LMFDB - Embedded newform 1098.2.e.f.367.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1098,2,Mod(367,1098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1098, 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("1098.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1098 = 2 \cdot 3^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1098.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:	$8.76757414194$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			367.1
Character	$\chi$	$=$	1098.367
Dual form			1098.2.e.f.733.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.70593 + 0.299644i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02139 - 3.50116i) q^{5} +(0.593468 - 1.62720i) q^{6} +(1.31426 - 2.27636i) q^{7} +1.00000 q^{8} +(2.82043 - 1.02235i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.70593 + 0.299644i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02139 - 3.50116i) q^{5} +(0.593468 - 1.62720i) q^{6} +(1.31426 - 2.27636i) q^{7} +1.00000 q^{8} +(2.82043 - 1.02235i) q^{9} +4.04279 q^{10} +(2.10717 - 3.64973i) q^{11} +(1.11247 + 1.32756i) q^{12} +(-3.06435 - 5.30761i) q^{13} +(1.31426 + 2.27636i) q^{14} +(4.49746 + 5.36704i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.44390 q^{17} +(-0.524836 + 2.95373i) q^{18} -4.44023 q^{19} +(-2.02139 + 3.50116i) q^{20} +(-1.55994 + 4.27714i) q^{21} +(2.10717 + 3.64973i) q^{22} +(0.820153 + 1.42055i) q^{23} +(-1.70593 + 0.299644i) q^{24} +(-5.67206 + 9.82430i) q^{25} +6.12870 q^{26} +(-4.50512 + 2.58918i) q^{27} -2.62852 q^{28} +(3.78780 - 6.56067i) q^{29} +(-6.89673 + 1.21140i) q^{30} +(-0.108453 - 0.187846i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.50108 + 6.85760i) q^{33} +(-2.72195 + 4.71455i) q^{34} -10.6265 q^{35} +(-2.29559 - 1.93139i) q^{36} +8.34941 q^{37} +(2.22011 - 3.84535i) q^{38} +(6.81797 + 8.13622i) q^{39} +(-2.02139 - 3.50116i) q^{40} +(-4.05327 - 7.02047i) q^{41} +(-2.92414 - 3.48952i) q^{42} +(-2.10813 + 3.65139i) q^{43} -4.21434 q^{44} +(-9.28058 - 7.80819i) q^{45} -1.64031 q^{46} +(3.17365 - 5.49692i) q^{47} +(0.593468 - 1.62720i) q^{48} +(0.0454480 + 0.0787182i) q^{49} +(-5.67206 - 9.82430i) q^{50} +(-9.28693 + 1.63123i) q^{51} +(-3.06435 + 5.30761i) q^{52} +5.78041 q^{53} +(0.0102666 - 5.19614i) q^{54} -17.0377 q^{55} +(1.31426 - 2.27636i) q^{56} +(7.57474 - 1.33049i) q^{57} +(3.78780 + 6.56067i) q^{58} +(-1.93757 - 3.35598i) q^{59} +(2.39926 - 6.57844i) q^{60} +(0.500000 - 0.866025i) q^{61} +0.216906 q^{62} +(1.37954 - 7.76394i) q^{63} +1.00000 q^{64} +(-12.3885 + 21.4575i) q^{65} +(-4.68832 - 5.59480i) q^{66} +(-3.28031 - 5.68167i) q^{67} +(-2.72195 - 4.71455i) q^{68} +(-1.82479 - 2.17761i) q^{69} +(5.31327 - 9.20285i) q^{70} +14.7541 q^{71} +(2.82043 - 1.02235i) q^{72} -7.90683 q^{73} +(-4.17470 + 7.23080i) q^{74} +(6.73237 - 18.4592i) q^{75} +(2.22011 + 3.84535i) q^{76} +(-5.53874 - 9.59338i) q^{77} +(-10.4552 + 1.83643i) q^{78} +(-5.86350 + 10.1559i) q^{79} +4.04279 q^{80} +(6.90962 - 5.76691i) q^{81} +8.10654 q^{82} +(-5.77258 + 9.99839i) q^{83} +(4.48408 - 0.787619i) q^{84} +(-11.0043 - 19.0599i) q^{85} +(-2.10813 - 3.65139i) q^{86} +(-4.49588 + 12.3271i) q^{87} +(2.10717 - 3.64973i) q^{88} -13.5586 q^{89} +(11.4024 - 4.13313i) q^{90} -16.1094 q^{91} +(0.820153 - 1.42055i) q^{92} +(0.241300 + 0.287956i) q^{93} +(3.17365 + 5.49692i) q^{94} +(8.97545 + 15.5459i) q^{95} +(1.11247 + 1.32756i) q^{96} +(1.99272 - 3.45149i) q^{97} -0.0908960 q^{98} +(2.21184 - 12.4481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 2 q^{3} - 17 q^{4} - 5 q^{5} - q^{6} - 11 q^{7} + 34 q^{8}+O(q^{10}) $ 34 * q - 17 * q^2 + 2 * q^3 - 17 * q^4 - 5 * q^5 - q^6 - 11 * q^7 + 34 * q^8	\( 34 q - 17 q^{2} + 2 q^{3} - 17 q^{4} - 5 q^{5} - q^{6} - 11 q^{7} + 34 q^{8} + 10 q^{10} - 3 q^{11} - q^{12} - 10 q^{13} - 11 q^{14} + q^{15} - 17 q^{16} + 16 q^{17} + 3 q^{18} + 22 q^{19} - 5 q^{20} - q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 32 q^{25} + 20 q^{26} - q^{27} + 22 q^{28} - 6 q^{29} - 5 q^{30} - 20 q^{31} - 17 q^{32} - 14 q^{33} - 8 q^{34} - 16 q^{35} - 3 q^{36} + 58 q^{37} - 11 q^{38} + 44 q^{39} - 5 q^{40} - 20 q^{41} + 8 q^{42} - 30 q^{43} + 6 q^{44} - 22 q^{45} + 10 q^{46} - 10 q^{47} - q^{48} - 42 q^{49} - 32 q^{50} - 49 q^{51} - 10 q^{52} + 4 q^{53} - 22 q^{54} + 30 q^{55} - 11 q^{56} + 27 q^{57} - 6 q^{58} + 3 q^{59} + 4 q^{60} + 17 q^{61} + 40 q^{62} - 45 q^{63} + 34 q^{64} - 28 q^{65} + 28 q^{66} - 11 q^{67} - 8 q^{68} - 32 q^{69} + 8 q^{70} + 126 q^{71} + 56 q^{73} - 29 q^{74} + 100 q^{75} - 11 q^{76} - 17 q^{77} - 16 q^{78} - 17 q^{79} + 10 q^{80} - 8 q^{81} + 40 q^{82} + 20 q^{83} - 7 q^{84} - 33 q^{85} - 30 q^{86} - 86 q^{87} - 3 q^{88} + 4 q^{89} + 23 q^{90} + 60 q^{91} - 5 q^{92} + 121 q^{93} - 10 q^{94} - q^{95} - q^{96} - 32 q^{97} + 84 q^{98} - 31 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 2 * q^3 - 17 * q^4 - 5 * q^5 - q^6 - 11 * q^7 + 34 * q^8 + 10 * q^10 - 3 * q^11 - q^12 - 10 * q^13 - 11 * q^14 + q^15 - 17 * q^16 + 16 * q^17 + 3 * q^18 + 22 * q^19 - 5 * q^20 - q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 32 * q^25 + 20 * q^26 - q^27 + 22 * q^28 - 6 * q^29 - 5 * q^30 - 20 * q^31 - 17 * q^32 - 14 * q^33 - 8 * q^34 - 16 * q^35 - 3 * q^36 + 58 * q^37 - 11 * q^38 + 44 * q^39 - 5 * q^40 - 20 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 22 * q^45 + 10 * q^46 - 10 * q^47 - q^48 - 42 * q^49 - 32 * q^50 - 49 * q^51 - 10 * q^52 + 4 * q^53 - 22 * q^54 + 30 * q^55 - 11 * q^56 + 27 * q^57 - 6 * q^58 + 3 * q^59 + 4 * q^60 + 17 * q^61 + 40 * q^62 - 45 * q^63 + 34 * q^64 - 28 * q^65 + 28 * q^66 - 11 * q^67 - 8 * q^68 - 32 * q^69 + 8 * q^70 + 126 * q^71 + 56 * q^73 - 29 * q^74 + 100 * q^75 - 11 * q^76 - 17 * q^77 - 16 * q^78 - 17 * q^79 + 10 * q^80 - 8 * q^81 + 40 * q^82 + 20 * q^83 - 7 * q^84 - 33 * q^85 - 30 * q^86 - 86 * q^87 - 3 * q^88 + 4 * q^89 + 23 * q^90 + 60 * q^91 - 5 * q^92 + 121 * q^93 - 10 * q^94 - q^95 - q^96 - 32 * q^97 + 84 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1098\mathbb{Z}\right)^\times$.

$n$	$245$	$307$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.70593	+	0.299644i	−0.984922	+	0.173000i
$3$	−1.70593	+	0.299644i	−0.984922	+	0.173000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.02139	−	3.50116i	−0.903994	−	1.56576i	−0.822261	−	0.569110i	$-0.807288\pi$
$5$	−2.02139	−	3.50116i	−0.903994	−	1.56576i	−0.0817331	−	0.996654i	$-0.526046\pi$
$6$	0.593468	−	1.62720i	0.242282	−	0.664304i
$7$	1.31426	−	2.27636i	0.496743	−	0.860384i	−0.503250	−	0.864141i	$-0.667862\pi$
$7$	1.31426	−	2.27636i	0.496743	−	0.860384i	0.999993	+	0.00375666i	$0.00119579\pi$
$8$	1.00000			0.353553
$9$	2.82043	−	1.02235i	0.940142	−	0.340782i
$10$	4.04279			1.27844
$11$	2.10717	−	3.64973i	0.635336	−	1.10043i	−0.351108	−	0.936335i	$-0.614195\pi$
$11$	2.10717	−	3.64973i	0.635336	−	1.10043i	0.986444	−	0.164100i	$-0.0524718\pi$
$12$	1.11247	+	1.32756i	0.321141	+	0.383234i
$13$	−3.06435	−	5.30761i	−0.849897	−	1.47207i	−0.881299	−	0.472558i	$-0.843331\pi$
$13$	−3.06435	−	5.30761i	−0.849897	−	1.47207i	0.0314022	−	0.999507i	$-0.490003\pi$
$14$	1.31426	+	2.27636i	0.351250	+	0.608384i
$15$	4.49746	+	5.36704i	1.16124	+	1.38576i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.44390			1.32034			0.660169	−	0.751117i	$-0.270484\pi$
$17$	5.44390			1.32034			0.660169	+	0.751117i	$0.270484\pi$
$18$	−0.524836	+	2.95373i	−0.123705	+	0.696202i
$19$	−4.44023			−1.01866			−0.509329	−	0.860572i	$-0.670106\pi$
$19$	−4.44023			−1.01866			−0.509329	+	0.860572i	$0.670106\pi$
$20$	−2.02139	+	3.50116i	−0.451997	+	0.782882i
$21$	−1.55994	+	4.27714i	−0.340407	+	0.933348i
$22$	2.10717	+	3.64973i	0.449251	+	0.778125i
$23$	0.820153	+	1.42055i	0.171014	+	0.296204i	0.938775	−	0.344532i	$-0.111962\pi$
$23$	0.820153	+	1.42055i	0.171014	+	0.296204i	−0.767761	+	0.640736i	$0.778629\pi$
$24$	−1.70593	+	0.299644i	−0.348222	+	0.0611646i
$25$	−5.67206	+	9.82430i	−1.13441	+	1.96486i
$26$	6.12870			1.20194
$27$	−4.50512	+	2.58918i	−0.867012	+	0.498288i
$28$	−2.62852			−0.496743
$29$	3.78780	−	6.56067i	0.703378	−	1.21829i	−0.263896	−	0.964551i	$-0.585008\pi$
$29$	3.78780	−	6.56067i	0.703378	−	1.21829i	0.967274	−	0.253735i	$-0.0816590\pi$
$30$	−6.89673	+	1.21140i	−1.25916	+	0.221170i
$31$	−0.108453	−	0.187846i	−0.0194787	−	0.0337381i	0.856122	−	0.516774i	$-0.172867\pi$
$31$	−0.108453	−	0.187846i	−0.0194787	−	0.0337381i	−0.875600	+	0.483036i	$0.839534\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.50108	+	6.85760i	−0.435382	+	1.19376i
$34$	−2.72195	+	4.71455i	−0.466810	+	0.808539i
$35$	−10.6265			−1.79621
$36$	−2.29559	−	1.93139i	−0.382599	−	0.321898i
$37$	8.34941			1.37263			0.686317	−	0.727303i	$-0.259226\pi$
$37$	8.34941			1.37263			0.686317	+	0.727303i	$0.259226\pi$
$38$	2.22011	−	3.84535i	0.360150	−	0.623798i
$39$	6.81797	+	8.13622i	1.09175	+	1.30284i
$40$	−2.02139	−	3.50116i	−0.319610	−	0.553581i
$41$	−4.05327	−	7.02047i	−0.633015	−	1.09641i	−0.986932	−	0.161137i	$-0.948484\pi$
$41$	−4.05327	−	7.02047i	−0.633015	−	1.09641i	0.353917	−	0.935277i	$-0.384849\pi$
$42$	−2.92414	−	3.48952i	−0.451204	−	0.538444i
$43$	−2.10813	+	3.65139i	−0.321487	+	0.556831i	−0.980795	−	0.195041i	$-0.937516\pi$
$43$	−2.10813	+	3.65139i	−0.321487	+	0.556831i	0.659308	+	0.751873i	$0.270849\pi$
$44$	−4.21434			−0.635336
$45$	−9.28058	−	7.80819i	−1.38347	−	1.16398i
$46$	−1.64031			−0.241850
$47$	3.17365	−	5.49692i	0.462924	−	0.801808i	−0.536181	−	0.844103i	$-0.680134\pi$
$47$	3.17365	−	5.49692i	0.462924	−	0.801808i	0.999105	+	0.0422950i	$0.0134669\pi$
$48$	0.593468	−	1.62720i	0.0856597	−	0.234867i
$49$	0.0454480	+	0.0787182i	0.00649257	+	0.0112455i
$50$	−5.67206	−	9.82430i	−0.802150	−	1.38937i
$51$	−9.28693	+	1.63123i	−1.30043	+	0.228418i
$52$	−3.06435	+	5.30761i	−0.424949	+	0.736033i
$53$	5.78041			0.794000			0.397000	−	0.917819i	$-0.370051\pi$
$53$	5.78041			0.794000			0.397000	+	0.917819i	$0.370051\pi$
$54$	0.0102666	−	5.19614i	0.00139711	−	0.707105i
$55$	−17.0377			−2.29736
$56$	1.31426	−	2.27636i	0.175625	−	0.304192i
$57$	7.57474	−	1.33049i	1.00330	−	0.176227i
$58$	3.78780	+	6.56067i	0.497363	+	0.861458i
$59$	−1.93757	−	3.35598i	−0.252251	−	0.436911i	0.711894	−	0.702286i	$-0.247837\pi$
$59$	−1.93757	−	3.35598i	−0.252251	−	0.436911i	−0.964145	+	0.265375i	$0.914504\pi$
$60$	2.39926	−	6.57844i	0.309744	−	0.849273i
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i
$62$	0.216906			0.0275471
$63$	1.37954	−	7.76394i	0.173806	−	0.978165i
$64$	1.00000			0.125000
$65$	−12.3885	+	21.4575i	−1.53660	+	2.66148i
$66$	−4.68832	−	5.59480i	−0.577092	−	0.688672i
$67$	−3.28031	−	5.68167i	−0.400754	−	0.694126i	0.593063	−	0.805156i	$-0.297918\pi$
$67$	−3.28031	−	5.68167i	−0.400754	−	0.694126i	−0.993817	+	0.111030i	$0.964585\pi$
$68$	−2.72195	−	4.71455i	−0.330085	−	0.571723i
$69$	−1.82479	−	2.17761i	−0.219678	−	0.262153i
$70$	5.31327	−	9.20285i	0.635057	−	1.09995i
$71$	14.7541			1.75099			0.875494	−	0.483229i	$-0.160536\pi$
$71$	14.7541			1.75099			0.875494	+	0.483229i	$0.160536\pi$
$72$	2.82043	−	1.02235i	0.332391	−	0.120485i
$73$	−7.90683			−0.925425			−0.462713	−	0.886508i	$-0.653124\pi$
$73$	−7.90683			−0.925425			−0.462713	+	0.886508i	$0.653124\pi$
$74$	−4.17470	+	7.23080i	−0.485299	+	0.840563i
$75$	6.73237	−	18.4592i	0.777387	−	2.13149i
$76$	2.22011	+	3.84535i	0.254665	+	0.441092i
$77$	−5.53874	−	9.59338i	−0.631198	−	1.09327i
$78$	−10.4552	+	1.83643i	−1.18381	+	0.207934i
$79$	−5.86350	+	10.1559i	−0.659695	+	1.14263i	0.320999	+	0.947079i	$0.395981\pi$
$79$	−5.86350	+	10.1559i	−0.659695	+	1.14263i	−0.980694	+	0.195546i	$0.937352\pi$
$80$	4.04279			0.451997
$81$	6.90962	−	5.76691i	0.767735	−	0.640767i
$82$	8.10654			0.895218
$83$	−5.77258	+	9.99839i	−0.633622	+	1.09747i	0.353183	+	0.935554i	$0.385099\pi$
$83$	−5.77258	+	9.99839i	−0.633622	+	1.09747i	−0.986805	+	0.161912i	$0.948234\pi$
$84$	4.48408	−	0.787619i	0.489253	−	0.0859363i
$85$	−11.0043	−	19.0599i	−1.19358	−	2.06734i
$86$	−2.10813	−	3.65139i	−0.227325	−	0.393739i
$87$	−4.49588	+	12.3271i	−0.482009	+	1.32160i
$88$	2.10717	−	3.64973i	0.224625	−	0.389062i
$89$	−13.5586			−1.43721			−0.718603	−	0.695421i	$-0.755218\pi$
$89$	−13.5586			−1.43721			−0.718603	+	0.695421i	$0.755218\pi$
$90$	11.4024	−	4.13313i	1.20192	−	0.435670i
$91$	−16.1094			−1.68872
$92$	0.820153	−	1.42055i	0.0855068	−	0.148102i
$93$	0.241300	+	0.287956i	0.0250217	+	0.0298596i
$94$	3.17365	+	5.49692i	0.327337	+	0.566964i
$95$	8.97545	+	15.5459i	0.920862	+	1.59498i
$96$	1.11247	+	1.32756i	0.113541	+	0.135494i
$97$	1.99272	−	3.45149i	0.202330	−	0.350446i	−0.746949	−	0.664882i	$-0.768482\pi$
$97$	1.99272	−	3.45149i	0.202330	−	0.350446i	0.949279	+	0.314436i	$0.101815\pi$
$98$	−0.0908960			−0.00918188
$99$	2.21184	−	12.4481i	0.222298	−	1.25108i
$100$	11.3441			1.13441
$101$	−1.42002	+	2.45955i	−0.141297	+	0.244734i	−0.927985	−	0.372617i	$-0.878461\pi$
$101$	−1.42002	+	2.45955i	−0.141297	+	0.244734i	0.786688	+	0.617351i	$0.211794\pi$
$102$	3.23078	−	8.85833i	0.319895	−	0.877106i
$103$	1.97710	+	3.42443i	0.194809	+	0.337419i	0.946838	−	0.321711i	$-0.104258\pi$
$103$	1.97710	+	3.42443i	0.194809	+	0.337419i	−0.752029	+	0.659130i	$0.770925\pi$
$104$	−3.06435	−	5.30761i	−0.300484	−	0.520454i
$105$	18.1282	−	3.18418i	1.76913	−	0.310744i
$106$	−2.89020	+	5.00598i	−0.280722	+	0.486224i
$107$	17.1906			1.66188			0.830938	−	0.556366i	$-0.187805\pi$
$107$	17.1906			1.66188			0.830938	+	0.556366i	$0.187805\pi$
$108$	4.49486	+	2.60696i	0.432518	+	0.250855i
$109$	−2.56099			−0.245299			−0.122649	−	0.992450i	$-0.539139\pi$
$109$	−2.56099			−0.245299			−0.122649	+	0.992450i	$0.539139\pi$
$110$	8.51885	−	14.7551i	0.812240	−	1.40684i
$111$	−14.2435	+	2.50185i	−1.35194	+	0.237465i
$112$	1.31426	+	2.27636i	0.124186	+	0.215096i
$113$	2.85907	+	4.95205i	0.268958	+	0.465850i	0.968593	−	0.248651i	$-0.0799873\pi$
$113$	2.85907	+	4.95205i	0.268958	+	0.465850i	−0.699635	+	0.714501i	$0.746654\pi$
$114$	−2.63513	+	7.22516i	−0.246803	+	0.676698i
$115$	3.31570	−	5.74296i	0.309191	−	0.535534i
$116$	−7.57561			−0.703378
$117$	−14.0690	−	11.8369i	−1.30068	−	1.09432i
$118$	3.87515			0.356736
$119$	7.15469	−	12.3923i	0.655869	−	1.13600i
$120$	4.49746	+	5.36704i	0.410560	+	0.489942i
$121$	−3.38035	−	5.85493i	−0.307304	−	0.532267i
$122$	0.500000	+	0.866025i	0.0452679	+	0.0784063i
$123$	9.01826	+	10.7619i	0.813149	+	0.970371i
$124$	−0.108453	+	0.187846i	−0.00973936	+	0.0168691i
$125$	25.6479			2.29402
$126$	6.03400	+	5.07669i	0.537552	+	0.452267i
$127$	−0.859611			−0.0762781			−0.0381391	−	0.999272i	$-0.512143\pi$
$127$	−0.859611			−0.0762781			−0.0381391	+	0.999272i	$0.512143\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.50221	−	6.86071i	0.220308	−	0.604052i
$130$	−12.3885	−	21.4575i	−1.08654	−	1.88195i
$131$	2.92515	+	5.06652i	0.255572	+	0.442664i	0.965051	−	0.262063i	$-0.0844029\pi$
$131$	2.92515	+	5.06652i	0.255572	+	0.442664i	−0.709479	+	0.704727i	$0.751070\pi$
$132$	7.18940	−	1.26280i	0.625757	−	0.109913i
$133$	−5.83561	+	10.1076i	−0.506012	+	0.876438i
$134$	6.56062			0.566751
$135$	18.1717	+	10.5394i	1.56398	+	0.907086i
$136$	5.44390			0.466810
$137$	4.90134	−	8.48938i	0.418750	−	0.725297i	−0.577064	−	0.816699i	$-0.695802\pi$
$137$	4.90134	−	8.48938i	0.418750	−	0.725297i	0.995814	+	0.0914025i	$0.0291350\pi$
$138$	2.79825	−	0.491508i	0.238203	−	0.0418399i
$139$	1.48451	+	2.57124i	0.125914	+	0.218090i	0.922090	−	0.386976i	$-0.126480\pi$
$139$	1.48451	+	2.57124i	0.125914	+	0.218090i	−0.796176	+	0.605065i	$0.793147\pi$
$140$	5.31327	+	9.20285i	0.449053	+	0.777783i
$141$	−3.76692	+	10.3283i	−0.317232	+	0.869804i
$142$	−7.37704	+	12.7774i	−0.619068	+	1.07226i
$143$	−25.8284			−2.15988
$144$	−0.524836	+	2.95373i	−0.0437363	+	0.246145i
$145$	−30.6266			−2.54340
$146$	3.95342	−	6.84752i	0.327187	−	0.566705i
$147$	−0.101119	−	0.120670i	−0.00834013	−	0.00995269i
$148$	−4.17470	−	7.23080i	−0.343158	−	0.594368i
$149$	−10.2299	−	17.7188i	−0.838070	−	1.45158i	−0.891506	−	0.453009i	$-0.850351\pi$
$149$	−10.2299	−	17.7188i	−0.838070	−	1.45158i	0.0534359	−	0.998571i	$-0.482983\pi$
$150$	12.6200	+	15.0600i	1.03042	+	1.22964i
$151$	0.332740	−	0.576323i	0.0270780	−	0.0469005i	−0.852169	−	0.523267i	$-0.824713\pi$
$151$	0.332740	−	0.576323i	0.0270780	−	0.0469005i	0.879247	+	0.476366i	$0.158046\pi$
$152$	−4.44023			−0.360150
$153$	15.3541	−	5.56555i	1.24131	−	0.449948i
$154$	11.0775			0.892649
$155$	−0.438452	+	0.759421i	−0.0352173	+	0.0609982i
$156$	3.63719	−	9.97264i	0.291208	−	0.798451i
$157$	4.10401	+	7.10836i	0.327536	+	0.567309i	0.982022	−	0.188765i	$-0.0604484\pi$
$157$	4.10401	+	7.10836i	0.327536	+	0.567309i	−0.654486	+	0.756074i	$0.727115\pi$
$158$	−5.86350	−	10.1559i	−0.466475	−	0.807958i
$159$	−9.86100	+	1.73207i	−0.782028	+	0.137362i
$160$	−2.02139	+	3.50116i	−0.159805	+	0.276791i
$161$	4.31157			0.339799
$162$	1.53948	+	8.86736i	0.120953	+	0.696685i
$163$	12.3611			0.968195			0.484097	−	0.875014i	$-0.339148\pi$
$163$	12.3611			0.968195			0.484097	+	0.875014i	$0.339148\pi$
$164$	−4.05327	+	7.02047i	−0.316507	+	0.548207i
$165$	29.0652	−	5.10524i	2.26272	−	0.397443i
$166$	−5.77258	−	9.99839i	−0.448039	−	0.776026i
$167$	12.7054	+	22.0064i	0.983172	+	1.70290i	0.649792	+	0.760112i	$0.274856\pi$
$167$	12.7054	+	22.0064i	0.983172	+	1.70290i	0.333380	+	0.942793i	$0.391811\pi$
$168$	−1.55994	+	4.27714i	−0.120352	+	0.329988i
$169$	−12.2805	+	21.2704i	−0.944650	+	1.63618i
$170$	22.0085			1.68798
$171$	−12.5233	+	4.53945i	−0.957684	+	0.347141i
$172$	4.21626			0.321487
$173$	−8.37516	+	14.5062i	−0.636752	+	1.10289i	0.349389	+	0.936978i	$0.386389\pi$
$173$	−8.37516	+	14.5062i	−0.636752	+	1.10289i	−0.986141	+	0.165909i	$0.946944\pi$
$174$	−8.42761	−	10.0571i	−0.638896	−	0.762425i
$175$	14.9091	+	25.8233i	1.12702	+	1.95206i
$176$	2.10717	+	3.64973i	0.158834	+	0.275109i
$177$	4.31097	+	5.14450i	0.324033	+	0.386684i
$178$	6.77928	−	11.7421i	0.508129	−	0.880105i
$179$	−10.9587			−0.819088			−0.409544	−	0.912290i	$-0.634312\pi$
$179$	−10.9587			−0.819088			−0.409544	+	0.912290i	$0.634312\pi$
$180$	−2.12180	+	11.9413i	−0.158150	+	0.890053i
$181$	−6.70682			−0.498514			−0.249257	−	0.968437i	$-0.580186\pi$
$181$	−6.70682			−0.498514			−0.249257	+	0.968437i	$0.580186\pi$
$182$	8.05469	−	13.9511i	0.597053	−	1.03413i
$183$	−0.593468	+	1.62720i	−0.0438704	+	0.120286i
$184$	0.820153	+	1.42055i	0.0604625	+	0.104724i
$185$	−16.8774	−	29.2326i	−1.24085	−	2.14922i
$186$	−0.370027	+	0.0649945i	−0.0271317	+	0.00476563i
$187$	11.4712	−	19.8687i	0.838859	−	1.45295i
$188$	−6.34729			−0.462924
$189$	−0.0269860	+	13.6582i	−0.00196295	+	0.993484i
$190$	−17.9509			−1.30229
$191$	−10.2059	+	17.6772i	−0.738475	+	1.27908i	0.214706	+	0.976679i	$0.431121\pi$
$191$	−10.2059	+	17.6772i	−0.738475	+	1.27908i	−0.953182	+	0.302398i	$0.902213\pi$
$192$	−1.70593	+	0.299644i	−0.123115	+	0.0216249i
$193$	−6.94154	−	12.0231i	−0.499663	−	0.865442i	0.500337	−	0.865831i	$-0.333210\pi$
$193$	−6.94154	−	12.0231i	−0.499663	−	0.865442i	−1.00000		0.000388994i	$0.999876\pi$
$194$	1.99272	+	3.45149i	0.143069	+	0.247803i
$195$	14.7044	−	40.3173i	1.05300	−	2.88718i
$196$	0.0454480	−	0.0787182i	0.00324628	−	0.00562273i
$197$	−19.8807			−1.41644			−0.708221	−	0.705991i	$-0.750502\pi$
$197$	−19.8807			−1.41644			−0.708221	+	0.705991i	$0.750502\pi$
$198$	9.67441	+	8.13953i	0.687530	+	0.578452i
$199$	15.2050			1.07785			0.538926	−	0.842353i	$-0.318830\pi$
$199$	15.2050			1.07785			0.538926	+	0.842353i	$0.318830\pi$
$200$	−5.67206	+	9.82430i	−0.401075	+	0.694683i
$201$	7.29847	+	8.70963i	0.514795	+	0.614330i
$202$	−1.42002	−	2.45955i	−0.0999123	−	0.173053i
$203$	−9.95631	−	17.2448i	−0.698796	−	1.21035i
$204$	6.05615	+	7.22710i	0.424016	+	0.505998i
$205$	−16.3865	+	28.3823i	−1.14448	+	1.98230i
$206$	−3.95419			−0.275502
$207$	3.76547	+	3.16807i	0.261718	+	0.220196i
$208$	6.12870			0.424949
$209$	−9.35633	+	16.2056i	−0.647191	+	1.12097i
$210$	−6.30651	+	17.2915i	−0.435190	+	1.19323i
$211$	−3.68758	−	6.38708i	−0.253864	−	0.439704i	0.710723	−	0.703472i	$-0.248368\pi$
$211$	−3.68758	−	6.38708i	−0.253864	−	0.439704i	−0.964586	+	0.263768i	$0.915035\pi$
$212$	−2.89020	−	5.00598i	−0.198500	−	0.343812i
$213$	−25.1695	+	4.42097i	−1.72459	+	0.302920i
$214$	−8.59528	+	14.8875i	−0.587562	+	1.01769i
$215$	17.0454			1.16249
$216$	−4.50512	+	2.58918i	−0.306535	+	0.176171i
$217$	−0.570141			−0.0387037
$218$	1.28050	−	2.21789i	0.0867262	−	0.150214i
$219$	13.4885	−	2.36924i	0.911471	−	0.160098i
$220$	8.51885	+	14.7551i	0.574340	+	0.994787i
$221$	−16.6820	−	28.8941i	−1.12215	−	1.94362i
$222$	4.95511	−	13.5862i	0.332565	−	0.911846i
$223$	−2.00471	+	3.47226i	−0.134245	+	0.232520i	−0.925309	−	0.379214i	$-0.876194\pi$
$223$	−2.00471	+	3.47226i	−0.134245	+	0.232520i	0.791064	+	0.611734i	$0.209528\pi$
$224$	−2.62852			−0.175625
$225$	−5.95380	+	33.5075i	−0.396920	+	2.23383i
$226$	−5.71813			−0.380365
$227$	−3.24262	+	5.61638i	−0.215220	+	0.372772i	−0.953341	−	0.301897i	$-0.902380\pi$
$227$	−3.24262	+	5.61638i	−0.215220	+	0.372772i	0.738121	+	0.674669i	$0.235714\pi$
$228$	−4.93961	−	5.89467i	−0.327133	−	0.390384i
$229$	4.81256	+	8.33559i	0.318023	+	0.550831i	0.980075	−	0.198626i	$-0.0636479\pi$
$229$	4.81256	+	8.33559i	0.318023	+	0.550831i	−0.662053	+	0.749457i	$0.730315\pi$
$230$	3.31570	+	5.74296i	0.218631	+	0.378680i
$231$	12.3233	+	14.7060i	0.810815	+	0.967585i
$232$	3.78780	−	6.56067i	0.248682	−	0.430729i
$233$	27.2350			1.78422			0.892112	−	0.451813i	$-0.149223\pi$
$233$	27.2350			1.78422			0.892112	+	0.451813i	$0.149223\pi$
$234$	17.2855	−	6.26565i	1.12999	−	0.409598i
$235$	−25.6608			−1.67392
$236$	−1.93757	+	3.35598i	−0.126125	+	0.218456i
$237$	6.95960	−	19.0822i	0.452075	−	1.23952i
$238$	7.15469	+	12.3923i	0.463770	+	0.803272i
$239$	0.843640	+	1.46123i	0.0545706	+	0.0945190i	0.892020	−	0.451995i	$-0.149288\pi$
$239$	0.843640	+	1.46123i	0.0545706	+	0.0945190i	−0.837450	+	0.546514i	$0.815954\pi$
$240$	−6.89673	+	1.21140i	−0.445182	+	0.0781953i
$241$	−7.71872	+	13.3692i	−0.497206	+	0.861187i	−0.999995	−	0.00322282i	$-0.998974\pi$
$241$	−7.71872	+	13.3692i	−0.497206	+	0.861187i	0.502788	+	0.864409i	$0.332307\pi$
$242$	6.76070			0.434594
$243$	−10.0593	+	11.9084i	−0.645307	+	0.763924i
$244$	−1.00000			−0.0640184
$245$	0.183736	−	0.318241i	0.0117385	−	0.0203317i
$246$	−13.8292	+	2.42908i	−0.881720	+	0.154872i
$247$	13.6064	+	23.5670i	0.865755	+	1.49953i
$248$	−0.108453	−	0.187846i	−0.00688677	−	0.0119282i
$249$	6.85168	−	18.7863i	0.434207	−	1.19053i
$250$	−12.8240	+	22.2117i	−0.811058	+	1.40479i
$251$	14.3588			0.906318			0.453159	−	0.891430i	$-0.350297\pi$
$251$	14.3588			0.906318			0.453159	+	0.891430i	$0.350297\pi$
$252$	−7.41354	+	2.68725i	−0.467009	+	0.169281i
$253$	6.91281			0.434605
$254$	0.429806	−	0.744445i	0.0269684	−	0.0467106i
$255$	24.4837	+	29.2176i	1.53323	+	1.82968i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.19936	+	9.00555i	0.324327	+	0.561751i	0.981376	−	0.192097i	$-0.0615289\pi$
$257$	5.19936	+	9.00555i	0.324327	+	0.561751i	−0.657049	+	0.753848i	$0.728196\pi$
$258$	4.69045	+	5.59734i	0.292014	+	0.348475i
$259$	10.9733	−	19.0063i	0.681846	−	1.18099i
$260$	24.7770			1.53660
$261$	3.97595	−	22.3763i	0.246105	−	1.38506i
$262$	−5.85031			−0.361433
$263$	3.87890	−	6.71846i	0.239183	−	0.414278i	−0.721297	−	0.692626i	$-0.756454\pi$
$263$	3.87890	−	6.71846i	0.239183	−	0.414278i	0.960480	+	0.278348i	$0.0897870\pi$
$264$	−2.50108	+	6.85760i	−0.153931	+	0.422056i
$265$	−11.6845	−	20.2381i	−0.717772	−	1.24322i
$266$	−5.83561	−	10.1076i	−0.357804	−	0.619735i
$267$	23.1300	−	4.06274i	1.41554	−	0.248636i
$268$	−3.28031	+	5.68167i	−0.200377	+	0.347063i
$269$	9.58542			0.584433			0.292217	−	0.956352i	$-0.405607\pi$
$269$	9.58542			0.584433			0.292217	+	0.956352i	$0.405607\pi$
$270$	−18.2133	+	10.4675i	−1.10842	+	0.637032i
$271$	1.47114			0.0893653			0.0446827	−	0.999001i	$-0.485772\pi$
$271$	1.47114			0.0893653			0.0446827	+	0.999001i	$0.485772\pi$
$272$	−2.72195	+	4.71455i	−0.165042	+	0.285862i
$273$	27.4816	−	4.82708i	1.66326	−	0.292148i
$274$	4.90134	+	8.48938i	0.296101	+	0.512862i
$275$	23.9040	+	41.4030i	1.44147	+	2.49669i
$276$	−0.973469	+	2.66911i	−0.0585959	+	0.160662i
$277$	10.5057	−	18.1965i	0.631229	−	1.09332i	−0.356072	−	0.934459i	$-0.615884\pi$
$277$	10.5057	−	18.1965i	0.631229	−	1.09332i	0.987301	−	0.158862i	$-0.0507826\pi$
$278$	−2.96901			−0.178070
$279$	−0.497927	−	0.418929i	−0.0298101	−	0.0250806i
$280$	−10.6265			−0.635057
$281$	15.4424	−	26.7470i	0.921217	−	1.59559i	0.123681	−	0.992322i	$-0.460530\pi$
$281$	15.4424	−	26.7470i	0.921217	−	1.59559i	0.797535	−	0.603272i	$-0.206137\pi$
$282$	−7.06115	−	8.42642i	−0.420486	−	0.501786i
$283$	6.23708	+	10.8029i	0.370756	+	0.642168i	0.989682	−	0.143281i	$-0.0457654\pi$
$283$	6.23708	+	10.8029i	0.370756	+	0.642168i	−0.618926	+	0.785449i	$0.712432\pi$
$284$	−7.37704	−	12.7774i	−0.437747	−	0.758200i
$285$	−19.9698	−	23.8309i	−1.18291	−	1.41162i
$286$	12.9142	−	22.3681i	0.763634	−	1.32265i
$287$	−21.3082			−1.25778
$288$	−2.29559	−	1.93139i	−0.135269	−	0.113808i
$289$	12.6360			0.743295
$290$	15.3133	−	26.5234i	0.899227	−	1.55751i
$291$	−2.36523	+	6.48512i	−0.138652	+	0.380165i
$292$	3.95342	+	6.84752i	0.231356	+	0.400721i
$293$	3.30883	+	5.73106i	0.193304	+	0.334812i	0.946343	−	0.323163i	$-0.104746\pi$
$293$	3.30883	+	5.73106i	0.193304	+	0.334812i	−0.753039	+	0.657976i	$0.771413\pi$
$294$	0.155063	−	0.0272364i	0.00904343	−	0.00158846i
$295$	−7.83320	+	13.5675i	−0.456067	+	0.789930i
$296$	8.34941			0.485299
$297$	−0.0432672	+	21.8983i	−0.00251062	+	1.27067i
$298$	20.4599			1.18521
$299$	5.02647	−	8.70609i	0.290688	−	0.503486i
$300$	−19.3523	+	3.39920i	−1.11731	+	0.196253i
$301$	5.54125	+	9.59773i	0.319393	+	0.553204i
$302$	0.332740	+	0.576323i	0.0191470	+	0.0331637i
$303$	1.68547	−	4.62133i	0.0968280	−	0.265488i
$304$	2.22011	−	3.84535i	0.127332	−	0.220546i
$305$	−4.04279			−0.231489
$306$	−2.85715	+	16.0798i	−0.163332	+	0.919222i
$307$	7.81948			0.446282			0.223141	−	0.974786i	$-0.428369\pi$
$307$	7.81948			0.446282			0.223141	+	0.974786i	$0.428369\pi$
$308$	−5.53874	+	9.59338i	−0.315599	+	0.546633i
$309$	−4.39891	−	5.24943i	−0.250245	−	0.298630i
$310$	−0.438452	−	0.759421i	−0.0249024	−	0.0431322i
$311$	−10.1691	−	17.6134i	−0.576638	−	0.998766i	−0.995862	−	0.0908829i	$-0.971031\pi$
$311$	−10.1691	−	17.6134i	−0.576638	−	0.998766i	0.419224	−	0.907883i	$-0.362302\pi$
$312$	6.81797	+	8.13622i	0.385992	+	0.460623i
$313$	13.5662	−	23.4974i	0.766809	−	1.32815i	−0.172475	−	0.985014i	$-0.555176\pi$
$313$	13.5662	−	23.4974i	0.766809	−	1.32815i	0.939285	−	0.343139i	$-0.111490\pi$
$314$	−8.20803			−0.463206
$315$	−29.9714	+	10.8640i	−1.68869	+	0.612117i
$316$	11.7270			0.659695
$317$	−4.29459	+	7.43844i	−0.241208	+	0.417785i	−0.961059	−	0.276344i	$-0.910877\pi$
$317$	−4.29459	+	7.43844i	−0.241208	+	0.417785i	0.719851	+	0.694129i	$0.244210\pi$
$318$	3.43049	−	9.40591i	0.192372	−	0.527457i
$319$	−15.9631	−	27.6489i	−0.893763	−	1.54804i
$320$	−2.02139	−	3.50116i	−0.112999	−	0.195721i
$321$	−29.3260	+	5.15105i	−1.63682	+	0.287504i
$322$	−2.15579	+	3.73393i	−0.120137	+	0.208084i
$323$	−24.1721			−1.34497
$324$	−8.44910	−	3.10045i	−0.469394	−	0.172247i
$325$	69.5247			3.85653
$326$	−6.18054	+	10.7050i	−0.342309	+	0.592896i
$327$	4.36889	−	0.767387i	0.241600	−	0.0424366i
$328$	−4.05327	−	7.02047i	−0.223804	−	0.387641i
$329$	−8.34199	−	14.4487i	−0.459909	−	0.796585i
$330$	−10.1113	+	27.7238i	−0.556610	+	1.52615i
$331$	1.71562	−	2.97153i	0.0942988	−	0.163330i	−0.815017	−	0.579437i	$-0.803272\pi$
$331$	1.71562	−	2.97153i	0.0942988	−	0.163330i	0.909316	+	0.416107i	$0.136606\pi$
$332$	11.5452			0.633622
$333$	23.5489	−	8.53598i	1.29047	−	0.467769i
$334$	−25.4108			−1.39042
$335$	−13.2616	+	22.9698i	−0.724558	+	1.25497i
$336$	−2.92414	−	3.48952i	−0.159525	−	0.190369i
$337$	−4.57183	−	7.91863i	−0.249043	−	0.431356i	0.714217	−	0.699924i	$-0.246783\pi$
$337$	−4.57183	−	7.91863i	−0.249043	−	0.431356i	−0.963261	+	0.268568i	$0.913449\pi$
$338$	−12.2805	−	21.2704i	−0.667969	−	1.15696i
$339$	−6.36123	−	7.59117i	−0.345495	−	0.412296i
$340$	−11.0043	+	19.0599i	−0.596790	+	1.03367i
$341$	−0.914116			−0.0495021
$342$	2.33039	−	13.1153i	0.126013	−	0.709192i
$343$	18.6385			1.00639
$344$	−2.10813	+	3.65139i	−0.113663	+	0.196870i
$345$	−3.93553	+	10.7907i	−0.211882	+	0.580949i
$346$	−8.37516	−	14.5062i	−0.450252	−	0.779859i
$347$	18.3901	+	31.8526i	0.987233	+	1.70994i	0.631560	+	0.775327i	$0.282415\pi$
$347$	18.3901	+	31.8526i	0.987233	+	1.70994i	0.355673	+	0.934610i	$0.384252\pi$
$348$	12.9235	−	2.26999i	0.692772	−	0.121684i
$349$	−8.50479	+	14.7307i	−0.455251	+	0.788518i	−0.998703	−	0.0509226i	$-0.983784\pi$
$349$	−8.50479	+	14.7307i	−0.455251	+	0.788518i	0.543452	+	0.839441i	$0.317117\pi$
$350$	−29.8182			−1.59385
$351$	27.5476	+	15.9773i	1.47038	+	0.852804i
$352$	−4.21434			−0.224625
$353$	13.1451	−	22.7680i	0.699644	−	1.21182i	−0.268946	−	0.963155i	$-0.586675\pi$
$353$	13.1451	−	22.7680i	0.699644	−	1.21182i	0.968590	−	0.248664i	$-0.0799914\pi$
$354$	−6.61075	+	1.16117i	−0.351358	+	0.0617152i
$355$	−29.8238	−	51.6563i	−1.58288	−	2.74163i
$356$	6.77928	+	11.7421i	0.359301	+	0.622328i
$357$	−8.49216	+	23.2843i	−0.449453	+	1.23234i
$358$	5.47933	−	9.49048i	0.289592	−	0.501587i
$359$	−17.1316			−0.904173			−0.452087	−	0.891974i	$-0.649320\pi$
$359$	−17.1316			−0.904173			−0.452087	+	0.891974i	$0.649320\pi$
$360$	−9.28058	−	7.80819i	−0.489130	−	0.411528i
$361$	0.715635			0.0376650
$362$	3.35341	−	5.80827i	0.176251	−	0.305276i
$363$	7.52105	+	8.97524i	0.394753	+	0.471078i
$364$	8.05469	+	13.9511i	0.422181	+	0.731238i
$365$	15.9828	+	27.6831i	0.836579	+	1.44900i
$366$	−1.11247	−	1.32756i	−0.0581496	−	0.0693927i
$367$	3.56149	−	6.16868i	0.185908	−	0.322002i	−0.757974	−	0.652285i	$-0.773811\pi$
$367$	3.56149	−	6.16868i	0.185908	−	0.322002i	0.943882	+	0.330282i	$0.107144\pi$
$368$	−1.64031			−0.0855068
$369$	−18.6093	−	15.6569i	−0.968762	−	0.815065i
$370$	33.7549			1.75483
$371$	7.59695	−	13.1583i	0.394414	−	0.683145i
$372$	0.128727	−	0.352950i	0.00667417	−	0.0182996i
$373$	6.50748	+	11.2713i	0.336944	+	0.583605i	0.983856	−	0.178960i	$-0.0572732\pi$
$373$	6.50748	+	11.2713i	0.336944	+	0.583605i	−0.646912	+	0.762565i	$0.723940\pi$
$374$	11.4712	+	19.8687i	0.593163	+	1.02739i
$375$	−43.7537	+	7.68524i	−2.25943	+	0.396864i
$376$	3.17365	−	5.49692i	0.163668	−	0.283482i
$377$	−46.4286			−2.39119
$378$	−11.8148	−	6.85245i	−0.607688	−	0.352452i
$379$	4.71603			0.242246			0.121123	−	0.992638i	$-0.461350\pi$
$379$	4.71603			0.242246			0.121123	+	0.992638i	$0.461350\pi$
$380$	8.97545	−	15.5459i	0.460431	−	0.797490i
$381$	1.46644	−	0.257577i	0.0751280	−	0.0131961i
$382$	−10.2059	−	17.6772i	−0.522181	−	0.904444i
$383$	2.13021	+	3.68962i	0.108848	+	0.188531i	0.915304	−	0.402764i	$-0.131950\pi$
$383$	2.13021	+	3.68962i	0.108848	+	0.188531i	−0.806456	+	0.591295i	$0.798617\pi$
$384$	0.593468	−	1.62720i	0.0302853	−	0.0830379i
$385$	−22.3919	+	38.7840i	−1.14120	+	1.97661i
$386$	13.8831			0.706630
$387$	−2.21284	+	12.4537i	−0.112485	+	0.633057i
$388$	−3.98544			−0.202330
$389$	13.2536	−	22.9558i	0.671982	−	1.16391i	−0.305359	−	0.952237i	$-0.598777\pi$
$389$	13.2536	−	22.9558i	0.671982	−	1.16391i	0.977341	−	0.211670i	$-0.0678901\pi$
$390$	27.5636	+	32.8930i	1.39574	+	1.66560i
$391$	4.46483	+	7.73331i	0.225796	+	0.391090i
$392$	0.0454480	+	0.0787182i	0.00229547	+	0.00397587i
$393$	−6.50827	−	7.76664i	−0.328299	−	0.391775i
$394$	9.94035	−	17.2172i	0.500788	−	0.867390i
$395$	47.4098			2.38544
$396$	−11.8862	+	4.30852i	−0.597307	+	0.216511i
$397$	8.28900			0.416013			0.208006	−	0.978127i	$-0.433303\pi$
$397$	8.28900			0.416013			0.208006	+	0.978127i	$0.433303\pi$
$398$	−7.60248	+	13.1679i	−0.381078	+	0.660046i
$399$	6.92650	−	18.9915i	0.346759	−	0.950762i
$400$	−5.67206	−	9.82430i	−0.283603	−	0.491215i
$401$	−10.9135	−	18.9027i	−0.544992	−	0.943955i	−0.998607	−	0.0527568i	$-0.983199\pi$
$401$	−10.9135	−	18.9027i	−0.544992	−	0.943955i	0.453615	−	0.891198i	$-0.350134\pi$
$402$	−11.1920	+	1.96585i	−0.558206	+	0.0980477i
$403$	−0.664675	+	1.15125i	−0.0331098	+	0.0573479i
$404$	2.84004			0.141297
$405$	−34.1579	−	12.5345i	−1.69732	−	0.622842i
$406$	19.9126			0.988247
$407$	17.5936	−	30.4731i	0.872084	−	1.51049i
$408$	−9.28693	+	1.63123i	−0.459772	+	0.0807580i
$409$	5.01967	+	8.69433i	0.248207	+	0.429907i	0.963028	−	0.269400i	$-0.0868254\pi$
$409$	5.01967	+	8.69433i	0.248207	+	0.429907i	−0.714822	+	0.699307i	$0.753492\pi$
$410$	−16.3865	−	28.3823i	−0.809272	−	1.40170i
$411$	−5.81758	+	15.9510i	−0.286960	+	0.786804i
$412$	1.97710	−	3.42443i	0.0974046	−	0.168710i
$413$	−10.1859			−0.501215
$414$	−4.62636	+	1.67696i	−0.227373	+	0.0824181i
$415$	46.6746			2.29116
$416$	−3.06435	+	5.30761i	−0.150242	+	0.260227i
$417$	−3.30293	−	3.94154i	−0.161745	−	0.193018i
$418$	−9.35633	−	16.2056i	−0.457633	−	0.792643i
$419$	−0.444905	−	0.770598i	−0.0217350	−	0.0376462i	0.854953	−	0.518705i	$-0.173586\pi$
$419$	−0.444905	−	0.770598i	−0.0217350	−	0.0376462i	−0.876688	+	0.481059i	$0.840252\pi$
$420$	−11.8217	−	14.1074i	−0.576838	−	0.688369i
$421$	−10.0991	+	17.4922i	−0.492202	+	0.852518i	−0.999960	−	0.00898145i	$-0.997141\pi$
$421$	−10.0991	+	17.4922i	−0.492202	+	0.852518i	0.507758	+	0.861500i	$0.330474\pi$
$422$	7.37516			0.359017
$423$	3.33129	−	18.7482i	0.161973	−	0.911570i
$424$	5.78041			0.280722
$425$	−30.8781	+	53.4825i	−1.49781	+	2.59428i
$426$	8.75608	−	24.0079i	0.424233	−	1.16319i
$427$	−1.31426	−	2.27636i	−0.0636014	−	0.110161i
$428$	−8.59528	−	14.8875i	−0.415469	−	0.719613i
$429$	44.0616	−	7.73933i	2.12732	−	0.373659i
$430$	−8.52271	+	14.7618i	−0.411002	+	0.711876i
$431$	−12.4423			−0.599322			−0.299661	−	0.954046i	$-0.596874\pi$
$431$	−12.4423			−0.599322			−0.299661	+	0.954046i	$0.596874\pi$
$432$	0.0102666	−	5.19614i	0.000493954	−	0.250000i
$433$	4.03198			0.193765			0.0968823	−	0.995296i	$-0.469113\pi$
$433$	4.03198			0.193765			0.0968823	+	0.995296i	$0.469113\pi$
$434$	0.285070	−	0.493756i	0.0136838	−	0.0237011i
$435$	52.2469	−	9.17707i	2.50505	−	0.440007i
$436$	1.28050	+	2.21789i	0.0613247	+	0.106217i
$437$	−3.64167	−	6.30755i	−0.174204	−	0.301731i
$438$	−4.69245	+	12.8660i	−0.224214	+	0.614763i
$439$	7.57067	−	13.1128i	0.361328	−	0.625839i	−0.626851	−	0.779139i	$-0.715657\pi$
$439$	7.57067	−	13.1128i	0.361328	−	0.625839i	0.988180	+	0.153300i	$0.0489901\pi$
$440$	−17.0377			−0.812240
$441$	0.208660	+	0.175555i	0.00993619	+	0.00835978i
$442$	33.3640			1.58696
$443$	0.517823	−	0.896895i	0.0246025	−	0.0426128i	−0.853462	−	0.521155i	$-0.825501\pi$
$443$	0.517823	−	0.896895i	0.0246025	−	0.0426128i	0.878065	+	0.478542i	$0.158835\pi$
$444$	9.28844	+	11.0843i	0.440810	+	0.526040i
$445$	27.4072	+	47.4707i	1.29923	+	2.25033i
$446$	−2.00471	−	3.47226i	−0.0949258	−	0.164416i
$447$	22.7610	+	27.1618i	1.07656	+	1.28471i
$448$	1.31426	−	2.27636i	0.0620929	−	0.107548i
$449$	−22.6531			−1.06907			−0.534534	−	0.845147i	$-0.679513\pi$
$449$	−22.6531			−1.06907			−0.534534	+	0.845147i	$0.679513\pi$
$450$	−26.0415	−	21.9099i	−1.22761	−	1.03284i
$451$	−34.1638			−1.60871
$452$	2.85907	−	4.95205i	0.134479	−	0.232925i
$453$	−0.394941	+	1.08287i	−0.0185560	+	0.0508778i
$454$	−3.24262	−	5.61638i	−0.152184	−	0.263590i
$455$	32.5634	+	56.4015i	1.52660	+	2.64414i
$456$	7.57474	−	1.33049i	0.354720	−	0.0623058i
$457$	−12.9650	+	22.4561i	−0.606479	+	1.05045i	0.385337	+	0.922776i	$0.374085\pi$
$457$	−12.9650	+	22.4561i	−0.606479	+	1.05045i	−0.991816	+	0.127676i	$0.959248\pi$
$458$	−9.62511			−0.449752
$459$	−24.5254	+	14.0952i	−1.14475	+	0.657909i
$460$	−6.63140			−0.309191
$461$	6.26415	−	10.8498i	0.291750	−	0.505326i	−0.682473	−	0.730910i	$-0.739096\pi$
$461$	6.26415	−	10.8498i	0.291750	−	0.505326i	0.974224	+	0.225584i	$0.0724290\pi$
$462$	−18.8975	+	3.31930i	−0.879189	+	0.154428i
$463$	4.69089	+	8.12485i	0.218004	+	0.377594i	0.954198	−	0.299177i	$-0.0967121\pi$
$463$	4.69089	+	8.12485i	0.218004	+	0.377594i	−0.736194	+	0.676771i	$0.763379\pi$
$464$	3.78780	+	6.56067i	0.175844	+	0.304571i
$465$	0.520414	−	1.42690i	0.0241336	−	0.0661710i
$466$	−13.6175	+	23.5862i	−0.630819	+	1.09261i
$467$	13.0532			0.604031			0.302015	−	0.953303i	$-0.402341\pi$
$467$	13.0532			0.604031			0.302015	+	0.953303i	$0.402341\pi$
$468$	−3.21656	+	18.1025i	−0.148685	+	0.836790i
$469$	−17.2447			−0.796287
$470$	12.8304	−	22.2229i	0.591821	−	1.02506i
$471$	−9.13115	−	10.8967i	−0.420741	−	0.502091i
$472$	−1.93757	−	3.35598i	−0.0891841	−	0.154471i
$473$	8.88438	+	15.3882i	0.408504	+	0.707550i
$474$	13.0459	+	15.5683i	0.599218	+	0.715076i
$475$	25.1852	−	43.6221i	1.15558	−	2.00152i
$476$	−14.3094			−0.655869
$477$	16.3032	−	5.90958i	0.746473	−	0.270581i
$478$	−1.68728			−0.0771744
$479$	20.5575	−	35.6066i	0.939295	−	1.62691i	0.172506	−	0.985009i	$-0.444814\pi$
$479$	20.5575	−	35.6066i	0.939295	−	1.62691i	0.766789	−	0.641899i	$-0.221853\pi$
$480$	2.39926	−	6.57844i	0.109511	−	0.300263i
$481$	−25.5855	−	44.3154i	−1.16660	−	2.02061i
$482$	−7.71872	−	13.3692i	−0.351578	−	0.608951i
$483$	−7.35526	+	1.29194i	−0.334676	+	0.0587851i
$484$	−3.38035	+	5.85493i	−0.153652	+	0.266133i
$485$	−16.1123			−0.731621
$486$	−5.28330	−	14.6658i	−0.239655	−	0.665256i
$487$	6.86990			0.311305			0.155652	−	0.987812i	$-0.450252\pi$
$487$	6.86990			0.311305			0.155652	+	0.987812i	$0.450252\pi$
$488$	0.500000	−	0.866025i	0.0226339	−	0.0392031i
$489$	−21.0872	+	3.70392i	−0.953596	+	0.167497i
$490$	0.183736	+	0.318241i	0.00830037	+	0.0143767i
$491$	10.1102	+	17.5114i	0.456267	+	0.790278i	0.998760	−	0.0497822i	$-0.0158527\pi$
$491$	10.1102	+	17.5114i	0.456267	+	0.790278i	−0.542493	+	0.840060i	$0.682519\pi$
$492$	4.81097	−	13.1910i	0.216895	−	0.594697i
$493$	20.6204	−	35.7156i	0.928697	−	1.60855i
$494$	−27.2128			−1.22436
$495$	−48.0536	+	17.4184i	−2.15985	+	0.782900i
$496$	0.216906			0.00973936
$497$	19.3907	−	33.5856i	0.869791	−	1.50652i
$498$	12.8436	+	15.3269i	0.575535	+	0.686814i
$499$	−5.63049	−	9.75229i	−0.252055	−	0.436573i	0.712036	−	0.702143i	$-0.247773\pi$
$499$	−5.63049	−	9.75229i	−0.252055	−	0.436573i	−0.964092	+	0.265570i	$0.914440\pi$
$500$	−12.8240	−	22.2117i	−0.573505	−	0.993340i
$501$	−28.2686	−	33.7343i	−1.26295	−	1.50714i
$502$	−7.17939	+	12.4351i	−0.320432	+	0.555004i
$503$	−15.6779			−0.699041			−0.349520	−	0.936929i	$-0.613655\pi$
$503$	−15.6779			−0.699041			−0.349520	+	0.936929i	$0.613655\pi$
$504$	1.37954	−	7.76394i	0.0614496	−	0.345833i
$505$	11.4817			0.510928
$506$	−3.45641	+	5.98667i	−0.153656	+	0.266140i
$507$	14.5761	−	39.9656i	0.647348	−	1.77494i
$508$	0.429806	+	0.744445i	0.0190695	+	0.0330294i
$509$	−11.3928	−	19.7328i	−0.504975	−	0.874642i	−0.999983	−	0.00575398i	$-0.998168\pi$
$509$	−11.3928	−	19.7328i	−0.504975	−	0.874642i	0.495009	−	0.868888i	$-0.335165\pi$
$510$	−37.5451	+	6.59472i	−1.66252	+	0.292019i
$511$	−10.3916	+	17.9988i	−0.459698	+	0.796221i
$512$	1.00000			0.0441942
$513$	20.0038	−	11.4966i	0.883189	−	0.507585i
$514$	−10.3987			−0.458668
$515$	7.99298	−	13.8442i	0.352213	−	0.610050i
$516$	−7.19266	+	1.26338i	−0.316639	+	0.0556170i
$517$	−13.3748	−	23.1659i	−0.588225	−	1.01884i
$518$	10.9733	+	19.0063i	0.482138	+	0.835088i
$519$	9.94078	−	27.2562i	0.436352	−	1.19641i
$520$	−12.3885	+	21.4575i	−0.543272	+	0.940974i
$521$	−29.8673			−1.30851			−0.654254	−	0.756275i	$-0.727017\pi$
$521$	−29.8673			−1.30851			−0.654254	+	0.756275i	$0.727017\pi$
$522$	17.3905	+	14.6314i	0.761162	+	0.640401i
$523$	−19.4600			−0.850927			−0.425464	−	0.904976i	$-0.639889\pi$
$523$	−19.4600			−0.850927			−0.425464	+	0.904976i	$0.639889\pi$
$524$	2.92515	−	5.06652i	0.127786	−	0.221332i
$525$	−33.1718	−	39.5855i	−1.44773	−	1.72765i
$526$	3.87890	+	6.71846i	0.169128	+	0.292939i
$527$	−0.590406	−	1.02261i	−0.0257185	−	0.0445458i
$528$	−4.68832	−	5.59480i	−0.204033	−	0.243482i
$529$	10.1547	−	17.5885i	0.441509	−	0.764715i
$530$	23.3690			1.01508
$531$	−8.89576	−	7.48442i	−0.386043	−	0.324796i
$532$	11.6712			0.506012
$533$	−24.8413	+	43.0263i	−1.07599	+	1.86368i
$534$	−8.04658	+	22.0626i	−0.348210	+	0.954741i
$535$	−34.7489	−	60.1869i	−1.50233	−	2.60210i
$536$	−3.28031	−	5.68167i	−0.141688	−	0.245411i
$537$	18.6948	−	3.28370i	0.806738	−	0.141702i
$538$	−4.79271	+	8.30122i	−0.206628	+	0.357891i
$539$	0.383067			0.0164999
$540$	0.0415058	−	21.0069i	0.00178613	−	0.903993i
$541$	−22.9150			−0.985193			−0.492596	−	0.870258i	$-0.663952\pi$
$541$	−22.9150			−0.985193			−0.492596	+	0.870258i	$0.663952\pi$
$542$	−0.735569	+	1.27404i	−0.0315954	+	0.0547249i
$543$	11.4414	−	2.00966i	0.490997	−	0.0862426i
$544$	−2.72195	−	4.71455i	−0.116703	−	0.202135i
$545$	5.17678	+	8.96644i	0.221749	+	0.384080i
$546$	−9.56041	+	26.2133i	−0.409148	+	1.12182i
$547$	−2.35184	+	4.07351i	−0.100558	+	0.174171i	−0.911915	−	0.410380i	$-0.865396\pi$
$547$	−2.35184	+	4.07351i	−0.100558	+	0.174171i	0.811357	+	0.584551i	$0.198729\pi$
$548$	−9.80269			−0.418750
$549$	0.524836	−	2.95373i	0.0223994	−	0.126062i
$550$	−47.8080			−2.03854
$551$	−16.8187	+	29.1309i	−0.716502	+	1.24102i
$552$	−1.82479	−	2.17761i	−0.0776680	−	0.0926850i
$553$	15.4123	+	26.6949i	0.655398	+	1.13518i
$554$	10.5057	+	18.1965i	0.446346	+	0.773095i
$555$	37.5512	+	44.8116i	1.59396	+	1.90215i
$556$	1.48451	−	2.57124i	0.0629571	−	0.109045i
$557$	27.2033			1.15264			0.576320	−	0.817224i	$-0.304488\pi$
$557$	27.2033			1.15264			0.576320	+	0.817224i	$0.304488\pi$
$558$	0.611767	−	0.221753i	0.0258982	−	0.00938754i
$559$	25.8402			1.09292
$560$	5.31327	−	9.20285i	0.224527	−	0.388891i
$561$	−13.6156	+	37.3321i	−0.574852	+	1.57616i
$562$	15.4424	+	26.7470i	0.651399	+	1.12826i
$563$	8.59186	+	14.8815i	0.362104	+	0.627182i	0.988307	−	0.152478i	$-0.0487253\pi$
$563$	8.59186	+	14.8815i	0.362104	+	0.627182i	−0.626203	+	0.779660i	$0.715392\pi$
$564$	10.8281	−	1.90193i	0.455944	−	0.0800856i
$565$	11.5586	−	20.0201i	0.486274	−	0.842251i
$566$	−12.4742			−0.524328
$567$	−4.04655	−	23.3080i	−0.169939	−	0.978844i
$568$	14.7541			0.619068
$569$	2.41374	−	4.18071i	0.101189	−	0.175265i	−0.810986	−	0.585066i	$-0.801069\pi$
$569$	2.41374	−	4.18071i	0.101189	−	0.175265i	0.912175	+	0.409801i	$0.134402\pi$
$570$	30.6231	−	5.37888i	1.28266	−	0.225296i
$571$	−17.0416	−	29.5169i	−0.713169	−	1.23525i	−0.963661	−	0.267127i	$-0.913926\pi$
$571$	−17.0416	−	29.5169i	−0.713169	−	1.23525i	0.250492	−	0.968119i	$-0.419407\pi$
$572$	12.9142	+	22.3681i	0.539971	+	0.935256i
$573$	12.1138	−	33.2143i	0.506061	−	1.38755i
$574$	10.6541	−	18.4534i	0.444693	−	0.770231i
$575$	−18.6078			−0.776000
$576$	2.82043	−	1.02235i	0.117518	−	0.0425978i
$577$	46.1916			1.92298			0.961490	−	0.274839i	$-0.0886247\pi$
$577$	46.1916			1.92298			0.961490	+	0.274839i	$0.0886247\pi$
$578$	−6.31800	+	10.9431i	−0.262794	+	0.455173i
$579$	15.4445	+	18.4306i	0.641850	+	0.765951i
$580$	15.3133	+	26.5234i	0.635849	+	1.10132i
$581$	15.1733	+	26.2810i	0.629495	+	1.09032i
$582$	−4.43367	−	5.29091i	−0.183781	−	0.219315i
$583$	12.1803	−	21.0969i	0.504457	−	0.873746i
$584$	−7.90683			−0.327187
$585$	−13.0039	+	73.1847i	−0.537643	+	3.02581i
$586$	−6.61766			−0.273373
$587$	5.58707	−	9.67708i	0.230603	−	0.399416i	−0.727383	−	0.686232i	$-0.759263\pi$
$587$	5.58707	−	9.67708i	0.230603	−	0.399416i	0.957986	+	0.286816i	$0.0925968\pi$
$588$	−0.0539439	+	0.147906i	−0.00222461	+	0.00609956i
$589$	0.481556	+	0.834079i	0.0198422	+	0.0343676i
$590$	−7.83320	−	13.5675i	−0.322488	−	0.558565i
$591$	33.9152	−	5.95713i	1.39508	−	0.245044i
$592$	−4.17470	+	7.23080i	−0.171579	+	0.297184i
$593$	−29.7071			−1.21992			−0.609962	−	0.792431i	$-0.708815\pi$
$593$	−29.7071			−1.21992			−0.609962	+	0.792431i	$0.708815\pi$
$594$	−18.9429	−	10.9866i	−0.777236	−	0.450787i
$595$	−57.8498			−2.37161
$596$	−10.2299	+	17.7188i	−0.419035	+	0.725790i
$597$	−25.9387	+	4.55608i	−1.06160	+	0.186468i
$598$	5.02647	+	8.70609i	0.205547	+	0.356019i
$599$	−20.1067	−	34.8259i	−0.821539	−	1.42295i	−0.904536	−	0.426398i	$-0.859782\pi$
$599$	−20.1067	−	34.8259i	−0.821539	−	1.42295i	0.0829964	−	0.996550i	$-0.473551\pi$
$600$	6.73237	−	18.4592i	0.274848	−	0.753594i
$601$	−8.79736	+	15.2375i	−0.358852	+	0.621550i	−0.987769	−	0.155922i	$-0.950165\pi$
$601$	−8.79736	+	15.2375i	−0.358852	+	0.621550i	0.628917	+	0.777472i	$0.283498\pi$
$602$	−11.0825			−0.451689
$603$	−15.0605	−	12.6711i	−0.613311	−	0.516007i
$604$	−0.665480			−0.0270780
$605$	−13.6660	+	23.6702i	−0.555603	+	0.962332i
$606$	3.15945	+	3.77033i	0.128344	+	0.153159i
$607$	0.420571	+	0.728451i	0.0170705	+	0.0295669i	0.874434	−	0.485144i	$-0.161233\pi$
$607$	0.420571	+	0.728451i	0.0170705	+	0.0295669i	−0.857364	+	0.514711i	$0.827899\pi$
$608$	2.22011	+	3.84535i	0.0900375	+	0.155950i
$609$	22.1521	+	26.4352i	0.897650	+	1.07121i
$610$	2.02139	−	3.50116i	0.0818438	−	0.141758i
$611$	−38.9006			−1.57375
$612$	−12.4970	−	10.5143i	−0.505160	−	0.425015i
$613$	24.2957			0.981294			0.490647	−	0.871358i	$-0.336760\pi$
$613$	24.2957			0.981294			0.490647	+	0.871358i	$0.336760\pi$
$614$	−3.90974	+	6.77187i	−0.157784	+	0.273291i
$615$	19.4497	−	53.3284i	0.784289	−	2.15041i
$616$	−5.53874	−	9.59338i	−0.223162	−	0.386528i
$617$	−2.17856	−	3.77337i	−0.0877054	−	0.151910i	0.818835	−	0.574028i	$-0.194620\pi$
$617$	−2.17856	−	3.77337i	−0.0877054	−	0.151910i	−0.906541	+	0.422118i	$0.861287\pi$
$618$	6.74560	−	1.18485i	0.271348	−	0.0476617i
$619$	12.3209	−	21.3405i	0.495220	−	0.857746i	−0.504765	−	0.863257i	$-0.668421\pi$
$619$	12.3209	−	21.3405i	0.495220	−	0.857746i	0.999985	+	0.00551106i	$0.00175423\pi$
$620$	0.876904			0.0352173
$621$	−7.37294	−	4.27621i	−0.295866	−	0.171599i
$622$	20.3382			0.815489
$623$	−17.8195	+	30.8642i	−0.713922	+	1.23655i
$624$	−10.4552	+	1.83643i	−0.418541	+	0.0735159i
$625$	−23.4842	−	40.6759i	−0.939369	−	1.62703i
$626$	13.5662	+	23.4974i	0.542216	+	0.939146i
$627$	11.1054	−	30.4493i	0.443505	−	1.21603i
$628$	4.10401	−	7.10836i	0.163768	−	0.283654i
$629$	45.4533			1.81234
$630$	5.57718	−	31.3880i	0.222200	−	1.25053i
$631$	7.91509			0.315095			0.157547	−	0.987511i	$-0.449641\pi$
$631$	7.91509			0.315095			0.157547	+	0.987511i	$0.449641\pi$
$632$	−5.86350	+	10.1559i	−0.233238	+	0.403979i
$633$	8.20462	+	9.79097i	0.326104	+	0.389156i
$634$	−4.29459	−	7.43844i	−0.170560	−	0.295418i
$635$	1.73761	+	3.00963i	0.0689550	+	0.119434i
$636$	6.43051	+	7.67385i	0.254986	+	0.304288i
$637$	0.278537	−	0.482440i	0.0110360	−	0.0191150i
$638$	31.9262			1.26397
$639$	41.6128	−	15.0838i	1.64618	−	0.596705i
$640$	4.04279			0.159805
$641$	1.97143	−	3.41461i	0.0778667	−	0.134869i	−0.824463	−	0.565916i	$-0.808522\pi$
$641$	1.97143	−	3.41461i	0.0778667	−	0.134869i	0.902329	+	0.431047i	$0.141856\pi$
$642$	10.2021	−	27.9726i	0.402643	−	1.10399i
$643$	−1.91502	−	3.31692i	−0.0755211	−	0.130806i	0.825792	−	0.563975i	$-0.190729\pi$
$643$	−1.91502	−	3.31692i	−0.0755211	−	0.130806i	−0.901313	+	0.433169i	$0.857395\pi$
$644$	−2.15579	−	3.73393i	−0.0849499	−	0.147137i
$645$	−29.0784	+	5.10756i	−1.14496	+	0.201110i
$646$	12.0861	−	20.9337i	0.475520	−	0.823625i
$647$	33.0472			1.29922			0.649610	−	0.760268i	$-0.274932\pi$
$647$	33.0472			1.29922			0.649610	+	0.760268i	$0.274932\pi$
$648$	6.90962	−	5.76691i	0.271435	−	0.226545i
$649$	−16.3312			−0.641056
$650$	−34.7623	+	60.2101i	−1.36349	+	2.36164i
$651$	0.972623	−	0.170839i	0.0381201	−	0.00669572i
$652$	−6.18054	−	10.7050i	−0.242049	−	0.419241i
$653$	22.7564	+	39.4153i	0.890528	+	1.54244i	0.839243	+	0.543756i	$0.182998\pi$
$653$	22.7564	+	39.4153i	0.890528	+	1.54244i	0.0512854	+	0.998684i	$0.483668\pi$
$654$	−1.51987	+	4.16726i	−0.0594316	+	0.162953i
$655$	11.8258	−	20.4828i	0.462071	−	0.800331i
$656$	8.10654			0.316507
$657$	−22.3006	+	8.08352i	−0.870031	+	0.315368i
$658$	16.6840			0.650409
$659$	−15.6698	+	27.1408i	−0.610407	+	1.05726i	0.380765	+	0.924672i	$0.375661\pi$
$659$	−15.6698	+	27.1408i	−0.610407	+	1.05726i	−0.991172	+	0.132584i	$0.957672\pi$
$660$	−18.9539	−	22.6186i	−0.737778	−	0.880427i
$661$	5.54920	+	9.61150i	0.215839	+	0.373844i	0.953532	−	0.301293i	$-0.0974181\pi$
$661$	5.54920	+	9.61150i	0.215839	+	0.373844i	−0.737693	+	0.675136i	$0.764085\pi$
$662$	1.71562	+	2.97153i	0.0666793	+	0.115492i
$663$	37.1163	+	44.2927i	1.44148	+	1.72019i
$664$	−5.77258	+	9.99839i	−0.224019	+	0.388013i
$665$	47.1842			1.82973
$666$	−4.38207	+	24.6619i	−0.169802	+	0.955630i
$667$	12.4263			0.481149
$668$	12.7054	−	22.0064i	0.491586	−	0.851452i
$669$	2.37946	−	6.52415i	0.0919953	−	0.252238i
$670$	−13.2616	−	22.9698i	−0.512340	−	0.887399i
$671$	−2.10717	−	3.64973i	−0.0813465	−	0.140896i
$672$	4.48408	−	0.787619i	0.172977	−	0.0303831i
$673$	−19.3083	+	33.4430i	−0.744281	+	1.28913i	0.206250	+	0.978499i	$0.433874\pi$
$673$	−19.3083	+	33.4430i	−0.744281	+	1.28913i	−0.950530	+	0.310632i	$0.899459\pi$
$674$	9.14365			0.352200
$675$	0.116466	−	58.9457i	0.00448278	−	2.26882i
$676$	24.5609			0.944650
$677$	15.4154	−	26.7002i	0.592461	−	1.02617i	−0.401439	−	0.915886i	$-0.631490\pi$
$677$	15.4154	−	26.7002i	0.592461	−	1.02617i	0.993900	−	0.110286i	$-0.0351768\pi$
$678$	9.75476	−	1.71340i	0.374629	−	0.0658029i
$679$	−5.23790	−	9.07230i	−0.201012	−	0.348163i
$680$	−11.0043	−	19.0599i	−0.421994	−	0.730915i
$681$	3.84878	−	10.5528i	0.147486	−	0.404384i
$682$	0.457058	−	0.791647i	0.0175016	−	0.0303137i
$683$	−20.2866			−0.776245			−0.388122	−	0.921608i	$-0.626876\pi$
$683$	−20.2866			−0.776245			−0.388122	+	0.921608i	$0.626876\pi$
$684$	10.1930	+	8.57581i	0.389737	+	0.327904i
$685$	−39.6302			−1.51419
$686$	−9.31927	+	16.1415i	−0.355811	+	0.616284i
$687$	−10.7076	−	12.7779i	−0.408521	−	0.487508i
$688$	−2.10813	−	3.65139i	−0.0803717	−	0.139208i
$689$	−17.7132	−	30.6801i	−0.674819	−	1.16882i
$690$	−7.37722	−	8.80359i	−0.280846	−	0.335147i
$691$	−11.0891	+	19.2069i	−0.421850	+	0.730666i	−0.996121	−	0.0879995i	$-0.971953\pi$
$691$	−11.0891	+	19.2069i	−0.421850	+	0.730666i	0.574270	+	0.818666i	$0.305286\pi$
$692$	16.7503			0.636752
$693$	−25.4294	−	21.3949i	−0.965981	−	0.812725i
$694$	−36.7802			−1.39616
$695$	6.00154	−	10.3950i	0.227651	−	0.394304i
$696$	−4.49588	+	12.3271i	−0.170416	+	0.467256i
$697$	−22.0656	−	38.2187i	−0.835794	−	1.44764i
$698$	−8.50479	−	14.7307i	−0.321911	−	0.557566i
$699$	−46.4612	+	8.16081i	−1.75732	+	0.308670i
$700$	14.9091	−	25.8233i	0.563511	−	0.976030i
$701$	14.5406			0.549189			0.274595	−	0.961560i	$-0.411456\pi$
$701$	14.5406			0.549189			0.274595	+	0.961560i	$0.411456\pi$
$702$	−27.6105	+	15.8683i	−1.04209	+	0.598910i
$703$	−37.0733			−1.39825
$704$	2.10717	−	3.64973i	0.0794170	−	0.137554i
$705$	43.7756	−	7.68909i	1.64868	−	0.289588i
$706$	13.1451	+	22.7680i	0.494723	+	0.856885i
$707$	3.73255	+	6.46497i	0.140377	+	0.243140i
$708$	2.29978	−	6.30566i	0.0864309	−	0.236981i
$709$	10.5471	−	18.2681i	0.396105	−	0.686073i	−0.597137	−	0.802139i	$-0.703695\pi$
$709$	10.5471	−	18.2681i	0.396105	−	0.686073i	0.993242	+	0.116066i	$0.0370284\pi$
$710$	59.6476			2.23853
$711$	−6.15475	+	34.6384i	−0.230821	+	1.29904i
$712$	−13.5586			−0.508129
$713$	0.177896	−	0.308125i	0.00666225	−	0.0115394i
$714$	−15.9187	−	18.9966i	−0.595743	−	0.710929i
$715$	52.2094	+	90.4294i	1.95252	+	3.38187i
$716$	5.47933	+	9.49048i	0.204772	+	0.354676i
$717$	−1.87704	−	2.23997i	−0.0700995	−	0.0836531i
$718$	8.56582	−	14.8364i	0.319674	−	0.553691i
$719$	24.8266			0.925877			0.462938	−	0.886390i	$-0.346795\pi$
$719$	24.8266			0.925877			0.462938	+	0.886390i	$0.346795\pi$
$720$	11.4024	−	4.13313i	0.424942	−	0.154033i
$721$	10.3937			0.387080
$722$	−0.357818	+	0.619758i	−0.0133166	+	0.0230650i
$723$	9.16163	−	25.1199i	0.340725	−	0.934218i
$724$	3.35341	+	5.80827i	0.124628	+	0.215863i
$725$	42.9693	+	74.4250i	1.59584	+	2.76408i
$726$	−11.5333	+	2.02580i	−0.428041	+	0.0751846i
$727$	−6.40686	+	11.0970i	−0.237617	+	0.411565i	−0.960030	−	0.279897i	$-0.909700\pi$
$727$	−6.40686	+	11.0970i	−0.237617	+	0.411565i	0.722413	+	0.691462i	$0.243033\pi$
$728$	−16.1094			−0.597053
$729$	13.5923	−	23.3292i	0.503418	−	0.864043i
$730$	−31.9656			−1.18310
$731$	−11.4764	+	19.8778i	−0.424471	+	0.735206i
$732$	1.70593	−	0.299644i	0.0630532	−	0.0110752i
$733$	−4.64425	−	8.04409i	−0.171539	−	0.297115i	0.767419	−	0.641146i	$-0.221541\pi$
$733$	−4.64425	−	8.04409i	−0.171539	−	0.297115i	−0.938958	+	0.344031i	$0.888207\pi$
$734$	3.56149	+	6.16868i	0.131457	+	0.227690i
$735$	−0.218083	+	0.597954i	−0.00804413	+	0.0220559i
$736$	0.820153	−	1.42055i	0.0302312	−	0.0523620i
$737$	−27.6487			−1.01845
$738$	22.8639	−	8.28769i	0.841632	−	0.305074i
$739$	−17.2041			−0.632861			−0.316431	−	0.948616i	$-0.602484\pi$
$739$	−17.2041			−0.632861			−0.316431	+	0.948616i	$0.602484\pi$
$740$	−16.8774	+	29.2326i	−0.620427	+	1.07461i
$741$	−30.2733	−	36.1267i	−1.11212	−	1.32715i
$742$	7.59695	+	13.1583i	0.278893	+	0.483057i
$743$	−0.0184581	−	0.0319704i	−0.000677162	−	0.00117288i	0.865687	−	0.500586i	$-0.166882\pi$
$743$	−0.0184581	−	0.0319704i	−0.000677162	−	0.00117288i	−0.866364	+	0.499413i	$0.833549\pi$
$744$	0.241300	+	0.287956i	0.00884650	+	0.0105570i
$745$	−41.3575	+	71.6333i	−1.51522	+	2.62444i
$746$	−13.0150			−0.476511
$747$	−6.05931	+	34.1013i	−0.221698	+	1.24770i
$748$	−22.9425			−0.838859
$749$	22.5929	−	39.1320i	0.825525	−	1.42985i
$750$	15.2212	−	41.7344i	0.555800	−	1.52393i
$751$	4.85261	+	8.40497i	0.177074	+	0.306702i	0.940877	−	0.338748i	$-0.110003\pi$
$751$	4.85261	+	8.40497i	0.177074	+	0.306702i	−0.763803	+	0.645450i	$0.776670\pi$
$752$	3.17365	+	5.49692i	0.115731	+	0.200452i
$753$	−24.4951	+	4.30252i	−0.892652	+	0.156793i
$754$	23.2143	−	40.2084i	0.845415	−	1.46430i
$755$	−2.69039			−0.0979135
$756$	11.8418	−	6.80570i	0.430682	−	0.247521i
$757$	−44.2726			−1.60912			−0.804558	−	0.593874i	$-0.797598\pi$
$757$	−44.2726			−1.60912			−0.804558	+	0.593874i	$0.797598\pi$
$758$	−2.35801	+	4.08420i	−0.0856469	+	0.148345i
$759$	−11.7928	+	2.07138i	−0.428052	+	0.0751864i
$760$	8.97545	+	15.5459i	0.325574	+	0.563910i
$761$	−6.07815	−	10.5277i	−0.220333	−	0.381628i	0.734576	−	0.678526i	$-0.237381\pi$
$761$	−6.07815	−	10.5277i	−0.220333	−	0.381628i	−0.954909	+	0.296898i	$0.904048\pi$
$762$	−0.510152	+	1.39876i	−0.0184808	+	0.0506718i
$763$	−3.36581	+	5.82975i	−0.121850	+	0.211051i
$764$	20.4119			0.738475
$765$	−50.5225	−	42.5070i	−1.82665	−	1.53684i
$766$	−4.26041			−0.153935
$767$	−11.8748	+	20.5678i	−0.428774	+	0.742659i
$768$	1.11247	+	1.32756i	0.0401427	+	0.0479042i
$769$	8.10259	+	14.0341i	0.292187	+	0.506083i	0.974327	−	0.225139i	$-0.0722837\pi$
$769$	8.10259	+	14.0341i	0.292187	+	0.506083i	−0.682140	+	0.731222i	$0.738950\pi$
$770$	−22.3919	−	38.7840i	−0.806949	−	1.39768i
$771$	−11.5682	−	13.8049i	−0.416619	−	0.497172i
$772$	−6.94154	+	12.0231i	−0.249832	+	0.432721i
$773$	−23.7724			−0.855032			−0.427516	−	0.904008i	$-0.640611\pi$
$773$	−23.7724			−0.855032			−0.427516	+	0.904008i	$0.640611\pi$
$774$	−9.67880	−	8.14323i	−0.347897	−	0.292702i
$775$	2.46061			0.0883875
$776$	1.99272	−	3.45149i	0.0715345	−	0.123901i
$777$	−13.0246	+	35.7115i	−0.467254	+	1.28114i
$778$	13.2536	+	22.9558i	0.475163	+	0.823006i
$779$	17.9975	+	31.1725i	0.644826	+	1.11687i
$780$	−42.2680	+	7.42428i	−1.51344	+	0.265832i
$781$	31.0894	−	53.8484i	1.11247	−	1.92685i
$782$	−8.92965			−0.319324
$783$	−0.0777761	+	39.3639i	−0.00277949	+	1.40675i
$784$	−0.0908960			−0.00324628
$785$	16.5916	−	28.7376i	0.592181	−	1.02569i
$786$	9.98025	−	1.75301i	0.355984	−	0.0625278i
$787$	−24.4808	−	42.4019i	−0.872645	−	1.51146i	−0.859251	−	0.511555i	$-0.829070\pi$
$787$	−24.4808	−	42.4019i	−0.872645	−	1.51146i	−0.0133939	−	0.999910i	$-0.504264\pi$
$788$	9.94035	+	17.2172i	0.354110	+	0.613337i
$789$	−4.60401	+	12.6235i	−0.163907	+	0.449410i
$790$	−23.7049	+	41.0581i	−0.843382	+	1.46078i
$791$	15.0302			0.534413
$792$	2.21184	−	12.4481i	0.0785942	−	0.442322i
$793$	−6.12870			−0.217636
$794$	−4.14450	+	7.17848i	−0.147083	+	0.254755i
$795$	25.9972	+	31.0237i	0.922025	+	1.10030i
$796$	−7.60248	−	13.1679i	−0.269463	−	0.466723i
$797$	4.10867	+	7.11643i	0.145537	+	0.252077i	0.929573	−	0.368638i	$-0.120176\pi$
$797$	4.10867	+	7.11643i	0.145537	+	0.252077i	−0.784036	+	0.620715i	$0.786842\pi$
$798$	12.9838	+	15.4943i	0.459623	+	0.548491i
$799$	17.2770	−	29.9247i	0.611217	−	1.05866i
$800$	11.3441			0.401075
$801$	−38.2410	+	13.8616i	−1.35118	+	0.489774i
$802$	21.8269			0.770736
$803$	−16.6611	+	28.8578i	−0.587956	+	1.01837i
$804$	3.89352	−	10.6755i	0.137314	−	0.376495i
$805$	−8.71538	−	15.0955i	−0.307177	−	0.532046i
$806$	−0.664675	−	1.15125i	−0.0234122	−	0.0405511i
$807$	−16.3521	+	2.87221i	−0.575621	+	0.101107i
$808$	−1.42002	+	2.45955i	−0.0499562	+	0.0865266i
$809$	26.7693			0.941159			0.470580	−	0.882358i	$-0.344045\pi$
$809$	26.7693			0.941159			0.470580	+	0.882358i	$0.344045\pi$
$810$	27.9341	−	23.3144i	0.981504	−	0.819183i
$811$	18.3883			0.645702			0.322851	−	0.946450i	$-0.395359\pi$
$811$	18.3883			0.645702			0.322851	+	0.946450i	$0.395359\pi$
$812$	−9.95631	+	17.2448i	−0.349398	+	0.605175i
$813$	−2.50967	+	0.440818i	−0.0880179	+	0.0154602i
$814$	17.5936	+	30.4731i	0.616657	+	1.06808i
$815$	−24.9866	−	43.2781i	−0.875243	−	1.51596i
$816$	3.23078	−	8.85833i	0.113100	−	0.310104i
$817$	9.36058	−	16.2130i	0.327485	−	0.567221i
$818$	−10.0393			−0.351017
$819$	−45.4353	+	16.4694i	−1.58764	+	0.575486i
$820$	32.7730			1.14448
$821$	5.64051	−	9.76966i	0.196855	−	0.340963i	−0.750652	−	0.660698i	$-0.770260\pi$
$821$	5.64051	−	9.76966i	0.196855	−	0.340963i	0.947507	+	0.319735i	$0.103594\pi$
$822$	−10.9052	−	13.0137i	−0.380361	−	0.453904i
$823$	10.5058	+	18.1966i	0.366209	+	0.634293i	0.988969	−	0.148120i	$-0.0473221\pi$
$823$	10.5058	+	18.1966i	0.366209	+	0.634293i	−0.622760	+	0.782413i	$0.713989\pi$
$824$	1.97710	+	3.42443i	0.0688754	+	0.119296i
$825$	−53.1848	−	63.4681i	−1.85166	−	2.20967i
$826$	5.09295	−	8.82125i	0.177206	−	0.306930i
$827$	−38.2016			−1.32840			−0.664200	−	0.747555i	$-0.731228\pi$
$827$	−38.2016			−1.32840			−0.664200	+	0.747555i	$0.731228\pi$
$828$	0.860891	−	4.84503i	0.0299180	−	0.168376i
$829$	36.5596			1.26977			0.634885	−	0.772607i	$-0.281048\pi$
$829$	36.5596			1.26977			0.634885	+	0.772607i	$0.281048\pi$
$830$	−23.3373	+	40.4214i	−0.810049	+	1.40305i
$831$	−12.4697	+	34.1900i	−0.432567	+	1.18604i
$832$	−3.06435	−	5.30761i	−0.106237	−	0.184008i
$833$	0.247414	+	0.428534i	0.00857239	+	0.0148478i
$834$	5.06494	−	0.889647i	0.175385	−	0.0308059i
$835$	51.3652	−	88.9671i	1.77756	−	3.07883i
$836$	18.7127			0.647191
$837$	0.974961	+	0.565465i	0.0336996	+	0.0195453i
$838$	0.889810			0.0307380
$839$	1.07344	−	1.85926i	0.0370594	−	0.0641887i	−0.846901	−	0.531751i	$-0.821534\pi$
$839$	1.07344	−	1.85926i	0.0370594	−	0.0641887i	0.883960	+	0.467562i	$0.154868\pi$
$840$	18.1282	−	3.18418i	0.625481	−	0.109865i
$841$	−14.1949	−	24.5863i	−0.489480	−	0.847805i
$842$	−10.0991	−	17.4922i	−0.348039	−	0.602821i
$843$	−18.3291	+	50.2559i	−0.631289	+	1.73091i
$844$	−3.68758	+	6.38708i	−0.126932	+	0.219852i
$845$	99.2945			3.41584
$846$	14.5708	+	12.2591i	0.500954	+	0.421476i
$847$	−17.7706			−0.610605
$848$	−2.89020	+	5.00598i	−0.0992500	+	0.171906i
$849$	−13.8771	−	16.5602i	−0.476260	−	0.568345i
$850$	−30.8781	−	53.4825i	−1.05911	−	1.83443i
$851$	6.84779	+	11.8607i	0.234739	+	0.406580i
$852$	16.4134	+	19.5869i	0.562315	+	0.671038i
$853$	−22.4142	+	38.8226i	−0.767448	+	1.32926i	0.171494	+	0.985185i	$0.445140\pi$
$853$	−22.4142	+	38.8226i	−0.767448	+	1.32926i	−0.938943	+	0.344074i	$0.888193\pi$
$854$	2.62852			0.0899460
$855$	41.2079	+	34.6702i	1.40928	+	1.18569i
$856$	17.1906			0.587562
$857$	24.2882	−	42.0684i	0.829669	−	1.43703i	−0.0686293	−	0.997642i	$-0.521863\pi$
$857$	24.2882	−	42.0684i	0.829669	−	1.43703i	0.898298	−	0.439386i	$-0.144804\pi$
$858$	−15.3284	+	42.0282i	−0.523301	+	1.43482i
$859$	13.3098	+	23.0532i	0.454125	+	0.786567i	0.998637	−	0.0521858i	$-0.0166188\pi$
$859$	13.3098	+	23.0532i	0.454125	+	0.786567i	−0.544513	+	0.838752i	$0.683285\pi$
$860$	−8.52271	−	14.7618i	−0.290622	−	0.503372i
$861$	36.3504	−	6.38487i	1.23882	−	0.217596i
$862$	6.22113	−	10.7753i	0.211893	−	0.367009i
$863$	−28.3414			−0.964753			−0.482377	−	0.875964i	$-0.660226\pi$
$863$	−28.3414			−0.964753			−0.482377	+	0.875964i	$0.660226\pi$
$864$	4.49486	+	2.60696i	0.152918	+	0.0886907i
$865$	67.7180			2.30248
$866$	−2.01599	+	3.49180i	−0.0685061	+	0.118656i
$867$	−21.5562	+	3.78630i	−0.732087	+	0.128590i
$868$	0.285070	+	0.493756i	0.00967592	+	0.0167592i
$869$	24.7108	+	42.8004i	0.838257	+	1.45190i
$870$	−18.1759	+	49.8357i	−0.616220	+	1.68959i
$871$	−20.1040	+	34.8212i	−0.681199	+	1.17987i
$872$	−2.56099			−0.0867262
$873$	2.09170	−	11.7719i	0.0707933	−	0.398419i
$874$	7.28333			0.246362
$875$	33.7080	−	58.3840i	1.13954	−	1.97374i
$876$	−8.79609	−	10.4968i	−0.297192	−	0.354654i
$877$	−8.76403	−	15.1797i	−0.295940	−	0.512584i	0.679263	−	0.733895i	$-0.262300\pi$
$877$	−8.76403	−	15.1797i	−0.295940	−	0.512584i	−0.975203	+	0.221311i	$0.928966\pi$
$878$	7.57067	+	13.1128i	0.255498	+	0.442535i
$879$	−7.36192	−	8.78534i	−0.248312	−	0.296322i
$880$	8.51885	−	14.7551i	0.287170	−	0.497393i
$881$	8.16640			0.275133			0.137566	−	0.990493i	$-0.456072\pi$
$881$	8.16640			0.275133			0.137566	+	0.990493i	$0.456072\pi$
$882$	−0.256365	+	0.0929272i	−0.00863227	+	0.00312902i
$883$	−17.8946			−0.602200			−0.301100	−	0.953592i	$-0.597354\pi$
$883$	−17.8946			−0.602200			−0.301100	+	0.953592i	$0.597354\pi$
$884$	−16.6820	+	28.8941i	−0.561076	+	0.971812i
$885$	9.29751	−	25.4924i	0.312532	−	0.856919i
$886$	0.517823	+	0.896895i	0.0173966	+	0.0301318i
$887$	−3.43066	−	5.94207i	−0.115190	−	0.199515i	0.802666	−	0.596429i	$-0.203414\pi$
$887$	−3.43066	−	5.94207i	−0.115190	−	0.199515i	−0.917856	+	0.396914i	$0.870081\pi$
$888$	−14.2435	+	2.50185i	−0.477982	+	0.0839566i
$889$	−1.12975	+	1.95679i	−0.0378906	+	0.0656285i
$890$	−54.8144			−1.83738
$891$	−6.48789	−	37.3701i	−0.217353	−	1.25195i
$892$	4.00942			0.134245
$893$	−14.0917	+	24.4076i	−0.471561	+	0.816768i
$894$	−34.9033	+	6.13069i	−1.16734	+	0.205041i
$895$	22.1518	+	38.3680i	0.740451	+	1.28250i
$896$	1.31426	+	2.27636i	0.0439063	+	0.0760479i
$897$	−5.96609	+	16.3582i	−0.199202	+	0.546184i
$898$	11.3266	−	19.6182i	0.377972	−	0.654667i
$899$	−1.64319			−0.0548036
$900$	31.9953	−	11.5976i	1.06651	−	0.386587i
$901$	31.4680			1.04835
$902$	17.0819	−	29.5867i	0.568764	−	0.985129i
$903$	−12.3289	−	14.7127i	−0.410281	−	0.489608i
$904$	2.85907	+	4.95205i	0.0950911	+	0.164703i
$905$	13.5571	+	23.4816i	0.450654	+	0.780555i
$906$	−0.740325	−	0.883466i	−0.0245956	−	0.0293512i
$907$	7.26087	−	12.5762i	0.241093	−	0.417586i	−0.719933	−	0.694044i	$-0.755827\pi$
$907$	7.26087	−	12.5762i	0.241093	−	0.417586i	0.961026	+	0.276458i	$0.0891607\pi$
$908$	6.48523			0.215220
$909$	−1.49056	+	8.38873i	−0.0494386	+	0.278237i
$910$	−65.1268			−2.15893
$911$	−20.9513	+	36.2887i	−0.694147	+	1.20230i	0.276321	+	0.961065i	$0.410885\pi$
$911$	−20.9513	+	36.2887i	−0.694147	+	1.20230i	−0.970468	+	0.241232i	$0.922449\pi$
$912$	−2.63513	+	7.22516i	−0.0872580	+	0.239249i
$913$	24.3276	+	42.1367i	0.805127	+	1.39452i
$914$	−12.9650	−	22.4561i	−0.428845	−	0.742782i
$915$	6.89673	−	1.21140i	0.227999	−	0.0400475i
$916$	4.81256	−	8.33559i	0.159011	−	0.275416i
$917$	15.3776			0.507814
$918$	0.0558905	−	28.2873i	0.00184466	−	0.933619i
$919$	−48.6533			−1.60493			−0.802463	−	0.596702i	$-0.796477\pi$
$919$	−48.6533			−1.60493			−0.802463	+	0.596702i	$0.796477\pi$
$920$	3.31570	−	5.74296i	0.109315	−	0.189340i
$921$	−13.3395	+	2.34306i	−0.439552	+	0.0772065i
$922$	6.26415	+	10.8498i	0.206299	+	0.357320i
$923$	−45.2116	−	78.3089i	−1.48816	−	2.57757i
$924$	6.57413	−	18.0253i	0.216273	−	0.592990i
$925$	−47.3583	+	82.0270i	−1.55713	+	2.69703i
$926$	−9.38177			−0.308304
$927$	9.07721	+	7.63708i	0.298135	+	0.250835i
$928$	−7.57561			−0.248682
$929$	2.01117	−	3.48345i	0.0659844	−	0.114288i	−0.831146	−	0.556054i	$-0.812315\pi$
$929$	2.01117	−	3.48345i	0.0659844	−	0.114288i	0.897130	+	0.441766i	$0.145648\pi$
$930$	0.975526	+	1.16414i	0.0319888	+	0.0381738i
$931$	−0.201799	−	0.349527i	−0.00661371	−	0.0114553i
$932$	−13.6175	−	23.5862i	−0.446056	−	0.772592i
$933$	22.6256	+	27.0002i	0.740729	+	0.883948i
$934$	−6.52661	+	11.3044i	−0.213557	+	0.369892i
$935$	−92.7514			−3.03330
$936$	−14.0690	−	11.8369i	−0.459859	−	0.386901i
$937$	−17.1767			−0.561138			−0.280569	−	0.959834i	$-0.590523\pi$
$937$	−17.1767			−0.561138			−0.280569	+	0.959834i	$0.590523\pi$
$938$	8.62235	−	14.9344i	0.281530	−	0.487624i
$939$	−16.1023	+	44.1501i	−0.525478	+	1.44078i
$940$	12.8304	+	22.2229i	0.418481	+	0.724830i
$941$	−16.9767	−	29.4046i	−0.553426	−	0.958562i	−0.998024	−	0.0628317i	$-0.979987\pi$
$941$	−16.9767	−	29.4046i	−0.553426	−	0.958562i	0.444598	−	0.895730i	$-0.353346\pi$
$942$	14.0024	−	2.45949i	0.456221	−	0.0801344i
$943$	6.64860	−	11.5157i	0.216508	−	0.375003i
$944$	3.87515			0.126125
$945$	47.8739	−	27.5140i	1.55734	−	0.895031i
$946$	−17.7688			−0.577712
$947$	15.8617	−	27.4734i	0.515438	−	0.892764i	−0.484402	−	0.874846i	$-0.660963\pi$
$947$	15.8617	−	27.4734i	0.515438	−	0.892764i	0.999839	−	0.0179184i	$-0.00570392\pi$
$948$	−20.0055	+	3.51393i	−0.649748	+	0.114127i
$949$	24.2293	+	41.9664i	0.786516	+	1.36229i
$950$	25.1852	+	43.6221i	0.817117	+	1.41529i
$951$	5.09740	−	13.9763i	0.165295	−	0.453214i
$952$	7.15469	−	12.3923i	0.231885	−	0.401636i
$953$	2.97694			0.0964327			0.0482163	−	0.998837i	$-0.484646\pi$
$953$	2.97694			0.0964327			0.0482163	+	0.998837i	$0.484646\pi$
$954$	−3.03377	+	17.0738i	−0.0982218	+	0.552785i
$955$	82.5208			2.67031
$956$	0.843640	−	1.46123i	0.0272853	−	0.0472595i
$957$	35.5169	+	42.3840i	1.14810	+	1.37008i
$958$	20.5575	+	35.6066i	0.664182	+	1.15040i
$959$	−12.8833	−	22.3145i	−0.416022	−	0.720572i
$960$	4.49746	+	5.36704i	0.145155	+	0.173221i
$961$	15.4765	−	26.8060i	0.499241	−	0.864711i
$962$	51.1710			1.64982
$963$	48.4847	−	17.5747i	1.56240	−	0.566337i
$964$	15.4374			0.497206
$965$	−28.0632	+	48.6068i	−0.903385	+	1.56471i
$966$	2.55878	−	7.01581i	0.0823274	−	0.225730i
$967$	10.4828	+	18.1567i	0.337104	+	0.583881i	0.983887	−	0.178793i	$-0.0572193\pi$
$967$	10.4828	+	18.1567i	0.337104	+	0.583881i	−0.646783	+	0.762674i	$0.723886\pi$
$968$	−3.38035	−	5.85493i	−0.108649	−	0.188185i
$969$	41.2361	−	7.24304i	1.32469	−	0.232680i
$970$	8.05614	−	13.9536i	0.258667	−	0.448024i
$971$	−46.8628			−1.50390			−0.751950	−	0.659220i	$-0.770887\pi$
$971$	−46.8628			−1.50390			−0.751950	+	0.659220i	$0.770887\pi$
$972$	15.3426	+	2.75745i	0.492115	+	0.0884451i
$973$	7.80410			0.250188
$974$	−3.43495	+	5.94951i	−0.110063	+	0.190635i
$975$	−118.605	+	20.8326i	−3.79838	+	0.667179i
$976$	0.500000	+	0.866025i	0.0160046	+	0.0277208i
$977$	12.8646	+	22.2822i	0.411576	+	0.712870i	0.995062	−	0.0992525i	$-0.0316452\pi$
$977$	12.8646	+	22.2822i	0.411576	+	0.712870i	−0.583486	+	0.812123i	$0.698312\pi$
$978$	7.33591	−	20.1140i	0.234577	−	0.643175i
$979$	−28.5702	+	49.4851i	−0.913109	+	1.58155i
$980$	−0.367473			−0.0117385
$981$	−7.22310	+	2.61822i	−0.230616	+	0.0835934i
$982$	−20.2204			−0.645259
$983$	16.7394	−	28.9936i	0.533905	−	0.924751i	−0.465310	−	0.885148i	$-0.654057\pi$
$983$	16.7394	−	28.9936i	0.533905	−	0.924751i	0.999215	−	0.0396032i	$-0.0126094\pi$
$984$	9.01826	+	10.7619i	0.287492	+	0.343078i
$985$	40.1867	+	69.6055i	1.28046	+	2.21781i
$986$	20.6204	+	35.7156i	0.656688	+	1.13742i
$987$	18.5604	+	22.1490i	0.590783	+	0.705010i
$988$	13.6064	−	23.5670i	0.432877	−	0.749766i
$989$	−6.91595			−0.219914
$990$	8.94199	−	50.3248i	0.284195	−	1.59943i
$991$	1.68880			0.0536466			0.0268233	−	0.999640i	$-0.491461\pi$
$991$	1.68880			0.0536466			0.0268233	+	0.999640i	$0.491461\pi$
$992$	−0.108453	+	0.187846i	−0.00344338	+	0.00596411i
$993$	−2.03633	+	5.58332i	−0.0646209	+	0.177181i
$994$	19.3907	+	33.5856i	0.615035	+	1.06527i
$995$	−30.7352	−	53.2349i	−0.974372	−	1.68766i
$996$	−19.6953	+	3.45943i	−0.624069	+	0.109616i
$997$	−13.6025	+	23.5602i	−0.430795	+	0.746160i	−0.996942	−	0.0781450i	$-0.975100\pi$
$997$	−13.6025	+	23.5602i	−0.430795	+	0.746160i	0.566147	+	0.824305i	$0.308434\pi$
$998$	11.2610			0.356460
$999$	−37.6151	+	21.6181i	−1.19009	+	0.683967i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1098.2.e.f.367.1	✓	34
9.2	odd	6		9882.2.a.bk.1.2		17
9.4	even	3	inner	1098.2.e.f.733.1	yes	34
9.7	even	3		9882.2.a.bm.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1098.2.e.f.367.1	✓	34	1.1	even	1	trivial
1098.2.e.f.733.1	yes	34	9.4	even	3	inner
9882.2.a.bk.1.2		17	9.2	odd	6
9882.2.a.bm.1.16		17	9.7	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:	\( N \)	\(=\)	\( 1098 = 2 \cdot 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1098.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.70593 + 0.299644i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02139 - 3.50116i) q^{5} +(0.593468 - 1.62720i) q^{6} +(1.31426 - 2.27636i) q^{7} +1.00000 q^{8} +(2.82043 - 1.02235i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.70593 + 0.299644i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.02139 - 3.50116i) q^{5} +(0.593468 - 1.62720i) q^{6} +(1.31426 - 2.27636i) q^{7} +1.00000 q^{8} +(2.82043 - 1.02235i) q^{9} +4.04279 q^{10} +(2.10717 - 3.64973i) q^{11} +(1.11247 + 1.32756i) q^{12} +(-3.06435 - 5.30761i) q^{13} +(1.31426 + 2.27636i) q^{14} +(4.49746 + 5.36704i) q^{15} +(-0.500000 + 0.866025i) q^{16} +5.44390 q^{17} +(-0.524836 + 2.95373i) q^{18} -4.44023 q^{19} +(-2.02139 + 3.50116i) q^{20} +(-1.55994 + 4.27714i) q^{21} +(2.10717 + 3.64973i) q^{22} +(0.820153 + 1.42055i) q^{23} +(-1.70593 + 0.299644i) q^{24} +(-5.67206 + 9.82430i) q^{25} +6.12870 q^{26} +(-4.50512 + 2.58918i) q^{27} -2.62852 q^{28} +(3.78780 - 6.56067i) q^{29} +(-6.89673 + 1.21140i) q^{30} +(-0.108453 - 0.187846i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.50108 + 6.85760i) q^{33} +(-2.72195 + 4.71455i) q^{34} -10.6265 q^{35} +(-2.29559 - 1.93139i) q^{36} +8.34941 q^{37} +(2.22011 - 3.84535i) q^{38} +(6.81797 + 8.13622i) q^{39} +(-2.02139 - 3.50116i) q^{40} +(-4.05327 - 7.02047i) q^{41} +(-2.92414 - 3.48952i) q^{42} +(-2.10813 + 3.65139i) q^{43} -4.21434 q^{44} +(-9.28058 - 7.80819i) q^{45} -1.64031 q^{46} +(3.17365 - 5.49692i) q^{47} +(0.593468 - 1.62720i) q^{48} +(0.0454480 + 0.0787182i) q^{49} +(-5.67206 - 9.82430i) q^{50} +(-9.28693 + 1.63123i) q^{51} +(-3.06435 + 5.30761i) q^{52} +5.78041 q^{53} +(0.0102666 - 5.19614i) q^{54} -17.0377 q^{55} +(1.31426 - 2.27636i) q^{56} +(7.57474 - 1.33049i) q^{57} +(3.78780 + 6.56067i) q^{58} +(-1.93757 - 3.35598i) q^{59} +(2.39926 - 6.57844i) q^{60} +(0.500000 - 0.866025i) q^{61} +0.216906 q^{62} +(1.37954 - 7.76394i) q^{63} +1.00000 q^{64} +(-12.3885 + 21.4575i) q^{65} +(-4.68832 - 5.59480i) q^{66} +(-3.28031 - 5.68167i) q^{67} +(-2.72195 - 4.71455i) q^{68} +(-1.82479 - 2.17761i) q^{69} +(5.31327 - 9.20285i) q^{70} +14.7541 q^{71} +(2.82043 - 1.02235i) q^{72} -7.90683 q^{73} +(-4.17470 + 7.23080i) q^{74} +(6.73237 - 18.4592i) q^{75} +(2.22011 + 3.84535i) q^{76} +(-5.53874 - 9.59338i) q^{77} +(-10.4552 + 1.83643i) q^{78} +(-5.86350 + 10.1559i) q^{79} +4.04279 q^{80} +(6.90962 - 5.76691i) q^{81} +8.10654 q^{82} +(-5.77258 + 9.99839i) q^{83} +(4.48408 - 0.787619i) q^{84} +(-11.0043 - 19.0599i) q^{85} +(-2.10813 - 3.65139i) q^{86} +(-4.49588 + 12.3271i) q^{87} +(2.10717 - 3.64973i) q^{88} -13.5586 q^{89} +(11.4024 - 4.13313i) q^{90} -16.1094 q^{91} +(0.820153 - 1.42055i) q^{92} +(0.241300 + 0.287956i) q^{93} +(3.17365 + 5.49692i) q^{94} +(8.97545 + 15.5459i) q^{95} +(1.11247 + 1.32756i) q^{96} +(1.99272 - 3.45149i) q^{97} -0.0908960 q^{98} +(2.21184 - 12.4481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 2 q^{3} - 17 q^{4} - 5 q^{5} - q^{6} - 11 q^{7} + 34 q^{8}+O(q^{10}) \) 34 * q - 17 * q^2 + 2 * q^3 - 17 * q^4 - 5 * q^5 - q^6 - 11 * q^7 + 34 * q^8	\( 34 q - 17 q^{2} + 2 q^{3} - 17 q^{4} - 5 q^{5} - q^{6} - 11 q^{7} + 34 q^{8} + 10 q^{10} - 3 q^{11} - q^{12} - 10 q^{13} - 11 q^{14} + q^{15} - 17 q^{16} + 16 q^{17} + 3 q^{18} + 22 q^{19} - 5 q^{20} - q^{21} - 3 q^{22} - 5 q^{23} + 2 q^{24} - 32 q^{25} + 20 q^{26} - q^{27} + 22 q^{28} - 6 q^{29} - 5 q^{30} - 20 q^{31} - 17 q^{32} - 14 q^{33} - 8 q^{34} - 16 q^{35} - 3 q^{36} + 58 q^{37} - 11 q^{38} + 44 q^{39} - 5 q^{40} - 20 q^{41} + 8 q^{42} - 30 q^{43} + 6 q^{44} - 22 q^{45} + 10 q^{46} - 10 q^{47} - q^{48} - 42 q^{49} - 32 q^{50} - 49 q^{51} - 10 q^{52} + 4 q^{53} - 22 q^{54} + 30 q^{55} - 11 q^{56} + 27 q^{57} - 6 q^{58} + 3 q^{59} + 4 q^{60} + 17 q^{61} + 40 q^{62} - 45 q^{63} + 34 q^{64} - 28 q^{65} + 28 q^{66} - 11 q^{67} - 8 q^{68} - 32 q^{69} + 8 q^{70} + 126 q^{71} + 56 q^{73} - 29 q^{74} + 100 q^{75} - 11 q^{76} - 17 q^{77} - 16 q^{78} - 17 q^{79} + 10 q^{80} - 8 q^{81} + 40 q^{82} + 20 q^{83} - 7 q^{84} - 33 q^{85} - 30 q^{86} - 86 q^{87} - 3 q^{88} + 4 q^{89} + 23 q^{90} + 60 q^{91} - 5 q^{92} + 121 q^{93} - 10 q^{94} - q^{95} - q^{96} - 32 q^{97} + 84 q^{98} - 31 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 2 * q^3 - 17 * q^4 - 5 * q^5 - q^6 - 11 * q^7 + 34 * q^8 + 10 * q^10 - 3 * q^11 - q^12 - 10 * q^13 - 11 * q^14 + q^15 - 17 * q^16 + 16 * q^17 + 3 * q^18 + 22 * q^19 - 5 * q^20 - q^21 - 3 * q^22 - 5 * q^23 + 2 * q^24 - 32 * q^25 + 20 * q^26 - q^27 + 22 * q^28 - 6 * q^29 - 5 * q^30 - 20 * q^31 - 17 * q^32 - 14 * q^33 - 8 * q^34 - 16 * q^35 - 3 * q^36 + 58 * q^37 - 11 * q^38 + 44 * q^39 - 5 * q^40 - 20 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 22 * q^45 + 10 * q^46 - 10 * q^47 - q^48 - 42 * q^49 - 32 * q^50 - 49 * q^51 - 10 * q^52 + 4 * q^53 - 22 * q^54 + 30 * q^55 - 11 * q^56 + 27 * q^57 - 6 * q^58 + 3 * q^59 + 4 * q^60 + 17 * q^61 + 40 * q^62 - 45 * q^63 + 34 * q^64 - 28 * q^65 + 28 * q^66 - 11 * q^67 - 8 * q^68 - 32 * q^69 + 8 * q^70 + 126 * q^71 + 56 * q^73 - 29 * q^74 + 100 * q^75 - 11 * q^76 - 17 * q^77 - 16 * q^78 - 17 * q^79 + 10 * q^80 - 8 * q^81 + 40 * q^82 + 20 * q^83 - 7 * q^84 - 33 * q^85 - 30 * q^86 - 86 * q^87 - 3 * q^88 + 4 * q^89 + 23 * q^90 + 60 * q^91 - 5 * q^92 + 121 * q^93 - 10 * q^94 - q^95 - q^96 - 32 * q^97 + 84 * q^98 - 31 * q^99

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