LMFDB - Embedded newform 5610.2.a.ck.1.4

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			1.4
Root			$1.83132$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.59911 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.59911 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +5.94482 q^{13} +2.59911 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.94482 q^{19} +1.00000 q^{20} +2.59911 q^{21} -1.00000 q^{22} -4.26174 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.94482 q^{26} +1.00000 q^{27} +2.59911 q^{28} +3.34571 q^{29} +1.00000 q^{30} -4.90728 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +2.59911 q^{35} +1.00000 q^{36} +9.22420 q^{37} -1.94482 q^{38} +5.94482 q^{39} +1.00000 q^{40} +3.66263 q^{41} +2.59911 q^{42} +4.96247 q^{43} -1.00000 q^{44} +1.00000 q^{45} -4.26174 q^{46} -3.66263 q^{47} +1.00000 q^{48} -0.244651 q^{49} +1.00000 q^{50} -1.00000 q^{51} +5.94482 q^{52} +9.97081 q^{53} +1.00000 q^{54} -1.00000 q^{55} +2.59911 q^{56} -1.94482 q^{57} +3.34571 q^{58} -11.1690 q^{59} +1.00000 q^{60} -9.45120 q^{61} -4.90728 q^{62} +2.59911 q^{63} +1.00000 q^{64} +5.94482 q^{65} -1.00000 q^{66} +10.4224 q^{67} -1.00000 q^{68} -4.26174 q^{69} +2.59911 q^{70} +3.27939 q^{71} +1.00000 q^{72} +4.64555 q^{73} +9.22420 q^{74} +1.00000 q^{75} -1.94482 q^{76} -2.59911 q^{77} +5.94482 q^{78} +2.38324 q^{79} +1.00000 q^{80} +1.00000 q^{81} +3.66263 q^{82} -11.4512 q^{83} +2.59911 q^{84} -1.00000 q^{85} +4.96247 q^{86} +3.34571 q^{87} -1.00000 q^{88} +0.691421 q^{89} +1.00000 q^{90} +15.4512 q^{91} -4.26174 q^{92} -4.90728 q^{93} -3.66263 q^{94} -1.94482 q^{95} +1.00000 q^{96} +2.98235 q^{97} -0.244651 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	2.59911	0.982370	0.491185	−	0.871055i	$-0.336564\pi$
$7$	2.59911	0.982370	0.491185	+	0.871055i	$0.336564\pi$
$8$	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
$13$	5.94482	1.64880	0.824398	−	0.566011i	$-0.191514\pi$
$13$	5.94482	1.64880	0.824398	+	0.566011i	$0.191514\pi$
$14$	2.59911	0.694640
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−1.94482	−0.446171	−0.223086	−	0.974799i	$-0.571613\pi$
$19$	−1.94482	−0.446171	−0.223086	+	0.974799i	$0.571613\pi$
$20$	1.00000	0.223607
$21$	2.59911	0.567171
$22$	−1.00000	−0.213201
$23$	−4.26174	−0.888634	−0.444317	−	0.895870i	$-0.646554\pi$
$23$	−4.26174	−0.888634	−0.444317	+	0.895870i	$0.646554\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	5.94482	1.16587
$27$	1.00000	0.192450
$28$	2.59911	0.491185
$29$	3.34571	0.621283	0.310641	−	0.950527i	$-0.399456\pi$
$29$	3.34571	0.621283	0.310641	+	0.950527i	$0.399456\pi$
$30$	1.00000	0.182574
$31$	−4.90728	−0.881374	−0.440687	−	0.897661i	$-0.645265\pi$
$31$	−4.90728	−0.881374	−0.440687	+	0.897661i	$0.645265\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	2.59911	0.439329
$36$	1.00000	0.166667
$37$	9.22420	1.51645	0.758225	−	0.651993i	$-0.226067\pi$
$37$	9.22420	1.51645	0.758225	+	0.651993i	$0.226067\pi$
$38$	−1.94482	−0.315491
$39$	5.94482	0.951932
$40$	1.00000	0.158114
$41$	3.66263	0.572007	0.286003	−	0.958229i	$-0.407673\pi$
$41$	3.66263	0.572007	0.286003	+	0.958229i	$0.407673\pi$
$42$	2.59911	0.401051
$43$	4.96247	0.756769	0.378385	−	0.925649i	$-0.376480\pi$
$43$	4.96247	0.756769	0.378385	+	0.925649i	$0.376480\pi$
$44$	−1.00000	−0.150756
$45$	1.00000	0.149071
$46$	−4.26174	−0.628359
$47$	−3.66263	−0.534250	−0.267125	−	0.963662i	$-0.586074\pi$
$47$	−3.66263	−0.534250	−0.267125	+	0.963662i	$0.586074\pi$
$48$	1.00000	0.144338
$49$	−0.244651	−0.0349501
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	5.94482	0.824398
$53$	9.97081	1.36960	0.684798	−	0.728733i	$-0.259890\pi$
$53$	9.97081	1.36960	0.684798	+	0.728733i	$0.259890\pi$
$54$	1.00000	0.136083
$55$	−1.00000	−0.134840
$56$	2.59911	0.347320
$57$	−1.94482	−0.257597
$58$	3.34571	0.439313
$59$	−11.1690	−1.45408	−0.727041	−	0.686594i	$-0.759105\pi$
$59$	−11.1690	−1.45408	−0.727041	+	0.686594i	$0.759105\pi$
$60$	1.00000	0.129099
$61$	−9.45120	−1.21010	−0.605051	−	0.796186i	$-0.706847\pi$
$61$	−9.45120	−1.21010	−0.605051	+	0.796186i	$0.706847\pi$
$62$	−4.90728	−0.623225
$63$	2.59911	0.327457
$64$	1.00000	0.125000
$65$	5.94482	0.737364
$66$	−1.00000	−0.123091
$67$	10.4224	1.27330	0.636650	−	0.771153i	$-0.280319\pi$
$67$	10.4224	1.27330	0.636650	+	0.771153i	$0.280319\pi$
$68$	−1.00000	−0.121268
$69$	−4.26174	−0.513053
$70$	2.59911	0.310653
$71$	3.27939	0.389192	0.194596	−	0.980884i	$-0.437660\pi$
$71$	3.27939	0.389192	0.194596	+	0.980884i	$0.437660\pi$
$72$	1.00000	0.117851
$73$	4.64555	0.543720	0.271860	−	0.962337i	$-0.412361\pi$
$73$	4.64555	0.543720	0.271860	+	0.962337i	$0.412361\pi$
$74$	9.22420	1.07229
$75$	1.00000	0.115470
$76$	−1.94482	−0.223086
$77$	−2.59911	−0.296196
$78$	5.94482	0.673118
$79$	2.38324	0.268136	0.134068	−	0.990972i	$-0.457196\pi$
$79$	2.38324	0.268136	0.134068	+	0.990972i	$0.457196\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	3.66263	0.404470
$83$	−11.4512	−1.25693	−0.628466	−	0.777837i	$-0.716317\pi$
$83$	−11.4512	−1.25693	−0.628466	+	0.777837i	$0.716317\pi$
$84$	2.59911	0.283586
$85$	−1.00000	−0.108465
$86$	4.96247	0.535117
$87$	3.34571	0.358698
$88$	−1.00000	−0.106600
$89$	0.691421	0.0732904	0.0366452	−	0.999328i	$-0.488333\pi$
$89$	0.691421	0.0732904	0.0366452	+	0.999328i	$0.488333\pi$
$90$	1.00000	0.105409
$91$	15.4512	1.61973
$92$	−4.26174	−0.444317
$93$	−4.90728	−0.508861
$94$	−3.66263	−0.377772
$95$	−1.94482	−0.199534
$96$	1.00000	0.102062
$97$	2.98235	0.302812	0.151406	−	0.988472i	$-0.451620\pi$
$97$	2.98235	0.302812	0.151406	+	0.988472i	$0.451620\pi$
$98$	−0.244651	−0.0247134
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−3.02879	−0.301376	−0.150688	−	0.988581i	$-0.548149\pi$
$101$	−3.02879	−0.301376	−0.150688	+	0.988581i	$0.548149\pi$
$102$	−1.00000	−0.0990148
$103$	−0.680282	−0.0670302	−0.0335151	−	0.999438i	$-0.510670\pi$
$103$	−0.680282	−0.0670302	−0.0335151	+	0.999438i	$0.510670\pi$
$104$	5.94482	0.582937
$105$	2.59911	0.253647
$106$	9.97081	0.968450
$107$	−15.4048	−1.48923	−0.744617	−	0.667492i	$-0.767368\pi$
$107$	−15.4048	−1.48923	−0.744617	+	0.667492i	$0.767368\pi$
$108$	1.00000	0.0962250
$109$	4.36336	0.417934	0.208967	−	0.977923i	$-0.432990\pi$
$109$	4.36336	0.417934	0.208967	+	0.977923i	$0.432990\pi$
$110$	−1.00000	−0.0953463
$111$	9.22420	0.875523
$112$	2.59911	0.245592
$113$	7.50639	0.706142	0.353071	−	0.935597i	$-0.385137\pi$
$113$	7.50639	0.706142	0.353071	+	0.935597i	$0.385137\pi$
$114$	−1.94482	−0.182149
$115$	−4.26174	−0.397409
$116$	3.34571	0.310641
$117$	5.94482	0.549598
$118$	−11.1690	−1.02819
$119$	−2.59911	−0.238260
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	−9.45120	−0.855672
$123$	3.66263	0.330248
$124$	−4.90728	−0.440687
$125$	1.00000	0.0894427
$126$	2.59911	0.231547
$127$	−8.86084	−0.786273	−0.393136	−	0.919480i	$-0.628610\pi$
$127$	−8.86084	−0.786273	−0.393136	+	0.919480i	$0.628610\pi$
$128$	1.00000	0.0883883
$129$	4.96247	0.436921
$130$	5.94482	0.521395
$131$	−18.7765	−1.64051	−0.820254	−	0.572000i	$-0.806168\pi$
$131$	−18.7765	−1.64051	−0.820254	+	0.572000i	$0.806168\pi$
$132$	−1.00000	−0.0870388
$133$	−5.05478	−0.438305
$134$	10.4224	0.900359
$135$	1.00000	0.0860663
$136$	−1.00000	−0.0857493
$137$	−2.68028	−0.228992	−0.114496	−	0.993424i	$-0.536525\pi$
$137$	−2.68028	−0.228992	−0.114496	+	0.993424i	$0.536525\pi$
$138$	−4.26174	−0.362783
$139$	−14.0962	−1.19562	−0.597811	−	0.801637i	$-0.703963\pi$
$139$	−14.0962	−1.19562	−0.597811	+	0.801637i	$0.703963\pi$
$140$	2.59911	0.219665
$141$	−3.66263	−0.308449
$142$	3.27939	0.275200
$143$	−5.94482	−0.497130
$144$	1.00000	0.0833333
$145$	3.34571	0.277846
$146$	4.64555	0.384468
$147$	−0.244651	−0.0201784
$148$	9.22420	0.758225
$149$	7.22420	0.591830	0.295915	−	0.955214i	$-0.404376\pi$
$149$	7.22420	0.591830	0.295915	+	0.955214i	$0.404376\pi$
$150$	1.00000	0.0816497
$151$	−19.1138	−1.55546	−0.777731	−	0.628597i	$-0.783629\pi$
$151$	−19.1138	−1.55546	−0.777731	+	0.628597i	$0.783629\pi$
$152$	−1.94482	−0.157745
$153$	−1.00000	−0.0808452
$154$	−2.59911	−0.209442
$155$	−4.90728	−0.394162
$156$	5.94482	0.475966
$157$	6.91842	0.552150	0.276075	−	0.961136i	$-0.410966\pi$
$157$	6.91842	0.552150	0.276075	+	0.961136i	$0.410966\pi$
$158$	2.38324	0.189601
$159$	9.97081	0.790737
$160$	1.00000	0.0790569
$161$	−11.0767	−0.872967
$162$	1.00000	0.0785674
$163$	16.8980	1.32355	0.661776	−	0.749702i	$-0.269803\pi$
$163$	16.8980	1.32355	0.661776	+	0.749702i	$0.269803\pi$
$164$	3.66263	0.286003
$165$	−1.00000	−0.0778499
$166$	−11.4512	−0.888786
$167$	4.86084	0.376143	0.188072	−	0.982155i	$-0.439776\pi$
$167$	4.86084	0.376143	0.188072	+	0.982155i	$0.439776\pi$
$168$	2.59911	0.200525
$169$	22.3408	1.71853
$170$	−1.00000	−0.0766965
$171$	−1.94482	−0.148724
$172$	4.96247	0.378385
$173$	−23.5103	−1.78745	−0.893726	−	0.448614i	$-0.851918\pi$
$173$	−23.5103	−1.78745	−0.893726	+	0.448614i	$0.851918\pi$
$174$	3.34571	0.253638
$175$	2.59911	0.196474
$176$	−1.00000	−0.0753778
$177$	−11.1690	−0.839515
$178$	0.691421	0.0518242
$179$	−0.282184	−0.0210914	−0.0105457	−	0.999944i	$-0.503357\pi$
$179$	−0.282184	−0.0210914	−0.0105457	+	0.999944i	$0.503357\pi$
$180$	1.00000	0.0745356
$181$	6.46885	0.480826	0.240413	−	0.970671i	$-0.422717\pi$
$181$	6.46885	0.480826	0.240413	+	0.970671i	$0.422717\pi$
$182$	15.4512	1.14532
$183$	−9.45120	−0.698653
$184$	−4.26174	−0.314179
$185$	9.22420	0.678177
$186$	−4.90728	−0.359819
$187$	1.00000	0.0731272
$188$	−3.66263	−0.267125
$189$	2.59911	0.189057
$190$	−1.94482	−0.141092
$191$	−9.34571	−0.676232	−0.338116	−	0.941104i	$-0.609790\pi$
$191$	−9.34571	−0.676232	−0.338116	+	0.941104i	$0.609790\pi$
$192$	1.00000	0.0721688
$193$	5.41203	0.389567	0.194783	−	0.980846i	$-0.437600\pi$
$193$	5.41203	0.389567	0.194783	+	0.980846i	$0.437600\pi$
$194$	2.98235	0.214120
$195$	5.94482	0.425717
$196$	−0.244651	−0.0174750
$197$	6.53278	0.465441	0.232721	−	0.972544i	$-0.425237\pi$
$197$	6.53278	0.465441	0.232721	+	0.972544i	$0.425237\pi$
$198$	−1.00000	−0.0710669
$199$	−12.5551	−0.890005	−0.445002	−	0.895529i	$-0.646797\pi$
$199$	−12.5551	−0.890005	−0.445002	+	0.895529i	$0.646797\pi$
$200$	1.00000	0.0707107
$201$	10.4224	0.735140
$202$	−3.02879	−0.213105
$203$	8.69585	0.610329
$204$	−1.00000	−0.0700140
$205$	3.66263	0.255809
$206$	−0.680282	−0.0473975
$207$	−4.26174	−0.296211
$208$	5.94482	0.412199
$209$	1.94482	0.134526
$210$	2.59911	0.179355
$211$	17.3297	1.19303	0.596513	−	0.802604i	$-0.296553\pi$
$211$	17.3297	1.19303	0.596513	+	0.802604i	$0.296553\pi$
$212$	9.97081	0.684798
$213$	3.27939	0.224700
$214$	−15.4048	−1.05305
$215$	4.96247	0.338437
$216$	1.00000	0.0680414
$217$	−12.7545	−0.865835
$218$	4.36336	0.295524
$219$	4.64555	0.313917
$220$	−1.00000	−0.0674200
$221$	−5.94482	−0.399892
$222$	9.22420	0.619088
$223$	8.47703	0.567664	0.283832	−	0.958874i	$-0.408394\pi$
$223$	8.47703	0.567664	0.283832	+	0.958874i	$0.408394\pi$
$224$	2.59911	0.173660
$225$	1.00000	0.0666667
$226$	7.50639	0.499317
$227$	29.4214	1.95277	0.976385	−	0.216038i	$-0.0693134\pi$
$227$	29.4214	1.95277	0.976385	+	0.216038i	$0.0693134\pi$
$228$	−1.94482	−0.128799
$229$	−22.8515	−1.51007	−0.755036	−	0.655683i	$-0.772381\pi$
$229$	−22.8515	−1.51007	−0.755036	+	0.655683i	$0.772381\pi$
$230$	−4.26174	−0.281011
$231$	−2.59911	−0.171009
$232$	3.34571	0.219657
$233$	23.9858	1.57136	0.785682	−	0.618631i	$-0.212312\pi$
$233$	23.9858	1.57136	0.785682	+	0.618631i	$0.212312\pi$
$234$	5.94482	0.388625
$235$	−3.66263	−0.238924
$236$	−11.1690	−0.727041
$237$	2.38324	0.154808
$238$	−2.59911	−0.168475
$239$	−15.5946	−1.00873	−0.504366	−	0.863490i	$-0.668274\pi$
$239$	−15.5946	−1.00873	−0.504366	+	0.863490i	$0.668274\pi$
$240$	1.00000	0.0645497
$241$	−1.49525	−0.0963174	−0.0481587	−	0.998840i	$-0.515335\pi$
$241$	−1.49525	−0.0963174	−0.0481587	+	0.998840i	$0.515335\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−9.45120	−0.605051
$245$	−0.244651	−0.0156302
$246$	3.66263	0.233521
$247$	−11.5616	−0.735645
$248$	−4.90728	−0.311613
$249$	−11.4512	−0.725691
$250$	1.00000	0.0632456
$251$	24.5849	1.55179	0.775893	−	0.630864i	$-0.217300\pi$
$251$	24.5849	1.55179	0.775893	+	0.630864i	$0.217300\pi$
$252$	2.59911	0.163728
$253$	4.26174	0.267933
$254$	−8.86084	−0.555979
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	6.18987	0.386113	0.193057	−	0.981188i	$-0.438160\pi$
$257$	6.18987	0.386113	0.193057	+	0.981188i	$0.438160\pi$
$258$	4.96247	0.308950
$259$	23.9747	1.48971
$260$	5.94482	0.368682
$261$	3.34571	0.207094
$262$	−18.7765	−1.16001
$263$	3.37170	0.207908	0.103954	−	0.994582i	$-0.466851\pi$
$263$	3.37170	0.207908	0.103954	+	0.994582i	$0.466851\pi$
$264$	−1.00000	−0.0615457
$265$	9.97081	0.612502
$266$	−5.05478	−0.309929
$267$	0.691421	0.0423143
$268$	10.4224	0.636650
$269$	−2.23631	−0.136350	−0.0681751	−	0.997673i	$-0.521718\pi$
$269$	−2.23631	−0.136350	−0.0681751	+	0.997673i	$0.521718\pi$
$270$	1.00000	0.0608581
$271$	−7.27064	−0.441660	−0.220830	−	0.975312i	$-0.570877\pi$
$271$	−7.27064	−0.441660	−0.220830	+	0.975312i	$0.570877\pi$
$272$	−1.00000	−0.0606339
$273$	15.4512	0.935149
$274$	−2.68028	−0.161922
$275$	−1.00000	−0.0603023
$276$	−4.26174	−0.256526
$277$	24.9024	1.49624	0.748120	−	0.663563i	$-0.230957\pi$
$277$	24.9024	1.49624	0.748120	+	0.663563i	$0.230957\pi$
$278$	−14.0962	−0.845433
$279$	−4.90728	−0.293791
$280$	2.59911	0.155326
$281$	−21.5894	−1.28792	−0.643958	−	0.765061i	$-0.722709\pi$
$281$	−21.5894	−1.28792	−0.643958	+	0.765061i	$0.722709\pi$
$282$	−3.66263	−0.218107
$283$	27.4259	1.63030	0.815150	−	0.579250i	$-0.196655\pi$
$283$	27.4259	1.63030	0.815150	+	0.579250i	$0.196655\pi$
$284$	3.27939	0.194596
$285$	−1.94482	−0.115201
$286$	−5.94482	−0.351524
$287$	9.51957	0.561922
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	3.34571	0.196467
$291$	2.98235	0.174828
$292$	4.64555	0.271860
$293$	−23.8012	−1.39048	−0.695240	−	0.718778i	$-0.744702\pi$
$293$	−23.8012	−1.39048	−0.695240	+	0.718778i	$0.744702\pi$
$294$	−0.244651	−0.0142683
$295$	−11.1690	−0.650285
$296$	9.22420	0.536146
$297$	−1.00000	−0.0580259
$298$	7.22420	0.418487
$299$	−25.3352	−1.46517
$300$	1.00000	0.0577350
$301$	12.8980	0.743427
$302$	−19.1138	−1.09988
$303$	−3.02879	−0.173999
$304$	−1.94482	−0.111543
$305$	−9.45120	−0.541174
$306$	−1.00000	−0.0571662
$307$	−6.69753	−0.382248	−0.191124	−	0.981566i	$-0.561213\pi$
$307$	−6.69753	−0.382248	−0.191124	+	0.981566i	$0.561213\pi$
$308$	−2.59911	−0.148098
$309$	−0.680282	−0.0386999
$310$	−4.90728	−0.278715
$311$	−9.20432	−0.521929	−0.260965	−	0.965348i	$-0.584041\pi$
$311$	−9.20432	−0.521929	−0.260965	+	0.965348i	$0.584041\pi$
$312$	5.94482	0.336559
$313$	−32.5539	−1.84006	−0.920028	−	0.391854i	$-0.871834\pi$
$313$	−32.5539	−1.84006	−0.920028	+	0.391854i	$0.871834\pi$
$314$	6.91842	0.390429
$315$	2.59911	0.146443
$316$	2.38324	0.134068
$317$	6.95636	0.390708	0.195354	−	0.980733i	$-0.437414\pi$
$317$	6.95636	0.390708	0.195354	+	0.980733i	$0.437414\pi$
$318$	9.97081	0.559135
$319$	−3.34571	−0.187324
$320$	1.00000	0.0559017
$321$	−15.4048	−0.859810
$322$	−11.0767	−0.617281
$323$	1.94482	0.108212
$324$	1.00000	0.0555556
$325$	5.94482	0.329759
$326$	16.8980	0.935892
$327$	4.36336	0.241294
$328$	3.66263	0.202235
$329$	−9.51957	−0.524831
$330$	−1.00000	−0.0550482
$331$	−4.95636	−0.272426	−0.136213	−	0.990680i	$-0.543493\pi$
$331$	−4.95636	−0.272426	−0.136213	+	0.990680i	$0.543493\pi$
$332$	−11.4512	−0.628466
$333$	9.22420	0.505483
$334$	4.86084	0.265973
$335$	10.4224	0.569437
$336$	2.59911	0.141793
$337$	−2.67972	−0.145974	−0.0729868	−	0.997333i	$-0.523253\pi$
$337$	−2.67972	−0.145974	−0.0729868	+	0.997333i	$0.523253\pi$
$338$	22.3408	1.21518
$339$	7.50639	0.407691
$340$	−1.00000	−0.0542326
$341$	4.90728	0.265744
$342$	−1.94482	−0.105164
$343$	−18.8296	−1.01670
$344$	4.96247	0.267558
$345$	−4.26174	−0.229444
$346$	−23.5103	−1.26392
$347$	27.8312	1.49406	0.747030	−	0.664791i	$-0.231479\pi$
$347$	27.8312	1.49406	0.747030	+	0.664791i	$0.231479\pi$
$348$	3.34571	0.179349
$349$	−17.0011	−0.910047	−0.455023	−	0.890480i	$-0.650369\pi$
$349$	−17.0011	−0.910047	−0.455023	+	0.890480i	$0.650369\pi$
$350$	2.59911	0.138928
$351$	5.94482	0.317311
$352$	−1.00000	−0.0533002
$353$	−23.9528	−1.27488	−0.637438	−	0.770501i	$-0.720006\pi$
$353$	−23.9528	−1.27488	−0.637438	+	0.770501i	$0.720006\pi$
$354$	−11.1690	−0.593627
$355$	3.27939	0.174052
$356$	0.691421	0.0366452
$357$	−2.59911	−0.137559
$358$	−0.282184	−0.0149139
$359$	28.8273	1.52145	0.760724	−	0.649075i	$-0.224844\pi$
$359$	28.8273	1.52145	0.760724	+	0.649075i	$0.224844\pi$
$360$	1.00000	0.0527046
$361$	−15.2177	−0.800931
$362$	6.46885	0.339995
$363$	1.00000	0.0524864
$364$	15.4512	0.809863
$365$	4.64555	0.243159
$366$	−9.45120	−0.494022
$367$	1.43563	0.0749393	0.0374697	−	0.999298i	$-0.488070\pi$
$367$	1.43563	0.0749393	0.0374697	+	0.999298i	$0.488070\pi$
$368$	−4.26174	−0.222158
$369$	3.66263	0.190669
$370$	9.22420	0.479543
$371$	25.9152	1.34545
$372$	−4.90728	−0.254431
$373$	4.64702	0.240614	0.120307	−	0.992737i	$-0.461612\pi$
$373$	4.64702	0.240614	0.120307	+	0.992737i	$0.461612\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	−3.66263	−0.188886
$377$	19.8896	1.02437
$378$	2.59911	0.133684
$379$	−3.39922	−0.174606	−0.0873031	−	0.996182i	$-0.527825\pi$
$379$	−3.39922	−0.174606	−0.0873031	+	0.996182i	$0.527825\pi$
$380$	−1.94482	−0.0997669
$381$	−8.86084	−0.453955
$382$	−9.34571	−0.478168
$383$	6.05905	0.309603	0.154802	−	0.987946i	$-0.450526\pi$
$383$	6.05905	0.309603	0.154802	+	0.987946i	$0.450526\pi$
$384$	1.00000	0.0510310
$385$	−2.59911	−0.132463
$386$	5.41203	0.275465
$387$	4.96247	0.252256
$388$	2.98235	0.151406
$389$	22.5942	1.14557	0.572786	−	0.819705i	$-0.305862\pi$
$389$	22.5942	1.14557	0.572786	+	0.819705i	$0.305862\pi$
$390$	5.94482	0.301027
$391$	4.26174	0.215525
$392$	−0.244651	−0.0123567
$393$	−18.7765	−0.947147
$394$	6.53278	0.329117
$395$	2.38324	0.119914
$396$	−1.00000	−0.0502519
$397$	19.4947	0.978410	0.489205	−	0.872169i	$-0.337287\pi$
$397$	19.4947	0.978410	0.489205	+	0.872169i	$0.337287\pi$
$398$	−12.5551	−0.629328
$399$	−5.05478	−0.253056
$400$	1.00000	0.0500000
$401$	−15.1976	−0.758934	−0.379467	−	0.925205i	$-0.623893\pi$
$401$	−15.1976	−0.758934	−0.379467	+	0.925205i	$0.623893\pi$
$402$	10.4224	0.519823
$403$	−29.1729	−1.45321
$404$	−3.02879	−0.150688
$405$	1.00000	0.0496904
$406$	8.69585	0.431568
$407$	−9.22420	−0.457227
$408$	−1.00000	−0.0495074
$409$	18.4131	0.910469	0.455235	−	0.890371i	$-0.349555\pi$
$409$	18.4131	0.910469	0.455235	+	0.890371i	$0.349555\pi$
$410$	3.66263	0.180884
$411$	−2.68028	−0.132209
$412$	−0.680282	−0.0335151
$413$	−29.0295	−1.42845
$414$	−4.26174	−0.209453
$415$	−11.4512	−0.562117
$416$	5.94482	0.291469
$417$	−14.0962	−0.690293
$418$	1.94482	0.0951241
$419$	−11.1763	−0.545997	−0.272999	−	0.962014i	$-0.588015\pi$
$419$	−11.1763	−0.545997	−0.272999	+	0.962014i	$0.588015\pi$
$420$	2.59911	0.126823
$421$	−12.4815	−0.608310	−0.304155	−	0.952623i	$-0.598374\pi$
$421$	−12.4815	−0.608310	−0.304155	+	0.952623i	$0.598374\pi$
$422$	17.3297	0.843596
$423$	−3.66263	−0.178083
$424$	9.97081	0.484225
$425$	−1.00000	−0.0485071
$426$	3.27939	0.158887
$427$	−24.5647	−1.18877
$428$	−15.4048	−0.744617
$429$	−5.94482	−0.287018
$430$	4.96247	0.239311
$431$	−19.6247	−0.945288	−0.472644	−	0.881253i	$-0.656700\pi$
$431$	−19.6247	−0.945288	−0.472644	+	0.881253i	$0.656700\pi$
$432$	1.00000	0.0481125
$433$	−19.0878	−0.917303	−0.458652	−	0.888616i	$-0.651667\pi$
$433$	−19.0878	−0.917303	−0.458652	+	0.888616i	$0.651667\pi$
$434$	−12.7545	−0.612238
$435$	3.34571	0.160415
$436$	4.36336	0.208967
$437$	8.28829	0.396483
$438$	4.64555	0.221973
$439$	10.0882	0.481486	0.240743	−	0.970589i	$-0.422609\pi$
$439$	10.0882	0.481486	0.240743	+	0.970589i	$0.422609\pi$
$440$	−1.00000	−0.0476731
$441$	−0.244651	−0.0116500
$442$	−5.94482	−0.282766
$443$	4.29480	0.204052	0.102026	−	0.994782i	$-0.467468\pi$
$443$	4.29480	0.204052	0.102026	+	0.994782i	$0.467468\pi$
$444$	9.22420	0.437761
$445$	0.691421	0.0327765
$446$	8.47703	0.401399
$447$	7.22420	0.341693
$448$	2.59911	0.122796
$449$	−34.3033	−1.61887	−0.809436	−	0.587208i	$-0.800227\pi$
$449$	−34.3033	−1.61887	−0.809436	+	0.587208i	$0.800227\pi$
$450$	1.00000	0.0471405
$451$	−3.66263	−0.172467
$452$	7.50639	0.353071
$453$	−19.1138	−0.898046
$454$	29.4214	1.38082
$455$	15.4512	0.724364
$456$	−1.94482	−0.0910743
$457$	−4.72448	−0.221002	−0.110501	−	0.993876i	$-0.535246\pi$
$457$	−4.72448	−0.221002	−0.110501	+	0.993876i	$0.535246\pi$
$458$	−22.8515	−1.06778
$459$	−1.00000	−0.0466760
$460$	−4.26174	−0.198705
$461$	27.7632	1.29306	0.646532	−	0.762887i	$-0.276219\pi$
$461$	27.7632	1.29306	0.646532	+	0.762887i	$0.276219\pi$
$462$	−2.59911	−0.120921
$463$	−19.6136	−0.911519	−0.455760	−	0.890103i	$-0.650632\pi$
$463$	−19.6136	−0.911519	−0.455760	+	0.890103i	$0.650632\pi$
$464$	3.34571	0.155321
$465$	−4.90728	−0.227570
$466$	23.9858	1.11112
$467$	−29.2857	−1.35518	−0.677589	−	0.735441i	$-0.736975\pi$
$467$	−29.2857	−1.35518	−0.677589	+	0.735441i	$0.736975\pi$
$468$	5.94482	0.274799
$469$	27.0890	1.25085
$470$	−3.66263	−0.168945
$471$	6.91842	0.318784
$472$	−11.1690	−0.514096
$473$	−4.96247	−0.228174
$474$	2.38324	0.109466
$475$	−1.94482	−0.0892343
$476$	−2.59911	−0.119130
$477$	9.97081	0.456532
$478$	−15.5946	−0.713282
$479$	7.35502	0.336059	0.168030	−	0.985782i	$-0.446260\pi$
$479$	7.35502	0.336059	0.168030	+	0.985782i	$0.446260\pi$
$480$	1.00000	0.0456435
$481$	54.8362	2.50032
$482$	−1.49525	−0.0681067
$483$	−11.0767	−0.504007
$484$	1.00000	0.0454545
$485$	2.98235	0.135422
$486$	1.00000	0.0453609
$487$	−27.6113	−1.25119	−0.625594	−	0.780149i	$-0.715143\pi$
$487$	−27.6113	−1.25119	−0.625594	+	0.780149i	$0.715143\pi$
$488$	−9.45120	−0.427836
$489$	16.8980	0.764153
$490$	−0.244651	−0.0110522
$491$	−6.43025	−0.290193	−0.145097	−	0.989418i	$-0.546349\pi$
$491$	−6.43025	−0.290193	−0.145097	+	0.989418i	$0.546349\pi$
$492$	3.66263	0.165124
$493$	−3.34571	−0.150683
$494$	−11.5616	−0.520180
$495$	−1.00000	−0.0449467
$496$	−4.90728	−0.220343
$497$	8.52347	0.382330
$498$	−11.4512	−0.513141
$499$	−22.4298	−1.00410	−0.502048	−	0.864840i	$-0.667420\pi$
$499$	−22.4298	−1.00410	−0.502048	+	0.864840i	$0.667420\pi$
$500$	1.00000	0.0447214
$501$	4.86084	0.217166
$502$	24.5849	1.09728
$503$	−28.8434	−1.28606	−0.643031	−	0.765840i	$-0.722323\pi$
$503$	−28.8434	−1.28606	−0.643031	+	0.765840i	$0.722323\pi$
$504$	2.59911	0.115773
$505$	−3.02879	−0.134779
$506$	4.26174	0.189457
$507$	22.3408	0.992191
$508$	−8.86084	−0.393136
$509$	−16.0874	−0.713063	−0.356532	−	0.934283i	$-0.616041\pi$
$509$	−16.0874	−0.713063	−0.356532	+	0.934283i	$0.616041\pi$
$510$	−1.00000	−0.0442807
$511$	12.0743	0.534134
$512$	1.00000	0.0441942
$513$	−1.94482	−0.0858657
$514$	6.18987	0.273023
$515$	−0.680282	−0.0299768
$516$	4.96247	0.218460
$517$	3.66263	0.161082
$518$	23.9747	1.05339
$519$	−23.5103	−1.03199
$520$	5.94482	0.260697
$521$	−34.6953	−1.52003	−0.760014	−	0.649907i	$-0.774808\pi$
$521$	−34.6953	−1.52003	−0.760014	+	0.649907i	$0.774808\pi$
$522$	3.34571	0.146438
$523$	17.5788	0.768668	0.384334	−	0.923194i	$-0.374431\pi$
$523$	17.5788	0.768668	0.384334	+	0.923194i	$0.374431\pi$
$524$	−18.7765	−0.820254
$525$	2.59911	0.113434
$526$	3.37170	0.147013
$527$	4.90728	0.213765
$528$	−1.00000	−0.0435194
$529$	−4.83760	−0.210330
$530$	9.97081	0.433104
$531$	−11.1690	−0.484694
$532$	−5.05478	−0.219153
$533$	21.7737	0.943122
$534$	0.691421	0.0299207
$535$	−15.4048	−0.666006
$536$	10.4224	0.450180
$537$	−0.282184	−0.0121772
$538$	−2.23631	−0.0964141
$539$	0.244651	0.0105378
$540$	1.00000	0.0430331
$541$	−31.2059	−1.34165	−0.670824	−	0.741616i	$-0.734060\pi$
$541$	−31.2059	−1.34165	−0.670824	+	0.741616i	$0.734060\pi$
$542$	−7.27064	−0.312301
$543$	6.46885	0.277605
$544$	−1.00000	−0.0428746
$545$	4.36336	0.186906
$546$	15.4512	0.661250
$547$	16.1768	0.691670	0.345835	−	0.938295i	$-0.387596\pi$
$547$	16.1768	0.691670	0.345835	+	0.938295i	$0.387596\pi$
$548$	−2.68028	−0.114496
$549$	−9.45120	−0.403368
$550$	−1.00000	−0.0426401
$551$	−6.50679	−0.277199
$552$	−4.26174	−0.181392
$553$	6.19430	0.263409
$554$	24.9024	1.05800
$555$	9.22420	0.391546
$556$	−14.0962	−0.597811
$557$	19.0083	0.805409	0.402705	−	0.915330i	$-0.368070\pi$
$557$	19.0083	0.805409	0.402705	+	0.915330i	$0.368070\pi$
$558$	−4.90728	−0.207742
$559$	29.5009	1.24776
$560$	2.59911	0.109832
$561$	1.00000	0.0422200
$562$	−21.5894	−0.910694
$563$	13.8476	0.583608	0.291804	−	0.956478i	$-0.405745\pi$
$563$	13.8476	0.583608	0.291804	+	0.956478i	$0.405745\pi$
$564$	−3.66263	−0.154225
$565$	7.50639	0.315796
$566$	27.4259	1.15280
$567$	2.59911	0.109152
$568$	3.27939	0.137600
$569$	−1.22273	−0.0512594	−0.0256297	−	0.999672i	$-0.508159\pi$
$569$	−1.22273	−0.0512594	−0.0256297	+	0.999672i	$0.508159\pi$
$570$	−1.94482	−0.0814594
$571$	36.9600	1.54673	0.773364	−	0.633963i	$-0.218573\pi$
$571$	36.9600	1.54673	0.773364	+	0.633963i	$0.218573\pi$
$572$	−5.94482	−0.248565
$573$	−9.34571	−0.390423
$574$	9.51957	0.397339
$575$	−4.26174	−0.177727
$576$	1.00000	0.0416667
$577$	25.1045	1.04512	0.522558	−	0.852604i	$-0.324978\pi$
$577$	25.1045	1.04512	0.522558	+	0.852604i	$0.324978\pi$
$578$	1.00000	0.0415945
$579$	5.41203	0.224916
$580$	3.34571	0.138923
$581$	−29.7629	−1.23477
$582$	2.98235	0.123622
$583$	−9.97081	−0.412949
$584$	4.64555	0.192234
$585$	5.94482	0.245788
$586$	−23.8012	−0.983218
$587$	−15.5283	−0.640922	−0.320461	−	0.947262i	$-0.603838\pi$
$587$	−15.5283	−0.640922	−0.320461	+	0.947262i	$0.603838\pi$
$588$	−0.244651	−0.0100892
$589$	9.54376	0.393244
$590$	−11.1690	−0.459821
$591$	6.53278	0.268723
$592$	9.22420	0.379112
$593$	−25.9416	−1.06529	−0.532647	−	0.846337i	$-0.678803\pi$
$593$	−25.9416	−1.06529	−0.532647	+	0.846337i	$0.678803\pi$
$594$	−1.00000	−0.0410305
$595$	−2.59911	−0.106553
$596$	7.22420	0.295915
$597$	−12.5551	−0.513844
$598$	−25.3352	−1.03604
$599$	−5.59951	−0.228790	−0.114395	−	0.993435i	$-0.536493\pi$
$599$	−5.59951	−0.228790	−0.114395	+	0.993435i	$0.536493\pi$
$600$	1.00000	0.0408248
$601$	31.8864	1.30067	0.650337	−	0.759646i	$-0.274628\pi$
$601$	31.8864	1.30067	0.650337	+	0.759646i	$0.274628\pi$
$602$	12.8980	0.525682
$603$	10.4224	0.424434
$604$	−19.1138	−0.777731
$605$	1.00000	0.0406558
$606$	−3.02879	−0.123036
$607$	−18.5460	−0.752757	−0.376379	−	0.926466i	$-0.622831\pi$
$607$	−18.5460	−0.752757	−0.376379	+	0.926466i	$0.622831\pi$
$608$	−1.94482	−0.0788727
$609$	8.69585	0.352374
$610$	−9.45120	−0.382668
$611$	−21.7737	−0.880868
$612$	−1.00000	−0.0404226
$613$	33.8091	1.36554	0.682769	−	0.730634i	$-0.260776\pi$
$613$	33.8091	1.36554	0.682769	+	0.730634i	$0.260776\pi$
$614$	−6.69753	−0.270290
$615$	3.66263	0.147692
$616$	−2.59911	−0.104721
$617$	13.0657	0.526006	0.263003	−	0.964795i	$-0.415287\pi$
$617$	13.0657	0.526006	0.263003	+	0.964795i	$0.415287\pi$
$618$	−0.680282	−0.0273650
$619$	45.2658	1.81938	0.909692	−	0.415283i	$-0.136317\pi$
$619$	45.2658	1.81938	0.909692	+	0.415283i	$0.136317\pi$
$620$	−4.90728	−0.197081
$621$	−4.26174	−0.171018
$622$	−9.20432	−0.369060
$623$	1.79708	0.0719983
$624$	5.94482	0.237983
$625$	1.00000	0.0400000
$626$	−32.5539	−1.30112
$627$	1.94482	0.0776685
$628$	6.91842	0.276075
$629$	−9.22420	−0.367793
$630$	2.59911	0.103551
$631$	17.2900	0.688303	0.344151	−	0.938914i	$-0.388167\pi$
$631$	17.2900	0.688303	0.344151	+	0.938914i	$0.388167\pi$
$632$	2.38324	0.0948004
$633$	17.3297	0.688794
$634$	6.95636	0.276272
$635$	−8.86084	−0.351632
$636$	9.97081	0.395368
$637$	−1.45440	−0.0576255
$638$	−3.34571	−0.132458
$639$	3.27939	0.129731
$640$	1.00000	0.0395285
$641$	−34.5210	−1.36350	−0.681749	−	0.731587i	$-0.738780\pi$
$641$	−34.5210	−1.36350	−0.681749	+	0.731587i	$0.738780\pi$
$642$	−15.4048	−0.607978
$643$	−12.2816	−0.484340	−0.242170	−	0.970234i	$-0.577859\pi$
$643$	−12.2816	−0.484340	−0.242170	+	0.970234i	$0.577859\pi$
$644$	−11.0767	−0.436483
$645$	4.96247	0.195397
$646$	1.94482	0.0765178
$647$	16.9128	0.664912	0.332456	−	0.943119i	$-0.392123\pi$
$647$	16.9128	0.664912	0.332456	+	0.943119i	$0.392123\pi$
$648$	1.00000	0.0392837
$649$	11.1690	0.438422
$650$	5.94482	0.233175
$651$	−12.7545	−0.499890
$652$	16.8980	0.661776
$653$	−24.3169	−0.951595	−0.475797	−	0.879555i	$-0.657840\pi$
$653$	−24.3169	−0.951595	−0.475797	+	0.879555i	$0.657840\pi$
$654$	4.36336	0.170621
$655$	−18.7765	−0.733657
$656$	3.66263	0.143002
$657$	4.64555	0.181240
$658$	−9.51957	−0.371111
$659$	40.2128	1.56647	0.783234	−	0.621726i	$-0.213568\pi$
$659$	40.2128	1.56647	0.783234	+	0.621726i	$0.213568\pi$
$660$	−1.00000	−0.0389249
$661$	−46.7675	−1.81905	−0.909523	−	0.415654i	$-0.863553\pi$
$661$	−46.7675	−1.81905	−0.909523	+	0.415654i	$0.863553\pi$
$662$	−4.95636	−0.192634
$663$	−5.94482	−0.230878
$664$	−11.4512	−0.444393
$665$	−5.05478	−0.196016
$666$	9.22420	0.357431
$667$	−14.2585	−0.552093
$668$	4.86084	0.188072
$669$	8.47703	0.327741
$670$	10.4224	0.402653
$671$	9.45120	0.364860
$672$	2.59911	0.100263
$673$	−9.61823	−0.370756	−0.185378	−	0.982667i	$-0.559351\pi$
$673$	−9.61823	−0.370756	−0.185378	+	0.982667i	$0.559351\pi$
$674$	−2.67972	−0.103219
$675$	1.00000	0.0384900
$676$	22.3408	0.859263
$677$	31.9487	1.22789	0.613944	−	0.789350i	$-0.289582\pi$
$677$	31.9487	1.22789	0.613944	+	0.789350i	$0.289582\pi$
$678$	7.50639	0.288281
$679$	7.75144	0.297473
$680$	−1.00000	−0.0383482
$681$	29.4214	1.12743
$682$	4.90728	0.187910
$683$	37.2063	1.42366	0.711829	−	0.702353i	$-0.247867\pi$
$683$	37.2063	1.42366	0.711829	+	0.702353i	$0.247867\pi$
$684$	−1.94482	−0.0743619
$685$	−2.68028	−0.102408
$686$	−18.8296	−0.718918
$687$	−22.8515	−0.871840
$688$	4.96247	0.189192
$689$	59.2746	2.25818
$690$	−4.26174	−0.162242
$691$	−38.5557	−1.46673	−0.733365	−	0.679836i	$-0.762051\pi$
$691$	−38.5557	−1.46673	−0.733365	+	0.679836i	$0.762051\pi$
$692$	−23.5103	−0.893726
$693$	−2.59911	−0.0987319
$694$	27.8312	1.05646
$695$	−14.0962	−0.534699
$696$	3.34571	0.126819
$697$	−3.66263	−0.138732
$698$	−17.0011	−0.643500
$699$	23.9858	0.907227
$700$	2.59911	0.0982370
$701$	−44.4380	−1.67840	−0.839200	−	0.543823i	$-0.816976\pi$
$701$	−44.4380	−1.67840	−0.839200	+	0.543823i	$0.816976\pi$
$702$	5.94482	0.224373
$703$	−17.9394	−0.676596
$704$	−1.00000	−0.0376889
$705$	−3.66263	−0.137943
$706$	−23.9528	−0.901474
$707$	−7.87214	−0.296062
$708$	−11.1690	−0.419757
$709$	−33.6704	−1.26452	−0.632259	−	0.774757i	$-0.717872\pi$
$709$	−33.6704	−1.26452	−0.632259	+	0.774757i	$0.717872\pi$
$710$	3.27939	0.123073
$711$	2.38324	0.0893786
$712$	0.691421	0.0259121
$713$	20.9135	0.783218
$714$	−2.59911	−0.0972691
$715$	−5.94482	−0.222324
$716$	−0.282184	−0.0105457
$717$	−15.5946	−0.582392
$718$	28.8273	1.07583
$719$	−11.8835	−0.443181	−0.221590	−	0.975140i	$-0.571125\pi$
$719$	−11.8835	−0.443181	−0.221590	+	0.975140i	$0.571125\pi$
$720$	1.00000	0.0372678
$721$	−1.76812	−0.0658484
$722$	−15.2177	−0.566344
$723$	−1.49525	−0.0556089
$724$	6.46885	0.240413
$725$	3.34571	0.124257
$726$	1.00000	0.0371135
$727$	31.2769	1.16000	0.579998	−	0.814618i	$-0.303053\pi$
$727$	31.2769	1.16000	0.579998	+	0.814618i	$0.303053\pi$
$728$	15.4512	0.572660
$729$	1.00000	0.0370370
$730$	4.64555	0.171939
$731$	−4.96247	−0.183543
$732$	−9.45120	−0.349327
$733$	−25.5617	−0.944144	−0.472072	−	0.881560i	$-0.656494\pi$
$733$	−25.5617	−0.944144	−0.472072	+	0.881560i	$0.656494\pi$
$734$	1.43563	0.0529901
$735$	−0.244651	−0.00902408
$736$	−4.26174	−0.157090
$737$	−10.4224	−0.383915
$738$	3.66263	0.134823
$739$	9.74157	0.358349	0.179175	−	0.983817i	$-0.442657\pi$
$739$	9.74157	0.358349	0.179175	+	0.983817i	$0.442657\pi$
$740$	9.22420	0.339088
$741$	−11.5616	−0.424725
$742$	25.9152	0.951376
$743$	−54.1942	−1.98819	−0.994096	−	0.108508i	$-0.965393\pi$
$743$	−54.1942	−1.98819	−0.994096	+	0.108508i	$0.965393\pi$
$744$	−4.90728	−0.179910
$745$	7.22420	0.264674
$746$	4.64702	0.170139
$747$	−11.4512	−0.418978
$748$	1.00000	0.0365636
$749$	−40.0386	−1.46298
$750$	1.00000	0.0365148
$751$	36.7891	1.34245	0.671226	−	0.741252i	$-0.265768\pi$
$751$	36.7891	1.34245	0.671226	+	0.741252i	$0.265768\pi$
$752$	−3.66263	−0.133562
$753$	24.5849	0.895924
$754$	19.8896	0.724338
$755$	−19.1138	−0.695624
$756$	2.59911	0.0945286
$757$	13.1027	0.476226	0.238113	−	0.971238i	$-0.423471\pi$
$757$	13.1027	0.476226	0.238113	+	0.971238i	$0.423471\pi$
$758$	−3.39922	−0.123465
$759$	4.26174	0.154691
$760$	−1.94482	−0.0705459
$761$	25.4500	0.922563	0.461282	−	0.887254i	$-0.347390\pi$
$761$	25.4500	0.922563	0.461282	+	0.887254i	$0.347390\pi$
$762$	−8.86084	−0.320994
$763$	11.3408	0.410566
$764$	−9.34571	−0.338116
$765$	−1.00000	−0.0361551
$766$	6.05905	0.218922
$767$	−66.3978	−2.39748
$768$	1.00000	0.0360844
$769$	−19.2725	−0.694983	−0.347492	−	0.937683i	$-0.612966\pi$
$769$	−19.2725	−0.694983	−0.347492	+	0.937683i	$0.612966\pi$
$770$	−2.59911	−0.0936653
$771$	6.18987	0.222923
$772$	5.41203	0.194783
$773$	12.5188	0.450270	0.225135	−	0.974328i	$-0.427718\pi$
$773$	12.5188	0.450270	0.225135	+	0.974328i	$0.427718\pi$
$774$	4.96247	0.178372
$775$	−4.90728	−0.176275
$776$	2.98235	0.107060
$777$	23.9747	0.860087
$778$	22.5942	0.810042
$779$	−7.12314	−0.255213
$780$	5.94482	0.212859
$781$	−3.27939	−0.117346
$782$	4.26174	0.152399
$783$	3.34571	0.119566
$784$	−0.244651	−0.00873752
$785$	6.91842	0.246929
$786$	−18.7765	−0.669734
$787$	2.97859	0.106175	0.0530876	−	0.998590i	$-0.483094\pi$
$787$	2.97859	0.106175	0.0530876	+	0.998590i	$0.483094\pi$
$788$	6.53278	0.232721
$789$	3.37170	0.120036
$790$	2.38324	0.0847920
$791$	19.5099	0.693692
$792$	−1.00000	−0.0355335
$793$	−56.1857	−1.99521
$794$	19.4947	0.691840
$795$	9.97081	0.353628
$796$	−12.5551	−0.445002
$797$	−17.0784	−0.604947	−0.302474	−	0.953158i	$-0.597812\pi$
$797$	−17.0784	−0.604947	−0.302474	+	0.953158i	$0.597812\pi$
$798$	−5.05478	−0.178937
$799$	3.66263	0.129575
$800$	1.00000	0.0353553
$801$	0.691421	0.0244301
$802$	−15.1976	−0.536648
$803$	−4.64555	−0.163938
$804$	10.4224	0.367570
$805$	−11.0767	−0.390403
$806$	−29.1729	−1.02757
$807$	−2.23631	−0.0787218
$808$	−3.02879	−0.106552
$809$	−11.1205	−0.390977	−0.195489	−	0.980706i	$-0.562629\pi$
$809$	−11.1205	−0.390977	−0.195489	+	0.980706i	$0.562629\pi$
$810$	1.00000	0.0351364
$811$	−49.2404	−1.72907	−0.864533	−	0.502576i	$-0.832386\pi$
$811$	−49.2404	−1.72907	−0.864533	+	0.502576i	$0.832386\pi$
$812$	8.69585	0.305165
$813$	−7.27064	−0.254993
$814$	−9.22420	−0.323308
$815$	16.8980	0.591910
$816$	−1.00000	−0.0350070
$817$	−9.65108	−0.337649
$818$	18.4131	0.643799
$819$	15.4512	0.539909
$820$	3.66263	0.127905
$821$	−34.7891	−1.21415	−0.607074	−	0.794646i	$-0.707657\pi$
$821$	−34.7891	−1.21415	−0.607074	+	0.794646i	$0.707657\pi$
$822$	−2.68028	−0.0934856
$823$	−2.67474	−0.0932355	−0.0466177	−	0.998913i	$-0.514844\pi$
$823$	−2.67474	−0.0932355	−0.0466177	+	0.998913i	$0.514844\pi$
$824$	−0.680282	−0.0236987
$825$	−1.00000	−0.0348155
$826$	−29.0295	−1.01006
$827$	−20.7133	−0.720274	−0.360137	−	0.932900i	$-0.617270\pi$
$827$	−20.7133	−0.720274	−0.360137	+	0.932900i	$0.617270\pi$
$828$	−4.26174	−0.148106
$829$	16.9452	0.588532	0.294266	−	0.955724i	$-0.404925\pi$
$829$	16.9452	0.588532	0.294266	+	0.955724i	$0.404925\pi$
$830$	−11.4512	−0.397477
$831$	24.9024	0.863855
$832$	5.94482	0.206099
$833$	0.244651	0.00847664
$834$	−14.0962	−0.488111
$835$	4.86084	0.168216
$836$	1.94482	0.0672629
$837$	−4.90728	−0.169620
$838$	−11.1763	−0.386078
$839$	38.1818	1.31818	0.659091	−	0.752063i	$-0.270941\pi$
$839$	38.1818	1.31818	0.659091	+	0.752063i	$0.270941\pi$
$840$	2.59911	0.0896777
$841$	−17.8062	−0.614008
$842$	−12.4815	−0.430140
$843$	−21.5894	−0.743578
$844$	17.3297	0.596513
$845$	22.3408	0.768548
$846$	−3.66263	−0.125924
$847$	2.59911	0.0893063
$848$	9.97081	0.342399
$849$	27.4259	0.941254
$850$	−1.00000	−0.0342997
$851$	−39.3111	−1.34757
$852$	3.27939	0.112350
$853$	−0.788410	−0.0269947	−0.0134973	−	0.999909i	$-0.504296\pi$
$853$	−0.788410	−0.0269947	−0.0134973	+	0.999909i	$0.504296\pi$
$854$	−24.5647	−0.840586
$855$	−1.94482	−0.0665113
$856$	−15.4048	−0.526524
$857$	−13.3011	−0.454357	−0.227178	−	0.973853i	$-0.572950\pi$
$857$	−13.3011	−0.454357	−0.227178	+	0.973853i	$0.572950\pi$
$858$	−5.94482	−0.202953
$859$	27.3861	0.934403	0.467202	−	0.884151i	$-0.345262\pi$
$859$	27.3861	0.934403	0.467202	+	0.884151i	$0.345262\pi$
$860$	4.96247	0.169219
$861$	9.51957	0.324426
$862$	−19.6247	−0.668420
$863$	−45.1238	−1.53603	−0.768016	−	0.640430i	$-0.778756\pi$
$863$	−45.1238	−1.53603	−0.768016	+	0.640430i	$0.778756\pi$
$864$	1.00000	0.0340207
$865$	−23.5103	−0.799373
$866$	−19.0878	−0.648631
$867$	1.00000	0.0339618
$868$	−12.7545	−0.432917
$869$	−2.38324	−0.0808460
$870$	3.34571	0.113430
$871$	61.9593	2.09941
$872$	4.36336	0.147762
$873$	2.98235	0.100937
$874$	8.28829	0.280356
$875$	2.59911	0.0878658
$876$	4.64555	0.156958
$877$	−6.58070	−0.222214	−0.111107	−	0.993808i	$-0.535440\pi$
$877$	−6.58070	−0.222214	−0.111107	+	0.993808i	$0.535440\pi$
$878$	10.0882	0.340462
$879$	−23.8012	−0.802794
$880$	−1.00000	−0.0337100
$881$	10.5210	0.354461	0.177231	−	0.984169i	$-0.443286\pi$
$881$	10.5210	0.354461	0.177231	+	0.984169i	$0.443286\pi$
$882$	−0.244651	−0.00823782
$883$	−18.4380	−0.620488	−0.310244	−	0.950657i	$-0.600411\pi$
$883$	−18.4380	−0.620488	−0.310244	+	0.950657i	$0.600411\pi$
$884$	−5.94482	−0.199946
$885$	−11.1690	−0.375442
$886$	4.29480	0.144287
$887$	−32.1244	−1.07863	−0.539315	−	0.842104i	$-0.681317\pi$
$887$	−32.1244	−1.07863	−0.539315	+	0.842104i	$0.681317\pi$
$888$	9.22420	0.309544
$889$	−23.0303	−0.772410
$890$	0.691421	0.0231765
$891$	−1.00000	−0.0335013
$892$	8.47703	0.283832
$893$	7.12314	0.238367
$894$	7.22420	0.241614
$895$	−0.282184	−0.00943238
$896$	2.59911	0.0868300
$897$	−25.3352	−0.845919
$898$	−34.3033	−1.14472
$899$	−16.4183	−0.547582
$900$	1.00000	0.0333333
$901$	−9.97081	−0.332176
$902$	−3.66263	−0.121952
$903$	12.8980	0.429218
$904$	7.50639	0.249659
$905$	6.46885	0.215032
$906$	−19.1138	−0.635015
$907$	−8.62046	−0.286238	−0.143119	−	0.989706i	$-0.545713\pi$
$907$	−8.62046	−0.286238	−0.143119	+	0.989706i	$0.545713\pi$
$908$	29.4214	0.976385
$909$	−3.02879	−0.100459
$910$	15.4512	0.512202
$911$	−18.0106	−0.596717	−0.298358	−	0.954454i	$-0.596439\pi$
$911$	−18.0106	−0.596717	−0.298358	+	0.954454i	$0.596439\pi$
$912$	−1.94482	−0.0643993
$913$	11.4512	0.378980
$914$	−4.72448	−0.156272
$915$	−9.45120	−0.312447
$916$	−22.8515	−0.755036
$917$	−48.8020	−1.61158
$918$	−1.00000	−0.0330049
$919$	−25.1171	−0.828538	−0.414269	−	0.910154i	$-0.635963\pi$
$919$	−25.1171	−0.828538	−0.414269	+	0.910154i	$0.635963\pi$
$920$	−4.26174	−0.140505
$921$	−6.69753	−0.220691
$922$	27.7632	0.914334
$923$	19.4954	0.641697
$924$	−2.59911	−0.0855043
$925$	9.22420	0.303290
$926$	−19.6136	−0.644541
$927$	−0.680282	−0.0223434
$928$	3.34571	0.109828
$929$	−18.7781	−0.616091	−0.308045	−	0.951372i	$-0.599675\pi$
$929$	−18.7781	−0.616091	−0.308045	+	0.951372i	$0.599675\pi$
$930$	−4.90728	−0.160916
$931$	0.475800	0.0155937
$932$	23.9858	0.785682
$933$	−9.20432	−0.301336
$934$	−29.2857	−0.958256
$935$	1.00000	0.0327035
$936$	5.94482	0.194312
$937$	−35.3984	−1.15642	−0.578208	−	0.815889i	$-0.696248\pi$
$937$	−35.3984	−1.15642	−0.578208	+	0.815889i	$0.696248\pi$
$938$	27.0890	0.884486
$939$	−32.5539	−1.06236
$940$	−3.66263	−0.119462
$941$	28.9671	0.944299	0.472149	−	0.881518i	$-0.343478\pi$
$941$	28.9671	0.944299	0.472149	+	0.881518i	$0.343478\pi$
$942$	6.91842	0.225414
$943$	−15.6092	−0.508305
$944$	−11.1690	−0.363521
$945$	2.59911	0.0845489
$946$	−4.96247	−0.161344
$947$	34.5888	1.12398	0.561992	−	0.827142i	$-0.310035\pi$
$947$	34.5888	1.12398	0.561992	+	0.827142i	$0.310035\pi$
$948$	2.38324	0.0774042
$949$	27.6169	0.896483
$950$	−1.94482	−0.0630982
$951$	6.95636	0.225575
$952$	−2.59911	−0.0842375
$953$	−10.1104	−0.327507	−0.163753	−	0.986501i	$-0.552360\pi$
$953$	−10.1104	−0.327507	−0.163753	+	0.986501i	$0.552360\pi$
$954$	9.97081	0.322817
$955$	−9.34571	−0.302420
$956$	−15.5946	−0.504366
$957$	−3.34571	−0.108151
$958$	7.35502	0.237630
$959$	−6.96634	−0.224955
$960$	1.00000	0.0322749
$961$	−6.91858	−0.223180
$962$	54.8362	1.76799
$963$	−15.4048	−0.496412
$964$	−1.49525	−0.0481587
$965$	5.41203	0.174220
$966$	−11.0767	−0.356387
$967$	0.296474	0.00953395	0.00476698	−	0.999989i	$-0.498483\pi$
$967$	0.296474	0.00953395	0.00476698	+	0.999989i	$0.498483\pi$
$968$	1.00000	0.0321412
$969$	1.94482	0.0624765
$970$	2.98235	0.0957575
$971$	−14.8632	−0.476984	−0.238492	−	0.971144i	$-0.576653\pi$
$971$	−14.8632	−0.476984	−0.238492	+	0.971144i	$0.576653\pi$
$972$	1.00000	0.0320750
$973$	−36.6375	−1.17454
$974$	−27.6113	−0.884724
$975$	5.94482	0.190386
$976$	−9.45120	−0.302526
$977$	11.8399	0.378792	0.189396	−	0.981901i	$-0.439347\pi$
$977$	11.8399	0.378792	0.189396	+	0.981901i	$0.439347\pi$
$978$	16.8980	0.540338
$979$	−0.691421	−0.0220979
$980$	−0.244651	−0.00781508
$981$	4.36336	0.139311
$982$	−6.43025	−0.205197
$983$	−20.3877	−0.650266	−0.325133	−	0.945668i	$-0.605409\pi$
$983$	−20.3877	−0.650266	−0.325133	+	0.945668i	$0.605409\pi$
$984$	3.66263	0.116760
$985$	6.53278	0.208152
$986$	−3.34571	−0.106549
$987$	−9.51957	−0.303011
$988$	−11.5616	−0.367823
$989$	−21.1487	−0.672490
$990$	−1.00000	−0.0317821
$991$	6.87311	0.218332	0.109166	−	0.994024i	$-0.465182\pi$
$991$	6.87311	0.218332	0.109166	+	0.994024i	$0.465182\pi$
$992$	−4.90728	−0.155806
$993$	−4.95636	−0.157285
$994$	8.52347	0.270348
$995$	−12.5551	−0.398022
$996$	−11.4512	−0.362845
$997$	28.8404	0.913384	0.456692	−	0.889625i	$-0.349034\pi$
$997$	28.8404	0.913384	0.456692	+	0.889625i	$0.349034\pi$
$998$	−22.4298	−0.710003
$999$	9.22420	0.291841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.ck.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ck.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.59911 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +2.59911 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +5.94482 q^{13} +2.59911 q^{14} +1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -1.94482 q^{19} +1.00000 q^{20} +2.59911 q^{21} -1.00000 q^{22} -4.26174 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.94482 q^{26} +1.00000 q^{27} +2.59911 q^{28} +3.34571 q^{29} +1.00000 q^{30} -4.90728 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +2.59911 q^{35} +1.00000 q^{36} +9.22420 q^{37} -1.94482 q^{38} +5.94482 q^{39} +1.00000 q^{40} +3.66263 q^{41} +2.59911 q^{42} +4.96247 q^{43} -1.00000 q^{44} +1.00000 q^{45} -4.26174 q^{46} -3.66263 q^{47} +1.00000 q^{48} -0.244651 q^{49} +1.00000 q^{50} -1.00000 q^{51} +5.94482 q^{52} +9.97081 q^{53} +1.00000 q^{54} -1.00000 q^{55} +2.59911 q^{56} -1.94482 q^{57} +3.34571 q^{58} -11.1690 q^{59} +1.00000 q^{60} -9.45120 q^{61} -4.90728 q^{62} +2.59911 q^{63} +1.00000 q^{64} +5.94482 q^{65} -1.00000 q^{66} +10.4224 q^{67} -1.00000 q^{68} -4.26174 q^{69} +2.59911 q^{70} +3.27939 q^{71} +1.00000 q^{72} +4.64555 q^{73} +9.22420 q^{74} +1.00000 q^{75} -1.94482 q^{76} -2.59911 q^{77} +5.94482 q^{78} +2.38324 q^{79} +1.00000 q^{80} +1.00000 q^{81} +3.66263 q^{82} -11.4512 q^{83} +2.59911 q^{84} -1.00000 q^{85} +4.96247 q^{86} +3.34571 q^{87} -1.00000 q^{88} +0.691421 q^{89} +1.00000 q^{90} +15.4512 q^{91} -4.26174 q^{92} -4.90728 q^{93} -3.66263 q^{94} -1.94482 q^{95} +1.00000 q^{96} +2.98235 q^{97} -0.244651 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 5 q^{5} + 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 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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