LMFDB - Embedded newform 380.3.x.a.197.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(197,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.x (of order $12$, degree $4$, 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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.3
Character	$\chi$	$=$	380.197
Dual form			380.3.x.a.353.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.39499 - 1.17763i) q^{3} +(4.76910 - 1.50189i) q^{5} +(2.17731 + 2.17731i) q^{7} +(10.1349 + 5.85137i) q^{9} +O(q^{10})$	\(q+(-4.39499 - 1.17763i) q^{3} +(4.76910 - 1.50189i) q^{5} +(2.17731 + 2.17731i) q^{7} +(10.1349 + 5.85137i) q^{9} -13.6120 q^{11} +(4.12219 + 15.3842i) q^{13} +(-22.7288 + 0.984556i) q^{15} +(-0.483152 + 1.80315i) q^{17} +(11.5760 - 15.0664i) q^{19} +(-7.00518 - 12.1333i) q^{21} +(-0.635421 - 2.37142i) q^{23} +(20.4886 - 14.3254i) q^{25} +(-8.69569 - 8.69569i) q^{27} +(40.5826 + 23.4304i) q^{29} +14.1381 q^{31} +(59.8248 + 16.0300i) q^{33} +(13.6539 + 7.11372i) q^{35} +(16.1016 + 16.1016i) q^{37} -72.4680i q^{39} +(-8.41028 - 14.5670i) q^{41} +(80.8819 + 21.6722i) q^{43} +(57.1224 + 12.6843i) q^{45} +(0.201661 - 0.0540349i) q^{47} -39.5186i q^{49} +(4.24689 - 7.35583i) q^{51} +(11.0149 + 41.1083i) q^{53} +(-64.9172 + 20.4438i) q^{55} +(-68.6190 + 52.5844i) q^{57} +(39.3120 - 22.6968i) q^{59} +(58.3324 - 101.035i) q^{61} +(9.32651 + 34.8070i) q^{63} +(42.7647 + 67.1779i) q^{65} +(-3.97436 + 1.06493i) q^{67} +11.1707i q^{69} +(-25.5943 - 44.3307i) q^{71} +(37.4121 + 10.0246i) q^{73} +(-106.917 + 38.8317i) q^{75} +(-29.6376 - 29.6376i) q^{77} +(-97.8112 + 56.4713i) q^{79} +(-24.6852 - 42.7561i) q^{81} +(-58.0168 + 58.0168i) q^{83} +(0.403937 + 9.32503i) q^{85} +(-150.768 - 150.768i) q^{87} +(92.4809 + 53.3939i) q^{89} +(-24.5210 + 42.4716i) q^{91} +(-62.1367 - 16.6495i) q^{93} +(32.5788 - 89.2391i) q^{95} +(-12.0651 + 45.0275i) q^{97} +(-137.956 - 79.6491i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{5} - 12 q^{7}+O(q^{10}) $ 80 * q + 2 * q^5 - 12 * q^7	$ 80 q + 2 q^{5} - 12 q^{7} - 16 q^{11} - 8 q^{13} - 6 q^{15} - 32 q^{17} + 24 q^{21} - 60 q^{23} - 50 q^{25} - 84 q^{27} + 112 q^{31} + 12 q^{33} + 76 q^{35} - 128 q^{37} - 40 q^{41} + 58 q^{43} - 116 q^{45} + 70 q^{47} - 8 q^{51} - 82 q^{53} - 136 q^{55} + 322 q^{57} + 104 q^{61} - 86 q^{63} + 280 q^{65} - 72 q^{67} - 32 q^{71} - 292 q^{73} + 108 q^{75} + 420 q^{77} + 336 q^{81} - 100 q^{83} - 296 q^{85} + 200 q^{87} + 112 q^{91} + 16 q^{93} - 308 q^{95} - 122 q^{97}+O(q^{100}) $ 80 * q + 2 * q^5 - 12 * q^7 - 16 * q^11 - 8 * q^13 - 6 * q^15 - 32 * q^17 + 24 * q^21 - 60 * q^23 - 50 * q^25 - 84 * q^27 + 112 * q^31 + 12 * q^33 + 76 * q^35 - 128 * q^37 - 40 * q^41 + 58 * q^43 - 116 * q^45 + 70 * q^47 - 8 * q^51 - 82 * q^53 - 136 * q^55 + 322 * q^57 + 104 * q^61 - 86 * q^63 + 280 * q^65 - 72 * q^67 - 32 * q^71 - 292 * q^73 + 108 * q^75 + 420 * q^77 + 336 * q^81 - 100 * q^83 - 296 * q^85 + 200 * q^87 + 112 * q^91 + 16 * q^93 - 308 * q^95 - 122 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−4.39499	−	1.17763i	−1.46500	−	0.392545i	−0.563784	−	0.825922i	$-0.690655\pi$
$3$	−4.39499	−	1.17763i	−1.46500	−	0.392545i	−0.901212	+	0.433378i	$0.857322\pi$
$4$		0			0
$5$	4.76910	−	1.50189i	0.953820	−	0.300379i
$5$	4.76910	−	1.50189i	0.953820	−	0.300379i
$6$		0			0
$7$	2.17731	+	2.17731i	0.311044	+	0.311044i	0.845314	−	0.534270i	$-0.179413\pi$
$7$	2.17731	+	2.17731i	0.311044	+	0.311044i	−0.534270	+	0.845314i	$0.679413\pi$
$8$		0			0
$9$	10.1349	+	5.85137i	1.12610	+	0.650152i
$10$		0			0
$11$	−13.6120			−1.23746			−0.618729	−	0.785604i	$-0.712352\pi$
$11$	−13.6120			−1.23746			−0.618729	+	0.785604i	$0.712352\pi$
$12$		0			0
$13$	4.12219	+	15.3842i	0.317092	+	1.18340i	0.922026	+	0.387128i	$0.126533\pi$
$13$	4.12219	+	15.3842i	0.317092	+	1.18340i	−0.604934	+	0.796275i	$0.706801\pi$
$14$		0			0
$15$	−22.7288	+	0.984556i	−1.51525	+	0.0656371i
$16$		0			0
$17$	−0.483152	+	1.80315i	−0.0284207	+	0.106067i	−0.978679	−	0.205395i	$-0.934152\pi$
$17$	−0.483152	+	1.80315i	−0.0284207	+	0.106067i	0.950258	+	0.311462i	$0.100819\pi$
$18$		0			0
$19$	11.5760	−	15.0664i	0.609262	−	0.792969i
$19$	11.5760	−	15.0664i	0.609262	−	0.792969i
$20$		0			0
$21$	−7.00518	−	12.1333i	−0.333580	−	0.577777i
$22$		0			0
$23$	−0.635421	−	2.37142i	−0.0276270	−	0.103105i	0.950736	−	0.310003i	$-0.100330\pi$
$23$	−0.635421	−	2.37142i	−0.0276270	−	0.103105i	−0.978363	+	0.206898i	$0.933663\pi$
$24$		0			0
$25$	20.4886	−	14.3254i	0.819545	−	0.573015i
$26$		0			0
$27$	−8.69569	−	8.69569i	−0.322063	−	0.322063i
$28$		0			0
$29$	40.5826	+	23.4304i	1.39940	+	0.807944i	0.994330	−	0.106342i	$-0.0339139\pi$
$29$	40.5826	+	23.4304i	1.39940	+	0.807944i	0.405070	+	0.914286i	$0.367247\pi$
$30$		0			0
$31$	14.1381			0.456067			0.228034	−	0.973653i	$-0.426770\pi$
$31$	14.1381			0.456067			0.228034	+	0.973653i	$0.426770\pi$
$32$		0			0
$33$	59.8248	+	16.0300i	1.81287	+	0.485757i
$34$		0			0
$35$	13.6539	+	7.11372i	0.390111	+	0.203249i
$36$		0			0
$37$	16.1016	+	16.1016i	0.435179	+	0.435179i	0.890386	−	0.455207i	$-0.150435\pi$
$37$	16.1016	+	16.1016i	0.435179	+	0.435179i	−0.455207	+	0.890386i	$0.650435\pi$
$38$		0			0
$39$		−	72.4680i		−	1.85815i
$40$		0			0
$41$	−8.41028	−	14.5670i	−0.205129	−	0.355293i	0.745045	−	0.667014i	$-0.232428\pi$
$41$	−8.41028	−	14.5670i	−0.205129	−	0.355293i	−0.950174	+	0.311721i	$0.899095\pi$
$42$		0			0
$43$	80.8819	+	21.6722i	1.88097	+	0.504006i	0.999495	+	0.0317832i	$0.0101186\pi$
$43$	80.8819	+	21.6722i	1.88097	+	0.504006i	0.881479	+	0.472222i	$0.156548\pi$
$44$		0			0
$45$	57.1224	+	12.6843i	1.26939	+	0.281873i
$46$		0			0
$47$	0.201661	−	0.0540349i	0.00429066	−	0.00114968i	−0.256673	−	0.966498i	$-0.582626\pi$
$47$	0.201661	−	0.0540349i	0.00429066	−	0.00114968i	0.260964	+	0.965349i	$0.415960\pi$
$48$		0			0
$49$		−	39.5186i		−	0.806503i
$50$		0			0
$51$	4.24689	−	7.35583i	0.0832724	−	0.144232i
$52$		0			0
$53$	11.0149	+	41.1083i	0.207829	+	0.775628i	0.988569	+	0.150771i	$0.0481758\pi$
$53$	11.0149	+	41.1083i	0.207829	+	0.775628i	−0.780740	+	0.624856i	$0.785158\pi$
$54$		0			0
$55$	−64.9172	+	20.4438i	−1.18031	+	0.371706i
$56$		0			0
$57$	−68.6190	+	52.5844i	−1.20384	+	0.922534i
$58$		0			0
$59$	39.3120	−	22.6968i	0.666305	−	0.384692i	−0.128370	−	0.991726i	$-0.540974\pi$
$59$	39.3120	−	22.6968i	0.666305	−	0.384692i	0.794675	+	0.607035i	$0.207641\pi$
$60$		0			0
$61$	58.3324	−	101.035i	0.956268	−	1.65631i	0.224830	−	0.974398i	$-0.427817\pi$
$61$	58.3324	−	101.035i	0.956268	−	1.65631i	0.731439	−	0.681907i	$-0.238849\pi$
$62$		0			0
$63$	9.32651	+	34.8070i	0.148040	+	0.552492i
$64$		0			0
$65$	42.7647	+	67.1779i	0.657918	+	1.03351i
$66$		0			0
$67$	−3.97436	+	1.06493i	−0.0593188	+	0.0158944i	−0.288356	−	0.957523i	$-0.593109\pi$
$67$	−3.97436	+	1.06493i	−0.0593188	+	0.0158944i	0.229038	+	0.973418i	$0.426442\pi$
$68$		0			0
$69$			11.1707i			0.161894i
$70$		0			0
$71$	−25.5943	−	44.3307i	−0.360483	−	0.624376i	0.627557	−	0.778571i	$-0.284055\pi$
$71$	−25.5943	−	44.3307i	−0.360483	−	0.624376i	−0.988040	+	0.154195i	$0.950722\pi$
$72$		0			0
$73$	37.4121	+	10.0246i	0.512495	+	0.137323i	0.505793	−	0.862655i	$-0.331200\pi$
$73$	37.4121	+	10.0246i	0.512495	+	0.137323i	0.00670217	+	0.999978i	$0.497867\pi$
$74$		0			0
$75$	−106.917	+	38.8317i	−1.42556	+	0.517756i
$76$		0			0
$77$	−29.6376	−	29.6376i	−0.384904	−	0.384904i
$78$		0			0
$79$	−97.8112	+	56.4713i	−1.23812	+	0.714827i	−0.968709	−	0.248199i	$-0.920161\pi$
$79$	−97.8112	+	56.4713i	−1.23812	+	0.714827i	−0.269407	+	0.963026i	$0.586828\pi$
$80$		0			0
$81$	−24.6852	−	42.7561i	−0.304756	−	0.527853i
$82$		0			0
$83$	−58.0168	+	58.0168i	−0.698998	+	0.698998i	−0.964194	−	0.265196i	$-0.914563\pi$
$83$	−58.0168	+	58.0168i	−0.698998	+	0.698998i	0.265196	+	0.964194i	$0.414563\pi$
$84$		0			0
$85$	0.403937	+	9.32503i	0.00475220	+	0.109706i
$86$		0			0
$87$	−150.768	−	150.768i	−1.73296	−	1.73296i
$88$		0			0
$89$	92.4809	+	53.3939i	1.03911	+	0.599931i	0.919581	−	0.392899i	$-0.128528\pi$
$89$	92.4809	+	53.3939i	1.03911	+	0.599931i	0.119530	+	0.992831i	$0.461861\pi$
$90$		0			0
$91$	−24.5210	+	42.4716i	−0.269461	+	0.466720i
$92$		0			0
$93$	−62.1367	−	16.6495i	−0.668137	−	0.179027i
$94$		0			0
$95$	32.5788	−	89.2391i	0.342935	−	0.939359i
$96$		0			0
$97$	−12.0651	+	45.0275i	−0.124382	+	0.464201i	−0.999817	−	0.0191353i	$-0.993909\pi$
$97$	−12.0651	+	45.0275i	−0.124382	+	0.464201i	0.875435	+	0.483337i	$0.160575\pi$
$98$		0			0
$99$	−137.956	−	79.6491i	−1.39350	−	0.804536i
$100$		0			0
$101$	13.9402	−	24.1451i	0.138021	−	0.239060i	−0.788726	−	0.614745i	$-0.789259\pi$
$101$	13.9402	−	24.1451i	0.138021	−	0.239060i	0.926748	+	0.375685i	$0.122592\pi$
$102$		0			0
$103$	−99.8449	+	99.8449i	−0.969368	+	0.969368i	−0.999545	−	0.0301762i	$-0.990393\pi$
$103$	−99.8449	+	99.8449i	−0.969368	+	0.969368i	0.0301762	+	0.999545i	$0.490393\pi$
$104$		0			0
$105$	−51.6314	−	47.3440i	−0.491727	−	0.450895i
$106$		0			0
$107$	73.6132	+	73.6132i	0.687974	+	0.687974i	0.961784	−	0.273810i	$-0.0882839\pi$
$107$	73.6132	+	73.6132i	0.687974	+	0.687974i	−0.273810	+	0.961784i	$0.588284\pi$
$108$		0			0
$109$	−81.9039	+	47.2873i	−0.751412	+	0.433828i	−0.826204	−	0.563371i	$-0.809504\pi$
$109$	−81.9039	+	47.2873i	−0.751412	+	0.433828i	0.0747917	+	0.997199i	$0.476171\pi$
$110$		0			0
$111$	−51.8047	−	89.7283i	−0.466709	−	0.808363i
$112$		0			0
$113$	−52.5274	+	52.5274i	−0.464844	+	0.464844i	−0.900240	−	0.435395i	$-0.856609\pi$
$113$	−52.5274	+	52.5274i	−0.464844	+	0.464844i	0.435395	+	0.900240i	$0.356609\pi$
$114$		0			0
$115$	−6.59201	−	10.3552i	−0.0573218	−	0.0900453i
$116$		0			0
$117$	−48.2410	+	180.038i	−0.412316	+	1.53878i
$118$		0			0
$119$	−4.97798	+	2.87404i	−0.0418317	+	0.0241516i
$120$		0			0
$121$	64.2876			0.531302
$122$		0			0
$123$	19.8085	+	73.9261i	0.161044	+	0.601026i
$124$		0			0
$125$	76.1971	−	99.0909i	0.609577	−	0.792727i
$126$		0			0
$127$	196.049	−	52.5313i	1.54370	−	0.413632i	0.616238	−	0.787560i	$-0.288656\pi$
$127$	196.049	−	52.5313i	1.54370	−	0.413632i	0.927458	+	0.373928i	$0.121989\pi$
$128$		0			0
$129$	−329.953	−	190.498i	−2.55778	−	1.47673i
$130$		0			0
$131$	54.2432	+	93.9520i	0.414070	+	0.717191i	0.995330	−	0.0965271i	$-0.0307735\pi$
$131$	54.2432	+	93.9520i	0.414070	+	0.717191i	−0.581260	+	0.813718i	$0.697440\pi$
$132$		0			0
$133$	58.0087	−	7.59976i	0.436156	−	0.0571410i
$134$		0			0
$135$	−54.5306	−	28.4106i	−0.403931	−	0.210449i
$136$		0			0
$137$	−34.2930	+	9.18879i	−0.250314	+	0.0670714i	−0.381794	−	0.924247i	$-0.624694\pi$
$137$	−34.2930	+	9.18879i	−0.250314	+	0.0670714i	0.131480	+	0.991319i	$0.458027\pi$
$138$		0			0
$139$	190.014	+	109.705i	1.36701	+	0.789244i	0.990545	−	0.137187i	$-0.0438061\pi$
$139$	190.014	+	109.705i	1.36701	+	0.789244i	0.376465	+	0.926431i	$0.377139\pi$
$140$		0			0
$141$	−0.949930			−0.00673709
$142$		0			0
$143$	−56.1115	−	209.411i	−0.392388	−	1.46441i
$144$		0			0
$145$	228.732	+	50.7910i	1.57746	+	0.350283i
$146$		0			0
$147$	−46.5385	+	173.684i	−0.316588	+	1.18152i
$148$		0			0
$149$	−83.0853	+	47.9693i	−0.557620	+	0.321942i	−0.752190	−	0.658947i	$-0.771002\pi$
$149$	−83.0853	+	47.9693i	−0.557620	+	0.321942i	0.194570	+	0.980889i	$0.437669\pi$
$150$		0			0
$151$	103.234			0.683668			0.341834	−	0.939760i	$-0.388952\pi$
$151$	103.234			0.683668			0.341834	+	0.939760i	$0.388952\pi$
$152$		0			0
$153$	−15.4476	+	15.4476i	−0.100964	+	0.100964i
$154$		0			0
$155$	67.4260	−	21.2339i	0.435006	−	0.136993i
$156$		0			0
$157$	35.6648	−	133.103i	0.227164	−	0.847789i	−0.754361	−	0.656459i	$-0.772053\pi$
$157$	35.6648	−	133.103i	0.227164	−	0.847789i	0.981526	−	0.191330i	$-0.0612800\pi$
$158$		0			0
$159$		−	193.642i		−	1.21787i
$160$		0			0
$161$	3.77981	−	6.54683i	0.0234771	−	0.0406635i
$162$		0			0
$163$	102.016	−	102.016i	0.625863	−	0.625863i	−0.321161	−	0.947025i	$-0.604073\pi$
$163$	102.016	−	102.016i	0.625863	−	0.625863i	0.947025	+	0.321161i	$0.104073\pi$
$164$		0			0
$165$	309.386	−	13.4018i	1.87506	−	0.0812231i
$166$		0			0
$167$	−125.723	+	33.6873i	−0.752830	+	0.201720i	−0.614773	−	0.788704i	$-0.710752\pi$
$167$	−125.723	+	33.6873i	−0.752830	+	0.201720i	−0.138057	+	0.990424i	$0.544086\pi$
$168$		0			0
$169$	−73.3241	+	42.3337i	−0.433870	+	0.250495i
$170$		0			0
$171$	205.480	−	84.9608i	1.20164	−	0.496847i
$172$		0			0
$173$	−12.9811	−	3.47829i	−0.0750355	−	0.0201057i	0.221106	−	0.975250i	$-0.429033\pi$
$173$	−12.9811	−	3.47829i	−0.0750355	−	0.0201057i	−0.296142	+	0.955144i	$0.595700\pi$
$174$		0			0
$175$	75.8009	+	13.4193i	0.433148	+	0.0766818i
$176$		0			0
$177$	−199.504	+	53.4570i	−1.12714	+	0.302017i
$178$		0			0
$179$		−	105.771i		−	0.590899i	−0.955358	−	0.295450i	$-0.904531\pi$
$179$		−	105.771i		−	0.590899i	0.955358	−	0.295450i	$-0.0954695\pi$
$180$		0			0
$181$	−116.077	+	201.051i	−0.641309	+	1.11078i	0.343831	+	0.939031i	$0.388275\pi$
$181$	−116.077	+	201.051i	−0.641309	+	1.11078i	−0.985141	+	0.171749i	$0.945058\pi$
$182$		0			0
$183$	−375.352	+	375.352i	−2.05110	+	2.05110i
$184$		0			0
$185$	100.973	+	52.6074i	0.545801	+	0.284364i
$186$		0			0
$187$	6.57668	−	24.5445i	0.0351694	−	0.131254i
$188$		0			0
$189$		−	37.8664i		−	0.200351i
$190$		0			0
$191$	−317.025			−1.65982			−0.829909	−	0.557900i	$-0.811607\pi$
$191$	−317.025			−1.65982			−0.829909	+	0.557900i	$0.811607\pi$
$192$		0			0
$193$	−9.44468	−	2.53069i	−0.0489361	−	0.0131124i	0.234268	−	0.972172i	$-0.424731\pi$
$193$	−9.44468	−	2.53069i	−0.0489361	−	0.0131124i	−0.283204	+	0.959060i	$0.591397\pi$
$194$		0			0
$195$	−108.839	−	345.607i	−0.558150	−	1.77234i
$196$		0			0
$197$	−220.185	−	220.185i	−1.11769	−	1.11769i	−0.992080	−	0.125610i	$-0.959911\pi$
$197$	−220.185	−	220.185i	−1.11769	−	1.11769i	−0.125610	−	0.992080i	$-0.540089\pi$
$198$		0			0
$199$	−129.811	−	74.9463i	−0.652316	−	0.376615i	0.137027	−	0.990567i	$-0.456245\pi$
$199$	−129.811	−	74.9463i	−0.652316	−	0.376615i	−0.789343	+	0.613953i	$0.789579\pi$
$200$		0			0
$201$	18.7214			0.0931411
$202$		0			0
$203$	37.3457	+	139.376i	0.183969	+	0.686581i
$204$		0			0
$205$	−61.9876	−	56.8403i	−0.302378	−	0.277270i
$206$		0			0
$207$	7.43617	−	27.7521i	0.0359235	−	0.134068i
$208$		0			0
$209$	−157.573	+	205.085i	−0.753936	+	0.981266i
$210$		0			0
$211$	136.325	+	236.122i	0.646091	+	1.11906i	0.984048	+	0.177901i	$0.0569307\pi$
$211$	136.325	+	236.122i	0.646091	+	1.11906i	−0.337958	+	0.941161i	$0.609736\pi$
$212$		0			0
$213$	60.2815	+	224.974i	0.283012	+	1.05621i
$214$		0			0
$215$	418.283	−	18.1190i	1.94550	−	0.0842744i
$216$		0			0
$217$	30.7830	+	30.7830i	0.141857	+	0.141857i
$218$		0			0
$219$	−152.621	−	88.1156i	−0.696898	−	0.402354i
$220$		0			0
$221$	−29.7317			−0.134532
$222$		0			0
$223$	44.9224	+	12.0369i	0.201446	+	0.0539772i	0.358131	−	0.933671i	$-0.383414\pi$
$223$	44.9224	+	12.0369i	0.201446	+	0.0539772i	−0.156685	+	0.987649i	$0.550081\pi$
$224$		0			0
$225$	291.473	−	25.2992i	1.29543	−	0.112441i
$226$		0			0
$227$	−258.953	−	258.953i	−1.14076	−	1.14076i	−0.988311	−	0.152453i	$-0.951283\pi$
$227$	−258.953	−	258.953i	−1.14076	−	1.14076i	−0.152453	−	0.988311i	$-0.548717\pi$
$228$		0			0
$229$			297.223i			1.29792i	0.760823	+	0.648959i	$0.224795\pi$
$229$			297.223i			1.29792i	−0.760823	+	0.648959i	$0.775205\pi$
$230$		0			0
$231$	95.3548	+	165.159i	0.412791	+	0.714975i
$232$		0			0
$233$	−46.3453	−	12.4182i	−0.198907	−	0.0532969i	0.157990	−	0.987441i	$-0.449499\pi$
$233$	−46.3453	−	12.4182i	−0.198907	−	0.0532969i	−0.356897	+	0.934144i	$0.616165\pi$
$234$		0			0
$235$	0.880586	−	0.560571i	0.00374717	−	0.00238541i
$236$		0			0
$237$	496.382	−	133.005i	2.09444	−	0.561203i
$238$		0			0
$239$		−	247.323i		−	1.03482i	−0.855737	−	0.517411i	$-0.826896\pi$
$239$		−	247.323i		−	1.03482i	0.855737	−	0.517411i	$-0.173104\pi$
$240$		0			0
$241$	197.031	−	341.268i	0.817557	−	1.41605i	−0.0899199	−	0.995949i	$-0.528661\pi$
$241$	197.031	−	341.268i	0.817557	−	1.41605i	0.907477	−	0.420102i	$-0.138006\pi$
$242$		0			0
$243$	86.7859	+	323.889i	0.357144	+	1.33288i
$244$		0			0
$245$	−59.3528	−	188.468i	−0.242256	−	0.769259i
$246$		0			0
$247$	279.504	+	115.981i	1.13159	+	0.469558i
$248$		0			0
$249$	323.306	−	186.661i	1.29842	−	0.749642i
$250$		0			0
$251$	78.4750	−	135.923i	0.312649	−	0.541525i	−0.666286	−	0.745697i	$-0.732117\pi$
$251$	78.4750	−	135.923i	0.312649	−	0.541525i	0.978935	+	0.204172i	$0.0654502\pi$
$252$		0			0
$253$	8.64937	+	32.2799i	0.0341872	+	0.127588i
$254$		0			0
$255$	9.20617	−	41.4591i	0.0361026	−	0.162585i
$256$		0			0
$257$	−248.353	+	66.5459i	−0.966353	+	0.258934i	−0.707287	−	0.706926i	$-0.750081\pi$
$257$	−248.353	+	66.5459i	−0.966353	+	0.258934i	−0.259066	+	0.965860i	$0.583415\pi$
$258$		0			0
$259$			70.1165i			0.270720i
$260$		0			0
$261$	274.200	+	474.928i	1.05057	+	1.81965i
$262$		0			0
$263$	−196.893	−	52.7572i	−0.748641	−	0.200598i	−0.135726	−	0.990746i	$-0.543337\pi$
$263$	−196.893	−	52.7572i	−0.748641	−	0.200598i	−0.612915	+	0.790149i	$0.710003\pi$
$264$		0			0
$265$	114.272	+	179.506i	0.431213	+	0.677382i
$266$		0			0
$267$	−343.574	−	343.574i	−1.28679	−	1.28679i
$268$		0			0
$269$	−335.868	+	193.914i	−1.24858	+	0.720869i	−0.970826	−	0.239783i	$-0.922924\pi$
$269$	−335.868	+	193.914i	−1.24858	+	0.720869i	−0.277755	+	0.960652i	$0.589590\pi$
$270$		0			0
$271$	126.579	+	219.242i	0.467083	+	0.809011i	0.999293	−	0.0376012i	$-0.0119717\pi$
$271$	126.579	+	219.242i	0.467083	+	0.809011i	−0.532210	+	0.846612i	$0.678638\pi$
$272$		0			0
$273$	157.785	−	157.785i	0.577968	−	0.577968i
$274$		0			0
$275$	−278.892	+	194.997i	−1.01415	+	0.709082i
$276$		0			0
$277$	−257.146	−	257.146i	−0.928324	−	0.928324i	0.0692741	−	0.997598i	$-0.477932\pi$
$277$	−257.146	−	257.146i	−0.928324	−	0.928324i	−0.997598	+	0.0692741i	$0.977932\pi$
$278$		0			0
$279$	143.288	+	82.7272i	0.513576	+	0.296513i
$280$		0			0
$281$	−55.7998	+	96.6481i	−0.198576	+	0.343943i	−0.948067	−	0.318071i	$-0.896965\pi$
$281$	−55.7998	+	96.6481i	−0.198576	+	0.343943i	0.749491	+	0.662014i	$0.230298\pi$
$282$		0			0
$283$	441.878	+	118.401i	1.56141	+	0.418378i	0.933109	−	0.359595i	$-0.117085\pi$
$283$	441.878	+	118.401i	1.56141	+	0.418378i	0.628298	+	0.777973i	$0.283752\pi$
$284$		0			0
$285$	−248.275	+	353.839i	−0.871139	+	1.24154i
$286$		0			0
$287$	13.4052	−	50.0287i	0.0467079	−	0.174316i
$288$		0			0
$289$	247.263	+	142.758i	0.855583	+	0.493971i
$290$		0			0
$291$	106.052	−	183.687i	0.364439	−	0.631228i
$292$		0			0
$293$	246.968	−	246.968i	0.842895	−	0.842895i	−0.146340	−	0.989234i	$-0.546749\pi$
$293$	246.968	−	246.968i	0.842895	−	0.842895i	0.989234	+	0.146340i	$0.0467492\pi$
$294$		0			0
$295$	153.395	−	167.286i	0.519982	−	0.567071i
$296$		0			0
$297$	118.366	+	118.366i	0.398539	+	0.398539i
$298$		0			0
$299$	33.8632	−	19.5509i	0.113255	−	0.0653877i
$300$		0			0
$301$	128.918	+	223.292i	0.428298	+	0.741834i
$302$		0			0
$303$	−89.7008	+	89.7008i	−0.296042	+	0.296042i
$304$		0			0
$305$	126.450	−	569.453i	0.414589	−	1.86706i
$306$		0			0
$307$	−88.4860	+	330.234i	−0.288228	+	1.07568i	0.658220	+	0.752825i	$0.271310\pi$
$307$	−88.4860	+	330.234i	−0.288228	+	1.07568i	−0.946448	+	0.322856i	$0.895357\pi$
$308$		0			0
$309$	556.398	−	321.237i	1.80064	−	1.03960i
$310$		0			0
$311$	−76.5432			−0.246120			−0.123060	−	0.992399i	$-0.539271\pi$
$311$	−76.5432			−0.246120			−0.123060	+	0.992399i	$0.539271\pi$
$312$		0			0
$313$	−100.819	−	376.261i	−0.322105	−	1.20211i	−0.917190	−	0.398450i	$-0.869548\pi$
$313$	−100.819	−	376.261i	−0.322105	−	1.20211i	0.595085	−	0.803663i	$-0.297118\pi$
$314$		0			0
$315$	96.7555	+	151.991i	0.307160	+	0.482510i
$316$		0			0
$317$	531.336	−	142.371i	1.67614	−	0.449120i	0.709384	−	0.704822i	$-0.248973\pi$
$317$	531.336	−	142.371i	1.67614	−	0.449120i	0.966756	+	0.255702i	$0.0823067\pi$
$318$		0			0
$319$	−552.412	−	318.935i	−1.73170	−	0.999796i
$320$		0			0
$321$	−236.840	−	410.219i	−0.737819	−	1.27794i
$322$		0			0
$323$	21.5740	+	28.1525i	0.0667925	+	0.0871596i
$324$		0			0
$325$	304.843	+	256.150i	0.937978	+	0.788154i
$326$		0			0
$327$	415.654	−	111.374i	1.27111	−	0.340594i
$328$		0			0
$329$	0.556729	+	0.321427i	0.00169218	+	0.000976983i
$330$		0			0
$331$	156.749			0.473562			0.236781	−	0.971563i	$-0.423908\pi$
$331$	156.749			0.473562			0.236781	+	0.971563i	$0.423908\pi$
$332$		0			0
$333$	68.9714	+	257.405i	0.207121	+	0.772987i
$334$		0			0
$335$	−17.3547	+	11.0478i	−0.0518051	+	0.0329785i
$336$		0			0
$337$	−38.7752	+	144.711i	−0.115060	+	0.429410i	−0.999291	−	0.0376395i	$-0.988016\pi$
$337$	−38.7752	+	144.711i	−0.115060	+	0.429410i	0.884231	+	0.467049i	$0.154683\pi$
$338$		0			0
$339$	292.715	−	168.999i	0.863468	−	0.498523i
$340$		0			0
$341$	−192.448			−0.564364
$342$		0			0
$343$	192.733	−	192.733i	0.561902	−	0.561902i
$344$		0			0
$345$	16.7772	+	53.2740i	0.0486294	+	0.154417i
$346$		0			0
$347$	−14.6394	+	54.6348i	−0.0421884	+	0.157449i	−0.983807	−	0.179233i	$-0.942638\pi$
$347$	−14.6394	+	54.6348i	−0.0421884	+	0.157449i	0.941618	+	0.336683i	$0.109305\pi$
$348$		0			0
$349$			239.484i			0.686200i	0.939299	+	0.343100i	$0.111477\pi$
$349$			239.484i			0.686200i	−0.939299	+	0.343100i	$0.888523\pi$
$350$		0			0
$351$	97.9313	−	169.622i	0.279006	−	0.483253i
$352$		0			0
$353$	−77.8369	+	77.8369i	−0.220501	+	0.220501i	−0.808709	−	0.588208i	$-0.799834\pi$
$353$	−77.8369	+	77.8369i	−0.220501	+	0.220501i	0.588208	+	0.808709i	$0.299834\pi$
$354$		0			0
$355$	−188.642	−	172.977i	−0.531386	−	0.487260i
$356$		0			0
$357$	25.2627	−	6.76913i	0.0707639	−	0.0189611i
$358$		0			0
$359$	28.9571	−	16.7184i	0.0806604	−	0.0465693i	−0.459127	−	0.888370i	$-0.651838\pi$
$359$	28.9571	−	16.7184i	0.0806604	−	0.0465693i	0.539788	+	0.841801i	$0.318504\pi$
$360$		0			0
$361$	−92.9935	−	348.817i	−0.257600	−	0.966252i
$362$		0			0
$363$	−282.543	−	75.7072i	−0.778356	−	0.208560i
$364$		0			0
$365$	193.478	−	8.38099i	0.530077	−	0.0229616i
$366$		0			0
$367$	−390.012	+	104.503i	−1.06270	+	0.284750i	−0.747491	−	0.664272i	$-0.768742\pi$
$367$	−390.012	+	104.503i	−1.06270	+	0.284750i	−0.315211	+	0.949022i	$0.602075\pi$
$368$		0			0
$369$		−	196.847i		−	0.533460i
$370$		0			0
$371$	−65.5225	+	113.488i	−0.176611	+	0.305899i
$372$		0			0
$373$	−281.906	+	281.906i	−0.755781	+	0.755781i	−0.975552	−	0.219770i	$-0.929469\pi$
$373$	−281.906	+	281.906i	−0.755781	+	0.755781i	0.219770	+	0.975552i	$0.429469\pi$
$374$		0			0
$375$	−451.578	+	345.771i	−1.20421	+	0.922056i
$376$		0			0
$377$	−193.169	+	720.917i	−0.512385	+	1.91225i
$378$		0			0
$379$		−	357.030i		−	0.942033i	−0.882125	−	0.471016i	$-0.843887\pi$
$379$		−	357.030i		−	0.942033i	0.882125	−	0.471016i	$-0.156113\pi$
$380$		0			0
$381$	−923.498			−2.42388
$382$		0			0
$383$	297.026	+	79.5878i	0.775524	+	0.207801i	0.624810	−	0.780777i	$-0.285176\pi$
$383$	297.026	+	79.5878i	0.775524	+	0.207801i	0.150713	+	0.988578i	$0.451843\pi$
$384$		0			0
$385$	−185.857	−	96.8322i	−0.482746	−	0.251512i
$386$		0			0
$387$	692.915	+	692.915i	1.79048	+	1.79048i
$388$		0			0
$389$	−149.767	−	86.4682i	−0.385006	−	0.222283i	0.294988	−	0.955501i	$-0.404684\pi$
$389$	−149.767	−	86.4682i	−0.385006	−	0.222283i	−0.679994	+	0.733218i	$0.738018\pi$
$390$		0			0
$391$	4.58302			0.0117213
$392$		0			0
$393$	−127.757	−	476.796i	−0.325082	−	1.21322i
$394$		0			0
$395$	−381.657	+	416.219i	−0.966221	+	1.05372i
$396$		0			0
$397$	−145.670	+	543.649i	−0.366928	+	1.36939i	0.497860	+	0.867257i	$0.334119\pi$
$397$	−145.670	+	543.649i	−0.366928	+	1.36939i	−0.864788	+	0.502137i	$0.832547\pi$
$398$		0			0
$399$	−263.897	−	34.9122i	−0.661397	−	0.0874992i
$400$		0			0
$401$	−358.817	−	621.489i	−0.894805	−	1.54985i	−0.834046	−	0.551695i	$-0.813981\pi$
$401$	−358.817	−	621.489i	−0.894805	−	1.54985i	−0.0607587	−	0.998152i	$-0.519352\pi$
$402$		0			0
$403$	58.2800	+	217.504i	0.144615	+	0.539712i
$404$		0			0
$405$	−181.941	−	166.833i	−0.449238	−	0.411934i
$406$		0			0
$407$	−219.176	−	219.176i	−0.538516	−	0.538516i
$408$		0			0
$409$	309.501	+	178.690i	0.756726	+	0.436896i	0.828119	−	0.560553i	$-0.189411\pi$
$409$	309.501	+	178.690i	0.756726	+	0.436896i	−0.0713933	+	0.997448i	$0.522745\pi$
$410$		0			0
$411$	161.538			0.393038
$412$		0			0
$413$	135.012	+	36.1765i	0.326907	+	0.0875944i
$414$		0			0
$415$	−189.553	+	363.823i	−0.456754	+	0.876683i
$416$		0			0
$417$	−705.919	−	705.919i	−1.69285	−	1.69285i
$418$		0			0
$419$			479.583i			1.14459i	0.820048	+	0.572295i	$0.193947\pi$
$419$			479.583i			1.14459i	−0.820048	+	0.572295i	$0.806053\pi$
$420$		0			0
$421$	−353.703	−	612.631i	−0.840149	−	1.45518i	−0.889768	−	0.456413i	$-0.849134\pi$
$421$	−353.703	−	612.631i	−0.840149	−	1.45518i	0.0496186	−	0.998768i	$-0.484199\pi$
$422$		0			0
$423$	2.35999	+	0.632356i	0.00557916	+	0.00149493i
$424$		0			0
$425$	15.9316	+	43.8653i	0.0374862	+	0.103212i
$426$		0			0
$427$	346.991	−	92.9760i	0.812626	−	0.217743i
$428$		0			0
$429$			986.437i			2.29939i
$430$		0			0
$431$	62.4782	−	108.215i	0.144961	−	0.251080i	−0.784397	−	0.620259i	$-0.787028\pi$
$431$	62.4782	−	108.215i	0.144961	−	0.251080i	0.929358	+	0.369179i	$0.120361\pi$
$432$		0			0
$433$	61.2538	+	228.602i	0.141464	+	0.527950i	0.999887	+	0.0150086i	$0.00477757\pi$
$433$	61.2538	+	228.602i	0.141464	+	0.527950i	−0.858424	+	0.512942i	$0.828556\pi$
$434$		0			0
$435$	−945.463	−	492.589i	−2.17348	−	1.13239i
$436$		0			0
$437$	−43.0844	−	17.8780i	−0.0985914	−	0.0409108i
$438$		0			0
$439$	2.50512	−	1.44633i	0.00570643	−	0.00329461i	−0.497144	−	0.867668i	$-0.665618\pi$
$439$	2.50512	−	1.44633i	0.00570643	−	0.00329461i	0.502851	+	0.864373i	$0.332285\pi$
$440$		0			0
$441$	231.238	−	400.516i	0.524350	−	0.908201i
$442$		0			0
$443$	113.898	+	425.073i	0.257106	+	0.959532i	0.966907	+	0.255130i	$0.0821182\pi$
$443$	113.898	+	425.073i	0.257106	+	0.959532i	−0.709801	+	0.704402i	$0.751215\pi$
$444$		0			0
$445$	521.243	+	115.744i	1.17133	+	0.260099i
$446$		0			0
$447$	421.649	−	112.981i	0.943287	−	0.252753i
$448$		0			0
$449$		−	707.493i		−	1.57571i	−0.615861	−	0.787855i	$-0.711192\pi$
$449$		−	707.493i		−	1.57571i	0.615861	−	0.787855i	$-0.288808\pi$
$450$		0			0
$451$	114.481	+	198.287i	0.253838	+	0.439661i
$452$		0			0
$453$	−453.711	−	121.572i	−1.00157	−	0.268370i
$454$		0			0
$455$	−53.1551	+	239.379i	−0.116824	+	0.526108i
$456$		0			0
$457$	−209.537	−	209.537i	−0.458505	−	0.458505i	0.439660	−	0.898164i	$-0.355099\pi$
$457$	−209.537	−	209.537i	−0.458505	−	0.458505i	−0.898164	+	0.439660i	$0.855099\pi$
$458$		0			0
$459$	19.8809	−	11.4783i	0.0433136	−	0.0250071i
$460$		0			0
$461$	231.634	+	401.201i	0.502459	+	0.870284i	0.999996	+	0.00284166i	$0.000904530\pi$
$461$	231.634	+	401.201i	0.502459	+	0.870284i	−0.497537	+	0.867443i	$0.665762\pi$
$462$		0			0
$463$	581.974	−	581.974i	1.25696	−	1.25696i	0.304428	−	0.952535i	$-0.401535\pi$
$463$	581.974	−	581.974i	1.25696	−	1.25696i	0.952535	−	0.304428i	$-0.0984654\pi$
$464$		0			0
$465$	−321.342	+	13.9197i	−0.691058	+	0.0299349i
$466$		0			0
$467$	90.1034	+	90.1034i	0.192941	+	0.192941i	0.796966	−	0.604025i	$-0.206437\pi$
$467$	90.1034	+	90.1034i	0.192941	+	0.192941i	−0.604025	+	0.796966i	$0.706437\pi$
$468$		0			0
$469$	−10.9721	−	6.33474i	−0.0233946	−	0.0135069i
$470$		0			0
$471$	−313.493	+	542.985i	−0.665590	+	1.15284i
$472$		0			0
$473$	−1100.97	−	295.003i	−2.32763	−	0.623686i
$474$		0			0
$475$	21.3440	−	474.520i	0.0449347	−	0.998990i
$476$		0			0
$477$	−128.905	+	481.080i	−0.270241	+	1.00855i
$478$		0			0
$479$	305.111	+	176.156i	0.636975	+	0.367758i	0.783448	−	0.621457i	$-0.213459\pi$
$479$	305.111	+	176.156i	0.636975	+	0.367758i	−0.146473	+	0.989215i	$0.546792\pi$
$480$		0			0
$481$	−181.337	+	314.086i	−0.377001	+	0.652984i
$482$		0			0
$483$	−24.3220	+	24.3220i	−0.0503561	+	0.0503561i
$484$		0			0
$485$	10.0870	+	232.861i	0.0207979	+	0.480126i
$486$		0			0
$487$	−279.209	−	279.209i	−0.573324	−	0.573324i	0.359732	−	0.933056i	$-0.382868\pi$
$487$	−279.209	−	279.209i	−0.573324	−	0.573324i	−0.933056	+	0.359732i	$0.882868\pi$
$488$		0			0
$489$	−568.495	+	328.221i	−1.16257	+	0.671208i
$490$		0			0
$491$	−396.750	−	687.192i	−0.808046	−	1.39958i	−0.914216	−	0.405228i	$-0.867192\pi$
$491$	−396.750	−	687.192i	−0.808046	−	1.39958i	0.106170	−	0.994348i	$-0.466141\pi$
$492$		0			0
$493$	−61.8559	+	61.8559i	−0.125468	+	0.125468i
$494$		0			0
$495$	−777.552	−	172.659i	−1.57081	−	0.348806i
$496$		0			0
$497$	40.7948	−	152.248i	0.0820822	−	0.306335i
$498$		0			0
$499$	−362.068	+	209.040i	−0.725588	+	0.418918i	−0.816806	−	0.576913i	$-0.804257\pi$
$499$	−362.068	+	209.040i	−0.725588	+	0.418918i	0.0912180	+	0.995831i	$0.470924\pi$
$500$		0			0
$501$	592.221			1.18208
$502$		0			0
$503$	19.9378	+	74.4088i	0.0396377	+	0.147930i	0.982909	−	0.184094i	$-0.0589351\pi$
$503$	19.9378	+	74.4088i	0.0396377	+	0.147930i	−0.943271	+	0.332024i	$0.892268\pi$
$504$		0			0
$505$	30.2187	−	136.087i	0.0598389	−	0.269479i
$506$		0			0
$507$	372.112	−	99.7071i	0.733949	−	0.196661i
$508$		0			0
$509$	346.871	+	200.266i	0.681475	+	0.393450i	0.800411	−	0.599452i	$-0.204615\pi$
$509$	346.871	+	200.266i	0.681475	+	0.393450i	−0.118935	+	0.992902i	$0.537948\pi$
$510$		0			0
$511$	59.6313	+	103.284i	0.116695	+	0.202122i
$512$		0			0
$513$	−231.674	+	30.3517i	−0.451606	+	0.0591652i
$514$		0			0
$515$	−326.214	+	626.127i	−0.633425	+	1.21578i
$516$		0			0
$517$	−2.74501	+	0.735525i	−0.00530951	+	0.00142268i
$518$		0			0
$519$	52.9558	+	30.5741i	0.102034	+	0.0589096i
$520$		0			0
$521$	−654.535			−1.25630			−0.628152	−	0.778090i	$-0.716189\pi$
$521$	−654.535			−1.25630			−0.628152	+	0.778090i	$0.716189\pi$
$522$		0			0
$523$	−210.328	−	784.953i	−0.402156	−	1.50087i	−0.809241	−	0.587476i	$-0.800122\pi$
$523$	−210.328	−	784.953i	−0.402156	−	1.50087i	0.407086	−	0.913390i	$-0.366545\pi$
$524$		0			0
$525$	−317.341	−	148.243i	−0.604459	−	0.282368i
$526$		0			0
$527$	−6.83084	+	25.4930i	−0.0129617	+	0.0483739i
$528$		0			0
$529$	452.908	−	261.486i	0.856158	−	0.494303i
$530$		0			0
$531$	531.230			1.00043
$532$		0			0
$533$	189.434	−	189.434i	0.355411	−	0.355411i
$534$		0			0
$535$	461.628	+	240.509i	0.862856	+	0.449550i
$536$		0			0
$537$	−124.559	+	464.862i	−0.231954	+	0.865665i
$538$		0			0
$539$			537.929i			0.998014i
$540$		0			0
$541$	166.859	−	289.008i	0.308427	−	0.534211i	−0.669591	−	0.742730i	$-0.733531\pi$
$541$	166.859	−	289.008i	0.308427	−	0.534211i	0.978018	+	0.208518i	$0.0668641\pi$
$542$		0			0
$543$	746.922	−	746.922i	1.37555	−	1.37555i
$544$		0			0
$545$	−319.588	+	348.529i	−0.586399	+	0.639502i
$546$		0			0
$547$	170.836	−	45.7752i	0.312314	−	0.0836842i	−0.0992577	−	0.995062i	$-0.531647\pi$
$547$	170.836	−	45.7752i	0.312314	−	0.0836842i	0.411571	+	0.911378i	$0.364980\pi$
$548$		0			0
$549$	1182.38	−	682.649i	2.15370	−	1.24344i
$550$		0			0
$551$	822.795	−	340.205i	1.49328	−	0.617431i
$552$		0			0
$553$	−335.921	−	90.0097i	−0.607452	−	0.162766i
$554$		0			0
$555$	−381.824	−	350.118i	−0.687971	−	0.630844i
$556$		0			0
$557$	−573.744	+	153.734i	−1.03006	+	0.276004i	−0.733989	−	0.679161i	$-0.762344\pi$
$557$	−573.744	+	153.734i	−1.03006	+	0.276004i	−0.296073	+	0.955165i	$0.595677\pi$
$558$		0			0
$559$			1333.64i			2.38577i
$560$		0			0
$561$	−57.8088	+	100.128i	−0.103046	+	0.178481i
$562$		0			0
$563$	548.124	−	548.124i	0.973576	−	0.973576i	−0.0260834	−	0.999660i	$-0.508304\pi$
$563$	548.124	−	548.124i	0.973576	−	0.973576i	0.999660	+	0.0260834i	$0.00830353\pi$
$564$		0			0
$565$	−171.618	+	329.399i	−0.303748	+	0.583007i
$566$		0			0
$567$	39.3458	−	146.841i	0.0693930	−	0.258978i
$568$		0			0
$569$		−	837.630i		−	1.47211i	−0.676923	−	0.736054i	$-0.736687\pi$
$569$		−	837.630i		−	1.47211i	0.676923	−	0.736054i	$-0.263313\pi$
$570$		0			0
$571$	−574.222			−1.00564			−0.502821	−	0.864390i	$-0.667705\pi$
$571$	−574.222			−1.00564			−0.502821	+	0.864390i	$0.667705\pi$
$572$		0			0
$573$	1393.32	+	373.339i	2.43163	+	0.651552i
$574$		0			0
$575$	−46.9904	−	39.4845i	−0.0817224	−	0.0686688i
$576$		0			0
$577$	−110.191	−	110.191i	−0.190972	−	0.190972i	0.605144	−	0.796116i	$-0.293115\pi$
$577$	−110.191	−	110.191i	−0.190972	−	0.190972i	−0.796116	+	0.605144i	$0.793115\pi$
$578$		0			0
$579$	38.5290	+	22.2447i	0.0665441	+	0.0384192i
$580$		0			0
$581$	−252.641			−0.434839
$582$		0			0
$583$	−149.936	−	559.567i	−0.257179	−	0.959807i
$584$		0			0
$585$	40.3317	+	931.071i	0.0689431	+	1.59157i
$586$		0			0
$587$	195.771	−	730.629i	0.333512	−	1.24468i	−0.571962	−	0.820280i	$-0.693817\pi$
$587$	195.771	−	730.629i	0.333512	−	1.24468i	0.905474	−	0.424403i	$-0.139516\pi$
$588$		0			0
$589$	163.662	−	213.010i	0.277865	−	0.361647i
$590$		0			0
$591$	708.413	+	1227.01i	1.19867	+	2.07615i
$592$		0			0
$593$	−188.391	−	703.086i	−0.317692	−	1.18564i	−0.921457	−	0.388480i	$-0.873000\pi$
$593$	−188.391	−	703.086i	−0.317692	−	1.18564i	0.603765	−	0.797162i	$-0.293666\pi$
$594$		0			0
$595$	−19.4240	+	21.1830i	−0.0326453	+	0.0356016i
$596$		0			0
$597$	482.258	+	482.258i	0.807802	+	0.807802i
$598$		0			0
$599$	623.190	+	359.799i	1.04038	+	0.600666i	0.919942	−	0.392054i	$-0.128235\pi$
$599$	623.190	+	359.799i	1.04038	+	0.600666i	0.120442	+	0.992720i	$0.461569\pi$
$600$		0			0
$601$	−75.9686			−0.126404			−0.0632018	−	0.998001i	$-0.520131\pi$
$601$	−75.9686			−0.126404			−0.0632018	+	0.998001i	$0.520131\pi$
$602$		0			0
$603$	−46.5109	−	12.4626i	−0.0771325	−	0.0206676i
$604$		0			0
$605$	306.594	−	96.5531i	0.506767	−	0.159592i
$606$		0			0
$607$	435.124	+	435.124i	0.716844	+	0.716844i	0.967958	−	0.251114i	$-0.0807968\pi$
$607$	435.124	+	435.124i	0.716844	+	0.716844i	−0.251114	+	0.967958i	$0.580797\pi$
$608$		0			0
$609$		−	656.536i		−	1.07806i
$610$		0			0
$611$	1.66257	+	2.87966i	0.00272106	+	0.00471302i
$612$		0			0
$613$	629.823	+	168.760i	1.02744	+	0.275303i	0.732901	−	0.680336i	$-0.238166\pi$
$613$	629.823	+	168.760i	1.02744	+	0.275303i	0.294543	+	0.955638i	$0.404833\pi$
$614$		0			0
$615$	205.498	+	322.811i	0.334143	+	0.524896i
$616$		0			0
$617$	552.380	−	148.010i	0.895268	−	0.239886i	0.218285	−	0.975885i	$-0.429954\pi$
$617$	552.380	−	148.010i	0.895268	−	0.239886i	0.676983	+	0.735999i	$0.263287\pi$
$618$		0			0
$619$			817.832i			1.32122i	0.750731	+	0.660608i	$0.229701\pi$
$619$			817.832i			1.32122i	−0.750731	+	0.660608i	$0.770299\pi$
$620$		0			0
$621$	−15.0957	+	26.1466i	−0.0243087	+	0.0421040i
$622$		0			0
$623$	85.1046	+	317.615i	0.136604	+	0.509815i
$624$		0			0
$625$	214.568	−	587.014i	0.343308	−	0.939223i
$626$		0			0
$627$	934.044	−	715.781i	1.48970	−	1.14160i
$628$		0			0
$629$	−36.8131	+	21.2541i	−0.0585264	+	0.0337903i
$630$		0			0
$631$	−420.746	+	728.754i	−0.666793	+	1.15492i	0.312003	+	0.950081i	$0.399000\pi$
$631$	−420.746	+	728.754i	−0.666793	+	1.15492i	−0.978796	+	0.204838i	$0.934333\pi$
$632$		0			0
$633$	−321.082	−	1198.30i	−0.507239	−	1.89304i
$634$		0			0
$635$	856.083	−	544.972i	1.34816	−	0.858224i
$636$		0			0
$637$	607.964	−	162.904i	0.954418	−	0.255736i
$638$		0			0
$639$		−	599.048i		−	0.937477i
$640$		0			0
$641$	58.4058	+	101.162i	0.0911167	+	0.157819i	0.907981	−	0.419011i	$-0.137623\pi$
$641$	58.4058	+	101.162i	0.0911167	+	0.157819i	−0.816865	+	0.576830i	$0.804290\pi$
$642$		0			0
$643$	−438.446	−	117.481i	−0.681875	−	0.182708i	−0.0987769	−	0.995110i	$-0.531493\pi$
$643$	−438.446	−	117.481i	−0.681875	−	0.182708i	−0.583098	+	0.812402i	$0.698160\pi$
$644$		0			0
$645$	−1859.69	−	412.952i	−2.88324	−	0.640235i
$646$		0			0
$647$	259.084	+	259.084i	0.400439	+	0.400439i	0.878388	−	0.477949i	$-0.158620\pi$
$647$	259.084	+	259.084i	0.400439	+	0.400439i	−0.477949	+	0.878388i	$0.658620\pi$
$648$		0			0
$649$	−535.117	+	308.950i	−0.824525	+	0.476040i
$650$		0			0
$651$	−99.0398	−	171.542i	−0.152135	−	0.263505i
$652$		0			0
$653$	−874.850	+	874.850i	−1.33974	+	1.33974i	−0.443431	+	0.896309i	$0.646239\pi$
$653$	−874.850	+	874.850i	−1.33974	+	1.33974i	−0.896309	+	0.443431i	$0.853761\pi$
$654$		0			0
$655$	399.797	+	366.599i	0.610377	+	0.559693i
$656$		0			0
$657$	320.510	+	320.510i	0.487839	+	0.487839i
$658$		0			0
$659$	482.622	+	278.642i	0.732354	+	0.422825i	0.819283	−	0.573390i	$-0.194372\pi$
$659$	482.622	+	278.642i	0.732354	+	0.422825i	−0.0869285	+	0.996215i	$0.527705\pi$
$660$		0			0
$661$	29.2059	−	50.5861i	0.0441844	−	0.0765297i	−0.843087	−	0.537777i	$-0.819264\pi$
$661$	29.2059	−	50.5861i	0.0441844	−	0.0765297i	0.887272	+	0.461247i	$0.152598\pi$
$662$		0			0
$663$	130.670	+	35.0130i	0.197090	+	0.0528100i
$664$		0			0
$665$	265.235	−	123.367i	0.398850	−	0.185514i
$666$		0			0
$667$	29.7763	−	111.127i	0.0446421	−	0.166607i
$668$		0			0
$669$	−183.258	−	105.804i	−0.273929	−	0.158153i
$670$		0			0
$671$	−794.022	+	1375.29i	−1.18334	+	2.04961i
$672$		0			0
$673$	14.0448	−	14.0448i	0.0208690	−	0.0208690i	−0.696595	−	0.717464i	$-0.745303\pi$
$673$	14.0448	−	14.0448i	0.0208690	−	0.0208690i	0.717464	+	0.696595i	$0.245303\pi$
$674$		0			0
$675$	−302.732	−	53.5938i	−0.448491	−	0.0793982i
$676$		0			0
$677$	−670.816	−	670.816i	−0.990865	−	0.990865i	0.00909337	−	0.999959i	$-0.497105\pi$
$677$	−670.816	−	670.816i	−0.990865	−	0.990865i	−0.999959	+	0.00909337i	$0.997105\pi$
$678$		0			0
$679$	−124.308	+	71.7695i	−0.183076	+	0.105699i
$680$		0			0
$681$	833.145	+	1443.05i	1.22341	+	2.11901i
$682$		0			0
$683$	70.1966	−	70.1966i	0.102777	−	0.102777i	−0.653849	−	0.756625i	$-0.726847\pi$
$683$	70.1966	−	70.1966i	0.102777	−	0.102777i	0.756625	+	0.653849i	$0.226847\pi$
$684$		0			0
$685$	−149.746	+	95.3267i	−0.218608	+	0.139163i
$686$		0			0
$687$	350.020	−	1306.29i	0.509491	−	1.90145i
$688$		0			0
$689$	−587.014	+	338.913i	−0.851979	+	0.491891i
$690$		0			0
$691$	276.641			0.400349			0.200174	−	0.979760i	$-0.435849\pi$
$691$	276.641			0.400349			0.200174	+	0.979760i	$0.435849\pi$
$692$		0			0
$693$	−126.953	−	473.794i	−0.183193	−	0.683686i
$694$		0			0
$695$	1070.96	+	237.812i	1.54095	+	0.342175i
$696$		0			0
$697$	30.3299	−	8.12688i	0.0435149	−	0.0116598i
$698$		0			0
$699$	189.063	+	109.156i	0.270476	+	0.156160i
$700$		0			0
$701$	−628.424	−	1088.46i	−0.896468	−	1.55273i	−0.831978	−	0.554809i	$-0.812791\pi$
$701$	−628.424	−	1088.46i	−0.896468	−	1.55273i	−0.0644897	−	0.997918i	$-0.520542\pi$
$702$		0			0
$703$	428.986	−	56.2017i	0.610222	−	0.0799455i
$704$		0			0
$705$	−4.53031	+	1.42669i	−0.00642598	+	0.00202368i
$706$		0			0
$707$	82.9233	−	22.2192i	0.117289	−	0.0314275i
$708$		0			0
$709$	362.753	+	209.436i	0.511641	+	0.295396i	0.733508	−	0.679681i	$-0.237882\pi$
$709$	362.753	+	209.436i	0.511641	+	0.295396i	−0.221867	+	0.975077i	$0.571215\pi$
$710$		0			0
$711$	−1321.74			−1.85899
$712$		0			0
$713$	−8.98363	−	33.5274i	−0.0125998	−	0.0470230i
$714$		0			0
$715$	−582.114	−	914.428i	−0.814146	−	1.27892i
$716$		0			0
$717$	−291.255	+	1086.98i	−0.406214	+	1.51601i
$718$		0			0
$719$	135.733	−	78.3656i	0.188781	−	0.108992i	−0.402631	−	0.915362i	$-0.631904\pi$
$719$	135.733	−	78.3656i	0.188781	−	0.108992i	0.591412	+	0.806370i	$0.298571\pi$
$720$		0			0
$721$	−434.787			−0.603033
$722$		0			0
$723$	−1267.84	+	1267.84i	−1.75358	+	1.75358i
$724$		0			0
$725$	1167.13	−	101.304i	1.60983	−	0.139730i
$726$		0			0
$727$	108.427	−	404.655i	0.149143	−	0.556610i	−0.850393	−	0.526148i	$-0.823636\pi$
$727$	108.427	−	404.655i	0.149143	−	0.556610i	0.999536	−	0.0304615i	$-0.00969769\pi$
$728$		0			0
$729$		−	1081.36i		−	1.48334i
$730$		0			0
$731$	−78.1564	+	135.371i	−0.106917	+	0.185186i
$732$		0			0
$733$	−896.106	+	896.106i	−1.22252	+	1.22252i	−0.255784	+	0.966734i	$0.582334\pi$
$733$	−896.106	+	896.106i	−1.22252	+	1.22252i	−0.966734	+	0.255784i	$0.917666\pi$
$734$		0			0
$735$	38.9083	+	898.212i	0.0529365	+	1.22206i
$736$		0			0
$737$	54.0991	−	14.4958i	0.0734045	−	0.0196687i
$738$		0			0
$739$	873.064	−	504.064i	1.18141	−	0.682089i	0.225071	−	0.974342i	$-0.427738\pi$
$739$	873.064	−	504.064i	1.18141	−	0.682089i	0.956341	+	0.292254i	$0.0944051\pi$
$740$		0			0
$741$	−1091.83	−	838.888i	−1.47346	−	1.13210i
$742$		0			0
$743$	598.485	+	160.364i	0.805498	+	0.215833i	0.637997	−	0.770039i	$-0.279763\pi$
$743$	598.485	+	160.364i	0.805498	+	0.215833i	0.167502	+	0.985872i	$0.446430\pi$
$744$		0			0
$745$	−324.197	+	353.556i	−0.435164	+	0.474572i
$746$		0			0
$747$	−927.472	+	248.515i	−1.24160	+	0.332684i
$748$		0			0
$749$			320.558i			0.427981i
$750$		0			0
$751$	−246.828	+	427.519i	−0.328666	+	0.569267i	−0.982247	−	0.187590i	$-0.939933\pi$
$751$	−246.828	+	427.519i	−0.328666	+	0.569267i	0.653581	+	0.756856i	$0.273266\pi$
$752$		0			0
$753$	−504.964	+	504.964i	−0.670603	+	0.670603i
$754$		0			0
$755$	492.332	−	155.046i	0.652096	−	0.205359i
$756$		0			0
$757$	−27.5620	+	102.863i	−0.0364095	+	0.135882i	−0.981738	−	0.190237i	$-0.939074\pi$
$757$	−27.5620	+	102.863i	−0.0364095	+	0.135882i	0.945329	+	0.326119i	$0.105741\pi$
$758$		0			0
$759$		−	152.056i		−	0.200337i
$760$		0			0
$761$	1092.24			1.43527			0.717637	−	0.696417i	$-0.245224\pi$
$761$	1092.24			1.43527			0.717637	+	0.696417i	$0.245224\pi$
$762$		0			0
$763$	−281.289	−	75.3712i	−0.368662	−	0.0987827i
$764$		0			0
$765$	−50.4703	+	96.8716i	−0.0659743	+	0.126629i
$766$		0			0
$767$	511.225	+	511.225i	0.666525	+	0.666525i
$768$		0			0
$769$	−368.972	−	213.026i	−0.479808	−	0.277017i	0.240529	−	0.970642i	$-0.422679\pi$
$769$	−368.972	−	213.026i	−0.479808	−	0.277017i	−0.720336	+	0.693625i	$0.756013\pi$
$770$		0			0
$771$	1169.87			1.51735
$772$		0			0
$773$	−316.908	−	1182.72i	−0.409971	−	1.53003i	−0.794700	−	0.607003i	$-0.792372\pi$
$773$	−316.908	−	1182.72i	−0.409971	−	1.53003i	0.384729	−	0.923030i	$-0.374295\pi$
$774$		0			0
$775$	289.670	−	202.533i	0.373768	−	0.261333i
$776$		0			0
$777$	82.5715	−	308.161i	0.106270	−	0.396604i
$778$		0			0
$779$	−316.830	−	41.9149i	−0.406714	−	0.0538060i
$780$		0			0
$781$	348.391	+	603.431i	0.446083	+	0.772639i
$782$		0			0
$783$	−149.150	−	556.637i	−0.190486	−	0.710903i
$784$		0			0
$785$	−29.8174	−	688.346i	−0.0379840	−	0.876873i
$786$		0			0
$787$	−757.924	−	757.924i	−0.963054	−	0.963054i	0.0362874	−	0.999341i	$-0.488447\pi$
$787$	−757.924	−	757.924i	−0.963054	−	0.963054i	−0.999341	+	0.0362874i	$0.988447\pi$
$788$		0			0
$789$	803.212	+	463.735i	1.01801	+	0.587750i
$790$		0			0
$791$	−228.737			−0.289174
$792$		0			0
$793$	1794.80	+	480.915i	2.26330	+	0.606450i
$794$		0			0
$795$	−290.830	−	923.498i	−0.365824	−	1.16163i
$796$		0			0
$797$	860.536	+	860.536i	1.07972	+	1.07972i	0.996534	+	0.0831843i	$0.0265090\pi$
$797$	860.536	+	860.536i	1.07972	+	1.07972i	0.0831843	+	0.996534i	$0.473491\pi$
$798$		0			0
$799$			0.389731i			0.000487773i
$800$		0			0
$801$	624.855	+	1082.28i	0.780094	+	1.35116i
$802$		0			0
$803$	−509.256	−	136.455i	−0.634191	−	0.169931i
$804$		0			0
$805$	8.19366	−	36.8994i	0.0101785	−	0.0458377i
$806$		0			0
$807$	1704.50	−	456.719i	2.11214	−	0.565946i
$808$		0			0
$809$			1260.14i			1.55765i	0.627238	+	0.778827i	$0.284185\pi$
$809$			1260.14i			1.55765i	−0.627238	+	0.778827i	$0.715815\pi$
$810$		0			0
$811$	601.138	−	1041.20i	0.741230	−	1.28385i	−0.210705	−	0.977550i	$-0.567576\pi$
$811$	601.138	−	1041.20i	0.741230	−	1.28385i	0.951935	−	0.306299i	$-0.0990907\pi$
$812$		0			0
$813$	−298.128	−	1112.63i	−0.366702	−	1.36855i
$814$		0			0
$815$	333.306	−	639.740i	0.408965	−	0.784957i
$816$		0			0
$817$	1262.81	−	967.723i	1.54567	−	1.18448i
$818$		0			0
$819$	−497.034	+	286.963i	−0.606879	+	0.350382i
$820$		0			0
$821$	423.055	−	732.752i	0.515292	−	0.892512i	−0.484550	−	0.874763i	$-0.661017\pi$
$821$	423.055	−	732.752i	0.515292	−	0.892512i	0.999842	−	0.0177487i	$-0.00564989\pi$
$822$		0			0
$823$	−171.155	−	638.761i	−0.207965	−	0.776137i	−0.988525	−	0.151056i	$-0.951733\pi$
$823$	−171.155	−	638.761i	−0.207965	−	0.776137i	0.780560	−	0.625081i	$-0.214934\pi$
$824$		0			0
$825$	1455.36	−	528.579i	1.76408	−	0.640702i
$826$		0			0
$827$	−1197.27	+	320.808i	−1.44773	+	0.387918i	−0.895233	−	0.445597i	$-0.852991\pi$
$827$	−1197.27	+	320.808i	−1.44773	+	0.387918i	−0.552496	+	0.833515i	$0.686325\pi$
$828$		0			0
$829$			428.790i			0.517237i	0.965980	+	0.258619i	$0.0832673\pi$
$829$			428.790i			0.517237i	−0.965980	+	0.258619i	$0.916733\pi$
$830$		0			0
$831$	827.329	+	1432.98i	0.995582	+	1.72440i
$832$		0			0
$833$	71.2579	+	19.0935i	0.0855437	+	0.0229214i
$834$		0			0
$835$	−548.989	+	349.480i	−0.657472	+	0.418539i
$836$		0			0
$837$	−122.940	−	122.940i	−0.146882	−	0.146882i
$838$		0			0
$839$	−1128.23	+	651.382i	−1.34473	+	0.776379i	−0.987497	−	0.157637i	$-0.949613\pi$
$839$	−1128.23	+	651.382i	−1.34473	+	0.776379i	−0.357231	+	0.934016i	$0.616279\pi$
$840$		0			0
$841$	677.464	+	1173.40i	0.805546	+	1.39525i
$842$		0			0
$843$	359.055	−	359.055i	0.425926	−	0.425926i
$844$		0			0
$845$	−286.109	+	312.018i	−0.338591	+	0.369253i
$846$		0			0
$847$	139.974	+	139.974i	0.165259	+	0.165259i
$848$		0			0
$849$	−1802.62	−	1040.74i	−2.12322	−	1.22584i
$850$		0			0
$851$	27.9525	−	48.4151i	0.0328466	−	0.0568920i
$852$		0			0
$853$	−853.417	−	228.672i	−1.00049	−	0.268080i	−0.278839	−	0.960338i	$-0.589950\pi$
$853$	−853.417	−	228.672i	−1.00049	−	0.268080i	−0.721650	+	0.692258i	$0.756616\pi$
$854$		0			0
$855$	852.354	−	713.796i	0.996905	−	0.834850i
$856$		0			0
$857$	−416.428	+	1554.13i	−0.485914	+	1.81345i	0.0899965	+	0.995942i	$0.471314\pi$
$857$	−416.428	+	1554.13i	−0.485914	+	1.81345i	−0.575910	+	0.817513i	$0.695352\pi$
$858$		0			0
$859$	−599.627	−	346.195i	−0.698052	−	0.403021i	0.108569	−	0.994089i	$-0.465373\pi$
$859$	−599.627	−	346.195i	−0.698052	−	0.403021i	−0.806622	+	0.591068i	$0.798706\pi$
$860$		0			0
$861$	−117.831	+	204.089i	−0.136854	+	0.237037i
$862$		0			0
$863$	595.374	−	595.374i	0.689889	−	0.689889i	−0.272318	−	0.962207i	$-0.587790\pi$
$863$	595.374	−	595.374i	0.689889	−	0.689889i	0.962207	+	0.272318i	$0.0877903\pi$
$864$		0			0
$865$	−67.1324	+	2.90801i	−0.0776097	+	0.00336186i
$866$		0			0
$867$	−918.604	−	918.604i	−1.05952	−	1.05952i
$868$		0			0
$869$	1331.41	−	768.690i	1.53212	−	0.884568i
$870$		0			0
$871$	−32.7662	−	56.7527i	−0.0376190	−	0.0651581i
$872$		0			0
$873$	−385.751	+	385.751i	−0.441868	+	0.441868i
$874$		0			0
$875$	381.656	−	49.8468i	0.436179	−	0.0569677i
$876$		0			0
$877$	198.982	−	742.610i	0.226889	−	0.846762i	−0.754750	−	0.656013i	$-0.772242\pi$
$877$	198.982	−	742.610i	0.226889	−	0.846762i	0.981639	−	0.190749i	$-0.0610917\pi$
$878$		0			0
$879$	−1376.26	+	794.584i	−1.56571	+	0.903964i
$880$		0			0
$881$	984.870			1.11790			0.558950	−	0.829201i	$-0.311204\pi$
$881$	984.870			1.11790			0.558950	+	0.829201i	$0.311204\pi$
$882$		0			0
$883$	231.258	+	863.066i	0.261900	+	0.977425i	0.964121	+	0.265465i	$0.0855255\pi$
$883$	231.258	+	863.066i	0.261900	+	0.977425i	−0.702220	+	0.711960i	$0.747808\pi$
$884$		0			0
$885$	−871.170	+	554.577i	−0.984372	+	0.626640i
$886$		0			0
$887$	−1378.80	+	369.449i	−1.55446	+	0.416515i	−0.930903	−	0.365265i	$-0.880978\pi$
$887$	−1378.80	+	369.449i	−1.55446	+	0.416515i	−0.623553	+	0.781781i	$0.714312\pi$
$888$		0			0
$889$	541.237	+	312.483i	0.608816	+	0.351500i
$890$		0			0
$891$	336.016	+	581.997i	0.377123	+	0.653196i
$892$		0			0
$893$	1.52031	−	3.66381i	0.00170247	−	0.00410281i
$894$		0			0
$895$	−158.857	−	504.432i	−0.177494	−	0.563612i
$896$		0			0
$897$	−171.852	+	46.0477i	−0.191585	+	0.0513352i
$898$		0			0
$899$	573.760	+	331.261i	0.638220	+	0.368477i
$900$		0			0
$901$	−79.4461			−0.0881755
$902$		0			0
$903$	−303.636	−	1133.18i	−0.336252	−	1.25491i
$904$		0			0
$905$	−251.625	+	1133.17i	−0.278039	+	1.25212i
$906$		0			0
$907$	315.549	−	1177.64i	0.347904	−	1.29839i	−0.541280	−	0.840843i	$-0.682060\pi$
$907$	315.549	−	1177.64i	0.347904	−	1.29839i	0.889183	−	0.457551i	$-0.151273\pi$
$908$		0			0
$909$	282.563	−	163.138i	0.310851	−	0.179470i
$910$		0			0
$911$	−627.447			−0.688746			−0.344373	−	0.938833i	$-0.611908\pi$
$911$	−627.447			−0.688746			−0.344373	+	0.938833i	$0.611908\pi$
$912$		0			0
$913$	789.727	−	789.727i	0.864981	−	0.864981i
$914$		0			0
$915$	−1226.35	+	2353.83i	−1.34028	+	2.57249i
$916$		0			0
$917$	−86.4583	+	322.667i	−0.0942839	+	0.351872i
$918$		0			0
$919$		−	36.5897i		−	0.0398146i	−0.999802	−	0.0199073i	$-0.993663\pi$
$919$		−	36.5897i		−	0.0398146i	0.999802	−	0.0199073i	$-0.00633711\pi$
$920$		0			0
$921$	777.790	−	1347.17i	0.844505	−	1.46273i
$922$		0			0
$923$	576.489	−	576.489i	0.624582	−	0.624582i
$924$		0			0
$925$	560.562	+	99.2385i	0.606013	+	0.107285i
$926$		0			0
$927$	−1596.15	+	427.686i	−1.72184	+	0.461366i
$928$		0			0
$929$	1581.77	−	913.237i	1.70266	−	0.983032i	0.759614	−	0.650374i	$-0.225388\pi$
$929$	1581.77	−	913.237i	1.70266	−	0.983032i	0.943047	−	0.332659i	$-0.107946\pi$
$930$		0			0
$931$	−595.404	−	457.467i	−0.639532	−	0.491372i
$932$		0			0
$933$	336.406	+	90.1398i	0.360564	+	0.0966129i
$934$		0			0
$935$	−5.49841	−	126.933i	−0.00588065	−	0.135757i
$936$		0			0
$937$	−35.7157	+	9.57000i	−0.0381171	+	0.0102134i	−0.277827	−	0.960631i	$-0.589614\pi$
$937$	−35.7157	+	9.57000i	−0.0381171	+	0.0102134i	0.239710	+	0.970845i	$0.422948\pi$
$938$		0			0
$939$			1772.39i			1.88753i
$940$		0			0
$941$	48.2942	−	83.6480i	0.0513222	−	0.0888926i	−0.839223	−	0.543787i	$-0.816990\pi$
$941$	48.2942	−	83.6480i	0.0513222	−	0.0888926i	0.890545	+	0.454895i	$0.150323\pi$
$942$		0			0
$943$	−29.2005	+	29.2005i	−0.0309655	+	0.0309655i
$944$		0			0
$945$	−56.8714	−	180.589i	−0.0601813	−	0.191099i
$946$		0			0
$947$	−285.388	+	1065.08i	−0.301360	+	1.12469i	0.634674	+	0.772780i	$0.281134\pi$
$947$	−285.388	+	1065.08i	−0.301360	+	1.12469i	−0.936034	+	0.351910i	$0.885532\pi$
$948$		0			0
$949$			616.881i			0.650032i
$950$		0			0
$951$	−2502.88			−2.63184
$952$		0			0
$953$	−1307.00	−	350.210i	−1.37146	−	0.367481i	−0.503448	−	0.864026i	$-0.667935\pi$
$953$	−1307.00	−	350.210i	−1.37146	−	0.367481i	−0.868011	+	0.496544i	$0.834602\pi$
$954$		0			0
$955$	−1511.92	+	476.138i	−1.58317	+	0.498574i
$956$		0			0
$957$	2052.25	+	2052.25i	2.14447	+	2.14447i
$958$		0			0
$959$	−94.6734	−	54.6597i	−0.0987209	−	0.0569965i
$960$		0			0
$961$	−761.114			−0.792002
$962$		0			0
$963$	315.322	+	1176.80i	0.327438	+	1.22201i
$964$		0			0
$965$	−48.8434	+	2.11578i	−0.0506150	+	0.00219251i
$966$		0			0
$967$	255.154	−	952.248i	0.263861	−	0.984744i	−0.699082	−	0.715041i	$-0.746408\pi$
$967$	255.154	−	952.248i	0.263861	−	0.984744i	0.962944	−	0.269703i	$-0.0869255\pi$
$968$		0			0
$969$	−61.6641	−	149.136i	−0.0636368	−	0.153907i
$970$		0			0
$971$	−476.315	−	825.002i	−0.490541	−	0.849641i	0.509400	−	0.860530i	$-0.329867\pi$
$971$	−476.315	−	825.002i	−0.490541	−	0.849641i	−0.999941	+	0.0108886i	$0.996534\pi$
$972$		0			0
$973$	174.859	+	652.582i	0.179711	+	0.670691i
$974$		0			0
$975$	−1038.13	−	1484.77i	−1.06475	−	1.52284i
$976$		0			0
$977$	−450.483	−	450.483i	−0.461088	−	0.461088i	0.437924	−	0.899012i	$-0.355714\pi$
$977$	−450.483	−	450.483i	−0.461088	−	0.461088i	−0.899012	+	0.437924i	$0.855714\pi$
$978$		0			0
$979$	−1258.85	−	726.799i	−1.28586	−	0.742390i
$980$		0			0
$981$	−1106.78			−1.12822
$982$		0			0
$983$	−762.845	−	204.404i	−0.776037	−	0.207939i	−0.151000	−	0.988534i	$-0.548249\pi$
$983$	−762.845	−	204.404i	−0.776037	−	0.207939i	−0.625037	+	0.780595i	$0.714916\pi$
$984$		0			0
$985$	−1380.78	−	719.389i	−1.40181	−	0.730344i
$986$		0			0
$987$	−2.06829	−	2.06829i	−0.00209553	−	0.00209553i
$988$		0			0
$989$		−	205.576i		−	0.207863i
$990$		0			0
$991$	−613.695	−	1062.95i	−0.619268	−	1.07260i	−0.989619	−	0.143713i	$-0.954096\pi$
$991$	−613.695	−	1062.95i	−0.619268	−	1.07260i	0.370351	−	0.928892i	$-0.379237\pi$
$992$		0			0
$993$	−688.910	−	184.593i	−0.693766	−	0.185894i
$994$		0			0
$995$	−731.642	−	162.464i	−0.735319	−	0.163281i
$996$		0			0
$997$	665.561	−	178.336i	0.667563	−	0.178873i	0.0909064	−	0.995859i	$-0.471024\pi$
$997$	665.561	−	178.336i	0.667563	−	0.178873i	0.576657	+	0.816986i	$0.304357\pi$
$998$		0			0
$999$		−	280.030i		−	0.280310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.x.a.197.3	✓	80
5.3	odd	4	inner	380.3.x.a.273.18	yes	80
19.11	even	3	inner	380.3.x.a.277.18	yes	80
95.68	odd	12	inner	380.3.x.a.353.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.x.a.197.3	✓	80	1.1	even	1	trivial
380.3.x.a.273.18	yes	80	5.3	odd	4	inner
380.3.x.a.277.18	yes	80	19.11	even	3	inner
380.3.x.a.353.3	yes	80	95.68	odd	12	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.39499 - 1.17763i) q^{3} +(4.76910 - 1.50189i) q^{5} +(2.17731 + 2.17731i) q^{7} +(10.1349 + 5.85137i) q^{9} +O(q^{10})\)	\(q+(-4.39499 - 1.17763i) q^{3} +(4.76910 - 1.50189i) q^{5} +(2.17731 + 2.17731i) q^{7} +(10.1349 + 5.85137i) q^{9} -13.6120 q^{11} +(4.12219 + 15.3842i) q^{13} +(-22.7288 + 0.984556i) q^{15} +(-0.483152 + 1.80315i) q^{17} +(11.5760 - 15.0664i) q^{19} +(-7.00518 - 12.1333i) q^{21} +(-0.635421 - 2.37142i) q^{23} +(20.4886 - 14.3254i) q^{25} +(-8.69569 - 8.69569i) q^{27} +(40.5826 + 23.4304i) q^{29} +14.1381 q^{31} +(59.8248 + 16.0300i) q^{33} +(13.6539 + 7.11372i) q^{35} +(16.1016 + 16.1016i) q^{37} -72.4680i q^{39} +(-8.41028 - 14.5670i) q^{41} +(80.8819 + 21.6722i) q^{43} +(57.1224 + 12.6843i) q^{45} +(0.201661 - 0.0540349i) q^{47} -39.5186i q^{49} +(4.24689 - 7.35583i) q^{51} +(11.0149 + 41.1083i) q^{53} +(-64.9172 + 20.4438i) q^{55} +(-68.6190 + 52.5844i) q^{57} +(39.3120 - 22.6968i) q^{59} +(58.3324 - 101.035i) q^{61} +(9.32651 + 34.8070i) q^{63} +(42.7647 + 67.1779i) q^{65} +(-3.97436 + 1.06493i) q^{67} +11.1707i q^{69} +(-25.5943 - 44.3307i) q^{71} +(37.4121 + 10.0246i) q^{73} +(-106.917 + 38.8317i) q^{75} +(-29.6376 - 29.6376i) q^{77} +(-97.8112 + 56.4713i) q^{79} +(-24.6852 - 42.7561i) q^{81} +(-58.0168 + 58.0168i) q^{83} +(0.403937 + 9.32503i) q^{85} +(-150.768 - 150.768i) q^{87} +(92.4809 + 53.3939i) q^{89} +(-24.5210 + 42.4716i) q^{91} +(-62.1367 - 16.6495i) q^{93} +(32.5788 - 89.2391i) q^{95} +(-12.0651 + 45.0275i) q^{97} +(-137.956 - 79.6491i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{5} - 12 q^{7}+O(q^{10}) \) 80 * q + 2 * q^5 - 12 * q^7	\( 80 q + 2 q^{5} - 12 q^{7} - 16 q^{11} - 8 q^{13} - 6 q^{15} - 32 q^{17} + 24 q^{21} - 60 q^{23} - 50 q^{25} - 84 q^{27} + 112 q^{31} + 12 q^{33} + 76 q^{35} - 128 q^{37} - 40 q^{41} + 58 q^{43} - 116 q^{45} + 70 q^{47} - 8 q^{51} - 82 q^{53} - 136 q^{55} + 322 q^{57} + 104 q^{61} - 86 q^{63} + 280 q^{65} - 72 q^{67} - 32 q^{71} - 292 q^{73} + 108 q^{75} + 420 q^{77} + 336 q^{81} - 100 q^{83} - 296 q^{85} + 200 q^{87} + 112 q^{91} + 16 q^{93} - 308 q^{95} - 122 q^{97}+O(q^{100}) \) 80 * q + 2 * q^5 - 12 * q^7 - 16 * q^11 - 8 * q^13 - 6 * q^15 - 32 * q^17 + 24 * q^21 - 60 * q^23 - 50 * q^25 - 84 * q^27 + 112 * q^31 + 12 * q^33 + 76 * q^35 - 128 * q^37 - 40 * q^41 + 58 * q^43 - 116 * q^45 + 70 * q^47 - 8 * q^51 - 82 * q^53 - 136 * q^55 + 322 * q^57 + 104 * q^61 - 86 * q^63 + 280 * q^65 - 72 * q^67 - 32 * q^71 - 292 * q^73 + 108 * q^75 + 420 * q^77 + 336 * q^81 - 100 * q^83 - 296 * q^85 + 200 * q^87 + 112 * q^91 + 16 * q^93 - 308 * q^95 - 122 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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