LMFDB - Embedded newform 276.2.i.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.1
Root			$1.84381 - 0.541390i$ of defining polynomial
Character	$\chi$	$=$	276.85
Dual form			276.2.i.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{3} +(-1.21471 - 2.65985i) q^{5} +(0.960219 - 0.281946i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{3} +(-1.21471 - 2.65985i) q^{5} +(0.960219 - 0.281946i) q^{7} +(0.415415 - 0.909632i) q^{9} +(-1.65056 - 1.90485i) q^{11} +(0.463267 + 0.136028i) q^{13} +(-2.45990 - 1.58088i) q^{15} +(0.446491 - 3.10542i) q^{17} +(-0.0786963 - 0.547345i) q^{19} +(0.655357 - 0.756322i) q^{21} +(3.87251 + 2.82908i) q^{23} +(-2.32496 + 2.68314i) q^{25} +(-0.142315 - 0.989821i) q^{27} +(-0.0173123 + 0.120410i) q^{29} +(6.92752 + 4.45205i) q^{31} +(-2.41838 - 0.710099i) q^{33} +(-1.91632 - 2.21155i) q^{35} +(-3.95959 + 8.67029i) q^{37} +(0.463267 - 0.136028i) q^{39} +(-0.578290 - 1.26628i) q^{41} +(5.21923 - 3.35419i) q^{43} -2.92409 q^{45} +8.69831 q^{47} +(-5.04625 + 3.24303i) q^{49} +(-1.30330 - 2.85383i) q^{51} +(-7.41370 + 2.17686i) q^{53} +(-3.06165 + 6.70407i) q^{55} +(-0.362120 - 0.417909i) q^{57} +(0.227334 + 0.0667513i) q^{59} +(-1.54102 - 0.990353i) q^{61} +(0.142423 - 0.990571i) q^{63} +(-0.200924 - 1.39745i) q^{65} +(1.83195 - 2.11418i) q^{67} +(4.78728 + 0.286340i) q^{69} +(-7.51699 + 8.67507i) q^{71} +(1.94856 + 13.5525i) q^{73} +(-0.505261 + 3.51417i) q^{75} +(-2.12196 - 1.36370i) q^{77} +(16.3977 + 4.81479i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(-3.34983 + 7.33511i) q^{83} +(-8.80229 + 2.58458i) q^{85} +(0.0505345 + 0.110655i) q^{87} +(4.15453 - 2.66995i) q^{89} +0.483191 q^{91} +8.23476 q^{93} +(-1.36026 + 0.874186i) q^{95} +(-6.49214 - 14.2158i) q^{97} +(-2.41838 + 0.710099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$		0			0
$5$	−1.21471	−	2.65985i	−0.543235	−	1.18952i	−0.959870	−	0.280445i	$-0.909518\pi$
$5$	−1.21471	−	2.65985i	−0.543235	−	1.18952i	0.416635	−	0.909074i	$-0.363209\pi$
$6$		0			0
$7$	0.960219	−	0.281946i	0.362929	−	0.106566i	−0.0951837	−	0.995460i	$-0.530344\pi$
$7$	0.960219	−	0.281946i	0.362929	−	0.106566i	0.458113	+	0.888894i	$0.348526\pi$
$8$		0			0
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$		0			0
$11$	−1.65056	−	1.90485i	−0.497662	−	0.574333i	0.450235	−	0.892910i	$-0.351340\pi$
$11$	−1.65056	−	1.90485i	−0.497662	−	0.574333i	−0.947897	+	0.318578i	$0.896795\pi$
$12$		0			0
$13$	0.463267	+	0.136028i	0.128487	+	0.0377273i	0.345344	−	0.938476i	$-0.387762\pi$
$13$	0.463267	+	0.136028i	0.128487	+	0.0377273i	−0.216857	+	0.976203i	$0.569580\pi$
$14$		0			0
$15$	−2.45990	−	1.58088i	−0.635144	−	0.408182i
$16$		0			0
$17$	0.446491	−	3.10542i	0.108290	−	0.753174i	−0.861239	−	0.508199i	$-0.830311\pi$
$17$	0.446491	−	3.10542i	0.108290	−	0.753174i	0.969529	−	0.244975i	$-0.0787796\pi$
$18$		0			0
$19$	−0.0786963	−	0.547345i	−0.0180542	−	0.125569i	0.978801	−	0.204813i	$-0.0656586\pi$
$19$	−0.0786963	−	0.547345i	−0.0180542	−	0.125569i	−0.996855	+	0.0792435i	$0.974750\pi$
$20$		0			0
$21$	0.655357	−	0.756322i	0.143011	−	0.165043i
$22$		0			0
$23$	3.87251	+	2.82908i	0.807473	+	0.589904i
$23$	3.87251	+	2.82908i	0.807473	+	0.589904i
$24$		0			0
$25$	−2.32496	+	2.68314i	−0.464991	+	0.536628i
$26$		0			0
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$		0			0
$29$	−0.0173123	+	0.120410i	−0.00321482	+	0.0223596i	−0.991366	−	0.131126i	$-0.958141\pi$
$29$	−0.0173123	+	0.120410i	−0.00321482	+	0.0223596i	0.988151	+	0.153486i	$0.0490499\pi$
$30$		0			0
$31$	6.92752	+	4.45205i	1.24422	+	0.799611i	0.986044	−	0.166487i	$-0.0532424\pi$
$31$	6.92752	+	4.45205i	1.24422	+	0.799611i	0.258175	+	0.966098i	$0.416879\pi$
$32$		0			0
$33$	−2.41838	−	0.710099i	−0.420985	−	0.123612i
$34$		0			0
$35$	−1.91632	−	2.21155i	−0.323917	−	0.373821i
$36$		0			0
$37$	−3.95959	+	8.67029i	−0.650952	+	1.42539i	0.239766	+	0.970831i	$0.422929\pi$
$37$	−3.95959	+	8.67029i	−0.650952	+	1.42539i	−0.890718	+	0.454556i	$0.849798\pi$
$38$		0			0
$39$	0.463267	−	0.136028i	0.0741822	−	0.0217818i
$40$		0			0
$41$	−0.578290	−	1.26628i	−0.0903137	−	0.197760i	0.859085	−	0.511833i	$-0.171033\pi$
$41$	−0.578290	−	1.26628i	−0.0903137	−	0.197760i	−0.949399	+	0.314074i	$0.898306\pi$
$42$		0			0
$43$	5.21923	−	3.35419i	0.795925	−	0.511510i	−0.0783589	−	0.996925i	$-0.524968\pi$
$43$	5.21923	−	3.35419i	0.795925	−	0.511510i	0.874284	+	0.485415i	$0.161332\pi$
$44$		0			0
$45$	−2.92409			−0.435898
$46$		0			0
$47$	8.69831			1.26878			0.634389	−	0.773014i	$-0.281252\pi$
$47$	8.69831			1.26878			0.634389	+	0.773014i	$0.281252\pi$
$48$		0			0
$49$	−5.04625	+	3.24303i	−0.720892	+	0.463289i
$50$		0			0
$51$	−1.30330	−	2.85383i	−0.182499	−	0.399617i
$52$		0			0
$53$	−7.41370	+	2.17686i	−1.01835	+	0.299015i	−0.747965	−	0.663738i	$-0.768969\pi$
$53$	−7.41370	+	2.17686i	−1.01835	+	0.299015i	−0.270385	+	0.962752i	$0.587151\pi$
$54$		0			0
$55$	−3.06165	+	6.70407i	−0.412832	+	0.903976i
$56$		0			0
$57$	−0.362120	−	0.417909i	−0.0479640	−	0.0553534i
$58$		0			0
$59$	0.227334	+	0.0667513i	0.0295964	+	0.00869028i	0.296497	−	0.955034i	$-0.404181\pi$
$59$	0.227334	+	0.0667513i	0.0295964	+	0.00869028i	−0.266901	+	0.963724i	$0.586000\pi$
$60$		0			0
$61$	−1.54102	−	0.990353i	−0.197307	−	0.126802i	0.438257	−	0.898850i	$-0.355596\pi$
$61$	−1.54102	−	0.990353i	−0.197307	−	0.126802i	−0.635564	+	0.772048i	$0.719232\pi$
$62$		0			0
$63$	0.142423	−	0.990571i	0.0179436	−	0.124800i
$64$		0			0
$65$	−0.200924	−	1.39745i	−0.0249215	−	0.173333i
$66$		0			0
$67$	1.83195	−	2.11418i	0.223808	−	0.258288i	−0.632730	−	0.774373i	$-0.718065\pi$
$67$	1.83195	−	2.11418i	0.223808	−	0.258288i	0.856538	+	0.516084i	$0.172611\pi$
$68$		0			0
$69$	4.78728	+	0.286340i	0.576320	+	0.0344712i
$70$		0			0
$71$	−7.51699	+	8.67507i	−0.892103	+	1.02954i	0.107274	+	0.994230i	$0.465788\pi$
$71$	−7.51699	+	8.67507i	−0.892103	+	1.02954i	−0.999376	+	0.0353118i	$0.988758\pi$
$72$		0			0
$73$	1.94856	+	13.5525i	0.228061	+	1.58620i	0.706261	+	0.707951i	$0.250380\pi$
$73$	1.94856	+	13.5525i	0.228061	+	1.58620i	−0.478200	+	0.878251i	$0.658711\pi$
$74$		0			0
$75$	−0.505261	+	3.51417i	−0.0583425	+	0.405781i
$76$		0			0
$77$	−2.12196	−	1.36370i	−0.241820	−	0.155408i
$78$		0			0
$79$	16.3977	+	4.81479i	1.84488	+	0.541706i	0.999977	+	0.00678681i	$0.00216032\pi$
$79$	16.3977	+	4.81479i	1.84488	+	0.541706i	0.844903	+	0.534919i	$0.179658\pi$
$80$		0			0
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$		0			0
$83$	−3.34983	+	7.33511i	−0.367692	+	0.805133i	0.631857	+	0.775085i	$0.282293\pi$
$83$	−3.34983	+	7.33511i	−0.367692	+	0.805133i	−0.999548	+	0.0300477i	$0.990434\pi$
$84$		0			0
$85$	−8.80229	+	2.58458i	−0.954742	+	0.280338i
$86$		0			0
$87$	0.0505345	+	0.110655i	0.00541787	+	0.0118635i
$88$		0			0
$89$	4.15453	−	2.66995i	0.440379	−	0.283015i	−0.301604	−	0.953433i	$-0.597522\pi$
$89$	4.15453	−	2.66995i	0.440379	−	0.283015i	0.741983	+	0.670419i	$0.233886\pi$
$90$		0			0
$91$	0.483191			0.0506522
$92$		0			0
$93$	8.23476			0.853904
$94$		0			0
$95$	−1.36026	+	0.874186i	−0.139560	+	0.0896896i
$96$		0			0
$97$	−6.49214	−	14.2158i	−0.659177	−	1.44340i	−0.883287	−	0.468833i	$-0.844675\pi$
$97$	−6.49214	−	14.2158i	−0.659177	−	1.44340i	0.224109	−	0.974564i	$-0.428053\pi$
$98$		0			0
$99$	−2.41838	+	0.710099i	−0.243056	+	0.0713676i
$100$		0			0
$101$	−1.35100	+	2.95829i	−0.134430	+	0.294361i	−0.964861	−	0.262761i	$-0.915367\pi$
$101$	−1.35100	+	2.95829i	−0.134430	+	0.294361i	0.830431	+	0.557121i	$0.188094\pi$
$102$		0			0
$103$	0.917997	+	1.05943i	0.0904529	+	0.104388i	0.799172	−	0.601103i	$-0.205272\pi$
$103$	0.917997	+	1.05943i	0.0904529	+	0.104388i	−0.708719	+	0.705491i	$0.750726\pi$
$104$		0			0
$105$	−2.80777	−	0.824435i	−0.274010	−	0.0804566i
$106$		0			0
$107$	−8.44978	−	5.43034i	−0.816871	−	0.524971i	0.0642102	−	0.997936i	$-0.479547\pi$
$107$	−8.44978	−	5.43034i	−0.816871	−	0.524971i	−0.881081	+	0.472965i	$0.843184\pi$
$108$		0			0
$109$	0.961777	−	6.68930i	0.0921215	−	0.640719i	−0.890484	−	0.455014i	$-0.849634\pi$
$109$	0.961777	−	6.68930i	0.0921215	−	0.640719i	0.982606	−	0.185705i	$-0.0594568\pi$
$110$		0			0
$111$	1.35649	+	9.43463i	0.128753	+	0.895495i
$112$		0			0
$113$	6.56447	−	7.57581i	0.617534	−	0.712672i	−0.357703	−	0.933835i	$-0.616440\pi$
$113$	6.56447	−	7.57581i	0.617534	−	0.712672i	0.975237	+	0.221164i	$0.0709854\pi$
$114$		0			0
$115$	2.82094	−	13.7368i	0.263054	−	1.28096i
$116$		0			0
$117$	0.316183	−	0.364895i	0.0292312	−	0.0337346i
$118$		0			0
$119$	−0.446829	−	3.10777i	−0.0409608	−	0.284889i
$120$		0			0
$121$	0.661368	−	4.59992i	0.0601244	−	0.418174i
$122$		0			0
$123$	−1.17109	−	0.752614i	−0.105594	−	0.0678609i
$124$		0			0
$125$	−4.06733	−	1.19428i	−0.363793	−	0.106819i
$126$		0			0
$127$	−10.9350	−	12.6197i	−0.970327	−	1.11982i	−0.992766	−	0.120069i	$-0.961689\pi$
$127$	−10.9350	−	12.6197i	−0.970327	−	1.11982i	0.0224388	−	0.999748i	$-0.492857\pi$
$128$		0			0
$129$	2.57728	−	5.64345i	0.226917	−	0.496878i
$130$		0			0
$131$	13.8070	−	4.05411i	1.20633	−	0.354209i	0.384057	−	0.923309i	$-0.374526\pi$
$131$	13.8070	−	4.05411i	1.20633	−	0.354209i	0.822268	+	0.569100i	$0.192708\pi$
$132$		0			0
$133$	−0.229887	−	0.503383i	−0.0199338	−	0.0436488i
$134$		0			0
$135$	−2.45990	+	1.58088i	−0.211715	+	0.136061i
$136$		0			0
$137$	1.88176			0.160769			0.0803847	−	0.996764i	$-0.474385\pi$
$137$	1.88176			0.160769			0.0803847	+	0.996764i	$0.474385\pi$
$138$		0			0
$139$	3.46292			0.293721			0.146860	−	0.989157i	$-0.453083\pi$
$139$	3.46292			0.293721			0.146860	+	0.989157i	$0.453083\pi$
$140$		0			0
$141$	7.31748	−	4.70266i	0.616243	−	0.396035i
$142$		0			0
$143$	−0.505538	−	1.10697i	−0.0422752	−	0.0925699i
$144$		0			0
$145$	0.341302	−	0.100215i	0.0283436	−	0.00832242i
$146$		0			0
$147$	−2.49186	+	5.45641i	−0.205525	+	0.450037i
$148$		0			0
$149$	14.1256	+	16.3019i	1.15722	+	1.33550i	0.932540	+	0.361067i	$0.117588\pi$
$149$	14.1256	+	16.3019i	1.15722	+	1.33550i	0.224678	+	0.974433i	$0.427867\pi$
$150$		0			0
$151$	−3.13983	−	0.921937i	−0.255516	−	0.0750262i	0.151466	−	0.988462i	$-0.451601\pi$
$151$	−3.13983	−	0.921937i	−0.255516	−	0.0750262i	−0.406982	+	0.913436i	$0.633419\pi$
$152$		0			0
$153$	−2.63931	−	1.69618i	−0.213375	−	0.137128i
$154$		0			0
$155$	3.42682	−	23.8341i	0.275249	−	1.91440i
$156$		0			0
$157$	−3.24424	−	22.5642i	−0.258919	−	1.80082i	−0.540567	−	0.841301i	$-0.681790\pi$
$157$	−3.24424	−	22.5642i	−0.258919	−	1.80082i	0.281649	−	0.959518i	$-0.409119\pi$
$158$		0			0
$159$	−5.05990	+	5.83944i	−0.401277	+	0.463098i
$160$		0			0
$161$	4.51610	+	1.62470i	0.355919	+	0.128044i
$162$		0			0
$163$	7.91542	−	9.13488i	0.619984	−	0.715499i	−0.355720	−	0.934592i	$-0.615764\pi$
$163$	7.91542	−	9.13488i	0.619984	−	0.715499i	0.975704	+	0.219093i	$0.0703099\pi$
$164$		0			0
$165$	1.04887	+	7.29507i	0.0816547	+	0.567921i
$166$		0			0
$167$	−1.18059	+	8.21115i	−0.0913565	+	0.635398i	0.891772	+	0.452484i	$0.149462\pi$
$167$	−1.18059	+	8.21115i	−0.0913565	+	0.635398i	−0.983129	+	0.182914i	$0.941447\pi$
$168$		0			0
$169$	−10.7402	−	6.90230i	−0.826168	−	0.530946i
$170$		0			0
$171$	−0.530574	−	0.155791i	−0.0405740	−	0.0119136i
$172$		0			0
$173$	13.5301	+	15.6146i	1.02868	+	1.18716i	0.982123	+	0.188241i	$0.0602786\pi$
$173$	13.5301	+	15.6146i	1.02868	+	1.18716i	0.0465543	+	0.998916i	$0.485176\pi$
$174$		0			0
$175$	−1.47597	+	3.23192i	−0.111573	+	0.244310i
$176$		0			0
$177$	0.227334	−	0.0667513i	0.0170875	−	0.00501733i
$178$		0			0
$179$	1.61211	+	3.53002i	0.120494	+	0.263846i	0.960262	−	0.279100i	$-0.0900361\pi$
$179$	1.61211	+	3.53002i	0.120494	+	0.263846i	−0.839768	+	0.542946i	$0.817309\pi$
$180$		0			0
$181$	6.70576	−	4.30953i	0.498435	−	0.320325i	−0.267155	−	0.963654i	$-0.586083\pi$
$181$	6.70576	−	4.30953i	0.498435	−	0.320325i	0.765590	+	0.643329i	$0.222447\pi$
$182$		0			0
$183$	−1.83181			−0.135412
$184$		0			0
$185$	27.8714			2.04915
$186$		0			0
$187$	−6.65230	+	4.27517i	−0.486464	+	0.312632i
$188$		0			0
$189$	−0.415730	−	0.910321i	−0.0302399	−	0.0662161i
$190$		0			0
$191$	−16.2019	+	4.75730i	−1.17233	+	0.344226i	−0.809211	−	0.587518i	$-0.800105\pi$
$191$	−16.2019	+	4.75730i	−1.17233	+	0.344226i	−0.363116	+	0.931744i	$0.618287\pi$
$192$		0			0
$193$	−8.84842	+	19.3753i	−0.636923	+	1.39467i	0.265624	+	0.964077i	$0.414422\pi$
$193$	−8.84842	+	19.3753i	−0.636923	+	1.39467i	−0.902547	+	0.430591i	$0.858305\pi$
$194$		0			0
$195$	−0.924549	−	1.06699i	−0.0662083	−	0.0764084i
$196$		0			0
$197$	−25.8424	−	7.58802i	−1.84120	−	0.540624i	−0.841196	−	0.540731i	$-0.818148\pi$
$197$	−25.8424	−	7.58802i	−1.84120	−	0.540624i	−1.00000		0.000106800i	$0.999966\pi$
$198$		0			0
$199$	−6.12918	−	3.93898i	−0.434486	−	0.279227i	0.305060	−	0.952333i	$-0.401323\pi$
$199$	−6.12918	−	3.93898i	−0.434486	−	0.279227i	−0.739546	+	0.673106i	$0.764960\pi$
$200$		0			0
$201$	0.398121	−	2.76899i	0.0280813	−	0.195309i
$202$		0			0
$203$	0.0173255	+	0.120501i	0.00121601	+	0.00845752i
$204$		0			0
$205$	−2.66565	+	3.07633i	−0.186177	+	0.214860i
$206$		0			0
$207$	4.18212	−	2.34731i	0.290677	−	0.163149i
$208$		0			0
$209$	−0.912714	+	1.05333i	−0.0631338	+	0.0728603i
$210$		0			0
$211$	−2.22131	−	15.4495i	−0.152921	−	1.06359i	−0.911290	−	0.411765i	$-0.864913\pi$
$211$	−2.22131	−	15.4495i	−0.152921	−	1.06359i	0.758369	−	0.651825i	$-0.225997\pi$
$212$		0			0
$213$	−1.63360	+	11.3619i	−0.111932	+	0.778506i
$214$		0			0
$215$	−15.2615	−	9.80797i	−1.04083	−	0.668898i
$216$		0			0
$217$	7.90717	+	2.32176i	0.536774	+	0.157611i
$218$		0			0
$219$	8.96628	+	10.3476i	0.605885	+	0.699228i
$220$		0			0
$221$	0.629267	−	1.37790i	0.0423291	−	0.0926878i
$222$		0			0
$223$	1.34888	−	0.396066i	0.0903274	−	0.0265225i	−0.236257	−	0.971691i	$-0.575921\pi$
$223$	1.34888	−	0.396066i	0.0903274	−	0.0265225i	0.326584	+	0.945168i	$0.394102\pi$
$224$		0			0
$225$	1.47485	+	3.22947i	0.0983233	+	0.215298i
$226$		0			0
$227$	−3.73511	+	2.40041i	−0.247908	+	0.159321i	−0.658694	−	0.752411i	$-0.728891\pi$
$227$	−3.73511	+	2.40041i	−0.247908	+	0.159321i	0.410786	+	0.911732i	$0.365254\pi$
$228$		0			0
$229$	−1.67523			−0.110702			−0.0553512	−	0.998467i	$-0.517628\pi$
$229$	−1.67523			−0.110702			−0.0553512	+	0.998467i	$0.517628\pi$
$230$		0			0
$231$	−2.52238			−0.165960
$232$		0			0
$233$	−18.3038	+	11.7632i	−1.19912	+	0.770630i	−0.978804	−	0.204798i	$-0.934346\pi$
$233$	−18.3038	+	11.7632i	−1.19912	+	0.770630i	−0.220319	+	0.975428i	$0.570710\pi$
$234$		0			0
$235$	−10.5659	−	23.1362i	−0.689245	−	1.50924i
$236$		0			0
$237$	16.3977	−	4.81479i	1.06514	−	0.312754i
$238$		0			0
$239$	−8.72594	+	19.1071i	−0.564434	+	1.23594i	0.385274	+	0.922802i	$0.374107\pi$
$239$	−8.72594	+	19.1071i	−0.564434	+	1.23594i	−0.949708	+	0.313136i	$0.898620\pi$
$240$		0			0
$241$	17.2462	+	19.9032i	1.11093	+	1.28208i	0.955746	+	0.294194i	$0.0950510\pi$
$241$	17.2462	+	19.9032i	1.11093	+	1.28208i	0.155182	+	0.987886i	$0.450404\pi$
$242$		0			0
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$		0			0
$245$	14.7557	+	9.48290i	0.942706	+	0.605840i
$246$		0			0
$247$	0.0379966	−	0.264272i	0.00241766	−	0.0168152i
$248$		0			0
$249$	1.14760	+	7.98174i	0.0727263	+	0.505823i
$250$		0			0
$251$	−17.0613	+	19.6898i	−1.07690	+	1.24281i	−0.108318	+	0.994116i	$0.534547\pi$
$251$	−17.0613	+	19.6898i	−1.07690	+	1.24281i	−0.968582	+	0.248693i	$0.919999\pi$
$252$		0			0
$253$	−1.00283	−	12.0461i	−0.0630476	−	0.757331i
$254$		0			0
$255$	−6.00762	+	6.93317i	−0.376212	+	0.434172i
$256$		0			0
$257$	−1.12414	−	7.81860i	−0.0701222	−	0.487711i	−0.994374	−	0.105927i	$-0.966219\pi$
$257$	−1.12414	−	7.81860i	−0.0701222	−	0.487711i	0.924252	−	0.381784i	$-0.124690\pi$
$258$		0			0
$259$	−1.35752	+	9.44177i	−0.0843523	+	0.586683i
$260$		0			0
$261$	0.102337	+	0.0657680i	0.00633450	+	0.00407094i
$262$		0			0
$263$	11.8421	+	3.47716i	0.730216	+	0.214411i	0.625646	−	0.780107i	$-0.284835\pi$
$263$	11.8421	+	3.47716i	0.730216	+	0.214411i	0.104570	+	0.994518i	$0.466653\pi$
$264$		0			0
$265$	14.7956	+	17.0751i	0.908888	+	1.04891i
$266$		0			0
$267$	2.05153	−	4.49222i	0.125551	−	0.274919i
$268$		0			0
$269$	10.7364	−	3.15249i	0.654610	−	0.192211i	0.0624710	−	0.998047i	$-0.480102\pi$
$269$	10.7364	−	3.15249i	0.654610	−	0.192211i	0.592139	+	0.805836i	$0.298284\pi$
$270$		0			0
$271$	9.90135	+	21.6809i	0.601464	+	1.31702i	0.928261	+	0.371929i	$0.121303\pi$
$271$	9.90135	+	21.6809i	0.601464	+	1.31702i	−0.326797	+	0.945095i	$0.605969\pi$
$272$		0			0
$273$	0.406486	−	0.261233i	0.0246016	−	0.0158105i
$274$		0			0
$275$	8.94844			0.539612
$276$		0			0
$277$	−17.8542			−1.07275			−0.536376	−	0.843979i	$-0.680207\pi$
$277$	−17.8542			−1.07275			−0.536376	+	0.843979i	$0.680207\pi$
$278$		0			0
$279$	6.92752	−	4.45205i	0.414740	−	0.266537i
$280$		0			0
$281$	−0.687581	−	1.50559i	−0.0410176	−	0.0898161i	0.888014	−	0.459817i	$-0.152085\pi$
$281$	−0.687581	−	1.50559i	−0.0410176	−	0.0898161i	−0.929032	+	0.370000i	$0.879358\pi$
$282$		0			0
$283$	1.30907	−	0.384378i	0.0778161	−	0.0228489i	−0.242593	−	0.970128i	$-0.577998\pi$
$283$	1.30907	−	0.384378i	0.0778161	−	0.0228489i	0.320409	+	0.947279i	$0.396180\pi$
$284$		0			0
$285$	−0.671703	+	1.47082i	−0.0397882	+	0.0871241i
$286$		0			0
$287$	−0.912307	−	1.05286i	−0.0538518	−	0.0621483i
$288$		0			0
$289$	6.86713	+	2.01637i	0.403949	+	0.118610i
$290$		0			0
$291$	−13.1472	−	8.44918i	−0.770702	−	0.495300i
$292$		0			0
$293$	1.50932	−	10.4975i	0.0881752	−	0.613272i	−0.897040	−	0.441950i	$-0.854287\pi$
$293$	1.50932	−	10.4975i	0.0881752	−	0.613272i	0.985215	−	0.171322i	$-0.0548039\pi$
$294$		0			0
$295$	−0.0985970	−	0.685757i	−0.00574054	−	0.0399263i
$296$		0			0
$297$	−1.65056	+	1.90485i	−0.0957751	+	0.110530i
$298$		0			0
$299$	1.40917	+	1.83739i	0.0814946	+	0.106259i
$300$		0			0
$301$	4.06590	−	4.69230i	0.234355	−	0.270460i
$302$		0			0
$303$	0.462834	+	3.21908i	0.0265891	+	0.184931i
$304$		0			0
$305$	−0.762294	+	5.30187i	−0.0436488	+	0.303584i
$306$		0			0
$307$	−8.68375	−	5.58071i	−0.495608	−	0.318508i	0.268849	−	0.963182i	$-0.413357\pi$
$307$	−8.68375	−	5.58071i	−0.495608	−	0.318508i	−0.764457	+	0.644674i	$0.776993\pi$
$308$		0			0
$309$	1.34504	+	0.394938i	0.0765165	+	0.0224673i
$310$		0			0
$311$	4.61609	+	5.32725i	0.261755	+	0.302081i	0.871380	−	0.490609i	$-0.163226\pi$
$311$	4.61609	+	5.32725i	0.261755	+	0.302081i	−0.609625	+	0.792690i	$0.708680\pi$
$312$		0			0
$313$	0.939900	−	2.05809i	0.0531263	−	0.116330i	−0.881207	−	0.472730i	$-0.843269\pi$
$313$	0.939900	−	2.05809i	0.0531263	−	0.116330i	0.934334	+	0.356400i	$0.115996\pi$
$314$		0			0
$315$	−2.80777	+	0.824435i	−0.158200	+	0.0464517i
$316$		0			0
$317$	−1.31835	−	2.88679i	−0.0740460	−	0.162138i	0.868989	−	0.494831i	$-0.164770\pi$
$317$	−1.31835	−	2.88679i	−0.0740460	−	0.162138i	−0.943035	+	0.332693i	$0.892043\pi$
$318$		0			0
$319$	0.257938	−	0.165766i	0.0144417	−	0.00928114i
$320$		0			0
$321$	−10.0443			−0.560616
$322$		0			0
$323$	−1.73487			−0.0965308
$324$		0			0
$325$	−1.44206	+	0.926754i	−0.0799909	+	0.0514071i
$326$		0			0
$327$	−2.80741	−	6.14738i	−0.155250	−	0.339951i
$328$		0			0
$329$	8.35228	−	2.45245i	0.460476	−	0.135208i
$330$		0			0
$331$	−8.63436	+	18.9066i	−0.474587	+	1.03920i	0.509329	+	0.860572i	$0.329894\pi$
$331$	−8.63436	+	18.9066i	−0.474587	+	1.03920i	−0.983916	+	0.178629i	$0.942834\pi$
$332$		0			0
$333$	6.24190	+	7.20354i	0.342054	+	0.394751i
$334$		0			0
$335$	−7.84869	−	2.30458i	−0.428820	−	0.125913i
$336$		0			0
$337$	−21.9636	−	14.1152i	−1.19644	−	0.768902i	−0.218099	−	0.975927i	$-0.569986\pi$
$337$	−21.9636	−	14.1152i	−1.19644	−	0.768902i	−0.978336	+	0.207024i	$0.933622\pi$
$338$		0			0
$339$	1.42660	−	9.92220i	0.0774821	−	0.538900i
$340$		0			0
$341$	−2.95381	−	20.5442i	−0.159958	−	1.11253i
$342$		0			0
$343$	−8.51864	+	9.83104i	−0.459963	+	0.530826i
$344$		0			0
$345$	−5.05354	−	13.0812i	−0.272073	−	0.704270i
$346$		0			0
$347$	7.52379	−	8.68291i	0.403898	−	0.466123i	−0.516967	−	0.856006i	$-0.672939\pi$
$347$	7.52379	−	8.68291i	0.403898	−	0.466123i	0.920865	+	0.389882i	$0.127484\pi$
$348$		0			0
$349$	4.15887	+	28.9256i	0.222619	+	1.54835i	0.728075	+	0.685497i	$0.240415\pi$
$349$	4.15887	+	28.9256i	0.222619	+	1.54835i	−0.505456	+	0.862852i	$0.668676\pi$
$350$		0			0
$351$	0.0687132	−	0.477911i	0.00366764	−	0.0255090i
$352$		0			0
$353$	−27.4206	−	17.6221i	−1.45945	−	0.937932i	−0.998730	−	0.0503875i	$-0.983954\pi$
$353$	−27.4206	−	17.6221i	−1.45945	−	0.937932i	−0.460721	−	0.887545i	$-0.652409\pi$
$354$		0			0
$355$	32.2053	+	9.45634i	1.70928	+	0.501890i
$356$		0			0
$357$	−2.05608	−	2.37285i	−0.108819	−	0.125584i
$358$		0			0
$359$	−12.1092	+	26.5155i	−0.639101	+	1.39944i	0.261678	+	0.965155i	$0.415724\pi$
$359$	−12.1092	+	26.5155i	−0.639101	+	1.39944i	−0.900778	+	0.434280i	$0.857003\pi$
$360$		0			0
$361$	17.9370	−	5.26677i	0.944051	−	0.277198i
$362$		0			0
$363$	−1.93052	−	4.22726i	−0.101326	−	0.221874i
$364$		0			0
$365$	33.6807	−	21.6453i	1.76293	−	1.13296i
$366$		0			0
$367$	−22.4367			−1.17119			−0.585593	−	0.810605i	$-0.699138\pi$
$367$	−22.4367			−1.17119			−0.585593	+	0.810605i	$0.699138\pi$
$368$		0			0
$369$	−1.39208			−0.0724687
$370$		0			0
$371$	−6.50502	+	4.18053i	−0.337724	+	0.217042i
$372$		0			0
$373$	−5.65832	−	12.3900i	−0.292977	−	0.641530i	0.704711	−	0.709495i	$-0.251077\pi$
$373$	−5.65832	−	12.3900i	−0.292977	−	0.641530i	−0.997688	+	0.0679649i	$0.978349\pi$
$374$		0			0
$375$	−4.06733	+	1.19428i	−0.210036	+	0.0616721i
$376$		0			0
$377$	−0.0243993	+	0.0534271i	−0.00125663	+	0.00275163i
$378$		0			0
$379$	−3.03505	−	3.50264i	−0.155900	−	0.179918i	0.672426	−	0.740164i	$-0.265252\pi$
$379$	−3.03505	−	3.50264i	−0.155900	−	0.179918i	−0.828327	+	0.560246i	$0.810707\pi$
$380$		0			0
$381$	−16.0219	−	4.70444i	−0.820824	−	0.241016i
$382$		0			0
$383$	25.6052	+	16.4555i	1.30837	+	0.840836i	0.994097	−	0.108498i	$-0.0346042\pi$
$383$	25.6052	+	16.4555i	1.30837	+	0.840836i	0.314269	+	0.949334i	$0.398241\pi$
$384$		0			0
$385$	−1.04967	+	7.30060i	−0.0534960	+	0.372073i
$386$		0			0
$387$	−0.882937	−	6.14096i	−0.0448822	−	0.312162i
$388$		0			0
$389$	−1.96796	+	2.27115i	−0.0997797	+	0.115152i	−0.803443	−	0.595382i	$-0.797001\pi$
$389$	−1.96796	+	2.27115i	−0.0997797	+	0.115152i	0.703663	+	0.710534i	$0.251546\pi$
$390$		0			0
$391$	10.5145	−	10.7626i	0.531742	−	0.544287i
$392$		0			0
$393$	9.42339	−	10.8752i	0.475347	−	0.548580i
$394$		0			0
$395$	−7.11182	−	49.4638i	−0.357835	−	2.48879i
$396$		0			0
$397$	1.38627	−	9.64170i	0.0695747	−	0.483903i	−0.925007	−	0.379949i	$-0.875942\pi$
$397$	1.38627	−	9.64170i	0.0695747	−	0.483903i	0.994582	−	0.103954i	$-0.0331494\pi$
$398$		0			0
$399$	−0.465543	−	0.299186i	−0.0233063	−	0.0149780i
$400$		0			0
$401$	−19.1560	−	5.62470i	−0.956603	−	0.280884i	−0.234069	−	0.972220i	$-0.575204\pi$
$401$	−19.1560	−	5.62470i	−0.956603	−	0.280884i	−0.722533	+	0.691336i	$0.757022\pi$
$402$		0			0
$403$	2.60369	+	3.00482i	0.129699	+	0.149681i
$404$		0			0
$405$	−1.21471	+	2.65985i	−0.0603595	+	0.132169i
$406$		0			0
$407$	23.0511	−	6.76841i	1.14260	−	0.335498i
$408$		0			0
$409$	10.1075	+	22.1323i	0.499784	+	1.09437i	0.976540	+	0.215338i	$0.0690853\pi$
$409$	10.1075	+	22.1323i	0.499784	+	1.09437i	−0.476756	+	0.879036i	$0.658187\pi$
$410$		0			0
$411$	1.58303	−	1.01735i	0.0780853	−	0.0501824i
$412$		0			0
$413$	0.237111			0.0116675
$414$		0			0
$415$	23.5793			1.15746
$416$		0			0
$417$	2.91319	−	1.87219i	0.142660	−	0.0916818i
$418$		0			0
$419$	5.43702	+	11.9054i	0.265616	+	0.581618i	0.994702	−	0.102805i	$-0.0327817\pi$
$419$	5.43702	+	11.9054i	0.265616	+	0.581618i	−0.729086	+	0.684422i	$0.760054\pi$
$420$		0			0
$421$	5.86675	−	1.72263i	0.285928	−	0.0839560i	−0.135624	−	0.990760i	$-0.543304\pi$
$421$	5.86675	−	1.72263i	0.285928	−	0.0839560i	0.421552	+	0.906804i	$0.361486\pi$
$422$		0			0
$423$	3.61341	−	7.91226i	0.175690	−	0.384707i
$424$		0			0
$425$	7.29420	+	8.41795i	0.353821	+	0.408331i
$426$		0			0
$427$	−1.75894	−	0.516472i	−0.0851212	−	0.0249938i
$428$		0			0
$429$	−1.02376	−	0.657932i	−0.0494277	−	0.0317652i
$430$		0			0
$431$	3.47655	−	24.1799i	0.167459	−	1.16471i	−0.716653	−	0.697430i	$-0.754327\pi$
$431$	3.47655	−	24.1799i	0.167459	−	1.16471i	0.884112	−	0.467275i	$-0.154764\pi$
$432$		0			0
$433$	2.34204	+	16.2892i	0.112551	+	0.782810i	0.965423	+	0.260690i	$0.0839499\pi$
$433$	2.34204	+	16.2892i	0.112551	+	0.782810i	−0.852872	+	0.522121i	$0.825141\pi$
$434$		0			0
$435$	0.232941	−	0.268828i	0.0111687	−	0.0128893i
$436$		0			0
$437$	1.24373	−	2.34223i	0.0594957	−	0.112044i
$438$		0			0
$439$	0.691787	−	0.798365i	0.0330172	−	0.0381039i	−0.739001	−	0.673705i	$-0.764702\pi$
$439$	0.691787	−	0.798365i	0.0330172	−	0.0381039i	0.772018	+	0.635601i	$0.219247\pi$
$440$		0			0
$441$	0.853673	+	5.93743i	0.0406511	+	0.282735i
$442$		0			0
$443$	2.83450	−	19.7144i	0.134671	−	0.936659i	−0.804681	−	0.593707i	$-0.797664\pi$
$443$	2.83450	−	19.7144i	0.134671	−	0.936659i	0.939353	−	0.342953i	$-0.111427\pi$
$444$		0			0
$445$	−12.1482	−	7.80719i	−0.575881	−	0.370096i
$446$		0			0
$447$	20.6967	+	6.07710i	0.978920	+	0.287437i
$448$		0			0
$449$	−16.0130	−	18.4800i	−0.755702	−	0.872127i	0.239406	−	0.970920i	$-0.423047\pi$
$449$	−16.0130	−	18.4800i	−0.755702	−	0.872127i	−0.995108	+	0.0987927i	$0.968502\pi$
$450$		0			0
$451$	−1.45756	+	3.19162i	−0.0686340	+	0.150288i
$452$		0			0
$453$	−3.13983	+	0.921937i	−0.147522	+	0.0433164i
$454$		0			0
$455$	−0.586937	−	1.28521i	−0.0275160	−	0.0602517i
$456$		0			0
$457$	8.21331	−	5.27838i	0.384203	−	0.246912i	−0.334255	−	0.942483i	$-0.608485\pi$
$457$	8.21331	−	5.27838i	0.384203	−	0.246912i	0.718458	+	0.695571i	$0.244848\pi$
$458$		0			0
$459$	−3.13735			−0.146439
$460$		0			0
$461$	28.8585			1.34408			0.672038	−	0.740517i	$-0.265419\pi$
$461$	28.8585			1.34408			0.672038	+	0.740517i	$0.265419\pi$
$462$		0			0
$463$	17.0636	−	10.9661i	0.793014	−	0.509639i	−0.0803151	−	0.996770i	$-0.525593\pi$
$463$	17.0636	−	10.9661i	0.793014	−	0.509639i	0.873329	+	0.487130i	$0.161956\pi$
$464$		0			0
$465$	−10.0028	−	21.9032i	−0.463871	−	1.01574i
$466$		0			0
$467$	−26.5386	+	7.79244i	−1.22806	+	0.360591i	−0.830518	−	0.556993i	$-0.811955\pi$
$467$	−26.5386	+	7.79244i	−1.22806	+	0.360591i	−0.397543	+	0.917584i	$0.630137\pi$
$468$		0			0
$469$	1.16299	−	2.54659i	0.0537018	−	0.117591i
$470$		0			0
$471$	−14.9284	−	17.2282i	−0.687862	−	0.793835i
$472$		0			0
$473$	−15.0039	−	4.40553i	−0.689878	−	0.202567i
$474$		0			0
$475$	1.65157	+	1.06140i	0.0757792	+	0.0487003i
$476$		0			0
$477$	−1.09962	+	7.64804i	−0.0503482	+	0.350180i
$478$		0			0
$479$	−2.91070	−	20.2444i	−0.132993	−	0.924988i	−0.941623	−	0.336670i	$-0.890699\pi$
$479$	−2.91070	−	20.2444i	−0.132993	−	0.924988i	0.808630	−	0.588318i	$-0.200210\pi$
$480$		0			0
$481$	−3.01375	+	3.47805i	−0.137415	+	0.158585i
$482$		0			0
$483$	4.67757	−	1.07480i	0.212837	−	0.0489053i
$484$		0			0
$485$	−29.9258	+	34.5362i	−1.35886	+	1.56821i
$486$		0			0
$487$	−0.443196	−	3.08250i	−0.0200831	−	0.139681i	0.977313	−	0.211801i	$-0.0679328\pi$
$487$	−0.443196	−	3.08250i	−0.0200831	−	0.139681i	−0.997396	+	0.0721195i	$0.977024\pi$
$488$		0			0
$489$	1.72019	−	11.9642i	0.0777895	−	0.541038i
$490$		0			0
$491$	−4.62679	−	2.97346i	−0.208804	−	0.134190i	0.432059	−	0.901845i	$-0.357787\pi$
$491$	−4.62679	−	2.97346i	−0.208804	−	0.134190i	−0.640863	+	0.767655i	$0.721424\pi$
$492$		0			0
$493$	0.366193	+	0.107524i	0.0164925	+	0.00484264i
$494$		0			0
$495$	4.82638	+	5.56994i	0.216930	+	0.250350i
$496$		0			0
$497$	−4.77206	+	10.4494i	−0.214056	+	0.468718i
$498$		0			0
$499$	−8.04956	+	2.36356i	−0.360348	+	0.105808i	−0.456895	−	0.889521i	$-0.651038\pi$
$499$	−8.04956	+	2.36356i	−0.360348	+	0.105808i	0.0965470	+	0.995328i	$0.469220\pi$
$500$		0			0
$501$	3.44611	+	7.54594i	0.153961	+	0.337128i
$502$		0			0
$503$	−1.42347	+	0.914807i	−0.0634693	+	0.0407892i	−0.571991	−	0.820260i	$-0.693829\pi$
$503$	−1.42347	+	0.914807i	−0.0634693	+	0.0407892i	0.508521	+	0.861049i	$0.330192\pi$
$504$		0			0
$505$	9.50967			0.423175
$506$		0			0
$507$	−12.7669			−0.566997
$508$		0			0
$509$	−12.2843	+	7.89467i	−0.544494	+	0.349925i	−0.783794	−	0.621021i	$-0.786718\pi$
$509$	−12.2843	+	7.89467i	−0.544494	+	0.349925i	0.239300	+	0.970946i	$0.423082\pi$
$510$		0			0
$511$	5.69212	+	12.4640i	0.251805	+	0.551375i
$512$		0			0
$513$	−0.530574	+	0.155791i	−0.0234254	+	0.00687832i
$514$		0			0
$515$	1.70281	−	3.72863i	0.0750346	−	0.164303i
$516$		0			0
$517$	−14.3571	−	16.5689i	−0.631423	−	0.728701i
$518$		0			0
$519$	19.8242	+	5.82090i	0.870184	+	0.255509i
$520$		0			0
$521$	−21.6860	−	13.9368i	−0.950083	−	0.610581i	−0.0288462	−	0.999584i	$-0.509183\pi$
$521$	−21.6860	−	13.9368i	−0.950083	−	0.610581i	−0.921237	+	0.389003i	$0.872820\pi$
$522$		0			0
$523$	−2.00234	+	13.9266i	−0.0875563	+	0.608967i	0.898048	+	0.439898i	$0.144985\pi$
$523$	−2.00234	+	13.9266i	−0.0875563	+	0.608967i	−0.985604	+	0.169070i	$0.945924\pi$
$524$		0			0
$525$	0.505644	+	3.51683i	0.0220681	+	0.153487i
$526$		0			0
$527$	16.9185	−	19.5250i	0.736983	−	0.850524i
$528$		0			0
$529$	6.99260	+	21.9113i	0.304026	+	0.952664i
$530$		0			0
$531$	0.155157	−	0.179061i	0.00673324	−	0.00777058i
$532$		0			0
$533$	−0.0956541	−	0.665289i	−0.00414324	−	0.0288169i
$534$		0			0
$535$	−4.17984	+	29.0714i	−0.180710	+	1.25687i
$536$		0			0
$537$	3.26466	+	2.09807i	0.140881	+	0.0905385i
$538$		0			0
$539$	14.5066	+	4.25952i	0.624843	+	0.183470i
$540$		0			0
$541$	11.8199	+	13.6409i	0.508177	+	0.586468i	0.950631	−	0.310324i	$-0.100437\pi$
$541$	11.8199	+	13.6409i	0.508177	+	0.586468i	−0.442454	+	0.896791i	$0.645892\pi$
$542$		0			0
$543$	3.31134	−	7.25082i	0.142103	−	0.311162i
$544$		0			0
$545$	−18.9608	+	5.56739i	−0.812191	+	0.238481i
$546$		0			0
$547$	−6.77596	−	14.8373i	−0.289719	−	0.634396i	0.707675	−	0.706538i	$-0.249744\pi$
$547$	−6.77596	−	14.8373i	−0.289719	−	0.634396i	−0.997394	+	0.0721416i	$0.977017\pi$
$548$		0			0
$549$	−1.54102	+	0.990353i	−0.0657691	+	0.0422672i
$550$		0			0
$551$	0.0672682			0.00286572
$552$		0			0
$553$	17.1029			0.727287
$554$		0			0
$555$	23.4469	−	15.0684i	0.995266	−	0.639619i
$556$		0			0
$557$	9.28190	+	20.3245i	0.393287	+	0.861178i	0.997907	+	0.0646639i	$0.0205975\pi$
$557$	9.28190	+	20.3245i	0.393287	+	0.861178i	−0.604620	+	0.796514i	$0.706675\pi$
$558$		0			0
$559$	2.87416	−	0.843930i	0.121564	−	0.0356944i
$560$		0			0
$561$	−3.28494	+	7.19301i	−0.138690	+	0.303689i
$562$		0			0
$563$	9.19015	+	10.6060i	0.387318	+	0.446989i	0.915606	−	0.402076i	$-0.131711\pi$
$563$	9.19015	+	10.6060i	0.387318	+	0.446989i	−0.528288	+	0.849065i	$0.677166\pi$
$564$		0			0
$565$	−28.1244	−	8.25807i	−1.18320	−	0.347420i
$566$		0			0
$567$	−0.841890	−	0.541050i	−0.0353561	−	0.0227220i
$568$		0			0
$569$	−5.30762	+	36.9153i	−0.222507	+	1.54757i	0.506002	+	0.862532i	$0.331123\pi$
$569$	−5.30762	+	36.9153i	−0.222507	+	1.54757i	−0.728509	+	0.685037i	$0.759786\pi$
$570$		0			0
$571$	5.24484	+	36.4787i	0.219490	+	1.52659i	0.739928	+	0.672686i	$0.234860\pi$
$571$	5.24484	+	36.4787i	0.219490	+	1.52659i	−0.520438	+	0.853899i	$0.674231\pi$
$572$		0			0
$573$	−11.0579	+	12.7615i	−0.461950	+	0.533119i
$574$		0			0
$575$	−16.5942	+	3.81299i	−0.692027	+	0.159013i
$576$		0			0
$577$	−13.7946	+	15.9198i	−0.574278	+	0.662752i	−0.966364	−	0.257177i	$-0.917208\pi$
$577$	−13.7946	+	15.9198i	−0.574278	+	0.662752i	0.392087	+	0.919928i	$0.371753\pi$
$578$		0			0
$579$	3.03133	+	21.0834i	0.125978	+	0.876196i
$580$		0			0
$581$	−1.14847	+	7.98779i	−0.0476466	+	0.331389i
$582$		0			0
$583$	16.3833	+	10.5289i	0.678528	+	0.436064i
$584$		0			0
$585$	−1.35464	−	0.397757i	−0.0560073	−	0.0164452i
$586$		0			0
$587$	−0.0269562	−	0.0311092i	−0.00111260	−	0.00128401i	0.755193	−	0.655503i	$-0.227543\pi$
$587$	−0.0269562	−	0.0311092i	−0.00111260	−	0.00128401i	−0.756306	+	0.654218i	$0.772998\pi$
$588$		0			0
$589$	1.89163	−	4.14210i	0.0779434	−	0.170672i
$590$		0			0
$591$	−25.8424	+	7.58802i	−1.06301	+	0.312129i
$592$		0			0
$593$	6.17509	+	13.5216i	0.253580	+	0.555264i	0.993018	−	0.117961i	$-0.0376358\pi$
$593$	6.17509	+	13.5216i	0.253580	+	0.555264i	−0.739438	+	0.673225i	$0.764909\pi$
$594$		0			0
$595$	−7.72341	+	4.96354i	−0.316629	+	0.203485i
$596$		0			0
$597$	−7.28577			−0.298187
$598$		0			0
$599$	44.0448			1.79962			0.899811	−	0.436280i	$-0.143704\pi$
$599$	44.0448			1.79962			0.899811	+	0.436280i	$0.143704\pi$
$600$		0			0
$601$	37.1322	−	23.8634i	1.51465	−	0.973409i	0.521932	−	0.852987i	$-0.325212\pi$
$601$	37.1322	−	23.8634i	1.51465	−	0.973409i	0.992723	−	0.120422i	$-0.0384248\pi$
$602$		0			0
$603$	−1.16211	−	2.54466i	−0.0473247	−	0.103627i
$604$		0			0
$605$	−13.0384	+	3.82843i	−0.530088	+	0.155648i
$606$		0			0
$607$	−8.82155	+	19.3165i	−0.358056	+	0.784032i	0.641797	+	0.766874i	$0.278189\pi$
$607$	−8.82155	+	19.3165i	−0.358056	+	0.784032i	−0.999853	+	0.0171579i	$0.994538\pi$
$608$		0			0
$609$	0.0797229	+	0.0920052i	0.00323054	+	0.00372824i
$610$		0			0
$611$	4.02964	+	1.18321i	0.163022	+	0.0478676i
$612$		0			0
$613$	−28.7218	−	18.4584i	−1.16006	−	0.745527i	−0.188445	−	0.982084i	$-0.560345\pi$
$613$	−28.7218	−	18.4584i	−1.16006	−	0.745527i	−0.971618	+	0.236557i	$0.923981\pi$
$614$		0			0
$615$	−0.579301	+	4.02913i	−0.0233597	+	0.162470i
$616$		0			0
$617$	−5.83677	−	40.5956i	−0.234980	−	1.63432i	−0.676057	−	0.736849i	$-0.736313\pi$
$617$	−5.83677	−	40.5956i	−0.234980	−	1.63432i	0.441077	−	0.897469i	$-0.354596\pi$
$618$		0			0
$619$	−4.61337	+	5.32411i	−0.185427	+	0.213994i	−0.840851	−	0.541267i	$-0.817945\pi$
$619$	−4.61337	+	5.32411i	−0.185427	+	0.213994i	0.655424	+	0.755262i	$0.272490\pi$
$620$		0			0
$621$	2.24917	−	4.23571i	0.0902561	−	0.169973i
$622$		0			0
$623$	3.23648	−	3.73510i	0.129667	−	0.149643i
$624$		0			0
$625$	4.29035	+	29.8400i	0.171614	+	1.19360i
$626$		0			0
$627$	−0.198352	+	1.37957i	−0.00792141	+	0.0550946i
$628$		0			0
$629$	25.1569	+	16.1674i	1.00307	+	0.644636i
$630$		0			0
$631$	−22.4420	−	6.58958i	−0.893403	−	0.262327i	−0.197364	−	0.980330i	$-0.563238\pi$
$631$	−22.4420	−	6.58958i	−0.893403	−	0.262327i	−0.696040	+	0.718003i	$0.745056\pi$
$632$		0			0
$633$	−10.2213	−	11.7961i	−0.406262	−	0.468851i
$634$		0			0
$635$	−20.2835	+	44.4148i	−0.804928	+	1.76255i
$636$		0			0
$637$	−2.77890	+	0.815959i	−0.110104	+	0.0323295i
$638$		0			0
$639$	4.76845	+	10.4414i	0.188637	+	0.413057i
$640$		0			0
$641$	13.9034	−	8.93518i	0.549152	−	0.352919i	−0.236457	−	0.971642i	$-0.575986\pi$
$641$	13.9034	−	8.93518i	0.549152	−	0.352919i	0.785609	+	0.618723i	$0.212350\pi$
$642$		0			0
$643$	−34.1400			−1.34635			−0.673176	−	0.739482i	$-0.735070\pi$
$643$	−34.1400			−1.34635			−0.673176	+	0.739482i	$0.735070\pi$
$644$		0			0
$645$	−18.1414			−0.714316
$646$		0			0
$647$	−8.12978	+	5.22469i	−0.319614	+	0.205404i	−0.690604	−	0.723233i	$-0.742655\pi$
$647$	−8.12978	+	5.22469i	−0.319614	+	0.205404i	0.370989	+	0.928637i	$0.379019\pi$
$648$		0			0
$649$	−0.248077	−	0.543213i	−0.00973788	−	0.0213230i
$650$		0			0
$651$	7.90717	−	2.32176i	0.309907	−	0.0909968i
$652$		0			0
$653$	2.47632	−	5.42237i	0.0969057	−	0.212194i	−0.854971	−	0.518677i	$-0.826425\pi$
$653$	2.47632	−	5.42237i	0.0969057	−	0.212194i	0.951876	+	0.306483i	$0.0991522\pi$
$654$		0			0
$655$	−27.5549	−	31.8000i	−1.07666	−	1.24253i
$656$		0			0
$657$	13.1373	+	3.85745i	0.512534	+	0.150493i
$658$		0			0
$659$	31.7171	+	20.3833i	1.23552	+	0.794021i	0.984742	−	0.174023i	$-0.0556766\pi$
$659$	31.7171	+	20.3833i	1.23552	+	0.794021i	0.250780	+	0.968044i	$0.419313\pi$
$660$		0			0
$661$	4.57689	−	31.8330i	0.178020	−	1.23816i	−0.683316	−	0.730123i	$-0.739463\pi$
$661$	4.57689	−	31.8330i	0.178020	−	1.23816i	0.861336	−	0.508036i	$-0.169628\pi$
$662$		0			0
$663$	−0.215577	−	1.49937i	−0.00837233	−	0.0582308i
$664$		0			0
$665$	−1.05967	+	1.22293i	−0.0410924	+	0.0474232i
$666$		0			0
$667$	−0.407692	+	0.417310i	−0.0157859	+	0.0161583i
$668$		0			0
$669$	0.920617	−	1.06245i	0.0355931	−	0.0410766i
$670$		0			0
$671$	0.657073	+	4.57004i	0.0253660	+	0.176424i
$672$		0			0
$673$	4.44939	−	30.9462i	0.171511	−	1.19289i	−0.704181	−	0.710020i	$-0.748686\pi$
$673$	4.44939	−	30.9462i	0.171511	−	1.19289i	0.875693	−	0.482868i	$-0.160405\pi$
$674$		0			0
$675$	2.98671	+	1.91944i	0.114958	+	0.0738793i
$676$		0			0
$677$	−5.24755	−	1.54082i	−0.201680	−	0.0592185i	0.179332	−	0.983789i	$-0.442606\pi$
$677$	−5.24755	−	1.54082i	−0.201680	−	0.0592185i	−0.381012	+	0.924570i	$0.624424\pi$
$678$		0			0
$679$	−10.2420	−	11.8199i	−0.393051	−	0.453605i
$680$		0			0
$681$	−1.84442	+	4.03871i	−0.0706782	+	0.154764i
$682$		0			0
$683$	31.9778	−	9.38953i	1.22360	−	0.359280i	0.394767	−	0.918781i	$-0.370825\pi$
$683$	31.9778	−	9.38953i	1.22360	−	0.359280i	0.828830	+	0.559501i	$0.189007\pi$
$684$		0			0
$685$	−2.28579	−	5.00518i	−0.0873356	−	0.191238i
$686$		0			0
$687$	−1.40929	+	0.905699i	−0.0537679	+	0.0345546i
$688$		0			0
$689$	−3.73064			−0.142126
$690$		0			0
$691$	23.4533			0.892206			0.446103	−	0.894982i	$-0.352811\pi$
$691$	23.4533			0.892206			0.446103	+	0.894982i	$0.352811\pi$
$692$		0			0
$693$	−2.12196	+	1.36370i	−0.0806067	+	0.0518028i
$694$		0			0
$695$	−4.20644	−	9.21083i	−0.159560	−	0.349387i
$696$		0			0
$697$	−4.19052	+	1.23045i	−0.158727	+	0.0466066i
$698$		0			0
$699$	−9.03851	+	19.7916i	−0.341868	+	0.748586i
$700$		0			0
$701$	−9.67059	−	11.1605i	−0.365253	−	0.421525i	0.543140	−	0.839642i	$-0.317235\pi$
$701$	−9.67059	−	11.1605i	−0.365253	−	0.421525i	−0.908393	+	0.418118i	$0.862690\pi$
$702$		0			0
$703$	5.05724	+	1.48494i	0.190737	+	0.0560056i
$704$		0			0
$705$	−21.3970	−	13.7510i	−0.805857	−	0.517893i
$706$		0			0
$707$	−0.463184	+	3.22152i	−0.0174198	+	0.121158i
$708$		0			0
$709$	−1.84594	−	12.8388i	−0.0693258	−	0.482172i	−0.994675	−	0.103057i	$-0.967138\pi$
$709$	−1.84594	−	12.8388i	−0.0693258	−	0.482172i	0.925350	−	0.379115i	$-0.123771\pi$
$710$		0			0
$711$	11.1915	−	12.9157i	0.419715	−	0.484376i
$712$		0			0
$713$	14.2317	+	36.8391i	0.532980	+	1.37963i
$714$		0			0
$715$	−2.33030	+	2.68931i	−0.0871482	+	0.100574i
$716$		0			0
$717$	2.98937	+	20.7916i	0.111640	+	0.776475i
$718$		0			0
$719$	2.59209	−	18.0284i	0.0966687	−	0.672345i	−0.882651	−	0.470028i	$-0.844244\pi$
$719$	2.59209	−	18.0284i	0.0966687	−	0.672345i	0.979320	−	0.202317i	$-0.0648472\pi$
$720$		0			0
$721$	1.18018	+	0.758455i	0.0439522	+	0.0282463i
$722$		0			0
$723$	25.2690	+	7.41964i	0.939763	+	0.275939i
$724$		0			0
$725$	−0.282827	−	0.326399i	−0.0105039	−	0.0121222i
$726$		0			0
$727$	3.56341	−	7.80279i	0.132160	−	0.289389i	−0.831970	−	0.554820i	$-0.812787\pi$
$727$	3.56341	−	7.80279i	0.132160	−	0.289389i	0.964130	+	0.265431i	$0.0855143\pi$
$728$		0			0
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$		0			0
$731$	−8.08583	−	17.7055i	−0.299065	−	0.654861i
$732$		0			0
$733$	−2.64399	+	1.69919i	−0.0976579	+	0.0627609i	−0.588558	−	0.808455i	$-0.700304\pi$
$733$	−2.64399	+	1.69919i	−0.0976579	+	0.0627609i	0.490900	+	0.871216i	$0.336668\pi$
$734$		0			0
$735$	17.5401			0.646977
$736$		0			0
$737$	−7.05093			−0.259724
$738$		0			0
$739$	18.9339	−	12.1681i	0.696494	−	0.447610i	−0.143895	−	0.989593i	$-0.545963\pi$
$739$	18.9339	−	12.1681i	0.696494	−	0.447610i	0.840389	+	0.541983i	$0.182326\pi$
$740$		0			0
$741$	−0.110911	−	0.242862i	−0.00407443	−	0.00892176i
$742$		0			0
$743$	−4.72970	+	1.38877i	−0.173516	+	0.0509489i	−0.367336	−	0.930088i	$-0.619730\pi$
$743$	−4.72970	+	1.38877i	−0.173516	+	0.0509489i	0.193821	+	0.981037i	$0.437912\pi$
$744$		0			0
$745$	26.2019	−	57.3741i	0.959962	−	2.10202i
$746$		0			0
$747$	5.28068	+	6.09423i	0.193210	+	0.222976i
$748$		0			0
$749$	−9.64470	−	2.83194i	−0.352410	−	0.103477i
$750$		0			0
$751$	0.881369	+	0.566421i	0.0321616	+	0.0206690i	0.556623	−	0.830765i	$-0.312097\pi$
$751$	0.881369	+	0.566421i	0.0321616	+	0.0206690i	−0.524461	+	0.851434i	$0.675733\pi$
$752$		0			0
$753$	−3.70778	+	25.7882i	−0.135119	+	0.939773i
$754$		0			0
$755$	1.36178	+	9.47135i	0.0495601	+	0.344698i
$756$		0			0
$757$	1.85765	−	2.14384i	0.0675173	−	0.0779192i	−0.720986	−	0.692950i	$-0.756311\pi$
$757$	1.85765	−	2.14384i	0.0675173	−	0.0779192i	0.788503	+	0.615030i	$0.210856\pi$
$758$		0			0
$759$	−7.35625	−	9.59164i	−0.267015	−	0.348155i
$760$		0			0
$761$	19.1081	−	22.0519i	0.692666	−	0.799380i	−0.295076	−	0.955474i	$-0.595345\pi$
$761$	19.1081	−	22.0519i	0.692666	−	0.799380i	0.987742	+	0.156094i	$0.0498904\pi$
$762$		0			0
$763$	−0.962505	−	6.69437i	−0.0348450	−	0.242352i
$764$		0			0
$765$	−1.30558	+	9.08052i	−0.0472034	+	0.328307i
$766$		0			0
$767$	0.0962364	+	0.0618474i	0.00347490	+	0.00223318i
$768$		0			0
$769$	−19.4993	−	5.72551i	−0.703163	−	0.206467i	−0.0894441	−	0.995992i	$-0.528509\pi$
$769$	−19.4993	−	5.72551i	−0.703163	−	0.206467i	−0.613719	+	0.789525i	$0.710327\pi$
$770$		0			0
$771$	−5.17274	−	5.96966i	−0.186292	−	0.214992i
$772$		0			0
$773$	−9.32220	+	20.4128i	−0.335296	+	0.734196i	−0.999916	−	0.0129858i	$-0.995866\pi$
$773$	−9.32220	+	20.4128i	−0.335296	+	0.734196i	0.664620	+	0.747182i	$0.268594\pi$
$774$		0			0
$775$	−28.0516	+	8.23670i	−1.00764	+	0.295871i
$776$		0			0
$777$	3.96259	+	8.67685i	0.142157	+	0.311280i
$778$		0			0
$779$	−0.647582	+	0.416175i	−0.0232020	+	0.0149110i
$780$		0			0
$781$	28.9319			1.03526
$782$		0			0
$783$	0.121648			0.00434735
$784$		0			0
$785$	−56.0765	+	36.0382i	−2.00145	+	1.28626i
$786$		0			0
$787$	−5.82947	−	12.7648i	−0.207798	−	0.455015i	0.776823	−	0.629720i	$-0.216830\pi$
$787$	−5.82947	−	12.7648i	−0.207798	−	0.455015i	−0.984621	+	0.174705i	$0.944103\pi$
$788$		0			0
$789$	11.8421	−	3.47716i	0.421591	−	0.123790i
$790$		0			0
$791$	4.16737	−	9.12526i	0.148175	−	0.324457i
$792$		0			0
$793$	−0.579189	−	0.668420i	−0.0205676	−	0.0237363i
$794$		0			0
$795$	21.6783	+	6.36533i	0.768851	+	0.225755i
$796$		0			0
$797$	44.3146	+	28.4792i	1.56970	+	1.00879i	0.979479	+	0.201547i	$0.0645968\pi$
$797$	44.3146	+	28.4792i	1.56970	+	1.00879i	0.590224	+	0.807240i	$0.299040\pi$
$798$		0			0
$799$	3.88372	−	27.0119i	0.137396	−	0.955611i
$800$		0			0
$801$	−0.702822	−	4.88823i	−0.0248330	−	0.172717i
$802$		0			0
$803$	22.5993	−	26.0809i	0.797510	−	0.920376i
$804$		0			0
$805$	−1.16430	−	13.9857i	−0.0410363	−	0.492931i
$806$		0			0
$807$	7.32767	−	8.45658i	0.257946	−	0.297686i
$808$		0			0
$809$	−7.51836	−	52.2913i	−0.264331	−	1.83847i	−0.499259	−	0.866453i	$-0.666394\pi$
$809$	−7.51836	−	52.2913i	−0.264331	−	1.83847i	0.234927	−	0.972013i	$-0.424515\pi$
$810$		0			0
$811$	−6.05545	+	42.1166i	−0.212636	+	1.47891i	0.551672	+	0.834061i	$0.313990\pi$
$811$	−6.05545	+	42.1166i	−0.212636	+	1.47891i	−0.764307	+	0.644852i	$0.776919\pi$
$812$		0			0
$813$	20.0511	+	12.8861i	0.703225	+	0.451935i
$814$		0			0
$815$	−33.9123	−	9.95756i	−1.18790	−	0.348798i
$816$		0			0
$817$	−2.24663	−	2.59275i	−0.0785998	−	0.0907090i
$818$		0			0
$819$	0.200725	−	0.439526i	0.00701389	−	0.0153583i
$820$		0			0
$821$	−9.90317	+	2.90783i	−0.345623	+	0.101484i	−0.449937	−	0.893060i	$-0.648554\pi$
$821$	−9.90317	+	2.90783i	−0.345623	+	0.101484i	0.104314	+	0.994544i	$0.466735\pi$
$822$		0			0
$823$	−22.5958	−	49.4779i	−0.787640	−	1.72469i	−0.683285	−	0.730151i	$-0.739450\pi$
$823$	−22.5958	−	49.4779i	−0.787640	−	1.72469i	−0.104355	−	0.994540i	$-0.533278\pi$
$824$		0			0
$825$	7.52791	−	4.83789i	0.262088	−	0.168434i
$826$		0			0
$827$	27.7576			0.965227			0.482613	−	0.875834i	$-0.339688\pi$
$827$	27.7576			0.965227			0.482613	+	0.875834i	$0.339688\pi$
$828$		0			0
$829$	−31.3925			−1.09031			−0.545153	−	0.838336i	$-0.683529\pi$
$829$	−31.3925			−1.09031			−0.545153	+	0.838336i	$0.683529\pi$
$830$		0			0
$831$	−15.0199	+	9.65268i	−0.521033	+	0.334848i
$832$		0			0
$833$	7.81784	+	17.1187i	0.270872	+	0.593127i
$834$		0			0
$835$	23.2745	−	6.83400i	0.805446	−	0.236500i
$836$		0			0
$837$	3.42084	−	7.49060i	0.118242	−	0.258913i
$838$		0			0
$839$	−2.24487	−	2.59072i	−0.0775017	−	0.0894417i	0.715674	−	0.698434i	$-0.246119\pi$
$839$	−2.24487	−	2.59072i	−0.0775017	−	0.0894417i	−0.793176	+	0.608992i	$0.791574\pi$
$840$		0			0
$841$	27.8111	+	8.16607i	0.959003	+	0.281589i
$842$		0			0
$843$	−1.39241	−	0.894851i	−0.0479573	−	0.0308203i
$844$		0			0
$845$	−5.31283	+	36.9515i	−0.182767	+	1.27117i
$846$		0			0
$847$	−0.661869	−	4.60340i	−0.0227421	−	0.158175i
$848$		0			0
$849$	0.893450	−	1.03110i	0.0306631	−	0.0353871i
$850$		0			0
$851$	−39.8625	+	22.3738i	−1.36647	+	0.766962i
$852$		0			0
$853$	−21.3027	+	24.5846i	−0.729390	+	0.841760i	−0.992403	−	0.123032i	$-0.960738\pi$
$853$	−21.3027	+	24.5846i	−0.729390	+	0.841760i	0.263013	+	0.964792i	$0.415284\pi$
$854$		0			0
$855$	0.230115	+	1.60049i	0.00786977	+	0.0547354i
$856$		0			0
$857$	5.10290	−	35.4914i	0.174312	−	1.21236i	−0.695334	−	0.718687i	$-0.744743\pi$
$857$	5.10290	−	35.4914i	0.174312	−	1.21236i	0.869645	−	0.493677i	$-0.164348\pi$
$858$		0			0
$859$	7.63096	+	4.90412i	0.260365	+	0.167326i	0.664311	−	0.747456i	$-0.268725\pi$
$859$	7.63096	+	4.90412i	0.260365	+	0.167326i	−0.403946	+	0.914783i	$0.632362\pi$
$860$		0			0
$861$	−1.33670	−	0.392491i	−0.0455546	−	0.0133760i
$862$		0			0
$863$	−27.7686	−	32.0467i	−0.945255	−	1.09088i	−0.995744	−	0.0921581i	$-0.970623\pi$
$863$	−27.7686	−	32.0467i	−0.945255	−	1.09088i	0.0504891	−	0.998725i	$-0.483922\pi$
$864$		0			0
$865$	25.0973	−	54.9553i	0.853332	−	1.86854i
$866$		0			0
$867$	6.86713	−	2.01637i	0.233220	−	0.0684795i
$868$		0			0
$869$	−17.8939	−	39.1821i	−0.607008	−	1.32916i
$870$		0			0
$871$	1.13627	−	0.730236i	0.0385010	−	0.0247431i
$872$		0			0
$873$	−15.6281			−0.528931
$874$		0			0
$875$	−4.24225			−0.143414
$876$		0			0
$877$	34.8182	−	22.3763i	1.17573	−	0.755594i	0.201132	−	0.979564i	$-0.435538\pi$
$877$	34.8182	−	22.3763i	1.17573	−	0.755594i	0.974596	+	0.223970i	$0.0719017\pi$
$878$		0			0
$879$	−4.40567	−	9.64707i	−0.148600	−	0.325388i
$880$		0			0
$881$	−17.0646	+	5.01061i	−0.574920	+	0.168812i	−0.556252	−	0.831014i	$-0.687761\pi$
$881$	−17.0646	+	5.01061i	−0.574920	+	0.168812i	−0.0186687	+	0.999826i	$0.505943\pi$
$882$		0			0
$883$	3.41762	−	7.48354i	0.115012	−	0.251841i	−0.843368	−	0.537336i	$-0.819431\pi$
$883$	3.41762	−	7.48354i	0.115012	−	0.251841i	0.958380	+	0.285495i	$0.0921580\pi$
$884$		0			0
$885$	−0.453693	−	0.523590i	−0.0152507	−	0.0176003i
$886$		0			0
$887$	42.8259	+	12.5748i	1.43795	+	0.422221i	0.905539	−	0.424263i	$-0.139467\pi$
$887$	42.8259	+	12.5748i	1.43795	+	0.422221i	0.532414	+	0.846484i	$0.321285\pi$
$888$		0			0
$889$	−14.0581	−	9.03459i	−0.471493	−	0.303010i
$890$		0			0
$891$	−0.358701	+	2.49482i	−0.0120169	+	0.0835795i
$892$		0			0
$893$	−0.684525	−	4.76097i	−0.0229067	−	0.159320i
$894$		0			0
$895$	7.43107	−	8.57591i	0.248393	−	0.286661i
$896$		0			0
$897$	2.17884	+	0.783853i	0.0727493	+	0.0261721i
$898$		0			0
$899$	−0.656002	+	0.757067i	−0.0218789	+	0.0252496i
$900$		0			0
$901$	3.44990	+	23.9946i	0.114933	+	0.799375i
$902$		0			0
$903$	0.883605	−	6.14561i	0.0294045	−	0.204513i
$904$		0			0
$905$	−19.6083	−	12.6015i	−0.651800	−	0.418887i
$906$		0			0
$907$	−39.2401	−	11.5219i	−1.30295	−	0.382580i	−0.444637	−	0.895711i	$-0.646667\pi$
$907$	−39.2401	−	11.5219i	−1.30295	−	0.382580i	−0.858310	+	0.513131i	$0.828486\pi$
$908$		0			0
$909$	2.12973	+	2.45783i	0.0706385	+	0.0815212i
$910$		0			0
$911$	0.360612	−	0.789631i	0.0119476	−	0.0261616i	−0.903564	−	0.428453i	$-0.859059\pi$
$911$	0.360612	−	0.789631i	0.0119476	−	0.0261616i	0.915512	+	0.402291i	$0.131786\pi$
$912$		0			0
$913$	19.5014	−	5.72611i	0.645401	−	0.189507i
$914$		0			0
$915$	2.22512	+	4.87234i	0.0735603	+	0.161075i
$916$		0			0
$917$	12.1147	−	7.78567i	0.400064	−	0.257105i
$918$		0			0
$919$	−53.6469			−1.76965			−0.884824	−	0.465926i	$-0.845721\pi$
$919$	−53.6469			−1.76965			−0.884824	+	0.465926i	$0.845721\pi$
$920$		0			0
$921$	−10.3224			−0.340135
$922$		0			0
$923$	−4.66243	+	2.99636i	−0.153466	+	0.0986264i
$924$		0			0
$925$	−14.0577	−	30.7822i	−0.462216	−	1.01211i
$926$		0			0
$927$	1.34504	−	0.394938i	0.0441768	−	0.0129715i
$928$		0			0
$929$	−1.81781	+	3.98044i	−0.0596403	+	0.130594i	−0.937105	−	0.349046i	$-0.886506\pi$
$929$	−1.81781	+	3.98044i	−0.0596403	+	0.130594i	0.877465	+	0.479640i	$0.159233\pi$
$930$		0			0
$931$	2.17217	+	2.50682i	0.0711901	+	0.0821578i
$932$		0			0
$933$	6.76343	+	1.98592i	0.221425	+	0.0650162i
$934$		0			0
$935$	19.4519	+	12.5010i	0.636146	+	0.408826i
$936$		0			0
$937$	−0.811889	+	5.64681i	−0.0265232	+	0.184473i	−0.998776	−	0.0494590i	$-0.984250\pi$
$937$	−0.811889	+	5.64681i	−0.0265232	+	0.184473i	0.972253	+	0.233932i	$0.0751594\pi$
$938$		0			0
$939$	−0.321995	−	2.23953i	−0.0105079	−	0.0730842i
$940$		0			0
$941$	7.27395	−	8.39458i	0.237124	−	0.273656i	−0.624698	−	0.780866i	$-0.714778\pi$
$941$	7.27395	−	8.39458i	0.237124	−	0.273656i	0.861822	+	0.507211i	$0.169323\pi$
$942$		0			0
$943$	1.34297	−	6.53970i	0.0437332	−	0.212962i
$944$		0			0
$945$	−1.91632	+	2.21155i	−0.0623380	+	0.0719418i
$946$		0			0
$947$	2.12760	+	14.7978i	0.0691376	+	0.480863i	0.994745	+	0.102379i	$0.0326454\pi$
$947$	2.12760	+	14.7978i	0.0691376	+	0.480863i	−0.925608	+	0.378484i	$0.876446\pi$
$948$		0			0
$949$	−0.940813	+	6.54350i	−0.0305401	+	0.212411i
$950$		0			0
$951$	−2.66978	−	1.71577i	−0.0865737	−	0.0556375i
$952$		0			0
$953$	28.3258	+	8.31722i	0.917564	+	0.269421i	0.706221	−	0.707991i	$-0.250398\pi$
$953$	28.3258	+	8.31722i	0.917564	+	0.269421i	0.211343	+	0.977412i	$0.432216\pi$
$954$		0			0
$955$	32.3343	+	37.3158i	1.04631	+	1.20751i
$956$		0			0
$957$	0.127371	−	0.278903i	0.00411731	−	0.00901566i
$958$		0			0
$959$	1.80690	−	0.530554i	0.0583478	−	0.0171325i
$960$		0			0
$961$	15.2919	+	33.4847i	0.493288	+	1.08015i
$962$		0			0
$963$	−8.44978	+	5.43034i	−0.272290	+	0.174990i
$964$		0			0
$965$	62.2837			2.00498
$966$		0			0
$967$	−44.5676			−1.43320			−0.716598	−	0.697486i	$-0.754302\pi$
$967$	−44.5676			−1.43320			−0.716598	+	0.697486i	$0.754302\pi$
$968$		0			0
$969$	−1.45947	+	0.937942i	−0.0468848	+	0.0301310i
$970$		0			0
$971$	22.1020	+	48.3967i	0.709288	+	1.55312i	0.828334	+	0.560235i	$0.189289\pi$
$971$	22.1020	+	48.3967i	0.709288	+	1.55312i	−0.119046	+	0.992889i	$0.537983\pi$
$972$		0			0
$973$	3.32516	−	0.976355i	0.106600	−	0.0313005i
$974$		0			0
$975$	−0.712095	+	1.55927i	−0.0228053	+	0.0499366i
$976$		0			0
$977$	24.1039	+	27.8174i	0.771151	+	0.889956i	0.996437	−	0.0843367i	$-0.0268771\pi$
$977$	24.1039	+	27.8174i	0.771151	+	0.889956i	−0.225286	+	0.974293i	$0.572332\pi$
$978$		0			0
$979$	−11.9431	−	3.50682i	−0.381705	−	0.112079i
$980$		0			0
$981$	−5.68527	−	3.65370i	−0.181517	−	0.116654i
$982$		0			0
$983$	5.86774	−	40.8111i	0.187152	−	1.30167i	−0.652185	−	0.758059i	$-0.726148\pi$
$983$	5.86774	−	40.8111i	0.187152	−	1.30167i	0.839337	−	0.543611i	$-0.182943\pi$
$984$		0			0
$985$	11.2081	+	77.9541i	0.357120	+	2.48382i
$986$		0			0
$987$	5.70049	−	6.57872i	0.181449	−	0.209403i
$988$		0			0
$989$	29.7008	+	1.77648i	0.944430	+	0.0564888i
$990$		0			0
$991$	26.4437	−	30.5176i	0.840011	−	0.969425i	−0.159832	−	0.987144i	$-0.551095\pi$
$991$	26.4437	−	30.5176i	0.840011	−	0.969425i	0.999843	+	0.0177197i	$0.00564066\pi$
$992$		0			0
$993$	2.95800	+	20.5733i	0.0938693	+	0.652875i
$994$		0			0
$995$	−3.03191	+	21.0874i	−0.0961180	+	0.668515i
$996$		0			0
$997$	22.2576	+	14.3041i	0.704905	+	0.453015i	0.843357	−	0.537354i	$-0.180576\pi$
$997$	22.2576	+	14.3041i	0.704905	+	0.453015i	−0.138451	+	0.990369i	$0.544212\pi$
$998$		0			0
$999$	9.14555	+	2.68537i	0.289352	+	0.0849615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.85.1	yes	20
3.2	odd	2		828.2.q.c.361.2		20
23.6	even	11		6348.2.a.s.1.2		10
23.13	even	11	inner	276.2.i.a.13.1	✓	20
23.17	odd	22		6348.2.a.t.1.9		10
69.59	odd	22		828.2.q.c.289.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.13.1	✓	20	23.13	even	11	inner
276.2.i.a.85.1	yes	20	1.1	even	1	trivial
828.2.q.c.289.2		20	69.59	odd	22
828.2.q.c.361.2		20	3.2	odd	2
6348.2.a.s.1.2		10	23.6	even	11
6348.2.a.t.1.9		10	23.17	odd	22

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{3} +(-1.21471 - 2.65985i) q^{5} +(0.960219 - 0.281946i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{3} +(-1.21471 - 2.65985i) q^{5} +(0.960219 - 0.281946i) q^{7} +(0.415415 - 0.909632i) q^{9} +(-1.65056 - 1.90485i) q^{11} +(0.463267 + 0.136028i) q^{13} +(-2.45990 - 1.58088i) q^{15} +(0.446491 - 3.10542i) q^{17} +(-0.0786963 - 0.547345i) q^{19} +(0.655357 - 0.756322i) q^{21} +(3.87251 + 2.82908i) q^{23} +(-2.32496 + 2.68314i) q^{25} +(-0.142315 - 0.989821i) q^{27} +(-0.0173123 + 0.120410i) q^{29} +(6.92752 + 4.45205i) q^{31} +(-2.41838 - 0.710099i) q^{33} +(-1.91632 - 2.21155i) q^{35} +(-3.95959 + 8.67029i) q^{37} +(0.463267 - 0.136028i) q^{39} +(-0.578290 - 1.26628i) q^{41} +(5.21923 - 3.35419i) q^{43} -2.92409 q^{45} +8.69831 q^{47} +(-5.04625 + 3.24303i) q^{49} +(-1.30330 - 2.85383i) q^{51} +(-7.41370 + 2.17686i) q^{53} +(-3.06165 + 6.70407i) q^{55} +(-0.362120 - 0.417909i) q^{57} +(0.227334 + 0.0667513i) q^{59} +(-1.54102 - 0.990353i) q^{61} +(0.142423 - 0.990571i) q^{63} +(-0.200924 - 1.39745i) q^{65} +(1.83195 - 2.11418i) q^{67} +(4.78728 + 0.286340i) q^{69} +(-7.51699 + 8.67507i) q^{71} +(1.94856 + 13.5525i) q^{73} +(-0.505261 + 3.51417i) q^{75} +(-2.12196 - 1.36370i) q^{77} +(16.3977 + 4.81479i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(-3.34983 + 7.33511i) q^{83} +(-8.80229 + 2.58458i) q^{85} +(0.0505345 + 0.110655i) q^{87} +(4.15453 - 2.66995i) q^{89} +0.483191 q^{91} +8.23476 q^{93} +(-1.36026 + 0.874186i) q^{95} +(-6.49214 - 14.2158i) q^{97} +(-2.41838 + 0.710099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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