LMFDB - Embedded newform 416.2.bf.a.53.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$416 = 2^{5} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			53.17
Character	$\chi$	$=$	416.53
Dual form			416.2.bf.a.157.17

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.706943 - 1.22484i) q^{2} +(-3.07212 + 1.27251i) q^{3} +(-1.00046 + 1.73178i) q^{4} +(0.840287 - 2.02863i) q^{5} +(3.73043 + 2.86325i) q^{6} +(-1.05731 - 1.05731i) q^{7} +(2.82843 + 0.00113391i) q^{8} +(5.69729 - 5.69729i) q^{9} +(-3.07878 + 0.404911i) q^{10} +(-2.23858 - 0.927249i) q^{11} +(0.869822 - 6.59334i) q^{12} +(-0.382683 - 0.923880i) q^{13} +(-0.547576 + 2.04249i) q^{14} +7.30147i q^{15} +(-1.99815 - 3.46517i) q^{16} +6.89532i q^{17} +(-11.0059 - 2.95060i) q^{18} +(-1.11025 - 2.68038i) q^{19} +(2.67248 + 3.48477i) q^{20} +(4.59361 + 1.90274i) q^{21} +(0.446816 + 3.39741i) q^{22} +(-1.82706 + 1.82706i) q^{23} +(-8.69070 + 3.59572i) q^{24} +(0.126266 + 0.126266i) q^{25} +(-0.861069 + 1.12186i) q^{26} +(-6.43532 + 15.5362i) q^{27} +(2.88883 - 0.773232i) q^{28} +(-6.09051 + 2.52277i) q^{29} +(8.94313 - 5.16172i) q^{30} +0.600079 q^{31} +(-2.83170 + 4.89709i) q^{32} +8.05711 q^{33} +(8.44566 - 4.87460i) q^{34} +(-3.03333 + 1.25645i) q^{35} +(4.16654 + 15.5664i) q^{36} +(-2.37525 + 5.73436i) q^{37} +(-2.49816 + 3.25476i) q^{38} +(2.35130 + 2.35130i) q^{39} +(2.37899 - 5.73689i) q^{40} +(-1.89745 + 1.89745i) q^{41} +(-0.916876 - 6.97157i) q^{42} +(7.35282 + 3.04564i) q^{43} +(3.84541 - 2.94905i) q^{44} +(-6.77035 - 16.3451i) q^{45} +(3.52948 + 0.946227i) q^{46} +8.80706i q^{47} +(10.5480 + 8.10274i) q^{48} -4.76420i q^{49} +(0.0653928 - 0.243919i) q^{50} +(-8.77438 - 21.1832i) q^{51} +(1.98282 + 0.261582i) q^{52} +(-10.9745 - 4.54578i) q^{53} +(23.5788 - 3.10100i) q^{54} +(-3.76210 + 3.76210i) q^{55} +(-2.98932 - 2.99172i) q^{56} +(6.82164 + 6.82164i) q^{57} +(7.39563 + 5.67644i) q^{58} +(2.29877 - 5.54971i) q^{59} +(-12.6446 - 7.30485i) q^{60} +(-11.6640 + 4.83140i) q^{61} +(-0.424222 - 0.735000i) q^{62} -12.0476 q^{63} +(8.00000 + 0.00641434i) q^{64} -2.19578 q^{65} +(-5.69592 - 9.86866i) q^{66} +(2.96767 - 1.22925i) q^{67} +(-11.9412 - 6.89852i) q^{68} +(3.28798 - 7.93789i) q^{69} +(3.68334 + 2.82711i) q^{70} +(-2.14910 - 2.14910i) q^{71} +(16.1208 - 16.1079i) q^{72} +(-0.189225 + 0.189225i) q^{73} +(8.70284 - 1.14457i) q^{74} +(-0.548580 - 0.227229i) q^{75} +(5.75261 + 0.758910i) q^{76} +(1.38648 + 3.34726i) q^{77} +(1.21773 - 4.54219i) q^{78} +5.43668i q^{79} +(-8.70858 + 1.14177i) q^{80} -31.7466i q^{81} +(3.66547 + 0.982684i) q^{82} +(5.85721 + 14.1406i) q^{83} +(-7.89087 + 6.05153i) q^{84} +(13.9881 + 5.79405i) q^{85} +(-1.46761 - 11.1591i) q^{86} +(15.5005 - 15.5005i) q^{87} +(-6.33060 - 2.62520i) q^{88} +(11.8476 + 11.8476i) q^{89} +(-15.2338 + 19.8476i) q^{90} +(-0.572211 + 1.38144i) q^{91} +(-1.33617 - 4.99197i) q^{92} +(-1.84351 + 0.763608i) q^{93} +(10.7872 - 6.22609i) q^{94} -6.37044 q^{95} +(2.46771 - 18.6478i) q^{96} -4.15797 q^{97} +(-5.83537 + 3.36802i) q^{98} +(-18.0366 + 7.47102i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100})$ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$ .

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.706943	−	1.22484i	−0.499884	−	0.866092i
$2$	−0.706943	−	1.22484i	−0.499884	−	0.866092i
$3$	−3.07212	+	1.27251i	−1.77369	+	0.734685i	−0.779577	+	0.626306i	$0.784566\pi$
$3$	−3.07212	+	1.27251i	−1.77369	+	0.734685i	−0.994110	+	0.108379i	$0.965434\pi$
$4$	−1.00046	+	1.73178i	−0.500231	+	0.865892i
$5$	0.840287	−	2.02863i	0.375788	−	0.907232i	−0.616958	−	0.786996i	$-0.711635\pi$
$5$	0.840287	−	2.02863i	0.375788	−	0.907232i	0.992745	−	0.120236i	$-0.0383650\pi$
$6$	3.73043	+	2.86325i	1.52294	+	1.16892i
$7$	−1.05731	−	1.05731i	−0.399625	−	0.399625i	0.478476	−	0.878101i	$-0.341189\pi$
$7$	−1.05731	−	1.05731i	−0.399625	−	0.399625i	−0.878101	+	0.478476i	$0.841189\pi$
$8$	2.82843	+	0.00113391i	1.00000	+	0.000400896i
$9$	5.69729	−	5.69729i	1.89910	−	1.89910i
$10$	−3.07878	+	0.404911i	−0.973597	+	0.128044i
$11$	−2.23858	−	0.927249i	−0.674957	−	0.279576i	0.0187602	−	0.999824i	$-0.494028\pi$
$11$	−2.23858	−	0.927249i	−0.674957	−	0.279576i	−0.693717	+	0.720248i	$0.744028\pi$
$12$	0.869822	−	6.59334i	0.251096	−	1.90333i
$13$	−0.382683	−	0.923880i	−0.106137	−	0.256238i
$13$	−0.382683	−	0.923880i	−0.106137	−	0.256238i
$14$	−0.547576	+	2.04249i	−0.146346	+	0.545879i
$15$			7.30147i			1.88523i
$16$	−1.99815	−	3.46517i	−0.499537	−	0.866293i
$17$			6.89532i			1.67236i	0.548454	+	0.836181i	$0.315217\pi$
$17$			6.89532i			1.67236i	−0.548454	+	0.836181i	$0.684783\pi$
$18$	−11.0059	−	2.95060i	−2.59412	−	0.695464i
$19$	−1.11025	−	2.68038i	−0.254709	−	0.614922i	0.743864	−	0.668332i	$-0.232991\pi$
$19$	−1.11025	−	2.68038i	−0.254709	−	0.614922i	−0.998573	+	0.0534092i	$0.982991\pi$
$20$	2.67248	+	3.48477i	0.597584	+	0.779218i
$21$	4.59361	+	1.90274i	1.00241	+	0.415211i
$22$	0.446816	+	3.39741i	0.0952615	+	0.724331i
$23$	−1.82706	+	1.82706i	−0.380968	+	0.380968i	−0.871451	−	0.490483i	$-0.836820\pi$
$23$	−1.82706	+	1.82706i	−0.380968	+	0.380968i	0.490483	+	0.871451i	$0.336820\pi$
$24$	−8.69070	+	3.59572i	−1.77398	+	0.733974i
$25$	0.126266	+	0.126266i	0.0252533	+	0.0252533i
$26$	−0.861069	+	1.12186i	−0.168869	+	0.220014i
$27$	−6.43532	+	15.5362i	−1.23848	+	2.98995i
$28$	2.88883	−	0.773232i	0.545937	−	0.146127i
$29$	−6.09051	+	2.52277i	−1.13098	+	0.468467i	−0.868113	−	0.496366i	$-0.834667\pi$
$29$	−6.09051	+	2.52277i	−1.13098	+	0.468467i	−0.262865	+	0.964833i	$0.584667\pi$
$30$	8.94313	−	5.16172i	1.63278	−	0.942397i
$31$	0.600079			0.107777			0.0538887	−	0.998547i	$-0.482838\pi$
$31$	0.600079			0.107777			0.0538887	+	0.998547i	$0.482838\pi$
$32$	−2.83170	+	4.89709i	−0.500579	+	0.865691i
$33$	8.05711			1.40256
$34$	8.44566	−	4.87460i	1.44842	−	0.835987i
$35$	−3.03333	+	1.25645i	−0.512727	+	0.212379i
$36$	4.16654	+	15.5664i	0.694424	+	2.59440i
$37$	−2.37525	+	5.73436i	−0.390489	+	0.942723i	0.599345	+	0.800491i	$0.295428\pi$
$37$	−2.37525	+	5.73436i	−0.390489	+	0.942723i	−0.989833	+	0.142232i	$0.954572\pi$
$38$	−2.49816	+	3.25476i	−0.405254	+	0.527992i
$39$	2.35130	+	2.35130i	0.376509	+	0.376509i
$40$	2.37899	−	5.73689i	0.376152	−	0.907081i
$41$	−1.89745	+	1.89745i	−0.296332	+	0.296332i	−0.839575	−	0.543243i	$-0.817196\pi$
$41$	−1.89745	+	1.89745i	−0.296332	+	0.296332i	0.543243	+	0.839575i	$0.317196\pi$
$42$	−0.916876	−	6.97157i	−0.141477	−	1.07574i
$43$	7.35282	+	3.04564i	1.12129	+	0.464455i	0.864813	−	0.502094i	$-0.167437\pi$
$43$	7.35282	+	3.04564i	1.12129	+	0.464455i	0.256481	+	0.966549i	$0.417437\pi$
$44$	3.84541	−	2.94905i	0.579717	−	0.444587i
$45$	−6.77035	−	16.3451i	−1.00926	−	2.43658i
$46$	3.52948	+	0.946227i	0.520393	+	0.139514i
$47$			8.80706i			1.28464i	0.766436	+	0.642321i	$0.222028\pi$
$47$			8.80706i			1.28464i	−0.766436	+	0.642321i	$0.777972\pi$
$48$	10.5480	+	8.10274i	1.52247	+	1.16953i
$49$		−	4.76420i		−	0.680599i
$50$	0.0653928	−	0.243919i	0.00924794	−	0.0344953i
$51$	−8.77438	−	21.1832i	−1.22866	−	2.96625i
$52$	1.98282	+	0.261582i	0.274968	+	0.0362749i
$53$	−10.9745	−	4.54578i	−1.50746	−	0.624411i	−0.532429	−	0.846474i	$-0.678721\pi$
$53$	−10.9745	−	4.54578i	−1.50746	−	0.624411i	−0.975032	+	0.222063i	$0.928721\pi$
$54$	23.5788	−	3.10100i	3.20867	−	0.421993i
$55$	−3.76210	+	3.76210i	−0.507281	+	0.507281i
$56$	−2.98932	−	2.99172i	−0.399465	−	0.399785i
$57$	6.82164	+	6.82164i	0.903548	+	0.903548i
$58$	7.39563	+	5.67644i	0.971094	+	0.745353i
$59$	2.29877	−	5.54971i	0.299274	−	0.722511i	−0.700685	−	0.713470i	$-0.747122\pi$
$59$	2.29877	−	5.54971i	0.299274	−	0.722511i	0.999959	−	0.00904045i	$-0.00287771\pi$
$60$	−12.6446	−	7.30485i	−1.63241	−	0.943052i
$61$	−11.6640	+	4.83140i	−1.49342	+	0.618597i	−0.972059	−	0.234736i	$-0.924577\pi$
$61$	−11.6640	+	4.83140i	−1.49342	+	0.618597i	−0.521366	+	0.853333i	$0.674577\pi$
$62$	−0.424222	−	0.735000i	−0.0538762	−	0.0933451i
$63$	−12.0476			−1.51785
$64$	8.00000	+	0.00641434i	1.00000	+	0.000801793i
$65$	−2.19578			−0.272353
$66$	−5.69592	−	9.86866i	−0.701119	−	1.21475i
$67$	2.96767	−	1.22925i	0.362559	−	0.150177i	−0.193965	−	0.981008i	$-0.562135\pi$
$67$	2.96767	−	1.22925i	0.362559	−	0.150177i	0.556524	+	0.830832i	$0.312135\pi$
$68$	−11.9412	−	6.89852i	−1.44808	−	0.836568i
$69$	3.28798	−	7.93789i	0.395826	−	0.955610i
$70$	3.68334	+	2.82711i	0.440244	+	0.337904i
$71$	−2.14910	−	2.14910i	−0.255051	−	0.255051i	0.567986	−	0.823038i	$-0.307723\pi$
$71$	−2.14910	−	2.14910i	−0.255051	−	0.255051i	−0.823038	+	0.567986i	$0.807723\pi$
$72$	16.1208	−	16.1079i	1.89986	−	1.89833i
$73$	−0.189225	+	0.189225i	−0.0221472	+	0.0221472i	−0.718094	−	0.695946i	$-0.754985\pi$
$73$	−0.189225	+	0.189225i	−0.0221472	+	0.0221472i	0.695946	+	0.718094i	$0.254985\pi$
$74$	8.70284	−	1.14457i	1.01168	−	0.133053i
$75$	−0.548580	−	0.227229i	−0.0633445	−	0.0262382i
$76$	5.75261	+	0.758910i	0.659870	+	0.0870529i
$77$	1.38648	+	3.34726i	0.158004	+	0.381455i
$78$	1.21773	−	4.54219i	0.137880	−	0.514302i
$79$			5.43668i			0.611674i	0.952084	+	0.305837i	$0.0989363\pi$
$79$			5.43668i			0.611674i	−0.952084	+	0.305837i	$0.901064\pi$
$80$	−8.70858	+	1.14177i	−0.973648	+	0.127654i
$81$		−	31.7466i		−	3.52740i
$82$	3.66547	+	0.982684i	0.404783	+	0.108519i
$83$	5.85721	+	14.1406i	0.642912	+	1.55213i	0.822733	+	0.568428i	$0.192448\pi$
$83$	5.85721	+	14.1406i	0.642912	+	1.55213i	−0.179821	+	0.983699i	$0.557552\pi$
$84$	−7.89087	+	6.05153i	−0.860964	+	0.660276i
$85$	13.9881	+	5.79405i	1.51722	+	0.628453i
$86$	−1.46761	−	11.1591i	−0.158256	−	1.20332i
$87$	15.5005	−	15.5005i	1.66183	−	1.66183i
$88$	−6.33060	−	2.62520i	−0.674845	−	0.279847i
$89$	11.8476	+	11.8476i	1.25584	+	1.25584i	0.953061	+	0.302777i	$0.0979137\pi$
$89$	11.8476	+	11.8476i	1.25584	+	1.25584i	0.302777	+	0.953061i	$0.402086\pi$
$90$	−15.2338	+	19.8476i	−1.60579	+	2.09212i
$91$	−0.572211	+	1.38144i	−0.0599841	+	0.144814i
$92$	−1.33617	−	4.99197i	−0.139305	−	0.520449i
$93$	−1.84351	+	0.763608i	−0.191163	+	0.0791824i
$94$	10.7872	−	6.22609i	1.11262	−	0.642172i
$95$	−6.37044			−0.653594
$96$	2.46771	−	18.6478i	0.251859	−	1.90323i
$97$	−4.15797			−0.422178			−0.211089	−	0.977467i	$-0.567701\pi$
$97$	−4.15797			−0.422178			−0.211089	+	0.977467i	$0.567701\pi$
$98$	−5.83537	+	3.36802i	−0.589462	+	0.340221i
$99$	−18.0366	+	7.47102i	−1.81275	+	0.750865i
$100$	−0.344991	+	0.0923411i	−0.0344991	+	0.00923411i
$101$	−4.93192	+	11.9067i	−0.490745	+	1.18476i	0.463597	+	0.886046i	$0.346559\pi$
$101$	−4.93192	+	11.9067i	−0.490745	+	1.18476i	−0.954342	+	0.298717i	$0.903441\pi$
$102$	−19.7431	+	25.7225i	−1.95486	+	2.54691i
$103$	1.21280	+	1.21280i	0.119501	+	0.119501i	0.764328	−	0.644827i	$-0.223071\pi$
$103$	1.21280	+	1.21280i	0.119501	+	0.119501i	−0.644827	+	0.764328i	$0.723071\pi$
$104$	−1.08134	−	2.61356i	−0.106035	−	0.256281i
$105$	7.71991	−	7.71991i	0.753386	−	0.753386i
$106$	2.19049	+	16.6556i	0.212759	+	1.61773i
$107$	−3.57812	−	1.48210i	−0.345910	−	0.143280i	0.202963	−	0.979186i	$-0.434943\pi$
$107$	−3.57812	−	1.48210i	−0.345910	−	0.143280i	−0.548873	+	0.835906i	$0.684943\pi$
$108$	−20.4671	−	26.6880i	−1.96945	−	2.56806i
$109$	−0.0783483	−	0.189150i	−0.00750441	−	0.0181172i	0.920083	−	0.391724i	$-0.128121\pi$
$109$	−0.0783483	−	0.189150i	−0.00750441	−	0.0181172i	−0.927587	+	0.373606i	$0.878121\pi$
$110$	7.26755	+	1.94838i	0.692934	+	0.185770i
$111$		−	20.6392i		−	1.95898i
$112$	−1.55110	+	5.77641i	−0.146565	+	0.545820i
$113$		−	14.4049i		−	1.35510i	−0.735478	−	0.677549i	$-0.763042\pi$
$113$		−	14.4049i		−	1.35510i	0.735478	−	0.677549i	$-0.236958\pi$
$114$	3.53290	−	13.1779i	0.330887	−	1.23423i
$115$	2.17118	+	5.24169i	0.202463	+	0.488790i
$116$	1.72443	−	13.0714i	0.160110	−	1.21365i
$117$	−7.44386	−	3.08335i	−0.688186	−	0.285056i
$118$	−8.42260	+	1.10771i	−0.775363	+	0.101973i
$119$	7.29049	−	7.29049i	0.668318	−	0.668318i
$120$	−0.00827918	+	20.6517i	−0.000755782	+	1.88523i
$121$	−3.62673	−	3.62673i	−0.329703	−	0.329703i
$122$	14.1635	+	10.8710i	1.28230	+	0.984217i
$123$	3.41466	−	8.24372i	0.307890	−	0.743312i
$124$	−0.600357	+	1.03921i	−0.0539136	+	0.0933235i
$125$	10.5054	−	4.35148i	0.939632	−	0.389209i
$126$	8.51696	+	14.7564i	0.758751	+	1.31460i
$127$	−0.940625			−0.0834670			−0.0417335	−	0.999129i	$-0.513288\pi$
$127$	−0.940625			−0.0834670			−0.0417335	+	0.999129i	$0.513288\pi$
$128$	−5.64769	−	9.80325i	−0.499190	−	0.866493i
$129$	−26.4643			−2.33005
$130$	1.55229	+	2.68947i	0.136145	+	0.235882i
$131$	−6.43157	+	2.66405i	−0.561929	+	0.232759i	−0.645523	−	0.763741i	$-0.723360\pi$
$131$	−6.43157	+	2.66405i	−0.561929	+	0.232759i	0.0835932	+	0.996500i	$0.473360\pi$
$132$	−8.06084	+	13.9532i	−0.701606	+	1.21447i
$133$	−1.66012	+	4.00787i	−0.143950	+	0.347527i
$134$	−3.60361	−	2.76591i	−0.311304	−	0.238938i
$135$	26.1098	+	26.1098i	2.24717	+	2.24717i
$136$	−0.00781865	+	19.5029i	−0.000670444	+	1.67236i
$137$	−8.86704	+	8.86704i	−0.757562	+	0.757562i	−0.975878	−	0.218316i	$-0.929944\pi$
$137$	−8.86704	+	8.86704i	−0.757562	+	0.757562i	0.218316	+	0.975878i	$0.429944\pi$
$138$	−12.0471	+	1.58439i	−1.02551	+	0.134872i
$139$	10.1791	+	4.21634i	0.863384	+	0.357625i	0.770030	−	0.638008i	$-0.220241\pi$
$139$	10.1791	+	4.21634i	0.863384	+	0.357625i	0.0933539	+	0.995633i	$0.470241\pi$
$140$	0.858842	−	6.51011i	0.0725854	−	0.550205i
$141$	−11.2071	−	27.0563i	−0.943807	−	2.27855i
$142$	−1.11301	+	4.15160i	−0.0934019	+	0.348394i
$143$			2.42302i			0.202623i
$144$	−31.1261	−	8.35805i	−2.59384	−	0.696504i
$145$			14.4753i			1.20210i
$146$	0.365542	+	0.0979991i	0.0302525	+	0.00811046i
$147$	6.06250	+	14.6362i	0.500026	+	1.20717i
$148$	−7.55432	−	9.85044i	−0.620962	−	0.809701i
$149$	2.09345	+	0.867136i	0.171502	+	0.0710386i	0.466783	−	0.884372i	$-0.345413\pi$
$149$	2.09345	+	0.867136i	0.171502	+	0.0710386i	−0.295280	+	0.955411i	$0.595413\pi$
$150$	0.109495	+	0.832560i	0.00894027	+	0.0679783i
$151$	8.41108	−	8.41108i	0.684484	−	0.684484i	−0.276523	−	0.961007i	$-0.589182\pi$
$151$	8.41108	−	8.41108i	0.684484	−	0.684484i	0.961007	+	0.276523i	$0.0891823\pi$
$152$	−3.13723	−	7.58253i	−0.254463	−	0.615024i
$153$	39.2846	+	39.2846i	3.17598	+	3.17598i
$154$	3.11969	−	4.06454i	0.251392	−	0.327530i
$155$	0.504239	−	1.21734i	0.0405014	−	0.0977791i
$156$	−6.42432	+	1.71955i	−0.514357	+	0.137674i
$157$	−1.29387	+	0.535938i	−0.103262	+	0.0427725i	−0.433716	−	0.901049i	$-0.642798\pi$
$157$	−1.29387	+	0.535938i	−0.103262	+	0.0427725i	0.330454	+	0.943822i	$0.392798\pi$
$158$	6.65906	−	3.84342i	0.529766	−	0.305766i
$159$	39.4994			3.13251
$160$	7.55495	+	9.85944i	0.597271	+	0.779457i
$161$	3.86353			0.304489
$162$	−38.8845	+	22.4431i	−3.05506	+	1.76329i
$163$	−3.84508	+	1.59268i	−0.301170	+	0.124749i	−0.528151	−	0.849151i	$-0.677114\pi$
$163$	−3.84508	+	1.59268i	−0.301170	+	0.124749i	0.226981	+	0.973899i	$0.427114\pi$
$164$	−1.38765	−	5.18431i	−0.108357	−	0.404826i
$165$	6.77028	−	16.3449i	0.527066	−	1.27245i
$166$	13.1792	−	17.1707i	1.02290	−	1.33271i
$167$	−14.9696	−	14.9696i	−1.15839	−	1.15839i	−0.984823	−	0.173563i	$-0.944472\pi$
$167$	−14.9696	−	14.9696i	−1.15839	−	1.15839i	−0.173563	−	0.984823i	$-0.555528\pi$
$168$	12.9905	+	5.38696i	1.00224	+	0.415613i
$169$	−0.707107	+	0.707107i	−0.0543928	+	0.0543928i
$170$	−2.79199	−	21.2292i	−0.214136	−	1.62821i
$171$	−21.5963	−	8.94550i	−1.65151	−	0.684079i
$172$	−12.6306	+	9.68645i	−0.963075	+	0.738585i
$173$	−0.551863	−	1.33231i	−0.0419573	−	0.101294i	0.901512	−	0.432755i	$-0.142458\pi$
$173$	−0.551863	−	1.33231i	−0.0419573	−	0.101294i	−0.943469	+	0.331461i	$0.892458\pi$
$174$	−29.9436	−	8.02764i	−2.27002	−	0.608574i
$175$		−	0.267005i		−	0.0201837i
$176$	1.25993	+	9.60984i	0.0949711	+	0.724369i
$177$			19.9746i			1.50138i
$178$	6.13580	−	22.8869i	0.459898	−	1.71545i
$179$	−3.89384	−	9.40055i	−0.291039	−	0.702630i	0.708958	−	0.705251i	$-0.249166\pi$
$179$	−3.89384	−	9.40055i	−0.291039	−	0.702630i	−0.999997	+	0.00262075i	$0.999166\pi$
$180$	35.0796	+	4.62785i	2.61468	+	0.344940i
$181$	2.94135	+	1.21835i	0.218629	+	0.0905590i	0.489310	−	0.872110i	$-0.337249\pi$
$181$	2.94135	+	1.21835i	0.218629	+	0.0905590i	−0.270681	+	0.962669i	$0.587249\pi$
$182$	2.09656	−	0.275733i	0.155408	−	0.0204387i
$183$	29.6852	−	29.6852i	2.19439	−	2.19439i
$184$	−5.16977	+	5.16563i	−0.381121	+	0.380815i
$185$	9.63702	+	9.63702i	0.708528	+	0.708528i
$186$	2.23855	+	1.71818i	0.164139	+	0.125983i
$187$	6.39369	−	15.4357i	0.467553	−	1.12877i
$188$	−15.2519	−	8.81114i	−1.11236	−	0.642618i
$189$	23.2307	−	9.62248i	1.68979	−	0.699933i
$190$	4.50354	+	7.80277i	0.326721	+	0.566072i
$191$	−19.7377			−1.42817			−0.714085	−	0.700059i	$-0.753157\pi$
$191$	−19.7377			−1.42817			−0.714085	+	0.700059i	$0.753157\pi$
$192$	−24.5851	+	10.1604i	−1.77428	+	0.733263i
$193$	7.01268			0.504784			0.252392	−	0.967625i	$-0.418783\pi$
$193$	7.01268			0.504784			0.252392	+	0.967625i	$0.418783\pi$
$194$	2.93945	+	5.09285i	0.211040	+	0.365645i
$195$	6.74568	−	2.79415i	0.483068	−	0.200093i
$196$	8.25056	+	4.76640i	0.589325	+	0.340457i
$197$	3.26525	−	7.88301i	0.232639	−	0.561641i	−0.763847	−	0.645398i	$-0.776692\pi$
$197$	3.26525	−	7.88301i	0.232639	−	0.561641i	0.996486	+	0.0837563i	$0.0266917\pi$
$198$	21.9017	+	16.8104i	1.55648	+	1.19466i
$199$	11.4609	+	11.4609i	0.812440	+	0.812440i	0.984999	−	0.172559i	$-0.0552035\pi$
$199$	11.4609	+	11.4609i	0.812440	+	0.812440i	−0.172559	+	0.984999i	$0.555204\pi$
$200$	0.356992	+	0.357278i	0.0252431	+	0.0252634i
$201$	−7.55279	+	7.55279i	−0.532733	+	0.532733i
$202$	18.0704	−	2.37656i	1.27143	−	0.167214i
$203$	9.10690	+	3.77220i	0.639179	+	0.264756i
$204$	45.4632	+	5.99771i	3.18306	+	0.419924i
$205$	2.25483	+	5.44364i	0.157484	+	0.380200i
$206$	0.628104	−	2.34286i	0.0437621	−	0.163235i
$207$			20.8186i			1.44699i
$208$	−2.43674	+	3.17211i	−0.168958	+	0.219946i
$209$			7.02973i			0.486257i
$210$	−14.9132	−	3.99811i	−1.02911	−	0.275896i
$211$	1.16190	+	2.80508i	0.0799886	+	0.193110i	0.958815	−	0.284033i	$-0.0916725\pi$
$211$	1.16190	+	2.80508i	0.0799886	+	0.193110i	−0.878826	+	0.477143i	$0.841673\pi$
$212$	18.8519	−	14.4575i	1.29475	−	0.992948i
$213$	9.33705	+	3.86753i	0.639764	+	0.264999i
$214$	0.714185	+	5.43038i	0.0488207	+	0.371213i
$215$	12.3570	−	12.3570i	0.842738	−	0.842738i
$216$	−18.2195	+	43.9358i	−1.23968	+	2.98945i
$217$	−0.634469	−	0.634469i	−0.0430705	−	0.0430705i
$218$	−0.176290	+	0.229682i	−0.0119399	+	0.0155560i
$219$	0.340531	−	0.822114i	0.0230109	−	0.0555533i
$220$	−2.75130	−	10.2790i	−0.185493	−	0.693008i
$221$	6.37045	−	2.63873i	0.428523	−	0.177500i
$222$	−25.2797	+	14.5907i	−1.69666	+	0.979264i
$223$	−22.9047			−1.53382			−0.766908	−	0.641758i	$-0.778206\pi$
$223$	−22.9047			−1.53382			−0.766908	+	0.641758i	$0.778206\pi$
$224$	8.17172	−	2.18375i	0.545996	−	0.145908i
$225$	1.43875			0.0959167
$226$	−17.6437	+	10.1834i	−1.17364	+	0.677392i
$227$	−23.7568	+	9.84040i	−1.57680	+	0.653130i	−0.987902	−	0.155080i	$-0.950436\pi$
$227$	−23.7568	+	9.84040i	−1.57680	+	0.653130i	−0.588894	+	0.808210i	$0.700436\pi$
$228$	−18.6384	+	4.98881i	−1.23436	+	0.330392i
$229$	9.97103	−	24.0722i	0.658904	−	1.59074i	−0.140595	−	0.990067i	$-0.544901\pi$
$229$	9.97103	−	24.0722i	0.658904	−	1.59074i	0.799499	−	0.600668i	$-0.205099\pi$
$230$	4.88532	−	6.36492i	0.322129	−	0.419690i
$231$	−8.51885	−	8.51885i	−0.560499	−	0.560499i
$232$	−17.2294	+	7.12857i	−1.13117	+	0.468013i
$233$	−15.9597	+	15.9597i	−1.04555	+	1.04555i	−0.0466402	+	0.998912i	$0.514851\pi$
$233$	−15.9597	+	15.9597i	−1.04555	+	1.04555i	−0.998912	+	0.0466402i	$0.985149\pi$
$234$	1.48578	+	11.2973i	0.0971285	+	0.738527i
$235$	17.8663	+	7.40046i	1.16547	+	0.482753i
$236$	7.31107	+	9.53325i	0.475910	+	0.620561i
$237$	−6.91824	−	16.7021i	−0.449388	−	1.08492i
$238$	−14.0836	−	3.77572i	−0.912907	−	0.244743i
$239$			12.3952i			0.801782i	0.916126	+	0.400891i	$0.131299\pi$
$239$			12.3952i			0.801782i	−0.916126	+	0.400891i	$0.868701\pi$
$240$	25.3008	−	14.5894i	1.63316	−	0.941743i
$241$		−	10.1671i		−	0.654919i	−0.944865	−	0.327459i	$-0.893808\pi$
$241$		−	10.1671i		−	0.654919i	0.944865	−	0.327459i	$-0.106192\pi$
$242$	−1.87827	+	7.00606i	−0.120740	+	0.450367i
$243$	21.0920	+	50.9206i	1.35305	+	3.26655i
$244$	3.30249	−	25.0332i	0.211420	−	1.60259i
$245$	−9.66480	−	4.00329i	−0.617462	−	0.255761i
$246$	−12.5112	+	1.64543i	−0.797686	+	0.104909i
$247$	−2.05148	+	2.05148i	−0.130532	+	0.130532i
$248$	1.69728		0.000680433i	0.107777		4.32076e-5i
$249$	−35.9880	−	35.9880i	−2.28065	−	2.28065i
$250$	−12.7566	−	9.79119i	−0.806798	−	0.619249i
$251$	−6.97038	+	16.8280i	−0.439966	+	1.06217i	0.535993	+	0.844222i	$0.319937\pi$
$251$	−6.97038	+	16.8280i	−0.439966	+	1.06217i	−0.975960	+	0.217951i	$0.930063\pi$
$252$	12.0532	−	20.8638i	0.759278	−	1.31430i
$253$	5.78415	−	2.39587i	0.363647	−	0.150627i
$254$	0.664968	+	1.15211i	0.0417238	+	0.0722901i
$255$	−50.3460			−3.15279
$256$	−8.01481	+	13.8478i	−0.500926	+	0.865490i
$257$	4.76471			0.297215			0.148607	−	0.988896i	$-0.452521\pi$
$257$	4.76471			0.297215			0.148607	+	0.988896i	$0.452521\pi$
$258$	18.7088	+	32.4146i	1.16476	+	2.01804i
$259$	8.57437	−	3.55162i	0.532785	−	0.220687i
$260$	2.19679	−	3.80261i	0.136239	−	0.235828i
$261$	−20.3264	+	49.0723i	−1.25817	+	3.03750i
$262$	7.80979	+	5.99432i	0.482490	+	0.370330i
$263$	−17.1628	−	17.1628i	−1.05830	−	1.05830i	−0.998192	−	0.0601097i	$-0.980855\pi$
$263$	−17.1628	−	17.1628i	−1.05830	−	1.05830i	−0.0601097	−	0.998192i	$-0.519145\pi$
$264$	22.7889	+	0.00913600i	1.40256	+	0.000562282i
$265$	−18.4434	+	18.4434i	−1.13297	+	1.13297i
$266$	6.08261	−	0.799964i	0.372949	−	0.0490489i
$267$	−51.4732	−	21.3209i	−3.15011	−	1.30482i
$268$	−0.840250	+	6.36918i	−0.0513265	+	0.389060i
$269$	−3.78114	−	9.12848i	−0.230540	−	0.556574i	0.765701	−	0.643197i	$-0.222392\pi$
$269$	−3.78114	−	9.12848i	−0.230540	−	0.556574i	−0.996241	+	0.0866234i	$0.972392\pi$
$270$	13.5222	−	50.4385i	0.822933	−	3.06959i
$271$		−	6.42480i		−	0.390279i	−0.980775	−	0.195140i	$-0.937484\pi$
$271$		−	6.42480i		−	0.390279i	0.980775	−	0.195140i	$-0.0625160\pi$
$272$	23.8935	−	13.7779i	1.44875	−	0.835407i
$273$		−	4.97209i		−	0.300925i
$274$	17.1292	+	4.59220i	1.03481	+	0.277425i
$275$	−0.165577	−	0.399737i	−0.00998464	−	0.0241051i
$276$	10.4572	+	13.6356i	0.629450	+	0.820769i
$277$	10.9274	+	4.52627i	0.656563	+	0.271957i	0.685992	−	0.727610i	$-0.259369\pi$
$277$	10.9274	+	4.52627i	0.656563	+	0.271957i	−0.0294284	+	0.999567i	$0.509369\pi$
$278$	−2.03174	−	15.4485i	−0.121856	−	0.926541i
$279$	3.41882	−	3.41882i	0.204680	−	0.204680i
$280$	−8.58099	+	3.55033i	−0.512812	+	0.212173i
$281$	12.3901	+	12.3901i	0.739132	+	0.739132i	0.972410	−	0.233278i	$-0.0749453\pi$
$281$	12.3901	+	12.3901i	0.739132	+	0.739132i	−0.233278	+	0.972410i	$0.574945\pi$
$282$	−25.2169	+	32.8541i	−1.50164	+	1.95644i
$283$	−7.52972	+	18.1784i	−0.447596	+	1.08059i	0.525625	+	0.850717i	$0.323832\pi$
$283$	−7.52972	+	18.1784i	−0.447596	+	1.08059i	−0.973220	+	0.229875i	$0.926168\pi$
$284$	5.87188	−	1.57168i	0.348432	−	0.0932622i
$285$	19.5707	−	8.10647i	1.15927	−	0.480186i
$286$	2.96781	−	1.71294i	0.175490	−	0.101288i
$287$	4.01239			0.236844
$288$	11.7671	+	44.0331i	0.693384	+	2.59468i
$289$	−30.5455			−1.79679
$290$	17.7299	−	10.2332i	1.04113	−	0.600913i
$291$	12.7738	−	5.29107i	0.748812	−	0.310168i
$292$	−0.138384	−	0.517010i	−0.00809834	−	0.0302557i
$293$	−1.83794	+	4.43719i	−0.107374	+	0.259223i	−0.968430	−	0.249287i	$-0.919804\pi$
$293$	−1.83794	+	4.43719i	−0.107374	+	0.259223i	0.861056	+	0.508511i	$0.169804\pi$
$294$	13.6411	−	17.7725i	0.795565	−	1.03651i
$295$	−9.32670	−	9.32670i	−0.543022	−	0.543022i
$296$	−6.72473	+	16.2165i	−0.390867	+	0.942567i
$297$	28.8119	−	28.8119i	1.67184	−	1.67184i
$298$	−0.417849	−	3.17716i	−0.0242053	−	0.184048i
$299$	2.38717	+	0.988797i	0.138053	+	0.0571836i
$300$	0.942346	−	0.722687i	0.0544064	−	0.0417244i
$301$	−4.55402	−	10.9944i	−0.262490	−	0.633706i
$302$	−16.2484	−	4.35607i	−0.934989	−	0.250663i
$303$		−	42.8547i		−	2.46194i
$304$	−7.06954	+	9.20301i	−0.405466	+	0.527829i
$305$			27.7218i			1.58734i
$306$	20.3454	−	75.8894i	1.16307	−	4.33831i
$307$	−5.24867	−	12.6714i	−0.299557	−	0.723195i	−0.999955	−	0.00944283i	$-0.996994\pi$
$307$	−5.24867	−	12.6714i	−0.299557	−	0.723195i	0.700398	−	0.713752i	$-0.253006\pi$
$308$	−7.18385	−	0.947725i	−0.409338	−	0.0540016i
$309$	−5.26916	−	2.18256i	−0.299752	−	0.124161i
$310$	−1.84751	+	0.242979i	−0.104932	+	0.0138003i
$311$	−7.60983	+	7.60983i	−0.431514	+	0.431514i	−0.889143	−	0.457629i	$-0.848699\pi$
$311$	−7.60983	+	7.60983i	−0.431514	+	0.431514i	0.457629	+	0.889143i	$0.348699\pi$
$312$	6.64780	+	6.65313i	0.376358	+	0.376660i
$313$	−7.75071	−	7.75071i	−0.438096	−	0.438096i	0.453275	−	0.891371i	$-0.350256\pi$
$313$	−7.75071	−	7.75071i	−0.438096	−	0.438096i	−0.891371	+	0.453275i	$0.850256\pi$
$314$	1.57113	+	1.20590i	0.0886640	+	0.0680531i
$315$	−10.1234	+	24.4401i	−0.570391	+	1.37704i
$316$	−9.41515	−	5.43920i	−0.529644	−	0.305979i
$317$	−19.1889	+	7.94830i	−1.07776	+	0.446421i	−0.849721	−	0.527232i	$-0.823230\pi$
$317$	−19.1889	+	7.94830i	−1.07776	+	0.446421i	−0.228034	+	0.973653i	$0.573230\pi$
$318$	−27.9239	−	48.3805i	−1.56589	−	2.71304i
$319$	15.9733			0.894334
$320$	6.73531	−	16.2237i	0.376515	−	0.906930i
$321$	12.8784			0.718802
$322$	−2.73130	−	4.73221i	−0.152209	−	0.263715i
$323$	18.4821	−	7.65554i	1.02837	−	0.425966i
$324$	54.9783	+	31.7613i	3.05435	+	1.76452i
$325$	0.0683348	−	0.164975i	0.00379053	−	0.00915116i
$326$	4.66903	+	3.58367i	0.258594	+	0.198481i
$327$	0.481390	+	0.481390i	0.0266209	+	0.0266209i
$328$	−5.36896	+	5.36465i	−0.296451	+	0.296213i
$329$	9.31178	−	9.31178i	0.513375	−	0.513375i
$330$	−24.8061	+	3.26241i	−1.36553	+	0.179590i
$331$	−10.6403	−	4.40736i	−0.584844	−	0.242250i	0.0705865	−	0.997506i	$-0.477513\pi$
$331$	−10.6403	−	4.40736i	−0.584844	−	0.242250i	−0.655431	+	0.755255i	$0.727513\pi$
$332$	−30.3483	−	4.00368i	−1.66558	−	0.219731i
$333$	19.1378	+	46.2028i	1.04875	+	2.53190i
$334$	−7.75272	+	28.9181i	−0.424210	+	1.58233i
$335$		−	7.05324i		−	0.385359i
$336$	−2.58541	−	19.7196i	−0.141046	−	1.07579i
$337$		−	30.9560i		−	1.68628i	−0.537692	−	0.843142i	$-0.680704\pi$
$337$		−	30.9560i		−	1.68628i	0.537692	−	0.843142i	$-0.319296\pi$
$338$	1.36598	+	0.366208i	0.0742993	+	0.0199191i
$339$	18.3304	+	44.2535i	0.995570	+	2.40352i
$340$	−24.0286	+	18.4276i	−1.30313	+	0.999376i
$341$	−1.34332	−	0.556423i	−0.0727450	−	0.0301320i
$342$	4.31059	+	32.7760i	0.233090	+	1.77232i
$343$	−12.4384	+	12.4384i	−0.671610	+	0.671610i
$344$	20.7935	+	8.62270i	1.12111	+	0.464905i
$345$	−13.3402	−	13.3402i	−0.718213	−	0.718213i
$346$	−1.24174	+	1.61781i	−0.0667561	+	0.0869742i
$347$	13.8421	−	33.4178i	0.743083	−	1.79396i	0.150229	−	0.988651i	$-0.451999\pi$
$347$	13.8421	−	33.4178i	0.743083	−	1.79396i	0.592854	−	0.805310i	$-0.298001\pi$
$348$	11.3358	+	42.3511i	0.607664	+	2.27026i
$349$	−0.579789	+	0.240157i	−0.0310354	+	0.0128553i	−0.398147	−	0.917322i	$-0.630347\pi$
$349$	−0.579789	+	0.240157i	−0.0310354	+	0.0128553i	0.367112	+	0.930177i	$0.380347\pi$
$350$	−0.327038	+	0.188757i	−0.0174809	+	0.0100895i
$351$	16.8163			0.897588
$352$	10.8798	−	8.33682i	0.579896	−	0.444354i
$353$	13.2078			0.702981			0.351491	−	0.936191i	$-0.385675\pi$
$353$	13.2078			0.702981			0.351491	+	0.936191i	$0.385675\pi$
$354$	24.4656	−	14.1209i	1.30033	−	0.750516i
$355$	−6.16560	+	2.55388i	−0.327236	+	0.135546i
$356$	−32.3704	+	8.66436i	−1.71563	+	0.459210i
$357$	−13.1200	+	31.6745i	−0.694383	+	1.67639i
$358$	−8.76145	+	11.4150i	−0.463057	+	0.603301i
$359$	−16.0663	−	16.0663i	−0.847947	−	0.847947i	0.141930	−	0.989877i	$-0.454669\pi$
$359$	−16.0663	−	16.0663i	−0.847947	−	0.847947i	−0.989877	+	0.141930i	$0.954669\pi$
$360$	−19.1309	−	46.2385i	−1.00829	−	2.43698i
$361$	7.48323	−	7.48323i	0.393854	−	0.393854i
$362$	−0.587088	−	4.46398i	−0.0308566	−	0.234622i
$363$	15.7568	+	6.52668i	0.827018	+	0.342562i
$364$	−1.81988	−	2.37303i	−0.0953876	−	0.124380i
$365$	0.224865	+	0.542872i	0.0117700	+	0.0284152i
$366$	−57.3454	−	15.3739i	−2.99749	−	0.803605i
$367$		−	2.33921i		−	0.122106i	−0.998135	−	0.0610530i	$-0.980554\pi$
$367$		−	2.33921i		−	0.122106i	0.998135	−	0.0610530i	$-0.0194459\pi$
$368$	9.98180	+	2.68034i	0.520338	+	0.139722i
$369$			21.6207i			1.12553i
$370$	4.99098	−	18.6166i	0.259469	−	0.967833i
$371$	6.79713	+	16.4097i	0.352889	+	0.851950i
$372$	0.521962	−	3.95652i	0.0270625	−	0.205136i
$373$	0.791362	+	0.327793i	0.0409752	+	0.0169725i	0.403077	−	0.915166i	$-0.367941\pi$
$373$	0.791362	+	0.327793i	0.0409752	+	0.0169725i	−0.362102	+	0.932139i	$0.617941\pi$
$374$	−23.4263	+	3.08094i	−1.21134	+	0.159312i
$375$	−26.7365	+	26.7365i	−1.38067	+	1.38067i
$376$	−0.00998638	+	24.9101i	−0.000515008	+	1.28464i
$377$	4.66147	+	4.66147i	0.240078	+	0.240078i
$378$	−28.2088	−	21.6514i	−1.45090	−	1.11363i
$379$	7.72848	−	18.6582i	0.396985	−	0.958407i	−0.591392	−	0.806384i	$-0.701421\pi$
$379$	7.72848	−	18.6582i	0.396985	−	0.958407i	0.988377	−	0.152023i	$-0.0485787\pi$
$380$	6.37339	−	11.0322i	0.326948	−	0.565941i
$381$	2.88971	−	1.19696i	0.148044	−	0.0613219i
$382$	13.9534	+	24.1755i	0.713920	+	1.23693i
$383$	−0.174067			−0.00889441			−0.00444720	−	0.999990i	$-0.501416\pi$
$383$	−0.174067			−0.00889441			−0.00444720	+	0.999990i	$0.501416\pi$
$384$	29.8251	+	22.9300i	1.52201	+	1.17014i
$385$	7.95540			0.405445
$386$	−4.95757	−	8.58941i	−0.252333	−	0.437189i
$387$	59.2430	−	24.5393i	3.01149	−	1.24740i
$388$	4.15990	−	7.20071i	0.211187	−	0.365560i
$389$	3.02359	−	7.29959i	0.153302	−	0.370104i	−0.828506	−	0.559980i	$-0.810809\pi$
$389$	3.02359	−	7.29959i	0.153302	−	0.370104i	0.981808	+	0.189876i	$0.0608087\pi$
$390$	−8.19120	−	6.28707i	−0.414777	−	0.318358i
$391$	−12.5982	−	12.5982i	−0.637116	−	0.637116i
$392$	0.00540215	−	13.4752i	0.000272850	−	0.680599i
$393$	16.3685	−	16.3685i	0.825682	−	0.825682i
$394$	−11.9638	+	1.57343i	−0.602726	+	0.0792684i
$395$	11.0290	+	4.56837i	0.554931	+	0.229860i
$396$	5.10680	−	38.7100i	0.256626	−	1.94525i
$397$	13.0731	+	31.5612i	0.656120	+	1.58401i	0.803748	+	0.594970i	$0.202836\pi$
$397$	13.0731	+	31.5612i	0.656120	+	1.58401i	−0.147628	+	0.989043i	$0.547164\pi$
$398$	5.93555	−	22.1399i	0.297522	−	1.10977i
$399$		−	14.4252i		−	0.722161i
$400$	0.185235	−	0.689833i	0.00926177	−	0.0344916i
$401$			27.1280i			1.35471i	0.735657	+	0.677355i	$0.236874\pi$
$401$			27.1280i			1.35471i	−0.735657	+	0.677355i	$0.763126\pi$
$402$	14.5904	+	3.91156i	0.727701	+	0.195091i
$403$	−0.229640	−	0.554401i	−0.0114392	−	0.0276167i
$404$	−15.6856	−	20.4533i	−0.780390	−	1.01759i
$405$	−64.4022	−	26.6763i	−3.20017	−	1.32555i
$406$	−1.81772	−	13.8212i	−0.0902118	−	0.685935i
$407$	10.6344	−	10.6344i	0.527126	−	0.527126i
$408$	−24.7937	−	59.9252i	−1.22747	−	2.96674i
$409$	−5.21955	−	5.21955i	−0.258090	−	0.258090i	0.566187	−	0.824277i	$-0.308418\pi$
$409$	−5.21955	−	5.21955i	−0.258090	−	0.258090i	−0.824277	+	0.566187i	$0.808418\pi$
$410$	5.07355	−	6.61015i	0.250565	−	0.326452i
$411$	15.9571	−	38.5240i	0.787108	−	1.90025i
$412$	−3.31367	+	0.886945i	−0.163253	+	0.0436967i
$413$	−8.29826	+	3.43725i	−0.408331	+	0.169136i
$414$	25.4994	−	14.7175i	1.25323	−	0.723327i
$415$	33.6077			1.64974
$416$	5.60796	+	0.742115i	0.274953	+	0.0363852i
$417$	−36.6369			−1.79411
$418$	8.61029	−	4.96962i	0.421143	−	0.243072i
$419$	4.25103	−	1.76084i	0.207677	−	0.0860224i	−0.276420	−	0.961037i	$-0.589148\pi$
$419$	4.25103	−	1.76084i	0.207677	−	0.0860224i	0.484097	+	0.875014i	$0.339148\pi$
$420$	5.64573	+	21.0927i	0.275483	+	1.02922i
$421$	13.0651	−	31.5420i	0.636755	−	1.53726i	−0.194222	−	0.980958i	$-0.562218\pi$
$421$	13.0651	−	31.5420i	0.636755	−	1.53726i	0.830977	−	0.556306i	$-0.187782\pi$
$422$	2.61437	−	3.40617i	0.127266	−	0.165810i
$423$	50.1763	+	50.1763i	2.43966	+	2.43966i
$424$	−31.0354	−	12.8699i	−1.50721	−	0.625015i
$425$	−0.870647	+	0.870647i	−0.0422326	+	0.0422326i
$426$	−1.86366	−	14.1705i	−0.0902944	−	0.686563i
$427$	17.4408	+	7.22420i	0.844017	+	0.349603i
$428$	6.14646	−	4.71373i	0.297100	−	0.227847i
$429$	−3.08332	−	7.44380i	−0.148864	−	0.359390i
$430$	−23.8710	−	6.39962i	−1.15116	−	0.308617i
$431$			3.06380i			0.147578i	0.997274	+	0.0737891i	$0.0235092\pi$
$431$			3.06380i			0.147578i	−0.997274	+	0.0737891i	$0.976491\pi$
$432$	66.6945	−	8.74423i	3.20884	−	0.420707i
$433$		−	2.48584i		−	0.119462i	−0.998215	−	0.0597309i	$-0.980976\pi$
$433$		−	2.48584i		−	0.119462i	0.998215	−	0.0597309i	$-0.0190242\pi$
$434$	−0.328589	+	1.22566i	−0.0157728	+	0.0588334i
$435$	−18.4199	−	44.4696i	−0.883168	−	2.13216i
$436$	0.405951	+	0.0535548i	0.0194415	+	0.00256481i
$437$	6.92571	+	2.86872i	0.331302	+	0.137230i
$438$	−1.24769	+	0.164092i	−0.0596171	+	0.00784063i
$439$	−7.47987	+	7.47987i	−0.356995	+	0.356995i	−0.862704	−	0.505709i	$-0.831231\pi$
$439$	−7.47987	+	7.47987i	−0.356995	+	0.356995i	0.505709	+	0.862704i	$0.331231\pi$
$440$	−10.6451	+	10.6366i	−0.507484	+	0.507078i
$441$	−27.1430	−	27.1430i	−1.29252	−	1.29252i
$442$	−7.73556	−	5.93735i	−0.367943	−	0.282411i
$443$	−0.376758	+	0.909574i	−0.0179003	+	0.0432152i	−0.932577	−	0.360971i	$-0.882445\pi$
$443$	−0.376758	+	0.909574i	−0.0179003	+	0.0432152i	0.914677	+	0.404186i	$0.132445\pi$
$444$	35.7426	+	20.6487i	1.69627	+	0.979945i
$445$	33.9897	−	14.0790i	1.61127	−	0.667408i
$446$	16.1924	+	28.0546i	0.766730	+	1.32843i
$447$	−7.53477			−0.356382
$448$	−8.45169	−	8.46525i	−0.399305	−	0.399945i
$449$	−37.9350			−1.79026			−0.895131	−	0.445804i	$-0.852918\pi$
$449$	−37.9350			−1.79026			−0.895131	+	0.445804i	$0.852918\pi$
$450$	−1.01711	−	1.76224i	−0.0479472	−	0.0830727i
$451$	6.00701	−	2.48818i	0.282859	−	0.117164i
$452$	24.9461	+	14.4116i	1.17337	+	0.677862i
$453$	−15.1366	+	36.5430i	−0.711180	+	1.71694i
$454$	28.8476	+	22.1417i	1.35389	+	1.03916i
$455$	2.32161	+	2.32161i	0.108839	+	0.108839i
$456$	19.2868	+	19.3022i	0.903186	+	0.903911i
$457$	−1.37762	+	1.37762i	−0.0644424	+	0.0644424i	−0.738593	−	0.674151i	$-0.764510\pi$
$457$	−1.37762	+	1.37762i	−0.0644424	+	0.0644424i	0.674151	+	0.738593i	$0.264510\pi$
$458$	−36.5335	+	4.80476i	−1.70710	+	0.224512i
$459$	−107.127	−	44.3736i	−5.00028	−	2.07118i
$460$	−11.2496	−	1.48410i	−0.524517	−	0.0691967i
$461$	14.2980	+	34.5185i	0.665925	+	1.60769i	0.788364	+	0.615209i	$0.210928\pi$
$461$	14.2980	+	34.5185i	0.665925	+	1.60769i	−0.122439	+	0.992476i	$0.539072\pi$
$462$	−4.41188	+	16.4566i	−0.205259	+	0.765629i
$463$		−	7.49178i		−	0.348172i	−0.984730	−	0.174086i	$-0.944303\pi$
$463$		−	7.49178i		−	0.348172i	0.984730	−	0.174086i	$-0.0556971\pi$
$464$	20.9116	+	16.0638i	0.970795	+	0.745742i
$465$			4.38146i			0.203185i
$466$	30.8306	+	8.26545i	1.42820	+	0.382889i
$467$	6.61649	+	15.9736i	0.306174	+	0.739171i	0.999822	+	0.0188561i	$0.00600245\pi$
$467$	6.61649	+	15.9736i	0.306174	+	0.739171i	−0.693648	+	0.720314i	$0.743998\pi$
$468$	12.7870	−	9.80638i	0.591079	−	0.453300i
$469$	−4.43744	−	1.83805i	−0.204902	−	0.0848732i
$470$	−3.56608	−	27.1150i	−0.164491	−	1.25072i
$471$	3.29293	−	3.29293i	0.151730	−	0.151730i
$472$	6.50818	−	15.6943i	0.299563	−	0.722391i
$473$	−13.6358	−	13.6358i	−0.626975	−	0.626975i
$474$	−15.5666	+	20.2812i	−0.714998	+	0.931545i
$475$	0.198255	−	0.478629i	0.00909655	−	0.0219610i
$476$	5.33168	+	19.9194i	0.244377	+	0.913005i
$477$	−88.4234	+	36.6262i	−4.04863	+	1.67700i
$478$	15.1822	−	8.76273i	0.694417	−	0.400798i
$479$	16.9849			0.776062			0.388031	−	0.921646i	$-0.373155\pi$
$479$	16.9849			0.776062			0.388031	+	0.921646i	$0.373155\pi$
$480$	−35.7559	−	20.6756i	−1.63203	−	0.943706i
$481$	6.20683			0.283007
$482$	−12.4530	+	7.18754i	−0.567220	+	0.327384i
$483$	−11.8692	+	4.91639i	−0.540068	+	0.223703i
$484$	9.90913	−	2.65231i	0.450415	−	0.120559i
$485$	−3.49389	+	8.43500i	−0.158649	+	0.383013i
$486$	47.4587	−	61.8322i	2.15277	−	2.80477i
$487$	−9.26893	−	9.26893i	−0.420015	−	0.420015i	0.465194	−	0.885209i	$-0.345985\pi$
$487$	−9.26893	−	9.26893i	−0.420015	−	0.420015i	−0.885209	+	0.465194i	$0.845985\pi$
$488$	−32.9963	+	13.6520i	−1.49367	+	0.617998i
$489$	9.78582	−	9.78582i	0.442530	−	0.442530i
$490$	1.92908	+	14.6679i	0.0871468	+	0.662630i
$491$	−6.57871	−	2.72499i	−0.296893	−	0.122977i	0.229265	−	0.973364i	$-0.426368\pi$
$491$	−6.57871	−	2.72499i	−0.296893	−	0.122977i	−0.526158	+	0.850387i	$0.676368\pi$
$492$	10.8601	+	14.1610i	0.489611	+	0.638427i
$493$	−17.3953	−	41.9960i	−0.783446	−	1.89141i
$494$	3.96301	+	1.06245i	0.178304	+	0.0478020i
$495$			42.8675i			1.92675i
$496$	−1.19905	−	2.07938i	−0.0538388	−	0.0933667i
$497$			4.54453i			0.203850i
$498$	−18.6381	+	69.5211i	−0.835192	+	3.11531i
$499$	4.21154	+	10.1675i	0.188534	+	0.455162i	0.989678	−	0.143310i	$-0.0457747\pi$
$499$	4.21154	+	10.1675i	0.188534	+	0.455162i	−0.801144	+	0.598472i	$0.795775\pi$
$500$	−2.97445	+	22.5466i	−0.133021	+	1.00831i
$501$	65.0375	+	26.9394i	2.90566	+	1.20356i
$502$	25.5392	−	3.35883i	1.13987	−	0.149912i
$503$	12.5177	−	12.5177i	0.558136	−	0.558136i	−0.370640	−	0.928777i	$-0.620862\pi$
$503$	12.5177	−	12.5177i	0.558136	−	0.558136i	0.928777	+	0.370640i	$0.120862\pi$
$504$	−34.0757	−	0.0136608i	−1.51785	−	0.000608502i
$505$	20.0101	+	20.0101i	0.890439	+	0.890439i
$506$	−7.02363	−	5.39091i	−0.312238	−	0.239655i
$507$	1.27251	−	3.07212i	0.0565142	−	0.136437i
$508$	0.941060	−	1.62896i	0.0417528	−	0.0722733i
$509$	7.38534	−	3.05911i	0.327349	−	0.135593i	−0.212955	−	0.977062i	$-0.568309\pi$
$509$	7.38534	−	3.05911i	0.327349	−	0.135593i	0.540305	+	0.841469i	$0.318309\pi$
$510$	35.5918	+	61.6658i	1.57603	+	2.73061i
$511$	0.400139			0.0177011
$512$	22.6274	+	0.0272137i	0.999999	+	0.00120269i
$513$	48.7879			2.15404
$514$	−3.36838	−	5.83601i	−0.148573	−	0.257415i
$515$	3.47942	−	1.44122i	0.153322	−	0.0635079i
$516$	26.4766	−	45.8305i	1.16557	−	2.01757i
$517$	8.16634	−	19.7153i	0.359155	−	0.867077i
$518$	−10.4118	−	7.99143i	−0.457466	−	0.351123i
$519$	3.39077	+	3.39077i	0.148838	+	0.148838i
$520$	−6.21059	−	0.00248980i	−0.272352	−	0.000109185i
$521$	−13.4672	+	13.4672i	−0.590007	+	0.590007i	−0.937633	−	0.347626i	$-0.886988\pi$
$521$	−13.4672	+	13.4672i	−0.590007	+	0.590007i	0.347626	+	0.937633i	$0.386988\pi$
$522$	74.4753	−	9.79474i	3.25970	−	0.428704i
$523$	30.8988	+	12.7987i	1.35111	+	0.559649i	0.936601	−	0.350396i	$-0.113953\pi$
$523$	30.8988	+	12.7987i	1.35111	+	0.559649i	0.414510	+	0.910045i	$0.363953\pi$
$524$	1.82100	−	13.8034i	0.0795508	−	0.603003i
$525$	0.339767	+	0.820270i	0.0148286	+	0.0357995i
$526$	−8.88853	+	33.1547i	−0.387558	+	1.44561i
$527$			4.13774i			0.180243i
$528$	−16.0993	−	27.9192i	−0.700632	−	1.21503i
$529$			16.3237i			0.709727i
$530$	35.6287	+	9.55179i	1.54761	+	0.414903i
$531$	−18.5216	−	44.7150i	−0.803768	−	1.94047i
$532$	−5.27988	−	6.88469i	−0.228912	−	0.298489i
$533$	2.47914	+	1.02689i	0.107384	+	0.0444797i
$534$	10.2740	+	78.1191i	0.444597	+	3.38054i
$535$	−6.01329	+	6.01329i	−0.259977	+	0.259977i
$536$	8.39523	−	3.47348i	0.362619	−	0.150031i
$537$	23.9246	+	23.9246i	1.03242	+	1.03242i
$538$	−8.50788	+	11.0846i	−0.366801	+	0.477892i
$539$	−4.41760	+	10.6650i	−0.190279	+	0.459375i
$540$	−71.3384	+	19.0946i	−3.06992	+	0.821703i
$541$	6.73799	−	2.79097i	0.289689	−	0.119993i	−0.233107	−	0.972451i	$-0.574889\pi$
$541$	6.73799	−	2.79097i	0.289689	−	0.119993i	0.522795	+	0.852458i	$0.324889\pi$
$542$	−7.86935	+	4.54197i	−0.338018	+	0.195094i
$543$	−10.5865			−0.454311
$544$	−33.7670	−	19.5255i	−1.44775	−	0.837148i
$545$	−0.449550			−0.0192566
$546$	−6.09001	+	3.51499i	−0.260628	+	0.150427i
$547$	5.92902	−	2.45588i	0.253506	−	0.105006i	−0.252311	−	0.967646i	$-0.581191\pi$
$547$	5.92902	−	2.45588i	0.253506	−	0.105006i	0.505818	+	0.862640i	$0.331191\pi$
$548$	−6.48465	−	24.2269i	−0.277010	−	1.03492i
$549$	−38.9274	+	93.9791i	−1.66138	+	4.01093i
$550$	−0.372561	+	0.485396i	−0.0158860	+	0.0206974i
$551$	13.5240	+	13.5240i	0.576141	+	0.576141i
$552$	9.30882	−	22.4480i	0.396210	−	0.955451i
$553$	5.74825	−	5.74825i	0.244441	−	0.244441i
$554$	−2.18109	−	16.5841i	−0.0926654	−	0.704591i
$555$	−41.8693	−	17.3428i	−1.77725	−	0.736162i
$556$	−17.4856	+	13.4098i	−0.741557	+	0.568702i
$557$	−5.76747	−	13.9239i	−0.244376	−	0.589975i	0.753332	−	0.657640i	$-0.228445\pi$
$557$	−5.76747	−	13.9239i	−0.244376	−	0.589975i	−0.997708	+	0.0676649i	$0.978445\pi$
$558$	−6.60442	−	1.77059i	−0.279587	−	0.0749553i
$559$		−	7.95864i		−	0.336614i
$560$	10.4149	+	8.00045i	0.440108	+	0.338081i
$561$			55.5564i			2.34559i
$562$	6.41679	−	23.9350i	0.270676	−	1.00964i
$563$	−0.808658	−	1.95227i	−0.0340809	−	0.0822785i	0.905923	−	0.423443i	$-0.139179\pi$
$563$	−0.808658	−	1.95227i	−0.0340809	−	0.0822785i	−0.940004	+	0.341165i	$0.889179\pi$
$564$	58.0679	+	7.66058i	2.44510	+	0.322569i
$565$	−29.2222	−	12.1042i	−1.22939	−	0.509229i
$566$	27.5887	−	3.62837i	1.15964	−	0.152512i
$567$	−33.5660	+	33.5660i	−1.40964	+	1.40964i
$568$	−6.07614	−	6.08101i	−0.254949	−	0.255154i
$569$	12.1946	+	12.1946i	0.511225	+	0.511225i	0.914902	−	0.403677i	$-0.132268\pi$
$569$	12.1946	+	12.1946i	0.511225	+	0.511225i	−0.403677	+	0.914902i	$0.632268\pi$
$570$	−23.7645	−	18.2402i	−0.995386	−	0.763998i
$571$	3.38345	−	8.16836i	0.141593	−	0.341835i	−0.837136	−	0.546995i	$-0.815772\pi$
$571$	3.38345	−	8.16836i	0.141593	−	0.341835i	0.978728	+	0.205160i	$0.0657715\pi$
$572$	−4.19615	−	2.42414i	−0.175450	−	0.101358i
$573$	60.6365	−	25.1165i	2.53313	−	1.04926i
$574$	−2.83653	−	4.91453i	−0.118394	−	0.205128i
$575$	−0.461392			−0.0192414
$576$	45.6148	−	45.5417i	1.90062	−	1.89757i
$577$	−16.6499			−0.693144			−0.346572	−	0.938023i	$-0.612654\pi$
$577$	−16.6499			−0.693144			−0.346572	+	0.938023i	$0.612654\pi$
$578$	21.5939	+	37.4133i	0.898189	+	1.55619i
$579$	−21.5438	+	8.92372i	−0.895328	+	0.370857i
$580$	−25.0680	−	14.4820i	−1.04089	−	0.601330i
$581$	8.75805	−	21.1438i	0.363345	−	0.877193i
$582$	−15.5110	−	11.9053i	−0.642953	−	0.493492i
$583$	20.3522	+	20.3522i	0.842901	+	0.842901i
$584$	−0.535425	+	0.534996i	−0.0221560	+	0.0221383i
$585$	−12.5100	+	12.5100i	−0.517223	+	0.517223i
$586$	6.73417	−	0.885654i	0.278186	−	0.0365860i
$587$	20.1309	+	8.33850i	0.830892	+	0.344167i	0.757256	−	0.653118i	$-0.226540\pi$
$587$	20.1309	+	8.33850i	0.830892	+	0.344167i	0.0736362	+	0.997285i	$0.476540\pi$
$588$	−31.4120	−	4.14400i	−1.29541	−	0.170896i
$589$	−0.666238	−	1.60844i	−0.0274519	−	0.0662747i
$590$	−4.83026	+	18.0172i	−0.198859	+	0.741755i
$591$			28.3726i			1.16709i
$592$	24.6166	−	3.22746i	1.01174	−	0.132648i
$593$		−	33.8758i		−	1.39111i	−0.718472	−	0.695556i	$-0.755158\pi$
$593$		−	33.8758i		−	1.39111i	0.718472	−	0.695556i	$-0.244842\pi$
$594$	−55.6584	−	14.9216i	−2.28369	−	0.612241i
$595$	−8.66362	−	20.9158i	−0.355174	−	0.857465i
$596$	−3.59611	+	2.75787i	−0.147303	+	0.112967i
$597$	−49.7933	−	20.6250i	−2.03790	−	0.844127i
$598$	−0.476474	−	3.62292i	−0.0194845	−	0.148152i
$599$	23.9653	−	23.9653i	0.979195	−	0.979195i	−0.0205931	−	0.999788i	$-0.506555\pi$
$599$	23.9653	−	23.9653i	0.979195	−	0.979195i	0.999788	+	0.0205931i	$0.00655546\pi$
$600$	−1.55136	−	0.643323i	−0.0633340	−	0.0262636i
$601$	10.5169	+	10.5169i	0.428994	+	0.428994i	0.888285	−	0.459292i	$-0.151897\pi$
$601$	10.5169	+	10.5169i	0.428994	+	0.428994i	−0.459292	+	0.888285i	$0.651897\pi$
$602$	−10.2469	+	13.3504i	−0.417633	+	0.544120i
$603$	9.90428	−	23.9111i	0.403334	−	0.973734i
$604$	6.15119	+	22.9811i	0.250289	+	0.935089i
$605$	−10.4048	+	4.30981i	−0.423016	+	0.175219i
$606$	−52.4902	+	30.2959i	−2.13227	+	1.23069i
$607$	−22.4386			−0.910754			−0.455377	−	0.890299i	$-0.650496\pi$
$607$	−22.4386			−0.910754			−0.455377	+	0.890299i	$0.650496\pi$
$608$	16.2700	+	2.15304i	0.659835	+	0.0873174i
$609$	−32.7776			−1.32822
$610$	33.9547	−	19.5977i	1.37479	−	0.793488i
$611$	8.13666	−	3.37032i	0.329174	−	0.136348i
$612$	−107.335	+	28.7297i	−4.33877	+	1.16133i
$613$	−3.12528	+	7.54510i	−0.126229	+	0.304744i	−0.974342	−	0.225071i	$-0.927739\pi$
$613$	−3.12528	+	7.54510i	−0.126229	+	0.304744i	0.848113	+	0.529815i	$0.177739\pi$
$614$	−11.8099	+	15.3867i	−0.476610	+	0.620958i
$615$	−13.8542	−	13.8542i	−0.558655	−	0.558655i
$616$	3.91776	+	9.46905i	0.157851	+	0.381519i
$617$	17.9078	−	17.9078i	0.720942	−	0.720942i	−0.247855	−	0.968797i	$-0.579726\pi$
$617$	17.9078	−	17.9078i	0.720942	−	0.720942i	0.968797	+	0.247855i	$0.0797256\pi$
$618$	1.05171	+	7.99682i	0.0423062	+	0.321679i
$619$	−12.9299	−	5.35573i	−0.519695	−	0.215265i	0.107388	−	0.994217i	$-0.465751\pi$
$619$	−12.9299	−	5.35573i	−0.519695	−	0.215265i	−0.627083	+	0.778952i	$0.715751\pi$
$620$	1.60370	+	2.09114i	0.0644060	+	0.0839820i
$621$	−16.6279	−	40.1433i	−0.667255	−	1.61090i
$622$	14.7005	+	3.94110i	0.589438	+	0.158024i
$623$		−	25.0531i		−	1.00373i
$624$	3.44940	−	12.8459i	0.138087	−	0.514247i
$625$		−	24.0753i		−	0.963011i
$626$	−4.01406	+	14.9727i	−0.160434	+	0.598429i
$627$	−8.94541	−	21.5961i	−0.357245	−	0.862467i
$628$	0.366339	−	2.77689i	0.0146185	−	0.110810i
$629$	−39.5403	−	16.3781i	−1.57657	−	0.653039i
$630$	37.0919	−	4.87820i	1.47778	−	0.194352i
$631$	−17.8488	+	17.8488i	−0.710551	+	0.710551i	−0.966650	−	0.256099i	$-0.917563\pi$
$631$	−17.8488	+	17.8488i	−0.710551	+	0.710551i	0.256099	+	0.966650i	$0.417563\pi$
$632$	−0.00616469	+	15.3773i	−0.000245218	+	0.611674i
$633$	−7.13899	−	7.13899i	−0.283750	−	0.283750i
$634$	23.3008	+	17.8843i	0.925394	+	0.710277i
$635$	−0.790395	+	1.90818i	−0.0313659	+	0.0757239i
$636$	−39.5177	+	68.4045i	−1.56698	+	2.71241i
$637$	−4.40154	+	1.82318i	−0.174395	+	0.0722370i
$638$	−11.2922	−	19.5647i	−0.447063	−	0.774576i
$639$	−24.4881			−0.968734
$640$	−24.6329	+	3.21954i	−0.973699	+	0.127263i
$641$	1.73963			0.0687112			0.0343556	−	0.999410i	$-0.489062\pi$
$641$	1.73963			0.0687112			0.0343556	+	0.999410i	$0.489062\pi$
$642$	−9.10429	−	15.7740i	−0.359318	−	0.622548i
$643$	−35.8108	+	14.8333i	−1.41224	+	0.584969i	−0.952898	−	0.303291i	$-0.901915\pi$
$643$	−35.8108	+	14.8333i	−1.41224	+	0.584969i	−0.459341	+	0.888260i	$0.651915\pi$
$644$	−3.86532	+	6.69080i	−0.152315	+	0.263654i
$645$	−22.2376	+	53.6864i	−0.875606	+	2.11390i
$646$	−22.4426	−	17.2256i	−0.882993	−	0.677732i
$647$	−10.5161	−	10.5161i	−0.413429	−	0.413429i	0.469502	−	0.882931i	$-0.344433\pi$
$647$	−10.5161	−	10.5161i	−0.413429	−	0.413429i	−0.882931	+	0.469502i	$0.844433\pi$
$648$	0.0359977	−	89.7930i	0.00141412	−	3.52740i
$649$	−10.2919	+	10.2919i	−0.403994	+	0.403994i
$650$	−0.250376	+	0.0329287i	−0.00982057	+	0.00129157i
$651$	2.75653	+	1.14179i	0.108037	+	0.0447504i
$652$	1.08868	−	8.25227i	0.0426358	−	0.323184i
$653$	17.9960	+	43.4462i	0.704238	+	1.70018i	0.713919	+	0.700228i	$0.246919\pi$
$653$	17.9960	+	43.4462i	0.704238	+	1.70018i	−0.00968055	+	0.999953i	$0.503081\pi$
$654$	0.249310	−	0.929941i	0.00974880	−	0.0363636i
$655$			15.2859i			0.597268i
$656$	10.3664	+	2.78360i	0.404739	+	0.108682i
$657$			2.15614i			0.0841191i
$658$	−17.9883	−	4.82254i	−0.701258	−	0.188002i
$659$	15.4907	+	37.3978i	0.603430	+	1.45681i	0.870028	+	0.493002i	$0.164100\pi$
$659$	15.4907	+	37.3978i	0.603430	+	1.45681i	−0.266598	+	0.963808i	$0.585900\pi$
$660$	21.5324	+	28.0771i	0.838149	+	1.09290i
$661$	−2.78800	−	1.15483i	−0.108441	−	0.0449176i	0.327803	−	0.944746i	$-0.393692\pi$
$661$	−2.78800	−	1.15483i	−0.108441	−	0.0449176i	−0.436244	+	0.899828i	$0.643692\pi$
$662$	2.12378	+	16.1484i	0.0825432	+	0.627626i
$663$	−16.2129	+	16.2129i	−0.629659	+	0.629659i
$664$	16.5507	+	40.0022i	0.642290	+	1.55238i
$665$	6.73553	+	6.73553i	0.261193	+	0.261193i
$666$	43.0616	−	56.1035i	1.66860	−	2.17397i
$667$	6.51846	−	15.7370i	0.252396	−	0.609338i
$668$	40.9007	−	10.9476i	1.58250	−	0.423576i
$669$	70.3660	−	29.1466i	2.72051	−	1.12687i
$670$	−8.63908	+	4.98624i	−0.333757	+	0.192635i
$671$	30.5907			1.18094
$672$	−22.3256	+	17.1074i	−0.861229	+	0.659930i
$673$	−30.3119			−1.16844			−0.584218	−	0.811597i	$-0.698599\pi$
$673$	−30.3119			−1.16844			−0.584218	+	0.811597i	$0.698599\pi$
$674$	−37.9162	+	21.8842i	−1.46048	+	0.842946i
$675$	−2.77427	+	1.14914i	−0.106782	+	0.0442304i
$676$	−0.517122	−	1.93199i	−0.0198893	−	0.0743073i
$677$	4.83251	−	11.6667i	0.185728	−	0.448388i	−0.803401	−	0.595439i	$-0.796978\pi$
$677$	4.83251	−	11.6667i	0.185728	−	0.448388i	0.989129	+	0.147051i	$0.0469782\pi$
$678$	41.2448	−	53.7365i	1.58400	−	2.06374i
$679$	4.39626	+	4.39626i	0.168713	+	0.168713i
$680$	39.5577	+	16.4039i	1.51697	+	0.629061i
$681$	60.4617	−	60.4617i	2.31690	−	2.31690i
$682$	0.268125	+	2.03871i	0.0102670	+	0.0780664i
$683$	−3.35397	−	1.38926i	−0.128336	−	0.0531586i	0.317591	−	0.948228i	$-0.397126\pi$
$683$	−3.35397	−	1.38926i	−0.128336	−	0.0531586i	−0.445927	+	0.895069i	$0.647126\pi$
$684$	37.0980	−	28.4505i	1.41848	−	1.08783i
$685$	10.5371	+	25.4388i	0.402602	+	0.971967i
$686$	24.0283	+	6.44179i	0.917403	+	0.245949i
$687$			86.6408i			3.30555i
$688$	−4.13837	−	31.5644i	−0.157774	−	1.20338i
$689$			11.8787i			0.452542i
$690$	−6.90885	+	25.7704i	−0.263015	+	0.981062i
$691$	5.86712	+	14.1645i	0.223196	+	0.538842i	0.995321	−	0.0966286i	$-0.0308059\pi$
$691$	5.86712	+	14.1645i	0.223196	+	0.538842i	−0.772125	+	0.635471i	$0.780806\pi$
$692$	2.85940	+	0.377224i	0.108698	+	0.0143399i
$693$	26.9695	+	11.1711i	1.02449	+	0.424356i
$694$	−50.7170	+	6.67013i	−1.92519	+	0.253195i
$695$	17.1068	−	17.1068i	0.648898	−	0.648898i
$696$	43.8596	−	43.8244i	1.66249	−	1.66116i
$697$	−13.0836	−	13.0836i	−0.495575	−	0.495575i
$698$	0.704031	+	0.540372i	0.0266480	+	0.0204534i
$699$	28.7211	−	69.3388i	1.08633	−	2.62263i
$700$	0.462395	+	0.267128i	0.0174769	+	0.0100965i
$701$	−31.5208	+	13.0563i	−1.19052	+	0.493131i	−0.887925	−	0.459988i	$-0.847854\pi$
$701$	−31.5208	+	13.0563i	−1.19052	+	0.493131i	−0.302598	+	0.953118i	$0.597854\pi$
$702$	−11.8882	−	20.5973i	−0.448690	−	0.777394i
$703$	18.0074			0.679163
$704$	−17.9027	−	7.43235i	−0.674732	−	0.280117i
$705$	−64.3045			−2.42185
$706$	−9.33718	−	16.1775i	−0.351409	−	0.608847i
$707$	17.8036	−	7.37451i	0.669575	−	0.277347i
$708$	−34.5916	−	19.9838i	−1.30003	−	0.751038i
$709$	10.5222	−	25.4028i	0.395169	−	0.954023i	−0.593625	−	0.804742i	$-0.702304\pi$
$709$	10.5222	−	25.4028i	0.395169	−	0.954023i	0.988795	−	0.149282i	$-0.0476961\pi$
$710$	7.48682	+	5.74643i	0.280975	+	0.215660i
$711$	30.9743	+	30.9743i	1.16163	+	1.16163i
$712$	33.4965	+	33.5234i	1.25533	+	1.25634i
$713$	−1.09638	+	1.09638i	−0.0410597	+	0.0410597i
$714$	48.0712	−	6.32216i	1.79902	−	0.236601i
$715$	4.91542	+	2.03603i	0.183826	+	0.0761433i
$716$	20.1754	+	2.66162i	0.753989	+	0.0994695i
$717$	−15.7731	−	38.0796i	−0.589057	−	1.42211i
$718$	−8.32068	+	31.0366i	−0.310525	+	1.15828i
$719$		−	14.6114i		−	0.544915i	−0.962168	−	0.272457i	$-0.912164\pi$
$719$		−	14.6114i		−	0.544915i	0.962168	−	0.272457i	$-0.0878364\pi$
$720$	−43.1103	+	56.1202i	−1.60662	+	2.09148i
$721$		−	2.56461i		−	0.0955110i
$722$	−14.4560	−	3.87554i	−0.537995	−	0.144233i
$723$	12.9377	+	31.2344i	0.481159	+	1.16162i
$724$	−5.05262	+	3.87487i	−0.187779	+	0.144008i
$725$	−1.08757	−	0.450485i	−0.0403912	−	0.0167306i
$726$	−3.14503	−	23.9136i	−0.116723	−	0.887515i
$727$	−2.11505	+	2.11505i	−0.0784430	+	0.0784430i	−0.745240	−	0.666797i	$-0.767665\pi$
$727$	−2.11505	+	2.11505i	−0.0784430	+	0.0784430i	0.666797	+	0.745240i	$0.267665\pi$
$728$	−1.62002	+	3.90666i	−0.0600421	+	0.144790i
$729$	−62.2493	−	62.2493i	−2.30553	−	2.30553i
$730$	0.505965	−	0.659204i	0.0187266	−	0.0243982i
$731$	−21.0007	+	50.7001i	−0.776738	+	1.87521i
$732$	21.7094	+	81.1073i	0.802403	+	2.99781i
$733$	12.5481	−	5.19758i	0.463473	−	0.191977i	−0.138713	−	0.990333i	$-0.544297\pi$
$733$	12.5481	−	5.19758i	0.463473	−	0.191977i	0.602186	+	0.798356i	$0.294297\pi$
$734$	−2.86516	+	1.65369i	−0.105755	+	0.0610388i
$735$	34.7856			1.28309
$736$	−3.77359	−	14.1210i	−0.139096	−	0.520505i
$737$	−7.78318			−0.286697
$738$	26.4818	−	15.2846i	0.974810	−	0.562633i
$739$	15.9988	−	6.62693i	0.588526	−	0.243776i	−0.0684902	−	0.997652i	$-0.521818\pi$
$739$	15.9988	−	6.62693i	0.588526	−	0.243776i	0.657016	+	0.753876i	$0.271818\pi$
$740$	−26.3307	+	7.04775i	−0.967936	+	0.259081i
$741$	3.69185	−	8.91290i	0.135623	−	0.327424i
$742$	15.2941	−	19.9261i	0.561463	−	0.731511i
$743$	7.33572	+	7.33572i	0.269121	+	0.269121i	0.828746	−	0.559625i	$-0.189055\pi$
$743$	7.33572	+	7.33572i	0.269121	+	0.269121i	−0.559625	+	0.828746i	$0.689055\pi$
$744$	−5.21510	+	2.15772i	−0.191195	+	0.0791058i
$745$	3.51820	−	3.51820i	0.128897	−	0.128897i
$746$	−0.157954	−	1.20102i	−0.00578312	−	0.0439726i
$747$	113.933	+	47.1926i	4.16859	+	1.72669i
$748$	20.3347	+	26.5153i	0.743510	+	0.969497i
$749$	2.21613	+	5.35022i	0.0809757	+	0.195493i
$750$	51.6491	+	13.8467i	1.88596	+	0.505612i
$751$			8.72743i			0.318468i	0.987241	+	0.159234i	$0.0509025\pi$
$751$			8.72743i			0.318468i	−0.987241	+	0.159234i	$0.949097\pi$
$752$	30.5180	−	17.5978i	1.11288	−	0.641726i
$753$		−	60.5674i		−	2.20720i
$754$	2.41416	−	9.00495i	0.0879185	−	0.327941i
$755$	−9.99527	−	24.1307i	−0.363765	−	0.878206i
$756$	−6.57743	+	49.8575i	−0.239219	+	1.81330i
$757$	−20.8782	−	8.64802i	−0.758830	−	0.314318i	−0.0304912	−	0.999535i	$-0.509707\pi$
$757$	−20.8782	−	8.64802i	−0.758830	−	0.314318i	−0.728339	+	0.685218i	$0.759707\pi$
$758$	−28.3169	+	3.72414i	−1.02852	+	0.135267i
$759$	−14.7208	+	14.7208i	−0.534332	+	0.534332i
$760$	−18.0183	−	0.00722349i	−0.653594	−	0.000262023i
$761$	11.8333	+	11.8333i	0.428956	+	0.428956i	0.888273	−	0.459317i	$-0.151906\pi$
$761$	11.8333	+	11.8333i	0.428956	+	0.428956i	−0.459317	+	0.888273i	$0.651906\pi$
$762$	−3.50894	−	2.69325i	−0.127115	−	0.0975661i
$763$	−0.117151	+	0.282828i	−0.00424116	+	0.0102391i
$764$	19.7468	−	34.1814i	0.714416	−	1.23664i
$765$	112.704	−	46.6837i	4.07484	−	1.68785i
$766$	0.123055	+	0.213204i	0.00444617	+	0.00770338i
$767$	−6.00696			−0.216899
$768$	7.00087	−	52.7411i	0.252622	−	1.90313i
$769$	19.7272			0.711380			0.355690	−	0.934604i	$-0.384246\pi$
$769$	19.7272			0.711380			0.355690	+	0.934604i	$0.384246\pi$
$770$	−5.62401	−	9.74408i	−0.202675	−	0.351152i
$771$	−14.6378	+	6.06316i	−0.527166	+	0.218359i
$772$	−7.01593	+	12.1444i	−0.252509	+	0.437088i
$773$	−1.85971	+	4.48974i	−0.0668891	+	0.161485i	−0.953789	−	0.300477i	$-0.902854\pi$
$773$	−1.85971	+	4.48974i	−0.0668891	+	0.161485i	0.886900	+	0.461962i	$0.152854\pi$
$774$	−71.9381	−	55.2153i	−2.58576	−	1.98467i
$775$	0.0757697	+	0.0757697i	0.00272173	+	0.00272173i
$776$	−11.7605	−	0.00471475i	−0.422178	−	0.000169250i
$777$	−21.8220	+	21.8220i	−0.782859	+	0.782859i
$778$	−11.0783	+	1.45698i	−0.397177	+	0.0522354i
$779$	7.19255	+	2.97925i	0.257700	+	0.106743i
$780$	−1.90994	+	14.4775i	−0.0683867	+	0.518378i
$781$	2.81818	+	6.80369i	0.100842	+	0.243455i
$782$	−6.52454	+	24.3369i	−0.233317	+	0.870286i
$783$		−	110.858i		−	3.96176i
$784$	−16.5087	+	9.51957i	−0.589598	+	0.339985i
$785$			3.07513i			0.109756i
$786$	−31.6204	−	8.47719i	−1.12786	−	0.302371i
$787$	18.3499	+	44.3006i	0.654103	+	1.57915i	0.806769	+	0.590867i	$0.201214\pi$
$787$	18.3499	+	44.3006i	0.654103	+	1.57915i	−0.152665	+	0.988278i	$0.548786\pi$
$788$	10.3849	+	13.5414i	0.369947	+	0.482391i
$789$	74.5658	+	30.8862i	2.65461	+	1.09958i
$790$	−2.20137	−	16.7384i	−0.0783213	−	0.595524i
$791$	−15.2304	+	15.2304i	−0.541531	+	0.541531i
$792$	−51.0238	+	21.1108i	−1.81305	+	0.750139i
$793$	8.92726	+	8.92726i	0.317016	+	0.317016i
$794$	29.4155	−	38.3244i	1.04392	−	1.36008i
$795$	33.1909	−	80.1299i	1.17716	−	2.84191i
$796$	−31.3139	+	8.38158i	−1.10989	+	0.297077i
$797$	−18.1187	+	7.50500i	−0.641796	+	0.265841i	−0.679756	−	0.733439i	$-0.737914\pi$
$797$	−18.1187	+	7.50500i	−0.641796	+	0.265841i	0.0379594	+	0.999279i	$0.487914\pi$
$798$	−17.6685	+	10.1978i	−0.625458	+	0.360997i
$799$	−60.7275			−2.14839
$800$	−0.975885	+	0.260789i	−0.0345028	+	0.00922028i
$801$	134.998			4.76991
$802$	33.2275	−	19.1780i	1.17330	−	0.677198i
$803$	0.599055	−	0.248137i	0.0211402	−	0.00875655i
$804$	−5.52351	−	20.6361i	−0.194799	−	0.727779i
$805$	3.24648	−	7.83769i	0.114423	−	0.276242i
$806$	−0.516709	+	0.673202i	−0.0182003	+	0.0237125i
$807$	23.2322	+	23.2322i	0.817813	+	0.817813i
$808$	−13.9631	+	33.6717i	−0.491220	+	1.18457i
$809$	22.6943	−	22.6943i	0.797888	−	0.797888i	−0.184874	−	0.982762i	$-0.559188\pi$
$809$	22.6943	−	22.6943i	0.797888	−	0.797888i	0.982762	+	0.184874i	$0.0591878\pi$
$810$	12.8546	+	97.7410i	0.451663	+	3.43427i
$811$	28.2189	+	11.6887i	0.990901	+	0.410444i	0.818453	−	0.574574i	$-0.194832\pi$
$811$	28.2189	+	11.6887i	0.990901	+	0.410444i	0.172448	+	0.985019i	$0.444832\pi$
$812$	−15.6437	+	11.9972i	−0.548988	+	0.421020i
$813$	8.17564	+	19.7377i	0.286732	+	0.692233i
$814$	−20.5433	−	5.50750i	−0.720042	−	0.193038i
$815$			9.13856i			0.320110i
$816$	−55.8710	+	72.7320i	−1.95588	+	2.54613i
$817$		−	23.0898i		−	0.807810i
$818$	−2.70318	+	10.0830i	−0.0945146	+	0.352545i
$819$	4.61041	+	11.1305i	0.161101	+	0.388932i
$820$	−11.6831	−	1.54128i	−0.407991	−	0.0538239i
$821$	24.4516	+	10.1282i	0.853367	+	0.353476i	0.766110	−	0.642709i	$-0.222190\pi$
$821$	24.4516	+	10.1282i	0.853367	+	0.353476i	0.0872574	+	0.996186i	$0.472190\pi$
$822$	−58.4665	+	7.68931i	−2.03925	+	0.268195i
$823$	−28.0998	+	28.0998i	−0.979499	+	0.979499i	−0.999794	−	0.0202955i	$-0.993539\pi$
$823$	−28.0998	+	28.0998i	−0.979499	+	0.979499i	0.0202955	+	0.999794i	$0.493539\pi$
$824$	3.42894	+	3.43169i	0.119453	+	0.119549i
$825$	1.01734	+	1.01734i	0.0354193	+	0.0354193i
$826$	10.0765	+	7.73410i	0.350606	+	0.269104i
$827$	−13.3667	+	32.2700i	−0.464805	+	1.12214i	0.501597	+	0.865101i	$0.332746\pi$
$827$	−13.3667	+	32.2700i	−0.464805	+	1.12214i	−0.966402	+	0.257036i	$0.917254\pi$
$828$	−36.0532	−	20.8282i	−1.25294	−	0.723830i
$829$	−21.1217	+	8.74888i	−0.733586	+	0.303861i	−0.718025	−	0.696018i	$-0.754953\pi$
$829$	−21.1217	+	8.74888i	−0.733586	+	0.303861i	−0.0155611	+	0.999879i	$0.504953\pi$
$830$	−23.7587	−	41.1641i	−0.824678	−	1.42883i
$831$	−39.3299			−1.36434
$832$	−3.05554	−	7.39349i	−0.105932	−	0.256323i
$833$	32.8507			1.13821
$834$	25.9002	+	44.8743i	0.896850	+	1.55387i
$835$	−42.9467	+	17.7891i	−1.48623	+	0.615617i
$836$	−12.1740	−	7.03298i	−0.421046	−	0.243241i
$837$	−3.86170	+	9.32297i	−0.133480	+	0.322249i
$838$	−5.16198	−	3.96202i	−0.178318	−	0.136866i
$839$	−31.4010	−	31.4010i	−1.08408	−	1.08408i	−0.996124	−	0.0879582i	$-0.971966\pi$
$839$	−31.4010	−	31.4010i	−1.08408	−	1.08408i	−0.0879582	−	0.996124i	$-0.528034\pi$
$840$	21.8439	−	21.8264i	0.753688	−	0.753084i
$841$	10.2238	−	10.2238i	0.352545	−	0.352545i
$842$	−47.8702	+	6.29572i	−1.64972	+	0.216965i
$843$	−53.8304	−	22.2973i	−1.85402	−	0.767959i
$844$	−6.02023	−	0.794215i	−0.207225	−	0.0273380i
$845$	0.840287	+	2.02863i	0.0289068	+	0.0697871i
$846$	25.9861	−	96.9298i	0.893422	−	3.33251i
$847$			7.66916i			0.263515i
$848$	6.17674	+	47.1116i	0.212110	+	1.61782i
$849$		−	65.4277i		−	2.24547i
$850$	1.68190	+	0.450905i	0.0576887	+	0.0154659i
$851$	−6.13730	−	14.8167i	−0.210384	−	0.507911i
$852$	−16.0391	+	12.3004i	−0.549490	+	0.421405i
$853$	17.3908	+	7.20352i	0.595451	+	0.246644i	0.659994	−	0.751271i	$-0.270559\pi$
$853$	17.3908	+	7.20352i	0.595451	+	0.246644i	−0.0645429	+	0.997915i	$0.520559\pi$
$854$	−3.48114	−	26.4692i	−0.119122	−	0.905758i
$855$	−36.2943	+	36.2943i	−1.24124	+	1.24124i
$856$	−10.1188	−	4.19608i	−0.345852	−	0.143419i
$857$	24.5001	+	24.5001i	0.836906	+	0.836906i	0.988450	−	0.151545i	$-0.0484247\pi$
$857$	24.5001	+	24.5001i	0.836906	+	0.836906i	−0.151545	+	0.988450i	$0.548425\pi$
$858$	−6.93772	+	9.03891i	−0.236850	+	0.308583i
$859$	3.03259	−	7.32131i	0.103471	−	0.249800i	−0.863663	−	0.504070i	$-0.831835\pi$
$859$	3.03259	−	7.32131i	0.103471	−	0.249800i	0.967133	+	0.254270i	$0.0818353\pi$
$860$	9.03690	+	33.7623i	0.308156	+	1.15128i
$861$	−12.3265	+	5.10581i	−0.420087	+	0.174006i
$862$	3.75267	−	2.16594i	0.127816	−	0.0737721i
$863$	−49.1381			−1.67268			−0.836340	−	0.548211i	$-0.815309\pi$
$863$	−49.1381			−1.67268			−0.836340	+	0.548211i	$0.815309\pi$
$864$	−57.8595	−	75.5083i	−1.96842	−	2.56885i
$865$	−3.16650			−0.107664
$866$	−3.04475	+	1.75735i	−0.103465	+	0.0597170i
$867$	93.8393	−	38.8695i	3.18695	−	1.32008i
$868$	1.73352	−	0.464000i	0.0588397	−	0.0157492i
$869$	5.04116	−	12.1704i	0.171010	−	0.412854i
$870$	−41.4463	+	53.9990i	−1.40516	+	1.83074i
$871$	−2.27136	−	2.27136i	−0.0769620	−	0.0769620i
$872$	−0.221388	−	0.535085i	−0.00749715	−	0.0181203i
$873$	−23.6892	+	23.6892i	−0.801756	+	0.801756i
$874$	−1.38236	−	10.5109i	−0.0467590	−	0.355537i
$875$	−15.7083	−	6.50660i	−0.531038	−	0.219963i
$876$	1.08303	+	1.41222i	0.0365924	+	0.0477145i
$877$	−16.9494	−	40.9194i	−0.572339	−	1.38175i	−0.899558	−	0.436801i	$-0.856112\pi$
$877$	−16.9494	−	40.9194i	−0.572339	−	1.38175i	0.327219	−	0.944948i	$-0.393888\pi$
$878$	14.4495	+	3.87380i	0.487646	+	0.130734i
$879$		−	15.9704i		−	0.538667i
$880$	20.5535	+	5.51908i	0.692859	+	0.186048i
$881$		−	41.3958i		−	1.39466i	−0.716750	−	0.697330i	$-0.754371\pi$
$881$		−	41.3958i		−	1.39466i	0.716750	−	0.697330i	$-0.245629\pi$
$882$	−14.0573	+	52.4344i	−0.473332	+	1.76556i
$883$	0.747150	+	1.80378i	0.0251436	+	0.0607020i	0.935953	−	0.352126i	$-0.114541\pi$
$883$	0.747150	+	1.80378i	0.0251436	+	0.0607020i	−0.910809	+	0.412828i	$0.864541\pi$
$884$	−1.80369	+	13.6722i	−0.0606648	+	0.459845i
$885$	40.5210	+	16.7844i	1.36210	+	0.564200i
$886$	1.38043	−	0.181549i	0.0463764	−	0.00609926i
$887$	−8.32657	+	8.32657i	−0.279579	+	0.279579i	−0.832941	−	0.553362i	$-0.813345\pi$
$887$	−8.32657	+	8.32657i	−0.279579	+	0.279579i	0.553362	+	0.832941i	$0.313345\pi$
$888$	0.0234029	−	58.3764i	0.000785349	−	1.95898i
$889$	0.994531	+	0.994531i	0.0333555	+	0.0333555i
$890$	−41.2733	−	31.6789i	−1.38348	−	1.06188i
$891$	−29.4370	+	71.0673i	−0.986178	+	2.38084i
$892$	22.9153	−	39.6661i	0.767263	−	1.32812i
$893$	23.6063	−	9.77805i	0.789955	−	0.327210i
$894$	5.32665	+	9.22888i	0.178150	+	0.308660i
$895$	−22.3422			−0.746818
$896$	−4.39371	+	16.3364i	−0.146784	+	0.545761i
$897$	−8.59191			−0.286876
$898$	26.8179	+	46.4642i	0.894924	+	1.55053i
$899$	−3.65478	+	1.51386i	−0.121894	+	0.0504901i
$900$	−1.43942	+	2.49160i	−0.0479805	+	0.0830535i
$901$	31.3446	−	75.6726i	1.04424	−	2.52102i
$902$	−7.29424	−	5.59862i	−0.242872	−	0.186413i
$903$	27.9810	+	27.9810i	0.931148	+	0.931148i
$904$	0.0163338	−	40.7432i	0.000543254	−	1.35510i
$905$	4.94316	−	4.94316i	0.164316	−	0.164316i
$906$	55.4600	−	7.29391i	1.84254	−	0.242324i
$907$	−9.40054	−	3.89383i	−0.312140	−	0.129293i	0.221114	−	0.975248i	$-0.429031\pi$
$907$	−9.40054	−	3.89383i	−0.312140	−	0.129293i	−0.533254	+	0.845955i	$0.679031\pi$
$908$	6.72638	−	50.9866i	0.223223	−	1.69205i
$909$	39.7374	+	95.9346i	1.31801	+	3.18195i
$910$	1.20235	−	4.48485i	0.0398577	−	0.148671i
$911$			40.8372i			1.35300i	0.736444	+	0.676499i	$0.236504\pi$
$911$			40.8372i			1.35300i	−0.736444	+	0.676499i	$0.763496\pi$
$912$	10.0075	−	37.2688i	0.331381	−	1.23409i
$913$		−	37.0858i		−	1.22736i
$914$	2.66126	+	0.713465i	0.0880268	+	0.0235993i
$915$	−35.2763	−	85.1645i	−1.16620	−	2.81545i
$916$	31.7122	+	41.3510i	1.04780	+	1.36628i
$917$	9.61688	+	3.98344i	0.317577	+	0.131545i
$918$	21.3824	+	162.584i	0.705725	+	5.36606i
$919$	−37.1208	+	37.1208i	−1.22450	+	1.22450i	−0.258488	+	0.966014i	$0.583224\pi$
$919$	−37.1208	+	37.1208i	−1.22450	+	1.22450i	−0.966014	+	0.258488i	$0.916776\pi$
$920$	6.13507	+	14.8282i	0.202267	+	0.488871i
$921$	32.2490	+	32.2490i	1.06264	+	1.06264i
$922$	32.1717	−	41.9154i	1.05952	−	1.38041i
$923$	−1.16309	+	2.80794i	−0.0382834	+	0.0924244i
$924$	23.2756	−	6.23001i	0.765711	−	0.204952i
$925$	−1.02397	+	0.424143i	−0.0336679	+	0.0139457i
$926$	−9.17622	+	5.29626i	−0.301549	+	0.174046i
$927$	13.8193			0.453886
$928$	4.89226	−	36.9695i	0.160596	−	1.21358i
$929$	2.46086			0.0807383			0.0403691	−	0.999185i	$-0.487147\pi$
$929$	2.46086			0.0807383			0.0403691	+	0.999185i	$0.487147\pi$
$930$	5.36658	−	3.09744i	0.175977	−	0.101569i
$931$	−12.7699	+	5.28946i	−0.418516	+	0.173355i
$932$	−11.6716	−	43.6057i	−0.382317	−	1.42835i
$933$	13.6947	−	33.0619i	0.448344	−	1.08240i
$934$	14.8876	−	19.3966i	0.487138	−	0.634675i
$935$	−25.9409	−	25.9409i	−0.848357	−	0.848357i
$936$	−21.0509	−	8.72947i	−0.688071	−	0.285332i
$937$	16.1090	−	16.1090i	0.526260	−	0.526260i	−0.393195	−	0.919455i	$-0.628630\pi$
$937$	16.1090	−	16.1090i	0.526260	−	0.526260i	0.919455	+	0.393195i	$0.128630\pi$
$938$	0.885704	+	6.73455i	0.0289193	+	0.219891i
$939$	33.6739	+	13.9482i	1.09891	+	0.455183i
$940$	−30.6905	+	23.5367i	−1.00102	+	0.767681i
$941$	−9.66357	−	23.3299i	−0.315023	−	0.760534i	−0.999504	−	0.0315023i	$-0.989971\pi$
$941$	−9.66357	−	23.3299i	−0.315023	−	0.760534i	0.684480	−	0.729031i	$-0.260029\pi$
$942$	−6.36122	−	1.70540i	−0.207260	−	0.0555648i
$943$		−	6.93352i		−	0.225786i
$944$	−23.8240	+	3.12353i	−0.775404	+	0.101662i
$945$		−	55.2123i		−	1.79606i
$946$	−7.06193	+	26.3414i	−0.229603	+	0.856433i
$947$	−4.95747	−	11.9684i	−0.161096	−	0.388920i	0.822634	−	0.568571i	$-0.192503\pi$
$947$	−4.95747	−	11.9684i	−0.161096	−	0.388920i	−0.983731	+	0.179650i	$0.942503\pi$
$948$	35.8459	+	4.72895i	1.16422	+	0.153589i
$949$	0.247235	+	0.102408i	0.00802558	+	0.00332431i
$950$	−0.726399	+	0.0955335i	−0.0235675	+	0.00309952i
$951$	48.8362	−	48.8362i	1.58362	−	1.58362i
$952$	20.6289	−	20.6123i	0.668586	−	0.668050i
$953$	9.34291	+	9.34291i	0.302646	+	0.302646i	0.842048	−	0.539402i	$-0.181350\pi$
$953$	9.34291	+	9.34291i	0.302646	+	0.302646i	−0.539402	+	0.842048i	$0.681350\pi$
$954$	107.372	+	82.4119i	3.47628	+	2.66818i
$955$	−16.5853	+	40.0406i	−0.536689	+	1.29568i
$956$	−21.4659	−	12.4010i	−0.694256	−	0.401076i
$957$	−49.0719	+	20.3262i	−1.58627	+	0.657054i
$958$	−12.0074	−	20.8038i	−0.387941	−	0.672141i
$959$	18.7504			0.605482
$960$	−0.0468341	+	58.4117i	−0.00151156	+	1.88523i
$961$	−30.6399			−0.988384
$962$	−4.38788	−	7.60237i	−0.141471	−	0.245110i
$963$	−28.8295	+	11.9416i	−0.929019	+	0.384812i
$964$	17.6072	+	10.1718i	0.567089	+	0.327611i
$965$	5.89267	−	14.2262i	0.189692	−	0.457956i
$966$	14.4126	+	11.0623i	0.463719	+	0.355923i
$967$	−10.2850	−	10.2850i	−0.330744	−	0.330744i	0.522125	−	0.852869i	$-0.325139\pi$
$967$	−10.2850	−	10.2850i	−0.330744	−	0.330744i	−0.852869	+	0.522125i	$0.825139\pi$
$968$	−10.2538	−	10.2621i	−0.329571	−	0.329835i
$969$	−47.0374	+	47.0374i	−1.51106	+	1.51106i
$970$	12.8015	−	1.68361i	0.411031	−	0.0540574i
$971$	−29.4022	−	12.1788i	−0.943562	−	0.390836i	−0.142754	−	0.989758i	$-0.545596\pi$
$971$	−29.4022	−	12.1788i	−0.943562	−	0.390836i	−0.800807	+	0.598922i	$0.795596\pi$
$972$	−109.285	−	14.4174i	−3.50532	−	0.462437i
$973$	−6.30453	−	15.2205i	−0.202114	−	0.487946i
$974$	−4.80035	+	17.9056i	−0.153813	+	0.573731i
$975$			0.593779i			0.0190161i
$976$	40.0481	+	30.7640i	1.28191	+	0.984731i
$977$			20.0011i			0.639893i	0.947436	+	0.319947i	$0.103665\pi$
$977$			20.0011i			0.639893i	−0.947436	+	0.319947i	$0.896335\pi$
$978$	−18.9041	−	5.06804i	−0.604486	−	0.162058i
$979$	−15.5360	−	37.5073i	−0.496534	−	1.19874i
$980$	16.6021	−	12.7322i	0.530335	−	0.406715i
$981$	−1.52401	−	0.631267i	−0.0486580	−	0.0201548i
$982$	1.31310	+	9.98428i	0.0419026	+	0.318611i
$983$	21.9840	−	21.9840i	0.701180	−	0.701180i	−0.263484	−	0.964664i	$-0.584871\pi$
$983$	21.9840	−	21.9840i	0.701180	−	0.701180i	0.964664	+	0.263484i	$0.0848715\pi$
$984$	9.66747	−	23.3129i	0.308188	−	0.743188i
$985$	−13.2480	−	13.2480i	−0.422116	−	0.422116i
$986$	−39.1409	+	50.9953i	−1.24650	+	1.62402i
$987$	−16.7575	+	40.4562i	−0.533398	+	1.28774i
$988$	−1.50029	−	5.60514i	−0.0477305	−	0.178323i
$989$	−18.9986	+	7.86948i	−0.604120	+	0.250235i
$990$	52.5058	−	30.3049i	1.66874	−	0.963152i
$991$	7.34402			0.233291			0.116645	−	0.993174i	$-0.462786\pi$
$991$	7.34402			0.233291			0.116645	+	0.993174i	$0.462786\pi$
$992$	−1.69924	+	2.93864i	−0.0539510	+	0.0933019i
$993$	38.2967			1.21531
$994$	5.56632	−	3.21272i	0.176553	−	0.101901i
$995$	32.8803	−	13.6195i	1.04238	−	0.431767i
$996$	98.3282	−	26.3188i	3.11565	−	0.833943i
$997$	−12.6055	+	30.4324i	−0.399221	+	0.963804i	0.588631	+	0.808402i	$0.299667\pi$
$997$	−12.6055	+	30.4324i	−0.399221	+	0.963804i	−0.987851	+	0.155402i	$0.950333\pi$
$998$	9.47629	−	12.3463i	0.299967	−	0.390816i
$999$	−73.8049	−	73.8049i	−2.33509	−	2.33509i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bf.a.53.17	✓	192
32.29	even	8	inner	416.2.bf.a.157.17	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bf.a.53.17	✓	192	1.1	even	1	trivial
416.2.bf.a.157.17	yes	192	32.29	even	8	inner

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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	416.2.bf.a.53.17

Level	$416$
Weight	$2$
Character	416.53
Analytic conductor	$3.322$
Analytic rank	$0$
Dimension	$192$
Inner twists	$2$