LMFDB - Embedded newform 1860.2.s.a.1177.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] 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("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1177.14
Character	$\chi$	$=$	1860.1177
Dual form			1860.2.s.a.433.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{3} +(-2.03335 + 0.930324i) q^{5} +(3.55204 + 3.55204i) q^{7} +1.00000i q^{9} -1.02375i q^{11} +(-2.14442 - 2.14442i) q^{13} +(2.09563 + 0.779955i) q^{15} +(4.10840 - 4.10840i) q^{17} +1.55305i q^{19} -5.02334i q^{21} +(1.29395 + 1.29395i) q^{23} +(3.26900 - 3.78334i) q^{25} +(0.707107 - 0.707107i) q^{27} +5.13268 q^{29} +(-3.42793 + 4.38740i) q^{31} +(-0.723899 + 0.723899i) q^{33} +(-10.5271 - 3.91798i) q^{35} +(-8.19054 + 8.19054i) q^{37} +3.03266i q^{39} +3.51578 q^{41} +(3.18311 + 3.18311i) q^{43} +(-0.930324 - 2.03335i) q^{45} +(4.33874 + 4.33874i) q^{47} +18.2339i q^{49} -5.81016 q^{51} +(-6.42067 - 6.42067i) q^{53} +(0.952417 + 2.08163i) q^{55} +(1.09817 - 1.09817i) q^{57} -1.91513i q^{59} +4.45240i q^{61} +(-3.55204 + 3.55204i) q^{63} +(6.35534 + 2.36534i) q^{65} +(0.870307 + 0.870307i) q^{67} -1.82992i q^{69} -9.24125 q^{71} +(2.35042 + 2.35042i) q^{73} +(-4.98675 + 0.363696i) q^{75} +(3.63639 - 3.63639i) q^{77} +3.74066 q^{79} -1.00000 q^{81} +(4.05436 + 4.05436i) q^{83} +(-4.53166 + 12.1760i) q^{85} +(-3.62935 - 3.62935i) q^{87} +13.1218 q^{89} -15.2341i q^{91} +(5.52627 - 0.678443i) q^{93} +(-1.44484 - 3.15789i) q^{95} +(5.44174 + 5.44174i) q^{97} +1.02375 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−2.03335	+	0.930324i	−0.909340	+	0.416053i
$5$	−2.03335	+	0.930324i	−0.909340	+	0.416053i
$6$		0			0
$7$	3.55204	+	3.55204i	1.34254	+	1.34254i	0.893520	+	0.449024i	$0.148228\pi$
$7$	3.55204	+	3.55204i	1.34254	+	1.34254i	0.449024	+	0.893520i	$0.351772\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$		−	1.02375i		−	0.308672i	−0.988018	−	0.154336i	$-0.950676\pi$
$11$		−	1.02375i		−	0.308672i	0.988018	−	0.154336i	$-0.0493238\pi$
$12$		0			0
$13$	−2.14442	−	2.14442i	−0.594754	−	0.594754i	0.344158	−	0.938912i	$-0.388165\pi$
$13$	−2.14442	−	2.14442i	−0.594754	−	0.594754i	−0.938912	+	0.344158i	$0.888165\pi$
$14$		0			0
$15$	2.09563	+	0.779955i	0.541090	+	0.201384i
$16$		0			0
$17$	4.10840	−	4.10840i	0.996434	−	0.996434i	−0.00355941	−	0.999994i	$-0.501133\pi$
$17$	4.10840	−	4.10840i	0.996434	−	0.996434i	0.999994	+	0.00355941i	$0.00113300\pi$
$18$		0			0
$19$			1.55305i			0.356295i	0.984004	+	0.178147i	$0.0570103\pi$
$19$			1.55305i			0.356295i	−0.984004	+	0.178147i	$0.942990\pi$
$20$		0			0
$21$		−	5.02334i		−	1.09618i
$22$		0			0
$23$	1.29395	+	1.29395i	0.269808	+	0.269808i	0.829023	−	0.559215i	$-0.188897\pi$
$23$	1.29395	+	1.29395i	0.269808	+	0.269808i	−0.559215	+	0.829023i	$0.688897\pi$
$24$		0			0
$25$	3.26900	−	3.78334i	0.653799	−	0.756668i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	5.13268			0.953115			0.476557	−	0.879143i	$-0.341884\pi$
$29$	5.13268			0.953115			0.476557	+	0.879143i	$0.341884\pi$
$30$		0			0
$31$	−3.42793	+	4.38740i	−0.615675	+	0.788000i
$31$	−3.42793	+	4.38740i	−0.615675	+	0.788000i
$32$		0			0
$33$	−0.723899	+	0.723899i	−0.126015	+	0.126015i
$34$		0			0
$35$	−10.5271	−	3.91798i	−1.77940	−	0.662259i
$36$		0			0
$37$	−8.19054	+	8.19054i	−1.34652	+	1.34652i	−0.457102	+	0.889414i	$0.651113\pi$
$37$	−8.19054	+	8.19054i	−1.34652	+	1.34652i	−0.889414	+	0.457102i	$0.848887\pi$
$38$		0			0
$39$			3.03266i			0.485615i
$40$		0			0
$41$	3.51578			0.549072			0.274536	−	0.961577i	$-0.411476\pi$
$41$	3.51578			0.549072			0.274536	+	0.961577i	$0.411476\pi$
$42$		0			0
$43$	3.18311	+	3.18311i	0.485419	+	0.485419i	0.906857	−	0.421438i	$-0.138475\pi$
$43$	3.18311	+	3.18311i	0.485419	+	0.485419i	−0.421438	+	0.906857i	$0.638475\pi$
$44$		0			0
$45$	−0.930324	−	2.03335i	−0.138684	−	0.303113i
$46$		0			0
$47$	4.33874	+	4.33874i	0.632871	+	0.632871i	0.948787	−	0.315916i	$-0.102312\pi$
$47$	4.33874	+	4.33874i	0.632871	+	0.632871i	−0.315916	+	0.948787i	$0.602312\pi$
$48$		0			0
$49$			18.2339i			2.60485i
$50$		0			0
$51$	−5.81016			−0.813585
$52$		0			0
$53$	−6.42067	−	6.42067i	−0.881947	−	0.881947i	0.111785	−	0.993732i	$-0.464343\pi$
$53$	−6.42067	−	6.42067i	−0.881947	−	0.881947i	−0.993732	+	0.111785i	$0.964343\pi$
$54$		0			0
$55$	0.952417	+	2.08163i	0.128424	+	0.280688i
$56$		0			0
$57$	1.09817	−	1.09817i	0.145457	−	0.145457i
$58$		0			0
$59$		−	1.91513i		−	0.249329i	−0.992199	−	0.124664i	$-0.960215\pi$
$59$		−	1.91513i		−	0.249329i	0.992199	−	0.124664i	$-0.0397854\pi$
$60$		0			0
$61$			4.45240i			0.570071i	0.958517	+	0.285036i	$0.0920055\pi$
$61$			4.45240i			0.570071i	−0.958517	+	0.285036i	$0.907995\pi$
$62$		0			0
$63$	−3.55204	+	3.55204i	−0.447515	+	0.447515i
$64$		0			0
$65$	6.35534	+	2.36534i	0.788283	+	0.293384i
$66$		0			0
$67$	0.870307	+	0.870307i	0.106325	+	0.106325i	0.758268	−	0.651943i	$-0.226046\pi$
$67$	0.870307	+	0.870307i	0.106325	+	0.106325i	−0.651943	+	0.758268i	$0.726046\pi$
$68$		0			0
$69$		−	1.82992i		−	0.220297i
$70$		0			0
$71$	−9.24125			−1.09673			−0.548367	−	0.836238i	$-0.684750\pi$
$71$	−9.24125			−1.09673			−0.548367	+	0.836238i	$0.684750\pi$
$72$		0			0
$73$	2.35042	+	2.35042i	0.275095	+	0.275095i	0.831147	−	0.556052i	$-0.187684\pi$
$73$	2.35042	+	2.35042i	0.275095	+	0.275095i	−0.556052	+	0.831147i	$0.687684\pi$
$74$		0			0
$75$	−4.98675	+	0.363696i	−0.575821	+	0.0419960i
$76$		0			0
$77$	3.63639	−	3.63639i	0.414405	−	0.414405i
$78$		0			0
$79$	3.74066			0.420857			0.210429	−	0.977609i	$-0.432514\pi$
$79$	3.74066			0.420857			0.210429	+	0.977609i	$0.432514\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	4.05436	+	4.05436i	0.445023	+	0.445023i	0.893696	−	0.448673i	$-0.148103\pi$
$83$	4.05436	+	4.05436i	0.445023	+	0.445023i	−0.448673	+	0.893696i	$0.648103\pi$
$84$		0			0
$85$	−4.53166	+	12.1760i	−0.491528	+	1.32067i
$86$		0			0
$87$	−3.62935	−	3.62935i	−0.389108	−	0.389108i
$88$		0			0
$89$	13.1218			1.39090			0.695452	−	0.718572i	$-0.255204\pi$
$89$	13.1218			1.39090			0.695452	+	0.718572i	$0.255204\pi$
$90$		0			0
$91$		−	15.2341i		−	1.59697i
$92$		0			0
$93$	5.52627	−	0.678443i	0.573048	−	0.0703513i
$94$		0			0
$95$	−1.44484	−	3.15789i	−0.148238	−	0.323993i
$96$		0			0
$97$	5.44174	+	5.44174i	0.552525	+	0.552525i	0.927169	−	0.374644i	$-0.122235\pi$
$97$	5.44174	+	5.44174i	0.552525	+	0.552525i	−0.374644	+	0.927169i	$0.622235\pi$
$98$		0			0
$99$	1.02375			0.102891
$100$		0			0
$101$	−7.13399			−0.709858			−0.354929	−	0.934893i	$-0.615495\pi$
$101$	−7.13399			−0.709858			−0.354929	+	0.934893i	$0.615495\pi$
$102$		0			0
$103$	−11.2107	+	11.2107i	−1.10463	+	1.10463i	−0.110782	+	0.993845i	$0.535336\pi$
$103$	−11.2107	+	11.2107i	−1.10463	+	1.10463i	−0.993845	+	0.110782i	$0.964664\pi$
$104$		0			0
$105$	4.67333	+	10.2142i	0.456070	+	0.996803i
$106$		0			0
$107$	10.0352	+	10.0352i	0.970140	+	0.970140i	0.999567	−	0.0294273i	$-0.00936834\pi$
$107$	10.0352	+	10.0352i	0.970140	+	0.970140i	−0.0294273	+	0.999567i	$0.509368\pi$
$108$		0			0
$109$			16.8305i			1.61207i	0.591865	+	0.806037i	$0.298392\pi$
$109$			16.8305i			1.61207i	−0.591865	+	0.806037i	$0.701608\pi$
$110$		0			0
$111$	11.5832			1.09943
$112$		0			0
$113$	−3.04324	+	3.04324i	−0.286284	+	0.286284i	−0.835609	−	0.549325i	$-0.814885\pi$
$113$	−3.04324	+	3.04324i	−0.286284	+	0.286284i	0.549325	+	0.835609i	$0.314885\pi$
$114$		0			0
$115$	−3.83485	−	1.42726i	−0.357601	−	0.133093i
$116$		0			0
$117$	2.14442	−	2.14442i	0.198251	−	0.198251i
$118$		0			0
$119$	29.1864			2.67551
$120$		0			0
$121$	9.95194			0.904722
$122$		0			0
$123$	−2.48603	−	2.48603i	−0.224158	−	0.224158i
$124$		0			0
$125$	−3.12727	+	10.7341i	−0.279712	+	0.960084i
$126$		0			0
$127$	10.0477	−	10.0477i	0.891586	−	0.891586i	−0.103086	−	0.994672i	$-0.532872\pi$
$127$	10.0477	−	10.0477i	0.891586	−	0.891586i	0.994672	+	0.103086i	$0.0328717\pi$
$128$		0			0
$129$		−	4.50159i		−	0.396343i
$130$		0			0
$131$	18.5042			1.61672			0.808360	−	0.588688i	$-0.200355\pi$
$131$	18.5042			1.61672			0.808360	+	0.588688i	$0.200355\pi$
$132$		0			0
$133$	−5.51650	+	5.51650i	−0.478341	+	0.478341i
$134$		0			0
$135$	−0.779955	+	2.09563i	−0.0671278	+	0.180363i
$136$		0			0
$137$	−9.90653	+	9.90653i	−0.846372	+	0.846372i	−0.989678	−	0.143306i	$-0.954227\pi$
$137$	−9.90653	+	9.90653i	−0.846372	+	0.846372i	0.143306	+	0.989678i	$0.454227\pi$
$138$		0			0
$139$	7.30205			0.619352			0.309676	−	0.950842i	$-0.399779\pi$
$139$	7.30205			0.619352			0.309676	+	0.950842i	$0.399779\pi$
$140$		0			0
$141$		−	6.13591i		−	0.516737i
$142$		0			0
$143$	−2.19534	+	2.19534i	−0.183584	+	0.183584i
$144$		0			0
$145$	−10.4365	+	4.77505i	−0.866706	+	0.396547i
$146$		0			0
$147$	12.8933	−	12.8933i	1.06342	−	1.06342i
$148$		0			0
$149$		−	4.76358i		−	0.390248i	−0.980779	−	0.195124i	$-0.937489\pi$
$149$		−	4.76358i		−	0.390248i	0.980779	−	0.195124i	$-0.0625109\pi$
$150$		0			0
$151$			12.1699i			0.990375i	0.868786	+	0.495188i	$0.164901\pi$
$151$			12.1699i			0.990375i	−0.868786	+	0.495188i	$0.835099\pi$
$152$		0			0
$153$	4.10840	+	4.10840i	0.332145	+	0.332145i
$154$		0			0
$155$	2.88848	−	12.1102i	0.232008	−	0.972714i
$156$		0			0
$157$	−8.33014	−	8.33014i	−0.664818	−	0.664818i	0.291694	−	0.956512i	$-0.405781\pi$
$157$	−8.33014	−	8.33014i	−0.664818	−	0.664818i	−0.956512	+	0.291694i	$0.905781\pi$
$158$		0			0
$159$			9.08020i			0.720107i
$160$		0			0
$161$			9.19233i			0.724457i
$162$		0			0
$163$	6.96331	−	6.96331i	0.545408	−	0.545408i	−0.379701	−	0.925109i	$-0.623973\pi$
$163$	6.96331	−	6.96331i	0.545408	−	0.545408i	0.925109	+	0.379701i	$0.123973\pi$
$164$		0			0
$165$	0.798478	−	2.14540i	0.0621614	−	0.167019i
$166$		0			0
$167$	−6.35870	+	6.35870i	−0.492051	+	0.492051i	−0.908952	−	0.416901i	$-0.863116\pi$
$167$	−6.35870	+	6.35870i	−0.492051	+	0.492051i	0.416901	+	0.908952i	$0.363116\pi$
$168$		0			0
$169$		−	3.80295i		−	0.292535i
$170$		0			0
$171$	−1.55305			−0.118765
$172$		0			0
$173$	2.44986	−	2.44986i	0.186259	−	0.186259i	−0.607817	−	0.794077i	$-0.707955\pi$
$173$	2.44986	−	2.44986i	0.186259	−	0.186259i	0.794077	+	0.607817i	$0.207955\pi$
$174$		0			0
$175$	25.0502	−	1.82697i	1.89361	−	0.138106i
$176$		0			0
$177$	−1.35420	+	1.35420i	−0.101788	+	0.101788i
$178$		0			0
$179$	−19.7597			−1.47691			−0.738454	−	0.674303i	$-0.764444\pi$
$179$	−19.7597			−1.47691			−0.738454	+	0.674303i	$0.764444\pi$
$180$		0			0
$181$		−	14.2138i		−	1.05651i	−0.849087	−	0.528253i	$-0.822847\pi$
$181$		−	14.2138i		−	1.05651i	0.849087	−	0.528253i	$-0.177153\pi$
$182$		0			0
$183$	3.14832	−	3.14832i	0.232731	−	0.232731i
$184$		0			0
$185$	9.03435	−	24.2741i	0.664219	−	1.78466i
$186$		0			0
$187$	−4.20597	−	4.20597i	−0.307571	−	0.307571i
$188$		0			0
$189$	5.02334			0.365394
$190$		0			0
$191$	8.65264			0.626083			0.313042	−	0.949739i	$-0.398652\pi$
$191$	8.65264			0.626083			0.313042	+	0.949739i	$0.398652\pi$
$192$		0			0
$193$	−8.36215	+	8.36215i	−0.601921	+	0.601921i	−0.940822	−	0.338901i	$-0.889945\pi$
$193$	−8.36215	+	8.36215i	−0.601921	+	0.601921i	0.338901	+	0.940822i	$0.389945\pi$
$194$		0			0
$195$	−2.82136	−	6.16646i	−0.202042	−	0.441589i
$196$		0			0
$197$	−19.7620	+	19.7620i	−1.40798	+	1.40798i	−0.637688	+	0.770295i	$0.720109\pi$
$197$	−19.7620	+	19.7620i	−1.40798	+	1.40798i	−0.770295	+	0.637688i	$0.779891\pi$
$198$		0			0
$199$	−1.98778			−0.140910			−0.0704551	−	0.997515i	$-0.522445\pi$
$199$	−1.98778			−0.140910			−0.0704551	+	0.997515i	$0.522445\pi$
$200$		0			0
$201$		−	1.23080i		−	0.0868139i
$202$		0			0
$203$	18.2315	+	18.2315i	1.27960	+	1.27960i
$204$		0			0
$205$	−7.14880	+	3.27081i	−0.499294	+	0.228443i
$206$		0			0
$207$	−1.29395	+	1.29395i	−0.0899359	+	0.0899359i
$208$		0			0
$209$	1.58993			0.109978
$210$		0			0
$211$	18.5123			1.27444			0.637218	−	0.770683i	$-0.280085\pi$
$211$	18.5123			1.27444			0.637218	+	0.770683i	$0.280085\pi$
$212$		0			0
$213$	6.53455	+	6.53455i	0.447740	+	0.447740i
$214$		0			0
$215$	−9.43368	−	3.51104i	−0.643371	−	0.239451i
$216$		0			0
$217$	−27.7603	+	3.40805i	−1.88450	+	0.231354i
$218$		0			0
$219$		−	3.32399i		−	0.224614i
$220$		0			0
$221$	−17.6203			−1.18527
$222$		0			0
$223$	−8.63066	−	8.63066i	−0.577952	−	0.577952i	0.356387	−	0.934338i	$-0.384009\pi$
$223$	−8.63066	−	8.63066i	−0.577952	−	0.577952i	−0.934338	+	0.356387i	$0.884009\pi$
$224$		0			0
$225$	3.78334	+	3.26900i	0.252223	+	0.217933i
$226$		0			0
$227$	−5.53685	−	5.53685i	−0.367494	−	0.367494i	0.499069	−	0.866563i	$-0.333676\pi$
$227$	−5.53685	−	5.53685i	−0.367494	−	0.367494i	−0.866563	+	0.499069i	$0.833676\pi$
$228$		0			0
$229$	5.41788			0.358023			0.179012	−	0.983847i	$-0.442710\pi$
$229$	5.41788			0.358023			0.179012	+	0.983847i	$0.442710\pi$
$230$		0			0
$231$	−5.14263			−0.338360
$232$		0			0
$233$	−9.98770	+	9.98770i	−0.654316	+	0.654316i	−0.954029	−	0.299713i	$-0.903109\pi$
$233$	−9.98770	+	9.98770i	−0.654316	+	0.654316i	0.299713	+	0.954029i	$0.403109\pi$
$234$		0			0
$235$	−12.8586	−	4.78574i	−0.838803	−	0.312187i
$236$		0			0
$237$	−2.64505	−	2.64505i	−0.171814	−	0.171814i
$238$		0			0
$239$	10.8859			0.704152			0.352076	−	0.935971i	$-0.385476\pi$
$239$	10.8859			0.704152			0.352076	+	0.935971i	$0.385476\pi$
$240$		0			0
$241$		−	20.2688i		−	1.30563i	−0.757518	−	0.652814i	$-0.773588\pi$
$241$		−	20.2688i		−	1.30563i	0.757518	−	0.652814i	$-0.226412\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−16.9635	−	37.0759i	−1.08376	−	2.36869i
$246$		0			0
$247$	3.33039	−	3.33039i	0.211908	−	0.211908i
$248$		0			0
$249$		−	5.73373i		−	0.363360i
$250$		0			0
$251$		−	23.0045i		−	1.45203i	−0.687679	−	0.726015i	$-0.741370\pi$
$251$		−	23.0045i		−	1.45203i	0.687679	−	0.726015i	$-0.258630\pi$
$252$		0			0
$253$	1.32468	−	1.32468i	0.0832820	−	0.0832820i
$254$		0			0
$255$	11.8141	−	5.40533i	0.739826	−	0.338495i
$256$		0			0
$257$	−7.01803	−	7.01803i	−0.437773	−	0.437773i	0.453489	−	0.891262i	$-0.350179\pi$
$257$	−7.01803	−	7.01803i	−0.437773	−	0.437773i	−0.891262	+	0.453489i	$0.850179\pi$
$258$		0			0
$259$	−58.1862			−3.61551
$260$		0			0
$261$			5.13268i			0.317705i
$262$		0			0
$263$	−7.85555	−	7.85555i	−0.484394	−	0.484394i	0.422138	−	0.906532i	$-0.361280\pi$
$263$	−7.85555	−	7.85555i	−0.484394	−	0.484394i	−0.906532	+	0.422138i	$0.861280\pi$
$264$		0			0
$265$	19.0288	+	7.08215i	1.16893	+	0.435053i
$266$		0			0
$267$	−9.27849	−	9.27849i	−0.567835	−	0.567835i
$268$		0			0
$269$	−25.9151			−1.58007			−0.790035	−	0.613062i	$-0.789938\pi$
$269$	−25.9151			−1.58007			−0.790035	+	0.613062i	$0.789938\pi$
$270$		0			0
$271$		−	22.4105i		−	1.36134i	−0.732589	−	0.680671i	$-0.761688\pi$
$271$		−	22.4105i		−	1.36134i	0.732589	−	0.680671i	$-0.238312\pi$
$272$		0			0
$273$	−10.7721	+	10.7721i	−0.651959	+	0.651959i
$274$		0			0
$275$	−3.87319	−	3.34663i	−0.233562	−	0.201809i
$276$		0			0
$277$	−12.5081	+	12.5081i	−0.751541	+	0.751541i	−0.974767	−	0.223225i	$-0.928341\pi$
$277$	−12.5081	+	12.5081i	−0.751541	+	0.751541i	0.223225	+	0.974767i	$0.428341\pi$
$278$		0			0
$279$	−4.38740	−	3.42793i	−0.262667	−	0.205225i
$280$		0			0
$281$	15.8320			0.944457			0.472228	−	0.881476i	$-0.343450\pi$
$281$	15.8320			0.944457			0.472228	+	0.881476i	$0.343450\pi$
$282$		0			0
$283$	6.74084	−	6.74084i	0.400701	−	0.400701i	−0.477779	−	0.878480i	$-0.658558\pi$
$283$	6.74084	−	6.74084i	0.400701	−	0.400701i	0.878480	+	0.477779i	$0.158558\pi$
$284$		0			0
$285$	−1.21131	+	3.25462i	−0.0717518	+	0.192787i
$286$		0			0
$287$	12.4882	+	12.4882i	0.737154	+	0.737154i
$288$		0			0
$289$		−	16.7580i		−	0.985762i
$290$		0			0
$291$		−	7.69578i		−	0.451135i
$292$		0			0
$293$	−5.81877	+	5.81877i	−0.339936	+	0.339936i	−0.856343	−	0.516407i	$-0.827269\pi$
$293$	−5.81877	+	5.81877i	−0.339936	+	0.339936i	0.516407	+	0.856343i	$0.327269\pi$
$294$		0			0
$295$	1.78169	+	3.89412i	0.103734	+	0.226725i
$296$		0			0
$297$	−0.723899	−	0.723899i	−0.0420049	−	0.0420049i
$298$		0			0
$299$		−	5.54955i		−	0.320939i
$300$		0			0
$301$			22.6130i			1.30339i
$302$		0			0
$303$	5.04449	+	5.04449i	0.289798	+	0.289798i
$304$		0			0
$305$	−4.14217	−	9.05327i	−0.237180	−	0.518389i
$306$		0			0
$307$	18.7305	+	18.7305i	1.06901	+	1.06901i	0.997436	+	0.0715707i	$0.0228011\pi$
$307$	18.7305	+	18.7305i	1.06901	+	1.06901i	0.0715707	+	0.997436i	$0.477199\pi$
$308$		0			0
$309$	15.8544			0.901924
$310$		0			0
$311$	34.5214			1.95753			0.978763	−	0.204993i	$-0.0657173\pi$
$311$	34.5214			1.95753			0.978763	+	0.204993i	$0.0657173\pi$
$312$		0			0
$313$	15.7212	+	15.7212i	0.888616	+	0.888616i	0.994390	−	0.105774i	$-0.0337320\pi$
$313$	15.7212	+	15.7212i	0.888616	+	0.888616i	−0.105774	+	0.994390i	$0.533732\pi$
$314$		0			0
$315$	3.91798	−	10.5271i	0.220753	−	0.593133i
$316$		0			0
$317$	−19.1093	−	19.1093i	−1.07328	−	1.07328i	−0.997093	−	0.0761895i	$-0.975725\pi$
$317$	−19.1093	−	19.1093i	−1.07328	−	1.07328i	−0.0761895	−	0.997093i	$-0.524275\pi$
$318$		0			0
$319$		−	5.25457i		−	0.294200i
$320$		0			0
$321$		−	14.1919i		−	0.792116i
$322$		0			0
$323$	6.38056	+	6.38056i	0.355024	+	0.355024i
$324$		0			0
$325$	−15.1232	+	1.10297i	−0.838881	+	0.0611816i
$326$		0			0
$327$	11.9010	−	11.9010i	0.658126	−	0.658126i
$328$		0			0
$329$			30.8228i			1.69931i
$330$		0			0
$331$			15.1665i			0.833624i	0.908993	+	0.416812i	$0.136853\pi$
$331$			15.1665i			0.833624i	−0.908993	+	0.416812i	$0.863147\pi$
$332$		0			0
$333$	−8.19054	−	8.19054i	−0.448839	−	0.448839i
$334$		0			0
$335$	−2.57930	−	0.959969i	−0.140922	−	0.0524487i
$336$		0			0
$337$	−25.4179	+	25.4179i	−1.38460	+	1.38460i	−0.548363	+	0.836240i	$0.684749\pi$
$337$	−25.4179	+	25.4179i	−1.38460	+	1.38460i	−0.836240	+	0.548363i	$0.815251\pi$
$338$		0			0
$339$	4.30380			0.233750
$340$		0			0
$341$	4.49159	+	3.50934i	0.243233	+	0.190042i
$342$		0			0
$343$	−39.9033	+	39.9033i	−2.15458	+	2.15458i
$344$		0			0
$345$	1.70242	+	3.72087i	0.0916553	+	0.200325i
$346$		0			0
$347$	−3.48531	+	3.48531i	−0.187101	+	0.187101i	−0.794442	−	0.607341i	$-0.792236\pi$
$347$	−3.48531	+	3.48531i	−0.187101	+	0.187101i	0.607341	+	0.794442i	$0.292236\pi$
$348$		0			0
$349$			4.83284i			0.258696i	0.991599	+	0.129348i	$0.0412884\pi$
$349$			4.83284i			0.258696i	−0.991599	+	0.129348i	$0.958712\pi$
$350$		0			0
$351$	−3.03266			−0.161872
$352$		0			0
$353$	22.4901	+	22.4901i	1.19703	+	1.19703i	0.975052	+	0.221975i	$0.0712504\pi$
$353$	22.4901	+	22.4901i	1.19703	+	1.19703i	0.221975	+	0.975052i	$0.428750\pi$
$354$		0			0
$355$	18.7907	−	8.59735i	0.997304	−	0.456300i
$356$		0			0
$357$	−20.6379	−	20.6379i	−1.09227	−	1.09227i
$358$		0			0
$359$		−	4.18262i		−	0.220750i	−0.993890	−	0.110375i	$-0.964795\pi$
$359$		−	4.18262i		−	0.220750i	0.993890	−	0.110375i	$-0.0352052\pi$
$360$		0			0
$361$	16.5880			0.873054
$362$		0			0
$363$	−7.03708	−	7.03708i	−0.369351	−	0.369351i
$364$		0			0
$365$	−6.96586	−	2.59256i	−0.364610	−	0.135701i
$366$		0			0
$367$	18.3267	−	18.3267i	0.956645	−	0.956645i	−0.0424530	−	0.999098i	$-0.513517\pi$
$367$	18.3267	−	18.3267i	0.956645	−	0.956645i	0.999098	+	0.0424530i	$0.0135173\pi$
$368$		0			0
$369$			3.51578i			0.183024i
$370$		0			0
$371$		−	45.6129i		−	2.36810i
$372$		0			0
$373$	2.05895	−	2.05895i	0.106608	−	0.106608i	−0.651791	−	0.758399i	$-0.725982\pi$
$373$	2.05895	−	2.05895i	0.106608	−	0.106608i	0.758399	+	0.651791i	$0.225982\pi$
$374$		0			0
$375$	9.80145	−	5.37882i	0.506144	−	0.277761i
$376$		0			0
$377$	−11.0066	−	11.0066i	−0.566869	−	0.566869i
$378$		0			0
$379$		−	1.81999i		−	0.0934868i	−0.998907	−	0.0467434i	$-0.985116\pi$
$379$		−	1.81999i		−	0.0934868i	0.998907	−	0.0467434i	$-0.0148843\pi$
$380$		0			0
$381$	−14.2095			−0.727977
$382$		0			0
$383$	−8.30075	−	8.30075i	−0.424148	−	0.424148i	0.462481	−	0.886629i	$-0.346959\pi$
$383$	−8.30075	−	8.30075i	−0.424148	−	0.424148i	−0.886629	+	0.462481i	$0.846959\pi$
$384$		0			0
$385$	−4.01102	+	10.7771i	−0.204421	+	0.549250i
$386$		0			0
$387$	−3.18311	+	3.18311i	−0.161806	+	0.161806i
$388$		0			0
$389$	20.6917			1.04911			0.524556	−	0.851376i	$-0.324231\pi$
$389$	20.6917			1.04911			0.524556	+	0.851376i	$0.324231\pi$
$390$		0			0
$391$	10.6322			0.537691
$392$		0			0
$393$	−13.0845	−	13.0845i	−0.660023	−	0.660023i
$394$		0			0
$395$	−7.60606	+	3.48002i	−0.382702	+	0.175099i
$396$		0			0
$397$	6.09112	+	6.09112i	0.305704	+	0.305704i	0.843241	−	0.537536i	$-0.180645\pi$
$397$	6.09112	+	6.09112i	0.305704	+	0.305704i	−0.537536	+	0.843241i	$0.680645\pi$
$398$		0			0
$399$	7.80151			0.390564
$400$		0			0
$401$		−	17.2360i		−	0.860724i	−0.902656	−	0.430362i	$-0.858386\pi$
$401$		−	17.2360i		−	0.860724i	0.902656	−	0.430362i	$-0.141614\pi$
$402$		0			0
$403$	16.7593	−	2.05749i	0.834842	−	0.102491i
$404$		0			0
$405$	2.03335	−	0.930324i	0.101038	−	0.0462281i
$406$		0			0
$407$	8.38505	+	8.38505i	0.415631	+	0.415631i
$408$		0			0
$409$	12.8179			0.633807			0.316903	−	0.948458i	$-0.397357\pi$
$409$	12.8179			0.633807			0.316903	+	0.948458i	$0.397357\pi$
$410$		0			0
$411$	14.0100			0.691060
$412$		0			0
$413$	6.80261	−	6.80261i	0.334735	−	0.334735i
$414$		0			0
$415$	−12.0158	−	4.47205i	−0.589831	−	0.219524i
$416$		0			0
$417$	−5.16333	−	5.16333i	−0.252849	−	0.252849i
$418$		0			0
$419$		−	33.2306i		−	1.62342i	−0.584059	−	0.811711i	$-0.698536\pi$
$419$		−	33.2306i		−	1.62342i	0.584059	−	0.811711i	$-0.301464\pi$
$420$		0			0
$421$	6.24017			0.304127			0.152064	−	0.988371i	$-0.451408\pi$
$421$	6.24017			0.304127			0.152064	+	0.988371i	$0.451408\pi$
$422$		0			0
$423$	−4.33874	+	4.33874i	−0.210957	+	0.210957i
$424$		0			0
$425$	−2.11313	−	28.9738i	−0.102502	−	1.40544i
$426$		0			0
$427$	−15.8151	+	15.8151i	−0.765346	+	0.765346i
$428$		0			0
$429$	3.10468			0.149896
$430$		0			0
$431$	−23.1353			−1.11439			−0.557193	−	0.830383i	$-0.688122\pi$
$431$	−23.1353			−1.11439			−0.557193	+	0.830383i	$0.688122\pi$
$432$		0			0
$433$	3.61218	+	3.61218i	0.173590	+	0.173590i	0.788555	−	0.614965i	$-0.210830\pi$
$433$	3.61218	+	3.61218i	0.173590	+	0.173590i	−0.614965	+	0.788555i	$0.710830\pi$
$434$		0			0
$435$	10.7562	+	4.00326i	0.515721	+	0.191942i
$436$		0			0
$437$	−2.00957	+	2.00957i	−0.0961310	+	0.0961310i
$438$		0			0
$439$			18.6910i			0.892074i	0.895015	+	0.446037i	$0.147165\pi$
$439$			18.6910i			0.892074i	−0.895015	+	0.446037i	$0.852835\pi$
$440$		0			0
$441$	−18.2339			−0.868282
$442$		0			0
$443$	−9.51625	+	9.51625i	−0.452131	+	0.452131i	−0.896061	−	0.443931i	$-0.853584\pi$
$443$	−9.51625	+	9.51625i	−0.452131	+	0.452131i	0.443931	+	0.896061i	$0.353584\pi$
$444$		0			0
$445$	−26.6811	+	12.2075i	−1.26481	+	0.578691i
$446$		0			0
$447$	−3.36836	+	3.36836i	−0.159318	+	0.159318i
$448$		0			0
$449$	7.11177			0.335625			0.167813	−	0.985819i	$-0.446330\pi$
$449$	7.11177			0.335625			0.167813	+	0.985819i	$0.446330\pi$
$450$		0			0
$451$		−	3.59927i		−	0.169483i
$452$		0			0
$453$	8.60544	−	8.60544i	0.404319	−	0.404319i
$454$		0			0
$455$	14.1726	+	30.9762i	0.664424	+	1.45219i
$456$		0			0
$457$	−2.85154	+	2.85154i	−0.133389	+	0.133389i	−0.770649	−	0.637260i	$-0.780068\pi$
$457$	−2.85154	+	2.85154i	−0.133389	+	0.133389i	0.637260	+	0.770649i	$0.280068\pi$
$458$		0			0
$459$		−	5.81016i		−	0.271195i
$460$		0			0
$461$		−	18.3405i		−	0.854200i	−0.904204	−	0.427100i	$-0.859535\pi$
$461$		−	18.3405i		−	0.854200i	0.904204	−	0.427100i	$-0.140465\pi$
$462$		0			0
$463$	−28.8325	−	28.8325i	−1.33996	−	1.33996i	−0.896091	−	0.443870i	$-0.853605\pi$
$463$	−28.8325	−	28.8325i	−1.33996	−	1.33996i	−0.443870	−	0.896091i	$-0.646395\pi$
$464$		0			0
$465$	−10.6057	+	6.52073i	−0.491826	+	0.302392i
$466$		0			0
$467$	−3.69035	−	3.69035i	−0.170769	−	0.170769i	0.616548	−	0.787317i	$-0.288531\pi$
$467$	−3.69035	−	3.69035i	−0.170769	−	0.170769i	−0.787317	+	0.616548i	$0.788531\pi$
$468$		0			0
$469$			6.18273i			0.285492i
$470$		0			0
$471$			11.7806i			0.542822i
$472$		0			0
$473$	3.25870	−	3.25870i	0.149835	−	0.149835i
$474$		0			0
$475$	5.87572	+	5.07692i	0.269597	+	0.232945i
$476$		0			0
$477$	6.42067	−	6.42067i	0.293982	−	0.293982i
$478$		0			0
$479$		−	4.52547i		−	0.206774i	−0.994641	−	0.103387i	$-0.967032\pi$
$479$		−	4.52547i		−	0.206774i	0.994641	−	0.103387i	$-0.0329680\pi$
$480$		0			0
$481$	35.1279			1.60169
$482$		0			0
$483$	6.49996	−	6.49996i	0.295758	−	0.295758i
$484$		0			0
$485$	−16.1275	−	6.00236i	−0.732313	−	0.272553i
$486$		0			0
$487$	5.17614	−	5.17614i	0.234553	−	0.234553i	−0.580037	−	0.814590i	$-0.696962\pi$
$487$	5.17614	−	5.17614i	0.234553	−	0.234553i	0.814590	+	0.580037i	$0.196962\pi$
$488$		0			0
$489$	−9.84761			−0.445324
$490$		0			0
$491$		−	5.26486i		−	0.237600i	−0.992918	−	0.118800i	$-0.962095\pi$
$491$		−	5.26486i		−	0.237600i	0.992918	−	0.118800i	$-0.0379047\pi$
$492$		0			0
$493$	21.0871	−	21.0871i	0.949716	−	0.949716i
$494$		0			0
$495$	−2.08163	+	0.952417i	−0.0935625	+	0.0428080i
$496$		0			0
$497$	−32.8252	−	32.8252i	−1.47241	−	1.47241i
$498$		0			0
$499$	2.40122			0.107493			0.0537466	−	0.998555i	$-0.482884\pi$
$499$	2.40122			0.107493			0.0537466	+	0.998555i	$0.482884\pi$
$500$		0			0
$501$	8.99256			0.401758
$502$		0			0
$503$	−11.1899	+	11.1899i	−0.498931	+	0.498931i	−0.911105	−	0.412174i	$-0.864770\pi$
$503$	−11.1899	+	11.1899i	−0.498931	+	0.498931i	0.412174	+	0.911105i	$0.364770\pi$
$504$		0			0
$505$	14.5059	−	6.63692i	0.645503	−	0.295339i
$506$		0			0
$507$	−2.68909	+	2.68909i	−0.119427	+	0.119427i
$508$		0			0
$509$	−22.8056			−1.01084			−0.505420	−	0.862873i	$-0.668662\pi$
$509$	−22.8056			−1.01084			−0.505420	+	0.862873i	$0.668662\pi$
$510$		0			0
$511$			16.6975i			0.738655i
$512$		0			0
$513$	1.09817	+	1.09817i	0.0484855	+	0.0484855i
$514$		0			0
$515$	12.3657	−	33.2249i	0.544898	−	1.46407i
$516$		0			0
$517$	4.44178	−	4.44178i	0.195349	−	0.195349i
$518$		0			0
$519$	−3.46462			−0.152080
$520$		0			0
$521$	11.1465			0.488337			0.244169	−	0.969733i	$-0.421485\pi$
$521$	11.1465			0.488337			0.244169	+	0.969733i	$0.421485\pi$
$522$		0			0
$523$	0.976480	+	0.976480i	0.0426985	+	0.0426985i	0.728134	−	0.685435i	$-0.240388\pi$
$523$	0.976480	+	0.976480i	0.0426985	+	0.0426985i	−0.685435	+	0.728134i	$0.740388\pi$
$524$		0			0
$525$	−19.0050	−	16.4213i	−0.829446	−	0.716683i
$526$		0			0
$527$	3.94186	+	32.1085i	0.171710	+	1.39867i
$528$		0			0
$529$		−	19.6514i		−	0.854408i
$530$		0			0
$531$	1.91513			0.0831095
$532$		0			0
$533$	−7.53930	−	7.53930i	−0.326563	−	0.326563i
$534$		0			0
$535$	−29.7410	−	11.0691i	−1.28582	−	0.478557i
$536$		0			0
$537$	13.9722	+	13.9722i	0.602946	+	0.602946i
$538$		0			0
$539$	18.6670			0.804043
$540$		0			0
$541$	10.4590			0.449668			0.224834	−	0.974397i	$-0.427816\pi$
$541$	10.4590			0.449668			0.224834	+	0.974397i	$0.427816\pi$
$542$		0			0
$543$	−10.0507	+	10.0507i	−0.431317	+	0.431317i
$544$		0			0
$545$	−15.6579	−	34.2223i	−0.670709	−	1.46592i
$546$		0			0
$547$	11.6513	+	11.6513i	0.498174	+	0.498174i	0.910869	−	0.412695i	$-0.135413\pi$
$547$	11.6513	+	11.6513i	0.498174	+	0.498174i	−0.412695	+	0.910869i	$0.635413\pi$
$548$		0			0
$549$	−4.45240			−0.190024
$550$		0			0
$551$			7.97132i			0.339590i
$552$		0			0
$553$	13.2870	+	13.2870i	0.565019	+	0.565019i
$554$		0			0
$555$	−23.5526	+	10.7761i	−0.999752	+	0.457420i
$556$		0			0
$557$	−7.51732	+	7.51732i	−0.318519	+	0.318519i	−0.848198	−	0.529679i	$-0.822312\pi$
$557$	−7.51732	+	7.51732i	−0.318519	+	0.318519i	0.529679	+	0.848198i	$0.322312\pi$
$558$		0			0
$559$		−	13.6518i		−	0.577410i
$560$		0			0
$561$			5.94814i			0.251131i
$562$		0			0
$563$	28.1064	−	28.1064i	1.18454	−	1.18454i	0.205988	−	0.978555i	$-0.433959\pi$
$563$	28.1064	−	28.1064i	1.18454	−	1.18454i	0.978555	−	0.205988i	$-0.0660407\pi$
$564$		0			0
$565$	3.35677	−	9.01917i	0.141220	−	0.379439i
$566$		0			0
$567$	−3.55204	−	3.55204i	−0.149172	−	0.149172i
$568$		0			0
$569$	−29.9106			−1.25392			−0.626959	−	0.779052i	$-0.715701\pi$
$569$	−29.9106			−1.25392			−0.626959	+	0.779052i	$0.715701\pi$
$570$		0			0
$571$			24.2546i			1.01502i	0.861645	+	0.507511i	$0.169434\pi$
$571$			24.2546i			1.01502i	−0.861645	+	0.507511i	$0.830566\pi$
$572$		0			0
$573$	−6.11834	−	6.11834i	−0.255597	−	0.255597i
$574$		0			0
$575$	9.12539	−	0.665536i	0.380555	−	0.0277548i
$576$		0			0
$577$	−25.4116	−	25.4116i	−1.05790	−	1.05790i	−0.998218	−	0.0596791i	$-0.980992\pi$
$577$	−25.4116	−	25.4116i	−1.05790	−	1.05790i	−0.0596791	−	0.998218i	$-0.519008\pi$
$578$		0			0
$579$	11.8259			0.491466
$580$		0			0
$581$			28.8024i			1.19493i
$582$		0			0
$583$	−6.57315	+	6.57315i	−0.272232	+	0.272232i
$584$		0			0
$585$	−2.36534	+	6.35534i	−0.0977948	+	0.262761i
$586$		0			0
$587$	10.2347	−	10.2347i	0.422430	−	0.422430i	−0.463610	−	0.886039i	$-0.653446\pi$
$587$	10.2347	−	10.2347i	0.422430	−	0.422430i	0.886039	+	0.463610i	$0.153446\pi$
$588$		0			0
$589$	−6.81386	−	5.32376i	−0.280760	−	0.219362i
$590$		0			0
$591$	27.9477			1.14961
$592$		0			0
$593$	25.4713	−	25.4713i	1.04598	−	1.04598i	0.0470910	−	0.998891i	$-0.485005\pi$
$593$	25.4713	−	25.4713i	1.04598	−	1.04598i	0.998891	−	0.0470910i	$-0.0149951\pi$
$594$		0			0
$595$	−59.3461	+	27.1528i	−2.43295	+	1.11316i
$596$		0			0
$597$	1.40558	+	1.40558i	0.0575264	+	0.0575264i
$598$		0			0
$599$		−	19.5400i		−	0.798381i	−0.916868	−	0.399191i	$-0.869291\pi$
$599$		−	19.5400i		−	0.798381i	0.916868	−	0.399191i	$-0.130709\pi$
$600$		0			0
$601$			18.3140i			0.747044i	0.927621	+	0.373522i	$0.121850\pi$
$601$			18.3140i			0.747044i	−0.927621	+	0.373522i	$0.878150\pi$
$602$		0			0
$603$	−0.870307	+	0.870307i	−0.0354416	+	0.0354416i
$604$		0			0
$605$	−20.2357	+	9.25852i	−0.822700	+	0.376413i
$606$		0			0
$607$	−26.3948	−	26.3948i	−1.07133	−	1.07133i	−0.997252	−	0.0740800i	$-0.976398\pi$
$607$	−26.3948	−	26.3948i	−1.07133	−	1.07133i	−0.0740800	−	0.997252i	$-0.523602\pi$
$608$		0			0
$609$		−	25.7832i		−	1.04479i
$610$		0			0
$611$		−	18.6082i		−	0.752805i
$612$		0			0
$613$	20.1925	+	20.1925i	0.815568	+	0.815568i	0.985462	−	0.169895i	$-0.0543427\pi$
$613$	20.1925	+	20.1925i	0.815568	+	0.815568i	−0.169895	+	0.985462i	$0.554343\pi$
$614$		0			0
$615$	7.36778	+	2.74215i	0.297097	+	0.110574i
$616$		0			0
$617$	18.3952	+	18.3952i	0.740563	+	0.740563i	0.972686	−	0.232123i	$-0.0745673\pi$
$617$	18.3952	+	18.3952i	0.740563	+	0.740563i	−0.232123	+	0.972686i	$0.574567\pi$
$618$		0			0
$619$	−14.1585			−0.569080			−0.284540	−	0.958664i	$-0.591841\pi$
$619$	−14.1585			−0.569080			−0.284540	+	0.958664i	$0.591841\pi$
$620$		0			0
$621$	1.82992			0.0734323
$622$		0			0
$623$	46.6090	+	46.6090i	1.86735	+	1.86735i
$624$		0			0
$625$	−3.62733	−	24.7355i	−0.145093	−	0.989418i
$626$		0			0
$627$	−1.12425	−	1.12425i	−0.0448983	−	0.0448983i
$628$		0			0
$629$			67.3001i			2.68343i
$630$		0			0
$631$		−	44.7781i		−	1.78259i	−0.453426	−	0.891294i	$-0.649798\pi$
$631$		−	44.7781i		−	1.78259i	0.453426	−	0.891294i	$-0.350202\pi$
$632$		0			0
$633$	−13.0901	−	13.0901i	−0.520286	−	0.520286i
$634$		0			0
$635$	−11.0828	+	29.7780i	−0.439808	+	1.18170i
$636$		0			0
$637$	39.1012	−	39.1012i	1.54924	−	1.54924i
$638$		0			0
$639$		−	9.24125i		−	0.365578i
$640$		0			0
$641$			13.5164i			0.533868i	0.963715	+	0.266934i	$0.0860105\pi$
$641$			13.5164i			0.533868i	−0.963715	+	0.266934i	$0.913989\pi$
$642$		0			0
$643$	−33.9393	−	33.9393i	−1.33844	−	1.33844i	−0.897575	−	0.440861i	$-0.854673\pi$
$643$	−33.9393	−	33.9393i	−1.33844	−	1.33844i	−0.440861	−	0.897575i	$-0.645327\pi$
$644$		0			0
$645$	4.18794	+	9.15330i	0.164900	+	0.360411i
$646$		0			0
$647$	18.7556	−	18.7556i	0.737358	−	0.737358i	−0.234708	−	0.972066i	$-0.575413\pi$
$647$	18.7556	−	18.7556i	0.737358	−	0.737358i	0.972066	+	0.234708i	$0.0754133\pi$
$648$		0			0
$649$	−1.96061			−0.0769607
$650$		0			0
$651$	22.0394	+	17.2197i	0.863792	+	0.674892i
$652$		0			0
$653$	16.1170	−	16.1170i	0.630709	−	0.630709i	−0.317537	−	0.948246i	$-0.602856\pi$
$653$	16.1170	−	16.1170i	0.630709	−	0.630709i	0.948246	+	0.317537i	$0.102856\pi$
$654$		0			0
$655$	−37.6255	+	17.2149i	−1.47015	+	0.672642i
$656$		0			0
$657$	−2.35042	+	2.35042i	−0.0916985	+	0.0916985i
$658$		0			0
$659$			29.1112i			1.13401i	0.823714	+	0.567006i	$0.191898\pi$
$659$			29.1112i			1.13401i	−0.823714	+	0.567006i	$0.808102\pi$
$660$		0			0
$661$	9.88998			0.384676			0.192338	−	0.981329i	$-0.438393\pi$
$661$	9.88998			0.384676			0.192338	+	0.981329i	$0.438393\pi$
$662$		0			0
$663$	12.4594	+	12.4594i	0.483883	+	0.483883i
$664$		0			0
$665$	6.08482	−	16.3491i	0.235959	−	0.633990i
$666$		0			0
$667$	6.64144	+	6.64144i	0.257158	+	0.257158i
$668$		0			0
$669$			12.2056i			0.471896i
$670$		0			0
$671$	4.55814			0.175965
$672$		0			0
$673$	−23.4547	−	23.4547i	−0.904114	−	0.904114i	0.0916753	−	0.995789i	$-0.470778\pi$
$673$	−23.4547	−	23.4547i	−0.904114	−	0.904114i	−0.995789	+	0.0916753i	$0.970778\pi$
$674$		0			0
$675$	−0.363696	−	4.98675i	−0.0139987	−	0.191940i
$676$		0			0
$677$	26.7263	−	26.7263i	1.02718	−	1.02718i	0.0275551	−	0.999620i	$-0.491228\pi$
$677$	26.7263	−	26.7263i	1.02718	−	1.02718i	0.999620	−	0.0275551i	$-0.00877216\pi$
$678$		0			0
$679$			38.6585i			1.48358i
$680$		0			0
$681$			7.83029i			0.300058i
$682$		0			0
$683$	24.5885	−	24.5885i	0.940852	−	0.940852i	−0.0574939	−	0.998346i	$-0.518311\pi$
$683$	24.5885	−	24.5885i	0.940852	−	0.940852i	0.998346	+	0.0574939i	$0.0183110\pi$
$684$		0			0
$685$	10.9271	−	29.3597i	0.417504	−	1.12178i
$686$		0			0
$687$	−3.83102	−	3.83102i	−0.146162	−	0.146162i
$688$		0			0
$689$			27.5372i			1.04908i
$690$		0			0
$691$	37.0886			1.41092			0.705459	−	0.708751i	$-0.250741\pi$
$691$	37.0886			1.41092			0.705459	+	0.708751i	$0.250741\pi$
$692$		0			0
$693$	3.63639	+	3.63639i	0.138135	+	0.138135i
$694$		0			0
$695$	−14.8476	+	6.79327i	−0.563202	+	0.257684i
$696$		0			0
$697$	14.4442	−	14.4442i	0.547115	−	0.547115i
$698$		0			0
$699$	14.1247			0.534247
$700$		0			0
$701$	−4.34949			−0.164278			−0.0821390	−	0.996621i	$-0.526175\pi$
$701$	−4.34949			−0.164278			−0.0821390	+	0.996621i	$0.526175\pi$
$702$		0			0
$703$	−12.7203	−	12.7203i	−0.479756	−	0.479756i
$704$		0			0
$705$	5.70838	+	12.4764i	0.214990	+	0.469890i
$706$		0			0
$707$	−25.3402	−	25.3402i	−0.953016	−	0.953016i
$708$		0			0
$709$	39.1189			1.46914			0.734571	−	0.678532i	$-0.237384\pi$
$709$	39.1189			1.46914			0.734571	+	0.678532i	$0.237384\pi$
$710$		0			0
$711$			3.74066i			0.140286i
$712$		0			0
$713$	−10.1127	+	1.24150i	−0.378722	+	0.0464945i
$714$		0			0
$715$	2.42151	−	6.50627i	0.0905595	−	0.243321i
$716$		0			0
$717$	−7.69751	−	7.69751i	−0.287469	−	0.287469i
$718$		0			0
$719$	−4.60677			−0.171804			−0.0859018	−	0.996304i	$-0.527377\pi$
$719$	−4.60677			−0.171804			−0.0859018	+	0.996304i	$0.527377\pi$
$720$		0			0
$721$	−79.6419			−2.96602
$722$		0			0
$723$	−14.3322	+	14.3322i	−0.533021	+	0.533021i
$724$		0			0
$725$	16.7787	−	19.4187i	0.623146	−	0.721192i
$726$		0			0
$727$	−7.67641	−	7.67641i	−0.284702	−	0.284702i	0.550279	−	0.834981i	$-0.314521\pi$
$727$	−7.67641	−	7.67641i	−0.284702	−	0.284702i	−0.834981	+	0.550279i	$0.814521\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	26.1550			0.967376
$732$		0			0
$733$	4.75239	−	4.75239i	0.175533	−	0.175533i	−0.613872	−	0.789405i	$-0.710389\pi$
$733$	4.75239	−	4.75239i	0.175533	−	0.175533i	0.789405	+	0.613872i	$0.210389\pi$
$734$		0			0
$735$	−14.2216	+	38.2116i	−0.524573	+	1.40946i
$736$		0			0
$737$	0.890975	−	0.890975i	0.0328195	−	0.0328195i
$738$		0			0
$739$	39.0534			1.43660			0.718300	−	0.695733i	$-0.244920\pi$
$739$	39.0534			1.43660			0.718300	+	0.695733i	$0.244920\pi$
$740$		0			0
$741$	−4.70988			−0.173022
$742$		0			0
$743$	19.7451	+	19.7451i	0.724378	+	0.724378i	0.969494	−	0.245115i	$-0.0788259\pi$
$743$	19.7451	+	19.7451i	0.724378	+	0.724378i	−0.245115	+	0.969494i	$0.578826\pi$
$744$		0			0
$745$	4.43167	+	9.68602i	0.162364	+	0.354868i
$746$		0			0
$747$	−4.05436	+	4.05436i	−0.148341	+	0.148341i
$748$		0			0
$749$			71.2908i			2.60491i
$750$		0			0
$751$	1.62333			0.0592362			0.0296181	−	0.999561i	$-0.490571\pi$
$751$	1.62333			0.0592362			0.0296181	+	0.999561i	$0.490571\pi$
$752$		0			0
$753$	−16.2666	+	16.2666i	−0.592788	+	0.592788i
$754$		0			0
$755$	−11.3220	−	24.7457i	−0.412049	−	0.900588i
$756$		0			0
$757$	6.73436	−	6.73436i	0.244765	−	0.244765i	−0.574053	−	0.818818i	$-0.694630\pi$
$757$	6.73436	−	6.73436i	0.244765	−	0.244765i	0.818818	+	0.574053i	$0.194630\pi$
$758$		0			0
$759$	−1.87338			−0.0679995
$760$		0			0
$761$		−	5.92302i		−	0.214709i	−0.994221	−	0.107355i	$-0.965762\pi$
$761$		−	5.92302i		−	0.214709i	0.994221	−	0.107355i	$-0.0342380\pi$
$762$		0			0
$763$	−59.7827	+	59.7827i	−2.16428	+	2.16428i
$764$		0			0
$765$	−12.1760	−	4.53166i	−0.440223	−	0.163843i
$766$		0			0
$767$	−4.10684	+	4.10684i	−0.148289	+	0.148289i
$768$		0			0
$769$			12.3215i			0.444325i	0.975010	+	0.222162i	$0.0713115\pi$
$769$			12.3215i			0.444325i	−0.975010	+	0.222162i	$0.928689\pi$
$770$		0			0
$771$			9.92500i			0.357440i
$772$		0			0
$773$	6.41615	+	6.41615i	0.230773	+	0.230773i	0.813015	−	0.582242i	$-0.197825\pi$
$773$	6.41615	+	6.41615i	0.230773	+	0.230773i	−0.582242	+	0.813015i	$0.697825\pi$
$774$		0			0
$775$	5.39311	+	27.3114i	0.193726	+	0.981056i
$776$		0			0
$777$	41.1439	+	41.1439i	1.47603	+	1.47603i
$778$		0			0
$779$			5.46019i			0.195631i
$780$		0			0
$781$			9.46071i			0.338531i
$782$		0			0
$783$	3.62935	−	3.62935i	0.129703	−	0.129703i
$784$		0			0
$785$	24.6878	+	9.18834i	0.881145	+	0.327946i
$786$		0			0
$787$	−1.14869	+	1.14869i	−0.0409463	+	0.0409463i	−0.727284	−	0.686337i	$-0.759217\pi$
$787$	−1.14869	+	1.14869i	−0.0409463	+	0.0409463i	0.686337	+	0.727284i	$0.259217\pi$
$788$		0			0
$789$			11.1094i			0.395506i
$790$		0			0
$791$	−21.6194			−0.768699
$792$		0			0
$793$	9.54780	−	9.54780i	0.339052	−	0.339052i
$794$		0			0
$795$	−8.44752	−	18.4632i	−0.299603	−	0.654822i
$796$		0			0
$797$	−7.73659	+	7.73659i	−0.274044	+	0.274044i	−0.830726	−	0.556682i	$-0.812074\pi$
$797$	−7.73659	+	7.73659i	−0.274044	+	0.274044i	0.556682	+	0.830726i	$0.312074\pi$
$798$		0			0
$799$	35.6506			1.26123
$800$		0			0
$801$			13.1218i			0.463635i
$802$		0			0
$803$	2.40623	−	2.40623i	0.0849142	−	0.0849142i
$804$		0			0
$805$	−8.55184	−	18.6912i	−0.301413	−	0.658778i
$806$		0			0
$807$	18.3247	+	18.3247i	0.645061	+	0.645061i
$808$		0			0
$809$	−41.7842			−1.46905			−0.734526	−	0.678580i	$-0.762596\pi$
$809$	−41.7842			−1.46905			−0.734526	+	0.678580i	$0.762596\pi$
$810$		0			0
$811$	16.2271			0.569811			0.284905	−	0.958556i	$-0.408038\pi$
$811$	16.2271			0.569811			0.284905	+	0.958556i	$0.408038\pi$
$812$		0			0
$813$	−15.8466	+	15.8466i	−0.555766	+	0.555766i
$814$		0			0
$815$	−7.68069	+	20.6370i	−0.269043	+	0.722881i
$816$		0			0
$817$	−4.94353	+	4.94353i	−0.172952	+	0.172952i
$818$		0			0
$819$	15.2341			0.532322
$820$		0			0
$821$		−	40.6044i		−	1.41710i	−0.705659	−	0.708552i	$-0.749349\pi$
$821$		−	40.6044i		−	1.41710i	0.705659	−	0.708552i	$-0.250651\pi$
$822$		0			0
$823$	15.3216	+	15.3216i	0.534076	+	0.534076i	0.921783	−	0.387707i	$-0.126733\pi$
$823$	15.3216	+	15.3216i	0.534076	+	0.534076i	−0.387707	+	0.921783i	$0.626733\pi$
$824$		0			0
$825$	0.372333	+	5.10518i	0.0129630	+	0.177740i
$826$		0			0
$827$	12.6570	−	12.6570i	0.440126	−	0.440126i	−0.451928	−	0.892054i	$-0.649264\pi$
$827$	12.6570	−	12.6570i	0.440126	−	0.440126i	0.892054	+	0.451928i	$0.149264\pi$
$828$		0			0
$829$	47.3287			1.64380			0.821898	−	0.569635i	$-0.192915\pi$
$829$	47.3287			1.64380			0.821898	+	0.569635i	$0.192915\pi$
$830$		0			0
$831$	17.6892			0.613631
$832$		0			0
$833$	74.9123	+	74.9123i	2.59556	+	2.59556i
$834$		0			0
$835$	7.01379	−	18.8451i	0.242722	−	0.652161i
$836$		0			0
$837$	0.678443	+	5.52627i	0.0234504	+	0.191016i
$838$		0			0
$839$			15.6057i			0.538770i	0.963033	+	0.269385i	$0.0868205\pi$
$839$			15.6057i			0.538770i	−0.963033	+	0.269385i	$0.913180\pi$
$840$		0			0
$841$	−2.65559			−0.0915720
$842$		0			0
$843$	−11.1949	−	11.1949i	−0.385573	−	0.385573i
$844$		0			0
$845$	3.53797	+	7.73272i	0.121710	+	0.266014i
$846$		0			0
$847$	35.3497	+	35.3497i	1.21463	+	1.21463i
$848$		0			0
$849$	−9.53299			−0.327171
$850$		0			0
$851$	−21.1963			−0.726601
$852$		0			0
$853$	27.4430	−	27.4430i	0.939630	−	0.939630i	−0.0586490	−	0.998279i	$-0.518679\pi$
$853$	27.4430	−	27.4430i	0.939630	−	0.939630i	0.998279	+	0.0586490i	$0.0186793\pi$
$854$		0			0
$855$	3.15789	−	1.44484i	0.107998	−	0.0494125i
$856$		0			0
$857$	−4.09409	−	4.09409i	−0.139851	−	0.139851i	0.633715	−	0.773567i	$-0.281529\pi$
$857$	−4.09409	−	4.09409i	−0.139851	−	0.139851i	−0.773567	+	0.633715i	$0.781529\pi$
$858$		0			0
$859$	−2.94083			−0.100340			−0.0501699	−	0.998741i	$-0.515976\pi$
$859$	−2.94083			−0.100340			−0.0501699	+	0.998741i	$0.515976\pi$
$860$		0			0
$861$		−	17.6609i		−	0.601883i
$862$		0			0
$863$	−14.4017	−	14.4017i	−0.490239	−	0.490239i	0.418143	−	0.908381i	$-0.362681\pi$
$863$	−14.4017	−	14.4017i	−0.490239	−	0.490239i	−0.908381	+	0.418143i	$0.862681\pi$
$864$		0			0
$865$	−2.70225	+	7.26057i	−0.0918793	+	0.246867i
$866$		0			0
$867$	−11.8497	+	11.8497i	−0.402436	+	0.402436i
$868$		0			0
$869$		−	3.82949i		−	0.129907i
$870$		0			0
$871$		−	3.73260i		−	0.126474i
$872$		0			0
$873$	−5.44174	+	5.44174i	−0.184175	+	0.184175i
$874$		0			0
$875$	−49.2360	+	27.0196i	−1.66448	+	0.913430i
$876$		0			0
$877$	17.5893	+	17.5893i	0.593947	+	0.593947i	0.938695	−	0.344748i	$-0.112036\pi$
$877$	17.5893	+	17.5893i	0.593947	+	0.593947i	−0.344748	+	0.938695i	$0.612036\pi$
$878$		0			0
$879$	8.22899			0.277557
$880$		0			0
$881$			14.9288i			0.502965i	0.967862	+	0.251482i	$0.0809180\pi$
$881$			14.9288i			0.502965i	−0.967862	+	0.251482i	$0.919082\pi$
$882$		0			0
$883$	−20.8754	−	20.8754i	−0.702512	−	0.702512i	0.262437	−	0.964949i	$-0.415474\pi$
$883$	−20.8754	−	20.8754i	−0.702512	−	0.702512i	−0.964949	+	0.262437i	$0.915474\pi$
$884$		0			0
$885$	1.49371	−	4.01340i	0.0502107	−	0.134909i
$886$		0			0
$887$	25.7169	+	25.7169i	0.863489	+	0.863489i	0.991742	−	0.128252i	$-0.0409367\pi$
$887$	25.7169	+	25.7169i	0.863489	+	0.863489i	−0.128252	+	0.991742i	$0.540937\pi$
$888$		0			0
$889$	71.3794			2.39399
$890$		0			0
$891$			1.02375i			0.0342969i
$892$		0			0
$893$	−6.73830	+	6.73830i	−0.225488	+	0.225488i
$894$		0			0
$895$	40.1783	−	18.3829i	1.34301	−	0.614473i
$896$		0			0
$897$	−3.92412	+	3.92412i	−0.131023	+	0.131023i
$898$		0			0
$899$	−17.5945	+	22.5191i	−0.586809	+	0.751055i
$900$		0			0
$901$	−52.7574			−1.75760
$902$		0			0
$903$	15.9898	−	15.9898i	0.532108	−	0.532108i
$904$		0			0
$905$	13.2235	+	28.9016i	0.439563	+	0.960723i
$906$		0			0
$907$	−39.1743	−	39.1743i	−1.30076	−	1.30076i	−0.927878	−	0.372883i	$-0.878369\pi$
$907$	−39.1743	−	39.1743i	−1.30076	−	1.30076i	−0.372883	−	0.927878i	$-0.621631\pi$
$908$		0			0
$909$		−	7.13399i		−	0.236619i
$910$		0			0
$911$		−	15.6644i		−	0.518985i	−0.965745	−	0.259493i	$-0.916445\pi$
$911$		−	15.6644i		−	0.518985i	0.965745	−	0.259493i	$-0.0835553\pi$
$912$		0			0
$913$	4.15064	−	4.15064i	0.137366	−	0.137366i
$914$		0			0
$915$	−3.47267	+	9.33059i	−0.114803	+	0.308460i
$916$		0			0
$917$	65.7276	+	65.7276i	2.17052	+	2.17052i
$918$		0			0
$919$			2.15744i			0.0711672i	0.999367	+	0.0355836i	$0.0113290\pi$
$919$			2.15744i			0.0711672i	−0.999367	+	0.0355836i	$0.988671\pi$
$920$		0			0
$921$		−	26.4889i		−	0.872840i
$922$		0			0
$923$	19.8171	+	19.8171i	0.652287	+	0.652287i
$924$		0			0
$925$	4.21275	+	57.7624i	0.138514	+	1.89922i
$926$		0			0
$927$	−11.2107	−	11.2107i	−0.368209	−	0.368209i
$928$		0			0
$929$	−54.5132			−1.78852			−0.894260	−	0.447549i	$-0.852297\pi$
$929$	−54.5132			−1.78852			−0.894260	+	0.447549i	$0.852297\pi$
$930$		0			0
$931$	−28.3182			−0.928093
$932$		0			0
$933$	−24.4103	−	24.4103i	−0.799157	−	0.799157i
$934$		0			0
$935$	12.4651	+	4.63928i	0.407653	+	0.151721i
$936$		0			0
$937$	−11.9539	−	11.9539i	−0.390516	−	0.390516i	0.484356	−	0.874871i	$-0.339054\pi$
$937$	−11.9539	−	11.9539i	−0.390516	−	0.390516i	−0.874871	+	0.484356i	$0.839054\pi$
$938$		0			0
$939$		−	22.2332i		−	0.725552i
$940$		0			0
$941$			23.0083i			0.750048i	0.927015	+	0.375024i	$0.122366\pi$
$941$			23.0083i			0.750048i	−0.927015	+	0.375024i	$0.877634\pi$
$942$		0			0
$943$	4.54925	+	4.54925i	0.148144	+	0.148144i
$944$		0			0
$945$	−10.2142	+	4.67333i	−0.332268	+	0.152023i
$946$		0			0
$947$	−42.7108	+	42.7108i	−1.38791	+	1.38791i	−0.558222	+	0.829691i	$0.688516\pi$
$947$	−42.7108	+	42.7108i	−1.38791	+	1.38791i	−0.829691	+	0.558222i	$0.811484\pi$
$948$		0			0
$949$		−	10.0805i		−	0.327228i
$950$		0			0
$951$			27.0246i			0.876332i
$952$		0			0
$953$	−12.1309	−	12.1309i	−0.392957	−	0.392957i	0.482783	−	0.875740i	$-0.339626\pi$
$953$	−12.1309	−	12.1309i	−0.392957	−	0.392957i	−0.875740	+	0.482783i	$0.839626\pi$
$954$		0			0
$955$	−17.5938	+	8.04976i	−0.569323	+	0.260484i
$956$		0			0
$957$	−3.71554	+	3.71554i	−0.120106	+	0.120106i
$958$		0			0
$959$	−70.3767			−2.27258
$960$		0			0
$961$	−7.49853	−	30.0794i	−0.241888	−	0.970304i
$962$		0			0
$963$	−10.0352	+	10.0352i	−0.323380	+	0.323380i
$964$		0			0
$965$	9.22364	−	24.7827i	0.296920	−	0.797782i
$966$		0			0
$967$	27.2341	−	27.2341i	0.875791	−	0.875791i	−0.117305	−	0.993096i	$-0.537426\pi$
$967$	27.2341	−	27.2341i	0.875791	−	0.875791i	0.993096	+	0.117305i	$0.0374256\pi$
$968$		0			0
$969$		−	9.02348i		−	0.289876i
$970$		0			0
$971$	−50.8704			−1.63251			−0.816254	−	0.577693i	$-0.803953\pi$
$971$	−50.8704			−1.63251			−0.816254	+	0.577693i	$0.803953\pi$
$972$		0			0
$973$	25.9372	+	25.9372i	0.831507	+	0.831507i
$974$		0			0
$975$	11.4736	+	9.91377i	0.367449	+	0.317495i
$976$		0			0
$977$	−43.9716	−	43.9716i	−1.40678	−	1.40678i	−0.775807	−	0.630970i	$-0.782657\pi$
$977$	−43.9716	−	43.9716i	−1.40678	−	1.40678i	−0.630970	−	0.775807i	$-0.717343\pi$
$978$		0			0
$979$		−	13.4334i		−	0.429333i
$980$		0			0
$981$	−16.8305			−0.537358
$982$		0			0
$983$	11.2694	+	11.2694i	0.359439	+	0.359439i	0.863606	−	0.504167i	$-0.168201\pi$
$983$	11.2694	+	11.2694i	0.359439	+	0.359439i	−0.504167	+	0.863606i	$0.668201\pi$
$984$		0			0
$985$	21.7979	−	58.5680i	0.694539	−	1.86613i
$986$		0			0
$987$	21.7950	−	21.7950i	0.693742	−	0.693742i
$988$		0			0
$989$			8.23757i			0.261940i
$990$		0			0
$991$		−	38.8970i		−	1.23561i	−0.786333	−	0.617803i	$-0.788023\pi$
$991$		−	38.8970i		−	1.23561i	0.786333	−	0.617803i	$-0.211977\pi$
$992$		0			0
$993$	10.7243	−	10.7243i	0.340325	−	0.340325i
$994$		0			0
$995$	4.04185	−	1.84928i	0.128135	−	0.0586262i
$996$		0			0
$997$	5.14799	+	5.14799i	0.163039	+	0.163039i	0.783911	−	0.620873i	$-0.213222\pi$
$997$	5.14799	+	5.14799i	0.163039	+	0.163039i	−0.620873	+	0.783911i	$0.713222\pi$
$998$		0			0
$999$			11.5832i			0.366475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.1177.14	yes	64
5.3	odd	4	inner	1860.2.s.a.433.21	yes	64
31.30	odd	2	inner	1860.2.s.a.1177.21	yes	64
155.123	even	4	inner	1860.2.s.a.433.14	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.14	✓	64	155.123	even	4	inner
1860.2.s.a.433.21	yes	64	5.3	odd	4	inner
1860.2.s.a.1177.14	yes	64	1.1	even	1	trivial
1860.2.s.a.1177.21	yes	64	31.30	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:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-2.03335 + 0.930324i) q^{5} +(3.55204 + 3.55204i) q^{7} +1.00000i q^{9} -1.02375i q^{11} +(-2.14442 - 2.14442i) q^{13} +(2.09563 + 0.779955i) q^{15} +(4.10840 - 4.10840i) q^{17} +1.55305i q^{19} -5.02334i q^{21} +(1.29395 + 1.29395i) q^{23} +(3.26900 - 3.78334i) q^{25} +(0.707107 - 0.707107i) q^{27} +5.13268 q^{29} +(-3.42793 + 4.38740i) q^{31} +(-0.723899 + 0.723899i) q^{33} +(-10.5271 - 3.91798i) q^{35} +(-8.19054 + 8.19054i) q^{37} +3.03266i q^{39} +3.51578 q^{41} +(3.18311 + 3.18311i) q^{43} +(-0.930324 - 2.03335i) q^{45} +(4.33874 + 4.33874i) q^{47} +18.2339i q^{49} -5.81016 q^{51} +(-6.42067 - 6.42067i) q^{53} +(0.952417 + 2.08163i) q^{55} +(1.09817 - 1.09817i) q^{57} -1.91513i q^{59} +4.45240i q^{61} +(-3.55204 + 3.55204i) q^{63} +(6.35534 + 2.36534i) q^{65} +(0.870307 + 0.870307i) q^{67} -1.82992i q^{69} -9.24125 q^{71} +(2.35042 + 2.35042i) q^{73} +(-4.98675 + 0.363696i) q^{75} +(3.63639 - 3.63639i) q^{77} +3.74066 q^{79} -1.00000 q^{81} +(4.05436 + 4.05436i) q^{83} +(-4.53166 + 12.1760i) q^{85} +(-3.62935 - 3.62935i) q^{87} +13.1218 q^{89} -15.2341i q^{91} +(5.52627 - 0.678443i) q^{93} +(-1.44484 - 3.15789i) q^{95} +(5.44174 + 5.44174i) q^{97} +1.02375 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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