LMFDB - Embedded newform 1360.2.bn.a.1327.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1360,2,Mod(783,1360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1360, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1360.783"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bn (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1327.4
Character	$\chi$	$=$	1360.1327
Dual form			1360.2.bn.a.783.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.62263 - 1.62263i) q^{3} +(1.74625 + 1.39664i) q^{5} +(-1.20200 + 1.20200i) q^{7} +2.26589i q^{9} +2.64044i q^{11} +(3.80108 - 3.80108i) q^{13} +(-0.567299 - 5.09977i) q^{15} +(-0.707107 - 0.707107i) q^{17} -4.76917 q^{19} +3.90082 q^{21} +(0.848105 + 0.848105i) q^{23} +(1.09881 + 4.87777i) q^{25} +(-1.19119 + 1.19119i) q^{27} +4.15666i q^{29} +3.91291i q^{31} +(4.28448 - 4.28448i) q^{33} +(-3.77776 + 0.420240i) q^{35} +(4.47368 + 4.47368i) q^{37} -12.3355 q^{39} -6.25974 q^{41} +(7.59005 + 7.59005i) q^{43} +(-3.16463 + 3.95682i) q^{45} +(6.80420 - 6.80420i) q^{47} +4.11038i q^{49} +2.29475i q^{51} +(-6.24599 + 6.24599i) q^{53} +(-3.68774 + 4.61088i) q^{55} +(7.73862 + 7.73862i) q^{57} +2.42164 q^{59} -0.875552 q^{61} +(-2.72360 - 2.72360i) q^{63} +(11.9464 - 1.32892i) q^{65} +(6.37536 - 6.37536i) q^{67} -2.75233i q^{69} -3.01403i q^{71} +(-1.95554 + 1.95554i) q^{73} +(6.13188 - 9.69780i) q^{75} +(-3.17382 - 3.17382i) q^{77} +17.1634 q^{79} +10.6634 q^{81} +(12.7110 + 12.7110i) q^{83} +(-0.247216 - 2.22236i) q^{85} +(6.74475 - 6.74475i) q^{87} -10.0727i q^{89} +9.13781i q^{91} +(6.34923 - 6.34923i) q^{93} +(-8.32818 - 6.66080i) q^{95} +(2.55854 + 2.55854i) q^{97} -5.98295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{13} - 16 q^{21} - 24 q^{25} + 8 q^{33} - 16 q^{41} + 24 q^{45} - 16 q^{53} + 32 q^{57} + 16 q^{61} + 56 q^{65} - 8 q^{73} + 40 q^{77} + 32 q^{81} + 56 q^{93} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^13 - 16 * q^21 - 24 * q^25 + 8 * q^33 - 16 * q^41 + 24 * q^45 - 16 * q^53 + 32 * q^57 + 16 * q^61 + 56 * q^65 - 8 * q^73 + 40 * q^77 + 32 * q^81 + 56 * q^93 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.62263	−	1.62263i	−0.936829	−	0.936829i	0.0612912	−	0.998120i	$-0.480478\pi$
$3$	−1.62263	−	1.62263i	−0.936829	−	0.936829i	−0.998120	+	0.0612912i	$0.980478\pi$
$4$		0			0
$5$	1.74625	+	1.39664i	0.780949	+	0.624595i
$5$	1.74625	+	1.39664i	0.780949	+	0.624595i
$6$		0			0
$7$	−1.20200	+	1.20200i	−0.454314	+	0.454314i	−0.896784	−	0.442469i	$-0.854103\pi$
$7$	−1.20200	+	1.20200i	−0.454314	+	0.454314i	0.442469	+	0.896784i	$0.354103\pi$
$8$		0			0
$9$			2.26589i			0.755296i
$10$		0			0
$11$			2.64044i			0.796124i	0.917359	+	0.398062i	$0.130317\pi$
$11$			2.64044i			0.796124i	−0.917359	+	0.398062i	$0.869683\pi$
$12$		0			0
$13$	3.80108	−	3.80108i	1.05423	−	1.05423i	0.0557864	−	0.998443i	$-0.482233\pi$
$13$	3.80108	−	3.80108i	1.05423	−	1.05423i	0.998443	−	0.0557864i	$-0.0177666\pi$
$14$		0			0
$15$	−0.567299	−	5.09977i	−0.146476	−	1.31675i
$16$		0			0
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$17$	−0.707107	−	0.707107i	−0.171499	−	0.171499i
$18$		0			0
$19$	−4.76917			−1.09412			−0.547061	−	0.837092i	$-0.684254\pi$
$19$	−4.76917			−1.09412			−0.547061	+	0.837092i	$0.684254\pi$
$20$		0			0
$21$	3.90082			0.851230
$22$		0			0
$23$	0.848105	+	0.848105i	0.176842	+	0.176842i	0.789978	−	0.613136i	$-0.210092\pi$
$23$	0.848105	+	0.848105i	0.176842	+	0.176842i	−0.613136	+	0.789978i	$0.710092\pi$
$24$		0			0
$25$	1.09881	+	4.87777i	0.219761	+	0.975554i
$26$		0			0
$27$	−1.19119	+	1.19119i	−0.229246	+	0.229246i
$28$		0			0
$29$			4.15666i			0.771873i	0.922525	+	0.385936i	$0.126122\pi$
$29$			4.15666i			0.771873i	−0.922525	+	0.385936i	$0.873878\pi$
$30$		0			0
$31$			3.91291i			0.702779i	0.936229	+	0.351390i	$0.114291\pi$
$31$			3.91291i			0.702779i	−0.936229	+	0.351390i	$0.885709\pi$
$32$		0			0
$33$	4.28448	−	4.28448i	0.745832	−	0.745832i
$34$		0			0
$35$	−3.77776	+	0.420240i	−0.638559	+	0.0710335i
$36$		0			0
$37$	4.47368	+	4.47368i	0.735468	+	0.735468i	0.971697	−	0.236230i	$-0.0759117\pi$
$37$	4.47368	+	4.47368i	0.735468	+	0.735468i	−0.236230	+	0.971697i	$0.575912\pi$
$38$		0			0
$39$	−12.3355			−1.97526
$40$		0			0
$41$	−6.25974			−0.977608			−0.488804	−	0.872394i	$-0.662567\pi$
$41$	−6.25974			−0.977608			−0.488804	+	0.872394i	$0.662567\pi$
$42$		0			0
$43$	7.59005	+	7.59005i	1.15747	+	1.15747i	0.985018	+	0.172453i	$0.0551694\pi$
$43$	7.59005	+	7.59005i	1.15747	+	1.15747i	0.172453	+	0.985018i	$0.444831\pi$
$44$		0			0
$45$	−3.16463	+	3.95682i	−0.471755	+	0.589847i
$46$		0			0
$47$	6.80420	−	6.80420i	0.992494	−	0.992494i	−0.00747772	−	0.999972i	$-0.502380\pi$
$47$	6.80420	−	6.80420i	0.992494	−	0.992494i	0.999972	+	0.00747772i	$0.00238025\pi$
$48$		0			0
$49$			4.11038i			0.587197i
$50$		0			0
$51$			2.29475i			0.321330i
$52$		0			0
$53$	−6.24599	+	6.24599i	−0.857953	+	0.857953i	−0.991097	−	0.133144i	$-0.957493\pi$
$53$	−6.24599	+	6.24599i	−0.857953	+	0.857953i	0.133144	+	0.991097i	$0.457493\pi$
$54$		0			0
$55$	−3.68774	+	4.61088i	−0.497255	+	0.621732i
$56$		0			0
$57$	7.73862	+	7.73862i	1.02501	+	1.02501i
$58$		0			0
$59$	2.42164			0.315270			0.157635	−	0.987497i	$-0.449613\pi$
$59$	2.42164			0.315270			0.157635	+	0.987497i	$0.449613\pi$
$60$		0			0
$61$	−0.875552			−0.112103			−0.0560515	−	0.998428i	$-0.517851\pi$
$61$	−0.875552			−0.112103			−0.0560515	+	0.998428i	$0.517851\pi$
$62$		0			0
$63$	−2.72360	−	2.72360i	−0.343142	−	0.343142i
$64$		0			0
$65$	11.9464	−	1.32892i	1.48177	−	0.164832i
$66$		0			0
$67$	6.37536	−	6.37536i	0.778874	−	0.778874i	−0.200765	−	0.979639i	$-0.564343\pi$
$67$	6.37536	−	6.37536i	0.778874	−	0.778874i	0.979639	+	0.200765i	$0.0643428\pi$
$68$		0			0
$69$		−	2.75233i		−	0.331342i
$70$		0			0
$71$		−	3.01403i		−	0.357700i	−0.983876	−	0.178850i	$-0.942762\pi$
$71$		−	3.01403i		−	0.357700i	0.983876	−	0.178850i	$-0.0572377\pi$
$72$		0			0
$73$	−1.95554	+	1.95554i	−0.228879	+	0.228879i	−0.812224	−	0.583345i	$-0.801744\pi$
$73$	−1.95554	+	1.95554i	−0.228879	+	0.228879i	0.583345	+	0.812224i	$0.301744\pi$
$74$		0			0
$75$	6.13188	−	9.69780i	0.708048	−	1.11981i
$76$		0			0
$77$	−3.17382	−	3.17382i	−0.361690	−	0.361690i
$78$		0			0
$79$	17.1634			1.93103			0.965516	−	0.260345i	$-0.0838364\pi$
$79$	17.1634			1.93103			0.965516	+	0.260345i	$0.0838364\pi$
$80$		0			0
$81$	10.6634			1.18482
$82$		0			0
$83$	12.7110	+	12.7110i	1.39521	+	1.39521i	0.813134	+	0.582076i	$0.197760\pi$
$83$	12.7110	+	12.7110i	1.39521	+	1.39521i	0.582076	+	0.813134i	$0.302240\pi$
$84$		0			0
$85$	−0.247216	−	2.22236i	−0.0268143	−	0.241049i
$86$		0			0
$87$	6.74475	−	6.74475i	0.723113	−	0.723113i
$88$		0			0
$89$		−	10.0727i		−	1.06770i	−0.845579	−	0.533850i	$-0.820745\pi$
$89$		−	10.0727i		−	1.06770i	0.845579	−	0.533850i	$-0.179255\pi$
$90$		0			0
$91$			9.13781i			0.957903i
$92$		0			0
$93$	6.34923	−	6.34923i	0.658384	−	0.658384i
$94$		0			0
$95$	−8.32818	−	6.66080i	−0.854454	−	0.683384i
$96$		0			0
$97$	2.55854	+	2.55854i	0.259780	+	0.259780i	0.824965	−	0.565184i	$-0.191195\pi$
$97$	2.55854	+	2.55854i	0.259780	+	0.259780i	−0.565184	+	0.824965i	$0.691195\pi$
$98$		0			0
$99$	−5.98295			−0.601309
$100$		0			0
$101$	−10.8276			−1.07739			−0.538693	−	0.842502i	$-0.681082\pi$
$101$	−10.8276			−1.07739			−0.538693	+	0.842502i	$0.681082\pi$
$102$		0			0
$103$	−8.82240	−	8.82240i	−0.869297	−	0.869297i	0.123097	−	0.992395i	$-0.460717\pi$
$103$	−8.82240	−	8.82240i	−0.869297	−	0.869297i	−0.992395	+	0.123097i	$0.960717\pi$
$104$		0			0
$105$	6.81183	+	5.44804i	0.664766	+	0.531674i
$106$		0			0
$107$	1.55754	−	1.55754i	0.150573	−	0.150573i	−0.627801	−	0.778374i	$-0.716045\pi$
$107$	1.55754	−	1.55754i	0.150573	−	0.150573i	0.778374	+	0.627801i	$0.216045\pi$
$108$		0			0
$109$			14.4651i			1.38551i	0.721174	+	0.692754i	$0.243603\pi$
$109$			14.4651i			1.38551i	−0.721174	+	0.692754i	$0.756397\pi$
$110$		0			0
$111$		−	14.5183i		−	1.37801i
$112$		0			0
$113$	1.97253	−	1.97253i	0.185560	−	0.185560i	−0.608214	−	0.793773i	$-0.708114\pi$
$113$	1.97253	−	1.97253i	0.185560	−	0.185560i	0.793773	+	0.608214i	$0.208114\pi$
$114$		0			0
$115$	0.296511	+	2.66550i	0.0276498	+	0.248559i
$116$		0			0
$117$	8.61282	+	8.61282i	0.796255	+	0.796255i
$118$		0			0
$119$	1.69989			0.155829
$120$		0			0
$121$	4.02806			0.366187
$122$		0			0
$123$	10.1573	+	10.1573i	0.915851	+	0.915851i
$124$		0			0
$125$	−4.89368	+	10.0525i	−0.437704	+	0.899119i
$126$		0			0
$127$	1.19937	−	1.19937i	0.106427	−	0.106427i	−0.651888	−	0.758315i	$-0.726023\pi$
$127$	1.19937	−	1.19937i	0.106427	−	0.106427i	0.758315	+	0.651888i	$0.226023\pi$
$128$		0			0
$129$		−	24.6317i		−	2.16870i
$130$		0			0
$131$			14.3026i			1.24962i	0.780776	+	0.624812i	$0.214824\pi$
$131$			14.3026i			1.24962i	−0.780776	+	0.624812i	$0.785176\pi$
$132$		0			0
$133$	5.73256	−	5.73256i	0.497076	−	0.497076i
$134$		0			0
$135$	−3.74380	+	0.416461i	−0.322215	+	0.0358433i
$136$		0			0
$137$	10.1291	+	10.1291i	0.865387	+	0.865387i	0.991958	−	0.126570i	$-0.0403970\pi$
$137$	10.1291	+	10.1291i	0.865387	+	0.865387i	−0.126570	+	0.991958i	$0.540397\pi$
$138$		0			0
$139$	−16.0334			−1.35994			−0.679969	−	0.733241i	$-0.738007\pi$
$139$	−16.0334			−1.35994			−0.679969	+	0.733241i	$0.738007\pi$
$140$		0			0
$141$	−22.0815			−1.85959
$142$		0			0
$143$	10.0365	+	10.0365i	0.839297	+	0.839297i
$144$		0			0
$145$	−5.80535	+	7.25859i	−0.482108	+	0.602793i
$146$		0			0
$147$	6.66964	−	6.66964i	0.550103	−	0.550103i
$148$		0			0
$149$			3.60173i			0.295065i	0.989057	+	0.147533i	$0.0471332\pi$
$149$			3.60173i			0.295065i	−0.989057	+	0.147533i	$0.952867\pi$
$150$		0			0
$151$			8.44607i			0.687331i	0.939092	+	0.343666i	$0.111669\pi$
$151$			8.44607i			0.687331i	−0.939092	+	0.343666i	$0.888331\pi$
$152$		0			0
$153$	1.60223	−	1.60223i	0.129532	−	0.129532i
$154$		0			0
$155$	−5.46492	+	6.83294i	−0.438953	+	0.548835i
$156$		0			0
$157$	10.8937	+	10.8937i	0.869415	+	0.869415i	0.992408	−	0.122993i	$-0.0392491\pi$
$157$	10.8937	+	10.8937i	0.869415	+	0.869415i	−0.122993	+	0.992408i	$0.539249\pi$
$158$		0			0
$159$	20.2699			1.60751
$160$		0			0
$161$	−2.03885			−0.160684
$162$		0			0
$163$	−3.49398	−	3.49398i	−0.273670	−	0.273670i	0.556906	−	0.830576i	$-0.311988\pi$
$163$	−3.49398	−	3.49398i	−0.273670	−	0.273670i	−0.830576	+	0.556906i	$0.811988\pi$
$164$		0			0
$165$	13.4656	−	1.49792i	1.04830	−	0.116613i
$166$		0			0
$167$	0.829798	−	0.829798i	0.0642117	−	0.0642117i	−0.674272	−	0.738483i	$-0.735542\pi$
$167$	0.829798	−	0.829798i	0.0642117	−	0.0642117i	0.738483	+	0.674272i	$0.235542\pi$
$168$		0			0
$169$		−	15.8964i		−	1.22280i
$170$		0			0
$171$		−	10.8064i		−	0.826387i
$172$		0			0
$173$	−2.62725	+	2.62725i	−0.199746	+	0.199746i	−0.799891	−	0.600145i	$-0.795110\pi$
$173$	−2.62725	+	2.62725i	−0.199746	+	0.199746i	0.600145	+	0.799891i	$0.295110\pi$
$174$		0			0
$175$	−7.18386	−	4.54232i	−0.543049	−	0.343367i
$176$		0			0
$177$	−3.92943	−	3.92943i	−0.295354	−	0.295354i
$178$		0			0
$179$	−13.2509			−0.990417			−0.495209	−	0.868774i	$-0.664908\pi$
$179$	−13.2509			−0.990417			−0.495209	+	0.868774i	$0.664908\pi$
$180$		0			0
$181$	−6.88026			−0.511406			−0.255703	−	0.966755i	$-0.582307\pi$
$181$	−6.88026			−0.511406			−0.255703	+	0.966755i	$0.582307\pi$
$182$		0			0
$183$	1.42070	+	1.42070i	0.105021	+	0.105021i
$184$		0			0
$185$	1.56407	+	14.0603i	0.114993	+	1.03373i
$186$		0			0
$187$	1.86708	−	1.86708i	0.136534	−	0.136534i
$188$		0			0
$189$		−	2.86364i		−	0.208299i
$190$		0			0
$191$			5.90023i			0.426925i	0.976951	+	0.213463i	$0.0684742\pi$
$191$			5.90023i			0.426925i	−0.976951	+	0.213463i	$0.931526\pi$
$192$		0			0
$193$	10.5763	−	10.5763i	0.761298	−	0.761298i	−0.215259	−	0.976557i	$-0.569060\pi$
$193$	10.5763	−	10.5763i	0.761298	−	0.761298i	0.976557	+	0.215259i	$0.0690596\pi$
$194$		0			0
$195$	−21.5410	−	17.2283i	−1.54258	−	1.23374i
$196$		0			0
$197$	3.61519	+	3.61519i	0.257572	+	0.257572i	0.824066	−	0.566494i	$-0.191701\pi$
$197$	3.61519	+	3.61519i	0.257572	+	0.257572i	−0.566494	+	0.824066i	$0.691701\pi$
$198$		0			0
$199$	7.33590			0.520028			0.260014	−	0.965605i	$-0.416273\pi$
$199$	7.33590			0.520028			0.260014	+	0.965605i	$0.416273\pi$
$200$		0			0
$201$	−20.6898			−1.45934
$202$		0			0
$203$	−4.99632	−	4.99632i	−0.350673	−	0.350673i
$204$		0			0
$205$	−10.9311	−	8.74260i	−0.763461	−	0.610609i
$206$		0			0
$207$	−1.92171	+	1.92171i	−0.133568	+	0.133568i
$208$		0			0
$209$		−	12.5927i		−	0.871057i
$210$		0			0
$211$			6.52445i			0.449162i	0.974455	+	0.224581i	$0.0721013\pi$
$211$			6.52445i			0.449162i	−0.974455	+	0.224581i	$0.927899\pi$
$212$		0			0
$213$	−4.89068	+	4.89068i	−0.335104	+	0.335104i
$214$		0			0
$215$	2.65360	+	23.8547i	0.180974	+	1.62688i
$216$		0			0
$217$	−4.70333	−	4.70333i	−0.319283	−	0.319283i
$218$		0			0
$219$	6.34627			0.428841
$220$		0			0
$221$	−5.37553			−0.361598
$222$		0			0
$223$	−17.8237	−	17.8237i	−1.19356	−	1.19356i	−0.976060	−	0.217500i	$-0.930210\pi$
$223$	−17.8237	−	17.8237i	−1.19356	−	1.19356i	−0.217500	−	0.976060i	$-0.569790\pi$
$224$		0			0
$225$	−11.0525	+	2.48977i	−0.736832	+	0.165985i
$226$		0			0
$227$	−5.06497	+	5.06497i	−0.336174	+	0.336174i	−0.854925	−	0.518751i	$-0.826397\pi$
$227$	−5.06497	+	5.06497i	−0.336174	+	0.336174i	0.518751	+	0.854925i	$0.326397\pi$
$228$		0			0
$229$		−	3.52529i		−	0.232958i	−0.993193	−	0.116479i	$-0.962839\pi$
$229$		−	3.52529i		−	0.232958i	0.993193	−	0.116479i	$-0.0371607\pi$
$230$		0			0
$231$			10.2999i			0.677684i
$232$		0			0
$233$	12.7321	−	12.7321i	0.834110	−	0.834110i	−0.153966	−	0.988076i	$-0.549205\pi$
$233$	12.7321	−	12.7321i	0.834110	−	0.834110i	0.988076	+	0.153966i	$0.0492046\pi$
$234$		0			0
$235$	21.3849	−	2.37886i	1.39499	−	0.155180i
$236$		0			0
$237$	−27.8499	−	27.8499i	−1.80905	−	1.80905i
$238$		0			0
$239$	−3.68172			−0.238151			−0.119075	−	0.992885i	$-0.537993\pi$
$239$	−3.68172			−0.238151			−0.119075	+	0.992885i	$0.537993\pi$
$240$		0			0
$241$	−6.53949			−0.421246			−0.210623	−	0.977567i	$-0.567549\pi$
$241$	−6.53949			−0.421246			−0.210623	+	0.977567i	$0.567549\pi$
$242$		0			0
$243$	−13.7292	−	13.7292i	−0.880731	−	0.880731i
$244$		0			0
$245$	−5.74071	+	7.17776i	−0.366760	+	0.458571i
$246$		0			0
$247$	−18.1280	+	18.1280i	−1.15346	+	1.15346i
$248$		0			0
$249$		−	41.2505i		−	2.61415i
$250$		0			0
$251$		−	14.2752i		−	0.901044i	−0.892765	−	0.450522i	$-0.851238\pi$
$251$		−	14.2752i		−	0.901044i	0.892765	−	0.450522i	$-0.148762\pi$
$252$		0			0
$253$	−2.23937	+	2.23937i	−0.140788	+	0.140788i
$254$		0			0
$255$	−3.20494	+	4.00722i	−0.200701	+	0.250942i
$256$		0			0
$257$	−12.0214	−	12.0214i	−0.749873	−	0.749873i	0.224583	−	0.974455i	$-0.427898\pi$
$257$	−12.0214	−	12.0214i	−0.749873	−	0.749873i	−0.974455	+	0.224583i	$0.927898\pi$
$258$		0			0
$259$	−10.7547			−0.668267
$260$		0			0
$261$	−9.41853			−0.582993
$262$		0			0
$263$	−21.6788	−	21.6788i	−1.33677	−	1.33677i	−0.899167	−	0.437606i	$-0.855826\pi$
$263$	−21.6788	−	21.6788i	−1.33677	−	1.33677i	−0.437606	−	0.899167i	$-0.644174\pi$
$264$		0			0
$265$	−19.6305	+	2.18370i	−1.20589	+	0.134144i
$266$		0			0
$267$	−16.3443	+	16.3443i	−1.00025	+	1.00025i
$268$		0			0
$269$			14.0117i			0.854306i	0.904179	+	0.427153i	$0.140483\pi$
$269$			14.0117i			0.854306i	−0.904179	+	0.427153i	$0.859517\pi$
$270$		0			0
$271$			13.4228i			0.815378i	0.913121	+	0.407689i	$0.133665\pi$
$271$			13.4228i			0.815378i	−0.913121	+	0.407689i	$0.866335\pi$
$272$		0			0
$273$	14.8273	−	14.8273i	0.897391	−	0.897391i
$274$		0			0
$275$	−12.8795	+	2.90133i	−0.776661	+	0.174957i
$276$		0			0
$277$	5.09588	+	5.09588i	0.306181	+	0.306181i	0.843426	−	0.537245i	$-0.180535\pi$
$277$	5.09588	+	5.09588i	0.306181	+	0.306181i	−0.537245	+	0.843426i	$0.680535\pi$
$278$		0			0
$279$	−8.86622			−0.530807
$280$		0			0
$281$	−3.76441			−0.224566			−0.112283	−	0.993676i	$-0.535816\pi$
$281$	−3.76441			−0.224566			−0.112283	+	0.993676i	$0.535816\pi$
$282$		0			0
$283$	16.3366	+	16.3366i	0.971111	+	0.971111i	0.999594	−	0.0284835i	$-0.00906781\pi$
$283$	16.3366	+	16.3366i	0.971111	+	0.971111i	−0.0284835	+	0.999594i	$0.509068\pi$
$284$		0			0
$285$	2.70555	+	24.3217i	0.160263	+	1.44069i
$286$		0			0
$287$	7.52423	−	7.52423i	0.444141	−	0.444141i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$		0			0
$291$		−	8.30315i		−	0.486739i
$292$		0			0
$293$	−11.4684	+	11.4684i	−0.669990	+	0.669990i	−0.957714	−	0.287723i	$-0.907102\pi$
$293$	−11.4684	+	11.4684i	−0.669990	+	0.669990i	0.287723	+	0.957714i	$0.407102\pi$
$294$		0			0
$295$	4.22880	+	3.38215i	0.246210	+	0.196916i
$296$		0			0
$297$	−3.14528	−	3.14528i	−0.182508	−	0.182508i
$298$		0			0
$299$	6.44743			0.372864
$300$		0			0
$301$	−18.2465			−1.05171
$302$		0			0
$303$	17.5692	+	17.5692i	1.00933	+	1.00933i
$304$		0			0
$305$	−1.52894	−	1.22283i	−0.0875467	−	0.0700190i
$306$		0			0
$307$	0.180986	−	0.180986i	0.0103294	−	0.0103294i	−0.701923	−	0.712253i	$-0.747675\pi$
$307$	0.180986	−	0.180986i	0.0103294	−	0.0103294i	0.712253	+	0.701923i	$0.247675\pi$
$308$		0			0
$309$			28.6311i			1.62877i
$310$		0			0
$311$			11.8937i			0.674432i	0.941427	+	0.337216i	$0.109485\pi$
$311$			11.8937i			0.674432i	−0.941427	+	0.337216i	$0.890515\pi$
$312$		0			0
$313$	8.10613	−	8.10613i	0.458186	−	0.458186i	−0.439874	−	0.898060i	$-0.644977\pi$
$313$	8.10613	−	8.10613i	0.458186	−	0.458186i	0.898060	+	0.439874i	$0.144977\pi$
$314$		0			0
$315$	−0.952216	−	8.55999i	−0.0536513	−	0.482301i
$316$		0			0
$317$	−15.4386	−	15.4386i	−0.867120	−	0.867120i	0.125032	−	0.992153i	$-0.460097\pi$
$317$	−15.4386	−	15.4386i	−0.867120	−	0.867120i	−0.992153	+	0.125032i	$0.960097\pi$
$318$		0			0
$319$	−10.9754			−0.614506
$320$		0			0
$321$	−5.05465			−0.282123
$322$		0			0
$323$	3.37231	+	3.37231i	0.187641	+	0.187641i
$324$		0			0
$325$	22.7174	+	14.3641i	1.26014	+	0.796778i
$326$		0			0
$327$	23.4716	−	23.4716i	1.29798	−	1.29798i
$328$		0			0
$329$			16.3573i			0.901809i
$330$		0			0
$331$		−	21.3694i		−	1.17457i	−0.809380	−	0.587285i	$-0.800197\pi$
$331$		−	21.3694i		−	1.17457i	0.809380	−	0.587285i	$-0.199803\pi$
$332$		0			0
$333$	−10.1369	+	10.1369i	−0.555496	+	0.555496i
$334$		0			0
$335$	20.0371	−	2.22893i	1.09474	−	0.121779i
$336$		0			0
$337$	−16.9583	−	16.9583i	−0.923776	−	0.923776i	0.0735176	−	0.997294i	$-0.476577\pi$
$337$	−16.9583	−	16.9583i	−0.923776	−	0.923776i	−0.997294	+	0.0735176i	$0.976577\pi$
$338$		0			0
$339$	−6.40138			−0.347675
$340$		0			0
$341$	−10.3318			−0.559499
$342$		0			0
$343$	−13.3547	−	13.3547i	−0.721086	−	0.721086i
$344$		0			0
$345$	3.84401	−	4.80627i	0.206954	−	0.258761i
$346$		0			0
$347$	22.0044	−	22.0044i	1.18126	−	1.18126i	0.201841	−	0.979418i	$-0.435307\pi$
$347$	22.0044	−	22.0044i	1.18126	−	1.18126i	0.979418	−	0.201841i	$-0.0646925\pi$
$348$		0			0
$349$		−	34.1564i		−	1.82835i	−0.405321	−	0.914174i	$-0.632840\pi$
$349$		−	34.1564i		−	1.82835i	0.405321	−	0.914174i	$-0.367160\pi$
$350$		0			0
$351$			9.05565i			0.483355i
$352$		0			0
$353$	−10.8601	+	10.8601i	−0.578025	+	0.578025i	−0.934359	−	0.356333i	$-0.884027\pi$
$353$	−10.8601	+	10.8601i	−0.578025	+	0.578025i	0.356333	+	0.934359i	$0.384027\pi$
$354$		0			0
$355$	4.20951	−	5.26327i	0.223418	−	0.279345i
$356$		0			0
$357$	−2.75830	−	2.75830i	−0.145985	−	0.145985i
$358$		0			0
$359$	−3.66807			−0.193593			−0.0967966	−	0.995304i	$-0.530860\pi$
$359$	−3.66807			−0.193593			−0.0967966	+	0.995304i	$0.530860\pi$
$360$		0			0
$361$	3.74499			0.197105
$362$		0			0
$363$	−6.53607	−	6.53607i	−0.343055	−	0.343055i
$364$		0			0
$365$	−6.14607	+	0.683690i	−0.321700	+	0.0357860i
$366$		0			0
$367$	−7.05281	+	7.05281i	−0.368154	+	0.368154i	−0.866804	−	0.498650i	$-0.833829\pi$
$367$	−7.05281	+	7.05281i	−0.368154	+	0.368154i	0.498650	+	0.866804i	$0.333829\pi$
$368$		0			0
$369$		−	14.1839i		−	0.738383i
$370$		0			0
$371$		−	15.0154i		−	0.779560i
$372$		0			0
$373$	26.9600	−	26.9600i	1.39594	−	1.39594i	0.584649	−	0.811286i	$-0.301232\pi$
$373$	26.9600	−	26.9600i	1.39594	−	1.39594i	0.811286	−	0.584649i	$-0.198768\pi$
$374$		0			0
$375$	24.2521	−	8.37081i	1.25237	−	0.432267i
$376$		0			0
$377$	15.7998	+	15.7998i	0.813731	+	0.813731i
$378$		0			0
$379$	17.9215			0.920566			0.460283	−	0.887772i	$-0.347748\pi$
$379$	17.9215			0.920566			0.460283	+	0.887772i	$0.347748\pi$
$380$		0			0
$381$	−3.89229			−0.199408
$382$		0			0
$383$	−8.16744	−	8.16744i	−0.417337	−	0.417337i	0.466948	−	0.884285i	$-0.345354\pi$
$383$	−8.16744	−	8.16744i	−0.417337	−	0.417337i	−0.884285	+	0.466948i	$0.845354\pi$
$384$		0			0
$385$	−1.10962	−	9.97497i	−0.0565514	−	0.508372i
$386$		0			0
$387$	−17.1982	+	17.1982i	−0.874233	+	0.874233i
$388$		0			0
$389$			8.86301i			0.449372i	0.974431	+	0.224686i	$0.0721357\pi$
$389$			8.86301i			0.449372i	−0.974431	+	0.224686i	$0.927864\pi$
$390$		0			0
$391$		−	1.19940i		−	0.0606563i
$392$		0			0
$393$	23.2079	−	23.2079i	1.17068	−	1.17068i
$394$		0			0
$395$	29.9716	+	23.9710i	1.50804	+	1.20611i
$396$		0			0
$397$	0.768547	+	0.768547i	0.0385722	+	0.0385722i	0.726130	−	0.687558i	$-0.241317\pi$
$397$	0.768547	+	0.768547i	0.0385722	+	0.0385722i	−0.687558	+	0.726130i	$0.741317\pi$
$398$		0			0
$399$	−18.6037			−0.931350
$400$		0			0
$401$	−35.0311			−1.74937			−0.874686	−	0.484690i	$-0.838932\pi$
$401$	−35.0311			−1.74937			−0.874686	+	0.484690i	$0.838932\pi$
$402$		0			0
$403$	14.8733	+	14.8733i	0.740891	+	0.740891i
$404$		0			0
$405$	18.6210	+	14.8929i	0.925286	+	0.740036i
$406$		0			0
$407$	−11.8125	+	11.8125i	−0.585523	+	0.585523i
$408$		0			0
$409$		−	35.5481i		−	1.75774i	−0.477063	−	0.878869i	$-0.658299\pi$
$409$		−	35.5481i		−	1.75774i	0.477063	−	0.878869i	$-0.341701\pi$
$410$		0			0
$411$		−	32.8717i		−	1.62144i
$412$		0			0
$413$	−2.91082	+	2.91082i	−0.143232	+	0.143232i
$414$		0			0
$415$	4.44396	+	39.9492i	0.218146	+	1.96103i
$416$		0			0
$417$	26.0164	+	26.0164i	1.27403	+	1.27403i
$418$		0			0
$419$	26.9073			1.31451			0.657254	−	0.753669i	$-0.271718\pi$
$419$	26.9073			1.31451			0.657254	+	0.753669i	$0.271718\pi$
$420$		0			0
$421$	−25.3667			−1.23630			−0.618148	−	0.786061i	$-0.712117\pi$
$421$	−25.3667			−1.23630			−0.618148	+	0.786061i	$0.712117\pi$
$422$		0			0
$423$	15.4176	+	15.4176i	0.749627	+	0.749627i
$424$		0			0
$425$	2.67213	−	4.22608i	0.129617	−	0.204995i
$426$		0			0
$427$	1.05242	−	1.05242i	0.0509300	−	0.0509300i
$428$		0			0
$429$		−	32.5712i		−	1.57255i
$430$		0			0
$431$			11.7901i			0.567908i	0.958838	+	0.283954i	$0.0916462\pi$
$431$			11.7901i			0.567908i	−0.958838	+	0.283954i	$0.908354\pi$
$432$		0			0
$433$	9.11541	−	9.11541i	0.438059	−	0.438059i	−0.453300	−	0.891358i	$-0.649753\pi$
$433$	9.11541	−	9.11541i	0.438059	−	0.438059i	0.891358	+	0.453300i	$0.149753\pi$
$434$		0			0
$435$	21.1980	−	2.35807i	1.01637	−	0.113061i
$436$		0			0
$437$	−4.04476	−	4.04476i	−0.193487	−	0.193487i
$438$		0			0
$439$	33.3994			1.59407			0.797034	−	0.603934i	$-0.206401\pi$
$439$	33.3994			1.59407			0.797034	+	0.603934i	$0.206401\pi$
$440$		0			0
$441$	−9.31366			−0.443508
$442$		0			0
$443$	−4.28922	−	4.28922i	−0.203787	−	0.203787i	0.597833	−	0.801620i	$-0.296028\pi$
$443$	−4.28922	−	4.28922i	−0.203787	−	0.203787i	−0.801620	+	0.597833i	$0.796028\pi$
$444$		0			0
$445$	14.0679	−	17.5894i	0.666881	−	0.833819i
$446$		0			0
$447$	5.84430	−	5.84430i	0.276426	−	0.276426i
$448$		0			0
$449$			31.4310i			1.48332i	0.670777	+	0.741659i	$0.265961\pi$
$449$			31.4310i			1.48332i	−0.670777	+	0.741659i	$0.734039\pi$
$450$		0			0
$451$		−	16.5285i		−	0.778297i
$452$		0			0
$453$	13.7049	−	13.7049i	0.643912	−	0.643912i
$454$		0			0
$455$	−12.7622	+	15.9569i	−0.598302	+	0.748073i
$456$		0			0
$457$	25.5007	+	25.5007i	1.19287	+	1.19287i	0.976257	+	0.216614i	$0.0695014\pi$
$457$	25.5007	+	25.5007i	1.19287	+	1.19287i	0.216614	+	0.976257i	$0.430499\pi$
$458$		0			0
$459$	1.68460			0.0786306
$460$		0			0
$461$	−27.0350			−1.25915			−0.629573	−	0.776942i	$-0.716770\pi$
$461$	−27.0350			−1.25915			−0.629573	+	0.776942i	$0.716770\pi$
$462$		0			0
$463$	12.1613	+	12.1613i	0.565185	+	0.565185i	0.930776	−	0.365591i	$-0.119133\pi$
$463$	12.1613	+	12.1613i	0.565185	+	0.565185i	−0.365591	+	0.930776i	$0.619133\pi$
$464$		0			0
$465$	19.9549	−	2.21979i	0.925388	−	0.102940i
$466$		0			0
$467$	−28.9190	+	28.9190i	−1.33821	+	1.33821i	−0.440422	+	0.897791i	$0.645171\pi$
$467$	−28.9190	+	28.9190i	−1.33821	+	1.33821i	−0.897791	+	0.440422i	$0.854829\pi$
$468$		0			0
$469$			15.3264i			0.707707i
$470$		0			0
$471$		−	35.3531i		−	1.62899i
$472$		0			0
$473$	−20.0411	+	20.0411i	−0.921490	+	0.921490i
$474$		0			0
$475$	−5.24039	−	23.2629i	−0.240446	−	1.06738i
$476$		0			0
$477$	−14.1527	−	14.1527i	−0.648008	−	0.648008i
$478$		0			0
$479$	8.00770			0.365881			0.182941	−	0.983124i	$-0.441438\pi$
$479$	8.00770			0.365881			0.182941	+	0.983124i	$0.441438\pi$
$480$		0			0
$481$	34.0096			1.55070
$482$		0			0
$483$	3.30831	+	3.30831i	0.150533	+	0.150533i
$484$		0			0
$485$	0.894507	+	8.04121i	0.0406175	+	0.365133i
$486$		0			0
$487$	−18.6236	+	18.6236i	−0.843918	+	0.843918i	−0.989366	−	0.145448i	$-0.953538\pi$
$487$	−18.6236	+	18.6236i	−0.843918	+	0.843918i	0.145448	+	0.989366i	$0.453538\pi$
$488$		0			0
$489$			11.3389i			0.512764i
$490$		0			0
$491$			41.5559i			1.87539i	0.347456	+	0.937696i	$0.387046\pi$
$491$			41.5559i			1.87539i	−0.347456	+	0.937696i	$0.612954\pi$
$492$		0			0
$493$	2.93920	−	2.93920i	0.132375	−	0.132375i
$494$		0			0
$495$	−10.4478	−	8.35601i	−0.469591	−	0.375575i
$496$		0			0
$497$	3.62288	+	3.62288i	0.162508	+	0.162508i
$498$		0			0
$499$	32.0111			1.43301			0.716506	−	0.697581i	$-0.245740\pi$
$499$	32.0111			1.43301			0.716506	+	0.697581i	$0.245740\pi$
$500$		0			0
$501$	−2.69292			−0.120311
$502$		0			0
$503$	−26.7786	−	26.7786i	−1.19400	−	1.19400i	−0.975934	−	0.218067i	$-0.930025\pi$
$503$	−26.7786	−	26.7786i	−1.19400	−	1.19400i	−0.218067	−	0.975934i	$-0.569975\pi$
$504$		0			0
$505$	−18.9077	−	15.1222i	−0.841382	−	0.672930i
$506$		0			0
$507$	−25.7940	+	25.7940i	−1.14555	+	1.14555i
$508$		0			0
$509$		−	0.975619i		−	0.0432436i	−0.999766	−	0.0216218i	$-0.993117\pi$
$509$		−	0.975619i		−	0.0432436i	0.999766	−	0.0216218i	$-0.00688296\pi$
$510$		0			0
$511$		−	4.70114i		−	0.207966i
$512$		0			0
$513$	5.68101	−	5.68101i	0.250823	−	0.250823i
$514$		0			0
$515$	−3.08445	−	27.7279i	−0.135917	−	1.22184i
$516$		0			0
$517$	17.9661	+	17.9661i	0.790148	+	0.790148i
$518$		0			0
$519$	8.52614			0.374256
$520$		0			0
$521$	31.9559			1.40001			0.700006	−	0.714136i	$-0.253180\pi$
$521$	31.9559			1.40001			0.700006	+	0.714136i	$0.253180\pi$
$522$		0			0
$523$	−20.8299	−	20.8299i	−0.910829	−	0.910829i	0.0855081	−	0.996337i	$-0.472749\pi$
$523$	−20.8299	−	20.8299i	−0.910829	−	0.910829i	−0.996337	+	0.0855081i	$0.972749\pi$
$524$		0			0
$525$	4.28625	+	19.0273i	0.187067	+	0.830420i
$526$		0			0
$527$	2.76685	−	2.76685i	0.120526	−	0.120526i
$528$		0			0
$529$		−	21.5614i		−	0.937454i
$530$		0			0
$531$			5.48716i			0.238123i
$532$		0			0
$533$	−23.7938	+	23.7938i	−1.03062	+	1.03062i
$534$		0			0
$535$	4.89519	−	0.544543i	0.211638	−	0.0235426i
$536$		0			0
$537$	21.5013	+	21.5013i	0.927851	+	0.927851i
$538$		0			0
$539$	−10.8532			−0.467481
$540$		0			0
$541$	1.41989			0.0610460			0.0305230	−	0.999534i	$-0.490283\pi$
$541$	1.41989			0.0610460			0.0305230	+	0.999534i	$0.490283\pi$
$542$		0			0
$543$	11.1642	+	11.1642i	0.479100	+	0.479100i
$544$		0			0
$545$	−20.2025	+	25.2598i	−0.865382	+	1.08201i
$546$		0			0
$547$	3.72598	−	3.72598i	0.159311	−	0.159311i	−0.622950	−	0.782262i	$-0.714066\pi$
$547$	3.72598	−	3.72598i	0.159311	−	0.159311i	0.782262	+	0.622950i	$0.214066\pi$
$548$		0			0
$549$		−	1.98390i		−	0.0846710i
$550$		0			0
$551$		−	19.8238i		−	0.844524i
$552$		0			0
$553$	−20.6304	+	20.6304i	−0.877295	+	0.877295i
$554$		0			0
$555$	20.2768	−	25.3526i	0.860702	−	1.07616i
$556$		0			0
$557$	8.92785	+	8.92785i	0.378285	+	0.378285i	0.870483	−	0.492198i	$-0.163806\pi$
$557$	8.92785	+	8.92785i	0.378285	+	0.378285i	−0.492198	+	0.870483i	$0.663806\pi$
$558$		0			0
$559$	57.7007			2.44048
$560$		0			0
$561$	−6.05916			−0.255818
$562$		0			0
$563$	4.73075	+	4.73075i	0.199377	+	0.199377i	0.799733	−	0.600356i	$-0.204974\pi$
$563$	4.73075	+	4.73075i	0.199377	+	0.199377i	−0.600356	+	0.799733i	$0.704974\pi$
$564$		0			0
$565$	6.19944	−	0.689627i	0.260812	−	0.0290128i
$566$		0			0
$567$	−12.8175	+	12.8175i	−0.538283	+	0.538283i
$568$		0			0
$569$		−	10.3040i		−	0.431965i	−0.976397	−	0.215982i	$-0.930705\pi$
$569$		−	10.3040i		−	0.431965i	0.976397	−	0.215982i	$-0.0692954\pi$
$570$		0			0
$571$		−	15.0575i		−	0.630138i	−0.949069	−	0.315069i	$-0.897972\pi$
$571$		−	15.0575i		−	0.630138i	0.949069	−	0.315069i	$-0.102028\pi$
$572$		0			0
$573$	9.57391	−	9.57391i	0.399956	−	0.399956i
$574$		0			0
$575$	−3.20496	+	5.06876i	−0.133656	+	0.211382i
$576$		0			0
$577$	−15.5222	−	15.5222i	−0.646199	−	0.646199i	0.305874	−	0.952072i	$-0.401052\pi$
$577$	−15.5222	−	15.5222i	−0.646199	−	0.646199i	−0.952072	+	0.305874i	$0.901052\pi$
$578$		0			0
$579$	−34.3229			−1.42641
$580$		0			0
$581$	−30.5572			−1.26773
$582$		0			0
$583$	−16.4922	−	16.4922i	−0.683036	−	0.683036i
$584$		0			0
$585$	3.01118	+	27.0692i	0.124497	+	1.11917i
$586$		0			0
$587$	12.8730	−	12.8730i	0.531327	−	0.531327i	−0.389640	−	0.920967i	$-0.627401\pi$
$587$	12.8730	−	12.8730i	0.531327	−	0.531327i	0.920967	+	0.389640i	$0.127401\pi$
$588$		0			0
$589$		−	18.6613i		−	0.768927i
$590$		0			0
$591$		−	11.7323i		−	0.482601i
$592$		0			0
$593$	−20.4257	+	20.4257i	−0.838785	+	0.838785i	−0.988699	−	0.149914i	$-0.952100\pi$
$593$	−20.4257	+	20.4257i	−0.838785	+	0.838785i	0.149914	+	0.988699i	$0.452100\pi$
$594$		0			0
$595$	2.96844	+	2.37413i	0.121694	+	0.0973298i
$596$		0			0
$597$	−11.9035	−	11.9035i	−0.487177	−	0.487177i
$598$		0			0
$599$	−36.0087			−1.47128			−0.735639	−	0.677374i	$-0.763118\pi$
$599$	−36.0087			−1.47128			−0.735639	+	0.677374i	$0.763118\pi$
$600$		0			0
$601$	−1.99521			−0.0813865			−0.0406932	−	0.999172i	$-0.512957\pi$
$601$	−1.99521			−0.0813865			−0.0406932	+	0.999172i	$0.512957\pi$
$602$		0			0
$603$	14.4459	+	14.4459i	0.588281	+	0.588281i
$604$		0			0
$605$	7.03401	+	5.62574i	0.285973	+	0.228719i
$606$		0			0
$607$	7.52888	−	7.52888i	0.305588	−	0.305588i	−0.537607	−	0.843195i	$-0.680672\pi$
$607$	7.52888	−	7.52888i	0.305588	−	0.305588i	0.843195	+	0.537607i	$0.180672\pi$
$608$		0			0
$609$			16.2144i			0.657041i
$610$		0			0
$611$		−	51.7266i		−	2.09263i
$612$		0			0
$613$	8.03392	−	8.03392i	0.324487	−	0.324487i	−0.525999	−	0.850485i	$-0.676308\pi$
$613$	8.03392	−	8.03392i	0.324487	−	0.324487i	0.850485	+	0.525999i	$0.176308\pi$
$614$		0			0
$615$	3.55115	+	31.9232i	0.143196	+	1.28727i
$616$		0			0
$617$	7.60146	+	7.60146i	0.306023	+	0.306023i	0.843365	−	0.537342i	$-0.180571\pi$
$617$	7.60146	+	7.60146i	0.306023	+	0.306023i	−0.537342	+	0.843365i	$0.680571\pi$
$618$		0			0
$619$	−37.9897			−1.52694			−0.763468	−	0.645846i	$-0.776505\pi$
$619$	−37.9897			−1.52694			−0.763468	+	0.645846i	$0.776505\pi$
$620$		0			0
$621$	−2.02052			−0.0810806
$622$		0			0
$623$	12.1074	+	12.1074i	0.485072	+	0.485072i
$624$		0			0
$625$	−22.5853	+	10.7194i	−0.903410	+	0.428778i
$626$		0			0
$627$	−20.4334	+	20.4334i	−0.816031	+	0.816031i
$628$		0			0
$629$		−	6.32673i		−	0.252263i
$630$		0			0
$631$			12.7035i			0.505718i	0.967503	+	0.252859i	$0.0813708\pi$
$631$			12.7035i			0.505718i	−0.967503	+	0.252859i	$0.918629\pi$
$632$		0			0
$633$	10.5868	−	10.5868i	0.420788	−	0.420788i
$634$		0			0
$635$	3.76950	−	0.419320i	0.149588	−	0.0166402i
$636$		0			0
$637$	15.6239	+	15.6239i	0.619040	+	0.619040i
$638$		0			0
$639$	6.82947			0.270169
$640$		0			0
$641$	−16.0173			−0.632643			−0.316322	−	0.948652i	$-0.602448\pi$
$641$	−16.0173			−0.632643			−0.316322	+	0.948652i	$0.602448\pi$
$642$		0			0
$643$	−26.9924	−	26.9924i	−1.06448	−	1.06448i	−0.997773	−	0.0667042i	$-0.978752\pi$
$643$	−26.9924	−	26.9924i	−1.06448	−	1.06448i	−0.0667042	−	0.997773i	$-0.521248\pi$
$644$		0			0
$645$	34.4016	−	43.0133i	1.35456	−	1.69365i
$646$		0			0
$647$	−12.3728	+	12.3728i	−0.486424	+	0.486424i	−0.907176	−	0.420752i	$-0.861766\pi$
$647$	−12.3728	+	12.3728i	−0.486424	+	0.486424i	0.420752	+	0.907176i	$0.361766\pi$
$648$		0			0
$649$			6.39420i			0.250994i
$650$		0			0
$651$			15.2636i			0.598227i
$652$		0			0
$653$	19.4689	−	19.4689i	0.761879	−	0.761879i	−0.214783	−	0.976662i	$-0.568904\pi$
$653$	19.4689	−	19.4689i	0.761879	−	0.761879i	0.976662	+	0.214783i	$0.0689044\pi$
$654$		0			0
$655$	−19.9755	+	24.9760i	−0.780509	+	0.975891i
$656$		0			0
$657$	−4.43105	−	4.43105i	−0.172872	−	0.172872i
$658$		0			0
$659$	8.17037			0.318273			0.159136	−	0.987257i	$-0.449129\pi$
$659$	8.17037			0.318273			0.159136	+	0.987257i	$0.449129\pi$
$660$		0			0
$661$	47.9393			1.86462			0.932312	−	0.361655i	$-0.117788\pi$
$661$	47.9393			1.86462			0.932312	+	0.361655i	$0.117788\pi$
$662$		0			0
$663$	8.72253	+	8.72253i	0.338755	+	0.338755i
$664$		0			0
$665$	18.0168	−	2.00419i	0.698662	−	0.0777193i
$666$		0			0
$667$	−3.52529	+	3.52529i	−0.136500	+	0.136500i
$668$		0			0
$669$			57.8426i			2.23632i
$670$		0			0
$671$		−	2.31185i		−	0.0892479i
$672$		0			0
$673$	16.0689	−	16.0689i	0.619410	−	0.619410i	−0.325970	−	0.945380i	$-0.605691\pi$
$673$	16.0689	−	16.0689i	0.619410	−	0.619410i	0.945380	+	0.325970i	$0.105691\pi$
$674$		0			0
$675$	−7.11927	−	4.50148i	−0.274021	−	0.173262i
$676$		0			0
$677$	−0.872671	−	0.872671i	−0.0335395	−	0.0335395i	0.690138	−	0.723678i	$-0.257550\pi$
$677$	−0.872671	−	0.872671i	−0.0335395	−	0.0335395i	−0.723678	+	0.690138i	$0.757550\pi$
$678$		0			0
$679$	−6.15074			−0.236044
$680$		0			0
$681$	16.4372			0.629875
$682$		0			0
$683$	14.5816	+	14.5816i	0.557948	+	0.557948i	0.928723	−	0.370775i	$-0.120908\pi$
$683$	14.5816	+	14.5816i	0.557948	+	0.557948i	−0.370775	+	0.928723i	$0.620908\pi$
$684$		0			0
$685$	3.54130	+	31.8347i	0.135306	+	1.21634i
$686$		0			0
$687$	−5.72026	+	5.72026i	−0.218242	+	0.218242i
$688$		0			0
$689$			47.4830i			1.80896i
$690$		0			0
$691$			21.9981i			0.836847i	0.908252	+	0.418423i	$0.137417\pi$
$691$			21.9981i			0.836847i	−0.908252	+	0.418423i	$0.862583\pi$
$692$		0			0
$693$	7.19152	−	7.19152i	0.273183	−	0.273183i
$694$		0			0
$695$	−27.9985	−	22.3929i	−1.06204	−	0.849411i
$696$		0			0
$697$	4.42631	+	4.42631i	0.167658	+	0.167658i
$698$		0			0
$699$	−41.3192			−1.56284
$700$		0			0
$701$	−4.15440			−0.156909			−0.0784547	−	0.996918i	$-0.524999\pi$
$701$	−4.15440			−0.156909			−0.0784547	+	0.996918i	$0.524999\pi$
$702$		0			0
$703$	−21.3357	−	21.3357i	−0.804692	−	0.804692i
$704$		0			0
$705$	−38.5598	−	30.8398i	−1.45225	−	1.16149i
$706$		0			0
$707$	13.0148	−	13.0148i	0.489472	−	0.489472i
$708$		0			0
$709$		−	42.6097i		−	1.60024i	−0.599839	−	0.800121i	$-0.704769\pi$
$709$		−	42.6097i		−	1.60024i	0.599839	−	0.800121i	$-0.295231\pi$
$710$		0			0
$711$			38.8903i			1.45850i
$712$		0			0
$713$	−3.31856	+	3.31856i	−0.124281	+	0.124281i
$714$		0			0
$715$	3.50893	+	31.5437i	0.131227	+	1.17967i
$716$		0			0
$717$	5.97409	+	5.97409i	0.223107	+	0.223107i
$718$		0			0
$719$	−30.9444			−1.15403			−0.577015	−	0.816734i	$-0.695783\pi$
$719$	−30.9444			−1.15403			−0.577015	+	0.816734i	$0.695783\pi$
$720$		0			0
$721$	21.2091			0.789868
$722$		0			0
$723$	10.6112	+	10.6112i	0.394635	+	0.394635i
$724$		0			0
$725$	−20.2752	+	4.56737i	−0.753003	+	0.169628i
$726$		0			0
$727$	13.8348	−	13.8348i	0.513105	−	0.513105i	−0.402371	−	0.915477i	$-0.631814\pi$
$727$	13.8348	−	13.8348i	0.513105	−	0.513105i	0.915477	+	0.402371i	$0.131814\pi$
$728$		0			0
$729$			12.5649i			0.465365i
$730$		0			0
$731$		−	10.7339i		−	0.397009i
$732$		0			0
$733$	−6.75386	+	6.75386i	−0.249459	+	0.249459i	−0.820749	−	0.571289i	$-0.806443\pi$
$733$	−6.75386	+	6.75386i	−0.249459	+	0.249459i	0.571289	+	0.820749i	$0.306443\pi$
$734$		0			0
$735$	20.9620	−	2.33182i	0.773194	−	0.0860103i
$736$		0			0
$737$	16.8338	+	16.8338i	0.620080	+	0.620080i
$738$		0			0
$739$	−2.36223			−0.0868962			−0.0434481	−	0.999056i	$-0.513834\pi$
$739$	−2.36223			−0.0868962			−0.0434481	+	0.999056i	$0.513834\pi$
$740$		0			0
$741$	58.8302			2.16118
$742$		0			0
$743$	−16.1834	−	16.1834i	−0.593710	−	0.593710i	0.344921	−	0.938632i	$-0.387906\pi$
$743$	−16.1834	−	16.1834i	−0.593710	−	0.593710i	−0.938632	+	0.344921i	$0.887906\pi$
$744$		0			0
$745$	−5.03032	+	6.28954i	−0.184297	+	0.230431i
$746$		0			0
$747$	−28.8016	+	28.8016i	−1.05380	+	1.05380i
$748$		0			0
$749$			3.74434i			0.136815i
$750$		0			0
$751$		−	48.2104i		−	1.75922i	−0.475692	−	0.879612i	$-0.657802\pi$
$751$		−	48.2104i		−	1.75922i	0.475692	−	0.879612i	$-0.342198\pi$
$752$		0			0
$753$	−23.1635	+	23.1635i	−0.844124	+	0.844124i
$754$		0			0
$755$	−11.7961	+	14.7490i	−0.429304	+	0.536770i
$756$		0			0
$757$	27.8759	+	27.8759i	1.01317	+	1.01317i	0.999912	+	0.0132549i	$0.00421930\pi$
$757$	27.8759	+	27.8759i	1.01317	+	1.01317i	0.0132549	+	0.999912i	$0.495781\pi$
$758$		0			0
$759$	7.26737			0.263789
$760$		0			0
$761$	44.9607			1.62982			0.814912	−	0.579584i	$-0.196785\pi$
$761$	44.9607			1.62982			0.814912	+	0.579584i	$0.196785\pi$
$762$		0			0
$763$	−17.3871	−	17.3871i	−0.629456	−	0.629456i
$764$		0			0
$765$	5.03562	−	0.560164i	0.182063	−	0.0202528i
$766$		0			0
$767$	9.20483	−	9.20483i	0.332367	−	0.332367i
$768$		0			0
$769$		−	37.8420i		−	1.36462i	−0.731064	−	0.682308i	$-0.760976\pi$
$769$		−	37.8420i		−	1.36462i	0.731064	−	0.682308i	$-0.239024\pi$
$770$		0			0
$771$			39.0126i			1.40500i
$772$		0			0
$773$	30.4766	−	30.4766i	1.09617	−	1.09617i	0.101311	−	0.994855i	$-0.467696\pi$
$773$	30.4766	−	30.4766i	1.09617	−	1.09617i	0.994855	−	0.101311i	$-0.0323036\pi$
$774$		0			0
$775$	−19.0863	+	4.29953i	−0.685599	+	0.154444i
$776$		0			0
$777$	17.4510	+	17.4510i	0.626052	+	0.626052i
$778$		0			0
$779$	29.8538			1.06962
$780$		0			0
$781$	7.95839			0.284773
$782$		0			0
$783$	−4.95140	−	4.95140i	−0.176948	−	0.176948i
$784$		0			0
$785$	3.80863	+	34.2378i	0.135936	+	1.22200i
$786$		0			0
$787$	−7.38453	+	7.38453i	−0.263230	+	0.263230i	−0.826365	−	0.563135i	$-0.809595\pi$
$787$	−7.38453	+	7.38453i	−0.263230	+	0.263230i	0.563135	+	0.826365i	$0.309595\pi$
$788$		0			0
$789$			70.3536i			2.50465i
$790$		0			0
$791$			4.74197i			0.168605i
$792$		0			0
$793$	−3.32804	+	3.32804i	−0.118182	+	0.118182i
$794$		0			0
$795$	35.3964	+	28.3097i	1.25538	+	1.00404i
$796$		0			0
$797$	−29.6225	−	29.6225i	−1.04928	−	1.04928i	−0.998721	−	0.0505617i	$-0.983899\pi$
$797$	−29.6225	−	29.6225i	−1.04928	−	1.04928i	−0.0505617	−	0.998721i	$-0.516101\pi$
$798$		0			0
$799$	−9.62259			−0.340423
$800$		0			0
$801$	22.8235			0.806430
$802$		0			0
$803$	−5.16351	−	5.16351i	−0.182216	−	0.182216i
$804$		0			0
$805$	−3.56035	−	2.84753i	−0.125486	−	0.100362i
$806$		0			0
$807$	22.7358	−	22.7358i	0.800338	−	0.800338i
$808$		0			0
$809$			38.4538i			1.35196i	0.736918	+	0.675982i	$0.236280\pi$
$809$			38.4538i			1.35196i	−0.736918	+	0.675982i	$0.763720\pi$
$810$		0			0
$811$			10.1069i			0.354902i	0.984130	+	0.177451i	$0.0567851\pi$
$811$			10.1069i			0.354902i	−0.984130	+	0.177451i	$0.943215\pi$
$812$		0			0
$813$	21.7803	−	21.7803i	0.763869	−	0.763869i
$814$		0			0
$815$	−1.22155	−	10.9812i	−0.0427891	−	0.384655i
$816$		0			0
$817$	−36.1982	−	36.1982i	−1.26642	−	1.26642i
$818$		0			0
$819$	−20.7053			−0.723500
$820$		0			0
$821$	18.7015			0.652685			0.326343	−	0.945252i	$-0.394184\pi$
$821$	18.7015			0.652685			0.326343	+	0.945252i	$0.394184\pi$
$822$		0			0
$823$	2.39249	+	2.39249i	0.0833970	+	0.0833970i	0.747575	−	0.664178i	$-0.231218\pi$
$823$	2.39249	+	2.39249i	0.0833970	+	0.0833970i	−0.664178	+	0.747575i	$0.731218\pi$
$824$		0			0
$825$	25.6065	+	16.1909i	0.891504	+	0.563694i
$826$		0			0
$827$	−9.10551	+	9.10551i	−0.316630	+	0.316630i	−0.847471	−	0.530842i	$-0.821876\pi$
$827$	−9.10551	+	9.10551i	−0.316630	+	0.316630i	0.530842	+	0.847471i	$0.321876\pi$
$828$		0			0
$829$		−	33.5611i		−	1.16563i	−0.812606	−	0.582813i	$-0.801952\pi$
$829$		−	33.5611i		−	1.16563i	0.812606	−	0.582813i	$-0.198048\pi$
$830$		0			0
$831$		−	16.5375i		−	0.573679i
$832$		0			0
$833$	2.90648	−	2.90648i	0.100703	−	0.100703i
$834$		0			0
$835$	2.60797	−	0.290111i	0.0902524	−	0.0100397i
$836$		0			0
$837$	−4.66104	−	4.66104i	−0.161109	−	0.161109i
$838$		0			0
$839$	46.0966			1.59143			0.795716	−	0.605670i	$-0.207095\pi$
$839$	46.0966			1.59143			0.795716	+	0.605670i	$0.207095\pi$
$840$		0			0
$841$	11.7222			0.404212
$842$		0			0
$843$	6.10826	+	6.10826i	0.210380	+	0.210380i
$844$		0			0
$845$	22.2015	−	27.7591i	0.763754	−	0.954942i
$846$		0			0
$847$	−4.84174	+	4.84174i	−0.166364	+	0.166364i
$848$		0			0
$849$		−	53.0167i		−	1.81953i
$850$		0			0
$851$			7.58829i			0.260123i
$852$		0			0
$853$	−26.5299	+	26.5299i	−0.908367	+	0.908367i	−0.996141	−	0.0877730i	$-0.972025\pi$
$853$	−26.5299	+	26.5299i	−0.908367	+	0.908367i	0.0877730	+	0.996141i	$0.472025\pi$
$854$		0			0
$855$	15.0926	−	18.8707i	0.516157	−	0.645366i
$856$		0			0
$857$	38.0282	+	38.0282i	1.29902	+	1.29902i	0.929041	+	0.369977i	$0.120634\pi$
$857$	38.0282	+	38.0282i	1.29902	+	1.29902i	0.369977	+	0.929041i	$0.379366\pi$
$858$		0			0
$859$	46.5438			1.58805			0.794027	−	0.607882i	$-0.207981\pi$
$859$	46.5438			1.58805			0.794027	+	0.607882i	$0.207981\pi$
$860$		0			0
$861$	−24.4182			−0.832169
$862$		0			0
$863$	11.5399	+	11.5399i	0.392822	+	0.392822i	0.875692	−	0.482870i	$-0.160406\pi$
$863$	11.5399	+	11.5399i	0.392822	+	0.392822i	−0.482870	+	0.875692i	$0.660406\pi$
$864$		0			0
$865$	−8.25717	+	0.918530i	−0.280752	+	0.0312309i
$866$		0			0
$867$	1.62263	−	1.62263i	0.0551076	−	0.0551076i
$868$		0			0
$869$			45.3189i			1.53734i
$870$		0			0
$871$		−	48.4665i		−	1.64222i
$872$		0			0
$873$	−5.79736	+	5.79736i	−0.196211	+	0.196211i
$874$		0			0
$875$	−6.20086	−	17.9653i	−0.209627	−	0.607338i
$876$		0			0
$877$	10.9661	+	10.9661i	0.370300	+	0.370300i	0.867586	−	0.497286i	$-0.165670\pi$
$877$	10.9661	+	10.9661i	0.370300	+	0.370300i	−0.497286	+	0.867586i	$0.665670\pi$
$878$		0			0
$879$	37.2180			1.25533
$880$		0			0
$881$	17.8076			0.599952			0.299976	−	0.953947i	$-0.403021\pi$
$881$	17.8076			0.599952			0.299976	+	0.953947i	$0.403021\pi$
$882$		0			0
$883$	22.1027	+	22.1027i	0.743815	+	0.743815i	0.973310	−	0.229495i	$-0.0737075\pi$
$883$	22.1027	+	22.1027i	0.743815	+	0.743815i	−0.229495	+	0.973310i	$0.573707\pi$
$884$		0			0
$885$	−1.37379	−	12.3498i	−0.0461796	−	0.415134i
$886$		0			0
$887$	37.4622	−	37.4622i	1.25786	−	1.25786i	0.305742	−	0.952114i	$-0.401095\pi$
$887$	37.4622	−	37.4622i	1.25786	−	1.25786i	0.952114	−	0.305742i	$-0.0989045\pi$
$888$		0			0
$889$			2.88330i			0.0967028i
$890$		0			0
$891$			28.1561i			0.943266i
$892$		0			0
$893$	−32.4504	+	32.4504i	−1.08591	+	1.08591i
$894$		0			0
$895$	−23.1394	−	18.5067i	−0.773465	−	0.618610i
$896$		0			0
$897$	−10.4618	−	10.4618i	−0.349310	−	0.349310i
$898$		0			0
$899$	−16.2646			−0.542456
$900$		0			0
$901$	8.83316			0.294275
$902$		0			0
$903$	29.6074	+	29.6074i	0.985274	+	0.985274i
$904$		0			0
$905$	−12.0147	−	9.60924i	−0.399382	−	0.319422i
$906$		0			0
$907$	−1.54841	+	1.54841i	−0.0514140	+	0.0514140i	−0.732346	−	0.680932i	$-0.761575\pi$
$907$	−1.54841	+	1.54841i	−0.0514140	+	0.0514140i	0.680932	+	0.732346i	$0.261575\pi$
$908$		0			0
$909$		−	24.5341i		−	0.813745i
$910$		0			0
$911$			41.9628i			1.39029i	0.718870	+	0.695145i	$0.244660\pi$
$911$			41.9628i			1.39029i	−0.718870	+	0.695145i	$0.755340\pi$
$912$		0			0
$913$	−33.5626	+	33.5626i	−1.11076	+	1.11076i
$914$		0			0
$915$	0.496700	+	4.46511i	0.0164204	+	0.147612i
$916$		0			0
$917$	−17.1918	−	17.1918i	−0.567722	−	0.567722i
$918$		0			0
$919$	−47.9702			−1.58239			−0.791195	−	0.611564i	$-0.790541\pi$
$919$	−47.9702			−1.58239			−0.791195	+	0.611564i	$0.790541\pi$
$920$		0			0
$921$	−0.587349			−0.0193538
$922$		0			0
$923$	−11.4566	−	11.4566i	−0.377098	−	0.377098i
$924$		0			0
$925$	−16.9059	+	26.7373i	−0.555861	+	0.879116i
$926$		0			0
$927$	19.9906	−	19.9906i	0.656577	−	0.656577i
$928$		0			0
$929$		−	16.2536i		−	0.533262i	−0.963799	−	0.266631i	$-0.914089\pi$
$929$		−	16.2536i		−	0.533262i	0.963799	−	0.266631i	$-0.0859106\pi$
$930$		0			0
$931$		−	19.6031i		−	0.642466i
$932$		0			0
$933$	19.2992	−	19.2992i	0.631828	−	0.631828i
$934$		0			0
$935$	5.86802	−	0.652760i	0.191905	−	0.0213475i
$936$		0			0
$937$	0.579498	+	0.579498i	0.0189314	+	0.0189314i	0.716509	−	0.697578i	$-0.245739\pi$
$937$	0.579498	+	0.579498i	0.0189314	+	0.0189314i	−0.697578	+	0.716509i	$0.745739\pi$
$938$		0			0
$939$	−26.3066			−0.858483
$940$		0			0
$941$	−10.6463			−0.347060			−0.173530	−	0.984829i	$-0.555517\pi$
$941$	−10.6463			−0.347060			−0.173530	+	0.984829i	$0.555517\pi$
$942$		0			0
$943$	−5.30892	−	5.30892i	−0.172882	−	0.172882i
$944$		0			0
$945$	3.99947	−	5.00064i	0.130103	−	0.162671i
$946$		0			0
$947$	17.7246	−	17.7246i	0.575973	−	0.575973i	−0.357818	−	0.933791i	$-0.616479\pi$
$947$	17.7246	−	17.7246i	0.575973	−	0.575973i	0.933791	+	0.357818i	$0.116479\pi$
$948$		0			0
$949$			14.8664i			0.482582i
$950$		0			0
$951$			50.1025i			1.62469i
$952$		0			0
$953$	20.9430	−	20.9430i	0.678411	−	0.678411i	−0.281229	−	0.959641i	$-0.590742\pi$
$953$	20.9430	−	20.9430i	0.678411	−	0.678411i	0.959641	+	0.281229i	$0.0907421\pi$
$954$		0			0
$955$	−8.24048	+	10.3033i	−0.266656	+	0.333407i
$956$		0			0
$957$	17.8091	+	17.8091i	0.575687	+	0.575687i
$958$		0			0
$959$	−24.3504			−0.786316
$960$		0			0
$961$	15.6891			0.506101
$962$		0			0
$963$	3.52922	+	3.52922i	0.113728	+	0.113728i
$964$		0			0
$965$	33.2401	−	3.69764i	1.07004	−	0.119031i
$966$		0			0
$967$	11.2472	−	11.2472i	0.361685	−	0.361685i	−0.502748	−	0.864433i	$-0.667678\pi$
$967$	11.2472	−	11.2472i	0.361685	−	0.361685i	0.864433	+	0.502748i	$0.167678\pi$
$968$		0			0
$969$		−	10.9441i		−	0.351574i
$970$		0			0
$971$		−	25.7004i		−	0.824765i	−0.911011	−	0.412383i	$-0.864697\pi$
$971$		−	25.7004i		−	0.824765i	0.911011	−	0.412383i	$-0.135303\pi$
$972$		0			0
$973$	19.2722	−	19.2722i	0.617840	−	0.617840i
$974$		0			0
$975$	−13.5543	−	60.1698i	−0.434086	−	1.92698i
$976$		0			0
$977$	−29.0277	−	29.0277i	−0.928678	−	0.928678i	0.0689424	−	0.997621i	$-0.478038\pi$
$977$	−29.0277	−	29.0277i	−0.928678	−	0.928678i	−0.997621	+	0.0689424i	$0.978038\pi$
$978$		0			0
$979$	26.5963			0.850022
$980$		0			0
$981$	−32.7764			−1.04647
$982$		0			0
$983$	−27.9994	−	27.9994i	−0.893042	−	0.893042i	0.101766	−	0.994808i	$-0.467551\pi$
$983$	−27.9994	−	27.9994i	−0.893042	−	0.893042i	−0.994808	+	0.101766i	$0.967551\pi$
$984$		0			0
$985$	1.26393	+	11.3621i	0.0402721	+	0.362028i
$986$		0			0
$987$	26.5420	−	26.5420i	0.844840	−	0.844840i
$988$		0			0
$989$			12.8743i			0.409379i
$990$		0			0
$991$			34.4814i			1.09534i	0.836695	+	0.547669i	$0.184485\pi$
$991$			34.4814i			1.09534i	−0.836695	+	0.547669i	$0.815515\pi$
$992$		0			0
$993$	−34.6748	+	34.6748i	−1.10037	+	1.10037i
$994$		0			0
$995$	12.8103	+	10.2456i	0.406115	+	0.324807i
$996$		0			0
$997$	−33.3082	−	33.3082i	−1.05488	−	1.05488i	−0.998404	−	0.0564788i	$-0.982013\pi$
$997$	−33.3082	−	33.3082i	−1.05488	−	1.05488i	−0.0564788	−	0.998404i	$-0.517987\pi$
$998$		0			0
$999$	−10.6580			−0.337205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bn.a.1327.4	yes	32
4.3	odd	2	inner	1360.2.bn.a.1327.13	yes	32
5.3	odd	4	inner	1360.2.bn.a.783.13	yes	32
20.3	even	4	inner	1360.2.bn.a.783.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1360.2.bn.a.783.4	✓	32	20.3	even	4	inner
1360.2.bn.a.783.13	yes	32	5.3	odd	4	inner
1360.2.bn.a.1327.4	yes	32	1.1	even	1	trivial
1360.2.bn.a.1327.13	yes	32	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bn (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62263 - 1.62263i) q^{3} +(1.74625 + 1.39664i) q^{5} +(-1.20200 + 1.20200i) q^{7} +2.26589i q^{9} +2.64044i q^{11} +(3.80108 - 3.80108i) q^{13} +(-0.567299 - 5.09977i) q^{15} +(-0.707107 - 0.707107i) q^{17} -4.76917 q^{19} +3.90082 q^{21} +(0.848105 + 0.848105i) q^{23} +(1.09881 + 4.87777i) q^{25} +(-1.19119 + 1.19119i) q^{27} +4.15666i q^{29} +3.91291i q^{31} +(4.28448 - 4.28448i) q^{33} +(-3.77776 + 0.420240i) q^{35} +(4.47368 + 4.47368i) q^{37} -12.3355 q^{39} -6.25974 q^{41} +(7.59005 + 7.59005i) q^{43} +(-3.16463 + 3.95682i) q^{45} +(6.80420 - 6.80420i) q^{47} +4.11038i q^{49} +2.29475i q^{51} +(-6.24599 + 6.24599i) q^{53} +(-3.68774 + 4.61088i) q^{55} +(7.73862 + 7.73862i) q^{57} +2.42164 q^{59} -0.875552 q^{61} +(-2.72360 - 2.72360i) q^{63} +(11.9464 - 1.32892i) q^{65} +(6.37536 - 6.37536i) q^{67} -2.75233i q^{69} -3.01403i q^{71} +(-1.95554 + 1.95554i) q^{73} +(6.13188 - 9.69780i) q^{75} +(-3.17382 - 3.17382i) q^{77} +17.1634 q^{79} +10.6634 q^{81} +(12.7110 + 12.7110i) q^{83} +(-0.247216 - 2.22236i) q^{85} +(6.74475 - 6.74475i) q^{87} -10.0727i q^{89} +9.13781i q^{91} +(6.34923 - 6.34923i) q^{93} +(-8.32818 - 6.66080i) q^{95} +(2.55854 + 2.55854i) q^{97} -5.98295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{13} - 16 q^{21} - 24 q^{25} + 8 q^{33} - 16 q^{41} + 24 q^{45} - 16 q^{53} + 32 q^{57} + 16 q^{61} + 56 q^{65} - 8 q^{73} + 40 q^{77} + 32 q^{81} + 56 q^{93} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^13 - 16 * q^21 - 24 * q^25 + 8 * q^33 - 16 * q^41 + 24 * q^45 - 16 * q^53 + 32 * q^57 + 16 * q^61 + 56 * q^65 - 8 * q^73 + 40 * q^77 + 32 * q^81 + 56 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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