LMFDB - Embedded newform 544.2.bb.d.321.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(161,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.161"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.bb (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,8,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 28 x^{14} - 36 x^{13} - 28 x^{12} + 20 x^{11} + 644 x^{10} - 2244 x^{9} + \cdots + 1394 $ x^16 - 8x^15 + 28x^14 - 36x^13 - 28x^12 + 20x^11 + 644x^10 - 2244x^9 + 3535x^8 - 2948x^7 + 1924x^6 - 5312x^5 + 14942x^4 - 22400x^3 + 18396x^2 - 7904*x + 1394
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			321.3
Root			$0.900800 - 0.239491i$ of defining polynomial
Character	$\chi$	$=$	544.321
Dual form			544.2.bb.d.161.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.433184 + 1.04580i) q^{3} +(2.16830 - 0.898138i) q^{5} +(-3.20687 - 1.32833i) q^{7} +(1.21528 - 1.21528i) q^{9} +(2.05797 - 4.96839i) q^{11} +0.828427i q^{13} +(1.87854 + 1.87854i) q^{15} +(3.79779 - 1.60525i) q^{17} +(-1.01217 - 1.01217i) q^{19} -3.92915i q^{21} +(0.316155 - 0.763265i) q^{23} +(0.359330 - 0.359330i) q^{25} +(4.93476 + 2.04405i) q^{27} +(-3.47274 + 1.43846i) q^{29} +(3.20687 + 7.74207i) q^{31} +6.08741 q^{33} -8.14648 q^{35} +(-1.37879 - 3.32869i) q^{37} +(-0.866367 + 0.358861i) q^{39} +(10.1101 + 4.18776i) q^{41} +(-9.11795 + 9.11795i) q^{43} +(1.54359 - 3.72657i) q^{45} -3.75708i q^{47} +(3.56982 + 3.56982i) q^{49} +(3.32390 + 3.27635i) q^{51} +(-5.17620 - 5.17620i) q^{53} -12.6213i q^{55} +(0.620073 - 1.49699i) q^{57} +(5.86838 - 5.86838i) q^{59} +(-2.27807 - 0.943606i) q^{61} +(-5.51152 + 2.28295i) q^{63} +(0.744042 + 1.79628i) q^{65} +8.93145 q^{67} +0.935174 q^{69} +(5.29847 + 12.7916i) q^{71} +(-1.86750 + 0.773543i) q^{73} +(0.531442 + 0.220130i) q^{75} +(-13.1993 + 13.1993i) q^{77} +(3.56573 - 8.60844i) q^{79} +0.890232i q^{81} +(-3.20203 - 3.20203i) q^{83} +(6.79300 - 6.89159i) q^{85} +(-3.00867 - 3.00867i) q^{87} -0.313491i q^{89} +(1.10042 - 2.65666i) q^{91} +(-6.70748 + 6.70748i) q^{93} +(-3.10377 - 1.28562i) q^{95} +(-11.5908 + 4.80106i) q^{97} +(-3.53695 - 8.53896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} - 8 q^{17} - 24 q^{25} + 8 q^{29} - 32 q^{33} + 56 q^{37} + 56 q^{41} + 72 q^{45} - 24 q^{49} - 56 q^{53} + 8 q^{57} - 24 q^{61} + 16 q^{65} + 64 q^{69} + 8 q^{73} - 88 q^{77} + 8 q^{85}+ \cdots - 16 q^{97}+O(q^{100}) $ 16 * q + 8 * q^5 - 8 * q^17 - 24 * q^25 + 8 * q^29 - 32 * q^33 + 56 * q^37 + 56 * q^41 + 72 * q^45 - 24 * q^49 - 56 * q^53 + 8 * q^57 - 24 * q^61 + 16 * q^65 + 64 * q^69 + 8 * q^73 - 88 * q^77 + 8 * q^85 + 24 * q^93 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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
$3$	0.433184	+	1.04580i	0.250099	+	0.603792i	0.998212	−	0.0597799i	$-0.0190399\pi$
$3$	0.433184	+	1.04580i	0.250099	+	0.603792i	−0.748113	+	0.663571i	$0.769040\pi$
$4$		0			0
$5$	2.16830	−	0.898138i	0.969692	−	0.401660i	0.159095	−	0.987263i	$-0.449142\pi$
$5$	2.16830	−	0.898138i	0.969692	−	0.401660i	0.810598	+	0.585604i	$0.199142\pi$
$6$		0			0
$7$	−3.20687	−	1.32833i	−1.21208	−	0.502061i	−0.317199	−	0.948359i	$-0.602742\pi$
$7$	−3.20687	−	1.32833i	−1.21208	−	0.502061i	−0.894885	+	0.446297i	$0.852742\pi$
$8$		0			0
$9$	1.21528	−	1.21528i	0.405092	−	0.405092i
$10$		0			0
$11$	2.05797	−	4.96839i	0.620502	−	1.49802i	−0.230613	−	0.973046i	$-0.574073\pi$
$11$	2.05797	−	4.96839i	0.620502	−	1.49802i	0.851115	−	0.524979i	$-0.175927\pi$
$12$		0			0
$13$			0.828427i			0.229764i	0.993379	+	0.114882i	$0.0366490\pi$
$13$			0.828427i			0.229764i	−0.993379	+	0.114882i	$0.963351\pi$
$14$		0			0
$15$	1.87854	+	1.87854i	0.485037	+	0.485037i
$16$		0			0
$17$	3.79779	−	1.60525i	0.921099	−	0.389329i
$17$	3.79779	−	1.60525i	0.921099	−	0.389329i
$18$		0			0
$19$	−1.01217	−	1.01217i	−0.232209	−	0.232209i	0.581405	−	0.813614i	$-0.302503\pi$
$19$	−1.01217	−	1.01217i	−0.232209	−	0.232209i	−0.813614	+	0.581405i	$0.802503\pi$
$20$		0			0
$21$		−	3.92915i		−	0.857411i
$22$		0			0
$23$	0.316155	−	0.763265i	0.0659228	−	0.159152i	−0.887485	−	0.460837i	$-0.847549\pi$
$23$	0.316155	−	0.763265i	0.0659228	−	0.159152i	0.953408	+	0.301685i	$0.0975492\pi$
$24$		0			0
$25$	0.359330	−	0.359330i	0.0718659	−	0.0718659i
$26$		0			0
$27$	4.93476	+	2.04405i	0.949696	+	0.393377i
$28$		0			0
$29$	−3.47274	+	1.43846i	−0.644872	+	0.267115i	−0.681057	−	0.732230i	$-0.738479\pi$
$29$	−3.47274	+	1.43846i	−0.644872	+	0.267115i	0.0361848	+	0.999345i	$0.488479\pi$
$30$		0			0
$31$	3.20687	+	7.74207i	0.575971	+	1.39052i	0.896400	+	0.443245i	$0.146173\pi$
$31$	3.20687	+	7.74207i	0.575971	+	1.39052i	−0.320429	+	0.947272i	$0.603827\pi$
$32$		0			0
$33$	6.08741			1.05968
$34$		0			0
$35$	−8.14648			−1.37701
$36$		0			0
$37$	−1.37879	−	3.32869i	−0.226671	−	0.547233i	0.769097	−	0.639132i	$-0.220706\pi$
$37$	−1.37879	−	3.32869i	−0.226671	−	0.547233i	−0.995768	+	0.0918989i	$0.970706\pi$
$38$		0			0
$39$	−0.866367	+	0.358861i	−0.138730	+	0.0574638i
$40$		0			0
$41$	10.1101	+	4.18776i	1.57894	+	0.654018i	0.988245	−	0.152878i	$-0.0488543\pi$
$41$	10.1101	+	4.18776i	1.57894	+	0.654018i	0.590693	+	0.806896i	$0.298854\pi$
$42$		0			0
$43$	−9.11795	+	9.11795i	−1.39047	+	1.39047i	−0.566222	+	0.824253i	$0.691596\pi$
$43$	−9.11795	+	9.11795i	−1.39047	+	1.39047i	−0.824253	+	0.566222i	$0.808404\pi$
$44$		0			0
$45$	1.54359	−	3.72657i	0.230105	−	0.555524i
$46$		0			0
$47$		−	3.75708i		−	0.548027i	−0.961726	−	0.274014i	$-0.911649\pi$
$47$		−	3.75708i		−	0.548027i	0.961726	−	0.274014i	$-0.0883513\pi$
$48$		0			0
$49$	3.56982	+	3.56982i	0.509974	+	0.509974i
$50$		0			0
$51$	3.32390	+	3.27635i	0.465439	+	0.458781i
$52$		0			0
$53$	−5.17620	−	5.17620i	−0.711006	−	0.711006i	0.255739	−	0.966746i	$-0.417681\pi$
$53$	−5.17620	−	5.17620i	−0.711006	−	0.711006i	−0.966746	+	0.255739i	$0.917681\pi$
$54$		0			0
$55$		−	12.6213i		−	1.70185i
$56$		0			0
$57$	0.620073	−	1.49699i	0.0821306	−	0.198281i
$58$		0			0
$59$	5.86838	−	5.86838i	0.763997	−	0.763997i	−0.213045	−	0.977042i	$-0.568338\pi$
$59$	5.86838	−	5.86838i	0.763997	−	0.763997i	0.977042	+	0.213045i	$0.0683381\pi$
$60$		0			0
$61$	−2.27807	−	0.943606i	−0.291676	−	0.120816i	0.232047	−	0.972705i	$-0.425458\pi$
$61$	−2.27807	−	0.943606i	−0.291676	−	0.120816i	−0.523724	+	0.851888i	$0.675458\pi$
$62$		0			0
$63$	−5.51152	+	2.28295i	−0.694386	+	0.287624i
$64$		0			0
$65$	0.744042	+	1.79628i	0.0922871	+	0.222801i
$66$		0			0
$67$	8.93145			1.09115			0.545575	−	0.838062i	$-0.316311\pi$
$67$	8.93145			1.09115			0.545575	+	0.838062i	$0.316311\pi$
$68$		0			0
$69$	0.935174			0.112582
$70$		0			0
$71$	5.29847	+	12.7916i	0.628812	+	1.51809i	0.841100	+	0.540880i	$0.181909\pi$
$71$	5.29847	+	12.7916i	0.628812	+	1.51809i	−0.212287	+	0.977207i	$0.568091\pi$
$72$		0			0
$73$	−1.86750	+	0.773543i	−0.218574	+	0.0905364i	−0.489284	−	0.872125i	$-0.662742\pi$
$73$	−1.86750	+	0.773543i	−0.218574	+	0.0905364i	0.270709	+	0.962661i	$0.412742\pi$
$74$		0			0
$75$	0.531442	+	0.220130i	0.0613656	+	0.0254185i
$76$		0			0
$77$	−13.1993	+	13.1993i	−1.50420	+	1.50420i
$78$		0			0
$79$	3.56573	−	8.60844i	0.401176	−	0.968525i	−0.586205	−	0.810163i	$-0.699379\pi$
$79$	3.56573	−	8.60844i	0.401176	−	0.968525i	0.987381	−	0.158362i	$-0.0506214\pi$
$80$		0			0
$81$			0.890232i			0.0989147i
$82$		0			0
$83$	−3.20203	−	3.20203i	−0.351468	−	0.351468i	0.509187	−	0.860656i	$-0.329946\pi$
$83$	−3.20203	−	3.20203i	−0.351468	−	0.351468i	−0.860656	+	0.509187i	$0.829946\pi$
$84$		0			0
$85$	6.79300	−	6.89159i	0.736805	−	0.747498i
$86$		0			0
$87$	−3.00867	−	3.00867i	−0.322563	−	0.322563i
$88$		0			0
$89$		−	0.313491i		−	0.0332300i	−0.999862	−	0.0166150i	$-0.994711\pi$
$89$		−	0.313491i		−	0.0332300i	0.999862	−	0.0166150i	$-0.00528896\pi$
$90$		0			0
$91$	1.10042	−	2.65666i	0.115356	−	0.278494i
$92$		0			0
$93$	−6.70748	+	6.70748i	−0.695533	+	0.695533i
$94$		0			0
$95$	−3.10377	−	1.28562i	−0.318440	−	0.131902i
$96$		0			0
$97$	−11.5908	+	4.80106i	−1.17687	+	0.487474i	−0.883457	−	0.468513i	$-0.844790\pi$
$97$	−11.5908	+	4.80106i	−1.17687	+	0.487474i	−0.293410	+	0.955987i	$0.594790\pi$
$98$		0			0
$99$	−3.53695	−	8.53896i	−0.355477	−	0.858198i
$100$		0			0
$101$	−11.1492			−1.10939			−0.554694	−	0.832054i	$-0.687165\pi$
$101$	−11.1492			−1.10939			−0.554694	+	0.832054i	$0.687165\pi$
$102$		0			0
$103$	4.18319			0.412182			0.206091	−	0.978533i	$-0.433926\pi$
$103$	4.18319			0.412182			0.206091	+	0.978533i	$0.433926\pi$
$104$		0			0
$105$	−3.52892	−	8.51957i	−0.344387	−	0.831425i
$106$		0			0
$107$	−11.1284	+	4.60952i	−1.07582	+	0.445620i	−0.849041	−	0.528327i	$-0.822820\pi$
$107$	−11.1284	+	4.60952i	−1.07582	+	0.445620i	−0.226780	+	0.973946i	$0.572820\pi$
$108$		0			0
$109$	2.16830	+	0.898138i	0.207685	+	0.0860261i	0.484101	−	0.875012i	$-0.339147\pi$
$109$	2.16830	+	0.898138i	0.207685	+	0.0860261i	−0.276416	+	0.961038i	$0.589147\pi$
$110$		0			0
$111$	2.88387	−	2.88387i	0.273725	−	0.273725i
$112$		0			0
$113$	−7.90642	+	19.0878i	−0.743773	+	1.79563i	−0.153978	+	0.988074i	$0.549208\pi$
$113$	−7.90642	+	19.0878i	−0.743773	+	1.79563i	−0.589795	+	0.807553i	$0.700792\pi$
$114$		0			0
$115$		−	1.93894i		−	0.180807i
$116$		0			0
$117$	1.00677	+	1.00677i	0.0930757	+	0.0930757i
$118$		0			0
$119$	−14.3113	+	0.103102i	−1.31192	+	0.00945132i
$120$		0			0
$121$	−12.6714	−	12.6714i	−1.15195	−	1.15195i
$122$		0			0
$123$			12.3872i			1.11692i
$124$		0			0
$125$	−4.03429	+	9.73963i	−0.360838	+	0.871139i
$126$		0			0
$127$	−5.33432	+	5.33432i	−0.473345	+	0.473345i	−0.902995	−	0.429651i	$-0.858637\pi$
$127$	−5.33432	+	5.33432i	−0.473345	+	0.473345i	0.429651	+	0.902995i	$0.358637\pi$
$128$		0			0
$129$	−13.4853	−	5.58579i	−1.18731	−	0.491801i
$130$		0			0
$131$	3.88897	−	1.61086i	0.339780	−	0.140742i	−0.206267	−	0.978496i	$-0.566132\pi$
$131$	3.88897	−	1.61086i	0.339780	−	0.140742i	0.546048	+	0.837754i	$0.316132\pi$
$132$		0			0
$133$	1.90141	+	4.59042i	0.164873	+	0.398040i
$134$		0			0
$135$	12.5359			1.07892
$136$		0			0
$137$	6.60889			0.564636			0.282318	−	0.959321i	$-0.408897\pi$
$137$	6.60889			0.564636			0.282318	+	0.959321i	$0.408897\pi$
$138$		0			0
$139$	−1.50575	−	3.63521i	−0.127716	−	0.308335i	0.847068	−	0.531485i	$-0.178366\pi$
$139$	−1.50575	−	3.63521i	−0.127716	−	0.308335i	−0.974784	+	0.223150i	$0.928366\pi$
$140$		0			0
$141$	3.92915	−	1.62751i	0.330894	−	0.137061i
$142$		0			0
$143$	4.11595	+	1.70488i	0.344193	+	0.142569i
$144$		0			0
$145$	−6.23801	+	6.23801i	−0.518038	+	0.518038i
$146$		0			0
$147$	−2.18692	+	5.27970i	−0.180374	+	0.435462i
$148$		0			0
$149$			7.14921i			0.585686i	0.956161	+	0.292843i	$0.0946014\pi$
$149$			7.14921i			0.585686i	−0.956161	+	0.292843i	$0.905399\pi$
$150$		0			0
$151$	11.1551	+	11.1551i	0.907793	+	0.907793i	0.996094	−	0.0883007i	$-0.0281436\pi$
$151$	11.1551	+	11.1551i	0.907793	+	0.907793i	−0.0883007	+	0.996094i	$0.528144\pi$
$152$		0			0
$153$	2.66454	−	6.56617i	0.215416	−	0.530844i
$154$		0			0
$155$	13.9069	+	13.9069i	1.11703	+	1.11703i
$156$		0			0
$157$		−	5.78973i		−	0.462071i	−0.972945	−	0.231035i	$-0.925789\pi$
$157$		−	5.78973i		−	0.462071i	0.972945	−	0.231035i	$-0.0742113\pi$
$158$		0			0
$159$	3.17102	−	7.65551i	0.251478	−	0.607121i
$160$		0			0
$161$	−2.02774	+	2.02774i	−0.159808	+	0.159808i
$162$		0			0
$163$	−8.53896	−	3.53695i	−0.668823	−	0.277036i	0.0223228	−	0.999751i	$-0.492894\pi$
$163$	−8.53896	−	3.53695i	−0.668823	−	0.277036i	−0.691146	+	0.722715i	$0.742894\pi$
$164$		0			0
$165$	13.1993	−	5.46733i	1.02756	−	0.425631i
$166$		0			0
$167$	−3.20687	−	7.74207i	−0.248155	−	0.599100i	0.749892	−	0.661560i	$-0.230105\pi$
$167$	−3.20687	−	7.74207i	−0.248155	−	0.599100i	−0.998047	+	0.0624603i	$0.980105\pi$
$168$		0			0
$169$	12.3137			0.947208
$170$		0			0
$171$	−2.46014			−0.188132
$172$		0			0
$173$	8.21024	+	19.8213i	0.624213	+	1.50698i	0.846713	+	0.532050i	$0.178578\pi$
$173$	8.21024	+	19.8213i	0.624213	+	1.50698i	−0.222500	+	0.974933i	$0.571422\pi$
$174$		0			0
$175$	−1.62963	+	0.675016i	−0.123189	+	0.0510264i
$176$		0			0
$177$	8.67922	+	3.59505i	0.652370	+	0.270220i
$178$		0			0
$179$	4.76926	−	4.76926i	0.356471	−	0.356471i	−0.506039	−	0.862510i	$-0.668891\pi$
$179$	4.76926	−	4.76926i	0.356471	−	0.356471i	0.862510	+	0.506039i	$0.168891\pi$
$180$		0			0
$181$	5.65108	−	13.6429i	0.420042	−	1.01407i	−0.562293	−	0.826938i	$-0.690081\pi$
$181$	5.65108	−	13.6429i	0.420042	−	1.01407i	0.982335	−	0.187132i	$-0.0599193\pi$
$182$		0			0
$183$		−	2.79115i		−	0.206328i
$184$		0			0
$185$	−5.97925	−	5.97925i	−0.439603	−	0.439603i
$186$		0			0
$187$	−0.159735	−	22.1724i	−0.0116810	−	1.62141i
$188$		0			0
$189$	−13.1100	−	13.1100i	−0.953611	−	0.953611i
$190$		0			0
$191$			3.62259i			0.262122i	0.991374	+	0.131061i	$0.0418383\pi$
$191$			3.62259i			0.262122i	−0.991374	+	0.131061i	$0.958162\pi$
$192$		0			0
$193$	−6.89965	+	16.6572i	−0.496648	+	1.19901i	0.454631	+	0.890680i	$0.349771\pi$
$193$	−6.89965	+	16.6572i	−0.496648	+	1.19901i	−0.951278	+	0.308333i	$0.900229\pi$
$194$		0			0
$195$	−1.55624	+	1.55624i	−0.111444	+	0.111444i
$196$		0			0
$197$	−13.5760	−	5.62335i	−0.967247	−	0.400647i	−0.157561	−	0.987509i	$-0.550363\pi$
$197$	−13.5760	−	5.62335i	−0.967247	−	0.400647i	−0.809687	+	0.586862i	$0.800363\pi$
$198$		0			0
$199$	−18.8534	+	7.80932i	−1.33648	+	0.553588i	−0.932497	−	0.361179i	$-0.882374\pi$
$199$	−18.8534	+	7.80932i	−1.33648	+	0.553588i	−0.403983	+	0.914767i	$0.632374\pi$
$200$		0			0
$201$	3.86896	+	9.34048i	0.272895	+	0.658827i
$202$		0			0
$203$	13.0474			0.915747
$204$		0			0
$205$	25.6830			1.79378
$206$		0			0
$207$	−0.543363	−	1.31179i	−0.0377663	−	0.0911759i
$208$		0			0
$209$	−7.11190	+	2.94585i	−0.491941	+	0.203768i
$210$		0			0
$211$	0.998248	+	0.413488i	0.0687222	+	0.0284657i	0.416780	−	0.909007i	$-0.363159\pi$
$211$	0.998248	+	0.413488i	0.0687222	+	0.0284657i	−0.348058	+	0.937473i	$0.613159\pi$
$212$		0			0
$213$	−11.0822	+	11.0822i	−0.759343	+	0.759343i
$214$		0			0
$215$	−11.5813	+	27.9596i	−0.789835	+	1.90683i
$216$		0			0
$217$		−	29.0876i		−	1.97460i
$218$		0			0
$219$	−1.61794	−	1.61794i	−0.109330	−	0.109330i
$220$		0			0
$221$	1.32983	+	3.14619i	0.0894540	+	0.211636i
$222$		0			0
$223$	6.98566	+	6.98566i	0.467794	+	0.467794i	0.901199	−	0.433405i	$-0.142688\pi$
$223$	6.98566	+	6.98566i	0.467794	+	0.467794i	−0.433405	+	0.901199i	$0.642688\pi$
$224$		0			0
$225$		−	0.873369i		−	0.0582246i
$226$		0			0
$227$	−5.77436	+	13.9405i	−0.383258	+	0.925266i	0.608074	+	0.793880i	$0.291942\pi$
$227$	−5.77436	+	13.9405i	−0.383258	+	0.925266i	−0.991331	+	0.131385i	$0.958058\pi$
$228$		0			0
$229$	15.6233	−	15.6233i	1.03242	−	1.03242i	0.0329608	−	0.999457i	$-0.489506\pi$
$229$	15.6233	−	15.6233i	1.03242	−	1.03242i	0.999457	−	0.0329608i	$-0.0104936\pi$
$230$		0			0
$231$	−19.5215	−	8.08608i	−1.28442	−	0.532025i
$232$		0			0
$233$	−7.61315	+	3.15347i	−0.498754	+	0.206591i	−0.617856	−	0.786291i	$-0.711999\pi$
$233$	−7.61315	+	3.15347i	−0.498754	+	0.206591i	0.119102	+	0.992882i	$0.461999\pi$
$234$		0			0
$235$	−3.37438	−	8.14648i	−0.220120	−	0.531418i
$236$		0			0
$237$	10.5473			0.685121
$238$		0			0
$239$	10.5115			0.679934			0.339967	−	0.940437i	$-0.389584\pi$
$239$	10.5115			0.679934			0.339967	+	0.940437i	$0.389584\pi$
$240$		0			0
$241$	−6.94298	−	16.7618i	−0.447237	−	1.07972i	−0.973353	−	0.229312i	$-0.926352\pi$
$241$	−6.94298	−	16.7618i	−0.447237	−	1.07972i	0.526116	−	0.850413i	$-0.323648\pi$
$242$		0			0
$243$	13.8733	−	5.74650i	0.889972	−	0.368638i
$244$		0			0
$245$	10.9466	+	4.53424i	0.699354	+	0.289682i
$246$		0			0
$247$	0.838513	−	0.838513i	0.0533533	−	0.0533533i
$248$		0			0
$249$	1.96161	−	4.73574i	0.124312	−	0.300115i
$250$		0			0
$251$		−	1.87169i		−	0.118140i	−0.998254	−	0.0590701i	$-0.981186\pi$
$251$		−	1.87169i		−	0.118140i	0.998254	−	0.0590701i	$-0.0188135\pi$
$252$		0			0
$253$	−3.14156	−	3.14156i	−0.197508	−	0.197508i
$254$		0			0
$255$	10.1498	+	4.11878i	0.635607	+	0.257928i
$256$		0			0
$257$	7.53377	+	7.53377i	0.469944	+	0.469944i	0.901896	−	0.431953i	$-0.142175\pi$
$257$	7.53377	+	7.53377i	0.469944	+	0.469944i	−0.431953	+	0.901896i	$0.642175\pi$
$258$		0			0
$259$			12.5062i			0.777095i
$260$		0			0
$261$	−2.47222	+	5.96846i	−0.153026	+	0.369439i
$262$		0			0
$263$	22.3450	−	22.3450i	1.37785	−	1.37785i	0.529612	−	0.848240i	$-0.322338\pi$
$263$	22.3450	−	22.3450i	1.37785	−	1.37785i	0.848240	−	0.529612i	$-0.177662\pi$
$264$		0			0
$265$	−15.8725	−	6.57461i	−0.975040	−	0.403875i
$266$		0			0
$267$	0.327848	−	0.135799i	0.0200640	−	0.00831077i
$268$		0			0
$269$	9.33332	+	22.5326i	0.569063	+	1.37384i	0.902346	+	0.431012i	$0.141843\pi$
$269$	9.33332	+	22.5326i	0.569063	+	1.37384i	−0.333284	+	0.942827i	$0.608157\pi$
$270$		0			0
$271$	−27.6373			−1.67885			−0.839424	−	0.543478i	$-0.817107\pi$
$271$	−27.6373			−1.67885			−0.839424	+	0.543478i	$0.817107\pi$
$272$		0			0
$273$	3.25501			0.197002
$274$		0			0
$275$	−1.04580	−	2.52478i	−0.0630640	−	0.152250i
$276$		0			0
$277$	21.4662	−	8.89159i	1.28978	−	0.534244i	0.370859	−	0.928689i	$-0.379063\pi$
$277$	21.4662	−	8.89159i	1.28978	−	0.534244i	0.918919	+	0.394445i	$0.129063\pi$
$278$		0			0
$279$	13.3060	+	5.51152i	0.796609	+	0.329966i
$280$		0			0
$281$	−2.98205	+	2.98205i	−0.177894	+	0.177894i	−0.790437	−	0.612543i	$-0.790147\pi$
$281$	−2.98205	+	2.98205i	−0.177894	+	0.177894i	0.612543	+	0.790437i	$0.290147\pi$
$282$		0			0
$283$	1.49291	−	3.60420i	0.0887442	−	0.214247i	−0.873276	−	0.487226i	$-0.838009\pi$
$283$	1.49291	−	3.60420i	0.0887442	−	0.214247i	0.962020	+	0.272979i	$0.0880088\pi$
$284$		0			0
$285$		−	3.80283i		−	0.225260i
$286$		0			0
$287$	−26.8592	−	26.8592i	−1.58545	−	1.58545i
$288$		0			0
$289$	11.8464	−	12.1928i	0.696846	−	0.717221i
$290$		0			0
$291$	−10.0419	−	10.0419i	−0.588665	−	0.588665i
$292$		0			0
$293$			2.47602i			0.144651i	0.997381	+	0.0723253i	$0.0230420\pi$
$293$			2.47602i			0.144651i	−0.997381	+	0.0723253i	$0.976958\pi$
$294$		0			0
$295$	7.45377	−	17.9950i	0.433975	−	1.04771i
$296$		0			0
$297$	20.3112	−	20.3112i	1.17858	−	1.17858i
$298$		0			0
$299$	0.632310	+	0.261911i	0.0365674	+	0.0151467i
$300$		0			0
$301$	41.3518	−	17.1285i	2.38348	−	0.987268i
$302$		0			0
$303$	−4.82965	−	11.6598i	−0.277456	−	0.669839i
$304$		0			0
$305$	−5.78701			−0.331363
$306$		0			0
$307$	22.1895			1.26642			0.633211	−	0.773979i	$-0.281737\pi$
$307$	22.1895			1.26642			0.633211	+	0.773979i	$0.281737\pi$
$308$		0			0
$309$	1.81209	+	4.37477i	0.103086	+	0.248872i
$310$		0			0
$311$	23.3720	−	9.68101i	1.32531	−	0.548960i	0.395993	−	0.918253i	$-0.370400\pi$
$311$	23.3720	−	9.68101i	1.32531	−	0.548960i	0.929313	+	0.369294i	$0.120400\pi$
$312$		0			0
$313$	11.1444	+	4.61617i	0.629920	+	0.260921i	0.674719	−	0.738075i	$-0.264265\pi$
$313$	11.1444	+	4.61617i	0.629920	+	0.260921i	−0.0447990	+	0.998996i	$0.514265\pi$
$314$		0			0
$315$	−9.90022	+	9.90022i	−0.557814	+	0.557814i
$316$		0			0
$317$	1.04874	−	2.53189i	0.0589032	−	0.142205i	−0.891688	−	0.452651i	$-0.850478\pi$
$317$	1.04874	−	2.53189i	0.0589032	−	0.142205i	0.950591	+	0.310446i	$0.100478\pi$
$318$		0			0
$319$			20.2142i			1.13178i
$320$		0			0
$321$	−9.64126	−	9.64126i	−0.538123	−	0.538123i
$322$		0			0
$323$	−5.46881	−	2.21924i	−0.304293	−	0.123482i
$324$		0			0
$325$	0.297678	+	0.297678i	0.0165122	+	0.0165122i
$326$		0			0
$327$			2.65666i			0.146914i
$328$		0			0
$329$	−4.99065	+	12.0485i	−0.275143	+	0.664255i
$330$		0			0
$331$	−12.7799	+	12.7799i	−0.702449	+	0.702449i	−0.964936	−	0.262487i	$-0.915457\pi$
$331$	−12.7799	+	12.7799i	−0.702449	+	0.702449i	0.262487	+	0.964936i	$0.415457\pi$
$332$		0			0
$333$	−5.72088	−	2.36967i	−0.313502	−	0.129857i
$334$		0			0
$335$	19.3660	−	8.02167i	1.05808	−	0.438271i
$336$		0			0
$337$	7.73463	+	18.6730i	0.421332	+	1.01719i	0.981955	+	0.189114i	$0.0605616\pi$
$337$	7.73463	+	18.6730i	0.421332	+	1.01719i	−0.560623	+	0.828071i	$0.689438\pi$
$338$		0			0
$339$	−23.3869			−1.27020
$340$		0			0
$341$	45.0653			2.44042
$342$		0			0
$343$	2.59225	+	6.25825i	0.139968	+	0.337914i
$344$		0			0
$345$	2.02774	−	0.839916i	0.109170	−	0.0452196i
$346$		0			0
$347$	−31.6311	−	13.1020i	−1.69804	−	0.703353i	−0.698124	−	0.715976i	$-0.745982\pi$
$347$	−31.6311	−	13.1020i	−1.69804	−	0.703353i	−0.999920	+	0.0126233i	$0.995982\pi$
$348$		0			0
$349$	−18.2018	+	18.2018i	−0.974320	+	0.974320i	−0.999678	−	0.0253582i	$-0.991927\pi$
$349$	−18.2018	+	18.2018i	−0.974320	+	0.974320i	0.0253582	+	0.999678i	$0.491927\pi$
$350$		0			0
$351$	−1.69334	+	4.08809i	−0.0903840	+	0.218206i
$352$		0			0
$353$		−	17.6506i		−	0.939447i	−0.882814	−	0.469724i	$-0.844354\pi$
$353$		−	17.6506i		−	0.939447i	0.882814	−	0.469724i	$-0.155646\pi$
$354$		0			0
$355$	22.9773	+	22.9773i	1.21951	+	1.21951i
$356$		0			0
$357$	−6.30725	−	14.9221i	−0.333815	−	0.789760i
$358$		0			0
$359$	15.2432	+	15.2432i	0.804507	+	0.804507i	0.983796	−	0.179289i	$-0.0573797\pi$
$359$	15.2432	+	15.2432i	0.804507	+	0.804507i	−0.179289	+	0.983796i	$0.557380\pi$
$360$		0			0
$361$		−	16.9510i		−	0.892158i
$362$		0			0
$363$	7.76269	−	18.7408i	0.407436	−	0.983637i
$364$		0			0
$365$	−3.35454	+	3.35454i	−0.175585	+	0.175585i
$366$		0			0
$367$	28.2251	+	11.6912i	1.47334	+	0.610276i	0.967617	−	0.252422i	$-0.0812271\pi$
$367$	28.2251	+	11.6912i	1.47334	+	0.610276i	0.505719	+	0.862698i	$0.331227\pi$
$368$		0			0
$369$	17.3759	−	7.19733i	0.904552	−	0.374678i
$370$		0			0
$371$	9.72372	+	23.4751i	0.504830	+	1.21877i
$372$		0			0
$373$	−6.56695			−0.340024			−0.170012	−	0.985442i	$-0.554381\pi$
$373$	−6.56695			−0.340024			−0.170012	+	0.985442i	$0.554381\pi$
$374$		0			0
$375$	−11.9333			−0.616231
$376$		0			0
$377$	−1.19166	−	2.87692i	−0.0613735	−	0.148169i
$378$		0			0
$379$	−7.20579	+	2.98474i	−0.370136	+	0.153316i	−0.559995	−	0.828496i	$-0.689197\pi$
$379$	−7.20579	+	2.98474i	−0.370136	+	0.153316i	0.189859	+	0.981811i	$0.439197\pi$
$380$		0			0
$381$	−7.88936	−	3.26788i	−0.404184	−	0.167419i
$382$		0			0
$383$	−13.6056	+	13.6056i	−0.695214	+	0.695214i	−0.963374	−	0.268160i	$-0.913584\pi$
$383$	−13.6056	+	13.6056i	−0.695214	+	0.695214i	0.268160	+	0.963374i	$0.413584\pi$
$384$		0			0
$385$	−16.7652	+	40.4748i	−0.854435	+	2.06279i
$386$		0			0
$387$			22.1617i			1.12654i
$388$		0			0
$389$	−14.0112	−	14.0112i	−0.710395	−	0.710395i	0.256223	−	0.966618i	$-0.417522\pi$
$389$	−14.0112	−	14.0112i	−0.710395	−	0.710395i	−0.966618	+	0.256223i	$0.917522\pi$
$390$		0			0
$391$	−0.0245392	−	3.40623i	−0.00124100	−	0.172260i
$392$		0			0
$393$	3.36927	+	3.36927i	0.169957	+	0.169957i
$394$		0			0
$395$		−	21.8682i		−	1.10031i
$396$		0			0
$397$	−12.3266	+	29.7589i	−0.618652	+	1.49356i	0.234617	+	0.972088i	$0.424616\pi$
$397$	−12.3266	+	29.7589i	−0.618652	+	1.49356i	−0.853269	+	0.521470i	$0.825384\pi$
$398$		0			0
$399$	−3.97699	+	3.97699i	−0.199098	+	0.199098i
$400$		0			0
$401$	−15.7229	−	6.51265i	−0.785165	−	0.325226i	−0.0461672	−	0.998934i	$-0.514701\pi$
$401$	−15.7229	−	6.51265i	−0.785165	−	0.325226i	−0.738998	+	0.673708i	$0.764701\pi$
$402$		0			0
$403$	−6.41374	+	2.65666i	−0.319491	+	0.132338i
$404$		0			0
$405$	0.799552	+	1.93029i	0.0397300	+	0.0959168i
$406$		0			0
$407$	−19.3757			−0.960419
$408$		0			0
$409$	−28.6315			−1.41574			−0.707868	−	0.706345i	$-0.750343\pi$
$409$	−28.6315			−1.41574			−0.707868	+	0.706345i	$0.750343\pi$
$410$		0			0
$411$	2.86286	+	6.91156i	0.141215	+	0.340922i
$412$		0			0
$413$	−26.6143	+	11.0240i	−1.30960	+	0.542455i
$414$		0			0
$415$	−9.81882	−	4.06709i	−0.481987	−	0.199645i
$416$		0			0
$417$	3.14943	−	3.14943i	0.154228	−	0.154228i
$418$		0			0
$419$	1.59117	−	3.84142i	0.0777336	−	0.187665i	−0.880235	−	0.474537i	$-0.842615\pi$
$419$	1.59117	−	3.84142i	0.0777336	−	0.187665i	0.957969	+	0.286872i	$0.0926154\pi$
$420$		0			0
$421$		−	34.1240i		−	1.66310i	−0.555447	−	0.831552i	$-0.687453\pi$
$421$		−	34.1240i		−	1.66310i	0.555447	−	0.831552i	$-0.312547\pi$
$422$		0			0
$423$	−4.56589	−	4.56589i	−0.222001	−	0.222001i
$424$		0			0
$425$	0.787845	−	1.94147i	0.0382161	−	0.0941751i
$426$		0			0
$427$	6.05205	+	6.05205i	0.292879	+	0.292879i
$428$		0			0
$429$			5.04297i			0.243477i
$430$		0			0
$431$	−7.23740	+	17.4726i	−0.348614	+	0.841628i	0.648171	+	0.761495i	$0.275534\pi$
$431$	−7.23740	+	17.4726i	−0.348614	+	0.841628i	−0.996784	+	0.0801324i	$0.974466\pi$
$432$		0			0
$433$	−0.558793	+	0.558793i	−0.0268539	+	0.0268539i	−0.720406	−	0.693552i	$-0.756045\pi$
$433$	−0.558793	+	0.558793i	−0.0268539	+	0.0268539i	0.693552	+	0.720406i	$0.256045\pi$
$434$		0			0
$435$	−9.22590	−	3.82149i	−0.442348	−	0.183227i
$436$		0			0
$437$	−1.09256	+	0.452554i	−0.0522643	+	0.0216486i
$438$		0			0
$439$	5.59008	+	13.4957i	0.266800	+	0.644112i	0.999329	−	0.0366234i	$-0.0116602\pi$
$439$	5.59008	+	13.4957i	0.266800	+	0.644112i	−0.732529	+	0.680736i	$0.761660\pi$
$440$		0			0
$441$	8.67663			0.413173
$442$		0			0
$443$	−18.7059			−0.888743			−0.444371	−	0.895843i	$-0.646573\pi$
$443$	−18.7059			−0.888743			−0.444371	+	0.895843i	$0.646573\pi$
$444$		0			0
$445$	−0.281558	−	0.679742i	−0.0133471	−	0.0322228i
$446$		0			0
$447$	−7.47663	+	3.09692i	−0.353632	+	0.146479i
$448$		0			0
$449$	19.2318	+	7.96609i	0.907606	+	0.375943i	0.787140	−	0.616775i	$-0.211561\pi$
$449$	19.2318	+	7.96609i	0.907606	+	0.375943i	0.120466	+	0.992717i	$0.461561\pi$
$450$		0			0
$451$	41.6128	−	41.6128i	1.95947	−	1.95947i
$452$		0			0
$453$	−6.83380	+	16.4983i	−0.321080	+	0.775156i
$454$		0			0
$455$		−	6.74876i		−	0.316387i
$456$		0			0
$457$	6.79186	+	6.79186i	0.317710	+	0.317710i	0.847887	−	0.530177i	$-0.177875\pi$
$457$	6.79186	+	6.79186i	0.317710	+	0.317710i	−0.530177	+	0.847887i	$0.677875\pi$
$458$		0			0
$459$	22.0224	−	0.158654i	1.02792	−	0.00740533i
$460$		0			0
$461$	−23.2317	−	23.2317i	−1.08201	−	1.08201i	−0.996322	−	0.0856848i	$-0.972692\pi$
$461$	−23.2317	−	23.2317i	−1.08201	−	1.08201i	−0.0856848	−	0.996322i	$-0.527308\pi$
$462$		0			0
$463$		−	14.5739i		−	0.677308i	−0.940911	−	0.338654i	$-0.890028\pi$
$463$		−	14.5739i		−	0.677308i	0.940911	−	0.338654i	$-0.109972\pi$
$464$		0			0
$465$	−8.51957	+	20.5681i	−0.395085	+	0.953821i
$466$		0			0
$467$	4.30114	−	4.30114i	0.199033	−	0.199033i	−0.600552	−	0.799585i	$-0.705053\pi$
$467$	4.30114	−	4.30114i	0.199033	−	0.199033i	0.799585	+	0.600552i	$0.205053\pi$
$468$		0			0
$469$	−28.6420	−	11.8639i	−1.32256	−	0.547824i
$470$		0			0
$471$	6.05488	−	2.50801i	0.278994	−	0.115563i
$472$		0			0
$473$	26.5370	+	64.0660i	1.22017	+	2.94576i
$474$		0			0
$475$	−0.727409			−0.0333758
$476$		0			0
$477$	−12.5810			−0.576046
$478$		0			0
$479$	−11.5060	−	27.7780i	−0.525723	−	1.26921i	−0.934301	−	0.356484i	$-0.883975\pi$
$479$	−11.5060	−	27.7780i	−0.525723	−	1.26921i	0.408578	−	0.912723i	$-0.366025\pi$
$480$		0			0
$481$	2.75758	−	1.14223i	0.125735	−	0.0520810i
$482$		0			0
$483$	−2.99898	−	1.24222i	−0.136458	−	0.0565230i
$484$		0			0
$485$	−20.8203	+	20.8203i	−0.945400	+	0.945400i
$486$		0			0
$487$	12.6321	−	30.4966i	0.572416	−	1.38193i	−0.327076	−	0.944998i	$-0.606063\pi$
$487$	12.6321	−	30.4966i	0.572416	−	1.38193i	0.899492	−	0.436937i	$-0.143937\pi$
$488$		0			0
$489$		−	10.4622i		−	0.473116i
$490$		0			0
$491$	11.8153	+	11.8153i	0.533218	+	0.533218i	0.921528	−	0.388311i	$-0.126941\pi$
$491$	11.8153	+	11.8153i	0.533218	+	0.533218i	−0.388311	+	0.921528i	$0.626941\pi$
$492$		0			0
$493$	−10.8797	+	11.0376i	−0.489995	+	0.497107i
$494$		0			0
$495$	−15.3383	−	15.3383i	−0.689407	−	0.689407i
$496$		0			0
$497$		−	48.0592i		−	2.15575i
$498$		0			0
$499$	−10.0952	+	24.3720i	−0.451923	+	1.09104i	0.519667	+	0.854369i	$0.326056\pi$
$499$	−10.0952	+	24.3720i	−0.451923	+	1.09104i	−0.971590	+	0.236670i	$0.923944\pi$
$500$		0			0
$501$	6.70748	−	6.70748i	0.299668	−	0.299668i
$502$		0			0
$503$	7.45731	+	3.08892i	0.332505	+	0.137728i	0.542689	−	0.839934i	$-0.317406\pi$
$503$	7.45731	+	3.08892i	0.332505	+	0.137728i	−0.210184	+	0.977662i	$0.567406\pi$
$504$		0			0
$505$	−24.1748	+	10.0135i	−1.07576	+	0.445596i
$506$		0			0
$507$	5.33410	+	12.8776i	0.236896	+	0.571916i
$508$		0			0
$509$	−0.0643005			−0.00285007			−0.00142503	−	0.999999i	$-0.500454\pi$
$509$	−0.0643005			−0.00285007			−0.00142503	+	0.999999i	$0.500454\pi$
$510$		0			0
$511$	7.01635			0.310385
$512$		0			0
$513$	−2.92591	−	7.06378i	−0.129182	−	0.311873i
$514$		0			0
$515$	9.07040	−	3.75708i	0.399690	−	0.165557i
$516$		0			0
$517$	−18.6666	−	7.73198i	−0.820958	−	0.340052i
$518$		0			0
$519$	−17.1725	+	17.1725i	−0.753789	+	0.753789i
$520$		0			0
$521$	−3.14015	+	7.58100i	−0.137573	+	0.332130i	−0.977618	−	0.210386i	$-0.932528\pi$
$521$	−3.14015	+	7.58100i	−0.137573	+	0.332130i	0.840046	+	0.542515i	$0.182528\pi$
$522$		0			0
$523$			9.10794i			0.398263i	0.979973	+	0.199131i	$0.0638120\pi$
$523$			9.10794i			0.398263i	−0.979973	+	0.199131i	$0.936188\pi$
$524$		0			0
$525$	−1.41186	−	1.41186i	−0.0616186	−	0.0616186i
$526$		0			0
$527$	24.6069	+	24.2549i	1.07190	+	1.05656i
$528$		0			0
$529$	15.7808	+	15.7808i	0.686123	+	0.686123i
$530$		0			0
$531$		−	14.2634i		−	0.618978i
$532$		0			0
$533$	−3.46925	+	8.37551i	−0.150270	+	0.362784i
$534$		0			0
$535$	−19.9896	+	19.9896i	−0.864228	+	0.864228i
$536$		0			0
$537$	7.05364	+	2.92172i	0.304387	+	0.126081i
$538$		0			0
$539$	25.0828	−	10.3897i	1.08039	−	0.447514i
$540$		0			0
$541$	−5.16424	−	12.4676i	−0.222028	−	0.536023i	0.773137	−	0.634239i	$-0.218687\pi$
$541$	−5.16424	−	12.4676i	−0.222028	−	0.536023i	−0.995165	+	0.0982156i	$0.968687\pi$
$542$		0			0
$543$	16.7157			0.717339
$544$		0			0
$545$	5.50817			0.235944
$546$		0			0
$547$	−11.2642	−	27.1941i	−0.481621	−	1.16274i	−0.958839	−	0.283951i	$-0.908355\pi$
$547$	−11.2642	−	27.1941i	−0.481621	−	1.16274i	0.477217	−	0.878785i	$-0.341645\pi$
$548$		0			0
$549$	−3.91522	+	1.62174i	−0.167097	+	0.0692140i
$550$		0			0
$551$	4.97100	+	2.05905i	0.211772	+	0.0877186i
$552$		0			0
$553$	−22.8697	+	22.8697i	−0.972518	+	0.972518i
$554$		0			0
$555$	3.66297	−	8.84320i	0.155484	−	0.375373i
$556$		0			0
$557$		−	18.6792i		−	0.791465i	−0.918366	−	0.395732i	$-0.870491\pi$
$557$		−	18.6792i		−	0.791465i	0.918366	−	0.395732i	$-0.129509\pi$
$558$		0			0
$559$	−7.55356	−	7.55356i	−0.319482	−	0.319482i
$560$		0			0
$561$	23.1187	−	9.77178i	0.976071	−	0.412565i
$562$		0			0
$563$	−20.6388	−	20.6388i	−0.869822	−	0.869822i	0.122630	−	0.992452i	$-0.460867\pi$
$563$	−20.6388	−	20.6388i	−0.869822	−	0.869822i	−0.992452	+	0.122630i	$0.960867\pi$
$564$		0			0
$565$			48.4890i			2.03995i
$566$		0			0
$567$	1.18252	−	2.85486i	0.0496613	−	0.119893i
$568$		0			0
$569$	16.7031	−	16.7031i	0.700229	−	0.700229i	−0.264231	−	0.964460i	$-0.585118\pi$
$569$	16.7031	−	16.7031i	0.700229	−	0.700229i	0.964460	+	0.264231i	$0.0851180\pi$
$570$		0			0
$571$	−14.0895	−	5.83606i	−0.589627	−	0.244232i	0.0678631	−	0.997695i	$-0.478382\pi$
$571$	−14.0895	−	5.83606i	−0.589627	−	0.244232i	−0.657490	+	0.753463i	$0.728382\pi$
$572$		0			0
$573$	−3.78850	+	1.56925i	−0.158267	+	0.0655563i
$574$		0			0
$575$	−0.160660	−	0.387868i	−0.00669999	−	0.0161752i
$576$		0			0
$577$	7.85403			0.326967			0.163484	−	0.986546i	$-0.447727\pi$
$577$	7.85403			0.326967			0.163484	+	0.986546i	$0.447727\pi$
$578$		0			0
$579$	−20.4089			−0.848165
$580$		0			0
$581$	6.01515	+	14.5218i	0.249550	+	0.602468i
$582$		0			0
$583$	−36.3699	+	15.0649i	−1.50629	+	0.623924i
$584$		0			0
$585$	3.08719	+	1.27876i	0.127640	+	0.0528700i
$586$		0			0
$587$	−19.8525	+	19.8525i	−0.819402	+	0.819402i	−0.986021	−	0.166619i	$-0.946715\pi$
$587$	−19.8525	+	19.8525i	−0.819402	+	0.819402i	0.166619	+	0.986021i	$0.446715\pi$
$588$		0			0
$589$	4.59042	−	11.0822i	0.189145	−	0.456636i
$590$		0			0
$591$		−	16.6337i		−	0.684217i
$592$		0			0
$593$	−10.8867	−	10.8867i	−0.447063	−	0.447063i	0.447314	−	0.894377i	$-0.352381\pi$
$593$	−10.8867	−	10.8867i	−0.447063	−	0.447063i	−0.894377	+	0.447314i	$0.852381\pi$
$594$		0			0
$595$	−30.9386	+	13.0771i	−1.26836	+	0.536109i
$596$		0			0
$597$	−16.3339	−	16.3339i	−0.668503	−	0.668503i
$598$		0			0
$599$			18.0394i			0.737069i	0.929614	+	0.368535i	$0.120140\pi$
$599$			18.0394i			0.737069i	−0.929614	+	0.368535i	$0.879860\pi$
$600$		0			0
$601$	−6.42665	+	15.5153i	−0.262149	+	0.632883i	−0.999071	−	0.0430947i	$-0.986278\pi$
$601$	−6.42665	+	15.5153i	−0.262149	+	0.632883i	0.736922	+	0.675977i	$0.236278\pi$
$602$		0			0
$603$	10.8542	−	10.8542i	0.442016	−	0.442016i
$604$		0			0
$605$	−38.8561	−	16.0947i	−1.57973	−	0.654344i
$606$		0			0
$607$	19.8148	−	8.20757i	0.804259	−	0.333135i	0.0575982	−	0.998340i	$-0.481656\pi$
$607$	19.8148	−	8.20757i	0.804259	−	0.333135i	0.746661	+	0.665205i	$0.231656\pi$
$608$		0			0
$609$	5.65192	+	13.6449i	0.229027	+	0.552920i
$610$		0			0
$611$	3.11247			0.125917
$612$		0			0
$613$	30.7109			1.24040			0.620200	−	0.784444i	$-0.287051\pi$
$613$	30.7109			1.24040			0.620200	+	0.784444i	$0.287051\pi$
$614$		0			0
$615$	11.1254	+	26.8592i	0.448621	+	1.08307i
$616$		0			0
$617$	−12.5311	+	5.19056i	−0.504484	+	0.208964i	−0.620386	−	0.784297i	$-0.713024\pi$
$617$	−12.5311	+	5.19056i	−0.504484	+	0.208964i	0.115902	+	0.993261i	$0.463024\pi$
$618$		0			0
$619$	20.7341	+	8.58836i	0.833375	+	0.345195i	0.758238	−	0.651978i	$-0.226060\pi$
$619$	20.7341	+	8.58836i	0.833375	+	0.345195i	0.0751374	+	0.997173i	$0.476060\pi$
$620$		0			0
$621$	3.12030	−	3.12030i	0.125213	−	0.125213i
$622$		0			0
$623$	−0.416419	+	1.00533i	−0.0166835	+	0.0402775i
$624$		0			0
$625$			27.2826i			1.09130i
$626$		0			0
$627$	−6.16152	−	6.16152i	−0.246067	−	0.246067i
$628$		0			0
$629$	−10.5797	−	10.4284i	−0.421841	−	0.415806i
$630$		0			0
$631$	−25.3981	−	25.3981i	−1.01108	−	1.01108i	−0.999938	−	0.0111430i	$-0.996453\pi$
$631$	−25.3981	−	25.3981i	−1.01108	−	1.01108i	−0.0111430	−	0.999938i	$-0.503547\pi$
$632$		0			0
$633$			1.22308i			0.0486131i
$634$		0			0
$635$	−6.77544	+	16.3574i	−0.268875	+	0.649122i
$636$		0			0
$637$	−2.95734	+	2.95734i	−0.117174	+	0.117174i
$638$		0			0
$639$	21.9845	+	9.10626i	0.869692	+	0.360238i
$640$		0			0
$641$	10.0617	−	4.16767i	0.397411	−	0.164613i	−0.175022	−	0.984565i	$-0.556000\pi$
$641$	10.0617	−	4.16767i	0.397411	−	0.164613i	0.572433	+	0.819951i	$0.306000\pi$
$642$		0			0
$643$	−4.14957	−	10.0179i	−0.163643	−	0.395069i	0.820694	−	0.571369i	$-0.193587\pi$
$643$	−4.14957	−	10.0179i	−0.163643	−	0.395069i	−0.984337	+	0.176299i	$0.943587\pi$
$644$		0			0
$645$	−34.2569			−1.34886
$646$		0			0
$647$	8.06107			0.316913			0.158457	−	0.987366i	$-0.449348\pi$
$647$	8.06107			0.316913			0.158457	+	0.987366i	$0.449348\pi$
$648$		0			0
$649$	−17.0794	−	41.2333i	−0.670425	−	1.61855i
$650$		0			0
$651$	30.4198	−	12.6003i	1.19224	−	0.493844i
$652$		0			0
$653$	38.0843	+	15.7751i	1.49036	+	0.617326i	0.971394	−	0.237472i	$-0.0763188\pi$
$653$	38.0843	+	15.7751i	1.49036	+	0.617326i	0.518961	+	0.854798i	$0.326319\pi$
$654$		0			0
$655$	6.98566	−	6.98566i	0.272952	−	0.272952i
$656$		0			0
$657$	−1.32946	+	3.20959i	−0.0518671	+	0.125218i
$658$		0			0
$659$		−	33.2980i		−	1.29710i	−0.761170	−	0.648552i	$-0.775375\pi$
$659$		−	33.2980i		−	1.29710i	0.761170	−	0.648552i	$-0.224625\pi$
$660$		0			0
$661$	−7.50126	−	7.50126i	−0.291765	−	0.291765i	0.546012	−	0.837777i	$-0.316145\pi$
$661$	−7.50126	−	7.50126i	−0.291765	−	0.291765i	−0.837777	+	0.546012i	$0.816145\pi$
$662$		0			0
$663$	−2.71422	+	2.75361i	−0.105411	+	0.106941i
$664$		0			0
$665$	8.24566	+	8.24566i	0.319753	+	0.319753i
$666$		0			0
$667$			3.10540i			0.120242i
$668$		0			0
$669$	−4.27951	+	10.3317i	−0.165456	+	0.399445i
$670$		0			0
$671$	−9.37639	+	9.37639i	−0.361972	+	0.361972i
$672$		0			0
$673$	−17.8537	−	7.39523i	−0.688208	−	0.285065i	0.0110455	−	0.999939i	$-0.496484\pi$
$673$	−17.8537	−	7.39523i	−0.688208	−	0.285065i	−0.699253	+	0.714874i	$0.746484\pi$
$674$		0			0
$675$	2.50769	−	1.03872i	0.0965211	−	0.0399804i
$676$		0			0
$677$	−1.46317	−	3.53241i	−0.0562343	−	0.135762i	0.893265	−	0.449530i	$-0.148408\pi$
$677$	−1.46317	−	3.53241i	−0.0562343	−	0.135762i	−0.949500	+	0.313768i	$0.898408\pi$
$678$		0			0
$679$	43.5476			1.67120
$680$		0			0
$681$	−17.0803			−0.654520
$682$		0			0
$683$	10.7023	+	25.8376i	0.409511	+	0.988647i	0.985267	+	0.171025i	$0.0547079\pi$
$683$	10.7023	+	25.8376i	0.409511	+	0.988647i	−0.575756	+	0.817622i	$0.695292\pi$
$684$		0			0
$685$	14.3300	−	5.93570i	0.547523	−	0.226791i
$686$		0			0
$687$	23.1066	+	9.57106i	0.881571	+	0.365159i
$688$		0			0
$689$	4.28811	−	4.28811i	0.163364	−	0.163364i
$690$		0			0
$691$	−10.2602	+	24.7702i	−0.390315	+	0.942303i	0.599556	+	0.800333i	$0.295344\pi$
$691$	−10.2602	+	24.7702i	−0.390315	+	0.942303i	−0.989871	+	0.141971i	$0.954656\pi$
$692$		0			0
$693$			32.0816i			1.21868i
$694$		0			0
$695$	−6.52985	−	6.52985i	−0.247691	−	0.247691i
$696$		0			0
$697$	45.1185	−	0.325043i	1.70899	−	0.0123119i
$698$		0			0
$699$	−6.59578	−	6.59578i	−0.249475	−	0.249475i
$700$		0			0
$701$		−	29.7543i		−	1.12380i	−0.827204	−	0.561902i	$-0.810070\pi$
$701$		−	29.7543i		−	1.12380i	0.827204	−	0.561902i	$-0.189930\pi$
$702$		0			0
$703$	−1.97364	+	4.76479i	−0.0744373	+	0.179708i
$704$		0			0
$705$	7.05784	−	7.05784i	0.265814	−	0.265814i
$706$		0			0
$707$	35.7541	+	14.8098i	1.34467	+	0.556981i
$708$		0			0
$709$	0.418231	−	0.173237i	0.0157070	−	0.00650605i	−0.374816	−	0.927099i	$-0.622294\pi$
$709$	0.418231	−	0.173237i	0.0157070	−	0.00650605i	0.390523	+	0.920593i	$0.372294\pi$
$710$		0			0
$711$	−6.12828	−	14.7950i	−0.229828	−	0.554855i
$712$		0			0
$713$	6.92313			0.259273
$714$		0			0
$715$	10.4558			0.391025
$716$		0			0
$717$	4.55342	+	10.9929i	0.170051	+	0.410538i
$718$		0			0
$719$	−19.7773	+	8.19202i	−0.737568	+	0.305511i	−0.719658	−	0.694329i	$-0.755701\pi$
$719$	−19.7773	+	8.19202i	−0.737568	+	0.305511i	−0.0179105	+	0.999840i	$0.505701\pi$
$720$		0			0
$721$	−13.4150	−	5.55666i	−0.499599	−	0.206941i
$722$		0			0
$723$	14.5219	−	14.5219i	0.540075	−	0.540075i
$724$		0			0
$725$	−0.730979	+	1.76474i	−0.0271479	+	0.0655408i
$726$		0			0
$727$		−	22.4811i		−	0.833779i	−0.908957	−	0.416889i	$-0.863120\pi$
$727$		−	22.4811i		−	0.833779i	0.908957	−	0.416889i	$-0.136880\pi$
$728$		0			0
$729$	13.9078	+	13.9078i	0.515105	+	0.515105i
$730$		0			0
$731$	−19.9915	+	49.2646i	−0.739412	+	1.82212i
$732$		0			0
$733$	−14.9436	−	14.9436i	−0.551953	−	0.551953i	0.375051	−	0.927004i	$-0.377625\pi$
$733$	−14.9436	−	14.9436i	−0.551953	−	0.551953i	−0.927004	+	0.375051i	$0.877625\pi$
$734$		0			0
$735$			13.4121i			0.494713i
$736$		0			0
$737$	18.3807	−	44.3749i	0.677061	−	1.63457i
$738$		0			0
$739$	−16.1375	+	16.1375i	−0.593626	+	0.593626i	−0.938609	−	0.344983i	$-0.887885\pi$
$739$	−16.1375	+	16.1375i	−0.593626	+	0.593626i	0.344983	+	0.938609i	$0.387885\pi$
$740$		0			0
$741$	1.24015	+	0.513685i	0.0455579	+	0.0188707i
$742$		0			0
$743$	−34.6827	+	14.3660i	−1.27238	+	0.527039i	−0.913688	−	0.406416i	$-0.866778\pi$
$743$	−34.6827	+	14.3660i	−1.27238	+	0.527039i	−0.358696	+	0.933455i	$0.616778\pi$
$744$		0			0
$745$	6.42098	+	15.5016i	0.235247	+	0.567935i
$746$		0			0
$747$	−7.78269			−0.284754
$748$		0			0
$749$	41.8102			1.52771
$750$		0			0
$751$	−16.0162	−	38.6665i	−0.584439	−	1.41096i	−0.888752	−	0.458389i	$-0.848427\pi$
$751$	−16.0162	−	38.6665i	−0.584439	−	1.41096i	0.304313	−	0.952572i	$-0.401573\pi$
$752$		0			0
$753$	1.95741	−	0.810786i	0.0713320	−	0.0295467i
$754$		0			0
$755$	34.2066	+	14.1688i	1.24490	+	0.515656i
$756$		0			0
$757$	1.75575	−	1.75575i	0.0638138	−	0.0638138i	−0.674480	−	0.738293i	$-0.735632\pi$
$757$	1.75575	−	1.75575i	0.0638138	−	0.0638138i	0.738293	+	0.674480i	$0.235632\pi$
$758$		0			0
$759$	1.92456	−	4.64631i	0.0698572	−	0.168650i
$760$		0			0
$761$		−	18.0881i		−	0.655695i	−0.944731	−	0.327847i	$-0.893677\pi$
$761$		−	18.0881i		−	0.655695i	0.944731	−	0.327847i	$-0.106323\pi$
$762$		0			0
$763$	−5.76043	−	5.76043i	−0.208542	−	0.208542i
$764$		0			0
$765$	−0.119810	−	16.6305i	−0.00433174	−	0.601279i
$766$		0			0
$767$	4.86152	+	4.86152i	0.175539	+	0.175539i
$768$		0			0
$769$		−	22.2047i		−	0.800721i	−0.916358	−	0.400360i	$-0.868885\pi$
$769$		−	22.2047i		−	0.800721i	0.916358	−	0.400360i	$-0.131115\pi$
$770$		0			0
$771$	−4.61529	+	11.1423i	−0.166216	+	0.401280i
$772$		0			0
$773$	−13.6919	+	13.6919i	−0.492463	+	0.492463i	−0.909081	−	0.416619i	$-0.863215\pi$
$773$	−13.6919	+	13.6919i	−0.492463	+	0.492463i	0.416619	+	0.909081i	$0.363215\pi$
$774$		0			0
$775$	3.93428	+	1.62963i	0.141324	+	0.0585381i
$776$		0			0
$777$	−13.0789	+	5.41747i	−0.469204	+	0.194351i
$778$		0			0
$779$	−5.99449	−	14.4720i	−0.214775	−	0.518512i
$780$		0			0
$781$	74.4579			2.66431
$782$		0			0
$783$	−20.0774			−0.717509
$784$		0			0
$785$	−5.19998	−	12.5539i	−0.185595	−	0.448066i
$786$		0			0
$787$	−22.8930	+	9.48258i	−0.816047	+	0.338018i	−0.751364	−	0.659888i	$-0.770604\pi$
$787$	−22.8930	+	9.48258i	−0.816047	+	0.338018i	−0.0646829	+	0.997906i	$0.520604\pi$
$788$		0			0
$789$	33.0478	+	13.6889i	1.17653	+	0.487336i
$790$		0			0
$791$	50.7097	−	50.7097i	1.80303	−	1.80303i
$792$		0			0
$793$	0.781709	−	1.88721i	0.0277593	−	0.0670168i
$794$		0			0
$795$		−	19.4474i		−	0.689729i
$796$		0			0
$797$	−16.0835	−	16.0835i	−0.569707	−	0.569707i	0.362339	−	0.932046i	$-0.381978\pi$
$797$	−16.0835	−	16.0835i	−0.569707	−	0.569707i	−0.932046	+	0.362339i	$0.881978\pi$
$798$		0			0
$799$	−6.03104	−	14.2686i	−0.213363	−	0.504787i
$800$		0			0
$801$	−0.380978	−	0.380978i	−0.0134612	−	0.0134612i
$802$		0			0
$803$			10.8704i			0.383607i
$804$		0			0
$805$	−2.57555	+	6.21792i	−0.0907762	+	0.219153i
$806$		0			0
$807$	−19.5215	+	19.5215i	−0.687190	+	0.687190i
$808$		0			0
$809$	44.2248	+	18.3185i	1.55486	+	0.644044i	0.984187	−	0.177134i	$-0.0566825\pi$
$809$	44.2248	+	18.3185i	1.55486	+	0.644044i	0.570673	+	0.821178i	$0.306682\pi$
$810$		0			0
$811$	−39.7135	+	16.4499i	−1.39453	+	0.577632i	−0.948325	−	0.317299i	$-0.897224\pi$
$811$	−39.7135	+	16.4499i	−1.39453	+	0.577632i	−0.446203	+	0.894932i	$0.647224\pi$
$812$		0			0
$813$	−11.9720	−	28.9030i	−0.419877	−	1.01367i
$814$		0			0
$815$	−21.6917			−0.759827
$816$		0			0
$817$	18.4579			0.645761
$818$		0			0
$819$	−1.89125	−	4.56589i	−0.0660858	−	0.159545i
$820$		0			0
$821$	30.8199	−	12.7660i	1.07562	−	0.445537i	0.226650	−	0.973976i	$-0.427223\pi$
$821$	30.8199	−	12.7660i	1.07562	−	0.445537i	0.848971	+	0.528440i	$0.177223\pi$
$822$		0			0
$823$	−8.35785	−	3.46193i	−0.291336	−	0.120675i	0.232229	−	0.972661i	$-0.425398\pi$
$823$	−8.35785	−	3.46193i	−0.291336	−	0.120675i	−0.523565	+	0.851986i	$0.675398\pi$
$824$		0			0
$825$	2.18739	−	2.18739i	0.0761550	−	0.0761550i
$826$		0			0
$827$	5.60353	−	13.5281i	0.194854	−	0.470419i	−0.796010	−	0.605283i	$-0.793060\pi$
$827$	5.60353	−	13.5281i	0.194854	−	0.470419i	0.990864	+	0.134864i	$0.0430598\pi$
$828$		0			0
$829$		−	30.5539i		−	1.06118i	−0.847629	−	0.530590i	$-0.821971\pi$
$829$		−	30.5539i		−	1.06118i	0.847629	−	0.530590i	$-0.178029\pi$
$830$		0			0
$831$	18.5976	+	18.5976i	0.645144	+	0.645144i
$832$		0			0
$833$	19.2879	+	7.82698i	0.668285	+	0.271189i
$834$		0			0
$835$	−13.9069	−	13.9069i	−0.481268	−	0.481268i
$836$		0			0
$837$			44.7603i			1.54714i
$838$		0			0
$839$	−2.37805	+	5.74111i	−0.0820993	+	0.198205i	−0.959599	−	0.281373i	$-0.909210\pi$
$839$	−2.37805	+	5.74111i	−0.0820993	+	0.198205i	0.877499	+	0.479578i	$0.159210\pi$
$840$		0			0
$841$	−10.5153	+	10.5153i	−0.362597	+	0.362597i
$842$		0			0
$843$	−4.41040	−	1.82685i	−0.151902	−	0.0629199i
$844$		0			0
$845$	26.6998	−	11.0594i	0.918501	−	0.380455i
$846$		0			0
$847$	23.8038	+	57.4675i	0.817909	+	1.97461i
$848$		0			0
$849$	4.41597			0.151556
$850$		0			0
$851$	−2.97658			−0.102036
$852$		0			0
$853$	9.58980	+	23.1518i	0.328349	+	0.792704i	0.998715	+	0.0506737i	$0.0161368\pi$
$853$	9.58980	+	23.1518i	0.328349	+	0.792704i	−0.670367	+	0.742030i	$0.733863\pi$
$854$		0			0
$855$	−5.33432	+	2.20955i	−0.182430	+	0.0755650i
$856$		0			0
$857$	13.3430	+	5.52685i	0.455788	+	0.188794i	0.598752	−	0.800934i	$-0.295663\pi$
$857$	13.3430	+	5.52685i	0.455788	+	0.188794i	−0.142964	+	0.989728i	$0.545663\pi$
$858$		0			0
$859$	14.8437	−	14.8437i	0.506460	−	0.506460i	−0.406978	−	0.913438i	$-0.633417\pi$
$859$	14.8437	−	14.8437i	0.506460	−	0.506460i	0.913438	+	0.406978i	$0.133417\pi$
$860$		0			0
$861$	16.4543	−	39.7243i	0.560762	−	1.35380i
$862$		0			0
$863$			12.3137i			0.419162i	0.977791	+	0.209581i	$0.0672100\pi$
$863$			12.3137i			0.419162i	−0.977791	+	0.209581i	$0.932790\pi$
$864$		0			0
$865$	35.6045	+	35.6045i	1.21059	+	1.21059i
$866$		0			0
$867$	17.8828	+	7.10721i	0.607332	+	0.241373i
$868$		0			0
$869$	−35.4319	−	35.4319i	−1.20194	−	1.20194i
$870$		0			0
$871$			7.39905i			0.250707i
$872$		0			0
$873$	−8.25139	+	19.9206i	−0.279267	+	0.674211i
$874$		0			0
$875$	25.8749	−	25.8749i	0.874731	−	0.874731i
$876$		0			0
$877$	30.0462	+	12.4455i	1.01459	+	0.420256i	0.827126	−	0.562016i	$-0.189974\pi$
$877$	30.0462	+	12.4455i	1.01459	+	0.420256i	0.187461	+	0.982272i	$0.439974\pi$
$878$		0			0
$879$	−2.58941	+	1.07257i	−0.0873388	+	0.0361769i
$880$		0			0
$881$	−13.8980	−	33.5528i	−0.468237	−	1.13042i	−0.964932	−	0.262499i	$-0.915453\pi$
$881$	−13.8980	−	33.5528i	−0.468237	−	1.13042i	0.496696	−	0.867925i	$-0.334547\pi$
$882$		0			0
$883$	31.0615			1.04530			0.522652	−	0.852546i	$-0.324943\pi$
$883$	31.0615			1.04530			0.522652	+	0.852546i	$0.324943\pi$
$884$		0			0
$885$	22.0480			0.741135
$886$		0			0
$887$	−18.5915	−	44.8837i	−0.624240	−	1.50705i	−0.846680	−	0.532102i	$-0.821402\pi$
$887$	−18.5915	−	44.8837i	−0.624240	−	1.50705i	0.222440	−	0.974946i	$-0.428598\pi$
$888$		0			0
$889$	24.1922	−	10.0208i	0.811381	−	0.336085i
$890$		0			0
$891$	4.42302	+	1.83207i	0.148177	+	0.0613768i
$892$		0			0
$893$	−3.80283	+	3.80283i	−0.127257	+	0.127257i
$894$		0			0
$895$	6.05772	−	14.6246i	0.202487	−	0.488847i
$896$		0			0
$897$			0.774724i			0.0258673i
$898$		0			0
$899$	−22.2733	−	22.2733i	−0.742856	−	0.742856i
$900$		0			0
$901$	−27.9672	−	11.3490i	−0.931723	−	0.378092i
$902$		0			0
$903$	35.8258	+	35.8258i	1.19221	+	1.19221i
$904$		0			0
$905$		−	34.6574i		−	1.15205i
$906$		0			0
$907$	3.76687	−	9.09402i	0.125077	−	0.301962i	−0.848921	−	0.528520i	$-0.822747\pi$
$907$	3.76687	−	9.09402i	0.125077	−	0.301962i	0.973998	+	0.226558i	$0.0727472\pi$
$908$		0			0
$909$	−13.5494	+	13.5494i	−0.449404	+	0.449404i
$910$		0			0
$911$	−5.84015	−	2.41907i	−0.193493	−	0.0801473i	0.283833	−	0.958874i	$-0.408394\pi$
$911$	−5.84015	−	2.41907i	−0.193493	−	0.0801473i	−0.477326	+	0.878726i	$0.658394\pi$
$912$		0			0
$913$	−22.4986	+	9.31922i	−0.744595	+	0.308421i
$914$		0			0
$915$	−2.50684	−	6.05205i	−0.0828736	−	0.200074i
$916$		0			0
$917$	−14.6112			−0.482503
$918$		0			0
$919$	35.0444			1.15601			0.578004	−	0.816034i	$-0.303832\pi$
$919$	35.0444			1.15601			0.578004	+	0.816034i	$0.303832\pi$
$920$		0			0
$921$	9.61213	+	23.2057i	0.316730	+	0.764655i
$922$		0			0
$923$	−10.5969	+	4.38939i	−0.348802	+	0.144479i
$924$		0			0
$925$	−1.69154	−	0.700657i	−0.0556174	−	0.0230375i
$926$		0			0
$927$	5.08373	−	5.08373i	0.166972	−	0.166972i
$928$		0			0
$929$	2.54453	−	6.14303i	0.0834832	−	0.201546i	−0.876625	−	0.481173i	$-0.840211\pi$
$929$	2.54453	−	6.14303i	0.0834832	−	0.201546i	0.960109	+	0.279627i	$0.0902108\pi$
$930$		0			0
$931$		−	7.22657i		−	0.236841i
$932$		0			0
$933$	20.2488	+	20.2488i	0.662915	+	0.662915i
$934$		0			0
$935$	−20.2603	−	47.9330i	−0.662581	−	1.56758i
$936$		0			0
$937$	−34.8896	−	34.8896i	−1.13979	−	1.13979i	−0.988487	−	0.151306i	$-0.951652\pi$
$937$	−34.8896	−	34.8896i	−1.13979	−	1.13979i	−0.151306	−	0.988487i	$-0.548348\pi$
$938$		0			0
$939$			13.6545i			0.445597i
$940$		0			0
$941$	15.8417	−	38.2453i	0.516425	−	1.24676i	−0.423661	−	0.905821i	$-0.639255\pi$
$941$	15.8417	−	38.2453i	0.516425	−	1.24676i	0.940085	−	0.340939i	$-0.110745\pi$
$942$		0			0
$943$	6.39274	−	6.39274i	0.208176	−	0.208176i
$944$		0			0
$945$	−40.2009	−	16.6518i	−1.30774	−	0.541682i
$946$		0			0
$947$	16.1545	−	6.69143i	0.524952	−	0.217442i	−0.104438	−	0.994531i	$-0.533305\pi$
$947$	16.1545	−	6.69143i	0.524952	−	0.217442i	0.629391	+	0.777089i	$0.283305\pi$
$948$		0			0
$949$	−0.640824	−	1.54709i	−0.0208020	−	0.0502206i
$950$		0			0
$951$	3.10214			0.100594
$952$		0			0
$953$	−54.4709			−1.76449			−0.882243	−	0.470794i	$-0.843968\pi$
$953$	−54.4709			−1.76449			−0.882243	+	0.470794i	$0.843968\pi$
$954$		0			0
$955$	3.25359	+	7.85486i	0.105284	+	0.254177i
$956$		0			0
$957$	−21.1400	+	8.75647i	−0.683359	+	0.283057i
$958$		0			0
$959$	−21.1939	−	8.77879i	−0.684386	−	0.283482i
$960$		0			0
$961$	−27.7354	+	27.7354i	−0.894689	+	0.894689i
$962$		0			0
$963$	−7.92220	+	19.1259i	−0.255289	+	0.616323i
$964$		0			0
$965$			42.3147i			1.36216i
$966$		0			0
$967$	7.54887	+	7.54887i	0.242755	+	0.242755i	0.817989	−	0.575234i	$-0.195089\pi$
$967$	7.54887	+	7.54887i	0.242755	+	0.242755i	−0.575234	+	0.817989i	$0.695089\pi$
$968$		0			0
$969$	−0.0481285	−	6.68061i	−0.00154611	−	0.214612i
$970$		0			0
$971$	−42.9911	−	42.9911i	−1.37965	−	1.37965i	−0.845199	−	0.534452i	$-0.820518\pi$
$971$	−42.9911	−	42.9911i	−1.37965	−	1.37965i	−0.534452	−	0.845199i	$-0.679482\pi$
$972$		0			0
$973$			13.6578i			0.437849i
$974$		0			0
$975$	−0.182362	+	0.440261i	−0.00584026	+	0.0140996i
$976$		0			0
$977$	8.40142	−	8.40142i	0.268785	−	0.268785i	−0.559825	−	0.828611i	$-0.689132\pi$
$977$	8.40142	−	8.40142i	0.268785	−	0.268785i	0.828611	+	0.559825i	$0.189132\pi$
$978$		0			0
$979$	−1.55754	−	0.645156i	−0.0497793	−	0.0206193i
$980$		0			0
$981$	3.72657	−	1.54359i	0.118980	−	0.0492832i
$982$		0			0
$983$	−10.0746	−	24.3222i	−0.321329	−	0.775757i	−0.999177	−	0.0405551i	$-0.987087\pi$
$983$	−10.0746	−	24.3222i	−0.321329	−	0.775757i	0.677848	−	0.735202i	$-0.262913\pi$
$984$		0			0
$985$	−34.4873			−1.09886
$986$		0			0
$987$	−14.7621			−0.469884
$988$		0			0
$989$	4.07673	+	9.84210i	0.129633	+	0.312961i
$990$		0			0
$991$	37.9278	−	15.7102i	1.20482	−	0.499051i	0.312264	−	0.949995i	$-0.398913\pi$
$991$	37.9278	−	15.7102i	1.20482	−	0.499051i	0.892552	+	0.450944i	$0.148913\pi$
$992$		0			0
$993$	−18.9013	−	7.82917i	−0.599814	−	0.248451i
$994$		0			0
$995$	−33.8659	+	33.8659i	−1.07362	+	1.07362i
$996$		0			0
$997$	2.79830	−	6.75570i	0.0886231	−	0.213955i	−0.873354	−	0.487087i	$-0.838060\pi$
$997$	2.79830	−	6.75570i	0.0886231	−	0.213955i	0.961977	+	0.273132i	$0.0880595\pi$
$998$		0			0
$999$		−	19.2446i		−	0.608872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.bb.d.321.3	yes	16
4.3	odd	2	inner	544.2.bb.d.321.2	yes	16
17.5	odd	16		9248.2.a.bx.1.7		16
17.8	even	8	inner	544.2.bb.d.161.3	yes	16
17.12	odd	16		9248.2.a.bx.1.10		16
68.39	even	16		9248.2.a.bx.1.9		16
68.59	odd	8	inner	544.2.bb.d.161.2	✓	16
68.63	even	16		9248.2.a.bx.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.bb.d.161.2	✓	16	68.59	odd	8	inner
544.2.bb.d.161.3	yes	16	17.8	even	8	inner
544.2.bb.d.321.2	yes	16	4.3	odd	2	inner
544.2.bb.d.321.3	yes	16	1.1	even	1	trivial
9248.2.a.bx.1.7		16	17.5	odd	16
9248.2.a.bx.1.8		16	68.63	even	16
9248.2.a.bx.1.9		16	68.39	even	16
9248.2.a.bx.1.10		16	17.12	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.bb (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.433184 + 1.04580i) q^{3} +(2.16830 - 0.898138i) q^{5} +(-3.20687 - 1.32833i) q^{7} +(1.21528 - 1.21528i) q^{9} +(2.05797 - 4.96839i) q^{11} +0.828427i q^{13} +(1.87854 + 1.87854i) q^{15} +(3.79779 - 1.60525i) q^{17} +(-1.01217 - 1.01217i) q^{19} -3.92915i q^{21} +(0.316155 - 0.763265i) q^{23} +(0.359330 - 0.359330i) q^{25} +(4.93476 + 2.04405i) q^{27} +(-3.47274 + 1.43846i) q^{29} +(3.20687 + 7.74207i) q^{31} +6.08741 q^{33} -8.14648 q^{35} +(-1.37879 - 3.32869i) q^{37} +(-0.866367 + 0.358861i) q^{39} +(10.1101 + 4.18776i) q^{41} +(-9.11795 + 9.11795i) q^{43} +(1.54359 - 3.72657i) q^{45} -3.75708i q^{47} +(3.56982 + 3.56982i) q^{49} +(3.32390 + 3.27635i) q^{51} +(-5.17620 - 5.17620i) q^{53} -12.6213i q^{55} +(0.620073 - 1.49699i) q^{57} +(5.86838 - 5.86838i) q^{59} +(-2.27807 - 0.943606i) q^{61} +(-5.51152 + 2.28295i) q^{63} +(0.744042 + 1.79628i) q^{65} +8.93145 q^{67} +0.935174 q^{69} +(5.29847 + 12.7916i) q^{71} +(-1.86750 + 0.773543i) q^{73} +(0.531442 + 0.220130i) q^{75} +(-13.1993 + 13.1993i) q^{77} +(3.56573 - 8.60844i) q^{79} +0.890232i q^{81} +(-3.20203 - 3.20203i) q^{83} +(6.79300 - 6.89159i) q^{85} +(-3.00867 - 3.00867i) q^{87} -0.313491i q^{89} +(1.10042 - 2.65666i) q^{91} +(-6.70748 + 6.70748i) q^{93} +(-3.10377 - 1.28562i) q^{95} +(-11.5908 + 4.80106i) q^{97} +(-3.53695 - 8.53896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} - 8 q^{17} - 24 q^{25} + 8 q^{29} - 32 q^{33} + 56 q^{37} + 56 q^{41} + 72 q^{45} - 24 q^{49} - 56 q^{53} + 8 q^{57} - 24 q^{61} + 16 q^{65} + 64 q^{69} + 8 q^{73} - 88 q^{77} + 8 q^{85}+ \cdots - 16 q^{97}+O(q^{100}) \) 16 * q + 8 * q^5 - 8 * q^17 - 24 * q^25 + 8 * q^29 - 32 * q^33 + 56 * q^37 + 56 * q^41 + 72 * q^45 - 24 * q^49 - 56 * q^53 + 8 * q^57 - 24 * q^61 + 16 * q^65 + 64 * q^69 + 8 * q^73 - 88 * q^77 + 8 * q^85 + 24 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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