LMFDB - Embedded newform 5610.2.a.ci.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:	5.5.18569692.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 23x^{3} - 32x^{2} + 26x - 4 $ x^5 - 23x^3 - 32x^2 + 26*x - 4
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			$0.228960$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.06482 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.06482 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +3.41051 q^{13} +3.06482 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.41051 q^{19} +1.00000 q^{20} -3.06482 q^{21} +1.00000 q^{22} -7.25619 q^{23} -1.00000 q^{24} +1.00000 q^{25} +3.41051 q^{26} -1.00000 q^{27} +3.06482 q^{28} +4.34569 q^{29} -1.00000 q^{30} +9.71411 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +3.06482 q^{35} +1.00000 q^{36} -3.86843 q^{37} +3.41051 q^{38} -3.41051 q^{39} +1.00000 q^{40} +12.3210 q^{41} -3.06482 q^{42} -11.8160 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.25619 q^{46} +12.3210 q^{47} -1.00000 q^{48} +2.39310 q^{49} +1.00000 q^{50} +1.00000 q^{51} +3.41051 q^{52} -1.14930 q^{53} -1.00000 q^{54} +1.00000 q^{55} +3.06482 q^{56} -3.41051 q^{57} +4.34569 q^{58} -6.36310 q^{59} -1.00000 q^{60} -12.1894 q^{61} +9.71411 q^{62} +3.06482 q^{63} +1.00000 q^{64} +3.41051 q^{65} -1.00000 q^{66} -5.08222 q^{67} -1.00000 q^{68} +7.25619 q^{69} +3.06482 q^{70} +4.45792 q^{71} +1.00000 q^{72} +3.14930 q^{73} -3.86843 q^{74} -1.00000 q^{75} +3.41051 q^{76} +3.06482 q^{77} -3.41051 q^{78} -10.7789 q^{79} +1.00000 q^{80} +1.00000 q^{81} +12.3210 q^{82} +13.2736 q^{83} -3.06482 q^{84} -1.00000 q^{85} -11.8160 q^{86} -4.34569 q^{87} +1.00000 q^{88} +2.69138 q^{89} +1.00000 q^{90} +10.4526 q^{91} -7.25619 q^{92} -9.71411 q^{93} +12.3210 q^{94} +3.41051 q^{95} -1.00000 q^{96} -16.5351 q^{97} +2.39310 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - q^{13} + 2 q^{14} - 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} - q^{19} + 5 q^{20} - 2 q^{21} + 5 q^{22} - 5 q^{24} + 5 q^{25} - q^{26} - 5 q^{27} + 2 q^{28} + 17 q^{29} - 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + q^{37} - q^{38} + q^{39} + 5 q^{40} + 12 q^{41} - 2 q^{42} + 7 q^{43} + 5 q^{44} + 5 q^{45} + 12 q^{47} - 5 q^{48} + 23 q^{49} + 5 q^{50} + 5 q^{51} - q^{52} + 6 q^{53} - 5 q^{54} + 5 q^{55} + 2 q^{56} + q^{57} + 17 q^{58} + 2 q^{59} - 5 q^{60} + 9 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} - q^{65} - 5 q^{66} + 17 q^{67} - 5 q^{68} + 2 q^{70} + 20 q^{71} + 5 q^{72} + 4 q^{73} + q^{74} - 5 q^{75} - q^{76} + 2 q^{77} + q^{78} - 2 q^{79} + 5 q^{80} + 5 q^{81} + 12 q^{82} + q^{83} - 2 q^{84} - 5 q^{85} + 7 q^{86} - 17 q^{87} + 5 q^{88} + 4 q^{89} + 5 q^{90} + 23 q^{91} - 10 q^{93} + 12 q^{94} - q^{95} - 5 q^{96} - 8 q^{97} + 23 q^{98} + 5 q^{99}+O(q^{100}) \) 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 - q^13 + 2 * q^14 - 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 - q^19 + 5 * q^20 - 2 * q^21 + 5 * q^22 - 5 * q^24 + 5 * q^25 - q^26 - 5 * q^27 + 2 * q^28 + 17 * q^29 - 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + q^37 - q^38 + q^39 + 5 * q^40 + 12 * q^41 - 2 * q^42 + 7 * q^43 + 5 * q^44 + 5 * q^45 + 12 * q^47 - 5 * q^48 + 23 * q^49 + 5 * q^50 + 5 * q^51 - q^52 + 6 * q^53 - 5 * q^54 + 5 * q^55 + 2 * q^56 + q^57 + 17 * q^58 + 2 * q^59 - 5 * q^60 + 9 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 - q^65 - 5 * q^66 + 17 * q^67 - 5 * q^68 + 2 * q^70 + 20 * q^71 + 5 * q^72 + 4 * q^73 + q^74 - 5 * q^75 - q^76 + 2 * q^77 + q^78 - 2 * q^79 + 5 * q^80 + 5 * q^81 + 12 * q^82 + q^83 - 2 * q^84 - 5 * q^85 + 7 * q^86 - 17 * q^87 + 5 * q^88 + 4 * q^89 + 5 * q^90 + 23 * q^91 - 10 * q^93 + 12 * q^94 - q^95 - 5 * q^96 - 8 * q^97 + 23 * 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
$7$	3.06482	1.15839	0.579196	−	0.815188i	$-0.303367\pi$
$7$	3.06482	1.15839	0.579196	+	0.815188i	$0.303367\pi$
$8$	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
$13$	3.41051	0.945905	0.472952	−	0.881088i	$-0.343188\pi$
$13$	3.41051	0.945905	0.472952	+	0.881088i	$0.343188\pi$
$14$	3.06482	0.819107
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	3.41051	0.782424	0.391212	−	0.920301i	$-0.372056\pi$
$19$	3.41051	0.782424	0.391212	+	0.920301i	$0.372056\pi$
$20$	1.00000	0.223607
$21$	−3.06482	−0.668798
$22$	1.00000	0.213201
$23$	−7.25619	−1.51302	−0.756511	−	0.653981i	$-0.773097\pi$
$23$	−7.25619	−1.51302	−0.756511	+	0.653981i	$0.773097\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	3.41051	0.668856
$27$	−1.00000	−0.192450
$28$	3.06482	0.579196
$29$	4.34569	0.806975	0.403487	−	0.914985i	$-0.367798\pi$
$29$	4.34569	0.806975	0.403487	+	0.914985i	$0.367798\pi$
$30$	−1.00000	−0.182574
$31$	9.71411	1.74471	0.872353	−	0.488876i	$-0.162593\pi$
$31$	9.71411	1.74471	0.872353	+	0.488876i	$0.162593\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	3.06482	0.518049
$36$	1.00000	0.166667
$37$	−3.86843	−0.635966	−0.317983	−	0.948096i	$-0.603005\pi$
$37$	−3.86843	−0.635966	−0.317983	+	0.948096i	$0.603005\pi$
$38$	3.41051	0.553258
$39$	−3.41051	−0.546118
$40$	1.00000	0.158114
$41$	12.3210	1.92422	0.962109	−	0.272664i	$-0.0879047\pi$
$41$	12.3210	1.92422	0.962109	+	0.272664i	$0.0879047\pi$
$42$	−3.06482	−0.472912
$43$	−11.8160	−1.80192	−0.900962	−	0.433898i	$-0.857138\pi$
$43$	−11.8160	−1.80192	−0.900962	+	0.433898i	$0.857138\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	−7.25619	−1.06987
$47$	12.3210	1.79720	0.898602	−	0.438764i	$-0.144584\pi$
$47$	12.3210	1.79720	0.898602	+	0.438764i	$0.144584\pi$
$48$	−1.00000	−0.144338
$49$	2.39310	0.341872
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	3.41051	0.472952
$53$	−1.14930	−0.157869	−0.0789344	−	0.996880i	$-0.525152\pi$
$53$	−1.14930	−0.157869	−0.0789344	+	0.996880i	$0.525152\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	3.06482	0.409553
$57$	−3.41051	−0.451733
$58$	4.34569	0.570617
$59$	−6.36310	−0.828405	−0.414202	−	0.910185i	$-0.635939\pi$
$59$	−6.36310	−0.828405	−0.414202	+	0.910185i	$0.635939\pi$
$60$	−1.00000	−0.129099
$61$	−12.1894	−1.56070	−0.780349	−	0.625344i	$-0.784959\pi$
$61$	−12.1894	−1.56070	−0.780349	+	0.625344i	$0.784959\pi$
$62$	9.71411	1.23369
$63$	3.06482	0.386131
$64$	1.00000	0.125000
$65$	3.41051	0.423021
$66$	−1.00000	−0.123091
$67$	−5.08222	−0.620892	−0.310446	−	0.950591i	$-0.600478\pi$
$67$	−5.08222	−0.620892	−0.310446	+	0.950591i	$0.600478\pi$
$68$	−1.00000	−0.121268
$69$	7.25619	0.873543
$70$	3.06482	0.366316
$71$	4.45792	0.529058	0.264529	−	0.964378i	$-0.414784\pi$
$71$	4.45792	0.529058	0.264529	+	0.964378i	$0.414784\pi$
$72$	1.00000	0.117851
$73$	3.14930	0.368598	0.184299	−	0.982870i	$-0.440999\pi$
$73$	3.14930	0.368598	0.184299	+	0.982870i	$0.440999\pi$
$74$	−3.86843	−0.449696
$75$	−1.00000	−0.115470
$76$	3.41051	0.391212
$77$	3.06482	0.349268
$78$	−3.41051	−0.386164
$79$	−10.7789	−1.21272	−0.606362	−	0.795189i	$-0.707372\pi$
$79$	−10.7789	−1.21272	−0.606362	+	0.795189i	$0.707372\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	12.3210	1.36063
$83$	13.2736	1.45697	0.728483	−	0.685063i	$-0.240226\pi$
$83$	13.2736	1.45697	0.728483	+	0.685063i	$0.240226\pi$
$84$	−3.06482	−0.334399
$85$	−1.00000	−0.108465
$86$	−11.8160	−1.27415
$87$	−4.34569	−0.465907
$88$	1.00000	0.106600
$89$	2.69138	0.285286	0.142643	−	0.989774i	$-0.454440\pi$
$89$	2.69138	0.285286	0.142643	+	0.989774i	$0.454440\pi$
$90$	1.00000	0.105409
$91$	10.4526	1.09573
$92$	−7.25619	−0.756511
$93$	−9.71411	−1.00731
$94$	12.3210	1.27082
$95$	3.41051	0.349911
$96$	−1.00000	−0.102062
$97$	−16.5351	−1.67889	−0.839444	−	0.543446i	$-0.817119\pi$
$97$	−16.5351	−1.67889	−0.839444	+	0.543446i	$0.817119\pi$
$98$	2.39310	0.241740
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	13.0124	1.29478	0.647391	−	0.762158i	$-0.275860\pi$
$101$	13.0124	1.29478	0.647391	+	0.762158i	$0.275860\pi$
$102$	1.00000	0.0990148
$103$	−5.91551	−0.582873	−0.291436	−	0.956590i	$-0.594133\pi$
$103$	−5.91551	−0.582873	−0.291436	+	0.956590i	$0.594133\pi$
$104$	3.41051	0.334428
$105$	−3.06482	−0.299096
$106$	−1.14930	−0.111630
$107$	−2.63189	−0.254435	−0.127217	−	0.991875i	$-0.540605\pi$
$107$	−2.63189	−0.254435	−0.127217	+	0.991875i	$0.540605\pi$
$108$	−1.00000	−0.0962250
$109$	3.23879	0.310220	0.155110	−	0.987897i	$-0.450427\pi$
$109$	3.23879	0.310220	0.155110	+	0.987897i	$0.450427\pi$
$110$	1.00000	0.0953463
$111$	3.86843	0.367175
$112$	3.06482	0.289598
$113$	12.2565	1.15300	0.576498	−	0.817098i	$-0.304419\pi$
$113$	12.2565	1.15300	0.576498	+	0.817098i	$0.304419\pi$
$114$	−3.41051	−0.319423
$115$	−7.25619	−0.676644
$116$	4.34569	0.403487
$117$	3.41051	0.315302
$118$	−6.36310	−0.585771
$119$	−3.06482	−0.280951
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−12.1894	−1.10358
$123$	−12.3210	−1.11095
$124$	9.71411	0.872353
$125$	1.00000	0.0894427
$126$	3.06482	0.273036
$127$	−13.5348	−1.20102	−0.600510	−	0.799617i	$-0.705036\pi$
$127$	−13.5348	−1.20102	−0.600510	+	0.799617i	$0.705036\pi$
$128$	1.00000	0.0883883
$129$	11.8160	1.04034
$130$	3.41051	0.299121
$131$	12.7512	1.11408	0.557038	−	0.830487i	$-0.311938\pi$
$131$	12.7512	1.11408	0.557038	+	0.830487i	$0.311938\pi$
$132$	−1.00000	−0.0870388
$133$	10.4526	0.906354
$134$	−5.08222	−0.439037
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−9.90549	−0.846283	−0.423142	−	0.906064i	$-0.639073\pi$
$137$	−9.90549	−0.846283	−0.423142	+	0.906064i	$0.639073\pi$
$138$	7.25619	0.617688
$139$	−15.5825	−1.32169	−0.660847	−	0.750521i	$-0.729803\pi$
$139$	−15.5825	−1.32169	−0.660847	+	0.750521i	$0.729803\pi$
$140$	3.06482	0.259024
$141$	−12.3210	−1.03762
$142$	4.45792	0.374100
$143$	3.41051	0.285201
$144$	1.00000	0.0833333
$145$	4.34569	0.360890
$146$	3.14930	0.260638
$147$	−2.39310	−0.197380
$148$	−3.86843	−0.317983
$149$	−18.5105	−1.51644	−0.758218	−	0.652002i	$-0.773930\pi$
$149$	−18.5105	−1.51644	−0.758218	+	0.652002i	$0.773930\pi$
$150$	−1.00000	−0.0816497
$151$	6.39084	0.520079	0.260040	−	0.965598i	$-0.416264\pi$
$151$	6.39084	0.520079	0.260040	+	0.965598i	$0.416264\pi$
$152$	3.41051	0.276629
$153$	−1.00000	−0.0808452
$154$	3.06482	0.246970
$155$	9.71411	0.780256
$156$	−3.41051	−0.273059
$157$	11.1072	0.886452	0.443226	−	0.896410i	$-0.353834\pi$
$157$	11.1072	0.886452	0.443226	+	0.896410i	$0.353834\pi$
$158$	−10.7789	−0.857526
$159$	1.14930	0.0911456
$160$	1.00000	0.0790569
$161$	−22.2389	−1.75267
$162$	1.00000	0.0785674
$163$	2.14429	0.167954	0.0839769	−	0.996468i	$-0.473238\pi$
$163$	2.14429	0.167954	0.0839769	+	0.996468i	$0.473238\pi$
$164$	12.3210	0.962109
$165$	−1.00000	−0.0778499
$166$	13.2736	1.03023
$167$	15.3665	1.18909	0.594547	−	0.804061i	$-0.297331\pi$
$167$	15.3665	1.18909	0.594547	+	0.804061i	$0.297331\pi$
$168$	−3.06482	−0.236456
$169$	−1.36843	−0.105264
$170$	−1.00000	−0.0766965
$171$	3.41051	0.260808
$172$	−11.8160	−0.900962
$173$	−16.7736	−1.27527	−0.637636	−	0.770337i	$-0.720088\pi$
$173$	−16.7736	−1.27527	−0.637636	+	0.770337i	$0.720088\pi$
$174$	−4.34569	−0.329446
$175$	3.06482	0.231678
$176$	1.00000	0.0753778
$177$	6.36310	0.478280
$178$	2.69138	0.201728
$179$	−23.0301	−1.72135	−0.860676	−	0.509153i	$-0.829959\pi$
$179$	−23.0301	−1.72135	−0.860676	+	0.509153i	$0.829959\pi$
$180$	1.00000	0.0745356
$181$	0.833292	0.0619381	0.0309691	−	0.999520i	$-0.490141\pi$
$181$	0.833292	0.0619381	0.0309691	+	0.999520i	$0.490141\pi$
$182$	10.4526	0.774797
$183$	12.1894	0.901069
$184$	−7.25619	−0.534934
$185$	−3.86843	−0.284412
$186$	−9.71411	−0.712273
$187$	−1.00000	−0.0731272
$188$	12.3210	0.898602
$189$	−3.06482	−0.222933
$190$	3.41051	0.247424
$191$	0.738469	0.0534338	0.0267169	−	0.999643i	$-0.491495\pi$
$191$	0.738469	0.0534338	0.0267169	+	0.999643i	$0.491495\pi$
$192$	−1.00000	−0.0721688
$193$	26.8755	1.93454	0.967270	−	0.253750i	$-0.0816640\pi$
$193$	26.8755	1.93454	0.967270	+	0.253750i	$0.0816640\pi$
$194$	−16.5351	−1.18715
$195$	−3.41051	−0.244232
$196$	2.39310	0.170936
$197$	−5.08222	−0.362093	−0.181047	−	0.983475i	$-0.557949\pi$
$197$	−5.08222	−0.362093	−0.181047	+	0.983475i	$0.557949\pi$
$198$	1.00000	0.0710669
$199$	0.693321	0.0491482	0.0245741	−	0.999698i	$-0.492177\pi$
$199$	0.693321	0.0491482	0.0245741	+	0.999698i	$0.492177\pi$
$200$	1.00000	0.0707107
$201$	5.08222	0.358472
$202$	13.0124	0.915549
$203$	13.3187	0.934793
$204$	1.00000	0.0700140
$205$	12.3210	0.860537
$206$	−5.91551	−0.412153
$207$	−7.25619	−0.504340
$208$	3.41051	0.236476
$209$	3.41051	0.235910
$210$	−3.06482	−0.211492
$211$	−5.97532	−0.411358	−0.205679	−	0.978620i	$-0.565940\pi$
$211$	−5.97532	−0.411358	−0.205679	+	0.978620i	$0.565940\pi$
$212$	−1.14930	−0.0789344
$213$	−4.45792	−0.305452
$214$	−2.63189	−0.179912
$215$	−11.8160	−0.805845
$216$	−1.00000	−0.0680414
$217$	29.7720	2.02105
$218$	3.23879	0.219358
$219$	−3.14930	−0.212810
$220$	1.00000	0.0674200
$221$	−3.41051	−0.229416
$222$	3.86843	0.259632
$223$	−26.0351	−1.74344	−0.871720	−	0.490003i	$-0.836996\pi$
$223$	−26.0351	−1.74344	−0.871720	+	0.490003i	$0.836996\pi$
$224$	3.06482	0.204777
$225$	1.00000	0.0666667
$226$	12.2565	0.815292
$227$	18.6667	1.23895	0.619476	−	0.785015i	$-0.287345\pi$
$227$	18.6667	1.23895	0.619476	+	0.785015i	$0.287345\pi$
$228$	−3.41051	−0.225866
$229$	12.8808	0.851189	0.425594	−	0.904914i	$-0.360065\pi$
$229$	12.8808	0.851189	0.425594	+	0.904914i	$0.360065\pi$
$230$	−7.25619	−0.478459
$231$	−3.06482	−0.201650
$232$	4.34569	0.285309
$233$	13.8457	0.907061	0.453531	−	0.891241i	$-0.350164\pi$
$233$	13.8457	0.907061	0.453531	+	0.891241i	$0.350164\pi$
$234$	3.41051	0.222952
$235$	12.3210	0.803734
$236$	−6.36310	−0.414202
$237$	10.7789	0.700167
$238$	−3.06482	−0.198663
$239$	15.4282	0.997969	0.498985	−	0.866611i	$-0.333706\pi$
$239$	15.4282	0.997969	0.498985	+	0.866611i	$0.333706\pi$
$240$	−1.00000	−0.0645497
$241$	11.3858	0.733426	0.366713	−	0.930334i	$-0.380483\pi$
$241$	11.3858	0.733426	0.366713	+	0.930334i	$0.380483\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−12.1894	−0.780349
$245$	2.39310	0.152890
$246$	−12.3210	−0.785559
$247$	11.6316	0.740099
$248$	9.71411	0.616847
$249$	−13.2736	−0.841180
$250$	1.00000	0.0632456
$251$	2.87569	0.181512	0.0907560	−	0.995873i	$-0.471072\pi$
$251$	2.87569	0.181512	0.0907560	+	0.995873i	$0.471072\pi$
$252$	3.06482	0.193065
$253$	−7.25619	−0.456193
$254$	−13.5348	−0.849249
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−8.92985	−0.557029	−0.278514	−	0.960432i	$-0.589842\pi$
$257$	−8.92985	−0.557029	−0.278514	+	0.960432i	$0.589842\pi$
$258$	11.8160	0.735632
$259$	−11.8560	−0.736697
$260$	3.41051	0.211511
$261$	4.34569	0.268992
$262$	12.7512	0.787771
$263$	9.11929	0.562319	0.281160	−	0.959661i	$-0.409281\pi$
$263$	9.11929	0.562319	0.281160	+	0.959661i	$0.409281\pi$
$264$	−1.00000	−0.0615457
$265$	−1.14930	−0.0706011
$266$	10.4526	0.640889
$267$	−2.69138	−0.164710
$268$	−5.08222	−0.310446
$269$	12.3291	0.751718	0.375859	−	0.926677i	$-0.377348\pi$
$269$	12.3291	0.751718	0.375859	+	0.926677i	$0.377348\pi$
$270$	−1.00000	−0.0608581
$271$	9.91358	0.602207	0.301103	−	0.953591i	$-0.402645\pi$
$271$	9.91358	0.602207	0.301103	+	0.953591i	$0.402645\pi$
$272$	−1.00000	−0.0606339
$273$	−10.4526	−0.632619
$274$	−9.90549	−0.598413
$275$	1.00000	0.0603023
$276$	7.25619	0.436772
$277$	21.5472	1.29465	0.647323	−	0.762216i	$-0.275888\pi$
$277$	21.5472	1.29465	0.647323	+	0.762216i	$0.275888\pi$
$278$	−15.5825	−0.934579
$279$	9.71411	0.581569
$280$	3.06482	0.183158
$281$	17.8457	1.06458	0.532292	−	0.846561i	$-0.321331\pi$
$281$	17.8457	1.06458	0.532292	+	0.846561i	$0.321331\pi$
$282$	−12.3210	−0.733706
$283$	15.0348	0.893726	0.446863	−	0.894602i	$-0.352541\pi$
$283$	15.0348	0.893726	0.446863	+	0.894602i	$0.352541\pi$
$284$	4.45792	0.264529
$285$	−3.41051	−0.202021
$286$	3.41051	0.201668
$287$	37.7616	2.22900
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	4.34569	0.255188
$291$	16.5351	0.969307
$292$	3.14930	0.184299
$293$	21.3087	1.24487	0.622435	−	0.782672i	$-0.286144\pi$
$293$	21.3087	1.24487	0.622435	+	0.782672i	$0.286144\pi$
$294$	−2.39310	−0.139569
$295$	−6.36310	−0.370474
$296$	−3.86843	−0.224848
$297$	−1.00000	−0.0580259
$298$	−18.5105	−1.07228
$299$	−24.7473	−1.43117
$300$	−1.00000	−0.0577350
$301$	−36.2139	−2.08733
$302$	6.39084	0.367752
$303$	−13.0124	−0.747543
$304$	3.41051	0.195606
$305$	−12.1894	−0.697965
$306$	−1.00000	−0.0571662
$307$	11.0545	0.630912	0.315456	−	0.948940i	$-0.397842\pi$
$307$	11.0545	0.630912	0.315456	+	0.948940i	$0.397842\pi$
$308$	3.06482	0.174634
$309$	5.91551	0.336522
$310$	9.71411	0.551725
$311$	−10.4479	−0.592446	−0.296223	−	0.955119i	$-0.595727\pi$
$311$	−10.4479	−0.592446	−0.296223	+	0.955119i	$0.595727\pi$
$312$	−3.41051	−0.193082
$313$	−21.7489	−1.22932	−0.614661	−	0.788791i	$-0.710707\pi$
$313$	−21.7489	−1.22932	−0.614661	+	0.788791i	$0.710707\pi$
$314$	11.1072	0.626817
$315$	3.06482	0.172683
$316$	−10.7789	−0.606362
$317$	9.62123	0.540382	0.270191	−	0.962807i	$-0.412913\pi$
$317$	9.62123	0.540382	0.270191	+	0.962807i	$0.412913\pi$
$318$	1.14930	0.0644497
$319$	4.34569	0.243312
$320$	1.00000	0.0559017
$321$	2.63189	0.146898
$322$	−22.2389	−1.23933
$323$	−3.41051	−0.189766
$324$	1.00000	0.0555556
$325$	3.41051	0.189181
$326$	2.14429	0.118761
$327$	−3.23879	−0.179105
$328$	12.3210	0.680314
$329$	37.7616	2.08187
$330$	−1.00000	−0.0550482
$331$	9.76154	0.536543	0.268271	−	0.963343i	$-0.413548\pi$
$331$	9.76154	0.536543	0.268271	+	0.963343i	$0.413548\pi$
$332$	13.2736	0.728483
$333$	−3.86843	−0.211989
$334$	15.3665	0.840817
$335$	−5.08222	−0.277671
$336$	−3.06482	−0.167199
$337$	−4.44790	−0.242292	−0.121146	−	0.992635i	$-0.538657\pi$
$337$	−4.44790	−0.242292	−0.121146	+	0.992635i	$0.538657\pi$
$338$	−1.36843	−0.0744329
$339$	−12.2565	−0.665683
$340$	−1.00000	−0.0542326
$341$	9.71411	0.526049
$342$	3.41051	0.184419
$343$	−14.1193	−0.762370
$344$	−11.8160	−0.637076
$345$	7.25619	0.390660
$346$	−16.7736	−0.901754
$347$	−8.90517	−0.478054	−0.239027	−	0.971013i	$-0.576829\pi$
$347$	−8.90517	−0.478054	−0.239027	+	0.971013i	$0.576829\pi$
$348$	−4.34569	−0.232954
$349$	15.3985	0.824265	0.412133	−	0.911124i	$-0.364784\pi$
$349$	15.3985	0.824265	0.412133	+	0.911124i	$0.364784\pi$
$350$	3.06482	0.163821
$351$	−3.41051	−0.182039
$352$	1.00000	0.0533002
$353$	−0.467241	−0.0248687	−0.0124344	−	0.999923i	$-0.503958\pi$
$353$	−0.467241	−0.0248687	−0.0124344	+	0.999923i	$0.503958\pi$
$354$	6.36310	0.338195
$355$	4.45792	0.236602
$356$	2.69138	0.142643
$357$	3.06482	0.162207
$358$	−23.0301	−1.21718
$359$	23.6875	1.25018	0.625089	−	0.780553i	$-0.285063\pi$
$359$	23.6875	1.25018	0.625089	+	0.780553i	$0.285063\pi$
$360$	1.00000	0.0527046
$361$	−7.36843	−0.387812
$362$	0.833292	0.0437969
$363$	−1.00000	−0.0524864
$364$	10.4526	0.547864
$365$	3.14930	0.164842
$366$	12.1894	0.637152
$367$	−12.8210	−0.669252	−0.334626	−	0.942351i	$-0.608610\pi$
$367$	−12.8210	−0.669252	−0.334626	+	0.942351i	$0.608610\pi$
$368$	−7.25619	−0.378255
$369$	12.3210	0.641406
$370$	−3.86843	−0.201110
$371$	−3.52240	−0.182874
$372$	−9.71411	−0.503653
$373$	−35.1965	−1.82241	−0.911203	−	0.411958i	$-0.864845\pi$
$373$	−35.1965	−1.82241	−0.911203	+	0.411958i	$0.864845\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	12.3210	0.635408
$377$	14.8210	0.763321
$378$	−3.06482	−0.157637
$379$	9.66703	0.496562	0.248281	−	0.968688i	$-0.420134\pi$
$379$	9.66703	0.496562	0.248281	+	0.968688i	$0.420134\pi$
$380$	3.41051	0.174955
$381$	13.5348	0.693409
$382$	0.738469	0.0377834
$383$	−28.3210	−1.44714	−0.723568	−	0.690253i	$-0.757499\pi$
$383$	−28.3210	−1.44714	−0.723568	+	0.690253i	$0.757499\pi$
$384$	−1.00000	−0.0510310
$385$	3.06482	0.156198
$386$	26.8755	1.36793
$387$	−11.8160	−0.600641
$388$	−16.5351	−0.839444
$389$	12.6493	0.641345	0.320672	−	0.947190i	$-0.396091\pi$
$389$	12.6493	0.641345	0.320672	+	0.947190i	$0.396091\pi$
$390$	−3.41051	−0.172698
$391$	7.25619	0.366962
$392$	2.39310	0.120870
$393$	−12.7512	−0.643212
$394$	−5.08222	−0.256039
$395$	−10.7789	−0.542347
$396$	1.00000	0.0502519
$397$	−2.05787	−0.103281	−0.0516407	−	0.998666i	$-0.516445\pi$
$397$	−2.05787	−0.103281	−0.0516407	+	0.998666i	$0.516445\pi$
$398$	0.693321	0.0347530
$399$	−10.4526	−0.523284
$400$	1.00000	0.0500000
$401$	−21.4437	−1.07085	−0.535424	−	0.844584i	$-0.679848\pi$
$401$	−21.4437	−1.07085	−0.535424	+	0.844584i	$0.679848\pi$
$402$	5.08222	0.253478
$403$	33.1301	1.65033
$404$	13.0124	0.647391
$405$	1.00000	0.0496904
$406$	13.3187	0.660998
$407$	−3.86843	−0.191751
$408$	1.00000	0.0495074
$409$	−34.2099	−1.69157	−0.845786	−	0.533523i	$-0.820868\pi$
$409$	−34.2099	−1.69157	−0.845786	+	0.533523i	$0.820868\pi$
$410$	12.3210	0.608491
$411$	9.90549	0.488602
$412$	−5.91551	−0.291436
$413$	−19.5017	−0.959617
$414$	−7.25619	−0.356623
$415$	13.2736	0.651575
$416$	3.41051	0.167214
$417$	15.5825	0.763080
$418$	3.41051	0.166813
$419$	−13.4877	−0.658918	−0.329459	−	0.944170i	$-0.606866\pi$
$419$	−13.4877	−0.658918	−0.329459	+	0.944170i	$0.606866\pi$
$420$	−3.06482	−0.149548
$421$	−15.7018	−0.765261	−0.382630	−	0.923901i	$-0.624982\pi$
$421$	−15.7018	−0.765261	−0.382630	+	0.923901i	$0.624982\pi$
$422$	−5.97532	−0.290874
$423$	12.3210	0.599068
$424$	−1.14930	−0.0558151
$425$	−1.00000	−0.0485071
$426$	−4.45792	−0.215987
$427$	−37.3584	−1.80790
$428$	−2.63189	−0.127217
$429$	−3.41051	−0.164661
$430$	−11.8160	−0.569818
$431$	11.3333	0.545906	0.272953	−	0.962027i	$-0.412000\pi$
$431$	11.3333	0.545906	0.272953	+	0.962027i	$0.412000\pi$
$432$	−1.00000	−0.0481125
$433$	9.03480	0.434185	0.217092	−	0.976151i	$-0.430343\pi$
$433$	9.03480	0.434185	0.217092	+	0.976151i	$0.430343\pi$
$434$	29.7720	1.42910
$435$	−4.34569	−0.208360
$436$	3.23879	0.155110
$437$	−24.7473	−1.18382
$438$	−3.14930	−0.150479
$439$	−16.8531	−0.804354	−0.402177	−	0.915562i	$-0.631746\pi$
$439$	−16.8531	−0.804354	−0.402177	+	0.915562i	$0.631746\pi$
$440$	1.00000	0.0476731
$441$	2.39310	0.113957
$442$	−3.41051	−0.162221
$443$	−20.4102	−0.969717	−0.484859	−	0.874593i	$-0.661129\pi$
$443$	−20.4102	−0.969717	−0.484859	+	0.874593i	$0.661129\pi$
$444$	3.86843	0.183587
$445$	2.69138	0.127584
$446$	−26.0351	−1.23280
$447$	18.5105	0.875514
$448$	3.06482	0.144799
$449$	20.3528	0.960506	0.480253	−	0.877130i	$-0.340545\pi$
$449$	20.3528	0.960506	0.480253	+	0.877130i	$0.340545\pi$
$450$	1.00000	0.0471405
$451$	12.3210	0.580174
$452$	12.2565	0.576498
$453$	−6.39084	−0.300268
$454$	18.6667	0.876072
$455$	10.4526	0.490025
$456$	−3.41051	−0.159712
$457$	35.2697	1.64985	0.824924	−	0.565244i	$-0.191218\pi$
$457$	35.2697	1.64985	0.824924	+	0.565244i	$0.191218\pi$
$458$	12.8808	0.601881
$459$	1.00000	0.0466760
$460$	−7.25619	−0.338322
$461$	−20.5455	−0.956898	−0.478449	−	0.878115i	$-0.658801\pi$
$461$	−20.5455	−0.956898	−0.478449	+	0.878115i	$0.658801\pi$
$462$	−3.06482	−0.142588
$463$	−16.8908	−0.784984	−0.392492	−	0.919755i	$-0.628387\pi$
$463$	−16.8908	−0.784984	−0.392492	+	0.919755i	$0.628387\pi$
$464$	4.34569	0.201744
$465$	−9.71411	−0.450481
$466$	13.8457	0.641389
$467$	19.6841	0.910871	0.455436	−	0.890269i	$-0.349483\pi$
$467$	19.6841	0.910871	0.455436	+	0.890269i	$0.349483\pi$
$468$	3.41051	0.157651
$469$	−15.5761	−0.719237
$470$	12.3210	0.568326
$471$	−11.1072	−0.511794
$472$	−6.36310	−0.292885
$473$	−11.8160	−0.543301
$474$	10.7789	0.495093
$475$	3.41051	0.156485
$476$	−3.06482	−0.140476
$477$	−1.14930	−0.0526229
$478$	15.4282	0.705671
$479$	7.83134	0.357823	0.178912	−	0.983865i	$-0.442742\pi$
$479$	7.83134	0.357823	0.178912	+	0.983865i	$0.442742\pi$
$480$	−1.00000	−0.0456435
$481$	−13.1933	−0.601563
$482$	11.3858	0.518610
$483$	22.2389	1.01191
$484$	1.00000	0.0454545
$485$	−16.5351	−0.750822
$486$	−1.00000	−0.0453609
$487$	−7.43825	−0.337059	−0.168530	−	0.985697i	$-0.553902\pi$
$487$	−7.43825	−0.337059	−0.168530	+	0.985697i	$0.553902\pi$
$488$	−12.1894	−0.551790
$489$	−2.14429	−0.0969682
$490$	2.39310	0.108109
$491$	−25.7492	−1.16205	−0.581023	−	0.813887i	$-0.697348\pi$
$491$	−25.7492	−1.16205	−0.581023	+	0.813887i	$0.697348\pi$
$492$	−12.3210	−0.555474
$493$	−4.34569	−0.195720
$494$	11.6316	0.523329
$495$	1.00000	0.0449467
$496$	9.71411	0.436177
$497$	13.6627	0.612856
$498$	−13.2736	−0.594804
$499$	8.38276	0.375264	0.187632	−	0.982239i	$-0.439919\pi$
$499$	8.38276	0.375264	0.187632	+	0.982239i	$0.439919\pi$
$500$	1.00000	0.0447214
$501$	−15.3665	−0.686524
$502$	2.87569	0.128348
$503$	−33.7593	−1.50525	−0.752626	−	0.658449i	$-0.771213\pi$
$503$	−33.7593	−1.50525	−0.752626	+	0.658449i	$0.771213\pi$
$504$	3.06482	0.136518
$505$	13.0124	0.579044
$506$	−7.25619	−0.322577
$507$	1.36843	0.0607742
$508$	−13.5348	−0.600510
$509$	31.1965	1.38276	0.691380	−	0.722491i	$-0.257003\pi$
$509$	31.1965	1.38276	0.691380	+	0.722491i	$0.257003\pi$
$510$	1.00000	0.0442807
$511$	9.65204	0.426981
$512$	1.00000	0.0441942
$513$	−3.41051	−0.150578
$514$	−8.92985	−0.393879
$515$	−5.91551	−0.260669
$516$	11.8160	0.520171
$517$	12.3210	0.541877
$518$	−11.8560	−0.520924
$519$	16.7736	0.736279
$520$	3.41051	0.149561
$521$	−4.42290	−0.193771	−0.0968854	−	0.995296i	$-0.530888\pi$
$521$	−4.42290	−0.193771	−0.0968854	+	0.995296i	$0.530888\pi$
$522$	4.34569	0.190206
$523$	−19.4726	−0.851476	−0.425738	−	0.904847i	$-0.639985\pi$
$523$	−19.4726	−0.851476	−0.425738	+	0.904847i	$0.639985\pi$
$524$	12.7512	0.557038
$525$	−3.06482	−0.133760
$526$	9.11929	0.397620
$527$	−9.71411	−0.423153
$528$	−1.00000	−0.0435194
$529$	29.6524	1.28923
$530$	−1.14930	−0.0499225
$531$	−6.36310	−0.276135
$532$	10.4526	0.453177
$533$	42.0209	1.82013
$534$	−2.69138	−0.116468
$535$	−2.63189	−0.113787
$536$	−5.08222	−0.219519
$537$	23.0301	0.993823
$538$	12.3291	0.531545
$539$	2.39310	0.103078
$540$	−1.00000	−0.0430331
$541$	39.2740	1.68852	0.844262	−	0.535931i	$-0.180039\pi$
$541$	39.2740	1.68852	0.844262	+	0.535931i	$0.180039\pi$
$542$	9.91358	0.425825
$543$	−0.833292	−0.0357600
$544$	−1.00000	−0.0428746
$545$	3.23879	0.138734
$546$	−10.4526	−0.447329
$547$	15.9756	0.683069	0.341534	−	0.939869i	$-0.389053\pi$
$547$	15.9756	0.683069	0.341534	+	0.939869i	$0.389053\pi$
$548$	−9.90549	−0.423142
$549$	−12.1894	−0.520233
$550$	1.00000	0.0426401
$551$	14.8210	0.631397
$552$	7.25619	0.308844
$553$	−33.0355	−1.40481
$554$	21.5472	0.915453
$555$	3.86843	0.164206
$556$	−15.5825	−0.660847
$557$	−15.6667	−0.663819	−0.331910	−	0.943311i	$-0.607693\pi$
$557$	−15.6667	−0.663819	−0.331910	+	0.943311i	$0.607693\pi$
$558$	9.71411	0.411231
$559$	−40.2986	−1.70445
$560$	3.06482	0.129512
$561$	1.00000	0.0422200
$562$	17.8457	0.752775
$563$	33.6525	1.41828	0.709141	−	0.705066i	$-0.249083\pi$
$563$	33.6525	1.41828	0.709141	+	0.705066i	$0.249083\pi$
$564$	−12.3210	−0.518808
$565$	12.2565	0.515636
$566$	15.0348	0.631960
$567$	3.06482	0.128710
$568$	4.45792	0.187050
$569$	−34.2249	−1.43478	−0.717391	−	0.696671i	$-0.754664\pi$
$569$	−34.2249	−1.43478	−0.717391	+	0.696671i	$0.754664\pi$
$570$	−3.41051	−0.142850
$571$	−26.8210	−1.12242	−0.561212	−	0.827672i	$-0.689665\pi$
$571$	−26.8210	−1.12242	−0.561212	+	0.827672i	$0.689665\pi$
$572$	3.41051	0.142601
$573$	−0.738469	−0.0308500
$574$	37.7616	1.57614
$575$	−7.25619	−0.302604
$576$	1.00000	0.0416667
$577$	16.2986	0.678520	0.339260	−	0.940693i	$-0.389823\pi$
$577$	16.2986	0.678520	0.339260	+	0.940693i	$0.389823\pi$
$578$	1.00000	0.0415945
$579$	−26.8755	−1.11691
$580$	4.34569	0.180445
$581$	40.6812	1.68774
$582$	16.5351	0.685403
$583$	−1.14930	−0.0475992
$584$	3.14930	0.130319
$585$	3.41051	0.141007
$586$	21.3087	0.880255
$587$	−38.0029	−1.56855	−0.784273	−	0.620416i	$-0.786964\pi$
$587$	−38.0029	−1.56855	−0.784273	+	0.620416i	$0.786964\pi$
$588$	−2.39310	−0.0986899
$589$	33.1301	1.36510
$590$	−6.36310	−0.261965
$591$	5.08222	0.209055
$592$	−3.86843	−0.158991
$593$	−26.6420	−1.09406	−0.547028	−	0.837114i	$-0.684241\pi$
$593$	−26.6420	−1.09406	−0.547028	+	0.837114i	$0.684241\pi$
$594$	−1.00000	−0.0410305
$595$	−3.06482	−0.125645
$596$	−18.5105	−0.758218
$597$	−0.693321	−0.0283757
$598$	−24.7473	−1.01199
$599$	−9.75280	−0.398489	−0.199244	−	0.979950i	$-0.563849\pi$
$599$	−9.75280	−0.398489	−0.199244	+	0.979950i	$0.563849\pi$
$600$	−1.00000	−0.0408248
$601$	−3.31956	−0.135408	−0.0677039	−	0.997705i	$-0.521567\pi$
$601$	−3.31956	−0.135408	−0.0677039	+	0.997705i	$0.521567\pi$
$602$	−36.2139	−1.47597
$603$	−5.08222	−0.206964
$604$	6.39084	0.260040
$605$	1.00000	0.0406558
$606$	−13.0124	−0.528592
$607$	−8.72151	−0.353995	−0.176998	−	0.984211i	$-0.556638\pi$
$607$	−8.72151	−0.353995	−0.176998	+	0.984211i	$0.556638\pi$
$608$	3.41051	0.138314
$609$	−13.3187	−0.539703
$610$	−12.1894	−0.493536
$611$	42.0209	1.69998
$612$	−1.00000	−0.0404226
$613$	−17.3862	−0.702221	−0.351110	−	0.936334i	$-0.614196\pi$
$613$	−17.3862	−0.702221	−0.351110	+	0.936334i	$0.614196\pi$
$614$	11.0545	0.446122
$615$	−12.3210	−0.496831
$616$	3.06482	0.123485
$617$	22.3407	0.899402	0.449701	−	0.893179i	$-0.351531\pi$
$617$	22.3407	0.899402	0.449701	+	0.893179i	$0.351531\pi$
$618$	5.91551	0.237957
$619$	−27.7219	−1.11424	−0.557118	−	0.830433i	$-0.688093\pi$
$619$	−27.7219	−1.11424	−0.557118	+	0.830433i	$0.688093\pi$
$620$	9.71411	0.390128
$621$	7.25619	0.291181
$622$	−10.4479	−0.418923
$623$	8.24860	0.330473
$624$	−3.41051	−0.136530
$625$	1.00000	0.0400000
$626$	−21.7489	−0.869262
$627$	−3.41051	−0.136203
$628$	11.1072	0.443226
$629$	3.86843	0.154244
$630$	3.06482	0.122105
$631$	−3.82553	−0.152292	−0.0761460	−	0.997097i	$-0.524262\pi$
$631$	−3.82553	−0.152292	−0.0761460	+	0.997097i	$0.524262\pi$
$632$	−10.7789	−0.428763
$633$	5.97532	0.237498
$634$	9.62123	0.382108
$635$	−13.5348	−0.537112
$636$	1.14930	0.0455728
$637$	8.16170	0.323378
$638$	4.34569	0.172048
$639$	4.45792	0.176353
$640$	1.00000	0.0395285
$641$	26.8553	1.06072	0.530361	−	0.847772i	$-0.322056\pi$
$641$	26.8553	1.06072	0.530361	+	0.847772i	$0.322056\pi$
$642$	2.63189	0.103872
$643$	16.7122	0.659063	0.329532	−	0.944144i	$-0.393109\pi$
$643$	16.7122	0.659063	0.329532	+	0.944144i	$0.393109\pi$
$644$	−22.2389	−0.876336
$645$	11.8160	0.465255
$646$	−3.41051	−0.134185
$647$	10.3110	0.405367	0.202683	−	0.979244i	$-0.435034\pi$
$647$	10.3110	0.405367	0.202683	+	0.979244i	$0.435034\pi$
$648$	1.00000	0.0392837
$649$	−6.36310	−0.249773
$650$	3.41051	0.133771
$651$	−29.7720	−1.16686
$652$	2.14429	0.0839769
$653$	−30.3087	−1.18607	−0.593036	−	0.805176i	$-0.702071\pi$
$653$	−30.3087	−1.18607	−0.593036	+	0.805176i	$0.702071\pi$
$654$	−3.23879	−0.126647
$655$	12.7512	0.498230
$656$	12.3210	0.481055
$657$	3.14930	0.122866
$658$	37.7616	1.47210
$659$	−28.4614	−1.10870	−0.554350	−	0.832284i	$-0.687033\pi$
$659$	−28.4614	−1.10870	−0.554350	+	0.832284i	$0.687033\pi$
$660$	−1.00000	−0.0389249
$661$	13.0205	0.506438	0.253219	−	0.967409i	$-0.418511\pi$
$661$	13.0205	0.506438	0.253219	+	0.967409i	$0.418511\pi$
$662$	9.76154	0.379393
$663$	3.41051	0.132453
$664$	13.2736	0.515116
$665$	10.4526	0.405334
$666$	−3.86843	−0.149899
$667$	−31.5332	−1.22097
$668$	15.3665	0.594547
$669$	26.0351	1.00658
$670$	−5.08222	−0.196343
$671$	−12.1894	−0.470568
$672$	−3.06482	−0.118228
$673$	17.1841	0.662398	0.331199	−	0.943561i	$-0.392547\pi$
$673$	17.1841	0.662398	0.331199	+	0.943561i	$0.392547\pi$
$674$	−4.44790	−0.171327
$675$	−1.00000	−0.0384900
$676$	−1.36843	−0.0526320
$677$	−38.5709	−1.48240	−0.741200	−	0.671284i	$-0.765743\pi$
$677$	−38.5709	−1.48240	−0.741200	+	0.671284i	$0.765743\pi$
$678$	−12.2565	−0.470709
$679$	−50.6771	−1.94481
$680$	−1.00000	−0.0383482
$681$	−18.6667	−0.715310
$682$	9.71411	0.371973
$683$	−48.9904	−1.87457	−0.937283	−	0.348569i	$-0.886668\pi$
$683$	−48.9904	−1.87457	−0.937283	+	0.348569i	$0.886668\pi$
$684$	3.41051	0.130404
$685$	−9.90549	−0.378469
$686$	−14.1193	−0.539077
$687$	−12.8808	−0.491434
$688$	−11.8160	−0.450481
$689$	−3.91971	−0.149329
$690$	7.25619	0.276239
$691$	−44.0946	−1.67744	−0.838719	−	0.544564i	$-0.816695\pi$
$691$	−44.0946	−1.67744	−0.838719	+	0.544564i	$0.816695\pi$
$692$	−16.7736	−0.637636
$693$	3.06482	0.116423
$694$	−8.90517	−0.338036
$695$	−15.5825	−0.591080
$696$	−4.34569	−0.164723
$697$	−12.3210	−0.466692
$698$	15.3985	0.582844
$699$	−13.8457	−0.523692
$700$	3.06482	0.115839
$701$	14.0517	0.530726	0.265363	−	0.964149i	$-0.414508\pi$
$701$	14.0517	0.530726	0.265363	+	0.964149i	$0.414508\pi$
$702$	−3.41051	−0.128721
$703$	−13.1933	−0.497595
$704$	1.00000	0.0376889
$705$	−12.3210	−0.464036
$706$	−0.467241	−0.0175848
$707$	39.8806	1.49986
$708$	6.36310	0.239140
$709$	13.6683	0.513324	0.256662	−	0.966501i	$-0.417377\pi$
$709$	13.6683	0.513324	0.256662	+	0.966501i	$0.417377\pi$
$710$	4.45792	0.167303
$711$	−10.7789	−0.404242
$712$	2.69138	0.100864
$713$	−70.4875	−2.63978
$714$	3.06482	0.114698
$715$	3.41051	0.127546
$716$	−23.0301	−0.860676
$717$	−15.4282	−0.576178
$718$	23.6875	0.884010
$719$	3.92484	0.146372	0.0731858	−	0.997318i	$-0.476683\pi$
$719$	3.92484	0.146372	0.0731858	+	0.997318i	$0.476683\pi$
$720$	1.00000	0.0372678
$721$	−18.1300	−0.675195
$722$	−7.36843	−0.274225
$723$	−11.3858	−0.423444
$724$	0.833292	0.0309691
$725$	4.34569	0.161395
$726$	−1.00000	−0.0371135
$727$	−17.2801	−0.640882	−0.320441	−	0.947268i	$-0.603831\pi$
$727$	−17.2801	−0.640882	−0.320441	+	0.947268i	$0.603831\pi$
$728$	10.4526	0.387399
$729$	1.00000	0.0370370
$730$	3.14930	0.116561
$731$	11.8160	0.437031
$732$	12.1894	0.450535
$733$	−9.11190	−0.336556	−0.168278	−	0.985740i	$-0.553821\pi$
$733$	−9.11190	−0.336556	−0.168278	+	0.985740i	$0.553821\pi$
$734$	−12.8210	−0.473232
$735$	−2.39310	−0.0882709
$736$	−7.25619	−0.267467
$737$	−5.08222	−0.187206
$738$	12.3210	0.453543
$739$	20.4560	0.752485	0.376242	−	0.926521i	$-0.377216\pi$
$739$	20.4560	0.752485	0.376242	+	0.926521i	$0.377216\pi$
$740$	−3.86843	−0.142206
$741$	−11.6316	−0.427296
$742$	−3.52240	−0.129311
$743$	−10.7593	−0.394719	−0.197360	−	0.980331i	$-0.563237\pi$
$743$	−10.7593	−0.394719	−0.197360	+	0.980331i	$0.563237\pi$
$744$	−9.71411	−0.356137
$745$	−18.5105	−0.678170
$746$	−35.1965	−1.28864
$747$	13.2736	0.485656
$748$	−1.00000	−0.0365636
$749$	−8.06627	−0.294735
$750$	−1.00000	−0.0365148
$751$	38.6197	1.40925	0.704627	−	0.709578i	$-0.251114\pi$
$751$	38.6197	1.40925	0.704627	+	0.709578i	$0.251114\pi$
$752$	12.3210	0.449301
$753$	−2.87569	−0.104796
$754$	14.8210	0.539750
$755$	6.39084	0.232586
$756$	−3.06482	−0.111466
$757$	−45.6852	−1.66046	−0.830229	−	0.557422i	$-0.811791\pi$
$757$	−45.6852	−1.66046	−0.830229	+	0.557422i	$0.811791\pi$
$758$	9.66703	0.351122
$759$	7.25619	0.263383
$760$	3.41051	0.123712
$761$	41.6423	1.50953	0.754767	−	0.655993i	$-0.227750\pi$
$761$	41.6423	1.50953	0.754767	+	0.655993i	$0.227750\pi$
$762$	13.5348	0.490314
$763$	9.92630	0.359356
$764$	0.738469	0.0267169
$765$	−1.00000	−0.0361551
$766$	−28.3210	−1.02328
$767$	−21.7014	−0.783592
$768$	−1.00000	−0.0360844
$769$	−10.6527	−0.384146	−0.192073	−	0.981381i	$-0.561521\pi$
$769$	−10.6527	−0.384146	−0.192073	+	0.981381i	$0.561521\pi$
$770$	3.06482	0.110448
$771$	8.92985	0.321601
$772$	26.8755	0.967270
$773$	−36.2601	−1.30418	−0.652092	−	0.758140i	$-0.726108\pi$
$773$	−36.2601	−1.30418	−0.652092	+	0.758140i	$0.726108\pi$
$774$	−11.8160	−0.424718
$775$	9.71411	0.348941
$776$	−16.5351	−0.593577
$777$	11.8560	0.425332
$778$	12.6493	0.453499
$779$	42.0209	1.50556
$780$	−3.41051	−0.122116
$781$	4.45792	0.159517
$782$	7.25619	0.259481
$783$	−4.34569	−0.155302
$784$	2.39310	0.0854680
$785$	11.1072	0.396434
$786$	−12.7512	−0.454820
$787$	33.9156	1.20896	0.604481	−	0.796620i	$-0.293381\pi$
$787$	33.9156	1.20896	0.604481	+	0.796620i	$0.293381\pi$
$788$	−5.08222	−0.181047
$789$	−9.11929	−0.324655
$790$	−10.7789	−0.383497
$791$	37.5640	1.33562
$792$	1.00000	0.0355335
$793$	−41.5722	−1.47627
$794$	−2.05787	−0.0730310
$795$	1.14930	0.0407616
$796$	0.693321	0.0245741
$797$	−29.4190	−1.04208	−0.521038	−	0.853534i	$-0.674455\pi$
$797$	−29.4190	−1.04208	−0.521038	+	0.853534i	$0.674455\pi$
$798$	−10.4526	−0.370017
$799$	−12.3210	−0.435886
$800$	1.00000	0.0353553
$801$	2.69138	0.0950953
$802$	−21.4437	−0.757203
$803$	3.14930	0.111136
$804$	5.08222	0.179236
$805$	−22.2389	−0.783819
$806$	33.1301	1.16696
$807$	−12.3291	−0.434005
$808$	13.0124	0.457774
$809$	21.9282	0.770956	0.385478	−	0.922717i	$-0.374037\pi$
$809$	21.9282	0.770956	0.385478	+	0.922717i	$0.374037\pi$
$810$	1.00000	0.0351364
$811$	28.6381	1.00562	0.502811	−	0.864397i	$-0.332299\pi$
$811$	28.6381	1.00562	0.502811	+	0.864397i	$0.332299\pi$
$812$	13.3187	0.467396
$813$	−9.91358	−0.347684
$814$	−3.86843	−0.135588
$815$	2.14429	0.0751112
$816$	1.00000	0.0350070
$817$	−40.2986	−1.40987
$818$	−34.2099	−1.19612
$819$	10.4526	0.365243
$820$	12.3210	0.430268
$821$	42.8542	1.49562	0.747811	−	0.663912i	$-0.231105\pi$
$821$	42.8542	1.49562	0.747811	+	0.663912i	$0.231105\pi$
$822$	9.90549	0.345494
$823$	−39.9013	−1.39087	−0.695436	−	0.718588i	$-0.744789\pi$
$823$	−39.9013	−1.39087	−0.695436	+	0.718588i	$0.744789\pi$
$824$	−5.91551	−0.206077
$825$	−1.00000	−0.0348155
$826$	−19.5017	−0.678552
$827$	−8.36810	−0.290987	−0.145494	−	0.989359i	$-0.546477\pi$
$827$	−8.36810	−0.290987	−0.145494	+	0.989359i	$0.546477\pi$
$828$	−7.25619	−0.252170
$829$	35.5329	1.23411	0.617054	−	0.786921i	$-0.288326\pi$
$829$	35.5329	1.23411	0.617054	+	0.786921i	$0.288326\pi$
$830$	13.2736	0.460733
$831$	−21.5472	−0.747464
$832$	3.41051	0.118238
$833$	−2.39310	−0.0829161
$834$	15.5825	0.539579
$835$	15.3665	0.531779
$836$	3.41051	0.117955
$837$	−9.71411	−0.335769
$838$	−13.4877	−0.465926
$839$	−45.8223	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$839$	−45.8223	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$840$	−3.06482	−0.105746
$841$	−10.1150	−0.348792
$842$	−15.7018	−0.541121
$843$	−17.8457	−0.614638
$844$	−5.97532	−0.205679
$845$	−1.36843	−0.0470755
$846$	12.3210	0.423605
$847$	3.06482	0.105308
$848$	−1.14930	−0.0394672
$849$	−15.0348	−0.515993
$850$	−1.00000	−0.0342997
$851$	28.0701	0.962229
$852$	−4.45792	−0.152726
$853$	−3.62738	−0.124199	−0.0620995	−	0.998070i	$-0.519780\pi$
$853$	−3.62738	−0.124199	−0.0620995	+	0.998070i	$0.519780\pi$
$854$	−37.3584	−1.27838
$855$	3.41051	0.116637
$856$	−2.63189	−0.0899562
$857$	−1.03514	−0.0353596	−0.0176798	−	0.999844i	$-0.505628\pi$
$857$	−1.03514	−0.0353596	−0.0176798	+	0.999844i	$0.505628\pi$
$858$	−3.41051	−0.116433
$859$	5.19364	0.177205	0.0886024	−	0.996067i	$-0.471760\pi$
$859$	5.19364	0.177205	0.0886024	+	0.996067i	$0.471760\pi$
$860$	−11.8160	−0.402922
$861$	−37.7616	−1.28691
$862$	11.3333	0.386014
$863$	30.7593	1.04706	0.523529	−	0.852008i	$-0.324615\pi$
$863$	30.7593	1.04706	0.523529	+	0.852008i	$0.324615\pi$
$864$	−1.00000	−0.0340207
$865$	−16.7736	−0.570319
$866$	9.03480	0.307015
$867$	−1.00000	−0.0339618
$868$	29.7720	1.01053
$869$	−10.7789	−0.365650
$870$	−4.34569	−0.147333
$871$	−17.3330	−0.587305
$872$	3.23879	0.109679
$873$	−16.5351	−0.559629
$874$	−24.7473	−0.837090
$875$	3.06482	0.103610
$876$	−3.14930	−0.106405
$877$	23.8911	0.806747	0.403373	−	0.915035i	$-0.367838\pi$
$877$	23.8911	0.806747	0.403373	+	0.915035i	$0.367838\pi$
$878$	−16.8531	−0.568764
$879$	−21.3087	−0.718725
$880$	1.00000	0.0337100
$881$	46.4287	1.56422	0.782112	−	0.623138i	$-0.214143\pi$
$881$	46.4287	1.56422	0.782112	+	0.623138i	$0.214143\pi$
$882$	2.39310	0.0805800
$883$	−28.9876	−0.975511	−0.487755	−	0.872980i	$-0.662184\pi$
$883$	−28.9876	−0.975511	−0.487755	+	0.872980i	$0.662184\pi$
$884$	−3.41051	−0.114708
$885$	6.36310	0.213893
$886$	−20.4102	−0.685694
$887$	−9.71995	−0.326364	−0.163182	−	0.986596i	$-0.552176\pi$
$887$	−9.71995	−0.326364	−0.163182	+	0.986596i	$0.552176\pi$
$888$	3.86843	0.129816
$889$	−41.4817	−1.39125
$890$	2.69138	0.0902154
$891$	1.00000	0.0335013
$892$	−26.0351	−0.871720
$893$	42.0209	1.40618
$894$	18.5105	0.619082
$895$	−23.0301	−0.769812
$896$	3.06482	0.102388
$897$	24.7473	0.826289
$898$	20.3528	0.679180
$899$	42.2145	1.40793
$900$	1.00000	0.0333333
$901$	1.14930	0.0382888
$902$	12.3210	0.410245
$903$	36.2139	1.20512
$904$	12.2565	0.407646
$905$	0.833292	0.0276996
$906$	−6.39084	−0.212321
$907$	14.2385	0.472780	0.236390	−	0.971658i	$-0.424036\pi$
$907$	14.2385	0.472780	0.236390	+	0.971658i	$0.424036\pi$
$908$	18.6667	0.619476
$909$	13.0124	0.431594
$910$	10.4526	0.346500
$911$	10.9849	0.363945	0.181972	−	0.983304i	$-0.441752\pi$
$911$	10.9849	0.363945	0.181972	+	0.983304i	$0.441752\pi$
$912$	−3.41051	−0.112933
$913$	13.2736	0.439292
$914$	35.2697	1.16662
$915$	12.1894	0.402970
$916$	12.8808	0.425594
$917$	39.0801	1.29054
$918$	1.00000	0.0330049
$919$	−42.2675	−1.39427	−0.697137	−	0.716938i	$-0.745543\pi$
$919$	−42.2675	−1.39427	−0.697137	+	0.716938i	$0.745543\pi$
$920$	−7.25619	−0.239230
$921$	−11.0545	−0.364257
$922$	−20.5455	−0.676629
$923$	15.2038	0.500438
$924$	−3.06482	−0.100825
$925$	−3.86843	−0.127193
$926$	−16.8908	−0.555068
$927$	−5.91551	−0.194291
$928$	4.34569	0.142654
$929$	32.8017	1.07619	0.538094	−	0.842885i	$-0.319145\pi$
$929$	32.8017	1.07619	0.538094	+	0.842885i	$0.319145\pi$
$930$	−9.71411	−0.318538
$931$	8.16170	0.267489
$932$	13.8457	0.453531
$933$	10.4479	0.342049
$934$	19.6841	0.644083
$935$	−1.00000	−0.0327035
$936$	3.41051	0.111476
$937$	−0.332972	−0.0108777	−0.00543886	−	0.999985i	$-0.501731\pi$
$937$	−0.332972	−0.0108777	−0.00543886	+	0.999985i	$0.501731\pi$
$938$	−15.5761	−0.508577
$939$	21.7489	0.709749
$940$	12.3210	0.401867
$941$	−28.1381	−0.917277	−0.458639	−	0.888623i	$-0.651663\pi$
$941$	−28.1381	−0.917277	−0.458639	+	0.888623i	$0.651663\pi$
$942$	−11.1072	−0.361893
$943$	−89.4037	−2.91138
$944$	−6.36310	−0.207101
$945$	−3.06482	−0.0996985
$946$	−11.8160	−0.384171
$947$	16.2886	0.529308	0.264654	−	0.964343i	$-0.414742\pi$
$947$	16.2886	0.529308	0.264654	+	0.964343i	$0.414742\pi$
$948$	10.7789	0.350083
$949$	10.7407	0.348659
$950$	3.41051	0.110652
$951$	−9.62123	−0.311990
$952$	−3.06482	−0.0993313
$953$	−41.3341	−1.33894	−0.669471	−	0.742838i	$-0.733479\pi$
$953$	−41.3341	−1.33894	−0.669471	+	0.742838i	$0.733479\pi$
$954$	−1.14930	−0.0372100
$955$	0.738469	0.0238963
$956$	15.4282	0.498985
$957$	−4.34569	−0.140476
$958$	7.83134	0.253019
$959$	−30.3585	−0.980328
$960$	−1.00000	−0.0322749
$961$	63.3640	2.04400
$962$	−13.1933	−0.425369
$963$	−2.63189	−0.0848115
$964$	11.3858	0.366713
$965$	26.8755	0.865153
$966$	22.2389	0.715525
$967$	3.28619	0.105677	0.0528384	−	0.998603i	$-0.483173\pi$
$967$	3.28619	0.105677	0.0528384	+	0.998603i	$0.483173\pi$
$968$	1.00000	0.0321412
$969$	3.41051	0.109561
$970$	−16.5351	−0.530911
$971$	−42.5425	−1.36525	−0.682627	−	0.730767i	$-0.739163\pi$
$971$	−42.5425	−1.36525	−0.682627	+	0.730767i	$0.739163\pi$
$972$	−1.00000	−0.0320750
$973$	−47.7576	−1.53104
$974$	−7.43825	−0.238337
$975$	−3.41051	−0.109224
$976$	−12.1894	−0.390174
$977$	−20.3184	−0.650044	−0.325022	−	0.945706i	$-0.605372\pi$
$977$	−20.3184	−0.650044	−0.325022	+	0.945706i	$0.605372\pi$
$978$	−2.14429	−0.0685669
$979$	2.69138	0.0860170
$980$	2.39310	0.0764449
$981$	3.23879	0.103407
$982$	−25.7492	−0.821691
$983$	−24.4063	−0.778440	−0.389220	−	0.921145i	$-0.627255\pi$
$983$	−24.4063	−0.778440	−0.389220	+	0.921145i	$0.627255\pi$
$984$	−12.3210	−0.392780
$985$	−5.08222	−0.161933
$986$	−4.34569	−0.138395
$987$	−37.7616	−1.20197
$988$	11.6316	0.370049
$989$	85.7392	2.72635
$990$	1.00000	0.0317821
$991$	1.94245	0.0617039	0.0308519	−	0.999524i	$-0.490178\pi$
$991$	1.94245	0.0617039	0.0308519	+	0.999524i	$0.490178\pi$
$992$	9.71411	0.308423
$993$	−9.76154	−0.309773
$994$	13.6627	0.433355
$995$	0.693321	0.0219798
$996$	−13.2736	−0.420590
$997$	16.0601	0.508629	0.254315	−	0.967122i	$-0.418150\pi$
$997$	16.0601	0.508629	0.254315	+	0.967122i	$0.418150\pi$
$998$	8.38276	0.265351
$999$	3.86843	0.122392

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ci.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.06482 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +3.06482 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +3.41051 q^{13} +3.06482 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +3.41051 q^{19} +1.00000 q^{20} -3.06482 q^{21} +1.00000 q^{22} -7.25619 q^{23} -1.00000 q^{24} +1.00000 q^{25} +3.41051 q^{26} -1.00000 q^{27} +3.06482 q^{28} +4.34569 q^{29} -1.00000 q^{30} +9.71411 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} +3.06482 q^{35} +1.00000 q^{36} -3.86843 q^{37} +3.41051 q^{38} -3.41051 q^{39} +1.00000 q^{40} +12.3210 q^{41} -3.06482 q^{42} -11.8160 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.25619 q^{46} +12.3210 q^{47} -1.00000 q^{48} +2.39310 q^{49} +1.00000 q^{50} +1.00000 q^{51} +3.41051 q^{52} -1.14930 q^{53} -1.00000 q^{54} +1.00000 q^{55} +3.06482 q^{56} -3.41051 q^{57} +4.34569 q^{58} -6.36310 q^{59} -1.00000 q^{60} -12.1894 q^{61} +9.71411 q^{62} +3.06482 q^{63} +1.00000 q^{64} +3.41051 q^{65} -1.00000 q^{66} -5.08222 q^{67} -1.00000 q^{68} +7.25619 q^{69} +3.06482 q^{70} +4.45792 q^{71} +1.00000 q^{72} +3.14930 q^{73} -3.86843 q^{74} -1.00000 q^{75} +3.41051 q^{76} +3.06482 q^{77} -3.41051 q^{78} -10.7789 q^{79} +1.00000 q^{80} +1.00000 q^{81} +12.3210 q^{82} +13.2736 q^{83} -3.06482 q^{84} -1.00000 q^{85} -11.8160 q^{86} -4.34569 q^{87} +1.00000 q^{88} +2.69138 q^{89} +1.00000 q^{90} +10.4526 q^{91} -7.25619 q^{92} -9.71411 q^{93} +12.3210 q^{94} +3.41051 q^{95} -1.00000 q^{96} -16.5351 q^{97} +2.39310 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 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	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - q^{13} + 2 q^{14} - 5 q^{15} + 5 q^{16} - 5 q^{17} + 5 q^{18} - q^{19} + 5 q^{20} - 2 q^{21} + 5 q^{22} - 5 q^{24} + 5 q^{25} - q^{26} - 5 q^{27} + 2 q^{28} + 17 q^{29} - 5 q^{30} + 10 q^{31} + 5 q^{32} - 5 q^{33} - 5 q^{34} + 2 q^{35} + 5 q^{36} + q^{37} - q^{38} + q^{39} + 5 q^{40} + 12 q^{41} - 2 q^{42} + 7 q^{43} + 5 q^{44} + 5 q^{45} + 12 q^{47} - 5 q^{48} + 23 q^{49} + 5 q^{50} + 5 q^{51} - q^{52} + 6 q^{53} - 5 q^{54} + 5 q^{55} + 2 q^{56} + q^{57} + 17 q^{58} + 2 q^{59} - 5 q^{60} + 9 q^{61} + 10 q^{62} + 2 q^{63} + 5 q^{64} - q^{65} - 5 q^{66} + 17 q^{67} - 5 q^{68} + 2 q^{70} + 20 q^{71} + 5 q^{72} + 4 q^{73} + q^{74} - 5 q^{75} - q^{76} + 2 q^{77} + q^{78} - 2 q^{79} + 5 q^{80} + 5 q^{81} + 12 q^{82} + q^{83} - 2 q^{84} - 5 q^{85} + 7 q^{86} - 17 q^{87} + 5 q^{88} + 4 q^{89} + 5 q^{90} + 23 q^{91} - 10 q^{93} + 12 q^{94} - q^{95} - 5 q^{96} - 8 q^{97} + 23 q^{98} + 5 q^{99}+O(q^{100}) \) 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 - q^13 + 2 * q^14 - 5 * q^15 + 5 * q^16 - 5 * q^17 + 5 * q^18 - q^19 + 5 * q^20 - 2 * q^21 + 5 * q^22 - 5 * q^24 + 5 * q^25 - q^26 - 5 * q^27 + 2 * q^28 + 17 * q^29 - 5 * q^30 + 10 * q^31 + 5 * q^32 - 5 * q^33 - 5 * q^34 + 2 * q^35 + 5 * q^36 + q^37 - q^38 + q^39 + 5 * q^40 + 12 * q^41 - 2 * q^42 + 7 * q^43 + 5 * q^44 + 5 * q^45 + 12 * q^47 - 5 * q^48 + 23 * q^49 + 5 * q^50 + 5 * q^51 - q^52 + 6 * q^53 - 5 * q^54 + 5 * q^55 + 2 * q^56 + q^57 + 17 * q^58 + 2 * q^59 - 5 * q^60 + 9 * q^61 + 10 * q^62 + 2 * q^63 + 5 * q^64 - q^65 - 5 * q^66 + 17 * q^67 - 5 * q^68 + 2 * q^70 + 20 * q^71 + 5 * q^72 + 4 * q^73 + q^74 - 5 * q^75 - q^76 + 2 * q^77 + q^78 - 2 * q^79 + 5 * q^80 + 5 * q^81 + 12 * q^82 + q^83 - 2 * q^84 - 5 * q^85 + 7 * q^86 - 17 * q^87 + 5 * q^88 + 4 * q^89 + 5 * q^90 + 23 * q^91 - 10 * q^93 + 12 * q^94 - q^95 - 5 * q^96 - 8 * q^97 + 23 * q^98 + 5 * q^99

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