LMFDB - Embedded newform 62.2.d.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(33,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("62.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.d (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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.511890625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 7x^{6} - 5x^{5} + 16x^{4} + 15x^{3} + 63x^{2} + 81x + 81 $ x^8 - 3x^7 + 7x^6 - 5x^5 + 16x^4 + 15x^3 + 63x^2 + 81*x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			47.2
Root			$0.639176 + 1.96718i$ of defining polynomial
Character	$\chi$	$=$	62.47
Dual form			62.2.d.a.33.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.364368 + 0.264729i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.34677 q^{5} -0.450384 q^{6} +(-1.39639 + 4.29764i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.864368 - 2.66025i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.364368 + 0.264729i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.34677 q^{5} -0.450384 q^{6} +(-1.39639 + 4.29764i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.864368 - 2.66025i) q^{9} +(-1.89858 + 1.37940i) q^{10} +(1.20405 - 3.70568i) q^{11} +(0.364368 - 0.264729i) q^{12} +(-3.65224 - 2.65351i) q^{13} +(-1.39639 - 4.29764i) q^{14} +(0.855089 + 0.621258i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.171195 + 0.526883i) q^{17} +(2.26295 + 1.64413i) q^{18} +(-3.17339 + 2.30560i) q^{19} +(0.725192 - 2.23191i) q^{20} +(-1.64651 + 1.19626i) q^{21} +(1.20405 + 3.70568i) q^{22} +(-0.478858 - 1.47377i) q^{23} +(-0.139176 + 0.428341i) q^{24} +0.507332 q^{25} +4.51442 q^{26} +(0.806826 - 2.48316i) q^{27} +(3.65579 + 2.65609i) q^{28} +(-0.398577 + 0.289583i) q^{29} -1.05695 q^{30} +(1.66251 + 5.31376i) q^{31} +1.00000 q^{32} +(1.41972 - 1.03149i) q^{33} +(-0.448193 - 0.325631i) q^{34} +(-3.27700 + 10.0856i) q^{35} -2.79715 q^{36} +11.5828 q^{37} +(1.21213 - 3.73054i) q^{38} +(-0.628300 - 1.93371i) q^{39} +(0.725192 + 2.23191i) q^{40} +(1.84896 - 1.34335i) q^{41} +(0.628910 - 1.93559i) q^{42} +(-2.66765 + 1.93816i) q^{43} +(-3.15224 - 2.29024i) q^{44} +(-2.02847 - 6.24300i) q^{45} +(1.25367 + 0.910841i) q^{46} +(-5.29715 - 3.84861i) q^{47} +(-0.139176 - 0.428341i) q^{48} +(-10.8567 - 7.88783i) q^{49} +(-0.410440 + 0.298202i) q^{50} +(-0.0771033 + 0.237300i) q^{51} +(-3.65224 + 2.65351i) q^{52} +(3.12158 + 9.60723i) q^{53} +(0.806826 + 2.48316i) q^{54} +(2.82563 - 8.69639i) q^{55} -4.51880 q^{56} -1.76664 q^{57} +(0.152243 - 0.468556i) q^{58} +(4.20405 + 3.05442i) q^{59} +(0.855089 - 0.621258i) q^{60} +2.57137 q^{61} +(-4.46835 - 3.32173i) q^{62} +12.6398 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-8.57098 - 6.22718i) q^{65} +(-0.542285 + 1.66898i) q^{66} -0.992911 q^{67} +0.553997 q^{68} +(0.215670 - 0.663763i) q^{69} +(-3.27700 - 10.0856i) q^{70} +(1.60263 + 4.93238i) q^{71} +(2.26295 - 1.64413i) q^{72} +(-3.52552 + 10.8504i) q^{73} +(-9.37071 + 6.80822i) q^{74} +(0.184855 + 0.134305i) q^{75} +(1.21213 + 3.73054i) q^{76} +(14.2444 + 10.3491i) q^{77} +(1.64491 + 1.19510i) q^{78} +(-4.32479 - 13.3103i) q^{79} +(-1.89858 - 1.37940i) q^{80} +(-5.83749 + 4.24119i) q^{81} +(-0.706240 + 2.17358i) q^{82} +(0.702846 - 0.510647i) q^{83} +(0.628910 + 1.93559i) q^{84} +(0.401754 + 1.23647i) q^{85} +(1.01895 - 3.13601i) q^{86} -0.221890 q^{87} +3.89639 q^{88} +(4.10996 - 12.6492i) q^{89} +(5.31061 + 3.85839i) q^{90} +(16.5038 - 11.9907i) q^{91} -1.54962 q^{92} +(-0.800941 + 2.37628i) q^{93} +6.54764 q^{94} +(-7.44721 + 5.41071i) q^{95} +(0.364368 + 0.264729i) q^{96} +(-2.28568 + 7.03461i) q^{97} +13.4196 q^{98} -10.8988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{12} - 11 q^{13} + 2 q^{14} + 21 q^{15} - 2 q^{16} - 7 q^{17} - 5 q^{18} - 14 q^{19} + q^{20} - 7 q^{21} - 2 q^{22} + 3 q^{23} + q^{24} + 14 q^{26} + 5 q^{27} + 2 q^{28} + 13 q^{29} - 14 q^{30} + 15 q^{31} + 8 q^{32} + 2 q^{33} + 3 q^{34} - 28 q^{35} + 10 q^{36} + 52 q^{37} + 21 q^{38} - 16 q^{39} + q^{40} - 11 q^{41} - 17 q^{42} - 22 q^{43} - 7 q^{44} - 19 q^{45} + 8 q^{46} - 10 q^{47} + q^{48} - 10 q^{49} - 15 q^{50} + 28 q^{51} - 11 q^{52} + 7 q^{53} + 5 q^{54} - 7 q^{55} - 8 q^{56} - 20 q^{57} - 17 q^{58} + 22 q^{59} + 21 q^{60} + 4 q^{61} + 5 q^{62} + 66 q^{63} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 8 q^{68} + 4 q^{69} - 28 q^{70} - 15 q^{71} - 5 q^{72} - 29 q^{73} - 23 q^{74} - 34 q^{75} + 21 q^{76} + 34 q^{77} - q^{78} - 2 q^{79} + q^{80} - 45 q^{81} + 9 q^{82} + 38 q^{83} - 17 q^{84} + 25 q^{85} + 18 q^{86} - 20 q^{87} + 18 q^{88} + q^{89} + 46 q^{90} + 38 q^{91} - 22 q^{92} + 21 q^{93} - 20 q^{94} - 12 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} + 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^12 - 11 * q^13 + 2 * q^14 + 21 * q^15 - 2 * q^16 - 7 * q^17 - 5 * q^18 - 14 * q^19 + q^20 - 7 * q^21 - 2 * q^22 + 3 * q^23 + q^24 + 14 * q^26 + 5 * q^27 + 2 * q^28 + 13 * q^29 - 14 * q^30 + 15 * q^31 + 8 * q^32 + 2 * q^33 + 3 * q^34 - 28 * q^35 + 10 * q^36 + 52 * q^37 + 21 * q^38 - 16 * q^39 + q^40 - 11 * q^41 - 17 * q^42 - 22 * q^43 - 7 * q^44 - 19 * q^45 + 8 * q^46 - 10 * q^47 + q^48 - 10 * q^49 - 15 * q^50 + 28 * q^51 - 11 * q^52 + 7 * q^53 + 5 * q^54 - 7 * q^55 - 8 * q^56 - 20 * q^57 - 17 * q^58 + 22 * q^59 + 21 * q^60 + 4 * q^61 + 5 * q^62 + 66 * q^63 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 8 * q^68 + 4 * q^69 - 28 * q^70 - 15 * q^71 - 5 * q^72 - 29 * q^73 - 23 * q^74 - 34 * q^75 + 21 * q^76 + 34 * q^77 - q^78 - 2 * q^79 + q^80 - 45 * q^81 + 9 * q^82 + 38 * q^83 - 17 * q^84 + 25 * q^85 + 18 * q^86 - 20 * q^87 + 18 * q^88 + q^89 + 46 * q^90 + 38 * q^91 - 22 * q^92 + 21 * q^93 - 20 * q^94 - 12 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.364368	+	0.264729i	0.210368	+	0.152841i	0.687980	−	0.725729i	$-0.258498\pi$
$3$	0.364368	+	0.264729i	0.210368	+	0.152841i	−0.477612	+	0.878571i	$0.658498\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.34677			1.04951			0.524754	−	0.851254i	$-0.324157\pi$
$5$	2.34677			1.04951			0.524754	+	0.851254i	$0.324157\pi$
$6$	−0.450384			−0.183868
$7$	−1.39639	+	4.29764i	−0.527785	+	1.62435i	0.230959	+	0.972964i	$0.425814\pi$
$7$	−1.39639	+	4.29764i	−0.527785	+	1.62435i	−0.758743	+	0.651390i	$0.774186\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.864368	−	2.66025i	−0.288123	−	0.886751i
$10$	−1.89858	+	1.37940i	−0.600383	+	0.436204i
$11$	1.20405	−	3.70568i	0.363035	−	1.11731i	−0.588168	−	0.808739i	$-0.700151\pi$
$11$	1.20405	−	3.70568i	0.363035	−	1.11731i	0.951203	−	0.308567i	$-0.0998494\pi$
$12$	0.364368	−	0.264729i	0.105184	−	0.0764207i
$13$	−3.65224	−	2.65351i	−1.01295	−	0.735951i	−0.0481242	−	0.998841i	$-0.515324\pi$
$13$	−3.65224	−	2.65351i	−1.01295	−	0.735951i	−0.964826	+	0.262890i	$0.915324\pi$
$14$	−1.39639	−	4.29764i	−0.373200	−	1.14859i
$15$	0.855089	+	0.621258i	0.220783	+	0.160408i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.171195	+	0.526883i	0.0415208	+	0.127788i	0.969668	−	0.244425i	$-0.0785992\pi$
$17$	0.171195	+	0.526883i	0.0415208	+	0.127788i	−0.928147	+	0.372213i	$0.878599\pi$
$18$	2.26295	+	1.64413i	0.533381	+	0.387524i
$19$	−3.17339	+	2.30560i	−0.728024	+	0.528941i	−0.888938	−	0.458028i	$-0.848556\pi$
$19$	−3.17339	+	2.30560i	−0.728024	+	0.528941i	0.160913	+	0.986969i	$0.448556\pi$
$20$	0.725192	−	2.23191i	0.162158	−	0.499071i
$21$	−1.64651	+	1.19626i	−0.359297	+	0.261045i
$22$	1.20405	+	3.70568i	0.256704	+	0.790054i
$23$	−0.478858	−	1.47377i	−0.0998487	−	0.307303i	0.888638	−	0.458609i	$-0.151652\pi$
$23$	−0.478858	−	1.47377i	−0.0998487	−	0.307303i	−0.988487	+	0.151306i	$0.951652\pi$
$24$	−0.139176	+	0.428341i	−0.0284092	+	0.0874346i
$25$	0.507332			0.101466
$26$	4.51442			0.885351
$27$	0.806826	−	2.48316i	0.155274	−	0.477884i
$28$	3.65579	+	2.65609i	0.690879	+	0.501953i
$29$	−0.398577	+	0.289583i	−0.0740139	+	0.0537743i	−0.624177	−	0.781283i	$-0.714566\pi$
$29$	−0.398577	+	0.289583i	−0.0740139	+	0.0537743i	0.550163	+	0.835057i	$0.314566\pi$
$30$	−1.05695			−0.192971
$31$	1.66251	+	5.31376i	0.298595	+	0.954380i
$31$	1.66251	+	5.31376i	0.298595	+	0.954380i
$32$	1.00000			0.176777
$33$	1.41972	−	1.03149i	0.247141	−	0.179559i
$34$	−0.448193	−	0.325631i	−0.0768645	−	0.0558453i
$35$	−3.27700	+	10.0856i	−0.553914	+	1.70477i
$36$	−2.79715			−0.466192
$37$	11.5828			1.90421			0.952103	−	0.305776i	$-0.0989159\pi$
$37$	11.5828			1.90421			0.952103	+	0.305776i	$0.0989159\pi$
$38$	1.21213	−	3.73054i	0.196633	−	0.605173i
$39$	−0.628300	−	1.93371i	−0.100609	−	0.309641i
$40$	0.725192	+	2.23191i	0.114663	+	0.352896i
$41$	1.84896	−	1.34335i	0.288759	−	0.209796i	−0.433970	−	0.900927i	$-0.642888\pi$
$41$	1.84896	−	1.34335i	0.288759	−	0.209796i	0.722729	+	0.691132i	$0.242888\pi$
$42$	0.628910	−	1.93559i	0.0970429	−	0.298667i
$43$	−2.66765	+	1.93816i	−0.406813	+	0.295567i	−0.772310	−	0.635246i	$-0.780899\pi$
$43$	−2.66765	+	1.93816i	−0.406813	+	0.295567i	0.365497	+	0.930812i	$0.380899\pi$
$44$	−3.15224	−	2.29024i	−0.475219	−	0.345266i
$45$	−2.02847	−	6.24300i	−0.302387	−	0.930652i
$46$	1.25367	+	0.910841i	0.184843	+	0.134296i
$47$	−5.29715	−	3.84861i	−0.772669	−	0.561377i	0.130101	−	0.991501i	$-0.458470\pi$
$47$	−5.29715	−	3.84861i	−0.772669	−	0.561377i	−0.902770	+	0.430124i	$0.858470\pi$
$48$	−0.139176	−	0.428341i	−0.0200884	−	0.0618256i
$49$	−10.8567	−	7.88783i	−1.55095	−	1.12683i
$50$	−0.410440	+	0.298202i	−0.0580450	+	0.0421721i
$51$	−0.0771033	+	0.237300i	−0.0107966	+	0.0332286i
$52$	−3.65224	+	2.65351i	−0.506475	+	0.367976i
$53$	3.12158	+	9.60723i	0.428782	+	1.31965i	0.899326	+	0.437278i	$0.144058\pi$
$53$	3.12158	+	9.60723i	0.428782	+	1.31965i	−0.470544	+	0.882376i	$0.655942\pi$
$54$	0.806826	+	2.48316i	0.109795	+	0.337915i
$55$	2.82563	−	8.69639i	0.381008	−	1.17262i
$56$	−4.51880			−0.603850
$57$	−1.76664			−0.233997
$58$	0.152243	−	0.468556i	0.0199905	−	0.0615244i
$59$	4.20405	+	3.05442i	0.547321	+	0.397652i	0.826797	−	0.562501i	$-0.190161\pi$
$59$	4.20405	+	3.05442i	0.547321	+	0.397652i	−0.279476	+	0.960153i	$0.590161\pi$
$60$	0.855089	−	0.621258i	0.110391	−	0.0802041i
$61$	2.57137			0.329230			0.164615	−	0.986358i	$-0.447362\pi$
$61$	2.57137			0.329230			0.164615	+	0.986358i	$0.447362\pi$
$62$	−4.46835	−	3.32173i	−0.567481	−	0.421860i
$63$	12.6398			1.59246
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−8.57098	−	6.22718i	−1.06310	−	0.772386i
$66$	−0.542285	+	1.66898i	−0.0667506	+	0.205437i
$67$	−0.992911			−0.121303			−0.0606517	−	0.998159i	$-0.519318\pi$
$67$	−0.992911			−0.121303			−0.0606517	+	0.998159i	$0.519318\pi$
$68$	0.553997			0.0671820
$69$	0.215670	−	0.663763i	0.0259636	−	0.0799077i
$70$	−3.27700	−	10.0856i	−0.391676	−	1.20546i
$71$	1.60263	+	4.93238i	0.190197	+	0.585366i	0.999999	−	0.00133726i	$-0.000425663\pi$
$71$	1.60263	+	4.93238i	0.190197	+	0.585366i	−0.809802	+	0.586703i	$0.800426\pi$
$72$	2.26295	−	1.64413i	0.266691	−	0.193762i
$73$	−3.52552	+	10.8504i	−0.412631	+	1.26995i	0.501721	+	0.865029i	$0.332700\pi$
$73$	−3.52552	+	10.8504i	−0.412631	+	1.26995i	−0.914352	+	0.404919i	$0.867300\pi$
$74$	−9.37071	+	6.80822i	−1.08932	+	0.791440i
$75$	0.184855	+	0.134305i	0.0213453	+	0.0155082i
$76$	1.21213	+	3.73054i	0.139040	+	0.427922i
$77$	14.2444	+	10.3491i	1.62330	+	1.17939i
$78$	1.64491	+	1.19510i	0.186250	+	0.135318i
$79$	−4.32479	−	13.3103i	−0.486577	−	1.49753i	−0.829684	−	0.558234i	$-0.811479\pi$
$79$	−4.32479	−	13.3103i	−0.486577	−	1.49753i	0.343107	−	0.939296i	$-0.388521\pi$
$80$	−1.89858	−	1.37940i	−0.212267	−	0.154221i
$81$	−5.83749	+	4.24119i	−0.648610	+	0.471243i
$82$	−0.706240	+	2.17358i	−0.0779912	+	0.240032i
$83$	0.702846	−	0.510647i	0.0771473	−	0.0560508i	−0.548543	−	0.836122i	$-0.684817\pi$
$83$	0.702846	−	0.510647i	0.0771473	−	0.0560508i	0.625690	+	0.780071i	$0.284817\pi$
$84$	0.628910	+	1.93559i	0.0686197	+	0.211190i
$85$	0.401754	+	1.23647i	0.0435764	+	0.134114i
$86$	1.01895	−	3.13601i	0.109876	−	0.338165i
$87$	−0.221890			−0.0237891
$88$	3.89639			0.415356
$89$	4.10996	−	12.6492i	0.435655	−	1.34081i	−0.456759	−	0.889590i	$-0.650990\pi$
$89$	4.10996	−	12.6492i	0.435655	−	1.34081i	0.892414	−	0.451217i	$-0.149010\pi$
$90$	5.31061	+	3.85839i	0.559788	+	0.406710i
$91$	16.5038	−	11.9907i	1.73006	−	1.25697i
$92$	−1.54962			−0.161559
$93$	−0.800941	+	2.37628i	−0.0830537	+	0.246409i
$94$	6.54764			0.675338
$95$	−7.44721	+	5.41071i	−0.764067	+	0.555127i
$96$	0.364368	+	0.264729i	0.0371882	+	0.0270188i
$97$	−2.28568	+	7.03461i	−0.232076	+	0.714257i	0.765420	+	0.643531i	$0.222531\pi$
$97$	−2.28568	+	7.03461i	−0.232076	+	0.714257i	−0.997496	+	0.0707253i	$0.977469\pi$
$98$	13.4196			1.35558
$99$	−10.8988			−1.09537
$100$	0.156774	−	0.482501i	0.0156774	−	0.0482501i
$101$	5.20306	+	16.0134i	0.517724	+	1.59339i	0.778270	+	0.627930i	$0.216097\pi$
$101$	5.20306	+	16.0134i	0.517724	+	1.59339i	−0.260546	+	0.965461i	$0.583903\pi$
$102$	−0.0771033	−	0.237300i	−0.00763436	−	0.0234962i
$103$	−4.22066	+	3.06649i	−0.415874	+	0.302150i	−0.775976	−	0.630763i	$-0.782742\pi$
$103$	−4.22066	+	3.06649i	−0.415874	+	0.302150i	0.360102	+	0.932913i	$0.382742\pi$
$104$	1.39503	−	4.29347i	0.136794	−	0.421009i
$105$	−3.86398	+	2.80734i	−0.377085	+	0.273969i
$106$	−8.17240	−	5.93760i	−0.793774	−	0.576710i
$107$	−4.83001	−	14.8652i	−0.466935	−	1.43708i	−0.856533	−	0.516092i	$-0.827386\pi$
$107$	−4.83001	−	14.8652i	−0.466935	−	1.43708i	0.389598	−	0.920985i	$-0.372614\pi$
$108$	−2.11230	−	1.53467i	−0.203256	−	0.147674i
$109$	5.25841	+	3.82046i	0.503665	+	0.365934i	0.810415	−	0.585856i	$-0.199242\pi$
$109$	5.25841	+	3.82046i	0.503665	+	0.365934i	−0.306750	+	0.951790i	$0.599242\pi$
$110$	2.82563	+	8.69639i	0.269413	+	0.829168i
$111$	4.22042	+	3.06631i	0.400584	+	0.291042i
$112$	3.65579	−	2.65609i	0.345439	−	0.250976i
$113$	2.34995	−	7.23240i	0.221064	−	0.680367i	−0.777603	−	0.628756i	$-0.783565\pi$
$113$	2.34995	−	7.23240i	0.221064	−	0.680367i	0.998667	−	0.0516107i	$-0.0164355\pi$
$114$	1.42924	−	1.03840i	0.133861	−	0.0972555i
$115$	−1.12377	−	3.45861i	−0.104792	−	0.322517i
$116$	0.152243	+	0.468556i	0.0141354	+	0.0435043i
$117$	−3.90212	+	12.0095i	−0.360751	+	1.11028i
$118$	−5.19649			−0.478376
$119$	−2.50340			−0.229487
$120$	−0.326615	+	1.00522i	−0.0298157	+	0.0917633i
$121$	−3.38317	−	2.45802i	−0.307561	−	0.223456i
$122$	−2.08028	+	1.51141i	−0.188340	+	0.136837i
$123$	1.02933			0.0928112
$124$	5.56743	+	0.0609025i	0.499970	+	0.00546920i
$125$	−10.5433			−0.943018
$126$	−10.2258	+	7.42948i	−0.910987	+	0.661871i
$127$	4.07196	+	2.95845i	0.361328	+	0.262520i	0.753606	−	0.657327i	$-0.228313\pi$
$127$	4.07196	+	2.95845i	0.361328	+	0.262520i	−0.392278	+	0.919847i	$0.628313\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−1.48509			−0.130755
$130$	10.5943			0.929182
$131$	1.05181	−	3.23713i	0.0918968	−	0.282829i	−0.894536	−	0.446996i	$-0.852494\pi$
$131$	1.05181	−	3.23713i	0.0918968	−	0.282829i	0.986433	+	0.164167i	$0.0524937\pi$
$132$	−0.542285	−	1.66898i	−0.0471998	−	0.145266i
$133$	−5.47735	−	16.8576i	−0.474947	−	1.46174i
$134$	0.803282	−	0.583618i	0.0693930	−	0.0504170i
$135$	1.89344	−	5.82740i	0.162961	−	0.501543i
$136$	−0.448193	+	0.325631i	−0.0384323	+	0.0279227i
$137$	−10.2728	−	7.46365i	−0.877668	−	0.637663i	0.0549659	−	0.998488i	$-0.482495\pi$
$137$	−10.2728	−	7.46365i	−0.877668	−	0.637663i	−0.932633	+	0.360825i	$0.882495\pi$
$138$	0.215670	+	0.663763i	0.0183590	+	0.0565033i
$139$	5.93060	+	4.30883i	0.503027	+	0.365470i	0.810172	−	0.586192i	$-0.199374\pi$
$139$	5.93060	+	4.30883i	0.503027	+	0.365470i	−0.307145	+	0.951663i	$0.599374\pi$
$140$	8.57929	+	6.23322i	0.725083	+	0.526803i
$141$	−0.911277	−	2.80462i	−0.0767433	−	0.236192i
$142$	−4.19573	−	3.04838i	−0.352098	−	0.255814i
$143$	−14.2306	+	10.3391i	−1.19002	+	0.864599i
$144$	−0.864368	+	2.66025i	−0.0720307	+	0.221688i
$145$	−0.935369	+	0.679585i	−0.0776782	+	0.0564365i
$146$	−3.52552	−	10.8504i	−0.291774	−	0.897989i
$147$	−1.86769	−	5.74815i	−0.154044	−	0.474099i
$148$	3.57929	−	11.0159i	0.294216	−	0.905504i
$149$	−5.33363			−0.436948			−0.218474	−	0.975843i	$-0.570108\pi$
$149$	−5.33363			−0.436948			−0.218474	+	0.975843i	$0.570108\pi$
$150$	−0.228494			−0.0186565
$151$	2.72738	−	8.39402i	0.221951	−	0.683096i	−0.776636	−	0.629950i	$-0.783075\pi$
$151$	2.72738	−	8.39402i	0.221951	−	0.683096i	0.998587	−	0.0531455i	$-0.0169247\pi$
$152$	−3.17339	−	2.30560i	−0.257396	−	0.187009i
$153$	1.25367	−	0.910841i	0.101353	−	0.0736372i
$154$	−17.6070			−1.41881
$155$	3.90153	+	12.4702i	0.313378	+	1.00163i
$156$	−2.03322			−0.162788
$157$	−0.461017	+	0.334949i	−0.0367932	+	0.0267318i	−0.606030	−	0.795442i	$-0.707239\pi$
$157$	−0.461017	+	0.334949i	−0.0367932	+	0.0267318i	0.569237	+	0.822174i	$0.307239\pi$
$158$	11.3225	+	8.22624i	0.900766	+	0.654445i
$159$	−1.40591	+	4.32694i	−0.111496	+	0.343149i
$160$	2.34677			0.185528
$161$	7.00241			0.551867
$162$	2.22972	−	6.86238i	0.175184	−	0.539160i
$163$	−0.655420	−	2.01718i	−0.0513365	−	0.157997i	0.922102	−	0.386948i	$-0.126471\pi$
$163$	−0.655420	−	2.01718i	−0.0513365	−	0.157997i	−0.973438	+	0.228950i	$0.926471\pi$
$164$	−0.706240	−	2.17358i	−0.0551481	−	0.169728i
$165$	3.33176	−	2.42066i	0.259377	−	0.188448i
$166$	−0.268463	+	0.826245i	−0.0208368	+	0.0641290i
$167$	14.6653	−	10.6550i	1.13483	−	0.824505i	0.148443	−	0.988921i	$-0.452574\pi$
$167$	14.6653	−	10.6550i	1.13483	−	0.824505i	0.986391	+	0.164416i	$0.0525739\pi$
$168$	−1.64651	−	1.19626i	−0.127031	−	0.0922933i
$169$	2.28054	+	7.01879i	0.175426	+	0.539907i
$170$	−1.05181	−	0.764182i	−0.0806699	−	0.0586101i
$171$	8.87645	+	6.44912i	0.678799	+	0.493176i
$172$	1.01895	+	3.13601i	0.0776943	+	0.239119i
$173$	11.1056	+	8.06867i	0.844341	+	0.613450i	0.923580	−	0.383406i	$-0.125249\pi$
$173$	11.1056	+	8.06867i	0.844341	+	0.613450i	−0.0792386	+	0.996856i	$0.525249\pi$
$174$	0.179513	−	0.130424i	0.0136088	−	0.00988739i
$175$	−0.708431	+	2.18033i	−0.0535523	+	0.164817i
$176$	−3.15224	+	2.29024i	−0.237609	+	0.172633i
$177$	0.723228	+	2.22587i	0.0543612	+	0.167306i
$178$	4.10996	+	12.6492i	0.308054	+	0.948094i
$179$	−2.03701	+	6.26927i	−0.152253	+	0.468587i	−0.997872	−	0.0651997i	$-0.979232\pi$
$179$	−2.03701	+	6.26927i	−0.152253	+	0.468587i	0.845619	+	0.533787i	$0.179232\pi$
$180$	−6.56428			−0.489272
$181$	−8.54813			−0.635377			−0.317689	−	0.948195i	$-0.602907\pi$
$181$	−8.54813			−0.635377			−0.317689	+	0.948195i	$0.602907\pi$
$182$	−6.30388	+	19.4013i	−0.467274	+	1.43812i
$183$	0.936925	+	0.680716i	0.0692595	+	0.0503200i
$184$	1.25367	−	0.910841i	0.0924215	−	0.0671481i
$185$	27.1823			1.99848
$186$	−0.748767	−	2.39323i	−0.0549023	−	0.175480i
$187$	2.15859			0.157852
$188$	−5.29715	+	3.84861i	−0.386335	+	0.280689i
$189$	9.54506	+	6.93489i	0.694301	+	0.504439i
$190$	2.84458	−	8.75472i	0.206368	−	0.635134i
$191$	−16.2456			−1.17549			−0.587744	−	0.809047i	$-0.699984\pi$
$191$	−16.2456			−1.17549			−0.587744	+	0.809047i	$0.699984\pi$
$192$	−0.450384			−0.0325037
$193$	−1.37562	+	4.23373i	−0.0990194	+	0.304750i	−0.988280	−	0.152650i	$-0.951219\pi$
$193$	−1.37562	+	4.23373i	−0.0990194	+	0.304750i	0.889261	+	0.457400i	$0.151219\pi$
$194$	−2.28568	−	7.03461i	−0.164103	−	0.505056i
$195$	−1.47448	−	4.53797i	−0.105589	−	0.324971i
$196$	−10.8567	+	7.88783i	−0.775476	+	0.563416i
$197$	7.56025	−	23.2681i	0.538645	−	1.65778i	−0.196992	−	0.980405i	$-0.563117\pi$
$197$	7.56025	−	23.2681i	0.538645	−	1.65778i	0.735638	−	0.677375i	$-0.236883\pi$
$198$	8.81731	−	6.40615i	0.626619	−	0.455265i
$199$	17.0892	+	12.4160i	1.21142	+	0.880148i	0.995359	−	0.0962316i	$-0.0306790\pi$
$199$	17.0892	+	12.4160i	1.21142	+	0.880148i	0.216061	+	0.976380i	$0.430679\pi$
$200$	0.156774	+	0.482501i	0.0110856	+	0.0341180i
$201$	−0.361785	−	0.262852i	−0.0255184	−	0.0185402i
$202$	−13.6218	−	9.89681i	−0.958426	−	0.696337i
$203$	−0.687956	−	2.11731i	−0.0482850	−	0.148606i
$204$	0.201859	+	0.146659i	0.0141330	+	0.0102682i
$205$	4.33909	−	3.15253i	0.303055	−	0.220182i
$206$	1.61215	−	4.96168i	0.112324	−	0.345697i
$207$	−3.50670	+	2.54776i	−0.243732	+	0.177082i
$208$	1.39503	+	4.29347i	0.0967281	+	0.297699i
$209$	4.72291	+	14.5356i	0.326690	+	1.00545i
$210$	1.47591	−	4.54238i	0.101847	−	0.313454i
$211$	6.43453			0.442971			0.221486	−	0.975164i	$-0.428909\pi$
$211$	6.43453			0.442971			0.221486	+	0.975164i	$0.428909\pi$
$212$	10.1016			0.693783
$213$	−0.721797	+	2.22146i	−0.0494567	+	0.152212i
$214$	12.6451	+	9.18722i	0.864403	+	0.628026i
$215$	−6.26036	+	4.54842i	−0.426953	+	0.310200i
$216$	2.61094			0.177652
$217$	−25.1581	−	0.275206i	−1.70784	−	0.0186822i
$218$	−6.49976			−0.440219
$219$	−4.15702	+	3.02025i	−0.280905	+	0.204090i
$220$	−7.39759	−	5.37466i	−0.498745	−	0.362360i
$221$	0.772844	−	2.37857i	0.0519871	−	0.160000i
$222$	−5.21672			−0.350124
$223$	−7.88294			−0.527881			−0.263940	−	0.964539i	$-0.585022\pi$
$223$	−7.88294			−0.527881			−0.263940	+	0.964539i	$0.585022\pi$
$224$	−1.39639	+	4.29764i	−0.0933000	+	0.287148i
$225$	−0.438521	−	1.34963i	−0.0292347	−	0.0899753i
$226$	2.34995	+	7.23240i	0.156316	+	0.481092i
$227$	6.99901	−	5.08508i	0.464541	−	0.337509i	−0.330769	−	0.943712i	$-0.607308\pi$
$227$	6.99901	−	5.08508i	0.464541	−	0.337509i	0.795310	+	0.606203i	$0.207308\pi$
$228$	−0.545922	+	1.68017i	−0.0361545	+	0.111272i
$229$	4.52016	−	3.28409i	0.298700	−	0.217018i	−0.428333	−	0.903621i	$-0.640899\pi$
$229$	4.52016	−	3.28409i	0.298700	−	0.217018i	0.727033	+	0.686603i	$0.240899\pi$
$230$	2.94207	+	2.13754i	0.193994	+	0.140945i
$231$	2.45048	+	7.54179i	0.161230	+	0.496213i
$232$	−0.398577	−	0.289583i	−0.0261679	−	0.0190121i
$233$	−17.7762	−	12.9152i	−1.16456	−	0.846102i	−0.174212	−	0.984708i	$-0.555738\pi$
$233$	−17.7762	−	12.9152i	−1.16456	−	0.846102i	−0.990348	+	0.138606i	$0.955738\pi$
$234$	−3.90212	−	12.0095i	−0.255090	−	0.785085i
$235$	−12.4312	−	9.03180i	−0.810922	−	0.589170i
$236$	4.20405	−	3.05442i	0.273660	−	0.198826i
$237$	1.94782	−	5.99476i	0.126524	−	0.389402i
$238$	2.02530	−	1.47146i	0.131280	−	0.0953808i
$239$	−5.57929	−	17.1713i	−0.360895	−	1.11072i	−0.952512	−	0.304500i	$-0.901510\pi$
$239$	−5.57929	−	17.1713i	−0.360895	−	1.11072i	0.591618	−	0.806219i	$-0.298490\pi$
$240$	−0.326615	−	1.00522i	−0.0210829	−	0.0648865i
$241$	6.57038	−	20.2216i	0.423235	−	1.30258i	−0.481438	−	0.876480i	$-0.659885\pi$
$241$	6.57038	−	20.2216i	0.423235	−	1.30258i	0.904674	−	0.426105i	$-0.140115\pi$
$242$	4.18183			0.268818
$243$	−11.0826			−0.710949
$244$	0.794596	−	2.44552i	0.0508688	−	0.156558i
$245$	−25.4781	−	18.5109i	−1.62774	−	1.18262i
$246$	−0.832742	+	0.605023i	−0.0530937	+	0.0385748i
$247$	17.7079			1.12673
$248$	−4.53994	+	3.22318i	−0.288287	+	0.204672i
$249$	0.391278			0.0247962
$250$	8.52968	−	6.19717i	0.539464	−	0.391944i
$251$	−5.70637	−	4.14592i	−0.360183	−	0.261688i	0.392946	−	0.919562i	$-0.371456\pi$
$251$	−5.70637	−	4.14592i	−0.360183	−	0.261688i	−0.753128	+	0.657874i	$0.771456\pi$
$252$	3.90591	−	12.0212i	0.246049	−	0.757261i
$253$	−6.03790			−0.379600
$254$	−5.03322			−0.315812
$255$	−0.180944	+	0.556888i	−0.0113311	+	0.0348736i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	4.41762	+	13.5960i	0.275564	+	0.848098i	0.989070	+	0.147449i	$0.0471061\pi$
$257$	4.41762	+	13.5960i	0.275564	+	0.848098i	−0.713506	+	0.700649i	$0.752894\pi$
$258$	1.20147	−	0.872917i	0.0748000	−	0.0543454i
$259$	−16.1741	+	49.7788i	−1.00501	+	3.09311i
$260$	−8.57098	+	6.22718i	−0.531549	+	0.386193i
$261$	1.11488	+	0.810009i	0.0690095	+	0.0501383i
$262$	1.05181	+	3.23713i	0.0649808	+	0.199990i
$263$	−22.2697	−	16.1799i	−1.37321	−	0.997692i	−0.997479	−	0.0709621i	$-0.977393\pi$
$263$	−22.2697	−	16.1799i	−1.37321	−	0.997692i	−0.375727	−	0.926730i	$-0.622607\pi$
$264$	1.41972	+	1.03149i	0.0873777	+	0.0634836i
$265$	7.32563	+	22.5460i	0.450010	+	1.38499i
$266$	14.3399	+	10.4185i	0.879236	+	0.638802i
$267$	4.84614	−	3.52092i	0.296579	−	0.215477i
$268$	−0.306826	+	0.944314i	−0.0187424	+	0.0576832i
$269$	7.80449	−	5.67029i	0.475848	−	0.345724i	−0.323868	−	0.946102i	$-0.604983\pi$
$269$	7.80449	−	5.67029i	0.475848	−	0.345724i	0.799716	+	0.600379i	$0.204983\pi$
$270$	1.89344	+	5.82740i	0.115231	+	0.354644i
$271$	3.02212	+	9.30113i	0.183581	+	0.565003i	0.999921	−	0.0125679i	$-0.00400060\pi$
$271$	3.02212	+	9.30113i	0.183581	+	0.565003i	−0.816340	+	0.577571i	$0.804001\pi$
$272$	0.171195	−	0.526883i	0.0103802	−	0.0319470i
$273$	9.18773			0.556067
$274$	12.6979			0.767110
$275$	0.610852	−	1.88001i	0.0368358	−	0.113369i
$276$	−0.564631	−	0.410228i	−0.0339868	−	0.0246928i
$277$	−12.5696	+	9.13236i	−0.755235	+	0.548711i	−0.897445	−	0.441126i	$-0.854579\pi$
$277$	−12.5696	+	9.13236i	−0.755235	+	0.548711i	0.142210	+	0.989837i	$0.454579\pi$
$278$	−7.33062			−0.439661
$279$	12.6989	−	9.01574i	0.760265	−	0.539758i
$280$	−10.6046			−0.633745
$281$	14.2137	−	10.3269i	0.847918	−	0.616049i	−0.0766532	−	0.997058i	$-0.524423\pi$
$281$	14.2137	−	10.3269i	0.847918	−	0.616049i	0.924571	+	0.381009i	$0.124423\pi$
$282$	2.38575	+	1.73335i	0.142070	+	0.103220i
$283$	−3.59945	+	11.0780i	−0.213965	+	0.658517i	0.785260	+	0.619166i	$0.212529\pi$
$283$	−3.59945	+	11.0780i	−0.213965	+	0.658517i	−0.999225	+	0.0393511i	$0.987471\pi$
$284$	5.18621			0.307745
$285$	−4.14590			−0.245582
$286$	5.43559	−	16.7290i	0.321413	−	0.989207i
$287$	3.19136	+	9.82200i	0.188380	+	0.579774i
$288$	−0.864368	−	2.66025i	−0.0509334	−	0.156757i
$289$	13.5050	−	9.81195i	0.794411	−	0.577174i
$290$	0.357279	−	1.09959i	0.0209802	−	0.0645703i
$291$	−2.69510	+	1.95810i	−0.157989	+	0.114786i
$292$	9.22994	+	6.70594i	0.540141	+	0.392436i
$293$	1.57393	+	4.84405i	0.0919497	+	0.282992i	0.986447	−	0.164082i	$-0.0524661\pi$
$293$	1.57393	+	4.84405i	0.0919497	+	0.282992i	−0.894497	+	0.447074i	$0.852466\pi$
$294$	4.88966	+	3.55255i	0.285171	+	0.207189i
$295$	9.86594	+	7.16802i	0.574417	+	0.417339i
$296$	3.57929	+	11.0159i	0.208042	+	0.640288i
$297$	−8.23033	−	5.97969i	−0.477572	−	0.346977i
$298$	4.31499	−	3.13503i	0.249961	−	0.181607i
$299$	−2.16177	+	6.65323i	−0.125018	+	0.384766i
$300$	0.184855	−	0.134305i	0.0106726	−	0.00775412i
$301$	−4.60444	−	14.1710i	−0.265396	−	0.816803i
$302$	2.72738	+	8.39402i	0.156943	+	0.483022i
$303$	−2.34338	+	7.21217i	−0.134623	+	0.414328i
$304$	3.92252			0.224972
$305$	6.03441			0.345529
$306$	−0.478858	+	1.47377i	−0.0273745	+	0.0842500i
$307$	−5.57317	−	4.04914i	−0.318077	−	0.231097i	0.417277	−	0.908779i	$-0.362984\pi$
$307$	−5.57317	−	4.04914i	−0.318077	−	0.231097i	−0.735355	+	0.677682i	$0.762984\pi$
$308$	14.2444	−	10.3491i	0.811648	−	0.589697i
$309$	−2.34966			−0.133668
$310$	−10.4862	−	7.79533i	−0.595576	−	0.442745i
$311$	−14.1586			−0.802860			−0.401430	−	0.915890i	$-0.631487\pi$
$311$	−14.1586			−0.802860			−0.401430	+	0.915890i	$0.631487\pi$
$312$	1.64491	−	1.19510i	0.0931248	−	0.0676591i
$313$	−6.66666	−	4.84361i	−0.376822	−	0.273777i	0.383212	−	0.923660i	$-0.374818\pi$
$313$	−6.66666	−	4.84361i	−0.376822	−	0.273777i	−0.760034	+	0.649883i	$0.774818\pi$
$314$	0.176093	−	0.541958i	0.00993750	−	0.0305845i
$315$	29.6627			1.67130
$316$	−13.9953			−0.787298
$317$	−6.52016	+	20.0670i	−0.366208	+	1.12707i	0.583012	+	0.812463i	$0.301874\pi$
$317$	−6.52016	+	20.0670i	−0.366208	+	1.12707i	−0.949221	+	0.314610i	$0.898126\pi$
$318$	−1.40591	−	4.32694i	−0.0788394	−	0.242643i
$319$	0.593197	+	1.82567i	0.0332127	+	0.102218i
$320$	−1.89858	+	1.37940i	−0.106134	+	0.0771106i
$321$	2.17536	−	6.69506i	0.121417	−	0.373682i
$322$	−5.66507	+	4.11591i	−0.315702	+	0.229371i
$323$	−1.75805	−	1.27730i	−0.0978204	−	0.0710706i
$324$	2.22972	+	6.86238i	0.123874	+	0.381243i
$325$	−1.85290	−	1.34621i	−0.102780	−	0.0746742i
$326$	1.71591	+	1.24668i	0.0950356	+	0.0690474i
$327$	0.904612	+	2.78411i	0.0500252	+	0.153962i
$328$	1.84896	+	1.34335i	0.102092	+	0.0741740i
$329$	23.9368	−	17.3911i	1.31968	−	0.958802i
$330$	−1.27262	+	3.91671i	−0.0700553	+	0.215608i
$331$	0.374852	−	0.272346i	0.0206037	−	0.0149695i	−0.577436	−	0.816436i	$-0.695947\pi$
$331$	0.374852	−	0.272346i	0.0206037	−	0.0149695i	0.598039	+	0.801467i	$0.295947\pi$
$332$	−0.268463	−	0.826245i	−0.0147338	−	0.0453461i
$333$	−10.0118	−	30.8133i	−0.548645	−	1.68856i
$334$	−5.60164	+	17.2401i	−0.306508	+	0.943335i
$335$	−2.33013			−0.127309
$336$	2.03520			0.111029
$337$	−10.8443	+	33.3753i	−0.590726	+	1.81807i	−0.0157789	+	0.999876i	$0.505023\pi$
$337$	−10.8443	+	33.3753i	−0.590726	+	1.81807i	−0.574947	+	0.818191i	$0.694977\pi$
$338$	−5.97054	−	4.33785i	−0.324755	−	0.235948i
$339$	2.77087	−	2.01316i	0.150493	−	0.109340i
$340$	1.30010			0.0705081
$341$	21.6929	+	0.237300i	1.17473	+	0.0128505i
$342$	−10.9719			−0.593292
$343$	23.4686	−	17.0509i	1.26718	−	0.920663i
$344$	−2.66765	−	1.93816i	−0.143830	−	0.104499i
$345$	0.506128	−	1.55770i	0.0272490	−	0.0838638i
$346$	−13.7272			−0.737981
$347$	8.09090			0.434343			0.217171	−	0.976134i	$-0.430317\pi$
$347$	8.09090			0.434343			0.217171	+	0.976134i	$0.430317\pi$
$348$	−0.0685678	+	0.211030i	−0.00367562	+	0.0113124i
$349$	−0.0982456	−	0.302369i	−0.00525897	−	0.0161854i	0.948393	−	0.317099i	$-0.102709\pi$
$349$	−0.0982456	−	0.302369i	−0.00525897	−	0.0161854i	−0.953652	+	0.300913i	$0.902709\pi$
$350$	−0.708431	−	2.18033i	−0.0378672	−	0.116543i
$351$	−9.53581	+	6.92817i	−0.508984	+	0.369798i
$352$	1.20405	−	3.70568i	0.0641761	−	0.197514i
$353$	7.79103	−	5.66051i	0.414675	−	0.301279i	−0.360817	−	0.932637i	$-0.617502\pi$
$353$	7.79103	−	5.66051i	0.414675	−	0.301279i	0.775492	+	0.631358i	$0.217502\pi$
$354$	−1.89344	−	1.37566i	−0.100635	−	0.0731156i
$355$	3.76100	+	11.5752i	0.199613	+	0.614346i
$356$	−10.7600	−	7.81761i	−0.570279	−	0.414332i
$357$	−0.912161	−	0.662724i	−0.0482767	−	0.0350751i
$358$	−2.03701	−	6.26927i	−0.107659	−	0.331341i
$359$	13.2229	+	9.60698i	0.697876	+	0.507037i	0.879240	−	0.476379i	$-0.158051\pi$
$359$	13.2229	+	9.60698i	0.697876	+	0.507037i	−0.181364	+	0.983416i	$0.558051\pi$
$360$	5.31061	−	3.85839i	0.279894	−	0.203355i
$361$	−1.11674	+	3.43696i	−0.0587757	+	0.180893i
$362$	6.91558	−	5.02446i	0.363475	−	0.264080i
$363$	−0.582011	−	1.79125i	−0.0305477	−	0.0940161i
$364$	−6.30388	−	19.4013i	−0.330413	−	1.01691i
$365$	−8.27359	+	25.4635i	−0.433060	+	1.33282i
$366$	−1.15810			−0.0605350
$367$	−20.2563			−1.05737			−0.528685	−	0.848818i	$-0.677315\pi$
$367$	−20.2563			−1.05737			−0.528685	+	0.848818i	$0.677315\pi$
$368$	−0.478858	+	1.47377i	−0.0249622	+	0.0768257i
$369$	−5.17183	−	3.75755i	−0.269235	−	0.195610i
$370$	−21.9909	+	15.9773i	−1.14325	+	0.830622i
$371$	−45.6473			−2.36989
$372$	2.01247	+	1.49605i	0.104342	+	0.0775667i
$373$	−1.39447			−0.0722029			−0.0361015	−	0.999348i	$-0.511494\pi$
$373$	−1.39447			−0.0722029			−0.0361015	+	0.999348i	$0.511494\pi$
$374$	−1.74633	+	1.26879i	−0.0903008	+	0.0656074i
$375$	−3.84163	−	2.79111i	−0.198381	−	0.144132i
$376$	2.02333	−	6.22718i	0.104345	−	0.321142i
$377$	2.22411			0.114548
$378$	−11.7983			−0.606841
$379$	9.37925	−	28.8664i	0.481780	−	1.48277i	−0.354812	−	0.934938i	$-0.615455\pi$
$379$	9.37925	−	28.8664i	0.481780	−	1.48277i	0.836591	−	0.547827i	$-0.184545\pi$
$380$	2.84458	+	8.75472i	0.145924	+	0.449107i
$381$	0.700505	+	2.15593i	0.0358880	+	0.110452i
$382$	13.1429	−	9.54890i	0.672451	−	0.488564i
$383$	−2.08027	+	6.40242i	−0.106297	+	0.327148i	−0.990033	−	0.140838i	$-0.955020\pi$
$383$	−2.08027	+	6.40242i	−0.106297	+	0.327148i	0.883736	+	0.467986i	$0.155020\pi$
$384$	0.364368	−	0.264729i	0.0185941	−	0.0135094i
$385$	33.4282	+	24.2870i	1.70366	+	1.23778i
$386$	−1.37562	−	4.23373i	−0.0700173	−	0.215491i
$387$	7.46183	+	5.42134i	0.379306	+	0.275582i
$388$	5.98400	+	4.34763i	0.303792	+	0.220717i
$389$	−7.11009	−	21.8826i	−0.360496	−	1.10949i	−0.952754	−	0.303744i	$-0.901763\pi$
$389$	−7.11009	−	21.8826i	−0.360496	−	1.10949i	0.592258	−	0.805749i	$-0.298237\pi$
$390$	3.86023	+	2.80462i	0.195470	+	0.142017i
$391$	0.694528	−	0.504604i	0.0351238	−	0.0255189i
$392$	4.14688	−	12.7628i	0.209449	−	0.644617i
$393$	1.24021	−	0.901063i	0.0625602	−	0.0454526i
$394$	7.56025	+	23.2681i	0.380880	+	1.17223i
$395$	−10.1493	−	31.2363i	−0.510666	−	1.57167i
$396$	−3.36791	+	10.3654i	−0.169244	+	0.520879i
$397$	1.29862			0.0651757			0.0325878	−	0.999469i	$-0.489625\pi$
$397$	1.29862			0.0651757			0.0325878	+	0.999469i	$0.489625\pi$
$398$	−21.1234			−1.05882
$399$	2.46691	−	7.59237i	0.123500	−	0.380094i
$400$	−0.410440	−	0.298202i	−0.0205220	−	0.0149101i
$401$	−10.5582	+	7.67095i	−0.527249	+	0.383069i	−0.819328	−	0.573325i	$-0.805653\pi$
$401$	−10.5582	+	7.67095i	−0.527249	+	0.383069i	0.292079	+	0.956394i	$0.405653\pi$
$402$	0.447191			0.0223039
$403$	8.02823	−	23.8186i	0.399915	−	1.18649i
$404$	16.8375			0.837695
$405$	−13.6993	+	9.95309i	−0.680721	+	0.494573i
$406$	1.80109	+	1.30857i	0.0893867	+	0.0649432i
$407$	13.9463	−	42.9223i	0.691293	−	2.12758i
$408$	−0.249511			−0.0123527
$409$	−19.7086			−0.974529			−0.487265	−	0.873254i	$-0.662005\pi$
$409$	−19.7086			−0.974529			−0.487265	+	0.873254i	$0.662005\pi$
$410$	−1.65738	+	5.10090i	−0.0818524	+	0.251916i
$411$	−1.76725	−	5.43903i	−0.0871720	−	0.268288i
$412$	1.61215	+	4.96168i	0.0794249	+	0.244445i
$413$	−18.9973	+	13.8023i	−0.934794	+	0.679168i
$414$	1.33944	−	4.12237i	0.0658298	−	0.202603i
$415$	1.64942	−	1.19837i	0.0809667	−	0.0588258i
$416$	−3.65224	−	2.65351i	−0.179066	−	0.130099i
$417$	1.02025	+	3.14000i	0.0499618	+	0.153767i
$418$	−12.3647	−	8.98351i	−0.604779	−	0.439398i
$419$	27.7414	+	20.1553i	1.35526	+	0.984651i	0.998731	+	0.0503655i	$0.0160386\pi$
$419$	27.7414	+	20.1553i	1.35526	+	0.984651i	0.356525	+	0.934286i	$0.383961\pi$
$420$	1.47591	+	4.54238i	0.0720169	+	0.221645i
$421$	8.68658	+	6.31117i	0.423358	+	0.307587i	0.778987	−	0.627039i	$-0.215734\pi$
$421$	8.68658	+	6.31117i	0.423358	+	0.307587i	−0.355630	+	0.934627i	$0.615734\pi$
$422$	−5.20565	+	3.78212i	−0.253407	+	0.184111i
$423$	−5.65957	+	17.4184i	−0.275178	+	0.846911i
$424$	−8.17240	+	5.93760i	−0.396887	+	0.288355i
$425$	0.0868524	+	0.267304i	0.00421296	+	0.0129662i
$426$	−0.721797	−	2.22146i	−0.0349712	−	0.107630i
$427$	−3.59062	+	11.0508i	−0.173762	+	0.534786i
$428$	−15.6302			−0.755516
$429$	−7.92222			−0.382488
$430$	2.39125	−	7.35950i	0.115316	−	0.354906i
$431$	22.5690	+	16.3973i	1.08711	+	0.789832i	0.978909	−	0.204297i	$-0.0654908\pi$
$431$	22.5690	+	16.3973i	1.08711	+	0.789832i	0.108202	+	0.994129i	$0.465491\pi$
$432$	−2.11230	+	1.53467i	−0.101628	+	0.0738371i
$433$	10.8746			0.522602			0.261301	−	0.965257i	$-0.415849\pi$
$433$	10.8746			0.522602			0.261301	+	0.965257i	$0.415849\pi$
$434$	20.5151	−	14.5649i	0.984757	−	0.699139i
$435$	−0.520725			−0.0249668
$436$	5.25841	−	3.82046i	0.251832	−	0.182967i
$437$	4.91753	+	3.57279i	0.235237	+	0.170910i
$438$	1.58784	−	4.88687i	0.0758699	−	0.233503i
$439$	−22.0368			−1.05176			−0.525881	−	0.850558i	$-0.676264\pi$
$439$	−22.0368			−1.05176			−0.525881	+	0.850558i	$0.676264\pi$
$440$	9.14392			0.435920
$441$	−11.5994	+	35.6994i	−0.552355	+	1.69997i
$442$	0.772844	+	2.37857i	0.0367605	+	0.113137i
$443$	−0.310840	−	0.956668i	−0.0147685	−	0.0454527i	0.943401	−	0.331655i	$-0.107607\pi$
$443$	−0.310840	−	0.956668i	−0.0147685	−	0.0454527i	−0.958169	+	0.286202i	$0.907607\pi$
$444$	4.22042	−	3.06631i	0.200292	−	0.145521i
$445$	9.64513	−	29.6847i	0.457223	−	1.40719i
$446$	6.37743	−	4.63348i	0.301980	−	0.219402i
$447$	−1.94340	−	1.41197i	−0.0919199	−	0.0667837i
$448$	−1.39639	−	4.29764i	−0.0659731	−	0.203044i
$449$	−2.13977	−	1.55463i	−0.100982	−	0.0733677i	0.536148	−	0.844124i	$-0.319879\pi$
$449$	−2.13977	−	1.55463i	−0.100982	−	0.0733677i	−0.637130	+	0.770756i	$0.719879\pi$
$450$	1.14806	+	0.834117i	0.0541202	+	0.0393207i
$451$	−2.75179	−	8.46912i	−0.129577	−	0.398795i
$452$	−6.15224	−	4.46987i	−0.289377	−	0.210245i
$453$	3.21591	−	2.33650i	0.151097	−	0.109778i
$454$	−2.67339	+	8.22783i	−0.125468	+	0.386151i
$455$	38.7305	−	28.1394i	1.81572	−	1.31919i
$456$	−0.545922	−	1.68017i	−0.0255651	−	0.0786814i
$457$	0.304016	+	0.935666i	0.0142213	+	0.0437686i	0.957915	−	0.287051i	$-0.0926749\pi$
$457$	0.304016	+	0.935666i	0.0142213	+	0.0437686i	−0.943694	+	0.330819i	$0.892675\pi$
$458$	−1.72655	+	5.31376i	−0.0806762	+	0.248296i
$459$	1.44646			0.0675148
$460$	−3.63659			−0.169557
$461$	−5.86035	+	18.0363i	−0.272944	+	0.840035i	0.716812	+	0.697266i	$0.245600\pi$
$461$	−5.86035	+	18.0363i	−0.272944	+	0.840035i	−0.989756	+	0.142769i	$0.954400\pi$
$462$	−6.41543	−	4.66108i	−0.298473	−	0.216853i
$463$	−18.0540	+	13.1170i	−0.839040	+	0.609598i	−0.922102	−	0.386946i	$-0.873530\pi$
$463$	−18.0540	+	13.1170i	−0.839040	+	0.609598i	0.0830624	+	0.996544i	$0.473530\pi$
$464$	0.492668			0.0228716
$465$	−1.87963	+	5.57658i	−0.0871655	+	0.258608i
$466$	21.9726			1.01786
$467$	20.8069	−	15.1171i	0.962828	−	0.699536i	0.00902235	−	0.999959i	$-0.497128\pi$
$467$	20.8069	−	15.1171i	0.962828	−	0.699536i	0.953806	+	0.300424i	$0.0971281\pi$
$468$	10.2159	+	7.42228i	0.472230	+	0.343095i
$469$	1.38649	−	4.26717i	0.0640220	−	0.197040i
$470$	15.3658			0.708772
$471$	−0.256651			−0.0118258
$472$	−1.60580	+	4.94216i	−0.0739131	+	0.227481i
$473$	3.97023	+	12.2191i	0.182551	+	0.561835i
$474$	1.94782	+	5.99476i	0.0894662	+	0.275349i
$475$	−1.60996	+	1.16970i	−0.0738700	+	0.0536697i
$476$	−0.773594	+	2.38088i	−0.0354576	+	0.109127i
$477$	22.8595	−	16.6084i	1.04666	−	0.760445i
$478$	14.6068	+	10.6124i	0.668099	+	0.485402i
$479$	12.5953	+	38.7643i	0.575494	+	1.77119i	0.634492	+	0.772929i	$0.281209\pi$
$479$	12.5953	+	38.7643i	0.575494	+	1.77119i	−0.0589982	+	0.998258i	$0.518791\pi$
$480$	0.855089	+	0.621258i	0.0390293	+	0.0283564i
$481$	−42.3033	−	30.7352i	−1.92887	−	1.40140i
$482$	6.57038	+	20.2216i	0.299273	+	0.921067i
$483$	2.55145	+	1.85374i	0.116095	+	0.0843481i
$484$	−3.38317	+	2.45802i	−0.153780	+	0.111728i
$485$	−5.36398	+	16.5086i	−0.243566	+	0.749618i
$486$	8.96601	−	6.51419i	0.406706	−	0.295489i
$487$	5.35312	+	16.4752i	0.242573	+	0.746562i	0.996026	+	0.0890610i	$0.0283866\pi$
$487$	5.35312	+	16.4752i	0.242573	+	0.746562i	−0.753453	+	0.657501i	$0.771613\pi$
$488$	0.794596	+	2.44552i	0.0359697	+	0.110703i
$489$	0.295191	−	0.908504i	0.0133490	−	0.0410840i
$490$	31.4926			1.42269
$491$	4.67620			0.211034			0.105517	−	0.994417i	$-0.466350\pi$
$491$	4.67620			0.211034			0.105517	+	0.994417i	$0.466350\pi$
$492$	0.318079	−	0.978947i	0.0143401	−	0.0441344i
$493$	−0.220811	−	0.160428i	−0.00994481	−	0.00722533i
$494$	−14.3260	+	10.4084i	−0.644557	+	0.468298i
$495$	−25.5770			−1.14960
$496$	1.77835	−	5.27612i	0.0798504	−	0.236905i
$497$	−23.4355			−1.05122
$498$	−0.316550	+	0.229987i	−0.0141850	+	0.0103060i
$499$	−7.21652	−	5.24311i	−0.323056	−	0.234714i	0.414422	−	0.910085i	$-0.363984\pi$
$499$	−7.21652	−	5.24311i	−0.323056	−	0.234714i	−0.737478	+	0.675371i	$0.763984\pi$
$500$	−3.25805	+	10.0272i	−0.145704	+	0.448432i
$501$	8.16424			0.364751
$502$	7.05346			0.314811
$503$	−2.88248	+	8.87137i	−0.128524	+	0.395555i	−0.994527	−	0.104484i	$-0.966681\pi$
$503$	−2.88248	+	8.87137i	−0.128524	+	0.395555i	0.866003	+	0.500039i	$0.166681\pi$
$504$	3.90591	+	12.0212i	0.173983	+	0.535465i
$505$	12.2104	+	37.5797i	0.543355	+	1.67228i
$506$	4.88477	−	3.54899i	0.217154	−	0.157772i
$507$	−1.02712	+	3.16115i	−0.0456160	+	0.140392i
$508$	4.07196	−	2.95845i	0.180664	−	0.131260i
$509$	−14.0049	−	10.1752i	−0.620757	−	0.451006i	0.232429	−	0.972613i	$-0.425333\pi$
$509$	−14.0049	−	10.1752i	−0.620757	−	0.451006i	−0.853186	+	0.521607i	$0.825333\pi$
$510$	−0.180944	−	0.556888i	−0.00801232	−	0.0246594i
$511$	−41.7083	−	30.3028i	−1.84507	−	1.34052i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	3.16479	+	9.74023i	0.139729	+	0.430042i
$514$	−11.5655	−	8.40282i	−0.510132	−	0.370632i
$515$	−9.90492	+	7.19635i	−0.436463	+	0.317109i
$516$	−0.458919	+	1.41241i	−0.0202028	+	0.0621778i
$517$	−20.6398	+	14.9957i	−0.907736	+	0.659509i
$518$	−16.1741	−	49.7788i	−0.710650	−	2.18716i
$519$	1.91051	+	5.87994i	0.0838620	+	0.258101i
$520$	3.27382	−	10.0758i	0.143567	−	0.441852i
$521$	32.2898			1.41464			0.707321	−	0.706893i	$-0.249904\pi$
$521$	32.2898			1.41464			0.707321	+	0.706893i	$0.249904\pi$
$522$	−1.37807			−0.0603165
$523$	13.1525	−	40.4791i	0.575117	−	1.77003i	−0.0606639	−	0.998158i	$-0.519322\pi$
$523$	13.1525	−	40.4791i	0.575117	−	1.77003i	0.635781	−	0.771870i	$-0.280678\pi$
$524$	−2.75367	−	2.00066i	−0.120294	−	0.0873990i
$525$	−0.835325	+	0.606899i	−0.0364566	+	0.0264873i
$526$	27.5268			1.20023
$527$	−2.51512	+	1.78563i	−0.109560	+	0.0777835i
$528$	−1.75487			−0.0763709
$529$	16.6647	−	12.1076i	0.724552	−	0.526418i
$530$	−19.1787	−	13.9342i	−0.833071	−	0.605262i
$531$	4.49168	−	13.8240i	0.194922	−	0.599909i
$532$	−17.7251			−0.768480
$533$	−10.3174			−0.446898
$534$	−1.85106	+	5.69697i	−0.0801032	+	0.246532i
$535$	−11.3349	−	34.8853i	−0.490051	−	1.50822i
$536$	−0.306826	−	0.944314i	−0.0132529	−	0.0407882i
$537$	−2.40188	+	1.74507i	−0.103649	+	0.0753052i
$538$	−2.98105	+	9.17472i	−0.128522	+	0.395550i
$539$	−42.3017	+	30.7340i	−1.82207	+	1.32381i
$540$	−4.95708	−	3.60153i	−0.213319	−	0.154985i
$541$	−7.39203	−	22.7503i	−0.317808	−	0.978112i	−0.974583	−	0.224026i	$-0.928080\pi$
$541$	−7.39203	−	22.7503i	−0.317808	−	0.978112i	0.656775	−	0.754086i	$-0.271920\pi$
$542$	−7.91201	−	5.74841i	−0.339850	−	0.246915i
$543$	−3.11467	−	2.26294i	−0.133663	−	0.0971119i
$544$	0.171195	+	0.526883i	0.00733991	+	0.0225899i
$545$	12.3403	+	8.96575i	0.528600	+	0.384050i
$546$	−7.43303	+	5.40041i	−0.318104	+	0.231116i
$547$	3.37193	−	10.3777i	0.144173	−	0.443719i	−0.852731	−	0.522351i	$-0.825055\pi$
$547$	3.37193	−	10.3777i	0.144173	−	0.443719i	0.996904	+	0.0786316i	$0.0250551\pi$
$548$	−10.2728	+	7.46365i	−0.438834	+	0.318831i
$549$	−2.22261	−	6.84049i	−0.0948586	−	0.291945i
$550$	0.610852	+	1.88001i	0.0260468	+	0.0801639i
$551$	0.597176	−	1.83792i	0.0254405	−	0.0782980i
$552$	0.697922			0.0297055
$553$	63.2421			2.68933
$554$	4.80117	−	14.7765i	0.203982	−	0.627792i
$555$	9.90435	+	7.19593i	0.420416	+	0.305450i
$556$	5.93060	−	4.30883i	0.251513	−	0.182735i
$557$	−35.6156			−1.50908			−0.754540	−	0.656254i	$-0.772140\pi$
$557$	−35.6156			−1.50908			−0.754540	+	0.656254i	$0.772140\pi$
$558$	−4.97433	+	14.7581i	−0.210580	+	0.624761i
$559$	14.8858			0.629604
$560$	8.57929	−	6.23322i	0.362541	−	0.263402i
$561$	0.786521	+	0.571441i	0.0332069	+	0.0241263i
$562$	−5.42915	+	16.7092i	−0.229015	+	0.704835i
$563$	−24.6955			−1.04079			−0.520396	−	0.853925i	$-0.674215\pi$
$563$	−24.6955			−1.04079			−0.520396	+	0.853925i	$0.674215\pi$
$564$	−2.94895			−0.124173
$565$	5.51479	−	16.9728i	0.232009	−	0.714050i
$566$	−3.59945	−	11.0780i	−0.151296	−	0.465642i
$567$	−10.0757	−	31.0097i	−0.423139	−	1.30229i
$568$	−4.19573	+	3.04838i	−0.176049	+	0.127907i
$569$	−5.32586	+	16.3913i	−0.223271	+	0.687159i	0.775191	+	0.631727i	$0.217654\pi$
$569$	−5.32586	+	16.3913i	−0.223271	+	0.687159i	−0.998462	+	0.0554320i	$0.982346\pi$
$570$	3.35410	−	2.43690i	0.140488	−	0.102070i
$571$	9.71832	+	7.06077i	0.406699	+	0.295484i	0.772264	−	0.635302i	$-0.219124\pi$
$571$	9.71832	+	7.06077i	0.406699	+	0.295484i	−0.365565	+	0.930786i	$0.619124\pi$
$572$	5.43559	+	16.7290i	0.227273	+	0.699475i
$573$	−5.91937	−	4.30067i	−0.247285	−	0.179663i
$574$	−8.35509	−	6.07033i	−0.348735	−	0.253371i
$575$	−0.242940	−	0.747691i	−0.0101313	−	0.0311809i
$576$	2.26295	+	1.64413i	0.0942894	+	0.0685053i
$577$	18.1017	−	13.1516i	0.753582	−	0.547509i	−0.143353	−	0.989672i	$-0.545789\pi$
$577$	18.1017	−	13.1516i	0.753582	−	0.547509i	0.896935	+	0.442162i	$0.145789\pi$
$578$	−5.15845	+	15.8761i	−0.214563	+	0.660357i
$579$	−1.62202	+	1.17847i	−0.0674090	+	0.0489755i
$580$	0.357279	+	1.09959i	0.0148352	+	0.0456581i
$581$	1.21313	+	3.73364i	0.0503292	+	0.154897i
$582$	1.02944	−	3.16828i	0.0426715	−	0.131329i
$583$	39.3599			1.63012
$584$	−11.4088			−0.472101
$585$	−9.15738	+	28.1835i	−0.378611	+	1.16525i
$586$	−4.12059	−	2.99379i	−0.170220	−	0.123672i
$587$	6.30998	−	4.58447i	0.260441	−	0.189221i	−0.449901	−	0.893079i	$-0.648541\pi$
$587$	6.30998	−	4.58447i	0.260441	−	0.189221i	0.710341	+	0.703857i	$0.248541\pi$
$588$	−6.04396			−0.249249
$589$	−17.5272	−	13.0295i	−0.722195	−	0.536873i
$590$	−12.1950			−0.502059
$591$	8.91444	−	6.47672i	0.366691	−	0.266417i
$592$	−9.37071	−	6.80822i	−0.385134	−	0.279816i
$593$	1.16024	−	3.57086i	0.0476454	−	0.146637i	−0.924403	−	0.381416i	$-0.875437\pi$
$593$	1.16024	−	3.57086i	0.0476454	−	0.146637i	0.972049	+	0.234779i	$0.0754365\pi$
$594$	10.1733			0.417414
$595$	−5.87492			−0.240848
$596$	−1.64818	+	5.07258i	−0.0675121	+	0.207781i
$597$	2.93988	+	9.04801i	0.120321	+	0.370310i
$598$	−2.16177	−	6.65323i	−0.0884011	−	0.272071i
$599$	−9.78226	+	7.10723i	−0.399692	+	0.290394i	−0.769416	−	0.638748i	$-0.779453\pi$
$599$	−9.78226	+	7.10723i	−0.399692	+	0.290394i	0.369723	+	0.929142i	$0.379453\pi$
$600$	−0.0706085	+	0.217311i	−0.00288258	+	0.00887167i
$601$	−0.370713	+	0.269339i	−0.0151217	+	0.0109866i	−0.595320	−	0.803488i	$-0.702975\pi$
$601$	−0.370713	+	0.269339i	−0.0151217	+	0.0109866i	0.580199	+	0.814475i	$0.302975\pi$
$602$	12.0546	+	8.75817i	0.491308	+	0.356956i
$603$	0.858241	+	2.64139i	0.0349503	+	0.107566i
$604$	−7.14038	−	5.18779i	−0.290538	−	0.211088i
$605$	−7.93952	−	5.76840i	−0.322788	−	0.234519i
$606$	−2.34338	−	7.21217i	−0.0951931	−	0.292974i
$607$	−9.38039	−	6.81525i	−0.380738	−	0.276622i	0.380912	−	0.924611i	$-0.375610\pi$
$607$	−9.38039	−	6.81525i	−0.380738	−	0.276622i	−0.761650	+	0.647989i	$0.775610\pi$
$608$	−3.17339	+	2.30560i	−0.128698	+	0.0935044i
$609$	0.309844	−	0.953602i	0.0125555	−	0.0386419i
$610$	−4.88194	+	3.54694i	−0.197664	+	0.143611i
$611$	9.13418	+	28.1121i	0.369529	+	1.13729i
$612$	−0.478858	−	1.47377i	−0.0193567	−	0.0595737i
$613$	6.58111	−	20.2546i	0.265808	−	0.818074i	−0.725698	−	0.688014i	$-0.758483\pi$
$613$	6.58111	−	20.2546i	0.265808	−	0.818074i	0.991506	−	0.130060i	$-0.0415171\pi$
$614$	6.88881			0.278010
$615$	2.41559			0.0974061
$616$	−5.44086	+	16.7453i	−0.219219	+	0.674685i
$617$	−2.83430	−	2.05924i	−0.114105	−	0.0829018i	0.529270	−	0.848454i	$-0.322466\pi$
$617$	−2.83430	−	2.05924i	−0.114105	−	0.0829018i	−0.643374	+	0.765552i	$0.722466\pi$
$618$	1.90092	−	1.38110i	0.0764661	−	0.0555559i
$619$	33.5950			1.35030			0.675149	−	0.737681i	$-0.264079\pi$
$619$	33.5950			1.35030			0.675149	+	0.737681i	$0.264079\pi$
$620$	13.0655	+	0.142924i	0.524722	+	0.00573997i
$621$	−4.04596			−0.162359
$622$	11.4545	−	8.32221i	0.459285	−	0.333690i
$623$	48.6224	+	35.3262i	1.94801	+	1.41531i
$624$	−0.628300	+	1.93371i	−0.0251521	+	0.0774103i
$625$	−27.2793			−1.09117
$626$	8.24045			0.329355
$627$	−2.12712	+	6.54661i	−0.0849491	+	0.261446i
$628$	0.176093	+	0.541958i	0.00702688	+	0.0216265i
$629$	1.98292	+	6.10280i	0.0790642	+	0.243335i
$630$	−23.9976	+	17.4353i	−0.956088	+	0.694638i
$631$	−4.64328	+	14.2906i	−0.184846	+	0.568898i	−0.999946	−	0.0104230i	$-0.996682\pi$
$631$	−4.64328	+	14.2906i	−0.184846	+	0.568898i	0.815100	+	0.579321i	$0.196682\pi$
$632$	11.3225	−	8.22624i	0.450383	−	0.327222i
$633$	2.34454	+	1.70341i	0.0931871	+	0.0677044i
$634$	−6.52016	−	20.0670i	−0.258948	−	0.796961i
$635$	9.55596	+	6.94281i	0.379217	+	0.275517i
$636$	3.68072	+	2.67420i	0.145950	+	0.106039i
$637$	18.7207	+	57.6165i	0.741743	+	2.28285i
$638$	−1.55301	−	1.12833i	−0.0614843	−	0.0446709i
$639$	11.7361	−	8.52678i	0.464273	−	0.337314i
$640$	0.725192	−	2.23191i	0.0286657	−	0.0882240i
$641$	−12.2466	+	8.89764i	−0.483710	+	0.351436i	−0.802760	−	0.596302i	$-0.796636\pi$
$641$	−12.2466	+	8.89764i	−0.483710	+	0.351436i	0.319050	+	0.947738i	$0.396636\pi$
$642$	2.17536	+	6.69506i	0.0858546	+	0.264233i
$643$	12.9751	+	39.9332i	0.511687	+	1.57481i	0.789230	+	0.614098i	$0.210480\pi$
$643$	12.9751	+	39.9332i	0.511687	+	1.57481i	−0.277543	+	0.960713i	$0.589520\pi$
$644$	2.16386	−	6.65969i	0.0852682	−	0.262428i
$645$	−3.48518			−0.137229
$646$	2.17307			0.0854981
$647$	5.71719	−	17.5957i	0.224766	−	0.691759i	−0.773549	−	0.633736i	$-0.781520\pi$
$647$	5.71719	−	17.5957i	0.224766	−	0.691759i	0.998315	−	0.0580226i	$-0.0184795\pi$
$648$	−5.83749	−	4.24119i	−0.229318	−	0.166609i
$649$	16.3806	−	11.9012i	0.642995	−	0.467163i
$650$	2.29031			0.0898333
$651$	−9.09396	−	6.76036i	−0.356421	−	0.264959i
$652$	−2.12098			−0.0830642
$653$	−14.2084	+	10.3230i	−0.556018	+	0.403971i	−0.830000	−	0.557764i	$-0.811659\pi$
$653$	−14.2084	+	10.3230i	−0.556018	+	0.403971i	0.273981	+	0.961735i	$0.411659\pi$
$654$	−2.36831	−	1.72067i	−0.0926081	−	0.0672837i
$655$	2.46835	−	7.59680i	0.0964464	−	0.296831i
$656$	−2.28544			−0.0892315
$657$	31.9123			1.24502
$658$	−9.14304	+	28.1394i	−0.356433	+	1.09699i
$659$	4.20074	+	12.9285i	0.163638	+	0.503625i	0.998933	−	0.0461763i	$-0.0147036\pi$
$659$	4.20074	+	12.9285i	0.163638	+	0.503625i	−0.835296	+	0.549801i	$0.814704\pi$
$660$	−1.27262	−	3.91671i	−0.0495366	−	0.152458i
$661$	14.2060	−	10.3212i	0.552548	−	0.401450i	−0.276176	−	0.961107i	$-0.589067\pi$
$661$	14.2060	−	10.3212i	0.552548	−	0.401450i	0.828724	+	0.559657i	$0.189067\pi$
$662$	−0.143181	+	0.440665i	−0.00556487	+	0.0171269i
$663$	0.911277	−	0.662081i	0.0353910	−	0.0257131i
$664$	0.702846	+	0.510647i	0.0272757	+	0.0198170i
$665$	−12.8541	−	39.5608i	−0.498460	−	1.53410i
$666$	26.2113	+	19.0436i	1.01567	+	0.737926i
$667$	0.617642	+	0.448743i	0.0239152	+	0.0173754i
$668$	−5.60164	−	17.2401i	−0.216734	−	0.667039i
$669$	−2.87229	−	2.08684i	−0.111049	−	0.0806820i
$670$	1.88512	−	1.36962i	0.0728285	−	0.0529130i
$671$	3.09605	−	9.52868i	0.119522	−	0.367851i
$672$	−1.64651	+	1.19626i	−0.0635154	+	0.0461467i
$673$	4.16091	+	12.8060i	0.160391	+	0.493634i	0.998667	−	0.0516125i	$-0.0164361\pi$
$673$	4.16091	+	12.8060i	0.160391	+	0.493634i	−0.838276	+	0.545246i	$0.816436\pi$
$674$	−10.8443	−	33.3753i	−0.417706	−	1.28557i
$675$	0.409328	−	1.25978i	0.0157551	−	0.0484891i
$676$	7.37999			0.283846
$677$	9.27008			0.356278			0.178139	−	0.984005i	$-0.442992\pi$
$677$	9.27008			0.356278			0.178139	+	0.984005i	$0.442992\pi$
$678$	−1.05838	+	3.25735i	−0.0406468	+	0.125098i
$679$	−27.0405	−	19.6461i	−1.03772	−	0.753947i
$680$	−1.05181	+	0.764182i	−0.0403349	+	0.0293051i
$681$	3.89639			0.149310
$682$	−17.6894	+	12.5588i	−0.677361	+	0.480900i
$683$	40.3516			1.54401			0.772005	−	0.635616i	$-0.219254\pi$
$683$	40.3516			1.54401			0.772005	+	0.635616i	$0.219254\pi$
$684$	8.87645	−	6.44912i	0.339399	−	0.246588i
$685$	−24.1080	−	17.5155i	−0.921119	−	0.669232i
$686$	−8.96420	+	27.5890i	−0.342255	+	1.05335i
$687$	2.51639			0.0960064
$688$	3.29740			0.125712
$689$	14.0921	−	43.3711i	0.536867	−	1.65231i
$690$	0.506128	+	1.55770i	0.0192679	+	0.0593006i
$691$	1.23019	+	3.78614i	0.0467987	+	0.144032i	0.971725	−	0.236114i	$-0.0758739\pi$
$691$	1.23019	+	3.78614i	0.0467987	+	0.144032i	−0.924927	+	0.380146i	$0.875874\pi$
$692$	11.1056	−	8.06867i	0.422171	−	0.306725i
$693$	15.2189	−	46.8391i	0.578119	−	1.77927i
$694$	−6.54568	+	4.75571i	−0.248471	+	0.180524i
$695$	13.9177	+	10.1118i	0.527930	+	0.383564i
$696$	−0.0685678	−	0.211030i	−0.00259905	−	0.00799907i
$697$	1.02432	+	0.744212i	0.0387989	+	0.0281890i
$698$	0.257210	+	0.186874i	0.00973555	+	0.00707329i
$699$	−3.05807	−	9.41177i	−0.115667	−	0.355986i
$700$	1.85470	+	1.34752i	0.0701009	+	0.0509313i
$701$	−2.90416	+	2.11000i	−0.109689	+	0.0796935i	−0.641277	−	0.767309i	$-0.721595\pi$
$701$	−2.90416	+	2.11000i	−0.109689	+	0.0796935i	0.531589	+	0.847003i	$0.321595\pi$
$702$	3.64235	−	11.2100i	0.137472	−	0.423095i
$703$	−36.7568	+	26.7054i	−1.38631	+	1.00721i
$704$	1.20405	+	3.70568i	0.0453793	+	0.139663i
$705$	−2.13856	−	6.58180i	−0.0805427	−	0.247885i
$706$	−2.97591	+	9.15890i	−0.112000	+	0.344700i
$707$	−76.0852			−2.86148
$708$	2.34042			0.0879582
$709$	−12.1791	+	37.4835i	−0.457396	+	1.40772i	0.410902	+	0.911680i	$0.365214\pi$
$709$	−12.1791	+	37.4835i	−0.457396	+	1.40772i	−0.868298	+	0.496042i	$0.834786\pi$
$710$	−9.84642	−	7.15384i	−0.369530	−	0.268479i
$711$	−31.6706	+	23.0101i	−1.18774	+	0.862945i
$712$	13.3001			0.498442
$713$	7.03517	−	4.99470i	0.263469	−	0.187053i
$714$	1.12749			0.0421954
$715$	−33.3958	+	24.2635i	−1.24893	+	0.907403i
$716$	5.33296	+	3.87462i	0.199302	+	0.144801i
$717$	2.51282	−	7.73368i	0.0938431	−	0.288819i
$718$	−16.3444			−0.609966
$719$	−17.4797			−0.651883			−0.325942	−	0.945390i	$-0.605681\pi$
$719$	−17.4797			−0.651883			−0.325942	+	0.945390i	$0.605681\pi$
$720$	−2.02847	+	6.24300i	−0.0755968	+	0.232663i
$721$	−7.28498	−	22.4209i	−0.271307	−	0.834997i
$722$	−1.11674	−	3.43696i	−0.0415607	−	0.127911i
$723$	7.74727	−	5.62872i	0.288124	−	0.209334i
$724$	−2.64152	+	8.12975i	−0.0981712	+	0.302140i
$725$	−0.202211	+	0.146915i	−0.00750992	+	0.00545628i
$726$	1.52373	+	1.10705i	0.0565507	+	0.0410865i
$727$	9.23205	+	28.4133i	0.342398	+	1.05379i	0.962962	+	0.269637i	$0.0869036\pi$
$727$	9.23205	+	28.4133i	0.342398	+	1.05379i	−0.620564	+	0.784156i	$0.713096\pi$
$728$	16.5038	+	11.9907i	0.611670	+	0.444404i
$729$	13.4743	+	9.78967i	0.499049	+	0.362580i
$730$	−8.27359	−	25.4635i	−0.306219	−	0.942447i
$731$	−1.47787	−	1.07374i	−0.0546610	−	0.0397136i
$732$	0.936925	−	0.680716i	0.0346297	−	0.0251600i
$733$	7.10623	−	21.8707i	0.262475	−	0.807814i	−0.729790	−	0.683671i	$-0.760382\pi$
$733$	7.10623	−	21.8707i	0.262475	−	0.807814i	0.992264	−	0.124142i	$-0.0396179\pi$
$734$	16.3877	−	11.9063i	0.604880	−	0.439471i
$735$	−4.38303	−	13.4896i	−0.161670	−	0.497571i
$736$	−0.478858	−	1.47377i	−0.0176509	−	0.0543240i
$737$	−1.19551	+	3.67941i	−0.0440373	+	0.135533i
$738$	6.39273			0.235320
$739$	−13.3526			−0.491185			−0.245592	−	0.969373i	$-0.578982\pi$
$739$	−13.3526			−0.491185			−0.245592	+	0.969373i	$0.578982\pi$
$740$	8.39978	−	25.8519i	0.308782	−	0.950334i
$741$	6.45220	+	4.68780i	0.237027	+	0.172210i
$742$	36.9294	−	26.8308i	1.35572	−	0.984990i
$743$	−21.9645			−0.805800			−0.402900	−	0.915244i	$-0.631998\pi$
$743$	−21.9645			−0.805800			−0.402900	+	0.915244i	$0.631998\pi$
$744$	−2.50748	−	0.0274295i	−0.0919287	−	0.00100561i
$745$	−12.5168			−0.458580
$746$	1.12815	−	0.819649i	0.0413045	−	0.0300095i
$747$	−1.96597	−	1.42836i	−0.0719310	−	0.0522609i
$748$	0.667040	−	2.05294i	0.0243894	−	0.0750629i
$749$	70.6300			2.58076
$750$	4.74852			0.173391
$751$	0.677265	−	2.08441i	0.0247137	−	0.0760611i	−0.937939	−	0.346800i	$-0.887268\pi$
$751$	0.677265	−	2.08441i	0.0247137	−	0.0760611i	0.962653	+	0.270739i	$0.0872681\pi$
$752$	2.02333	+	6.22718i	0.0737834	+	0.227082i
$753$	−0.981674	−	3.02128i	−0.0357742	−	0.110102i
$754$	−1.79934	+	1.30730i	−0.0655283	+	0.0476091i
$755$	6.40054	−	19.6988i	0.232940	−	0.716914i
$756$	9.54506	−	6.93489i	0.347150	−	0.252220i
$757$	−17.9961	−	13.0749i	−0.654078	−	0.475215i	0.210580	−	0.977577i	$-0.432465\pi$
$757$	−17.9961	−	13.0749i	−0.654078	−	0.475215i	−0.864658	+	0.502361i	$0.832465\pi$
$758$	9.37925	+	28.8664i	0.340670	+	1.04847i
$759$	−2.20002	−	1.59841i	−0.0798557	−	0.0580185i
$760$	−7.44721	−	5.41071i	−0.270139	−	0.196267i
$761$	−4.98686	−	15.3480i	−0.180774	−	0.556364i	0.819076	−	0.573684i	$-0.194486\pi$
$761$	−4.98686	−	15.3480i	−0.180774	−	0.556364i	−0.999850	+	0.0173206i	$0.994486\pi$
$762$	−1.83395	−	1.33244i	−0.0664369	−	0.0482692i
$763$	−23.7617	+	17.2639i	−0.860232	+	0.624995i
$764$	−5.02016	+	15.4505i	−0.181623	+	0.558978i
$765$	2.94207	−	2.13754i	0.106371	−	0.0772828i
$766$	−2.08027	−	6.40242i	−0.0751632	−	0.231329i
$767$	−7.24927	−	22.3110i	−0.261756	−	0.805603i
$768$	−0.139176	+	0.428341i	−0.00502209	+	0.0154564i
$769$	−45.4393			−1.63858			−0.819291	−	0.573377i	$-0.805633\pi$
$769$	−45.4393			−1.63858			−0.819291	+	0.573377i	$0.805633\pi$
$770$	−41.3196			−1.48905
$771$	−1.98963	+	6.12344i	−0.0716546	+	0.220530i
$772$	3.60142	+	2.61659i	0.129618	+	0.0941730i
$773$	−4.72595	+	3.43360i	−0.169981	+	0.123498i	−0.669523	−	0.742791i	$-0.733501\pi$
$773$	−4.72595	+	3.43360i	−0.169981	+	0.123498i	0.499542	+	0.866289i	$0.333501\pi$
$774$	−9.22333			−0.331526
$775$	0.843443	+	2.69584i	0.0302974	+	0.0968374i
$776$	−7.39663			−0.265524
$777$	−19.0712	+	13.8561i	−0.684177	+	0.497083i
$778$	18.6145	+	13.5242i	0.667361	+	0.484866i
$779$	−2.77024	+	8.52593i	−0.0992542	+	0.305473i
$780$	−4.77151			−0.170847
$781$	20.2075			0.723080
$782$	−0.265286	+	0.816466i	−0.00948660	+	0.0291968i
$783$	0.397498	+	1.22337i	0.0142054	+	0.0437198i
$784$	4.14688	+	12.7628i	0.148103	+	0.455813i
$785$	−1.08190	+	0.786048i	−0.0386147	+	0.0280553i
$786$	−0.473717	+	1.45795i	−0.0168969	+	0.0520034i
$787$	−15.5409	+	11.2911i	−0.553974	+	0.402486i	−0.829249	−	0.558880i	$-0.811231\pi$
$787$	−15.5409	+	11.2911i	−0.553974	+	0.402486i	0.275275	+	0.961366i	$0.411231\pi$
$788$	−19.7930	−	14.3804i	−0.705096	−	0.512282i
$789$	−3.83108	−	11.7908i	−0.136390	−	0.419765i
$790$	26.5712	+	19.3051i	0.945361	+	0.686845i
$791$	27.8008	+	20.1984i	0.988481	+	0.718174i
$792$	−3.36791	−	10.3654i	−0.119674	−	0.368317i
$793$	−9.39126	−	6.82315i	−0.333493	−	0.242297i
$794$	−1.05060	+	0.763308i	−0.0372845	+	0.0270888i
$795$	−3.29934	+	10.1543i	−0.117016	+	0.360137i
$796$	17.0892	−	12.4160i	0.605710	−	0.440074i
$797$	−6.81862	−	20.9855i	−0.241528	−	0.743346i	−0.996188	−	0.0872304i	$-0.972198\pi$
$797$	−6.81862	−	20.9855i	−0.241528	−	0.743346i	0.754660	−	0.656116i	$-0.227802\pi$
$798$	2.46691	+	7.59237i	0.0873277	+	0.268767i
$799$	1.12092	−	3.44984i	0.0396553	−	0.122047i
$800$	0.507332			0.0179369
$801$	−37.2024			−1.31448
$802$	4.03286	−	12.4119i	0.142405	−	0.438278i
$803$	35.9634	+	26.1290i	1.26912	+	0.922071i
$804$	−0.361785	+	0.262852i	−0.0127592	+	0.00927009i
$805$	16.4330			0.579189
$806$	7.50527	+	23.9886i	0.264362	+	0.844961i
$807$	4.34480			0.152944
$808$	−13.6218	+	9.89681i	−0.479213	+	0.348169i
$809$	−35.1560	−	25.5423i	−1.23602	−	0.898020i	−0.238692	−	0.971095i	$-0.576719\pi$
$809$	−35.1560	−	25.5423i	−1.23602	−	0.898020i	−0.997326	+	0.0730754i	$0.976719\pi$
$810$	5.23265	−	16.1044i	0.183857	−	0.565852i
$811$	26.7525			0.939406			0.469703	−	0.882824i	$-0.344361\pi$
$811$	26.7525			0.939406			0.469703	+	0.882824i	$0.344361\pi$
$812$	−2.22627			−0.0781268
$813$	−1.36111	+	4.18908i	−0.0477363	+	0.146917i
$814$	13.9463	+	42.9223i	0.488818	+	1.50443i
$815$	−1.53812	−	4.73385i	−0.0538780	−	0.165819i
$816$	0.201859	−	0.146659i	0.00706648	−	0.00513410i
$817$	3.99686	−	12.3011i	0.139832	−	0.430360i
$818$	15.9446	−	11.5844i	0.557491	−	0.405041i
$819$	−46.1636	−	33.5398i	−1.61309	−	1.17198i
$820$	−1.65738	−	5.10090i	−0.0578784	−	0.178131i
$821$	41.6692	+	30.2745i	1.45427	+	1.05659i	0.984811	+	0.173629i	$0.0555494\pi$
$821$	41.6692	+	30.2745i	1.45427	+	1.05659i	0.469454	+	0.882957i	$0.344451\pi$
$822$	4.62672	+	3.36151i	0.161375	+	0.117246i
$823$	6.74405	+	20.7561i	0.235083	+	0.723511i	0.997110	+	0.0759660i	$0.0242040\pi$
$823$	6.74405	+	20.7561i	0.235083	+	0.723511i	−0.762028	+	0.647545i	$0.775796\pi$
$824$	−4.22066	−	3.06649i	−0.147034	−	0.106826i
$825$	0.720268	−	0.523306i	0.0250765	−	0.0182192i
$826$	7.25631	−	22.3326i	0.252479	−	0.777051i
$827$	38.5697	−	28.0225i	1.34120	−	0.974438i	0.341800	−	0.939773i	$-0.388964\pi$
$827$	38.5697	−	28.0225i	1.34120	−	0.974438i	0.999399	−	0.0346650i	$-0.0110364\pi$
$828$	1.33944	+	4.12237i	0.0465487	+	0.143262i
$829$	12.2864	+	37.8136i	0.426723	+	1.31332i	0.901334	+	0.433124i	$0.142589\pi$
$829$	12.2864	+	37.8136i	0.426723	+	1.31332i	−0.474611	+	0.880196i	$0.657411\pi$
$830$	−0.630021	+	1.93901i	−0.0218684	+	0.0673039i
$831$	−6.99757			−0.242743
$832$	4.51442			0.156509
$833$	2.29736	−	7.07054i	0.0795987	−	0.244980i
$834$	−2.67104	−	1.94063i	−0.0924907	−	0.0671984i
$835$	34.4161	−	25.0047i	1.19102	−	0.865324i
$836$	15.2837			0.528596
$837$	14.5363	+	0.159013i	0.502447	+	0.00549629i
$838$	−34.2903			−1.18454
$839$	−39.9822	+	29.0488i	−1.38034	+	1.00288i	−0.383492	+	0.923544i	$0.625279\pi$
$839$	−39.9822	+	29.0488i	−1.38034	+	1.00288i	−0.996848	+	0.0793318i	$0.974721\pi$
$840$	−3.86398	−	2.80734i	−0.133320	−	0.0968625i
$841$	−8.88649	+	27.3498i	−0.306431	+	0.943096i
$842$	−10.7372			−0.370028
$843$	7.91284			0.272533
$844$	1.98838	−	6.11960i	0.0684429	−	0.210645i
$845$	5.35191	+	16.4715i	0.184111	+	0.566636i
$846$	−5.65957	−	17.4184i	−0.194580	−	0.598856i
$847$	15.2879	−	11.1073i	0.525298	−	0.381651i
$848$	3.12158	−	9.60723i	0.107195	−	0.329914i
$849$	−4.24418	+	3.08358i	−0.145660	+	0.105828i
$850$	−0.227383	−	0.165203i	−0.00779916	−	0.00566642i
$851$	−5.54653	−	17.0705i	−0.190133	−	0.585168i
$852$	1.88969	+	1.37294i	0.0647397	+	0.0470362i
$853$	7.76940	+	5.64480i	0.266019	+	0.193274i	0.712796	−	0.701371i	$-0.247428\pi$
$853$	7.76940	+	5.64480i	0.266019	+	0.193274i	−0.446777	+	0.894645i	$0.647428\pi$
$854$	−3.59062	−	11.0508i	−0.122869	−	0.378151i
$855$	20.8310	+	15.1346i	0.712405	+	0.517592i
$856$	12.6451	−	9.18722i	0.432202	−	0.314013i
$857$	9.96965	−	30.6834i	0.340557	−	1.04813i	−0.623363	−	0.781932i	$-0.714234\pi$
$857$	9.96965	−	30.6834i	0.340557	−	1.04813i	0.963920	−	0.266193i	$-0.0857658\pi$
$858$	6.40921	−	4.65656i	0.218807	−	0.158972i
$859$	1.41883	+	4.36670i	0.0484097	+	0.148990i	0.972339	−	0.233573i	$-0.0750417\pi$
$859$	1.41883	+	4.36670i	0.0484097	+	0.148990i	−0.923930	+	0.382562i	$0.875042\pi$
$860$	2.39125	+	7.35950i	0.0815408	+	0.250957i
$861$	−1.43734	+	4.42367i	−0.0489843	+	0.150758i
$862$	−27.8968			−0.950170
$863$	41.2988			1.40583			0.702913	−	0.711276i	$-0.251882\pi$
$863$	41.2988			1.40583			0.702913	+	0.711276i	$0.251882\pi$
$864$	0.806826	−	2.48316i	0.0274488	−	0.0844787i
$865$	26.0622	+	18.9353i	0.886143	+	0.643820i
$866$	−8.79776	+	6.39195i	−0.298960	+	0.217207i
$867$	7.51830			0.255335
$868$	−8.03602	+	23.8417i	−0.272760	+	0.809242i
$869$	−54.5312			−1.84984
$870$	0.421275	−	0.306074i	0.0142826	−	0.0103769i
$871$	3.62635	+	2.63470i	0.122874	+	0.0892734i
$872$	−2.00854	+	6.18164i	−0.0680176	+	0.209337i
$873$	20.6895			0.700234
$874$	−6.07840			−0.205605
$875$	14.7225	−	45.3111i	0.497710	−	1.53179i
$876$	1.58784	+	4.88687i	0.0536481	+	0.165112i
$877$	9.87961	+	30.4063i	0.333611	+	1.02675i	0.967402	+	0.253244i	$0.0814977\pi$
$877$	9.87961	+	30.4063i	0.333611	+	1.02675i	−0.633792	+	0.773504i	$0.718502\pi$
$878$	17.8282	−	12.9529i	0.601672	−	0.437140i
$879$	−0.708871	+	2.18168i	−0.0239096	+	0.0735863i
$880$	−7.39759	+	5.37466i	−0.249373	+	0.181180i
$881$	−35.4991	−	25.7916i	−1.19599	−	0.868941i	−0.202110	−	0.979363i	$-0.564780\pi$
$881$	−35.4991	−	25.7916i	−1.19599	−	0.868941i	−0.993885	+	0.110422i	$0.964780\pi$
$882$	−11.5994	−	35.6994i	−0.390574	−	1.20206i
$883$	3.42984	+	2.49192i	0.115423	+	0.0838598i	0.643999	−	0.765026i	$-0.277274\pi$
$883$	3.42984	+	2.49192i	0.115423	+	0.0838598i	−0.528576	+	0.848886i	$0.677274\pi$
$884$	−2.02333	−	1.47004i	−0.0680521	−	0.0494427i
$885$	1.69725	+	5.22360i	0.0570525	+	0.175589i
$886$	0.813791	+	0.591254i	0.0273398	+	0.0198635i
$887$	−36.6576	+	26.6333i	−1.23084	+	0.894259i	−0.996953	−	0.0780048i	$-0.975145\pi$
$887$	−36.6576	+	26.6333i	−1.23084	+	0.894259i	−0.233888	+	0.972263i	$0.575145\pi$
$888$	−1.61206	+	4.96140i	−0.0540971	+	0.166494i
$889$	−18.4004	+	13.3687i	−0.617129	+	0.448371i
$890$	9.64513	+	29.6847i	0.323305	+	0.995032i
$891$	8.68786	+	26.7385i	0.291054	+	0.895773i
$892$	−2.43596	+	7.49712i	−0.0815621	+	0.251022i
$893$	25.6833			0.859457
$894$	2.40218			0.0803409
$895$	−4.78039	+	14.7125i	−0.159791	+	0.491786i
$896$	3.65579	+	2.65609i	0.122131	+	0.0887336i
$897$	−2.54898	+	1.85194i	−0.0851080	+	0.0618346i
$898$	2.64490			0.0882615
$899$	−2.20141	−	1.63651i	−0.0734213	−	0.0545806i
$900$	−1.41908			−0.0473028
$901$	−4.52749	+	3.28941i	−0.150832	+	0.109586i
$902$	7.20427	+	5.23421i	0.239876	+	0.174280i
$903$	2.07377	−	6.38240i	0.0690106	−	0.212393i
$904$	7.60459			0.252925
$905$	−20.0605			−0.666833
$906$	−1.22837	+	3.78053i	−0.0408098	+	0.125600i
$907$	−14.2818	−	43.9547i	−0.474218	−	1.45949i	−0.847010	−	0.531578i	$-0.821599\pi$
$907$	−14.2818	−	43.9547i	−0.474218	−	1.45949i	0.372792	−	0.927915i	$-0.378401\pi$
$908$	−2.67339	−	8.22783i	−0.0887194	−	0.273050i
$909$	38.1023	−	27.6829i	1.26377	−	0.918184i
$910$	−14.7938	+	45.5305i	−0.490408	+	1.50932i
$911$	14.4786	−	10.5193i	0.479698	−	0.348521i	−0.321510	−	0.946906i	$-0.604191\pi$
$911$	14.4786	−	10.5193i	0.479698	−	0.348521i	0.801209	+	0.598385i	$0.204191\pi$
$912$	1.42924	+	1.03840i	0.0473269	+	0.0343850i
$913$	−1.04604	−	3.21937i	−0.0346187	−	0.106546i
$914$	−0.795925	−	0.578274i	−0.0263269	−	0.0191276i
$915$	2.19875	+	1.59748i	0.0726884	+	0.0528112i
$916$	−1.72655	−	5.31376i	−0.0570467	−	0.175572i
$917$	12.4433	+	9.04056i	0.410913	+	0.298546i
$918$	−1.17021	+	0.850206i	−0.0386226	+	0.0280610i
$919$	−11.6470	+	35.8459i	−0.384200	+	1.18245i	0.552859	+	0.833275i	$0.313537\pi$
$919$	−11.6470	+	35.8459i	−0.384200	+	1.18245i	−0.937059	+	0.349171i	$0.886463\pi$
$920$	2.94207	−	2.13754i	0.0969970	−	0.0704725i
$921$	−0.958759	−	2.95076i	−0.0315922	−	0.0972308i
$922$	−5.86035	−	18.0363i	−0.193000	−	0.593994i
$923$	7.23493	−	22.2668i	0.238141	−	0.732922i
$924$	7.92991			0.260875
$925$	5.87634			0.193213
$926$	6.89601	−	21.2237i	0.226617	−	0.697455i
$927$	11.8058	+	8.57744i	0.387755	+	0.281720i
$928$	−0.398577	+	0.289583i	−0.0130839	+	0.00950604i
$929$	−5.12810			−0.168248			−0.0841238	−	0.996455i	$-0.526809\pi$
$929$	−5.12810			−0.168248			−0.0841238	+	0.996455i	$0.526809\pi$
$930$	−1.75719	−	5.61637i	−0.0576204	−	0.184168i
$931$	52.6385			1.72516
$932$	−17.7762	+	12.9152i	−0.582280	+	0.423051i
$933$	−5.15894	−	3.74819i	−0.168896	−	0.122710i
$934$	−7.94753	+	24.4600i	−0.260051	+	0.800355i
$935$	5.06571			0.165666
$936$	−12.6275			−0.412744
$937$	5.09540	−	15.6820i	0.166459	−	0.512309i	−0.832681	−	0.553752i	$-0.813195\pi$
$937$	5.09540	−	15.6820i	0.166459	−	0.512309i	0.999141	+	0.0414429i	$0.0131955\pi$
$938$	1.38649	+	4.26717i	0.0452704	+	0.139328i
$939$	−1.14688	−	3.52972i	−0.0374269	−	0.115188i
$940$	−12.4312	+	9.03180i	−0.405461	+	0.294585i
$941$	−11.1640	+	34.3593i	−0.363936	+	1.12008i	0.586709	+	0.809798i	$0.300423\pi$
$941$	−11.1640	+	34.3593i	−0.363936	+	1.12008i	−0.950645	+	0.310282i	$0.899577\pi$
$942$	0.207635	−	0.150856i	0.00676511	−	0.00491514i
$943$	−2.86518	−	2.08168i	−0.0933031	−	0.0677887i
$944$	−1.60580	−	4.94216i	−0.0522645	−	0.160854i
$945$	22.4001	+	16.2746i	0.728674	+	0.529413i
$946$	−10.3942	−	7.55183i	−0.337944	−	0.245531i
$947$	−10.0662	−	30.9807i	−0.327109	−	1.00674i	−0.970480	−	0.241182i	$-0.922465\pi$
$947$	−10.0662	−	30.9807i	−0.327109	−	1.00674i	0.643371	−	0.765554i	$-0.277535\pi$
$948$	−5.09945	−	3.70497i	−0.165622	−	0.120332i
$949$	41.6678	−	30.2735i	1.35260	−	0.982718i
$950$	0.614949	−	1.89262i	0.0199516	−	0.0614047i
$951$	−7.68805	+	5.58569i	−0.249302	+	0.181129i
$952$	−0.773594	−	2.38088i	−0.0250723	−	0.0771647i
$953$	11.6147	+	35.7463i	0.376237	+	1.15794i	0.942641	+	0.333809i	$0.108334\pi$
$953$	11.6147	+	35.7463i	0.376237	+	1.15794i	−0.566404	+	0.824128i	$0.691666\pi$
$954$	−8.73154	+	26.8729i	−0.282694	+	0.870042i
$955$	−38.1246			−1.23368
$956$	−18.0550			−0.583940
$957$	−0.267167	+	0.822254i	−0.00863627	+	0.0265797i
$958$	−32.9749	−	23.9577i	−1.06537	−	0.774037i
$959$	46.4209	−	33.7268i	1.49901	−	1.08909i
$960$	−1.05695			−0.0341128
$961$	−25.4721	+	17.6684i	−0.821681	+	0.569947i
$962$	52.2898			1.68589
$963$	−35.3704	+	25.6981i	−1.13979	+	0.828109i
$964$	−17.2015	−	12.4976i	−0.554022	−	0.402521i
$965$	−3.22827	+	9.93558i	−0.103922	+	0.319838i
$966$	−3.15377			−0.101471
$967$	−2.28904			−0.0736105			−0.0368053	−	0.999322i	$-0.511718\pi$
$967$	−2.28904			−0.0736105			−0.0368053	+	0.999322i	$0.511718\pi$
$968$	1.29226	−	3.97715i	0.0415347	−	0.127831i
$969$	−0.302439	−	0.930812i	−0.00971575	−	0.0299020i
$970$	−5.36398	−	16.5086i	−0.172227	−	0.530060i
$971$	−32.7888	+	23.8225i	−1.05224	+	0.764500i	−0.972638	−	0.232327i	$-0.925366\pi$
$971$	−32.7888	+	23.8225i	−1.05224	+	0.764500i	−0.0796057	+	0.996826i	$0.525366\pi$
$972$	−3.42471	+	10.5402i	−0.109848	+	0.338076i
$973$	−26.7992	+	19.4707i	−0.859142	+	0.624204i
$974$	−14.0146	−	10.1822i	−0.449058	−	0.326260i
$975$	−0.318757	−	0.981032i	−0.0102084	−	0.0314182i
$976$	−2.08028	−	1.51141i	−0.0665882	−	0.0483791i
$977$	26.8806	+	19.5299i	0.859987	+	0.624817i	0.927881	−	0.372876i	$-0.121628\pi$
$977$	26.8806	+	19.5299i	0.859987	+	0.624817i	−0.0678947	+	0.997692i	$0.521628\pi$
$978$	0.295191	+	0.908504i	0.00943916	+	0.0290507i
$979$	−41.9252	−	30.4604i	−1.33993	−	0.973519i
$980$	−25.4781	+	18.5109i	−0.813868	+	0.591309i
$981$	5.61818	−	17.2910i	0.179375	−	0.552059i
$982$	−3.78313	+	2.74860i	−0.120724	+	0.0877114i
$983$	−4.69827	−	14.4598i	−0.149852	−	0.461196i	0.847751	−	0.530394i	$-0.177956\pi$
$983$	−4.69827	−	14.4598i	−0.149852	−	0.461196i	−0.997603	+	0.0691982i	$0.977956\pi$
$984$	0.318079	+	0.978947i	0.0101400	+	0.0312077i
$985$	17.7422	−	54.6048i	0.565313	−	1.73985i
$986$	0.272937			0.00869209
$987$	13.3257			0.424163
$988$	5.47204	−	16.8412i	0.174089	−	0.535791i
$989$	4.13383	+	3.00341i	0.131448	+	0.0955028i
$990$	20.6922	−	15.0338i	0.657641	−	0.477804i
$991$	−5.97603			−0.189835			−0.0949173	−	0.995485i	$-0.530259\pi$
$991$	−5.97603			−0.189835			−0.0949173	+	0.995485i	$0.530259\pi$
$992$	1.66251	+	5.31376i	0.0527847	+	0.168712i
$993$	0.208682			0.00662232
$994$	18.9597	−	13.7750i	0.601365	−	0.436917i
$995$	40.1044	+	29.1375i	1.27139	+	0.923722i
$996$	0.120911	−	0.372127i	0.00383123	−	0.0117913i
$997$	−27.0384			−0.856314			−0.428157	−	0.903704i	$-0.640837\pi$
$997$	−27.0384			−0.856314			−0.428157	+	0.903704i	$0.640837\pi$
$998$	8.92011			0.282361
$999$	9.34534	−	28.7620i	0.295673	−	0.909989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.d.a.47.2	yes	8
3.2	odd	2		558.2.i.i.109.1		8
4.3	odd	2		496.2.n.e.481.1		8
31.2	even	5	inner	62.2.d.a.33.2	✓	8
31.8	even	5		1922.2.a.r.1.2		4
31.23	odd	10		1922.2.a.n.1.3		4
93.2	odd	10		558.2.i.i.343.1		8
124.95	odd	10		496.2.n.e.33.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.d.a.33.2	✓	8	31.2	even	5	inner
62.2.d.a.47.2	yes	8	1.1	even	1	trivial
496.2.n.e.33.1		8	124.95	odd	10
496.2.n.e.481.1		8	4.3	odd	2
558.2.i.i.109.1		8	3.2	odd	2
558.2.i.i.343.1		8	93.2	odd	10
1922.2.a.n.1.3		4	31.23	odd	10
1922.2.a.r.1.2		4	31.8	even	5

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.364368 + 0.264729i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.34677 q^{5} -0.450384 q^{6} +(-1.39639 + 4.29764i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.864368 - 2.66025i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.364368 + 0.264729i) q^{3} +(0.309017 - 0.951057i) q^{4} +2.34677 q^{5} -0.450384 q^{6} +(-1.39639 + 4.29764i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.864368 - 2.66025i) q^{9} +(-1.89858 + 1.37940i) q^{10} +(1.20405 - 3.70568i) q^{11} +(0.364368 - 0.264729i) q^{12} +(-3.65224 - 2.65351i) q^{13} +(-1.39639 - 4.29764i) q^{14} +(0.855089 + 0.621258i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.171195 + 0.526883i) q^{17} +(2.26295 + 1.64413i) q^{18} +(-3.17339 + 2.30560i) q^{19} +(0.725192 - 2.23191i) q^{20} +(-1.64651 + 1.19626i) q^{21} +(1.20405 + 3.70568i) q^{22} +(-0.478858 - 1.47377i) q^{23} +(-0.139176 + 0.428341i) q^{24} +0.507332 q^{25} +4.51442 q^{26} +(0.806826 - 2.48316i) q^{27} +(3.65579 + 2.65609i) q^{28} +(-0.398577 + 0.289583i) q^{29} -1.05695 q^{30} +(1.66251 + 5.31376i) q^{31} +1.00000 q^{32} +(1.41972 - 1.03149i) q^{33} +(-0.448193 - 0.325631i) q^{34} +(-3.27700 + 10.0856i) q^{35} -2.79715 q^{36} +11.5828 q^{37} +(1.21213 - 3.73054i) q^{38} +(-0.628300 - 1.93371i) q^{39} +(0.725192 + 2.23191i) q^{40} +(1.84896 - 1.34335i) q^{41} +(0.628910 - 1.93559i) q^{42} +(-2.66765 + 1.93816i) q^{43} +(-3.15224 - 2.29024i) q^{44} +(-2.02847 - 6.24300i) q^{45} +(1.25367 + 0.910841i) q^{46} +(-5.29715 - 3.84861i) q^{47} +(-0.139176 - 0.428341i) q^{48} +(-10.8567 - 7.88783i) q^{49} +(-0.410440 + 0.298202i) q^{50} +(-0.0771033 + 0.237300i) q^{51} +(-3.65224 + 2.65351i) q^{52} +(3.12158 + 9.60723i) q^{53} +(0.806826 + 2.48316i) q^{54} +(2.82563 - 8.69639i) q^{55} -4.51880 q^{56} -1.76664 q^{57} +(0.152243 - 0.468556i) q^{58} +(4.20405 + 3.05442i) q^{59} +(0.855089 - 0.621258i) q^{60} +2.57137 q^{61} +(-4.46835 - 3.32173i) q^{62} +12.6398 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-8.57098 - 6.22718i) q^{65} +(-0.542285 + 1.66898i) q^{66} -0.992911 q^{67} +0.553997 q^{68} +(0.215670 - 0.663763i) q^{69} +(-3.27700 - 10.0856i) q^{70} +(1.60263 + 4.93238i) q^{71} +(2.26295 - 1.64413i) q^{72} +(-3.52552 + 10.8504i) q^{73} +(-9.37071 + 6.80822i) q^{74} +(0.184855 + 0.134305i) q^{75} +(1.21213 + 3.73054i) q^{76} +(14.2444 + 10.3491i) q^{77} +(1.64491 + 1.19510i) q^{78} +(-4.32479 - 13.3103i) q^{79} +(-1.89858 - 1.37940i) q^{80} +(-5.83749 + 4.24119i) q^{81} +(-0.706240 + 2.17358i) q^{82} +(0.702846 - 0.510647i) q^{83} +(0.628910 + 1.93559i) q^{84} +(0.401754 + 1.23647i) q^{85} +(1.01895 - 3.13601i) q^{86} -0.221890 q^{87} +3.89639 q^{88} +(4.10996 - 12.6492i) q^{89} +(5.31061 + 3.85839i) q^{90} +(16.5038 - 11.9907i) q^{91} -1.54962 q^{92} +(-0.800941 + 2.37628i) q^{93} +6.54764 q^{94} +(-7.44721 + 5.41071i) q^{95} +(0.364368 + 0.264729i) q^{96} +(-2.28568 + 7.03461i) q^{97} +13.4196 q^{98} -10.8988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 4 q^{5} + 6 q^{6} + 2 q^{7} - 2 q^{8} + q^{10} - 2 q^{11} - 4 q^{12} - 11 q^{13} + 2 q^{14} + 21 q^{15} - 2 q^{16} - 7 q^{17} - 5 q^{18} - 14 q^{19} + q^{20} - 7 q^{21} - 2 q^{22} + 3 q^{23} + q^{24} + 14 q^{26} + 5 q^{27} + 2 q^{28} + 13 q^{29} - 14 q^{30} + 15 q^{31} + 8 q^{32} + 2 q^{33} + 3 q^{34} - 28 q^{35} + 10 q^{36} + 52 q^{37} + 21 q^{38} - 16 q^{39} + q^{40} - 11 q^{41} - 17 q^{42} - 22 q^{43} - 7 q^{44} - 19 q^{45} + 8 q^{46} - 10 q^{47} + q^{48} - 10 q^{49} - 15 q^{50} + 28 q^{51} - 11 q^{52} + 7 q^{53} + 5 q^{54} - 7 q^{55} - 8 q^{56} - 20 q^{57} - 17 q^{58} + 22 q^{59} + 21 q^{60} + 4 q^{61} + 5 q^{62} + 66 q^{63} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 8 q^{68} + 4 q^{69} - 28 q^{70} - 15 q^{71} - 5 q^{72} - 29 q^{73} - 23 q^{74} - 34 q^{75} + 21 q^{76} + 34 q^{77} - q^{78} - 2 q^{79} + q^{80} - 45 q^{81} + 9 q^{82} + 38 q^{83} - 17 q^{84} + 25 q^{85} + 18 q^{86} - 20 q^{87} + 18 q^{88} + q^{89} + 46 q^{90} + 38 q^{91} - 22 q^{92} + 21 q^{93} - 20 q^{94} - 12 q^{95} - 4 q^{96} - 10 q^{97} + 60 q^{98} + 14 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 4 * q^5 + 6 * q^6 + 2 * q^7 - 2 * q^8 + q^10 - 2 * q^11 - 4 * q^12 - 11 * q^13 + 2 * q^14 + 21 * q^15 - 2 * q^16 - 7 * q^17 - 5 * q^18 - 14 * q^19 + q^20 - 7 * q^21 - 2 * q^22 + 3 * q^23 + q^24 + 14 * q^26 + 5 * q^27 + 2 * q^28 + 13 * q^29 - 14 * q^30 + 15 * q^31 + 8 * q^32 + 2 * q^33 + 3 * q^34 - 28 * q^35 + 10 * q^36 + 52 * q^37 + 21 * q^38 - 16 * q^39 + q^40 - 11 * q^41 - 17 * q^42 - 22 * q^43 - 7 * q^44 - 19 * q^45 + 8 * q^46 - 10 * q^47 + q^48 - 10 * q^49 - 15 * q^50 + 28 * q^51 - 11 * q^52 + 7 * q^53 + 5 * q^54 - 7 * q^55 - 8 * q^56 - 20 * q^57 - 17 * q^58 + 22 * q^59 + 21 * q^60 + 4 * q^61 + 5 * q^62 + 66 * q^63 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 8 * q^68 + 4 * q^69 - 28 * q^70 - 15 * q^71 - 5 * q^72 - 29 * q^73 - 23 * q^74 - 34 * q^75 + 21 * q^76 + 34 * q^77 - q^78 - 2 * q^79 + q^80 - 45 * q^81 + 9 * q^82 + 38 * q^83 - 17 * q^84 + 25 * q^85 + 18 * q^86 - 20 * q^87 + 18 * q^88 + q^89 + 46 * q^90 + 38 * q^91 - 22 * q^92 + 21 * q^93 - 20 * q^94 - 12 * q^95 - 4 * q^96 - 10 * q^97 + 60 * q^98 + 14 * q^99

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