LMFDB - Embedded newform 1044.2.z.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1044,2,Mod(109,1044)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1044, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

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

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

chi := DirichletCharacter("1044.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1044 = 2^{2} \cdot 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1044.z (of order $14$, degree $6$, 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:	$8.33638197102$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			361.1
Character	$\chi$	$=$	1044.361
Dual form			1044.2.z.c.937.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.10154 - 1.01205i) q^{5} +(-2.51961 + 3.15949i) q^{7} +O(q^{10})$	$q+(-2.10154 - 1.01205i) q^{5} +(-2.51961 + 3.15949i) q^{7} +(1.80218 + 0.411337i) q^{11} +(0.177678 - 0.778456i) q^{13} -6.12795i q^{17} +(0.496881 - 0.396249i) q^{19} +(5.06999 - 2.44158i) q^{23} +(0.274787 + 0.344572i) q^{25} +(5.15591 + 1.55453i) q^{29} +(-0.776281 + 1.61196i) q^{31} +(8.49262 - 4.08983i) q^{35} +(6.78673 - 1.54903i) q^{37} -10.0006i q^{41} +(-1.73210 - 3.59675i) q^{43} +(7.60533 + 1.73587i) q^{47} +(-2.07630 - 9.09685i) q^{49} +(-7.82784 - 3.76969i) q^{53} +(-3.37107 - 2.68834i) q^{55} -0.770551 q^{59} +(-2.48461 - 1.98141i) q^{61} +(-1.16123 + 1.45614i) q^{65} +(-0.719935 - 3.15424i) q^{67} +(2.20838 - 9.67555i) q^{71} +(5.21215 + 10.8231i) q^{73} +(-5.84041 + 4.65757i) q^{77} +(8.51225 - 1.94287i) q^{79} +(-4.83430 - 6.06201i) q^{83} +(-6.20179 + 12.8781i) q^{85} +(0.850890 - 1.76689i) q^{89} +(2.01185 + 2.52277i) q^{91} +(-1.44524 + 0.329867i) q^{95} +(-4.74439 + 3.78352i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) $ 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1044\mathbb{Z}\right)^\times$.

$n$	$523$	$901$	$929$
$\chi(n)$	$1$	$e\left(\frac{9}{14}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	−2.10154	−	1.01205i	−0.939838	−	0.452602i	−0.0997261	−	0.995015i	$-0.531797\pi$
$5$	−2.10154	−	1.01205i	−0.939838	−	0.452602i	−0.840112	+	0.542413i	$0.817511\pi$
$6$		0			0
$7$	−2.51961	+	3.15949i	−0.952322	+	1.19417i	0.0285637	+	0.999592i	$0.490907\pi$
$7$	−2.51961	+	3.15949i	−0.952322	+	1.19417i	−0.980886	+	0.194583i	$0.937665\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.80218	+	0.411337i	0.543379	+	0.124023i	0.485395	−	0.874295i	$-0.338676\pi$
$11$	1.80218	+	0.411337i	0.543379	+	0.124023i	0.0579838	+	0.998318i	$0.481533\pi$
$12$		0			0
$13$	0.177678	−	0.778456i	0.0492789	−	0.215905i	−0.944293	−	0.329105i	$-0.893253\pi$
$13$	0.177678	−	0.778456i	0.0492789	−	0.215905i	0.993572	+	0.113200i	$0.0361101\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	6.12795i		−	1.48625i	−0.669155	−	0.743123i	$-0.733344\pi$
$17$		−	6.12795i		−	1.48625i	0.669155	−	0.743123i	$-0.266656\pi$
$18$		0			0
$19$	0.496881	−	0.396249i	0.113992	−	0.0909058i	−0.564835	−	0.825204i	$-0.691060\pi$
$19$	0.496881	−	0.396249i	0.113992	−	0.0909058i	0.678827	+	0.734298i	$0.262489\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.06999	−	2.44158i	1.05717	−	0.509105i	0.177217	−	0.984172i	$-0.443290\pi$
$23$	5.06999	−	2.44158i	1.05717	−	0.509105i	0.879950	+	0.475067i	$0.157576\pi$
$24$		0			0
$25$	0.274787	+	0.344572i	0.0549575	+	0.0689145i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.15591	+	1.55453i	0.957429	+	0.288669i
$29$	5.15591	+	1.55453i	0.957429	+	0.288669i
$30$		0			0
$31$	−0.776281	+	1.61196i	−0.139424	+	0.289517i	−0.958976	−	0.283488i	$-0.908508\pi$
$31$	−0.776281	+	1.61196i	−0.139424	+	0.289517i	0.819552	+	0.573005i	$0.194223\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	8.49262	−	4.08983i	1.43552	−	0.691308i
$36$		0			0
$37$	6.78673	−	1.54903i	1.11573	−	0.254658i	0.375375	−	0.926873i	$-0.377514\pi$
$37$	6.78673	−	1.54903i	1.11573	−	0.254658i	0.740356	+	0.672215i	$0.234657\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	10.0006i		−	1.56183i	−0.624639	−	0.780914i	$-0.714754\pi$
$41$		−	10.0006i		−	1.56183i	0.624639	−	0.780914i	$-0.285246\pi$
$42$		0			0
$43$	−1.73210	−	3.59675i	−0.264143	−	0.548499i	0.726143	−	0.687544i	$-0.241311\pi$
$43$	−1.73210	−	3.59675i	−0.264143	−	0.548499i	−0.990286	+	0.139045i	$0.955597\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.60533	+	1.73587i	1.10935	+	0.253202i	0.737672	−	0.675159i	$-0.235925\pi$
$47$	7.60533	+	1.73587i	1.10935	+	0.253202i	0.371679	+	0.928361i	$0.378782\pi$
$48$		0			0
$49$	−2.07630	−	9.09685i	−0.296614	−	1.29955i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−7.82784	−	3.76969i	−1.07524	−	0.517807i	−0.189446	−	0.981891i	$-0.560669\pi$
$53$	−7.82784	−	3.76969i	−1.07524	−	0.517807i	−0.885791	+	0.464085i	$0.846383\pi$
$54$		0			0
$55$	−3.37107	−	2.68834i	−0.454555	−	0.362496i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.770551			−0.100317			−0.0501586	−	0.998741i	$-0.515973\pi$
$59$	−0.770551			−0.100317			−0.0501586	+	0.998741i	$0.515973\pi$
$60$		0			0
$61$	−2.48461	−	1.98141i	−0.318121	−	0.253693i	0.451390	−	0.892327i	$-0.350929\pi$
$61$	−2.48461	−	1.98141i	−0.318121	−	0.253693i	−0.769511	+	0.638634i	$0.779500\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.16123	+	1.45614i	−0.144033	+	0.180612i
$66$		0			0
$67$	−0.719935	−	3.15424i	−0.0879540	−	0.385352i	0.911722	−	0.410808i	$-0.134753\pi$
$67$	−0.719935	−	3.15424i	−0.0879540	−	0.385352i	−0.999676	+	0.0254561i	$0.991896\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.20838	−	9.67555i	0.262087	−	1.14828i	−0.656897	−	0.753981i	$-0.728131\pi$
$71$	2.20838	−	9.67555i	0.262087	−	1.14828i	0.918983	−	0.394296i	$-0.129012\pi$
$72$		0			0
$73$	5.21215	+	10.8231i	0.610036	+	1.26675i	0.945783	+	0.324800i	$0.105297\pi$
$73$	5.21215	+	10.8231i	0.610036	+	1.26675i	−0.335747	+	0.941952i	$0.608989\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.84041	+	4.65757i	−0.665577	+	0.530780i
$78$		0			0
$79$	8.51225	−	1.94287i	0.957703	−	0.218589i	0.285021	−	0.958521i	$-0.407999\pi$
$79$	8.51225	−	1.94287i	0.957703	−	0.218589i	0.672682	+	0.739932i	$0.265142\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.83430	−	6.06201i	−0.530633	−	0.665393i	0.442196	−	0.896918i	$-0.354200\pi$
$83$	−4.83430	−	6.06201i	−0.530633	−	0.665393i	−0.972829	+	0.231526i	$0.925628\pi$
$84$		0			0
$85$	−6.20179	+	12.8781i	−0.672678	+	1.39683i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.850890	−	1.76689i	0.0901942	−	0.187290i	−0.850992	−	0.525179i	$-0.823998\pi$
$89$	0.850890	−	1.76689i	0.0901942	−	0.187290i	0.941186	+	0.337889i	$0.109713\pi$
$90$		0			0
$91$	2.01185	+	2.52277i	0.210899	+	0.264459i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.44524	+	0.329867i	−0.148278	+	0.0338436i
$96$		0			0
$97$	−4.74439	+	3.78352i	−0.481720	+	0.384159i	−0.834025	−	0.551727i	$-0.813969\pi$
$97$	−4.74439	+	3.78352i	−0.481720	+	0.384159i	0.352306	+	0.935885i	$0.385398\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.48957	+	9.32269i	0.446729	+	0.927642i	0.995773	+	0.0918488i	$0.0292777\pi$
$101$	4.48957	+	9.32269i	0.446729	+	0.927642i	−0.549044	+	0.835793i	$0.685008\pi$
$102$		0			0
$103$	−2.93819	+	12.8730i	−0.289508	+	1.26842i	0.595694	+	0.803211i	$0.296877\pi$
$103$	−2.93819	+	12.8730i	−0.289508	+	1.26842i	−0.885202	+	0.465206i	$0.845980\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.07198	−	4.69664i	−0.103632	−	0.454041i	−0.999944	−	0.0106168i	$-0.996621\pi$
$107$	−1.07198	−	4.69664i	−0.103632	−	0.454041i	0.896312	−	0.443425i	$-0.146237\pi$
$108$		0			0
$109$	8.66850	−	10.8700i	0.830292	−	1.04115i	−0.168172	−	0.985758i	$-0.553787\pi$
$109$	8.66850	−	10.8700i	0.830292	−	1.04115i	0.998464	−	0.0553958i	$-0.0176420\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.95721	−	7.94061i	−0.936696	−	0.746990i	0.0308926	−	0.999523i	$-0.490165\pi$
$113$	−9.95721	−	7.94061i	−0.936696	−	0.746990i	−0.967588	+	0.252533i	$0.918736\pi$
$114$		0			0
$115$	−13.1258			−1.22399
$116$		0			0
$117$		0			0
$118$		0			0
$119$	19.3612	+	15.4400i	1.77484	+	1.41539i
$120$		0			0
$121$	−6.83199	−	3.29011i	−0.621090	−	0.299101i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.36644	+	10.3680i	0.211661	+	0.927346i
$126$		0			0
$127$	18.3267	+	4.18294i	1.62623	+	0.371176i	0.935885	−	0.352306i	$-0.114602\pi$
$127$	18.3267	+	4.18294i	1.62623	+	0.371176i	0.690343	+	0.723482i	$0.257459\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.19081	−	10.7788i	−0.453523	−	0.941751i	−0.994890	−	0.100964i	$-0.967807\pi$
$131$	−5.19081	−	10.7788i	−0.453523	−	0.941751i	0.541367	−	0.840787i	$-0.317907\pi$
$132$		0			0
$133$			2.56828i			0.222698i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.25623	−	2.11267i	0.790813	−	0.180498i	0.192009	−	0.981393i	$-0.438500\pi$
$137$	9.25623	−	2.11267i	0.790813	−	0.180498i	0.598804	+	0.800895i	$0.295643\pi$
$138$		0			0
$139$	−11.1209	+	5.35553i	−0.943260	+	0.454250i	−0.841318	−	0.540540i	$-0.818220\pi$
$139$	−11.1209	+	5.35553i	−0.943260	+	0.454250i	−0.101942	+	0.994790i	$0.532506\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.640415	−	1.32984i	0.0535542	−	0.111206i
$144$		0			0
$145$	−9.26210	−	8.48495i	−0.769176	−	0.704637i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.96429	+	4.97107i	0.324768	+	0.407246i	0.917234	−	0.398350i	$-0.130417\pi$
$149$	3.96429	+	4.97107i	0.324768	+	0.407246i	−0.592466	+	0.805595i	$0.701846\pi$
$150$		0			0
$151$	21.0814	−	10.1523i	1.71558	−	0.826180i	0.725081	−	0.688664i	$-0.241802\pi$
$151$	21.0814	−	10.1523i	1.71558	−	0.826180i	0.990499	−	0.137516i	$-0.0439120\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.26278	−	2.60198i	0.262072	−	0.208996i
$156$		0			0
$157$		−	9.48242i		−	0.756780i	−0.925646	−	0.378390i	$-0.876478\pi$
$157$		−	9.48242i		−	0.756780i	0.925646	−	0.378390i	$-0.123522\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.06025	+	22.1704i	−0.398804	+	1.74727i
$162$		0			0
$163$	−10.8495	−	2.47632i	−0.849796	−	0.193960i	−0.224622	−	0.974446i	$-0.572115\pi$
$163$	−10.8495	−	2.47632i	−0.849796	−	0.193960i	−0.625174	+	0.780485i	$0.714972\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.38553	+	5.49927i	−0.339362	+	0.425547i	−0.922003	−	0.387183i	$-0.873448\pi$
$167$	−4.38553	+	5.49927i	−0.339362	+	0.425547i	0.582641	+	0.812730i	$0.302020\pi$
$168$		0			0
$169$	11.1382	+	5.36386i	0.856782	+	0.412605i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−22.7743			−1.73150			−0.865748	−	0.500480i	$-0.833157\pi$
$173$	−22.7743			−1.73150			−0.865748	+	0.500480i	$0.833157\pi$
$174$		0			0
$175$	−1.78103			−0.134633
$176$		0			0
$177$		0			0
$178$		0			0
$179$	16.7988	+	8.08988i	1.25560	+	0.604666i	0.939008	−	0.343896i	$-0.111747\pi$
$179$	16.7988	+	8.08988i	1.25560	+	0.604666i	0.316593	+	0.948561i	$0.397461\pi$
$180$		0			0
$181$	−7.11504	+	8.92198i	−0.528857	+	0.663165i	−0.972463	−	0.233056i	$-0.925127\pi$
$181$	−7.11504	+	8.92198i	−0.528857	+	0.663165i	0.443607	+	0.896222i	$0.353699\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−15.8303	−	3.61316i	−1.16387	−	0.265645i
$186$		0			0
$187$	2.52065	−	11.0437i	0.184328	−	0.807595i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	0.431460i		−	0.0312193i	−0.999878	−	0.0156097i	$-0.995031\pi$
$191$		−	0.431460i		−	0.0312193i	0.999878	−	0.0156097i	$-0.00496891\pi$
$192$		0			0
$193$	3.83179	−	3.05575i	0.275818	−	0.219958i	−0.475804	−	0.879551i	$-0.657843\pi$
$193$	3.83179	−	3.05575i	0.275818	−	0.219958i	0.751623	+	0.659593i	$0.229272\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.4979	+	6.98182i	−1.03293	+	0.497434i	−0.871987	−	0.489529i	$-0.837169\pi$
$197$	−14.4979	+	6.98182i	−1.03293	+	0.497434i	−0.160945	+	0.986963i	$0.551454\pi$
$198$		0			0
$199$	2.26603	+	2.84152i	0.160635	+	0.201430i	0.855635	−	0.517580i	$-0.173167\pi$
$199$	2.26603	+	2.84152i	0.160635	+	0.201430i	−0.695000	+	0.719010i	$0.744596\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−17.9024	+	12.3732i	−1.25650	+	0.868431i
$204$		0			0
$205$	−10.1211	+	21.0166i	−0.706887	+	1.46787i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.05846	−	0.509729i	0.0732154	−	0.0352587i
$210$		0			0
$211$	27.4264	−	6.25991i	1.88811	−	0.430950i	0.888504	−	0.458870i	$-0.151746\pi$
$211$	27.4264	−	6.25991i	1.88811	−	0.430950i	0.999610	+	0.0279201i	$0.00888838\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			9.31169i			0.635052i
$216$		0			0
$217$	−3.13706	−	6.51417i	−0.212957	−	0.442211i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.77034	−	1.08880i	−0.320888	−	0.0732405i
$222$		0			0
$223$	−4.86527	−	21.3162i	−0.325803	−	1.42744i	−0.827049	−	0.562130i	$-0.809982\pi$
$223$	−4.86527	−	21.3162i	−0.325803	−	1.42744i	0.501246	−	0.865305i	$-0.332875\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.06138	+	0.992706i	0.136818	+	0.0658882i	0.501040	−	0.865424i	$-0.332951\pi$
$227$	2.06138	+	0.992706i	0.136818	+	0.0658882i	−0.364222	+	0.931312i	$0.618665\pi$
$228$		0			0
$229$	−7.31496	−	5.83349i	−0.483386	−	0.385488i	0.351256	−	0.936279i	$-0.385755\pi$
$229$	−7.31496	−	5.83349i	−0.483386	−	0.385488i	−0.834643	+	0.550791i	$0.814326\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.7560			−1.22874			−0.614372	−	0.789017i	$-0.710590\pi$
$233$	−18.7560			−1.22874			−0.614372	+	0.789017i	$0.710590\pi$
$234$		0			0
$235$	−14.2261	−	11.3450i	−0.928011	−	0.740064i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−15.2672	+	19.1444i	−0.987552	+	1.23835i	−0.0164058	+	0.999865i	$0.505222\pi$
$239$	−15.2672	+	19.1444i	−0.987552	+	1.23835i	−0.971146	+	0.238485i	$0.923349\pi$
$240$		0			0
$241$	−1.09596	−	4.80171i	−0.0705969	−	0.309305i	0.927285	−	0.374356i	$-0.122136\pi$
$241$	−1.09596	−	4.80171i	−0.0705969	−	0.309305i	−0.997882	+	0.0650508i	$0.979279\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.84304	+	21.2187i	−0.309410	+	1.35562i
$246$		0			0
$247$	−0.220178	−	0.457204i	−0.0140096	−	0.0290912i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.85006	−	1.47537i	0.116774	−	0.0931245i	−0.563362	−	0.826211i	$-0.690492\pi$
$251$	1.85006	−	1.47537i	0.116774	−	0.0931245i	0.680136	+	0.733086i	$0.261921\pi$
$252$		0			0
$253$	10.1414	−	2.31470i	0.637583	−	0.145524i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.73307	−	5.93508i	−0.295241	−	0.370220i	0.611981	−	0.790872i	$-0.290373\pi$
$257$	−4.73307	−	5.93508i	−0.295241	−	0.370220i	−0.907222	+	0.420652i	$0.861801\pi$
$258$		0			0
$259$	−12.2058	+	25.3455i	−0.758429	+	1.57490i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.89058	−	6.00236i	0.178241	−	0.370121i	−0.792638	−	0.609693i	$-0.791293\pi$
$263$	2.89058	−	6.00236i	0.178241	−	0.370121i	0.970879	+	0.239572i	$0.0770070\pi$
$264$		0			0
$265$	12.6354	+	15.8443i	0.776188	+	0.973309i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.20629	+	2.10128i	−0.561317	+	0.128117i	−0.493760	−	0.869598i	$-0.664378\pi$
$269$	−9.20629	+	2.10128i	−0.561317	+	0.128117i	−0.0675575	+	0.997715i	$0.521521\pi$
$270$		0			0
$271$	−8.13602	+	6.48826i	−0.494228	+	0.394134i	−0.838641	−	0.544685i	$-0.816649\pi$
$271$	−8.13602	+	6.48826i	−0.494228	+	0.394134i	0.344413	+	0.938818i	$0.388078\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.353482	+	0.734013i	0.0213158	+	0.0442627i
$276$		0			0
$277$	−1.08942	+	4.77306i	−0.0654569	+	0.286785i	−0.997054	−	0.0767082i	$-0.975559\pi$
$277$	−1.08942	+	4.77306i	−0.0654569	+	0.286785i	0.931597	+	0.363494i	$0.118416\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.144212	+	0.631832i	0.00860294	+	0.0376919i	0.979047	−	0.203633i	$-0.0652751\pi$
$281$	0.144212	+	0.631832i	0.00860294	+	0.0376919i	−0.970444	+	0.241325i	$0.922418\pi$
$282$		0			0
$283$	9.02782	−	11.3205i	0.536648	−	0.672935i	−0.437402	−	0.899266i	$-0.644101\pi$
$283$	9.02782	−	11.3205i	0.536648	−	0.672935i	0.974051	+	0.226330i	$0.0726729\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	31.5967	+	25.1975i	1.86510	+	1.48736i
$288$		0			0
$289$	−20.5518			−1.20893
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−8.48446	−	6.76613i	−0.495667	−	0.395281i	0.343502	−	0.939152i	$-0.388387\pi$
$293$	−8.48446	−	6.76613i	−0.495667	−	0.395281i	−0.839169	+	0.543871i	$0.816958\pi$
$294$		0			0
$295$	1.61934	+	0.779835i	0.0942819	+	0.0454038i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.999839	−	4.38058i	−0.0578222	−	0.253336i
$300$		0			0
$301$	15.7281	+	3.58984i	0.906553	+	0.206915i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.21622	+	6.67856i	0.184160	+	0.382413i
$306$		0			0
$307$			17.5893i			1.00387i	0.864904	+	0.501937i	$0.167379\pi$
$307$			17.5893i			1.00387i	−0.864904	+	0.501937i	$0.832621\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	29.6848	−	6.77536i	1.68327	−	0.384195i	0.729323	−	0.684170i	$-0.239835\pi$
$311$	29.6848	−	6.77536i	1.68327	−	0.384195i	0.953947	+	0.299975i	$0.0969782\pi$
$312$		0			0
$313$	12.5545	−	6.04593i	0.709623	−	0.341736i	−0.0440109	−	0.999031i	$-0.514014\pi$
$313$	12.5545	−	6.04593i	0.709623	−	0.341736i	0.753634	+	0.657295i	$0.228299\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.7913	−	24.4848i	0.662263	−	1.37520i	−0.251061	−	0.967971i	$-0.580780\pi$
$317$	11.7913	−	24.4848i	0.662263	−	1.37520i	0.913325	−	0.407232i	$-0.133506\pi$
$318$		0			0
$319$	8.65247	+	4.92237i	0.484445	+	0.275600i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−2.42819	−	3.04486i	−0.135108	−	0.169421i
$324$		0			0
$325$	0.317058	−	0.152687i	0.0175872	−	0.00846956i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−24.6469	+	19.6552i	−1.35883	+	1.08363i
$330$		0			0
$331$			6.18522i			0.339970i	0.985447	+	0.169985i	$0.0543720\pi$
$331$			6.18522i			0.339970i	−0.985447	+	0.169985i	$0.945628\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.67927	+	7.35738i	−0.0917485	+	0.401977i
$336$		0			0
$337$	−7.58050	−	1.73020i	−0.412936	−	0.0942500i	0.0110055	−	0.999939i	$-0.496497\pi$
$337$	−7.58050	−	1.73020i	−0.412936	−	0.0942500i	−0.423942	+	0.905689i	$0.639354\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.06206	+	2.58574i	−0.111667	+	0.140026i
$342$		0			0
$343$	8.48629	+	4.08678i	0.458217	+	0.220665i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−24.6006			−1.32063			−0.660316	−	0.750988i	$-0.729578\pi$
$347$	−24.6006			−1.32063			−0.660316	+	0.750988i	$0.729578\pi$
$348$		0			0
$349$	5.10179			0.273092			0.136546	−	0.990634i	$-0.456400\pi$
$349$	5.10179			0.273092			0.136546	+	0.990634i	$0.456400\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	20.3269	+	9.78893i	1.08189	+	0.521012i	0.887922	−	0.459995i	$-0.152149\pi$
$353$	20.3269	+	9.78893i	1.08189	+	0.521012i	0.193972	+	0.981007i	$0.437863\pi$
$354$		0			0
$355$	−14.4331	+	18.0986i	−0.766032	+	0.960574i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	31.3875	+	7.16399i	1.65657	+	0.378101i	0.945653	−	0.325177i	$-0.105424\pi$
$359$	31.3875	+	7.16399i	1.65657	+	0.378101i	0.710915	+	0.703278i	$0.248281\pi$
$360$		0			0
$361$	−4.13802	+	18.1299i	−0.217791	+	0.954203i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	28.0202i		−	1.46665i
$366$		0			0
$367$	−19.1871	+	15.3012i	−1.00156	+	0.798716i	−0.979583	−	0.201042i	$-0.935567\pi$
$367$	−19.1871	+	15.3012i	−1.00156	+	0.798716i	−0.0219761	+	0.999758i	$0.506996\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	31.6334	−	15.2338i	1.64232	−	0.790901i
$372$		0			0
$373$	−23.1575	−	29.0385i	−1.19905	−	1.50356i	−0.814205	−	0.580577i	$-0.802827\pi$
$373$	−23.1575	−	29.0385i	−1.19905	−	1.50356i	−0.384843	−	0.922982i	$-0.625744\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.12622	−	3.73745i	0.109506	−	0.192488i
$378$		0			0
$379$	5.27182	−	10.9470i	0.270795	−	0.562312i	−0.720579	−	0.693373i	$-0.756124\pi$
$379$	5.27182	−	10.9470i	0.270795	−	0.562312i	0.991374	+	0.131061i	$0.0418382\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−24.3079	+	11.7060i	−1.24207	+	0.598151i	−0.935376	−	0.353656i	$-0.884938\pi$
$383$	−24.3079	+	11.7060i	−1.24207	+	0.598151i	−0.306698	+	0.951807i	$0.599224\pi$
$384$		0			0
$385$	16.9876	−	3.87730i	0.865767	−	0.197606i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	5.24356i		−	0.265859i	−0.991125	−	0.132930i	$-0.957562\pi$
$389$		−	5.24356i		−	0.265859i	0.991125	−	0.132930i	$-0.0424384\pi$
$390$		0			0
$391$	−14.9619	−	31.0687i	−0.756655	−	1.57121i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−19.8551	−	4.53180i	−0.999020	−	0.228020i
$396$		0			0
$397$	−7.05702	−	30.9188i	−0.354182	−	1.55177i	−0.767417	−	0.641148i	$-0.778459\pi$
$397$	−7.05702	−	30.9188i	−0.354182	−	1.55177i	0.413235	−	0.910624i	$-0.364399\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−12.9425	−	6.23279i	−0.646318	−	0.311250i	0.0818543	−	0.996644i	$-0.473916\pi$
$401$	−12.9425	−	6.23279i	−0.646318	−	0.311250i	−0.728173	+	0.685394i	$0.759630\pi$
$402$		0			0
$403$	1.11692	+	0.890711i	0.0556375	+	0.0443695i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.8681			0.637849
$408$		0			0
$409$	16.6203	+	13.2543i	0.821823	+	0.655382i	0.941344	−	0.337450i	$-0.109564\pi$
$409$	16.6203	+	13.2543i	0.821823	+	0.655382i	−0.119520	+	0.992832i	$0.538136\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.94149	−	2.43455i	0.0955343	−	0.119796i
$414$		0			0
$415$	4.02442	+	17.6321i	0.197551	+	0.865527i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	4.27476	−	18.7290i	0.208836	−	0.914969i	−0.756507	−	0.653985i	$-0.773096\pi$
$419$	4.27476	−	18.7290i	0.208836	−	0.914969i	0.965343	−	0.260984i	$-0.0840470\pi$
$420$		0			0
$421$	−1.24866	−	2.59286i	−0.0608558	−	0.126368i	0.868323	−	0.496000i	$-0.165198\pi$
$421$	−1.24866	−	2.59286i	−0.0608558	−	0.126368i	−0.929179	+	0.369631i	$0.879484\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.11152	−	1.68388i	0.102424	−	0.0816803i
$426$		0			0
$427$	12.5205	−	2.85772i	0.605908	−	0.138295i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	7.59988	+	9.52995i	0.366073	+	0.459042i	0.930419	−	0.366497i	$-0.119443\pi$
$431$	7.59988	+	9.52995i	0.366073	+	0.459042i	−0.564346	+	0.825538i	$0.690872\pi$
$432$		0			0
$433$	−7.71536	+	16.0211i	−0.370777	+	0.769926i	−0.999973	−	0.00732066i	$-0.997670\pi$
$433$	−7.71536	+	16.0211i	−0.370777	+	0.769926i	0.629197	+	0.777246i	$0.283384\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.55171	−	3.22216i	0.0742283	−	0.154137i
$438$		0			0
$439$	−1.11635	−	1.39985i	−0.0532803	−	0.0668114i	0.754477	−	0.656326i	$-0.227890\pi$
$439$	−1.11635	−	1.39985i	−0.0532803	−	0.0668114i	−0.807758	+	0.589515i	$0.799319\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−25.6566	+	5.85595i	−1.21898	+	0.278224i	−0.783166	−	0.621812i	$-0.786397\pi$
$443$	−25.6566	+	5.85595i	−1.21898	+	0.278224i	−0.435814	+	0.900037i	$0.643540\pi$
$444$		0			0
$445$	−3.57636	+	2.85206i	−0.169536	+	0.135200i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.39621	−	13.2819i	−0.301856	−	0.626810i	0.693774	−	0.720192i	$-0.255947\pi$
$449$	−6.39621	−	13.2819i	−0.301856	−	0.626810i	−0.995630	+	0.0933820i	$0.970232\pi$
$450$		0			0
$451$	4.11361	−	18.0229i	0.193702	−	0.848665i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.67481	−	7.33781i	−0.0785161	−	0.344002i
$456$		0			0
$457$	12.1927	−	15.2891i	0.570350	−	0.715196i	−0.410084	−	0.912048i	$-0.634500\pi$
$457$	12.1927	−	15.2891i	0.570350	−	0.715196i	0.980433	+	0.196852i	$0.0630719\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.2070	+	8.93728i	0.521962	+	0.416251i	0.848708	−	0.528861i	$-0.177381\pi$
$461$	11.2070	+	8.93728i	0.521962	+	0.416251i	−0.326746	+	0.945112i	$0.605952\pi$
$462$		0			0
$463$	26.4802			1.23064			0.615320	−	0.788278i	$-0.289027\pi$
$463$	26.4802			1.23064			0.615320	+	0.788278i	$0.289027\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−27.5004	−	21.9309i	−1.27257	−	1.01484i	−0.998589	−	0.0531036i	$-0.983089\pi$
$467$	−27.5004	−	21.9309i	−1.27257	−	1.01484i	−0.273979	−	0.961736i	$-0.588340\pi$
$468$		0			0
$469$	11.7797	+	5.67282i	0.543938	+	0.261947i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.64209	−	7.19448i	−0.0755035	−	0.330803i
$474$		0			0
$475$	0.273073	+	0.0623271i	0.0125295	+	0.00285977i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.05052	−	16.7171i	−0.367838	−	0.763823i	0.632101	−	0.774886i	$-0.282193\pi$
$479$	−8.05052	−	16.7171i	−0.367838	−	0.763823i	−0.999939	+	0.0110632i	$0.996478\pi$
$480$		0			0
$481$		−	5.55840i		−	0.253441i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.7996	−	3.14968i	0.626610	−	0.143020i
$486$		0			0
$487$	−11.0896	+	5.34048i	−0.502518	+	0.242000i	−0.667929	−	0.744225i	$-0.732819\pi$
$487$	−11.0896	+	5.34048i	−0.502518	+	0.242000i	0.165411	+	0.986225i	$0.447105\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.53323	−	11.4899i	0.249711	−	0.518531i	−0.738004	−	0.674797i	$-0.764231\pi$
$491$	5.53323	−	11.4899i	0.249711	−	0.518531i	0.987715	+	0.156266i	$0.0499457\pi$
$492$		0			0
$493$	9.52609	−	31.5952i	0.429034	−	1.42297i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	25.0055	+	31.3560i	1.12165	+	1.40651i
$498$		0			0
$499$	12.8732	−	6.19939i	0.576282	−	0.277523i	−0.122956	−	0.992412i	$-0.539237\pi$
$499$	12.8732	−	6.19939i	0.576282	−	0.277523i	0.699238	+	0.714889i	$0.253523\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.16349	−	3.32027i	0.185641	−	0.148044i	−0.526260	−	0.850324i	$-0.676406\pi$
$503$	4.16349	−	3.32027i	0.185641	−	0.148044i	0.711901	+	0.702280i	$0.247835\pi$
$504$		0			0
$505$		−	24.1357i		−	1.07402i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	8.76475	−	38.4009i	0.388491	−	1.70209i	−0.281368	−	0.959600i	$-0.590788\pi$
$509$	8.76475	−	38.4009i	0.388491	−	1.70209i	0.669859	−	0.742489i	$-0.266355\pi$
$510$		0			0
$511$	−47.3282	−	10.8023i	−2.09367	−	0.477868i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	19.2029	−	24.0796i	0.846179	−	1.06108i
$516$		0			0
$517$	12.9922	+	6.25670i	0.571395	+	0.275169i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.9022			1.17861			0.589304	−	0.807911i	$-0.299402\pi$
$521$	26.9022			1.17861			0.589304	+	0.807911i	$0.299402\pi$
$522$		0			0
$523$	−9.57862			−0.418844			−0.209422	−	0.977825i	$-0.567158\pi$
$523$	−9.57862			−0.418844			−0.209422	+	0.977825i	$0.567158\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.87804	+	4.75701i	0.430294	+	0.207219i
$528$		0			0
$529$	5.40327	−	6.77548i	0.234925	−	0.294586i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.78501	−	1.77688i	−0.337206	−	0.0769651i
$534$		0			0
$535$	−2.50043	+	10.9551i	−0.108103	+	0.473630i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	17.2483i		−	0.742935i
$540$		0			0
$541$	−26.6558	+	21.2573i	−1.14602	+	0.913924i	−0.997188	−	0.0749383i	$-0.976124\pi$
$541$	−26.6558	+	21.2573i	−1.14602	+	0.913924i	−0.148836	+	0.988862i	$0.547553\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−29.2182	+	14.0707i	−1.25157	+	0.602724i
$546$		0			0
$547$	−5.91800	−	7.42094i	−0.253035	−	0.317296i	0.639048	−	0.769167i	$-0.279328\pi$
$547$	−5.91800	−	7.42094i	−0.253035	−	0.317296i	−0.892084	+	0.451870i	$0.850757\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.17786	−	1.27061i	0.135381	−	0.0541298i
$552$		0			0
$553$	−15.3091	+	31.7896i	−0.651008	+	1.35183i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	37.7606	−	18.1846i	1.59997	−	0.770505i	0.600396	−	0.799703i	$-0.295010\pi$
$557$	37.7606	−	18.1846i	1.59997	−	0.770505i	0.999574	+	0.0291983i	$0.00929543\pi$
$558$		0			0
$559$	−3.10767	+	0.709305i	−0.131440	+	0.0300004i
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	7.91358i		−	0.333518i	−0.985998	−	0.166759i	$-0.946670\pi$
$563$		−	7.91358i		−	0.333518i	0.985998	−	0.166759i	$-0.0533301\pi$
$564$		0			0
$565$	12.8892	+	26.7647i	0.542253	+	1.12600i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	30.2361	+	6.90120i	1.26756	+	0.289313i	0.802868	−	0.596157i	$-0.203306\pi$
$569$	30.2361	+	6.90120i	1.26756	+	0.289313i	0.464696	+	0.885470i	$0.346164\pi$
$570$		0			0
$571$	6.67941	+	29.2644i	0.279524	+	1.22468i	0.898397	+	0.439185i	$0.144733\pi$
$571$	6.67941	+	29.2644i	0.279524	+	1.22468i	−0.618872	+	0.785492i	$0.712410\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.23447	+	1.07606i	0.0931839	+	0.0448750i
$576$		0			0
$577$	29.3666	+	23.4191i	1.22255	+	0.974948i	1.00000		2.60869e-5i	$8.30371e-6\pi$
$577$	29.3666	+	23.4191i	1.22255	+	0.974948i	0.222546	+	0.974922i	$0.428563\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	31.3334			1.29993
$582$		0			0
$583$	−12.5566	−	10.0136i	−0.520041	−	0.414719i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.4296	−	20.6021i	0.678123	−	0.850339i	−0.317057	−	0.948407i	$-0.602695\pi$
$587$	16.4296	−	20.6021i	0.678123	−	0.850339i	0.995180	+	0.0980673i	$0.0312660\pi$
$588$		0			0
$589$	0.253020	+	1.10855i	0.0104255	+	0.0456772i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	3.36965	−	14.7634i	0.138375	−	0.606260i	−0.857417	−	0.514622i	$-0.827932\pi$
$593$	3.36965	−	14.7634i	0.138375	−	0.606260i	0.995792	−	0.0916385i	$-0.0292104\pi$
$594$		0			0
$595$	−25.0623	−	52.0424i	−1.02745	−	2.13353i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.93060	+	5.52697i	−0.283177	+	0.225826i	−0.754769	−	0.655991i	$-0.772251\pi$
$599$	−6.93060	+	5.52697i	−0.283177	+	0.225826i	0.471592	+	0.881817i	$0.343679\pi$
$600$		0			0
$601$	−1.18785	+	0.271118i	−0.0484533	+	0.0110592i	−0.246679	−	0.969097i	$-0.579339\pi$
$601$	−1.18785	+	0.271118i	−0.0484533	+	0.0110592i	0.198226	+	0.980156i	$0.436482\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	11.0280	+	13.8286i	0.448350	+	0.562213i
$606$		0			0
$607$	−18.4501	+	38.3121i	−0.748868	+	1.55504i	0.0807663	+	0.996733i	$0.474263\pi$
$607$	−18.4501	+	38.3121i	−0.748868	+	1.55504i	−0.829634	+	0.558307i	$0.811451\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.70259	−	5.61199i	0.109335	−	0.227037i
$612$		0			0
$613$	18.7146	+	23.4673i	0.755874	+	0.947835i	0.999759	−	0.0219687i	$-0.00699341\pi$
$613$	18.7146	+	23.4673i	0.755874	+	0.947835i	−0.243885	+	0.969804i	$0.578422\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.2749	−	4.62761i	0.816236	−	0.186300i	0.206032	−	0.978545i	$-0.433945\pi$
$617$	20.2749	−	4.62761i	0.816236	−	0.186300i	0.610203	+	0.792245i	$0.291088\pi$
$618$		0			0
$619$	5.90472	−	4.70885i	0.237331	−	0.189265i	−0.497601	−	0.867406i	$-0.665786\pi$
$619$	5.90472	−	4.70885i	0.237331	−	0.189265i	0.734932	+	0.678141i	$0.237214\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.43857	+	7.14025i	0.137763	+	0.286068i
$624$		0			0
$625$	6.01015	−	26.3322i	0.240406	−	1.05329i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−9.49236	−	41.5887i	−0.378485	−	1.65825i
$630$		0			0
$631$	−6.59947	+	8.27547i	−0.262721	+	0.329441i	−0.895643	−	0.444774i	$-0.853284\pi$
$631$	−6.59947	+	8.27547i	−0.262721	+	0.329441i	0.632922	+	0.774215i	$0.281855\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−34.2809	−	27.3381i	−1.36040	−	1.08488i
$636$		0			0
$637$	−7.45041			−0.295196
$638$		0			0
$639$		0			0
$640$		0			0
$641$	32.7080	+	26.0837i	1.29189	+	1.03025i	0.997210	+	0.0746482i	$0.0237834\pi$
$641$	32.7080	+	26.0837i	1.29189	+	1.03025i	0.294677	+	0.955597i	$0.404788\pi$
$642$		0			0
$643$	40.0983	+	19.3103i	1.58132	+	0.761525i	0.998688	−	0.0512084i	$-0.0163073\pi$
$643$	40.0983	+	19.3103i	1.58132	+	0.761525i	0.582635	+	0.812734i	$0.302022\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.832486	−	3.64736i	−0.0327284	−	0.143393i	0.955924	−	0.293615i	$-0.0948583\pi$
$647$	−0.832486	−	3.64736i	−0.0327284	−	0.143393i	−0.988652	+	0.150222i	$0.952001\pi$
$648$		0			0
$649$	−1.38867	−	0.316956i	−0.0545102	−	0.0124416i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.186189	−	0.386625i	−0.00728612	−	0.0151298i	0.897294	−	0.441433i	$-0.145530\pi$
$653$	−0.186189	−	0.386625i	−0.00728612	−	0.0151298i	−0.904580	+	0.426304i	$0.859816\pi$
$654$		0			0
$655$			27.9055i			1.09036i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.7892	+	4.06027i	−0.692969	+	0.158166i	−0.554479	−	0.832198i	$-0.687082\pi$
$659$	−17.7892	+	4.06027i	−0.692969	+	0.158166i	−0.138491	+	0.990364i	$0.544225\pi$
$660$		0			0
$661$	22.6534	−	10.9093i	0.881116	−	0.424323i	0.0620842	−	0.998071i	$-0.480225\pi$
$661$	22.6534	−	10.9093i	0.881116	−	0.424323i	0.819032	+	0.573748i	$0.194511\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.59923	−	5.39735i	0.100794	−	0.209300i
$666$		0			0
$667$	29.9360	−	4.70711i	1.15913	−	0.182260i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.66269	−	4.59287i	−0.141397	−	0.177306i
$672$		0			0
$673$	−0.249098	+	0.119959i	−0.00960201	+	0.00462409i	−0.438679	−	0.898644i	$-0.644553\pi$
$673$	−0.249098	+	0.119959i	−0.00960201	+	0.00462409i	0.429077	+	0.903268i	$0.358839\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.90142	+	3.90875i	−0.188377	+	0.150225i	−0.713137	−	0.701025i	$-0.752726\pi$
$677$	−4.90142	+	3.90875i	−0.188377	+	0.150225i	0.524760	+	0.851250i	$0.324155\pi$
$678$		0			0
$679$		−	24.5228i		−	0.941100i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.82096	+	34.2659i	−0.299261	+	1.31115i	0.571971	+	0.820274i	$0.306179\pi$
$683$	−7.82096	+	34.2659i	−0.299261	+	1.31115i	−0.871231	+	0.490873i	$0.836678\pi$
$684$		0			0
$685$	−21.5905	−	4.92789i	−0.824930	−	0.188285i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−4.32537	+	5.42384i	−0.164783	+	0.206632i
$690$		0			0
$691$	41.7251	+	20.0938i	1.58730	+	0.764402i	0.999020	−	0.0442566i	$-0.0140919\pi$
$691$	41.7251	+	20.0938i	1.58730	+	0.764402i	0.588278	+	0.808659i	$0.299806\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	28.7911			1.09211
$696$		0			0
$697$	−61.2830			−2.32126
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−19.0313	−	9.16497i	−0.718801	−	0.346156i	0.0384676	−	0.999260i	$-0.487752\pi$
$701$	−19.0313	−	9.16497i	−0.718801	−	0.346156i	−0.757269	+	0.653104i	$0.773467\pi$
$702$		0			0
$703$	2.75839	−	3.45892i	0.104035	−	0.130456i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−40.7669	−	9.30478i	−1.53320	−	0.349942i
$708$		0			0
$709$	−8.20271	+	35.9384i	−0.308059	+	1.34970i	0.549579	+	0.835442i	$0.314788\pi$
$709$	−8.20271	+	35.9384i	−0.308059	+	1.34970i	−0.857638	+	0.514254i	$0.828069\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			10.0680i			0.377050i
$714$		0			0
$715$	−2.69172	+	2.14658i	−0.100665	+	0.0802774i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.26759	+	3.01831i	−0.233742	+	0.112564i	−0.547089	−	0.837075i	$-0.684264\pi$
$719$	−6.26759	+	3.01831i	−0.233742	+	0.112564i	0.313347	+	0.949639i	$0.398550\pi$
$720$		0			0
$721$	−33.2691	−	41.7182i	−1.23901	−	1.55367i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.881130	+	2.20375i	0.0327244	+	0.0818453i
$726$		0			0
$727$	16.7401	−	34.7612i	0.620856	−	1.28922i	−0.319034	−	0.947743i	$-0.603358\pi$
$727$	16.7401	−	34.7612i	0.620856	−	1.28922i	0.939890	−	0.341477i	$-0.110927\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−22.0407	+	10.6142i	−0.815204	+	0.392582i
$732$		0			0
$733$	−35.9697	+	8.20985i	−1.32857	+	0.303238i	−0.827158	−	0.561970i	$-0.810044\pi$
$733$	−35.9697	+	8.20985i	−1.32857	+	0.303238i	−0.501414	+	0.865208i	$0.667187\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	5.98066i		−	0.220300i
$738$		0			0
$739$	−5.70395	−	11.8444i	−0.209823	−	0.435702i	0.769323	−	0.638860i	$-0.220594\pi$
$739$	−5.70395	−	11.8444i	−0.209823	−	0.435702i	−0.979146	+	0.203158i	$0.934880\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−38.2632	−	8.73333i	−1.40374	−	0.320395i	−0.547428	−	0.836853i	$-0.684393\pi$
$743$	−38.2632	−	8.73333i	−1.40374	−	0.320395i	−0.856313	+	0.516458i	$0.827250\pi$
$744$		0			0
$745$	−3.30017	−	14.4590i	−0.120909	−	0.529736i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	17.5400	+	8.44680i	0.640896	+	0.308639i
$750$		0			0
$751$	−12.2655	−	9.78138i	−0.447573	−	0.356928i	0.373616	−	0.927583i	$-0.378118\pi$
$751$	−12.2655	−	9.78138i	−0.447573	−	0.356928i	−0.821189	+	0.570656i	$0.806689\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−54.5781			−1.98630
$756$		0			0
$757$	18.1042	+	14.4376i	0.658010	+	0.524745i	0.894602	−	0.446864i	$-0.147459\pi$
$757$	18.1042	+	14.4376i	0.658010	+	0.524745i	−0.236592	+	0.971609i	$0.576031\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.3967	−	16.7989i	0.485630	−	0.608960i	−0.477291	−	0.878745i	$-0.658381\pi$
$761$	13.3967	−	16.7989i	0.485630	−	0.608960i	0.962921	+	0.269785i	$0.0869526\pi$
$762$		0			0
$763$	12.5023	+	54.7761i	0.452613	+	1.98303i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.136910	+	0.599840i	−0.00494352	+	0.0216590i
$768$		0			0
$769$	−21.1881	−	43.9975i	−0.764062	−	1.58659i	−0.809147	−	0.587607i	$-0.800070\pi$
$769$	−21.1881	−	43.9975i	−0.764062	−	1.58659i	0.0450850	−	0.998983i	$-0.485644\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.5225	+	8.39144i	−0.378469	+	0.301819i	−0.794186	−	0.607675i	$-0.792102\pi$
$773$	−10.5225	+	8.39144i	−0.378469	+	0.301819i	0.415717	+	0.909494i	$0.363531\pi$
$774$		0			0
$775$	−0.768751	+	0.175462i	−0.0276143	+	0.00630279i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.96272	−	4.96909i	−0.141979	−	0.178036i
$780$		0			0
$781$	7.95982	−	16.5287i	0.284825	−	0.591445i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.59668	+	19.9277i	−0.342520	+	0.711251i
$786$		0			0
$787$	6.33379	+	7.94233i	0.225775	+	0.283113i	0.881797	−	0.471628i	$-0.156334\pi$
$787$	6.33379	+	7.94233i	0.225775	+	0.283113i	−0.656022	+	0.754742i	$0.727762\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	50.1766	−	11.4525i	1.78407	−	0.407203i
$792$		0			0
$793$	−1.98390	+	1.58211i	−0.0704503	+	0.0561822i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.145085	+	0.301272i	0.00513917	+	0.0106716i	0.903523	−	0.428540i	$-0.140972\pi$
$797$	0.145085	+	0.301272i	0.00513917	+	0.0106716i	−0.898383	+	0.439212i	$0.855258\pi$
$798$		0			0
$799$	10.6373	−	46.6051i	0.376321	−	1.64877i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.94130	+	21.6492i	0.174375	+	0.763985i
$804$		0			0
$805$	33.0719	−	41.4709i	1.16563	−	1.46166i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−23.4260	−	18.6816i	−0.823614	−	0.656810i	0.118183	−	0.992992i	$-0.462293\pi$
$809$	−23.4260	−	18.6816i	−0.823614	−	0.656810i	−0.941797	+	0.336182i	$0.890864\pi$
$810$		0			0
$811$	10.8754			0.381888			0.190944	−	0.981601i	$-0.438845\pi$
$811$	10.8754			0.381888			0.190944	+	0.981601i	$0.438845\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	20.2945	+	16.1843i	0.710884	+	0.566911i
$816$		0			0
$817$	−2.28586	−	1.10081i	−0.0799720	−	0.0385125i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.6322	+	50.9640i	0.405967	+	1.77866i	0.602457	+	0.798151i	$0.294189\pi$
$821$	11.6322	+	50.9640i	0.405967	+	1.77866i	−0.196490	+	0.980506i	$0.562954\pi$
$822$		0			0
$823$	8.84960	+	2.01986i	0.308478	+	0.0704080i	0.373957	−	0.927446i	$-0.378001\pi$
$823$	8.84960	+	2.01986i	0.308478	+	0.0704080i	−0.0654797	+	0.997854i	$0.520858\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.1350	+	37.6578i	0.630617	+	1.30949i	0.934222	+	0.356691i	$0.116095\pi$
$827$	18.1350	+	37.6578i	0.630617	+	1.30949i	−0.303605	+	0.952798i	$0.598190\pi$
$828$		0			0
$829$			23.7963i			0.826478i	0.910623	+	0.413239i	$0.135603\pi$
$829$			23.7963i			0.826478i	−0.910623	+	0.413239i	$0.864397\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−55.7451	+	12.7234i	−1.93145	+	0.440841i
$834$		0			0
$835$	14.7819	−	7.11859i	0.511549	−	0.246349i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.7987	+	24.5002i	−0.407335	+	0.845839i	0.591873	+	0.806032i	$0.298389\pi$
$839$	−11.7987	+	24.5002i	−0.407335	+	0.845839i	−0.999207	+	0.0398079i	$0.987325\pi$
$840$		0			0
$841$	24.1669	+	16.0301i	0.833340	+	0.552761i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−17.9788	−	22.5448i	−0.618491	−	0.775563i
$846$		0			0
$847$	27.6090	−	13.2958i	0.948657	−	0.456849i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	30.6266	−	24.4239i	1.04987	−	0.837241i
$852$		0			0
$853$			24.0457i			0.823310i	0.911340	+	0.411655i	$0.135049\pi$
$853$			24.0457i			0.823310i	−0.911340	+	0.411655i	$0.864951\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.47740	−	41.5232i	0.323742	−	1.41841i	−0.507095	−	0.861890i	$-0.669281\pi$
$857$	9.47740	−	41.5232i	0.323742	−	1.41841i	0.830837	−	0.556516i	$-0.187862\pi$
$858$		0			0
$859$	−51.7042	−	11.8011i	−1.76413	−	0.402650i	−0.787280	−	0.616596i	$-0.788511\pi$
$859$	−51.7042	−	11.8011i	−1.76413	−	0.402650i	−0.976845	+	0.213946i	$0.931368\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−29.7946	+	37.3613i	−1.01422	+	1.27179i	−0.0522510	+	0.998634i	$0.516640\pi$
$863$	−29.7946	+	37.3613i	−1.01422	+	1.27179i	−0.961969	+	0.273158i	$0.911932\pi$
$864$		0			0
$865$	47.8611	+	23.0487i	1.62733	+	0.783679i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	16.1398			0.547506
$870$		0			0
$871$	−2.58335			−0.0875336
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−38.7202	−	18.6467i	−1.30898	−	0.630372i
$876$		0			0
$877$	16.9686	−	21.2780i	0.572990	−	0.718506i	−0.407910	−	0.913022i	$-0.633742\pi$
$877$	16.9686	−	21.2780i	0.572990	−	0.718506i	0.980899	+	0.194516i	$0.0623136\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	48.3636	+	11.0387i	1.62941	+	0.371902i	0.936925	−	0.349530i	$-0.113659\pi$
$881$	48.3636	+	11.0387i	1.62941	+	0.371902i	0.692485	+	0.721433i	$0.256516\pi$
$882$		0			0
$883$	−0.621812	+	2.72434i	−0.0209256	+	0.0916812i	−0.984312	−	0.176434i	$-0.943544\pi$
$883$	−0.621812	+	2.72434i	−0.0209256	+	0.0916812i	0.963387	+	0.268115i	$0.0864009\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			52.1075i			1.74960i	0.484486	+	0.874799i	$0.339007\pi$
$887$			52.1075i			1.74960i	−0.484486	+	0.874799i	$0.660993\pi$
$888$		0			0
$889$	−59.3920	+	47.3635i	−1.99194	+	1.58852i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.46678	−	2.15109i	0.149475	−	0.0719833i
$894$		0			0
$895$	−27.1160	−	34.0024i	−0.906389	−	1.13658i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.50829	+	7.10439i	−0.217064	+	0.236945i
$900$		0			0
$901$	−23.1005	+	47.9686i	−0.769588	+	1.59807i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.9820	−	11.5491i	0.797190	−	0.383906i
$906$		0			0
$907$	−18.0202	+	4.11299i	−0.598351	+	0.136570i	−0.510960	−	0.859604i	$-0.670710\pi$
$907$	−18.0202	+	4.11299i	−0.598351	+	0.136570i	−0.0873908	+	0.996174i	$0.527853\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			10.9764i			0.363664i	0.983330	+	0.181832i	$0.0582028\pi$
$911$			10.9764i			0.363664i	−0.983330	+	0.181832i	$0.941797\pi$
$912$		0			0
$913$	−6.21876	−	12.9134i	−0.205811	−	0.427371i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	47.1344	+	10.7581i	1.55652	+	0.355264i
$918$		0			0
$919$	5.20088	+	22.7865i	0.171561	+	0.751658i	0.985356	+	0.170507i	$0.0545405\pi$
$919$	5.20088	+	22.7865i	0.171561	+	0.751658i	−0.813795	+	0.581151i	$0.802602\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−7.13961	−	3.43826i	−0.235003	−	0.113172i
$924$		0			0
$925$	2.39866	+	1.91287i	0.0788674	+	0.0628947i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−25.3721			−0.832431			−0.416215	−	0.909266i	$-0.636644\pi$
$929$	−25.3721			−0.832431			−0.416215	+	0.909266i	$0.636644\pi$
$930$		0			0
$931$	−4.63629	−	3.69732i	−0.151948	−	0.121175i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.4740	+	20.6578i	−0.538758	+	0.675581i
$936$		0			0
$937$	−0.984625	−	4.31392i	−0.0321663	−	0.140930i	0.956295	−	0.292404i	$-0.0944551\pi$
$937$	−0.984625	−	4.31392i	−0.0321663	−	0.140930i	−0.988461	+	0.151474i	$0.951598\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.79830	−	7.87888i	0.0586230	−	0.256844i	−0.937121	−	0.349004i	$-0.886520\pi$
$941$	1.79830	−	7.87888i	0.0586230	−	0.256844i	0.995744	+	0.0921598i	$0.0293771\pi$
$942$		0			0
$943$	−24.4172	−	50.7029i	−0.795134	−	1.65111i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.90123	−	1.51618i	0.0617816	−	0.0492692i	−0.592112	−	0.805856i	$-0.701706\pi$
$947$	1.90123	−	1.51618i	0.0617816	−	0.0492692i	0.653894	+	0.756586i	$0.273134\pi$
$948$		0			0
$949$	9.35142	−	2.13440i	0.303560	−	0.0692856i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−8.50087	−	10.6597i	−0.275370	−	0.345303i	0.624845	−	0.780749i	$-0.285162\pi$
$953$	−8.50087	−	10.6597i	−0.275370	−	0.345303i	−0.900215	+	0.435446i	$0.856591\pi$
$954$		0			0
$955$	−0.436659	+	0.906731i	−0.0141299	+	0.0293411i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−16.6471	+	34.5681i	−0.537563	+	1.11626i
$960$		0			0
$961$	17.3324	+	21.7341i	0.559109	+	0.701100i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−11.1452	+	2.54383i	−0.358778	+	0.0818887i
$966$		0			0
$967$	−12.2046	+	9.73285i	−0.392474	+	0.312987i	−0.799767	−	0.600310i	$-0.795044\pi$
$967$	−12.2046	+	9.73285i	−0.392474	+	0.312987i	0.407294	+	0.913297i	$0.366472\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.25716	−	8.84008i	−0.136619	−	0.283692i	0.821424	−	0.570319i	$-0.193180\pi$
$971$	−4.25716	−	8.84008i	−0.136619	−	0.283692i	−0.958042	+	0.286627i	$0.907466\pi$
$972$		0			0
$973$	11.0995	−	48.6301i	0.355834	−	1.55901i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.20476	+	40.3287i	0.294486	+	1.29023i	0.878209	+	0.478277i	$0.158738\pi$
$977$	9.20476	+	40.3287i	0.294486	+	1.29023i	−0.583723	+	0.811953i	$0.698405\pi$
$978$		0			0
$979$	2.26025	−	2.83426i	0.0722379	−	0.0905834i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	36.6749	+	29.2472i	1.16975	+	0.932842i	0.998626	−	0.0524086i	$-0.0166898\pi$
$983$	36.6749	+	29.2472i	1.16975	+	0.932842i	0.171121	+	0.985250i	$0.445261\pi$
$984$		0			0
$985$	37.5339			1.19593
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−17.5635	−	14.0064i	−0.558487	−	0.445378i
$990$		0			0
$991$	31.0460	+	14.9510i	0.986210	+	0.474934i	0.856237	−	0.516584i	$-0.172797\pi$
$991$	31.0460	+	14.9510i	0.986210	+	0.474934i	0.129973	+	0.991518i	$0.458511\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.88641	−	8.26491i	−0.0598032	−	0.262015i
$996$		0			0
$997$	−27.7893	−	6.34272i	−0.880095	−	0.200876i	−0.241483	−	0.970405i	$-0.577634\pi$
$997$	−27.7893	−	6.34272i	−0.880095	−	0.200876i	−0.638612	+	0.769529i	$0.720491\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1044.2.z.c.361.1	✓	24
3.2	odd	2	inner	1044.2.z.c.361.4	yes	24
29.9	even	14	inner	1044.2.z.c.937.1	yes	24
87.38	odd	14	inner	1044.2.z.c.937.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1044.2.z.c.361.1	✓	24	1.1	even	1	trivial
1044.2.z.c.361.4	yes	24	3.2	odd	2	inner
1044.2.z.c.937.1	yes	24	29.9	even	14	inner
1044.2.z.c.937.4	yes	24	87.38	odd	14	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1044 = 2^{2} \cdot 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1044.z (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10154 - 1.01205i) q^{5} +(-2.51961 + 3.15949i) q^{7} +O(q^{10})\)	\(q+(-2.10154 - 1.01205i) q^{5} +(-2.51961 + 3.15949i) q^{7} +(1.80218 + 0.411337i) q^{11} +(0.177678 - 0.778456i) q^{13} -6.12795i q^{17} +(0.496881 - 0.396249i) q^{19} +(5.06999 - 2.44158i) q^{23} +(0.274787 + 0.344572i) q^{25} +(5.15591 + 1.55453i) q^{29} +(-0.776281 + 1.61196i) q^{31} +(8.49262 - 4.08983i) q^{35} +(6.78673 - 1.54903i) q^{37} -10.0006i q^{41} +(-1.73210 - 3.59675i) q^{43} +(7.60533 + 1.73587i) q^{47} +(-2.07630 - 9.09685i) q^{49} +(-7.82784 - 3.76969i) q^{53} +(-3.37107 - 2.68834i) q^{55} -0.770551 q^{59} +(-2.48461 - 1.98141i) q^{61} +(-1.16123 + 1.45614i) q^{65} +(-0.719935 - 3.15424i) q^{67} +(2.20838 - 9.67555i) q^{71} +(5.21215 + 10.8231i) q^{73} +(-5.84041 + 4.65757i) q^{77} +(8.51225 - 1.94287i) q^{79} +(-4.83430 - 6.06201i) q^{83} +(-6.20179 + 12.8781i) q^{85} +(0.850890 - 1.76689i) q^{89} +(2.01185 + 2.52277i) q^{91} +(-1.44524 + 0.329867i) q^{95} +(-4.74439 + 3.78352i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} - 10 q^{13} - 10 q^{25} - 28 q^{31} + 28 q^{37} - 14 q^{43} - 4 q^{49} + 14 q^{55} - 56 q^{61} - 20 q^{67} + 14 q^{79} + 14 q^{85} + 46 q^{91} + 28 q^{97}+O(q^{100}) \) 24 * q - 4 * q^7 - 10 * q^13 - 10 * q^25 - 28 * q^31 + 28 * q^37 - 14 * q^43 - 4 * q^49 + 14 * q^55 - 56 * q^61 - 20 * q^67 + 14 * q^79 + 14 * q^85 + 46 * q^91 + 28 * q^97

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