LMFDB - Embedded newform 480.2.b.a.431.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [480,2,Mod(431,480)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(480, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("480.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 480 = 2^{5} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	480.b (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:	$3.83281929702$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1649659456.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{5} + 4x^{4} - 4x^{3} - 8x + 16 $ x^8 - x^7 - 2x^5 + 4x^4 - 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			431.3
Root			$-0.578647 + 1.29041i$ of defining polynomial
Character	$\chi$	$=$	480.431
Dual form			480.2.b.a.431.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.751690 - 1.56044i) q^{3} -1.00000 q^{5} -4.28591i q^{7} +(-1.86993 + 2.34593i) q^{9} +O(q^{10})$	\(q+(-0.751690 - 1.56044i) q^{3} -1.00000 q^{5} -4.28591i q^{7} +(-1.86993 + 2.34593i) q^{9} +2.44673i q^{11} -2.71493i q^{13} +(0.751690 + 1.56044i) q^{15} +1.16504i q^{17} -6.05444 q^{19} +(-6.68789 + 3.22167i) q^{21} -7.55782 q^{23} +1.00000 q^{25} +(5.06628 + 1.15449i) q^{27} -0.733092 q^{29} -0.469799i q^{31} +(3.81797 - 1.83918i) q^{33} +4.28591i q^{35} -1.36664i q^{37} +(-4.23647 + 2.04078i) q^{39} -4.69186i q^{41} +1.50338 q^{43} +(1.86993 - 2.34593i) q^{45} -4.07812 q^{47} -11.3690 q^{49} +(1.81797 - 0.875746i) q^{51} -1.00676 q^{53} -2.44673i q^{55} +(4.55106 + 9.44757i) q^{57} -1.63484i q^{59} -10.9336i q^{61} +(10.0544 + 8.01433i) q^{63} +2.71493i q^{65} +9.97632 q^{67} +(5.68113 + 11.7935i) q^{69} +11.6359 q^{71} -9.63593 q^{73} +(-0.751690 - 1.56044i) q^{75} +10.4865 q^{77} +3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} -5.45095i q^{83} -1.16504i q^{85} +(0.551058 + 1.14394i) q^{87} -7.75993i q^{89} -11.6359 q^{91} +(-0.733092 + 0.353143i) q^{93} +6.05444 q^{95} +17.1156 q^{97} +(-5.73985 - 4.57520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{5}+O(q^{10}) $ 8 * q - 8 * q^5	$ 8 q - 8 q^{5} + 4 q^{19} - 4 q^{21} + 4 q^{23} + 8 q^{25} + 12 q^{27} - 4 q^{33} - 16 q^{39} - 28 q^{47} - 16 q^{49} - 20 q^{51} + 16 q^{53} - 4 q^{57} + 28 q^{63} + 32 q^{67} + 20 q^{69} + 24 q^{71} - 8 q^{73} + 8 q^{81} - 36 q^{87} - 24 q^{91} - 4 q^{95} + 8 q^{97} - 16 q^{99}+O(q^{100}) $ 8 * q - 8 * q^5 + 4 * q^19 - 4 * q^21 + 4 * q^23 + 8 * q^25 + 12 * q^27 - 4 * q^33 - 16 * q^39 - 28 * q^47 - 16 * q^49 - 20 * q^51 + 16 * q^53 - 4 * q^57 + 28 * q^63 + 32 * q^67 + 20 * q^69 + 24 * q^71 - 8 * q^73 + 8 * q^81 - 36 * q^87 - 24 * q^91 - 4 * q^95 + 8 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$421$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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
$3$	−0.751690	−	1.56044i	−0.433988	−	0.900919i
$3$	−0.751690	−	1.56044i	−0.433988	−	0.900919i
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$		−	4.28591i		−	1.61992i	−0.586484	−	0.809961i	$-0.699488\pi$
$7$		−	4.28591i		−	1.61992i	0.586484	−	0.809961i	$-0.300512\pi$
$8$		0			0
$9$	−1.86993	+	2.34593i	−0.623308	+	0.781976i
$10$		0			0
$11$			2.44673i			0.737717i	0.929486	+	0.368858i	$0.120251\pi$
$11$			2.44673i			0.737717i	−0.929486	+	0.368858i	$0.879749\pi$
$12$		0			0
$13$		−	2.71493i		−	0.752985i	−0.926420	−	0.376493i	$-0.877130\pi$
$13$		−	2.71493i		−	0.752985i	0.926420	−	0.376493i	$-0.122870\pi$
$14$		0			0
$15$	0.751690	+	1.56044i	0.194085	+	0.402903i
$16$		0			0
$17$			1.16504i			0.282563i	0.989969	+	0.141281i	$0.0451222\pi$
$17$			1.16504i			0.282563i	−0.989969	+	0.141281i	$0.954878\pi$
$18$		0			0
$19$	−6.05444			−1.38898			−0.694492	−	0.719501i	$-0.744371\pi$
$19$	−6.05444			−1.38898			−0.694492	+	0.719501i	$0.744371\pi$
$20$		0			0
$21$	−6.68789	+	3.22167i	−1.45942	+	0.703027i
$22$		0			0
$23$	−7.55782			−1.57591			−0.787957	−	0.615731i	$-0.788861\pi$
$23$	−7.55782			−1.57591			−0.787957	+	0.615731i	$0.788861\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	5.06628	+	1.15449i	0.975005	+	0.222182i
$28$		0			0
$29$	−0.733092			−0.136132			−0.0680659	−	0.997681i	$-0.521683\pi$
$29$	−0.733092			−0.136132			−0.0680659	+	0.997681i	$0.521683\pi$
$30$		0			0
$31$		−	0.469799i		−	0.0843784i	−0.999110	−	0.0421892i	$-0.986567\pi$
$31$		−	0.469799i		−	0.0843784i	0.999110	−	0.0421892i	$-0.0134332\pi$
$32$		0			0
$33$	3.81797	−	1.83918i	0.664623	−	0.320160i
$34$		0			0
$35$			4.28591i			0.724451i
$36$		0			0
$37$		−	1.36664i		−	0.224674i	−0.993670	−	0.112337i	$-0.964166\pi$
$37$		−	1.36664i		−	0.224674i	0.993670	−	0.112337i	$-0.0358336\pi$
$38$		0			0
$39$	−4.23647	+	2.04078i	−0.678378	+	0.326787i
$40$		0			0
$41$		−	4.69186i		−	0.732745i	−0.930468	−	0.366372i	$-0.880600\pi$
$41$		−	4.69186i		−	0.732745i	0.930468	−	0.366372i	$-0.119400\pi$
$42$		0			0
$43$	1.50338			0.229263			0.114632	−	0.993408i	$-0.463431\pi$
$43$	1.50338			0.229263			0.114632	+	0.993408i	$0.463431\pi$
$44$		0			0
$45$	1.86993	−	2.34593i	0.278752	−	0.349710i
$46$		0			0
$47$	−4.07812			−0.594854			−0.297427	−	0.954745i	$-0.596129\pi$
$47$	−4.07812			−0.594854			−0.297427	+	0.954745i	$0.596129\pi$
$48$		0			0
$49$	−11.3690			−1.62415
$50$		0			0
$51$	1.81797	−	0.875746i	0.254566	−	0.122629i
$52$		0			0
$53$	−1.00676			−0.138289			−0.0691445	−	0.997607i	$-0.522027\pi$
$53$	−1.00676			−0.138289			−0.0691445	+	0.997607i	$0.522027\pi$
$54$		0			0
$55$		−	2.44673i		−	0.329917i
$56$		0			0
$57$	4.55106	+	9.44757i	0.602802	+	1.25136i
$58$		0			0
$59$		−	1.63484i		−	0.212837i	−0.994321	−	0.106419i	$-0.966062\pi$
$59$		−	1.63484i		−	0.212837i	0.994321	−	0.106419i	$-0.0339384\pi$
$60$		0			0
$61$		−	10.9336i		−	1.39990i	−0.714190	−	0.699952i	$-0.753205\pi$
$61$		−	10.9336i		−	1.39990i	0.714190	−	0.699952i	$-0.246795\pi$
$62$		0			0
$63$	10.0544	+	8.01433i	1.26674	+	1.00971i
$64$		0			0
$65$			2.71493i			0.336745i
$66$		0			0
$67$	9.97632			1.21880			0.609401	−	0.792862i	$-0.291410\pi$
$67$	9.97632			1.21880			0.609401	+	0.792862i	$0.291410\pi$
$68$		0			0
$69$	5.68113	+	11.7935i	0.683928	+	1.41977i
$70$		0			0
$71$	11.6359			1.38093			0.690465	−	0.723365i	$-0.257406\pi$
$71$	11.6359			1.38093			0.690465	+	0.723365i	$0.257406\pi$
$72$		0			0
$73$	−9.63593			−1.12780			−0.563900	−	0.825843i	$-0.690700\pi$
$73$	−9.63593			−1.12780			−0.563900	+	0.825843i	$0.690700\pi$
$74$		0			0
$75$	−0.751690	−	1.56044i	−0.0867976	−	0.180184i
$76$		0			0
$77$	10.4865			1.19504
$78$		0			0
$79$			3.61177i			0.406355i	0.979142	+	0.203178i	$0.0651269\pi$
$79$			3.61177i			0.406355i	−0.979142	+	0.203178i	$0.934873\pi$
$80$		0			0
$81$	−2.00676	−	8.77342i	−0.222973	−	0.974825i
$82$		0			0
$83$		−	5.45095i		−	0.598319i	−0.954203	−	0.299160i	$-0.903294\pi$
$83$		−	5.45095i		−	0.598319i	0.954203	−	0.299160i	$-0.0967063\pi$
$84$		0			0
$85$		−	1.16504i		−	0.126366i
$86$		0			0
$87$	0.551058	+	1.14394i	0.0590796	+	0.122644i
$88$		0			0
$89$		−	7.75993i		−	0.822551i	−0.911511	−	0.411275i	$-0.865083\pi$
$89$		−	7.75993i		−	0.822551i	0.911511	−	0.411275i	$-0.134917\pi$
$90$		0			0
$91$	−11.6359			−1.21978
$92$		0			0
$93$	−0.733092	+	0.353143i	−0.0760181	+	0.0366192i
$94$		0			0
$95$	6.05444			0.621172
$96$		0			0
$97$	17.1156			1.73783			0.868915	−	0.494962i	$-0.164818\pi$
$97$	17.1156			1.73783			0.868915	+	0.494962i	$0.164818\pi$
$98$		0			0
$99$	−5.73985	−	4.57520i	−0.576877	−	0.459825i
$100$		0			0
$101$	5.36226			0.533565			0.266783	−	0.963757i	$-0.414039\pi$
$101$	5.36226			0.533565			0.266783	+	0.963757i	$0.414039\pi$
$102$		0			0
$103$		−	13.0910i		−	1.28990i	−0.764225	−	0.644949i	$-0.776878\pi$
$103$		−	13.0910i		−	1.28990i	0.764225	−	0.644949i	$-0.223122\pi$
$104$		0			0
$105$	6.68789	−	3.22167i	0.652671	−	0.314403i
$106$		0			0
$107$		−	8.82622i		−	0.853263i	−0.904425	−	0.426632i	$-0.859700\pi$
$107$		−	8.82622i		−	0.853263i	0.904425	−	0.426632i	$-0.140300\pi$
$108$		0			0
$109$			0.780183i			0.0747280i	0.999302	+	0.0373640i	$0.0118961\pi$
$109$			0.780183i			0.0747280i	−0.999302	+	0.0373640i	$0.988104\pi$
$110$		0			0
$111$	−2.13255	+	1.02729i	−0.202413	+	0.0975058i
$112$		0			0
$113$		−	2.91653i		−	0.274364i	−0.990546	−	0.137182i	$-0.956195\pi$
$113$		−	2.91653i		−	0.274364i	0.990546	−	0.137182i	$-0.0438045\pi$
$114$		0			0
$115$	7.55782			0.704770
$116$		0			0
$117$	6.36902	+	5.07671i	0.588816	+	0.469342i
$118$		0			0
$119$	4.99324			0.457730
$120$		0			0
$121$	5.01352			0.455774
$122$		0			0
$123$	−7.32134	+	3.52682i	−0.660143	+	0.318003i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	2.93762i		−	0.260672i	−0.991470	−	0.130336i	$-0.958394\pi$
$127$		−	2.93762i		−	0.260672i	0.991470	−	0.130336i	$-0.0416056\pi$
$128$		0			0
$129$	−1.13007	−	2.34593i	−0.0994975	−	0.206547i
$130$		0			0
$131$			7.87658i			0.688180i	0.938937	+	0.344090i	$0.111813\pi$
$131$			7.87658i			0.688180i	−0.938937	+	0.344090i	$0.888187\pi$
$132$		0			0
$133$			25.9488i			2.25004i
$134$		0			0
$135$	−5.06628	−	1.15449i	−0.436036	−	0.0993627i
$136$		0			0
$137$			2.51333i			0.214728i	0.994220	+	0.107364i	$0.0342410\pi$
$137$			2.51333i			0.214728i	−0.994220	+	0.107364i	$0.965759\pi$
$138$		0			0
$139$	−2.57474			−0.218386			−0.109193	−	0.994021i	$-0.534827\pi$
$139$	−2.57474			−0.218386			−0.109193	+	0.994021i	$0.534827\pi$
$140$		0			0
$141$	3.06548	+	6.36364i	0.258160	+	0.535915i
$142$		0			0
$143$	6.64269			0.555490
$144$		0			0
$145$	0.733092			0.0608800
$146$		0			0
$147$	8.54598	+	17.7406i	0.704860	+	1.46322i
$148$		0			0
$149$	−16.1224			−1.32080			−0.660399	−	0.750915i	$-0.729613\pi$
$149$	−16.1224			−1.32080			−0.660399	+	0.750915i	$0.729613\pi$
$150$		0			0
$151$			17.8468i			1.45235i	0.687511	+	0.726174i	$0.258703\pi$
$151$			17.8468i			1.45235i	−0.687511	+	0.726174i	$0.741297\pi$
$152$		0			0
$153$	−2.73309	−	2.17853i	−0.220957	−	0.176124i
$154$		0			0
$155$			0.469799i			0.0377352i
$156$		0			0
$157$		−	23.2338i		−	1.85426i	−0.374737	−	0.927131i	$-0.622267\pi$
$157$		−	23.2338i		−	1.85426i	0.374737	−	0.927131i	$-0.377733\pi$
$158$		0			0
$159$	0.756770	+	1.57098i	0.0600158	+	0.124587i
$160$		0			0
$161$			32.3921i			2.55286i
$162$		0			0
$163$	−6.96956			−0.545898			−0.272949	−	0.962028i	$-0.587999\pi$
$163$	−6.96956			−0.545898			−0.272949	+	0.962028i	$0.587999\pi$
$164$		0			0
$165$	−3.81797	+	1.83918i	−0.297228	+	0.143180i
$166$		0			0
$167$	9.93540			0.768825			0.384412	−	0.923162i	$-0.374404\pi$
$167$	9.93540			0.768825			0.384412	+	0.923162i	$0.374404\pi$
$168$		0			0
$169$	5.62917			0.433013
$170$		0			0
$171$	11.3213	−	14.2033i	0.865765	−	1.08615i
$172$		0			0
$173$	8.01352			0.609256			0.304628	−	0.952471i	$-0.401468\pi$
$173$	8.01352			0.609256			0.304628	+	0.952471i	$0.401468\pi$
$174$		0			0
$175$		−	4.28591i		−	0.323984i
$176$		0			0
$177$	−2.55106	+	1.22889i	−0.191749	+	0.0923690i
$178$		0			0
$179$		−	23.5020i		−	1.75663i	−0.478087	−	0.878313i	$-0.658670\pi$
$179$		−	23.5020i		−	1.75663i	0.478087	−	0.878313i	$-0.341330\pi$
$180$		0			0
$181$			9.92011i			0.737356i	0.929557	+	0.368678i	$0.120189\pi$
$181$			9.92011i			0.737356i	−0.929557	+	0.368678i	$0.879811\pi$
$182$		0			0
$183$	−17.0612	+	8.21868i	−1.26120	+	0.607542i
$184$		0			0
$185$			1.36664i			0.100477i
$186$		0			0
$187$	−2.85053			−0.208451
$188$		0			0
$189$	4.94804	−	21.7136i	0.359917	−	1.57943i
$190$		0			0
$191$	−22.4865			−1.62706			−0.813532	−	0.581521i	$-0.802458\pi$
$191$	−22.4865			−1.62706			−0.813532	+	0.581521i	$0.802458\pi$
$192$		0			0
$193$	−13.1156			−0.944084			−0.472042	−	0.881576i	$-0.656483\pi$
$193$	−13.1156			−0.944084			−0.472042	+	0.881576i	$0.656483\pi$
$194$		0			0
$195$	4.23647	−	2.04078i	0.303380	−	0.146143i
$196$		0			0
$197$	−24.2786			−1.72978			−0.864890	−	0.501961i	$-0.832612\pi$
$197$	−24.2786			−1.72978			−0.864890	+	0.501961i	$0.832612\pi$
$198$		0			0
$199$		−	1.81809i		−	0.128881i	−0.997922	−	0.0644404i	$-0.979474\pi$
$199$		−	1.81809i		−	0.128881i	0.997922	−	0.0644404i	$-0.0205262\pi$
$200$		0			0
$201$	−7.49910	−	15.5674i	−0.528946	−	1.09804i
$202$		0			0
$203$			3.14197i			0.220523i
$204$		0			0
$205$			4.69186i			0.327693i
$206$		0			0
$207$	14.1326	−	17.7301i	0.982280	−	1.23233i
$208$		0			0
$209$		−	14.8136i		−	1.02468i
$210$		0			0
$211$	−1.06120			−0.0730557			−0.0365279	−	0.999333i	$-0.511630\pi$
$211$	−1.06120			−0.0730557			−0.0365279	+	0.999333i	$0.511630\pi$
$212$		0			0
$213$	−8.74661	−	18.1571i	−0.599308	−	1.24411i
$214$		0			0
$215$	−1.50338			−0.102530
$216$		0			0
$217$	−2.01352			−0.136686
$218$		0			0
$219$	7.24323	+	15.0363i	0.489452	+	1.01606i
$220$		0			0
$221$	3.16299			0.212766
$222$		0			0
$223$			5.22551i			0.349926i	0.984575	+	0.174963i	$0.0559806\pi$
$223$			5.22551i			0.349926i	−0.984575	+	0.174963i	$0.944019\pi$
$224$		0			0
$225$	−1.86993	+	2.34593i	−0.124662	+	0.156395i
$226$		0			0
$227$			13.8951i			0.922248i	0.887336	+	0.461124i	$0.152554\pi$
$227$			13.8951i			0.922248i	−0.887336	+	0.461124i	$0.847446\pi$
$228$		0			0
$229$			0.233312i			0.0154177i	0.999970	+	0.00770885i	$0.00245383\pi$
$229$			0.233312i			0.0154177i	−0.999970	+	0.00770885i	$0.997546\pi$
$230$		0			0
$231$	−7.88256	−	16.3635i	−0.518635	−	1.07664i
$232$		0			0
$233$			8.62188i			0.564838i	0.959291	+	0.282419i	$0.0911369\pi$
$233$			8.62188i			0.564838i	−0.959291	+	0.282419i	$0.908863\pi$
$234$		0			0
$235$	4.07812			0.266027
$236$		0			0
$237$	5.63593	−	2.71493i	0.366093	−	0.176353i
$238$		0			0
$239$	−20.1089			−1.30073			−0.650367	−	0.759620i	$-0.725385\pi$
$239$	−20.1089			−1.30073			−0.650367	+	0.759620i	$0.725385\pi$
$240$		0			0
$241$	−9.12420			−0.587741			−0.293871	−	0.955845i	$-0.594943\pi$
$241$	−9.12420			−0.587741			−0.293871	+	0.955845i	$0.594943\pi$
$242$		0			0
$243$	−12.1819	+	9.72631i	−0.781470	+	0.623943i
$244$		0			0
$245$	11.3690			0.726340
$246$		0			0
$247$			16.4374i			1.04588i
$248$		0			0
$249$	−8.50586	+	4.09742i	−0.539037	+	0.259663i
$250$		0			0
$251$			13.3064i			0.839895i	0.907548	+	0.419947i	$0.137951\pi$
$251$			13.3064i			0.839895i	−0.907548	+	0.419947i	$0.862049\pi$
$252$		0			0
$253$		−	18.4919i		−	1.16258i
$254$		0			0
$255$	−1.81797	+	0.875746i	−0.113845	+	0.0548413i
$256$		0			0
$257$		−	30.2136i		−	1.88467i	−0.334668	−	0.942336i	$-0.608624\pi$
$257$		−	30.2136i		−	1.88467i	0.334668	−	0.942336i	$-0.391376\pi$
$258$		0			0
$259$	−5.85729			−0.363954
$260$		0			0
$261$	1.37083	−	1.71978i	0.0848521	−	0.106452i
$262$		0			0
$263$	14.9286			0.920540			0.460270	−	0.887779i	$-0.347753\pi$
$263$	14.9286			0.920540			0.460270	+	0.887779i	$0.347753\pi$
$264$		0			0
$265$	1.00676			0.0618447
$266$		0			0
$267$	−12.1089	+	5.83306i	−0.741051	+	0.356977i
$268$		0			0
$269$	4.85053			0.295742			0.147871	−	0.989007i	$-0.452758\pi$
$269$	4.85053			0.295742			0.147871	+	0.989007i	$0.452758\pi$
$270$		0			0
$271$		−	14.8802i		−	0.903906i	−0.892042	−	0.451953i	$-0.850728\pi$
$271$		−	14.8802i		−	0.903906i	0.892042	−	0.451953i	$-0.149272\pi$
$272$		0			0
$273$	8.74661	+	18.1571i	0.529369	+	1.09892i
$274$		0			0
$275$			2.44673i			0.147543i
$276$		0			0
$277$			19.6832i			1.18265i	0.806434	+	0.591324i	$0.201395\pi$
$277$			19.6832i			1.18265i	−0.806434	+	0.591324i	$0.798605\pi$
$278$		0			0
$279$	1.10212	+	0.878490i	0.0659819	+	0.0525938i
$280$		0			0
$281$			2.29836i			0.137109i	0.997647	+	0.0685544i	$0.0218387\pi$
$281$			2.29836i			0.137109i	−0.997647	+	0.0685544i	$0.978161\pi$
$282$		0			0
$283$	21.6123			1.28472			0.642358	−	0.766405i	$-0.277956\pi$
$283$	21.6123			1.28472			0.642358	+	0.766405i	$0.277956\pi$
$284$		0			0
$285$	−4.55106	−	9.44757i	−0.269581	−	0.559625i
$286$		0			0
$287$	−20.1089			−1.18699
$288$		0			0
$289$	15.6427			0.920158
$290$		0			0
$291$	−12.8656	−	26.7079i	−0.754197	−	1.56564i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$			1.63484i			0.0951838i
$296$		0			0
$297$	−2.82472	+	12.3958i	−0.163907	+	0.719278i
$298$		0			0
$299$			20.5189i			1.18664i
$300$		0			0
$301$		−	6.44335i		−	0.371388i
$302$		0			0
$303$	−4.03076	−	8.36747i	−0.231561	−	0.480699i
$304$		0			0
$305$			10.9336i			0.626056i
$306$		0			0
$307$	4.98308			0.284399			0.142200	−	0.989838i	$-0.454582\pi$
$307$	4.98308			0.284399			0.142200	+	0.989838i	$0.454582\pi$
$308$		0			0
$309$	−20.4277	+	9.84040i	−1.16209	+	0.559801i
$310$		0			0
$311$	11.0886			0.628777			0.314388	−	0.949294i	$-0.398201\pi$
$311$	11.0886			0.628777			0.314388	+	0.949294i	$0.398201\pi$
$312$		0			0
$313$	11.2583			0.636359			0.318180	−	0.948030i	$-0.396928\pi$
$313$	11.2583			0.636359			0.318180	+	0.948030i	$0.396928\pi$
$314$		0			0
$315$	−10.0544	−	8.01433i	−0.566503	−	0.451556i
$316$		0			0
$317$	−27.2110			−1.52832			−0.764161	−	0.645026i	$-0.776847\pi$
$317$	−27.2110			−1.52832			−0.764161	+	0.645026i	$0.776847\pi$
$318$		0			0
$319$		−	1.79368i		−	0.100427i
$320$		0			0
$321$	−13.7728	+	6.63458i	−0.768721	+	0.370306i
$322$		0			0
$323$		−	7.05364i		−	0.392475i
$324$		0			0
$325$		−	2.71493i		−	0.150597i
$326$		0			0
$327$	1.21743	−	0.586455i	0.0673238	−	0.0324311i
$328$		0			0
$329$			17.4784i			0.963617i
$330$		0			0
$331$	18.3195			1.00693			0.503467	−	0.864015i	$-0.332058\pi$
$331$	18.3195			1.00693			0.503467	+	0.864015i	$0.332058\pi$
$332$		0			0
$333$	3.20603	+	2.55551i	0.175690	+	0.140041i
$334$		0			0
$335$	−9.97632			−0.545065
$336$		0			0
$337$	2.54733			0.138762			0.0693810	−	0.997590i	$-0.477898\pi$
$337$	2.54733			0.138762			0.0693810	+	0.997590i	$0.477898\pi$
$338$		0			0
$339$	−4.55106	+	2.19232i	−0.247180	+	0.119071i
$340$		0			0
$341$	1.14947			0.0622474
$342$		0			0
$343$			18.7252i			1.01107i
$344$		0			0
$345$	−5.68113	−	11.7935i	−0.305862	−	0.634940i
$346$		0			0
$347$		−	29.3727i		−	1.57681i	−0.615156	−	0.788405i	$-0.710907\pi$
$347$		−	29.3727i		−	1.57681i	0.615156	−	0.788405i	$-0.289093\pi$
$348$		0			0
$349$			23.5131i			1.25863i	0.777152	+	0.629313i	$0.216664\pi$
$349$			23.5131i			1.25863i	−0.777152	+	0.629313i	$0.783336\pi$
$350$		0			0
$351$	3.13436	−	13.7546i	0.167300	−	0.734165i
$352$		0			0
$353$		−	31.0677i		−	1.65357i	−0.562522	−	0.826783i	$-0.690169\pi$
$353$		−	31.0677i		−	1.65357i	0.562522	−	0.826783i	$-0.309831\pi$
$354$		0			0
$355$	−11.6359			−0.617571
$356$		0			0
$357$	−3.75337	−	7.79164i	−0.198649	−	0.412377i
$358$		0			0
$359$	11.3979			0.601556			0.300778	−	0.953694i	$-0.402754\pi$
$359$	11.3979			0.601556			0.300778	+	0.953694i	$0.402754\pi$
$360$		0			0
$361$	17.6562			0.929274
$362$		0			0
$363$	−3.76861	−	7.82328i	−0.197801	−	0.410616i
$364$		0			0
$365$	9.63593			0.504368
$366$		0			0
$367$			21.0209i			1.09728i	0.836059	+	0.548640i	$0.184854\pi$
$367$			21.0209i			1.09728i	−0.836059	+	0.548640i	$0.815146\pi$
$368$		0			0
$369$	11.0068	+	8.77342i	0.572989	+	0.456726i
$370$		0			0
$371$			4.31488i			0.224017i
$372$		0			0
$373$			10.3471i			0.535755i	0.963453	+	0.267878i	$0.0863223\pi$
$373$			10.3471i			0.535755i	−0.963453	+	0.267878i	$0.913678\pi$
$374$		0			0
$375$	0.751690	+	1.56044i	0.0388171	+	0.0805806i
$376$		0			0
$377$			1.99029i			0.102505i
$378$		0			0
$379$	17.5341			0.900668			0.450334	−	0.892860i	$-0.351305\pi$
$379$	17.5341			0.900668			0.450334	+	0.892860i	$0.351305\pi$
$380$		0			0
$381$	−4.58397	+	2.20818i	−0.234844	+	0.113128i
$382$		0			0
$383$	−24.7343			−1.26386			−0.631932	−	0.775023i	$-0.717738\pi$
$383$	−24.7343			−1.26386			−0.631932	+	0.775023i	$0.717738\pi$
$384$		0			0
$385$	−10.4865			−0.534439
$386$		0			0
$387$	−2.81121	+	3.52682i	−0.142902	+	0.179278i
$388$		0			0
$389$	24.2313			1.22857			0.614287	−	0.789083i	$-0.289444\pi$
$389$	24.2313			1.22857			0.614287	+	0.789083i	$0.289444\pi$
$390$		0			0
$391$		−	8.80513i		−	0.445295i
$392$		0			0
$393$	12.2909	−	5.92075i	0.619994	−	0.298662i
$394$		0			0
$395$		−	3.61177i		−	0.181728i
$396$		0			0
$397$			21.8856i			1.09840i	0.835689	+	0.549202i	$0.185068\pi$
$397$			21.8856i			1.09840i	−0.835689	+	0.549202i	$0.814932\pi$
$398$		0			0
$399$	40.4914	−	19.5054i	2.02711	−	0.976493i
$400$		0			0
$401$			21.4163i			1.06948i	0.845016	+	0.534740i	$0.179591\pi$
$401$			21.4163i			1.06948i	−0.845016	+	0.534740i	$0.820409\pi$
$402$		0			0
$403$	−1.27547			−0.0635357
$404$		0			0
$405$	2.00676	+	8.77342i	0.0997166	+	0.435955i
$406$		0			0
$407$	3.34379			0.165746
$408$		0			0
$409$	−21.5455			−1.06536			−0.532679	−	0.846317i	$-0.678815\pi$
$409$	−21.5455			−1.06536			−0.532679	+	0.846317i	$0.678815\pi$
$410$		0			0
$411$	3.92188	−	1.88924i	0.193452	−	0.0931894i
$412$		0			0
$413$	−7.00676			−0.344780
$414$		0			0
$415$			5.45095i			0.267576i
$416$		0			0
$417$	1.93540	+	4.01771i	0.0947771	+	0.196748i
$418$		0			0
$419$			14.6547i			0.715930i	0.933735	+	0.357965i	$0.116529\pi$
$419$			14.6547i			0.715930i	−0.933735	+	0.357965i	$0.883471\pi$
$420$		0			0
$421$			19.0967i			0.930718i	0.885122	+	0.465359i	$0.154075\pi$
$421$			19.0967i			0.930718i	−0.885122	+	0.465359i	$0.845925\pi$
$422$		0			0
$423$	7.62577	−	9.56697i	0.370778	−	0.465162i
$424$		0			0
$425$			1.16504i			0.0565126i
$426$		0			0
$427$	−46.8604			−2.26774
$428$		0			0
$429$	−4.99324	−	10.3655i	−0.241076	−	0.500451i
$430$		0			0
$431$	27.8537			1.34166			0.670832	−	0.741609i	$-0.265937\pi$
$431$	27.8537			1.34166			0.670832	+	0.741609i	$0.265937\pi$
$432$		0			0
$433$	24.0750			1.15697			0.578486	−	0.815692i	$-0.303644\pi$
$433$	24.0750			1.15697			0.578486	+	0.815692i	$0.303644\pi$
$434$		0			0
$435$	−0.551058	−	1.14394i	−0.0264212	−	0.0548479i
$436$		0			0
$437$	45.7583			2.18892
$438$		0			0
$439$			24.6249i			1.17528i	0.809122	+	0.587641i	$0.199943\pi$
$439$			24.6249i			1.17528i	−0.809122	+	0.587641i	$0.800057\pi$
$440$		0			0
$441$	21.2592	−	26.6709i	1.01234	−	1.27004i
$442$		0			0
$443$			7.61113i			0.361616i	0.983518	+	0.180808i	$0.0578712\pi$
$443$			7.61113i			0.361616i	−0.983518	+	0.180808i	$0.942129\pi$
$444$		0			0
$445$			7.75993i			0.367856i
$446$		0			0
$447$	12.1190	+	25.1580i	0.573211	+	1.18993i
$448$		0			0
$449$		−	11.2946i		−	0.533026i	−0.963831	−	0.266513i	$-0.914128\pi$
$449$		−	11.2946i		−	0.533026i	0.963831	−	0.266513i	$-0.0858715\pi$
$450$		0			0
$451$	11.4797			0.540558
$452$		0			0
$453$	27.8487	−	13.4152i	1.30845	−	0.630302i
$454$		0			0
$455$	11.6359			0.545501
$456$		0			0
$457$	−29.5067			−1.38027			−0.690133	−	0.723682i	$-0.742448\pi$
$457$	−29.5067			−1.38027			−0.690133	+	0.723682i	$0.742448\pi$
$458$		0			0
$459$	−1.34502	+	5.90240i	−0.0627803	+	0.275500i
$460$		0			0
$461$	28.9508			1.34838			0.674188	−	0.738560i	$-0.264494\pi$
$461$	28.9508			1.34838			0.674188	+	0.738560i	$0.264494\pi$
$462$		0			0
$463$		−	22.6025i		−	1.05043i	−0.850971	−	0.525213i	$-0.823986\pi$
$463$		−	22.6025i		−	1.05043i	0.850971	−	0.525213i	$-0.176014\pi$
$464$		0			0
$465$	0.733092	−	0.353143i	0.0339963	−	0.0163766i
$466$		0			0
$467$		−	13.6141i		−	0.629984i	−0.949094	−	0.314992i	$-0.897998\pi$
$467$		−	13.6141i		−	0.629984i	0.949094	−	0.314992i	$-0.102002\pi$
$468$		0			0
$469$		−	42.7576i		−	1.97436i
$470$		0			0
$471$	−36.2549	+	17.4646i	−1.67054	+	0.804728i
$472$		0			0
$473$			3.67836i			0.169131i
$474$		0			0
$475$	−6.05444			−0.277797
$476$		0			0
$477$	1.88256	−	2.36178i	0.0861967	−	0.108139i
$478$		0			0
$479$	−0.411425			−0.0187985			−0.00939924	−	0.999956i	$-0.502992\pi$
$479$	−0.411425			−0.0187985			−0.00939924	+	0.999956i	$0.502992\pi$
$480$		0			0
$481$	−3.71032			−0.169176
$482$		0			0
$483$	50.5459	−	24.3488i	2.29992	−	1.10791i
$484$		0			0
$485$	−17.1156			−0.777181
$486$		0			0
$487$		−	32.2250i		−	1.46025i	−0.683312	−	0.730126i	$-0.739461\pi$
$487$		−	32.2250i		−	1.46025i	0.683312	−	0.730126i	$-0.260539\pi$
$488$		0			0
$489$	5.23895	+	10.8756i	0.236913	+	0.491810i
$490$		0			0
$491$			14.1605i			0.639055i	0.947577	+	0.319528i	$0.103524\pi$
$491$			14.1605i			0.639055i	−0.947577	+	0.319528i	$0.896476\pi$
$492$		0			0
$493$		−	0.854079i		−	0.0384658i
$494$		0			0
$495$	5.73985	+	4.57520i	0.257987	+	0.205640i
$496$		0			0
$497$		−	49.8706i		−	2.23700i
$498$		0			0
$499$	14.6018			0.653665			0.326833	−	0.945082i	$-0.394019\pi$
$499$	14.6018			0.653665			0.326833	+	0.945082i	$0.394019\pi$
$500$		0			0
$501$	−7.46834	−	15.5036i	−0.333661	−	0.692648i
$502$		0			0
$503$	30.2823			1.35022			0.675112	−	0.737716i	$-0.264095\pi$
$503$	30.2823			1.35022			0.675112	+	0.737716i	$0.264095\pi$
$504$		0			0
$505$	−5.36226			−0.238618
$506$		0			0
$507$	−4.23139	−	8.78397i	−0.187923	−	0.390110i
$508$		0			0
$509$	8.84197			0.391913			0.195957	−	0.980613i	$-0.437219\pi$
$509$	8.84197			0.391913			0.195957	+	0.980613i	$0.437219\pi$
$510$		0			0
$511$			41.2987i			1.82695i
$512$		0			0
$513$	−30.6734	−	6.98979i	−1.35427	−	0.308607i
$514$		0			0
$515$			13.0910i			0.576860i
$516$		0			0
$517$		−	9.97804i		−	0.438834i
$518$		0			0
$519$	−6.02368	−	12.5046i	−0.264410	−	0.548890i
$520$		0			0
$521$		−	38.6076i		−	1.69143i	−0.533634	−	0.845716i	$-0.679174\pi$
$521$		−	38.6076i		−	1.69143i	0.533634	−	0.845716i	$-0.320826\pi$
$522$		0			0
$523$	13.8674			0.606381			0.303191	−	0.952930i	$-0.401948\pi$
$523$	13.8674			0.606381			0.303191	+	0.952930i	$0.401948\pi$
$524$		0			0
$525$	−6.68789	+	3.22167i	−0.291883	+	0.140605i
$526$		0			0
$527$	0.547333			0.0238422
$528$		0			0
$529$	34.1206			1.48350
$530$		0			0
$531$	3.83521	+	3.05702i	0.166434	+	0.132663i
$532$		0			0
$533$	−12.7380			−0.551746
$534$		0			0
$535$			8.82622i			0.381591i
$536$		0			0
$537$	−36.6734	+	17.6662i	−1.58258	+	0.762355i
$538$		0			0
$539$		−	27.8169i		−	1.19816i
$540$		0			0
$541$		−	5.19654i		−	0.223417i	−0.993741	−	0.111708i	$-0.964368\pi$
$541$		−	5.19654i		−	0.223417i	0.993741	−	0.111708i	$-0.0356323\pi$
$542$		0			0
$543$	15.4797	−	7.45684i	0.664298	−	0.320004i
$544$		0			0
$545$		−	0.780183i		−	0.0334194i
$546$		0			0
$547$	13.1393			0.561796			0.280898	−	0.959738i	$-0.409368\pi$
$547$	13.1393			0.561796			0.280898	+	0.959738i	$0.409368\pi$
$548$		0			0
$549$	25.6494	+	20.4450i	1.09469	+	0.872572i
$550$		0			0
$551$	4.43846			0.189085
$552$		0			0
$553$	15.4797			0.658264
$554$		0			0
$555$	2.13255	−	1.02729i	0.0905218	−	0.0436059i
$556$		0			0
$557$	0.506781			0.0214730			0.0107365	−	0.999942i	$-0.496582\pi$
$557$	0.506781			0.0214730			0.0107365	+	0.999942i	$0.496582\pi$
$558$		0			0
$559$		−	4.08156i		−	0.172632i
$560$		0			0
$561$	2.14271	+	4.44807i	0.0904654	+	0.187798i
$562$		0			0
$563$			13.0410i			0.549612i	0.961500	+	0.274806i	$0.0886136\pi$
$563$			13.0410i			0.549612i	−0.961500	+	0.274806i	$0.911386\pi$
$564$		0			0
$565$			2.91653i			0.122699i
$566$		0			0
$567$	−37.6021	+	8.60079i	−1.57914	+	0.361199i
$568$		0			0
$569$			30.7683i			1.28988i	0.764235	+	0.644938i	$0.223117\pi$
$569$			30.7683i			1.28988i	−0.764235	+	0.644938i	$0.776883\pi$
$570$		0			0
$571$	−27.6769			−1.15824			−0.579120	−	0.815242i	$-0.696604\pi$
$571$	−27.6769			−1.15824			−0.579120	+	0.815242i	$0.696604\pi$
$572$		0			0
$573$	16.9028	+	35.0887i	0.706126	+	1.46585i
$574$		0			0
$575$	−7.55782			−0.315183
$576$		0			0
$577$	−33.4626			−1.39307			−0.696533	−	0.717525i	$-0.745275\pi$
$577$	−33.4626			−1.39307			−0.696533	+	0.717525i	$0.745275\pi$
$578$		0			0
$579$	9.85889	+	20.4661i	0.409721	+	0.850543i
$580$		0			0
$581$	−23.3623			−0.969230
$582$		0			0
$583$		−	2.46327i		−	0.102018i
$584$		0			0
$585$	−6.36902	−	5.07671i	−0.263327	−	0.209896i
$586$		0			0
$587$		−	28.7031i		−	1.18471i	−0.805679	−	0.592353i	$-0.798199\pi$
$587$		−	28.7031i		−	1.18471i	0.805679	−	0.592353i	$-0.201801\pi$
$588$		0			0
$589$			2.84437i			0.117200i
$590$		0			0
$591$	18.2500	+	37.8853i	0.750704	+	1.55839i
$592$		0			0
$593$			44.2574i			1.81744i	0.417411	+	0.908718i	$0.362938\pi$
$593$			44.2574i			1.81744i	−0.417411	+	0.908718i	$0.637062\pi$
$594$		0			0
$595$	−4.99324			−0.204703
$596$		0			0
$597$	−2.83701	+	1.36664i	−0.116111	+	0.0559328i
$598$		0			0
$599$	−24.1359			−0.986166			−0.493083	−	0.869982i	$-0.664130\pi$
$599$	−24.1359			−0.986166			−0.493083	+	0.869982i	$0.664130\pi$
$600$		0			0
$601$	19.7669			0.806308			0.403154	−	0.915132i	$-0.367914\pi$
$601$	19.7669			0.806308			0.403154	+	0.915132i	$0.367914\pi$
$602$		0			0
$603$	−18.6550	+	23.4037i	−0.759689	+	0.953074i
$604$		0			0
$605$	−5.01352			−0.203828
$606$		0			0
$607$		−	7.68877i		−	0.312078i	−0.987751	−	0.156039i	$-0.950127\pi$
$607$		−	7.68877i		−	0.312078i	0.987751	−	0.156039i	$-0.0498725\pi$
$608$		0			0
$609$	4.90284	−	2.36178i	0.198673	−	0.0957043i
$610$		0			0
$611$			11.0718i			0.447916i
$612$		0			0
$613$		−	26.6091i		−	1.07473i	−0.843349	−	0.537366i	$-0.819419\pi$
$613$		−	26.6091i		−	1.07473i	0.843349	−	0.537366i	$-0.180581\pi$
$614$		0			0
$615$	7.32134	−	3.52682i	0.295225	−	0.142215i
$616$		0			0
$617$			25.0592i			1.00885i	0.863456	+	0.504423i	$0.168295\pi$
$617$			25.0592i			1.00885i	−0.863456	+	0.504423i	$0.831705\pi$
$618$		0			0
$619$	20.1498			0.809889			0.404944	−	0.914341i	$-0.367291\pi$
$619$	20.1498			0.809889			0.404944	+	0.914341i	$0.367291\pi$
$620$		0			0
$621$	−38.2900	−	8.72542i	−1.53652	−	0.350139i
$622$		0			0
$623$	−33.2583			−1.33247
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−23.1156	+	11.1352i	−0.923149	+	0.444697i
$628$		0			0
$629$	1.59218			0.0634845
$630$		0			0
$631$		−	27.8036i		−	1.10684i	−0.832902	−	0.553421i	$-0.813322\pi$
$631$		−	27.8036i		−	1.10684i	0.832902	−	0.553421i	$-0.186678\pi$
$632$		0			0
$633$	0.797690	+	1.65593i	0.0317053	+	0.0658173i
$634$		0			0
$635$			2.93762i			0.116576i
$636$		0			0
$637$			30.8661i			1.22296i
$638$		0			0
$639$	−21.7583	+	27.2971i	−0.860746	+	1.07986i
$640$		0			0
$641$			36.3093i			1.43413i	0.697006	+	0.717065i	$0.254515\pi$
$641$			36.3093i			1.43413i	−0.697006	+	0.717065i	$0.745485\pi$
$642$		0			0
$643$	−32.8571			−1.29576			−0.647878	−	0.761744i	$-0.724344\pi$
$643$	−32.8571			−1.29576			−0.647878	+	0.761744i	$0.724344\pi$
$644$		0			0
$645$	1.13007	+	2.34593i	0.0444966	+	0.0923708i
$646$		0			0
$647$	−17.1329			−0.673563			−0.336781	−	0.941583i	$-0.609338\pi$
$647$	−17.1329			−0.673563			−0.336781	+	0.941583i	$0.609338\pi$
$648$		0			0
$649$	4.00000			0.157014
$650$		0			0
$651$	1.51354	+	3.14197i	0.0593203	+	0.123143i
$652$		0			0
$653$	−27.7583			−1.08627			−0.543134	−	0.839646i	$-0.682762\pi$
$653$	−27.7583			−1.08627			−0.543134	+	0.839646i	$0.682762\pi$
$654$		0			0
$655$		−	7.87658i		−	0.307764i
$656$		0			0
$657$	18.0185	−	22.6052i	0.702968	−	0.881913i
$658$		0			0
$659$		−	15.3389i		−	0.597519i	−0.954328	−	0.298760i	$-0.903427\pi$
$659$		−	15.3389i		−	0.597519i	0.954328	−	0.298760i	$-0.0965729\pi$
$660$		0			0
$661$		−	38.9369i		−	1.51447i	−0.653141	−	0.757236i	$-0.726549\pi$
$661$		−	38.9369i		−	1.51447i	0.653141	−	0.757236i	$-0.273451\pi$
$662$		0			0
$663$	−2.37759	−	4.93564i	−0.0923378	−	0.191685i
$664$		0			0
$665$		−	25.9488i		−	1.00625i
$666$		0			0
$667$	5.54057			0.214532
$668$		0			0
$669$	8.15407	−	3.92796i	0.315255	−	0.151864i
$670$		0			0
$671$	26.7516			1.03273
$672$		0			0
$673$	−6.78966			−0.261722			−0.130861	−	0.991401i	$-0.541774\pi$
$673$	−6.78966			−0.261722			−0.130861	+	0.991401i	$0.541774\pi$
$674$		0			0
$675$	5.06628	+	1.15449i	0.195001	+	0.0444363i
$676$		0			0
$677$	−40.6772			−1.56335			−0.781675	−	0.623685i	$-0.785635\pi$
$677$	−40.6772			−1.56335			−0.781675	+	0.623685i	$0.785635\pi$
$678$		0			0
$679$		−	73.3561i		−	2.81515i
$680$		0			0
$681$	21.6824	−	10.4448i	0.830870	−	0.400245i
$682$		0			0
$683$			8.14204i			0.311546i	0.987793	+	0.155773i	$0.0497869\pi$
$683$			8.14204i			0.311546i	−0.987793	+	0.155773i	$0.950213\pi$
$684$		0			0
$685$		−	2.51333i		−	0.0960292i
$686$		0			0
$687$	0.364069	−	0.175378i	0.0138901	−	0.00669110i
$688$		0			0
$689$			2.73328i			0.104130i
$690$		0			0
$691$	2.10179			0.0799560			0.0399780	−	0.999201i	$-0.487271\pi$
$691$	2.10179			0.0799560			0.0399780	+	0.999201i	$0.487271\pi$
$692$		0			0
$693$	−19.6089	+	24.6005i	−0.744880	+	0.934495i
$694$		0			0
$695$	2.57474			0.0976653
$696$		0			0
$697$	5.46618			0.207046
$698$		0			0
$699$	13.4539	−	6.48098i	0.508873	−	0.245133i
$700$		0			0
$701$	−20.0135			−0.755900			−0.377950	−	0.925826i	$-0.623371\pi$
$701$	−20.0135			−0.755900			−0.377950	+	0.925826i	$0.623371\pi$
$702$		0			0
$703$			8.27422i			0.312068i
$704$		0			0
$705$	−3.06548	−	6.36364i	−0.115453	−	0.239669i
$706$		0			0
$707$		−	22.9822i		−	0.864334i
$708$		0			0
$709$		−	15.3500i		−	0.576480i	−0.957558	−	0.288240i	$-0.906930\pi$
$709$		−	15.3500i		−	0.576480i	0.957558	−	0.288240i	$-0.0930701\pi$
$710$		0			0
$711$	−8.47294	−	6.75373i	−0.317760	−	0.253285i
$712$		0			0
$713$			3.55066i			0.132973i
$714$		0			0
$715$	−6.64269			−0.248423
$716$		0			0
$717$	15.1156	+	31.3786i	0.564504	+	1.17186i
$718$		0			0
$719$	−5.77864			−0.215507			−0.107754	−	0.994178i	$-0.534366\pi$
$719$	−5.77864			−0.215507			−0.107754	+	0.994178i	$0.534366\pi$
$720$		0			0
$721$	−56.1070			−2.08953
$722$		0			0
$723$	6.85856	+	14.2377i	0.255073	+	0.529507i
$724$		0			0
$725$	−0.733092			−0.0272264
$726$		0			0
$727$			25.0657i			0.929636i	0.885406	+	0.464818i	$0.153880\pi$
$727$			25.0657i			0.929636i	−0.885406	+	0.464818i	$0.846120\pi$
$728$		0			0
$729$	24.3343	+	11.6979i	0.901271	+	0.433257i
$730$		0			0
$731$			1.75149i			0.0647813i
$732$		0			0
$733$		−	14.9596i		−	0.552546i	−0.961079	−	0.276273i	$-0.910901\pi$
$733$		−	14.9596i		−	0.552546i	0.961079	−	0.276273i	$-0.0890994\pi$
$734$		0			0
$735$	−8.54598	−	17.7406i	−0.315223	−	0.654373i
$736$		0			0
$737$			24.4094i			0.899130i
$738$		0			0
$739$	−9.76476			−0.359202			−0.179601	−	0.983739i	$-0.557481\pi$
$739$	−9.76476			−0.359202			−0.179601	+	0.983739i	$0.557481\pi$
$740$		0			0
$741$	25.6494	−	12.3558i	0.942256	−	0.453901i
$742$		0			0
$743$	13.6457			0.500613			0.250307	−	0.968167i	$-0.419469\pi$
$743$	13.6457			0.500613			0.250307	+	0.968167i	$0.419469\pi$
$744$		0			0
$745$	16.1224			0.590679
$746$		0			0
$747$	12.7875	+	10.1929i	0.467871	+	0.372937i
$748$		0			0
$749$	−37.8284			−1.38222
$750$		0			0
$751$		−	36.7841i		−	1.34227i	−0.741335	−	0.671135i	$-0.765807\pi$
$751$		−	36.7841i		−	1.34227i	0.741335	−	0.671135i	$-0.234193\pi$
$752$		0			0
$753$	20.7639	−	10.0023i	0.756677	−	0.364504i
$754$		0			0
$755$		−	17.8468i		−	0.649510i
$756$		0			0
$757$		−	10.1994i		−	0.370702i	−0.982672	−	0.185351i	$-0.940658\pi$
$757$		−	10.1994i		−	0.370702i	0.982672	−	0.185351i	$-0.0593422\pi$
$758$		0			0
$759$	−28.8555	+	13.9002i	−1.04739	+	0.504545i
$760$		0			0
$761$		−	28.0668i		−	1.01742i	−0.860938	−	0.508710i	$-0.830123\pi$
$761$		−	28.0668i		−	1.01742i	0.860938	−	0.508710i	$-0.169877\pi$
$762$		0			0
$763$	3.34379			0.121053
$764$		0			0
$765$	2.73309	+	2.17853i	0.0988151	+	0.0787650i
$766$		0			0
$767$	−4.43846			−0.160263
$768$		0			0
$769$	16.3302			0.588883			0.294442	−	0.955669i	$-0.404866\pi$
$769$	16.3302			0.588883			0.294442	+	0.955669i	$0.404866\pi$
$770$		0			0
$771$	−47.1464	+	22.7112i	−1.69794	+	0.817925i
$772$		0			0
$773$	42.5099			1.52897			0.764487	−	0.644639i	$-0.222992\pi$
$773$	42.5099			1.52897			0.764487	+	0.644639i	$0.222992\pi$
$774$		0			0
$775$		−	0.469799i		−	0.0168757i
$776$		0			0
$777$	4.40286	+	9.13993i	0.157952	+	0.327893i
$778$		0			0
$779$			28.4065i			1.01777i
$780$		0			0
$781$			28.4700i			1.01874i
$782$		0			0
$783$	−3.71405	−	0.846347i	−0.132729	−	0.0302460i
$784$		0			0
$785$			23.2338i			0.829251i
$786$		0			0
$787$	−27.9997			−0.998083			−0.499042	−	0.866578i	$-0.666315\pi$
$787$	−27.9997			−0.998083			−0.499042	+	0.866578i	$0.666315\pi$
$788$		0			0
$789$	−11.2217	−	23.2952i	−0.399503	−	0.829331i
$790$		0			0
$791$	−12.5000			−0.444448
$792$		0			0
$793$	−29.6839			−1.05411
$794$		0			0
$795$	−0.756770	−	1.57098i	−0.0268399	−	0.0557170i
$796$		0			0
$797$	1.92561			0.0682086			0.0341043	−	0.999418i	$-0.489142\pi$
$797$	1.92561			0.0682086			0.0341043	+	0.999418i	$0.489142\pi$
$798$		0			0
$799$		−	4.75115i		−	0.168084i
$800$		0			0
$801$	18.2042	+	14.5105i	0.643215	+	0.512703i
$802$		0			0
$803$		−	23.5765i		−	0.831997i
$804$		0			0
$805$		−	32.3921i		−	1.14167i
$806$		0			0
$807$	−3.64609	−	7.56894i	−0.128349	−	0.266439i
$808$		0			0
$809$		−	30.3334i		−	1.06647i	−0.845968	−	0.533233i	$-0.820977\pi$
$809$		−	30.3334i		−	1.06647i	0.845968	−	0.533233i	$-0.179023\pi$
$810$		0			0
$811$	−7.56798			−0.265748			−0.132874	−	0.991133i	$-0.542421\pi$
$811$	−7.56798			−0.265748			−0.132874	+	0.991133i	$0.542421\pi$
$812$		0			0
$813$	−23.2196	+	11.1853i	−0.814345	+	0.392284i
$814$		0			0
$815$	6.96956			0.244133
$816$		0			0
$817$	−9.10212			−0.318443
$818$		0			0
$819$	21.7583	−	27.2971i	0.760297	−	0.953836i
$820$		0			0
$821$	28.8505			1.00689			0.503445	−	0.864027i	$-0.332066\pi$
$821$	28.8505			1.00689			0.503445	+	0.864027i	$0.332066\pi$
$822$		0			0
$823$			15.3789i			0.536076i	0.963408	+	0.268038i	$0.0863752\pi$
$823$			15.3789i			0.536076i	−0.963408	+	0.268038i	$0.913625\pi$
$824$		0			0
$825$	3.81797	−	1.83918i	0.132925	−	0.0640321i
$826$		0			0
$827$			48.0070i			1.66937i	0.550731	+	0.834683i	$0.314349\pi$
$827$			48.0070i			1.66937i	−0.550731	+	0.834683i	$0.685651\pi$
$828$		0			0
$829$			19.0600i			0.661982i	0.943634	+	0.330991i	$0.107383\pi$
$829$			19.0600i			0.661982i	−0.943634	+	0.330991i	$0.892617\pi$
$830$		0			0
$831$	30.7144	−	14.7956i	1.06547	−	0.513255i
$832$		0			0
$833$		−	13.2453i		−	0.458923i
$834$		0			0
$835$	−9.93540			−0.343829
$836$		0			0
$837$	0.542379	−	2.38013i	0.0187473	−	0.0822694i
$838$		0			0
$839$	56.8469			1.96257			0.981287	−	0.192552i	$-0.0616763\pi$
$839$	56.8469			1.96257			0.981287	+	0.192552i	$0.0616763\pi$
$840$		0			0
$841$	−28.4626			−0.981468
$842$		0			0
$843$	3.58645	−	1.72766i	0.123524	−	0.0595036i
$844$		0			0
$845$	−5.62917			−0.193649
$846$		0			0
$847$		−	21.4875i		−	0.738319i
$848$		0			0
$849$	−16.2457	−	33.7246i	−0.557551	−	1.15742i
$850$		0			0
$851$			10.3288i			0.354067i
$852$		0			0
$853$		−	29.3057i		−	1.00341i	−0.865039	−	0.501704i	$-0.832707\pi$
$853$		−	29.3057i		−	1.00341i	0.865039	−	0.501704i	$-0.167293\pi$
$854$		0			0
$855$	−11.3213	+	14.2033i	−0.387182	+	0.485742i
$856$		0			0
$857$			30.9833i			1.05837i	0.848507	+	0.529185i	$0.177502\pi$
$857$			30.9833i			1.05837i	−0.848507	+	0.529185i	$0.822498\pi$
$858$		0			0
$859$	1.13559			0.0387457			0.0193729	−	0.999812i	$-0.493833\pi$
$859$	1.13559			0.0387457			0.0193729	+	0.999812i	$0.493833\pi$
$860$		0			0
$861$	15.1156	+	31.3786i	0.515139	+	1.06938i
$862$		0			0
$863$	−12.8678			−0.438024			−0.219012	−	0.975722i	$-0.570283\pi$
$863$	−12.8678			−0.438024			−0.219012	+	0.975722i	$0.570283\pi$
$864$		0			0
$865$	−8.01352			−0.272468
$866$		0			0
$867$	−11.7584	−	24.4094i	−0.399338	−	0.828988i
$868$		0			0
$869$	−8.83701			−0.299775
$870$		0			0
$871$		−	27.0850i		−	0.917740i
$872$		0			0
$873$	−32.0050	+	40.1520i	−1.08320	+	1.35894i
$874$		0			0
$875$			4.28591i			0.144890i
$876$		0			0
$877$		−	35.8017i		−	1.20894i	−0.796629	−	0.604469i	$-0.793385\pi$
$877$		−	35.8017i		−	1.20894i	0.796629	−	0.604469i	$-0.206615\pi$
$878$		0			0
$879$	4.51014	+	9.36262i	0.152123	+	0.315793i
$880$		0			0
$881$			26.0081i			0.876234i	0.898918	+	0.438117i	$0.144354\pi$
$881$			26.0081i			0.876234i	−0.898918	+	0.438117i	$0.855646\pi$
$882$		0			0
$883$	−41.3226			−1.39062			−0.695308	−	0.718712i	$-0.744732\pi$
$883$	−41.3226			−1.39062			−0.695308	+	0.718712i	$0.744732\pi$
$884$		0			0
$885$	2.55106	−	1.22889i	0.0857529	−	0.0413087i
$886$		0			0
$887$	−14.9286			−0.501255			−0.250627	−	0.968084i	$-0.580637\pi$
$887$	−14.9286			−0.501255			−0.250627	+	0.968084i	$0.580637\pi$
$888$		0			0
$889$	−12.5904			−0.422268
$890$		0			0
$891$	21.4662	−	4.90999i	0.719144	−	0.164491i
$892$		0			0
$893$	24.6907			0.826242
$894$		0			0
$895$			23.5020i			0.785587i
$896$		0			0
$897$	32.0185	−	15.4239i	1.06907	−	0.514988i
$898$		0			0
$899$			0.344406i			0.0114866i
$900$		0			0
$901$		−	1.17291i		−	0.0390753i
$902$		0			0
$903$	−10.0544	+	4.84340i	−0.334591	+	0.161178i
$904$		0			0
$905$		−	9.92011i		−	0.329756i
$906$		0			0
$907$	39.4794			1.31089			0.655447	−	0.755241i	$-0.272480\pi$
$907$	39.4794			1.31089			0.655447	+	0.755241i	$0.272480\pi$
$908$		0			0
$909$	−10.0270	+	12.5795i	−0.332576	+	0.417235i
$910$		0			0
$911$	−47.8266			−1.58457			−0.792284	−	0.610153i	$-0.791108\pi$
$911$	−47.8266			−1.58457			−0.792284	+	0.610153i	$0.791108\pi$
$912$		0			0
$913$	13.3370			0.441390
$914$		0			0
$915$	17.0612	−	8.21868i	0.564026	−	0.271701i
$916$		0			0
$917$	33.7583			1.11480
$918$		0			0
$919$			30.2025i			0.996290i	0.867094	+	0.498145i	$0.165985\pi$
$919$			30.2025i			0.996290i	−0.867094	+	0.498145i	$0.834015\pi$
$920$		0			0
$921$	−3.74573	−	7.77578i	−0.123426	−	0.256221i
$922$		0			0
$923$		−	31.5907i		−	1.03982i
$924$		0			0
$925$		−	1.36664i		−	0.0449348i
$926$		0			0
$927$	30.7106	+	24.4793i	1.00867	+	0.804005i
$928$		0			0
$929$		−	2.81266i		−	0.0922804i	−0.998935	−	0.0461402i	$-0.985308\pi$
$929$		−	2.81266i		−	0.0922804i	0.998935	−	0.0461402i	$-0.0146921\pi$
$930$		0			0
$931$	68.8330			2.25591
$932$		0			0
$933$	−8.33518	−	17.3031i	−0.272882	−	0.566477i
$934$		0			0
$935$	2.85053			0.0932223
$936$		0			0
$937$	−20.7171			−0.676798			−0.338399	−	0.941003i	$-0.609885\pi$
$937$	−20.7171			−0.676798			−0.338399	+	0.941003i	$0.609885\pi$
$938$		0			0
$939$	−8.46278	−	17.5679i	−0.276172	−	0.573308i
$940$		0			0
$941$	−41.0867			−1.33939			−0.669695	−	0.742636i	$-0.733575\pi$
$941$	−41.0867			−1.33939			−0.669695	+	0.742636i	$0.733575\pi$
$942$		0			0
$943$			35.4602i			1.15474i
$944$		0			0
$945$	−4.94804	+	21.7136i	−0.160960	+	0.706344i
$946$		0			0
$947$			12.3990i			0.402913i	0.979497	+	0.201456i	$0.0645674\pi$
$947$			12.3990i			0.402913i	−0.979497	+	0.201456i	$0.935433\pi$
$948$		0			0
$949$			26.1608i			0.849217i
$950$		0			0
$951$	20.4542	+	42.4610i	0.663274	+	1.37689i
$952$		0			0
$953$		−	24.4649i		−	0.792496i	−0.918144	−	0.396248i	$-0.870312\pi$
$953$		−	24.4649i		−	0.792496i	0.918144	−	0.396248i	$-0.129688\pi$
$954$		0			0
$955$	22.4865			0.727645
$956$		0			0
$957$	−2.79892	+	1.34829i	−0.0904762	+	0.0435840i
$958$		0			0
$959$	10.7719			0.347842
$960$		0			0
$961$	30.7793			0.992880
$962$		0			0
$963$	20.7057	+	16.5044i	0.667232	+	0.531846i
$964$		0			0
$965$	13.1156			0.422207
$966$		0			0
$967$		−	3.64391i		−	0.117180i	−0.998282	−	0.0585901i	$-0.981340\pi$
$967$		−	3.64391i		−	0.117180i	0.998282	−	0.0585901i	$-0.0186605\pi$
$968$		0			0
$969$	−11.0068	+	5.30215i	−0.353588	+	0.170330i
$970$		0			0
$971$		−	27.1170i		−	0.870225i	−0.900376	−	0.435113i	$-0.856709\pi$
$971$		−	27.1170i		−	0.870225i	0.900376	−	0.435113i	$-0.143291\pi$
$972$		0			0
$973$			11.0351i			0.353769i
$974$		0			0
$975$	−4.23647	+	2.04078i	−0.135676	+	0.0653573i
$976$		0			0
$977$		−	41.8998i		−	1.34049i	−0.742139	−	0.670246i	$-0.766188\pi$
$977$		−	41.8998i		−	1.34049i	0.742139	−	0.670246i	$-0.233812\pi$
$978$		0			0
$979$	18.9864			0.606809
$980$		0			0
$981$	−1.83025	−	1.45888i	−0.0584355	−	0.0465786i
$982$		0			0
$983$	−0.734322			−0.0234212			−0.0117106	−	0.999931i	$-0.503728\pi$
$983$	−0.734322			−0.0234212			−0.0117106	+	0.999931i	$0.503728\pi$
$984$		0			0
$985$	24.2786			0.773581
$986$		0			0
$987$	27.2740	−	13.1384i	0.868141	−	0.418199i
$988$		0			0
$989$	−11.3623			−0.361299
$990$		0			0
$991$			25.5433i			0.811408i	0.914004	+	0.405704i	$0.132974\pi$
$991$			25.5433i			0.811408i	−0.914004	+	0.405704i	$0.867026\pi$
$992$		0			0
$993$	−13.7706	−	28.5865i	−0.436997	−	0.907165i
$994$		0			0
$995$			1.81809i			0.0576373i
$996$		0			0
$997$		−	23.4092i		−	0.741378i	−0.928757	−	0.370689i	$-0.879122\pi$
$997$		−	23.4092i		−	0.741378i	0.928757	−	0.370689i	$-0.120878\pi$
$998$		0			0
$999$	1.57777	−	6.92377i	0.0499184	−	0.219058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	480.2.b.a.431.3		8
3.2	odd	2		480.2.b.b.431.4		8
4.3	odd	2		120.2.b.b.11.4	yes	8
5.2	odd	4		2400.2.m.c.1199.4		16
5.3	odd	4		2400.2.m.c.1199.13		16
5.4	even	2		2400.2.b.e.2351.6		8
8.3	odd	2		480.2.b.b.431.3		8
8.5	even	2		120.2.b.a.11.6	yes	8
12.11	even	2		120.2.b.a.11.5	✓	8
15.2	even	4		2400.2.m.d.1199.14		16
15.8	even	4		2400.2.m.d.1199.3		16
15.14	odd	2		2400.2.b.f.2351.5		8
20.3	even	4		600.2.m.d.299.16		16
20.7	even	4		600.2.m.d.299.1		16
20.19	odd	2		600.2.b.e.251.5		8
24.5	odd	2		120.2.b.b.11.3	yes	8
24.11	even	2	inner	480.2.b.a.431.4		8
40.3	even	4		2400.2.m.d.1199.13		16
40.13	odd	4		600.2.m.c.299.15		16
40.19	odd	2		2400.2.b.f.2351.6		8
40.27	even	4		2400.2.m.d.1199.4		16
40.29	even	2		600.2.b.f.251.3		8
40.37	odd	4		600.2.m.c.299.2		16
60.23	odd	4		600.2.m.c.299.1		16
60.47	odd	4		600.2.m.c.299.16		16
60.59	even	2		600.2.b.f.251.4		8
120.29	odd	2		600.2.b.e.251.6		8
120.53	even	4		600.2.m.d.299.2		16
120.59	even	2		2400.2.b.e.2351.5		8
120.77	even	4		600.2.m.d.299.15		16
120.83	odd	4		2400.2.m.c.1199.3		16
120.107	odd	4		2400.2.m.c.1199.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.5	✓	8	12.11	even	2
120.2.b.a.11.6	yes	8	8.5	even	2
120.2.b.b.11.3	yes	8	24.5	odd	2
120.2.b.b.11.4	yes	8	4.3	odd	2
480.2.b.a.431.3		8	1.1	even	1	trivial
480.2.b.a.431.4		8	24.11	even	2	inner
480.2.b.b.431.3		8	8.3	odd	2
480.2.b.b.431.4		8	3.2	odd	2
600.2.b.e.251.5		8	20.19	odd	2
600.2.b.e.251.6		8	120.29	odd	2
600.2.b.f.251.3		8	40.29	even	2
600.2.b.f.251.4		8	60.59	even	2
600.2.m.c.299.1		16	60.23	odd	4
600.2.m.c.299.2		16	40.37	odd	4
600.2.m.c.299.15		16	40.13	odd	4
600.2.m.c.299.16		16	60.47	odd	4
600.2.m.d.299.1		16	20.7	even	4
600.2.m.d.299.2		16	120.53	even	4
600.2.m.d.299.15		16	120.77	even	4
600.2.m.d.299.16		16	20.3	even	4
2400.2.b.e.2351.5		8	120.59	even	2
2400.2.b.e.2351.6		8	5.4	even	2
2400.2.b.f.2351.5		8	15.14	odd	2
2400.2.b.f.2351.6		8	40.19	odd	2
2400.2.m.c.1199.3		16	120.83	odd	4
2400.2.m.c.1199.4		16	5.2	odd	4
2400.2.m.c.1199.13		16	5.3	odd	4
2400.2.m.c.1199.14		16	120.107	odd	4
2400.2.m.d.1199.3		16	15.8	even	4
2400.2.m.d.1199.4		16	40.27	even	4
2400.2.m.d.1199.13		16	40.3	even	4
2400.2.m.d.1199.14		16	15.2	even	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:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.751690 - 1.56044i) q^{3} -1.00000 q^{5} -4.28591i q^{7} +(-1.86993 + 2.34593i) q^{9} +O(q^{10})\)	\(q+(-0.751690 - 1.56044i) q^{3} -1.00000 q^{5} -4.28591i q^{7} +(-1.86993 + 2.34593i) q^{9} +2.44673i q^{11} -2.71493i q^{13} +(0.751690 + 1.56044i) q^{15} +1.16504i q^{17} -6.05444 q^{19} +(-6.68789 + 3.22167i) q^{21} -7.55782 q^{23} +1.00000 q^{25} +(5.06628 + 1.15449i) q^{27} -0.733092 q^{29} -0.469799i q^{31} +(3.81797 - 1.83918i) q^{33} +4.28591i q^{35} -1.36664i q^{37} +(-4.23647 + 2.04078i) q^{39} -4.69186i q^{41} +1.50338 q^{43} +(1.86993 - 2.34593i) q^{45} -4.07812 q^{47} -11.3690 q^{49} +(1.81797 - 0.875746i) q^{51} -1.00676 q^{53} -2.44673i q^{55} +(4.55106 + 9.44757i) q^{57} -1.63484i q^{59} -10.9336i q^{61} +(10.0544 + 8.01433i) q^{63} +2.71493i q^{65} +9.97632 q^{67} +(5.68113 + 11.7935i) q^{69} +11.6359 q^{71} -9.63593 q^{73} +(-0.751690 - 1.56044i) q^{75} +10.4865 q^{77} +3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} -5.45095i q^{83} -1.16504i q^{85} +(0.551058 + 1.14394i) q^{87} -7.75993i q^{89} -11.6359 q^{91} +(-0.733092 + 0.353143i) q^{93} +6.05444 q^{95} +17.1156 q^{97} +(-5.73985 - 4.57520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{5}+O(q^{10}) \) 8 * q - 8 * q^5	\( 8 q - 8 q^{5} + 4 q^{19} - 4 q^{21} + 4 q^{23} + 8 q^{25} + 12 q^{27} - 4 q^{33} - 16 q^{39} - 28 q^{47} - 16 q^{49} - 20 q^{51} + 16 q^{53} - 4 q^{57} + 28 q^{63} + 32 q^{67} + 20 q^{69} + 24 q^{71} - 8 q^{73} + 8 q^{81} - 36 q^{87} - 24 q^{91} - 4 q^{95} + 8 q^{97} - 16 q^{99}+O(q^{100}) \) 8 * q - 8 * q^5 + 4 * q^19 - 4 * q^21 + 4 * q^23 + 8 * q^25 + 12 * q^27 - 4 * q^33 - 16 * q^39 - 28 * q^47 - 16 * q^49 - 20 * q^51 + 16 * q^53 - 4 * q^57 + 28 * q^63 + 32 * q^67 + 20 * q^69 + 24 * q^71 - 8 * q^73 + 8 * q^81 - 36 * q^87 - 24 * q^91 - 4 * q^95 + 8 * q^97 - 16 * q^99

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