LMFDB - Embedded newform 550.2.t.a.419.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(89,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("550.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.t (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			419.2
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	550.419
Dual form			550.2.t.a.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(1.64204 + 2.26007i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(2.26007 + 1.64204i) q^{6} +1.72654i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.48459 + 4.56909i) q^{9} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(1.64204 + 2.26007i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(2.26007 + 1.64204i) q^{6} +1.72654i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.48459 + 4.56909i) q^{9} +(-1.70582 + 1.44575i) q^{10} +(-0.309017 - 0.951057i) q^{11} +(2.65688 + 0.863271i) q^{12} +(2.50000 + 0.812299i) q^{13} +(0.533531 + 1.64204i) q^{14} +(-5.31375 - 3.28408i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.00531 + 2.76007i) q^{17} +4.80423i q^{18} +(-0.322921 - 0.234616i) q^{19} +(-1.17557 + 1.90211i) q^{20} +(-3.90211 + 2.83505i) q^{21} +(-0.587785 - 0.809017i) q^{22} +(3.23842 - 1.05223i) q^{23} +2.79360 q^{24} +(3.56227 - 3.50859i) q^{25} +2.62866 q^{26} +(-4.79360 + 1.55754i) q^{27} +(1.01484 + 1.39680i) q^{28} +(-2.40211 + 1.74524i) q^{29} +(-6.06851 - 1.48131i) q^{30} +(0.0738814 + 0.0536780i) q^{31} -1.00000i q^{32} +(1.64204 - 2.26007i) q^{33} +(-1.05425 + 3.24466i) q^{34} +(-1.46386 - 3.57237i) q^{35} +(1.48459 + 4.56909i) q^{36} +(3.66994 + 1.19244i) q^{37} +(-0.379616 - 0.123345i) q^{38} +(2.26924 + 6.98401i) q^{39} +(-0.530249 + 2.17229i) q^{40} +(2.82974 - 8.70905i) q^{41} +(-2.83505 + 3.90211i) q^{42} -6.85816i q^{43} +(-0.809017 - 0.587785i) q^{44} +(-0.802198 - 10.7126i) q^{45} +(2.75476 - 2.00145i) q^{46} +(-1.43564 - 1.97599i) q^{47} +(2.65688 - 0.863271i) q^{48} +4.01905 q^{49} +(2.30371 - 4.43767i) q^{50} -9.53077 q^{51} +(2.50000 - 0.812299i) q^{52} +(1.12428 + 1.54743i) q^{53} +(-4.07768 + 2.96261i) q^{54} +(1.44575 + 1.70582i) q^{55} +(1.39680 + 1.01484i) q^{56} -1.11507i q^{57} +(-1.74524 + 2.40211i) q^{58} +(-3.45309 + 10.6275i) q^{59} +(-6.22925 + 0.466469i) q^{60} +(-3.43294 - 10.5655i) q^{61} +(0.0868528 + 0.0282202i) q^{62} +(-7.88873 - 2.56320i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-5.86144 + 0.438926i) q^{65} +(0.863271 - 2.65688i) q^{66} +(3.74779 - 5.15838i) q^{67} +3.41164i q^{68} +(7.69572 + 5.59127i) q^{69} +(-2.49614 - 2.94517i) q^{70} +(-8.84072 + 6.42316i) q^{71} +(2.82385 + 3.88670i) q^{72} +(10.0753 - 3.27366i) q^{73} +3.85880 q^{74} +(13.7791 + 2.28975i) q^{75} -0.399152 q^{76} +(1.64204 - 0.533531i) q^{77} +(4.31636 + 5.94095i) q^{78} +(-3.30272 + 2.39956i) q^{79} +(0.166977 + 2.22982i) q^{80} +(0.268667 + 0.195198i) q^{81} -9.15723i q^{82} +(8.12334 - 11.1808i) q^{83} +(-1.49047 + 4.58721i) q^{84} +(1.80902 - 7.41106i) q^{85} +(-2.11929 - 6.52250i) q^{86} +(-7.88873 - 2.56320i) q^{87} +(-0.951057 - 0.309017i) q^{88} +(-4.06227 - 12.5024i) q^{89} +(-4.07331 - 9.94038i) q^{90} +(-1.40247 + 4.31636i) q^{91} +(2.00145 - 2.75476i) q^{92} +0.255119i q^{93} +(-1.97599 - 1.43564i) q^{94} +(0.867073 + 0.211650i) q^{95} +(2.26007 - 1.64204i) q^{96} +(8.53258 + 11.7441i) q^{97} +(3.82234 - 1.24196i) q^{98} +4.80423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9	$ 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9} + 2 q^{11} + 20 q^{13} - 2 q^{14} - 2 q^{16} - 10 q^{17} + 16 q^{19} - 16 q^{21} + 10 q^{23} + 4 q^{24} - 10 q^{25} - 20 q^{27} - 10 q^{28} - 4 q^{29} + 10 q^{31} + 10 q^{33} - 10 q^{34} + 10 q^{35} - 2 q^{36} + 20 q^{37} - 10 q^{38} + 30 q^{39} + 26 q^{41} - 20 q^{42} - 2 q^{44} + 20 q^{45} + 16 q^{46} + 10 q^{47} + 8 q^{49} + 20 q^{50} - 40 q^{51} + 20 q^{52} - 10 q^{53} - 8 q^{54} + 10 q^{55} + 2 q^{56} - 20 q^{58} - 16 q^{59} - 10 q^{60} - 40 q^{61} - 30 q^{63} + 2 q^{64} - 10 q^{65} + 4 q^{66} + 28 q^{69} + 10 q^{70} - 26 q^{71} - 10 q^{73} + 8 q^{74} + 10 q^{75} + 4 q^{76} + 10 q^{77} + 20 q^{78} + 32 q^{79} - 18 q^{81} + 50 q^{83} - 24 q^{84} + 10 q^{85} - 10 q^{86} - 30 q^{87} + 6 q^{89} - 10 q^{90} + 40 q^{91} - 20 q^{92} - 10 q^{94} - 30 q^{95} + 6 q^{96} - 40 q^{97} - 20 q^{98} + 8 q^{99}+O(q^{100}) $ 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9 + 2 * q^11 + 20 * q^13 - 2 * q^14 - 2 * q^16 - 10 * q^17 + 16 * q^19 - 16 * q^21 + 10 * q^23 + 4 * q^24 - 10 * q^25 - 20 * q^27 - 10 * q^28 - 4 * q^29 + 10 * q^31 + 10 * q^33 - 10 * q^34 + 10 * q^35 - 2 * q^36 + 20 * q^37 - 10 * q^38 + 30 * q^39 + 26 * q^41 - 20 * q^42 - 2 * q^44 + 20 * q^45 + 16 * q^46 + 10 * q^47 + 8 * q^49 + 20 * q^50 - 40 * q^51 + 20 * q^52 - 10 * q^53 - 8 * q^54 + 10 * q^55 + 2 * q^56 - 20 * q^58 - 16 * q^59 - 10 * q^60 - 40 * q^61 - 30 * q^63 + 2 * q^64 - 10 * q^65 + 4 * q^66 + 28 * q^69 + 10 * q^70 - 26 * q^71 - 10 * q^73 + 8 * q^74 + 10 * q^75 + 4 * q^76 + 10 * q^77 + 20 * q^78 + 32 * q^79 - 18 * q^81 + 50 * q^83 - 24 * q^84 + 10 * q^85 - 10 * q^86 - 30 * q^87 + 6 * q^89 - 10 * q^90 + 40 * q^91 - 20 * q^92 - 10 * q^94 - 30 * q^95 + 6 * q^96 - 40 * q^97 - 20 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$	1.64204	+	2.26007i	0.948032	+	1.30485i	0.952396	+	0.304864i	$0.0986109\pi$
$3$	1.64204	+	2.26007i	0.948032	+	1.30485i	−0.00436407	+	0.999990i	$0.501389\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−2.06909	+	0.847859i	−0.925325	+	0.379174i
$5$	−2.06909	+	0.847859i	−0.925325	+	0.379174i
$6$	2.26007	+	1.64204i	0.922671	+	0.670360i
$7$			1.72654i			0.652572i	0.945271	+	0.326286i	$0.105797\pi$
$7$			1.72654i			0.652572i	−0.945271	+	0.326286i	$0.894203\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−1.48459	+	4.56909i	−0.494862	+	1.52303i
$10$	−1.70582	+	1.44575i	−0.539427	+	0.457185i
$11$	−0.309017	−	0.951057i	−0.0931721	−	0.286754i
$11$	−0.309017	−	0.951057i	−0.0931721	−	0.286754i
$12$	2.65688	+	0.863271i	0.766974	+	0.249205i
$13$	2.50000	+	0.812299i	0.693375	+	0.225291i	0.634442	−	0.772971i	$-0.281230\pi$
$13$	2.50000	+	0.812299i	0.693375	+	0.225291i	0.0589335	+	0.998262i	$0.481230\pi$
$14$	0.533531	+	1.64204i	0.142592	+	0.438854i
$15$	−5.31375	−	3.28408i	−1.37200	−	0.847946i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−2.00531	+	2.76007i	−0.486359	+	0.669416i	−0.979711	−	0.200414i	$-0.935771\pi$
$17$	−2.00531	+	2.76007i	−0.486359	+	0.669416i	0.493352	+	0.869830i	$0.335771\pi$
$18$			4.80423i			1.13237i
$19$	−0.322921	−	0.234616i	−0.0740831	−	0.0538245i	0.550127	−	0.835081i	$-0.314579\pi$
$19$	−0.322921	−	0.234616i	−0.0740831	−	0.0538245i	−0.624210	+	0.781256i	$0.714579\pi$
$20$	−1.17557	+	1.90211i	−0.262866	+	0.425325i
$21$	−3.90211	+	2.83505i	−0.851511	+	0.618659i
$22$	−0.587785	−	0.809017i	−0.125316	−	0.172483i
$23$	3.23842	−	1.05223i	0.675257	−	0.219404i	0.0487392	−	0.998812i	$-0.484480\pi$
$23$	3.23842	−	1.05223i	0.675257	−	0.219404i	0.626518	+	0.779407i	$0.284480\pi$
$24$	2.79360			0.570242
$25$	3.56227	−	3.50859i	0.712454	−	0.701719i
$26$	2.62866			0.515522
$27$	−4.79360	+	1.55754i	−0.922530	+	0.299748i
$28$	1.01484	+	1.39680i	0.191786	+	0.263971i
$29$	−2.40211	+	1.74524i	−0.446061	+	0.324082i	−0.788039	−	0.615626i	$-0.788903\pi$
$29$	−2.40211	+	1.74524i	−0.446061	+	0.324082i	0.341977	+	0.939708i	$0.388903\pi$
$30$	−6.06851	−	1.48131i	−1.10795	−	0.270448i
$31$	0.0738814	+	0.0536780i	0.0132695	+	0.00964085i	0.594400	−	0.804169i	$-0.297390\pi$
$31$	0.0738814	+	0.0536780i	0.0132695	+	0.00964085i	−0.581131	+	0.813810i	$0.697390\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.64204	−	2.26007i	0.285842	−	0.393428i
$34$	−1.05425	+	3.24466i	−0.180803	+	0.556455i
$35$	−1.46386	−	3.57237i	−0.247438	−	0.603841i
$36$	1.48459	+	4.56909i	0.247431	+	0.761515i
$37$	3.66994	+	1.19244i	0.603334	+	0.196035i	0.594727	−	0.803928i	$-0.297260\pi$
$37$	3.66994	+	1.19244i	0.603334	+	0.196035i	0.00860726	+	0.999963i	$0.497260\pi$
$38$	−0.379616	−	0.123345i	−0.0615819	−	0.0200092i
$39$	2.26924	+	6.98401i	0.363370	+	1.11834i
$40$	−0.530249	+	2.17229i	−0.0838397	+	0.343469i
$41$	2.82974	−	8.70905i	0.441931	−	1.36012i	−0.443883	−	0.896085i	$-0.646399\pi$
$41$	2.82974	−	8.70905i	0.441931	−	1.36012i	0.885814	−	0.464040i	$-0.153601\pi$
$42$	−2.83505	+	3.90211i	−0.437458	+	0.602109i
$43$		−	6.85816i		−	1.04586i	−0.852376	−	0.522930i	$-0.824839\pi$
$43$		−	6.85816i		−	1.04586i	0.852376	−	0.522930i	$-0.175161\pi$
$44$	−0.809017	−	0.587785i	−0.121964	−	0.0886120i
$45$	−0.802198	−	10.7126i	−0.119585	−	1.59694i
$46$	2.75476	−	2.00145i	0.406168	−	0.295098i
$47$	−1.43564	−	1.97599i	−0.209410	−	0.288228i	0.691373	−	0.722498i	$-0.257006\pi$
$47$	−1.43564	−	1.97599i	−0.209410	−	0.288228i	−0.900783	+	0.434270i	$0.857006\pi$
$48$	2.65688	−	0.863271i	0.383487	−	0.124602i
$49$	4.01905			0.574150
$50$	2.30371	−	4.43767i	0.325793	−	0.627582i
$51$	−9.53077			−1.33457
$52$	2.50000	−	0.812299i	0.346688	−	0.112646i
$53$	1.12428	+	1.54743i	0.154431	+	0.212557i	0.879222	−	0.476413i	$-0.158063\pi$
$53$	1.12428	+	1.54743i	0.154431	+	0.212557i	−0.724790	+	0.688970i	$0.758063\pi$
$54$	−4.07768	+	2.96261i	−0.554902	+	0.403160i
$55$	1.44575	+	1.70582i	0.194944	+	0.230013i
$56$	1.39680	+	1.01484i	0.186656	+	0.135613i
$57$		−	1.11507i		−	0.147695i
$58$	−1.74524	+	2.40211i	−0.229161	+	0.315413i
$59$	−3.45309	+	10.6275i	−0.449553	+	1.38358i	0.427859	+	0.903846i	$0.359268\pi$
$59$	−3.45309	+	10.6275i	−0.449553	+	1.38358i	−0.877412	+	0.479737i	$0.840732\pi$
$60$	−6.22925	+	0.466469i	−0.804193	+	0.0602209i
$61$	−3.43294	−	10.5655i	−0.439543	−	1.35277i	−0.888359	−	0.459149i	$-0.848154\pi$
$61$	−3.43294	−	10.5655i	−0.439543	−	1.35277i	0.448816	−	0.893624i	$-0.351846\pi$
$62$	0.0868528	+	0.0282202i	0.0110303	+	0.00358397i
$63$	−7.88873	−	2.56320i	−0.993886	−	0.322933i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−5.86144	+	0.438926i	−0.727022	+	0.0544421i
$66$	0.863271	−	2.65688i	0.106261	−	0.327039i
$67$	3.74779	−	5.15838i	0.457865	−	0.630197i	−0.516199	−	0.856468i	$-0.672654\pi$
$67$	3.74779	−	5.15838i	0.457865	−	0.630197i	0.974064	+	0.226271i	$0.0726537\pi$
$68$			3.41164i			0.413722i
$69$	7.69572	+	5.59127i	0.926456	+	0.673109i
$70$	−2.49614	−	2.94517i	−0.298346	−	0.352015i
$71$	−8.84072	+	6.42316i	−1.04920	+	0.762289i	−0.972060	−	0.234732i	$-0.924579\pi$
$71$	−8.84072	+	6.42316i	−1.04920	+	0.762289i	−0.0771400	+	0.997020i	$0.524579\pi$
$72$	2.82385	+	3.88670i	0.332794	+	0.458052i
$73$	10.0753	−	3.27366i	1.17922	−	0.383152i	0.347144	−	0.937812i	$-0.387151\pi$
$73$	10.0753	−	3.27366i	1.17922	−	0.383152i	0.832078	+	0.554659i	$0.187151\pi$
$74$	3.85880			0.448577
$75$	13.7791	+	2.28975i	1.59107	+	0.264397i
$76$	−0.399152			−0.0457859
$77$	1.64204	−	0.533531i	0.187128	−	0.0608015i
$78$	4.31636	+	5.94095i	0.488731	+	0.672681i
$79$	−3.30272	+	2.39956i	−0.371585	+	0.269972i	−0.757868	−	0.652408i	$-0.773759\pi$
$79$	−3.30272	+	2.39956i	−0.371585	+	0.269972i	0.386283	+	0.922380i	$0.373759\pi$
$80$	0.166977	+	2.22982i	0.0186686	+	0.249302i
$81$	0.268667	+	0.195198i	0.0298518	+	0.0216886i
$82$		−	9.15723i		−	1.01125i
$83$	8.12334	−	11.1808i	0.891653	−	1.22725i	−0.0814020	−	0.996681i	$-0.525940\pi$
$83$	8.12334	−	11.1808i	0.891653	−	1.22725i	0.973055	−	0.230574i	$-0.0740603\pi$
$84$	−1.49047	+	4.58721i	−0.162624	+	0.500506i
$85$	1.80902	−	7.41106i	0.196215	−	0.803843i
$86$	−2.11929	−	6.52250i	−0.228529	−	0.703339i
$87$	−7.88873	−	2.56320i	−0.845761	−	0.274804i
$88$	−0.951057	−	0.309017i	−0.101383	−	0.0329413i
$89$	−4.06227	−	12.5024i	−0.430600	−	1.32525i	−0.897529	−	0.440955i	$-0.854640\pi$
$89$	−4.06227	−	12.5024i	−0.430600	−	1.32525i	0.466929	−	0.884295i	$-0.345360\pi$
$90$	−4.07331	−	9.94038i	−0.429364	−	1.04781i
$91$	−1.40247	+	4.31636i	−0.147019	+	0.452477i
$92$	2.00145	−	2.75476i	0.208666	−	0.287204i
$93$			0.255119i			0.0264546i
$94$	−1.97599	−	1.43564i	−0.203808	−	0.148075i
$95$	0.867073	+	0.211650i	0.0889599	+	0.0217148i
$96$	2.26007	−	1.64204i	0.230668	−	0.167590i
$97$	8.53258	+	11.7441i	0.866352	+	1.19243i	0.980017	+	0.198912i	$0.0637408\pi$
$97$	8.53258	+	11.7441i	0.866352	+	1.19243i	−0.113665	+	0.993519i	$0.536259\pi$
$98$	3.82234	−	1.24196i	0.386115	−	0.125456i
$99$	4.80423			0.482843
$100$	0.819639	−	4.93236i	0.0819639	−	0.493236i
$101$	9.32032			0.927406			0.463703	−	0.885991i	$-0.346520\pi$
$101$	9.32032			0.927406			0.463703	+	0.885991i	$0.346520\pi$
$102$	−9.06430	+	2.94517i	−0.897499	+	0.291615i
$103$	8.18504	+	11.2657i	0.806496	+	1.11005i	0.991855	+	0.127375i	$0.0406553\pi$
$103$	8.18504	+	11.2657i	0.806496	+	1.11005i	−0.185359	+	0.982671i	$0.559345\pi$
$104$	2.12663	−	1.54508i	0.208533	−	0.151508i
$105$	5.67010	−	9.17442i	0.553345	−	0.895332i
$106$	1.54743	+	1.12428i	0.150300	+	0.109199i
$107$		−	6.03258i		−	0.583191i	−0.956542	−	0.291596i	$-0.905814\pi$
$107$		−	6.03258i		−	0.583191i	0.956542	−	0.291596i	$-0.0941862\pi$
$108$	−2.96261	+	4.07768i	−0.285077	+	0.392375i
$109$	−1.56706	+	4.82292i	−0.150097	+	0.461952i	−0.997631	−	0.0687892i	$-0.978086\pi$
$109$	−1.56706	+	4.82292i	−0.150097	+	0.461952i	0.847534	+	0.530741i	$0.178086\pi$
$110$	1.90211	+	1.17557i	0.181359	+	0.112086i
$111$	3.33119	+	10.2524i	0.316183	+	0.973111i
$112$	1.64204	+	0.533531i	0.155158	+	0.0504139i
$113$	−12.6756	−	4.11855i	−1.19242	−	0.387441i	−0.355453	−	0.934694i	$-0.615674\pi$
$113$	−12.6756	−	4.11855i	−1.19242	−	0.387441i	−0.836967	+	0.547253i	$0.815674\pi$
$114$	−0.344577	−	1.06050i	−0.0322725	−	0.0993247i
$115$	−5.80844	+	4.92287i	−0.541640	+	0.459060i
$116$	−0.917526	+	2.82385i	−0.0851901	+	0.262188i
$117$	−7.42294	+	10.2168i	−0.686251	+	0.944543i
$118$			11.1744i			1.02869i
$119$	−4.76538	−	3.46225i	−0.436842	−	0.317384i
$120$	−5.78022	+	2.36858i	−0.527660	+	0.216221i
$121$	−0.809017	+	0.587785i	−0.0735470	+	0.0534350i
$122$	−6.52984	−	8.98755i	−0.591184	−	0.813694i
$123$	24.3296	−	7.90518i	2.19373	−	0.712786i
$124$	0.0913225			0.00820100
$125$	−4.39587	+	10.2799i	−0.393179	+	0.919462i
$126$	−8.29470			−0.738951
$127$	−16.4866	+	5.35681i	−1.46295	+	0.475340i	−0.928968	−	0.370159i	$-0.879303\pi$
$127$	−16.4866	+	5.35681i	−1.46295	+	0.475340i	−0.533977	+	0.845499i	$0.679303\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$	15.4999	−	11.2614i	1.36469	−	0.991508i
$130$	−5.43893	+	2.22873i	−0.477025	+	0.195472i
$131$	13.4432	+	9.76709i	1.17454	+	0.853355i	0.991546	−	0.129759i	$-0.0414203\pi$
$131$	13.4432	+	9.76709i	1.17454	+	0.853355i	0.182996	+	0.983114i	$0.441420\pi$
$132$		−	2.79360i		−	0.243152i
$133$	0.405074	−	0.557537i	0.0351244	−	0.0483445i
$134$	1.97033	−	6.06404i	0.170210	−	0.523854i
$135$	8.59783	−	7.28698i	0.739983	−	0.627164i
$136$	1.05425	+	3.24466i	0.0904016	+	0.278227i
$137$	−16.1341	−	5.24228i	−1.37843	−	0.447878i	−0.476275	−	0.879297i	$-0.658013\pi$
$137$	−16.1341	−	5.24228i	−1.37843	−	0.447878i	−0.902152	+	0.431419i	$0.858013\pi$
$138$	9.04686	+	2.93950i	0.770120	+	0.250227i
$139$	−1.93690	−	5.96116i	−0.164286	−	0.505619i	0.834697	−	0.550709i	$-0.185643\pi$
$139$	−1.93690	−	5.96116i	−0.164286	−	0.505619i	−0.998983	+	0.0450900i	$0.985643\pi$
$140$	−3.28408	−	2.02967i	−0.277555	−	0.171539i
$141$	2.10851	−	6.48932i	0.177568	−	0.546500i
$142$	−6.42316	+	8.84072i	−0.539019	+	0.741897i
$143$		−	2.62866i		−	0.219819i
$144$	3.88670	+	2.82385i	0.323892	+	0.235321i
$145$	3.49047	−	5.64771i	0.289868	−	0.469016i
$146$	8.57054	−	6.22686i	0.709303	−	0.515339i
$147$	6.59944	+	9.08335i	0.544313	+	0.749182i
$148$	3.66994	−	1.19244i	0.301667	−	0.0980176i
$149$	−20.9691			−1.71785			−0.858926	−	0.512099i	$-0.828868\pi$
$149$	−20.9691			−1.71785			−0.858926	+	0.512099i	$0.828868\pi$
$150$	13.8122	−	2.08029i	1.12776	−	0.169855i
$151$	3.06154			0.249144			0.124572	−	0.992211i	$-0.460244\pi$
$151$	3.06154			0.249144			0.124572	+	0.992211i	$0.460244\pi$
$152$	−0.379616	+	0.123345i	−0.0307909	+	0.0100046i
$153$	−9.63397	−	13.2600i	−0.778860	−	1.07201i
$154$	1.39680	−	1.01484i	0.112558	−	0.0817778i
$155$	−0.198379	−	0.0484236i	−0.0159342	−	0.00388948i
$156$	5.94095	+	4.31636i	0.475657	+	0.345585i
$157$		−	11.8646i		−	0.946899i	−0.880821	−	0.473450i	$-0.843009\pi$
$157$		−	11.8646i		−	0.946899i	0.880821	−	0.473450i	$-0.156991\pi$
$158$	−2.39956	+	3.30272i	−0.190899	+	0.262750i
$159$	−1.65121	+	5.08190i	−0.130949	+	0.403021i
$160$	0.847859	+	2.06909i	0.0670291	+	0.163576i
$161$	1.81671	+	5.59127i	0.143177	+	0.440653i
$162$	0.315836	+	0.102621i	0.0248145	+	0.00806271i
$163$	−22.2538	−	7.23070i	−1.74305	−	0.566352i	−0.747822	−	0.663899i	$-0.768900\pi$
$163$	−22.2538	−	7.23070i	−1.74305	−	0.566352i	−0.995231	+	0.0975472i	$0.968900\pi$
$164$	−2.82974	−	8.70905i	−0.220966	−	0.680062i
$165$	−1.48131	+	6.06851i	−0.115319	+	0.472433i
$166$	4.27070	−	13.1438i	0.331470	−	1.02016i
$167$	−0.835306	+	1.14970i	−0.0646379	+	0.0889665i	−0.840112	−	0.542413i	$-0.817511\pi$
$167$	−0.835306	+	1.14970i	−0.0646379	+	0.0889665i	0.775474	+	0.631379i	$0.217511\pi$
$168$			4.82328i			0.372124i
$169$	−4.92705	−	3.57971i	−0.379004	−	0.275362i
$170$	−0.569667	−	7.60736i	−0.0436914	−	0.583458i
$171$	1.55138	−	1.12715i	0.118637	−	0.0861951i
$172$	−4.03112	−	5.54837i	−0.307370	−	0.423059i
$173$	−16.5747	+	5.38545i	−1.26015	+	0.409448i	−0.861548	−	0.507676i	$-0.830505\pi$
$173$	−16.5747	+	5.38545i	−1.26015	+	0.409448i	−0.398603	+	0.917124i	$0.630505\pi$
$174$	−8.29470			−0.628820
$175$	6.05774	+	6.15041i	0.457922	+	0.464927i
$176$	−1.00000			−0.0753778
$177$	−29.6890	+	9.64655i	−2.23156	+	0.725079i
$178$	−7.72690	−	10.6352i	−0.579156	−	0.797139i
$179$	14.8487	−	10.7882i	1.10985	−	0.806351i	0.127207	−	0.991876i	$-0.459399\pi$
$179$	14.8487	−	10.7882i	1.10985	−	0.806351i	0.982639	+	0.185525i	$0.0593987\pi$
$180$	−6.94569	−	8.19514i	−0.517701	−	0.610830i
$181$	1.16370	+	0.845474i	0.0864968	+	0.0628436i	0.630193	−	0.776438i	$-0.282976\pi$
$181$	1.16370	+	0.845474i	0.0864968	+	0.0628436i	−0.543696	+	0.839282i	$0.682976\pi$
$182$			4.53849i			0.336415i
$183$	18.2418	−	25.1077i	1.34847	−	1.85601i
$184$	1.05223	−	3.23842i	0.0775711	−	0.238739i
$185$	−8.60445	+	0.644333i	−0.632612	+	0.0473723i
$186$	0.0788361	+	0.242632i	0.00578054	+	0.0177907i
$187$	3.24466	+	1.05425i	0.237273	+	0.0770947i
$188$	−2.32292	−	0.754763i	−0.169416	−	0.0550467i
$189$	−2.68915	−	8.27636i	−0.195607	−	0.602017i
$190$	0.890039	−	0.0666494i	0.0645702	−	0.00483526i
$191$	−6.51925	+	20.0642i	−0.471716	+	1.45179i	0.378619	+	0.925553i	$0.376399\pi$
$191$	−6.51925	+	20.0642i	−0.471716	+	1.45179i	−0.850335	+	0.526241i	$0.823601\pi$
$192$	1.64204	−	2.26007i	0.118504	−	0.163107i
$193$		−	3.06591i		−	0.220689i	−0.993893	−	0.110344i	$-0.964805\pi$
$193$		−	3.06591i		−	0.220689i	0.993893	−	0.110344i	$-0.0351954\pi$
$194$	11.7441	+	8.53258i	0.843176	+	0.612603i
$195$	−10.6167	−	12.5266i	−0.760279	−	0.897045i
$196$	3.25148	−	2.36234i	0.232249	−	0.168738i
$197$	−11.9489	−	16.4463i	−0.851326	−	1.17175i	−0.983569	−	0.180533i	$-0.942218\pi$
$197$	−11.9489	−	16.4463i	−0.851326	−	1.17175i	0.132242	−	0.991217i	$-0.457782\pi$
$198$	4.56909	−	1.48459i	0.324711	−	0.105505i
$199$	−9.79432			−0.694301			−0.347150	−	0.937809i	$-0.612851\pi$
$199$	−9.79432			−0.694301			−0.347150	+	0.937809i	$0.612851\pi$
$200$	−0.744661	−	4.94424i	−0.0526555	−	0.349610i
$201$	17.8123			1.25639
$202$	8.86415	−	2.88014i	0.623679	−	0.202646i
$203$	−3.01323	−	4.14735i	−0.211487	−	0.291087i
$204$	−7.71055	+	5.60205i	−0.539847	+	0.392222i
$205$	1.52905	+	20.4190i	0.106794	+	1.42613i
$206$	11.2657	+	8.18504i	0.784921	+	0.570279i
$207$			16.3587i			1.13701i
$208$	1.54508	−	2.12663i	0.107132	−	0.147455i
$209$	−0.123345	+	0.379616i	−0.00853194	+	0.0262586i
$210$	2.55754	−	10.4775i	0.176487	−	0.723019i
$211$	4.95418	+	15.2474i	0.341060	+	1.04967i	0.963659	+	0.267134i	$0.0860766\pi$
$211$	4.95418	+	15.2474i	0.341060	+	1.04967i	−0.622600	+	0.782541i	$0.713923\pi$
$212$	1.81912	+	0.591067i	0.124938	+	0.0405947i
$213$	−29.0336	−	9.43359i	−1.98935	−	0.646379i
$214$	−1.86417	−	5.73732i	−0.127432	−	0.392195i
$215$	5.81475	+	14.1902i	0.396563	+	0.967760i
$216$	−1.55754	+	4.79360i	−0.105977	+	0.326163i
$217$	−0.0926774	+	0.127559i	−0.00629135	+	0.00865930i
$218$			5.07112i			0.343460i
$219$	23.9427	+	17.3954i	1.61790	+	1.17547i
$220$	2.17229	+	0.530249i	0.146456	+	0.0357494i
$221$	−7.25528	+	5.27127i	−0.488043	+	0.354584i
$222$	6.33630	+	8.72118i	0.425265	+	0.585327i
$223$	21.1302	−	6.86562i	1.41498	−	0.459756i	0.500979	−	0.865460i	$-0.332973\pi$
$223$	21.1302	−	6.86562i	1.41498	−	0.459756i	0.914005	+	0.405704i	$0.132973\pi$
$224$	1.72654			0.115359
$225$	10.7426	+	21.4852i	0.716172	+	1.43234i
$226$	−13.3279			−0.886560
$227$	−19.2992	+	6.27070i	−1.28093	+	0.416201i	−0.868909	−	0.494972i	$-0.835178\pi$
$227$	−19.2992	+	6.27070i	−1.28093	+	0.416201i	−0.412025	+	0.911173i	$0.635178\pi$
$228$	−0.655423	−	0.902113i	−0.0434065	−	0.0597439i
$229$	−12.9563	+	9.41331i	−0.856177	+	0.622049i	−0.926842	−	0.375451i	$-0.877488\pi$
$229$	−12.9563	+	9.41331i	−0.856177	+	0.622049i	0.0706651	+	0.997500i	$0.477488\pi$
$230$	−4.00290	+	6.47684i	−0.263944	+	0.427070i
$231$	3.90211	+	2.83505i	0.256740	+	0.186533i
$232$			2.96917i			0.194936i
$233$	6.66463	−	9.17307i	0.436614	−	0.600948i	−0.532841	−	0.846215i	$-0.678876\pi$
$233$	6.66463	−	9.17307i	0.436614	−	0.600948i	0.969456	+	0.245267i	$0.0788757\pi$
$234$	−3.90247	+	12.0106i	−0.255112	+	0.785155i
$235$	4.64584	+	2.87129i	0.303061	+	0.187302i
$236$	3.45309	+	10.6275i	0.224777	+	0.691792i
$237$	−10.8464	−	3.52420i	−0.704548	−	0.228922i
$238$	−5.60205	−	1.82021i	−0.363127	−	0.117987i
$239$	−1.98005	−	6.09397i	−0.128079	−	0.394186i	0.866371	−	0.499402i	$-0.166447\pi$
$239$	−1.98005	−	6.09397i	−0.128079	−	0.394186i	−0.994449	+	0.105215i	$0.966447\pi$
$240$	−4.76538	+	4.03884i	−0.307604	+	0.260706i
$241$	−1.71139	+	5.26710i	−0.110240	+	0.339284i	−0.990925	−	0.134419i	$-0.957083\pi$
$241$	−1.71139	+	5.26710i	−0.110240	+	0.339284i	0.880685	+	0.473703i	$0.157083\pi$
$242$	−0.587785	+	0.809017i	−0.0377843	+	0.0520056i
$243$			16.0486i			1.02952i
$244$	−8.98755	−	6.52984i	−0.575369	−	0.418030i
$245$	−8.31578	+	3.40759i	−0.531276	+	0.217703i
$246$	20.6960	−	15.0365i	1.31953	−	0.958695i
$247$	−0.616724	−	0.848848i	−0.0392412	−	0.0540109i
$248$	0.0868528	−	0.0282202i	0.00551516	−	0.00179198i
$249$	38.6083			2.44670
$250$	−1.00406	+	11.1352i	−0.0635021	+	0.704250i
$251$	6.37708			0.402518			0.201259	−	0.979538i	$-0.435497\pi$
$251$	6.37708			0.402518			0.201259	+	0.979538i	$0.435497\pi$
$252$	−7.88873	+	2.56320i	−0.496943	+	0.161467i
$253$	−2.00145	−	2.75476i	−0.125830	−	0.173190i
$254$	−14.0243	+	10.1893i	−0.879963	+	0.639331i
$255$	19.7200	−	8.08075i	1.23492	−	0.506036i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$			29.2562i			1.82495i	0.409134	+	0.912475i	$0.365831\pi$
$257$			29.2562i			1.82495i	−0.409134	+	0.912475i	$0.634169\pi$
$258$	11.2614	−	15.4999i	0.701102	−	0.964984i
$259$	−2.05879	+	6.33630i	−0.127927	+	0.393719i
$260$	−4.48401	+	3.80037i	−0.278087	+	0.235689i
$261$	−4.40800	−	13.5664i	−0.272848	−	0.839741i
$262$	15.8035	+	5.13486i	0.976343	+	0.317233i
$263$	−0.164281	−	0.0533783i	−0.0101300	−	0.00329144i	0.303948	−	0.952689i	$-0.401695\pi$
$263$	−0.164281	−	0.0533783i	−0.0101300	−	0.00329144i	−0.314078	+	0.949397i	$0.601695\pi$
$264$	−0.863271	−	2.65688i	−0.0531307	−	0.163519i
$265$	−3.63824	−	2.24855i	−0.223495	−	0.138128i
$266$	0.212960	−	0.655423i	0.0130574	−	0.0401866i
$267$	21.5859	−	29.7104i	1.32104	−	1.81825i
$268$		−	6.37611i		−	0.389483i
$269$	14.4084	+	10.4683i	0.878493	+	0.638263i	0.932852	−	0.360259i	$-0.117312\pi$
$269$	14.4084	+	10.4683i	0.878493	+	0.638263i	−0.0543594	+	0.998521i	$0.517312\pi$
$270$	5.92522	−	9.58721i	0.360597	−	0.583459i
$271$	3.72394	−	2.70560i	0.226213	−	0.164353i	−0.468906	−	0.883248i	$-0.655352\pi$
$271$	3.72394	−	2.70560i	0.226213	−	0.164353i	0.695119	+	0.718895i	$0.255352\pi$
$272$	2.00531	+	2.76007i	0.121590	+	0.167354i
$273$	−12.0582	+	3.91794i	−0.729795	+	0.237125i
$274$	−16.9644			−1.02485
$275$	−4.43767	−	2.30371i	−0.267602	−	0.138919i
$276$	9.51243			0.572581
$277$	12.0788	−	3.92464i	0.725746	−	0.235809i	0.0772331	−	0.997013i	$-0.475391\pi$
$277$	12.0788	−	3.92464i	0.725746	−	0.235809i	0.648512	+	0.761204i	$0.275391\pi$
$278$	−3.68420	−	5.07086i	−0.220964	−	0.304130i
$279$	−0.354943	+	0.257881i	−0.0212499	+	0.0154389i
$280$	−3.75055	−	0.915497i	−0.224138	−	0.0547114i
$281$	5.69900	+	4.14057i	0.339974	+	0.247005i	0.744651	−	0.667454i	$-0.232616\pi$
$281$	5.69900	+	4.14057i	0.339974	+	0.247005i	−0.404677	+	0.914460i	$0.632616\pi$
$282$		−	6.82328i		−	0.406320i
$283$	2.01223	−	2.76960i	0.119615	−	0.164636i	−0.745011	−	0.667052i	$-0.767556\pi$
$283$	2.01223	−	2.76960i	0.119615	−	0.164636i	0.864626	+	0.502417i	$0.167556\pi$
$284$	−3.37685	+	10.3929i	−0.200379	+	0.616704i
$285$	0.945424	+	2.30719i	0.0560021	+	0.136666i
$286$	−0.812299	−	2.50000i	−0.0480323	−	0.147828i
$287$	15.0365	+	4.88567i	0.887579	+	0.288392i
$288$	4.56909	+	1.48459i	0.269236	+	0.0874802i
$289$	1.65655	+	5.09835i	0.0974444	+	0.299903i
$290$	1.57440	−	6.44990i	0.0924520	−	0.378751i
$291$	−12.5317	+	38.5685i	−0.734619	+	2.26093i
$292$	6.22686	−	8.57054i	0.364400	−	0.501553i
$293$		−	33.4085i		−	1.95175i	−0.218339	−	0.975873i	$-0.570064\pi$
$293$		−	33.4085i		−	1.95175i	0.218339	−	0.975873i	$-0.429936\pi$
$294$	9.08335	+	6.59944i	0.529752	+	0.384887i
$295$	−1.86588	−	24.9170i	−0.108636	−	1.45072i
$296$	3.12184	−	2.26815i	0.181453	−	0.131833i
$297$	2.96261	+	4.07768i	0.171908	+	0.236611i
$298$	−19.9428	+	6.47980i	−1.15525	+	0.375365i
$299$	8.95077			0.517636
$300$	12.4934	−	6.24669i	0.721306	−	0.360653i
$301$	11.8409			0.682498
$302$	2.91169	−	0.946067i	0.167549	−	0.0544400i
$303$	15.3043	+	21.0646i	0.879211	+	1.21013i
$304$	−0.322921	+	0.234616i	−0.0185208	+	0.0134561i
$305$	16.0611	+	18.9503i	0.919656	+	1.08509i
$306$	−13.2600	−	9.63397i	−0.758025	−	0.550737i
$307$		−	0.519637i		−	0.0296573i	−0.999890	−	0.0148286i	$-0.995280\pi$
$307$		−	0.519637i		−	0.0296573i	0.999890	−	0.0148286i	$-0.00472027\pi$
$308$	1.01484	−	1.39680i	0.0578257	−	0.0795902i
$309$	−12.0212	+	36.9976i	−0.683865	+	2.10472i
$310$	−0.203633	+	0.0152488i	−0.0115656	+	0.000866073i
$311$	4.95685	+	15.2556i	0.281077	+	0.865066i	0.987547	+	0.157323i	$0.0502864\pi$
$311$	4.95685	+	15.2556i	0.281077	+	0.865066i	−0.706470	+	0.707743i	$0.749714\pi$
$312$	6.98401	+	2.26924i	0.395392	+	0.128471i
$313$	7.62646	+	2.47799i	0.431073	+	0.140064i	0.516513	−	0.856279i	$-0.327230\pi$
$313$	7.62646	+	2.47799i	0.431073	+	0.140064i	−0.0854402	+	0.996343i	$0.527230\pi$
$314$	−3.66637	−	11.2839i	−0.206905	−	0.636788i
$315$	18.4957	−	1.38503i	1.04212	−	0.0780375i
$316$	−1.26153	+	3.88258i	−0.0709664	+	0.218412i
$317$	−6.06050	+	8.34156i	−0.340391	+	0.468509i	−0.944556	−	0.328351i	$-0.893507\pi$
$317$	−6.06050	+	8.34156i	−0.340391	+	0.468509i	0.604164	+	0.796860i	$0.293507\pi$
$318$			5.34342i			0.299644i
$319$	2.40211	+	1.74524i	0.134493	+	0.0977145i
$320$	1.44575	+	1.70582i	0.0808196	+	0.0953582i
$321$	13.6341	−	9.90573i	0.760979	−	0.552884i
$322$	3.45559	+	4.75621i	0.192573	+	0.265053i
$323$	1.29511	−	0.420808i	0.0720620	−	0.0234144i
$324$	0.332090			0.0184495
$325$	11.7557	−	5.87785i	0.652089	−	0.326045i
$326$	−23.3990			−1.29595
$327$	−13.4733	+	4.37775i	−0.745077	+	0.242090i
$328$	−5.38249	−	7.40836i	−0.297198	−	0.409058i
$329$	3.41164	−	2.47870i	0.188090	−	0.136655i
$330$	0.466469	+	6.22925i	0.0256783	+	0.342909i
$331$	15.4321	+	11.2121i	0.848227	+	0.616273i	0.924657	−	0.380802i	$-0.124352\pi$
$331$	15.4321	+	11.2121i	0.848227	+	0.616273i	−0.0764295	+	0.997075i	$0.524352\pi$
$332$		−	13.8203i		−	0.758485i
$333$	−10.8967	+	14.9980i	−0.597135	+	0.821886i
$334$	−0.439146	+	1.35155i	−0.0240290	+	0.0739537i
$335$	−3.38093	+	13.8508i	−0.184720	+	0.756748i
$336$	1.49047	+	4.58721i	0.0813121	+	0.250253i
$337$	11.6518	+	3.78589i	0.634712	+	0.206230i	0.608661	−	0.793430i	$-0.291707\pi$
$337$	11.6518	+	3.78589i	0.634712	+	0.206230i	0.0260507	+	0.999661i	$0.491707\pi$
$338$	−5.79210	−	1.88197i	−0.315048	−	0.102365i
$339$	−11.5056	−	35.4106i	−0.624899	−	1.92324i
$340$	−2.89259	−	7.05899i	−0.156873	−	0.382827i
$341$	0.0282202	−	0.0868528i	0.00152821	−	0.00470334i
$342$	1.12715	−	1.55138i	0.0609491	−	0.0838893i
$343$			19.0249i			1.02725i
$344$	−5.54837	−	4.03112i	−0.299148	−	0.217344i
$345$	−20.6637	−	5.04395i	−1.11250	−	0.271557i
$346$	−14.0993	+	10.2437i	−0.757982	+	0.550706i
$347$	−15.6937	−	21.6005i	−0.842480	−	1.15957i	−0.985470	−	0.169850i	$-0.945672\pi$
$347$	−15.6937	−	21.6005i	−0.842480	−	1.15957i	0.142990	−	0.989724i	$-0.454328\pi$
$348$	−7.88873	+	2.56320i	−0.422880	+	0.137402i
$349$	−1.49715			−0.0801407			−0.0400704	−	0.999197i	$-0.512758\pi$
$349$	−1.49715			−0.0801407			−0.0400704	+	0.999197i	$0.512758\pi$
$350$	7.66183	+	3.97745i	0.409542	+	0.212603i
$351$	−13.2492			−0.707190
$352$	−0.951057	+	0.309017i	−0.0506915	+	0.0164707i
$353$	7.77997	+	10.7082i	0.414086	+	0.569940i	0.964209	−	0.265143i	$-0.0854193\pi$
$353$	7.77997	+	10.7082i	0.414086	+	0.569940i	−0.550123	+	0.835083i	$0.685419\pi$
$354$	−25.2550	+	18.3488i	−1.34229	+	0.975230i
$355$	12.8463	−	20.7858i	0.681812	−	1.10319i
$356$	−10.6352	−	7.72690i	−0.563663	−	0.409525i
$357$		−	16.4553i		−	0.870906i
$358$	10.7882	−	14.8487i	0.570176	−	0.784780i
$359$	5.99869	−	18.4621i	0.316599	−	0.974391i	−0.658493	−	0.752587i	$-0.728806\pi$
$359$	5.99869	−	18.4621i	0.316599	−	0.974391i	0.975091	−	0.221804i	$-0.0711944\pi$
$360$	−9.13818	−	5.64771i	−0.481624	−	0.297660i
$361$	−5.82209	−	17.9185i	−0.306426	−	0.943082i
$362$	1.36801	+	0.444492i	0.0719008	+	0.0233620i
$363$	−2.65688	−	0.863271i	−0.139450	−	0.0453100i
$364$	1.40247	+	4.31636i	0.0735094	+	0.226239i
$365$	−18.0711	+	15.3159i	−0.945883	+	0.801671i
$366$	9.59027	−	29.5158i	0.501292	−	1.54282i
$367$	3.79897	−	5.22884i	0.198305	−	0.272943i	−0.698271	−	0.715833i	$-0.746047\pi$
$367$	3.79897	−	5.22884i	0.198305	−	0.272943i	0.896576	+	0.442890i	$0.146047\pi$
$368$		−	3.40507i		−	0.177502i
$369$	35.5914	+	25.8587i	1.85282	+	1.34615i
$370$	−7.98421	+	3.27172i	−0.415079	+	0.170089i
$371$	−2.67171	+	1.94111i	−0.138708	+	0.100778i
$372$	0.149955	+	0.206396i	0.00777481	+	0.0107011i
$373$	−28.3126	+	9.19932i	−1.46597	+	0.476323i	−0.929888	−	0.367843i	$-0.880097\pi$
$373$	−28.3126	+	9.19932i	−1.46597	+	0.476323i	−0.536083	+	0.844165i	$0.680097\pi$
$374$	3.41164			0.176412
$375$	−30.4515	+	6.94501i	−1.57251	+	0.358639i
$376$	−2.44246			−0.125960
$377$	−7.42294	+	2.41186i	−0.382301	+	0.124217i
$378$	−5.11507	−	7.04029i	−0.263091	−	0.362114i
$379$	−9.12950	+	6.63297i	−0.468951	+	0.340713i	−0.797032	−	0.603937i	$-0.793598\pi$
$379$	−9.12950	+	6.63297i	−0.468951	+	0.340713i	0.328081	+	0.944649i	$0.393598\pi$
$380$	0.825882	−	0.338425i	0.0423668	−	0.0173608i
$381$	−39.1784	−	28.4647i	−2.00717	−	1.45829i
$382$			21.0967i			1.07940i
$383$	−19.3763	+	26.6692i	−0.990085	+	1.36273i	−0.0588695	+	0.998266i	$0.518750\pi$
$383$	−19.3763	+	26.6692i	−0.990085	+	1.36273i	−0.931215	+	0.364469i	$0.881250\pi$
$384$	0.863271	−	2.65688i	0.0440536	−	0.135583i
$385$	−2.94517	+	2.49614i	−0.150100	+	0.127215i
$386$	−0.947418	−	2.91585i	−0.0482223	−	0.148413i
$387$	31.3355	+	10.1815i	1.59288	+	0.517557i
$388$	13.8060	+	4.48584i	0.700893	+	0.227734i
$389$	−9.14170	−	28.1352i	−0.463502	−	1.42651i	−0.860856	−	0.508848i	$-0.830071\pi$
$389$	−9.14170	−	28.1352i	−0.463502	−	1.42651i	0.397354	−	0.917665i	$-0.369929\pi$
$390$	−13.9680	−	8.63271i	−0.707298	−	0.437134i
$391$	−3.58981	+	11.0483i	−0.181545	+	0.558737i
$392$	2.36234	−	3.25148i	0.119316	−	0.164225i
$393$			46.4207i			2.34161i
$394$	−16.4463	−	11.9489i	−0.828553	−	0.601979i
$395$	4.79913	−	7.76515i	0.241470	−	0.390707i
$396$	3.88670	−	2.82385i	0.195314	−	0.141904i
$397$	−0.535581	−	0.737164i	−0.0268800	−	0.0369972i	0.795365	−	0.606130i	$-0.207279\pi$
$397$	−0.535581	−	0.737164i	−0.0268800	−	0.0369972i	−0.822245	+	0.569133i	$0.807279\pi$
$398$	−9.31495	+	3.02661i	−0.466916	+	0.151710i
$399$	1.92522			0.0963816
$400$	−2.23607	−	4.47214i	−0.111803	−	0.223607i
$401$	−11.0249			−0.550557			−0.275279	−	0.961364i	$-0.588770\pi$
$401$	−11.0249			−0.550557			−0.275279	+	0.961364i	$0.588770\pi$
$402$	16.9405	−	5.50432i	0.844917	−	0.274530i
$403$	0.141101	+	0.194209i	0.00702874	+	0.00967423i
$404$	7.54029	−	5.47834i	0.375144	−	0.272558i
$405$	−0.721395	−	0.176090i	−0.0358464	−	0.00875000i
$406$	−4.14735	−	3.01323i	−0.205830	−	0.149544i
$407$		−	3.85880i		−	0.191274i
$408$	−5.60205	+	7.71055i	−0.277343	+	0.381729i
$409$	4.95215	−	15.2412i	0.244868	−	0.753627i	−0.750790	−	0.660541i	$-0.770327\pi$
$409$	4.95215	−	15.2412i	0.244868	−	0.753627i	0.995658	−	0.0930857i	$-0.0296731\pi$
$410$	7.76404	+	18.9471i	0.383439	+	0.935733i
$411$	−14.6448	−	45.0722i	−0.722377	−	2.22325i
$412$	13.2437	+	4.30313i	0.652469	+	0.212000i
$413$	−18.3488	−	5.96190i	−0.902887	−	0.293366i
$414$	5.05513	+	15.5581i	0.248446	+	0.764638i
$415$	−7.32818	+	30.0216i	−0.359726	+	1.47370i
$416$	0.812299	−	2.50000i	0.0398262	−	0.122573i
$417$	10.2922	−	14.1660i	0.504011	−	0.693711i
$418$			0.399152i			0.0195232i
$419$	−12.8967	−	9.37003i	−0.630047	−	0.457756i	0.226369	−	0.974042i	$-0.427314\pi$
$419$	−12.8967	−	9.37003i	−0.630047	−	0.457756i	−0.856417	+	0.516285i	$0.827314\pi$
$420$	−0.805379	−	10.7551i	−0.0392985	−	0.524793i
$421$	−3.72884	+	2.70916i	−0.181732	+	0.132036i	−0.674932	−	0.737880i	$-0.735827\pi$
$421$	−3.72884	+	2.70916i	−0.181732	+	0.132036i	0.493200	+	0.869916i	$0.335827\pi$
$422$	9.42341	+	12.9702i	0.458725	+	0.631380i
$423$	11.1598	−	3.62605i	0.542610	−	0.176305i
$424$	1.91273			0.0928906
$425$	2.54051	+	16.8679i	0.123233	+	0.818216i
$426$	−30.5278			−1.47907
$427$	18.2418	−	5.92711i	0.882782	−	0.286833i
$428$	−3.54586	−	4.88046i	−0.171396	−	0.235906i
$429$	5.94095	−	4.31636i	0.286832	−	0.208396i
$430$	9.91515	+	11.6988i	0.478151	+	0.564165i
$431$	22.6784	+	16.4768i	1.09238	+	0.793661i	0.979800	−	0.199981i	$-0.0640881\pi$
$431$	22.6784	+	16.4768i	1.09238	+	0.793661i	0.112581	+	0.993643i	$0.464088\pi$
$432$			5.04029i			0.242501i
$433$	11.7969	−	16.2370i	0.566921	−	0.780300i	−0.425264	−	0.905069i	$-0.639819\pi$
$433$	11.7969	−	16.2370i	0.566921	−	0.780300i	0.992186	+	0.124769i	$0.0398189\pi$
$434$	−0.0487234	+	0.149955i	−0.00233880	+	0.00719808i
$435$	18.4957	−	1.38503i	0.886802	−	0.0664070i
$436$	1.56706	+	4.82292i	0.0750487	+	0.230976i
$437$	−1.29262	−	0.419998i	−0.0618345	−	0.0200912i
$438$	28.1463	+	9.14530i	1.34488	+	0.436979i
$439$	6.85816	+	21.1072i	0.327322	+	1.00739i	0.970382	+	0.241577i	$0.0776648\pi$
$439$	6.85816	+	21.1072i	0.327322	+	1.00739i	−0.643059	+	0.765816i	$0.722335\pi$
$440$	2.22982	−	0.166977i	0.106303	−	0.00796034i
$441$	−5.96663	+	18.3634i	−0.284125	+	0.874448i
$442$	−5.27127	+	7.25528i	−0.250729	+	0.345099i
$443$			11.8071i			0.560974i	0.959858	+	0.280487i	$0.0904959\pi$
$443$			11.8071i			0.560974i	−0.959858	+	0.280487i	$0.909504\pi$
$444$	8.72118	+	6.33630i	0.413889	+	0.300708i
$445$	19.0055	+	22.4243i	0.900945	+	1.06302i
$446$	17.9744	−	13.0592i	0.851114	−	0.618370i
$447$	−34.4320	−	47.3916i	−1.62858	−	2.24155i
$448$	1.64204	−	0.533531i	0.0775791	−	0.0252070i
$449$	−18.8115			−0.887770			−0.443885	−	0.896084i	$-0.646400\pi$
$449$	−18.8115			−0.887770			−0.443885	+	0.896084i	$0.646400\pi$
$450$	16.8561	+	17.1140i	0.794603	+	0.806760i
$451$	−9.15723			−0.431197
$452$	−12.6756	+	4.11855i	−0.596210	+	0.193720i
$453$	5.02717	+	6.91930i	0.236197	+	0.325097i
$454$	−16.4169	+	11.9276i	−0.770483	+	0.559789i
$455$	−0.757825	−	10.1200i	−0.0355274	−	0.474434i
$456$	−0.902113	−	0.655423i	−0.0422453	−	0.0306930i
$457$		−	38.3795i		−	1.79532i	−0.440692	−	0.897658i	$-0.645267\pi$
$457$		−	38.3795i		−	1.79532i	0.440692	−	0.897658i	$-0.354733\pi$
$458$	−9.41331	+	12.9563i	−0.439855	+	0.605409i
$459$	5.31375	−	16.3540i	0.248025	−	0.763341i
$460$	−1.80554	+	7.39680i	−0.0841836	+	0.344878i
$461$	−8.00293	−	24.6305i	−0.372733	−	1.14716i	−0.944995	−	0.327084i	$-0.893934\pi$
$461$	−8.00293	−	24.6305i	−0.372733	−	1.14716i	0.572262	−	0.820071i	$-0.306066\pi$
$462$	4.58721	+	1.49047i	0.213416	+	0.0693432i
$463$	30.6502	+	9.95885i	1.42444	+	0.462827i	0.917009	−	0.398868i	$-0.130597\pi$
$463$	30.6502	+	9.95885i	1.42444	+	0.462827i	0.507427	+	0.861695i	$0.330597\pi$
$464$	0.917526	+	2.82385i	0.0425951	+	0.131094i
$465$	−0.216305	−	0.527864i	−0.0100309	−	0.0244791i
$466$	3.50380	−	10.7836i	0.162310	−	0.499540i
$467$	14.6718	−	20.1940i	0.678929	−	0.934466i	−0.320991	−	0.947082i	$-0.604016\pi$
$467$	14.6718	−	20.1940i	0.678929	−	0.934466i	0.999920	+	0.0126163i	$0.00401599\pi$
$468$			12.6287i			0.583760i
$469$	8.90617	+	6.47071i	0.411249	+	0.298790i
$470$	5.30573	+	1.29511i	0.244735	+	0.0597391i
$471$	26.8149	−	19.4822i	1.23557	−	0.897691i
$472$	6.56816	+	9.04029i	0.302324	+	0.416113i
$473$	−6.52250	+	2.11929i	−0.299905	+	0.0974450i
$474$	−11.4046			−0.523829
$475$	−1.97350	+	0.297233i	−0.0905505	+	0.0136380i
$476$	−5.89034			−0.269983
$477$	−8.73946	+	2.83962i	−0.400152	+	0.130017i
$478$	−3.76628	−	5.18384i	−0.172266	−	0.237103i
$479$	−19.1778	+	13.9335i	−0.876256	+	0.636638i	−0.932258	−	0.361793i	$-0.882165\pi$
$479$	−19.1778	+	13.9335i	−0.876256	+	0.636638i	0.0560020	+	0.998431i	$0.482165\pi$
$480$	−3.28408	+	5.31375i	−0.149897	+	0.242538i
$481$	8.20623	+	5.96218i	0.374172	+	0.271852i
$482$			5.53816i			0.252256i
$483$	−9.65356	+	13.2870i	−0.439252	+	0.604579i
$484$	−0.309017	+	0.951057i	−0.0140462	+	0.0432298i
$485$	−27.6120	−	17.0652i	−1.25380	−	0.774889i
$486$	4.95929	+	15.2631i	0.224958	+	0.692350i
$487$	25.7389	+	8.36307i	1.16634	+	0.378967i	0.827276	−	0.561796i	$-0.189889\pi$
$487$	25.7389	+	8.36307i	1.16634	+	0.378967i	0.339065	+	0.940763i	$0.389889\pi$
$488$	−10.5655	−	3.43294i	−0.478278	−	0.155402i
$489$	−20.1997	−	62.1683i	−0.913463	−	2.81135i
$490$	−6.85577	+	5.81053i	−0.309712	+	0.262493i
$491$	−8.56525	+	26.3611i	−0.386544	+	1.18966i	0.548809	+	0.835948i	$0.315081\pi$
$491$	−8.56525	+	26.3611i	−0.386544	+	1.18966i	−0.935354	+	0.353714i	$0.884919\pi$
$492$	15.0365	−	20.6960i	0.677899	−	0.933049i
$493$		−	10.1298i		−	0.456221i
$494$	−0.848848	−	0.616724i	−0.0381915	−	0.0277477i
$495$	−9.94038	+	4.07331i	−0.446787	+	0.183081i
$496$	0.0738814	−	0.0536780i	0.00331737	−	0.00241021i
$497$	−11.0899	−	15.2639i	−0.497448	−	0.684678i
$498$	36.7187	−	11.9306i	1.64540	−	0.534624i
$499$	−14.2580			−0.638277			−0.319138	−	0.947708i	$-0.603393\pi$
$499$	−14.2580			−0.638277			−0.319138	+	0.947708i	$0.603393\pi$
$500$	2.48604	+	10.9004i	0.111179	+	0.487483i
$501$	−3.97001			−0.177367
$502$	6.06497	−	1.97063i	0.270693	−	0.0879534i
$503$	−1.06887	−	1.47117i	−0.0476584	−	0.0655962i	0.784523	−	0.620100i	$-0.212908\pi$
$503$	−1.06887	−	1.47117i	−0.0476584	−	0.0655962i	−0.832181	+	0.554504i	$0.812908\pi$
$504$	−6.71055	+	4.87550i	−0.298912	+	0.217172i
$505$	−19.2846	+	7.90231i	−0.858152	+	0.351648i
$506$	−2.75476	−	2.00145i	−0.122464	−	0.0889754i
$507$		−	17.0135i		−	0.755597i
$508$	−10.1893	+	14.0243i	−0.452075	+	0.622228i
$509$	0.954017	−	2.93616i	0.0422861	−	0.130143i	−0.927685	−	0.373364i	$-0.878204\pi$
$509$	0.954017	−	2.93616i	0.0422861	−	0.130143i	0.969971	+	0.243221i	$0.0782041\pi$
$510$	16.2578	−	13.7791i	0.719906	−	0.610147i
$511$	5.65211	+	17.3954i	0.250034	+	0.769527i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	1.91338	+	0.621694i	0.0844777	+	0.0274485i
$514$	9.04065	+	27.8243i	0.398766	+	1.22728i
$515$	−26.4873	−	16.3701i	−1.16717	−	0.721352i
$516$	5.92045	−	18.2213i	0.260633	−	0.802147i
$517$	−1.43564	+	1.97599i	−0.0631396	+	0.0869041i
$518$			6.66239i			0.292728i
$519$	−39.3878	−	28.6169i	−1.72893	−	1.25614i
$520$	−3.09017	+	5.00000i	−0.135513	+	0.219265i
$521$	26.5622	−	19.2985i	1.16371	−	0.845484i	0.173467	−	0.984840i	$-0.444503\pi$
$521$	26.5622	−	19.2985i	1.16371	−	0.845484i	0.990242	+	0.139355i	$0.0445031\pi$
$522$	−8.38451	−	11.5403i	−0.366980	−	0.505105i
$523$	17.5105	−	5.68950i	0.765679	−	0.248784i	0.0999649	−	0.994991i	$-0.468127\pi$
$523$	17.5105	−	5.68950i	0.765679	−	0.248784i	0.665714	+	0.746207i	$0.268127\pi$
$524$	16.6168			0.725907
$525$	−3.95334	+	23.7901i	−0.172538	+	1.03829i
$526$	−0.172736			−0.00753163
$527$	−0.296310	+	0.0962771i	−0.0129075	+	0.00419390i
$528$	−1.64204	−	2.26007i	−0.0714606	−	0.0983571i
$529$	−9.22722	+	6.70397i	−0.401183	+	0.291477i
$530$	−4.15501	−	1.01423i	−0.180482	−	0.0440551i
$531$	−43.4316	−	31.5549i	−1.88477	−	1.36937i
$532$		−	0.689153i		−	0.0298786i
$533$	14.1487	−	19.4740i	0.612848	−	0.843513i
$534$	11.3484	−	34.9267i	0.491092	−	1.51143i
$535$	5.11477	+	12.4819i	0.221131	+	0.539642i
$536$	−1.97033	−	6.06404i	−0.0851052	−	0.261927i
$537$	48.7644	+	15.8445i	2.10434	+	0.683742i
$538$	16.9380	+	5.50350i	0.730251	+	0.237273i
$539$	−1.24196	−	3.82234i	−0.0534948	−	0.164640i
$540$	2.67261	−	10.9490i	0.115011	−	0.471169i
$541$	9.45080	−	29.0866i	0.406322	−	1.25053i	−0.513465	−	0.858111i	$-0.671638\pi$
$541$	9.45080	−	29.0866i	0.406322	−	1.25053i	0.919787	−	0.392419i	$-0.128362\pi$
$542$	2.70560	−	3.72394i	0.116215	−	0.159957i
$543$			4.01834i			0.172443i
$544$	2.76007	+	2.00531i	0.118337	+	0.0859770i
$545$	−0.846763	−	11.3077i	−0.0362713	−	0.484369i
$546$	−10.2573	+	7.45237i	−0.438972	+	0.318932i
$547$	2.05789	+	2.83245i	0.0879891	+	0.121107i	0.850742	−	0.525583i	$-0.176153\pi$
$547$	2.05789	+	2.83245i	0.0879891	+	0.121107i	−0.762753	+	0.646690i	$0.776153\pi$
$548$	−16.1341	+	5.24228i	−0.689213	+	0.223939i
$549$	53.3712			2.27783
$550$	−4.93236	−	0.819639i	−0.210317	−	0.0349495i
$551$	1.18515			0.0504892
$552$	9.04686	−	2.93950i	0.385060	−	0.125114i
$553$	−4.14295	−	5.70228i	−0.176176	−	0.242486i
$554$	10.2749	−	7.46512i	0.436537	−	0.317162i
$555$	−15.5851	−	18.3887i	−0.661550	−	0.780556i
$556$	−5.07086	−	3.68420i	−0.215053	−	0.156245i
$557$		−	11.1072i		−	0.470626i	−0.971920	−	0.235313i	$-0.924388\pi$
$557$		−	11.1072i		−	0.470626i	0.971920	−	0.235313i	$-0.0756115\pi$
$558$	−0.257881	+	0.354943i	−0.0109170	+	0.0150259i
$559$	5.57088	−	17.1454i	0.235623	−	0.725173i
$560$	−3.84989	+	0.288294i	−0.162687	+	0.0121826i
$561$	2.94517	+	9.06430i	0.124345	+	0.382695i
$562$	6.69958	+	2.17682i	0.282605	+	0.0918238i
$563$	−20.6413	−	6.70675i	−0.869925	−	0.282656i	−0.160157	−	0.987091i	$-0.551200\pi$
$563$	−20.6413	−	6.70675i	−0.869925	−	0.282656i	−0.709768	+	0.704436i	$0.751200\pi$
$564$	−2.10851	−	6.48932i	−0.0887842	−	0.273250i
$565$	29.7189	−	2.22546i	1.25028	−	0.0936259i
$566$	1.05789	−	3.25586i	0.0444665	−	0.136854i
$567$	−0.337017	+	0.463864i	−0.0141534	+	0.0194805i
$568$			10.9277i			0.458517i
$569$	27.6873	+	20.1160i	1.16071	+	0.843306i	0.989868	−	0.141992i	$-0.0453508\pi$
$569$	27.6873	+	20.1160i	1.16071	+	0.843306i	0.170843	+	0.985298i	$0.445351\pi$
$570$	1.61211	+	1.90211i	0.0675239	+	0.0796707i
$571$	−9.03414	+	6.56369i	−0.378067	+	0.274682i	−0.760548	−	0.649282i	$-0.775070\pi$
$571$	−9.03414	+	6.56369i	−0.378067	+	0.274682i	0.382481	+	0.923963i	$0.375070\pi$
$572$	−1.54508	−	2.12663i	−0.0646032	−	0.0889187i
$573$	−56.0514	+	18.2122i	−2.34158	+	0.760826i
$574$	15.8104			0.659911
$575$	7.84429	−	15.1106i	0.327130	−	0.630156i
$576$	4.80423			0.200176
$577$	12.2634	−	3.98461i	0.510531	−	0.165881i	−0.0424130	−	0.999100i	$-0.513505\pi$
$577$	12.2634	−	3.98461i	0.510531	−	0.165881i	0.552944	+	0.833219i	$0.313505\pi$
$578$	3.15095	+	4.33692i	0.131062	+	0.180392i
$579$	6.92918	−	5.03434i	0.287967	−	0.209220i
$580$	−0.495785	−	6.62074i	−0.0205864	−	0.274911i
$581$	19.3042	+	14.0253i	0.800872	+	0.581867i
$582$			40.5533i			1.68099i
$583$	1.12428	−	1.54743i	0.0465628	−	0.0640882i
$584$	3.27366	−	10.0753i	0.135465	−	0.416918i
$585$	6.69633	−	27.4331i	0.276859	−	1.13422i
$586$	−10.3238	−	31.7734i	−0.426472	−	1.31255i
$587$	26.4309	+	8.58792i	1.09092	+	0.354461i	0.798602	−	0.601860i	$-0.205573\pi$
$587$	26.4309	+	8.58792i	1.09092	+	0.354461i	0.292318	+	0.956321i	$0.405573\pi$
$588$	10.6781	+	3.46953i	0.440358	+	0.143081i
$589$	−0.0112642	−	0.0346675i	−0.000464131	−	0.00142845i
$590$	−9.47433	−	23.1209i	−0.390052	−	0.951872i
$591$	17.5492	−	54.0110i	0.721879	−	2.22171i
$592$	2.26815	−	3.12184i	0.0932203	−	0.128307i
$593$		−	47.3083i		−	1.94272i	−0.237615	−	0.971359i	$-0.576366\pi$
$593$		−	47.3083i		−	1.94272i	0.237615	−	0.971359i	$-0.423634\pi$
$594$	4.07768	+	2.96261i	0.167309	+	0.121557i
$595$	12.7955	+	3.12334i	0.524565	+	0.128045i
$596$	−16.9643	+	12.3253i	−0.694886	+	0.504864i
$597$	−16.0827	−	22.1359i	−0.658219	−	0.905961i
$598$	8.51268	−	2.76594i	0.348110	−	0.113108i
$599$	−35.6545			−1.45680			−0.728401	−	0.685151i	$-0.759736\pi$
$599$	−35.6545			−1.45680			−0.728401	+	0.685151i	$0.759736\pi$
$600$	9.95158	−	9.80162i	0.406271	−	0.400150i
$601$	−9.08245			−0.370481			−0.185240	−	0.982693i	$-0.559306\pi$
$601$	−9.08245			−0.370481			−0.185240	+	0.982693i	$0.559306\pi$
$602$	11.2614	−	3.65904i	0.458979	−	0.149131i
$603$	18.0052	+	24.7820i	0.733229	+	1.00920i
$604$	2.47684	−	1.79953i	0.100781	−	0.0732217i
$605$	1.17557	−	1.90211i	0.0477937	−	0.0773319i
$606$	21.0646	+	15.3043i	0.855691	+	0.621696i
$607$			41.6350i			1.68991i	0.534836	+	0.844956i	$0.320374\pi$
$607$			41.6350i			1.68991i	−0.534836	+	0.844956i	$0.679626\pi$
$608$	−0.234616	+	0.322921i	−0.00951492	+	0.0130962i
$609$	4.42548	−	13.6202i	0.179329	−	0.551919i
$610$	21.1310	+	13.0597i	0.855569	+	0.528771i
$611$	−1.98401	−	6.10616i	−0.0802645	−	0.247029i
$612$	−15.5881	−	5.06488i	−0.630111	−	0.204735i
$613$	9.03615	+	2.93602i	0.364966	+	0.118585i	0.485759	−	0.874093i	$-0.338543\pi$
$613$	9.03615	+	2.93602i	0.364966	+	0.118585i	−0.120792	+	0.992678i	$0.538543\pi$
$614$	−0.160577	−	0.494204i	−0.00648035	−	0.0199445i
$615$	−43.6377	+	36.9846i	−1.75964	+	1.49136i
$616$	0.533531	−	1.64204i	0.0214966	−	0.0661597i
$617$	−2.77634	+	3.82130i	−0.111771	+	0.153840i	−0.861238	−	0.508202i	$-0.830310\pi$
$617$	−2.77634	+	3.82130i	−0.111771	+	0.153840i	0.749466	+	0.662042i	$0.230310\pi$
$618$			38.9016i			1.56485i
$619$	−9.86827	−	7.16972i	−0.396639	−	0.288175i	0.371531	−	0.928420i	$-0.378833\pi$
$619$	−9.86827	−	7.16972i	−0.396639	−	0.288175i	−0.768171	+	0.640245i	$0.778833\pi$
$620$	−0.188954	+	0.0774286i	−0.00758859	+	0.00310961i
$621$	−13.8848	+	10.0879i	−0.557178	+	0.404814i
$622$	9.42848	+	12.9772i	0.378048	+	0.520338i
$623$	21.5859	−	7.01368i	0.864821	−	0.280997i
$624$	7.34342			0.293972
$625$	0.379550	−	24.9971i	0.0151820	−	0.999885i
$626$	8.01894			0.320501
$627$	−1.06050	+	0.344577i	−0.0423522	+	0.0137611i
$628$	−6.97384	−	9.59867i	−0.278287	−	0.383029i
$629$	−10.6506	+	7.73810i	−0.424666	+	0.308538i
$630$	17.1625	−	7.03273i	0.683770	−	0.280191i
$631$	−26.3767	−	19.1638i	−1.05004	−	0.762898i	−0.0778188	−	0.996968i	$-0.524796\pi$
$631$	−26.3767	−	19.1638i	−1.05004	−	0.762898i	−0.972220	+	0.234070i	$0.924796\pi$
$632$			4.08238i			0.162388i
$633$	−26.3253	+	36.2337i	−1.04634	+	1.44016i
$634$	−3.18619	+	9.80609i	−0.126540	+	0.389450i
$635$	29.5704	−	25.0620i	1.17346	−	0.994555i
$636$	1.65121	+	5.08190i	0.0654747	+	0.201510i
$637$	10.0476	+	3.26467i	0.398101	+	0.129351i
$638$	2.82385	+	0.917526i	0.111797	+	0.0363252i
$639$	−16.2232	−	49.9298i	−0.641779	−	1.97519i
$640$	1.90211	+	1.17557i	0.0751876	+	0.0464685i
$641$	−10.3699	+	31.9152i	−0.409586	+	1.26057i	0.507420	+	0.861699i	$0.330599\pi$
$641$	−10.3699	+	31.9152i	−0.409586	+	1.26057i	−0.917005	+	0.398875i	$0.869401\pi$
$642$	9.90573	−	13.6341i	0.390948	−	0.538094i
$643$		−	37.7412i		−	1.48837i	−0.667974	−	0.744185i	$-0.732838\pi$
$643$		−	37.7412i		−	1.48837i	0.667974	−	0.744185i	$-0.267162\pi$
$644$	4.75621	+	3.45559i	0.187421	+	0.136169i
$645$	−22.5227	+	36.4426i	−0.886832	+	1.43492i
$646$	1.10169	−	0.800424i	0.0433454	−	0.0314923i
$647$	3.16270	+	4.35308i	0.124338	+	0.171137i	0.866648	−	0.498920i	$-0.166270\pi$
$647$	3.16270	+	4.35308i	0.124338	+	0.171137i	−0.742310	+	0.670057i	$0.766270\pi$
$648$	0.315836	−	0.102621i	0.0124072	−	0.00403135i
$649$	11.1744			0.438634
$650$	9.36398	−	9.22288i	0.367286	−	0.361751i
$651$	−0.440474			−0.0172635
$652$	−22.2538	+	7.23070i	−0.871526	+	0.283176i
$653$	10.9112	+	15.0179i	0.426986	+	0.587696i	0.967258	−	0.253794i	$-0.0816786\pi$
$653$	10.9112	+	15.0179i	0.426986	+	0.587696i	−0.540272	+	0.841491i	$0.681679\pi$
$654$	−11.4611	+	8.32698i	−0.448165	+	0.325611i
$655$	−36.0964	−	8.81102i	−1.41040	−	0.344275i
$656$	−7.40836	−	5.38249i	−0.289248	−	0.210151i
$657$			50.8949i			1.98560i
$658$	2.47870	−	3.41164i	0.0966298	−	0.133000i
$659$	5.57820	−	17.1679i	0.217296	−	0.668767i	−0.781687	−	0.623671i	$-0.785640\pi$
$659$	5.57820	−	17.1679i	0.217296	−	0.668767i	0.998983	−	0.0450964i	$-0.0143595\pi$
$660$	2.36858	+	5.78022i	0.0921969	+	0.224995i
$661$	−9.97279	−	30.6931i	−0.387897	−	1.19382i	−0.934357	−	0.356338i	$-0.884025\pi$
$661$	−9.97279	−	30.6931i	−0.387897	−	1.19382i	0.546460	−	0.837485i	$-0.315975\pi$
$662$	18.1416	+	5.89455i	0.705092	+	0.229098i
$663$	−23.8269	−	7.74184i	−0.925361	−	0.300668i
$664$	−4.27070	−	13.1438i	−0.165735	−	0.510080i
$665$	−0.365423	+	1.49704i	−0.0141705	+	0.0580527i
$666$	−5.72873	+	17.6312i	−0.221984	+	0.683196i
$667$	−5.94266	+	8.17937i	−0.230101	+	0.316707i
$668$			1.42111i			0.0549843i
$669$	50.2134	+	36.4822i	1.94136	+	1.41048i
$670$	1.06467	+	14.2176i	0.0411317	+	0.549274i
$671$	−8.98755	+	6.52984i	−0.346960	+	0.252082i
$672$	2.83505	+	3.90211i	0.109364	+	0.150527i
$673$	28.0837	−	9.12493i	1.08255	−	0.351740i	0.287184	−	0.957876i	$-0.407281\pi$
$673$	28.0837	−	9.12493i	1.08255	−	0.351740i	0.795362	+	0.606135i	$0.207281\pi$
$674$	12.2514			0.471906
$675$	−11.6114	+	22.3672i	−0.446921	+	0.860913i
$676$	−6.09017			−0.234237
$677$	0.0431986	−	0.0140361i	0.00166026	−	0.000539450i	−0.308187	−	0.951326i	$-0.599722\pi$
$677$	0.0431986	−	0.0140361i	0.00166026	−	0.000539450i	0.309847	+	0.950786i	$0.399722\pi$
$678$	−21.8850	−	30.1221i	−0.840487	−	1.15683i
$679$	−20.2767	+	14.7319i	−0.778147	+	0.565357i
$680$	−4.93236	−	5.81964i	−0.189147	−	0.223173i
$681$	−45.8623	−	33.3209i	−1.75745	−	1.27686i
$682$		−	0.0913225i		−	0.00349692i
$683$	−1.70527	+	2.34711i	−0.0652505	+	0.0898096i	−0.840395	−	0.541974i	$-0.817677\pi$
$683$	−1.70527	+	2.34711i	−0.0652505	+	0.0898096i	0.775145	+	0.631784i	$0.217677\pi$
$684$	0.592576	−	1.82376i	0.0226577	−	0.0697333i
$685$	37.8276	−	2.83267i	1.44532	−	0.108231i
$686$	5.87901	+	18.0937i	0.224461	+	0.690821i
$687$	−42.5495	−	13.8252i	−1.62337	−	0.527464i
$688$	−6.52250	−	2.11929i	−0.248668	−	0.0807971i
$689$	1.55371	+	4.78184i	0.0591917	+	0.182173i
$690$	−21.2111	+	1.58836i	−0.807491	+	0.0604679i
$691$	−7.86196	+	24.1966i	−0.299083	+	0.920483i	0.682736	+	0.730665i	$0.260790\pi$
$691$	−7.86196	+	24.1966i	−0.299083	+	0.920483i	−0.981819	+	0.189818i	$0.939210\pi$
$692$	−10.2437	+	14.0993i	−0.389408	+	0.535974i
$693$			8.29470i			0.315090i
$694$	−21.6005	−	15.6937i	−0.819943	−	0.595723i
$695$	9.06184	+	10.6920i	0.343735	+	0.405569i
$696$	−6.71055	+	4.87550i	−0.254363	+	0.184805i
$697$	18.3631	+	25.2746i	0.695552	+	0.957345i
$698$	−1.42388	+	0.462645i	−0.0538945	+	0.0175114i
$699$	31.6754			1.19807
$700$	8.51593	+	1.41514i	0.321872	+	0.0534873i
$701$	5.83132			0.220246			0.110123	−	0.993918i	$-0.464876\pi$
$701$	5.83132			0.220246			0.110123	+	0.993918i	$0.464876\pi$
$702$	−12.6007	+	4.09423i	−0.475584	+	0.154527i
$703$	−0.905335	−	1.24609i	−0.0341454	−	0.0469971i
$704$	−0.809017	+	0.587785i	−0.0304910	+	0.0221530i
$705$	1.13933	+	15.2147i	0.0429098	+	0.573019i
$706$	10.7082	+	7.77997i	0.403009	+	0.292803i
$707$			16.0919i			0.605199i
$708$	−18.3488	+	25.2550i	−0.689591	+	0.949141i
$709$	−2.40453	+	7.40039i	−0.0903041	+	0.277927i	−0.986001	−	0.166737i	$-0.946677\pi$
$709$	−2.40453	+	7.40039i	−0.0903041	+	0.277927i	0.895697	+	0.444664i	$0.146677\pi$
$710$	5.79441	−	23.7382i	0.217460	−	0.890878i
$711$	−6.06066	−	18.6528i	−0.227292	−	0.699534i
$712$	−12.5024	−	4.06227i	−0.468547	−	0.152240i
$713$	0.295740	+	0.0960919i	0.0110756	+	0.00359867i
$714$	−5.08496	−	15.6499i	−0.190300	−	0.585683i
$715$	2.22873	+	5.43893i	0.0833497	+	0.203404i
$716$	5.67171	−	17.4557i	0.211962	−	0.652351i
$717$	10.5215	−	14.4816i	0.392933	−	0.540825i
$718$		−	19.4122i		−	0.724456i
$719$	−12.5315	−	9.10465i	−0.467345	−	0.339546i	0.329060	−	0.944309i	$-0.393268\pi$
$719$	−12.5315	−	9.10465i	−0.467345	−	0.339546i	−0.796406	+	0.604763i	$0.793268\pi$
$720$	−10.4362	−	2.54743i	−0.388933	−	0.0949373i
$721$	−19.4508	+	14.1318i	−0.724385	+	0.526296i
$722$	−11.0743	−	15.2424i	−0.412142	−	0.567264i
$723$	−14.7142	+	4.78093i	−0.547227	+	0.177805i
$724$	1.43841			0.0534580
$725$	−2.43365	+	14.6450i	−0.0903835	+	0.543903i
$726$	−2.79360			−0.103680
$727$	10.3832	−	3.37369i	0.385090	−	0.125123i	−0.110073	−	0.993924i	$-0.535108\pi$
$727$	10.3832	−	3.37369i	0.385090	−	0.125123i	0.495163	+	0.868800i	$0.335108\pi$
$728$	2.66765	+	3.67171i	0.0988699	+	0.136083i
$729$	−35.4650	+	25.7669i	−1.31352	+	0.954328i
$730$	−12.4537	+	20.1506i	−0.460933	+	0.745805i
$731$	18.9290	+	13.7527i	0.700115	+	0.508663i
$732$		−	31.0348i		−	1.14708i
$733$	−3.58521	+	4.93462i	−0.132423	+	0.182264i	−0.870079	−	0.492912i	$-0.835932\pi$
$733$	−3.58521	+	4.93462i	−0.132423	+	0.182264i	0.737656	+	0.675176i	$0.235932\pi$
$734$	1.99724	−	6.14687i	0.0737194	−	0.226885i
$735$	−21.3562	−	13.1989i	−0.787737	−	0.486848i
$736$	−1.05223	−	3.23842i	−0.0387856	−	0.119370i
$737$	−6.06404	−	1.97033i	−0.223372	−	0.0725779i
$738$	41.8402	+	13.5947i	1.54016	+	0.500428i
$739$	−1.37630	−	4.23581i	−0.0506280	−	0.155817i	0.922546	−	0.385887i	$-0.126104\pi$
$739$	−1.37630	−	4.23581i	−0.0506280	−	0.155817i	−0.973174	+	0.230070i	$0.926104\pi$
$740$	−6.58242	+	5.57885i	−0.241975	+	0.205082i
$741$	0.905773	−	2.78768i	0.0332744	−	0.102408i
$742$	−1.94111	+	2.67171i	−0.0712605	+	0.0980816i
$743$			6.08141i			0.223105i	0.993759	+	0.111553i	$0.0355824\pi$
$743$			6.08141i			0.223105i	−0.993759	+	0.111553i	$0.964418\pi$
$744$	0.206396	+	0.149955i	0.00756683	+	0.00549762i
$745$	43.3869	−	17.7788i	1.58957	−	0.651365i
$746$	−24.0841	+	17.4981i	−0.881783	+	0.640653i
$747$	39.0264	+	53.7152i	1.42790	+	1.96534i
$748$	3.24466	−	1.05425i	0.118637	−	0.0385474i
$749$	10.4155			0.380574
$750$	−26.8150	+	16.0151i	−0.979145	+	0.584790i
$751$	−6.67648			−0.243628			−0.121814	−	0.992553i	$-0.538871\pi$
$751$	−6.67648			−0.243628			−0.121814	+	0.992553i	$0.538871\pi$
$752$	−2.32292	+	0.754763i	−0.0847082	+	0.0275234i
$753$	10.4714	+	14.4127i	0.381600	+	0.525227i
$754$	−6.31433	+	4.58763i	−0.229954	+	0.167072i
$755$	−6.33460	+	2.59575i	−0.230540	+	0.0944691i
$756$	−7.04029	−	5.11507i	−0.256053	−	0.186033i
$757$		−	35.2257i		−	1.28030i	−0.768251	−	0.640149i	$-0.778873\pi$
$757$		−	35.2257i		−	1.28030i	0.768251	−	0.640149i	$-0.221127\pi$
$758$	−6.63297	+	9.12950i	−0.240920	+	0.331598i
$759$	2.93950	−	9.04686i	0.106697	−	0.328380i
$760$	0.680881	−	0.577072i	0.0246982	−	0.0209326i
$761$	−10.2209	−	31.4566i	−0.370506	−	1.14030i	−0.946461	−	0.322818i	$-0.895370\pi$
$761$	−10.2209	−	31.4566i	−0.370506	−	1.14030i	0.575955	−	0.817481i	$-0.304630\pi$
$762$	−46.0569	−	14.9648i	−1.66847	−	0.542118i
$763$	−8.32698	−	2.70560i	−0.301457	−	0.0979493i
$764$	6.51925	+	20.0642i	0.235858	+	0.725897i
$765$	31.1762	+	19.2679i	1.12718	+	0.696634i
$766$	−10.1867	+	31.3516i	−0.368062	+	1.13278i
$767$	−17.2654	+	23.7638i	−0.623418	+	0.858062i
$768$		−	2.79360i		−	0.100806i
$769$	26.4151	+	19.1917i	0.952552	+	0.692069i	0.951409	−	0.307930i	$-0.0996362\pi$
$769$	26.4151	+	19.1917i	0.952552	+	0.692069i	0.00114284	+	0.999999i	$0.499636\pi$
$770$	−2.02967	+	3.28408i	−0.0731443	+	0.118350i
$771$	−66.1211	+	48.0398i	−2.38129	+	1.73011i
$772$	−1.80210	−	2.48037i	−0.0648589	−	0.0892706i
$773$	16.2857	−	5.29155i	0.585757	−	0.190324i	−0.00112099	−	0.999999i	$-0.500357\pi$
$773$	16.2857	−	5.29155i	0.585757	−	0.190324i	0.586878	+	0.809675i	$0.300357\pi$
$774$	32.9481			1.18430
$775$	0.451520	−	0.0680043i	0.0162191	−	0.00244279i
$776$	14.5165			0.521112
$777$	−17.7011	+	5.75145i	−0.635024	+	0.206332i
$778$	−17.3885	−	23.9333i	−0.623409	−	0.858049i
$779$	−2.95706	+	2.14843i	−0.105948	+	0.0769755i
$780$	−15.9520	−	3.89384i	−0.571174	−	0.139422i
$781$	8.84072	+	6.42316i	0.316346	+	0.229839i
$782$			11.6169i			0.415419i
$783$	8.79651	−	12.1074i	0.314362	−	0.432682i
$784$	1.24196	−	3.82234i	0.0443555	−	0.136512i
$785$	10.0595	+	24.5490i	0.359039	+	0.876190i
$786$	14.3448	+	44.1487i	0.511661	+	1.57473i
$787$	−8.97775	−	2.91705i	−0.320022	−	0.103981i	0.144601	−	0.989490i	$-0.453810\pi$
$787$	−8.97775	−	2.91705i	−0.320022	−	0.103981i	−0.464623	+	0.885509i	$0.653810\pi$
$788$	−19.3338	−	6.28193i	−0.688738	−	0.223784i
$789$	−0.149118	−	0.458937i	−0.00530873	−	0.0163386i
$790$	2.16468	−	8.86811i	0.0770158	−	0.315513i
$791$	7.11086	−	21.8850i	0.252833	−	0.778140i
$792$	2.82385	−	3.88670i	0.100341	−	0.138108i
$793$		−	29.2023i		−	1.03700i
$794$	−0.737164	−	0.535581i	−0.0261610	−	0.0190071i
$795$	−0.892231	−	11.9149i	−0.0316442	−	0.422578i
$796$	−7.92377	+	5.75695i	−0.280851	+	0.204050i
$797$	−0.726165	−	0.999480i	−0.0257221	−	0.0354034i	0.795962	−	0.605346i	$-0.206965\pi$
$797$	−0.726165	−	0.999480i	−0.0257221	−	0.0354034i	−0.821684	+	0.569943i	$0.806965\pi$
$798$	1.83099	−	0.594926i	0.0648165	−	0.0210602i
$799$	8.33280			0.294793
$800$	−3.50859	−	3.56227i	−0.124047	−	0.125945i
$801$	63.1553			2.23148
$802$	−10.4853	+	3.40688i	−0.370249	+	0.120301i
$803$	−6.22686	−	8.57054i	−0.219741	−	0.302448i
$804$	14.4105	−	10.4698i	0.508219	−	0.369242i
$805$	−8.49955	−	10.0285i	−0.299570	−	0.353459i
$806$	0.194209	+	0.141101i	0.00684071	+	0.00497007i
$807$			49.7533i			1.75140i
$808$	5.47834	−	7.54029i	0.192727	−	0.265267i
$809$	15.6367	−	48.1249i	0.549758	−	1.69198i	−0.159640	−	0.987175i	$-0.551033\pi$
$809$	15.6367	−	48.1249i	0.549758	−	1.69198i	0.709399	−	0.704807i	$-0.248967\pi$
$810$	−0.740503	+	0.0554516i	−0.0260186	+	0.00194837i
$811$	−13.8127	−	42.5111i	−0.485030	−	1.49277i	−0.831938	−	0.554868i	$-0.812769\pi$
$811$	−13.8127	−	42.5111i	−0.485030	−	1.49277i	0.346909	−	0.937899i	$-0.387231\pi$
$812$	−4.87550	−	1.58415i	−0.171097	−	0.0555927i
$813$	12.2297	+	3.97367i	0.428915	+	0.139363i
$814$	−1.19244	−	3.66994i	−0.0417948	−	0.128631i
$815$	52.1758	−	3.90711i	1.82764	−	0.136860i
$816$	−2.94517	+	9.06430i	−0.103102	+	0.317314i
$817$	−1.60903	+	2.21464i	−0.0562929	+	0.0774805i
$818$		−	16.0255i		−	0.560319i
$819$	−17.6397	−	12.8160i	−0.616382	−	0.447828i
$820$	13.2390	+	15.6206i	0.462327	+	0.545494i
$821$	6.03269	−	4.38301i	0.210542	−	0.152968i	−0.477517	−	0.878623i	$-0.658463\pi$
$821$	6.03269	−	4.38301i	0.210542	−	0.152968i	0.688059	+	0.725655i	$0.258463\pi$
$822$	−27.8562	−	38.3407i	−0.971595	−	1.33729i
$823$	−22.0861	+	7.17621i	−0.769873	+	0.250147i	−0.667511	−	0.744600i	$-0.732640\pi$
$823$	−22.0861	+	7.17621i	−0.769873	+	0.250147i	−0.102363	+	0.994747i	$0.532640\pi$
$824$	13.9252			0.485108
$825$	−2.08029	−	13.8122i	−0.0724263	−	0.480881i
$826$	−19.2931			−0.671293
$827$	31.4094	−	10.2055i	1.09221	−	0.354881i	0.293112	−	0.956078i	$-0.405309\pi$
$827$	31.4094	−	10.2055i	1.09221	−	0.354881i	0.799101	+	0.601197i	$0.205309\pi$
$828$	9.61543	+	13.2345i	0.334159	+	0.459931i
$829$	−23.8420	+	17.3222i	−0.828065	+	0.601625i	−0.919011	−	0.394231i	$-0.871011\pi$
$829$	−23.8420	+	17.3222i	−0.828065	+	0.601625i	0.0909461	+	0.995856i	$0.471011\pi$
$830$	2.30767	+	30.8168i	0.0801005	+	1.06967i
$831$	28.7039	+	20.8546i	0.995726	+	0.723438i
$832$		−	2.62866i		−	0.0911322i
$833$	−8.05945	+	11.0929i	−0.279243	+	0.384345i
$834$	5.41093	−	16.6531i	0.187365	−	0.576650i
$835$	0.753540	−	3.08706i	0.0260773	−	0.106832i
$836$	0.123345	+	0.379616i	0.00426597	+	0.0131293i
$837$	−0.437764	−	0.142238i	−0.0151313	−	0.00491647i
$838$	−15.1610	−	4.92612i	−0.523729	−	0.170170i
$839$	0.326678	+	1.00541i	0.0112782	+	0.0347107i	0.956537	−	0.291610i	$-0.0941910\pi$
$839$	0.326678	+	1.00541i	0.0112782	+	0.0347107i	−0.945259	+	0.326321i	$0.894191\pi$
$840$	−4.08946	−	9.97980i	−0.141100	−	0.344336i
$841$	−6.23720	+	19.1961i	−0.215076	+	0.661935i
$842$	−2.70916	+	3.72884i	−0.0933637	+	0.128504i
$843$			19.6791i			0.677785i
$844$	12.9702	+	9.42341i	0.446453	+	0.324367i
$845$	13.2296	+	3.22930i	0.455112	+	0.111091i
$846$	9.49312	−	6.89716i	0.326380	−	0.237129i
$847$	−1.01484	−	1.39680i	−0.0348702	−	0.0479947i
$848$	1.81912	−	0.591067i	0.0624688	−	0.0202973i
$849$	9.56366			0.328224
$850$	7.62866	+	15.2573i	0.261661	+	0.523321i
$851$	13.1395			0.450416
$852$	−29.0336	+	9.43359i	−0.994675	+	0.323190i
$853$	−6.02139	−	8.28773i	−0.206168	−	0.283767i	0.693394	−	0.720559i	$-0.256115\pi$
$853$	−6.02139	−	8.28773i	−0.206168	−	0.283767i	−0.899563	+	0.436792i	$0.856115\pi$
$854$	15.5174	−	11.2740i	0.530994	−	0.385790i
$855$	−2.25429	+	3.64752i	−0.0770952	+	0.124743i
$856$	−4.88046	−	3.54586i	−0.166811	−	0.121195i
$857$		−	40.0473i		−	1.36799i	−0.729487	−	0.683994i	$-0.760241\pi$
$857$		−	40.0473i		−	1.36799i	0.729487	−	0.683994i	$-0.239759\pi$
$858$	4.31636	−	5.94095i	0.147358	−	0.202821i
$859$	−15.4298	+	47.4882i	−0.526459	+	1.62027i	0.234953	+	0.972007i	$0.424506\pi$
$859$	−15.4298	+	47.4882i	−0.526459	+	1.62027i	−0.761412	+	0.648268i	$0.775494\pi$
$860$	13.0450	+	8.06225i	0.444831	+	0.274920i
$861$	13.6486	+	42.0061i	0.465144	+	1.43157i
$862$	26.6601	+	8.66239i	0.908046	+	0.295042i
$863$	44.9115	+	14.5926i	1.52880	+	0.496739i	0.948261	−	0.317491i	$-0.102840\pi$
$863$	44.9115	+	14.5926i	1.52880	+	0.496739i	0.580543	+	0.814230i	$0.302840\pi$
$864$	1.55754	+	4.79360i	0.0529885	+	0.163082i
$865$	29.7285	−	25.1960i	1.01080	−	0.856689i
$866$	6.20198	−	19.0877i	0.210752	−	0.648628i
$867$	−8.80252	+	12.1156i	−0.298949	+	0.411468i
$868$			0.157672i			0.00535174i
$869$	3.30272	+	2.39956i	0.112037	+	0.0813997i
$870$	17.1625	−	7.03273i	0.581863	−	0.238432i
$871$	13.5596	−	9.85164i	0.459450	−	0.333810i
$872$	2.98073	+	4.10262i	0.100940	+	0.138932i
$873$	−66.3271	+	21.5510i	−2.24483	+	0.729391i
$874$	−1.35914			−0.0459737
$875$	−17.7487	−	7.58966i	−0.600015	−	0.256577i
$876$	29.5948			0.999916
$877$	−16.0485	+	5.21447i	−0.541919	+	0.176080i	−0.567170	−	0.823601i	$-0.691962\pi$
$877$	−16.0485	+	5.21447i	−0.541919	+	0.176080i	0.0252507	+	0.999681i	$0.491962\pi$
$878$	13.0450	+	17.9549i	0.440247	+	0.605948i
$879$	75.5057	−	54.8581i	2.54674	−	1.85032i
$880$	2.06909	−	0.847859i	0.0697490	−	0.0285813i
$881$	19.2877	+	14.0133i	0.649819	+	0.472121i	0.863210	−	0.504846i	$-0.168451\pi$
$881$	19.2877	+	14.0133i	0.649819	+	0.472121i	−0.213391	+	0.976967i	$0.568451\pi$
$882$			19.3084i			0.650149i
$883$	−7.67012	+	10.5570i	−0.258120	+	0.355272i	−0.918334	−	0.395806i	$-0.870465\pi$
$883$	−7.67012	+	10.5570i	−0.258120	+	0.355272i	0.660214	+	0.751077i	$0.270465\pi$
$884$	−2.77127	+	8.52910i	−0.0932079	+	0.286865i
$885$	53.2504	−	45.1317i	1.78999	−	1.51709i
$886$	3.64860	+	11.2292i	0.122577	+	0.377254i
$887$	22.6572	+	7.36176i	0.760753	+	0.247184i	0.663602	−	0.748086i	$-0.269027\pi$
$887$	22.6572	+	7.36176i	0.760753	+	0.247184i	0.0971515	+	0.995270i	$0.469027\pi$
$888$	10.2524	+	3.33119i	0.344047	+	0.111788i
$889$	−9.24876	−	28.4647i	−0.310193	−	0.954677i
$890$	25.0048	+	15.4538i	0.838162	+	0.518012i
$891$	0.102621	−	0.315836i	0.00343795	−	0.0105809i
$892$	13.0592	−	17.9744i	0.437254	−	0.601828i
$893$			0.974914i			0.0326243i
$894$	−47.3916	−	34.4320i	−1.58501	−	1.15158i
$895$	−21.5765	+	34.9115i	−0.721222	+	1.16696i
$896$	1.39680	−	1.01484i	0.0466639	−	0.0339033i
$897$	14.6975	+	20.2294i	0.490736	+	0.675440i
$898$	−17.8908	+	5.81307i	−0.597024	+	0.193985i
$899$	−0.271152			−0.00904344
$900$	21.3196	+	11.0675i	0.710653	+	0.368918i
$901$	−6.52556			−0.217398
$902$	−8.70905	+	2.82974i	−0.289979	+	0.0942200i
$903$	19.4432	+	26.7613i	0.647030	+	0.890561i
$904$	−10.7825	+	7.83395i	−0.358621	+	0.260553i
$905$	−3.12463	−	0.762713i	−0.103866	−	0.0253534i
$906$	6.91930	+	5.02717i	0.229878	+	0.167016i
$907$			33.4702i			1.11136i	0.831396	+	0.555680i	$0.187542\pi$
$907$			33.4702i			1.11136i	−0.831396	+	0.555680i	$0.812458\pi$
$908$	−11.9276	+	16.4169i	−0.395830	+	0.544814i
$909$	−13.8368	+	42.5854i	−0.458939	+	1.41247i
$910$	−3.84799	−	9.39054i	−0.127560	−	0.311293i
$911$	8.81250	+	27.1221i	0.291971	+	0.898595i	0.984222	+	0.176938i	$0.0566191\pi$
$911$	8.81250	+	27.1221i	0.291971	+	0.898595i	−0.692251	+	0.721657i	$0.743381\pi$
$912$	−1.06050	−	0.344577i	−0.0351166	−	0.0114101i
$913$	−13.1438	−	4.27070i	−0.434998	−	0.141339i
$914$	−11.8599	−	36.5011i	−0.392291	−	1.20735i
$915$	−16.4561	+	67.4165i	−0.544023	+	2.22872i
$916$	−4.94887	+	15.2311i	−0.163515	+	0.503248i
$917$	−16.8633	+	23.2103i	−0.556875	+	0.766473i
$918$		−	17.1957i		−	0.567541i
$919$	16.1336	+	11.7218i	0.532200	+	0.386666i	0.821180	−	0.570669i	$-0.193316\pi$
$919$	16.1336	+	11.7218i	0.532200	+	0.386666i	−0.288980	+	0.957335i	$0.593316\pi$
$920$	0.568571	+	7.59272i	0.0187452	+	0.250325i
$921$	1.17442	−	0.853265i	0.0386984	−	0.0281160i
$922$	−15.2225	−	20.9519i	−0.501325	−	0.690015i
$923$	−27.3193	+	8.87659i	−0.899226	+	0.292176i
$924$	4.82328			0.158674
$925$	17.2571	−	8.62854i	0.567409	−	0.283705i
$926$	32.2275			1.05906
$927$	−63.6256	+	20.6732i	−2.08974	+	0.678997i
$928$	1.74524	+	2.40211i	0.0572902	+	0.0788532i
$929$	2.91652	−	2.11898i	0.0956879	−	0.0695214i	−0.538913	−	0.842362i	$-0.681165\pi$
$929$	2.91652	−	2.11898i	0.0956879	−	0.0695214i	0.634600	+	0.772840i	$0.281165\pi$
$930$	−0.368837	−	0.435187i	−0.0120946	−	0.0142703i
$931$	−1.29784	−	0.942932i	−0.0425348	−	0.0309034i
$932$		−	11.3385i		−	0.371406i
$933$	−26.3394	+	36.2531i	−0.862315	+	1.18687i
$934$	7.71341	−	23.7394i	0.252391	−	0.776778i
$935$	−7.60736	+	0.569667i	−0.248787	+	0.0186301i
$936$	3.90247	+	12.0106i	0.127556	+	0.392578i
$937$	−11.5489	−	3.75248i	−0.377288	−	0.122588i	0.114233	−	0.993454i	$-0.463559\pi$
$937$	−11.5489	−	3.75248i	−0.377288	−	0.122588i	−0.491521	+	0.870866i	$0.663559\pi$
$938$	10.4698	+	3.40185i	0.341852	+	0.111074i
$939$	6.92252	+	21.3053i	0.225908	+	0.695273i
$940$	5.44627	−	0.407836i	0.177638	−	0.0133022i
$941$	−13.6532	+	42.0203i	−0.445082	+	1.36982i	0.437311	+	0.899310i	$0.355931\pi$
$941$	−13.6532	+	42.0203i	−0.445082	+	1.36982i	−0.882393	+	0.470512i	$0.844069\pi$
$942$	19.4822	−	26.8149i	0.634763	−	0.873676i
$943$		−	31.1811i		−	1.01539i
$944$	9.04029	+	6.56816i	0.294237	+	0.213775i
$945$	12.5813	+	14.8445i	0.409269	+	0.482892i
$946$	−5.54837	+	4.03112i	−0.180393	+	0.131063i
$947$	−13.1934	−	18.1591i	−0.428726	−	0.590091i	0.538934	−	0.842348i	$-0.318827\pi$
$947$	−13.1934	−	18.1591i	−0.428726	−	0.590091i	−0.967660	+	0.252257i	$0.918827\pi$
$948$	−10.8464	+	3.52420i	−0.352274	+	0.114461i
$949$	27.8474			0.903964
$950$	−1.78506	+	0.892531i	−0.0579151	+	0.0289575i
$951$	−28.8041			−0.934037
$952$	−5.60205	+	1.82021i	−0.181563	+	0.0589935i
$953$	28.6926	+	39.4919i	0.929443	+	1.27927i	0.960076	+	0.279738i	$0.0902476\pi$
$953$	28.6926	+	39.4919i	0.929443	+	1.27927i	−0.0306333	+	0.999531i	$0.509752\pi$
$954$	−7.43423	+	5.40128i	−0.240692	+	0.174873i
$955$	−3.52268	−	47.0420i	−0.113991	−	1.52224i
$956$	−5.18384	−	3.76628i	−0.167657	−	0.121810i
$957$			8.29470i			0.268130i
$958$	−13.9335	+	19.1778i	−0.450171	+	0.619607i
$959$	9.05101	−	27.8562i	0.292272	−	0.899522i
$960$	−1.48131	+	6.06851i	−0.0478089	+	0.195860i
$961$	−9.57695	−	29.4748i	−0.308934	−	0.950801i
$962$	9.64700	+	3.13450i	0.311032	+	0.101060i
$963$	27.5634	+	8.95589i	0.888218	+	0.288599i
$964$	1.71139	+	5.26710i	0.0551200	+	0.169642i
$965$	2.59946	+	6.34364i	0.0836795	+	0.204209i
$966$	−5.07518	+	15.6198i	−0.163291	+	0.502558i
$967$	−8.99207	+	12.3765i	−0.289166	+	0.398002i	−0.928743	−	0.370725i	$-0.879109\pi$
$967$	−8.99207	+	12.3765i	−0.289166	+	0.398002i	0.639577	+	0.768727i	$0.279109\pi$
$968$			1.00000i			0.0321412i
$969$	3.07768	+	2.23607i	0.0988694	+	0.0718329i
$970$	−31.5340	−	7.69735i	−1.01250	−	0.247147i
$971$	−46.6129	+	33.8662i	−1.49588	+	1.08682i	−0.523890	+	0.851786i	$0.675520\pi$
$971$	−46.6129	+	33.8662i	−1.49588	+	1.08682i	−0.971987	+	0.235033i	$0.924480\pi$
$972$	9.43314	+	12.9836i	0.302568	+	0.416449i
$973$	10.2922	−	3.34414i	0.329953	−	0.107208i
$974$	27.0635			0.867170
$975$	32.5877	+	16.9171i	1.04364	+	0.541781i
$976$	−11.1092			−0.355597
$977$	9.42586	−	3.06265i	0.301560	−	0.0979828i	−0.154329	−	0.988020i	$-0.549321\pi$
$977$	9.42586	−	3.06265i	0.301560	−	0.0979828i	0.455889	+	0.890037i	$0.349321\pi$
$978$	−38.4221	−	52.8835i	−1.22860	−	1.69103i
$979$	−10.6352	+	7.72690i	−0.339901	+	0.246953i
$980$	−4.72468	+	7.64469i	−0.150924	+	0.244201i
$981$	−19.7099	−	14.3201i	−0.629289	−	0.457205i
$982$			27.7177i			0.884509i
$983$	−0.138824	+	0.191074i	−0.00442778	+	0.00609432i	−0.811225	−	0.584734i	$-0.801199\pi$
$983$	−0.138824	+	0.191074i	−0.00442778	+	0.00609432i	0.806797	+	0.590828i	$0.201199\pi$
$984$	7.90518	−	24.3296i	0.252008	−	0.775600i
$985$	38.6676	+	23.8979i	1.23205	+	0.761450i
$986$	−3.13027	−	9.63397i	−0.0996880	−	0.306808i
$987$	11.2041	+	3.64043i	0.356630	+	0.115876i
$988$	−0.997880	−	0.324231i	−0.0317468	−	0.0103152i
$989$	−7.21633	−	22.2096i	−0.229466	−	0.706224i
$990$	−8.19514	+	6.94569i	−0.260459	+	0.220748i
$991$	10.7564	−	33.1047i	0.341687	−	1.05161i	−0.621646	−	0.783298i	$-0.713536\pi$
$991$	10.7564	−	33.1047i	0.341687	−	1.05161i	0.963333	−	0.268307i	$-0.0864643\pi$
$992$	0.0536780	−	0.0738814i	0.00170428	−	0.00234574i
$993$			53.2885i			1.69106i
$994$	−15.2639	−	11.0899i	−0.484141	−	0.351749i
$995$	20.2653	−	8.30420i	0.642454	−	0.263261i
$996$	31.2348	−	22.6934i	0.989713	−	0.719068i
$997$	−8.88306	−	12.2265i	−0.281329	−	0.387217i	0.644844	−	0.764314i	$-0.276922\pi$
$997$	−8.88306	−	12.2265i	−0.281329	−	0.387217i	−0.926174	+	0.377097i	$0.876922\pi$
$998$	−13.5602	+	4.40597i	−0.429240	+	0.139469i
$999$	−19.4495			−0.615355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.t.a.419.2	✓	8
25.4	even	10	inner	550.2.t.a.529.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.t.a.419.2	✓	8	1.1	even	1	trivial
550.2.t.a.529.2	yes	8	25.4	even	10	inner

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.t (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.64204 + 2.26007i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(2.26007 + 1.64204i) q^{6} +1.72654i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.48459 + 4.56909i) q^{9} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(1.64204 + 2.26007i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-2.06909 + 0.847859i) q^{5} +(2.26007 + 1.64204i) q^{6} +1.72654i q^{7} +(0.587785 - 0.809017i) q^{8} +(-1.48459 + 4.56909i) q^{9} +(-1.70582 + 1.44575i) q^{10} +(-0.309017 - 0.951057i) q^{11} +(2.65688 + 0.863271i) q^{12} +(2.50000 + 0.812299i) q^{13} +(0.533531 + 1.64204i) q^{14} +(-5.31375 - 3.28408i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-2.00531 + 2.76007i) q^{17} +4.80423i q^{18} +(-0.322921 - 0.234616i) q^{19} +(-1.17557 + 1.90211i) q^{20} +(-3.90211 + 2.83505i) q^{21} +(-0.587785 - 0.809017i) q^{22} +(3.23842 - 1.05223i) q^{23} +2.79360 q^{24} +(3.56227 - 3.50859i) q^{25} +2.62866 q^{26} +(-4.79360 + 1.55754i) q^{27} +(1.01484 + 1.39680i) q^{28} +(-2.40211 + 1.74524i) q^{29} +(-6.06851 - 1.48131i) q^{30} +(0.0738814 + 0.0536780i) q^{31} -1.00000i q^{32} +(1.64204 - 2.26007i) q^{33} +(-1.05425 + 3.24466i) q^{34} +(-1.46386 - 3.57237i) q^{35} +(1.48459 + 4.56909i) q^{36} +(3.66994 + 1.19244i) q^{37} +(-0.379616 - 0.123345i) q^{38} +(2.26924 + 6.98401i) q^{39} +(-0.530249 + 2.17229i) q^{40} +(2.82974 - 8.70905i) q^{41} +(-2.83505 + 3.90211i) q^{42} -6.85816i q^{43} +(-0.809017 - 0.587785i) q^{44} +(-0.802198 - 10.7126i) q^{45} +(2.75476 - 2.00145i) q^{46} +(-1.43564 - 1.97599i) q^{47} +(2.65688 - 0.863271i) q^{48} +4.01905 q^{49} +(2.30371 - 4.43767i) q^{50} -9.53077 q^{51} +(2.50000 - 0.812299i) q^{52} +(1.12428 + 1.54743i) q^{53} +(-4.07768 + 2.96261i) q^{54} +(1.44575 + 1.70582i) q^{55} +(1.39680 + 1.01484i) q^{56} -1.11507i q^{57} +(-1.74524 + 2.40211i) q^{58} +(-3.45309 + 10.6275i) q^{59} +(-6.22925 + 0.466469i) q^{60} +(-3.43294 - 10.5655i) q^{61} +(0.0868528 + 0.0282202i) q^{62} +(-7.88873 - 2.56320i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-5.86144 + 0.438926i) q^{65} +(0.863271 - 2.65688i) q^{66} +(3.74779 - 5.15838i) q^{67} +3.41164i q^{68} +(7.69572 + 5.59127i) q^{69} +(-2.49614 - 2.94517i) q^{70} +(-8.84072 + 6.42316i) q^{71} +(2.82385 + 3.88670i) q^{72} +(10.0753 - 3.27366i) q^{73} +3.85880 q^{74} +(13.7791 + 2.28975i) q^{75} -0.399152 q^{76} +(1.64204 - 0.533531i) q^{77} +(4.31636 + 5.94095i) q^{78} +(-3.30272 + 2.39956i) q^{79} +(0.166977 + 2.22982i) q^{80} +(0.268667 + 0.195198i) q^{81} -9.15723i q^{82} +(8.12334 - 11.1808i) q^{83} +(-1.49047 + 4.58721i) q^{84} +(1.80902 - 7.41106i) q^{85} +(-2.11929 - 6.52250i) q^{86} +(-7.88873 - 2.56320i) q^{87} +(-0.951057 - 0.309017i) q^{88} +(-4.06227 - 12.5024i) q^{89} +(-4.07331 - 9.94038i) q^{90} +(-1.40247 + 4.31636i) q^{91} +(2.00145 - 2.75476i) q^{92} +0.255119i q^{93} +(-1.97599 - 1.43564i) q^{94} +(0.867073 + 0.211650i) q^{95} +(2.26007 - 1.64204i) q^{96} +(8.53258 + 11.7441i) q^{97} +(3.82234 - 1.24196i) q^{98} +4.80423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9	\( 8 q + 10 q^{3} + 2 q^{4} + 6 q^{6} + 2 q^{9} + 2 q^{11} + 20 q^{13} - 2 q^{14} - 2 q^{16} - 10 q^{17} + 16 q^{19} - 16 q^{21} + 10 q^{23} + 4 q^{24} - 10 q^{25} - 20 q^{27} - 10 q^{28} - 4 q^{29} + 10 q^{31} + 10 q^{33} - 10 q^{34} + 10 q^{35} - 2 q^{36} + 20 q^{37} - 10 q^{38} + 30 q^{39} + 26 q^{41} - 20 q^{42} - 2 q^{44} + 20 q^{45} + 16 q^{46} + 10 q^{47} + 8 q^{49} + 20 q^{50} - 40 q^{51} + 20 q^{52} - 10 q^{53} - 8 q^{54} + 10 q^{55} + 2 q^{56} - 20 q^{58} - 16 q^{59} - 10 q^{60} - 40 q^{61} - 30 q^{63} + 2 q^{64} - 10 q^{65} + 4 q^{66} + 28 q^{69} + 10 q^{70} - 26 q^{71} - 10 q^{73} + 8 q^{74} + 10 q^{75} + 4 q^{76} + 10 q^{77} + 20 q^{78} + 32 q^{79} - 18 q^{81} + 50 q^{83} - 24 q^{84} + 10 q^{85} - 10 q^{86} - 30 q^{87} + 6 q^{89} - 10 q^{90} + 40 q^{91} - 20 q^{92} - 10 q^{94} - 30 q^{95} + 6 q^{96} - 40 q^{97} - 20 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 10 * q^3 + 2 * q^4 + 6 * q^6 + 2 * q^9 + 2 * q^11 + 20 * q^13 - 2 * q^14 - 2 * q^16 - 10 * q^17 + 16 * q^19 - 16 * q^21 + 10 * q^23 + 4 * q^24 - 10 * q^25 - 20 * q^27 - 10 * q^28 - 4 * q^29 + 10 * q^31 + 10 * q^33 - 10 * q^34 + 10 * q^35 - 2 * q^36 + 20 * q^37 - 10 * q^38 + 30 * q^39 + 26 * q^41 - 20 * q^42 - 2 * q^44 + 20 * q^45 + 16 * q^46 + 10 * q^47 + 8 * q^49 + 20 * q^50 - 40 * q^51 + 20 * q^52 - 10 * q^53 - 8 * q^54 + 10 * q^55 + 2 * q^56 - 20 * q^58 - 16 * q^59 - 10 * q^60 - 40 * q^61 - 30 * q^63 + 2 * q^64 - 10 * q^65 + 4 * q^66 + 28 * q^69 + 10 * q^70 - 26 * q^71 - 10 * q^73 + 8 * q^74 + 10 * q^75 + 4 * q^76 + 10 * q^77 + 20 * q^78 + 32 * q^79 - 18 * q^81 + 50 * q^83 - 24 * q^84 + 10 * q^85 - 10 * q^86 - 30 * q^87 + 6 * q^89 - 10 * q^90 + 40 * q^91 - 20 * q^92 - 10 * q^94 - 30 * q^95 + 6 * q^96 - 40 * q^97 - 20 * q^98 + 8 * q^99

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