LMFDB - Embedded newform 574.2.e.g.247.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(165,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("574.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 11 x^{10} - 8 x^{9} + 85 x^{8} - 60 x^{7} + 305 x^{6} - 145 x^{5} + 748 x^{4} + \cdots + 1 $ x^12 - x^11 + 11x^10 - 8x^9 + 85x^8 - 60x^7 + 305x^6 - 145x^5 + 748x^4 - 450x^3 + 300x^2 - 18x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.4
Root			$1.14160 + 1.97731i$ of defining polynomial
Character	$\chi$	$=$	574.247
Dual form			574.2.e.g.165.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.243160 + 0.421166i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.308156 + 0.533741i) q^{5} +0.486321 q^{6} +(-0.833444 + 2.51105i) q^{7} -1.00000 q^{8} +(1.38175 - 2.39325i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.243160 + 0.421166i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.308156 + 0.533741i) q^{5} +0.486321 q^{6} +(-0.833444 + 2.51105i) q^{7} -1.00000 q^{8} +(1.38175 - 2.39325i) q^{9} +(0.308156 + 0.533741i) q^{10} +(0.840241 + 1.45534i) q^{11} +(0.243160 - 0.421166i) q^{12} +5.11251 q^{13} +(1.75791 + 1.97731i) q^{14} -0.299725 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.18990 + 3.79302i) q^{17} +(-1.38175 - 2.39325i) q^{18} +(3.82849 - 6.63113i) q^{19} +0.616311 q^{20} +(-1.26023 + 0.259569i) q^{21} +1.68048 q^{22} +(-1.20166 + 2.08133i) q^{23} +(-0.243160 - 0.421166i) q^{24} +(2.31008 + 4.00118i) q^{25} +(2.55626 - 4.42756i) q^{26} +2.80291 q^{27} +(2.59135 - 0.533741i) q^{28} +4.00988 q^{29} +(-0.149862 + 0.259569i) q^{30} +(-2.01174 - 3.48443i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.408627 + 0.707762i) q^{33} +4.37980 q^{34} +(-1.08342 - 1.21864i) q^{35} -2.76349 q^{36} +(-2.07634 + 3.59632i) q^{37} +(-3.82849 - 6.63113i) q^{38} +(1.24316 + 2.15322i) q^{39} +(0.308156 - 0.533741i) q^{40} +1.00000 q^{41} +(-0.405321 + 1.22118i) q^{42} -9.35336 q^{43} +(0.840241 - 1.45534i) q^{44} +(0.851585 + 1.47499i) q^{45} +(1.20166 + 2.08133i) q^{46} +(-1.45469 + 2.51960i) q^{47} -0.486321 q^{48} +(-5.61074 - 4.18564i) q^{49} +4.62016 q^{50} +(-1.06500 + 1.84463i) q^{51} +(-2.55626 - 4.42756i) q^{52} +(2.91511 + 5.04913i) q^{53} +(1.40145 - 2.42739i) q^{54} -1.03570 q^{55} +(0.833444 - 2.51105i) q^{56} +3.72375 q^{57} +(2.00494 - 3.47266i) q^{58} +(-5.67294 - 9.82582i) q^{59} +(0.149862 + 0.259569i) q^{60} +(0.539580 - 0.934580i) q^{61} -4.02347 q^{62} +(4.85797 + 5.46428i) q^{63} +1.00000 q^{64} +(-1.57545 + 2.72876i) q^{65} +(0.408627 + 0.707762i) q^{66} +(-6.31561 - 10.9390i) q^{67} +(2.18990 - 3.79302i) q^{68} -1.16878 q^{69} +(-1.59708 + 0.328950i) q^{70} +6.87059 q^{71} +(-1.38175 + 2.39325i) q^{72} +(2.29262 + 3.97093i) q^{73} +(2.07634 + 3.59632i) q^{74} +(-1.12344 + 1.94586i) q^{75} -7.65697 q^{76} +(-4.35473 + 0.896942i) q^{77} +2.48632 q^{78} +(-4.74642 + 8.22104i) q^{79} +(-0.308156 - 0.533741i) q^{80} +(-3.46368 - 5.99927i) q^{81} +(0.500000 - 0.866025i) q^{82} +4.98021 q^{83} +(0.854909 + 0.961607i) q^{84} -2.69932 q^{85} +(-4.67668 + 8.10025i) q^{86} +(0.975044 + 1.68883i) q^{87} +(-0.840241 - 1.45534i) q^{88} +(1.10797 - 1.91905i) q^{89} +1.70317 q^{90} +(-4.26099 + 12.8378i) q^{91} +2.40331 q^{92} +(0.978349 - 1.69455i) q^{93} +(1.45469 + 2.51960i) q^{94} +(2.35954 + 4.08684i) q^{95} +(-0.243160 + 0.421166i) q^{96} -15.8435 q^{97} +(-6.43024 + 2.76622i) q^{98} +4.64400 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9	$ 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9} - q^{11} - q^{12} + 8 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} + q^{17} + 5 q^{18} + 3 q^{19} - 6 q^{21} - 2 q^{22} - 21 q^{23} + q^{24} + 4 q^{26} + 26 q^{27} + 2 q^{28} + 10 q^{29} + 2 q^{30} - 3 q^{31} + 6 q^{32} + 19 q^{33} + 2 q^{34} - 51 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 11 q^{39} + 12 q^{41} - 6 q^{42} + 24 q^{43} - q^{44} - 28 q^{45} + 21 q^{46} + 18 q^{47} + 2 q^{48} - 15 q^{49} - 13 q^{51} - 4 q^{52} - 14 q^{53} + 13 q^{54} - 14 q^{55} + q^{56} + 10 q^{57} + 5 q^{58} - 16 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{62} - 41 q^{63} + 12 q^{64} - 18 q^{65} - 19 q^{66} + 13 q^{67} + q^{68} + 30 q^{69} - 12 q^{70} + 22 q^{71} + 5 q^{72} - q^{73} - 2 q^{74} + 23 q^{75} - 6 q^{76} - 11 q^{77} + 22 q^{78} - 19 q^{79} + 6 q^{81} + 6 q^{82} + 30 q^{83} - 4 q^{85} + 12 q^{86} - 10 q^{87} + q^{88} + 14 q^{89} - 56 q^{90} + 5 q^{91} + 42 q^{92} - 35 q^{93} - 18 q^{94} - 24 q^{95} + q^{96} + 2 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9 - q^11 - q^12 + 8 * q^13 + q^14 + 4 * q^15 - 6 * q^16 + q^17 + 5 * q^18 + 3 * q^19 - 6 * q^21 - 2 * q^22 - 21 * q^23 + q^24 + 4 * q^26 + 26 * q^27 + 2 * q^28 + 10 * q^29 + 2 * q^30 - 3 * q^31 + 6 * q^32 + 19 * q^33 + 2 * q^34 - 51 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 12 * q^41 - 6 * q^42 + 24 * q^43 - q^44 - 28 * q^45 + 21 * q^46 + 18 * q^47 + 2 * q^48 - 15 * q^49 - 13 * q^51 - 4 * q^52 - 14 * q^53 + 13 * q^54 - 14 * q^55 + q^56 + 10 * q^57 + 5 * q^58 - 16 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^62 - 41 * q^63 + 12 * q^64 - 18 * q^65 - 19 * q^66 + 13 * q^67 + q^68 + 30 * q^69 - 12 * q^70 + 22 * q^71 + 5 * q^72 - q^73 - 2 * q^74 + 23 * q^75 - 6 * q^76 - 11 * q^77 + 22 * q^78 - 19 * q^79 + 6 * q^81 + 6 * q^82 + 30 * q^83 - 4 * q^85 + 12 * q^86 - 10 * q^87 + q^88 + 14 * q^89 - 56 * q^90 + 5 * q^91 + 42 * q^92 - 35 * q^93 - 18 * q^94 - 24 * q^95 + q^96 + 2 * q^97 + 6 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.243160	+	0.421166i	0.140389	+	0.243160i	0.927643	−	0.373468i	$-0.121831\pi$
$3$	0.243160	+	0.421166i	0.140389	+	0.243160i	−0.787254	+	0.616628i	$0.788498\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.308156	+	0.533741i	−0.137811	+	0.238696i	−0.926668	−	0.375881i	$-0.877340\pi$
$5$	−0.308156	+	0.533741i	−0.137811	+	0.238696i	0.788857	+	0.614577i	$0.210673\pi$
$6$	0.486321			0.198540
$7$	−0.833444	+	2.51105i	−0.315012	+	0.949088i
$7$	−0.833444	+	2.51105i	−0.315012	+	0.949088i
$8$	−1.00000			−0.353553
$9$	1.38175	−	2.39325i	0.460582	−	0.797751i
$10$	0.308156	+	0.533741i	0.0974473	+	0.168784i
$11$	0.840241	+	1.45534i	0.253342	+	0.438802i	0.964444	−	0.264288i	$-0.0851368\pi$
$11$	0.840241	+	1.45534i	0.253342	+	0.438802i	−0.711102	+	0.703089i	$0.751803\pi$
$12$	0.243160	−	0.421166i	0.0701944	−	0.121580i
$13$	5.11251			1.41796			0.708978	−	0.705231i	$-0.249157\pi$
$13$	5.11251			1.41796			0.708978	+	0.705231i	$0.249157\pi$
$14$	1.75791	+	1.97731i	0.469821	+	0.528458i
$15$	−0.299725			−0.0773887
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.18990	+	3.79302i	0.531129	+	0.919943i	0.999340	+	0.0363259i	$0.0115654\pi$
$17$	2.18990	+	3.79302i	0.531129	+	0.919943i	−0.468211	+	0.883617i	$0.655101\pi$
$18$	−1.38175	−	2.39325i	−0.325681	−	0.564095i
$19$	3.82849	−	6.63113i	0.878315	−	1.52129i	0.0251263	−	0.999684i	$-0.492001\pi$
$19$	3.82849	−	6.63113i	0.878315	−	1.52129i	0.853189	−	0.521602i	$-0.174665\pi$
$20$	0.616311			0.137811
$21$	−1.26023	+	0.259569i	−0.275005	+	0.0566427i
$22$	1.68048			0.358280
$23$	−1.20166	+	2.08133i	−0.250563	+	0.433987i	−0.963681	−	0.267057i	$-0.913949\pi$
$23$	−1.20166	+	2.08133i	−0.250563	+	0.433987i	0.713118	+	0.701044i	$0.247282\pi$
$24$	−0.243160	−	0.421166i	−0.0496349	−	0.0859702i
$25$	2.31008	+	4.00118i	0.462016	+	0.800235i
$26$	2.55626	−	4.42756i	0.501323	−	0.868317i
$27$	2.80291			0.539420
$28$	2.59135	−	0.533741i	0.489720	−	0.100868i
$29$	4.00988			0.744616			0.372308	−	0.928109i	$-0.378567\pi$
$29$	4.00988			0.744616			0.372308	+	0.928109i	$0.378567\pi$
$30$	−0.149862	+	0.259569i	−0.0273610	+	0.0473907i
$31$	−2.01174	−	3.48443i	−0.361318	−	0.625822i	0.626860	−	0.779132i	$-0.284340\pi$
$31$	−2.01174	−	3.48443i	−0.361318	−	0.625822i	−0.988178	+	0.153310i	$0.951007\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.408627	+	0.707762i	−0.0711328	+	0.123206i
$34$	4.37980			0.751130
$35$	−1.08342	−	1.21864i	−0.183131	−	0.205987i
$36$	−2.76349			−0.460582
$37$	−2.07634	+	3.59632i	−0.341348	+	0.591232i	−0.984683	−	0.174352i	$-0.944217\pi$
$37$	−2.07634	+	3.59632i	−0.341348	+	0.591232i	0.643335	+	0.765585i	$0.277550\pi$
$38$	−3.82849	−	6.63113i	−0.621063	−	1.07571i
$39$	1.24316	+	2.15322i	0.199065	+	0.344791i
$40$	0.308156	−	0.533741i	0.0487237	−	0.0843919i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−0.405321	+	1.22118i	−0.0625425	+	0.188432i
$43$	−9.35336			−1.42637			−0.713187	−	0.700974i	$-0.752749\pi$
$43$	−9.35336			−1.42637			−0.713187	+	0.700974i	$0.752749\pi$
$44$	0.840241	−	1.45534i	0.126671	−	0.219401i
$45$	0.851585	+	1.47499i	0.126947	+	0.219878i
$46$	1.20166	+	2.08133i	0.177174	+	0.306875i
$47$	−1.45469	+	2.51960i	−0.212189	+	0.367522i	−0.952399	−	0.304853i	$-0.901393\pi$
$47$	−1.45469	+	2.51960i	−0.212189	+	0.367522i	0.740210	+	0.672375i	$0.234726\pi$
$48$	−0.486321			−0.0701944
$49$	−5.61074	−	4.18564i	−0.801534	−	0.597949i
$50$	4.62016			0.653389
$51$	−1.06500	+	1.84463i	−0.149129	+	0.258299i
$52$	−2.55626	−	4.42756i	−0.354489	−	0.613993i
$53$	2.91511	+	5.04913i	0.400422	+	0.693551i	0.993777	−	0.111390i	$-0.0355303\pi$
$53$	2.91511	+	5.04913i	0.400422	+	0.693551i	−0.593355	+	0.804941i	$0.702197\pi$
$54$	1.40145	−	2.42739i	0.190714	−	0.330326i
$55$	−1.03570			−0.139654
$56$	0.833444	−	2.51105i	0.111374	−	0.335553i
$57$	3.72375			0.493222
$58$	2.00494	−	3.47266i	0.263261	−	0.455982i
$59$	−5.67294	−	9.82582i	−0.738554	−	1.27921i	−0.953146	−	0.302510i	$-0.902176\pi$
$59$	−5.67294	−	9.82582i	−0.738554	−	1.27921i	0.214592	−	0.976704i	$-0.431158\pi$
$60$	0.149862	+	0.259569i	0.0193472	+	0.0335103i
$61$	0.539580	−	0.934580i	0.0690861	−	0.119661i	−0.829413	−	0.558636i	$-0.811325\pi$
$61$	0.539580	−	0.934580i	0.0690861	−	0.119661i	0.898499	+	0.438975i	$0.144658\pi$
$62$	−4.02347			−0.510981
$63$	4.85797	+	5.46428i	0.612047	+	0.688434i
$64$	1.00000			0.125000
$65$	−1.57545	+	2.72876i	−0.195410	+	0.338461i
$66$	0.408627	+	0.707762i	0.0502985	+	0.0871195i
$67$	−6.31561	−	10.9390i	−0.771575	−	1.33641i	−0.936699	−	0.350134i	$-0.886136\pi$
$67$	−6.31561	−	10.9390i	−0.771575	−	1.33641i	0.165124	−	0.986273i	$-0.447197\pi$
$68$	2.18990	−	3.79302i	0.265565	−	0.459971i
$69$	−1.16878			−0.140705
$70$	−1.59708	+	0.328950i	−0.190888	+	0.0393171i
$71$	6.87059			0.815389			0.407695	−	0.913118i	$-0.366333\pi$
$71$	6.87059			0.815389			0.407695	+	0.913118i	$0.366333\pi$
$72$	−1.38175	+	2.39325i	−0.162840	+	0.282048i
$73$	2.29262	+	3.97093i	0.268331	+	0.464762i	0.968431	−	0.249282i	$-0.0801947\pi$
$73$	2.29262	+	3.97093i	0.268331	+	0.464762i	−0.700100	+	0.714045i	$0.746861\pi$
$74$	2.07634	+	3.59632i	0.241370	+	0.418064i
$75$	−1.12344	+	1.94586i	−0.129724	+	0.224688i
$76$	−7.65697			−0.878315
$77$	−4.35473	+	0.896942i	−0.496267	+	0.102216i
$78$	2.48632			0.281520
$79$	−4.74642	+	8.22104i	−0.534014	+	0.924940i	0.465196	+	0.885208i	$0.345984\pi$
$79$	−4.74642	+	8.22104i	−0.534014	+	0.924940i	−0.999210	+	0.0397321i	$0.987350\pi$
$80$	−0.308156	−	0.533741i	−0.0344528	−	0.0596741i
$81$	−3.46368	−	5.99927i	−0.384854	−	0.666586i
$82$	0.500000	−	0.866025i	0.0552158	−	0.0956365i
$83$	4.98021			0.546649			0.273324	−	0.961922i	$-0.411877\pi$
$83$	4.98021			0.546649			0.273324	+	0.961922i	$0.411877\pi$
$84$	0.854909	+	0.961607i	0.0932782	+	0.104920i
$85$	−2.69932			−0.292782
$86$	−4.67668	+	8.10025i	−0.504300	+	0.873472i
$87$	0.975044	+	1.68883i	0.104536	+	0.181061i
$88$	−0.840241	−	1.45534i	−0.0895700	−	0.155140i
$89$	1.10797	−	1.91905i	0.117444	−	0.203419i	−0.801310	−	0.598249i	$-0.795863\pi$
$89$	1.10797	−	1.91905i	0.117444	−	0.203419i	0.918754	+	0.394830i	$0.129197\pi$
$90$	1.70317			0.179530
$91$	−4.26099	+	12.8378i	−0.446673	+	1.34576i
$92$	2.40331			0.250563
$93$	0.978349	−	1.69455i	0.101450	−	0.175717i
$94$	1.45469	+	2.51960i	0.150040	+	0.259877i
$95$	2.35954	+	4.08684i	0.242084	+	0.419301i
$96$	−0.243160	+	0.421166i	−0.0248175	+	0.0429851i
$97$	−15.8435			−1.60867			−0.804334	−	0.594178i	$-0.797477\pi$
$97$	−15.8435			−1.60867			−0.804334	+	0.594178i	$0.797477\pi$
$98$	−6.43024	+	2.76622i	−0.649552	+	0.279431i
$99$	4.64400			0.466739
$100$	2.31008	−	4.00118i	0.231008	−	0.400118i
$101$	−1.45005	−	2.51156i	−0.144286	−	0.249910i	0.784821	−	0.619723i	$-0.212755\pi$
$101$	−1.45005	−	2.51156i	−0.144286	−	0.249910i	−0.929106	+	0.369813i	$0.879422\pi$
$102$	1.06500	+	1.84463i	0.105450	+	0.182645i
$103$	4.72199	−	8.17872i	0.465271	−	0.805873i	−0.533943	−	0.845521i	$-0.679290\pi$
$103$	4.72199	−	8.17872i	0.465271	−	0.805873i	0.999214	+	0.0396474i	$0.0126235\pi$
$104$	−5.11251			−0.501323
$105$	0.249804	−	0.752624i	0.0243784	−	0.0734486i
$106$	5.83023			0.566282
$107$	−9.56832	+	16.5728i	−0.925005	+	1.60216i	−0.133451	+	0.991055i	$0.542606\pi$
$107$	−9.56832	+	16.5728i	−0.925005	+	1.60216i	−0.791553	+	0.611100i	$0.790727\pi$
$108$	−1.40145	−	2.42739i	−0.134855	−	0.233576i
$109$	−2.66993	−	4.62445i	−0.255733	−	0.442942i	0.709362	−	0.704845i	$-0.248983\pi$
$109$	−2.66993	−	4.62445i	−0.255733	−	0.442942i	−0.965094	+	0.261903i	$0.915650\pi$
$110$	−0.517850	+	0.896942i	−0.0493750	+	0.0855201i
$111$	−2.01953			−0.191686
$112$	−1.75791	−	1.97731i	−0.166107	−	0.186838i
$113$	7.95104			0.747971			0.373986	−	0.927435i	$-0.377991\pi$
$113$	7.95104			0.747971			0.373986	+	0.927435i	$0.377991\pi$
$114$	1.86187	−	3.22486i	0.174380	−	0.302036i
$115$	−0.740594	−	1.28275i	−0.0690607	−	0.119617i
$116$	−2.00494	−	3.47266i	−0.186154	−	0.322428i
$117$	7.06419	−	12.2355i	0.653085	−	1.13118i
$118$	−11.3459			−1.04447
$119$	−11.3496	+	2.33768i	−1.04042	+	0.214295i
$120$	0.299725			0.0273610
$121$	4.08799	−	7.08061i	0.371635	−	0.643691i
$122$	−0.539580	−	0.934580i	−0.0488513	−	0.0846129i
$123$	0.243160	+	0.421166i	0.0219250	+	0.0379753i
$124$	−2.01174	+	3.48443i	−0.180659	+	0.312911i
$125$	−5.92901			−0.530307
$126$	7.16119	−	1.47499i	0.637969	−	0.131402i
$127$	−12.2391			−1.08605			−0.543023	−	0.839718i	$-0.682720\pi$
$127$	−12.2391			−1.08605			−0.543023	+	0.839718i	$0.682720\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−2.27437	−	3.93932i	−0.200247	−	0.346838i
$130$	1.57545	+	2.72876i	0.138176	+	0.239328i
$131$	−0.619016	+	1.07217i	−0.0540837	+	0.0936757i	−0.891800	−	0.452430i	$-0.850557\pi$
$131$	−0.619016	+	1.07217i	−0.0540837	+	0.0936757i	0.837716	+	0.546106i	$0.183890\pi$
$132$	0.817254			0.0711328
$133$	13.4603	+	15.1402i	1.16715	+	1.31282i
$134$	−12.6312			−1.09117
$135$	−0.863731	+	1.49603i	−0.0743381	+	0.128757i
$136$	−2.18990	−	3.79302i	−0.187783	−	0.325249i
$137$	−7.75680	−	13.4352i	−0.662708	−	1.14784i	−0.979901	−	0.199484i	$-0.936074\pi$
$137$	−7.75680	−	13.4352i	−0.662708	−	1.14784i	0.317193	−	0.948361i	$-0.397260\pi$
$138$	−0.584390	+	1.01219i	−0.0497466	+	0.0861637i
$139$	17.9970			1.52649			0.763243	−	0.646112i	$-0.223606\pi$
$139$	17.9970			1.52649			0.763243	+	0.646112i	$0.223606\pi$
$140$	−0.513661	+	1.54759i	−0.0434123	+	0.130795i
$141$	−1.41490			−0.119156
$142$	3.43530	−	5.95011i	0.288284	−	0.499322i
$143$	4.29574	+	7.44044i	0.359228	+	0.622201i
$144$	1.38175	+	2.39325i	0.115145	+	0.199438i
$145$	−1.23567	+	2.14024i	−0.102616	+	0.177737i
$146$	4.58524			0.379477
$147$	0.398540	−	3.38084i	0.0328710	−	0.278847i
$148$	4.15268			0.341348
$149$	−7.23394	+	12.5296i	−0.592628	+	1.02646i	0.401249	+	0.915969i	$0.368576\pi$
$149$	−7.23394	+	12.5296i	−0.592628	+	1.02646i	−0.993877	+	0.110492i	$0.964757\pi$
$150$	1.12344	+	1.94586i	0.0917285	+	0.158878i
$151$	−1.07063	−	1.85438i	−0.0871265	−	0.150908i	0.819169	−	0.573552i	$-0.194435\pi$
$151$	−1.07063	−	1.85438i	−0.0871265	−	0.150908i	−0.906295	+	0.422645i	$0.861102\pi$
$152$	−3.82849	+	6.63113i	−0.310531	+	0.537856i
$153$	12.1035			0.978514
$154$	−1.40059	+	4.21977i	−0.112863	+	0.340039i
$155$	2.47971			0.199175
$156$	1.24316	−	2.15322i	0.0995325	−	0.172395i
$157$	2.68916	+	4.65776i	0.214618	+	0.371730i	0.953154	−	0.302484i	$-0.0978159\pi$
$157$	2.68916	+	4.65776i	0.214618	+	0.371730i	−0.738536	+	0.674214i	$0.764483\pi$
$158$	4.74642	+	8.22104i	0.377605	+	0.654031i
$159$	−1.41768	+	2.45550i	−0.112429	+	0.194733i
$160$	−0.616311			−0.0487237
$161$	−4.22481	−	4.75209i	−0.332961	−	0.374517i
$162$	−6.92736			−0.544265
$163$	−4.22210	+	7.31289i	−0.330700	+	0.572790i	−0.982649	−	0.185473i	$-0.940618\pi$
$163$	−4.22210	+	7.31289i	−0.330700	+	0.572790i	0.651949	+	0.758263i	$0.273952\pi$
$164$	−0.500000	−	0.866025i	−0.0390434	−	0.0676252i
$165$	−0.251841	−	0.436202i	−0.0196058	−	0.0339583i
$166$	2.49010	−	4.31299i	0.193270	−	0.334753i
$167$	−13.3726			−1.03481			−0.517403	−	0.855742i	$-0.673101\pi$
$167$	−13.3726			−1.03481			−0.517403	+	0.855742i	$0.673101\pi$
$168$	1.26023	−	0.259569i	0.0972289	−	0.0200262i
$169$	13.1378			1.01060
$170$	−1.34966	+	2.33768i	−0.103514	+	0.179292i
$171$	−10.5800	−	18.3251i	−0.809072	−	1.40135i
$172$	4.67668	+	8.10025i	0.356594	+	0.617638i
$173$	1.85534	−	3.21355i	0.141059	−	0.244321i	−0.786837	−	0.617161i	$-0.788283\pi$
$173$	1.85534	−	3.21355i	0.141059	−	0.244321i	0.927896	+	0.372840i	$0.121616\pi$
$174$	1.95009			0.147836
$175$	−11.9725	+	2.46597i	−0.905034	+	0.186410i
$176$	−1.68048			−0.126671
$177$	2.75887	−	4.77850i	0.207369	−	0.359174i
$178$	−1.10797	−	1.91905i	−0.0830455	−	0.143839i
$179$	3.01323	+	5.21906i	0.225219	+	0.390091i	0.956385	−	0.292109i	$-0.0943569\pi$
$179$	3.01323	+	5.21906i	0.225219	+	0.390091i	−0.731166	+	0.682199i	$0.761024\pi$
$180$	0.851585	−	1.47499i	0.0634734	−	0.109939i
$181$	−11.8265			−0.879053			−0.439527	−	0.898230i	$-0.644854\pi$
$181$	−11.8265			−0.879053			−0.439527	+	0.898230i	$0.644854\pi$
$182$	8.98734	+	10.1090i	0.666186	+	0.749330i
$183$	0.524818			0.0387957
$184$	1.20166	−	2.08133i	0.0885872	−	0.153438i
$185$	−1.27967	−	2.21645i	−0.0940833	−	0.162957i
$186$	−0.978349	−	1.69455i	−0.0717361	−	0.124250i
$187$	−3.68009	+	6.37410i	−0.269115	+	0.466121i
$188$	2.90939			0.212189
$189$	−2.33607	+	7.03824i	−0.169924	+	0.511957i
$190$	4.71908			0.342358
$191$	−3.76217	+	6.51627i	−0.272221	+	0.471501i	−0.969430	−	0.245367i	$-0.921092\pi$
$191$	−3.76217	+	6.51627i	−0.272221	+	0.471501i	0.697209	+	0.716868i	$0.254425\pi$
$192$	0.243160	+	0.421166i	0.0175486	+	0.0303951i
$193$	−0.859793	−	1.48920i	−0.0618892	−	0.107195i	0.833421	−	0.552639i	$-0.186379\pi$
$193$	−0.859793	−	1.48920i	−0.0618892	−	0.107195i	−0.895310	+	0.445444i	$0.853046\pi$
$194$	−7.92177	+	13.7209i	−0.568750	+	0.985103i
$195$	−1.53235			−0.109734
$196$	−0.819500	+	6.95186i	−0.0585357	+	0.496562i
$197$	17.3709			1.23763			0.618813	−	0.785538i	$-0.287614\pi$
$197$	17.3709			1.23763			0.618813	+	0.785538i	$0.287614\pi$
$198$	2.32200	−	4.02182i	0.165017	−	0.285818i
$199$	−10.0157	−	17.3478i	−0.709997	−	1.22975i	−0.964858	−	0.262773i	$-0.915363\pi$
$199$	−10.0157	−	17.3478i	−0.709997	−	1.22975i	0.254860	−	0.966978i	$-0.417971\pi$
$200$	−2.31008	−	4.00118i	−0.163347	−	0.282926i
$201$	3.07142	−	5.31985i	0.216641	−	0.375233i
$202$	−2.90010			−0.204051
$203$	−3.34201	+	10.0690i	−0.234563	+	0.706706i
$204$	2.12999			0.149129
$205$	−0.308156	+	0.533741i	−0.0215225	+	0.0372781i
$206$	−4.72199	−	8.17872i	−0.328996	−	0.569839i
$207$	3.32077	+	5.75173i	0.230809	+	0.399773i
$208$	−2.55626	+	4.42756i	−0.177244	+	0.306996i
$209$	12.8674			0.890057
$210$	−0.526890	−	0.592649i	−0.0363588	−	0.0408967i
$211$	−3.19398			−0.219883			−0.109941	−	0.993938i	$-0.535066\pi$
$211$	−3.19398			−0.219883			−0.109941	+	0.993938i	$0.535066\pi$
$212$	2.91511	−	5.04913i	0.200211	−	0.346775i
$213$	1.67066	+	2.89366i	0.114472	+	0.198270i
$214$	9.56832	+	16.5728i	0.654077	+	1.13289i
$215$	2.88229	−	4.99227i	0.196571	−	0.340470i
$216$	−2.80291			−0.190714
$217$	10.4262	−	2.14749i	0.707780	−	0.145781i
$218$	−5.33986			−0.361661
$219$	−1.11495	+	1.93115i	−0.0753412	+	0.130495i
$220$	0.517850	+	0.896942i	0.0349134	+	0.0604718i
$221$	11.1959	+	19.3919i	0.753117	+	1.30444i
$222$	−1.00977	+	1.74897i	−0.0677711	+	0.117383i
$223$	3.67068			0.245807			0.122903	−	0.992419i	$-0.460779\pi$
$223$	3.67068			0.245807			0.122903	+	0.992419i	$0.460779\pi$
$224$	−2.59135	+	0.533741i	−0.173142	+	0.0356621i
$225$	12.7678			0.851185
$226$	3.97552	−	6.88580i	0.264448	−	0.458037i
$227$	4.53263	+	7.85075i	0.300841	+	0.521072i	0.976327	−	0.216301i	$-0.0693992\pi$
$227$	4.53263	+	7.85075i	0.300841	+	0.521072i	−0.675486	+	0.737373i	$0.736066\pi$
$228$	−1.86187	−	3.22486i	−0.123306	−	0.213572i
$229$	8.50486	−	14.7308i	0.562017	−	0.973442i	−0.435303	−	0.900284i	$-0.643359\pi$
$229$	8.50486	−	14.7308i	0.562017	−	0.973442i	0.997320	−	0.0731580i	$-0.0233077\pi$
$230$	−1.48119			−0.0976666
$231$	−1.43666	−	1.61596i	−0.0945252	−	0.106323i
$232$	−4.00988			−0.263261
$233$	−2.41717	+	4.18667i	−0.158354	+	0.274278i	−0.934275	−	0.356552i	$-0.883952\pi$
$233$	−2.41717	+	4.18667i	−0.158354	+	0.274278i	0.775921	+	0.630830i	$0.217285\pi$
$234$	−7.06419	−	12.2355i	−0.461801	−	0.799862i
$235$	−0.896544	−	1.55286i	−0.0584841	−	0.101297i
$236$	−5.67294	+	9.82582i	−0.369277	+	0.639607i
$237$	−4.61657			−0.299878
$238$	−3.65032	+	10.9979i	−0.236615	+	0.712888i
$239$	9.41859			0.609238			0.304619	−	0.952474i	$-0.401471\pi$
$239$	9.41859			0.609238			0.304619	+	0.952474i	$0.401471\pi$
$240$	0.149862	−	0.259569i	0.00967358	−	0.0167551i
$241$	−13.6864	−	23.7056i	−0.881620	−	1.52701i	−0.849539	−	0.527526i	$-0.823120\pi$
$241$	−13.6864	−	23.7056i	−0.881620	−	1.52701i	−0.0320818	−	0.999485i	$-0.510214\pi$
$242$	−4.08799	−	7.08061i	−0.262786	−	0.455159i
$243$	5.88882	−	10.1997i	0.377768	−	0.654314i
$244$	−1.07916			−0.0690861
$245$	3.96303	−	1.70485i	0.253189	−	0.108919i
$246$	0.486321			0.0310067
$247$	19.5732	−	33.9017i	1.24541	−	2.15712i
$248$	2.01174	+	3.48443i	0.127745	+	0.221261i
$249$	1.21099	+	2.09750i	0.0767433	+	0.132923i
$250$	−2.96451	+	5.13467i	−0.187492	+	0.324745i
$251$	−27.5767			−1.74062			−0.870311	−	0.492502i	$-0.836083\pi$
$251$	−27.5767			−1.74062			−0.870311	+	0.492502i	$0.836083\pi$
$252$	2.30322	−	6.93927i	0.145089	−	0.437133i
$253$	−4.03872			−0.253912
$254$	−6.11955	+	10.5994i	−0.383975	+	0.665064i
$255$	−0.656368	−	1.13686i	−0.0411034	−	0.0711931i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.41129	−	4.17648i	0.150412	−	0.260521i	−0.780967	−	0.624572i	$-0.785273\pi$
$257$	2.41129	−	4.17648i	0.150412	−	0.260521i	0.931379	+	0.364051i	$0.118607\pi$
$258$	−4.54874			−0.283192
$259$	−7.30004	−	8.21113i	−0.453602	−	0.510215i
$260$	3.15090			0.195410
$261$	5.54063	−	9.59666i	0.342957	−	0.594018i
$262$	0.619016	+	1.07217i	0.0382429	+	0.0662387i
$263$	−13.3254	−	23.0802i	−0.821678	−	1.42319i	−0.904432	−	0.426618i	$-0.859705\pi$
$263$	−13.3254	−	23.0802i	−0.821678	−	1.42319i	0.0827542	−	0.996570i	$-0.473628\pi$
$264$	0.408627	−	0.707762i	0.0251492	−	0.0435598i
$265$	−3.59323			−0.220731
$266$	19.8419	−	4.08684i	1.21659	−	0.250580i
$267$	1.07765			0.0659514
$268$	−6.31561	+	10.9390i	−0.385788	+	0.668204i
$269$	10.4544	+	18.1076i	0.637416	+	1.10404i	0.985998	+	0.166759i	$0.0533302\pi$
$269$	10.4544	+	18.1076i	0.637416	+	1.10404i	−0.348581	+	0.937279i	$0.613336\pi$
$270$	0.863731	+	1.49603i	0.0525650	+	0.0910453i
$271$	10.5084	−	18.2011i	0.638341	−	1.10564i	−0.347456	−	0.937696i	$-0.612954\pi$
$271$	10.5084	−	18.2011i	0.638341	−	1.10564i	0.985797	−	0.167943i	$-0.0537124\pi$
$272$	−4.37980			−0.265565
$273$	−6.44294	+	1.32705i	−0.389944	+	0.0803168i
$274$	−15.5136			−0.937211
$275$	−3.88205	+	6.72391i	−0.234096	+	0.405467i
$276$	0.584390	+	1.01219i	0.0351762	+	0.0609269i
$277$	0.449228	+	0.778086i	0.0269915	+	0.0467507i	0.879206	−	0.476442i	$-0.158074\pi$
$277$	0.449228	+	0.778086i	0.0269915	+	0.0467507i	−0.852214	+	0.523193i	$0.824741\pi$
$278$	8.99850	−	15.5859i	0.539694	−	0.934777i
$279$	−11.1188			−0.665667
$280$	1.08342	+	1.21864i	0.0647467	+	0.0728275i
$281$	30.0786			1.79434			0.897171	−	0.441684i	$-0.145619\pi$
$281$	30.0786			1.79434			0.897171	+	0.441684i	$0.145619\pi$
$282$	−0.707448	+	1.22534i	−0.0421279	+	0.0729677i
$283$	−9.80094	−	16.9757i	−0.582605	−	1.00910i	−0.995169	−	0.0981733i	$-0.968700\pi$
$283$	−9.80094	−	16.9757i	−0.582605	−	1.00910i	0.412564	−	0.910929i	$-0.364633\pi$
$284$	−3.43530	−	5.95011i	−0.203847	−	0.353074i
$285$	−1.14749	+	1.98752i	−0.0679716	+	0.117730i
$286$	8.59148			0.508025
$287$	−0.833444	+	2.51105i	−0.0491967	+	0.148223i
$288$	2.76349			0.162840
$289$	−1.09134	+	1.89025i	−0.0641963	+	0.111191i
$290$	1.23567	+	2.14024i	0.0725608	+	0.125679i
$291$	−3.85252	−	6.67276i	−0.225839	−	0.391164i
$292$	2.29262	−	3.97093i	0.134165	−	0.232381i
$293$	25.7367			1.50356			0.751778	−	0.659417i	$-0.229197\pi$
$293$	25.7367			1.50356			0.751778	+	0.659417i	$0.229197\pi$
$294$	−2.72862	−	2.03556i	−0.159136	−	0.118717i
$295$	6.99259			0.407125
$296$	2.07634	−	3.59632i	0.120685	−	0.209032i
$297$	2.35512	+	4.07918i	0.136658	+	0.236698i
$298$	7.23394	+	12.5296i	0.419051	+	0.725818i
$299$	−6.14348	+	10.6408i	−0.355286	+	0.615374i
$300$	2.24688			0.129724
$301$	7.79551	−	23.4868i	0.449326	−	1.35375i
$302$	−2.14126			−0.123216
$303$	0.705191	−	1.22143i	0.0405122	−	0.0701691i
$304$	3.82849	+	6.63113i	0.219579	+	0.380322i
$305$	0.332549	+	0.575992i	0.0190417	+	0.0329812i
$306$	6.05177	−	10.4820i	0.345957	−	0.599215i
$307$	17.4198			0.994199			0.497100	−	0.867694i	$-0.334398\pi$
$307$	17.4198			0.994199			0.497100	+	0.867694i	$0.334398\pi$
$308$	2.95414	+	3.32283i	0.168328	+	0.189336i
$309$	4.59280			0.261275
$310$	1.23986	−	2.14749i	0.0704190	−	0.121969i
$311$	11.5044	+	19.9263i	0.652357	+	1.12992i	0.982549	+	0.186002i	$0.0595531\pi$
$311$	11.5044	+	19.9263i	0.652357	+	1.12992i	−0.330192	+	0.943914i	$0.607114\pi$
$312$	−1.24316	−	2.15322i	−0.0703801	−	0.121902i
$313$	−3.83277	+	6.63855i	−0.216641	+	0.375233i	−0.953779	−	0.300509i	$-0.902843\pi$
$313$	−3.83277	+	6.63855i	−0.216641	+	0.375233i	0.737138	+	0.675742i	$0.236177\pi$
$314$	5.37832			0.303516
$315$	−4.41352	+	0.909052i	−0.248674	+	0.0512193i
$316$	9.49284			0.534014
$317$	2.06562	−	3.57776i	0.116017	−	0.200947i	−0.802169	−	0.597097i	$-0.796321\pi$
$317$	2.06562	−	3.57776i	0.116017	−	0.200947i	0.918186	+	0.396150i	$0.129654\pi$
$318$	1.41768	+	2.45550i	0.0794996	+	0.137697i
$319$	3.36926	+	5.83574i	0.188643	+	0.326739i
$320$	−0.308156	+	0.533741i	−0.0172264	+	0.0298370i
$321$	−9.30655			−0.519441
$322$	−6.22783	+	1.28275i	−0.347064	+	0.0714846i
$323$	33.5360			1.86599
$324$	−3.46368	+	5.99927i	−0.192427	+	0.333293i
$325$	11.8103	+	20.4561i	0.655118	+	1.13470i
$326$	4.22210	+	7.31289i	0.233840	+	0.405023i
$327$	1.29844	−	2.24897i	0.0718040	−	0.124368i
$328$	−1.00000			−0.0552158
$329$	−5.11445	−	5.75276i	−0.281969	−	0.317160i
$330$	−0.503682			−0.0277268
$331$	1.96096	−	3.39648i	0.107784	−	0.186687i	−0.807088	−	0.590431i	$-0.798958\pi$
$331$	1.96096	−	3.39648i	0.107784	−	0.186687i	0.914872	+	0.403743i	$0.132291\pi$
$332$	−2.49010	−	4.31299i	−0.136662	−	0.236706i
$333$	5.73795	+	9.93841i	0.314438	+	0.544622i
$334$	−6.68632	+	11.5811i	−0.365859	+	0.633687i
$335$	7.78476			0.425327
$336$	0.405321	−	1.22118i	0.0221121	−	0.0666206i
$337$	−32.3835			−1.76404			−0.882021	−	0.471210i	$-0.843818\pi$
$337$	−32.3835			−1.76404			−0.882021	+	0.471210i	$0.843818\pi$
$338$	6.56888	−	11.3776i	0.357300	−	0.618862i
$339$	1.93338	+	3.34871i	0.105007	+	0.181877i
$340$	1.34966	+	2.33768i	0.0731956	+	0.126779i
$341$	3.38069	−	5.85552i	0.183074	−	0.317094i
$342$	−21.1600			−1.14420
$343$	15.1866	−	10.6004i	0.819999	−	0.572365i
$344$	9.35336			0.504300
$345$	0.360166	−	0.623826i	0.0193907	−	0.0335857i
$346$	−1.85534	−	3.21355i	−0.0997438	−	0.172761i
$347$	−12.1454	−	21.0365i	−0.651999	−	1.12930i	−0.982637	−	0.185538i	$-0.940597\pi$
$347$	−12.1454	−	21.0365i	−0.651999	−	1.12930i	0.330638	−	0.943758i	$-0.392736\pi$
$348$	0.975044	−	1.68883i	0.0522678	−	0.0905306i
$349$	15.8847			0.850287			0.425143	−	0.905126i	$-0.360224\pi$
$349$	15.8847			0.850287			0.425143	+	0.905126i	$0.360224\pi$
$350$	−3.85065	+	11.6015i	−0.205826	+	0.620124i
$351$	14.3299			0.764873
$352$	−0.840241	+	1.45534i	−0.0447850	+	0.0775699i
$353$	−11.6540	−	20.1853i	−0.620278	−	1.07435i	−0.989434	−	0.144985i	$-0.953687\pi$
$353$	−11.6540	−	20.1853i	−0.620278	−	1.07435i	0.369156	−	0.929367i	$-0.379647\pi$
$354$	−2.75887	−	4.77850i	−0.146632	−	0.253975i
$355$	−2.11721	+	3.66712i	−0.112370	+	0.194630i
$356$	−2.21593			−0.117444
$357$	−3.74433	−	4.21165i	−0.198171	−	0.222904i
$358$	6.02645			0.318508
$359$	−15.4687	+	26.7926i	−0.816408	+	1.41406i	0.0919043	+	0.995768i	$0.470705\pi$
$359$	−15.4687	+	26.7926i	−0.816408	+	1.41406i	−0.908312	+	0.418292i	$0.862629\pi$
$360$	−0.851585	−	1.47499i	−0.0448825	−	0.0777387i
$361$	−19.8146	−	34.3199i	−1.04287	−	1.80631i
$362$	−5.91323	+	10.2420i	−0.310792	+	0.538308i
$363$	3.97615			0.208694
$364$	13.2483	−	2.72876i	0.694401	−	0.143026i
$365$	−2.82593			−0.147916
$366$	0.262409	−	0.454506i	0.0137163	−	0.0237574i
$367$	−9.52435	−	16.4967i	−0.497167	−	0.861119i	0.502827	−	0.864387i	$-0.332293\pi$
$367$	−9.52435	−	16.4967i	−0.497167	−	0.861119i	−0.999995	+	0.00326794i	$0.998960\pi$
$368$	−1.20166	−	2.08133i	−0.0626406	−	0.108497i
$369$	1.38175	−	2.39325i	0.0719308	−	0.124588i
$370$	−2.55934			−0.133054
$371$	−15.1082	+	3.11183i	−0.784378	+	0.161558i
$372$	−1.95670			−0.101450
$373$	−8.42659	+	14.5953i	−0.436312	+	0.755715i	−0.997402	−	0.0720400i	$-0.977049\pi$
$373$	−8.42659	+	14.5953i	−0.436312	+	0.755715i	0.561089	+	0.827755i	$0.310382\pi$
$374$	3.68009	+	6.37410i	0.190293	+	0.329597i
$375$	−1.44170	−	2.49710i	−0.0744491	−	0.128950i
$376$	1.45469	−	2.51960i	0.0750201	−	0.129939i
$377$	20.5005			1.05583
$378$	4.92726	+	5.54221i	0.253431	+	0.285061i
$379$	26.6798			1.37045			0.685224	−	0.728332i	$-0.259704\pi$
$379$	26.6798			1.37045			0.685224	+	0.728332i	$0.259704\pi$
$380$	2.35954	−	4.08684i	0.121042	−	0.209651i
$381$	−2.97607	−	5.15470i	−0.152469	−	0.264083i
$382$	3.76217	+	6.51627i	0.192489	+	0.333401i
$383$	−15.3384	+	26.5669i	−0.783755	+	1.35750i	0.145986	+	0.989287i	$0.453365\pi$
$383$	−15.3384	+	26.5669i	−0.783755	+	1.35750i	−0.929740	+	0.368216i	$0.879969\pi$
$384$	0.486321			0.0248175
$385$	0.863198	−	2.60069i	0.0439926	−	0.132544i
$386$	−1.71959			−0.0875246
$387$	−12.9240	+	22.3850i	−0.656962	+	1.13789i
$388$	7.92177	+	13.7209i	0.402167	+	0.696573i
$389$	−7.79160	−	13.4955i	−0.395050	−	0.684247i	0.598058	−	0.801453i	$-0.295939\pi$
$389$	−7.79160	−	13.4955i	−0.395050	−	0.684247i	−0.993108	+	0.117207i	$0.962606\pi$
$390$	−0.766173	+	1.32705i	−0.0387967	+	0.0671979i
$391$	−10.5260			−0.532324
$392$	5.61074	+	4.18564i	0.283385	+	0.211407i
$393$	−0.602081			−0.0303710
$394$	8.68546	−	15.0437i	0.437567	−	0.757888i
$395$	−2.92527	−	5.06672i	−0.147186	−	0.254934i
$396$	−2.32200	−	4.02182i	−0.116685	−	0.202104i
$397$	3.00250	−	5.20049i	0.150691	−	0.261005i	−0.780790	−	0.624793i	$-0.785183\pi$
$397$	3.00250	−	5.20049i	0.150691	−	0.261005i	0.931482	+	0.363788i	$0.118517\pi$
$398$	−20.0315			−1.00409
$399$	−3.10354	+	9.35051i	−0.155371	+	0.468111i
$400$	−4.62016			−0.231008
$401$	−4.87822	+	8.44933i	−0.243607	+	0.421940i	−0.961739	−	0.273967i	$-0.911664\pi$
$401$	−4.87822	+	8.44933i	−0.243607	+	0.421940i	0.718132	+	0.695907i	$0.244997\pi$
$402$	−3.07142	−	5.31985i	−0.153188	−	0.265330i
$403$	−10.2850	−	17.8142i	−0.512333	−	0.887387i
$404$	−1.45005	+	2.51156i	−0.0721428	+	0.124955i
$405$	4.26941			0.212149
$406$	7.04901	+	7.92877i	0.349836	+	0.393498i
$407$	−6.97850			−0.345911
$408$	1.06500	−	1.84463i	0.0527251	−	0.0913226i
$409$	1.21922	+	2.11175i	0.0602866	+	0.104419i	0.894593	−	0.446881i	$-0.147465\pi$
$409$	1.21922	+	2.11175i	0.0602866	+	0.104419i	−0.834307	+	0.551300i	$0.814132\pi$
$410$	0.308156	+	0.533741i	0.0152187	+	0.0263596i
$411$	3.77230	−	6.53381i	0.186074	−	0.322289i
$412$	−9.44397			−0.465271
$413$	29.4012	−	6.05576i	1.44674	−	0.297985i
$414$	6.64153			0.326413
$415$	−1.53468	+	2.65814i	−0.0753344	+	0.130483i
$416$	2.55626	+	4.42756i	0.125331	+	0.217079i
$417$	4.37616	+	7.57973i	0.214301	+	0.371181i
$418$	6.43370	−	11.1435i	0.314683	−	0.545047i
$419$	4.49210			0.219453			0.109727	−	0.993962i	$-0.465002\pi$
$419$	4.49210			0.219453			0.109727	+	0.993962i	$0.465002\pi$
$420$	−0.776694	+	0.159976i	−0.0378988	+	0.00780601i
$421$	−38.1666			−1.86013			−0.930064	−	0.367398i	$-0.880249\pi$
$421$	−38.1666			−1.86013			−0.930064	+	0.367398i	$0.880249\pi$
$422$	−1.59699	+	2.76607i	−0.0777403	+	0.134650i
$423$	4.02004	+	6.96291i	0.195461	+	0.338548i
$424$	−2.91511	−	5.04913i	−0.141570	−	0.245207i
$425$	−10.1177	+	17.5244i	−0.490780	+	0.850057i
$426$	3.34131			0.161887
$427$	1.89707	+	2.13383i	0.0918055	+	0.103263i
$428$	19.1366			0.925005
$429$	−2.08911	+	3.61844i	−0.100863	+	0.174700i
$430$	−2.88229	−	4.99227i	−0.138996	−	0.240749i
$431$	15.5791	+	26.9838i	0.750420	+	1.29976i	0.947619	+	0.319401i	$0.103482\pi$
$431$	15.5791	+	26.9838i	0.750420	+	1.29976i	−0.197200	+	0.980363i	$0.563185\pi$
$432$	−1.40145	+	2.42739i	−0.0674275	+	0.116788i
$433$	11.5301			0.554101			0.277051	−	0.960855i	$-0.410643\pi$
$433$	11.5301			0.554101			0.277051	+	0.960855i	$0.410643\pi$
$434$	3.35334	−	10.1031i	0.160965	−	0.484966i
$435$	−1.20186			−0.0576248
$436$	−2.66993	+	4.62445i	−0.127866	+	0.221471i
$437$	9.20105	+	15.9367i	0.440146	+	0.762355i
$438$	1.11495	+	1.93115i	0.0532743	+	0.0922738i
$439$	−13.9570	+	24.1742i	−0.666131	+	1.15377i	0.312847	+	0.949804i	$0.398717\pi$
$439$	−13.9570	+	24.1742i	−0.666131	+	1.15377i	−0.978977	+	0.203969i	$0.934616\pi$
$440$	1.03570			0.0493750
$441$	−17.7699	+	7.64444i	−0.846187	+	0.364021i
$442$	22.3918			1.06507
$443$	−6.34720	+	10.9937i	−0.301565	+	0.522326i	−0.976491	−	0.215560i	$-0.930842\pi$
$443$	−6.34720	+	10.9937i	−0.301565	+	0.522326i	0.674926	+	0.737886i	$0.264176\pi$
$444$	1.00977	+	1.74897i	0.0479214	+	0.0830024i
$445$	0.682852	+	1.18273i	0.0323703	+	0.0560669i
$446$	1.83534	−	3.17890i	0.0869058	−	0.150525i
$447$	−7.03604			−0.332793
$448$	−0.833444	+	2.51105i	−0.0393765	+	0.118636i
$449$	−38.5081			−1.81731			−0.908656	−	0.417546i	$-0.862890\pi$
$449$	−38.5081			−1.81731			−0.908656	+	0.417546i	$0.862890\pi$
$450$	6.38389	−	11.0572i	0.300939	−	0.521242i
$451$	0.840241	+	1.45534i	0.0395654	+	0.0685293i
$452$	−3.97552	−	6.88580i	−0.186993	−	0.323881i
$453$	0.520669	−	0.901826i	0.0244632	−	0.0423715i
$454$	9.06526			0.425454
$455$	−5.53899	−	6.23029i	−0.259672	−	0.292081i
$456$	−3.72375			−0.174380
$457$	2.68412	−	4.64904i	0.125558	−	0.217473i	−0.796393	−	0.604779i	$-0.793261\pi$
$457$	2.68412	−	4.64904i	0.125558	−	0.217473i	0.921951	+	0.387307i	$0.126595\pi$
$458$	−8.50486	−	14.7308i	−0.397406	−	0.688327i
$459$	6.13809	+	10.6315i	0.286502	+	0.496235i
$460$	−0.740594	+	1.28275i	−0.0345304	+	0.0598083i
$461$	29.6642			1.38160			0.690799	−	0.723047i	$-0.257259\pi$
$461$	29.6642			1.38160			0.690799	+	0.723047i	$0.257259\pi$
$462$	−2.11779	+	0.436202i	−0.0985287	+	0.0202939i
$463$	26.0446			1.21039			0.605197	−	0.796076i	$-0.293094\pi$
$463$	26.0446			1.21039			0.605197	+	0.796076i	$0.293094\pi$
$464$	−2.00494	+	3.47266i	−0.0930770	+	0.161214i
$465$	0.602968	+	1.04437i	0.0279619	+	0.0484315i
$466$	2.41717	+	4.18667i	0.111973	+	0.193944i
$467$	5.25480	−	9.10158i	0.243163	−	0.421171i	−0.718450	−	0.695578i	$-0.755148\pi$
$467$	5.25480	−	9.10158i	0.243163	−	0.421171i	0.961614	+	0.274407i	$0.0884816\pi$
$468$	−14.1284			−0.653085
$469$	32.7320	−	6.74180i	1.51142	−	0.311308i
$470$	−1.79309			−0.0827090
$471$	−1.30779	+	2.26517i	−0.0602600	+	0.104373i
$472$	5.67294	+	9.82582i	0.261118	+	0.452270i
$473$	−7.85908	−	13.6123i	−0.361361	−	0.625895i
$474$	−2.30828	+	3.99807i	−0.106023	+	0.183637i
$475$	35.3764			1.62318
$476$	7.69930	+	8.66022i	0.352897	+	0.396941i
$477$	16.1118			0.737708
$478$	4.70930	−	8.15674i	0.215398	−	0.373081i
$479$	5.30853	+	9.19464i	0.242553	+	0.420114i	0.961441	−	0.275012i	$-0.0886819\pi$
$479$	5.30853	+	9.19464i	0.242553	+	0.420114i	−0.718888	+	0.695126i	$0.755349\pi$
$480$	−0.149862	−	0.259569i	−0.00684026	−	0.0118477i
$481$	−10.6153	+	18.3862i	−0.484016	+	0.838341i
$482$	−27.3729			−1.24680
$483$	0.974113	−	2.93487i	0.0443237	−	0.133541i
$484$	−8.17598			−0.371635
$485$	4.88227	−	8.45634i	0.221693	−	0.383983i
$486$	−5.88882	−	10.1997i	−0.267122	−	0.462670i
$487$	−0.175163	−	0.303391i	−0.00793739	−	0.0137480i	0.862029	−	0.506858i	$-0.169193\pi$
$487$	−0.175163	−	0.303391i	−0.00793739	−	0.0137480i	−0.869967	+	0.493110i	$0.835860\pi$
$488$	−0.539580	+	0.934580i	−0.0244256	+	0.0423064i
$489$	−4.10659			−0.185706
$490$	0.505067	−	4.28451i	0.0228166	−	0.193554i
$491$	−29.9266			−1.35057			−0.675285	−	0.737557i	$-0.735979\pi$
$491$	−29.9266			−1.35057			−0.675285	+	0.737557i	$0.735979\pi$
$492$	0.243160	−	0.421166i	0.0109625	−	0.0189876i
$493$	8.78124	+	15.2096i	0.395487	+	0.685004i
$494$	−19.5732	−	33.9017i	−0.880639	−	1.52531i
$495$	−1.43107	+	2.47869i	−0.0643220	+	0.111409i
$496$	4.02347			0.180659
$497$	−5.72626	+	17.2524i	−0.256858	+	0.773876i
$498$	2.42198			0.108531
$499$	−17.2189	+	29.8240i	−0.770823	+	1.33510i	0.166289	+	0.986077i	$0.446821\pi$
$499$	−17.2189	+	29.8240i	−0.770823	+	1.33510i	−0.937112	+	0.349028i	$0.886512\pi$
$500$	2.96451	+	5.13467i	0.132577	+	0.229630i
$501$	−3.25170	−	5.63211i	−0.145275	−	0.251624i
$502$	−13.7883	+	23.8821i	−0.615403	+	1.06591i
$503$	−12.7817			−0.569907			−0.284953	−	0.958541i	$-0.591978\pi$
$503$	−12.7817			−0.569907			−0.284953	+	0.958541i	$0.591978\pi$
$504$	−4.85797	−	5.46428i	−0.216391	−	0.243398i
$505$	1.78737			0.0795368
$506$	−2.01936	+	3.49764i	−0.0897715	+	0.155489i
$507$	3.19458	+	5.53318i	0.141876	+	0.245737i
$508$	6.11955	+	10.5994i	0.271511	+	0.470271i
$509$	−18.3317	+	31.7515i	−0.812541	+	1.40736i	0.0985400	+	0.995133i	$0.468583\pi$
$509$	−18.3317	+	31.7515i	−0.812541	+	1.40736i	−0.911081	+	0.412228i	$0.864751\pi$
$510$	−1.31274			−0.0581289
$511$	−11.8820	+	2.44733i	−0.525628	+	0.108263i
$512$	−1.00000			−0.0441942
$513$	10.7309	−	18.5865i	0.473780	−	0.820612i
$514$	−2.41129	−	4.17648i	−0.106357	−	0.184217i
$515$	2.91021	+	5.04064i	0.128239	+	0.222117i
$516$	−2.27437	+	3.93932i	−0.100123	+	0.173419i
$517$	−4.88918			−0.215026
$518$	−10.7611	+	2.21645i	−0.472814	+	0.0973854i
$519$	1.80458			0.0792124
$520$	1.57545	−	2.72876i	0.0690880	−	0.119664i
$521$	−1.68022	−	2.91023i	−0.0736119	−	0.127500i	0.826870	−	0.562393i	$-0.190119\pi$
$521$	−1.68022	−	2.91023i	−0.0736119	−	0.127500i	−0.900482	+	0.434894i	$0.856786\pi$
$522$	−5.54063	−	9.59666i	−0.242507	−	0.420034i
$523$	−11.8788	+	20.5746i	−0.519423	+	0.899666i	0.480322	+	0.877092i	$0.340520\pi$
$523$	−11.8788	+	20.5746i	−0.519423	+	0.899666i	−0.999745	+	0.0225745i	$0.992814\pi$
$524$	1.23803			0.0540837
$525$	−3.94982	−	4.44278i	−0.172384	−	0.193899i
$526$	−26.6507			−1.16203
$527$	8.81101	−	15.2611i	0.383813	−	0.664784i
$528$	−0.408627	−	0.707762i	−0.0177832	−	0.0308014i
$529$	8.61205	+	14.9165i	0.374437	+	0.648544i
$530$	−1.79662	+	3.11183i	−0.0780401	+	0.135169i
$531$	−31.3543			−1.36066
$532$	6.38166	−	19.2270i	0.276680	−	0.833598i
$533$	5.11251			0.221447
$534$	0.538827	−	0.933276i	0.0233173	−	0.0403868i
$535$	−5.89706	−	10.2140i	−0.254952	−	0.441590i
$536$	6.31561	+	10.9390i	0.272793	+	0.472491i
$537$	−1.46539	+	2.53814i	−0.0632364	+	0.109529i
$538$	20.9088			0.901443
$539$	1.37715	−	11.6825i	0.0593182	−	0.503200i
$540$	1.72746			0.0743381
$541$	2.16789	−	3.75489i	0.0932047	−	0.161435i	−0.815653	−	0.578541i	$-0.803622\pi$
$541$	2.16789	−	3.75489i	0.0932047	−	0.161435i	0.908858	+	0.417106i	$0.136956\pi$
$542$	−10.5084	−	18.2011i	−0.451375	−	0.781805i
$543$	−2.87573	−	4.98090i	−0.123409	−	0.213751i
$544$	−2.18990	+	3.79302i	−0.0938913	+	0.162624i
$545$	3.29101			0.140971
$546$	−2.07221	+	6.24328i	−0.0886824	+	0.267188i
$547$	25.3371			1.08334			0.541669	−	0.840592i	$-0.317793\pi$
$547$	25.3371			1.08334			0.541669	+	0.840592i	$0.317793\pi$
$548$	−7.75680	+	13.4352i	−0.331354	+	0.573922i
$549$	−1.49112	−	2.58270i	−0.0636397	−	0.110227i
$550$	3.88205	+	6.72391i	0.165531	+	0.286708i
$551$	15.3518	−	26.5900i	0.654007	−	1.13277i
$552$	1.16878			0.0497466
$553$	−16.6876	−	18.7703i	−0.709628	−	0.798194i
$554$	0.898457			0.0381718
$555$	0.622331	−	1.07791i	0.0264165	−	0.0457547i
$556$	−8.99850	−	15.5859i	−0.381621	−	0.660987i
$557$	−16.7791	−	29.0623i	−0.710953	−	1.23141i	−0.964500	−	0.264084i	$-0.914930\pi$
$557$	−16.7791	−	29.0623i	−0.710953	−	1.23141i	0.253546	−	0.967323i	$-0.418403\pi$
$558$	−5.55942	+	9.62919i	−0.235349	+	0.407636i
$559$	−47.8192			−2.02254
$560$	1.59708	−	0.328950i	0.0674890	−	0.0139007i
$561$	−3.57941			−0.151123
$562$	15.0393	−	26.0489i	0.634395	−	1.09881i
$563$	−4.03827	−	6.99449i	−0.170193	−	0.294782i	0.768294	−	0.640097i	$-0.221106\pi$
$563$	−4.03827	−	6.99449i	−0.170193	−	0.294782i	−0.938487	+	0.345314i	$0.887772\pi$
$564$	0.707448	+	1.22534i	0.0297890	+	0.0515960i
$565$	−2.45016	+	4.24380i	−0.103079	+	0.178538i
$566$	−19.6019			−0.823928
$567$	17.9513	−	3.69742i	0.753882	−	0.155277i
$568$	−6.87059			−0.288284
$569$	−11.7314	+	20.3194i	−0.491806	+	0.851833i	−0.999955	−	0.00943620i	$-0.996996\pi$
$569$	−11.7314	+	20.3194i	−0.491806	+	0.851833i	0.508150	+	0.861269i	$0.330330\pi$
$570$	1.14749	+	1.98752i	0.0480632	+	0.0832479i
$571$	−2.52782	−	4.37831i	−0.105786	−	0.183227i	0.808273	−	0.588808i	$-0.200402\pi$
$571$	−2.52782	−	4.37831i	−0.105786	−	0.183227i	−0.914059	+	0.405581i	$0.867069\pi$
$572$	4.29574	−	7.44044i	0.179614	−	0.311101i
$573$	−3.65924			−0.152867
$574$	1.75791	+	1.97731i	0.0733738	+	0.0825313i
$575$	−11.1037			−0.463056
$576$	1.38175	−	2.39325i	0.0575727	−	0.0997189i
$577$	7.52319	+	13.0306i	0.313195	+	0.542469i	0.979052	−	0.203610i	$-0.0652674\pi$
$577$	7.52319	+	13.0306i	0.313195	+	0.542469i	−0.665857	+	0.746079i	$0.731934\pi$
$578$	1.09134	+	1.89025i	0.0453936	+	0.0786241i
$579$	0.418135	−	0.724231i	0.0173771	−	0.0300980i
$580$	2.47133			0.102616
$581$	−4.15072	+	12.5055i	−0.172201	+	0.518818i
$582$	−7.70504			−0.319384
$583$	−4.89880	+	8.48497i	−0.202887	+	0.351411i
$584$	−2.29262	−	3.97093i	−0.0948692	−	0.164318i
$585$	4.35374	+	7.54090i	0.180005	+	0.311778i
$586$	12.8684	−	22.2887i	0.531587	−	0.920736i
$587$	9.33886			0.385456			0.192728	−	0.981252i	$-0.438266\pi$
$587$	9.33886			0.385456			0.192728	+	0.981252i	$0.438266\pi$
$588$	−3.12716	+	1.34527i	−0.128962	+	0.0554781i
$589$	−30.8076			−1.26941
$590$	3.49630	−	6.05576i	0.143940	−	0.249312i
$591$	4.22392	+	7.31605i	0.173749	+	0.300942i
$592$	−2.07634	−	3.59632i	−0.0853370	−	0.147808i
$593$	23.9526	−	41.4872i	0.983617	−	1.70367i	0.335687	−	0.941974i	$-0.391032\pi$
$593$	23.9526	−	41.4872i	0.983617	−	1.70367i	0.647929	−	0.761700i	$-0.275635\pi$
$594$	4.71024			0.193263
$595$	2.24973	−	6.77813i	0.0922301	−	0.277876i
$596$	14.4679			0.592628
$597$	4.87087	−	8.43659i	0.199351	−	0.345287i
$598$	6.14348	+	10.6408i	0.251225	+	0.435135i
$599$	−13.1289	−	22.7399i	−0.536433	−	0.929129i	−0.999093	−	0.0425929i	$-0.986438\pi$
$599$	−13.1289	−	22.7399i	−0.536433	−	0.929129i	0.462660	−	0.886536i	$-0.346895\pi$
$600$	1.12344	−	1.94586i	0.0458643	−	0.0794392i
$601$	−34.5798			−1.41054			−0.705269	−	0.708939i	$-0.749174\pi$
$601$	−34.5798			−1.41054			−0.705269	+	0.708939i	$0.749174\pi$
$602$	−16.4424	−	18.4945i	−0.670141	−	0.753779i
$603$	−34.9063			−1.42149
$604$	−1.07063	+	1.85438i	−0.0435633	+	0.0754538i
$605$	2.51947	+	4.36386i	0.102431	+	0.177416i
$606$	−0.705191	−	1.22143i	−0.0286464	−	0.0496170i
$607$	4.01054	−	6.94645i	0.162783	−	0.281948i	−0.773083	−	0.634305i	$-0.781286\pi$
$607$	4.01054	−	6.94645i	0.162783	−	0.281948i	0.935866	+	0.352357i	$0.114620\pi$
$608$	7.65697			0.310531
$609$	−5.05337	+	1.04084i	−0.204773	+	0.0421770i
$610$	0.665098			0.0269290
$611$	−7.43714	+	12.8815i	−0.300874	+	0.521130i
$612$	−6.05177	−	10.4820i	−0.244629	−	0.423709i
$613$	1.12512	+	1.94876i	0.0454430	+	0.0787096i	0.887852	−	0.460129i	$-0.152197\pi$
$613$	1.12512	+	1.94876i	0.0454430	+	0.0787096i	−0.842409	+	0.538838i	$0.818863\pi$
$614$	8.70989	−	15.0860i	0.351502	−	0.608820i
$615$	−0.299725			−0.0120861
$616$	4.35473	−	0.896942i	0.175457	−	0.0361388i
$617$	−38.9683			−1.56880			−0.784402	−	0.620252i	$-0.787030\pi$
$617$	−38.9683			−1.56880			−0.784402	+	0.620252i	$0.787030\pi$
$618$	2.29640	−	3.97748i	0.0923748	−	0.159998i
$619$	−7.99446	−	13.8468i	−0.321324	−	0.556550i	0.659437	−	0.751760i	$-0.270795\pi$
$619$	−7.99446	−	13.8468i	−0.321324	−	0.556550i	−0.980762	+	0.195210i	$0.937461\pi$
$620$	−1.23986	−	2.14749i	−0.0497938	−	0.0862454i
$621$	−3.36813	+	5.83377i	−0.135158	+	0.234101i
$622$	23.0089			0.922572
$623$	3.89541	+	4.38158i	0.156066	+	0.175544i
$624$	−2.48632			−0.0995325
$625$	−9.72334	+	16.8413i	−0.388934	+	0.673653i
$626$	3.83277	+	6.63855i	0.153188	+	0.265330i
$627$	3.12885	+	5.41932i	0.124954	+	0.216427i
$628$	2.68916	−	4.65776i	0.107309	−	0.185865i
$629$	−18.1879			−0.725200
$630$	−1.41950	+	4.27675i	−0.0565541	+	0.170390i
$631$	9.44784			0.376113			0.188056	−	0.982158i	$-0.439781\pi$
$631$	9.44784			0.376113			0.188056	+	0.982158i	$0.439781\pi$
$632$	4.74642	−	8.22104i	0.188803	−	0.327016i
$633$	−0.776651	−	1.34520i	−0.0308691	−	0.0534668i
$634$	−2.06562	−	3.57776i	−0.0820362	−	0.142091i
$635$	3.77155	−	6.53251i	0.149669	−	0.259235i
$636$	2.83536			0.112429
$637$	−28.6850	−	21.3991i	−1.13654	−	0.847864i
$638$	6.73853			0.266781
$639$	9.49341	−	16.4431i	0.375554	−	0.650478i
$640$	0.308156	+	0.533741i	0.0121809	+	0.0210980i
$641$	−6.40453	−	11.0930i	−0.252964	−	0.438146i	0.711377	−	0.702811i	$-0.248072\pi$
$641$	−6.40453	−	11.0930i	−0.252964	−	0.438146i	−0.964340	+	0.264665i	$0.914739\pi$
$642$	−4.65328	+	8.05971i	−0.183650	+	0.318091i
$643$	12.3360			0.486486			0.243243	−	0.969965i	$-0.421789\pi$
$643$	12.3360			0.486486			0.243243	+	0.969965i	$0.421789\pi$
$644$	−2.00303	+	6.03483i	−0.0789303	+	0.237806i
$645$	2.80344			0.110385
$646$	16.7680	−	29.0431i	0.659729	−	1.14268i
$647$	24.8579	+	43.0551i	0.977265	+	1.69267i	0.672249	+	0.740325i	$0.265329\pi$
$647$	24.8579	+	43.0551i	0.977265	+	1.69267i	0.305016	+	0.952347i	$0.401338\pi$
$648$	3.46368	+	5.99927i	0.136066	+	0.235674i
$649$	9.53328	−	16.5121i	0.374214	−	0.648158i
$650$	23.6206			0.926477
$651$	3.43970	+	3.86900i	0.134813	+	0.151638i
$652$	8.44420			0.330700
$653$	−22.6700	+	39.2656i	−0.887145	+	1.53658i	−0.0439096	+	0.999036i	$0.513981\pi$
$653$	−22.6700	+	39.2656i	−0.887145	+	1.53658i	−0.843235	+	0.537545i	$0.819352\pi$
$654$	−1.29844	−	2.24897i	−0.0507731	−	0.0879416i
$655$	−0.381506	−	0.660788i	−0.0149067	−	0.0258191i
$656$	−0.500000	+	0.866025i	−0.0195217	+	0.0338126i
$657$	12.6713			0.494353
$658$	−7.53926	+	1.55286i	−0.293911	+	0.0605368i
$659$	2.23227			0.0869570			0.0434785	−	0.999054i	$-0.486156\pi$
$659$	2.23227			0.0869570			0.0434785	+	0.999054i	$0.486156\pi$
$660$	−0.251841	+	0.436202i	−0.00980291	+	0.0169791i
$661$	22.0641	+	38.2162i	0.858195	+	1.48644i	0.873649	+	0.486557i	$0.161748\pi$
$661$	22.0641	+	38.2162i	0.858195	+	1.48644i	−0.0154532	+	0.999881i	$0.504919\pi$
$662$	−1.96096	−	3.39648i	−0.0762148	−	0.132008i
$663$	−5.44480	+	9.43067i	−0.211458	+	0.366257i
$664$	−4.98021			−0.193270
$665$	−12.2288	+	2.51876i	−0.474213	+	0.0976735i
$666$	11.4759			0.444682
$667$	−4.81849	+	8.34587i	−0.186573	+	0.323154i
$668$	6.68632	+	11.5811i	0.258702	+	0.448084i
$669$	0.892564	+	1.54597i	0.0345085	+	0.0597705i
$670$	3.89238	−	6.74180i	0.150376	−	0.260459i
$671$	1.81351			0.0700097
$672$	−0.854909	−	0.961607i	−0.0329788	−	0.0370948i
$673$	−27.0400			−1.04231			−0.521157	−	0.853461i	$-0.674499\pi$
$673$	−27.0400			−1.04231			−0.521157	+	0.853461i	$0.674499\pi$
$674$	−16.1918	+	28.0449i	−0.623683	+	1.08025i
$675$	6.47494	+	11.2149i	0.249221	+	0.431663i
$676$	−6.56888	−	11.3776i	−0.252649	−	0.437601i
$677$	−5.79372	+	10.0350i	−0.222671	+	0.385677i	−0.955618	−	0.294608i	$-0.904811\pi$
$677$	−5.79372	+	10.0350i	−0.222671	+	0.385677i	0.732947	+	0.680285i	$0.238144\pi$
$678$	3.86676			0.148502
$679$	13.2047	−	39.7839i	0.506750	−	1.52677i
$680$	2.69932			0.103514
$681$	−2.20431	+	3.81798i	−0.0844695	+	0.146305i
$682$	−3.38069	−	5.85552i	−0.129453	−	0.224219i
$683$	21.0022	+	36.3769i	0.803627	+	1.39192i	0.917214	+	0.398394i	$0.130432\pi$
$683$	21.0022	+	36.3769i	0.803627	+	1.39192i	−0.113587	+	0.993528i	$0.536234\pi$
$684$	−10.5800	+	18.3251i	−0.404536	+	0.700677i
$685$	9.56121			0.365315
$686$	−1.58688	−	18.4521i	−0.0605874	−	0.704506i
$687$	8.27218			0.315603
$688$	4.67668	−	8.10025i	0.178297	−	0.308819i
$689$	14.9036	+	25.8137i	0.567780	+	0.983424i
$690$	−0.360166	−	0.623826i	−0.0137113	−	0.0237487i
$691$	1.00062	−	1.73313i	0.0380655	−	0.0659314i	−0.846365	−	0.532603i	$-0.821214\pi$
$691$	1.00062	−	1.73313i	0.0380655	−	0.0659314i	0.884431	+	0.466672i	$0.154547\pi$
$692$	−3.71068			−0.141059
$693$	−3.87051	+	11.6613i	−0.147029	+	0.442977i
$694$	−24.2908			−0.922066
$695$	−5.54587	+	9.60573i	−0.210367	+	0.364366i
$696$	−0.975044	−	1.68883i	−0.0369589	−	0.0640148i
$697$	2.18990	+	3.79302i	0.0829484	+	0.143671i
$698$	7.94233	−	13.7565i	0.300622	−	0.520692i
$699$	−2.35104			−0.0889247
$700$	8.12183	+	9.13548i	0.306976	+	0.345289i
$701$	−44.6984			−1.68823			−0.844117	−	0.536159i	$-0.819875\pi$
$701$	−44.6984			−1.68823			−0.844117	+	0.536159i	$0.819875\pi$
$702$	7.16495	−	12.4100i	0.270423	−	0.468387i
$703$	15.8985	+	27.5370i	0.599622	+	1.03858i
$704$	0.840241	+	1.45534i	0.0316678	+	0.0548502i
$705$	0.436008	−	0.755188i	0.0164210	−	0.0284420i
$706$	−23.3079			−0.877205
$707$	7.51520	−	1.54790i	0.282638	−	0.0582149i
$708$	−5.51774			−0.207369
$709$	6.56813	−	11.3763i	0.246671	−	0.427247i	−0.715929	−	0.698173i	$-0.753997\pi$
$709$	6.56813	−	11.3763i	0.246671	−	0.427247i	0.962600	+	0.270926i	$0.0873299\pi$
$710$	2.11721	+	3.66712i	0.0794575	+	0.137624i
$711$	13.1167	+	22.7188i	0.491915	+	0.852021i
$712$	−1.10797	+	1.91905i	−0.0415228	+	0.0719196i
$713$	9.66966			0.362131
$714$	−5.51956	+	1.13686i	−0.206564	+	0.0425460i
$715$	−5.29503			−0.198023
$716$	3.01323	−	5.21906i	0.112610	−	0.195045i
$717$	2.29023	+	3.96679i	0.0855302	+	0.148143i
$718$	15.4687	+	26.7926i	0.577288	+	0.999892i
$719$	7.09058	−	12.2812i	0.264434	−	0.458013i	−0.702981	−	0.711208i	$-0.748148\pi$
$719$	7.09058	−	12.2812i	0.264434	−	0.458013i	0.967415	+	0.253195i	$0.0814816\pi$
$720$	−1.70317			−0.0634734
$721$	16.6017	+	18.6737i	0.618278	+	0.695443i
$722$	−39.6292			−1.47485
$723$	6.65600	−	11.5285i	0.247539	−	0.428751i
$724$	5.91323	+	10.2420i	0.219763	+	0.380641i
$725$	9.26314	+	16.0442i	0.344024	+	0.595868i
$726$	1.98808	−	3.44345i	0.0737844	−	0.127798i
$727$	−19.8678			−0.736857			−0.368428	−	0.929656i	$-0.620104\pi$
$727$	−19.8678			−0.736857			−0.368428	+	0.929656i	$0.620104\pi$
$728$	4.26099	−	12.8378i	0.157923	−	0.475799i
$729$	−15.0544			−0.557569
$730$	−1.41297	+	2.44733i	−0.0522962	+	0.0905797i
$731$	−20.4829	−	35.4775i	−0.757589	−	1.31218i
$732$	−0.262409	−	0.454506i	−0.00969892	−	0.0167990i
$733$	−2.19963	+	3.80988i	−0.0812453	+	0.140721i	−0.903785	−	0.427987i	$-0.859223\pi$
$733$	−2.19963	+	3.80988i	−0.0812453	+	0.140721i	0.822540	+	0.568708i	$0.192556\pi$
$734$	−19.0487			−0.703101
$735$	1.68168	+	1.25454i	0.0620297	+	0.0462744i
$736$	−2.40331			−0.0885872
$737$	10.6133	−	18.3827i	0.390945	−	0.677137i
$738$	−1.38175	−	2.39325i	−0.0508628	−	0.0880969i
$739$	24.8043	+	42.9623i	0.912440	+	1.58039i	0.810607	+	0.585590i	$0.199137\pi$
$739$	24.8043	+	42.9623i	0.912440	+	1.58039i	0.101833	+	0.994802i	$0.467529\pi$
$740$	−1.27967	+	2.21645i	−0.0470416	+	0.0814785i
$741$	19.0377			0.699367
$742$	−4.85917	+	14.6400i	−0.178386	+	0.537451i
$743$	37.2462			1.36643			0.683215	−	0.730217i	$-0.260581\pi$
$743$	37.2462			1.36643			0.683215	+	0.730217i	$0.260581\pi$
$744$	−0.978349	+	1.69455i	−0.0358680	+	0.0621252i
$745$	−4.45836	−	7.72210i	−0.163342	−	0.282916i
$746$	8.42659	+	14.5953i	0.308519	+	0.534371i
$747$	6.88138	−	11.9189i	0.251777	−	0.436090i
$748$	7.36018			0.269115
$749$	−33.6405	−	37.8391i	−1.22920	−	1.38261i
$750$	−2.88340			−0.105287
$751$	22.0394	−	38.1734i	0.804230	−	1.39297i	−0.112579	−	0.993643i	$-0.535911\pi$
$751$	22.0394	−	38.1734i	0.804230	−	1.39297i	0.916809	−	0.399325i	$-0.130755\pi$
$752$	−1.45469	−	2.51960i	−0.0530472	−	0.0918805i
$753$	−6.70555	−	11.6144i	−0.244364	−	0.423251i
$754$	10.2503	−	17.7540i	0.373293	−	0.646562i
$755$	1.31968			0.0480281
$756$	7.26333	−	1.49603i	0.264165	−	0.0544100i
$757$	49.7382			1.80777			0.903883	−	0.427779i	$-0.140704\pi$
$757$	49.7382			1.80777			0.903883	+	0.427779i	$0.140704\pi$
$758$	13.3399	−	23.1054i	0.484527	−	0.839225i
$759$	−0.982058	−	1.70097i	−0.0356464	−	0.0617414i
$760$	−2.35954	−	4.08684i	−0.0855895	−	0.148245i
$761$	4.58778	−	7.94626i	0.166307	−	0.288052i	−0.770812	−	0.637063i	$-0.780149\pi$
$761$	4.58778	−	7.94626i	0.166307	−	0.288052i	0.937119	+	0.349011i	$0.113482\pi$
$762$	−5.95214			−0.215623
$763$	13.8375	−	2.85010i	0.500950	−	0.103181i
$764$	7.52434			0.272221
$765$	−3.72978	+	6.46016i	−0.134850	+	0.233568i
$766$	15.3384	+	26.5669i	0.554198	+	0.959899i
$767$	−29.0030	−	50.2346i	−1.04724	−	1.81387i
$768$	0.243160	−	0.421166i	0.00877430	−	0.0151975i
$769$	6.52990			0.235474			0.117737	−	0.993045i	$-0.462436\pi$
$769$	6.52990			0.235474			0.117737	+	0.993045i	$0.462436\pi$
$770$	−1.82067	−	2.04790i	−0.0656123	−	0.0738011i
$771$	2.34532			0.0844647
$772$	−0.859793	+	1.48920i	−0.0309446	+	0.0535976i
$773$	1.78589	+	3.09324i	0.0642338	+	0.111256i	0.896354	−	0.443339i	$-0.146206\pi$
$773$	1.78589	+	3.09324i	0.0642338	+	0.111256i	−0.832120	+	0.554596i	$0.812873\pi$
$774$	12.9240	+	22.3850i	0.464543	+	0.804611i
$775$	9.29454	−	16.0986i	0.333870	−	0.578280i
$776$	15.8435			0.568750
$777$	1.68317	−	5.07115i	0.0603834	−	0.181927i
$778$	−15.5832			−0.558685
$779$	3.82849	−	6.63113i	0.137170	−	0.237585i
$780$	0.766173	+	1.32705i	0.0274334	+	0.0475161i
$781$	5.77295	+	9.99905i	0.206573	+	0.357794i
$782$	−5.26301	+	9.11581i	−0.188205	+	0.325981i
$783$	11.2393			0.401660
$784$	6.43024	−	2.76622i	0.229651	−	0.0987937i
$785$	−3.31472			−0.118307
$786$	−0.301040	+	0.521417i	−0.0107378	+	0.0185983i
$787$	5.19992	+	9.00653i	0.185357	+	0.321048i	0.943697	−	0.330812i	$-0.107322\pi$
$787$	5.19992	+	9.00653i	0.185357	+	0.321048i	−0.758340	+	0.651860i	$0.773989\pi$
$788$	−8.68546	−	15.0437i	−0.309407	−	0.535908i
$789$	6.48041	−	11.2244i	0.230709	−	0.399599i
$790$	−5.85054			−0.208153
$791$	−6.62675	+	19.9655i	−0.235620	+	0.709890i
$792$	−4.64400			−0.165017
$793$	2.75861	−	4.77805i	0.0979611	−	0.169674i
$794$	−3.00250	−	5.20049i	−0.106555	−	0.184559i
$795$	−0.873733	−	1.51335i	−0.0309881	−	0.0536730i
$796$	−10.0157	+	17.3478i	−0.354999	+	0.614876i
$797$	18.3777			0.650971			0.325485	−	0.945547i	$-0.394472\pi$
$797$	18.3777			0.650971			0.325485	+	0.945547i	$0.394472\pi$
$798$	6.54601	+	7.36300i	0.231726	+	0.260647i
$799$	−12.7425			−0.450799
$800$	−2.31008	+	4.00118i	−0.0816737	+	0.141463i
$801$	−3.06185	−	5.30329i	−0.108185	−	0.187382i
$802$	4.87822	+	8.44933i	0.172256	+	0.298356i
$803$	−3.85270	+	6.67308i	−0.135959	+	0.235488i
$804$	−6.14283			−0.216641
$805$	3.83828	−	0.790570i	0.135282	−	0.0278639i
$806$	−20.5700			−0.724549
$807$	−5.08420	+	8.80609i	−0.178972	+	0.309989i
$808$	1.45005	+	2.51156i	0.0510127	+	0.0883565i
$809$	−4.86690	−	8.42971i	−0.171111	−	0.296373i	0.767698	−	0.640812i	$-0.221402\pi$
$809$	−4.86690	−	8.42971i	−0.171111	−	0.296373i	−0.938809	+	0.344439i	$0.888069\pi$
$810$	2.13471	−	3.69742i	0.0750059	−	0.129914i
$811$	31.2917			1.09880			0.549401	−	0.835559i	$-0.314856\pi$
$811$	31.2917			1.09880			0.549401	+	0.835559i	$0.314856\pi$
$812$	10.3910	−	2.14024i	0.364653	−	0.0751076i
$813$	10.2209			0.358464
$814$	−3.48925	+	6.04356i	−0.122298	+	0.211827i
$815$	−2.60213	−	4.50701i	−0.0911485	−	0.157874i
$816$	−1.06500	−	1.84463i	−0.0372823	−	0.0645748i
$817$	−35.8092	+	62.0234i	−1.25281	+	2.16992i
$818$	2.43844			0.0852581
$819$	24.8364	+	27.9362i	0.867855	+	0.976169i
$820$	0.616311			0.0215225
$821$	18.6492	−	32.3013i	0.650861	−	1.12732i	−0.332053	−	0.943261i	$-0.607741\pi$
$821$	18.6492	−	32.3013i	0.650861	−	1.12732i	0.982914	−	0.184064i	$-0.0589253\pi$
$822$	−3.77230	−	6.53381i	−0.131574	−	0.227893i
$823$	−2.12943	−	3.68829i	−0.0742274	−	0.128566i	0.826523	−	0.562904i	$-0.190316\pi$
$823$	−2.12943	−	3.68829i	−0.0742274	−	0.128566i	−0.900750	+	0.434338i	$0.856982\pi$
$824$	−4.72199	+	8.17872i	−0.164498	+	0.284919i
$825$	−3.77584			−0.131458
$826$	9.45616	−	28.4901i	0.329022	−	0.991297i
$827$	−7.45576			−0.259262			−0.129631	−	0.991562i	$-0.541379\pi$
$827$	−7.45576			−0.259262			−0.129631	+	0.991562i	$0.541379\pi$
$828$	3.32077	−	5.75173i	0.115405	−	0.199887i
$829$	24.6747	+	42.7378i	0.856987	+	1.48434i	0.874789	+	0.484503i	$0.161000\pi$
$829$	24.6747	+	42.7378i	0.856987	+	1.48434i	−0.0178025	+	0.999842i	$0.505667\pi$
$830$	1.53468	+	2.65814i	0.0532695	+	0.0922654i
$831$	−0.218469	+	0.378400i	−0.00757861	+	0.0131265i
$832$	5.11251			0.177244
$833$	3.58925	−	30.4478i	0.124360	−	1.05495i
$834$	8.75232			0.303068
$835$	4.12086	−	7.13753i	0.142608	−	0.247004i
$836$	−6.43370	−	11.1435i	−0.222514	−	0.385406i
$837$	−5.63871	−	9.76653i	−0.194902	−	0.337581i
$838$	2.24605	−	3.89027i	0.0775885	−	0.134387i
$839$	33.1222			1.14351			0.571753	−	0.820426i	$-0.306264\pi$
$839$	33.1222			1.14351			0.571753	+	0.820426i	$0.306264\pi$
$840$	−0.249804	+	0.752624i	−0.00861906	+	0.0259680i
$841$	−12.9209			−0.445547
$842$	−19.0833	+	33.0533i	−0.657654	+	1.13909i
$843$	7.31394	+	12.6681i	0.251905	+	0.436313i
$844$	1.59699	+	2.76607i	0.0549707	+	0.0952121i
$845$	−4.04847	+	7.01216i	−0.139272	+	0.241226i
$846$	8.04007			0.276423
$847$	14.3726	+	16.1664i	0.493850	+	0.555485i
$848$	−5.83023			−0.200211
$849$	4.76640	−	8.25565i	0.163582	−	0.283333i
$850$	10.1177	+	17.5244i	0.347034	+	0.601081i
$851$	−4.99009	−	8.64309i	−0.171058	−	0.296281i
$852$	1.67066	−	2.89366i	0.0572358	−	0.0991352i
$853$	18.9524			0.648917			0.324458	−	0.945900i	$-0.394818\pi$
$853$	18.9524			0.648917			0.324458	+	0.945900i	$0.394818\pi$
$854$	2.79649	−	0.575992i	0.0956938	−	0.0197100i
$855$	13.0411			0.445997
$856$	9.56832	−	16.5728i	0.327039	−	0.566447i
$857$	−0.0122798	−	0.0212692i	−0.000419470	−	0.000726543i	0.865816	−	0.500363i	$-0.166800\pi$
$857$	−0.0122798	−	0.0212692i	−0.000419470	−	0.000726543i	−0.866235	+	0.499637i	$0.833467\pi$
$858$	2.08911	+	3.61844i	0.0713210	+	0.123532i
$859$	−2.32376	+	4.02486i	−0.0792855	+	0.137327i	−0.902942	−	0.429763i	$-0.858597\pi$
$859$	−2.32376	+	4.02486i	−0.0792855	+	0.137327i	0.823656	+	0.567089i	$0.191931\pi$
$860$	−5.76458			−0.196571
$861$	−1.26023	+	0.259569i	−0.0429485	+	0.00884610i
$862$	31.1582			1.06125
$863$	−0.759521	+	1.31553i	−0.0258544	+	0.0447811i	−0.878663	−	0.477442i	$-0.841564\pi$
$863$	−0.759521	+	1.31553i	−0.0258544	+	0.0447811i	0.852809	+	0.522223i	$0.174897\pi$
$864$	1.40145	+	2.42739i	0.0476784	+	0.0825814i
$865$	1.14347	+	1.98054i	0.0388791	+	0.0673405i
$866$	5.76505	−	9.98536i	0.195904	−	0.339316i
$867$	−1.06148			−0.0360497
$868$	−7.07290	−	7.95565i	−0.240070	−	0.270032i
$869$	−15.9526			−0.541153
$870$	−0.600930	+	1.04084i	−0.0203734	+	0.0352878i
$871$	−32.2886	−	55.9256i	−1.09406	−	1.89497i
$872$	2.66993	+	4.62445i	0.0904152	+	0.156604i
$873$	−21.8917	+	37.9176i	−0.740923	+	1.28332i
$874$	18.4021			0.622460
$875$	4.94150	−	14.8880i	0.167053	−	0.503308i
$876$	2.22990			0.0753412
$877$	18.5702	−	32.1646i	0.627073	−	1.08612i	−0.361063	−	0.932541i	$-0.617586\pi$
$877$	18.5702	−	32.1646i	0.627073	−	1.08612i	0.988136	−	0.153581i	$-0.0490805\pi$
$878$	13.9570	+	24.1742i	0.471026	+	0.815840i
$879$	6.25815	+	10.8394i	0.211082	+	0.365605i
$880$	0.517850	−	0.896942i	0.0174567	−	0.0302359i
$881$	27.1593			0.915021			0.457511	−	0.889204i	$-0.348741\pi$
$881$	27.1593			0.915021			0.457511	+	0.889204i	$0.348741\pi$
$882$	−2.26468	+	19.2114i	−0.0762558	+	0.646882i
$883$	−22.3915			−0.753534			−0.376767	−	0.926308i	$-0.622964\pi$
$883$	−22.3915			−0.753534			−0.376767	+	0.926308i	$0.622964\pi$
$884$	11.1959	−	19.3919i	0.376559	−	0.652219i
$885$	1.70032	+	2.94505i	0.0571557	+	0.0989966i
$886$	6.34720	+	10.9937i	0.213239	+	0.369340i
$887$	8.36573	−	14.4899i	0.280894	−	0.486522i	−0.690711	−	0.723131i	$-0.742702\pi$
$887$	8.36573	−	14.4899i	0.280894	−	0.486522i	0.971605	+	0.236608i	$0.0760358\pi$
$888$	2.01953			0.0677711
$889$	10.2006	−	30.7330i	0.342118	−	1.03075i
$890$	1.36570			0.0457785
$891$	5.82066	−	10.0817i	0.194999	−	0.337749i
$892$	−1.83534	−	3.17890i	−0.0614517	−	0.106437i
$893$	11.1386	+	19.2925i	0.372738	+	0.645600i
$894$	−3.51802	+	6.09339i	−0.117660	+	0.203793i
$895$	−3.71417			−0.124151
$896$	1.75791	+	1.97731i	0.0587277	+	0.0660572i
$897$	−5.97540			−0.199513
$898$	−19.2541	+	33.3490i	−0.642517	+	1.11287i
$899$	−8.06682	−	13.9721i	−0.269043	−	0.465997i
$900$	−6.38389	−	11.0572i	−0.212796	−	0.368574i
$901$	−12.7676	+	22.1142i	−0.425351	+	0.736730i
$902$	1.68048			0.0559539
$903$	11.7874	−	2.42785i	0.392260	−	0.0807937i
$904$	−7.95104			−0.264448
$905$	3.64439	−	6.31226i	0.121143	−	0.209827i
$906$	−0.520669	−	0.901826i	−0.0172981	−	0.0299612i
$907$	−5.36630	−	9.29471i	−0.178185	−	0.308626i	0.763074	−	0.646311i	$-0.223689\pi$
$907$	−5.36630	−	9.29471i	−0.178185	−	0.308626i	−0.941259	+	0.337686i	$0.890356\pi$
$908$	4.53263	−	7.85075i	0.150421	−	0.260536i
$909$	−8.01441			−0.265821
$910$	−8.16509	+	1.68176i	−0.270670	+	0.0557499i
$911$	−3.97142			−0.131579			−0.0657896	−	0.997834i	$-0.520957\pi$
$911$	−3.97142			−0.131579			−0.0657896	+	0.997834i	$0.520957\pi$
$912$	−1.86187	+	3.22486i	−0.0616528	+	0.106786i
$913$	4.18457	+	7.24790i	0.138489	+	0.239870i
$914$	−2.68412	−	4.64904i	−0.0887829	−	0.153776i
$915$	−0.161726	+	0.280117i	−0.00534648	+	0.00926038i
$916$	−17.0097			−0.562017
$917$	−2.17635	−	2.44797i	−0.0718694	−	0.0808391i
$918$	12.2762			0.405174
$919$	20.7902	−	36.0097i	0.685805	−	1.18785i	−0.287378	−	0.957817i	$-0.592784\pi$
$919$	20.7902	−	36.0097i	0.685805	−	1.18785i	0.973183	−	0.230032i	$-0.0738831\pi$
$920$	0.740594	+	1.28275i	0.0244166	+	0.0422909i
$921$	4.23580	+	7.33662i	0.139574	+	0.241750i
$922$	14.8321	−	25.6899i	0.488469	−	0.846053i
$923$	35.1260			1.15619
$924$	−0.681135	+	2.05216i	−0.0224077	+	0.0675113i
$925$	−19.1860			−0.630833
$926$	13.0223	−	22.5553i	0.427939	−	0.741212i
$927$	−13.0492	−	22.6018i	−0.428591	−	0.742342i
$928$	2.00494	+	3.47266i	0.0658154	+	0.113996i
$929$	22.8415	−	39.5627i	0.749406	−	1.29801i	−0.198701	−	0.980060i	$-0.563672\pi$
$929$	22.8415	−	39.5627i	0.749406	−	1.29801i	0.948108	−	0.317950i	$-0.102994\pi$
$930$	1.20594			0.0395442
$931$	−49.2362	+	21.1809i	−1.61365	+	0.694176i
$932$	4.83435			0.158354
$933$	−5.59485	+	9.69057i	−0.183167	+	0.317255i
$934$	−5.25480	−	9.10158i	−0.171942	−	0.297813i
$935$	−2.26808	−	3.92843i	−0.0741742	−	0.128473i
$936$	−7.06419	+	12.2355i	−0.230900	+	0.399931i
$937$	6.29104			0.205519			0.102760	−	0.994706i	$-0.467233\pi$
$937$	6.29104			0.205519			0.102760	+	0.994706i	$0.467233\pi$
$938$	10.5274	−	31.7176i	0.343733	−	1.03562i
$939$	−3.72791			−0.121656
$940$	−0.896544	+	1.55286i	−0.0292420	+	0.0506487i
$941$	−15.9434	−	27.6147i	−0.519739	−	0.900214i	−0.999737	−	0.0229445i	$-0.992696\pi$
$941$	−15.9434	−	27.6147i	−0.519739	−	0.900214i	0.479998	−	0.877270i	$-0.340637\pi$
$942$	1.30779	+	2.26517i	0.0426102	+	0.0738031i
$943$	−1.20166	+	2.08133i	−0.0391313	+	0.0677774i
$944$	11.3459			0.369277
$945$	−3.03672	−	3.41573i	−0.0987847	−	0.111114i
$946$	−15.7182			−0.511041
$947$	7.68282	−	13.3070i	0.249658	−	0.432421i	−0.713773	−	0.700377i	$-0.753015\pi$
$947$	7.68282	−	13.3070i	0.249658	−	0.432421i	0.963431	+	0.267957i	$0.0863484\pi$
$948$	2.30828	+	3.99807i	0.0749696	+	0.129851i
$949$	11.7210	+	20.3014i	0.380481	+	0.659012i
$950$	17.6882	−	30.6369i	0.573882	−	0.993992i
$951$	2.00911			0.0651498
$952$	11.3496	−	2.33768i	0.367843	−	0.0757647i
$953$	25.8172			0.836301			0.418150	−	0.908378i	$-0.362679\pi$
$953$	25.8172			0.836301			0.418150	+	0.908378i	$0.362679\pi$
$954$	8.05589	−	13.9532i	0.260819	−	0.451752i
$955$	−2.31867	−	4.01605i	−0.0750303	−	0.129956i
$956$	−4.70930	−	8.15674i	−0.152310	−	0.263808i
$957$	−1.63854	+	2.83804i	−0.0529666	+	0.0917409i
$958$	10.6171			0.343021
$959$	40.2013	−	8.28025i	1.29817	−	0.267383i
$960$	−0.299725			−0.00967358
$961$	7.40584	−	12.8273i	0.238898	−	0.413783i
$962$	10.6153	+	18.3862i	0.342251	+	0.592796i
$963$	26.4420	+	45.7989i	0.852081	+	1.47585i
$964$	−13.6864	+	23.7056i	−0.440810	+	0.763506i
$965$	1.05980			0.0341161
$966$	−2.05461	−	2.31104i	−0.0661061	−	0.0743565i
$967$	18.6448			0.599577			0.299789	−	0.954006i	$-0.403084\pi$
$967$	18.6448			0.599577			0.299789	+	0.954006i	$0.403084\pi$
$968$	−4.08799	+	7.08061i	−0.131393	+	0.227579i
$969$	8.15464	+	14.1242i	0.261965	+	0.453736i
$970$	−4.88227	−	8.45634i	−0.156760	−	0.271517i
$971$	5.64351	−	9.77485i	0.181109	−	0.313690i	−0.761149	−	0.648577i	$-0.775365\pi$
$971$	5.64351	−	9.77485i	0.181109	−	0.313690i	0.942258	+	0.334887i	$0.108698\pi$
$972$	−11.7776			−0.377768
$973$	−14.9995	+	45.1914i	−0.480862	+	1.44877i
$974$	−0.350326			−0.0112252
$975$	−5.74360	+	9.94821i	−0.183942	+	0.318598i
$976$	0.539580	+	0.934580i	0.0172715	+	0.0299152i
$977$	17.7501	+	30.7441i	0.567877	+	0.983592i	0.996776	+	0.0802393i	$0.0255684\pi$
$977$	17.7501	+	30.7441i	0.567877	+	0.983592i	−0.428899	+	0.903353i	$0.641098\pi$
$978$	−2.05329	+	3.55641i	−0.0656571	+	0.113721i
$979$	3.72383			0.119014
$980$	−3.45796	−	2.57966i	−0.110461	−	0.0824041i
$981$	−14.7567			−0.471144
$982$	−14.9633	+	25.9172i	−0.477499	+	0.827052i
$983$	5.88131	+	10.1867i	0.187585	+	0.324906i	0.944444	−	0.328671i	$-0.106601\pi$
$983$	5.88131	+	10.1867i	0.187585	+	0.324906i	−0.756860	+	0.653577i	$0.773267\pi$
$984$	−0.243160	−	0.421166i	−0.00775167	−	0.0134263i
$985$	−5.35294	+	9.27157i	−0.170559	+	0.295417i
$986$	17.5625			0.559303
$987$	1.17924	−	3.55288i	0.0375355	−	0.113089i
$988$	−39.1464			−1.24541
$989$	11.2395	−	19.4674i	0.357396	−	0.619028i
$990$	1.43107	+	2.47869i	0.0454825	+	0.0787780i
$991$	−15.8403	−	27.4363i	−0.503185	−	0.871541i	−0.999993	−	0.00368124i	$-0.998828\pi$
$991$	−15.8403	−	27.4363i	−0.503185	−	0.871541i	0.496809	−	0.867860i	$-0.334505\pi$
$992$	2.01174	−	3.48443i	0.0638727	−	0.110631i
$993$	1.90731			0.0605267
$994$	12.0779	+	13.5853i	0.383087	+	0.430899i
$995$	12.3456			0.391383
$996$	1.21099	−	2.09750i	0.0383717	−	0.0664617i
$997$	3.49449	+	6.05264i	0.110672	+	0.191689i	0.916041	−	0.401084i	$-0.131366\pi$
$997$	3.49449	+	6.05264i	0.110672	+	0.191689i	−0.805370	+	0.592773i	$0.798033\pi$
$998$	17.2189	+	29.8240i	0.545054	+	0.944062i
$999$	−5.81979	+	10.0802i	−0.184130	+	0.318922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.e.g.247.4	yes	12
7.2	even	3		4018.2.a.bo.1.3		6
7.4	even	3	inner	574.2.e.g.165.4	✓	12
7.5	odd	6		4018.2.a.bn.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.g.165.4	✓	12	7.4	even	3	inner
574.2.e.g.247.4	yes	12	1.1	even	1	trivial
4018.2.a.bn.1.4		6	7.5	odd	6
4018.2.a.bo.1.3		6	7.2	even	3

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.243160 + 0.421166i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.308156 + 0.533741i) q^{5} +0.486321 q^{6} +(-0.833444 + 2.51105i) q^{7} -1.00000 q^{8} +(1.38175 - 2.39325i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.243160 + 0.421166i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.308156 + 0.533741i) q^{5} +0.486321 q^{6} +(-0.833444 + 2.51105i) q^{7} -1.00000 q^{8} +(1.38175 - 2.39325i) q^{9} +(0.308156 + 0.533741i) q^{10} +(0.840241 + 1.45534i) q^{11} +(0.243160 - 0.421166i) q^{12} +5.11251 q^{13} +(1.75791 + 1.97731i) q^{14} -0.299725 q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.18990 + 3.79302i) q^{17} +(-1.38175 - 2.39325i) q^{18} +(3.82849 - 6.63113i) q^{19} +0.616311 q^{20} +(-1.26023 + 0.259569i) q^{21} +1.68048 q^{22} +(-1.20166 + 2.08133i) q^{23} +(-0.243160 - 0.421166i) q^{24} +(2.31008 + 4.00118i) q^{25} +(2.55626 - 4.42756i) q^{26} +2.80291 q^{27} +(2.59135 - 0.533741i) q^{28} +4.00988 q^{29} +(-0.149862 + 0.259569i) q^{30} +(-2.01174 - 3.48443i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.408627 + 0.707762i) q^{33} +4.37980 q^{34} +(-1.08342 - 1.21864i) q^{35} -2.76349 q^{36} +(-2.07634 + 3.59632i) q^{37} +(-3.82849 - 6.63113i) q^{38} +(1.24316 + 2.15322i) q^{39} +(0.308156 - 0.533741i) q^{40} +1.00000 q^{41} +(-0.405321 + 1.22118i) q^{42} -9.35336 q^{43} +(0.840241 - 1.45534i) q^{44} +(0.851585 + 1.47499i) q^{45} +(1.20166 + 2.08133i) q^{46} +(-1.45469 + 2.51960i) q^{47} -0.486321 q^{48} +(-5.61074 - 4.18564i) q^{49} +4.62016 q^{50} +(-1.06500 + 1.84463i) q^{51} +(-2.55626 - 4.42756i) q^{52} +(2.91511 + 5.04913i) q^{53} +(1.40145 - 2.42739i) q^{54} -1.03570 q^{55} +(0.833444 - 2.51105i) q^{56} +3.72375 q^{57} +(2.00494 - 3.47266i) q^{58} +(-5.67294 - 9.82582i) q^{59} +(0.149862 + 0.259569i) q^{60} +(0.539580 - 0.934580i) q^{61} -4.02347 q^{62} +(4.85797 + 5.46428i) q^{63} +1.00000 q^{64} +(-1.57545 + 2.72876i) q^{65} +(0.408627 + 0.707762i) q^{66} +(-6.31561 - 10.9390i) q^{67} +(2.18990 - 3.79302i) q^{68} -1.16878 q^{69} +(-1.59708 + 0.328950i) q^{70} +6.87059 q^{71} +(-1.38175 + 2.39325i) q^{72} +(2.29262 + 3.97093i) q^{73} +(2.07634 + 3.59632i) q^{74} +(-1.12344 + 1.94586i) q^{75} -7.65697 q^{76} +(-4.35473 + 0.896942i) q^{77} +2.48632 q^{78} +(-4.74642 + 8.22104i) q^{79} +(-0.308156 - 0.533741i) q^{80} +(-3.46368 - 5.99927i) q^{81} +(0.500000 - 0.866025i) q^{82} +4.98021 q^{83} +(0.854909 + 0.961607i) q^{84} -2.69932 q^{85} +(-4.67668 + 8.10025i) q^{86} +(0.975044 + 1.68883i) q^{87} +(-0.840241 - 1.45534i) q^{88} +(1.10797 - 1.91905i) q^{89} +1.70317 q^{90} +(-4.26099 + 12.8378i) q^{91} +2.40331 q^{92} +(0.978349 - 1.69455i) q^{93} +(1.45469 + 2.51960i) q^{94} +(2.35954 + 4.08684i) q^{95} +(-0.243160 + 0.421166i) q^{96} -15.8435 q^{97} +(-6.43024 + 2.76622i) q^{98} +4.64400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9	\( 12 q + 6 q^{2} - q^{3} - 6 q^{4} - 2 q^{6} - q^{7} - 12 q^{8} - 5 q^{9} - q^{11} - q^{12} + 8 q^{13} + q^{14} + 4 q^{15} - 6 q^{16} + q^{17} + 5 q^{18} + 3 q^{19} - 6 q^{21} - 2 q^{22} - 21 q^{23} + q^{24} + 4 q^{26} + 26 q^{27} + 2 q^{28} + 10 q^{29} + 2 q^{30} - 3 q^{31} + 6 q^{32} + 19 q^{33} + 2 q^{34} - 51 q^{35} + 10 q^{36} + 2 q^{37} - 3 q^{38} + 11 q^{39} + 12 q^{41} - 6 q^{42} + 24 q^{43} - q^{44} - 28 q^{45} + 21 q^{46} + 18 q^{47} + 2 q^{48} - 15 q^{49} - 13 q^{51} - 4 q^{52} - 14 q^{53} + 13 q^{54} - 14 q^{55} + q^{56} + 10 q^{57} + 5 q^{58} - 16 q^{59} - 2 q^{60} + 20 q^{61} - 6 q^{62} - 41 q^{63} + 12 q^{64} - 18 q^{65} - 19 q^{66} + 13 q^{67} + q^{68} + 30 q^{69} - 12 q^{70} + 22 q^{71} + 5 q^{72} - q^{73} - 2 q^{74} + 23 q^{75} - 6 q^{76} - 11 q^{77} + 22 q^{78} - 19 q^{79} + 6 q^{81} + 6 q^{82} + 30 q^{83} - 4 q^{85} + 12 q^{86} - 10 q^{87} + q^{88} + 14 q^{89} - 56 q^{90} + 5 q^{91} + 42 q^{92} - 35 q^{93} - 18 q^{94} - 24 q^{95} + q^{96} + 2 q^{97} + 6 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - q^3 - 6 * q^4 - 2 * q^6 - q^7 - 12 * q^8 - 5 * q^9 - q^11 - q^12 + 8 * q^13 + q^14 + 4 * q^15 - 6 * q^16 + q^17 + 5 * q^18 + 3 * q^19 - 6 * q^21 - 2 * q^22 - 21 * q^23 + q^24 + 4 * q^26 + 26 * q^27 + 2 * q^28 + 10 * q^29 + 2 * q^30 - 3 * q^31 + 6 * q^32 + 19 * q^33 + 2 * q^34 - 51 * q^35 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 11 * q^39 + 12 * q^41 - 6 * q^42 + 24 * q^43 - q^44 - 28 * q^45 + 21 * q^46 + 18 * q^47 + 2 * q^48 - 15 * q^49 - 13 * q^51 - 4 * q^52 - 14 * q^53 + 13 * q^54 - 14 * q^55 + q^56 + 10 * q^57 + 5 * q^58 - 16 * q^59 - 2 * q^60 + 20 * q^61 - 6 * q^62 - 41 * q^63 + 12 * q^64 - 18 * q^65 - 19 * q^66 + 13 * q^67 + q^68 + 30 * q^69 - 12 * q^70 + 22 * q^71 + 5 * q^72 - q^73 - 2 * q^74 + 23 * q^75 - 6 * q^76 - 11 * q^77 + 22 * q^78 - 19 * q^79 + 6 * q^81 + 6 * q^82 + 30 * q^83 - 4 * q^85 + 12 * q^86 - 10 * q^87 + q^88 + 14 * q^89 - 56 * q^90 + 5 * q^91 + 42 * q^92 - 35 * q^93 - 18 * q^94 - 24 * q^95 + q^96 + 2 * q^97 + 6 * q^98 + 20 * q^99

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