LMFDB - Embedded newform 950.2.u.d.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.2
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	950.499
Dual form			950.2.u.d.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.342020 + 0.939693i) q^{2} +(-2.49362 - 0.439693i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.439693 - 2.49362i) q^{6} +(0.565258 - 0.326352i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(3.20574 + 1.16679i) q^{9} +O(q^{10})$	\(q+(0.342020 + 0.939693i) q^{2} +(-2.49362 - 0.439693i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.439693 - 2.49362i) q^{6} +(0.565258 - 0.326352i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(3.20574 + 1.16679i) q^{9} +(0.500000 - 0.866025i) q^{11} +(2.19285 - 1.26604i) q^{12} +(-2.83564 + 0.500000i) q^{13} +(0.500000 + 0.419550i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.160035 + 0.439693i) q^{17} +3.41147i q^{18} +(4.07398 - 1.55007i) q^{19} +(-1.55303 + 0.565258i) q^{21} +(0.984808 + 0.173648i) q^{22} +(-2.15160 - 2.56418i) q^{23} +(1.93969 + 1.62760i) q^{24} +(-1.43969 - 2.49362i) q^{26} +(-0.902302 - 0.520945i) q^{27} +(-0.223238 + 0.613341i) q^{28} +(6.41147 + 2.33359i) q^{29} +(2.03209 + 3.51968i) q^{31} +(0.984808 - 0.173648i) q^{32} +(-1.62760 + 1.93969i) q^{33} +(-0.358441 + 0.300767i) q^{34} +(-3.20574 + 1.16679i) q^{36} +7.63816i q^{37} +(2.84997 + 3.29813i) q^{38} +7.29086 q^{39} +(-0.854570 + 4.84651i) q^{41} +(-1.06234 - 1.26604i) q^{42} +(-2.02022 + 2.40760i) q^{43} +(0.173648 + 0.984808i) q^{44} +(1.67365 - 2.89884i) q^{46} +(-2.19285 + 6.02481i) q^{47} +(-0.866025 + 2.37939i) q^{48} +(-3.28699 + 5.69323i) q^{49} +(-0.205737 - 1.16679i) q^{51} +(1.85083 - 2.20574i) q^{52} +(2.48427 + 2.96064i) q^{53} +(0.180922 - 1.02606i) q^{54} -0.652704 q^{56} +(-10.8405 + 2.07398i) q^{57} +6.82295i q^{58} +(-5.68479 + 2.06910i) q^{59} +(-3.96064 + 3.32337i) q^{61} +(-2.61240 + 3.11334i) q^{62} +(2.19285 - 0.386659i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-2.37939 - 0.866025i) q^{66} +(0.300767 - 0.826352i) q^{67} +(-0.405223 - 0.233956i) q^{68} +(4.23783 + 7.34013i) q^{69} +(9.35504 + 7.84981i) q^{71} +(-2.19285 - 2.61334i) q^{72} +(0.502055 + 0.0885259i) q^{73} +(-7.17752 + 2.61240i) q^{74} +(-2.12449 + 3.80612i) q^{76} -0.652704i q^{77} +(2.49362 + 6.85117i) q^{78} +(1.51367 - 8.58445i) q^{79} +(-5.81908 - 4.88279i) q^{81} +(-4.84651 + 0.854570i) q^{82} +(15.5100 - 8.95471i) q^{83} +(0.826352 - 1.43128i) q^{84} +(-2.95336 - 1.07494i) q^{86} +(-14.9617 - 8.63816i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(3.06418 + 17.3778i) q^{89} +(-1.43969 + 1.20805i) q^{91} +(3.29644 + 0.581252i) q^{92} +(-3.51968 - 9.67024i) q^{93} -6.41147 q^{94} -2.53209 q^{96} +(4.96032 + 13.6284i) q^{97} +(-6.47410 - 1.14156i) q^{98} +(2.61334 - 2.19285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{6} + 18 q^{9}+O(q^{10}) $ 12 * q + 6 * q^6 + 18 * q^9	$ 12 q + 6 q^{6} + 18 q^{9} + 6 q^{11} + 6 q^{14} + 18 q^{19} + 6 q^{21} + 12 q^{24} - 6 q^{26} + 36 q^{29} + 6 q^{31} + 12 q^{34} - 18 q^{36} + 24 q^{39} - 42 q^{41} + 18 q^{46} - 24 q^{49} + 18 q^{51} + 36 q^{54} - 12 q^{56} - 54 q^{59} - 30 q^{61} + 6 q^{64} - 6 q^{66} + 12 q^{69} + 12 q^{71} - 36 q^{74} - 24 q^{79} - 36 q^{81} + 12 q^{84} + 18 q^{86} - 6 q^{91} - 36 q^{94} - 12 q^{96} + 18 q^{99}+O(q^{100}) $ 12 * q + 6 * q^6 + 18 * q^9 + 6 * q^11 + 6 * q^14 + 18 * q^19 + 6 * q^21 + 12 * q^24 - 6 * q^26 + 36 * q^29 + 6 * q^31 + 12 * q^34 - 18 * q^36 + 24 * q^39 - 42 * q^41 + 18 * q^46 - 24 * q^49 + 18 * q^51 + 36 * q^54 - 12 * q^56 - 54 * q^59 - 30 * q^61 + 6 * q^64 - 6 * q^66 + 12 * q^69 + 12 * q^71 - 36 * q^74 - 24 * q^79 - 36 * q^81 + 12 * q^84 + 18 * q^86 - 6 * q^91 - 36 * q^94 - 12 * q^96 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$3$	−2.49362	−	0.439693i	−1.43969	−	0.253857i	−0.601344	−	0.798991i	$-0.705368\pi$
$3$	−2.49362	−	0.439693i	−1.43969	−	0.253857i	−0.838349	+	0.545134i	$0.816479\pi$
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.439693	−	2.49362i	−0.179504	−	1.01802i
$7$	0.565258	−	0.326352i	0.213647	−	0.123349i	−0.389358	−	0.921087i	$-0.627303\pi$
$7$	0.565258	−	0.326352i	0.213647	−	0.123349i	0.603005	+	0.797737i	$0.293970\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	3.20574	+	1.16679i	1.06858	+	0.388931i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$	2.19285	−	1.26604i	0.633022	−	0.365476i
$13$	−2.83564	+	0.500000i	−0.786465	+	0.138675i	−0.552437	−	0.833555i	$-0.686302\pi$
$13$	−2.83564	+	0.500000i	−0.786465	+	0.138675i	−0.234028	+	0.972230i	$0.575191\pi$
$14$	0.500000	+	0.419550i	0.133631	+	0.112129i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	0.160035	+	0.439693i	0.0388142	+	0.106641i	0.957586	−	0.288149i	$-0.0930397\pi$
$17$	0.160035	+	0.439693i	0.0388142	+	0.106641i	−0.918772	+	0.394790i	$0.870817\pi$
$18$			3.41147i			0.804092i
$19$	4.07398	−	1.55007i	0.934635	−	0.355609i
$19$	4.07398	−	1.55007i	0.934635	−	0.355609i
$20$		0			0
$21$	−1.55303	+	0.565258i	−0.338900	+	0.123349i
$22$	0.984808	+	0.173648i	0.209962	+	0.0370219i
$23$	−2.15160	−	2.56418i	−0.448640	−	0.534668i	0.493564	−	0.869710i	$-0.335694\pi$
$23$	−2.15160	−	2.56418i	−0.448640	−	0.534668i	−0.942203	+	0.335042i	$0.891250\pi$
$24$	1.93969	+	1.62760i	0.395938	+	0.332232i
$25$		0			0
$26$	−1.43969	−	2.49362i	−0.282347	−	0.489039i
$27$	−0.902302	−	0.520945i	−0.173648	−	0.100256i
$28$	−0.223238	+	0.613341i	−0.0421880	+	0.115911i
$29$	6.41147	+	2.33359i	1.19058	+	0.433336i	0.859927	−	0.510416i	$-0.170509\pi$
$29$	6.41147	+	2.33359i	1.19058	+	0.433336i	0.330653	+	0.943752i	$0.392731\pi$
$30$		0			0
$31$	2.03209	+	3.51968i	0.364974	+	0.632153i	0.988772	−	0.149432i	$-0.0477446\pi$
$31$	2.03209	+	3.51968i	0.364974	+	0.632153i	−0.623798	+	0.781586i	$0.714411\pi$
$32$	0.984808	−	0.173648i	0.174091	−	0.0306970i
$33$	−1.62760	+	1.93969i	−0.283328	+	0.337657i
$34$	−0.358441	+	0.300767i	−0.0614721	+	0.0515812i
$35$		0			0
$36$	−3.20574	+	1.16679i	−0.534290	+	0.194465i
$37$			7.63816i			1.25571i	0.778332	+	0.627853i	$0.216066\pi$
$37$			7.63816i			1.25571i	−0.778332	+	0.627853i	$0.783934\pi$
$38$	2.84997	+	3.29813i	0.462326	+	0.535028i
$39$	7.29086			1.16747
$40$		0			0
$41$	−0.854570	+	4.84651i	−0.133461	+	0.756898i	0.842457	+	0.538763i	$0.181108\pi$
$41$	−0.854570	+	4.84651i	−0.133461	+	0.756898i	−0.975919	+	0.218134i	$0.930003\pi$
$42$	−1.06234	−	1.26604i	−0.163922	−	0.195355i
$43$	−2.02022	+	2.40760i	−0.308081	+	0.367156i	−0.897763	−	0.440479i	$-0.854809\pi$
$43$	−2.02022	+	2.40760i	−0.308081	+	0.367156i	0.589682	+	0.807635i	$0.299253\pi$
$44$	0.173648	+	0.984808i	0.0261784	+	0.148465i
$45$		0			0
$46$	1.67365	−	2.89884i	0.246766	−	0.427411i
$47$	−2.19285	+	6.02481i	−0.319861	+	0.878810i	0.670699	+	0.741729i	$0.265994\pi$
$47$	−2.19285	+	6.02481i	−0.319861	+	0.878810i	−0.990560	+	0.137080i	$0.956228\pi$
$48$	−0.866025	+	2.37939i	−0.125000	+	0.343435i
$49$	−3.28699	+	5.69323i	−0.469570	+	0.813319i
$50$		0			0
$51$	−0.205737	−	1.16679i	−0.0288090	−	0.163384i
$52$	1.85083	−	2.20574i	0.256664	−	0.305881i
$53$	2.48427	+	2.96064i	0.341241	+	0.406675i	0.909185	−	0.416392i	$-0.136706\pi$
$53$	2.48427	+	2.96064i	0.341241	+	0.406675i	−0.567944	+	0.823067i	$0.692261\pi$
$54$	0.180922	−	1.02606i	0.0246204	−	0.139629i
$55$		0			0
$56$	−0.652704			−0.0872212
$57$	−10.8405	+	2.07398i	−1.43586	+	0.274705i
$58$			6.82295i			0.895897i
$59$	−5.68479	+	2.06910i	−0.740097	+	0.269373i	−0.684432	−	0.729076i	$-0.739950\pi$
$59$	−5.68479	+	2.06910i	−0.740097	+	0.269373i	−0.0556645	+	0.998450i	$0.517728\pi$
$60$		0			0
$61$	−3.96064	+	3.32337i	−0.507108	+	0.425514i	−0.860110	−	0.510109i	$-0.829605\pi$
$61$	−3.96064	+	3.32337i	−0.507108	+	0.425514i	0.353002	+	0.935622i	$0.385161\pi$
$62$	−2.61240	+	3.11334i	−0.331776	+	0.395395i
$63$	2.19285	−	0.386659i	0.276274	−	0.0487145i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−2.37939	−	0.866025i	−0.292882	−	0.106600i
$67$	0.300767	−	0.826352i	0.0367446	−	0.100955i	−0.919964	−	0.392004i	$-0.871782\pi$
$67$	0.300767	−	0.826352i	0.0367446	−	0.100955i	0.956708	+	0.291049i	$0.0940042\pi$
$68$	−0.405223	−	0.233956i	−0.0491405	−	0.0283713i
$69$	4.23783	+	7.34013i	0.510174	+	0.883648i
$70$		0			0
$71$	9.35504	+	7.84981i	1.11024	+	0.931601i	0.998071	−	0.0620884i	$-0.0197761\pi$
$71$	9.35504	+	7.84981i	1.11024	+	0.931601i	0.112168	+	0.993689i	$0.464221\pi$
$72$	−2.19285	−	2.61334i	−0.258430	−	0.307985i
$73$	0.502055	+	0.0885259i	0.0587611	+	0.0103612i	0.202951	−	0.979189i	$-0.434947\pi$
$73$	0.502055	+	0.0885259i	0.0587611	+	0.0103612i	−0.144190	+	0.989550i	$0.546058\pi$
$74$	−7.17752	+	2.61240i	−0.834370	+	0.303686i
$75$		0			0
$76$	−2.12449	+	3.80612i	−0.243695	+	0.436592i
$77$		−	0.652704i		−	0.0743825i
$78$	2.49362	+	6.85117i	0.282347	+	0.775742i
$79$	1.51367	−	8.58445i	0.170301	−	0.965826i	−0.773127	−	0.634251i	$-0.781309\pi$
$79$	1.51367	−	8.58445i	0.170301	−	0.965826i	0.943429	−	0.331576i	$-0.107580\pi$
$80$		0			0
$81$	−5.81908	−	4.88279i	−0.646564	−	0.542532i
$82$	−4.84651	+	0.854570i	−0.535207	+	0.0943715i
$83$	15.5100	−	8.95471i	1.70244	−	0.982907i	0.759170	−	0.650892i	$-0.225605\pi$
$83$	15.5100	−	8.95471i	1.70244	−	0.982907i	0.943274	−	0.332015i	$-0.107728\pi$
$84$	0.826352	−	1.43128i	0.0901624	−	0.156166i
$85$		0			0
$86$	−2.95336	−	1.07494i	−0.318469	−	0.115913i
$87$	−14.9617	−	8.63816i	−1.60407	−	0.926108i
$88$	−0.866025	+	0.500000i	−0.0923186	+	0.0533002i
$89$	3.06418	+	17.3778i	0.324802	+	1.84204i	0.511061	+	0.859544i	$0.329252\pi$
$89$	3.06418	+	17.3778i	0.324802	+	1.84204i	−0.186259	+	0.982501i	$0.559636\pi$
$90$		0			0
$91$	−1.43969	+	1.20805i	−0.150921	+	0.126638i
$92$	3.29644	+	0.581252i	0.343678	+	0.0605997i
$93$	−3.51968	−	9.67024i	−0.364974	−	1.00276i
$94$	−6.41147			−0.661293
$95$		0			0
$96$	−2.53209			−0.258430
$97$	4.96032	+	13.6284i	0.503644	+	1.38375i	0.887692	+	0.460437i	$0.152307\pi$
$97$	4.96032	+	13.6284i	0.503644	+	1.38375i	−0.384049	+	0.923313i	$0.625471\pi$
$98$	−6.47410	−	1.14156i	−0.653983	−	0.115315i
$99$	2.61334	−	2.19285i	0.262651	−	0.220390i
$100$		0			0
$101$	−2.59580	−	14.7215i	−0.258292	−	1.46485i	−0.787480	−	0.616341i	$-0.788614\pi$
$101$	−2.59580	−	14.7215i	−0.258292	−	1.46485i	0.529188	−	0.848505i	$-0.322497\pi$
$102$	1.02606	−	0.592396i	0.101595	−	0.0586560i
$103$	6.25849	+	3.61334i	0.616667	+	0.356033i	0.775570	−	0.631261i	$-0.217462\pi$
$103$	6.25849	+	3.61334i	0.616667	+	0.356033i	−0.158903	+	0.987294i	$0.550796\pi$
$104$	2.70574	+	0.984808i	0.265319	+	0.0965683i
$105$		0			0
$106$	−1.93242	+	3.34705i	−0.187693	+	0.325094i
$107$	6.29477	−	3.63429i	0.608538	−	0.351340i	−0.163855	−	0.986484i	$-0.552393\pi$
$107$	6.29477	−	3.63429i	0.608538	−	0.351340i	0.772393	+	0.635145i	$0.219060\pi$
$108$	1.02606	−	0.180922i	0.0987327	−	0.0174092i
$109$	−6.77584	−	5.68561i	−0.649008	−	0.544583i	0.257762	−	0.966209i	$-0.417015\pi$
$109$	−6.77584	−	5.68561i	−0.649008	−	0.544583i	−0.906770	+	0.421626i	$0.861460\pi$
$110$		0			0
$111$	3.35844	−	19.0467i	0.318769	−	1.80783i
$112$	−0.223238	−	0.613341i	−0.0210940	−	0.0579553i
$113$			1.49020i			0.140186i	0.997540	+	0.0700931i	$0.0223296\pi$
$113$			1.49020i			0.140186i	−0.997540	+	0.0700931i	$0.977670\pi$
$114$	−5.65657	−	9.47740i	−0.529787	−	0.887640i
$115$		0			0
$116$	−6.41147	+	2.33359i	−0.595290	+	0.216668i
$117$	−9.67372	−	1.70574i	−0.894335	−	0.157695i
$118$	−3.88863	−	4.63429i	−0.357977	−	0.426621i
$119$	0.233956	+	0.196312i	0.0214467	+	0.0179959i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−4.47756	−	2.58512i	−0.405380	−	0.234046i
$123$	4.26195	−	11.7096i	0.384287	−	1.05582i
$124$	−3.81908	−	1.39003i	−0.342963	−	0.124828i
$125$		0			0
$126$	1.11334	+	1.92836i	0.0991843	+	0.171792i
$127$	18.0569	−	3.18392i	1.60229	−	0.282527i	0.700158	−	0.713988i	$-0.253113\pi$
$127$	18.0569	−	3.18392i	1.60229	−	0.282527i	0.902131	+	0.431461i	$0.142002\pi$
$128$	−0.642788	+	0.766044i	−0.0568149	+	0.0677094i
$129$	6.09627	−	5.11538i	0.536746	−	0.450384i
$130$		0			0
$131$	−6.72416	+	2.44739i	−0.587492	+	0.213830i	−0.618626	−	0.785686i	$-0.712310\pi$
$131$	−6.72416	+	2.44739i	−0.587492	+	0.213830i	0.0311339	+	0.999515i	$0.490088\pi$
$132$		−	2.53209i		−	0.220390i
$133$	1.79698	−	2.20574i	0.155818	−	0.191262i
$134$	0.879385			0.0759673
$135$		0			0
$136$	0.0812519	−	0.460802i	0.00696729	−	0.0395135i
$137$	10.8961	+	12.9855i	0.930916	+	1.10942i	0.993776	+	0.111400i	$0.0355334\pi$
$137$	10.8961	+	12.9855i	0.930916	+	1.10942i	−0.0628601	+	0.998022i	$0.520022\pi$
$138$	−5.44804	+	6.49273i	−0.463768	+	0.552698i
$139$	−2.20321	−	12.4950i	−0.186874	−	1.05981i	−0.923524	−	0.383541i	$-0.874705\pi$
$139$	−2.20321	−	12.4950i	−0.186874	−	1.05981i	0.736650	−	0.676274i	$-0.236406\pi$
$140$		0			0
$141$	8.11721	−	14.0594i	0.683592	−	1.18402i
$142$	−4.17680	+	11.4757i	−0.350509	+	0.963015i
$143$	−0.984808	+	2.70574i	−0.0823538	+	0.226265i
$144$	1.70574	−	2.95442i	0.142145	−	0.246202i
$145$		0			0
$146$	0.0885259	+	0.502055i	0.00732645	+	0.0415504i
$147$	10.6998	−	12.7515i	0.882503	−	1.05173i
$148$	−4.90971	−	5.85117i	−0.403576	−	0.480963i
$149$	0.593740	−	3.36727i	0.0486411	−	0.275857i	−0.950780	−	0.309865i	$-0.899716\pi$
$149$	0.593740	−	3.36727i	0.0486411	−	0.275857i	0.999422	+	0.0340079i	$0.0108271\pi$
$150$		0			0
$151$	15.5594			1.26621			0.633104	−	0.774067i	$-0.281780\pi$
$151$	15.5594			1.26621			0.633104	+	0.774067i	$0.281780\pi$
$152$	−4.30320	−	0.694593i	−0.349036	−	0.0563389i
$153$			1.59627i			0.129051i
$154$	0.613341	−	0.223238i	0.0494244	−	0.0179890i
$155$		0			0
$156$	−5.58512	+	4.68647i	−0.447168	+	0.375218i
$157$	−8.53882	+	10.1762i	−0.681472	+	0.812147i	−0.990296	−	0.138972i	$-0.955620\pi$
$157$	−8.53882	+	10.1762i	−0.681472	+	0.812147i	0.308824	+	0.951119i	$0.400065\pi$
$158$	8.58445	−	1.51367i	0.682942	−	0.120421i
$159$	−4.89306	−	8.47502i	−0.388045	−	0.672113i
$160$		0			0
$161$	−2.05303	−	0.747243i	−0.161802	−	0.0588910i
$162$	2.59808	−	7.13816i	0.204124	−	0.560826i
$163$	−4.56504	−	2.63563i	−0.357562	−	0.206438i	0.310449	−	0.950590i	$-0.399521\pi$
$163$	−4.56504	−	2.63563i	−0.357562	−	0.206438i	−0.668011	+	0.744152i	$0.732854\pi$
$164$	−2.46064	−	4.26195i	−0.192143	−	0.332802i
$165$		0			0
$166$	13.7194	+	11.5119i	1.06483	+	0.893501i
$167$	−1.39998	−	1.66843i	−0.108334	−	0.129107i	0.709153	−	0.705055i	$-0.249078\pi$
$167$	−1.39998	−	1.66843i	−0.108334	−	0.129107i	−0.817487	+	0.575948i	$0.804633\pi$
$168$	1.62760	+	0.286989i	0.125572	+	0.0221417i
$169$	−4.42514	+	1.61062i	−0.340396	+	0.123894i
$170$		0			0
$171$	14.8687	−	0.215615i	1.13704	−	0.0164885i
$172$		−	3.14290i		−	0.239644i
$173$	−2.54747	−	6.99912i	−0.193681	−	0.532133i	0.804398	−	0.594091i	$-0.202488\pi$
$173$	−2.54747	−	6.99912i	−0.193681	−	0.532133i	−0.998079	+	0.0619572i	$0.980266\pi$
$174$	3.00000	−	17.0138i	0.227429	−	1.28982i
$175$		0			0
$176$	−0.766044	−	0.642788i	−0.0577428	−	0.0484519i
$177$	15.0855	−	2.65998i	1.13389	−	0.199936i
$178$	−15.2818	+	8.82295i	−1.14542	+	0.661308i
$179$	3.17617	−	5.50130i	0.237398	−	0.411186i	−0.722569	−	0.691299i	$-0.757039\pi$
$179$	3.17617	−	5.50130i	0.237398	−	0.411186i	0.959967	+	0.280113i	$0.0903720\pi$
$180$		0			0
$181$	−12.5449	−	4.56596i	−0.932454	−	0.339385i	−0.169272	−	0.985569i	$-0.554142\pi$
$181$	−12.5449	−	4.56596i	−0.932454	−	0.339385i	−0.763182	+	0.646184i	$0.776364\pi$
$182$	−1.62760	−	0.939693i	−0.120645	−	0.0696547i
$183$	11.3376	−	6.54576i	0.838099	−	0.483876i
$184$	0.581252	+	3.29644i	0.0428505	+	0.243017i
$185$		0			0
$186$	7.88326	−	6.61484i	0.578028	−	0.485023i
$187$	0.460802	+	0.0812519i	0.0336972	+	0.00594173i
$188$	−2.19285	−	6.02481i	−0.159930	−	0.439405i
$189$	−0.680045			−0.0494660
$190$		0			0
$191$	9.17530			0.663901			0.331951	−	0.943297i	$-0.392293\pi$
$191$	9.17530			0.663901			0.331951	+	0.943297i	$0.392293\pi$
$192$	−0.866025	−	2.37939i	−0.0625000	−	0.171717i
$193$	−14.9734	−	2.64022i	−1.07781	−	0.190047i	−0.393563	−	0.919298i	$-0.628758\pi$
$193$	−14.9734	−	2.64022i	−1.07781	−	0.190047i	−0.684246	+	0.729251i	$0.739869\pi$
$194$	−11.1099	+	9.32234i	−0.797647	+	0.669305i
$195$		0			0
$196$	−1.14156	−	6.47410i	−0.0815399	−	0.462436i
$197$	15.5522	−	8.97906i	1.10805	−	0.639731i	0.169724	−	0.985492i	$-0.445712\pi$
$197$	15.5522	−	8.97906i	1.10805	−	0.639731i	0.938323	+	0.345760i	$0.112379\pi$
$198$	2.95442	+	1.70574i	0.209962	+	0.121221i
$199$	−23.2729	−	8.47065i	−1.64977	−	0.600468i	−0.661065	−	0.750328i	$-0.729895\pi$
$199$	−23.2729	−	8.47065i	−1.64977	−	0.600468i	−0.988707	+	0.149860i	$0.952118\pi$
$200$		0			0
$201$	−1.11334	+	1.92836i	−0.0785290	+	0.136016i
$202$	12.9459	−	7.47431i	0.910869	−	0.525890i
$203$	4.38571	−	0.773318i	0.307816	−	0.0542763i
$204$	0.907604	+	0.761570i	0.0635450	+	0.0533206i
$205$		0			0
$206$	−1.25490	+	7.11689i	−0.0874330	+	0.495857i
$207$	−3.90560	−	10.7306i	−0.271458	−	0.745825i
$208$			2.87939i			0.199649i
$209$	0.694593	−	4.30320i	0.0480460	−	0.297659i
$210$		0			0
$211$	−10.0522	+	3.65869i	−0.692019	+	0.251874i	−0.663999	−	0.747733i	$-0.731142\pi$
$211$	−10.0522	+	3.65869i	−0.692019	+	0.251874i	−0.0280195	+	0.999607i	$0.508920\pi$
$212$	−3.80612	−	0.671122i	−0.261406	−	0.0460928i
$213$	−19.8764	−	23.6878i	−1.36191	−	1.62306i
$214$	5.56805	+	4.67215i	0.380624	+	0.319381i
$215$		0			0
$216$	0.520945	+	0.902302i	0.0354458	+	0.0613939i
$217$	2.29731	+	1.32635i	0.155951	+	0.0900386i
$218$	3.02525	−	8.31180i	0.204896	−	0.562946i
$219$	−1.21301	−	0.441500i	−0.0819677	−	0.0298338i
$220$		0			0
$221$	−0.673648	−	1.16679i	−0.0453145	−	0.0784870i
$222$	19.0467	−	3.35844i	1.27833	−	0.225404i
$223$	−7.35770	+	8.76857i	−0.492708	+	0.587187i	−0.953904	−	0.300111i	$-0.902976\pi$
$223$	−7.35770	+	8.76857i	−0.492708	+	0.587187i	0.461196	+	0.887298i	$0.347421\pi$
$224$	0.500000	−	0.419550i	0.0334077	−	0.0280324i
$225$		0			0
$226$	−1.40033	+	0.509678i	−0.0931486	+	0.0339033i
$227$		−	14.3250i		−	0.950784i	−0.879774	−	0.475392i	$-0.842306\pi$
$227$		−	14.3250i		−	0.950784i	0.879774	−	0.475392i	$-0.157694\pi$
$228$	6.97118	−	8.55690i	0.461678	−	0.566695i
$229$	6.08647			0.402205			0.201103	−	0.979570i	$-0.435548\pi$
$229$	6.08647			0.402205			0.201103	+	0.979570i	$0.435548\pi$
$230$		0			0
$231$	−0.286989	+	1.62760i	−0.0188825	+	0.107088i
$232$	−4.38571	−	5.22668i	−0.287936	−	0.343148i
$233$	7.10257	−	8.46451i	0.465305	−	0.554528i	−0.481455	−	0.876471i	$-0.659891\pi$
$233$	7.10257	−	8.46451i	0.465305	−	0.554528i	0.946759	+	0.321943i	$0.104336\pi$
$234$	−1.70574	−	9.67372i	−0.111508	−	0.632391i
$235$		0			0
$236$	3.02481	−	5.23913i	0.196899	−	0.341039i
$237$	−7.54904	+	20.7408i	−0.490363	+	1.34726i
$238$	−0.104455	+	0.286989i	−0.00677084	+	0.0186027i
$239$	−4.02481	+	6.97118i	−0.260344	+	0.450928i	−0.966333	−	0.257294i	$-0.917169\pi$
$239$	−4.02481	+	6.97118i	−0.260344	+	0.450928i	0.705990	+	0.708222i	$0.250503\pi$
$240$		0			0
$241$	4.80019	+	27.2232i	0.309208	+	1.75360i	0.603007	+	0.797736i	$0.293969\pi$
$241$	4.80019	+	27.2232i	0.309208	+	1.75360i	−0.293799	+	0.955867i	$0.594920\pi$
$242$	−6.42788	+	7.66044i	−0.413200	+	0.492432i
$243$	14.3728	+	17.1288i	0.922015	+	1.09881i
$244$	0.897804	−	5.09170i	0.0574760	−	0.325962i
$245$		0			0
$246$	12.4611			0.794491
$247$	−10.7773	+	6.43242i	−0.685744	+	0.409285i
$248$		−	4.06418i		−	0.258076i
$249$	−42.6134	+	15.5100i	−2.70051	+	0.982907i
$250$		0			0
$251$	−16.8648	+	14.1513i	−1.06450	+	0.893221i	−0.994543	−	0.104329i	$-0.966730\pi$
$251$	−16.8648	+	14.1513i	−1.06450	+	0.893221i	−0.0699563	+	0.997550i	$0.522286\pi$
$252$	−1.43128	+	1.70574i	−0.0901624	+	0.107451i
$253$	−3.29644	+	0.581252i	−0.207246	+	0.0365430i
$254$	9.16772	+	15.8790i	0.575234	+	0.996334i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	4.89711	−	13.4547i	0.305474	−	0.839282i	−0.688051	−	0.725662i	$-0.741533\pi$
$257$	4.89711	−	13.4547i	0.305474	−	0.839282i	0.993524	−	0.113619i	$-0.0362444\pi$
$258$	6.89193	+	3.97906i	0.429073	+	0.247725i
$259$	2.49273	+	4.31753i	0.154890	+	0.268278i
$260$		0			0
$261$	17.8307	+	14.9617i	1.10369	+	0.926108i
$262$	−4.59959	−	5.48158i	−0.284164	−	0.338653i
$263$	4.69815	+	0.828411i	0.289701	+	0.0510820i	0.316610	−	0.948556i	$-0.397455\pi$
$263$	4.69815	+	0.828411i	0.289701	+	0.0510820i	−0.0269093	+	0.999638i	$0.508567\pi$
$264$	2.37939	−	0.866025i	0.146441	−	0.0533002i
$265$		0			0
$266$	2.68732	+	0.934204i	0.164770	+	0.0572797i
$267$		−	44.6810i		−	2.73443i
$268$	0.300767	+	0.826352i	0.0183723	+	0.0504775i
$269$	−0.384133	+	2.17853i	−0.0234210	+	0.132827i	−0.994276	−	0.106839i	$-0.965927\pi$
$269$	−0.384133	+	2.17853i	−0.0234210	+	0.132827i	0.970855	+	0.239666i	$0.0770381\pi$
$270$		0			0
$271$	16.3917	+	13.7543i	0.995726	+	0.835513i	0.986387	−	0.164443i	$-0.0525828\pi$
$271$	16.3917	+	13.7543i	0.995726	+	0.835513i	0.00933905	+	0.999956i	$0.497027\pi$
$272$	0.460802	−	0.0812519i	0.0279403	−	0.00492662i
$273$	4.12122	−	2.37939i	0.249427	−	0.144007i
$274$	−8.47565	+	14.6803i	−0.512033	+	0.886867i
$275$		0			0
$276$	−7.96451	−	2.89884i	−0.479407	−	0.174490i
$277$	−6.70669	−	3.87211i	−0.402966	−	0.232653i	0.284797	−	0.958588i	$-0.408074\pi$
$277$	−6.70669	−	3.87211i	−0.402966	−	0.232653i	−0.687763	+	0.725935i	$0.741407\pi$
$278$	10.9879	−	6.34389i	0.659013	−	0.380481i
$279$	2.40760	+	13.6542i	0.144139	+	0.817456i
$280$		0			0
$281$	−10.7968	+	9.05958i	−0.644082	+	0.540449i	−0.905269	−	0.424839i	$-0.860331\pi$
$281$	−10.7968	+	9.05958i	−0.644082	+	0.540449i	0.261186	+	0.965288i	$0.415886\pi$
$282$	15.9878	+	2.81908i	0.952059	+	0.167874i
$283$	−1.78001	−	4.89053i	−0.105810	−	0.290712i	0.875477	−	0.483259i	$-0.160547\pi$
$283$	−1.78001	−	4.89053i	−0.105810	−	0.290712i	−0.981288	+	0.192548i	$0.938325\pi$
$284$	−12.2121			−0.724657
$285$		0			0
$286$	−2.87939			−0.170262
$287$	1.09861	+	3.01842i	0.0648492	+	0.178172i
$288$	3.35965	+	0.592396i	0.197969	+	0.0349073i
$289$	12.8550	−	10.7867i	0.756179	−	0.634509i
$290$		0			0
$291$	−6.37686	−	36.1650i	−0.373818	−	2.12003i
$292$	−0.441500	+	0.254900i	−0.0258368	+	0.0149169i
$293$	23.0953	+	13.3341i	1.34924	+	0.778986i	0.988142	−	0.153541i	$-0.0490676\pi$
$293$	23.0953	+	13.3341i	1.34924	+	0.778986i	0.361101	+	0.932527i	$0.382401\pi$
$294$	15.6420	+	5.69323i	0.912261	+	0.332036i
$295$		0			0
$296$	3.81908	−	6.61484i	0.221979	−	0.384480i
$297$	−0.902302	+	0.520945i	−0.0523569	+	0.0302283i
$298$	3.36727	−	0.593740i	0.195061	−	0.0343945i
$299$	7.38326	+	6.19529i	0.426985	+	0.358283i
$300$		0			0
$301$	−0.356219	+	2.02022i	−0.0205321	+	0.116444i
$302$	5.32164	+	14.6211i	0.306226	+	0.841349i
$303$			37.8512i			2.17450i
$304$	−0.819078	−	4.28125i	−0.0469773	−	0.245547i
$305$		0			0
$306$	−1.50000	+	0.545955i	−0.0857493	+	0.0312102i
$307$	−33.5130	−	5.90925i	−1.91269	−	0.337259i	−0.914899	−	0.403684i	$-0.867730\pi$
$307$	−33.5130	−	5.90925i	−1.91269	−	0.337259i	−0.997791	+	0.0664248i	$0.978841\pi$
$308$	0.419550	+	0.500000i	0.0239061	+	0.0284901i
$309$	−14.0175	−	11.7621i	−0.797430	−	0.669123i
$310$		0			0
$311$	9.52347	+	16.4951i	0.540026	+	0.935353i	0.998902	+	0.0468526i	$0.0149191\pi$
$311$	9.52347	+	16.4951i	0.540026	+	0.935353i	−0.458875	+	0.888501i	$0.651748\pi$
$312$	−6.31407	−	3.64543i	−0.357464	−	0.206382i
$313$	−1.22735	+	3.37211i	−0.0693738	+	0.190603i	−0.969534	−	0.244955i	$-0.921227\pi$
$313$	−1.22735	+	3.37211i	−0.0693738	+	0.190603i	0.900161	+	0.435558i	$0.143449\pi$
$314$	−12.4829	−	4.54341i	−0.704452	−	0.256400i
$315$		0			0
$316$	4.35844	+	7.54904i	0.245181	+	0.424667i
$317$	27.7795	−	4.89827i	1.56025	−	0.275114i	0.674145	−	0.738599i	$-0.264512\pi$
$317$	27.7795	−	4.89827i	1.56025	−	0.275114i	0.886105	+	0.463484i	$0.153401\pi$
$318$	6.29039	−	7.49660i	0.352748	−	0.420388i
$319$	5.22668	−	4.38571i	0.292638	−	0.245552i
$320$		0			0
$321$	−17.2947	+	6.29477i	−0.965298	+	0.351340i
$322$		−	2.18479i		−	0.121754i
$323$	1.33353	+	1.54323i	0.0741997	+	0.0858678i
$324$	7.59627			0.422015
$325$		0			0
$326$	0.915345	−	5.19118i	0.0506962	−	0.287513i
$327$	14.3965	+	17.1570i	0.796126	+	0.948787i
$328$	3.16333	−	3.76991i	0.174666	−	0.208159i
$329$	0.726682	+	4.12122i	0.0400633	+	0.227210i
$330$		0			0
$331$	−4.12108	+	7.13792i	−0.226515	+	0.392336i	−0.956773	−	0.290836i	$-0.906067\pi$
$331$	−4.12108	+	7.13792i	−0.226515	+	0.392336i	0.730258	+	0.683172i	$0.239400\pi$
$332$	−6.12538	+	16.8293i	−0.336174	+	0.923630i
$333$	−8.91215	+	24.4859i	−0.488383	+	1.34182i
$334$	1.08899	−	1.88619i	0.0595870	−	0.103208i
$335$		0			0
$336$	0.286989	+	1.62760i	0.0156565	+	0.0887926i
$337$	2.64695	−	3.15451i	0.144189	−	0.171837i	−0.689117	−	0.724650i	$-0.742001\pi$
$337$	2.64695	−	3.15451i	0.144189	−	0.171837i	0.833305	+	0.552813i	$0.186446\pi$
$338$	−3.02698	−	3.60741i	−0.164646	−	0.196217i
$339$	0.655230	−	3.71599i	0.0355872	−	0.201825i
$340$		0			0
$341$	4.06418			0.220088
$342$	5.28801	+	13.8983i	0.285943	+	0.751532i
$343$			8.85978i			0.478383i
$344$	2.95336	−	1.07494i	0.159235	−	0.0579567i
$345$		0			0
$346$	5.70574	−	4.78768i	0.306742	−	0.257387i
$347$	0.601535	−	0.716881i	0.0322921	−	0.0384842i	−0.749657	−	0.661827i	$-0.769781\pi$
$347$	0.601535	−	0.716881i	0.0322921	−	0.0384842i	0.781949	+	0.623343i	$0.214226\pi$
$348$	17.0138	−	3.00000i	0.912038	−	0.160817i
$349$	−7.03936	−	12.1925i	−0.376808	−	0.652651i	0.613787	−	0.789471i	$-0.289645\pi$
$349$	−7.03936	−	12.1925i	−0.376808	−	0.652651i	−0.990596	+	0.136820i	$0.956312\pi$
$350$		0			0
$351$	2.81908	+	1.02606i	0.150471	+	0.0547671i
$352$	0.342020	−	0.939693i	0.0182297	−	0.0500858i
$353$	16.2775	+	9.39780i	0.866362	+	0.500195i	0.866138	−	0.499805i	$-0.166595\pi$
$353$	16.2775	+	9.39780i	0.866362	+	0.500195i	0.000224734		1.00000i	$0.499928\pi$
$354$	7.65910	+	13.2660i	0.407077	+	0.705077i
$355$		0			0
$356$	−13.5175	−	11.3426i	−0.716428	−	0.601155i
$357$	−0.497079	−	0.592396i	−0.0263082	−	0.0313529i
$358$	6.25584	+	1.10307i	0.330632	+	0.0582993i
$359$	27.3307	−	9.94756i	1.44246	−	0.525012i	0.501984	−	0.864877i	$-0.332604\pi$
$359$	27.3307	−	9.94756i	1.44246	−	0.525012i	0.940474	+	0.339865i	$0.110381\pi$
$360$		0			0
$361$	14.1946	−	12.6299i	0.747084	−	0.664730i
$362$		−	13.3500i		−	0.701660i
$363$	−8.66025	−	23.7939i	−0.454545	−	1.24885i
$364$	0.326352	−	1.85083i	0.0171055	−	0.0970100i
$365$		0			0
$366$	10.0287	+	8.41507i	0.524208	+	0.439863i
$367$	−16.7207	+	2.94831i	−0.872813	+	0.153901i	−0.592074	−	0.805883i	$-0.701691\pi$
$367$	−16.7207	+	2.94831i	−0.872813	+	0.153901i	−0.280739	+	0.959784i	$0.590580\pi$
$368$	−2.89884	+	1.67365i	−0.151113	+	0.0872449i
$369$	−8.39440	+	14.5395i	−0.436995	+	0.756898i
$370$		0			0
$371$	2.37046	+	0.862778i	0.123068	+	0.0447932i
$372$	8.91215	+	5.14543i	0.462073	+	0.266778i
$373$	−3.57445	+	2.06371i	−0.185078	+	0.106855i	−0.589676	−	0.807640i	$-0.700745\pi$
$373$	−3.57445	+	2.06371i	−0.185078	+	0.106855i	0.404598	+	0.914495i	$0.367411\pi$
$374$	0.0812519	+	0.460802i	0.00420144	+	0.0238275i
$375$		0			0
$376$	4.91147	−	4.12122i	0.253290	−	0.212535i
$377$	−19.3474	−	3.41147i	−0.996443	−	0.175700i
$378$	−0.232589	−	0.639033i	−0.0119631	−	0.0328683i
$379$	23.1702			1.19018			0.595088	−	0.803661i	$-0.297117\pi$
$379$	23.1702			1.19018			0.595088	+	0.803661i	$0.297117\pi$
$380$		0			0
$381$	−46.4270			−2.37852
$382$	3.13814	+	8.62196i	0.160561	+	0.441138i
$383$	−31.4565	−	5.54664i	−1.60735	−	0.283420i	−0.703318	−	0.710876i	$-0.748299\pi$
$383$	−31.4565	−	5.54664i	−1.60735	−	0.283420i	−0.904036	+	0.427456i	$0.859410\pi$
$384$	1.93969	−	1.62760i	0.0989845	−	0.0830579i
$385$		0			0
$386$	−2.64022	−	14.9734i	−0.134383	−	0.762126i
$387$	−9.28547	+	5.36097i	−0.472007	+	0.272513i
$388$	−12.5600	−	7.25150i	−0.637635	−	0.368139i
$389$	−25.8717	−	9.41653i	−1.31175	−	0.477437i	−0.410943	−	0.911661i	$-0.634800\pi$
$389$	−25.8717	−	9.41653i	−1.31175	−	0.477437i	−0.900805	+	0.434224i	$0.857023\pi$
$390$		0			0
$391$	0.783119	−	1.35640i	0.0396040	−	0.0685962i
$392$	5.69323	−	3.28699i	0.287552	−	0.166018i
$393$	17.8436	−	3.14631i	0.900090	−	0.158710i
$394$	13.7567	+	11.5433i	0.693053	+	0.581541i
$395$		0			0
$396$	−0.592396	+	3.35965i	−0.0297690	+	0.168829i
$397$	9.38960	+	25.7977i	0.471251	+	1.29475i	0.916748	+	0.399467i	$0.130805\pi$
$397$	9.38960	+	25.7977i	0.471251	+	1.29475i	−0.445497	+	0.895284i	$0.646973\pi$
$398$		−	24.7665i		−	1.24143i
$399$	−5.45084	+	4.71015i	−0.272883	+	0.235803i
$400$		0			0
$401$	−24.0624	+	8.75801i	−1.20162	+	0.437354i	−0.863789	−	0.503853i	$-0.831915\pi$
$401$	−24.0624	+	8.75801i	−1.20162	+	0.437354i	−0.337831	+	0.941207i	$0.609693\pi$
$402$	−2.19285	−	0.386659i	−0.109370	−	0.0192848i
$403$	−7.52211	−	8.96451i	−0.374703	−	0.446554i
$404$	11.4513	+	9.60878i	0.569724	+	0.478055i
$405$		0			0
$406$	2.22668	+	3.85673i	0.110508	+	0.191406i
$407$	6.61484	+	3.81908i	0.327885	+	0.189305i
$408$	−0.405223	+	1.11334i	−0.0200615	+	0.0551186i
$409$	−16.4675	−	5.99368i	−0.814265	−	0.296368i	−0.0988809	−	0.995099i	$-0.531526\pi$
$409$	−16.4675	−	5.99368i	−0.814265	−	0.296368i	−0.715385	+	0.698731i	$0.753748\pi$
$410$		0			0
$411$	−21.4611	−	37.1717i	−1.05860	−	1.83355i
$412$	−7.11689	+	1.25490i	−0.350624	+	0.0618245i
$413$	−2.53812	+	3.02481i	−0.124893	+	0.148841i
$414$	8.74763	−	7.34013i	0.429922	−	0.360748i
$415$		0			0
$416$	−2.70574	+	0.984808i	−0.132660	+	0.0482842i
$417$			32.1266i			1.57325i
$418$	4.28125	−	0.819078i	0.209403	−	0.0400624i
$419$	32.8776			1.60618			0.803089	−	0.595860i	$-0.203188\pi$
$419$	32.8776			1.60618			0.803089	+	0.595860i	$0.203188\pi$
$420$		0			0
$421$	−0.931074	+	5.28039i	−0.0453778	+	0.257350i	−0.999054	−	0.0434844i	$-0.986154\pi$
$421$	−0.931074	+	5.28039i	−0.0453778	+	0.257350i	0.953676	+	0.300835i	$0.0972652\pi$
$422$	−6.87608	−	8.19459i	−0.334722	−	0.398907i
$423$	−14.0594	+	16.7554i	−0.683592	+	0.814674i
$424$	−0.671122	−	3.80612i	−0.0325926	−	0.184842i
$425$		0			0
$426$	15.4611	−	26.7794i	0.749093	−	1.29747i
$427$	−1.15419	+	3.17112i	−0.0558554	+	0.153461i
$428$	−2.48600	+	6.83022i	−0.120165	+	0.330151i
$429$	3.64543	−	6.31407i	0.176003	−	0.304846i
$430$		0			0
$431$	−3.80557	−	21.5825i	−0.183308	−	1.03959i	−0.928110	−	0.372305i	$-0.878567\pi$
$431$	−3.80557	−	21.5825i	−0.183308	−	1.03959i	0.744802	−	0.667285i	$-0.232544\pi$
$432$	−0.669713	+	0.798133i	−0.0322216	+	0.0384002i
$433$	5.13122	+	6.11515i	0.246591	+	0.293875i	0.875115	−	0.483914i	$-0.160785\pi$
$433$	5.13122	+	6.11515i	0.246591	+	0.293875i	−0.628525	+	0.777790i	$0.716341\pi$
$434$	−0.460637	+	2.61240i	−0.0221113	+	0.125399i
$435$		0			0
$436$	8.84524			0.423610
$437$	−12.7402	−	7.11128i	−0.609447	−	0.340179i
$438$		−	1.29086i		−	0.0616796i
$439$	−26.2456	+	9.55261i	−1.25263	+	0.455921i	−0.881290	−	0.472575i	$-0.843325\pi$
$439$	−26.2456	+	9.55261i	−1.25263	+	0.455921i	−0.371342	+	0.928496i	$0.621102\pi$
$440$		0			0
$441$	−17.1800	+	14.4158i	−0.818097	+	0.686465i
$442$	0.866025	−	1.03209i	0.0411926	−	0.0490915i
$443$	−7.54671	+	1.33069i	−0.358555	+	0.0632229i	−0.350024	−	0.936741i	$-0.613827\pi$
$443$	−7.54671	+	1.33069i	−0.358555	+	0.0632229i	−0.00853096	+	0.999964i	$0.502716\pi$
$444$	9.67024	+	16.7494i	0.458929	+	0.794889i
$445$		0			0
$446$	−10.7562	−	3.91495i	−0.509323	−	0.185378i
$447$	−2.96113	+	8.13563i	−0.140057	+	0.384802i
$448$	0.565258	+	0.326352i	0.0267059	+	0.0154187i
$449$	10.4807	+	18.1531i	0.494615	+	0.856698i	0.999981	−	0.00620692i	$-0.00197574\pi$
$449$	10.4807	+	18.1531i	0.494615	+	0.856698i	−0.505366	+	0.862905i	$0.668642\pi$
$450$		0			0
$451$	3.76991	+	3.16333i	0.177518	+	0.148956i
$452$	−0.957882	−	1.14156i	−0.0450550	−	0.0536944i
$453$	−38.7993	−	6.84137i	−1.82295	−	0.321435i
$454$	13.4611	−	4.89944i	0.631761	−	0.229942i
$455$		0			0
$456$	10.4251	+	3.62414i	0.488202	+	0.169716i
$457$		−	26.6563i		−	1.24693i	−0.781851	−	0.623465i	$-0.785724\pi$
$457$		−	26.6563i		−	1.24693i	0.781851	−	0.623465i	$-0.214276\pi$
$458$	2.08169	+	5.71941i	0.0972712	+	0.267250i
$459$	0.0846555	−	0.480105i	0.00395138	−	0.0224094i
$460$		0			0
$461$	−4.47178	−	3.75227i	−0.208272	−	0.174761i	0.532685	−	0.846314i	$-0.321183\pi$
$461$	−4.47178	−	3.75227i	−0.208272	−	0.174761i	−0.740957	+	0.671553i	$0.765628\pi$
$462$	−1.62760	+	0.286989i	−0.0757226	+	0.0133519i
$463$	−24.0079	+	13.8610i	−1.11574	+	0.644174i	−0.940310	−	0.340318i	$-0.889465\pi$
$463$	−24.0079	+	13.8610i	−1.11574	+	0.644174i	−0.175431	+	0.984492i	$0.556132\pi$
$464$	3.41147	−	5.90885i	0.158374	−	0.274311i
$465$		0			0
$466$	10.3833	+	3.77920i	0.480995	+	0.175068i
$467$	−17.3746	−	10.0312i	−0.803999	−	0.464189i	0.0408685	−	0.999165i	$-0.486988\pi$
$467$	−17.3746	−	10.0312i	−0.803999	−	0.464189i	−0.844868	+	0.534975i	$0.820321\pi$
$468$	8.50692	−	4.91147i	0.393233	−	0.227033i
$469$	−0.0996702	−	0.565258i	−0.00460234	−	0.0261012i
$470$		0			0
$471$	25.7670	−	21.6211i	1.18728	−	0.996246i
$472$	5.95772	+	1.05051i	0.274226	+	0.0483535i
$473$	1.07494	+	2.95336i	0.0494256	+	0.135796i
$474$	−22.0719			−1.01380
$475$		0			0
$476$	−0.305407			−0.0139983
$477$	4.50946	+	12.3897i	0.206474	+	0.567283i
$478$	−7.92734	−	1.39780i	−0.362588	−	0.0639340i
$479$	14.9199	−	12.5193i	0.681709	−	0.572022i	−0.234796	−	0.972045i	$-0.575442\pi$
$479$	14.9199	−	12.5193i	0.681709	−	0.572022i	0.916505	+	0.400023i	$0.130998\pi$
$480$		0			0
$481$	−3.81908	−	21.6591i	−0.174135	−	0.987568i
$482$	−23.9397	+	13.8216i	−1.09042	+	0.629557i
$483$	4.79093	+	2.76604i	0.217995	+	0.125859i
$484$	−9.39693	−	3.42020i	−0.427133	−	0.155464i
$485$		0			0
$486$	−11.1800	+	19.3644i	−0.507137	+	0.878387i
$487$	−26.6742	+	15.4003i	−1.20872	+	0.697856i	−0.962480	−	0.271353i	$-0.912529\pi$
$487$	−26.6742	+	15.4003i	−1.20872	+	0.697856i	−0.246241	+	0.969209i	$0.579196\pi$
$488$	5.09170	−	0.897804i	0.230490	−	0.0406417i
$489$	10.2246	+	8.57948i	0.462373	+	0.387977i
$490$		0			0
$491$	1.82383	−	10.3434i	0.0823081	−	0.466792i	−0.915597	−	0.402097i	$-0.868281\pi$
$491$	1.82383	−	10.3434i	0.0823081	−	0.466792i	0.997905	−	0.0646952i	$-0.0206075\pi$
$492$	4.26195	+	11.7096i	0.192143	+	0.527910i
$493$			3.19253i			0.143784i
$494$	−9.73055	−	7.92734i	−0.437798	−	0.356668i
$495$		0			0
$496$	3.81908	−	1.39003i	0.171482	−	0.0624142i
$497$	7.84981	+	1.38413i	0.352112	+	0.0620868i
$498$	−29.1493	−	34.7388i	−1.30621	−	1.55668i
$499$	−6.10085	−	5.11922i	−0.273112	−	0.229168i	0.495936	−	0.868359i	$-0.334825\pi$
$499$	−6.10085	−	5.11922i	−0.273112	−	0.229168i	−0.769048	+	0.639191i	$0.779269\pi$
$500$		0			0
$501$	2.75743	+	4.77600i	0.123193	+	0.213376i
$502$	−19.0660	−	11.0077i	−0.850956	−	0.491300i
$503$	4.07001	−	11.1823i	0.181473	−	0.498593i	−0.815284	−	0.579061i	$-0.803419\pi$
$503$	4.07001	−	11.1823i	0.181473	−	0.498593i	0.996757	+	0.0804683i	$0.0256416\pi$
$504$	−2.09240	−	0.761570i	−0.0932027	−	0.0339230i
$505$		0			0
$506$	−1.67365	−	2.89884i	−0.0744027	−	0.128869i
$507$	11.7428	−	2.07057i	0.521517	−	0.0919574i
$508$	−11.7858	+	14.0458i	−0.522910	+	0.623180i
$509$	9.73442	−	8.16815i	0.431471	−	0.362047i	−0.401036	−	0.916062i	$-0.631350\pi$
$509$	9.73442	−	8.16815i	0.431471	−	0.362047i	0.832506	+	0.554016i	$0.186905\pi$
$510$		0			0
$511$	0.312681	−	0.113807i	0.0138322	−	0.00503451i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.48346	−	0.723689i	−0.197950	−	0.0319516i
$514$	14.3182			0.631549
$515$		0			0
$516$	−1.38191	+	7.83721i	−0.0608353	+	0.345014i
$517$	4.12122	+	4.91147i	0.181251	+	0.216006i
$518$	−3.20459	+	3.81908i	−0.140801	+	0.167801i
$519$	3.27497	+	18.5733i	0.143755	+	0.815276i
$520$		0			0
$521$	12.6138	−	21.8478i	0.552621	−	0.957168i	−0.445463	−	0.895300i	$-0.646961\pi$
$521$	12.6138	−	21.8478i	0.552621	−	0.957168i	0.998084	−	0.0618674i	$-0.0197056\pi$
$522$	−7.96097	+	21.8726i	−0.348442	+	0.957337i
$523$	−15.0832	+	41.4406i	−0.659540	+	1.81207i	−0.0805294	+	0.996752i	$0.525661\pi$
$523$	−15.0832	+	41.4406i	−0.659540	+	1.81207i	−0.579011	+	0.815320i	$0.696561\pi$
$524$	3.57785	−	6.19702i	0.156299	−	0.270718i
$525$		0			0
$526$	0.828411	+	4.69815i	0.0361204	+	0.204849i
$527$	−1.22237	+	1.45677i	−0.0532474	+	0.0634578i
$528$	1.62760	+	1.93969i	0.0708320	+	0.0844143i
$529$	2.04829	−	11.6164i	0.0890559	−	0.505061i
$530$		0			0
$531$	−20.6382			−0.895620
$532$	0.0412527	+	2.84477i	0.00178853	+	0.123336i
$533$		−	14.1702i		−	0.613781i
$534$	41.9864	−	15.2818i	1.81693	−	0.661308i
$535$		0			0
$536$	−0.673648	+	0.565258i	−0.0290972	+	0.0244154i
$537$	−10.3391	+	12.3216i	−0.446163	+	0.531716i
$538$	−2.17853	+	0.384133i	−0.0939229	+	0.0165611i
$539$	3.28699	+	5.69323i	0.141581	+	0.245225i
$540$		0			0
$541$	31.7759	+	11.5655i	1.36615	+	0.497239i	0.917951	−	0.396694i	$-0.129842\pi$
$541$	31.7759	+	11.5655i	1.36615	+	0.497239i	0.448202	+	0.893933i	$0.352065\pi$
$542$	−7.31850	+	20.1074i	−0.314356	+	0.863687i
$543$	29.2746	+	16.9017i	1.25629	+	0.725320i
$544$	0.233956	+	0.405223i	0.0100308	+	0.0173738i
$545$		0			0
$546$	3.64543	+	3.05888i	0.156010	+	0.130908i
$547$	16.7239	+	19.9308i	0.715064	+	0.852181i	0.994141	−	0.108088i	$-0.0344729\pi$
$547$	16.7239	+	19.9308i	0.715064	+	0.852181i	−0.279077	+	0.960269i	$0.590028\pi$
$548$	−16.6938	−	2.94356i	−0.713123	−	0.125743i
$549$	−16.5744	+	6.03260i	−0.707380	+	0.257465i
$550$		0			0
$551$	29.7374	−	0.431229i	1.26686	−	0.0183710i
$552$		−	8.47565i		−	0.360748i
$553$	−1.94594	−	5.34642i	−0.0827497	−	0.227353i
$554$	1.34477	−	7.62657i	0.0571338	−	0.324022i
$555$		0			0
$556$	9.71941	+	8.15555i	0.412195	+	0.345872i
$557$	18.8697	−	3.32723i	0.799533	−	0.140979i	0.241069	−	0.970508i	$-0.422502\pi$
$557$	18.8697	−	3.32723i	0.799533	−	0.140979i	0.558464	+	0.829529i	$0.311391\pi$
$558$	−12.0073	+	6.93242i	−0.508310	+	0.293473i
$559$	4.52481	−	7.83721i	0.191379	−	0.331479i
$560$		0			0
$561$	−1.11334	−	0.405223i	−0.0470053	−	0.0171085i
$562$	−12.2059	−	7.04710i	−0.514877	−	0.297264i
$563$	−6.87262	+	3.96791i	−0.289647	+	0.167228i	−0.637782	−	0.770217i	$-0.720148\pi$
$563$	−6.87262	+	3.96791i	−0.289647	+	0.167228i	0.348136	+	0.937444i	$0.386815\pi$
$564$	2.81908	+	15.9878i	0.118705	+	0.673207i
$565$		0			0
$566$	3.98680	−	3.34532i	0.167578	−	0.140614i
$567$	−4.88279	−	0.860967i	−0.205058	−	0.0361572i
$568$	−4.17680	−	11.4757i	−0.175254	−	0.481508i
$569$	−9.12929			−0.382720			−0.191360	−	0.981520i	$-0.561290\pi$
$569$	−9.12929			−0.382720			−0.191360	+	0.981520i	$0.561290\pi$
$570$		0			0
$571$	−21.4587			−0.898020			−0.449010	−	0.893527i	$-0.648223\pi$
$571$	−21.4587			−0.898020			−0.449010	+	0.893527i	$0.648223\pi$
$572$	−0.984808	−	2.70574i	−0.0411769	−	0.113133i
$573$	−22.8797	−	4.03431i	−0.955814	−	0.168536i
$574$	−2.46064	+	2.06472i	−0.102705	+	0.0861797i
$575$		0			0
$576$	0.592396	+	3.35965i	0.0246832	+	0.139985i
$577$	−29.7382	+	17.1694i	−1.23802	+	0.714770i	−0.968689	−	0.248278i	$-0.920135\pi$
$577$	−29.7382	+	17.1694i	−1.23802	+	0.714770i	−0.269329	+	0.963048i	$0.586802\pi$
$578$	14.5328	+	8.39053i	0.604486	+	0.349000i
$579$	36.1771	+	13.1674i	1.50347	+	0.547218i
$580$		0			0
$581$	5.84477	−	10.1234i	0.242482	−	0.419991i
$582$	31.8029	−	18.3614i	1.31827	−	0.761106i
$583$	3.80612	−	0.671122i	0.157633	−	0.0277950i
$584$	−0.390530	−	0.327693i	−0.0161602	−	0.0135600i
$585$		0			0
$586$	−4.63088	+	26.2630i	−0.191300	+	1.08492i
$587$	−7.73195	−	21.2433i	−0.319132	−	0.876807i	−0.990724	−	0.135886i	$-0.956612\pi$
$587$	−7.73195	−	21.2433i	−0.319132	−	0.876807i	0.671593	−	0.740920i	$-0.265610\pi$
$588$			16.6459i			0.686465i
$589$	13.7344	+	11.1892i	0.565917	+	0.461044i
$590$		0			0
$591$	−42.7293	+	15.5522i	−1.75765	+	0.639731i
$592$	7.52211	+	1.32635i	0.309157	+	0.0545127i
$593$	20.7440	+	24.7217i	0.851852	+	1.01520i	0.999657	+	0.0261814i	$0.00833476\pi$
$593$	20.7440	+	24.7217i	0.851852	+	1.01520i	−0.147805	+	0.989017i	$0.547221\pi$
$594$	−0.798133	−	0.669713i	−0.0327478	−	0.0274787i
$595$		0			0
$596$	1.70961	+	2.96113i	0.0700283	+	0.121292i
$597$	54.3093	+	31.3555i	2.22273	+	1.28330i
$598$	−3.29644	+	9.05690i	−0.134802	+	0.370364i
$599$	−5.03849	−	1.83386i	−0.205867	−	0.0749294i	0.237029	−	0.971503i	$-0.423827\pi$
$599$	−5.03849	−	1.83386i	−0.205867	−	0.0749294i	−0.442895	+	0.896573i	$0.646049\pi$
$600$		0			0
$601$	−17.8319	−	30.8857i	−0.727377	−	1.25985i	−0.957988	−	0.286808i	$-0.907406\pi$
$601$	−17.8319	−	30.8857i	−0.727377	−	1.25985i	0.230611	−	0.973046i	$-0.425928\pi$
$602$	−2.02022	+	0.356219i	−0.0823380	+	0.0145184i
$603$	1.92836	−	2.29813i	0.0785290	−	0.0935872i
$604$	−11.9192	+	10.0014i	−0.484986	+	0.406952i
$605$		0			0
$606$	−35.5685	+	12.9459i	−1.44487	+	0.525890i
$607$		−	6.93077i		−	0.281311i	−0.990059	−	0.140656i	$-0.955079\pi$
$607$		−	6.93077i		−	0.281311i	0.990059	−	0.140656i	$-0.0449210\pi$
$608$	3.74292	−	2.23396i	0.151795	−	0.0905989i
$609$	−11.2763			−0.456939
$610$		0			0
$611$	3.20574	−	18.1806i	0.129690	−	0.735510i
$612$	−1.02606	−	1.22281i	−0.0414760	−	0.0494292i
$613$	13.2291	−	15.7658i	0.534317	−	0.636775i	−0.429586	−	0.903026i	$-0.641341\pi$
$613$	13.2291	−	15.7658i	0.534317	−	0.636775i	0.963904	+	0.266251i	$0.0857851\pi$
$614$	−5.90925	−	33.5130i	−0.238478	−	1.35248i
$615$		0			0
$616$	−0.326352	+	0.565258i	−0.0131491	+	0.0227749i
$617$	9.13478	−	25.0976i	0.367753	−	1.01039i	−0.608462	−	0.793583i	$-0.708213\pi$
$617$	9.13478	−	25.0976i	0.367753	−	1.01039i	0.976214	−	0.216808i	$-0.0695647\pi$
$618$	6.25849	−	17.1951i	0.251753	−	0.691687i
$619$	−2.15405	+	3.73092i	−0.0865785	+	0.149958i	−0.906063	−	0.423143i	$-0.860927\pi$
$619$	−2.15405	+	3.73092i	−0.0865785	+	0.149958i	0.819484	+	0.573102i	$0.194260\pi$
$620$		0			0
$621$	0.605600	+	3.43453i	0.0243019	+	0.137823i
$622$	−12.2431	+	14.5908i	−0.490905	+	0.585038i
$623$	7.40333	+	8.82295i	0.296608	+	0.353484i
$624$	1.26604	−	7.18009i	0.0506823	−	0.287434i
$625$		0			0
$626$	−3.58853			−0.143426
$627$	−3.62414	+	10.4251i	−0.144734	+	0.416340i
$628$		−	13.2841i		−	0.530091i
$629$	−3.35844	+	1.22237i	−0.133910	+	0.0487392i
$630$		0			0
$631$	−10.5988	+	8.89344i	−0.421931	+	0.354042i	−0.828897	−	0.559401i	$-0.811031\pi$
$631$	−10.5988	+	8.89344i	−0.421931	+	0.354042i	0.406966	+	0.913443i	$0.366587\pi$
$632$	−5.60310	+	6.67752i	−0.222879	+	0.265617i
$633$	26.6750	−	4.70352i	1.06023	−	0.186948i
$634$	14.1040	+	24.4289i	0.560142	+	0.970194i
$635$		0			0
$636$	9.19594	+	3.34705i	0.364643	+	0.132719i
$637$	6.47410	−	17.7875i	0.256513	−	0.704765i
$638$	5.90885	+	3.41147i	0.233933	+	0.135062i
$639$	20.8307	+	36.0798i	0.824049	+	1.42730i
$640$		0			0
$641$	2.43969	+	2.04715i	0.0963621	+	0.0808574i	0.689696	−	0.724099i	$-0.257744\pi$
$641$	2.43969	+	2.04715i	0.0963621	+	0.0808574i	−0.593334	+	0.804956i	$0.702189\pi$
$642$	−11.8303	−	14.0988i	−0.466904	−	0.556435i
$643$	11.8715	+	2.09327i	0.468168	+	0.0825507i	0.402755	−	0.915308i	$-0.368053\pi$
$643$	11.8715	+	2.09327i	0.468168	+	0.0825507i	0.0654126	+	0.997858i	$0.479164\pi$
$644$	2.05303	−	0.747243i	0.0809009	−	0.0294455i
$645$		0			0
$646$	−0.994070	+	1.78093i	−0.0391112	+	0.0700696i
$647$		−	25.3105i		−	0.995057i	−0.867448	−	0.497528i	$-0.834241\pi$
$647$		−	25.3105i		−	0.995057i	0.867448	−	0.497528i	$-0.165759\pi$
$648$	2.59808	+	7.13816i	0.102062	+	0.280413i
$649$	−1.05051	+	5.95772i	−0.0412360	+	0.233861i
$650$		0			0
$651$	−5.14543	−	4.31753i	−0.201665	−	0.169217i
$652$	5.19118	−	0.915345i	0.203302	−	0.0358477i
$653$	1.24400	−	0.718226i	0.0486816	−	0.0281063i	−0.475462	−	0.879736i	$-0.657719\pi$
$653$	1.24400	−	0.718226i	0.0486816	−	0.0281063i	0.524143	+	0.851630i	$0.324386\pi$
$654$	−11.1985	+	19.3963i	−0.437895	+	0.758456i
$655$		0			0
$656$	4.62449	+	1.68317i	0.180556	+	0.0657169i
$657$	1.50617	+	0.869585i	0.0587611	+	0.0339257i
$658$	−3.62414	+	2.09240i	−0.141284	+	0.0815701i
$659$	0.0736733	+	0.417822i	0.00286990	+	0.0162760i	0.986209	−	0.165504i	$-0.0529252\pi$
$659$	0.0736733	+	0.417822i	0.00286990	+	0.0162760i	−0.983339	+	0.181780i	$0.941814\pi$
$660$		0			0
$661$	−8.34074	+	6.99871i	−0.324417	+	0.272218i	−0.790420	−	0.612565i	$-0.790138\pi$
$661$	−8.34074	+	6.99871i	−0.324417	+	0.272218i	0.466003	+	0.884783i	$0.345693\pi$
$662$	−8.11695	−	1.43124i	−0.315474	−	0.0556266i
$663$	1.16679	+	3.20574i	0.0453145	+	0.124501i
$664$	−17.9094			−0.695020
$665$		0			0
$666$	−26.0574			−1.00970
$667$	−7.81120	−	21.4611i	−0.302451	−	0.830977i
$668$	2.14490	+	0.378203i	0.0829886	+	0.0146331i
$669$	22.2028	−	18.6304i	0.858410	−	0.720291i
$670$		0			0
$671$	0.897804	+	5.09170i	0.0346593	+	0.196563i
$672$	−1.43128	+	0.826352i	−0.0552130	+	0.0318772i
$673$	30.6274	+	17.6827i	1.18060	+	0.681619i	0.956153	−	0.292867i	$-0.0946094\pi$
$673$	30.6274	+	17.6827i	1.18060	+	0.681619i	0.224446	+	0.974487i	$0.427943\pi$
$674$	3.86959	+	1.40841i	0.149051	+	0.0542501i
$675$		0			0
$676$	2.35457	−	4.07824i	0.0905604	−	0.156855i
$677$	27.6706	−	15.9757i	1.06347	−	0.613994i	0.137079	−	0.990560i	$-0.456228\pi$
$677$	27.6706	−	15.9757i	1.06347	−	0.613994i	0.926390	+	0.376566i	$0.122895\pi$
$678$	3.71599	−	0.655230i	0.142712	−	0.0251640i
$679$	7.25150	+	6.08473i	0.278287	+	0.233510i
$680$		0			0
$681$	−6.29860	+	35.7211i	−0.241363	+	1.36884i
$682$	1.39003	+	3.81908i	0.0532270	+	0.146240i
$683$			30.2327i			1.15682i	0.815746	+	0.578410i	$0.196327\pi$
$683$			30.2327i			1.15682i	−0.815746	+	0.578410i	$0.803673\pi$
$684$	−11.2515	+	9.72259i	−0.430212	+	0.371753i
$685$		0			0
$686$	−8.32547	+	3.03022i	−0.317868	+	0.115695i
$687$	−15.1773	−	2.67617i	−0.579052	−	0.102102i
$688$	2.02022	+	2.40760i	0.0770201	+	0.0917890i
$689$	−8.52481	−	7.15317i	−0.324770	−	0.272514i
$690$		0			0
$691$	20.5829	+	35.6506i	0.783010	+	1.35621i	0.930180	+	0.367103i	$0.119650\pi$
$691$	20.5829	+	35.6506i	0.783010	+	1.35621i	−0.147170	+	0.989111i	$0.547016\pi$
$692$	6.45043	+	3.72416i	0.245208	+	0.141571i
$693$	0.761570	−	2.09240i	0.0289297	−	0.0794836i
$694$	0.879385	+	0.320070i	0.0333810	+	0.0121497i
$695$		0			0
$696$	8.63816	+	14.9617i	0.327428	+	0.567123i
$697$	−2.26774	+	0.399863i	−0.0858966	+	0.0151459i
$698$	9.04963	−	10.7849i	0.342534	−	0.408216i
$699$	−21.4329	+	17.9843i	−0.810666	+	0.680230i
$700$		0			0
$701$	17.5373	−	6.38306i	0.662375	−	0.241085i	0.0111135	−	0.999938i	$-0.496462\pi$
$701$	17.5373	−	6.38306i	0.662375	−	0.241085i	0.651261	+	0.758854i	$0.274240\pi$
$702$			3.00000i			0.113228i
$703$	11.8396	+	31.1177i	0.446541	+	1.17363i
$704$	1.00000			0.0376889
$705$		0			0
$706$	−3.26382	+	18.5101i	−0.122836	+	0.696635i
$707$	−6.27169	−	7.47431i	−0.235871	−	0.281100i
$708$	−9.84635	+	11.7344i	−0.370048	+	0.441007i
$709$	6.62536	+	37.5743i	0.248821	+	1.41113i	0.811449	+	0.584423i	$0.198679\pi$
$709$	6.62536	+	37.5743i	0.248821	+	1.41113i	−0.562629	+	0.826710i	$0.690210\pi$
$710$		0			0
$711$	14.8687	−	25.7534i	0.557620	−	0.965826i
$712$	6.03525	−	16.5817i	0.226181	−	0.621426i
$713$	4.65284	−	12.7836i	0.174250	−	0.478749i
$714$	0.386659	−	0.669713i	0.0144704	−	0.0250634i
$715$		0			0
$716$	1.10307	+	6.25584i	0.0412238	+	0.233792i
$717$	13.1015	−	15.6138i	0.489286	−	0.583108i
$718$	18.6953	+	22.2802i	0.697702	+	0.831489i
$719$	−2.94516	+	16.7028i	−0.109836	+	0.622910i	0.879342	+	0.476190i	$0.157983\pi$
$719$	−2.94516	+	16.7028i	−0.109836	+	0.622910i	−0.989178	+	0.146720i	$0.953129\pi$
$720$		0			0
$721$	4.71688			0.175666
$722$	16.7230	+	9.01889i	0.622367	+	0.335648i
$723$		−	69.9951i		−	2.60314i
$724$	12.5449	−	4.56596i	0.466227	−	0.169693i
$725$		0			0
$726$	19.3969	−	16.2760i	0.719887	−	0.604057i
$727$	−20.0584	+	23.9047i	−0.743925	+	0.886575i	−0.996719	−	0.0809452i	$-0.974206\pi$
$727$	−20.0584	+	23.9047i	−0.743925	+	0.886575i	0.252794	+	0.967520i	$0.418651\pi$
$728$	1.85083	−	0.326352i	0.0685964	−	0.0120954i
$729$	−16.9145	−	29.2967i	−0.626462	−	1.08506i
$730$		0			0
$731$	−1.38191	−	0.502975i	−0.0511118	−	0.0186032i
$732$	−4.47756	+	12.3020i	−0.165495	+	0.454695i
$733$	−9.60197	−	5.54370i	−0.354657	−	0.204761i	0.312078	−	0.950057i	$-0.398975\pi$
$733$	−9.60197	−	5.54370i	−0.354657	−	0.204761i	−0.666734	+	0.745295i	$0.732308\pi$
$734$	−8.48932	−	14.7039i	−0.313347	−	0.542732i
$735$		0			0
$736$	−2.56418	−	2.15160i	−0.0945168	−	0.0793091i
$737$	−0.565258	−	0.673648i	−0.0208215	−	0.0248141i
$738$	−16.5337	−	2.91534i	−0.608615	−	0.107315i
$739$	−11.0842	+	4.03434i	−0.407741	+	0.148405i	−0.537744	−	0.843108i	$-0.680723\pi$
$739$	−11.0842	+	4.03434i	−0.407741	+	0.148405i	0.130004	+	0.991514i	$0.458501\pi$
$740$		0			0
$741$	29.7028	−	11.3013i	1.09116	−	0.415164i
$742$			2.52259i			0.0926073i
$743$	3.92928	+	10.7956i	0.144151	+	0.396052i	0.990666	−	0.136313i	$-0.0435254\pi$
$743$	3.92928	+	10.7956i	0.144151	+	0.396052i	−0.846514	+	0.532366i	$0.821303\pi$
$744$	−1.78699	+	10.1345i	−0.0655142	+	0.371549i
$745$		0			0
$746$	−3.16179	−	2.65306i	−0.115761	−	0.0971353i
$747$	60.1693	−	10.6095i	2.20148	−	0.388180i
$748$	−0.405223	+	0.233956i	−0.0148164	+	0.00855426i
$749$	2.37211	−	4.10862i	0.0866751	−	0.150126i
$750$		0			0
$751$	39.2717	+	14.2937i	1.43305	+	0.521586i	0.937803	−	0.347169i	$-0.112857\pi$
$751$	39.2717	+	14.2937i	1.43305	+	0.521586i	0.495243	+	0.868755i	$0.335079\pi$
$752$	5.55250	+	3.20574i	0.202479	+	0.116901i
$753$	48.2767	−	27.8726i	1.75930	−	1.01573i
$754$	−3.41147	−	19.3474i	−0.124239	−	0.704592i
$755$		0			0
$756$	0.520945	−	0.437124i	0.0189466	−	0.0158981i
$757$	−44.3392	−	7.81820i	−1.61154	−	0.284157i	−0.705932	−	0.708280i	$-0.749471\pi$
$757$	−44.3392	−	7.81820i	−1.61154	−	0.284157i	−0.905605	+	0.424123i	$0.860583\pi$
$758$	7.92469	+	21.7729i	0.287838	+	0.790828i
$759$	8.47565			0.307647
$760$		0			0
$761$	−27.3604			−0.991814			−0.495907	−	0.868376i	$-0.665164\pi$
$761$	−27.3604			−0.991814			−0.495907	+	0.868376i	$0.665164\pi$
$762$	−15.8790	−	43.6271i	−0.575234	−	1.58044i
$763$	−5.68561	−	1.00253i	−0.205833	−	0.0362939i
$764$	−7.02869	+	5.89777i	−0.254289	+	0.213374i
$765$		0			0
$766$	−5.54664	−	31.4565i	−0.200408	−	1.13657i
$767$	15.0855	−	8.70961i	0.544705	−	0.314486i
$768$	2.19285	+	1.26604i	0.0791278	+	0.0456844i
$769$	−31.2704	−	11.3815i	−1.12764	−	0.410427i	−0.290204	−	0.956965i	$-0.593723\pi$
$769$	−31.2704	−	11.3815i	−1.12764	−	0.410427i	−0.837434	+	0.546538i	$0.815945\pi$
$770$		0			0
$771$	−18.1275	+	31.3977i	−0.652845	+	1.13076i
$772$	13.1674	−	7.60220i	0.473905	−	0.273609i
$773$	−27.9485	+	4.92808i	−1.00524	+	0.177251i	−0.651949	−	0.758263i	$-0.726048\pi$
$773$	−27.9485	+	4.92808i	−1.00524	+	0.177251i	−0.353290	+	0.935514i	$0.614937\pi$
$774$	−8.21348	−	6.89193i	−0.295227	−	0.247725i
$775$		0			0
$776$	2.51842	−	14.2827i	0.0904059	−	0.512718i
$777$	−4.31753	−	11.8623i	−0.154890	−	0.425558i
$778$		−	27.5321i		−	0.987073i
$779$	4.03091	+	21.0692i	0.144422	+	0.754883i
$780$		0			0
$781$	11.4757	−	4.17680i	0.410631	−	0.149458i
$782$	1.54244	+	0.271974i	0.0551576	+	0.00972578i
$783$	−4.56942	−	5.44562i	−0.163298	−	0.194611i
$784$	5.03596	+	4.22567i	0.179856	+	0.150917i
$785$		0			0
$786$	9.05943	+	15.6914i	0.323139	+	0.559693i
$787$	19.5422	+	11.2827i	0.696605	+	0.402185i	0.806082	−	0.591804i	$-0.201584\pi$
$787$	19.5422	+	11.2827i	0.696605	+	0.402185i	−0.109477	+	0.993989i	$0.534917\pi$
$788$	−6.14204	+	16.8751i	−0.218801	+	0.601151i
$789$	−11.3512	−	4.13149i	−0.404112	−	0.147085i
$790$		0			0
$791$	0.486329	+	0.842347i	0.0172919	+	0.0299504i
$792$	−3.35965	+	0.592396i	−0.119380	+	0.0210499i
$793$	9.56926	−	11.4042i	0.339814	−	0.404975i
$794$	−21.0305	+	17.6467i	−0.746344	+	0.626257i
$795$		0			0
$796$	23.2729	−	8.47065i	0.824886	−	0.300234i
$797$			30.1320i			1.06733i	0.845696	+	0.533665i	$0.179186\pi$
$797$			30.1320i			1.06733i	−0.845696	+	0.533665i	$0.820814\pi$
$798$	−6.29039	−	3.51114i	−0.222677	−	0.124293i
$799$	−3.00000			−0.106132
$800$		0			0
$801$	−10.4534	+	59.2840i	−0.369351	+	2.09470i
$802$	−16.4597	−	19.6159i	−0.581211	−	0.692660i
$803$	0.327693	−	0.390530i	0.0115640	−	0.0137815i
$804$	−0.386659	−	2.19285i	−0.0136364	−	0.0773360i
$805$		0			0
$806$	5.85117	−	10.1345i	0.206099	−	0.356973i
$807$	1.91576	−	5.26352i	0.0674381	−	0.185285i
$808$	−5.11273	+	14.0471i	−0.179865	+	0.494175i
$809$	−6.59714	+	11.4266i	−0.231943	+	0.401737i	−0.958380	−	0.285496i	$-0.907842\pi$
$809$	−6.59714	+	11.4266i	−0.231943	+	0.401737i	0.726437	+	0.687233i	$0.241175\pi$
$810$		0			0
$811$	−5.92144	−	33.5821i	−0.207930	−	1.17923i	−0.892762	−	0.450528i	$-0.851236\pi$
$811$	−5.92144	−	33.5821i	−0.207930	−	1.17923i	0.684833	−	0.728700i	$-0.259875\pi$
$812$	−2.86257	+	3.41147i	−0.100456	+	0.119719i
$813$	−34.8271	−	41.5053i	−1.22144	−	1.45565i
$814$	−1.32635	+	7.52211i	−0.0464886	+	0.263650i
$815$		0			0
$816$	−1.18479			−0.0414760
$817$	−4.49839	+	12.9400i	−0.157379	+	0.452713i
$818$		−	17.5243i		−	0.612724i
$819$	−6.02481	+	2.19285i	−0.210524	+	0.0766245i
$820$		0			0
$821$	4.27173	−	3.58440i	0.149084	−	0.125097i	−0.565195	−	0.824957i	$-0.691199\pi$
$821$	4.27173	−	3.58440i	0.149084	−	0.125097i	0.714279	+	0.699861i	$0.246755\pi$
$822$	27.5899	−	32.8803i	0.962307	−	1.14683i
$823$	−7.01244	+	1.23648i	−0.244438	+	0.0431010i	−0.294525	−	0.955644i	$-0.595161\pi$
$823$	−7.01244	+	1.23648i	−0.244438	+	0.0431010i	0.0500866	+	0.998745i	$0.484050\pi$
$824$	−3.61334	−	6.25849i	−0.125877	−	0.218025i
$825$		0			0
$826$	−3.71048	−	1.35051i	−0.129104	−	0.0469901i
$827$	−0.873538	+	2.40003i	−0.0303759	+	0.0834570i	−0.953954	−	0.299954i	$-0.903029\pi$
$827$	−0.873538	+	2.40003i	−0.0303759	+	0.0834570i	0.923578	+	0.383411i	$0.125251\pi$
$828$	9.88933	+	5.70961i	0.343678	+	0.198423i
$829$	−16.1022	−	27.8898i	−0.559252	−	0.968654i	−0.997559	−	0.0698281i	$-0.977755\pi$
$829$	−16.1022	−	27.8898i	−0.559252	−	0.968654i	0.438307	−	0.898826i	$-0.355578\pi$
$830$		0			0
$831$	15.0214	+	12.6045i	0.521087	+	0.437244i
$832$	−1.85083	−	2.20574i	−0.0641661	−	0.0764702i
$833$	−3.02931	−	0.534148i	−0.104959	−	0.0185071i
$834$	−30.1891	+	10.9879i	−1.04536	+	0.380481i
$835$		0			0
$836$	2.23396	+	3.74292i	0.0772630	+	0.129452i
$837$		−	4.23442i		−	0.146363i
$838$	11.2448	+	30.8949i	0.388446	+	1.06725i
$839$	7.29039	−	41.3459i	0.251692	−	1.42742i	−0.552730	−	0.833360i	$-0.686414\pi$
$839$	7.29039	−	41.3459i	0.251692	−	1.42742i	0.804422	−	0.594058i	$-0.202475\pi$
$840$		0			0
$841$	13.4461	+	11.2826i	0.463658	+	0.389055i
$842$	−5.28039	+	0.931074i	−0.181974	+	0.0320869i
$843$	30.9065	−	17.8439i	1.06448	−	0.614576i
$844$	5.34864	−	9.26412i	0.184108	−	0.318884i
$845$		0			0
$846$	−20.5535	−	7.48086i	−0.706644	−	0.257197i
$847$	5.65258	+	3.26352i	0.194225	+	0.112136i
$848$	3.34705	−	1.93242i	0.114938	−	0.0663595i
$849$	2.28833	+	12.9778i	0.0785354	+	0.445396i
$850$		0			0
$851$	19.5856	−	16.4343i	0.671385	−	0.563359i
$852$	30.4524	+	5.36959i	1.04328	+	0.183959i
$853$	−12.5296	−	34.4247i	−0.429005	−	1.17868i	−0.946418	−	0.322945i	$-0.895327\pi$
$853$	−12.5296	−	34.4247i	−0.429005	−	1.17868i	0.517413	−	0.855736i	$-0.326895\pi$
$854$	−3.37464			−0.115478
$855$		0			0
$856$	−7.26857			−0.248435
$857$	−13.9170	−	38.2365i	−0.475394	−	1.30614i	−0.913363	−	0.407145i	$-0.866524\pi$
$857$	−13.9170	−	38.2365i	−0.475394	−	1.30614i	0.437969	−	0.898990i	$-0.355698\pi$
$858$	7.18009	+	1.26604i	0.245124	+	0.0432220i
$859$	10.0018	−	8.39252i	0.341257	−	0.286349i	−0.456011	−	0.889974i	$-0.650722\pi$
$859$	10.0018	−	8.39252i	0.341257	−	0.286349i	0.797268	+	0.603625i	$0.206278\pi$
$860$		0			0
$861$	−1.41235	−	8.00984i	−0.0481328	−	0.272975i
$862$	18.9793	−	10.9577i	0.646437	−	0.373221i
$863$	−39.3728	−	22.7319i	−1.34027	−	0.773803i	−0.353420	−	0.935465i	$-0.614981\pi$
$863$	−39.3728	−	22.7319i	−1.34027	−	0.773803i	−0.986846	+	0.161662i	$0.948315\pi$
$864$	−0.979055	−	0.356347i	−0.0333081	−	0.0121232i
$865$		0			0
$866$	−3.99138	+	6.91328i	−0.135633	+	0.234923i
$867$	−36.7984	+	21.2456i	−1.24974	+	0.721537i
$868$	−2.61240	+	0.460637i	−0.0886707	+	0.0156350i
$869$	−6.67752	−	5.60310i	−0.226519	−	0.190072i
$870$		0			0
$871$	−0.439693	+	2.49362i	−0.0148984	+	0.0844931i
$872$	3.02525	+	8.31180i	0.102448	+	0.281473i
$873$			49.4766i			1.67453i
$874$	2.32501	−	14.4041i	0.0786446	−	0.487226i
$875$		0			0
$876$	1.21301	−	0.441500i	0.0409838	−	0.0149169i
$877$	52.7090	+	9.29401i	1.77986	+	0.313837i	0.964294	−	0.264834i	$-0.0853171\pi$
$877$	52.7090	+	9.29401i	1.77986	+	0.313837i	0.815562	+	0.578670i	$0.196428\pi$
$878$	−17.9530	−	21.3956i	−0.605885	−	0.722066i
$879$	−51.7281	−	43.4050i	−1.74474	−	1.46401i
$880$		0			0
$881$	−4.08781	−	7.08030i	−0.137722	−	0.238541i	0.788912	−	0.614506i	$-0.210645\pi$
$881$	−4.08781	−	7.08030i	−0.137722	−	0.238541i	−0.926634	+	0.375965i	$0.877311\pi$
$882$	−19.4223	−	11.2135i	−0.653983	−	0.377577i
$883$	10.5796	−	29.0672i	0.356031	−	0.978188i	−0.624362	−	0.781136i	$-0.714641\pi$
$883$	10.5796	−	29.0672i	0.356031	−	0.978188i	0.980393	−	0.197053i	$-0.0631370\pi$
$884$	1.26604	+	0.460802i	0.0425817	+	0.0154985i
$885$		0			0
$886$	−3.83157	−	6.63647i	−0.128724	−	0.222956i
$887$	−10.2986	+	1.81592i	−0.345793	+	0.0609727i	−0.343848	−	0.939025i	$-0.611730\pi$
$887$	−10.2986	+	1.81592i	−0.345793	+	0.0609727i	−0.00194565	+	0.999998i	$0.500619\pi$
$888$	−12.4318	+	14.8157i	−0.417185	+	0.497181i
$889$	9.16772	−	7.69263i	0.307475	−	0.258002i
$890$		0			0
$891$	−7.13816	+	2.59808i	−0.239137	+	0.0870388i
$892$		−	11.4466i		−	0.383259i
$893$	0.405223	+	27.9440i	0.0135603	+	0.935111i
$894$	−8.65776			−0.289559
$895$		0			0
$896$	−0.113341	+	0.642788i	−0.00378645	+	0.0214740i
$897$	−15.6870	−	18.6951i	−0.523774	−	0.624210i
$898$	−13.4737	+	16.0574i	−0.449624	+	0.535841i
$899$	4.81521	+	27.3084i	0.160596	+	0.910786i
$900$		0			0
$901$	−0.904200	+	1.56612i	−0.0301233	+	0.0521750i
$902$	−1.68317	+	4.62449i	−0.0560436	+	0.153979i
$903$	1.77655	−	4.88103i	0.0591199	−	0.162431i
$904$	0.745100	−	1.29055i	0.0247817	−	0.0429231i
$905$		0			0
$906$	−6.84137	−	38.7993i	−0.227289	−	1.28902i
$907$	−15.7602	+	18.7822i	−0.523308	+	0.623654i	−0.961360	−	0.275296i	$-0.911224\pi$
$907$	−15.7602	+	18.7822i	−0.523308	+	0.623654i	0.438052	+	0.898950i	$0.355669\pi$
$908$	9.20794	+	10.9736i	0.305576	+	0.364171i
$909$	8.85550	−	50.2221i	0.293719	−	1.66576i
$910$		0			0
$911$	44.2927			1.46748			0.733742	−	0.679428i	$-0.237772\pi$
$911$	44.2927			1.46748			0.733742	+	0.679428i	$0.237772\pi$
$912$	0.160035	+	11.0360i	0.00529929	+	0.365437i
$913$		−	17.9094i		−	0.592715i
$914$	25.0488	−	9.11700i	0.828539	−	0.301564i
$915$		0			0
$916$	−4.66250	+	3.91231i	−0.154053	+	0.129266i
$917$	−3.00217	+	3.57785i	−0.0991404	+	0.118151i
$918$	0.480105	−	0.0846555i	0.0158458	−	0.00279405i
$919$	−24.4636	−	42.3723i	−0.806981	−	1.39773i	−0.914946	−	0.403577i	$-0.867767\pi$
$919$	−24.4636	−	42.3723i	−0.806981	−	1.39773i	0.107965	−	0.994155i	$-0.465567\pi$
$920$		0			0
$921$	80.9705	+	29.4709i	2.66807	+	0.971098i
$922$	1.99654	−	5.48545i	0.0657526	−	0.180654i
$923$	−30.4524	−	17.5817i	−1.00235	−	0.578709i
$924$	−0.826352	−	1.43128i	−0.0271850	−	0.0470858i
$925$		0			0
$926$	−21.2362	−	17.8193i	−0.697866	−	0.585579i
$927$	15.8471	+	18.8858i	0.520485	+	0.620290i
$928$	6.71929	+	1.18479i	0.220572	+	0.0388927i
$929$	29.5685	−	10.7621i	0.970112	−	0.353092i	0.192123	−	0.981371i	$-0.438463\pi$
$929$	29.5685	−	10.7621i	0.970112	−	0.353092i	0.777988	+	0.628279i	$0.216240\pi$
$930$		0			0
$931$	−4.56624	+	28.2892i	−0.149652	+	0.927139i
$932$			11.0496i			0.361943i
$933$	−16.4951	−	45.3200i	−0.540026	−	1.48371i
$934$	3.48380	−	19.7576i	0.113994	−	0.646489i
$935$		0			0
$936$	7.52481	+	6.31407i	0.245956	+	0.206382i
$937$	6.56504	−	1.15759i	0.214471	−	0.0378169i	−0.0653804	−	0.997860i	$-0.520826\pi$
$937$	6.56504	−	1.15759i	0.214471	−	0.0378169i	0.279851	+	0.960043i	$0.409715\pi$
$938$	0.497079	−	0.286989i	0.0162302	−	0.00937052i
$939$	4.54323	−	7.86911i	0.148263	−	0.256799i
$940$		0			0
$941$	−19.0415	−	6.93053i	−0.620734	−	0.225929i	0.0124591	−	0.999922i	$-0.496034\pi$
$941$	−19.0415	−	6.93053i	−0.620734	−	0.225929i	−0.633194	+	0.773994i	$0.718256\pi$
$942$	29.1300	+	16.8182i	0.949106	+	0.547967i
$943$	14.2660	−	8.23648i	0.464565	−	0.268217i
$944$	1.05051	+	5.95772i	0.0341911	+	0.193907i
$945$		0			0
$946$	−2.40760	+	2.02022i	−0.0782779	+	0.0656830i
$947$	−5.45475	−	0.961819i	−0.177255	−	0.0312549i	0.0843158	−	0.996439i	$-0.473130\pi$
$947$	−5.45475	−	0.961819i	−0.177255	−	0.0312549i	−0.261571	+	0.965184i	$0.584241\pi$
$948$	−7.54904	−	20.7408i	−0.245181	−	0.673630i
$949$	−1.46791			−0.0476504
$950$		0			0
$951$	−71.4252			−2.31612
$952$	−0.104455	−	0.286989i	−0.00338542	−	0.00930137i
$953$	−36.1784	−	6.37922i	−1.17193	−	0.206643i	−0.446401	−	0.894833i	$-0.647295\pi$
$953$	−36.1784	−	6.37922i	−1.17193	−	0.206643i	−0.725531	+	0.688190i	$0.758406\pi$
$954$	−10.1001	+	8.47502i	−0.327004	+	0.274389i
$955$		0			0
$956$	−1.39780	−	7.92734i	−0.0452082	−	0.256388i
$957$	−14.9617	+	8.63816i	−0.483644	+	0.279232i
$958$	16.8672	+	9.73829i	0.544955	+	0.314630i
$959$	10.3969	+	3.78417i	0.335734	+	0.122197i
$960$		0			0
$961$	7.24123	−	12.5422i	0.233588	−	0.404586i
$962$	19.0467	−	10.9966i	0.614089	−	0.354544i
$963$	24.4198	−	4.30587i	0.786918	−	0.138755i
$964$	−21.1759	−	17.7687i	−0.682031	−	0.572292i
$965$		0			0
$966$	−0.960637	+	5.44804i	−0.0309080	+	0.175288i
$967$	−19.5885	−	53.8188i	−0.629922	−	1.73070i	−0.681286	−	0.732017i	$-0.738579\pi$
$967$	−19.5885	−	53.8188i	−0.629922	−	1.73070i	0.0513643	−	0.998680i	$-0.483643\pi$
$968$		−	10.0000i		−	0.321412i
$969$	−2.64677	−	4.43458i	−0.0850266	−	0.142459i
$970$		0			0
$971$	−1.88191	+	0.684960i	−0.0603934	+	0.0219814i	−0.372040	−	0.928217i	$-0.621342\pi$
$971$	−1.88191	+	0.684960i	−0.0603934	+	0.0219814i	0.311647	+	0.950198i	$0.399119\pi$
$972$	−22.0204	−	3.88279i	−0.706304	−	0.124541i
$973$	−5.32316	−	6.34389i	−0.170653	−	0.203376i
$974$	−23.5947	−	19.7983i	−0.756022	−	0.634378i
$975$		0			0
$976$	2.58512	+	4.47756i	0.0827477	+	0.143323i
$977$	23.6161	+	13.6348i	0.755545	+	0.436214i	0.827694	−	0.561180i	$-0.189652\pi$
$977$	23.6161	+	13.6348i	0.755545	+	0.436214i	−0.0721487	+	0.997394i	$0.522986\pi$
$978$	−4.56504	+	12.5424i	−0.145974	+	0.401060i
$979$	16.5817	+	6.03525i	0.529954	+	0.192887i
$980$		0			0
$981$	−15.0876	−	26.1326i	−0.481712	−	0.834349i
$982$	10.3434	−	1.82383i	0.330072	−	0.0582006i
$983$	23.8250	−	28.3935i	0.759899	−	0.905613i	−0.237942	−	0.971279i	$-0.576473\pi$
$983$	23.8250	−	28.3935i	0.759899	−	0.905613i	0.997842	+	0.0656666i	$0.0209174\pi$
$984$	−9.54576	+	8.00984i	−0.304308	+	0.255344i
$985$		0			0
$986$	−3.00000	+	1.09191i	−0.0955395	+	0.0347735i
$987$		−	10.5963i		−	0.337283i
$988$	4.12122	−	11.8550i	0.131113	−	0.377159i
$989$	10.5202			0.334524
$990$		0			0
$991$	2.61112	−	14.8084i	0.0829449	−	0.470404i	−0.914836	−	0.403825i	$-0.867680\pi$
$991$	2.61112	−	14.8084i	0.0829449	−	0.470404i	0.997781	−	0.0665790i	$-0.0212085\pi$
$992$	2.61240	+	3.11334i	0.0829439	+	0.0988487i
$993$	13.4149	−	15.9873i	0.425709	−	0.507340i
$994$	1.38413	+	7.84981i	0.0439020	+	0.248981i
$995$		0			0
$996$	22.6741	−	39.2727i	0.718457	−	1.24440i
$997$	5.27552	−	14.4944i	0.167077	−	0.459041i	−0.827693	−	0.561182i	$-0.810347\pi$
$997$	5.27552	−	14.4944i	0.167077	−	0.459041i	0.994770	+	0.102140i	$0.0325691\pi$
$998$	2.72388	−	7.48380i	0.0862230	−	0.236896i
$999$	3.97906	−	6.89193i	0.125892	−	0.218051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.d.499.2		12
5.2	odd	4		950.2.l.e.651.1	yes	6
5.3	odd	4		950.2.l.b.651.1	yes	6
5.4	even	2	inner	950.2.u.d.499.1		12
19.4	even	9	inner	950.2.u.d.99.1		12
95.4	even	18	inner	950.2.u.d.99.2		12
95.23	odd	36		950.2.l.b.251.1	✓	6
95.42	odd	36		950.2.l.e.251.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.b.251.1	✓	6	95.23	odd	36
950.2.l.b.651.1	yes	6	5.3	odd	4
950.2.l.e.251.1	yes	6	95.42	odd	36
950.2.l.e.651.1	yes	6	5.2	odd	4
950.2.u.d.99.1		12	19.4	even	9	inner
950.2.u.d.99.2		12	95.4	even	18	inner
950.2.u.d.499.1		12	5.4	even	2	inner
950.2.u.d.499.2		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 + 0.939693i) q^{2} +(-2.49362 - 0.439693i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.439693 - 2.49362i) q^{6} +(0.565258 - 0.326352i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(3.20574 + 1.16679i) q^{9} +O(q^{10})\)	\(q+(0.342020 + 0.939693i) q^{2} +(-2.49362 - 0.439693i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.439693 - 2.49362i) q^{6} +(0.565258 - 0.326352i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(3.20574 + 1.16679i) q^{9} +(0.500000 - 0.866025i) q^{11} +(2.19285 - 1.26604i) q^{12} +(-2.83564 + 0.500000i) q^{13} +(0.500000 + 0.419550i) q^{14} +(0.173648 - 0.984808i) q^{16} +(0.160035 + 0.439693i) q^{17} +3.41147i q^{18} +(4.07398 - 1.55007i) q^{19} +(-1.55303 + 0.565258i) q^{21} +(0.984808 + 0.173648i) q^{22} +(-2.15160 - 2.56418i) q^{23} +(1.93969 + 1.62760i) q^{24} +(-1.43969 - 2.49362i) q^{26} +(-0.902302 - 0.520945i) q^{27} +(-0.223238 + 0.613341i) q^{28} +(6.41147 + 2.33359i) q^{29} +(2.03209 + 3.51968i) q^{31} +(0.984808 - 0.173648i) q^{32} +(-1.62760 + 1.93969i) q^{33} +(-0.358441 + 0.300767i) q^{34} +(-3.20574 + 1.16679i) q^{36} +7.63816i q^{37} +(2.84997 + 3.29813i) q^{38} +7.29086 q^{39} +(-0.854570 + 4.84651i) q^{41} +(-1.06234 - 1.26604i) q^{42} +(-2.02022 + 2.40760i) q^{43} +(0.173648 + 0.984808i) q^{44} +(1.67365 - 2.89884i) q^{46} +(-2.19285 + 6.02481i) q^{47} +(-0.866025 + 2.37939i) q^{48} +(-3.28699 + 5.69323i) q^{49} +(-0.205737 - 1.16679i) q^{51} +(1.85083 - 2.20574i) q^{52} +(2.48427 + 2.96064i) q^{53} +(0.180922 - 1.02606i) q^{54} -0.652704 q^{56} +(-10.8405 + 2.07398i) q^{57} +6.82295i q^{58} +(-5.68479 + 2.06910i) q^{59} +(-3.96064 + 3.32337i) q^{61} +(-2.61240 + 3.11334i) q^{62} +(2.19285 - 0.386659i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-2.37939 - 0.866025i) q^{66} +(0.300767 - 0.826352i) q^{67} +(-0.405223 - 0.233956i) q^{68} +(4.23783 + 7.34013i) q^{69} +(9.35504 + 7.84981i) q^{71} +(-2.19285 - 2.61334i) q^{72} +(0.502055 + 0.0885259i) q^{73} +(-7.17752 + 2.61240i) q^{74} +(-2.12449 + 3.80612i) q^{76} -0.652704i q^{77} +(2.49362 + 6.85117i) q^{78} +(1.51367 - 8.58445i) q^{79} +(-5.81908 - 4.88279i) q^{81} +(-4.84651 + 0.854570i) q^{82} +(15.5100 - 8.95471i) q^{83} +(0.826352 - 1.43128i) q^{84} +(-2.95336 - 1.07494i) q^{86} +(-14.9617 - 8.63816i) q^{87} +(-0.866025 + 0.500000i) q^{88} +(3.06418 + 17.3778i) q^{89} +(-1.43969 + 1.20805i) q^{91} +(3.29644 + 0.581252i) q^{92} +(-3.51968 - 9.67024i) q^{93} -6.41147 q^{94} -2.53209 q^{96} +(4.96032 + 13.6284i) q^{97} +(-6.47410 - 1.14156i) q^{98} +(2.61334 - 2.19285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{6} + 18 q^{9}+O(q^{10}) \) 12 * q + 6 * q^6 + 18 * q^9	\( 12 q + 6 q^{6} + 18 q^{9} + 6 q^{11} + 6 q^{14} + 18 q^{19} + 6 q^{21} + 12 q^{24} - 6 q^{26} + 36 q^{29} + 6 q^{31} + 12 q^{34} - 18 q^{36} + 24 q^{39} - 42 q^{41} + 18 q^{46} - 24 q^{49} + 18 q^{51} + 36 q^{54} - 12 q^{56} - 54 q^{59} - 30 q^{61} + 6 q^{64} - 6 q^{66} + 12 q^{69} + 12 q^{71} - 36 q^{74} - 24 q^{79} - 36 q^{81} + 12 q^{84} + 18 q^{86} - 6 q^{91} - 36 q^{94} - 12 q^{96} + 18 q^{99}+O(q^{100}) \) 12 * q + 6 * q^6 + 18 * q^9 + 6 * q^11 + 6 * q^14 + 18 * q^19 + 6 * q^21 + 12 * q^24 - 6 * q^26 + 36 * q^29 + 6 * q^31 + 12 * q^34 - 18 * q^36 + 24 * q^39 - 42 * q^41 + 18 * q^46 - 24 * q^49 + 18 * q^51 + 36 * q^54 - 12 * q^56 - 54 * q^59 - 30 * q^61 + 6 * q^64 - 6 * q^66 + 12 * q^69 + 12 * q^71 - 36 * q^74 - 24 * q^79 - 36 * q^81 + 12 * q^84 + 18 * q^86 - 6 * q^91 - 36 * q^94 - 12 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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