LMFDB - Embedded newform 946.2.f.f.861.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(345,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("946.345");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.f (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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			861.5
Character	$\chi$	$=$	946.861
Dual form			946.2.f.f.345.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.367924 - 1.13235i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.00998 + 2.18688i) q^{5} +(0.963238 + 0.699834i) q^{6} +(-0.576083 + 1.77300i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.28019 - 0.930114i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.367924 - 1.13235i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.00998 + 2.18688i) q^{5} +(0.963238 + 0.699834i) q^{6} +(-0.576083 + 1.77300i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.28019 - 0.930114i) q^{9} -3.72054 q^{10} +(0.520653 - 3.27550i) q^{11} -1.19063 q^{12} +(2.34118 - 1.70097i) q^{13} +(-0.576083 - 1.77300i) q^{14} +(1.36888 - 4.21298i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.172711 + 0.125482i) q^{17} +(-0.488990 + 1.50496i) q^{18} +(-0.698960 - 2.15118i) q^{19} +(3.00998 - 2.18688i) q^{20} +2.21962 q^{21} +(1.50408 + 2.95597i) q^{22} +6.98931 q^{23} +(0.963238 - 0.699834i) q^{24} +(2.73247 + 8.40967i) q^{25} +(-0.894251 + 2.75222i) q^{26} +(-4.41395 - 3.20692i) q^{27} +(1.50821 + 1.09578i) q^{28} +(-1.11731 + 3.43873i) q^{29} +(1.36888 + 4.21298i) q^{30} +(-7.33391 + 5.32839i) q^{31} +1.00000 q^{32} +(-3.90059 + 0.615574i) q^{33} -0.213483 q^{34} +(-5.61135 + 4.07688i) q^{35} +(-0.488990 - 1.50496i) q^{36} +(2.20596 - 6.78926i) q^{37} +(1.82990 + 1.32950i) q^{38} +(-2.78747 - 2.02522i) q^{39} +(-1.14971 + 3.53845i) q^{40} +(-0.00918817 - 0.0282783i) q^{41} +(-1.79571 + 1.30466i) q^{42} +1.00000 q^{43} +(-2.95430 - 1.50736i) q^{44} +5.88741 q^{45} +(-5.65447 + 4.10821i) q^{46} +(0.0181195 + 0.0557660i) q^{47} +(-0.367924 + 1.13235i) q^{48} +(2.85145 + 2.07170i) q^{49} +(-7.15369 - 5.19746i) q^{50} +(0.0785456 - 0.241738i) q^{51} +(-0.894251 - 2.75222i) q^{52} +(3.19890 - 2.32414i) q^{53} +5.45594 q^{54} +(8.73029 - 8.72060i) q^{55} -1.86425 q^{56} +(-2.17873 + 1.58294i) q^{57} +(-1.11731 - 3.43873i) q^{58} +(2.44983 - 7.53980i) q^{59} +(-3.58377 - 2.60376i) q^{60} +(6.58667 + 4.78550i) q^{61} +(2.80130 - 8.62152i) q^{62} +(0.911597 + 2.80561i) q^{63} +(-0.809017 + 0.587785i) q^{64} +10.7667 q^{65} +(2.79382 - 2.79072i) q^{66} +7.67996 q^{67} +(0.172711 - 0.125482i) q^{68} +(-2.57154 - 7.91437i) q^{69} +(2.14334 - 6.59653i) q^{70} +(6.07435 + 4.41327i) q^{71} +(1.28019 + 0.930114i) q^{72} +(-3.92031 + 12.0655i) q^{73} +(2.20596 + 6.78926i) q^{74} +(8.51739 - 6.18824i) q^{75} -2.26188 q^{76} +(5.50754 + 2.81008i) q^{77} +3.44551 q^{78} +(-3.19939 + 2.32450i) q^{79} +(-1.14971 - 3.53845i) q^{80} +(-0.540403 + 1.66319i) q^{81} +(0.0240549 + 0.0174769i) q^{82} +(-9.92036 - 7.20756i) q^{83} +(0.685901 - 2.11099i) q^{84} +(0.245444 + 0.755398i) q^{85} +(-0.809017 + 0.587785i) q^{86} +4.30495 q^{87} +(3.27608 - 0.517016i) q^{88} -1.66755 q^{89} +(-4.76301 + 3.46053i) q^{90} +(1.66710 + 5.13082i) q^{91} +(2.15981 - 6.64722i) q^{92} +(8.73195 + 6.34414i) q^{93} +(-0.0474374 - 0.0344653i) q^{94} +(2.60051 - 8.00355i) q^{95} +(-0.367924 - 1.13235i) q^{96} +(4.32973 - 3.14573i) q^{97} -3.52459 q^{98} +(-2.38006 - 4.67754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} + 13 q^{6} + 10 q^{7} - 8 q^{8} - 14 q^{9}+O(q^{10}) $ 32 * q - 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^5 + 13 * q^6 + 10 * q^7 - 8 * q^8 - 14 * q^9	\( 32 q - 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} + 13 q^{6} + 10 q^{7} - 8 q^{8} - 14 q^{9} + 2 q^{10} + q^{11} - 22 q^{12} + 11 q^{13} + 10 q^{14} + 8 q^{15} - 8 q^{16} - 13 q^{17} + q^{18} + 39 q^{19} + 2 q^{20} - 2 q^{21} + 6 q^{22} - 26 q^{23} + 13 q^{24} - 28 q^{25} - 4 q^{26} + 28 q^{27} - 16 q^{29} + 8 q^{30} + 7 q^{31} + 32 q^{32} + 4 q^{33} + 12 q^{34} - 52 q^{35} + q^{36} + 20 q^{37} + 14 q^{38} + 6 q^{39} - 3 q^{40} + q^{41} + 8 q^{42} + 32 q^{43} + 11 q^{44} + 64 q^{45} + 14 q^{46} + 47 q^{47} - 2 q^{48} + 4 q^{49} - 3 q^{50} + 8 q^{51} - 4 q^{52} + 25 q^{53} - 82 q^{54} - 11 q^{55} - 20 q^{56} - 81 q^{57} - 16 q^{58} + 45 q^{59} - 2 q^{60} + 2 q^{62} + 36 q^{63} - 8 q^{64} - 106 q^{65} - q^{66} - 48 q^{67} - 13 q^{68} - 35 q^{69} + 48 q^{70} + 45 q^{71} - 14 q^{72} - 20 q^{73} + 20 q^{74} + 66 q^{75} - 106 q^{76} - 10 q^{77} - 34 q^{78} - 38 q^{79} - 3 q^{80} + 69 q^{81} + 36 q^{82} + 58 q^{83} - 7 q^{84} + 59 q^{85} - 8 q^{86} - 58 q^{87} + q^{88} - 12 q^{89} - 31 q^{90} - 9 q^{91} - q^{92} + 19 q^{93} - 18 q^{94} - 46 q^{95} - 2 q^{96} + 80 q^{97} + 44 q^{98} + 5 q^{99}+O(q^{100}) \) 32 * q - 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^5 + 13 * q^6 + 10 * q^7 - 8 * q^8 - 14 * q^9 + 2 * q^10 + q^11 - 22 * q^12 + 11 * q^13 + 10 * q^14 + 8 * q^15 - 8 * q^16 - 13 * q^17 + q^18 + 39 * q^19 + 2 * q^20 - 2 * q^21 + 6 * q^22 - 26 * q^23 + 13 * q^24 - 28 * q^25 - 4 * q^26 + 28 * q^27 - 16 * q^29 + 8 * q^30 + 7 * q^31 + 32 * q^32 + 4 * q^33 + 12 * q^34 - 52 * q^35 + q^36 + 20 * q^37 + 14 * q^38 + 6 * q^39 - 3 * q^40 + q^41 + 8 * q^42 + 32 * q^43 + 11 * q^44 + 64 * q^45 + 14 * q^46 + 47 * q^47 - 2 * q^48 + 4 * q^49 - 3 * q^50 + 8 * q^51 - 4 * q^52 + 25 * q^53 - 82 * q^54 - 11 * q^55 - 20 * q^56 - 81 * q^57 - 16 * q^58 + 45 * q^59 - 2 * q^60 + 2 * q^62 + 36 * q^63 - 8 * q^64 - 106 * q^65 - q^66 - 48 * q^67 - 13 * q^68 - 35 * q^69 + 48 * q^70 + 45 * q^71 - 14 * q^72 - 20 * q^73 + 20 * q^74 + 66 * q^75 - 106 * q^76 - 10 * q^77 - 34 * q^78 - 38 * q^79 - 3 * q^80 + 69 * q^81 + 36 * q^82 + 58 * q^83 - 7 * q^84 + 59 * q^85 - 8 * q^86 - 58 * q^87 + q^88 - 12 * q^89 - 31 * q^90 - 9 * q^91 - q^92 + 19 * q^93 - 18 * q^94 - 46 * q^95 - 2 * q^96 + 80 * q^97 + 44 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.367924	−	1.13235i	−0.212421	−	0.653765i	−0.999327	−	0.0366916i	$-0.988318\pi$
$3$	−0.367924	−	1.13235i	−0.212421	−	0.653765i	0.786905	−	0.617074i	$-0.211682\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	3.00998	+	2.18688i	1.34611	+	0.978003i	0.999195	+	0.0401045i	$0.0127691\pi$
$5$	3.00998	+	2.18688i	1.34611	+	0.978003i	0.346910	+	0.937898i	$0.387231\pi$
$6$	0.963238	+	0.699834i	0.393240	+	0.285706i
$7$	−0.576083	+	1.77300i	−0.217739	+	0.670132i	0.781209	+	0.624270i	$0.214603\pi$
$7$	−0.576083	+	1.77300i	−0.217739	+	0.670132i	−0.998948	+	0.0458620i	$0.985397\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	1.28019	−	0.930114i	0.426731	−	0.310038i
$10$	−3.72054			−1.17654
$11$	0.520653	−	3.27550i	0.156983	−	0.987601i
$11$	0.520653	−	3.27550i	0.156983	−	0.987601i
$12$	−1.19063			−0.343705
$13$	2.34118	−	1.70097i	0.649326	−	0.471763i	−0.213715	−	0.976896i	$-0.568556\pi$
$13$	2.34118	−	1.70097i	0.649326	−	0.471763i	0.863042	+	0.505133i	$0.168556\pi$
$14$	−0.576083	−	1.77300i	−0.153965	−	0.473855i
$15$	1.36888	−	4.21298i	0.353443	−	1.08779i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.172711	+	0.125482i	0.0418887	+	0.0304339i	0.608533	−	0.793529i	$-0.291758\pi$
$17$	0.172711	+	0.125482i	0.0418887	+	0.0304339i	−0.566644	+	0.823963i	$0.691758\pi$
$18$	−0.488990	+	1.50496i	−0.115256	+	0.354722i
$19$	−0.698960	−	2.15118i	−0.160352	−	0.493514i	0.838311	−	0.545192i	$-0.183543\pi$
$19$	−0.698960	−	2.15118i	−0.160352	−	0.493514i	−0.998664	+	0.0516776i	$0.983543\pi$
$20$	3.00998	−	2.18688i	0.673053	−	0.489001i
$21$	2.21962			0.484361
$22$	1.50408	+	2.95597i	0.320670	+	0.630215i
$23$	6.98931			1.45737			0.728685	−	0.684848i	$-0.240132\pi$
$23$	6.98931			1.45737			0.728685	+	0.684848i	$0.240132\pi$
$24$	0.963238	−	0.699834i	0.196620	−	0.142853i
$25$	2.73247	+	8.40967i	0.546493	+	1.68193i
$26$	−0.894251	+	2.75222i	−0.175377	+	0.539755i
$27$	−4.41395	−	3.20692i	−0.849465	−	0.617172i
$28$	1.50821	+	1.09578i	0.285024	+	0.207082i
$29$	−1.11731	+	3.43873i	−0.207480	+	0.638556i	0.792123	+	0.610362i	$0.208976\pi$
$29$	−1.11731	+	3.43873i	−0.207480	+	0.638556i	−0.999602	+	0.0281947i	$0.991024\pi$
$30$	1.36888	+	4.21298i	0.249922	+	0.769181i
$31$	−7.33391	+	5.32839i	−1.31721	+	0.957008i	−0.317246	+	0.948343i	$0.602758\pi$
$31$	−7.33391	+	5.32839i	−1.31721	+	0.957008i	−0.999962	+	0.00866451i	$0.997242\pi$
$32$	1.00000			0.176777
$33$	−3.90059	+	0.615574i	−0.679006	+	0.107158i
$34$	−0.213483			−0.0366120
$35$	−5.61135	+	4.07688i	−0.948491	+	0.689119i
$36$	−0.488990	−	1.50496i	−0.0814983	−	0.250826i
$37$	2.20596	−	6.78926i	0.362658	−	1.11615i	−0.588776	−	0.808296i	$-0.700390\pi$
$37$	2.20596	−	6.78926i	0.362658	−	1.11615i	0.951434	−	0.307851i	$-0.0996100\pi$
$38$	1.82990	+	1.32950i	0.296849	+	0.215674i
$39$	−2.78747	−	2.02522i	−0.446353	−	0.324294i
$40$	−1.14971	+	3.53845i	−0.181785	+	0.559478i
$41$	−0.00918817	−	0.0282783i	−0.00143495	−	0.00441632i	0.950336	−	0.311224i	$-0.100739\pi$
$41$	−0.00918817	−	0.0282783i	−0.00143495	−	0.00441632i	−0.951771	+	0.306808i	$0.900739\pi$
$42$	−1.79571	+	1.30466i	−0.277084	+	0.201314i
$43$	1.00000			0.152499
$43$	1.00000			0.152499
$44$	−2.95430	−	1.50736i	−0.445377	−	0.227243i
$45$	5.88741			0.877643
$46$	−5.65447	+	4.10821i	−0.833706	+	0.605723i
$47$	0.0181195	+	0.0557660i	0.00264300	+	0.00813430i	0.952369	−	0.304947i	$-0.0986388\pi$
$47$	0.0181195	+	0.0557660i	0.00264300	+	0.00813430i	−0.949726	+	0.313081i	$0.898639\pi$
$48$	−0.367924	+	1.13235i	−0.0531053	+	0.163441i
$49$	2.85145	+	2.07170i	0.407350	+	0.295957i
$50$	−7.15369	−	5.19746i	−1.01168	−	0.735032i
$51$	0.0785456	−	0.241738i	0.0109986	−	0.0338502i
$52$	−0.894251	−	2.75222i	−0.124010	−	0.381664i
$53$	3.19890	−	2.32414i	0.439403	−	0.319245i	−0.345995	−	0.938236i	$-0.612458\pi$
$53$	3.19890	−	2.32414i	0.439403	−	0.319245i	0.785398	+	0.618991i	$0.212458\pi$
$54$	5.45594			0.742459
$55$	8.73029	−	8.72060i	1.17719	−	1.17589i
$56$	−1.86425			−0.249120
$57$	−2.17873	+	1.58294i	−0.288580	+	0.209666i
$58$	−1.11731	−	3.43873i	−0.146710	−	0.451527i
$59$	2.44983	−	7.53980i	0.318941	−	0.981598i	−0.655161	−	0.755489i	$-0.727399\pi$
$59$	2.44983	−	7.53980i	0.318941	−	0.981598i	0.974102	−	0.226109i	$-0.0726007\pi$
$60$	−3.58377	−	2.60376i	−0.462663	−	0.336144i
$61$	6.58667	+	4.78550i	0.843337	+	0.612720i	0.923301	−	0.384078i	$-0.125481\pi$
$61$	6.58667	+	4.78550i	0.843337	+	0.612720i	−0.0799641	+	0.996798i	$0.525481\pi$
$62$	2.80130	−	8.62152i	0.355766	−	1.09493i
$63$	0.911597	+	2.80561i	0.114850	+	0.353473i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	10.7667			1.33545
$66$	2.79382	−	2.79072i	0.343895	−	0.343514i
$67$	7.67996			0.938257			0.469128	−	0.883130i	$-0.344568\pi$
$67$	7.67996			0.938257			0.469128	+	0.883130i	$0.344568\pi$
$68$	0.172711	−	0.125482i	0.0209443	−	0.0152169i
$69$	−2.57154	−	7.91437i	−0.309576	−	0.952778i
$70$	2.14334	−	6.59653i	0.256179	−	0.788437i
$71$	6.07435	+	4.41327i	0.720892	+	0.523759i	0.886669	−	0.462404i	$-0.153013\pi$
$71$	6.07435	+	4.41327i	0.720892	+	0.523759i	−0.165777	+	0.986163i	$0.553013\pi$
$72$	1.28019	+	0.930114i	0.150872	+	0.109615i
$73$	−3.92031	+	12.0655i	−0.458838	+	1.41216i	0.407732	+	0.913102i	$0.366320\pi$
$73$	−3.92031	+	12.0655i	−0.458838	+	1.41216i	−0.866570	+	0.499056i	$0.833680\pi$
$74$	2.20596	+	6.78926i	0.256438	+	0.789236i
$75$	8.51739	−	6.18824i	0.983503	−	0.714557i
$76$	−2.26188			−0.259456
$77$	5.50754	+	2.81008i	0.627642	+	0.320239i
$78$	3.44551			0.390127
$79$	−3.19939	+	2.32450i	−0.359960	+	0.261526i	−0.753035	−	0.657980i	$-0.771411\pi$
$79$	−3.19939	+	2.32450i	−0.359960	+	0.261526i	0.393076	+	0.919506i	$0.371411\pi$
$80$	−1.14971	−	3.53845i	−0.128542	−	0.395610i
$81$	−0.540403	+	1.66319i	−0.0600448	+	0.184799i
$82$	0.0240549	+	0.0174769i	0.00265642	+	0.00193000i
$83$	−9.92036	−	7.20756i	−1.08890	−	0.791133i	−0.109688	−	0.993966i	$-0.534985\pi$
$83$	−9.92036	−	7.20756i	−1.08890	−	0.791133i	−0.979213	+	0.202833i	$0.934985\pi$
$84$	0.685901	−	2.11099i	0.0748379	−	0.230328i
$85$	0.245444	+	0.755398i	0.0266221	+	0.0819345i
$86$	−0.809017	+	0.587785i	−0.0872385	+	0.0633825i
$87$	4.30495			0.461539
$88$	3.27608	−	0.517016i	0.349231	−	0.0551141i
$89$	−1.66755			−0.176760			−0.0883802	−	0.996087i	$-0.528169\pi$
$89$	−1.66755			−0.176760			−0.0883802	+	0.996087i	$0.528169\pi$
$90$	−4.76301	+	3.46053i	−0.502066	+	0.364772i
$91$	1.66710	+	5.13082i	0.174760	+	0.537856i
$92$	2.15981	−	6.64722i	0.225176	−	0.693021i
$93$	8.73195	+	6.34414i	0.905461	+	0.657856i
$94$	−0.0474374	−	0.0344653i	−0.00489279	−	0.00355482i
$95$	2.60051	−	8.00355i	0.266807	−	0.821147i
$96$	−0.367924	−	1.13235i	−0.0375511	−	0.115570i
$97$	4.32973	−	3.14573i	0.439617	−	0.319401i	−0.345866	−	0.938284i	$-0.612415\pi$
$97$	4.32973	−	3.14573i	0.439617	−	0.319401i	0.785483	+	0.618883i	$0.212415\pi$
$98$	−3.52459			−0.356037
$99$	−2.38006	−	4.67754i	−0.239205	−	0.470111i
$100$	8.84245			0.884245
$101$	−13.9893	+	10.1638i	−1.39199	+	1.01134i	−0.396342	+	0.918103i	$0.629721\pi$
$101$	−13.9893	+	10.1638i	−1.39199	+	1.01134i	−0.995644	+	0.0932342i	$0.970279\pi$
$102$	0.0785456	+	0.241738i	0.00777717	+	0.0239357i
$103$	4.60384	−	14.1692i	0.453630	−	1.39613i	−0.419106	−	0.907937i	$-0.637657\pi$
$103$	4.60384	−	14.1692i	0.453630	−	1.39613i	0.872736	−	0.488192i	$-0.162343\pi$
$104$	2.34118	+	1.70097i	0.229572	+	0.166793i
$105$	6.68103	+	4.85405i	0.652001	+	0.473707i
$106$	−1.22187	+	3.76054i	−0.118679	+	0.365256i
$107$	−2.02333	−	6.22716i	−0.195602	−	0.602002i	−0.999969	−	0.00786908i	$-0.997495\pi$
$107$	−2.02333	−	6.22716i	−0.195602	−	0.602002i	0.804367	−	0.594133i	$-0.202505\pi$
$108$	−4.41395	+	3.20692i	−0.424732	+	0.308586i
$109$	14.7311			1.41098			0.705489	−	0.708721i	$-0.250727\pi$
$109$	14.7311			1.41098			0.705489	+	0.708721i	$0.250727\pi$
$110$	−1.93711	+	12.1867i	−0.184696	+	1.16195i
$111$	−8.49948			−0.806735
$112$	1.50821	−	1.09578i	0.142512	−	0.103541i
$113$	−0.0435238	−	0.133952i	−0.00409437	−	0.0126012i	0.948988	−	0.315311i	$-0.102109\pi$
$113$	−0.0435238	−	0.133952i	−0.00409437	−	0.0126012i	−0.953083	+	0.302710i	$0.902109\pi$
$114$	0.832202	−	2.56125i	0.0779428	−	0.239883i
$115$	21.0377	+	15.2848i	1.96178	+	1.42531i
$116$	2.92516	+	2.12525i	0.271594	+	0.197325i
$117$	1.41507	−	4.35513i	0.130823	−	0.402632i
$118$	2.44983	+	7.53980i	0.225525	+	0.694095i
$119$	−0.321976	+	0.233929i	−0.0295155	+	0.0214443i
$120$	4.42978			0.404382
$121$	−10.4578	−	3.41080i	−0.950713	−	0.310073i
$122$	−8.14157			−0.737103
$123$	−0.0286405	+	0.0208085i	−0.00258243	+	0.00187624i
$124$	2.80130	+	8.62152i	0.251564	+	0.774236i
$125$	−4.41771	+	13.5963i	−0.395132	+	1.21609i
$126$	−2.38659	−	1.73396i	−0.212615	−	0.154474i
$127$	7.75657	+	5.63548i	0.688285	+	0.500068i	0.876096	−	0.482137i	$-0.160139\pi$
$127$	7.75657	+	5.63548i	0.688285	+	0.500068i	−0.187811	+	0.982205i	$0.560139\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.367924	−	1.13235i	−0.0323939	−	0.0996983i
$130$	−8.71046	+	6.32852i	−0.763958	+	0.555048i
$131$	−11.8154			−1.03231			−0.516157	−	0.856494i	$-0.672638\pi$
$131$	−11.8154			−1.03231			−0.516157	+	0.856494i	$0.672638\pi$
$132$	−0.619904	+	3.89991i	−0.0539557	+	0.339443i
$133$	4.21670			0.365635
$134$	−6.21322	+	4.51417i	−0.536741	+	0.389965i
$135$	−6.27276	−	19.3056i	−0.539873	−	1.66156i
$136$	−0.0659699	+	0.203034i	−0.00565687	+	0.0174101i
$137$	8.35197	+	6.06806i	0.713557	+	0.518429i	0.884319	−	0.466883i	$-0.154623\pi$
$137$	8.35197	+	6.06806i	0.713557	+	0.518429i	−0.170762	+	0.985312i	$0.554623\pi$
$138$	6.73237	+	4.89135i	0.573097	+	0.416379i
$139$	−2.73155	+	8.40684i	−0.231687	+	0.713059i	0.765857	+	0.643011i	$0.222315\pi$
$139$	−2.73155	+	8.40684i	−0.231687	+	0.713059i	−0.997544	+	0.0700475i	$0.977685\pi$
$140$	2.14334	+	6.59653i	0.181146	+	0.557509i
$141$	0.0564803	−	0.0410353i	0.00475650	−	0.00345580i
$142$	−7.50830			−0.630083
$143$	−4.35258	−	8.55415i	−0.363981	−	0.715334i
$144$	−1.58240			−0.131867
$145$	−10.8832	+	7.90710i	−0.903799	+	0.656649i
$146$	−3.92031	−	12.0655i	−0.324447	−	0.998546i
$147$	1.29678	−	3.99109i	0.106957	−	0.329179i
$148$	−5.77529	−	4.19599i	−0.474726	−	0.344909i
$149$	6.49234	+	4.71696i	0.531873	+	0.386429i	0.821058	−	0.570845i	$-0.193384\pi$
$149$	6.49234	+	4.71696i	0.531873	+	0.386429i	−0.289185	+	0.957273i	$0.593384\pi$
$150$	−3.25335	+	10.0128i	−0.265635	+	0.817541i
$151$	0.233029	+	0.717188i	0.0189636	+	0.0583639i	0.960091	−	0.279690i	$-0.0902315\pi$
$151$	0.233029	+	0.717188i	0.0189636	+	0.0583639i	−0.941127	+	0.338053i	$0.890232\pi$
$152$	1.82990	−	1.32950i	0.148425	−	0.107837i
$153$	0.337817			0.0273108
$154$	−6.10741	+	0.963844i	−0.492149	+	0.0776688i
$155$	−33.7275			−2.70906
$156$	−2.78747	+	2.02522i	−0.223177	+	0.162147i
$157$	−7.00251	−	21.5515i	−0.558861	−	1.72000i	−0.685523	−	0.728051i	$-0.740427\pi$
$157$	−7.00251	−	21.5515i	−0.558861	−	1.72000i	0.126662	−	0.991946i	$-0.459573\pi$
$158$	1.22206	−	3.76111i	0.0972218	−	0.299218i
$159$	−3.80870	−	2.76719i	−0.302050	−	0.219452i
$160$	3.00998	+	2.18688i	0.237960	+	0.172888i
$161$	−4.02642	+	12.3921i	−0.317327	+	0.976631i
$162$	−0.540403	−	1.66319i	−0.0424581	−	0.130672i
$163$	−12.6454	+	9.18742i	−0.990464	+	0.719614i	−0.960023	−	0.279922i	$-0.909691\pi$
$163$	−12.6454	+	9.18742i	−0.990464	+	0.719614i	−0.0304416	+	0.999537i	$0.509691\pi$
$164$	−0.0297335			−0.00232180
$165$	−13.0869	−	6.67726i	−1.01881	−	0.519824i
$166$	12.2622			0.951734
$167$	−0.743785	+	0.540392i	−0.0575558	+	0.0418168i	−0.616191	−	0.787597i	$-0.711325\pi$
$167$	−0.743785	+	0.540392i	−0.0575558	+	0.0418168i	0.558635	+	0.829413i	$0.311325\pi$
$168$	0.685901	+	2.11099i	0.0529184	+	0.162866i
$169$	−1.42939	+	4.39920i	−0.109953	+	0.338400i
$170$	−0.642580	−	0.466862i	−0.0492837	−	0.0358067i
$171$	−2.89565	−	2.10381i	−0.221436	−	0.160882i
$172$	0.309017	−	0.951057i	0.0235623	−	0.0725174i
$173$	−4.23217	−	13.0253i	−0.321766	−	0.990293i	−0.972879	−	0.231313i	$-0.925698\pi$
$173$	−4.23217	−	13.0253i	−0.321766	−	0.990293i	0.651114	−	0.758980i	$-0.274302\pi$
$174$	−3.48278	+	2.53039i	−0.264029	+	0.191828i
$175$	−16.4845			−1.24611
$176$	−2.34651	+	2.34391i	−0.176875	+	0.176679i
$177$	−9.43908			−0.709485
$178$	1.34908	−	0.980164i	0.101118	−	0.0734664i
$179$	7.75520	+	23.8681i	0.579651	+	1.78398i	0.619765	+	0.784788i	$0.287228\pi$
$179$	7.75520	+	23.8681i	0.579651	+	1.78398i	−0.0401138	+	0.999195i	$0.512772\pi$
$180$	1.81931	−	5.59926i	0.135603	−	0.417344i
$181$	−0.976936	−	0.709786i	−0.0726151	−	0.0527580i	0.550885	−	0.834581i	$-0.314290\pi$
$181$	−0.976936	−	0.709786i	−0.0726151	−	0.0527580i	−0.623501	+	0.781823i	$0.714290\pi$
$182$	−4.36453	−	3.17102i	−0.323521	−	0.235052i
$183$	2.99548	−	9.21915i	0.221432	−	0.681499i
$184$	2.15981	+	6.64722i	0.159224	+	0.490040i
$185$	21.4872	−	15.6114i	1.57977	−	1.14777i
$186$	−10.7933			−0.791402
$187$	0.500940	−	0.500384i	0.0366323	−	0.0365917i
$188$	0.0586358			0.00427646
$189$	8.22868	−	5.97849i	0.598548	−	0.434871i
$190$	2.60051	+	8.00355i	0.188661	+	0.580639i
$191$	−3.32171	+	10.2232i	−0.240351	+	0.739723i	0.756016	+	0.654553i	$0.227143\pi$
$191$	−3.32171	+	10.2232i	−0.240351	+	0.739723i	−0.996366	+	0.0851699i	$0.972857\pi$
$192$	0.963238	+	0.699834i	0.0695157	+	0.0505061i
$193$	15.2850	+	11.1052i	1.10024	+	0.799370i	0.981099	−	0.193507i	$-0.0619862\pi$
$193$	15.2850	+	11.1052i	1.10024	+	0.799370i	0.119140	+	0.992877i	$0.461986\pi$
$194$	−1.65381	+	5.08990i	−0.118737	+	0.365434i
$195$	−3.96134	−	12.1917i	−0.283677	−	0.873069i
$196$	2.85145	−	2.07170i	0.203675	−	0.147979i
$197$	−24.8249			−1.76870			−0.884352	−	0.466821i	$-0.845399\pi$
$197$	−24.8249			−1.76870			−0.884352	+	0.466821i	$0.845399\pi$
$198$	4.67490	+	2.38525i	0.332230	+	0.169512i
$199$	−14.6158			−1.03609			−0.518045	−	0.855354i	$-0.673340\pi$
$199$	−14.6158			−1.03609			−0.518045	+	0.855354i	$0.673340\pi$
$200$	−7.15369	+	5.19746i	−0.505842	+	0.367516i
$201$	−2.82565	−	8.69644i	−0.199306	−	0.613400i
$202$	5.34343	−	16.4454i	0.375963	−	1.15709i
$203$	−5.45321	−	3.96199i	−0.382741	−	0.278077i
$204$	−0.205635	−	0.149403i	−0.0143973	−	0.0104603i
$205$	0.0341850	−	0.105211i	0.00238758	−	0.00734822i
$206$	4.60384	+	14.1692i	0.320765	+	0.987213i
$207$	8.94766	−	6.50085i	0.621905	−	0.451840i
$208$	−2.89386			−0.200653
$209$	−7.41011	+	1.16943i	−0.512568	+	0.0808911i
$210$	−8.25820			−0.569870
$211$	−6.97279	+	5.06603i	−0.480027	+	0.348760i	−0.801336	−	0.598214i	$-0.795877\pi$
$211$	−6.97279	+	5.06603i	−0.480027	+	0.348760i	0.321309	+	0.946974i	$0.395877\pi$
$212$	−1.22187	−	3.76054i	−0.0839185	−	0.258275i
$213$	2.76249	−	8.50206i	0.189283	−	0.582552i
$214$	5.29714	+	3.84860i	0.362105	+	0.263085i
$215$	3.00998	+	2.18688i	0.205279	+	0.149144i
$216$	1.68598	−	5.18891i	0.114716	−	0.353060i
$217$	−5.22231	−	16.0726i	−0.354514	−	1.09108i
$218$	−11.9177	+	8.65869i	−0.807166	+	0.586441i
$219$	15.1048			1.02069
$220$	−5.59598	−	10.9978i	−0.377281	−	0.741473i
$221$	0.617789			0.0415570
$222$	6.87622	−	4.99587i	0.461502	−	0.335301i
$223$	−0.0812599	−	0.250092i	−0.00544157	−	0.0167474i	0.948299	−	0.317379i	$-0.102803\pi$
$223$	−0.0812599	−	0.250092i	−0.00544157	−	0.0167474i	−0.953740	+	0.300631i	$0.902803\pi$
$224$	−0.576083	+	1.77300i	−0.0384912	+	0.118464i
$225$	11.3200	+	8.22449i	0.754669	+	0.548299i
$226$	0.113947	+	0.0827872i	0.00757962	+	0.00550692i
$227$	6.87494	−	21.1589i	0.456306	−	1.40437i	−0.413289	−	0.910600i	$-0.635620\pi$
$227$	6.87494	−	21.1589i	0.456306	−	1.40437i	0.869595	−	0.493766i	$-0.164380\pi$
$228$	0.832202	+	2.56125i	0.0551139	+	0.169623i
$229$	18.2760	−	13.2783i	1.20771	−	0.877453i	0.212689	−	0.977120i	$-0.431778\pi$
$229$	18.2760	−	13.2783i	1.20771	−	0.877453i	0.995021	+	0.0996674i	$0.0317779\pi$
$230$	−26.0040			−1.71465
$231$	1.15565	−	7.27038i	0.0760364	−	0.478356i
$232$	−3.61570			−0.237382
$233$	−11.5648	+	8.40230i	−0.757633	+	0.550453i	−0.898184	−	0.439621i	$-0.855113\pi$
$233$	−11.5648	+	8.40230i	−0.757633	+	0.550453i	0.140550	+	0.990074i	$0.455113\pi$
$234$	1.41507	+	4.35513i	0.0925058	+	0.284704i
$235$	−0.0674143	+	0.207480i	−0.00439762	+	0.0135345i
$236$	−6.41374	−	4.65985i	−0.417499	−	0.303331i
$237$	3.80929	+	2.76761i	0.247440	+	0.179776i
$238$	0.122984	−	0.378506i	0.00797187	−	0.0245349i
$239$	−4.15007	−	12.7726i	−0.268445	−	0.826190i	−0.990880	−	0.134750i	$-0.956977\pi$
$239$	−4.15007	−	12.7726i	−0.268445	−	0.826190i	0.722434	−	0.691440i	$-0.243023\pi$
$240$	−3.58377	+	2.60376i	−0.231331	+	0.168072i
$241$	3.21525			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$241$	3.21525			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$242$	10.4654	−	3.38757i	0.672741	−	0.217761i
$243$	−14.2857			−0.916426
$244$	6.58667	−	4.78550i	0.421668	−	0.306360i
$245$	4.05226	+	12.4716i	0.258889	+	0.796780i
$246$	0.0109397	−	0.0336689i	0.000697489	−	0.00214665i
$247$	−5.29547	−	3.84739i	−0.336943	−	0.244803i
$248$	−7.33391	−	5.32839i	−0.465703	−	0.338353i
$249$	−4.51158	+	13.8852i	−0.285910	+	0.879939i
$250$	−4.41771	−	13.5963i	−0.279400	−	0.859906i
$251$	−21.7056	+	15.7700i	−1.37005	+	0.995396i	−0.372312	+	0.928108i	$0.621435\pi$
$251$	−21.7056	+	15.7700i	−1.37005	+	0.995396i	−0.997734	+	0.0672885i	$0.978565\pi$
$252$	2.94999			0.185832
$253$	3.63900	−	22.8935i	0.228782	−	1.43930i
$254$	−9.58765			−0.601583
$255$	0.765074	−	0.555859i	0.0479108	−	0.0348092i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−5.91770	+	18.2128i	−0.369136	+	1.13608i	0.578215	+	0.815885i	$0.303750\pi$
$257$	−5.91770	+	18.2128i	−0.369136	+	1.13608i	−0.947350	+	0.320199i	$0.896250\pi$
$258$	0.963238	+	0.699834i	0.0599686	+	0.0435697i
$259$	10.7666	+	7.82236i	0.669001	+	0.486058i
$260$	3.32710	−	10.2398i	0.206338	−	0.635043i
$261$	1.76804	+	5.44146i	0.109439	+	0.336818i
$262$	9.55884	−	6.94490i	0.590547	−	0.429058i
$263$	−15.9195			−0.981640			−0.490820	−	0.871261i	$-0.663303\pi$
$263$	−15.9195			−0.981640			−0.490820	+	0.871261i	$0.663303\pi$
$264$	−1.79079	−	3.51946i	−0.110216	−	0.216608i
$265$	14.7113			0.903706
$266$	−3.41139	+	2.47852i	−0.209165	+	0.151968i
$267$	0.613534	+	1.88826i	0.0375476	+	0.115560i
$268$	2.37324	−	7.30408i	0.144969	−	0.446168i
$269$	−18.0700	−	13.1286i	−1.10175	−	0.800465i	−0.120401	−	0.992725i	$-0.538418\pi$
$269$	−18.0700	−	13.1286i	−1.10175	−	0.800465i	−0.981344	+	0.192261i	$0.938418\pi$
$270$	16.4223	+	11.9315i	0.999429	+	0.726127i
$271$	3.16035	−	9.72656i	0.191978	−	0.590846i	−0.808021	−	0.589154i	$-0.799461\pi$
$271$	3.16035	−	9.72656i	0.191978	−	0.590846i	0.999999	−	0.00169261i	$-0.000538773\pi$
$272$	−0.0659699	−	0.203034i	−0.00400001	−	0.0123108i
$273$	5.19653	−	3.77550i	0.314509	−	0.228504i
$274$	−10.3236			−0.623671
$275$	28.9686	−	4.57169i	1.74687	−	0.275683i
$276$	−8.32166			−0.500905
$277$	−9.59377	+	6.97028i	−0.576434	+	0.418804i	−0.837437	−	0.546534i	$-0.815947\pi$
$277$	−9.59377	+	6.97028i	−0.576434	+	0.418804i	0.261003	+	0.965338i	$0.415947\pi$
$278$	−2.73155	−	8.40684i	−0.163827	−	0.504209i
$279$	−4.43279	+	13.6427i	−0.265384	+	0.816769i
$280$	−5.61135	−	4.07688i	−0.335342	−	0.243640i
$281$	−19.9764	−	14.5137i	−1.19169	−	0.865815i	−0.198250	−	0.980151i	$-0.563526\pi$
$281$	−19.9764	−	14.5137i	−1.19169	−	0.865815i	−0.993442	+	0.114336i	$0.963526\pi$
$282$	−0.0215735	+	0.0663965i	−0.00128469	+	0.00395386i
$283$	−1.12177	−	3.45245i	−0.0666822	−	0.205227i	0.912164	−	0.409826i	$-0.134411\pi$
$283$	−1.12177	−	3.45245i	−0.0666822	−	0.205227i	−0.978846	+	0.204600i	$0.934411\pi$
$284$	6.07435	−	4.41327i	0.360446	−	0.261879i
$285$	−10.0197			−0.593513
$286$	8.54932	+	4.36207i	0.505532	+	0.257935i
$287$	0.0554306			0.00327196
$288$	1.28019	−	0.930114i	0.0754361	−	0.0548075i
$289$	−5.23921	−	16.1246i	−0.308189	−	0.948507i
$290$	4.15701	−	12.7939i	0.244108	−	0.751287i
$291$	−5.15510	−	3.74540i	−0.302197	−	0.219559i
$292$	10.2635	+	7.45688i	0.600626	+	0.436381i
$293$	0.219294	−	0.674917i	0.0128113	−	0.0394291i	−0.944447	−	0.328665i	$-0.893401\pi$
$293$	0.219294	−	0.674917i	0.0128113	−	0.0394291i	0.957258	+	0.289236i	$0.0934012\pi$
$294$	1.29678	+	3.99109i	0.0756299	+	0.232765i
$295$	23.8626	−	17.3372i	1.38933	−	1.00941i
$296$	7.13865			0.414926
$297$	−12.8024	+	12.7882i	−0.742871	+	0.742047i
$298$	−8.02497			−0.464874
$299$	16.3632	−	11.8886i	0.946309	−	0.687534i
$300$	−3.25335	−	10.0128i	−0.187832	−	0.578089i
$301$	−0.576083	+	1.77300i	−0.0332049	+	0.102194i
$302$	−0.610077	−	0.443247i	−0.0351060	−	0.0255060i
$303$	16.6560	+	12.1013i	0.956864	+	0.695203i
$304$	−0.698960	+	2.15118i	−0.0400881	+	0.123379i
$305$	9.36046	+	28.8085i	0.535978	+	1.64957i
$306$	−0.273299	+	0.198564i	−0.0156235	+	0.0113511i
$307$	−18.8654			−1.07671			−0.538353	−	0.842719i	$-0.680953\pi$
$307$	−18.8654			−1.07671			−0.538353	+	0.842719i	$0.680953\pi$
$308$	4.37447	−	4.36961i	0.249258	−	0.248982i
$309$	−17.7384			−1.00910
$310$	27.2861	−	19.8245i	1.54975	−	1.12596i
$311$	0.917629	+	2.82417i	0.0520339	+	0.160144i	0.973697	−	0.227848i	$-0.0731689\pi$
$311$	0.917629	+	2.82417i	0.0520339	+	0.160144i	−0.921663	+	0.387992i	$0.873169\pi$
$312$	1.06472	−	3.27687i	0.0602779	−	0.185516i
$313$	3.04794	+	2.21446i	0.172280	+	0.125169i	0.670584	−	0.741834i	$-0.266044\pi$
$313$	3.04794	+	2.21446i	0.172280	+	0.125169i	−0.498304	+	0.867002i	$0.666044\pi$
$314$	18.3328	+	13.3196i	1.03458	+	0.751666i
$315$	−3.39164	+	10.4384i	−0.191097	+	0.588136i
$316$	1.22206	+	3.76111i	0.0687462	+	0.211579i
$317$	−21.7813	+	15.8250i	−1.22336	+	0.888822i	−0.996374	−	0.0850762i	$-0.972887\pi$
$317$	−21.7813	+	15.8250i	−1.22336	+	0.888822i	−0.226984	+	0.973898i	$0.572887\pi$
$318$	4.70782			0.264001
$319$	10.6818	+	5.45014i	0.598068	+	0.305149i
$320$	−3.72054			−0.207985
$321$	−6.30692	+	4.58225i	−0.352018	+	0.255756i
$322$	−4.02642	−	12.3921i	−0.224384	−	0.690582i
$323$	0.149216	−	0.459240i	0.00830261	−	0.0255528i
$324$	1.41479	+	1.02791i	0.0785996	+	0.0571060i
$325$	20.7018	+	15.0407i	1.14833	+	0.834308i
$326$	4.83011	−	14.8656i	0.267515	−	0.823327i
$327$	−5.41991	−	16.6808i	−0.299722	−	0.922449i
$328$	0.0240549	−	0.0174769i	0.00132821	−	0.000965002i
$329$	−0.109312			−0.00602654
$330$	14.5123	−	2.29027i	0.798877	−	0.126075i
$331$	19.1696			1.05366			0.526828	−	0.849972i	$-0.323381\pi$
$331$	19.1696			1.05366			0.526828	+	0.849972i	$0.323381\pi$
$332$	−9.92036	+	7.20756i	−0.544450	+	0.395566i
$333$	−3.49073	−	10.7434i	−0.191291	−	0.588732i
$334$	0.284101	−	0.874372i	0.0155453	−	0.0478435i
$335$	23.1166	+	16.7952i	1.26299	+	0.917618i
$336$	−1.79571	−	1.30466i	−0.0979641	−	0.0711751i
$337$	−2.30190	+	7.08453i	−0.125393	+	0.385919i	−0.993972	−	0.109631i	$-0.965033\pi$
$337$	−2.30190	+	7.08453i	−0.125393	+	0.385919i	0.868580	+	0.495549i	$0.165033\pi$
$338$	−1.42939	−	4.39920i	−0.0777484	−	0.239285i
$339$	−0.135668	+	0.0985687i	−0.00736848	+	0.00535352i
$340$	0.794273			0.0430755
$341$	13.6348	+	26.7965i	0.738363	+	1.45111i
$342$	3.57921			0.193542
$343$	−15.8732	+	11.5326i	−0.857075	+	0.622701i
$344$	0.309017	+	0.951057i	0.0166611	+	0.0512775i
$345$	9.56751	−	29.4458i	0.515097	−	1.58531i
$346$	11.0800	+	8.05006i	0.595662	+	0.432774i
$347$	−14.4103	−	10.4697i	−0.773584	−	0.562042i	0.129462	−	0.991584i	$-0.458675\pi$
$347$	−14.4103	−	10.4697i	−0.773584	−	0.562042i	−0.903047	+	0.429542i	$0.858675\pi$
$348$	1.33030	−	4.09425i	0.0713117	−	0.219475i
$349$	0.206790	+	0.636433i	0.0110692	+	0.0340675i	0.956439	−	0.291934i	$-0.0942987\pi$
$349$	0.206790	+	0.636433i	0.0110692	+	0.0340675i	−0.945369	+	0.326001i	$0.894299\pi$
$350$	13.3362	−	9.68934i	0.712852	−	0.517917i
$351$	−15.7887			−0.842739
$352$	0.520653	−	3.27550i	0.0277509	−	0.174585i
$353$	−22.2855			−1.18614			−0.593068	−	0.805153i	$-0.702083\pi$
$353$	−22.2855			−1.18614			−0.593068	+	0.805153i	$0.702083\pi$
$354$	7.63638	−	5.54815i	0.405869	−	0.294881i
$355$	8.63238	+	26.5677i	0.458159	+	1.41007i
$356$	−0.515303	+	1.58594i	−0.0273110	+	0.0840546i
$357$	0.383354	+	0.278523i	0.0202892	+	0.0147410i
$358$	−20.3034	−	14.7513i	−1.07307	−	0.779629i
$359$	−0.705121	+	2.17014i	−0.0372149	+	0.114536i	−0.967938	−	0.251188i	$-0.919179\pi$
$359$	−0.705121	+	2.17014i	−0.0372149	+	0.114536i	0.930723	+	0.365724i	$0.119179\pi$
$360$	1.81931	+	5.59926i	0.0958860	+	0.295107i
$361$	11.2323	−	8.16074i	0.591174	−	0.429513i
$362$	1.20756			0.0634679
$363$	−0.0145404	+	13.0969i	−0.000763170	+	0.687409i
$364$	5.39486			0.282767
$365$	−38.1858	+	27.7436i	−1.99874	+	1.45217i
$366$	2.99548	+	9.21915i	0.156576	+	0.481892i
$367$	0.916910	−	2.82196i	0.0478623	−	0.147305i	−0.924269	−	0.381741i	$-0.875324\pi$
$367$	0.916910	−	2.82196i	0.0478623	−	0.147305i	0.972131	+	0.234436i	$0.0753245\pi$
$368$	−5.65447	−	4.10821i	−0.294759	−	0.214155i
$369$	−0.0380646	−	0.0276556i	−0.00198157	−	0.00143969i
$370$	−8.20739	+	25.2597i	−0.426682	+	1.31319i
$371$	2.27787	+	7.01056i	0.118261	+	0.363970i
$372$	8.73195	−	6.34414i	0.452731	−	0.328928i
$373$	10.8112			0.559781			0.279891	−	0.960032i	$-0.409702\pi$
$373$	10.8112			0.559781			0.279891	+	0.960032i	$0.409702\pi$
$374$	−0.111151	+	0.699264i	−0.00574746	+	0.0361581i
$375$	17.0212			0.878972
$376$	−0.0474374	+	0.0344653i	−0.00244640	+	0.00177741i
$377$	3.23334	+	9.95120i	0.166525	+	0.512513i
$378$	−3.14308	+	9.67339i	−0.161662	+	0.497546i
$379$	−17.7050	−	12.8635i	−0.909447	−	0.660752i	0.0314282	−	0.999506i	$-0.489994\pi$
$379$	−17.7050	−	12.8635i	−0.909447	−	0.660752i	−0.940875	+	0.338754i	$0.889994\pi$
$380$	−6.80823	−	4.94647i	−0.349255	−	0.253748i
$381$	3.52753	−	10.8566i	0.180721	−	0.556202i
$382$	−3.32171	−	10.2232i	−0.169954	−	0.523063i
$383$	15.5898	−	11.3266i	0.796600	−	0.578764i	−0.113314	−	0.993559i	$-0.536147\pi$
$383$	15.5898	−	11.3266i	0.796600	−	0.578764i	0.909915	+	0.414795i	$0.136147\pi$
$384$	−1.19063			−0.0607590
$385$	10.4323	+	20.5026i	0.531678	+	1.04491i
$386$	−18.8933			−0.961644
$387$	1.28019	−	0.930114i	0.0650758	−	0.0472804i
$388$	−1.65381	−	5.08990i	−0.0839594	−	0.258401i
$389$	2.67319	−	8.22723i	0.135536	−	0.417137i	−0.860137	−	0.510063i	$-0.829622\pi$
$389$	2.67319	−	8.22723i	0.135536	−	0.417137i	0.995673	+	0.0929260i	$0.0296220\pi$
$390$	10.3709	+	7.53491i	0.525152	+	0.381545i
$391$	1.20713	+	0.877033i	0.0610473	+	0.0443535i
$392$	−1.08916	+	3.35208i	−0.0550108	+	0.169306i
$393$	4.34716	+	13.3792i	0.219285	+	0.674891i
$394$	20.0838	−	14.5917i	1.01181	−	0.735121i
$395$	−14.7135			−0.740317
$396$	−5.18408	+	0.818129i	−0.260510	+	0.0411125i
$397$	−2.55624			−0.128294			−0.0641469	−	0.997940i	$-0.520433\pi$
$397$	−2.55624			−0.128294			−0.0641469	+	0.997940i	$0.520433\pi$
$398$	11.8245	−	8.59098i	0.592707	−	0.430627i
$399$	−1.55143	−	4.77480i	−0.0776685	−	0.239039i
$400$	2.73247	−	8.40967i	0.136623	−	0.420483i
$401$	−3.85021	−	2.79734i	−0.192271	−	0.139693i	0.487485	−	0.873131i	$-0.337914\pi$
$401$	−3.85021	−	2.79734i	−0.192271	−	0.139693i	−0.679756	+	0.733438i	$0.737914\pi$
$402$	7.39764	+	5.37470i	0.368961	+	0.268066i
$403$	−8.10657	+	24.9495i	−0.403817	+	1.24282i
$404$	5.34343	+	16.4454i	0.265846	+	0.818189i
$405$	−5.26380	+	3.82437i	−0.261560	+	0.190035i
$406$	6.74054			0.334528
$407$	−21.0897	−	10.7605i	−1.04538	−	0.533378i
$408$	0.254179			0.0125837
$409$	13.6567	−	9.92215i	0.675279	−	0.490619i	−0.196509	−	0.980502i	$-0.562961\pi$
$409$	13.6567	−	9.92215i	0.675279	−	0.490619i	0.871788	+	0.489883i	$0.162961\pi$
$410$	0.0341850	+	0.105211i	0.00168828	+	0.00519598i
$411$	3.79830	−	11.6900i	0.187356	−	0.576624i
$412$	−12.0530	−	8.75703i	−0.593809	−	0.431428i
$413$	11.9568	+	8.68711i	0.588355	+	0.427465i
$414$	−3.41770	+	10.5186i	−0.167971	+	0.516961i
$415$	−14.0980	−	43.3893i	−0.692045	−	2.12990i
$416$	2.34118	−	1.70097i	0.114786	−	0.0833967i
$417$	10.5245			0.515388
$418$	5.30753	−	5.30164i	0.259600	−	0.259312i
$419$	−1.00961			−0.0493225			−0.0246613	−	0.999696i	$-0.507851\pi$
$419$	−1.00961			−0.0493225			−0.0246613	+	0.999696i	$0.507851\pi$
$420$	6.68103	−	4.85405i	0.326001	−	0.236853i
$421$	−0.275929	−	0.849221i	−0.0134479	−	0.0413885i	0.944107	−	0.329638i	$-0.106927\pi$
$421$	−0.275929	−	0.849221i	−0.0134479	−	0.0413885i	−0.957555	+	0.288250i	$0.906927\pi$
$422$	2.66337	−	8.19701i	0.129651	−	0.399024i
$423$	0.0750651	+	0.0545380i	0.00364979	+	0.00265173i
$424$	3.19890	+	2.32414i	0.155352	+	0.112870i
$425$	−0.583335	+	1.79532i	−0.0282959	+	0.0870859i
$426$	2.76249	+	8.50206i	0.133843	+	0.411926i
$427$	−12.2792	+	8.92134i	−0.594230	+	0.431734i
$428$	−6.54762			−0.316491
$429$	−8.08492	+	8.07594i	−0.390343	+	0.389910i
$430$	−3.72054			−0.179421
$431$	−13.4759	+	9.79084i	−0.649113	+	0.471608i	−0.862969	−	0.505257i	$-0.831398\pi$
$431$	−13.4759	+	9.79084i	−0.649113	+	0.471608i	0.213856	+	0.976865i	$0.431398\pi$
$432$	1.68598	+	5.18891i	0.0811167	+	0.249651i
$433$	−5.51756	+	16.9813i	−0.265157	+	0.816069i	0.726500	+	0.687166i	$0.241146\pi$
$433$	−5.51756	+	16.9813i	−0.265157	+	0.816069i	−0.991657	+	0.128903i	$0.958854\pi$
$434$	13.6722	+	9.93343i	0.656286	+	0.476820i
$435$	12.9578	+	9.41441i	0.621280	+	0.451386i
$436$	4.55214	−	14.0101i	0.218008	−	0.670960i
$437$	−4.88525	−	15.0352i	−0.233693	−	0.719233i
$438$	−12.2200	+	8.87837i	−0.583895	+	0.424225i
$439$	17.0412			0.813334			0.406667	−	0.913576i	$-0.366691\pi$
$439$	17.0412			0.813334			0.406667	+	0.913576i	$0.366691\pi$
$440$	10.9916	+	5.60819i	0.524004	+	0.267360i
$441$	5.57733			0.265587
$442$	−0.499802	+	0.363127i	−0.0237732	+	0.0172722i
$443$	4.77897	+	14.7081i	0.227056	+	0.698805i	0.998076	+	0.0619953i	$0.0197464\pi$
$443$	4.77897	+	14.7081i	0.227056	+	0.698805i	−0.771021	+	0.636810i	$0.780254\pi$
$444$	−2.62648	+	8.08348i	−0.124647	+	0.383625i
$445$	−5.01931	−	3.64674i	−0.237938	−	0.172872i
$446$	0.212741	+	0.154566i	0.0100736	+	0.00731889i
$447$	2.95258	−	9.08712i	0.139652	−	0.429806i
$448$	−0.576083	−	1.77300i	−0.0272174	−	0.0837665i
$449$	−7.56926	+	5.49939i	−0.357216	+	0.259532i	−0.751890	−	0.659289i	$-0.770857\pi$
$449$	−7.56926	+	5.49939i	−0.357216	+	0.259532i	0.394674	+	0.918821i	$0.370857\pi$
$450$	−13.9923			−0.659605
$451$	−0.0974094	+	0.0153727i	−0.00458683	+	0.000723873i
$452$	−0.140846			−0.00662483
$453$	0.726374	−	0.527742i	0.0341280	−	0.0247955i
$454$	6.87494	+	21.1589i	0.322657	+	0.993036i
$455$	−6.20253	+	19.0894i	−0.290779	+	0.894926i
$456$	−2.17873	−	1.58294i	−0.102028	−	0.0741280i
$457$	−16.7757	−	12.1882i	−0.784732	−	0.570141i	0.121663	−	0.992571i	$-0.461177\pi$
$457$	−16.7757	−	12.1882i	−0.784732	−	0.570141i	−0.906395	+	0.422430i	$0.861177\pi$
$458$	−6.98080	+	21.4847i	−0.326191	+	1.00391i
$459$	−0.359928	−	1.10774i	−0.0168000	−	0.0517050i
$460$	21.0377	−	15.2848i	0.980888	−	0.712657i
$461$	−0.154766			−0.00720819			−0.00360409	−	0.999994i	$-0.501147\pi$
$461$	−0.154766			−0.00720819			−0.00360409	+	0.999994i	$0.501147\pi$
$462$	3.33848	+	6.56114i	0.155320	+	0.305252i
$463$	9.10549			0.423168			0.211584	−	0.977360i	$-0.432138\pi$
$463$	9.10549			0.423168			0.211584	+	0.977360i	$0.432138\pi$
$464$	2.92516	−	2.12525i	0.135797	−	0.0986624i
$465$	12.4092	+	38.1915i	0.575461	+	1.77109i
$466$	4.41735	−	13.5952i	0.204630	−	0.629786i
$467$	22.3875	+	16.2655i	1.03597	+	0.752678i	0.969495	−	0.245110i	$-0.0788242\pi$
$467$	22.3875	+	16.2655i	1.03597	+	0.752678i	0.0664767	+	0.997788i	$0.478824\pi$
$468$	−3.70469	−	2.69162i	−0.171250	−	0.124420i
$469$	−4.42430	+	13.6166i	−0.204295	+	0.628756i
$470$	−0.0674143	−	0.207480i	−0.00310959	−	0.00957033i
$471$	−21.8275	+	15.8586i	−1.00576	+	0.730727i
$472$	7.92782			0.364907
$473$	0.520653	−	3.27550i	0.0239396	−	0.150608i
$474$	−4.70854			−0.216270
$475$	16.1808	−	11.7560i	0.742427	−	0.539404i
$476$	0.122984	+	0.378506i	0.00563696	+	0.0173488i
$477$	1.93350	−	5.95069i	0.0885287	−	0.272463i
$478$	10.8650	+	7.89390i	0.496954	+	0.361058i
$479$	31.1051	+	22.5992i	1.42123	+	1.03258i	0.991567	+	0.129594i	$0.0413675\pi$
$479$	31.1051	+	22.5992i	1.42123	+	1.03258i	0.429663	+	0.902989i	$0.358632\pi$
$480$	1.36888	−	4.21298i	0.0624805	−	0.192295i
$481$	−6.38375	−	19.6472i	−0.291074	−	0.895833i
$482$	−2.60119	+	1.88988i	−0.118481	+	0.0860815i
$483$	15.5136			0.705894
$484$	−6.47551	+	8.89200i	−0.294342	+	0.404182i
$485$	19.9117			0.904146
$486$	11.5574	−	8.39691i	0.524252	−	0.380891i
$487$	5.42645	+	16.7009i	0.245896	+	0.756790i	0.995488	+	0.0948894i	$0.0302497\pi$
$487$	5.42645	+	16.7009i	0.245896	+	0.756790i	−0.749592	+	0.661900i	$0.769750\pi$
$488$	−2.51588	+	7.74309i	−0.113889	+	0.350513i
$489$	15.0560	+	10.9388i	0.680855	+	0.494670i
$490$	−10.6090	−	7.70786i	−0.479264	−	0.348206i
$491$	−5.01922	+	15.4476i	−0.226514	+	0.697139i	0.771620	+	0.636084i	$0.219447\pi$
$491$	−5.01922	+	15.4476i	−0.226514	+	0.697139i	−0.998134	+	0.0610556i	$0.980553\pi$
$492$	0.0109397	+	0.0336689i	0.000493199	+	0.00151791i
$493$	−0.624472	+	0.453705i	−0.0281248	+	0.0204339i
$494$	6.54557			0.294499
$495$	3.06529	−	19.2842i	0.137775	−	0.866761i
$496$	9.06521			0.407040
$497$	−11.3241	+	8.22742i	−0.507954	+	0.369050i
$498$	−4.51158	−	13.8852i	−0.202169	−	0.622211i
$499$	−9.02974	+	27.7907i	−0.404227	+	1.24408i	0.517312	+	0.855797i	$0.326933\pi$
$499$	−9.02974	+	27.7907i	−0.404227	+	1.24408i	−0.921539	+	0.388286i	$0.873067\pi$
$500$	11.5657	+	8.40298i	0.517234	+	0.375793i
$501$	0.885572	+	0.643405i	0.0395644	+	0.0287452i
$502$	8.29080	−	25.5165i	0.370037	−	1.13886i
$503$	−6.56091	−	20.1924i	−0.292536	−	0.900335i	−0.984038	−	0.177959i	$-0.943050\pi$
$503$	−6.56091	−	20.1924i	−0.292536	−	0.900335i	0.691501	−	0.722375i	$-0.256950\pi$
$504$	−2.38659	+	1.73396i	−0.106307	+	0.0772368i
$505$	−64.3346			−2.86285
$506$	10.5124	+	20.6602i	0.467335	+	0.918457i
$507$	5.50736			0.244590
$508$	7.75657	−	5.63548i	0.344142	−	0.250034i
$509$	−3.43898	−	10.5841i	−0.152430	−	0.469132i	0.845461	−	0.534037i	$-0.179326\pi$
$509$	−3.43898	−	10.5841i	−0.152430	−	0.469132i	−0.997891	+	0.0649050i	$0.979326\pi$
$510$	−0.292232	+	0.899399i	−0.0129403	+	0.0398260i
$511$	−19.1337	−	13.9014i	−0.846425	−	0.614964i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−3.81348	+	11.7367i	−0.168369	+	0.518188i
$514$	−5.91770	−	18.2128i	−0.261018	−	0.803332i
$515$	44.8438	−	32.5809i	1.97605	−	1.43569i
$516$	−1.19063			−0.0524145
$517$	0.192096	−	0.0303157i	0.00844835	−	0.00133328i
$518$	−13.3082			−0.584729
$519$	−13.1921	+	9.58462i	−0.579069	+	0.420718i
$520$	3.32710	+	10.2398i	0.145903	+	0.449043i
$521$	−0.328033	+	1.00958i	−0.0143714	+	0.0442306i	−0.957985	−	0.286818i	$-0.907402\pi$
$521$	−0.328033	+	1.00958i	−0.0143714	+	0.0442306i	0.943614	+	0.331049i	$0.107402\pi$
$522$	−4.62879	−	3.36301i	−0.202596	−	0.147195i
$523$	13.8204	+	10.0411i	0.604324	+	0.439067i	0.847411	−	0.530937i	$-0.178160\pi$
$523$	13.8204	+	10.0411i	0.604324	+	0.439067i	−0.243087	+	0.970004i	$0.578160\pi$
$524$	−3.65115	+	11.2371i	−0.159501	+	0.490894i
$525$	6.06504	+	18.6663i	0.264700	+	0.814664i
$526$	12.8792	−	9.35726i	0.561558	−	0.407996i
$527$	−1.93527			−0.0843016
$528$	3.51747	+	1.79470i	0.153078	+	0.0781043i
$529$	25.8504			1.12393
$530$	−11.9017	+	8.64706i	−0.516975	+	0.375604i
$531$	−3.87662	−	11.9310i	−0.168231	−	0.517762i
$532$	1.30303	−	4.01032i	0.0564937	−	0.173870i
$533$	−0.0696115	−	0.0505757i	−0.00301521	−	0.00219068i
$534$	−1.60625	−	1.16701i	−0.0695093	−	0.0505015i
$535$	7.52788	−	23.1684i	0.325459	−	1.00166i
$536$	2.37324	+	7.30408i	0.102508	+	0.315488i
$537$	24.1738	−	17.5633i	1.04318	−	0.757911i
$538$	22.3357			0.962960
$539$	8.27048	−	8.26131i	0.356235	−	0.355840i
$540$	−20.2991			−0.873533
$541$	10.7390	−	7.80238i	0.461708	−	0.335450i	−0.332493	−	0.943106i	$-0.607890\pi$
$541$	10.7390	−	7.80238i	0.461708	−	0.335450i	0.794201	+	0.607655i	$0.207890\pi$
$542$	3.16035	+	9.72656i	0.135749	+	0.417791i
$543$	−0.444291	+	1.36739i	−0.0190663	+	0.0586801i
$544$	0.172711	+	0.125482i	0.00740494	+	0.00538000i
$545$	44.3402	+	32.2151i	1.89933	+	1.37994i
$546$	−1.98490	+	6.10889i	−0.0849459	+	0.261436i
$547$	−7.44717	−	22.9200i	−0.318418	−	0.979990i	−0.974325	−	0.225148i	$-0.927714\pi$
$547$	−7.44717	−	22.9200i	−0.318418	−	0.979990i	0.655907	−	0.754842i	$-0.272286\pi$
$548$	8.35197	−	6.06806i	0.356778	−	0.259215i
$549$	12.8833			0.549844
$550$	−20.7489	+	20.7259i	−0.884736	+	0.883754i
$551$	8.17828			0.348406
$552$	6.73237	−	4.89135i	0.286549	−	0.208190i
$553$	−2.27822	−	7.01164i	−0.0968797	−	0.298165i
$554$	3.66449	−	11.2781i	0.155689	−	0.479163i
$555$	−25.5833	−	18.5873i	−1.08595	−	0.788989i
$556$	7.15128	+	5.19571i	0.303282	+	0.220347i
$557$	10.6156	−	32.6716i	0.449799	−	1.38434i	−0.427335	−	0.904094i	$-0.640547\pi$
$557$	10.6156	−	32.6716i	0.449799	−	1.38434i	0.877134	−	0.480246i	$-0.159453\pi$
$558$	−4.43279	−	13.6427i	−0.187655	−	0.577543i
$559$	2.34118	−	1.70097i	0.0990213	−	0.0719432i
$560$	6.93601			0.293100
$561$	−0.750920	−	0.383138i	−0.0317039	−	0.0161761i
$562$	24.6922			1.04158
$563$	33.5031	−	24.3414i	1.41199	−	1.02587i	0.418956	−	0.908006i	$-0.362396\pi$
$563$	33.5031	−	24.3414i	1.41199	−	1.02587i	0.993030	−	0.117862i	$-0.0376039\pi$
$564$	−0.0215735	−	0.0663965i	−0.000908410	−	0.00279580i
$565$	0.161932	−	0.498376i	0.00681254	−	0.0209668i
$566$	2.93683	+	2.13373i	0.123444	+	0.0896874i
$567$	−2.63752	−	1.91627i	−0.110765	−	0.0804758i
$568$	−2.32019	+	7.14082i	−0.0973532	+	0.299622i
$569$	−7.66021	−	23.5757i	−0.321133	−	0.988345i	−0.973156	−	0.230146i	$-0.926080\pi$
$569$	−7.66021	−	23.5757i	−0.321133	−	0.988345i	0.652023	−	0.758199i	$-0.273920\pi$
$570$	8.10607	−	5.88940i	0.339526	−	0.246680i
$571$	37.3690			1.56385			0.781923	−	0.623375i	$-0.214239\pi$
$571$	37.3690			1.56385			0.781923	+	0.623375i	$0.214239\pi$
$572$	−9.48050	+	1.49617i	−0.396400	+	0.0625580i
$573$	12.7984			0.534661
$574$	−0.0448443	+	0.0325813i	−0.00187176	+	0.00135992i
$575$	19.0980	+	58.7777i	0.796444	+	2.45120i
$576$	−0.488990	+	1.50496i	−0.0203746	+	0.0627065i
$577$	−30.2950	−	22.0106i	−1.26120	−	0.916313i	−0.262380	−	0.964965i	$-0.584508\pi$
$577$	−30.2950	−	22.0106i	−1.26120	−	0.916313i	−0.998816	+	0.0486518i	$0.984508\pi$
$578$	13.7164	+	9.96556i	0.570528	+	0.414513i
$579$	6.95131	−	21.3939i	0.288887	−	0.889101i
$580$	4.15701	+	12.7939i	0.172610	+	0.531240i
$581$	18.4940	−	13.4367i	0.767260	−	0.557447i
$582$	6.37205			0.264130
$583$	−5.94721	−	11.6881i	−0.246308	−	0.484071i
$584$	−12.6864			−0.524967
$585$	13.7835	−	10.0143i	0.569877	−	0.414040i
$586$	0.219294	+	0.674917i	0.00905895	+	0.0278806i
$587$	12.9553	−	39.8723i	0.534722	−	1.64570i	−0.209528	−	0.977803i	$-0.567193\pi$
$587$	12.9553	−	39.8723i	0.534722	−	1.64570i	0.744250	−	0.667902i	$-0.232807\pi$
$588$	−3.39502	−	2.46663i	−0.140008	−	0.101722i
$589$	16.5884	+	12.0522i	0.683515	+	0.496602i
$590$	−9.11470	+	28.0522i	−0.375246	+	1.15489i
$591$	9.13370	+	28.1106i	0.375710	+	1.15632i
$592$	−5.77529	+	4.19599i	−0.237363	+	0.172454i
$593$	−13.1121			−0.538450			−0.269225	−	0.963077i	$-0.586768\pi$
$593$	−13.1121			−0.538450			−0.269225	+	0.963077i	$0.586768\pi$
$594$	2.84065	−	17.8709i	0.116553	−	0.733254i
$595$	−1.48072			−0.0607036
$596$	6.49234	−	4.71696i	0.265937	−	0.193214i
$597$	5.37752	+	16.5503i	0.220087	+	0.677359i
$598$	−6.25019	+	19.2361i	−0.255589	+	0.786623i
$599$	−30.0573	−	21.8379i	−1.22811	−	0.892272i	−0.231360	−	0.972868i	$-0.574318\pi$
$599$	−30.0573	−	21.8379i	−1.22811	−	0.892272i	−0.996747	+	0.0805960i	$0.974318\pi$
$600$	8.51739	+	6.18824i	0.347721	+	0.252634i
$601$	−13.5425	+	41.6794i	−0.552409	+	1.70014i	0.150280	+	0.988643i	$0.451982\pi$
$601$	−13.5425	+	41.6794i	−0.552409	+	1.70014i	−0.702689	+	0.711497i	$0.748018\pi$
$602$	−0.576083	−	1.77300i	−0.0234794	−	0.0722622i
$603$	9.83183	−	7.14324i	0.400383	−	0.290895i
$604$	0.754096			0.0306837
$605$	−24.0189	−	33.1365i	−0.976508	−	1.34719i
$606$	−20.5880			−0.836330
$607$	27.7712	−	20.1769i	1.12720	−	0.818957i	0.141913	−	0.989879i	$-0.454675\pi$
$607$	27.7712	−	20.1769i	1.12720	−	0.818957i	0.985285	+	0.170922i	$0.0546746\pi$
$608$	−0.698960	−	2.15118i	−0.0283466	−	0.0872418i
$609$	−2.48001	+	7.63268i	−0.100495	+	0.309292i
$610$	−24.5060	−	17.8046i	−0.992219	−	0.720889i
$611$	0.137277	+	0.0997376i	0.00555363	+	0.00403495i
$612$	0.104391	−	0.321283i	0.00421976	−	0.0129871i
$613$	11.5407	+	35.5186i	0.466125	+	1.43458i	0.857562	+	0.514380i	$0.171978\pi$
$613$	11.5407	+	35.5186i	0.466125	+	1.43458i	−0.391438	+	0.920205i	$0.628022\pi$
$614$	15.2624	−	11.0888i	0.615942	−	0.447508i
$615$	−0.131713			−0.00531119
$616$	−0.970624	+	6.10634i	−0.0391076	+	0.246031i
$617$	−42.1641			−1.69746			−0.848731	−	0.528824i	$-0.822633\pi$
$617$	−42.1641			−1.69746			−0.848731	+	0.528824i	$0.822633\pi$
$618$	14.3507	−	10.4264i	0.577268	−	0.419410i
$619$	−0.841647	−	2.59032i	−0.0338287	−	0.104114i	0.932716	−	0.360611i	$-0.117432\pi$
$619$	−0.841647	−	2.59032i	−0.0338287	−	0.104114i	−0.966545	+	0.256497i	$0.917432\pi$
$620$	−10.4224	+	32.0768i	−0.418572	+	1.28823i
$621$	−30.8504	−	22.4142i	−1.23799	−	0.899449i
$622$	−2.40238	−	1.74543i	−0.0963268	−	0.0699855i
$623$	0.960650	−	2.95658i	0.0384876	−	0.118453i
$624$	1.06472	+	3.27687i	0.0426229	+	0.131180i
$625$	−7.26226	+	5.27634i	−0.290490	+	0.211054i
$626$	−3.76746			−0.150578
$627$	4.05057	+	7.96061i	0.161764	+	0.317916i
$628$	−22.6606			−0.904256
$629$	1.23293	−	0.895773i	0.0491600	−	0.0357168i
$630$	−3.39164	−	10.4384i	−0.135126	−	0.415875i
$631$	−7.65239	+	23.5516i	−0.304637	+	0.937576i	0.675176	+	0.737657i	$0.264068\pi$
$631$	−7.65239	+	23.5516i	−0.304637	+	0.937576i	−0.979812	+	0.199919i	$0.935932\pi$
$632$	−3.19939	−	2.32450i	−0.127265	−	0.0924635i
$633$	8.30200	+	6.03176i	0.329975	+	0.239741i
$634$	8.31971	−	25.6054i	0.330418	−	1.01692i
$635$	11.0230	+	33.9254i	0.437436	+	1.34629i
$636$	−3.80870	+	2.76719i	−0.151025	+	0.109726i
$637$	10.1997			0.404125
$638$	−11.8453	+	1.86937i	−0.468960	+	0.0740092i
$639$	11.8812			0.470012
$640$	3.00998	−	2.18688i	0.118980	−	0.0864441i
$641$	−7.89453	−	24.2969i	−0.311815	−	0.959669i	−0.977046	−	0.213030i	$-0.931667\pi$
$641$	−7.89453	−	24.2969i	−0.311815	−	0.959669i	0.665230	−	0.746638i	$-0.268333\pi$
$642$	2.40903	−	7.41423i	0.0950768	−	0.292616i
$643$	−30.0929	−	21.8638i	−1.18675	−	0.862224i	−0.193832	−	0.981035i	$-0.562092\pi$
$643$	−30.0929	−	21.8638i	−1.18675	−	0.862224i	−0.992917	+	0.118811i	$0.962092\pi$
$644$	10.5413	+	7.65871i	0.415386	+	0.301796i
$645$	1.36888	−	4.21298i	0.0538995	−	0.165886i
$646$	0.149216	+	0.459240i	0.00587083	+	0.0180686i
$647$	40.7628	−	29.6159i	1.60255	−	1.16432i	0.720156	−	0.693813i	$-0.244070\pi$
$647$	40.7628	−	29.6159i	1.60255	−	1.16432i	0.882395	−	0.470509i	$-0.155930\pi$
$648$	−1.74878			−0.0686986
$649$	−23.4211	−	11.9500i	−0.919360	−	0.469080i
$650$	−25.5888			−1.00367
$651$	−16.2785	+	11.8270i	−0.638005	+	0.463538i
$652$	4.83011	+	14.8656i	0.189162	+	0.582180i
$653$	3.21727	−	9.90173i	0.125901	−	0.387485i	−0.868163	−	0.496279i	$-0.834699\pi$
$653$	3.21727	−	9.90173i	0.125901	−	0.387485i	0.994064	+	0.108795i	$0.0346992\pi$
$654$	14.1895	+	10.3093i	0.554854	+	0.403125i
$655$	−35.5641	−	25.8388i	−1.38960	−	1.00961i
$656$	−0.00918817	+	0.0282783i	−0.000358738	+	0.00110408i
$657$	6.20352	+	19.0925i	0.242022	+	0.744868i
$658$	0.0884349	−	0.0642517i	0.00344755	−	0.00250479i
$659$	11.7405			0.457344			0.228672	−	0.973504i	$-0.426562\pi$
$659$	11.7405			0.457344			0.228672	+	0.973504i	$0.426562\pi$
$660$	−10.3945	+	10.3830i	−0.404607	+	0.404158i
$661$	−30.8617			−1.20038			−0.600190	−	0.799857i	$-0.704909\pi$
$661$	−30.8617			−1.20038			−0.600190	+	0.799857i	$0.704909\pi$
$662$	−15.5085	+	11.2676i	−0.602756	+	0.437928i
$663$	−0.227300	−	0.699556i	−0.00882759	−	0.0271685i
$664$	3.78924	−	11.6621i	0.147051	−	0.452577i
$665$	12.6922	+	9.22143i	0.492183	+	0.357592i
$666$	9.13885	+	6.63976i	0.354123	+	0.257286i
$667$	−7.80923	+	24.0343i	−0.302375	+	0.930613i
$668$	0.284101	+	0.874372i	0.0109922	+	0.0338305i
$669$	−0.253296	+	0.184030i	−0.00979297	+	0.00711501i
$670$	−28.5736			−1.10390
$671$	19.1043	−	19.0831i	0.737512	−	0.736694i
$672$	2.21962			0.0856238
$673$	15.7113	−	11.4149i	0.605626	−	0.440013i	−0.242246	−	0.970215i	$-0.577884\pi$
$673$	15.7113	−	11.4149i	0.605626	−	0.440013i	0.847871	+	0.530202i	$0.177884\pi$
$674$	−2.30190	−	7.08453i	−0.0886660	−	0.272886i
$675$	14.9082	−	45.8826i	0.573816	−	1.76602i
$676$	3.74218	+	2.71885i	0.143930	+	0.104571i
$677$	6.12834	+	4.45250i	0.235531	+	0.171123i	0.699290	−	0.714838i	$-0.253500\pi$
$677$	6.12834	+	4.45250i	0.235531	+	0.171123i	−0.463759	+	0.885961i	$0.653500\pi$
$678$	0.0518206	−	0.159488i	0.00199016	−	0.00612508i
$679$	3.08311	+	9.48882i	0.118319	+	0.364148i
$680$	−0.642580	+	0.466862i	−0.0246418	+	0.0179033i
$681$	−26.4888			−1.01505
$682$	−26.7813	−	13.6645i	−1.02551	−	0.523241i
$683$	2.04832			0.0783766			0.0391883	−	0.999232i	$-0.487523\pi$
$683$	2.04832			0.0783766			0.0391883	+	0.999232i	$0.487523\pi$
$684$	−2.89565	+	2.10381i	−0.110718	+	0.0804412i
$685$	11.8692	+	36.5295i	0.453497	+	1.39572i
$686$	6.06304	−	18.6601i	0.231488	−	0.712447i
$687$	−21.7599	−	15.8095i	−0.830191	−	0.603169i
$688$	−0.809017	−	0.587785i	−0.0308435	−	0.0224091i
$689$	3.53592	−	10.8825i	0.134708	−	0.414588i
$690$	9.56751	+	29.4458i	0.364229	+	1.12098i
$691$	−21.9026	+	15.9131i	−0.833213	+	0.605365i	−0.920467	−	0.390821i	$-0.872191\pi$
$691$	−21.9026	+	15.9131i	−0.833213	+	0.605365i	0.0872535	+	0.996186i	$0.472191\pi$
$692$	−13.6956			−0.520628
$693$	9.66440	−	1.52519i	0.367120	−	0.0579373i
$694$	17.8121			0.676137
$695$	−26.6067	+	19.3309i	−1.00925	+	0.733262i
$696$	1.33030	+	4.09425i	0.0504250	+	0.155192i
$697$	0.00196152	−	0.00603693i	7.42978e−5	−	0.000228665i
$698$	−0.541382	−	0.393337i	−0.0204916	−	0.0148880i
$699$	13.7693	+	10.0040i	0.520804	+	0.378386i
$700$	−5.09399	+	15.6777i	−0.192535	+	0.592561i
$701$	−6.28967	−	19.3576i	−0.237558	−	0.731128i	−0.996772	−	0.0802866i	$-0.974416\pi$
$701$	−6.28967	−	19.3576i	−0.237558	−	0.731128i	0.759214	−	0.650841i	$-0.225584\pi$
$702$	12.7733	−	9.28037i	0.482098	−	0.350265i
$703$	−16.1468			−0.608988
$704$	1.50408	+	2.95597i	0.0566870	+	0.111407i
$705$	0.259744			0.00978253
$706$	18.0293	−	13.0991i	0.678542	−	0.492990i
$707$	−9.96147	−	30.6582i	−0.374640	−	1.15302i
$708$	−2.91684	+	8.97710i	−0.109621	+	0.337380i
$709$	15.3379	+	11.1436i	0.576026	+	0.418508i	0.837289	−	0.546760i	$-0.184139\pi$
$709$	15.3379	+	11.1436i	0.576026	+	0.418508i	−0.261263	+	0.965268i	$0.584139\pi$
$710$	−22.5999	−	16.4198i	−0.848158	−	0.616223i
$711$	−1.93379	+	5.95160i	−0.0725229	+	0.223203i
$712$	−0.515303	−	1.58594i	−0.0193118	−	0.0594355i
$713$	−51.2589	+	37.2418i	−1.91966	+	1.39472i
$714$	−0.473852			−0.0177335
$715$	5.60572	−	35.2664i	0.209642	−	1.31889i
$716$	25.0964			0.937895
$717$	−12.9362	+	9.39869i	−0.483111	+	0.351001i
$718$	−0.705121	−	2.17014i	−0.0263149	−	0.0809889i
$719$	−5.51930	+	16.9867i	−0.205835	+	0.633496i	0.793843	+	0.608123i	$0.208077\pi$
$719$	−5.51930	+	16.9867i	−0.205835	+	0.633496i	−0.999678	+	0.0253729i	$0.991923\pi$
$720$	−4.76301	−	3.46053i	−0.177507	−	0.128966i
$721$	22.4698	+	16.3252i	0.836818	+	0.607984i
$722$	−4.29036	+	13.2044i	−0.159671	+	0.491415i
$723$	−1.18297	−	3.64080i	−0.0439950	−	0.135403i
$724$	−0.976936	+	0.709786i	−0.0363076	+	0.0263790i
$725$	−31.9716			−1.18740
$726$	−7.68640	−	10.6042i	−0.285269	−	0.393557i
$727$	−30.2703			−1.12266			−0.561331	−	0.827591i	$-0.689711\pi$
$727$	−30.2703			−1.12266			−0.561331	+	0.827591i	$0.689711\pi$
$728$	−4.36453	+	3.17102i	−0.161760	+	0.117526i
$729$	6.87725	+	21.1660i	0.254713	+	0.783926i
$730$	14.5857	−	44.8901i	0.539841	−	1.66146i
$731$	0.172711	+	0.125482i	0.00638796	+	0.00464113i
$732$	−7.84227	−	5.69774i	−0.289859	−	0.210595i
$733$	10.1589	−	31.2660i	0.375229	−	1.15484i	−0.568095	−	0.822963i	$-0.692319\pi$
$733$	10.1589	−	31.2660i	0.375229	−	1.15484i	0.943324	−	0.331873i	$-0.107681\pi$
$734$	0.916910	+	2.82196i	0.0338438	+	0.104160i
$735$	12.6313	−	9.17719i	0.465913	−	0.338506i
$736$	6.98931			0.257629
$737$	3.99859	−	25.1557i	0.147290	−	0.926624i
$738$	0.0470505			0.00173195
$739$	−24.3130	+	17.6644i	−0.894369	+	0.649797i	−0.937014	−	0.349293i	$-0.886422\pi$
$739$	−24.3130	+	17.6644i	−0.894369	+	0.649797i	0.0426443	+	0.999090i	$0.486422\pi$
$740$	−8.20739	−	25.2597i	−0.301710	−	0.928567i
$741$	−2.40827	+	7.41190i	−0.0884701	+	0.272283i
$742$	−5.96354	−	4.33276i	−0.218928	−	0.159061i
$743$	−30.0162	−	21.8080i	−1.10119	−	0.800059i	−0.119933	−	0.992782i	$-0.538268\pi$
$743$	−30.0162	−	21.8080i	−1.10119	−	0.800059i	−0.981253	+	0.192723i	$0.938268\pi$
$744$	−3.33531	+	10.2650i	−0.122278	+	0.376334i
$745$	9.22640	+	28.3959i	0.338029	+	1.04035i
$746$	−8.74642	+	6.35465i	−0.320229	+	0.232660i
$747$	−19.4038			−0.709949
$748$	−0.321095	−	0.631049i	−0.0117404	−	0.0230734i
$749$	12.2064			0.446011
$750$	−13.7705	+	10.0048i	−0.502826	+	0.365324i
$751$	12.1251	+	37.3172i	0.442451	+	1.36172i	0.885255	+	0.465105i	$0.153984\pi$
$751$	12.1251	+	37.3172i	0.442451	+	1.36172i	−0.442805	+	0.896618i	$0.646016\pi$
$752$	0.0181195	−	0.0557660i	0.000660749	−	0.00203358i
$753$	25.8433	+	18.7763i	0.941782	+	0.684245i
$754$	−8.46499	−	6.15018i	−0.308277	−	0.223976i
$755$	−0.866993	+	2.66833i	−0.0315531	+	0.0971105i
$756$	−3.14308	−	9.67339i	−0.114313	−	0.351818i
$757$	22.5728	−	16.4001i	0.820422	−	0.596071i	−0.0964115	−	0.995342i	$-0.530736\pi$
$757$	22.5728	−	16.4001i	0.820422	−	0.596071i	0.916833	+	0.399270i	$0.130736\pi$
$758$	21.8846			0.794886
$759$	−27.2624	+	4.30243i	−0.989563	+	0.156168i
$760$	8.41543			0.305260
$761$	−19.4288	+	14.1158i	−0.704293	+	0.511699i	−0.881327	−	0.472506i	$-0.843349\pi$
$761$	−19.4288	+	14.1158i	−0.704293	+	0.511699i	0.177035	+	0.984205i	$0.443349\pi$
$762$	3.52753	+	10.8566i	0.127789	+	0.393294i
$763$	−8.48631	+	26.1182i	−0.307225	+	0.945542i
$764$	8.69636	+	6.31827i	0.314623	+	0.228587i
$765$	1.01682	+	0.738764i	0.0367633	+	0.0267101i
$766$	−5.95477	+	18.3269i	−0.215154	+	0.662177i
$767$	−7.08946	−	21.8191i	−0.255985	−	0.787842i
$768$	0.963238	−	0.699834i	0.0347579	−	0.0252531i
$769$	−34.0272			−1.22705			−0.613527	−	0.789674i	$-0.710250\pi$
$769$	−34.0272			−1.22705			−0.613527	+	0.789674i	$0.710250\pi$
$770$	−20.4910	−	10.4550i	−0.738445	−	0.376773i
$771$	22.8006			0.821144
$772$	15.2850	−	11.1052i	0.550120	−	0.399685i
$773$	−7.33118	−	22.5630i	−0.263684	−	0.811536i	−0.991994	−	0.126288i	$-0.959694\pi$
$773$	−7.33118	−	22.5630i	−0.263684	−	0.811536i	0.728309	−	0.685248i	$-0.240306\pi$
$774$	−0.488990	+	1.50496i	−0.0175764	+	0.0540945i
$775$	−64.8497	−	47.1160i	−2.32947	−	1.69246i
$776$	4.32973	+	3.14573i	0.155428	+	0.112925i
$777$	4.89641	−	15.0696i	0.175658	−	0.540619i
$778$	2.67319	+	8.22723i	0.0958385	+	0.294961i
$779$	−0.0544094	+	0.0395308i	−0.00194942	+	0.00141634i
$780$	−12.8192			−0.459000
$781$	17.6183	−	17.5988i	0.630433	−	0.629733i
$782$	−1.49210			−0.0533573
$783$	15.9595	−	11.5952i	0.570346	−	0.414380i
$784$	−1.08916	−	3.35208i	−0.0388985	−	0.119717i
$785$	26.0531	−	80.1833i	0.929876	−	2.86186i
$786$	−11.3810	−	8.26880i	−0.405948	−	0.294938i
$787$	44.5538	+	32.3703i	1.58817	+	1.15388i	0.906490	+	0.422228i	$0.138752\pi$
$787$	44.5538	+	32.3703i	1.58817	+	1.15388i	0.681684	+	0.731647i	$0.261248\pi$
$788$	−7.67133	+	23.6099i	−0.273280	+	0.841069i
$789$	5.85718	+	18.0265i	0.208521	+	0.641762i
$790$	11.9035	−	8.64839i	0.423507	−	0.307696i
$791$	0.262571			0.00933596
$792$	3.71313	−	3.70901i	0.131940	−	0.131794i
$793$	23.5605			0.836659
$794$	2.06804	−	1.50252i	0.0733919	−	0.0533224i
$795$	−5.41263	−	16.6584i	−0.191966	−	0.590811i
$796$	−4.51654	+	13.9005i	−0.160085	+	0.492690i
$797$	4.31938	+	3.13822i	0.153000	+	0.111161i	0.661652	−	0.749811i	$-0.269856\pi$
$797$	4.31938	+	3.13822i	0.153000	+	0.111161i	−0.508651	+	0.860973i	$0.669856\pi$
$798$	4.06169	+	2.95099i	0.143782	+	0.104464i
$799$	−0.00386820	+	0.0119051i	−0.000136847	+	0.000421172i
$800$	2.73247	+	8.40967i	0.0966073	+	0.297327i
$801$	−2.13479	+	1.55102i	−0.0754291	+	0.0548024i
$802$	4.75913			0.168051
$803$	37.4794	+	19.1229i	1.32262	+	0.674833i
$804$	−9.14398			−0.322483
$805$	−39.2194	+	28.4946i	−1.38230	+	1.00430i
$806$	−8.10657	−	24.9495i	−0.285542	−	0.878807i
$807$	−8.21785	+	25.2919i	−0.289282	+	0.890318i
$808$	−13.9893	−	10.1638i	−0.492141	−	0.357562i
$809$	−7.85742	−	5.70875i	−0.276252	−	0.200709i	0.441029	−	0.897493i	$-0.354614\pi$
$809$	−7.85742	−	5.70875i	−0.276252	−	0.200709i	−0.717281	+	0.696784i	$0.754614\pi$
$810$	2.01059	−	6.18797i	0.0706450	−	0.217423i
$811$	−9.40358	−	28.9412i	−0.330204	−	1.01626i	−0.969036	−	0.246918i	$-0.920582\pi$
$811$	−9.40358	−	28.9412i	−0.330204	−	1.01626i	0.638832	−	0.769346i	$-0.279418\pi$
$812$	−5.45321	+	3.96199i	−0.191370	+	0.139039i
$813$	−12.1767			−0.427055
$814$	23.3868	−	3.69080i	0.819706	−	0.129362i
$815$	−58.1542			−2.03705
$816$	−0.205635	+	0.149403i	−0.00719866	+	0.00523014i
$817$	−0.698960	−	2.15118i	−0.0244535	−	0.0752602i
$818$	−5.21638	+	16.0544i	−0.182387	+	0.561328i
$819$	6.90646	+	5.01783i	0.241331	+	0.175337i
$820$	−0.0894974	−	0.0650237i	−0.00312539	−	0.00227073i
$821$	−16.2938	+	50.1472i	−0.568658	+	1.75015i	0.0881670	+	0.996106i	$0.471899\pi$
$821$	−16.2938	+	50.1472i	−0.568658	+	1.75015i	−0.656825	+	0.754043i	$0.728101\pi$
$822$	3.79830	+	11.6900i	0.132481	+	0.407735i
$823$	−42.6809	+	31.0095i	−1.48776	+	1.08092i	−0.512811	+	0.858501i	$0.671396\pi$
$823$	−42.6809	+	31.0095i	−1.48776	+	1.08092i	−0.974951	+	0.222421i	$0.928604\pi$
$824$	14.8983			0.519008
$825$	−15.8350	−	31.1206i	−0.551304	−	1.08348i
$826$	−14.7794			−0.514241
$827$	−8.68807	+	6.31226i	−0.302114	+	0.219499i	−0.728505	−	0.685040i	$-0.759785\pi$
$827$	−8.68807	+	6.31226i	−0.302114	+	0.219499i	0.426391	+	0.904539i	$0.359785\pi$
$828$	−3.41770	−	10.5186i	−0.118773	−	0.365547i
$829$	−9.22339	+	28.3867i	−0.320342	+	0.985910i	0.653158	+	0.757222i	$0.273444\pi$
$829$	−9.22339	+	28.3867i	−0.320342	+	0.985910i	−0.973500	+	0.228688i	$0.926556\pi$
$830$	36.9091	+	26.8161i	1.28113	+	0.930799i
$831$	11.4226	+	8.29901i	0.396246	+	0.287889i
$832$	−0.894251	+	2.75222i	−0.0310026	+	0.0954161i
$833$	0.232517	+	0.715613i	0.00805623	+	0.0247945i
$834$	−8.51452	+	6.18616i	−0.294834	+	0.214209i
$835$	−3.42055			−0.118373
$836$	−1.17766	+	7.40880i	−0.0407301	+	0.256239i
$837$	49.4592			1.70956
$838$	0.816789	−	0.593432i	0.0282155	−	0.0204998i
$839$	−11.4087	−	35.1123i	−0.393871	−	1.21221i	−0.929837	−	0.367972i	$-0.880052\pi$
$839$	−11.4087	−	35.1123i	−0.393871	−	1.21221i	0.535966	−	0.844240i	$-0.319948\pi$
$840$	−2.55193	+	7.85402i	−0.0880498	+	0.270989i
$841$	12.8850	+	9.36151i	0.444311	+	0.322811i
$842$	0.722391	+	0.524847i	0.0248952	+	0.0180874i
$843$	−9.08486	+	27.9603i	−0.312899	+	0.963005i
$844$	2.66337	+	8.19701i	0.0916770	+	0.282153i
$845$	−13.9230	+	10.1156i	−0.478964	+	0.347988i
$846$	−0.0927856			−0.00319003
$847$	12.0719	−	16.5769i	0.414797	−	0.569588i
$848$	−3.95406			−0.135783
$849$	−3.49667	+	2.54048i	−0.120005	+	0.0871890i
$850$	−0.583335	−	1.79532i	−0.0200082	−	0.0615790i
$851$	15.4182	−	47.4522i	0.528528	−	1.62664i
$852$	−7.23229	−	5.25456i	−0.247774	−	0.180018i
$853$	37.8066	+	27.4681i	1.29447	+	0.940491i	0.999885	−	0.0151332i	$-0.00481724\pi$
$853$	37.8066	+	27.4681i	1.29447	+	0.940491i	0.294589	+	0.955624i	$0.404817\pi$
$854$	4.69022	−	14.4350i	0.160496	−	0.493956i
$855$	−4.11506	−	12.6649i	−0.140732	−	0.433129i
$856$	5.29714	−	3.84860i	0.181052	−	0.131542i
$857$	40.6408			1.38826			0.694131	−	0.719848i	$-0.255789\pi$
$857$	40.6408			1.38826			0.694131	+	0.719848i	$0.255789\pi$
$858$	1.79391	−	11.2858i	0.0612432	−	0.385290i
$859$	−25.7538			−0.878708			−0.439354	−	0.898314i	$-0.644793\pi$
$859$	−25.7538			−0.878708			−0.439354	+	0.898314i	$0.644793\pi$
$860$	3.00998	−	2.18688i	0.102640	−	0.0745720i
$861$	−0.0203943	−	0.0627671i	−0.000695035	−	0.00213910i
$862$	5.14735	−	15.8419i	0.175319	−	0.539578i
$863$	39.9353	+	29.0147i	1.35941	+	0.987672i	0.998482	+	0.0550804i	$0.0175415\pi$
$863$	39.9353	+	29.0147i	1.35941	+	0.987672i	0.360932	+	0.932592i	$0.382458\pi$
$864$	−4.41395	−	3.20692i	−0.150166	−	0.109102i
$865$	15.7460	−	48.4611i	0.535379	−	1.64773i
$866$	−5.51756	−	16.9813i	−0.187494	−	0.577048i
$867$	−16.3312	+	11.8653i	−0.554635	+	0.402966i
$868$	−16.8998			−0.573615
$869$	5.94812	+	11.6899i	0.201776	+	0.396552i
$870$	−16.0168			−0.543019
$871$	17.9802	−	13.0634i	0.609235	−	0.442635i
$872$	4.55214	+	14.0101i	0.154155	+	0.474441i
$873$	2.61700	−	8.05428i	0.0885719	−	0.272596i
$874$	12.7897	+	9.29229i	0.432619	+	0.314316i
$875$	−21.5613	−	15.6652i	−0.728905	−	0.529581i
$876$	4.66763	−	14.3655i	0.157705	−	0.485365i
$877$	1.60638	+	4.94394i	0.0542438	+	0.166945i	0.974508	−	0.224352i	$-0.0720265\pi$
$877$	1.60638	+	4.94394i	0.0542438	+	0.166945i	−0.920264	+	0.391297i	$0.872027\pi$
$878$	−13.7867	+	10.0166i	−0.465277	+	0.338044i
$879$	−0.844929			−0.0284988
$880$	−12.1888	+	1.92358i	−0.410884	+	0.0648439i
$881$	−16.1650			−0.544612			−0.272306	−	0.962211i	$-0.587786\pi$
$881$	−16.1650			−0.544612			−0.272306	+	0.962211i	$0.587786\pi$
$882$	−4.51215	+	3.27827i	−0.151932	+	0.110385i
$883$	11.8451	+	36.4554i	0.398619	+	1.22682i	0.926107	+	0.377260i	$0.123134\pi$
$883$	11.8451	+	36.4554i	0.398619	+	1.22682i	−0.527489	+	0.849562i	$0.676866\pi$
$884$	0.190907	−	0.587552i	0.00642091	−	0.0197615i
$885$	−28.4115	−	20.6421i	−0.955041	−	0.693878i
$886$	−12.5115	−	9.09014i	−0.420332	−	0.305389i
$887$	8.35951	−	25.7279i	0.280685	−	0.863859i	−0.706974	−	0.707239i	$-0.749940\pi$
$887$	8.35951	−	25.7279i	0.280685	−	0.863859i	0.987659	−	0.156620i	$-0.0500597\pi$
$888$	−2.62648	−	8.08348i	−0.0881390	−	0.271264i
$889$	−14.4602	+	10.5059i	−0.484978	+	0.352357i
$890$	6.20421			0.207966
$891$	5.16642	+	2.63604i	0.173082	+	0.0883105i
$892$	−0.262963			−0.00880464
$893$	0.107298	−	0.0779564i	0.00359058	−	0.00260871i
$894$	2.95258	+	9.08712i	0.0987491	+	0.303919i
$895$	−28.8536	+	88.8022i	−0.964469	+	2.96833i
$896$	1.50821	+	1.09578i	0.0503856	+	0.0366073i
$897$	−19.4825	−	14.1549i	−0.650502	−	0.472617i
$898$	2.89120	−	8.89820i	0.0964806	−	0.296937i
$899$	−10.1287	−	31.1728i	−0.337810	−	1.03967i
$900$	11.3200	−	8.22449i	0.377334	−	0.274150i
$901$	0.844125			0.0281219
$902$	0.0697700	−	0.0696926i	0.00232309	−	0.00232051i
$903$	2.21962			0.0738644
$904$	0.113947	−	0.0827872i	0.00378981	−	0.00275346i
$905$	−1.38835	−	4.27289i	−0.0461502	−	0.142036i
$906$	−0.277450	+	0.853904i	−0.00921767	+	0.0283691i
$907$	29.6727	+	21.5585i	0.985267	+	0.715838i	0.958880	−	0.283813i	$-0.0915997\pi$
$907$	29.6727	+	21.5585i	0.985267	+	0.715838i	0.0263874	+	0.999652i	$0.491600\pi$
$908$	−17.9988	−	13.0769i	−0.597312	−	0.433973i
$909$	−8.45547	+	26.0233i	−0.280450	+	0.863137i
$910$	−6.20253	−	19.0894i	−0.205612	−	0.632808i
$911$	−36.0756	+	26.2104i	−1.19524	+	0.868391i	−0.993808	−	0.111112i	$-0.964559\pi$
$911$	−36.0756	+	26.2104i	−1.19524	+	0.868391i	−0.201429	+	0.979503i	$0.564559\pi$
$912$	2.69306			0.0891762
$913$	−28.7735	+	28.7415i	−0.952263	+	0.951206i
$914$	20.7359			0.685881
$915$	29.1775	−	21.1987i	0.964579	−	0.700808i
$916$	−6.98080	−	21.4847i	−0.230652	−	0.709874i
$917$	6.80664	−	20.9487i	0.224775	−	0.691787i
$918$	0.942303	+	0.684623i	0.0311006	+	0.0225959i
$919$	1.16621	+	0.847303i	0.0384698	+	0.0279500i	0.606854	−	0.794813i	$-0.292431\pi$
$919$	1.16621	+	0.847303i	0.0384698	+	0.0279500i	−0.568384	+	0.822763i	$0.692431\pi$
$920$	−8.03568	+	24.7313i	−0.264929	+	0.815367i
$921$	6.94105	+	21.3623i	0.228715	+	0.703913i
$922$	0.125209	−	0.0909694i	0.00412353	−	0.00299592i
$923$	21.7280			0.715184
$924$	−6.55743	−	3.34576i	−0.215723	−	0.110067i
$925$	63.1232			2.07548
$926$	−7.36650	+	5.35208i	−0.242078	+	0.175880i
$927$	−7.28514	−	22.4214i	−0.239275	−	0.736414i
$928$	−1.11731	+	3.43873i	−0.0366775	+	0.112882i
$929$	21.7709	+	15.8175i	0.714281	+	0.518956i	0.884552	−	0.466442i	$-0.154464\pi$
$929$	21.7709	+	15.8175i	0.714281	+	0.518956i	−0.170271	+	0.985397i	$0.554464\pi$
$930$	−32.4876	−	23.6036i	−1.06531	−	0.773994i
$931$	2.46355	−	7.58202i	0.0807395	−	0.248491i
$932$	4.41735	+	13.5952i	0.144695	+	0.445326i
$933$	2.86034	−	2.07816i	0.0936435	−	0.0680360i
$934$	−27.6725			−0.905473
$935$	2.60210	−	0.410652i	0.0850978	−	0.0134297i
$936$	4.57925			0.149678
$937$	23.5089	−	17.0802i	0.768002	−	0.557986i	−0.133352	−	0.991069i	$-0.542574\pi$
$937$	23.5089	−	17.0802i	0.768002	−	0.557986i	0.901354	+	0.433083i	$0.142574\pi$
$938$	−4.42430	−	13.6166i	−0.144459	−	0.444598i
$939$	1.38614	−	4.26610i	0.0452350	−	0.139219i
$940$	0.176493	+	0.128230i	0.00575656	+	0.00418239i
$941$	−14.1316	−	10.2672i	−0.460678	−	0.334702i	0.333119	−	0.942885i	$-0.391899\pi$
$941$	−14.1316	−	10.2672i	−0.460678	−	0.334702i	−0.793797	+	0.608182i	$0.791899\pi$
$942$	8.33738	−	25.6598i	0.271647	−	0.836042i
$943$	−0.0642189	−	0.197645i	−0.00209126	−	0.00643622i
$944$	−6.41374	+	4.65985i	−0.208749	+	0.151665i
$945$	37.8424			1.23101
$946$	1.50408	+	2.95597i	0.0489017	+	0.0961069i
$947$	−12.8200			−0.416593			−0.208297	−	0.978066i	$-0.566792\pi$
$947$	−12.8200			−0.416593			−0.208297	+	0.978066i	$0.566792\pi$
$948$	3.80929	−	2.76761i	0.123720	−	0.0898878i
$949$	11.3448	+	34.9158i	0.368268	+	1.13341i
$950$	−6.18052	+	19.0217i	−0.200523	+	0.617145i
$951$	25.9334	+	18.8417i	0.840948	+	0.610985i
$952$	−0.321976	−	0.233929i	−0.0104353	−	0.00758170i
$953$	−9.08770	+	27.9691i	−0.294380	+	0.906007i	0.689050	+	0.724714i	$0.258028\pi$
$953$	−9.08770	+	27.9691i	−0.294380	+	0.906007i	−0.983429	+	0.181293i	$0.941972\pi$
$954$	1.93350	+	5.95069i	0.0625993	+	0.192661i
$955$	−32.3552	+	23.5074i	−1.04699	+	0.760682i
$956$	−13.4299			−0.434354
$957$	2.24138	−	14.1009i	0.0724536	−	0.455816i
$958$	−38.4481			−1.24220
$959$	−15.5701	+	11.3123i	−0.502785	+	0.365295i
$960$	1.36888	+	4.21298i	0.0441804	+	0.135973i
$961$	15.8149	−	48.6731i	0.510157	−	1.57010i
$962$	16.7129	+	12.1426i	0.538844	+	0.391493i
$963$	−8.38222	−	6.09004i	−0.270113	−	0.196249i
$964$	0.993566	−	3.05788i	0.0320006	−	0.0984878i
$965$	21.7219	+	66.8530i	0.699251	+	2.15207i
$966$	−12.5508	+	9.11868i	−0.403815	+	0.293389i
$967$	2.09608			0.0674054			0.0337027	−	0.999432i	$-0.489270\pi$
$967$	2.09608			0.0674054			0.0337027	+	0.999432i	$0.489270\pi$
$968$	0.0122123	−	11.0000i	0.000392519	−	0.353553i
$969$	−0.574923			−0.0184692
$970$	−16.1089	+	11.7038i	−0.517227	+	0.375787i
$971$	−4.16156	−	12.8080i	−0.133551	−	0.411027i	0.861811	−	0.507230i	$-0.169330\pi$
$971$	−4.16156	−	12.8080i	−0.133551	−	0.411027i	−0.995362	+	0.0962024i	$0.969330\pi$
$972$	−4.41452	+	13.5865i	−0.141596	+	0.435787i
$973$	−13.3317	−	9.68608i	−0.427396	−	0.310521i
$974$	−14.2066	−	10.3217i	−0.455210	−	0.330729i
$975$	9.41473	−	28.9756i	0.301513	−	0.927961i
$976$	−2.51588	−	7.74309i	−0.0805315	−	0.247850i
$977$	−19.7314	+	14.3357i	−0.631264	+	0.458640i	−0.856838	−	0.515586i	$-0.827574\pi$
$977$	−19.7314	+	14.3357i	−0.631264	+	0.458640i	0.225574	+	0.974226i	$0.427574\pi$
$978$	−18.6102			−0.595089
$979$	−0.868217	+	5.46208i	−0.0277483	+	0.174569i
$980$	13.1134			0.418892
$981$	18.8586	−	13.7016i	0.602108	−	0.437457i
$982$	−5.01922	−	15.4476i	−0.160170	−	0.492952i
$983$	−1.43603	+	4.41964i	−0.0458022	+	0.140965i	−0.971342	−	0.237685i	$-0.923611\pi$
$983$	−1.43603	+	4.41964i	−0.0458022	+	0.140965i	0.925540	+	0.378650i	$0.123611\pi$
$984$	−0.0286405	−	0.0208085i	−0.000913025	−	0.000663352i
$985$	−74.7227	−	54.2892i	−2.38086	−	1.72980i
$986$	0.238527	−	0.734111i	0.00759625	−	0.0233788i
$987$	0.0402184	+	0.123779i	0.00128016	+	0.00393994i
$988$	−5.29547	+	3.84739i	−0.168471	+	0.122402i
$989$	6.98931			0.222247
$990$	8.85510	+	17.4030i	0.281434	+	0.553104i
$991$	−19.8349			−0.630075			−0.315038	−	0.949079i	$-0.602017\pi$
$991$	−19.8349			−0.630075			−0.315038	+	0.949079i	$0.602017\pi$
$992$	−7.33391	+	5.32839i	−0.232852	+	0.169177i
$993$	−7.05296	−	21.7068i	−0.223819	−	0.688844i
$994$	4.32541	−	13.3122i	0.137194	−	0.422239i
$995$	−43.9934	−	31.9631i	−1.39469	−	1.01330i
$996$	11.8115	+	8.58153i	0.374260	+	0.271916i
$997$	4.94008	−	15.2040i	0.156454	−	0.481516i	−0.841851	−	0.539709i	$-0.818534\pi$
$997$	4.94008	−	15.2040i	0.156454	−	0.481516i	0.998305	+	0.0581937i	$0.0185341\pi$
$998$	−9.02974	−	27.7907i	−0.285832	−	0.879699i
$999$	−31.5096	+	22.8931i	−0.996921	+	0.724305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.f.f.861.5	yes	32
11.4	even	5	inner	946.2.f.f.345.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.f.f.345.5	✓	32	11.4	even	5	inner
946.2.f.f.861.5	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.367924 - 1.13235i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.00998 + 2.18688i) q^{5} +(0.963238 + 0.699834i) q^{6} +(-0.576083 + 1.77300i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.28019 - 0.930114i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.367924 - 1.13235i) q^{3} +(0.309017 - 0.951057i) q^{4} +(3.00998 + 2.18688i) q^{5} +(0.963238 + 0.699834i) q^{6} +(-0.576083 + 1.77300i) q^{7} +(0.309017 + 0.951057i) q^{8} +(1.28019 - 0.930114i) q^{9} -3.72054 q^{10} +(0.520653 - 3.27550i) q^{11} -1.19063 q^{12} +(2.34118 - 1.70097i) q^{13} +(-0.576083 - 1.77300i) q^{14} +(1.36888 - 4.21298i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.172711 + 0.125482i) q^{17} +(-0.488990 + 1.50496i) q^{18} +(-0.698960 - 2.15118i) q^{19} +(3.00998 - 2.18688i) q^{20} +2.21962 q^{21} +(1.50408 + 2.95597i) q^{22} +6.98931 q^{23} +(0.963238 - 0.699834i) q^{24} +(2.73247 + 8.40967i) q^{25} +(-0.894251 + 2.75222i) q^{26} +(-4.41395 - 3.20692i) q^{27} +(1.50821 + 1.09578i) q^{28} +(-1.11731 + 3.43873i) q^{29} +(1.36888 + 4.21298i) q^{30} +(-7.33391 + 5.32839i) q^{31} +1.00000 q^{32} +(-3.90059 + 0.615574i) q^{33} -0.213483 q^{34} +(-5.61135 + 4.07688i) q^{35} +(-0.488990 - 1.50496i) q^{36} +(2.20596 - 6.78926i) q^{37} +(1.82990 + 1.32950i) q^{38} +(-2.78747 - 2.02522i) q^{39} +(-1.14971 + 3.53845i) q^{40} +(-0.00918817 - 0.0282783i) q^{41} +(-1.79571 + 1.30466i) q^{42} +1.00000 q^{43} +(-2.95430 - 1.50736i) q^{44} +5.88741 q^{45} +(-5.65447 + 4.10821i) q^{46} +(0.0181195 + 0.0557660i) q^{47} +(-0.367924 + 1.13235i) q^{48} +(2.85145 + 2.07170i) q^{49} +(-7.15369 - 5.19746i) q^{50} +(0.0785456 - 0.241738i) q^{51} +(-0.894251 - 2.75222i) q^{52} +(3.19890 - 2.32414i) q^{53} +5.45594 q^{54} +(8.73029 - 8.72060i) q^{55} -1.86425 q^{56} +(-2.17873 + 1.58294i) q^{57} +(-1.11731 - 3.43873i) q^{58} +(2.44983 - 7.53980i) q^{59} +(-3.58377 - 2.60376i) q^{60} +(6.58667 + 4.78550i) q^{61} +(2.80130 - 8.62152i) q^{62} +(0.911597 + 2.80561i) q^{63} +(-0.809017 + 0.587785i) q^{64} +10.7667 q^{65} +(2.79382 - 2.79072i) q^{66} +7.67996 q^{67} +(0.172711 - 0.125482i) q^{68} +(-2.57154 - 7.91437i) q^{69} +(2.14334 - 6.59653i) q^{70} +(6.07435 + 4.41327i) q^{71} +(1.28019 + 0.930114i) q^{72} +(-3.92031 + 12.0655i) q^{73} +(2.20596 + 6.78926i) q^{74} +(8.51739 - 6.18824i) q^{75} -2.26188 q^{76} +(5.50754 + 2.81008i) q^{77} +3.44551 q^{78} +(-3.19939 + 2.32450i) q^{79} +(-1.14971 - 3.53845i) q^{80} +(-0.540403 + 1.66319i) q^{81} +(0.0240549 + 0.0174769i) q^{82} +(-9.92036 - 7.20756i) q^{83} +(0.685901 - 2.11099i) q^{84} +(0.245444 + 0.755398i) q^{85} +(-0.809017 + 0.587785i) q^{86} +4.30495 q^{87} +(3.27608 - 0.517016i) q^{88} -1.66755 q^{89} +(-4.76301 + 3.46053i) q^{90} +(1.66710 + 5.13082i) q^{91} +(2.15981 - 6.64722i) q^{92} +(8.73195 + 6.34414i) q^{93} +(-0.0474374 - 0.0344653i) q^{94} +(2.60051 - 8.00355i) q^{95} +(-0.367924 - 1.13235i) q^{96} +(4.32973 - 3.14573i) q^{97} -3.52459 q^{98} +(-2.38006 - 4.67754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} + 13 q^{6} + 10 q^{7} - 8 q^{8} - 14 q^{9}+O(q^{10}) \) 32 * q - 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^5 + 13 * q^6 + 10 * q^7 - 8 * q^8 - 14 * q^9	\( 32 q - 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{5} + 13 q^{6} + 10 q^{7} - 8 q^{8} - 14 q^{9} + 2 q^{10} + q^{11} - 22 q^{12} + 11 q^{13} + 10 q^{14} + 8 q^{15} - 8 q^{16} - 13 q^{17} + q^{18} + 39 q^{19} + 2 q^{20} - 2 q^{21} + 6 q^{22} - 26 q^{23} + 13 q^{24} - 28 q^{25} - 4 q^{26} + 28 q^{27} - 16 q^{29} + 8 q^{30} + 7 q^{31} + 32 q^{32} + 4 q^{33} + 12 q^{34} - 52 q^{35} + q^{36} + 20 q^{37} + 14 q^{38} + 6 q^{39} - 3 q^{40} + q^{41} + 8 q^{42} + 32 q^{43} + 11 q^{44} + 64 q^{45} + 14 q^{46} + 47 q^{47} - 2 q^{48} + 4 q^{49} - 3 q^{50} + 8 q^{51} - 4 q^{52} + 25 q^{53} - 82 q^{54} - 11 q^{55} - 20 q^{56} - 81 q^{57} - 16 q^{58} + 45 q^{59} - 2 q^{60} + 2 q^{62} + 36 q^{63} - 8 q^{64} - 106 q^{65} - q^{66} - 48 q^{67} - 13 q^{68} - 35 q^{69} + 48 q^{70} + 45 q^{71} - 14 q^{72} - 20 q^{73} + 20 q^{74} + 66 q^{75} - 106 q^{76} - 10 q^{77} - 34 q^{78} - 38 q^{79} - 3 q^{80} + 69 q^{81} + 36 q^{82} + 58 q^{83} - 7 q^{84} + 59 q^{85} - 8 q^{86} - 58 q^{87} + q^{88} - 12 q^{89} - 31 q^{90} - 9 q^{91} - q^{92} + 19 q^{93} - 18 q^{94} - 46 q^{95} - 2 q^{96} + 80 q^{97} + 44 q^{98} + 5 q^{99}+O(q^{100}) \) 32 * q - 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^5 + 13 * q^6 + 10 * q^7 - 8 * q^8 - 14 * q^9 + 2 * q^10 + q^11 - 22 * q^12 + 11 * q^13 + 10 * q^14 + 8 * q^15 - 8 * q^16 - 13 * q^17 + q^18 + 39 * q^19 + 2 * q^20 - 2 * q^21 + 6 * q^22 - 26 * q^23 + 13 * q^24 - 28 * q^25 - 4 * q^26 + 28 * q^27 - 16 * q^29 + 8 * q^30 + 7 * q^31 + 32 * q^32 + 4 * q^33 + 12 * q^34 - 52 * q^35 + q^36 + 20 * q^37 + 14 * q^38 + 6 * q^39 - 3 * q^40 + q^41 + 8 * q^42 + 32 * q^43 + 11 * q^44 + 64 * q^45 + 14 * q^46 + 47 * q^47 - 2 * q^48 + 4 * q^49 - 3 * q^50 + 8 * q^51 - 4 * q^52 + 25 * q^53 - 82 * q^54 - 11 * q^55 - 20 * q^56 - 81 * q^57 - 16 * q^58 + 45 * q^59 - 2 * q^60 + 2 * q^62 + 36 * q^63 - 8 * q^64 - 106 * q^65 - q^66 - 48 * q^67 - 13 * q^68 - 35 * q^69 + 48 * q^70 + 45 * q^71 - 14 * q^72 - 20 * q^73 + 20 * q^74 + 66 * q^75 - 106 * q^76 - 10 * q^77 - 34 * q^78 - 38 * q^79 - 3 * q^80 + 69 * q^81 + 36 * q^82 + 58 * q^83 - 7 * q^84 + 59 * q^85 - 8 * q^86 - 58 * q^87 + q^88 - 12 * q^89 - 31 * q^90 - 9 * q^91 - q^92 + 19 * q^93 - 18 * q^94 - 46 * q^95 - 2 * q^96 + 80 * q^97 + 44 * q^98 + 5 * q^99

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