338931\pi$
$920$	9.36130	0.308633
$921$	20.3490	0.670524
$922$	−6.13735	−0.202123
$923$	−74.1262	−2.43989
$924$	−1.23070	−0.0404869
$925$	−10.3405	−0.339993
$926$	21.3522	0.701677
$927$	16.4437	0.540082
$928$	3.64185	0.119550
$929$	38.0184	1.24734	0.623672	−	0.781686i	$-0.285640\pi$
$929$	38.0184	1.24734	0.623672	+	0.781686i	$0.285640\pi$
$930$	2.10662	0.0690787
$931$	4.78626	0.156863
$932$	5.00144	0.163827
$933$	21.1713	0.693119
$934$	−16.6143	−0.543636
$935$	1.00000	0.0327035
$936$	4.87255	0.159264
$937$	−49.4931	−1.61687	−0.808435	−	0.588585i	$-0.799685\pi$
$937$	−49.4931	−1.61687	−0.808435	+	0.588585i	$0.799685\pi$
$938$	−14.6195	−0.477345
$939$	16.3262	0.532784
$940$	8.59200	0.280240
$941$	51.6792	1.68469	0.842347	−	0.538936i	$-0.181174\pi$
$941$	51.6792	1.68469	0.842347	+	0.538936i	$0.181174\pi$
$942$	17.6208	0.574117
$943$	−80.4323	−2.61924
$944$	9.46792	0.308155
$945$	1.23070	0.0400346
$946$	0.979164	0.0318354
$947$	−4.56453	−0.148327	−0.0741637	−	0.997246i	$-0.523629\pi$
$947$	−4.56453	−0.148327	−0.0741637	+	0.997246i	$0.523629\pi$
$948$	8.62102	0.279998
$949$	54.8390	1.78015
$950$	−0.872548	−0.0283092
$951$	28.6536	0.929156
$952$	−1.23070	−0.0398871
$953$	−12.2549	−0.396975	−0.198488	−	0.980103i	$-0.563603\pi$
$953$	−12.2549	−0.396975	−0.198488	+	0.980103i	$0.563603\pi$
$954$	−7.92931	−0.256721
$955$	−9.64185	−0.312003
$956$	−7.38418	−0.238821
$957$	−3.64185	−0.117724
$958$	14.7403	0.476237
$959$	17.7758	0.574012
$960$	1.00000	0.0322749
$961$	−26.5622	−0.856844
$962$	−50.3844	−1.62446
$963$	2.02736	0.0653309
$964$	24.6033	0.792420
$965$	24.4967	0.788577
$966$	11.5209	0.370680
$967$	−37.0597	−1.19176	−0.595880	−	0.803074i	$-0.703197\pi$
$967$	−37.0597	−1.19176	−0.595880	+	0.803074i	$0.703197\pi$
$968$	1.00000	0.0321412
$969$	0.872548	0.0280303
$970$	7.85171	0.252103
$971$	−24.4933	−0.786029	−0.393014	−	0.919532i	$-0.628568\pi$
$971$	−24.4933	−0.786029	−0.393014	+	0.919532i	$0.628568\pi$
$972$	1.00000	0.0320750
$973$	3.37661	0.108249
$974$	4.51612	0.144706
$975$	4.87255	0.156046
$976$	0.00337115	0.000107908 0
$977$	34.5127	1.10416	0.552080	−	0.833791i	$-0.313834\pi$
$977$	34.5127	1.10416	0.552080	+	0.833791i	$0.313834\pi$
$978$	2.79495	0.0893725
$979$	−1.28370	−0.0410273
$980$	−5.48539	−0.175224
$981$	−0.209861	−0.00670034
$982$	−34.6400	−1.10541
$983$	−21.8193	−0.695928	−0.347964	−	0.937508i	$-0.613127\pi$
$983$	−21.8193	−0.695928	−0.347964	+	0.937508i	$0.613127\pi$
$984$	−8.59200	−0.273903
$985$	−13.6242	−0.434102
$986$	−3.64185	−0.115980
$987$	10.5741	0.336579
$988$	−4.25153	−0.135259
$989$	−9.16625	−0.291470
$990$	−1.00000	−0.0317821
$991$	37.5868	1.19398	0.596991	−	0.802248i	$-0.296363\pi$
$991$	37.5868	1.19398	0.596991	+	0.802248i	$0.296363\pi$
$992$	2.10662	0.0668851
$993$	−26.6536	−0.845826
$994$	−18.7226	−0.593845
$995$	−27.8307	−0.882291
$996$	−1.99663	−0.0632656
$997$	−10.9565	−0.346995	−0.173497	−	0.984834i	$-0.555507\pi$
$997$	−10.9565	−0.346995	−0.173497	+	0.984834i	$0.555507\pi$
$998$	30.8778	0.977420
$999$	−10.3405	−0.327158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.ck.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ck.1.3	✓	5	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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.23070 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.23070 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.87255 q^{13} +1.23070 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -0.872548 q^{19} +1.00000 q^{20} +1.23070 q^{21} -1.00000 q^{22} +9.36130 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.87255 q^{26} +1.00000 q^{27} +1.23070 q^{28} +3.64185 q^{29} +1.00000 q^{30} +2.10662 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +1.23070 q^{35} +1.00000 q^{36} -10.3405 q^{37} -0.872548 q^{38} +4.87255 q^{39} +1.00000 q^{40} -8.59200 q^{41} +1.23070 q^{42} -0.979164 q^{43} -1.00000 q^{44} +1.00000 q^{45} +9.36130 q^{46} +8.59200 q^{47} +1.00000 q^{48} -5.48539 q^{49} +1.00000 q^{50} -1.00000 q^{51} +4.87255 q^{52} -7.92931 q^{53} +1.00000 q^{54} -1.00000 q^{55} +1.23070 q^{56} -0.872548 q^{57} +3.64185 q^{58} +9.46792 q^{59} +1.00000 q^{60} +0.00337115 q^{61} +2.10662 q^{62} +1.23070 q^{63} +1.00000 q^{64} +4.87255 q^{65} -1.00000 q^{66} -11.8791 q^{67} -1.00000 q^{68} +9.36130 q^{69} +1.23070 q^{70} -15.2130 q^{71} +1.00000 q^{72} +11.2547 q^{73} -10.3405 q^{74} +1.00000 q^{75} -0.872548 q^{76} -1.23070 q^{77} +4.87255 q^{78} +8.62102 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.59200 q^{82} -1.99663 q^{83} +1.23070 q^{84} -1.00000 q^{85} -0.979164 q^{86} +3.64185 q^{87} -1.00000 q^{88} +1.28370 q^{89} +1.00000 q^{90} +5.99663 q^{91} +9.36130 q^{92} +2.10662 q^{93} +8.59200 q^{94} -0.872548 q^{95} +1.00000 q^{96} +7.85171 q^{97} -5.48539 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} - 5 q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} + 11 q^{19} + 5 q^{20} + 2 q^{21} - 5 q^{22} + 4 q^{23} + 5 q^{24} + 5 q^{25} + 9 q^{26} + 5 q^{27} + 2 q^{28} + 7 q^{29} + 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + 7 q^{37} + 11 q^{38} + 9 q^{39} + 5 q^{40} + 4 q^{41} + 2 q^{42} + 11 q^{43} - 5 q^{44} + 5 q^{45} + 4 q^{46} - 4 q^{47} + 5 q^{48} + 19 q^{49} + 5 q^{50} - 5 q^{51} + 9 q^{52} + 12 q^{53} + 5 q^{54} - 5 q^{55} + 2 q^{56} + 11 q^{57} + 7 q^{58} + 4 q^{59} + 5 q^{60} + 19 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} - 5 q^{68} + 4 q^{69} + 2 q^{70} - 2 q^{71} + 5 q^{72} + 14 q^{73} + 7 q^{74} + 5 q^{75} + 11 q^{76} - 2 q^{77} + 9 q^{78} + 16 q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} + 9 q^{83} + 2 q^{84} - 5 q^{85} + 11 q^{86} + 7 q^{87} - 5 q^{88} - 16 q^{89} + 5 q^{90} + 11 q^{91} + 4 q^{92} + 10 q^{93} - 4 q^{94} + 11 q^{95} + 5 q^{96} + 8 q^{97} + 19 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 5 * q^5 + 5 * q^6 + 2 * q^7 + 5 * q^8 + 5 * q^9 + 5 * q^10 - 5 * q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 + 11 * q^19 + 5 * q^20 + 2 * q^21 - 5 * q^22 + 4 * q^23 + 5 * q^24 + 5 * q^25 + 9 * q^26 + 5 * q^27 + 2 * q^28 + 7 * q^29 + 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + 7 * q^37 + 11 * q^38 + 9 * q^39 + 5 * q^40 + 4 * q^41 + 2 * q^42 + 11 * q^43 - 5 * q^44 + 5 * q^45 + 4 * q^46 - 4 * q^47 + 5 * q^48 + 19 * q^49 + 5 * q^50 - 5 * q^51 + 9 * q^52 + 12 * q^53 + 5 * q^54 - 5 * q^55 + 2 * q^56 + 11 * q^57 + 7 * q^58 + 4 * q^59 + 5 * q^60 + 19 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 - 5 * q^68 + 4 * q^69 + 2 * q^70 - 2 * q^71 + 5 * q^72 + 14 * q^73 + 7 * q^74 + 5 * q^75 + 11 * q^76 - 2 * q^77 + 9 * q^78 + 16 * q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 + 9 * q^83 + 2 * q^84 - 5 * q^85 + 11 * q^86 + 7 * q^87 - 5 * q^88 - 16 * q^89 + 5 * q^90 + 11 * q^91 + 4 * q^92 + 10 * q^93 - 4 * q^94 + 11 * q^95 + 5 * q^96 + 8 * q^97 + 19 * q^98 - 5 * q^99

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