LMFDB - Embedded newform 1044.2.z.c.613.2

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			613.2
Character	$\chi$	$=$	1044.613
Dual form			1044.2.z.c.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0963412 + 0.422098i) q^{5} +(-1.75124 + 0.843350i) q^{7} +O(q^{10})$	$q+(-0.0963412 + 0.422098i) q^{5} +(-1.75124 + 0.843350i) q^{7} +(1.32188 - 1.05417i) q^{11} +(-0.887715 - 1.11316i) q^{13} +5.95728i q^{17} +(0.940312 - 1.95258i) q^{19} +(1.63470 + 7.16209i) q^{23} +(4.33596 + 2.08809i) q^{25} +(-3.16210 + 4.35903i) q^{29} +(2.38239 + 0.543766i) q^{31} +(-0.187261 - 0.820443i) q^{35} +(-2.79472 - 2.22872i) q^{37} +5.11072i q^{41} +(-7.35452 + 1.67862i) q^{43} +(-1.35380 + 1.07962i) q^{47} +(-2.00884 + 2.51901i) q^{49} +(-2.56097 + 11.2203i) q^{53} +(0.317610 + 0.659524i) q^{55} +12.0447 q^{59} +(0.325228 + 0.675343i) q^{61} +(0.555386 - 0.267460i) q^{65} +(4.67843 - 5.86657i) q^{67} +(-0.751759 - 0.942676i) q^{71} +(-3.72297 + 0.849744i) q^{73} +(-1.42589 + 2.96090i) q^{77} +(6.97885 + 5.56545i) q^{79} +(-9.33814 - 4.49701i) q^{83} +(-2.51456 - 0.573931i) q^{85} +(10.1011 + 2.30550i) q^{89} +(2.49338 + 1.20075i) q^{91} +(0.733589 + 0.585018i) q^{95} +(4.81459 - 9.99761i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1044\mathbb{Z}\right)^\times$.

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

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
$5$	−0.0963412	+	0.422098i	−0.0430851	+	0.188768i	−0.991891	−	0.127092i	$-0.959436\pi$
$5$	−0.0963412	+	0.422098i	−0.0430851	+	0.188768i	0.948806	+	0.315860i	$0.102293\pi$
$6$		0			0
$7$	−1.75124	+	0.843350i	−0.661905	+	0.318757i	−0.734504	−	0.678605i	$-0.762585\pi$
$7$	−1.75124	+	0.843350i	−0.661905	+	0.318757i	0.0725989	+	0.997361i	$0.476871\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.32188	−	1.05417i	0.398562	−	0.317843i	−0.403615	−	0.914929i	$-0.632246\pi$
$11$	1.32188	−	1.05417i	0.398562	−	0.317843i	0.802177	+	0.597086i	$0.203675\pi$
$12$		0			0
$13$	−0.887715	−	1.11316i	−0.246208	−	0.308735i	0.643337	−	0.765583i	$-0.277550\pi$
$13$	−0.887715	−	1.11316i	−0.246208	−	0.308735i	−0.889545	+	0.456848i	$0.848978\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			5.95728i			1.44485i	0.691448	+	0.722426i	$0.256973\pi$
$17$			5.95728i			1.44485i	−0.691448	+	0.722426i	$0.743027\pi$
$18$		0			0
$19$	0.940312	−	1.95258i	0.215722	−	0.447952i	−0.764824	−	0.644239i	$-0.777174\pi$
$19$	0.940312	−	1.95258i	0.215722	−	0.447952i	0.980546	+	0.196287i	$0.0628885\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.63470	+	7.16209i	0.340858	+	1.49340i	0.797266	+	0.603628i	$0.206279\pi$
$23$	1.63470	+	7.16209i	0.340858	+	1.49340i	−0.456408	+	0.889771i	$0.650864\pi$
$24$		0			0
$25$	4.33596	+	2.08809i	0.867192	+	0.417618i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.16210	+	4.35903i	−0.587188	+	0.809451i
$29$	−3.16210	+	4.35903i	−0.587188	+	0.809451i
$30$		0			0
$31$	2.38239	+	0.543766i	0.427891	+	0.0976632i	0.431042	−	0.902332i	$-0.358146\pi$
$31$	2.38239	+	0.543766i	0.427891	+	0.0976632i	−0.00315157	+	0.999995i	$0.501003\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.187261	−	0.820443i	−0.0316528	−	0.138680i
$36$		0			0
$37$	−2.79472	−	2.22872i	−0.459449	−	0.366399i	0.366243	−	0.930519i	$-0.380644\pi$
$37$	−2.79472	−	2.22872i	−0.459449	−	0.366399i	−0.825692	+	0.564121i	$0.809215\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			5.11072i			0.798161i	0.916916	+	0.399080i	$0.130671\pi$
$41$			5.11072i			0.798161i	−0.916916	+	0.399080i	$0.869329\pi$
$42$		0			0
$43$	−7.35452	+	1.67862i	−1.12155	+	0.255987i	−0.742802	−	0.669511i	$-0.766504\pi$
$43$	−7.35452	+	1.67862i	−1.12155	+	0.255987i	−0.378752	+	0.925498i	$0.623647\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.35380	+	1.07962i	−0.197472	+	0.157479i	−0.717234	−	0.696832i	$-0.754592\pi$
$47$	−1.35380	+	1.07962i	−0.197472	+	0.157479i	0.519762	+	0.854311i	$0.326021\pi$
$48$		0			0
$49$	−2.00884	+	2.51901i	−0.286978	+	0.359859i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.56097	+	11.2203i	−0.351776	+	1.54123i	0.421301	+	0.906921i	$0.361574\pi$
$53$	−2.56097	+	11.2203i	−0.351776	+	1.54123i	−0.773077	+	0.634312i	$0.781283\pi$
$54$		0			0
$55$	0.317610	+	0.659524i	0.0428265	+	0.0889301i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	12.0447			1.56808			0.784042	−	0.620707i	$-0.213155\pi$
$59$	12.0447			1.56808			0.784042	+	0.620707i	$0.213155\pi$
$60$		0			0
$61$	0.325228	+	0.675343i	0.0416412	+	0.0864688i	0.920752	−	0.390149i	$-0.127577\pi$
$61$	0.325228	+	0.675343i	0.0416412	+	0.0864688i	−0.879110	+	0.476618i	$0.841862\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.555386	−	0.267460i	0.0688872	−	0.0331743i
$66$		0			0
$67$	4.67843	−	5.86657i	0.571562	−	0.716716i	−0.409086	−	0.912496i	$-0.634152\pi$
$67$	4.67843	−	5.86657i	0.571562	−	0.716716i	0.980648	+	0.195780i	$0.0627239\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.751759	−	0.942676i	−0.0892174	−	0.111875i	0.735219	−	0.677829i	$-0.237079\pi$
$71$	−0.751759	−	0.942676i	−0.0892174	−	0.111875i	−0.824437	+	0.565954i	$0.808508\pi$
$72$		0			0
$73$	−3.72297	+	0.849744i	−0.435741	+	0.0994551i	−0.434764	−	0.900544i	$-0.643168\pi$
$73$	−3.72297	+	0.849744i	−0.435741	+	0.0994551i	−0.000977188		1.00000i	$0.500311\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.42589	+	2.96090i	−0.162496	+	0.337426i
$78$		0			0
$79$	6.97885	+	5.56545i	0.785182	+	0.626162i	0.931776	−	0.363035i	$-0.118259\pi$
$79$	6.97885	+	5.56545i	0.785182	+	0.626162i	−0.146593	+	0.989197i	$0.546831\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−9.33814	−	4.49701i	−1.02499	−	0.493611i	−0.155647	−	0.987813i	$-0.549746\pi$
$83$	−9.33814	−	4.49701i	−1.02499	−	0.493611i	−0.869347	+	0.494201i	$0.835461\pi$
$84$		0			0
$85$	−2.51456	−	0.573931i	−0.272742	−	0.0622516i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	10.1011	+	2.30550i	1.07071	+	0.244383i	0.721325	−	0.692597i	$-0.243533\pi$
$89$	10.1011	+	2.30550i	1.07071	+	0.244383i	0.349385	+	0.936979i	$0.386391\pi$
$90$		0			0
$91$	2.49338	+	1.20075i	0.261378	+	0.125873i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.733589	+	0.585018i	0.0752646	+	0.0600215i
$96$		0			0
$97$	4.81459	−	9.99761i	0.488848	−	1.01510i	−0.499979	−	0.866037i	$-0.666659\pi$
$97$	4.81459	−	9.99761i	0.488848	−	1.01510i	0.988827	−	0.149066i	$-0.0476266\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.21548	+	1.41864i	−0.618463	+	0.141160i	−0.520263	−	0.854006i	$-0.674166\pi$
$101$	−6.21548	+	1.41864i	−0.618463	+	0.141160i	−0.0982009	+	0.995167i	$0.531309\pi$
$102$		0			0
$103$	−2.81831	−	3.53405i	−0.277696	−	0.348220i	0.623350	−	0.781943i	$-0.285771\pi$
$103$	−2.81831	−	3.53405i	−0.277696	−	0.348220i	−0.901046	+	0.433723i	$0.857200\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.62166	−	4.54141i	0.350119	−	0.439035i	−0.575322	−	0.817927i	$-0.695123\pi$
$107$	3.62166	−	4.54141i	0.350119	−	0.439035i	0.925441	+	0.378892i	$0.123695\pi$
$108$		0			0
$109$	3.51868	−	1.69451i	0.337029	−	0.162305i	−0.257713	−	0.966222i	$-0.582969\pi$
$109$	3.51868	−	1.69451i	0.337029	−	0.162305i	0.594741	+	0.803917i	$0.297254\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.62135	+	7.51982i	0.340668	+	0.707405i	0.998971	−	0.0453481i	$-0.0144397\pi$
$113$	3.62135	+	7.51982i	0.340668	+	0.707405i	−0.658303	+	0.752753i	$0.728725\pi$
$114$		0			0
$115$	−3.18059			−0.296592
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.02407	−	10.4326i	−0.460556	−	0.956354i
$120$		0			0
$121$	−1.81162	+	7.93724i	−0.164693	+	0.721568i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−2.64882	+	3.32151i	−0.236918	+	0.297085i
$126$		0			0
$127$	−3.20204	+	2.55354i	−0.284135	+	0.226590i	−0.755178	−	0.655520i	$-0.772449\pi$
$127$	−3.20204	+	2.55354i	−0.284135	+	0.226590i	0.471042	+	0.882111i	$0.343878\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.04366	−	1.15118i	0.440667	−	0.100579i	0.00356964	−	0.999994i	$-0.498864\pi$
$131$	5.04366	−	1.15118i	0.440667	−	0.100579i	0.437097	+	0.899414i	$0.356007\pi$
$132$		0			0
$133$			4.21244i			0.365264i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.22939	−	2.57536i	−0.275906	−	0.220027i	0.475754	−	0.879578i	$-0.342175\pi$
$137$	−3.22939	−	2.57536i	−0.275906	−	0.220027i	−0.751660	+	0.659551i	$0.770747\pi$
$138$		0			0
$139$	1.70031	+	7.44955i	0.144219	+	0.631863i	0.994428	+	0.105418i	$0.0336181\pi$
$139$	1.70031	+	7.44955i	0.144219	+	0.631863i	−0.850209	+	0.526445i	$0.823525\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.34691	−	0.535667i	−0.196258	−	0.0447947i
$144$		0			0
$145$	−1.53530	−	1.75467i	−0.127499	−	0.145718i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.32987	−	1.60358i	−0.272794	−	0.131371i	0.292486	−	0.956270i	$-0.405518\pi$
$149$	−3.32987	−	1.60358i	−0.272794	−	0.131371i	−0.565280	+	0.824899i	$0.691232\pi$
$150$		0			0
$151$	−4.74613	−	20.7941i	−0.386234	−	1.69220i	−0.677469	−	0.735552i	$-0.736923\pi$
$151$	−4.74613	−	20.7941i	−0.386234	−	1.69220i	0.291234	−	0.956652i	$-0.405934\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.459045	+	0.953217i	−0.0368714	+	0.0765643i
$156$		0			0
$157$			20.3852i			1.62691i	0.581625	+	0.813457i	$0.302417\pi$
$157$			20.3852i			1.62691i	−0.581625	+	0.813457i	$0.697583\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.90289	−	11.1639i	−0.701646	−	0.879837i
$162$		0			0
$163$	−1.01141	+	0.806573i	−0.0792198	+	0.0631757i	−0.662299	−	0.749240i	$-0.730419\pi$
$163$	−1.01141	+	0.806573i	−0.0792198	+	0.0631757i	0.583079	+	0.812415i	$0.301848\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.63302	−	1.74957i	0.281131	−	0.135386i	−0.288005	−	0.957629i	$-0.592992\pi$
$167$	3.63302	−	1.74957i	0.281131	−	0.135386i	0.569136	+	0.822243i	$0.307278\pi$
$168$		0			0
$169$	2.44169	−	10.6977i	0.187822	−	0.822902i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.16558			0.316703			0.158352	−	0.987383i	$-0.449382\pi$
$173$	4.16558			0.316703			0.158352	+	0.987383i	$0.449382\pi$
$174$		0			0
$175$	−9.35427			−0.707117
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.19981	−	14.0193i	0.239165	−	1.04785i	−0.702601	−	0.711584i	$-0.747978\pi$
$179$	3.19981	−	14.0193i	0.239165	−	1.04785i	0.941767	−	0.336267i	$-0.109165\pi$
$180$		0			0
$181$	6.94665	−	3.34533i	0.516340	−	0.248656i	−0.157519	−	0.987516i	$-0.550350\pi$
$181$	6.94665	−	3.34533i	0.516340	−	0.248656i	0.673859	+	0.738860i	$0.264635\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.20998	−	0.964930i	0.0889598	−	0.0709431i
$186$		0			0
$187$	6.27995	+	7.87481i	0.459236	+	0.575863i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	12.4812i		−	0.903107i	−0.892244	−	0.451554i	$-0.850870\pi$
$191$		−	12.4812i		−	0.903107i	0.892244	−	0.451554i	$-0.149130\pi$
$192$		0			0
$193$	5.79612	−	12.0358i	0.417214	−	0.866354i	−0.581395	−	0.813622i	$-0.697493\pi$
$193$	5.79612	−	12.0358i	0.417214	−	0.866354i	0.998609	−	0.0527322i	$-0.0167930\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.32730	−	5.81530i	−0.0945664	−	0.414323i	0.905381	−	0.424601i	$-0.139585\pi$
$197$	−1.32730	−	5.81530i	−0.0945664	−	0.414323i	−0.999947	+	0.0102780i	$0.996728\pi$
$198$		0			0
$199$	8.54219	+	4.11370i	0.605540	+	0.291613i	0.711421	−	0.702766i	$-0.248052\pi$
$199$	8.54219	+	4.11370i	0.605540	+	0.291613i	−0.105881	+	0.994379i	$0.533766\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.86140	−	10.3004i	0.130645	−	0.722949i
$204$		0			0
$205$	−2.15723	−	0.492373i	−0.150667	−	0.0343888i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.815359	−	3.57232i	−0.0563995	−	0.247103i
$210$		0			0
$211$	1.06476	+	0.849120i	0.0733013	+	0.0584558i	0.659455	−	0.751744i	$-0.270787\pi$
$211$	1.06476	+	0.849120i	0.0733013	+	0.0584558i	−0.586154	+	0.810200i	$0.699359\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	3.26605i		−	0.222743i
$216$		0			0
$217$	−4.63072	+	1.05693i	−0.314354	+	0.0717492i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	6.63140	−	5.28837i	0.446076	−	0.355734i
$222$		0			0
$223$	−5.70643	+	7.15564i	−0.382131	+	0.479177i	−0.935282	−	0.353904i	$-0.884854\pi$
$223$	−5.70643	+	7.15564i	−0.382131	+	0.479177i	0.553151	+	0.833081i	$0.313425\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.41656	−	23.7315i	0.359510	−	1.57512i	−0.394908	−	0.918721i	$-0.629223\pi$
$227$	5.41656	−	23.7315i	0.359510	−	1.57512i	0.754418	−	0.656395i	$-0.227919\pi$
$228$		0			0
$229$	−7.61533	−	15.8134i	−0.503235	−	1.04498i	−0.985613	−	0.169016i	$-0.945941\pi$
$229$	−7.61533	−	15.8134i	−0.503235	−	1.04498i	0.482378	−	0.875963i	$-0.339773\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−22.8668			−1.49806			−0.749028	−	0.662538i	$-0.769479\pi$
$233$	−22.8668			−1.49806			−0.749028	+	0.662538i	$0.769479\pi$
$234$		0			0
$235$	−0.325280	−	0.675450i	−0.0212189	−	0.0440615i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.02735	−	3.38419i	0.454562	−	0.218905i	−0.192571	−	0.981283i	$-0.561682\pi$
$239$	7.02735	−	3.38419i	0.454562	−	0.218905i	0.647132	+	0.762378i	$0.275968\pi$
$240$		0			0
$241$	−11.9036	+	14.9266i	−0.766778	+	0.961509i	−0.999940	−	0.0109286i	$-0.996521\pi$
$241$	−11.9036	+	14.9266i	−0.766778	+	0.961509i	0.233162	+	0.972438i	$0.425093\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.869736	−	1.09061i	−0.0555654	−	0.0696768i
$246$		0			0
$247$	−3.00826	+	0.686616i	−0.191411	+	0.0436883i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.2483	−	25.4339i	0.773106	−	1.60537i	−0.0226424	−	0.999744i	$-0.507208\pi$
$251$	12.2483	−	25.4339i	0.773106	−	1.60537i	0.795748	−	0.605627i	$-0.207078\pi$
$252$		0			0
$253$	9.71090	+	7.74419i	0.610519	+	0.486873i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.7330	+	5.16873i	0.669505	+	0.322417i	0.737576	−	0.675264i	$-0.235970\pi$
$257$	10.7330	+	5.16873i	0.669505	+	0.322417i	−0.0680713	+	0.997680i	$0.521685\pi$
$258$		0			0
$259$	6.77381	+	1.54608i	0.420904	+	0.0960685i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−28.7419	−	6.56015i	−1.77230	−	0.404516i	−0.793375	−	0.608733i	$-0.791678\pi$
$263$	−28.7419	−	6.56015i	−1.77230	−	0.404516i	−0.978926	+	0.204217i	$0.934535\pi$
$264$		0			0
$265$	−4.48936	−	2.16196i	−0.275779	−	0.132808i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.0387	−	8.00563i	−0.612073	−	0.488112i	0.267702	−	0.963502i	$-0.413736\pi$
$269$	−10.0387	−	8.00563i	−0.612073	−	0.488112i	−0.879775	+	0.475390i	$0.842307\pi$
$270$		0			0
$271$	3.42755	−	7.11738i	0.208209	−	0.432350i	−0.770546	−	0.637384i	$-0.780016\pi$
$271$	3.42755	−	7.11738i	0.208209	−	0.432350i	0.978755	+	0.205034i	$0.0657307\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.93281	−	1.81061i	0.478367	−	0.109184i
$276$		0			0
$277$	−7.86099	−	9.85736i	−0.472321	−	0.592272i	0.487417	−	0.873169i	$-0.337939\pi$
$277$	−7.86099	−	9.85736i	−0.472321	−	0.592272i	−0.959738	+	0.280898i	$0.909368\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.90268	+	9.90965i	−0.471434	+	0.591160i	−0.959522	−	0.281635i	$-0.909123\pi$
$281$	−7.90268	+	9.90965i	−0.471434	+	0.591160i	0.488087	+	0.872795i	$0.337695\pi$
$282$		0			0
$283$	17.0092	−	8.19118i	1.01109	−	0.486915i	0.146402	−	0.989225i	$-0.453231\pi$
$283$	17.0092	−	8.19118i	1.01109	−	0.486915i	0.864688	+	0.502310i	$0.167516\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.31013	−	8.95008i	−0.254419	−	0.528306i
$288$		0			0
$289$	−18.4891			−1.08760
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.4099	+	27.8460i	0.783417	+	1.62678i	0.779187	+	0.626791i	$0.215632\pi$
$293$	13.4099	+	27.8460i	0.783417	+	1.62678i	0.00422967	+	0.999991i	$0.498654\pi$
$294$		0			0
$295$	−1.16040	+	5.08404i	−0.0675611	+	0.296004i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.52140	−	8.17758i	0.377142	−	0.472921i
$300$		0			0
$301$	11.4638	−	9.14210i	0.660764	−	0.526942i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.316394	+	0.0722149i	−0.0181167	+	0.00413501i
$306$		0			0
$307$			12.6938i			0.724475i	0.932086	+	0.362238i	$0.117987\pi$
$307$			12.6938i			0.724475i	−0.932086	+	0.362238i	$0.882013\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.79029	+	3.02266i	0.214928	+	0.171399i	0.725036	−	0.688711i	$-0.241823\pi$
$311$	3.79029	+	3.02266i	0.214928	+	0.171399i	−0.510108	+	0.860110i	$0.670395\pi$
$312$		0			0
$313$	6.68813	+	29.3026i	0.378036	+	1.65628i	0.703475	+	0.710720i	$0.251631\pi$
$313$	6.68813	+	29.3026i	0.378036	+	1.65628i	−0.325440	+	0.945563i	$0.605512\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.7095	−	3.58560i	−0.882335	−	0.201387i	−0.242733	−	0.970093i	$-0.578044\pi$
$317$	−15.7095	−	3.58560i	−0.882335	−	0.201387i	−0.639602	+	0.768706i	$0.720901\pi$
$318$		0			0
$319$	0.415208	+	9.09549i	0.0232472	+	0.509250i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	11.6320	+	5.60170i	0.647224	+	0.311687i
$324$		0			0
$325$	−1.52472	−	6.68024i	−0.0845764	−	0.370553i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.46033	−	3.03240i	0.0805105	−	0.167182i
$330$		0			0
$331$		−	4.89986i		−	0.269321i	−0.990892	−	0.134660i	$-0.957006\pi$
$331$		−	4.89986i		−	0.269321i	0.990892	−	0.134660i	$-0.0429944\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.02554	+	2.53995i	0.110667	+	0.138772i
$336$		0			0
$337$	17.9039	−	14.2779i	0.975290	−	0.777768i	0.000296158	−	1.00000i	$-0.499906\pi$
$337$	17.9039	−	14.2779i	0.975290	−	0.777768i	0.974994	+	0.222232i	$0.0713343\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.72246	−	1.79264i	0.201583	−	0.0970771i
$342$		0			0
$343$	4.42119	−	19.3705i	0.238722	−	1.04591i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.88764			0.369748			0.184874	−	0.982762i	$-0.440812\pi$
$347$	6.88764			0.369748			0.184874	+	0.982762i	$0.440812\pi$
$348$		0			0
$349$	−6.50303			−0.348099			−0.174050	−	0.984737i	$-0.555685\pi$
$349$	−6.50303			−0.348099			−0.174050	+	0.984737i	$0.555685\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.02836	+	13.2681i	−0.161183	+	0.706190i	0.828148	+	0.560509i	$0.189394\pi$
$353$	−3.02836	+	13.2681i	−0.161183	+	0.706190i	−0.989332	+	0.145681i	$0.953463\pi$
$354$		0			0
$355$	0.470327	−	0.226498i	0.0249624	−	0.0120212i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.8253	+	16.6077i	−1.09912	+	0.876519i	−0.993033	−	0.117838i	$-0.962404\pi$
$359$	−20.8253	+	16.6077i	−1.09912	+	0.876519i	−0.106087	+	0.994357i	$0.533832\pi$
$360$		0			0
$361$	8.91793	+	11.1827i	0.469365	+	0.588565i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	1.65333i		−	0.0865391i
$366$		0			0
$367$	6.51834	−	13.5355i	0.340255	−	0.706546i	−0.658693	−	0.752412i	$-0.728890\pi$
$367$	6.51834	−	13.5355i	0.340255	−	0.706546i	0.998948	+	0.0458658i	$0.0146047\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.97782	−	21.8093i	−0.258436	−	1.13228i
$372$		0			0
$373$	16.8929	+	8.13518i	0.874680	+	0.421224i	0.816679	−	0.577093i	$-0.195813\pi$
$373$	16.8929	+	8.13518i	0.874680	+	0.421224i	0.0580015	+	0.998316i	$0.481527\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.65934	−	0.349648i	0.394476	−	0.0180078i
$378$		0			0
$379$	−31.6853	−	7.23197i	−1.62757	−	0.371481i	−0.691244	−	0.722622i	$-0.742937\pi$
$379$	−31.6853	−	7.23197i	−1.62757	−	0.371481i	−0.936323	+	0.351140i	$0.885794\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	5.91987	+	25.9367i	0.302491	+	1.32530i	0.866353	+	0.499432i	$0.166458\pi$
$383$	5.91987	+	25.9367i	0.302491	+	1.32530i	−0.563862	+	0.825869i	$0.690685\pi$
$384$		0			0
$385$	−1.11242	−	0.887125i	−0.0566941	−	0.0452121i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	14.1922i		−	0.719571i	−0.933035	−	0.359786i	$-0.882850\pi$
$389$		−	14.1922i		−	0.719571i	0.933035	−	0.359786i	$-0.117150\pi$
$390$		0			0
$391$	−42.6665	+	9.73835i	−2.15774	+	0.492490i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.02152	+	2.40958i	−0.152029	+	0.121239i
$396$		0			0
$397$	−6.70269	+	8.40491i	−0.336398	+	0.421830i	−0.921044	−	0.389459i	$-0.872662\pi$
$397$	−6.70269	+	8.40491i	−0.336398	+	0.421830i	0.584646	+	0.811289i	$0.301234\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.72927	−	16.3390i	0.186231	−	0.815930i	−0.792350	−	0.610067i	$-0.791143\pi$
$401$	3.72927	−	16.3390i	0.186231	−	0.815930i	0.978581	−	0.205863i	$-0.0660002\pi$
$402$		0			0
$403$	−1.50959	−	3.13469i	−0.0751980	−	0.156150i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.04373			−0.299576
$408$		0			0
$409$	−3.67081	−	7.62251i	−0.181510	−	0.376909i	0.790284	−	0.612740i	$-0.209933\pi$
$409$	−3.67081	−	7.62251i	−0.181510	−	0.376909i	−0.971794	+	0.235832i	$0.924219\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−21.0931	+	10.1579i	−1.03792	+	0.499837i
$414$		0			0
$415$	2.79783	−	3.50837i	0.137340	−	0.172219i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.11639	+	7.66971i	0.298805	+	0.374690i	0.908456	−	0.417980i	$-0.137262\pi$
$419$	6.11639	+	7.66971i	0.298805	+	0.374690i	−0.609651	+	0.792670i	$0.708690\pi$
$420$		0			0
$421$	1.96908	−	0.449429i	0.0959669	−	0.0219038i	−0.174268	−	0.984698i	$-0.555756\pi$
$421$	1.96908	−	0.449429i	0.0959669	−	0.0219038i	0.270235	+	0.962794i	$0.412899\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−12.4393	+	25.8305i	−0.603395	+	1.25296i
$426$		0			0
$427$	−1.13910	−	0.908404i	−0.0551250	−	0.0439607i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.7529	+	6.62303i	0.662452	+	0.319020i	0.734725	−	0.678365i	$-0.237311\pi$
$431$	13.7529	+	6.62303i	0.662452	+	0.319020i	−0.0722732	+	0.997385i	$0.523025\pi$
$432$		0			0
$433$	4.75418	+	1.08511i	0.228471	+	0.0521471i	0.335224	−	0.942139i	$-0.391188\pi$
$433$	4.75418	+	1.08511i	0.228471	+	0.0521471i	−0.106752	+	0.994286i	$0.534045\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.5217	+	3.54272i	0.742501	+	0.169471i
$438$		0			0
$439$	19.1494	+	9.22187i	0.913951	+	0.440136i	0.830908	−	0.556410i	$-0.187822\pi$
$439$	19.1494	+	9.22187i	0.913951	+	0.440136i	0.0830435	+	0.996546i	$0.473536\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.62456	+	6.08039i	0.362254	+	0.288888i	0.787654	−	0.616117i	$-0.211295\pi$
$443$	7.62456	+	6.08039i	0.362254	+	0.288888i	−0.425400	+	0.905005i	$0.639867\pi$
$444$		0			0
$445$	−1.94630	+	4.04153i	−0.0922633	+	0.191587i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	25.7295	−	5.87259i	1.21425	−	0.277145i	0.433018	−	0.901385i	$-0.357449\pi$
$449$	25.7295	−	5.87259i	1.21425	−	0.277145i	0.781232	+	0.624240i	$0.214591\pi$
$450$		0			0
$451$	5.38755	+	6.75577i	0.253690	+	0.318117i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.747050	+	0.936771i	−0.0350222	+	0.0439165i
$456$		0			0
$457$	18.8934	−	9.09861i	0.883798	−	0.425615i	0.0637879	−	0.997963i	$-0.479682\pi$
$457$	18.8934	−	9.09861i	0.883798	−	0.425615i	0.820010	+	0.572349i	$0.193968\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.27642	+	10.9566i	0.245747	+	0.510300i	0.986959	−	0.160972i	$-0.0514628\pi$
$461$	5.27642	+	10.9566i	0.245747	+	0.510300i	−0.741212	+	0.671271i	$0.765749\pi$
$462$		0			0
$463$	13.9533			0.648466			0.324233	−	0.945977i	$-0.394894\pi$
$463$	13.9533			0.648466			0.324233	+	0.945977i	$0.394894\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.78283	−	3.70209i	−0.0824997	−	0.171312i	0.855638	−	0.517575i	$-0.173165\pi$
$467$	−1.78283	−	3.70209i	−0.0824997	−	0.171312i	−0.938138	+	0.346262i	$0.887451\pi$
$468$		0			0
$469$	−3.24546	+	14.2193i	−0.149862	+	0.656586i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.95226	+	9.97182i	−0.365645	+	0.458505i
$474$		0			0
$475$	8.15431	−	6.50284i	0.374145	−	0.298371i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−27.8033	+	6.34591i	−1.27036	+	0.289952i	−0.803994	−	0.594638i	$-0.797296\pi$
$479$	−27.8033	+	6.34591i	−1.27036	+	0.289952i	−0.466370	+	0.884590i	$0.654438\pi$
$480$		0			0
$481$			5.08944i			0.232058i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.75613	+	2.99541i	0.170557	+	0.136015i
$486$		0			0
$487$	5.98820	+	26.2360i	0.271351	+	1.18887i	0.908419	+	0.418060i	$0.137290\pi$
$487$	5.98820	+	26.2360i	0.271351	+	1.18887i	−0.637068	+	0.770808i	$0.719853\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	31.6134	+	7.21556i	1.42669	+	0.325633i	0.865025	−	0.501729i	$-0.167302\pi$
$491$	31.6134	+	7.21556i	1.42669	+	0.325633i	0.561669	+	0.827362i	$0.310160\pi$
$492$		0			0
$493$	−25.9679	−	18.8375i	−1.16954	−	0.848399i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.11151	+	1.01685i	0.0947143	+	0.0456120i
$498$		0			0
$499$	−2.84199	−	12.4516i	−0.127225	−	0.557409i	−0.997855	−	0.0654698i	$-0.979145\pi$
$499$	−2.84199	−	12.4516i	−0.127225	−	0.557409i	0.870630	−	0.491939i	$-0.163712\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.72416	+	20.1924i	−0.433579	+	0.900336i	0.563655	+	0.826010i	$0.309395\pi$
$503$	−9.72416	+	20.1924i	−0.433579	+	0.900336i	−0.997234	+	0.0743254i	$0.976320\pi$
$504$		0			0
$505$		−	2.76022i		−	0.122828i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	15.4906	+	19.4246i	0.686608	+	0.860979i	0.995944	−	0.0899735i	$-0.0286782\pi$
$509$	15.4906	+	19.4246i	0.686608	+	0.860979i	−0.309336	+	0.950953i	$0.600107\pi$
$510$		0			0
$511$	5.80317	−	4.62787i	0.256717	−	0.204725i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.76324	−	0.849130i	0.0776974	−	0.0374171i
$516$		0			0
$517$	−0.651467	+	2.85426i	−0.0286515	+	0.125530i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−31.1593			−1.36512			−0.682558	−	0.730832i	$-0.739132\pi$
$521$	−31.1593			−1.36512			−0.682558	+	0.730832i	$0.739132\pi$
$522$		0			0
$523$	−15.3737			−0.672244			−0.336122	−	0.941819i	$-0.609115\pi$
$523$	−15.3737			−0.672244			−0.336122	+	0.941819i	$0.609115\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.23936	+	14.1926i	−0.141109	+	0.618238i
$528$		0			0
$529$	−27.9010	+	13.4364i	−1.21308	+	0.584191i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.68905	−	4.53687i	0.246420	−	0.196514i
$534$		0			0
$535$	1.56801	+	1.96622i	0.0677909	+	0.0850071i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			5.44749i			0.234640i
$540$		0			0
$541$	13.5367	−	28.1092i	0.581988	−	1.20851i	−0.377303	−	0.926090i	$-0.623148\pi$
$541$	13.5367	−	28.1092i	0.581988	−	1.20851i	0.959291	−	0.282420i	$-0.0911373\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.376255	+	1.64848i	0.0161170	+	0.0706132i
$546$		0			0
$547$	−3.37150	−	1.62363i	−0.144155	−	0.0694214i	0.360416	−	0.932792i	$-0.382635\pi$
$547$	−3.37150	−	1.62363i	−0.144155	−	0.0694214i	−0.504571	+	0.863370i	$0.668349\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.53797	+	10.2731i	0.235926	+	0.437649i
$552$		0			0
$553$	−16.9152	−	3.86079i	−0.719309	−	0.164178i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.770954	−	3.37777i	−0.0326664	−	0.143121i	0.955965	−	0.293481i	$-0.0948138\pi$
$557$	−0.770954	−	3.37777i	−0.0326664	−	0.143121i	−0.988631	+	0.150360i	$0.951957\pi$
$558$		0			0
$559$	8.39729	+	6.69662i	0.355168	+	0.283237i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			30.4884i			1.28493i	0.766314	+	0.642467i	$0.222089\pi$
$563$			30.4884i			1.28493i	−0.766314	+	0.642467i	$0.777911\pi$
$564$		0			0
$565$	−3.52299	+	0.804099i	−0.148213	+	0.0338287i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.53091	+	4.41075i	−0.231868	+	0.184908i	−0.732531	−	0.680734i	$-0.761661\pi$
$569$	−5.53091	+	4.41075i	−0.231868	+	0.184908i	0.500663	+	0.865642i	$0.333090\pi$
$570$		0			0
$571$	−19.0819	+	23.9280i	−0.798554	+	1.00136i	0.201208	+	0.979549i	$0.435513\pi$
$571$	−19.0819	+	23.9280i	−0.798554	+	1.00136i	−0.999762	+	0.0218070i	$0.993058\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.86707	+	34.4679i	−0.328080	+	1.43741i
$576$		0			0
$577$	−13.2950	−	27.6073i	−0.553478	−	1.14931i	−0.970653	−	0.240482i	$-0.922694\pi$
$577$	−13.2950	−	27.6073i	−0.553478	−	1.14931i	0.417176	−	0.908826i	$-0.363020\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	20.1458			0.835790
$582$		0			0
$583$	8.44280	+	17.5317i	0.349665	+	0.726087i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.9703	+	5.28300i	−0.452791	+	0.218053i	−0.646358	−	0.763034i	$-0.723709\pi$
$587$	−10.9703	+	5.28300i	−0.452791	+	0.218053i	0.193567	+	0.981087i	$0.437994\pi$
$588$		0			0
$589$	3.30194	−	4.14050i	0.136054	−	0.170606i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.0747	+	16.3952i	0.536915	+	0.673270i	0.974104	−	0.226099i	$-0.0725974\pi$
$593$	13.0747	+	16.3952i	0.536915	+	0.673270i	−0.437189	+	0.899370i	$0.644026\pi$
$594$		0			0
$595$	4.88760	−	1.11556i	0.200372	−	0.0457337i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−19.9534	+	41.4337i	−0.815274	+	1.69293i	−0.0990301	+	0.995084i	$0.531574\pi$
$599$	−19.9534	+	41.4337i	−0.815274	+	1.69293i	−0.716244	+	0.697850i	$0.754140\pi$
$600$		0			0
$601$	14.6593	+	11.6904i	0.597965	+	0.476861i	0.875082	−	0.483975i	$-0.160807\pi$
$601$	14.6593	+	11.6904i	0.597965	+	0.476861i	−0.277117	+	0.960836i	$0.589379\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.17576	−	1.52937i	−0.129113	−	0.0621776i
$606$		0			0
$607$	4.32543	+	0.987252i	0.175564	+	0.0400713i	0.309399	−	0.950932i	$-0.399872\pi$
$607$	4.32543	+	0.987252i	0.175564	+	0.0400713i	−0.133835	+	0.991004i	$0.542729\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.40358	+	0.548602i	0.0972386	+	0.0221941i
$612$		0			0
$613$	16.7023	+	8.04343i	0.674601	+	0.324871i	0.739631	−	0.673012i	$-0.235000\pi$
$613$	16.7023	+	8.04343i	0.674601	+	0.324871i	−0.0650298	+	0.997883i	$0.520714\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.22184	+	4.16428i	0.210223	+	0.167648i	0.722941	−	0.690910i	$-0.242790\pi$
$617$	5.22184	+	4.16428i	0.210223	+	0.167648i	−0.512718	+	0.858557i	$0.671361\pi$
$618$		0			0
$619$	19.0962	−	39.6536i	0.767540	−	1.59381i	−0.0365691	−	0.999331i	$-0.511643\pi$
$619$	19.0962	−	39.6536i	0.767540	−	1.59381i	0.804109	−	0.594482i	$-0.202643\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−19.6337	+	4.48126i	−0.786607	+	0.179538i
$624$		0			0
$625$	13.8561	+	17.3750i	0.554243	+	0.694998i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	13.2771	−	16.6489i	0.529392	−	0.663836i
$630$		0			0
$631$	31.2602	−	15.0541i	1.24445	−	0.599295i	0.308431	−	0.951247i	$-0.400196\pi$
$631$	31.2602	−	15.0541i	1.24445	−	0.599295i	0.936018	+	0.351951i	$0.114482\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.769358	−	1.59759i	−0.0305310	−	0.0633983i
$636$		0			0
$637$	4.58734			0.181757
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.73140	−	18.1309i	−0.344870	−	0.716129i	0.654327	−	0.756212i	$-0.272952\pi$
$641$	−8.73140	−	18.1309i	−0.344870	−	0.716129i	−0.999196	+	0.0400828i	$0.987238\pi$
$642$		0			0
$643$	3.72670	−	16.3277i	0.146967	−	0.643903i	−0.846751	−	0.531989i	$-0.821445\pi$
$643$	3.72670	−	16.3277i	0.146967	−	0.643903i	0.993718	−	0.111914i	$-0.0356981\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.14721	+	1.43856i	−0.0451015	+	0.0565555i	−0.803871	−	0.594804i	$-0.797230\pi$
$647$	−1.14721	+	1.43856i	−0.0451015	+	0.0565555i	0.758769	+	0.651360i	$0.225801\pi$
$648$		0			0
$649$	15.9216	−	12.6971i	0.624979	−	0.498404i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.8412	−	2.70267i	0.463380	−	0.105764i	0.0155442	−	0.999879i	$-0.495052\pi$
$653$	11.8412	−	2.70267i	0.463380	−	0.105764i	0.447836	+	0.894116i	$0.352195\pi$
$654$		0			0
$655$			2.23983i			0.0875173i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−11.9109	−	9.49865i	−0.463984	−	0.370015i	0.363417	−	0.931627i	$-0.381610\pi$
$659$	−11.9109	−	9.49865i	−0.463984	−	0.370015i	−0.827401	+	0.561612i	$0.810181\pi$
$660$		0			0
$661$	8.36834	+	36.6641i	0.325491	+	1.42607i	0.827627	+	0.561279i	$0.189690\pi$
$661$	8.36834	+	36.6641i	0.325491	+	1.42607i	−0.502136	+	0.864789i	$0.667452\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.77806	−	0.405831i	−0.0689503	−	0.0157375i
$666$		0			0
$667$	−36.3888	−	15.5216i	−1.40898	−	0.600997i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.14184	+	0.549879i	0.0440801	+	0.0212279i
$672$		0			0
$673$	−3.69074	−	16.1702i	−0.142267	−	0.623315i	−0.994905	−	0.100812i	$-0.967856\pi$
$673$	−3.69074	−	16.1702i	−0.142267	−	0.623315i	0.852638	−	0.522502i	$-0.175001\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.8265	−	30.7875i	0.569827	−	1.18326i	−0.394586	−	0.918859i	$-0.629112\pi$
$677$	14.8265	−	30.7875i	0.569827	−	1.18326i	0.964413	−	0.264399i	$-0.0851736\pi$
$678$		0			0
$679$			21.5685i			0.827725i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	13.9745	+	17.5235i	0.534720	+	0.670518i	0.973662	−	0.227998i	$-0.0732179\pi$
$683$	13.9745	+	17.5235i	0.534720	+	0.670518i	−0.438941	+	0.898516i	$0.644646\pi$
$684$		0			0
$685$	1.39818	−	1.11501i	0.0534216	−	0.0426023i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	14.7635	−	7.10970i	0.562443	−	0.270858i
$690$		0			0
$691$	−6.47809	+	28.3824i	−0.246438	+	1.07972i	0.688592	+	0.725149i	$0.258229\pi$
$691$	−6.47809	+	28.3824i	−0.246438	+	1.07972i	−0.935030	+	0.354568i	$0.884628\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.30825			−0.125489
$696$		0			0
$697$	−30.4460			−1.15322
$698$		0			0
$699$		0			0
$700$		0			0
$701$	0.613668	−	2.68865i	0.0231779	−	0.101549i	−0.962016	−	0.272993i	$-0.911986\pi$
$701$	0.613668	−	2.68865i	0.0231779	−	0.101549i	0.985194	+	0.171444i	$0.0548434\pi$
$702$		0			0
$703$	−6.97965	+	3.36122i	−0.263243	+	0.126771i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.68836	−	7.72621i	0.364368	−	0.290574i
$708$		0			0
$709$	17.7622	+	22.2731i	0.667073	+	0.836483i	0.994093	−	0.108534i	$-0.0346158\pi$
$709$	17.7622	+	22.2731i	0.667073	+	0.836483i	−0.327020	+	0.945018i	$0.606044\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			17.9518i			0.672300i
$714$		0			0
$715$	0.452208	−	0.939020i	0.0169116	−	0.0351173i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.08002	+	39.7822i	0.338628	+	1.48362i	0.801927	+	0.597422i	$0.203808\pi$
$719$	9.08002	+	39.7822i	0.338628	+	1.48362i	−0.463299	+	0.886202i	$0.653334\pi$
$720$		0			0
$721$	7.91597	+	3.81213i	0.294806	+	0.141971i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−22.8128	+	12.2978i	−0.847245	+	0.456729i
$726$		0			0
$727$	−42.7877	−	9.76600i	−1.58691	−	0.362201i	−0.664155	−	0.747595i	$-0.731208\pi$
$727$	−42.7877	−	9.76600i	−1.58691	−	0.362201i	−0.922752	+	0.385394i	$0.874065\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−10.0000	−	43.8129i	−0.369864	−	1.62048i
$732$		0			0
$733$	−36.4916	−	29.1011i	−1.34785	−	1.07487i	−0.989996	−	0.141097i	$-0.954937\pi$
$733$	−36.4916	−	29.1011i	−1.34785	−	1.07487i	−0.357854	−	0.933778i	$-0.616491\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	12.6868i		−	0.467323i
$738$		0			0
$739$	−37.3865	+	8.53323i	−1.37529	+	0.313900i	−0.845384	−	0.534159i	$-0.820628\pi$
$739$	−37.3865	+	8.53323i	−1.37529	+	0.313900i	−0.529902	+	0.848059i	$0.677771\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.468173	+	0.373355i	−0.0171756	+	0.0136971i	−0.632040	−	0.774936i	$-0.717782\pi$
$743$	−0.468173	+	0.373355i	−0.0171756	+	0.0136971i	0.614864	+	0.788633i	$0.289211\pi$
$744$		0			0
$745$	0.997674	−	1.25104i	0.0365519	−	0.0458347i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.51237	+	11.0074i	−0.0918000	+	0.402202i
$750$		0			0
$751$	−14.0057	−	29.0831i	−0.511075	−	1.06126i	−0.983671	−	0.179978i	$-0.942397\pi$
$751$	−14.0057	−	29.0831i	−0.511075	−	1.06126i	0.472596	−	0.881279i	$-0.343317\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.23442			0.336075
$756$		0			0
$757$	9.55590	+	19.8430i	0.347315	+	0.721207i	0.999315	−	0.0370122i	$-0.0117840\pi$
$757$	9.55590	+	19.8430i	0.347315	+	0.721207i	−0.652000	+	0.758219i	$0.726070\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.7535	−	12.8838i	0.969815	−	0.467038i	0.119225	−	0.992867i	$-0.461959\pi$
$761$	26.7535	−	12.8838i	0.969815	−	0.467038i	0.850590	+	0.525829i	$0.176245\pi$
$762$		0			0
$763$	−4.73298	+	5.93497i	−0.171345	+	0.214860i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.6923	−	13.4077i	−0.386075	−	0.484123i
$768$		0			0
$769$	42.1532	−	9.62119i	1.52008	−	0.346949i	0.620678	−	0.784065i	$-0.286857\pi$
$769$	42.1532	−	9.62119i	1.52008	−	0.346949i	0.899405	+	0.437116i	$0.144000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	13.1484	−	27.3029i	0.472914	−	0.982016i	−0.518961	−	0.854798i	$-0.673681\pi$
$773$	13.1484	−	27.3029i	0.472914	−	0.982016i	0.991875	−	0.127218i	$-0.0406048\pi$
$774$		0			0
$775$	9.19453	+	7.33239i	0.330277	+	0.263387i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	9.97908	+	4.80567i	0.357538	+	0.172181i
$780$		0			0
$781$	−1.98747	−	0.453628i	−0.0711174	−	0.0162321i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.60455	−	1.96393i	−0.307109	−	0.0700957i
$786$		0			0
$787$	30.5730	+	14.7232i	1.08981	+	0.524824i	0.890440	−	0.455100i	$-0.150396\pi$
$787$	30.5730	+	14.7232i	1.08981	+	0.524824i	0.199369	+	0.979925i	$0.436111\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−12.6837	−	10.1149i	−0.450980	−	0.359645i
$792$		0			0
$793$	0.463055	−	0.961544i	0.0164436	−	0.0341454i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−35.1637	+	8.02589i	−1.24556	+	0.284292i	−0.793984	−	0.607939i	$-0.791996\pi$
$797$	−35.1637	+	8.02589i	−1.24556	+	0.284292i	−0.451580	+	0.892231i	$0.649139\pi$
$798$		0			0
$799$	−6.43160	−	8.06498i	−0.227534	−	0.285318i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.02556	+	5.04789i	−0.142059	+	0.178136i
$804$		0			0
$805$	5.56997	−	2.68235i	0.196316	−	0.0945406i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−19.6314	−	40.7650i	−0.690203	−	1.43322i	−0.891192	−	0.453627i	$-0.850130\pi$
$809$	−19.6314	−	40.7650i	−0.690203	−	1.43322i	0.200989	−	0.979594i	$-0.435585\pi$
$810$		0			0
$811$	28.4728			0.999816			0.499908	−	0.866079i	$-0.333367\pi$
$811$	28.4728			0.999816			0.499908	+	0.866079i	$0.333367\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.243013	−	0.504621i	−0.00851236	−	0.0176761i
$816$		0			0
$817$	−3.63790	+	15.9387i	−0.127274	+	0.557624i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.8304	−	23.6126i	0.657187	−	0.824086i	−0.335847	−	0.941917i	$-0.609023\pi$
$821$	18.8304	−	23.6126i	0.657187	−	0.824086i	0.993034	+	0.117831i	$0.0375940\pi$
$822$		0			0
$823$	17.8279	−	14.2172i	0.621440	−	0.495582i	−0.261415	−	0.965226i	$-0.584189\pi$
$823$	17.8279	−	14.2172i	0.621440	−	0.495582i	0.882856	+	0.469644i	$0.155618\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	38.6650	−	8.82504i	1.34452	−	0.306877i	0.511099	−	0.859522i	$-0.329239\pi$
$827$	38.6650	−	8.82504i	1.34452	−	0.306877i	0.833417	+	0.552645i	$0.186382\pi$
$828$		0			0
$829$			24.5919i			0.854113i	0.904225	+	0.427057i	$0.140449\pi$
$829$			24.5919i			0.854113i	−0.904225	+	0.427057i	$0.859551\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15.0064	−	11.9672i	−0.519942	−	0.414640i
$834$		0			0
$835$	0.388481	+	1.70205i	0.0134439	+	0.0589018i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−24.0410	−	5.48720i	−0.829987	−	0.189439i	−0.213639	−	0.976913i	$-0.568532\pi$
$839$	−24.0410	−	5.48720i	−0.829987	−	0.189439i	−0.616348	+	0.787474i	$0.711389\pi$
$840$		0			0
$841$	−9.00221	−	27.5674i	−0.310421	−	0.950599i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.28026	+	2.06126i	0.147245	+	0.0709096i
$846$		0			0
$847$	−3.52130	−	15.4278i	−0.120993	−	0.530106i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	11.3937	−	23.6593i	0.390572	−	0.811031i
$852$		0			0
$853$		−	4.39087i		−	0.150340i	−0.997171	−	0.0751702i	$-0.976050\pi$
$853$		−	4.39087i		−	0.150340i	0.997171	−	0.0751702i	$-0.0239500\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.1744	−	12.7582i	−0.347549	−	0.435813i	0.577076	−	0.816690i	$-0.304193\pi$
$857$	−10.1744	−	12.7582i	−0.347549	−	0.435813i	−0.924626	+	0.380877i	$0.875622\pi$
$858$		0			0
$859$	44.9846	−	35.8740i	1.53485	−	1.22401i	0.648295	−	0.761389i	$-0.275482\pi$
$859$	44.9846	−	35.8740i	1.53485	−	1.22401i	0.886559	−	0.462616i	$-0.153089\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−43.8178	+	21.1015i	−1.49158	+	0.718305i	−0.989231	−	0.146362i	$-0.953243\pi$
$863$	−43.8178	+	21.1015i	−1.49158	+	0.718305i	−0.502345	+	0.864667i	$0.667529\pi$
$864$		0			0
$865$	−0.401317	+	1.75828i	−0.0136452	+	0.0597835i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	15.0921			0.511965
$870$		0			0
$871$	−10.6835			−0.361998
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.83751	−	8.05064i	0.0621190	−	0.272161i
$876$		0			0
$877$	−20.1316	+	9.69489i	−0.679797	+	0.327373i	−0.741722	−	0.670708i	$-0.765990\pi$
$877$	−20.1316	+	9.69489i	−0.679797	+	0.327373i	0.0619246	+	0.998081i	$0.480276\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	33.7190	−	26.8900i	1.13602	−	0.905947i	0.139579	−	0.990211i	$-0.455425\pi$
$881$	33.7190	−	26.8900i	1.13602	−	0.905947i	0.996443	+	0.0842637i	$0.0268538\pi$
$882$		0			0
$883$	23.1185	+	28.9897i	0.778001	+	0.975582i	1.00000		0.000535025i	$0.000170304\pi$
$883$	23.1185	+	28.9897i	0.778001	+	0.975582i	−0.221999	+	0.975047i	$0.571258\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			9.85868i			0.331022i	0.986208	+	0.165511i	$0.0529274\pi$
$887$			9.85868i			0.331022i	−0.986208	+	0.165511i	$0.947073\pi$
$888$		0			0
$889$	3.45400	−	7.17230i	0.115843	−	0.240551i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.835048	+	3.65859i	0.0279438	+	0.122430i
$894$		0			0
$895$	5.60924	+	2.70127i	0.187496	+	0.0902935i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−9.90366	+	8.66547i	−0.330306	+	0.289010i
$900$		0			0
$901$	−66.8427	−	15.2564i	−2.22685	−	0.508265i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.742810	+	3.25446i	0.0246918	+	0.108182i
$906$		0			0
$907$	27.4973	+	21.9283i	0.913032	+	0.728119i	0.962678	−	0.270648i	$-0.0872380\pi$
$907$	27.4973	+	21.9283i	0.913032	+	0.728119i	−0.0496462	+	0.998767i	$0.515809\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			1.18602i			0.0392944i	0.999807	+	0.0196472i	$0.00625431\pi$
$911$			1.18602i			0.0392944i	−0.999807	+	0.0196472i	$0.993746\pi$
$912$		0			0
$913$	−17.0845	+	3.89943i	−0.565415	+	0.129052i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.86179	+	6.26957i	−0.259619	+	0.207039i
$918$		0			0
$919$	−17.0281	+	21.3525i	−0.561704	+	0.704354i	−0.978872	−	0.204475i	$-0.934451\pi$
$919$	−17.0281	+	21.3525i	−0.561704	+	0.704354i	0.417168	+	0.908829i	$0.363023\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.382001	+	1.67366i	−0.0125737	+	0.0550891i
$924$		0			0
$925$	−7.46404	−	15.4992i	−0.245416	−	0.509612i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.3286			0.404488			0.202244	−	0.979335i	$-0.435177\pi$
$929$	12.3286			0.404488			0.202244	+	0.979335i	$0.435177\pi$
$930$		0			0
$931$	3.02962	+	6.29108i	0.0992919	+	0.206182i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.92896	+	1.89209i	−0.128491	+	0.0618779i
$936$		0			0
$937$	−11.7177	+	14.6936i	−0.382801	+	0.480018i	−0.935481	−	0.353376i	$-0.885034\pi$
$937$	−11.7177	+	14.6936i	−0.382801	+	0.480018i	0.552680	+	0.833393i	$0.313605\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−33.1286	−	41.5419i	−1.07996	−	1.35423i	−0.930847	−	0.365409i	$-0.880929\pi$
$941$	−33.1286	−	41.5419i	−1.07996	−	1.35423i	−0.149114	−	0.988820i	$-0.547642\pi$
$942$		0			0
$943$	−36.6034	+	8.35449i	−1.19197	+	0.272060i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	12.3494	−	25.6439i	0.401303	−	0.833314i	−0.598186	−	0.801357i	$-0.704112\pi$
$947$	12.3494	−	25.6439i	0.401303	−	0.833314i	0.999489	−	0.0319571i	$-0.0101740\pi$
$948$		0			0
$949$	4.25084	+	3.38993i	0.137988	+	0.110042i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−35.3452	−	17.0213i	−1.14494	−	0.551375i	−0.237432	−	0.971404i	$-0.576306\pi$
$953$	−35.3452	−	17.0213i	−1.14494	−	0.551375i	−0.907511	+	0.420029i	$0.862020\pi$
$954$		0			0
$955$	5.26829	+	1.20245i	0.170478	+	0.0389105i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.82735	+	1.78654i	0.252758	+	0.0576905i
$960$		0			0
$961$	−22.5499	−	10.8595i	−0.727417	−	0.350305i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.52187	+	3.60607i	0.145564	+	0.116084i
$966$		0			0
$967$	13.6513	−	28.3472i	0.438996	−	0.911584i	−0.557676	−	0.830059i	$-0.688307\pi$
$967$	13.6513	−	28.3472i	0.438996	−	0.911584i	0.996671	−	0.0815250i	$-0.0259790\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	25.2465	−	5.76235i	0.810199	−	0.184923i	0.202698	−	0.979241i	$-0.435029\pi$
$971$	25.2465	−	5.76235i	0.810199	−	0.184923i	0.607501	+	0.794319i	$0.292172\pi$
$972$		0			0
$973$	−9.26023	−	11.6120i	−0.296869	−	0.372262i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.6190	−	23.3475i	0.595675	−	0.746953i	−0.389022	−	0.921229i	$-0.627187\pi$
$977$	18.6190	−	23.3475i	0.595675	−	0.746953i	0.984697	+	0.174276i	$0.0557583\pi$
$978$		0			0
$979$	15.7828	−	7.60059i	0.504420	−	0.242916i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	17.4717	+	36.2803i	0.557259	+	1.15716i	0.969274	+	0.245984i	$0.0791109\pi$
$983$	17.4717	+	36.2803i	0.557259	+	1.15716i	−0.412015	+	0.911177i	$0.635175\pi$
$984$		0			0
$985$	2.58250			0.0822853
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−24.0449	−	49.9297i	−0.764582	−	1.58767i
$990$		0			0
$991$	3.75293	−	16.4426i	0.119216	−	0.522318i	−0.879690	−	0.475548i	$-0.842250\pi$
$991$	3.75293	−	16.4426i	0.119216	−	0.522318i	0.998906	−	0.0467703i	$-0.0148929\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.55935	+	3.20933i	−0.0811369	+	0.101742i
$996$		0			0
$997$	38.6311	−	30.8072i	1.22346	−	0.975675i	0.223458	−	0.974714i	$-0.428265\pi$
$997$	38.6311	−	30.8072i	1.22346	−	0.975675i	1.00000		0.000961406i	$-0.000306025\pi$
$998$		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.613.2	yes	24
3.2	odd	2	inner	1044.2.z.c.613.3	yes	24
29.22	even	14	inner	1044.2.z.c.109.2	✓	24
87.80	odd	14	inner	1044.2.z.c.109.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1044.2.z.c.109.2	✓	24	29.22	even	14	inner
1044.2.z.c.109.3	yes	24	87.80	odd	14	inner
1044.2.z.c.613.2	yes	24	1.1	even	1	trivial
1044.2.z.c.613.3	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.0963412 + 0.422098i) q^{5} +(-1.75124 + 0.843350i) q^{7} +O(q^{10})\)	\(q+(-0.0963412 + 0.422098i) q^{5} +(-1.75124 + 0.843350i) q^{7} +(1.32188 - 1.05417i) q^{11} +(-0.887715 - 1.11316i) q^{13} +5.95728i q^{17} +(0.940312 - 1.95258i) q^{19} +(1.63470 + 7.16209i) q^{23} +(4.33596 + 2.08809i) q^{25} +(-3.16210 + 4.35903i) q^{29} +(2.38239 + 0.543766i) q^{31} +(-0.187261 - 0.820443i) q^{35} +(-2.79472 - 2.22872i) q^{37} +5.11072i q^{41} +(-7.35452 + 1.67862i) q^{43} +(-1.35380 + 1.07962i) q^{47} +(-2.00884 + 2.51901i) q^{49} +(-2.56097 + 11.2203i) q^{53} +(0.317610 + 0.659524i) q^{55} +12.0447 q^{59} +(0.325228 + 0.675343i) q^{61} +(0.555386 - 0.267460i) q^{65} +(4.67843 - 5.86657i) q^{67} +(-0.751759 - 0.942676i) q^{71} +(-3.72297 + 0.849744i) q^{73} +(-1.42589 + 2.96090i) q^{77} +(6.97885 + 5.56545i) q^{79} +(-9.33814 - 4.49701i) q^{83} +(-2.51456 - 0.573931i) q^{85} +(10.1011 + 2.30550i) q^{89} +(2.49338 + 1.20075i) q^{91} +(0.733589 + 0.585018i) q^{95} +(4.81459 - 9.99761i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more