LMFDB - Embedded newform 650.2.l.c.131.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(131,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("650.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.l (of order $5$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			131.3
Character	$\chi$	$=$	650.131
Dual form			650.2.l.c.521.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.892707 + 0.648590i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.63942 - 1.52062i) q^{5} +(-0.892707 - 0.648590i) q^{6} +4.94642 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.550793 + 1.69517i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.892707 + 0.648590i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.63942 - 1.52062i) q^{5} +(-0.892707 - 0.648590i) q^{6} +4.94642 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.550793 + 1.69517i) q^{9} +(0.939587 - 2.02908i) q^{10} +(-0.745048 - 2.29302i) q^{11} +(0.340984 - 1.04944i) q^{12} +(0.309017 - 0.951057i) q^{13} +(1.52853 + 4.70432i) q^{14} +(2.44979 + 0.294157i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.90688 + 2.83851i) q^{17} -1.78240 q^{18} +(4.56778 + 3.31869i) q^{19} +(2.22012 + 0.266580i) q^{20} +(-4.41570 + 3.20820i) q^{21} +(1.95056 - 1.41716i) q^{22} +(0.0249333 + 0.0767368i) q^{23} +1.10345 q^{24} +(0.375420 + 4.98589i) q^{25} +1.00000 q^{26} +(-1.63072 - 5.01885i) q^{27} +(-4.00174 + 2.90743i) q^{28} +(0.133335 - 0.0968736i) q^{29} +(0.477266 + 2.42078i) q^{30} +(4.56829 + 3.31906i) q^{31} +1.00000 q^{32} +(2.15234 + 1.56377i) q^{33} +(-1.49229 + 4.59281i) q^{34} +(-8.10927 - 7.52163i) q^{35} +(-0.550793 - 1.69517i) q^{36} +(-2.24247 + 6.90160i) q^{37} +(-1.74474 + 5.36975i) q^{38} +(0.340984 + 1.04944i) q^{39} +(0.432523 + 2.19384i) q^{40} +(-1.66842 + 5.13486i) q^{41} +(-4.41570 - 3.20820i) q^{42} -0.386159 q^{43} +(1.95056 + 1.41716i) q^{44} +(3.48069 - 1.94155i) q^{45} +(-0.0652763 + 0.0474260i) q^{46} +(-7.76553 + 5.64199i) q^{47} +(0.340984 + 1.04944i) q^{48} +17.4671 q^{49} +(-4.62585 + 1.89777i) q^{50} -5.32873 q^{51} +(0.309017 + 0.951057i) q^{52} +(9.03260 - 6.56257i) q^{53} +(4.26929 - 3.10182i) q^{54} +(-2.26537 + 4.89217i) q^{55} +(-4.00174 - 2.90743i) q^{56} -6.23016 q^{57} +(0.133335 + 0.0968736i) q^{58} +(-1.02835 + 3.16494i) q^{59} +(-2.15482 + 1.20197i) q^{60} +(-2.04676 - 6.29928i) q^{61} +(-1.74493 + 5.37035i) q^{62} +(-2.72445 + 8.38501i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.95281 + 1.08929i) q^{65} +(-0.822120 + 2.53023i) q^{66} +(4.97383 + 3.61370i) q^{67} -4.82917 q^{68} +(-0.0720289 - 0.0523320i) q^{69} +(4.64759 - 10.0367i) q^{70} +(4.34304 - 3.15540i) q^{71} +(1.44200 - 1.04767i) q^{72} +(-1.94749 - 5.99375i) q^{73} -7.25677 q^{74} +(-3.56893 - 4.20744i) q^{75} -5.64609 q^{76} +(-3.68532 - 11.3422i) q^{77} +(-0.892707 + 0.648590i) q^{78} +(8.65414 - 6.28760i) q^{79} +(-1.95281 + 1.08929i) q^{80} +(0.384945 + 0.279679i) q^{81} -5.39911 q^{82} +(-4.41495 - 3.20765i) q^{83} +(1.68665 - 5.19097i) q^{84} +(-2.08872 - 10.5944i) q^{85} +(-0.119330 - 0.367259i) q^{86} +(-0.0561980 + 0.172960i) q^{87} +(-0.745048 + 2.29302i) q^{88} +(-1.69610 - 5.22006i) q^{89} +(2.92212 + 2.71036i) q^{90} +(1.52853 - 4.70432i) q^{91} +(-0.0652763 - 0.0474260i) q^{92} -6.23085 q^{93} +(-7.76553 - 5.64199i) q^{94} +(-2.44206 - 12.3866i) q^{95} +(-0.892707 + 0.648590i) q^{96} +(-6.02114 + 4.37462i) q^{97} +(5.39762 + 16.6122i) q^{98} +4.29742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.892707	+	0.648590i	−0.515405	+	0.374464i	−0.814870	−	0.579644i	$-0.803192\pi$
$3$	−0.892707	+	0.648590i	−0.515405	+	0.374464i	0.299465	+	0.954107i	$0.403192\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.63942	−	1.52062i	−0.733173	−	0.680043i
$5$	−1.63942	−	1.52062i	−0.733173	−	0.680043i
$6$	−0.892707	−	0.648590i	−0.364446	−	0.264786i
$7$	4.94642			1.86957			0.934785	−	0.355214i	$-0.115592\pi$
$7$	4.94642			1.86957			0.934785	+	0.355214i	$0.115592\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.550793	+	1.69517i	−0.183598	+	0.565056i
$10$	0.939587	−	2.02908i	0.297124	−	0.641652i
$11$	−0.745048	−	2.29302i	−0.224640	−	0.691372i	−0.998328	−	0.0578045i	$-0.981590\pi$
$11$	−0.745048	−	2.29302i	−0.224640	−	0.691372i	0.773688	−	0.633567i	$-0.218410\pi$
$12$	0.340984	−	1.04944i	0.0984336	−	0.302947i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i
$14$	1.52853	+	4.70432i	0.408516	+	1.25728i
$15$	2.44979	+	0.294157i	0.632532	+	0.0759509i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.90688	+	2.83851i	0.947557	+	0.688440i	0.950228	−	0.311556i	$-0.100850\pi$
$17$	3.90688	+	2.83851i	0.947557	+	0.688440i	−0.00267083	+	0.999996i	$0.500850\pi$
$18$	−1.78240			−0.420117
$19$	4.56778	+	3.31869i	1.04792	+	0.761359i	0.971816	−	0.235741i	$-0.0757516\pi$
$19$	4.56778	+	3.31869i	1.04792	+	0.761359i	0.0761050	+	0.997100i	$0.475752\pi$
$20$	2.22012	+	0.266580i	0.496434	+	0.0596090i
$21$	−4.41570	+	3.20820i	−0.963586	+	0.700086i
$22$	1.95056	−	1.41716i	0.415861	−	0.302141i
$23$	0.0249333	+	0.0767368i	0.00519895	+	0.0160007i	0.953622	−	0.301006i	$-0.0973223\pi$
$23$	0.0249333	+	0.0767368i	0.00519895	+	0.0160007i	−0.948423	+	0.317006i	$0.897322\pi$
$24$	1.10345			0.225240
$25$	0.375420	+	4.98589i	0.0750839	+	0.997177i
$26$	1.00000			0.196116
$27$	−1.63072	−	5.01885i	−0.313833	−	0.965878i
$28$	−4.00174	+	2.90743i	−0.756257	+	0.549453i
$29$	0.133335	−	0.0968736i	0.0247597	−	0.0179890i	−0.575337	−	0.817917i	$-0.695129\pi$
$29$	0.133335	−	0.0968736i	0.0247597	−	0.0179890i	0.600096	+	0.799928i	$0.295129\pi$
$30$	0.477266	+	2.42078i	0.0871364	+	0.441973i
$31$	4.56829	+	3.31906i	0.820489	+	0.596120i	0.916853	−	0.399226i	$-0.130721\pi$
$31$	4.56829	+	3.31906i	0.820489	+	0.596120i	−0.0963635	+	0.995346i	$0.530721\pi$
$32$	1.00000			0.176777
$33$	2.15234	+	1.56377i	0.374674	+	0.272217i
$34$	−1.49229	+	4.59281i	−0.255926	+	0.787660i
$35$	−8.10927	−	7.52163i	−1.37072	−	1.27139i
$36$	−0.550793	−	1.69517i	−0.0917989	−	0.282528i
$37$	−2.24247	+	6.90160i	−0.368659	+	1.13462i	0.578999	+	0.815329i	$0.303444\pi$
$37$	−2.24247	+	6.90160i	−0.368659	+	1.13462i	−0.947658	+	0.319288i	$0.896556\pi$
$38$	−1.74474	+	5.36975i	−0.283034	+	0.871088i
$39$	0.340984	+	1.04944i	0.0546011	+	0.168045i
$40$	0.432523	+	2.19384i	0.0683878	+	0.346876i
$41$	−1.66842	+	5.13486i	−0.260563	+	0.801930i	0.732120	+	0.681176i	$0.238531\pi$
$41$	−1.66842	+	5.13486i	−0.260563	+	0.801930i	−0.992682	+	0.120754i	$0.961469\pi$
$42$	−4.41570	−	3.20820i	−0.681358	−	0.495035i
$43$	−0.386159			−0.0588887			−0.0294443	−	0.999566i	$-0.509374\pi$
$43$	−0.386159			−0.0588887			−0.0294443	+	0.999566i	$0.509374\pi$
$44$	1.95056	+	1.41716i	0.294058	+	0.213646i
$45$	3.48069	−	1.94155i	0.518871	−	0.289429i
$46$	−0.0652763	+	0.0474260i	−0.00962446	+	0.00699258i
$47$	−7.76553	+	5.64199i	−1.13272	+	0.822969i	−0.986088	−	0.166223i	$-0.946843\pi$
$47$	−7.76553	+	5.64199i	−1.13272	+	0.822969i	−0.146631	+	0.989191i	$0.546843\pi$
$48$	0.340984	+	1.04944i	0.0492168	+	0.151474i
$49$	17.4671			2.49529
$50$	−4.62585	+	1.89777i	−0.654194	+	0.268385i
$51$	−5.32873			−0.746171
$52$	0.309017	+	0.951057i	0.0428529	+	0.131888i
$53$	9.03260	−	6.56257i	1.24072	−	0.901438i	0.243077	−	0.970007i	$-0.421843\pi$
$53$	9.03260	−	6.56257i	1.24072	−	0.901438i	0.997646	+	0.0685692i	$0.0218434\pi$
$54$	4.26929	−	3.10182i	0.580976	−	0.422104i
$55$	−2.26537	+	4.89217i	−0.305462	+	0.659660i
$56$	−4.00174	−	2.90743i	−0.534755	−	0.388522i
$57$	−6.23016			−0.825205
$58$	0.133335	+	0.0968736i	0.0175077	+	0.0127201i
$59$	−1.02835	+	3.16494i	−0.133880	+	0.412040i	−0.995414	−	0.0956594i	$-0.969504\pi$
$59$	−1.02835	+	3.16494i	−0.133880	+	0.412040i	0.861534	+	0.507700i	$0.169504\pi$
$60$	−2.15482	+	1.20197i	−0.278186	+	0.155174i
$61$	−2.04676	−	6.29928i	−0.262061	−	0.806540i	−0.992356	−	0.123409i	$-0.960617\pi$
$61$	−2.04676	−	6.29928i	−0.262061	−	0.806540i	0.730295	−	0.683132i	$-0.239383\pi$
$62$	−1.74493	+	5.37035i	−0.221607	+	0.682035i
$63$	−2.72445	+	8.38501i	−0.343249	+	1.05641i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.95281	+	1.08929i	−0.242216	+	0.135109i
$66$	−0.822120	+	2.53023i	−0.101196	+	0.311449i
$67$	4.97383	+	3.61370i	0.607650	+	0.441484i	0.848586	−	0.529057i	$-0.177454\pi$
$67$	4.97383	+	3.61370i	0.607650	+	0.441484i	−0.240936	+	0.970541i	$0.577454\pi$
$68$	−4.82917			−0.585622
$69$	−0.0720289	−	0.0523320i	−0.00867126	−	0.00630004i
$70$	4.64759	−	10.0367i	0.555493	−	1.19961i
$71$	4.34304	−	3.15540i	0.515424	−	0.374477i	−0.299453	−	0.954111i	$-0.596804\pi$
$71$	4.34304	−	3.15540i	0.515424	−	0.374477i	0.814877	+	0.579633i	$0.196804\pi$
$72$	1.44200	−	1.04767i	0.169941	−	0.123469i
$73$	−1.94749	−	5.99375i	−0.227936	−	0.701516i	−0.997980	−	0.0635249i	$-0.979766\pi$
$73$	−1.94749	−	5.99375i	−0.227936	−	0.701516i	0.770044	−	0.637991i	$-0.220234\pi$
$74$	−7.25677			−0.843583
$75$	−3.56893	−	4.20744i	−0.412105	−	0.485834i
$76$	−5.64609			−0.647651
$77$	−3.68532	−	11.3422i	−0.419981	−	1.29257i
$78$	−0.892707	+	0.648590i	−0.101079	+	0.0734383i
$79$	8.65414	−	6.28760i	0.973666	−	0.707410i	0.0173822	−	0.999849i	$-0.494467\pi$
$79$	8.65414	−	6.28760i	0.973666	−	0.707410i	0.956284	+	0.292439i	$0.0944668\pi$
$80$	−1.95281	+	1.08929i	−0.218330	+	0.121786i
$81$	0.384945	+	0.279679i	0.0427717	+	0.0310755i
$82$	−5.39911			−0.596232
$83$	−4.41495	−	3.20765i	−0.484603	−	0.352085i	0.318502	−	0.947922i	$-0.396820\pi$
$83$	−4.41495	−	3.20765i	−0.484603	−	0.352085i	−0.803105	+	0.595837i	$0.796820\pi$
$84$	1.68665	−	5.19097i	0.184028	−	0.566381i
$85$	−2.08872	−	10.5944i	−0.226554	−	1.14912i
$86$	−0.119330	−	0.367259i	−0.0128677	−	0.0396026i
$87$	−0.0561980	+	0.172960i	−0.00602505	+	0.0185432i
$88$	−0.745048	+	2.29302i	−0.0794223	+	0.244437i
$89$	−1.69610	−	5.22006i	−0.179786	−	0.553325i	0.820033	−	0.572316i	$-0.193955\pi$
$89$	−1.69610	−	5.22006i	−0.179786	−	0.553325i	−0.999820	+	0.0189905i	$0.993955\pi$
$90$	2.92212	+	2.71036i	0.308018	+	0.285697i
$91$	1.52853	−	4.70432i	0.160233	−	0.493147i
$92$	−0.0652763	−	0.0474260i	−0.00680552	−	0.00494450i
$93$	−6.23085			−0.646109
$94$	−7.76553	−	5.64199i	−0.800953	−	0.581927i
$95$	−2.44206	−	12.3866i	−0.250550	−	1.27084i
$96$	−0.892707	+	0.648590i	−0.0911116	+	0.0661964i
$97$	−6.02114	+	4.37462i	−0.611355	+	0.444175i	−0.849891	−	0.526958i	$-0.823332\pi$
$97$	−6.02114	+	4.37462i	−0.611355	+	0.444175i	0.238536	+	0.971134i	$0.423332\pi$
$98$	5.39762	+	16.6122i	0.545242	+	1.67808i
$99$	4.29742			0.431907
$100$	−3.23435	−	3.81300i	−0.323435	−	0.381300i
$101$	14.6833			1.46104			0.730519	−	0.682892i	$-0.239278\pi$
$101$	14.6833			1.46104			0.730519	+	0.682892i	$0.239278\pi$
$102$	−1.64667	−	5.06792i	−0.163044	−	0.501799i
$103$	1.19432	−	0.867726i	0.117680	−	0.0854996i	−0.527389	−	0.849624i	$-0.676829\pi$
$103$	1.19432	−	0.867726i	0.117680	−	0.0854996i	0.645069	+	0.764125i	$0.276829\pi$
$104$	−0.809017	+	0.587785i	−0.0793306	+	0.0576371i
$105$	12.1177	+	1.45502i	1.18256	+	0.141996i
$106$	9.03260	+	6.56257i	0.877324	+	0.637413i
$107$	−4.92611			−0.476226			−0.238113	−	0.971238i	$-0.576529\pi$
$107$	−4.92611			−0.476226			−0.238113	+	0.971238i	$0.576529\pi$
$108$	4.26929	+	3.10182i	0.410812	+	0.298473i
$109$	5.04800	−	15.5361i	0.483511	−	1.48809i	−0.350616	−	0.936519i	$-0.614028\pi$
$109$	5.04800	−	15.5361i	0.483511	−	1.48809i	0.834127	−	0.551573i	$-0.185972\pi$
$110$	−5.35276	−	0.642730i	−0.510366	−	0.0612819i
$111$	−2.47444	−	7.61555i	−0.234864	−	0.722836i
$112$	1.52853	−	4.70432i	0.144432	−	0.444517i
$113$	−3.59268	+	11.0571i	−0.337971	+	1.04017i	0.627269	+	0.778803i	$0.284173\pi$
$113$	−3.59268	+	11.0571i	−0.337971	+	1.04017i	−0.965240	+	0.261365i	$0.915827\pi$
$114$	−1.92523	−	5.92523i	−0.180314	−	0.554949i
$115$	0.0758114	−	0.163718i	0.00706945	−	0.0152668i
$116$	−0.0509295	+	0.156745i	−0.00472868	+	0.0145534i
$117$	1.44200	+	1.04767i	0.133313	+	0.0968572i
$118$	−3.32782			−0.306350
$119$	19.3250	+	14.0405i	1.77152	+	1.28709i
$120$	−1.80902	−	1.67793i	−0.165140	−	0.153173i
$121$	4.19634	−	3.04882i	0.381485	−	0.277165i
$122$	5.35849	−	3.89317i	0.485135	−	0.352471i
$123$	−1.84101	−	5.66604i	−0.165998	−	0.510890i
$124$	−5.64672			−0.507090
$125$	6.96617	−	8.74485i	0.623074	−	0.782163i
$126$	−8.81652			−0.785438
$127$	1.74849	+	5.38131i	0.155154	+	0.477514i	0.998176	−	0.0603638i	$-0.0192261\pi$
$127$	1.74849	+	5.38131i	0.155154	+	0.477514i	−0.843023	+	0.537878i	$0.819226\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	0.344727	−	0.250459i	0.0303515	−	0.0220517i
$130$	−1.63942	−	1.52062i	−0.143787	−	0.133367i
$131$	−6.43093	−	4.67234i	−0.561873	−	0.408225i	0.270271	−	0.962784i	$-0.412887\pi$
$131$	−6.43093	−	4.67234i	−0.561873	−	0.408225i	−0.832144	+	0.554560i	$0.812887\pi$
$132$	−2.66044			−0.231561
$133$	22.5942	+	16.4156i	1.95916	+	1.42341i
$134$	−1.89984	+	5.84709i	−0.164121	+	0.505112i
$135$	−4.95832	+	10.7077i	−0.426745	+	0.921575i
$136$	−1.49229	−	4.59281i	−0.127963	−	0.393830i
$137$	4.32804	−	13.3203i	0.369769	−	1.13803i	−0.577171	−	0.816623i	$-0.695843\pi$
$137$	4.32804	−	13.3203i	0.369769	−	1.13803i	0.946940	−	0.321410i	$-0.104157\pi$
$138$	0.0275126	−	0.0846750i	0.00234203	−	0.00720802i
$139$	4.27188	+	13.1475i	0.362336	+	1.11515i	0.951633	+	0.307238i	$0.0994048\pi$
$139$	4.27188	+	13.1475i	0.362336	+	1.11515i	−0.589297	+	0.807917i	$0.700595\pi$
$140$	10.9816	+	1.31861i	0.928118	+	0.111443i
$141$	3.27301	−	10.0733i	0.275637	−	0.848324i
$142$	4.34304	+	3.15540i	0.364460	+	0.264796i
$143$	−2.41102			−0.201620
$144$	1.44200	+	1.04767i	0.120166	+	0.0873059i
$145$	−0.365901	−	0.0439353i	−0.0303864	−	0.00364863i
$146$	5.09859	−	3.70434i	0.421962	−	0.306574i
$147$	−15.5930	+	11.3290i	−1.28609	+	0.934396i
$148$	−2.24247	−	6.90160i	−0.184330	−	0.567308i
$149$	14.9689			1.22630			0.613152	−	0.789965i	$-0.289901\pi$
$149$	14.9689			1.22630			0.613152	+	0.789965i	$0.289901\pi$
$150$	2.89866	−	4.69443i	0.236674	−	0.383299i
$151$	−10.5564			−0.859068			−0.429534	−	0.903051i	$-0.641322\pi$
$151$	−10.5564			−0.859068			−0.429534	+	0.903051i	$0.641322\pi$
$152$	−1.74474	−	5.36975i	−0.141517	−	0.435544i
$153$	−6.96364	+	5.05938i	−0.562977	+	0.409027i
$154$	9.64828	−	7.00989i	0.777481	−	0.564873i
$155$	−2.44233	−	12.3880i	−0.196173	−	0.995027i
$156$	−0.892707	−	0.648590i	−0.0714738	−	0.0519287i
$157$	−20.3428			−1.62353			−0.811767	−	0.583982i	$-0.801494\pi$
$157$	−20.3428			−1.62353			−0.811767	+	0.583982i	$0.801494\pi$
$158$	8.65414	+	6.28760i	0.688486	+	0.500214i
$159$	−3.80705	+	11.7169i	−0.301919	+	0.929211i
$160$	−1.63942	−	1.52062i	−0.129608	−	0.120216i
$161$	0.123331	+	0.379572i	0.00971981	+	0.0299145i
$162$	−0.147036	+	0.452530i	−0.0115522	+	0.0355542i
$163$	−4.81942	+	14.8326i	−0.377486	+	1.16178i	0.564300	+	0.825570i	$0.309146\pi$
$163$	−4.81942	+	14.8326i	−0.377486	+	1.16178i	−0.941786	+	0.336213i	$0.890854\pi$
$164$	−1.66842	−	5.13486i	−0.130281	−	0.400965i
$165$	−1.15070	−	5.83657i	−0.0895818	−	0.454376i
$166$	1.68636	−	5.19008i	0.130887	−	0.402828i
$167$	−6.44840	−	4.68503i	−0.498992	−	0.362539i	0.309640	−	0.950854i	$-0.399791\pi$
$167$	−6.44840	−	4.68503i	−0.498992	−	0.362539i	−0.808632	+	0.588315i	$0.799791\pi$
$168$	5.45811			0.421102
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	9.43043	−	5.26035i	0.723281	−	0.403450i
$171$	−8.14164	+	5.91524i	−0.622606	+	0.452350i
$172$	0.312409	−	0.226979i	0.0238210	−	0.0173070i
$173$	−6.86465	−	21.1272i	−0.521910	−	1.60627i	−0.770346	−	0.637626i	$-0.779917\pi$
$173$	−6.86465	−	21.1272i	−0.521910	−	1.60627i	0.248436	−	0.968648i	$-0.420083\pi$
$174$	−0.181860			−0.0137868
$175$	1.85698	+	24.6623i	0.140375	+	1.86429i
$176$	−2.41102			−0.181738
$177$	−1.13473	−	3.49234i	−0.0852917	−	0.262501i
$178$	4.44045	−	3.22617i	0.332826	−	0.241812i
$179$	−15.8621	+	11.5245i	−1.18559	+	0.861381i	−0.992791	−	0.119858i	$-0.961756\pi$
$179$	−15.8621	+	11.5245i	−1.18559	+	0.861381i	−0.192798	+	0.981239i	$0.561756\pi$
$180$	−1.67473	+	3.61665i	−0.124827	+	0.269569i
$181$	−1.71061	−	1.24283i	−0.127148	−	0.0923788i	0.522393	−	0.852705i	$-0.325039\pi$
$181$	−1.71061	−	1.24283i	−0.127148	−	0.0923788i	−0.649542	+	0.760326i	$0.725039\pi$
$182$	4.94642			0.366653
$183$	5.91281	+	4.29591i	0.437087	+	0.317563i
$184$	0.0249333	−	0.0767368i	0.00183811	−	0.00565711i
$185$	14.1711	−	7.90471i	1.04188	−	0.581166i
$186$	−1.92544	−	5.92589i	−0.141180	−	0.434508i
$187$	3.59796	−	11.0734i	0.263109	−	0.809765i
$188$	2.96617	−	9.12893i	0.216330	−	0.665796i
$189$	−8.06624	−	24.8253i	−0.586732	−	1.80578i
$190$	11.0257	−	6.15021i	0.799890	−	0.446183i
$191$	3.05820	−	9.41218i	0.221284	−	0.681041i	−0.777364	−	0.629051i	$-0.783444\pi$
$191$	3.05820	−	9.41218i	0.221284	−	0.681041i	0.998648	−	0.0519901i	$-0.0165564\pi$
$192$	−0.892707	−	0.648590i	−0.0644256	−	0.0468079i
$193$	−23.0107			−1.65635			−0.828175	−	0.560470i	$-0.810621\pi$
$193$	−23.0107			−1.65635			−0.828175	+	0.560470i	$0.810621\pi$
$194$	−6.02114	−	4.37462i	−0.432293	−	0.314079i
$195$	1.03678	−	2.23898i	0.0742457	−	0.160337i
$196$	−14.1311	+	10.2669i	−1.00937	+	0.733348i
$197$	−14.5689	+	10.5849i	−1.03799	+	0.754144i	−0.969892	−	0.243534i	$-0.921693\pi$
$197$	−14.5689	+	10.5849i	−1.03799	+	0.754144i	−0.0680984	+	0.997679i	$0.521693\pi$
$198$	1.32798	+	4.08709i	0.0943752	+	0.290457i
$199$	−13.2631			−0.940200			−0.470100	−	0.882613i	$-0.655782\pi$
$199$	−13.2631			−0.940200			−0.470100	+	0.882613i	$0.655782\pi$
$200$	2.62691	−	4.25433i	0.185751	−	0.300827i
$201$	−6.78399			−0.478506
$202$	4.53738	+	13.9646i	0.319249	+	0.982546i
$203$	0.659531	−	0.479177i	0.0462900	−	0.0336316i
$204$	4.31103	−	3.13215i	0.301833	−	0.219294i
$205$	10.5434	−	5.88118i	0.736384	−	0.410759i
$206$	1.19432	+	0.867726i	0.0832124	+	0.0604573i
$207$	−0.143815			−0.00999583
$208$	−0.809017	−	0.587785i	−0.0560952	−	0.0407556i
$209$	4.20660	−	12.9466i	0.290977	−	0.895535i
$210$	2.36076	+	11.9742i	0.162908	+	0.826299i
$211$	2.37833	+	7.31975i	0.163731	+	0.503912i	0.998941	−	0.0460195i	$-0.0146536\pi$
$211$	2.37833	+	7.31975i	0.163731	+	0.503912i	−0.835209	+	0.549932i	$0.814654\pi$
$212$	−3.45015	+	10.6185i	−0.236957	+	0.729279i
$213$	−1.83050	+	5.63370i	−0.125424	+	0.386015i
$214$	−1.52225	−	4.68501i	−0.104059	−	0.320261i
$215$	0.633078	+	0.587202i	0.0431756	+	0.0400468i
$216$	−1.63072	+	5.01885i	−0.110957	+	0.341489i
$217$	22.5967	+	16.4174i	1.53396	+	1.11449i
$218$	16.3357			1.10639
$219$	5.62602	+	4.08755i	0.380172	+	0.276211i
$220$	−1.04282	−	5.28940i	−0.0703071	−	0.356611i
$221$	3.90688	−	2.83851i	0.262805	−	0.190939i
$222$	6.47817	−	4.70667i	0.434787	−	0.315891i
$223$	−7.99963	−	24.6203i	−0.535695	−	1.64870i	−0.742143	−	0.670242i	$-0.766190\pi$
$223$	−7.99963	−	24.6203i	−0.535695	−	1.64870i	0.206448	−	0.978458i	$-0.433810\pi$
$224$	4.94642			0.330496
$225$	−8.65869	−	2.10979i	−0.577246	−	0.140653i
$226$	−11.6262			−0.773361
$227$	−5.98467	−	18.4189i	−0.397217	−	1.22251i	−0.927222	−	0.374513i	$-0.877810\pi$
$227$	−5.98467	−	18.4189i	−0.397217	−	1.22251i	0.530005	−	0.847994i	$-0.322190\pi$
$228$	5.04030	−	3.66200i	0.333802	−	0.242522i
$229$	6.55724	−	4.76411i	0.433314	−	0.314821i	−0.349658	−	0.936877i	$-0.613702\pi$
$229$	6.55724	−	4.76411i	0.433314	−	0.314821i	0.782973	+	0.622056i	$0.213702\pi$
$230$	0.179132	+	0.0215092i	0.0118116	+	0.00141828i
$231$	10.6464	+	7.73504i	0.700480	+	0.508928i
$232$	−0.164811			−0.0108204
$233$	−6.62963	−	4.81671i	−0.434321	−	0.315553i	0.349053	−	0.937103i	$-0.386503\pi$
$233$	−6.62963	−	4.81671i	−0.434321	−	0.315553i	−0.783374	+	0.621550i	$0.786503\pi$
$234$	−0.550793	+	1.69517i	−0.0360065	+	0.110817i
$235$	21.3103	+	2.55883i	1.39013	+	0.166919i
$236$	−1.02835	−	3.16494i	−0.0669400	−	0.206020i
$237$	−3.64754	+	11.2260i	−0.236933	+	0.729205i
$238$	−7.38151	+	22.7180i	−0.478472	+	1.47259i
$239$	7.93233	+	24.4132i	0.513100	+	1.57916i	0.786713	+	0.617319i	$0.211781\pi$
$239$	7.93233	+	24.4132i	0.513100	+	1.57916i	−0.273613	+	0.961840i	$0.588219\pi$
$240$	1.03678	−	2.23898i	0.0669242	−	0.144526i
$241$	2.48779	−	7.65663i	0.160253	−	0.493207i	−0.838403	−	0.545052i	$-0.816510\pi$
$241$	2.48779	−	7.65663i	0.160253	−	0.493207i	0.998655	+	0.0518447i	$0.0165101\pi$
$242$	4.19634	+	3.04882i	0.269751	+	0.195986i
$243$	15.3063			0.981903
$244$	5.35849	+	3.89317i	0.343042	+	0.249235i
$245$	−28.6359	−	26.5608i	−1.82948	−	1.69691i
$246$	4.81982	−	3.50181i	0.307301	−	0.223267i
$247$	4.56778	−	3.31869i	0.290641	−	0.211163i
$248$	−1.74493	−	5.37035i	−0.110803	−	0.341017i
$249$	6.02170			0.381610
$250$	10.4695	+	3.92292i	0.662150	+	0.248107i
$251$	−22.9616			−1.44933			−0.724663	−	0.689104i	$-0.758004\pi$
$251$	−22.9616			−1.44933			−0.724663	+	0.689104i	$0.758004\pi$
$252$	−2.72445	−	8.38501i	−0.171624	−	0.528206i
$253$	0.157383	−	0.114345i	0.00989456	−	0.00718882i
$254$	−4.57762	+	3.32583i	−0.287225	+	0.208681i
$255$	8.73604	+	8.10298i	0.547072	+	0.507428i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	15.4808			0.965663			0.482832	−	0.875713i	$-0.339608\pi$
$257$	15.4808			0.965663			0.482832	+	0.875713i	$0.339608\pi$
$258$	0.344727	+	0.250459i	0.0214618	+	0.0155929i
$259$	−11.0922	+	34.1382i	−0.689234	+	2.12124i
$260$	0.939587	−	2.02908i	0.0582707	−	0.125838i
$261$	0.0907769	+	0.279383i	0.00561895	+	0.0172933i
$262$	2.45640	−	7.56001i	0.151757	−	0.467059i
$263$	1.34025	−	4.12487i	0.0826434	−	0.254350i	−0.901194	−	0.433417i	$-0.857308\pi$
$263$	1.34025	−	4.12487i	0.0826434	−	0.254350i	0.983837	+	0.179067i	$0.0573078\pi$
$264$	−0.822120	−	2.53023i	−0.0505980	−	0.155725i
$265$	−24.7874	−	2.97634i	−1.52268	−	0.182835i
$266$	−8.63020	+	26.5610i	−0.529152	+	1.62856i
$267$	4.89980	+	3.55991i	0.299863	+	0.217863i
$268$	−6.14800			−0.375549
$269$	−2.04220	−	1.48374i	−0.124515	−	0.0904653i	0.523785	−	0.851851i	$-0.324520\pi$
$269$	−2.04220	−	1.48374i	−0.124515	−	0.0904653i	−0.648300	+	0.761385i	$0.724520\pi$
$270$	−11.7159	−	1.40678i	−0.713005	−	0.0856137i
$271$	−14.1908	+	10.3102i	−0.862031	+	0.626302i	−0.928437	−	0.371491i	$-0.878847\pi$
$271$	−14.1908	+	10.3102i	−0.862031	+	0.626302i	0.0664058	+	0.997793i	$0.478847\pi$
$272$	3.90688	−	2.83851i	0.236889	−	0.172110i
$273$	1.68665	+	5.19097i	0.102081	+	0.314172i
$274$	14.0058			0.846123
$275$	11.1530	−	4.57557i	0.672553	−	0.275917i
$276$	0.0890326			0.00535913
$277$	−0.465592	−	1.43295i	−0.0279747	−	0.0860974i	0.936094	−	0.351749i	$-0.114413\pi$
$277$	−0.465592	−	1.43295i	−0.0279747	−	0.0860974i	−0.964069	+	0.265652i	$0.914413\pi$
$278$	−11.1839	+	8.12559i	−0.670767	+	0.487340i
$279$	−8.14254	+	5.91590i	−0.487481	+	0.354176i
$280$	2.13944	+	10.8516i	0.127856	+	0.648509i
$281$	25.2641	+	18.3554i	1.50713	+	1.09499i	0.967431	+	0.253135i	$0.0814616\pi$
$281$	25.2641	+	18.3554i	1.50713	+	1.09499i	0.539698	+	0.841859i	$0.318538\pi$
$282$	10.5917			0.630726
$283$	−0.705809	−	0.512800i	−0.0419560	−	0.0304828i	0.566610	−	0.823986i	$-0.308255\pi$
$283$	−0.705809	−	0.512800i	−0.0419560	−	0.0304828i	−0.608566	+	0.793504i	$0.708255\pi$
$284$	−1.65889	+	5.10555i	−0.0984372	+	0.302959i
$285$	10.2139	+	9.47372i	0.605017	+	0.561174i
$286$	−0.745048	−	2.29302i	−0.0440556	−	0.135589i
$287$	−8.25269	+	25.3992i	−0.487141	+	1.49926i
$288$	−0.550793	+	1.69517i	−0.0324558	+	0.0998887i
$289$	1.95325	+	6.01148i	0.114897	+	0.353617i
$290$	−0.0712846	−	0.361569i	−0.00418597	−	0.0212321i
$291$	2.53779	−	7.81051i	0.148768	−	0.457860i
$292$	5.09859	+	3.70434i	0.298372	+	0.216780i
$293$	−5.99361			−0.350150			−0.175075	−	0.984555i	$-0.556017\pi$
$293$	−5.99361			−0.350150			−0.175075	+	0.984555i	$0.556017\pi$
$294$	−15.5930	−	11.3290i	−0.909400	−	0.660718i
$295$	6.49858	−	3.62495i	0.378362	−	0.211052i
$296$	5.87085	−	4.26542i	0.341236	−	0.247923i
$297$	−10.2934	+	7.47856i	−0.597281	+	0.433950i
$298$	4.62566	+	14.2363i	0.267957	+	0.824687i
$299$	0.0806859			0.00466619
$300$	5.36040	+	1.30613i	0.309483	+	0.0754092i
$301$	−1.91010			−0.110097
$302$	−3.26211	−	10.0397i	−0.187713	−	0.577722i
$303$	−13.1079	+	9.52341i	−0.753026	+	0.547106i
$304$	4.56778	−	3.31869i	0.261980	−	0.190340i
$305$	−6.22332	+	13.4395i	−0.356346	+	0.769546i
$306$	−6.96364	−	5.05938i	−0.398085	−	0.289225i
$307$	−17.1856			−0.980837			−0.490418	−	0.871487i	$-0.663156\pi$
$307$	−17.1856			−0.980837			−0.490418	+	0.871487i	$0.663156\pi$
$308$	9.64828	+	7.00989i	0.549762	+	0.399425i
$309$	−0.503382	+	1.54925i	−0.0286364	+	0.0881338i
$310$	11.0269	−	6.15089i	0.626289	−	0.349347i
$311$	−0.898034	−	2.76387i	−0.0509229	−	0.156724i	0.922361	−	0.386328i	$-0.126257\pi$
$311$	−0.898034	−	2.76387i	−0.0509229	−	0.156724i	−0.973284	+	0.229604i	$0.926257\pi$
$312$	0.340984	−	1.04944i	0.0193044	−	0.0594129i
$313$	6.21489	−	19.1275i	0.351286	−	1.08115i	−0.606845	−	0.794820i	$-0.707565\pi$
$313$	6.21489	−	19.1275i	0.351286	−	1.08115i	0.958132	−	0.286328i	$-0.0924347\pi$
$314$	−6.28628	−	19.3472i	−0.354755	−	1.09182i
$315$	17.2170	−	9.60372i	0.970066	−	0.541108i
$316$	−3.30559	+	10.1735i	−0.185954	+	0.572307i
$317$	−5.38769	−	3.91439i	−0.302603	−	0.219854i	0.426113	−	0.904670i	$-0.359883\pi$
$317$	−5.38769	−	3.91439i	−0.302603	−	0.219854i	−0.728716	+	0.684816i	$0.759883\pi$
$318$	−12.3199			−0.690865
$319$	−0.321474	−	0.233565i	−0.0179991	−	0.0130771i
$320$	0.939587	−	2.02908i	0.0525245	−	0.113429i
$321$	4.39758	−	3.19503i	0.245449	−	0.178329i
$322$	−0.322884	+	0.234589i	−0.0179936	+	0.0130731i
$323$	8.42563	+	25.9314i	0.468814	+	1.44286i
$324$	−0.475819			−0.0264344
$325$	4.85787	+	1.18368i	0.269466	+	0.0656587i
$326$	−15.5960			−0.863781
$327$	5.57020	+	17.1433i	0.308033	+	0.948027i
$328$	4.36797	−	3.17352i	0.241181	−	0.175228i
$329$	−38.4116	+	27.9076i	−2.11770	+	1.53860i
$330$	5.19532	−	2.89798i	0.285993	−	0.159528i
$331$	−24.9954	−	18.1603i	−1.37387	−	0.998178i	−0.997423	−	0.0717414i	$-0.977144\pi$
$331$	−24.9954	−	18.1603i	−1.37387	−	0.998178i	−0.376451	−	0.926437i	$-0.622856\pi$
$332$	5.45717			0.299501
$333$	−10.4642	−	7.60271i	−0.573437	−	0.416626i
$334$	2.46307	−	7.58054i	0.134773	−	0.414789i
$335$	−2.65915	−	13.4877i	−0.145285	−	0.736912i
$336$	1.68665	+	5.19097i	0.0920142	+	0.283191i
$337$	1.11415	−	3.42899i	0.0606915	−	0.186789i	−0.916114	−	0.400918i	$-0.868691\pi$
$337$	1.11415	−	3.42899i	0.0606915	−	0.186789i	0.976805	+	0.214129i	$0.0686912\pi$
$338$	0.309017	−	0.951057i	0.0168083	−	0.0517307i
$339$	−3.96433	−	12.2010i	−0.215313	−	0.662666i
$340$	7.91705	+	7.34333i	0.429362	+	0.398248i
$341$	4.20707	−	12.9480i	0.227826	−	0.701176i
$342$	−8.14164	−	5.91524i	−0.440249	−	0.319860i
$343$	51.7744			2.79556
$344$	0.312409	+	0.226979i	0.0168440	+	0.0122379i
$345$	0.0385086	+	0.195323i	0.00207323	+	0.0105158i
$346$	17.9719	−	13.0573i	0.966175	−	0.701967i
$347$	−7.58351	+	5.50974i	−0.407104	+	0.295779i	−0.772428	−	0.635102i	$-0.780958\pi$
$347$	−7.58351	+	5.50974i	−0.407104	+	0.295779i	0.365324	+	0.930880i	$0.380958\pi$
$348$	−0.0561980	−	0.172960i	−0.00301253	−	0.00927160i
$349$	25.7423			1.37795			0.688976	−	0.724784i	$-0.258061\pi$
$349$	25.7423			1.37795			0.688976	+	0.724784i	$0.258061\pi$
$350$	−22.8814	+	9.38716i	−1.22306	+	0.501765i
$351$	−5.27713			−0.281672
$352$	−0.745048	−	2.29302i	−0.0397112	−	0.122218i
$353$	4.25015	−	3.08792i	0.226213	−	0.164353i	−0.468906	−	0.883248i	$-0.655352\pi$
$353$	4.25015	−	3.08792i	0.226213	−	0.164353i	0.695119	+	0.718895i	$0.255352\pi$
$354$	2.97077	−	2.15839i	0.157894	−	0.114717i
$355$	−11.9183	−	1.43108i	−0.632555	−	0.0759537i
$356$	4.44045	+	3.22617i	0.235343	+	0.170987i
$357$	−26.3581			−1.39502
$358$	−15.8621	−	11.5245i	−0.838338	−	0.609088i
$359$	−4.61422	+	14.2011i	−0.243529	+	0.749507i	0.752345	+	0.658769i	$0.228922\pi$
$359$	−4.61422	+	14.2011i	−0.243529	+	0.749507i	−0.995875	+	0.0907377i	$0.971078\pi$
$360$	−3.95715	−	0.475153i	−0.208560	−	0.0250428i
$361$	3.97962	+	12.2480i	0.209454	+	0.644632i
$362$	0.653394	−	2.01094i	0.0343416	−	0.105693i
$363$	−1.76867	+	5.44341i	−0.0928311	+	0.285705i
$364$	1.52853	+	4.70432i	0.0801166	+	0.246574i
$365$	−5.92147	+	12.7877i	−0.309944	+	0.669338i
$366$	−2.25849	+	6.95092i	−0.118053	+	0.363331i
$367$	14.3057	+	10.3937i	0.746749	+	0.542545i	0.894817	−	0.446432i	$-0.147306\pi$
$367$	14.3057	+	10.3937i	0.746749	+	0.542545i	−0.148069	+	0.988977i	$0.547306\pi$
$368$	0.0806859			0.00420604
$369$	−7.78549	−	5.65649i	−0.405297	−	0.294465i
$370$	11.8969	+	11.0348i	0.618492	+	0.573672i
$371$	44.6790	−	32.4612i	2.31962	−	1.68530i
$372$	5.04087	−	3.66240i	0.261357	−	0.189887i
$373$	9.56215	+	29.4293i	0.495109	+	1.52379i	0.816786	+	0.576941i	$0.195754\pi$
$373$	9.56215	+	29.4293i	0.495109	+	1.52379i	−0.321677	+	0.946850i	$0.604246\pi$
$374$	11.6432			0.602057
$375$	−0.546934	+	12.3248i	−0.0282436	+	0.636449i
$376$	9.59872			0.495016
$377$	−0.0509295	−	0.156745i	−0.00262300	−	0.00807277i
$378$	21.1177	−	15.3429i	1.08618	−	0.789153i
$379$	22.6932	−	16.4876i	1.16567	−	0.846909i	0.175187	−	0.984535i	$-0.443947\pi$
$379$	22.6932	−	16.4876i	1.16567	−	0.846909i	0.990484	+	0.137626i	$0.0439471\pi$
$380$	9.25633	+	8.58556i	0.474840	+	0.440430i
$381$	−5.05116	−	3.66988i	−0.258779	−	0.188014i
$382$	9.89655			0.506351
$383$	−21.8394	−	15.8673i	−1.11594	−	0.810779i	−0.132353	−	0.991203i	$-0.542253\pi$
$383$	−21.8394	−	15.8673i	−1.11594	−	0.810779i	−0.983589	+	0.180424i	$0.942253\pi$
$384$	0.340984	−	1.04944i	0.0174008	−	0.0535540i
$385$	−11.2055	+	24.1987i	−0.571083	+	1.23328i
$386$	−7.11071	−	21.8845i	−0.361926	−	1.11389i
$387$	0.212694	−	0.654604i	0.0108118	−	0.0332754i
$388$	2.29987	−	7.07828i	0.116758	−	0.359345i
$389$	0.0470968	+	0.144949i	0.00238790	+	0.00734921i	0.952243	−	0.305340i	$-0.0987701\pi$
$389$	0.0470968	+	0.144949i	0.00238790	+	0.00734921i	−0.949855	+	0.312689i	$0.898770\pi$
$390$	2.44979	+	0.294157i	0.124050	+	0.0148952i
$391$	−0.120407	+	0.370575i	−0.00608925	+	0.0187408i
$392$	−14.1311	−	10.2669i	−0.713730	−	0.518556i
$393$	8.77137			0.442457
$394$	−14.5689	−	10.5849i	−0.733970	−	0.533261i
$395$	−23.7489	−	2.85163i	−1.19493	−	0.143481i
$396$	−3.47669	+	2.52596i	−0.174710	+	0.126934i
$397$	−29.8967	+	21.7212i	−1.50047	+	1.09016i	−0.530280	+	0.847823i	$0.677913\pi$
$397$	−29.8967	+	21.7212i	−1.50047	+	1.09016i	−0.970193	+	0.242334i	$0.922087\pi$
$398$	−4.09854	−	12.6140i	−0.205441	−	0.632283i
$399$	−30.8170			−1.54278
$400$	4.85787	+	1.18368i	0.242894	+	0.0591839i
$401$	−22.9444			−1.14579			−0.572894	−	0.819629i	$-0.694179\pi$
$401$	−22.9444			−1.14579			−0.572894	+	0.819629i	$0.694179\pi$
$402$	−2.09637	−	6.45196i	−0.104557	−	0.321794i
$403$	4.56829	−	3.31906i	0.227563	−	0.165334i
$404$	−11.8790	+	8.63060i	−0.591003	+	0.429389i
$405$	−0.205802	−	1.04387i	−0.0102264	−	0.0518703i
$406$	0.659531	+	0.479177i	0.0327320	+	0.0237812i
$407$	17.4963			0.867257
$408$	4.31103	+	3.13215i	0.213428	+	0.155064i
$409$	3.84203	−	11.8245i	0.189976	−	0.584686i	−0.810023	−	0.586399i	$-0.800545\pi$
$409$	3.84203	−	11.8245i	0.189976	−	0.584686i	0.999999	+	0.00171285i	$0.000545217\pi$
$410$	8.85143	+	8.21000i	0.437141	+	0.405463i
$411$	4.77576	+	14.6983i	0.235571	+	0.725013i
$412$	−0.456190	+	1.40401i	−0.0224749	+	0.0691706i
$413$	−5.08666	+	15.6551i	−0.250298	+	0.770338i
$414$	−0.0444412	−	0.136776i	−0.00218417	−	0.00672218i
$415$	2.36035	+	11.9722i	0.115865	+	0.587690i
$416$	0.309017	−	0.951057i	0.0151508	−	0.0466294i
$417$	−12.3409	−	8.96616i	−0.604334	−	0.439075i
$418$	13.6129			0.665827
$419$	−23.1540	−	16.8224i	−1.13115	−	0.821828i	−0.145288	−	0.989389i	$-0.546411\pi$
$419$	−23.1540	−	16.8224i	−1.13115	−	0.821828i	−0.985862	+	0.167561i	$0.946411\pi$
$420$	−10.6586	+	5.94545i	−0.520088	+	0.290108i
$421$	23.2626	−	16.9013i	1.13375	−	0.823717i	0.147513	−	0.989060i	$-0.452873\pi$
$421$	23.2626	−	16.9013i	1.13375	−	0.823717i	0.986236	+	0.165343i	$0.0528732\pi$
$422$	−6.22655	+	4.52386i	−0.303104	+	0.220218i
$423$	−5.28691	−	16.2714i	−0.257059	−	0.791145i
$424$	−11.1649			−0.542216
$425$	−12.6858	+	20.5449i	−0.615351	+	0.996573i
$426$	−5.92363			−0.287001
$427$	−10.1241	−	31.1589i	−0.489941	−	1.50788i
$428$	3.98531	−	2.89550i	0.192637	−	0.139959i
$429$	2.15234	−	1.56377i	0.103916	−	0.0754993i
$430$	−0.362830	+	0.783548i	−0.0174972	+	0.0377861i
$431$	1.84290	+	1.33895i	0.0887695	+	0.0644948i	0.631285	−	0.775551i	$-0.282528\pi$
$431$	1.84290	+	1.33895i	0.0887695	+	0.0644948i	−0.542515	+	0.840046i	$0.682528\pi$
$432$	−5.27713			−0.253896
$433$	13.2589	+	9.63318i	0.637184	+	0.462941i	0.858882	−	0.512174i	$-0.171160\pi$
$433$	13.2589	+	9.63318i	0.637184	+	0.462941i	−0.221698	+	0.975115i	$0.571160\pi$
$434$	−8.63116	+	26.5640i	−0.414309	+	1.27511i
$435$	0.355138	−	0.198098i	0.0170276	−	0.00949808i
$436$	5.04800	+	15.5361i	0.241755	+	0.744046i
$437$	−0.140776	+	0.433263i	−0.00673421	+	0.0207258i
$438$	−2.14895	+	6.61379i	−0.102681	+	0.316019i
$439$	4.58792	+	14.1202i	0.218970	+	0.673919i	0.998848	+	0.0479879i	$0.0152809\pi$
$439$	4.58792	+	14.1202i	0.218970	+	0.673919i	−0.779878	+	0.625931i	$0.784719\pi$
$440$	4.70827	−	2.62630i	0.224458	−	0.125204i
$441$	−9.62074	+	29.6096i	−0.458130	+	1.40998i
$442$	3.90688	+	2.83851i	0.185831	+	0.135014i
$443$	34.1306			1.62159			0.810796	−	0.585329i	$-0.199035\pi$
$443$	34.1306			1.62159			0.810796	+	0.585329i	$0.199035\pi$
$444$	6.47817	+	4.70667i	0.307441	+	0.223369i
$445$	−5.15711	+	11.1370i	−0.244470	+	0.527945i
$446$	20.9433	−	15.2162i	0.991694	−	0.720508i
$447$	−13.3629	+	9.70870i	−0.632043	+	0.459206i
$448$	1.52853	+	4.70432i	0.0722161	+	0.222258i
$449$	−27.5497			−1.30015			−0.650074	−	0.759871i	$-0.725262\pi$
$449$	−27.5497			−1.30015			−0.650074	+	0.759871i	$0.725262\pi$
$450$	−0.669150	−	8.88687i	−0.0315440	−	0.418931i
$451$	13.0174			0.612965
$452$	−3.59268	−	11.0571i	−0.168986	−	0.520084i
$453$	9.42378	−	6.84678i	0.442768	−	0.321690i
$454$	15.6681	−	11.3835i	0.735339	−	0.534255i
$455$	−9.65940	+	5.38807i	−0.452840	+	0.252596i
$456$	5.04030	+	3.66200i	0.236034	+	0.171489i
$457$	35.1719			1.64527			0.822635	−	0.568570i	$-0.192503\pi$
$457$	35.1719			1.64527			0.822635	+	0.568570i	$0.192503\pi$
$458$	6.55724	+	4.76411i	0.306400	+	0.222612i
$459$	7.87503	−	24.2369i	0.367575	−	1.13128i
$460$	0.0348985	+	0.177012i	0.00162715	+	0.00825321i
$461$	8.23438	+	25.3428i	0.383513	+	1.18033i	0.937553	+	0.347842i	$0.113086\pi$
$461$	8.23438	+	25.3428i	0.383513	+	1.18033i	−0.554040	+	0.832490i	$0.686914\pi$
$462$	−4.06655	+	12.5156i	−0.189193	+	0.582276i
$463$	0.451399	−	1.38926i	0.0209783	−	0.0645646i	−0.940019	−	0.341121i	$-0.889193\pi$
$463$	0.451399	−	1.38926i	0.0209783	−	0.0645646i	0.960998	+	0.276557i	$0.0891933\pi$
$464$	−0.0509295	−	0.156745i	−0.00236434	−	0.00727669i
$465$	10.2150	+	9.47477i	0.473710	+	0.439382i
$466$	2.53229	−	7.79359i	0.117306	−	0.361031i
$467$	23.5661	+	17.1217i	1.09051	+	0.792300i	0.979485	−	0.201518i	$-0.0645875\pi$
$467$	23.5661	+	17.1217i	1.09051	+	0.792300i	0.111022	+	0.993818i	$0.464588\pi$
$468$	−1.78240			−0.0823917
$469$	24.6027	+	17.8749i	1.13605	+	0.825385i
$470$	4.15166	+	21.0580i	0.191502	+	0.971335i
$471$	18.1602	−	13.1941i	0.836777	−	0.607954i
$472$	2.69226	−	1.95604i	0.123921	−	0.0900341i
$473$	0.287707	+	0.885471i	0.0132288	+	0.0407140i
$474$	−11.8037			−0.542161
$475$	−14.8318	+	24.0203i	−0.680528	+	1.10213i
$476$	−23.8871			−1.09486
$477$	6.14956	+	18.9264i	0.281569	+	0.866580i
$478$	−20.7671	+	15.0882i	−0.949866	+	0.690118i
$479$	−2.21956	+	1.61261i	−0.101414	+	0.0736819i	−0.637337	−	0.770585i	$-0.719964\pi$
$479$	−2.21956	+	1.61261i	−0.101414	+	0.0736819i	0.535922	+	0.844267i	$0.319964\pi$
$480$	2.44979	+	0.294157i	0.111817	+	0.0134264i
$481$	5.87085	+	4.26542i	0.267688	+	0.194487i
$482$	8.05066			0.366697
$483$	−0.356285	−	0.258856i	−0.0162115	−	0.0117784i
$484$	−1.60286	+	4.93309i	−0.0728572	+	0.224232i
$485$	16.5233	+	1.98403i	0.750286	+	0.0900902i
$486$	4.72992	+	14.5572i	0.214554	+	0.660328i
$487$	2.54732	−	7.83984i	0.115430	−	0.355257i	−0.876606	−	0.481208i	$-0.840198\pi$
$487$	2.54732	−	7.83984i	0.115430	−	0.355257i	0.992036	+	0.125951i	$0.0401982\pi$
$488$	−2.04676	+	6.29928i	−0.0926525	+	0.285155i
$489$	−5.31797	−	16.3670i	−0.240487	−	0.740143i
$490$	16.4118	−	35.4421i	0.741411	−	1.60111i
$491$	−7.58664	+	23.3493i	−0.342380	+	1.05374i	0.620591	+	0.784134i	$0.286893\pi$
$491$	−7.58664	+	23.3493i	−0.342380	+	1.05374i	−0.962971	+	0.269604i	$0.913107\pi$
$492$	4.81982	+	3.50181i	0.217294	+	0.157874i
$493$	0.795901			0.0358456
$494$	4.56778	+	3.31869i	0.205514	+	0.149315i
$495$	−7.04529	−	6.53475i	−0.316662	−	0.293715i
$496$	4.56829	−	3.31906i	0.205122	−	0.149030i
$497$	21.4825	−	15.6079i	0.963621	−	0.700112i
$498$	1.86081	+	5.72698i	0.0833848	+	0.256632i
$499$	−6.52212			−0.291970			−0.145985	−	0.989287i	$-0.546635\pi$
$499$	−6.52212			−0.291970			−0.145985	+	0.989287i	$0.546635\pi$
$500$	−0.495660	+	11.1693i	−0.0221666	+	0.499508i
$501$	8.79520			0.392940
$502$	−7.09554	−	21.8378i	−0.316689	−	0.974669i
$503$	−10.3600	+	7.52696i	−0.461929	+	0.335611i	−0.794287	−	0.607542i	$-0.792156\pi$
$503$	−10.3600	+	7.52696i	−0.461929	+	0.335611i	0.332359	+	0.943153i	$0.392156\pi$
$504$	7.13271	−	5.18222i	0.317716	−	0.230834i
$505$	−24.0721	−	22.3277i	−1.07119	−	0.993569i
$506$	0.157383	+	0.114345i	0.00699651	+	0.00508326i
$507$	1.10345			0.0490058
$508$	−4.57762	−	3.32583i	−0.203099	−	0.147560i
$509$	4.66714	−	14.3640i	0.206867	−	0.636673i	−0.792764	−	0.609529i	$-0.791359\pi$
$509$	4.66714	−	14.3640i	0.206867	−	0.636673i	0.999632	−	0.0271440i	$-0.00864127\pi$
$510$	−5.00681	+	10.8124i	−0.221705	+	0.478782i
$511$	−9.63309	−	29.6476i	−0.426143	−	1.31153i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	9.20721	−	28.3369i	0.406508	−	1.25110i
$514$	4.78382	+	14.7231i	0.211005	+	0.649407i
$515$	−3.27748	−	0.393542i	−0.144423	−	0.0173415i
$516$	−0.131674	+	0.405251i	−0.00579662	+	0.0178402i
$517$	18.7229	+	13.6030i	0.823432	+	0.598258i
$518$	−35.8950			−1.57714
$519$	19.8310	+	14.4081i	0.870486	+	0.632445i
$520$	2.22012	+	0.266580i	0.0973587	+	0.0116903i
$521$	30.2879	−	22.0055i	1.32694	−	0.964077i	0.327120	−	0.944983i	$-0.393922\pi$
$521$	30.2879	−	22.0055i	1.32694	−	0.964077i	0.999818	−	0.0190942i	$-0.00607825\pi$
$522$	−0.237657	+	0.172668i	−0.0104020	+	0.00755747i
$523$	−10.0362	−	30.8882i	−0.438852	−	1.35065i	−0.889087	−	0.457737i	$-0.848660\pi$
$523$	−10.0362	−	30.8882i	−0.438852	−	1.35065i	0.450236	−	0.892910i	$-0.351340\pi$
$524$	7.94907			0.347257
$525$	−17.6534	−	20.8118i	−0.770459	−	0.908300i
$526$	4.33714			0.189108
$527$	8.42656	+	25.9343i	0.367067	+	1.12972i
$528$	2.15234	−	1.56377i	0.0936685	−	0.0680542i
$529$	18.6021	−	13.5152i	0.808788	−	0.587619i
$530$	−4.82907	−	24.4940i	−0.209762	−	1.06395i
$531$	−4.79870	−	3.48646i	−0.208246	−	0.151299i
$532$	−27.9279			−1.21083
$533$	4.36797	+	3.17352i	0.189198	+	0.137460i
$534$	−1.87156	+	5.76006i	−0.0809902	+	0.249262i
$535$	8.07599	+	7.49076i	0.349155	+	0.323854i
$536$	−1.89984	−	5.84709i	−0.0820604	−	0.252556i
$537$	6.68554	−	20.5760i	0.288503	−	0.887919i
$538$	0.780049	−	2.40074i	0.0336303	−	0.103503i
$539$	−13.0138	−	40.0523i	−0.560543	−	1.72517i
$540$	−2.28248	−	11.5772i	−0.0982222	−	0.498202i
$541$	0.380973	−	1.17251i	0.0163793	−	0.0504103i	−0.942533	−	0.334114i	$-0.891563\pi$
$541$	0.380973	−	1.17251i	0.0163793	−	0.0504103i	0.958912	+	0.283703i	$0.0915631\pi$
$542$	−14.1908	−	10.3102i	−0.609548	−	0.442863i
$543$	2.33316			0.100125
$544$	3.90688	+	2.83851i	0.167506	+	0.121700i
$545$	−31.9004	+	17.7942i	−1.36646	+	0.762221i
$546$	−4.41570	+	3.20820i	−0.188975	+	0.137298i
$547$	−19.9959	+	14.5279i	−0.854964	+	0.621168i	−0.926510	−	0.376270i	$-0.877207\pi$
$547$	−19.9959	+	14.5279i	−0.854964	+	0.621168i	0.0715461	+	0.997437i	$0.477207\pi$
$548$	4.32804	+	13.3203i	0.184885	+	0.569016i
$549$	11.8057			0.503854
$550$	7.79810	+	9.19324i	0.332512	+	0.392001i
$551$	0.930539			0.0396423
$552$	0.0275126	+	0.0846750i	0.00117101	+	0.00360401i
$553$	42.8070	−	31.1011i	1.82034	−	1.32255i
$554$	1.21894	−	0.885609i	0.0517876	−	0.0376259i
$555$	−7.52371	+	16.2478i	−0.319364	+	0.689681i
$556$	−11.1839	−	8.12559i	−0.474304	−	0.344602i
$557$	27.0866			1.14770			0.573849	−	0.818961i	$-0.305450\pi$
$557$	27.0866			1.14770			0.573849	+	0.818961i	$0.305450\pi$
$558$	−8.14254	−	5.91590i	−0.344701	−	0.250440i
$559$	−0.119330	+	0.367259i	−0.00504711	+	0.0155334i
$560$	−9.65940	+	5.38807i	−0.408184	+	0.227687i
$561$	3.97016	+	12.2189i	0.167620	+	0.515882i
$562$	−9.65002	+	29.6997i	−0.407062	+	1.25281i
$563$	8.50967	−	26.1901i	0.358640	−	1.10378i	−0.595229	−	0.803556i	$-0.702939\pi$
$563$	8.50967	−	26.1901i	0.358640	−	1.10378i	0.953869	−	0.300224i	$-0.0970614\pi$
$564$	3.27301	+	10.0733i	0.137819	+	0.424162i
$565$	22.7037	−	12.6642i	0.955150	−	0.532788i
$566$	0.269595	−	0.829728i	0.0113319	−	0.0348761i
$567$	1.90410	+	1.38341i	0.0799647	+	0.0580978i
$568$	−5.36829			−0.225249
$569$	−25.2572	−	18.3504i	−1.05884	−	0.769290i	−0.0849637	−	0.996384i	$-0.527077\pi$
$569$	−25.2572	−	18.3504i	−1.05884	−	0.769290i	−0.973873	+	0.227094i	$0.927077\pi$
$570$	−5.85378	+	12.6415i	−0.245188	+	0.529494i
$571$	27.4008	−	19.9079i	1.14669	−	0.833118i	0.158652	−	0.987335i	$-0.449285\pi$
$571$	27.4008	−	19.9079i	1.14669	−	0.833118i	0.988037	+	0.154216i	$0.0492853\pi$
$572$	1.95056	−	1.41716i	0.0815570	−	0.0592546i
$573$	3.37456	+	10.3858i	0.140974	+	0.433875i
$574$	−26.7063			−1.11470
$575$	−0.373241	+	0.153123i	−0.0155652	+	0.00638568i
$576$	−1.78240			−0.0742669
$577$	−11.1980	−	34.4638i	−0.466178	−	1.43475i	−0.857496	−	0.514491i	$-0.827981\pi$
$577$	−11.1980	−	34.4638i	−0.466178	−	1.43475i	0.391318	−	0.920256i	$-0.372019\pi$
$578$	−5.11367	+	3.71530i	−0.212701	+	0.154536i
$579$	20.5419	−	14.9245i	0.853691	−	0.620242i
$580$	0.321844	−	0.179527i	0.0133639	−	0.00745444i
$581$	−21.8382	−	15.8664i	−0.906000	−	0.658247i
$582$	8.21245			0.340417
$583$	−21.7778	−	15.8225i	−0.901945	−	0.655301i
$584$	−1.94749	+	5.99375i	−0.0805876	+	0.248023i
$585$	−0.770930	−	3.91031i	−0.0318740	−	0.161671i
$586$	−1.85213	−	5.70026i	−0.0765107	−	0.235476i
$587$	6.62522	−	20.3903i	0.273452	−	0.841599i	−0.716173	−	0.697923i	$-0.754108\pi$
$587$	6.62522	−	20.3903i	0.273452	−	0.841599i	0.989625	−	0.143676i	$-0.0458922\pi$
$588$	5.95598	−	18.3306i	0.245621	−	0.755942i
$589$	9.85204	+	30.3215i	0.405946	+	1.24937i
$590$	5.45570	+	5.06035i	0.224608	+	0.208331i
$591$	6.14049	−	18.8985i	0.252586	−	0.777379i
$592$	5.87085	+	4.26542i	0.241291	+	0.175308i
$593$	−39.4365			−1.61946			−0.809732	−	0.586800i	$-0.800387\pi$
$593$	−39.4365			−1.61946			−0.809732	+	0.586800i	$0.800387\pi$
$594$	−10.2934	−	7.47856i	−0.422342	−	0.306849i
$595$	−10.3317	−	52.4044i	−0.423558	−	2.14837i
$596$	−12.1101	+	8.79852i	−0.496050	+	0.360402i
$597$	11.8401	−	8.60234i	0.484583	−	0.352070i
$598$	0.0249333	+	0.0767368i	0.00101960	+	0.00313800i
$599$	27.8976			1.13986			0.569932	−	0.821692i	$-0.306969\pi$
$599$	27.8976			1.13986			0.569932	+	0.821692i	$0.306969\pi$
$600$	0.414256	+	5.50166i	0.0169119	+	0.224604i
$601$	−26.7032			−1.08925			−0.544623	−	0.838681i	$-0.683327\pi$
$601$	−26.7032			−1.08925			−0.544623	+	0.838681i	$0.683327\pi$
$602$	−0.590255	−	1.81662i	−0.0240570	−	0.0740398i
$603$	−8.86538	+	6.44108i	−0.361026	+	0.262301i
$604$	8.54031	−	6.20490i	0.347500	−	0.252474i
$605$	−11.5157	−	1.38274i	−0.468179	−	0.0562163i
$606$	−13.1079	−	9.52341i	−0.532470	−	0.386862i
$607$	17.9414			0.728219			0.364110	−	0.931356i	$-0.381373\pi$
$607$	17.9414			0.728219			0.364110	+	0.931356i	$0.381373\pi$
$608$	4.56778	+	3.31869i	0.185248	+	0.134591i
$609$	−0.277979	+	0.855530i	−0.0112643	+	0.0346678i
$610$	−14.7049	−	1.76568i	−0.595383	−	0.0714903i
$611$	2.96617	+	9.12893i	0.119998	+	0.369317i
$612$	2.65987	−	8.18625i	0.107519	−	0.330909i
$613$	0.490169	−	1.50859i	0.0197978	−	0.0609312i	−0.940670	−	0.339324i	$-0.889802\pi$
$613$	0.490169	−	1.50859i	0.0197978	−	0.0609312i	0.960467	+	0.278393i	$0.0898017\pi$
$614$	−5.31066	−	16.3445i	−0.214321	−	0.659611i
$615$	−5.59771	+	12.0885i	−0.225722	+	0.487456i
$616$	−3.68532	+	11.3422i	−0.148486	+	0.456992i
$617$	12.3996	+	9.00884i	0.499189	+	0.362682i	0.808707	−	0.588211i	$-0.200168\pi$
$617$	12.3996	+	9.00884i	0.499189	+	0.362682i	−0.309518	+	0.950894i	$0.600168\pi$
$618$	−1.62898			−0.0655271
$619$	−18.0271	−	13.0974i	−0.724568	−	0.526430i	0.163272	−	0.986581i	$-0.447795\pi$
$619$	−18.0271	−	13.0974i	−0.724568	−	0.526430i	−0.887840	+	0.460151i	$0.847795\pi$
$620$	9.25736	+	8.58652i	0.371785	+	0.344843i
$621$	0.344471	−	0.250273i	0.0138232	−	0.0100431i
$622$	2.35108	−	1.70816i	0.0942699	−	0.0684911i
$623$	−8.38962	−	25.8206i	−0.336123	−	1.03448i
$624$	1.10345			0.0441732
$625$	−24.7181	+	3.74360i	−0.988725	+	0.149744i
$626$	20.1118			0.803829
$627$	4.64176	+	14.2859i	0.185374	+	0.570523i
$628$	16.4577	−	11.9572i	0.656733	−	0.477144i
$629$	−28.3513	+	20.5984i	−1.13044	+	0.821314i
$630$	14.4540	+	13.4066i	0.575862	+	0.534131i
$631$	10.8337	+	7.87116i	0.431284	+	0.313346i	0.782162	−	0.623075i	$-0.214117\pi$
$631$	10.8337	+	7.87116i	0.431284	+	0.313346i	−0.350878	+	0.936421i	$0.614117\pi$
$632$	−10.6971			−0.425508
$633$	−6.87067	−	4.99183i	−0.273085	−	0.198408i
$634$	2.05792	−	6.33361i	0.0817303	−	0.251540i
$635$	5.31642	−	11.4811i	0.210976	−	0.455612i
$636$	−3.80705	−	11.7169i	−0.150959	−	0.464605i
$637$	5.39762	−	16.6122i	0.213861	−	0.658197i
$638$	0.122792	−	0.377915i	0.00486139	−	0.0149618i
$639$	2.95682	+	9.10016i	0.116970	+	0.359997i
$640$	2.22012	+	0.266580i	0.0877580	+	0.0105375i
$641$	−0.487794	+	1.50128i	−0.0192667	+	0.0592968i	−0.960228	−	0.279218i	$-0.909925\pi$
$641$	−0.487794	+	1.50128i	−0.0192667	+	0.0592968i	0.940961	+	0.338515i	$0.109925\pi$
$642$	4.39758	+	3.19503i	0.173559	+	0.126098i
$643$	−43.2032			−1.70377			−0.851883	−	0.523732i	$-0.824539\pi$
$643$	−43.2032			−1.70377			−0.851883	+	0.523732i	$0.824539\pi$
$644$	−0.322884	−	0.234589i	−0.0127234	−	0.00924409i
$645$	−0.946007	−	0.113591i	−0.0372490	−	0.00447265i
$646$	−22.0586	+	16.0265i	−0.867883	+	0.630554i
$647$	2.51092	−	1.82429i	0.0987143	−	0.0717201i	−0.537333	−	0.843370i	$-0.680568\pi$
$647$	2.51092	−	1.82429i	0.0987143	−	0.0717201i	0.636047	+	0.771650i	$0.280568\pi$
$648$	−0.147036	−	0.452530i	−0.00577612	−	0.0177771i
$649$	8.02345			0.314948
$650$	0.375420	+	4.98589i	0.0147252	+	0.195563i
$651$	−30.8204			−1.20795
$652$	−4.81942	−	14.8326i	−0.188743	−	0.580891i
$653$	7.91915	−	5.75360i	0.309900	−	0.225156i	−0.421953	−	0.906618i	$-0.638655\pi$
$653$	7.91915	−	5.75360i	0.309900	−	0.225156i	0.731854	+	0.681462i	$0.238655\pi$
$654$	−14.5830	+	10.5951i	−0.570239	+	0.414303i
$655$	3.43815	+	17.4390i	0.134340	+	0.681397i
$656$	4.36797	+	3.17352i	0.170541	+	0.123905i
$657$	11.2331			0.438244
$658$	−38.4116	−	27.9076i	−1.49744	−	1.08795i
$659$	−4.37889	+	13.4768i	−0.170577	+	0.524983i	−0.999404	−	0.0345224i	$-0.989009\pi$
$659$	−4.37889	+	13.4768i	−0.170577	+	0.524983i	0.828827	+	0.559506i	$0.189009\pi$
$660$	4.36158	+	4.04552i	0.169774	+	0.157472i
$661$	9.42088	+	28.9945i	0.366430	+	1.12775i	0.949081	+	0.315032i	$0.102015\pi$
$661$	9.42088	+	28.9945i	0.366430	+	1.12775i	−0.582651	+	0.812722i	$0.697985\pi$
$662$	9.54741	−	29.3839i	0.371071	−	1.14204i
$663$	−1.64667	+	5.06792i	−0.0639513	+	0.196822i
$664$	1.68636	+	5.19008i	0.0654434	+	0.201414i
$665$	−12.0795	−	61.2693i	−0.468421	−	2.37592i
$666$	3.99698	−	12.3014i	0.154880	−	0.476671i
$667$	0.0107583	+	0.00781633i	0.000416561	+	0.000302650i
$668$	7.97066			0.308394
$669$	23.1098	+	16.7903i	0.893477	+	0.649149i
$670$	12.0058	−	6.69693i	0.463826	−	0.258725i
$671$	−12.9194	+	9.38653i	−0.498750	+	0.362363i
$672$	−4.41570	+	3.20820i	−0.170339	+	0.123759i
$673$	−5.51655	−	16.9782i	−0.212647	−	0.654461i	−0.999312	−	0.0370809i	$-0.988194\pi$
$673$	−5.51655	−	16.9782i	−0.212647	−	0.654461i	0.786665	−	0.617380i	$-0.211806\pi$
$674$	3.60546			0.138877
$675$	24.4112	−	10.0148i	0.939588	−	0.385469i
$676$	1.00000			0.0384615
$677$	0.552592	+	1.70070i	0.0212378	+	0.0653633i	0.961114	−	0.276153i	$-0.0890596\pi$
$677$	0.552592	+	1.70070i	0.0212378	+	0.0653633i	−0.939876	+	0.341516i	$0.889060\pi$
$678$	10.3788	−	7.54061i	0.398594	−	0.289596i
$679$	−29.7831	+	21.6387i	−1.14297	+	0.830417i
$680$	−4.53742	+	9.79878i	−0.174002	+	0.375766i
$681$	17.2889	+	12.5611i	0.662512	+	0.481343i
$682$	13.6144			0.521321
$683$	−15.2834	−	11.1040i	−0.584802	−	0.424883i	0.255650	−	0.966769i	$-0.417710\pi$
$683$	−15.2834	−	11.1040i	−0.584802	−	0.424883i	−0.840452	+	0.541886i	$0.817710\pi$
$684$	3.10983	−	9.57107i	0.118907	−	0.365959i
$685$	−27.3507	+	15.2564i	−1.04502	+	0.582916i
$686$	15.9992	+	49.2404i	0.610851	+	1.88001i
$687$	−2.76374	+	8.50591i	−0.105443	+	0.324521i
$688$	−0.119330	+	0.367259i	−0.00454940	+	0.0140016i
$689$	−3.45015	−	10.6185i	−0.131440	−	0.404531i
$690$	−0.173863	+	0.0969820i	−0.00661887	+	0.00369204i
$691$	−6.57624	+	20.2396i	−0.250172	+	0.769950i	0.744571	+	0.667543i	$0.232654\pi$
$691$	−6.57624	+	20.2396i	−0.250172	+	0.769950i	−0.994743	+	0.102406i	$0.967346\pi$
$692$	17.9719	+	13.0573i	0.683189	+	0.496366i
$693$	21.2568			0.807481
$694$	−7.58351	−	5.50974i	−0.287866	−	0.209147i
$695$	12.9889	−	28.0502i	0.492698	−	1.06400i
$696$	0.147128	−	0.106895i	0.00557688	−	0.00405184i
$697$	−21.0937	+	15.3254i	−0.798979	+	0.580492i
$698$	7.95479	+	24.4823i	0.301093	+	0.926670i
$699$	9.04238			0.342014
$700$	−15.9985	−	18.8607i	−0.604685	−	0.712867i
$701$	15.3134			0.578381			0.289190	−	0.957272i	$-0.406614\pi$
$701$	15.3134			0.578381			0.289190	+	0.957272i	$0.406614\pi$
$702$	−1.63072	−	5.01885i	−0.0615477	−	0.189424i
$703$	−33.1474	+	24.0830i	−1.25018	+	0.908306i
$704$	1.95056	−	1.41716i	0.0735145	−	0.0534114i
$705$	−20.6835	+	11.5374i	−0.778986	+	0.434523i
$706$	4.25015	+	3.08792i	0.159957	+	0.116215i
$707$	72.6295			2.73151
$708$	2.97077	+	2.15839i	0.111648	+	0.0811172i
$709$	4.54438	−	13.9862i	0.170668	−	0.525262i	−0.828741	−	0.559632i	$-0.810943\pi$
$709$	4.54438	−	13.9862i	0.170668	−	0.525262i	0.999409	+	0.0343702i	$0.0109425\pi$
$710$	−2.32191	−	11.7772i	−0.0871396	−	0.441989i
$711$	5.89189	+	18.1334i	0.220963	+	0.680055i
$712$	−1.69610	+	5.22006i	−0.0635640	+	0.195630i
$713$	−0.140791	+	0.433311i	−0.00527268	+	0.0162276i
$714$	−8.14511	−	25.0681i	−0.304823	−	0.938149i
$715$	3.95269	+	3.66626i	0.147822	+	0.137110i
$716$	6.05878	−	18.6470i	0.226427	−	0.696872i
$717$	−22.9154	−	16.6490i	−0.855791	−	0.621769i
$718$	−14.9319			−0.557255
$719$	−22.4680	−	16.3240i	−0.837916	−	0.608782i	0.0838715	−	0.996477i	$-0.473271\pi$
$719$	−22.4680	−	16.3240i	−0.837916	−	0.608782i	−0.921788	+	0.387695i	$0.873271\pi$
$720$	−0.770930	−	3.91031i	−0.0287309	−	0.145729i
$721$	5.90762	−	4.29213i	0.220011	−	0.159847i
$722$	−10.4188	+	7.56969i	−0.387747	+	0.281715i
$723$	2.74514	+	8.44868i	0.102093	+	0.314210i
$724$	2.11443			0.0785821
$725$	0.533057	+	0.628425i	0.0197972	+	0.0233391i
$726$	−5.72354			−0.212420
$727$	−2.96640	−	9.12965i	−0.110018	−	0.338600i	0.880858	−	0.473381i	$-0.156967\pi$
$727$	−2.96640	−	9.12965i	−0.110018	−	0.338600i	−0.990875	+	0.134781i	$0.956967\pi$
$728$	−4.00174	+	2.90743i	−0.148314	+	0.107757i
$729$	−14.8189	+	10.7666i	−0.548849	+	0.398762i
$730$	−13.9917	−	1.68004i	−0.517854	−	0.0621811i
$731$	−1.50868	−	1.09612i	−0.0558004	−	0.0405414i
$732$	−7.30863			−0.270135
$733$	−22.6012	−	16.4207i	−0.834793	−	0.606513i	0.0861181	−	0.996285i	$-0.472554\pi$
$733$	−22.6012	−	16.4207i	−0.834793	−	0.606513i	−0.920911	+	0.389772i	$0.872554\pi$
$734$	−5.46427	+	16.8173i	−0.201690	+	0.620738i
$735$	42.7905	+	5.13805i	1.57835	+	0.189520i
$736$	0.0249333	+	0.0767368i	0.000919054	+	0.00282856i
$737$	4.58055	−	14.0975i	0.168727	−	0.519287i
$738$	2.97379	−	9.15240i	0.109467	−	0.336904i
$739$	−3.36957	−	10.3705i	−0.123952	−	0.381484i	0.869757	−	0.493480i	$-0.164275\pi$
$739$	−3.36957	−	10.3705i	−0.123952	−	0.381484i	−0.993709	+	0.111996i	$0.964275\pi$
$740$	−6.81837	+	14.7246i	−0.250648	+	0.541287i
$741$	−1.92523	+	5.92523i	−0.0707249	+	0.217669i
$742$	44.6790	+	32.4612i	1.64022	+	1.19169i
$743$	−29.9780			−1.09979			−0.549893	−	0.835235i	$-0.685331\pi$
$743$	−29.9780			−1.09979			−0.549893	+	0.835235i	$0.685331\pi$
$744$	5.04087	+	3.66240i	0.184807	+	0.134270i
$745$	−24.5404	−	22.7621i	−0.899092	−	0.833939i
$746$	−25.0340	+	18.1883i	−0.916561	+	0.665921i
$747$	7.86922	−	5.71732i	0.287920	−	0.209186i
$748$	3.59796	+	11.0734i	0.131554	+	0.404883i
$749$	−24.3666			−0.890337
$750$	−11.8906	+	3.28840i	−0.434182	+	0.120075i
$751$	15.1137			0.551506			0.275753	−	0.961228i	$-0.411073\pi$
$751$	15.1137			0.551506			0.275753	+	0.961228i	$0.411073\pi$
$752$	2.96617	+	9.12893i	0.108165	+	0.332898i
$753$	20.4980	−	14.8927i	0.746989	−	0.542720i
$754$	0.133335	−	0.0968736i	0.00485578	−	0.00352793i
$755$	17.3064	+	16.0523i	0.629845	+	0.584203i
$756$	21.1177	+	15.3429i	0.768043	+	0.558016i
$757$	8.77515			0.318938			0.159469	−	0.987203i	$-0.449022\pi$
$757$	8.77515			0.318938			0.159469	+	0.987203i	$0.449022\pi$
$758$	22.6932	+	16.4876i	0.824254	+	0.598855i
$759$	−0.0663335	+	0.204154i	−0.00240775	+	0.00741030i
$760$	−5.30499	+	11.4564i	−0.192432	+	0.415567i
$761$	−9.29884	−	28.6189i	−0.337083	−	1.03743i	−0.965687	−	0.259709i	$-0.916373\pi$
$761$	−9.29884	−	28.6189i	−0.337083	−	1.03743i	0.628604	−	0.777725i	$-0.283627\pi$
$762$	1.92937	−	5.93799i	0.0698937	−	0.215111i
$763$	24.9695	−	76.8483i	0.903957	−	2.78209i
$764$	3.05820	+	9.41218i	0.110642	+	0.340521i
$765$	19.1098	+	2.29459i	0.690915	+	0.0829612i
$766$	8.34191	−	25.6738i	0.301406	−	0.927631i
$767$	2.69226	+	1.95604i	0.0972119	+	0.0706286i
$768$	1.10345			0.0398172
$769$	28.6400	+	20.8082i	1.03278	+	0.750362i	0.968864	−	0.247593i	$-0.0796396\pi$
$769$	28.6400	+	20.8082i	1.03278	+	0.750362i	0.0639206	+	0.997955i	$0.479640\pi$
$770$	−26.4770	−	3.17921i	−0.954165	−	0.114571i
$771$	−13.8198	+	10.0407i	−0.497708	+	0.361606i
$772$	18.6161	−	13.5254i	0.670007	−	0.486789i
$773$	10.5640	+	32.5127i	0.379961	+	1.16940i	0.940070	+	0.340980i	$0.110759\pi$
$773$	10.5640	+	32.5127i	0.379961	+	1.16940i	−0.560110	+	0.828418i	$0.689241\pi$
$774$	0.688292			0.0247401
$775$	−14.8334	+	24.0230i	−0.532832	+	0.862932i
$776$	7.44254			0.267172
$777$	−12.2396	−	37.6697i	−0.439094	−	1.35139i
$778$	−0.123301	+	0.0895835i	−0.00442056	+	0.00321172i
$779$	−24.6620	+	17.9180i	−0.883606	+	0.641977i
$780$	0.477266	+	2.42078i	0.0170889	+	0.0866780i
$781$	−10.4712	−	7.60775i	−0.374688	−	0.272227i
$782$	−0.389646			−0.0139337
$783$	−0.703626	−	0.511214i	−0.0251456	−	0.0182693i
$784$	5.39762	−	16.6122i	0.192772	−	0.593291i
$785$	33.3505	+	30.9337i	1.19033	+	1.10407i
$786$	2.71050	+	8.34207i	0.0966804	+	0.297552i
$787$	−10.1054	+	31.1012i	−0.360219	+	1.10864i	0.592702	+	0.805422i	$0.298061\pi$
$787$	−10.1054	+	31.1012i	−0.360219	+	1.10864i	−0.952921	+	0.303218i	$0.901939\pi$
$788$	5.56482	−	17.1268i	0.198239	−	0.610116i
$789$	1.47890	+	4.55157i	0.0526501	+	0.162040i
$790$	−4.62674	−	23.4677i	−0.164612	−	0.834943i
$791$	−17.7709	+	54.6932i	−0.631861	+	1.94467i
$792$	−3.47669	−	2.52596i	−0.123539	−	0.0897561i
$793$	−6.62346			−0.235206
$794$	−29.8967	−	21.7212i	−1.06099	−	0.770858i
$795$	24.0584	−	13.4199i	0.853262	−	0.475954i
$796$	10.7301	−	7.79588i	0.380319	−	0.276318i
$797$	−16.3075	+	11.8481i	−0.577640	+	0.419680i	−0.837872	−	0.545866i	$-0.816201\pi$
$797$	−16.3075	+	11.8481i	−0.577640	+	0.419680i	0.260233	+	0.965546i	$0.416201\pi$
$798$	−9.52297	−	29.3087i	−0.337109	−	1.03752i
$799$	−46.3538			−1.63988
$800$	0.375420	+	4.98589i	0.0132731	+	0.176278i
$801$	9.78308			0.345668
$802$	−7.09021	−	21.8214i	−0.250364	−	0.770541i
$803$	−12.2928	+	8.93126i	−0.433804	+	0.315177i
$804$	5.48836	−	3.98753i	0.193560	−	0.140629i
$805$	0.374995	−	0.809819i	0.0132168	−	0.0285424i
$806$	4.56829	+	3.31906i	0.160911	+	0.116909i
$807$	2.78542			0.0980515
$808$	−11.8790	−	8.63060i	−0.417902	−	0.303624i
$809$	1.15751	−	3.56243i	0.0406957	−	0.125249i	−0.928645	−	0.370971i	$-0.879025\pi$
$809$	1.15751	−	3.56243i	0.0406957	−	0.125249i	0.969340	+	0.245722i	$0.0790251\pi$
$810$	0.929182	−	0.518303i	0.0326481	−	0.0182113i
$811$	4.34200	+	13.3633i	0.152468	+	0.469249i	0.997896	−	0.0648413i	$-0.0206541\pi$
$811$	4.34200	+	13.3633i	0.152468	+	0.469249i	−0.845427	+	0.534091i	$0.820654\pi$
$812$	−0.251918	+	0.775325i	−0.00884060	+	0.0272086i
$813$	5.98114	−	18.4080i	0.209768	−	0.645598i
$814$	5.40664	+	16.6399i	0.189503	+	0.583229i
$815$	30.4559	−	16.9885i	1.06682	−	0.595080i
$816$	−1.64667	+	5.06792i	−0.0576449	+	0.177413i
$817$	−1.76389	−	1.28154i	−0.0617107	−	0.0448354i
$818$	12.4331			0.434712
$819$	7.13271	+	5.18222i	0.249237	+	0.181081i
$820$	−5.07293	+	10.9552i	−0.177155	+	0.382573i
$821$	−5.14392	+	3.73728i	−0.179524	+	0.130432i	−0.673918	−	0.738806i	$-0.735390\pi$
$821$	−5.14392	+	3.73728i	−0.179524	+	0.130432i	0.494394	+	0.869238i	$0.335390\pi$
$822$	−12.5031	+	9.08404i	−0.436096	+	0.316842i
$823$	−16.2579	−	50.0366i	−0.566714	−	1.74417i	−0.662802	−	0.748794i	$-0.730633\pi$
$823$	−16.2579	−	50.0366i	−0.566714	−	1.74417i	0.0960882	−	0.995373i	$-0.469367\pi$
$824$	−1.47626			−0.0514281
$825$	−6.98873	+	11.3184i	−0.243316	+	0.394056i
$826$	−16.4608			−0.572743
$827$	−3.71190	−	11.4240i	−0.129075	−	0.397253i	0.865546	−	0.500829i	$-0.166971\pi$
$827$	−3.71190	−	11.4240i	−0.129075	−	0.397253i	−0.994622	+	0.103576i	$0.966971\pi$
$828$	0.116349	−	0.0845323i	0.00404340	−	0.00293770i
$829$	32.8147	−	23.8413i	1.13970	−	0.828042i	0.152625	−	0.988284i	$-0.451227\pi$
$829$	32.8147	−	23.8413i	1.13970	−	0.828042i	0.987078	+	0.160242i	$0.0512274\pi$
$830$	−10.6568	+	5.94443i	−0.369903	+	0.206334i
$831$	1.34503	+	0.977223i	0.0466586	+	0.0338995i
$832$	1.00000			0.0346688
$833$	68.2416	+	49.5804i	2.36443	+	1.71786i
$834$	4.71379	−	14.5075i	0.163225	−	0.502355i
$835$	3.44749	+	17.4863i	0.119305	+	0.605139i
$836$	4.20660	+	12.9466i	0.145488	+	0.447767i
$837$	9.20823	−	28.3400i	0.318283	−	0.979574i
$838$	8.84406	−	27.2192i	0.305513	−	0.940272i
$839$	−7.87786	−	24.2455i	−0.271974	−	0.837049i	−0.990004	−	0.141038i	$-0.954956\pi$
$839$	−7.87786	−	24.2455i	−0.271974	−	0.837049i	0.718030	−	0.696012i	$-0.245044\pi$
$840$	−8.94815	−	8.29972i	−0.308741	−	0.286368i
$841$	−8.95310	+	27.5548i	−0.308728	+	0.950166i
$842$	23.2626	+	16.9013i	0.801682	+	0.582456i
$843$	−34.4586			−1.18682
$844$	−6.22655	−	4.52386i	−0.214327	−	0.155718i
$845$	0.432523	+	2.19384i	0.0148792	+	0.0754703i
$846$	13.8413	−	10.0563i	0.475874	−	0.345743i
$847$	20.7569	−	15.0807i	0.713214	−	0.518180i
$848$	−3.45015	−	10.6185i	−0.118478	−	0.364639i
$849$	0.962677			0.0330390
$850$	−23.4595	−	5.71618i	−0.804653	−	0.196063i
$851$	−0.585519			−0.0200713
$852$	−1.83050	−	5.63370i	−0.0627119	−	0.193008i
$853$	−25.9108	+	18.8253i	−0.887168	+	0.644565i	−0.935138	−	0.354284i	$-0.884725\pi$
$853$	−25.9108	+	18.8253i	−0.887168	+	0.644565i	0.0479703	+	0.998849i	$0.484725\pi$
$854$	26.5053	−	19.2572i	0.906994	−	0.658970i
$855$	22.3424	+	2.68276i	0.764095	+	0.0917483i
$856$	3.98531	+	2.89550i	0.136215	+	0.0989661i
$857$	56.4226			1.92736			0.963679	−	0.267062i	$-0.0860529\pi$
$857$	56.4226			1.92736			0.963679	+	0.267062i	$0.0860529\pi$
$858$	2.15234	+	1.56377i	0.0734796	+	0.0533861i
$859$	−1.44914	+	4.46000i	−0.0494441	+	0.152173i	−0.972730	−	0.231940i	$-0.925493\pi$
$859$	−1.44914	+	4.46000i	−0.0494441	+	0.152173i	0.923286	+	0.384113i	$0.125493\pi$
$860$	−0.857320	−	0.102942i	−0.0292344	−	0.00351030i
$861$	−9.10640	−	28.0266i	−0.310345	−	0.955145i
$862$	−0.703926	+	2.16646i	−0.0239758	+	0.0737900i
$863$	−17.6928	+	54.4529i	−0.602270	+	1.85360i	−0.0877035	+	0.996147i	$0.527953\pi$
$863$	−17.6928	+	54.4529i	−0.602270	+	1.85360i	−0.514567	+	0.857450i	$0.672047\pi$
$864$	−1.63072	−	5.01885i	−0.0554783	−	0.170745i
$865$	−20.8725	+	45.0750i	−0.709685	+	1.53260i
$866$	−5.06446	+	15.5868i	−0.172098	+	0.529662i
$867$	−5.64267	−	4.09964i	−0.191635	−	0.139231i
$868$	−27.9310			−0.948041
$869$	−20.8653	−	15.1596i	−0.707808	−	0.514253i
$870$	0.298146	+	0.276541i	0.0101081	+	0.00937561i
$871$	4.97383	−	3.61370i	0.168532	−	0.122446i
$872$	−13.2158	+	9.60186i	−0.447545	+	0.325160i
$873$	−4.09930	−	12.6164i	−0.138740	−	0.426999i
$874$	−0.455560			−0.0154095
$875$	34.4576	−	43.2557i	1.16488	−	1.46231i
$876$	−6.95415			−0.234959
$877$	−1.39701	−	4.29955i	−0.0471736	−	0.145185i	0.924695	−	0.380708i	$-0.124320\pi$
$877$	−1.39701	−	4.29955i	−0.0471736	−	0.145185i	−0.971869	+	0.235523i	$0.924320\pi$
$878$	−12.0113	+	8.72675i	−0.405363	+	0.294513i
$879$	5.35054	−	3.88739i	0.180469	−	0.131119i
$880$	3.95269	+	3.66626i	0.133245	+	0.123589i
$881$	41.2104	+	29.9411i	1.38841	+	1.00874i	0.996037	+	0.0889370i	$0.0283470\pi$
$881$	41.2104	+	29.9411i	1.38841	+	1.00874i	0.392377	+	0.919805i	$0.371653\pi$
$882$	−31.1334			−1.04831
$883$	11.1643	+	8.11137i	0.375710	+	0.272969i	0.759575	−	0.650420i	$-0.225407\pi$
$883$	11.1643	+	8.11137i	0.375710	+	0.272969i	−0.383865	+	0.923389i	$0.625407\pi$
$884$	−1.49229	+	4.59281i	−0.0501913	+	0.154473i
$885$	−3.45023	+	7.45093i	−0.115978	+	0.250460i
$886$	10.5469	+	32.4601i	0.354331	+	1.09052i
$887$	−12.3757	+	38.0886i	−0.415536	+	1.27889i	0.496234	+	0.868189i	$0.334716\pi$
$887$	−12.3757	+	38.0886i	−0.415536	+	1.27889i	−0.911770	+	0.410700i	$0.865284\pi$
$888$	−2.47444	+	7.61555i	−0.0830369	+	0.255561i
$889$	8.64879	+	26.6182i	0.290071	+	0.892747i
$890$	−12.1856	−	1.46317i	−0.408461	−	0.0490457i
$891$	0.354508	−	1.09106i	0.0118764	−	0.0365520i
$892$	20.9433	+	15.2162i	0.701234	+	0.509476i
$893$	−54.1952			−1.81357
$894$	−13.3629	−	9.70870i	−0.446922	−	0.324708i
$895$	43.5291	+	5.22673i	1.45502	+	0.174710i
$896$	−4.00174	+	2.90743i	−0.133689	+	0.0971305i
$897$	−0.0720289	+	0.0523320i	−0.00240497	+	0.00174732i
$898$	−8.51331	−	26.2013i	−0.284093	−	0.874348i
$899$	0.930642			0.0310386
$900$	8.24513	−	3.38259i	0.274838	−	0.112753i
$901$	53.9172			1.79624
$902$	4.02259	+	12.3803i	0.133938	+	0.412218i
$903$	1.70516	−	1.23887i	0.0567443	−	0.0412271i
$904$	9.40577	−	6.83369i	0.312831	−	0.227285i
$905$	0.914538	+	4.63871i	0.0304003	+	0.154196i
$906$	9.42378	+	6.84678i	0.313084	+	0.227469i
$907$	−49.2834			−1.63643			−0.818214	−	0.574914i	$-0.805035\pi$
$907$	−49.2834			−1.63643			−0.818214	+	0.574914i	$0.805035\pi$
$908$	15.6681	+	11.3835i	0.519963	+	0.377775i
$909$	−8.08744	+	24.8906i	−0.268243	+	0.825569i
$910$	−8.10927	−	7.52163i	−0.268820	−	0.249340i
$911$	−4.64549	−	14.2973i	−0.153912	−	0.473692i	0.844137	−	0.536127i	$-0.180113\pi$
$911$	−4.64549	−	14.2973i	−0.153912	−	0.473692i	−0.998049	+	0.0624354i	$0.980113\pi$
$912$	−1.92523	+	5.92523i	−0.0637506	+	0.196204i
$913$	−4.06585	+	12.5134i	−0.134560	+	0.414133i
$914$	10.8687	+	33.4504i	0.359505	+	1.10644i
$915$	−3.16115	−	16.0340i	−0.104504	−	0.530066i
$916$	−2.50464	+	7.70849i	−0.0827557	+	0.254696i
$917$	−31.8101	−	23.1114i	−1.05046	−	0.763205i
$918$	25.4841			0.841102
$919$	41.6603	+	30.2680i	1.37425	+	0.998449i	0.997392	+	0.0721773i	$0.0229948\pi$
$919$	41.6603	+	30.2680i	1.37425	+	0.998449i	0.376856	+	0.926272i	$0.377005\pi$
$920$	−0.157564	+	0.0878900i	−0.00519473	+	0.00289765i
$921$	15.3418	−	11.1464i	0.505528	−	0.367288i
$922$	−21.5579	+	15.6627i	−0.709971	+	0.515824i
$923$	−1.65889	−	5.10555i	−0.0546032	−	0.168051i
$924$	−13.1596			−0.432920
$925$	−35.2525	−	8.58969i	−1.15909	−	0.282427i
$926$	1.46076			0.0480035
$927$	0.813116	+	2.50251i	0.0267062	+	0.0821933i
$928$	0.133335	−	0.0968736i	0.00437694	−	0.00318003i
$929$	−22.6975	+	16.4907i	−0.744680	+	0.541042i	−0.894173	−	0.447721i	$-0.852236\pi$
$929$	−22.6975	+	16.4907i	−0.744680	+	0.541042i	0.149493	+	0.988763i	$0.452236\pi$
$930$	−5.85443	+	12.6429i	−0.191974	+	0.414577i
$931$	79.7857	+	57.9677i	2.61487	+	1.89981i
$932$	8.19467			0.268425
$933$	2.59430	+	1.88487i	0.0849335	+	0.0617078i
$934$	−9.00143	+	27.7036i	−0.294536	+	0.906488i
$935$	−22.7370	+	12.6828i	−0.743579	+	0.414773i
$936$	−0.550793	−	1.69517i	−0.0180032	−	0.0554083i
$937$	9.58989	−	29.5147i	0.313288	−	0.964202i	−0.663165	−	0.748473i	$-0.730787\pi$
$937$	9.58989	−	29.5147i	0.313288	−	0.964202i	0.976453	−	0.215729i	$-0.0692127\pi$
$938$	−9.39738	+	28.9222i	−0.306835	+	0.944342i
$939$	6.85780	+	21.1061i	0.223796	+	0.688773i
$940$	−18.7445	+	10.4558i	−0.611377	+	0.341029i
$941$	−2.94114	+	9.05190i	−0.0958784	+	0.295083i	−0.987482	−	0.157734i	$-0.949581\pi$
$941$	−2.94114	+	9.05190i	−0.0958784	+	0.295083i	0.891603	+	0.452818i	$0.149581\pi$
$942$	18.1602	+	13.1941i	0.591691	+	0.429888i
$943$	−0.435632			−0.0141861
$944$	2.69226	+	1.95604i	0.0876256	+	0.0636637i
$945$	−24.5259	+	52.9649i	−0.797829	+	1.72295i
$946$	−0.753226	+	0.547251i	−0.0244895	+	0.0177927i
$947$	21.7619	−	15.8110i	0.707167	−	0.513787i	−0.175091	−	0.984552i	$-0.556022\pi$
$947$	21.7619	−	15.8110i	0.707167	−	0.513787i	0.882259	+	0.470765i	$0.156022\pi$
$948$	−3.64754	−	11.2260i	−0.118467	−	0.364603i
$949$	−6.30220			−0.204578
$950$	−27.4280	−	6.68315i	−0.889881	−	0.216830i
$951$	7.34847			0.238290
$952$	−7.38151	−	22.7180i	−0.239236	−	0.736293i
$953$	−17.5395	+	12.7432i	−0.568161	+	0.412793i	−0.834437	−	0.551104i	$-0.814207\pi$
$953$	−17.5395	+	12.7432i	−0.568161	+	0.412793i	0.266275	+	0.963897i	$0.414207\pi$
$954$	−16.0997	+	11.6972i	−0.521249	+	0.378709i
$955$	−19.3260	+	10.7802i	−0.625376	+	0.348838i
$956$	−20.7671	−	15.0882i	−0.671656	−	0.487987i
$957$	0.438470			0.0141737
$958$	−2.21956	−	1.61261i	−0.0717108	−	0.0521009i
$959$	21.4083	−	65.8879i	0.691310	−	2.12763i
$960$	0.477266	+	2.42078i	0.0154037	+	0.0781305i
$961$	0.273606	+	0.842074i	0.00882601	+	0.0271637i
$962$	−2.24247	+	6.90160i	−0.0723000	+	0.222517i
$963$	2.71327	−	8.35059i	0.0874340	−	0.269094i
$964$	2.48779	+	7.65663i	0.0801263	+	0.246603i
$965$	37.7244	+	34.9906i	1.21439	+	1.12639i
$966$	0.136089	−	0.418838i	0.00437858	−	0.0134759i
$967$	−36.3102	−	26.3809i	−1.16766	−	0.848353i	−0.176931	−	0.984223i	$-0.556617\pi$
$967$	−36.3102	−	26.3809i	−1.16766	−	0.848353i	−0.990727	+	0.135871i	$0.956617\pi$
$968$	−5.18696			−0.166715
$969$	−24.3405	−	17.6844i	−0.781929	−	0.568104i
$970$	3.21907	+	16.3277i	0.103358	+	0.524252i
$971$	−11.0582	+	8.03422i	−0.354873	+	0.257830i	−0.750911	−	0.660404i	$-0.770385\pi$
$971$	−11.0582	+	8.03422i	−0.354873	+	0.257830i	0.396037	+	0.918234i	$0.370385\pi$
$972$	−12.3831	+	8.99685i	−0.397188	+	0.288574i
$973$	21.1305	+	65.0329i	0.677412	+	2.08486i
$974$	8.24330			0.264132
$975$	−5.10438	+	2.09409i	−0.163471	+	0.0670645i
$976$	−6.62346			−0.212012
$977$	−7.95287	−	24.4764i	−0.254435	−	0.783070i	−0.993940	−	0.109920i	$-0.964941\pi$
$977$	−7.95287	−	24.4764i	−0.254435	−	0.783070i	0.739506	−	0.673150i	$-0.235059\pi$
$978$	13.9226	−	10.1154i	0.445197	−	0.323454i
$979$	−10.7060	+	7.77838i	−0.342166	+	0.248598i
$980$	38.7790	+	4.65636i	1.23875	+	0.148742i
$981$	23.5560	+	17.1144i	0.752084	+	0.546421i
$982$	−24.5509			−0.783450
$983$	12.9127	+	9.38166i	0.411853	+	0.299228i	0.774351	−	0.632756i	$-0.218076\pi$
$983$	12.9127	+	9.38166i	0.411853	+	0.299228i	−0.362499	+	0.931984i	$0.618076\pi$
$984$	−1.84101	+	5.66604i	−0.0586892	+	0.180627i
$985$	39.9803	+	4.80061i	1.27388	+	0.152960i
$986$	0.245947	+	0.756946i	0.00783254	+	0.0241061i
$987$	16.1897	−	49.8267i	0.515323	−	1.58600i
$988$	−1.74474	+	5.36975i	−0.0555075	+	0.170834i
$989$	−0.00962822	−	0.0296326i	−0.000306160	−	0.000942263i
$990$	4.03780	−	8.71982i	0.128330	−	0.277134i
$991$	0.337329	−	1.03819i	0.0107156	−	0.0329793i	−0.945556	−	0.325460i	$-0.894481\pi$
$991$	0.337329	−	1.03819i	0.0107156	−	0.0329793i	0.956271	+	0.292481i	$0.0944808\pi$
$992$	4.56829	+	3.31906i	0.145043	+	0.105380i
$993$	34.0922			1.08188
$994$	21.4825	+	15.6079i	0.681383	+	0.495054i
$995$	21.7439	+	20.1682i	0.689329	+	0.639376i
$996$	−4.87166	+	3.53947i	−0.154364	+	0.112152i
$997$	1.53505	−	1.11528i	0.0486155	−	0.0353212i	−0.563212	−	0.826312i	$-0.690435\pi$
$997$	1.53505	−	1.11528i	0.0486155	−	0.0353212i	0.611828	+	0.790991i	$0.290435\pi$
$998$	−2.01545	−	6.20290i	−0.0637978	−	0.196349i
$999$	38.2949			1.21160

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.l.c.131.3	✓	24
25.21	even	5	inner	650.2.l.c.521.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.l.c.131.3	✓	24	1.1	even	1	trivial
650.2.l.c.521.3	yes	24	25.21	even	5	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.892707 + 0.648590i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.63942 - 1.52062i) q^{5} +(-0.892707 - 0.648590i) q^{6} +4.94642 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.550793 + 1.69517i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.892707 + 0.648590i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.63942 - 1.52062i) q^{5} +(-0.892707 - 0.648590i) q^{6} +4.94642 q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.550793 + 1.69517i) q^{9} +(0.939587 - 2.02908i) q^{10} +(-0.745048 - 2.29302i) q^{11} +(0.340984 - 1.04944i) q^{12} +(0.309017 - 0.951057i) q^{13} +(1.52853 + 4.70432i) q^{14} +(2.44979 + 0.294157i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.90688 + 2.83851i) q^{17} -1.78240 q^{18} +(4.56778 + 3.31869i) q^{19} +(2.22012 + 0.266580i) q^{20} +(-4.41570 + 3.20820i) q^{21} +(1.95056 - 1.41716i) q^{22} +(0.0249333 + 0.0767368i) q^{23} +1.10345 q^{24} +(0.375420 + 4.98589i) q^{25} +1.00000 q^{26} +(-1.63072 - 5.01885i) q^{27} +(-4.00174 + 2.90743i) q^{28} +(0.133335 - 0.0968736i) q^{29} +(0.477266 + 2.42078i) q^{30} +(4.56829 + 3.31906i) q^{31} +1.00000 q^{32} +(2.15234 + 1.56377i) q^{33} +(-1.49229 + 4.59281i) q^{34} +(-8.10927 - 7.52163i) q^{35} +(-0.550793 - 1.69517i) q^{36} +(-2.24247 + 6.90160i) q^{37} +(-1.74474 + 5.36975i) q^{38} +(0.340984 + 1.04944i) q^{39} +(0.432523 + 2.19384i) q^{40} +(-1.66842 + 5.13486i) q^{41} +(-4.41570 - 3.20820i) q^{42} -0.386159 q^{43} +(1.95056 + 1.41716i) q^{44} +(3.48069 - 1.94155i) q^{45} +(-0.0652763 + 0.0474260i) q^{46} +(-7.76553 + 5.64199i) q^{47} +(0.340984 + 1.04944i) q^{48} +17.4671 q^{49} +(-4.62585 + 1.89777i) q^{50} -5.32873 q^{51} +(0.309017 + 0.951057i) q^{52} +(9.03260 - 6.56257i) q^{53} +(4.26929 - 3.10182i) q^{54} +(-2.26537 + 4.89217i) q^{55} +(-4.00174 - 2.90743i) q^{56} -6.23016 q^{57} +(0.133335 + 0.0968736i) q^{58} +(-1.02835 + 3.16494i) q^{59} +(-2.15482 + 1.20197i) q^{60} +(-2.04676 - 6.29928i) q^{61} +(-1.74493 + 5.37035i) q^{62} +(-2.72445 + 8.38501i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.95281 + 1.08929i) q^{65} +(-0.822120 + 2.53023i) q^{66} +(4.97383 + 3.61370i) q^{67} -4.82917 q^{68} +(-0.0720289 - 0.0523320i) q^{69} +(4.64759 - 10.0367i) q^{70} +(4.34304 - 3.15540i) q^{71} +(1.44200 - 1.04767i) q^{72} +(-1.94749 - 5.99375i) q^{73} -7.25677 q^{74} +(-3.56893 - 4.20744i) q^{75} -5.64609 q^{76} +(-3.68532 - 11.3422i) q^{77} +(-0.892707 + 0.648590i) q^{78} +(8.65414 - 6.28760i) q^{79} +(-1.95281 + 1.08929i) q^{80} +(0.384945 + 0.279679i) q^{81} -5.39911 q^{82} +(-4.41495 - 3.20765i) q^{83} +(1.68665 - 5.19097i) q^{84} +(-2.08872 - 10.5944i) q^{85} +(-0.119330 - 0.367259i) q^{86} +(-0.0561980 + 0.172960i) q^{87} +(-0.745048 + 2.29302i) q^{88} +(-1.69610 - 5.22006i) q^{89} +(2.92212 + 2.71036i) q^{90} +(1.52853 - 4.70432i) q^{91} +(-0.0652763 - 0.0474260i) q^{92} -6.23085 q^{93} +(-7.76553 - 5.64199i) q^{94} +(-2.44206 - 12.3866i) q^{95} +(-0.892707 + 0.648590i) q^{96} +(-6.02114 + 4.37462i) q^{97} +(5.39762 + 16.6122i) q^{98} +4.29742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - q^{5} + 3 q^{6} - 6 q^{8} + 7 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 20 q^{15} - 6 q^{16} + 9 q^{17} + 22 q^{18} + 12 q^{19} + 4 q^{20} + 25 q^{21} + 2 q^{22} - 6 q^{23} - 2 q^{24} - 41 q^{25} + 24 q^{26} - 6 q^{27} - 2 q^{29} + 10 q^{30} + 13 q^{31} + 24 q^{32} - 34 q^{33} + 14 q^{34} + 7 q^{36} + 5 q^{37} + 22 q^{38} - 2 q^{39} - q^{40} - 10 q^{41} + 25 q^{42} - 18 q^{43} + 2 q^{44} + 3 q^{45} + 9 q^{46} - 5 q^{47} - 2 q^{48} + 32 q^{49} - 11 q^{50} - 56 q^{51} - 6 q^{52} + 34 q^{53} + 19 q^{54} + 20 q^{55} - 12 q^{57} - 2 q^{58} - 15 q^{60} - 2 q^{61} - 12 q^{62} + 10 q^{63} - 6 q^{64} - q^{65} + 26 q^{66} + 2 q^{67} - 46 q^{68} + 33 q^{69} - 20 q^{70} + 29 q^{71} - 18 q^{72} - 11 q^{73} - 30 q^{74} - 25 q^{75} - 68 q^{76} + 15 q^{77} + 3 q^{78} + 20 q^{79} - q^{80} - 9 q^{81} - 20 q^{82} - 69 q^{83} - 20 q^{84} - 27 q^{85} + 22 q^{86} - 18 q^{87} + 2 q^{88} + 19 q^{89} + 8 q^{90} + 9 q^{92} + 40 q^{93} - 5 q^{94} + 78 q^{95} + 3 q^{96} - 49 q^{97} + 2 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - q^5 + 3 * q^6 - 6 * q^8 + 7 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 20 * q^15 - 6 * q^16 + 9 * q^17 + 22 * q^18 + 12 * q^19 + 4 * q^20 + 25 * q^21 + 2 * q^22 - 6 * q^23 - 2 * q^24 - 41 * q^25 + 24 * q^26 - 6 * q^27 - 2 * q^29 + 10 * q^30 + 13 * q^31 + 24 * q^32 - 34 * q^33 + 14 * q^34 + 7 * q^36 + 5 * q^37 + 22 * q^38 - 2 * q^39 - q^40 - 10 * q^41 + 25 * q^42 - 18 * q^43 + 2 * q^44 + 3 * q^45 + 9 * q^46 - 5 * q^47 - 2 * q^48 + 32 * q^49 - 11 * q^50 - 56 * q^51 - 6 * q^52 + 34 * q^53 + 19 * q^54 + 20 * q^55 - 12 * q^57 - 2 * q^58 - 15 * q^60 - 2 * q^61 - 12 * q^62 + 10 * q^63 - 6 * q^64 - q^65 + 26 * q^66 + 2 * q^67 - 46 * q^68 + 33 * q^69 - 20 * q^70 + 29 * q^71 - 18 * q^72 - 11 * q^73 - 30 * q^74 - 25 * q^75 - 68 * q^76 + 15 * q^77 + 3 * q^78 + 20 * q^79 - q^80 - 9 * q^81 - 20 * q^82 - 69 * q^83 - 20 * q^84 - 27 * q^85 + 22 * q^86 - 18 * q^87 + 2 * q^88 + 19 * q^89 + 8 * q^90 + 9 * q^92 + 40 * q^93 - 5 * q^94 + 78 * q^95 + 3 * q^96 - 49 * q^97 + 2 * q^98 - 28 * q^99

Introduction

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