LMFDB - Embedded newform 722.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.17557$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.28408 q^{3} +1.00000 q^{4} +3.69572 q^{5} +1.28408 q^{6} -0.442463 q^{7} +1.00000 q^{8} -1.35114 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.28408 q^{3} +1.00000 q^{4} +3.69572 q^{5} +1.28408 q^{6} -0.442463 q^{7} +1.00000 q^{8} -1.35114 q^{9} +3.69572 q^{10} -4.02967 q^{11} +1.28408 q^{12} +4.89149 q^{13} -0.442463 q^{14} +4.74559 q^{15} +1.00000 q^{16} +0.266893 q^{17} -1.35114 q^{18} +3.69572 q^{20} -0.568158 q^{21} -4.02967 q^{22} -9.20930 q^{23} +1.28408 q^{24} +8.65833 q^{25} +4.89149 q^{26} -5.58721 q^{27} -0.442463 q^{28} -0.223582 q^{29} +4.74559 q^{30} +3.47985 q^{31} +1.00000 q^{32} -5.17442 q^{33} +0.266893 q^{34} -1.63522 q^{35} -1.35114 q^{36} +1.44903 q^{37} +6.28106 q^{39} +3.69572 q^{40} -7.86472 q^{41} -0.568158 q^{42} -5.63522 q^{43} -4.02967 q^{44} -4.99344 q^{45} -9.20930 q^{46} +2.19868 q^{47} +1.28408 q^{48} -6.80423 q^{49} +8.65833 q^{50} +0.342712 q^{51} +4.89149 q^{52} +9.94241 q^{53} -5.58721 q^{54} -14.8925 q^{55} -0.442463 q^{56} -0.223582 q^{58} -3.50953 q^{59} +4.74559 q^{60} +4.07955 q^{61} +3.47985 q^{62} +0.597831 q^{63} +1.00000 q^{64} +18.0776 q^{65} -5.17442 q^{66} +0.147763 q^{67} +0.266893 q^{68} -11.8255 q^{69} -1.63522 q^{70} +11.4691 q^{71} -1.35114 q^{72} +1.42226 q^{73} +1.44903 q^{74} +11.1180 q^{75} +1.78298 q^{77} +6.28106 q^{78} +10.2034 q^{79} +3.69572 q^{80} -3.12099 q^{81} -7.86472 q^{82} -3.28878 q^{83} -0.568158 q^{84} +0.986361 q^{85} -5.63522 q^{86} -0.287096 q^{87} -4.02967 q^{88} -5.96075 q^{89} -4.99344 q^{90} -2.16431 q^{91} -9.20930 q^{92} +4.46841 q^{93} +2.19868 q^{94} +1.28408 q^{96} +4.08476 q^{97} -6.80423 q^{98} +5.44466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{29} + 4 q^{30} + 26 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} + 6 q^{35} + 4 q^{36} + 4 q^{37} - 6 q^{39} - 2 q^{40} - 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} - 10 q^{46} - 12 q^{47} + 2 q^{48} - 12 q^{49} + 6 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} - 4 q^{54} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} + 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} - 4 q^{65} + 16 q^{66} + 10 q^{67} + 6 q^{68} - 20 q^{69} + 6 q^{70} + 4 q^{72} - 14 q^{73} + 4 q^{74} + 8 q^{75} + 4 q^{77} - 6 q^{78} + 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 18 q^{85} - 10 q^{86} - 26 q^{87} + 2 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 8 q^{93} - 12 q^{94} + 2 q^{96} + 28 q^{97} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 - 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^29 + 4 * q^30 + 26 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 + 6 * q^35 + 4 * q^36 + 4 * q^37 - 6 * q^39 - 2 * q^40 - 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 - 10 * q^46 - 12 * q^47 + 2 * q^48 - 12 * q^49 + 6 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 - 4 * q^54 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 + 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 - 4 * q^65 + 16 * q^66 + 10 * q^67 + 6 * q^68 - 20 * q^69 + 6 * q^70 + 4 * q^72 - 14 * q^73 + 4 * q^74 + 8 * q^75 + 4 * q^77 - 6 * q^78 + 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 18 * q^85 - 10 * q^86 - 26 * q^87 + 2 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 8 * q^93 - 12 * q^94 + 2 * q^96 + 28 * q^97 - 12 * q^98 + 22 * 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
$3$	1.28408	0.741363	0.370682	−	0.928760i	$-0.379124\pi$
$3$	1.28408	0.741363	0.370682	+	0.928760i	$0.379124\pi$
$4$	1.00000	0.500000
$5$	3.69572	1.65278	0.826388	−	0.563102i	$-0.190392\pi$
$5$	3.69572	1.65278	0.826388	+	0.563102i	$0.190392\pi$
$6$	1.28408	0.524223
$7$	−0.442463	−0.167235	−0.0836177	−	0.996498i	$-0.526647\pi$
$7$	−0.442463	−0.167235	−0.0836177	+	0.996498i	$0.526647\pi$
$8$	1.00000	0.353553
$9$	−1.35114	−0.450380
$10$	3.69572	1.16869
$11$	−4.02967	−1.21499	−0.607496	−	0.794323i	$-0.707826\pi$
$11$	−4.02967	−1.21499	−0.607496	+	0.794323i	$0.707826\pi$
$12$	1.28408	0.370682
$13$	4.89149	1.35666	0.678328	−	0.734759i	$-0.262705\pi$
$13$	4.89149	1.35666	0.678328	+	0.734759i	$0.262705\pi$
$14$	−0.442463	−0.118253
$15$	4.74559	1.22531
$16$	1.00000	0.250000
$17$	0.266893	0.0647311	0.0323655	−	0.999476i	$-0.489696\pi$
$17$	0.266893	0.0647311	0.0323655	+	0.999476i	$0.489696\pi$
$18$	−1.35114	−0.318467
$19$	0	0
$19$	0	0
$20$	3.69572	0.826388
$21$	−0.568158	−0.123982
$22$	−4.02967	−0.859129
$23$	−9.20930	−1.92027	−0.960136	−	0.279534i	$-0.909820\pi$
$23$	−9.20930	−1.92027	−0.960136	+	0.279534i	$0.909820\pi$
$24$	1.28408	0.262112
$25$	8.65833	1.73167
$26$	4.89149	0.959300
$27$	−5.58721	−1.07526
$28$	−0.442463	−0.0836177
$29$	−0.223582	−0.0415181	−0.0207590	−	0.999785i	$-0.506608\pi$
$29$	−0.223582	−0.0415181	−0.0207590	+	0.999785i	$0.506608\pi$
$30$	4.74559	0.866423
$31$	3.47985	0.625000	0.312500	−	0.949918i	$-0.398834\pi$
$31$	3.47985	0.625000	0.312500	+	0.949918i	$0.398834\pi$
$32$	1.00000	0.176777
$33$	−5.17442	−0.900751
$34$	0.266893	0.0457718
$35$	−1.63522	−0.276403
$36$	−1.35114	−0.225190
$37$	1.44903	0.238219	0.119109	−	0.992881i	$-0.461996\pi$
$37$	1.44903	0.238219	0.119109	+	0.992881i	$0.461996\pi$
$38$	0	0
$39$	6.28106	1.00577
$40$	3.69572	0.584344
$41$	−7.86472	−1.22826	−0.614132	−	0.789204i	$-0.710494\pi$
$41$	−7.86472	−1.22826	−0.614132	+	0.789204i	$0.710494\pi$
$42$	−0.568158	−0.0876687
$43$	−5.63522	−0.859363	−0.429682	−	0.902981i	$-0.641374\pi$
$43$	−5.63522	−0.859363	−0.429682	+	0.902981i	$0.641374\pi$
$44$	−4.02967	−0.607496
$45$	−4.99344	−0.744377
$46$	−9.20930	−1.35784
$47$	2.19868	0.320710	0.160355	−	0.987059i	$-0.448736\pi$
$47$	2.19868	0.320710	0.160355	+	0.987059i	$0.448736\pi$
$48$	1.28408	0.185341
$49$	−6.80423	−0.972032
$50$	8.65833	1.22447
$51$	0.342712	0.0479892
$52$	4.89149	0.678328
$53$	9.94241	1.36569	0.682847	−	0.730561i	$-0.260741\pi$
$53$	9.94241	1.36569	0.682847	+	0.730561i	$0.260741\pi$
$54$	−5.58721	−0.760323
$55$	−14.8925	−2.00811
$56$	−0.442463	−0.0591267
$57$	0	0
$58$	−0.223582	−0.0293577
$59$	−3.50953	−0.456901	−0.228451	−	0.973555i	$-0.573366\pi$
$59$	−3.50953	−0.456901	−0.228451	+	0.973555i	$0.573366\pi$
$60$	4.74559	0.612653
$61$	4.07955	0.522333	0.261166	−	0.965294i	$-0.415893\pi$
$61$	4.07955	0.522333	0.261166	+	0.965294i	$0.415893\pi$
$62$	3.47985	0.441942
$63$	0.597831	0.0753196
$64$	1.00000	0.125000
$65$	18.0776	2.24225
$66$	−5.17442	−0.636927
$67$	0.147763	0.0180521	0.00902605	−	0.999959i	$-0.497127\pi$
$67$	0.147763	0.0180521	0.00902605	+	0.999959i	$0.497127\pi$
$68$	0.266893	0.0323655
$69$	−11.8255	−1.42362
$70$	−1.63522	−0.195446
$71$	11.4691	1.36113	0.680567	−	0.732686i	$-0.261734\pi$
$71$	11.4691	1.36113	0.680567	+	0.732686i	$0.261734\pi$
$72$	−1.35114	−0.159233
$73$	1.42226	0.166463	0.0832315	−	0.996530i	$-0.473476\pi$
$73$	1.42226	0.166463	0.0832315	+	0.996530i	$0.473476\pi$
$74$	1.44903	0.168446
$75$	11.1180	1.28379
$76$	0	0
$77$	1.78298	0.203190
$78$	6.28106	0.711190
$79$	10.2034	1.14797	0.573985	−	0.818866i	$-0.305397\pi$
$79$	10.2034	1.14797	0.573985	+	0.818866i	$0.305397\pi$
$80$	3.69572	0.413194
$81$	−3.12099	−0.346777
$82$	−7.86472	−0.868513
$83$	−3.28878	−0.360990	−0.180495	−	0.983576i	$-0.557770\pi$
$83$	−3.28878	−0.360990	−0.180495	+	0.983576i	$0.557770\pi$
$84$	−0.568158	−0.0619911
$85$	0.986361	0.106986
$86$	−5.63522	−0.607661
$87$	−0.287096	−0.0307800
$88$	−4.02967	−0.429565
$89$	−5.96075	−0.631838	−0.315919	−	0.948786i	$-0.602313\pi$
$89$	−5.96075	−0.631838	−0.315919	+	0.948786i	$0.602313\pi$
$90$	−4.99344	−0.526354
$91$	−2.16431	−0.226881
$92$	−9.20930	−0.960136
$93$	4.46841	0.463352
$94$	2.19868	0.226776
$95$	0	0
$96$	1.28408	0.131056
$97$	4.08476	0.414744	0.207372	−	0.978262i	$-0.433509\pi$
$97$	4.08476	0.414744	0.207372	+	0.978262i	$0.433509\pi$
$98$	−6.80423	−0.687331
$99$	5.44466	0.547208
$100$	8.65833	0.865833
$101$	0.425277	0.0423167	0.0211583	−	0.999776i	$-0.493265\pi$
$101$	0.425277	0.0423167	0.0211583	+	0.999776i	$0.493265\pi$
$102$	0.342712	0.0339335
$103$	−4.53618	−0.446963	−0.223482	−	0.974708i	$-0.571742\pi$
$103$	−4.53618	−0.446963	−0.223482	+	0.974708i	$0.571742\pi$
$104$	4.89149	0.479650
$105$	−2.09975	−0.204915
$106$	9.94241	0.965692
$107$	−3.17151	−0.306602	−0.153301	−	0.988180i	$-0.548990\pi$
$107$	−3.17151	−0.306602	−0.153301	+	0.988180i	$0.548990\pi$
$108$	−5.58721	−0.537629
$109$	−6.78112	−0.649513	−0.324757	−	0.945798i	$-0.605282\pi$
$109$	−6.78112	−0.649513	−0.324757	+	0.945798i	$0.605282\pi$
$110$	−14.8925	−1.41995
$111$	1.86067	0.176607
$112$	−0.442463	−0.0418089
$113$	−10.0444	−0.944893	−0.472447	−	0.881359i	$-0.656629\pi$
$113$	−10.0444	−0.944893	−0.472447	+	0.881359i	$0.656629\pi$
$114$	0	0
$115$	−34.0350	−3.17378
$116$	−0.223582	−0.0207590
$117$	−6.60909	−0.611011
$118$	−3.50953	−0.323078
$119$	−0.118090	−0.0108253
$120$	4.74559	0.433211
$121$	5.23826	0.476205
$122$	4.07955	0.369345
$123$	−10.0989	−0.910590
$124$	3.47985	0.312500
$125$	13.5201	1.20928
$126$	0.597831	0.0532590
$127$	14.0806	1.24945	0.624725	−	0.780845i	$-0.285211\pi$
$127$	14.0806	1.24945	0.624725	+	0.780845i	$0.285211\pi$
$128$	1.00000	0.0883883
$129$	−7.23607	−0.637100
$130$	18.0776	1.58551
$131$	15.8415	1.38408	0.692039	−	0.721860i	$-0.256712\pi$
$131$	15.8415	1.38408	0.692039	+	0.721860i	$0.256712\pi$
$132$	−5.17442	−0.450375
$133$	0	0
$134$	0.147763	0.0127648
$135$	−20.6487	−1.77716
$136$	0.266893	0.0228859
$137$	2.20744	0.188594	0.0942970	−	0.995544i	$-0.469940\pi$
$137$	2.20744	0.188594	0.0942970	+	0.995544i	$0.469940\pi$
$138$	−11.8255	−1.00665
$139$	−17.0644	−1.44739	−0.723694	−	0.690121i	$-0.757557\pi$
$139$	−17.0644	−1.44739	−0.723694	+	0.690121i	$0.757557\pi$
$140$	−1.63522	−0.138201
$141$	2.82328	0.237763
$142$	11.4691	0.962467
$143$	−19.7111	−1.64833
$144$	−1.35114	−0.112595
$145$	−0.826294	−0.0686200
$146$	1.42226	0.117707
$147$	−8.73716	−0.720629
$148$	1.44903	0.119109
$149$	13.5458	1.10971	0.554856	−	0.831946i	$-0.312773\pi$
$149$	13.5458	1.10971	0.554856	+	0.831946i	$0.312773\pi$
$150$	11.1180	0.907779
$151$	−9.15317	−0.744875	−0.372437	−	0.928057i	$-0.621478\pi$
$151$	−9.15317	−0.744875	−0.372437	+	0.928057i	$0.621478\pi$
$152$	0	0
$153$	−0.360610	−0.0291536
$154$	1.78298	0.143677
$155$	12.8606	1.03298
$156$	6.28106	0.502887
$157$	−16.3903	−1.30809	−0.654043	−	0.756457i	$-0.726929\pi$
$157$	−16.3903	−1.30809	−0.654043	+	0.756457i	$0.726929\pi$
$158$	10.2034	0.811737
$159$	12.7668	1.01248
$160$	3.69572	0.292172
$161$	4.07478	0.321138
$162$	−3.12099	−0.245209
$163$	−13.7722	−1.07873	−0.539363	−	0.842073i	$-0.681335\pi$
$163$	−13.7722	−1.07873	−0.539363	+	0.842073i	$0.681335\pi$
$164$	−7.86472	−0.614132
$165$	−19.1232	−1.48874
$166$	−3.28878	−0.255259
$167$	−10.3328	−0.799576	−0.399788	−	0.916608i	$-0.630916\pi$
$167$	−10.3328	−0.799576	−0.399788	+	0.916608i	$0.630916\pi$
$168$	−0.568158	−0.0438343
$169$	10.9267	0.840515
$170$	0.986361	0.0756504
$171$	0	0
$172$	−5.63522	−0.429682
$173$	−9.81201	−0.745994	−0.372997	−	0.927833i	$-0.621670\pi$
$173$	−9.81201	−0.745994	−0.372997	+	0.927833i	$0.621670\pi$
$174$	−0.287096	−0.0217647
$175$	−3.83099	−0.289596
$176$	−4.02967	−0.303748
$177$	−4.50651	−0.338730
$178$	−5.96075	−0.446777
$179$	−8.79830	−0.657616	−0.328808	−	0.944397i	$-0.606647\pi$
$179$	−8.79830	−0.657616	−0.328808	+	0.944397i	$0.606647\pi$
$180$	−4.99344	−0.372189
$181$	14.5278	1.07984	0.539920	−	0.841717i	$-0.318455\pi$
$181$	14.5278	1.07984	0.539920	+	0.841717i	$0.318455\pi$
$182$	−2.16431	−0.160429
$183$	5.23846	0.387238
$184$	−9.20930	−0.678919
$185$	5.35520	0.393722
$186$	4.46841	0.327639
$187$	−1.07549	−0.0786477
$188$	2.19868	0.160355
$189$	2.47214	0.179821
$190$	0	0
$191$	12.7302	0.921122	0.460561	−	0.887628i	$-0.347648\pi$
$191$	12.7302	0.921122	0.460561	+	0.887628i	$0.347648\pi$
$192$	1.28408	0.0926704
$193$	17.4781	1.25810	0.629049	−	0.777366i	$-0.283444\pi$
$193$	17.4781	1.25810	0.629049	+	0.777366i	$0.283444\pi$
$194$	4.08476	0.293269
$195$	23.2130	1.66232
$196$	−6.80423	−0.486016
$197$	−24.5113	−1.74636	−0.873178	−	0.487401i	$-0.837945\pi$
$197$	−24.5113	−1.74636	−0.873178	+	0.487401i	$0.837945\pi$
$198$	5.44466	0.386935
$199$	16.4661	1.16725	0.583625	−	0.812023i	$-0.301634\pi$
$199$	16.4661	1.16725	0.583625	+	0.812023i	$0.301634\pi$
$200$	8.65833	0.612236
$201$	0.189739	0.0133832
$202$	0.425277	0.0299224
$203$	0.0989267	0.00694329
$204$	0.342712	0.0239946
$205$	−29.0658	−2.03004
$206$	−4.53618	−0.316051
$207$	12.4431	0.864853
$208$	4.89149	0.339164
$209$	0	0
$210$	−2.09975	−0.144897
$211$	27.4805	1.89183	0.945916	−	0.324411i	$-0.105166\pi$
$211$	27.4805	1.89183	0.945916	+	0.324411i	$0.105166\pi$
$212$	9.94241	0.682847
$213$	14.7273	1.00909
$214$	−3.17151	−0.216800
$215$	−20.8262	−1.42033
$216$	−5.58721	−0.380161
$217$	−1.53971	−0.104522
$218$	−6.78112	−0.459275
$219$	1.82629	0.123410
$220$	−14.8925	−1.00405
$221$	1.30550	0.0878178
$222$	1.86067	0.124880
$223$	20.3706	1.36412	0.682058	−	0.731298i	$-0.261085\pi$
$223$	20.3706	1.36412	0.682058	+	0.731298i	$0.261085\pi$
$224$	−0.442463	−0.0295633
$225$	−11.6986	−0.779908
$226$	−10.0444	−0.668140
$227$	−22.1493	−1.47010	−0.735051	−	0.678011i	$-0.762842\pi$
$227$	−22.1493	−1.47010	−0.735051	+	0.678011i	$0.762842\pi$
$228$	0	0
$229$	12.7148	0.840216	0.420108	−	0.907474i	$-0.361992\pi$
$229$	12.7148	0.840216	0.420108	+	0.907474i	$0.361992\pi$
$230$	−34.0350	−2.24420
$231$	2.28949	0.150637
$232$	−0.223582	−0.0146788
$233$	−8.68176	−0.568761	−0.284381	−	0.958711i	$-0.591788\pi$
$233$	−8.68176	−0.568761	−0.284381	+	0.958711i	$0.591788\pi$
$234$	−6.60909	−0.432050
$235$	8.12569	0.530062
$236$	−3.50953	−0.228451
$237$	13.1019	0.851063
$238$	−0.118090	−0.00765466
$239$	21.8749	1.41497	0.707485	−	0.706728i	$-0.249830\pi$
$239$	21.8749	1.41497	0.707485	+	0.706728i	$0.249830\pi$
$240$	4.74559	0.306327
$241$	−18.9632	−1.22153	−0.610764	−	0.791813i	$-0.709138\pi$
$241$	−18.9632	−1.22153	−0.610764	+	0.791813i	$0.709138\pi$
$242$	5.23826	0.336728
$243$	12.7540	0.818171
$244$	4.07955	0.261166
$245$	−25.1465	−1.60655
$246$	−10.0989	−0.643884
$247$	0	0
$248$	3.47985	0.220971
$249$	−4.22305	−0.267625
$250$	13.5201	0.855089
$251$	2.90276	0.183220	0.0916102	−	0.995795i	$-0.470799\pi$
$251$	2.90276	0.183220	0.0916102	+	0.995795i	$0.470799\pi$
$252$	0.597831	0.0376598
$253$	37.1105	2.33311
$254$	14.0806	0.883495
$255$	1.26657	0.0793154
$256$	1.00000	0.0625000
$257$	22.9050	1.42878	0.714388	−	0.699750i	$-0.246705\pi$
$257$	22.9050	1.42878	0.714388	+	0.699750i	$0.246705\pi$
$258$	−7.23607	−0.450498
$259$	−0.641142	−0.0398386
$260$	18.0776	1.12112
$261$	0.302090	0.0186989
$262$	15.8415	0.978691
$263$	−5.06236	−0.312159	−0.156079	−	0.987745i	$-0.549886\pi$
$263$	−5.06236	−0.312159	−0.156079	+	0.987745i	$0.549886\pi$
$264$	−5.17442	−0.318463
$265$	36.7443	2.25719
$266$	0	0
$267$	−7.65407	−0.468421
$268$	0.147763	0.00902605
$269$	−20.7419	−1.26466	−0.632329	−	0.774700i	$-0.717901\pi$
$269$	−20.7419	−1.26466	−0.632329	+	0.774700i	$0.717901\pi$
$270$	−20.6487	−1.25664
$271$	6.29470	0.382376	0.191188	−	0.981553i	$-0.438766\pi$
$271$	6.29470	0.382376	0.191188	+	0.981553i	$0.438766\pi$
$272$	0.266893	0.0161828
$273$	−2.77914	−0.168201
$274$	2.20744	0.133356
$275$	−34.8902	−2.10396
$276$	−11.8255	−0.711810
$277$	7.17608	0.431169	0.215584	−	0.976485i	$-0.430834\pi$
$277$	7.17608	0.431169	0.215584	+	0.976485i	$0.430834\pi$
$278$	−17.0644	−1.02346
$279$	−4.70177	−0.281488
$280$	−1.63522	−0.0977231
$281$	2.77391	0.165478	0.0827388	−	0.996571i	$-0.473633\pi$
$281$	2.77391	0.165478	0.0827388	+	0.996571i	$0.473633\pi$
$282$	2.82328	0.168124
$283$	7.74861	0.460607	0.230304	−	0.973119i	$-0.426028\pi$
$283$	7.74861	0.460607	0.230304	+	0.973119i	$0.426028\pi$
$284$	11.4691	0.680567
$285$	0	0
$286$	−19.7111	−1.16554
$287$	3.47985	0.205409
$288$	−1.35114	−0.0796167
$289$	−16.9288	−0.995810
$290$	−0.826294	−0.0485217
$291$	5.24515	0.307476
$292$	1.42226	0.0832315
$293$	−0.782870	−0.0457358	−0.0228679	−	0.999738i	$-0.507280\pi$
$293$	−0.782870	−0.0457358	−0.0228679	+	0.999738i	$0.507280\pi$
$294$	−8.73716	−0.509562
$295$	−12.9702	−0.755155
$296$	1.44903	0.0842230
$297$	22.5146	1.30643
$298$	13.5458	0.784685
$299$	−45.0472	−2.60515
$300$	11.1180	0.641897
$301$	2.49338	0.143716
$302$	−9.15317	−0.526706
$303$	0.546090	0.0313720
$304$	0	0
$305$	15.0769	0.863298
$306$	−0.360610	−0.0206147
$307$	−28.1688	−1.60768	−0.803839	−	0.594847i	$-0.797212\pi$
$307$	−28.1688	−1.60768	−0.803839	+	0.594847i	$0.797212\pi$
$308$	1.78298	0.101595
$309$	−5.82481	−0.331362
$310$	12.8606	0.730430
$311$	3.86827	0.219350	0.109675	−	0.993968i	$-0.465019\pi$
$311$	3.86827	0.219350	0.109675	+	0.993968i	$0.465019\pi$
$312$	6.28106	0.355595
$313$	30.3878	1.71762	0.858809	−	0.512295i	$-0.171205\pi$
$313$	30.3878	1.71762	0.858809	+	0.512295i	$0.171205\pi$
$314$	−16.3903	−0.924957
$315$	2.20941	0.124486
$316$	10.2034	0.573985
$317$	5.32803	0.299252	0.149626	−	0.988743i	$-0.452193\pi$
$317$	5.32803	0.299252	0.149626	+	0.988743i	$0.452193\pi$
$318$	12.7668	0.715929
$319$	0.900961	0.0504441
$320$	3.69572	0.206597
$321$	−4.07247	−0.227303
$322$	4.07478	0.227079
$323$	0	0
$324$	−3.12099	−0.173389
$325$	42.3521	2.34927
$326$	−13.7722	−0.762774
$327$	−8.70749	−0.481525
$328$	−7.86472	−0.434257
$329$	−0.972835	−0.0536341
$330$	−19.1232	−1.05270
$331$	−20.5480	−1.12942	−0.564711	−	0.825289i	$-0.691012\pi$
$331$	−20.5480	−1.12942	−0.564711	+	0.825289i	$0.691012\pi$
$332$	−3.28878	−0.180495
$333$	−1.95784	−0.107289
$334$	−10.3328	−0.565386
$335$	0.546090	0.0298361
$336$	−0.568158	−0.0309956
$337$	13.2824	0.723539	0.361770	−	0.932268i	$-0.382173\pi$
$337$	13.2824	0.723539	0.361770	+	0.932268i	$0.382173\pi$
$338$	10.9267	0.594334
$339$	−12.8977	−0.700509
$340$	0.986361	0.0534929
$341$	−14.0227	−0.759370
$342$	0	0
$343$	6.10787	0.329794
$344$	−5.63522	−0.303831
$345$	−43.7036	−2.35292
$346$	−9.81201	−0.527497
$347$	30.1423	1.61812	0.809062	−	0.587723i	$-0.199975\pi$
$347$	30.1423	1.61812	0.809062	+	0.587723i	$0.199975\pi$
$348$	−0.287096	−0.0153900
$349$	35.0653	1.87700	0.938501	−	0.345277i	$-0.112215\pi$
$349$	35.0653	1.87700	0.938501	+	0.345277i	$0.112215\pi$
$350$	−3.83099	−0.204775
$351$	−27.3298	−1.45876
$352$	−4.02967	−0.214782
$353$	13.5411	0.720718	0.360359	−	0.932814i	$-0.382654\pi$
$353$	13.5411	0.720718	0.360359	+	0.932814i	$0.382654\pi$
$354$	−4.50651	−0.239518
$355$	42.3866	2.24965
$356$	−5.96075	−0.315919
$357$	−0.151637	−0.00802550
$358$	−8.79830	−0.465005
$359$	−23.5072	−1.24066	−0.620332	−	0.784339i	$-0.713002\pi$
$359$	−23.5072	−1.24066	−0.620332	+	0.784339i	$0.713002\pi$
$360$	−4.99344	−0.263177
$361$	0	0
$362$	14.5278	0.763562
$363$	6.72634	0.353041
$364$	−2.16431	−0.113440
$365$	5.25627	0.275126
$366$	5.23846	0.273819
$367$	−12.6929	−0.662563	−0.331282	−	0.943532i	$-0.607481\pi$
$367$	−12.6929	−0.662563	−0.331282	+	0.943532i	$0.607481\pi$
$368$	−9.20930	−0.480068
$369$	10.6264	0.553186
$370$	5.35520	0.278403
$371$	−4.39915	−0.228393
$372$	4.46841	0.231676
$373$	2.64950	0.137186	0.0685930	−	0.997645i	$-0.478149\pi$
$373$	2.64950	0.137186	0.0685930	+	0.997645i	$0.478149\pi$
$374$	−1.07549	−0.0556123
$375$	17.3609	0.896515
$376$	2.19868	0.113388
$377$	−1.09365	−0.0563257
$378$	2.47214	0.127153
$379$	18.1672	0.933187	0.466593	−	0.884472i	$-0.345481\pi$
$379$	18.1672	0.933187	0.466593	+	0.884472i	$0.345481\pi$
$380$	0	0
$381$	18.0806	0.926297
$382$	12.7302	0.651332
$383$	23.0083	1.17567	0.587835	−	0.808981i	$-0.299980\pi$
$383$	23.0083	1.17567	0.587835	+	0.808981i	$0.299980\pi$
$384$	1.28408	0.0655279
$385$	6.58940	0.335827
$386$	17.4781	0.889610
$387$	7.61398	0.387040
$388$	4.08476	0.207372
$389$	−16.5706	−0.840164	−0.420082	−	0.907486i	$-0.637999\pi$
$389$	−16.5706	−0.840164	−0.420082	+	0.907486i	$0.637999\pi$
$390$	23.2130	1.17544
$391$	−2.45790	−0.124301
$392$	−6.80423	−0.343665
$393$	20.3417	1.02611
$394$	−24.5113	−1.23486
$395$	37.7088	1.89734
$396$	5.44466	0.273604
$397$	−17.7948	−0.893097	−0.446548	−	0.894759i	$-0.647347\pi$
$397$	−17.7948	−0.893097	−0.446548	+	0.894759i	$0.647347\pi$
$398$	16.4661	0.825371
$399$	0	0
$400$	8.65833	0.432916
$401$	30.6215	1.52916	0.764582	−	0.644527i	$-0.222946\pi$
$401$	30.6215	1.52916	0.764582	+	0.644527i	$0.222946\pi$
$402$	0.189739	0.00946333
$403$	17.0217	0.847910
$404$	0.425277	0.0211583
$405$	−11.5343	−0.573145
$406$	0.0989267	0.00490965
$407$	−5.83911	−0.289434
$408$	0.342712	0.0169668
$409$	9.14328	0.452106	0.226053	−	0.974115i	$-0.427418\pi$
$409$	9.14328	0.452106	0.226053	+	0.974115i	$0.427418\pi$
$410$	−29.0658	−1.43546
$411$	2.83452	0.139817
$412$	−4.53618	−0.223482
$413$	1.55284	0.0764101
$414$	12.4431	0.611543
$415$	−12.1544	−0.596636
$416$	4.89149	0.239825
$417$	−21.9121	−1.07304
$418$	0	0
$419$	12.6157	0.616315	0.308158	−	0.951335i	$-0.400288\pi$
$419$	12.6157	0.616315	0.308158	+	0.951335i	$0.400288\pi$
$420$	−2.09975	−0.102457
$421$	33.2553	1.62077	0.810383	−	0.585901i	$-0.199259\pi$
$421$	33.2553	1.62077	0.810383	+	0.585901i	$0.199259\pi$
$422$	27.4805	1.33773
$423$	−2.97072	−0.144442
$424$	9.94241	0.482846
$425$	2.31085	0.112093
$426$	14.7273	0.713538
$427$	−1.80505	−0.0873525
$428$	−3.17151	−0.153301
$429$	−25.3106	−1.22201
$430$	−20.8262	−1.00433
$431$	−22.9915	−1.10746	−0.553730	−	0.832696i	$-0.686796\pi$
$431$	−22.9915	−1.10746	−0.553730	+	0.832696i	$0.686796\pi$
$432$	−5.58721	−0.268815
$433$	34.7092	1.66802	0.834010	−	0.551749i	$-0.186040\pi$
$433$	34.7092	1.66802	0.834010	+	0.551749i	$0.186040\pi$
$434$	−1.53971	−0.0739083
$435$	−1.06103	−0.0508724
$436$	−6.78112	−0.324757
$437$	0	0
$438$	1.82629	0.0872637
$439$	−36.4818	−1.74118	−0.870591	−	0.492007i	$-0.836263\pi$
$439$	−36.4818	−1.74118	−0.870591	+	0.492007i	$0.836263\pi$
$440$	−14.8925	−0.709974
$441$	9.19347	0.437784
$442$	1.30550	0.0620965
$443$	11.7583	0.558653	0.279327	−	0.960196i	$-0.409889\pi$
$443$	11.7583	0.558653	0.279327	+	0.960196i	$0.409889\pi$
$444$	1.86067	0.0883033
$445$	−22.0292	−1.04429
$446$	20.3706	0.964575
$447$	17.3938	0.822700
$448$	−0.442463	−0.0209044
$449$	−8.69102	−0.410154	−0.205077	−	0.978746i	$-0.565745\pi$
$449$	−8.69102	−0.410154	−0.205077	+	0.978746i	$0.565745\pi$
$450$	−11.6986	−0.551478
$451$	31.6923	1.49233
$452$	−10.0444	−0.472447
$453$	−11.7534	−0.552223
$454$	−22.1493	−1.03952
$455$	−7.99866	−0.374983
$456$	0	0
$457$	−13.0286	−0.609454	−0.304727	−	0.952440i	$-0.598565\pi$
$457$	−13.0286	−0.609454	−0.304727	+	0.952440i	$0.598565\pi$
$458$	12.7148	0.594122
$459$	−1.49119	−0.0696026
$460$	−34.0350	−1.58689
$461$	9.04260	0.421156	0.210578	−	0.977577i	$-0.432465\pi$
$461$	9.04260	0.421156	0.210578	+	0.977577i	$0.432465\pi$
$462$	2.28949	0.106517
$463$	−17.7205	−0.823542	−0.411771	−	0.911287i	$-0.635090\pi$
$463$	−17.7205	−0.823542	−0.411771	+	0.911287i	$0.635090\pi$
$464$	−0.223582	−0.0103795
$465$	16.5140	0.765817
$466$	−8.68176	−0.402175
$467$	−7.87772	−0.364537	−0.182269	−	0.983249i	$-0.558344\pi$
$467$	−7.87772	−0.364537	−0.182269	+	0.983249i	$0.558344\pi$
$468$	−6.60909	−0.305506
$469$	−0.0653797	−0.00301895
$470$	8.12569	0.374810
$471$	−21.0464	−0.969768
$472$	−3.50953	−0.161539
$473$	22.7081	1.04412
$474$	13.1019	0.601792
$475$	0	0
$476$	−0.118090	−0.00541266
$477$	−13.4336	−0.615082
$478$	21.8749	1.00053
$479$	−30.1798	−1.37895	−0.689476	−	0.724309i	$-0.742159\pi$
$479$	−30.1798	−1.37895	−0.689476	+	0.724309i	$0.742159\pi$
$480$	4.74559	0.216606
$481$	7.08791	0.323181
$482$	−18.9632	−0.863751
$483$	5.23234	0.238080
$484$	5.23826	0.238103
$485$	15.0961	0.685479
$486$	12.7540	0.578534
$487$	35.7699	1.62089	0.810445	−	0.585814i	$-0.199225\pi$
$487$	35.7699	1.62089	0.810445	+	0.585814i	$0.199225\pi$
$488$	4.07955	0.184672
$489$	−17.6847	−0.799728
$490$	−25.1465	−1.13600
$491$	−18.2726	−0.824632	−0.412316	−	0.911041i	$-0.635280\pi$
$491$	−18.2726	−0.824632	−0.412316	+	0.911041i	$0.635280\pi$
$492$	−10.0989	−0.455295
$493$	−0.0596724	−0.00268751
$494$	0	0
$495$	20.1219	0.904413
$496$	3.47985	0.156250
$497$	−5.07467	−0.227630
$498$	−4.22305	−0.189239
$499$	17.6980	0.792270	0.396135	−	0.918192i	$-0.370351\pi$
$499$	17.6980	0.792270	0.396135	+	0.918192i	$0.370351\pi$
$500$	13.5201	0.604639
$501$	−13.2681	−0.592777
$502$	2.90276	0.129556
$503$	−10.1902	−0.454361	−0.227180	−	0.973853i	$-0.572951\pi$
$503$	−10.1902	−0.454361	−0.227180	+	0.973853i	$0.572951\pi$
$504$	0.597831	0.0266295
$505$	1.57171	0.0699400
$506$	37.1105	1.64976
$507$	14.0307	0.623127
$508$	14.0806	0.624725
$509$	−8.43621	−0.373929	−0.186964	−	0.982367i	$-0.559865\pi$
$509$	−8.43621	−0.373929	−0.186964	+	0.982367i	$0.559865\pi$
$510$	1.26657	0.0560845
$511$	−0.629298	−0.0278385
$512$	1.00000	0.0441942
$513$	0	0
$514$	22.9050	1.01030
$515$	−16.7644	−0.738730
$516$	−7.23607	−0.318550
$517$	−8.85995	−0.389660
$518$	−0.641142	−0.0281702
$519$	−12.5994	−0.553052
$520$	18.0776	0.792754
$521$	8.96365	0.392705	0.196352	−	0.980533i	$-0.437090\pi$
$521$	8.96365	0.392705	0.196352	+	0.980533i	$0.437090\pi$
$522$	0.302090	0.0132221
$523$	−2.13993	−0.0935727	−0.0467864	−	0.998905i	$-0.514898\pi$
$523$	−2.13993	−0.0935727	−0.0467864	+	0.998905i	$0.514898\pi$
$524$	15.8415	0.692039
$525$	−4.91930	−0.214696
$526$	−5.06236	−0.220729
$527$	0.928748	0.0404569
$528$	−5.17442	−0.225188
$529$	61.8112	2.68744
$530$	36.7443	1.59607
$531$	4.74186	0.205779
$532$	0	0
$533$	−38.4702	−1.66633
$534$	−7.65407	−0.331224
$535$	−11.7210	−0.506744
$536$	0.147763	0.00638238
$537$	−11.2977	−0.487533
$538$	−20.7419	−0.894248
$539$	27.4188	1.18101
$540$	−20.6487	−0.888581
$541$	−11.7115	−0.503519	−0.251759	−	0.967790i	$-0.581009\pi$
$541$	−11.7115	−0.503519	−0.251759	+	0.967790i	$0.581009\pi$
$542$	6.29470	0.270381
$543$	18.6548	0.800553
$544$	0.266893	0.0114429
$545$	−25.0611	−1.07350
$546$	−2.77914	−0.118936
$547$	−24.9897	−1.06848	−0.534240	−	0.845333i	$-0.679402\pi$
$547$	−24.9897	−1.06848	−0.534240	+	0.845333i	$0.679402\pi$
$548$	2.20744	0.0942970
$549$	−5.51205	−0.235248
$550$	−34.8902	−1.48772
$551$	0	0
$552$	−11.8255	−0.503325
$553$	−4.51462	−0.191981
$554$	7.17608	0.304882
$555$	6.87650	0.291891
$556$	−17.0644	−0.723694
$557$	9.19566	0.389633	0.194816	−	0.980840i	$-0.437589\pi$
$557$	9.19566	0.389633	0.194816	+	0.980840i	$0.437589\pi$
$558$	−4.70177	−0.199042
$559$	−27.5646	−1.16586
$560$	−1.63522	−0.0691007
$561$	−1.38102	−0.0583065
$562$	2.77391	0.117010
$563$	19.7224	0.831202	0.415601	−	0.909547i	$-0.363571\pi$
$563$	19.7224	0.831202	0.415601	+	0.909547i	$0.363571\pi$
$564$	2.82328	0.118881
$565$	−37.1211	−1.56170
$566$	7.74861	0.325698
$567$	1.38093	0.0579935
$568$	11.4691	0.481234
$569$	22.1469	0.928446	0.464223	−	0.885718i	$-0.346334\pi$
$569$	22.1469	0.928446	0.464223	+	0.885718i	$0.346334\pi$
$570$	0	0
$571$	−3.02145	−0.126444	−0.0632218	−	0.998000i	$-0.520138\pi$
$571$	−3.02145	−0.126444	−0.0632218	+	0.998000i	$0.520138\pi$
$572$	−19.7111	−0.824163
$573$	16.3465	0.682886
$574$	3.47985	0.145246
$575$	−79.7371	−3.32527
$576$	−1.35114	−0.0562975
$577$	2.30938	0.0961407	0.0480704	−	0.998844i	$-0.484693\pi$
$577$	2.30938	0.0961407	0.0480704	+	0.998844i	$0.484693\pi$
$578$	−16.9288	−0.704144
$579$	22.4432	0.932708
$580$	−0.826294	−0.0343100
$581$	1.45516	0.0603704
$582$	5.24515	0.217419
$583$	−40.0646	−1.65931
$584$	1.42226	0.0588535
$585$	−24.4253	−1.00986
$586$	−0.782870	−0.0323401
$587$	28.0890	1.15936	0.579679	−	0.814845i	$-0.303178\pi$
$587$	28.0890	1.15936	0.579679	+	0.814845i	$0.303178\pi$
$588$	−8.73716	−0.360315
$589$	0	0
$590$	−12.9702	−0.533975
$591$	−31.4744	−1.29468
$592$	1.44903	0.0595547
$593$	−12.0939	−0.496637	−0.248318	−	0.968678i	$-0.579878\pi$
$593$	−12.0939	−0.496637	−0.248318	+	0.968678i	$0.579878\pi$
$594$	22.5146	0.923786
$595$	−0.436429	−0.0178918
$596$	13.5458	0.554856
$597$	21.1438	0.865357
$598$	−45.0472	−1.84212
$599$	19.5025	0.796851	0.398426	−	0.917201i	$-0.369557\pi$
$599$	19.5025	0.796851	0.398426	+	0.917201i	$0.369557\pi$
$600$	11.1180	0.453890
$601$	−38.9632	−1.58934	−0.794671	−	0.607040i	$-0.792357\pi$
$601$	−38.9632	−1.58934	−0.794671	+	0.607040i	$0.792357\pi$
$602$	2.49338	0.101623
$603$	−0.199648	−0.00813031
$604$	−9.15317	−0.372437
$605$	19.3591	0.787061
$606$	0.546090	0.0221834
$607$	8.46029	0.343393	0.171696	−	0.985150i	$-0.445075\pi$
$607$	8.46029	0.343393	0.171696	+	0.985150i	$0.445075\pi$
$608$	0	0
$609$	0.127030	0.00514750
$610$	15.0769	0.610444
$611$	10.7548	0.435093
$612$	−0.360610	−0.0145768
$613$	−2.91493	−0.117733	−0.0588664	−	0.998266i	$-0.518749\pi$
$613$	−2.91493	−0.117733	−0.0588664	+	0.998266i	$0.518749\pi$
$614$	−28.1688	−1.13680
$615$	−37.3228	−1.50500
$616$	1.78298	0.0718384
$617$	−3.01905	−0.121542	−0.0607712	−	0.998152i	$-0.519356\pi$
$617$	−3.01905	−0.121542	−0.0607712	+	0.998152i	$0.519356\pi$
$618$	−5.82481	−0.234308
$619$	−3.92813	−0.157885	−0.0789423	−	0.996879i	$-0.525154\pi$
$619$	−3.92813	−0.157885	−0.0789423	+	0.996879i	$0.525154\pi$
$620$	12.8606	0.516492
$621$	51.4543	2.06479
$622$	3.86827	0.155104
$623$	2.63741	0.105666
$624$	6.28106	0.251444
$625$	6.67500	0.267000
$626$	30.3878	1.21454
$627$	0	0
$628$	−16.3903	−0.654043
$629$	0.386735	0.0154201
$630$	2.20941	0.0880251
$631$	10.1367	0.403536	0.201768	−	0.979433i	$-0.435331\pi$
$631$	10.1367	0.403536	0.201768	+	0.979433i	$0.435331\pi$
$632$	10.2034	0.405869
$633$	35.2871	1.40254
$634$	5.32803	0.211603
$635$	52.0379	2.06506
$636$	12.7668	0.506238
$637$	−33.2828	−1.31871
$638$	0.900961	0.0356694
$639$	−15.4964	−0.613028
$640$	3.69572	0.146086
$641$	8.28031	0.327052	0.163526	−	0.986539i	$-0.447713\pi$
$641$	8.28031	0.327052	0.163526	+	0.986539i	$0.447713\pi$
$642$	−4.07247	−0.160728
$643$	36.8541	1.45338	0.726691	−	0.686964i	$-0.241057\pi$
$643$	36.8541	1.45338	0.726691	+	0.686964i	$0.241057\pi$
$644$	4.07478	0.160569
$645$	−26.7425	−1.05298
$646$	0	0
$647$	−20.1901	−0.793753	−0.396876	−	0.917872i	$-0.629906\pi$
$647$	−20.1901	−0.793753	−0.396876	+	0.917872i	$0.629906\pi$
$648$	−3.12099	−0.122604
$649$	14.1422	0.555131
$650$	42.3521	1.66119
$651$	−1.97711	−0.0774889
$652$	−13.7722	−0.539363
$653$	−22.0387	−0.862443	−0.431221	−	0.902246i	$-0.641917\pi$
$653$	−22.0387	−0.862443	−0.431221	+	0.902246i	$0.641917\pi$
$654$	−8.70749	−0.340490
$655$	58.5457	2.28757
$656$	−7.86472	−0.307066
$657$	−1.92167	−0.0749716
$658$	−0.972835	−0.0379251
$659$	−27.2216	−1.06040	−0.530202	−	0.847872i	$-0.677884\pi$
$659$	−27.2216	−1.06040	−0.530202	+	0.847872i	$0.677884\pi$
$660$	−19.1232	−0.744369
$661$	−8.90825	−0.346491	−0.173245	−	0.984879i	$-0.555425\pi$
$661$	−8.90825	−0.346491	−0.173245	+	0.984879i	$0.555425\pi$
$662$	−20.5480	−0.798622
$663$	1.67637	0.0651049
$664$	−3.28878	−0.127629
$665$	0	0
$666$	−1.95784	−0.0758648
$667$	2.05903	0.0797260
$668$	−10.3328	−0.399788
$669$	26.1574	1.01131
$670$	0.546090	0.0210973
$671$	−16.4392	−0.634630
$672$	−0.568158	−0.0219172
$673$	35.7010	1.37617	0.688087	−	0.725629i	$-0.258451\pi$
$673$	35.7010	1.37617	0.688087	+	0.725629i	$0.258451\pi$
$674$	13.2824	0.511620
$675$	−48.3759	−1.86199
$676$	10.9267	0.420257
$677$	−27.3849	−1.05249	−0.526243	−	0.850334i	$-0.676400\pi$
$677$	−27.3849	−1.05249	−0.526243	+	0.850334i	$0.676400\pi$
$678$	−12.8977	−0.495335
$679$	−1.80736	−0.0693600
$680$	0.986361	0.0378252
$681$	−28.4415	−1.08988
$682$	−14.0227	−0.536956
$683$	−38.1521	−1.45985	−0.729925	−	0.683528i	$-0.760445\pi$
$683$	−38.1521	−1.45985	−0.729925	+	0.683528i	$0.760445\pi$
$684$	0	0
$685$	8.15806	0.311703
$686$	6.10787	0.233199
$687$	16.3268	0.622905
$688$	−5.63522	−0.214841
$689$	48.6332	1.85278
$690$	−43.7036	−1.66377
$691$	−28.2058	−1.07300	−0.536499	−	0.843901i	$-0.680254\pi$
$691$	−28.2058	−1.07300	−0.536499	+	0.843901i	$0.680254\pi$
$692$	−9.81201	−0.372997
$693$	−2.40906	−0.0915127
$694$	30.1423	1.14419
$695$	−63.0654	−2.39221
$696$	−0.287096	−0.0108824
$697$	−2.09904	−0.0795068
$698$	35.0653	1.32724
$699$	−11.1481	−0.421659
$700$	−3.83099	−0.144798
$701$	42.6148	1.60954	0.804769	−	0.593588i	$-0.202289\pi$
$701$	42.6148	1.60954	0.804769	+	0.593588i	$0.202289\pi$
$702$	−27.3298	−1.03150
$703$	0	0
$704$	−4.02967	−0.151874
$705$	10.4340	0.392968
$706$	13.5411	0.509625
$707$	−0.188170	−0.00707685
$708$	−4.50651	−0.169365
$709$	−22.6892	−0.852110	−0.426055	−	0.904697i	$-0.640097\pi$
$709$	−22.6892	−0.852110	−0.426055	+	0.904697i	$0.640097\pi$
$710$	42.3866	1.59074
$711$	−13.7862	−0.517023
$712$	−5.96075	−0.223388
$713$	−32.0470	−1.20017
$714$	−0.151637	−0.00567489
$715$	−72.8467	−2.72431
$716$	−8.79830	−0.328808
$717$	28.0891	1.04901
$718$	−23.5072	−0.877282
$719$	−37.8324	−1.41091	−0.705456	−	0.708754i	$-0.749258\pi$
$719$	−37.8324	−1.41091	−0.705456	+	0.708754i	$0.749258\pi$
$720$	−4.99344	−0.186094
$721$	2.00709	0.0747481
$722$	0	0
$723$	−24.3503	−0.905596
$724$	14.5278	0.539920
$725$	−1.93584	−0.0718954
$726$	6.72634	0.249638
$727$	−19.5403	−0.724710	−0.362355	−	0.932040i	$-0.618027\pi$
$727$	−19.5403	−0.724710	−0.362355	+	0.932040i	$0.618027\pi$
$728$	−2.16431	−0.0802145
$729$	25.7402	0.953339
$730$	5.25627	0.194543
$731$	−1.50400	−0.0556275
$732$	5.23846	0.193619
$733$	35.1101	1.29682	0.648410	−	0.761291i	$-0.275434\pi$
$733$	35.1101	1.29682	0.648410	+	0.761291i	$0.275434\pi$
$734$	−12.6929	−0.468503
$735$	−32.2901	−1.19104
$736$	−9.20930	−0.339459
$737$	−0.595436	−0.0219332
$738$	10.6264	0.391161
$739$	−16.2775	−0.598776	−0.299388	−	0.954131i	$-0.596783\pi$
$739$	−16.2775	−0.598776	−0.299388	+	0.954131i	$0.596783\pi$
$740$	5.35520	0.196861
$741$	0	0
$742$	−4.39915	−0.161498
$743$	33.3085	1.22197	0.610986	−	0.791641i	$-0.290773\pi$
$743$	33.3085	1.22197	0.610986	+	0.791641i	$0.290773\pi$
$744$	4.46841	0.163820
$745$	50.0613	1.83410
$746$	2.64950	0.0970051
$747$	4.44360	0.162583
$748$	−1.07549	−0.0393239
$749$	1.40328	0.0512747
$750$	17.3609	0.633932
$751$	19.2599	0.702804	0.351402	−	0.936225i	$-0.385705\pi$
$751$	19.2599	0.702804	0.351402	+	0.936225i	$0.385705\pi$
$752$	2.19868	0.0801776
$753$	3.72737	0.135833
$754$	−1.09365	−0.0398283
$755$	−33.8275	−1.23111
$756$	2.47214	0.0899107
$757$	−23.9454	−0.870311	−0.435156	−	0.900355i	$-0.643307\pi$
$757$	−23.9454	−0.870311	−0.435156	+	0.900355i	$0.643307\pi$
$758$	18.1672	0.659863
$759$	47.6528	1.72969
$760$	0	0
$761$	−44.7968	−1.62388	−0.811941	−	0.583739i	$-0.801589\pi$
$761$	−44.7968	−1.62388	−0.811941	+	0.583739i	$0.801589\pi$
$762$	18.0806	0.654991
$763$	3.00040	0.108622
$764$	12.7302	0.460561
$765$	−1.33271	−0.0481843
$766$	23.0083	0.831324
$767$	−17.1668	−0.619858
$768$	1.28408	0.0463352
$769$	−31.7367	−1.14446	−0.572228	−	0.820095i	$-0.693921\pi$
$769$	−31.7367	−1.14446	−0.572228	+	0.820095i	$0.693921\pi$
$770$	6.58940	0.237466
$771$	29.4119	1.05924
$772$	17.4781	0.629049
$773$	−22.2307	−0.799582	−0.399791	−	0.916606i	$-0.630917\pi$
$773$	−22.2307	−0.799582	−0.399791	+	0.916606i	$0.630917\pi$
$774$	7.61398	0.273679
$775$	30.1297	1.08229
$776$	4.08476	0.146634
$777$	−0.823277	−0.0295349
$778$	−16.5706	−0.594086
$779$	0	0
$780$	23.2130	0.831160
$781$	−46.2168	−1.65377
$782$	−2.45790	−0.0878942
$783$	1.24920	0.0446427
$784$	−6.80423	−0.243008
$785$	−60.5739	−2.16197
$786$	20.3417	0.725566
$787$	24.4596	0.871891	0.435945	−	0.899973i	$-0.356414\pi$
$787$	24.4596	0.871891	0.435945	+	0.899973i	$0.356414\pi$
$788$	−24.5113	−0.873178
$789$	−6.50047	−0.231423
$790$	37.7088	1.34162
$791$	4.44426	0.158020
$792$	5.44466	0.193467
$793$	19.9551	0.708626
$794$	−17.7948	−0.631515
$795$	47.1826	1.67340
$796$	16.4661	0.583625
$797$	41.6933	1.47685	0.738426	−	0.674334i	$-0.235569\pi$
$797$	41.6933	1.47685	0.738426	+	0.674334i	$0.235569\pi$
$798$	0	0
$799$	0.586812	0.0207599
$800$	8.65833	0.306118
$801$	8.05381	0.284567
$802$	30.6215	1.08128
$803$	−5.73124	−0.202251
$804$	0.189739	0.00669159
$805$	15.0592	0.530768
$806$	17.0217	0.599563
$807$	−26.6343	−0.937571
$808$	0.425277	0.0149612
$809$	−49.2488	−1.73150	−0.865748	−	0.500481i	$-0.833157\pi$
$809$	−49.2488	−1.73150	−0.865748	+	0.500481i	$0.833157\pi$
$810$	−11.5343	−0.405275
$811$	52.0455	1.82756	0.913782	−	0.406205i	$-0.133148\pi$
$811$	52.0455	1.82756	0.913782	+	0.406205i	$0.133148\pi$
$812$	0.0989267	0.00347165
$813$	8.08289	0.283479
$814$	−5.83911	−0.204661
$815$	−50.8983	−1.78289
$816$	0.342712	0.0119973
$817$	0	0
$818$	9.14328	0.319687
$819$	2.92428	0.102183
$820$	−29.0658	−1.01502
$821$	−42.2582	−1.47482	−0.737411	−	0.675444i	$-0.763952\pi$
$821$	−42.2582	−1.47482	−0.737411	+	0.675444i	$0.763952\pi$
$822$	2.83452	0.0988653
$823$	32.4771	1.13208	0.566041	−	0.824377i	$-0.308475\pi$
$823$	32.4771	1.13208	0.566041	+	0.824377i	$0.308475\pi$
$824$	−4.53618	−0.158025
$825$	−44.8018	−1.55980
$826$	1.55284	0.0540301
$827$	−21.5156	−0.748172	−0.374086	−	0.927394i	$-0.622044\pi$
$827$	−21.5156	−0.748172	−0.374086	+	0.927394i	$0.622044\pi$
$828$	12.4431	0.432426
$829$	5.65061	0.196254	0.0981269	−	0.995174i	$-0.468715\pi$
$829$	5.65061	0.196254	0.0981269	+	0.995174i	$0.468715\pi$
$830$	−12.1544	−0.421885
$831$	9.21465	0.319653
$832$	4.89149	0.169582
$833$	−1.81600	−0.0629207
$834$	−21.9121	−0.758754
$835$	−38.1871	−1.32152
$836$	0	0
$837$	−19.4427	−0.672037
$838$	12.6157	0.435801
$839$	−10.6766	−0.368598	−0.184299	−	0.982870i	$-0.559001\pi$
$839$	−10.6766	−0.368598	−0.184299	+	0.982870i	$0.559001\pi$
$840$	−2.09975	−0.0724483
$841$	−28.9500	−0.998276
$842$	33.2553	1.14605
$843$	3.56192	0.122679
$844$	27.4805	0.945916
$845$	40.3820	1.38918
$846$	−2.97072	−0.102136
$847$	−2.31774	−0.0796385
$848$	9.94241	0.341424
$849$	9.94983	0.341477
$850$	2.31085	0.0792614
$851$	−13.3445	−0.457445
$852$	14.7273	0.504547
$853$	10.2666	0.351521	0.175760	−	0.984433i	$-0.443762\pi$
$853$	10.2666	0.351521	0.175760	+	0.984433i	$0.443762\pi$
$854$	−1.80505	−0.0617676
$855$	0	0
$856$	−3.17151	−0.108400
$857$	−37.3387	−1.27547	−0.637734	−	0.770257i	$-0.720128\pi$
$857$	−37.3387	−1.27547	−0.637734	+	0.770257i	$0.720128\pi$
$858$	−25.3106	−0.864090
$859$	−24.2890	−0.828729	−0.414365	−	0.910111i	$-0.635996\pi$
$859$	−24.2890	−0.828729	−0.414365	+	0.910111i	$0.635996\pi$
$860$	−20.8262	−0.710167
$861$	4.46841	0.152283
$862$	−22.9915	−0.783092
$863$	−23.5728	−0.802427	−0.401214	−	0.915985i	$-0.631412\pi$
$863$	−23.5728	−0.802427	−0.401214	+	0.915985i	$0.631412\pi$
$864$	−5.58721	−0.190081
$865$	−36.2624	−1.23296
$866$	34.7092	1.17947
$867$	−21.7379	−0.738257
$868$	−1.53971	−0.0522611
$869$	−41.1163	−1.39477
$870$	−1.06103	−0.0359722
$871$	0.722781	0.0244905
$872$	−6.78112	−0.229638
$873$	−5.51908	−0.186793
$874$	0	0
$875$	−5.98217	−0.202234
$876$	1.82629	0.0617048
$877$	−31.4382	−1.06159	−0.530796	−	0.847500i	$-0.678107\pi$
$877$	−31.4382	−1.06159	−0.530796	+	0.847500i	$0.678107\pi$
$878$	−36.4818	−1.23120
$879$	−1.00527	−0.0339068
$880$	−14.8925	−0.502027
$881$	−41.7600	−1.40693	−0.703466	−	0.710729i	$-0.748365\pi$
$881$	−41.7600	−1.40693	−0.703466	+	0.710729i	$0.748365\pi$
$882$	9.19347	0.309560
$883$	0.543040	0.0182748	0.00913738	−	0.999958i	$-0.497091\pi$
$883$	0.543040	0.0182748	0.00913738	+	0.999958i	$0.497091\pi$
$884$	1.30550	0.0439089
$885$	−16.6548	−0.559844
$886$	11.7583	0.395028
$887$	11.3248	0.380250	0.190125	−	0.981760i	$-0.439111\pi$
$887$	11.3248	0.380250	0.190125	+	0.981760i	$0.439111\pi$
$888$	1.86067	0.0624399
$889$	−6.23015	−0.208952
$890$	−22.0292	−0.738422
$891$	12.5766	0.421332
$892$	20.3706	0.682058
$893$	0	0
$894$	17.3938	0.581737
$895$	−32.5160	−1.08689
$896$	−0.442463	−0.0147817
$897$	−57.8442	−1.93136
$898$	−8.69102	−0.290023
$899$	−0.778031	−0.0259488
$900$	−11.6986	−0.389954
$901$	2.65356	0.0884029
$902$	31.6923	1.05524
$903$	3.20170	0.106546
$904$	−10.0444	−0.334070
$905$	53.6905	1.78473
$906$	−11.7534	−0.390481
$907$	10.9258	0.362787	0.181393	−	0.983411i	$-0.441939\pi$
$907$	10.9258	0.362787	0.181393	+	0.983411i	$0.441939\pi$
$908$	−22.1493	−0.735051
$909$	−0.574610	−0.0190586
$910$	−7.99866	−0.265153
$911$	47.4159	1.57096	0.785479	−	0.618888i	$-0.212416\pi$
$911$	47.4159	1.57096	0.785479	+	0.618888i	$0.212416\pi$
$912$	0	0
$913$	13.2527	0.438600
$914$	−13.0286	−0.430949
$915$	19.3599	0.640018
$916$	12.7148	0.420108
$917$	−7.00929	−0.231467
$918$	−1.49119	−0.0492165
$919$	5.11069	0.168586	0.0842930	−	0.996441i	$-0.473137\pi$
$919$	5.11069	0.168586	0.0842930	+	0.996441i	$0.473137\pi$
$920$	−34.0350	−1.12210
$921$	−36.1709	−1.19187
$922$	9.04260	0.297802
$923$	56.1011	1.84659
$924$	2.28949	0.0753187
$925$	12.5462	0.412515
$926$	−17.7205	−0.582332
$927$	6.12902	0.201303
$928$	−0.223582	−0.00733942
$929$	−42.8442	−1.40567	−0.702837	−	0.711351i	$-0.748084\pi$
$929$	−42.8442	−1.40567	−0.702837	+	0.711351i	$0.748084\pi$
$930$	16.5140	0.541514
$931$	0	0
$932$	−8.68176	−0.284381
$933$	4.96717	0.162618
$934$	−7.87772	−0.257767
$935$	−3.97471	−0.129987
$936$	−6.60909	−0.216025
$937$	−3.67885	−0.120183	−0.0600913	−	0.998193i	$-0.519139\pi$
$937$	−3.67885	−0.120183	−0.0600913	+	0.998193i	$0.519139\pi$
$938$	−0.0653797	−0.00213472
$939$	39.0203	1.27338
$940$	8.12569	0.265031
$941$	18.3795	0.599154	0.299577	−	0.954072i	$-0.403154\pi$
$941$	18.3795	0.599154	0.299577	+	0.954072i	$0.403154\pi$
$942$	−21.0464	−0.685729
$943$	72.4286	2.35860
$944$	−3.50953	−0.114225
$945$	9.13632	0.297204
$946$	22.7081	0.738304
$947$	46.7590	1.51946	0.759732	−	0.650237i	$-0.225330\pi$
$947$	46.7590	1.51946	0.759732	+	0.650237i	$0.225330\pi$
$948$	13.1019	0.425531
$949$	6.95697	0.225833
$950$	0	0
$951$	6.84162	0.221855
$952$	−0.118090	−0.00382733
$953$	25.0551	0.811613	0.405807	−	0.913959i	$-0.366991\pi$
$953$	25.0551	0.811613	0.405807	+	0.913959i	$0.366991\pi$
$954$	−13.4336	−0.434929
$955$	47.0471	1.52241
$956$	21.8749	0.707485
$957$	1.15690	0.0373974
$958$	−30.1798	−0.975066
$959$	−0.976709	−0.0315396
$960$	4.74559	0.153163
$961$	−18.8906	−0.609375
$962$	7.08791	0.228523
$963$	4.28516	0.138087
$964$	−18.9632	−0.610764
$965$	64.5940	2.07935
$966$	5.23234	0.168348
$967$	7.10627	0.228522	0.114261	−	0.993451i	$-0.463550\pi$
$967$	7.10627	0.228522	0.114261	+	0.993451i	$0.463550\pi$
$968$	5.23826	0.168364
$969$	0	0
$970$	15.0961	0.484707
$971$	60.7543	1.94970	0.974848	−	0.222869i	$-0.0715422\pi$
$971$	60.7543	1.94970	0.974848	+	0.222869i	$0.0715422\pi$
$972$	12.7540	0.409085
$973$	7.55039	0.242054
$974$	35.7699	1.14614
$975$	54.3835	1.74167
$976$	4.07955	0.130583
$977$	−38.5412	−1.23304	−0.616520	−	0.787339i	$-0.711458\pi$
$977$	−38.5412	−1.23304	−0.616520	+	0.787339i	$0.711458\pi$
$978$	−17.6847	−0.565493
$979$	24.0199	0.767678
$980$	−25.1465	−0.803275
$981$	9.16225	0.292528
$982$	−18.2726	−0.583103
$983$	−7.50529	−0.239381	−0.119691	−	0.992811i	$-0.538190\pi$
$983$	−7.50529	−0.239381	−0.119691	+	0.992811i	$0.538190\pi$
$984$	−10.0989	−0.321942
$985$	−90.5868	−2.88633
$986$	−0.0596724	−0.00190035
$987$	−1.24920	−0.0397624
$988$	0	0
$989$	51.8964	1.65021
$990$	20.1219	0.639516
$991$	−21.4221	−0.680496	−0.340248	−	0.940336i	$-0.610511\pi$
$991$	−21.4221	−0.680496	−0.340248	+	0.940336i	$0.610511\pi$
$992$	3.47985	0.110485
$993$	−26.3853	−0.837312
$994$	−5.07467	−0.160959
$995$	60.8541	1.92920
$996$	−4.22305	−0.133813
$997$	−41.0005	−1.29850	−0.649250	−	0.760575i	$-0.724917\pi$
$997$	−41.0005	−1.29850	−0.649250	+	0.760575i	$0.724917\pi$
$998$	17.6980	0.560220
$999$	−8.09602	−0.256147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.a.n.1.3	yes	4
3.2	odd	2		6498.2.a.bx.1.1		4
4.3	odd	2		5776.2.a.bt.1.2		4
19.2	odd	18		722.2.e.s.99.2		24
19.3	odd	18		722.2.e.s.389.2		24
19.4	even	9		722.2.e.r.415.2		24
19.5	even	9		722.2.e.r.595.2		24
19.6	even	9		722.2.e.r.245.3		24
19.7	even	3		722.2.c.m.429.2		8
19.8	odd	6		722.2.c.n.653.3		8
19.9	even	9		722.2.e.r.423.3		24
19.10	odd	18		722.2.e.s.423.2		24
19.11	even	3		722.2.c.m.653.2		8
19.12	odd	6		722.2.c.n.429.3		8
19.13	odd	18		722.2.e.s.245.2		24
19.14	odd	18		722.2.e.s.595.3		24
19.15	odd	18		722.2.e.s.415.3		24
19.16	even	9		722.2.e.r.389.3		24
19.17	even	9		722.2.e.r.99.3		24
19.18	odd	2		722.2.a.m.1.2	✓	4
57.56	even	2		6498.2.a.ca.1.1		4
76.75	even	2		5776.2.a.bv.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.2	✓	4	19.18	odd	2
722.2.a.n.1.3	yes	4	1.1	even	1	trivial
722.2.c.m.429.2		8	19.7	even	3
722.2.c.m.653.2		8	19.11	even	3
722.2.c.n.429.3		8	19.12	odd	6
722.2.c.n.653.3		8	19.8	odd	6
722.2.e.r.99.3		24	19.17	even	9
722.2.e.r.245.3		24	19.6	even	9
722.2.e.r.389.3		24	19.16	even	9
722.2.e.r.415.2		24	19.4	even	9
722.2.e.r.423.3		24	19.9	even	9
722.2.e.r.595.2		24	19.5	even	9
722.2.e.s.99.2		24	19.2	odd	18
722.2.e.s.245.2		24	19.13	odd	18
722.2.e.s.389.2		24	19.3	odd	18
722.2.e.s.415.3		24	19.15	odd	18
722.2.e.s.423.2		24	19.10	odd	18
722.2.e.s.595.3		24	19.14	odd	18
5776.2.a.bt.1.2		4	4.3	odd	2
5776.2.a.bv.1.3		4	76.75	even	2
6498.2.a.bx.1.1		4	3.2	odd	2
6498.2.a.ca.1.1		4	57.56	even	2

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.28408 q^{3} +1.00000 q^{4} +3.69572 q^{5} +1.28408 q^{6} -0.442463 q^{7} +1.00000 q^{8} -1.35114 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.28408 q^{3} +1.00000 q^{4} +3.69572 q^{5} +1.28408 q^{6} -0.442463 q^{7} +1.00000 q^{8} -1.35114 q^{9} +3.69572 q^{10} -4.02967 q^{11} +1.28408 q^{12} +4.89149 q^{13} -0.442463 q^{14} +4.74559 q^{15} +1.00000 q^{16} +0.266893 q^{17} -1.35114 q^{18} +3.69572 q^{20} -0.568158 q^{21} -4.02967 q^{22} -9.20930 q^{23} +1.28408 q^{24} +8.65833 q^{25} +4.89149 q^{26} -5.58721 q^{27} -0.442463 q^{28} -0.223582 q^{29} +4.74559 q^{30} +3.47985 q^{31} +1.00000 q^{32} -5.17442 q^{33} +0.266893 q^{34} -1.63522 q^{35} -1.35114 q^{36} +1.44903 q^{37} +6.28106 q^{39} +3.69572 q^{40} -7.86472 q^{41} -0.568158 q^{42} -5.63522 q^{43} -4.02967 q^{44} -4.99344 q^{45} -9.20930 q^{46} +2.19868 q^{47} +1.28408 q^{48} -6.80423 q^{49} +8.65833 q^{50} +0.342712 q^{51} +4.89149 q^{52} +9.94241 q^{53} -5.58721 q^{54} -14.8925 q^{55} -0.442463 q^{56} -0.223582 q^{58} -3.50953 q^{59} +4.74559 q^{60} +4.07955 q^{61} +3.47985 q^{62} +0.597831 q^{63} +1.00000 q^{64} +18.0776 q^{65} -5.17442 q^{66} +0.147763 q^{67} +0.266893 q^{68} -11.8255 q^{69} -1.63522 q^{70} +11.4691 q^{71} -1.35114 q^{72} +1.42226 q^{73} +1.44903 q^{74} +11.1180 q^{75} +1.78298 q^{77} +6.28106 q^{78} +10.2034 q^{79} +3.69572 q^{80} -3.12099 q^{81} -7.86472 q^{82} -3.28878 q^{83} -0.568158 q^{84} +0.986361 q^{85} -5.63522 q^{86} -0.287096 q^{87} -4.02967 q^{88} -5.96075 q^{89} -4.99344 q^{90} -2.16431 q^{91} -9.20930 q^{92} +4.46841 q^{93} +2.19868 q^{94} +1.28408 q^{96} +4.08476 q^{97} -6.80423 q^{98} +5.44466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 2 q^{11} + 2 q^{12} + 18 q^{13} - 2 q^{14} + 4 q^{15} + 4 q^{16} + 6 q^{17} + 4 q^{18} - 2 q^{20} + 4 q^{21} + 2 q^{22} - 10 q^{23} + 2 q^{24} + 6 q^{25} + 18 q^{26} - 4 q^{27} - 2 q^{28} - 2 q^{29} + 4 q^{30} + 26 q^{31} + 4 q^{32} + 16 q^{33} + 6 q^{34} + 6 q^{35} + 4 q^{36} + 4 q^{37} - 6 q^{39} - 2 q^{40} - 12 q^{41} + 4 q^{42} - 10 q^{43} + 2 q^{44} - 22 q^{45} - 10 q^{46} - 12 q^{47} + 2 q^{48} - 12 q^{49} + 6 q^{50} - 2 q^{51} + 18 q^{52} + 8 q^{53} - 4 q^{54} - 26 q^{55} - 2 q^{56} - 2 q^{58} - 8 q^{59} + 4 q^{60} + 26 q^{62} - 22 q^{63} + 4 q^{64} - 4 q^{65} + 16 q^{66} + 10 q^{67} + 6 q^{68} - 20 q^{69} + 6 q^{70} + 4 q^{72} - 14 q^{73} + 4 q^{74} + 8 q^{75} + 4 q^{77} - 6 q^{78} + 22 q^{79} - 2 q^{80} - 4 q^{81} - 12 q^{82} - 12 q^{83} + 4 q^{84} - 18 q^{85} - 10 q^{86} - 26 q^{87} + 2 q^{88} - 16 q^{89} - 22 q^{90} - 4 q^{91} - 10 q^{92} + 8 q^{93} - 12 q^{94} + 2 q^{96} + 28 q^{97} - 12 q^{98} + 22 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 2 * q^11 + 2 * q^12 + 18 * q^13 - 2 * q^14 + 4 * q^15 + 4 * q^16 + 6 * q^17 + 4 * q^18 - 2 * q^20 + 4 * q^21 + 2 * q^22 - 10 * q^23 + 2 * q^24 + 6 * q^25 + 18 * q^26 - 4 * q^27 - 2 * q^28 - 2 * q^29 + 4 * q^30 + 26 * q^31 + 4 * q^32 + 16 * q^33 + 6 * q^34 + 6 * q^35 + 4 * q^36 + 4 * q^37 - 6 * q^39 - 2 * q^40 - 12 * q^41 + 4 * q^42 - 10 * q^43 + 2 * q^44 - 22 * q^45 - 10 * q^46 - 12 * q^47 + 2 * q^48 - 12 * q^49 + 6 * q^50 - 2 * q^51 + 18 * q^52 + 8 * q^53 - 4 * q^54 - 26 * q^55 - 2 * q^56 - 2 * q^58 - 8 * q^59 + 4 * q^60 + 26 * q^62 - 22 * q^63 + 4 * q^64 - 4 * q^65 + 16 * q^66 + 10 * q^67 + 6 * q^68 - 20 * q^69 + 6 * q^70 + 4 * q^72 - 14 * q^73 + 4 * q^74 + 8 * q^75 + 4 * q^77 - 6 * q^78 + 22 * q^79 - 2 * q^80 - 4 * q^81 - 12 * q^82 - 12 * q^83 + 4 * q^84 - 18 * q^85 - 10 * q^86 - 26 * q^87 + 2 * q^88 - 16 * q^89 - 22 * q^90 - 4 * q^91 - 10 * q^92 + 8 * q^93 - 12 * q^94 + 2 * q^96 + 28 * q^97 - 12 * q^98 + 22 * q^99

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