LMFDB - Embedded newform 784.2.x.m.557.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.4
Character	$\chi$	$=$	784.557
Dual form			784.2.x.m.373.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.545265 - 1.30487i) q^{2} +(0.569433 - 0.152579i) q^{3} +(-1.40537 - 1.42300i) q^{4} +(-1.54592 - 0.414228i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(-2.29710 + 1.32623i) q^{9} +O(q^{10})$	\(q+(0.545265 - 1.30487i) q^{2} +(0.569433 - 0.152579i) q^{3} +(-1.40537 - 1.42300i) q^{4} +(-1.54592 - 0.414228i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(-2.29710 + 1.32623i) q^{9} +(-1.38345 + 1.79136i) q^{10} +(1.41182 + 5.26900i) q^{11} +(-1.01739 - 0.595873i) q^{12} +(-4.66311 - 4.66311i) q^{13} -0.943500 q^{15} +(-0.0498554 + 3.99969i) q^{16} +(-2.66615 + 4.61791i) q^{17} +(0.478033 + 3.72057i) q^{18} +(0.936730 - 3.49592i) q^{19} +(1.58315 + 2.78199i) q^{20} +(7.64518 + 1.03075i) q^{22} +(-2.25586 + 1.30242i) q^{23} +(-1.33228 + 1.00265i) q^{24} +(-2.11185 - 1.21928i) q^{25} +(-8.62739 + 3.54213i) q^{26} +(-2.35625 + 2.35625i) q^{27} +(-1.22279 - 1.22279i) q^{29} +(-0.514457 + 1.23115i) q^{30} +(-0.416854 + 0.722013i) q^{31} +(5.19189 + 2.24594i) q^{32} +(1.60788 + 2.78493i) q^{33} +(4.57201 + 5.99696i) q^{34} +(5.11551 + 1.40492i) q^{36} +(6.05105 + 1.62137i) q^{37} +(-4.05096 - 3.12852i) q^{38} +(-3.36683 - 1.94384i) q^{39} +(4.49336 - 0.548881i) q^{40} +0.263382i q^{41} +(1.25233 - 1.25233i) q^{43} +(5.51365 - 9.41394i) q^{44} +(4.10050 - 1.09872i) q^{45} +(0.469450 + 3.65377i) q^{46} +(-5.37795 - 9.31488i) q^{47} +(0.581880 + 2.28516i) q^{48} +(-2.74251 + 2.09086i) q^{50} +(-0.813598 + 3.03639i) q^{51} +(-0.0821962 + 13.1890i) q^{52} +(0.0174309 + 0.0650529i) q^{53} +(1.78982 + 4.35939i) q^{54} -8.73026i q^{55} -2.13362i q^{57} +(-2.26233 + 0.928839i) q^{58} +(1.32019 + 4.92700i) q^{59} +(1.32597 + 1.34260i) q^{60} +(-1.63393 + 6.09793i) q^{61} +(0.714837 + 0.937629i) q^{62} +(5.76162 - 5.55011i) q^{64} +(5.27720 + 9.14038i) q^{65} +(4.51069 - 0.579551i) q^{66} +(-12.9904 + 3.48077i) q^{67} +(10.3182 - 2.69595i) q^{68} +(-1.08584 + 1.08584i) q^{69} +2.05301i q^{71} +(4.62255 - 5.90903i) q^{72} +(-4.74814 - 2.74134i) q^{73} +(5.41510 - 7.01175i) q^{74} +(-1.38859 - 0.372072i) q^{75} +(-6.29115 + 3.58011i) q^{76} +(-4.37227 + 3.33337i) q^{78} +(-2.60788 - 4.51698i) q^{79} +(1.73385 - 6.16254i) q^{80} +(2.99648 - 5.19006i) q^{81} +(0.343679 + 0.143613i) q^{82} +(-5.84045 - 5.84045i) q^{83} +(6.03452 - 6.03452i) q^{85} +(-0.951279 - 2.31699i) q^{86} +(-0.882871 - 0.509726i) q^{87} +(-9.27757 - 12.3277i) q^{88} +(5.47892 - 3.16326i) q^{89} +(0.802163 - 5.94971i) q^{90} +(5.02367 + 1.37970i) q^{92} +(-0.127207 + 0.474741i) q^{93} +(-15.0871 + 1.93845i) q^{94} +(-2.89622 + 5.01639i) q^{95} +(3.29912 + 0.486741i) q^{96} -18.8089 q^{97} +(-10.2310 - 10.2310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.545265	−	1.30487i	0.385560	−	0.922683i
$2$	0.545265	−	1.30487i	0.385560	−	0.922683i
$3$	0.569433	−	0.152579i	0.328762	−	0.0880916i	−0.0906624	−	0.995882i	$-0.528898\pi$
$3$	0.569433	−	0.152579i	0.328762	−	0.0880916i	0.419425	+	0.907790i	$0.362232\pi$
$4$	−1.40537	−	1.42300i	−0.702686	−	0.711500i
$5$	−1.54592	−	0.414228i	−0.691356	−	0.185248i	−0.104000	−	0.994577i	$-0.533164\pi$
$5$	−1.54592	−	0.414228i	−0.691356	−	0.185248i	−0.587356	+	0.809329i	$0.699831\pi$
$6$	0.111396	−	0.826233i	0.0454772	−	0.337308i
$7$		0			0
$7$		0			0
$8$	−2.62313	+	1.05792i	−0.927416	+	0.374030i
$9$	−2.29710	+	1.32623i	−0.765701	+	0.442078i
$10$	−1.38345	+	1.79136i	−0.437485	+	0.566478i
$11$	1.41182	+	5.26900i	0.425681	+	1.58866i	0.762431	+	0.647069i	$0.224006\pi$
$11$	1.41182	+	5.26900i	0.425681	+	1.58866i	−0.336750	+	0.941594i	$0.609328\pi$
$12$	−1.01739	−	0.595873i	−0.293694	−	0.172014i
$13$	−4.66311	−	4.66311i	−1.29332	−	1.29332i	−0.932724	−	0.360591i	$-0.882575\pi$
$13$	−4.66311	−	4.66311i	−1.29332	−	1.29332i	−0.360591	−	0.932724i	$-0.617425\pi$
$14$		0			0
$15$	−0.943500			−0.243611
$16$	−0.0498554	+	3.99969i	−0.0124639	+	0.999922i
$17$	−2.66615	+	4.61791i	−0.646637	+	1.12001i	0.337284	+	0.941403i	$0.390492\pi$
$17$	−2.66615	+	4.61791i	−0.646637	+	1.12001i	−0.983921	+	0.178605i	$0.942842\pi$
$18$	0.478033	+	3.72057i	0.112673	+	0.876946i
$19$	0.936730	−	3.49592i	0.214901	−	0.802020i	−0.771301	−	0.636471i	$-0.780394\pi$
$19$	0.936730	−	3.49592i	0.214901	−	0.802020i	0.986202	−	0.165549i	$-0.0529397\pi$
$20$	1.58315	+	2.78199i	0.354002	+	0.622071i
$21$		0			0
$22$	7.64518	+	1.03075i	1.62996	+	0.219757i
$23$	−2.25586	+	1.30242i	−0.470379	+	0.271574i	−0.716399	−	0.697691i	$-0.754211\pi$
$23$	−2.25586	+	1.30242i	−0.470379	+	0.271574i	0.246019	+	0.969265i	$0.420877\pi$
$24$	−1.33228	+	1.00265i	−0.271951	+	0.204665i
$25$	−2.11185	−	1.21928i	−0.422370	−	0.243855i
$26$	−8.62739	+	3.54213i	−1.69197	+	0.694668i
$27$	−2.35625	+	2.35625i	−0.453461	+	0.453461i
$28$		0			0
$29$	−1.22279	−	1.22279i	−0.227067	−	0.227067i	0.584399	−	0.811466i	$-0.301330\pi$
$29$	−1.22279	−	1.22279i	−0.227067	−	0.227067i	−0.811466	+	0.584399i	$0.801330\pi$
$30$	−0.514457	+	1.23115i	−0.0939266	+	0.224775i
$31$	−0.416854	+	0.722013i	−0.0748692	+	0.129677i	−0.901029	−	0.433758i	$-0.857187\pi$
$31$	−0.416854	+	0.722013i	−0.0748692	+	0.129677i	0.826160	+	0.563435i	$0.190521\pi$
$32$	5.19189	+	2.24594i	0.917805	+	0.397031i
$33$	1.60788	+	2.78493i	0.279896	+	0.484794i
$34$	4.57201	+	5.99696i	0.784094	+	1.02847i
$35$		0			0
$36$	5.11551	+	1.40492i	0.852586	+	0.234154i
$37$	6.05105	+	1.62137i	0.994786	+	0.266552i	0.719260	−	0.694741i	$-0.244481\pi$
$37$	6.05105	+	1.62137i	0.994786	+	0.266552i	0.275526	+	0.961294i	$0.411148\pi$
$38$	−4.05096	−	3.12852i	−0.657153	−	0.507512i
$39$	−3.36683	−	1.94384i	−0.539124	−	0.311263i
$40$	4.49336	−	0.548881i	0.710463	−	0.0867857i
$41$			0.263382i			0.0411333i	0.999788	+	0.0205667i	$0.00654703\pi$
$41$			0.263382i			0.0411333i	−0.999788	+	0.0205667i	$0.993453\pi$
$42$		0			0
$43$	1.25233	−	1.25233i	0.190979	−	0.190979i	−0.605140	−	0.796119i	$-0.706883\pi$
$43$	1.25233	−	1.25233i	0.190979	−	0.190979i	0.796119	+	0.605140i	$0.206883\pi$
$44$	5.51365	−	9.41394i	0.831213	−	1.41920i
$45$	4.10050	−	1.09872i	0.611266	−	0.163788i
$46$	0.469450	+	3.65377i	0.0692166	+	0.538719i
$47$	−5.37795	−	9.31488i	−0.784455	−	1.35872i	−0.929324	−	0.369265i	$-0.879610\pi$
$47$	−5.37795	−	9.31488i	−0.784455	−	1.35872i	0.144870	−	0.989451i	$-0.453724\pi$
$48$	0.581880	+	2.28516i	0.0839872	+	0.329835i
$49$		0			0
$50$	−2.74251	+	2.09086i	−0.387850	+	0.295692i
$51$	−0.813598	+	3.03639i	−0.113927	+	0.425180i
$52$	−0.0821962	+	13.1890i	−0.0113986	+	1.82899i
$53$	0.0174309	+	0.0650529i	0.00239432	+	0.00893571i	0.967113	−	0.254348i	$-0.0818610\pi$
$53$	0.0174309	+	0.0650529i	0.00239432	+	0.00893571i	−0.964718	+	0.263284i	$0.915194\pi$
$54$	1.78982	+	4.35939i	0.243564	+	0.593237i
$55$		−	8.73026i		−	1.17719i
$56$		0			0
$57$		−	2.13362i		−	0.282605i
$58$	−2.26233	+	0.928839i	−0.297058	+	0.121963i
$59$	1.32019	+	4.92700i	0.171874	+	0.641441i	0.997063	+	0.0765850i	$0.0244016\pi$
$59$	1.32019	+	4.92700i	0.171874	+	0.641441i	−0.825189	+	0.564856i	$0.808932\pi$
$60$	1.32597	+	1.34260i	0.171182	+	0.173329i
$61$	−1.63393	+	6.09793i	−0.209204	+	0.780760i	0.778923	+	0.627120i	$0.215766\pi$
$61$	−1.63393	+	6.09793i	−0.209204	+	0.780760i	−0.988127	+	0.153640i	$0.950900\pi$
$62$	0.714837	+	0.937629i	0.0907844	+	0.119079i
$63$		0			0
$64$	5.76162	−	5.55011i	0.720203	−	0.693764i
$65$	5.27720	+	9.14038i	0.654557	+	1.13373i
$66$	4.51069	−	0.579551i	0.555228	−	0.0713377i
$67$	−12.9904	+	3.48077i	−1.58703	+	0.425244i	−0.941094	−	0.338146i	$-0.890200\pi$
$67$	−12.9904	+	3.48077i	−1.58703	+	0.425244i	−0.645938	+	0.763390i	$0.723533\pi$
$68$	10.3182	−	2.69595i	1.25127	−	0.326932i
$69$	−1.08584	+	1.08584i	−0.130720	+	0.130720i
$70$		0			0
$71$			2.05301i			0.243647i	0.992552	+	0.121824i	$0.0388743\pi$
$71$			2.05301i			0.243647i	−0.992552	+	0.121824i	$0.961126\pi$
$72$	4.62255	−	5.90903i	0.544773	−	0.696385i
$73$	−4.74814	−	2.74134i	−0.555728	−	0.320850i	0.195701	−	0.980664i	$-0.437302\pi$
$73$	−4.74814	−	2.74134i	−0.555728	−	0.320850i	−0.751429	+	0.659814i	$0.770635\pi$
$74$	5.41510	−	7.01175i	0.629493	−	0.815100i
$75$	−1.38859	−	0.372072i	−0.160341	−	0.0429632i
$76$	−6.29115	+	3.58011i	−0.721645	+	0.410667i
$77$		0			0
$78$	−4.37227	+	3.33337i	−0.495062	+	0.377429i
$79$	−2.60788	−	4.51698i	−0.293409	−	0.508200i	0.681204	−	0.732093i	$-0.261457\pi$
$79$	−2.60788	−	4.51698i	−0.293409	−	0.508200i	−0.974614	+	0.223893i	$0.928123\pi$
$80$	1.73385	−	6.16254i	0.193851	−	0.688993i
$81$	2.99648	−	5.19006i	0.332943	−	0.576674i
$82$	0.343679	+	0.143613i	0.0379530	+	0.0158594i
$83$	−5.84045	−	5.84045i	−0.641073	−	0.641073i	0.309746	−	0.950819i	$-0.399756\pi$
$83$	−5.84045	−	5.84045i	−0.641073	−	0.641073i	−0.950819	+	0.309746i	$0.899756\pi$
$84$		0			0
$85$	6.03452	−	6.03452i	0.654535	−	0.654535i
$86$	−0.951279	−	2.31699i	−0.102579	−	0.249847i
$87$	−0.882871	−	0.509726i	−0.0946537	−	0.0546483i
$88$	−9.27757	−	12.3277i	−0.988992	−	1.31414i
$89$	5.47892	−	3.16326i	0.580764	−	0.335304i	−0.180673	−	0.983543i	$-0.557828\pi$
$89$	5.47892	−	3.16326i	0.580764	−	0.335304i	0.761437	+	0.648239i	$0.224494\pi$
$90$	0.802163	−	5.94971i	0.0845554	−	0.627154i
$91$		0			0
$92$	5.02367	+	1.37970i	0.523754	+	0.143844i
$93$	−0.127207	+	0.474741i	−0.0131907	+	0.0492284i
$94$	−15.0871	+	1.93845i	−1.55612	+	0.199936i
$95$	−2.89622	+	5.01639i	−0.297146	+	0.514671i
$96$	3.29912	+	0.486741i	0.336715	+	0.0496778i
$97$	−18.8089			−1.90976			−0.954878	−	0.296999i	$-0.904014\pi$
$97$	−18.8089			−1.90976			−0.954878	+	0.296999i	$0.904014\pi$
$98$		0			0
$99$	−10.2310	−	10.2310i	−1.02826	−	1.02826i
$100$	1.23290	+	4.71869i	0.123290	+	0.471869i
$101$	1.05607	+	3.94130i	0.105083	+	0.392174i	0.998355	−	0.0573431i	$-0.0182629\pi$
$101$	1.05607	+	3.94130i	0.105083	+	0.392174i	−0.893272	+	0.449517i	$0.851596\pi$
$102$	3.51847	+	2.71728i	0.348380	+	0.269050i
$103$	6.70338	−	3.87020i	0.660504	−	0.381342i	−0.131965	−	0.991254i	$-0.542129\pi$
$103$	6.70338	−	3.87020i	0.660504	−	0.381342i	0.792469	+	0.609912i	$0.208795\pi$
$104$	17.1651	+	7.29876i	1.68318	+	0.715703i
$105$		0			0
$106$	0.0943901	+	0.0127260i	0.00916798	+	0.00123606i
$107$	3.18895	+	0.854476i	0.308287	+	0.0826053i	0.409646	−	0.912245i	$-0.365652\pi$
$107$	3.18895	+	0.854476i	0.308287	+	0.0826053i	−0.101359	+	0.994850i	$0.532319\pi$
$108$	6.66436	+	0.0415334i	0.641279	+	0.00399656i
$109$	6.73214	−	1.80387i	0.644822	−	0.172779i	0.0784353	−	0.996919i	$-0.475008\pi$
$109$	6.73214	−	1.80387i	0.644822	−	0.172779i	0.566387	+	0.824140i	$0.308341\pi$
$110$	−11.3919	−	4.76030i	−1.08617	−	0.453877i
$111$	3.69306			0.350529
$112$		0			0
$113$	5.24381			0.493296			0.246648	−	0.969105i	$-0.420671\pi$
$113$	5.24381			0.493296			0.246648	+	0.969105i	$0.420671\pi$
$114$	−2.78410	−	1.16339i	−0.260755	−	0.108961i
$115$	4.02688	−	1.07900i	0.375508	−	0.100617i
$116$	−0.0215540	+	3.45851i	−0.00200124	+	0.321115i
$117$	16.8960	+	4.52728i	1.56204	+	0.418547i
$118$	7.14895	+	0.963849i	0.658114	+	0.0887295i
$119$		0			0
$120$	2.47492	−	0.998145i	0.225929	−	0.0911178i
$121$	−16.2428	+	9.37781i	−1.47662	+	0.852528i
$122$	7.06608	+	5.45706i	0.639732	+	0.494059i
$123$	0.0401866	+	0.149978i	0.00362350	+	0.0135231i
$124$	1.61326	−	0.421513i	0.144875	−	0.0378530i
$125$	8.41814	+	8.41814i	0.752941	+	0.752941i
$126$		0			0
$127$	−17.6789			−1.56875			−0.784373	−	0.620290i	$-0.787015\pi$
$127$	−17.6789			−1.56875			−0.784373	+	0.620290i	$0.787015\pi$
$128$	−4.10056	−	10.5444i	−0.362442	−	0.932006i
$129$	0.522040	−	0.904200i	0.0459631	−	0.0796104i
$130$	14.8045	−	1.90214i	1.29844	−	0.166828i
$131$	0.797610	−	2.97672i	0.0696875	−	0.260077i	−0.922289	−	0.386502i	$-0.873683\pi$
$131$	0.797610	−	2.97672i	0.0696875	−	0.260077i	0.991976	+	0.126424i	$0.0403501\pi$
$132$	1.70328	−	6.20188i	0.148252	−	0.539804i
$133$		0			0
$134$	−2.54126	+	18.8487i	−0.219531	+	1.62828i
$135$	4.61860	−	2.66655i	0.397506	−	0.229500i
$136$	2.10829	−	14.9339i	0.180785	−	1.28057i
$137$	−7.40148	−	4.27325i	−0.632351	−	0.365088i	0.149311	−	0.988790i	$-0.452295\pi$
$137$	−7.40148	−	4.27325i	−0.632351	−	0.365088i	−0.781662	+	0.623702i	$0.785628\pi$
$138$	0.824810	+	2.00895i	0.0702125	+	0.171013i
$139$	5.72549	−	5.72549i	0.485629	−	0.485629i	−0.421295	−	0.906924i	$-0.638424\pi$
$139$	5.72549	−	5.72549i	0.485629	−	0.485629i	0.906924	+	0.421295i	$0.138424\pi$
$140$		0			0
$141$	−4.48364	−	4.48364i	−0.377591	−	0.377591i
$142$	2.67891	+	1.11943i	0.224809	+	0.0939408i
$143$	17.9865	−	31.1535i	1.50410	−	2.60518i
$144$	−5.19000	−	9.25382i	−0.432500	−	0.771151i
$145$	1.38382	+	2.39685i	0.114920	+	0.199048i
$146$	−6.16609	+	4.70095i	−0.510309	+	0.389054i
$147$		0			0
$148$	−6.19676	−	10.8893i	−0.509371	−	0.895092i
$149$	−0.539794	−	0.144637i	−0.0442217	−	0.0118492i	0.236640	−	0.971597i	$-0.423954\pi$
$149$	−0.539794	−	0.144637i	−0.0442217	−	0.0118492i	−0.280862	+	0.959748i	$0.590620\pi$
$150$	−1.24266	+	1.60906i	−0.101462	+	0.131379i
$151$	3.21780	+	1.85780i	0.261861	+	0.151185i	0.625183	−	0.780478i	$-0.285024\pi$
$151$	3.21780	+	1.85780i	0.261861	+	0.151185i	−0.363322	+	0.931663i	$0.618358\pi$
$152$	1.24123	+	10.1612i	0.100677	+	0.824186i
$153$		−	14.1437i		−	1.14345i
$154$		0			0
$155$	0.943500	−	0.943500i	0.0757837	−	0.0757837i
$156$	1.96557	+	7.52281i	0.157371	+	0.602307i
$157$	5.45784	−	1.46242i	0.435583	−	0.116714i	−0.0343627	−	0.999409i	$-0.510940\pi$
$157$	5.45784	−	1.46242i	0.435583	−	0.116714i	0.469946	+	0.882695i	$0.344273\pi$
$158$	−7.31606	+	0.939995i	−0.582034	+	0.0747819i
$159$	0.0198514	+	0.0343837i	0.00157432	+	0.00272681i
$160$	−7.09591	−	5.62267i	−0.560981	−	0.444511i
$161$		0			0
$162$	−5.13848	−	6.73998i	−0.403717	−	0.529543i
$163$	1.23412	−	4.60580i	0.0966638	−	0.360754i	−0.900603	−	0.434643i	$-0.856874\pi$
$163$	1.23412	−	4.60580i	0.0966638	−	0.360754i	0.997266	+	0.0738892i	$0.0235411\pi$
$164$	0.374792	−	0.370150i	0.0292663	−	0.0289038i
$165$	−1.33206	−	4.97130i	−0.103700	−	0.387015i
$166$	−10.8056	+	4.43644i	−0.838679	+	0.344335i
$167$			12.4233i			0.961345i	0.876900	+	0.480673i	$0.159607\pi$
$167$			12.4233i			0.961345i	−0.876900	+	0.480673i	$0.840393\pi$
$168$		0			0
$169$			30.4893i			2.34533i
$170$	−4.58385	−	11.1647i	−0.351565	−	0.856291i
$171$	2.48464	+	9.27282i	0.190005	+	0.709110i
$172$	−3.54206	−	0.0220747i	−0.270080	−	0.00168318i
$173$	−3.38906	+	12.6481i	−0.257665	+	0.961620i	0.708923	+	0.705286i	$0.249181\pi$
$173$	−3.38906	+	12.6481i	−0.257665	+	0.961620i	−0.966588	+	0.256334i	$0.917485\pi$
$174$	−1.14652	+	0.874097i	−0.0869178	+	0.0662651i
$175$		0			0
$176$	−21.1448	+	5.38417i	−1.59385	+	0.405847i
$177$	1.50352	+	2.60417i	0.113011	+	0.195741i
$178$	−1.14018	−	8.87409i	−0.0854598	−	0.665141i
$179$	13.5991	−	3.64387i	1.01644	−	0.272355i	0.288124	−	0.957593i	$-0.406968\pi$
$179$	13.5991	−	3.64387i	1.01644	−	0.272355i	0.728319	+	0.685238i	$0.240302\pi$
$180$	−7.32621	−	4.29089i	−0.546063	−	0.319824i
$181$	5.08125	−	5.08125i	0.377687	−	0.377687i	−0.492580	−	0.870267i	$-0.663946\pi$
$181$	5.08125	−	5.08125i	0.377687	−	0.377687i	0.870267	+	0.492580i	$0.163946\pi$
$182$		0			0
$183$			3.72167i			0.275114i
$184$	4.53956	−	5.80294i	0.334661	−	0.427798i
$185$	−8.68281	−	5.01302i	−0.638373	−	0.368565i
$186$	0.550114	+	0.424848i	0.0403364	+	0.0311513i
$187$	−28.0959	−	7.52827i	−2.05458	−	0.550522i
$188$	−5.69705	+	20.7437i	−0.415500	+	1.51289i
$189$		0			0
$190$	4.96654	+	6.51445i	0.360311	+	0.472608i
$191$	−10.3964	−	18.0070i	−0.752254	−	1.30294i	−0.946728	−	0.322035i	$-0.895633\pi$
$191$	−10.3964	−	18.0070i	−0.752254	−	1.30294i	0.194474	−	0.980908i	$-0.437700\pi$
$192$	2.43403	−	4.03952i	0.175661	−	0.291527i
$193$	−6.67236	+	11.5569i	−0.480287	+	0.831882i	−0.999744	−	0.0226149i	$-0.992801\pi$
$193$	−6.67236	+	11.5569i	−0.480287	+	0.831882i	0.519457	+	0.854496i	$0.326134\pi$
$194$	−10.2558	+	24.5432i	−0.736326	+	1.76210i
$195$	4.39965	+	4.39965i	0.315065	+	0.315065i
$196$		0			0
$197$	0.194462	−	0.194462i	0.0138549	−	0.0138549i	−0.700145	−	0.714000i	$-0.746882\pi$
$197$	0.194462	−	0.194462i	0.0138549	−	0.0138549i	0.714000	+	0.700145i	$0.246882\pi$
$198$	−18.9288	+	7.77154i	−1.34521	+	0.552300i
$199$	−12.4710	−	7.20013i	−0.884045	−	0.510403i	−0.0120548	−	0.999927i	$-0.503837\pi$
$199$	−12.4710	−	7.20013i	−0.884045	−	0.510403i	−0.871990	+	0.489524i	$0.837171\pi$
$200$	6.82954	+	0.964158i	0.482922	+	0.0681763i
$201$	−6.86608	+	3.96413i	−0.484296	+	0.279608i
$202$	5.71872	+	0.771019i	0.402367	+	0.0542487i
$203$		0			0
$204$	5.46419	−	3.10951i	0.382570	−	0.217709i
$205$	0.109100	−	0.407167i	0.00761987	−	0.0284378i
$206$	−1.39499	−	10.8573i	−0.0971935	−	0.756465i
$207$	3.45463	−	5.98359i	0.240113	−	0.415888i
$208$	18.8835	−	18.4185i	1.30933	−	1.27709i
$209$	19.7425			1.36562
$210$		0			0
$211$	7.72356	+	7.72356i	0.531711	+	0.531711i	0.921081	−	0.389370i	$-0.127307\pi$
$211$	7.72356	+	7.72356i	0.531711	+	0.531711i	−0.389370	+	0.921081i	$0.627307\pi$
$212$	0.0680734	−	0.116228i	0.00467530	−	0.00798255i
$213$	0.313247	+	1.16905i	0.0214633	+	0.0801021i
$214$	2.85380	−	3.69525i	0.195082	−	0.252602i
$215$	−2.45476	+	1.41725i	−0.167413	+	0.0966559i
$216$	3.68804	−	8.67348i	0.250939	−	0.590156i
$217$		0			0
$218$	1.31698	−	9.76815i	0.0891971	−	0.661583i
$219$	−3.12202	−	0.836543i	−0.210967	−	0.0565284i
$220$	−12.4232	+	12.2693i	−0.837569	+	0.827194i
$221$	33.9664	−	9.10127i	2.28483	−	0.612218i
$222$	2.01369	−	4.81896i	0.135150	−	0.323427i
$223$	7.06285			0.472963			0.236482	−	0.971636i	$-0.424006\pi$
$223$	7.06285			0.472963			0.236482	+	0.971636i	$0.424006\pi$
$224$		0			0
$225$	6.46817			0.431212
$226$	2.85926	−	6.84249i	0.190195	−	0.455156i
$227$	−16.1503	+	4.32747i	−1.07193	+	0.287224i	−0.751288	−	0.659975i	$-0.770567\pi$
$227$	−16.1503	+	4.32747i	−1.07193	+	0.287224i	−0.320647	+	0.947199i	$0.603900\pi$
$228$	−3.03614	+	2.99853i	−0.201073	+	0.198583i
$229$	−12.8108	−	3.43264i	−0.846561	−	0.226835i	−0.190636	−	0.981661i	$-0.561055\pi$
$229$	−12.8108	−	3.43264i	−0.846561	−	0.226835i	−0.655926	+	0.754826i	$0.727722\pi$
$230$	0.787761	−	5.84289i	0.0519434	−	0.385269i
$231$		0			0
$232$	4.50115	+	1.91393i	0.295515	+	0.125656i
$233$	21.1644	−	12.2193i	1.38653	−	0.800511i	0.393604	−	0.919280i	$-0.371228\pi$
$233$	21.1644	−	12.2193i	1.38653	−	0.800511i	0.992922	+	0.118769i	$0.0378948\pi$
$234$	15.1203	−	19.5786i	0.988446	−	1.27989i
$235$	4.45539	+	16.6277i	0.290638	+	1.08467i
$236$	5.15577	−	8.80290i	0.335612	−	0.573020i
$237$	−2.17421	−	2.17421i	−0.141230	−	0.141230i
$238$		0			0
$239$	−6.27660			−0.406000			−0.203000	−	0.979179i	$-0.565069\pi$
$239$	−6.27660			−0.406000			−0.203000	+	0.979179i	$0.565069\pi$
$240$	0.0470386	−	3.77371i	0.00303633	−	0.243592i
$241$	−7.50621	+	13.0011i	−0.483517	+	0.837476i	−0.999821	−	0.0189293i	$-0.993974\pi$
$241$	−7.50621	+	13.0011i	−0.483517	+	0.837476i	0.516304	+	0.856406i	$0.327308\pi$
$242$	3.38017	+	26.3082i	0.217286	+	1.69115i
$243$	3.50175	−	13.0687i	0.224637	−	0.838358i
$244$	10.9736	−	6.24477i	0.702515	−	0.399781i
$245$		0			0
$246$	0.217615	+	0.0293396i	0.0138746	+	0.00187063i
$247$	−20.6700	+	11.9338i	−1.31520	+	0.759330i
$248$	0.329633	−	2.33493i	0.0209317	−	0.148268i
$249$	−4.21688	−	2.43462i	−0.267234	−	0.154288i
$250$	15.5747	−	6.39447i	0.985030	−	0.404422i
$251$	−11.7926	+	11.7926i	−0.744339	+	0.744339i	−0.973410	−	0.229071i	$-0.926431\pi$
$251$	−11.7926	+	11.7926i	−0.744339	+	0.744339i	0.229071	+	0.973410i	$0.426431\pi$
$252$		0			0
$253$	−10.0473	−	10.0473i	−0.631671	−	0.631671i
$254$	−9.63966	+	23.0686i	−0.604846	+	1.44745i
$255$	2.51551	−	4.35700i	0.157528	−	0.272846i
$256$	−15.9950	−	0.398812i	−0.999689	−	0.0249258i
$257$	10.1988	+	17.6649i	0.636186	+	1.10191i	0.986263	+	0.165186i	$0.0528223\pi$
$257$	10.1988	+	17.6649i	0.636186	+	1.10191i	−0.350076	+	0.936721i	$0.613844\pi$
$258$	−0.895214	−	1.17422i	−0.0557336	−	0.0731039i
$259$		0			0
$260$	5.59033	−	20.3551i	0.346697	−	1.26237i
$261$	4.43058	+	1.18717i	0.274246	+	0.0734841i
$262$	−3.44933	−	2.66388i	−0.213100	−	0.164575i
$263$	−20.2176	−	11.6726i	−1.24667	−	0.719764i	−0.276225	−	0.961093i	$-0.589083\pi$
$263$	−20.2176	−	11.6726i	−1.24667	−	0.719764i	−0.970443	+	0.241329i	$0.922417\pi$
$264$	−7.16390	−	5.60423i	−0.440908	−	0.344916i
$265$		−	0.107787i		−	0.00662130i
$266$		0			0
$267$	2.63723	−	2.63723i	0.161396	−	0.161396i
$268$	23.2095	+	13.5936i	1.41775	+	0.830360i
$269$	30.1489	−	8.07837i	1.83821	−	0.492547i	0.839502	−	0.543356i	$-0.182847\pi$
$269$	30.1489	−	8.07837i	1.83821	−	0.492547i	0.998708	+	0.0508094i	$0.0161801\pi$
$270$	−0.961142	−	7.48065i	−0.0584932	−	0.455258i
$271$	0.731959	+	1.26779i	0.0444633	+	0.0770127i	0.887401	−	0.460999i	$-0.152509\pi$
$271$	0.731959	+	1.26779i	0.0444633	+	0.0770127i	−0.842937	+	0.538012i	$0.819176\pi$
$272$	−18.3373	−	10.8940i	−1.11186	−	0.660546i
$273$		0			0
$274$	−9.61180	+	7.32792i	−0.580670	+	0.442696i
$275$	3.44281	−	12.8487i	0.207609	−	0.774808i
$276$	3.07116	+	0.0191400i	0.184862	+	0.00115209i
$277$	−0.509633	−	1.90198i	−0.0306209	−	0.114279i	0.948924	−	0.315505i	$-0.102174\pi$
$277$	−0.509633	−	1.90198i	−0.0306209	−	0.114279i	−0.979545	+	0.201226i	$0.935507\pi$
$278$	−4.34911	−	10.5929i	−0.260842	−	0.635321i
$279$		−	2.21138i		−	0.132392i
$280$		0			0
$281$		−	5.66742i		−	0.338090i	−0.985608	−	0.169045i	$-0.945932\pi$
$281$		−	5.66742i		−	0.338090i	0.985608	−	0.169045i	$-0.0540683\pi$
$282$	−8.29534	+	3.40580i	−0.493980	+	0.202812i
$283$	6.09854	+	22.7600i	0.362520	+	1.35294i	0.870751	+	0.491724i	$0.163633\pi$
$283$	6.09854	+	22.7600i	0.362520	+	1.35294i	−0.508231	+	0.861221i	$0.669700\pi$
$284$	2.92143	−	2.88524i	0.173355	−	0.171208i
$285$	−0.883805	+	3.29840i	−0.0523521	+	0.195381i
$286$	−30.8438	−	40.4569i	−1.82383	−	2.39226i
$287$		0			0
$288$	−14.9050	+	1.72649i	−0.878283	+	0.101734i
$289$	−5.71672	−	9.90165i	−0.336278	−	0.582450i
$290$	3.88213	−	0.498790i	0.227966	−	0.0292900i
$291$	−10.7104	+	2.86985i	−0.627856	+	0.168234i
$292$	2.77198	+	10.6092i	0.162218	+	0.620857i
$293$	−17.1121	+	17.1121i	−0.999698	+	0.999698i	−1.00000		0.000302098i	$-0.999904\pi$
$293$	−17.1121	+	17.1121i	−0.999698	+	0.999698i	0.000302098		1.00000i	$0.499904\pi$
$294$		0			0
$295$		−	8.16360i		−	0.475303i
$296$	−17.5880	+	2.14844i	−1.02228	+	0.124875i
$297$	−15.7417	−	9.08849i	−0.913427	−	0.527367i
$298$	−0.483064	+	0.625496i	−0.0279831	+	0.0362340i
$299$	16.5927	+	4.44599i	0.959579	+	0.257118i
$300$	1.42203	+	2.49887i	0.0821010	+	0.144272i
$301$		0			0
$302$	4.17874	−	3.18582i	0.240459	−	0.183323i
$303$	1.20272	+	2.08317i	0.0690944	+	0.119675i
$304$	13.9359	+	3.92092i	0.799279	+	0.224880i
$305$	5.05186	−	8.75008i	0.289269	−	0.501028i
$306$	−18.4558	−	7.71209i	−1.05505	−	0.440871i
$307$	9.59837	+	9.59837i	0.547808	+	0.547808i	0.925806	−	0.377998i	$-0.123388\pi$
$307$	9.59837	+	9.59837i	0.547808	+	0.547808i	−0.377998	+	0.925806i	$0.623388\pi$
$308$		0			0
$309$	3.22662	−	3.22662i	0.183556	−	0.183556i
$310$	−0.716688	−	1.74560i	−0.0407051	−	0.0991436i
$311$	−16.6161	−	9.59331i	−0.942213	−	0.543987i	−0.0515594	−	0.998670i	$-0.516419\pi$
$311$	−16.6161	−	9.59331i	−0.942213	−	0.543987i	−0.890653	+	0.454683i	$0.849752\pi$
$312$	10.8880	+	1.53712i	0.616414	+	0.0870220i
$313$	4.36445	−	2.51982i	0.246693	−	0.142428i	−0.371556	−	0.928411i	$-0.621176\pi$
$313$	4.36445	−	2.51982i	0.246693	−	0.142428i	0.618249	+	0.785982i	$0.287842\pi$
$314$	1.06769	−	7.91918i	0.0602535	−	0.446905i
$315$		0			0
$316$	−2.76262	+	10.0591i	−0.155409	+	0.565866i
$317$	2.02264	−	7.54861i	0.113603	−	0.423972i	−0.885576	−	0.464495i	$-0.846236\pi$
$317$	2.02264	−	7.54861i	0.113603	−	0.423972i	0.999179	+	0.0405232i	$0.0129025\pi$
$318$	0.0556906	−	0.00715533i	0.00312297	−	0.000401251i
$319$	4.71652	−	8.16926i	0.264075	−	0.457391i
$320$	−11.2060	+	6.19339i	−0.626435	+	0.346221i
$321$	1.94627			0.108630
$322$		0			0
$323$	13.6464	+	13.6464i	0.759306	+	0.759306i
$324$	−11.5966	+	3.02998i	−0.644257	+	0.168332i
$325$	4.16216	+	15.5334i	0.230875	+	0.861638i
$326$	−5.33705	−	4.12175i	−0.295592	−	0.228282i
$327$	3.55827	−	2.05437i	0.196773	−	0.113607i
$328$	−0.278636	−	0.690885i	−0.0153851	−	0.0381477i
$329$		0			0
$330$	−7.21323	−	0.972515i	−0.397075	−	0.0535352i
$331$	20.1508	+	5.39940i	1.10759	+	0.296778i	0.765852	−	0.643017i	$-0.222318\pi$
$331$	20.1508	+	5.39940i	1.10759	+	0.296778i	0.341739	+	0.939795i	$0.388984\pi$
$332$	−0.102949	+	16.5190i	−0.00565006	+	0.906597i
$333$	−16.0502	+	4.30064i	−0.879545	+	0.235673i
$334$	16.2108	+	6.77400i	0.887016	+	0.370657i
$335$	21.5239			1.17598
$336$		0			0
$337$	16.7111			0.910311			0.455156	−	0.890412i	$-0.349584\pi$
$337$	16.7111			0.910311			0.455156	+	0.890412i	$0.349584\pi$
$338$	39.7845	+	16.6247i	2.16399	+	0.904266i
$339$	2.98600	−	0.800096i	0.162177	−	0.0434552i
$340$	−17.0679	−	0.106370i	−0.925635	−	0.00576871i
$341$	−4.39281	−	1.17705i	−0.237884	−	0.0637408i
$342$	13.4546	+	1.81400i	0.727542	+	0.0980900i
$343$		0			0
$344$	−1.96017	+	4.60990i	−0.105685	+	0.248549i
$345$	2.12840	−	1.22883i	0.114589	−	0.0661582i
$346$	14.6562	+	11.3189i	0.787925	+	0.608506i
$347$	2.04215	+	7.62139i	0.109628	+	0.409138i	0.998829	−	0.0483791i	$-0.0154056\pi$
$347$	2.04215	+	7.62139i	0.109628	+	0.409138i	−0.889201	+	0.457517i	$0.848739\pi$
$348$	0.515423	+	1.97268i	0.0276296	+	0.105747i
$349$	17.9789	+	17.9789i	0.962388	+	0.962388i	0.999318	−	0.0369299i	$-0.0117578\pi$
$349$	17.9789	+	17.9789i	0.962388	+	0.962388i	−0.0369299	+	0.999318i	$0.511758\pi$
$350$		0			0
$351$	21.9750			1.17294
$352$	−4.50384	+	30.5270i	−0.240056	+	1.62709i
$353$	−12.5159	+	21.6782i	−0.666155	+	1.15381i	0.312816	+	0.949814i	$0.398728\pi$
$353$	−12.5159	+	21.6782i	−0.666155	+	1.15381i	−0.978971	+	0.204000i	$0.934606\pi$
$354$	4.21791	−	0.541933i	0.224180	−	0.0288034i
$355$	0.850413	−	3.17379i	0.0451352	−	0.168447i
$356$	−12.2012	−	3.35095i	−0.646664	−	0.177600i
$357$		0			0
$358$	2.66033	−	19.7319i	0.140603	−	1.04286i
$359$	15.5806	−	8.99548i	0.822314	−	0.474763i	−0.0288999	−	0.999582i	$-0.509200\pi$
$359$	15.5806	−	8.99548i	0.822314	−	0.474763i	0.851214	+	0.524819i	$0.175867\pi$
$360$	−9.59377	+	7.22008i	−0.505636	+	0.380532i
$361$	5.11046	+	2.95053i	0.268972	+	0.155291i
$362$	−3.85975	−	9.40101i	−0.202864	−	0.494106i
$363$	−7.81836	+	7.81836i	−0.410357	+	0.410357i
$364$		0			0
$365$	6.20470	+	6.20470i	0.324769	+	0.324769i
$366$	4.85629	+	2.02929i	0.253842	+	0.106073i
$367$	5.15387	−	8.92677i	0.269030	−	0.465974i	−0.699582	−	0.714553i	$-0.746630\pi$
$367$	5.15387	−	8.92677i	0.269030	−	0.465974i	0.968612	+	0.248579i	$0.0799636\pi$
$368$	−5.09681	−	9.08767i	−0.265690	−	0.473728i
$369$	−0.349306	−	0.605015i	−0.0181841	−	0.0314958i
$370$	−11.2758	+	8.59651i	−0.586199	+	0.446911i
$371$		0			0
$372$	0.854329	−	0.486174i	0.0442949	−	0.0252069i
$373$	−21.9323	−	5.87673i	−1.13561	−	0.304286i	−0.358425	−	0.933558i	$-0.616686\pi$
$373$	−21.9323	−	5.87673i	−1.13561	−	0.304286i	−0.777184	+	0.629273i	$0.783353\pi$
$374$	−25.1431	+	32.5566i	−1.30012	+	1.68346i
$375$	6.07800	+	3.50914i	0.313867	+	0.181211i
$376$	23.9614	+	18.7447i	1.23572	+	0.966685i
$377$			11.4040i			0.587338i
$378$		0			0
$379$	15.7922	−	15.7922i	0.811190	−	0.811190i	−0.173622	−	0.984812i	$-0.555547\pi$
$379$	15.7922	−	15.7922i	0.811190	−	0.811190i	0.984812	+	0.173622i	$0.0555471\pi$
$380$	11.2086	−	2.92859i	0.574988	−	0.150233i
$381$	−10.0669	+	2.69743i	−0.515745	+	0.138193i
$382$	−29.1656	+	3.74730i	−1.49224	+	0.191729i
$383$	9.18163	+	15.9031i	0.469160	+	0.812608i	0.999378	−	0.0352526i	$-0.0112236\pi$
$383$	9.18163	+	15.9031i	0.469160	+	0.812608i	−0.530219	+	0.847861i	$0.677890\pi$
$384$	−3.94386	−	5.37870i	−0.201259	−	0.274481i
$385$		0			0
$386$	11.4420	+	15.0081i	0.582383	+	0.763893i
$387$	−1.21585	+	4.53762i	−0.0618052	+	0.230660i
$388$	26.4335	+	26.7651i	1.34196	+	1.35879i
$389$	5.10801	+	19.0634i	0.258987	+	0.966551i	0.965829	+	0.259180i	$0.0834523\pi$
$389$	5.10801	+	19.0634i	0.258987	+	0.966551i	−0.706842	+	0.707371i	$0.749881\pi$
$390$	8.13994	−	3.34200i	0.412182	−	0.169229i
$391$		−	13.8898i		−	0.702438i
$392$		0			0
$393$		−	1.81674i		−	0.0916426i
$394$	−0.147715	−	0.359781i	−0.00744175	−	0.0181255i
$395$	2.16051	+	8.06314i	0.108707	+	0.405701i
$396$	−0.180341	+	28.9372i	−0.00906249	+	1.45415i
$397$	0.412931	−	1.54108i	0.0207244	−	0.0773446i	−0.954789	−	0.297284i	$-0.903919\pi$
$397$	0.412931	−	1.54108i	0.0207244	−	0.0773446i	0.975514	+	0.219939i	$0.0705859\pi$
$398$	−16.1952	+	12.3470i	−0.811793	+	0.618901i
$399$		0			0
$400$	4.98201	−	8.38595i	0.249101	−	0.419297i
$401$	7.17349	+	12.4248i	0.358227	+	0.620467i	0.987665	−	0.156584i	$-0.0500481\pi$
$401$	7.17349	+	12.4248i	0.358227	+	0.620467i	−0.629438	+	0.777051i	$0.716715\pi$
$402$	1.42885	+	11.1208i	0.0712645	+	0.554657i
$403$	5.31066	−	1.42299i	0.264543	−	0.0708841i
$404$	4.12430	−	7.04177i	0.205191	−	0.350341i
$405$	−6.78219	+	6.78219i	−0.337010	+	0.337010i
$406$		0			0
$407$			34.1721i			1.69385i
$408$	−1.07808	−	8.82557i	−0.0533727	−	0.436931i
$409$	−33.9931	−	19.6259i	−1.68085	−	0.970438i	−0.961099	−	0.276204i	$-0.910923\pi$
$409$	−33.9931	−	19.6259i	−1.68085	−	0.970438i	−0.719749	−	0.694234i	$-0.755743\pi$
$410$	−0.471811	−	0.364375i	−0.0233011	−	0.0179952i
$411$	−4.86666	−	1.30402i	−0.240055	−	0.0643224i
$412$	−14.9280	−	4.09984i	−0.735451	−	0.201984i
$413$		0			0
$414$	−5.92412	−	7.77048i	−0.291155	−	0.381898i
$415$	6.60959	+	11.4481i	0.324452	+	0.561967i
$416$	−13.7373	−	34.6835i	−0.673526	−	1.70050i
$417$	2.38669	−	4.13387i	0.116877	−	0.202437i
$418$	10.7649	−	25.7614i	0.526529	−	1.26003i
$419$	4.41473	+	4.41473i	0.215673	+	0.215673i	0.806672	−	0.590999i	$-0.201266\pi$
$419$	4.41473	+	4.41473i	0.215673	+	0.215673i	−0.590999	+	0.806672i	$0.701266\pi$
$420$		0			0
$421$	−7.57494	+	7.57494i	−0.369180	+	0.369180i	−0.867178	−	0.497998i	$-0.834069\pi$
$421$	−7.57494	+	7.57494i	−0.369180	+	0.369180i	0.497998	+	0.867178i	$0.334069\pi$
$422$	14.2896	−	5.86685i	0.695608	−	0.285594i
$423$	24.7074	+	14.2648i	1.20132	+	0.693580i
$424$	−0.114544	−	0.152202i	−0.00556275	−	0.00739158i
$425$	11.2610	−	6.50155i	0.546239	−	0.315371i
$426$	1.69626	+	0.228697i	0.0821842	+	0.0110804i
$427$		0			0
$428$	−3.26574	−	5.73873i	−0.157856	−	0.277392i
$429$	5.48872	−	20.4842i	0.264998	−	0.988985i
$430$	0.510841	+	3.97592i	0.0246349	+	0.191736i
$431$	9.26979	−	16.0558i	0.446510	−	0.773378i	−0.551646	−	0.834078i	$-0.686000\pi$
$431$	9.26979	−	16.0558i	0.446510	−	0.773378i	0.998156	+	0.0607001i	$0.0193333\pi$
$432$	−9.30681	−	9.54175i	−0.447774	−	0.459078i
$433$	−7.21190			−0.346582			−0.173291	−	0.984871i	$-0.555440\pi$
$433$	−7.21190			−0.346582			−0.173291	+	0.984871i	$0.555440\pi$
$434$		0			0
$435$	1.15370	+	1.15370i	0.0553159	+	0.0553159i
$436$	−12.0281	−	7.04472i	−0.576040	−	0.337381i
$437$	2.44003	+	9.10633i	0.116723	+	0.435615i
$438$	−2.79391	+	3.61770i	−0.133498	+	0.172860i
$439$	−13.1302	+	7.58073i	−0.626671	+	0.361809i	−0.779462	−	0.626450i	$-0.784507\pi$
$439$	−13.1302	+	7.58073i	−0.626671	+	0.361809i	0.152791	+	0.988259i	$0.451174\pi$
$440$	9.23590	+	22.9006i	0.440304	+	1.09174i
$441$		0			0
$442$	6.64471	−	49.2843i	0.316056	−	2.34422i
$443$	2.89250	+	0.775043i	0.137427	+	0.0368234i	0.326877	−	0.945067i	$-0.394004\pi$
$443$	2.89250	+	0.775043i	0.137427	+	0.0368234i	−0.189450	+	0.981890i	$0.560670\pi$
$444$	−5.19012	−	5.25522i	−0.246312	−	0.249402i
$445$	−9.78027	+	2.62062i	−0.463629	+	0.124229i
$446$	3.85112	−	9.21610i	0.182356	−	0.436395i
$447$	−0.329445			−0.0155822
$448$		0			0
$449$	4.29509			0.202698			0.101349	−	0.994851i	$-0.467684\pi$
$449$	4.29509			0.202698			0.101349	+	0.994851i	$0.467684\pi$
$450$	3.52687	−	8.44013i	0.166258	−	0.397871i
$451$	−1.38776	+	0.371849i	−0.0653470	+	0.0175097i
$452$	−7.36950	−	7.46193i	−0.346632	−	0.350980i
$453$	2.11578	+	0.566922i	0.0994082	+	0.0266363i
$454$	−3.15942	+	23.4337i	−0.148279	+	1.09980i
$455$		0			0
$456$	2.25719	+	5.59676i	0.105703	+	0.262093i
$457$	−24.0610	+	13.8916i	−1.12553	+	0.649823i	−0.942806	−	0.333342i	$-0.891824\pi$
$457$	−24.0610	+	13.8916i	−1.12553	+	0.649823i	−0.182721	+	0.983165i	$0.558490\pi$
$458$	−11.4644	+	14.8447i	−0.535698	+	0.693648i
$459$	−4.59884	−	17.1631i	−0.214655	−	0.801104i
$460$	−7.19467	−	4.21385i	−0.335453	−	0.196472i
$461$	6.50912	+	6.50912i	0.303160	+	0.303160i	0.842249	−	0.539089i	$-0.181231\pi$
$461$	6.50912	+	6.50912i	0.303160	+	0.303160i	−0.539089	+	0.842249i	$0.681231\pi$
$462$		0			0
$463$	−39.1018			−1.81722			−0.908608	−	0.417650i	$-0.862854\pi$
$463$	−39.1018			−1.81722			−0.908608	+	0.417650i	$0.862854\pi$
$464$	4.95175	−	4.82982i	0.229879	−	0.224219i
$465$	0.393302	−	0.681219i	0.0182389	−	0.0315908i
$466$	−4.40436	−	34.2795i	−0.204028	−	1.58797i
$467$	−6.02544	+	22.4873i	−0.278824	+	1.04059i	0.674411	+	0.738356i	$0.264398\pi$
$467$	−6.02544	+	22.4873i	−0.278824	+	1.04059i	−0.953235	+	0.302230i	$0.902269\pi$
$468$	−17.3029	−	30.4055i	−0.799827	−	1.40550i
$469$		0			0
$470$	24.1264	+	3.25282i	1.11287	+	0.150041i
$471$	2.88474	−	1.66551i	0.132922	−	0.0767424i
$472$	−8.67538	−	11.5275i	−0.399317	−	0.530597i
$473$	8.36662	+	4.83047i	0.384698	+	0.222105i
$474$	−4.02258	+	1.65154i	−0.184763	+	0.0758579i
$475$	−6.24073	+	6.24073i	−0.286344	+	0.286344i
$476$		0			0
$477$	−0.126316	−	0.126316i	−0.00578361	−	0.00578361i
$478$	−3.42241	+	8.19015i	−0.156537	+	0.374609i
$479$	−18.6282	+	32.2650i	−0.851145	+	1.47423i	0.0290300	+	0.999579i	$0.490758\pi$
$479$	−18.6282	+	32.2650i	−0.851145	+	1.47423i	−0.880175	+	0.474649i	$0.842575\pi$
$480$	−4.89855	−	2.11905i	−0.223587	−	0.0967209i
$481$	−20.6561	−	35.7774i	−0.941836	−	1.63131i
$482$	12.8719	+	16.8837i	0.586300	+	0.769031i
$483$		0			0
$484$	36.1719	+	9.93424i	1.64418	+	0.451556i
$485$	29.0770	+	7.79117i	1.32032	+	0.353779i
$486$	−15.1436	−	11.6952i	−0.686927	−	0.530506i
$487$	33.2743	+	19.2110i	1.50780	+	0.870531i	0.999959	+	0.00908353i	$0.00289142\pi$
$487$	33.2743	+	19.2110i	1.50780	+	0.870531i	0.507846	+	0.861448i	$0.330442\pi$
$488$	−2.16508	−	17.7242i	−0.0980086	−	0.802338i
$489$		−	2.81100i		−	0.127118i
$490$		0			0
$491$	9.52330	−	9.52330i	0.429781	−	0.429781i	−0.458773	−	0.888554i	$-0.651711\pi$
$491$	9.52330	−	9.52330i	0.429781	−	0.429781i	0.888554	+	0.458773i	$0.151711\pi$
$492$	0.156942	−	0.267961i	0.00707549	−	0.0120806i
$493$	8.90689	−	2.38659i	0.401146	−	0.107487i
$494$	4.30147	+	33.4787i	0.193532	+	1.50628i
$495$	11.5784	+	20.0543i	0.520409	+	0.901374i
$496$	−2.86704	−	1.70328i	−0.128734	−	0.0764797i
$497$		0			0
$498$	−5.47618	+	4.17497i	−0.245393	+	0.187085i
$499$	3.58042	−	13.3623i	0.160282	−	0.598180i	−0.838313	−	0.545189i	$-0.816458\pi$
$499$	3.58042	−	13.3623i	0.160282	−	0.598180i	0.998595	−	0.0529909i	$-0.0168754\pi$
$500$	0.148386	−	23.8096i	0.00663601	−	1.06480i
$501$	1.89554	+	7.07425i	0.0846865	+	0.316054i
$502$	8.95769	+	21.8178i	0.399801	+	0.973777i
$503$			11.0554i			0.492938i	0.969151	+	0.246469i	$0.0792703\pi$
$503$			11.0554i			0.492938i	−0.969151	+	0.246469i	$0.920730\pi$
$504$		0			0
$505$		−	6.53038i		−	0.290598i
$506$	−18.5889	+	7.63201i	−0.826379	+	0.339284i
$507$	4.65203	+	17.3616i	0.206604	+	0.771056i
$508$	24.8454	+	25.1570i	1.10234	+	1.11616i
$509$	0.0634101	−	0.236650i	0.00281060	−	0.0104893i	−0.964506	−	0.264060i	$-0.914938\pi$
$509$	0.0634101	−	0.236650i	0.00281060	−	0.0104893i	0.967317	+	0.253571i	$0.0816050\pi$
$510$	−4.31369	−	5.65814i	−0.191014	−	0.250546i
$511$		0			0
$512$	−9.24192	+	20.6540i	−0.408439	+	0.912786i
$513$	6.03011	+	10.4445i	0.266236	+	0.461134i
$514$	28.6115	−	3.67611i	1.26200	−	0.162146i
$515$	−11.9660	+	3.20629i	−0.527286	+	0.141286i
$516$	−2.02034	+	0.527875i	−0.0889404	+	0.0232384i
$517$	41.4874	−	41.4874i	1.82461	−	1.82461i
$518$		0			0
$519$			7.71937i			0.338843i
$520$	−23.5126	−	18.3936i	−1.03109	−	0.806611i
$521$	25.9687	+	14.9930i	1.13771	+	0.656857i	0.945862	−	0.324568i	$-0.105219\pi$
$521$	25.9687	+	14.9930i	1.13771	+	0.656857i	0.191847	+	0.981425i	$0.438552\pi$
$522$	3.96495	−	5.13401i	0.173541	−	0.224710i
$523$	2.03443	+	0.545124i	0.0889594	+	0.0238366i	0.303024	−	0.952983i	$-0.402004\pi$
$523$	2.03443	+	0.545124i	0.0889594	+	0.0238366i	−0.214065	+	0.976819i	$0.568670\pi$
$524$	−5.35681	+	3.04840i	−0.234013	+	0.133170i
$525$		0			0
$526$	−26.2552	+	20.0166i	−1.14478	+	0.872766i
$527$	−2.22279	−	3.84999i	−0.0968263	−	0.167708i
$528$	−11.2190	+	6.29218i	−0.488245	+	0.273832i
$529$	−8.10740	+	14.0424i	−0.352495	+	0.610540i
$530$	−0.140648	−	0.0587724i	−0.00610935	−	0.00255291i
$531$	−9.56695	−	9.56695i	−0.415170	−	0.415170i
$532$		0			0
$533$	1.22818	−	1.22818i	0.0531983	−	0.0531983i
$534$	−2.00326	−	4.87923i	−0.0866894	−	0.211145i
$535$	−4.57591	−	2.64190i	−0.197834	−	0.114219i
$536$	30.3932	−	22.8733i	1.31279	−	0.987976i
$537$	7.18780	−	4.14988i	0.310176	−	0.179080i
$538$	5.89790	−	43.7452i	0.254277	−	1.88599i
$539$		0			0
$540$	−10.2854	−	2.82477i	−0.442611	−	0.121559i
$541$	4.42294	−	16.5066i	0.190157	−	0.709676i	−0.803310	−	0.595561i	$-0.796930\pi$
$541$	4.42294	−	16.5066i	0.190157	−	0.709676i	0.993467	−	0.114115i	$-0.0364034\pi$
$542$	2.05341	−	0.263830i	0.0882016	−	0.0113325i
$543$	2.11814	−	3.66873i	0.0908982	−	0.157440i
$544$	−24.2139	+	17.9877i	−1.03816	+	0.771214i
$545$	−11.1545			−0.477808
$546$		0			0
$547$	12.2663	+	12.2663i	0.524468	+	0.524468i	0.918918	−	0.394449i	$-0.129065\pi$
$547$	12.2663	+	12.2663i	0.524468	+	0.524468i	−0.394449	+	0.918918i	$0.629065\pi$
$548$	4.32101	+	16.5378i	0.184584	+	0.706460i
$549$	−4.33395	−	16.1745i	−0.184969	−	0.690312i
$550$	−14.8887	−	11.4984i	−0.634856	−	0.490292i
$551$	−5.42021	+	3.12936i	−0.230909	+	0.133315i
$552$	1.69957	−	3.99703i	0.0723385	−	0.170125i
$553$		0			0
$554$	−2.75972	−	0.372076i	−0.117249	−	0.0158080i
$555$	−5.70916	−	1.52977i	−0.242340	−	0.0649349i
$556$	−16.1938	−	0.100923i	−0.686770	−	0.00428007i
$557$	3.17901	−	0.851813i	0.134699	−	0.0360925i	−0.190840	−	0.981621i	$-0.561121\pi$
$557$	3.17901	−	0.851813i	0.134699	−	0.0360925i	0.325539	+	0.945529i	$0.394454\pi$
$558$	−2.88557	−	1.20579i	−0.122156	−	0.0510451i
$559$	−11.6795			−0.493992
$560$		0			0
$561$	−17.1474			−0.723964
$562$	−7.39524	−	3.09024i	−0.311950	−	0.130354i
$563$	−16.4703	+	4.41321i	−0.694141	+	0.185994i	−0.588605	−	0.808421i	$-0.700323\pi$
$563$	−16.4703	+	4.41321i	−0.694141	+	0.185994i	−0.105536	+	0.994415i	$0.533656\pi$
$564$	−0.0790327	+	12.6814i	−0.00332788	+	0.533984i
$565$	−8.10650	−	2.17213i	−0.341043	−	0.0913822i
$566$	33.0242	+	4.45245i	1.38811	+	0.187151i
$567$		0			0
$568$	−2.17191	−	5.38531i	−0.0911315	−	0.225963i
$569$	−6.92621	+	3.99885i	−0.290362	+	0.167641i	−0.638105	−	0.769949i	$-0.720281\pi$
$569$	−6.92621	+	3.99885i	−0.290362	+	0.167641i	0.347743	+	0.937590i	$0.386948\pi$
$570$	3.82208	+	2.95175i	0.160089	+	0.123635i
$571$	8.07146	+	30.1231i	0.337780	+	1.26061i	0.900824	+	0.434185i	$0.142964\pi$
$571$	8.07146	+	30.1231i	0.337780	+	1.26061i	−0.563044	+	0.826427i	$0.690370\pi$
$572$	−69.6090	+	18.1875i	−2.91050	+	0.760457i
$573$	−8.66753	−	8.66753i	−0.362091	−	0.362091i
$574$		0			0
$575$	6.35204			0.264899
$576$	−5.87430	+	20.3904i	−0.244762	+	0.849601i
$577$	21.7100	−	37.6028i	0.903798	−	1.56542i	0.0812747	−	0.996692i	$-0.474101\pi$
$577$	21.7100	−	37.6028i	0.903798	−	1.56542i	0.822523	−	0.568732i	$-0.192566\pi$
$578$	−16.0375	+	2.06056i	−0.667072	+	0.0857079i
$579$	−2.03613	+	7.59893i	−0.0846185	+	0.315801i
$580$	1.46593	−	5.33765i	0.0608695	−	0.221634i
$581$		0			0
$582$	−2.09524	+	15.5405i	−0.0868503	+	0.644176i
$583$	−0.318155	+	0.183687i	−0.0131766	+	0.00760752i
$584$	15.3551	+	2.16775i	0.635399	+	0.0897022i
$585$	−24.2446	−	13.9976i	−1.00239	−	0.578730i
$586$	12.9984	+	31.6596i	0.536960	+	1.30785i
$587$	18.2274	−	18.2274i	0.752326	−	0.752326i	−0.222587	−	0.974913i	$-0.571450\pi$
$587$	18.2274	−	18.2274i	0.752326	−	0.752326i	0.974913	+	0.222587i	$0.0714502\pi$
$588$		0			0
$589$	2.13362	+	2.13362i	0.0879143	+	0.0879143i
$590$	−10.6524	−	4.45132i	−0.438554	−	0.183258i
$591$	0.0810624	−	0.140404i	0.00333446	−	0.00577546i
$592$	−6.78667	+	24.1215i	−0.278930	+	0.991386i
$593$	−19.8757	−	34.4257i	−0.816197	−	1.41370i	−0.908465	−	0.417961i	$-0.862745\pi$
$593$	−19.8757	−	34.4257i	−0.816197	−	1.41370i	0.0922677	−	0.995734i	$-0.470588\pi$
$594$	−20.4427	+	15.5853i	−0.838774	+	0.639471i
$595$		0			0
$596$	0.552793	+	0.971396i	0.0226433	+	0.0397899i
$597$	−8.19998	−	2.19718i	−0.335603	−	0.0899246i
$598$	14.8488	−	19.2270i	0.607214	−	0.786252i
$599$	−32.5016	−	18.7648i	−1.32798	−	0.766708i	−0.342991	−	0.939339i	$-0.611440\pi$
$599$	−32.5016	−	18.7648i	−1.32798	−	0.766708i	−0.984987	+	0.172631i	$0.944773\pi$
$600$	4.03608	−	0.493022i	0.164772	−	0.0201276i
$601$		−	3.99899i		−	0.163122i	−0.996668	−	0.0815611i	$-0.974009\pi$
$601$		−	3.99899i		−	0.163122i	0.996668	−	0.0815611i	$-0.0259906\pi$
$602$		0			0
$603$	25.2240	−	25.2240i	1.02720	−	1.02720i
$604$	−1.87856	−	7.18982i	−0.0764376	−	0.292550i
$605$	28.9947	−	7.76910i	1.17880	−	0.315859i
$606$	3.37407	−	0.433513i	0.137062	−	0.0176103i
$607$	−12.1836	−	21.1026i	−0.494517	−	0.856529i	0.505463	−	0.862848i	$-0.331322\pi$
$607$	−12.1836	−	21.1026i	−0.494517	−	0.856529i	−0.999980	+	0.00631933i	$0.997988\pi$
$608$	12.7151	−	16.0466i	0.515663	−	0.650776i
$609$		0			0
$610$	−8.66311	−	11.3631i	−0.350759	−	0.460080i
$611$	−18.3584	+	68.5144i	−0.742700	+	2.77179i
$612$	−20.1265	+	19.8772i	−0.813567	+	0.803489i
$613$	−6.11872	−	22.8354i	−0.247133	−	0.922312i	−0.972299	−	0.233739i	$-0.924904\pi$
$613$	−6.11872	−	22.8354i	−0.247133	−	0.922312i	0.725167	−	0.688573i	$-0.241763\pi$
$614$	17.7583	−	7.29097i	0.716666	−	0.294240i
$615$		−	0.248501i		−	0.0100205i
$616$		0			0
$617$			2.64202i			0.106364i	0.998585	+	0.0531819i	$0.0169363\pi$
$617$			2.64202i			0.106364i	−0.998585	+	0.0531819i	$0.983064\pi$
$618$	−2.45095	−	5.96967i	−0.0985919	−	0.240136i
$619$	−9.87436	−	36.8516i	−0.396884	−	1.48119i	−0.818548	−	0.574439i	$-0.805220\pi$
$619$	−9.87436	−	36.8516i	−0.396884	−	1.48119i	0.421664	−	0.906752i	$-0.361446\pi$
$620$	−2.66857	−	0.0166310i	−0.107172	−	0.000667916i
$621$	2.24654	−	8.38421i	0.0901507	−	0.336447i
$622$	−21.5782	+	16.4510i	−0.865207	+	0.659623i
$623$		0			0
$624$	7.94260	−	13.3693i	0.317959	−	0.535202i
$625$	−3.43035	−	5.94155i	−0.137214	−	0.237662i
$626$	−0.908252	−	7.06901i	−0.0363011	−	0.282534i
$627$	11.2421	−	3.01230i	0.448964	−	0.120300i
$628$	−9.75133	−	5.71125i	−0.389120	−	0.227904i
$629$	−23.6204	+	23.6204i	−0.941805	+	0.941805i
$630$		0			0
$631$		−	18.9710i		−	0.755223i	−0.925964	−	0.377611i	$-0.876746\pi$
$631$		−	18.9710i		−	0.755223i	0.925964	−	0.377611i	$-0.123254\pi$
$632$	11.6194	+	9.08971i	0.462195	+	0.361569i
$633$	5.57650	+	3.21960i	0.221646	+	0.127967i
$634$	−8.74708	−	6.75528i	−0.347391	−	0.268286i
$635$	27.3301	+	7.32308i	1.08456	+	0.290607i
$636$	0.0210293	−	0.0765705i	0.000833867	−	0.00303622i
$637$		0			0
$638$	−8.08807	−	10.6089i	−0.320210	−	0.420009i
$639$	−2.72277	−	4.71597i	−0.107711	−	0.186561i
$640$	1.97134	+	17.9994i	0.0779239	+	0.711490i
$641$	−15.6881	+	27.1726i	−0.619643	+	1.07325i	0.369908	+	0.929068i	$0.379389\pi$
$641$	−15.6881	+	27.1726i	−0.619643	+	1.07325i	−0.989551	+	0.144184i	$0.953944\pi$
$642$	1.06123	−	2.53963i	0.0418835	−	0.100231i
$643$	−13.5690	−	13.5690i	−0.535110	−	0.535110i	0.386978	−	0.922089i	$-0.373519\pi$
$643$	−13.5690	−	13.5690i	−0.535110	−	0.535110i	−0.922089	+	0.386978i	$0.873519\pi$
$644$		0			0
$645$	−1.18158	+	1.18158i	−0.0465245	+	0.0465245i
$646$	25.2477	−	10.3659i	0.993356	−	0.407840i
$647$	−34.3455	−	19.8294i	−1.35026	−	0.779573i	−0.361974	−	0.932188i	$-0.617897\pi$
$647$	−34.3455	−	19.8294i	−1.35026	−	0.779573i	−0.988286	+	0.152615i	$0.951230\pi$
$648$	−2.36951	+	16.7842i	−0.0930831	+	0.659347i
$649$	−24.0965	+	13.9121i	−0.945871	+	0.546099i
$650$	22.5386	+	3.03874i	0.884035	+	0.119189i
$651$		0			0
$652$	−8.28845	+	4.71671i	−0.324601	+	0.184721i
$653$	1.08587	−	4.05251i	0.0424933	−	0.158587i	−0.941419	−	0.337239i	$-0.890507\pi$
$653$	1.08587	−	4.05251i	0.0424933	−	0.158587i	0.983912	+	0.178652i	$0.0571736\pi$
$654$	−0.740485	−	5.76326i	−0.0289552	−	0.225361i
$655$	−2.46608	+	4.27138i	−0.0963577	+	0.166896i
$656$	−1.05345	−	0.0131310i	−0.0411301	−	0.000512680i
$657$	14.5426			0.567362
$658$		0			0
$659$	−19.5078	−	19.5078i	−0.759915	−	0.759915i	0.216391	−	0.976307i	$-0.430571\pi$
$659$	−19.5078	−	19.5078i	−0.759915	−	0.759915i	−0.976307	+	0.216391i	$0.930571\pi$
$660$	−5.20213	+	8.88205i	−0.202492	+	0.345733i
$661$	−4.38283	−	16.3569i	−0.170472	−	0.636212i	−0.997279	−	0.0737248i	$-0.976511\pi$
$661$	−4.38283	−	16.3569i	−0.170472	−	0.636212i	0.826806	−	0.562487i	$-0.190155\pi$
$662$	18.0331	−	23.3501i	0.700875	−	0.907529i
$663$	17.9529	−	10.3651i	0.697234	−	0.402548i
$664$	21.4990	+	9.14155i	0.834323	+	0.354761i
$665$		0			0
$666$	−3.13983	+	23.2884i	−0.121666	+	0.902407i
$667$	4.35104	+	1.16586i	0.168473	+	0.0451422i
$668$	17.6784	−	17.4594i	0.683997	−	0.675524i
$669$	4.02182	−	1.07764i	0.155493	−	0.0416641i
$670$	11.7363	−	28.0860i	0.453411	−	1.08506i
$671$	−34.4368			−1.32942
$672$		0			0
$673$	−30.9400			−1.19265			−0.596324	−	0.802744i	$-0.703373\pi$
$673$	−30.9400			−1.19265			−0.596324	+	0.802744i	$0.703373\pi$
$674$	9.11197	−	21.8058i	0.350980	−	0.839929i
$675$	7.84897	−	2.10313i	0.302107	−	0.0809493i
$676$	43.3862	−	42.8488i	1.66870	−	1.64803i
$677$	−0.0168505	−	0.00451508i	−0.000647617	−	0.000173529i	0.258495	−	0.966013i	$-0.416773\pi$
$677$	−0.0168505	−	0.00451508i	−0.000647617	−	0.000173529i	−0.259143	+	0.965839i	$0.583440\pi$
$678$	0.584138	−	4.33260i	0.0224337	−	0.166393i
$679$		0			0
$680$	−9.44530	+	22.2133i	−0.362211	+	0.851843i
$681$	−8.53625	+	4.92841i	−0.327110	+	0.188857i
$682$	−3.93114	+	5.09024i	−0.150531	+	0.194915i
$683$	−5.17376	−	19.3087i	−0.197969	−	0.738829i	−0.991478	−	0.130271i	$-0.958415\pi$
$683$	−5.17376	−	19.3087i	−0.197969	−	0.738829i	0.793510	−	0.608557i	$-0.208251\pi$
$684$	9.70336	−	16.5674i	0.371017	−	0.633471i
$685$	9.67199	+	9.67199i	0.369548	+	0.369548i
$686$		0			0
$687$	−7.81864			−0.298300
$688$	4.94651	+	5.07138i	0.188584	+	0.193345i
$689$	0.222067	−	0.384631i	0.00846008	−	0.0146533i
$690$	−0.442926	−	3.44733i	−0.0168619	−	0.131238i
$691$	−11.5428	+	43.0783i	−0.439109	+	1.63878i	0.291929	+	0.956440i	$0.405703\pi$
$691$	−11.5428	+	43.0783i	−0.439109	+	1.63878i	−0.731038	+	0.682337i	$0.760964\pi$
$692$	22.7612	−	12.9527i	0.865250	−	0.492388i
$693$		0			0
$694$	11.0584	+	1.49094i	0.419773	+	0.0565954i
$695$	−11.2228	+	6.47948i	−0.425705	+	0.245781i
$696$	2.85513	+	0.403072i	0.108224	+	0.0152784i
$697$	−1.21627	−	0.702215i	−0.0460696	−	0.0265983i
$698$	33.2634	−	13.6569i	1.25904	−	0.516920i
$699$	10.1873	−	10.1873i	0.385319	−	0.385319i
$700$		0			0
$701$	−16.8654	−	16.8654i	−0.636998	−	0.636998i	0.312816	−	0.949814i	$-0.398728\pi$
$701$	−16.8654	−	16.8654i	−0.636998	−	0.636998i	−0.949814	+	0.312816i	$0.898728\pi$
$702$	11.9822	−	28.6745i	0.452238	−	1.08225i
$703$	11.3364	−	19.6352i	0.427560	−	0.740556i
$704$	37.3779	+	22.5222i	1.40873	+	0.848838i
$705$	5.07410	+	8.78859i	0.191102	+	0.330998i
$706$	21.4627	+	28.1520i	0.807761	+	1.05951i
$707$		0			0
$708$	1.59273	−	5.79933i	0.0598583	−	0.217952i
$709$	−29.5530	−	7.91870i	−1.10989	−	0.297393i	−0.343102	−	0.939298i	$-0.611478\pi$
$709$	−29.5530	−	7.91870i	−1.10989	−	0.297393i	−0.766784	+	0.641905i	$0.778144\pi$
$710$	−3.67768	−	2.84023i	−0.138021	−	0.106592i
$711$	11.9811	+	6.91731i	0.449328	+	0.259419i
$712$	−11.0255	+	14.0939i	−0.413196	+	0.528190i
$713$		−	2.17168i		−	0.0813300i
$714$		0			0
$715$	−40.7102	+	40.7102i	−1.52248	+	1.52248i
$716$	−24.2970	−	14.2305i	−0.908022	−	0.531819i
$717$	−3.57411	+	0.957679i	−0.133477	+	0.0357652i
$718$	−3.24237	−	25.2356i	−0.121004	−	0.941785i
$719$	20.1849	+	34.9613i	0.752769	+	1.30383i	0.946476	+	0.322775i	$0.104616\pi$
$719$	20.1849	+	34.9613i	0.752769	+	1.30383i	−0.193706	+	0.981060i	$0.562051\pi$
$720$	4.19012	+	16.4555i	0.156157	+	0.613260i
$721$		0			0
$722$	6.63661	−	5.05967i	0.246989	−	0.188302i
$723$	−2.29058	+	8.54857i	−0.0851876	+	0.317925i
$724$	−14.3717	−	0.0895667i	−0.534119	−	0.00332872i
$725$	1.09143	+	4.07327i	0.0405347	+	0.151277i
$726$	5.93887	+	14.4650i	0.220412	+	0.536847i
$727$			3.43634i			0.127447i	0.997968	+	0.0637234i	$0.0202976\pi$
$727$			3.43634i			0.127447i	−0.997968	+	0.0637234i	$0.979702\pi$
$728$		0			0
$729$			10.0029i			0.370476i
$730$	11.4795	−	4.71313i	0.424877	−	0.174441i
$731$	2.44425	+	9.12207i	0.0904039	+	0.337392i
$732$	5.29593	−	5.23033i	0.195743	−	0.193319i
$733$	10.0069	−	37.3462i	0.369613	−	1.37941i	−0.491446	−	0.870908i	$-0.663531\pi$
$733$	10.0069	−	37.3462i	0.369613	−	1.37941i	0.861059	−	0.508506i	$-0.169802\pi$
$734$	−8.83805	−	11.5926i	−0.326218	−	0.427890i
$735$		0			0
$736$	−14.6373	+	1.69549i	−0.539540	+	0.0624967i
$737$	−36.6804	−	63.5323i	−1.35114	−	2.34024i
$738$	−0.979930	+	0.125905i	−0.0360717	+	0.00463463i
$739$	38.7393	−	10.3802i	1.42505	−	0.381841i	0.537777	−	0.843087i	$-0.319264\pi$
$739$	38.7393	−	10.3802i	1.42505	−	0.381841i	0.887272	+	0.461247i	$0.152598\pi$
$740$	5.06905	+	19.4008i	0.186342	+	0.713187i
$741$	−9.94932	+	9.94932i	−0.365497	+	0.365497i
$742$		0			0
$743$		−	34.1733i		−	1.25370i	−0.779141	−	0.626848i	$-0.784344\pi$
$743$		−	34.1733i		−	1.25370i	0.779141	−	0.626848i	$-0.215656\pi$
$744$	−0.168558	−	1.37988i	−0.00617963	−	0.0505889i
$745$	0.774565	+	0.447195i	0.0283779	+	0.0163840i
$746$	−19.6273	+	25.4144i	−0.718605	+	0.930487i
$747$	21.1619	+	5.67032i	0.774274	+	0.207466i
$748$	28.7725	+	50.5605i	1.05203	+	1.84867i
$749$		0			0
$750$	7.89309	−	6.01760i	0.288215	−	0.219732i
$751$	−4.27895	−	7.41136i	−0.156141	−	0.270445i	0.777333	−	0.629090i	$-0.216572\pi$
$751$	−4.27895	−	7.41136i	−0.156141	−	0.270445i	−0.933474	+	0.358645i	$0.883239\pi$
$752$	37.5248	−	21.0457i	1.36839	−	0.767459i
$753$	−4.91577	+	8.51437i	−0.179141	+	0.310281i
$754$	14.8808	+	6.21822i	0.541926	+	0.226454i
$755$	−4.20490	−	4.20490i	−0.153032	−	0.153032i
$756$		0			0
$757$	−25.0492	+	25.0492i	−0.910428	+	0.910428i	−0.996306	−	0.0858779i	$-0.972631\pi$
$757$	−25.0492	+	25.0492i	−0.910428	+	0.910428i	0.0858779	+	0.996306i	$0.472631\pi$
$758$	−11.9958	−	29.2177i	−0.435708	−	1.06123i
$759$	−7.25431	−	4.18827i	−0.263315	−	0.152025i
$760$	2.29022	−	16.2226i	0.0830751	−	0.588456i
$761$	−24.6145	+	14.2112i	−0.892274	+	0.515155i	−0.874686	−	0.484691i	$-0.838932\pi$
$761$	−24.6145	+	14.2112i	−0.892274	+	0.515155i	−0.0175884	+	0.999845i	$0.505599\pi$
$762$	−1.96935	+	14.6069i	−0.0713421	+	0.529151i
$763$		0			0
$764$	−11.0132	+	40.1006i	−0.398445	+	1.45079i
$765$	−5.85873	+	21.8651i	−0.211823	+	0.790533i
$766$	25.7578	−	3.30946i	0.930669	−	0.119576i
$767$	16.8190	−	29.1314i	0.607299	−	1.05187i
$768$	−9.16895	+	2.21341i	−0.330856	+	0.0798696i
$769$	12.0189			0.433413			0.216707	−	0.976237i	$-0.430469\pi$
$769$	12.0189			0.433413			0.216707	+	0.976237i	$0.430469\pi$
$770$		0			0
$771$	8.50286	+	8.50286i	0.306223	+	0.306223i
$772$	25.8226	−	6.74694i	0.929375	−	0.242828i
$773$	−1.85543	−	6.92456i	−0.0667352	−	0.249059i	0.924497	−	0.381189i	$-0.124485\pi$
$773$	−1.85543	−	6.92456i	−0.0667352	−	0.249059i	−0.991232	+	0.132130i	$0.957818\pi$
$774$	5.25805	+	4.06074i	0.188997	+	0.145960i
$775$	1.76066	−	1.01652i	0.0632449	−	0.0365145i
$776$	49.3382	−	19.8983i	1.77114	−	0.714306i
$777$		0			0
$778$	27.6604	+	3.72929i	0.991675	+	0.133701i
$779$	0.920763	+	0.246718i	0.0329897	+	0.00883957i
$780$	0.0775521	−	12.4438i	0.00277681	−	0.445561i
$781$	−10.8173	+	2.89849i	−0.387074	+	0.103716i
$782$	−18.1244	−	7.57362i	−0.648127	−	0.270832i
$783$	5.76241			0.205932
$784$		0			0
$785$	−9.04315			−0.322764
$786$	−2.37061	−	0.990606i	−0.0845570	−	0.0353337i
$787$	23.1726	−	6.20908i	0.826014	−	0.221330i	0.179040	−	0.983842i	$-0.442701\pi$
$787$	23.1726	−	6.20908i	0.826014	−	0.221330i	0.646974	+	0.762512i	$0.276034\pi$
$788$	−0.550012	−	0.00342776i	−0.0195934	−	0.000122109i
$789$	−13.2936	−	3.56200i	−0.473263	−	0.126810i
$790$	11.6994	+	1.57736i	0.416246	+	0.0561199i
$791$		0			0
$792$	37.6609	+	16.0137i	1.33822	+	0.569023i
$793$	36.0546	−	20.8161i	1.28033	−	0.739202i
$794$	−1.78575	−	1.37912i	−0.0633740	−	0.0489431i
$795$	−0.0164460	−	0.0613774i	−0.000583281	−	0.00217683i
$796$	7.28060	+	27.8651i	0.258054	+	0.987651i
$797$	−35.5609	−	35.5609i	−1.25963	−	1.25963i	−0.951268	−	0.308366i	$-0.900218\pi$
$797$	−35.5609	−	35.5609i	−1.25963	−	1.25963i	−0.308366	−	0.951268i	$-0.599782\pi$
$798$		0			0
$799$	57.3537			2.02903
$800$	−8.22606	−	11.0734i	−0.290835	−	0.391505i
$801$	−8.39042	+	14.5326i	−0.296461	+	0.513486i
$802$	20.1243	−	2.58564i	0.710612	−	0.0913021i
$803$	7.74059	−	28.8883i	0.273159	−	1.01944i
$804$	15.2904	+	4.19934i	0.539249	+	0.148099i
$805$		0			0
$806$	1.03890	−	7.70563i	0.0365938	−	0.271419i
$807$	15.9352	−	9.20019i	0.560945	−	0.323862i
$808$	−6.93977	−	9.22130i	−0.244140	−	0.324404i
$809$	−10.2729	−	5.93106i	−0.361176	−	0.208525i	0.308421	−	0.951250i	$-0.400200\pi$
$809$	−10.2729	−	5.93106i	−0.361176	−	0.208525i	−0.669596	+	0.742725i	$0.733533\pi$
$810$	5.15179	+	12.5480i	0.181015	+	0.440890i
$811$	−20.4859	+	20.4859i	−0.719357	+	0.719357i	−0.968473	−	0.249117i	$-0.919860\pi$
$811$	−20.4859	+	20.4859i	−0.719357	+	0.719357i	0.249117	+	0.968473i	$0.419860\pi$
$812$		0			0
$813$	0.610240	+	0.610240i	0.0214020	+	0.0214020i
$814$	44.5901	+	18.6328i	1.56288	+	0.653080i
$815$	−3.81570	+	6.60898i	−0.133658	+	0.231503i
$816$	−12.1041	−	3.40552i	−0.423727	−	0.119217i
$817$	−3.20496	−	5.55116i	−0.112127	−	0.194210i
$818$	−44.1445	+	33.6552i	−1.54347	+	1.17673i
$819$		0			0
$820$	−0.732724	+	0.416972i	−0.0255878	+	0.0145613i
$821$	39.7113	+	10.6406i	1.38594	+	0.371360i	0.873274	−	0.487230i	$-0.161993\pi$
$821$	39.7113	+	10.6406i	1.38594	+	0.371360i	0.512662	+	0.858591i	$0.328659\pi$
$822$	−4.35519	+	5.63933i	−0.151905	+	0.196694i
$823$	−44.4787	−	25.6798i	−1.55043	−	0.895140i	−0.998107	−	0.0615092i	$-0.980409\pi$
$823$	−44.4787	−	25.6798i	−1.55043	−	0.895140i	−0.552322	−	0.833631i	$-0.686258\pi$
$824$	−13.4895	+	17.2437i	−0.469928	+	0.600711i
$825$		−	7.84180i		−	0.273016i
$826$		0			0
$827$	−24.4414	+	24.4414i	−0.849912	+	0.849912i	−0.990122	−	0.140210i	$-0.955222\pi$
$827$	−24.4414	+	24.4414i	−0.849912	+	0.849912i	0.140210	+	0.990122i	$0.455222\pi$
$828$	−13.3697	+	3.49324i	−0.464629	+	0.121399i
$829$	−15.5537	+	4.16759i	−0.540201	+	0.144746i	−0.518595	−	0.855020i	$-0.673545\pi$
$829$	−15.5537	+	4.16759i	−0.540201	+	0.144746i	−0.0216062	+	0.999767i	$0.506878\pi$
$830$	18.5423	−	2.38239i	0.643613	−	0.0826938i
$831$	−0.580404	−	1.00529i	−0.0201340	−	0.0348731i
$832$	−52.7479	−	0.986303i	−1.82870	−	0.0341939i
$833$		0			0
$834$	−4.09279	−	5.36838i	−0.141722	−	0.185892i
$835$	5.14608	−	19.2054i	0.178087	−	0.664632i
$836$	−27.7456	−	28.0936i	−0.959602	−	0.971638i
$837$	−0.719031	−	2.68346i	−0.0248533	−	0.0927539i
$838$	8.16784	−	3.35345i	0.282153	−	0.115843i
$839$		−	35.2906i		−	1.21837i	−0.793029	−	0.609184i	$-0.791497\pi$
$839$		−	35.2906i		−	1.21837i	0.793029	−	0.609184i	$-0.208503\pi$
$840$		0			0
$841$		−	26.0096i		−	0.896881i
$842$	5.75397	+	14.0147i	0.198295	+	0.482977i
$843$	−0.864730	−	3.22722i	−0.0297829	−	0.111151i
$844$	0.136142	−	21.8451i	0.00468621	−	0.751939i
$845$	12.6295	−	47.1339i	0.434468	−	1.62146i
$846$	32.0858	−	24.4619i	1.10313	−	0.841016i
$847$		0			0
$848$	−0.261061	+	0.0664749i	−0.00896486	+	0.00228276i
$849$	6.94542	+	12.0298i	0.238366	+	0.412862i
$850$	−2.34344	−	18.2392i	−0.0803794	−	0.625600i
$851$	−15.7620	+	4.22342i	−0.540315	+	0.144777i
$852$	1.22333	−	2.08870i	0.0419107	−	0.0715578i
$853$	6.93449	−	6.93449i	0.237432	−	0.237432i	−0.578354	−	0.815786i	$-0.696305\pi$
$853$	6.93449	−	6.93449i	0.237432	−	0.237432i	0.815786	+	0.578354i	$0.196305\pi$
$854$		0			0
$855$		−	15.3642i		−	0.525445i
$856$	−9.26899	+	1.13224i	−0.316808	+	0.0386992i
$857$	25.2698	+	14.5895i	0.863200	+	0.498369i	0.865083	−	0.501630i	$-0.167266\pi$
$857$	25.2698	+	14.5895i	0.863200	+	0.498369i	−0.00188263	+	0.999998i	$0.500599\pi$
$858$	−23.7364	−	18.3314i	−0.810347	−	0.625822i
$859$	−2.22135	−	0.595210i	−0.0757916	−	0.0203083i	0.220724	−	0.975336i	$-0.429158\pi$
$859$	−2.22135	−	0.595210i	−0.0757916	−	0.0203083i	−0.296516	+	0.955028i	$0.595825\pi$
$860$	5.46660	+	1.50135i	0.186409	+	0.0511955i
$861$		0			0
$862$	−15.8962	−	20.8505i	−0.541426	−	0.710171i
$863$	16.8529	+	29.1902i	0.573681	+	0.993645i	0.996184	+	0.0872830i	$0.0278184\pi$
$863$	16.8529	+	29.1902i	0.573681	+	0.993645i	−0.422503	+	0.906362i	$0.638848\pi$
$864$	−17.5254	+	6.94140i	−0.596227	+	0.236151i
$865$	10.4784	−	18.1491i	0.356277	−	0.617090i
$866$	−3.93239	+	9.41059i	−0.133628	+	0.319785i
$867$	−4.76608	−	4.76608i	−0.161864	−	0.161864i
$868$		0			0
$869$	20.1181	−	20.1181i	0.682460	−	0.682460i
$870$	2.13451	−	0.876360i	0.0723666	−	0.0297114i
$871$	76.8070	+	44.3445i	2.60251	+	1.50256i
$872$	−15.7509	+	11.8538i	−0.533394	+	0.401421i
$873$	43.2060	−	24.9450i	1.46230	−	0.844260i
$874$	13.2130	+	1.78143i	0.446938	+	0.0602579i
$875$		0			0
$876$	3.19720	+	5.61829i	0.108024	+	0.189824i
$877$	−9.29142	+	34.6760i	−0.313749	+	1.17093i	0.611400	+	0.791322i	$0.290607\pi$
$877$	−9.29142	+	34.6760i	−0.313749	+	1.17093i	−0.925149	+	0.379605i	$0.876060\pi$
$878$	2.73243	+	21.2667i	0.0922150	+	0.717717i
$879$	−7.13324	+	12.3551i	−0.240598	+	0.416728i
$880$	34.9183	+	0.435251i	1.17710	+	0.0146723i
$881$	−13.0482			−0.439606			−0.219803	−	0.975544i	$-0.570541\pi$
$881$	−13.0482			−0.439606			−0.219803	+	0.975544i	$0.570541\pi$
$882$		0			0
$883$	−24.2895	−	24.2895i	−0.817407	−	0.817407i	0.168325	−	0.985732i	$-0.446164\pi$
$883$	−24.2895	−	24.2895i	−0.817407	−	0.817407i	−0.985732	+	0.168325i	$0.946164\pi$
$884$	−60.6865	−	35.5435i	−2.04111	−	1.19546i
$885$	−1.24560	−	4.64863i	−0.0418702	−	0.156262i
$886$	2.58851	−	3.35173i	0.0869627	−	0.112604i
$887$	17.1896	−	9.92445i	0.577172	−	0.333230i	−0.182837	−	0.983143i	$-0.558528\pi$
$887$	17.1896	−	9.92445i	0.577172	−	0.333230i	0.760009	+	0.649913i	$0.225195\pi$
$888$	−9.68736	+	3.90695i	−0.325087	+	0.131109i
$889$		0			0
$890$	−1.91327	+	14.1909i	−0.0641331	+	0.475680i
$891$	31.5770	+	8.46102i	1.05787	+	0.283455i
$892$	−9.92593	−	10.0504i	−0.332345	−	0.336513i
$893$	−37.6018	+	10.0754i	−1.25830	+	0.337160i
$894$	−0.179635	+	0.429884i	−0.00600789	+	0.0143775i
$895$	−22.5325			−0.753178
$896$		0			0
$897$	10.1268			0.338124
$898$	2.34196	−	5.60454i	0.0781523	−	0.187026i
$899$	1.39260	−	0.373145i	0.0464457	−	0.0124451i
$900$	−9.09019	−	9.20421i	−0.303006	−	0.306807i
$901$	−0.346882	−	0.0929467i	−0.0115563	−	0.00309650i
$902$	−0.271481	+	2.01360i	−0.00903935	+	0.0670456i
$903$		0			0
$904$	−13.7552	+	5.54751i	−0.457491	+	0.184508i
$905$	−9.96000	+	5.75041i	−0.331082	+	0.191150i
$906$	1.89342	−	2.45170i	0.0629047	−	0.0814523i
$907$	−14.5025	−	54.1242i	−0.481549	−	1.79716i	−0.595122	−	0.803635i	$-0.702896\pi$
$907$	−14.5025	−	54.1242i	−0.481549	−	1.79716i	0.113573	−	0.993530i	$-0.463770\pi$
$908$	28.8552	+	16.9002i	0.957594	+	0.560853i
$909$	−7.65297	−	7.65297i	−0.253833	−	0.253833i
$910$		0			0
$911$	11.6260			0.385188			0.192594	−	0.981279i	$-0.438310\pi$
$911$	11.6260			0.385188			0.192594	+	0.981279i	$0.438310\pi$
$912$	8.53382	+	0.106373i	0.282583	+	0.00352235i
$913$	22.5277	−	39.0191i	0.745557	−	1.29134i
$914$	5.00715	+	38.9711i	0.165622	+	1.28905i
$915$	1.54162	−	5.75339i	0.0509643	−	0.190201i
$916$	13.1193	+	23.0539i	0.433474	+	0.761722i
$917$		0			0
$918$	−24.9032	−	3.35754i	−0.821928	−	0.110815i
$919$	−36.4646	+	21.0528i	−1.20285	+	0.694468i	−0.961189	−	0.275891i	$-0.911027\pi$
$919$	−36.4646	+	21.0528i	−1.20285	+	0.694468i	−0.241666	+	0.970360i	$0.577694\pi$
$920$	−9.42153	+	7.09045i	−0.310619	+	0.233765i
$921$	6.93014	+	4.00112i	0.228356	+	0.131841i
$922$	12.0427	−	4.94436i	0.396607	−	0.162834i
$923$	9.57342	−	9.57342i	0.315113	−	0.315113i
$924$		0			0
$925$	−10.8020	−	10.8020i	−0.355167	−	0.355167i
$926$	−21.3208	+	51.0228i	−0.700646	+	1.67671i
$927$	−10.2656	+	17.7805i	−0.337165	+	0.583988i
$928$	−3.60228	−	9.09492i	−0.118251	−	0.298556i
$929$	15.1619	+	26.2612i	0.497447	+	0.861603i	0.999996	−	0.00294569i	$-0.000937644\pi$
$929$	15.1619	+	26.2612i	0.497447	+	0.861603i	−0.502549	+	0.864549i	$0.667604\pi$
$930$	−0.674449	−	0.884653i	−0.0221160	−	0.0290089i
$931$		0			0
$932$	−47.1319	−	12.9443i	−1.54386	−	0.424005i
$933$	−10.9255	−	2.92748i	−0.357685	−	0.0958414i
$934$	26.0575	+	20.1239i	0.852628	+	0.658475i
$935$	40.3156	+	23.2762i	1.31846	+	0.761213i
$936$	−49.1100	+	5.99896i	−1.60521	+	0.196082i
$937$		−	17.7772i		−	0.580757i	−0.956912	−	0.290378i	$-0.906219\pi$
$937$		−	17.7772i		−	0.580757i	0.956912	−	0.290378i	$-0.0937812\pi$
$938$		0			0
$939$	2.10079	−	2.10079i	0.0685567	−	0.0685567i
$940$	17.3998	−	29.7082i	0.567519	−	0.968975i
$941$	−28.9045	+	7.74494i	−0.942260	+	0.252478i	−0.697075	−	0.716998i	$-0.745516\pi$
$941$	−28.9045	+	7.74494i	−0.942260	+	0.252478i	−0.245186	+	0.969476i	$0.578849\pi$
$942$	−0.600321	−	4.67235i	−0.0195595	−	0.152233i
$943$	−0.343034	−	0.594153i	−0.0111707	−	0.0193483i
$944$	−19.7723	+	5.03470i	−0.643533	+	0.163865i
$945$		0			0
$946$	10.8652	−	8.28347i	0.353257	−	0.269319i
$947$	4.33732	−	16.1871i	0.140944	−	0.526010i	−0.858959	−	0.512045i	$-0.828888\pi$
$947$	4.33732	−	16.1871i	0.140944	−	0.526010i	0.999902	−	0.0139648i	$-0.00444527\pi$
$948$	−0.0383246	+	6.14948i	−0.00124472	+	0.199726i
$949$	9.35794	+	34.9243i	0.303772	+	1.13369i
$950$	4.74049	+	11.5462i	0.153802	+	0.374608i
$951$		−	4.60704i		−	0.149394i
$952$		0			0
$953$		−	14.1855i		−	0.459513i	−0.973248	−	0.229757i	$-0.926207\pi$
$953$		−	14.1855i		−	0.459513i	0.973248	−	0.229757i	$-0.0737930\pi$
$954$	−0.233701	+	0.0959502i	−0.00756636	+	0.00310650i
$955$	8.61292	+	32.1438i	0.278707	+	1.04015i
$956$	8.82096	+	8.93160i	0.285290	+	0.288869i
$957$	1.43929	−	5.37149i	0.0465255	−	0.173636i
$958$	31.9444	+	41.9004i	1.03208	+	1.35374i
$959$		0			0
$960$	−5.43609	+	5.23653i	−0.175449	+	0.169008i
$961$	15.1525	+	26.2448i	0.488789	+	0.846608i
$962$	−57.9479	+	7.44536i	−1.86831	+	0.240048i
$963$	−8.45857	+	2.26647i	−0.272574	+	0.0730359i
$964$	29.0496	−	7.59010i	0.935625	−	0.244461i
$965$	15.1021	−	15.1021i	0.486154	−	0.486154i
$966$		0			0
$967$			8.54873i			0.274909i	0.990508	+	0.137454i	$0.0438920\pi$
$967$			8.54873i			0.274909i	−0.990508	+	0.137454i	$0.956108\pi$
$968$	32.6861	−	41.7828i	1.05057	−	1.34295i
$969$	9.85287	+	5.68855i	0.316520	+	0.182743i
$970$	26.0212	−	33.6935i	0.835489	−	1.08183i
$971$	−34.8458	−	9.33690i	−1.11825	−	0.299635i	−0.348077	−	0.937466i	$-0.613165\pi$
$971$	−34.8458	−	9.33690i	−1.11825	−	0.299635i	−0.770177	+	0.637831i	$0.779832\pi$
$972$	−23.5180	+	13.3834i	−0.754341	+	0.429273i
$973$		0			0
$974$	43.2111	−	32.9437i	1.38457	−	1.05558i
$975$	4.74015	+	8.21018i	0.151806	+	0.262936i
$976$	−24.3084	−	6.83925i	−0.778091	−	0.218919i
$977$	−6.61877	+	11.4640i	−0.211753	+	0.366767i	−0.952263	−	0.305278i	$-0.901251\pi$
$977$	−6.61877	+	11.4640i	−0.211753	+	0.366767i	0.740510	+	0.672045i	$0.234584\pi$
$978$	−3.66799	−	1.53274i	−0.117289	−	0.0490115i
$979$	24.4025	+	24.4025i	0.779906	+	0.779906i
$980$		0			0
$981$	−13.0721	+	13.0721i	−0.417359	+	0.417359i
$982$	−7.23395	−	17.6194i	−0.230845	−	0.562257i
$983$	−17.2541	−	9.96166i	−0.550320	−	0.317727i	0.198931	−	0.980014i	$-0.436253\pi$
$983$	−17.2541	−	9.96166i	−0.550320	−	0.317727i	−0.749251	+	0.662286i	$0.769586\pi$
$984$	−0.264079	−	0.350899i	−0.00841854	−	0.0111862i
$985$	−0.381174	+	0.220071i	−0.0121452	+	0.00701205i
$986$	1.74242	−	12.9237i	0.0554899	−	0.411573i
$987$		0			0
$988$	46.0308	+	12.6419i	1.46444	+	0.402193i
$989$	−1.19402	+	4.45615i	−0.0379677	+	0.141697i
$990$	32.4815	−	4.17335i	1.03233	−	0.132638i
$991$	−27.1797	+	47.0767i	−0.863392	+	1.49544i	0.00524220	+	0.999986i	$0.498331\pi$
$991$	−27.1797	+	47.0767i	−0.863392	+	1.49544i	−0.868635	+	0.495453i	$0.835002\pi$
$992$	−3.78586	+	2.81238i	−0.120201	+	0.0892931i
$993$	12.2984			0.390278
$994$		0			0
$995$	16.2966	+	16.2966i	0.516638	+	0.516638i
$996$	2.46183	+	9.42216i	0.0780061	+	0.298553i
$997$	−5.27193	−	19.6751i	−0.166964	−	0.623117i	−0.997782	−	0.0665726i	$-0.978794\pi$
$997$	−5.27193	−	19.6751i	−0.166964	−	0.623117i	0.830818	−	0.556544i	$-0.187873\pi$
$998$	−15.4838	−	11.9580i	−0.490132	−	0.378524i
$999$	−18.0782	+	10.4374i	−0.571968	+	0.330226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.m.557.4		24
7.2	even	3	inner	784.2.x.m.765.1		24
7.3	odd	6		112.2.m.d.29.5	✓	12
7.4	even	3		784.2.m.h.589.5		12
7.5	odd	6		784.2.x.l.765.1		24
7.6	odd	2		784.2.x.l.557.4		24
16.5	even	4	inner	784.2.x.m.165.1		24
28.3	even	6		448.2.m.d.337.4		12
56.3	even	6		896.2.m.h.673.3		12
56.45	odd	6		896.2.m.g.673.4		12
112.3	even	12		896.2.m.h.225.3		12
112.5	odd	12		784.2.x.l.373.4		24
112.37	even	12	inner	784.2.x.m.373.4		24
112.45	odd	12		896.2.m.g.225.4		12
112.53	even	12		784.2.m.h.197.5		12
112.59	even	12		448.2.m.d.113.4		12
112.69	odd	4		784.2.x.l.165.1		24
112.101	odd	12		112.2.m.d.85.5	yes	12
224.59	even	24		7168.2.a.bi.1.7		12
224.101	odd	24		7168.2.a.bj.1.6		12
224.171	even	24		7168.2.a.bi.1.6		12
224.213	odd	24		7168.2.a.bj.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.5	✓	12	7.3	odd	6
112.2.m.d.85.5	yes	12	112.101	odd	12
448.2.m.d.113.4		12	112.59	even	12
448.2.m.d.337.4		12	28.3	even	6
784.2.m.h.197.5		12	112.53	even	12
784.2.m.h.589.5		12	7.4	even	3
784.2.x.l.165.1		24	112.69	odd	4
784.2.x.l.373.4		24	112.5	odd	12
784.2.x.l.557.4		24	7.6	odd	2
784.2.x.l.765.1		24	7.5	odd	6
784.2.x.m.165.1		24	16.5	even	4	inner
784.2.x.m.373.4		24	112.37	even	12	inner
784.2.x.m.557.4		24	1.1	even	1	trivial
784.2.x.m.765.1		24	7.2	even	3	inner
896.2.m.g.225.4		12	112.45	odd	12
896.2.m.g.673.4		12	56.45	odd	6
896.2.m.h.225.3		12	112.3	even	12
896.2.m.h.673.3		12	56.3	even	6
7168.2.a.bi.1.6		12	224.171	even	24
7168.2.a.bi.1.7		12	224.59	even	24
7168.2.a.bj.1.6		12	224.101	odd	24
7168.2.a.bj.1.7		12	224.213	odd	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.545265 - 1.30487i) q^{2} +(0.569433 - 0.152579i) q^{3} +(-1.40537 - 1.42300i) q^{4} +(-1.54592 - 0.414228i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(-2.29710 + 1.32623i) q^{9} +O(q^{10})\)	\(q+(0.545265 - 1.30487i) q^{2} +(0.569433 - 0.152579i) q^{3} +(-1.40537 - 1.42300i) q^{4} +(-1.54592 - 0.414228i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(-2.29710 + 1.32623i) q^{9} +(-1.38345 + 1.79136i) q^{10} +(1.41182 + 5.26900i) q^{11} +(-1.01739 - 0.595873i) q^{12} +(-4.66311 - 4.66311i) q^{13} -0.943500 q^{15} +(-0.0498554 + 3.99969i) q^{16} +(-2.66615 + 4.61791i) q^{17} +(0.478033 + 3.72057i) q^{18} +(0.936730 - 3.49592i) q^{19} +(1.58315 + 2.78199i) q^{20} +(7.64518 + 1.03075i) q^{22} +(-2.25586 + 1.30242i) q^{23} +(-1.33228 + 1.00265i) q^{24} +(-2.11185 - 1.21928i) q^{25} +(-8.62739 + 3.54213i) q^{26} +(-2.35625 + 2.35625i) q^{27} +(-1.22279 - 1.22279i) q^{29} +(-0.514457 + 1.23115i) q^{30} +(-0.416854 + 0.722013i) q^{31} +(5.19189 + 2.24594i) q^{32} +(1.60788 + 2.78493i) q^{33} +(4.57201 + 5.99696i) q^{34} +(5.11551 + 1.40492i) q^{36} +(6.05105 + 1.62137i) q^{37} +(-4.05096 - 3.12852i) q^{38} +(-3.36683 - 1.94384i) q^{39} +(4.49336 - 0.548881i) q^{40} +0.263382i q^{41} +(1.25233 - 1.25233i) q^{43} +(5.51365 - 9.41394i) q^{44} +(4.10050 - 1.09872i) q^{45} +(0.469450 + 3.65377i) q^{46} +(-5.37795 - 9.31488i) q^{47} +(0.581880 + 2.28516i) q^{48} +(-2.74251 + 2.09086i) q^{50} +(-0.813598 + 3.03639i) q^{51} +(-0.0821962 + 13.1890i) q^{52} +(0.0174309 + 0.0650529i) q^{53} +(1.78982 + 4.35939i) q^{54} -8.73026i q^{55} -2.13362i q^{57} +(-2.26233 + 0.928839i) q^{58} +(1.32019 + 4.92700i) q^{59} +(1.32597 + 1.34260i) q^{60} +(-1.63393 + 6.09793i) q^{61} +(0.714837 + 0.937629i) q^{62} +(5.76162 - 5.55011i) q^{64} +(5.27720 + 9.14038i) q^{65} +(4.51069 - 0.579551i) q^{66} +(-12.9904 + 3.48077i) q^{67} +(10.3182 - 2.69595i) q^{68} +(-1.08584 + 1.08584i) q^{69} +2.05301i q^{71} +(4.62255 - 5.90903i) q^{72} +(-4.74814 - 2.74134i) q^{73} +(5.41510 - 7.01175i) q^{74} +(-1.38859 - 0.372072i) q^{75} +(-6.29115 + 3.58011i) q^{76} +(-4.37227 + 3.33337i) q^{78} +(-2.60788 - 4.51698i) q^{79} +(1.73385 - 6.16254i) q^{80} +(2.99648 - 5.19006i) q^{81} +(0.343679 + 0.143613i) q^{82} +(-5.84045 - 5.84045i) q^{83} +(6.03452 - 6.03452i) q^{85} +(-0.951279 - 2.31699i) q^{86} +(-0.882871 - 0.509726i) q^{87} +(-9.27757 - 12.3277i) q^{88} +(5.47892 - 3.16326i) q^{89} +(0.802163 - 5.94971i) q^{90} +(5.02367 + 1.37970i) q^{92} +(-0.127207 + 0.474741i) q^{93} +(-15.0871 + 1.93845i) q^{94} +(-2.89622 + 5.01639i) q^{95} +(3.29912 + 0.486741i) q^{96} -18.8089 q^{97} +(-10.2310 - 10.2310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

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