LMFDB - Embedded newform 841.2.e.k.267.4

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			267.4
Character	$\chi$	$=$	841.267
Dual form			841.2.e.k.63.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88751 + 1.50524i) q^{2} +(2.35368 + 0.537213i) q^{3} +(0.851905 + 3.73244i) q^{4} +(0.623490 - 0.781831i) q^{5} +(3.63396 + 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-1.91526 + 3.97707i) q^{8} +(2.54832 + 1.22721i) q^{9} +O(q^{10})$	\(q+(1.88751 + 1.50524i) q^{2} +(2.35368 + 0.537213i) q^{3} +(0.851905 + 3.73244i) q^{4} +(0.623490 - 0.781831i) q^{5} +(3.63396 + 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-1.91526 + 3.97707i) q^{8} +(2.54832 + 1.22721i) q^{9} +(2.35368 - 0.537213i) q^{10} +(-0.179721 - 0.373194i) q^{11} +9.24264i q^{12} +(-3.44929 + 1.66109i) q^{13} +(5.33868 - 4.25745i) q^{14} +(1.88751 - 1.50524i) q^{15} +(-2.70291 + 1.30165i) q^{16} -0.828427i q^{17} +(2.96274 + 6.15220i) q^{18} +(-5.84957 + 1.33513i) q^{19} +(3.44929 + 1.66109i) q^{20} +(2.96274 - 6.15220i) q^{21} +(0.222521 - 0.974928i) q^{22} +(2.28001 + 2.85904i) q^{23} +(-6.64444 + 8.33186i) q^{24} +(0.890084 + 3.89971i) q^{25} +(-9.01091 - 2.05668i) q^{26} +(-0.323845 - 0.258258i) q^{27} +10.8284 q^{28} +5.82843 q^{30} +(-7.87388 - 6.27921i) q^{31} +(1.54603 + 0.352871i) q^{32} +(-0.222521 - 0.974928i) q^{33} +(1.24698 - 1.56366i) q^{34} +(-1.76350 - 2.21135i) q^{35} +(-2.40955 + 10.5569i) q^{36} +(-1.73553 + 3.60388i) q^{37} +(-13.0508 - 6.28493i) q^{38} +(-9.01091 + 2.05668i) q^{39} +(1.91526 + 3.97707i) q^{40} -4.48528i q^{41} +(14.8527 - 7.15270i) q^{42} +(2.80348 - 2.23570i) q^{43} +(1.23982 - 0.988722i) q^{44} +(2.54832 - 1.22721i) q^{45} +8.82843i q^{46} +(1.40693 + 2.92152i) q^{47} +(-7.06105 + 1.61164i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(-4.18995 + 8.70053i) q^{50} +(0.445042 - 1.94986i) q^{51} +(-9.13840 - 11.4592i) q^{52} +(5.91398 - 7.41589i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(-0.403828 - 0.0921712i) q^{55} +(9.76139 + 7.78445i) q^{56} -14.4853 q^{57} -3.65685 q^{59} +(7.22619 + 5.76269i) q^{60} +(-4.70737 - 1.07443i) q^{61} +(-5.41031 - 23.7041i) q^{62} +(4.98792 - 6.25465i) q^{63} +(6.12792 + 7.68417i) q^{64} +(-0.851905 + 3.73244i) q^{65} +(1.04749 - 2.17513i) q^{66} +(5.09665 + 2.45442i) q^{67} +(3.09205 - 0.705741i) q^{68} +(3.83051 + 7.95414i) q^{69} -6.82843i q^{70} +(-7.95414 + 3.83051i) q^{71} +(-9.76139 + 7.78445i) q^{72} +(-3.12733 + 2.49396i) q^{73} +(-8.70053 + 4.18995i) q^{74} +9.65685i q^{75} +(-9.96655 - 20.6958i) q^{76} +(-1.14220 + 0.260699i) q^{77} +(-20.1040 - 9.68156i) q^{78} +(1.04749 - 2.17513i) q^{79} +(-0.667563 + 2.92478i) q^{80} +(-5.91398 - 7.41589i) q^{81} +(6.75141 - 8.46601i) q^{82} +(-1.70381 - 7.46488i) q^{83} +(25.4867 + 5.81717i) q^{84} +(-0.647690 - 0.516516i) q^{85} +8.65685 q^{86} +1.82843 q^{88} +(9.76139 + 7.78445i) q^{89} +(6.65722 + 1.51947i) q^{90} +(2.40955 + 10.5569i) q^{91} +(-8.72886 + 10.9456i) q^{92} +(-15.1593 - 19.0092i) q^{93} +(-1.74199 + 7.63215i) q^{94} +(-2.60330 + 5.40581i) q^{95} +(3.44929 + 1.66109i) q^{96} +(4.37283 - 0.998069i) q^{97} +(-1.04749 - 2.17513i) q^{98} -1.17157i 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 $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{14}\right)$

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 $

$2$	1.88751	+	1.50524i	1.33467	+	1.06436i	0.992176	+	0.124843i	$0.0398429\pi$
$2$	1.88751	+	1.50524i	1.33467	+	1.06436i	0.342493	+	0.939520i	$0.388729\pi$
$3$	2.35368	+	0.537213i	1.35890	+	0.310160i	0.839030	−	0.544085i	$-0.183123\pi$
$3$	2.35368	+	0.537213i	1.35890	+	0.310160i	0.519870	+	0.854245i	$0.325980\pi$
$4$	0.851905	+	3.73244i	0.425953	+	1.86622i
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i	−0.622619	−	0.782526i	$-0.713931\pi$
$5$	0.623490	−	0.781831i	0.278833	−	0.349646i	0.901452	+	0.432880i	$0.142503\pi$
$6$	3.63396	+	4.55685i	1.48356	+	1.86033i
$7$	0.629384	−	2.75751i	0.237885	−	1.04224i	−0.705022	−	0.709185i	$-0.749063\pi$
$7$	0.629384	−	2.75751i	0.237885	−	1.04224i	0.942907	−	0.333056i	$-0.108080\pi$
$8$	−1.91526	+	3.97707i	−0.677145	+	1.40611i
$9$	2.54832	+	1.22721i	0.849442	+	0.409070i
$10$	2.35368	−	0.537213i	0.744300	−	0.169882i
$11$	−0.179721	−	0.373194i	−0.0541878	−	0.112522i	0.872117	−	0.489298i	$-0.162747\pi$
$11$	−0.179721	−	0.373194i	−0.0541878	−	0.112522i	−0.926304	+	0.376776i	$0.877033\pi$
$12$			9.24264i			2.66812i
$13$	−3.44929	+	1.66109i	−0.956662	+	0.460704i	−0.846017	−	0.533156i	$-0.821006\pi$
$13$	−3.44929	+	1.66109i	−0.956662	+	0.460704i	−0.110645	+	0.993860i	$0.535292\pi$
$14$	5.33868	−	4.25745i	1.42682	−	1.13785i
$15$	1.88751	−	1.50524i	0.487353	−	0.388651i
$16$	−2.70291	+	1.30165i	−0.675727	+	0.325413i
$17$		−	0.828427i		−	0.200923i	−0.994941	−	0.100462i	$-0.967968\pi$
$17$		−	0.828427i		−	0.200923i	0.994941	−	0.100462i	$-0.0320319\pi$
$18$	2.96274	+	6.15220i	0.698325	+	1.45009i
$19$	−5.84957	+	1.33513i	−1.34198	+	0.306299i	−0.832425	−	0.554138i	$-0.813048\pi$
$19$	−5.84957	+	1.33513i	−1.34198	+	0.306299i	−0.509558	+	0.860436i	$0.670191\pi$
$20$	3.44929	+	1.66109i	0.771286	+	0.371432i
$21$	2.96274	−	6.15220i	0.646524	−	1.34252i
$22$	0.222521	−	0.974928i	0.0474416	−	0.207855i
$23$	2.28001	+	2.85904i	0.475415	+	0.596152i	0.960488	−	0.278322i	$-0.0897783\pi$
$23$	2.28001	+	2.85904i	0.475415	+	0.596152i	−0.485073	+	0.874474i	$0.661207\pi$
$24$	−6.64444	+	8.33186i	−1.35629	+	1.70073i
$25$	0.890084	+	3.89971i	0.178017	+	0.779942i
$26$	−9.01091	−	2.05668i	−1.76718	−	0.403348i
$27$	−0.323845	−	0.258258i	−0.0623240	−	0.0497018i
$28$	10.8284			2.04638
$29$		0			0
$29$		0			0
$30$	5.82843			1.06412
$31$	−7.87388	−	6.27921i	−1.41419	−	1.12778i	−0.973118	−	0.230307i	$-0.926027\pi$
$31$	−7.87388	−	6.27921i	−1.41419	−	1.12778i	−0.441072	−	0.897472i	$-0.645402\pi$
$32$	1.54603	+	0.352871i	0.273302	+	0.0623793i
$33$	−0.222521	−	0.974928i	−0.0387359	−	0.169713i
$34$	1.24698	−	1.56366i	0.213855	−	0.268166i
$35$	−1.76350	−	2.21135i	−0.298085	−	0.373787i
$36$	−2.40955	+	10.5569i	−0.401592	+	1.75949i
$37$	−1.73553	+	3.60388i	−0.285320	+	0.592473i	−0.993535	−	0.113523i	$-0.963786\pi$
$37$	−1.73553	+	3.60388i	−0.285320	+	0.592473i	0.708215	+	0.705997i	$0.249501\pi$
$38$	−13.0508	−	6.28493i	−2.11712	−	1.01955i
$39$	−9.01091	+	2.05668i	−1.44290	+	0.329333i
$40$	1.91526	+	3.97707i	0.302828	+	0.628830i
$41$		−	4.48528i		−	0.700483i	−0.936659	−	0.350242i	$-0.886099\pi$
$41$		−	4.48528i		−	0.700483i	0.936659	−	0.350242i	$-0.113901\pi$
$42$	14.8527	−	7.15270i	2.29183	−	1.10368i
$43$	2.80348	−	2.23570i	0.427527	−	0.340941i	−0.385969	−	0.922512i	$-0.626133\pi$
$43$	2.80348	−	2.23570i	0.427527	−	0.340941i	0.813496	+	0.581570i	$0.197562\pi$
$44$	1.23982	−	0.988722i	0.186910	−	0.149055i
$45$	2.54832	−	1.22721i	0.379882	−	0.182941i
$46$			8.82843i			1.30168i
$47$	1.40693	+	2.92152i	0.205222	+	0.426147i	0.978022	−	0.208502i	$-0.0668588\pi$
$47$	1.40693	+	2.92152i	0.205222	+	0.426147i	−0.772800	+	0.634649i	$0.781145\pi$
$48$	−7.06105	+	1.61164i	−1.01918	+	0.232620i
$49$	−0.900969	−	0.433884i	−0.128710	−	0.0619834i
$50$	−4.18995	+	8.70053i	−0.592549	+	1.23044i
$51$	0.445042	−	1.94986i	0.0623183	−	0.273034i
$52$	−9.13840	−	11.4592i	−1.26727	−	1.58910i
$53$	5.91398	−	7.41589i	0.812347	−	1.01865i	−0.186994	−	0.982361i	$-0.559875\pi$
$53$	5.91398	−	7.41589i	0.812347	−	1.01865i	0.999341	−	0.0362900i	$-0.0115540\pi$
$54$	−0.222521	−	0.974928i	−0.0302813	−	0.132671i
$55$	−0.403828	−	0.0921712i	−0.0544522	−	0.0124284i
$56$	9.76139	+	7.78445i	1.30442	+	1.04024i
$57$	−14.4853			−1.91862
$58$		0			0
$59$	−3.65685			−0.476082			−0.238041	−	0.971255i	$-0.576505\pi$
$59$	−3.65685			−0.476082			−0.238041	+	0.971255i	$0.576505\pi$
$60$	7.22619	+	5.76269i	0.932897	+	0.743960i
$61$	−4.70737	−	1.07443i	−0.602717	−	0.137566i	−0.0897350	−	0.995966i	$-0.528602\pi$
$61$	−4.70737	−	1.07443i	−0.602717	−	0.137566i	−0.512982	+	0.858400i	$0.671459\pi$
$62$	−5.41031	−	23.7041i	−0.687110	−	3.01043i
$63$	4.98792	−	6.25465i	0.628419	−	0.788012i
$64$	6.12792	+	7.68417i	0.765991	+	0.960522i
$65$	−0.851905	+	3.73244i	−0.105666	+	0.462952i
$66$	1.04749	−	2.17513i	0.128937	−	0.267740i
$67$	5.09665	+	2.45442i	0.622655	+	0.299855i	0.718484	−	0.695543i	$-0.244836\pi$
$67$	5.09665	+	2.45442i	0.622655	+	0.299855i	−0.0958296	+	0.995398i	$0.530550\pi$
$68$	3.09205	−	0.705741i	0.374967	−	0.0855837i
$69$	3.83051	+	7.95414i	0.461139	+	0.957566i
$70$		−	6.82843i		−	0.816153i
$71$	−7.95414	+	3.83051i	−0.943983	+	0.454598i	−0.841572	−	0.540144i	$-0.818370\pi$
$71$	−7.95414	+	3.83051i	−0.943983	+	0.454598i	−0.102410	+	0.994742i	$0.532655\pi$
$72$	−9.76139	+	7.78445i	−1.15039	+	0.917406i
$73$	−3.12733	+	2.49396i	−0.366026	+	0.291896i	−0.789180	−	0.614162i	$-0.789494\pi$
$73$	−3.12733	+	2.49396i	−0.366026	+	0.291896i	0.423154	+	0.906058i	$0.360923\pi$
$74$	−8.70053	+	4.18995i	−1.01142	+	0.487072i
$75$			9.65685i			1.11508i
$76$	−9.96655	−	20.6958i	−1.14324	−	2.37397i
$77$	−1.14220	+	0.260699i	−0.130166	+	0.0297095i
$78$	−20.1040	−	9.68156i	−2.27632	−	1.09622i
$79$	1.04749	−	2.17513i	0.117852	−	0.244721i	−0.833695	−	0.552224i	$-0.813779\pi$
$79$	1.04749	−	2.17513i	0.117852	−	0.244721i	0.951547	+	0.307503i	$0.0994934\pi$
$80$	−0.667563	+	2.92478i	−0.0746358	+	0.327001i
$81$	−5.91398	−	7.41589i	−0.657108	−	0.823988i
$82$	6.75141	−	8.46601i	0.745569	−	0.934914i
$83$	−1.70381	−	7.46488i	−0.187017	−	0.819377i	−0.978178	−	0.207769i	$-0.933380\pi$
$83$	−1.70381	−	7.46488i	−0.187017	−	0.819377i	0.791161	−	0.611609i	$-0.209477\pi$
$84$	25.4867	+	5.81717i	2.78083	+	0.634706i
$85$	−0.647690	−	0.516516i	−0.0702519	−	0.0560240i
$86$	8.65685			0.933493
$87$		0			0
$88$	1.82843			0.194911
$89$	9.76139	+	7.78445i	1.03470	+	0.825150i	0.984815	−	0.173605i	$-0.0555417\pi$
$89$	9.76139	+	7.78445i	1.03470	+	0.825150i	0.0498895	+	0.998755i	$0.484113\pi$
$90$	6.65722	+	1.51947i	0.701733	+	0.160166i
$91$	2.40955	+	10.5569i	0.252590	+	1.10667i
$92$	−8.72886	+	10.9456i	−0.910046	+	1.14116i
$93$	−15.1593	−	19.0092i	−1.57195	−	1.97116i
$94$	−1.74199	+	7.63215i	−0.179672	+	0.787196i
$95$	−2.60330	+	5.40581i	−0.267093	+	0.554625i
$96$	3.44929	+	1.66109i	0.352042	+	0.169535i
$97$	4.37283	−	0.998069i	0.443993	−	0.101339i	0.00532129	−	0.999986i	$-0.498306\pi$
$97$	4.37283	−	0.998069i	0.443993	−	0.101339i	0.438672	+	0.898647i	$0.355449\pi$
$98$	−1.04749	−	2.17513i	−0.105812	−	0.219721i
$99$		−	1.17157i		−	0.117748i
$100$	−13.7972	+	6.64437i	−1.37972	+	0.664437i
$101$	−1.83195	+	1.46093i	−0.182285	+	0.145368i	−0.710381	−	0.703817i	$-0.751478\pi$
$101$	−1.83195	+	1.46093i	−0.182285	+	0.145368i	0.528096	+	0.849185i	$0.322906\pi$
$102$	3.77502	−	3.01048i	0.373782	−	0.298081i
$103$	4.35026	−	2.09498i	0.428644	−	0.206424i	−0.207107	−	0.978318i	$-0.566405\pi$
$103$	4.35026	−	2.09498i	0.428644	−	0.206424i	0.635751	+	0.771894i	$0.280691\pi$
$104$		−	16.8995i		−	1.65713i
$105$	−2.96274	−	6.15220i	−0.289134	−	0.600393i
$106$	22.3254	−	5.09562i	2.16843	−	0.494930i
$107$	13.3600	+	6.43381i	1.29156	+	0.621980i	0.948334	−	0.317274i	$-0.102768\pi$
$107$	13.3600	+	6.43381i	1.29156	+	0.621980i	0.343221	+	0.939255i	$0.388482\pi$
$108$	0.688047	−	1.42874i	0.0662073	−	0.137481i
$109$	2.81642	−	12.3395i	0.269764	−	1.18191i	−0.640525	−	0.767937i	$-0.721283\pi$
$109$	2.81642	−	12.3395i	0.269764	−	1.18191i	0.910289	−	0.413974i	$-0.135860\pi$
$110$	−0.623490	−	0.781831i	−0.0594474	−	0.0745447i
$111$	−6.02095	+	7.55003i	−0.571483	+	0.716617i
$112$	1.88815	+	8.27254i	0.178414	+	0.781681i
$113$	12.9799	+	2.96258i	1.22105	+	0.278696i	0.784010	−	0.620748i	$-0.213171\pi$
$113$	12.9799	+	2.96258i	1.22105	+	0.278696i	0.437037	+	0.899444i	$0.356028\pi$
$114$	−27.3411	−	21.8038i	−2.56073	−	2.04211i
$115$	3.65685			0.341003
$116$		0			0
$117$	−10.8284			−1.00109
$118$	−6.90234	−	5.50443i	−0.635412	−	0.506724i
$119$	−2.28440	−	0.521399i	−0.209410	−	0.0477966i
$120$	2.37137	+	10.3897i	0.216476	+	0.948442i
$121$	6.75141	−	8.46601i	0.613765	−	0.769637i
$122$	−7.26793	−	9.11370i	−0.658007	−	0.825115i
$123$	2.40955	−	10.5569i	0.217262	−	0.951887i
$124$	16.7290	−	34.7381i	1.50231	−	3.11957i
$125$	8.10872	+	3.90495i	0.725266	+	0.349270i
$126$	18.8295	−	4.29770i	1.67746	−	0.382870i
$127$	−1.88442	−	3.91304i	−0.167215	−	0.347226i	0.800476	−	0.599365i	$-0.204580\pi$
$127$	−1.88442	−	3.91304i	−0.167215	−	0.347226i	−0.967691	+	0.252139i	$0.918866\pi$
$128$			20.5563i			1.81694i
$129$	7.79956	−	3.75607i	0.686713	−	0.330703i
$130$	−7.22619	+	5.76269i	−0.633779	+	0.505422i
$131$	−16.6637	+	13.2889i	−1.45592	+	1.16105i	−0.500522	+	0.865724i	$0.666858\pi$
$131$	−16.6637	+	13.2889i	−1.45592	+	1.16105i	−0.955395	+	0.295331i	$0.904570\pi$
$132$	3.44929	−	1.66109i	0.300222	−	0.144580i
$133$			16.9706i			1.47153i
$134$	5.92549	+	12.3044i	0.511884	+	1.06294i
$135$	−0.403828	+	0.0921712i	−0.0347560	+	0.00793283i
$136$	3.29471	+	1.58665i	0.282519	+	0.136054i
$137$	−5.20660	+	10.8116i	−0.444830	+	0.923700i	0.551174	+	0.834391i	$0.314180\pi$
$137$	−5.20660	+	10.8116i	−0.444830	+	0.923700i	−0.996004	+	0.0893090i	$0.971534\pi$
$138$	−4.74275	+	20.7793i	−0.403729	+	1.76885i
$139$	8.72886	+	10.9456i	0.740372	+	0.928397i	0.999297	−	0.0375004i	$-0.0119395\pi$
$139$	8.72886	+	10.9456i	0.740372	+	0.928397i	−0.258925	+	0.965898i	$0.583368\pi$
$140$	6.75141	−	8.46601i	0.570599	−	0.715508i
$141$	1.74199	+	7.63215i	0.146702	+	0.642743i
$142$	−20.7793	−	4.74275i	−1.74376	−	0.398002i
$143$	1.23982	+	0.988722i	0.103679	+	0.0826811i
$144$	−8.48528			−0.707107
$145$		0			0
$146$	−9.65685			−0.799207
$147$	−1.88751	−	1.50524i	−0.155679	−	0.124150i
$148$	−14.9298	−	3.40762i	−1.22722	−	0.280105i
$149$	−1.74199	−	7.63215i	−0.142709	−	0.625250i	−0.994799	−	0.101855i	$-0.967522\pi$
$149$	−1.74199	−	7.63215i	−0.142709	−	0.625250i	0.852090	−	0.523395i	$-0.175335\pi$
$150$	−14.5359	+	18.2274i	−1.18685	+	1.48826i
$151$	8.81748	+	11.0568i	0.717556	+	0.899787i	0.998197	−	0.0600260i	$-0.0191184\pi$
$151$	8.81748	+	11.0568i	0.717556	+	0.899787i	−0.280641	+	0.959813i	$0.590547\pi$
$152$	5.89353	−	25.8212i	0.478028	−	2.09438i
$153$	1.01665	−	2.11110i	0.0821915	−	0.170672i
$154$	−2.54832	−	1.22721i	−0.205350	−	0.0988913i
$155$	−9.81857	+	2.24102i	−0.788646	+	0.180003i
$156$	−15.3529	−	31.8806i	−1.22921	−	2.55249i
$157$			8.48528i			0.677199i	0.940931	+	0.338600i	$0.109953\pi$
$157$			8.48528i			0.677199i	−0.940931	+	0.338600i	$0.890047\pi$
$158$	5.25123	−	2.52886i	0.417766	−	0.201185i
$159$	17.9035	−	14.2776i	1.41984	−	1.13229i
$160$	1.23982	−	0.988722i	0.0980162	−	0.0781653i
$161$	9.31885	−	4.48772i	0.734428	−	0.353682i
$162$		−	22.8995i		−	1.79915i
$163$	−1.70470	−	3.53985i	−0.133522	−	0.277262i	0.823478	−	0.567348i	$-0.192030\pi$
$163$	−1.70470	−	3.53985i	−0.133522	−	0.277262i	−0.957001	+	0.290086i	$0.906316\pi$
$164$	16.7410	−	3.82103i	1.30726	−	0.298373i
$165$	−0.900969	−	0.433884i	−0.0701403	−	0.0337778i
$166$	8.02046	−	16.6547i	0.622509	−	1.29265i
$167$	−0.705741	+	3.09205i	−0.0546119	+	0.239270i	−0.994866	−	0.101204i	$-0.967731\pi$
$167$	−0.705741	+	3.09205i	−0.0546119	+	0.239270i	0.940254	+	0.340474i	$0.110588\pi$
$168$	18.7933	+	23.5661i	1.44994	+	1.81816i
$169$	1.03303	−	1.29538i	0.0794640	−	0.0996447i
$170$	−0.445042	−	1.94986i	−0.0341332	−	0.149547i
$171$	−16.5451	−	3.77631i	−1.26523	−	0.288781i
$172$	10.7329	+	8.55922i	0.818378	+	0.652634i
$173$	−12.3431			−0.938432			−0.469216	−	0.883083i	$-0.655463\pi$
$173$	−12.3431			−0.938432			−0.469216	+	0.883083i	$0.655463\pi$
$174$		0			0
$175$	11.3137			0.855236
$176$	0.971536	+	0.774774i	0.0732323	+	0.0584008i
$177$	−8.60708	−	1.96451i	−0.646948	−	0.147662i
$178$	6.70726	+	29.3864i	0.502730	+	2.20260i
$179$	4.04351	−	5.07040i	0.302226	−	0.378979i	−0.607408	−	0.794390i	$-0.707791\pi$
$179$	4.04351	−	5.07040i	0.302226	−	0.378979i	0.909634	+	0.415411i	$0.136362\pi$
$180$	6.75141	+	8.46601i	0.503221	+	0.631019i
$181$	−1.84997	+	8.10527i	−0.137507	+	0.602460i	0.858471	+	0.512863i	$0.171415\pi$
$181$	−1.84997	+	8.10527i	−0.137507	+	0.602460i	−0.995978	+	0.0895969i	$0.971442\pi$
$182$	−11.3426	+	23.5533i	−0.840773	+	1.74588i
$183$	−10.5025	−	5.05772i	−0.776364	−	0.373877i
$184$	−15.7374	+	3.59196i	−1.16018	+	0.264803i
$185$	1.73553	+	3.60388i	0.127599	+	0.264962i
$186$		−	58.6985i		−	4.30398i
$187$	−0.309164	+	0.148885i	−0.0226083	+	0.0108876i
$188$	−9.70582	+	7.74014i	−0.707870	+	0.564507i
$189$	−0.915973	+	0.730464i	−0.0666272	+	0.0531334i
$190$	−13.0508	+	6.28493i	−0.946804	+	0.455957i
$191$		−	25.3137i		−	1.83164i	−0.401594	−	0.915818i	$-0.631544\pi$
$191$		−	25.3137i		−	1.83164i	0.401594	−	0.915818i	$-0.368456\pi$
$192$	10.2952	+	21.3781i	0.742989	+	1.54283i
$193$	5.04191	−	1.15078i	0.362925	−	0.0828352i	−0.0371701	−	0.999309i	$-0.511834\pi$
$193$	5.04191	−	1.15078i	0.362925	−	0.0828352i	0.400095	+	0.916474i	$0.368977\pi$
$194$	9.75608	+	4.69828i	0.700445	+	0.337317i
$195$	−4.01023	+	8.32733i	−0.287179	+	0.596333i
$196$	0.851905	−	3.73244i	0.0608504	−	0.266603i
$197$	1.24698	+	1.56366i	0.0888436	+	0.111406i	0.824266	−	0.566202i	$-0.191588\pi$
$197$	1.24698	+	1.56366i	0.0888436	+	0.111406i	−0.735423	+	0.677609i	$0.763016\pi$
$198$	1.76350	−	2.21135i	0.125326	−	0.157154i
$199$	0.107985	+	0.473114i	0.00765487	+	0.0335382i	0.978611	−	0.205719i	$-0.0659533\pi$
$199$	0.107985	+	0.473114i	0.00765487	+	0.0335382i	−0.970956	+	0.239257i	$0.923096\pi$
$200$	−17.2142	−	3.92902i	−1.21722	−	0.277824i
$201$	10.6774	+	8.51491i	0.753123	+	0.600595i
$202$	−5.65685			−0.398015
$203$		0			0
$204$	7.65685			0.536087
$205$	−3.50673	−	2.79653i	−0.244921	−	0.195318i
$206$	11.3646	+	2.59389i	0.791809	+	0.180725i
$207$	2.30157	+	10.0838i	0.159970	+	0.700874i
$208$	7.16096	−	8.97955i	0.496523	−	0.622620i
$209$	1.54955	+	1.94307i	0.107184	+	0.134405i
$210$	3.66832	−	16.0720i	0.253138	−	1.10907i
$211$	−8.41074	+	17.4651i	−0.579019	+	1.20235i	0.381561	+	0.924344i	$0.375387\pi$
$211$	−8.41074	+	17.4651i	−0.579019	+	1.20235i	−0.960580	+	0.278002i	$0.910328\pi$
$212$	32.7175	+	15.7559i	2.24705	+	1.08212i
$213$	−20.7793	+	4.74275i	−1.42378	+	0.324968i
$214$	15.5326	+	32.2538i	1.06179	+	2.20482i
$215$		−	3.58579i		−	0.244549i
$216$	1.64736	−	0.793325i	0.112088	−	0.0539789i
$217$	−22.2707	+	17.7603i	−1.51183	+	1.20565i
$218$	23.8899	−	19.0516i	1.61803	−	1.29034i
$219$	−8.70053	+	4.18995i	−0.587927	+	0.283131i
$220$		−	1.58579i		−	0.106914i
$221$	1.37609	+	2.85749i	0.0925661	+	0.192215i
$222$	−22.7292	+	5.18779i	−1.52548	+	0.348182i
$223$	2.85749	+	1.37609i	0.191352	+	0.0921501i	0.527106	−	0.849799i	$-0.323277\pi$
$223$	2.85749	+	1.37609i	0.191352	+	0.0921501i	−0.335755	+	0.941949i	$0.608991\pi$
$224$	1.94609	−	4.04110i	0.130029	−	0.270007i
$225$	−2.51754	+	11.0301i	−0.167836	+	0.735337i
$226$	20.0403	+	25.1297i	1.33306	+	1.67161i
$227$	−5.07654	+	6.36578i	−0.336942	+	0.422512i	−0.921220	−	0.389042i	$-0.872806\pi$
$227$	−5.07654	+	6.36578i	−0.336942	+	0.422512i	0.584278	+	0.811553i	$0.301378\pi$
$228$	−12.3401	−	54.0655i	−0.817242	−	3.58057i
$229$	3.42660	+	0.782098i	0.226436	+	0.0516825i	0.334233	−	0.942490i	$-0.391523\pi$
$229$	3.42660	+	0.782098i	0.226436	+	0.0516825i	−0.107797	+	0.994173i	$0.534380\pi$
$230$	6.90234	+	5.50443i	0.455127	+	0.362952i
$231$	−2.82843			−0.186097
$232$		0			0
$233$	18.3137			1.19977			0.599885	−	0.800086i	$-0.295213\pi$
$233$	18.3137			1.19977			0.599885	+	0.800086i	$0.295213\pi$
$234$	−20.4387	−	16.2994i	−1.33612	−	1.06552i
$235$	3.16134	+	0.721555i	0.206223	+	0.0470691i
$236$	−3.11529	−	13.6490i	−0.202788	−	0.888474i
$237$	3.63396	−	4.55685i	0.236051	−	0.295999i
$238$	−3.52699	−	4.42271i	−0.228621	−	0.286681i
$239$	4.37406	−	19.1640i	0.282935	−	1.23962i	−0.611076	−	0.791572i	$-0.709263\pi$
$239$	4.37406	−	19.1640i	0.282935	−	1.23962i	0.894011	−	0.448045i	$-0.147880\pi$
$240$	−3.14246	+	6.52539i	−0.202845	+	0.421212i
$241$	−16.5001	−	7.94602i	−1.06286	−	0.511848i	−0.181064	−	0.983471i	$-0.557954\pi$
$241$	−16.5001	−	7.94602i	−1.06286	−	0.511848i	−0.881800	+	0.471623i	$0.843668\pi$
$242$	25.4867	−	5.81717i	1.63835	−	0.373942i
$243$	−9.39656	−	19.5122i	−0.602789	−	1.25171i
$244$		−	18.4853i		−	1.18340i
$245$	−0.900969	+	0.433884i	−0.0575608	+	0.0277198i
$246$	20.4387	−	16.2994i	1.30313	−	1.03921i
$247$	17.9591	−	14.3219i	1.14271	−	0.911281i
$248$	40.0533	−	19.2887i	2.54339	−	1.22483i
$249$		−	18.4853i		−	1.17146i
$250$	9.42739	+	19.5762i	0.596241	+	1.23811i
$251$	−19.5678	+	4.46623i	−1.23511	+	0.281906i	−0.789741	−	0.613440i	$-0.789785\pi$
$251$	−19.5678	+	4.46623i	−1.23511	+	0.281906i	−0.445370	+	0.895346i	$0.646928\pi$
$252$	27.5943	+	13.2887i	1.73828	+	0.837112i
$253$	0.657212	−	1.36471i	0.0413186	−	0.0857989i
$254$	2.33319	−	10.2224i	0.146398	−	0.641410i
$255$	−1.24698	−	1.56366i	−0.0780889	−	0.0979204i
$256$	−18.6863	+	23.4319i	−1.16790	+	1.46450i
$257$	4.04356	+	17.7160i	0.252230	+	1.10509i	0.929344	+	0.369214i	$0.120373\pi$
$257$	4.04356	+	17.7160i	0.252230	+	1.10509i	−0.677114	+	0.735878i	$0.736770\pi$
$258$	20.3755	+	4.65058i	1.26852	+	0.289532i
$259$	8.84541	+	7.05398i	0.549627	+	0.438313i
$260$	−14.6569			−0.908980
$261$		0			0
$262$	−51.4558			−3.17895
$263$	−2.15579	−	1.71919i	−0.132932	−	0.106010i	0.554767	−	0.832006i	$-0.312807\pi$
$263$	−2.15579	−	1.71919i	−0.132932	−	0.106010i	−0.687699	+	0.725996i	$0.741379\pi$
$264$	4.30354	+	0.982255i	0.264865	+	0.0604536i
$265$	−2.11067	−	9.24747i	−0.129658	−	0.568067i
$266$	−25.5447	+	32.0321i	−1.56625	+	1.96401i
$267$	18.7933	+	23.5661i	1.15013	+	1.44222i
$268$	−4.81910	+	21.1139i	−0.294374	+	1.28973i
$269$	13.6482	−	28.3407i	0.832144	−	1.72797i	0.160575	−	0.987024i	$-0.448665\pi$
$269$	13.6482	−	28.3407i	0.832144	−	1.72797i	0.671570	−	0.740941i	$-0.265620\pi$
$270$	−0.900969	−	0.433884i	−0.0548312	−	0.0264053i
$271$	16.1412	−	3.68413i	0.980511	−	0.223795i	0.297916	−	0.954592i	$-0.403708\pi$
$271$	16.1412	−	3.68413i	0.980511	−	0.223795i	0.682595	+	0.730797i	$0.260851\pi$
$272$	1.07832	+	2.23916i	0.0653829	+	0.135769i
$273$			26.1421i			1.58219i
$274$	−26.1016	+	12.5699i	−1.57685	+	0.759373i
$275$	1.29538	−	1.03303i	0.0781144	−	0.0622942i
$276$	−26.4251	+	21.0733i	−1.59060	+	1.26847i
$277$	15.5991	−	7.51214i	0.937260	−	0.451361i	0.0980580	−	0.995181i	$-0.468737\pi$
$277$	15.5991	−	7.51214i	0.937260	−	0.451361i	0.839202	+	0.543820i	$0.183023\pi$
$278$			33.7990i			2.02713i
$279$	−12.3593	−	25.6644i	−0.739932	−	1.53648i
$280$	12.1722	−	2.77824i	0.727431	−	0.166031i
$281$	−28.8045	−	13.8715i	−1.71833	−	0.827505i	−0.989795	−	0.142497i	$-0.954487\pi$
$281$	−28.8045	−	13.8715i	−1.71833	−	0.827505i	−0.728536	−	0.685007i	$-0.759799\pi$
$282$	−8.20018	+	17.0279i	−0.488314	+	1.01399i
$283$	2.59389	−	11.3646i	0.154191	−	0.675555i	−0.837449	−	0.546516i	$-0.815954\pi$
$283$	2.59389	−	11.3646i	0.154191	−	0.675555i	0.991640	−	0.129039i	$-0.0411892\pi$
$284$	−21.0733	−	26.4251i	−1.25047	−	1.56804i
$285$	−9.03143	+	11.3250i	−0.534975	+	0.670838i
$286$	0.851905	+	3.73244i	0.0503742	+	0.220704i
$287$	−12.3682	−	2.82297i	−0.730073	−	0.166634i
$288$	3.50673	+	2.79653i	0.206636	+	0.164787i
$289$	16.3137			0.959630
$290$		0			0
$291$	10.8284			0.634774
$292$	−11.9727	−	9.54794i	−0.700652	−	0.558751i
$293$	7.46488	+	1.70381i	0.436103	+	0.0995377i	0.434935	−	0.900462i	$-0.356771\pi$
$293$	7.46488	+	1.70381i	0.436103	+	0.0995377i	0.00116759	+	0.999999i	$0.499628\pi$
$294$	−1.29695	−	5.68230i	−0.0756395	−	0.331398i
$295$	−2.28001	+	2.85904i	−0.132747	+	0.166460i
$296$	−11.0089	−	13.8047i	−0.639877	−	0.802381i
$297$	−0.0381786	+	0.167271i	−0.00221534	+	0.00970606i
$298$	8.20018	−	17.0279i	0.475024	−	0.986397i
$299$	−12.6136	−	6.07437i	−0.729461	−	0.351290i
$300$	−36.0436	+	8.22672i	−2.08098	+	0.474970i
$301$	−4.40051	−	9.13775i	−0.253641	−	0.526691i
$302$			34.1421i			1.96466i
$303$	−5.09665	+	2.45442i	−0.292795	+	0.141003i
$304$	14.0730	−	11.2228i	0.807140	−	0.643673i
$305$	−3.77502	+	3.01048i	−0.216157	+	0.172379i
$306$	5.09665	−	2.45442i	0.291356	−	0.140310i
$307$		−	2.89949i		−	0.165483i	−0.996571	−	0.0827415i	$-0.973632\pi$
$307$		−	2.89949i		−	0.165483i	0.996571	−	0.0827415i	$-0.0263676\pi$
$308$	−1.94609	−	4.04110i	−0.110889	−	0.230263i
$309$	11.3646	−	2.59389i	0.646509	−	0.147561i
$310$	−21.9059	−	10.5493i	−1.24417	−	0.599161i
$311$	−1.16554	+	2.42027i	−0.0660916	+	0.137241i	−0.931398	−	0.364003i	$-0.881410\pi$
$311$	−1.16554	+	2.42027i	−0.0660916	+	0.137241i	0.865306	+	0.501244i	$0.167124\pi$
$312$	9.07863	−	39.7761i	0.513976	−	2.25188i
$313$	6.12792	+	7.68417i	0.346371	+	0.434335i	0.924250	−	0.381787i	$-0.124691\pi$
$313$	6.12792	+	7.68417i	0.346371	+	0.434335i	−0.577880	+	0.816122i	$0.696120\pi$
$314$	−12.7724	+	16.0160i	−0.720786	+	0.903837i
$315$	−1.78017	−	7.79942i	−0.100301	−	0.439448i
$316$	9.01091	+	2.05668i	0.506903	+	0.115697i
$317$	−24.5932	−	19.6124i	−1.38129	−	1.10154i	−0.982862	−	0.184342i	$-0.940984\pi$
$317$	−24.5932	−	19.6124i	−1.38129	−	1.10154i	−0.398428	−	0.917200i	$-0.630444\pi$
$318$	55.2843			3.10019
$319$		0			0
$320$	9.82843			0.549426
$321$	27.9888	+	22.3203i	1.56218	+	1.24580i
$322$	24.3445	+	5.55647i	1.35667	+	0.309650i
$323$	1.10605	+	4.84594i	0.0615425	+	0.269635i
$324$	22.6412	−	28.3912i	1.25785	−	1.57729i
$325$	−9.54794	−	11.9727i	−0.529624	−	0.664128i
$326$	2.11067	−	9.24747i	0.116899	−	0.512170i
$327$	13.2579	−	27.5303i	0.733164	−	1.52243i
$328$	17.8383	+	8.59046i	0.984954	+	0.474329i
$329$	8.94162	−	2.04087i	0.492968	−	0.112517i
$330$	−1.04749	−	2.17513i	−0.0576623	−	0.119737i
$331$		−	2.41421i		−	0.132697i	−0.997797	−	0.0663486i	$-0.978865\pi$
$331$		−	2.41421i		−	0.132697i	0.997797	−	0.0663486i	$-0.0211349\pi$
$332$	26.4107	−	12.7187i	1.44948	−	0.698032i
$333$	−8.84541	+	7.05398i	−0.484726	+	0.386556i
$334$	−5.98637	+	4.77397i	−0.327560	+	0.261220i
$335$	5.09665	−	2.45442i	0.278460	−	0.134099i
$336$			20.4853i			1.11756i
$337$	−9.45823	−	19.6402i	−0.515222	−	1.06987i	−0.982587	−	0.185806i	$-0.940511\pi$
$337$	−9.45823	−	19.6402i	−0.515222	−	1.06987i	0.467364	−	0.884065i	$-0.345204\pi$
$338$	3.89971	−	0.890084i	0.212116	−	0.0484142i
$339$	28.9591	+	13.9459i	1.57284	+	0.757440i
$340$	1.37609	−	2.85749i	0.0746292	−	0.154969i
$341$	−0.928262	+	4.06698i	−0.0502682	+	0.220239i
$342$	−25.5447	−	32.0321i	−1.38130	−	1.73210i
$343$	10.5810	−	13.2681i	0.571319	−	0.716411i
$344$	3.52216	+	15.4316i	0.189902	+	0.832015i
$345$	8.60708	+	1.96451i	0.463390	+	0.105766i
$346$	−23.2978	−	18.5794i	−1.25250	−	0.998833i
$347$	−2.48528			−0.133417			−0.0667084	−	0.997773i	$-0.521250\pi$
$347$	−2.48528			−0.133417			−0.0667084	+	0.997773i	$0.521250\pi$
$348$		0			0
$349$	−5.14214			−0.275252			−0.137626	−	0.990484i	$-0.543947\pi$
$349$	−5.14214			−0.275252			−0.137626	+	0.990484i	$0.543947\pi$
$350$	21.3547	+	17.0298i	1.14146	+	0.910282i
$351$	1.54603	+	0.352871i	0.0825208	+	0.0188348i
$352$	−0.146164	−	0.640386i	−0.00779056	−	0.0341327i
$353$	−16.8159	+	21.0864i	−0.895018	+	1.12232i	0.0968814	+	0.995296i	$0.469113\pi$
$353$	−16.8159	+	21.0864i	−0.895018	+	1.12232i	−0.991900	+	0.127022i	$0.959458\pi$
$354$	−13.2889	−	16.6637i	−0.706296	−	0.885667i
$355$	−1.96451	+	8.60708i	−0.104265	+	0.456816i
$356$	−20.7392	+	43.0654i	−1.09918	+	2.28246i
$357$	−5.09665	−	2.45442i	−0.269743	−	0.129902i
$358$	15.2643	−	3.48398i	0.806744	−	0.184134i
$359$	1.70470	+	3.53985i	0.0899706	+	0.186826i	0.941099	−	0.338132i	$-0.109795\pi$
$359$	1.70470	+	3.53985i	0.0899706	+	0.186826i	−0.851128	+	0.524958i	$0.824081\pi$
$360$			12.4853i			0.658032i
$361$	15.3165	−	7.37602i	0.806130	−	0.388212i
$362$	−15.6922	+	12.5141i	−0.824763	+	0.657727i
$363$	20.4387	−	16.2994i	1.07276	−	0.855494i
$364$	−37.3504	+	17.9870i	−1.95769	+	0.942776i
$365$			4.00000i			0.209370i
$366$	−12.2104	−	25.3552i	−0.638249	−	1.32534i
$367$	−17.5487	+	4.00538i	−0.916035	+	0.209079i	−0.654453	−	0.756102i	$-0.727101\pi$
$367$	−17.5487	+	4.00538i	−0.916035	+	0.209079i	−0.261582	+	0.965181i	$0.584244\pi$
$368$	−9.88414	−	4.75995i	−0.515246	−	0.248129i
$369$	5.50438	−	11.4300i	0.286546	−	0.595020i
$370$	−2.14885	+	9.41474i	−0.111714	+	0.489449i
$371$	−16.7273	−	20.9753i	−0.868436	−	1.08898i
$372$	58.0365	−	72.7754i	3.00905	−	3.77323i
$373$	5.85535	+	25.6540i	0.303179	+	1.32831i	0.865299	+	0.501257i	$0.167129\pi$
$373$	5.85535	+	25.6540i	0.303179	+	1.32831i	−0.562120	+	0.827056i	$0.690014\pi$
$374$	−0.807657	−	0.184342i	−0.0417629	−	0.00953212i
$375$	16.9876	+	13.5471i	0.877235	+	0.699571i
$376$	−14.3137			−0.738173
$377$		0			0
$378$	−2.82843			−0.145479
$379$	5.44981	+	4.34607i	0.279938	+	0.223243i	0.753386	−	0.657579i	$-0.228419\pi$
$379$	5.44981	+	4.34607i	0.279938	+	0.223243i	−0.473448	+	0.880822i	$0.656991\pi$
$380$	−22.3946	−	5.11143i	−1.14882	−	0.262211i
$381$	−2.33319	−	10.2224i	−0.119533	−	0.523709i
$382$	38.1031	−	47.7798i	1.94953	−	2.44463i
$383$	2.19139	+	2.74792i	0.111975	+	0.140412i	0.834660	−	0.550765i	$-0.185664\pi$
$383$	2.19139	+	2.74792i	0.111975	+	0.140412i	−0.722686	+	0.691177i	$0.757093\pi$
$384$	−11.0431	+	48.3832i	−0.563543	+	2.46904i
$385$	−0.508326	+	1.05555i	−0.0259067	+	0.0537958i
$386$	11.2488	+	5.41716i	0.572551	+	0.275726i
$387$	9.88785	−	2.25684i	0.502628	−	0.114721i
$388$	7.45047	+	15.4711i	0.378240	+	0.785424i
$389$			3.02944i			0.153599i	0.997047	+	0.0767993i	$0.0244701\pi$
$389$			3.02944i			0.153599i	−0.997047	+	0.0767993i	$0.975530\pi$
$390$	−20.1040	+	9.68156i	−1.01800	+	0.490245i
$391$	2.36851	−	1.88882i	0.119781	−	0.0955219i
$392$	3.45117	−	2.75222i	0.174310	−	0.139008i
$393$	−46.3601	+	22.3259i	−2.33856	+	1.12619i
$394$			4.82843i			0.243253i
$395$	−1.04749	−	2.17513i	−0.0527048	−	0.109443i
$396$	4.37283	−	0.998069i	0.219743	−	0.0501549i
$397$	−17.4276	−	8.39268i	−0.874665	−	0.421216i	−0.0579918	−	0.998317i	$-0.518470\pi$
$397$	−17.4276	−	8.39268i	−0.874665	−	0.421216i	−0.816673	+	0.577101i	$0.804184\pi$
$398$	−0.508326	+	1.05555i	−0.0254801	+	0.0529100i
$399$	−9.11681	+	39.9433i	−0.456411	+	1.99967i
$400$	−7.48188	−	9.38198i	−0.374094	−	0.469099i
$401$	−11.6324	+	14.5865i	−0.580892	+	0.728416i	−0.982265	−	0.187499i	$-0.939962\pi$
$401$	−11.6324	+	14.5865i	−0.580892	+	0.728416i	0.401373	+	0.915915i	$0.368533\pi$
$402$	7.33664	+	32.1439i	0.365918	+	1.60319i
$403$	37.5897	+	8.57959i	1.87247	+	0.427380i
$404$	−7.01347	−	5.59305i	−0.348933	−	0.278265i
$405$	−9.48528			−0.471327
$406$		0			0
$407$	1.65685			0.0821272
$408$	6.90234	+	5.50443i	0.341717	+	0.272510i
$409$	−18.4949	−	4.22135i	−0.914515	−	0.208732i	−0.260730	−	0.965412i	$-0.583963\pi$
$409$	−18.4949	−	4.22135i	−0.914515	−	0.208732i	−0.653786	+	0.756680i	$0.726820\pi$
$410$	−2.40955	−	10.5569i	−0.118999	−	0.521370i
$411$	−18.0629	+	22.6501i	−0.890975	+	1.11725i
$412$	11.5254	+	14.4524i	0.567815	+	0.712017i
$413$	−2.30157	+	10.0838i	−0.113253	+	0.496192i
$414$	−10.8343	+	22.4977i	−0.532478	+	1.10570i
$415$	−6.89859	−	3.32218i	−0.338638	−	0.163080i
$416$	−5.91885	+	1.35094i	−0.290196	+	0.0662353i
$417$	14.6648	+	30.4518i	0.718140	+	1.49123i
$418$			6.00000i			0.293470i
$419$	−8.57247	+	4.12828i	−0.418792	+	0.201680i	−0.631399	−	0.775458i	$-0.717519\pi$
$419$	−8.57247	+	4.12828i	−0.418792	+	0.201680i	0.212607	+	0.977138i	$0.431805\pi$
$420$	20.4387	−	16.2994i	0.997309	−	0.795327i
$421$	−29.0159	+	23.1394i	−1.41415	+	1.12774i	−0.441015	+	0.897500i	$0.645381\pi$
$421$	−29.0159	+	23.1394i	−1.41415	+	1.12774i	−0.973133	+	0.230245i	$0.926047\pi$
$422$	−42.1644	+	20.3053i	−2.05253	+	0.988448i
$423$			9.17157i			0.445937i
$424$	18.1667	+	37.7236i	0.882255	+	1.83202i
$425$	3.23063	−	0.737370i	0.156708	−	0.0357677i
$426$	−46.3601	−	22.3259i	−2.24615	−	1.08169i
$427$	−5.92549	+	12.3044i	−0.286754	+	0.595452i
$428$	−12.6324	+	55.3462i	−0.610611	+	2.67526i
$429$	2.38699	+	2.99318i	0.115245	+	0.144512i
$430$	5.39746	−	6.76820i	0.260289	−	0.326392i
$431$	−4.37406	−	19.1640i	−0.210691	−	0.923098i	−0.964099	−	0.265544i	$-0.914448\pi$
$431$	−4.37406	−	19.1640i	−0.210691	−	0.923098i	0.753408	−	0.657554i	$-0.228409\pi$
$432$	1.21149	+	0.276514i	0.0582876	+	0.0133038i
$433$	23.9455	+	19.0959i	1.15075	+	0.917690i	0.997512	−	0.0705003i	$-0.0224596\pi$
$433$	23.9455	+	19.0959i	1.15075	+	0.917690i	0.153235	+	0.988190i	$0.451031\pi$
$434$	−68.7696			−3.30104
$435$		0			0
$436$	48.4558			2.32061
$437$	−17.1543	−	13.6801i	−0.820600	−	0.654406i
$438$	−22.7292	−	5.18779i	−1.08604	−	0.247882i
$439$	−0.0763571	−	0.334542i	−0.00364433	−	0.0159668i	0.973073	−	0.230497i	$-0.0740352\pi$
$439$	−0.0763571	−	0.334542i	−0.00364433	−	0.0159668i	−0.976717	+	0.214530i	$0.931178\pi$
$440$	1.14001	−	1.42952i	0.0543476	−	0.0681498i
$441$	−1.76350	−	2.21135i	−0.0839760	−	0.105303i
$442$	−1.70381	+	7.46488i	−0.0810420	+	0.355068i
$443$	−10.5621	+	21.9324i	−0.501820	+	1.04204i	0.484129	+	0.874997i	$0.339136\pi$
$443$	−10.5621	+	21.9324i	−0.501820	+	1.04204i	−0.985949	+	0.167044i	$0.946578\pi$
$444$	−33.3093	−	16.0409i	−1.58079	−	0.761269i
$445$	12.1722	−	2.77824i	0.577020	−	0.131701i
$446$	3.32218	+	6.89859i	0.157310	+	0.326658i
$447$		−	18.8995i		−	0.893915i
$448$	25.0460	−	12.0615i	1.18331	−	0.569854i
$449$	−27.3411	+	21.8038i	−1.29031	+	1.02898i	−0.292964	+	0.956124i	$0.594641\pi$
$449$	−27.3411	+	21.8038i	−1.29031	+	1.02898i	−0.997342	+	0.0728608i	$0.976787\pi$
$450$	−21.3547	+	17.0298i	−1.00667	+	0.802793i
$451$	−1.67388	+	0.806097i	−0.0788198	+	0.0379576i
$452$			50.9706i			2.39745i
$453$	14.8137	+	30.7610i	0.696009	+	1.44528i
$454$	−19.1640	+	4.37406i	−0.899412	+	0.205285i
$455$	9.75608	+	4.69828i	0.457372	+	0.220259i
$456$	27.7430	−	57.6090i	1.29919	−	2.69779i
$457$	0.229071	−	1.00363i	0.0107155	−	0.0469477i	−0.969288	−	0.245930i	$-0.920907\pi$
$457$	0.229071	−	1.00363i	0.0107155	−	0.0469477i	0.980003	+	0.198983i	$0.0637637\pi$
$458$	5.29049	+	6.63406i	0.247208	+	0.309989i
$459$	−0.213948	+	0.268282i	−0.00998623	+	0.0125223i
$460$	3.11529	+	13.6490i	0.145251	+	0.636387i
$461$	−13.6490	−	3.11529i	−0.635697	−	0.145094i	−0.107486	−	0.994207i	$-0.534280\pi$
$461$	−13.6490	−	3.11529i	−0.635697	−	0.145094i	−0.528211	+	0.849113i	$0.677137\pi$
$462$	−5.33868	−	4.25745i	−0.248378	−	0.198075i
$463$	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
$465$	−24.3137			−1.12752
$466$	34.5673	+	27.5665i	1.60130	+	1.27699i
$467$	−37.3937	−	8.53487i	−1.73037	−	0.394946i	−0.762620	−	0.646846i	$-0.776087\pi$
$467$	−37.3937	−	8.53487i	−1.73037	−	0.394946i	−0.967753	+	0.251900i	$0.918945\pi$
$468$	−9.22479	−	40.4165i	−0.426416	−	1.86825i
$469$	9.97584	−	12.5093i	0.460641	−	0.577626i
$470$	4.88094	+	6.12051i	0.225141	+	0.282318i
$471$	−4.55840	+	19.9717i	−0.210040	+	0.920246i
$472$	7.00381	−	14.5436i	0.322376	−	0.669422i
$473$	−1.33819	−	0.644439i	−0.0615301	−	0.0296314i
$474$	13.7183	−	3.13111i	0.630101	−	0.143817i
$475$	−10.4132	−	21.6233i	−0.477791	−	0.992143i
$476$		−	8.97056i		−	0.411165i
$477$	24.1716	−	11.6404i	1.10674	−	0.532978i
$478$	37.1025	−	29.5882i	1.69703	−	1.35333i
$479$	−5.39424	+	4.30176i	−0.246469	+	0.196553i	−0.738930	−	0.673782i	$-0.764669\pi$
$479$	−5.39424	+	4.30176i	−0.246469	+	0.196553i	0.492461	+	0.870334i	$0.336097\pi$
$480$	3.44929	−	1.66109i	0.157438	−	0.0758181i
$481$		−	15.3137i		−	0.698245i
$482$	−19.1834	−	39.8347i	−0.873779	−	1.81442i
$483$	24.3445	−	5.55647i	1.10771	−	0.252828i
$484$	37.3504	+	17.9870i	1.69775	+	0.817592i
$485$	1.94609	−	4.04110i	0.0883674	−	0.183497i
$486$	11.6343	−	50.9734i	0.527745	−	2.31220i
$487$	−7.17931	−	9.00257i	−0.325326	−	0.407945i	0.592093	−	0.805870i	$-0.298302\pi$
$487$	−7.17931	−	9.00257i	−0.325326	−	0.407945i	−0.917418	+	0.397925i	$0.869731\pi$
$488$	13.2889	−	16.6637i	0.601559	−	0.754332i
$489$	−2.11067	−	9.24747i	−0.0954480	−	0.418185i
$490$	−2.35368	−	0.537213i	−0.106329	−	0.0242688i
$491$	−16.6082	−	13.2446i	−0.749516	−	0.597719i	0.172437	−	0.985021i	$-0.444836\pi$
$491$	−16.6082	−	13.2446i	−0.749516	−	0.597719i	−0.921953	+	0.387301i	$0.873407\pi$
$492$	41.4558			1.86897
$493$		0			0
$494$	55.4558			2.49508
$495$	−0.915973	−	0.730464i	−0.0411699	−	0.0328319i
$496$	29.4557	+	6.72307i	1.32260	+	0.301875i
$497$	5.55647	+	24.3445i	0.249242	+	1.09200i
$498$	27.8247	−	34.8911i	1.24686	−	1.56351i
$499$	−11.8280	−	14.8318i	−0.529492	−	0.663962i	0.443102	−	0.896471i	$-0.353878\pi$
$499$	−11.8280	−	14.8318i	−0.529492	−	0.663962i	−0.972594	+	0.232509i	$0.925306\pi$
$500$	−7.66715	+	33.5920i	−0.342885	+	1.50228i
$501$	−3.32218	+	6.89859i	−0.148424	+	0.308206i
$502$	−43.6572	−	21.0242i	−1.94852	−	0.938356i
$503$	0.265256	−	0.0605430i	0.0118272	−	0.00269948i	−0.216603	−	0.976260i	$-0.569498\pi$
$503$	0.265256	−	0.0605430i	0.0118272	−	0.00269948i	0.228430	+	0.973560i	$0.426641\pi$
$504$	15.3220	+	31.8166i	0.682498	+	1.41722i
$505$			2.34315i			0.104269i
$506$	3.29471	−	1.58665i	0.146468	−	0.0705352i
$507$	3.12733	−	2.49396i	0.138889	−	0.110761i
$508$	12.9998	−	10.3670i	0.576775	−	0.459962i
$509$	9.47343	−	4.56217i	0.419903	−	0.202214i	−0.211988	−	0.977272i	$-0.567994\pi$
$509$	9.47343	−	4.56217i	0.419903	−	0.202214i	0.631890	+	0.775058i	$0.282279\pi$
$510$		−	4.82843i		−	0.213806i
$511$	4.90883	+	10.1933i	0.217154	+	0.450925i
$512$	−30.4593	+	6.95214i	−1.34612	+	0.307244i
$513$	2.23916	+	1.07832i	0.0988614	+	0.0476091i
$514$	−19.0345	+	39.5256i	−0.839576	+	1.74340i
$515$	1.07443	−	4.70737i	0.0473449	−	0.207431i
$516$	20.6638	+	25.9116i	0.909672	+	1.14069i
$517$	0.837438	−	1.05011i	0.0368305	−	0.0461839i
$518$	6.07787	+	26.6289i	0.267046	+	1.17001i
$519$	−29.0519	−	6.63090i	−1.27524	−	0.291064i
$520$	−13.2126	−	10.5367i	−0.579409	−	0.462063i
$521$	29.1421			1.27674			0.638370	−	0.769730i	$-0.279609\pi$
$521$	29.1421			1.27674			0.638370	+	0.769730i	$0.279609\pi$
$522$		0			0
$523$	4.68629			0.204917			0.102459	−	0.994737i	$-0.467329\pi$
$523$	4.68629			0.204917			0.102459	+	0.994737i	$0.467329\pi$
$524$	−63.7959	−	50.8755i	−2.78694	−	2.22251i
$525$	26.6289	+	6.07787i	1.16218	+	0.265260i
$526$	−1.48129	−	6.48995i	−0.0645873	−	0.282975i
$527$	−5.20187	+	6.52293i	−0.226597	+	0.284143i
$528$	1.87047	+	2.34549i	0.0814017	+	0.102075i
$529$	2.14230	−	9.38604i	0.0931436	−	0.408089i
$530$	9.93572	−	20.6317i	0.431580	−	0.896185i
$531$	−9.31885	−	4.48772i	−0.404404	−	0.194751i
$532$	−63.3416	+	14.4573i	−2.74621	+	0.626804i
$533$	7.45047	+	15.4711i	0.322716	+	0.670126i
$534$			72.7696i			3.14905i
$535$	13.3600	−	6.43381i	0.577601	−	0.278158i
$536$	−19.5228	+	15.5689i	−0.843255	+	0.672474i
$537$	12.2410	−	9.76189i	0.528239	−	0.421257i
$538$	68.4206	−	32.9496i	2.94982	−	1.42056i
$539$			0.414214i			0.0178414i
$540$	−0.688047	−	1.42874i	−0.0296088	−	0.0614834i
$541$	10.0838	−	2.30157i	0.433537	−	0.0989521i	−0.000182215	−	1.00000i	$-0.500058\pi$
$541$	10.0838	−	2.30157i	0.433537	−	0.0989521i	0.433720	+	0.901048i	$0.357201\pi$
$542$	36.0122	+	17.3426i	1.54686	+	0.744927i
$543$	−8.70851	+	18.0834i	−0.373718	+	0.776033i
$544$	0.292328	−	1.28077i	0.0125334	−	0.0549126i
$545$	−7.89142	−	9.89553i	−0.338031	−	0.423878i
$546$	−39.3501	+	49.3435i	−1.68403	+	2.11171i
$547$	−7.96602	−	34.9014i	−0.340603	−	1.49228i	−0.797805	−	0.602915i	$-0.794006\pi$
$547$	−7.96602	−	34.9014i	−0.340603	−	1.49228i	0.457203	−	0.889362i	$-0.348851\pi$
$548$	−44.7893	−	10.2229i	−1.91330	−	0.436699i
$549$	−10.6774	−	8.51491i	−0.455699	−	0.363407i
$550$	4.00000			0.170561
$551$		0			0
$552$	−38.9706			−1.65870
$553$	−5.33868	−	4.25745i	−0.227024	−	0.181045i
$554$	40.7510	+	9.30115i	1.73134	+	0.395168i
$555$	2.14885	+	9.41474i	0.0912137	+	0.399633i
$556$	−33.4178	+	41.9046i	−1.41723	+	1.77715i
$557$	10.7949	+	13.5364i	0.457395	+	0.573556i	0.956035	−	0.293254i	$-0.0947381\pi$
$557$	10.7949	+	13.5364i	0.457395	+	0.573556i	−0.498639	+	0.866810i	$0.666167\pi$
$558$	15.3027	−	67.0454i	0.647813	−	2.83826i
$559$	−5.95632	+	12.3684i	−0.251926	+	0.523129i
$560$	7.64497	+	3.68163i	0.323059	+	0.155577i
$561$	−0.807657	+	0.184342i	−0.0340993	+	0.00778294i
$562$	−33.4888	−	69.5402i	−1.41264	−	2.93338i
$563$		−	0.757359i		−	0.0319189i	−0.999873	−	0.0159594i	$-0.994920\pi$
$563$		−	0.757359i		−	0.0319189i	0.999873	−	0.0159594i	$-0.00508026\pi$
$564$	−27.0025	+	13.0037i	−1.13701	+	0.547556i
$565$	10.4091	−	8.30096i	0.437913	−	0.349224i
$566$	22.0024	−	17.5463i	0.924830	−	0.737527i
$567$	−24.1716	+	11.6404i	−1.01511	+	0.488852i
$568$		−	38.9706i		−	1.63517i
$569$	17.2065	+	35.7296i	0.721333	+	1.49786i	0.861513	+	0.507736i	$0.169518\pi$
$569$	17.2065	+	35.7296i	0.721333	+	1.49786i	−0.140180	+	0.990126i	$0.544768\pi$
$570$	−34.0938	+	7.78168i	−1.42803	+	0.325939i
$571$	−13.1788	−	6.34660i	−0.551518	−	0.265597i	0.137303	−	0.990529i	$-0.456157\pi$
$571$	−13.1788	−	6.34660i	−0.551518	−	0.265597i	−0.688820	+	0.724932i	$0.741871\pi$
$572$	−2.63414	+	5.46984i	−0.110139	+	0.228706i
$573$	13.5989	−	59.5805i	0.568100	−	2.48901i
$574$	−19.0959	−	23.9455i	−0.797047	−	0.999465i
$575$	−9.12005	+	11.4362i	−0.380332	+	0.476921i
$576$	6.18586	+	27.1020i	0.257744	+	1.12925i
$577$	29.0519	+	6.63090i	1.20945	+	0.276048i	0.779265	−	0.626695i	$-0.215593\pi$
$577$	29.0519	+	6.63090i	1.20945	+	0.276048i	0.430180	+	0.902743i	$0.358450\pi$
$578$	30.7923	+	24.5560i	1.28079	+	1.02140i
$579$	12.4853			0.518871
$580$		0			0
$581$	−21.6569			−0.898478
$582$	20.4387	+	16.2994i	0.847213	+	0.675630i
$583$	−3.83043	−	0.874270i	−0.158640	−	0.0362085i
$584$	−3.92902	−	17.2142i	−0.162584	−	0.712327i
$585$	−6.75141	+	8.46601i	−0.279137	+	0.350026i
$586$	11.5254	+	14.4524i	0.476109	+	0.597022i
$587$	−1.70381	+	7.46488i	−0.0703238	+	0.308109i	−0.997841	−	0.0656710i	$-0.979081\pi$
$587$	−1.70381	+	7.46488i	−0.0703238	+	0.308109i	0.927518	+	0.373780i	$0.121938\pi$
$588$	4.01023	−	8.32733i	0.165379	−	0.343413i
$589$	54.4423	+	26.2180i	2.24326	+	1.08030i
$590$	−8.60708	+	1.96451i	−0.354348	+	0.0808776i
$591$	2.09498	+	4.35026i	0.0861758	+	0.178946i
$592$		−	12.0000i		−	0.493197i
$593$	−17.5556	+	8.45435i	−0.720923	+	0.347178i	−0.758107	−	0.652130i	$-0.773876\pi$
$593$	−17.5556	+	8.45435i	−0.720923	+	0.347178i	0.0371837	+	0.999308i	$0.488161\pi$
$594$	−0.323845	+	0.258258i	−0.0132875	+	0.0105965i
$595$	−1.83195	+	1.46093i	−0.0751024	+	0.0598922i
$596$	27.0025	−	13.0037i	1.10607	−	0.532654i
$597$			1.17157i			0.0479493i
$598$	−14.6648	−	30.4518i	−0.599690	−	1.24527i
$599$	−9.62259	+	2.19629i	−0.393169	+	0.0897382i	−0.414535	−	0.910034i	$-0.636056\pi$
$599$	−9.62259	+	2.19629i	−0.393169	+	0.0897382i	0.0213660	+	0.999772i	$0.493198\pi$
$600$	−38.4060	−	18.4953i	−1.56792	−	0.755069i
$601$	7.45047	−	15.4711i	0.303911	−	0.631077i	−0.691952	−	0.721943i	$-0.743249\pi$
$601$	7.45047	−	15.4711i	0.303911	−	0.631077i	0.995863	+	0.0908658i	$0.0289634\pi$
$602$	5.44849	−	23.8714i	0.222064	−	0.972925i
$603$	9.97584	+	12.5093i	0.406247	+	0.509418i
$604$	−33.7571	+	42.3300i	−1.37356	+	1.72238i
$605$	−2.40955	−	10.5569i	−0.0979622	−	0.429200i
$606$	−13.3144	−	3.03894i	−0.540862	−	0.123448i
$607$	−6.04193	−	4.81828i	−0.245234	−	0.195568i	0.493157	−	0.869940i	$-0.335843\pi$
$607$	−6.04193	−	4.81828i	−0.245234	−	0.195568i	−0.738391	+	0.674372i	$0.764414\pi$
$608$	−9.51472			−0.385873
$609$		0			0
$610$	−11.6569			−0.471972
$611$	−9.70582	−	7.74014i	−0.392656	−	0.313132i
$612$	8.74565	+	1.99614i	0.353522	+	0.0806891i
$613$	−2.00269	−	8.77435i	−0.0808878	−	0.354393i	0.918246	−	0.396011i	$-0.129606\pi$
$613$	−2.00269	−	8.77435i	−0.0808878	−	0.354393i	−0.999134	+	0.0416183i	$0.986749\pi$
$614$	4.36443	−	5.47282i	0.176134	−	0.220865i
$615$	−6.75141	−	8.46601i	−0.272243	−	0.341382i
$616$	1.15078	−	5.04191i	0.0463664	−	0.203144i
$617$	0.297771	−	0.618327i	0.0119878	−	0.0248929i	−0.894889	−	0.446289i	$-0.852745\pi$
$617$	0.297771	−	0.618327i	0.0119878	−	0.0248929i	0.906877	+	0.421396i	$0.138460\pi$
$618$	25.3552	+	12.2104i	1.01994	+	0.491175i
$619$	32.7437	−	7.47354i	1.31608	−	0.300387i	0.493853	−	0.869545i	$-0.335588\pi$
$619$	32.7437	−	7.47354i	1.31608	−	0.300387i	0.822228	+	0.569158i	$0.192731\pi$
$620$	−16.7290	−	34.7381i	−0.671852	−	1.39511i
$621$		−	1.51472i		−	0.0607836i
$622$	−5.84304	+	2.81386i	−0.234284	+	0.112825i
$623$	27.6094	−	22.0177i	1.10615	−	0.882122i
$624$	21.6786	−	17.2881i	0.867837	−	0.692077i
$625$	−9.91066	+	4.77272i	−0.396426	+	0.190909i
$626$			23.7279i			0.948358i
$627$	2.60330	+	5.40581i	0.103966	+	0.215887i
$628$	−31.6708	+	7.22866i	−1.26380	+	0.288455i
$629$	2.98555	+	1.43776i	0.119042	+	0.0573274i
$630$	8.37990	−	17.4011i	0.333863	−	0.693274i
$631$	−8.19510	+	35.9051i	−0.326242	+	1.42936i	0.499992	+	0.866030i	$0.333336\pi$
$631$	−8.19510	+	35.9051i	−0.326242	+	1.42936i	−0.826233	+	0.563328i	$0.809521\pi$
$632$	6.64444	+	8.33186i	0.264302	+	0.331424i
$633$	−29.1787	+	36.5889i	−1.15975	+	1.45428i
$634$	−16.8985	−	74.0371i	−0.671125	−	2.94039i
$635$	−4.23425	−	0.966441i	−0.168031	−	0.0383520i
$636$	68.5424	+	54.6608i	2.71788	+	2.16744i
$637$	3.82843			0.151688
$638$		0			0
$639$	−24.9706			−0.987820
$640$	16.0716	+	12.8167i	0.635286	+	0.506624i
$641$	17.3527	+	3.96065i	0.685392	+	0.156436i	0.551017	−	0.834494i	$-0.314240\pi$
$641$	17.3527	+	3.96065i	0.685392	+	0.156436i	0.134375	+	0.990931i	$0.457097\pi$
$642$	19.2317	+	84.2595i	0.759014	+	3.32546i
$643$	−20.2542	+	25.3980i	−0.798749	+	1.00160i	0.201008	+	0.979590i	$0.435578\pi$
$643$	−20.2542	+	25.3980i	−0.798749	+	1.00160i	−0.999758	+	0.0220105i	$0.992993\pi$
$644$	24.6889	+	30.9589i	0.972880	+	1.21995i
$645$	1.92633	−	8.43981i	0.0758492	−	0.332317i
$646$	−5.20660	+	10.8116i	−0.204851	+	0.425378i
$647$	35.7296	+	17.2065i	1.40468	+	0.676456i	0.974104	−	0.226101i	$-0.0725978\pi$
$647$	35.7296	+	17.2065i	1.40468	+	0.676456i	0.430571	+	0.902557i	$0.358312\pi$
$648$	40.8203	−	9.31696i	1.60357	−	0.366005i
$649$	0.657212	+	1.36471i	0.0257978	+	0.0535697i
$650$		−	36.9706i		−	1.45010i
$651$	−61.9592	+	29.8380i	−2.42837	+	1.16944i
$652$	11.7600	−	9.37830i	0.460558	−	0.367283i
$653$	23.5661	−	18.7933i	0.922212	−	0.735439i	−0.0424037	−	0.999101i	$-0.513502\pi$
$653$	23.5661	−	18.7933i	0.922212	−	0.735439i	0.964615	+	0.263661i	$0.0849301\pi$
$654$	66.4641	−	32.0074i	2.59895	−	1.25159i
$655$			21.3137i			0.832796i
$656$	5.83827	+	12.1233i	0.227946	+	0.473335i
$657$	−11.0301	+	2.51754i	−0.430323	+	0.0982185i
$658$	19.9494	+	9.60711i	0.777708	+	0.374524i
$659$	−6.25409	+	12.9868i	−0.243625	+	0.505892i	−0.986545	−	0.163487i	$-0.947726\pi$
$659$	−6.25409	+	12.9868i	−0.243625	+	0.505892i	0.742921	+	0.669380i	$0.233440\pi$
$660$	0.851905	−	3.73244i	0.0331604	−	0.145285i
$661$	20.7708	+	26.0457i	0.807889	+	1.01306i	0.999501	+	0.0315898i	$0.0100570\pi$
$661$	20.7708	+	26.0457i	0.807889	+	1.01306i	−0.191612	+	0.981471i	$0.561372\pi$
$662$	3.63396	−	4.55685i	0.141238	−	0.177107i
$663$	1.70381	+	7.46488i	0.0661705	+	0.289912i
$664$	32.9516	+	7.52098i	1.27877	+	0.291871i
$665$	13.2681	+	10.5810i	0.514516	+	0.410313i
$666$	−27.3137			−1.05838
$667$		0			0
$668$	−12.1421			−0.469793
$669$	5.98637	+	4.77397i	0.231446	+	0.184572i
$670$	13.3144	+	3.03894i	0.514382	+	0.117404i
$671$	0.445042	+	1.94986i	0.0171807	+	0.0752733i
$672$	6.75141	−	8.46601i	0.260441	−	0.326583i
$673$	13.4845	+	16.9090i	0.519788	+	0.651794i	0.970564	−	0.240843i	$-0.0774240\pi$
$673$	13.4845	+	16.9090i	0.519788	+	0.651794i	−0.450776	+	0.892637i	$0.648853\pi$
$674$	11.7107	−	51.3079i	0.451079	−	1.97631i
$675$	0.718882	−	1.49277i	0.0276698	−	0.0574569i
$676$	5.71498	+	2.75219i	0.219807	+	0.105853i
$677$	−21.4484	+	4.89546i	−0.824330	+	0.188148i	−0.613822	−	0.789444i	$-0.710369\pi$
$677$	−21.4484	+	4.89546i	−0.824330	+	0.188148i	−0.210507	+	0.977592i	$0.567512\pi$
$678$	33.6685	+	69.9134i	1.29303	+	2.68501i
$679$		−	12.6863i		−	0.486855i
$680$	3.29471	−	1.58665i	0.126346	−	0.0608452i
$681$	−15.3683	+	12.2558i	−0.588916	+	0.469645i
$682$	−7.87388	+	6.27921i	−0.301506	+	0.240443i
$683$	−18.8938	+	9.09879i	−0.722952	+	0.348155i	−0.758908	−	0.651198i	$-0.774267\pi$
$683$	−18.8938	+	9.09879i	−0.722952	+	0.348155i	0.0359558	+	0.999353i	$0.488552\pi$
$684$		−	64.9706i		−	2.48421i
$685$	5.20660	+	10.8116i	0.198934	+	0.413091i
$686$	39.9433	−	9.11681i	1.52504	−	0.348081i
$687$	7.64497	+	3.68163i	0.291674	+	0.140463i
$688$	−4.66744	+	9.69205i	−0.177945	+	0.369506i
$689$	−8.08056	+	35.4032i	−0.307845	+	1.34876i
$690$	13.2889	+	16.6637i	0.505899	+	0.634377i
$691$	29.9275	−	37.5279i	1.13850	−	1.42763i	0.250298	−	0.968169i	$-0.419471\pi$
$691$	29.9275	−	37.5279i	1.13850	−	1.42763i	0.888198	−	0.459460i	$-0.151957\pi$
$692$	−10.5152	−	46.0701i	−0.399728	−	1.75132i
$693$	−3.23063	−	0.737370i	−0.122721	−	0.0280104i
$694$	−4.69099	−	3.74094i	−0.178068	−	0.142004i
$695$	14.0000			0.531050
$696$		0			0
$697$	−3.71573			−0.140743
$698$	−9.70582	−	7.74014i	−0.367371	−	0.292968i
$699$	43.1047	+	9.83836i	1.63037	+	0.372121i
$700$	9.63821	+	42.2277i	0.364290	+	1.59606i
$701$	25.0099	−	31.3614i	0.944609	−	1.18450i	−0.0380862	−	0.999274i	$-0.512126\pi$
$701$	25.0099	−	31.3614i	0.944609	−	1.18450i	0.982696	−	0.185228i	$-0.0593024\pi$
$702$	2.38699	+	2.99318i	0.0900910	+	0.112970i
$703$	5.34050	−	23.3983i	0.201421	−	0.882482i
$704$	1.76637	−	3.66791i	0.0665726	−	0.138239i
$705$	7.05317	+	3.39663i	0.265638	+	0.127924i
$706$	−63.4802	+	14.4889i	−2.38911	+	0.545298i
$707$	2.87553	+	5.97110i	0.108145	+	0.224566i
$708$		−	33.7990i		−	1.27024i
$709$	26.2562	−	12.6443i	0.986071	−	0.474867i	0.129882	−	0.991529i	$-0.458540\pi$
$709$	26.2562	−	12.6443i	0.986071	−	0.474867i	0.856189	+	0.516663i	$0.172826\pi$
$710$	−16.6637	+	13.2889i	−0.625379	+	0.498723i
$711$	5.33868	−	4.25745i	0.200216	−	0.159667i
$712$	−49.6548	+	23.9125i	−1.86089	+	0.896159i
$713$		−	36.8284i		−	1.37924i
$714$	−5.92549	−	12.3044i	−0.221756	−	0.460481i
$715$	1.54603	−	0.352871i	0.0578181	−	0.0131966i
$716$	22.3696	+	10.7727i	0.835993	+	0.402593i
$717$	20.5903	−	42.7562i	0.768960	−	1.59676i
$718$	−2.11067	+	9.24747i	−0.0787696	+	0.345112i
$719$	−12.5584	−	15.7478i	−0.468350	−	0.587292i	0.490416	−	0.871488i	$-0.336845\pi$
$719$	−12.5584	−	15.7478i	−0.468350	−	0.587292i	−0.958766	+	0.284196i	$0.908273\pi$
$720$	−5.29049	+	6.63406i	−0.197165	+	0.247237i
$721$	−3.03894	−	13.3144i	−0.113176	−	0.495856i
$722$	40.0126	+	9.13262i	1.48912	+	0.339881i
$723$	−34.5673	−	27.5665i	−1.28557	−	1.02521i
$724$	−31.8284			−1.18289
$725$		0			0
$726$	63.1127			2.34233
$727$	−1.02710	−	0.819084i	−0.0380930	−	0.0303781i	0.604258	−	0.796789i	$-0.293470\pi$
$727$	−1.02710	−	0.819084i	−0.0380930	−	0.0303781i	−0.642351	+	0.766410i	$0.722041\pi$
$728$	−46.6006	−	10.6363i	−1.72713	−	0.394207i
$729$	−5.30232	−	23.2310i	−0.196382	−	0.860407i
$730$	−6.02095	+	7.55003i	−0.222845	+	0.279439i
$731$	−1.85212	−	2.32248i	−0.0685030	−	0.0859000i
$732$	9.93053	−	43.5085i	0.367043	−	1.60812i
$733$	−17.8998	+	37.1693i	−0.661144	+	1.37288i	0.252990	+	0.967469i	$0.418586\pi$
$733$	−17.8998	+	37.1693i	−0.661144	+	1.37288i	−0.914134	+	0.405411i	$0.867128\pi$
$734$	−39.1524	−	18.8548i	−1.44514	−	0.695943i
$735$	−2.35368	+	0.537213i	−0.0868169	+	0.0198154i
$736$	2.51609	+	5.22471i	0.0927442	+	0.192585i
$737$		−	2.34315i		−	0.0863109i
$738$	27.5943	−	13.2887i	1.01576	−	0.489165i
$739$	3.18289	−	2.53827i	0.117084	−	0.0933717i	−0.563197	−	0.826323i	$-0.690429\pi$
$739$	3.18289	−	2.53827i	0.117084	−	0.0933717i	0.680282	+	0.732951i	$0.261857\pi$
$740$	−11.9727	+	9.54794i	−0.440127	+	0.350989i
$741$	49.9640	−	24.0614i	1.83547	−	0.883917i
$742$		−	64.7696i		−	2.37777i
$743$	−10.2643	−	21.3141i	−0.376562	−	0.781938i	−1.00000		6.56698e-5i	$-0.999979\pi$
$743$	−10.2643	−	21.3141i	−0.376562	−	0.781938i	0.623438	−	0.781872i	$-0.285735\pi$
$744$	104.635	−	23.8823i	3.83611	−	0.875566i
$745$	−7.05317	−	3.39663i	−0.258408	−	0.124443i
$746$	−27.5633	+	57.2358i	−1.00916	+	2.09555i
$747$	4.81910	−	21.1139i	0.176322	−	0.772516i
$748$	−0.819084	−	1.02710i	−0.0299487	−	0.0375544i
$749$	26.1499	−	32.7909i	0.955495	−	1.19815i
$750$	11.6725	+	51.1407i	0.426220	+	1.86739i
$751$	−24.6790	−	5.63283i	−0.900551	−	0.205545i	−0.252909	−	0.967490i	$-0.581387\pi$
$751$	−24.6790	−	5.63283i	−0.900551	−	0.205545i	−0.647642	+	0.761945i	$0.724245\pi$
$752$	−7.60560	−	6.06526i	−0.277348	−	0.221177i
$753$	−48.4558			−1.76583
$754$		0			0
$755$	14.1421			0.514685
$756$	−3.50673	−	2.79653i	−0.127539	−	0.101709i
$757$	24.8750	+	5.67756i	0.904098	+	0.206354i	0.649204	−	0.760615i	$-0.275102\pi$
$757$	24.8750	+	5.67756i	0.904098	+	0.206354i	0.254894	+	0.966969i	$0.417959\pi$
$758$	3.74468	+	16.4065i	0.136013	+	0.595911i
$759$	2.28001	−	2.85904i	0.0827592	−	0.103777i
$760$	−16.5133	−	20.7070i	−0.599000	−	0.751123i
$761$	−10.1465	+	44.4547i	−0.367811	+	1.61148i	0.364971	+	0.931019i	$0.381079\pi$
$761$	−10.1465	+	44.4547i	−0.367811	+	1.61148i	−0.732781	+	0.680464i	$0.761778\pi$
$762$	10.9832	−	22.8069i	0.397880	−	0.826205i
$763$	−32.2538	−	15.5326i	−1.16767	−	0.562318i
$764$	94.4819	−	21.5649i	3.41824	−	0.780190i
$765$	−1.01665	−	2.11110i	−0.0367572	−	0.0763270i
$766$			8.48528i			0.306586i
$767$	12.6136	−	6.07437i	0.455449	−	0.219333i
$768$	−56.5697	+	45.1128i	−2.04128	+	1.62787i
$769$	38.3979	−	30.6213i	1.38466	−	1.10423i	0.402662	−	0.915349i	$-0.368085\pi$
$769$	38.3979	−	30.6213i	1.38466	−	1.10423i	0.982000	−	0.188883i	$-0.0604865\pi$
$770$	−2.54832	+	1.22721i	−0.0918353	+	0.0442255i
$771$			43.8701i			1.57994i
$772$	8.59046	+	17.8383i	0.309177	+	0.642014i
$773$	19.0254	−	4.34243i	0.684298	−	0.156186i	0.133781	−	0.991011i	$-0.457288\pi$
$773$	19.0254	−	4.34243i	0.684298	−	0.156186i	0.550516	+	0.834824i	$0.314431\pi$
$774$	22.0605	+	10.6238i	0.792947	+	0.381863i
$775$	17.4787	−	36.2949i	0.627853	−	1.30375i
$776$	−4.40569	+	19.3026i	−0.158155	+	0.692923i
$777$	17.0298	+	21.3547i	0.610941	+	0.766096i
$778$	−4.56002	+	5.71809i	−0.163485	+	0.205003i
$779$	5.98841	+	26.2370i	0.214557	+	0.940037i
$780$	−34.4976	−	7.87385i	−1.23521	−	0.281929i
$781$	2.85904	+	2.28001i	0.102305	+	0.0815852i
$782$	7.31371			0.261538
$783$		0			0
$784$	3.00000			0.107143
$785$	6.63406	+	5.29049i	0.236780	+	0.188826i
$786$	−121.111	−	27.6428i	−4.31988	−	0.985984i
$787$	−12.0347	−	52.7273i	−0.428989	−	1.87952i	−0.473977	−	0.880537i	$-0.657182\pi$
$787$	−12.0347	−	52.7273i	−0.428989	−	1.87952i	0.0449881	−	0.998988i	$-0.485675\pi$
$788$	−4.77397	+	5.98637i	−0.170066	+	0.213256i
$789$	−4.15048	−	5.20454i	−0.147761	−	0.185286i
$790$	1.29695	−	5.68230i	0.0461433	−	0.202167i
$791$	16.3387	−	33.9277i	0.580937	−	1.20633i
$792$	4.65943	+	2.24386i	0.165565	+	0.0797321i
$793$	18.0218	−	4.11336i	0.639973	−	0.146070i
$794$	−20.2617	−	42.0739i	−0.719061	−	1.49315i
$795$		−	22.8995i		−	0.812161i
$796$	−1.67388	+	0.806097i	−0.0593290	+	0.0285714i
$797$	40.4521	−	32.2594i	1.43289	−	1.14269i	0.466832	−	0.884346i	$-0.345395\pi$
$797$	40.4521	−	32.2594i	1.43289	−	1.14269i	0.966054	−	0.258342i	$-0.0831760\pi$
$798$	−77.3323	+	61.6704i	−2.73753	+	2.18311i
$799$	2.42027	−	1.16554i	0.0856228	−	0.0412338i
$800$			6.34315i			0.224264i
$801$	15.3220	+	31.8166i	0.541378	+	1.12418i
$802$	−43.9123	+	10.0227i	−1.55060	+	0.353914i
$803$	1.49277	+	0.718882i	0.0526789	+	0.0253688i
$804$	−22.6853	+	47.1065i	−0.800049	+	1.66132i
$805$	2.30157	−	10.0838i	0.0811196	−	0.355408i
$806$	58.0365	+	72.7754i	2.04425	+	2.56340i
$807$	47.3485	−	59.3732i	1.66675	−	2.09003i
$808$	−2.30157	−	10.0838i	−0.0809688	−	0.354748i
$809$	−35.3745	−	8.07401i	−1.24370	−	0.283867i	−0.450473	−	0.892790i	$-0.648745\pi$
$809$	−35.3745	−	8.07401i	−1.24370	−	0.283867i	−0.793230	+	0.608923i	$0.791602\pi$
$810$	−17.9035	−	14.2776i	−0.629066	−	0.501664i
$811$	−10.8284			−0.380238			−0.190119	−	0.981761i	$-0.560887\pi$
$811$	−10.8284			−0.380238			−0.190119	+	0.981761i	$0.560887\pi$
$812$		0			0
$813$	39.9706			1.40183
$814$	3.12733	+	2.49396i	0.109613	+	0.0874132i
$815$	−3.83043	−	0.874270i	−0.134174	−	0.0306243i
$816$	1.33513	+	5.84957i	0.0467387	+	0.204776i
$817$	−13.4142	+	16.8209i	−0.469304	+	0.588488i
$818$	−28.5552	−	35.8071i	−0.998409	−	1.25197i
$819$	−6.81524	+	29.8595i	−0.238144	+	1.04338i
$820$	7.45047	−	15.4711i	0.260182	−	0.540273i
$821$	−1.33819	−	0.644439i	−0.0467032	−	0.0224911i	0.410386	−	0.911912i	$-0.365394\pi$
$821$	−1.33819	−	0.644439i	−0.0467032	−	0.0224911i	−0.457090	+	0.889421i	$0.651108\pi$
$822$	−68.1876	+	15.5634i	−2.37831	+	0.542835i
$823$	−23.5531	−	48.9084i	−0.821008	−	1.70484i	−0.702265	−	0.711916i	$-0.747828\pi$
$823$	−23.5531	−	48.9084i	−0.821008	−	1.70484i	−0.118744	−	0.992925i	$-0.537887\pi$
$824$			21.3137i			0.742498i
$825$	3.60388	−	1.73553i	0.125471	−	0.0604236i
$826$	−19.5228	+	15.5689i	−0.679284	+	0.541711i
$827$	−25.7219	+	20.5125i	−0.894437	+	0.713289i	−0.958632	−	0.284648i	$-0.908123\pi$
$827$	−25.7219	+	20.5125i	−0.894437	+	0.713289i	0.0641954	+	0.997937i	$0.479552\pi$
$828$	−35.6765	+	17.1809i	−1.23985	+	0.597078i
$829$			29.7990i			1.03496i	0.855695	+	0.517481i	$0.173130\pi$
$829$			29.7990i			1.03496i	−0.855695	+	0.517481i	$0.826870\pi$
$830$	−8.02046	−	16.6547i	−0.278394	−	0.578092i
$831$	40.7510	−	9.30115i	1.41364	−	0.322653i
$832$	−33.9011	−	16.3259i	−1.17531	−	0.566000i
$833$	−0.359441	+	0.746387i	−0.0124539	+	0.0258608i
$834$	−18.1573	+	79.5521i	−0.628734	+	2.75467i
$835$	1.97744	+	2.47964i	0.0684322	+	0.0858113i
$836$	−5.93233	+	7.43891i	−0.205174	+	0.257280i
$837$	0.928262	+	4.06698i	0.0320854	+	0.140575i
$838$	−22.3946	−	5.11143i	−0.773610	−	0.176571i
$839$	−6.19909	−	4.94361i	−0.214016	−	0.170672i	0.510614	−	0.859810i	$-0.329418\pi$
$839$	−6.19909	−	4.94361i	−0.214016	−	0.170672i	−0.724630	+	0.689138i	$0.757990\pi$
$840$	30.1421			1.04000
$841$		0			0
$842$	−89.5980			−3.08775
$843$	−60.3447	−	48.1233i	−2.07838	−	1.65745i
$844$	−72.3525	−	16.5140i	−2.49048	−	0.568435i
$845$	−0.368685	−	1.61531i	−0.0126831	−	0.0555685i
$846$	−13.8054	+	17.3114i	−0.474639	+	0.595179i
$847$	−19.0959	−	23.9455i	−0.656142	−	0.822776i
$848$	−6.33202	+	27.7424i	−0.217442	+	0.952678i
$849$	12.2104	−	25.3552i	0.419060	−	0.870188i
$850$	7.20775	+	3.47107i	0.247224	+	0.119057i
$851$	−14.2607	+	3.25491i	−0.488850	+	0.111577i
$852$	−35.4040	−	73.5172i	−1.21292	−	2.51866i
$853$		−	22.9706i		−	0.786497i	−0.919432	−	0.393249i	$-0.871351\pi$
$853$		−	22.9706i		−	0.786497i	0.919432	−	0.393249i	$-0.128649\pi$
$854$	−29.7055	+	14.3054i	−1.01650	+	0.489520i
$855$	−13.2681	+	10.5810i	−0.453760	+	0.361862i
$856$	−51.1754	+	40.8111i	−1.74914	+	1.39489i
$857$	5.56040	−	2.67775i	0.189939	−	0.0914700i	−0.336497	−	0.941685i	$-0.609242\pi$
$857$	5.56040	−	2.67775i	0.189939	−	0.0914700i	0.526436	+	0.850215i	$0.323528\pi$
$858$			9.24264i			0.315539i
$859$	−8.55962	−	17.7742i	−0.292051	−	0.606449i	0.702385	−	0.711797i	$-0.252119\pi$
$859$	−8.55962	−	17.7742i	−0.292051	−	0.606449i	−0.994435	+	0.105348i	$0.966404\pi$
$860$	13.3837	−	3.05475i	0.456382	−	0.104166i
$861$	−27.5943	−	13.2887i	−0.940413	−	0.452879i
$862$	20.5903	−	42.7562i	0.701309	−	1.45628i
$863$	3.80793	−	16.6836i	0.129624	−	0.567918i	−0.867847	−	0.496832i	$-0.834496\pi$
$863$	3.80793	−	16.6836i	0.129624	−	0.567918i	0.997470	−	0.0710858i	$-0.0226464\pi$
$864$	−0.409542	−	0.513549i	−0.0139329	−	0.0174713i
$865$	−7.69583	+	9.65026i	−0.261666	+	0.328119i
$866$	16.4534	+	72.0873i	0.559111	+	2.44963i
$867$	38.3973	+	8.76394i	1.30404	+	0.297639i
$868$	−85.2617	−	67.9939i	−2.89397	−	2.30786i
$869$	−1.00000			−0.0339227
$870$		0			0
$871$	−21.6569			−0.733815
$872$	43.6810	+	34.8344i	1.47922	+	1.17964i
$873$	12.3682	+	2.82297i	0.418601	+	0.0955429i
$874$	−11.7871	−	51.6425i	−0.398703	−	1.74683i
$875$	15.8715	−	19.9022i	0.536553	−	0.672816i
$876$	−23.0508	−	28.9047i	−0.778813	−	0.976601i
$877$	8.26490	−	36.2109i	0.279086	−	1.22276i	−0.619866	−	0.784708i	$-0.712813\pi$
$877$	8.26490	−	36.2109i	0.279086	−	1.22276i	0.898952	−	0.438048i	$-0.144330\pi$
$878$	0.359441	−	0.746387i	0.0121305	−	0.0251893i
$879$	16.6547	+	8.02046i	0.561748	+	0.270524i
$880$	1.21149	−	0.276514i	0.0408392	−	0.00932127i
$881$	6.07437	+	12.6136i	0.204651	+	0.424962i	0.977881	−	0.209164i	$-0.0670743\pi$
$881$	6.07437	+	12.6136i	0.204651	+	0.424962i	−0.773230	+	0.634126i	$0.781360\pi$
$882$		−	6.82843i		−	0.229925i
$883$	34.6210	−	16.6726i	1.16509	−	0.561077i	0.251557	−	0.967843i	$-0.419058\pi$
$883$	34.6210	−	16.6726i	1.16509	−	0.561077i	0.913533	+	0.406765i	$0.133343\pi$
$884$	−9.49310	+	7.57050i	−0.319288	+	0.254623i
$885$	−6.90234	+	5.50443i	−0.232020	+	0.185030i
$886$	−52.9495	+	25.4992i	−1.77887	+	0.856661i
$887$		−	17.1005i		−	0.574179i	−0.957904	−	0.287089i	$-0.907312\pi$
$887$		−	17.1005i		−	0.574179i	0.957904	−	0.287089i	$-0.0926877\pi$
$888$	−18.4953	−	38.4060i	−0.620663	−	1.28882i
$889$	−11.9763	+	2.73351i	−0.401672	+	0.0916789i
$890$	27.1571	+	13.0782i	0.910309	+	0.438382i
$891$	−1.70470	+	3.53985i	−0.0571096	+	0.118589i
$892$	−2.70188	+	11.8377i	−0.0904656	+	0.396356i
$893$	−12.1305	−	15.2112i	−0.405932	−	0.509023i
$894$	28.4482	−	35.6730i	0.951451	−	1.19308i
$895$	−1.44311	−	6.32268i	−0.0482379	−	0.211344i
$896$	56.6844	+	12.9378i	1.89369	+	0.432223i
$897$	−26.4251	−	21.0733i	−0.882309	−	0.703618i
$898$	−84.4264			−2.81735
$899$		0			0
$900$	−43.3137			−1.44379
$901$	−6.14353	−	4.89930i	−0.204671	−	0.163219i
$902$	−4.37283	−	0.998069i	−0.145599	−	0.0332321i
$903$	−5.44849	−	23.8714i	−0.181314	−	0.794390i
$904$	−36.6422	+	45.9479i	−1.21870	+	1.52820i
$905$	5.18351	+	6.49992i	0.172306	+	0.216065i
$906$	−18.3416	+	80.3598i	−0.609359	+	2.66978i
$907$	9.66878	−	20.0774i	0.321047	−	0.666660i	−0.676517	−	0.736427i	$-0.736511\pi$
$907$	9.66878	−	20.0774i	0.321047	−	0.666660i	0.997563	+	0.0697671i	$0.0222256\pi$
$908$	−28.0846	−	13.5248i	−0.932021	−	0.448838i
$909$	−6.46125	+	1.47474i	−0.214306	+	0.0489140i
$910$	11.3426	+	23.5533i	0.376005	+	0.780783i
$911$		−	15.4437i		−	0.511671i	−0.966720	−	0.255835i	$-0.917649\pi$
$911$		−	15.4437i		−	0.511671i	0.966720	−	0.255835i	$-0.0823505\pi$
$912$	39.1524	−	18.8548i	1.29646	−	0.624344i
$913$	−2.47964	+	1.97744i	−0.0820640	+	0.0654438i
$914$	1.94307	−	1.54955i	0.0642711	−	0.0512545i
$915$	−10.5025	+	5.05772i	−0.347201	+	0.167203i
$916$			13.4558i			0.444594i
$917$	26.1564	+	54.3143i	0.863759	+	1.79361i
$918$	−0.807657	+	0.184342i	−0.0266566	+	0.00608421i
$919$	−7.33581	−	3.53274i	−0.241986	−	0.116534i	0.308960	−	0.951075i	$-0.400019\pi$
$919$	−7.33581	−	3.53274i	−0.241986	−	0.116534i	−0.550947	+	0.834541i	$0.685733\pi$
$920$	−7.00381	+	14.5436i	−0.230909	+	0.479487i
$921$	1.55765	−	6.82450i	0.0513262	−	0.224875i
$922$	−21.0733	−	26.4251i	−0.694013	−	0.870265i
$923$	21.0733	−	26.4251i	0.693637	−	0.869793i
$924$	−2.40955	−	10.5569i	−0.0792684	−	0.347298i
$925$	−15.5988	−	3.56033i	−0.512887	−	0.117063i
$926$	49.0752	+	39.1362i	1.61271	+	1.28609i
$927$	13.6569			0.448550
$928$		0			0
$929$	18.6863			0.613077			0.306539	−	0.951858i	$-0.400829\pi$
$929$	18.6863			0.613077			0.306539	+	0.951858i	$0.400829\pi$
$930$	−45.8923	−	36.5979i	−1.50487	−	1.20009i
$931$	5.84957	+	1.33513i	0.191712	+	0.0437570i
$932$	15.6015	+	68.3548i	0.511046	+	2.23904i
$933$	−4.04351	+	5.07040i	−0.132378	+	0.165997i
$934$	−57.7339	−	72.3960i	−1.88911	−	2.36887i
$935$	−0.0763571	+	0.334542i	−0.00249714	+	0.0109407i
$936$	20.7392	−	43.0654i	0.677882	−	1.40764i
$937$	−14.9808	−	7.21437i	−0.489401	−	0.235683i	0.172874	−	0.984944i	$-0.444695\pi$
$937$	−14.9808	−	7.21437i	−0.489401	−	0.235683i	−0.662275	+	0.749261i	$0.730409\pi$
$938$	37.6589	−	8.59541i	1.22961	−	0.280650i
$939$	10.2952	+	21.3781i	0.335970	+	0.697649i
$940$			12.4142i			0.404907i
$941$	−50.9930	+	24.5569i	−1.66232	+	0.800533i	−0.663706	+	0.747994i	$0.731017\pi$
$941$	−50.9930	+	24.5569i	−1.66232	+	0.800533i	−0.998619	+	0.0525400i	$0.983268\pi$
$942$	−38.6661	+	30.8352i	−1.25981	+	1.00467i
$943$	12.8236	−	10.2265i	0.417594	−	0.333020i
$944$	9.88414	−	4.75995i	0.321701	−	0.154923i
$945$			1.17157i			0.0381113i
$946$	−1.55581	−	3.23068i	−0.0505839	−	0.105039i
$947$	−2.54965	+	0.581942i	−0.0828526	+	0.0189106i	−0.263746	−	0.964592i	$-0.584958\pi$
$947$	−2.54965	+	0.581942i	−0.0828526	+	0.0189106i	0.180894	+	0.983503i	$0.442101\pi$
$948$	20.1040	+	9.68156i	0.652946	+	0.314442i
$949$	6.64437	−	13.7972i	0.215685	−	0.447875i
$950$	12.8931	−	56.4884i	0.418308	−	1.83273i
$951$	−47.3485	−	59.3732i	−1.53538	−	1.92531i
$952$	6.44885	−	8.08660i	0.209008	−	0.262088i
$953$	7.92785	+	34.7342i	0.256808	+	1.12515i	0.924641	+	0.380839i	$0.124365\pi$
$953$	7.92785	+	34.7342i	0.256808	+	1.12515i	−0.667833	+	0.744311i	$0.732778\pi$
$954$	63.1456	+	14.4126i	2.04442	+	0.466625i
$955$	−19.7911	−	15.7828i	−0.640423	−	0.510721i
$956$	75.2548			2.43392
$957$		0			0
$958$	−16.6569			−0.538159
$959$	26.5362	+	21.1619i	0.856900	+	0.683355i
$960$	23.1330	+	5.27996i	0.746615	+	0.170410i
$961$	15.6713	+	68.6607i	0.505527	+	2.21486i
$962$	23.0508	−	28.9047i	0.743187	−	0.931927i
$963$	26.1499	+	32.7909i	0.842668	+	1.05667i
$964$	15.6015	−	68.3548i	0.502492	−	2.20156i
$965$	2.24386	−	4.65943i	0.0722325	−	0.149992i
$966$	54.3143	+	26.1564i	1.74753	+	0.841567i
$967$	−34.3590	+	7.84223i	−1.10491	+	0.252189i	−0.735802	−	0.677197i	$-0.763195\pi$
$967$	−34.3590	+	7.84223i	−1.10491	+	0.252189i	−0.369110	+	0.929386i	$0.620337\pi$
$968$	20.7392	+	43.0654i	0.666583	+	1.38417i
$969$			12.0000i			0.385496i
$970$	9.75608	−	4.69828i	0.313249	−	0.150853i
$971$	−12.2410	+	9.76189i	−0.392833	+	0.313274i	−0.799910	−	0.600120i	$-0.795120\pi$
$971$	−12.2410	+	9.76189i	−0.392833	+	0.313274i	0.407077	+	0.913394i	$0.366548\pi$
$972$	64.8230	−	51.6946i	2.07920	−	1.65810i
$973$	35.6765	−	17.1809i	1.14374	−	0.550795i
$974$		−	27.7990i		−	0.890737i
$975$	−16.0409	−	33.3093i	−0.513721	−	1.06675i
$976$	14.1221	−	3.22328i	0.452038	−	0.103175i
$977$	−32.5895	−	15.6943i	−1.04263	−	0.502104i	−0.167439	−	0.985882i	$-0.553550\pi$
$977$	−32.5895	−	15.6943i	−1.04263	−	0.502104i	−0.875190	+	0.483779i	$0.839264\pi$
$978$	9.93572	−	20.6317i	0.317709	−	0.659730i
$979$	1.15078	−	5.04191i	0.0367792	−	0.161140i
$980$	−2.38699	−	2.99318i	−0.0762494	−	0.0956138i
$981$	22.3203	−	27.9888i	0.712632	−	0.893613i
$982$	−11.4118	−	49.9985i	−0.364166	−	1.59552i
$983$	21.3217	+	4.86655i	0.680058	+	0.155219i	0.548577	−	0.836100i	$-0.315170\pi$
$983$	21.3217	+	4.86655i	0.680058	+	0.155219i	0.131481	+	0.991319i	$0.458027\pi$
$984$	37.3708	+	29.8022i	1.19134	+	0.950059i
$985$	2.00000			0.0637253
$986$		0			0
$987$	22.1421			0.704792
$988$	68.7551	+	54.8304i	2.18739	+	1.74439i
$989$	12.7839	+	2.91785i	0.406506	+	0.0927822i
$990$	−0.629384	−	2.75751i	−0.0200031	−	0.0876395i
$991$	7.99839	−	10.0297i	0.254077	−	0.318603i	−0.638392	−	0.769712i	$-0.720400\pi$
$991$	7.99839	−	10.0297i	0.254077	−	0.318603i	0.892469	+	0.451109i	$0.148971\pi$
$992$	−9.95748	−	12.4863i	−0.316150	−	0.396440i
$993$	1.29695	−	5.68230i	0.0411574	−	0.180322i
$994$	−26.1564	+	54.3143i	−0.829630	+	1.72274i
$995$	0.437223	+	0.210556i	0.0138609	+	0.00667506i
$996$	68.9952	−	15.7477i	2.18620	−	0.498985i
$997$	12.2721	+	25.4832i	0.388661	+	0.807063i	0.999878	+	0.0155999i	$0.00496579\pi$
$997$	12.2721	+	25.4832i	0.388661	+	0.807063i	−0.611217	+	0.791463i	$0.709320\pi$
$998$		−	45.7990i		−	1.44974i
$999$	1.49277	−	0.718882i	0.0472293	−	0.0227444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.k.267.4		24
29.2	odd	28		841.2.d.f.778.2		12
29.3	odd	28		841.2.d.f.605.1		12
29.4	even	14	inner	841.2.e.k.270.4		24
29.5	even	14	inner	841.2.e.k.63.4		24
29.6	even	14	inner	841.2.e.k.651.1		24
29.7	even	7	inner	841.2.e.k.236.1		24
29.8	odd	28		841.2.d.j.645.2		12
29.9	even	14	inner	841.2.e.k.196.1		24
29.10	odd	28		841.2.d.j.571.2		12
29.11	odd	28		841.2.a.d.1.2		2
29.12	odd	4		841.2.d.j.574.1		12
29.13	even	14		841.2.b.a.840.1		4
29.14	odd	28		841.2.d.f.190.1		12
29.15	odd	28		841.2.d.j.190.2		12
29.16	even	7		841.2.b.a.840.4		4
29.17	odd	4		841.2.d.f.574.2		12
29.18	odd	28		29.2.a.a.1.1	✓	2
29.19	odd	28		841.2.d.f.571.1		12
29.20	even	7	inner	841.2.e.k.196.4		24
29.21	odd	28		841.2.d.f.645.1		12
29.22	even	14	inner	841.2.e.k.236.4		24
29.23	even	7	inner	841.2.e.k.651.4		24
29.24	even	7	inner	841.2.e.k.63.1		24
29.25	even	7	inner	841.2.e.k.270.1		24
29.26	odd	28		841.2.d.j.605.2		12
29.27	odd	28		841.2.d.j.778.1		12
29.28	even	2	inner	841.2.e.k.267.1		24
87.11	even	28		7569.2.a.c.1.1		2
87.47	even	28		261.2.a.d.1.2		2
116.47	even	28		464.2.a.h.1.1		2
145.18	even	28		725.2.b.b.349.4		4
145.47	even	28		725.2.b.b.349.1		4
145.134	odd	28		725.2.a.b.1.2		2
203.76	even	28		1421.2.a.j.1.1		2
232.163	even	28		1856.2.a.w.1.2		2
232.221	odd	28		1856.2.a.r.1.1		2
319.76	even	28		3509.2.a.j.1.2		2
348.47	odd	28		4176.2.a.bq.1.2		2
377.337	odd	28		4901.2.a.g.1.2		2
435.134	even	28		6525.2.a.o.1.1		2
493.424	odd	28		8381.2.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.a.a.1.1	✓	2	29.18	odd	28
261.2.a.d.1.2		2	87.47	even	28
464.2.a.h.1.1		2	116.47	even	28
725.2.a.b.1.2		2	145.134	odd	28
725.2.b.b.349.1		4	145.47	even	28
725.2.b.b.349.4		4	145.18	even	28
841.2.a.d.1.2		2	29.11	odd	28
841.2.b.a.840.1		4	29.13	even	14
841.2.b.a.840.4		4	29.16	even	7
841.2.d.f.190.1		12	29.14	odd	28
841.2.d.f.571.1		12	29.19	odd	28
841.2.d.f.574.2		12	29.17	odd	4
841.2.d.f.605.1		12	29.3	odd	28
841.2.d.f.645.1		12	29.21	odd	28
841.2.d.f.778.2		12	29.2	odd	28
841.2.d.j.190.2		12	29.15	odd	28
841.2.d.j.571.2		12	29.10	odd	28
841.2.d.j.574.1		12	29.12	odd	4
841.2.d.j.605.2		12	29.26	odd	28
841.2.d.j.645.2		12	29.8	odd	28
841.2.d.j.778.1		12	29.27	odd	28
841.2.e.k.63.1		24	29.24	even	7	inner
841.2.e.k.63.4		24	29.5	even	14	inner
841.2.e.k.196.1		24	29.9	even	14	inner
841.2.e.k.196.4		24	29.20	even	7	inner
841.2.e.k.236.1		24	29.7	even	7	inner
841.2.e.k.236.4		24	29.22	even	14	inner
841.2.e.k.267.1		24	29.28	even	2	inner
841.2.e.k.267.4		24	1.1	even	1	trivial
841.2.e.k.270.1		24	29.25	even	7	inner
841.2.e.k.270.4		24	29.4	even	14	inner
841.2.e.k.651.1		24	29.6	even	14	inner
841.2.e.k.651.4		24	29.23	even	7	inner
1421.2.a.j.1.1		2	203.76	even	28
1856.2.a.r.1.1		2	232.221	odd	28
1856.2.a.w.1.2		2	232.163	even	28
3509.2.a.j.1.2		2	319.76	even	28
4176.2.a.bq.1.2		2	348.47	odd	28
4901.2.a.g.1.2		2	377.337	odd	28
6525.2.a.o.1.1		2	435.134	even	28
7569.2.a.c.1.1		2	87.11	even	28
8381.2.a.e.1.1		2	493.424	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)

\(f(q)\)	\(=\)	\(q+(1.88751 + 1.50524i) q^{2} +(2.35368 + 0.537213i) q^{3} +(0.851905 + 3.73244i) q^{4} +(0.623490 - 0.781831i) q^{5} +(3.63396 + 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-1.91526 + 3.97707i) q^{8} +(2.54832 + 1.22721i) q^{9} +O(q^{10})\)	\(q+(1.88751 + 1.50524i) q^{2} +(2.35368 + 0.537213i) q^{3} +(0.851905 + 3.73244i) q^{4} +(0.623490 - 0.781831i) q^{5} +(3.63396 + 4.55685i) q^{6} +(0.629384 - 2.75751i) q^{7} +(-1.91526 + 3.97707i) q^{8} +(2.54832 + 1.22721i) q^{9} +(2.35368 - 0.537213i) q^{10} +(-0.179721 - 0.373194i) q^{11} +9.24264i q^{12} +(-3.44929 + 1.66109i) q^{13} +(5.33868 - 4.25745i) q^{14} +(1.88751 - 1.50524i) q^{15} +(-2.70291 + 1.30165i) q^{16} -0.828427i q^{17} +(2.96274 + 6.15220i) q^{18} +(-5.84957 + 1.33513i) q^{19} +(3.44929 + 1.66109i) q^{20} +(2.96274 - 6.15220i) q^{21} +(0.222521 - 0.974928i) q^{22} +(2.28001 + 2.85904i) q^{23} +(-6.64444 + 8.33186i) q^{24} +(0.890084 + 3.89971i) q^{25} +(-9.01091 - 2.05668i) q^{26} +(-0.323845 - 0.258258i) q^{27} +10.8284 q^{28} +5.82843 q^{30} +(-7.87388 - 6.27921i) q^{31} +(1.54603 + 0.352871i) q^{32} +(-0.222521 - 0.974928i) q^{33} +(1.24698 - 1.56366i) q^{34} +(-1.76350 - 2.21135i) q^{35} +(-2.40955 + 10.5569i) q^{36} +(-1.73553 + 3.60388i) q^{37} +(-13.0508 - 6.28493i) q^{38} +(-9.01091 + 2.05668i) q^{39} +(1.91526 + 3.97707i) q^{40} -4.48528i q^{41} +(14.8527 - 7.15270i) q^{42} +(2.80348 - 2.23570i) q^{43} +(1.23982 - 0.988722i) q^{44} +(2.54832 - 1.22721i) q^{45} +8.82843i q^{46} +(1.40693 + 2.92152i) q^{47} +(-7.06105 + 1.61164i) q^{48} +(-0.900969 - 0.433884i) q^{49} +(-4.18995 + 8.70053i) q^{50} +(0.445042 - 1.94986i) q^{51} +(-9.13840 - 11.4592i) q^{52} +(5.91398 - 7.41589i) q^{53} +(-0.222521 - 0.974928i) q^{54} +(-0.403828 - 0.0921712i) q^{55} +(9.76139 + 7.78445i) q^{56} -14.4853 q^{57} -3.65685 q^{59} +(7.22619 + 5.76269i) q^{60} +(-4.70737 - 1.07443i) q^{61} +(-5.41031 - 23.7041i) q^{62} +(4.98792 - 6.25465i) q^{63} +(6.12792 + 7.68417i) q^{64} +(-0.851905 + 3.73244i) q^{65} +(1.04749 - 2.17513i) q^{66} +(5.09665 + 2.45442i) q^{67} +(3.09205 - 0.705741i) q^{68} +(3.83051 + 7.95414i) q^{69} -6.82843i q^{70} +(-7.95414 + 3.83051i) q^{71} +(-9.76139 + 7.78445i) q^{72} +(-3.12733 + 2.49396i) q^{73} +(-8.70053 + 4.18995i) q^{74} +9.65685i q^{75} +(-9.96655 - 20.6958i) q^{76} +(-1.14220 + 0.260699i) q^{77} +(-20.1040 - 9.68156i) q^{78} +(1.04749 - 2.17513i) q^{79} +(-0.667563 + 2.92478i) q^{80} +(-5.91398 - 7.41589i) q^{81} +(6.75141 - 8.46601i) q^{82} +(-1.70381 - 7.46488i) q^{83} +(25.4867 + 5.81717i) q^{84} +(-0.647690 - 0.516516i) q^{85} +8.65685 q^{86} +1.82843 q^{88} +(9.76139 + 7.78445i) q^{89} +(6.65722 + 1.51947i) q^{90} +(2.40955 + 10.5569i) q^{91} +(-8.72886 + 10.9456i) q^{92} +(-15.1593 - 19.0092i) q^{93} +(-1.74199 + 7.63215i) q^{94} +(-2.60330 + 5.40581i) q^{95} +(3.44929 + 1.66109i) q^{96} +(4.37283 - 0.998069i) q^{97} +(-1.04749 - 2.17513i) q^{98} -1.17157i 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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