LMFDB - Embedded newform 2738.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, 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("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.79129$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -2.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +4.79129 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -2.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +4.79129 q^{9} -3.79129 q^{10} -3.79129 q^{11} +2.79129 q^{12} -0.791288 q^{13} +2.00000 q^{14} +10.5826 q^{15} +1.00000 q^{16} +1.58258 q^{17} -4.79129 q^{18} +7.58258 q^{19} +3.79129 q^{20} -5.58258 q^{21} +3.79129 q^{22} -0.791288 q^{23} -2.79129 q^{24} +9.37386 q^{25} +0.791288 q^{26} +5.00000 q^{27} -2.00000 q^{28} -0.791288 q^{29} -10.5826 q^{30} +5.37386 q^{31} -1.00000 q^{32} -10.5826 q^{33} -1.58258 q^{34} -7.58258 q^{35} +4.79129 q^{36} -7.58258 q^{38} -2.20871 q^{39} -3.79129 q^{40} -5.20871 q^{41} +5.58258 q^{42} +6.00000 q^{43} -3.79129 q^{44} +18.1652 q^{45} +0.791288 q^{46} +1.58258 q^{47} +2.79129 q^{48} -3.00000 q^{49} -9.37386 q^{50} +4.41742 q^{51} -0.791288 q^{52} +7.58258 q^{53} -5.00000 q^{54} -14.3739 q^{55} +2.00000 q^{56} +21.1652 q^{57} +0.791288 q^{58} +7.58258 q^{59} +10.5826 q^{60} +8.20871 q^{61} -5.37386 q^{62} -9.58258 q^{63} +1.00000 q^{64} -3.00000 q^{65} +10.5826 q^{66} +7.37386 q^{67} +1.58258 q^{68} -2.20871 q^{69} +7.58258 q^{70} +9.16515 q^{71} -4.79129 q^{72} -9.37386 q^{73} +26.1652 q^{75} +7.58258 q^{76} +7.58258 q^{77} +2.20871 q^{78} -12.7913 q^{79} +3.79129 q^{80} -0.417424 q^{81} +5.20871 q^{82} -3.16515 q^{83} -5.58258 q^{84} +6.00000 q^{85} -6.00000 q^{86} -2.20871 q^{87} +3.79129 q^{88} +6.00000 q^{89} -18.1652 q^{90} +1.58258 q^{91} -0.791288 q^{92} +15.0000 q^{93} -1.58258 q^{94} +28.7477 q^{95} -2.79129 q^{96} +4.41742 q^{97} +3.00000 q^{98} -18.1652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + q^{12} + 3 q^{13} + 4 q^{14} + 12 q^{15} + 2 q^{16} - 6 q^{17} - 5 q^{18} + 6 q^{19} + 3 q^{20} - 2 q^{21} + 3 q^{22} + 3 q^{23} - q^{24} + 5 q^{25} - 3 q^{26} + 10 q^{27} - 4 q^{28} + 3 q^{29} - 12 q^{30} - 3 q^{31} - 2 q^{32} - 12 q^{33} + 6 q^{34} - 6 q^{35} + 5 q^{36} - 6 q^{38} - 9 q^{39} - 3 q^{40} - 15 q^{41} + 2 q^{42} + 12 q^{43} - 3 q^{44} + 18 q^{45} - 3 q^{46} - 6 q^{47} + q^{48} - 6 q^{49} - 5 q^{50} + 18 q^{51} + 3 q^{52} + 6 q^{53} - 10 q^{54} - 15 q^{55} + 4 q^{56} + 24 q^{57} - 3 q^{58} + 6 q^{59} + 12 q^{60} + 21 q^{61} + 3 q^{62} - 10 q^{63} + 2 q^{64} - 6 q^{65} + 12 q^{66} + q^{67} - 6 q^{68} - 9 q^{69} + 6 q^{70} - 5 q^{72} - 5 q^{73} + 34 q^{75} + 6 q^{76} + 6 q^{77} + 9 q^{78} - 21 q^{79} + 3 q^{80} - 10 q^{81} + 15 q^{82} + 12 q^{83} - 2 q^{84} + 12 q^{85} - 12 q^{86} - 9 q^{87} + 3 q^{88} + 12 q^{89} - 18 q^{90} - 6 q^{91} + 3 q^{92} + 30 q^{93} + 6 q^{94} + 30 q^{95} - q^{96} + 18 q^{97} + 6 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + q^12 + 3 * q^13 + 4 * q^14 + 12 * q^15 + 2 * q^16 - 6 * q^17 - 5 * q^18 + 6 * q^19 + 3 * q^20 - 2 * q^21 + 3 * q^22 + 3 * q^23 - q^24 + 5 * q^25 - 3 * q^26 + 10 * q^27 - 4 * q^28 + 3 * q^29 - 12 * q^30 - 3 * q^31 - 2 * q^32 - 12 * q^33 + 6 * q^34 - 6 * q^35 + 5 * q^36 - 6 * q^38 - 9 * q^39 - 3 * q^40 - 15 * q^41 + 2 * q^42 + 12 * q^43 - 3 * q^44 + 18 * q^45 - 3 * q^46 - 6 * q^47 + q^48 - 6 * q^49 - 5 * q^50 + 18 * q^51 + 3 * q^52 + 6 * q^53 - 10 * q^54 - 15 * q^55 + 4 * q^56 + 24 * q^57 - 3 * q^58 + 6 * q^59 + 12 * q^60 + 21 * q^61 + 3 * q^62 - 10 * q^63 + 2 * q^64 - 6 * q^65 + 12 * q^66 + q^67 - 6 * q^68 - 9 * q^69 + 6 * q^70 - 5 * q^72 - 5 * q^73 + 34 * q^75 + 6 * q^76 + 6 * q^77 + 9 * q^78 - 21 * q^79 + 3 * q^80 - 10 * q^81 + 15 * q^82 + 12 * q^83 - 2 * q^84 + 12 * q^85 - 12 * q^86 - 9 * q^87 + 3 * q^88 + 12 * q^89 - 18 * q^90 - 6 * q^91 + 3 * q^92 + 30 * q^93 + 6 * q^94 + 30 * q^95 - q^96 + 18 * q^97 + 6 * q^98 - 18 * 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
$3$	2.79129	1.61155	0.805775	−	0.592221i	$-0.201749\pi$
$3$	2.79129	1.61155	0.805775	+	0.592221i	$0.201749\pi$
$4$	1.00000	0.500000
$5$	3.79129	1.69552	0.847758	−	0.530384i	$-0.177952\pi$
$5$	3.79129	1.69552	0.847758	+	0.530384i	$0.177952\pi$
$6$	−2.79129	−1.13954
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	4.79129	1.59710
$10$	−3.79129	−1.19891
$11$	−3.79129	−1.14312	−0.571558	−	0.820562i	$-0.693661\pi$
$11$	−3.79129	−1.14312	−0.571558	+	0.820562i	$0.693661\pi$
$12$	2.79129	0.805775
$13$	−0.791288	−0.219464	−0.109732	−	0.993961i	$-0.534999\pi$
$13$	−0.791288	−0.219464	−0.109732	+	0.993961i	$0.534999\pi$
$14$	2.00000	0.534522
$15$	10.5826	2.73241
$16$	1.00000	0.250000
$17$	1.58258	0.383831	0.191915	−	0.981411i	$-0.438530\pi$
$17$	1.58258	0.383831	0.191915	+	0.981411i	$0.438530\pi$
$18$	−4.79129	−1.12932
$19$	7.58258	1.73956	0.869781	−	0.493438i	$-0.164260\pi$
$19$	7.58258	1.73956	0.869781	+	0.493438i	$0.164260\pi$
$20$	3.79129	0.847758
$21$	−5.58258	−1.21822
$22$	3.79129	0.808305
$23$	−0.791288	−0.164995	−0.0824975	−	0.996591i	$-0.526290\pi$
$23$	−0.791288	−0.164995	−0.0824975	+	0.996591i	$0.526290\pi$
$24$	−2.79129	−0.569769
$25$	9.37386	1.87477
$26$	0.791288	0.155184
$27$	5.00000	0.962250
$28$	−2.00000	−0.377964
$29$	−0.791288	−0.146938	−0.0734692	−	0.997297i	$-0.523407\pi$
$29$	−0.791288	−0.146938	−0.0734692	+	0.997297i	$0.523407\pi$
$30$	−10.5826	−1.93211
$31$	5.37386	0.965174	0.482587	−	0.875848i	$-0.339697\pi$
$31$	5.37386	0.965174	0.482587	+	0.875848i	$0.339697\pi$
$32$	−1.00000	−0.176777
$33$	−10.5826	−1.84219
$34$	−1.58258	−0.271409
$35$	−7.58258	−1.28169
$36$	4.79129	0.798548
$37$	0	0
$37$	0	0
$38$	−7.58258	−1.23006
$39$	−2.20871	−0.353677
$40$	−3.79129	−0.599455
$41$	−5.20871	−0.813464	−0.406732	−	0.913547i	$-0.633332\pi$
$41$	−5.20871	−0.813464	−0.406732	+	0.913547i	$0.633332\pi$
$42$	5.58258	0.861410
$43$	6.00000	0.914991	0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000	0.914991	0.457496	+	0.889212i	$0.348747\pi$
$44$	−3.79129	−0.571558
$45$	18.1652	2.70790
$46$	0.791288	0.116669
$47$	1.58258	0.230842	0.115421	−	0.993317i	$-0.463178\pi$
$47$	1.58258	0.230842	0.115421	+	0.993317i	$0.463178\pi$
$48$	2.79129	0.402888
$49$	−3.00000	−0.428571
$50$	−9.37386	−1.32566
$51$	4.41742	0.618563
$52$	−0.791288	−0.109732
$53$	7.58258	1.04155	0.520773	−	0.853695i	$-0.325644\pi$
$53$	7.58258	1.04155	0.520773	+	0.853695i	$0.325644\pi$
$54$	−5.00000	−0.680414
$55$	−14.3739	−1.93817
$56$	2.00000	0.267261
$57$	21.1652	2.80339
$58$	0.791288	0.103901
$59$	7.58258	0.987167	0.493584	−	0.869698i	$-0.335687\pi$
$59$	7.58258	0.987167	0.493584	+	0.869698i	$0.335687\pi$
$60$	10.5826	1.36620
$61$	8.20871	1.05102	0.525509	−	0.850788i	$-0.323875\pi$
$61$	8.20871	1.05102	0.525509	+	0.850788i	$0.323875\pi$
$62$	−5.37386	−0.682481
$63$	−9.58258	−1.20729
$64$	1.00000	0.125000
$65$	−3.00000	−0.372104
$66$	10.5826	1.30263
$67$	7.37386	0.900861	0.450430	−	0.892812i	$-0.351271\pi$
$67$	7.37386	0.900861	0.450430	+	0.892812i	$0.351271\pi$
$68$	1.58258	0.191915
$69$	−2.20871	−0.265898
$70$	7.58258	0.906291
$71$	9.16515	1.08770	0.543852	−	0.839181i	$-0.316965\pi$
$71$	9.16515	1.08770	0.543852	+	0.839181i	$0.316965\pi$
$72$	−4.79129	−0.564659
$73$	−9.37386	−1.09713	−0.548564	−	0.836109i	$-0.684825\pi$
$73$	−9.37386	−1.09713	−0.548564	+	0.836109i	$0.684825\pi$
$74$	0	0
$75$	26.1652	3.02129
$76$	7.58258	0.869781
$77$	7.58258	0.864115
$78$	2.20871	0.250087
$79$	−12.7913	−1.43913	−0.719566	−	0.694424i	$-0.755659\pi$
$79$	−12.7913	−1.43913	−0.719566	+	0.694424i	$0.755659\pi$
$80$	3.79129	0.423879
$81$	−0.417424	−0.0463805
$82$	5.20871	0.575206
$83$	−3.16515	−0.347421	−0.173710	−	0.984797i	$-0.555576\pi$
$83$	−3.16515	−0.347421	−0.173710	+	0.984797i	$0.555576\pi$
$84$	−5.58258	−0.609109
$85$	6.00000	0.650791
$86$	−6.00000	−0.646997
$87$	−2.20871	−0.236799
$88$	3.79129	0.404153
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−18.1652	−1.91478
$91$	1.58258	0.165899
$92$	−0.791288	−0.0824975
$93$	15.0000	1.55543
$94$	−1.58258	−0.163230
$95$	28.7477	2.94945
$96$	−2.79129	−0.284885
$97$	4.41742	0.448521	0.224261	−	0.974529i	$-0.428003\pi$
$97$	4.41742	0.448521	0.224261	+	0.974529i	$0.428003\pi$
$98$	3.00000	0.303046
$99$	−18.1652	−1.82567
$100$	9.37386	0.937386
$101$	1.58258	0.157472	0.0787361	−	0.996895i	$-0.474912\pi$
$101$	1.58258	0.157472	0.0787361	+	0.996895i	$0.474912\pi$
$102$	−4.41742	−0.437390
$103$	2.20871	0.217631	0.108815	−	0.994062i	$-0.465294\pi$
$103$	2.20871	0.217631	0.108815	+	0.994062i	$0.465294\pi$
$104$	0.791288	0.0775922
$105$	−21.1652	−2.06551
$106$	−7.58258	−0.736485
$107$	8.37386	0.809532	0.404766	−	0.914420i	$-0.367353\pi$
$107$	8.37386	0.809532	0.404766	+	0.914420i	$0.367353\pi$
$108$	5.00000	0.481125
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	14.3739	1.37049
$111$	0	0
$112$	−2.00000	−0.188982
$113$	−19.5826	−1.84217	−0.921087	−	0.389357i	$-0.872697\pi$
$113$	−19.5826	−1.84217	−0.921087	+	0.389357i	$0.872697\pi$
$114$	−21.1652	−1.98230
$115$	−3.00000	−0.279751
$116$	−0.791288	−0.0734692
$117$	−3.79129	−0.350505
$118$	−7.58258	−0.698033
$119$	−3.16515	−0.290149
$120$	−10.5826	−0.966053
$121$	3.37386	0.306715
$122$	−8.20871	−0.743182
$123$	−14.5390	−1.31094
$124$	5.37386	0.482587
$125$	16.5826	1.48319
$126$	9.58258	0.853684
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	16.7477	1.47456
$130$	3.00000	0.263117
$131$	−10.7477	−0.939033	−0.469517	−	0.882924i	$-0.655572\pi$
$131$	−10.7477	−0.939033	−0.469517	+	0.882924i	$0.655572\pi$
$132$	−10.5826	−0.921095
$133$	−15.1652	−1.31499
$134$	−7.37386	−0.637005
$135$	18.9564	1.63151
$136$	−1.58258	−0.135705
$137$	−17.3739	−1.48435	−0.742175	−	0.670207i	$-0.766206\pi$
$137$	−17.3739	−1.48435	−0.742175	+	0.670207i	$0.766206\pi$
$138$	2.20871	0.188018
$139$	−0.373864	−0.0317107	−0.0158553	−	0.999874i	$-0.505047\pi$
$139$	−0.373864	−0.0317107	−0.0158553	+	0.999874i	$0.505047\pi$
$140$	−7.58258	−0.640845
$141$	4.41742	0.372014
$142$	−9.16515	−0.769122
$143$	3.00000	0.250873
$144$	4.79129	0.399274
$145$	−3.00000	−0.249136
$146$	9.37386	0.775786
$147$	−8.37386	−0.690665
$148$	0	0
$149$	−13.5826	−1.11273	−0.556364	−	0.830939i	$-0.687804\pi$
$149$	−13.5826	−1.11273	−0.556364	+	0.830939i	$0.687804\pi$
$150$	−26.1652	−2.13638
$151$	−12.7477	−1.03740	−0.518698	−	0.854958i	$-0.673583\pi$
$151$	−12.7477	−1.03740	−0.518698	+	0.854958i	$0.673583\pi$
$152$	−7.58258	−0.615028
$153$	7.58258	0.613015
$154$	−7.58258	−0.611021
$155$	20.3739	1.63647
$156$	−2.20871	−0.176838
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	12.7913	1.01762
$159$	21.1652	1.67851
$160$	−3.79129	−0.299728
$161$	1.58258	0.124724
$162$	0.417424	0.0327960
$163$	10.4174	0.815956	0.407978	−	0.912992i	$-0.366234\pi$
$163$	10.4174	0.815956	0.407978	+	0.912992i	$0.366234\pi$
$164$	−5.20871	−0.406732
$165$	−40.1216	−3.12346
$166$	3.16515	0.245663
$167$	−0.956439	−0.0740115	−0.0370057	−	0.999315i	$-0.511782\pi$
$167$	−0.956439	−0.0740115	−0.0370057	+	0.999315i	$0.511782\pi$
$168$	5.58258	0.430705
$169$	−12.3739	−0.951836
$170$	−6.00000	−0.460179
$171$	36.3303	2.77825
$172$	6.00000	0.457496
$173$	3.16515	0.240642	0.120321	−	0.992735i	$-0.461608\pi$
$173$	3.16515	0.240642	0.120321	+	0.992735i	$0.461608\pi$
$174$	2.20871	0.167442
$175$	−18.7477	−1.41719
$176$	−3.79129	−0.285779
$177$	21.1652	1.59087
$178$	−6.00000	−0.449719
$179$	−7.58258	−0.566748	−0.283374	−	0.959009i	$-0.591454\pi$
$179$	−7.58258	−0.566748	−0.283374	+	0.959009i	$0.591454\pi$
$180$	18.1652	1.35395
$181$	−18.7477	−1.39351	−0.696754	−	0.717310i	$-0.745373\pi$
$181$	−18.7477	−1.39351	−0.696754	+	0.717310i	$0.745373\pi$
$182$	−1.58258	−0.117308
$183$	22.9129	1.69377
$184$	0.791288	0.0583345
$185$	0	0
$186$	−15.0000	−1.09985
$187$	−6.00000	−0.438763
$188$	1.58258	0.115421
$189$	−10.0000	−0.727393
$190$	−28.7477	−2.08558
$191$	5.37386	0.388839	0.194420	−	0.980918i	$-0.437718\pi$
$191$	5.37386	0.388839	0.194420	+	0.980918i	$0.437718\pi$
$192$	2.79129	0.201444
$193$	−18.3303	−1.31944	−0.659722	−	0.751510i	$-0.729326\pi$
$193$	−18.3303	−1.31944	−0.659722	+	0.751510i	$0.729326\pi$
$194$	−4.41742	−0.317153
$195$	−8.37386	−0.599665
$196$	−3.00000	−0.214286
$197$	25.9129	1.84622	0.923108	−	0.384541i	$-0.125640\pi$
$197$	25.9129	1.84622	0.923108	+	0.384541i	$0.125640\pi$
$198$	18.1652	1.29094
$199$	3.16515	0.224372	0.112186	−	0.993687i	$-0.464215\pi$
$199$	3.16515	0.224372	0.112186	+	0.993687i	$0.464215\pi$
$200$	−9.37386	−0.662832
$201$	20.5826	1.45178
$202$	−1.58258	−0.111350
$203$	1.58258	0.111075
$204$	4.41742	0.309282
$205$	−19.7477	−1.37924
$206$	−2.20871	−0.153888
$207$	−3.79129	−0.263513
$208$	−0.791288	−0.0548659
$209$	−28.7477	−1.98852
$210$	21.1652	1.46053
$211$	−3.37386	−0.232266	−0.116133	−	0.993234i	$-0.537050\pi$
$211$	−3.37386	−0.232266	−0.116133	+	0.993234i	$0.537050\pi$
$212$	7.58258	0.520773
$213$	25.5826	1.75289
$214$	−8.37386	−0.572426
$215$	22.7477	1.55138
$216$	−5.00000	−0.340207
$217$	−10.7477	−0.729603
$218$	6.00000	0.406371
$219$	−26.1652	−1.76808
$220$	−14.3739	−0.969086
$221$	−1.25227	−0.0842370
$222$	0	0
$223$	14.0000	0.937509	0.468755	−	0.883328i	$-0.344703\pi$
$223$	14.0000	0.937509	0.468755	+	0.883328i	$0.344703\pi$
$224$	2.00000	0.133631
$225$	44.9129	2.99419
$226$	19.5826	1.30261
$227$	−19.9129	−1.32166	−0.660832	−	0.750534i	$-0.729796\pi$
$227$	−19.9129	−1.32166	−0.660832	+	0.750534i	$0.729796\pi$
$228$	21.1652	1.40170
$229$	−20.7477	−1.37105	−0.685524	−	0.728050i	$-0.740427\pi$
$229$	−20.7477	−1.37105	−0.685524	+	0.728050i	$0.740427\pi$
$230$	3.00000	0.197814
$231$	21.1652	1.39256
$232$	0.791288	0.0519506
$233$	−25.1216	−1.64577	−0.822885	−	0.568208i	$-0.807637\pi$
$233$	−25.1216	−1.64577	−0.822885	+	0.568208i	$0.807637\pi$
$234$	3.79129	0.247844
$235$	6.00000	0.391397
$236$	7.58258	0.493584
$237$	−35.7042	−2.31923
$238$	3.16515	0.205166
$239$	−24.9564	−1.61430	−0.807149	−	0.590348i	$-0.798991\pi$
$239$	−24.9564	−1.61430	−0.807149	+	0.590348i	$0.798991\pi$
$240$	10.5826	0.683102
$241$	−13.5826	−0.874931	−0.437465	−	0.899235i	$-0.644124\pi$
$241$	−13.5826	−0.874931	−0.437465	+	0.899235i	$0.644124\pi$
$242$	−3.37386	−0.216880
$243$	−16.1652	−1.03699
$244$	8.20871	0.525509
$245$	−11.3739	−0.726649
$246$	14.5390	0.926974
$247$	−6.00000	−0.381771
$248$	−5.37386	−0.341241
$249$	−8.83485	−0.559886
$250$	−16.5826	−1.04877
$251$	13.5826	0.857325	0.428662	−	0.903465i	$-0.358985\pi$
$251$	13.5826	0.857325	0.428662	+	0.903465i	$0.358985\pi$
$252$	−9.58258	−0.603646
$253$	3.00000	0.188608
$254$	−8.00000	−0.501965
$255$	16.7477	1.04878
$256$	1.00000	0.0625000
$257$	−22.7477	−1.41896	−0.709482	−	0.704723i	$-0.751071\pi$
$257$	−22.7477	−1.41896	−0.709482	+	0.704723i	$0.751071\pi$
$258$	−16.7477	−1.04267
$259$	0	0
$260$	−3.00000	−0.186052
$261$	−3.79129	−0.234675
$262$	10.7477	0.663997
$263$	8.83485	0.544780	0.272390	−	0.962187i	$-0.412186\pi$
$263$	8.83485	0.544780	0.272390	+	0.962187i	$0.412186\pi$
$264$	10.5826	0.651313
$265$	28.7477	1.76596
$266$	15.1652	0.929835
$267$	16.7477	1.02494
$268$	7.37386	0.450430
$269$	−10.7477	−0.655300	−0.327650	−	0.944799i	$-0.606257\pi$
$269$	−10.7477	−0.655300	−0.327650	+	0.944799i	$0.606257\pi$
$270$	−18.9564	−1.15365
$271$	22.0000	1.33640	0.668202	−	0.743980i	$-0.267064\pi$
$271$	22.0000	1.33640	0.668202	+	0.743980i	$0.267064\pi$
$272$	1.58258	0.0959577
$273$	4.41742	0.267355
$274$	17.3739	1.04959
$275$	−35.5390	−2.14308
$276$	−2.20871	−0.132949
$277$	−23.3739	−1.40440	−0.702200	−	0.711980i	$-0.747799\pi$
$277$	−23.3739	−1.40440	−0.702200	+	0.711980i	$0.747799\pi$
$278$	0.373864	0.0224228
$279$	25.7477	1.54148
$280$	7.58258	0.453146
$281$	0	0		−	1.00000i	$-0.5\pi$
$281$	0	0			1.00000i	$0.5\pi$
$282$	−4.41742	−0.263054
$283$	24.0000	1.42665	0.713326	−	0.700832i	$-0.247188\pi$
$283$	24.0000	1.42665	0.713326	+	0.700832i	$0.247188\pi$
$284$	9.16515	0.543852
$285$	80.2432	4.75320
$286$	−3.00000	−0.177394
$287$	10.4174	0.614921
$288$	−4.79129	−0.282329
$289$	−14.4955	−0.852674
$290$	3.00000	0.176166
$291$	12.3303	0.722815
$292$	−9.37386	−0.548564
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	8.37386	0.488374
$295$	28.7477	1.67376
$296$	0	0
$297$	−18.9564	−1.09996
$298$	13.5826	0.786817
$299$	0.626136	0.0362104
$300$	26.1652	1.51065
$301$	−12.0000	−0.691669
$302$	12.7477	0.733549
$303$	4.41742	0.253774
$304$	7.58258	0.434891
$305$	31.1216	1.78202
$306$	−7.58258	−0.433467
$307$	12.3739	0.706214	0.353107	−	0.935583i	$-0.385125\pi$
$307$	12.3739	0.706214	0.353107	+	0.935583i	$0.385125\pi$
$308$	7.58258	0.432057
$309$	6.16515	0.350723
$310$	−20.3739	−1.15716
$311$	−9.62614	−0.545848	−0.272924	−	0.962036i	$-0.587991\pi$
$311$	−9.62614	−0.545848	−0.272924	+	0.962036i	$0.587991\pi$
$312$	2.20871	0.125044
$313$	33.1652	1.87461	0.937303	−	0.348517i	$-0.113315\pi$
$313$	33.1652	1.87461	0.937303	+	0.348517i	$0.113315\pi$
$314$	2.00000	0.112867
$315$	−36.3303	−2.04698
$316$	−12.7913	−0.719566
$317$	1.25227	0.0703347	0.0351673	−	0.999381i	$-0.488804\pi$
$317$	1.25227	0.0703347	0.0351673	+	0.999381i	$0.488804\pi$
$318$	−21.1652	−1.18688
$319$	3.00000	0.167968
$320$	3.79129	0.211939
$321$	23.3739	1.30460
$322$	−1.58258	−0.0881935
$323$	12.0000	0.667698
$324$	−0.417424	−0.0231902
$325$	−7.41742	−0.411445
$326$	−10.4174	−0.576968
$327$	−16.7477	−0.926151
$328$	5.20871	0.287603
$329$	−3.16515	−0.174500
$330$	40.1216	2.20862
$331$	16.4174	0.902383	0.451192	−	0.892427i	$-0.350999\pi$
$331$	16.4174	0.902383	0.451192	+	0.892427i	$0.350999\pi$
$332$	−3.16515	−0.173710
$333$	0	0
$334$	0.956439	0.0523340
$335$	27.9564	1.52742
$336$	−5.58258	−0.304554
$337$	8.12159	0.442411	0.221206	−	0.975227i	$-0.429001\pi$
$337$	8.12159	0.442411	0.221206	+	0.975227i	$0.429001\pi$
$338$	12.3739	0.673049
$339$	−54.6606	−2.96876
$340$	6.00000	0.325396
$341$	−20.3739	−1.10331
$342$	−36.3303	−1.96452
$343$	20.0000	1.07990
$344$	−6.00000	−0.323498
$345$	−8.37386	−0.450834
$346$	−3.16515	−0.170160
$347$	−1.58258	−0.0849571	−0.0424786	−	0.999097i	$-0.513525\pi$
$347$	−1.58258	−0.0849571	−0.0424786	+	0.999097i	$0.513525\pi$
$348$	−2.20871	−0.118399
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	18.7477	1.00211
$351$	−3.95644	−0.211179
$352$	3.79129	0.202076
$353$	7.58258	0.403580	0.201790	−	0.979429i	$-0.435324\pi$
$353$	7.58258	0.403580	0.201790	+	0.979429i	$0.435324\pi$
$354$	−21.1652	−1.12492
$355$	34.7477	1.84422
$356$	6.00000	0.317999
$357$	−8.83485	−0.467590
$358$	7.58258	0.400752
$359$	−27.1652	−1.43372	−0.716861	−	0.697216i	$-0.754422\pi$
$359$	−27.1652	−1.43372	−0.716861	+	0.697216i	$0.754422\pi$
$360$	−18.1652	−0.957388
$361$	38.4955	2.02608
$362$	18.7477	0.985359
$363$	9.41742	0.494287
$364$	1.58258	0.0829495
$365$	−35.5390	−1.86020
$366$	−22.9129	−1.19768
$367$	−32.7477	−1.70942	−0.854709	−	0.519108i	$-0.826264\pi$
$367$	−32.7477	−1.70942	−0.854709	+	0.519108i	$0.826264\pi$
$368$	−0.791288	−0.0412487
$369$	−24.9564	−1.29918
$370$	0	0
$371$	−15.1652	−0.787335
$372$	15.0000	0.777714
$373$	−14.7477	−0.763608	−0.381804	−	0.924243i	$-0.624697\pi$
$373$	−14.7477	−0.763608	−0.381804	+	0.924243i	$0.624697\pi$
$374$	6.00000	0.310253
$375$	46.2867	2.39024
$376$	−1.58258	−0.0816151
$377$	0.626136	0.0322477
$378$	10.0000	0.514344
$379$	−21.1216	−1.08494	−0.542472	−	0.840074i	$-0.682511\pi$
$379$	−21.1216	−1.08494	−0.542472	+	0.840074i	$0.682511\pi$
$380$	28.7477	1.47473
$381$	22.3303	1.14402
$382$	−5.37386	−0.274951
$383$	−18.3303	−0.936635	−0.468317	−	0.883560i	$-0.655140\pi$
$383$	−18.3303	−0.936635	−0.468317	+	0.883560i	$0.655140\pi$
$384$	−2.79129	−0.142442
$385$	28.7477	1.46512
$386$	18.3303	0.932988
$387$	28.7477	1.46133
$388$	4.41742	0.224261
$389$	35.8693	1.81865	0.909323	−	0.416090i	$-0.136600\pi$
$389$	35.8693	1.81865	0.909323	+	0.416090i	$0.136600\pi$
$390$	8.37386	0.424027
$391$	−1.25227	−0.0633302
$392$	3.00000	0.151523
$393$	−30.0000	−1.51330
$394$	−25.9129	−1.30547
$395$	−48.4955	−2.44007
$396$	−18.1652	−0.912833
$397$	12.7477	0.639790	0.319895	−	0.947453i	$-0.396352\pi$
$397$	12.7477	0.639790	0.319895	+	0.947453i	$0.396352\pi$
$398$	−3.16515	−0.158655
$399$	−42.3303	−2.11917
$400$	9.37386	0.468693
$401$	10.7477	0.536716	0.268358	−	0.963319i	$-0.413519\pi$
$401$	10.7477	0.536716	0.268358	+	0.963319i	$0.413519\pi$
$402$	−20.5826	−1.02657
$403$	−4.25227	−0.211821
$404$	1.58258	0.0787361
$405$	−1.58258	−0.0786388
$406$	−1.58258	−0.0785419
$407$	0	0
$408$	−4.41742	−0.218695
$409$	8.83485	0.436855	0.218428	−	0.975853i	$-0.429907\pi$
$409$	8.83485	0.436855	0.218428	+	0.975853i	$0.429907\pi$
$410$	19.7477	0.975271
$411$	−48.4955	−2.39210
$412$	2.20871	0.108815
$413$	−15.1652	−0.746228
$414$	3.79129	0.186332
$415$	−12.0000	−0.589057
$416$	0.791288	0.0387961
$417$	−1.04356	−0.0511034
$418$	28.7477	1.40610
$419$	6.79129	0.331776	0.165888	−	0.986145i	$-0.446951\pi$
$419$	6.79129	0.331776	0.165888	+	0.986145i	$0.446951\pi$
$420$	−21.1652	−1.03275
$421$	3.95644	0.192825	0.0964125	−	0.995341i	$-0.469263\pi$
$421$	3.95644	0.192825	0.0964125	+	0.995341i	$0.469263\pi$
$422$	3.37386	0.164237
$423$	7.58258	0.368677
$424$	−7.58258	−0.368242
$425$	14.8348	0.719596
$426$	−25.5826	−1.23948
$427$	−16.4174	−0.794495
$428$	8.37386	0.404766
$429$	8.37386	0.404294
$430$	−22.7477	−1.09699
$431$	−27.1652	−1.30850	−0.654250	−	0.756279i	$-0.727015\pi$
$431$	−27.1652	−1.30850	−0.654250	+	0.756279i	$0.727015\pi$
$432$	5.00000	0.240563
$433$	24.3739	1.17133	0.585667	−	0.810552i	$-0.300833\pi$
$433$	24.3739	1.17133	0.585667	+	0.810552i	$0.300833\pi$
$434$	10.7477	0.515907
$435$	−8.37386	−0.401496
$436$	−6.00000	−0.287348
$437$	−6.00000	−0.287019
$438$	26.1652	1.25022
$439$	26.3739	1.25876	0.629378	−	0.777099i	$-0.283310\pi$
$439$	26.3739	1.25876	0.629378	+	0.777099i	$0.283310\pi$
$440$	14.3739	0.685247
$441$	−14.3739	−0.684470
$442$	1.25227	0.0595645
$443$	−5.04356	−0.239627	−0.119813	−	0.992796i	$-0.538230\pi$
$443$	−5.04356	−0.239627	−0.119813	+	0.992796i	$0.538230\pi$
$444$	0	0
$445$	22.7477	1.07835
$446$	−14.0000	−0.662919
$447$	−37.9129	−1.79322
$448$	−2.00000	−0.0944911
$449$	21.1652	0.998845	0.499423	−	0.866358i	$-0.333546\pi$
$449$	21.1652	0.998845	0.499423	+	0.866358i	$0.333546\pi$
$450$	−44.9129	−2.11721
$451$	19.7477	0.929884
$452$	−19.5826	−0.921087
$453$	−35.5826	−1.67182
$454$	19.9129	0.934558
$455$	6.00000	0.281284
$456$	−21.1652	−0.991149
$457$	−33.4955	−1.56685	−0.783426	−	0.621486i	$-0.786529\pi$
$457$	−33.4955	−1.56685	−0.783426	+	0.621486i	$0.786529\pi$
$458$	20.7477	0.969478
$459$	7.91288	0.369342
$460$	−3.00000	−0.139876
$461$	24.3303	1.13318	0.566588	−	0.824002i	$-0.308263\pi$
$461$	24.3303	1.13318	0.566588	+	0.824002i	$0.308263\pi$
$462$	−21.1652	−0.984692
$463$	20.7042	0.962204	0.481102	−	0.876665i	$-0.340237\pi$
$463$	20.7042	0.962204	0.481102	+	0.876665i	$0.340237\pi$
$464$	−0.791288	−0.0367346
$465$	56.8693	2.63725
$466$	25.1216	1.16374
$467$	−25.5826	−1.18382	−0.591910	−	0.806004i	$-0.701626\pi$
$467$	−25.5826	−1.18382	−0.591910	+	0.806004i	$0.701626\pi$
$468$	−3.79129	−0.175252
$469$	−14.7477	−0.680987
$470$	−6.00000	−0.276759
$471$	−5.58258	−0.257232
$472$	−7.58258	−0.349016
$473$	−22.7477	−1.04594
$474$	35.7042	1.63995
$475$	71.0780	3.26128
$476$	−3.16515	−0.145074
$477$	36.3303	1.66345
$478$	24.9564	1.14148
$479$	0.791288	0.0361549	0.0180774	−	0.999837i	$-0.494245\pi$
$479$	0.791288	0.0361549	0.0180774	+	0.999837i	$0.494245\pi$
$480$	−10.5826	−0.483026
$481$	0	0
$482$	13.5826	0.618669
$483$	4.41742	0.201000
$484$	3.37386	0.153357
$485$	16.7477	0.760475
$486$	16.1652	0.733266
$487$	36.6606	1.66125	0.830625	−	0.556832i	$-0.187983\pi$
$487$	36.6606	1.66125	0.830625	+	0.556832i	$0.187983\pi$
$488$	−8.20871	−0.371591
$489$	29.0780	1.31495
$490$	11.3739	0.513819
$491$	−8.37386	−0.377907	−0.188954	−	0.981986i	$-0.560510\pi$
$491$	−8.37386	−0.377907	−0.188954	+	0.981986i	$0.560510\pi$
$492$	−14.5390	−0.655469
$493$	−1.25227	−0.0563995
$494$	6.00000	0.269953
$495$	−68.8693	−3.09545
$496$	5.37386	0.241294
$497$	−18.3303	−0.822226
$498$	8.83485	0.395899
$499$	16.7477	0.749731	0.374866	−	0.927079i	$-0.377689\pi$
$499$	16.7477	0.749731	0.374866	+	0.927079i	$0.377689\pi$
$500$	16.5826	0.741595
$501$	−2.66970	−0.119273
$502$	−13.5826	−0.606220
$503$	−29.3739	−1.30972	−0.654858	−	0.755752i	$-0.727272\pi$
$503$	−29.3739	−1.30972	−0.654858	+	0.755752i	$0.727272\pi$
$504$	9.58258	0.426842
$505$	6.00000	0.266996
$506$	−3.00000	−0.133366
$507$	−34.5390	−1.53393
$508$	8.00000	0.354943
$509$	−13.5826	−0.602037	−0.301019	−	0.953618i	$-0.597327\pi$
$509$	−13.5826	−0.602037	−0.301019	+	0.953618i	$0.597327\pi$
$510$	−16.7477	−0.741602
$511$	18.7477	0.829351
$512$	−1.00000	−0.0441942
$513$	37.9129	1.67389
$514$	22.7477	1.00336
$515$	8.37386	0.368997
$516$	16.7477	0.737278
$517$	−6.00000	−0.263880
$518$	0	0
$519$	8.83485	0.387807
$520$	3.00000	0.131559
$521$	−9.16515	−0.401533	−0.200766	−	0.979639i	$-0.564343\pi$
$521$	−9.16515	−0.401533	−0.200766	+	0.979639i	$0.564343\pi$
$522$	3.79129	0.165940
$523$	3.16515	0.138402	0.0692012	−	0.997603i	$-0.477955\pi$
$523$	3.16515	0.138402	0.0692012	+	0.997603i	$0.477955\pi$
$524$	−10.7477	−0.469517
$525$	−52.3303	−2.28388
$526$	−8.83485	−0.385218
$527$	8.50455	0.370464
$528$	−10.5826	−0.460547
$529$	−22.3739	−0.972777
$530$	−28.7477	−1.24872
$531$	36.3303	1.57660
$532$	−15.1652	−0.657493
$533$	4.12159	0.178526
$534$	−16.7477	−0.724745
$535$	31.7477	1.37257
$536$	−7.37386	−0.318502
$537$	−21.1652	−0.913344
$538$	10.7477	0.463367
$539$	11.3739	0.489907
$540$	18.9564	0.815755
$541$	8.20871	0.352920	0.176460	−	0.984308i	$-0.443535\pi$
$541$	8.20871	0.352920	0.176460	+	0.984308i	$0.443535\pi$
$542$	−22.0000	−0.944981
$543$	−52.3303	−2.24571
$544$	−1.58258	−0.0678524
$545$	−22.7477	−0.974406
$546$	−4.41742	−0.189048
$547$	19.9129	0.851413	0.425707	−	0.904861i	$-0.360026\pi$
$547$	19.9129	0.851413	0.425707	+	0.904861i	$0.360026\pi$
$548$	−17.3739	−0.742175
$549$	39.3303	1.67858
$550$	35.5390	1.51539
$551$	−6.00000	−0.255609
$552$	2.20871	0.0940090
$553$	25.5826	1.08788
$554$	23.3739	0.993060
$555$	0	0
$556$	−0.373864	−0.0158553
$557$	41.7042	1.76706	0.883531	−	0.468372i	$-0.155159\pi$
$557$	41.7042	1.76706	0.883531	+	0.468372i	$0.155159\pi$
$558$	−25.7477	−1.08999
$559$	−4.74773	−0.200807
$560$	−7.58258	−0.320422
$561$	−16.7477	−0.707090
$562$	0	0
$563$	16.7477	0.705833	0.352916	−	0.935655i	$-0.385190\pi$
$563$	16.7477	0.705833	0.352916	+	0.935655i	$0.385190\pi$
$564$	4.41742	0.186007
$565$	−74.2432	−3.12343
$566$	−24.0000	−1.00880
$567$	0.834849	0.0350603
$568$	−9.16515	−0.384561
$569$	−26.8348	−1.12498	−0.562488	−	0.826806i	$-0.690156\pi$
$569$	−26.8348	−1.12498	−0.562488	+	0.826806i	$0.690156\pi$
$570$	−80.2432	−3.36102
$571$	−28.3739	−1.18741	−0.593705	−	0.804683i	$-0.702335\pi$
$571$	−28.3739	−1.18741	−0.593705	+	0.804683i	$0.702335\pi$
$572$	3.00000	0.125436
$573$	15.0000	0.626634
$574$	−10.4174	−0.434815
$575$	−7.41742	−0.309328
$576$	4.79129	0.199637
$577$	4.41742	0.183900	0.0919499	−	0.995764i	$-0.470690\pi$
$577$	4.41742	0.183900	0.0919499	+	0.995764i	$0.470690\pi$
$578$	14.4955	0.602931
$579$	−51.1652	−2.12635
$580$	−3.00000	−0.124568
$581$	6.33030	0.262625
$582$	−12.3303	−0.511107
$583$	−28.7477	−1.19061
$584$	9.37386	0.387893
$585$	−14.3739	−0.594286
$586$	6.00000	0.247858
$587$	−25.9129	−1.06954	−0.534769	−	0.844998i	$-0.679602\pi$
$587$	−25.9129	−1.06954	−0.534769	+	0.844998i	$0.679602\pi$
$588$	−8.37386	−0.345332
$589$	40.7477	1.67898
$590$	−28.7477	−1.18353
$591$	72.3303	2.97527
$592$	0	0
$593$	−14.2087	−0.583482	−0.291741	−	0.956497i	$-0.594235\pi$
$593$	−14.2087	−0.583482	−0.291741	+	0.956497i	$0.594235\pi$
$594$	18.9564	0.777792
$595$	−12.0000	−0.491952
$596$	−13.5826	−0.556364
$597$	8.83485	0.361586
$598$	−0.626136	−0.0256046
$599$	27.1652	1.10994	0.554969	−	0.831871i	$-0.312730\pi$
$599$	27.1652	1.10994	0.554969	+	0.831871i	$0.312730\pi$
$600$	−26.1652	−1.06819
$601$	8.12159	0.331287	0.165643	−	0.986186i	$-0.447030\pi$
$601$	8.12159	0.331287	0.165643	+	0.986186i	$0.447030\pi$
$602$	12.0000	0.489083
$603$	35.3303	1.43876
$604$	−12.7477	−0.518698
$605$	12.7913	0.520040
$606$	−4.41742	−0.179446
$607$	−5.53901	−0.224822	−0.112411	−	0.993662i	$-0.535857\pi$
$607$	−5.53901	−0.224822	−0.112411	+	0.993662i	$0.535857\pi$
$608$	−7.58258	−0.307514
$609$	4.41742	0.179003
$610$	−31.1216	−1.26008
$611$	−1.25227	−0.0506615
$612$	7.58258	0.306507
$613$	−5.49545	−0.221959	−0.110980	−	0.993823i	$-0.535399\pi$
$613$	−5.49545	−0.221959	−0.110980	+	0.993823i	$0.535399\pi$
$614$	−12.3739	−0.499368
$615$	−55.1216	−2.22272
$616$	−7.58258	−0.305511
$617$	45.9564	1.85014	0.925068	−	0.379801i	$-0.124007\pi$
$617$	45.9564	1.85014	0.925068	+	0.379801i	$0.124007\pi$
$618$	−6.16515	−0.247999
$619$	−6.12159	−0.246048	−0.123024	−	0.992404i	$-0.539259\pi$
$619$	−6.12159	−0.246048	−0.123024	+	0.992404i	$0.539259\pi$
$620$	20.3739	0.818234
$621$	−3.95644	−0.158766
$622$	9.62614	0.385973
$623$	−12.0000	−0.480770
$624$	−2.20871	−0.0884192
$625$	16.0000	0.640000
$626$	−33.1652	−1.32555
$627$	−80.2432	−3.20460
$628$	−2.00000	−0.0798087
$629$	0	0
$630$	36.3303	1.44743
$631$	−3.95644	−0.157503	−0.0787517	−	0.996894i	$-0.525093\pi$
$631$	−3.95644	−0.157503	−0.0787517	+	0.996894i	$0.525093\pi$
$632$	12.7913	0.508810
$633$	−9.41742	−0.374309
$634$	−1.25227	−0.0497341
$635$	30.3303	1.20362
$636$	21.1652	0.839253
$637$	2.37386	0.0940559
$638$	−3.00000	−0.118771
$639$	43.9129	1.73717
$640$	−3.79129	−0.149864
$641$	−35.5390	−1.40371	−0.701853	−	0.712321i	$-0.747644\pi$
$641$	−35.5390	−1.40371	−0.701853	+	0.712321i	$0.747644\pi$
$642$	−23.3739	−0.922493
$643$	15.4955	0.611081	0.305541	−	0.952179i	$-0.401163\pi$
$643$	15.4955	0.611081	0.305541	+	0.952179i	$0.401163\pi$
$644$	1.58258	0.0623622
$645$	63.4955	2.50013
$646$	−12.0000	−0.472134
$647$	−32.7042	−1.28573	−0.642867	−	0.765978i	$-0.722255\pi$
$647$	−32.7042	−1.28573	−0.642867	+	0.765978i	$0.722255\pi$
$648$	0.417424	0.0163980
$649$	−28.7477	−1.12845
$650$	7.41742	0.290935
$651$	−30.0000	−1.17579
$652$	10.4174	0.407978
$653$	14.3739	0.562493	0.281246	−	0.959636i	$-0.409252\pi$
$653$	14.3739	0.562493	0.281246	+	0.959636i	$0.409252\pi$
$654$	16.7477	0.654888
$655$	−40.7477	−1.59215
$656$	−5.20871	−0.203366
$657$	−44.9129	−1.75222
$658$	3.16515	0.123390
$659$	−33.9564	−1.32276	−0.661378	−	0.750053i	$-0.730028\pi$
$659$	−33.9564	−1.32276	−0.661378	+	0.750053i	$0.730028\pi$
$660$	−40.1216	−1.56173
$661$	36.7913	1.43102	0.715508	−	0.698605i	$-0.246195\pi$
$661$	36.7913	1.43102	0.715508	+	0.698605i	$0.246195\pi$
$662$	−16.4174	−0.638081
$663$	−3.49545	−0.135752
$664$	3.16515	0.122832
$665$	−57.4955	−2.22958
$666$	0	0
$667$	0.626136	0.0242441
$668$	−0.956439	−0.0370057
$669$	39.0780	1.51084
$670$	−27.9564	−1.08005
$671$	−31.1216	−1.20144
$672$	5.58258	0.215353
$673$	5.12159	0.197423	0.0987114	−	0.995116i	$-0.468528\pi$
$673$	5.12159	0.197423	0.0987114	+	0.995116i	$0.468528\pi$
$674$	−8.12159	−0.312832
$675$	46.8693	1.80400
$676$	−12.3739	−0.475918
$677$	9.16515	0.352245	0.176123	−	0.984368i	$-0.443644\pi$
$677$	9.16515	0.352245	0.176123	+	0.984368i	$0.443644\pi$
$678$	54.6606	2.09923
$679$	−8.83485	−0.339050
$680$	−6.00000	−0.230089
$681$	−55.5826	−2.12993
$682$	20.3739	0.780156
$683$	22.4174	0.857779	0.428889	−	0.903357i	$-0.358905\pi$
$683$	22.4174	0.857779	0.428889	+	0.903357i	$0.358905\pi$
$684$	36.3303	1.38912
$685$	−65.8693	−2.51674
$686$	−20.0000	−0.763604
$687$	−57.9129	−2.20951
$688$	6.00000	0.228748
$689$	−6.00000	−0.228582
$690$	8.37386	0.318788
$691$	29.4955	1.12206	0.561030	−	0.827795i	$-0.310405\pi$
$691$	29.4955	1.12206	0.561030	+	0.827795i	$0.310405\pi$
$692$	3.16515	0.120321
$693$	36.3303	1.38007
$694$	1.58258	0.0600738
$695$	−1.41742	−0.0537660
$696$	2.20871	0.0837210
$697$	−8.24318	−0.312233
$698$	−10.0000	−0.378506
$699$	−70.1216	−2.65224
$700$	−18.7477	−0.708597
$701$	18.9564	0.715975	0.357987	−	0.933726i	$-0.383463\pi$
$701$	18.9564	0.715975	0.357987	+	0.933726i	$0.383463\pi$
$702$	3.95644	0.149326
$703$	0	0
$704$	−3.79129	−0.142890
$705$	16.7477	0.630756
$706$	−7.58258	−0.285374
$707$	−3.16515	−0.119038
$708$	21.1652	0.795435
$709$	−27.7913	−1.04372	−0.521862	−	0.853030i	$-0.674762\pi$
$709$	−27.7913	−1.04372	−0.521862	+	0.853030i	$0.674762\pi$
$710$	−34.7477	−1.30406
$711$	−61.2867	−2.29843
$712$	−6.00000	−0.224860
$713$	−4.25227	−0.159249
$714$	8.83485	0.330636
$715$	11.3739	0.425358
$716$	−7.58258	−0.283374
$717$	−69.6606	−2.60152
$718$	27.1652	1.01379
$719$	−2.83485	−0.105722	−0.0528610	−	0.998602i	$-0.516834\pi$
$719$	−2.83485	−0.105722	−0.0528610	+	0.998602i	$0.516834\pi$
$720$	18.1652	0.676975
$721$	−4.41742	−0.164513
$722$	−38.4955	−1.43265
$723$	−37.9129	−1.41000
$724$	−18.7477	−0.696754
$725$	−7.41742	−0.275476
$726$	−9.41742	−0.349513
$727$	28.1216	1.04297	0.521486	−	0.853260i	$-0.325378\pi$
$727$	28.1216	1.04297	0.521486	+	0.853260i	$0.325378\pi$
$728$	−1.58258	−0.0586542
$729$	−43.8693	−1.62479
$730$	35.5390	1.31536
$731$	9.49545	0.351202
$732$	22.9129	0.846884
$733$	7.49545	0.276851	0.138425	−	0.990373i	$-0.455796\pi$
$733$	7.49545	0.276851	0.138425	+	0.990373i	$0.455796\pi$
$734$	32.7477	1.20874
$735$	−31.7477	−1.17103
$736$	0.791288	0.0291673
$737$	−27.9564	−1.02979
$738$	24.9564	0.918659
$739$	−6.12159	−0.225186	−0.112593	−	0.993641i	$-0.535916\pi$
$739$	−6.12159	−0.225186	−0.112593	+	0.993641i	$0.535916\pi$
$740$	0	0
$741$	−16.7477	−0.615243
$742$	15.1652	0.556730
$743$	3.16515	0.116118	0.0580591	−	0.998313i	$-0.481509\pi$
$743$	3.16515	0.116118	0.0580591	+	0.998313i	$0.481509\pi$
$744$	−15.0000	−0.549927
$745$	−51.4955	−1.88665
$746$	14.7477	0.539953
$747$	−15.1652	−0.554864
$748$	−6.00000	−0.219382
$749$	−16.7477	−0.611949
$750$	−46.2867	−1.69015
$751$	−13.4955	−0.492456	−0.246228	−	0.969212i	$-0.579191\pi$
$751$	−13.4955	−0.492456	−0.246228	+	0.969212i	$0.579191\pi$
$752$	1.58258	0.0577106
$753$	37.9129	1.38162
$754$	−0.626136	−0.0228025
$755$	−48.3303	−1.75892
$756$	−10.0000	−0.363696
$757$	39.7913	1.44624	0.723119	−	0.690723i	$-0.242708\pi$
$757$	39.7913	1.44624	0.723119	+	0.690723i	$0.242708\pi$
$758$	21.1216	0.767171
$759$	8.37386	0.303952
$760$	−28.7477	−1.04279
$761$	−18.7913	−0.681184	−0.340592	−	0.940211i	$-0.610627\pi$
$761$	−18.7913	−0.681184	−0.340592	+	0.940211i	$0.610627\pi$
$762$	−22.3303	−0.808942
$763$	12.0000	0.434429
$764$	5.37386	0.194420
$765$	28.7477	1.03938
$766$	18.3303	0.662301
$767$	−6.00000	−0.216647
$768$	2.79129	0.100722
$769$	−48.3303	−1.74284	−0.871418	−	0.490542i	$-0.836799\pi$
$769$	−48.3303	−1.74284	−0.871418	+	0.490542i	$0.836799\pi$
$770$	−28.7477	−1.03600
$771$	−63.4955	−2.28673
$772$	−18.3303	−0.659722
$773$	−13.9129	−0.500411	−0.250206	−	0.968193i	$-0.580498\pi$
$773$	−13.9129	−0.500411	−0.250206	+	0.968193i	$0.580498\pi$
$774$	−28.7477	−1.03332
$775$	50.3739	1.80948
$776$	−4.41742	−0.158576
$777$	0	0
$778$	−35.8693	−1.28598
$779$	−39.4955	−1.41507
$780$	−8.37386	−0.299832
$781$	−34.7477	−1.24337
$782$	1.25227	0.0447812
$783$	−3.95644	−0.141392
$784$	−3.00000	−0.107143
$785$	−7.58258	−0.270634
$786$	30.0000	1.07006
$787$	8.00000	0.285169	0.142585	−	0.989783i	$-0.454459\pi$
$787$	8.00000	0.285169	0.142585	+	0.989783i	$0.454459\pi$
$788$	25.9129	0.923108
$789$	24.6606	0.877941
$790$	48.4955	1.72539
$791$	39.1652	1.39255
$792$	18.1652	0.645471
$793$	−6.49545	−0.230660
$794$	−12.7477	−0.452400
$795$	80.2432	2.84593
$796$	3.16515	0.112186
$797$	21.6261	0.766037	0.383019	−	0.923741i	$-0.374885\pi$
$797$	21.6261	0.766037	0.383019	+	0.923741i	$0.374885\pi$
$798$	42.3303	1.49848
$799$	2.50455	0.0886045
$800$	−9.37386	−0.331416
$801$	28.7477	1.01575
$802$	−10.7477	−0.379515
$803$	35.5390	1.25414
$804$	20.5826	0.725891
$805$	6.00000	0.211472
$806$	4.25227	0.149780
$807$	−30.0000	−1.05605
$808$	−1.58258	−0.0556748
$809$	11.0780	0.389483	0.194741	−	0.980855i	$-0.437613\pi$
$809$	11.0780	0.389483	0.194741	+	0.980855i	$0.437613\pi$
$810$	1.58258	0.0556060
$811$	48.8693	1.71603	0.858017	−	0.513621i	$-0.171696\pi$
$811$	48.8693	1.71603	0.858017	+	0.513621i	$0.171696\pi$
$812$	1.58258	0.0555375
$813$	61.4083	2.15368
$814$	0	0
$815$	39.4955	1.38347
$816$	4.41742	0.154641
$817$	45.4955	1.59168
$818$	−8.83485	−0.308903
$819$	7.58258	0.264957
$820$	−19.7477	−0.689621
$821$	−15.1652	−0.529267	−0.264634	−	0.964349i	$-0.585251\pi$
$821$	−15.1652	−0.529267	−0.264634	+	0.964349i	$0.585251\pi$
$822$	48.4955	1.69147
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−2.20871	−0.0769441
$825$	−99.1996	−3.45369
$826$	15.1652	0.527663
$827$	−14.8348	−0.515858	−0.257929	−	0.966164i	$-0.583040\pi$
$827$	−14.8348	−0.515858	−0.257929	+	0.966164i	$0.583040\pi$
$828$	−3.79129	−0.131756
$829$	39.9564	1.38774	0.693872	−	0.720098i	$-0.255903\pi$
$829$	39.9564	1.38774	0.693872	+	0.720098i	$0.255903\pi$
$830$	12.0000	0.416526
$831$	−65.2432	−2.26326
$832$	−0.791288	−0.0274330
$833$	−4.74773	−0.164499
$834$	1.04356	0.0361356
$835$	−3.62614	−0.125488
$836$	−28.7477	−0.994261
$837$	26.8693	0.928739
$838$	−6.79129	−0.234601
$839$	51.4955	1.77782	0.888910	−	0.458081i	$-0.151463\pi$
$839$	51.4955	1.77782	0.888910	+	0.458081i	$0.151463\pi$
$840$	21.1652	0.730267
$841$	−28.3739	−0.978409
$842$	−3.95644	−0.136348
$843$	0	0
$844$	−3.37386	−0.116133
$845$	−46.9129	−1.61385
$846$	−7.58258	−0.260694
$847$	−6.74773	−0.231855
$848$	7.58258	0.260387
$849$	66.9909	2.29912
$850$	−14.8348	−0.508831
$851$	0	0
$852$	25.5826	0.876445
$853$	−5.70417	−0.195307	−0.0976535	−	0.995220i	$-0.531134\pi$
$853$	−5.70417	−0.195307	−0.0976535	+	0.995220i	$0.531134\pi$
$854$	16.4174	0.561793
$855$	137.739	4.71056
$856$	−8.37386	−0.286213
$857$	−14.8348	−0.506749	−0.253374	−	0.967368i	$-0.581540\pi$
$857$	−14.8348	−0.506749	−0.253374	+	0.967368i	$0.581540\pi$
$858$	−8.37386	−0.285879
$859$	−54.6606	−1.86500	−0.932498	−	0.361175i	$-0.882376\pi$
$859$	−54.6606	−1.86500	−0.932498	+	0.361175i	$0.882376\pi$
$860$	22.7477	0.775691
$861$	29.0780	0.990977
$862$	27.1652	0.925249
$863$	−46.7477	−1.59131	−0.795656	−	0.605749i	$-0.792873\pi$
$863$	−46.7477	−1.59131	−0.795656	+	0.605749i	$0.792873\pi$
$864$	−5.00000	−0.170103
$865$	12.0000	0.408012
$866$	−24.3739	−0.828258
$867$	−40.4610	−1.37413
$868$	−10.7477	−0.364802
$869$	48.4955	1.64510
$870$	8.37386	0.283901
$871$	−5.83485	−0.197706
$872$	6.00000	0.203186
$873$	21.1652	0.716332
$874$	6.00000	0.202953
$875$	−33.1652	−1.12119
$876$	−26.1652	−0.884039
$877$	38.7477	1.30842	0.654209	−	0.756314i	$-0.273002\pi$
$877$	38.7477	1.30842	0.654209	+	0.756314i	$0.273002\pi$
$878$	−26.3739	−0.890075
$879$	−16.7477	−0.564887
$880$	−14.3739	−0.484543
$881$	−28.1216	−0.947440	−0.473720	−	0.880675i	$-0.657089\pi$
$881$	−28.1216	−0.947440	−0.473720	+	0.880675i	$0.657089\pi$
$882$	14.3739	0.483993
$883$	−13.9129	−0.468206	−0.234103	−	0.972212i	$-0.575215\pi$
$883$	−13.9129	−0.468206	−0.234103	+	0.972212i	$0.575215\pi$
$884$	−1.25227	−0.0421185
$885$	80.2432	2.69735
$886$	5.04356	0.169442
$887$	−33.8258	−1.13576	−0.567879	−	0.823112i	$-0.692236\pi$
$887$	−33.8258	−1.13576	−0.567879	+	0.823112i	$0.692236\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	−22.7477	−0.762506
$891$	1.58258	0.0530183
$892$	14.0000	0.468755
$893$	12.0000	0.401565
$894$	37.9129	1.26800
$895$	−28.7477	−0.960931
$896$	2.00000	0.0668153
$897$	1.74773	0.0583549
$898$	−21.1652	−0.706290
$899$	−4.25227	−0.141821
$900$	44.9129	1.49710
$901$	12.0000	0.399778
$902$	−19.7477	−0.657527
$903$	−33.4955	−1.11466
$904$	19.5826	0.651307
$905$	−71.0780	−2.36271
$906$	35.5826	1.18215
$907$	−6.33030	−0.210194	−0.105097	−	0.994462i	$-0.533515\pi$
$907$	−6.33030	−0.210194	−0.105097	+	0.994462i	$0.533515\pi$
$908$	−19.9129	−0.660832
$909$	7.58258	0.251498
$910$	−6.00000	−0.198898
$911$	−54.3303	−1.80004	−0.900022	−	0.435845i	$-0.856449\pi$
$911$	−54.3303	−1.80004	−0.900022	+	0.435845i	$0.856449\pi$
$912$	21.1652	0.700848
$913$	12.0000	0.397142
$914$	33.4955	1.10793
$915$	86.8693	2.87181
$916$	−20.7477	−0.685524
$917$	21.4955	0.709842
$918$	−7.91288	−0.261164
$919$	36.0000	1.18753	0.593765	−	0.804638i	$-0.297641\pi$
$919$	36.0000	1.18753	0.593765	+	0.804638i	$0.297641\pi$
$920$	3.00000	0.0989071
$921$	34.5390	1.13810
$922$	−24.3303	−0.801276
$923$	−7.25227	−0.238711
$924$	21.1652	0.696282
$925$	0	0
$926$	−20.7042	−0.680381
$927$	10.5826	0.347577
$928$	0.791288	0.0259753
$929$	5.37386	0.176311	0.0881554	−	0.996107i	$-0.471903\pi$
$929$	5.37386	0.176311	0.0881554	+	0.996107i	$0.471903\pi$
$930$	−56.8693	−1.86482
$931$	−22.7477	−0.745527
$932$	−25.1216	−0.822885
$933$	−26.8693	−0.879662
$934$	25.5826	0.837087
$935$	−22.7477	−0.743930
$936$	3.79129	0.123922
$937$	−33.8693	−1.10646	−0.553231	−	0.833028i	$-0.686605\pi$
$937$	−33.8693	−1.10646	−0.553231	+	0.833028i	$0.686605\pi$
$938$	14.7477	0.481530
$939$	92.5735	3.02102
$940$	6.00000	0.195698
$941$	33.4955	1.09192	0.545960	−	0.837811i	$-0.316165\pi$
$941$	33.4955	1.09192	0.545960	+	0.837811i	$0.316165\pi$
$942$	5.58258	0.181890
$943$	4.12159	0.134217
$944$	7.58258	0.246792
$945$	−37.9129	−1.23331
$946$	22.7477	0.739592
$947$	28.7477	0.934176	0.467088	−	0.884211i	$-0.345303\pi$
$947$	28.7477	0.934176	0.467088	+	0.884211i	$0.345303\pi$
$948$	−35.7042	−1.15962
$949$	7.41742	0.240780
$950$	−71.0780	−2.30608
$951$	3.49545	0.113348
$952$	3.16515	0.102583
$953$	46.4519	1.50472	0.752362	−	0.658750i	$-0.228914\pi$
$953$	46.4519	1.50472	0.752362	+	0.658750i	$0.228914\pi$
$954$	−36.3303	−1.17624
$955$	20.3739	0.659283
$956$	−24.9564	−0.807149
$957$	8.37386	0.270689
$958$	−0.791288	−0.0255653
$959$	34.7477	1.12206
$960$	10.5826	0.341551
$961$	−2.12159	−0.0684384
$962$	0	0
$963$	40.1216	1.29290
$964$	−13.5826	−0.437465
$965$	−69.4955	−2.23714
$966$	−4.41742	−0.142128
$967$	−0.956439	−0.0307570	−0.0153785	−	0.999882i	$-0.504895\pi$
$967$	−0.956439	−0.0307570	−0.0153785	+	0.999882i	$0.504895\pi$
$968$	−3.37386	−0.108440
$969$	33.4955	1.07603
$970$	−16.7477	−0.537737
$971$	36.6261	1.17539	0.587694	−	0.809083i	$-0.300036\pi$
$971$	36.6261	1.17539	0.587694	+	0.809083i	$0.300036\pi$
$972$	−16.1652	−0.518497
$973$	0.747727	0.0239710
$974$	−36.6606	−1.17468
$975$	−20.7042	−0.663064
$976$	8.20871	0.262754
$977$	−23.0780	−0.738332	−0.369166	−	0.929364i	$-0.620357\pi$
$977$	−23.0780	−0.738332	−0.369166	+	0.929364i	$0.620357\pi$
$978$	−29.0780	−0.929813
$979$	−22.7477	−0.727021
$980$	−11.3739	−0.363325
$981$	−28.7477	−0.917844
$982$	8.37386	0.267221
$983$	−18.3303	−0.584646	−0.292323	−	0.956320i	$-0.594428\pi$
$983$	−18.3303	−0.584646	−0.292323	+	0.956320i	$0.594428\pi$
$984$	14.5390	0.463487
$985$	98.2432	3.13029
$986$	1.25227	0.0398805
$987$	−8.83485	−0.281216
$988$	−6.00000	−0.190885
$989$	−4.74773	−0.150969
$990$	68.8693	2.18881
$991$	−3.95644	−0.125680	−0.0628402	−	0.998024i	$-0.520016\pi$
$991$	−3.95644	−0.125680	−0.0628402	+	0.998024i	$0.520016\pi$
$992$	−5.37386	−0.170620
$993$	45.8258	1.45424
$994$	18.3303	0.581402
$995$	12.0000	0.380426
$996$	−8.83485	−0.279943
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	−16.7477	−0.530140
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.h.1.2		2
37.6	odd	4		74.2.b.a.73.3	yes	4
37.31	odd	4		74.2.b.a.73.1	✓	4
37.36	even	2		2738.2.a.k.1.2		2
111.68	even	4		666.2.c.b.73.4		4
111.80	even	4		666.2.c.b.73.1		4
148.31	even	4		592.2.g.c.369.3		4
148.43	even	4		592.2.g.c.369.4		4
185.43	even	4		1850.2.c.h.1849.1		4
185.68	even	4		1850.2.c.g.1849.1		4
185.117	even	4		1850.2.c.g.1849.4		4
185.142	even	4		1850.2.c.h.1849.4		4
185.154	odd	4		1850.2.d.e.1701.2		4
185.179	odd	4		1850.2.d.e.1701.4		4
296.43	even	4		2368.2.g.h.961.1		4
296.117	odd	4		2368.2.g.j.961.3		4
296.179	even	4		2368.2.g.h.961.2		4
296.253	odd	4		2368.2.g.j.961.4		4
444.179	odd	4		5328.2.h.m.2737.4		4
444.191	odd	4		5328.2.h.m.2737.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.b.a.73.1	✓	4	37.31	odd	4
74.2.b.a.73.3	yes	4	37.6	odd	4
592.2.g.c.369.3		4	148.31	even	4
592.2.g.c.369.4		4	148.43	even	4
666.2.c.b.73.1		4	111.80	even	4
666.2.c.b.73.4		4	111.68	even	4
1850.2.c.g.1849.1		4	185.68	even	4
1850.2.c.g.1849.4		4	185.117	even	4
1850.2.c.h.1849.1		4	185.43	even	4
1850.2.c.h.1849.4		4	185.142	even	4
1850.2.d.e.1701.2		4	185.154	odd	4
1850.2.d.e.1701.4		4	185.179	odd	4
2368.2.g.h.961.1		4	296.43	even	4
2368.2.g.h.961.2		4	296.179	even	4
2368.2.g.j.961.3		4	296.117	odd	4
2368.2.g.j.961.4		4	296.253	odd	4
2738.2.a.h.1.2		2	1.1	even	1	trivial
2738.2.a.k.1.2		2	37.36	even	2
5328.2.h.m.2737.1		4	444.191	odd	4
5328.2.h.m.2737.4		4	444.179	odd	4

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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -2.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +4.79129 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.79129 q^{3} +1.00000 q^{4} +3.79129 q^{5} -2.79129 q^{6} -2.00000 q^{7} -1.00000 q^{8} +4.79129 q^{9} -3.79129 q^{10} -3.79129 q^{11} +2.79129 q^{12} -0.791288 q^{13} +2.00000 q^{14} +10.5826 q^{15} +1.00000 q^{16} +1.58258 q^{17} -4.79129 q^{18} +7.58258 q^{19} +3.79129 q^{20} -5.58258 q^{21} +3.79129 q^{22} -0.791288 q^{23} -2.79129 q^{24} +9.37386 q^{25} +0.791288 q^{26} +5.00000 q^{27} -2.00000 q^{28} -0.791288 q^{29} -10.5826 q^{30} +5.37386 q^{31} -1.00000 q^{32} -10.5826 q^{33} -1.58258 q^{34} -7.58258 q^{35} +4.79129 q^{36} -7.58258 q^{38} -2.20871 q^{39} -3.79129 q^{40} -5.20871 q^{41} +5.58258 q^{42} +6.00000 q^{43} -3.79129 q^{44} +18.1652 q^{45} +0.791288 q^{46} +1.58258 q^{47} +2.79129 q^{48} -3.00000 q^{49} -9.37386 q^{50} +4.41742 q^{51} -0.791288 q^{52} +7.58258 q^{53} -5.00000 q^{54} -14.3739 q^{55} +2.00000 q^{56} +21.1652 q^{57} +0.791288 q^{58} +7.58258 q^{59} +10.5826 q^{60} +8.20871 q^{61} -5.37386 q^{62} -9.58258 q^{63} +1.00000 q^{64} -3.00000 q^{65} +10.5826 q^{66} +7.37386 q^{67} +1.58258 q^{68} -2.20871 q^{69} +7.58258 q^{70} +9.16515 q^{71} -4.79129 q^{72} -9.37386 q^{73} +26.1652 q^{75} +7.58258 q^{76} +7.58258 q^{77} +2.20871 q^{78} -12.7913 q^{79} +3.79129 q^{80} -0.417424 q^{81} +5.20871 q^{82} -3.16515 q^{83} -5.58258 q^{84} +6.00000 q^{85} -6.00000 q^{86} -2.20871 q^{87} +3.79129 q^{88} +6.00000 q^{89} -18.1652 q^{90} +1.58258 q^{91} -0.791288 q^{92} +15.0000 q^{93} -1.58258 q^{94} +28.7477 q^{95} -2.79129 q^{96} +4.41742 q^{97} +3.00000 q^{98} -18.1652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + q^{12} + 3 q^{13} + 4 q^{14} + 12 q^{15} + 2 q^{16} - 6 q^{17} - 5 q^{18} + 6 q^{19} + 3 q^{20} - 2 q^{21} + 3 q^{22} + 3 q^{23} - q^{24} + 5 q^{25} - 3 q^{26} + 10 q^{27} - 4 q^{28} + 3 q^{29} - 12 q^{30} - 3 q^{31} - 2 q^{32} - 12 q^{33} + 6 q^{34} - 6 q^{35} + 5 q^{36} - 6 q^{38} - 9 q^{39} - 3 q^{40} - 15 q^{41} + 2 q^{42} + 12 q^{43} - 3 q^{44} + 18 q^{45} - 3 q^{46} - 6 q^{47} + q^{48} - 6 q^{49} - 5 q^{50} + 18 q^{51} + 3 q^{52} + 6 q^{53} - 10 q^{54} - 15 q^{55} + 4 q^{56} + 24 q^{57} - 3 q^{58} + 6 q^{59} + 12 q^{60} + 21 q^{61} + 3 q^{62} - 10 q^{63} + 2 q^{64} - 6 q^{65} + 12 q^{66} + q^{67} - 6 q^{68} - 9 q^{69} + 6 q^{70} - 5 q^{72} - 5 q^{73} + 34 q^{75} + 6 q^{76} + 6 q^{77} + 9 q^{78} - 21 q^{79} + 3 q^{80} - 10 q^{81} + 15 q^{82} + 12 q^{83} - 2 q^{84} + 12 q^{85} - 12 q^{86} - 9 q^{87} + 3 q^{88} + 12 q^{89} - 18 q^{90} - 6 q^{91} + 3 q^{92} + 30 q^{93} + 6 q^{94} + 30 q^{95} - q^{96} + 18 q^{97} + 6 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 2 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + q^12 + 3 * q^13 + 4 * q^14 + 12 * q^15 + 2 * q^16 - 6 * q^17 - 5 * q^18 + 6 * q^19 + 3 * q^20 - 2 * q^21 + 3 * q^22 + 3 * q^23 - q^24 + 5 * q^25 - 3 * q^26 + 10 * q^27 - 4 * q^28 + 3 * q^29 - 12 * q^30 - 3 * q^31 - 2 * q^32 - 12 * q^33 + 6 * q^34 - 6 * q^35 + 5 * q^36 - 6 * q^38 - 9 * q^39 - 3 * q^40 - 15 * q^41 + 2 * q^42 + 12 * q^43 - 3 * q^44 + 18 * q^45 - 3 * q^46 - 6 * q^47 + q^48 - 6 * q^49 - 5 * q^50 + 18 * q^51 + 3 * q^52 + 6 * q^53 - 10 * q^54 - 15 * q^55 + 4 * q^56 + 24 * q^57 - 3 * q^58 + 6 * q^59 + 12 * q^60 + 21 * q^61 + 3 * q^62 - 10 * q^63 + 2 * q^64 - 6 * q^65 + 12 * q^66 + q^67 - 6 * q^68 - 9 * q^69 + 6 * q^70 - 5 * q^72 - 5 * q^73 + 34 * q^75 + 6 * q^76 + 6 * q^77 + 9 * q^78 - 21 * q^79 + 3 * q^80 - 10 * q^81 + 15 * q^82 + 12 * q^83 - 2 * q^84 + 12 * q^85 - 12 * q^86 - 9 * q^87 + 3 * q^88 + 12 * q^89 - 18 * q^90 - 6 * q^91 + 3 * q^92 + 30 * q^93 + 6 * q^94 + 30 * q^95 - q^96 + 18 * q^97 + 6 * q^98 - 18 * q^99

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