LMFDB - Embedded newform 1850.2.c.g.1849.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1849,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("1850.1849");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 11x^{2} + 25 $ x^4 + 11*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1849.4
Root			$2.79129i$ of defining polynomial
Character	$\chi$	$=$	1850.1849
Dual form			1850.2.c.g.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.79129i q^{3} +1.00000 q^{4} -2.79129i q^{6} -2.00000i q^{7} -1.00000 q^{8} -4.79129 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.79129i q^{3} +1.00000 q^{4} -2.79129i q^{6} -2.00000i q^{7} -1.00000 q^{8} -4.79129 q^{9} +3.79129 q^{11} +2.79129i q^{12} -0.791288 q^{13} +2.00000i q^{14} +1.00000 q^{16} -1.58258 q^{17} +4.79129 q^{18} -7.58258i q^{19} +5.58258 q^{21} -3.79129 q^{22} -0.791288 q^{23} -2.79129i q^{24} +0.791288 q^{26} -5.00000i q^{27} -2.00000i q^{28} -0.791288i q^{29} -5.37386i q^{31} -1.00000 q^{32} +10.5826i q^{33} +1.58258 q^{34} -4.79129 q^{36} +(4.58258 + 4.00000i) q^{37} +7.58258i q^{38} -2.20871i q^{39} +5.20871 q^{41} -5.58258 q^{42} +6.00000 q^{43} +3.79129 q^{44} +0.791288 q^{46} +1.58258i q^{47} +2.79129i q^{48} +3.00000 q^{49} -4.41742i q^{51} -0.791288 q^{52} -7.58258i q^{53} +5.00000i q^{54} +2.00000i q^{56} +21.1652 q^{57} +0.791288i q^{58} -7.58258i q^{59} -8.20871i q^{61} +5.37386i q^{62} +9.58258i q^{63} +1.00000 q^{64} -10.5826i q^{66} -7.37386i q^{67} -1.58258 q^{68} -2.20871i q^{69} +9.16515 q^{71} +4.79129 q^{72} -9.37386i q^{73} +(-4.58258 - 4.00000i) q^{74} -7.58258i q^{76} -7.58258i q^{77} +2.20871i q^{78} +12.7913i q^{79} -0.417424 q^{81} -5.20871 q^{82} +3.16515i q^{83} +5.58258 q^{84} -6.00000 q^{86} +2.20871 q^{87} -3.79129 q^{88} +6.00000i q^{89} +1.58258i q^{91} -0.791288 q^{92} +15.0000 q^{93} -1.58258i q^{94} -2.79129i q^{96} -4.41742 q^{97} -3.00000 q^{98} -18.1652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 10 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 10 * q^9	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 10 q^{9} + 6 q^{11} + 6 q^{13} + 4 q^{16} + 12 q^{17} + 10 q^{18} + 4 q^{21} - 6 q^{22} + 6 q^{23} - 6 q^{26} - 4 q^{32} - 12 q^{34} - 10 q^{36} + 30 q^{41} - 4 q^{42} + 24 q^{43} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 6 q^{52} + 48 q^{57} + 4 q^{64} + 12 q^{68} + 10 q^{72} - 20 q^{81} - 30 q^{82} + 4 q^{84} - 24 q^{86} + 18 q^{87} - 6 q^{88} + 6 q^{92} + 60 q^{93} - 36 q^{97} - 12 q^{98} - 36 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 10 * q^9 + 6 * q^11 + 6 * q^13 + 4 * q^16 + 12 * q^17 + 10 * q^18 + 4 * q^21 - 6 * q^22 + 6 * q^23 - 6 * q^26 - 4 * q^32 - 12 * q^34 - 10 * q^36 + 30 * q^41 - 4 * q^42 + 24 * q^43 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 6 * q^52 + 48 * q^57 + 4 * q^64 + 12 * q^68 + 10 * q^72 - 20 * q^81 - 30 * q^82 + 4 * q^84 - 24 * q^86 + 18 * q^87 - 6 * q^88 + 6 * q^92 + 60 * q^93 - 36 * q^97 - 12 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times$.

$n$	$1001$	$1777$
$\chi(n)$	$-1$	$-1$

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
$3$			2.79129i			1.61155i	0.592221	+	0.805775i	$0.298251\pi$
$3$			2.79129i			1.61155i	−0.592221	+	0.805775i	$0.701749\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	2.79129i		−	1.13954i
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	−1.00000			−0.353553
$9$	−4.79129			−1.59710
$10$		0			0
$11$	3.79129			1.14312			0.571558	−	0.820562i	$-0.306339\pi$
$11$	3.79129			1.14312			0.571558	+	0.820562i	$0.306339\pi$
$12$			2.79129i			0.805775i
$13$	−0.791288			−0.219464			−0.109732	−	0.993961i	$-0.534999\pi$
$13$	−0.791288			−0.219464			−0.109732	+	0.993961i	$0.534999\pi$
$14$			2.00000i			0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.58258			−0.383831			−0.191915	−	0.981411i	$-0.561470\pi$
$17$	−1.58258			−0.383831			−0.191915	+	0.981411i	$0.561470\pi$
$18$	4.79129			1.12932
$19$		−	7.58258i		−	1.73956i	−0.493438	−	0.869781i	$-0.664260\pi$
$19$		−	7.58258i		−	1.73956i	0.493438	−	0.869781i	$-0.335740\pi$
$20$		0			0
$21$	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	$0.526290\pi$
$24$		−	2.79129i		−	0.569769i
$25$		0			0
$26$	0.791288			0.155184
$27$		−	5.00000i		−	0.962250i
$28$		−	2.00000i		−	0.377964i
$29$		−	0.791288i		−	0.146938i	−0.997297	−	0.0734692i	$-0.976593\pi$
$29$		−	0.791288i		−	0.146938i	0.997297	−	0.0734692i	$-0.0234071\pi$
$30$		0			0
$31$		−	5.37386i		−	0.965174i	−0.875848	−	0.482587i	$-0.839697\pi$
$31$		−	5.37386i		−	0.965174i	0.875848	−	0.482587i	$-0.160303\pi$
$32$	−1.00000			−0.176777
$33$			10.5826i			1.84219i
$34$	1.58258			0.271409
$35$		0			0
$36$	−4.79129			−0.798548
$37$	4.58258	+	4.00000i	0.753371	+	0.657596i
$37$	4.58258	+	4.00000i	0.753371	+	0.657596i
$38$			7.58258i			1.23006i
$39$		−	2.20871i		−	0.353677i
$40$		0			0
$41$	5.20871			0.813464			0.406732	−	0.913547i	$-0.366668\pi$
$41$	5.20871			0.813464			0.406732	+	0.913547i	$0.366668\pi$
$42$	−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
$45$		0			0
$46$	0.791288			0.116669
$47$			1.58258i			0.230842i	0.993317	+	0.115421i	$0.0368218\pi$
$47$			1.58258i			0.230842i	−0.993317	+	0.115421i	$0.963178\pi$
$48$			2.79129i			0.402888i
$49$	3.00000			0.428571
$50$		0			0
$51$		−	4.41742i		−	0.618563i
$52$	−0.791288			−0.109732
$53$		−	7.58258i		−	1.04155i	−0.853695	−	0.520773i	$-0.825644\pi$
$53$		−	7.58258i		−	1.04155i	0.853695	−	0.520773i	$-0.174356\pi$
$54$			5.00000i			0.680414i
$55$		0			0
$56$			2.00000i			0.267261i
$57$	21.1652			2.80339
$58$			0.791288i			0.103901i
$59$		−	7.58258i		−	0.987167i	−0.869698	−	0.493584i	$-0.835687\pi$
$59$		−	7.58258i		−	0.987167i	0.869698	−	0.493584i	$-0.164313\pi$
$60$		0			0
$61$		−	8.20871i		−	1.05102i	−0.850788	−	0.525509i	$-0.823875\pi$
$61$		−	8.20871i		−	1.05102i	0.850788	−	0.525509i	$-0.176125\pi$
$62$			5.37386i			0.682481i
$63$			9.58258i			1.20729i
$64$	1.00000			0.125000
$65$		0			0
$66$		−	10.5826i		−	1.30263i
$67$		−	7.37386i		−	0.900861i	−0.892812	−	0.450430i	$-0.851271\pi$
$67$		−	7.37386i		−	0.900861i	0.892812	−	0.450430i	$-0.148729\pi$
$68$	−1.58258			−0.191915
$69$		−	2.20871i		−	0.265898i
$70$		0			0
$71$	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
$73$		−	9.37386i		−	1.09713i	−0.836109	−	0.548564i	$-0.815175\pi$
$73$		−	9.37386i		−	1.09713i	0.836109	−	0.548564i	$-0.184825\pi$
$74$	−4.58258	−	4.00000i	−0.532714	−	0.464991i
$75$		0			0
$76$		−	7.58258i		−	0.869781i
$77$		−	7.58258i		−	0.864115i
$78$			2.20871i			0.250087i
$79$			12.7913i			1.43913i	0.694424	+	0.719566i	$0.255659\pi$
$79$			12.7913i			1.43913i	−0.694424	+	0.719566i	$0.744341\pi$
$80$		0			0
$81$	−0.417424			−0.0463805
$82$	−5.20871			−0.575206
$83$			3.16515i			0.347421i	0.984797	+	0.173710i	$0.0555756\pi$
$83$			3.16515i			0.347421i	−0.984797	+	0.173710i	$0.944424\pi$
$84$	5.58258			0.609109
$85$		0			0
$86$	−6.00000			−0.646997
$87$	2.20871			0.236799
$88$	−3.79129			−0.404153
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$		0			0
$91$			1.58258i			0.165899i
$92$	−0.791288			−0.0824975
$93$	15.0000			1.55543
$94$		−	1.58258i		−	0.163230i
$95$		0			0
$96$		−	2.79129i		−	0.284885i
$97$	−4.41742			−0.448521			−0.224261	−	0.974529i	$-0.571997\pi$
$97$	−4.41742			−0.448521			−0.224261	+	0.974529i	$0.571997\pi$
$98$	−3.00000			−0.303046
$99$	−18.1652			−1.82567
$100$		0			0
$101$	−1.58258			−0.157472			−0.0787361	−	0.996895i	$-0.525088\pi$
$101$	−1.58258			−0.157472			−0.0787361	+	0.996895i	$0.525088\pi$
$102$			4.41742i			0.437390i
$103$	−2.20871			−0.217631			−0.108815	−	0.994062i	$-0.534706\pi$
$103$	−2.20871			−0.217631			−0.108815	+	0.994062i	$0.534706\pi$
$104$	0.791288			0.0775922
$105$		0			0
$106$			7.58258i			0.736485i
$107$			8.37386i			0.809532i	0.914420	+	0.404766i	$0.132647\pi$
$107$			8.37386i			0.809532i	−0.914420	+	0.404766i	$0.867353\pi$
$108$		−	5.00000i		−	0.481125i
$109$			6.00000i			0.574696i	0.957826	+	0.287348i	$0.0927736\pi$
$109$			6.00000i			0.574696i	−0.957826	+	0.287348i	$0.907226\pi$
$110$		0			0
$111$	−11.1652	+	12.7913i	−1.05975	+	1.21410i
$112$		−	2.00000i		−	0.188982i
$113$	19.5826			1.84217			0.921087	−	0.389357i	$-0.127303\pi$
$113$	19.5826			1.84217			0.921087	+	0.389357i	$0.127303\pi$
$114$	−21.1652			−1.98230
$115$		0			0
$116$		−	0.791288i		−	0.0734692i
$117$	3.79129			0.350505
$118$			7.58258i			0.698033i
$119$			3.16515i			0.290149i
$120$		0			0
$121$	3.37386			0.306715
$122$			8.20871i			0.743182i
$123$			14.5390i			1.31094i
$124$		−	5.37386i		−	0.482587i
$125$		0			0
$126$		−	9.58258i		−	0.853684i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	−1.00000			−0.0883883
$129$			16.7477i			1.47456i
$130$		0			0
$131$			10.7477i			0.939033i	0.882924	+	0.469517i	$0.155572\pi$
$131$			10.7477i			0.939033i	−0.882924	+	0.469517i	$0.844428\pi$
$132$			10.5826i			0.921095i
$133$	−15.1652			−1.31499
$134$			7.37386i			0.637005i
$135$		0			0
$136$	1.58258			0.135705
$137$		−	17.3739i		−	1.48435i	−0.670207	−	0.742175i	$-0.733794\pi$
$137$		−	17.3739i		−	1.48435i	0.670207	−	0.742175i	$-0.266206\pi$
$138$			2.20871i			0.188018i
$139$	−0.373864			−0.0317107			−0.0158553	−	0.999874i	$-0.505047\pi$
$139$	−0.373864			−0.0317107			−0.0158553	+	0.999874i	$0.505047\pi$
$140$		0			0
$141$	−4.41742			−0.372014
$142$	−9.16515			−0.769122
$143$	−3.00000			−0.250873
$144$	−4.79129			−0.399274
$145$		0			0
$146$			9.37386i			0.775786i
$147$			8.37386i			0.690665i
$148$	4.58258	+	4.00000i	0.376685	+	0.328798i
$149$	13.5826			1.11273			0.556364	−	0.830939i	$-0.312196\pi$
$149$	13.5826			1.11273			0.556364	+	0.830939i	$0.312196\pi$
$150$		0			0
$151$	12.7477			1.03740			0.518698	−	0.854958i	$-0.326417\pi$
$151$	12.7477			1.03740			0.518698	+	0.854958i	$0.326417\pi$
$152$			7.58258i			0.615028i
$153$	7.58258			0.613015
$154$			7.58258i			0.611021i
$155$		0			0
$156$		−	2.20871i		−	0.176838i
$157$		−	2.00000i		−	0.159617i	−0.996810	−	0.0798087i	$-0.974569\pi$
$157$		−	2.00000i		−	0.159617i	0.996810	−	0.0798087i	$-0.0254309\pi$
$158$		−	12.7913i		−	1.01762i
$159$	21.1652			1.67851
$160$		0			0
$161$			1.58258i			0.124724i
$162$	0.417424			0.0327960
$163$	−10.4174			−0.815956			−0.407978	−	0.912992i	$-0.633766\pi$
$163$	−10.4174			−0.815956			−0.407978	+	0.912992i	$0.633766\pi$
$164$	5.20871			0.406732
$165$		0			0
$166$		−	3.16515i		−	0.245663i
$167$	0.956439			0.0740115			0.0370057	−	0.999315i	$-0.488218\pi$
$167$	0.956439			0.0740115			0.0370057	+	0.999315i	$0.488218\pi$
$168$	−5.58258			−0.430705
$169$	−12.3739			−0.951836
$170$		0			0
$171$			36.3303i			2.77825i
$172$	6.00000			0.457496
$173$			3.16515i			0.240642i	0.992735	+	0.120321i	$0.0383924\pi$
$173$			3.16515i			0.240642i	−0.992735	+	0.120321i	$0.961608\pi$
$174$	−2.20871			−0.167442
$175$		0			0
$176$	3.79129			0.285779
$177$	21.1652			1.59087
$178$		−	6.00000i		−	0.449719i
$179$		−	7.58258i		−	0.566748i	−0.959009	−	0.283374i	$-0.908546\pi$
$179$		−	7.58258i		−	0.566748i	0.959009	−	0.283374i	$-0.0914538\pi$
$180$		0			0
$181$	−18.7477			−1.39351			−0.696754	−	0.717310i	$-0.745373\pi$
$181$	−18.7477			−1.39351			−0.696754	+	0.717310i	$0.745373\pi$
$182$		−	1.58258i		−	0.117308i
$183$	22.9129			1.69377
$184$	0.791288			0.0583345
$185$		0			0
$186$	−15.0000			−1.09985
$187$	−6.00000			−0.438763
$188$			1.58258i			0.115421i
$189$	−10.0000			−0.727393
$190$		0			0
$191$			5.37386i			0.388839i	0.980918	+	0.194420i	$0.0622823\pi$
$191$			5.37386i			0.388839i	−0.980918	+	0.194420i	$0.937718\pi$
$192$			2.79129i			0.201444i
$193$	−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
$195$		0			0
$196$	3.00000			0.214286
$197$			25.9129i			1.84622i	0.384541	+	0.923108i	$0.374360\pi$
$197$			25.9129i			1.84622i	−0.384541	+	0.923108i	$0.625640\pi$
$198$	18.1652			1.29094
$199$			3.16515i			0.224372i	0.993687	+	0.112186i	$0.0357852\pi$
$199$			3.16515i			0.224372i	−0.993687	+	0.112186i	$0.964215\pi$
$200$		0			0
$201$	20.5826			1.45178
$202$	1.58258			0.111350
$203$	−1.58258			−0.111075
$204$		−	4.41742i		−	0.309282i
$205$		0			0
$206$	2.20871			0.153888
$207$	3.79129			0.263513
$208$	−0.791288			−0.0548659
$209$		−	28.7477i		−	1.98852i
$210$		0			0
$211$	−3.37386			−0.232266			−0.116133	−	0.993234i	$-0.537050\pi$
$211$	−3.37386			−0.232266			−0.116133	+	0.993234i	$0.537050\pi$
$212$		−	7.58258i		−	0.520773i
$213$			25.5826i			1.75289i
$214$		−	8.37386i		−	0.572426i
$215$		0			0
$216$			5.00000i			0.340207i
$217$	−10.7477			−0.729603
$218$		−	6.00000i		−	0.406371i
$219$	26.1652			1.76808
$220$		0			0
$221$	1.25227			0.0842370
$222$	11.1652	−	12.7913i	0.749356	−	0.858495i
$223$		−	14.0000i		−	0.937509i	−0.883328	−	0.468755i	$-0.844703\pi$
$223$		−	14.0000i		−	0.937509i	0.883328	−	0.468755i	$-0.155297\pi$
$224$			2.00000i			0.133631i
$225$		0			0
$226$	−19.5826			−1.30261
$227$	19.9129			1.32166			0.660832	−	0.750534i	$-0.270204\pi$
$227$	19.9129			1.32166			0.660832	+	0.750534i	$0.270204\pi$
$228$	21.1652			1.40170
$229$	20.7477			1.37105			0.685524	−	0.728050i	$-0.259573\pi$
$229$	20.7477			1.37105			0.685524	+	0.728050i	$0.259573\pi$
$230$		0			0
$231$	21.1652			1.39256
$232$			0.791288i			0.0519506i
$233$		−	25.1216i		−	1.64577i	−0.568208	−	0.822885i	$-0.692363\pi$
$233$		−	25.1216i		−	1.64577i	0.568208	−	0.822885i	$-0.307637\pi$
$234$	−3.79129			−0.247844
$235$		0			0
$236$		−	7.58258i		−	0.493584i
$237$	−35.7042			−2.31923
$238$		−	3.16515i		−	0.205166i
$239$			24.9564i			1.61430i	0.590348	+	0.807149i	$0.298991\pi$
$239$			24.9564i			1.61430i	−0.590348	+	0.807149i	$0.701009\pi$
$240$		0			0
$241$		−	13.5826i		−	0.874931i	−0.899235	−	0.437465i	$-0.855876\pi$
$241$		−	13.5826i		−	0.874931i	0.899235	−	0.437465i	$-0.144124\pi$
$242$	−3.37386			−0.216880
$243$		−	16.1652i		−	1.03699i
$244$		−	8.20871i		−	0.525509i
$245$		0			0
$246$		−	14.5390i		−	0.926974i
$247$			6.00000i			0.381771i
$248$			5.37386i			0.341241i
$249$	−8.83485			−0.559886
$250$		0			0
$251$		−	13.5826i		−	0.857325i	−0.903465	−	0.428662i	$-0.858985\pi$
$251$		−	13.5826i		−	0.857325i	0.903465	−	0.428662i	$-0.141015\pi$
$252$			9.58258i			0.603646i
$253$	−3.00000			−0.188608
$254$		−	8.00000i		−	0.501965i
$255$		0			0
$256$	1.00000			0.0625000
$257$	22.7477			1.41896			0.709482	−	0.704723i	$-0.248929\pi$
$257$	22.7477			1.41896			0.709482	+	0.704723i	$0.248929\pi$
$258$		−	16.7477i		−	1.04267i
$259$	8.00000	−	9.16515i	0.497096	−	0.569495i
$260$		0			0
$261$			3.79129i			0.234675i
$262$		−	10.7477i		−	0.663997i
$263$			8.83485i			0.544780i	0.962187	+	0.272390i	$0.0878141\pi$
$263$			8.83485i			0.544780i	−0.962187	+	0.272390i	$0.912186\pi$
$264$		−	10.5826i		−	0.651313i
$265$		0			0
$266$	15.1652			0.929835
$267$	−16.7477			−1.02494
$268$		−	7.37386i		−	0.450430i
$269$	10.7477			0.655300			0.327650	−	0.944799i	$-0.393743\pi$
$269$	10.7477			0.655300			0.327650	+	0.944799i	$0.393743\pi$
$270$		0			0
$271$	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
$274$			17.3739i			1.04959i
$275$		0			0
$276$		−	2.20871i		−	0.132949i
$277$	−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
$279$			25.7477i			1.54148i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	4.41742			0.263054
$283$	−24.0000			−1.42665			−0.713326	−	0.700832i	$-0.752812\pi$
$283$	−24.0000			−1.42665			−0.713326	+	0.700832i	$0.752812\pi$
$284$	9.16515			0.543852
$285$		0			0
$286$	3.00000			0.177394
$287$		−	10.4174i		−	0.614921i
$288$	4.79129			0.282329
$289$	−14.4955			−0.852674
$290$		0			0
$291$		−	12.3303i		−	0.722815i
$292$		−	9.37386i		−	0.548564i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		−	8.37386i		−	0.488374i
$295$		0			0
$296$	−4.58258	−	4.00000i	−0.266357	−	0.232495i
$297$		−	18.9564i		−	1.09996i
$298$	−13.5826			−0.786817
$299$	0.626136			0.0362104
$300$		0			0
$301$		−	12.0000i		−	0.691669i
$302$	−12.7477			−0.733549
$303$		−	4.41742i		−	0.253774i
$304$		−	7.58258i		−	0.434891i
$305$		0			0
$306$	−7.58258			−0.433467
$307$		−	12.3739i		−	0.706214i	−0.935583	−	0.353107i	$-0.885125\pi$
$307$		−	12.3739i		−	0.706214i	0.935583	−	0.353107i	$-0.114875\pi$
$308$		−	7.58258i		−	0.432057i
$309$		−	6.16515i		−	0.350723i
$310$		0			0
$311$			9.62614i			0.545848i	0.962036	+	0.272924i	$0.0879908\pi$
$311$			9.62614i			0.545848i	−0.962036	+	0.272924i	$0.912009\pi$
$312$			2.20871i			0.125044i
$313$	33.1652			1.87461			0.937303	−	0.348517i	$-0.113315\pi$
$313$	33.1652			1.87461			0.937303	+	0.348517i	$0.113315\pi$
$314$			2.00000i			0.112867i
$315$		0			0
$316$			12.7913i			0.719566i
$317$		−	1.25227i		−	0.0703347i	−0.999381	−	0.0351673i	$-0.988804\pi$
$317$		−	1.25227i		−	0.0703347i	0.999381	−	0.0351673i	$-0.0111964\pi$
$318$	−21.1652			−1.18688
$319$		−	3.00000i		−	0.167968i
$320$		0			0
$321$	−23.3739			−1.30460
$322$		−	1.58258i		−	0.0881935i
$323$			12.0000i			0.667698i
$324$	−0.417424			−0.0231902
$325$		0			0
$326$	10.4174			0.576968
$327$	−16.7477			−0.926151
$328$	−5.20871			−0.287603
$329$	3.16515			0.174500
$330$		0			0
$331$			16.4174i			0.902383i	0.892427	+	0.451192i	$0.149001\pi$
$331$			16.4174i			0.902383i	−0.892427	+	0.451192i	$0.850999\pi$
$332$			3.16515i			0.173710i
$333$	−21.9564	−	19.1652i	−1.20321	−	1.05024i
$334$	−0.956439			−0.0523340
$335$		0			0
$336$	5.58258			0.304554
$337$		−	8.12159i		−	0.442411i	−0.975227	−	0.221206i	$-0.929001\pi$
$337$		−	8.12159i		−	0.442411i	0.975227	−	0.221206i	$-0.0709992\pi$
$338$	12.3739			0.673049
$339$			54.6606i			2.96876i
$340$		0			0
$341$		−	20.3739i		−	1.10331i
$342$		−	36.3303i		−	1.96452i
$343$		−	20.0000i		−	1.07990i
$344$	−6.00000			−0.323498
$345$		0			0
$346$		−	3.16515i		−	0.170160i
$347$	−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	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$			3.95644i			0.211179i
$352$	−3.79129			−0.202076
$353$	−7.58258			−0.403580			−0.201790	−	0.979429i	$-0.564676\pi$
$353$	−7.58258			−0.403580			−0.201790	+	0.979429i	$0.564676\pi$
$354$	−21.1652			−1.12492
$355$		0			0
$356$			6.00000i			0.317999i
$357$	−8.83485			−0.467590
$358$			7.58258i			0.400752i
$359$	27.1652			1.43372			0.716861	−	0.697216i	$-0.245578\pi$
$359$	27.1652			1.43372			0.716861	+	0.697216i	$0.245578\pi$
$360$		0			0
$361$	−38.4955			−2.02608
$362$	18.7477			0.985359
$363$			9.41742i			0.494287i
$364$			1.58258i			0.0829495i
$365$		0			0
$366$	−22.9129			−1.19768
$367$		−	32.7477i		−	1.70942i	−0.519108	−	0.854709i	$-0.673736\pi$
$367$		−	32.7477i		−	1.70942i	0.519108	−	0.854709i	$-0.326264\pi$
$368$	−0.791288			−0.0412487
$369$	−24.9564			−1.29918
$370$		0			0
$371$	−15.1652			−0.787335
$372$	15.0000			0.777714
$373$		−	14.7477i		−	0.763608i	−0.924243	−	0.381804i	$-0.875303\pi$
$373$		−	14.7477i		−	0.763608i	0.924243	−	0.381804i	$-0.124697\pi$
$374$	6.00000			0.310253
$375$		0			0
$376$		−	1.58258i		−	0.0816151i
$377$			0.626136i			0.0322477i
$378$	10.0000			0.514344
$379$	21.1216			1.08494			0.542472	−	0.840074i	$-0.317489\pi$
$379$	21.1216			1.08494			0.542472	+	0.840074i	$0.317489\pi$
$380$		0			0
$381$	−22.3303			−1.14402
$382$		−	5.37386i		−	0.274951i
$383$	−18.3303			−0.936635			−0.468317	−	0.883560i	$-0.655140\pi$
$383$	−18.3303			−0.936635			−0.468317	+	0.883560i	$0.655140\pi$
$384$		−	2.79129i		−	0.142442i
$385$		0			0
$386$	18.3303			0.932988
$387$	−28.7477			−1.46133
$388$	−4.41742			−0.224261
$389$		−	35.8693i		−	1.81865i	−0.416090	−	0.909323i	$-0.636600\pi$
$389$		−	35.8693i		−	1.81865i	0.416090	−	0.909323i	$-0.363400\pi$
$390$		0			0
$391$	1.25227			0.0633302
$392$	−3.00000			−0.151523
$393$	−30.0000			−1.51330
$394$		−	25.9129i		−	1.30547i
$395$		0			0
$396$	−18.1652			−0.912833
$397$		−	12.7477i		−	0.639790i	−0.947453	−	0.319895i	$-0.896352\pi$
$397$		−	12.7477i		−	0.639790i	0.947453	−	0.319895i	$-0.103648\pi$
$398$		−	3.16515i		−	0.158655i
$399$		−	42.3303i		−	2.11917i
$400$		0			0
$401$		−	10.7477i		−	0.536716i	−0.963319	−	0.268358i	$-0.913519\pi$
$401$		−	10.7477i		−	0.536716i	0.963319	−	0.268358i	$-0.0864810\pi$
$402$	−20.5826			−1.02657
$403$			4.25227i			0.211821i
$404$	−1.58258			−0.0787361
$405$		0			0
$406$	1.58258			0.0785419
$407$	17.3739	+	15.1652i	0.861190	+	0.751709i
$408$			4.41742i			0.218695i
$409$			8.83485i			0.436855i	0.975853	+	0.218428i	$0.0700927\pi$
$409$			8.83485i			0.436855i	−0.975853	+	0.218428i	$0.929907\pi$
$410$		0			0
$411$	48.4955			2.39210
$412$	−2.20871			−0.108815
$413$	−15.1652			−0.746228
$414$	−3.79129			−0.186332
$415$		0			0
$416$	0.791288			0.0387961
$417$		−	1.04356i		−	0.0511034i
$418$			28.7477i			1.40610i
$419$	−6.79129			−0.331776			−0.165888	−	0.986145i	$-0.553049\pi$
$419$	−6.79129			−0.331776			−0.165888	+	0.986145i	$0.553049\pi$
$420$		0			0
$421$		−	3.95644i		−	0.192825i	−0.995341	−	0.0964125i	$-0.969263\pi$
$421$		−	3.95644i		−	0.192825i	0.995341	−	0.0964125i	$-0.0307368\pi$
$422$	3.37386			0.164237
$423$		−	7.58258i		−	0.368677i
$424$			7.58258i			0.368242i
$425$		0			0
$426$		−	25.5826i		−	1.23948i
$427$	−16.4174			−0.794495
$428$			8.37386i			0.404766i
$429$		−	8.37386i		−	0.404294i
$430$		0			0
$431$			27.1652i			1.30850i	0.756279	+	0.654250i	$0.227015\pi$
$431$			27.1652i			1.30850i	−0.756279	+	0.654250i	$0.772985\pi$
$432$		−	5.00000i		−	0.240563i
$433$		−	24.3739i		−	1.17133i	−0.810552	−	0.585667i	$-0.800833\pi$
$433$		−	24.3739i		−	1.17133i	0.810552	−	0.585667i	$-0.199167\pi$
$434$	10.7477			0.515907
$435$		0			0
$436$			6.00000i			0.287348i
$437$			6.00000i			0.287019i
$438$	−26.1652			−1.25022
$439$			26.3739i			1.25876i	0.777099	+	0.629378i	$0.216690\pi$
$439$			26.3739i			1.25876i	−0.777099	+	0.629378i	$0.783310\pi$
$440$		0			0
$441$	−14.3739			−0.684470
$442$	−1.25227			−0.0595645
$443$		−	5.04356i		−	0.239627i	−0.992796	−	0.119813i	$-0.961770\pi$
$443$		−	5.04356i		−	0.239627i	0.992796	−	0.119813i	$-0.0382296\pi$
$444$	−11.1652	+	12.7913i	−0.529875	+	0.607048i
$445$		0			0
$446$			14.0000i			0.662919i
$447$			37.9129i			1.79322i
$448$		−	2.00000i		−	0.0944911i
$449$		−	21.1652i		−	0.998845i	−0.866358	−	0.499423i	$-0.833546\pi$
$449$		−	21.1652i		−	0.998845i	0.866358	−	0.499423i	$-0.166454\pi$
$450$		0			0
$451$	19.7477			0.929884
$452$	19.5826			0.921087
$453$			35.5826i			1.67182i
$454$	−19.9129			−0.934558
$455$		0			0
$456$	−21.1652			−0.991149
$457$	33.4955			1.56685			0.783426	−	0.621486i	$-0.213471\pi$
$457$	33.4955			1.56685			0.783426	+	0.621486i	$0.213471\pi$
$458$	−20.7477			−0.969478
$459$			7.91288i			0.369342i
$460$		0			0
$461$			24.3303i			1.13318i	0.824002	+	0.566588i	$0.191737\pi$
$461$			24.3303i			1.13318i	−0.824002	+	0.566588i	$0.808263\pi$
$462$	−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	$0.340237\pi$
$464$		−	0.791288i		−	0.0367346i
$465$		0			0
$466$			25.1216i			1.16374i
$467$	25.5826			1.18382			0.591910	−	0.806004i	$-0.298374\pi$
$467$	25.5826			1.18382			0.591910	+	0.806004i	$0.298374\pi$
$468$	3.79129			0.175252
$469$	−14.7477			−0.680987
$470$		0			0
$471$	5.58258			0.257232
$472$			7.58258i			0.349016i
$473$	22.7477			1.04594
$474$	35.7042			1.63995
$475$		0			0
$476$			3.16515i			0.145074i
$477$			36.3303i			1.66345i
$478$		−	24.9564i		−	1.14148i
$479$		−	0.791288i		−	0.0361549i	−0.999837	−	0.0180774i	$-0.994245\pi$
$479$		−	0.791288i		−	0.0361549i	0.999837	−	0.0180774i	$-0.00575454\pi$
$480$		0			0
$481$	−3.62614	−	3.16515i	−0.165338	−	0.144318i
$482$			13.5826i			0.618669i
$483$	−4.41742			−0.201000
$484$	3.37386			0.153357
$485$		0			0
$486$			16.1652i			0.733266i
$487$	−36.6606			−1.66125			−0.830625	−	0.556832i	$-0.812017\pi$
$487$	−36.6606			−1.66125			−0.830625	+	0.556832i	$0.812017\pi$
$488$			8.20871i			0.371591i
$489$		−	29.0780i		−	1.31495i
$490$		0			0
$491$	−8.37386			−0.377907			−0.188954	−	0.981986i	$-0.560510\pi$
$491$	−8.37386			−0.377907			−0.188954	+	0.981986i	$0.560510\pi$
$492$			14.5390i			0.655469i
$493$			1.25227i			0.0563995i
$494$		−	6.00000i		−	0.269953i
$495$		0			0
$496$		−	5.37386i		−	0.241294i
$497$		−	18.3303i		−	0.822226i
$498$	8.83485			0.395899
$499$			16.7477i			0.749731i	0.927079	+	0.374866i	$0.122311\pi$
$499$			16.7477i			0.749731i	−0.927079	+	0.374866i	$0.877689\pi$
$500$		0			0
$501$			2.66970i			0.119273i
$502$			13.5826i			0.606220i
$503$	−29.3739			−1.30972			−0.654858	−	0.755752i	$-0.727272\pi$
$503$	−29.3739			−1.30972			−0.654858	+	0.755752i	$0.727272\pi$
$504$		−	9.58258i		−	0.426842i
$505$		0			0
$506$	3.00000			0.133366
$507$		−	34.5390i		−	1.53393i
$508$			8.00000i			0.354943i
$509$	−13.5826			−0.602037			−0.301019	−	0.953618i	$-0.597327\pi$
$509$	−13.5826			−0.602037			−0.301019	+	0.953618i	$0.597327\pi$
$510$		0			0
$511$	−18.7477			−0.829351
$512$	−1.00000			−0.0441942
$513$	−37.9129			−1.67389
$514$	−22.7477			−1.00336
$515$		0			0
$516$			16.7477i			0.737278i
$517$			6.00000i			0.263880i
$518$	−8.00000	+	9.16515i	−0.351500	+	0.402694i
$519$	−8.83485			−0.387807
$520$		0			0
$521$	9.16515			0.401533			0.200766	−	0.979639i	$-0.435657\pi$
$521$	9.16515			0.401533			0.200766	+	0.979639i	$0.435657\pi$
$522$		−	3.79129i		−	0.165940i
$523$	3.16515			0.138402			0.0692012	−	0.997603i	$-0.477955\pi$
$523$	3.16515			0.138402			0.0692012	+	0.997603i	$0.477955\pi$
$524$			10.7477i			0.469517i
$525$		0			0
$526$		−	8.83485i		−	0.385218i
$527$			8.50455i			0.370464i
$528$			10.5826i			0.460547i
$529$	−22.3739			−0.972777
$530$		0			0
$531$			36.3303i			1.57660i
$532$	−15.1652			−0.657493
$533$	−4.12159			−0.178526
$534$	16.7477			0.724745
$535$		0			0
$536$			7.37386i			0.318502i
$537$	21.1652			0.913344
$538$	−10.7477			−0.463367
$539$	11.3739			0.489907
$540$		0			0
$541$			8.20871i			0.352920i	0.984308	+	0.176460i	$0.0564646\pi$
$541$			8.20871i			0.352920i	−0.984308	+	0.176460i	$0.943535\pi$
$542$	−22.0000			−0.944981
$543$		−	52.3303i		−	2.24571i
$544$	1.58258			0.0678524
$545$		0			0
$546$	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	$0.360026\pi$
$548$		−	17.3739i		−	0.742175i
$549$			39.3303i			1.67858i
$550$		0			0
$551$	−6.00000			−0.255609
$552$			2.20871i			0.0940090i
$553$	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	$0.155159\pi$
$558$		−	25.7477i		−	1.08999i
$559$	−4.74773			−0.200807
$560$		0			0
$561$		−	16.7477i		−	0.707090i
$562$		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
$565$		0			0
$566$	24.0000			1.00880
$567$			0.834849i			0.0350603i
$568$	−9.16515			−0.384561
$569$		−	26.8348i		−	1.12498i	−0.826806	−	0.562488i	$-0.809844\pi$
$569$		−	26.8348i		−	1.12498i	0.826806	−	0.562488i	$-0.190156\pi$
$570$		0			0
$571$	−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
$574$			10.4174i			0.434815i
$575$		0			0
$576$	−4.79129			−0.199637
$577$	−4.41742			−0.183900			−0.0919499	−	0.995764i	$-0.529310\pi$
$577$	−4.41742			−0.183900			−0.0919499	+	0.995764i	$0.529310\pi$
$578$	14.4955			0.602931
$579$		−	51.1652i		−	2.12635i
$580$		0			0
$581$	6.33030			0.262625
$582$			12.3303i			0.511107i
$583$		−	28.7477i		−	1.19061i
$584$			9.37386i			0.387893i
$585$		0			0
$586$		−	6.00000i		−	0.247858i
$587$	−25.9129			−1.06954			−0.534769	−	0.844998i	$-0.679602\pi$
$587$	−25.9129			−1.06954			−0.534769	+	0.844998i	$0.679602\pi$
$588$			8.37386i			0.345332i
$589$	−40.7477			−1.67898
$590$		0			0
$591$	−72.3303			−2.97527
$592$	4.58258	+	4.00000i	0.188343	+	0.164399i
$593$			14.2087i			0.583482i	0.956497	+	0.291741i	$0.0942345\pi$
$593$			14.2087i			0.583482i	−0.956497	+	0.291741i	$0.905765\pi$
$594$			18.9564i			0.777792i
$595$		0			0
$596$	13.5826			0.556364
$597$	−8.83485			−0.361586
$598$	−0.626136			−0.0256046
$599$	−27.1652			−1.10994			−0.554969	−	0.831871i	$-0.687270\pi$
$599$	−27.1652			−1.10994			−0.554969	+	0.831871i	$0.687270\pi$
$600$		0			0
$601$	8.12159			0.331287			0.165643	−	0.986186i	$-0.447030\pi$
$601$	8.12159			0.331287			0.165643	+	0.986186i	$0.447030\pi$
$602$			12.0000i			0.489083i
$603$			35.3303i			1.43876i
$604$	12.7477			0.518698
$605$		0			0
$606$			4.41742i			0.179446i
$607$	−5.53901			−0.224822			−0.112411	−	0.993662i	$-0.535857\pi$
$607$	−5.53901			−0.224822			−0.112411	+	0.993662i	$0.535857\pi$
$608$			7.58258i			0.307514i
$609$		−	4.41742i		−	0.179003i
$610$		0			0
$611$		−	1.25227i		−	0.0506615i
$612$	7.58258			0.306507
$613$		−	5.49545i		−	0.221959i	−0.993823	−	0.110980i	$-0.964601\pi$
$613$		−	5.49545i		−	0.221959i	0.993823	−	0.110980i	$-0.0353988\pi$
$614$			12.3739i			0.499368i
$615$		0			0
$616$			7.58258i			0.305511i
$617$		−	45.9564i		−	1.85014i	−0.379801	−	0.925068i	$-0.624007\pi$
$617$		−	45.9564i		−	1.85014i	0.379801	−	0.925068i	$-0.375993\pi$
$618$			6.16515i			0.247999i
$619$	−6.12159			−0.246048			−0.123024	−	0.992404i	$-0.539259\pi$
$619$	−6.12159			−0.246048			−0.123024	+	0.992404i	$0.539259\pi$
$620$		0			0
$621$			3.95644i			0.158766i
$622$		−	9.62614i		−	0.385973i
$623$	12.0000			0.480770
$624$		−	2.20871i		−	0.0884192i
$625$		0			0
$626$	−33.1652			−1.32555
$627$	80.2432			3.20460
$628$		−	2.00000i		−	0.0798087i
$629$	−7.25227	−	6.33030i	−0.289167	−	0.252406i
$630$		0			0
$631$			3.95644i			0.157503i	0.996894	+	0.0787517i	$0.0250934\pi$
$631$			3.95644i			0.157503i	−0.996894	+	0.0787517i	$0.974907\pi$
$632$		−	12.7913i		−	0.508810i
$633$		−	9.41742i		−	0.374309i
$634$			1.25227i			0.0497341i
$635$		0			0
$636$	21.1652			0.839253
$637$	−2.37386			−0.0940559
$638$			3.00000i			0.118771i
$639$	−43.9129			−1.73717
$640$		0			0
$641$	−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	$-0.598837\pi$
$643$	−15.4955			−0.611081			−0.305541	+	0.952179i	$0.598837\pi$
$644$			1.58258i			0.0623622i
$645$		0			0
$646$		−	12.0000i		−	0.472134i
$647$	−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
$649$		−	28.7477i		−	1.12845i
$650$		0			0
$651$		−	30.0000i		−	1.17579i
$652$	−10.4174			−0.407978
$653$	−14.3739			−0.562493			−0.281246	−	0.959636i	$-0.590748\pi$
$653$	−14.3739			−0.562493			−0.281246	+	0.959636i	$0.590748\pi$
$654$	16.7477			0.654888
$655$		0			0
$656$	5.20871			0.203366
$657$			44.9129i			1.75222i
$658$	−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	$0.730028\pi$
$660$		0			0
$661$		−	36.7913i		−	1.43102i	−0.698605	−	0.715508i	$-0.746195\pi$
$661$		−	36.7913i		−	1.43102i	0.698605	−	0.715508i	$-0.253805\pi$
$662$		−	16.4174i		−	0.638081i
$663$			3.49545i			0.135752i
$664$		−	3.16515i		−	0.122832i
$665$		0			0
$666$	21.9564	+	19.1652i	0.850795	+	0.742635i
$667$			0.626136i			0.0242441i
$668$	0.956439			0.0370057
$669$	39.0780			1.51084
$670$		0			0
$671$		−	31.1216i		−	1.20144i
$672$	−5.58258			−0.215353
$673$		−	5.12159i		−	0.197423i	−0.995116	−	0.0987114i	$-0.968528\pi$
$673$		−	5.12159i		−	0.197423i	0.995116	−	0.0987114i	$-0.0314721\pi$
$674$			8.12159i			0.312832i
$675$		0			0
$676$	−12.3739			−0.475918
$677$		−	9.16515i		−	0.352245i	−0.984368	−	0.176123i	$-0.943644\pi$
$677$		−	9.16515i		−	0.352245i	0.984368	−	0.176123i	$-0.0563555\pi$
$678$		−	54.6606i		−	2.09923i
$679$			8.83485i			0.339050i
$680$		0			0
$681$			55.5826i			2.12993i
$682$			20.3739i			0.780156i
$683$	22.4174			0.857779			0.428889	−	0.903357i	$-0.358905\pi$
$683$	22.4174			0.857779			0.428889	+	0.903357i	$0.358905\pi$
$684$			36.3303i			1.38912i
$685$		0			0
$686$			20.0000i			0.763604i
$687$			57.9129i			2.20951i
$688$	6.00000			0.228748
$689$			6.00000i			0.228582i
$690$		0			0
$691$	−29.4955			−1.12206			−0.561030	−	0.827795i	$-0.689595\pi$
$691$	−29.4955			−1.12206			−0.561030	+	0.827795i	$0.689595\pi$
$692$			3.16515i			0.120321i
$693$			36.3303i			1.38007i
$694$	1.58258			0.0600738
$695$		0			0
$696$	−2.20871			−0.0837210
$697$	−8.24318			−0.312233
$698$	10.0000			0.378506
$699$	70.1216			2.65224
$700$		0			0
$701$			18.9564i			0.715975i	0.933726	+	0.357987i	$0.116537\pi$
$701$			18.9564i			0.715975i	−0.933726	+	0.357987i	$0.883463\pi$
$702$		−	3.95644i		−	0.149326i
$703$	30.3303	−	34.7477i	1.14393	−	1.31054i
$704$	3.79129			0.142890
$705$		0			0
$706$	7.58258			0.285374
$707$			3.16515i			0.119038i
$708$	21.1652			0.795435
$709$			27.7913i			1.04372i	0.853030	+	0.521862i	$0.174762\pi$
$709$			27.7913i			1.04372i	−0.853030	+	0.521862i	$0.825238\pi$
$710$		0			0
$711$		−	61.2867i		−	2.29843i
$712$		−	6.00000i		−	0.224860i
$713$			4.25227i			0.159249i
$714$	8.83485			0.330636
$715$		0			0
$716$		−	7.58258i		−	0.283374i
$717$	−69.6606			−2.60152
$718$	−27.1652			−1.01379
$719$	2.83485			0.105722			0.0528610	−	0.998602i	$-0.483166\pi$
$719$	2.83485			0.105722			0.0528610	+	0.998602i	$0.483166\pi$
$720$		0			0
$721$			4.41742i			0.164513i
$722$	38.4955			1.43265
$723$	37.9129			1.41000
$724$	−18.7477			−0.696754
$725$		0			0
$726$		−	9.41742i		−	0.349513i
$727$	28.1216			1.04297			0.521486	−	0.853260i	$-0.325378\pi$
$727$	28.1216			1.04297			0.521486	+	0.853260i	$0.325378\pi$
$728$		−	1.58258i		−	0.0586542i
$729$	43.8693			1.62479
$730$		0			0
$731$	−9.49545			−0.351202
$732$	22.9129			0.846884
$733$			7.49545i			0.276851i	0.990373	+	0.138425i	$0.0442041\pi$
$733$			7.49545i			0.276851i	−0.990373	+	0.138425i	$0.955796\pi$
$734$			32.7477i			1.20874i
$735$		0			0
$736$	0.791288			0.0291673
$737$		−	27.9564i		−	1.02979i
$738$	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
$743$			3.16515i			0.116118i	0.998313	+	0.0580591i	$0.0184912\pi$
$743$			3.16515i			0.116118i	−0.998313	+	0.0580591i	$0.981509\pi$
$744$	−15.0000			−0.549927
$745$		0			0
$746$			14.7477i			0.539953i
$747$		−	15.1652i		−	0.554864i
$748$	−6.00000			−0.219382
$749$	16.7477			0.611949
$750$		0			0
$751$	13.4955			0.492456			0.246228	−	0.969212i	$-0.420809\pi$
$751$	13.4955			0.492456			0.246228	+	0.969212i	$0.420809\pi$
$752$			1.58258i			0.0577106i
$753$	37.9129			1.38162
$754$		−	0.626136i		−	0.0228025i
$755$		0			0
$756$	−10.0000			−0.363696
$757$	−39.7913			−1.44624			−0.723119	−	0.690723i	$-0.757292\pi$
$757$	−39.7913			−1.44624			−0.723119	+	0.690723i	$0.757292\pi$
$758$	−21.1216			−0.767171
$759$		−	8.37386i		−	0.303952i
$760$		0			0
$761$	18.7913			0.681184			0.340592	−	0.940211i	$-0.389373\pi$
$761$	18.7913			0.681184			0.340592	+	0.940211i	$0.389373\pi$
$762$	22.3303			0.808942
$763$	12.0000			0.434429
$764$			5.37386i			0.194420i
$765$		0			0
$766$	18.3303			0.662301
$767$			6.00000i			0.216647i
$768$			2.79129i			0.100722i
$769$		−	48.3303i		−	1.74284i	−0.490542	−	0.871418i	$-0.663201\pi$
$769$		−	48.3303i		−	1.74284i	0.490542	−	0.871418i	$-0.336799\pi$
$770$		0			0
$771$			63.4955i			2.28673i
$772$	−18.3303			−0.659722
$773$			13.9129i			0.500411i	0.968193	+	0.250206i	$0.0804983\pi$
$773$			13.9129i			0.500411i	−0.968193	+	0.250206i	$0.919502\pi$
$774$	28.7477			1.03332
$775$		0			0
$776$	4.41742			0.158576
$777$	25.5826	+	22.3303i	0.917770	+	0.801095i
$778$			35.8693i			1.28598i
$779$		−	39.4955i		−	1.41507i
$780$		0			0
$781$	34.7477			1.24337
$782$	−1.25227			−0.0447812
$783$	−3.95644			−0.141392
$784$	3.00000			0.107143
$785$		0			0
$786$	30.0000			1.07006
$787$			8.00000i			0.285169i	0.989783	+	0.142585i	$0.0455413\pi$
$787$			8.00000i			0.285169i	−0.989783	+	0.142585i	$0.954459\pi$
$788$			25.9129i			0.923108i
$789$	−24.6606			−0.877941
$790$		0			0
$791$		−	39.1652i		−	1.39255i
$792$	18.1652			0.645471
$793$			6.49545i			0.230660i
$794$			12.7477i			0.452400i
$795$		0			0
$796$			3.16515i			0.112186i
$797$	21.6261			0.766037			0.383019	−	0.923741i	$-0.374885\pi$
$797$	21.6261			0.766037			0.383019	+	0.923741i	$0.374885\pi$
$798$			42.3303i			1.49848i
$799$		−	2.50455i		−	0.0886045i
$800$		0			0
$801$		−	28.7477i		−	1.01575i
$802$			10.7477i			0.379515i
$803$		−	35.5390i		−	1.25414i
$804$	20.5826			0.725891
$805$		0			0
$806$		−	4.25227i		−	0.149780i
$807$			30.0000i			1.05605i
$808$	1.58258			0.0556748
$809$			11.0780i			0.389483i	0.980855	+	0.194741i	$0.0623868\pi$
$809$			11.0780i			0.389483i	−0.980855	+	0.194741i	$0.937613\pi$
$810$		0			0
$811$	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
$813$			61.4083i			2.15368i
$814$	−17.3739	−	15.1652i	−0.608954	−	0.531538i
$815$		0			0
$816$		−	4.41742i		−	0.154641i
$817$		−	45.4955i		−	1.59168i
$818$		−	8.83485i		−	0.308903i
$819$		−	7.58258i		−	0.264957i
$820$		0			0
$821$	−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
$823$			16.0000i			0.557725i	0.960331	+	0.278862i	$0.0899574\pi$
$823$			16.0000i			0.557725i	−0.960331	+	0.278862i	$0.910043\pi$
$824$	2.20871			0.0769441
$825$		0			0
$826$	15.1652			0.527663
$827$	14.8348			0.515858			0.257929	−	0.966164i	$-0.416960\pi$
$827$	14.8348			0.515858			0.257929	+	0.966164i	$0.416960\pi$
$828$	3.79129			0.131756
$829$			39.9564i			1.38774i	0.720098	+	0.693872i	$0.244097\pi$
$829$			39.9564i			1.38774i	−0.720098	+	0.693872i	$0.755903\pi$
$830$		0			0
$831$		−	65.2432i		−	2.26326i
$832$	−0.791288			−0.0274330
$833$	−4.74773			−0.164499
$834$			1.04356i			0.0361356i
$835$		0			0
$836$		−	28.7477i		−	0.994261i
$837$	−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	$0.151463\pi$
$840$		0			0
$841$	28.3739			0.978409
$842$			3.95644i			0.136348i
$843$		0			0
$844$	−3.37386			−0.116133
$845$		0			0
$846$			7.58258i			0.260694i
$847$		−	6.74773i		−	0.231855i
$848$		−	7.58258i		−	0.260387i
$849$		−	66.9909i		−	2.29912i
$850$		0			0
$851$	−3.62614	−	3.16515i	−0.124302	−	0.108500i
$852$			25.5826i			0.876445i
$853$	5.70417			0.195307			0.0976535	−	0.995220i	$-0.468866\pi$
$853$	5.70417			0.195307			0.0976535	+	0.995220i	$0.468866\pi$
$854$	16.4174			0.561793
$855$		0			0
$856$		−	8.37386i		−	0.286213i
$857$	14.8348			0.506749			0.253374	−	0.967368i	$-0.418460\pi$
$857$	14.8348			0.506749			0.253374	+	0.967368i	$0.418460\pi$
$858$			8.37386i			0.285879i
$859$			54.6606i			1.86500i	0.361175	+	0.932498i	$0.382376\pi$
$859$			54.6606i			1.86500i	−0.361175	+	0.932498i	$0.617624\pi$
$860$		0			0
$861$	29.0780			0.990977
$862$		−	27.1652i		−	0.925249i
$863$			46.7477i			1.59131i	0.605749	+	0.795656i	$0.292873\pi$
$863$			46.7477i			1.59131i	−0.605749	+	0.795656i	$0.707127\pi$
$864$			5.00000i			0.170103i
$865$		0			0
$866$			24.3739i			0.828258i
$867$		−	40.4610i		−	1.37413i
$868$	−10.7477			−0.364802
$869$			48.4955i			1.64510i
$870$		0			0
$871$			5.83485i			0.197706i
$872$		−	6.00000i		−	0.203186i
$873$	21.1652			0.716332
$874$		−	6.00000i		−	0.202953i
$875$		0			0
$876$	26.1652			0.884039
$877$			38.7477i			1.30842i	0.756314	+	0.654209i	$0.226998\pi$
$877$			38.7477i			1.30842i	−0.756314	+	0.654209i	$0.773002\pi$
$878$		−	26.3739i		−	0.890075i
$879$	−16.7477			−0.564887
$880$		0			0
$881$	28.1216			0.947440			0.473720	−	0.880675i	$-0.342911\pi$
$881$	28.1216			0.947440			0.473720	+	0.880675i	$0.342911\pi$
$882$	14.3739			0.483993
$883$	13.9129			0.468206			0.234103	−	0.972212i	$-0.424785\pi$
$883$	13.9129			0.468206			0.234103	+	0.972212i	$0.424785\pi$
$884$	1.25227			0.0421185
$885$		0			0
$886$			5.04356i			0.169442i
$887$			33.8258i			1.13576i	0.823112	+	0.567879i	$0.192236\pi$
$887$			33.8258i			1.13576i	−0.823112	+	0.567879i	$0.807764\pi$
$888$	11.1652	−	12.7913i	0.374678	−	0.429248i
$889$	16.0000			0.536623
$890$		0			0
$891$	−1.58258			−0.0530183
$892$		−	14.0000i		−	0.468755i
$893$	12.0000			0.401565
$894$		−	37.9129i		−	1.26800i
$895$		0			0
$896$			2.00000i			0.0668153i
$897$			1.74773i			0.0583549i
$898$			21.1652i			0.706290i
$899$	−4.25227			−0.141821
$900$		0			0
$901$			12.0000i			0.399778i
$902$	−19.7477			−0.657527
$903$	33.4955			1.11466
$904$	−19.5826			−0.651307
$905$		0			0
$906$		−	35.5826i		−	1.18215i
$907$	6.33030			0.210194			0.105097	−	0.994462i	$-0.466485\pi$
$907$	6.33030			0.210194			0.105097	+	0.994462i	$0.466485\pi$
$908$	19.9129			0.660832
$909$	7.58258			0.251498
$910$		0			0
$911$		−	54.3303i		−	1.80004i	−0.435845	−	0.900022i	$-0.643551\pi$
$911$		−	54.3303i		−	1.80004i	0.435845	−	0.900022i	$-0.356449\pi$
$912$	21.1652			0.700848
$913$			12.0000i			0.397142i
$914$	−33.4955			−1.10793
$915$		0			0
$916$	20.7477			0.685524
$917$	21.4955			0.709842
$918$		−	7.91288i		−	0.261164i
$919$			36.0000i			1.18753i	0.804638	+	0.593765i	$0.202359\pi$
$919$			36.0000i			1.18753i	−0.804638	+	0.593765i	$0.797641\pi$
$920$		0			0
$921$	34.5390			1.13810
$922$		−	24.3303i		−	0.801276i
$923$	−7.25227			−0.238711
$924$	21.1652			0.696282
$925$		0			0
$926$	−20.7042			−0.680381
$927$	10.5826			0.347577
$928$			0.791288i			0.0259753i
$929$	5.37386			0.176311			0.0881554	−	0.996107i	$-0.471903\pi$
$929$	5.37386			0.176311			0.0881554	+	0.996107i	$0.471903\pi$
$930$		0			0
$931$		−	22.7477i		−	0.745527i
$932$		−	25.1216i		−	0.822885i
$933$	−26.8693			−0.879662
$934$	−25.5826			−0.837087
$935$		0			0
$936$	−3.79129			−0.123922
$937$		−	33.8693i		−	1.10646i	−0.833028	−	0.553231i	$-0.813395\pi$
$937$		−	33.8693i		−	1.10646i	0.833028	−	0.553231i	$-0.186605\pi$
$938$	14.7477			0.481530
$939$			92.5735i			3.02102i
$940$		0			0
$941$	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
$944$		−	7.58258i		−	0.246792i
$945$		0			0
$946$	−22.7477			−0.739592
$947$	−28.7477			−0.934176			−0.467088	−	0.884211i	$-0.654697\pi$
$947$	−28.7477			−0.934176			−0.467088	+	0.884211i	$0.654697\pi$
$948$	−35.7042			−1.15962
$949$			7.41742i			0.240780i
$950$		0			0
$951$	3.49545			0.113348
$952$		−	3.16515i		−	0.102583i
$953$			46.4519i			1.50472i	0.658750	+	0.752362i	$0.271086\pi$
$953$			46.4519i			1.50472i	−0.658750	+	0.752362i	$0.728914\pi$
$954$		−	36.3303i		−	1.17624i
$955$		0			0
$956$			24.9564i			0.807149i
$957$	8.37386			0.270689
$958$			0.791288i			0.0255653i
$959$	−34.7477			−1.12206
$960$		0			0
$961$	2.12159			0.0684384
$962$	3.62614	+	3.16515i	0.116911	+	0.102049i
$963$		−	40.1216i		−	1.29290i
$964$		−	13.5826i		−	0.437465i
$965$		0			0
$966$	4.41742			0.142128
$967$	0.956439			0.0307570			0.0153785	−	0.999882i	$-0.495105\pi$
$967$	0.956439			0.0307570			0.0153785	+	0.999882i	$0.495105\pi$
$968$	−3.37386			−0.108440
$969$	−33.4955			−1.07603
$970$		0			0
$971$	36.6261			1.17539			0.587694	−	0.809083i	$-0.300036\pi$
$971$	36.6261			1.17539			0.587694	+	0.809083i	$0.300036\pi$
$972$		−	16.1652i		−	0.518497i
$973$			0.747727i			0.0239710i
$974$	36.6606			1.17468
$975$		0			0
$976$		−	8.20871i		−	0.262754i
$977$	−23.0780			−0.738332			−0.369166	−	0.929364i	$-0.620357\pi$
$977$	−23.0780			−0.738332			−0.369166	+	0.929364i	$0.620357\pi$
$978$			29.0780i			0.929813i
$979$			22.7477i			0.727021i
$980$		0			0
$981$		−	28.7477i		−	0.917844i
$982$	8.37386			0.267221
$983$		−	18.3303i		−	0.584646i	−0.956320	−	0.292323i	$-0.905572\pi$
$983$		−	18.3303i		−	0.584646i	0.956320	−	0.292323i	$-0.0944282\pi$
$984$		−	14.5390i		−	0.463487i
$985$		0			0
$986$		−	1.25227i		−	0.0398805i
$987$			8.83485i			0.281216i
$988$			6.00000i			0.190885i
$989$	−4.74773			−0.150969
$990$		0			0
$991$			3.95644i			0.125680i	0.998024	+	0.0628402i	$0.0200159\pi$
$991$			3.95644i			0.125680i	−0.998024	+	0.0628402i	$0.979984\pi$
$992$			5.37386i			0.170620i
$993$	−45.8258			−1.45424
$994$			18.3303i			0.581402i
$995$		0			0
$996$	−8.83485			−0.279943
$997$	−18.0000			−0.570066			−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000			−0.570066			−0.285033	+	0.958518i	$0.592005\pi$
$998$		−	16.7477i		−	0.530140i
$999$	20.0000	−	22.9129i	0.632772	−	0.724931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.c.g.1849.4		4
5.2	odd	4		1850.2.d.e.1701.2		4
5.3	odd	4		74.2.b.a.73.3	yes	4
5.4	even	2		1850.2.c.h.1849.1		4
15.8	even	4		666.2.c.b.73.1		4
20.3	even	4		592.2.g.c.369.4		4
37.36	even	2		1850.2.c.h.1849.4		4
40.3	even	4		2368.2.g.h.961.1		4
40.13	odd	4		2368.2.g.j.961.3		4
60.23	odd	4		5328.2.h.m.2737.1		4
185.43	even	4		2738.2.a.k.1.2		2
185.68	even	4		2738.2.a.h.1.2		2
185.73	odd	4		74.2.b.a.73.1	✓	4
185.147	odd	4		1850.2.d.e.1701.4		4
185.184	even	2	inner	1850.2.c.g.1849.1		4
555.443	even	4		666.2.c.b.73.4		4
740.443	even	4		592.2.g.c.369.3		4
1480.443	even	4		2368.2.g.h.961.2		4
1480.813	odd	4		2368.2.g.j.961.4		4
2220.443	odd	4		5328.2.h.m.2737.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.b.a.73.1	✓	4	185.73	odd	4
74.2.b.a.73.3	yes	4	5.3	odd	4
592.2.g.c.369.3		4	740.443	even	4
592.2.g.c.369.4		4	20.3	even	4
666.2.c.b.73.1		4	15.8	even	4
666.2.c.b.73.4		4	555.443	even	4
1850.2.c.g.1849.1		4	185.184	even	2	inner
1850.2.c.g.1849.4		4	1.1	even	1	trivial
1850.2.c.h.1849.1		4	5.4	even	2
1850.2.c.h.1849.4		4	37.36	even	2
1850.2.d.e.1701.2		4	5.2	odd	4
1850.2.d.e.1701.4		4	185.147	odd	4
2368.2.g.h.961.1		4	40.3	even	4
2368.2.g.h.961.2		4	1480.443	even	4
2368.2.g.j.961.3		4	40.13	odd	4
2368.2.g.j.961.4		4	1480.813	odd	4
2738.2.a.h.1.2		2	185.68	even	4
2738.2.a.k.1.2		2	185.43	even	4
5328.2.h.m.2737.1		4	60.23	odd	4
5328.2.h.m.2737.4		4	2220.443	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:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.79129i q^{3} +1.00000 q^{4} -2.79129i q^{6} -2.00000i q^{7} -1.00000 q^{8} -4.79129 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.79129i q^{3} +1.00000 q^{4} -2.79129i q^{6} -2.00000i q^{7} -1.00000 q^{8} -4.79129 q^{9} +3.79129 q^{11} +2.79129i q^{12} -0.791288 q^{13} +2.00000i q^{14} +1.00000 q^{16} -1.58258 q^{17} +4.79129 q^{18} -7.58258i q^{19} +5.58258 q^{21} -3.79129 q^{22} -0.791288 q^{23} -2.79129i q^{24} +0.791288 q^{26} -5.00000i q^{27} -2.00000i q^{28} -0.791288i q^{29} -5.37386i q^{31} -1.00000 q^{32} +10.5826i q^{33} +1.58258 q^{34} -4.79129 q^{36} +(4.58258 + 4.00000i) q^{37} +7.58258i q^{38} -2.20871i q^{39} +5.20871 q^{41} -5.58258 q^{42} +6.00000 q^{43} +3.79129 q^{44} +0.791288 q^{46} +1.58258i q^{47} +2.79129i q^{48} +3.00000 q^{49} -4.41742i q^{51} -0.791288 q^{52} -7.58258i q^{53} +5.00000i q^{54} +2.00000i q^{56} +21.1652 q^{57} +0.791288i q^{58} -7.58258i q^{59} -8.20871i q^{61} +5.37386i q^{62} +9.58258i q^{63} +1.00000 q^{64} -10.5826i q^{66} -7.37386i q^{67} -1.58258 q^{68} -2.20871i q^{69} +9.16515 q^{71} +4.79129 q^{72} -9.37386i q^{73} +(-4.58258 - 4.00000i) q^{74} -7.58258i q^{76} -7.58258i q^{77} +2.20871i q^{78} +12.7913i q^{79} -0.417424 q^{81} -5.20871 q^{82} +3.16515i q^{83} +5.58258 q^{84} -6.00000 q^{86} +2.20871 q^{87} -3.79129 q^{88} +6.00000i q^{89} +1.58258i q^{91} -0.791288 q^{92} +15.0000 q^{93} -1.58258i q^{94} -2.79129i q^{96} -4.41742 q^{97} -3.00000 q^{98} -18.1652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 10 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 10 * q^9	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 10 q^{9} + 6 q^{11} + 6 q^{13} + 4 q^{16} + 12 q^{17} + 10 q^{18} + 4 q^{21} - 6 q^{22} + 6 q^{23} - 6 q^{26} - 4 q^{32} - 12 q^{34} - 10 q^{36} + 30 q^{41} - 4 q^{42} + 24 q^{43} + 6 q^{44} - 6 q^{46} + 12 q^{49} + 6 q^{52} + 48 q^{57} + 4 q^{64} + 12 q^{68} + 10 q^{72} - 20 q^{81} - 30 q^{82} + 4 q^{84} - 24 q^{86} + 18 q^{87} - 6 q^{88} + 6 q^{92} + 60 q^{93} - 36 q^{97} - 12 q^{98} - 36 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 10 * q^9 + 6 * q^11 + 6 * q^13 + 4 * q^16 + 12 * q^17 + 10 * q^18 + 4 * q^21 - 6 * q^22 + 6 * q^23 - 6 * q^26 - 4 * q^32 - 12 * q^34 - 10 * q^36 + 30 * q^41 - 4 * q^42 + 24 * q^43 + 6 * q^44 - 6 * q^46 + 12 * q^49 + 6 * q^52 + 48 * q^57 + 4 * q^64 + 12 * q^68 + 10 * q^72 - 20 * q^81 - 30 * q^82 + 4 * q^84 - 24 * q^86 + 18 * q^87 - 6 * q^88 + 6 * q^92 + 60 * q^93 - 36 * q^97 - 12 * q^98 - 36 * q^99

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