LMFDB - Embedded newform 1380.2.r.c.737.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(737,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("1380.737");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.r (of order $4$, degree $2$, 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:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.17
Character	$\chi$	$=$	1380.737
Dual form			1380.2.r.c.1013.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.118851 - 1.72797i) q^{3} +(0.238514 + 2.22331i) q^{5} +(2.86460 + 2.86460i) q^{7} +(-2.97175 + 0.410741i) q^{9} +O(q^{10})$	\(q+(-0.118851 - 1.72797i) q^{3} +(0.238514 + 2.22331i) q^{5} +(2.86460 + 2.86460i) q^{7} +(-2.97175 + 0.410741i) q^{9} +0.979600i q^{11} +(-0.371384 + 0.371384i) q^{13} +(3.81346 - 0.676387i) q^{15} +(-2.74647 + 2.74647i) q^{17} -0.0365351i q^{19} +(4.60948 - 5.29040i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-4.88622 + 1.06058i) q^{25} +(1.06294 + 5.08627i) q^{27} -8.55018 q^{29} -4.25537 q^{31} +(1.69272 - 0.116426i) q^{33} +(-5.68565 + 7.05214i) q^{35} +(1.18118 + 1.18118i) q^{37} +(0.685879 + 0.597600i) q^{39} +3.46350i q^{41} +(-8.36498 + 8.36498i) q^{43} +(-1.62201 - 6.50915i) q^{45} +(4.20045 - 4.20045i) q^{47} +9.41186i q^{49} +(5.07223 + 4.41939i) q^{51} +(-4.49366 - 4.49366i) q^{53} +(-2.17796 + 0.233648i) q^{55} +(-0.0631315 + 0.00434223i) q^{57} +2.38445 q^{59} +12.8261 q^{61} +(-9.68948 - 7.33626i) q^{63} +(-0.914281 - 0.737121i) q^{65} +(-4.68784 - 4.68784i) q^{67} +(1.13782 - 1.30590i) q^{69} +15.3783i q^{71} +(8.21790 - 8.21790i) q^{73} +(2.41338 + 8.31719i) q^{75} +(-2.80616 + 2.80616i) q^{77} -9.27494i q^{79} +(8.66258 - 2.44124i) q^{81} +(3.54552 + 3.54552i) q^{83} +(-6.76132 - 5.45118i) q^{85} +(1.01620 + 14.7744i) q^{87} +8.84660 q^{89} -2.12773 q^{91} +(0.505755 + 7.35315i) q^{93} +(0.0812288 - 0.00871412i) q^{95} +(3.88352 + 3.88352i) q^{97} +(-0.402362 - 2.91113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{3}+O(q^{10}) $ 80 * q + 8 * q^3	$ 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) $ 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$1$

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
$3$	−0.118851	−	1.72797i	−0.0686186	−	0.997643i
$3$	−0.118851	−	1.72797i	−0.0686186	−	0.997643i
$4$		0			0
$5$	0.238514	+	2.22331i	0.106667	+	0.994295i
$5$	0.238514	+	2.22331i	0.106667	+	0.994295i
$6$		0			0
$7$	2.86460	+	2.86460i	1.08272	+	1.08272i	0.996255	+	0.0864618i	$0.0275561\pi$
$7$	2.86460	+	2.86460i	1.08272	+	1.08272i	0.0864618	+	0.996255i	$0.472444\pi$
$8$		0			0
$9$	−2.97175	+	0.410741i	−0.990583	+	0.136914i
$10$		0			0
$11$			0.979600i			0.295361i	0.989035	+	0.147680i	$0.0471807\pi$
$11$			0.979600i			0.295361i	−0.989035	+	0.147680i	$0.952819\pi$
$12$		0			0
$13$	−0.371384	+	0.371384i	−0.103003	+	0.103003i	−0.756730	−	0.653727i	$-0.773204\pi$
$13$	−0.371384	+	0.371384i	−0.103003	+	0.103003i	0.653727	+	0.756730i	$0.273204\pi$
$14$		0			0
$15$	3.81346	−	0.676387i	0.984632	−	0.174642i
$16$		0			0
$17$	−2.74647	+	2.74647i	−0.666116	+	0.666116i	−0.956815	−	0.290699i	$-0.906112\pi$
$17$	−2.74647	+	2.74647i	−0.666116	+	0.666116i	0.290699	+	0.956815i	$0.406112\pi$
$18$		0			0
$19$		−	0.0365351i		−	0.00838172i	−0.999991	−	0.00419086i	$-0.998666\pi$
$19$		−	0.0365351i		−	0.00838172i	0.999991	−	0.00419086i	$-0.00133400\pi$
$20$		0			0
$21$	4.60948	−	5.29040i	1.00587	−	1.15446i
$22$		0			0
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$23$	0.707107	+	0.707107i	0.147442	+	0.147442i
$24$		0			0
$25$	−4.88622	+	1.06058i	−0.977244	+	0.212116i
$26$		0			0
$27$	1.06294	+	5.08627i	0.204564	+	0.978853i
$28$		0			0
$29$	−8.55018			−1.58773			−0.793864	−	0.608095i	$-0.791934\pi$
$29$	−8.55018			−1.58773			−0.793864	+	0.608095i	$0.791934\pi$
$30$		0			0
$31$	−4.25537			−0.764287			−0.382144	−	0.924103i	$-0.624814\pi$
$31$	−4.25537			−0.764287			−0.382144	+	0.924103i	$0.624814\pi$
$32$		0			0
$33$	1.69272	−	0.116426i	0.294664	−	0.0202672i
$34$		0			0
$35$	−5.68565	+	7.05214i	−0.961050	+	1.19203i
$36$		0			0
$37$	1.18118	+	1.18118i	0.194184	+	0.194184i	0.797501	−	0.603317i	$-0.206155\pi$
$37$	1.18118	+	1.18118i	0.194184	+	0.194184i	−0.603317	+	0.797501i	$0.706155\pi$
$38$		0			0
$39$	0.685879	+	0.597600i	0.109828	+	0.0956926i
$40$		0			0
$41$			3.46350i			0.540908i	0.962733	+	0.270454i	$0.0871738\pi$
$41$			3.46350i			0.540908i	−0.962733	+	0.270454i	$0.912826\pi$
$42$		0			0
$43$	−8.36498	+	8.36498i	−1.27565	+	1.27565i	−0.332568	+	0.943079i	$0.607915\pi$
$43$	−8.36498	+	8.36498i	−1.27565	+	1.27565i	−0.943079	+	0.332568i	$0.892085\pi$
$44$		0			0
$45$	−1.62201	−	6.50915i	−0.241795	−	0.970327i
$46$		0			0
$47$	4.20045	−	4.20045i	0.612699	−	0.612699i	−0.330949	−	0.943648i	$-0.607369\pi$
$47$	4.20045	−	4.20045i	0.612699	−	0.612699i	0.943648	+	0.330949i	$0.107369\pi$
$48$		0			0
$49$			9.41186i			1.34455i
$50$		0			0
$51$	5.07223	+	4.41939i	0.710254	+	0.618838i
$52$		0			0
$53$	−4.49366	−	4.49366i	−0.617252	−	0.617252i	0.327574	−	0.944826i	$-0.393769\pi$
$53$	−4.49366	−	4.49366i	−0.617252	−	0.617252i	−0.944826	+	0.327574i	$0.893769\pi$
$54$		0			0
$55$	−2.17796	+	0.233648i	−0.293676	+	0.0315051i
$56$		0			0
$57$	−0.0631315	+	0.00434223i	−0.00836197	+	0.000575142i
$58$		0			0
$59$	2.38445			0.310429			0.155214	−	0.987881i	$-0.450393\pi$
$59$	2.38445			0.310429			0.155214	+	0.987881i	$0.450393\pi$
$60$		0			0
$61$	12.8261			1.64221			0.821104	−	0.570779i	$-0.193359\pi$
$61$	12.8261			1.64221			0.821104	+	0.570779i	$0.193359\pi$
$62$		0			0
$63$	−9.68948	−	7.33626i	−1.22076	−	0.924282i
$64$		0			0
$65$	−0.914281	−	0.737121i	−0.113403	−	0.0914286i
$66$		0			0
$67$	−4.68784	−	4.68784i	−0.572711	−	0.572711i	0.360174	−	0.932885i	$-0.382717\pi$
$67$	−4.68784	−	4.68784i	−0.572711	−	0.572711i	−0.932885	+	0.360174i	$0.882717\pi$
$68$		0			0
$69$	1.13782	−	1.30590i	0.136977	−	0.157212i
$70$		0			0
$71$			15.3783i			1.82507i	0.408998	+	0.912535i	$0.365878\pi$
$71$			15.3783i			1.82507i	−0.408998	+	0.912535i	$0.634122\pi$
$72$		0			0
$73$	8.21790	−	8.21790i	0.961833	−	0.961833i	−0.0374653	−	0.999298i	$-0.511928\pi$
$73$	8.21790	−	8.21790i	0.961833	−	0.961833i	0.999298	+	0.0374653i	$0.0119284\pi$
$74$		0			0
$75$	2.41338	+	8.31719i	0.278673	+	0.960386i
$76$		0			0
$77$	−2.80616	+	2.80616i	−0.319792	+	0.319792i
$78$		0			0
$79$		−	9.27494i		−	1.04351i	−0.853095	−	0.521756i	$-0.825277\pi$
$79$		−	9.27494i		−	1.04351i	0.853095	−	0.521756i	$-0.174723\pi$
$80$		0			0
$81$	8.66258	−	2.44124i	0.962509	−	0.271249i
$82$		0			0
$83$	3.54552	+	3.54552i	0.389171	+	0.389171i	0.874392	−	0.485220i	$-0.161261\pi$
$83$	3.54552	+	3.54552i	0.389171	+	0.389171i	−0.485220	+	0.874392i	$0.661261\pi$
$84$		0			0
$85$	−6.76132	−	5.45118i	−0.733368	−	0.591263i
$86$		0			0
$87$	1.01620	+	14.7744i	0.108948	+	1.58399i
$88$		0			0
$89$	8.84660			0.937738			0.468869	−	0.883268i	$-0.344662\pi$
$89$	8.84660			0.937738			0.468869	+	0.883268i	$0.344662\pi$
$90$		0			0
$91$	−2.12773			−0.223047
$92$		0			0
$93$	0.505755	+	7.35315i	0.0524443	+	0.762486i
$94$		0			0
$95$	0.0812288	−	0.00871412i	0.00833390	−	0.000894050i
$96$		0			0
$97$	3.88352	+	3.88352i	0.394312	+	0.394312i	0.876221	−	0.481909i	$-0.160056\pi$
$97$	3.88352	+	3.88352i	0.394312	+	0.394312i	−0.481909	+	0.876221i	$0.660056\pi$
$98$		0			0
$99$	−0.402362	−	2.91113i	−0.0404389	−	0.292579i
$100$		0			0
$101$			3.75009i			0.373148i	0.982441	+	0.186574i	$0.0597385\pi$
$101$			3.75009i			0.373148i	−0.982441	+	0.186574i	$0.940262\pi$
$102$		0			0
$103$	−1.78704	+	1.78704i	−0.176082	+	0.176082i	−0.789646	−	0.613563i	$-0.789736\pi$
$103$	−1.78704	+	1.78704i	−0.176082	+	0.176082i	0.613563	+	0.789646i	$0.289736\pi$
$104$		0			0
$105$	12.8616	+	8.98647i	1.25517	+	0.876989i
$106$		0			0
$107$	4.78625	−	4.78625i	0.462704	−	0.462704i	−0.436837	−	0.899541i	$-0.643901\pi$
$107$	4.78625	−	4.78625i	0.462704	−	0.462704i	0.899541	+	0.436837i	$0.143901\pi$
$108$		0			0
$109$			7.69227i			0.736786i	0.929670	+	0.368393i	$0.120092\pi$
$109$			7.69227i			0.736786i	−0.929670	+	0.368393i	$0.879908\pi$
$110$		0			0
$111$	1.90065	−	2.18142i	0.180402	−	0.207051i
$112$		0			0
$113$	5.63596	+	5.63596i	0.530186	+	0.530186i	0.920628	−	0.390441i	$-0.127678\pi$
$113$	5.63596	+	5.63596i	0.530186	+	0.530186i	−0.390441	+	0.920628i	$0.627678\pi$
$114$		0			0
$115$	−1.40346	+	1.74077i	−0.130874	+	0.162328i
$116$		0			0
$117$	0.951116	−	1.25620i	0.0879307	−	0.116136i
$118$		0			0
$119$	−15.7351			−1.44243
$120$		0			0
$121$	10.0404			0.912762
$122$		0			0
$123$	5.98482	−	0.411641i	0.539633	−	0.0371164i
$124$		0			0
$125$	−3.52343	−	10.6106i	−0.315145	−	0.949043i
$126$		0			0
$127$	8.01054	+	8.01054i	0.710820	+	0.710820i	0.966707	−	0.255886i	$-0.0823673\pi$
$127$	8.01054	+	8.01054i	0.710820	+	0.710820i	−0.255886	+	0.966707i	$0.582367\pi$
$128$		0			0
$129$	15.4486	+	13.4602i	1.36017	+	1.18511i
$130$		0			0
$131$		−	3.22086i		−	0.281408i	−0.990052	−	0.140704i	$-0.955063\pi$
$131$		−	3.22086i		−	0.281408i	0.990052	−	0.140704i	$-0.0449366\pi$
$132$		0			0
$133$	0.104658	−	0.104658i	0.00907503	−	0.00907503i
$134$		0			0
$135$	−11.0548	+	3.57640i	−0.951449	+	0.307807i
$136$		0			0
$137$	8.37811	−	8.37811i	0.715790	−	0.715790i	−0.251950	−	0.967740i	$-0.581072\pi$
$137$	8.37811	−	8.37811i	0.715790	−	0.715790i	0.967740	+	0.251950i	$0.0810718\pi$
$138$		0			0
$139$			21.3432i			1.81031i	0.425083	+	0.905154i	$0.360245\pi$
$139$			21.3432i			1.81031i	−0.425083	+	0.905154i	$0.639755\pi$
$140$		0			0
$141$	−7.75748	−	6.75902i	−0.653297	−	0.569212i
$142$		0			0
$143$	−0.363808	−	0.363808i	−0.0304231	−	0.0304231i
$144$		0			0
$145$	−2.03934	−	19.0097i	−0.169358	−	1.57867i
$146$		0			0
$147$	16.2634	−	1.11861i	1.34138	−	0.0922613i
$148$		0			0
$149$	18.6662			1.52920			0.764598	−	0.644508i	$-0.222938\pi$
$149$	18.6662			1.52920			0.764598	+	0.644508i	$0.222938\pi$
$150$		0			0
$151$	−3.28286			−0.267155			−0.133578	−	0.991038i	$-0.542647\pi$
$151$	−3.28286			−0.267155			−0.133578	+	0.991038i	$0.542647\pi$
$152$		0			0
$153$	7.03372	−	9.28990i	0.568643	−	0.751044i
$154$		0			0
$155$	−1.01496	−	9.46101i	−0.0815239	−	0.759927i
$156$		0			0
$157$	−16.2435	−	16.2435i	−1.29637	−	1.29637i	−0.930771	−	0.365603i	$-0.880863\pi$
$157$	−16.2435	−	16.2435i	−1.29637	−	1.29637i	−0.365603	−	0.930771i	$-0.619137\pi$
$158$		0			0
$159$	−7.23083	+	8.29898i	−0.573442	+	0.658152i
$160$		0			0
$161$			4.05116i			0.319276i
$162$		0			0
$163$	−9.06097	+	9.06097i	−0.709710	+	0.709710i	−0.966474	−	0.256764i	$-0.917344\pi$
$163$	−9.06097	+	9.06097i	−0.709710	+	0.709710i	0.256764	+	0.966474i	$0.417344\pi$
$164$		0			0
$165$	0.662589	+	3.73567i	0.0515825	+	0.290821i
$166$		0			0
$167$	−4.41233	+	4.41233i	−0.341437	+	0.341437i	−0.856907	−	0.515471i	$-0.827617\pi$
$167$	−4.41233	+	4.41233i	−0.341437	+	0.341437i	0.515471	+	0.856907i	$0.327617\pi$
$168$		0			0
$169$			12.7241i			0.978781i
$170$		0			0
$171$	0.0150065	+	0.108573i	0.00114757	+	0.00830279i
$172$		0			0
$173$	−6.35293	−	6.35293i	−0.483005	−	0.483005i	0.423085	−	0.906090i	$-0.360947\pi$
$173$	−6.35293	−	6.35293i	−0.483005	−	0.483005i	−0.906090	+	0.423085i	$0.860947\pi$
$174$		0			0
$175$	−17.0352	−	10.9589i	−1.28774	−	0.828417i
$176$		0			0
$177$	−0.283394	−	4.12025i	−0.0213012	−	0.309697i
$178$		0			0
$179$	21.3828			1.59823			0.799113	−	0.601181i	$-0.205303\pi$
$179$	21.3828			1.59823			0.799113	+	0.601181i	$0.205303\pi$
$180$		0			0
$181$	−7.19936			−0.535124			−0.267562	−	0.963541i	$-0.586218\pi$
$181$	−7.19936			−0.535124			−0.267562	+	0.963541i	$0.586218\pi$
$182$		0			0
$183$	−1.52439	−	22.1630i	−0.112686	−	1.63834i
$184$		0			0
$185$	−2.34440	+	2.90785i	−0.172364	+	0.213790i
$186$		0			0
$187$	−2.69044	−	2.69044i	−0.196744	−	0.196744i
$188$		0			0
$189$	−11.5252	+	17.6150i	−0.838337	+	1.28131i
$190$		0			0
$191$			12.0194i			0.869695i	0.900504	+	0.434848i	$0.143198\pi$
$191$			12.0194i			0.869695i	−0.900504	+	0.434848i	$0.856802\pi$
$192$		0			0
$193$	11.7576	−	11.7576i	0.846330	−	0.846330i	−0.143343	−	0.989673i	$-0.545785\pi$
$193$	11.7576	−	11.7576i	0.846330	−	0.846330i	0.989673	+	0.143343i	$0.0457852\pi$
$194$		0			0
$195$	−1.16506	+	1.66746i	−0.0834316	+	0.119409i
$196$		0			0
$197$	8.90705	−	8.90705i	0.634601	−	0.634601i	−0.314617	−	0.949219i	$-0.601876\pi$
$197$	8.90705	−	8.90705i	0.634601	−	0.634601i	0.949219	+	0.314617i	$0.101876\pi$
$198$		0			0
$199$			7.13057i			0.505473i	0.967535	+	0.252736i	$0.0813305\pi$
$199$			7.13057i			0.505473i	−0.967535	+	0.252736i	$0.918669\pi$
$200$		0			0
$201$	−7.54328	+	8.65759i	−0.532062	+	0.610659i
$202$		0			0
$203$	−24.4928	−	24.4928i	−1.71906	−	1.71906i
$204$		0			0
$205$	−7.70044	+	0.826093i	−0.537822	+	0.0576968i
$206$		0			0
$207$	−2.39178	−	1.81091i	−0.166240	−	0.125867i
$208$		0			0
$209$	0.0357898			0.00247563
$210$		0			0
$211$	−23.2958			−1.60375			−0.801875	−	0.597492i	$-0.796164\pi$
$211$	−23.2958			−1.60375			−0.801875	+	0.597492i	$0.796164\pi$
$212$		0			0
$213$	26.5732	−	1.82773i	1.82077	−	0.125234i
$214$		0			0
$215$	−20.5931	−	16.6028i	−1.40444	−	1.13230i
$216$		0			0
$217$	−12.1899	−	12.1899i	−0.827507	−	0.827507i
$218$		0			0
$219$	−15.1770	−	13.2236i	−1.02557	−	0.893566i
$220$		0			0
$221$		−	2.03999i		−	0.137224i
$222$		0			0
$223$	8.11541	−	8.11541i	0.543448	−	0.543448i	−0.381090	−	0.924538i	$-0.624451\pi$
$223$	8.11541	−	8.11541i	0.543448	−	0.543448i	0.924538	+	0.381090i	$0.124451\pi$
$224$		0			0
$225$	14.0850	−	5.15875i	0.939000	−	0.343917i
$226$		0			0
$227$	4.59897	−	4.59897i	0.305245	−	0.305245i	−0.537817	−	0.843062i	$-0.680751\pi$
$227$	4.59897	−	4.59897i	0.305245	−	0.305245i	0.843062	+	0.537817i	$0.180751\pi$
$228$		0			0
$229$		−	12.9894i		−	0.858364i	−0.903218	−	0.429182i	$-0.858802\pi$
$229$		−	12.9894i		−	0.858364i	0.903218	−	0.429182i	$-0.141198\pi$
$230$		0			0
$231$	5.18248	+	4.51545i	0.340982	+	0.297094i
$232$		0			0
$233$	−2.39926	−	2.39926i	−0.157181	−	0.157181i	0.624135	−	0.781316i	$-0.285451\pi$
$233$	−2.39926	−	2.39926i	−0.157181	−	0.157181i	−0.781316	+	0.624135i	$0.785451\pi$
$234$		0			0
$235$	10.3408	+	8.33705i	0.674558	+	0.543849i
$236$		0			0
$237$	−16.0268	+	1.10234i	−1.04105	+	0.0716044i
$238$		0			0
$239$	−2.38693			−0.154398			−0.0771988	−	0.997016i	$-0.524598\pi$
$239$	−2.38693			−0.154398			−0.0771988	+	0.997016i	$0.524598\pi$
$240$		0			0
$241$	−15.4824			−0.997306			−0.498653	−	0.866802i	$-0.666172\pi$
$241$	−15.4824			−0.997306			−0.498653	+	0.866802i	$0.666172\pi$
$242$		0			0
$243$	−5.24794	−	14.6785i	−0.336656	−	0.941628i
$244$		0			0
$245$	−20.9255	+	2.24486i	−1.33688	+	0.143419i
$246$		0			0
$247$	0.0135685	+	0.0135685i	0.000863345	+	0.000863345i
$248$		0			0
$249$	5.70516	−	6.54793i	0.361550	−	0.414958i
$250$		0			0
$251$		−	11.4240i		−	0.721074i	−0.932745	−	0.360537i	$-0.882594\pi$
$251$		−	11.4240i		−	0.721074i	0.932745	−	0.360537i	$-0.117406\pi$
$252$		0			0
$253$	−0.692682	+	0.692682i	−0.0435485	+	0.0435485i
$254$		0			0
$255$	−8.61587	+	12.3312i	−0.539547	+	0.772211i
$256$		0			0
$257$	8.92626	−	8.92626i	0.556805	−	0.556805i	−0.371591	−	0.928396i	$-0.621188\pi$
$257$	8.92626	−	8.92626i	0.556805	−	0.556805i	0.928396	+	0.371591i	$0.121188\pi$
$258$		0			0
$259$			6.76720i			0.420493i
$260$		0			0
$261$	25.4090	−	3.51191i	1.57278	−	0.217382i
$262$		0			0
$263$	−0.432955	−	0.432955i	−0.0266972	−	0.0266972i	0.693632	−	0.720329i	$-0.256009\pi$
$263$	−0.432955	−	0.432955i	−0.0266972	−	0.0266972i	−0.720329	+	0.693632i	$0.756009\pi$
$264$		0			0
$265$	8.91901	−	11.0626i	0.547890	−	0.679571i
$266$		0			0
$267$	−1.05143	−	15.2866i	−0.0643463	−	0.935527i
$268$		0			0
$269$	17.9180			1.09248			0.546241	−	0.837628i	$-0.316058\pi$
$269$	17.9180			1.09248			0.546241	+	0.837628i	$0.316058\pi$
$270$		0			0
$271$	−15.1348			−0.919373			−0.459686	−	0.888081i	$-0.652038\pi$
$271$	−15.1348			−0.919373			−0.459686	+	0.888081i	$0.652038\pi$
$272$		0			0
$273$	0.252883	+	3.67665i	0.0153052	+	0.222521i
$274$		0			0
$275$	−1.03894	−	4.78654i	−0.0626507	−	0.288639i
$276$		0			0
$277$	8.90799	+	8.90799i	0.535229	+	0.535229i	0.922124	−	0.386895i	$-0.126452\pi$
$277$	8.90799	+	8.90799i	0.535229	+	0.535229i	−0.386895	+	0.922124i	$0.626452\pi$
$278$		0			0
$279$	12.6459	−	1.74786i	0.757090	−	0.104641i
$280$		0			0
$281$			28.9417i			1.72652i	0.504764	+	0.863258i	$0.331580\pi$
$281$			28.9417i			1.72652i	−0.504764	+	0.863258i	$0.668420\pi$
$282$		0			0
$283$	0.952502	−	0.952502i	0.0566204	−	0.0566204i	−0.678230	−	0.734850i	$-0.737253\pi$
$283$	0.952502	−	0.952502i	0.0566204	−	0.0566204i	0.734850	+	0.678230i	$0.237253\pi$
$284$		0			0
$285$	−0.0247118	−	0.139325i	−0.00146380	−	0.00825291i
$286$		0			0
$287$	−9.92155	+	9.92155i	−0.585650	+	0.585650i
$288$		0			0
$289$			1.91384i			0.112579i
$290$		0			0
$291$	6.24905	−	7.17217i	0.366326	−	0.420440i
$292$		0			0
$293$	−10.4394	−	10.4394i	−0.609874	−	0.609874i	0.333039	−	0.942913i	$-0.391926\pi$
$293$	−10.4394	−	10.4394i	−0.609874	−	0.609874i	−0.942913	+	0.333039i	$0.891926\pi$
$294$		0			0
$295$	0.568724	+	5.30137i	0.0331124	+	0.308658i
$296$		0			0
$297$	−4.98251	+	1.04126i	−0.289115	+	0.0604200i
$298$		0			0
$299$	−0.525216			−0.0303740
$300$		0			0
$301$	−47.9246			−2.76233
$302$		0			0
$303$	6.48004	−	0.445702i	0.372269	−	0.0256049i
$304$		0			0
$305$	3.05919	+	28.5163i	0.175169	+	1.63284i
$306$		0			0
$307$	−1.73844	−	1.73844i	−0.0992182	−	0.0992182i	0.655755	−	0.754973i	$-0.272350\pi$
$307$	−1.73844	−	1.73844i	−0.0992182	−	0.0992182i	−0.754973	+	0.655755i	$0.772350\pi$
$308$		0			0
$309$	3.30034	+	2.87556i	0.187750	+	0.163585i
$310$		0			0
$311$			10.6035i			0.601270i	0.953739	+	0.300635i	$0.0971986\pi$
$311$			10.6035i			0.601270i	−0.953739	+	0.300635i	$0.902801\pi$
$312$		0			0
$313$	−22.9105	+	22.9105i	−1.29498	+	1.29498i	−0.363307	+	0.931670i	$0.618352\pi$
$313$	−22.9105	+	22.9105i	−1.29498	+	1.29498i	−0.931670	+	0.363307i	$0.881648\pi$
$314$		0			0
$315$	13.9997	−	23.2925i	0.788795	−	1.31239i
$316$		0			0
$317$	−11.8239	+	11.8239i	−0.664097	+	0.664097i	−0.956343	−	0.292246i	$-0.905597\pi$
$317$	−11.8239	+	11.8239i	−0.664097	+	0.664097i	0.292246	+	0.956343i	$0.405597\pi$
$318$		0			0
$319$		−	8.37576i		−	0.468953i
$320$		0			0
$321$	−8.83933	−	7.70163i	−0.493363	−	0.429863i
$322$		0			0
$323$	0.100342	+	0.100342i	0.00558320	+	0.00558320i
$324$		0			0
$325$	1.42078	−	2.20855i	0.0788107	−	0.122508i
$326$		0			0
$327$	13.2920	−	0.914234i	0.735049	−	0.0505572i
$328$		0			0
$329$	24.0652			1.32676
$330$		0			0
$331$	0.565521			0.0310839			0.0155419	−	0.999879i	$-0.495053\pi$
$331$	0.565521			0.0310839			0.0155419	+	0.999879i	$0.495053\pi$
$332$		0			0
$333$	−3.99532	−	3.02500i	−0.218942	−	0.165769i
$334$		0			0
$335$	9.30441	−	11.5406i	0.508354	−	0.630532i
$336$		0			0
$337$	−10.2688	−	10.2688i	−0.559375	−	0.559375i	0.369755	−	0.929129i	$-0.379442\pi$
$337$	−10.2688	−	10.2688i	−0.559375	−	0.559375i	−0.929129	+	0.369755i	$0.879442\pi$
$338$		0			0
$339$	9.06892	−	10.4086i	0.492556	−	0.565317i
$340$		0			0
$341$		−	4.16856i		−	0.225740i
$342$		0			0
$343$	−6.90903	+	6.90903i	−0.373052	+	0.373052i
$344$		0			0
$345$	3.17480	+	2.21825i	0.170926	+	0.119426i
$346$		0			0
$347$	20.5918	−	20.5918i	1.10543	−	1.10543i	0.111682	−	0.993744i	$-0.464376\pi$
$347$	20.5918	−	20.5918i	1.10543	−	1.10543i	0.993744	−	0.111682i	$-0.0356239\pi$
$348$		0			0
$349$		−	4.11593i		−	0.220321i	−0.993914	−	0.110160i	$-0.964864\pi$
$349$		−	4.11593i		−	0.220321i	0.993914	−	0.110160i	$-0.0351365\pi$
$350$		0			0
$351$	−2.28372	−	1.49420i	−0.121896	−	0.0797544i
$352$		0			0
$353$	5.92298	+	5.92298i	0.315248	+	0.315248i	0.846939	−	0.531690i	$-0.178443\pi$
$353$	5.92298	+	5.92298i	0.315248	+	0.315248i	−0.531690	+	0.846939i	$0.678443\pi$
$354$		0			0
$355$	−34.1908	+	3.66794i	−1.81466	+	0.194674i
$356$		0			0
$357$	1.87013	+	27.1897i	0.0989776	+	1.43903i
$358$		0			0
$359$	6.15663			0.324934			0.162467	−	0.986714i	$-0.448055\pi$
$359$	6.15663			0.324934			0.162467	+	0.986714i	$0.448055\pi$
$360$		0			0
$361$	18.9987			0.999930
$362$		0			0
$363$	−1.19331	−	17.3495i	−0.0626325	−	0.910611i
$364$		0			0
$365$	20.2310	+	16.3109i	1.05894	+	0.853750i
$366$		0			0
$367$	11.6858	+	11.6858i	0.609991	+	0.609991i	0.942944	−	0.332952i	$-0.108045\pi$
$367$	11.6858	+	11.6858i	0.609991	+	0.609991i	−0.332952	+	0.942944i	$0.608045\pi$
$368$		0			0
$369$	−1.42260	−	10.2927i	−0.0740578	−	0.535814i
$370$		0			0
$371$		−	25.7451i		−	1.33662i
$372$		0			0
$373$	22.9924	−	22.9924i	1.19050	−	1.19050i	0.213576	−	0.976926i	$-0.431489\pi$
$373$	22.9924	−	22.9924i	1.19050	−	1.19050i	0.976926	−	0.213576i	$-0.0685110\pi$
$374$		0			0
$375$	−17.9161	+	7.34946i	−0.925182	+	0.379525i
$376$		0			0
$377$	3.17540	−	3.17540i	0.163541	−	0.163541i
$378$		0			0
$379$		−	12.4724i		−	0.640666i	−0.947305	−	0.320333i	$-0.896205\pi$
$379$		−	12.4724i		−	0.640666i	0.947305	−	0.320333i	$-0.103795\pi$
$380$		0			0
$381$	12.8899	−	14.7940i	0.660369	−	0.757921i
$382$		0			0
$383$	−5.49762	−	5.49762i	−0.280916	−	0.280916i	0.552559	−	0.833474i	$-0.313652\pi$
$383$	−5.49762	−	5.49762i	−0.280916	−	0.280916i	−0.833474	+	0.552559i	$0.813652\pi$
$384$		0			0
$385$	−6.90828	−	5.56966i	−0.352079	−	0.283856i
$386$		0			0
$387$	21.4228	−	28.2945i	1.08898	−	1.43829i
$388$		0			0
$389$	−3.81556			−0.193456			−0.0967282	−	0.995311i	$-0.530838\pi$
$389$	−3.81556			−0.193456			−0.0967282	+	0.995311i	$0.530838\pi$
$390$		0			0
$391$	−3.88409			−0.196427
$392$		0			0
$393$	−5.56555	+	0.382803i	−0.280745	+	0.0193098i
$394$		0			0
$395$	20.6211	−	2.21220i	1.03756	−	0.111308i
$396$		0			0
$397$	7.73487	+	7.73487i	0.388202	+	0.388202i	0.874046	−	0.485844i	$-0.161488\pi$
$397$	7.73487	+	7.73487i	0.388202	+	0.388202i	−0.485844	+	0.874046i	$0.661488\pi$
$398$		0			0
$399$	−0.193285	−	0.168408i	−0.00967636	−	0.00843093i
$400$		0			0
$401$		−	12.2234i		−	0.610406i	−0.952287	−	0.305203i	$-0.901276\pi$
$401$		−	12.2234i		−	0.610406i	0.952287	−	0.305203i	$-0.0987243\pi$
$402$		0			0
$403$	1.58038	−	1.58038i	0.0787241	−	0.0787241i
$404$		0			0
$405$	7.49378	+	18.6773i	0.372369	+	0.928085i
$406$		0			0
$407$	−1.15708	+	1.15708i	−0.0573544	+	0.0573544i
$408$		0			0
$409$			16.6028i			0.820956i	0.911871	+	0.410478i	$0.134638\pi$
$409$			16.6028i			0.820956i	−0.911871	+	0.410478i	$0.865362\pi$
$410$		0			0
$411$	−15.4729	−	13.4814i	−0.763220	−	0.664987i
$412$		0			0
$413$	6.83049	+	6.83049i	0.336107	+	0.336107i
$414$		0			0
$415$	−7.03714	+	8.72845i	−0.345439	+	0.428463i
$416$		0			0
$417$	36.8804	−	2.53666i	1.80604	−	0.124221i
$418$		0			0
$419$	34.3360			1.67742			0.838712	−	0.544576i	$-0.183309\pi$
$419$	34.3360			1.67742			0.838712	+	0.544576i	$0.183309\pi$
$420$		0			0
$421$	−36.8024			−1.79364			−0.896819	−	0.442398i	$-0.854128\pi$
$421$	−36.8024			−1.79364			−0.896819	+	0.442398i	$0.854128\pi$
$422$		0			0
$423$	−10.7574	+	14.2080i	−0.523042	+	0.690816i
$424$		0			0
$425$	10.5070	−	16.3327i	0.509664	−	0.792252i
$426$		0			0
$427$	36.7415	+	36.7415i	1.77805	+	1.77805i
$428$		0			0
$429$	−0.585409	+	0.671887i	−0.0282638	+	0.0324390i
$430$		0			0
$431$		−	24.7800i		−	1.19361i	−0.802386	−	0.596805i	$-0.796437\pi$
$431$		−	24.7800i		−	1.19361i	0.802386	−	0.596805i	$-0.203563\pi$
$432$		0			0
$433$	24.7689	−	24.7689i	1.19032	−	1.19032i	0.213338	−	0.976978i	$-0.431566\pi$
$433$	24.7689	−	24.7689i	1.19032	−	1.19032i	0.976978	−	0.213338i	$-0.0684335\pi$
$434$		0			0
$435$	−32.6058	+	5.78323i	−1.56333	+	0.277285i
$436$		0			0
$437$	0.0258342	−	0.0258342i	0.00123582	−	0.00123582i
$438$		0			0
$439$			2.78166i			0.132762i	0.997794	+	0.0663808i	$0.0211452\pi$
$439$			2.78166i			0.132762i	−0.997794	+	0.0663808i	$0.978855\pi$
$440$		0			0
$441$	−3.86584	−	27.9697i	−0.184088	−	1.33189i
$442$		0			0
$443$	−25.3492	−	25.3492i	−1.20438	−	1.20438i	−0.972822	−	0.231554i	$-0.925619\pi$
$443$	−25.3492	−	25.3492i	−1.20438	−	1.20438i	−0.231554	−	0.972822i	$-0.574381\pi$
$444$		0			0
$445$	2.11004	+	19.6687i	0.100025	+	0.932388i
$446$		0			0
$447$	−2.21850	−	32.2546i	−0.104931	−	1.52559i
$448$		0			0
$449$	31.6178			1.49214			0.746068	−	0.665869i	$-0.231939\pi$
$449$	31.6178			1.49214			0.746068	+	0.665869i	$0.231939\pi$
$450$		0			0
$451$	−3.39285			−0.159763
$452$		0			0
$453$	0.390171	+	5.67268i	0.0183318	+	0.266526i
$454$		0			0
$455$	−0.507493	−	4.73061i	−0.0237916	−	0.221774i
$456$		0			0
$457$	−5.22794	−	5.22794i	−0.244553	−	0.244553i	0.574178	−	0.818731i	$-0.305322\pi$
$457$	−5.22794	−	5.22794i	−0.244553	−	0.244553i	−0.818731	+	0.574178i	$0.805322\pi$
$458$		0			0
$459$	−16.8886	−	11.0499i	−0.788293	−	0.515767i
$460$		0			0
$461$			2.58356i			0.120329i	0.998188	+	0.0601643i	$0.0191625\pi$
$461$			2.58356i			0.120329i	−0.998188	+	0.0601643i	$0.980838\pi$
$462$		0			0
$463$	−7.54194	+	7.54194i	−0.350504	+	0.350504i	−0.860297	−	0.509793i	$-0.829722\pi$
$463$	−7.54194	+	7.54194i	−0.350504	+	0.350504i	0.509793	+	0.860297i	$0.329722\pi$
$464$		0			0
$465$	−16.2277	+	2.87828i	−0.752542	+	0.133477i
$466$		0			0
$467$	−9.21019	+	9.21019i	−0.426197	+	0.426197i	−0.887331	−	0.461134i	$-0.847443\pi$
$467$	−9.21019	+	9.21019i	−0.426197	+	0.426197i	0.461134	+	0.887331i	$0.347443\pi$
$468$		0			0
$469$		−	26.8576i		−	1.24017i
$470$		0			0
$471$	−26.1377	+	29.9988i	−1.20436	+	1.38227i
$472$		0			0
$473$	−8.19433	−	8.19433i	−0.376776	−	0.376776i
$474$		0			0
$475$	0.0387484	+	0.178519i	0.00177790	+	0.00819099i
$476$		0			0
$477$	15.1998	+	11.5083i	0.695950	+	0.526929i
$478$		0			0
$479$	−6.73288			−0.307633			−0.153816	−	0.988099i	$-0.549156\pi$
$479$	−6.73288			−0.307633			−0.153816	+	0.988099i	$0.549156\pi$
$480$		0			0
$481$	−0.877340			−0.0400033
$482$		0			0
$483$	7.00027	−	0.481484i	0.318523	−	0.0219083i
$484$		0			0
$485$	−7.70801	+	9.56056i	−0.350003	+	0.434123i
$486$		0			0
$487$	1.51387	+	1.51387i	0.0685998	+	0.0685998i	0.740574	−	0.671975i	$-0.234554\pi$
$487$	1.51387	+	1.51387i	0.0685998	+	0.0685998i	−0.671975	+	0.740574i	$0.734554\pi$
$488$		0			0
$489$	16.7340	+	14.5802i	0.756736	+	0.659338i
$490$		0			0
$491$			42.2018i			1.90454i	0.305257	+	0.952270i	$0.401258\pi$
$491$			42.2018i			1.90454i	−0.305257	+	0.952270i	$0.598742\pi$
$492$		0			0
$493$	23.4828	−	23.4828i	1.05761	−	1.05761i
$494$		0			0
$495$	6.37637	−	1.58892i	0.286596	−	0.0714167i
$496$		0			0
$497$	−44.0527	+	44.0527i	−1.97603	+	1.97603i
$498$		0			0
$499$		−	10.7169i		−	0.479756i	−0.970803	−	0.239878i	$-0.922893\pi$
$499$		−	10.7169i		−	0.479756i	0.970803	−	0.239878i	$-0.0771075\pi$
$500$		0			0
$501$	8.14878	+	7.09996i	0.364061	+	0.317203i
$502$		0			0
$503$	15.7243	+	15.7243i	0.701110	+	0.701110i	0.964649	−	0.263539i	$-0.0848897\pi$
$503$	15.7243	+	15.7243i	0.701110	+	0.701110i	−0.263539	+	0.964649i	$0.584890\pi$
$504$		0			0
$505$	−8.33762	+	0.894449i	−0.371019	+	0.0398025i
$506$		0			0
$507$	21.9869	−	1.51228i	0.976474	−	0.0671626i
$508$		0			0
$509$	−33.8195			−1.49902			−0.749511	−	0.661992i	$-0.769711\pi$
$509$	−33.8195			−1.49902			−0.749511	+	0.661992i	$0.769711\pi$
$510$		0			0
$511$	47.0820			2.08279
$512$		0			0
$513$	0.185827	−	0.0388347i	0.00820448	−	0.00171459i
$514$		0			0
$515$	−4.39938	−	3.54691i	−0.193860	−	0.156296i
$516$		0			0
$517$	4.11476	+	4.11476i	0.180967	+	0.180967i
$518$		0			0
$519$	−10.2226	+	11.7327i	−0.448723	+	0.515009i
$520$		0			0
$521$			5.18366i			0.227100i	0.993532	+	0.113550i	$0.0362222\pi$
$521$			5.18366i			0.227100i	−0.993532	+	0.113550i	$0.963778\pi$
$522$		0			0
$523$	9.96371	−	9.96371i	0.435682	−	0.435682i	−0.454874	−	0.890556i	$-0.650316\pi$
$523$	9.96371	−	9.96371i	0.435682	−	0.435682i	0.890556	+	0.454874i	$0.150316\pi$
$524$		0			0
$525$	−16.9120	+	30.7388i	−0.738102	+	1.34155i
$526$		0			0
$527$	11.6872	−	11.6872i	0.509104	−	0.509104i
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	−7.08598	+	0.979392i	−0.307505	+	0.0425020i
$532$		0			0
$533$	−1.28629	−	1.28629i	−0.0557153	−	0.0557153i
$534$		0			0
$535$	11.7829	+	9.49973i	0.509419	+	0.410709i
$536$		0			0
$537$	−2.54137	−	36.9488i	−0.109668	−	1.59446i
$538$		0			0
$539$	−9.21986			−0.397128
$540$		0			0
$541$	−5.35341			−0.230161			−0.115080	−	0.993356i	$-0.536713\pi$
$541$	−5.35341			−0.230161			−0.115080	+	0.993356i	$0.536713\pi$
$542$		0			0
$543$	0.855651	+	12.4403i	0.0367195	+	0.533863i
$544$		0			0
$545$	−17.1023	+	1.83471i	−0.732582	+	0.0785905i
$546$		0			0
$547$	14.3234	+	14.3234i	0.612426	+	0.612426i	0.943578	−	0.331151i	$-0.107437\pi$
$547$	14.3234	+	14.3234i	0.612426	+	0.612426i	−0.331151	+	0.943578i	$0.607437\pi$
$548$		0			0
$549$	−38.1158	+	5.26819i	−1.62674	+	0.224841i
$550$		0			0
$551$			0.312382i			0.0133079i
$552$		0			0
$553$	26.5690	−	26.5690i	1.12983	−	1.12983i
$554$		0			0
$555$	5.30331	+	3.70544i	0.225113	+	0.157287i
$556$		0			0
$557$	14.0434	−	14.0434i	0.595039	−	0.595039i	−0.343949	−	0.938988i	$-0.611765\pi$
$557$	14.0434	−	14.0434i	0.595039	−	0.595039i	0.938988	+	0.343949i	$0.111765\pi$
$558$		0			0
$559$		−	6.21323i		−	0.262792i
$560$		0			0
$561$	−4.32923	+	4.96875i	−0.182780	+	0.209781i
$562$		0			0
$563$	27.3965	+	27.3965i	1.15462	+	1.15462i	0.985615	+	0.169008i	$0.0540564\pi$
$563$	27.3965	+	27.3965i	1.15462	+	1.15462i	0.169008	+	0.985615i	$0.445944\pi$
$564$		0			0
$565$	−11.1862	+	13.8747i	−0.470608	+	0.583715i
$566$		0			0
$567$	31.8080	+	17.8217i	1.33581	+	0.748439i
$568$		0			0
$569$	41.6400			1.74564			0.872819	−	0.488044i	$-0.162289\pi$
$569$	41.6400			1.74564			0.872819	+	0.488044i	$0.162289\pi$
$570$		0			0
$571$	−39.6019			−1.65729			−0.828643	−	0.559777i	$-0.810887\pi$
$571$	−39.6019			−1.65729			−0.828643	+	0.559777i	$0.810887\pi$
$572$		0			0
$573$	20.7692	−	1.42852i	0.867645	−	0.0596773i
$574$		0			0
$575$	−4.20502	−	2.70514i	−0.175362	−	0.112812i
$576$		0			0
$577$	−24.4391	−	24.4391i	−1.01741	−	1.01741i	−0.999846	−	0.0175673i	$-0.994408\pi$
$577$	−24.4391	−	24.4391i	−1.01741	−	1.01741i	−0.0175673	−	0.999846i	$-0.505592\pi$
$578$		0			0
$579$	−21.7141	−	18.9193i	−0.902409	−	0.786261i
$580$		0			0
$581$			20.3130i			0.842725i
$582$		0			0
$583$	4.40199	−	4.40199i	0.182312	−	0.182312i
$584$		0			0
$585$	3.01978	+	1.81501i	0.124853	+	0.0750413i
$586$		0			0
$587$	−30.4887	+	30.4887i	−1.25841	+	1.25841i	−0.306551	+	0.951854i	$0.599175\pi$
$587$	−30.4887	+	30.4887i	−1.25841	+	1.25841i	−0.951854	+	0.306551i	$0.900825\pi$
$588$		0			0
$589$			0.155470i			0.00640604i
$590$		0			0
$591$	−16.4497	−	14.3325i	−0.676651	−	0.589560i
$592$		0			0
$593$	−33.8921	−	33.8921i	−1.39178	−	1.39178i	−0.821333	−	0.570449i	$-0.806769\pi$
$593$	−33.8921	−	33.8921i	−1.39178	−	1.39178i	−0.570449	−	0.821333i	$-0.693231\pi$
$594$		0			0
$595$	−3.75303	−	34.9839i	−0.153859	−	1.43420i
$596$		0			0
$597$	12.3214	−	0.847475i	0.504281	−	0.0346849i
$598$		0			0
$599$	2.82212			0.115309			0.0576543	−	0.998337i	$-0.481638\pi$
$599$	2.82212			0.115309			0.0576543	+	0.998337i	$0.481638\pi$
$600$		0			0
$601$	36.7391			1.49862			0.749310	−	0.662219i	$-0.230385\pi$
$601$	36.7391			1.49862			0.749310	+	0.662219i	$0.230385\pi$
$602$		0			0
$603$	15.8566	+	12.0056i	0.645730	+	0.488906i
$604$		0			0
$605$	2.39477	+	22.3229i	0.0973612	+	0.907555i
$606$		0			0
$607$	24.3692	+	24.3692i	0.989115	+	0.989115i	0.999941	−	0.0108266i	$-0.00344628\pi$
$607$	24.3692	+	24.3692i	0.989115	+	0.989115i	−0.0108266	+	0.999941i	$0.503446\pi$
$608$		0			0
$609$	−39.4119	+	45.2339i	−1.59705	+	1.83297i
$610$		0			0
$611$			3.11996i			0.126220i
$612$		0			0
$613$	16.7487	−	16.7487i	0.676474	−	0.676474i	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	16.7487	−	16.7487i	0.676474	−	0.676474i	0.959200	+	0.282727i	$0.0912390\pi$
$614$		0			0
$615$	2.34267	+	13.2079i	0.0944655	+	0.532595i
$616$		0			0
$617$	−7.94538	+	7.94538i	−0.319869	+	0.319869i	−0.848717	−	0.528848i	$-0.822624\pi$
$617$	−7.94538	+	7.94538i	−0.319869	+	0.319869i	0.528848	+	0.848717i	$0.322624\pi$
$618$		0			0
$619$			29.1075i			1.16993i	0.811060	+	0.584964i	$0.198891\pi$
$619$			29.1075i			1.16993i	−0.811060	+	0.584964i	$0.801109\pi$
$620$		0			0
$621$	−2.84492	+	4.34815i	−0.114163	+	0.174485i
$622$		0			0
$623$	25.3420	+	25.3420i	1.01530	+	1.01530i
$624$		0			0
$625$	22.7503	−	10.3645i	0.910014	−	0.414579i
$626$		0			0
$627$	−0.00425365	−	0.0618436i	−0.000169874	−	0.00246980i
$628$		0			0
$629$	−6.48813			−0.258699
$630$		0			0
$631$	28.2822			1.12590			0.562948	−	0.826492i	$-0.309667\pi$
$631$	28.2822			1.12590			0.562948	+	0.826492i	$0.309667\pi$
$632$		0			0
$633$	2.76873	+	40.2544i	0.110047	+	1.59997i
$634$		0			0
$635$	−15.8993	+	19.7205i	−0.630944	+	0.782586i
$636$		0			0
$637$	−3.49541	−	3.49541i	−0.138493	−	0.138493i
$638$		0			0
$639$	−6.31651	−	45.7005i	−0.249877	−	1.80788i
$640$		0			0
$641$		−	20.9173i		−	0.826184i	−0.910689	−	0.413092i	$-0.864449\pi$
$641$		−	20.9173i		−	0.826184i	0.910689	−	0.413092i	$-0.135551\pi$
$642$		0			0
$643$	−31.9708	+	31.9708i	−1.26081	+	1.26081i	−0.310105	+	0.950702i	$0.600364\pi$
$643$	−31.9708	+	31.9708i	−1.26081	+	1.26081i	−0.950702	+	0.310105i	$0.899636\pi$
$644$		0			0
$645$	−26.2416	+	37.5575i	−1.03326	+	1.47882i
$646$		0			0
$647$	−27.7371	+	27.7371i	−1.09046	+	1.09046i	−0.0949788	+	0.995479i	$0.530278\pi$
$647$	−27.7371	+	27.7371i	−1.09046	+	1.09046i	−0.995479	+	0.0949788i	$0.969722\pi$
$648$		0			0
$649$			2.33581i			0.0916884i
$650$		0			0
$651$	−19.6150	+	22.5126i	−0.768774	+	0.882339i
$652$		0			0
$653$	−21.6190	−	21.6190i	−0.846018	−	0.846018i	0.143615	−	0.989634i	$-0.454127\pi$
$653$	−21.6190	−	21.6190i	−0.846018	−	0.846018i	−0.989634	+	0.143615i	$0.954127\pi$
$654$		0			0
$655$	7.16098	−	0.768220i	0.279803	−	0.0300169i
$656$		0			0
$657$	−21.0461	+	27.7970i	−0.821087	+	1.08446i
$658$		0			0
$659$	−10.2034			−0.397468			−0.198734	−	0.980053i	$-0.563683\pi$
$659$	−10.2034			−0.397468			−0.198734	+	0.980053i	$0.563683\pi$
$660$		0			0
$661$	26.8842			1.04567			0.522836	−	0.852433i	$-0.324874\pi$
$661$	26.8842			1.04567			0.522836	+	0.852433i	$0.324874\pi$
$662$		0			0
$663$	−3.52503	+	0.242454i	−0.136901	+	0.00941614i
$664$		0			0
$665$	0.257651	+	0.207726i	0.00999126	+	0.00805526i
$666$		0			0
$667$	−6.04589	−	6.04589i	−0.234098	−	0.234098i
$668$		0			0
$669$	−14.9877	−	13.0587i	−0.579458	−	0.504877i
$670$		0			0
$671$			12.5644i			0.485043i
$672$		0			0
$673$	−7.68913	+	7.68913i	−0.296394	+	0.296394i	−0.839600	−	0.543205i	$-0.817210\pi$
$673$	−7.68913	+	7.68913i	−0.296394	+	0.296394i	0.543205	+	0.839600i	$0.317210\pi$
$674$		0			0
$675$	−10.5882	−	23.7253i	−0.407539	−	0.913188i
$676$		0			0
$677$	−5.77117	+	5.77117i	−0.221804	+	0.221804i	−0.809258	−	0.587454i	$-0.800130\pi$
$677$	−5.77117	+	5.77117i	−0.221804	+	0.221804i	0.587454	+	0.809258i	$0.300130\pi$
$678$		0			0
$679$			22.2495i			0.853857i
$680$		0			0
$681$	−8.49348	−	7.40029i	−0.325471	−	0.283580i
$682$		0			0
$683$	−30.6661	−	30.6661i	−1.17341	−	1.17341i	−0.981392	−	0.192014i	$-0.938498\pi$
$683$	−30.6661	−	30.6661i	−1.17341	−	1.17341i	−0.192014	−	0.981392i	$-0.561502\pi$
$684$		0			0
$685$	20.6254	+	16.6289i	0.788058	+	0.635356i
$686$		0			0
$687$	−22.4453	+	1.54380i	−0.856341	+	0.0588998i
$688$		0			0
$689$	3.33775			0.127158
$690$		0			0
$691$	34.9110			1.32808			0.664038	−	0.747699i	$-0.268841\pi$
$691$	34.9110			1.32808			0.664038	+	0.747699i	$0.268841\pi$
$692$		0			0
$693$	7.18660	−	9.49182i	0.272997	−	0.360564i
$694$		0			0
$695$	−47.4526	+	5.09065i	−1.79998	+	0.193099i
$696$		0			0
$697$	−9.51239	−	9.51239i	−0.360308	−	0.360308i
$698$		0			0
$699$	−3.86069	+	4.43100i	−0.146025	+	0.167596i
$700$		0			0
$701$			7.54148i			0.284838i	0.989806	+	0.142419i	$0.0454880\pi$
$701$			7.54148i			0.284838i	−0.989806	+	0.142419i	$0.954512\pi$
$702$		0			0
$703$	0.0431544	−	0.0431544i	0.00162760	−	0.00162760i
$704$		0			0
$705$	13.1771	−	18.8594i	0.496280	−	0.710286i
$706$		0			0
$707$	−10.7425	+	10.7425i	−0.404014	+	0.404014i
$708$		0			0
$709$		−	23.1020i		−	0.867616i	−0.901005	−	0.433808i	$-0.857170\pi$
$709$		−	23.1020i		−	0.867616i	0.901005	−	0.433808i	$-0.142830\pi$
$710$		0			0
$711$	3.80960	+	27.5628i	0.142871	+	1.03369i
$712$		0			0
$713$	−3.00900	−	3.00900i	−0.112688	−	0.112688i
$714$		0			0
$715$	0.722084	−	0.895630i	0.0270044	−	0.0334947i
$716$		0			0
$717$	0.283689	+	4.12454i	0.0105946	+	0.154034i
$718$		0			0
$719$	−19.8717			−0.741090			−0.370545	−	0.928815i	$-0.620829\pi$
$719$	−19.8717			−0.741090			−0.370545	+	0.928815i	$0.620829\pi$
$720$		0			0
$721$	−10.2383			−0.381295
$722$		0			0
$723$	1.84009	+	26.7530i	0.0684338	+	0.994955i
$724$		0			0
$725$	41.7781	−	9.06816i	1.55160	−	0.336783i
$726$		0			0
$727$	22.6210	+	22.6210i	0.838965	+	0.838965i	0.988723	−	0.149758i	$-0.0478493\pi$
$727$	22.6210	+	22.6210i	0.838965	+	0.838965i	−0.149758	+	0.988723i	$0.547849\pi$
$728$		0			0
$729$	−24.7403	+	10.8128i	−0.916308	+	0.400475i
$730$		0			0
$731$		−	45.9483i		−	1.69946i
$732$		0			0
$733$	12.3202	−	12.3202i	0.455056	−	0.455056i	−0.441972	−	0.897029i	$-0.645721\pi$
$733$	12.3202	−	12.3202i	0.455056	−	0.455056i	0.897029	+	0.441972i	$0.145721\pi$
$734$		0			0
$735$	6.36606	+	35.8918i	0.234816	+	1.32389i
$736$		0			0
$737$	4.59221	−	4.59221i	0.169156	−	0.169156i
$738$		0			0
$739$		−	35.3176i		−	1.29918i	−0.760286	−	0.649589i	$-0.774941\pi$
$739$		−	35.3176i		−	1.29918i	0.760286	−	0.649589i	$-0.225059\pi$
$740$		0			0
$741$	0.0218334	−	0.0250586i	0.000802069	−	0.000920552i
$742$		0			0
$743$	5.38471	+	5.38471i	0.197546	+	0.197546i	0.798947	−	0.601401i	$-0.205391\pi$
$743$	5.38471	+	5.38471i	0.197546	+	0.197546i	−0.601401	+	0.798947i	$0.705391\pi$
$744$		0			0
$745$	4.45215	+	41.5008i	0.163114	+	1.52047i
$746$		0			0
$747$	−11.9927	−	9.08010i	−0.438789	−	0.332224i
$748$		0			0
$749$	27.4214			1.00195
$750$		0			0
$751$	34.1344			1.24558			0.622792	−	0.782388i	$-0.285998\pi$
$751$	34.1344			1.24558			0.622792	+	0.782388i	$0.285998\pi$
$752$		0			0
$753$	−19.7402	+	1.35775i	−0.719374	+	0.0494791i
$754$		0			0
$755$	−0.783007	−	7.29882i	−0.0284965	−	0.265631i
$756$		0			0
$757$	−28.6049	−	28.6049i	−1.03966	−	1.03966i	−0.999180	−	0.0404838i	$-0.987110\pi$
$757$	−28.6049	−	28.6049i	−1.03966	−	1.03966i	−0.0404838	−	0.999180i	$-0.512890\pi$
$758$		0			0
$759$	1.27926	+	1.11461i	0.0464341	+	0.0404577i
$760$		0			0
$761$			36.1534i			1.31056i	0.755386	+	0.655281i	$0.227450\pi$
$761$			36.1534i			1.31056i	−0.755386	+	0.655281i	$0.772550\pi$
$762$		0			0
$763$	−22.0353	+	22.0353i	−0.797731	+	0.797731i
$764$		0			0
$765$	22.3320	+	13.4224i	0.807414	+	0.485287i
$766$		0			0
$767$	−0.885545	+	0.885545i	−0.0319752	+	0.0319752i
$768$		0			0
$769$			17.2214i			0.621020i	0.950570	+	0.310510i	$0.100500\pi$
$769$			17.2214i			0.621020i	−0.950570	+	0.310510i	$0.899500\pi$
$770$		0			0
$771$	−16.4852	−	14.3634i	−0.593700	−	0.517285i
$772$		0			0
$773$	−23.4545	−	23.4545i	−0.843598	−	0.843598i	0.145727	−	0.989325i	$-0.453448\pi$
$773$	−23.4545	−	23.4545i	−0.843598	−	0.843598i	−0.989325	+	0.145727i	$0.953448\pi$
$774$		0			0
$775$	20.7927	−	4.51316i	0.746895	−	0.162118i
$776$		0			0
$777$	11.6935	−	0.804288i	0.419502	−	0.0288537i
$778$		0			0
$779$	0.126539			0.00453374
$780$		0			0
$781$	−15.0646			−0.539054
$782$		0			0
$783$	−9.08836	−	43.4885i	−0.324791	−	1.55415i
$784$		0			0
$785$	32.2401	−	39.9887i	1.15070	−	1.42726i
$786$		0			0
$787$	15.1406	+	15.1406i	0.539703	+	0.539703i	0.923442	−	0.383738i	$-0.125364\pi$
$787$	15.1406	+	15.1406i	0.539703	+	0.539703i	−0.383738	+	0.923442i	$0.625364\pi$
$788$		0			0
$789$	−0.696676	+	0.799590i	−0.0248023	+	0.0284662i
$790$		0			0
$791$			32.2895i			1.14808i
$792$		0			0
$793$	−4.76339	+	4.76339i	−0.169153	+	0.169153i
$794$		0			0
$795$	−20.1759	−	14.0970i	−0.715565	−	0.499968i
$796$		0			0
$797$	26.2486	−	26.2486i	0.929773	−	0.929773i	−0.0679180	−	0.997691i	$-0.521636\pi$
$797$	26.2486	−	26.2486i	0.929773	−	0.929773i	0.997691	+	0.0679180i	$0.0216356\pi$
$798$		0			0
$799$			23.0728i			0.816257i
$800$		0			0
$801$	−26.2899	+	3.63366i	−0.928907	+	0.128389i
$802$		0			0
$803$	8.05026	+	8.05026i	0.284087	+	0.284087i
$804$		0			0
$805$	−9.00698	+	0.966257i	−0.317454	+	0.0340561i
$806$		0			0
$807$	−2.12958	−	30.9618i	−0.0749646	−	1.08991i
$808$		0			0
$809$	15.5327			0.546099			0.273050	−	0.962000i	$-0.411968\pi$
$809$	15.5327			0.546099			0.273050	+	0.962000i	$0.411968\pi$
$810$		0			0
$811$	−36.2208			−1.27189			−0.635943	−	0.771736i	$-0.719389\pi$
$811$	−36.2208			−1.27189			−0.635943	+	0.771736i	$0.719389\pi$
$812$		0			0
$813$	1.79878	+	26.1524i	0.0630861	+	0.917206i
$814$		0			0
$815$	−22.3065	−	17.9842i	−0.781363	−	0.629959i
$816$		0			0
$817$	0.305615	+	0.305615i	0.0106921	+	0.0106921i
$818$		0			0
$819$	6.32308	−	0.873947i	0.220946	−	0.0305382i
$820$		0			0
$821$		−	20.6691i		−	0.721358i	−0.932690	−	0.360679i	$-0.882545\pi$
$821$		−	20.6691i		−	0.721358i	0.932690	−	0.360679i	$-0.117455\pi$
$822$		0			0
$823$	19.9338	−	19.9338i	0.694849	−	0.694849i	−0.268446	−	0.963295i	$-0.586510\pi$
$823$	19.9338	−	19.9338i	0.694849	−	0.694849i	0.963295	+	0.268446i	$0.0865100\pi$
$824$		0			0
$825$	−8.14752	+	2.36415i	−0.283660	+	0.0823091i
$826$		0			0
$827$	1.03302	−	1.03302i	0.0359217	−	0.0359217i	−0.688918	−	0.724839i	$-0.741914\pi$
$827$	1.03302	−	1.03302i	0.0359217	−	0.0359217i	0.724839	+	0.688918i	$0.241914\pi$
$828$		0			0
$829$		−	22.9602i		−	0.797441i	−0.917072	−	0.398721i	$-0.869454\pi$
$829$		−	22.9602i		−	0.797441i	0.917072	−	0.398721i	$-0.130546\pi$
$830$		0			0
$831$	14.3340	−	16.4514i	0.497241	−	0.570694i
$832$		0			0
$833$	−25.8494	−	25.8494i	−0.895628	−	0.895628i
$834$		0			0
$835$	−10.8624	−	8.75758i	−0.375908	−	0.303069i
$836$		0			0
$837$	−4.52322	−	21.6440i	−0.156345	−	0.748125i
$838$		0			0
$839$	−34.0650			−1.17605			−0.588026	−	0.808842i	$-0.700095\pi$
$839$	−34.0650			−1.17605			−0.588026	+	0.808842i	$0.700095\pi$
$840$		0			0
$841$	44.1056			1.52088
$842$		0			0
$843$	50.0103	−	3.43974i	1.72245	−	0.118471i
$844$		0			0
$845$	−28.2897	+	3.03488i	−0.973197	+	0.104403i
$846$		0			0
$847$	28.7617	+	28.7617i	0.988263	+	0.988263i
$848$		0			0
$849$	−1.75910	−	1.53269i	−0.0603721	−	0.0526017i
$850$		0			0
$851$			1.67044i			0.0572619i
$852$		0			0
$853$	5.77822	−	5.77822i	0.197843	−	0.197843i	−0.601232	−	0.799075i	$-0.705323\pi$
$853$	5.77822	−	5.77822i	0.197843	−	0.197843i	0.799075	+	0.601232i	$0.205323\pi$
$854$		0			0
$855$	−0.237812	+	0.0592602i	−0.00813302	+	0.00202666i
$856$		0			0
$857$	−18.4168	+	18.4168i	−0.629106	+	0.629106i	−0.947843	−	0.318737i	$-0.896741\pi$
$857$	−18.4168	+	18.4168i	−0.629106	+	0.629106i	0.318737	+	0.947843i	$0.396741\pi$
$858$		0			0
$859$			13.8386i			0.472165i	0.971733	+	0.236083i	$0.0758636\pi$
$859$			13.8386i			0.472165i	−0.971733	+	0.236083i	$0.924136\pi$
$860$		0			0
$861$	18.3233	+	15.9649i	0.624457	+	0.544084i
$862$		0			0
$863$	12.4841	+	12.4841i	0.424964	+	0.424964i	0.886909	−	0.461945i	$-0.152848\pi$
$863$	12.4841	+	12.4841i	0.424964	+	0.424964i	−0.461945	+	0.886909i	$0.652848\pi$
$864$		0			0
$865$	12.6093	−	15.6398i	0.428729	−	0.531770i
$866$		0			0
$867$	3.30706	−	0.227462i	0.112314	−	0.00772502i
$868$		0			0
$869$	9.08574			0.308213
$870$		0			0
$871$	3.48197			0.117982
$872$		0			0
$873$	−13.1360	−	9.94574i	−0.444586	−	0.336612i
$874$		0			0
$875$	20.3020	−	40.4884i	0.686332	−	1.36876i
$876$		0			0
$877$	38.2405	+	38.2405i	1.29129	+	1.29129i	0.933989	+	0.357301i	$0.116303\pi$
$877$	38.2405	+	38.2405i	1.29129	+	1.29129i	0.357301	+	0.933989i	$0.383697\pi$
$878$		0			0
$879$	−16.7982	+	19.2796i	−0.566588	+	0.650285i
$880$		0			0
$881$			28.8129i			0.970732i	0.874311	+	0.485366i	$0.161314\pi$
$881$			28.8129i			0.970732i	−0.874311	+	0.485366i	$0.838686\pi$
$882$		0			0
$883$	37.5541	−	37.5541i	1.26380	−	1.26380i	0.314560	−	0.949238i	$-0.398143\pi$
$883$	37.5541	−	37.5541i	1.26380	−	1.26380i	0.949238	−	0.314560i	$-0.101857\pi$
$884$		0			0
$885$	9.09301	−	1.61281i	0.305658	−	0.0542140i
$886$		0			0
$887$	−19.9797	+	19.9797i	−0.670854	+	0.670854i	−0.957913	−	0.287059i	$-0.907322\pi$
$887$	−19.9797	+	19.9797i	−0.670854	+	0.670854i	0.287059	+	0.957913i	$0.407322\pi$
$888$		0			0
$889$			45.8940i			1.53923i
$890$		0			0
$891$	2.39144	+	8.48587i	0.0801162	+	0.284287i
$892$		0			0
$893$	−0.153464	−	0.153464i	−0.00513547	−	0.00513547i
$894$		0			0
$895$	5.10009	+	47.5406i	0.170477	+	1.58911i
$896$		0			0
$897$	0.0624224	+	0.907556i	0.00208422	+	0.0303024i
$898$		0			0
$899$	36.3842			1.21348
$900$		0			0
$901$	24.6834			0.822323
$902$		0			0
$903$	5.69589	+	82.8122i	0.189547	+	2.75582i
$904$		0			0
$905$	−1.71715	−	16.0064i	−0.0570799	−	0.532071i
$906$		0			0
$907$	−2.95460	−	2.95460i	−0.0981058	−	0.0981058i	0.656350	−	0.754456i	$-0.272099\pi$
$907$	−2.95460	−	2.95460i	−0.0981058	−	0.0981058i	−0.754456	+	0.656350i	$0.772099\pi$
$908$		0			0
$909$	−1.54032	−	11.1443i	−0.0510891	−	0.369634i
$910$		0			0
$911$			16.7204i			0.553971i	0.960874	+	0.276986i	$0.0893354\pi$
$911$			16.7204i			0.553971i	−0.960874	+	0.276986i	$0.910665\pi$
$912$		0			0
$913$	−3.47319	+	3.47319i	−0.114946	+	0.114946i
$914$		0			0
$915$	48.9117	−	8.67537i	1.61697	−	0.286799i
$916$		0			0
$917$	9.22648	−	9.22648i	0.304685	−	0.304685i
$918$		0			0
$919$			32.2932i			1.06526i	0.846349	+	0.532628i	$0.178796\pi$
$919$			32.2932i			1.06526i	−0.846349	+	0.532628i	$0.821204\pi$
$920$		0			0
$921$	−2.79736	+	3.21059i	−0.0921761	+	0.105793i
$922$		0			0
$923$	−5.71126	−	5.71126i	−0.187988	−	0.187988i
$924$		0			0
$925$	−7.02423	−	4.51876i	−0.230955	−	0.148576i
$926$		0			0
$927$	4.57663	−	6.04465i	0.150316	−	0.198532i
$928$		0			0
$929$	7.49440			0.245883			0.122942	−	0.992414i	$-0.460767\pi$
$929$	7.49440			0.245883			0.122942	+	0.992414i	$0.460767\pi$
$930$		0			0
$931$	0.343863			0.0112697
$932$		0			0
$933$	18.3225	−	1.26024i	0.599853	−	0.0412583i
$934$		0			0
$935$	5.33998	−	6.62339i	0.174636	−	0.216608i
$936$		0			0
$937$	−33.8386	−	33.8386i	−1.10546	−	1.10546i	−0.993740	−	0.111718i	$-0.964365\pi$
$937$	−33.8386	−	33.8386i	−1.10546	−	1.10546i	−0.111718	−	0.993740i	$-0.535635\pi$
$938$		0			0
$939$	42.3115	+	36.8656i	1.38078	+	1.20306i
$940$		0			0
$941$			48.0105i			1.56510i	0.622590	+	0.782548i	$0.286080\pi$
$941$			48.0105i			1.56510i	−0.622590	+	0.782548i	$0.713920\pi$
$942$		0			0
$943$	−2.44907	+	2.44907i	−0.0797526	+	0.0797526i
$944$		0			0
$945$	−41.9126	−	21.4227i	−1.36342	−	0.696881i
$946$		0			0
$947$	−15.6561	+	15.6561i	−0.508754	+	0.508754i	−0.914144	−	0.405390i	$-0.867136\pi$
$947$	−15.6561	+	15.6561i	−0.508754	+	0.508754i	0.405390	+	0.914144i	$0.367136\pi$
$948$		0			0
$949$			6.10399i			0.198144i
$950$		0			0
$951$	21.8366	+	19.0261i	0.708101	+	0.616962i
$952$		0			0
$953$	6.48804	+	6.48804i	0.210168	+	0.210168i	0.804339	−	0.594171i	$-0.202520\pi$
$953$	6.48804	+	6.48804i	0.210168	+	0.210168i	−0.594171	+	0.804339i	$0.702520\pi$
$954$		0			0
$955$	−26.7229	+	2.86680i	−0.864733	+	0.0927674i
$956$		0			0
$957$	−14.4730	+	0.995467i	−0.467847	+	0.0321789i
$958$		0			0
$959$	47.9999			1.55000
$960$		0			0
$961$	−12.8918			−0.415865
$962$		0			0
$963$	−12.2576	+	16.1894i	−0.394996	+	0.521697i
$964$		0			0
$965$	28.9451	+	23.3364i	0.931777	+	0.751226i
$966$		0			0
$967$	−8.51246	−	8.51246i	−0.273742	−	0.273742i	0.556863	−	0.830605i	$-0.312005\pi$
$967$	−8.51246	−	8.51246i	−0.273742	−	0.273742i	−0.830605	+	0.556863i	$0.812005\pi$
$968$		0			0
$969$	0.161463	−	0.185314i	0.00518693	−	0.00595315i
$970$		0			0
$971$		−	33.5907i		−	1.07798i	−0.842313	−	0.538989i	$-0.818806\pi$
$971$		−	33.5907i		−	1.07798i	0.842313	−	0.538989i	$-0.181194\pi$
$972$		0			0
$973$	−61.1398	+	61.1398i	−1.96005	+	1.96005i
$974$		0			0
$975$	−3.98516	−	2.19258i	−0.127627	−	0.0702187i
$976$		0			0
$977$	−23.6065	+	23.6065i	−0.755239	+	0.755239i	−0.975452	−	0.220213i	$-0.929325\pi$
$977$	−23.6065	+	23.6065i	−0.755239	+	0.755239i	0.220213	+	0.975452i	$0.429325\pi$
$978$		0			0
$979$			8.66613i			0.276971i
$980$		0			0
$981$	−3.15953	−	22.8595i	−0.100876	−	0.729848i
$982$		0			0
$983$	33.5917	+	33.5917i	1.07141	+	1.07141i	0.997246	+	0.0741633i	$0.0236286\pi$
$983$	33.5917	+	33.5917i	1.07141	+	1.07141i	0.0741633	+	0.997246i	$0.476371\pi$
$984$		0			0
$985$	21.9276	+	17.6787i	0.698671	+	0.563290i
$986$		0			0
$987$	−2.86018	−	41.5840i	−0.0910404	−	1.32363i
$988$		0			0
$989$	−11.8299			−0.376168
$990$		0			0
$991$	0.835595			0.0265435			0.0132718	−	0.999912i	$-0.495775\pi$
$991$	0.835595			0.0265435			0.0132718	+	0.999912i	$0.495775\pi$
$992$		0			0
$993$	−0.0672127	−	0.977203i	−0.00213293	−	0.0310106i
$994$		0			0
$995$	−15.8535	+	1.70074i	−0.502589	+	0.0539171i
$996$		0			0
$997$	−3.47311	−	3.47311i	−0.109994	−	0.109994i	0.649968	−	0.759962i	$-0.274782\pi$
$997$	−3.47311	−	3.47311i	−0.109994	−	0.109994i	−0.759962	+	0.649968i	$0.774782\pi$
$998$		0			0
$999$	−4.75226	+	7.26331i	−0.150355	+	0.229801i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.r.c.737.17	✓	80
3.2	odd	2	inner	1380.2.r.c.737.39	yes	80
5.3	odd	4	inner	1380.2.r.c.1013.39	yes	80
15.8	even	4	inner	1380.2.r.c.1013.17	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.r.c.737.17	✓	80	1.1	even	1	trivial
1380.2.r.c.737.39	yes	80	3.2	odd	2	inner
1380.2.r.c.1013.17	yes	80	15.8	even	4	inner
1380.2.r.c.1013.39	yes	80	5.3	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:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.118851 - 1.72797i) q^{3} +(0.238514 + 2.22331i) q^{5} +(2.86460 + 2.86460i) q^{7} +(-2.97175 + 0.410741i) q^{9} +O(q^{10})\)	\(q+(-0.118851 - 1.72797i) q^{3} +(0.238514 + 2.22331i) q^{5} +(2.86460 + 2.86460i) q^{7} +(-2.97175 + 0.410741i) q^{9} +0.979600i q^{11} +(-0.371384 + 0.371384i) q^{13} +(3.81346 - 0.676387i) q^{15} +(-2.74647 + 2.74647i) q^{17} -0.0365351i q^{19} +(4.60948 - 5.29040i) q^{21} +(0.707107 + 0.707107i) q^{23} +(-4.88622 + 1.06058i) q^{25} +(1.06294 + 5.08627i) q^{27} -8.55018 q^{29} -4.25537 q^{31} +(1.69272 - 0.116426i) q^{33} +(-5.68565 + 7.05214i) q^{35} +(1.18118 + 1.18118i) q^{37} +(0.685879 + 0.597600i) q^{39} +3.46350i q^{41} +(-8.36498 + 8.36498i) q^{43} +(-1.62201 - 6.50915i) q^{45} +(4.20045 - 4.20045i) q^{47} +9.41186i q^{49} +(5.07223 + 4.41939i) q^{51} +(-4.49366 - 4.49366i) q^{53} +(-2.17796 + 0.233648i) q^{55} +(-0.0631315 + 0.00434223i) q^{57} +2.38445 q^{59} +12.8261 q^{61} +(-9.68948 - 7.33626i) q^{63} +(-0.914281 - 0.737121i) q^{65} +(-4.68784 - 4.68784i) q^{67} +(1.13782 - 1.30590i) q^{69} +15.3783i q^{71} +(8.21790 - 8.21790i) q^{73} +(2.41338 + 8.31719i) q^{75} +(-2.80616 + 2.80616i) q^{77} -9.27494i q^{79} +(8.66258 - 2.44124i) q^{81} +(3.54552 + 3.54552i) q^{83} +(-6.76132 - 5.45118i) q^{85} +(1.01620 + 14.7744i) q^{87} +8.84660 q^{89} -2.12773 q^{91} +(0.505755 + 7.35315i) q^{93} +(0.0812288 - 0.00871412i) q^{95} +(3.88352 + 3.88352i) q^{97} +(-0.402362 - 2.91113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{3}+O(q^{10}) \) 80 * q + 8 * q^3	\( 80 q + 8 q^{3} + 32 q^{13} + 24 q^{21} - 32 q^{25} - 28 q^{27} - 32 q^{31} - 44 q^{33} + 24 q^{37} - 32 q^{43} + 88 q^{45} + 16 q^{51} + 8 q^{55} + 16 q^{57} - 32 q^{61} - 12 q^{63} - 16 q^{67} - 32 q^{73} + 4 q^{75} - 64 q^{81} - 32 q^{85} + 64 q^{91} + 8 q^{93} - 96 q^{97}+O(q^{100}) \) 80 * q + 8 * q^3 + 32 * q^13 + 24 * q^21 - 32 * q^25 - 28 * q^27 - 32 * q^31 - 44 * q^33 + 24 * q^37 - 32 * q^43 + 88 * q^45 + 16 * q^51 + 8 * q^55 + 16 * q^57 - 32 * q^61 - 12 * q^63 - 16 * q^67 - 32 * q^73 + 4 * q^75 - 64 * q^81 - 32 * q^85 + 64 * q^91 + 8 * q^93 - 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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