LMFDB - Embedded newform 946.2.f.g.861.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("946.345");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			861.10
Character	$\chi$	$=$	946.861
Dual form			946.2.f.g.345.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.972426 + 2.99282i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.26325 + 0.917804i) q^{5} +(-2.54584 - 1.84966i) q^{6} +(-0.230171 + 0.708394i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-5.58431 + 4.05724i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.972426 + 2.99282i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.26325 + 0.917804i) q^{5} +(-2.54584 - 1.84966i) q^{6} +(-0.230171 + 0.708394i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-5.58431 + 4.05724i) q^{9} -1.56146 q^{10} +(-1.40816 - 3.00285i) q^{11} +3.14684 q^{12} +(-2.96347 + 2.15309i) q^{13} +(-0.230171 - 0.708394i) q^{14} +(-1.51841 + 4.67317i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.72326 - 4.15819i) q^{17} +(2.13302 - 6.56475i) q^{18} +(-0.247011 - 0.760220i) q^{19} +(1.26325 - 0.917804i) q^{20} -2.34392 q^{21} +(2.90425 + 1.60166i) q^{22} +3.53402 q^{23} +(-2.54584 + 1.84966i) q^{24} +(-0.791652 - 2.43646i) q^{25} +(1.13194 - 3.48377i) q^{26} +(-9.93537 - 7.21847i) q^{27} +(0.602596 + 0.437811i) q^{28} +(-1.71245 + 5.27039i) q^{29} +(-1.51841 - 4.67317i) q^{30} +(-5.63921 + 4.09712i) q^{31} +1.00000 q^{32} +(7.61766 - 7.13441i) q^{33} +7.07434 q^{34} +(-0.940930 + 0.683625i) q^{35} +(2.13302 + 6.56475i) q^{36} +(-2.62166 + 8.06865i) q^{37} +(0.646682 + 0.469842i) q^{38} +(-9.32555 - 6.77541i) q^{39} +(-0.482518 + 1.48504i) q^{40} +(2.99591 + 9.22045i) q^{41} +(1.89627 - 1.37772i) q^{42} -1.00000 q^{43} +(-3.29102 + 0.411305i) q^{44} -10.7781 q^{45} +(-2.85908 + 2.07724i) q^{46} +(1.56585 + 4.81918i) q^{47} +(0.972426 - 2.99282i) q^{48} +(5.21428 + 3.78839i) q^{49} +(2.07257 + 1.50581i) q^{50} +(6.87928 - 21.1722i) q^{51} +(1.13194 + 3.48377i) q^{52} +(4.20710 - 3.05664i) q^{53} +12.2808 q^{54} +(0.977174 - 5.08575i) q^{55} -0.744849 q^{56} +(2.03500 - 1.47852i) q^{57} +(-1.71245 - 5.27039i) q^{58} +(-4.21396 + 12.9692i) q^{59} +(3.97524 + 2.88818i) q^{60} +(-5.93060 - 4.30883i) q^{61} +(2.15399 - 6.62928i) q^{62} +(-1.58878 - 4.88975i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.71970 q^{65} +(-1.96931 + 10.2494i) q^{66} +5.13712 q^{67} +(-5.72326 + 4.15819i) q^{68} +(3.43657 + 10.5767i) q^{69} +(0.359403 - 1.10613i) q^{70} +(6.75568 + 4.90829i) q^{71} +(-5.58431 - 4.05724i) q^{72} +(1.74332 - 5.36540i) q^{73} +(-2.62166 - 8.06865i) q^{74} +(6.52205 - 4.73855i) q^{75} -0.799343 q^{76} +(2.45132 - 0.306360i) q^{77} +11.5270 q^{78} +(-1.86572 + 1.35553i) q^{79} +(-0.482518 - 1.48504i) q^{80} +(5.54312 - 17.0600i) q^{81} +(-7.84339 - 5.69855i) q^{82} +(5.54008 + 4.02510i) q^{83} +(-0.724311 + 2.22920i) q^{84} +(-3.41350 - 10.5057i) q^{85} +(0.809017 - 0.587785i) q^{86} -17.4386 q^{87} +(2.42073 - 2.26717i) q^{88} +7.18187 q^{89} +(8.71968 - 6.33522i) q^{90} +(-0.843128 - 2.59488i) q^{91} +(1.09207 - 3.36105i) q^{92} +(-17.7457 - 12.8930i) q^{93} +(-4.09944 - 2.97842i) q^{94} +(0.385697 - 1.18705i) q^{95} +(0.972426 + 2.99282i) q^{96} +(10.1064 - 7.34272i) q^{97} -6.44520 q^{98} +(20.0468 + 11.0556i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9}+O(q^{10}) $ 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 5 q^{14} - 23 q^{15} - 10 q^{16} - 5 q^{17} + 9 q^{18} - 21 q^{19} + 8 q^{20} + 20 q^{21} + 6 q^{22} + 24 q^{23} - 5 q^{24} - 16 q^{25} - 18 q^{26} - 10 q^{27} - 20 q^{28} + 7 q^{29} - 23 q^{30} - 15 q^{31} + 40 q^{32} + 36 q^{33} + 10 q^{34} + 50 q^{35} + 9 q^{36} + 2 q^{37} - 21 q^{38} - 70 q^{39} - 7 q^{40} - 20 q^{41} - 10 q^{42} - 40 q^{43} + 6 q^{44} - 14 q^{45} - q^{46} - 8 q^{47} + 5 q^{48} + 5 q^{49} - 11 q^{50} + 13 q^{51} - 18 q^{52} + 24 q^{53} + 38 q^{55} + 30 q^{56} + 62 q^{57} + 7 q^{58} - 27 q^{59} + 2 q^{60} - 49 q^{61} + 20 q^{62} - 5 q^{63} - 10 q^{64} - 4 q^{65} - 34 q^{66} - 26 q^{67} - 5 q^{68} + 73 q^{69} - 65 q^{70} - 5 q^{71} - 31 q^{72} + 22 q^{73} + 2 q^{74} - 60 q^{75} + 84 q^{76} - 20 q^{77} + 30 q^{78} + 81 q^{79} - 7 q^{80} - 38 q^{81} - 25 q^{82} + 3 q^{83} - 38 q^{85} + 10 q^{86} + 28 q^{87} - 14 q^{88} - 56 q^{89} - 4 q^{90} + 10 q^{91} - 11 q^{92} - 16 q^{93} - 23 q^{94} + 66 q^{95} + 5 q^{96} - 20 q^{97} + 50 q^{98} + 94 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 5 * q^14 - 23 * q^15 - 10 * q^16 - 5 * q^17 + 9 * q^18 - 21 * q^19 + 8 * q^20 + 20 * q^21 + 6 * q^22 + 24 * q^23 - 5 * q^24 - 16 * q^25 - 18 * q^26 - 10 * q^27 - 20 * q^28 + 7 * q^29 - 23 * q^30 - 15 * q^31 + 40 * q^32 + 36 * q^33 + 10 * q^34 + 50 * q^35 + 9 * q^36 + 2 * q^37 - 21 * q^38 - 70 * q^39 - 7 * q^40 - 20 * q^41 - 10 * q^42 - 40 * q^43 + 6 * q^44 - 14 * q^45 - q^46 - 8 * q^47 + 5 * q^48 + 5 * q^49 - 11 * q^50 + 13 * q^51 - 18 * q^52 + 24 * q^53 + 38 * q^55 + 30 * q^56 + 62 * q^57 + 7 * q^58 - 27 * q^59 + 2 * q^60 - 49 * q^61 + 20 * q^62 - 5 * q^63 - 10 * q^64 - 4 * q^65 - 34 * q^66 - 26 * q^67 - 5 * q^68 + 73 * q^69 - 65 * q^70 - 5 * q^71 - 31 * q^72 + 22 * q^73 + 2 * q^74 - 60 * q^75 + 84 * q^76 - 20 * q^77 + 30 * q^78 + 81 * q^79 - 7 * q^80 - 38 * q^81 - 25 * q^82 + 3 * q^83 - 38 * q^85 + 10 * q^86 + 28 * q^87 - 14 * q^88 - 56 * q^89 - 4 * q^90 + 10 * q^91 - 11 * q^92 - 16 * q^93 - 23 * q^94 + 66 * q^95 + 5 * q^96 - 20 * q^97 + 50 * q^98 + 94 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.972426	+	2.99282i	0.561430	+	1.72791i	0.678326	+	0.734761i	$0.262706\pi$
$3$	0.972426	+	2.99282i	0.561430	+	1.72791i	−0.116895	+	0.993144i	$0.537294\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	1.26325	+	0.917804i	0.564942	+	0.410454i	0.833264	−	0.552875i	$-0.186469\pi$
$5$	1.26325	+	0.917804i	0.564942	+	0.410454i	−0.268322	+	0.963329i	$0.586469\pi$
$6$	−2.54584	−	1.84966i	−1.03934	−	0.755122i
$7$	−0.230171	+	0.708394i	−0.0869965	+	0.267748i	−0.985085	−	0.172066i	$-0.944956\pi$
$7$	−0.230171	+	0.708394i	−0.0869965	+	0.267748i	0.898089	+	0.439814i	$0.144956\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−5.58431	+	4.05724i	−1.86144	+	1.35241i
$10$	−1.56146			−0.493777
$11$	−1.40816	−	3.00285i	−0.424575	−	0.905393i
$11$	−1.40816	−	3.00285i	−0.424575	−	0.905393i
$12$	3.14684			0.908414
$13$	−2.96347	+	2.15309i	−0.821918	+	0.597158i	−0.917261	−	0.398286i	$-0.869605\pi$
$13$	−2.96347	+	2.15309i	−0.821918	+	0.597158i	0.0953432	+	0.995444i	$0.469605\pi$
$14$	−0.230171	−	0.708394i	−0.0615158	−	0.189326i
$15$	−1.51841	+	4.67317i	−0.392051	+	1.20661i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.72326	−	4.15819i	−1.38810	−	1.00851i	−0.996071	−	0.0885554i	$-0.971775\pi$
$17$	−5.72326	−	4.15819i	−1.38810	−	1.00851i	−0.392024	−	0.919955i	$-0.628225\pi$
$18$	2.13302	−	6.56475i	0.502757	−	1.54733i
$19$	−0.247011	−	0.760220i	−0.0566681	−	0.174407i	0.918716	−	0.394919i	$-0.129227\pi$
$19$	−0.247011	−	0.760220i	−0.0566681	−	0.174407i	−0.975384	+	0.220512i	$0.929227\pi$
$20$	1.26325	−	0.917804i	0.282471	−	0.205227i
$21$	−2.34392			−0.511485
$22$	2.90425	+	1.60166i	0.619189	+	0.341475i
$23$	3.53402			0.736894			0.368447	−	0.929649i	$-0.379890\pi$
$23$	3.53402			0.736894			0.368447	+	0.929649i	$0.379890\pi$
$24$	−2.54584	+	1.84966i	−0.519668	+	0.377561i
$25$	−0.791652	−	2.43646i	−0.158330	−	0.487291i
$26$	1.13194	−	3.48377i	0.221992	−	0.683223i
$27$	−9.93537	−	7.21847i	−1.91206	−	1.38920i
$28$	0.602596	+	0.437811i	0.113880	+	0.0827386i
$29$	−1.71245	+	5.27039i	−0.317995	+	0.978687i	0.656510	+	0.754318i	$0.272032\pi$
$29$	−1.71245	+	5.27039i	−0.317995	+	0.978687i	−0.974504	+	0.224369i	$0.927968\pi$
$30$	−1.51841	−	4.67317i	−0.277222	−	0.853200i
$31$	−5.63921	+	4.09712i	−1.01283	+	0.735865i	−0.964801	−	0.262981i	$-0.915294\pi$
$31$	−5.63921	+	4.09712i	−1.01283	+	0.735865i	−0.0480303	+	0.998846i	$0.515294\pi$
$32$	1.00000			0.176777
$33$	7.61766	−	7.13441i	1.32606	−	1.24194i
$34$	7.07434			1.21324
$35$	−0.940930	+	0.683625i	−0.159046	+	0.115554i
$36$	2.13302	+	6.56475i	0.355503	+	1.09412i
$37$	−2.62166	+	8.06865i	−0.430999	+	1.32648i	0.466132	+	0.884715i	$0.345647\pi$
$37$	−2.62166	+	8.06865i	−0.430999	+	1.32648i	−0.897131	+	0.441764i	$0.854353\pi$
$38$	0.646682	+	0.469842i	0.104906	+	0.0762184i
$39$	−9.32555	−	6.77541i	−1.49328	−	1.08493i
$40$	−0.482518	+	1.48504i	−0.0762928	+	0.234805i
$41$	2.99591	+	9.22045i	0.467882	+	1.43999i	0.855321	+	0.518098i	$0.173360\pi$
$41$	2.99591	+	9.22045i	0.467882	+	1.43999i	−0.387439	+	0.921895i	$0.626640\pi$
$42$	1.89627	−	1.37772i	0.292601	−	0.212587i
$43$	−1.00000			−0.152499
$43$	−1.00000			−0.152499
$44$	−3.29102	+	0.411305i	−0.496140	+	0.0620065i
$45$	−10.7781			−1.60671
$46$	−2.85908	+	2.07724i	−0.421548	+	0.306273i
$47$	1.56585	+	4.81918i	0.228402	+	0.702949i	0.997928	+	0.0643343i	$0.0204924\pi$
$47$	1.56585	+	4.81918i	0.228402	+	0.702949i	−0.769526	+	0.638615i	$0.779508\pi$
$48$	0.972426	−	2.99282i	0.140358	−	0.431976i
$49$	5.21428	+	3.78839i	0.744897	+	0.541199i
$50$	2.07257	+	1.50581i	0.293106	+	0.212954i
$51$	6.87928	−	21.1722i	0.963291	−	2.96471i
$52$	1.13194	+	3.48377i	0.156972	+	0.483111i
$53$	4.20710	−	3.05664i	0.577890	−	0.419862i	−0.260073	−	0.965589i	$-0.583747\pi$
$53$	4.20710	−	3.05664i	0.577890	−	0.419862i	0.837963	+	0.545727i	$0.183747\pi$
$54$	12.2808			1.67120
$55$	0.977174	−	5.08575i	0.131762	−	0.685763i
$56$	−0.744849			−0.0995347
$57$	2.03500	−	1.47852i	0.269543	−	0.195834i
$58$	−1.71245	−	5.27039i	−0.224856	−	0.692036i
$59$	−4.21396	+	12.9692i	−0.548611	+	1.68845i	0.163635	+	0.986521i	$0.447678\pi$
$59$	−4.21396	+	12.9692i	−0.548611	+	1.68845i	−0.712246	+	0.701930i	$0.752322\pi$
$60$	3.97524	+	2.88818i	0.513201	+	0.372862i
$61$	−5.93060	−	4.30883i	−0.759335	−	0.551689i	0.139371	−	0.990240i	$-0.455492\pi$
$61$	−5.93060	−	4.30883i	−0.759335	−	0.551689i	−0.898706	+	0.438551i	$0.855492\pi$
$62$	2.15399	−	6.62928i	0.273556	−	0.841920i
$63$	−1.58878	−	4.88975i	−0.200167	−	0.616050i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−5.71970			−0.709442
$66$	−1.96931	+	10.2494i	−0.242406	+	1.26161i
$67$	5.13712			0.627599			0.313799	−	0.949489i	$-0.398398\pi$
$67$	5.13712			0.627599			0.313799	+	0.949489i	$0.398398\pi$
$68$	−5.72326	+	4.15819i	−0.694048	+	0.504255i
$69$	3.43657	+	10.5767i	0.413715	+	1.27328i
$70$	0.359403	−	1.10613i	0.0429569	−	0.132208i
$71$	6.75568	+	4.90829i	0.801752	+	0.582507i	0.911428	−	0.411461i	$-0.134981\pi$
$71$	6.75568	+	4.90829i	0.801752	+	0.582507i	−0.109676	+	0.993967i	$0.534981\pi$
$72$	−5.58431	−	4.05724i	−0.658117	−	0.478150i
$73$	1.74332	−	5.36540i	0.204040	−	0.627972i	−0.795711	−	0.605677i	$-0.792903\pi$
$73$	1.74332	−	5.36540i	0.204040	−	0.627972i	0.999751	−	0.0222955i	$-0.00709745\pi$
$74$	−2.62166	−	8.06865i	−0.304762	−	0.937962i
$75$	6.52205	−	4.73855i	0.753101	−	0.547160i
$76$	−0.799343			−0.0916909
$77$	2.45132	−	0.306360i	0.279353	−	0.0349130i
$78$	11.5270			1.30518
$79$	−1.86572	+	1.35553i	−0.209910	+	0.152509i	−0.687773	−	0.725926i	$-0.741412\pi$
$79$	−1.86572	+	1.35553i	−0.209910	+	0.152509i	0.477863	+	0.878434i	$0.341412\pi$
$80$	−0.482518	−	1.48504i	−0.0539471	−	0.166032i
$81$	5.54312	−	17.0600i	0.615902	−	1.89555i
$82$	−7.84339	−	5.69855i	−0.866157	−	0.629300i
$83$	5.54008	+	4.02510i	0.608103	+	0.441812i	0.848746	−	0.528801i	$-0.177358\pi$
$83$	5.54008	+	4.02510i	0.608103	+	0.441812i	−0.240643	+	0.970614i	$0.577358\pi$
$84$	−0.724311	+	2.22920i	−0.0790288	+	0.243226i
$85$	−3.41350	−	10.5057i	−0.370246	−	1.13950i
$86$	0.809017	−	0.587785i	0.0872385	−	0.0633825i
$87$	−17.4386			−1.86961
$88$	2.42073	−	2.26717i	0.258051	−	0.241681i
$89$	7.18187			0.761276			0.380638	−	0.924724i	$-0.375704\pi$
$89$	7.18187			0.761276			0.380638	+	0.924724i	$0.375704\pi$
$90$	8.71968	−	6.33522i	0.919135	−	0.667790i
$91$	−0.843128	−	2.59488i	−0.0883838	−	0.272017i
$92$	1.09207	−	3.36105i	0.113856	−	0.350414i
$93$	−17.7457	−	12.8930i	−1.84014	−	1.33694i
$94$	−4.09944	−	2.97842i	−0.422825	−	0.307200i
$95$	0.385697	−	1.18705i	0.0395717	−	0.121789i
$96$	0.972426	+	2.99282i	0.0992478	+	0.305453i
$97$	10.1064	−	7.34272i	1.02615	−	0.745540i	0.0586137	−	0.998281i	$-0.481332\pi$
$97$	10.1064	−	7.34272i	1.02615	−	0.745540i	0.967534	+	0.252741i	$0.0813320\pi$
$98$	−6.44520			−0.651063
$99$	20.0468	+	11.0556i	2.01478	+	1.11113i
$100$	−2.56184			−0.256184
$101$	7.52347	−	5.46612i	0.748613	−	0.543899i	−0.146784	−	0.989169i	$-0.546892\pi$
$101$	7.52347	−	5.46612i	0.748613	−	0.543899i	0.895397	+	0.445270i	$0.146892\pi$
$102$	6.87928	+	21.1722i	0.681150	+	2.09636i
$103$	1.35517	−	4.17078i	0.133529	−	0.410959i	−0.861830	−	0.507198i	$-0.830681\pi$
$103$	1.35517	−	4.17078i	0.133529	−	0.410959i	0.995358	+	0.0962389i	$0.0306813\pi$
$104$	−2.96347	−	2.15309i	−0.290592	−	0.211127i
$105$	−2.96095	−	2.15126i	−0.288959	−	0.209941i
$106$	−1.60697	+	4.94575i	−0.156083	+	0.480373i
$107$	0.189012	+	0.581720i	0.0182725	+	0.0562370i	0.959777	−	0.280763i	$-0.0905876\pi$
$107$	0.189012	+	0.581720i	0.0182725	+	0.0562370i	−0.941505	+	0.337000i	$0.890588\pi$
$108$	−9.93537	+	7.21847i	−0.956031	+	0.694598i
$109$	14.9455			1.43152			0.715759	−	0.698347i	$-0.246081\pi$
$109$	14.9455			1.43152			0.715759	+	0.698347i	$0.246081\pi$
$110$	2.19878	+	4.68883i	0.209645	+	0.447062i
$111$	−26.6974			−2.53401
$112$	0.602596	−	0.437811i	0.0569400	−	0.0413693i
$113$	3.59379	+	11.0605i	0.338075	+	1.04049i	0.965187	+	0.261559i	$0.0842367\pi$
$113$	3.59379	+	11.0605i	0.338075	+	1.04049i	−0.627112	+	0.778929i	$0.715763\pi$
$114$	−0.777302	+	2.39229i	−0.0728010	+	0.224058i
$115$	4.46434	+	3.24353i	0.416302	+	0.302461i
$116$	4.48326	+	3.25728i	0.416260	+	0.302431i
$117$	7.81334	−	24.0470i	0.722343	−	2.22314i
$118$	−4.21396	−	12.9692i	−0.387927	−	1.19392i
$119$	4.26297	−	3.09723i	0.390786	−	0.283922i
$120$	−4.91366			−0.448554
$121$	−7.03419	+	8.45696i	−0.639472	+	0.768814i
$122$	7.33062			0.663683
$123$	−24.6819	+	17.9324i	−2.22549	+	1.61691i
$124$	2.15399	+	6.62928i	0.193434	+	0.595327i
$125$	3.64872	−	11.2296i	0.326352	−	1.00441i
$126$	4.15947	+	3.02203i	0.370555	+	0.269224i
$127$	−13.3698	−	9.71376i	−1.18638	−	0.861956i	−0.193504	−	0.981099i	$-0.561985\pi$
$127$	−13.3698	−	9.71376i	−1.18638	−	0.861956i	−0.992877	+	0.119143i	$0.961985\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−0.972426	−	2.99282i	−0.0856173	−	0.263503i
$130$	4.62734	−	3.36196i	0.405844	−	0.294863i
$131$	−14.8957			−1.30145			−0.650723	−	0.759315i	$-0.725534\pi$
$131$	−14.8957			−1.30145			−0.650723	+	0.759315i	$0.725534\pi$
$132$	−4.43124	−	9.44947i	−0.385690	−	0.822471i
$133$	0.595390			0.0516269
$134$	−4.15601	+	3.01952i	−0.359025	+	0.260847i
$135$	−5.92570	−	18.2374i	−0.510003	−	1.56963i
$136$	2.18609	−	6.72810i	0.187456	−	0.576930i
$137$	−8.02372	−	5.82958i	−0.685513	−	0.498054i	0.189669	−	0.981848i	$-0.439258\pi$
$137$	−8.02372	−	5.82958i	−0.685513	−	0.498054i	−0.875182	+	0.483794i	$0.839258\pi$
$138$	−8.99706	−	6.53675i	−0.765881	−	0.556445i
$139$	2.72959	−	8.40081i	0.231521	−	0.712547i	−0.766043	−	0.642789i	$-0.777777\pi$
$139$	2.72959	−	8.40081i	0.231521	−	0.712547i	0.997564	−	0.0697582i	$-0.0222228\pi$
$140$	0.359403	+	1.10613i	0.0303751	+	0.0934850i
$141$	−12.9003	+	9.37259i	−1.08640	+	0.789314i
$142$	−8.35048			−0.700757
$143$	10.6384	+	5.86696i	0.889629	+	0.490620i
$144$	6.90258			0.575215
$145$	−7.00044	+	5.08611i	−0.581355	+	0.422379i
$146$	1.74332	+	5.36540i	0.144278	+	0.444043i
$147$	−6.26748	+	19.2893i	−0.516933	+	1.59096i
$148$	6.86361	+	4.98670i	0.564185	+	0.409904i
$149$	18.5390	+	13.4694i	1.51878	+	1.10345i	0.962090	+	0.272731i	$0.0879271\pi$
$149$	18.5390	+	13.4694i	1.51878	+	1.10345i	0.556685	+	0.830723i	$0.312073\pi$
$150$	−2.49120	+	7.66713i	−0.203406	+	0.626018i
$151$	−1.10696	−	3.40687i	−0.0900831	−	0.277247i	0.895858	−	0.444340i	$-0.146562\pi$
$151$	−1.10696	−	3.40687i	−0.0900831	−	0.277247i	−0.985941	+	0.167093i	$0.946562\pi$
$152$	0.646682	−	0.469842i	0.0524528	−	0.0381092i
$153$	48.8312			3.94777
$154$	−1.80308	+	1.68870i	−0.145297	+	0.136079i
$155$	−10.8841			−0.874230
$156$	−9.32555	+	6.77541i	−0.746641	+	0.542467i
$157$	0.407612	+	1.25450i	0.0325309	+	0.100120i	0.966004	−	0.258529i	$-0.0832376\pi$
$157$	0.407612	+	1.25450i	0.0325309	+	0.100120i	−0.933473	+	0.358649i	$0.883238\pi$
$158$	0.712642	−	2.19329i	0.0566948	−	0.174489i
$159$	13.2391	+	9.61875i	1.04993	+	0.762816i
$160$	1.26325	+	0.917804i	0.0998685	+	0.0725587i
$161$	−0.813429	+	2.50348i	−0.0641072	+	0.197302i
$162$	5.54312	+	17.0600i	0.435508	+	1.34036i
$163$	−8.47386	+	6.15662i	−0.663724	+	0.482224i	−0.867918	−	0.496707i	$-0.834542\pi$
$163$	−8.47386	+	6.15662i	−0.663724	+	0.482224i	0.204195	+	0.978930i	$0.434542\pi$
$164$	9.69496			0.757049
$165$	16.1710	−	2.02101i	1.25891	−	0.157336i
$166$	−6.84791			−0.531501
$167$	−12.9654	+	9.41993i	−1.00329	+	0.728936i	−0.962792	−	0.270243i	$-0.912896\pi$
$167$	−12.9654	+	9.41993i	−1.00329	+	0.728936i	−0.0405027	+	0.999179i	$0.512896\pi$
$168$	−0.724311	−	2.22920i	−0.0558818	−	0.171987i
$169$	0.129143	−	0.397461i	0.00993408	−	0.0305739i
$170$	8.93665	+	6.49286i	0.685410	+	0.497979i
$171$	4.46378	+	3.24312i	0.341354	+	0.248008i
$172$	−0.309017	+	0.951057i	−0.0235623	+	0.0725174i
$173$	3.83540	+	11.8041i	0.291600	+	0.897453i	0.984342	+	0.176267i	$0.0564023\pi$
$173$	3.83540	+	11.8041i	0.291600	+	0.897453i	−0.692742	+	0.721185i	$0.743598\pi$
$174$	14.1081	−	10.2501i	1.06953	−	0.777060i
$175$	1.90819			0.144245
$176$	−0.625808	+	3.25705i	−0.0471720	+	0.245509i
$177$	−42.9124			−3.22549
$178$	−5.81025	+	4.22140i	−0.435497	+	0.316407i
$179$	1.98616	+	6.11279i	0.148453	+	0.456891i	0.997439	−	0.0715243i	$-0.0227864\pi$
$179$	1.98616	+	6.11279i	0.148453	+	0.456891i	−0.848986	+	0.528415i	$0.822786\pi$
$180$	−3.33062	+	10.2506i	−0.248250	+	0.764034i
$181$	12.7970	+	9.29753i	0.951190	+	0.691080i	0.951088	−	0.308920i	$-0.0999674\pi$
$181$	12.7970	+	9.29753i	0.951190	+	0.691080i	0.000102269		1.00000i	$0.499967\pi$
$182$	2.20734	+	1.60372i	0.163619	+	0.118876i
$183$	7.12849	−	21.9392i	0.526953	−	1.62179i
$184$	1.09207	+	3.36105i	0.0805086	+	0.247780i
$185$	−10.7173	+	7.78654i	−0.787948	+	0.572478i
$186$	21.9348			1.60834
$187$	−4.42718	+	23.0415i	−0.323747	+	1.68496i
$188$	5.06718			0.369562
$189$	7.40035	−	5.37667i	0.538297	−	0.391095i
$190$	0.385697	+	1.18705i	0.0279814	+	0.0861180i
$191$	−3.61603	+	11.1290i	−0.261646	+	0.805265i	0.730801	+	0.682591i	$0.239147\pi$
$191$	−3.61603	+	11.1290i	−0.261646	+	0.805265i	−0.992447	+	0.122674i	$0.960853\pi$
$192$	−2.54584	−	1.84966i	−0.183731	−	0.133488i
$193$	−15.5111	−	11.2695i	−1.11651	−	0.811194i	−0.132836	−	0.991138i	$-0.542408\pi$
$193$	−15.5111	−	11.2695i	−1.11651	−	0.811194i	−0.983677	+	0.179944i	$0.942408\pi$
$194$	−3.86029	+	11.8808i	−0.277153	+	0.852989i
$195$	−5.56199	−	17.1180i	−0.398302	−	1.22585i
$196$	5.21428	−	3.78839i	0.372448	−	0.270600i
$197$	19.7827			1.40946			0.704731	−	0.709474i	$-0.251068\pi$
$197$	19.7827			1.40946			0.704731	+	0.709474i	$0.251068\pi$
$198$	−22.7166	+	2.83907i	−1.61440	+	0.201764i
$199$	−13.1481			−0.932047			−0.466023	−	0.884772i	$-0.654314\pi$
$199$	−13.1481			−0.932047			−0.466023	+	0.884772i	$0.654314\pi$
$200$	2.07257	−	1.50581i	0.146553	−	0.106477i
$201$	4.99547	+	15.3745i	0.352353	+	1.08443i
$202$	−2.87371	+	8.84436i	−0.202193	+	0.622287i
$203$	−3.33935	−	2.42618i	−0.234377	−	0.170285i
$204$	−18.0102	−	13.0852i	−1.26096	−	0.916145i
$205$	−4.67799	+	14.3974i	−0.326725	+	1.00556i
$206$	1.35517	+	4.17078i	0.0944190	+	0.290592i
$207$	−19.7350	+	14.3383i	−1.37168	+	0.996584i
$208$	3.66305			0.253987
$209$	−1.93500	+	1.81224i	−0.133847	+	0.125356i
$210$	3.65994			0.252560
$211$	−3.34208	+	2.42817i	−0.230079	+	0.167162i	−0.696852	−	0.717215i	$-0.745416\pi$
$211$	−3.34208	+	2.42817i	−0.230079	+	0.167162i	0.466773	+	0.884377i	$0.345416\pi$
$212$	−1.60697	−	4.94575i	−0.110367	−	0.339675i
$213$	−8.12023	+	24.9915i	−0.556389	+	1.71239i
$214$	−0.494840	−	0.359523i	−0.0338266	−	0.0245765i
$215$	−1.26325	−	0.917804i	−0.0861528	−	0.0625937i
$216$	3.79497	−	11.6797i	0.258215	−	0.794705i
$217$	−1.60439	−	4.93782i	−0.108913	−	0.335201i
$218$	−12.0912	+	8.78474i	−0.818916	+	0.594977i
$219$	17.7529			1.19963
$220$	−4.53488	−	2.50093i	−0.305741	−	0.168613i
$221$	25.9137			1.74314
$222$	21.5987	−	15.6923i	1.44961	−	1.05320i
$223$	−8.60698	−	26.4896i	−0.576366	−	1.77387i	−0.631479	−	0.775393i	$-0.717552\pi$
$223$	−8.60698	−	26.4896i	−0.576366	−	1.77387i	0.0551130	−	0.998480i	$-0.482448\pi$
$224$	−0.230171	+	0.708394i	−0.0153790	+	0.0473316i
$225$	14.3061	+	10.3940i	0.953740	+	0.692933i
$226$	−9.40866	−	6.83579i	−0.625855	−	0.454710i
$227$	7.43598	−	22.8856i	0.493543	−	1.51897i	−0.325672	−	0.945483i	$-0.605590\pi$
$227$	7.43598	−	22.8856i	0.493543	−	1.51897i	0.819215	−	0.573487i	$-0.194410\pi$
$228$	−0.777302	−	2.39229i	−0.0514781	−	0.158433i
$229$	0.229840	−	0.166988i	0.0151882	−	0.0110349i	−0.580165	−	0.814499i	$-0.697012\pi$
$229$	0.229840	−	0.166988i	0.0151882	−	0.0110349i	0.595353	+	0.803464i	$0.297012\pi$
$230$	−5.51823			−0.363861
$231$	3.30060	+	7.03843i	0.217164	+	0.463095i
$232$	−5.54162			−0.363825
$233$	14.1196	−	10.2585i	0.925003	−	0.672054i	−0.0197612	−	0.999805i	$-0.506291\pi$
$233$	14.1196	−	10.2585i	0.925003	−	0.672054i	0.944764	+	0.327751i	$0.106291\pi$
$234$	7.81334	+	24.0470i	0.510774	+	1.57200i
$235$	−2.44501	+	7.52496i	−0.159495	+	0.490874i
$236$	11.0323	+	8.01543i	0.718141	+	0.521760i
$237$	−5.87112	−	4.26562i	−0.381370	−	0.277082i
$238$	−1.62831	+	5.01142i	−0.105548	+	0.324842i
$239$	4.90786	+	15.1048i	0.317463	+	0.977051i	0.974729	+	0.223392i	$0.0717129\pi$
$239$	4.90786	+	15.1048i	0.317463	+	0.977051i	−0.657266	+	0.753659i	$0.728287\pi$
$240$	3.97524	−	2.88818i	0.256600	−	0.186431i
$241$	5.54473			0.357168			0.178584	−	0.983925i	$-0.442848\pi$
$241$	5.54473			0.357168			0.178584	+	0.983925i	$0.442848\pi$
$242$	0.719907	−	10.9764i	0.0462774	−	0.705591i
$243$	19.6053			1.25768
$244$	−5.93060	+	4.30883i	−0.379668	+	0.275845i
$245$	3.10992	+	9.57136i	0.198686	+	0.611492i
$246$	9.42763	−	29.0153i	0.601084	−	1.84995i
$247$	2.36883	+	1.72105i	0.150725	+	0.109508i
$248$	−5.63921	−	4.09712i	−0.358090	−	0.260168i
$249$	−6.65909	+	20.4946i	−0.422003	+	1.29879i
$250$	3.64872	+	11.2296i	0.230766	+	0.710223i
$251$	4.13154	−	3.00174i	0.260780	−	0.189468i	−0.449711	−	0.893174i	$-0.648473\pi$
$251$	4.13154	−	3.00174i	0.260780	−	0.189468i	0.710491	+	0.703706i	$0.248473\pi$
$252$	−5.14138			−0.323877
$253$	−4.97645	−	10.6121i	−0.312867	−	0.667178i
$254$	16.5260			1.03694
$255$	28.1222	−	20.4320i	1.76108	−	1.27950i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	7.29476	−	22.4510i	0.455035	−	1.40045i	−0.416059	−	0.909337i	$-0.636589\pi$
$257$	7.29476	−	22.4510i	0.455035	−	1.40045i	0.871094	−	0.491116i	$-0.163411\pi$
$258$	2.54584	+	1.84966i	0.158497	+	0.115155i
$259$	−5.11235	−	3.71434i	−0.317666	−	0.230798i
$260$	−1.76749	+	5.43976i	−0.109615	+	0.337360i
$261$	−11.8204	−	36.3793i	−0.731661	−	2.25182i
$262$	12.0509	−	8.75549i	0.744507	−	0.540916i
$263$	−0.344345			−0.0212332			−0.0106166	−	0.999944i	$-0.503379\pi$
$263$	−0.344345			−0.0212332			−0.0106166	+	0.999944i	$0.503379\pi$
$264$	9.13921	+	5.04017i	0.562479	+	0.310201i
$265$	8.12001			0.498808
$266$	−0.481681	+	0.349962i	−0.0295337	+	0.0214575i
$267$	6.98383	+	21.4940i	0.427404	+	1.31541i
$268$	1.58746	−	4.88569i	0.0969693	−	0.298441i
$269$	8.80409	+	6.39655i	0.536795	+	0.390004i	0.822893	−	0.568196i	$-0.192358\pi$
$269$	8.80409	+	6.39655i	0.536795	+	0.390004i	−0.286098	+	0.958200i	$0.592358\pi$
$270$	15.5137	+	11.2714i	0.944133	+	0.685953i
$271$	−7.00767	+	21.5674i	−0.425686	+	1.31013i	0.476650	+	0.879093i	$0.341851\pi$
$271$	−7.00767	+	21.5674i	−0.425686	+	1.31013i	−0.902336	+	0.431033i	$0.858149\pi$
$272$	2.18609	+	6.72810i	0.132551	+	0.407951i
$273$	6.94613	−	5.04666i	0.420399	−	0.305438i
$274$	9.91787			0.599160
$275$	−6.20154	+	5.80812i	−0.373967	+	0.350243i
$276$	11.1210			0.669404
$277$	15.6273	−	11.3539i	0.938954	−	0.682190i	−0.00921486	−	0.999958i	$-0.502933\pi$
$277$	15.6273	−	11.3539i	0.938954	−	0.682190i	0.948169	+	0.317768i	$0.102933\pi$
$278$	2.72959	+	8.40081i	0.163710	+	0.503847i
$279$	14.8681	−	45.7592i	0.890128	−	2.73953i
$280$	−0.940930	−	0.683625i	−0.0562313	−	0.0408544i
$281$	−4.67311	−	3.39521i	−0.278774	−	0.202541i	0.439608	−	0.898190i	$-0.355117\pi$
$281$	−4.67311	−	3.39521i	−0.278774	−	0.202541i	−0.718383	+	0.695648i	$0.755117\pi$
$282$	4.92746	−	15.1652i	0.293426	−	0.903073i
$283$	0.603230	+	1.85655i	0.0358583	+	0.110361i	0.967384	−	0.253316i	$-0.0815213\pi$
$283$	0.603230	+	1.85655i	0.0358583	+	0.110361i	−0.931525	+	0.363677i	$0.881521\pi$
$284$	6.75568	−	4.90829i	0.400876	−	0.291253i
$285$	3.92770			0.232657
$286$	−12.0552	+	1.50663i	−0.712837	+	0.0890889i
$287$	−7.22128			−0.426259
$288$	−5.58431	+	4.05724i	−0.329058	+	0.239075i
$289$	10.2119	+	31.4289i	0.600699	+	1.84876i
$290$	2.67393	−	8.22951i	0.157018	−	0.483253i
$291$	31.8031	+	23.1063i	1.86433	+	1.35452i
$292$	−4.56408	−	3.31600i	−0.267092	−	0.194054i
$293$	−2.01792	+	6.21052i	−0.117888	+	0.362822i	−0.992538	−	0.121932i	$-0.961091\pi$
$293$	−2.01792	+	6.21052i	−0.117888	+	0.362822i	0.874650	+	0.484754i	$0.161091\pi$
$294$	−6.26748	−	19.2893i	−0.365527	−	1.12498i
$295$	−17.2265	+	12.5158i	−1.00297	+	0.728697i
$296$	−8.48388			−0.493116
$297$	−7.68541	+	39.9991i	−0.445953	+	2.32099i
$298$	−22.9155			−1.32746
$299$	−10.4729	+	7.60904i	−0.605666	+	0.440042i
$300$	−2.49120	−	7.66713i	−0.143830	−	0.442662i
$301$	0.230171	−	0.708394i	0.0132668	−	0.0408311i
$302$	2.89806	+	2.10556i	0.166764	+	0.121161i
$303$	23.6751	+	17.2010i	1.36010	+	0.988171i
$304$	−0.247011	+	0.760220i	−0.0141670	+	0.0436016i
$305$	−3.53716	−	10.8862i	−0.202537	−	0.623345i
$306$	−39.5053	+	28.7023i	−2.25837	+	1.64080i
$307$	−18.1071			−1.03343			−0.516713	−	0.856159i	$-0.672845\pi$
$307$	−18.1071			−1.03343			−0.516713	+	0.856159i	$0.672845\pi$
$308$	0.466132	−	2.42601i	0.0265604	−	0.138235i
$309$	13.8002			0.785065
$310$	8.80540	−	6.39750i	0.500113	−	0.363353i
$311$	−2.42939	−	7.47689i	−0.137758	−	0.423976i	0.858251	−	0.513231i	$-0.171551\pi$
$311$	−2.42939	−	7.47689i	−0.137758	−	0.423976i	−0.996009	+	0.0892549i	$0.971551\pi$
$312$	3.56204	−	10.9628i	0.201661	−	0.620649i
$313$	−17.9767	−	13.0608i	−1.01610	−	0.738241i	−0.0506212	−	0.998718i	$-0.516120\pi$
$313$	−17.9767	−	13.0608i	−1.01610	−	0.738241i	−0.965480	+	0.260477i	$0.916120\pi$
$314$	−1.06714	−	0.775323i	−0.0602223	−	0.0437540i
$315$	2.48081	−	7.63515i	0.139778	−	0.430192i
$316$	0.712642	+	2.19329i	0.0400893	+	0.123382i
$317$	15.4944	−	11.2574i	0.870255	−	0.632277i	−0.0604005	−	0.998174i	$-0.519238\pi$
$317$	15.4944	−	11.2574i	0.870255	−	0.632277i	0.930655	+	0.365897i	$0.119238\pi$
$318$	−16.3644			−0.917669
$319$	18.2376	−	2.27929i	1.02111	−	0.127616i
$320$	−1.56146			−0.0872883
$321$	−1.55718	+	1.13136i	−0.0869134	+	0.0631463i
$322$	−0.813429	−	2.50348i	−0.0453306	−	0.139513i
$323$	−1.74744	+	5.37806i	−0.0972300	+	0.299243i
$324$	−14.5121	−	10.5436i	−0.806226	−	0.585758i
$325$	7.59193	+	5.51586i	0.421125	+	0.305965i
$326$	3.23673	−	9.96162i	0.179266	−	0.551723i
$327$	14.5334	+	44.7291i	0.803698	+	2.47353i
$328$	−7.84339	+	5.69855i	−0.433079	+	0.314650i
$329$	−3.77429			−0.208083
$330$	−11.8947	+	11.1401i	−0.654780	+	0.613242i
$331$	−1.30601			−0.0717845			−0.0358923	−	0.999356i	$-0.511427\pi$
$331$	−1.30601			−0.0717845			−0.0358923	+	0.999356i	$0.511427\pi$
$332$	5.54008	−	4.02510i	0.304051	−	0.220906i
$333$	−18.0963	−	55.6946i	−0.991669	−	3.05204i
$334$	4.95235	−	15.2418i	0.270981	−	0.833993i
$335$	6.48945	+	4.71486i	0.354557	+	0.257600i
$336$	1.89627	+	1.37772i	0.103450	+	0.0751609i
$337$	−10.9454	+	33.6864i	−0.596232	+	1.83501i	−0.0477378	+	0.998860i	$0.515201\pi$
$337$	−10.9454	+	33.6864i	−0.596232	+	1.83501i	−0.548494	+	0.836154i	$0.684799\pi$
$338$	0.129143	+	0.397461i	0.00702445	+	0.0216190i
$339$	−29.6075	+	21.5111i	−1.60806	+	1.16832i
$340$	−11.0463			−0.599070
$341$	20.2439	+	11.1643i	1.09627	+	0.604580i
$342$	−5.51753			−0.298354
$343$	−8.10202	+	5.88646i	−0.437468	+	0.317839i
$344$	−0.309017	−	0.951057i	−0.0166611	−	0.0512775i
$345$	−5.36607	+	16.5151i	−0.288900	+	0.889141i
$346$	−10.0412	−	7.29536i	−0.539819	−	0.392201i
$347$	−9.29556	−	6.75362i	−0.499012	−	0.362553i	0.309628	−	0.950858i	$-0.399796\pi$
$347$	−9.29556	−	6.75362i	−0.499012	−	0.362553i	−0.808639	+	0.588305i	$0.799796\pi$
$348$	−5.38881	+	16.5851i	−0.288871	+	0.889052i
$349$	0.515982	+	1.58803i	0.0276199	+	0.0850052i	0.963916	−	0.266206i	$-0.0857700\pi$
$349$	0.515982	+	1.58803i	0.0276199	+	0.0850052i	−0.936296	+	0.351211i	$0.885770\pi$
$350$	−1.54375	+	1.12160i	−0.0825171	+	0.0599522i
$351$	44.9851			2.40113
$352$	−1.40816	−	3.00285i	−0.0750550	−	0.160052i
$353$	3.47036			0.184708			0.0923542	−	0.995726i	$-0.470561\pi$
$353$	3.47036			0.184708			0.0923542	+	0.995726i	$0.470561\pi$
$354$	34.7168	−	25.2233i	1.84518	−	1.34060i
$355$	4.02926	+	12.4008i	0.213851	+	0.658165i
$356$	2.21932	−	6.83036i	0.117624	−	0.362008i
$357$	13.4149	+	9.74647i	0.709990	+	0.515838i
$358$	−5.19985	−	3.77791i	−0.274820	−	0.199669i
$359$	2.29373	−	7.05936i	0.121058	−	0.372579i	−0.872104	−	0.489320i	$-0.837245\pi$
$359$	2.29373	−	7.05936i	0.121058	−	0.372579i	0.993162	+	0.116741i	$0.0372449\pi$
$360$	−3.33062	−	10.2506i	−0.175539	−	0.540254i
$361$	14.8544	−	10.7924i	0.781811	−	0.568019i
$362$	−15.8179			−0.831371
$363$	−32.1504	−	12.8283i	−1.68746	−	0.673312i
$364$	−2.72842			−0.143008
$365$	7.12663	−	5.17780i	0.373025	−	0.271018i
$366$	7.12849	+	21.9392i	0.372612	+	1.14678i
$367$	−5.79430	+	17.8330i	−0.302460	+	0.930876i	0.678153	+	0.734921i	$0.262781\pi$
$367$	−5.79430	+	17.8330i	−0.302460	+	0.930876i	−0.980613	+	0.195955i	$0.937219\pi$
$368$	−2.85908	−	2.07724i	−0.149040	−	0.108284i
$369$	−54.1396	−	39.3347i	−2.81840	−	2.04768i
$370$	4.09363	−	12.5989i	0.212817	−	0.654985i
$371$	1.19695	+	3.68384i	0.0621426	+	0.191255i
$372$	−17.7457	+	12.8930i	−0.920070	+	0.668470i
$373$	−10.3723			−0.537058			−0.268529	−	0.963272i	$-0.586538\pi$
$373$	−10.3723			−0.537058			−0.268529	+	0.963272i	$0.586538\pi$
$374$	−9.96178	−	21.2432i	−0.515111	−	1.09846i
$375$	37.1563			1.91874
$376$	−4.09944	+	2.97842i	−0.211412	+	0.153600i
$377$	−6.27280	−	19.3057i	−0.323065	−	0.994293i
$378$	−2.82668	+	8.69964i	−0.145389	+	0.447461i
$379$	6.58623	+	4.78518i	0.338312	+	0.245798i	0.743949	−	0.668236i	$-0.232950\pi$
$379$	6.58623	+	4.78518i	0.338312	+	0.245798i	−0.405637	+	0.914034i	$0.632950\pi$
$380$	−1.00977	−	0.733640i	−0.0518000	−	0.0376349i
$381$	16.0703	−	49.4594i	0.823308	−	2.53388i
$382$	−3.61603	−	11.1290i	−0.185012	−	0.569408i
$383$	−4.46486	+	3.24391i	−0.228143	+	0.165756i	−0.695985	−	0.718057i	$-0.745032\pi$
$383$	−4.46486	+	3.24391i	−0.228143	+	0.165756i	0.467841	+	0.883813i	$0.345032\pi$
$384$	3.14684			0.160586
$385$	3.37780	+	1.86282i	0.172149	+	0.0949380i
$386$	19.1728			0.975868
$387$	5.58431	−	4.05724i	0.283866	−	0.206241i
$388$	−3.86029	−	11.8808i	−0.195977	−	0.603154i
$389$	−7.62360	+	23.4630i	−0.386532	+	1.18962i	0.548831	+	0.835933i	$0.315073\pi$
$389$	−7.62360	+	23.4630i	−0.386532	+	1.18962i	−0.935363	+	0.353689i	$0.884927\pi$
$390$	14.5615	+	10.5795i	0.737349	+	0.535715i
$391$	−20.2261	−	14.6951i	−1.02288	−	0.743165i
$392$	−1.99168	+	6.12975i	−0.100595	+	0.309599i
$393$	−14.4850	−	44.5802i	−0.730671	−	2.24878i
$394$	−16.0046	+	11.6280i	−0.806299	+	0.585811i
$395$	−3.60098			−0.181185
$396$	16.7093	−	15.6493i	0.839675	−	0.786407i
$397$	−22.0520			−1.10676			−0.553378	−	0.832930i	$-0.686661\pi$
$397$	−22.0520			−1.10676			−0.553378	+	0.832930i	$0.686661\pi$
$398$	10.6371	−	7.72828i	0.533188	−	0.387384i
$399$	0.578973	+	1.78190i	0.0289849	+	0.0892063i
$400$	−0.791652	+	2.43646i	−0.0395826	+	0.121823i
$401$	−14.5949	−	10.6039i	−0.728837	−	0.529531i	0.160358	−	0.987059i	$-0.448735\pi$
$401$	−14.5949	−	10.6039i	−0.728837	−	0.529531i	−0.889195	+	0.457528i	$0.848735\pi$
$402$	−13.0783	−	9.50194i	−0.652286	−	0.473914i
$403$	7.89015	−	24.2834i	0.393036	−	1.20964i
$404$	−2.87371	−	8.84436i	−0.142972	−	0.440024i
$405$	22.6600	−	16.4635i	1.12599	−	0.818077i
$406$	4.12767			0.204853
$407$	27.9207	−	3.48946i	1.38398	−	0.172966i
$408$	22.2618			1.10212
$409$	−10.3515	+	7.52080i	−0.511848	+	0.371879i	−0.813524	−	0.581531i	$-0.802454\pi$
$409$	−10.3515	+	7.52080i	−0.511848	+	0.371879i	0.301676	+	0.953410i	$0.402454\pi$
$410$	−4.67799	−	14.3974i	−0.231029	−	0.711036i
$411$	9.64439	−	29.6824i	0.475723	−	1.46412i
$412$	−3.54788	−	2.57768i	−0.174791	−	0.126993i
$413$	−8.21740	−	5.97029i	−0.404352	−	0.293779i
$414$	7.53812	−	23.1999i	0.370478	−	1.14021i
$415$	3.30424	+	10.1694i	0.162199	+	0.499196i
$416$	−2.96347	+	2.15309i	−0.145296	+	0.105564i
$417$	27.7964			1.36120
$418$	0.500235	−	2.60350i	0.0244673	−	0.127341i
$419$	−27.2610			−1.33179			−0.665895	−	0.746046i	$-0.731950\pi$
$419$	−27.2610			−1.33179			−0.665895	+	0.746046i	$0.731950\pi$
$420$	−2.96095	+	2.15126i	−0.144480	+	0.104971i
$421$	−9.08194	−	27.9513i	−0.442626	−	1.36226i	−0.885066	−	0.465466i	$-0.845887\pi$
$421$	−9.08194	−	27.9513i	−0.442626	−	1.36226i	0.442439	−	0.896798i	$-0.354113\pi$
$422$	1.27656	−	3.92886i	0.0621421	−	0.191254i
$423$	−28.2967	−	20.5588i	−1.37583	−	0.999601i
$424$	4.20710	+	3.05664i	0.204315	+	0.148444i
$425$	−5.60042	+	17.2363i	−0.271660	+	0.836084i
$426$	−8.12023	−	24.9915i	−0.393426	−	1.21084i
$427$	4.41740	−	3.20943i	0.213773	−	0.155315i
$428$	0.611656			0.0295655
$429$	−7.21369	+	37.5440i	−0.348280	+	1.81264i
$430$	1.56146			0.0753003
$431$	21.7014	−	15.7670i	1.04532	−	0.759469i	0.0740030	−	0.997258i	$-0.476423\pi$
$431$	21.7014	−	15.7670i	1.04532	−	0.759469i	0.971317	+	0.237789i	$0.0764226\pi$
$432$	3.79497	+	11.6797i	0.182586	+	0.561941i
$433$	−9.63381	+	29.6498i	−0.462971	+	1.42488i	0.398545	+	0.917149i	$0.369515\pi$
$433$	−9.63381	+	29.6498i	−0.462971	+	1.42488i	−0.861516	+	0.507730i	$0.830485\pi$
$434$	4.20036	+	3.05174i	0.201624	+	0.146488i
$435$	−22.0292	−	16.0052i	−1.05622	−	0.767389i
$436$	4.61841	−	14.2140i	0.221182	−	0.680727i
$437$	−0.872940	−	2.68663i	−0.0417584	−	0.128519i
$438$	−14.3624	+	10.4349i	−0.686262	+	0.498599i
$439$	2.84100			0.135594			0.0677968	−	0.997699i	$-0.478403\pi$
$439$	2.84100			0.135594			0.0677968	+	0.997699i	$0.478403\pi$
$440$	5.13880	−	0.642236i	0.244983	−	0.0306174i
$441$	−44.4885			−2.11850
$442$	−20.9646	+	15.2317i	−0.997184	+	0.724496i
$443$	7.28767	+	22.4292i	0.346248	+	1.06564i	0.960912	+	0.276853i	$0.0892914\pi$
$443$	7.28767	+	22.4292i	0.346248	+	1.06564i	−0.614665	+	0.788789i	$0.710709\pi$
$444$	−8.24995	+	25.3907i	−0.391525	+	1.20499i
$445$	9.07248	+	6.59154i	0.430077	+	0.312469i
$446$	22.5334	+	16.3715i	1.06699	+	0.775211i
$447$	−22.2836	+	68.5819i	−1.05398	+	3.24381i
$448$	−0.230171	−	0.708394i	−0.0108746	−	0.0334685i
$449$	−12.4354	+	9.03484i	−0.586862	+	0.426380i	−0.841191	−	0.540737i	$-0.818145\pi$
$449$	−12.4354	+	9.03484i	−0.586862	+	0.426380i	0.254329	+	0.967118i	$0.418145\pi$
$450$	−17.6833			−0.833600
$451$	23.4689	−	21.9801i	1.10511	−	1.03500i
$452$	11.6297			0.547017
$453$	9.11971	−	6.62586i	0.428482	−	0.311310i
$454$	7.43598	+	22.8856i	0.348988	+	1.07407i
$455$	1.31651	−	4.05180i	0.0617190	−	0.189951i
$456$	2.03500	+	1.47852i	0.0952977	+	0.0692379i
$457$	−13.1096	−	9.52471i	−0.613243	−	0.445547i	0.237312	−	0.971433i	$-0.423734\pi$
$457$	−13.1096	−	9.52471i	−0.613243	−	0.445547i	−0.850555	+	0.525887i	$0.823734\pi$
$458$	−0.0877910	+	0.270193i	−0.00410220	+	0.0126253i
$459$	26.8469	+	82.6264i	1.25311	+	3.85667i
$460$	4.46434	−	3.24353i	0.208151	−	0.151231i
$461$	−4.62392			−0.215357			−0.107679	−	0.994186i	$-0.534342\pi$
$461$	−4.62392			−0.215357			−0.107679	+	0.994186i	$0.534342\pi$
$462$	−6.80733	−	3.75417i	−0.316706	−	0.174660i
$463$	39.3229			1.82749			0.913746	−	0.406286i	$-0.133176\pi$
$463$	39.3229			1.82749			0.913746	+	0.406286i	$0.133176\pi$
$464$	4.48326	−	3.25728i	0.208130	−	0.151215i
$465$	−10.5840	−	32.5741i	−0.490819	−	1.51059i
$466$	−5.39319	+	16.5985i	−0.249835	+	0.768912i
$467$	−14.9064	−	10.8301i	−0.689786	−	0.501159i	0.186804	−	0.982397i	$-0.440187\pi$
$467$	−14.9064	−	10.8301i	−0.689786	−	0.501159i	−0.876590	+	0.481238i	$0.840187\pi$
$468$	−20.4556	−	14.8618i	−0.945560	−	0.686989i
$469$	−1.18242	+	3.63910i	−0.0545989	+	0.168038i
$470$	−2.44501	−	7.52496i	−0.112780	−	0.347100i
$471$	−3.35812	+	2.43982i	−0.154734	+	0.112421i
$472$	−13.6367			−0.627678
$473$	1.40816	+	3.00285i	0.0647471	+	0.138071i
$474$	7.25711			0.333330
$475$	−1.65670	+	1.20366i	−0.0760144	+	0.0552277i
$476$	−1.62831	−	5.01142i	−0.0746334	−	0.229698i
$477$	−11.0922	+	34.1384i	−0.507879	+	1.56309i
$478$	−12.8489	−	9.33530i	−0.587697	−	0.426987i
$479$	−14.9312	−	10.8481i	−0.682222	−	0.495663i	0.191872	−	0.981420i	$-0.438544\pi$
$479$	−14.9312	−	10.8481i	−0.682222	−	0.495663i	−0.874094	+	0.485757i	$0.838544\pi$
$480$	−1.51841	+	4.67317i	−0.0693054	+	0.213300i
$481$	−9.60328	−	29.5559i	−0.437872	−	1.34763i
$482$	−4.48578	+	3.25911i	−0.204322	+	0.148448i
$483$	−8.28345			−0.376910
$484$	5.86936	+	9.30326i	0.266789	+	0.422875i
$485$	19.5060			0.885724
$486$	−15.8610	+	11.5237i	−0.719470	+	0.522726i
$487$	−2.01417	−	6.19897i	−0.0912707	−	0.280902i	0.894993	−	0.446080i	$-0.147180\pi$
$487$	−2.01417	−	6.19897i	−0.0912707	−	0.280902i	−0.986264	+	0.165178i	$0.947180\pi$
$488$	2.26529	−	6.97184i	0.102545	−	0.315600i
$489$	−26.6659	−	19.3739i	−1.20587	−	0.876117i
$490$	−8.14189	−	5.91543i	−0.367813	−	0.267232i
$491$	−1.71297	+	5.27196i	−0.0773050	+	0.237920i	−0.982240	−	0.187630i	$-0.939919\pi$
$491$	−1.71297	+	5.27196i	−0.0773050	+	0.237920i	0.904935	+	0.425550i	$0.139919\pi$
$492$	9.42763	+	29.0153i	0.425030	+	1.30811i
$493$	31.7161	−	23.0431i	1.42842	−	1.03781i
$494$	−2.92803			−0.131738
$495$	15.1773	+	32.3650i	0.682167	+	1.45470i
$496$	6.97044			0.312982
$497$	−5.03196	+	3.65594i	−0.225714	+	0.163991i
$498$	−6.65909	−	20.4946i	−0.298401	−	0.918384i
$499$	10.5246	−	32.3914i	0.471146	−	1.45004i	−0.379940	−	0.925011i	$-0.624055\pi$
$499$	10.5246	−	32.3914i	0.471146	−	1.45004i	0.851086	−	0.525026i	$-0.175945\pi$
$500$	−9.55248	−	6.94028i	−0.427200	−	0.310379i
$501$	−40.8001	−	29.6430i	−1.82281	−	1.32435i
$502$	−1.57811	+	4.85692i	−0.0704344	+	0.216775i
$503$	−5.66713	−	17.4416i	−0.252685	−	0.777684i	−0.994277	−	0.106833i	$-0.965929\pi$
$503$	−5.66713	−	17.4416i	−0.252685	−	0.777684i	0.741592	−	0.670851i	$-0.234071\pi$
$504$	4.15947	−	3.02203i	0.185277	−	0.134612i
$505$	14.5208			0.646168
$506$	10.2637	+	5.66030i	0.456276	+	0.251631i
$507$	1.31511			0.0584062
$508$	−13.3698	+	9.71376i	−0.593191	+	0.430978i
$509$	−12.7864	−	39.3525i	−0.566748	−	1.74427i	−0.662700	−	0.748885i	$-0.730590\pi$
$509$	−12.7864	−	39.3525i	−0.566748	−	1.74427i	0.0959520	−	0.995386i	$-0.469410\pi$
$510$	−10.7417	+	33.0596i	−0.475651	+	1.46390i
$511$	3.39955	+	2.46992i	0.150387	+	0.109263i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−3.03349	+	9.33611i	−0.133932	+	0.412199i
$514$	7.29476	+	22.4510i	0.321758	+	0.990270i
$515$	5.53987	−	4.02495i	0.244116	−	0.177361i
$516$	−3.14684			−0.138532
$517$	12.2663	−	11.4882i	0.539471	−	0.505248i
$518$	6.31922			0.277650
$519$	−31.5980	+	22.9573i	−1.38700	+	1.00771i
$520$	−1.76749	−	5.43976i	−0.0775094	−	0.238549i
$521$	−7.69146	+	23.6719i	−0.336969	+	1.03708i	0.628775	+	0.777587i	$0.283557\pi$
$521$	−7.69146	+	23.6719i	−0.336969	+	1.03708i	−0.965744	+	0.259496i	$0.916443\pi$
$522$	30.9461	+	22.4836i	1.35447	+	0.984082i
$523$	29.3745	+	21.3418i	1.28446	+	0.933213i	0.999678	−	0.0253801i	$-0.00807959\pi$
$523$	29.3745	+	21.3418i	1.28446	+	0.933213i	0.284780	+	0.958593i	$0.408080\pi$
$524$	−4.60303	+	14.1667i	−0.201084	+	0.618874i
$525$	1.85557	+	5.71086i	0.0809837	+	0.249242i
$526$	0.278581	−	0.202401i	0.0121467	−	0.00882510i
$527$	49.3113			2.14803
$528$	−10.3563	+	1.29431i	−0.450701	+	0.0563276i
$529$	−10.5107			−0.456988
$530$	−6.56923	+	4.77282i	−0.285349	+	0.207318i
$531$	−29.0872	−	89.5212i	−1.26228	−	3.88489i
$532$	0.183986	−	0.566250i	0.00797679	−	0.0245500i
$533$	−28.7307	−	20.8741i	−1.24446	−	0.904156i
$534$	−18.2839	−	13.2840i	−0.791222	−	0.574857i
$535$	−0.295135	+	0.908332i	−0.0127598	+	0.0392706i
$536$	1.58746	+	4.88569i	0.0685677	+	0.211030i
$537$	−16.3631	+	11.8885i	−0.706119	+	0.513025i
$538$	−10.8825			−0.469176
$539$	4.03346	−	20.9923i	0.173733	−	0.904204i
$540$	−19.1760			−0.825203
$541$	5.76009	−	4.18495i	0.247646	−	0.179925i	−0.457037	−	0.889448i	$-0.651089\pi$
$541$	5.76009	−	4.18495i	0.247646	−	0.179925i	0.704683	+	0.709523i	$0.251089\pi$
$542$	−7.00767	−	21.5674i	−0.301005	−	0.926399i
$543$	−15.3817	+	47.3402i	−0.660094	+	2.03156i
$544$	−5.72326	−	4.15819i	−0.245383	−	0.178281i
$545$	18.8799	+	13.7170i	0.808724	+	0.587573i
$546$	−2.65319	+	8.16566i	−0.113546	+	0.349458i
$547$	0.570368	+	1.75541i	0.0243872	+	0.0750560i	0.962509	−	0.271248i	$-0.0874365\pi$
$547$	0.570368	+	1.75541i	0.0243872	+	0.0750560i	−0.938122	+	0.346304i	$0.887436\pi$
$548$	−8.02372	+	5.82958i	−0.342756	+	0.249027i
$549$	50.6002			2.15957
$550$	1.60322	−	8.34404i	0.0683615	−	0.355791i
$551$	4.42965			0.188709
$552$	−8.99706	+	6.53675i	−0.382940	+	0.278222i
$553$	−0.530811	−	1.63367i	−0.0225724	−	0.0694707i
$554$	−5.96910	+	18.3710i	−0.253603	+	0.780509i
$555$	−33.7254	−	24.5030i	−1.43157	−	1.04009i
$556$	−7.14615	−	5.19198i	−0.303064	−	0.220189i
$557$	−11.2133	+	34.5109i	−0.475121	+	1.46227i	0.370673	+	0.928764i	$0.379127\pi$
$557$	−11.2133	+	34.5109i	−0.475121	+	1.46227i	−0.845794	+	0.533509i	$0.820873\pi$
$558$	14.8681	+	45.7592i	0.629415	+	1.93714i
$559$	2.96347	−	2.15309i	0.125341	−	0.0910658i
$560$	1.16305			0.0491480
$561$	−73.2641	+	9.15639i	−3.09321	+	0.386583i
$562$	5.77628			0.243658
$563$	30.6780	−	22.2889i	1.29292	−	0.939363i	0.293063	−	0.956093i	$-0.405326\pi$
$563$	30.6780	−	22.2889i	1.29292	−	0.939363i	0.999860	+	0.0167300i	$0.00532556\pi$
$564$	4.92746	+	15.1652i	0.207484	+	0.638569i
$565$	−5.61156	+	17.2706i	−0.236080	+	0.726580i
$566$	−1.57928	−	1.14741i	−0.0663820	−	0.0482293i
$567$	10.8093	+	7.85342i	0.453948	+	0.329813i
$568$	−2.58044	+	7.94178i	−0.108273	+	0.333230i
$569$	7.13701	+	21.9655i	0.299199	+	0.920841i	0.981778	+	0.190029i	$0.0608582\pi$
$569$	7.13701	+	21.9655i	0.299199	+	0.920841i	−0.682579	+	0.730812i	$0.739142\pi$
$570$	−3.17758	+	2.30864i	−0.133094	+	0.0966985i
$571$	24.9337			1.04344			0.521722	−	0.853116i	$-0.325290\pi$
$571$	24.9337			1.04344			0.521722	+	0.853116i	$0.325290\pi$
$572$	8.86726	−	8.30474i	0.370759	−	0.347239i
$573$	−36.8234			−1.53832
$574$	5.84214	−	4.24456i	0.243846	−	0.177165i
$575$	−2.79771	−	8.61048i	−0.116673	−	0.359082i
$576$	2.13302	−	6.56475i	0.0888756	−	0.273531i
$577$	−10.1486	−	7.37335i	−0.422490	−	0.306957i	0.356149	−	0.934429i	$-0.384090\pi$
$577$	−10.1486	−	7.37335i	−0.422490	−	0.306957i	−0.778639	+	0.627472i	$0.784090\pi$
$578$	−26.7350	−	19.4241i	−1.11203	−	0.807938i
$579$	18.6441	−	57.3807i	0.774823	−	2.38466i
$580$	2.67393	+	8.22951i	0.111029	+	0.341712i
$581$	−4.12652	+	2.99809i	−0.171197	+	0.124382i
$582$	−39.3108			−1.62949
$583$	−15.1029	−	8.32907i	−0.625497	−	0.344955i
$584$	5.64151			0.233447
$585$	31.9406	−	23.2062i	1.32058	−	0.959458i
$586$	−2.01792	−	6.21052i	−0.0833595	−	0.256554i
$587$	−6.91734	+	21.2894i	−0.285509	+	0.878707i	0.700737	+	0.713420i	$0.252855\pi$
$587$	−6.91734	+	21.2894i	−0.285509	+	0.878707i	−0.986246	+	0.165286i	$0.947145\pi$
$588$	16.4085	+	11.9215i	0.676674	+	0.491633i
$589$	4.50766	+	3.27501i	0.185735	+	0.134944i
$590$	6.57993	−	20.2510i	0.270892	−	0.833719i
$591$	19.2373	+	59.2062i	0.791315	+	2.43542i
$592$	6.86361	−	4.98670i	0.282093	−	0.204952i
$593$	26.1069			1.07208			0.536041	−	0.844192i	$-0.319919\pi$
$593$	26.1069			1.07208			0.536041	+	0.844192i	$0.319919\pi$
$594$	−17.2933	−	36.8774i	−0.709552	−	1.51310i
$595$	8.22784			0.337308
$596$	18.5390	−	13.4694i	0.759388	−	0.551727i
$597$	−12.7856	−	39.3500i	−0.523279	−	1.61049i
$598$	4.00031	−	12.3117i	0.163585	−	0.503462i
$599$	12.0784	+	8.77551i	0.493512	+	0.358557i	0.806533	−	0.591189i	$-0.201341\pi$
$599$	12.0784	+	8.77551i	0.493512	+	0.358557i	−0.313021	+	0.949746i	$0.601341\pi$
$600$	6.52205	+	4.73855i	0.266262	+	0.193450i
$601$	−1.29021	+	3.97087i	−0.0526289	+	0.161975i	−0.973916	−	0.226907i	$-0.927139\pi$
$601$	−1.29021	+	3.97087i	−0.0526289	+	0.161975i	0.921288	+	0.388882i	$0.127139\pi$
$602$	0.230171	+	0.708394i	0.00938107	+	0.0288720i
$603$	−28.6872	+	20.8425i	−1.16823	+	0.848772i
$604$	−3.58220			−0.145757
$605$	−16.6478	+	4.22723i	−0.676828	+	0.171861i
$606$	−29.2641			−1.18877
$607$	1.45704	−	1.05860i	0.0591393	−	0.0429672i	−0.557823	−	0.829960i	$-0.688363\pi$
$607$	1.45704	−	1.05860i	0.0591393	−	0.0429672i	0.616962	+	0.786993i	$0.288363\pi$
$608$	−0.247011	−	0.760220i	−0.0100176	−	0.0308310i
$609$	4.01385	−	12.3534i	0.162650	−	0.500584i
$610$	9.26040	+	6.72807i	0.374942	+	0.272412i
$611$	−15.0164	−	10.9101i	−0.607500	−	0.441375i
$612$	15.0897	−	46.4413i	0.609964	−	1.87728i
$613$	−0.682283	−	2.09985i	−0.0275571	−	0.0848122i	0.936332	−	0.351116i	$-0.114198\pi$
$613$	−0.682283	−	2.09985i	−0.0275571	−	0.0848122i	−0.963889	+	0.266304i	$0.914198\pi$
$614$	14.6489	−	10.6431i	0.591183	−	0.429520i
$615$	−47.6377			−1.92094
$616$	1.04886	+	2.23667i	0.0422599	+	0.0901180i
$617$	23.9334			0.963521			0.481761	−	0.876303i	$-0.339997\pi$
$617$	23.9334			0.963521			0.481761	+	0.876303i	$0.339997\pi$
$618$	−11.1646	+	8.11155i	−0.449106	+	0.326294i
$619$	−8.17301	−	25.1539i	−0.328501	−	1.01102i	−0.969835	−	0.243760i	$-0.921619\pi$
$619$	−8.17301	−	25.1539i	−0.328501	−	1.01102i	0.641335	−	0.767261i	$-0.278381\pi$
$620$	−3.36336	+	10.3514i	−0.135076	+	0.415721i
$621$	−35.1118	−	25.5102i	−1.40899	−	1.02369i
$622$	6.36022	+	4.62097i	0.255022	+	0.185284i
$623$	−1.65306	+	5.08759i	−0.0662284	+	0.203830i
$624$	3.56204	+	10.9628i	0.142596	+	0.438865i
$625$	4.55296	−	3.30792i	0.182118	−	0.132317i
$626$	22.2204			0.888105
$627$	−7.30536	−	4.02882i	−0.291748	−	0.160896i
$628$	1.31906			0.0526362
$629$	48.5555	−	35.2776i	1.93604	−	1.40661i
$630$	2.48081	+	7.63515i	0.0988378	+	0.304192i
$631$	3.70482	−	11.4023i	0.147487	−	0.453917i	−0.849836	−	0.527048i	$-0.823299\pi$
$631$	3.70482	−	11.4023i	0.147487	−	0.453917i	0.997322	+	0.0731305i	$0.0232989\pi$
$632$	−1.86572	−	1.35553i	−0.0742144	−	0.0539199i
$633$	−10.5170	−	7.64104i	−0.418013	−	0.303704i
$634$	−5.91835	+	18.2148i	−0.235048	+	0.723403i
$635$	−7.97410	−	24.5418i	−0.316443	−	0.973910i
$636$	13.2391	−	9.61875i	0.524963	−	0.381408i
$637$	−23.6091			−0.935425
$638$	−13.4148	+	12.5638i	−0.531096	+	0.497404i
$639$	−57.6399			−2.28020
$640$	1.26325	−	0.917804i	0.0499343	−	0.0362794i
$641$	13.9197	+	42.8404i	0.549795	+	1.69210i	0.709307	+	0.704900i	$0.249008\pi$
$641$	13.9197	+	42.8404i	0.549795	+	1.69210i	−0.159512	+	0.987196i	$0.550992\pi$
$642$	0.594791	−	1.83058i	0.0234745	−	0.0722471i
$643$	−26.0117	−	18.8986i	−1.02580	−	0.745288i	−0.0583368	−	0.998297i	$-0.518580\pi$
$643$	−26.0117	−	18.8986i	−1.02580	−	0.745288i	−0.967464	+	0.253009i	$0.918580\pi$
$644$	2.12958	+	1.54723i	0.0839174	+	0.0609695i
$645$	1.51841	−	4.67317i	0.0597871	−	0.184006i
$646$	−1.74744	−	5.37806i	−0.0687520	−	0.211597i
$647$	10.2472	−	7.44504i	0.402860	−	0.292695i	−0.367845	−	0.929887i	$-0.619904\pi$
$647$	10.2472	−	7.44504i	0.402860	−	0.292695i	0.770705	+	0.637192i	$0.219904\pi$
$648$	17.9379			0.704667
$649$	44.8786	−	5.60883i	1.76164	−	0.220166i
$650$	−9.38414			−0.368076
$651$	13.2178	−	9.60333i	0.518048	−	0.376384i
$652$	3.23673	+	9.96162i	0.126760	+	0.390127i
$653$	10.2340	−	31.4971i	0.400489	−	1.23258i	−0.524114	−	0.851648i	$-0.675604\pi$
$653$	10.2340	−	31.4971i	0.400489	−	1.23258i	0.924604	−	0.380931i	$-0.124396\pi$
$654$	−38.0489	−	27.6441i	−1.48783	−	1.08097i
$655$	−18.8170	−	13.6714i	−0.735241	−	0.534184i
$656$	2.99591	−	9.22045i	0.116971	−	0.359998i
$657$	12.0334	+	37.0351i	0.469469	+	1.44488i
$658$	3.05346	−	2.21847i	0.119036	−	0.0864850i
$659$	−23.7011			−0.923263			−0.461631	−	0.887072i	$-0.652736\pi$
$659$	−23.7011			−0.923263			−0.461631	+	0.887072i	$0.652736\pi$
$660$	3.07501	−	16.0040i	0.119695	−	0.622956i
$661$	37.5441			1.46030			0.730149	−	0.683288i	$-0.239451\pi$
$661$	37.5441			1.46030			0.730149	+	0.683288i	$0.239451\pi$
$662$	1.05658	−	0.767651i	0.0410652	−	0.0298356i
$663$	25.1991	+	77.5549i	0.978653	+	3.01198i
$664$	−2.11612	+	6.51275i	−0.0821214	+	0.252744i
$665$	0.752125	+	0.546451i	0.0291662	+	0.0211905i
$666$	47.3766	+	34.4211i	1.83581	+	1.33379i
$667$	−6.05184	+	18.6257i	−0.234328	+	0.721188i
$668$	4.95235	+	15.2418i	0.191612	+	0.589722i
$669$	70.9089	−	51.5183i	2.74149	−	1.99181i
$670$	−8.02140			−0.309894
$671$	−4.58756	+	23.8762i	−0.177101	+	0.921730i
$672$	−2.34392			−0.0904187
$673$	10.4207	−	7.57109i	0.401689	−	0.291844i	−0.368540	−	0.929612i	$-0.620142\pi$
$673$	10.4207	−	7.57109i	0.401689	−	0.291844i	0.770229	+	0.637768i	$0.220142\pi$
$674$	−10.9454	−	33.6864i	−0.421600	−	1.29755i
$675$	−9.72212	+	29.9216i	−0.374205	+	1.15168i
$676$	−0.338101	−	0.245645i	−0.0130039	−	0.00944787i
$677$	36.1494	+	26.2641i	1.38933	+	1.00941i	0.995938	+	0.0900411i	$0.0286998\pi$
$677$	36.1494	+	26.2641i	1.38933	+	1.00941i	0.393396	+	0.919369i	$0.371300\pi$
$678$	11.3091	−	34.8057i	0.434322	−	1.33671i
$679$	2.87534	+	8.84938i	0.110345	+	0.339608i
$680$	8.93665	−	6.49286i	0.342705	−	0.248990i
$681$	75.7234			2.90173
$682$	−22.9399	+	2.86698i	−0.878413	+	0.109782i
$683$	38.6706			1.47969			0.739845	−	0.672777i	$-0.234899\pi$
$683$	38.6706			1.47969			0.739845	+	0.672777i	$0.234899\pi$
$684$	4.46378	−	3.24312i	0.170677	−	0.124004i
$685$	−4.78555	−	14.7284i	−0.182846	−	0.562743i
$686$	3.09470	−	9.52450i	0.118156	−	0.363647i
$687$	0.723269	+	0.525485i	0.0275944	+	0.0200485i
$688$	0.809017	+	0.587785i	0.0308435	+	0.0224091i
$689$	−5.88641	+	18.1165i	−0.224254	+	0.690184i
$690$	−5.36607	−	16.5151i	−0.204283	−	0.628718i
$691$	2.39330	−	1.73883i	0.0910454	−	0.0661484i	−0.541331	−	0.840809i	$-0.682080\pi$
$691$	2.39330	−	1.73883i	0.0910454	−	0.0661484i	0.632377	+	0.774661i	$0.282080\pi$
$692$	12.4116			0.471819
$693$	−12.4459	+	11.6564i	−0.472782	+	0.442789i
$694$	11.4899			0.436152
$695$	11.1584	−	8.10708i	0.423264	−	0.307519i
$696$	−5.38881	−	16.5851i	−0.204262	−	0.628655i
$697$	21.1941	−	65.2287i	0.802783	−	2.47071i
$698$	−1.35086	−	0.981455i	−0.0511307	−	0.0371486i
$699$	44.4319	+	32.2817i	1.68057	+	1.22101i
$700$	0.589662	−	1.81479i	0.0222871	−	0.0685927i
$701$	−9.32129	−	28.6880i	−0.352060	−	1.08353i	−0.957695	−	0.287787i	$-0.907081\pi$
$701$	−9.32129	−	28.6880i	−0.352060	−	1.08353i	0.605634	−	0.795743i	$-0.292919\pi$
$702$	−36.3937	+	26.4416i	−1.37359	+	0.997974i
$703$	6.78153			0.255770
$704$	2.90425	+	1.60166i	0.109458	+	0.0603649i
$705$	−24.8984			−0.937729
$706$	−2.80758	+	2.03982i	−0.105665	+	0.0767698i
$707$	2.14048	+	6.58772i	0.0805010	+	0.247757i
$708$	−13.2606	+	40.8121i	−0.498366	+	1.53381i
$709$	11.7131	+	8.51009i	0.439896	+	0.319603i	0.785594	−	0.618743i	$-0.212358\pi$
$709$	11.7131	+	8.51009i	0.439896	+	0.319603i	−0.345698	+	0.938346i	$0.612358\pi$
$710$	−10.5487	−	7.66410i	−0.395887	−	0.287629i
$711$	4.91907	−	15.1394i	0.184480	−	0.567770i
$712$	2.21932	+	6.83036i	0.0831725	+	0.255979i
$713$	−19.9291	+	14.4793i	−0.746349	+	0.542254i
$714$	−16.5817			−0.620554
$715$	8.05424	+	17.1754i	0.301211	+	0.642324i
$716$	6.42736			0.240202
$717$	−40.4335	+	29.3767i	−1.51002	+	1.09709i
$718$	2.29373	+	7.05936i	0.0856011	+	0.263453i
$719$	−10.0934	+	31.0643i	−0.376421	+	1.15850i	0.566095	+	0.824340i	$0.308454\pi$
$719$	−10.0934	+	31.0643i	−0.376421	+	1.15850i	−0.942515	+	0.334163i	$0.891546\pi$
$720$	8.71968	+	6.33522i	0.324963	+	0.236100i
$721$	2.64263	+	1.91999i	0.0984168	+	0.0715040i
$722$	−5.67388	+	17.4624i	−0.211160	+	0.649883i
$723$	5.39184	+	16.5944i	0.200525	+	0.617152i
$724$	12.7970	−	9.29753i	0.475595	−	0.345540i
$725$	14.1967			0.527254
$726$	33.5505	−	8.51920i	1.24518	−	0.316177i
$727$	6.76237			0.250802			0.125401	−	0.992106i	$-0.459978\pi$
$727$	6.76237			0.250802			0.125401	+	0.992106i	$0.459978\pi$
$728$	2.20734	−	1.60372i	0.0818093	−	0.0594380i
$729$	2.43534	+	7.49520i	0.0901977	+	0.277600i
$730$	−2.72213	+	8.37785i	−0.100751	+	0.310078i
$731$	5.72326	+	4.15819i	0.211683	+	0.153796i
$732$	−18.6626	−	13.5592i	−0.689791	−	0.501162i
$733$	−0.405555	+	1.24817i	−0.0149795	+	0.0461023i	−0.958267	−	0.285875i	$-0.907716\pi$
$733$	−0.405555	+	1.24817i	−0.0149795	+	0.0461023i	0.943287	+	0.331977i	$0.107716\pi$
$734$	−5.79430	−	17.8330i	−0.213871	−	0.658229i
$735$	−25.6212	+	18.6149i	−0.945052	+	0.686620i
$736$	3.53402			0.130266
$737$	−7.23386	−	15.4260i	−0.266463	−	0.568223i
$738$	66.9203			2.46337
$739$	−1.94968	+	1.41653i	−0.0717202	+	0.0521078i	−0.623068	−	0.782168i	$-0.714114\pi$
$739$	−1.94968	+	1.41653i	−0.0717202	+	0.0521078i	0.551347	+	0.834276i	$0.314114\pi$
$740$	4.09363	+	12.5989i	0.150485	+	0.463144i
$741$	−2.84729	+	8.76307i	−0.104598	+	0.321919i
$742$	−3.13366	−	2.27674i	−0.115040	−	0.0835816i
$743$	6.23840	+	4.53246i	0.228865	+	0.166280i	0.696308	−	0.717743i	$-0.254825\pi$
$743$	6.23840	+	4.53246i	0.228865	+	0.166280i	−0.467443	+	0.884023i	$0.654825\pi$
$744$	6.77824	−	20.8613i	0.248502	−	0.764812i
$745$	11.0571	+	34.0304i	0.405102	+	1.24678i
$746$	8.39138	−	6.09669i	0.307230	−	0.223216i
$747$	−47.2683			−1.72946
$748$	20.5457	+	11.3307i	0.751224	+	0.414292i
$749$	−0.455592			−0.0166470
$750$	−30.0601	+	21.8399i	−1.09764	+	0.797482i
$751$	−11.7133	−	36.0499i	−0.427425	−	1.31548i	−0.900653	−	0.434539i	$-0.856911\pi$
$751$	−11.7133	−	36.0499i	−0.427425	−	1.31548i	0.473228	−	0.880940i	$-0.343089\pi$
$752$	1.56585	−	4.81918i	0.0571005	−	0.175737i
$753$	13.0013	+	9.44598i	0.473793	+	0.344231i
$754$	16.4224	+	11.9316i	0.598068	+	0.434522i
$755$	1.72847	−	5.31969i	0.0629056	−	0.193603i
$756$	−2.82668	−	8.69964i	−0.102805	−	0.316403i
$757$	25.6731	−	18.6526i	0.933105	−	0.677940i	−0.0136462	−	0.999907i	$-0.504344\pi$
$757$	25.6731	−	18.6526i	0.933105	−	0.677940i	0.946751	+	0.321967i	$0.104344\pi$
$758$	−8.14103			−0.295695
$759$	26.9209	−	25.2131i	0.977168	−	0.915178i
$760$	1.24814			0.0452749
$761$	−9.00532	+	6.54275i	−0.326443	+	0.237174i	−0.738920	−	0.673794i	$-0.764664\pi$
$761$	−9.00532	+	6.54275i	−0.326443	+	0.237174i	0.412477	+	0.910968i	$0.364664\pi$
$762$	16.0703	+	49.4594i	0.582167	+	1.79173i
$763$	−3.44002	+	10.5873i	−0.124537	+	0.383286i
$764$	9.46688	+	6.87809i	0.342500	+	0.248841i
$765$	61.6860	+	44.8175i	2.23026	+	1.62038i
$766$	1.70542	−	5.24875i	0.0616194	−	0.189645i
$767$	−15.4359	−	47.5069i	−0.557359	−	1.71538i
$768$	−2.54584	+	1.84966i	−0.0918653	+	0.0667440i
$769$	−17.5577			−0.633145			−0.316573	−	0.948568i	$-0.602532\pi$
$769$	−17.5577			−0.633145			−0.316573	+	0.948568i	$0.602532\pi$
$770$	−3.82763	+	0.478369i	−0.137938	+	0.0172392i
$771$	74.2854			2.67532
$772$	−15.5111	+	11.2695i	−0.558257	+	0.405597i
$773$	−9.00633	−	27.7186i	−0.323935	−	0.996969i	−0.971919	−	0.235316i	$-0.924388\pi$
$773$	−9.00633	−	27.7186i	−0.323935	−	0.996969i	0.647984	−	0.761654i	$-0.275612\pi$
$774$	−2.13302	+	6.56475i	−0.0766697	+	0.235965i
$775$	14.4467	+	10.4962i	0.518943	+	0.377034i
$776$	10.1064	+	7.34272i	0.362798	+	0.263588i
$777$	6.14497	−	18.9123i	0.220450	−	0.678474i
$778$	−7.62360	−	23.4630i	−0.273319	−	0.841190i
$779$	6.26956	−	4.55510i	0.224630	−	0.163203i
$780$	−17.9990			−0.644467
$781$	5.22580	−	27.1979i	0.186994	−	0.973218i
$782$	25.0009			0.894029
$783$	55.0580	−	40.0020i	1.96761	−	1.42955i
$784$	−1.99168	−	6.12975i	−0.0711313	−	0.218920i
$785$	−0.636469	+	1.95885i	−0.0227166	+	0.0699144i
$786$	37.9222	+	27.5521i	1.35264	+	0.982751i
$787$	11.4262	+	8.30161i	0.407300	+	0.295920i	0.772508	−	0.635005i	$-0.219002\pi$
$787$	11.4262	+	8.30161i	0.407300	+	0.295920i	−0.365208	+	0.930926i	$0.619002\pi$
$788$	6.11321	−	18.8145i	0.217774	−	0.670239i
$789$	−0.334850	−	1.03056i	−0.0119210	−	0.0366890i
$790$	2.91325	−	2.11660i	0.103649	−	0.0753053i
$791$	−8.66241			−0.308000
$792$	−4.31969	+	22.4820i	−0.153493	+	0.798865i
$793$	26.8524			0.953557
$794$	17.8404	−	12.9618i	0.633132	−	0.459998i
$795$	7.89611	+	24.3017i	0.280046	+	0.861894i
$796$	−4.06300	+	12.5046i	−0.144009	+	0.443214i
$797$	3.62552	+	2.63409i	0.128422	+	0.0933044i	0.650142	−	0.759813i	$-0.274709\pi$
$797$	3.62552	+	2.63409i	0.128422	+	0.0933044i	−0.521720	+	0.853117i	$0.674709\pi$
$798$	−1.51577	−	1.10127i	−0.0536577	−	0.0389846i
$799$	11.0773	−	34.0925i	0.391888	−	1.20611i
$800$	−0.791652	−	2.43646i	−0.0279891	−	0.0861417i
$801$	−40.1057	+	29.1385i	−1.41707	+	1.02956i
$802$	18.0403			0.637027
$803$	−18.5663	+	2.32038i	−0.655192	+	0.0818845i
$804$	16.1657			0.570119
$805$	−3.32526	+	2.41594i	−0.117200	+	0.0851509i
$806$	7.89015	+	24.2834i	0.277919	+	0.855346i
$807$	−10.5824	+	32.5692i	−0.372517	+	1.14649i
$808$	7.52347	+	5.46612i	0.264675	+	0.192297i
$809$	9.72921	+	7.06868i	0.342061	+	0.248522i	0.745531	−	0.666471i	$-0.232196\pi$
$809$	9.72921	+	7.06868i	0.342061	+	0.248522i	−0.403470	+	0.914993i	$0.632196\pi$
$810$	−8.65536	+	26.6385i	−0.304118	+	0.935980i
$811$	1.93180	+	5.94546i	0.0678345	+	0.208773i	0.979228	−	0.202763i	$-0.0649922\pi$
$811$	1.93180	+	5.94546i	0.0678345	+	0.208773i	−0.911393	+	0.411537i	$0.864992\pi$
$812$	−3.33935	+	2.42618i	−0.117188	+	0.0851423i
$813$	−71.3618			−2.50277
$814$	−20.5372	+	19.2344i	−0.719830	+	0.674165i
$815$	−16.3552			−0.572896
$816$	−18.0102	+	13.0852i	−0.630482	+	0.458072i
$817$	0.247011	+	0.760220i	0.00864181	+	0.0265967i
$818$	3.95392	−	12.1689i	0.138245	−	0.425476i
$819$	15.2363	+	11.0698i	0.532400	+	0.386811i
$820$	12.2471	+	8.89807i	0.427689	+	0.310734i
$821$	−8.23170	+	25.3346i	−0.287288	+	0.884182i	0.698415	+	0.715693i	$0.253889\pi$
$821$	−8.23170	+	25.3346i	−0.287288	+	0.884182i	−0.985703	+	0.168489i	$0.946111\pi$
$822$	9.64439	+	29.6824i	0.336387	+	1.03529i
$823$	−21.0722	+	15.3098i	−0.734530	+	0.533667i	−0.890993	−	0.454017i	$-0.849991\pi$
$823$	−21.0722	+	15.3098i	−0.734530	+	0.533667i	0.156463	+	0.987684i	$0.449991\pi$
$824$	4.38542			0.152773
$825$	−23.4132	−	12.9121i	−0.815143	−	0.449542i
$826$	10.1573			0.353416
$827$	−17.0807	+	12.4099i	−0.593954	+	0.431533i	−0.843728	−	0.536771i	$-0.819644\pi$
$827$	−17.0807	+	12.4099i	−0.593954	+	0.431533i	0.249774	+	0.968304i	$0.419644\pi$
$828$	7.53812	+	23.1999i	0.261968	+	0.806253i
$829$	−0.301336	+	0.927418i	−0.0104658	+	0.0322105i	−0.956153	−	0.292867i	$-0.905391\pi$
$829$	−0.301336	+	0.927418i	−0.0104658	+	0.0322105i	0.945687	+	0.325078i	$0.105391\pi$
$830$	−8.65061	−	6.28504i	−0.300267	−	0.218157i
$831$	49.1766	+	35.7289i	1.70592	+	1.23942i
$832$	1.13194	−	3.48377i	0.0392431	−	0.120778i
$833$	−14.0898	−	43.3639i	−0.488183	−	1.50247i
$834$	−22.4878	+	16.3383i	−0.778688	+	0.565750i
$835$	−25.0242			−0.865998
$836$	1.12560	+	2.40031i	0.0389297	+	0.0830163i
$837$	85.6026			2.95886
$838$	22.0546	−	16.0236i	0.761865	−	0.553527i
$839$	−4.11288	−	12.6582i	−0.141993	−	0.437008i	0.854619	−	0.519255i	$-0.173790\pi$
$839$	−4.11288	−	12.6582i	−0.141993	−	0.437008i	−0.996612	+	0.0822468i	$0.973790\pi$
$840$	1.13098	−	3.48081i	0.0390226	−	0.120099i
$841$	−1.38301	−	1.00482i	−0.0476901	−	0.0346489i
$842$	23.7768	+	17.2749i	0.819403	+	0.595331i
$843$	5.61701	−	17.2874i	0.193460	−	0.595409i
$844$	1.27656	+	3.92886i	0.0439411	+	0.135237i
$845$	0.527931	−	0.383564i	0.0181614	−	0.0131950i
$846$	34.9767			1.20252
$847$	−4.37179	−	6.92953i	−0.150216	−	0.238101i
$848$	−5.20027			−0.178578
$849$	−4.96973	+	3.61072i	−0.170561	+	0.123920i
$850$	−5.60042	−	17.2363i	−0.192093	−	0.591201i
$851$	−9.26501	+	28.5148i	−0.317600	+	0.977474i
$852$	21.2590	+	15.4456i	0.728322	+	0.529157i
$853$	−28.8357	−	20.9503i	−0.987314	−	0.717326i	−0.0279831	−	0.999608i	$-0.508908\pi$
$853$	−28.8357	−	20.9503i	−0.987314	−	0.717326i	−0.959331	+	0.282282i	$0.908908\pi$
$854$	−1.68730	+	5.19297i	−0.0577381	+	0.177700i
$855$	2.66231	+	8.19374i	0.0910490	+	0.280220i
$856$	−0.494840	+	0.359523i	−0.0169133	+	0.0122882i
$857$	−27.9052			−0.953223			−0.476611	−	0.879114i	$-0.658135\pi$
$857$	−27.9052			−0.953223			−0.476611	+	0.879114i	$0.658135\pi$
$858$	−16.2318	−	34.6139i	−0.554146	−	1.18170i
$859$	−37.3468			−1.27425			−0.637127	−	0.770758i	$-0.719878\pi$
$859$	−37.3468			−1.27425			−0.637127	+	0.770758i	$0.719878\pi$
$860$	−1.26325	+	0.917804i	−0.0430764	+	0.0312968i
$861$	−7.02216	−	21.6120i	−0.239315	−	0.736535i
$862$	−8.28920	+	25.5115i	−0.282331	+	0.868926i
$863$	−1.30180	−	0.945810i	−0.0443137	−	0.0321958i	0.565408	−	0.824811i	$-0.308719\pi$
$863$	−1.30180	−	0.945810i	−0.0443137	−	0.0321958i	−0.609722	+	0.792616i	$0.708719\pi$
$864$	−9.93537	−	7.21847i	−0.338008	−	0.245577i
$865$	−5.98883	+	18.4317i	−0.203626	+	0.626697i
$866$	−9.63381	−	29.6498i	−0.327370	−	1.00754i
$867$	−84.1308	+	61.1246i	−2.85723	+	2.07590i
$868$	−5.19193			−0.176226
$869$	6.69767	+	3.69369i	0.227203	+	0.125300i
$870$	27.2296			0.923171
$871$	−15.2237	+	11.0606i	−0.515835	+	0.374776i
$872$	4.61841	+	14.2140i	0.156399	+	0.481347i
$873$	−26.6460	+	82.0080i	−0.901831	+	2.77555i
$874$	2.28539	+	1.66043i	0.0773043	+	0.0561649i
$875$	7.11516	+	5.16947i	0.240536	+	0.174760i
$876$	5.48595	−	16.8840i	0.185353	−	0.570458i
$877$	12.2368	+	37.6609i	0.413207	+	1.27172i	0.913845	+	0.406063i	$0.133099\pi$
$877$	12.2368	+	37.6609i	0.413207	+	1.27172i	−0.500638	+	0.865657i	$0.666901\pi$
$878$	−2.29842	+	1.66990i	−0.0775679	+	0.0563564i
$879$	−20.5492			−0.693108
$880$	−3.77988	+	3.54009i	−0.127420	+	0.119336i
$881$	41.6876			1.40449			0.702246	−	0.711935i	$-0.252181\pi$
$881$	41.6876			1.40449			0.702246	+	0.711935i	$0.252181\pi$
$882$	35.9920	−	26.1497i	1.21191	−	0.880506i
$883$	−8.10724	−	24.9515i	−0.272830	−	0.839686i	−0.989785	−	0.142566i	$-0.954465\pi$
$883$	−8.10724	−	24.9515i	−0.272830	−	0.839686i	0.716955	−	0.697120i	$-0.245535\pi$
$884$	8.00776	−	24.6453i	0.269330	−	0.828913i
$885$	−54.2090	−	39.3851i	−1.82221	−	1.32392i
$886$	−19.0794	−	13.8620i	−0.640984	−	0.465702i
$887$	−13.8048	+	42.4868i	−0.463520	+	1.42657i	0.397314	+	0.917683i	$0.369942\pi$
$887$	−13.8048	+	42.4868i	−0.463520	+	1.42657i	−0.860834	+	0.508886i	$0.830058\pi$
$888$	−8.24995	−	25.3907i	−0.276850	−	0.852057i
$889$	9.95851	−	7.23528i	0.333998	−	0.242664i
$890$	−11.2142			−0.375901
$891$	−59.0340	+	7.37795i	−1.97772	+	0.247171i
$892$	−27.8528			−0.932580
$893$	3.27686	−	2.38078i	0.109656	−	0.0796696i
$894$	−22.2836	−	68.5819i	−0.745276	−	2.29372i
$895$	−3.10132	+	9.54488i	−0.103666	+	0.319050i
$896$	0.602596	+	0.437811i	0.0201313	+	0.0146263i
$897$	−32.9567	−	23.9444i	−1.10039	−	0.799481i
$898$	4.74989	−	14.6187i	0.158506	−	0.487831i
$899$	−11.9366	−	36.7369i	−0.398106	−	1.22525i
$900$	14.3061	−	10.3940i	0.476870	−	0.346466i
$901$	−36.7885			−1.22560
$902$	−6.06718	+	31.5769i	−0.202015	+	1.05140i
$903$	2.34392			0.0780008
$904$	−9.40866	+	6.83579i	−0.312927	+	0.227355i
$905$	7.63242	+	23.4902i	0.253710	+	0.780840i
$906$	−3.48342	+	10.7209i	−0.115729	+	0.356177i
$907$	30.1511	+	21.9060i	1.00115	+	0.727378i	0.962334	−	0.271869i	$-0.0876417\pi$
$907$	30.1511	+	21.9060i	1.00115	+	0.727378i	0.0388151	+	0.999246i	$0.487642\pi$
$908$	−19.4676	−	14.1441i	−0.646056	−	0.469387i
$909$	−19.8360	+	61.0490i	−0.657919	+	2.02487i
$910$	1.31651	+	4.05180i	0.0436419	+	0.134316i
$911$	32.2335	−	23.4190i	1.06794	−	0.775907i	0.0924029	−	0.995722i	$-0.470545\pi$
$911$	32.2335	−	23.4190i	1.06794	−	0.775907i	0.975542	+	0.219815i	$0.0705452\pi$
$912$	−2.51540			−0.0832933
$913$	4.28548	−	22.3040i	0.141829	−	0.738154i
$914$	16.2044			0.535994
$915$	29.1410	−	21.1721i	0.963370	−	0.699930i
$916$	−0.0877910	−	0.270193i	−0.00290070	−	0.00892743i
$917$	3.42857	−	10.5520i	0.113221	−	0.348459i
$918$	−70.2862	−	51.0659i	−2.31979	−	1.68543i
$919$	−10.6345	−	7.72645i	−0.350801	−	0.254872i	0.398404	−	0.917210i	$-0.369564\pi$
$919$	−10.6345	−	7.72645i	−0.350801	−	0.254872i	−0.749205	+	0.662338i	$0.769564\pi$
$920$	−1.70523	+	5.24815i	−0.0562197	+	0.173026i
$921$	−17.6078	−	54.1912i	−0.580197	−	1.78566i
$922$	3.74083	−	2.71787i	0.123198	−	0.0895084i
$923$	−30.5882			−1.00682
$924$	7.71389	−	0.964066i	0.253768	−	0.0317154i
$925$	21.7344			0.714621
$926$	−31.8129	+	23.1134i	−1.04544	+	0.759555i
$927$	9.35416	+	28.7891i	0.307231	+	0.945560i
$928$	−1.71245	+	5.27039i	−0.0562140	+	0.173009i
$929$	−22.7657	−	16.5402i	−0.746918	−	0.542668i	0.147952	−	0.988995i	$-0.452732\pi$
$929$	−22.7657	−	16.5402i	−0.746918	−	0.542668i	−0.894870	+	0.446327i	$0.852732\pi$
$930$	27.7092	+	20.1319i	0.908619	+	0.660150i
$931$	1.59203	−	4.89977i	0.0521768	−	0.160584i
$932$	−5.39319	−	16.5985i	−0.176660	−	0.543703i
$933$	20.0146	−	14.5414i	0.655248	−	0.476066i
$934$	18.4253			0.602895
$935$	−26.7402	+	25.0438i	−0.874497	+	0.819021i
$936$	25.2845			0.826449
$937$	−21.7461	+	15.7995i	−0.710416	+	0.516147i	−0.883308	−	0.468794i	$-0.844689\pi$
$937$	−21.7461	+	15.7995i	−0.710416	+	0.516147i	0.172892	+	0.984941i	$0.444689\pi$
$938$	−1.18242	−	3.63910i	−0.0386072	−	0.118821i
$939$	21.6077	−	66.5016i	0.705140	−	2.17020i
$940$	6.40111	+	4.65068i	0.208781	+	0.151688i
$941$	−21.2864	−	15.4655i	−0.693918	−	0.504161i	0.184028	−	0.982921i	$-0.441086\pi$
$941$	−21.2864	−	15.4655i	−0.693918	−	0.504161i	−0.877946	+	0.478760i	$0.841086\pi$
$942$	1.28269	−	3.94771i	0.0417922	−	0.128623i
$943$	10.5876	+	32.5852i	0.344779	+	1.06112i
$944$	11.0323	−	8.01543i	0.359071	−	0.260880i
$945$	14.2832			0.464633
$946$	−2.90425	−	1.60166i	−0.0944254	−	0.0520745i
$947$	−41.2948			−1.34190			−0.670951	−	0.741502i	$-0.734114\pi$
$947$	−41.2948			−1.34190			−0.670951	+	0.741502i	$0.734114\pi$
$948$	−5.87112	+	4.26562i	−0.190685	+	0.138541i
$949$	6.38587	+	19.6537i	0.207294	+	0.637986i
$950$	0.632802	−	1.94756i	0.0205308	−	0.0631873i
$951$	48.7585	+	35.4251i	1.58110	+	1.14874i
$952$	4.26297	+	3.09723i	0.138164	+	0.100382i
$953$	1.10044	−	3.38681i	0.0356468	−	0.109709i	−0.931650	−	0.363357i	$-0.881630\pi$
$953$	1.10044	−	3.38681i	0.0356468	−	0.109709i	0.967297	+	0.253648i	$0.0816304\pi$
$954$	−11.0922	−	34.1384i	−0.359125	−	1.10527i
$955$	−14.7822	+	10.7399i	−0.478339	+	0.347534i
$956$	15.8822			0.513666
$957$	24.5562	+	52.3653i	0.793790	+	1.69273i
$958$	18.4559			0.596284
$959$	5.97646	−	4.34216i	0.192990	−	0.140216i
$960$	−1.51841	−	4.67317i	−0.0490063	−	0.150826i
$961$	5.43470	−	16.7263i	0.175313	−	0.539558i
$962$	25.1417	+	18.2665i	0.810602	+	0.588936i
$963$	−3.41568	−	2.48163i	−0.110069	−	0.0799695i
$964$	1.71342	−	5.27335i	0.0551854	−	0.169843i
$965$	−9.25121	−	28.4723i	−0.297807	−	0.916555i
$966$	6.70145	−	4.86889i	0.215616	−	0.156654i
$967$	52.0359			1.67336			0.836682	−	0.547690i	$-0.184492\pi$
$967$	52.0359			1.67336			0.836682	+	0.547690i	$0.184492\pi$
$968$	−10.2167	−	4.07657i	−0.328378	−	0.131026i
$969$	−17.7948			−0.571652
$970$	−15.7807	+	11.4654i	−0.506688	+	0.368131i
$971$	7.35254	+	22.6288i	0.235954	+	0.726192i	0.996993	+	0.0774863i	$0.0246894\pi$
$971$	7.35254	+	22.6288i	0.235954	+	0.726192i	−0.761039	+	0.648706i	$0.775311\pi$
$972$	6.05837	−	18.6457i	0.194322	−	0.598062i
$973$	5.32281	+	3.86725i	0.170641	+	0.123978i
$974$	5.27316	+	3.83118i	0.168963	+	0.122759i
$975$	−9.12539	+	28.0851i	−0.292246	+	0.899442i
$976$	2.26529	+	6.97184i	0.0725101	+	0.223163i
$977$	18.4887	−	13.4328i	0.591506	−	0.429755i	−0.251348	−	0.967897i	$-0.580874\pi$
$977$	18.4887	−	13.4328i	0.591506	−	0.429755i	0.842854	+	0.538142i	$0.180874\pi$
$978$	32.9608			1.05397
$979$	−10.1132	−	21.5661i	−0.323219	−	0.689254i
$980$	10.0639			0.321480
$981$	−83.4602	+	60.6374i	−2.66468	+	1.93600i
$982$	−1.71297	−	5.27196i	−0.0546629	−	0.168235i
$983$	−1.00856	+	3.10403i	−0.0321681	+	0.0990031i	−0.965851	−	0.259097i	$-0.916575\pi$
$983$	−1.00856	+	3.10403i	−0.0321681	+	0.0990031i	0.933683	+	0.358100i	$0.116575\pi$
$984$	−24.6819	−	17.9324i	−0.786829	−	0.571665i
$985$	24.9905	+	18.1567i	0.796264	+	0.578520i
$986$	−12.1145	+	37.2845i	−0.385804	+	1.18738i
$987$	−3.67022	−	11.2958i	−0.116824	−	0.359548i
$988$	2.36883	−	1.72105i	0.0753624	−	0.0547540i
$989$	−3.53402			−0.112375
$990$	−31.3024	−	17.2629i	−0.994854	−	0.548651i
$991$	17.2132			0.546796			0.273398	−	0.961901i	$-0.411852\pi$
$991$	17.2132			0.546796			0.273398	+	0.961901i	$0.411852\pi$
$992$	−5.63921	+	4.09712i	−0.179045	+	0.130084i
$993$	−1.26999	−	3.90864i	−0.0403020	−	0.124037i
$994$	1.92204	−	5.91543i	0.0609634	−	0.187626i
$995$	−16.6094	−	12.0674i	−0.526552	−	0.382562i
$996$	17.4337	+	12.6663i	0.552409	+	0.401348i
$997$	−5.20543	+	16.0207i	−0.164858	+	0.507380i	−0.999026	−	0.0441306i	$-0.985948\pi$
$997$	−5.20543	+	16.0207i	−0.164858	+	0.507380i	0.834168	+	0.551510i	$0.185948\pi$
$998$	10.5246	+	32.3914i	0.333150	+	1.02533i
$999$	84.2905	−	61.2407i	2.66683	−	1.93757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.f.g.861.10	yes	40
11.4	even	5	inner	946.2.f.g.345.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.f.g.345.10	✓	40	11.4	even	5	inner
946.2.f.g.861.10	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.972426 + 2.99282i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.26325 + 0.917804i) q^{5} +(-2.54584 - 1.84966i) q^{6} +(-0.230171 + 0.708394i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-5.58431 + 4.05724i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.972426 + 2.99282i) q^{3} +(0.309017 - 0.951057i) q^{4} +(1.26325 + 0.917804i) q^{5} +(-2.54584 - 1.84966i) q^{6} +(-0.230171 + 0.708394i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-5.58431 + 4.05724i) q^{9} -1.56146 q^{10} +(-1.40816 - 3.00285i) q^{11} +3.14684 q^{12} +(-2.96347 + 2.15309i) q^{13} +(-0.230171 - 0.708394i) q^{14} +(-1.51841 + 4.67317i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.72326 - 4.15819i) q^{17} +(2.13302 - 6.56475i) q^{18} +(-0.247011 - 0.760220i) q^{19} +(1.26325 - 0.917804i) q^{20} -2.34392 q^{21} +(2.90425 + 1.60166i) q^{22} +3.53402 q^{23} +(-2.54584 + 1.84966i) q^{24} +(-0.791652 - 2.43646i) q^{25} +(1.13194 - 3.48377i) q^{26} +(-9.93537 - 7.21847i) q^{27} +(0.602596 + 0.437811i) q^{28} +(-1.71245 + 5.27039i) q^{29} +(-1.51841 - 4.67317i) q^{30} +(-5.63921 + 4.09712i) q^{31} +1.00000 q^{32} +(7.61766 - 7.13441i) q^{33} +7.07434 q^{34} +(-0.940930 + 0.683625i) q^{35} +(2.13302 + 6.56475i) q^{36} +(-2.62166 + 8.06865i) q^{37} +(0.646682 + 0.469842i) q^{38} +(-9.32555 - 6.77541i) q^{39} +(-0.482518 + 1.48504i) q^{40} +(2.99591 + 9.22045i) q^{41} +(1.89627 - 1.37772i) q^{42} -1.00000 q^{43} +(-3.29102 + 0.411305i) q^{44} -10.7781 q^{45} +(-2.85908 + 2.07724i) q^{46} +(1.56585 + 4.81918i) q^{47} +(0.972426 - 2.99282i) q^{48} +(5.21428 + 3.78839i) q^{49} +(2.07257 + 1.50581i) q^{50} +(6.87928 - 21.1722i) q^{51} +(1.13194 + 3.48377i) q^{52} +(4.20710 - 3.05664i) q^{53} +12.2808 q^{54} +(0.977174 - 5.08575i) q^{55} -0.744849 q^{56} +(2.03500 - 1.47852i) q^{57} +(-1.71245 - 5.27039i) q^{58} +(-4.21396 + 12.9692i) q^{59} +(3.97524 + 2.88818i) q^{60} +(-5.93060 - 4.30883i) q^{61} +(2.15399 - 6.62928i) q^{62} +(-1.58878 - 4.88975i) q^{63} +(-0.809017 + 0.587785i) q^{64} -5.71970 q^{65} +(-1.96931 + 10.2494i) q^{66} +5.13712 q^{67} +(-5.72326 + 4.15819i) q^{68} +(3.43657 + 10.5767i) q^{69} +(0.359403 - 1.10613i) q^{70} +(6.75568 + 4.90829i) q^{71} +(-5.58431 - 4.05724i) q^{72} +(1.74332 - 5.36540i) q^{73} +(-2.62166 - 8.06865i) q^{74} +(6.52205 - 4.73855i) q^{75} -0.799343 q^{76} +(2.45132 - 0.306360i) q^{77} +11.5270 q^{78} +(-1.86572 + 1.35553i) q^{79} +(-0.482518 - 1.48504i) q^{80} +(5.54312 - 17.0600i) q^{81} +(-7.84339 - 5.69855i) q^{82} +(5.54008 + 4.02510i) q^{83} +(-0.724311 + 2.22920i) q^{84} +(-3.41350 - 10.5057i) q^{85} +(0.809017 - 0.587785i) q^{86} -17.4386 q^{87} +(2.42073 - 2.26717i) q^{88} +7.18187 q^{89} +(8.71968 - 6.33522i) q^{90} +(-0.843128 - 2.59488i) q^{91} +(1.09207 - 3.36105i) q^{92} +(-17.7457 - 12.8930i) q^{93} +(-4.09944 - 2.97842i) q^{94} +(0.385697 - 1.18705i) q^{95} +(0.972426 + 2.99282i) q^{96} +(10.1064 - 7.34272i) q^{97} -6.44520 q^{98} +(20.0468 + 11.0556i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9}+O(q^{10}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9	\( 40 q - 10 q^{2} + 5 q^{3} - 10 q^{4} + 8 q^{5} - 5 q^{6} + 5 q^{7} - 10 q^{8} - 31 q^{9} - 2 q^{10} + 6 q^{11} + 2 q^{13} + 5 q^{14} - 23 q^{15} - 10 q^{16} - 5 q^{17} + 9 q^{18} - 21 q^{19} + 8 q^{20} + 20 q^{21} + 6 q^{22} + 24 q^{23} - 5 q^{24} - 16 q^{25} - 18 q^{26} - 10 q^{27} - 20 q^{28} + 7 q^{29} - 23 q^{30} - 15 q^{31} + 40 q^{32} + 36 q^{33} + 10 q^{34} + 50 q^{35} + 9 q^{36} + 2 q^{37} - 21 q^{38} - 70 q^{39} - 7 q^{40} - 20 q^{41} - 10 q^{42} - 40 q^{43} + 6 q^{44} - 14 q^{45} - q^{46} - 8 q^{47} + 5 q^{48} + 5 q^{49} - 11 q^{50} + 13 q^{51} - 18 q^{52} + 24 q^{53} + 38 q^{55} + 30 q^{56} + 62 q^{57} + 7 q^{58} - 27 q^{59} + 2 q^{60} - 49 q^{61} + 20 q^{62} - 5 q^{63} - 10 q^{64} - 4 q^{65} - 34 q^{66} - 26 q^{67} - 5 q^{68} + 73 q^{69} - 65 q^{70} - 5 q^{71} - 31 q^{72} + 22 q^{73} + 2 q^{74} - 60 q^{75} + 84 q^{76} - 20 q^{77} + 30 q^{78} + 81 q^{79} - 7 q^{80} - 38 q^{81} - 25 q^{82} + 3 q^{83} - 38 q^{85} + 10 q^{86} + 28 q^{87} - 14 q^{88} - 56 q^{89} - 4 q^{90} + 10 q^{91} - 11 q^{92} - 16 q^{93} - 23 q^{94} + 66 q^{95} + 5 q^{96} - 20 q^{97} + 50 q^{98} + 94 q^{99}+O(q^{100}) \) 40 * q - 10 * q^2 + 5 * q^3 - 10 * q^4 + 8 * q^5 - 5 * q^6 + 5 * q^7 - 10 * q^8 - 31 * q^9 - 2 * q^10 + 6 * q^11 + 2 * q^13 + 5 * q^14 - 23 * q^15 - 10 * q^16 - 5 * q^17 + 9 * q^18 - 21 * q^19 + 8 * q^20 + 20 * q^21 + 6 * q^22 + 24 * q^23 - 5 * q^24 - 16 * q^25 - 18 * q^26 - 10 * q^27 - 20 * q^28 + 7 * q^29 - 23 * q^30 - 15 * q^31 + 40 * q^32 + 36 * q^33 + 10 * q^34 + 50 * q^35 + 9 * q^36 + 2 * q^37 - 21 * q^38 - 70 * q^39 - 7 * q^40 - 20 * q^41 - 10 * q^42 - 40 * q^43 + 6 * q^44 - 14 * q^45 - q^46 - 8 * q^47 + 5 * q^48 + 5 * q^49 - 11 * q^50 + 13 * q^51 - 18 * q^52 + 24 * q^53 + 38 * q^55 + 30 * q^56 + 62 * q^57 + 7 * q^58 - 27 * q^59 + 2 * q^60 - 49 * q^61 + 20 * q^62 - 5 * q^63 - 10 * q^64 - 4 * q^65 - 34 * q^66 - 26 * q^67 - 5 * q^68 + 73 * q^69 - 65 * q^70 - 5 * q^71 - 31 * q^72 + 22 * q^73 + 2 * q^74 - 60 * q^75 + 84 * q^76 - 20 * q^77 + 30 * q^78 + 81 * q^79 - 7 * q^80 - 38 * q^81 - 25 * q^82 + 3 * q^83 - 38 * q^85 + 10 * q^86 + 28 * q^87 - 14 * q^88 - 56 * q^89 - 4 * q^90 + 10 * q^91 - 11 * q^92 - 16 * q^93 - 23 * q^94 + 66 * q^95 + 5 * q^96 - 20 * q^97 + 50 * q^98 + 94 * q^99

Introduction

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