LMFDB - Embedded newform 5610.2.a.ci.1.2

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			1.2
Root			$-2.65676$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.13372 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.13372 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -6.38639 q^{13} -3.13372 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -6.38639 q^{19} +1.00000 q^{20} +3.13372 q^{21} +1.00000 q^{22} -7.44697 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.38639 q^{26} -1.00000 q^{27} -3.13372 q^{28} +0.747335 q^{29} -1.00000 q^{30} +4.13346 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -3.13372 q^{35} +1.00000 q^{36} +11.6999 q^{37} -6.38639 q^{38} +6.38639 q^{39} +1.00000 q^{40} +6.31325 q^{41} +3.13372 q^{42} +10.7583 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.44697 q^{46} +6.31325 q^{47} -1.00000 q^{48} +2.82021 q^{49} +1.00000 q^{50} +1.00000 q^{51} -6.38639 q^{52} +11.8188 q^{53} -1.00000 q^{54} +1.00000 q^{55} -3.13372 q^{56} +6.38639 q^{57} +0.747335 q^{58} +7.45926 q^{59} -1.00000 q^{60} +9.38665 q^{61} +4.13346 q^{62} -3.13372 q^{63} +1.00000 q^{64} -6.38639 q^{65} -1.00000 q^{66} +11.3403 q^{67} -1.00000 q^{68} +7.44697 q^{69} -3.13372 q^{70} -1.31351 q^{71} +1.00000 q^{72} -9.81884 q^{73} +11.6999 q^{74} -1.00000 q^{75} -6.38639 q^{76} -3.13372 q^{77} +6.38639 q^{78} +1.00027 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.31325 q^{82} +3.24038 q^{83} +3.13372 q^{84} -1.00000 q^{85} +10.7583 q^{86} -0.747335 q^{87} +1.00000 q^{88} -4.50533 q^{89} +1.00000 q^{90} +20.0131 q^{91} -7.44697 q^{92} -4.13346 q^{93} +6.31325 q^{94} -6.38639 q^{95} -1.00000 q^{96} +8.63932 q^{97} +2.82021 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−3.13372	−1.18444	−0.592218	−	0.805778i	$-0.701747\pi$
$7$	−3.13372	−1.18444	−0.592218	+	0.805778i	$0.701747\pi$
$8$	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
$13$	−6.38639	−1.77126	−0.885632	−	0.464387i	$-0.846275\pi$
$13$	−6.38639	−1.77126	−0.885632	+	0.464387i	$0.846275\pi$
$14$	−3.13372	−0.837522
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−6.38639	−1.46514	−0.732569	−	0.680693i	$-0.761679\pi$
$19$	−6.38639	−1.46514	−0.732569	+	0.680693i	$0.761679\pi$
$20$	1.00000	0.223607
$21$	3.13372	0.683834
$22$	1.00000	0.213201
$23$	−7.44697	−1.55280	−0.776400	−	0.630240i	$-0.782956\pi$
$23$	−7.44697	−1.55280	−0.776400	+	0.630240i	$0.782956\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−6.38639	−1.25247
$27$	−1.00000	−0.192450
$28$	−3.13372	−0.592218
$29$	0.747335	0.138777	0.0693883	−	0.997590i	$-0.477895\pi$
$29$	0.747335	0.138777	0.0693883	+	0.997590i	$0.477895\pi$
$30$	−1.00000	−0.182574
$31$	4.13346	0.742391	0.371195	−	0.928555i	$-0.378948\pi$
$31$	4.13346	0.742391	0.371195	+	0.928555i	$0.378948\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−1.00000	−0.171499
$35$	−3.13372	−0.529695
$36$	1.00000	0.166667
$37$	11.6999	1.92345	0.961726	−	0.274013i	$-0.0883513\pi$
$37$	11.6999	1.92345	0.961726	+	0.274013i	$0.0883513\pi$
$38$	−6.38639	−1.03601
$39$	6.38639	1.02264
$40$	1.00000	0.158114
$41$	6.31325	0.985964	0.492982	−	0.870040i	$-0.335907\pi$
$41$	6.31325	0.985964	0.492982	+	0.870040i	$0.335907\pi$
$42$	3.13372	0.483544
$43$	10.7583	1.64062	0.820310	−	0.571920i	$-0.193801\pi$
$43$	10.7583	1.64062	0.820310	+	0.571920i	$0.193801\pi$
$44$	1.00000	0.150756
$45$	1.00000	0.149071
$46$	−7.44697	−1.09800
$47$	6.31325	0.920882	0.460441	−	0.887690i	$-0.347691\pi$
$47$	6.31325	0.920882	0.460441	+	0.887690i	$0.347691\pi$
$48$	−1.00000	−0.144338
$49$	2.82021	0.402887
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	−6.38639	−0.885632
$53$	11.8188	1.62344	0.811722	−	0.584045i	$-0.198531\pi$
$53$	11.8188	1.62344	0.811722	+	0.584045i	$0.198531\pi$
$54$	−1.00000	−0.136083
$55$	1.00000	0.134840
$56$	−3.13372	−0.418761
$57$	6.38639	0.845897
$58$	0.747335	0.0981299
$59$	7.45926	0.971112	0.485556	−	0.874205i	$-0.338617\pi$
$59$	7.45926	0.971112	0.485556	+	0.874205i	$0.338617\pi$
$60$	−1.00000	−0.129099
$61$	9.38665	1.20184	0.600919	−	0.799310i	$-0.294802\pi$
$61$	9.38665	1.20184	0.600919	+	0.799310i	$0.294802\pi$
$62$	4.13346	0.524949
$63$	−3.13372	−0.394812
$64$	1.00000	0.125000
$65$	−6.38639	−0.792134
$66$	−1.00000	−0.123091
$67$	11.3403	1.38544	0.692720	−	0.721207i	$-0.256412\pi$
$67$	11.3403	1.38544	0.692720	+	0.721207i	$0.256412\pi$
$68$	−1.00000	−0.121268
$69$	7.44697	0.896510
$70$	−3.13372	−0.374551
$71$	−1.31351	−0.155886	−0.0779428	−	0.996958i	$-0.524835\pi$
$71$	−1.31351	−0.155886	−0.0779428	+	0.996958i	$0.524835\pi$
$72$	1.00000	0.117851
$73$	−9.81884	−1.14921	−0.574604	−	0.818431i	$-0.694844\pi$
$73$	−9.81884	−1.14921	−0.574604	+	0.818431i	$0.694844\pi$
$74$	11.6999	1.36009
$75$	−1.00000	−0.115470
$76$	−6.38639	−0.732569
$77$	−3.13372	−0.357121
$78$	6.38639	0.723116
$79$	1.00027	0.112539	0.0562693	−	0.998416i	$-0.482079\pi$
$79$	1.00027	0.112539	0.0562693	+	0.998416i	$0.482079\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	6.31325	0.697182
$83$	3.24038	0.355678	0.177839	−	0.984060i	$-0.443089\pi$
$83$	3.24038	0.355678	0.177839	+	0.984060i	$0.443089\pi$
$84$	3.13372	0.341917
$85$	−1.00000	−0.108465
$86$	10.7583	1.16009
$87$	−0.747335	−0.0801228
$88$	1.00000	0.106600
$89$	−4.50533	−0.477564	−0.238782	−	0.971073i	$-0.576748\pi$
$89$	−4.50533	−0.477564	−0.238782	+	0.971073i	$0.576748\pi$
$90$	1.00000	0.105409
$91$	20.0131	2.09795
$92$	−7.44697	−0.776400
$93$	−4.13346	−0.428619
$94$	6.31325	0.651162
$95$	−6.38639	−0.655229
$96$	−1.00000	−0.102062
$97$	8.63932	0.877190	0.438595	−	0.898685i	$-0.355476\pi$
$97$	8.63932	0.877190	0.438595	+	0.898685i	$0.355476\pi$
$98$	2.82021	0.284884
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	−0.192080	−0.0191127	−0.00955635	−	0.999954i	$-0.503042\pi$
$101$	−0.192080	−0.0191127	−0.00955635	+	0.999954i	$0.503042\pi$
$102$	1.00000	0.0990148
$103$	−12.6851	−1.24990	−0.624951	−	0.780664i	$-0.714881\pi$
$103$	−12.6851	−1.24990	−0.624951	+	0.780664i	$0.714881\pi$
$104$	−6.38639	−0.626237
$105$	3.13372	0.305820
$106$	11.8188	1.14795
$107$	−13.4738	−1.30256	−0.651279	−	0.758838i	$-0.725767\pi$
$107$	−13.4738	−1.30256	−0.651279	+	0.758838i	$0.725767\pi$
$108$	−1.00000	−0.0962250
$109$	13.6536	1.30777	0.653887	−	0.756592i	$-0.273137\pi$
$109$	13.6536	1.30777	0.653887	+	0.756592i	$0.273137\pi$
$110$	1.00000	0.0953463
$111$	−11.6999	−1.11051
$112$	−3.13372	−0.296109
$113$	−5.86518	−0.551750	−0.275875	−	0.961194i	$-0.588968\pi$
$113$	−5.86518	−0.551750	−0.275875	+	0.961194i	$0.588968\pi$
$114$	6.38639	0.598140
$115$	−7.44697	−0.694434
$116$	0.747335	0.0693883
$117$	−6.38639	−0.590422
$118$	7.45926	0.686680
$119$	3.13372	0.287268
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	9.38665	0.849827
$123$	−6.31325	−0.569247
$124$	4.13346	0.371195
$125$	1.00000	0.0894427
$126$	−3.13372	−0.279174
$127$	−6.67284	−0.592119	−0.296059	−	0.955170i	$-0.595673\pi$
$127$	−6.67284	−0.592119	−0.296059	+	0.955170i	$0.595673\pi$
$128$	1.00000	0.0883883
$129$	−10.7583	−0.947212
$130$	−6.38639	−0.560123
$131$	−3.62454	−0.316677	−0.158339	−	0.987385i	$-0.550614\pi$
$131$	−3.62454	−0.316677	−0.158339	+	0.987385i	$0.550614\pi$
$132$	−1.00000	−0.0870388
$133$	20.0131	1.73536
$134$	11.3403	0.979654
$135$	−1.00000	−0.0860663
$136$	−1.00000	−0.0857493
$137$	−10.7141	−0.915371	−0.457686	−	0.889114i	$-0.651321\pi$
$137$	−10.7141	−0.915371	−0.457686	+	0.889114i	$0.651321\pi$
$138$	7.44697	0.633928
$139$	5.56644	0.472140	0.236070	−	0.971736i	$-0.424141\pi$
$139$	5.56644	0.472140	0.236070	+	0.971736i	$0.424141\pi$
$140$	−3.13372	−0.264848
$141$	−6.31325	−0.531672
$142$	−1.31351	−0.110228
$143$	−6.38639	−0.534056
$144$	1.00000	0.0833333
$145$	0.747335	0.0620628
$146$	−9.81884	−0.812613
$147$	−2.82021	−0.232607
$148$	11.6999	0.961726
$149$	9.07340	0.743322	0.371661	−	0.928369i	$-0.378788\pi$
$149$	9.07340	0.743322	0.371661	+	0.928369i	$0.378788\pi$
$150$	−1.00000	−0.0816497
$151$	−2.83498	−0.230708	−0.115354	−	0.993324i	$-0.536800\pi$
$151$	−2.83498	−0.230708	−0.115354	+	0.993324i	$0.536800\pi$
$152$	−6.38639	−0.518004
$153$	−1.00000	−0.0808452
$154$	−3.13372	−0.252522
$155$	4.13346	0.332007
$156$	6.38639	0.511320
$157$	5.95366	0.475154	0.237577	−	0.971369i	$-0.423647\pi$
$157$	5.95366	0.475154	0.237577	+	0.971369i	$0.423647\pi$
$158$	1.00027	0.0795768
$159$	−11.8188	−0.937295
$160$	1.00000	0.0790569
$161$	23.3367	1.83919
$162$	1.00000	0.0785674
$163$	−13.8043	−1.08124	−0.540619	−	0.841267i	$-0.681810\pi$
$163$	−13.8043	−1.08124	−0.540619	+	0.841267i	$0.681810\pi$
$164$	6.31325	0.492982
$165$	−1.00000	−0.0778499
$166$	3.24038	0.251502
$167$	−14.5812	−1.12833	−0.564164	−	0.825662i	$-0.690802\pi$
$167$	−14.5812	−1.12833	−0.564164	+	0.825662i	$0.690802\pi$
$168$	3.13372	0.241772
$169$	27.7859	2.13738
$170$	−1.00000	−0.0766965
$171$	−6.38639	−0.488379
$172$	10.7583	0.820310
$173$	−20.3264	−1.54539	−0.772694	−	0.634779i	$-0.781091\pi$
$173$	−20.3264	−1.54539	−0.772694	+	0.634779i	$0.781091\pi$
$174$	−0.747335	−0.0566553
$175$	−3.13372	−0.236887
$176$	1.00000	0.0753778
$177$	−7.45926	−0.560672
$178$	−4.50533	−0.337689
$179$	−8.46122	−0.632421	−0.316211	−	0.948689i	$-0.602411\pi$
$179$	−8.46122	−0.632421	−0.316211	+	0.948689i	$0.602411\pi$
$180$	1.00000	0.0745356
$181$	24.0254	1.78580	0.892898	−	0.450258i	$-0.148668\pi$
$181$	24.0254	1.78580	0.892898	+	0.450258i	$0.148668\pi$
$182$	20.0131	1.48347
$183$	−9.38665	−0.693881
$184$	−7.44697	−0.548998
$185$	11.6999	0.860194
$186$	−4.13346	−0.303080
$187$	−1.00000	−0.0731272
$188$	6.31325	0.460441
$189$	3.13372	0.227945
$190$	−6.38639	−0.463317
$191$	15.8797	1.14901	0.574507	−	0.818500i	$-0.305194\pi$
$191$	15.8797	1.14901	0.574507	+	0.818500i	$0.305194\pi$
$192$	−1.00000	−0.0721688
$193$	13.4347	0.967050	0.483525	−	0.875331i	$-0.339356\pi$
$193$	13.4347	0.967050	0.483525	+	0.875331i	$0.339356\pi$
$194$	8.63932	0.620267
$195$	6.38639	0.457339
$196$	2.82021	0.201443
$197$	11.3403	0.807964	0.403982	−	0.914767i	$-0.367626\pi$
$197$	11.3403	0.807964	0.403982	+	0.914767i	$0.367626\pi$
$198$	1.00000	0.0710669
$199$	21.4620	1.52140	0.760701	−	0.649103i	$-0.224855\pi$
$199$	21.4620	1.52140	0.760701	+	0.649103i	$0.224855\pi$
$200$	1.00000	0.0707107
$201$	−11.3403	−0.799884
$202$	−0.192080	−0.0135147
$203$	−2.34194	−0.164372
$204$	1.00000	0.0700140
$205$	6.31325	0.440936
$206$	−12.6851	−0.883814
$207$	−7.44697	−0.517600
$208$	−6.38639	−0.442816
$209$	−6.38639	−0.441756
$210$	3.13372	0.216247
$211$	−3.56591	−0.245488	−0.122744	−	0.992438i	$-0.539169\pi$
$211$	−3.56591	−0.245488	−0.122744	+	0.992438i	$0.539169\pi$
$212$	11.8188	0.811722
$213$	1.31351	0.0900005
$214$	−13.4738	−0.921048
$215$	10.7583	0.733707
$216$	−1.00000	−0.0680414
$217$	−12.9531	−0.879313
$218$	13.6536	0.924736
$219$	9.81884	0.663496
$220$	1.00000	0.0674200
$221$	6.38639	0.429595
$222$	−11.6999	−0.785246
$223$	−14.4467	−0.967423	−0.483711	−	0.875228i	$-0.660712\pi$
$223$	−14.4467	−0.967423	−0.483711	+	0.875228i	$0.660712\pi$
$224$	−3.13372	−0.209381
$225$	1.00000	0.0666667
$226$	−5.86518	−0.390146
$227$	9.06058	0.601372	0.300686	−	0.953723i	$-0.402784\pi$
$227$	9.06058	0.601372	0.300686	+	0.953723i	$0.402784\pi$
$228$	6.38639	0.422949
$229$	−15.8920	−1.05017	−0.525086	−	0.851049i	$-0.675967\pi$
$229$	−15.8920	−1.05017	−0.525086	+	0.851049i	$0.675967\pi$
$230$	−7.44697	−0.491039
$231$	3.13372	0.206184
$232$	0.747335	0.0490650
$233$	23.8334	1.56138	0.780688	−	0.624922i	$-0.214869\pi$
$233$	23.8334	1.56138	0.780688	+	0.624922i	$0.214869\pi$
$234$	−6.38639	−0.417491
$235$	6.31325	0.411831
$236$	7.45926	0.485556
$237$	−1.00027	−0.0649742
$238$	3.13372	0.203129
$239$	4.26691	0.276004	0.138002	−	0.990432i	$-0.455932\pi$
$239$	4.26691	0.276004	0.138002	+	0.990432i	$0.455932\pi$
$240$	−1.00000	−0.0645497
$241$	−0.820472	−0.0528512	−0.0264256	−	0.999651i	$-0.508413\pi$
$241$	−0.820472	−0.0528512	−0.0264256	+	0.999651i	$0.508413\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	9.38665	0.600919
$245$	2.82021	0.180176
$246$	−6.31325	−0.402518
$247$	40.7859	2.59515
$248$	4.13346	0.262475
$249$	−3.24038	−0.205351
$250$	1.00000	0.0632456
$251$	27.1128	1.71135	0.855673	−	0.517517i	$-0.173144\pi$
$251$	27.1128	1.71135	0.855673	+	0.517517i	$0.173144\pi$
$252$	−3.13372	−0.197406
$253$	−7.44697	−0.468187
$254$	−6.67284	−0.418691
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−30.4604	−1.90007	−0.950033	−	0.312149i	$-0.898951\pi$
$257$	−30.4604	−1.90007	−0.950033	+	0.312149i	$0.898951\pi$
$258$	−10.7583	−0.669780
$259$	−36.6642	−2.27820
$260$	−6.38639	−0.396067
$261$	0.747335	0.0462589
$262$	−3.62454	−0.223925
$263$	9.07373	0.559510	0.279755	−	0.960071i	$-0.409747\pi$
$263$	9.07373	0.559510	0.279755	+	0.960071i	$0.409747\pi$
$264$	−1.00000	−0.0615457
$265$	11.8188	0.726026
$266$	20.0131	1.22708
$267$	4.50533	0.275722
$268$	11.3403	0.692720
$269$	−15.6831	−0.956216	−0.478108	−	0.878301i	$-0.658677\pi$
$269$	−15.6831	−0.956216	−0.478108	+	0.878301i	$0.658677\pi$
$270$	−1.00000	−0.0608581
$271$	−11.2822	−0.685346	−0.342673	−	0.939455i	$-0.611332\pi$
$271$	−11.2822	−0.685346	−0.342673	+	0.939455i	$0.611332\pi$
$272$	−1.00000	−0.0606339
$273$	−20.0131	−1.21125
$274$	−10.7141	−0.647265
$275$	1.00000	0.0603023
$276$	7.44697	0.448255
$277$	−25.6913	−1.54364	−0.771820	−	0.635841i	$-0.780653\pi$
$277$	−25.6913	−1.54364	−0.771820	+	0.635841i	$0.780653\pi$
$278$	5.56644	0.333853
$279$	4.13346	0.247464
$280$	−3.13372	−0.187276
$281$	27.8334	1.66040	0.830199	−	0.557467i	$-0.188227\pi$
$281$	27.8334	1.66040	0.830199	+	0.557467i	$0.188227\pi$
$282$	−6.31325	−0.375949
$283$	21.7589	1.29343	0.646715	−	0.762732i	$-0.276142\pi$
$283$	21.7589	1.29343	0.646715	+	0.762732i	$0.276142\pi$
$284$	−1.31351	−0.0779428
$285$	6.38639	0.378297
$286$	−6.38639	−0.377635
$287$	−19.7840	−1.16781
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	0.747335	0.0438850
$291$	−8.63932	−0.506446
$292$	−9.81884	−0.574604
$293$	−0.312917	−0.0182808	−0.00914040	−	0.999958i	$-0.502910\pi$
$293$	−0.312917	−0.0182808	−0.00914040	+	0.999958i	$0.502910\pi$
$294$	−2.82021	−0.164478
$295$	7.45926	0.434295
$296$	11.6999	0.680043
$297$	−1.00000	−0.0580259
$298$	9.07340	0.525608
$299$	47.5592	2.75042
$300$	−1.00000	−0.0577350
$301$	−33.7134	−1.94321
$302$	−2.83498	−0.163135
$303$	0.192080	0.0110347
$304$	−6.38639	−0.366284
$305$	9.38665	0.537478
$306$	−1.00000	−0.0571662
$307$	−9.96459	−0.568709	−0.284354	−	0.958719i	$-0.591779\pi$
$307$	−9.96459	−0.568709	−0.284354	+	0.958719i	$0.591779\pi$
$308$	−3.13372	−0.178560
$309$	12.6851	0.721631
$310$	4.13346	0.234764
$311$	1.28449	0.0728368	0.0364184	−	0.999337i	$-0.488405\pi$
$311$	1.28449	0.0728368	0.0364184	+	0.999337i	$0.488405\pi$
$312$	6.38639	0.361558
$313$	4.27973	0.241905	0.120952	−	0.992658i	$-0.461405\pi$
$313$	4.27973	0.241905	0.120952	+	0.992658i	$0.461405\pi$
$314$	5.95366	0.335985
$315$	−3.13372	−0.176565
$316$	1.00027	0.0562693
$317$	23.9551	1.34545	0.672725	−	0.739893i	$-0.265124\pi$
$317$	23.9551	1.34545	0.672725	+	0.739893i	$0.265124\pi$
$318$	−11.8188	−0.662768
$319$	0.747335	0.0418427
$320$	1.00000	0.0559017
$321$	13.4738	0.752032
$322$	23.3367	1.30050
$323$	6.38639	0.355348
$324$	1.00000	0.0555556
$325$	−6.38639	−0.354253
$326$	−13.8043	−0.764551
$327$	−13.6536	−0.755044
$328$	6.31325	0.348591
$329$	−19.7840	−1.09073
$330$	−1.00000	−0.0550482
$331$	−18.9657	−1.04245	−0.521225	−	0.853419i	$-0.674525\pi$
$331$	−18.9657	−1.04245	−0.521225	+	0.853419i	$0.674525\pi$
$332$	3.24038	0.177839
$333$	11.6999	0.641151
$334$	−14.5812	−0.797849
$335$	11.3403	0.619587
$336$	3.13372	0.170958
$337$	7.28449	0.396812	0.198406	−	0.980120i	$-0.436424\pi$
$337$	7.28449	0.396812	0.198406	+	0.980120i	$0.436424\pi$
$338$	27.7859	1.51135
$339$	5.86518	0.318553
$340$	−1.00000	−0.0542326
$341$	4.13346	0.223839
$342$	−6.38639	−0.345336
$343$	13.0983	0.707242
$344$	10.7583	0.580046
$345$	7.44697	0.400931
$346$	−20.3264	−1.09275
$347$	−28.0263	−1.50453	−0.752265	−	0.658860i	$-0.771039\pi$
$347$	−28.0263	−1.50453	−0.752265	+	0.658860i	$0.771039\pi$
$348$	−0.747335	−0.0400614
$349$	−28.3247	−1.51619	−0.758093	−	0.652146i	$-0.773869\pi$
$349$	−28.3247	−1.51619	−0.758093	+	0.652146i	$0.773869\pi$
$350$	−3.13372	−0.167504
$351$	6.38639	0.340880
$352$	1.00000	0.0533002
$353$	−6.47626	−0.344696	−0.172348	−	0.985036i	$-0.555135\pi$
$353$	−6.47626	−0.344696	−0.172348	+	0.985036i	$0.555135\pi$
$354$	−7.45926	−0.396455
$355$	−1.31351	−0.0697141
$356$	−4.50533	−0.238782
$357$	−3.13372	−0.165854
$358$	−8.46122	−0.447189
$359$	−12.2680	−0.647479	−0.323739	−	0.946146i	$-0.604940\pi$
$359$	−12.2680	−0.647479	−0.323739	+	0.946146i	$0.604940\pi$
$360$	1.00000	0.0527046
$361$	21.7859	1.14663
$362$	24.0254	1.26275
$363$	−1.00000	−0.0524864
$364$	20.0131	1.04897
$365$	−9.81884	−0.513942
$366$	−9.38665	−0.490648
$367$	6.77277	0.353536	0.176768	−	0.984253i	$-0.443436\pi$
$367$	6.77277	0.353536	0.176768	+	0.984253i	$0.443436\pi$
$368$	−7.44697	−0.388200
$369$	6.31325	0.328655
$370$	11.6999	0.608249
$371$	−37.0370	−1.92286
$372$	−4.13346	−0.214310
$373$	−15.7479	−0.815397	−0.407699	−	0.913117i	$-0.633669\pi$
$373$	−15.7479	−0.815397	−0.407699	+	0.913117i	$0.633669\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	6.31325	0.325581
$377$	−4.77277	−0.245810
$378$	3.13372	0.161181
$379$	−18.2516	−0.937520	−0.468760	−	0.883326i	$-0.655299\pi$
$379$	−18.2516	−0.937520	−0.468760	+	0.883326i	$0.655299\pi$
$380$	−6.38639	−0.327615
$381$	6.67284	0.341860
$382$	15.8797	0.812476
$383$	−22.3132	−1.14015	−0.570077	−	0.821591i	$-0.693087\pi$
$383$	−22.3132	−1.14015	−0.570077	+	0.821591i	$0.693087\pi$
$384$	−1.00000	−0.0510310
$385$	−3.13372	−0.159709
$386$	13.4347	0.683807
$387$	10.7583	0.546873
$388$	8.63932	0.438595
$389$	13.2672	0.672673	0.336336	−	0.941742i	$-0.390812\pi$
$389$	13.2672	0.672673	0.336336	+	0.941742i	$0.390812\pi$
$390$	6.38639	0.323387
$391$	7.44697	0.376609
$392$	2.82021	0.142442
$393$	3.62454	0.182834
$394$	11.3403	0.571317
$395$	1.00027	0.0503288
$396$	1.00000	0.0502519
$397$	35.0866	1.76094	0.880472	−	0.474099i	$-0.157226\pi$
$397$	35.0866	1.76094	0.880472	+	0.474099i	$0.157226\pi$
$398$	21.4620	1.07579
$399$	−20.0131	−1.00191
$400$	1.00000	0.0500000
$401$	27.9070	1.39361	0.696805	−	0.717261i	$-0.254604\pi$
$401$	27.9070	1.39361	0.696805	+	0.717261i	$0.254604\pi$
$402$	−11.3403	−0.565603
$403$	−26.3978	−1.31497
$404$	−0.192080	−0.00955635
$405$	1.00000	0.0496904
$406$	−2.34194	−0.116229
$407$	11.6999	0.579943
$408$	1.00000	0.0495074
$409$	−4.59694	−0.227304	−0.113652	−	0.993521i	$-0.536255\pi$
$409$	−4.59694	−0.227304	−0.113652	+	0.993521i	$0.536255\pi$
$410$	6.31325	0.311789
$411$	10.7141	0.528490
$412$	−12.6851	−0.624951
$413$	−23.3752	−1.15022
$414$	−7.44697	−0.365999
$415$	3.24038	0.159064
$416$	−6.38639	−0.313118
$417$	−5.56644	−0.272590
$418$	−6.38639	−0.312368
$419$	15.7122	0.767591	0.383795	−	0.923418i	$-0.374617\pi$
$419$	15.7122	0.767591	0.383795	+	0.923418i	$0.374617\pi$
$420$	3.13372	0.152910
$421$	32.6648	1.59198	0.795991	−	0.605308i	$-0.206950\pi$
$421$	32.6648	1.59198	0.795991	+	0.605308i	$0.206950\pi$
$422$	−3.56591	−0.173586
$423$	6.31325	0.306961
$424$	11.8188	0.573974
$425$	−1.00000	−0.0485071
$426$	1.31351	0.0636400
$427$	−29.4151	−1.42350
$428$	−13.4738	−0.651279
$429$	6.38639	0.308338
$430$	10.7583	0.518809
$431$	20.9394	1.00862	0.504308	−	0.863524i	$-0.331748\pi$
$431$	20.9394	1.00862	0.504308	+	0.863524i	$0.331748\pi$
$432$	−1.00000	−0.0481125
$433$	15.7589	0.757322	0.378661	−	0.925535i	$-0.376385\pi$
$433$	15.7589	0.757322	0.378661	+	0.925535i	$0.376385\pi$
$434$	−12.9531	−0.621768
$435$	−0.747335	−0.0358320
$436$	13.6536	0.653887
$437$	47.5592	2.27507
$438$	9.81884	0.469163
$439$	16.5163	0.788278	0.394139	−	0.919051i	$-0.371043\pi$
$439$	16.5163	0.788278	0.394139	+	0.919051i	$0.371043\pi$
$440$	1.00000	0.0476731
$441$	2.82021	0.134296
$442$	6.38639	0.303769
$443$	−28.9258	−1.37430	−0.687152	−	0.726513i	$-0.741140\pi$
$443$	−28.9258	−1.37430	−0.687152	+	0.726513i	$0.741140\pi$
$444$	−11.6999	−0.555253
$445$	−4.50533	−0.213573
$446$	−14.4467	−0.684071
$447$	−9.07340	−0.429157
$448$	−3.13372	−0.148054
$449$	−8.29012	−0.391235	−0.195618	−	0.980680i	$-0.562671\pi$
$449$	−8.29012	−0.391235	−0.195618	+	0.980680i	$0.562671\pi$
$450$	1.00000	0.0471405
$451$	6.31325	0.297279
$452$	−5.86518	−0.275875
$453$	2.83498	0.133199
$454$	9.06058	0.425234
$455$	20.0131	0.938231
$456$	6.38639	0.299070
$457$	−30.6943	−1.43582	−0.717910	−	0.696136i	$-0.754901\pi$
$457$	−30.6943	−1.43582	−0.717910	+	0.696136i	$0.754901\pi$
$458$	−15.8920	−0.742583
$459$	1.00000	0.0466760
$460$	−7.44697	−0.347217
$461$	−10.1915	−0.474668	−0.237334	−	0.971428i	$-0.576274\pi$
$461$	−10.1915	−0.474668	−0.237334	+	0.971428i	$0.576274\pi$
$462$	3.13372	0.145794
$463$	5.92100	0.275172	0.137586	−	0.990490i	$-0.456066\pi$
$463$	5.92100	0.275172	0.137586	+	0.990490i	$0.456066\pi$
$464$	0.747335	0.0346942
$465$	−4.13346	−0.191684
$466$	23.8334	1.10406
$467$	27.0260	1.25062	0.625308	−	0.780378i	$-0.284973\pi$
$467$	27.0260	1.25062	0.625308	+	0.780378i	$0.284973\pi$
$468$	−6.38639	−0.295211
$469$	−35.5374	−1.64096
$470$	6.31325	0.291208
$471$	−5.95366	−0.274330
$472$	7.45926	0.343340
$473$	10.7583	0.494665
$474$	−1.00027	−0.0459437
$475$	−6.38639	−0.293027
$476$	3.13372	0.143634
$477$	11.8188	0.541148
$478$	4.26691	0.195164
$479$	30.2301	1.38125	0.690625	−	0.723213i	$-0.257336\pi$
$479$	30.2301	1.38125	0.690625	+	0.723213i	$0.257336\pi$
$480$	−1.00000	−0.0456435
$481$	−74.7201	−3.40694
$482$	−0.820472	−0.0373715
$483$	−23.3367	−1.06186
$484$	1.00000	0.0454545
$485$	8.63932	0.392291
$486$	−1.00000	−0.0453609
$487$	−2.23789	−0.101408	−0.0507042	−	0.998714i	$-0.516147\pi$
$487$	−2.23789	−0.101408	−0.0507042	+	0.998714i	$0.516147\pi$
$488$	9.38665	0.424914
$489$	13.8043	0.624253
$490$	2.82021	0.127404
$491$	−8.58016	−0.387217	−0.193609	−	0.981079i	$-0.562019\pi$
$491$	−8.58016	−0.387217	−0.193609	+	0.981079i	$0.562019\pi$
$492$	−6.31325	−0.284623
$493$	−0.747335	−0.0336583
$494$	40.7859	1.83505
$495$	1.00000	0.0449467
$496$	4.13346	0.185598
$497$	4.11619	0.184636
$498$	−3.24038	−0.145205
$499$	21.1614	0.947314	0.473657	−	0.880710i	$-0.342934\pi$
$499$	21.1614	0.947314	0.473657	+	0.880710i	$0.342934\pi$
$500$	1.00000	0.0447214
$501$	14.5812	0.651441
$502$	27.1128	1.21010
$503$	−22.5511	−1.00551	−0.502753	−	0.864430i	$-0.667679\pi$
$503$	−22.5511	−1.00551	−0.502753	+	0.864430i	$0.667679\pi$
$504$	−3.13372	−0.139587
$505$	−0.192080	−0.00854746
$506$	−7.44697	−0.331058
$507$	−27.7859	−1.23402
$508$	−6.67284	−0.296059
$509$	11.7479	0.520718	0.260359	−	0.965512i	$-0.416159\pi$
$509$	11.7479	0.520718	0.260359	+	0.965512i	$0.416159\pi$
$510$	1.00000	0.0442807
$511$	30.7695	1.36116
$512$	1.00000	0.0441942
$513$	6.38639	0.281966
$514$	−30.4604	−1.34355
$515$	−12.6851	−0.558973
$516$	−10.7583	−0.473606
$517$	6.31325	0.277656
$518$	−36.6642	−1.61093
$519$	20.3264	0.892230
$520$	−6.38639	−0.280062
$521$	18.5785	0.813937	0.406969	−	0.913442i	$-0.366586\pi$
$521$	18.5785	0.813937	0.406969	+	0.913442i	$0.366586\pi$
$522$	0.747335	0.0327100
$523$	−37.3216	−1.63196	−0.815981	−	0.578079i	$-0.803802\pi$
$523$	−37.3216	−1.63196	−0.815981	+	0.578079i	$0.803802\pi$
$524$	−3.62454	−0.158339
$525$	3.13372	0.136767
$526$	9.07373	0.395634
$527$	−4.13346	−0.180056
$528$	−1.00000	−0.0435194
$529$	32.4574	1.41119
$530$	11.8188	0.513378
$531$	7.45926	0.323704
$532$	20.0131	0.867680
$533$	−40.3188	−1.74640
$534$	4.50533	0.194965
$535$	−13.4738	−0.582522
$536$	11.3403	0.489827
$537$	8.46122	0.365128
$538$	−15.6831	−0.676147
$539$	2.82021	0.121475
$540$	−1.00000	−0.0430331
$541$	−45.0621	−1.93737	−0.968685	−	0.248294i	$-0.920130\pi$
$541$	−45.0621	−1.93737	−0.968685	+	0.248294i	$0.920130\pi$
$542$	−11.2822	−0.484613
$543$	−24.0254	−1.03103
$544$	−1.00000	−0.0428746
$545$	13.6536	0.584854
$546$	−20.0131	−0.856484
$547$	22.4258	0.958858	0.479429	−	0.877581i	$-0.340844\pi$
$547$	22.4258	0.958858	0.479429	+	0.877581i	$0.340844\pi$
$548$	−10.7141	−0.457686
$549$	9.38665	0.400612
$550$	1.00000	0.0426401
$551$	−4.77277	−0.203327
$552$	7.44697	0.316964
$553$	−3.13455	−0.133295
$554$	−25.6913	−1.09152
$555$	−11.6999	−0.496633
$556$	5.56644	0.236070
$557$	−33.2326	−1.40811	−0.704056	−	0.710145i	$-0.748630\pi$
$557$	−33.2326	−1.40811	−0.704056	+	0.710145i	$0.748630\pi$
$558$	4.13346	0.174983
$559$	−68.7064	−2.90597
$560$	−3.13372	−0.132424
$561$	1.00000	0.0422200
$562$	27.8334	1.17408
$563$	−19.5329	−0.823215	−0.411607	−	0.911361i	$-0.635032\pi$
$563$	−19.5329	−0.823215	−0.411607	+	0.911361i	$0.635032\pi$
$564$	−6.31325	−0.265836
$565$	−5.86518	−0.246750
$566$	21.7589	0.914593
$567$	−3.13372	−0.131604
$568$	−1.31351	−0.0551138
$569$	44.4241	1.86236	0.931178	−	0.364564i	$-0.118782\pi$
$569$	44.4241	1.86236	0.931178	+	0.364564i	$0.118782\pi$
$570$	6.38639	0.267496
$571$	−7.22723	−0.302450	−0.151225	−	0.988499i	$-0.548322\pi$
$571$	−7.22723	−0.302450	−0.151225	+	0.988499i	$0.548322\pi$
$572$	−6.38639	−0.267028
$573$	−15.8797	−0.663384
$574$	−19.7840	−0.825767
$575$	−7.44697	−0.310560
$576$	1.00000	0.0416667
$577$	−9.63769	−0.401222	−0.200611	−	0.979671i	$-0.564293\pi$
$577$	−9.63769	−0.401222	−0.200611	+	0.979671i	$0.564293\pi$
$578$	1.00000	0.0415945
$579$	−13.4347	−0.558326
$580$	0.747335	0.0310314
$581$	−10.1544	−0.421277
$582$	−8.63932	−0.358111
$583$	11.8188	0.489487
$584$	−9.81884	−0.406307
$585$	−6.38639	−0.264045
$586$	−0.312917	−0.0129265
$587$	−2.51205	−0.103684	−0.0518418	−	0.998655i	$-0.516509\pi$
$587$	−2.51205	−0.103684	−0.0518418	+	0.998655i	$0.516509\pi$
$588$	−2.82021	−0.116303
$589$	−26.3978	−1.08770
$590$	7.45926	0.307093
$591$	−11.3403	−0.466478
$592$	11.6999	0.480863
$593$	−14.6265	−0.600638	−0.300319	−	0.953839i	$-0.597093\pi$
$593$	−14.6265	−0.600638	−0.300319	+	0.953839i	$0.597093\pi$
$594$	−1.00000	−0.0410305
$595$	3.13372	0.128470
$596$	9.07340	0.371661
$597$	−21.4620	−0.878382
$598$	47.5592	1.94484
$599$	−39.6550	−1.62026	−0.810129	−	0.586252i	$-0.800603\pi$
$599$	−39.6550	−1.62026	−0.810129	+	0.586252i	$0.800603\pi$
$600$	−1.00000	−0.0408248
$601$	−41.4026	−1.68885	−0.844423	−	0.535677i	$-0.820056\pi$
$601$	−41.4026	−1.68885	−0.844423	+	0.535677i	$0.820056\pi$
$602$	−33.7134	−1.37405
$603$	11.3403	0.461813
$604$	−2.83498	−0.115354
$605$	1.00000	0.0406558
$606$	0.192080	0.00780272
$607$	40.2162	1.63232	0.816162	−	0.577824i	$-0.196098\pi$
$607$	40.2162	1.63232	0.816162	+	0.577824i	$0.196098\pi$
$608$	−6.38639	−0.259002
$609$	2.34194	0.0949002
$610$	9.38665	0.380054
$611$	−40.3188	−1.63113
$612$	−1.00000	−0.0404226
$613$	40.3047	1.62789	0.813945	−	0.580942i	$-0.197316\pi$
$613$	40.3047	1.62789	0.813945	+	0.580942i	$0.197316\pi$
$614$	−9.96459	−0.402138
$615$	−6.31325	−0.254575
$616$	−3.13372	−0.126261
$617$	42.9339	1.72845	0.864227	−	0.503103i	$-0.167808\pi$
$617$	42.9339	1.72845	0.864227	+	0.503103i	$0.167808\pi$
$618$	12.6851	0.510270
$619$	−45.6213	−1.83367	−0.916837	−	0.399261i	$-0.869267\pi$
$619$	−45.6213	−1.83367	−0.916837	+	0.399261i	$0.869267\pi$
$620$	4.13346	0.166004
$621$	7.44697	0.298837
$622$	1.28449	0.0515034
$623$	14.1184	0.565644
$624$	6.38639	0.255660
$625$	1.00000	0.0400000
$626$	4.27973	0.171052
$627$	6.38639	0.255048
$628$	5.95366	0.237577
$629$	−11.6999	−0.466506
$630$	−3.13372	−0.124850
$631$	−30.7096	−1.22253	−0.611266	−	0.791425i	$-0.709339\pi$
$631$	−30.7096	−1.22253	−0.611266	+	0.791425i	$0.709339\pi$
$632$	1.00027	0.0397884
$633$	3.56591	0.141732
$634$	23.9551	0.951377
$635$	−6.67284	−0.264803
$636$	−11.8188	−0.468648
$637$	−18.0109	−0.713619
$638$	0.747335	0.0295873
$639$	−1.31351	−0.0519618
$640$	1.00000	0.0395285
$641$	30.3110	1.19721	0.598606	−	0.801044i	$-0.295722\pi$
$641$	30.3110	1.19721	0.598606	+	0.801044i	$0.295722\pi$
$642$	13.4738	0.531767
$643$	10.3382	0.407697	0.203849	−	0.979002i	$-0.434655\pi$
$643$	10.3382	0.407697	0.203849	+	0.979002i	$0.434655\pi$
$644$	23.3367	0.919596
$645$	−10.7583	−0.423606
$646$	6.38639	0.251269
$647$	−1.65773	−0.0651720	−0.0325860	−	0.999469i	$-0.510374\pi$
$647$	−1.65773	−0.0651720	−0.0325860	+	0.999469i	$0.510374\pi$
$648$	1.00000	0.0392837
$649$	7.45926	0.292801
$650$	−6.38639	−0.250495
$651$	12.9531	0.507672
$652$	−13.8043	−0.540619
$653$	18.4850	0.723372	0.361686	−	0.932300i	$-0.382201\pi$
$653$	18.4850	0.723372	0.361686	+	0.932300i	$0.382201\pi$
$654$	−13.6536	−0.533897
$655$	−3.62454	−0.141622
$656$	6.31325	0.246491
$657$	−9.81884	−0.383070
$658$	−19.7840	−0.771259
$659$	49.4258	1.92535	0.962677	−	0.270652i	$-0.0872393\pi$
$659$	49.4258	1.92535	0.962677	+	0.270652i	$0.0872393\pi$
$660$	−1.00000	−0.0389249
$661$	−22.1884	−0.863030	−0.431515	−	0.902106i	$-0.642021\pi$
$661$	−22.1884	−0.863030	−0.431515	+	0.902106i	$0.642021\pi$
$662$	−18.9657	−0.737123
$663$	−6.38639	−0.248027
$664$	3.24038	0.125751
$665$	20.0131	0.776077
$666$	11.6999	0.453362
$667$	−5.56538	−0.215493
$668$	−14.5812	−0.564164
$669$	14.4467	0.558542
$670$	11.3403	0.438114
$671$	9.38665	0.362368
$672$	3.13372	0.120886
$673$	38.1121	1.46911	0.734556	−	0.678548i	$-0.237391\pi$
$673$	38.1121	1.46911	0.734556	+	0.678548i	$0.237391\pi$
$674$	7.28449	0.280588
$675$	−1.00000	−0.0384900
$676$	27.7859	1.06869
$677$	34.8169	1.33812	0.669061	−	0.743207i	$-0.266696\pi$
$677$	34.8169	1.33812	0.669061	+	0.743207i	$0.266696\pi$
$678$	5.86518	0.225251
$679$	−27.0732	−1.03897
$680$	−1.00000	−0.0383482
$681$	−9.06058	−0.347202
$682$	4.13346	0.158278
$683$	4.10138	0.156935	0.0784674	−	0.996917i	$-0.474997\pi$
$683$	4.10138	0.156935	0.0784674	+	0.996917i	$0.474997\pi$
$684$	−6.38639	−0.244190
$685$	−10.7141	−0.409366
$686$	13.0983	0.500096
$687$	15.8920	0.606317
$688$	10.7583	0.410155
$689$	−75.4797	−2.87555
$690$	7.44697	0.283501
$691$	−14.4676	−0.550374	−0.275187	−	0.961391i	$-0.588740\pi$
$691$	−14.4676	−0.550374	−0.275187	+	0.961391i	$0.588740\pi$
$692$	−20.3264	−0.772694
$693$	−3.13372	−0.119040
$694$	−28.0263	−1.06386
$695$	5.56644	0.211147
$696$	−0.747335	−0.0283277
$697$	−6.31325	−0.239131
$698$	−28.3247	−1.07211
$699$	−23.8334	−0.901460
$700$	−3.13372	−0.118444
$701$	26.8772	1.01514	0.507568	−	0.861612i	$-0.330545\pi$
$701$	26.8772	1.01514	0.507568	+	0.861612i	$0.330545\pi$
$702$	6.38639	0.241039
$703$	−74.7201	−2.81812
$704$	1.00000	0.0376889
$705$	−6.31325	−0.237771
$706$	−6.47626	−0.243737
$707$	0.601926	0.0226377
$708$	−7.45926	−0.280336
$709$	50.3401	1.89056	0.945281	−	0.326258i	$-0.105788\pi$
$709$	50.3401	1.89056	0.945281	+	0.326258i	$0.105788\pi$
$710$	−1.31351	−0.0492953
$711$	1.00027	0.0375129
$712$	−4.50533	−0.168844
$713$	−30.7817	−1.15278
$714$	−3.13372	−0.117277
$715$	−6.38639	−0.238837
$716$	−8.46122	−0.316211
$717$	−4.26691	−0.159351
$718$	−12.2680	−0.457837
$719$	22.4749	0.838172	0.419086	−	0.907946i	$-0.362351\pi$
$719$	22.4749	0.838172	0.419086	+	0.907946i	$0.362351\pi$
$720$	1.00000	0.0372678
$721$	39.7516	1.48043
$722$	21.7859	0.810788
$723$	0.820472	0.0305137
$724$	24.0254	0.892898
$725$	0.747335	0.0277553
$726$	−1.00000	−0.0371135
$727$	33.8634	1.25593	0.627963	−	0.778243i	$-0.283889\pi$
$727$	33.8634	1.25593	0.627963	+	0.778243i	$0.283889\pi$
$728$	20.0131	0.741737
$729$	1.00000	0.0370370
$730$	−9.81884	−0.363412
$731$	−10.7583	−0.397909
$732$	−9.38665	−0.346941
$733$	−25.2513	−0.932678	−0.466339	−	0.884606i	$-0.654427\pi$
$733$	−25.2513	−0.932678	−0.466339	+	0.884606i	$0.654427\pi$
$734$	6.77277	0.249988
$735$	−2.82021	−0.104025
$736$	−7.44697	−0.274499
$737$	11.3403	0.417726
$738$	6.31325	0.232394
$739$	41.0632	1.51054	0.755268	−	0.655417i	$-0.227507\pi$
$739$	41.0632	1.51054	0.755268	+	0.655417i	$0.227507\pi$
$740$	11.6999	0.430097
$741$	−40.7859	−1.49831
$742$	−37.0370	−1.35967
$743$	27.6209	1.01331	0.506656	−	0.862148i	$-0.330881\pi$
$743$	27.6209	1.01331	0.506656	+	0.862148i	$0.330881\pi$
$744$	−4.13346	−0.151540
$745$	9.07340	0.332424
$746$	−15.7479	−0.576573
$747$	3.24038	0.118559
$748$	−1.00000	−0.0365636
$749$	42.2230	1.54280
$750$	−1.00000	−0.0365148
$751$	−22.1427	−0.807998	−0.403999	−	0.914759i	$-0.632380\pi$
$751$	−22.1427	−0.807998	−0.403999	+	0.914759i	$0.632380\pi$
$752$	6.31325	0.230221
$753$	−27.1128	−0.988046
$754$	−4.77277	−0.173814
$755$	−2.83498	−0.103176
$756$	3.13372	0.113972
$757$	27.0952	0.984792	0.492396	−	0.870371i	$-0.336121\pi$
$757$	27.0952	0.984792	0.492396	+	0.870371i	$0.336121\pi$
$758$	−18.2516	−0.662927
$759$	7.44697	0.270308
$760$	−6.38639	−0.231659
$761$	11.3143	0.410145	0.205072	−	0.978747i	$-0.434257\pi$
$761$	11.3143	0.410145	0.205072	+	0.978747i	$0.434257\pi$
$762$	6.67284	0.241731
$763$	−42.7865	−1.54897
$764$	15.8797	0.574507
$765$	−1.00000	−0.0361551
$766$	−22.3132	−0.806210
$767$	−47.6377	−1.72010
$768$	−1.00000	−0.0360844
$769$	32.0268	1.15492	0.577459	−	0.816420i	$-0.304045\pi$
$769$	32.0268	1.15492	0.577459	+	0.816420i	$0.304045\pi$
$770$	−3.13372	−0.112931
$771$	30.4604	1.09700
$772$	13.4347	0.483525
$773$	23.1719	0.833436	0.416718	−	0.909036i	$-0.363180\pi$
$773$	23.1719	0.833436	0.416718	+	0.909036i	$0.363180\pi$
$774$	10.7583	0.386698
$775$	4.13346	0.148478
$776$	8.63932	0.310133
$777$	36.6642	1.31532
$778$	13.2672	0.475651
$779$	−40.3188	−1.44457
$780$	6.38639	0.228669
$781$	−1.31351	−0.0470012
$782$	7.44697	0.266303
$783$	−0.747335	−0.0267076
$784$	2.82021	0.100722
$785$	5.95366	0.212495
$786$	3.62454	0.129283
$787$	11.8669	0.423008	0.211504	−	0.977377i	$-0.432164\pi$
$787$	11.8669	0.423008	0.211504	+	0.977377i	$0.432164\pi$
$788$	11.3403	0.403982
$789$	−9.07373	−0.323033
$790$	1.00027	0.0355878
$791$	18.3798	0.653512
$792$	1.00000	0.0355335
$793$	−59.9468	−2.12877
$794$	35.0866	1.24518
$795$	−11.8188	−0.419171
$796$	21.4620	0.760701
$797$	22.3411	0.791363	0.395681	−	0.918388i	$-0.370508\pi$
$797$	22.3411	0.791363	0.395681	+	0.918388i	$0.370508\pi$
$798$	−20.0131	−0.708458
$799$	−6.31325	−0.223347
$800$	1.00000	0.0353553
$801$	−4.50533	−0.159188
$802$	27.9070	0.985431
$803$	−9.81884	−0.346499
$804$	−11.3403	−0.399942
$805$	23.3367	0.822511
$806$	−26.3978	−0.929824
$807$	15.6831	0.552072
$808$	−0.192080	−0.00675736
$809$	−2.81911	−0.0991146	−0.0495573	−	0.998771i	$-0.515781\pi$
$809$	−2.81911	−0.0991146	−0.0495573	+	0.998771i	$0.515781\pi$
$810$	1.00000	0.0351364
$811$	−39.3082	−1.38030	−0.690149	−	0.723668i	$-0.742455\pi$
$811$	−39.3082	−1.38030	−0.690149	+	0.723668i	$0.742455\pi$
$812$	−2.34194	−0.0821860
$813$	11.2822	0.395685
$814$	11.6999	0.410081
$815$	−13.8043	−0.483545
$816$	1.00000	0.0350070
$817$	−68.7064	−2.40373
$818$	−4.59694	−0.160728
$819$	20.0131	0.699316
$820$	6.31325	0.220468
$821$	−16.2934	−0.568644	−0.284322	−	0.958729i	$-0.591768\pi$
$821$	−16.2934	−0.568644	−0.284322	+	0.958729i	$0.591768\pi$
$822$	10.7141	0.373699
$823$	24.0804	0.839391	0.419695	−	0.907665i	$-0.362137\pi$
$823$	24.0804	0.839391	0.419695	+	0.907665i	$0.362137\pi$
$824$	−12.6851	−0.441907
$825$	−1.00000	−0.0348155
$826$	−23.3752	−0.813328
$827$	−24.6983	−0.858843	−0.429422	−	0.903104i	$-0.641283\pi$
$827$	−24.6983	−0.858843	−0.429422	+	0.903104i	$0.641283\pi$
$828$	−7.44697	−0.258800
$829$	0.705495	0.0245029	0.0122514	−	0.999925i	$-0.496100\pi$
$829$	0.705495	0.0245029	0.0122514	+	0.999925i	$0.496100\pi$
$830$	3.24038	0.112475
$831$	25.6913	0.891221
$832$	−6.38639	−0.221408
$833$	−2.82021	−0.0977144
$834$	−5.56644	−0.192750
$835$	−14.5812	−0.504604
$836$	−6.38639	−0.220878
$837$	−4.13346	−0.142873
$838$	15.7122	0.542768
$839$	55.5402	1.91746	0.958731	−	0.284316i	$-0.0917666\pi$
$839$	55.5402	1.91746	0.958731	+	0.284316i	$0.0917666\pi$
$840$	3.13372	0.108124
$841$	−28.4415	−0.980741
$842$	32.6648	1.12570
$843$	−27.8334	−0.958632
$844$	−3.56591	−0.122744
$845$	27.7859	0.955865
$846$	6.31325	0.217054
$847$	−3.13372	−0.107676
$848$	11.8188	0.405861
$849$	−21.7589	−0.746762
$850$	−1.00000	−0.0342997
$851$	−87.1288	−2.98674
$852$	1.31351	0.0450003
$853$	32.0087	1.09596	0.547978	−	0.836493i	$-0.315398\pi$
$853$	32.0087	1.09596	0.547978	+	0.836493i	$0.315398\pi$
$854$	−29.4151	−1.00657
$855$	−6.38639	−0.218410
$856$	−13.4738	−0.460524
$857$	37.7253	1.28867	0.644336	−	0.764742i	$-0.277134\pi$
$857$	37.7253	1.28867	0.644336	+	0.764742i	$0.277134\pi$
$858$	6.38639	0.218028
$859$	21.2359	0.724559	0.362279	−	0.932070i	$-0.381999\pi$
$859$	21.2359	0.724559	0.362279	+	0.932070i	$0.381999\pi$
$860$	10.7583	0.366854
$861$	19.7840	0.674236
$862$	20.9394	0.713199
$863$	−7.62090	−0.259419	−0.129709	−	0.991552i	$-0.541404\pi$
$863$	−7.62090	−0.259419	−0.129709	+	0.991552i	$0.541404\pi$
$864$	−1.00000	−0.0340207
$865$	−20.3264	−0.691118
$866$	15.7589	0.535508
$867$	−1.00000	−0.0339618
$868$	−12.9531	−0.439657
$869$	1.00027	0.0339317
$870$	−0.747335	−0.0253370
$871$	−72.4236	−2.45398
$872$	13.6536	0.462368
$873$	8.63932	0.292397
$874$	47.5592	1.60871
$875$	−3.13372	−0.105939
$876$	9.81884	0.331748
$877$	37.1109	1.25315	0.626573	−	0.779362i	$-0.284457\pi$
$877$	37.1109	1.25315	0.626573	+	0.779362i	$0.284457\pi$
$878$	16.5163	0.557397
$879$	0.312917	0.0105544
$880$	1.00000	0.0337100
$881$	18.9420	0.638173	0.319086	−	0.947726i	$-0.396624\pi$
$881$	18.9420	0.638173	0.319086	+	0.947726i	$0.396624\pi$
$882$	2.82021	0.0949613
$883$	−42.1921	−1.41988	−0.709938	−	0.704264i	$-0.751277\pi$
$883$	−42.1921	−1.41988	−0.709938	+	0.704264i	$0.751277\pi$
$884$	6.38639	0.214797
$885$	−7.45926	−0.250740
$886$	−28.9258	−0.971780
$887$	54.6901	1.83632	0.918158	−	0.396215i	$-0.129677\pi$
$887$	54.6901	1.83632	0.918158	+	0.396215i	$0.129677\pi$
$888$	−11.6999	−0.392623
$889$	20.9108	0.701326
$890$	−4.50533	−0.151019
$891$	1.00000	0.0335013
$892$	−14.4467	−0.483711
$893$	−40.3188	−1.34922
$894$	−9.07340	−0.303460
$895$	−8.46122	−0.282827
$896$	−3.13372	−0.104690
$897$	−47.5592	−1.58796
$898$	−8.29012	−0.276645
$899$	3.08908	0.103026
$900$	1.00000	0.0333333
$901$	−11.8188	−0.393743
$902$	6.31325	0.210208
$903$	33.7134	1.12191
$904$	−5.86518	−0.195073
$905$	24.0254	0.798633
$906$	2.83498	0.0941860
$907$	42.9657	1.42665	0.713327	−	0.700832i	$-0.247188\pi$
$907$	42.9657	1.42665	0.713327	+	0.700832i	$0.247188\pi$
$908$	9.06058	0.300686
$909$	−0.192080	−0.00637090
$910$	20.0131	0.663429
$911$	30.8618	1.02250	0.511248	−	0.859433i	$-0.329183\pi$
$911$	30.8618	1.02250	0.511248	+	0.859433i	$0.329183\pi$
$912$	6.38639	0.211474
$913$	3.24038	0.107241
$914$	−30.6943	−1.01528
$915$	−9.38665	−0.310313
$916$	−15.8920	−0.525086
$917$	11.3583	0.375084
$918$	1.00000	0.0330049
$919$	33.3495	1.10010	0.550049	−	0.835132i	$-0.314609\pi$
$919$	33.3495	1.10010	0.550049	+	0.835132i	$0.314609\pi$
$920$	−7.44697	−0.245519
$921$	9.96459	0.328344
$922$	−10.1915	−0.335641
$923$	8.38861	0.276114
$924$	3.13372	0.103092
$925$	11.6999	0.384690
$926$	5.92100	0.194576
$927$	−12.6851	−0.416634
$928$	0.747335	0.0245325
$929$	−4.53352	−0.148740	−0.0743700	−	0.997231i	$-0.523695\pi$
$929$	−4.53352	−0.148740	−0.0743700	+	0.997231i	$0.523695\pi$
$930$	−4.13346	−0.135541
$931$	−18.0109	−0.590284
$932$	23.8334	0.780688
$933$	−1.28449	−0.0420524
$934$	27.0260	0.884319
$935$	−1.00000	−0.0327035
$936$	−6.38639	−0.208746
$937$	−28.2516	−0.922938	−0.461469	−	0.887156i	$-0.652678\pi$
$937$	−28.2516	−0.922938	−0.461469	+	0.887156i	$0.652678\pi$
$938$	−35.5374	−1.16034
$939$	−4.27973	−0.139664
$940$	6.31325	0.205915
$941$	26.2222	0.854818	0.427409	−	0.904058i	$-0.359426\pi$
$941$	26.2222	0.854818	0.427409	+	0.904058i	$0.359426\pi$
$942$	−5.95366	−0.193981
$943$	−47.0146	−1.53101
$944$	7.45926	0.242778
$945$	3.13372	0.101940
$946$	10.7583	0.349781
$947$	−15.6087	−0.507213	−0.253607	−	0.967307i	$-0.581617\pi$
$947$	−15.6087	−0.507213	−0.253607	+	0.967307i	$0.581617\pi$
$948$	−1.00027	−0.0324871
$949$	62.7069	2.03555
$950$	−6.38639	−0.207202
$951$	−23.9551	−0.776796
$952$	3.13372	0.101564
$953$	14.5031	0.469803	0.234901	−	0.972019i	$-0.424523\pi$
$953$	14.5031	0.469803	0.234901	+	0.972019i	$0.424523\pi$
$954$	11.8188	0.382649
$955$	15.8797	0.513855
$956$	4.26691	0.138002
$957$	−0.747335	−0.0241579
$958$	30.2301	0.976691
$959$	33.5751	1.08420
$960$	−1.00000	−0.0322749
$961$	−13.9145	−0.448856
$962$	−74.7201	−2.40907
$963$	−13.4738	−0.434186
$964$	−0.820472	−0.0264256
$965$	13.4347	0.432478
$966$	−23.3367	−0.750847
$967$	44.8985	1.44384	0.721919	−	0.691978i	$-0.243260\pi$
$967$	44.8985	1.44384	0.721919	+	0.691978i	$0.243260\pi$
$968$	1.00000	0.0321412
$969$	−6.38639	−0.205160
$970$	8.63932	0.277392
$971$	−1.18312	−0.0379680	−0.0189840	−	0.999820i	$-0.506043\pi$
$971$	−1.18312	−0.0379680	−0.0189840	+	0.999820i	$0.506043\pi$
$972$	−1.00000	−0.0320750
$973$	−17.4437	−0.559219
$974$	−2.23789	−0.0717066
$975$	6.38639	0.204528
$976$	9.38665	0.300459
$977$	−22.9702	−0.734882	−0.367441	−	0.930047i	$-0.619766\pi$
$977$	−22.9702	−0.734882	−0.367441	+	0.930047i	$0.619766\pi$
$978$	13.8043	0.441414
$979$	−4.50533	−0.143991
$980$	2.82021	0.0900882
$981$	13.6536	0.435925
$982$	−8.58016	−0.273804
$983$	23.0089	0.733870	0.366935	−	0.930246i	$-0.380407\pi$
$983$	23.0089	0.733870	0.366935	+	0.930246i	$0.380407\pi$
$984$	−6.31325	−0.201259
$985$	11.3403	0.361332
$986$	−0.747335	−0.0238000
$987$	19.7840	0.629730
$988$	40.7859	1.29757
$989$	−80.1164	−2.54755
$990$	1.00000	0.0317821
$991$	47.9464	1.52307	0.761534	−	0.648124i	$-0.224446\pi$
$991$	47.9464	1.52307	0.761534	+	0.648124i	$0.224446\pi$
$992$	4.13346	0.131237
$993$	18.9657	0.601859
$994$	4.11619	0.130558
$995$	21.4620	0.680392
$996$	−3.24038	−0.102675
$997$	15.7407	0.498512	0.249256	−	0.968438i	$-0.419814\pi$
$997$	15.7407	0.498512	0.249256	+	0.968438i	$0.419814\pi$
$998$	21.1614	0.669852
$999$	−11.6999	−0.370168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.ci.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.ci.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.13372 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.13372 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} -6.38639 q^{13} -3.13372 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -6.38639 q^{19} +1.00000 q^{20} +3.13372 q^{21} +1.00000 q^{22} -7.44697 q^{23} -1.00000 q^{24} +1.00000 q^{25} -6.38639 q^{26} -1.00000 q^{27} -3.13372 q^{28} +0.747335 q^{29} -1.00000 q^{30} +4.13346 q^{31} +1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -3.13372 q^{35} +1.00000 q^{36} +11.6999 q^{37} -6.38639 q^{38} +6.38639 q^{39} +1.00000 q^{40} +6.31325 q^{41} +3.13372 q^{42} +10.7583 q^{43} +1.00000 q^{44} +1.00000 q^{45} -7.44697 q^{46} +6.31325 q^{47} -1.00000 q^{48} +2.82021 q^{49} +1.00000 q^{50} +1.00000 q^{51} -6.38639 q^{52} +11.8188 q^{53} -1.00000 q^{54} +1.00000 q^{55} -3.13372 q^{56} +6.38639 q^{57} +0.747335 q^{58} +7.45926 q^{59} -1.00000 q^{60} +9.38665 q^{61} +4.13346 q^{62} -3.13372 q^{63} +1.00000 q^{64} -6.38639 q^{65} -1.00000 q^{66} +11.3403 q^{67} -1.00000 q^{68} +7.44697 q^{69} -3.13372 q^{70} -1.31351 q^{71} +1.00000 q^{72} -9.81884 q^{73} +11.6999 q^{74} -1.00000 q^{75} -6.38639 q^{76} -3.13372 q^{77} +6.38639 q^{78} +1.00027 q^{79} +1.00000 q^{80} +1.00000 q^{81} +6.31325 q^{82} +3.24038 q^{83} +3.13372 q^{84} -1.00000 q^{85} +10.7583 q^{86} -0.747335 q^{87} +1.00000 q^{88} -4.50533 q^{89} +1.00000 q^{90} +20.0131 q^{91} -7.44697 q^{92} -4.13346 q^{93} +6.31325 q^{94} -6.38639 q^{95} -1.00000 q^{96} +8.63932 q^{97} +2.82021 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} + 2 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 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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