LMFDB - Embedded newform 32.3.h.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [32,3,Mod(3,32)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(32, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("32.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 32 = 2^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	32.h (of order $8$, 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:	$0.871936845953$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	32.11
Dual form			32.3.h.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46783 - 1.35848i) q^{2} +(2.10187 + 5.07436i) q^{3} +(0.309042 + 3.98804i) q^{4} +(1.74699 - 4.21761i) q^{5} +(3.80826 - 10.3037i) q^{6} +(-0.392379 + 0.392379i) q^{7} +(4.96407 - 6.27359i) q^{8} +(-14.9674 + 14.9674i) q^{9} +O(q^{10})$	\(q+(-1.46783 - 1.35848i) q^{2} +(2.10187 + 5.07436i) q^{3} +(0.309042 + 3.98804i) q^{4} +(1.74699 - 4.21761i) q^{5} +(3.80826 - 10.3037i) q^{6} +(-0.392379 + 0.392379i) q^{7} +(4.96407 - 6.27359i) q^{8} +(-14.9674 + 14.9674i) q^{9} +(-8.29385 + 3.81747i) q^{10} +(2.90924 - 7.02353i) q^{11} +(-19.5872 + 9.95055i) q^{12} +(-4.50555 - 10.8774i) q^{13} +(1.10898 - 0.0429045i) q^{14} +25.0737 q^{15} +(-15.8090 + 2.46495i) q^{16} -10.5402i q^{17} +(42.3024 - 1.63660i) q^{18} +(-1.88707 + 0.781651i) q^{19} +(17.3599 + 5.66366i) q^{20} +(-2.81580 - 1.16634i) q^{21} +(-13.8116 + 6.35718i) q^{22} +(-0.445453 - 0.445453i) q^{23} +(42.2683 + 12.0032i) q^{24} +(2.94139 + 2.94139i) q^{25} +(-8.16334 + 22.0868i) q^{26} +(-61.7400 - 25.5735i) q^{27} +(-1.68608 - 1.44356i) q^{28} +(0.741814 - 0.307270i) q^{29} +(-36.8038 - 34.0622i) q^{30} +47.6947i q^{31} +(26.5535 + 17.8581i) q^{32} +41.7548 q^{33} +(-14.3187 + 15.4712i) q^{34} +(0.969419 + 2.34038i) q^{35} +(-64.3160 - 55.0649i) q^{36} +(14.5080 - 35.0255i) q^{37} +(3.83176 + 1.41623i) q^{38} +(45.7256 - 45.7256i) q^{39} +(-17.7874 - 31.8965i) q^{40} +(-11.3365 + 11.3365i) q^{41} +(2.54866 + 5.53721i) q^{42} +(-14.6421 + 35.3493i) q^{43} +(28.9092 + 9.43161i) q^{44} +(36.9787 + 89.2744i) q^{45} +(0.0487080 + 1.25899i) q^{46} -80.5164 q^{47} +(-45.7365 - 75.0396i) q^{48} +48.6921i q^{49} +(-0.321625 - 8.31328i) q^{50} +(53.4849 - 22.1542i) q^{51} +(41.9870 - 21.3299i) q^{52} +(-66.6128 - 27.5919i) q^{53} +(55.8825 + 121.410i) q^{54} +(-24.5401 - 24.5401i) q^{55} +(0.513828 + 4.40942i) q^{56} +(-7.93277 - 7.93277i) q^{57} +(-1.50628 - 0.556724i) q^{58} +(65.0706 + 26.9531i) q^{59} +(7.74883 + 99.9949i) q^{60} +(87.4322 - 36.2156i) q^{61} +(64.7925 - 70.0077i) q^{62} -11.7457i q^{63} +(-14.7160 - 62.2852i) q^{64} -53.7476 q^{65} +(-61.2889 - 56.7232i) q^{66} +(-7.12379 - 17.1984i) q^{67} +(42.0348 - 3.25737i) q^{68} +(1.32411 - 3.19668i) q^{69} +(1.75643 - 4.75222i) q^{70} +(-14.8103 + 14.8103i) q^{71} +(19.6001 + 168.198i) q^{72} +(18.6720 - 18.6720i) q^{73} +(-68.8769 + 31.7025i) q^{74} +(-8.74326 + 21.1081i) q^{75} +(-3.70044 - 7.28417i) q^{76} +(1.61436 + 3.89741i) q^{77} +(-129.235 + 4.99985i) q^{78} -36.2398 q^{79} +(-17.2220 + 70.9824i) q^{80} -176.540i q^{81} +(32.0406 - 1.23959i) q^{82} +(27.0868 - 11.2197i) q^{83} +(3.78122 - 11.5900i) q^{84} +(-44.4545 - 18.4137i) q^{85} +(69.5135 - 31.9955i) q^{86} +(3.11840 + 3.11840i) q^{87} +(-29.6211 - 53.1167i) q^{88} +(-56.4944 - 56.4944i) q^{89} +(66.9995 - 181.274i) q^{90} +(6.03592 + 2.50016i) q^{91} +(1.63882 - 1.91415i) q^{92} +(-242.020 + 100.248i) q^{93} +(118.184 + 109.380i) q^{94} +9.32448i q^{95} +(-34.8067 + 172.278i) q^{96} +158.579 q^{97} +(66.1474 - 71.4716i) q^{98} +(61.5800 + 148.667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/32\mathbb{Z}\right)^\times$.

$n$	$5$	$31$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−1.46783	−	1.35848i	−0.733914	−	0.679242i
$2$	−1.46783	−	1.35848i	−0.733914	−	0.679242i
$3$	2.10187	+	5.07436i	0.700624	+	1.69145i	0.722197	+	0.691688i	$0.243133\pi$
$3$	2.10187	+	5.07436i	0.700624	+	1.69145i	−0.0215732	+	0.999767i	$0.506867\pi$
$4$	0.309042	+	3.98804i	0.0772606	+	0.997011i
$5$	1.74699	−	4.21761i	0.349399	−	0.843523i	−0.647293	−	0.762242i	$-0.724099\pi$
$5$	1.74699	−	4.21761i	0.349399	−	0.843523i	0.996691	−	0.0812812i	$-0.0259012\pi$
$6$	3.80826	−	10.3037i	0.634710	−	1.71728i
$7$	−0.392379	+	0.392379i	−0.0560541	+	0.0560541i	−0.734578	−	0.678524i	$-0.762620\pi$
$7$	−0.392379	+	0.392379i	−0.0560541	+	0.0560541i	0.678524	+	0.734578i	$0.262620\pi$
$8$	4.96407	−	6.27359i	0.620509	−	0.784199i
$9$	−14.9674	+	14.9674i	−1.66304	+	1.66304i
$10$	−8.29385	+	3.81747i	−0.829385	+	0.381747i
$11$	2.90924	−	7.02353i	0.264477	−	0.638503i	−0.734729	−	0.678361i	$-0.762691\pi$
$11$	2.90924	−	7.02353i	0.264477	−	0.638503i	0.999205	+	0.0398581i	$0.0126906\pi$
$12$	−19.5872	+	9.95055i	−1.63227	+	0.829212i
$13$	−4.50555	−	10.8774i	−0.346581	−	0.836720i	−0.997019	−	0.0771604i	$-0.975415\pi$
$13$	−4.50555	−	10.8774i	−0.346581	−	0.836720i	0.650438	−	0.759559i	$-0.274585\pi$
$14$	1.10898	−	0.0429045i	0.0792132	−	0.00306461i
$15$	25.0737			1.67158
$16$	−15.8090	+	2.46495i	−0.988062	+	0.154059i
$17$		−	10.5402i		−	0.620012i	−0.950735	−	0.310006i	$-0.899669\pi$
$17$		−	10.5402i		−	0.620012i	0.950735	−	0.310006i	$-0.100331\pi$
$18$	42.3024	−	1.63660i	2.35014	−	0.0909223i
$19$	−1.88707	+	0.781651i	−0.0993196	+	0.0411395i	−0.431790	−	0.901974i	$-0.642118\pi$
$19$	−1.88707	+	0.781651i	−0.0993196	+	0.0411395i	0.332470	+	0.943114i	$0.392118\pi$
$20$	17.3599	+	5.66366i	0.867996	+	0.283183i
$21$	−2.81580	−	1.16634i	−0.134086	−	0.0555401i
$22$	−13.8116	+	6.35718i	−0.627801	+	0.288963i
$23$	−0.445453	−	0.445453i	−0.0193675	−	0.0193675i	0.697357	−	0.716724i	$-0.254359\pi$
$23$	−0.445453	−	0.445453i	−0.0193675	−	0.0193675i	−0.716724	+	0.697357i	$0.754359\pi$
$24$	42.2683	+	12.0032i	1.76118	+	0.500135i
$25$	2.94139	+	2.94139i	0.117656	+	0.117656i
$26$	−8.16334	+	22.0868i	−0.313975	+	0.849493i
$27$	−61.7400	−	25.5735i	−2.28667	−	0.947168i
$28$	−1.68608	−	1.44356i	−0.0602173	−	0.0515558i
$29$	0.741814	−	0.307270i	0.0255798	−	0.0105955i	−0.369857	−	0.929089i	$-0.620593\pi$
$29$	0.741814	−	0.307270i	0.0255798	−	0.0105955i	0.395437	+	0.918493i	$0.370593\pi$
$30$	−36.8038	−	34.0622i	−1.22679	−	1.13541i
$31$			47.6947i			1.53854i	0.638924	+	0.769270i	$0.279380\pi$
$31$			47.6947i			1.53854i	−0.638924	+	0.769270i	$0.720620\pi$
$32$	26.5535	+	17.8581i	0.829796	+	0.558067i
$33$	41.7548			1.26530
$34$	−14.3187	+	15.4712i	−0.421138	+	0.455036i
$35$	0.969419	+	2.34038i	0.0276977	+	0.0668681i
$36$	−64.3160	−	55.0649i	−1.78656	−	1.52958i
$37$	14.5080	−	35.0255i	0.392109	−	0.946635i	−0.597371	−	0.801965i	$-0.703788\pi$
$37$	14.5080	−	35.0255i	0.392109	−	0.946635i	0.989480	−	0.144670i	$-0.0462120\pi$
$38$	3.83176	+	1.41623i	0.100836	+	0.0372692i
$39$	45.7256	−	45.7256i	1.17245	−	1.17245i
$40$	−17.7874	−	31.8965i	−0.444685	−	0.797412i
$41$	−11.3365	+	11.3365i	−0.276501	+	0.276501i	−0.831711	−	0.555209i	$-0.812638\pi$
$41$	−11.3365	+	11.3365i	−0.276501	+	0.276501i	0.555209	+	0.831711i	$0.312638\pi$
$42$	2.54866	+	5.53721i	0.0606823	+	0.131838i
$43$	−14.6421	+	35.3493i	−0.340515	+	0.822076i	0.657149	+	0.753761i	$0.271762\pi$
$43$	−14.6421	+	35.3493i	−0.340515	+	0.822076i	−0.997664	+	0.0683149i	$0.978238\pi$
$44$	28.9092	+	9.43161i	0.657028	+	0.214355i
$45$	36.9787	+	89.2744i	0.821748	+	1.98388i
$46$	0.0487080	+	1.25899i	0.00105887	+	0.0273694i
$47$	−80.5164			−1.71312			−0.856558	−	0.516051i	$-0.827402\pi$
$47$	−80.5164			−1.71312			−0.856558	+	0.516051i	$0.827402\pi$
$48$	−45.7365	−	75.0396i	−0.952844	−	1.56332i
$49$			48.6921i			0.993716i
$50$	−0.321625	−	8.31328i	−0.00643251	−	0.166266i
$51$	53.4849	−	22.1542i	1.04872	−	0.434395i
$52$	41.9870	−	21.3299i	0.807442	−	0.410190i
$53$	−66.6128	−	27.5919i	−1.25685	−	0.520602i	−0.347905	−	0.937530i	$-0.613107\pi$
$53$	−66.6128	−	27.5919i	−1.25685	−	0.520602i	−0.908940	+	0.416927i	$0.863107\pi$
$54$	55.8825	+	121.410i	1.03486	+	2.24834i
$55$	−24.5401	−	24.5401i	−0.446184	−	0.446184i
$56$	0.513828	+	4.40942i	0.00917551	+	0.0787396i
$57$	−7.93277	−	7.93277i	−0.139171	−	0.139171i
$58$	−1.50628	−	0.556724i	−0.0259703	−	0.00959869i
$59$	65.0706	+	26.9531i	1.10289	+	0.456833i	0.858484	−	0.512840i	$-0.171406\pi$
$59$	65.0706	+	26.9531i	1.10289	+	0.456833i	0.244408	+	0.969673i	$0.421406\pi$
$60$	7.74883	+	99.9949i	0.129147	+	1.66658i
$61$	87.4322	−	36.2156i	1.43331	−	0.593698i	0.475147	−	0.879906i	$-0.342395\pi$
$61$	87.4322	−	36.2156i	1.43331	−	0.593698i	0.958168	+	0.286208i	$0.0923948\pi$
$62$	64.7925	−	70.0077i	1.04504	−	1.12916i
$63$		−	11.7457i		−	0.186440i
$64$	−14.7160	−	62.2852i	−0.229937	−	0.973205i
$65$	−53.7476			−0.826887
$66$	−61.2889	−	56.7232i	−0.928620	−	0.859443i
$67$	−7.12379	−	17.1984i	−0.106325	−	0.256692i	0.861759	−	0.507319i	$-0.169363\pi$
$67$	−7.12379	−	17.1984i	−0.106325	−	0.256692i	−0.968084	+	0.250627i	$0.919363\pi$
$68$	42.0348	−	3.25737i	0.618159	−	0.0479025i
$69$	1.32411	−	3.19668i	0.0191900	−	0.0463287i
$70$	1.75643	−	4.75222i	0.0250919	−	0.0678889i
$71$	−14.8103	+	14.8103i	−0.208596	+	0.208596i	−0.803671	−	0.595074i	$-0.797123\pi$
$71$	−14.8103	+	14.8103i	−0.208596	+	0.208596i	0.595074	+	0.803671i	$0.297123\pi$
$72$	19.6001	+	168.198i	0.272223	+	2.33609i
$73$	18.6720	−	18.6720i	0.255781	−	0.255781i	−0.567555	−	0.823336i	$-0.692110\pi$
$73$	18.6720	−	18.6720i	0.255781	−	0.255781i	0.823336	+	0.567555i	$0.192110\pi$
$74$	−68.8769	+	31.7025i	−0.930769	+	0.428412i
$75$	−8.74326	+	21.1081i	−0.116577	+	0.281441i
$76$	−3.70044	−	7.28417i	−0.0486901	−	0.0958443i
$77$	1.61436	+	3.89741i	0.0209657	+	0.0506157i
$78$	−129.235	+	4.99985i	−1.65686	+	0.0641007i
$79$	−36.2398			−0.458732			−0.229366	−	0.973340i	$-0.573665\pi$
$79$	−36.2398			−0.458732			−0.229366	+	0.973340i	$0.573665\pi$
$80$	−17.2220	+	70.9824i	−0.215275	+	0.887281i
$81$		−	176.540i		−	2.17951i
$82$	32.0406	−	1.23959i	0.390739	−	0.0151170i
$83$	27.0868	−	11.2197i	0.326347	−	0.135177i	−0.213494	−	0.976944i	$-0.568484\pi$
$83$	27.0868	−	11.2197i	0.326347	−	0.135177i	0.539841	+	0.841767i	$0.318484\pi$
$84$	3.78122	−	11.5900i	0.0450146	−	0.137976i
$85$	−44.4545	−	18.4137i	−0.522994	−	0.216631i
$86$	69.5135	−	31.9955i	0.808297	−	0.372041i
$87$	3.11840	+	3.11840i	0.0358436	+	0.0358436i
$88$	−29.6211	−	53.1167i	−0.336603	−	0.603599i
$89$	−56.4944	−	56.4944i	−0.634769	−	0.634769i	0.314491	−	0.949260i	$-0.398166\pi$
$89$	−56.4944	−	56.4944i	−0.634769	−	0.634769i	−0.949260	+	0.314491i	$0.898166\pi$
$90$	66.9995	−	181.274i	0.744439	−	2.01416i
$91$	6.03592	+	2.50016i	0.0663288	+	0.0274743i
$92$	1.63882	−	1.91415i	0.0178133	−	0.0208060i
$93$	−242.020	+	100.248i	−2.60237	+	1.07794i
$94$	118.184	+	109.380i	1.25728	+	1.16362i
$95$			9.32448i			0.0981525i
$96$	−34.8067	+	172.278i	−0.362570	+	1.79456i
$97$	158.579			1.63484			0.817419	−	0.576043i	$-0.195404\pi$
$97$	158.579			1.63484			0.817419	+	0.576043i	$0.195404\pi$
$98$	66.1474	−	71.4716i	0.674974	−	0.729302i
$99$	61.5800	+	148.667i	0.622021	+	1.50169i
$100$	−10.8214	+	12.6394i	−0.108214	+	0.126394i
$101$	−53.8420	+	129.986i	−0.533089	+	1.28699i	0.396379	+	0.918087i	$0.370267\pi$
$101$	−53.8420	+	129.986i	−0.533089	+	1.28699i	−0.929468	+	0.368903i	$0.879733\pi$
$102$	−108.603	−	40.1398i	−1.06473	−	0.393528i
$103$	9.94607	−	9.94607i	0.0965638	−	0.0965638i	−0.657175	−	0.753738i	$-0.728249\pi$
$103$	9.94607	−	9.94607i	0.0965638	−	0.0965638i	0.753738	+	0.657175i	$0.228249\pi$
$104$	−90.6060	−	25.7300i	−0.871211	−	0.247404i
$105$	−9.83837	+	9.83837i	−0.0936987	+	0.0936987i
$106$	60.2930	+	130.993i	0.568802	+	1.23578i
$107$	68.8129	−	166.129i	0.643111	−	1.55261i	−0.179350	−	0.983785i	$-0.557399\pi$
$107$	68.8129	−	166.129i	0.643111	−	1.55261i	0.822461	−	0.568822i	$-0.192601\pi$
$108$	82.9081	−	254.125i	0.767668	−	2.35301i
$109$	3.61301	+	8.72257i	0.0331469	+	0.0800236i	0.939586	−	0.342313i	$-0.111210\pi$
$109$	3.61301	+	8.72257i	0.0331469	+	0.0800236i	−0.906439	+	0.422336i	$0.861210\pi$
$110$	2.68333	+	69.3580i	0.0243939	+	0.630528i
$111$	208.226			1.87591
$112$	5.23591	−	7.17030i	0.0467492	−	0.0640205i
$113$			85.8345i			0.759598i	0.925069	+	0.379799i	$0.124007\pi$
$113$			85.8345i			0.759598i	−0.925069	+	0.379799i	$0.875993\pi$
$114$	0.867406	+	22.4205i	0.00760883	+	0.196671i
$115$	−2.65695	+	1.10055i	−0.0231039	+	0.00956997i
$116$	1.45466	+	2.86343i	0.0125401	+	0.0246847i
$117$	230.241	+	95.3691i	1.96788	+	0.815121i
$118$	−58.8971	−	127.960i	−0.499128	−	1.08441i
$119$	4.13575	+	4.13575i	0.0347542	+	0.0347542i
$120$	124.467	−	157.302i	1.03723	−	1.31085i
$121$	44.6936	+	44.6936i	0.369369	+	0.369369i
$122$	−177.534	−	65.6169i	−1.45520	−	0.537844i
$123$	−81.3537	−	33.6978i	−0.661412	−	0.273966i
$124$	−190.209	+	14.7397i	−1.53394	+	0.118869i
$125$	122.985	−	50.9419i	0.983877	−	0.407535i
$126$	−15.9564	+	17.2407i	−0.126638	+	0.136831i
$127$			17.2873i			0.136120i	0.997681	+	0.0680601i	$0.0216810\pi$
$127$			17.2873i			0.136120i	−0.997681	+	0.0680601i	$0.978319\pi$
$128$	−63.0128	+	111.415i	−0.492288	+	0.870432i
$129$	−210.151			−1.62908
$130$	78.8923	+	73.0153i	0.606864	+	0.561656i
$131$	−40.2223	−	97.1053i	−0.307041	−	0.741262i	−0.999798	−	0.0200911i	$-0.993604\pi$
$131$	−40.2223	−	97.1053i	−0.307041	−	0.741262i	0.692758	−	0.721171i	$-0.256396\pi$
$132$	12.9040	+	166.520i	0.0977576	+	1.26152i
$133$	0.433744	−	1.04715i	0.00326123	−	0.00787331i
$134$	−12.9072	+	34.9218i	−0.0963223	+	0.260610i
$135$	−215.719	+	215.719i	−1.59792	+	1.59792i
$136$	−66.1250	−	52.3224i	−0.486213	−	0.384723i
$137$	25.5351	−	25.5351i	0.186387	−	0.186387i	−0.607745	−	0.794132i	$-0.707926\pi$
$137$	25.5351	−	25.5351i	0.186387	−	0.186387i	0.794132	+	0.607745i	$0.207926\pi$
$138$	−6.28620	+	2.89340i	−0.0455522	+	0.0209666i
$139$	−52.2202	+	126.071i	−0.375685	+	0.906984i	0.617079	+	0.786901i	$0.288316\pi$
$139$	−52.2202	+	126.071i	−0.375685	+	0.906984i	−0.992764	+	0.120083i	$0.961684\pi$
$140$	−9.03396	+	4.58936i	−0.0645283	+	0.0327812i
$141$	−169.235	−	408.570i	−1.20025	−	2.89766i
$142$	41.8587	−	1.61943i	0.294779	−	0.0114045i
$143$	−89.5052			−0.625910
$144$	199.725	−	273.513i	1.38698	−	1.89939i
$145$		−	3.66548i		−	0.0252792i
$146$	−52.7730	+	2.04169i	−0.361459	+	0.0139842i
$147$	−247.081	+	102.344i	−1.68083	+	0.696221i
$148$	144.167	+	47.0343i	0.974100	+	0.317799i
$149$	151.298	+	62.6697i	1.01542	+	0.420602i	0.827430	−	0.561569i	$-0.189802\pi$
$149$	151.298	+	62.6697i	1.01542	+	0.420602i	0.187993	+	0.982170i	$0.439802\pi$
$150$	41.5086	−	19.1055i	0.276724	−	0.127370i
$151$	−123.292	−	123.292i	−0.816505	−	0.816505i	0.169095	−	0.985600i	$-0.445916\pi$
$151$	−123.292	−	123.292i	−0.816505	−	0.816505i	−0.985600	+	0.169095i	$0.945916\pi$
$152$	−4.46380	+	15.7189i	−0.0293671	+	0.103414i
$153$	157.759	+	157.759i	1.03111	+	1.03111i
$154$	2.92496	−	7.91381i	0.0189933	−	0.0513883i
$155$	201.158	+	83.3223i	1.29779	+	0.537563i
$156$	196.487	+	168.225i	1.25953	+	1.07836i
$157$	107.069	−	44.3494i	0.681968	−	0.282480i	−0.0146813	−	0.999892i	$-0.504673\pi$
$157$	107.069	−	44.3494i	0.681968	−	0.282480i	0.696649	+	0.717412i	$0.254673\pi$
$158$	53.1939	+	49.2312i	0.336670	+	0.311590i
$159$		−	396.012i		−	2.49064i
$160$	121.707	−	80.7943i	0.760671	−	0.504964i
$161$	0.349573			0.00217126
$162$	−239.827	+	259.131i	−1.48041	+	1.59957i
$163$	−48.6441	−	117.437i	−0.298430	−	0.720474i	−0.999969	−	0.00784306i	$-0.997503\pi$
$163$	−48.6441	−	117.437i	−0.298430	−	0.720474i	0.701539	−	0.712631i	$-0.252497\pi$
$164$	−48.7141	−	41.7072i	−0.297037	−	0.254312i
$165$	72.9453	−	176.106i	0.442093	−	1.06731i
$166$	−55.0006	−	20.3284i	−0.331329	−	0.122460i
$167$	88.6392	−	88.6392i	0.530774	−	0.530774i	−0.390029	−	0.920803i	$-0.627535\pi$
$167$	88.6392	−	88.6392i	0.530774	−	0.530774i	0.920803	+	0.390029i	$0.127535\pi$
$168$	−21.2950	+	11.8754i	−0.126756	+	0.0706868i
$169$	21.4841	−	21.4841i	0.127125	−	0.127125i
$170$	40.2370	+	87.4189i	0.236688	+	0.514229i
$171$	16.5452	−	39.9437i	0.0967558	−	0.233589i
$172$	−145.499	−	47.4691i	−0.845927	−	0.275983i
$173$	87.2836	+	210.721i	0.504530	+	1.21804i	0.946993	+	0.321255i	$0.104105\pi$
$173$	87.2836	+	210.721i	0.504530	+	1.21804i	−0.442463	+	0.896787i	$0.645895\pi$
$174$	−0.340980	−	8.81356i	−0.00195966	−	0.0506527i
$175$	−2.30827			−0.0131901
$176$	−28.6795	+	118.206i	−0.162952	+	0.671625i
$177$			386.844i			2.18556i
$178$	6.17737	+	159.671i	0.0347043	+	0.897028i
$179$	−5.53118	+	2.29109i	−0.0309005	+	0.0127994i	−0.398080	−	0.917351i	$-0.630323\pi$
$179$	−5.53118	+	2.29109i	−0.0309005	+	0.0127994i	0.367180	+	0.930150i	$0.380323\pi$
$180$	−344.602	+	175.062i	−1.91446	+	0.972567i
$181$	−273.836	−	113.427i	−1.51291	−	0.626666i	−0.536751	−	0.843741i	$-0.680348\pi$
$181$	−273.836	−	113.427i	−1.51291	−	0.626666i	−0.976155	+	0.217075i	$0.930348\pi$
$182$	−5.46327	−	11.8695i	−0.0300180	−	0.0652171i
$183$	367.542	+	367.542i	2.00843	+	2.00843i
$184$	−5.00586	+	0.583331i	−0.0272057	+	0.00317028i
$185$	−122.379	−	122.379i	−0.661506	−	0.661506i
$186$	491.430	+	181.634i	2.64210	+	0.976526i
$187$	−74.0295	−	30.6640i	−0.395880	−	0.163979i
$188$	−24.8830	−	321.103i	−0.132356	−	1.70800i
$189$	34.2600	−	14.1909i	0.181270	−	0.0750843i
$190$	12.6672	−	13.6867i	0.0666693	−	0.0720355i
$191$			140.503i			0.735620i	0.929901	+	0.367810i	$0.119892\pi$
$191$			140.503i			0.735620i	−0.929901	+	0.367810i	$0.880108\pi$
$192$	285.126	−	205.590i	1.48503	−	1.07078i
$193$	−159.719			−0.827560			−0.413780	−	0.910377i	$-0.635792\pi$
$193$	−159.719			−0.827560			−0.413780	+	0.910377i	$0.635792\pi$
$194$	−232.767	−	215.427i	−1.19983	−	1.11045i
$195$	−112.971	−	272.735i	−0.579336	−	1.39864i
$196$	−194.186	+	15.0479i	−0.990746	+	0.0767751i
$197$	−23.3511	+	56.3745i	−0.118533	+	0.286165i	−0.971999	−	0.234984i	$-0.924496\pi$
$197$	−23.3511	+	56.3745i	−0.118533	+	0.286165i	0.853466	+	0.521149i	$0.174496\pi$
$198$	111.573	−	301.874i	0.563501	−	1.52461i
$199$	138.741	−	138.741i	0.697191	−	0.697191i	−0.266613	−	0.963804i	$-0.585904\pi$
$199$	138.741	−	138.741i	0.697191	−	0.697191i	0.963804	+	0.266613i	$0.0859044\pi$
$200$	33.0543	−	3.85181i	0.165272	−	0.0192591i
$201$	72.2974	−	72.2974i	0.359689	−	0.359689i
$202$	255.615	−	117.654i	1.26542	−	0.582444i
$203$	−0.170506	+	0.411638i	−0.000839931	+	0.00202777i
$204$	104.881	+	206.453i	0.514122	+	1.01203i
$205$	28.0083	+	67.6180i	0.136626	+	0.329844i
$206$	−28.1107	+	1.08755i	−0.136460	+	0.00527937i
$207$	13.3345			0.0644180
$208$	98.0403	+	160.854i	0.471348	+	0.773337i
$209$			15.5279i			0.0742963i
$210$	27.8063	−	1.07577i	0.132411	−	0.00512273i
$211$	−194.276	+	80.4718i	−0.920740	+	0.381383i	−0.792158	−	0.610316i	$-0.791043\pi$
$211$	−194.276	+	80.4718i	−0.920740	+	0.381383i	−0.128582	+	0.991699i	$0.541043\pi$
$212$	89.4516	−	274.182i	0.421942	−	1.29331i
$213$	−106.283	−	44.0237i	−0.498979	−	0.206684i
$214$	−326.689	+	150.368i	−1.52658	+	0.702653i
$215$	123.510	+	123.510i	0.574464	+	0.574464i
$216$	−466.920	+	260.383i	−2.16167	+	1.20548i
$217$	−18.7144	−	18.7144i	−0.0862414	−	0.0862414i
$218$	6.54620	−	17.7115i	0.0300284	−	0.0812452i
$219$	133.995	+	55.5025i	0.611849	+	0.253436i
$220$	90.2831	−	105.451i	0.410378	−	0.479323i
$221$	−114.650	+	47.4894i	−0.518776	+	0.214884i
$222$	−305.640	−	282.872i	−1.37676	−	1.27420i
$223$			285.957i			1.28232i	0.767408	+	0.641160i	$0.221546\pi$
$223$			285.957i			1.28232i	−0.767408	+	0.641160i	$0.778454\pi$
$224$	−17.4262	+	3.41187i	−0.0777954	+	0.0152316i
$225$	−88.0496			−0.391332
$226$	116.605	−	125.990i	0.515951	−	0.557480i
$227$	8.02885	+	19.3834i	0.0353694	+	0.0853893i	0.940577	−	0.339580i	$-0.110285\pi$
$227$	8.02885	+	19.3834i	0.0353694	+	0.0853893i	−0.905208	+	0.424969i	$0.860285\pi$
$228$	29.1847	−	34.0878i	0.128003	−	0.149508i
$229$	−66.9028	+	161.518i	−0.292152	+	0.705317i	−0.999999	−	0.00104819i	$-0.999666\pi$
$229$	−66.9028	+	161.518i	−0.292152	+	0.705317i	0.707848	+	0.706365i	$0.249666\pi$
$230$	5.39503	+	1.99402i	0.0234566	+	0.00866963i
$231$	−16.3837	+	16.3837i	−0.0709251	+	0.0709251i
$232$	1.75474	−	6.17915i	0.00756352	−	0.0266343i
$233$	282.286	−	282.286i	1.21153	−	1.21153i	0.241001	−	0.970525i	$-0.422524\pi$
$233$	282.286	−	282.286i	1.21153	−	1.21153i	0.970525	−	0.241001i	$-0.0774758\pi$
$234$	−208.398	−	452.765i	−0.890588	−	1.93489i
$235$	−140.662	+	339.587i	−0.598560	+	1.44505i
$236$	−87.3807	+	267.834i	−0.370257	+	1.13489i
$237$	−76.1714	−	183.894i	−0.321398	−	0.775925i
$238$	−0.452223	−	11.6889i	−0.00190010	−	0.0491131i
$239$	13.1618			0.0550704			0.0275352	−	0.999621i	$-0.491234\pi$
$239$	13.1618			0.0550704			0.0275352	+	0.999621i	$0.491234\pi$
$240$	−396.389	+	61.8053i	−1.65162	+	0.257522i
$241$		−	231.745i		−	0.961599i	−0.876830	−	0.480800i	$-0.840346\pi$
$241$		−	231.745i		−	0.961599i	0.876830	−	0.480800i	$-0.159654\pi$
$242$	−4.88701	−	126.318i	−0.0201943	−	0.521976i
$243$	340.169	−	140.903i	1.39987	−	0.579847i
$244$	171.450	+	337.491i	0.702663	+	1.38316i
$245$	205.364	+	85.0647i	0.838222	+	0.347203i
$246$	73.6354	+	159.980i	0.299331	+	0.650327i
$247$	17.0046	+	17.0046i	0.0688445	+	0.0688445i
$248$	299.217	+	236.760i	1.20652	+	0.954678i
$249$	113.866	+	113.866i	0.457293	+	0.457293i
$250$	−249.724	−	92.2986i	−0.998896	−	0.369194i
$251$	131.701	+	54.5521i	0.524703	+	0.217339i	0.629281	−	0.777177i	$-0.283349\pi$
$251$	131.701	+	54.5521i	0.524703	+	0.217339i	−0.104578	+	0.994517i	$0.533349\pi$
$252$	46.8425	−	3.62993i	0.185883	−	0.0144045i
$253$	−4.42459	+	1.83272i	−0.0174885	+	0.00724397i
$254$	23.4845	−	25.3748i	0.0924586	−	0.0999006i
$255$		−	264.282i		−	1.03640i
$256$	243.848	−	77.9367i	0.952531	−	0.304440i
$257$	−70.0955			−0.272745			−0.136373	−	0.990658i	$-0.543544\pi$
$257$	−70.0955			−0.272745			−0.136373	+	0.990658i	$0.543544\pi$
$258$	308.466	+	285.487i	1.19560	+	1.10654i
$259$	8.05061	+	19.4359i	0.0310834	+	0.0750420i
$260$	−16.6103	−	214.348i	−0.0638858	−	0.824415i
$261$	−6.50399	+	15.7020i	−0.0249195	+	0.0601610i
$262$	−72.8765	+	197.175i	−0.278155	+	0.752577i
$263$	−245.883	+	245.883i	−0.934916	+	0.934916i	−0.998008	−	0.0630921i	$-0.979904\pi$
$263$	−245.883	+	245.883i	−0.934916	+	0.934916i	0.0630921	+	0.998008i	$0.479904\pi$
$264$	207.274	−	261.953i	0.785128	−	0.992245i
$265$	−232.744	+	232.744i	−0.878280	+	0.878280i
$266$	−2.05920	+	0.947803i	−0.00774135	+	0.00356317i
$267$	167.929	−	405.417i	0.628949	−	1.51842i
$268$	66.3862	−	33.7250i	0.247710	−	0.125840i
$269$	7.33716	+	17.7135i	0.0272757	+	0.0658493i	0.936931	−	0.349516i	$-0.113654\pi$
$269$	7.33716	+	17.7135i	0.0272757	+	0.0658493i	−0.909655	+	0.415365i	$0.863654\pi$
$270$	609.688	−	23.5877i	2.25811	−	0.0873619i
$271$	327.600			1.20886			0.604429	−	0.796659i	$-0.293401\pi$
$271$	327.600			1.20886			0.604429	+	0.796659i	$0.293401\pi$
$272$	25.9811	+	166.630i	0.0955187	+	0.612610i
$273$			35.8835i			0.131441i
$274$	−72.1701	+	2.79213i	−0.263394	+	0.0101902i
$275$	29.2161	−	12.1017i	0.106240	−	0.0440063i
$276$	13.1577	+	4.29269i	0.0476728	+	0.0155532i
$277$	−31.9345	−	13.2277i	−0.115287	−	0.0477535i	0.324294	−	0.945956i	$-0.394873\pi$
$277$	−31.9345	−	13.2277i	−0.115287	−	0.0477535i	−0.439581	+	0.898203i	$0.644873\pi$
$278$	247.916	−	114.110i	0.891783	−	0.410468i
$279$	−713.864	−	713.864i	−2.55865	−	2.55865i
$280$	19.4949	+	5.53609i	0.0696246	+	0.0197718i
$281$	−263.413	−	263.413i	−0.937413	−	0.937413i	0.0607409	−	0.998154i	$-0.480654\pi$
$281$	−263.413	−	263.413i	−0.937413	−	0.937413i	−0.998154	+	0.0607409i	$0.980654\pi$
$282$	−306.627	+	829.614i	−1.08733	+	2.94189i
$283$	−268.113	−	111.056i	−0.947397	−	0.392425i	−0.145145	−	0.989410i	$-0.546365\pi$
$283$	−268.113	−	111.056i	−0.947397	−	0.392425i	−0.802252	+	0.596986i	$0.796365\pi$
$284$	−63.6413	−	54.4873i	−0.224089	−	0.191857i
$285$	−47.3158	+	19.5989i	−0.166020	+	0.0687679i
$286$	131.378	+	121.591i	0.459365	+	0.425145i
$287$		−	8.89644i		−	0.0309980i
$288$	−664.724	+	130.146i	−2.30807	+	0.451897i
$289$	177.904			0.615585
$290$	−4.97950	+	5.38030i	−0.0171707	+	0.0185528i
$291$	333.313	+	804.689i	1.14541	+	2.76526i
$292$	80.2353	+	68.6944i	0.274778	+	0.235255i
$293$	44.7772	−	108.102i	0.152823	−	0.368948i	−0.828863	−	0.559451i	$-0.811012\pi$
$293$	44.7772	−	108.102i	0.152823	−	0.368948i	0.981687	+	0.190503i	$0.0610120\pi$
$294$	501.706	+	185.432i	1.70648	+	0.630721i
$295$	227.356	−	227.356i	0.770698	−	0.770698i
$296$	−147.717	−	264.887i	−0.499043	−	0.894887i
$297$	−359.233	+	359.233i	−1.20954	+	1.20954i
$298$	−136.944	−	297.524i	−0.459543	−	0.998404i
$299$	−2.83834	+	6.85237i	−0.00949279	+	0.0229176i
$300$	−86.8820	−	28.3452i	−0.289607	−	0.0944840i
$301$	−8.12503	−	19.6155i	−0.0269934	−	0.0651679i
$302$	13.4814	+	348.462i	0.0446403	+	1.15385i
$303$	−772.765			−2.55038
$304$	27.9060	−	17.0087i	0.0917960	−	0.0559495i
$305$		−	432.024i		−	1.41647i
$306$	−17.2501	−	445.876i	−0.0563730	−	1.45711i
$307$	430.497	−	178.318i	1.40227	−	0.580839i	0.451930	−	0.892054i	$-0.350736\pi$
$307$	430.497	−	178.318i	1.40227	−	0.580839i	0.950340	+	0.311215i	$0.100736\pi$
$308$	−15.0441	+	7.64260i	−0.0488446	+	0.0248136i
$309$	71.3754	+	29.5646i	0.230988	+	0.0956784i
$310$	−182.073	−	395.573i	−0.587333	−	1.27604i
$311$	−61.3250	−	61.3250i	−0.197187	−	0.197187i	0.601606	−	0.798793i	$-0.294528\pi$
$311$	−61.3250	−	61.3250i	−0.197187	−	0.197187i	−0.798793	+	0.601606i	$0.794528\pi$
$312$	−59.8787	−	513.849i	−0.191919	−	1.64695i
$313$	129.308	+	129.308i	0.413124	+	0.413124i	0.882826	−	0.469701i	$-0.155638\pi$
$313$	129.308	+	129.308i	0.413124	+	0.413124i	−0.469701	+	0.882826i	$0.655638\pi$
$314$	−217.407	−	80.3541i	−0.692379	−	0.255905i
$315$	−49.5390	−	20.5197i	−0.157267	−	0.0651420i
$316$	−11.1996	−	144.526i	−0.0354419	−	0.457361i
$317$	−286.711	+	118.760i	−0.904452	+	0.374636i	−0.785930	−	0.618315i	$-0.787816\pi$
$317$	−286.711	+	118.760i	−0.904452	+	0.374636i	−0.118522	+	0.992951i	$0.537816\pi$
$318$	−537.976	+	581.278i	−1.69175	+	1.82792i
$319$		−	6.10408i		−	0.0191350i
$320$	−288.403	−	46.7454i	−0.901261	−	0.146079i
$321$	987.635			3.07674
$322$	−0.513113	−	0.474889i	−0.00159352	−	0.00147481i
$323$	8.23877	+	19.8901i	0.0255070	+	0.0615794i
$324$	704.050	−	54.5584i	2.17299	−	0.168390i
$325$	18.7420	−	45.2471i	0.0576676	−	0.139222i
$326$	−88.1354	+	238.460i	−0.270354	+	0.731472i
$327$	−36.6674	+	36.6674i	−0.112133	+	0.112133i
$328$	14.8455	+	127.396i	0.0452606	+	0.388403i
$329$	31.5929	−	31.5929i	0.0960271	−	0.0960271i
$330$	−346.308	+	159.398i	−1.04942	+	0.483024i
$331$	123.164	−	297.345i	0.372098	−	0.898324i	−0.621297	−	0.783575i	$-0.713394\pi$
$331$	123.164	−	297.345i	0.372098	−	0.898324i	0.993395	−	0.114748i	$-0.0366061\pi$
$332$	53.1158	+	104.556i	0.159987	+	0.314928i
$333$	307.092	+	741.386i	0.922198	+	2.22638i
$334$	−250.522	+	9.69223i	−0.750066	+	0.0290187i
$335$	−84.9812			−0.253675
$336$	47.3899	+	11.4979i	0.141041	+	0.0342199i
$337$		−	263.653i		−	0.782354i	−0.920315	−	0.391177i	$-0.872068\pi$
$337$		−	263.653i		−	0.782354i	0.920315	−	0.391177i	$-0.127932\pi$
$338$	−60.7209	+	2.34918i	−0.179648	+	0.00695023i
$339$	−435.556	+	180.413i	−1.28483	+	0.532192i
$340$	59.6962	−	182.977i	0.175577	−	0.538168i
$341$	334.985	+	138.755i	0.982362	+	0.406908i
$342$	−78.5485	+	36.1541i	−0.229674	+	0.105714i
$343$	−38.3323	−	38.3323i	−0.111756	−	0.111756i
$344$	149.082	+	267.335i	0.433379	+	0.777137i
$345$	−11.1691	−	11.1691i	−0.0323743	−	0.0323743i
$346$	158.144	−	427.876i	0.457064	−	1.23664i
$347$	−388.417	−	160.888i	−1.11936	−	0.463653i	−0.255208	−	0.966886i	$-0.582144\pi$
$347$	−388.417	−	160.888i	−1.11936	−	0.463653i	−0.864151	+	0.503233i	$0.832144\pi$
$348$	−11.4726	+	13.4000i	−0.0329672	+	0.0385058i
$349$	448.277	−	185.683i	1.28446	−	0.532042i	0.367132	−	0.930169i	$-0.380340\pi$
$349$	448.277	−	185.683i	1.28446	−	0.532042i	0.917330	+	0.398127i	$0.130340\pi$
$350$	3.38815	+	3.13575i	0.00968044	+	0.00895930i
$351$			786.791i			2.24157i
$352$	202.678	−	134.546i	0.575789	−	0.382232i
$353$	−106.951			−0.302976			−0.151488	−	0.988459i	$-0.548407\pi$
$353$	−106.951			−0.302976			−0.151488	+	0.988459i	$0.548407\pi$
$354$	525.522	−	567.821i	1.48452	−	1.60401i
$355$	36.5908	+	88.3379i	0.103073	+	0.248839i
$356$	207.843	−	242.761i	0.583829	−	0.681914i
$357$	−12.2935	+	29.6791i	−0.0344356	+	0.0831348i
$358$	11.2312	+	4.15109i	0.0313722	+	0.0115952i
$359$	−208.761	+	208.761i	−0.581508	+	0.581508i	−0.935317	−	0.353810i	$-0.884886\pi$
$359$	−208.761	+	208.761i	−0.581508	+	0.581508i	0.353810	+	0.935317i	$0.384886\pi$
$360$	743.636	+	211.175i	2.06566	+	0.586598i
$361$	−252.315	+	252.315i	−0.698935	+	0.698935i
$362$	247.856	+	538.492i	0.684685	+	1.48755i
$363$	−132.852	+	320.732i	−0.365982	+	0.883559i
$364$	−8.10539	+	24.8442i	−0.0222676	+	0.0682532i
$365$	−46.1315	−	111.371i	−0.126388	−	0.305127i
$366$	−40.1888	−	1038.79i	−0.109806	−	2.83822i
$367$	711.002			1.93734			0.968668	−	0.248361i	$-0.0798919\pi$
$367$	711.002			1.93734			0.968668	+	0.248361i	$0.0798919\pi$
$368$	8.14019	+	5.94415i	0.0221201	+	0.0161526i
$369$		−	339.356i		−	0.919665i
$370$	13.3815	+	345.880i	0.0361661	+	0.934811i
$371$	36.9639	−	15.3110i	0.0996332	−	0.0412694i
$372$	−474.589	−	934.207i	−1.27578	−	2.51131i
$373$	−587.430	−	243.321i	−1.57488	−	0.652336i	−0.587287	−	0.809379i	$-0.699804\pi$
$373$	−587.430	−	243.321i	−1.57488	−	0.652336i	−0.987592	+	0.157043i	$0.949804\pi$
$374$	67.0060	+	145.577i	0.179160	+	0.389244i
$375$	516.995	+	516.995i	1.37865	+	1.37865i
$376$	−399.689	+	505.128i	−1.06300	+	1.34342i
$377$	−6.68456	−	6.68456i	−0.0177309	−	0.0177309i
$378$	−69.5659	−	25.7117i	−0.184037	−	0.0680205i
$379$	−34.5203	−	14.2988i	−0.0910825	−	0.0377276i	0.336677	−	0.941620i	$-0.390697\pi$
$379$	−34.5203	−	14.2988i	−0.0910825	−	0.0377276i	−0.427759	+	0.903893i	$0.640697\pi$
$380$	−37.1864	+	2.88166i	−0.0978591	+	0.00758332i
$381$	−87.7220	+	36.3356i	−0.230241	+	0.0953691i
$382$	190.872	−	206.235i	0.499664	−	0.539882i
$383$		−	347.623i		−	0.907631i	−0.891096	−	0.453815i	$-0.850063\pi$
$383$		−	347.623i		−	0.907631i	0.891096	−	0.453815i	$-0.149937\pi$
$384$	−697.807	−	85.5695i	−1.81721	−	0.222837i
$385$	19.2580			0.0500209
$386$	234.440	+	216.976i	0.607359	+	0.562114i
$387$	−309.931	−	748.239i	−0.800855	−	1.93343i
$388$	49.0077	+	632.421i	0.126309	+	1.62995i
$389$	−60.7529	+	146.670i	−0.156177	+	0.377045i	−0.982529	−	0.186109i	$-0.940412\pi$
$389$	−60.7529	+	146.670i	−0.156177	+	0.377045i	0.826352	+	0.563154i	$0.190412\pi$
$390$	−204.685	+	553.797i	−0.524833	+	1.41999i
$391$	−4.69517	+	4.69517i	−0.0120081	+	0.0120081i
$392$	305.474	+	241.711i	0.779271	+	0.616610i
$393$	408.205	−	408.205i	1.03869	−	1.03869i
$394$	110.859	−	51.0260i	0.281368	−	0.129508i
$395$	−63.3107	+	152.846i	−0.160280	+	0.386951i
$396$	−573.861	+	291.528i	−1.44914	+	0.736183i
$397$	179.460	+	433.255i	0.452041	+	1.09132i	0.971545	+	0.236855i	$0.0761165\pi$
$397$	179.460	+	433.255i	0.452041	+	1.09132i	−0.519505	+	0.854468i	$0.673883\pi$
$398$	−392.126	+	15.1706i	−0.985240	+	0.0381171i
$399$	6.22529			0.0156022
$400$	−53.7507	−	39.2500i	−0.134377	−	0.0981250i
$401$			680.550i			1.69713i	0.529089	+	0.848566i	$0.322534\pi$
$401$			680.550i			1.69713i	−0.529089	+	0.848566i	$0.677466\pi$
$402$	−204.335	+	7.90535i	−0.508297	+	0.0196650i
$403$	518.792	−	214.891i	1.28733	−	0.533228i
$404$	−535.029	−	174.553i	−1.32433	−	0.432062i
$405$	−744.578	−	308.414i	−1.83847	−	0.761517i
$406$	0.809477	−	0.372584i	0.00199379	−	0.000917696i
$407$	−203.795	−	203.795i	−0.500725	−	0.500725i
$408$	126.517	−	445.517i	0.310090	−	1.09195i
$409$	239.915	+	239.915i	0.586589	+	0.586589i	0.936706	−	0.350117i	$-0.113858\pi$
$409$	239.915	+	239.915i	0.586589	+	0.586589i	−0.350117	+	0.936706i	$0.613858\pi$
$410$	50.7466	−	137.301i	0.123772	−	0.334879i
$411$	183.246	+	75.9028i	0.445853	+	0.184678i
$412$	42.7391	+	36.5916i	0.103736	+	0.0888146i
$413$	−36.1082	+	14.9565i	−0.0874289	+	0.0362143i
$414$	−19.5728	−	18.1147i	−0.0472773	−	0.0437554i
$415$		−	133.843i		−	0.322512i
$416$	74.6112	−	369.292i	0.179354	−	0.887722i
$417$	−749.489			−1.79734
$418$	21.0944	−	22.7923i	0.0504652	−	0.0545271i
$419$	33.5102	+	80.9009i	0.0799767	+	0.193081i	0.958810	−	0.284048i	$-0.0916775\pi$
$419$	33.5102	+	80.9009i	0.0799767	+	0.193081i	−0.878833	+	0.477129i	$0.841678\pi$
$420$	−42.2763	−	36.1954i	−0.100658	−	0.0861794i
$421$	37.2975	−	90.0441i	0.0885926	−	0.213882i	−0.873373	−	0.487052i	$-0.838072\pi$
$421$	37.2975	−	90.0441i	0.0885926	−	0.213882i	0.961966	+	0.273170i	$0.0880723\pi$
$422$	394.484	+	145.802i	0.934796	+	0.345503i
$423$	1205.12	−	1205.12i	2.84898	−	2.84898i
$424$	−503.771	+	280.933i	−1.18814	+	0.662579i
$425$	31.0028	−	31.0028i	0.0729479	−	0.0729479i
$426$	96.1991	+	209.002i	0.225820	+	0.490616i
$427$	−20.0963	+	48.5167i	−0.0470639	+	0.113622i
$428$	683.796	+	223.088i	1.59765	+	0.521233i
$429$	−188.128	−	454.182i	−0.438527	−	1.05870i
$430$	−13.5051	−	349.077i	−0.0314073	−	0.811808i
$431$	−509.094			−1.18119			−0.590596	−	0.806967i	$-0.701107\pi$
$431$	−509.094			−1.18119			−0.590596	+	0.806967i	$0.701107\pi$
$432$	1039.08	+	252.106i	2.40529	+	0.583578i
$433$		−	66.0083i		−	0.152444i	−0.997091	−	0.0762220i	$-0.975714\pi$
$433$		−	66.0083i		−	0.152444i	0.997091	−	0.0762220i	$-0.0242858\pi$
$434$	2.04632	+	52.8927i	0.00471502	+	0.121873i
$435$	18.6000	−	7.70438i	0.0427586	−	0.0177112i
$436$	−33.6694	+	17.1045i	−0.0772235	+	0.0392305i
$437$	1.18879	+	0.492414i	0.00272035	+	0.00112681i
$438$	−121.282	−	263.498i	−0.276900	−	0.601593i
$439$	−39.8501	−	39.8501i	−0.0907747	−	0.0907747i	0.660261	−	0.751036i	$-0.270446\pi$
$439$	−39.8501	−	39.8501i	−0.0907747	−	0.0907747i	−0.751036	+	0.660261i	$0.770446\pi$
$440$	−275.774	+	32.1358i	−0.626758	+	0.0730360i
$441$	−728.792	−	728.792i	−1.65259	−	1.65259i
$442$	232.800	+	86.0433i	0.526696	+	0.194668i
$443$	−193.778	−	80.2656i	−0.437423	−	0.181187i	0.153094	−	0.988212i	$-0.451076\pi$
$443$	−193.778	−	80.2656i	−0.437423	−	0.181187i	−0.590517	+	0.807025i	$0.701076\pi$
$444$	64.3507	+	830.415i	0.144934	+	1.87030i
$445$	−336.967	+	139.576i	−0.757229	+	0.313655i
$446$	388.468	−	419.736i	0.871005	−	0.941113i
$447$			899.465i			2.01223i
$448$	30.2136	+	18.6651i	0.0674410	+	0.0416632i
$449$	124.217			0.276652			0.138326	−	0.990387i	$-0.455828\pi$
$449$	124.217			0.276652			0.138326	+	0.990387i	$0.455828\pi$
$450$	129.242	+	119.614i	0.287204	+	0.265809i
$451$	46.6418	+	112.603i	0.103419	+	0.249675i
$452$	−342.312	+	26.5265i	−0.757327	+	0.0586870i
$453$	366.485	−	884.774i	0.809019	−	1.95314i
$454$	14.5470	−	39.3585i	0.0320419	−	0.0866928i
$455$	21.0894	−	21.0894i	0.0463504	−	0.0463504i
$456$	−89.1458	+	10.3881i	−0.195495	+	0.0227810i
$457$	−573.100	+	573.100i	−1.25405	+	1.25405i	−0.300159	+	0.953889i	$0.597040\pi$
$457$	−573.100	+	573.100i	−1.25405	+	1.25405i	−0.953889	+	0.300159i	$0.902960\pi$
$458$	317.621	−	146.194i	0.693495	−	0.319200i
$459$	−269.550	+	650.752i	−0.587256	+	1.41776i
$460$	−5.21014	−	10.2559i	−0.0113264	−	0.0222955i
$461$	−86.0707	−	207.793i	−0.186704	−	0.450744i	0.802617	−	0.596495i	$-0.203440\pi$
$461$	−86.0707	−	207.793i	−0.186704	−	0.450744i	−0.989321	+	0.145750i	$0.953440\pi$
$462$	46.3054	−	1.79147i	0.100228	−	0.00387764i
$463$	−555.587			−1.19997			−0.599986	−	0.800010i	$-0.704827\pi$
$463$	−555.587			−1.19997			−0.599986	+	0.800010i	$0.704827\pi$
$464$	−10.9699	+	6.68616i	−0.0236421	+	0.0144098i
$465$			1195.88i			2.57179i
$466$	−797.827	+	30.8664i	−1.71208	+	0.0662370i
$467$	−319.806	+	132.468i	−0.684809	+	0.283657i	−0.697835	−	0.716258i	$-0.745853\pi$
$467$	−319.806	+	132.468i	−0.684809	+	0.283657i	0.0130269	+	0.999915i	$0.495853\pi$
$468$	−309.182	+	947.686i	−0.660645	+	2.02497i
$469$	9.54349	+	3.95304i	0.0203486	+	0.00842866i
$470$	667.791	−	307.369i	1.42083	−	0.653977i
$471$	450.090	+	450.090i	0.955606	+	0.955606i
$472$	492.108	−	274.429i	1.04260	−	0.581418i
$473$	205.679	+	205.679i	0.434839	+	0.434839i
$474$	−138.011	+	373.403i	−0.291162	+	0.787769i
$475$	−7.84975	−	3.25147i	−0.0165258	−	0.00684521i
$476$	−15.2154	+	17.7717i	−0.0319652	+	0.0373355i
$477$	1410.00	−	584.039i	2.95597	−	1.22440i
$478$	−19.3193	−	17.8801i	−0.0404170	−	0.0374061i
$479$		−	239.576i		−	0.500159i	−0.968225	−	0.250079i	$-0.919543\pi$
$479$		−	239.576i		−	0.500159i	0.968225	−	0.250079i	$-0.0804567\pi$
$480$	665.793	+	447.769i	1.38707	+	0.932852i
$481$	−446.351			−0.927965
$482$	−314.822	+	340.163i	−0.653159	+	0.705732i
$483$	0.734757	+	1.77386i	0.00152124	+	0.00367259i
$484$	−164.428	+	192.052i	−0.339727	+	0.396802i
$485$	277.037	−	668.826i	0.571210	−	1.37902i
$486$	−690.725	−	255.294i	−1.42124	−	0.525295i
$487$	−269.525	+	269.525i	−0.553439	+	0.553439i	−0.927432	−	0.373992i	$-0.877989\pi$
$487$	−269.525	+	269.525i	−0.553439	+	0.553439i	0.373992	+	0.927432i	$0.377989\pi$
$488$	206.818	−	728.291i	0.423807	−	1.49240i
$489$	493.676	−	493.676i	1.00956	−	1.00956i
$490$	−185.881	−	403.845i	−0.379348	−	0.824173i
$491$	285.394	−	689.002i	0.581250	−	1.40326i	−0.310430	−	0.950596i	$-0.600473\pi$
$491$	285.394	−	689.002i	0.581250	−	1.40326i	0.891680	−	0.452666i	$-0.149527\pi$
$492$	109.247	−	334.856i	0.222046	−	0.680602i
$493$	−3.23869	−	7.81888i	−0.00656934	−	0.0158598i
$494$	−1.85936	−	48.0603i	−0.00376389	−	0.0972881i
$495$	734.601			1.48404
$496$	−117.565	−	754.005i	−0.237026	−	1.52017i
$497$		−	11.6225i		−	0.0233854i
$498$	−12.4507	−	321.821i	−0.0250013	−	0.646227i
$499$	581.267	−	240.769i	1.16486	−	0.482503i	0.285373	−	0.958417i	$-0.407883\pi$
$499$	581.267	−	240.769i	1.16486	−	0.482503i	0.879492	+	0.475914i	$0.157883\pi$
$500$	241.166	+	474.725i	0.482332	+	0.949449i
$501$	636.096	+	263.479i	1.26965	+	0.525907i
$502$	−119.206	−	258.986i	−0.237461	−	0.515909i
$503$	204.189	+	204.189i	0.405942	+	0.405942i	0.880321	−	0.474379i	$-0.157327\pi$
$503$	204.189	+	204.189i	0.405942	+	0.405942i	−0.474379	+	0.880321i	$0.657327\pi$
$504$	−73.6880	−	58.3067i	−0.146206	−	0.115688i
$505$	454.169	+	454.169i	0.899345	+	0.899345i
$506$	8.98426	+	3.32061i	0.0177555	+	0.00656246i
$507$	154.175	+	63.8615i	0.304093	+	0.125960i
$508$	−68.9424	+	5.34250i	−0.135713	+	0.0105167i
$509$	−397.562	+	164.676i	−0.781066	+	0.323528i	−0.737345	−	0.675516i	$-0.763921\pi$
$509$	−397.562	+	164.676i	−0.781066	+	0.323528i	−0.0437202	+	0.999044i	$0.513921\pi$
$510$	−359.022	+	387.920i	−0.703965	+	0.760628i
$511$			14.6530i			0.0286751i
$512$	−463.803	−	216.866i	−0.905865	−	0.423566i
$513$	136.497			0.266077
$514$	102.888	+	95.2236i	0.200172	+	0.185260i
$515$	−24.5730	−	59.3244i	−0.0477145	−	0.115193i
$516$	−64.9456	−	838.091i	−0.125863	−	1.62421i
$517$	−234.242	+	565.510i	−0.453079	+	1.09383i
$518$	14.5864	−	39.4652i	0.0281591	−	0.0761876i
$519$	−885.818	+	885.818i	−1.70678	+	1.70678i
$520$	−266.807	+	337.191i	−0.513091	+	0.648444i
$521$	−333.835	+	333.835i	−0.640759	+	0.640759i	−0.950742	−	0.309983i	$-0.899676\pi$
$521$	−333.835	+	333.835i	−0.640759	+	0.640759i	0.309983	+	0.950742i	$0.399676\pi$
$522$	30.8777	−	14.2123i	0.0591526	−	0.0272266i
$523$	−211.672	+	511.022i	−0.404727	+	0.977097i	0.581775	+	0.813350i	$0.302358\pi$
$523$	−211.672	+	511.022i	−0.404727	+	0.977097i	−0.986502	+	0.163748i	$0.947642\pi$
$524$	374.830	−	190.418i	0.715324	−	0.363393i
$525$	−4.85170	−	11.7130i	−0.00924132	−	0.0223105i
$526$	694.942	−	26.8860i	1.32118	−	0.0511141i
$527$	502.712			0.953913
$528$	−660.101	+	102.924i	−1.25019	+	0.194931i
$529$		−	528.603i		−	0.999250i
$530$	657.808	−	25.4494i	1.24115	−	0.0480177i
$531$	−1377.35	+	570.518i	−2.59388	+	1.07442i
$532$	4.31013	+	1.40618i	0.00810174	+	0.00264319i
$533$	174.389	+	72.2343i	0.327184	+	0.135524i
$534$	−797.245	+	366.954i	−1.49297	+	0.687180i
$535$	−580.452	−	580.452i	−1.08496	−	1.08496i
$536$	−143.259	−	40.6821i	−0.267273	−	0.0758994i
$537$	−23.2517	−	23.2517i	−0.0432992	−	0.0432992i
$538$	13.2938	−	35.9677i	0.0247096	−	0.0668545i
$539$	341.990	+	141.657i	0.634490	+	0.262815i
$540$	−926.962	−	793.629i	−1.71660	−	1.46968i
$541$	−529.582	+	219.360i	−0.978896	+	0.405472i	−0.814016	−	0.580842i	$-0.802723\pi$
$541$	−529.582	+	219.360i	−0.978896	+	0.405472i	−0.164879	+	0.986314i	$0.552723\pi$
$542$	−480.861	−	445.040i	−0.887198	−	0.821107i
$543$		−	1627.95i		−	2.99807i
$544$	188.228	−	279.879i	0.346008	−	0.514484i
$545$	43.1003			0.0790832
$546$	48.7471	−	52.6708i	0.0892805	−	0.0964667i
$547$	−68.4960	−	165.364i	−0.125221	−	0.302311i	0.848820	−	0.528682i	$-0.177314\pi$
$547$	−68.4960	−	165.364i	−0.125221	−	0.302311i	−0.974041	+	0.226371i	$0.927314\pi$
$548$	109.726	+	93.9435i	0.200231	+	0.171430i
$549$	−766.577	+	1850.68i	−1.39632	+	3.37100i
$550$	−59.3243	−	21.9264i	−0.107862	−	0.0398662i
$551$	−1.15968	+	1.15968i	−0.00210468	+	0.00210468i
$552$	−13.4817	−	24.1755i	−0.0244234	−	0.0437961i
$553$	14.2197	−	14.2197i	0.0257138	−	0.0257138i
$554$	28.9048	+	62.7986i	0.0521747	+	0.113355i
$555$	363.770	−	878.217i	0.655441	−	1.58237i
$556$	−518.914	−	169.295i	−0.933299	−	0.304488i
$557$	−308.610	−	745.049i	−0.554057	−	1.33761i	−0.914408	−	0.404794i	$-0.867343\pi$
$557$	−308.610	−	745.049i	−0.554057	−	1.33761i	0.360351	−	0.932817i	$-0.382657\pi$
$558$	78.0573	+	2017.60i	0.139888	+	3.61578i
$559$	450.477			0.805863
$560$	−21.0945	−	34.6095i	−0.0376687	−	0.0618027i
$561$		−	440.104i		−	0.784500i
$562$	28.8028	+	744.487i	0.0512506	+	1.32471i
$563$	−347.195	+	143.813i	−0.616687	+	0.255440i	−0.669085	−	0.743186i	$-0.733314\pi$
$563$	−347.195	+	143.813i	−0.616687	+	0.255440i	0.0523978	+	0.998626i	$0.483314\pi$
$564$	1577.09	−	801.183i	2.79626	−	1.42054i
$565$	362.017	+	149.952i	0.640738	+	0.265402i
$566$	242.676	+	527.239i	0.428757	+	0.931518i
$567$	69.2706	+	69.2706i	0.122170	+	0.122170i
$568$	19.3945	+	166.434i	0.0341452	+	0.293017i
$569$	717.322	+	717.322i	1.26067	+	1.26067i	0.950768	+	0.309903i	$0.100297\pi$
$569$	717.322	+	717.322i	1.26067	+	1.26067i	0.309903	+	0.950768i	$0.399703\pi$
$570$	96.0763	+	35.5100i	0.168555	+	0.0622983i
$571$	−327.041	−	135.465i	−0.572751	−	0.237241i	0.0774591	−	0.996996i	$-0.475319\pi$
$571$	−327.041	−	135.465i	−0.572751	−	0.237241i	−0.650210	+	0.759754i	$0.725319\pi$
$572$	−27.6609	−	356.951i	−0.0483582	−	0.624039i
$573$	−712.966	+	295.320i	−1.24427	+	0.515393i
$574$	−12.0857	+	13.0584i	−0.0210552	+	0.0227499i
$575$		−	2.62050i		−	0.00455740i
$576$	1152.50	+	711.985i	2.00087	+	1.23608i
$577$	531.710			0.921507			0.460754	−	0.887528i	$-0.347579\pi$
$577$	531.710			0.921507			0.460754	+	0.887528i	$0.347579\pi$
$578$	−261.133	−	241.680i	−0.451787	−	0.418131i
$579$	−335.709	−	810.473i	−0.579808	−	1.39978i
$580$	14.6181	−	1.13279i	0.0252036	−	0.00195309i
$581$	−6.22591	+	15.0307i	−0.0107158	+	0.0258703i
$582$	603.911	−	1633.95i	1.03765	−	2.80747i
$583$	−387.585	+	387.585i	−0.664812	+	0.664812i
$584$	−24.4514	−	209.830i	−0.0418689	−	0.359298i
$585$	804.460	−	804.460i	1.37515	−	1.37515i
$586$	−212.580	+	97.8456i	−0.362764	+	0.166972i
$587$	105.581	−	254.894i	0.179865	−	0.434232i	−0.808073	−	0.589082i	$-0.799490\pi$
$587$	105.581	−	254.894i	0.179865	−	0.434232i	0.987938	+	0.154850i	$0.0494895\pi$
$588$	−484.513	−	953.743i	−0.824001	−	1.62201i
$589$	−37.2806	−	90.0034i	−0.0632948	−	0.152807i
$590$	−642.579	+	24.8602i	−1.08912	+	0.0421359i
$591$	−335.145			−0.567082
$592$	−143.021	+	589.479i	−0.241590	+	0.995742i
$593$		−	405.861i		−	0.684419i	−0.939624	−	0.342210i	$-0.888825\pi$
$593$		−	405.861i		−	0.684419i	0.939624	−	0.342210i	$-0.111175\pi$
$594$	1015.31	−	39.2803i	1.70927	−	0.0661284i
$595$	24.6681	−	10.2179i	0.0414590	−	0.0171729i
$596$	−203.172	+	622.751i	−0.340892	+	1.04488i
$597$	995.638	+	412.407i	1.66774	+	0.690799i
$598$	13.4750	−	6.20226i	0.0225335	−	0.0103717i
$599$	561.484	+	561.484i	0.937370	+	0.937370i	0.998151	−	0.0607815i	$-0.0193593\pi$
$599$	561.484	+	561.484i	0.937370	+	0.937370i	−0.0607815	+	0.998151i	$0.519359\pi$
$600$	89.0215	+	159.634i	0.148369	+	0.266056i
$601$	−358.762	−	358.762i	−0.596941	−	0.596941i	0.342556	−	0.939497i	$-0.388707\pi$
$601$	−358.762	−	358.762i	−0.596941	−	0.596941i	−0.939497	+	0.342556i	$0.888707\pi$
$602$	−14.7213	+	39.8300i	−0.0244539	+	0.0661628i
$603$	364.038	+	150.790i	0.603712	+	0.250066i
$604$	453.592	−	529.797i	0.750981	−	0.877148i
$605$	266.580	−	110.421i	0.440628	−	0.182514i
$606$	1134.29	+	1049.79i	1.87176	+	1.73233i
$607$			571.923i			0.942213i	0.882076	+	0.471107i	$0.156145\pi$
$607$			571.923i			0.942213i	−0.882076	+	0.471107i	$0.843855\pi$
$608$	−64.0672	−	12.9440i	−0.105374	−	0.0212895i
$609$	−2.44718			−0.00401836
$610$	−586.897	+	634.137i	−0.962126	+	1.03957i
$611$	362.771	+	875.806i	0.593733	+	1.43340i
$612$	−580.396	+	677.904i	−0.948359	+	1.10769i
$613$	401.254	−	968.712i	0.654574	−	1.58028i	−0.151494	−	0.988458i	$-0.548409\pi$
$613$	401.254	−	968.712i	0.654574	−	1.58028i	0.806068	−	0.591823i	$-0.201591\pi$
$614$	−874.137	−	323.083i	−1.42368	−	0.526194i
$615$	−284.249	+	284.249i	−0.462193	+	0.462193i
$616$	32.4645	+	9.21918i	0.0527022	+	0.0149662i
$617$	−151.870	+	151.870i	−0.246143	+	0.246143i	−0.819386	−	0.573242i	$-0.805685\pi$
$617$	−151.870	+	151.870i	−0.246143	+	0.246143i	0.573242	+	0.819386i	$0.305685\pi$
$618$	−64.6037	−	140.358i	−0.104537	−	0.227117i
$619$	146.518	−	353.725i	0.236701	−	0.571446i	−0.760237	−	0.649646i	$-0.774917\pi$
$619$	146.518	−	353.725i	0.236701	−	0.571446i	0.996938	+	0.0781999i	$0.0249173\pi$
$620$	−270.127	+	827.977i	−0.435688	+	1.33545i
$621$	16.1105	+	38.8941i	0.0259428	+	0.0626314i
$622$	6.70557	+	173.324i	0.0107807	+	0.278656i
$623$	44.3344			0.0711628
$624$	−610.164	+	835.587i	−0.977827	+	1.33908i
$625$		−	503.703i		−	0.805924i
$626$	−14.1391	−	365.465i	−0.0225865	−	0.583809i
$627$	−78.7944	+	32.6377i	−0.125669	+	0.0520537i
$628$	209.956	+	413.290i	0.334325	+	0.658105i
$629$	−369.176	−	152.918i	−0.586925	−	0.243112i
$630$	44.8390	+	97.4174i	0.0711731	+	0.154631i
$631$	−682.535	−	682.535i	−1.08167	−	1.08167i	−0.996354	−	0.0853189i	$-0.972809\pi$
$631$	−682.535	−	682.535i	−1.08167	−	1.08167i	−0.0853189	−	0.996354i	$-0.527191\pi$
$632$	−179.897	+	227.354i	−0.284647	+	0.359737i
$633$	−816.687	−	816.687i	−1.29018	−	1.29018i
$634$	582.176	+	215.174i	0.918259	+	0.339391i
$635$	72.9111	+	30.2007i	0.114821	+	0.0475602i
$636$	1579.31	−	122.385i	2.48320	−	0.192429i
$637$	529.641	−	219.385i	0.831462	−	0.344403i
$638$	−8.29229	+	8.95974i	−0.0129973	+	0.0140435i
$639$		−	443.344i		−	0.693808i
$640$	359.824	+	460.406i	0.562225	+	0.719384i
$641$	38.9310			0.0607348			0.0303674	−	0.999539i	$-0.490332\pi$
$641$	38.9310			0.0607348			0.0303674	+	0.999539i	$0.490332\pi$
$642$	−1449.68	−	1341.69i	−2.25807	−	2.08985i
$643$	318.631	+	769.243i	0.495538	+	1.19633i	0.951864	+	0.306522i	$0.0991652\pi$
$643$	318.631	+	769.243i	0.495538	+	1.19633i	−0.456326	+	0.889813i	$0.650835\pi$
$644$	0.108033	+	1.39411i	0.000167753	+	0.00216477i
$645$	−367.132	+	886.335i	−0.569197	+	1.37416i
$646$	14.9273	−	40.3876i	0.0231073	−	0.0625194i
$647$	−157.445	+	157.445i	−0.243346	+	0.243346i	−0.818233	−	0.574887i	$-0.805046\pi$
$647$	−157.445	+	157.445i	−0.243346	+	0.243346i	0.574887	+	0.818233i	$0.305046\pi$
$648$	−1107.54	−	876.358i	−1.70917	−	1.35240i
$649$	378.612	−	378.612i	0.583378	−	0.583378i
$650$	−88.9774	+	40.9543i	−0.136888	+	0.0630067i
$651$	55.6284	−	134.299i	0.0854507	−	0.206296i
$652$	453.312	−	230.288i	0.695264	−	0.353202i
$653$	−15.6861	−	37.8696i	−0.0240216	−	0.0579933i	0.911414	−	0.411492i	$-0.134992\pi$
$653$	−15.6861	−	37.8696i	−0.0240216	−	0.0579933i	−0.935435	+	0.353498i	$0.884992\pi$
$654$	103.634	−	4.00939i	0.158461	−	0.00613057i
$655$	−479.821			−0.732551
$656$	151.275	−	207.163i	0.230603	−	0.315798i
$657$			558.942i			0.850748i
$658$	−89.2915	+	3.45452i	−0.135701	+	0.00525003i
$659$	187.169	−	77.5281i	0.284020	−	0.117645i	−0.236125	−	0.971723i	$-0.575878\pi$
$659$	187.169	−	77.5281i	0.284020	−	0.117645i	0.520146	+	0.854078i	$0.325878\pi$
$660$	724.860	+	236.485i	1.09827	+	0.358311i
$661$	30.1818	+	12.5017i	0.0456608	+	0.0189133i	0.405397	−	0.914141i	$-0.367133\pi$
$661$	30.1818	+	12.5017i	0.0456608	+	0.0189133i	−0.359736	+	0.933054i	$0.617133\pi$
$662$	−584.723	+	269.135i	−0.883267	+	0.406548i
$663$	−481.957	−	481.957i	−0.726934	−	0.726934i
$664$	64.0729	−	225.627i	0.0964954	−	0.339800i
$665$	−3.65873	−	3.65873i	−0.00550184	−	0.00550184i
$666$	556.402	−	1505.41i	0.835439	−	2.26037i
$667$	−0.467318	−	0.193569i	−0.000700627	−	0.000290209i
$668$	380.890	+	326.104i	0.570195	+	0.488179i
$669$	−1451.05	+	601.045i	−2.16899	+	0.898423i
$670$	124.738	+	115.446i	0.186176	+	0.172307i
$671$		−	719.443i		−	1.07219i
$672$	−53.9406	−	81.2554i	−0.0802688	−	0.120916i
$673$	−327.878			−0.487189			−0.243595	−	0.969877i	$-0.578327\pi$
$673$	−327.878			−0.487189			−0.243595	+	0.969877i	$0.578327\pi$
$674$	−358.169	+	386.998i	−0.531408	+	0.574181i
$675$	−106.380	−	256.823i	−0.157599	−	0.380479i
$676$	92.3192	+	79.0402i	0.136567	+	0.116923i
$677$	117.661	−	284.058i	0.173797	−	0.419583i	−0.812846	−	0.582478i	$-0.802083\pi$
$677$	117.661	−	284.058i	0.173797	−	0.419583i	0.986643	+	0.162895i	$0.0520832\pi$
$678$	884.410	+	326.880i	1.30444	+	0.482124i
$679$	−62.2231	+	62.2231i	−0.0916393	+	0.0916393i
$680$	−336.195	+	187.483i	−0.494405	+	0.275710i
$681$	−81.4826	+	81.4826i	−0.119651	+	0.119651i
$682$	−303.204	−	658.741i	−0.444581	−	0.965897i
$683$	−324.811	+	784.162i	−0.475564	+	1.14811i	0.486104	+	0.873901i	$0.338417\pi$
$683$	−324.811	+	784.162i	−0.475564	+	1.14811i	−0.961669	+	0.274213i	$0.911583\pi$
$684$	164.411	+	53.6388i	0.240366	+	0.0784193i
$685$	−63.0875	−	152.307i	−0.0920985	−	0.222345i
$686$	4.19143	+	108.339i	0.00610996	+	0.157929i
$687$	−960.220			−1.39770
$688$	144.343	−	594.928i	0.209801	−	0.864721i
$689$			848.888i			1.23206i
$690$	1.22129	+	31.5675i	0.00176998	+	0.0457500i
$691$	826.286	−	342.259i	1.19578	−	0.495309i	0.306149	−	0.951984i	$-0.400959\pi$
$691$	826.286	−	342.259i	1.19578	−	0.495309i	0.889634	+	0.456674i	$0.150959\pi$
$692$	−813.391	+	413.213i	−1.17542	+	0.597128i
$693$	−82.4966	−	34.1712i	−0.119043	−	0.0493091i
$694$	351.567	+	763.815i	0.506580	+	1.10060i
$695$	440.490	+	440.490i	0.633798	+	0.633798i
$696$	35.0435	−	4.08361i	0.0503499	−	0.00586726i
$697$	119.490	+	119.490i	0.171434	+	0.171434i
$698$	−910.241	−	336.427i	−1.30407	−	0.481988i
$699$	2025.75	+	839.092i	2.89807	+	1.20042i
$700$	−0.713355	−	9.20550i	−0.00101908	−	0.0131507i
$701$	430.597	−	178.359i	0.614260	−	0.254435i	−0.0537885	−	0.998552i	$-0.517130\pi$
$701$	430.597	−	178.359i	0.614260	−	0.254435i	0.668049	+	0.744117i	$0.267130\pi$
$702$	1068.84	−	1154.87i	1.52257	−	1.64512i
$703$			77.4359i			0.110151i
$704$	−480.274	−	77.8444i	−0.682207	−	0.110574i
$705$	−2018.84			−2.86361
$706$	156.985	+	145.291i	0.222359	+	0.205794i
$707$	−29.8773	−	72.1301i	−0.0422592	−	0.102023i
$708$	−1542.75	+	119.551i	−2.17903	+	0.168858i
$709$	−77.1066	+	186.152i	−0.108754	+	0.262555i	−0.968882	−	0.247523i	$-0.920384\pi$
$709$	−77.1066	+	186.152i	−0.108754	+	0.262555i	0.860128	+	0.510078i	$0.170384\pi$
$710$	66.2967	−	179.373i	0.0933756	−	0.252638i
$711$	542.414	−	542.414i	0.762889	−	0.762889i
$712$	−634.866	+	73.9807i	−0.891665	+	0.103906i
$713$	21.2458	−	21.2458i	0.0297977	−	0.0297977i
$714$	58.3634	−	26.8634i	0.0817414	−	0.0376238i
$715$	−156.365	+	377.498i	−0.218692	+	0.527970i
$716$	−10.8463	−	21.3506i	−0.0151485	−	0.0298192i
$717$	27.6645	+	66.7879i	0.0385836	+	0.0931491i
$718$	590.025	−	22.8270i	0.821762	−	0.0317924i
$719$	809.898			1.12642			0.563212	−	0.826313i	$-0.309566\pi$
$719$	809.898			1.12642			0.563212	+	0.826313i	$0.309566\pi$
$720$	−804.652	−	1320.19i	−1.11757	−	1.83359i
$721$			7.80525i			0.0108256i
$722$	713.122	−	27.5894i	0.987704	−	0.0382124i
$723$	1175.96	−	487.099i	1.62650	−	0.673719i
$724$	367.723	−	1127.12i	0.507905	−	1.55680i
$725$	3.08576	+	1.27817i	0.00425623	+	0.00176299i
$726$	630.713	−	290.303i	0.868750	−	0.399866i
$727$	542.456	+	542.456i	0.746156	+	0.746156i	0.973755	−	0.227599i	$-0.0730875\pi$
$727$	542.456	+	542.456i	0.746156	+	0.746156i	−0.227599	+	0.973755i	$0.573087\pi$
$728$	45.6477	−	25.4559i	0.0627029	−	0.0349670i
$729$	306.489	+	306.489i	0.420424	+	0.420424i
$730$	−83.5830	+	226.143i	−0.114497	+	0.309785i
$731$	372.588	+	154.331i	0.509697	+	0.211123i
$732$	−1352.19	+	1579.36i	−1.84725	+	2.15760i
$733$	562.276	−	232.903i	0.767089	−	0.317739i	0.0353965	−	0.999373i	$-0.488731\pi$
$733$	562.276	−	232.903i	0.767089	−	0.317739i	0.731693	+	0.681635i	$0.238731\pi$
$734$	−1043.63	−	965.885i	−1.42184	−	1.31592i
$735$			1220.89i			1.66107i
$736$	−3.87337	−	19.7833i	−0.00526273	−	0.0268795i
$737$	−141.518			−0.192019
$738$	−461.010	+	498.117i	−0.624675	+	0.674955i
$739$	−305.819	−	738.312i	−0.413828	−	0.999070i	−0.984100	−	0.177614i	$-0.943162\pi$
$739$	−305.819	−	738.312i	−0.413828	−	0.999070i	0.570272	−	0.821456i	$-0.306838\pi$
$740$	450.231	−	525.871i	0.608420	−	0.710637i
$741$	−50.5461	+	122.029i	−0.0682133	+	0.164681i
$742$	−75.0564	−	27.7410i	−0.101154	−	0.0373868i
$743$	581.334	−	581.334i	0.782414	−	0.782414i	−0.197823	−	0.980238i	$-0.563387\pi$
$743$	581.334	−	581.334i	0.782414	−	0.782414i	0.980238	+	0.197823i	$0.0633873\pi$
$744$	−572.491	+	2015.98i	−0.769477	+	2.70965i
$745$	528.633	−	528.633i	0.709574	−	0.709574i
$746$	531.698	+	1155.17i	0.712732	+	1.54848i
$747$	−237.488	+	573.348i	−0.317923	+	0.767534i
$748$	99.4112	−	304.709i	0.132903	−	0.407365i
$749$	38.1847	+	92.1861i	0.0509810	+	0.123079i
$750$	−56.5307	−	1461.19i	−0.0753743	−	1.94825i
$751$	−187.901			−0.250201			−0.125100	−	0.992144i	$-0.539925\pi$
$751$	−187.901			−0.250201			−0.125100	+	0.992144i	$0.539925\pi$
$752$	1272.88	−	198.469i	1.69266	−	0.263922i
$753$			782.958i			1.03978i
$754$	0.730922	+	18.8927i	0.000969392	+	0.0250566i
$755$	−735.390	+	304.608i	−0.974026	+	0.403455i
$756$	67.1819	+	132.245i	0.0888649	+	0.174927i
$757$	−168.645	−	69.8549i	−0.222780	−	0.0922786i	0.268502	−	0.963279i	$-0.413472\pi$
$757$	−168.645	−	69.8549i	−0.222780	−	0.0922786i	−0.491282	+	0.871001i	$0.663472\pi$
$758$	31.2452	+	67.8833i	0.0412206	+	0.0895559i
$759$	−18.5998	−	18.5998i	−0.0245057	−	0.0245057i
$760$	58.4980	+	46.2874i	0.0769711	+	0.0609045i
$761$	391.406	+	391.406i	0.514331	+	0.514331i	0.915850	−	0.401520i	$-0.131518\pi$
$761$	391.406	+	391.406i	0.514331	+	0.514331i	−0.401520	+	0.915850i	$0.631518\pi$
$762$	178.122	+	65.8344i	0.233756	+	0.0863968i
$763$	−4.84022	−	2.00488i	−0.00634367	−	0.00262763i
$764$	−560.334	+	43.4215i	−0.733421	+	0.0568345i
$765$	940.971	−	389.763i	1.23003	−	0.509494i
$766$	−472.240	+	510.250i	−0.616501	+	0.666123i
$767$		−	829.235i		−	1.08114i
$768$	908.016	+	1073.56i	1.18231	+	1.39787i
$769$	184.433			0.239835			0.119918	−	0.992784i	$-0.461737\pi$
$769$	184.433			0.239835			0.119918	+	0.992784i	$0.461737\pi$
$770$	−28.2675	−	26.1617i	−0.0367110	−	0.0339763i
$771$	−147.332	−	355.690i	−0.191092	−	0.461336i
$772$	−49.3600	−	636.967i	−0.0639378	−	0.825087i
$773$	−140.532	+	339.275i	−0.181801	+	0.438907i	−0.988338	−	0.152277i	$-0.951339\pi$
$773$	−140.532	+	339.275i	−0.181801	+	0.438907i	0.806537	+	0.591184i	$0.201339\pi$
$774$	−561.545	+	1519.32i	−0.725511	+	1.96295i
$775$	−140.289	+	140.289i	−0.181018	+	0.181018i
$776$	787.199	−	994.862i	1.01443	−	1.28204i
$777$	−81.7035	+	81.7035i	−0.105152	+	0.105152i
$778$	288.424	−	132.755i	0.370725	−	0.170637i
$779$	12.5317	−	30.2541i	0.0160869	−	0.0388371i
$780$	1052.77	−	534.818i	1.34970	−	0.685665i
$781$	60.9340	+	147.108i	0.0780206	+	0.188358i
$782$	13.2700	−	0.513392i	0.0169693	−	0.000656512i
$783$	−53.6576			−0.0685282
$784$	−120.024	−	769.772i	−0.153091	−	0.981852i
$785$		−	529.054i		−	0.673954i
$786$	−1153.72	+	44.6351i	−1.46783	+	0.0567877i
$787$	−926.743	+	383.870i	−1.17756	+	0.487763i	−0.883686	−	0.468080i	$-0.844946\pi$
$787$	−926.743	+	383.870i	−1.17756	+	0.487763i	−0.293878	+	0.955843i	$0.594946\pi$
$788$	−232.040	−	75.7030i	−0.294467	−	0.0960697i
$789$	−1764.51	−	730.885i	−2.23639	−	0.926344i
$790$	300.568	−	138.345i	0.380465	−	0.175120i
$791$	−33.6796	−	33.6796i	−0.0425785	−	0.0425785i
$792$	1238.37	+	351.667i	1.56359	+	0.444024i
$793$	−787.860	−	787.860i	−0.993518	−	0.993518i
$794$	325.153	−	879.738i	0.409513	−	1.10798i
$795$	−1670.23	−	691.831i	−2.10091	−	0.870227i
$796$	596.182	+	510.428i	0.748973	+	0.641242i
$797$	−871.860	+	361.136i	−1.09393	+	0.453119i	−0.855374	−	0.518010i	$-0.826673\pi$
$797$	−871.860	+	361.136i	−1.09393	+	0.453119i	−0.238553	+	0.971130i	$0.576673\pi$
$798$	−9.13767	−	8.45696i	−0.0114507	−	0.0105977i
$799$			848.660i			1.06215i
$800$	25.5764	+	130.632i	0.0319705	+	0.163290i
$801$	1691.14			2.11129
$802$	924.516	−	998.931i	1.15276	−	1.24555i
$803$	−76.8221	−	185.465i	−0.0956689	−	0.230965i
$804$	310.668	+	265.982i	0.386403	+	0.330824i
$805$	0.610701	−	1.47436i	0.000758635	−	0.00183151i
$806$	−1053.42	−	389.348i	−1.30698	−	0.483062i
$807$	−74.4628	+	74.4628i	−0.0922711	+	0.0922711i
$808$	548.204	+	983.042i	0.678470	+	1.21664i
$809$	744.003	−	744.003i	0.919658	−	0.919658i	−0.0773465	−	0.997004i	$-0.524645\pi$
$809$	744.003	−	744.003i	0.919658	−	0.919658i	0.997004	+	0.0773465i	$0.0246448\pi$
$810$	673.937	+	1464.20i	0.832021	+	1.80765i
$811$	−307.315	+	741.925i	−0.378934	+	0.914827i	0.613233	+	0.789902i	$0.289869\pi$
$811$	−307.315	+	741.925i	−0.378934	+	0.914827i	−0.992166	+	0.124924i	$0.960131\pi$
$812$	−1.69432	−	0.552772i	−0.00208661	−	0.000680754i
$813$	688.574	+	1662.36i	0.846954	+	2.04473i
$814$	22.2839	+	575.989i	0.0273758	+	0.707603i
$815$	−580.286			−0.712007
$816$	−790.933	+	482.072i	−0.969280	+	0.590775i
$817$		−	78.1517i		−	0.0956569i
$818$	−26.2335	−	678.075i	−0.0320702	−	0.828943i
$819$	−127.763	+	52.9210i	−0.155998	+	0.0646166i
$820$	−261.008	+	132.595i	−0.318302	+	0.161701i
$821$	−948.269	−	392.786i	−1.15502	−	0.478424i	−0.278804	−	0.960348i	$-0.589938\pi$
$821$	−948.269	−	392.786i	−1.15502	−	0.478424i	−0.876213	+	0.481924i	$0.839938\pi$
$822$	−165.860	−	360.349i	−0.201777	−	0.438380i
$823$	492.275	+	492.275i	0.598147	+	0.598147i	0.939819	−	0.341672i	$-0.110993\pi$
$823$	492.275	+	492.275i	0.598147	+	0.598147i	−0.341672	+	0.939819i	$0.610993\pi$
$824$	−13.0246	−	111.771i	−0.0158066	−	0.135644i
$825$	122.817	+	122.817i	0.148869	+	0.148869i
$826$	73.3187	+	27.0988i	0.0887636	+	0.0328072i
$827$	−1350.77	−	559.506i	−1.63333	−	0.676549i	−0.637734	−	0.770257i	$-0.720128\pi$
$827$	−1350.77	−	559.506i	−1.63333	−	0.676549i	−0.995600	+	0.0937082i	$0.970128\pi$
$828$	4.12093	+	53.1786i	0.00497697	+	0.0642254i
$829$	441.547	−	182.895i	0.532627	−	0.220621i	−0.100127	−	0.994975i	$-0.531925\pi$
$829$	441.547	−	182.895i	0.532627	−	0.220621i	0.632753	+	0.774354i	$0.281925\pi$
$830$	−181.823	+	196.458i	−0.219064	+	0.236696i
$831$		−	189.850i		−	0.228460i
$832$	−611.194	+	440.700i	−0.734608	+	0.529687i
$833$	513.225			0.616116
$834$	1100.12	+	1018.17i	1.31909	+	1.22083i
$835$	−218.994	−	528.698i	−0.262268	−	0.633171i
$836$	−61.9260	+	4.79879i	−0.0740742	+	0.00574018i
$837$	1219.72	−	2944.67i	1.45726	−	3.51813i
$838$	60.7152	−	164.272i	0.0724526	−	0.196028i
$839$	849.569	−	849.569i	1.01260	−	1.01260i	0.0126775	−	0.999920i	$-0.495965\pi$
$839$	849.569	−	849.569i	1.01260	−	1.01260i	0.999920	−	0.0126775i	$-0.00403549\pi$
$840$	12.8836	+	110.560i	0.0153376	+	0.131619i
$841$	−594.221	+	594.221i	−0.706565	+	0.706565i
$842$	−177.070	+	81.5013i	−0.210297	+	0.0967949i
$843$	782.994	−	1890.31i	0.928818	−	2.24236i
$844$	−380.965	−	749.913i	−0.451380	−	0.888522i
$845$	−53.0792	−	128.144i	−0.0628156	−	0.151650i
$846$	−3406.04	+	131.773i	−4.02605	+	0.155760i
$847$	−35.0736			−0.0414093
$848$	1121.09	+	272.003i	1.32204	+	0.320758i
$849$		−	1593.93i		−	1.87742i
$850$	−87.6237	+	3.39000i	−0.103087	+	0.00398823i
$851$	−22.0649	+	9.13957i	−0.0259282	+	0.0107398i
$852$	142.723	−	437.465i	0.167515	−	0.513456i
$853$	773.493	+	320.391i	0.906791	+	0.375605i	0.786827	−	0.617173i	$-0.211722\pi$
$853$	773.493	+	320.391i	0.906791	+	0.375605i	0.119964	+	0.992778i	$0.461722\pi$
$854$	95.4071	−	43.9138i	0.111718	−	0.0514213i
$855$	−139.563	−	139.563i	−0.163231	−	0.163231i
$856$	−700.634	−	1256.38i	−0.818497	−	1.46773i
$857$	−259.040	−	259.040i	−0.302264	−	0.302264i	0.539635	−	0.841899i	$-0.318562\pi$
$857$	−259.040	−	259.040i	−0.302264	−	0.302264i	−0.841899	+	0.539635i	$0.818562\pi$
$858$	−340.859	+	922.230i	−0.397271	+	1.07486i
$859$	−762.123	−	315.682i	−0.887221	−	0.367499i	−0.107928	−	0.994159i	$-0.534422\pi$
$859$	−762.123	−	315.682i	−0.887221	−	0.367499i	−0.779293	+	0.626660i	$0.784422\pi$
$860$	−454.393	+	530.732i	−0.528364	+	0.617130i
$861$	45.1438	−	18.6992i	0.0524318	−	0.0217180i
$862$	747.263	+	691.596i	0.866894	+	0.802316i
$863$			1078.25i			1.24942i	0.780855	+	0.624712i	$0.214784\pi$
$863$			1078.25i			1.24942i	−0.780855	+	0.624712i	$0.785216\pi$
$864$	−1182.72	−	1781.63i	−1.36888	−	2.06207i
$865$	1041.22			1.20373
$866$	−89.6712	+	96.8888i	−0.103546	+	0.111881i
$867$	373.931	+	902.750i	0.431293	+	1.04123i
$868$	68.8502	−	80.4173i	0.0793206	−	0.0926467i
$869$	−105.430	+	254.532i	−0.121324	+	0.292902i
$870$	−37.7679	−	13.9591i	−0.0434114	−	0.0160450i
$871$	−154.976	+	154.976i	−0.177929	+	0.177929i
$872$	72.6571	+	20.6329i	0.0833224	+	0.0236616i
$873$	−2373.51	+	2373.51i	−2.71880	+	2.71880i
$874$	−1.07601	−	2.33773i	−0.00123113	−	0.00267475i
$875$	−28.2680	+	68.2450i	−0.0323063	+	0.0779943i
$876$	−179.936	+	551.530i	−0.205407	+	0.629600i
$877$	387.984	+	936.676i	0.442399	+	1.06805i	0.975105	+	0.221745i	$0.0711753\pi$
$877$	387.984	+	936.676i	0.442399	+	1.06805i	−0.532706	+	0.846301i	$0.678825\pi$
$878$	4.35740	+	112.629i	0.00496287	+	0.128279i
$879$	642.663			0.731130
$880$	448.444	+	327.464i	0.509596	+	0.372118i
$881$			1281.50i			1.45460i	0.686318	+	0.727301i	$0.259226\pi$
$881$			1281.50i			1.45460i	−0.686318	+	0.727301i	$0.740774\pi$
$882$	79.6896	+	2059.79i	0.0903510	+	2.33537i
$883$	−1014.19	+	420.092i	−1.14857	+	0.475755i	−0.874055	−	0.485826i	$-0.838519\pi$
$883$	−1014.19	+	420.092i	−1.14857	+	0.475755i	−0.274519	+	0.961582i	$0.588519\pi$
$884$	−224.821	−	442.551i	−0.254323	−	0.500624i
$885$	1631.56	+	675.814i	1.84357	+	0.763632i
$886$	175.394	+	381.061i	0.197961	+	0.430091i
$887$	−57.0987	−	57.0987i	−0.0643728	−	0.0643728i	0.674187	−	0.738560i	$-0.264494\pi$
$887$	−57.0987	−	57.0987i	−0.0643728	−	0.0643728i	−0.738560	+	0.674187i	$0.764494\pi$
$888$	1033.65	−	1306.33i	1.16402	−	1.47109i
$889$	−6.78316	−	6.78316i	−0.00763010	−	0.00763010i
$890$	684.222	+	252.890i	0.768789	+	0.284146i
$891$	−1239.94	−	513.598i	−1.39162	−	0.576429i
$892$	−1140.41	+	88.3729i	−1.27849	+	0.0990728i
$893$	151.940	−	62.9358i	0.170146	−	0.0704768i
$894$	1221.91	−	1320.26i	1.36679	−	1.47680i
$895$			27.3309i			0.0305373i
$896$	−18.9921	−	68.4419i	−0.0211965	−	0.0763860i
$897$	−40.7372			−0.0454150
$898$	−182.329	−	168.747i	−0.203039	−	0.187914i
$899$	14.6551	+	35.3806i	0.0163016	+	0.0393555i
$900$	−27.2111	−	351.146i	−0.0302345	−	0.390162i
$901$	−290.825	+	702.113i	−0.322780	+	0.779260i
$902$	84.5076	−	228.645i	0.0936892	−	0.253486i
$903$	82.4587	−	82.4587i	0.0913164	−	0.0913164i
$904$	538.491	+	426.089i	0.595676	+	0.471337i
$905$	−956.779	+	956.779i	−1.05721	+	1.05721i
$906$	−1739.89	+	800.832i	−1.92041	+	0.883921i
$907$	312.323	−	754.015i	0.344348	−	0.831329i	−0.652918	−	0.757429i	$-0.726455\pi$
$907$	312.323	−	754.015i	0.344348	−	0.831329i	0.997266	−	0.0739002i	$-0.0235446\pi$
$908$	−74.8204	+	38.0097i	−0.0824014	+	0.0418609i
$909$	−1139.67	−	2751.42i	−1.25377	−	3.02686i
$910$	−59.6053	+	2.30602i	−0.0655003	+	0.00253409i
$911$	1374.15			1.50840			0.754201	−	0.656644i	$-0.228024\pi$
$911$	1374.15			1.50840			0.754201	+	0.656644i	$0.228024\pi$
$912$	144.963	+	105.855i	0.158951	+	0.116069i
$913$		−	222.886i		−	0.244125i
$914$	1619.76	−	62.6655i	1.77217	−	0.0685618i
$915$	2192.25	−	908.058i	2.39590	−	0.992413i
$916$	−664.815	−	216.895i	−0.725781	−	0.236785i
$917$	53.8844	+	22.3196i	0.0587616	+	0.0243399i
$918$	1279.69	−	589.013i	1.39400	−	0.641627i
$919$	−317.523	−	317.523i	−0.345510	−	0.345510i	0.512924	−	0.858434i	$-0.328562\pi$
$919$	−317.523	−	317.523i	−0.345510	−	0.345510i	−0.858434	+	0.512924i	$0.828562\pi$
$920$	−6.28493	+	22.1318i	−0.00683145	+	0.0240564i
$921$	1809.70	+	1809.70i	1.96493	+	1.96493i
$922$	−155.947	+	421.930i	−0.169139	+	0.457625i
$923$	227.826	+	94.3687i	0.246832	+	0.102241i
$924$	−70.4021	−	60.2756i	−0.0761928	−	0.0652333i
$925$	145.697	−	60.3498i	0.157511	−	0.0652430i
$926$	815.507	+	754.756i	0.880677	+	0.815071i
$927$			297.733i			0.321179i
$928$	25.1850	+	5.08834i	0.0271390	+	0.00548313i
$929$	−46.9926			−0.0505841			−0.0252920	−	0.999680i	$-0.508052\pi$
$929$	−46.9926			−0.0505841			−0.0252920	+	0.999680i	$0.508052\pi$
$930$	1624.59	−	1755.35i	1.74687	−	1.88747i
$931$	−38.0602	−	91.8855i	−0.0408810	−	0.0986955i
$932$	1213.01	+	1038.53i	1.30151	+	1.11430i
$933$	182.288	−	440.083i	0.195379	−	0.471686i
$934$	649.375	+	240.011i	0.695263	+	0.256971i
$935$	−258.658	+	258.658i	−0.276640	+	0.276640i
$936$	1741.24	−	971.022i	1.86030	−	1.03742i
$937$	381.311	−	381.311i	0.406949	−	0.406949i	−0.473724	−	0.880673i	$-0.657091\pi$
$937$	381.311	−	381.311i	0.406949	−	0.406949i	0.880673	+	0.473724i	$0.157091\pi$
$938$	−8.63806	−	18.7671i	−0.00920902	−	0.0200075i
$939$	−384.367	+	927.944i	−0.409337	+	0.988226i
$940$	−1397.76	−	456.018i	−1.48698	−	0.485125i
$941$	319.284	+	770.819i	0.339303	+	0.819149i	0.997783	+	0.0665513i	$0.0211996\pi$
$941$	319.284	+	770.819i	0.339303	+	0.819149i	−0.658480	+	0.752598i	$0.728800\pi$
$942$	−49.2150	−	1272.10i	−0.0522452	−	1.35042i
$943$	10.0998			0.0107103
$944$	−1095.14	−	265.706i	−1.16010	−	0.281468i
$945$		−	169.287i		−	0.179139i
$946$	−22.4899	−	581.313i	−0.0237737	−	0.614496i
$947$	−46.3711	+	19.2075i	−0.0489663	+	0.0202825i	−0.407032	−	0.913414i	$-0.633436\pi$
$947$	−46.3711	+	19.2075i	−0.0489663	+	0.0202825i	0.358066	+	0.933696i	$0.383436\pi$
$948$	709.838	−	360.606i	0.748774	−	0.380386i
$949$	−287.230	−	118.975i	−0.302666	−	0.125368i
$950$	7.10502	+	15.4364i	0.00747897	+	0.0162488i
$951$	−1205.26	−	1205.26i	−1.26736	−	1.26736i
$952$	46.4762	−	5.41586i	0.0488195	−	0.00568893i
$953$	−456.351	−	456.351i	−0.478858	−	0.478858i	0.425909	−	0.904766i	$-0.359955\pi$
$953$	−456.351	−	456.351i	−0.478858	−	0.478858i	−0.904766	+	0.425909i	$0.859955\pi$
$954$	−2863.04	−	1058.19i	−3.00109	−	1.10921i
$955$	592.589	+	245.459i	0.620512	+	0.257025i
$956$	4.06756	+	52.4899i	0.00425477	+	0.0549058i
$957$	30.9743	−	12.8300i	0.0323661	−	0.0134065i
$958$	−325.460	+	351.657i	−0.339729	+	0.367074i
$959$			20.0388i			0.0208955i
$960$	−368.983	−	1561.72i	−0.384358	−	1.62679i
$961$	−1313.79			−1.36710
$962$	655.167	+	606.361i	0.681047	+	0.630313i
$963$	1456.56	+	3516.46i	1.51253	+	3.65157i
$964$	924.211	−	71.6192i	0.958725	−	0.0742938i
$965$	−279.028	+	673.634i	−0.289148	+	0.698066i
$966$	1.33126	−	3.60188i	0.00137812	−	0.00372865i
$967$	476.069	−	476.069i	0.492316	−	0.492316i	−0.416719	−	0.909035i	$-0.636820\pi$
$967$	476.069	−	476.069i	0.492316	−	0.492316i	0.909035	+	0.416719i	$0.136820\pi$
$968$	502.252	−	58.5273i	0.518855	−	0.0604621i
$969$	−83.6130	+	83.6130i	−0.0862879	+	0.0862879i
$970$	−1315.23	+	605.372i	−1.35591	+	0.624095i
$971$	−502.303	+	1212.67i	−0.517305	+	1.24888i	0.422248	+	0.906480i	$0.361241\pi$
$971$	−502.303	+	1212.67i	−0.517305	+	1.24888i	−0.939553	+	0.342404i	$0.888759\pi$
$972$	667.053	+	1313.07i	0.686269	+	1.35089i
$973$	−28.9774	−	69.9576i	−0.0297815	−	0.0718988i
$974$	761.762	−	29.4711i	0.782096	−	0.0302579i
$975$	268.993			0.275891
$976$	−1292.94	+	788.048i	−1.32474	+	0.807426i
$977$		−	1.17535i		−	0.00120302i	−1.00000		0.000601512i	$-0.999809\pi$
$977$		−	1.17535i		−	0.00120302i	1.00000		0.000601512i	$-0.000191467\pi$
$978$	−1395.28	+	53.9809i	−1.42667	+	0.0551952i
$979$	−561.146	+	232.434i	−0.573183	+	0.237420i
$980$	−275.775	+	845.291i	−0.281404	+	0.862542i
$981$	−184.631	−	76.4767i	−0.188207	−	0.0779579i
$982$	−1354.91	+	623.634i	−1.37974	+	0.635065i
$983$	−1006.98	−	1006.98i	−1.02439	−	1.02439i	−0.999695	−	0.0246998i	$-0.992137\pi$
$983$	−1006.98	−	1006.98i	−1.02439	−	1.02439i	−0.0246998	−	0.999695i	$-0.507863\pi$
$984$	−615.252	+	343.102i	−0.625256	+	0.348681i
$985$	196.972	+	196.972i	0.199971	+	0.199971i
$986$	−5.86799	+	15.8765i	−0.00595130	+	0.0161019i
$987$	226.718	+	93.9098i	0.229704	+	0.0951467i
$988$	−62.5599	+	73.0702i	−0.0633198	+	0.0739577i
$989$	22.2688	−	9.22405i	0.0225165	−	0.00932665i
$990$	−1078.27	−	997.944i	−1.08916	−	1.00802i
$991$		−	1294.48i		−	1.30624i	−0.757256	−	0.653118i	$-0.773461\pi$
$991$		−	1294.48i		−	1.30624i	0.757256	−	0.653118i	$-0.226539\pi$
$992$	−851.739	+	1266.46i	−0.858607	+	1.27667i
$993$	1767.71			1.78017
$994$	−15.7890	+	17.0599i	−0.0158843	+	0.0171629i
$995$	−342.777	−	827.536i	−0.344499	−	0.831694i
$996$	−418.913	+	489.292i	−0.420596	+	0.491257i
$997$	82.2498	−	198.568i	0.0824973	−	0.199166i	−0.877248	−	0.480037i	$-0.840623\pi$
$997$	82.2498	−	198.568i	0.0824973	−	0.199166i	0.959746	+	0.280871i	$0.0906233\pi$
$998$	−1180.28	−	436.235i	−1.18265	−	0.437109i
$999$	−1791.45	+	1791.45i	−1.79325	+	1.79325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	32.3.h.a.11.2	yes	28
3.2	odd	2		288.3.u.a.235.6		28
4.3	odd	2		128.3.h.a.79.1		28
8.3	odd	2		256.3.h.a.159.7		28
8.5	even	2		256.3.h.b.159.1		28
32.3	odd	8	inner	32.3.h.a.3.2	✓	28
32.13	even	8		256.3.h.a.95.7		28
32.19	odd	8		256.3.h.b.95.1		28
32.29	even	8		128.3.h.a.47.1		28
96.35	even	8		288.3.u.a.163.6		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.3.2	✓	28	32.3	odd	8	inner
32.3.h.a.11.2	yes	28	1.1	even	1	trivial
128.3.h.a.47.1		28	32.29	even	8
128.3.h.a.79.1		28	4.3	odd	2
256.3.h.a.95.7		28	32.13	even	8
256.3.h.a.159.7		28	8.3	odd	2
256.3.h.b.95.1		28	32.19	odd	8
256.3.h.b.159.1		28	8.5	even	2
288.3.u.a.163.6		28	96.35	even	8
288.3.u.a.235.6		28	3.2	odd	2

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:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	32.h (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46783 - 1.35848i) q^{2} +(2.10187 + 5.07436i) q^{3} +(0.309042 + 3.98804i) q^{4} +(1.74699 - 4.21761i) q^{5} +(3.80826 - 10.3037i) q^{6} +(-0.392379 + 0.392379i) q^{7} +(4.96407 - 6.27359i) q^{8} +(-14.9674 + 14.9674i) q^{9} +O(q^{10})\)	\(q+(-1.46783 - 1.35848i) q^{2} +(2.10187 + 5.07436i) q^{3} +(0.309042 + 3.98804i) q^{4} +(1.74699 - 4.21761i) q^{5} +(3.80826 - 10.3037i) q^{6} +(-0.392379 + 0.392379i) q^{7} +(4.96407 - 6.27359i) q^{8} +(-14.9674 + 14.9674i) q^{9} +(-8.29385 + 3.81747i) q^{10} +(2.90924 - 7.02353i) q^{11} +(-19.5872 + 9.95055i) q^{12} +(-4.50555 - 10.8774i) q^{13} +(1.10898 - 0.0429045i) q^{14} +25.0737 q^{15} +(-15.8090 + 2.46495i) q^{16} -10.5402i q^{17} +(42.3024 - 1.63660i) q^{18} +(-1.88707 + 0.781651i) q^{19} +(17.3599 + 5.66366i) q^{20} +(-2.81580 - 1.16634i) q^{21} +(-13.8116 + 6.35718i) q^{22} +(-0.445453 - 0.445453i) q^{23} +(42.2683 + 12.0032i) q^{24} +(2.94139 + 2.94139i) q^{25} +(-8.16334 + 22.0868i) q^{26} +(-61.7400 - 25.5735i) q^{27} +(-1.68608 - 1.44356i) q^{28} +(0.741814 - 0.307270i) q^{29} +(-36.8038 - 34.0622i) q^{30} +47.6947i q^{31} +(26.5535 + 17.8581i) q^{32} +41.7548 q^{33} +(-14.3187 + 15.4712i) q^{34} +(0.969419 + 2.34038i) q^{35} +(-64.3160 - 55.0649i) q^{36} +(14.5080 - 35.0255i) q^{37} +(3.83176 + 1.41623i) q^{38} +(45.7256 - 45.7256i) q^{39} +(-17.7874 - 31.8965i) q^{40} +(-11.3365 + 11.3365i) q^{41} +(2.54866 + 5.53721i) q^{42} +(-14.6421 + 35.3493i) q^{43} +(28.9092 + 9.43161i) q^{44} +(36.9787 + 89.2744i) q^{45} +(0.0487080 + 1.25899i) q^{46} -80.5164 q^{47} +(-45.7365 - 75.0396i) q^{48} +48.6921i q^{49} +(-0.321625 - 8.31328i) q^{50} +(53.4849 - 22.1542i) q^{51} +(41.9870 - 21.3299i) q^{52} +(-66.6128 - 27.5919i) q^{53} +(55.8825 + 121.410i) q^{54} +(-24.5401 - 24.5401i) q^{55} +(0.513828 + 4.40942i) q^{56} +(-7.93277 - 7.93277i) q^{57} +(-1.50628 - 0.556724i) q^{58} +(65.0706 + 26.9531i) q^{59} +(7.74883 + 99.9949i) q^{60} +(87.4322 - 36.2156i) q^{61} +(64.7925 - 70.0077i) q^{62} -11.7457i q^{63} +(-14.7160 - 62.2852i) q^{64} -53.7476 q^{65} +(-61.2889 - 56.7232i) q^{66} +(-7.12379 - 17.1984i) q^{67} +(42.0348 - 3.25737i) q^{68} +(1.32411 - 3.19668i) q^{69} +(1.75643 - 4.75222i) q^{70} +(-14.8103 + 14.8103i) q^{71} +(19.6001 + 168.198i) q^{72} +(18.6720 - 18.6720i) q^{73} +(-68.8769 + 31.7025i) q^{74} +(-8.74326 + 21.1081i) q^{75} +(-3.70044 - 7.28417i) q^{76} +(1.61436 + 3.89741i) q^{77} +(-129.235 + 4.99985i) q^{78} -36.2398 q^{79} +(-17.2220 + 70.9824i) q^{80} -176.540i q^{81} +(32.0406 - 1.23959i) q^{82} +(27.0868 - 11.2197i) q^{83} +(3.78122 - 11.5900i) q^{84} +(-44.4545 - 18.4137i) q^{85} +(69.5135 - 31.9955i) q^{86} +(3.11840 + 3.11840i) q^{87} +(-29.6211 - 53.1167i) q^{88} +(-56.4944 - 56.4944i) q^{89} +(66.9995 - 181.274i) q^{90} +(6.03592 + 2.50016i) q^{91} +(1.63882 - 1.91415i) q^{92} +(-242.020 + 100.248i) q^{93} +(118.184 + 109.380i) q^{94} +9.32448i q^{95} +(-34.8067 + 172.278i) q^{96} +158.579 q^{97} +(66.1474 - 71.4716i) q^{98} +(61.5800 + 148.667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 28 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} - 44 q^{10} - 4 q^{11} - 52 q^{12} - 4 q^{13} - 20 q^{14} - 8 q^{15} + 16 q^{16} + 56 q^{18} - 4 q^{19} + 76 q^{20} - 4 q^{21} + 144 q^{22} - 68 q^{23} + 208 q^{24} - 4 q^{25} + 96 q^{26} - 100 q^{27} + 56 q^{28} - 4 q^{29} + 20 q^{30} - 24 q^{32} - 8 q^{33} - 48 q^{34} + 92 q^{35} - 336 q^{36} - 4 q^{37} - 396 q^{38} + 188 q^{39} - 408 q^{40} - 4 q^{41} - 424 q^{42} + 92 q^{43} - 188 q^{44} - 40 q^{45} - 36 q^{46} - 8 q^{47} + 48 q^{48} + 308 q^{50} + 224 q^{51} + 420 q^{52} - 164 q^{53} + 592 q^{54} + 252 q^{55} + 552 q^{56} - 4 q^{57} + 528 q^{58} + 124 q^{59} + 440 q^{60} - 68 q^{61} + 216 q^{62} - 232 q^{64} - 8 q^{65} - 580 q^{66} - 164 q^{67} - 368 q^{68} + 188 q^{69} - 664 q^{70} - 260 q^{71} - 748 q^{72} - 4 q^{73} - 532 q^{74} - 488 q^{75} - 516 q^{76} + 220 q^{77} - 236 q^{78} - 520 q^{79} + 312 q^{80} + 636 q^{82} - 484 q^{83} + 992 q^{84} + 96 q^{85} + 688 q^{86} - 452 q^{87} + 672 q^{88} - 4 q^{89} + 872 q^{90} - 196 q^{91} + 616 q^{92} + 32 q^{93} + 40 q^{94} - 128 q^{96} - 8 q^{97} - 328 q^{98} + 216 q^{99}+O(q^{100}) \) 28 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 44 * q^10 - 4 * q^11 - 52 * q^12 - 4 * q^13 - 20 * q^14 - 8 * q^15 + 16 * q^16 + 56 * q^18 - 4 * q^19 + 76 * q^20 - 4 * q^21 + 144 * q^22 - 68 * q^23 + 208 * q^24 - 4 * q^25 + 96 * q^26 - 100 * q^27 + 56 * q^28 - 4 * q^29 + 20 * q^30 - 24 * q^32 - 8 * q^33 - 48 * q^34 + 92 * q^35 - 336 * q^36 - 4 * q^37 - 396 * q^38 + 188 * q^39 - 408 * q^40 - 4 * q^41 - 424 * q^42 + 92 * q^43 - 188 * q^44 - 40 * q^45 - 36 * q^46 - 8 * q^47 + 48 * q^48 + 308 * q^50 + 224 * q^51 + 420 * q^52 - 164 * q^53 + 592 * q^54 + 252 * q^55 + 552 * q^56 - 4 * q^57 + 528 * q^58 + 124 * q^59 + 440 * q^60 - 68 * q^61 + 216 * q^62 - 232 * q^64 - 8 * q^65 - 580 * q^66 - 164 * q^67 - 368 * q^68 + 188 * q^69 - 664 * q^70 - 260 * q^71 - 748 * q^72 - 4 * q^73 - 532 * q^74 - 488 * q^75 - 516 * q^76 + 220 * q^77 - 236 * q^78 - 520 * q^79 + 312 * q^80 + 636 * q^82 - 484 * q^83 + 992 * q^84 + 96 * q^85 + 688 * q^86 - 452 * q^87 + 672 * q^88 - 4 * q^89 + 872 * q^90 - 196 * q^91 + 616 * q^92 + 32 * q^93 + 40 * q^94 - 128 * q^96 - 8 * q^97 - 328 * q^98 + 216 * q^99

Introduction

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