LMFDB - Embedded newform 1920.2.m.t.959.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1920,2,Mod(959,1920)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1920, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1920.959"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.m (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2,0,4,0,-4,0,0,0,0,0,8,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			959.1
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	1920.959
Dual form			1920.2.m.t.959.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.618034 - 1.61803i) q^{3} +(1.00000 + 2.00000i) q^{5} +1.23607 q^{7} +(-2.23607 + 2.00000i) q^{9} -4.00000i q^{11} -2.47214 q^{13} +(2.61803 - 2.85410i) q^{15} -2.47214 q^{17} -6.47214 q^{19} +(-0.763932 - 2.00000i) q^{21} +3.23607i q^{23} +(-3.00000 + 4.00000i) q^{25} +(4.61803 + 2.38197i) q^{27} +4.47214 q^{29} -6.47214i q^{31} +(-6.47214 + 2.47214i) q^{33} +(1.23607 + 2.47214i) q^{35} -10.4721 q^{37} +(1.52786 + 4.00000i) q^{39} -4.00000i q^{41} -4.76393i q^{43} +(-6.23607 - 2.47214i) q^{45} +4.76393i q^{47} -5.47214 q^{49} +(1.52786 + 4.00000i) q^{51} -8.94427i q^{53} +(8.00000 - 4.00000i) q^{55} +(4.00000 + 10.4721i) q^{57} -8.94427i q^{59} -12.9443i q^{61} +(-2.76393 + 2.47214i) q^{63} +(-2.47214 - 4.94427i) q^{65} -1.70820i q^{67} +(5.23607 - 2.00000i) q^{69} +12.9443i q^{73} +(8.32624 + 2.38197i) q^{75} -4.94427i q^{77} -1.52786i q^{79} +(1.00000 - 8.94427i) q^{81} -14.1803 q^{83} +(-2.47214 - 4.94427i) q^{85} +(-2.76393 - 7.23607i) q^{87} +8.00000i q^{89} -3.05573 q^{91} +(-10.4721 + 4.00000i) q^{93} +(-6.47214 - 12.9443i) q^{95} +4.94427i q^{97} +(8.00000 + 8.94427i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 8 q^{13} + 6 q^{15} + 8 q^{17} - 8 q^{19} - 12 q^{21} - 12 q^{25} + 14 q^{27} - 8 q^{33} - 4 q^{35} - 24 q^{37} + 24 q^{39} - 16 q^{45} - 4 q^{49} + 24 q^{51} + 32 q^{55}+ \cdots + 32 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 8 * q^13 + 6 * q^15 + 8 * q^17 - 8 * q^19 - 12 * q^21 - 12 * q^25 + 14 * q^27 - 8 * q^33 - 4 * q^35 - 24 * q^37 + 24 * q^39 - 16 * q^45 - 4 * q^49 + 24 * q^51 + 32 * q^55 + 16 * q^57 - 20 * q^63 + 8 * q^65 + 12 * q^69 + 2 * q^75 + 4 * q^81 - 12 * q^83 + 8 * q^85 - 20 * q^87 - 48 * q^91 - 24 * q^93 - 8 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$3$	−0.618034	−	1.61803i	−0.356822	−	0.934172i
$4$		0			0
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$	1.23607			0.467190			0.233595	−	0.972334i	$-0.424951\pi$
$7$	1.23607			0.467190			0.233595	+	0.972334i	$0.424951\pi$
$8$		0			0
$9$	−2.23607	+	2.00000i	−0.745356	+	0.666667i
$10$		0			0
$11$		−	4.00000i		−	1.20605i	−0.797724	−	0.603023i	$-0.793963\pi$
$11$		−	4.00000i		−	1.20605i	0.797724	−	0.603023i	$-0.206037\pi$
$12$		0			0
$13$	−2.47214			−0.685647			−0.342824	−	0.939400i	$-0.611383\pi$
$13$	−2.47214			−0.685647			−0.342824	+	0.939400i	$0.611383\pi$
$14$		0			0
$15$	2.61803	−	2.85410i	0.675973	−	0.736926i
$16$		0			0
$17$	−2.47214			−0.599581			−0.299791	−	0.954005i	$-0.596917\pi$
$17$	−2.47214			−0.599581			−0.299791	+	0.954005i	$0.596917\pi$
$18$		0			0
$19$	−6.47214			−1.48481			−0.742405	−	0.669951i	$-0.766315\pi$
$19$	−6.47214			−1.48481			−0.742405	+	0.669951i	$0.766315\pi$
$20$		0			0
$21$	−0.763932	−	2.00000i	−0.166704	−	0.436436i
$22$		0			0
$23$			3.23607i			0.674767i	0.941367	+	0.337383i	$0.109542\pi$
$23$			3.23607i			0.674767i	−0.941367	+	0.337383i	$0.890458\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$	4.61803	+	2.38197i	0.888741	+	0.458410i
$28$		0			0
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$		0			0
$31$		−	6.47214i		−	1.16243i	−0.813750	−	0.581215i	$-0.802578\pi$
$31$		−	6.47214i		−	1.16243i	0.813750	−	0.581215i	$-0.197422\pi$
$32$		0			0
$33$	−6.47214	+	2.47214i	−1.12665	+	0.430344i
$34$		0			0
$35$	1.23607	+	2.47214i	0.208934	+	0.417867i
$36$		0			0
$37$	−10.4721			−1.72161			−0.860804	−	0.508936i	$-0.830039\pi$
$37$	−10.4721			−1.72161			−0.860804	+	0.508936i	$0.830039\pi$
$38$		0			0
$39$	1.52786	+	4.00000i	0.244654	+	0.640513i
$40$		0			0
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$		0			0
$43$		−	4.76393i		−	0.726493i	−0.931693	−	0.363246i	$-0.881668\pi$
$43$		−	4.76393i		−	0.726493i	0.931693	−	0.363246i	$-0.118332\pi$
$44$		0			0
$45$	−6.23607	−	2.47214i	−0.929618	−	0.368524i
$46$		0			0
$47$			4.76393i			0.694891i	0.937700	+	0.347445i	$0.112951\pi$
$47$			4.76393i			0.694891i	−0.937700	+	0.347445i	$0.887049\pi$
$48$		0			0
$49$	−5.47214			−0.781734
$50$		0			0
$51$	1.52786	+	4.00000i	0.213944	+	0.560112i
$52$		0			0
$53$		−	8.94427i		−	1.22859i	−0.789076	−	0.614295i	$-0.789440\pi$
$53$		−	8.94427i		−	1.22859i	0.789076	−	0.614295i	$-0.210560\pi$
$54$		0			0
$55$	8.00000	−	4.00000i	1.07872	−	0.539360i
$56$		0			0
$57$	4.00000	+	10.4721i	0.529813	+	1.38707i
$58$		0			0
$59$		−	8.94427i		−	1.16445i	−0.813029	−	0.582223i	$-0.802183\pi$
$59$		−	8.94427i		−	1.16445i	0.813029	−	0.582223i	$-0.197817\pi$
$60$		0			0
$61$		−	12.9443i		−	1.65734i	−0.559734	−	0.828672i	$-0.689097\pi$
$61$		−	12.9443i		−	1.65734i	0.559734	−	0.828672i	$-0.310903\pi$
$62$		0			0
$63$	−2.76393	+	2.47214i	−0.348223	+	0.311460i
$64$		0			0
$65$	−2.47214	−	4.94427i	−0.306631	−	0.613261i
$66$		0			0
$67$		−	1.70820i		−	0.208690i	−0.994541	−	0.104345i	$-0.966725\pi$
$67$		−	1.70820i		−	0.208690i	0.994541	−	0.104345i	$-0.0332747\pi$
$68$		0			0
$69$	5.23607	−	2.00000i	0.630349	−	0.240772i
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$			12.9443i			1.51501i	0.652828	+	0.757506i	$0.273582\pi$
$73$			12.9443i			1.51501i	−0.652828	+	0.757506i	$0.726418\pi$
$74$		0			0
$75$	8.32624	+	2.38197i	0.961431	+	0.275046i
$76$		0			0
$77$		−	4.94427i		−	0.563452i
$78$		0			0
$79$		−	1.52786i		−	0.171898i	−0.996300	−	0.0859491i	$-0.972608\pi$
$79$		−	1.52786i		−	0.171898i	0.996300	−	0.0859491i	$-0.0273922\pi$
$80$		0			0
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$		0			0
$83$	−14.1803			−1.55649			−0.778247	−	0.627958i	$-0.783891\pi$
$83$	−14.1803			−1.55649			−0.778247	+	0.627958i	$0.783891\pi$
$84$		0			0
$85$	−2.47214	−	4.94427i	−0.268141	−	0.536282i
$86$		0			0
$87$	−2.76393	−	7.23607i	−0.296325	−	0.775788i
$88$		0			0
$89$			8.00000i			0.847998i	0.905663	+	0.423999i	$0.139374\pi$
$89$			8.00000i			0.847998i	−0.905663	+	0.423999i	$0.860626\pi$
$90$		0			0
$91$	−3.05573			−0.320327
$92$		0			0
$93$	−10.4721	+	4.00000i	−1.08591	+	0.414781i
$94$		0			0
$95$	−6.47214	−	12.9443i	−0.664027	−	1.32805i
$96$		0			0
$97$			4.94427i			0.502015i	0.967985	+	0.251007i	$0.0807618\pi$
$97$			4.94427i			0.502015i	−0.967985	+	0.251007i	$0.919238\pi$
$98$		0			0
$99$	8.00000	+	8.94427i	0.804030	+	0.898933i
$100$		0			0
$101$	−12.4721			−1.24102			−0.620512	−	0.784197i	$-0.713075\pi$
$101$	−12.4721			−1.24102			−0.620512	+	0.784197i	$0.713075\pi$
$102$		0			0
$103$	−11.7082			−1.15364			−0.576822	−	0.816870i	$-0.695707\pi$
$103$	−11.7082			−1.15364			−0.576822	+	0.816870i	$0.695707\pi$
$104$		0			0
$105$	3.23607	−	3.52786i	0.315808	−	0.344284i
$106$		0			0
$107$	3.70820			0.358486			0.179243	−	0.983805i	$-0.442635\pi$
$107$	3.70820			0.358486			0.179243	+	0.983805i	$0.442635\pi$
$108$		0			0
$109$			4.94427i			0.473575i	0.971561	+	0.236788i	$0.0760946\pi$
$109$			4.94427i			0.473575i	−0.971561	+	0.236788i	$0.923905\pi$
$110$		0			0
$111$	6.47214	+	16.9443i	0.614308	+	1.60828i
$112$		0			0
$113$	5.52786			0.520018			0.260009	−	0.965606i	$-0.416275\pi$
$113$	5.52786			0.520018			0.260009	+	0.965606i	$0.416275\pi$
$114$		0			0
$115$	−6.47214	+	3.23607i	−0.603530	+	0.301765i
$116$		0			0
$117$	5.52786	−	4.94427i	0.511051	−	0.457098i
$118$		0			0
$119$	−3.05573			−0.280118
$120$		0			0
$121$	−5.00000			−0.454545
$122$		0			0
$123$	−6.47214	+	2.47214i	−0.583573	+	0.222905i
$124$		0			0
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	6.76393			0.600202			0.300101	−	0.953907i	$-0.402980\pi$
$127$	6.76393			0.600202			0.300101	+	0.953907i	$0.402980\pi$
$128$		0			0
$129$	−7.70820	+	2.94427i	−0.678670	+	0.259229i
$130$		0			0
$131$			16.9443i			1.48043i	0.672371	+	0.740214i	$0.265276\pi$
$131$			16.9443i			1.48043i	−0.672371	+	0.740214i	$0.734724\pi$
$132$		0			0
$133$	−8.00000			−0.693688
$134$		0			0
$135$	−0.145898	+	11.6180i	−0.0125569	+	0.999921i
$136$		0			0
$137$	−10.4721			−0.894695			−0.447347	−	0.894360i	$-0.647631\pi$
$137$	−10.4721			−0.894695			−0.447347	+	0.894360i	$0.647631\pi$
$138$		0			0
$139$	3.41641			0.289776			0.144888	−	0.989448i	$-0.453718\pi$
$139$	3.41641			0.289776			0.144888	+	0.989448i	$0.453718\pi$
$140$		0			0
$141$	7.70820	−	2.94427i	0.649148	−	0.247952i
$142$		0			0
$143$			9.88854i			0.826922i
$144$		0			0
$145$	4.47214	+	8.94427i	0.371391	+	0.742781i
$146$		0			0
$147$	3.38197	+	8.85410i	0.278940	+	0.730274i
$148$		0			0
$149$	23.8885			1.95703			0.978513	−	0.206186i	$-0.0661051\pi$
$149$	23.8885			1.95703			0.978513	+	0.206186i	$0.0661051\pi$
$150$		0			0
$151$		−	1.52786i		−	0.124336i	−0.998066	−	0.0621679i	$-0.980199\pi$
$151$		−	1.52786i		−	0.124336i	0.998066	−	0.0621679i	$-0.0198014\pi$
$152$		0			0
$153$	5.52786	−	4.94427i	0.446901	−	0.399721i
$154$		0			0
$155$	12.9443	−	6.47214i	1.03971	−	0.519854i
$156$		0			0
$157$	−10.4721			−0.835767			−0.417884	−	0.908501i	$-0.637228\pi$
$157$	−10.4721			−0.835767			−0.417884	+	0.908501i	$0.637228\pi$
$158$		0			0
$159$	−14.4721	+	5.52786i	−1.14772	+	0.438388i
$160$		0			0
$161$			4.00000i			0.315244i
$162$		0			0
$163$		−	19.2361i		−	1.50669i	−0.657628	−	0.753343i	$-0.728440\pi$
$163$		−	19.2361i		−	1.50669i	0.657628	−	0.753343i	$-0.271560\pi$
$164$		0			0
$165$	−11.4164	−	10.4721i	−0.888766	−	0.815255i
$166$		0			0
$167$		−	3.23607i		−	0.250414i	−0.992131	−	0.125207i	$-0.960040\pi$
$167$		−	3.23607i		−	0.250414i	0.992131	−	0.125207i	$-0.0399596\pi$
$168$		0			0
$169$	−6.88854			−0.529888
$170$		0			0
$171$	14.4721	−	12.9443i	1.10671	−	0.989873i
$172$		0			0
$173$			4.00000i			0.304114i	0.988372	+	0.152057i	$0.0485898\pi$
$173$			4.00000i			0.304114i	−0.988372	+	0.152057i	$0.951410\pi$
$174$		0			0
$175$	−3.70820	+	4.94427i	−0.280314	+	0.373752i
$176$		0			0
$177$	−14.4721	+	5.52786i	−1.08779	+	0.415500i
$178$		0			0
$179$			16.9443i			1.26647i	0.773958	+	0.633237i	$0.218274\pi$
$179$			16.9443i			1.26647i	−0.773958	+	0.633237i	$0.781726\pi$
$180$		0			0
$181$			16.9443i			1.25946i	0.776815	+	0.629729i	$0.216834\pi$
$181$			16.9443i			1.25946i	−0.776815	+	0.629729i	$0.783166\pi$
$182$		0			0
$183$	−20.9443	+	8.00000i	−1.54825	+	0.591377i
$184$		0			0
$185$	−10.4721	−	20.9443i	−0.769927	−	1.53985i
$186$		0			0
$187$			9.88854i			0.723122i
$188$		0			0
$189$	5.70820	+	2.94427i	0.415211	+	0.214164i
$190$		0			0
$191$	−12.9443			−0.936615			−0.468307	−	0.883566i	$-0.655136\pi$
$191$	−12.9443			−0.936615			−0.468307	+	0.883566i	$0.655136\pi$
$192$		0			0
$193$			3.05573i			0.219956i	0.993934	+	0.109978i	$0.0350781\pi$
$193$			3.05573i			0.219956i	−0.993934	+	0.109978i	$0.964922\pi$
$194$		0			0
$195$	−6.47214	+	7.05573i	−0.463479	+	0.505271i
$196$		0			0
$197$			8.94427i			0.637253i	0.947880	+	0.318626i	$0.103222\pi$
$197$			8.94427i			0.637253i	−0.947880	+	0.318626i	$0.896778\pi$
$198$		0			0
$199$		−	22.4721i		−	1.59301i	−0.604634	−	0.796504i	$-0.706680\pi$
$199$		−	22.4721i		−	1.59301i	0.604634	−	0.796504i	$-0.293320\pi$
$200$		0			0
$201$	−2.76393	+	1.05573i	−0.194953	+	0.0744653i
$202$		0			0
$203$	5.52786			0.387980
$204$		0			0
$205$	8.00000	−	4.00000i	0.558744	−	0.279372i
$206$		0			0
$207$	−6.47214	−	7.23607i	−0.449845	−	0.502941i
$208$		0			0
$209$			25.8885i			1.79075i
$210$		0			0
$211$	−19.4164			−1.33668			−0.668340	−	0.743856i	$-0.732995\pi$
$211$	−19.4164			−1.33668			−0.668340	+	0.743856i	$0.732995\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.52786	−	4.76393i	0.649795	−	0.324897i
$216$		0			0
$217$		−	8.00000i		−	0.543075i
$218$		0			0
$219$	20.9443	−	8.00000i	1.41528	−	0.540590i
$220$		0			0
$221$	6.11146			0.411101
$222$		0			0
$223$	19.1246			1.28068			0.640339	−	0.768092i	$-0.278794\pi$
$223$	19.1246			1.28068			0.640339	+	0.768092i	$0.278794\pi$
$224$		0			0
$225$	−1.29180	−	14.9443i	−0.0861197	−	0.996285i
$226$		0			0
$227$	−17.2361			−1.14400			−0.571999	−	0.820254i	$-0.693832\pi$
$227$	−17.2361			−1.14400			−0.571999	+	0.820254i	$0.693832\pi$
$228$		0			0
$229$		−	7.05573i		−	0.466256i	−0.972446	−	0.233128i	$-0.925104\pi$
$229$		−	7.05573i		−	0.466256i	0.972446	−	0.233128i	$-0.0748961\pi$
$230$		0			0
$231$	−8.00000	+	3.05573i	−0.526361	+	0.201052i
$232$		0			0
$233$	−18.4721			−1.21015			−0.605075	−	0.796169i	$-0.706857\pi$
$233$	−18.4721			−1.21015			−0.605075	+	0.796169i	$0.706857\pi$
$234$		0			0
$235$	−9.52786	+	4.76393i	−0.621529	+	0.310765i
$236$		0			0
$237$	−2.47214	+	0.944272i	−0.160582	+	0.0613371i
$238$		0			0
$239$	28.9443			1.87225			0.936125	−	0.351668i	$-0.114386\pi$
$239$	28.9443			1.87225			0.936125	+	0.351668i	$0.114386\pi$
$240$		0			0
$241$	−3.52786			−0.227250			−0.113625	−	0.993524i	$-0.536246\pi$
$241$	−3.52786			−0.227250			−0.113625	+	0.993524i	$0.536246\pi$
$242$		0			0
$243$	−15.0902	+	3.90983i	−0.968035	+	0.250816i
$244$		0			0
$245$	−5.47214	−	10.9443i	−0.349602	−	0.699204i
$246$		0			0
$247$	16.0000			1.01806
$248$		0			0
$249$	8.76393	+	22.9443i	0.555392	+	1.45403i
$250$		0			0
$251$		−	13.8885i		−	0.876637i	−0.898820	−	0.438319i	$-0.855574\pi$
$251$		−	13.8885i		−	0.876637i	0.898820	−	0.438319i	$-0.144426\pi$
$252$		0			0
$253$	12.9443			0.813799
$254$		0			0
$255$	−6.47214	+	7.05573i	−0.405301	+	0.441847i
$256$		0			0
$257$	31.4164			1.95970			0.979851	−	0.199731i	$-0.0640067\pi$
$257$	31.4164			1.95970			0.979851	+	0.199731i	$0.0640067\pi$
$258$		0			0
$259$	−12.9443			−0.804318
$260$		0			0
$261$	−10.0000	+	8.94427i	−0.618984	+	0.553637i
$262$		0			0
$263$		−	8.18034i		−	0.504421i	−0.967672	−	0.252211i	$-0.918842\pi$
$263$		−	8.18034i		−	0.504421i	0.967672	−	0.252211i	$-0.0811576\pi$
$264$		0			0
$265$	17.8885	−	8.94427i	1.09888	−	0.549442i
$266$		0			0
$267$	12.9443	−	4.94427i	0.792177	−	0.302585i
$268$		0			0
$269$	15.8885			0.968742			0.484371	−	0.874863i	$-0.339049\pi$
$269$	15.8885			0.968742			0.484371	+	0.874863i	$0.339049\pi$
$270$		0			0
$271$		−	17.5279i		−	1.06474i	−0.846511	−	0.532371i	$-0.821301\pi$
$271$		−	17.5279i		−	1.06474i	0.846511	−	0.532371i	$-0.178699\pi$
$272$		0			0
$273$	1.88854	+	4.94427i	0.114300	+	0.299241i
$274$		0			0
$275$	16.0000	+	12.0000i	0.964836	+	0.723627i
$276$		0			0
$277$	15.4164			0.926282			0.463141	−	0.886285i	$-0.346722\pi$
$277$	15.4164			0.926282			0.463141	+	0.886285i	$0.346722\pi$
$278$		0			0
$279$	12.9443	+	14.4721i	0.774953	+	0.866424i
$280$		0			0
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$		0			0
$283$		−	9.70820i		−	0.577093i	−0.957466	−	0.288546i	$-0.906828\pi$
$283$		−	9.70820i		−	0.577093i	0.957466	−	0.288546i	$-0.0931720\pi$
$284$		0			0
$285$	−16.9443	+	18.4721i	−1.00369	+	1.09419i
$286$		0			0
$287$		−	4.94427i		−	0.291851i
$288$		0			0
$289$	−10.8885			−0.640503
$290$		0			0
$291$	8.00000	−	3.05573i	0.468968	−	0.179130i
$292$		0			0
$293$			21.8885i			1.27874i	0.768898	+	0.639371i	$0.220805\pi$
$293$			21.8885i			1.27874i	−0.768898	+	0.639371i	$0.779195\pi$
$294$		0			0
$295$	17.8885	−	8.94427i	1.04151	−	0.520756i
$296$		0			0
$297$	9.52786	−	18.4721i	0.552863	−	1.07186i
$298$		0			0
$299$		−	8.00000i		−	0.462652i
$300$		0			0
$301$		−	5.88854i		−	0.339410i
$302$		0			0
$303$	7.70820	+	20.1803i	0.442825	+	1.15933i
$304$		0			0
$305$	25.8885	−	12.9443i	1.48237	−	0.741187i
$306$		0			0
$307$		−	24.1803i		−	1.38004i	−0.723788	−	0.690022i	$-0.757601\pi$
$307$		−	24.1803i		−	1.38004i	0.723788	−	0.690022i	$-0.242399\pi$
$308$		0			0
$309$	7.23607	+	18.9443i	0.411646	+	1.07770i
$310$		0			0
$311$	16.0000			0.907277			0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000			0.907277			0.453638	+	0.891186i	$0.350126\pi$
$312$		0			0
$313$		−	24.0000i		−	1.35656i	−0.734803	−	0.678280i	$-0.762726\pi$
$313$		−	24.0000i		−	1.35656i	0.734803	−	0.678280i	$-0.237274\pi$
$314$		0			0
$315$	−7.70820	−	3.05573i	−0.434308	−	0.172171i
$316$		0			0
$317$			0.944272i			0.0530356i	0.999648	+	0.0265178i	$0.00844187\pi$
$317$			0.944272i			0.0530356i	−0.999648	+	0.0265178i	$0.991558\pi$
$318$		0			0
$319$		−	17.8885i		−	1.00157i
$320$		0			0
$321$	−2.29180	−	6.00000i	−0.127916	−	0.334887i
$322$		0			0
$323$	16.0000			0.890264
$324$		0			0
$325$	7.41641	−	9.88854i	0.411388	−	0.548518i
$326$		0			0
$327$	8.00000	−	3.05573i	0.442401	−	0.168982i
$328$		0			0
$329$			5.88854i			0.324646i
$330$		0			0
$331$	−6.47214			−0.355741			−0.177870	−	0.984054i	$-0.556921\pi$
$331$	−6.47214			−0.355741			−0.177870	+	0.984054i	$0.556921\pi$
$332$		0			0
$333$	23.4164	−	20.9443i	1.28321	−	1.14774i
$334$		0			0
$335$	3.41641	−	1.70820i	0.186658	−	0.0933292i
$336$		0			0
$337$		−	17.8885i		−	0.974451i	−0.873276	−	0.487226i	$-0.838009\pi$
$337$		−	17.8885i		−	0.974451i	0.873276	−	0.487226i	$-0.161991\pi$
$338$		0			0
$339$	−3.41641	−	8.94427i	−0.185554	−	0.485786i
$340$		0			0
$341$	−25.8885			−1.40194
$342$		0			0
$343$	−15.4164			−0.832408
$344$		0			0
$345$	9.23607	+	8.47214i	0.497253	+	0.456124i
$346$		0			0
$347$	−9.23607			−0.495818			−0.247909	−	0.968783i	$-0.579743\pi$
$347$	−9.23607			−0.495818			−0.247909	+	0.968783i	$0.579743\pi$
$348$		0			0
$349$			34.8328i			1.86456i	0.361740	+	0.932279i	$0.382183\pi$
$349$			34.8328i			1.86456i	−0.361740	+	0.932279i	$0.617817\pi$
$350$		0			0
$351$	−11.4164	−	5.88854i	−0.609363	−	0.314307i
$352$		0			0
$353$	15.4164			0.820533			0.410266	−	0.911966i	$-0.365436\pi$
$353$	15.4164			0.820533			0.410266	+	0.911966i	$0.365436\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.88854	+	4.94427i	0.0999523	+	0.261679i
$358$		0			0
$359$	−22.8328			−1.20507			−0.602535	−	0.798092i	$-0.705843\pi$
$359$	−22.8328			−1.20507			−0.602535	+	0.798092i	$0.705843\pi$
$360$		0			0
$361$	22.8885			1.20466
$362$		0			0
$363$	3.09017	+	8.09017i	0.162192	+	0.424624i
$364$		0			0
$365$	−25.8885	+	12.9443i	−1.35507	+	0.677534i
$366$		0			0
$367$	−16.6525			−0.869252			−0.434626	−	0.900611i	$-0.643119\pi$
$367$	−16.6525			−0.869252			−0.434626	+	0.900611i	$0.643119\pi$
$368$		0			0
$369$	8.00000	+	8.94427i	0.416463	+	0.465620i
$370$		0			0
$371$		−	11.0557i		−	0.573985i
$372$		0			0
$373$	21.5279			1.11467			0.557335	−	0.830288i	$-0.311824\pi$
$373$	21.5279			1.11467			0.557335	+	0.830288i	$0.311824\pi$
$374$		0			0
$375$	3.56231	+	19.0344i	0.183957	+	0.982934i
$376$		0			0
$377$	−11.0557			−0.569399
$378$		0			0
$379$	−35.4164			−1.81922			−0.909609	−	0.415465i	$-0.863619\pi$
$379$	−35.4164			−1.81922			−0.909609	+	0.415465i	$0.863619\pi$
$380$		0			0
$381$	−4.18034	−	10.9443i	−0.214165	−	0.560692i
$382$		0			0
$383$			0.180340i			0.00921494i	0.999989	+	0.00460747i	$0.00146661\pi$
$383$			0.180340i			0.00921494i	−0.999989	+	0.00460747i	$0.998533\pi$
$384$		0			0
$385$	9.88854	−	4.94427i	0.503967	−	0.251983i
$386$		0			0
$387$	9.52786	+	10.6525i	0.484329	+	0.541496i
$388$		0			0
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$		−	8.00000i		−	0.404577i
$392$		0			0
$393$	27.4164	−	10.4721i	1.38297	−	0.528249i
$394$		0			0
$395$	3.05573	−	1.52786i	0.153750	−	0.0768752i
$396$		0			0
$397$	23.4164			1.17524			0.587618	−	0.809139i	$-0.300066\pi$
$397$	23.4164			1.17524			0.587618	+	0.809139i	$0.300066\pi$
$398$		0			0
$399$	4.94427	+	12.9443i	0.247523	+	0.648024i
$400$		0			0
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$			16.0000i			0.797017i
$404$		0			0
$405$	18.8885	−	6.94427i	0.938579	−	0.345064i
$406$		0			0
$407$			41.8885i			2.07634i
$408$		0			0
$409$	4.47214			0.221133			0.110566	−	0.993869i	$-0.464734\pi$
$409$	4.47214			0.221133			0.110566	+	0.993869i	$0.464734\pi$
$410$		0			0
$411$	6.47214	+	16.9443i	0.319247	+	0.835799i
$412$		0			0
$413$		−	11.0557i		−	0.544017i
$414$		0			0
$415$	−14.1803	−	28.3607i	−0.696086	−	1.39217i
$416$		0			0
$417$	−2.11146	−	5.52786i	−0.103398	−	0.270701i
$418$		0			0
$419$		−	4.00000i		−	0.195413i	−0.995215	−	0.0977064i	$-0.968849\pi$
$419$		−	4.00000i		−	0.195413i	0.995215	−	0.0977064i	$-0.0311506\pi$
$420$		0			0
$421$			12.9443i			0.630865i	0.948948	+	0.315433i	$0.102150\pi$
$421$			12.9443i			0.630865i	−0.948948	+	0.315433i	$0.897850\pi$
$422$		0			0
$423$	−9.52786	−	10.6525i	−0.463261	−	0.517941i
$424$		0			0
$425$	7.41641	−	9.88854i	0.359749	−	0.479665i
$426$		0			0
$427$		−	16.0000i		−	0.774294i
$428$		0			0
$429$	16.0000	−	6.11146i	0.772487	−	0.295064i
$430$		0			0
$431$	35.7771			1.72332			0.861661	−	0.507485i	$-0.169425\pi$
$431$	35.7771			1.72332			0.861661	+	0.507485i	$0.169425\pi$
$432$		0			0
$433$		−	20.9443i		−	1.00652i	−0.864136	−	0.503259i	$-0.832134\pi$
$433$		−	20.9443i		−	1.00652i	0.864136	−	0.503259i	$-0.167866\pi$
$434$		0			0
$435$	11.7082	−	12.7639i	0.561365	−	0.611984i
$436$		0			0
$437$		−	20.9443i		−	1.00190i
$438$		0			0
$439$			19.4164i			0.926695i	0.886177	+	0.463347i	$0.153352\pi$
$439$			19.4164i			0.926695i	−0.886177	+	0.463347i	$0.846648\pi$
$440$		0			0
$441$	12.2361	−	10.9443i	0.582670	−	0.521156i
$442$		0			0
$443$	6.18034			0.293637			0.146818	−	0.989163i	$-0.453097\pi$
$443$	6.18034			0.293637			0.146818	+	0.989163i	$0.453097\pi$
$444$		0			0
$445$	−16.0000	+	8.00000i	−0.758473	+	0.379236i
$446$		0			0
$447$	−14.7639	−	38.6525i	−0.698310	−	1.82820i
$448$		0			0
$449$			37.8885i			1.78807i	0.447996	+	0.894035i	$0.352138\pi$
$449$			37.8885i			1.78807i	−0.447996	+	0.894035i	$0.647862\pi$
$450$		0			0
$451$	−16.0000			−0.753411
$452$		0			0
$453$	−2.47214	+	0.944272i	−0.116151	+	0.0443658i
$454$		0			0
$455$	−3.05573	−	6.11146i	−0.143255	−	0.286509i
$456$		0			0
$457$			6.11146i			0.285882i	0.989731	+	0.142941i	$0.0456559\pi$
$457$			6.11146i			0.285882i	−0.989731	+	0.142941i	$0.954344\pi$
$458$		0			0
$459$	−11.4164	−	5.88854i	−0.532872	−	0.274854i
$460$		0			0
$461$	−11.5279			−0.536906			−0.268453	−	0.963293i	$-0.586512\pi$
$461$	−11.5279			−0.536906			−0.268453	+	0.963293i	$0.586512\pi$
$462$		0			0
$463$	35.7082			1.65950			0.829750	−	0.558135i	$-0.188483\pi$
$463$	35.7082			1.65950			0.829750	+	0.558135i	$0.188483\pi$
$464$		0			0
$465$	−18.4721	−	16.9443i	−0.856625	−	0.785772i
$466$		0			0
$467$	−14.7639			−0.683193			−0.341597	−	0.939847i	$-0.610968\pi$
$467$	−14.7639			−0.683193			−0.341597	+	0.939847i	$0.610968\pi$
$468$		0			0
$469$		−	2.11146i		−	0.0974980i
$470$		0			0
$471$	6.47214	+	16.9443i	0.298220	+	0.780751i
$472$		0			0
$473$	−19.0557			−0.876183
$474$		0			0
$475$	19.4164	−	25.8885i	0.890886	−	1.18785i
$476$		0			0
$477$	17.8885	+	20.0000i	0.819060	+	0.915737i
$478$		0			0
$479$	−38.8328			−1.77432			−0.887158	−	0.461465i	$-0.847324\pi$
$479$	−38.8328			−1.77432			−0.887158	+	0.461465i	$0.847324\pi$
$480$		0			0
$481$	25.8885			1.18042
$482$		0			0
$483$	6.47214	−	2.47214i	0.294492	−	0.112486i
$484$		0			0
$485$	−9.88854	+	4.94427i	−0.449016	+	0.224508i
$486$		0			0
$487$	24.6525			1.11711			0.558555	−	0.829467i	$-0.311356\pi$
$487$	24.6525			1.11711			0.558555	+	0.829467i	$0.311356\pi$
$488$		0			0
$489$	−31.1246	+	11.8885i	−1.40750	+	0.537619i
$490$		0			0
$491$			16.9443i			0.764684i	0.924021	+	0.382342i	$0.124882\pi$
$491$			16.9443i			0.764684i	−0.924021	+	0.382342i	$0.875118\pi$
$492$		0			0
$493$	−11.0557			−0.497925
$494$		0			0
$495$	−9.88854	+	24.9443i	−0.444457	+	1.12116i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	16.3607			0.732405			0.366202	−	0.930535i	$-0.380658\pi$
$499$	16.3607			0.732405			0.366202	+	0.930535i	$0.380658\pi$
$500$		0			0
$501$	−5.23607	+	2.00000i	−0.233930	+	0.0893534i
$502$		0			0
$503$		−	39.0132i		−	1.73951i	−0.493483	−	0.869755i	$-0.664277\pi$
$503$		−	39.0132i		−	1.73951i	0.493483	−	0.869755i	$-0.335723\pi$
$504$		0			0
$505$	−12.4721	−	24.9443i	−0.555003	−	1.11001i
$506$		0			0
$507$	4.25735	+	11.1459i	0.189076	+	0.495007i
$508$		0			0
$509$	21.4164			0.949266			0.474633	−	0.880184i	$-0.342581\pi$
$509$	21.4164			0.949266			0.474633	+	0.880184i	$0.342581\pi$
$510$		0			0
$511$			16.0000i			0.707798i
$512$		0			0
$513$	−29.8885	−	15.4164i	−1.31961	−	0.680651i
$514$		0			0
$515$	−11.7082	−	23.4164i	−0.515925	−	1.03185i
$516$		0			0
$517$	19.0557			0.838070
$518$		0			0
$519$	6.47214	−	2.47214i	0.284095	−	0.108515i
$520$		0			0
$521$		−	8.00000i		−	0.350486i	−0.984525	−	0.175243i	$-0.943929\pi$
$521$		−	8.00000i		−	0.350486i	0.984525	−	0.175243i	$-0.0560712\pi$
$522$		0			0
$523$			9.70820i			0.424510i	0.977214	+	0.212255i	$0.0680808\pi$
$523$			9.70820i			0.424510i	−0.977214	+	0.212255i	$0.931919\pi$
$524$		0			0
$525$	10.2918	+	2.94427i	0.449171	+	0.128499i
$526$		0			0
$527$			16.0000i			0.696971i
$528$		0			0
$529$	12.5279			0.544690
$530$		0			0
$531$	17.8885	+	20.0000i	0.776297	+	0.867926i
$532$		0			0
$533$			9.88854i			0.428320i
$534$		0			0
$535$	3.70820	+	7.41641i	0.160320	+	0.320639i
$536$		0			0
$537$	27.4164	−	10.4721i	1.18311	−	0.451906i
$538$		0			0
$539$			21.8885i			0.942806i
$540$		0			0
$541$		−	24.9443i		−	1.07244i	−0.844079	−	0.536219i	$-0.819852\pi$
$541$		−	24.9443i		−	1.07244i	0.844079	−	0.536219i	$-0.180148\pi$
$542$		0			0
$543$	27.4164	−	10.4721i	1.17655	−	0.449402i
$544$		0			0
$545$	−9.88854	+	4.94427i	−0.423579	+	0.211789i
$546$		0			0
$547$			19.2361i			0.822475i	0.911528	+	0.411237i	$0.134903\pi$
$547$			19.2361i			0.822475i	−0.911528	+	0.411237i	$0.865097\pi$
$548$		0			0
$549$	25.8885	+	28.9443i	1.10490	+	1.23531i
$550$		0			0
$551$	−28.9443			−1.23307
$552$		0			0
$553$		−	1.88854i		−	0.0803091i
$554$		0			0
$555$	−27.4164	+	29.8885i	−1.16376	+	1.26870i
$556$		0			0
$557$			29.8885i			1.26642i	0.773981	+	0.633209i	$0.218263\pi$
$557$			29.8885i			1.26642i	−0.773981	+	0.633209i	$0.781737\pi$
$558$		0			0
$559$			11.7771i			0.498118i
$560$		0			0
$561$	16.0000	−	6.11146i	0.675521	−	0.258026i
$562$		0			0
$563$	11.1246			0.468846			0.234423	−	0.972135i	$-0.424680\pi$
$563$	11.1246			0.468846			0.234423	+	0.972135i	$0.424680\pi$
$564$		0			0
$565$	5.52786	+	11.0557i	0.232559	+	0.465118i
$566$		0			0
$567$	1.23607	−	11.0557i	0.0519100	−	0.464297i
$568$		0			0
$569$			39.7771i			1.66754i	0.552110	+	0.833771i	$0.313823\pi$
$569$			39.7771i			1.66754i	−0.552110	+	0.833771i	$0.686177\pi$
$570$		0			0
$571$	9.52786			0.398729			0.199364	−	0.979925i	$-0.436112\pi$
$571$	9.52786			0.398729			0.199364	+	0.979925i	$0.436112\pi$
$572$		0			0
$573$	8.00000	+	20.9443i	0.334205	+	0.874960i
$574$		0			0
$575$	−12.9443	−	9.70820i	−0.539813	−	0.404860i
$576$		0			0
$577$			8.00000i			0.333044i	0.986038	+	0.166522i	$0.0532537\pi$
$577$			8.00000i			0.333044i	−0.986038	+	0.166522i	$0.946746\pi$
$578$		0			0
$579$	4.94427	−	1.88854i	0.205477	−	0.0784852i
$580$		0			0
$581$	−17.5279			−0.727178
$582$		0			0
$583$	−35.7771			−1.48174
$584$		0			0
$585$	15.4164	+	6.11146i	0.637390	+	0.252678i
$586$		0			0
$587$	−41.2361			−1.70199			−0.850997	−	0.525170i	$-0.824002\pi$
$587$	−41.2361			−1.70199			−0.850997	+	0.525170i	$0.824002\pi$
$588$		0			0
$589$			41.8885i			1.72599i
$590$		0			0
$591$	14.4721	−	5.52786i	0.595304	−	0.227386i
$592$		0			0
$593$	21.5279			0.884043			0.442022	−	0.897004i	$-0.354261\pi$
$593$	21.5279			0.884043			0.442022	+	0.897004i	$0.354261\pi$
$594$		0			0
$595$	−3.05573	−	6.11146i	−0.125273	−	0.250545i
$596$		0			0
$597$	−36.3607	+	13.8885i	−1.48814	+	0.568420i
$598$		0			0
$599$	12.9443			0.528889			0.264444	−	0.964401i	$-0.414811\pi$
$599$	12.9443			0.528889			0.264444	+	0.964401i	$0.414811\pi$
$600$		0			0
$601$	−4.47214			−0.182422			−0.0912111	−	0.995832i	$-0.529074\pi$
$601$	−4.47214			−0.182422			−0.0912111	+	0.995832i	$0.529074\pi$
$602$		0			0
$603$	3.41641	+	3.81966i	0.139127	+	0.155549i
$604$		0			0
$605$	−5.00000	−	10.0000i	−0.203279	−	0.406558i
$606$		0			0
$607$	−25.8197			−1.04799			−0.523994	−	0.851722i	$-0.675559\pi$
$607$	−25.8197			−1.04799			−0.523994	+	0.851722i	$0.675559\pi$
$608$		0			0
$609$	−3.41641	−	8.94427i	−0.138440	−	0.362440i
$610$		0			0
$611$		−	11.7771i		−	0.476450i
$612$		0			0
$613$	7.41641			0.299546			0.149773	−	0.988720i	$-0.452146\pi$
$613$	7.41641			0.299546			0.149773	+	0.988720i	$0.452146\pi$
$614$		0			0
$615$	−11.4164	−	10.4721i	−0.460354	−	0.422277i
$616$		0			0
$617$	−8.58359			−0.345562			−0.172781	−	0.984960i	$-0.555275\pi$
$617$	−8.58359			−0.345562			−0.172781	+	0.984960i	$0.555275\pi$
$618$		0			0
$619$	25.5279			1.02605			0.513026	−	0.858373i	$-0.328525\pi$
$619$	25.5279			1.02605			0.513026	+	0.858373i	$0.328525\pi$
$620$		0			0
$621$	−7.70820	+	14.9443i	−0.309320	+	0.599693i
$622$		0			0
$623$			9.88854i			0.396176i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		0			0
$627$	41.8885	−	16.0000i	1.67287	−	0.638978i
$628$		0			0
$629$	25.8885			1.03224
$630$		0			0
$631$		−	22.4721i		−	0.894602i	−0.894384	−	0.447301i	$-0.852385\pi$
$631$		−	22.4721i		−	0.894602i	0.894384	−	0.447301i	$-0.147615\pi$
$632$		0			0
$633$	12.0000	+	31.4164i	0.476957	+	1.24869i
$634$		0			0
$635$	6.76393	+	13.5279i	0.268418	+	0.536837i
$636$		0			0
$637$	13.5279			0.535993
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	21.8885i		−	0.864546i	−0.901743	−	0.432273i	$-0.857712\pi$
$641$		−	21.8885i		−	0.864546i	0.901743	−	0.432273i	$-0.142288\pi$
$642$		0			0
$643$			27.5967i			1.08831i	0.838985	+	0.544155i	$0.183150\pi$
$643$			27.5967i			1.08831i	−0.838985	+	0.544155i	$0.816850\pi$
$644$		0			0
$645$	−13.5967	−	12.4721i	−0.535371	−	0.491090i
$646$		0			0
$647$			33.7082i			1.32521i	0.748971	+	0.662603i	$0.230548\pi$
$647$			33.7082i			1.32521i	−0.748971	+	0.662603i	$0.769452\pi$
$648$		0			0
$649$	−35.7771			−1.40437
$650$		0			0
$651$	−12.9443	+	4.94427i	−0.507326	+	0.193781i
$652$		0			0
$653$			15.0557i			0.589176i	0.955624	+	0.294588i	$0.0951824\pi$
$653$			15.0557i			0.589176i	−0.955624	+	0.294588i	$0.904818\pi$
$654$		0			0
$655$	−33.8885	+	16.9443i	−1.32413	+	0.662067i
$656$		0			0
$657$	−25.8885	−	28.9443i	−1.01001	−	1.12922i
$658$		0			0
$659$		−	24.9443i		−	0.971691i	−0.874045	−	0.485845i	$-0.838512\pi$
$659$		−	24.9443i		−	0.971691i	0.874045	−	0.485845i	$-0.161488\pi$
$660$		0			0
$661$		−	20.9443i		−	0.814638i	−0.913286	−	0.407319i	$-0.866464\pi$
$661$		−	20.9443i		−	0.814638i	0.913286	−	0.407319i	$-0.133536\pi$
$662$		0			0
$663$	−3.77709	−	9.88854i	−0.146690	−	0.384039i
$664$		0			0
$665$	−8.00000	−	16.0000i	−0.310227	−	0.620453i
$666$		0			0
$667$			14.4721i			0.560363i
$668$		0			0
$669$	−11.8197	−	30.9443i	−0.456974	−	1.19637i
$670$		0			0
$671$	−51.7771			−1.99883
$672$		0			0
$673$		−	11.0557i		−	0.426167i	−0.977034	−	0.213083i	$-0.931649\pi$
$673$		−	11.0557i		−	0.426167i	0.977034	−	0.213083i	$-0.0683506\pi$
$674$		0			0
$675$	−23.3820	+	11.3262i	−0.899972	+	0.435947i
$676$		0			0
$677$			7.05573i			0.271174i	0.990765	+	0.135587i	$0.0432920\pi$
$677$			7.05573i			0.271174i	−0.990765	+	0.135587i	$0.956708\pi$
$678$		0			0
$679$			6.11146i			0.234536i
$680$		0			0
$681$	10.6525	+	27.8885i	0.408204	+	1.06869i
$682$		0			0
$683$	6.76393			0.258815			0.129407	−	0.991592i	$-0.458693\pi$
$683$	6.76393			0.258815			0.129407	+	0.991592i	$0.458693\pi$
$684$		0			0
$685$	−10.4721	−	20.9443i	−0.400120	−	0.800239i
$686$		0			0
$687$	−11.4164	+	4.36068i	−0.435563	+	0.166370i
$688$		0			0
$689$			22.1115i			0.842379i
$690$		0			0
$691$	45.3050			1.72348			0.861741	−	0.507349i	$-0.169374\pi$
$691$	45.3050			1.72348			0.861741	+	0.507349i	$0.169374\pi$
$692$		0			0
$693$	9.88854	+	11.0557i	0.375635	+	0.419972i
$694$		0			0
$695$	3.41641	+	6.83282i	0.129592	+	0.259183i
$696$		0			0
$697$			9.88854i			0.374555i
$698$		0			0
$699$	11.4164	+	29.8885i	0.431808	+	1.13049i
$700$		0			0
$701$	10.0000			0.377695			0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000			0.377695			0.188847	+	0.982006i	$0.439525\pi$
$702$		0			0
$703$	67.7771			2.55626
$704$		0			0
$705$	13.5967	+	12.4721i	0.512083	+	0.469728i
$706$		0			0
$707$	−15.4164			−0.579794
$708$		0			0
$709$		−	15.0557i		−	0.565430i	−0.959204	−	0.282715i	$-0.908765\pi$
$709$		−	15.0557i		−	0.565430i	0.959204	−	0.282715i	$-0.0912350\pi$
$710$		0			0
$711$	3.05573	+	3.41641i	0.114599	+	0.128125i
$712$		0			0
$713$	20.9443			0.784369
$714$		0			0
$715$	−19.7771	+	9.88854i	−0.739621	+	0.369811i
$716$		0			0
$717$	−17.8885	−	46.8328i	−0.668060	−	1.74900i
$718$		0			0
$719$	9.88854			0.368780			0.184390	−	0.982853i	$-0.440969\pi$
$719$	9.88854			0.368780			0.184390	+	0.982853i	$0.440969\pi$
$720$		0			0
$721$	−14.4721			−0.538971
$722$		0			0
$723$	2.18034	+	5.70820i	0.0810877	+	0.212290i
$724$		0			0
$725$	−13.4164	+	17.8885i	−0.498273	+	0.664364i
$726$		0			0
$727$	−17.2361			−0.639250			−0.319625	−	0.947544i	$-0.603557\pi$
$727$	−17.2361			−0.639250			−0.319625	+	0.947544i	$0.603557\pi$
$728$		0			0
$729$	15.6525	+	22.0000i	0.579721	+	0.814815i
$730$		0			0
$731$			11.7771i			0.435591i
$732$		0			0
$733$	−10.4721			−0.386797			−0.193399	−	0.981120i	$-0.561951\pi$
$733$	−10.4721			−0.386797			−0.193399	+	0.981120i	$0.561951\pi$
$734$		0			0
$735$	−14.3262	+	15.6180i	−0.528431	+	0.576080i
$736$		0			0
$737$	−6.83282			−0.251690
$738$		0			0
$739$	−9.52786			−0.350488			−0.175244	−	0.984525i	$-0.556071\pi$
$739$	−9.52786			−0.350488			−0.175244	+	0.984525i	$0.556071\pi$
$740$		0			0
$741$	−9.88854	−	25.8885i	−0.363265	−	0.951039i
$742$		0			0
$743$		−	37.4853i		−	1.37520i	−0.726089	−	0.687601i	$-0.758664\pi$
$743$		−	37.4853i		−	1.37520i	0.726089	−	0.687601i	$-0.241336\pi$
$744$		0			0
$745$	23.8885	+	47.7771i	0.875209	+	1.75042i
$746$		0			0
$747$	31.7082	−	28.3607i	1.16014	−	1.03766i
$748$		0			0
$749$	4.58359			0.167481
$750$		0			0
$751$			45.3050i			1.65320i	0.562789	+	0.826601i	$0.309728\pi$
$751$			45.3050i			1.65320i	−0.562789	+	0.826601i	$0.690272\pi$
$752$		0			0
$753$	−22.4721	+	8.58359i	−0.818930	+	0.312803i
$754$		0			0
$755$	3.05573	−	1.52786i	0.111209	−	0.0556047i
$756$		0			0
$757$	−0.583592			−0.0212110			−0.0106055	−	0.999944i	$-0.503376\pi$
$757$	−0.583592			−0.0212110			−0.0106055	+	0.999944i	$0.503376\pi$
$758$		0			0
$759$	−8.00000	−	20.9443i	−0.290382	−	0.760229i
$760$		0			0
$761$		−	25.8885i		−	0.938459i	−0.883076	−	0.469229i	$-0.844532\pi$
$761$		−	25.8885i		−	0.938459i	0.883076	−	0.469229i	$-0.155468\pi$
$762$		0			0
$763$			6.11146i			0.221250i
$764$		0			0
$765$	15.4164	+	6.11146i	0.557381	+	0.220960i
$766$		0			0
$767$			22.1115i			0.798398i
$768$		0			0
$769$	−7.88854			−0.284468			−0.142234	−	0.989833i	$-0.545429\pi$
$769$	−7.88854			−0.284468			−0.142234	+	0.989833i	$0.545429\pi$
$770$		0			0
$771$	−19.4164	−	50.8328i	−0.699265	−	1.83070i
$772$		0			0
$773$		−	36.7214i		−	1.32078i	−0.750925	−	0.660388i	$-0.770392\pi$
$773$		−	36.7214i		−	1.32078i	0.750925	−	0.660388i	$-0.229608\pi$
$774$		0			0
$775$	25.8885	+	19.4164i	0.929944	+	0.697458i
$776$		0			0
$777$	8.00000	+	20.9443i	0.286998	+	0.751372i
$778$		0			0
$779$			25.8885i			0.927553i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	20.6525	+	10.6525i	0.738059	+	0.380688i
$784$		0			0
$785$	−10.4721	−	20.9443i	−0.373767	−	0.747533i
$786$		0			0
$787$		−	8.18034i		−	0.291598i	−0.989314	−	0.145799i	$-0.953425\pi$
$787$		−	8.18034i		−	0.291598i	0.989314	−	0.145799i	$-0.0465752\pi$
$788$		0			0
$789$	−13.2361	+	5.05573i	−0.471216	+	0.179989i
$790$		0			0
$791$	6.83282			0.242947
$792$		0			0
$793$			32.0000i			1.13635i
$794$		0			0
$795$	−25.5279	−	23.4164i	−0.905380	−	0.830494i
$796$		0			0
$797$		−	40.9443i		−	1.45032i	−0.688580	−	0.725160i	$-0.741766\pi$
$797$		−	40.9443i		−	1.45032i	0.688580	−	0.725160i	$-0.258234\pi$
$798$		0			0
$799$		−	11.7771i		−	0.416643i
$800$		0			0
$801$	−16.0000	−	17.8885i	−0.565332	−	0.632061i
$802$		0			0
$803$	51.7771			1.82717
$804$		0			0
$805$	−8.00000	+	4.00000i	−0.281963	+	0.140981i
$806$		0			0
$807$	−9.81966	−	25.7082i	−0.345668	−	0.904972i
$808$		0			0
$809$		−	40.0000i		−	1.40633i	−0.711029	−	0.703163i	$-0.751771\pi$
$809$		−	40.0000i		−	1.40633i	0.711029	−	0.703163i	$-0.248229\pi$
$810$		0			0
$811$	−35.4164			−1.24364			−0.621819	−	0.783161i	$-0.713606\pi$
$811$	−35.4164			−1.24364			−0.621819	+	0.783161i	$0.713606\pi$
$812$		0			0
$813$	−28.3607	+	10.8328i	−0.994652	+	0.379923i
$814$		0			0
$815$	38.4721	−	19.2361i	1.34762	−	0.673810i
$816$		0			0
$817$			30.8328i			1.07870i
$818$		0			0
$819$	6.83282	−	6.11146i	0.238758	−	0.213552i
$820$		0			0
$821$	39.8885			1.39212			0.696060	−	0.717984i	$-0.254935\pi$
$821$	39.8885			1.39212			0.696060	+	0.717984i	$0.254935\pi$
$822$		0			0
$823$	−27.7082			−0.965847			−0.482924	−	0.875662i	$-0.660425\pi$
$823$	−27.7082			−0.965847			−0.482924	+	0.875662i	$0.660425\pi$
$824$		0			0
$825$	9.52786	−	33.3050i	0.331718	−	1.15953i
$826$		0			0
$827$	−42.5410			−1.47930			−0.739648	−	0.672994i	$-0.765008\pi$
$827$	−42.5410			−1.47930			−0.739648	+	0.672994i	$0.765008\pi$
$828$		0			0
$829$			3.05573i			0.106130i	0.998591	+	0.0530649i	$0.0168990\pi$
$829$			3.05573i			0.106130i	−0.998591	+	0.0530649i	$0.983101\pi$
$830$		0			0
$831$	−9.52786	−	24.9443i	−0.330518	−	0.865307i
$832$		0			0
$833$	13.5279			0.468713
$834$		0			0
$835$	6.47214	−	3.23607i	0.223978	−	0.111989i
$836$		0			0
$837$	15.4164	−	29.8885i	0.532869	−	1.03310i
$838$		0			0
$839$	22.8328			0.788276			0.394138	−	0.919051i	$-0.371043\pi$
$839$	22.8328			0.788276			0.394138	+	0.919051i	$0.371043\pi$
$840$		0			0
$841$	−9.00000			−0.310345
$842$		0			0
$843$	−19.4164	+	7.41641i	−0.668737	+	0.255435i
$844$		0			0
$845$	−6.88854	−	13.7771i	−0.236973	−	0.473946i
$846$		0			0
$847$	−6.18034			−0.212359
$848$		0			0
$849$	−15.7082	+	6.00000i	−0.539104	+	0.205919i
$850$		0			0
$851$		−	33.8885i		−	1.16168i
$852$		0			0
$853$	−50.4721			−1.72813			−0.864067	−	0.503378i	$-0.832090\pi$
$853$	−50.4721			−1.72813			−0.864067	+	0.503378i	$0.832090\pi$
$854$		0			0
$855$	40.3607	+	16.0000i	1.38031	+	0.547188i
$856$		0			0
$857$	−4.36068			−0.148958			−0.0744790	−	0.997223i	$-0.523729\pi$
$857$	−4.36068			−0.148958			−0.0744790	+	0.997223i	$0.523729\pi$
$858$		0			0
$859$	12.5836			0.429347			0.214673	−	0.976686i	$-0.431131\pi$
$859$	12.5836			0.429347			0.214673	+	0.976686i	$0.431131\pi$
$860$		0			0
$861$	−8.00000	+	3.05573i	−0.272639	+	0.104139i
$862$		0			0
$863$		−	43.2361i		−	1.47177i	−0.677105	−	0.735886i	$-0.736766\pi$
$863$		−	43.2361i		−	1.47177i	0.677105	−	0.735886i	$-0.263234\pi$
$864$		0			0
$865$	−8.00000	+	4.00000i	−0.272008	+	0.136004i
$866$		0			0
$867$	6.72949	+	17.6180i	0.228545	+	0.598340i
$868$		0			0
$869$	−6.11146			−0.207317
$870$		0			0
$871$			4.22291i			0.143088i
$872$		0			0
$873$	−9.88854	−	11.0557i	−0.334677	−	0.374180i
$874$		0			0
$875$	−13.5967	−	2.47214i	−0.459654	−	0.0835734i
$876$		0			0
$877$	−42.4721			−1.43418			−0.717091	−	0.696979i	$-0.754527\pi$
$877$	−42.4721			−1.43418			−0.717091	+	0.696979i	$0.754527\pi$
$878$		0			0
$879$	35.4164	−	13.5279i	1.19457	−	0.456284i
$880$		0			0
$881$		−	5.88854i		−	0.198390i	−0.995068	−	0.0991950i	$-0.968373\pi$
$881$		−	5.88854i		−	0.198390i	0.995068	−	0.0991950i	$-0.0316268\pi$
$882$		0			0
$883$		−	3.23607i		−	0.108902i	−0.998516	−	0.0544512i	$-0.982659\pi$
$883$		−	3.23607i		−	0.108902i	0.998516	−	0.0544512i	$-0.0173409\pi$
$884$		0			0
$885$	−25.5279	−	23.4164i	−0.858110	−	0.787134i
$886$		0			0
$887$			27.5967i			0.926608i	0.886199	+	0.463304i	$0.153336\pi$
$887$			27.5967i			0.926608i	−0.886199	+	0.463304i	$0.846664\pi$
$888$		0			0
$889$	8.36068			0.280408
$890$		0			0
$891$	−35.7771	−	4.00000i	−1.19858	−	0.134005i
$892$		0			0
$893$		−	30.8328i		−	1.03178i
$894$		0			0
$895$	−33.8885	+	16.9443i	−1.13277	+	0.566385i
$896$		0			0
$897$	−12.9443	+	4.94427i	−0.432197	+	0.165084i
$898$		0			0
$899$		−	28.9443i		−	0.965346i
$900$		0			0
$901$			22.1115i			0.736639i
$902$		0			0
$903$	−9.52786	+	3.63932i	−0.317067	+	0.121109i
$904$		0			0
$905$	−33.8885	+	16.9443i	−1.12649	+	0.563247i
$906$		0			0
$907$		−	29.4853i		−	0.979043i	−0.871991	−	0.489522i	$-0.837171\pi$
$907$		−	29.4853i		−	0.979043i	0.871991	−	0.489522i	$-0.162829\pi$
$908$		0			0
$909$	27.8885	−	24.9443i	0.925005	−	0.827349i
$910$		0			0
$911$	22.1115			0.732585			0.366293	−	0.930500i	$-0.380627\pi$
$911$	22.1115			0.732585			0.366293	+	0.930500i	$0.380627\pi$
$912$		0			0
$913$			56.7214i			1.87720i
$914$		0			0
$915$	−36.9443	−	33.8885i	−1.22134	−	1.12032i
$916$		0			0
$917$			20.9443i			0.691641i
$918$		0			0
$919$		−	33.5279i		−	1.10598i	−0.833187	−	0.552991i	$-0.813486\pi$
$919$		−	33.5279i		−	1.10598i	0.833187	−	0.552991i	$-0.186514\pi$
$920$		0			0
$921$	−39.1246	+	14.9443i	−1.28920	+	0.492431i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	31.4164	−	41.8885i	1.03297	−	1.37729i
$926$		0			0
$927$	26.1803	−	23.4164i	0.859875	−	0.769096i
$928$		0			0
$929$		−	18.1115i		−	0.594218i	−0.954844	−	0.297109i	$-0.903978\pi$
$929$		−	18.1115i		−	0.594218i	0.954844	−	0.297109i	$-0.0960224\pi$
$930$		0			0
$931$	35.4164			1.16073
$932$		0			0
$933$	−9.88854	−	25.8885i	−0.323736	−	0.847553i
$934$		0			0
$935$	−19.7771	+	9.88854i	−0.646780	+	0.323390i
$936$		0			0
$937$			14.8328i			0.484567i	0.970206	+	0.242283i	$0.0778964\pi$
$937$			14.8328i			0.484567i	−0.970206	+	0.242283i	$0.922104\pi$
$938$		0			0
$939$	−38.8328	+	14.8328i	−1.26726	+	0.484051i
$940$		0			0
$941$	−26.5836			−0.866600			−0.433300	−	0.901250i	$-0.642651\pi$
$941$	−26.5836			−0.866600			−0.433300	+	0.901250i	$0.642651\pi$
$942$		0			0
$943$	12.9443			0.421523
$944$		0			0
$945$	−0.180340	+	14.3607i	−0.00586646	+	0.467153i
$946$		0			0
$947$	8.06888			0.262203			0.131102	−	0.991369i	$-0.458149\pi$
$947$	8.06888			0.262203			0.131102	+	0.991369i	$0.458149\pi$
$948$		0			0
$949$		−	32.0000i		−	1.03876i
$950$		0			0
$951$	1.52786	−	0.583592i	0.0495444	−	0.0189243i
$952$		0			0
$953$	−10.4721			−0.339226			−0.169613	−	0.985511i	$-0.554252\pi$
$953$	−10.4721			−0.339226			−0.169613	+	0.985511i	$0.554252\pi$
$954$		0			0
$955$	−12.9443	−	25.8885i	−0.418867	−	0.837734i
$956$		0			0
$957$	−28.9443	+	11.0557i	−0.935635	+	0.357381i
$958$		0			0
$959$	−12.9443			−0.417992
$960$		0			0
$961$	−10.8885			−0.351243
$962$		0			0
$963$	−8.29180	+	7.41641i	−0.267199	+	0.238990i
$964$		0			0
$965$	−6.11146	+	3.05573i	−0.196735	+	0.0983674i
$966$		0			0
$967$	5.59675			0.179979			0.0899896	−	0.995943i	$-0.471317\pi$
$967$	5.59675			0.179979			0.0899896	+	0.995943i	$0.471317\pi$
$968$		0			0
$969$	−9.88854	−	25.8885i	−0.317666	−	0.831660i
$970$		0			0
$971$			28.0000i			0.898563i	0.893390	+	0.449281i	$0.148320\pi$
$971$			28.0000i			0.898563i	−0.893390	+	0.449281i	$0.851680\pi$
$972$		0			0
$973$	4.22291			0.135380
$974$		0			0
$975$	−20.5836	−	5.88854i	−0.659203	−	0.188584i
$976$		0			0
$977$	39.4164			1.26104			0.630521	−	0.776172i	$-0.282841\pi$
$977$	39.4164			1.26104			0.630521	+	0.776172i	$0.282841\pi$
$978$		0			0
$979$	32.0000			1.02272
$980$		0			0
$981$	−9.88854	−	11.0557i	−0.315717	−	0.352982i
$982$		0			0
$983$		−	1.70820i		−	0.0544832i	−0.999629	−	0.0272416i	$-0.991328\pi$
$983$		−	1.70820i		−	0.0544832i	0.999629	−	0.0272416i	$-0.00867235\pi$
$984$		0			0
$985$	−17.8885	+	8.94427i	−0.569976	+	0.284988i
$986$		0			0
$987$	9.52786	−	3.63932i	0.303275	−	0.115841i
$988$		0			0
$989$	15.4164			0.490213
$990$		0			0
$991$		−	47.1935i		−	1.49915i	−0.661919	−	0.749575i	$-0.730258\pi$
$991$		−	47.1935i		−	1.49915i	0.661919	−	0.749575i	$-0.269742\pi$
$992$		0			0
$993$	4.00000	+	10.4721i	0.126936	+	0.332323i
$994$		0			0
$995$	44.9443	−	22.4721i	1.42483	−	0.712415i
$996$		0			0
$997$	−38.2492			−1.21137			−0.605683	−	0.795706i	$-0.707100\pi$
$997$	−38.2492			−1.21137			−0.605683	+	0.795706i	$0.707100\pi$
$998$		0			0
$999$	−48.3607	−	24.9443i	−1.53006	−	0.789202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.m.t.959.1	yes	4
3.2	odd	2		1920.2.m.d.959.3	yes	4
4.3	odd	2		1920.2.m.h.959.4	yes	4
5.4	even	2		1920.2.m.g.959.4	yes	4
8.3	odd	2		1920.2.m.o.959.1	yes	4
8.5	even	2		1920.2.m.c.959.4	yes	4
12.11	even	2		1920.2.m.p.959.2	yes	4
15.14	odd	2		1920.2.m.o.959.2	yes	4
20.19	odd	2		1920.2.m.s.959.1	yes	4
24.5	odd	2		1920.2.m.s.959.2	yes	4
24.11	even	2		1920.2.m.g.959.3	yes	4
40.19	odd	2		1920.2.m.d.959.4	yes	4
40.29	even	2		1920.2.m.p.959.1	yes	4
60.59	even	2		1920.2.m.c.959.3	✓	4
120.29	odd	2		1920.2.m.h.959.3	yes	4
120.59	even	2	inner	1920.2.m.t.959.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1920.2.m.c.959.3	✓	4	60.59	even	2
1920.2.m.c.959.4	yes	4	8.5	even	2
1920.2.m.d.959.3	yes	4	3.2	odd	2
1920.2.m.d.959.4	yes	4	40.19	odd	2
1920.2.m.g.959.3	yes	4	24.11	even	2
1920.2.m.g.959.4	yes	4	5.4	even	2
1920.2.m.h.959.3	yes	4	120.29	odd	2
1920.2.m.h.959.4	yes	4	4.3	odd	2
1920.2.m.o.959.1	yes	4	8.3	odd	2
1920.2.m.o.959.2	yes	4	15.14	odd	2
1920.2.m.p.959.1	yes	4	40.29	even	2
1920.2.m.p.959.2	yes	4	12.11	even	2
1920.2.m.s.959.1	yes	4	20.19	odd	2
1920.2.m.s.959.2	yes	4	24.5	odd	2
1920.2.m.t.959.1	yes	4	1.1	even	1	trivial
1920.2.m.t.959.2	yes	4	120.59	even	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.618034 - 1.61803i) q^{3} +(1.00000 + 2.00000i) q^{5} +1.23607 q^{7} +(-2.23607 + 2.00000i) q^{9} -4.00000i q^{11} -2.47214 q^{13} +(2.61803 - 2.85410i) q^{15} -2.47214 q^{17} -6.47214 q^{19} +(-0.763932 - 2.00000i) q^{21} +3.23607i q^{23} +(-3.00000 + 4.00000i) q^{25} +(4.61803 + 2.38197i) q^{27} +4.47214 q^{29} -6.47214i q^{31} +(-6.47214 + 2.47214i) q^{33} +(1.23607 + 2.47214i) q^{35} -10.4721 q^{37} +(1.52786 + 4.00000i) q^{39} -4.00000i q^{41} -4.76393i q^{43} +(-6.23607 - 2.47214i) q^{45} +4.76393i q^{47} -5.47214 q^{49} +(1.52786 + 4.00000i) q^{51} -8.94427i q^{53} +(8.00000 - 4.00000i) q^{55} +(4.00000 + 10.4721i) q^{57} -8.94427i q^{59} -12.9443i q^{61} +(-2.76393 + 2.47214i) q^{63} +(-2.47214 - 4.94427i) q^{65} -1.70820i q^{67} +(5.23607 - 2.00000i) q^{69} +12.9443i q^{73} +(8.32624 + 2.38197i) q^{75} -4.94427i q^{77} -1.52786i q^{79} +(1.00000 - 8.94427i) q^{81} -14.1803 q^{83} +(-2.47214 - 4.94427i) q^{85} +(-2.76393 - 7.23607i) q^{87} +8.00000i q^{89} -3.05573 q^{91} +(-10.4721 + 4.00000i) q^{93} +(-6.47214 - 12.9443i) q^{95} +4.94427i q^{97} +(8.00000 + 8.94427i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 4 q^{5} - 4 q^{7} + 8 q^{13} + 6 q^{15} + 8 q^{17} - 8 q^{19} - 12 q^{21} - 12 q^{25} + 14 q^{27} - 8 q^{33} - 4 q^{35} - 24 q^{37} + 24 q^{39} - 16 q^{45} - 4 q^{49} + 24 q^{51} + 32 q^{55}+ \cdots + 32 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 4 * q^5 - 4 * q^7 + 8 * q^13 + 6 * q^15 + 8 * q^17 - 8 * q^19 - 12 * q^21 - 12 * q^25 + 14 * q^27 - 8 * q^33 - 4 * q^35 - 24 * q^37 + 24 * q^39 - 16 * q^45 - 4 * q^49 + 24 * q^51 + 32 * q^55 + 16 * q^57 - 20 * q^63 + 8 * q^65 + 12 * q^69 + 2 * q^75 + 4 * q^81 - 12 * q^83 + 8 * q^85 - 20 * q^87 - 48 * q^91 - 24 * q^93 - 8 * q^95 + 32 * q^99

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