LMFDB - Embedded newform 169.2.c.c.146.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,2,Mod(22,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("169.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	169.c (of order $3$, degree $2$, not 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:	$1.34947179416$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			146.3
Root			$0.900969 + 1.56052i$ of defining polynomial
Character	$\chi$	$=$	169.146
Dual form			169.2.c.c.22.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12349 + 1.94594i) q^{2} +(0.277479 + 0.480608i) q^{3} +(-1.52446 + 2.64044i) q^{4} -1.44504 q^{5} +(-0.623490 + 1.07992i) q^{6} +(-1.02446 + 1.77441i) q^{7} -2.35690 q^{8} +(1.34601 - 2.33136i) q^{9} +O(q^{10})$	\(q+(1.12349 + 1.94594i) q^{2} +(0.277479 + 0.480608i) q^{3} +(-1.52446 + 2.64044i) q^{4} -1.44504 q^{5} +(-0.623490 + 1.07992i) q^{6} +(-1.02446 + 1.77441i) q^{7} -2.35690 q^{8} +(1.34601 - 2.33136i) q^{9} +(-1.62349 - 2.81197i) q^{10} +(1.27748 + 2.21266i) q^{11} -1.69202 q^{12} -4.60388 q^{14} +(-0.400969 - 0.694498i) q^{15} +(0.400969 + 0.694498i) q^{16} +(2.64795 - 4.58638i) q^{17} +6.04892 q^{18} +(2.92543 - 5.06699i) q^{19} +(2.20291 - 3.81555i) q^{20} -1.13706 q^{21} +(-2.87047 + 4.97180i) q^{22} +(0.945042 + 1.63686i) q^{23} +(-0.653989 - 1.13274i) q^{24} -2.91185 q^{25} +3.15883 q^{27} +(-3.12349 - 5.41004i) q^{28} +(-1.13437 - 1.96480i) q^{29} +(0.900969 - 1.56052i) q^{30} -4.26875 q^{31} +(-3.25786 + 5.64279i) q^{32} +(-0.708947 + 1.22793i) q^{33} +11.8998 q^{34} +(1.48039 - 2.56410i) q^{35} +(4.10388 + 7.10812i) q^{36} +(-2.67845 - 4.63921i) q^{37} +13.1468 q^{38} +3.40581 q^{40} +(-0.637063 - 1.10343i) q^{41} +(-1.27748 - 2.21266i) q^{42} +(-3.06853 + 5.31485i) q^{43} -7.78986 q^{44} +(-1.94504 + 3.36891i) q^{45} +(-2.12349 + 3.67799i) q^{46} -2.95108 q^{47} +(-0.222521 + 0.385418i) q^{48} +(1.40097 + 2.42655i) q^{49} +(-3.27144 - 5.66630i) q^{50} +2.93900 q^{51} +5.52111 q^{53} +(3.54892 + 6.14691i) q^{54} +(-1.84601 - 3.19738i) q^{55} +(2.41454 - 4.18211i) q^{56} +3.24698 q^{57} +(2.54892 - 4.41485i) q^{58} +(6.10388 - 10.5722i) q^{59} +2.44504 q^{60} +(-4.28232 + 7.41720i) q^{61} +(-4.79590 - 8.30674i) q^{62} +(2.75786 + 4.77676i) q^{63} -13.0368 q^{64} -3.18598 q^{66} +(-0.288364 - 0.499461i) q^{67} +(8.07338 + 13.9835i) q^{68} +(-0.524459 + 0.908389i) q^{69} +6.65279 q^{70} +(2.29709 - 3.97868i) q^{71} +(-3.17241 + 5.49477i) q^{72} -10.5526 q^{73} +(6.01842 - 10.4242i) q^{74} +(-0.807979 - 1.39946i) q^{75} +(8.91939 + 15.4488i) q^{76} -5.23490 q^{77} -15.7778 q^{79} +(-0.579417 - 1.00358i) q^{80} +(-3.16152 - 5.47592i) q^{81} +(1.43147 - 2.47938i) q^{82} +7.72348 q^{83} +(1.73341 - 3.00235i) q^{84} +(-3.82640 + 6.62751i) q^{85} -13.7899 q^{86} +(0.629531 - 1.09038i) q^{87} +(-3.01089 - 5.21501i) q^{88} +(-3.30678 - 5.72751i) q^{89} -8.74094 q^{90} -5.76271 q^{92} +(-1.18449 - 2.05159i) q^{93} +(-3.31551 - 5.74263i) q^{94} +(-4.22737 + 7.32201i) q^{95} -3.61596 q^{96} +(-5.96346 + 10.3290i) q^{97} +(-3.14795 + 5.45241i) q^{98} +6.87800 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9	$ 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 5 q^{10} + 8 q^{11} - 10 q^{14} + 2 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 4 q^{19} + 4 q^{21} - 3 q^{22} + 5 q^{23} - 9 q^{24} - 10 q^{25} + 2 q^{27} - 14 q^{28} + q^{29} + q^{30} - 10 q^{31} - 7 q^{32} - 10 q^{33} + 26 q^{34} - 4 q^{35} + 7 q^{36} - 12 q^{37} + 24 q^{38} - 6 q^{40} + 7 q^{41} - 8 q^{42} - 13 q^{43} - 11 q^{45} - 8 q^{46} - 36 q^{47} - q^{48} + 4 q^{49} - q^{50} - 2 q^{51} + 2 q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} + 10 q^{57} - 3 q^{58} + 19 q^{59} + 14 q^{60} - 4 q^{61} - q^{62} + 4 q^{63} - 22 q^{64} + 10 q^{66} + q^{67} + 21 q^{68} + 6 q^{69} + 4 q^{70} + 27 q^{71} + 4 q^{72} + 18 q^{73} + 8 q^{74} - 15 q^{75} + 21 q^{76} + 16 q^{77} - 10 q^{79} + 5 q^{80} + q^{81} + 14 q^{82} - 14 q^{83} + 7 q^{84} - 5 q^{85} - 36 q^{86} + 18 q^{87} - 15 q^{88} + 11 q^{89} - 24 q^{90} - 22 q^{93} - 5 q^{94} - 3 q^{95} - 42 q^{96} - 7 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 5 * q^10 + 8 * q^11 - 10 * q^14 + 2 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 4 * q^19 + 4 * q^21 - 3 * q^22 + 5 * q^23 - 9 * q^24 - 10 * q^25 + 2 * q^27 - 14 * q^28 + q^29 + q^30 - 10 * q^31 - 7 * q^32 - 10 * q^33 + 26 * q^34 - 4 * q^35 + 7 * q^36 - 12 * q^37 + 24 * q^38 - 6 * q^40 + 7 * q^41 - 8 * q^42 - 13 * q^43 - 11 * q^45 - 8 * q^46 - 36 * q^47 - q^48 + 4 * q^49 - q^50 - 2 * q^51 + 2 * q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 + 10 * q^57 - 3 * q^58 + 19 * q^59 + 14 * q^60 - 4 * q^61 - q^62 + 4 * q^63 - 22 * q^64 + 10 * q^66 + q^67 + 21 * q^68 + 6 * q^69 + 4 * q^70 + 27 * q^71 + 4 * q^72 + 18 * q^73 + 8 * q^74 - 15 * q^75 + 21 * q^76 + 16 * q^77 - 10 * q^79 + 5 * q^80 + q^81 + 14 * q^82 - 14 * q^83 + 7 * q^84 - 5 * q^85 - 36 * q^86 + 18 * q^87 - 15 * q^88 + 11 * q^89 - 24 * q^90 - 22 * q^93 - 5 * q^94 - 3 * q^95 - 42 * q^96 - 7 * q^97 - 5 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.12349	+	1.94594i	0.794427	+	1.37599i	0.923202	+	0.384315i	$0.125562\pi$
$2$	1.12349	+	1.94594i	0.794427	+	1.37599i	−0.128775	+	0.991674i	$0.541104\pi$
$3$	0.277479	+	0.480608i	0.160203	+	0.277479i	0.934941	−	0.354803i	$-0.115452\pi$
$3$	0.277479	+	0.480608i	0.160203	+	0.277479i	−0.774739	+	0.632282i	$0.782119\pi$
$4$	−1.52446	+	2.64044i	−0.762229	+	1.32022i
$5$	−1.44504			−0.646242			−0.323121	−	0.946358i	$-0.604732\pi$
$5$	−1.44504			−0.646242			−0.323121	+	0.946358i	$0.604732\pi$
$6$	−0.623490	+	1.07992i	−0.254539	+	0.440874i
$7$	−1.02446	+	1.77441i	−0.387209	+	0.670666i	−0.992073	−	0.125663i	$-0.959894\pi$
$7$	−1.02446	+	1.77441i	−0.387209	+	0.670666i	0.604864	+	0.796329i	$0.293227\pi$
$8$	−2.35690			−0.833289
$9$	1.34601	−	2.33136i	0.448670	−	0.777120i
$10$	−1.62349	−	2.81197i	−0.513393	−	0.889222i
$11$	1.27748	+	2.21266i	0.385174	+	0.667142i	0.991793	−	0.127851i	$-0.0408079\pi$
$11$	1.27748	+	2.21266i	0.385174	+	0.667142i	−0.606619	+	0.794993i	$0.707475\pi$
$12$	−1.69202			−0.488445
$13$		0			0
$13$		0			0
$14$	−4.60388			−1.23044
$15$	−0.400969	−	0.694498i	−0.103530	−	0.179319i
$16$	0.400969	+	0.694498i	0.100242	+	0.173625i
$17$	2.64795	−	4.58638i	0.642222	−	1.11236i	−0.342714	−	0.939440i	$-0.611346\pi$
$17$	2.64795	−	4.58638i	0.642222	−	1.11236i	0.984936	−	0.172921i	$-0.0553205\pi$
$18$	6.04892			1.42574
$19$	2.92543	−	5.06699i	0.671139	−	1.16245i	−0.306442	−	0.951889i	$-0.599139\pi$
$19$	2.92543	−	5.06699i	0.671139	−	1.16245i	0.977581	−	0.210558i	$-0.0675280\pi$
$20$	2.20291	−	3.81555i	0.492585	−	0.853182i
$21$	−1.13706			−0.248128
$22$	−2.87047	+	4.97180i	−0.611986	+	1.05999i
$23$	0.945042	+	1.63686i	0.197055	+	0.341309i	0.947572	−	0.319542i	$-0.103529\pi$
$23$	0.945042	+	1.63686i	0.197055	+	0.341309i	−0.750517	+	0.660851i	$0.770196\pi$
$24$	−0.653989	−	1.13274i	−0.133495	−	0.231220i
$25$	−2.91185			−0.582371
$26$		0			0
$27$	3.15883			0.607918
$28$	−3.12349	−	5.41004i	−0.590284	−	1.02240i
$29$	−1.13437	−	1.96480i	−0.210648	−	0.364853i	0.741269	−	0.671208i	$-0.234224\pi$
$29$	−1.13437	−	1.96480i	−0.210648	−	0.364853i	−0.951918	+	0.306354i	$0.900891\pi$
$30$	0.900969	−	1.56052i	0.164494	−	0.284911i
$31$	−4.26875			−0.766690			−0.383345	−	0.923605i	$-0.625228\pi$
$31$	−4.26875			−0.766690			−0.383345	+	0.923605i	$0.625228\pi$
$32$	−3.25786	+	5.64279i	−0.575915	+	0.997513i
$33$	−0.708947	+	1.22793i	−0.123412	+	0.213756i
$34$	11.8998			2.04079
$35$	1.48039	−	2.56410i	0.250231	−	0.433413i
$36$	4.10388	+	7.10812i	0.683979	+	1.18469i
$37$	−2.67845	−	4.63921i	−0.440334	−	0.762681i	0.557380	−	0.830258i	$-0.311807\pi$
$37$	−2.67845	−	4.63921i	−0.440334	−	0.762681i	−0.997714	+	0.0675764i	$0.978473\pi$
$38$	13.1468			2.13268
$39$		0			0
$40$	3.40581			0.538506
$41$	−0.637063	−	1.10343i	−0.0994926	−	0.172326i	0.811982	−	0.583682i	$-0.198389\pi$
$41$	−0.637063	−	1.10343i	−0.0994926	−	0.172326i	−0.911475	+	0.411356i	$0.865055\pi$
$42$	−1.27748	−	2.21266i	−0.197119	−	0.341421i
$43$	−3.06853	+	5.31485i	−0.467947	+	0.810507i	−0.999329	−	0.0366246i	$-0.988339\pi$
$43$	−3.06853	+	5.31485i	−0.467947	+	0.810507i	0.531382	+	0.847132i	$0.321673\pi$
$44$	−7.78986			−1.17437
$45$	−1.94504	+	3.36891i	−0.289950	+	0.502208i
$46$	−2.12349	+	3.67799i	−0.313091	+	0.542290i
$47$	−2.95108			−0.430460			−0.215230	−	0.976563i	$-0.569050\pi$
$47$	−2.95108			−0.430460			−0.215230	+	0.976563i	$0.569050\pi$
$48$	−0.222521	+	0.385418i	−0.0321181	+	0.0556302i
$49$	1.40097	+	2.42655i	0.200138	+	0.346650i
$50$	−3.27144	−	5.66630i	−0.462651	−	0.801335i
$51$	2.93900			0.411542
$52$		0			0
$53$	5.52111			0.758382			0.379191	−	0.925318i	$-0.376202\pi$
$53$	5.52111			0.758382			0.379191	+	0.925318i	$0.376202\pi$
$54$	3.54892	+	6.14691i	0.482946	+	0.836488i
$55$	−1.84601	−	3.19738i	−0.248916	−	0.431135i
$56$	2.41454	−	4.18211i	0.322657	−	0.558858i
$57$	3.24698			0.430073
$58$	2.54892	−	4.41485i	0.334689	−	0.579699i
$59$	6.10388	−	10.5722i	0.794657	−	1.37639i	−0.128400	−	0.991722i	$-0.540984\pi$
$59$	6.10388	−	10.5722i	0.794657	−	1.37639i	0.923057	−	0.384664i	$-0.125683\pi$
$60$	2.44504			0.315654
$61$	−4.28232	+	7.41720i	−0.548295	+	0.949675i	0.450096	+	0.892980i	$0.351390\pi$
$61$	−4.28232	+	7.41720i	−0.548295	+	0.949675i	−0.998392	+	0.0566953i	$0.981944\pi$
$62$	−4.79590	−	8.30674i	−0.609080	−	1.05496i
$63$	2.75786	+	4.77676i	0.347458	+	0.601815i
$64$	−13.0368			−1.62960
$65$		0			0
$66$	−3.18598			−0.392167
$67$	−0.288364	−	0.499461i	−0.0352293	−	0.0610189i	0.847873	−	0.530199i	$-0.177883\pi$
$67$	−0.288364	−	0.499461i	−0.0352293	−	0.0610189i	−0.883102	+	0.469180i	$0.844549\pi$
$68$	8.07338	+	13.9835i	0.979041	+	1.69575i
$69$	−0.524459	+	0.908389i	−0.0631374	+	0.109357i
$70$	6.65279			0.795161
$71$	2.29709	−	3.97868i	0.272615	−	0.472183i	−0.696916	−	0.717153i	$-0.745445\pi$
$71$	2.29709	−	3.97868i	0.272615	−	0.472183i	0.969531	+	0.244970i	$0.0787782\pi$
$72$	−3.17241	+	5.49477i	−0.373872	+	0.647565i
$73$	−10.5526			−1.23508			−0.617542	−	0.786538i	$-0.711872\pi$
$73$	−10.5526			−1.23508			−0.617542	+	0.786538i	$0.711872\pi$
$74$	6.01842	−	10.4242i	0.699627	−	1.21179i
$75$	−0.807979	−	1.39946i	−0.0932973	−	0.161596i
$76$	8.91939	+	15.4488i	1.02312	+	1.77210i
$77$	−5.23490			−0.596572
$78$		0			0
$79$	−15.7778			−1.77514			−0.887569	−	0.460674i	$-0.847608\pi$
$79$	−15.7778			−1.77514			−0.887569	+	0.460674i	$0.847608\pi$
$80$	−0.579417	−	1.00358i	−0.0647808	−	0.112204i
$81$	−3.16152	−	5.47592i	−0.351280	−	0.608435i
$82$	1.43147	−	2.47938i	0.158079	−	0.273801i
$83$	7.72348			0.847762			0.423881	−	0.905718i	$-0.360667\pi$
$83$	7.72348			0.847762			0.423881	+	0.905718i	$0.360667\pi$
$84$	1.73341	−	3.00235i	0.189130	−	0.327583i
$85$	−3.82640	+	6.62751i	−0.415031	+	0.718855i
$86$	−13.7899			−1.48700
$87$	0.629531	−	1.09038i	0.0674928	−	0.116901i
$88$	−3.01089	−	5.21501i	−0.320961	−	0.555922i
$89$	−3.30678	−	5.72751i	−0.350518	−	0.607115i	0.635822	−	0.771836i	$-0.280661\pi$
$89$	−3.30678	−	5.72751i	−0.350518	−	0.607115i	−0.986340	+	0.164720i	$0.947328\pi$
$90$	−8.74094			−0.921376
$91$		0			0
$92$	−5.76271			−0.600804
$93$	−1.18449	−	2.05159i	−0.122826	−	0.212740i
$94$	−3.31551	−	5.74263i	−0.341969	−	0.592307i
$95$	−4.22737	+	7.32201i	−0.433719	+	0.751223i
$96$	−3.61596			−0.369052
$97$	−5.96346	+	10.3290i	−0.605498	+	1.04875i	0.386475	+	0.922300i	$0.373693\pi$
$97$	−5.96346	+	10.3290i	−0.605498	+	1.04875i	−0.991973	+	0.126453i	$0.959641\pi$
$98$	−3.14795	+	5.45241i	−0.317991	+	0.550776i
$99$	6.87800			0.691265
$100$	4.43900	−	7.68858i	0.443900	−	0.768858i
$101$	−6.53199	−	11.3137i	−0.649957	−	1.12576i	−0.983133	−	0.182894i	$-0.941453\pi$
$101$	−6.53199	−	11.3137i	−0.649957	−	1.12576i	0.333175	−	0.942865i	$-0.391880\pi$
$102$	3.30194	+	5.71912i	0.326941	+	0.566278i
$103$	9.16852			0.903401			0.451701	−	0.892170i	$-0.350818\pi$
$103$	9.16852			0.903401			0.451701	+	0.892170i	$0.350818\pi$
$104$		0			0
$105$	1.64310			0.160351
$106$	6.20291	+	10.7437i	0.602480	+	1.04353i
$107$	3.44989	+	5.97538i	0.333513	+	0.577662i	0.983198	−	0.182542i	$-0.0584325\pi$
$107$	3.44989	+	5.97538i	0.333513	+	0.577662i	−0.649685	+	0.760204i	$0.725099\pi$
$108$	−4.81551	+	8.34071i	−0.463373	+	0.802585i
$109$	0.121998			0.0116853			0.00584264	−	0.999983i	$-0.498140\pi$
$109$	0.121998			0.0116853			0.00584264	+	0.999983i	$0.498140\pi$
$110$	4.14795	−	7.18446i	0.395491	−	0.685011i
$111$	1.48643	−	2.57457i	0.141085	−	0.244367i
$112$	−1.64310			−0.155259
$113$	−3.65399	+	6.32890i	−0.343738	+	0.595372i	−0.985124	−	0.171847i	$-0.945027\pi$
$113$	−3.65399	+	6.32890i	−0.343738	+	0.595372i	0.641385	+	0.767219i	$0.278360\pi$
$114$	3.64795	+	6.31843i	0.341662	+	0.591775i
$115$	−1.36563	−	2.36533i	−0.127345	−	0.220568i
$116$	6.91723			0.642249
$117$		0			0
$118$	27.4306			2.52519
$119$	5.42543	+	9.39712i	0.497348	+	0.861432i
$120$	0.945042	+	1.63686i	0.0862701	+	0.149424i
$121$	2.23609	−	3.87303i	0.203281	−	0.352094i
$122$	−19.2446			−1.74232
$123$	0.353543	−	0.612355i	0.0318779	−	0.0552142i
$124$	6.50753	−	11.2714i	0.584394	−	1.01220i
$125$	11.4330			1.02260
$126$	−6.19687	+	10.7333i	−0.552061	+	0.956197i
$127$	9.48523	+	16.4289i	0.841678	+	1.45783i	0.888475	+	0.458925i	$0.151765\pi$
$127$	9.48523	+	16.4289i	0.841678	+	1.45783i	−0.0467971	+	0.998904i	$0.514901\pi$
$128$	−8.13102	−	14.0833i	−0.718688	−	1.24480i
$129$	−3.40581			−0.299865
$130$		0			0
$131$	3.25667			0.284536			0.142268	−	0.989828i	$-0.454560\pi$
$131$	3.25667			0.284536			0.142268	+	0.989828i	$0.454560\pi$
$132$	−2.16152	−	3.74387i	−0.188136	−	0.325862i
$133$	5.99396	+	10.3818i	0.519742	+	0.900220i
$134$	0.647948	−	1.12228i	0.0559742	−	0.0969502i
$135$	−4.56465			−0.392862
$136$	−6.24094	+	10.8096i	−0.535156	+	0.926918i
$137$	−0.396125	+	0.686108i	−0.0338432	+	0.0586181i	−0.882451	−	0.470405i	$-0.844108\pi$
$137$	−0.396125	+	0.686108i	−0.0338432	+	0.0586181i	0.848608	+	0.529023i	$0.177441\pi$
$138$	−2.35690			−0.200632
$139$	5.66972	−	9.82024i	0.480899	−	0.832942i	−0.518861	−	0.854859i	$-0.673644\pi$
$139$	5.66972	−	9.82024i	0.480899	−	0.832942i	0.999760	+	0.0219169i	$0.00697694\pi$
$140$	4.51357	+	7.81774i	0.381467	+	0.660720i
$141$	−0.818864	−	1.41831i	−0.0689608	−	0.119444i
$142$	10.3230			0.866291
$143$		0			0
$144$	2.15883			0.179903
$145$	1.63922	+	2.83921i	0.136130	+	0.235784i
$146$	−11.8557	−	20.5347i	−0.981185	−	1.69946i
$147$	−0.777479	+	1.34663i	−0.0641254	+	0.111068i
$148$	16.3327			1.34254
$149$	−4.20291	+	7.27965i	−0.344316	+	0.596372i	−0.985229	−	0.171241i	$-0.945222\pi$
$149$	−4.20291	+	7.27965i	−0.344316	+	0.596372i	0.640914	+	0.767613i	$0.278556\pi$
$150$	1.81551	−	3.14456i	0.148236	−	0.256752i
$151$	14.1293			1.14983			0.574913	−	0.818215i	$-0.305036\pi$
$151$	14.1293			1.14983			0.574913	+	0.818215i	$0.305036\pi$
$152$	−6.89493	+	11.9424i	−0.559253	+	0.968654i
$153$	−7.12833	−	12.3466i	−0.576292	−	0.998166i
$154$	−5.88135	−	10.1868i	−0.473933	−	0.820876i
$155$	6.16852			0.495468
$156$		0			0
$157$	−9.43296			−0.752832			−0.376416	−	0.926451i	$-0.622844\pi$
$157$	−9.43296			−0.752832			−0.376416	+	0.926451i	$0.622844\pi$
$158$	−17.7262	−	30.7026i	−1.41022	−	2.44257i
$159$	1.53199	+	2.65349i	0.121495	+	0.210435i
$160$	4.70775	−	8.15406i	0.372180	−	0.644635i
$161$	−3.87263			−0.305206
$162$	7.10388	−	12.3043i	0.558133	−	0.966715i
$163$	−4.35205	+	7.53797i	−0.340879	+	0.590420i	−0.984596	−	0.174844i	$-0.944058\pi$
$163$	−4.35205	+	7.53797i	−0.340879	+	0.590420i	0.643717	+	0.765263i	$0.277391\pi$
$164$	3.88471			0.303345
$165$	1.02446	−	1.77441i	0.0797540	−	0.138138i
$166$	8.67725	+	15.0294i	0.673485	+	1.16651i
$167$	11.9269	+	20.6580i	0.922933	+	1.59857i	0.794853	+	0.606803i	$0.207548\pi$
$167$	11.9269	+	20.6580i	0.922933	+	1.59857i	0.128080	+	0.991764i	$0.459119\pi$
$168$	2.67994			0.206762
$169$		0			0
$170$	−17.1957			−1.31885
$171$	−7.87531	−	13.6404i	−0.602240	−	1.04311i
$172$	−9.35570	−	16.2045i	−0.713365	−	1.23559i
$173$	9.42758	−	16.3291i	0.716766	−	1.24147i	−0.245509	−	0.969394i	$-0.578955\pi$
$173$	9.42758	−	16.3291i	0.716766	−	1.24147i	0.962274	−	0.272081i	$-0.0877117\pi$
$174$	2.82908			0.214472
$175$	2.98307	−	5.16684i	0.225499	−	0.390576i
$176$	−1.02446	+	1.77441i	−0.0772215	+	0.133752i
$177$	6.77479			0.509224
$178$	7.43027	−	12.8696i	0.556922	−	0.964618i
$179$	−3.01089	−	5.21501i	−0.225044	−	0.389788i	0.731289	−	0.682068i	$-0.238919\pi$
$179$	−3.01089	−	5.21501i	−0.225044	−	0.389788i	−0.956333	+	0.292280i	$0.905586\pi$
$180$	−5.93027	−	10.2715i	−0.442016	−	0.765595i
$181$	−4.77777			−0.355129			−0.177565	−	0.984109i	$-0.556822\pi$
$181$	−4.77777			−0.355129			−0.177565	+	0.984109i	$0.556822\pi$
$182$		0			0
$183$	−4.75302			−0.351353
$184$	−2.22737	−	3.85791i	−0.164204	−	0.284409i
$185$	3.87047	+	6.70385i	0.284563	+	0.492877i
$186$	2.66152	−	4.60989i	0.195152	−	0.338014i
$187$	13.5308			0.989470
$188$	4.49880	−	7.79216i	0.328109	−	0.568301i
$189$	−3.23609	+	5.60508i	−0.235391	+	0.407710i
$190$	−18.9976			−1.37823
$191$	−9.21528	+	15.9613i	−0.666795	+	1.15492i	0.312001	+	0.950082i	$0.399001\pi$
$191$	−9.21528	+	15.9613i	−0.666795	+	1.15492i	−0.978795	+	0.204840i	$0.934333\pi$
$192$	−3.61745	−	6.26561i	−0.261067	−	0.452181i
$193$	−3.02715	−	5.24317i	−0.217899	−	0.377412i	0.736267	−	0.676692i	$-0.236587\pi$
$193$	−3.02715	−	5.24317i	−0.217899	−	0.377412i	−0.954165	+	0.299280i	$0.903254\pi$
$194$	−26.7995			−1.92410
$195$		0			0
$196$	−8.54288			−0.610205
$197$	5.70775	+	9.88611i	0.406660	+	0.704357i	0.994513	−	0.104611i	$-0.0333599\pi$
$197$	5.70775	+	9.88611i	0.406660	+	0.704357i	−0.587853	+	0.808968i	$0.700027\pi$
$198$	7.72737	+	13.3842i	0.549160	+	0.951173i
$199$	6.95257	−	12.0422i	0.492855	−	0.853650i	−0.507111	−	0.861881i	$-0.669287\pi$
$199$	6.95257	−	12.0422i	0.492855	−	0.853650i	0.999966	+	0.00823084i	$0.00261999\pi$
$200$	6.86294			0.485283
$201$	0.160030	−	0.277180i	0.0112876	−	0.0195508i
$202$	14.6773	−	25.4217i	1.03269	−	1.78867i
$203$	4.64848			0.326259
$204$	−4.48039	+	7.76026i	−0.313690	+	0.543327i
$205$	0.920583	+	1.59450i	0.0642963	+	0.111364i
$206$	10.3007	+	17.8414i	0.717687	+	1.24307i
$207$	5.08815			0.353651
$208$		0			0
$209$	14.9487			1.03402
$210$	1.84601	+	3.19738i	0.127387	+	0.220640i
$211$	6.62229	+	11.4701i	0.455897	+	0.789638i	0.998739	−	0.0501974i	$-0.0159850\pi$
$211$	6.62229	+	11.4701i	0.455897	+	0.789638i	−0.542842	+	0.839835i	$0.682652\pi$
$212$	−8.41670	+	14.5781i	−0.578061	+	1.00123i
$213$	2.54958			0.174694
$214$	−7.75182	+	13.4266i	−0.529904	+	0.917820i
$215$	4.43416	−	7.68018i	0.302407	−	0.523784i
$216$	−7.44504			−0.506571
$217$	4.37316	−	7.57453i	0.296869	−	0.514193i
$218$	0.137063	+	0.237401i	0.00928310	+	0.0160788i
$219$	−2.92812	−	5.07165i	−0.197864	−	0.342710i
$220$	11.2567			0.758924
$221$		0			0
$222$	6.67994			0.448328
$223$	3.66756	+	6.35241i	0.245598	+	0.425389i	0.962300	−	0.271992i	$-0.0876823\pi$
$223$	3.66756	+	6.35241i	0.245598	+	0.425389i	−0.716701	+	0.697380i	$0.754349\pi$
$224$	−6.67510	−	11.5616i	−0.445999	−	0.772492i
$225$	−3.91939	+	6.78858i	−0.261292	+	0.452572i
$226$	−16.4209			−1.09230
$227$	4.33728	−	7.51239i	0.287875	−	0.498615i	−0.685427	−	0.728141i	$-0.740384\pi$
$227$	4.33728	−	7.51239i	0.287875	−	0.498615i	0.973302	+	0.229526i	$0.0737177\pi$
$228$	−4.94989	+	8.57345i	−0.327814	+	0.567791i
$229$	−13.6866			−0.904439			−0.452219	−	0.891907i	$-0.649368\pi$
$229$	−13.6866			−0.904439			−0.452219	+	0.891907i	$0.649368\pi$
$230$	3.06853	−	5.31485i	0.202333	−	0.350451i
$231$	−1.45257	−	2.51593i	−0.0955724	−	0.165536i
$232$	2.67360	+	4.63082i	0.175531	+	0.304028i
$233$	−5.08815			−0.333336			−0.166668	−	0.986013i	$-0.553301\pi$
$233$	−5.08815			−0.333336			−0.166668	+	0.986013i	$0.553301\pi$
$234$		0			0
$235$	4.26444			0.278181
$236$	18.6102	+	32.2338i	1.21142	+	2.09824i
$237$	−4.37800	−	7.58292i	−0.284382	−	0.492564i
$238$	−12.1908	+	21.1151i	−0.790214	+	1.36869i
$239$	−10.9239			−0.706611			−0.353305	−	0.935508i	$-0.614942\pi$
$239$	−10.9239			−0.706611			−0.353305	+	0.935508i	$0.614942\pi$
$240$	0.321552	−	0.556945i	0.0207561	−	0.0359506i
$241$	−5.95742	+	10.3186i	−0.383751	+	0.664676i	−0.991595	−	0.129380i	$-0.958701\pi$
$241$	−5.95742	+	10.3186i	−0.383751	+	0.664676i	0.607844	+	0.794056i	$0.292035\pi$
$242$	10.0489			0.645969
$243$	6.49276	−	11.2458i	0.416511	−	0.721418i
$244$	−13.0565	−	22.6144i	−0.835854	−	1.44774i
$245$	−2.02446	−	3.50647i	−0.129338	−	0.224020i
$246$	1.58881			0.101299
$247$		0			0
$248$	10.0610			0.638874
$249$	2.14310	+	3.71197i	0.135814	+	0.235236i
$250$	12.8448	+	22.2479i	0.812377	+	1.40708i
$251$	−11.1739	+	19.3538i	−0.705290	+	1.22160i	0.261296	+	0.965259i	$0.415850\pi$
$251$	−11.1739	+	19.3538i	−0.705290	+	1.22160i	−0.966587	+	0.256340i	$0.917483\pi$
$252$	−16.8170			−1.05937
$253$	−2.41454	+	4.18211i	−0.151801	+	0.262927i
$254$	−21.3131	+	36.9154i	−1.33730	+	2.31628i
$255$	−4.24698			−0.265956
$256$	5.23341	−	9.06453i	0.327088	−	0.566533i
$257$	9.33004	+	16.1601i	0.581992	+	1.00804i	0.995243	+	0.0974228i	$0.0310599\pi$
$257$	9.33004	+	16.1601i	0.581992	+	1.00804i	−0.413251	+	0.910617i	$0.635607\pi$
$258$	−3.82640	−	6.62751i	−0.238221	−	0.412611i
$259$	10.9758			0.682005
$260$		0			0
$261$	−6.10752			−0.378046
$262$	3.65883	+	6.33729i	0.226043	+	0.391519i
$263$	−7.19955	−	12.4700i	−0.443944	−	0.768933i	0.554034	−	0.832494i	$-0.313088\pi$
$263$	−7.19955	−	12.4700i	−0.443944	−	0.768933i	−0.997978	+	0.0635610i	$0.979754\pi$
$264$	1.67092	−	2.89411i	0.102838	−	0.178120i
$265$	−7.97823			−0.490099
$266$	−13.4683	+	23.3278i	−0.825795	+	1.43032i
$267$	1.83513	−	3.17853i	0.112308	−	0.194523i
$268$	1.75840			0.107411
$269$	−0.326396	+	0.565335i	−0.0199007	+	0.0344691i	−0.875804	−	0.482666i	$-0.839668\pi$
$269$	−0.326396	+	0.565335i	−0.0199007	+	0.0344691i	0.855904	+	0.517136i	$0.173002\pi$
$270$	−5.12833	−	8.88254i	−0.312100	−	0.540574i
$271$	0.997844	+	1.72832i	0.0606147	+	0.104988i	0.894740	−	0.446587i	$-0.147361\pi$
$271$	0.997844	+	1.72832i	0.0606147	+	0.104988i	−0.834126	+	0.551574i	$0.814027\pi$
$272$	4.24698			0.257511
$273$		0			0
$274$	−1.78017			−0.107544
$275$	−3.71983	−	6.44294i	−0.224314	−	0.388524i
$276$	−1.59903	−	2.76960i	−0.0962504	−	0.166711i
$277$	−5.89224	+	10.2057i	−0.354030	+	0.613199i	−0.986952	−	0.161018i	$-0.948522\pi$
$277$	−5.89224	+	10.2057i	−0.354030	+	0.613199i	0.632921	+	0.774216i	$0.281856\pi$
$278$	25.4795			1.52816
$279$	−5.74578	+	9.95199i	−0.343991	+	0.595810i
$280$	−3.48911	+	6.04332i	−0.208514	+	0.361158i
$281$	−6.47219			−0.386098			−0.193049	−	0.981189i	$-0.561838\pi$
$281$	−6.47219			−0.386098			−0.193049	+	0.981189i	$0.561838\pi$
$282$	1.83997	−	3.18692i	0.109569	−	0.189778i
$283$	−3.29052	−	5.69935i	−0.195601	−	0.338791i	0.751496	−	0.659737i	$-0.229332\pi$
$283$	−3.29052	−	5.69935i	−0.195601	−	0.338791i	−0.947097	+	0.320946i	$0.895999\pi$
$284$	7.00365	+	12.1307i	0.415590	+	0.719823i
$285$	−4.69202			−0.277931
$286$		0			0
$287$	2.61058			0.154098
$288$	8.77024	+	15.1905i	0.516791	+	0.895109i
$289$	−5.52326	−	9.56657i	−0.324898	−	0.562739i
$290$	−3.68329	+	6.37965i	−0.216290	+	0.374626i
$291$	−6.61894			−0.388009
$292$	16.0869	−	27.8634i	0.941418	−	1.63058i
$293$	12.1691	−	21.0774i	0.710924	−	1.23136i	−0.253587	−	0.967313i	$-0.581610\pi$
$293$	12.1691	−	21.0774i	0.710924	−	1.23136i	0.964511	−	0.264044i	$-0.0850563\pi$
$294$	−3.49396			−0.203772
$295$	−8.82036	+	15.2773i	−0.513541	+	0.889479i
$296$	6.31282	+	10.9341i	0.366925	+	0.635533i
$297$	4.03534	+	6.98942i	0.234154	+	0.405567i
$298$	−18.8877			−1.09413
$299$		0			0
$300$	4.92692			0.284456
$301$	−6.28717	−	10.8897i	−0.362386	−	0.627672i
$302$	15.8741	+	27.4948i	0.913453	+	1.58215i
$303$	3.62498	−	6.27865i	0.208250	−	0.360699i
$304$	4.69202			0.269106
$305$	6.18814	−	10.7182i	0.354332	−	0.613720i
$306$	16.0172	−	27.7426i	0.915644	−	1.58594i
$307$	−14.0737			−0.803227			−0.401613	−	0.915809i	$-0.631550\pi$
$307$	−14.0737			−0.803227			−0.401613	+	0.915809i	$0.631550\pi$
$308$	7.98039	−	13.8224i	0.454725	−	0.787606i
$309$	2.54407	+	4.40646i	0.144727	+	0.250675i
$310$	6.93027	+	12.0036i	0.393613	+	0.681758i
$311$	−29.7700			−1.68810			−0.844051	−	0.536263i	$-0.819836\pi$
$311$	−29.7700			−1.68810			−0.844051	+	0.536263i	$0.819836\pi$
$312$		0			0
$313$	−7.47889			−0.422732			−0.211366	−	0.977407i	$-0.567791\pi$
$313$	−7.47889			−0.422732			−0.211366	+	0.977407i	$0.567791\pi$
$314$	−10.5978	−	18.3560i	−0.598070	−	1.03589i
$315$	−3.98523	−	6.90262i	−0.224542	−	0.388919i
$316$	24.0526	−	41.6603i	1.35306	−	2.34357i
$317$	30.0301			1.68666			0.843330	−	0.537396i	$-0.180592\pi$
$317$	30.0301			1.68666			0.843330	+	0.537396i	$0.180592\pi$
$318$	−3.44235	+	5.96233i	−0.193038	+	0.334351i
$319$	2.89828	−	5.01997i	0.162273	−	0.281064i
$320$	18.8388			1.05312
$321$	−1.91454	+	3.31608i	−0.106859	+	0.185086i
$322$	−4.35086	−	7.53590i	−0.242464	−	0.419959i
$323$	−15.4928	−	26.8343i	−0.862040	−	1.49310i
$324$	19.2784			1.07102
$325$		0			0
$326$	−19.5579			−1.08321
$327$	0.0338518	+	0.0586331i	0.00187201	+	0.00324242i
$328$	1.50149	+	2.60066i	0.0829060	+	0.143597i
$329$	3.02326	−	5.23644i	0.166678	−	0.288694i
$330$	4.60388			0.253435
$331$	7.85839	−	13.6111i	0.431936	−	0.748135i	−0.565104	−	0.825020i	$-0.691164\pi$
$331$	7.85839	−	13.6111i	0.431936	−	0.748135i	0.997040	+	0.0768845i	$0.0244973\pi$
$332$	−11.7741	+	20.3934i	−0.646189	+	1.11923i
$333$	−14.4209			−0.790259
$334$	−26.7995	+	46.4182i	−1.46641	+	2.53989i
$335$	0.416698	+	0.721743i	0.0227667	+	0.0394330i
$336$	−0.455927	−	0.789689i	−0.0248729	−	0.0430811i
$337$	1.95407			0.106445			0.0532224	−	0.998583i	$-0.483051\pi$
$337$	1.95407			0.106445			0.0532224	+	0.998583i	$0.483051\pi$
$338$		0			0
$339$	−4.05562			−0.220271
$340$	−11.6664	−	20.2067i	−0.632698	−	1.09586i
$341$	−5.45324	−	9.44529i	−0.295309	−	0.511491i
$342$	17.6957	−	30.6498i	0.956872	−	1.65735i
$343$	−20.0834			−1.08440
$344$	7.23221	−	12.5266i	0.389935	−	0.675387i
$345$	0.757865	−	1.31266i	0.0408021	−	0.0706713i
$346$	42.3672			2.27767
$347$	8.56249	−	14.8307i	0.459659	−	0.796152i	−0.539284	−	0.842124i	$-0.681305\pi$
$347$	8.56249	−	14.8307i	0.459659	−	0.796152i	0.998943	+	0.0459718i	$0.0146384\pi$
$348$	1.91939	+	3.32448i	0.102890	+	0.178211i
$349$	5.23341	+	9.06453i	0.280138	+	0.485213i	0.971418	−	0.237373i	$-0.0762865\pi$
$349$	5.23341	+	9.06453i	0.280138	+	0.485213i	−0.691281	+	0.722586i	$0.742953\pi$
$350$	13.4058			0.716571
$351$		0			0
$352$	−16.6474			−0.887310
$353$	−7.76540	−	13.4501i	−0.413310	−	0.715875i	0.581939	−	0.813232i	$-0.302294\pi$
$353$	−7.76540	−	13.4501i	−0.413310	−	0.715875i	−0.995249	+	0.0973578i	$0.968961\pi$
$354$	7.61141	+	13.1833i	0.404542	+	0.700687i
$355$	−3.31940	+	5.74936i	−0.176175	+	0.305144i
$356$	20.1642			1.06870
$357$	−3.01089	+	5.21501i	−0.159353	+	0.276007i
$358$	6.76540	−	11.7180i	0.357562	−	0.619316i
$359$	−21.4263			−1.13083			−0.565417	−	0.824805i	$-0.691285\pi$
$359$	−21.4263			−1.13083			−0.565417	+	0.824805i	$0.691285\pi$
$360$	4.58426	−	7.94017i	0.241612	−	0.418484i
$361$	−7.61625	−	13.1917i	−0.400855	−	0.694302i
$362$	−5.36778	−	9.29727i	−0.282124	−	0.488654i
$363$	2.48188			0.130265
$364$		0			0
$365$	15.2489			0.798164
$366$	−5.33997	−	9.24910i	−0.279125	−	0.483458i
$367$	−17.1516	−	29.7074i	−0.895306	−	1.55072i	−0.833425	−	0.552632i	$-0.813624\pi$
$367$	−17.1516	−	29.7074i	−0.895306	−	1.55072i	−0.0618807	−	0.998084i	$-0.519710\pi$
$368$	−0.757865	+	1.31266i	−0.0395064	+	0.0684271i
$369$	−3.42998			−0.178557
$370$	−8.69687	+	15.0634i	−0.452129	+	0.783110i
$371$	−5.65615	+	9.79673i	−0.293652	+	0.508621i
$372$	7.22282			0.374486
$373$	6.29805	−	10.9085i	0.326101	−	0.564823i	−0.655634	−	0.755079i	$-0.727598\pi$
$373$	6.29805	−	10.9085i	0.326101	−	0.564823i	0.981735	+	0.190256i	$0.0609318\pi$
$374$	15.2017	+	26.3301i	0.786062	+	1.36150i
$375$	3.17241	+	5.49477i	0.163822	+	0.283749i
$376$	6.95539			0.358697
$377$		0			0
$378$	−14.5429			−0.748005
$379$	−8.26928	−	14.3228i	−0.424765	−	0.735714i	0.571634	−	0.820509i	$-0.306310\pi$
$379$	−8.26928	−	14.3228i	−0.424765	−	0.735714i	−0.996398	+	0.0847951i	$0.972976\pi$
$380$	−12.8889	−	22.3242i	−0.661186	−	1.14521i
$381$	−5.26391	+	9.11735i	−0.269678	+	0.467096i
$382$	−41.4131			−2.11888
$383$	−3.76809	+	6.52652i	−0.192540	+	0.333489i	−0.946091	−	0.323900i	$-0.895006\pi$
$383$	−3.76809	+	6.52652i	−0.192540	+	0.333489i	0.753551	+	0.657389i	$0.228339\pi$
$384$	4.51238	−	7.81567i	0.230271	−	0.398842i
$385$	7.56465			0.385530
$386$	6.80194	−	11.7813i	0.346210	−	0.599652i
$387$	8.26055	+	14.3077i	0.419908	+	0.727301i
$388$	−18.1821	−	31.4923i	−0.923056	−	1.59878i
$389$	35.5555			1.80274			0.901369	−	0.433052i	$-0.142563\pi$
$389$	35.5555			1.80274			0.901369	+	0.433052i	$0.142563\pi$
$390$		0			0
$391$	10.0097			0.506212
$392$	−3.30194	−	5.71912i	−0.166773	−	0.288859i
$393$	0.903657	+	1.56518i	0.0455835	+	0.0789529i
$394$	−12.8252	+	22.2139i	−0.646124	+	1.11912i
$395$	22.7995			1.14717
$396$	−10.4852	+	18.1610i	−0.526903	+	0.912622i
$397$	−0.675760	+	1.17045i	−0.0339154	+	0.0587432i	−0.882485	−	0.470341i	$-0.844131\pi$
$397$	−0.675760	+	1.17045i	−0.0339154	+	0.0587432i	0.848569	+	0.529084i	$0.177464\pi$
$398$	31.2446			1.56615
$399$	−3.32640	+	5.76149i	−0.166528	+	0.288435i
$400$	−1.16756	−	2.02228i	−0.0583781	−	0.101114i
$401$	−0.289561	−	0.501534i	−0.0144600	−	0.0250454i	0.858705	−	0.512470i	$-0.171270\pi$
$401$	−0.289561	−	0.501534i	−0.0144600	−	0.0250454i	−0.873165	+	0.487425i	$0.837936\pi$
$402$	0.719169			0.0358689
$403$		0			0
$404$	39.8310			1.98167
$405$	4.56853	+	7.91293i	0.227012	+	0.393197i
$406$	5.22252	+	9.04567i	0.259189	+	0.448929i
$407$	6.84332	−	11.8530i	0.339211	−	0.587531i
$408$	−6.92692			−0.342934
$409$	7.57875	−	13.1268i	0.374745	−	0.649078i	−0.615544	−	0.788103i	$-0.711064\pi$
$409$	7.57875	−	13.1268i	0.374745	−	0.649078i	0.990289	+	0.139025i	$0.0443969\pi$
$410$	−2.06853	+	3.58280i	−0.102157	+	0.176942i
$411$	−0.439665			−0.0216871
$412$	−13.9770	+	24.2089i	−0.688599	+	1.19269i
$413$	12.5063	+	21.6616i	0.615397	+	1.06590i
$414$	5.71648	+	9.90123i	0.280950	+	0.486619i
$415$	−11.1608			−0.547860
$416$		0			0
$417$	6.29291			0.308165
$418$	16.7947	+	29.0893i	0.821456	+	1.42280i
$419$	17.8617	+	30.9374i	0.872603	+	1.51139i	0.859294	+	0.511481i	$0.170903\pi$
$419$	17.8617	+	30.9374i	0.872603	+	1.51139i	0.0133088	+	0.999911i	$0.495764\pi$
$420$	−2.50484	+	4.33852i	−0.122224	+	0.211698i
$421$	−35.0465			−1.70806			−0.854032	−	0.520221i	$-0.825849\pi$
$421$	−35.0465			−1.70806			−0.854032	+	0.520221i	$0.825849\pi$
$422$	−14.8802	+	25.7732i	−0.724355	+	1.25462i
$423$	−3.97219	+	6.88003i	−0.193134	+	0.334519i
$424$	−13.0127			−0.631951
$425$	−7.71044	+	13.3549i	−0.374011	+	0.647806i
$426$	2.86443	+	4.96134i	0.138782	+	0.240378i
$427$	−8.77413	−	15.1972i	−0.424610	−	0.735446i
$428$	−21.0368			−1.01685
$429$		0			0
$430$	19.9269			0.960961
$431$	17.1407	+	29.6886i	0.825639	+	1.43005i	0.901430	+	0.432925i	$0.142519\pi$
$431$	17.1407	+	29.6886i	0.825639	+	1.43005i	−0.0757909	+	0.997124i	$0.524148\pi$
$432$	1.26659	+	2.19381i	0.0609390	+	0.105549i
$433$	−6.86927	+	11.8979i	−0.330116	+	0.571778i	−0.982534	−	0.186081i	$-0.940421\pi$
$433$	−6.86927	+	11.8979i	−0.330116	+	0.571778i	0.652418	+	0.757859i	$0.273755\pi$
$434$	19.6528			0.943364
$435$	−0.909698	+	1.57564i	−0.0436167	+	0.0755463i
$436$	−0.185981	+	0.322128i	−0.00890686	+	0.0154271i
$437$	11.0586			0.529005
$438$	6.57942	−	11.3959i	0.314377	−	0.544516i
$439$	−5.12014	−	8.86834i	−0.244371	−	0.423263i	0.717584	−	0.696472i	$-0.245248\pi$
$439$	−5.12014	−	8.86834i	−0.244371	−	0.423263i	−0.961955	+	0.273210i	$0.911915\pi$
$440$	4.35086	+	7.53590i	0.207419	+	0.359260i
$441$	7.54288			0.359185
$442$		0			0
$443$	12.1763			0.578513			0.289257	−	0.957252i	$-0.406592\pi$
$443$	12.1763			0.578513			0.289257	+	0.957252i	$0.406592\pi$
$444$	4.53199	+	7.84964i	0.215079	+	0.372527i
$445$	4.77844	+	8.27650i	0.226520	+	0.392344i
$446$	−8.24094	+	14.2737i	−0.390220	+	0.675880i
$447$	−4.66487			−0.220641
$448$	13.3557	−	23.1327i	0.630997	−	1.09292i
$449$	6.45257	−	11.1762i	0.304516	−	0.527437i	−0.672638	−	0.739972i	$-0.734839\pi$
$449$	6.45257	−	11.1762i	0.304516	−	0.527437i	0.977153	+	0.212535i	$0.0681720\pi$
$450$	−17.6136			−0.830311
$451$	1.62767	−	2.81921i	0.0766440	−	0.132751i
$452$	−11.1407	−	19.2963i	−0.524015	−	0.907621i
$453$	3.92058	+	6.79065i	0.184205	+	0.319053i
$454$	19.4916			0.914785
$455$		0			0
$456$	−7.65279			−0.358375
$457$	−2.32855	−	4.03317i	−0.108925	−	0.188664i	0.806410	−	0.591357i	$-0.201408\pi$
$457$	−2.32855	−	4.03317i	−0.108925	−	0.188664i	−0.915335	+	0.402693i	$0.868074\pi$
$458$	−15.3768	−	26.6334i	−0.718511	−	1.24450i
$459$	8.36443	−	14.4876i	0.390418	−	0.676224i
$460$	8.32736			0.388265
$461$	15.7702	−	27.3149i	0.734493	−	1.27218i	−0.220452	−	0.975398i	$-0.570753\pi$
$461$	15.7702	−	27.3149i	0.734493	−	1.27218i	0.954945	−	0.296782i	$-0.0959135\pi$
$462$	3.26391	−	5.65325i	0.151851	−	0.263013i
$463$	17.6504			0.820284			0.410142	−	0.912022i	$-0.365479\pi$
$463$	17.6504			0.820284			0.410142	+	0.912022i	$0.365479\pi$
$464$	0.909698	−	1.57564i	0.0422317	−	0.0731474i
$465$	1.71164	+	2.96464i	0.0793752	+	0.137482i
$466$	−5.71648	−	9.90123i	−0.264811	−	0.458666i
$467$	−32.1726			−1.48877			−0.744385	−	0.667751i	$-0.767257\pi$
$467$	−32.1726			−1.48877			−0.744385	+	0.667751i	$0.767257\pi$
$468$		0			0
$469$	1.18167			0.0545644
$470$	4.79105	+	8.29835i	0.220995	+	0.382774i
$471$	−2.61745	−	4.53355i	−0.120606	−	0.208895i
$472$	−14.3862	+	24.9176i	−0.662178	+	1.14693i
$473$	−15.6799			−0.720964
$474$	9.83728	−	17.0387i	0.451841	−	0.782612i
$475$	−8.51842	+	14.7543i	−0.390852	+	0.676975i
$476$	−33.0834			−1.51637
$477$	7.43147	−	12.8717i	0.340264	−	0.589354i
$478$	−12.2729	−	21.2573i	−0.561351	−	0.972288i
$479$	17.4499	+	30.2241i	0.797306	+	1.38097i	0.921365	+	0.388699i	$0.127075\pi$
$479$	17.4499	+	30.2241i	0.797306	+	1.38097i	−0.124059	+	0.992275i	$0.539591\pi$
$480$	5.22521			0.238497
$481$		0			0
$482$	−26.7724			−1.21945
$483$	−1.07457	−	1.86121i	−0.0488947	−	0.0846882i
$484$	6.81767	+	11.8085i	0.309894	+	0.536752i
$485$	8.61745	−	14.9259i	0.391298	−	0.677748i
$486$	29.1782			1.32355
$487$	−20.9175	+	36.2302i	−0.947864	+	1.64175i	−0.197950	+	0.980212i	$0.563428\pi$
$487$	−20.9175	+	36.2302i	−0.947864	+	1.64175i	−0.749914	+	0.661536i	$0.769905\pi$
$488$	10.0930	−	17.4816i	0.456888	−	0.791354i
$489$	−4.83041			−0.218439
$490$	4.54892	−	7.87896i	0.205499	−	0.355935i
$491$	−10.9227	−	18.9187i	−0.492936	−	0.853791i	0.507031	−	0.861928i	$-0.330743\pi$
$491$	−10.9227	−	18.9187i	−0.492936	−	0.853791i	−0.999967	+	0.00813732i	$0.997410\pi$
$492$	1.07792	+	1.86702i	0.0485966	+	0.0841718i
$493$	−12.0151			−0.541131
$494$		0			0
$495$	−9.93900			−0.446725
$496$	−1.71164	−	2.96464i	−0.0768547	−	0.133116i
$497$	4.70655	+	8.15199i	0.211118	+	0.365667i
$498$	−4.81551	+	8.34071i	−0.215788	+	0.373756i
$499$	23.5472			1.05412			0.527058	−	0.849829i	$-0.323295\pi$
$499$	23.5472			1.05412			0.527058	+	0.849829i	$0.323295\pi$
$500$	−17.4291	+	30.1880i	−0.779452	+	1.35005i
$501$	−6.61894	+	11.4643i	−0.295712	+	0.512189i
$502$	−50.2150			−2.24121
$503$	3.54341	−	6.13736i	0.157993	−	0.273652i	−0.776152	−	0.630546i	$-0.782831\pi$
$503$	3.54341	−	6.13736i	0.157993	−	0.273652i	0.934145	+	0.356894i	$0.116164\pi$
$504$	−6.50000	−	11.2583i	−0.289533	−	0.501486i
$505$	9.43900	+	16.3488i	0.420030	+	0.727513i
$506$	−10.8509			−0.482379
$507$		0			0
$508$	−57.8394			−2.56621
$509$	−3.80947	−	6.59820i	−0.168852	−	0.292460i	0.769165	−	0.639051i	$-0.220673\pi$
$509$	−3.80947	−	6.59820i	−0.168852	−	0.292460i	−0.938016	+	0.346591i	$0.887339\pi$
$510$	−4.77144	−	8.26437i	−0.211283	−	0.365953i
$511$	10.8107	−	18.7246i	0.478236	−	0.828329i
$512$	−9.00538			−0.397985
$513$	9.24094	−	16.0058i	0.407997	−	0.706672i
$514$	−20.9644	+	36.3114i	−0.924701	+	1.60163i
$515$	−13.2489			−0.583816
$516$	5.19202	−	8.99284i	0.228566	−	0.395888i
$517$	−3.76995	−	6.52974i	−0.165802	−	0.287178i
$518$	12.3312	+	21.3583i	0.541804	+	0.938431i
$519$	10.4638			0.459311
$520$		0			0
$521$	−39.5133			−1.73111			−0.865555	−	0.500813i	$-0.833034\pi$
$521$	−39.5133			−1.73111			−0.865555	+	0.500813i	$0.833034\pi$
$522$	−6.86174	−	11.8849i	−0.300330	−	0.520187i
$523$	7.90970	+	13.7000i	0.345867	+	0.599059i	0.985511	−	0.169612i	$-0.0542515\pi$
$523$	7.90970	+	13.7000i	0.345867	+	0.599059i	−0.639644	+	0.768671i	$0.720918\pi$
$524$	−4.96466	+	8.59904i	−0.216882	+	0.375651i
$525$	3.31096			0.144502
$526$	16.1773	−	28.0198i	0.705362	−	1.22172i
$527$	−11.3034	+	19.5781i	−0.492385	+	0.852836i
$528$	−1.13706			−0.0494843
$529$	9.71379	−	16.8248i	0.422339	−	0.731512i
$530$	−8.96346	−	15.5252i	−0.389348	−	0.674370i
$531$	−16.4318	−	28.4606i	−0.713078	−	1.23509i
$532$	−36.5502			−1.58465
$533$		0			0
$534$	8.24698			0.356882
$535$	−4.98523	−	8.63467i	−0.215530	−	0.373309i
$536$	0.679644	+	1.17718i	0.0293562	+	0.0508464i
$537$	1.67092	−	2.89411i	0.0721053	−	0.124890i
$538$	−1.46681			−0.0632388
$539$	−3.57942	+	6.19973i	−0.154176	+	0.267041i
$540$	6.95862	−	12.0527i	0.299451	−	0.518665i
$541$	34.4819			1.48249			0.741246	−	0.671234i	$-0.234235\pi$
$541$	34.4819			1.48249			0.741246	+	0.671234i	$0.234235\pi$
$542$	−2.24214	+	3.88349i	−0.0963080	+	0.166810i
$543$	−1.32573	−	2.29624i	−0.0568926	−	0.0985409i
$544$	17.2533	+	29.8836i	0.739730	+	1.28125i
$545$	−0.176292			−0.00755152
$546$		0			0
$547$	36.8582			1.57594			0.787970	−	0.615713i	$-0.211132\pi$
$547$	36.8582			1.57594			0.787970	+	0.615713i	$0.211132\pi$
$548$	−1.20775	−	2.09189i	−0.0515926	−	0.0893609i
$549$	11.5281	+	19.9673i	0.492008	+	0.852182i
$550$	8.35839	−	14.4772i	0.356403	−	0.617308i
$551$	−13.2741			−0.565497
$552$	1.23609	−	2.14098i	0.0526117	−	0.0911261i
$553$	16.1637	−	27.9963i	0.687350	−	1.19052i
$554$	−26.4795			−1.12501
$555$	−2.14795	+	3.72036i	−0.0911753	+	0.157920i
$556$	17.2865	+	29.9411i	0.733111	+	1.26979i
$557$	−0.638260	−	1.10550i	−0.0270439	−	0.0468415i	0.852187	−	0.523238i	$-0.175276\pi$
$557$	−0.638260	−	1.10550i	−0.0270439	−	0.0468415i	−0.879231	+	0.476396i	$0.841943\pi$
$558$	−25.8213			−1.09310
$559$		0			0
$560$	2.37435			0.100335
$561$	3.75451	+	6.50301i	0.158516	+	0.274557i
$562$	−7.27144	−	12.5945i	−0.306727	−	0.531267i
$563$	4.56369	−	7.90454i	0.192336	−	0.333137i	−0.753688	−	0.657233i	$-0.771727\pi$
$563$	4.56369	−	7.90454i	0.192336	−	0.333137i	0.946024	+	0.324096i	$0.105060\pi$
$564$	4.99330			0.210256
$565$	5.28017	−	9.14552i	0.222138	−	0.384755i
$566$	7.39373	−	12.8063i	0.310782	−	0.538290i
$567$	12.9554			0.544075
$568$	−5.41401	+	9.37734i	−0.227167	+	0.393464i
$569$	2.86078	+	4.95502i	0.119930	+	0.207725i	0.919740	−	0.392529i	$-0.128400\pi$
$569$	2.86078	+	4.95502i	0.119930	+	0.207725i	−0.799810	+	0.600254i	$0.795066\pi$
$570$	−5.27144	−	9.13040i	−0.220796	−	0.382430i
$571$	7.60148			0.318112			0.159056	−	0.987270i	$-0.449155\pi$
$571$	7.60148			0.318112			0.159056	+	0.987270i	$0.449155\pi$
$572$		0			0
$573$	−10.2282			−0.427289
$574$	2.93296	+	5.08004i	0.122419	+	0.212037i
$575$	−2.75182	−	4.76630i	−0.114759	−	0.198768i
$576$	−17.5477	+	30.3935i	−0.731155	+	1.26640i
$577$	45.1564			1.87989			0.939944	−	0.341330i	$-0.110877\pi$
$577$	45.1564			1.87989			0.939944	+	0.341330i	$0.110877\pi$
$578$	12.4107	−	21.4959i	0.516215	−	0.894111i
$579$	1.67994	−	2.90974i	0.0698159	−	0.120925i
$580$	−9.99569			−0.415048
$581$	−7.91239	+	13.7047i	−0.328261	+	0.568565i
$582$	−7.43631	−	12.8801i	−0.308245	−	0.533896i
$583$	7.05310	+	12.2163i	0.292109	+	0.505948i
$584$	24.8713			1.02918
$585$		0			0
$586$	54.6872			2.25911
$587$	16.2020	+	28.0627i	0.668728	+	1.15827i	0.978260	+	0.207382i	$0.0664944\pi$
$587$	16.2020	+	28.0627i	0.668728	+	1.15827i	−0.309532	+	0.950889i	$0.600172\pi$
$588$	−2.37047	−	4.10577i	−0.0977565	−	0.169319i
$589$	−12.4879	+	21.6297i	−0.514556	+	0.891237i
$590$	−39.6383			−1.63188
$591$	−3.16756	+	5.48638i	−0.130296	+	0.225680i
$592$	2.14795	−	3.72036i	0.0882801	−	0.152906i
$593$	36.6848			1.50647			0.753233	−	0.657754i	$-0.228493\pi$
$593$	36.6848			1.50647			0.753233	+	0.657754i	$0.228493\pi$
$594$	−9.06734	+	15.7051i	−0.372037	+	0.644387i
$595$	−7.83997	−	13.5792i	−0.321407	−	0.556694i
$596$	−12.8143	−	22.1950i	−0.524895	−	0.909144i
$597$	7.71678			0.315827
$598$		0			0
$599$	−9.99223			−0.408271			−0.204136	−	0.978943i	$-0.565438\pi$
$599$	−9.99223			−0.408271			−0.204136	+	0.978943i	$0.565438\pi$
$600$	1.90432	+	3.29838i	0.0777436	+	0.134656i
$601$	0.905813	+	1.56891i	0.0369489	+	0.0639974i	0.883908	−	0.467660i	$-0.154903\pi$
$601$	0.905813	+	1.56891i	0.0369489	+	0.0639974i	−0.846960	+	0.531657i	$0.821569\pi$
$602$	14.1271	−	24.4689i	0.575779	−	0.997279i
$603$	−1.55257			−0.0632253
$604$	−21.5395	+	37.3076i	−0.876431	+	1.51802i
$605$	−3.23125	+	5.59669i	−0.131369	+	0.227538i
$606$	16.2905			0.661757
$607$	−5.60806	+	9.71344i	−0.227624	+	0.394256i	−0.957103	−	0.289746i	$-0.906429\pi$
$607$	−5.60806	+	9.71344i	−0.227624	+	0.394256i	0.729479	+	0.684003i	$0.239762\pi$
$608$	19.0613	+	33.0151i	0.773038	+	1.33894i
$609$	1.28986	+	2.23410i	0.0522676	+	0.0905302i
$610$	27.8092			1.12596
$611$		0			0
$612$	43.4674			1.75707
$613$	10.4472	+	18.0951i	0.421958	+	0.730853i	0.996131	−	0.0878810i	$-0.0280095\pi$
$613$	10.4472	+	18.0951i	0.421958	+	0.730853i	−0.574173	+	0.818734i	$0.694676\pi$
$614$	−15.8116	−	27.3865i	−0.638105	−	1.10523i
$615$	−0.510885	+	0.884879i	−0.0206009	+	0.0356818i
$616$	12.3381			0.497117
$617$	−6.04958	+	10.4782i	−0.243547	+	0.421836i	−0.961722	−	0.274027i	$-0.911644\pi$
$617$	−6.04958	+	10.4782i	−0.243547	+	0.421836i	0.718175	+	0.695862i	$0.244978\pi$
$618$	−5.71648	+	9.90123i	−0.229951	+	0.398286i
$619$	−10.5526			−0.424143			−0.212072	−	0.977254i	$-0.568021\pi$
$619$	−10.5526			−0.424143			−0.212072	+	0.977254i	$0.568021\pi$
$620$	−9.40366	+	16.2876i	−0.377660	+	0.654126i
$621$	2.98523	+	5.17057i	0.119793	+	0.207488i
$622$	−33.4463	−	57.9307i	−1.34107	−	2.32281i
$623$	13.5506			0.542895
$624$		0			0
$625$	−1.96184			−0.0784735
$626$	−8.40246	−	14.5535i	−0.335830	−	0.581674i
$627$	4.14795	+	7.18446i	0.165653	+	0.286920i
$628$	14.3802	−	24.9072i	0.573831	−	0.993904i
$629$	−28.3696			−1.13117
$630$	8.95473	−	15.5100i	0.356765	−	0.617935i
$631$	6.92572	−	11.9957i	0.275709	−	0.477541i	−0.694605	−	0.719391i	$-0.744421\pi$
$631$	6.92572	−	11.9957i	0.275709	−	0.477541i	0.970314	+	0.241850i	$0.0777542\pi$
$632$	37.1866			1.47920
$633$	−3.67510	+	6.36545i	−0.146072	+	0.253004i
$634$	33.7385	+	58.4369i	1.33993	+	2.32082i
$635$	−13.7066	−	23.7404i	−0.543928	−	0.942111i
$636$	−9.34183			−0.370428
$637$		0			0
$638$	13.0248			0.515655
$639$	−6.18382	−	10.7107i	−0.244628	−	0.423709i
$640$	11.7497	+	20.3510i	0.464446	+	0.804445i
$641$	−17.4804	+	30.2769i	−0.690434	+	1.19587i	0.281262	+	0.959631i	$0.409247\pi$
$641$	−17.4804	+	30.2769i	−0.690434	+	1.19587i	−0.971696	+	0.236235i	$0.924086\pi$
$642$	−8.60388			−0.339568
$643$	−16.6990	+	28.9236i	−0.658545	+	1.14063i	0.322447	+	0.946587i	$0.395495\pi$
$643$	−16.6990	+	28.9236i	−0.658545	+	1.14063i	−0.980992	+	0.194046i	$0.937839\pi$
$644$	5.90366	−	10.2254i	0.232637	−	0.402939i
$645$	4.92154			0.193786
$646$	34.8119	−	60.2960i	1.36966	−	2.37232i
$647$	−1.16421	−	2.01647i	−0.0457698	−	0.0792757i	0.842233	−	0.539114i	$-0.181241\pi$
$647$	−1.16421	−	2.01647i	−0.0457698	−	0.0792757i	−0.888003	+	0.459838i	$0.847907\pi$
$648$	7.45138	+	12.9062i	0.292718	+	0.507002i
$649$	31.1903			1.22433
$650$		0			0
$651$	4.85384			0.190237
$652$	−13.2690	−	22.9827i	−0.519656	−	0.900070i
$653$	−7.28568	−	12.6192i	−0.285111	−	0.493826i	0.687525	−	0.726160i	$-0.258697\pi$
$653$	−7.28568	−	12.6192i	−0.285111	−	0.493826i	−0.972636	+	0.232334i	$0.925364\pi$
$654$	−0.0760644	+	0.131747i	−0.00297435	+	0.00515173i
$655$	−4.70602			−0.183879
$656$	0.510885	−	0.884879i	0.0199467	−	0.0345487i
$657$	−14.2039	+	24.6018i	−0.554146	+	0.959808i
$658$	13.5864			0.529654
$659$	−5.56973	+	9.64705i	−0.216966	+	0.375796i	−0.953879	−	0.300192i	$-0.902949\pi$
$659$	−5.56973	+	9.64705i	−0.216966	+	0.375796i	0.736913	+	0.675988i	$0.236283\pi$
$660$	3.12349	+	5.41004i	0.121582	+	0.210586i
$661$	6.92490	+	11.9943i	0.269347	+	0.466523i	0.968693	−	0.248260i	$-0.0798587\pi$
$661$	6.92490	+	11.9943i	0.269347	+	0.466523i	−0.699346	+	0.714783i	$0.746525\pi$
$662$	35.3153			1.37257
$663$		0			0
$664$	−18.2034			−0.706430
$665$	−8.66152	−	15.0022i	−0.335879	−	0.581760i
$666$	−16.2017	−	28.0622i	−0.627804	−	1.08739i
$667$	2.14406	−	3.71363i	0.0830185	−	0.143792i
$668$	−72.7284			−2.81395
$669$	−2.03534	+	3.52532i	−0.0786909	+	0.136297i
$670$	−0.936313	+	1.62174i	−0.0361729	+	0.0626533i
$671$	−21.8823			−0.844757
$672$	3.70440	−	6.41621i	0.142900	−	0.247511i
$673$	3.26487	+	5.65491i	0.125851	+	0.217981i	0.922065	−	0.387034i	$-0.126500\pi$
$673$	3.26487	+	5.65491i	0.125851	+	0.217981i	−0.796214	+	0.605015i	$0.793167\pi$
$674$	2.19537	+	3.80250i	0.0845626	+	0.146467i
$675$	−9.19806			−0.354034
$676$		0			0
$677$	−11.3104			−0.434693			−0.217346	−	0.976095i	$-0.569740\pi$
$677$	−11.3104			−0.434693			−0.217346	+	0.976095i	$0.569740\pi$
$678$	−4.55645	−	7.89200i	−0.174989	−	0.303091i
$679$	−12.2186	−	21.1633i	−0.468908	−	0.812173i
$680$	9.01842	−	15.6204i	0.345841	−	0.599013i
$681$	4.81402			0.184474
$682$	12.2533	−	21.2234i	0.469204	−	0.812685i
$683$	−7.08964	+	12.2796i	−0.271277	+	0.469866i	−0.969189	−	0.246317i	$-0.920779\pi$
$683$	−7.08964	+	12.2796i	−0.271277	+	0.469866i	0.697912	+	0.716184i	$0.254113\pi$
$684$	48.0224			1.83618
$685$	0.572417	−	0.991455i	0.0218709	−	0.0378815i
$686$	−22.5635	−	39.0810i	−0.861477	−	1.49212i
$687$	−3.79776	−	6.57791i	−0.144893	−	0.250963i
$688$	−4.92154			−0.187632
$689$		0			0
$690$	3.40581			0.129657
$691$	−15.3976	−	26.6695i	−0.585753	−	1.01455i	−0.994781	−	0.102032i	$-0.967466\pi$
$691$	−15.3976	−	26.6695i	−0.585753	−	1.01455i	0.409028	−	0.912522i	$-0.365868\pi$
$692$	28.7439	+	49.7859i	1.09268	+	1.89258i
$693$	−7.04623	+	12.2044i	−0.267664	+	0.463608i
$694$	38.4795			1.46066
$695$	−8.19298	+	14.1907i	−0.310777	+	0.538282i
$696$	−1.48374	+	2.56991i	−0.0562409	+	0.0974122i
$697$	−6.74764			−0.255585
$698$	−11.7594	+	20.3678i	−0.445098	+	0.770933i
$699$	−1.41185	−	2.44540i	−0.0534012	−	0.0924936i
$700$	9.09515	+	15.7533i	0.343764	+	0.595417i
$701$	6.73184			0.254258			0.127129	−	0.991886i	$-0.459424\pi$
$701$	6.73184			0.254258			0.127129	+	0.991886i	$0.459424\pi$
$702$		0			0
$703$	−31.3424			−1.18210
$704$	−16.6543	−	28.8461i	−0.627682	−	1.08718i
$705$	1.18329	+	2.04952i	0.0445654	+	0.0771895i
$706$	17.4487	−	30.2220i	0.656690	−	1.13742i
$707$	26.7670			1.00668
$708$	−10.3279	+	17.8884i	−0.388146	+	0.672288i
$709$	23.8126	−	41.2446i	0.894300	−	1.54897i	0.0596324	−	0.998220i	$-0.481007\pi$
$709$	23.8126	−	41.2446i	0.894300	−	1.54897i	0.834668	−	0.550753i	$-0.185660\pi$
$710$	−14.9172			−0.559834
$711$	−21.2371	+	36.7837i	−0.796452	+	1.37949i
$712$	7.79374	+	13.4992i	0.292083	+	0.505902i
$713$	−4.03415	−	6.98735i	−0.151080	−	0.261678i
$714$	−13.5308			−0.506377
$715$		0			0
$716$	18.3599			0.686141
$717$	−3.03116	−	5.25013i	−0.113201	−	0.196070i
$718$	−24.0722	−	41.6942i	−0.898366	−	1.55602i
$719$	2.99665	−	5.19035i	0.111756	−	0.193567i	−0.804722	−	0.593651i	$-0.797686\pi$
$719$	2.99665	−	5.19035i	0.111756	−	0.193567i	0.916478	+	0.400084i	$0.131019\pi$
$720$	−3.11960			−0.116261
$721$	−9.39277	+	16.2688i	−0.349805	+	0.605880i
$722$	17.1136	−	29.6416i	0.636901	−	1.10314i
$723$	−6.61224			−0.245912
$724$	7.28352	−	12.6154i	0.270690	−	0.468849i
$725$	3.30313	+	5.72120i	0.122675	+	0.212480i
$726$	2.78836	+	4.82959i	0.103486	+	0.179243i
$727$	−24.1226			−0.894657			−0.447329	−	0.894370i	$-0.647625\pi$
$727$	−24.1226			−0.894657			−0.447329	+	0.894370i	$0.647625\pi$
$728$		0			0
$729$	−11.7627			−0.435656
$730$	17.1320	+	29.6735i	0.634083	+	1.09826i
$731$	16.2506	+	28.1469i	0.601051	+	1.04105i
$732$	7.24578	−	12.5501i	0.267812	−	0.463864i
$733$	36.0646			1.33208			0.666038	−	0.745918i	$-0.267989\pi$
$733$	36.0646			1.33208			0.666038	+	0.745918i	$0.267989\pi$
$734$	38.5393	−	66.7520i	1.42251	−	2.46386i
$735$	1.12349	−	1.94594i	0.0414405	−	0.0717771i
$736$	−12.3153			−0.453947
$737$	0.736758	−	1.27610i	0.0271388	−	0.0470059i
$738$	−3.85354	−	6.67453i	−0.141851	−	0.245693i
$739$	−13.7627	−	23.8377i	−0.506269	−	0.876884i	−0.999974	−	0.00725452i	$-0.997691\pi$
$739$	−13.7627	−	23.8377i	−0.506269	−	0.876884i	0.493704	−	0.869630i	$-0.335643\pi$
$740$	−23.6015			−0.867608
$741$		0			0
$742$	−25.4185			−0.933142
$743$	5.23460	+	9.06660i	0.192039	+	0.332621i	0.945926	−	0.324383i	$-0.105157\pi$
$743$	5.23460	+	9.06660i	0.192039	+	0.332621i	−0.753887	+	0.657004i	$0.771823\pi$
$744$	2.79172	+	4.83539i	0.102349	+	0.177274i
$745$	6.07338	−	10.5194i	0.222511	−	0.385401i
$746$	28.3032			1.03625
$747$	10.3959	−	18.0062i	0.380366	−	0.658813i
$748$	−20.6271	+	35.7273i	−0.754203	+	1.30632i
$749$	−14.1371			−0.516557
$750$	−7.12833	+	12.3466i	−0.260290	+	0.450835i
$751$	−2.03385	−	3.52273i	−0.0742163	−	0.128546i	0.826529	−	0.562894i	$-0.190312\pi$
$751$	−2.03385	−	3.52273i	−0.0742163	−	0.128546i	−0.900745	+	0.434348i	$0.856979\pi$
$752$	−1.18329	−	2.04952i	−0.0431502	−	0.0747384i
$753$	−12.4021			−0.451957
$754$		0			0
$755$	−20.4174			−0.743066
$756$	−9.86658	−	17.0894i	−0.358844	−	0.621536i
$757$	−10.2168	−	17.6960i	−0.371335	−	0.643171i	0.618436	−	0.785835i	$-0.287767\pi$
$757$	−10.2168	−	17.6960i	−0.371335	−	0.643171i	−0.989771	+	0.142664i	$0.954433\pi$
$758$	18.5809	−	32.1831i	0.674889	−	1.16894i
$759$	−2.67994			−0.0972757
$760$	9.96346	−	17.2572i	0.361413	−	0.625985i
$761$	13.5118	−	23.4032i	0.489804	−	0.848365i	−0.510127	−	0.860099i	$-0.670402\pi$
$761$	13.5118	−	23.4032i	0.489804	−	0.848365i	0.999931	+	0.0117336i	$0.00373501\pi$
$762$	−23.6558			−0.856958
$763$	−0.124982	+	0.216475i	−0.00452464	+	0.00783691i
$764$	−28.0966	−	48.6648i	−1.01650	−	1.76063i
$765$	10.3007	+	17.8414i	0.372424	+	0.645057i
$766$	−16.9336			−0.611837
$767$		0			0
$768$	5.80864			0.209601
$769$	18.9703	+	32.8576i	0.684088	+	1.18487i	0.973723	+	0.227737i	$0.0731327\pi$
$769$	18.9703	+	32.8576i	0.684088	+	1.18487i	−0.289635	+	0.957137i	$0.593534\pi$
$770$	8.49880	+	14.7204i	0.306276	+	0.530485i
$771$	−5.17778	+	8.96818i	−0.186473	+	0.322981i
$772$	18.4590			0.664355
$773$	8.16876	−	14.1487i	0.293810	−	0.508894i	−0.680897	−	0.732379i	$-0.738410\pi$
$773$	8.16876	−	14.1487i	0.293810	−	0.508894i	0.974707	+	0.223485i	$0.0717434\pi$
$774$	−18.5613	+	32.1491i	−0.667172	+	1.15558i
$775$	12.4300			0.446498
$776$	14.0553	−	24.3444i	0.504554	−	0.873914i
$777$	3.04556	+	5.27507i	0.109259	+	0.189242i
$778$	39.9463	+	69.1890i	1.43214	+	2.48055i
$779$	−7.45473			−0.267093
$780$		0			0
$781$	11.7380			0.420017
$782$	11.2458	+	19.4783i	0.402148	+	0.696541i
$783$	−3.58330	−	6.20646i	−0.128057	−	0.221801i
$784$	−1.12349	+	1.94594i	−0.0401246	+	0.0694979i
$785$	13.6310			0.486512
$786$	−2.03050	+	3.51693i	−0.0724255	+	0.125445i
$787$	9.34535	−	16.1866i	0.333126	−	0.576991i	−0.649997	−	0.759936i	$-0.725230\pi$
$787$	9.34535	−	16.1866i	0.333126	−	0.576991i	0.983123	+	0.182946i	$0.0585633\pi$
$788$	−34.8049			−1.23987
$789$	3.99545	−	6.92032i	0.142242	−	0.246370i
$790$	25.6151	+	44.3666i	0.911343	+	1.57849i
$791$	−7.48672	−	12.9674i	−0.266197	−	0.461067i
$792$	−16.2107			−0.576023
$793$		0			0
$794$	−3.03684			−0.107773
$795$	−2.21379	−	3.83440i	−0.0785151	−	0.135992i
$796$	21.1978	+	36.7157i	0.751337	+	1.30135i
$797$	−14.6259	+	25.3329i	−0.518077	+	0.897336i	0.481702	+	0.876335i	$0.340019\pi$
$797$	−14.6259	+	25.3329i	−0.518077	+	0.897336i	−0.999779	+	0.0210013i	$0.993315\pi$
$798$	−14.9487			−0.529178
$799$	−7.81431	+	13.5348i	−0.276451	+	0.478826i
$800$	9.48643	−	16.4310i	0.335396	−	0.580923i
$801$	−17.8039			−0.629068
$802$	0.650637	−	1.12694i	0.0229748	−	0.0397935i
$803$	−13.4807	−	23.3492i	−0.475723	−	0.823976i
$804$	0.487918	+	0.845099i	0.0172076	+	0.0298044i
$805$	5.59611			0.197237
$806$		0			0
$807$	−0.362273			−0.0127526
$808$	15.3952	+	26.6653i	0.541602	+	0.938082i
$809$	3.32544	+	5.75983i	0.116916	+	0.202505i	0.918544	−	0.395319i	$-0.129366\pi$
$809$	3.32544	+	5.75983i	0.116916	+	0.202505i	−0.801628	+	0.597823i	$0.796032\pi$
$810$	−10.2654	+	17.7802i	−0.360689	+	0.624732i
$811$	3.89200			0.136667			0.0683333	−	0.997663i	$-0.478232\pi$
$811$	3.89200			0.136667			0.0683333	+	0.997663i	$0.478232\pi$
$812$	−7.08642	+	12.2740i	−0.248684	+	0.430734i
$813$	−0.553762	+	0.959143i	−0.0194213	+	0.0336386i
$814$	30.7536			1.07791
$815$	6.28890	−	10.8927i	0.220290	−	0.381554i
$816$	1.17845	+	2.04113i	0.0412539	+	0.0714539i
$817$	17.9535	+	31.0964i	0.628115	+	1.08793i
$818$	34.0586			1.19083
$819$		0			0
$820$	−5.61356			−0.196034
$821$	−22.9991	−	39.8356i	−0.802674	−	1.39027i	−0.917850	−	0.396927i	$-0.870077\pi$
$821$	−22.9991	−	39.8356i	−0.802674	−	1.39027i	0.115176	−	0.993345i	$-0.463257\pi$
$822$	−0.493959	−	0.855562i	−0.0172288	−	0.0298412i
$823$	−3.97650	+	6.88750i	−0.138612	+	0.240083i	−0.926971	−	0.375132i	$-0.877597\pi$
$823$	−3.97650	+	6.88750i	−0.138612	+	0.240083i	0.788359	+	0.615215i	$0.210931\pi$
$824$	−21.6093			−0.752794
$825$	2.06435	−	3.57556i	0.0718715	−	0.124485i
$826$	−28.1015	+	48.6732i	−0.977776	+	1.69356i
$827$	27.9648			0.972432			0.486216	−	0.873839i	$-0.338377\pi$
$827$	27.9648			0.972432			0.486216	+	0.873839i	$0.338377\pi$
$828$	−7.75667	+	13.4349i	−0.269563	+	0.466897i
$829$	−13.8155	−	23.9292i	−0.479833	−	0.831094i	0.519900	−	0.854227i	$-0.325969\pi$
$829$	−13.8155	−	23.9292i	−0.479833	−	0.831094i	−0.999732	+	0.0231329i	$0.992636\pi$
$830$	−12.5390	−	21.7182i	−0.435235	−	0.753849i
$831$	−6.53989			−0.226866
$832$		0			0
$833$	14.8388			0.514133
$834$	7.07002	+	12.2456i	0.244815	+	0.424032i
$835$	−17.2349	−	29.8517i	−0.596438	−	1.03306i
$836$	−22.7887	+	39.4711i	−0.788162	+	1.36514i
$837$	−13.4843			−0.466085
$838$	−40.1350	+	69.5158i	−1.38644	+	2.40138i
$839$	−14.3424	+	24.8418i	−0.495155	+	0.857634i	−0.999984	−	0.00558509i	$-0.998222\pi$
$839$	−14.3424	+	24.8418i	−0.495155	+	0.857634i	0.504829	+	0.863219i	$0.331556\pi$
$840$	−3.87263			−0.133618
$841$	11.9264	−	20.6571i	0.411255	−	0.712314i
$842$	−39.3744	−	68.1985i	−1.35693	−	2.35027i
$843$	−1.79590	−	3.11058i	−0.0618540	−	0.107134i
$844$	−40.3817			−1.38999
$845$		0			0
$846$	−17.8509			−0.613725
$847$	4.58157	+	7.93552i	0.157425	+	0.272668i
$848$	2.21379	+	3.83440i	0.0760219	+	0.131674i
$849$	1.82610	−	3.16290i	0.0626716	−	0.108550i
$850$	−34.6504			−1.18850
$851$	5.06249	−	8.76849i	0.173540	−	0.300580i
$852$	−3.88673	+	6.73202i	−0.133157	+	0.230635i
$853$	−43.2078			−1.47941			−0.739703	−	0.672934i	$-0.765034\pi$
$853$	−43.2078			−1.47941			−0.739703	+	0.672934i	$0.765034\pi$
$854$	19.7153	−	34.1479i	0.674643	−	1.16852i
$855$	11.3802	+	19.7110i	0.389193	+	0.674102i
$856$	−8.13102	−	14.0833i	−0.277913	−	0.481359i
$857$	35.1685			1.20133			0.600667	−	0.799499i	$-0.294902\pi$
$857$	35.1685			1.20133			0.600667	+	0.799499i	$0.294902\pi$
$858$		0			0
$859$	27.3793			0.934168			0.467084	−	0.884213i	$-0.345305\pi$
$859$	27.3793			0.934168			0.467084	+	0.884213i	$0.345305\pi$
$860$	13.5194	+	23.4162i	0.461007	+	0.798487i
$861$	0.724381	+	1.25467i	0.0246869	+	0.0427589i
$862$	−38.5148	+	66.7096i	−1.31182	+	2.27214i
$863$	−41.3913			−1.40898			−0.704489	−	0.709715i	$-0.748824\pi$
$863$	−41.3913			−1.40898			−0.704489	+	0.709715i	$0.748824\pi$
$864$	−10.2911	+	17.8246i	−0.350109	+	0.606406i
$865$	−13.6233	+	23.5962i	−0.463204	+	0.802294i
$866$	−30.8702			−1.04901
$867$	3.06518	−	5.30905i	0.104099	−	0.180305i
$868$	13.3334	+	23.0941i	0.452565	+	0.783866i
$869$	−20.1558	−	34.9108i	−0.683738	−	1.18427i
$870$	−4.08815			−0.138601
$871$		0			0
$872$	−0.287536			−0.00973721
$873$	16.0538	+	27.8059i	0.543338	+	0.941088i
$874$	12.4242	+	21.5194i	0.420256	+	0.727905i
$875$	−11.7126	+	20.2868i	−0.395958	+	0.685819i
$876$	17.8552			0.603270
$877$	12.3736	−	21.4317i	0.417826	−	0.723696i	−0.577894	−	0.816112i	$-0.696125\pi$
$877$	12.3736	−	21.4317i	0.417826	−	0.723696i	0.995721	+	0.0924153i	$0.0294587\pi$
$878$	11.5048	−	19.9270i	0.388270	−	0.672503i
$879$	13.5066			0.455567
$880$	1.48039	−	2.56410i	0.0499038	−	0.0864359i
$881$	14.2937	+	24.7575i	0.481568	+	0.834101i	0.999776	−	0.0211538i	$-0.00673397\pi$
$881$	14.2937	+	24.7575i	0.481568	+	0.834101i	−0.518208	+	0.855255i	$0.673401\pi$
$882$	8.47434	+	14.6780i	0.285346	+	0.494234i
$883$	9.61702			0.323639			0.161819	−	0.986820i	$-0.448264\pi$
$883$	9.61702			0.323639			0.161819	+	0.986820i	$0.448264\pi$
$884$		0			0
$885$	−9.78986			−0.329082
$886$	13.6799	+	23.6944i	0.459587	+	0.796027i
$887$	−7.98307	−	13.8271i	−0.268045	−	0.464268i	0.700312	−	0.713837i	$-0.253044\pi$
$887$	−7.98307	−	13.8271i	−0.268045	−	0.464268i	−0.968357	+	0.249569i	$0.919711\pi$
$888$	−3.50335	+	6.06798i	−0.117565	+	0.203628i
$889$	−38.8689			−1.30362
$890$	−10.7371	+	18.5971i	−0.359907	+	0.623377i
$891$	8.07756	−	13.9907i	0.270608	−	0.468707i
$892$	−22.3642			−0.748809
$893$	−8.63318	+	14.9531i	−0.288898	+	0.500387i
$894$	−5.24094	−	9.07757i	−0.175283	−	0.303599i
$895$	4.35086	+	7.53590i	0.145433	+	0.251897i
$896$	33.3196			1.11313
$897$		0			0
$898$	28.9976			0.967663
$899$	4.84236	+	8.38722i	0.161502	+	0.279729i
$900$	−11.9499	−	20.6978i	−0.398330	−	0.689927i
$901$	14.6196	−	25.3219i	0.487050	−	0.843595i
$902$	7.31468			0.243552
$903$	3.48911	−	6.04332i	0.116110	−	0.201109i
$904$	8.61207	−	14.9165i	0.286433	−	0.496117i
$905$	6.90408			0.229500
$906$	−8.80947	+	15.2585i	−0.292675	+	0.506928i
$907$	14.4182	+	24.9730i	0.478748	+	0.829216i	0.999703	−	0.0243681i	$-0.00775737\pi$
$907$	14.4182	+	24.9730i	0.478748	+	0.829216i	−0.520955	+	0.853584i	$0.674424\pi$
$908$	13.2240	+	22.9047i	0.438854	+	0.760118i
$909$	−35.1685			−1.16647
$910$		0			0
$911$	38.5633			1.27766			0.638830	−	0.769348i	$-0.279419\pi$
$911$	38.5633			1.27766			0.638830	+	0.769348i	$0.279419\pi$
$912$	1.30194	+	2.25502i	0.0431115	+	0.0746713i
$913$	9.86658	+	17.0894i	0.326536	+	0.565577i
$914$	5.23221	−	9.06245i	0.173066	−	0.299759i
$915$	6.86831			0.227059
$916$	20.8647	−	36.1388i	0.689390	−	1.19406i
$917$	−3.33632	+	5.77868i	−0.110175	+	0.190829i
$918$	37.5894			1.24064
$919$	−4.43751	+	7.68599i	−0.146380	+	0.253537i	−0.929887	−	0.367845i	$-0.880096\pi$
$919$	−4.43751	+	7.68599i	−0.146380	+	0.253537i	0.783507	+	0.621383i	$0.213429\pi$
$920$	3.21864	+	5.57484i	0.106115	+	0.183797i
$921$	−3.90515	−	6.76392i	−0.128679	−	0.222879i
$922$	70.8708			2.33401
$923$		0			0
$924$	8.85756			0.291392
$925$	7.79925	+	13.5087i	0.256438	+	0.444163i
$926$	19.8300	+	34.3466i	0.651656	+	1.12870i
$927$	12.3409	−	21.3751i	0.405329	−	0.702051i
$928$	14.7826			0.485261
$929$	−12.1148	+	20.9834i	−0.397472	+	0.688442i	−0.993413	−	0.114586i	$-0.963446\pi$
$929$	−12.1148	+	20.9834i	−0.397472	+	0.688442i	0.595941	+	0.803028i	$0.296779\pi$
$930$	−3.84601	+	6.66149i	−0.126116	+	0.218439i
$931$	16.3937			0.537283
$932$	7.75667	−	13.4349i	0.254078	−	0.440076i
$933$	−8.26055	−	14.3077i	−0.270438	−	0.468413i
$934$	−36.1456	−	62.6059i	−1.18272	−	2.04853i
$935$	−19.5526			−0.639437
$936$		0			0
$937$	17.2644			0.564005			0.282002	−	0.959414i	$-0.409001\pi$
$937$	17.2644			0.564005			0.282002	+	0.959414i	$0.409001\pi$
$938$	1.32759	+	2.29946i	0.0433474	+	0.0750800i
$939$	−2.07524	−	3.59441i	−0.0677228	−	0.117299i
$940$	−6.50096	+	11.2600i	−0.212038	+	0.367260i
$941$	4.34050			0.141496			0.0707482	−	0.997494i	$-0.477461\pi$
$941$	4.34050			0.141496			0.0707482	+	0.997494i	$0.477461\pi$
$942$	5.88135	−	10.1868i	0.191625	−	0.331904i
$943$	1.20410	−	2.08557i	0.0392110	−	0.0679154i
$944$	9.78986			0.318633
$945$	4.67629	−	8.09958i	0.152120	−	0.263479i
$946$	−17.6163	−	30.5122i	−0.572754	−	0.992039i
$947$	22.5073	+	38.9838i	0.731389	+	1.26680i	0.956290	+	0.292421i	$0.0944608\pi$
$947$	22.5073	+	38.9838i	0.731389	+	1.26680i	−0.224901	+	0.974382i	$0.572206\pi$
$948$	26.6963			0.867057
$949$		0			0
$950$	−38.2814			−1.24201
$951$	8.33273	+	14.4327i	0.270207	+	0.468013i
$952$	−12.7872	−	22.1480i	−0.414434	−	0.717822i
$953$	23.4429	−	40.6044i	0.759391	−	1.31530i	−0.183770	−	0.982969i	$-0.558830\pi$
$953$	23.4429	−	40.6044i	0.759391	−	1.31530i	0.943161	−	0.332335i	$-0.107837\pi$
$954$	33.3967			1.08126
$955$	13.3165	−	23.0648i	0.430911	−	0.746360i
$956$	16.6531	−	28.8440i	0.538599	−	0.932881i
$957$	3.21685			0.103986
$958$	−39.2095	+	67.9129i	−1.26680	+	2.19417i
$959$	−0.811626	−	1.40578i	−0.0262088	−	0.0453949i
$960$	5.22737	+	9.05406i	0.168712	+	0.292219i
$961$	−12.7778			−0.412186
$962$		0			0
$963$	18.5743			0.598550
$964$	−18.1637	−	31.4604i	−0.585013	−	1.01327i
$965$	4.37435	+	7.57660i	0.140815	+	0.243900i
$966$	2.41454	−	4.18211i	0.0776866	−	0.134557i
$967$	6.29457			0.202420			0.101210	−	0.994865i	$-0.467729\pi$
$967$	6.29457			0.202420			0.101210	+	0.994865i	$0.467729\pi$
$968$	−5.27024	+	9.12833i	−0.169392	+	0.293396i
$969$	8.59783	−	14.8919i	0.276202	−	0.478396i
$970$	38.7265			1.24343
$971$	20.9034	−	36.2058i	0.670823	−	1.16190i	−0.306848	−	0.951758i	$-0.599274\pi$
$971$	20.9034	−	36.2058i	0.670823	−	1.16190i	0.977671	−	0.210141i	$-0.0673922\pi$
$972$	19.7959	+	34.2875i	0.634954	+	1.09977i
$973$	11.6168	+	20.1209i	0.372417	+	0.645045i
$974$	−94.0025			−3.01203
$975$		0			0
$976$	−6.86831			−0.219849
$977$	−11.8765	−	20.5707i	−0.379963	−	0.658116i	0.611093	−	0.791559i	$-0.290730\pi$
$977$	−11.8765	−	20.5707i	−0.379963	−	0.658116i	−0.991056	+	0.133443i	$0.957397\pi$
$978$	−5.42692	−	9.39970i	−0.173534	−	0.300569i
$979$	8.44869	−	14.6336i	0.270021	−	0.467691i
$980$	12.3448			0.394341
$981$	0.164210	−	0.284421i	0.00524284	−	0.00908086i
$982$	24.5432	−	42.5100i	0.783204	−	1.35655i
$983$	−55.7251			−1.77736			−0.888678	−	0.458532i	$-0.848375\pi$
$983$	−55.7251			−1.77736			−0.888678	+	0.458532i	$0.848375\pi$
$984$	−0.833265	+	1.44326i	−0.0265635	+	0.0460094i
$985$	−8.24794	−	14.2858i	−0.262801	−	0.455185i
$986$	−13.4988	−	23.3806i	−0.429889	−	0.744590i
$987$	3.35557			0.106809
$988$		0			0
$989$	−11.5996			−0.368845
$990$	−11.1664	−	19.3407i	−0.354890	−	0.614688i
$991$	17.7756	+	30.7883i	0.564661	+	0.978022i	0.997081	+	0.0763495i	$0.0243265\pi$
$991$	17.7756	+	30.7883i	0.564661	+	0.978022i	−0.432420	+	0.901672i	$0.642340\pi$
$992$	13.9070	−	24.0876i	0.441548	−	0.764784i
$993$	8.72215			0.276789
$994$	−10.5755	+	18.3174i	−0.335436	+	0.580991i
$995$	−10.0468	+	17.4015i	−0.318504	+	0.551665i
$996$	−13.0683			−0.414085
$997$	−3.30529	+	5.72493i	−0.104680	+	0.181310i	−0.913607	−	0.406598i	$-0.866715\pi$
$997$	−3.30529	+	5.72493i	−0.104680	+	0.181310i	0.808928	+	0.587908i	$0.200048\pi$
$998$	26.4550	+	45.8214i	0.837419	+	1.45045i
$999$	−8.46077	−	14.6545i	−0.267687	−	0.463647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.2.c.c.146.3		6
13.2	odd	12		169.2.b.b.168.6		6
13.3	even	3		169.2.a.b.1.1	✓	3
13.4	even	6		169.2.c.b.22.1		6
13.5	odd	4		169.2.e.b.23.6		12
13.6	odd	12		169.2.e.b.147.1		12
13.7	odd	12		169.2.e.b.147.6		12
13.8	odd	4		169.2.e.b.23.1		12
13.9	even	3	inner	169.2.c.c.22.3		6
13.10	even	6		169.2.a.c.1.3	yes	3
13.11	odd	12		169.2.b.b.168.1		6
13.12	even	2		169.2.c.b.146.1		6
39.2	even	12		1521.2.b.l.1351.1		6
39.11	even	12		1521.2.b.l.1351.6		6
39.23	odd	6		1521.2.a.o.1.1		3
39.29	odd	6		1521.2.a.r.1.3		3
52.3	odd	6		2704.2.a.z.1.2		3
52.11	even	12		2704.2.f.o.337.3		6
52.15	even	12		2704.2.f.o.337.4		6
52.23	odd	6		2704.2.a.ba.1.2		3
65.29	even	6		4225.2.a.bg.1.3		3
65.49	even	6		4225.2.a.bb.1.1		3
91.55	odd	6		8281.2.a.bf.1.1		3
91.62	odd	6		8281.2.a.bj.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.2.a.b.1.1	✓	3	13.3	even	3
169.2.a.c.1.3	yes	3	13.10	even	6
169.2.b.b.168.1		6	13.11	odd	12
169.2.b.b.168.6		6	13.2	odd	12
169.2.c.b.22.1		6	13.4	even	6
169.2.c.b.146.1		6	13.12	even	2
169.2.c.c.22.3		6	13.9	even	3	inner
169.2.c.c.146.3		6	1.1	even	1	trivial
169.2.e.b.23.1		12	13.8	odd	4
169.2.e.b.23.6		12	13.5	odd	4
169.2.e.b.147.1		12	13.6	odd	12
169.2.e.b.147.6		12	13.7	odd	12
1521.2.a.o.1.1		3	39.23	odd	6
1521.2.a.r.1.3		3	39.29	odd	6
1521.2.b.l.1351.1		6	39.2	even	12
1521.2.b.l.1351.6		6	39.11	even	12
2704.2.a.z.1.2		3	52.3	odd	6
2704.2.a.ba.1.2		3	52.23	odd	6
2704.2.f.o.337.3		6	52.11	even	12
2704.2.f.o.337.4		6	52.15	even	12
4225.2.a.bb.1.1		3	65.49	even	6
4225.2.a.bg.1.3		3	65.29	even	6
8281.2.a.bf.1.1		3	91.55	odd	6
8281.2.a.bj.1.3		3	91.62	odd	6

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	169.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12349 + 1.94594i) q^{2} +(0.277479 + 0.480608i) q^{3} +(-1.52446 + 2.64044i) q^{4} -1.44504 q^{5} +(-0.623490 + 1.07992i) q^{6} +(-1.02446 + 1.77441i) q^{7} -2.35690 q^{8} +(1.34601 - 2.33136i) q^{9} +O(q^{10})\)	\(q+(1.12349 + 1.94594i) q^{2} +(0.277479 + 0.480608i) q^{3} +(-1.52446 + 2.64044i) q^{4} -1.44504 q^{5} +(-0.623490 + 1.07992i) q^{6} +(-1.02446 + 1.77441i) q^{7} -2.35690 q^{8} +(1.34601 - 2.33136i) q^{9} +(-1.62349 - 2.81197i) q^{10} +(1.27748 + 2.21266i) q^{11} -1.69202 q^{12} -4.60388 q^{14} +(-0.400969 - 0.694498i) q^{15} +(0.400969 + 0.694498i) q^{16} +(2.64795 - 4.58638i) q^{17} +6.04892 q^{18} +(2.92543 - 5.06699i) q^{19} +(2.20291 - 3.81555i) q^{20} -1.13706 q^{21} +(-2.87047 + 4.97180i) q^{22} +(0.945042 + 1.63686i) q^{23} +(-0.653989 - 1.13274i) q^{24} -2.91185 q^{25} +3.15883 q^{27} +(-3.12349 - 5.41004i) q^{28} +(-1.13437 - 1.96480i) q^{29} +(0.900969 - 1.56052i) q^{30} -4.26875 q^{31} +(-3.25786 + 5.64279i) q^{32} +(-0.708947 + 1.22793i) q^{33} +11.8998 q^{34} +(1.48039 - 2.56410i) q^{35} +(4.10388 + 7.10812i) q^{36} +(-2.67845 - 4.63921i) q^{37} +13.1468 q^{38} +3.40581 q^{40} +(-0.637063 - 1.10343i) q^{41} +(-1.27748 - 2.21266i) q^{42} +(-3.06853 + 5.31485i) q^{43} -7.78986 q^{44} +(-1.94504 + 3.36891i) q^{45} +(-2.12349 + 3.67799i) q^{46} -2.95108 q^{47} +(-0.222521 + 0.385418i) q^{48} +(1.40097 + 2.42655i) q^{49} +(-3.27144 - 5.66630i) q^{50} +2.93900 q^{51} +5.52111 q^{53} +(3.54892 + 6.14691i) q^{54} +(-1.84601 - 3.19738i) q^{55} +(2.41454 - 4.18211i) q^{56} +3.24698 q^{57} +(2.54892 - 4.41485i) q^{58} +(6.10388 - 10.5722i) q^{59} +2.44504 q^{60} +(-4.28232 + 7.41720i) q^{61} +(-4.79590 - 8.30674i) q^{62} +(2.75786 + 4.77676i) q^{63} -13.0368 q^{64} -3.18598 q^{66} +(-0.288364 - 0.499461i) q^{67} +(8.07338 + 13.9835i) q^{68} +(-0.524459 + 0.908389i) q^{69} +6.65279 q^{70} +(2.29709 - 3.97868i) q^{71} +(-3.17241 + 5.49477i) q^{72} -10.5526 q^{73} +(6.01842 - 10.4242i) q^{74} +(-0.807979 - 1.39946i) q^{75} +(8.91939 + 15.4488i) q^{76} -5.23490 q^{77} -15.7778 q^{79} +(-0.579417 - 1.00358i) q^{80} +(-3.16152 - 5.47592i) q^{81} +(1.43147 - 2.47938i) q^{82} +7.72348 q^{83} +(1.73341 - 3.00235i) q^{84} +(-3.82640 + 6.62751i) q^{85} -13.7899 q^{86} +(0.629531 - 1.09038i) q^{87} +(-3.01089 - 5.21501i) q^{88} +(-3.30678 - 5.72751i) q^{89} -8.74094 q^{90} -5.76271 q^{92} +(-1.18449 - 2.05159i) q^{93} +(-3.31551 - 5.74263i) q^{94} +(-4.22737 + 7.32201i) q^{95} -3.61596 q^{96} +(-5.96346 + 10.3290i) q^{97} +(-3.14795 + 5.45241i) q^{98} +6.87800 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9	\( 6 q + 2 q^{2} + 2 q^{3} - 8 q^{5} + q^{6} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 5 q^{10} + 8 q^{11} - 10 q^{14} + 2 q^{15} - 2 q^{16} + 2 q^{17} + 18 q^{18} + 4 q^{19} + 4 q^{21} - 3 q^{22} + 5 q^{23} - 9 q^{24} - 10 q^{25} + 2 q^{27} - 14 q^{28} + q^{29} + q^{30} - 10 q^{31} - 7 q^{32} - 10 q^{33} + 26 q^{34} - 4 q^{35} + 7 q^{36} - 12 q^{37} + 24 q^{38} - 6 q^{40} + 7 q^{41} - 8 q^{42} - 13 q^{43} - 11 q^{45} - 8 q^{46} - 36 q^{47} - q^{48} + 4 q^{49} - q^{50} - 2 q^{51} + 2 q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} + 10 q^{57} - 3 q^{58} + 19 q^{59} + 14 q^{60} - 4 q^{61} - q^{62} + 4 q^{63} - 22 q^{64} + 10 q^{66} + q^{67} + 21 q^{68} + 6 q^{69} + 4 q^{70} + 27 q^{71} + 4 q^{72} + 18 q^{73} + 8 q^{74} - 15 q^{75} + 21 q^{76} + 16 q^{77} - 10 q^{79} + 5 q^{80} + q^{81} + 14 q^{82} - 14 q^{83} + 7 q^{84} - 5 q^{85} - 36 q^{86} + 18 q^{87} - 15 q^{88} + 11 q^{89} - 24 q^{90} - 22 q^{93} - 5 q^{94} - 3 q^{95} - 42 q^{96} - 7 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 2 * q^3 - 8 * q^5 + q^6 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 5 * q^10 + 8 * q^11 - 10 * q^14 + 2 * q^15 - 2 * q^16 + 2 * q^17 + 18 * q^18 + 4 * q^19 + 4 * q^21 - 3 * q^22 + 5 * q^23 - 9 * q^24 - 10 * q^25 + 2 * q^27 - 14 * q^28 + q^29 + q^30 - 10 * q^31 - 7 * q^32 - 10 * q^33 + 26 * q^34 - 4 * q^35 + 7 * q^36 - 12 * q^37 + 24 * q^38 - 6 * q^40 + 7 * q^41 - 8 * q^42 - 13 * q^43 - 11 * q^45 - 8 * q^46 - 36 * q^47 - q^48 + 4 * q^49 - q^50 - 2 * q^51 + 2 * q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 + 10 * q^57 - 3 * q^58 + 19 * q^59 + 14 * q^60 - 4 * q^61 - q^62 + 4 * q^63 - 22 * q^64 + 10 * q^66 + q^67 + 21 * q^68 + 6 * q^69 + 4 * q^70 + 27 * q^71 + 4 * q^72 + 18 * q^73 + 8 * q^74 - 15 * q^75 + 21 * q^76 + 16 * q^77 - 10 * q^79 + 5 * q^80 + q^81 + 14 * q^82 - 14 * q^83 + 7 * q^84 - 5 * q^85 - 36 * q^86 + 18 * q^87 - 15 * q^88 + 11 * q^89 - 24 * q^90 - 22 * q^93 - 5 * q^94 - 3 * q^95 - 42 * q^96 - 7 * q^97 - 5 * q^98 + 2 * q^99

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