LMFDB - Embedded newform 1344.2.u.a.559.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(559,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 2]))

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

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

chi := DirichletCharacter("1344.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.u (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			559.7
Character	$\chi$	$=$	1344.559
Dual form			1344.2.u.a.1231.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +(-1.07201 - 1.07201i) q^{5} +(-0.929507 - 2.47710i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.07201 - 1.07201i) q^{5} +(-0.929507 - 2.47710i) q^{7} +1.00000i q^{9} +(1.12178 + 1.12178i) q^{11} +(-0.380324 + 0.380324i) q^{13} +1.51606i q^{15} -4.93076i q^{17} +(-0.00735220 - 0.00735220i) q^{19} +(-1.09431 + 2.40883i) q^{21} -1.62475 q^{23} -2.70157i q^{25} +(0.707107 - 0.707107i) q^{27} +(-3.69584 - 3.69584i) q^{29} -1.21242 q^{31} -1.58643i q^{33} +(-1.65904 + 3.65193i) q^{35} +(-6.70001 + 6.70001i) q^{37} +0.537859 q^{39} -2.08793 q^{41} +(7.89391 + 7.89391i) q^{43} +(1.07201 - 1.07201i) q^{45} -2.09637 q^{47} +(-5.27203 + 4.60496i) q^{49} +(-3.48657 + 3.48657i) q^{51} +(-5.28124 + 5.28124i) q^{53} -2.40512i q^{55} +0.0103976i q^{57} +(-9.39247 + 9.39247i) q^{59} +(2.45118 - 2.45118i) q^{61} +(2.47710 - 0.929507i) q^{63} +0.815426 q^{65} +(-4.70113 + 4.70113i) q^{67} +(1.14887 + 1.14887i) q^{69} -5.16953 q^{71} +7.83339 q^{73} +(-1.91030 + 1.91030i) q^{75} +(1.73605 - 3.82145i) q^{77} -4.65497i q^{79} -1.00000 q^{81} +(-0.694961 - 0.694961i) q^{83} +(-5.28584 + 5.28584i) q^{85} +5.22671i q^{87} -16.3938 q^{89} +(1.29561 + 0.588586i) q^{91} +(0.857310 + 0.857310i) q^{93} +0.0157633i q^{95} +15.8094i q^{97} +(-1.12178 + 1.12178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) $ 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		0			0
$5$	−1.07201	−	1.07201i	−0.479420	−	0.479420i	0.425526	−	0.904946i	$-0.360089\pi$
$5$	−1.07201	−	1.07201i	−0.479420	−	0.479420i	−0.904946	+	0.425526i	$0.860089\pi$
$6$		0			0
$7$	−0.929507	−	2.47710i	−0.351321	−	0.936255i
$7$	−0.929507	−	2.47710i	−0.351321	−	0.936255i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	1.12178	+	1.12178i	0.338229	+	0.338229i	0.855700	−	0.517472i	$-0.173127\pi$
$11$	1.12178	+	1.12178i	0.338229	+	0.338229i	−0.517472	+	0.855700i	$0.673127\pi$
$12$		0			0
$13$	−0.380324	+	0.380324i	−0.105483	+	0.105483i	−0.757879	−	0.652396i	$-0.773764\pi$
$13$	−0.380324	+	0.380324i	−0.105483	+	0.105483i	0.652396	+	0.757879i	$0.273764\pi$
$14$		0			0
$15$			1.51606i			0.391444i
$16$		0			0
$17$		−	4.93076i		−	1.19588i	−0.801539	−	0.597942i	$-0.795985\pi$
$17$		−	4.93076i		−	1.19588i	0.801539	−	0.597942i	$-0.204015\pi$
$18$		0			0
$19$	−0.00735220	−	0.00735220i	−0.00168671	−	0.00168671i	0.706263	−	0.707950i	$-0.250380\pi$
$19$	−0.00735220	−	0.00735220i	−0.00168671	−	0.00168671i	−0.707950	+	0.706263i	$0.750380\pi$
$20$		0			0
$21$	−1.09431	+	2.40883i	−0.238798	+	0.525651i
$22$		0			0
$23$	−1.62475			−0.338783			−0.169392	−	0.985549i	$-0.554180\pi$
$23$	−1.62475			−0.338783			−0.169392	+	0.985549i	$0.554180\pi$
$24$		0			0
$25$		−	2.70157i		−	0.540314i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$	−3.69584	−	3.69584i	−0.686301	−	0.686301i	0.275112	−	0.961412i	$-0.411285\pi$
$29$	−3.69584	−	3.69584i	−0.686301	−	0.686301i	−0.961412	+	0.275112i	$0.911285\pi$
$30$		0			0
$31$	−1.21242			−0.217757			−0.108878	−	0.994055i	$-0.534726\pi$
$31$	−1.21242			−0.217757			−0.108878	+	0.994055i	$0.534726\pi$
$32$		0			0
$33$		−	1.58643i		−	0.276162i
$34$		0			0
$35$	−1.65904	+	3.65193i	−0.280429	+	0.617289i
$36$		0			0
$37$	−6.70001	+	6.70001i	−1.10148	+	1.10148i	−0.107243	+	0.994233i	$0.534202\pi$
$37$	−6.70001	+	6.70001i	−1.10148	+	1.10148i	−0.994233	+	0.107243i	$0.965798\pi$
$38$		0			0
$39$	0.537859			0.0861264
$40$		0			0
$41$	−2.08793			−0.326080			−0.163040	−	0.986619i	$-0.552130\pi$
$41$	−2.08793			−0.326080			−0.163040	+	0.986619i	$0.552130\pi$
$42$		0			0
$43$	7.89391	+	7.89391i	1.20381	+	1.20381i	0.972998	+	0.230812i	$0.0741383\pi$
$43$	7.89391	+	7.89391i	1.20381	+	1.20381i	0.230812	+	0.972998i	$0.425862\pi$
$44$		0			0
$45$	1.07201	−	1.07201i	0.159807	−	0.159807i
$46$		0			0
$47$	−2.09637			−0.305787			−0.152894	−	0.988243i	$-0.548859\pi$
$47$	−2.09637			−0.305787			−0.152894	+	0.988243i	$0.548859\pi$
$48$		0			0
$49$	−5.27203	+	4.60496i	−0.753148	+	0.657852i
$50$		0			0
$51$	−3.48657	+	3.48657i	−0.488218	+	0.488218i
$52$		0			0
$53$	−5.28124	+	5.28124i	−0.725434	+	0.725434i	−0.969707	−	0.244272i	$-0.921451\pi$
$53$	−5.28124	+	5.28124i	−0.725434	+	0.725434i	0.244272	+	0.969707i	$0.421451\pi$
$54$		0			0
$55$		−	2.40512i		−	0.324307i
$56$		0			0
$57$			0.0103976i			0.00137719i
$58$		0			0
$59$	−9.39247	+	9.39247i	−1.22280	+	1.22280i	−0.256162	+	0.966634i	$0.582458\pi$
$59$	−9.39247	+	9.39247i	−1.22280	+	1.22280i	−0.966634	+	0.256162i	$0.917542\pi$
$60$		0			0
$61$	2.45118	−	2.45118i	0.313841	−	0.313841i	−0.532555	−	0.846396i	$-0.678768\pi$
$61$	2.45118	−	2.45118i	0.313841	−	0.313841i	0.846396	+	0.532555i	$0.178768\pi$
$62$		0			0
$63$	2.47710	−	0.929507i	0.312085	−	0.117107i
$64$		0			0
$65$	0.815426			0.101141
$66$		0			0
$67$	−4.70113	+	4.70113i	−0.574334	+	0.574334i	−0.933337	−	0.359002i	$-0.883117\pi$
$67$	−4.70113	+	4.70113i	−0.574334	+	0.574334i	0.359002	+	0.933337i	$0.383117\pi$
$68$		0			0
$69$	1.14887	+	1.14887i	0.138308	+	0.138308i
$70$		0			0
$71$	−5.16953			−0.613510			−0.306755	−	0.951789i	$-0.599243\pi$
$71$	−5.16953			−0.613510			−0.306755	+	0.951789i	$0.599243\pi$
$72$		0			0
$73$	7.83339			0.916828			0.458414	−	0.888739i	$-0.348418\pi$
$73$	7.83339			0.916828			0.458414	+	0.888739i	$0.348418\pi$
$74$		0			0
$75$	−1.91030	+	1.91030i	−0.220582	+	0.220582i
$76$		0			0
$77$	1.73605	−	3.82145i	0.197842	−	0.435495i
$78$		0			0
$79$		−	4.65497i		−	0.523725i	−0.965105	−	0.261863i	$-0.915663\pi$
$79$		−	4.65497i		−	0.523725i	0.965105	−	0.261863i	$-0.0843368\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−0.694961	−	0.694961i	−0.0762819	−	0.0762819i	0.667936	−	0.744218i	$-0.267178\pi$
$83$	−0.694961	−	0.694961i	−0.0762819	−	0.0762819i	−0.744218	+	0.667936i	$0.767178\pi$
$84$		0			0
$85$	−5.28584	+	5.28584i	−0.573330	+	0.573330i
$86$		0			0
$87$			5.22671i			0.560362i
$88$		0			0
$89$	−16.3938			−1.73774			−0.868869	−	0.495043i	$-0.835152\pi$
$89$	−16.3938			−1.73774			−0.868869	+	0.495043i	$0.835152\pi$
$90$		0			0
$91$	1.29561	+	0.588586i	0.135817	+	0.0617006i
$92$		0			0
$93$	0.857310	+	0.857310i	0.0888989	+	0.0888989i
$94$		0			0
$95$			0.0157633i			0.00161728i
$96$		0			0
$97$			15.8094i			1.60520i	0.596516	+	0.802601i	$0.296551\pi$
$97$			15.8094i			1.60520i	−0.596516	+	0.802601i	$0.703449\pi$
$98$		0			0
$99$	−1.12178	+	1.12178i	−0.112743	+	0.112743i
$100$		0			0
$101$	−11.6943	−	11.6943i	−1.16363	−	1.16363i	−0.983676	−	0.179951i	$-0.942406\pi$
$101$	−11.6943	−	11.6943i	−1.16363	−	1.16363i	−0.179951	−	0.983676i	$-0.557594\pi$
$102$		0			0
$103$		−	17.2578i		−	1.70046i	−0.526408	−	0.850232i	$-0.676461\pi$
$103$		−	17.2578i		−	1.70046i	0.526408	−	0.850232i	$-0.323539\pi$
$104$		0			0
$105$	3.75542	−	1.40919i	0.366492	−	0.137523i
$106$		0			0
$107$	0.486324	+	0.486324i	0.0470148	+	0.0470148i	0.730223	−	0.683209i	$-0.239416\pi$
$107$	0.486324	+	0.486324i	0.0470148	+	0.0470148i	−0.683209	+	0.730223i	$0.739416\pi$
$108$		0			0
$109$	4.59269	+	4.59269i	0.439900	+	0.439900i	0.891978	−	0.452078i	$-0.149317\pi$
$109$	4.59269	+	4.59269i	0.439900	+	0.439900i	−0.452078	+	0.891978i	$0.649317\pi$
$110$		0			0
$111$	9.47525			0.899351
$112$		0			0
$113$	16.4776			1.55009			0.775043	−	0.631908i	$-0.217728\pi$
$113$	16.4776			1.55009			0.775043	+	0.631908i	$0.217728\pi$
$114$		0			0
$115$	1.74175	+	1.74175i	0.162419	+	0.162419i
$116$		0			0
$117$	−0.380324	−	0.380324i	−0.0351610	−	0.0351610i
$118$		0			0
$119$	−12.2140	+	4.58317i	−1.11965	+	0.420139i
$120$		0			0
$121$		−	8.48323i		−	0.771203i
$122$		0			0
$123$	1.47639	+	1.47639i	0.133122	+	0.133122i
$124$		0			0
$125$	−8.25620	+	8.25620i	−0.738457	+	0.738457i
$126$		0			0
$127$		−	11.8244i		−	1.04925i	−0.851335	−	0.524623i	$-0.824206\pi$
$127$		−	11.8244i		−	1.04925i	0.851335	−	0.524623i	$-0.175794\pi$
$128$		0			0
$129$		−	11.1637i		−	0.982907i
$130$		0			0
$131$	−9.68747	−	9.68747i	−0.846398	−	0.846398i	0.143283	−	0.989682i	$-0.454234\pi$
$131$	−9.68747	−	9.68747i	−0.846398	−	0.846398i	−0.989682	+	0.143283i	$0.954234\pi$
$132$		0			0
$133$	−0.0113782	+	0.0250460i	−0.000986615	+	0.00217177i
$134$		0			0
$135$	−1.51606			−0.130481
$136$		0			0
$137$		−	0.638902i		−	0.0545851i	−0.999627	−	0.0272925i	$-0.991311\pi$
$137$		−	0.638902i		−	0.0545851i	0.999627	−	0.0272925i	$-0.00868856\pi$
$138$		0			0
$139$	8.78705	−	8.78705i	0.745308	−	0.745308i	−0.228286	−	0.973594i	$-0.573312\pi$
$139$	8.78705	−	8.78705i	0.745308	−	0.745308i	0.973594	+	0.228286i	$0.0733121\pi$
$140$		0			0
$141$	1.48236	+	1.48236i	0.124837	+	0.124837i
$142$		0			0
$143$	−0.853277			−0.0713546
$144$		0			0
$145$			7.92400i			0.658052i
$146$		0			0
$147$	6.98409	+	0.471690i	0.576038	+	0.0389044i
$148$		0			0
$149$	−6.68763	+	6.68763i	−0.547872	+	0.547872i	−0.925825	−	0.377953i	$-0.876628\pi$
$149$	−6.68763	+	6.68763i	−0.547872	+	0.547872i	0.377953	+	0.925825i	$0.376628\pi$
$150$		0			0
$151$	−11.7089			−0.952854			−0.476427	−	0.879214i	$-0.658068\pi$
$151$	−11.7089			−0.952854			−0.476427	+	0.879214i	$0.658068\pi$
$152$		0			0
$153$	4.93076			0.398628
$154$		0			0
$155$	1.29973	+	1.29973i	0.104397	+	0.104397i
$156$		0			0
$157$	7.87159	−	7.87159i	0.628221	−	0.628221i	−0.319399	−	0.947620i	$-0.603481\pi$
$157$	7.87159	−	7.87159i	0.628221	−	0.628221i	0.947620	+	0.319399i	$0.103481\pi$
$158$		0			0
$159$	7.46881			0.592315
$160$		0			0
$161$	1.51021	+	4.02466i	0.119022	+	0.317188i
$162$		0			0
$163$	−4.16256	+	4.16256i	−0.326037	+	0.326037i	−0.851077	−	0.525041i	$-0.824050\pi$
$163$	−4.16256	+	4.16256i	−0.326037	+	0.326037i	0.525041	+	0.851077i	$0.324050\pi$
$164$		0			0
$165$	−1.70068	+	1.70068i	−0.132398	+	0.132398i
$166$		0			0
$167$			5.10931i			0.395370i	0.980266	+	0.197685i	$0.0633423\pi$
$167$			5.10931i			0.395370i	−0.980266	+	0.197685i	$0.936658\pi$
$168$		0			0
$169$			12.7107i			0.977747i
$170$		0			0
$171$	0.00735220	−	0.00735220i	0.000562237	−	0.000562237i
$172$		0			0
$173$	−6.04872	+	6.04872i	−0.459876	+	0.459876i	−0.898615	−	0.438739i	$-0.855425\pi$
$173$	−6.04872	+	6.04872i	−0.459876	+	0.459876i	0.438739	+	0.898615i	$0.355425\pi$
$174$		0			0
$175$	−6.69205	+	2.51113i	−0.505871	+	0.189823i
$176$		0			0
$177$	13.2830			0.998409
$178$		0			0
$179$	11.3303	−	11.3303i	0.846868	−	0.846868i	−0.142873	−	0.989741i	$-0.545634\pi$
$179$	11.3303	−	11.3303i	0.846868	−	0.846868i	0.989741	+	0.142873i	$0.0456340\pi$
$180$		0			0
$181$	3.12921	+	3.12921i	0.232593	+	0.232593i	0.813774	−	0.581181i	$-0.197409\pi$
$181$	3.12921	+	3.12921i	0.232593	+	0.232593i	−0.581181	+	0.813774i	$0.697409\pi$
$182$		0			0
$183$	−3.46649			−0.256250
$184$		0			0
$185$	14.3650			1.05614
$186$		0			0
$187$	5.53121	−	5.53121i	0.404482	−	0.404482i
$188$		0			0
$189$	−2.40883	−	1.09431i	−0.175217	−	0.0795995i
$190$		0			0
$191$		−	11.2514i		−	0.814126i	−0.913400	−	0.407063i	$-0.866553\pi$
$191$		−	11.2514i		−	0.814126i	0.913400	−	0.407063i	$-0.133447\pi$
$192$		0			0
$193$	15.6044			1.12323			0.561613	−	0.827400i	$-0.310181\pi$
$193$	15.6044			1.12323			0.561613	+	0.827400i	$0.310181\pi$
$194$		0			0
$195$	−0.576593	−	0.576593i	−0.0412907	−	0.0412907i
$196$		0			0
$197$	6.75482	−	6.75482i	0.481261	−	0.481261i	−0.424273	−	0.905534i	$-0.639470\pi$
$197$	6.75482	−	6.75482i	0.481261	−	0.481261i	0.905534	+	0.424273i	$0.139470\pi$
$198$		0			0
$199$			22.4644i			1.59246i	0.604996	+	0.796229i	$0.293175\pi$
$199$			22.4644i			1.59246i	−0.604996	+	0.796229i	$0.706825\pi$
$200$		0			0
$201$	6.64840			0.468942
$202$		0			0
$203$	−5.71965	+	12.5903i	−0.401441	+	0.883664i
$204$		0			0
$205$	2.23829	+	2.23829i	0.156329	+	0.156329i
$206$		0			0
$207$		−	1.62475i		−	0.112928i
$208$		0			0
$209$		−	0.0164951i		−	0.00114099i
$210$		0			0
$211$	−3.76337	+	3.76337i	−0.259081	+	0.259081i	−0.824680	−	0.565599i	$-0.808645\pi$
$211$	−3.76337	+	3.76337i	−0.259081	+	0.259081i	0.565599	+	0.824680i	$0.308645\pi$
$212$		0			0
$213$	3.65541	+	3.65541i	0.250464	+	0.250464i
$214$		0			0
$215$		−	16.9248i		−	1.15426i
$216$		0			0
$217$	1.12695	+	3.00328i	0.0765025	+	0.203876i
$218$		0			0
$219$	−5.53904	−	5.53904i	−0.374294	−	0.374294i
$220$		0			0
$221$	1.87528	+	1.87528i	0.126145	+	0.126145i
$222$		0			0
$223$	14.0828			0.943054			0.471527	−	0.881852i	$-0.343703\pi$
$223$	14.0828			0.943054			0.471527	+	0.881852i	$0.343703\pi$
$224$		0			0
$225$	2.70157			0.180105
$226$		0			0
$227$	−18.0404	−	18.0404i	−1.19738	−	1.19738i	−0.974947	−	0.222436i	$-0.928599\pi$
$227$	−18.0404	−	18.0404i	−1.19738	−	1.19738i	−0.222436	−	0.974947i	$-0.571401\pi$
$228$		0			0
$229$	−16.6213	−	16.6213i	−1.09837	−	1.09837i	−0.994602	−	0.103767i	$-0.966910\pi$
$229$	−16.6213	−	16.6213i	−1.09837	−	1.09837i	−0.103767	−	0.994602i	$-0.533090\pi$
$230$		0			0
$231$	−3.92975	+	1.47460i	−0.258559	+	0.0970216i
$232$		0			0
$233$		−	9.67000i		−	0.633503i	−0.948509	−	0.316751i	$-0.897408\pi$
$233$		−	9.67000i		−	0.633503i	0.948509	−	0.316751i	$-0.102592\pi$
$234$		0			0
$235$	2.24734	+	2.24734i	0.146600	+	0.146600i
$236$		0			0
$237$	−3.29156	+	3.29156i	−0.213810	+	0.213810i
$238$		0			0
$239$		−	22.0336i		−	1.42523i	−0.701553	−	0.712617i	$-0.747510\pi$
$239$		−	22.0336i		−	1.42523i	0.701553	−	0.712617i	$-0.252490\pi$
$240$		0			0
$241$		−	2.30808i		−	0.148676i	−0.997233	−	0.0743382i	$-0.976316\pi$
$241$		−	2.30808i		−	0.148676i	0.997233	−	0.0743382i	$-0.0236844\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$		0			0
$245$	10.5883	+	0.715110i	0.676461	+	0.0456867i
$246$		0			0
$247$	0.00559243			0.000355838
$248$		0			0
$249$			0.982823i			0.0622839i
$250$		0			0
$251$	1.88634	−	1.88634i	0.119065	−	0.119065i	−0.645064	−	0.764129i	$-0.723169\pi$
$251$	1.88634	−	1.88634i	0.119065	−	0.119065i	0.764129	+	0.645064i	$0.223169\pi$
$252$		0			0
$253$	−1.82261	−	1.82261i	−0.114586	−	0.114586i
$254$		0			0
$255$	7.47531			0.468122
$256$		0			0
$257$		−	3.19078i		−	0.199036i	−0.995036	−	0.0995178i	$-0.968270\pi$
$257$		−	3.19078i		−	0.199036i	0.995036	−	0.0995178i	$-0.0317300\pi$
$258$		0			0
$259$	22.8243	+	10.3689i	1.41823	+	0.644291i
$260$		0			0
$261$	3.69584	−	3.69584i	0.228767	−	0.228767i
$262$		0			0
$263$	20.1194			1.24061			0.620306	−	0.784360i	$-0.287008\pi$
$263$	20.1194			1.24061			0.620306	+	0.784360i	$0.287008\pi$
$264$		0			0
$265$	11.3231			0.695575
$266$		0			0
$267$	11.5922	+	11.5922i	0.709428	+	0.709428i
$268$		0			0
$269$	−16.4208	+	16.4208i	−1.00119	+	1.00119i	−0.00119219	+	0.999999i	$0.500379\pi$
$269$	−16.4208	+	16.4208i	−1.00119	+	1.00119i	−0.999999	+	0.00119219i	$0.999621\pi$
$270$		0			0
$271$	−30.3695			−1.84481			−0.922407	−	0.386218i	$-0.873781\pi$
$271$	−30.3695			−1.84481			−0.922407	+	0.386218i	$0.873781\pi$
$272$		0			0
$273$	−0.499944	−	1.33233i	−0.0302580	−	0.0806363i
$274$		0			0
$275$	3.03056	−	3.03056i	0.182750	−	0.182750i
$276$		0			0
$277$	20.2331	−	20.2331i	1.21569	−	1.21569i	0.246563	−	0.969127i	$-0.420699\pi$
$277$	20.2331	−	20.2331i	1.21569	−	1.21569i	0.969127	−	0.246563i	$-0.0793011\pi$
$278$		0			0
$279$		−	1.21242i		−	0.0725857i
$280$		0			0
$281$		−	28.4713i		−	1.69846i	−0.528026	−	0.849228i	$-0.677068\pi$
$281$		−	28.4713i		−	1.69846i	0.528026	−	0.849228i	$-0.322932\pi$
$282$		0			0
$283$	6.05298	−	6.05298i	0.359813	−	0.359813i	−0.503931	−	0.863744i	$-0.668114\pi$
$283$	6.05298	−	6.05298i	0.359813	−	0.359813i	0.863744	+	0.503931i	$0.168114\pi$
$284$		0			0
$285$	0.0111464	−	0.0111464i	0.000660253	−	0.000660253i
$286$		0			0
$287$	1.94075	+	5.17201i	0.114559	+	0.305294i
$288$		0			0
$289$	−7.31235			−0.430138
$290$		0			0
$291$	11.1789	−	11.1789i	0.655321	−	0.655321i
$292$		0			0
$293$	11.2656	+	11.2656i	0.658142	+	0.658142i	0.954940	−	0.296798i	$-0.0959189\pi$
$293$	11.2656	+	11.2656i	0.658142	+	0.658142i	−0.296798	+	0.954940i	$0.595919\pi$
$294$		0			0
$295$	20.1377			1.17246
$296$		0			0
$297$	1.58643			0.0920542
$298$		0			0
$299$	0.617930	−	0.617930i	0.0357358	−	0.0357358i
$300$		0			0
$301$	12.2165	−	26.8914i	0.704150	−	1.55000i
$302$		0			0
$303$			16.5382i			0.950097i
$304$		0			0
$305$	−5.25540			−0.300923
$306$		0			0
$307$	19.9262	+	19.9262i	1.13725	+	1.13725i	0.988942	+	0.148305i	$0.0473818\pi$
$307$	19.9262	+	19.9262i	1.13725	+	1.13725i	0.148305	+	0.988942i	$0.452618\pi$
$308$		0			0
$309$	−12.2031	+	12.2031i	−0.694212	+	0.694212i
$310$		0			0
$311$			8.15514i			0.462436i	0.972902	+	0.231218i	$0.0742710\pi$
$311$			8.15514i			0.462436i	−0.972902	+	0.231218i	$0.925729\pi$
$312$		0			0
$313$	−28.5813			−1.61551			−0.807754	−	0.589520i	$-0.799317\pi$
$313$	−28.5813			−1.61551			−0.807754	+	0.589520i	$0.799317\pi$
$314$		0			0
$315$	−3.65193	−	1.65904i	−0.205763	−	0.0934764i
$316$		0			0
$317$	−12.7765	−	12.7765i	−0.717599	−	0.717599i	0.250514	−	0.968113i	$-0.419400\pi$
$317$	−12.7765	−	12.7765i	−0.717599	−	0.717599i	−0.968113	+	0.250514i	$0.919400\pi$
$318$		0			0
$319$		−	8.29182i		−	0.464253i
$320$		0			0
$321$		−	0.687767i		−	0.0383874i
$322$		0			0
$323$	−0.0362519	+	0.0362519i	−0.00201711	+	0.00201711i
$324$		0			0
$325$	1.02747	+	1.02747i	0.0569938	+	0.0569938i
$326$		0			0
$327$		−	6.49505i		−	0.359177i
$328$		0			0
$329$	1.94859	+	5.19292i	0.107429	+	0.286295i
$330$		0			0
$331$	15.1140	+	15.1140i	0.830739	+	0.830739i	0.987618	−	0.156879i	$-0.0501432\pi$
$331$	15.1140	+	15.1140i	0.830739	+	0.830739i	−0.156879	+	0.987618i	$0.550143\pi$
$332$		0			0
$333$	−6.70001	−	6.70001i	−0.367159	−	0.367159i
$334$		0			0
$335$	10.0794			0.550694
$336$		0			0
$337$	−7.12166			−0.387942			−0.193971	−	0.981007i	$-0.562137\pi$
$337$	−7.12166			−0.387942			−0.193971	+	0.981007i	$0.562137\pi$
$338$		0			0
$339$	−11.6515	−	11.6515i	−0.632820	−	0.632820i
$340$		0			0
$341$	−1.36006	−	1.36006i	−0.0736516	−	0.0736516i
$342$		0			0
$343$	16.3073	+	8.77900i	0.880513	+	0.474021i
$344$		0			0
$345$		−	2.46321i		−	0.132615i
$346$		0			0
$347$	−0.263964	−	0.263964i	−0.0141704	−	0.0141704i	0.699986	−	0.714156i	$-0.253190\pi$
$347$	−0.263964	−	0.263964i	−0.0141704	−	0.0141704i	−0.714156	+	0.699986i	$0.753190\pi$
$348$		0			0
$349$	4.37893	−	4.37893i	0.234399	−	0.234399i	−0.580127	−	0.814526i	$-0.696997\pi$
$349$	4.37893	−	4.37893i	0.234399	−	0.234399i	0.814526	+	0.580127i	$0.196997\pi$
$350$		0			0
$351$			0.537859i			0.0287088i
$352$		0			0
$353$		−	16.9515i		−	0.902238i	−0.892464	−	0.451119i	$-0.851025\pi$
$353$		−	16.9515i		−	0.902238i	0.892464	−	0.451119i	$-0.148975\pi$
$354$		0			0
$355$	5.54181	+	5.54181i	0.294129	+	0.294129i
$356$		0			0
$357$	11.8774	+	5.39579i	0.628617	+	0.285575i
$358$		0			0
$359$	29.7322			1.56921			0.784603	−	0.619998i	$-0.212867\pi$
$359$	29.7322			1.56921			0.784603	+	0.619998i	$0.212867\pi$
$360$		0			0
$361$		−	18.9999i		−	0.999994i
$362$		0			0
$363$	−5.99855	+	5.99855i	−0.314842	+	0.314842i
$364$		0			0
$365$	−8.39751	−	8.39751i	−0.439546	−	0.439546i
$366$		0			0
$367$	−6.27534			−0.327570			−0.163785	−	0.986496i	$-0.552370\pi$
$367$	−6.27534			−0.327570			−0.163785	+	0.986496i	$0.552370\pi$
$368$		0			0
$369$		−	2.08793i		−	0.108693i
$370$		0			0
$371$	17.9911	+	8.17320i	0.934052	+	0.424332i
$372$		0			0
$373$	0.151895	−	0.151895i	0.00786483	−	0.00786483i	−0.703163	−	0.711028i	$-0.748230\pi$
$373$	0.151895	−	0.151895i	0.00786483	−	0.00786483i	0.711028	+	0.703163i	$0.248230\pi$
$374$		0			0
$375$	11.6760			0.602947
$376$		0			0
$377$	2.81123			0.144786
$378$		0			0
$379$	−12.6234	−	12.6234i	−0.648420	−	0.648420i	0.304191	−	0.952611i	$-0.401614\pi$
$379$	−12.6234	−	12.6234i	−0.648420	−	0.648420i	−0.952611	+	0.304191i	$0.901614\pi$
$380$		0			0
$381$	−8.36112	+	8.36112i	−0.428353	+	0.428353i
$382$		0			0
$383$	−21.5769			−1.10253			−0.551263	−	0.834331i	$-0.685854\pi$
$383$	−21.5769			−1.10253			−0.551263	+	0.834331i	$0.685854\pi$
$384$		0			0
$385$	−5.95773	+	2.23558i	−0.303634	+	0.113936i
$386$		0			0
$387$	−7.89391	+	7.89391i	−0.401270	+	0.401270i
$388$		0			0
$389$	−4.93088	+	4.93088i	−0.250006	+	0.250006i	−0.820973	−	0.570967i	$-0.806568\pi$
$389$	−4.93088	+	4.93088i	−0.250006	+	0.250006i	0.570967	+	0.820973i	$0.306568\pi$
$390$		0			0
$391$			8.01123i			0.405146i
$392$		0			0
$393$			13.7002i			0.691081i
$394$		0			0
$395$	−4.99020	+	4.99020i	−0.251084	+	0.251084i
$396$		0			0
$397$	21.5942	−	21.5942i	1.08378	−	1.08378i	0.0876282	−	0.996153i	$-0.472071\pi$
$397$	21.5942	−	21.5942i	1.08378	−	1.08378i	0.996153	−	0.0876282i	$-0.0279287\pi$
$398$		0			0
$399$	0.0257558	−	0.00966463i	0.00128940	−	0.000483837i
$400$		0			0
$401$	−8.58725			−0.428827			−0.214414	−	0.976743i	$-0.568784\pi$
$401$	−8.58725			−0.428827			−0.214414	+	0.976743i	$0.568784\pi$
$402$		0			0
$403$	0.461112	−	0.461112i	0.0229696	−	0.0229696i
$404$		0			0
$405$	1.07201	+	1.07201i	0.0532688	+	0.0532688i
$406$		0			0
$407$	−15.0318			−0.745101
$408$		0			0
$409$	6.59158			0.325933			0.162966	−	0.986632i	$-0.447894\pi$
$409$	6.59158			0.325933			0.162966	+	0.986632i	$0.447894\pi$
$410$		0			0
$411$	−0.451772	+	0.451772i	−0.0222843	+	0.0222843i
$412$		0			0
$413$	31.9965	+	14.5357i	1.57444	+	0.715256i
$414$		0			0
$415$			1.49002i			0.0731421i
$416$		0			0
$417$	−12.4268			−0.608542
$418$		0			0
$419$	−3.50670	−	3.50670i	−0.171313	−	0.171313i	0.616243	−	0.787556i	$-0.288654\pi$
$419$	−3.50670	−	3.50670i	−0.171313	−	0.171313i	−0.787556	+	0.616243i	$0.788654\pi$
$420$		0			0
$421$	12.7198	−	12.7198i	0.619924	−	0.619924i	−0.325588	−	0.945512i	$-0.605562\pi$
$421$	12.7198	−	12.7198i	0.619924	−	0.619924i	0.945512	+	0.325588i	$0.105562\pi$
$422$		0			0
$423$		−	2.09637i		−	0.101929i
$424$		0			0
$425$	−13.3208			−0.646152
$426$		0			0
$427$	−8.35019	−	3.79342i	−0.404094	−	0.183576i
$428$		0			0
$429$	0.603358	+	0.603358i	0.0291304	+	0.0291304i
$430$		0			0
$431$			35.1089i			1.69114i	0.533867	+	0.845568i	$0.320738\pi$
$431$			35.1089i			1.69114i	−0.533867	+	0.845568i	$0.679262\pi$
$432$		0			0
$433$			27.6070i			1.32671i	0.748306	+	0.663353i	$0.230867\pi$
$433$			27.6070i			1.32671i	−0.748306	+	0.663353i	$0.769133\pi$
$434$		0			0
$435$	5.60311	−	5.60311i	0.268649	−	0.268649i
$436$		0			0
$437$	0.0119455	+	0.0119455i	0.000571429	+	0.000571429i
$438$		0			0
$439$		−	18.3491i		−	0.875753i	−0.899035	−	0.437877i	$-0.855731\pi$
$439$		−	18.3491i		−	0.875753i	0.899035	−	0.437877i	$-0.144269\pi$
$440$		0			0
$441$	−4.60496	−	5.27203i	−0.219284	−	0.251049i
$442$		0			0
$443$	−14.7001	−	14.7001i	−0.698421	−	0.698421i	0.265649	−	0.964070i	$-0.414414\pi$
$443$	−14.7001	−	14.7001i	−0.698421	−	0.698421i	−0.964070	+	0.265649i	$0.914414\pi$
$444$		0			0
$445$	17.5744	+	17.5744i	0.833105	+	0.833105i
$446$		0			0
$447$	9.45774			0.447336
$448$		0			0
$449$	−5.70106			−0.269050			−0.134525	−	0.990910i	$-0.542951\pi$
$449$	−5.70106			−0.269050			−0.134525	+	0.990910i	$0.542951\pi$
$450$		0			0
$451$	−2.34219	−	2.34219i	−0.110290	−	0.110290i
$452$		0			0
$453$	8.27942	+	8.27942i	0.389001	+	0.389001i
$454$		0			0
$455$	−0.757944	−	2.01989i	−0.0355330	−	0.0946939i
$456$		0			0
$457$		−	8.58548i		−	0.401612i	−0.979631	−	0.200806i	$-0.935644\pi$
$457$		−	8.58548i		−	0.401612i	0.979631	−	0.200806i	$-0.0643561\pi$
$458$		0			0
$459$	−3.48657	−	3.48657i	−0.162739	−	0.162739i
$460$		0			0
$461$	−21.5957	+	21.5957i	−1.00581	+	1.00581i	−0.00582709	+	0.999983i	$0.501855\pi$
$461$	−21.5957	+	21.5957i	−1.00581	+	1.00581i	−0.999983	+	0.00582709i	$0.998145\pi$
$462$		0			0
$463$			22.5950i			1.05008i	0.851078	+	0.525039i	$0.175949\pi$
$463$			22.5950i			1.05008i	−0.851078	+	0.525039i	$0.824051\pi$
$464$		0			0
$465$		−	1.83810i		−	0.0852398i
$466$		0			0
$467$	7.33529	+	7.33529i	0.339437	+	0.339437i	0.856155	−	0.516719i	$-0.172847\pi$
$467$	7.33529	+	7.33529i	0.339437	+	0.339437i	−0.516719	+	0.856155i	$0.672847\pi$
$468$		0			0
$469$	16.0149	+	7.27542i	0.739499	+	0.335948i
$470$		0			0
$471$	−11.1321			−0.512940
$472$		0			0
$473$			17.7104i			0.814326i
$474$		0			0
$475$	−0.0198625	+	0.0198625i	−0.000911353	+	0.000911353i
$476$		0			0
$477$	−5.28124	−	5.28124i	−0.241811	−	0.241811i
$478$		0			0
$479$	30.2356			1.38150			0.690749	−	0.723095i	$-0.257281\pi$
$479$	30.2356			1.38150			0.690749	+	0.723095i	$0.257281\pi$
$480$		0			0
$481$		−	5.09635i		−	0.232374i
$482$		0			0
$483$	1.77798	−	3.91375i	0.0809010	−	0.178082i
$484$		0			0
$485$	16.9479	−	16.9479i	0.769565	−	0.769565i
$486$		0			0
$487$	−16.2232			−0.735144			−0.367572	−	0.929995i	$-0.619811\pi$
$487$	−16.2232			−0.735144			−0.367572	+	0.929995i	$0.619811\pi$
$488$		0			0
$489$	5.88675			0.266208
$490$		0			0
$491$	−14.8388	−	14.8388i	−0.669668	−	0.669668i	0.287971	−	0.957639i	$-0.407019\pi$
$491$	−14.8388	−	14.8388i	−0.669668	−	0.669668i	−0.957639	+	0.287971i	$0.907019\pi$
$492$		0			0
$493$	−18.2233	+	18.2233i	−0.820736	+	0.820736i
$494$		0			0
$495$	2.40512			0.108102
$496$		0			0
$497$	4.80511	+	12.8054i	0.215539	+	0.574402i
$498$		0			0
$499$	16.1057	−	16.1057i	0.720990	−	0.720990i	−0.247817	−	0.968807i	$-0.579713\pi$
$499$	16.1057	−	16.1057i	0.720990	−	0.720990i	0.968807	+	0.247817i	$0.0797132\pi$
$500$		0			0
$501$	3.61283	−	3.61283i	0.161409	−	0.161409i
$502$		0			0
$503$			6.58635i			0.293671i	0.989161	+	0.146835i	$0.0469088\pi$
$503$			6.58635i			0.293671i	−0.989161	+	0.146835i	$0.953091\pi$
$504$		0			0
$505$			25.0729i			1.11573i
$506$		0			0
$507$	8.98783	−	8.98783i	0.399163	−	0.399163i
$508$		0			0
$509$	22.6237	−	22.6237i	1.00278	−	1.00278i	0.00278262	−	0.999996i	$-0.499114\pi$
$509$	22.6237	−	22.6237i	1.00278	−	1.00278i	0.999996	−	0.00278262i	$-0.000885738\pi$
$510$		0			0
$511$	−7.28119	−	19.4041i	−0.322101	−	0.858385i
$512$		0			0
$513$	−0.0103976			−0.000459064
$514$		0			0
$515$	−18.5006	+	18.5006i	−0.815236	+	0.815236i
$516$		0			0
$517$	−2.35166	−	2.35166i	−0.103426	−	0.103426i
$518$		0			0
$519$	8.55419			0.375487
$520$		0			0
$521$	−4.23960			−0.185740			−0.0928701	−	0.995678i	$-0.529604\pi$
$521$	−4.23960			−0.185740			−0.0928701	+	0.995678i	$0.529604\pi$
$522$		0			0
$523$	−10.3026	+	10.3026i	−0.450501	+	0.450501i	−0.895521	−	0.445020i	$-0.853197\pi$
$523$	−10.3026	+	10.3026i	−0.450501	+	0.450501i	0.445020	+	0.895521i	$0.353197\pi$
$524$		0			0
$525$	6.50763	+	2.95636i	0.284016	+	0.129026i
$526$		0			0
$527$			5.97814i			0.260412i
$528$		0			0
$529$	−20.3602			−0.885226
$530$		0			0
$531$	−9.39247	−	9.39247i	−0.407599	−	0.407599i
$532$		0			0
$533$	0.794090	−	0.794090i	0.0343959	−	0.0343959i
$534$		0			0
$535$		−	1.04269i		−	0.0450796i
$536$		0			0
$537$	−16.0235			−0.691465
$538$		0			0
$539$	−11.0798	−	0.748305i	−0.477240	−	0.0322318i
$540$		0			0
$541$	12.0207	+	12.0207i	0.516810	+	0.516810i	0.916605	−	0.399795i	$-0.130919\pi$
$541$	12.0207	+	12.0207i	0.516810	+	0.516810i	−0.399795	+	0.916605i	$0.630919\pi$
$542$		0			0
$543$		−	4.42537i		−	0.189911i
$544$		0			0
$545$		−	9.84687i		−	0.421794i
$546$		0			0
$547$	−23.7257	+	23.7257i	−1.01444	+	1.01444i	−0.0145455	+	0.999894i	$0.504630\pi$
$547$	−23.7257	+	23.7257i	−1.01444	+	1.01444i	−0.999894	+	0.0145455i	$0.995370\pi$
$548$		0			0
$549$	2.45118	+	2.45118i	0.104614	+	0.104614i
$550$		0			0
$551$			0.0543451i			0.00231518i
$552$		0			0
$553$	−11.5308	+	4.32683i	−0.490341	+	0.183996i
$554$		0			0
$555$	−10.1576	−	10.1576i	−0.431167	−	0.431167i
$556$		0			0
$557$	−0.791262	−	0.791262i	−0.0335269	−	0.0335269i	0.690145	−	0.723671i	$-0.257547\pi$
$557$	−0.791262	−	0.791262i	−0.0335269	−	0.0335269i	−0.723671	+	0.690145i	$0.757547\pi$
$558$		0			0
$559$	−6.00449			−0.253963
$560$		0			0
$561$	−7.82231			−0.330258
$562$		0			0
$563$	−27.1409	−	27.1409i	−1.14385	−	1.14385i	−0.987739	−	0.156114i	$-0.950103\pi$
$563$	−27.1409	−	27.1409i	−1.14385	−	1.14385i	−0.156114	−	0.987739i	$-0.549897\pi$
$564$		0			0
$565$	−17.6643	−	17.6643i	−0.743142	−	0.743142i
$566$		0			0
$567$	0.929507	+	2.47710i	0.0390356	+	0.104028i
$568$		0			0
$569$			46.0744i			1.93154i	0.259403	+	0.965769i	$0.416474\pi$
$569$			46.0744i			1.93154i	−0.259403	+	0.965769i	$0.583526\pi$
$570$		0			0
$571$	−27.3445	−	27.3445i	−1.14433	−	1.14433i	−0.987649	−	0.156684i	$-0.949920\pi$
$571$	−27.3445	−	27.3445i	−1.14433	−	1.14433i	−0.156684	−	0.987649i	$-0.550080\pi$
$572$		0			0
$573$	−7.95597	+	7.95597i	−0.332365	+	0.332365i
$574$		0			0
$575$			4.38937i			0.183049i
$576$		0			0
$577$		−	6.45943i		−	0.268910i	−0.990920	−	0.134455i	$-0.957072\pi$
$577$		−	6.45943i		−	0.268910i	0.990920	−	0.134455i	$-0.0429283\pi$
$578$		0			0
$579$	−11.0339	−	11.0339i	−0.458555	−	0.458555i
$580$		0			0
$581$	−1.07552	+	2.36746i	−0.0446199	+	0.0982187i
$582$		0			0
$583$	−11.8488			−0.490725
$584$		0			0
$585$			0.815426i			0.0337137i
$586$		0			0
$587$	21.6920	−	21.6920i	0.895325	−	0.895325i	−0.0996934	−	0.995018i	$-0.531786\pi$
$587$	21.6920	−	21.6920i	0.895325	−	0.895325i	0.995018	+	0.0996934i	$0.0317862\pi$
$588$		0			0
$589$	0.00891395	+	0.00891395i	0.000367293	+	0.000367293i
$590$		0			0
$591$	−9.55275			−0.392948
$592$		0			0
$593$		−	33.5016i		−	1.37575i	−0.725831	−	0.687873i	$-0.758544\pi$
$593$		−	33.5016i		−	1.37575i	0.725831	−	0.687873i	$-0.241456\pi$
$594$		0			0
$595$	18.0068	+	8.18032i	0.738206	+	0.335361i
$596$		0			0
$597$	15.8847	−	15.8847i	0.650118	−	0.650118i
$598$		0			0
$599$	−2.91644			−0.119162			−0.0595812	−	0.998223i	$-0.518977\pi$
$599$	−2.91644			−0.119162			−0.0595812	+	0.998223i	$0.518977\pi$
$600$		0			0
$601$	4.37362			0.178404			0.0892018	−	0.996014i	$-0.471568\pi$
$601$	4.37362			0.178404			0.0892018	+	0.996014i	$0.471568\pi$
$602$		0			0
$603$	−4.70113	−	4.70113i	−0.191445	−	0.191445i
$604$		0			0
$605$	−9.09415	+	9.09415i	−0.369730	+	0.369730i
$606$		0			0
$607$	−29.8679			−1.21230			−0.606150	−	0.795350i	$-0.707287\pi$
$607$	−29.8679			−1.21230			−0.606150	+	0.795350i	$0.707287\pi$
$608$		0			0
$609$	12.9471	−	4.85827i	0.524642	−	0.196867i
$610$		0			0
$611$	0.797300	−	0.797300i	0.0322553	−	0.0322553i
$612$		0			0
$613$	4.86096	−	4.86096i	0.196333	−	0.196333i	−0.602093	−	0.798426i	$-0.705666\pi$
$613$	4.86096	−	4.86096i	0.196333	−	0.196333i	0.798426	+	0.602093i	$0.205666\pi$
$614$		0			0
$615$		−	3.16542i		−	0.127642i
$616$		0			0
$617$			3.74665i			0.150835i	0.997152	+	0.0754173i	$0.0240289\pi$
$617$			3.74665i			0.150835i	−0.997152	+	0.0754173i	$0.975971\pi$
$618$		0			0
$619$	19.0497	−	19.0497i	0.765671	−	0.765671i	−0.211670	−	0.977341i	$-0.567890\pi$
$619$	19.0497	−	19.0497i	0.765671	−	0.765671i	0.977341	+	0.211670i	$0.0678903\pi$
$620$		0			0
$621$	−1.14887	+	1.14887i	−0.0461026	+	0.0461026i
$622$		0			0
$623$	15.2381	+	40.6090i	0.610503	+	1.62697i
$624$		0			0
$625$	4.19369			0.167748
$626$		0			0
$627$	−0.0116638	+	0.0116638i	−0.000465806	+	0.000465806i
$628$		0			0
$629$	33.0361	+	33.0361i	1.31724	+	1.31724i
$630$		0			0
$631$	−28.4844			−1.13395			−0.566974	−	0.823736i	$-0.691886\pi$
$631$	−28.4844			−1.13395			−0.566974	+	0.823736i	$0.691886\pi$
$632$		0			0
$633$	5.32221			0.211539
$634$		0			0
$635$	−12.6759	+	12.6759i	−0.503029	+	0.503029i
$636$		0			0
$637$	0.253703	−	3.75646i	0.0100521	−	0.148836i
$638$		0			0
$639$		−	5.16953i		−	0.204503i
$640$		0			0
$641$	−23.3813			−0.923506			−0.461753	−	0.887009i	$-0.652779\pi$
$641$	−23.3813			−0.923506			−0.461753	+	0.887009i	$0.652779\pi$
$642$		0			0
$643$	−4.17454	−	4.17454i	−0.164628	−	0.164628i	0.619985	−	0.784613i	$-0.287138\pi$
$643$	−4.17454	−	4.17454i	−0.164628	−	0.164628i	−0.784613	+	0.619985i	$0.787138\pi$
$644$		0			0
$645$	−11.9676	+	11.9676i	−0.471225	+	0.471225i
$646$		0			0
$647$			17.1525i			0.674335i	0.941445	+	0.337168i	$0.109469\pi$
$647$			17.1525i			0.674335i	−0.941445	+	0.337168i	$0.890531\pi$
$648$		0			0
$649$	−21.0725			−0.827169
$650$		0			0
$651$	1.32677	−	2.92052i	0.0520000	−	0.114464i
$652$		0			0
$653$	6.83742	+	6.83742i	0.267569	+	0.267569i	0.828120	−	0.560551i	$-0.189411\pi$
$653$	6.83742	+	6.83742i	0.267569	+	0.267569i	−0.560551	+	0.828120i	$0.689411\pi$
$654$		0			0
$655$			20.7702i			0.811560i
$656$		0			0
$657$			7.83339i			0.305609i
$658$		0			0
$659$	18.8182	−	18.8182i	0.733054	−	0.733054i	−0.238170	−	0.971224i	$-0.576547\pi$
$659$	18.8182	−	18.8182i	0.733054	−	0.733054i	0.971224	+	0.238170i	$0.0765475\pi$
$660$		0			0
$661$	−23.9718	−	23.9718i	−0.932396	−	0.932396i	0.0654588	−	0.997855i	$-0.479149\pi$
$661$	−23.9718	−	23.9718i	−0.932396	−	0.932396i	−0.997855	+	0.0654588i	$0.979149\pi$
$662$		0			0
$663$		−	2.65205i		−	0.102997i
$664$		0			0
$665$	0.0390473	−	0.0146521i	0.00151419	−	0.000568185i
$666$		0			0
$667$	6.00481	+	6.00481i	0.232507	+	0.232507i
$668$		0			0
$669$	−9.95804	−	9.95804i	−0.385000	−	0.385000i
$670$		0			0
$671$	5.49935			0.212300
$672$		0			0
$673$	3.36157			0.129579			0.0647896	−	0.997899i	$-0.479362\pi$
$673$	3.36157			0.129579			0.0647896	+	0.997899i	$0.479362\pi$
$674$		0			0
$675$	−1.91030	−	1.91030i	−0.0735274	−	0.0735274i
$676$		0			0
$677$	−16.3331	−	16.3331i	−0.627731	−	0.627731i	0.319766	−	0.947497i	$-0.396396\pi$
$677$	−16.3331	−	16.3331i	−0.627731	−	0.627731i	−0.947497	+	0.319766i	$0.896396\pi$
$678$		0			0
$679$	39.1615	−	14.6950i	1.50288	−	0.563941i
$680$		0			0
$681$			25.5130i			0.977659i
$682$		0			0
$683$	6.36376	+	6.36376i	0.243503	+	0.243503i	0.818298	−	0.574795i	$-0.194918\pi$
$683$	6.36376	+	6.36376i	0.243503	+	0.243503i	−0.574795	+	0.818298i	$0.694918\pi$
$684$		0			0
$685$	−0.684912	+	0.684912i	−0.0261691	+	0.0261691i
$686$		0			0
$687$			23.5061i			0.896814i
$688$		0			0
$689$		−	4.01717i		−	0.153042i
$690$		0			0
$691$	5.76023	+	5.76023i	0.219129	+	0.219129i	0.808131	−	0.589002i	$-0.200479\pi$
$691$	5.76023	+	5.76023i	0.219129	+	0.219129i	−0.589002	+	0.808131i	$0.700479\pi$
$692$		0			0
$693$	3.82145	+	1.73605i	0.145165	+	0.0659472i
$694$		0			0
$695$	−18.8397			−0.714631
$696$		0			0
$697$			10.2951i			0.389954i
$698$		0			0
$699$	−6.83772	+	6.83772i	−0.258626	+	0.258626i
$700$		0			0
$701$	−2.52774	−	2.52774i	−0.0954714	−	0.0954714i	0.657758	−	0.753229i	$-0.271505\pi$
$701$	−2.52774	−	2.52774i	−0.0954714	−	0.0954714i	−0.753229	+	0.657758i	$0.771505\pi$
$702$		0			0
$703$	0.0985197			0.00371574
$704$		0			0
$705$		−	3.17822i		−	0.119699i
$706$		0			0
$707$	−18.0980	+	39.8379i	−0.680645	+	1.49826i
$708$		0			0
$709$	−25.4224	+	25.4224i	−0.954759	+	0.954759i	−0.999020	−	0.0442613i	$-0.985907\pi$
$709$	−25.4224	+	25.4224i	−0.954759	+	0.954759i	0.0442613	+	0.999020i	$0.485907\pi$
$710$		0			0
$711$	4.65497			0.174575
$712$		0			0
$713$	1.96988			0.0737724
$714$		0			0
$715$	0.914726	+	0.914726i	0.0342088	+	0.0342088i
$716$		0			0
$717$	−15.5801	+	15.5801i	−0.581849	+	0.581849i
$718$		0			0
$719$	−8.26294			−0.308156			−0.154078	−	0.988059i	$-0.549241\pi$
$719$	−8.26294			−0.308156			−0.154078	+	0.988059i	$0.549241\pi$
$720$		0			0
$721$	−42.7493	+	16.0413i	−1.59207	+	0.597408i
$722$		0			0
$723$	−1.63206	+	1.63206i	−0.0606969	+	0.0606969i
$724$		0			0
$725$	−9.98457	+	9.98457i	−0.370818	+	0.370818i
$726$		0			0
$727$			3.21095i			0.119087i	0.998226	+	0.0595437i	$0.0189646\pi$
$727$			3.21095i			0.119087i	−0.998226	+	0.0595437i	$0.981035\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	38.9230	−	38.9230i	1.43962	−	1.43962i
$732$		0			0
$733$	9.97638	−	9.97638i	0.368486	−	0.368486i	−0.498439	−	0.866925i	$-0.666093\pi$
$733$	9.97638	−	9.97638i	0.368486	−	0.368486i	0.866925	+	0.498439i	$0.166093\pi$
$734$		0			0
$735$	−6.98139	−	7.99271i	−0.257512	−	0.294815i
$736$		0			0
$737$	−10.5472			−0.388513
$738$		0			0
$739$	−14.7848	+	14.7848i	−0.543868	+	0.543868i	−0.924660	−	0.380793i	$-0.875651\pi$
$739$	−14.7848	+	14.7848i	−0.543868	+	0.543868i	0.380793	+	0.924660i	$0.375651\pi$
$740$		0			0
$741$	−0.00395445	−	0.00395445i	−0.000145270	−	0.000145270i
$742$		0			0
$743$	24.4950			0.898634			0.449317	−	0.893372i	$-0.351667\pi$
$743$	24.4950			0.898634			0.449317	+	0.893372i	$0.351667\pi$
$744$		0			0
$745$	14.3385			0.525322
$746$		0			0
$747$	0.694961	−	0.694961i	0.0254273	−	0.0254273i
$748$		0			0
$749$	0.752631	−	1.65672i	0.0275006	−	0.0605351i
$750$		0			0
$751$			9.30768i			0.339642i	0.985475	+	0.169821i	$0.0543190\pi$
$751$			9.30768i			0.339642i	−0.985475	+	0.169821i	$0.945681\pi$
$752$		0			0
$753$	−2.66769			−0.0972159
$754$		0			0
$755$	12.5521	+	12.5521i	0.456817	+	0.456817i
$756$		0			0
$757$	4.71911	−	4.71911i	0.171519	−	0.171519i	−0.616127	−	0.787647i	$-0.711299\pi$
$757$	4.71911	−	4.71911i	0.171519	−	0.171519i	0.787647	+	0.616127i	$0.211299\pi$
$758$		0			0
$759$			2.57755i			0.0935593i
$760$		0			0
$761$	6.21468			0.225282			0.112641	−	0.993636i	$-0.464069\pi$
$761$	6.21468			0.225282			0.112641	+	0.993636i	$0.464069\pi$
$762$		0			0
$763$	7.10761	−	15.6455i	0.257313	−	0.566405i
$764$		0			0
$765$	−5.28584	−	5.28584i	−0.191110	−	0.191110i
$766$		0			0
$767$		−	7.14436i		−	0.257968i
$768$		0			0
$769$		−	36.6035i		−	1.31995i	−0.751286	−	0.659977i	$-0.770566\pi$
$769$		−	36.6035i		−	1.31995i	0.751286	−	0.659977i	$-0.229434\pi$
$770$		0			0
$771$	−2.25622	+	2.25622i	−0.0812559	+	0.0812559i
$772$		0			0
$773$	14.9532	+	14.9532i	0.537831	+	0.537831i	0.922891	−	0.385061i	$-0.125819\pi$
$773$	14.9532	+	14.9532i	0.537831	+	0.537831i	−0.385061	+	0.922891i	$0.625819\pi$
$774$		0			0
$775$			3.27543i			0.117657i
$776$		0			0
$777$	−8.80731	−	23.4711i	−0.315961	−	0.842022i
$778$		0			0
$779$	0.0153509	+	0.0153509i	0.000550003	+	0.000550003i
$780$		0			0
$781$	−5.79906	−	5.79906i	−0.207507	−	0.207507i
$782$		0			0
$783$	−5.22671			−0.186787
$784$		0			0
$785$	−16.8769			−0.602363
$786$		0			0
$787$	−28.5199	−	28.5199i	−1.01662	−	1.01662i	−0.999859	−	0.0167646i	$-0.994663\pi$
$787$	−28.5199	−	28.5199i	−1.01662	−	1.01662i	−0.0167646	−	0.999859i	$-0.505337\pi$
$788$		0			0
$789$	−14.2265	−	14.2265i	−0.506478	−	0.506478i
$790$		0			0
$791$	−15.3161	−	40.8167i	−0.544577	−	1.45128i
$792$		0			0
$793$			1.86448i			0.0662097i
$794$		0			0
$795$	−8.00667	−	8.00667i	−0.283967	−	0.283967i
$796$		0			0
$797$	30.0556	−	30.0556i	1.06462	−	1.06462i	0.0668612	−	0.997762i	$-0.478702\pi$
$797$	30.0556	−	30.0556i	1.06462	−	1.06462i	0.997762	−	0.0668612i	$-0.0212985\pi$
$798$		0			0
$799$			10.3367i			0.365686i
$800$		0			0
$801$		−	16.3938i		−	0.579246i
$802$		0			0
$803$	8.78731	+	8.78731i	0.310098	+	0.310098i
$804$		0			0
$805$	2.69552	−	5.93347i	0.0950047	−	0.209127i
$806$		0			0
$807$	23.2225			0.817469
$808$		0			0
$809$			42.1631i			1.48238i	0.671297	+	0.741188i	$0.265737\pi$
$809$			42.1631i			1.48238i	−0.671297	+	0.741188i	$0.734263\pi$
$810$		0			0
$811$	−25.2514	+	25.2514i	−0.886696	+	0.886696i	−0.994204	−	0.107508i	$-0.965713\pi$
$811$	−25.2514	+	25.2514i	−0.886696	+	0.886696i	0.107508	+	0.994204i	$0.465713\pi$
$812$		0			0
$813$	21.4745	+	21.4745i	0.753142	+	0.753142i
$814$		0			0
$815$	8.92465			0.312617
$816$		0			0
$817$		−	0.116075i		−	0.00406096i
$818$		0			0
$819$	−0.588586	+	1.29561i	−0.0205669	+	0.0452724i
$820$		0			0
$821$	20.8479	−	20.8479i	0.727597	−	0.727597i	−0.242544	−	0.970140i	$-0.577982\pi$
$821$	20.8479	−	20.8479i	0.727597	−	0.727597i	0.970140	+	0.242544i	$0.0779818\pi$
$822$		0			0
$823$	−22.9417			−0.799696			−0.399848	−	0.916582i	$-0.630937\pi$
$823$	−22.9417			−0.799696			−0.399848	+	0.916582i	$0.630937\pi$
$824$		0			0
$825$	−4.28586			−0.149214
$826$		0			0
$827$	−16.6173	−	16.6173i	−0.577841	−	0.577841i	0.356467	−	0.934308i	$-0.383981\pi$
$827$	−16.6173	−	16.6173i	−0.577841	−	0.577841i	−0.934308	+	0.356467i	$0.883981\pi$
$828$		0			0
$829$	−37.4650	+	37.4650i	−1.30121	+	1.30121i	−0.373641	+	0.927573i	$0.621891\pi$
$829$	−37.4650	+	37.4650i	−1.30121	+	1.30121i	−0.927573	+	0.373641i	$0.878109\pi$
$830$		0			0
$831$	−28.6139			−0.992606
$832$		0			0
$833$	22.7059	+	25.9951i	0.786714	+	0.900677i
$834$		0			0
$835$	5.47725	−	5.47725i	0.189548	−	0.189548i
$836$		0			0
$837$	−0.857310	+	0.857310i	−0.0296330	+	0.0296330i
$838$		0			0
$839$			46.1798i			1.59431i	0.603778	+	0.797153i	$0.293661\pi$
$839$			46.1798i			1.59431i	−0.603778	+	0.797153i	$0.706339\pi$
$840$		0			0
$841$		−	1.68150i		−	0.0579827i
$842$		0			0
$843$	−20.1323	+	20.1323i	−0.693392	+	0.693392i
$844$		0			0
$845$	13.6261	−	13.6261i	0.468751	−	0.468751i
$846$		0			0
$847$	−21.0138	+	7.88523i	−0.722043	+	0.270940i
$848$		0			0
$849$	−8.56021			−0.293786
$850$		0			0
$851$	10.8858	−	10.8858i	0.373162	−	0.373162i
$852$		0			0
$853$	−12.7966	−	12.7966i	−0.438147	−	0.438147i	0.453241	−	0.891388i	$-0.350268\pi$
$853$	−12.7966	−	12.7966i	−0.438147	−	0.438147i	−0.891388	+	0.453241i	$0.850268\pi$
$854$		0			0
$855$	−0.0157633			−0.000539095
$856$		0			0
$857$	50.6120			1.72887			0.864437	−	0.502741i	$-0.167675\pi$
$857$	50.6120			1.72887			0.864437	+	0.502741i	$0.167675\pi$
$858$		0			0
$859$	18.5878	−	18.5878i	0.634209	−	0.634209i	−0.314912	−	0.949121i	$-0.601975\pi$
$859$	18.5878	−	18.5878i	0.634209	−	0.634209i	0.949121	+	0.314912i	$0.101975\pi$
$860$		0			0
$861$	2.28485	−	5.02948i	0.0778674	−	0.171404i
$862$		0			0
$863$			11.9291i			0.406072i	0.979171	+	0.203036i	$0.0650809\pi$
$863$			11.9291i			0.406072i	−0.979171	+	0.203036i	$0.934919\pi$
$864$		0			0
$865$	12.9686			0.440947
$866$		0			0
$867$	5.17061	+	5.17061i	0.175603	+	0.175603i
$868$		0			0
$869$	5.22184	−	5.22184i	0.177139	−	0.177139i
$870$		0			0
$871$		−	3.57590i		−	0.121165i
$872$		0			0
$873$	−15.8094			−0.535067
$874$		0			0
$875$	28.1256	+	12.7772i	0.950819	+	0.431949i
$876$		0			0
$877$	0.656007	+	0.656007i	0.0221518	+	0.0221518i	0.718096	−	0.695944i	$-0.245014\pi$
$877$	0.656007	+	0.656007i	0.0221518	+	0.0221518i	−0.695944	+	0.718096i	$0.745014\pi$
$878$		0			0
$879$		−	15.9319i		−	0.537371i
$880$		0			0
$881$		−	25.1066i		−	0.845862i	−0.906162	−	0.422931i	$-0.861001\pi$
$881$		−	25.1066i		−	0.845862i	0.906162	−	0.422931i	$-0.138999\pi$
$882$		0			0
$883$	−23.0181	+	23.0181i	−0.774622	+	0.774622i	−0.978911	−	0.204289i	$-0.934512\pi$
$883$	−23.0181	+	23.0181i	−0.774622	+	0.774622i	0.204289	+	0.978911i	$0.434512\pi$
$884$		0			0
$885$	−14.2395	−	14.2395i	−0.478657	−	0.478657i
$886$		0			0
$887$		−	35.2156i		−	1.18243i	−0.806516	−	0.591213i	$-0.798649\pi$
$887$		−	35.2156i		−	1.18243i	0.806516	−	0.591213i	$-0.201351\pi$
$888$		0			0
$889$	−29.2902	+	10.9909i	−0.982362	+	0.368622i
$890$		0			0
$891$	−1.12178	−	1.12178i	−0.0375810	−	0.0375810i
$892$		0			0
$893$	0.0154129	+	0.0154129i	0.000515774	+	0.000515774i
$894$		0			0
$895$	−24.2925			−0.812010
$896$		0			0
$897$	−0.873886			−0.0291782
$898$		0			0
$899$	4.48091	+	4.48091i	0.149447	+	0.149447i
$900$		0			0
$901$	26.0405	+	26.0405i	0.867535	+	0.867535i
$902$		0			0
$903$	−27.6535	+	10.3767i	−0.920252	+	0.345316i
$904$		0			0
$905$		−	6.70912i		−	0.223019i
$906$		0			0
$907$	−1.59277	−	1.59277i	−0.0528870	−	0.0528870i	0.680169	−	0.733056i	$-0.261907\pi$
$907$	−1.59277	−	1.59277i	−0.0528870	−	0.0528870i	−0.733056	+	0.680169i	$0.761907\pi$
$908$		0			0
$909$	11.6943	−	11.6943i	0.387876	−	0.387876i
$910$		0			0
$911$		−	19.7779i		−	0.655273i	−0.944804	−	0.327636i	$-0.893748\pi$
$911$		−	19.7779i		−	0.655273i	0.944804	−	0.327636i	$-0.106252\pi$
$912$		0			0
$913$		−	1.55918i		−	0.0516014i
$914$		0			0
$915$	3.71613	+	3.71613i	0.122851	+	0.122851i
$916$		0			0
$917$	−14.9922	+	33.0014i	−0.495088	+	1.08980i
$918$		0			0
$919$	−13.7184			−0.452528			−0.226264	−	0.974066i	$-0.572651\pi$
$919$	−13.7184			−0.452528			−0.226264	+	0.974066i	$0.572651\pi$
$920$		0			0
$921$		−	28.1799i		−	0.928558i
$922$		0			0
$923$	1.96609	−	1.96609i	0.0647148	−	0.0647148i
$924$		0			0
$925$	18.1005	+	18.1005i	0.595142	+	0.595142i
$926$		0			0
$927$	17.2578			0.566821
$928$		0			0
$929$			37.2406i			1.22182i	0.791698	+	0.610912i	$0.209197\pi$
$929$			37.2406i			1.22182i	−0.791698	+	0.610912i	$0.790803\pi$
$930$		0			0
$931$	0.0726176	+	0.00490444i	0.00237995	+	0.000160736i
$932$		0			0
$933$	5.76655	−	5.76655i	0.188789	−	0.188789i
$934$		0			0
$935$	−11.8591			−0.387833
$936$		0			0
$937$	13.5853			0.443813			0.221906	−	0.975068i	$-0.428772\pi$
$937$	13.5853			0.443813			0.221906	+	0.975068i	$0.428772\pi$
$938$		0			0
$939$	20.2100	+	20.2100i	0.659528	+	0.659528i
$940$		0			0
$941$	−18.5023	+	18.5023i	−0.603158	+	0.603158i	−0.941149	−	0.337991i	$-0.890253\pi$
$941$	−18.5023	+	18.5023i	−0.603158	+	0.603158i	0.337991	+	0.941149i	$0.390253\pi$
$942$		0			0
$943$	3.39236			0.110471
$944$		0			0
$945$	1.40919	+	3.75542i	0.0458409	+	0.122164i
$946$		0			0
$947$	−1.34969	+	1.34969i	−0.0438590	+	0.0438590i	−0.728696	−	0.684837i	$-0.759873\pi$
$947$	−1.34969	+	1.34969i	−0.0438590	+	0.0438590i	0.684837	+	0.728696i	$0.259873\pi$
$948$		0			0
$949$	−2.97922	+	2.97922i	−0.0967097	+	0.0967097i
$950$		0			0
$951$			18.0687i			0.585917i
$952$		0			0
$953$		−	42.8779i		−	1.38895i	−0.719516	−	0.694476i	$-0.755636\pi$
$953$		−	42.8779i		−	1.38895i	0.719516	−	0.694476i	$-0.244364\pi$
$954$		0			0
$955$	−12.0617	+	12.0617i	−0.390308	+	0.390308i
$956$		0			0
$957$	−5.86320	+	5.86320i	−0.189530	+	0.189530i
$958$		0			0
$959$	−1.58262	+	0.593864i	−0.0511055	+	0.0191769i
$960$		0			0
$961$	−29.5300			−0.952582
$962$		0			0
$963$	−0.486324	+	0.486324i	−0.0156716	+	0.0156716i
$964$		0			0
$965$	−16.7281	−	16.7281i	−0.538496	−	0.538496i
$966$		0			0
$967$	51.9878			1.67181			0.835907	−	0.548871i	$-0.184942\pi$
$967$	51.9878			1.67181			0.835907	+	0.548871i	$0.184942\pi$
$968$		0			0
$969$	0.0512679			0.00164696
$970$		0			0
$971$	−0.444804	+	0.444804i	−0.0142744	+	0.0142744i	−0.714208	−	0.699934i	$-0.753213\pi$
$971$	−0.444804	+	0.444804i	−0.0142744	+	0.0142744i	0.699934	+	0.714208i	$0.253213\pi$
$972$		0			0
$973$	−29.9340	−	13.5988i	−0.959641	−	0.435956i
$974$		0			0
$975$		−	1.45306i		−	0.0465353i
$976$		0			0
$977$	−8.31426			−0.265997			−0.132998	−	0.991116i	$-0.542461\pi$
$977$	−8.31426			−0.265997			−0.132998	+	0.991116i	$0.542461\pi$
$978$		0			0
$979$	−18.3902	−	18.3902i	−0.587752	−	0.587752i
$980$		0			0
$981$	−4.59269	+	4.59269i	−0.146633	+	0.146633i
$982$		0			0
$983$			20.8780i			0.665903i	0.942944	+	0.332952i	$0.108045\pi$
$983$			20.8780i			0.665903i	−0.942944	+	0.332952i	$0.891955\pi$
$984$		0			0
$985$	−14.4825			−0.461452
$986$		0			0
$987$	2.29409	−	5.04981i	0.0730215	−	0.160737i
$988$		0			0
$989$	−12.8256	−	12.8256i	−0.407831	−	0.407831i
$990$		0			0
$991$		−	36.7988i		−	1.16895i	−0.811411	−	0.584476i	$-0.801300\pi$
$991$		−	36.7988i		−	1.16895i	0.811411	−	0.584476i	$-0.198700\pi$
$992$		0			0
$993$		−	21.3744i		−	0.678296i
$994$		0			0
$995$	24.0821	−	24.0821i	0.763455	−	0.763455i
$996$		0			0
$997$	14.9272	+	14.9272i	0.472748	+	0.472748i	0.902803	−	0.430055i	$-0.141506\pi$
$997$	14.9272	+	14.9272i	0.472748	+	0.472748i	−0.430055	+	0.902803i	$0.641506\pi$
$998$		0			0
$999$			9.47525i			0.299784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.u.a.559.7		64
4.3	odd	2		336.2.u.a.307.32	yes	64
7.6	odd	2	inner	1344.2.u.a.559.26		64
16.5	even	4		336.2.u.a.139.31	✓	64
16.11	odd	4	inner	1344.2.u.a.1231.26		64
28.27	even	2		336.2.u.a.307.31	yes	64
112.27	even	4	inner	1344.2.u.a.1231.7		64
112.69	odd	4		336.2.u.a.139.32	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.31	✓	64	16.5	even	4
336.2.u.a.139.32	yes	64	112.69	odd	4
336.2.u.a.307.31	yes	64	28.27	even	2
336.2.u.a.307.32	yes	64	4.3	odd	2
1344.2.u.a.559.7		64	1.1	even	1	trivial
1344.2.u.a.559.26		64	7.6	odd	2	inner
1344.2.u.a.1231.7		64	112.27	even	4	inner
1344.2.u.a.1231.26		64	16.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.u (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.07201 - 1.07201i) q^{5} +(-0.929507 - 2.47710i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +(-1.07201 - 1.07201i) q^{5} +(-0.929507 - 2.47710i) q^{7} +1.00000i q^{9} +(1.12178 + 1.12178i) q^{11} +(-0.380324 + 0.380324i) q^{13} +1.51606i q^{15} -4.93076i q^{17} +(-0.00735220 - 0.00735220i) q^{19} +(-1.09431 + 2.40883i) q^{21} -1.62475 q^{23} -2.70157i q^{25} +(0.707107 - 0.707107i) q^{27} +(-3.69584 - 3.69584i) q^{29} -1.21242 q^{31} -1.58643i q^{33} +(-1.65904 + 3.65193i) q^{35} +(-6.70001 + 6.70001i) q^{37} +0.537859 q^{39} -2.08793 q^{41} +(7.89391 + 7.89391i) q^{43} +(1.07201 - 1.07201i) q^{45} -2.09637 q^{47} +(-5.27203 + 4.60496i) q^{49} +(-3.48657 + 3.48657i) q^{51} +(-5.28124 + 5.28124i) q^{53} -2.40512i q^{55} +0.0103976i q^{57} +(-9.39247 + 9.39247i) q^{59} +(2.45118 - 2.45118i) q^{61} +(2.47710 - 0.929507i) q^{63} +0.815426 q^{65} +(-4.70113 + 4.70113i) q^{67} +(1.14887 + 1.14887i) q^{69} -5.16953 q^{71} +7.83339 q^{73} +(-1.91030 + 1.91030i) q^{75} +(1.73605 - 3.82145i) q^{77} -4.65497i q^{79} -1.00000 q^{81} +(-0.694961 - 0.694961i) q^{83} +(-5.28584 + 5.28584i) q^{85} +5.22671i q^{87} -16.3938 q^{89} +(1.29561 + 0.588586i) q^{91} +(0.857310 + 0.857310i) q^{93} +0.0157633i q^{95} +15.8094i q^{97} +(-1.12178 + 1.12178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99}+O(q^{100}) \) 64 * q - 8 * q^11 + 16 * q^23 + 16 * q^29 - 24 * q^35 + 16 * q^37 + 8 * q^43 + 16 * q^53 - 56 * q^67 + 128 * q^71 - 64 * q^81 - 8 * q^91 + 8 * q^99

Introduction

L-functions

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