LMFDB - Embedded newform 224.3.w.a.99.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,3,Mod(43,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 0]))

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

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

chi := DirichletCharacter("224.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	224.w (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:	$6.10355792167$
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			99.13
Character	$\chi$	$=$	224.99
Dual form			224.3.w.a.43.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40435 - 1.42401i) q^{2} +(-1.23085 + 2.97155i) q^{3} +(-0.0555981 + 3.99961i) q^{4} +(0.908665 + 2.19371i) q^{5} +(5.96006 - 2.42035i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.77356 - 5.53769i) q^{8} +(-0.951124 - 0.951124i) q^{9} +O(q^{10})$	\(q+(-1.40435 - 1.42401i) q^{2} +(-1.23085 + 2.97155i) q^{3} +(-0.0555981 + 3.99961i) q^{4} +(0.908665 + 2.19371i) q^{5} +(5.96006 - 2.42035i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.77356 - 5.53769i) q^{8} +(-0.951124 - 0.951124i) q^{9} +(1.84778 - 4.37468i) q^{10} +(0.333793 + 0.805848i) q^{11} +(-11.8166 - 5.08816i) q^{12} +(-0.135317 + 0.326684i) q^{13} +(0.0367756 - 5.29137i) q^{14} -7.63715 q^{15} +(-15.9938 - 0.444742i) q^{16} +16.7741i q^{17} +(-0.0186966 + 2.69012i) q^{18} +(-19.8537 - 8.22367i) q^{19} +(-8.82451 + 3.51234i) q^{20} +(-7.86197 + 3.25654i) q^{21} +(0.678771 - 1.60702i) q^{22} +(-25.3488 + 25.3488i) q^{23} +(9.34908 + 23.9725i) q^{24} +(13.6910 - 13.6910i) q^{25} +(0.655233 - 0.266086i) q^{26} +(-22.7469 + 9.42208i) q^{27} +(-7.58661 + 7.37858i) q^{28} +(-4.81426 - 1.99413i) q^{29} +(10.7252 + 10.8754i) q^{30} +28.7483i q^{31} +(21.8276 + 23.3999i) q^{32} -2.80547 q^{33} +(23.8865 - 23.5567i) q^{34} +(-2.40410 + 5.80401i) q^{35} +(3.85701 - 3.75125i) q^{36} +(-15.4691 - 37.3456i) q^{37} +(16.1710 + 39.8208i) q^{38} +(-0.804201 - 0.804201i) q^{39} +(17.3943 + 7.63362i) q^{40} +(17.6512 + 17.6512i) q^{41} +(15.6783 + 6.62219i) q^{42} +(3.86180 + 9.32321i) q^{43} +(-3.24164 + 1.29024i) q^{44} +(1.22224 - 2.95074i) q^{45} +(71.6955 + 0.498291i) q^{46} -0.603030 q^{47} +(21.0076 - 46.9790i) q^{48} +7.00000i q^{49} +(-38.7230 - 0.269129i) q^{50} +(-49.8450 - 20.6465i) q^{51} +(-1.29909 - 0.559378i) q^{52} +(-12.2763 + 5.08500i) q^{53} +(45.3618 + 19.1599i) q^{54} +(-1.46449 + 1.46449i) q^{55} +(21.1614 + 0.441278i) q^{56} +(48.8741 - 48.8741i) q^{57} +(3.92125 + 9.65600i) q^{58} +(-73.4795 + 30.4362i) q^{59} +(0.424611 - 30.5456i) q^{60} +(-10.6864 - 4.42646i) q^{61} +(40.9379 - 40.3727i) q^{62} -3.55878i q^{63} +(2.66802 - 63.9444i) q^{64} -0.839607 q^{65} +(3.93986 + 3.99501i) q^{66} +(27.8797 - 67.3075i) q^{67} +(-67.0900 - 0.932609i) q^{68} +(-44.1245 - 106.526i) q^{69} +(11.6412 - 4.72741i) q^{70} +(-26.0262 - 26.0262i) q^{71} +(-10.7584 - 0.224345i) q^{72} +(55.0444 + 55.0444i) q^{73} +(-31.4565 + 74.4744i) q^{74} +(23.8318 + 57.5350i) q^{75} +(33.9953 - 78.9499i) q^{76} +(-0.883134 + 2.13207i) q^{77} +(-0.0158085 + 2.27457i) q^{78} -42.0771 q^{79} +(-13.5574 - 35.4899i) q^{80} -91.2966i q^{81} +(0.346975 - 49.9238i) q^{82} +(96.5828 + 40.0059i) q^{83} +(-12.5878 - 31.6259i) q^{84} +(-36.7975 + 15.2420i) q^{85} +(7.85300 - 18.5923i) q^{86} +(11.8513 - 11.8513i) q^{87} +(6.38971 + 2.80417i) q^{88} +(31.7987 - 31.7987i) q^{89} +(-5.91833 + 2.40340i) q^{90} +(-0.864324 + 0.358015i) q^{91} +(-99.9761 - 102.795i) q^{92} +(-85.4270 - 35.3850i) q^{93} +(0.846866 + 0.858720i) q^{94} -51.0258i q^{95} +(-96.4005 + 36.0599i) q^{96} +76.5787 q^{97} +(9.96806 - 9.83046i) q^{98} +(0.448983 - 1.08394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) $ 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−1.40435	−	1.42401i	−0.702175	−	0.712004i
$2$	−1.40435	−	1.42401i	−0.702175	−	0.712004i
$3$	−1.23085	+	2.97155i	−0.410285	+	0.990516i	0.574776	+	0.818311i	$0.305089\pi$
$3$	−1.23085	+	2.97155i	−0.410285	+	0.990516i	−0.985061	+	0.172205i	$0.944911\pi$
$4$	−0.0555981	+	3.99961i	−0.0138995	+	0.999903i
$5$	0.908665	+	2.19371i	0.181733	+	0.438742i	0.988324	−	0.152368i	$-0.0486899\pi$
$5$	0.908665	+	2.19371i	0.181733	+	0.438742i	−0.806591	+	0.591110i	$0.798690\pi$
$6$	5.96006	−	2.42035i	0.993343	−	0.403391i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$7$	1.87083	+	1.87083i	0.267261	+	0.267261i
$8$	5.77356	−	5.53769i	0.721695	−	0.692211i
$9$	−0.951124	−	0.951124i	−0.105680	−	0.105680i
$10$	1.84778	−	4.37468i	0.184778	−	0.437468i
$11$	0.333793	+	0.805848i	0.0303448	+	0.0732589i	0.938326	−	0.345753i	$-0.112377\pi$
$11$	0.333793	+	0.805848i	0.0303448	+	0.0732589i	−0.907981	+	0.419012i	$0.862377\pi$
$12$	−11.8166	−	5.08816i	−0.984717	−	0.424013i
$13$	−0.135317	+	0.326684i	−0.0104090	+	0.0251295i	−0.928999	−	0.370083i	$-0.879329\pi$
$13$	−0.135317	+	0.326684i	−0.0104090	+	0.0251295i	0.918590	+	0.395213i	$0.129329\pi$
$14$	0.0367756	−	5.29137i	0.00262683	−	0.377955i
$15$	−7.63715			−0.509143
$16$	−15.9938	−	0.444742i	−0.999614	−	0.0277964i
$17$			16.7741i			0.986712i	0.869827	+	0.493356i	$0.164230\pi$
$17$			16.7741i			0.986712i	−0.869827	+	0.493356i	$0.835770\pi$
$18$	−0.0186966	+	2.69012i	−0.00103870	+	0.149451i
$19$	−19.8537	−	8.22367i	−1.04493	−	0.432825i	−0.206852	−	0.978372i	$-0.566322\pi$
$19$	−19.8537	−	8.22367i	−1.04493	−	0.432825i	−0.838080	+	0.545547i	$0.816322\pi$
$20$	−8.82451	+	3.51234i	−0.441226	+	0.175617i
$21$	−7.86197	+	3.25654i	−0.374380	+	0.155073i
$22$	0.678771	−	1.60702i	0.0308532	−	0.0730462i
$23$	−25.3488	+	25.3488i	−1.10212	+	1.10212i	−0.107968	+	0.994154i	$0.534434\pi$
$23$	−25.3488	+	25.3488i	−1.10212	+	1.10212i	−0.994154	+	0.107968i	$0.965566\pi$
$24$	9.34908	+	23.9725i	0.389545	+	0.998854i
$25$	13.6910	−	13.6910i	0.547639	−	0.547639i
$26$	0.655233	−	0.266086i	0.0252013	−	0.0102341i
$27$	−22.7469	+	9.42208i	−0.842478	+	0.348966i
$28$	−7.58661	+	7.37858i	−0.270950	+	0.263521i
$29$	−4.81426	−	1.99413i	−0.166009	−	0.0687632i	0.298131	−	0.954525i	$-0.403637\pi$
$29$	−4.81426	−	1.99413i	−0.166009	−	0.0687632i	−0.464140	+	0.885762i	$0.653637\pi$
$30$	10.7252	+	10.8754i	0.357508	+	0.362512i
$31$			28.7483i			0.927366i	0.886001	+	0.463683i	$0.153472\pi$
$31$			28.7483i			0.927366i	−0.886001	+	0.463683i	$0.846528\pi$
$32$	21.8276	+	23.3999i	0.682113	+	0.731247i
$33$	−2.80547			−0.0850141
$34$	23.8865	−	23.5567i	0.702543	−	0.692845i
$35$	−2.40410	+	5.80401i	−0.0686886	+	0.165829i
$36$	3.85701	−	3.75125i	0.107139	−	0.104201i
$37$	−15.4691	−	37.3456i	−0.418083	−	1.00934i	−0.982903	−	0.184127i	$-0.941054\pi$
$37$	−15.4691	−	37.3456i	−0.418083	−	1.00934i	0.564820	−	0.825214i	$-0.308946\pi$
$38$	16.1710	+	39.8208i	0.425552	+	1.04791i
$39$	−0.804201	−	0.804201i	−0.0206205	−	0.0206205i
$40$	17.3943	+	7.63362i	0.434858	+	0.190840i
$41$	17.6512	+	17.6512i	0.430516	+	0.430516i	0.888804	−	0.458288i	$-0.151537\pi$
$41$	17.6512	+	17.6512i	0.430516	+	0.430516i	−0.458288	+	0.888804i	$0.651537\pi$
$42$	15.6783	+	6.62219i	0.373293	+	0.157671i
$43$	3.86180	+	9.32321i	0.0898093	+	0.216819i	0.962402	−	0.271630i	$-0.0875628\pi$
$43$	3.86180	+	9.32321i	0.0898093	+	0.216819i	−0.872592	+	0.488449i	$0.837563\pi$
$44$	−3.24164	+	1.29024i	−0.0736736	+	0.0293236i
$45$	1.22224	−	2.95074i	0.0271608	−	0.0655721i
$46$	71.6955	+	0.498291i	1.55860	+	0.0108324i
$47$	−0.603030			−0.0128304			−0.00641522	−	0.999979i	$-0.502042\pi$
$47$	−0.603030			−0.0128304			−0.00641522	+	0.999979i	$0.502042\pi$
$48$	21.0076	−	46.9790i	0.437659	−	0.978728i
$49$			7.00000i			0.142857i
$50$	−38.7230	−	0.269129i	−0.774460	−	0.00538257i
$51$	−49.8450	−	20.6465i	−0.977354	−	0.404833i
$52$	−1.29909	−	0.559378i	−0.0249824	−	0.0107573i
$53$	−12.2763	+	5.08500i	−0.231628	+	0.0959434i	−0.495479	−	0.868620i	$-0.665007\pi$
$53$	−12.2763	+	5.08500i	−0.231628	+	0.0959434i	0.263851	+	0.964563i	$0.415007\pi$
$54$	45.3618	+	19.1599i	0.840033	+	0.354813i
$55$	−1.46449	+	1.46449i	−0.0266271	+	0.0266271i
$56$	21.1614	+	0.441278i	0.377882	+	0.00787997i
$57$	48.8741	−	48.8741i	0.857440	−	0.857440i
$58$	3.92125	+	9.65600i	0.0676077	+	0.166483i
$59$	−73.4795	+	30.4362i	−1.24541	+	0.515868i	−0.905403	−	0.424554i	$-0.860431\pi$
$59$	−73.4795	+	30.4362i	−1.24541	+	0.515868i	−0.340012	+	0.940421i	$0.610431\pi$
$60$	0.424611	−	30.5456i	0.00707685	−	0.509094i
$61$	−10.6864	−	4.42646i	−0.175187	−	0.0725648i	0.293366	−	0.956000i	$-0.405225\pi$
$61$	−10.6864	−	4.42646i	−0.175187	−	0.0725648i	−0.468553	+	0.883435i	$0.655225\pi$
$62$	40.9379	−	40.3727i	0.660288	−	0.651173i
$63$		−	3.55878i		−	0.0564886i
$64$	2.66802	−	63.9444i	0.0416878	−	0.999131i
$65$	−0.839607			−0.0129170
$66$	3.93986	+	3.99501i	0.0596948	+	0.0605304i
$67$	27.8797	−	67.3075i	0.416114	−	1.00459i	−0.567348	−	0.823478i	$-0.692031\pi$
$67$	27.8797	−	67.3075i	0.416114	−	1.00459i	0.983463	−	0.181111i	$-0.0579694\pi$
$68$	−67.0900	−	0.932609i	−0.986617	−	0.0137148i
$69$	−44.1245	−	106.526i	−0.639485	−	1.54385i
$70$	11.6412	−	4.72741i	0.166302	−	0.0675344i
$71$	−26.0262	−	26.0262i	−0.366566	−	0.366566i	0.499657	−	0.866223i	$-0.333459\pi$
$71$	−26.0262	−	26.0262i	−0.366566	−	0.366566i	−0.866223	+	0.499657i	$0.833459\pi$
$72$	−10.7584	−	0.224345i	−0.149422	−	0.00311590i
$73$	55.0444	+	55.0444i	0.754033	+	0.754033i	0.975229	−	0.221196i	$-0.0709962\pi$
$73$	55.0444	+	55.0444i	0.754033	+	0.754033i	−0.221196	+	0.975229i	$0.570996\pi$
$74$	−31.4565	+	74.4744i	−0.425088	+	1.00641i
$75$	23.8318	+	57.5350i	0.317757	+	0.767133i
$76$	33.9953	−	78.9499i	0.447307	−	1.03881i
$77$	−0.883134	+	2.13207i	−0.0114693	+	0.0276893i
$78$	−0.0158085	+	2.27457i	−0.000202673	+	0.0291611i
$79$	−42.0771			−0.532621			−0.266311	−	0.963887i	$-0.585805\pi$
$79$	−42.0771			−0.532621			−0.266311	+	0.963887i	$0.585805\pi$
$80$	−13.5574	−	35.4899i	−0.169467	−	0.443624i
$81$		−	91.2966i		−	1.12712i
$82$	0.346975	−	49.9238i	0.00423141	−	0.608827i
$83$	96.5828	+	40.0059i	1.16365	+	0.481999i	0.879088	−	0.476659i	$-0.158152\pi$
$83$	96.5828	+	40.0059i	1.16365	+	0.481999i	0.284560	+	0.958658i	$0.408152\pi$
$84$	−12.5878	−	31.6259i	−0.149854	−	0.376499i
$85$	−36.7975	+	15.2420i	−0.432912	+	0.179318i
$86$	7.85300	−	18.5923i	0.0913140	−	0.216189i
$87$	11.8513	−	11.8513i	0.136222	−	0.136222i
$88$	6.38971	+	2.80417i	0.0726103	+	0.0318656i
$89$	31.7987	−	31.7987i	0.357289	−	0.357289i	−0.505524	−	0.862813i	$-0.668701\pi$
$89$	31.7987	−	31.7987i	0.357289	−	0.357289i	0.862813	+	0.505524i	$0.168701\pi$
$90$	−5.91833	+	2.40340i	−0.0657592	+	0.0267045i
$91$	−0.864324	+	0.358015i	−0.00949807	+	0.00393423i
$92$	−99.9761	−	102.795i	−1.08670	−	1.11733i
$93$	−85.4270	−	35.3850i	−0.918570	−	0.380484i
$94$	0.846866	+	0.858720i	0.00900922	+	0.00913532i
$95$		−	51.0258i		−	0.537114i
$96$	−96.4005	+	36.0599i	−1.00417	+	0.375624i
$97$	76.5787			0.789472			0.394736	−	0.918795i	$-0.370836\pi$
$97$	76.5787			0.789472			0.394736	+	0.918795i	$0.370836\pi$
$98$	9.96806	−	9.83046i	0.101715	−	0.100311i
$99$	0.448983	−	1.08394i	0.00453518	−	0.0109489i
$100$	53.9974	+	55.5198i	0.539974	+	0.555198i
$101$	−3.16067	−	7.63054i	−0.0312938	−	0.0755499i	0.907460	−	0.420138i	$-0.138018\pi$
$101$	−3.16067	−	7.63054i	−0.0312938	−	0.0755499i	−0.938754	+	0.344588i	$0.888018\pi$
$102$	40.5991	+	99.9747i	0.398031	+	0.980144i
$103$	115.509	+	115.509i	1.12145	+	1.12145i	0.991524	+	0.129921i	$0.0414724\pi$
$103$	115.509	+	115.509i	1.12145	+	1.12145i	0.129921	+	0.991524i	$0.458528\pi$
$104$	1.02781	+	2.63547i	0.00988281	+	0.0253411i
$105$	−14.2878	−	14.2878i	−0.136074	−	0.136074i
$106$	24.4813	+	10.3404i	0.230955	+	0.0975508i
$107$	62.4749	+	150.828i	0.583878	+	1.40961i	0.889272	+	0.457380i	$0.151212\pi$
$107$	62.4749	+	150.828i	0.583878	+	1.40961i	−0.305394	+	0.952226i	$0.598788\pi$
$108$	−36.4200	−	91.5027i	−0.337222	−	0.847247i
$109$	48.9263	−	118.119i	0.448865	−	1.08366i	−0.523883	−	0.851790i	$-0.675517\pi$
$109$	48.9263	−	118.119i	0.448865	−	1.08366i	0.972748	−	0.231866i	$-0.0744830\pi$
$110$	4.14211	+	0.0287880i	0.0376555	+	0.000261709i
$111$	130.014			1.17130
$112$	−29.0897	−	30.7537i	−0.259729	−	0.274587i
$113$			198.203i			1.75401i	0.480482	+	0.877005i	$0.340462\pi$
$113$			198.203i			1.75401i	−0.480482	+	0.877005i	$0.659538\pi$
$114$	−138.233	−	0.960735i	−1.21257	−	0.00842750i
$115$	−78.6415	−	32.5744i	−0.683839	−	0.283255i
$116$	8.24342	−	19.1443i	0.0710640	−	0.165037i
$117$	0.439420	−	0.182014i	0.00375572	−	0.00155567i
$118$	146.532	+	61.8923i	1.24180	+	0.524511i
$119$	−31.3815	+	31.3815i	−0.263710	+	0.263710i
$120$	−44.0935	+	42.2921i	−0.367446	+	0.352434i
$121$	85.0219	−	85.0219i	0.702661	−	0.702661i
$122$	8.70416	+	21.4338i	0.0713456	+	0.175687i
$123$	−74.1772	+	30.7252i	−0.603067	+	0.249798i
$124$	−114.982	−	1.59835i	−0.927276	−	0.0128899i
$125$	97.3173	+	40.3101i	0.778538	+	0.322481i
$126$	−5.06773	+	4.99778i	−0.0402201	+	0.0396649i
$127$		−	39.9658i		−	0.314691i	−0.987544	−	0.157346i	$-0.949706\pi$
$127$		−	39.9658i		−	0.314691i	0.987544	−	0.157346i	$-0.0502936\pi$
$128$	−94.8041	+	86.0010i	−0.740657	+	0.671883i
$129$	−32.4577			−0.251610
$130$	1.17910	+	1.19561i	0.00907002	+	0.00919698i
$131$	−12.8494	+	31.0212i	−0.0980871	+	0.236803i	−0.965305	−	0.261126i	$-0.915906\pi$
$131$	−12.8494	+	31.0212i	−0.0980871	+	0.236803i	0.867218	+	0.497929i	$0.165906\pi$
$132$	0.155979	−	11.2208i	0.00118166	−	0.0850059i
$133$	−21.7578	−	52.5280i	−0.163592	−	0.394947i
$134$	−134.999	+	54.8224i	−1.00746	+	0.409123i
$135$	−41.3386	−	41.3386i	−0.306212	−	0.306212i
$136$	92.8898	+	96.8463i	0.683013	+	0.712105i
$137$	74.9065	+	74.9065i	0.546763	+	0.546763i	0.925503	−	0.378740i	$-0.123643\pi$
$137$	74.9065	+	74.9065i	0.546763	+	0.546763i	−0.378740	+	0.925503i	$0.623643\pi$
$138$	−89.7275	+	212.433i	−0.650199	+	1.53937i
$139$	103.084	+	248.866i	0.741609	+	1.79040i	0.599207	+	0.800594i	$0.295483\pi$
$139$	103.084	+	248.866i	0.741609	+	1.79040i	0.142402	+	0.989809i	$0.454517\pi$
$140$	−23.0801	−	9.93816i	−0.164858	−	0.0709869i
$141$	0.742243	−	1.79193i	0.00526413	−	0.0127087i
$142$	−0.511606	+	73.6114i	−0.00360286	+	0.518390i
$143$	−0.308425			−0.00215682
$144$	14.7891	+	15.6351i	0.102702	+	0.108577i
$145$		−	12.3731i		−	0.0853316i
$146$	1.08203	−	155.685i	0.00741115	−	1.06634i
$147$	−20.8008	−	8.61598i	−0.141502	−	0.0586121i
$148$	150.228	−	59.7939i	1.01505	−	0.404013i
$149$	−146.387	+	60.6355i	−0.982463	+	0.406949i	−0.815337	−	0.578986i	$-0.803448\pi$
$149$	−146.387	+	60.6355i	−0.982463	+	0.406949i	−0.167125	+	0.985936i	$0.553448\pi$
$150$	48.4621	−	114.736i	0.323081	−	0.764906i
$151$	178.520	−	178.520i	1.18225	−	1.18225i	0.203094	−	0.979159i	$-0.434900\pi$
$151$	178.520	−	178.520i	1.18225	−	1.18225i	0.979159	−	0.203094i	$-0.0650998\pi$
$152$	−160.167	+	62.4637i	−1.05373	+	0.410946i
$153$	15.9543	−	15.9543i	0.104276	−	0.104276i
$154$	4.27632	−	1.73659i	0.0277683	−	0.0112766i
$155$	−63.0655	+	26.1226i	−0.406874	+	0.168533i
$156$	3.26120	−	3.17178i	0.0209052	−	0.0203319i
$157$	94.7012	+	39.2265i	0.603192	+	0.249850i	0.663315	−	0.748341i	$-0.269149\pi$
$157$	94.7012	+	39.2265i	0.603192	+	0.249850i	−0.0601224	+	0.998191i	$0.519149\pi$
$158$	59.0910	+	59.9181i	0.373994	+	0.379229i
$159$		−	42.7384i		−	0.268795i
$160$	−31.4986	+	69.1461i	−0.196866	+	0.432163i
$161$	−94.8465			−0.589109
$162$	−130.007	+	128.212i	−0.802513	+	0.791434i
$163$	−34.4391	+	83.1433i	−0.211283	+	0.510081i	−0.993621	−	0.112772i	$-0.964027\pi$
$163$	−34.4391	+	83.1433i	−0.211283	+	0.510081i	0.782338	+	0.622854i	$0.214027\pi$
$164$	−71.5792	+	69.6164i	−0.436458	+	0.424490i
$165$	−2.54923	−	6.15438i	−0.0154499	−	0.0372993i
$166$	−78.6674	−	193.717i	−0.473900	−	1.16697i
$167$	−1.51404	−	1.51404i	−0.00906611	−	0.00906611i	0.702559	−	0.711625i	$-0.252041\pi$
$167$	−1.51404	−	1.51404i	−0.00906611	−	0.00906611i	−0.711625	+	0.702559i	$0.752041\pi$
$168$	−27.3579	+	62.3390i	−0.162845	+	0.371065i
$169$	119.413	+	119.413i	0.706584	+	0.706584i
$170$	73.3814	+	30.9948i	0.431655	+	0.182322i
$171$	11.0616	+	26.7051i	0.0646877	+	0.156170i
$172$	−37.5039	+	14.9274i	−0.218046	+	0.0867869i
$173$	39.2972	−	94.8718i	0.227151	−	0.548392i	−0.768677	−	0.639637i	$-0.779085\pi$
$173$	39.2972	−	94.8718i	0.227151	−	0.548392i	0.995828	+	0.0912450i	$0.0290846\pi$
$174$	−33.5198	−	0.232966i	−0.192642	−	0.00133888i
$175$	51.2269			0.292725
$176$	−4.98023	−	13.0370i	−0.0282968	−	0.0740741i
$177$		−	255.810i		−	1.44526i
$178$	−89.9382	−	0.625079i	−0.505271	−	0.00351168i
$179$	−171.842	−	71.1793i	−0.960012	−	0.397650i	−0.153027	−	0.988222i	$-0.548902\pi$
$179$	−171.842	−	71.1793i	−0.960012	−	0.397650i	−0.806985	+	0.590572i	$0.798902\pi$
$180$	11.7339	+	5.05253i	0.0651882	+	0.0280696i
$181$	−20.5449	+	8.50998i	−0.113508	+	0.0470165i	−0.438715	−	0.898626i	$-0.644566\pi$
$181$	−20.5449	+	8.50998i	−0.113508	+	0.0470165i	0.325207	+	0.945643i	$0.394566\pi$
$182$	1.72363	+	0.728026i	0.00947049	+	0.00400014i
$183$	26.3068	−	26.3068i	0.143753	−	0.143753i
$184$	−5.97911	+	286.727i	−0.0324951	+	1.55830i
$185$	67.8693	−	67.8693i	0.366861	−	0.366861i
$186$	69.5809	+	171.342i	0.374091	+	0.921192i
$187$	−13.5174	+	5.59908i	−0.0722855	+	0.0299416i
$188$	0.0335273	−	2.41189i	0.000178337	−	0.0128292i
$189$	−60.1827	−	24.9285i	−0.318427	−	0.131897i
$190$	−72.6612	+	71.6582i	−0.382427	+	0.377148i
$191$		−	164.910i		−	0.863404i	−0.902016	−	0.431702i	$-0.857913\pi$
$191$		−	164.910i		−	0.863404i	0.902016	−	0.431702i	$-0.142087\pi$
$192$	186.730	+	86.6344i	0.972551	+	0.451221i
$193$	−187.552			−0.971772			−0.485886	−	0.874022i	$-0.661503\pi$
$193$	−187.552			−0.971772			−0.485886	+	0.874022i	$0.661503\pi$
$194$	−107.543	−	109.049i	−0.554347	−	0.562107i
$195$	1.03343	−	2.49493i	0.00529966	−	0.0127945i
$196$	−27.9973	−	0.389187i	−0.142843	−	0.00198565i
$197$	71.8958	+	173.572i	0.364953	+	0.881075i	0.994560	+	0.104161i	$0.0332158\pi$
$197$	71.8958	+	173.572i	0.364953	+	0.881075i	−0.629607	+	0.776914i	$0.716784\pi$
$198$	−2.17407	+	0.882877i	−0.0109801	+	0.00445897i
$199$	−236.861	−	236.861i	−1.19026	−	1.19026i	−0.976995	−	0.213260i	$-0.931592\pi$
$199$	−236.861	−	236.861i	−1.19026	−	1.19026i	−0.213260	−	0.976995i	$-0.568408\pi$
$200$	3.22934	−	154.862i	0.0161467	−	0.774310i
$201$	165.691	+	165.691i	0.824336	+	0.824336i
$202$	−6.42726	+	15.2168i	−0.0318181	+	0.0753306i
$203$	−5.27598	−	12.7373i	−0.0259900	−	0.0627455i
$204$	85.3493	−	198.213i	0.418379	−	0.971632i
$205$	−22.6825	+	54.7605i	−0.110647	+	0.267124i
$206$	2.27060	−	326.701i	0.0110223	−	1.58592i
$207$	48.2197			0.232945
$208$	2.30952	−	5.16474i	0.0111035	−	0.0248305i
$209$		−	18.7441i		−	0.0896845i
$210$	−0.280860	+	40.4110i	−0.00133743	+	0.192433i
$211$	−57.0854	−	23.6456i	−0.270547	−	0.112064i	0.243286	−	0.969955i	$-0.421775\pi$
$211$	−57.0854	−	23.6456i	−0.270547	−	0.112064i	−0.513833	+	0.857890i	$0.671775\pi$
$212$	−19.6555	−	49.3831i	−0.0927146	−	0.232939i
$213$	109.372	−	45.3036i	0.513486	−	0.212693i
$214$	127.043	−	300.780i	0.593660	−	1.40551i
$215$	−16.9433	+	16.9433i	−0.0788062	+	0.0788062i
$216$	−79.1542	+	180.364i	−0.366454	+	0.835020i
$217$	−53.7832	+	53.7832i	−0.247849	+	0.247849i
$218$	−236.911	+	96.2084i	−1.08675	+	0.441323i
$219$	−231.319	+	95.8153i	−1.05625	+	0.437513i
$220$	−5.77597	−	5.93882i	−0.0262544	−	0.0269946i
$221$	−5.47983	−	2.26982i	−0.0247956	−	0.0102707i
$222$	−182.586	−	185.142i	−0.822459	−	0.833971i
$223$		−	252.834i		−	1.13379i	−0.823792	−	0.566893i	$-0.808145\pi$
$223$		−	252.834i		−	1.13379i	0.823792	−	0.566893i	$-0.191855\pi$
$224$	−2.94148	+	84.6129i	−0.0131316	+	0.377736i
$225$	−26.0436			−0.115749
$226$	282.243	−	278.347i	1.24886	−	1.23162i
$227$	66.8039	−	161.279i	0.294290	−	0.710479i	−0.705708	−	0.708503i	$-0.749371\pi$
$227$	66.8039	−	161.279i	0.294290	−	0.710479i	0.999998	−	0.00197642i	$-0.000629114\pi$
$228$	192.760	+	198.195i	0.845439	+	0.869275i
$229$	4.81730	+	11.6300i	0.0210362	+	0.0507860i	0.934049	−	0.357146i	$-0.116250\pi$
$229$	4.81730	+	11.6300i	0.0210362	+	0.0507860i	−0.913012	+	0.407932i	$0.866250\pi$
$230$	64.0541	+	157.732i	0.278496	+	0.685791i
$231$	−5.24854	−	5.24854i	−0.0227210	−	0.0227210i
$232$	−38.8383	+	15.1466i	−0.167406	+	0.0652872i
$233$	172.377	+	172.377i	0.739815	+	0.739815i	0.972542	−	0.232727i	$-0.0747648\pi$
$233$	172.377	+	172.377i	0.739815	+	0.739815i	−0.232727	+	0.972542i	$0.574765\pi$
$234$	−0.876288	−	0.370126i	−0.00374482	−	0.00158174i
$235$	−0.547952	−	1.32287i	−0.00233171	−	0.00562925i
$236$	−117.648	−	295.582i	−0.498507	−	1.25246i
$237$	51.7908	−	125.034i	0.218527	−	0.527570i
$238$	88.7581	+	0.616877i	0.372933	+	0.00259192i
$239$	163.034			0.682149			0.341075	−	0.940036i	$-0.389209\pi$
$239$	163.034			0.682149			0.341075	+	0.940036i	$0.389209\pi$
$240$	122.147	+	3.39656i	0.508946	+	0.0141523i
$241$			175.777i			0.729365i	0.931132	+	0.364682i	$0.118822\pi$
$241$			175.777i			0.729365i	−0.931132	+	0.364682i	$0.881178\pi$
$242$	−240.473	−	1.67131i	−0.993688	−	0.00690623i
$243$	66.5697	+	27.5741i	0.273950	+	0.113474i
$244$	18.2983	−	42.4954i	0.0749929	−	0.174161i
$245$	−15.3560	+	6.36065i	−0.0626774	+	0.0259618i
$246$	147.924	+	62.4800i	0.601316	+	0.253984i
$247$	5.37308	−	5.37308i	0.0217534	−	0.0217534i
$248$	159.199	+	165.980i	0.641933	+	0.669275i
$249$	−237.759	+	237.759i	−0.954855	+	0.954855i
$250$	−79.2656	−	195.190i	−0.317063	−	0.780761i
$251$	154.370	−	63.9420i	0.615018	−	0.254749i	−0.0533543	−	0.998576i	$-0.516991\pi$
$251$	154.370	−	63.9420i	0.615018	−	0.254749i	0.668372	+	0.743827i	$0.266991\pi$
$252$	14.2337	+	0.197861i	0.0564831	+	0.000785164i
$253$	−28.8885	−	11.9660i	−0.114184	−	0.0472965i
$254$	−56.9116	+	56.1259i	−0.224061	+	0.220968i
$255$		−	128.106i		−	0.502378i
$256$	255.604	+	14.2262i	0.998455	+	0.0555712i
$257$	69.6311			0.270938			0.135469	−	0.990782i	$-0.456746\pi$
$257$	69.6311			0.270938			0.135469	+	0.990782i	$0.456746\pi$
$258$	45.5819	+	46.2200i	0.176674	+	0.179147i
$259$	40.9273	−	98.8072i	0.158020	−	0.381495i
$260$	0.0466806	−	3.35810i	0.000179541	−	0.0129158i
$261$	2.68229	+	6.47562i	0.0102770	+	0.0248108i
$262$	62.2195	−	25.2670i	0.237479	−	0.0964390i
$263$	20.9352	+	20.9352i	0.0796014	+	0.0796014i	0.745786	−	0.666185i	$-0.232074\pi$
$263$	20.9352	+	20.9352i	0.0796014	+	0.0796014i	−0.666185	+	0.745786i	$0.732074\pi$
$264$	−16.1975	+	15.5358i	−0.0613543	+	0.0588477i
$265$	−22.3100	−	22.3100i	−0.0841888	−	0.0841888i
$266$	−44.2447	+	104.751i	−0.166333	+	0.393801i
$267$	55.3518	+	133.631i	0.207310	+	0.500491i
$268$	267.654	+	115.250i	0.998708	+	0.430038i
$269$	168.969	−	407.928i	0.628139	−	1.51646i	−0.213794	−	0.976879i	$-0.568582\pi$
$269$	168.969	−	407.928i	0.628139	−	1.51646i	0.841933	−	0.539583i	$-0.181418\pi$
$270$	−0.812609	+	116.920i	−0.00300966	+	0.433039i
$271$	384.304			1.41809			0.709047	−	0.705161i	$-0.249125\pi$
$271$	384.304			1.41809			0.709047	+	0.705161i	$0.249125\pi$
$272$	7.46015	−	268.282i	0.0274270	−	0.986331i
$273$		−	3.00904i		−	0.0110221i
$274$	1.47247	−	211.863i	0.00537396	−	0.773221i
$275$	15.6028	+	6.46289i	0.0567374	+	0.0235014i
$276$	428.515	−	170.558i	1.55259	−	0.617964i
$277$	−430.107	+	178.156i	−1.55273	+	0.643164i	−0.983808	−	0.179225i	$-0.942641\pi$
$277$	−430.107	+	178.156i	−1.55273	+	0.643164i	−0.568926	+	0.822389i	$0.692641\pi$
$278$	209.622	−	496.287i	0.754034	−	1.78521i
$279$	27.3432	−	27.3432i	0.0980044	−	0.0980044i
$280$	18.2606	+	46.8230i	0.0652164	+	0.167225i
$281$	−101.697	+	101.697i	−0.361910	+	0.361910i	−0.864516	−	0.502606i	$-0.832375\pi$
$281$	−101.697	+	101.697i	−0.361910	+	0.361910i	0.502606	+	0.864516i	$0.332375\pi$
$282$	−3.59410	+	1.45954i	−0.0127450	+	0.00517568i
$283$	−79.9520	+	33.1172i	−0.282516	+	0.117022i	−0.519442	−	0.854506i	$-0.673860\pi$
$283$	−79.9520	+	33.1172i	−0.282516	+	0.117022i	0.236926	+	0.971528i	$0.423860\pi$
$284$	105.542	−	102.648i	0.371626	−	0.361435i
$285$	151.626	+	62.8054i	0.532020	+	0.220370i
$286$	0.433137	+	0.439200i	0.00151447	+	0.00153566i
$287$			66.0446i			0.230120i
$288$	1.49544	−	43.0170i	0.00519250	−	0.149364i
$289$	7.62928			0.0263989
$290$	−17.6194	+	17.3762i	−0.0607565	+	0.0599178i
$291$	−94.2573	+	227.557i	−0.323908	+	0.781984i
$292$	−223.217	+	217.096i	−0.764441	+	0.743479i
$293$	161.516	+	389.935i	0.551250	+	1.33083i	0.916541	+	0.399941i	$0.130969\pi$
$293$	161.516	+	389.935i	0.551250	+	1.33083i	−0.365291	+	0.930893i	$0.619031\pi$
$294$	16.9424	+	41.7204i	0.0576273	+	0.141906i
$295$	−133.536	−	133.536i	−0.452666	−	0.452666i
$296$	−296.120	−	129.954i	−1.00041	−	0.439035i
$297$	−15.1855	−	15.1855i	−0.0511297	−	0.0511297i
$298$	291.924	+	123.303i	0.979611	+	0.413768i
$299$	−4.85092	−	11.7112i	−0.0162238	−	0.0391678i
$300$	−231.443	+	92.1190i	−0.771476	+	0.307063i
$301$	−10.2174	+	24.6669i	−0.0339447	+	0.0819498i
$302$	−504.919	−	3.50924i	−1.67192	−	0.0116200i
$303$	26.5648			0.0876728
$304$	313.879	+	140.358i	1.03250	+	0.461703i
$305$		−	27.4650i		−	0.0900493i
$306$	−45.1244	−	0.313619i	−0.147465	−	0.00102490i
$307$	209.762	+	86.8863i	0.683264	+	0.283017i	0.697190	−	0.716886i	$-0.254433\pi$
$307$	209.762	+	86.8863i	0.683264	+	0.283017i	−0.0139268	+	0.999903i	$0.504433\pi$
$308$	−8.47837	−	3.65073i	−0.0275272	−	0.0118530i
$309$	−485.415	+	201.065i	−1.57092	+	0.650697i
$310$	125.765	+	53.1205i	0.405693	+	0.171357i
$311$	−334.289	+	334.289i	−1.07488	+	1.07488i	−0.0779240	+	0.996959i	$0.524829\pi$
$311$	−334.289	+	334.289i	−1.07488	+	1.07488i	−0.996959	+	0.0779240i	$0.975171\pi$
$312$	−9.09651	−	0.189689i	−0.0291555	−	0.000607979i
$313$	−162.999	+	162.999i	−0.520765	+	0.520765i	−0.917802	−	0.397038i	$-0.870038\pi$
$313$	−162.999	+	162.999i	−0.520765	+	0.520765i	0.397038	+	0.917802i	$0.370038\pi$
$314$	−77.1348	−	189.943i	−0.245652	−	0.604914i
$315$	7.80693	−	3.23374i	0.0247839	−	0.0102658i
$316$	2.33941	−	168.292i	0.00740318	−	0.532570i
$317$	−165.147	−	68.4062i	−0.520969	−	0.215792i	0.106673	−	0.994294i	$-0.465980\pi$
$317$	−165.147	−	68.4062i	−0.520969	−	0.215792i	−0.627643	+	0.778502i	$0.715980\pi$
$318$	−60.8598	+	60.0197i	−0.191383	+	0.188741i
$319$		−	4.54519i		−	0.0142482i
$320$	142.700	−	52.2511i	0.445937	−	0.163285i
$321$	−525.089			−1.63579
$322$	133.198	+	135.062i	0.413658	+	0.419448i
$323$	137.945	−	333.028i	0.427074	−	1.03105i
$324$	365.151	+	5.07592i	1.12701	+	0.0156664i
$325$	2.62000	+	6.32524i	0.00806154	+	0.0194623i
$326$	166.761	−	67.7208i	0.511538	−	0.207733i
$327$	290.773	+	290.773i	0.889216	+	0.889216i
$328$	199.657	+	4.16343i	0.608709	+	0.0126934i
$329$	−1.12817	−	1.12817i	−0.00342908	−	0.00342908i
$330$	−5.18388	+	12.2730i	−0.0157087	+	0.0371910i
$331$	−126.009	−	304.214i	−0.380693	−	0.919075i	−0.991832	−	0.127551i	$-0.959288\pi$
$331$	−126.009	−	304.214i	−0.380693	−	0.919075i	0.611139	−	0.791523i	$-0.290712\pi$
$332$	−165.378	+	384.070i	−0.498127	+	1.15684i
$333$	−20.8073	+	50.2333i	−0.0624844	+	0.150851i
$334$	−0.0297620	+	4.28225i	−8.91079e−5	+	0.0128211i
$335$	172.986			0.516377
$336$	127.191	−	48.5879i	0.378545	−	0.144607i
$337$		−	134.073i		−	0.397844i	−0.980015	−	0.198922i	$-0.936256\pi$
$337$		−	134.073i		−	0.397844i	0.980015	−	0.198922i	$-0.0637440\pi$
$338$	2.34734	−	337.742i	0.00694479	−	0.999236i
$339$	−588.970	−	243.959i	−1.73737	−	0.719644i
$340$	−58.9164	−	148.023i	−0.173283	−	0.435363i
$341$	−23.1668	+	9.59600i	−0.0679378	+	0.0281408i
$342$	22.4939	−	53.2551i	0.0657715	−	0.155717i
$343$	−13.0958	+	13.0958i	−0.0381802	+	0.0381802i
$344$	73.9253	+	32.4427i	0.214899	+	0.0943101i
$345$	193.593	−	193.593i	0.561138	−	0.561138i
$346$	−190.285	+	77.2738i	−0.549958	+	0.223335i
$347$	336.081	−	139.209i	0.968532	−	0.401179i	0.158366	−	0.987380i	$-0.449377\pi$
$347$	336.081	−	139.209i	0.968532	−	0.401179i	0.810165	+	0.586201i	$0.199377\pi$
$348$	46.7417	+	48.0596i	0.134315	+	0.138102i
$349$	−620.815	−	257.150i	−1.77884	−	0.736820i	−0.992961	−	0.118440i	$-0.962211\pi$
$349$	−620.815	−	257.150i	−1.77884	−	0.736820i	−0.785879	−	0.618380i	$-0.787789\pi$
$350$	−71.9406	−	72.9476i	−0.205545	−	0.208422i
$351$		−	8.70601i		−	0.0248035i
$352$	−11.5709	+	25.4005i	−0.0328717	+	0.0721604i
$353$	156.550			0.443485			0.221743	−	0.975105i	$-0.428826\pi$
$353$	156.550			0.443485			0.221743	+	0.975105i	$0.428826\pi$
$354$	−364.276	+	359.247i	−1.02903	+	1.01482i
$355$	33.4448	−	80.7430i	0.0942108	−	0.227445i
$356$	125.415	+	128.951i	0.352288	+	0.362221i
$357$	−54.6255	−	131.878i	−0.153013	−	0.369405i
$358$	139.967	+	344.665i	0.390968	+	0.962752i
$359$	−400.957	−	400.957i	−1.11687	−	1.11687i	−0.992198	−	0.124675i	$-0.960211\pi$
$359$	−400.957	−	400.957i	−1.11687	−	1.11687i	−0.124675	−	0.992198i	$-0.539789\pi$
$360$	−9.28363	−	23.8047i	−0.0257879	−	0.0661241i
$361$	71.2752	+	71.2752i	0.197438	+	0.197438i
$362$	40.9705	+	17.3051i	0.113178	+	0.0478042i
$363$	147.997	+	357.296i	0.407705	+	0.984287i
$364$	−1.38387	−	3.47687i	−0.00380183	−	0.00955183i
$365$	−70.7346	+	170.768i	−0.193793	+	0.467859i
$366$	−74.4052	−	0.517123i	−0.203293	−	0.00141291i
$367$	212.537			0.579121			0.289561	−	0.957160i	$-0.406491\pi$
$367$	212.537			0.579121			0.289561	+	0.957160i	$0.406491\pi$
$368$	416.698	−	394.150i	1.13233	−	1.07106i
$369$		−	33.5769i		−	0.0909942i
$370$	−191.959	−	1.33413i	−0.518807	−	0.00360576i
$371$	−32.4800	−	13.4536i	−0.0875471	−	0.0362632i
$372$	146.276	−	339.708i	0.393215	−	0.913193i
$373$	−639.264	+	264.792i	−1.71384	+	0.709897i	−0.713890	+	0.700258i	$0.753068\pi$
$373$	−639.264	+	264.792i	−1.71384	+	0.709897i	−0.999954	+	0.00963962i	$0.996932\pi$
$374$	26.9563	+	11.3858i	0.0720756	+	0.0304433i
$375$	−239.567	+	239.567i	−0.638845	+	0.638845i
$376$	−3.48163	+	3.33939i	−0.00925966	+	0.00888137i
$377$	1.30290	−	1.30290i	0.00345597	−	0.00345597i
$378$	49.0192	+	120.709i	0.129680	+	0.319336i
$379$	603.746	−	250.080i	1.59300	−	0.659841i	0.602593	−	0.798049i	$-0.294134\pi$
$379$	603.746	−	250.080i	1.59300	−	0.659841i	0.990403	+	0.138208i	$0.0441342\pi$
$380$	204.084	+	2.83694i	0.537062	+	0.00746563i
$381$	118.760	+	49.1920i	0.311706	+	0.129113i
$382$	−234.833	+	231.592i	−0.614747	+	0.606261i
$383$			431.080i			1.12554i	0.826615	+	0.562768i	$0.190264\pi$
$383$			431.080i			1.12554i	−0.826615	+	0.562768i	$0.809736\pi$
$384$	−138.866	−	387.570i	−0.361630	−	1.00930i
$385$	−5.47962			−0.0142328
$386$	263.389	+	267.076i	0.682355	+	0.691906i
$387$	5.19448	−	12.5406i	0.0134224	−	0.0324046i
$388$	−4.25763	+	306.285i	−0.0109733	+	0.789395i
$389$	107.499	+	259.525i	0.276347	+	0.667160i	0.999729	−	0.0232881i	$-0.00741349\pi$
$389$	107.499	+	259.525i	0.276347	+	0.667160i	−0.723382	+	0.690448i	$0.757413\pi$
$390$	−5.00411	+	2.03214i	−0.0128310	+	0.00521062i
$391$	−425.204	−	425.204i	−1.08748	−	1.08748i
$392$	38.7638	+	40.4149i	0.0988873	+	0.103099i
$393$	−76.3652	−	76.3652i	−0.194314	−	0.194314i
$394$	146.201	−	346.136i	0.371068	−	0.878517i
$395$	−38.2340	−	92.3049i	−0.0967948	−	0.233683i
$396$	4.31038	+	1.85602i	0.0108848	+	0.00468692i
$397$	143.741	−	347.022i	0.362069	−	0.874112i	−0.632928	−	0.774210i	$-0.718147\pi$
$397$	143.741	−	347.022i	0.362069	−	0.874112i	0.994997	−	0.0999013i	$-0.0318527\pi$
$398$	−4.65606	+	669.927i	−0.0116986	+	1.68323i
$399$	182.870			0.458321
$400$	−225.060	+	212.882i	−0.562650	+	0.532205i
$401$		−	304.430i		−	0.759177i	−0.925155	−	0.379589i	$-0.876066\pi$
$401$		−	304.430i		−	0.759177i	0.925155	−	0.379589i	$-0.123934\pi$
$402$	3.25706	−	468.635i	0.00810214	−	1.16576i
$403$	−9.39161	−	3.89013i	−0.0233043	−	0.00965294i
$404$	30.6949	−	12.2172i	0.0759776	−	0.0302407i
$405$	200.278	−	82.9579i	0.494514	−	0.204834i
$406$	−10.7287	+	25.4007i	−0.0264255	+	0.0625633i
$407$	24.9314	−	24.9314i	0.0612566	−	0.0612566i
$408$	−402.117	+	156.823i	−0.985582	+	0.384369i
$409$	−137.631	+	137.631i	−0.336505	+	0.336505i	−0.855050	−	0.518545i	$-0.826474\pi$
$409$	−137.631	+	137.631i	−0.336505	+	0.336505i	0.518545	+	0.855050i	$0.326474\pi$
$410$	109.834	−	44.6028i	0.267887	−	0.108787i
$411$	−314.787	+	130.389i	−0.765906	+	0.317249i
$412$	−468.413	+	455.569i	−1.13692	+	1.10575i
$413$	−194.408	−	80.5266i	−0.470722	−	0.194980i
$414$	−67.7174	−	68.6653i	−0.163569	−	0.165858i
$415$			248.227i			0.598137i
$416$	−10.5980	+	3.96433i	−0.0254760	+	0.00952963i
$417$	−866.398			−2.07769
$418$	−26.6917	+	26.3232i	−0.0638558	+	0.0629743i
$419$	84.9271	−	205.032i	0.202690	−	0.489337i	−0.789548	−	0.613688i	$-0.789685\pi$
$419$	84.9271	−	205.032i	0.202690	−	0.489337i	0.992238	+	0.124352i	$0.0396851\pi$
$420$	57.9400	−	56.3513i	0.137952	−	0.134170i
$421$	−42.8465	−	103.441i	−0.101773	−	0.245702i	0.864789	−	0.502136i	$-0.167452\pi$
$421$	−42.8465	−	103.441i	−0.101773	−	0.245702i	−0.966562	+	0.256434i	$0.917452\pi$
$422$	46.4965	+	114.497i	0.110181	+	0.271319i
$423$	0.573557	+	0.573557i	0.00135593	+	0.00135593i
$424$	−42.7187	+	97.3407i	−0.100752	+	0.229577i
$425$	229.654	+	229.654i	0.540362	+	0.540362i
$426$	−218.110	−	92.1252i	−0.511995	−	0.216256i
$427$	−11.7113	−	28.2736i	−0.0274269	−	0.0662145i
$428$	−606.726	+	241.490i	−1.41759	+	0.564229i
$429$	0.379627	−	0.916500i	0.000884911	−	0.00213636i
$430$	47.9218	+	0.333061i	0.111446	+	0.000774561i
$431$	−59.4083			−0.137838			−0.0689191	−	0.997622i	$-0.521955\pi$
$431$	−59.4083			−0.137838			−0.0689191	+	0.997622i	$0.521955\pi$
$432$	368.000	−	140.579i	0.851853	−	0.325413i
$433$			225.917i			0.521747i	0.965373	+	0.260874i	$0.0840106\pi$
$433$			225.917i			0.521747i	−0.965373	+	0.260874i	$0.915989\pi$
$434$	152.118	+	1.05724i	0.350503	+	0.00243603i
$435$	36.7672	+	15.2295i	0.0845223	+	0.0350103i
$436$	469.708	+	202.253i	1.07731	+	0.463884i
$437$	711.728	−	294.807i	1.62867	−	0.674616i
$438$	461.294	+	194.841i	1.05318	+	0.444843i
$439$	−447.200	+	447.200i	−1.01868	+	1.01868i	−0.0188562	+	0.999822i	$0.506002\pi$
$439$	−447.200	+	447.200i	−1.01868	+	1.01868i	−0.999822	+	0.0188562i	$0.993998\pi$
$440$	−0.345434	+	16.5652i	−0.000785078	+	0.0376482i
$441$	6.65787	−	6.65787i	0.0150972	−	0.0150972i
$442$	4.46336	+	10.9909i	0.0100981	+	0.0248664i
$443$	443.273	−	183.610i	1.00062	−	0.414469i	0.178593	−	0.983923i	$-0.442845\pi$
$443$	443.273	−	183.610i	1.00062	−	0.414469i	0.822023	+	0.569454i	$0.192845\pi$
$444$	−7.22855	+	520.007i	−0.0162805	+	1.17119i
$445$	98.6516	+	40.8628i	0.221689	+	0.0918266i
$446$	−360.038	+	355.068i	−0.807260	+	0.796116i
$447$		−	509.629i		−	1.14011i
$448$	124.620	−	114.638i	0.278170	−	0.255887i
$449$	854.775			1.90373			0.951866	−	0.306516i	$-0.0991632\pi$
$449$	854.775			1.90373			0.951866	+	0.306516i	$0.0991632\pi$
$450$	36.5744	+	37.0863i	0.0812764	+	0.0824141i
$451$	−8.33231	+	20.1160i	−0.0184752	+	0.0446031i
$452$	−792.736	−	11.0197i	−1.75384	−	0.0243799i
$453$	310.749	+	750.214i	0.685980	+	1.65610i
$454$	−323.478	+	131.363i	−0.712507	+	0.289345i
$455$	−1.57076	−	1.57076i	−0.00345222	−	0.00345222i
$456$	11.5281	−	552.827i	0.0252809	−	1.21234i
$457$	324.480	+	324.480i	0.710021	+	0.710021i	0.966539	−	0.256518i	$-0.0825755\pi$
$457$	324.480	+	324.480i	0.710021	+	0.710021i	−0.256518	+	0.966539i	$0.582575\pi$
$458$	9.79602	−	23.1925i	0.0213887	−	0.0506386i
$459$	−158.047	−	381.559i	−0.344329	−	0.831284i
$460$	134.657	−	312.725i	0.292733	−	0.679836i
$461$	−100.109	+	241.684i	−0.217155	+	0.524259i	−0.994490	−	0.104827i	$-0.966571\pi$
$461$	−100.109	+	241.684i	−0.217155	+	0.524259i	0.777335	+	0.629087i	$0.216571\pi$
$462$	−0.103173	+	14.8448i	−0.000223317	+	0.0321315i
$463$	802.486			1.73323			0.866616	−	0.498976i	$-0.166290\pi$
$463$	802.486			1.73323			0.866616	+	0.498976i	$0.166290\pi$
$464$	76.1115	+	34.0349i	0.164033	+	0.0733510i
$465$		−	219.555i		−	0.472162i
$466$	3.38848	−	487.544i	0.00727141	−	1.04623i
$467$	418.346	+	173.285i	0.895817	+	0.371059i	0.782610	−	0.622512i	$-0.213888\pi$
$467$	418.346	+	173.285i	0.895817	+	0.371059i	0.113207	+	0.993571i	$0.463888\pi$
$468$	0.703553	+	1.76763i	0.00150332	+	0.00377699i
$469$	178.079	−	73.7627i	0.379699	−	0.157276i
$470$	−1.11427	+	2.63807i	−0.00237078	+	0.00561291i
$471$	−233.127	+	233.127i	−0.494961	+	0.494961i
$472$	−255.692	+	582.632i	−0.541720	+	1.23439i
$473$	−6.22404	+	6.22404i	−0.0131587	+	0.0131587i
$474$	−250.782	+	101.841i	−0.529076	+	0.214855i
$475$	−384.407	+	159.226i	−0.809277	+	0.335214i
$476$	−123.769	−	127.259i	−0.260019	−	0.267350i
$477$	16.5127	+	6.83979i	0.0346179	+	0.0143392i
$478$	−228.956	−	232.161i	−0.478988	−	0.485693i
$479$			503.112i			1.05034i	0.850998	+	0.525169i	$0.175998\pi$
$479$			503.112i			1.05034i	−0.850998	+	0.525169i	$0.824002\pi$
$480$	−166.701	−	178.708i	−0.347293	−	0.372309i
$481$	14.2934			0.0297161
$482$	250.308	−	246.852i	0.519310	−	0.512142i
$483$	116.742	−	281.841i	0.241703	−	0.583522i
$484$	335.328	+	344.782i	0.692826	+	0.712359i
$485$	69.5844	+	167.992i	0.143473	+	0.346374i
$486$	−54.2215	−	133.520i	−0.111567	−	0.274732i
$487$	153.636	+	153.636i	0.315475	+	0.315475i	0.847026	−	0.531551i	$-0.178391\pi$
$487$	153.636	+	153.636i	0.315475	+	0.315475i	−0.531551	+	0.847026i	$0.678391\pi$
$488$	−86.2110	+	33.6216i	−0.176662	+	0.0688967i
$489$	−204.675	−	204.675i	−0.418558	−	0.418558i
$490$	30.6228	+	12.9344i	0.0624955	+	0.0263968i
$491$	168.070	+	405.757i	0.342302	+	0.826390i	0.997482	+	0.0709174i	$0.0225927\pi$
$491$	168.070	+	405.757i	0.342302	+	0.826390i	−0.655180	+	0.755473i	$0.727407\pi$
$492$	−118.765	−	298.389i	−0.241392	−	0.606481i
$493$	33.4498	−	80.7549i	0.0678494	−	0.163803i
$494$	−15.1970	−	0.105621i	−0.0307632	−	0.000213807i
$495$	2.78582			0.00562793
$496$	12.7856	−	459.796i	0.0257774	−	0.927007i
$497$		−	97.3811i		−	0.195938i
$498$	672.468	+	4.67372i	1.35034	+	0.00938497i
$499$	37.4967	+	15.5317i	0.0751438	+	0.0311256i	0.419939	−	0.907552i	$-0.362052\pi$
$499$	37.4967	+	15.5317i	0.0751438	+	0.0311256i	−0.344795	+	0.938678i	$0.612052\pi$
$500$	−166.636	+	386.990i	−0.333271	+	0.773981i
$501$	6.36260	−	2.63548i	0.0126998	−	0.00526043i
$502$	−307.843	−	130.027i	−0.613233	−	0.259017i
$503$	−287.800	+	287.800i	−0.572167	+	0.572167i	−0.932734	−	0.360566i	$-0.882583\pi$
$503$	−287.800	+	287.800i	−0.572167	+	0.572167i	0.360566	+	0.932734i	$0.382583\pi$
$504$	−19.7074	−	20.5468i	−0.0391020	−	0.0407675i
$505$	13.8672	−	13.8672i	0.0274598	−	0.0274598i
$506$	23.5299	+	57.9420i	0.0465018	+	0.114510i
$507$	−501.820	+	207.861i	−0.989783	+	0.409981i
$508$	159.848	+	2.22202i	0.314661	+	0.00437406i
$509$	693.906	+	287.425i	1.36327	+	0.564686i	0.939956	−	0.341296i	$-0.110866\pi$
$509$	693.906	+	287.425i	1.36327	+	0.564686i	0.423317	+	0.905982i	$0.360866\pi$
$510$	−182.424	+	179.906i	−0.357695	+	0.352757i
$511$			205.957i			0.403048i
$512$	−338.700	−	383.961i	−0.661523	−	0.749925i
$513$	529.095			1.03137
$514$	−97.7864	−	99.1552i	−0.190246	−	0.192909i
$515$	−148.434	+	358.352i	−0.288222	+	0.695829i
$516$	1.80458	−	129.818i	0.00349726	−	0.251585i
$517$	−0.201287	−	0.485951i	−0.000389337	−	0.000939943i
$518$	−198.179	+	80.4792i	−0.382584	+	0.155365i
$519$	233.547	+	233.547i	0.449994	+	0.449994i
$520$	−4.84752	+	4.64948i	−0.00932216	+	0.00894131i
$521$	−166.292	−	166.292i	−0.319178	−	0.319178i	0.529273	−	0.848451i	$-0.322465\pi$
$521$	−166.292	−	166.292i	−0.319178	−	0.319178i	−0.848451	+	0.529273i	$0.822465\pi$
$522$	5.45446	−	12.9137i	0.0104492	−	0.0247388i
$523$	−326.711	−	788.750i	−0.624686	−	1.50813i	−0.846143	−	0.532956i	$-0.821081\pi$
$523$	−326.711	−	788.750i	−0.624686	−	1.50813i	0.221457	−	0.975170i	$-0.428919\pi$
$524$	−123.358	−	53.1174i	−0.235417	−	0.101369i
$525$	−63.0529	+	152.223i	−0.120101	+	0.289949i
$526$	0.411530	−	59.2122i	0.000782377	−	0.112571i
$527$	−482.228			−0.915043
$528$	44.8701	+	1.24771i	0.0849812	+	0.00236308i
$529$		−	756.124i		−	1.42935i
$530$	−0.438556	+	63.1008i	−0.000827465	+	0.119058i
$531$	98.8367	+	40.9395i	0.186133	+	0.0770988i
$532$	211.301	−	84.1023i	0.397183	−	0.158087i
$533$	−8.15484	+	3.37785i	−0.0152999	+	0.00633742i
$534$	112.558	−	266.486i	0.210783	−	0.499038i
$535$	−274.104	+	274.104i	−0.512344	+	0.512344i
$536$	−211.763	−	542.993i	−0.395080	−	1.01305i
$537$	423.025	−	423.025i	0.787757	−	0.787757i
$538$	−818.185	+	332.260i	−1.52079	+	0.617584i
$539$	−5.64093	+	2.33655i	−0.0104656	+	0.00433498i
$540$	167.637	−	163.040i	0.310439	−	0.301926i
$541$	149.859	+	62.0738i	0.277005	+	0.114739i	0.516861	−	0.856069i	$-0.327100\pi$
$541$	149.859	+	62.0738i	0.277005	+	0.114739i	−0.239856	+	0.970808i	$0.577100\pi$
$542$	−539.697	−	547.251i	−0.995751	−	1.00969i
$543$		−	71.5247i		−	0.131721i
$544$	−392.512	+	366.139i	−0.721530	+	0.673049i
$545$	303.575			0.557019
$546$	−4.28490	+	4.22575i	−0.00784781	+	0.00773947i
$547$	297.772	−	718.886i	0.544373	−	1.31423i	−0.377237	−	0.926117i	$-0.623126\pi$
$547$	297.772	−	718.886i	0.544373	−	1.31423i	0.921610	−	0.388117i	$-0.126874\pi$
$548$	−303.762	+	295.433i	−0.554310	+	0.539111i
$549$	5.95399	+	14.3742i	0.0108452	+	0.0261825i
$550$	−12.7086	−	31.2947i	−0.0231065	−	0.0568994i
$551$	79.1818	+	79.1818i	0.143706	+	0.143706i
$552$	−844.662	−	370.686i	−1.53019	−	0.671533i
$553$	−78.7190	−	78.7190i	−0.142349	−	0.142349i
$554$	857.718	+	362.282i	1.54823	+	0.653939i
$555$	118.139	+	285.214i	0.212864	+	0.513899i
$556$	−1001.10	+	398.458i	−1.80054	+	0.716652i
$557$	345.009	−	832.926i	0.619406	−	1.49538i	−0.232989	−	0.972479i	$-0.574851\pi$
$557$	345.009	−	832.926i	0.619406	−	1.49538i	0.852395	−	0.522899i	$-0.175149\pi$
$558$	−77.3365	−	0.537496i	−0.138596	−	0.000963255i
$559$	−3.56831			−0.00638338
$560$	41.0320	−	91.7591i	0.0732715	−	0.163856i
$561$		−	47.0592i		−	0.0838845i
$562$	287.635	+	1.99909i	0.511805	+	0.00355710i
$563$	−425.585	−	176.283i	−0.755923	−	0.313114i	−0.0287674	−	0.999586i	$-0.509158\pi$
$563$	−425.585	−	176.283i	−0.755923	−	0.313114i	−0.727156	+	0.686473i	$0.759158\pi$
$564$	7.12577	+	3.06831i	0.0126343	+	0.00544027i
$565$	−434.800	+	180.100i	−0.769558	+	0.318761i
$566$	159.440	+	67.3441i	0.281696	+	0.118983i
$567$	170.800	−	170.800i	0.301235	−	0.301235i
$568$	−294.389	−	6.13888i	−0.518290	−	0.0108079i
$569$	596.225	−	596.225i	1.04785	−	1.04785i	0.0490502	−	0.998796i	$-0.484381\pi$
$569$	596.225	−	596.225i	1.04785	−	1.04785i	0.998796	−	0.0490502i	$-0.0156194\pi$
$570$	−123.500	−	304.117i	−0.216667	−	0.533538i
$571$	745.482	−	308.789i	1.30557	−	0.540786i	0.381983	−	0.924169i	$-0.375241\pi$
$571$	745.482	−	308.789i	1.30557	−	0.540786i	0.923589	+	0.383383i	$0.125241\pi$
$572$	0.0171479	−	1.23358i	2.99788e−5	−	0.00215661i
$573$	490.038	+	202.980i	0.855215	+	0.354242i
$574$	94.0480	−	92.7497i	0.163847	−	0.161585i
$575$			694.100i			1.20713i
$576$	−63.3566	+	58.2814i	−0.109994	+	0.101183i
$577$	−17.8294			−0.0309002			−0.0154501	−	0.999881i	$-0.504918\pi$
$577$	−17.8294			−0.0309002			−0.0154501	+	0.999881i	$0.504918\pi$
$578$	−10.7142	−	10.8642i	−0.0185367	−	0.0187961i
$579$	230.849	−	557.320i	0.398704	−	0.962556i
$580$	49.4876	+	0.687920i	0.0853234	+	0.00118607i
$581$	105.846	+	255.534i	0.182179	+	0.439818i
$582$	456.414	−	185.347i	0.784216	−	0.318466i
$583$	−8.19547	−	8.19547i	−0.0140574	−	0.0140574i
$584$	622.621	+	12.9835i	1.06613	+	0.0222320i
$585$	0.798570	+	0.798570i	0.00136508	+	0.00136508i
$586$	328.445	−	777.605i	0.560486	−	1.32697i
$587$	217.595	+	525.322i	0.370691	+	0.894927i	0.993634	+	0.112659i	$0.0359369\pi$
$587$	217.595	+	525.322i	0.370691	+	0.894927i	−0.622943	+	0.782267i	$0.714063\pi$
$588$	35.6171	−	82.7162i	0.0605733	−	0.140674i
$589$	236.417	−	570.761i	0.401387	−	0.969034i
$590$	−2.62497	+	377.689i	−0.00444911	+	0.640150i
$591$	−604.270			−1.02245
$592$	230.800	+	604.179i	0.389865	+	1.02057i
$593$		−	181.883i		−	0.306716i	−0.988171	−	0.153358i	$-0.950991\pi$
$593$		−	181.883i		−	0.306716i	0.988171	−	0.153358i	$-0.0490088\pi$
$594$	−0.298508	+	42.9501i	−0.000502538	+	0.0723066i
$595$	−97.3571	−	40.3266i	−0.163625	−	0.0677759i
$596$	−234.380	−	588.862i	−0.393254	−	0.988024i
$597$	995.384	−	412.302i	1.66731	−	0.690623i
$598$	−9.86439	+	23.3543i	−0.0164956	+	0.0390541i
$599$	481.710	−	481.710i	0.804190	−	0.804190i	−0.179558	−	0.983747i	$-0.557467\pi$
$599$	481.710	−	481.710i	0.804190	−	0.804190i	0.983747	+	0.179558i	$0.0574667\pi$
$600$	456.205	+	200.209i	0.760342	+	0.333681i
$601$	−834.807	+	834.807i	−1.38903	+	1.38903i	−0.561664	+	0.827365i	$0.689839\pi$
$601$	−834.807	+	834.807i	−1.38903	+	1.38903i	−0.827365	+	0.561664i	$0.810161\pi$
$602$	49.4746	−	20.0914i	0.0821837	−	0.0333744i
$603$	−90.5348	+	37.5007i	−0.150141	+	0.0621903i
$604$	704.087	+	723.937i	1.16571	+	1.19857i
$605$	263.770	+	109.257i	0.435983	+	0.180590i
$606$	−37.3064	−	37.8286i	−0.0615616	−	0.0624234i
$607$		−	397.316i		−	0.654557i	−0.944928	−	0.327279i	$-0.893868\pi$
$607$		−	397.316i		−	0.654557i	0.944928	−	0.327279i	$-0.106132\pi$
$608$	−240.926	−	644.078i	−0.396260	−	1.05934i
$609$	44.3435			0.0728137
$610$	−39.1105	+	38.5706i	−0.0641155	+	0.0632304i
$611$	0.0816002	−	0.197000i	0.000133552	−	0.000322423i
$612$	62.9238	+	64.6979i	0.102817	+	0.105715i
$613$	−174.226	−	420.618i	−0.284218	−	0.686163i	0.715707	−	0.698401i	$-0.246105\pi$
$613$	−174.226	−	420.618i	−0.284218	−	0.686163i	−0.999925	+	0.0122376i	$0.996105\pi$
$614$	−170.853	−	420.722i	−0.278262	−	0.685214i
$615$	−134.804	−	134.804i	−0.219194	−	0.219194i
$616$	6.70793	+	17.2002i	0.0108895	+	0.0279224i
$617$	−782.576	−	782.576i	−1.26836	−	1.26836i	−0.946937	−	0.321420i	$-0.895840\pi$
$617$	−782.576	−	782.576i	−1.26836	−	1.26836i	−0.321420	−	0.946937i	$-0.604160\pi$
$618$	968.011	+	408.868i	1.56636	+	0.661599i
$619$	400.709	+	967.398i	0.647350	+	1.56284i	0.816560	+	0.577260i	$0.195878\pi$
$619$	400.709	+	967.398i	0.647350	+	1.56284i	−0.169211	+	0.985580i	$0.554122\pi$
$620$	−100.974	−	253.690i	−0.162861	−	0.409178i
$621$	337.769	−	815.446i	0.543911	−	1.31312i
$622$	945.488	+	6.57124i	1.52008	+	0.0105647i
$623$	118.980			0.190979
$624$	12.5046	+	13.2199i	0.0200394	+	0.0211857i
$625$		−	233.935i		−	0.374296i
$626$	461.021	+	3.20414i	0.736455	+	0.00511843i
$627$	55.6989	+	23.0712i	0.0888339	+	0.0367962i
$628$	−162.156	+	376.587i	−0.258210	+	0.599661i
$629$	626.439	−	259.480i	0.995929	−	0.412527i
$630$	−15.5685	−	6.57583i	−0.0247120	−	0.0104378i
$631$	−301.421	+	301.421i	−0.477688	+	0.477688i	−0.904392	−	0.426703i	$-0.859675\pi$
$631$	−301.421	+	301.421i	−0.477688	+	0.477688i	0.426703	+	0.904392i	$0.359675\pi$
$632$	−242.935	+	233.010i	−0.384390	+	0.368686i
$633$	140.528	−	140.528i	0.222003	−	0.222003i
$634$	134.514	+	331.237i	0.212167	+	0.522456i
$635$	87.6733	−	36.3155i	0.138068	−	0.0571897i
$636$	170.937	+	2.37617i	0.268769	+	0.00373612i
$637$	−2.28679	−	0.947218i	−0.00358993	−	0.00148700i
$638$	−6.47238	+	6.38304i	−0.0101448	+	0.0100048i
$639$			49.5082i			0.0774777i
$640$	−274.806	−	129.827i	−0.429385	−	0.202854i
$641$	−1235.67			−1.92773			−0.963864	−	0.266395i	$-0.914167\pi$
$641$	−1235.67			−1.92773			−0.963864	+	0.266395i	$0.914167\pi$
$642$	737.410	+	747.732i	1.14861	+	1.16469i
$643$	33.1893	−	80.1260i	0.0516163	−	0.124613i	−0.895968	−	0.444119i	$-0.853517\pi$
$643$	33.1893	−	80.1260i	0.0516163	−	0.124613i	0.947584	+	0.319506i	$0.103517\pi$
$644$	5.27329	−	379.350i	0.00818833	−	0.589052i
$645$	−29.4931	−	71.2027i	−0.0457258	−	0.110392i
$646$	−667.958	+	271.254i	−1.03399	+	0.419898i
$647$	−497.471	−	497.471i	−0.768888	−	0.768888i	0.209023	−	0.977911i	$-0.432972\pi$
$647$	−497.471	−	497.471i	−0.768888	−	0.768888i	−0.977911	+	0.209023i	$0.932972\pi$
$648$	−505.572	−	527.106i	−0.780203	−	0.813436i
$649$	−49.0539	−	49.0539i	−0.0755838	−	0.0755838i
$650$	5.32779	−	12.6138i	0.00819660	−	0.0194058i
$651$	−93.6200	−	226.019i	−0.143810	−	0.347187i
$652$	−330.626	−	142.366i	−0.507095	−	0.218352i
$653$	−267.649	+	646.162i	−0.409876	+	0.989528i	0.575294	+	0.817947i	$0.304888\pi$
$653$	−267.649	+	646.162i	−0.409876	+	0.989528i	−0.985170	+	0.171581i	$0.945112\pi$
$654$	5.71584	−	822.412i	0.00873982	−	1.25751i
$655$	−79.7274			−0.121721
$656$	−274.459	−	290.160i	−0.418383	−	0.442316i
$657$		−	104.708i		−	0.159373i
$658$	−0.0221768	+	3.19086i	−3.37033e−5	+	0.00484933i
$659$	252.729	+	104.684i	0.383503	+	0.158852i	0.566102	−	0.824335i	$-0.308451\pi$
$659$	252.729	+	104.684i	0.383503	+	0.158852i	−0.182599	+	0.983188i	$0.558451\pi$
$660$	24.7569	−	9.85375i	0.0375104	−	0.0149299i
$661$	644.295	−	266.876i	0.974728	−	0.403745i	0.162258	−	0.986748i	$-0.448122\pi$
$661$	644.295	−	266.876i	0.974728	−	0.403745i	0.812470	+	0.583003i	$0.198122\pi$
$662$	−256.241	+	606.661i	−0.387071	+	0.916407i
$663$	13.4897	−	13.4897i	0.0203465	−	0.0203465i
$664$	779.167	−	303.869i	1.17344	−	0.457634i
$665$	95.4606	−	95.4606i	0.143550	−	0.143550i
$666$	100.753	−	40.9154i	0.151281	−	0.0614345i
$667$	172.585	−	71.4869i	0.258747	−	0.107177i
$668$	6.13975	−	5.97140i	0.00919125	−	0.00893922i
$669$	751.308	+	311.202i	1.12303	+	0.465175i
$670$	−242.934	−	246.334i	−0.362587	−	0.367663i
$671$		−	10.0891i		−	0.0150360i
$672$	−247.811	−	112.887i	−0.368766	−	0.167987i
$673$	−849.641			−1.26247			−0.631234	−	0.775592i	$-0.717451\pi$
$673$	−849.641			−1.26247			−0.631234	+	0.775592i	$0.717451\pi$
$674$	−190.922	+	188.286i	−0.283266	+	0.279356i
$675$	−182.430	+	440.425i	−0.270267	+	0.652481i
$676$	−484.244	+	470.965i	−0.716337	+	0.696694i
$677$	−149.170	−	360.128i	−0.220340	−	0.531947i	0.774597	−	0.632456i	$-0.217953\pi$
$677$	−149.170	−	360.128i	−0.220340	−	0.531947i	−0.994936	+	0.100509i	$0.967953\pi$
$678$	479.720	+	1181.30i	0.707552	+	1.74233i
$679$	143.266	+	143.266i	0.210995	+	0.210995i
$680$	−128.047	+	291.774i	−0.188305	+	0.429080i
$681$	397.022	+	397.022i	0.582998	+	0.582998i
$682$	46.1991	+	19.5135i	0.0677406	+	0.0286122i
$683$	−58.5669	−	141.393i	−0.0857494	−	0.207017i	0.875188	−	0.483783i	$-0.160738\pi$
$683$	−58.5669	−	141.393i	−0.0857494	−	0.207017i	−0.960938	+	0.276765i	$0.910738\pi$
$684$	−107.425	+	42.7574i	−0.157054	+	0.0625108i
$685$	−96.2583	+	232.388i	−0.140523	+	0.339253i
$686$	37.0396	+	0.257429i	0.0539936	+	0.000375261i
$687$	−40.4885			−0.0589352
$688$	−57.6185	−	150.831i	−0.0837478	−	0.219231i
$689$		−	4.69854i		−	0.00681937i
$690$	−547.549	−	3.80552i	−0.793549	−	0.00551525i
$691$	−584.351	−	242.046i	−0.845659	−	0.350284i	−0.0825768	−	0.996585i	$-0.526315\pi$
$691$	−584.351	−	242.046i	−0.845659	−	0.350284i	−0.763082	+	0.646301i	$0.776315\pi$
$692$	377.266	+	162.448i	0.545182	+	0.234752i
$693$	2.86784	−	1.18790i	0.00413829	−	0.00171414i
$694$	−670.210	−	283.083i	−0.965720	−	0.407901i
$695$	−452.271	+	452.271i	−0.650750	+	0.650750i
$696$	2.79541	−	134.053i	0.00401639	−	0.192605i
$697$	−296.082	+	296.082i	−0.424795	+	0.424795i
$698$	505.659	+	1245.18i	0.724439	+	1.78392i
$699$	−724.397	+	300.055i	−1.03633	+	0.429263i
$700$	−2.84812	+	204.888i	−0.00406874	+	0.292697i
$701$	−779.866	−	323.031i	−1.11250	−	0.460815i	−0.250705	−	0.968063i	$-0.580663\pi$
$701$	−779.866	−	323.031i	−1.11250	−	0.460815i	−0.861800	+	0.507249i	$0.830663\pi$
$702$	−12.3974	+	12.2263i	−0.0176602	+	0.0174164i
$703$			868.661i			1.23565i
$704$	52.4200	−	19.1942i	0.0744602	−	0.0272644i
$705$	4.60543			0.00653253
$706$	−219.851	−	222.929i	−0.311404	−	0.315763i
$707$	8.36236	−	20.1885i	0.0118279	−	0.0285552i
$708$	1023.14	+	14.2226i	1.44512	+	0.0200884i
$709$	146.369	+	353.367i	0.206445	+	0.498402i	0.992858	−	0.119298i	$-0.0380644\pi$
$709$	146.369	+	353.367i	0.206445	+	0.498402i	−0.786414	+	0.617700i	$0.788064\pi$
$710$	−161.947	+	65.7657i	−0.228094	+	0.0926278i
$711$	40.0205	+	40.0205i	0.0562877	+	0.0562877i
$712$	7.50047	−	359.683i	0.0105344	−	0.505173i
$713$	−728.736	−	728.736i	−1.02207	−	1.02207i
$714$	−111.081	+	262.990i	−0.155576	+	0.368333i
$715$	−0.280255	−	0.676596i	−0.000391965	−	0.000946288i
$716$	294.244	−	683.345i	0.410955	−	0.954392i
$717$	−200.671	+	484.462i	−0.279875	+	0.675679i
$718$	−7.88177	+	1134.05i	−0.0109774	+	1.57946i
$719$	−1364.51			−1.89779			−0.948893	−	0.315598i	$-0.897795\pi$
$719$	−1364.51			−1.89779			−0.948893	+	0.315598i	$0.897795\pi$
$720$	−20.8606	+	46.6501i	−0.0289730	+	0.0647918i
$721$			432.195i			0.599438i
$722$	1.40108	−	201.592i	0.00194056	−	0.279213i
$723$	−522.329	−	216.356i	−0.722447	−	0.299247i
$724$	−32.8944	−	82.6448i	−0.0454342	−	0.114150i
$725$	−93.2135	+	38.6103i	−0.128570	+	0.0532556i
$726$	300.953	−	712.518i	0.414536	−	0.981430i
$727$	362.040	−	362.040i	0.497992	−	0.497992i	−0.412820	−	0.910813i	$-0.635456\pi$
$727$	362.040	−	362.040i	0.497992	−	0.497992i	0.910813	+	0.412820i	$0.135456\pi$
$728$	−3.00765	+	6.85338i	−0.00413139	+	0.00941398i
$729$	417.132	−	417.132i	0.572198	−	0.572198i
$730$	342.512	−	139.092i	0.469194	−	0.190537i
$731$	−156.388	+	64.7782i	−0.213938	+	0.0886159i
$732$	103.755	+	106.680i	0.141741	+	0.145737i
$733$	−460.885	−	190.905i	−0.628766	−	0.260443i	0.0454627	−	0.998966i	$-0.485524\pi$
$733$	−460.885	−	190.905i	−0.628766	−	0.260443i	−0.674229	+	0.738523i	$0.735524\pi$
$734$	−298.477	−	302.655i	−0.406645	−	0.412337i
$735$		−	53.4600i		−	0.0727347i
$736$	−1146.46	−	39.8556i	−1.55769	−	0.0541516i
$737$	63.5456			0.0862220
$738$	−47.8137	+	47.1537i	−0.0647883	+	0.0638939i
$739$	−339.313	+	819.175i	−0.459152	+	1.10849i	0.509589	+	0.860418i	$0.329797\pi$
$739$	−339.313	+	819.175i	−0.459152	+	1.10849i	−0.968741	+	0.248073i	$0.920203\pi$
$740$	267.678	+	275.224i	0.361726	+	0.371925i
$741$	9.35288	+	22.5798i	0.0126220	+	0.0304721i
$742$	26.4552	+	65.1454i	0.0356539	+	0.0877970i
$743$	994.064	+	994.064i	1.33791	+	1.33791i	0.898086	+	0.439821i	$0.144958\pi$
$743$	994.064	+	994.064i	1.33791	+	1.33791i	0.439821	+	0.898086i	$0.355042\pi$
$744$	−689.169	+	268.771i	−0.926303	+	0.361251i
$745$	−266.033	−	266.033i	−0.357092	−	0.357092i
$746$	1274.82	+	538.456i	1.70887	+	0.721791i
$747$	−53.8117	−	129.913i	−0.0720370	−	0.173913i
$748$	−21.6426	−	54.3756i	−0.0289340	−	0.0726946i
$749$	−165.293	+	399.053i	−0.220685	+	0.532781i
$750$	677.581	+	4.70926i	0.903442	+	0.00627901i
$751$	−200.166			−0.266533			−0.133267	−	0.991080i	$-0.542547\pi$
$751$	−200.166			−0.266533			−0.133267	+	0.991080i	$0.542547\pi$
$752$	9.64476	+	0.268193i	0.0128255	+	0.000356639i
$753$			537.419i			0.713705i
$754$	−3.68507	−	0.0256116i	−0.00488736	−	3.39676e-5i
$755$	553.837	+	229.407i	0.733559	+	0.303850i
$756$	103.050	−	239.321i	0.136310	−	0.316563i
$757$	−905.427	+	375.040i	−1.19607	+	0.495429i	−0.889728	−	0.456491i	$-0.849106\pi$
$757$	−905.427	+	375.040i	−1.19607	+	0.495429i	−0.306345	+	0.951921i	$0.599106\pi$
$758$	−1203.99	−	508.539i	−1.58837	−	0.670896i
$759$	71.1152	−	71.1152i	0.0936959	−	0.0936959i
$760$	−282.565	−	294.601i	−0.371796	−	0.387633i
$761$	−296.180	+	296.180i	−0.389198	+	0.389198i	−0.874401	−	0.485203i	$-0.838746\pi$
$761$	−296.180	+	296.180i	−0.389198	+	0.389198i	0.485203	+	0.874401i	$0.338746\pi$
$762$	−96.7310	−	238.198i	−0.126944	−	0.312596i
$763$	312.512	−	129.447i	0.409583	−	0.169655i
$764$	659.577	+	9.16869i	0.863321	+	0.0120009i
$765$	49.4961	+	20.5019i	0.0647008	+	0.0267999i
$766$	613.862	−	605.388i	0.801386	−	0.790323i
$767$		−	28.1231i		−	0.0366663i
$768$	−356.886	+	742.030i	−0.464695	+	0.966185i
$769$	−1356.19			−1.76358			−0.881788	−	0.471646i	$-0.843660\pi$
$769$	−1356.19			−1.76358			−0.881788	+	0.471646i	$0.843660\pi$
$770$	7.69531	+	7.80303i	0.00999391	+	0.0101338i
$771$	−85.7057	+	206.912i	−0.111162	+	0.268368i
$772$	10.4275	−	750.136i	0.0135072	−	0.971678i
$773$	135.246	+	326.513i	0.174962	+	0.422397i	0.986897	−	0.161352i	$-0.0515854\pi$
$773$	135.246	+	326.513i	0.174962	+	0.422397i	−0.811935	+	0.583749i	$0.801585\pi$
$774$	−25.1527	+	10.2144i	−0.0324971	+	0.0131969i
$775$	393.593	+	393.593i	0.507862	+	0.507862i
$776$	442.132	−	424.069i	0.569758	−	0.546481i
$777$	243.235	+	243.235i	0.313043	+	0.313043i
$778$	218.600	−	517.544i	0.280977	−	0.665223i
$779$	−205.283	−	495.598i	−0.263522	−	0.636198i
$780$	9.92131	+	4.27205i	0.0127196	+	0.00547699i
$781$	12.2858	−	29.6605i	0.0157308	−	0.0379776i
$782$	−8.35839	+	1202.63i	−0.0106885	+	1.53789i
$783$	128.298			0.163855
$784$	3.11319	−	111.957i	0.00397091	−	0.142802i
$785$			243.391i			0.310052i
$786$	−1.50114	+	215.988i	−0.00190985	+	0.274794i
$787$	170.398	+	70.5811i	0.216516	+	0.0896837i	0.488305	−	0.872673i	$-0.337615\pi$
$787$	170.398	+	70.5811i	0.216516	+	0.0896837i	−0.271789	+	0.962357i	$0.587615\pi$
$788$	−698.217	+	277.905i	−0.886062	+	0.352671i
$789$	−87.9780	+	36.4417i	−0.111506	+	0.0461872i
$790$	−77.7491	+	184.074i	−0.0984166	+	0.233005i
$791$	−370.804	+	370.804i	−0.468779	+	0.468779i
$792$	−3.41029	−	8.74452i	−0.00430592	−	0.0110411i
$793$	2.89210	−	2.89210i	0.00364704	−	0.00364704i
$794$	−696.026	+	282.652i	−0.876607	+	0.355985i
$795$	93.7557	−	38.8349i	0.117932	−	0.0488489i
$796$	960.521	−	934.183i	1.20668	−	1.17360i
$797$	1277.16	+	529.016i	1.60246	+	0.663759i	0.991760	−	0.128107i	$-0.0408902\pi$
$797$	1277.16	+	529.016i	1.60246	+	0.663759i	0.610695	+	0.791866i	$0.290890\pi$
$798$	−256.814	−	260.408i	−0.321822	−	0.326326i
$799$		−	10.1153i		−	0.0126599i
$800$	619.209	+	21.5261i	0.774011	+	0.0269077i
$801$	−60.4891			−0.0755169
$802$	−433.511	+	427.527i	−0.540537	+	0.533075i
$803$	−25.9840	+	62.7309i	−0.0323586	+	0.0781206i
$804$	−671.914	+	653.490i	−0.835714	+	0.812798i
$805$	−86.1837	−	208.066i	−0.107060	−	0.258467i
$806$	7.64954	+	18.8368i	0.00949074	+	0.0233708i
$807$	1004.20	+	1004.20i	1.24436	+	1.24436i
$808$	−60.5039	−	26.5526i	−0.0748811	−	0.0328621i
$809$	511.195	+	511.195i	0.631885	+	0.631885i	0.948541	−	0.316656i	$-0.102560\pi$
$809$	511.195	+	511.195i	0.631885	+	0.631885i	−0.316656	+	0.948541i	$0.602560\pi$
$810$	−399.394	−	168.696i	−0.493079	−	0.208266i
$811$	209.710	+	506.285i	0.258582	+	0.624273i	0.998845	−	0.0480447i	$-0.0152990\pi$
$811$	209.710	+	506.285i	0.258582	+	0.624273i	−0.740263	+	0.672317i	$0.765299\pi$
$812$	51.2377	−	20.3937i	0.0631007	−	0.0251154i
$813$	−473.022	+	1141.98i	−0.581823	+	1.40464i
$814$	−70.5150	−	0.490086i	−0.0866278	−	0.000602072i
$815$	−213.686			−0.262191
$816$	788.030	+	352.384i	0.965723	+	0.431844i
$817$		−	216.858i		−	0.265433i
$818$	389.269	+	2.70546i	0.475879	+	0.00330740i
$819$	1.16260	+	0.481563i	0.00141953	+	0.000587989i
$820$	−217.760	−	93.7660i	−0.265561	−	0.114349i
$821$	−383.682	+	158.926i	−0.467335	+	0.193577i	−0.603909	−	0.797053i	$-0.706391\pi$
$821$	−383.682	+	158.926i	−0.467335	+	0.193577i	0.136574	+	0.990630i	$0.456391\pi$
$822$	627.747	+	265.148i	0.763683	+	0.322564i
$823$	775.615	−	775.615i	0.942425	−	0.942425i	−0.0560059	−	0.998430i	$-0.517837\pi$
$823$	775.615	−	775.615i	0.942425	−	0.942425i	0.998430	+	0.0560059i	$0.0178366\pi$
$824$	1306.55	+	27.2455i	1.58562	+	0.0330649i
$825$	−38.4096	+	38.4096i	−0.0465570	+	0.0465570i
$826$	158.347	+	389.927i	0.191703	+	0.472066i
$827$	−339.642	+	140.684i	−0.410692	+	0.170114i	−0.578457	−	0.815713i	$-0.696345\pi$
$827$	−339.642	+	140.684i	−0.410692	+	0.170114i	0.167765	+	0.985827i	$0.446345\pi$
$828$	−2.68092	+	192.860i	−0.00323783	+	0.232923i
$829$	509.962	+	211.233i	0.615153	+	0.254805i	0.668430	−	0.743775i	$-0.266967\pi$
$829$	509.962	+	211.233i	0.615153	+	0.254805i	−0.0532772	+	0.998580i	$0.516967\pi$
$830$	353.477	−	348.597i	0.425876	−	0.419997i
$831$		−	1497.37i		−	1.80189i
$832$	20.5286	+	9.52435i	0.0246737	+	0.0114475i
$833$	−117.419			−0.140959
$834$	1216.73	+	1233.76i	1.45890	+	1.47933i
$835$	1.94561	−	4.69712i	0.00233007	−	0.00562529i
$836$	74.9690	+	1.04213i	0.0896759	+	0.00124657i
$837$	−270.869	−	653.936i	−0.323619	−	0.781285i
$838$	−411.235	+	167.000i	−0.490734	+	0.199284i
$839$	−962.454	−	962.454i	−1.14714	−	1.14714i	−0.987112	−	0.160033i	$-0.948840\pi$
$839$	−962.454	−	962.454i	−1.14714	−	1.14714i	−0.160033	−	0.987112i	$-0.551160\pi$
$840$	−161.613	−	3.37011i	−0.192396	−	0.00401203i
$841$	−575.476	−	575.476i	−0.684276	−	0.684276i
$842$	−87.1287	+	206.281i	−0.103478	+	0.244989i
$843$	−177.022	−	427.370i	−0.209991	−	0.506963i
$844$	97.7469	−	227.005i	0.115814	−	0.268963i
$845$	−153.451	+	370.463i	−0.181598	+	0.438417i
$846$	0.0112746	−	1.62222i	1.33270e−5	−	0.00191752i
$847$	318.123			0.375588
$848$	198.606	−	75.8688i	0.234205	−	0.0894679i
$849$		−	278.343i		−	0.327849i
$850$	4.51439	−	649.544i	0.00531105	−	0.764169i
$851$	1338.79	+	554.545i	1.57320	+	0.651639i
$852$	175.116	+	439.966i	0.205535	+	0.516392i
$853$	−95.7966	+	39.6803i	−0.112306	+	0.0465185i	−0.438129	−	0.898912i	$-0.644359\pi$
$853$	−95.7966	+	39.6803i	−0.112306	+	0.0465185i	0.325823	+	0.945431i	$0.394359\pi$
$854$	−23.8150	+	56.3830i	−0.0278865	+	0.0660223i
$855$	−48.5319	+	48.5319i	−0.0567624	+	0.0567624i
$856$	1195.94	+	524.847i	1.39713	+	0.613139i
$857$	714.548	−	714.548i	0.833778	−	0.833778i	−0.154254	−	0.988031i	$-0.549297\pi$
$857$	714.548	−	714.548i	0.833778	−	0.833778i	0.988031	+	0.154254i	$0.0492972\pi$
$858$	−1.83823	+	0.746496i	−0.00214246	+	0.000870042i
$859$	−830.152	+	343.860i	−0.966417	+	0.400303i	−0.809377	−	0.587289i	$-0.800195\pi$
$859$	−830.152	+	343.860i	−0.966417	+	0.400303i	−0.157040	+	0.987592i	$0.550195\pi$
$860$	−66.8248	−	68.7088i	−0.0777032	−	0.0798940i
$861$	−196.254	−	81.2913i	−0.227938	−	0.0944150i
$862$	83.4301	+	84.5979i	0.0967866	+	0.0981414i
$863$			387.999i			0.449593i	0.974406	+	0.224796i	$0.0721717\pi$
$863$			387.999i			0.449593i	−0.974406	+	0.224796i	$0.927828\pi$
$864$	−716.987	−	326.614i	−0.829846	−	0.378025i
$865$	243.829			0.281884
$866$	321.707	−	317.266i	0.371486	−	0.366358i
$867$	−9.39054	+	22.6708i	−0.0108311	+	0.0261485i
$868$	−212.122	−	218.102i	−0.244380	−	0.251270i
$869$	−14.0450	−	33.9077i	−0.0161623	−	0.0390193i
$870$	−29.9472	−	73.7443i	−0.0344220	−	0.0847636i
$871$	18.2157	+	18.2157i	0.0209135	+	0.0209135i
$872$	−371.625	−	952.903i	−0.426175	−	1.09278i
$873$	−72.8359	−	72.8359i	−0.0834317	−	0.0834317i
$874$	−1419.32	−	599.493i	−1.62394	−	0.685919i
$875$	106.651	+	257.477i	0.121886	+	0.294260i
$876$	−370.363	−	930.512i	−0.422789	−	1.06223i
$877$	56.4105	−	136.187i	0.0643221	−	0.155287i	−0.888450	−	0.458973i	$-0.848217\pi$
$877$	56.4105	−	136.187i	0.0643221	−	0.155287i	0.952772	+	0.303686i	$0.0982174\pi$
$878$	1264.84	+	8.79077i	1.44059	+	0.0100123i
$879$	−1357.51			−1.54438
$880$	24.0741	−	22.7715i	0.0273570	−	0.0258767i
$881$			1219.92i			1.38469i	0.721564	+	0.692347i	$0.243423\pi$
$881$			1219.92i			1.38469i	−0.721564	+	0.692347i	$0.756577\pi$
$882$	−18.8308	−	0.130876i	−0.0213502	−	0.000148386i
$883$	369.935	+	153.232i	0.418952	+	0.173536i	0.582193	−	0.813050i	$-0.302195\pi$
$883$	369.935	+	153.232i	0.418952	+	0.173536i	−0.163241	+	0.986586i	$0.552195\pi$
$884$	9.38307	−	21.7910i	0.0106143	−	0.0246505i
$885$	561.173	−	232.446i	0.634094	−	0.262650i
$886$	−883.973	−	373.372i	−0.997712	−	0.421413i
$887$	−170.587	+	170.587i	−0.192319	+	0.192319i	−0.796697	−	0.604378i	$-0.793422\pi$
$887$	−170.587	+	170.587i	−0.192319	+	0.192319i	0.604378	+	0.796697i	$0.293422\pi$
$888$	750.646	−	719.979i	0.845322	−	0.810788i
$889$	74.7691	−	74.7691i	0.0841047	−	0.0841047i
$890$	−80.3524	−	197.866i	−0.0902836	−	0.222322i
$891$	73.5711	−	30.4742i	0.0825714	−	0.0342022i
$892$	1011.24	+	14.0571i	1.13368	+	0.0157591i
$893$	11.9724	+	4.95913i	0.0134069	+	0.00555333i
$894$	−725.716	+	715.698i	−0.811763	+	0.800557i
$895$		−	441.650i		−	0.493464i
$896$	−338.255	−	16.4691i	−0.377517	−	0.0183807i
$897$	40.7710			0.0454527
$898$	−1200.40	−	1217.21i	−1.33675	−	1.35546i
$899$	57.3280	−	138.402i	0.0637686	−	0.153951i
$900$	1.44798	−	104.164i	0.00160886	−	0.115738i
$901$	−85.2963	−	205.924i	−0.0946685	−	0.228550i
$902$	40.3468	−	16.3846i	0.0447304	−	0.0181648i
$903$	−60.7227	−	60.7227i	−0.0672455	−	0.0672455i
$904$	1097.59	+	1144.34i	1.21414	+	1.26586i
$905$	−37.3369	−	37.3369i	−0.0412562	−	0.0412562i
$906$	631.910	−	1496.07i	0.697473	−	1.65129i
$907$	305.804	+	738.277i	0.337160	+	0.813977i	0.997986	+	0.0634374i	$0.0202063\pi$
$907$	305.804	+	738.277i	0.337160	+	0.813977i	−0.660826	+	0.750540i	$0.729794\pi$
$908$	641.339	+	276.156i	0.706320	+	0.304137i
$909$	−4.25140	+	10.2638i	−0.00467701	+	0.0112913i
$910$	−0.0308770	+	4.44268i	−3.39308e−5	+	0.00488206i
$911$	−501.039			−0.549988			−0.274994	−	0.961446i	$-0.588676\pi$
$911$	−501.039			−0.549988			−0.274994	+	0.961446i	$0.588676\pi$
$912$	−803.419	+	759.946i	−0.880942	+	0.833275i
$913$			91.1848i			0.0998738i
$914$	6.37841	−	917.745i	0.00697857	−	1.00410i
$915$	81.6137	+	33.8055i	0.0891953	+	0.0369459i
$916$	−46.7833	+	18.6207i	−0.0510735	+	0.0203283i
$917$	−82.0744	+	33.9963i	−0.0895032	+	0.0370734i
$918$	−321.390	+	760.903i	−0.350098	+	0.828871i
$919$	925.881	−	925.881i	1.00749	−	1.00749i	0.00751566	−	0.999972i	$-0.497608\pi$
$919$	925.881	−	925.881i	1.00749	−	1.00749i	0.999972	−	0.00751566i	$-0.00239233\pi$
$920$	−634.428	+	247.422i	−0.689596	+	0.268937i
$921$	−516.373	+	516.373i	−0.560666	+	0.560666i
$922$	484.747	−	196.853i	0.525756	−	0.213507i
$923$	12.0241	−	4.98055i	0.0130272	−	0.00539605i
$924$	21.2840	−	20.7003i	0.0230346	−	0.0224030i
$925$	−723.085	−	299.511i	−0.781713	−	0.323796i
$926$	−1126.97	−	1142.75i	−1.21703	−	1.23407i
$927$		−	219.726i		−	0.237030i
$928$	−58.4213	−	156.180i	−0.0629540	−	0.168298i
$929$	1248.93			1.34439			0.672193	−	0.740376i	$-0.265353\pi$
$929$	1248.93			1.34439			0.672193	+	0.740376i	$0.265353\pi$
$930$	−312.648	+	308.333i	−0.336181	+	0.331540i
$931$	57.5657	−	138.976i	0.0618321	−	0.149276i
$932$	−699.025	+	679.857i	−0.750027	+	0.729461i
$933$	−581.894	−	1404.82i	−0.623680	−	1.50570i
$934$	−340.746	−	839.081i	−0.364825	−	0.898374i
$935$	−24.5655	−	24.5655i	−0.0262733	−	0.0262733i
$936$	1.52908	−	3.48424i	0.00163364	−	0.00372248i
$937$	−784.600	−	784.600i	−0.837353	−	0.837353i	0.151157	−	0.988510i	$-0.451700\pi$
$937$	−784.600	−	784.600i	−0.837353	−	0.837353i	−0.988510	+	0.151157i	$0.951700\pi$
$938$	−355.124	−	149.997i	−0.378597	−	0.159912i
$939$	−283.732	−	684.989i	−0.302164	−	0.729487i
$940$	5.32145	−	2.11805i	0.00566112	−	0.00225324i
$941$	−145.458	+	351.167i	−0.154578	+	0.373185i	−0.982130	−	0.188205i	$-0.939733\pi$
$941$	−145.458	+	351.167i	−0.154578	+	0.373185i	0.827551	+	0.561390i	$0.189733\pi$
$942$	659.366	+	4.58266i	0.699964	+	0.00486482i
$943$	−894.871			−0.948962
$944$	1188.75	−	454.111i	1.25927	−	0.481050i
$945$		−	154.675i		−	0.163677i
$946$	17.6038	+	0.122348i	0.0186087	+	0.000129332i
$947$	−1335.26	−	553.083i	−1.40999	−	0.584037i	−0.457666	−	0.889124i	$-0.651315\pi$
$947$	−1335.26	−	553.083i	−1.40999	−	0.584037i	−0.952325	+	0.305087i	$0.901315\pi$
$948$	497.208	+	214.095i	0.524481	+	0.225838i
$949$	−25.4305	+	10.5337i	−0.0267972	+	0.0110998i
$950$	766.582	+	323.788i	0.806928	+	0.340830i
$951$	406.544	−	406.544i	0.427492	−	0.427492i
$952$	−7.40205	+	354.964i	−0.00777527	+	0.372861i
$953$	200.833	−	200.833i	0.210738	−	0.210738i	−0.593843	−	0.804581i	$-0.702390\pi$
$953$	200.833	−	200.833i	0.210738	−	0.210738i	0.804581	+	0.593843i	$0.202390\pi$
$954$	−13.4497	−	33.1197i	−0.0140982	−	0.0347167i
$955$	361.765	−	149.848i	0.378812	−	0.156909i
$956$	−9.06436	+	652.071i	−0.00948155	+	0.682083i
$957$	13.5062	+	5.59447i	0.0141131	+	0.00584584i
$958$	716.435	−	706.546i	0.747845	−	0.737521i
$959$			280.275i			0.292257i
$960$	−20.3761	+	488.352i	−0.0212251	+	0.508700i
$961$	134.533			0.139993
$962$	−20.0730	−	20.3540i	−0.0208659	−	0.0211580i
$963$	84.0345	−	202.877i	0.0872633	−	0.210672i
$964$	−703.039	−	9.77286i	−0.729294	−	0.0101378i
$965$	−170.422	−	411.435i	−0.176603	−	0.426357i
$966$	−565.291	+	229.561i	−0.585187	+	0.237641i
$967$	−690.877	−	690.877i	−0.714454	−	0.714454i	0.253010	−	0.967464i	$-0.418580\pi$
$967$	−690.877	−	690.877i	−0.714454	−	0.714454i	−0.967464	+	0.253010i	$0.918580\pi$
$968$	20.0544	−	961.704i	0.0207174	−	0.993496i
$969$	819.819	+	819.819i	0.846046	+	0.846046i
$970$	141.500	−	335.008i	0.145877	−	0.345369i
$971$	−638.663	−	1541.87i	−0.657737	−	1.58792i	−0.801291	−	0.598275i	$-0.795853\pi$
$971$	−638.663	−	1541.87i	−0.657737	−	1.58792i	0.143553	−	0.989643i	$-0.454147\pi$
$972$	−113.987	+	264.720i	−0.117270	+	0.272346i
$973$	−272.734	+	658.438i	−0.280302	+	0.676709i
$974$	3.02008	−	434.538i	0.00310070	−	0.446138i
$975$	−22.0206			−0.0225852
$976$	168.948	+	75.5486i	0.173102	+	0.0774064i
$977$		−	1089.31i		−	1.11496i	−0.830192	−	0.557478i	$-0.811769\pi$
$977$		−	1089.31i		−	1.11496i	0.830192	−	0.557478i	$-0.188231\pi$
$978$	−4.02336	+	578.893i	−0.00411387	+	0.591915i
$979$	36.2391	+	15.0107i	0.0370165	+	0.0153327i
$980$	−24.5864	−	61.7716i	−0.0250881	−	0.0630322i
$981$	−158.880	+	65.8104i	−0.161957	+	0.0670850i
$982$	341.772	−	809.159i	0.348037	−	0.823991i
$983$	458.104	−	458.104i	0.466027	−	0.466027i	−0.434598	−	0.900625i	$-0.643110\pi$
$983$	458.104	−	458.104i	0.466027	−	0.466027i	0.900625	+	0.434598i	$0.143110\pi$
$984$	−258.120	+	588.164i	−0.262317	+	0.597728i
$985$	−315.437	+	315.437i	−0.320241	+	0.320241i
$986$	−161.971	+	65.7755i	−0.164271	+	0.0667094i
$987$	4.74101	−	1.96379i	0.00480345	−	0.00198966i
$988$	21.1915	+	21.7890i	0.0214489	+	0.0220536i
$989$	−334.224	−	138.440i	−0.337941	−	0.139980i
$990$	−3.91227	−	3.96704i	−0.00395179	−	0.00400711i
$991$			444.592i			0.448630i	0.974517	+	0.224315i	$0.0720144\pi$
$991$			444.592i			0.448630i	−0.974517	+	0.224315i	$0.927986\pi$
$992$	−672.708	+	627.508i	−0.678133	+	0.632568i
$993$	1059.08			1.06655
$994$	−138.671	+	136.757i	−0.139508	+	0.137583i
$995$	304.377	−	734.831i	0.305907	−	0.738524i
$996$	−937.725	−	964.163i	−0.941491	−	0.968035i
$997$	−433.214	−	1045.87i	−0.434517	−	1.04902i	−0.977814	−	0.209476i	$-0.932824\pi$
$997$	−433.214	−	1045.87i	−0.434517	−	1.04902i	0.543297	−	0.839541i	$-0.317176\pi$
$998$	−30.5414	−	75.2075i	−0.0306026	−	0.0753583i
$999$	703.747	+	703.747i	0.704451	+	0.704451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.3.w.a.99.13	yes	192
32.11	odd	8	inner	224.3.w.a.43.13	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.3.w.a.43.13	✓	192	32.11	odd	8	inner
224.3.w.a.99.13	yes	192	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	224.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40435 - 1.42401i) q^{2} +(-1.23085 + 2.97155i) q^{3} +(-0.0555981 + 3.99961i) q^{4} +(0.908665 + 2.19371i) q^{5} +(5.96006 - 2.42035i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.77356 - 5.53769i) q^{8} +(-0.951124 - 0.951124i) q^{9} +O(q^{10})\)	\(q+(-1.40435 - 1.42401i) q^{2} +(-1.23085 + 2.97155i) q^{3} +(-0.0555981 + 3.99961i) q^{4} +(0.908665 + 2.19371i) q^{5} +(5.96006 - 2.42035i) q^{6} +(1.87083 + 1.87083i) q^{7} +(5.77356 - 5.53769i) q^{8} +(-0.951124 - 0.951124i) q^{9} +(1.84778 - 4.37468i) q^{10} +(0.333793 + 0.805848i) q^{11} +(-11.8166 - 5.08816i) q^{12} +(-0.135317 + 0.326684i) q^{13} +(0.0367756 - 5.29137i) q^{14} -7.63715 q^{15} +(-15.9938 - 0.444742i) q^{16} +16.7741i q^{17} +(-0.0186966 + 2.69012i) q^{18} +(-19.8537 - 8.22367i) q^{19} +(-8.82451 + 3.51234i) q^{20} +(-7.86197 + 3.25654i) q^{21} +(0.678771 - 1.60702i) q^{22} +(-25.3488 + 25.3488i) q^{23} +(9.34908 + 23.9725i) q^{24} +(13.6910 - 13.6910i) q^{25} +(0.655233 - 0.266086i) q^{26} +(-22.7469 + 9.42208i) q^{27} +(-7.58661 + 7.37858i) q^{28} +(-4.81426 - 1.99413i) q^{29} +(10.7252 + 10.8754i) q^{30} +28.7483i q^{31} +(21.8276 + 23.3999i) q^{32} -2.80547 q^{33} +(23.8865 - 23.5567i) q^{34} +(-2.40410 + 5.80401i) q^{35} +(3.85701 - 3.75125i) q^{36} +(-15.4691 - 37.3456i) q^{37} +(16.1710 + 39.8208i) q^{38} +(-0.804201 - 0.804201i) q^{39} +(17.3943 + 7.63362i) q^{40} +(17.6512 + 17.6512i) q^{41} +(15.6783 + 6.62219i) q^{42} +(3.86180 + 9.32321i) q^{43} +(-3.24164 + 1.29024i) q^{44} +(1.22224 - 2.95074i) q^{45} +(71.6955 + 0.498291i) q^{46} -0.603030 q^{47} +(21.0076 - 46.9790i) q^{48} +7.00000i q^{49} +(-38.7230 - 0.269129i) q^{50} +(-49.8450 - 20.6465i) q^{51} +(-1.29909 - 0.559378i) q^{52} +(-12.2763 + 5.08500i) q^{53} +(45.3618 + 19.1599i) q^{54} +(-1.46449 + 1.46449i) q^{55} +(21.1614 + 0.441278i) q^{56} +(48.8741 - 48.8741i) q^{57} +(3.92125 + 9.65600i) q^{58} +(-73.4795 + 30.4362i) q^{59} +(0.424611 - 30.5456i) q^{60} +(-10.6864 - 4.42646i) q^{61} +(40.9379 - 40.3727i) q^{62} -3.55878i q^{63} +(2.66802 - 63.9444i) q^{64} -0.839607 q^{65} +(3.93986 + 3.99501i) q^{66} +(27.8797 - 67.3075i) q^{67} +(-67.0900 - 0.932609i) q^{68} +(-44.1245 - 106.526i) q^{69} +(11.6412 - 4.72741i) q^{70} +(-26.0262 - 26.0262i) q^{71} +(-10.7584 - 0.224345i) q^{72} +(55.0444 + 55.0444i) q^{73} +(-31.4565 + 74.4744i) q^{74} +(23.8318 + 57.5350i) q^{75} +(33.9953 - 78.9499i) q^{76} +(-0.883134 + 2.13207i) q^{77} +(-0.0158085 + 2.27457i) q^{78} -42.0771 q^{79} +(-13.5574 - 35.4899i) q^{80} -91.2966i q^{81} +(0.346975 - 49.9238i) q^{82} +(96.5828 + 40.0059i) q^{83} +(-12.5878 - 31.6259i) q^{84} +(-36.7975 + 15.2420i) q^{85} +(7.85300 - 18.5923i) q^{86} +(11.8513 - 11.8513i) q^{87} +(6.38971 + 2.80417i) q^{88} +(31.7987 - 31.7987i) q^{89} +(-5.91833 + 2.40340i) q^{90} +(-0.864324 + 0.358015i) q^{91} +(-99.9761 - 102.795i) q^{92} +(-85.4270 - 35.3850i) q^{93} +(0.846866 + 0.858720i) q^{94} -51.0258i q^{95} +(-96.4005 + 36.0599i) q^{96} +76.5787 q^{97} +(9.96806 - 9.83046i) q^{98} +(0.448983 - 1.08394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 80 q^{10} + 96 q^{12} - 20 q^{16} - 60 q^{18} - 260 q^{22} + 64 q^{23} - 144 q^{24} - 200 q^{26} + 192 q^{27} - 40 q^{30} + 40 q^{32} + 120 q^{34} + 464 q^{36} + 504 q^{38} - 384 q^{39} + 360 q^{40} - 96 q^{43} + 52 q^{44} + 64 q^{46} - 104 q^{48} - 312 q^{50} - 384 q^{51} - 320 q^{52} + 160 q^{53} - 576 q^{54} - 512 q^{55} - 196 q^{56} - 360 q^{58} - 872 q^{60} + 128 q^{61} - 408 q^{62} + 832 q^{66} + 160 q^{67} + 856 q^{68} - 384 q^{69} + 336 q^{70} + 1488 q^{72} + 308 q^{74} + 768 q^{75} + 1024 q^{76} - 224 q^{77} - 408 q^{78} + 1024 q^{79} - 1040 q^{80} - 240 q^{82} - 1384 q^{86} + 896 q^{87} - 560 q^{88} - 1320 q^{90} - 380 q^{92} - 936 q^{94} - 1088 q^{96} - 512 q^{99}+O(q^{100}) \) 192 * q + 80 * q^10 + 96 * q^12 - 20 * q^16 - 60 * q^18 - 260 * q^22 + 64 * q^23 - 144 * q^24 - 200 * q^26 + 192 * q^27 - 40 * q^30 + 40 * q^32 + 120 * q^34 + 464 * q^36 + 504 * q^38 - 384 * q^39 + 360 * q^40 - 96 * q^43 + 52 * q^44 + 64 * q^46 - 104 * q^48 - 312 * q^50 - 384 * q^51 - 320 * q^52 + 160 * q^53 - 576 * q^54 - 512 * q^55 - 196 * q^56 - 360 * q^58 - 872 * q^60 + 128 * q^61 - 408 * q^62 + 832 * q^66 + 160 * q^67 + 856 * q^68 - 384 * q^69 + 336 * q^70 + 1488 * q^72 + 308 * q^74 + 768 * q^75 + 1024 * q^76 - 224 * q^77 - 408 * q^78 + 1024 * q^79 - 1040 * q^80 - 240 * q^82 - 1384 * q^86 + 896 * q^87 - 560 * q^88 - 1320 * q^90 - 380 * q^92 - 936 * q^94 - 1088 * q^96 - 512 * q^99

Introduction

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