LMFDB - Embedded newform 841.2.e.k.196.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{14})$
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			196.2
Character	$\chi$	$=$	841.196
Dual form			841.2.e.k.236.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.403828 + 0.0921712i) q^{2} +(0.179721 - 0.373194i) q^{3} +(-1.64736 + 0.793325i) q^{4} +(-0.222521 - 0.974928i) q^{5} +(-0.0381786 + 0.167271i) q^{6} +(-2.54832 - 1.22721i) q^{7} +(1.23982 - 0.988722i) q^{8} +(1.76350 + 2.21135i) q^{9} +O(q^{10})$	\(q+(-0.403828 + 0.0921712i) q^{2} +(0.179721 - 0.373194i) q^{3} +(-1.64736 + 0.793325i) q^{4} +(-0.222521 - 0.974928i) q^{5} +(-0.0381786 + 0.167271i) q^{6} +(-2.54832 - 1.22721i) q^{7} +(1.23982 - 0.988722i) q^{8} +(1.76350 + 2.21135i) q^{9} +(0.179721 + 0.373194i) q^{10} +(-1.88751 - 1.50524i) q^{11} +0.757359i q^{12} +(-1.14001 + 1.42952i) q^{13} +(1.14220 + 0.260699i) q^{14} +(-0.403828 - 0.0921712i) q^{15} +(1.87047 - 2.34549i) q^{16} +4.82843i q^{17} +(-0.915973 - 0.730464i) q^{18} +(2.60330 + 5.40581i) q^{19} +(1.14001 + 1.42952i) q^{20} +(-0.915973 + 0.730464i) q^{21} +(0.900969 + 0.433884i) q^{22} +(1.70381 - 7.46488i) q^{23} +(-0.146164 - 0.640386i) q^{24} +(3.60388 - 1.73553i) q^{25} +(0.328606 - 0.682357i) q^{26} +(2.35368 - 0.537213i) q^{27} +5.17157 q^{28} +0.171573 q^{30} +(3.96900 - 0.905898i) q^{31} +(-1.91526 + 3.97707i) q^{32} +(-0.900969 + 0.433884i) q^{33} +(-0.445042 - 1.94986i) q^{34} +(-0.629384 + 2.75751i) q^{35} +(-4.65943 - 2.24386i) q^{36} +(3.12733 - 2.49396i) q^{37} +(-1.54955 - 1.94307i) q^{38} +(0.328606 + 0.682357i) q^{39} +(-1.23982 - 0.988722i) q^{40} +12.4853i q^{41} +(0.302568 - 0.379408i) q^{42} +(6.25340 + 1.42730i) q^{43} +(4.30354 + 0.982255i) q^{44} +(1.76350 - 2.21135i) q^{45} +3.17157i q^{46} +(4.09886 + 3.26873i) q^{47} +(-0.539162 - 1.11958i) q^{48} +(0.623490 + 0.781831i) q^{49} +(-1.29538 + 1.03303i) q^{50} +(1.80194 + 0.867767i) q^{51} +(0.743920 - 3.25933i) q^{52} +(1.66563 + 7.29761i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(-1.04749 + 2.17513i) q^{55} +(-4.37283 + 0.998069i) q^{56} +2.48528 q^{57} +7.65685 q^{59} +(0.738371 - 0.168528i) q^{60} +(-0.359441 + 0.746387i) q^{61} +(-1.51930 + 0.731654i) q^{62} +(-1.78017 - 7.79942i) q^{63} +(-0.928262 + 4.06698i) q^{64} +(1.64736 + 0.793325i) q^{65} +(0.323845 - 0.258258i) q^{66} +(3.52699 + 4.42271i) q^{67} +(-3.83051 - 7.95414i) q^{68} +(-2.47964 - 1.97744i) q^{69} -1.17157i q^{70} +(1.97744 - 2.47964i) q^{71} +(4.37283 + 0.998069i) q^{72} +(-3.89971 - 0.890084i) q^{73} +(-1.03303 + 1.29538i) q^{74} -1.65685i q^{75} +(-8.57713 - 6.84003i) q^{76} +(2.96274 + 6.15220i) q^{77} +(-0.195594 - 0.245267i) q^{78} +(0.323845 - 0.258258i) q^{79} +(-2.70291 - 1.30165i) q^{80} +(-1.66563 + 7.29761i) q^{81} +(-1.15078 - 5.04191i) q^{82} +(3.29471 - 1.58665i) q^{83} +(0.929438 - 1.93000i) q^{84} +(4.70737 - 1.07443i) q^{85} -2.65685 q^{86} -3.82843 q^{88} +(-4.37283 + 0.998069i) q^{89} +(-0.508326 + 1.05555i) q^{90} +(4.65943 - 2.24386i) q^{91} +(3.11529 + 13.6490i) q^{92} +(0.375235 - 1.64401i) q^{93} +(-1.95652 - 0.942210i) q^{94} +(4.69099 - 3.74094i) q^{95} +(1.14001 + 1.42952i) q^{96} +(5.41716 + 11.2488i) q^{97} +(-0.323845 - 0.258258i) q^{98} -6.82843i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	$ 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) $ 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{14}\right)$

Coefficient data

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

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

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

$2$	−0.403828	+	0.0921712i	−0.285550	+	0.0651749i	−0.362897	−	0.931829i	$-0.618212\pi$
$2$	−0.403828	+	0.0921712i	−0.285550	+	0.0651749i	0.0773470	+	0.997004i	$0.475355\pi$
$3$	0.179721	−	0.373194i	0.103762	−	0.215463i	−0.842624	−	0.538502i	$-0.818990\pi$
$3$	0.179721	−	0.373194i	0.103762	−	0.215463i	0.946386	+	0.323039i	$0.104705\pi$
$4$	−1.64736	+	0.793325i	−0.823678	+	0.396662i
$5$	−0.222521	−	0.974928i	−0.0995144	−	0.436001i	−0.999999	−	0.00111393i	$-0.999645\pi$
$5$	−0.222521	−	0.974928i	−0.0995144	−	0.436001i	0.900485	−	0.434887i	$-0.143212\pi$
$6$	−0.0381786	+	0.167271i	−0.0155863	+	0.0682882i
$7$	−2.54832	−	1.22721i	−0.963176	−	0.463841i	−0.114889	−	0.993378i	$-0.536651\pi$
$7$	−2.54832	−	1.22721i	−0.963176	−	0.463841i	−0.848287	+	0.529537i	$0.822366\pi$
$8$	1.23982	−	0.988722i	0.438342	−	0.349566i
$9$	1.76350	+	2.21135i	0.587832	+	0.737118i
$10$	0.179721	+	0.373194i	0.0568326	+	0.118014i
$11$	−1.88751	−	1.50524i	−0.569105	−	0.453846i	0.296176	−	0.955133i	$-0.404289\pi$
$11$	−1.88751	−	1.50524i	−0.569105	−	0.453846i	−0.865281	+	0.501287i	$0.832860\pi$
$12$			0.757359i			0.218631i
$13$	−1.14001	+	1.42952i	−0.316181	+	0.396478i	−0.914372	−	0.404875i	$-0.867315\pi$
$13$	−1.14001	+	1.42952i	−0.316181	+	0.396478i	0.598191	+	0.801353i	$0.295886\pi$
$14$	1.14220	+	0.260699i	0.305266	+	0.0696749i
$15$	−0.403828	−	0.0921712i	−0.104268	−	0.0237985i
$16$	1.87047	−	2.34549i	0.467617	−	0.586374i
$17$			4.82843i			1.17107i	0.810649	+	0.585533i	$0.199115\pi$
$17$			4.82843i			1.17107i	−0.810649	+	0.585533i	$0.800885\pi$
$18$	−0.915973	−	0.730464i	−0.215897	−	0.172172i
$19$	2.60330	+	5.40581i	0.597239	+	1.24018i	0.952251	+	0.305317i	$0.0987624\pi$
$19$	2.60330	+	5.40581i	0.597239	+	1.24018i	−0.355012	+	0.934862i	$0.615523\pi$
$20$	1.14001	+	1.42952i	0.254913	+	0.319651i
$21$	−0.915973	+	0.730464i	−0.199882	+	0.159400i
$22$	0.900969	+	0.433884i	0.192087	+	0.0925043i
$23$	1.70381	−	7.46488i	0.355269	−	1.55654i	−0.409549	−	0.912288i	$-0.634314\pi$
$23$	1.70381	−	7.46488i	0.355269	−	1.55654i	0.764818	−	0.644247i	$-0.222829\pi$
$24$	−0.146164	−	0.640386i	−0.0298356	−	0.130718i
$25$	3.60388	−	1.73553i	0.720775	−	0.347107i
$26$	0.328606	−	0.682357i	0.0644449	−	0.133821i
$27$	2.35368	−	0.537213i	0.452967	−	0.103387i
$28$	5.17157			0.977335
$29$		0			0
$29$		0			0
$30$	0.171573			0.0313248
$31$	3.96900	−	0.905898i	0.712853	−	0.162704i	0.149310	−	0.988790i	$-0.452295\pi$
$31$	3.96900	−	0.905898i	0.712853	−	0.162704i	0.563543	+	0.826086i	$0.309438\pi$
$32$	−1.91526	+	3.97707i	−0.338573	+	0.703053i
$33$	−0.900969	+	0.433884i	−0.156839	+	0.0755295i
$34$	−0.445042	−	1.94986i	−0.0763241	−	0.334398i
$35$	−0.629384	+	2.75751i	−0.106385	+	0.466105i
$36$	−4.65943	−	2.24386i	−0.776571	−	0.373977i
$37$	3.12733	−	2.49396i	0.514129	−	0.410004i	−0.331759	−	0.943364i	$-0.607642\pi$
$37$	3.12733	−	2.49396i	0.514129	−	0.410004i	0.845889	+	0.533360i	$0.179071\pi$
$38$	−1.54955	−	1.94307i	−0.251370	−	0.315208i
$39$	0.328606	+	0.682357i	0.0526191	+	0.109265i
$40$	−1.23982	−	0.988722i	−0.196032	−	0.156331i
$41$			12.4853i			1.94987i	0.222483	+	0.974937i	$0.428584\pi$
$41$			12.4853i			1.94987i	−0.222483	+	0.974937i	$0.571416\pi$
$42$	0.302568	−	0.379408i	0.0466873	−	0.0585440i
$43$	6.25340	+	1.42730i	0.953634	+	0.217661i	0.670908	−	0.741540i	$-0.265904\pi$
$43$	6.25340	+	1.42730i	0.953634	+	0.217661i	0.282725	+	0.959201i	$0.408761\pi$
$44$	4.30354	+	0.982255i	0.648783	+	0.148081i
$45$	1.76350	−	2.21135i	0.262886	−	0.329649i
$46$			3.17157i			0.467623i
$47$	4.09886	+	3.26873i	0.597880	+	0.476794i	0.875053	−	0.484026i	$-0.160826\pi$
$47$	4.09886	+	3.26873i	0.597880	+	0.476794i	−0.277173	+	0.960820i	$0.589398\pi$
$48$	−0.539162	−	1.11958i	−0.0778213	−	0.161598i
$49$	0.623490	+	0.781831i	0.0890700	+	0.111690i
$50$	−1.29538	+	1.03303i	−0.183195	+	0.146093i
$51$	1.80194	+	0.867767i	0.252322	+	0.121512i
$52$	0.743920	−	3.25933i	0.103163	−	0.451987i
$53$	1.66563	+	7.29761i	0.228792	+	1.00240i	0.950626	+	0.310338i	$0.100442\pi$
$53$	1.66563	+	7.29761i	0.228792	+	1.00240i	−0.721834	+	0.692066i	$0.756701\pi$
$54$	−0.900969	+	0.433884i	−0.122606	+	0.0590441i
$55$	−1.04749	+	2.17513i	−0.141243	+	0.293295i
$56$	−4.37283	+	0.998069i	−0.584343	+	0.133373i
$57$	2.48528			0.329184
$58$		0			0
$59$	7.65685			0.996838			0.498419	−	0.866936i	$-0.333914\pi$
$59$	7.65685			0.996838			0.498419	+	0.866936i	$0.333914\pi$
$60$	0.738371	−	0.168528i	0.0953233	−	0.0217569i
$61$	−0.359441	+	0.746387i	−0.0460217	+	0.0955651i	−0.922712	−	0.385491i	$-0.874032\pi$
$61$	−0.359441	+	0.746387i	−0.0460217	+	0.0955651i	0.876690	+	0.481056i	$0.159747\pi$
$62$	−1.51930	+	0.731654i	−0.192951	+	0.0929202i
$63$	−1.78017	−	7.79942i	−0.224280	−	0.982635i
$64$	−0.928262	+	4.06698i	−0.116033	+	0.508373i
$65$	1.64736	+	0.793325i	0.204329	+	0.0983998i
$66$	0.323845	−	0.258258i	0.0398626	−	0.0317894i
$67$	3.52699	+	4.42271i	0.430891	+	0.540320i	0.949117	−	0.314924i	$-0.101979\pi$
$67$	3.52699	+	4.42271i	0.430891	+	0.540320i	−0.518226	+	0.855243i	$0.673408\pi$
$68$	−3.83051	−	7.95414i	−0.464518	−	0.964581i
$69$	−2.47964	−	1.97744i	−0.298513	−	0.238056i
$70$		−	1.17157i		−	0.140030i
$71$	1.97744	−	2.47964i	0.234679	−	0.294279i	−0.650521	−	0.759488i	$-0.725450\pi$
$71$	1.97744	−	2.47964i	0.234679	−	0.294279i	0.885201	+	0.465209i	$0.154021\pi$
$72$	4.37283	+	0.998069i	0.515342	+	0.117624i
$73$	−3.89971	−	0.890084i	−0.456427	−	0.104176i	−0.0118748	−	0.999929i	$-0.503780\pi$
$73$	−3.89971	−	0.890084i	−0.456427	−	0.104176i	−0.444552	+	0.895753i	$0.646637\pi$
$74$	−1.03303	+	1.29538i	−0.120087	+	0.150585i
$75$		−	1.65685i		−	0.191317i
$76$	−8.57713	−	6.84003i	−0.983864	−	0.784606i
$77$	2.96274	+	6.15220i	0.337636	+	0.701108i
$78$	−0.195594	−	0.245267i	−0.0221467	−	0.0277710i
$79$	0.323845	−	0.258258i	0.0364354	−	0.0290563i	−0.605103	−	0.796147i	$-0.706868\pi$
$79$	0.323845	−	0.258258i	0.0364354	−	0.0290563i	0.641538	+	0.767091i	$0.278297\pi$
$80$	−2.70291	−	1.30165i	−0.302194	−	0.145529i
$81$	−1.66563	+	7.29761i	−0.185070	+	0.810846i
$82$	−1.15078	−	5.04191i	−0.127083	−	0.556786i
$83$	3.29471	−	1.58665i	0.361642	−	0.174157i	−0.244235	−	0.969716i	$-0.578537\pi$
$83$	3.29471	−	1.58665i	0.361642	−	0.174157i	0.605877	+	0.795559i	$0.292823\pi$
$84$	0.929438	−	1.93000i	0.101410	−	0.210580i
$85$	4.70737	−	1.07443i	0.510586	−	0.116538i
$86$	−2.65685			−0.286496
$87$		0			0
$88$	−3.82843			−0.408112
$89$	−4.37283	+	0.998069i	−0.463519	+	0.105795i	−0.447901	−	0.894083i	$-0.647828\pi$
$89$	−4.37283	+	0.998069i	−0.463519	+	0.105795i	−0.0156172	+	0.999878i	$0.504971\pi$
$90$	−0.508326	+	1.05555i	−0.0535823	+	0.111265i
$91$	4.65943	−	2.24386i	0.488441	−	0.235221i
$92$	3.11529	+	13.6490i	0.324792	+	1.42301i
$93$	0.375235	−	1.64401i	0.0389101	−	0.170476i
$94$	−1.95652	−	0.942210i	−0.201800	−	0.0971816i
$95$	4.69099	−	3.74094i	0.481285	−	0.383812i
$96$	1.14001	+	1.42952i	0.116351	+	0.145900i
$97$	5.41716	+	11.2488i	0.550029	+	1.14215i	0.971879	+	0.235482i	$0.0756668\pi$
$97$	5.41716	+	11.2488i	0.550029	+	1.14215i	−0.421849	+	0.906666i	$0.638619\pi$
$98$	−0.323845	−	0.258258i	−0.0327133	−	0.0260880i
$99$		−	6.82843i		−	0.686283i
$100$	−4.56002	+	5.71809i	−0.456002	+	0.571809i
$101$	−13.3144	−	3.03894i	−1.32484	−	0.302385i	−0.499151	−	0.866515i	$-0.666355\pi$
$101$	−13.3144	−	3.03894i	−1.32484	−	0.302385i	−0.825686	+	0.564130i	$0.809212\pi$
$102$	−0.807657	−	0.184342i	−0.0799699	−	0.0182526i
$103$	0.516516	−	0.647690i	0.0508938	−	0.0638188i	−0.755733	−	0.654880i	$-0.772719\pi$
$103$	0.516516	−	0.647690i	0.0508938	−	0.0638188i	0.806627	+	0.591061i	$0.201291\pi$
$104$			2.89949i			0.284319i
$105$	0.915973	+	0.730464i	0.0893898	+	0.0712860i
$106$	−1.34526	−	2.79346i	−0.130663	−	0.271325i
$107$	−5.71838	−	7.17062i	−0.552817	−	0.693210i	0.424395	−	0.905477i	$-0.360487\pi$
$107$	−5.71838	−	7.17062i	−0.552817	−	0.693210i	−0.977212	+	0.212267i	$0.931915\pi$
$108$	−3.45117	+	2.75222i	−0.332089	+	0.264832i
$109$	1.21013	+	0.582769i	0.115910	+	0.0558192i	0.490940	−	0.871193i	$-0.336653\pi$
$109$	1.21013	+	0.582769i	0.115910	+	0.0558192i	−0.375030	+	0.927013i	$0.622368\pi$
$110$	0.222521	−	0.974928i	0.0212165	−	0.0929557i
$111$	−0.368685	−	1.61531i	−0.0349940	−	0.153319i
$112$	−7.64497	+	3.68163i	−0.722382	+	0.347881i
$113$	4.04107	−	8.39136i	0.380152	−	0.789393i	−0.619838	−	0.784730i	$-0.712802\pi$
$113$	4.04107	−	8.39136i	0.380152	−	0.789393i	0.999989	−	0.00466273i	$-0.00148420\pi$
$114$	−1.00363	+	0.229071i	−0.0939983	+	0.0214545i
$115$	−7.65685			−0.714005
$116$		0			0
$117$	−5.17157			−0.478112
$118$	−3.09205	+	0.705741i	−0.284647	+	0.0649688i
$119$	5.92549	−	12.3044i	0.543189	−	1.12794i
$120$	−0.591805	+	0.284998i	−0.0540242	+	0.0260167i
$121$	−1.15078	−	5.04191i	−0.104617	−	0.458356i
$122$	0.0763571	−	0.334542i	0.00691305	−	0.0302880i
$123$	4.65943	+	2.24386i	0.420126	+	0.202322i
$124$	−5.81968	+	4.64104i	−0.522623	+	0.416778i
$125$	−5.61141	−	7.03648i	−0.501900	−	0.629362i
$126$	1.43776	+	2.98555i	0.128086	+	0.265974i
$127$	12.2410	+	9.76189i	1.08622	+	0.866228i	0.991607	−	0.129287i	$-0.0412689\pi$
$127$	12.2410	+	9.76189i	1.08622	+	0.866228i	0.0946078	+	0.995515i	$0.469840\pi$
$128$		−	10.5563i		−	0.933058i
$129$	1.65652	−	2.07721i	0.145849	−	0.182888i
$130$	−0.738371	−	0.168528i	−0.0647594	−	0.0147809i
$131$	1.28077	+	0.292328i	0.111901	+	0.0255408i	0.278105	−	0.960551i	$-0.410294\pi$
$131$	1.28077	+	0.292328i	0.111901	+	0.0255408i	−0.166203	+	0.986091i	$0.553151\pi$
$132$	1.14001	−	1.42952i	0.0992248	−	0.124424i
$133$		−	16.9706i		−	1.47153i
$134$	−1.83195	−	1.46093i	−0.158256	−	0.126205i
$135$	−1.04749	−	2.17513i	−0.0901534	−	0.187205i
$136$	4.77397	+	5.98637i	0.409365	+	0.513327i
$137$	9.38198	−	7.48188i	0.801556	−	0.639220i	−0.134562	−	0.990905i	$-0.542963\pi$
$137$	9.38198	−	7.48188i	0.801556	−	0.639220i	0.936118	+	0.351685i	$0.114391\pi$
$138$	1.18361	+	0.569997i	0.100756	+	0.0485213i
$139$	−3.11529	+	13.6490i	−0.264236	+	1.15769i	0.652370	+	0.757900i	$0.273775\pi$
$139$	−3.11529	+	13.6490i	−0.264236	+	1.15769i	−0.916606	+	0.399792i	$0.869082\pi$
$140$	−1.15078	−	5.04191i	−0.0972589	−	0.426119i
$141$	1.95652	−	0.942210i	0.164769	−	0.0793484i
$142$	−0.569997	+	1.18361i	−0.0478331	+	0.0993264i
$143$	4.30354	−	0.982255i	0.359880	−	0.0821403i
$144$	8.48528			0.707107
$145$		0			0
$146$	1.65685			0.137122
$147$	0.403828	−	0.0921712i	0.0333072	−	0.00760215i
$148$	−3.17330	+	6.58942i	−0.260844	+	0.541647i
$149$	−1.95652	+	0.942210i	−0.160284	+	0.0771889i	−0.512306	−	0.858803i	$-0.671209\pi$
$149$	−1.95652	+	0.942210i	−0.160284	+	0.0771889i	0.352022	+	0.935992i	$0.385494\pi$
$150$	0.152714	+	0.669085i	0.0124691	+	0.0546305i
$151$	3.14692	−	13.7876i	0.256093	−	1.12202i	−0.669296	−	0.742996i	$-0.733404\pi$
$151$	3.14692	−	13.7876i	0.256093	−	1.12202i	0.925389	−	0.379020i	$-0.123739\pi$
$152$	8.57247	+	4.12828i	0.695319	+	0.334848i
$153$	−10.6774	+	8.51491i	−0.863213	+	0.688390i
$154$	−1.76350	−	2.21135i	−0.142107	−	0.178196i
$155$	−1.76637	−	3.66791i	−0.141878	−	0.294613i
$156$	−1.08266	−	0.863394i	−0.0866823	−	0.0691268i
$157$		−	8.48528i		−	0.677199i	−0.940931	−	0.338600i	$-0.890047\pi$
$157$		−	8.48528i		−	0.677199i	0.940931	−	0.338600i	$-0.109953\pi$
$158$	−0.106974	+	0.134141i	−0.00851039	+	0.0106717i
$159$	3.02277	+	0.689927i	0.239721	+	0.0547148i
$160$	4.30354	+	0.982255i	0.340225	+	0.0776541i
$161$	−13.5028	+	16.9320i	−1.06417	+	1.33443i
$162$		−	3.10051i		−	0.243599i
$163$	14.1285	+	11.2671i	1.10663	+	0.882509i	0.993809	−	0.111106i	$-0.0354392\pi$
$163$	14.1285	+	11.2671i	1.10663	+	0.882509i	0.112823	+	0.993615i	$0.464011\pi$
$164$	−9.90488	−	20.5677i	−0.773441	−	1.60607i
$165$	0.623490	+	0.781831i	0.0485386	+	0.0608655i
$166$	−1.18425	+	0.944412i	−0.0919160	+	0.0733006i
$167$	−7.95414	−	3.83051i	−0.615510	−	0.296414i	0.100032	−	0.994984i	$-0.468106\pi$
$167$	−7.95414	−	3.83051i	−0.615510	−	0.296414i	−0.715541	+	0.698570i	$0.753820\pi$
$168$	−0.413414	+	1.81128i	−0.0318956	+	0.139744i
$169$	2.14885	+	9.41474i	0.165296	+	0.724211i
$170$	−1.80194	+	0.867767i	−0.138202	+	0.0665547i
$171$	−7.36325	+	15.2899i	−0.563082	+	1.16925i
$172$	−11.4339	+	2.60971i	−0.871825	+	0.198988i
$173$	−23.6569			−1.79860			−0.899299	−	0.437335i	$-0.855922\pi$
$173$	−23.6569			−1.79860			−0.899299	+	0.437335i	$0.855922\pi$
$174$		0			0
$175$	−11.3137			−0.855236
$176$	−7.06105	+	1.61164i	−0.532247	+	0.121482i
$177$	1.37609	−	2.85749i	0.103434	−	0.214782i
$178$	1.67388	−	0.806097i	0.125462	−	0.0604195i
$179$	2.33319	+	10.2224i	0.174391	+	0.764058i	0.984156	+	0.177303i	$0.0567374\pi$
$179$	2.33319	+	10.2224i	0.174391	+	0.764058i	−0.809765	+	0.586754i	$0.800405\pi$
$180$	−1.15078	+	5.04191i	−0.0857743	+	0.375802i
$181$	12.8962	+	6.21049i	0.958567	+	0.461622i	0.846682	−	0.532099i	$-0.178597\pi$
$181$	12.8962	+	6.21049i	0.958567	+	0.461622i	0.111886	+	0.993721i	$0.464311\pi$
$182$	−1.67479	+	1.33560i	−0.124144	+	0.0990012i
$183$	0.213948	+	0.268282i	0.0158155	+	0.0198320i
$184$	−5.26828	−	10.9397i	−0.388382	−	0.806484i
$185$	−3.12733	−	2.49396i	−0.229926	−	0.183360i
$186$			0.698485i			0.0512154i
$187$	7.26793	−	9.11370i	0.531484	−	0.666459i
$188$	−9.34545	−	2.13304i	−0.681587	−	0.155568i
$189$	−6.65722	−	1.51947i	−0.484242	−	0.110525i
$190$	−1.54955	+	1.94307i	−0.112416	+	0.140965i
$191$		−	2.68629i		−	0.194373i	−0.995266	−	0.0971866i	$-0.969016\pi$
$191$		−	2.68629i		−	0.194373i	0.995266	−	0.0971866i	$-0.0309844\pi$
$192$	1.35094	+	1.07734i	0.0974960	+	0.0777504i
$193$	−4.69828	−	9.75608i	−0.338189	−	0.702258i	0.660636	−	0.750706i	$-0.270287\pi$
$193$	−4.69828	−	9.75608i	−0.338189	−	0.702258i	−0.998826	+	0.0484485i	$0.984572\pi$
$194$	−3.22442	−	4.04330i	−0.231500	−	0.290292i
$195$	0.592127	−	0.472206i	0.0424031	−	0.0338154i
$196$	−1.64736	−	0.793325i	−0.117668	−	0.0566661i
$197$	−0.445042	+	1.94986i	−0.0317079	+	0.138921i	−0.988304	−	0.152495i	$-0.951269\pi$
$197$	−0.445042	+	1.94986i	−0.0317079	+	0.138921i	0.956596	+	0.291416i	$0.0941264\pi$
$198$	0.629384	+	2.75751i	0.0447284	+	0.195968i
$199$	−14.8527	+	7.15270i	−1.05288	+	0.507041i	−0.878552	−	0.477646i	$-0.841490\pi$
$199$	−14.8527	+	7.15270i	−1.05288	+	0.507041i	−0.174330	+	0.984687i	$0.555776\pi$
$200$	2.75219	−	5.71498i	0.194609	−	0.404110i
$201$	2.28440	−	0.521399i	0.161129	−	0.0367766i
$202$	5.65685			0.398015
$203$		0			0
$204$	−3.65685			−0.256031
$205$	12.1722	−	2.77824i	0.850147	−	0.194040i
$206$	−0.148885	+	0.309164i	−0.0103733	+	0.0215405i
$207$	19.5122	−	9.39656i	1.35619	−	0.653106i
$208$	1.22059	+	5.34775i	0.0846327	+	0.370800i
$209$	3.22328	−	14.1221i	0.222959	−	0.976846i
$210$	−0.437223	−	0.210556i	−0.0301713	−	0.0145297i
$211$	−13.5920	+	10.8392i	−0.935709	+	0.746203i	−0.967389	−	0.253295i	$-0.918486\pi$
$211$	−13.5920	+	10.8392i	−0.935709	+	0.746203i	0.0316797	+	0.999498i	$0.489914\pi$
$212$	−8.53326	−	10.7004i	−0.586067	−	0.734905i
$213$	−0.569997	−	1.18361i	−0.0390555	−	0.0810997i
$214$	2.97017	+	2.36863i	0.203037	+	0.161916i
$215$		−	6.41421i		−	0.437446i
$216$	2.38699	−	2.99318i	0.162414	−	0.203660i
$217$	−11.2260	−	2.56227i	−0.762072	−	0.173938i
$218$	−0.542400	−	0.123799i	−0.0367360	−	0.00838475i
$219$	−1.03303	+	1.29538i	−0.0698058	+	0.0875337i
$220$		−	4.41421i		−	0.297606i
$221$	−6.90234	−	5.50443i	−0.464302	−	0.370268i
$222$	0.297771	+	0.618327i	0.0199851	+	0.0414994i
$223$	−5.50443	−	6.90234i	−0.368604	−	0.462215i	0.562591	−	0.826735i	$-0.309804\pi$
$223$	−5.50443	−	6.90234i	−0.368604	−	0.462215i	−0.931196	+	0.364520i	$0.881233\pi$
$224$	9.76139	−	7.78445i	0.652210	−	0.520120i
$225$	10.1933	+	4.90883i	0.679553	+	0.327256i
$226$	−0.858456	+	3.76114i	−0.0571036	+	0.250187i
$227$	−4.48205	−	19.6371i	−0.297484	−	1.30336i	−0.873860	−	0.486178i	$-0.838391\pi$
$227$	−4.48205	−	19.6371i	−0.297484	−	1.30336i	0.576376	−	0.817185i	$-0.304466\pi$
$228$	−4.09414	+	1.97164i	−0.271141	+	0.130575i
$229$	−8.88823	+	18.4566i	−0.587351	+	1.21965i	0.369544	+	0.929213i	$0.379514\pi$
$229$	−8.88823	+	18.4566i	−0.587351	+	1.21965i	−0.956895	+	0.290433i	$0.906201\pi$
$230$	3.09205	−	0.705741i	0.203884	−	0.0465352i
$231$	2.82843			0.186097
$232$		0			0
$233$	−4.31371			−0.282600			−0.141300	−	0.989967i	$-0.545128\pi$
$233$	−4.31371			−0.282600			−0.141300	+	0.989967i	$0.545128\pi$
$234$	2.08843	−	0.476670i	0.136525	−	0.0311609i
$235$	2.27470	−	4.72346i	0.148385	−	0.308124i
$236$	−12.6136	+	6.07437i	−0.821073	+	0.395408i
$237$	−0.0381786	−	0.167271i	−0.00247996	−	0.0108654i
$238$	−1.25877	+	5.51503i	−0.0815938	+	0.357486i
$239$	7.51691	+	3.61996i	0.486229	+	0.234155i	0.660904	−	0.750471i	$-0.270173\pi$
$239$	7.51691	+	3.61996i	0.486229	+	0.234155i	−0.174675	+	0.984626i	$0.555887\pi$
$240$	−0.971536	+	0.774774i	−0.0627124	+	0.0500114i
$241$	−2.68955	−	3.37259i	−0.173249	−	0.217248i	0.687624	−	0.726067i	$-0.258654\pi$
$241$	−2.68955	−	3.37259i	−0.173249	−	0.217248i	−0.860874	+	0.508819i	$0.830082\pi$
$242$	0.929438	+	1.93000i	0.0597465	+	0.124065i
$243$	8.08660	+	6.44885i	0.518755	+	0.413694i
$244$		−	1.51472i		−	0.0969699i
$245$	0.623490	−	0.781831i	0.0398333	−	0.0499494i
$246$	−2.08843	−	0.476670i	−0.133153	−	0.0303914i
$247$	−10.6955	−	2.44118i	−0.680539	−	0.155329i
$248$	4.02515	−	5.04738i	0.255597	−	0.320509i
$249$		−	1.51472i		−	0.0959914i
$250$	2.91461	+	2.32432i	0.184336	+	0.147003i
$251$	2.57247	+	5.34178i	0.162373	+	0.337170i	0.966242	−	0.257635i	$-0.0829433\pi$
$251$	2.57247	+	5.34178i	0.162373	+	0.337170i	−0.803870	+	0.594806i	$0.797229\pi$
$252$	9.12005	+	11.4362i	0.574509	+	0.720411i
$253$	−14.4524	+	11.5254i	−0.908613	+	0.724595i
$254$	−5.84304	−	2.81386i	−0.366625	−	0.176557i
$255$	0.445042	−	1.94986i	0.0278696	−	0.122105i
$256$	−0.883533	−	3.87101i	−0.0552208	−	0.241938i
$257$	21.4687	−	10.3388i	1.33918	−	0.644915i	0.379285	−	0.925280i	$-0.376170\pi$
$257$	21.4687	−	10.3388i	1.33918	−	0.644915i	0.959893	+	0.280365i	$0.0904555\pi$
$258$	−0.477491	+	0.991521i	−0.0297273	+	0.0617294i
$259$	−11.0301	+	2.51754i	−0.685374	+	0.156432i
$260$	−3.34315			−0.207333
$261$		0			0
$262$	−0.544156			−0.0336181
$263$	−10.9608	+	2.50172i	−0.675870	+	0.154263i	−0.546660	−	0.837354i	$-0.684101\pi$
$263$	−10.9608	+	2.50172i	−0.675870	+	0.154263i	−0.129209	+	0.991617i	$0.541244\pi$
$264$	−0.688047	+	1.42874i	−0.0423464	+	0.0879331i
$265$	6.74401	−	3.24774i	0.414281	−	0.199507i
$266$	1.56420	+	6.85319i	0.0959071	+	0.420196i
$267$	−0.413414	+	1.81128i	−0.0253005	+	0.110849i
$268$	−9.31885	−	4.48772i	−0.569240	−	0.274131i
$269$	15.2112	−	12.1305i	0.927443	−	0.739611i	−0.0382582	−	0.999268i	$-0.512181\pi$
$269$	15.2112	−	12.1305i	0.927443	−	0.739611i	0.965701	+	0.259657i	$0.0836095\pi$
$270$	0.623490	+	0.781831i	0.0379444	+	0.0475807i
$271$	6.31576	+	13.1148i	0.383655	+	0.796668i	0.999958	+	0.00915912i	$0.00291548\pi$
$271$	6.31576	+	13.1148i	0.383655	+	0.796668i	−0.616303	+	0.787509i	$0.711370\pi$
$272$	11.3250	+	9.03143i	0.686682	+	0.547611i
$273$		−	2.14214i		−	0.129648i
$274$	−3.09910	+	3.88614i	−0.187223	+	0.234770i
$275$	−9.41474	−	2.14885i	−0.567730	−	0.129581i
$276$	5.65360	+	1.29040i	0.340307	+	0.0776728i
$277$	3.31304	−	4.15442i	0.199061	−	0.249615i	−0.672275	−	0.740302i	$-0.734683\pi$
$277$	3.31304	−	4.15442i	0.199061	−	0.249615i	0.871336	+	0.490687i	$0.163254\pi$
$278$		−	5.79899i		−	0.347800i
$279$	9.00257	+	7.17931i	0.538970	+	0.429814i
$280$	1.94609	+	4.04110i	0.116301	+	0.241502i
$281$	−1.22863	−	1.54065i	−0.0732937	−	0.0919074i	0.743833	−	0.668366i	$-0.233006\pi$
$281$	−1.22863	−	1.54065i	−0.0732937	−	0.0919074i	−0.817127	+	0.576458i	$0.804434\pi$
$282$	−0.703253	+	0.560826i	−0.0418781	+	0.0333967i
$283$	0.309164	+	0.148885i	0.0183779	+	0.00885032i	0.443050	−	0.896497i	$-0.353896\pi$
$283$	0.309164	+	0.148885i	0.0183779	+	0.00885032i	−0.424672	+	0.905347i	$0.639611\pi$
$284$	−1.29040	+	5.65360i	−0.0765710	+	0.335479i
$285$	−0.553027	−	2.42297i	−0.0327585	−	0.143524i
$286$	−1.64736	+	0.793325i	−0.0974102	+	0.0469103i
$287$	15.3220	−	31.8166i	0.904432	−	1.87807i
$288$	−12.1722	+	2.77824i	−0.717257	+	0.163709i
$289$	−6.31371			−0.371395
$290$		0			0
$291$	5.17157			0.303163
$292$	7.13034	−	1.62745i	0.417272	−	0.0952395i
$293$	1.58665	−	3.29471i	0.0926931	−	0.192479i	−0.849468	−	0.527641i	$-0.823077\pi$
$293$	1.58665	−	3.29471i	0.0926931	−	0.192479i	0.942161	+	0.335162i	$0.108791\pi$
$294$	−0.154582	+	0.0744427i	−0.00901539	+	0.00434159i
$295$	−1.70381	−	7.46488i	−0.0991997	−	0.434622i
$296$	1.41148	−	6.18411i	0.0820408	−	0.359444i
$297$	−5.25123	−	2.52886i	−0.304707	−	0.146739i
$298$	0.703253	−	0.560826i	0.0407384	−	0.0324878i
$299$	8.72886	+	10.9456i	0.504803	+	0.633003i
$300$	1.31442	+	2.72943i	0.0758883	+	0.157584i
$301$	−14.1841	−	11.3114i	−0.817558	−	0.651980i
$302$			5.85786i			0.337082i
$303$	−3.52699	+	4.42271i	−0.202620	+	0.254078i
$304$	17.5487	+	4.00538i	1.00649	+	0.229724i
$305$	0.807657	+	0.184342i	0.0462463	+	0.0105554i
$306$	3.52699	−	4.42271i	0.201625	−	0.252829i
$307$			16.8995i			0.964505i	0.876032	+	0.482253i	$0.160181\pi$
$307$			16.8995i			0.964505i	−0.876032	+	0.482253i	$0.839819\pi$
$308$	−9.76139	−	7.78445i	−0.556207	−	0.443560i
$309$	−0.148885	−	0.309164i	−0.00846979	−	0.0175877i
$310$	1.05139	+	1.31840i	0.0597147	+	0.0748798i
$311$	19.7911	−	15.7828i	1.12225	−	0.894963i	0.126958	−	0.991908i	$-0.459479\pi$
$311$	19.7911	−	15.7828i	1.12225	−	0.894963i	0.995290	+	0.0969454i	$0.0309072\pi$
$312$	1.08207	+	0.521099i	0.0612603	+	0.0295014i
$313$	−0.928262	+	4.06698i	−0.0524685	+	0.229879i	−0.994363	−	0.106029i	$-0.966186\pi$
$313$	−0.928262	+	4.06698i	−0.0524685	+	0.229879i	0.941895	+	0.335909i	$0.109043\pi$
$314$	0.782098	+	3.42660i	0.0441364	+	0.193374i
$315$	−7.20775	+	3.47107i	−0.406111	+	0.195573i
$316$	−0.328606	+	0.682357i	−0.0184855	+	0.0383856i
$317$	18.9680	−	4.32933i	1.06535	−	0.243160i	0.346305	−	0.938122i	$-0.387436\pi$
$317$	18.9680	−	4.32933i	1.06535	−	0.243160i	0.719046	+	0.694962i	$0.244579\pi$
$318$	−1.28427			−0.0720184
$319$		0			0
$320$	4.17157			0.233198
$321$	−3.70374	+	0.845355i	−0.206723	+	0.0471831i
$322$	3.89218	−	8.08220i	0.216903	−	0.450403i
$323$	−26.1016	+	12.5699i	−1.45233	+	0.699406i
$324$	−3.04549	−	13.3431i	−0.169194	−	0.741286i
$325$	−1.62745	+	7.13034i	−0.0902749	+	0.395520i
$326$	−6.74401	−	3.24774i	−0.373516	−	0.179876i
$327$	0.434971	−	0.346878i	0.0240540	−	0.0191824i
$328$	12.3445	+	15.4795i	0.681609	+	0.854711i
$329$	−6.43381	−	13.3600i	−0.354708	−	0.736558i
$330$	−0.323845	−	0.258258i	−0.0178271	−	0.0142166i
$331$			0.414214i			0.0227672i	0.999935	+	0.0113836i	$0.00362360\pi$
$331$			0.414214i			0.0227672i	−0.999935	+	0.0113836i	$0.996376\pi$
$332$	−4.16883	+	5.22755i	−0.228795	+	0.286899i
$333$	11.0301	+	2.51754i	0.604443	+	0.137960i
$334$	3.56517	+	0.813727i	0.195077	+	0.0445251i
$335$	3.52699	−	4.42271i	0.192700	−	0.241638i
$336$			3.51472i			0.191744i
$337$	−13.9158	−	11.0975i	−0.758043	−	0.604519i	0.166303	−	0.986075i	$-0.446817\pi$
$337$	−13.9158	−	11.0975i	−0.758043	−	0.604519i	−0.924346	+	0.381556i	$0.875388\pi$
$338$	−1.73553	−	3.60388i	−0.0944007	−	0.196025i
$339$	−2.40534	−	3.01620i	−0.130640	−	0.163817i
$340$	−6.90234	+	5.50443i	−0.374332	+	0.298520i
$341$	−8.85511	−	4.26439i	−0.479531	−	0.230930i
$342$	1.56420	−	6.85319i	0.0845821	−	0.370578i
$343$	3.77631	+	16.5451i	0.203901	+	0.893350i
$344$	9.16427	−	4.41328i	0.494104	−	0.237948i
$345$	−1.37609	+	2.85749i	−0.0740864	+	0.153842i
$346$	9.55331	−	2.18048i	0.513589	−	0.117223i
$347$	14.4853			0.777611			0.388805	−	0.921320i	$-0.372888\pi$
$347$	14.4853			0.777611			0.388805	+	0.921320i	$0.372888\pi$
$348$		0			0
$349$	23.1421			1.23877			0.619385	−	0.785087i	$-0.287382\pi$
$349$	23.1421			1.23877			0.619385	+	0.785087i	$0.287382\pi$
$350$	4.56880	−	1.04280i	0.244212	−	0.0557399i
$351$	−1.91526	+	3.97707i	−0.102229	+	0.212280i
$352$	9.60149	−	4.62384i	0.511761	−	0.246451i
$353$	−1.55110	−	6.79580i	−0.0825565	−	0.361704i	0.916729	−	0.399511i	$-0.130820\pi$
$353$	−1.55110	−	6.79580i	−0.0825565	−	0.361704i	−0.999285	+	0.0378069i	$0.987963\pi$
$354$	−0.292328	+	1.28077i	−0.0155370	+	0.0680722i
$355$	−2.85749	−	1.37609i	−0.151660	−	0.0730355i
$356$	6.41181	−	5.11325i	0.339825	−	0.271002i
$357$	−3.52699	−	4.42271i	−0.186668	−	0.234074i
$358$	−1.88442	−	3.91304i	−0.0995947	−	0.206811i
$359$	−14.1285	−	11.2671i	−0.745675	−	0.594656i	0.175191	−	0.984534i	$-0.443946\pi$
$359$	−14.1285	−	11.2671i	−0.745675	−	0.594656i	−0.920866	+	0.389878i	$0.872517\pi$
$360$		−	4.48528i		−	0.236395i
$361$	−10.5993	+	13.2911i	−0.557859	+	0.699533i
$362$	−5.78028	−	1.31931i	−0.303805	−	0.0693415i
$363$	−2.08843	−	0.476670i	−0.109614	−	0.0250187i
$364$	−5.89562	+	7.39288i	−0.309015	+	0.387492i
$365$			4.00000i			0.209370i
$366$	−0.111126	−	0.0886201i	−0.00580865	−	0.00463225i
$367$	7.80991	+	16.2174i	0.407674	+	0.846543i	0.999190	+	0.0402500i	$0.0128154\pi$
$367$	7.80991	+	16.2174i	0.407674	+	0.846543i	−0.591516	+	0.806293i	$0.701470\pi$
$368$	−14.3219	−	17.9591i	−0.746581	−	0.936183i
$369$	−27.6094	+	22.0177i	−1.43729	+	1.14620i
$370$	1.49277	+	0.718882i	0.0776056	+	0.0373729i
$371$	4.71112	−	20.6408i	0.244589	−	1.07161i
$372$	0.686090	+	3.00596i	0.0355721	+	0.155852i
$373$	3.32123	−	1.59942i	0.171967	−	0.0828149i	−0.345920	−	0.938264i	$-0.612433\pi$
$373$	3.32123	−	1.59942i	0.171967	−	0.0828149i	0.517887	+	0.855449i	$0.326719\pi$
$374$	−2.09498	+	4.35026i	−0.108329	+	0.224947i
$375$	−3.63446	+	0.829541i	−0.187682	+	0.0428373i
$376$	8.31371			0.428747
$377$		0			0
$378$	2.82843			0.145479
$379$	−26.2944	+	6.00151i	−1.35065	+	0.308277i	−0.835815	−	0.549012i	$-0.815004\pi$
$379$	−26.2944	+	6.00151i	−1.35065	+	0.308277i	−0.514836	+	0.857289i	$0.672147\pi$
$380$	−4.75995	+	9.88414i	−0.244180	+	0.507045i
$381$	5.84304	−	2.81386i	0.299348	−	0.144158i
$382$	0.247599	+	1.08480i	0.0126683	+	0.0555032i
$383$	−4.55840	+	19.9717i	−0.232924	+	1.02050i	0.714277	+	0.699863i	$0.246756\pi$
$383$	−4.55840	+	19.9717i	−0.232924	+	1.02050i	−0.947201	+	0.320642i	$0.896101\pi$
$384$	−3.93956	−	1.89719i	−0.201040	−	0.0968157i
$385$	5.33868	−	4.25745i	0.272084	−	0.216980i
$386$	2.79653	+	3.50673i	0.142339	+	0.178488i
$387$	7.87158	+	16.3455i	0.400135	+	0.830888i
$388$	−17.8480	−	14.2333i	−0.906094	−	0.722586i
$389$			36.9706i			1.87448i	0.348682	+	0.937241i	$0.386629\pi$
$389$			36.9706i			1.87448i	−0.348682	+	0.937241i	$0.613371\pi$
$390$	−0.195594	+	0.245267i	−0.00990429	+	0.0124196i
$391$	36.0436	+	8.22672i	1.82280	+	0.416043i
$392$	1.54603	+	0.352871i	0.0780862	+	0.0178227i
$393$	0.339276	−	0.425438i	0.0171142	−	0.0214605i
$394$		−	0.828427i		−	0.0417356i
$395$	−0.323845	−	0.258258i	−0.0162944	−	0.0129944i
$396$	5.41716	+	11.2488i	0.272223	+	0.565276i
$397$	19.1142	+	23.9685i	0.959316	+	1.20294i	0.979150	+	0.203141i	$0.0651150\pi$
$397$	19.1142	+	23.9685i	0.959316	+	1.20294i	−0.0198335	+	0.999803i	$0.506314\pi$
$398$	5.33868	−	4.25745i	0.267604	−	0.213407i
$399$	−6.33330	−	3.04996i	−0.317062	−	0.152689i
$400$	2.67025	−	11.6991i	0.133513	−	0.584957i
$401$	1.63400	+	7.15904i	0.0815982	+	0.357505i	0.999200	−	0.0399961i	$-0.0127345\pi$
$401$	1.63400	+	7.15904i	0.0815982	+	0.357505i	−0.917602	+	0.397501i	$0.869877\pi$
$402$	−0.874447	+	0.421111i	−0.0436134	+	0.0210031i
$403$	−3.22968	+	6.70650i	−0.160882	+	0.334074i
$404$	24.3445	−	5.55647i	1.21118	−	0.276445i
$405$	7.48528			0.371947
$406$		0			0
$407$	−9.65685			−0.478672
$408$	3.09205	−	0.705741i	0.153080	−	0.0349394i
$409$	−6.49548	+	13.4880i	−0.321181	+	0.666939i	−0.997575	−	0.0696008i	$-0.977827\pi$
$409$	−6.49548	+	13.4880i	−0.321181	+	0.666939i	0.676394	+	0.736540i	$0.263542\pi$
$410$	−4.65943	+	2.24386i	−0.230113	+	0.110816i
$411$	−1.10605	−	4.84594i	−0.0545576	−	0.239033i
$412$	−0.337057	+	1.47674i	−0.0166056	+	0.0727538i
$413$	−19.5122	−	9.39656i	−0.960130	−	0.462374i
$414$	−7.01347	+	5.59305i	−0.344693	+	0.274884i
$415$	−2.28001	−	2.85904i	−0.111921	−	0.140345i
$416$	−3.50191	−	7.27178i	−0.171695	−	0.356528i
$417$	4.53383	+	3.61561i	0.222023	+	0.177057i
$418$			6.00000i			0.293470i
$419$	16.5133	−	20.7070i	0.806728	−	1.01160i	−0.192811	−	0.981236i	$-0.561760\pi$
$419$	16.5133	−	20.7070i	0.806728	−	1.01160i	0.999539	−	0.0303686i	$-0.00966810\pi$
$420$	−2.08843	−	0.476670i	−0.101905	−	0.0232591i
$421$	24.4831	+	5.58810i	1.19323	+	0.272347i	0.772605	−	0.634887i	$-0.218953\pi$
$421$	24.4831	+	5.58810i	1.19323	+	0.272347i	0.420626	+	0.907234i	$0.361810\pi$
$422$	4.48976	−	5.62998i	0.218558	−	0.274063i
$423$			14.8284i			0.720983i
$424$	9.28038	+	7.40086i	0.450695	+	0.359418i
$425$	8.37990	+	17.4011i	0.406485	+	0.844075i
$426$	0.339276	+	0.425438i	0.0164380	+	0.0206125i
$427$	1.83195	−	1.46093i	0.0886540	−	0.0706992i
$428$	15.1088	+	7.27604i	0.730314	+	0.351700i
$429$	0.406863	−	1.78258i	0.0196435	−	0.0860640i
$430$	0.591206	+	2.59024i	0.0285105	+	0.124913i
$431$	−7.51691	+	3.61996i	−0.362077	+	0.174367i	−0.606073	−	0.795409i	$-0.707256\pi$
$431$	−7.51691	+	3.61996i	−0.362077	+	0.174367i	0.243996	+	0.969776i	$0.421542\pi$
$432$	3.14246	−	6.52539i	0.151192	−	0.313953i
$433$	−14.2607	+	3.25491i	−0.685324	+	0.156421i	−0.550986	−	0.834515i	$-0.685748\pi$
$433$	−14.2607	+	3.25491i	−0.685324	+	0.156421i	−0.134339	+	0.990935i	$0.542891\pi$
$434$	4.76955			0.228946
$435$		0			0
$436$	−2.45584			−0.117614
$437$	44.7893	−	10.2229i	2.14256	−	0.489026i
$438$	0.297771	−	0.618327i	0.0142280	−	0.0295448i
$439$	−10.5025	+	5.05772i	−0.501255	+	0.241392i	−0.667386	−	0.744712i	$-0.732587\pi$
$439$	−10.5025	+	5.05772i	−0.501255	+	0.241392i	0.166131	+	0.986104i	$0.446873\pi$
$440$	0.851905	+	3.73244i	0.0406130	+	0.177937i
$441$	−0.629384	+	2.75751i	−0.0299707	+	0.131310i
$442$	3.29471	+	1.58665i	0.156713	+	0.0754692i
$443$	27.8777	−	22.2317i	1.32451	−	1.05626i	0.330865	−	0.943678i	$-0.392660\pi$
$443$	27.8777	−	22.2317i	1.32451	−	1.05626i	0.993643	−	0.112581i	$-0.0359118\pi$
$444$	1.88882	+	2.36851i	0.0896396	+	0.112404i
$445$	1.94609	+	4.04110i	0.0922535	+	0.191566i
$446$	2.85904	+	2.28001i	0.135380	+	0.107962i
$447$			0.899495i			0.0425447i
$448$	7.35655	−	9.22482i	0.347564	−	0.435832i
$449$	−1.00363	−	0.229071i	−0.0473641	−	0.0108105i	0.198773	−	0.980046i	$-0.436304\pi$
$449$	−1.00363	−	0.229071i	−0.0473641	−	0.0108105i	−0.246137	+	0.969235i	$0.579161\pi$
$450$	−4.56880	−	1.04280i	−0.215375	−	0.0491580i
$451$	18.7933	−	23.5661i	0.884943	−	1.10968i
$452$			17.0294i			0.800997i
$453$	−4.57986	−	3.65232i	−0.215181	−	0.171601i
$454$	3.61996	+	7.51691i	0.169893	+	0.352786i
$455$	−3.22442	−	4.04330i	−0.151163	−	0.189553i
$456$	3.08130	−	2.45725i	0.144295	−	0.115071i
$457$	31.5074	+	15.1732i	1.47385	+	0.709770i	0.986550	−	0.163462i	$-0.0522661\pi$
$457$	31.5074	+	15.1732i	1.47385	+	0.709770i	0.487304	+	0.873232i	$0.337980\pi$
$458$	1.88815	−	8.27254i	0.0882276	−	0.386550i
$459$	2.59389	+	11.3646i	0.121073	+	0.530454i
$460$	12.6136	−	6.07437i	0.588110	−	0.283219i
$461$	6.07437	−	12.6136i	0.282912	−	0.587472i	−0.710286	−	0.703913i	$-0.751434\pi$
$461$	6.07437	−	12.6136i	0.282912	−	0.587472i	0.993198	+	0.116441i	$0.0371486\pi$
$462$	−1.14220	+	0.260699i	−0.0531399	+	0.0121288i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$		0			0
$465$	−1.68629			−0.0781999
$466$	1.74200	−	0.397600i	0.0806965	−	0.0184184i
$467$	−14.0385	+	29.1512i	−0.649622	+	1.34895i	0.272537	+	0.962145i	$0.412137\pi$
$467$	−14.0385	+	29.1512i	−0.649622	+	1.34895i	−0.922160	+	0.386809i	$0.873577\pi$
$468$	8.51942	−	4.10274i	0.393810	−	0.189649i
$469$	−3.56033	−	15.5988i	−0.164401	−	0.720288i
$470$	−0.483220	+	2.11713i	−0.0222893	+	0.0976558i
$471$	−3.16665	−	1.52498i	−0.145912	−	0.0702673i
$472$	9.49310	−	7.57050i	0.436956	−	0.348460i
$473$	−9.65492	−	12.1069i	−0.443933	−	0.556675i
$474$	0.0308352	+	0.0640299i	0.00141631	+	0.00294099i
$475$	18.7640	+	14.9638i	0.860949	+	0.686584i
$476$			24.9706i			1.14452i
$477$	−13.2003	+	16.5526i	−0.604398	+	0.757892i
$478$	−3.36920	−	0.768998i	−0.154104	−	0.0351731i
$479$	12.5761	+	2.87041i	0.574616	+	0.131152i	0.499947	−	0.866056i	$-0.333353\pi$
$479$	12.5761	+	2.87041i	0.574616	+	0.131152i	0.0746688	+	0.997208i	$0.476210\pi$
$480$	1.14001	−	1.42952i	0.0520339	−	0.0652484i
$481$			7.31371i			0.333476i
$482$	1.39697	+	1.11405i	0.0636304	+	0.0507436i
$483$	3.89218	+	8.08220i	0.177100	+	0.367753i
$484$	5.89562	+	7.39288i	0.267983	+	0.336040i
$485$	9.76139	−	7.78445i	0.443242	−	0.353473i
$486$	−3.86000	−	1.85888i	−0.175093	−	0.0843203i
$487$	6.33857	−	27.7711i	0.287228	−	1.25843i	−0.601083	−	0.799187i	$-0.705264\pi$
$487$	6.33857	−	27.7711i	0.287228	−	1.25843i	0.888311	−	0.459242i	$-0.151879\pi$
$488$	0.292328	+	1.28077i	0.0132331	+	0.0579778i
$489$	6.74401	−	3.24774i	0.304974	−	0.146868i
$490$	−0.179721	+	0.373194i	−0.00811895	+	0.0168592i
$491$	−12.4375	+	2.83878i	−0.561297	+	0.128112i	−0.493750	−	0.869604i	$-0.664374\pi$
$491$	−12.4375	+	2.83878i	−0.561297	+	0.128112i	−0.0675466	+	0.997716i	$0.521517\pi$
$492$	−9.45584			−0.426302
$493$		0			0
$494$	4.54416			0.204451
$495$	−6.65722	+	1.51947i	−0.299220	+	0.0682950i
$496$	5.29911	−	11.0037i	0.237937	−	0.494081i
$497$	−8.08220	+	3.89218i	−0.362536	+	0.174588i
$498$	0.139613	+	0.611686i	0.00625623	+	0.0274103i
$499$	−3.33126	+	14.5952i	−0.149128	+	0.653372i	0.844001	+	0.536342i	$0.180194\pi$
$499$	−3.33126	+	14.5952i	−0.149128	+	0.653372i	−0.993128	+	0.117030i	$0.962663\pi$
$500$	14.8262	+	7.13992i	0.663048	+	0.319307i
$501$	−2.85904	+	2.28001i	−0.127733	+	0.101863i
$502$	−1.53119	−	1.92006i	−0.0683405	−	0.0856963i
$503$	−11.1629	−	23.1801i	−0.497730	−	1.03355i	−0.986896	−	0.161357i	$-0.948413\pi$
$503$	−11.1629	−	23.1801i	−0.497730	−	1.03355i	0.489166	−	0.872191i	$-0.337301\pi$
$504$	−9.91854	−	7.90977i	−0.441807	−	0.352329i
$505$			13.6569i			0.607722i
$506$	4.77397	−	5.98637i	0.212229	−	0.266127i
$507$	3.89971	+	0.890084i	0.173192	+	0.0395300i
$508$	−27.9097	−	6.37020i	−1.23829	−	0.282632i
$509$	−17.1368	+	21.4889i	−0.759575	+	0.952477i	−0.999834	−	0.0182320i	$-0.994196\pi$
$509$	−17.1368	+	21.4889i	−0.759575	+	0.952477i	0.240259	+	0.970709i	$0.422768\pi$
$510$			0.828427i			0.0366834i
$511$	8.84541	+	7.05398i	0.391298	+	0.312050i
$512$	9.87405	+	20.5037i	0.436375	+	0.906143i
$513$	9.03143	+	11.3250i	0.398747	+	0.500013i
$514$	−7.71672	+	6.15388i	−0.340370	+	0.271436i
$515$	−0.746387	−	0.359441i	−0.0328897	−	0.0158389i
$516$	−1.08098	+	4.73607i	−0.0475873	+	0.208494i
$517$	−2.81642	−	12.3395i	−0.123866	−	0.542691i
$518$	4.22220	−	2.03331i	0.185513	−	0.0893383i
$519$	−4.25162	+	8.82858i	−0.186626	+	0.387532i
$520$	2.82680	−	0.645198i	0.123963	−	0.0282938i
$521$	0.857864			0.0375837			0.0187919	−	0.999823i	$-0.494018\pi$
$521$	0.857864			0.0375837			0.0187919	+	0.999823i	$0.494018\pi$
$522$		0			0
$523$	27.3137			1.19435			0.597173	−	0.802113i	$-0.296291\pi$
$523$	27.3137			1.19435			0.597173	+	0.802113i	$0.296291\pi$
$524$	−2.34180	+	0.534500i	−0.102302	+	0.0233497i
$525$	−2.03331	+	4.22220i	−0.0887407	+	0.184272i
$526$	4.19568	−	2.02053i	0.182940	−	0.0880994i
$527$	4.37406	+	19.1640i	0.190537	+	0.834798i
$528$	−0.667563	+	2.92478i	−0.0290519	+	0.127285i
$529$	−32.0992	−	15.4582i	−1.39562	−	0.672094i
$530$	−2.42407	+	1.93313i	−0.105295	+	0.0839699i
$531$	13.5028	+	16.9320i	0.585973	+	0.734787i
$532$	13.4632	+	27.9566i	0.583702	+	1.21207i
$533$	−17.8480	−	14.2333i	−0.773082	−	0.616512i
$534$		−	0.769553i		−	0.0333018i
$535$	−5.71838	+	7.17062i	−0.247227	+	0.310013i
$536$	8.74565	+	1.99614i	0.377755	+	0.0862200i
$537$	4.23425	+	0.966441i	0.182722	+	0.0417050i
$538$	−5.02463	+	6.30068i	−0.216627	+	0.271642i
$539$		−	2.41421i		−	0.103988i
$540$	3.45117	+	2.75222i	0.148515	+	0.118437i
$541$	−9.39656	−	19.5122i	−0.403990	−	0.838893i	−0.999371	−	0.0354501i	$-0.988714\pi$
$541$	−9.39656	−	19.5122i	−0.403990	−	0.838893i	0.595382	−	0.803443i	$-0.297001\pi$
$542$	−3.75929	−	4.71400i	−0.161475	−	0.202484i
$543$	4.63543	−	3.69663i	0.198925	−	0.158638i
$544$	−19.2030	−	9.24767i	−0.823321	−	0.396491i
$545$	0.298878	−	1.30947i	0.0128025	−	0.0560915i
$546$	0.197443	+	0.865055i	0.00844979	+	0.0370209i
$547$	3.42277	−	1.64832i	0.146347	−	0.0704771i	−0.359277	−	0.933231i	$-0.616977\pi$
$547$	3.42277	−	1.64832i	0.146347	−	0.0704771i	0.505624	+	0.862754i	$0.331262\pi$
$548$	−9.51990	+	19.7683i	−0.406670	+	0.844459i
$549$	−2.28440	+	0.521399i	−0.0974957	+	0.0222528i
$550$	4.00000			0.170561
$551$		0			0
$552$	−5.02944			−0.214067
$553$	−1.14220	+	0.260699i	−0.0485712	+	0.0110861i
$554$	−0.954983	+	1.98304i	−0.0405733	+	0.0842514i
$555$	−1.49277	+	0.718882i	−0.0633647	+	0.0305148i
$556$	−5.69609	−	24.9562i	−0.241568	−	1.05838i
$557$	1.18241	−	5.18048i	0.0501004	−	0.219504i	−0.943680	−	0.330858i	$-0.892662\pi$
$557$	1.18241	−	5.18048i	0.0501004	−	0.219504i	0.993781	+	0.111354i	$0.0355189\pi$
$558$	−4.29722	−	2.06943i	−0.181916	−	0.0876060i
$559$	−9.16926	+	7.31224i	−0.387818	+	0.309275i
$560$	5.29049	+	6.63406i	0.223564	+	0.280340i
$561$	−2.09498	−	4.35026i	−0.0884500	−	0.183668i
$562$	0.638157	+	0.508913i	0.0269190	+	0.0214672i
$563$		−	9.24264i		−	0.389531i	−0.980850	−	0.194765i	$-0.937605\pi$
$563$		−	9.24264i		−	0.389531i	0.980850	−	0.194765i	$-0.0623946\pi$
$564$	−2.47561	+	3.10431i	−0.104242	+	0.130715i
$565$	−9.08019	−	2.07250i	−0.382007	−	0.0871905i
$566$	−0.138572	−	0.0316282i	−0.00582462	−	0.00132943i
$567$	13.2003	−	16.5526i	0.554359	−	0.695144i
$568$		−	5.02944i		−	0.211030i
$569$	−22.1596	−	17.6717i	−0.928977	−	0.740835i	0.0370396	−	0.999314i	$-0.488207\pi$
$569$	−22.1596	−	17.6717i	−0.928977	−	0.740835i	−0.966017	+	0.258479i	$0.916779\pi$
$570$	0.446656	+	0.927491i	0.0187084	+	0.0388483i
$571$	−19.0959	−	23.9455i	−0.799138	−	1.00209i	−0.999749	−	0.0224161i	$-0.992864\pi$
$571$	−19.0959	−	23.9455i	−0.799138	−	1.00209i	0.200611	−	0.979671i	$-0.435707\pi$
$572$	−6.31021	+	5.03223i	−0.263843	+	0.210408i
$573$	−1.00251	−	0.482782i	−0.0418803	−	0.0201685i
$574$	−3.25491	+	14.2607i	−0.135857	+	0.595229i
$575$	−6.81524	−	29.8595i	−0.284215	−	1.24523i
$576$	−10.6305	+	5.11939i	−0.442938	+	0.213308i
$577$	4.25162	−	8.82858i	0.176997	−	0.367539i	−0.793530	−	0.608532i	$-0.791759\pi$
$577$	4.25162	−	8.82858i	0.176997	−	0.367539i	0.970527	+	0.240993i	$0.0774731\pi$
$578$	2.54965	−	0.581942i	0.106052	−	0.0242056i
$579$	−4.48528			−0.186402
$580$		0			0
$581$	−10.3431			−0.429106
$582$	−2.08843	+	0.476670i	−0.0865681	+	0.0197586i
$583$	7.84074	−	16.2815i	0.324730	−	0.674310i
$584$	−5.71498	+	2.75219i	−0.236487	+	0.113886i
$585$	1.15078	+	5.04191i	0.0475790	+	0.208457i
$586$	−0.337057	+	1.47674i	−0.0139237	+	0.0610036i
$587$	3.29471	+	1.58665i	0.135987	+	0.0654880i	0.500640	−	0.865656i	$-0.333098\pi$
$587$	3.29471	+	1.58665i	0.135987	+	0.0654880i	−0.364653	+	0.931144i	$0.618812\pi$
$588$	−0.592127	+	0.472206i	−0.0244189	+	0.0194734i
$589$	15.2296	+	19.0973i	0.627525	+	0.786892i
$590$	1.37609	+	2.85749i	0.0566529	+	0.117641i
$591$	0.647690	+	0.516516i	0.0266424	+	0.0212466i
$592$		−	12.0000i		−	0.493197i
$593$	1.56790	−	1.96609i	0.0643860	−	0.0807375i	−0.748596	−	0.663027i	$-0.769272\pi$
$593$	1.56790	−	1.96609i	0.0643860	−	0.0807375i	0.812982	+	0.582289i	$0.197843\pi$
$594$	2.35368	+	0.537213i	0.0965728	+	0.0220421i
$595$	−13.3144	−	3.03894i	−0.545839	−	0.124584i
$596$	2.47561	−	3.10431i	0.101405	−	0.127158i
$597$			6.82843i			0.279469i
$598$	−4.53383	−	3.61561i	−0.185402	−	0.147853i
$599$	−19.0345	−	39.5256i	−0.777729	−	1.61497i	−0.788505	−	0.615029i	$-0.789144\pi$
$599$	−19.0345	−	39.5256i	−0.777729	−	1.61497i	0.0107761	−	0.999942i	$-0.496570\pi$
$600$	−1.63817	−	2.05420i	−0.0668779	−	0.0838623i
$601$	−17.8480	+	14.2333i	−0.728034	+	0.580588i	−0.915804	−	0.401625i	$-0.868446\pi$
$601$	−17.8480	+	14.2333i	−0.728034	+	0.580588i	0.187770	+	0.982213i	$0.439874\pi$
$602$	6.77053	+	3.26051i	0.275946	+	0.132889i
$603$	−3.56033	+	15.5988i	−0.144988	+	0.635234i
$604$	5.75392	+	25.2096i	0.234124	+	1.02576i
$605$	−4.65943	+	2.24386i	−0.189433	+	0.0912259i
$606$	1.01665	−	2.11110i	0.0412987	−	0.0857576i
$607$	17.2834	−	3.94483i	0.701513	−	0.160116i	0.143136	−	0.989703i	$-0.454281\pi$
$607$	17.2834	−	3.94483i	0.701513	−	0.160116i	0.558377	+	0.829587i	$0.311424\pi$
$608$	−26.4853			−1.07412
$609$		0			0
$610$	−0.343146			−0.0138936
$611$	−9.34545	+	2.13304i	−0.378076	+	0.0862935i
$612$	10.8343	−	22.4977i	0.437951	−	0.909416i
$613$	−8.10872	+	3.90495i	−0.327508	+	0.157720i	−0.590411	−	0.807103i	$-0.701034\pi$
$613$	−8.10872	+	3.90495i	−0.327508	+	0.157720i	0.262903	+	0.964822i	$0.415320\pi$
$614$	−1.55765	−	6.82450i	−0.0628615	−	0.275414i
$615$	1.15078	−	5.04191i	0.0464041	−	0.203309i
$616$	9.75608	+	4.69828i	0.393083	+	0.189299i
$617$	−18.2274	+	14.5359i	−0.733807	+	0.585192i	−0.917473	−	0.397797i	$-0.869775\pi$
$617$	−18.2274	+	14.5359i	−0.733807	+	0.585192i	0.183666	+	0.982989i	$0.441203\pi$
$618$	0.0886201	+	0.111126i	0.00356482	+	0.00447015i
$619$	−15.7995	−	32.8081i	−0.635037	−	1.31867i	−0.931541	−	0.363636i	$-0.881535\pi$
$619$	−15.7995	−	32.8081i	−0.635037	−	1.31867i	0.296504	−	0.955032i	$-0.404179\pi$
$620$	5.81968	+	4.64104i	0.233724	+	0.186389i
$621$		−	18.4853i		−	0.741789i
$622$	−6.53747	+	8.19772i	−0.262129	+	0.328699i
$623$	12.3682	+	2.82297i	0.495522	+	0.113100i
$624$	2.21511	+	0.505585i	0.0886755	+	0.0202396i
$625$	6.85839	−	8.60015i	0.274336	−	0.344006i
$626$		−	1.72792i		−	0.0690617i
$627$	−4.69099	−	3.74094i	−0.187340	−	0.149399i
$628$	6.73158	+	13.9783i	0.268619	+	0.557794i
$629$	12.0419	+	15.1001i	0.480142	+	0.602079i
$630$	2.59076	−	2.06606i	0.103218	−	0.0823139i
$631$	−28.0846	−	13.5248i	−1.11803	−	0.538415i	−0.218747	−	0.975782i	$-0.570197\pi$
$631$	−28.0846	−	13.5248i	−1.11803	−	0.538415i	−0.899284	+	0.437366i	$0.855911\pi$
$632$	0.146164	−	0.640386i	0.00581408	−	0.0254732i
$633$	1.60238	+	7.02047i	0.0636887	+	0.279038i
$634$	−7.26080	+	3.49661i	−0.288363	+	0.138868i
$635$	6.79325	−	14.1063i	0.269582	−	0.559793i
$636$	−5.52691	+	1.26148i	−0.219156	+	0.0500210i
$637$	−1.82843			−0.0724449
$638$		0			0
$639$	8.97056			0.354870
$640$	−10.2917	+	2.34901i	−0.406814	+	0.0928527i
$641$	9.45823	−	19.6402i	0.373578	−	0.775742i	−0.626415	−	0.779489i	$-0.715479\pi$
$641$	9.45823	−	19.6402i	0.373578	−	0.775742i	0.999993	+	0.00374766i	$0.00119292\pi$
$642$	1.41776	−	0.682756i	0.0559545	−	0.0269462i
$643$	3.45235	+	15.1257i	0.136147	+	0.596501i	0.996261	+	0.0863977i	$0.0275356\pi$
$643$	3.45235	+	15.1257i	0.136147	+	0.596501i	−0.860113	+	0.510103i	$0.829607\pi$
$644$	8.81138	−	38.6052i	0.347217	−	1.52126i
$645$	−2.39374	−	1.15277i	−0.0942535	−	0.0453901i
$646$	9.38198	−	7.48188i	0.369129	−	0.294371i
$647$	−17.6717	−	22.1596i	−0.694745	−	0.871182i	0.301874	−	0.953348i	$-0.402388\pi$
$647$	−17.6717	−	22.1596i	−0.694745	−	0.871182i	−0.996619	+	0.0821655i	$0.973816\pi$
$648$	5.15023	+	10.6946i	0.202320	+	0.420122i
$649$	−14.4524	−	11.5254i	−0.567305	−	0.452411i
$650$		−	3.02944i		−	0.118824i
$651$	−2.97377	+	3.72899i	−0.116551	+	0.146150i
$652$	−32.2132	−	7.35245i	−1.26157	−	0.287944i
$653$	1.81128	+	0.413414i	0.0708810	+	0.0161781i	0.257814	−	0.966194i	$-0.416998\pi$
$653$	1.81128	+	0.413414i	0.0708810	+	0.0161781i	−0.186933	+	0.982373i	$0.559855\pi$
$654$	−0.143682	+	0.180171i	−0.00561839	+	0.00704524i
$655$		−	1.31371i		−	0.0513308i
$656$	29.2842	+	23.3533i	1.14335	+	0.911795i
$657$	−4.90883	−	10.1933i	−0.191512	−	0.397678i
$658$	3.82956	+	4.80212i	0.149292	+	0.187206i
$659$	9.05813	−	7.22362i	0.352855	−	0.281392i	−0.430980	−	0.902361i	$-0.641832\pi$
$659$	9.05813	−	7.22362i	0.352855	−	0.281392i	0.783835	+	0.620969i	$0.213261\pi$
$660$	−1.64736	−	0.793325i	−0.0641232	−	0.0308801i
$661$	−2.37792	+	10.4184i	−0.0924905	+	0.405227i	−0.999887	−	0.0150488i	$-0.995210\pi$
$661$	−2.37792	+	10.4184i	−0.0924905	+	0.405227i	0.907396	+	0.420276i	$0.138067\pi$
$662$	−0.0381786	−	0.167271i	−0.00148385	−	0.00650118i
$663$	−3.29471	+	1.58665i	−0.127956	+	0.0616204i
$664$	2.51609	−	5.22471i	0.0976431	−	0.202758i
$665$	−16.5451	+	3.77631i	−0.641591	+	0.146439i
$666$	−4.68629			−0.181590
$667$		0			0
$668$	16.1421			0.624558
$669$	−3.56517	+	0.813727i	−0.137837	+	0.0314605i
$670$	−1.01665	+	2.11110i	−0.0392767	+	0.0815590i
$671$	1.80194	−	0.867767i	0.0695630	−	0.0334998i
$672$	−1.15078	−	5.04191i	−0.0443924	−	0.194496i
$673$	5.25759	−	23.0350i	0.202665	−	0.887935i	−0.766640	−	0.642077i	$-0.778073\pi$
$673$	5.25759	−	23.0350i	0.202665	−	0.887935i	0.969306	−	0.245858i	$-0.0790698\pi$
$674$	6.64247	+	3.19884i	0.255858	+	0.123215i
$675$	7.55003	−	6.02095i	0.290601	−	0.231746i
$676$	−11.0089	−	13.8047i	−0.423418	−	0.530949i
$677$	9.54544	+	19.8213i	0.366861	+	0.761795i	0.999924	−	0.0123051i	$-0.00391695\pi$
$677$	9.54544	+	19.8213i	0.366861	+	0.761795i	−0.633063	+	0.774100i	$0.718203\pi$
$678$	1.24935	+	0.996324i	0.0479810	+	0.0382636i
$679$		−	35.3137i		−	1.35522i
$680$	4.77397	−	5.98637i	0.183073	−	0.229567i
$681$	−8.13397	−	1.85652i	−0.311694	−	0.0711422i
$682$	3.96900	+	0.905898i	0.151981	+	0.0346886i
$683$	−8.08701	+	10.1408i	−0.309441	+	0.388027i	−0.912097	−	0.409974i	$-0.865538\pi$
$683$	−8.08701	+	10.1408i	−0.309441	+	0.388027i	0.602656	+	0.798001i	$0.294109\pi$
$684$		−	31.0294i		−	1.18644i
$685$	−9.38198	−	7.48188i	−0.358467	−	0.285868i
$686$	−3.04996	−	6.33330i	−0.116448	−	0.241807i
$687$	5.29049	+	6.63406i	0.201845	+	0.253105i
$688$	15.0445	−	11.9976i	0.573566	−	0.457404i
$689$	−12.3309	−	5.93826i	−0.469771	−	0.226230i
$690$	0.292328	−	1.28077i	0.0111287	−	0.0487581i
$691$	−10.6810	−	46.7965i	−0.406325	−	1.78022i	−0.600887	−	0.799334i	$-0.705186\pi$
$691$	−10.6810	−	46.7965i	−0.406325	−	1.78022i	0.194562	−	0.980890i	$-0.437671\pi$
$692$	38.9713	−	18.7676i	1.48146	−	0.713436i
$693$	−8.37990	+	17.4011i	−0.318326	+	0.661011i
$694$	−5.84957	+	1.33513i	−0.222047	+	0.0506807i
$695$	14.0000			0.531050
$696$		0			0
$697$	−60.2843			−2.28343
$698$	−9.34545	+	2.13304i	−0.353731	+	0.0807367i
$699$	−0.775262	+	1.60985i	−0.0293231	+	0.0608900i
$700$	18.6377	−	8.97545i	0.704439	−	0.339240i
$701$	4.92054	+	21.5583i	0.185846	+	0.814245i	0.978776	+	0.204932i	$0.0656975\pi$
$701$	4.92054	+	21.5583i	0.185846	+	0.814245i	−0.792930	+	0.609313i	$0.791445\pi$
$702$	0.406863	−	1.78258i	0.0153561	−	0.0672793i
$703$	21.6233	+	10.4132i	0.815536	+	0.392742i
$704$	7.87388	−	6.27921i	0.296758	−	0.236657i
$705$	−1.35395	−	1.69780i	−0.0509928	−	0.0639430i
$706$	1.25275	+	2.60137i	0.0471480	+	0.0979038i
$707$	30.2001	+	24.0838i	1.13579	+	0.905765i
$708$			5.79899i			0.217939i
$709$	−0.534870	+	0.670705i	−0.0200875	+	0.0251889i	−0.791774	−	0.610814i	$-0.790842\pi$
$709$	−0.534870	+	0.670705i	−0.0200875	+	0.0251889i	0.771686	+	0.636003i	$0.219414\pi$
$710$	1.28077	+	0.292328i	0.0480665	+	0.0109709i
$711$	1.14220	+	0.260699i	0.0428358	+	0.00977699i
$712$	−4.43469	+	5.56093i	−0.166197	+	0.208405i
$713$		−	31.1716i		−	1.16738i
$714$	1.83195	+	1.46093i	0.0685588	+	0.0546738i
$715$	−1.91526	−	3.97707i	−0.0716265	−	0.148734i
$716$	−11.9533	−	14.9889i	−0.446715	−	0.560163i
$717$	2.70189	−	2.15468i	0.100904	−	0.0804681i
$718$	6.74401	+	3.24774i	0.251684	+	0.121205i
$719$	−1.81180	+	7.93800i	−0.0675686	+	0.296037i	−0.997410	−	0.0719227i	$-0.977087\pi$
$719$	−1.81180	+	7.93800i	−0.0675686	+	0.296037i	0.929842	+	0.367960i	$0.119944\pi$
$720$	−1.88815	−	8.27254i	−0.0703673	−	0.308299i
$721$	−2.11110	+	1.01665i	−0.0786215	+	0.0378621i
$722$	3.05525	−	6.34429i	0.113705	−	0.236110i
$723$	−1.74200	+	0.397600i	−0.0647856	+	0.0147869i
$724$	−26.1716			−0.972659
$725$		0			0
$726$	0.887302			0.0329309
$727$	20.7793	−	4.74275i	0.770663	−	0.175899i	0.180929	−	0.983496i	$-0.442090\pi$
$727$	20.7793	−	4.74275i	0.770663	−	0.175899i	0.589734	+	0.807598i	$0.299233\pi$
$728$	3.55828	−	7.38885i	0.131879	−	0.273849i
$729$	−16.3720	+	7.88435i	−0.606371	+	0.292013i
$730$	−0.368685	−	1.61531i	−0.0136456	−	0.0597854i
$731$	−6.89160	+	30.1941i	−0.254895	+	1.11677i
$732$	−0.565283	−	0.272226i	−0.0208935	−	0.0100618i
$733$	−38.5090	+	30.7099i	−1.42236	+	1.13430i	−0.452177	+	0.891928i	$0.649352\pi$
$733$	−38.5090	+	30.7099i	−1.42236	+	1.13430i	−0.970185	+	0.242367i	$0.922076\pi$
$734$	−4.64864	−	5.82921i	−0.171585	−	0.215160i
$735$	−0.179721	−	0.373194i	−0.00662909	−	0.0137655i
$736$	26.4251	+	21.0733i	0.974043	+	0.776773i
$737$		−	13.6569i		−	0.503057i
$738$	9.12005	−	11.4362i	0.335714	−	0.420971i
$739$	−9.81857	−	2.24102i	−0.361182	−	0.0824374i	0.0380792	−	0.999275i	$-0.487876\pi$
$739$	−9.81857	−	2.24102i	−0.361182	−	0.0824374i	−0.399261	+	0.916837i	$0.630733\pi$
$740$	7.13034	+	1.62745i	0.262116	+	0.0598264i
$741$	−2.83323	+	3.55276i	−0.104081	+	0.130514i
$742$			8.76955i			0.321940i
$743$	9.65026	+	7.69583i	0.354034	+	0.282332i	0.784315	−	0.620362i	$-0.213014\pi$
$743$	9.65026	+	7.69583i	0.354034	+	0.282332i	−0.430282	+	0.902695i	$0.641586\pi$
$744$	−1.16025	−	2.40928i	−0.0425367	−	0.0883285i
$745$	1.35395	+	1.69780i	0.0496050	+	0.0622027i
$746$	−1.19379	+	0.952014i	−0.0437077	+	0.0348557i
$747$	9.31885	+	4.48772i	0.340959	+	0.164197i
$748$	−4.74275	+	20.7793i	−0.173412	+	0.759768i
$749$	5.77244	+	25.2907i	0.210920	+	0.924103i
$750$	1.39124	−	0.669984i	0.0508008	−	0.0244644i
$751$	1.16554	−	2.42027i	0.0425311	−	0.0883167i	−0.878621	−	0.477521i	$-0.841536\pi$
$751$	1.16554	−	2.42027i	0.0425311	−	0.0883167i	0.921152	+	0.389204i	$0.127250\pi$
$752$	15.3336	−	3.49979i	0.559159	−	0.127624i
$753$	2.45584			0.0894959
$754$		0			0
$755$	−14.1421			−0.514685
$756$	12.1722	−	2.77824i	0.442700	−	0.101043i
$757$	−18.4337	+	38.2779i	−0.669983	+	1.39123i	0.237600	+	0.971363i	$0.423639\pi$
$757$	−18.4337	+	38.2779i	−0.669983	+	1.39123i	−0.907584	+	0.419872i	$0.862075\pi$
$758$	10.0652	−	4.84716i	0.365586	−	0.176057i
$759$	1.70381	+	7.46488i	0.0618444	+	0.270958i
$760$	2.11722	−	9.27616i	0.0767998	−	0.336482i
$761$	30.2707	+	14.5776i	1.09731	+	0.528438i	0.892813	−	0.450428i	$-0.148729\pi$
$761$	30.2707	+	14.5776i	1.09731	+	0.528438i	0.204501	+	0.978866i	$0.434443\pi$
$762$	−2.10023	+	1.67488i	−0.0760832	+	0.0606743i
$763$	−2.36863	−	2.97017i	−0.0857502	−	0.107527i
$764$	2.13110	+	4.42528i	0.0771006	+	0.160101i
$765$	10.6774	+	8.51491i	0.386041	+	0.307857i
$766$		−	8.48528i		−	0.306586i
$767$	−8.72886	+	10.9456i	−0.315181	+	0.395224i
$768$	−1.60343	−	0.365971i	−0.0578586	−	0.0132059i
$769$	−12.7839	−	2.91785i	−0.461001	−	0.105220i	−0.0142880	−	0.999898i	$-0.504548\pi$
$769$	−12.7839	−	2.91785i	−0.461001	−	0.105220i	−0.446713	+	0.894678i	$0.647405\pi$
$770$	−1.76350	+	2.21135i	−0.0635520	+	0.0796916i
$771$		−	9.87006i		−	0.355461i
$772$	15.4795	+	12.3445i	0.557118	+	0.444287i
$773$	−15.8304	−	32.8721i	−0.569379	−	1.18233i	−0.964594	−	0.263739i	$-0.915044\pi$
$773$	−15.8304	−	32.8721i	−0.569379	−	1.18233i	0.395215	−	0.918589i	$-0.370670\pi$
$774$	−4.68535	−	5.87524i	−0.168411	−	0.211181i
$775$	12.7316	−	10.1531i	0.457331	−	0.364709i
$776$	17.8383	+	8.59046i	0.640357	+	0.308380i
$777$	−1.04280	+	4.56880i	−0.0374102	+	0.163905i
$778$	−3.40762	−	14.9298i	−0.122169	−	0.535258i
$779$	−67.4931	+	32.5030i	−2.41819	+	1.16454i
$780$	−0.600832	+	1.24764i	−0.0215132	+	0.0446727i
$781$	−7.46488	+	1.70381i	−0.267114	+	0.0609671i
$782$	−15.3137			−0.547617
$783$		0			0
$784$	3.00000			0.107143
$785$	−8.27254	+	1.88815i	−0.295260	+	0.0673911i
$786$	−0.0977960	+	0.203075i	−0.00348827	+	0.00724346i
$787$	37.9157	−	18.2592i	1.35155	−	0.650872i	0.388814	−	0.921316i	$-0.372885\pi$
$787$	37.9157	−	18.2592i	1.35155	−	0.650872i	0.962735	+	0.270445i	$0.0871707\pi$
$788$	−0.813727	−	3.56517i	−0.0289878	−	0.127004i
$789$	−1.03625	+	4.54010i	−0.0368914	+	0.161632i
$790$	0.154582	+	0.0744427i	0.00549977	+	0.00264855i
$791$	−20.5959	+	16.4247i	−0.732306	+	0.583994i
$792$	−6.75141	−	8.46601i	−0.239901	−	0.300826i
$793$	−0.657212	−	1.36471i	−0.0233383	−	0.0484624i
$794$	−9.92808	−	7.91738i	−0.352334	−	0.280977i
$795$		−	3.10051i		−	0.109964i
$796$	18.7933	−	23.5661i	0.666111	−	0.835277i
$797$	−54.3426	−	12.4033i	−1.92491	−	0.439349i	−0.997935	−	0.0642348i	$-0.979539\pi$
$797$	−54.3426	−	12.4033i	−1.92491	−	0.439349i	−0.926979	−	0.375114i	$-0.877604\pi$
$798$	2.83869	+	0.647912i	0.100488	+	0.0229358i
$799$	−15.7828	+	19.7911i	−0.558357	+	0.700157i
$800$			17.6569i			0.624264i
$801$	−9.91854	−	7.90977i	−0.350454	−	0.279478i
$802$	−1.31971	−	2.74041i	−0.0466007	−	0.0967674i
$803$	6.02095	+	7.55003i	0.212475	+	0.266435i
$804$	−3.34958	+	2.67120i	−0.118131	+	0.0942059i
$805$	19.5122	+	9.39656i	0.687713	+	0.331185i
$806$	0.686090	−	3.00596i	0.0241665	−	0.105880i
$807$	−1.79327	−	7.85682i	−0.0631260	−	0.276573i
$808$	−19.5122	+	9.39656i	−0.686435	+	0.330570i
$809$	−8.80102	+	18.2755i	−0.309427	+	0.642532i	−0.996458	−	0.0840964i	$-0.973200\pi$
$809$	−8.80102	+	18.2755i	−0.309427	+	0.642532i	0.687030	+	0.726629i	$0.258914\pi$
$810$	−3.02277	+	0.689927i	−0.106209	+	0.0242416i
$811$	−5.17157			−0.181598			−0.0907992	−	0.995869i	$-0.528942\pi$
$811$	−5.17157			−0.181598			−0.0907992	+	0.995869i	$0.528942\pi$
$812$		0			0
$813$	6.02944			0.211462
$814$	3.89971	−	0.890084i	0.136685	−	0.0311974i
$815$	7.84074	−	16.2815i	0.274649	−	0.570315i
$816$	5.40581	−	2.60330i	0.189241	−	0.0911338i
$817$	8.56378	+	37.5204i	0.299609	+	1.31267i
$818$	1.37985	−	6.04554i	0.0482455	−	0.211377i
$819$	13.1788	+	6.34660i	0.460506	+	0.221768i
$820$	−17.8480	+	14.2333i	−0.623279	+	0.497048i
$821$	−9.65492	−	12.1069i	−0.336959	−	0.422533i	0.584267	−	0.811562i	$-0.301382\pi$
$821$	−9.65492	−	12.1069i	−0.336959	−	0.422533i	−0.921226	+	0.389029i	$0.872811\pi$
$822$	0.893312	+	1.85498i	0.0311578	+	0.0646999i
$823$	−1.78592	−	1.42422i	−0.0622531	−	0.0496452i	0.591869	−	0.806034i	$-0.298390\pi$
$823$	−1.78592	−	1.42422i	−0.0622531	−	0.0496452i	−0.654122	+	0.756389i	$0.726962\pi$
$824$		−	1.31371i		−	0.0457652i
$825$	−2.49396	+	3.12733i	−0.0868285	+	0.108880i
$826$	8.74565	+	1.99614i	0.304300	+	0.0694545i
$827$	−12.7720	−	2.91514i	−0.444128	−	0.101369i	−0.00539209	−	0.999985i	$-0.501716\pi$
$827$	−12.7720	−	2.91514i	−0.444128	−	0.101369i	−0.438736	+	0.898616i	$0.644574\pi$
$828$	−24.6889	+	30.9589i	−0.858000	+	1.07590i
$829$		−	9.79899i		−	0.340333i	−0.985415	−	0.170166i	$-0.945569\pi$
$829$		−	9.79899i		−	0.340333i	0.985415	−	0.170166i	$-0.0544306\pi$
$830$	1.18425	+	0.944412i	0.0411061	+	0.0327810i
$831$	−0.954983	−	1.98304i	−0.0331280	−	0.0687910i
$832$	−4.75562	−	5.96335i	−0.164871	−	0.206742i
$833$	−3.77502	+	3.01048i	−0.130797	+	0.104307i
$834$	−2.16415	−	1.04220i	−0.0749382	−	0.0360883i
$835$	−1.96451	+	8.60708i	−0.0679847	+	0.297860i
$836$	5.89353	+	25.8212i	0.203832	+	0.893046i
$837$	8.85511	−	4.26439i	0.306077	−	0.147399i
$838$	−4.75995	+	9.88414i	−0.164430	+	0.341442i
$839$	−21.5177	+	4.91127i	−0.742874	+	0.169556i	−0.577175	−	0.816620i	$-0.695845\pi$
$839$	−21.5177	+	4.91127i	−0.742874	+	0.169556i	−0.165698	+	0.986176i	$0.552988\pi$
$840$	1.85786			0.0641024
$841$		0			0
$842$	−10.4020			−0.358477
$843$	−0.795769	+	0.181629i	−0.0274077	+	0.00625564i
$844$	13.7918	−	28.6389i	0.474732	−	0.985792i
$845$	8.70053	−	4.18995i	0.299307	−	0.144139i
$846$	−1.36675	−	5.98814i	−0.0469900	−	0.205876i
$847$	−3.25491	+	14.2607i	−0.111840	+	0.490003i
$848$	20.2320	+	9.74323i	0.694770	+	0.334584i
$849$	0.111126	−	0.0886201i	0.00381384	−	0.00304143i
$850$	−4.98792	−	6.25465i	−0.171084	−	0.214533i
$851$	−13.2887	−	27.5943i	−0.455532	−	0.945922i
$852$	1.87798	+	1.49764i	0.0643384	+	0.0513081i
$853$			10.9706i			0.375625i	0.982205	+	0.187812i	$0.0601397\pi$
$853$			10.9706i			0.375625i	−0.982205	+	0.187812i	$0.939860\pi$
$854$	−0.605136	+	0.758817i	−0.0207073	+	0.0259662i
$855$	16.5451	+	3.77631i	0.565830	+	0.129147i
$856$	−14.1795	−	3.23638i	−0.484645	−	0.110617i
$857$	−7.37490	+	9.24784i	−0.251922	+	0.315900i	−0.891671	−	0.452684i	$-0.850467\pi$
$857$	−7.37490	+	9.24784i	−0.251922	+	0.315900i	0.639749	+	0.768584i	$0.279038\pi$
$858$			0.757359i			0.0258558i
$859$	−4.47827	−	3.57130i	−0.152797	−	0.121851i	0.544108	−	0.839015i	$-0.316868\pi$
$859$	−4.47827	−	3.57130i	−0.152797	−	0.121851i	−0.696904	+	0.717164i	$0.745440\pi$
$860$	5.08855	+	10.5665i	0.173518	+	0.360314i
$861$	−9.12005	−	11.4362i	−0.310810	−	0.389744i
$862$	2.70189	−	2.15468i	0.0920267	−	0.0733888i
$863$	−40.6451	−	19.5737i	−1.38358	−	0.666295i	−0.413818	−	0.910360i	$-0.635805\pi$
$863$	−40.6451	−	19.5737i	−1.38358	−	0.666295i	−0.969759	+	0.244064i	$0.921519\pi$
$864$	−2.37137	+	10.3897i	−0.0806758	+	0.353464i
$865$	5.26415	+	23.0637i	0.178986	+	0.784190i
$866$	5.45886	−	2.62885i	0.185500	−	0.0893319i
$867$	−1.13470	+	2.35624i	−0.0385365	+	0.0800219i
$868$	20.5260	−	4.68492i	0.696696	−	0.159016i
$869$	−1.00000			−0.0339227
$870$		0			0
$871$	−10.3431			−0.350464
$872$	2.07654	−	0.473957i	0.0703205	−	0.0160502i
$873$	−15.3220	+	31.8166i	−0.518573	+	1.07683i
$874$	−17.1449	+	8.25656i	−0.579936	+	0.279282i
$875$	5.66446	+	24.8176i	0.191494	+	0.838988i
$876$	0.674113	−	2.95348i	0.0227762	−	0.0997889i
$877$	7.98066	+	3.84328i	0.269488	+	0.129778i	0.563748	−	0.825947i	$-0.309359\pi$
$877$	7.98066	+	3.84328i	0.269488	+	0.129778i	−0.294260	+	0.955725i	$0.595073\pi$
$878$	3.77502	−	3.01048i	0.127401	−	0.101599i
$879$	−0.944412	−	1.18425i	−0.0318542	−	0.0399439i
$880$	3.14246	+	6.52539i	0.105932	+	0.219971i
$881$	−10.9456	−	8.72886i	−0.368768	−	0.294083i	0.421519	−	0.906820i	$-0.361497\pi$
$881$	−10.9456	−	8.72886i	−0.368768	−	0.294083i	−0.790287	+	0.612737i	$0.790069\pi$
$882$		−	1.17157i		−	0.0394489i
$883$	28.9464	−	36.2976i	0.974124	−	1.22151i	−0.00103381	−	0.999999i	$-0.500329\pi$
$883$	28.9464	−	36.2976i	0.974124	−	1.22151i	0.975157	−	0.221513i	$-0.0710995\pi$
$884$	15.7374	+	3.59196i	0.529307	+	0.120811i
$885$	−3.09205	−	0.705741i	−0.103938	−	0.0237232i
$886$	−9.20867	+	11.5473i	−0.309371	+	0.387939i
$887$		−	36.8995i		−	1.23896i	−0.785011	−	0.619482i	$-0.787343\pi$
$887$		−	36.8995i		−	1.23896i	0.785011	−	0.619482i	$-0.212657\pi$
$888$	−2.05420	−	1.63817i	−0.0689343	−	0.0549733i
$889$	−19.2142	−	39.8987i	−0.644424	−	1.33816i
$890$	−1.15836	−	1.45254i	−0.0388283	−	0.0486891i
$891$	14.1285	−	11.2671i	0.473324	−	0.377463i
$892$	14.5436	+	7.00381i	0.486954	+	0.234505i
$893$	−6.99958	+	30.6672i	−0.234232	+	1.02624i
$894$	−0.0829075	−	0.363242i	−0.00277284	−	0.0121486i
$895$	9.44691	−	4.54939i	0.315775	−	0.152069i
$896$	−12.9548	+	26.9010i	−0.432791	+	0.898700i
$897$	5.65360	−	1.29040i	0.188768	−	0.0430851i
$898$	0.426407			0.0142294
$899$		0			0
$900$	−20.6863			−0.689543
$901$	−35.2360	+	8.04238i	−1.17388	+	0.267931i
$902$	−5.41716	+	11.2488i	−0.180372	+	0.374546i
$903$	−6.77053	+	3.26051i	−0.225309	+	0.108503i
$904$	−3.28653	−	14.3992i	−0.109309	−	0.478912i
$905$	3.18510	−	13.9548i	0.105876	−	0.463874i
$906$	2.18612	+	1.05278i	0.0726289	+	0.0349762i
$907$	26.8045	−	21.3759i	0.890030	−	0.709775i	−0.0676200	−	0.997711i	$-0.521541\pi$
$907$	26.8045	−	21.3759i	0.890030	−	0.709775i	0.957650	+	0.287936i	$0.0929691\pi$
$908$	22.9621	+	28.7936i	0.762026	+	0.955550i
$909$	−16.7598	−	34.8021i	−0.555888	−	1.15431i
$910$	1.67479	+	1.33560i	0.0555187	+	0.0442747i
$911$		−	46.5563i		−	1.54248i	−0.636544	−	0.771240i	$-0.719637\pi$
$911$		−	46.5563i		−	1.54248i	0.636544	−	0.771240i	$-0.280363\pi$
$912$	4.64864	−	5.82921i	0.153932	−	0.193025i
$913$	−8.60708	−	1.96451i	−0.284853	−	0.0650158i
$914$	−14.1221	−	3.22328i	−0.467118	−	0.106617i
$915$	0.213948	−	0.268282i	0.00707290	−	0.00886913i
$916$		−	37.4558i		−	1.23758i
$917$	−2.90507	−	2.31672i	−0.0959340	−	0.0765048i
$918$	−2.09498	−	4.35026i	−0.0691445	−	0.143580i
$919$	−12.5584	−	15.7478i	−0.414264	−	0.519471i	0.530295	−	0.847813i	$-0.322081\pi$
$919$	−12.5584	−	15.7478i	−0.414264	−	0.519471i	−0.944559	+	0.328343i	$0.893510\pi$
$920$	−9.49310	+	7.57050i	−0.312978	+	0.249592i
$921$	6.30678	+	3.03719i	0.207816	+	0.100079i
$922$	−1.29040	+	5.65360i	−0.0424970	+	0.186191i
$923$	1.29040	+	5.65360i	0.0424739	+	0.186090i
$924$	−4.65943	+	2.24386i	−0.153284	+	0.0738176i
$925$	6.94214	−	14.4155i	0.228256	−	0.473979i
$926$	−10.4995	+	2.39645i	−0.345036	+	0.0787523i
$927$	2.34315			0.0769590
$928$		0			0
$929$	41.3137			1.35546			0.677729	−	0.735311i	$-0.262964\pi$
$929$	41.3137			1.35546			0.677729	+	0.735311i	$0.262964\pi$
$930$	0.680972	−	0.155427i	0.0223300	−	0.00509667i
$931$	−2.60330	+	5.40581i	−0.0853198	+	0.177168i
$932$	7.10621	−	3.42217i	0.232772	−	0.112097i
$933$	−2.33319	−	10.2224i	−0.0763854	−	0.334666i
$934$	2.98223	−	13.0660i	0.0975815	−	0.427533i
$935$	−10.5025	−	5.05772i	−0.343467	−	0.165405i
$936$	−6.41181	+	5.11325i	−0.209576	+	0.167132i
$937$	−17.8489	−	22.3818i	−0.583098	−	0.731182i	0.399540	−	0.916716i	$-0.369170\pi$
$937$	−17.8489	−	22.3818i	−0.583098	−	0.731182i	−0.982638	+	0.185534i	$0.940599\pi$
$938$	2.87553	+	5.97110i	0.0938893	+	0.194963i
$939$	1.35094	+	1.07734i	0.0440864	+	0.0351577i
$940$			9.58579i			0.312654i
$941$	−14.0896	+	17.6678i	−0.459308	+	0.575954i	−0.956517	−	0.291677i	$-0.905787\pi$
$941$	−14.0896	+	17.6678i	−0.459308	+	0.575954i	0.497209	+	0.867631i	$0.334358\pi$
$942$	1.41934	+	0.323956i	0.0462447	+	0.0105551i
$943$	93.2011	+	21.2726i	3.03505	+	0.692730i
$944$	14.3219	−	17.9591i	0.466139	−	0.584519i
$945$			6.82843i			0.222129i
$946$	5.01483	+	3.99920i	0.163046	+	0.130025i
$947$	17.0884	+	35.4845i	0.555299	+	1.15309i	0.969994	+	0.243129i	$0.0781740\pi$
$947$	17.0884	+	35.4845i	0.555299	+	1.15309i	−0.414695	+	0.909960i	$0.636112\pi$
$948$	0.195594	+	0.245267i	0.00635260	+	0.00796591i
$949$	5.71809	−	4.56002i	0.185617	−	0.148025i
$950$	−8.95664	−	4.31329i	−0.290592	−	0.139942i
$951$	1.79327	−	7.85682i	0.0581507	−	0.254775i
$952$	−4.81910	−	21.1139i	−0.156188	−	0.684305i
$953$	−8.67400	+	4.17718i	−0.280979	+	0.135312i	−0.569066	−	0.822292i	$-0.692695\pi$
$953$	−8.67400	+	4.17718i	−0.280979	+	0.135312i	0.288087	+	0.957604i	$0.406981\pi$
$954$	3.80497	−	7.90109i	0.123190	−	0.255807i
$955$	−2.61894	+	0.597756i	−0.0847469	+	0.0193429i
$956$	−15.2548			−0.493377
$957$		0			0
$958$	−5.34315			−0.172629
$959$	−33.0902	+	7.55261i	−1.06854	+	0.243887i
$960$	0.749717	−	1.55680i	0.0241970	−	0.0502456i
$961$	−12.9977	+	6.25938i	−0.419282	+	0.201916i
$962$	−0.674113	−	2.95348i	−0.0217343	−	0.0952241i
$963$	5.77244	−	25.2907i	0.186014	−	0.814982i
$964$	7.10621	+	3.42217i	0.228876	+	0.110221i
$965$	−8.46601	+	6.75141i	−0.272530	+	0.217336i
$966$	−2.31672	−	2.90507i	−0.0745392	−	0.0934692i
$967$	11.6096	+	24.1075i	0.373339	+	0.775246i	0.999992	−	0.00405213i	$-0.00128984\pi$
$967$	11.6096	+	24.1075i	0.373339	+	0.775246i	−0.626653	+	0.779299i	$0.715576\pi$
$968$	−6.41181	−	5.11325i	−0.206083	−	0.164346i
$969$			12.0000i			0.385496i
$970$	−3.22442	+	4.04330i	−0.103530	+	0.129822i
$971$	−4.23425	−	0.966441i	−0.135884	−	0.0310146i	0.154038	−	0.988065i	$-0.450772\pi$
$971$	−4.23425	−	0.966441i	−0.135884	−	0.0310146i	−0.289922	+	0.957050i	$0.593629\pi$
$972$	−18.4375	−	4.20825i	−0.591384	−	0.134980i
$973$	24.6889	−	30.9589i	0.791491	−	0.992498i
$974$			11.7990i			0.378064i
$975$	2.36851	+	1.88882i	0.0758530	+	0.0604908i
$976$	1.07832	+	2.23916i	0.0345163	+	0.0716738i
$977$	26.0796	+	32.7028i	0.834360	+	1.04625i	0.998212	+	0.0597697i	$0.0190366\pi$
$977$	26.0796	+	32.7028i	0.834360	+	1.04625i	−0.163852	+	0.986485i	$0.552392\pi$
$978$	−2.42407	+	1.93313i	−0.0775133	+	0.0618148i
$979$	9.75608	+	4.69828i	0.311806	+	0.150158i
$980$	−0.406863	+	1.78258i	−0.0129968	+	0.0569426i
$981$	0.845355	+	3.70374i	0.0269901	+	0.118251i
$982$	4.76096	−	2.29276i	0.151928	−	0.0731649i
$983$	13.8279	−	28.7139i	0.441042	−	0.915832i	−0.555403	−	0.831581i	$-0.687436\pi$
$983$	13.8279	−	28.7139i	0.441042	−	0.915832i	0.996445	−	0.0842508i	$-0.0268497\pi$
$984$	7.99539	−	1.82490i	0.254884	−	0.0581756i
$985$	2.00000			0.0637253
$986$		0			0
$987$	−6.14214			−0.195506
$988$	19.5560	−	4.46352i	0.622158	−	0.142003i
$989$	21.3092	−	44.2490i	0.677593	−	1.40704i
$990$	2.54832	−	1.22721i	0.0809911	−	0.0390032i
$991$	−1.59583	−	6.99177i	−0.0506931	−	0.222101i	0.943236	−	0.332123i	$-0.107765\pi$
$991$	−1.59583	−	6.99177i	−0.0506931	−	0.222101i	−0.993929	+	0.110022i	$0.964908\pi$
$992$	−3.99883	+	17.5200i	−0.126963	+	0.556261i
$993$	0.154582	+	0.0744427i	0.00490551	+	0.00236237i
$994$	2.90507	−	2.31672i	0.0921433	−	0.0734819i
$995$	10.2784	+	12.8887i	0.325847	+	0.408600i
$996$	1.20166	+	2.49528i	0.0380762	+	0.0790660i
$997$	22.1135	+	17.6350i	0.700343	+	0.558505i	0.907628	−	0.419776i	$-0.137891\pi$
$997$	22.1135	+	17.6350i	0.700343	+	0.558505i	−0.207285	+	0.978281i	$0.566463\pi$
$998$		−	6.20101i		−	0.196290i
$999$	6.02095	−	7.55003i	0.190494	−	0.238872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.k.196.2		24
29.2	odd	28		841.2.a.d.1.1		2
29.3	odd	28		841.2.d.f.778.1		12
29.4	even	14	inner	841.2.e.k.236.2		24
29.5	even	14		841.2.b.a.840.3		4
29.6	even	14	inner	841.2.e.k.270.2		24
29.7	even	7	inner	841.2.e.k.63.3		24
29.8	odd	28		841.2.d.j.190.1		12
29.9	even	14	inner	841.2.e.k.651.3		24
29.10	odd	28		841.2.d.j.605.1		12
29.11	odd	28		841.2.d.f.574.1		12
29.12	odd	4		841.2.d.j.645.1		12
29.13	even	14	inner	841.2.e.k.267.3		24
29.14	odd	28		841.2.d.f.571.2		12
29.15	odd	28		841.2.d.j.571.1		12
29.16	even	7	inner	841.2.e.k.267.2		24
29.17	odd	4		841.2.d.f.645.2		12
29.18	odd	28		841.2.d.j.574.2		12
29.19	odd	28		841.2.d.f.605.2		12
29.20	even	7	inner	841.2.e.k.651.2		24
29.21	odd	28		841.2.d.f.190.2		12
29.22	even	14	inner	841.2.e.k.63.2		24
29.23	even	7	inner	841.2.e.k.270.3		24
29.24	even	7		841.2.b.a.840.2		4
29.25	even	7	inner	841.2.e.k.236.3		24
29.26	odd	28		841.2.d.j.778.2		12
29.27	odd	28		29.2.a.a.1.2	✓	2
29.28	even	2	inner	841.2.e.k.196.3		24
87.2	even	28		7569.2.a.c.1.2		2
87.56	even	28		261.2.a.d.1.1		2
116.27	even	28		464.2.a.h.1.2		2
145.27	even	28		725.2.b.b.349.3		4
145.114	odd	28		725.2.a.b.1.1		2
145.143	even	28		725.2.b.b.349.2		4
203.27	even	28		1421.2.a.j.1.2		2
232.27	even	28		1856.2.a.w.1.1		2
232.85	odd	28		1856.2.a.r.1.2		2
319.230	even	28		3509.2.a.j.1.1		2
348.143	odd	28		4176.2.a.bq.1.1		2
377.259	odd	28		4901.2.a.g.1.1		2
435.404	even	28		6525.2.a.o.1.2		2
493.288	odd	28		8381.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.2	✓	2	29.27	odd	28
261.2.a.d.1.1		2	87.56	even	28
464.2.a.h.1.2		2	116.27	even	28
725.2.a.b.1.1		2	145.114	odd	28
725.2.b.b.349.2		4	145.143	even	28
725.2.b.b.349.3		4	145.27	even	28
841.2.a.d.1.1		2	29.2	odd	28
841.2.b.a.840.2		4	29.24	even	7
841.2.b.a.840.3		4	29.5	even	14
841.2.d.f.190.2		12	29.21	odd	28
841.2.d.f.571.2		12	29.14	odd	28
841.2.d.f.574.1		12	29.11	odd	28
841.2.d.f.605.2		12	29.19	odd	28
841.2.d.f.645.2		12	29.17	odd	4
841.2.d.f.778.1		12	29.3	odd	28
841.2.d.j.190.1		12	29.8	odd	28
841.2.d.j.571.1		12	29.15	odd	28
841.2.d.j.574.2		12	29.18	odd	28
841.2.d.j.605.1		12	29.10	odd	28
841.2.d.j.645.1		12	29.12	odd	4
841.2.d.j.778.2		12	29.26	odd	28
841.2.e.k.63.2		24	29.22	even	14	inner
841.2.e.k.63.3		24	29.7	even	7	inner
841.2.e.k.196.2		24	1.1	even	1	trivial
841.2.e.k.196.3		24	29.28	even	2	inner
841.2.e.k.236.2		24	29.4	even	14	inner
841.2.e.k.236.3		24	29.25	even	7	inner
841.2.e.k.267.2		24	29.16	even	7	inner
841.2.e.k.267.3		24	29.13	even	14	inner
841.2.e.k.270.2		24	29.6	even	14	inner
841.2.e.k.270.3		24	29.23	even	7	inner
841.2.e.k.651.2		24	29.20	even	7	inner
841.2.e.k.651.3		24	29.9	even	14	inner
1421.2.a.j.1.2		2	203.27	even	28
1856.2.a.r.1.2		2	232.85	odd	28
1856.2.a.w.1.1		2	232.27	even	28
3509.2.a.j.1.1		2	319.230	even	28
4176.2.a.bq.1.1		2	348.143	odd	28
4901.2.a.g.1.1		2	377.259	odd	28
6525.2.a.o.1.2		2	435.404	even	28
7569.2.a.c.1.2		2	87.2	even	28
8381.2.a.e.1.2		2	493.288	odd	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.403828 + 0.0921712i) q^{2} +(0.179721 - 0.373194i) q^{3} +(-1.64736 + 0.793325i) q^{4} +(-0.222521 - 0.974928i) q^{5} +(-0.0381786 + 0.167271i) q^{6} +(-2.54832 - 1.22721i) q^{7} +(1.23982 - 0.988722i) q^{8} +(1.76350 + 2.21135i) q^{9} +O(q^{10})\)	\(q+(-0.403828 + 0.0921712i) q^{2} +(0.179721 - 0.373194i) q^{3} +(-1.64736 + 0.793325i) q^{4} +(-0.222521 - 0.974928i) q^{5} +(-0.0381786 + 0.167271i) q^{6} +(-2.54832 - 1.22721i) q^{7} +(1.23982 - 0.988722i) q^{8} +(1.76350 + 2.21135i) q^{9} +(0.179721 + 0.373194i) q^{10} +(-1.88751 - 1.50524i) q^{11} +0.757359i q^{12} +(-1.14001 + 1.42952i) q^{13} +(1.14220 + 0.260699i) q^{14} +(-0.403828 - 0.0921712i) q^{15} +(1.87047 - 2.34549i) q^{16} +4.82843i q^{17} +(-0.915973 - 0.730464i) q^{18} +(2.60330 + 5.40581i) q^{19} +(1.14001 + 1.42952i) q^{20} +(-0.915973 + 0.730464i) q^{21} +(0.900969 + 0.433884i) q^{22} +(1.70381 - 7.46488i) q^{23} +(-0.146164 - 0.640386i) q^{24} +(3.60388 - 1.73553i) q^{25} +(0.328606 - 0.682357i) q^{26} +(2.35368 - 0.537213i) q^{27} +5.17157 q^{28} +0.171573 q^{30} +(3.96900 - 0.905898i) q^{31} +(-1.91526 + 3.97707i) q^{32} +(-0.900969 + 0.433884i) q^{33} +(-0.445042 - 1.94986i) q^{34} +(-0.629384 + 2.75751i) q^{35} +(-4.65943 - 2.24386i) q^{36} +(3.12733 - 2.49396i) q^{37} +(-1.54955 - 1.94307i) q^{38} +(0.328606 + 0.682357i) q^{39} +(-1.23982 - 0.988722i) q^{40} +12.4853i q^{41} +(0.302568 - 0.379408i) q^{42} +(6.25340 + 1.42730i) q^{43} +(4.30354 + 0.982255i) q^{44} +(1.76350 - 2.21135i) q^{45} +3.17157i q^{46} +(4.09886 + 3.26873i) q^{47} +(-0.539162 - 1.11958i) q^{48} +(0.623490 + 0.781831i) q^{49} +(-1.29538 + 1.03303i) q^{50} +(1.80194 + 0.867767i) q^{51} +(0.743920 - 3.25933i) q^{52} +(1.66563 + 7.29761i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(-1.04749 + 2.17513i) q^{55} +(-4.37283 + 0.998069i) q^{56} +2.48528 q^{57} +7.65685 q^{59} +(0.738371 - 0.168528i) q^{60} +(-0.359441 + 0.746387i) q^{61} +(-1.51930 + 0.731654i) q^{62} +(-1.78017 - 7.79942i) q^{63} +(-0.928262 + 4.06698i) q^{64} +(1.64736 + 0.793325i) q^{65} +(0.323845 - 0.258258i) q^{66} +(3.52699 + 4.42271i) q^{67} +(-3.83051 - 7.95414i) q^{68} +(-2.47964 - 1.97744i) q^{69} -1.17157i q^{70} +(1.97744 - 2.47964i) q^{71} +(4.37283 + 0.998069i) q^{72} +(-3.89971 - 0.890084i) q^{73} +(-1.03303 + 1.29538i) q^{74} -1.65685i q^{75} +(-8.57713 - 6.84003i) q^{76} +(2.96274 + 6.15220i) q^{77} +(-0.195594 - 0.245267i) q^{78} +(0.323845 - 0.258258i) q^{79} +(-2.70291 - 1.30165i) q^{80} +(-1.66563 + 7.29761i) q^{81} +(-1.15078 - 5.04191i) q^{82} +(3.29471 - 1.58665i) q^{83} +(0.929438 - 1.93000i) q^{84} +(4.70737 - 1.07443i) q^{85} -2.65685 q^{86} -3.82843 q^{88} +(-4.37283 + 0.998069i) q^{89} +(-0.508326 + 1.05555i) q^{90} +(4.65943 - 2.24386i) q^{91} +(3.11529 + 13.6490i) q^{92} +(0.375235 - 1.64401i) q^{93} +(-1.95652 - 0.942210i) q^{94} +(4.69099 - 3.74094i) q^{95} +(1.14001 + 1.42952i) q^{96} +(5.41716 + 11.2488i) q^{97} +(-0.323845 - 0.258258i) q^{98} -6.82843i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6}+O(q^{10}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6	\( 24 q + 4 q^{4} - 4 q^{5} - 12 q^{6} - 4 q^{13} - 12 q^{16} + 4 q^{20} + 4 q^{22} + 8 q^{23} + 20 q^{24} + 16 q^{25} + 192 q^{28} + 72 q^{30} - 4 q^{33} - 8 q^{34} - 32 q^{36} - 24 q^{38} + 32 q^{42} - 4 q^{49} + 8 q^{51} + 36 q^{52} - 4 q^{53} - 4 q^{54} - 144 q^{57} + 48 q^{59} - 52 q^{62} - 32 q^{63} - 28 q^{64} - 4 q^{65} - 24 q^{71} - 16 q^{74} - 44 q^{78} - 12 q^{80} + 4 q^{81} - 32 q^{82} - 8 q^{83} + 72 q^{86} - 24 q^{88} + 32 q^{91} + 56 q^{92} + 52 q^{93} - 20 q^{94} + 4 q^{96}+O(q^{100}) \) 24 * q + 4 * q^4 - 4 * q^5 - 12 * q^6 - 4 * q^13 - 12 * q^16 + 4 * q^20 + 4 * q^22 + 8 * q^23 + 20 * q^24 + 16 * q^25 + 192 * q^28 + 72 * q^30 - 4 * q^33 - 8 * q^34 - 32 * q^36 - 24 * q^38 + 32 * q^42 - 4 * q^49 + 8 * q^51 + 36 * q^52 - 4 * q^53 - 4 * q^54 - 144 * q^57 + 48 * q^59 - 52 * q^62 - 32 * q^63 - 28 * q^64 - 4 * q^65 - 24 * q^71 - 16 * q^74 - 44 * q^78 - 12 * q^80 + 4 * q^81 - 32 * q^82 - 8 * q^83 + 72 * q^86 - 24 * q^88 + 32 * q^91 + 56 * q^92 + 52 * q^93 - 20 * q^94 + 4 * q^96

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