LMFDB - Embedded newform 160.4.z.a.29.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(29,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("160.29");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.z (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:	$9.44030560092$
Analytic rank:	$0$
Dimension:	$280$
Relative dimension:	$70$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.14
Character	$\chi$	$=$	160.29
Dual form			160.4.z.a.149.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.31596 - 1.62368i) q^{2} +(-2.87385 + 6.93809i) q^{3} +(2.72732 + 7.52075i) q^{4} +(11.1803 + 0.0240294i) q^{5} +(17.9210 - 11.4021i) q^{6} +(-23.8772 - 23.8772i) q^{7} +(5.89493 - 21.8460i) q^{8} +(-20.7862 - 20.7862i) q^{9} +(-25.8541 - 18.2089i) q^{10} +(48.2332 - 19.9788i) q^{11} +(-60.0176 - 2.69111i) q^{12} +(14.1490 + 5.86071i) q^{13} +(16.5296 + 94.0674i) q^{14} +(-32.2973 + 77.5010i) q^{15} +(-49.1234 + 41.0230i) q^{16} +37.9265 q^{17} +(14.3898 + 81.8902i) q^{18} +(10.7644 - 25.9876i) q^{19} +(30.3116 + 84.1499i) q^{20} +(234.281 - 97.0425i) q^{21} +(-144.145 - 32.0451i) q^{22} +(-26.7657 + 26.7657i) q^{23} +(134.629 + 103.682i) q^{24} +(124.999 + 0.537312i) q^{25} +(-23.2526 - 36.5466i) q^{26} +(16.6248 - 6.88621i) q^{27} +(114.453 - 244.695i) q^{28} +(195.727 + 81.0727i) q^{29} +(200.636 - 127.049i) q^{30} +11.6590 q^{31} +(180.376 - 15.2469i) q^{32} +392.063i q^{33} +(-87.8362 - 61.5805i) q^{34} +(-266.380 - 267.528i) q^{35} +(99.6373 - 213.019i) q^{36} +(270.084 - 111.872i) q^{37} +(-67.1255 + 42.7082i) q^{38} +(-81.3243 + 81.3243i) q^{39} +(66.4321 - 244.104i) q^{40} +(-275.599 - 275.599i) q^{41} +(-700.152 - 155.652i) q^{42} +(3.11016 + 7.50859i) q^{43} +(281.803 + 308.261i) q^{44} +(-231.897 - 232.896i) q^{45} +(105.447 - 18.5293i) q^{46} +410.590 q^{47} +(-143.448 - 458.717i) q^{48} +797.237i q^{49} +(-288.620 - 204.203i) q^{50} +(-108.995 + 263.138i) q^{51} +(-5.48803 + 122.395i) q^{52} +(172.825 + 417.236i) q^{53} +(-49.6833 - 11.0452i) q^{54} +(539.742 - 222.211i) q^{55} +(-662.376 + 380.867i) q^{56} +(149.369 + 149.369i) q^{57} +(-321.659 - 505.559i) q^{58} +(-163.843 - 395.553i) q^{59} +(-670.951 - 31.5296i) q^{60} +(480.706 + 199.115i) q^{61} +(-27.0017 - 18.9304i) q^{62} +992.632i q^{63} +(-442.500 - 257.562i) q^{64} +(158.049 + 65.8646i) q^{65} +(636.584 - 908.001i) q^{66} +(-250.968 + 605.890i) q^{67} +(103.438 + 285.236i) q^{68} +(-108.782 - 262.623i) q^{69} +(182.546 + 1052.10i) q^{70} +(136.726 - 136.726i) q^{71} +(-576.630 + 331.563i) q^{72} +(746.457 - 746.457i) q^{73} +(-807.148 - 179.438i) q^{74} +(-362.956 + 865.709i) q^{75} +(224.804 + 10.0799i) q^{76} +(-1628.71 - 674.634i) q^{77} +(320.388 - 56.2990i) q^{78} -580.678i q^{79} +(-550.201 + 457.470i) q^{80} -658.562i q^{81} +(190.791 + 1085.76i) q^{82} +(-560.369 - 232.112i) q^{83} +(1368.79 + 1497.31i) q^{84} +(424.030 + 0.911351i) q^{85} +(4.98855 - 22.4395i) q^{86} +(-1124.98 + 1124.98i) q^{87} +(-152.127 - 1171.48i) q^{88} +(37.8550 - 37.8550i) q^{89} +(158.915 + 915.904i) q^{90} +(-197.901 - 477.775i) q^{91} +(-274.296 - 128.299i) q^{92} +(-33.5061 + 80.8909i) q^{93} +(-950.908 - 666.666i) q^{94} +(120.974 - 290.291i) q^{95} +(-412.590 + 1295.28i) q^{96} -584.915i q^{97} +(1294.46 - 1846.37i) q^{98} +(-1417.87 - 587.301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) $ 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−2.31596	−	1.62368i	−0.818815	−	0.574058i
$2$	−2.31596	−	1.62368i	−0.818815	−	0.574058i
$3$	−2.87385	+	6.93809i	−0.553073	+	1.33524i	0.362086	+	0.932145i	$0.382065\pi$
$3$	−2.87385	+	6.93809i	−0.553073	+	1.33524i	−0.915159	+	0.403092i	$0.867935\pi$
$4$	2.72732	+	7.52075i	0.340915	+	0.940094i
$5$	11.1803	+	0.0240294i	0.999998	+	0.00214925i
$5$	11.1803	+	0.0240294i	0.999998	+	0.00214925i
$6$	17.9210	−	11.4021i	1.21937	−	0.775816i
$7$	−23.8772	−	23.8772i	−1.28925	−	1.28925i	−0.935246	−	0.354000i	$-0.884821\pi$
$7$	−23.8772	−	23.8772i	−1.28925	−	1.28925i	−0.354000	−	0.935246i	$-0.615179\pi$
$8$	5.89493	−	21.8460i	0.260522	−	0.965468i
$9$	−20.7862	−	20.7862i	−0.769860	−	0.769860i
$10$	−25.8541	−	18.2089i	−0.817579	−	0.575816i
$11$	48.2332	−	19.9788i	1.32208	−	0.547623i	0.393693	−	0.919242i	$-0.371197\pi$
$11$	48.2332	−	19.9788i	1.32208	−	0.547623i	0.928385	+	0.371620i	$0.121197\pi$
$12$	−60.0176	−	2.69111i	−1.44380	−	0.0647380i
$13$	14.1490	+	5.86071i	0.301864	+	0.125036i	0.528474	−	0.848949i	$-0.322764\pi$
$13$	14.1490	+	5.86071i	0.301864	+	0.125036i	−0.226610	+	0.973985i	$0.572764\pi$
$14$	16.5296	+	94.0674i	0.315552	+	1.79575i
$15$	−32.2973	+	77.5010i	−0.555942	+	1.33404i
$16$	−49.1234	+	41.0230i	−0.767553	+	0.640985i
$17$	37.9265			0.541090			0.270545	−	0.962707i	$-0.412796\pi$
$17$	37.9265			0.541090			0.270545	+	0.962707i	$0.412796\pi$
$18$	14.3898	+	81.8902i	0.188429	+	1.07232i
$19$	10.7644	−	25.9876i	0.129975	−	0.313788i	−0.845473	−	0.534019i	$-0.820681\pi$
$19$	10.7644	−	25.9876i	0.129975	−	0.313788i	0.975448	+	0.220231i	$0.0706811\pi$
$20$	30.3116	+	84.1499i	0.338894	+	0.940825i
$21$	234.281	−	97.0425i	2.43449	−	1.00840i
$22$	−144.145	−	32.0451i	−1.39690	−	0.310548i
$23$	−26.7657	+	26.7657i	−0.242653	+	0.242653i	−0.817947	−	0.575294i	$-0.804888\pi$
$23$	−26.7657	+	26.7657i	−0.242653	+	0.242653i	0.575294	+	0.817947i	$0.304888\pi$
$24$	134.629	+	103.682i	1.14504	+	0.881832i
$25$	124.999	+	0.537312i	0.999991	+	0.00429850i
$26$	−23.2526	−	36.5466i	−0.175393	−	0.275669i
$27$	16.6248	−	6.88621i	0.118498	−	0.0490834i
$28$	114.453	−	244.695i	0.772488	−	1.65154i
$29$	195.727	+	81.0727i	1.25330	+	0.519132i	0.907845	−	0.419305i	$-0.137726\pi$
$29$	195.727	+	81.0727i	1.25330	+	0.519132i	0.345450	+	0.938437i	$0.387726\pi$
$30$	200.636	−	127.049i	1.22103	−	0.773193i
$31$	11.6590			0.0675487			0.0337744	−	0.999429i	$-0.489247\pi$
$31$	11.6590			0.0675487			0.0337744	+	0.999429i	$0.489247\pi$
$32$	180.376	−	15.2469i	0.996447	−	0.0842281i
$33$			392.063i			2.06816i
$34$	−87.8362	−	61.5805i	−0.443052	−	0.310617i
$35$	−266.380	−	267.528i	−1.28647	−	1.29201i
$36$	99.6373	−	213.019i	0.461284	−	0.986198i
$37$	270.084	−	111.872i	1.20004	−	0.497073i	0.309029	−	0.951053i	$-0.399996\pi$
$37$	270.084	−	111.872i	1.20004	−	0.497073i	0.891012	+	0.453979i	$0.149996\pi$
$38$	−67.1255	+	42.7082i	−0.286558	+	0.182321i
$39$	−81.3243	+	81.3243i	−0.333905	+	0.333905i
$40$	66.4321	−	244.104i	0.262596	−	0.964906i
$41$	−275.599	−	275.599i	−1.04979	−	1.04979i	−0.998694	−	0.0510939i	$-0.983729\pi$
$41$	−275.599	−	275.599i	−1.04979	−	1.04979i	−0.0510939	−	0.998694i	$-0.516271\pi$
$42$	−700.152	−	155.652i	−2.57228	−	0.571847i
$43$	3.11016	+	7.50859i	0.0110301	+	0.0266291i	0.929299	−	0.369329i	$-0.120413\pi$
$43$	3.11016	+	7.50859i	0.0110301	+	0.0266291i	−0.918269	+	0.395958i	$0.870413\pi$
$44$	281.803	+	308.261i	0.965533	+	1.05618i
$45$	−231.897	−	232.896i	−0.768204	−	0.771513i
$46$	105.447	−	18.5293i	0.337985	−	0.0593911i
$47$	410.590			1.27427			0.637135	−	0.770752i	$-0.280119\pi$
$47$	410.590			1.27427			0.637135	+	0.770752i	$0.280119\pi$
$48$	−143.448	−	458.717i	−0.431354	−	1.37938i
$49$			797.237i			2.32431i
$50$	−288.620	−	204.203i	−0.816340	−	0.577572i
$51$	−108.995	+	263.138i	−0.299262	+	0.722483i
$52$	−5.48803	+	122.395i	−0.0146356	+	0.326407i
$53$	172.825	+	417.236i	0.447912	+	1.08135i	0.973103	+	0.230370i	$0.0739937\pi$
$53$	172.825	+	417.236i	0.447912	+	1.08135i	−0.525191	+	0.850984i	$0.676006\pi$
$54$	−49.6833	−	11.0452i	−0.125204	−	0.0278344i
$55$	539.742	−	222.211i	1.32325	−	0.544780i
$56$	−662.376	+	380.867i	−1.58060	+	0.908849i
$57$	149.369	+	149.369i	0.347095	+	0.347095i
$58$	−321.659	−	505.559i	−0.728205	−	1.14454i
$59$	−163.843	−	395.553i	−0.361535	−	0.872823i	−0.995076	−	0.0991138i	$-0.968399\pi$
$59$	−163.843	−	395.553i	−0.361535	−	0.872823i	0.633541	−	0.773709i	$-0.281601\pi$
$60$	−670.951	−	31.5296i	−1.44366	−	0.0678409i
$61$	480.706	+	199.115i	1.00899	+	0.417936i	0.825085	−	0.565009i	$-0.191127\pi$
$61$	480.706	+	199.115i	1.00899	+	0.417936i	0.183901	+	0.982945i	$0.441127\pi$
$62$	−27.0017	−	18.9304i	−0.0553099	−	0.0387769i
$63$			992.632i			1.98508i
$64$	−442.500	−	257.562i	−0.864257	−	0.503051i
$65$	158.049	+	65.8646i	0.301594	+	0.125685i
$66$	636.584	−	908.001i	1.18724	−	1.69344i
$67$	−250.968	+	605.890i	−0.457621	+	1.10480i	0.511736	+	0.859142i	$0.329002\pi$
$67$	−250.968	+	605.890i	−0.457621	+	1.10480i	−0.969358	+	0.245653i	$0.920998\pi$
$68$	103.438	+	285.236i	0.184466	+	0.508675i
$69$	−108.782	−	262.623i	−0.189795	−	0.458204i
$70$	182.546	+	1052.10i	0.311692	+	1.79643i
$71$	136.726	−	136.726i	0.228541	−	0.228541i	−0.583542	−	0.812083i	$-0.698334\pi$
$71$	136.726	−	136.726i	0.228541	−	0.228541i	0.812083	+	0.583542i	$0.198334\pi$
$72$	−576.630	+	331.563i	−0.943841	+	0.542710i
$73$	746.457	−	746.457i	1.19680	−	1.19680i	0.221676	−	0.975120i	$-0.428847\pi$
$73$	746.457	−	746.457i	1.19680	−	1.19680i	0.975120	−	0.221676i	$-0.0711528\pi$
$74$	−807.148	−	179.438i	−1.26796	−	0.281882i
$75$	−362.956	+	865.709i	−0.558808	+	1.33285i
$76$	224.804	+	10.0799i	0.339300	+	0.0152138i
$77$	−1628.71	−	674.634i	−2.41050	−	0.998463i
$78$	320.388	−	56.2990i	0.465088	−	0.0817257i
$79$		−	580.678i		−	0.826980i	−0.910509	−	0.413490i	$-0.864310\pi$
$79$		−	580.678i		−	0.826980i	0.910509	−	0.413490i	$-0.135690\pi$
$80$	−550.201	+	457.470i	−0.768929	+	0.639334i
$81$		−	658.562i		−	0.903377i
$82$	190.791	+	1085.76i	0.256943	+	1.46222i
$83$	−560.369	−	232.112i	−0.741065	−	0.306959i	−0.0199752	−	0.999800i	$-0.506359\pi$
$83$	−560.369	−	232.112i	−0.741065	−	0.306959i	−0.721090	+	0.692841i	$0.756359\pi$
$84$	1368.79	+	1497.31i	1.77795	+	1.94487i
$85$	424.030	+	0.911351i	0.541089	+	0.00116294i
$86$	4.98855	−	22.4395i	0.00625499	−	0.0281362i
$87$	−1124.98	+	1124.98i	−1.38633	+	1.38633i
$88$	−152.127	−	1171.48i	−0.184282	−	1.41909i
$89$	37.8550	−	37.8550i	0.0450856	−	0.0450856i	−0.684205	−	0.729290i	$-0.739850\pi$
$89$	37.8550	−	37.8550i	0.0450856	−	0.0450856i	0.729290	+	0.684205i	$0.239850\pi$
$90$	158.915	+	915.904i	0.186124	+	1.07272i
$91$	−197.901	−	477.775i	−0.227974	−	0.550378i
$92$	−274.296	−	128.299i	−0.310841	−	0.145393i
$93$	−33.5061	+	80.8909i	−0.0373594	+	0.0901935i
$94$	−950.908	−	666.666i	−1.04339	−	0.731504i
$95$	120.974	−	290.291i	0.130649	−	0.313508i
$96$	−412.590	+	1295.28i	−0.438643	+	1.37708i
$97$		−	584.915i		−	0.612259i	−0.951990	−	0.306129i	$-0.900966\pi$
$97$		−	584.915i		−	0.612259i	0.951990	−	0.306129i	$-0.0990340\pi$
$98$	1294.46	−	1846.37i	1.33429	−	1.90318i
$99$	−1417.87	−	587.301i	−1.43941	−	0.596222i
$100$	336.871	+	941.551i	0.336871	+	0.941551i
$101$	−417.368	−	1007.62i	−0.411185	−	0.992688i	−0.984820	−	0.173577i	$-0.944467\pi$
$101$	−417.368	−	1007.62i	−0.411185	−	0.992688i	0.573635	−	0.819111i	$-0.305533\pi$
$102$	679.679	−	432.442i	0.659787	−	0.419786i
$103$	979.034	+	979.034i	0.936573	+	0.936573i	0.998105	−	0.0615318i	$-0.0195985\pi$
$103$	979.034	+	979.034i	0.936573	+	0.936573i	−0.0615318	+	0.998105i	$0.519599\pi$
$104$	211.441	−	274.551i	0.199360	−	0.258865i
$105$	2621.67	−	1079.34i	2.43666	−	1.00317i
$106$	277.203	−	1246.91i	0.254003	−	1.14256i
$107$	−230.999	−	557.681i	−0.208706	−	0.503860i	0.784514	−	0.620111i	$-0.212912\pi$
$107$	−230.999	−	557.681i	−0.208706	−	0.503860i	−0.993220	+	0.116251i	$0.962912\pi$
$108$	97.1306	+	106.250i	0.0865407	+	0.0946657i
$109$	109.910	−	265.347i	0.0965824	−	0.233171i	−0.868203	−	0.496210i	$-0.834725\pi$
$109$	109.910	−	265.347i	0.0965824	−	0.233171i	0.964785	+	0.263039i	$0.0847248\pi$
$110$	−1610.82	−	361.738i	−1.39623	−	0.313549i
$111$			2195.37i			1.87726i
$112$	2152.44	+	193.414i	1.81595	+	0.163178i
$113$	−2055.04			−1.71081			−0.855405	−	0.517959i	$-0.826692\pi$
$113$	−2055.04			−1.71081			−0.855405	+	0.517959i	$0.826692\pi$
$114$	−103.405	−	588.460i	−0.0849540	−	0.483459i
$115$	−299.892	+	298.605i	−0.243174	+	0.242131i
$116$	−75.9174	+	1693.12i	−0.0607651	+	1.35520i
$117$	−172.282	−	415.926i	−0.136133	−	0.328653i
$118$	−262.797	+	1182.11i	−0.205020	+	0.922222i
$119$	−905.577	−	905.577i	−0.697597	−	0.697597i
$120$	1502.70	+	1162.43i	1.14314	+	0.884291i
$121$	986.127	−	986.127i	0.740892	−	0.740892i
$122$	−789.997	−	1241.66i	−0.586253	−	0.921428i
$123$	2704.16	−	1120.10i	1.98232	−	0.821106i
$124$	31.7977	+	87.6841i	0.0230284	+	0.0635021i
$125$	1397.51	+	9.01097i	0.999979	+	0.00644772i
$126$	1611.72	−	2298.89i	1.13955	−	1.62541i
$127$		−	1494.18i		−	1.04400i	−0.852947	−	0.521998i	$-0.825187\pi$
$127$		−	1494.18i		−	1.04400i	0.852947	−	0.521998i	$-0.174813\pi$
$128$	606.612	+	1314.98i	0.418886	+	0.908039i
$129$	−61.0334			−0.0416565
$130$	−259.093	−	409.161i	−0.174800	−	0.276045i
$131$	1610.74	+	667.189i	1.07428	+	0.444982i	0.848499	−	0.529196i	$-0.177507\pi$
$131$	1610.74	+	667.189i	1.07428	+	0.444982i	0.225781	+	0.974178i	$0.427507\pi$
$132$	−2948.61	+	1069.28i	−1.94427	+	0.705068i
$133$	−877.534	+	363.486i	−0.572119	+	0.236980i
$134$	1565.00	−	995.725i	1.00892	−	0.641922i
$135$	186.036	−	76.5905i	0.118603	−	0.0488286i
$136$	223.574	−	828.544i	0.140966	−	0.522405i
$137$	−1174.26	+	1174.26i	−0.732289	+	0.732289i	−0.971073	−	0.238784i	$-0.923251\pi$
$137$	−1174.26	+	1174.26i	−0.732289	+	0.732289i	0.238784	+	0.971073i	$0.423251\pi$
$138$	−174.481	+	784.851i	−0.107629	+	0.484138i
$139$	−614.225	+	254.420i	−0.374805	+	0.155249i	−0.562130	−	0.827049i	$-0.690018\pi$
$139$	−614.225	+	254.420i	−0.374805	+	0.155249i	0.187325	+	0.982298i	$0.440018\pi$
$140$	1285.51	−	2733.02i	0.776036	−	1.64987i
$141$	−1179.97	+	2848.71i	−0.704764	+	1.70145i
$142$	−538.651	+	94.6523i	−0.318328	+	0.0559370i
$143$	799.542			0.467560
$144$	1873.80	+	168.376i	1.08438	+	0.0974399i
$145$	2186.34	+	911.122i	1.25218	+	0.521824i
$146$	−2940.77	+	516.755i	−1.66698	+	0.292924i
$147$	−5531.31	−	2291.14i	−3.10350	−	1.28551i
$148$	1577.97	+	1726.12i	0.876408	+	0.958692i
$149$	589.982	−	244.379i	0.324384	−	0.134364i	−0.214548	−	0.976713i	$-0.568828\pi$
$149$	589.982	−	244.379i	0.324384	−	0.134364i	0.538932	+	0.842349i	$0.318828\pi$
$150$	2246.23	−	1415.62i	1.22269	−	0.770567i
$151$	2044.55	+	2044.55i	1.10187	+	1.10187i	0.994185	+	0.107688i	$0.0343448\pi$
$151$	2044.55	+	2044.55i	1.10187	+	1.10187i	0.107688	+	0.994185i	$0.465655\pi$
$152$	−504.271	−	388.355i	−0.269091	−	0.207235i
$153$	−788.349	−	788.349i	−0.416563	−	0.416563i
$154$	2676.63	+	4206.93i	1.40058	+	2.20132i
$155$	130.351	+	0.280158i	0.0675486	+	0.000145179i
$156$	−833.417	−	389.822i	−0.427736	−	0.200069i
$157$	94.8251	−	228.928i	0.0482030	−	0.116372i	−0.897944	−	0.440110i	$-0.854940\pi$
$157$	94.8251	−	228.928i	0.0482030	−	0.116372i	0.946147	+	0.323738i	$0.104940\pi$
$158$	−942.836	+	1344.83i	−0.474734	+	0.677143i
$159$	−3391.50			−1.69159
$160$	2017.03	−	166.131i	0.996625	−	0.0820862i
$161$	1278.18			0.625679
$162$	−1069.29	+	1525.20i	−0.518591	+	0.739699i
$163$	488.296	−	1178.85i	0.234640	−	0.566471i	−0.762073	−	0.647492i	$-0.775818\pi$
$163$	488.296	−	1178.85i	0.234640	−	0.566471i	0.996712	+	0.0810210i	$0.0258181\pi$
$164$	1321.06	−	2824.36i	0.629010	−	1.34479i
$165$	−9.42103	+	4383.38i	−0.00444501	+	2.06816i
$166$	920.914	+	1447.42i	0.430583	+	0.676757i
$167$	2877.46	+	2877.46i	1.33332	+	1.33332i	0.902380	+	0.430942i	$0.141819\pi$
$167$	2877.46	+	2877.46i	1.33332	+	1.33332i	0.430942	+	0.902380i	$0.358181\pi$
$168$	−738.923	−	5690.18i	−0.339340	−	2.61314i
$169$	−1387.67	−	1387.67i	−0.631619	−	0.631619i
$170$	−980.556	−	690.600i	−0.442384	−	0.311568i
$171$	−763.936	+	316.433i	−0.341635	+	0.141510i
$172$	−47.9878	+	43.8691i	−0.0212735	+	0.0194476i
$173$	138.324	+	57.2956i	0.0607894	+	0.0251798i	0.412871	−	0.910790i	$-0.364526\pi$
$173$	138.324	+	57.2956i	0.0607894	+	0.0251798i	−0.352082	+	0.935969i	$0.614526\pi$
$174$	4432.02	−	778.799i	1.93098	−	0.339314i
$175$	−2971.79	−	2997.45i	−1.28369	−	1.29478i
$176$	−1549.79	+	2960.10i	−0.663747	+	1.26776i
$177$	3215.24			1.36538
$178$	−149.135	+	26.2061i	−0.0627985	+	0.0110350i
$179$	298.570	−	720.812i	0.124671	−	0.300983i	−0.849205	−	0.528064i	$-0.822918\pi$
$179$	298.570	−	720.812i	0.124671	−	0.300983i	0.973876	+	0.227081i	$0.0729181\pi$
$180$	1119.09	−	2379.22i	0.463402	−	0.985204i
$181$	−2509.35	+	1039.41i	−1.03049	+	0.426842i	−0.832889	−	0.553440i	$-0.813315\pi$
$181$	−2509.35	+	1039.41i	−1.03049	+	0.426842i	−0.197600	+	0.980283i	$0.563315\pi$
$182$	−317.424	+	1427.83i	−0.129280	+	0.581528i
$183$	−2762.96	+	2762.96i	−1.11609	+	1.11609i
$184$	426.942	+	742.505i	0.171058	+	0.297490i
$185$	3022.31	−	1244.28i	1.20111	−	0.494493i
$186$	208.940	−	132.937i	0.0823667	−	0.0524053i
$187$	1829.32	−	757.727i	0.715363	−	0.296313i
$188$	1119.81	+	3087.94i	0.434418	+	1.19793i
$189$	−561.375	−	232.529i	−0.216053	−	0.0894922i
$190$	−751.511	+	475.878i	−0.286949	+	0.181704i
$191$	−2784.25			−1.05477			−0.527385	−	0.849626i	$-0.676827\pi$
$191$	−2784.25			−1.05477			−0.527385	+	0.849626i	$0.676827\pi$
$192$	3058.67	−	2329.91i	1.14969	−	0.875764i
$193$			197.316i			0.0735911i	0.999323	+	0.0367956i	$0.0117150\pi$
$193$			197.316i			0.0735911i	−0.999323	+	0.0367956i	$0.988285\pi$
$194$	−949.715	+	1354.64i	−0.351472	+	0.501326i
$195$	−911.185	+	907.277i	−0.334622	+	0.333187i
$196$	−5995.82	+	2174.32i	−2.18507	+	0.792392i
$197$	−1905.01	+	789.080i	−0.688966	+	0.285379i	−0.699569	−	0.714565i	$-0.746625\pi$
$197$	−1905.01	+	789.080i	−0.688966	+	0.285379i	0.0106036	+	0.999944i	$0.496625\pi$
$198$	2330.14	+	3662.33i	0.836342	+	1.31450i
$199$	334.374	−	334.374i	0.119111	−	0.119111i	−0.645039	−	0.764150i	$-0.723159\pi$
$199$	334.374	−	334.374i	0.119111	−	0.119111i	0.764150	+	0.645039i	$0.223159\pi$
$200$	748.598	−	2727.56i	0.264669	−	0.964339i
$201$	−3482.48	−	3482.48i	−1.22207	−	1.22207i
$202$	−669.439	+	3011.27i	−0.233176	+	1.04887i
$203$	−2737.62	−	6609.19i	−0.946517	−	2.28509i
$204$	−2276.26	−	102.064i	−0.781225	−	0.0350291i
$205$	−3074.66	−	3087.90i	−1.04753	−	1.05204i
$206$	−677.763	−	3857.04i	−0.229233	−	1.30453i
$207$	1112.71			0.373618
$208$	−935.472	+	292.537i	−0.311843	+	0.0975183i
$209$		−	1468.53i		−	0.486029i
$210$	−7824.18	−	1757.06i	−2.57105	−	0.577374i
$211$	−1092.02	+	2636.38i	−0.356294	+	0.860169i	0.639521	+	0.768774i	$0.279133\pi$
$211$	−1092.02	+	2636.38i	−0.356294	+	0.860169i	−0.995815	+	0.0913955i	$0.970867\pi$
$212$	−2666.58	+	2437.71i	−0.863875	+	0.789729i
$213$	555.687	+	1341.55i	0.178756	+	0.431556i
$214$	−370.512	+	1666.63i	−0.118354	+	0.532377i
$215$	34.5921	+	84.0231i	0.0109729	+	0.0266527i
$216$	−52.4345	−	403.779i	−0.0165172	−	0.127193i
$217$	−278.383	−	278.383i	−0.0870869	−	0.0870869i
$218$	−685.386	+	436.073i	−0.212937	+	0.135480i
$219$	3033.78	+	7324.19i	0.936090	+	2.25992i
$220$	3143.24	+	3453.23i	0.963261	+	1.05826i
$221$	536.622	+	222.276i	0.163335	+	0.0676557i
$222$	3564.58	−	5084.39i	1.07765	−	1.53713i
$223$		−	1498.22i		−	0.449903i	−0.974370	−	0.224951i	$-0.927778\pi$
$223$		−	1498.22i		−	0.449903i	0.974370	−	0.224951i	$-0.0722223\pi$
$224$	−4670.92	−	3942.82i	−1.39325	−	1.17607i
$225$	−2587.09	−	2609.42i	−0.766544	−	0.773162i
$226$	4759.38	+	3336.72i	1.40084	+	0.982104i
$227$	962.950	−	2324.77i	0.281556	−	0.679737i	−0.718316	−	0.695717i	$-0.755087\pi$
$227$	962.950	−	2324.77i	0.281556	−	0.679737i	0.999872	+	0.0159802i	$0.00508686\pi$
$228$	−715.990	+	1530.75i	−0.207972	+	0.444632i
$229$	−561.454	−	1355.47i	−0.162017	−	0.391144i	0.821934	−	0.569583i	$-0.192895\pi$
$229$	−561.454	−	1355.47i	−0.162017	−	0.391144i	−0.983951	+	0.178439i	$0.942895\pi$
$230$	1179.38	−	204.629i	0.338112	−	0.0586645i
$231$	9361.34	−	9361.34i	2.66637	−	2.66637i
$232$	2924.92	−	3797.94i	0.827716	−	1.07477i
$233$	2166.57	−	2166.57i	0.609170	−	0.609170i	−0.333559	−	0.942729i	$-0.608250\pi$
$233$	2166.57	−	2166.57i	0.609170	−	0.609170i	0.942729	+	0.333559i	$0.108250\pi$
$234$	−276.333	+	1243.00i	−0.0771985	+	0.347254i
$235$	4590.52	+	9.86622i	1.27427	+	0.00273873i
$236$	2528.00	−	2311.02i	0.697283	−	0.637436i
$237$	4028.80	+	1668.78i	1.10421	+	0.457380i
$238$	626.911	+	3567.65i	0.170742	+	0.971664i
$239$		−	1358.81i		−	0.367757i	−0.982949	−	0.183878i	$-0.941135\pi$
$239$		−	1358.81i		−	0.367757i	0.982949	−	0.183878i	$-0.0588652\pi$
$240$	−1592.77	−	5132.05i	−0.428388	−	1.38030i
$241$			2800.80i			0.748611i	0.927305	+	0.374306i	$0.122119\pi$
$241$			2800.80i			0.748611i	−0.927305	+	0.374306i	$0.877881\pi$
$242$	−3884.99	+	682.674i	−1.03197	+	0.181339i
$243$	5018.03	+	2078.54i	1.32472	+	0.548717i
$244$	−186.454	+	4158.32i	−0.0489200	+	1.09102i
$245$	−19.1571	+	8913.36i	−0.00499553	+	2.32430i
$246$	−8081.41	−	1796.59i	−2.09452	−	0.465635i
$247$	304.612	−	304.612i	0.0784695	−	0.0784695i
$248$	68.7287	−	254.702i	0.0175979	−	0.0652161i
$249$	3220.83	−	3220.83i	0.819727	−	0.819727i
$250$	−3221.95	−	2289.98i	−0.815096	−	0.579325i
$251$	203.624	+	491.591i	0.0512057	+	0.123621i	0.947412	−	0.320015i	$-0.103688\pi$
$251$	203.624	+	491.591i	0.0512057	+	0.123621i	−0.896207	+	0.443637i	$0.853688\pi$
$252$	−7465.34	+	2707.23i	−1.86616	+	0.676743i
$253$	−756.246	+	1825.74i	−0.187924	+	0.453689i
$254$	−2426.08	+	3460.47i	−0.599313	+	0.854839i
$255$	−1224.92	+	2939.34i	−0.300814	+	0.721838i
$256$	730.220	−	4030.38i	0.178276	−	0.983980i
$257$			7545.13i			1.83133i	0.401942	+	0.915665i	$0.368335\pi$
$257$			7545.13i			1.83133i	−0.401942	+	0.915665i	$0.631665\pi$
$258$	141.351	+	99.0988i	0.0341090	+	0.0239133i
$259$	−9120.03	−	3777.64i	−2.18800	−	0.906298i
$260$	−64.2990	+	1368.28i	−0.0153371	+	0.326375i
$261$	−2383.23	−	5753.62i	−0.565203	−	1.36452i
$262$	−2647.10	−	4160.51i	−0.624192	−	0.981057i
$263$	−3400.93	−	3400.93i	−0.797379	−	0.797379i	0.185303	−	0.982681i	$-0.440673\pi$
$263$	−3400.93	−	3400.93i	−0.797379	−	0.797379i	−0.982681	+	0.185303i	$0.940673\pi$
$264$	8565.02	+	2311.18i	1.99674	+	0.538801i
$265$	1922.21	+	4668.98i	0.445586	+	1.08231i
$266$	2622.52	+	583.015i	0.604500	+	0.134387i
$267$	153.852	+	371.431i	0.0352643	+	0.0851356i
$268$	−5241.22	−	235.009i	−1.19462	−	0.0535652i
$269$	−1236.78	+	2985.86i	−0.280327	+	0.676769i	−0.999843	−	0.0177065i	$-0.994364\pi$
$269$	−1236.78	+	2985.86i	−0.280327	+	0.676769i	0.719516	+	0.694476i	$0.244364\pi$
$270$	−555.209	−	124.682i	−0.125144	−	0.0281034i
$271$			4148.88i			0.929988i	0.885314	+	0.464994i	$0.153943\pi$
$271$			4148.88i			0.929988i	−0.885314	+	0.464994i	$0.846057\pi$
$272$	−1863.08	+	1555.86i	−0.415315	+	0.346830i
$273$	3883.59			0.860972
$274$	4626.15	−	812.912i	1.01998	−	0.179233i
$275$	6039.83	−	2471.42i	1.32442	−	0.541934i
$276$	1678.44	−	1534.38i	0.366051	−	0.334634i
$277$	−2110.52	−	5095.24i	−0.457793	−	1.10521i	−0.969289	−	0.245925i	$-0.920908\pi$
$277$	−2110.52	−	5095.24i	−0.457793	−	1.10521i	0.511495	−	0.859286i	$-0.329092\pi$
$278$	1835.62	+	408.078i	0.396018	+	0.0880392i
$279$	−242.346	−	242.346i	−0.0520031	−	0.0520031i
$280$	−7414.72	+	4242.30i	−1.58255	+	0.905450i
$281$	−3631.29	+	3631.29i	−0.770905	+	0.770905i	−0.978265	−	0.207360i	$-0.933513\pi$
$281$	−3631.29	+	3631.29i	−0.770905	+	0.770905i	0.207360	+	0.978265i	$0.433513\pi$
$282$	7358.16	−	4681.59i	1.55380	−	0.988598i
$283$	2363.02	−	978.795i	0.496350	−	0.205595i	−0.120443	−	0.992720i	$-0.538432\pi$
$283$	2363.02	−	978.795i	0.496350	−	0.205595i	0.616793	+	0.787125i	$0.288432\pi$
$284$	1401.18	+	655.386i	0.292763	+	0.136937i
$285$	1666.40	+	1673.58i	0.346348	+	0.347840i
$286$	−1851.71	−	1298.20i	−0.382845	−	0.268406i
$287$			13161.0i			2.70687i
$288$	−4066.26	−	3432.41i	−0.831968	−	0.702281i
$289$	−3474.58			−0.707222
$290$	−3584.10	−	5660.04i	−0.725744	−	1.14610i
$291$	4058.19	+	1680.96i	0.817510	+	0.338624i
$292$	7649.74	+	3578.09i	1.53311	+	0.717095i
$293$	−7951.83	+	3293.75i	−1.58550	+	0.656734i	−0.989272	−	0.146083i	$-0.953333\pi$
$293$	−7951.83	+	3293.75i	−1.58550	+	0.656734i	−0.596225	+	0.802818i	$0.703333\pi$
$294$	9090.19	+	14287.3i	1.80323	+	2.83418i
$295$	−1822.31	−	4426.34i	−0.359658	−	0.873598i
$296$	−851.844	−	6559.75i	−0.167272	−	1.28810i
$297$	664.287	−	664.287i	0.129784	−	0.129784i
$298$	−1763.17	−	391.972i	−0.342743	−	0.0761957i
$299$	−535.573	+	221.842i	−0.103589	+	0.0429078i
$300$	−7500.68	−	368.634i	−1.44351	−	0.0709436i
$301$	105.022	−	253.546i	0.0201109	−	0.0485519i
$302$	−1415.39	−	8054.77i	−0.269691	−	1.53477i
$303$	8190.38			1.55289
$304$	537.306	+	1718.19i	0.101370	+	0.324161i
$305$	5369.66	+	2237.72i	1.00809	+	0.420103i
$306$	545.756	+	3105.81i	0.101957	+	0.580220i
$307$	−3938.42	−	1631.35i	−0.732175	−	0.303277i	−0.0147294	−	0.999892i	$-0.504689\pi$
$307$	−3938.42	−	1631.35i	−0.732175	−	0.303277i	−0.717445	+	0.696615i	$0.754689\pi$
$308$	631.734	−	14089.1i	0.116871	−	2.60649i
$309$	−9606.22	+	3979.03i	−1.76854	+	0.732553i
$310$	−301.432	−	212.297i	−0.0552264	−	0.0388956i
$311$	4258.17	+	4258.17i	0.776395	+	0.776395i	0.979216	−	0.202821i	$-0.0650109\pi$
$311$	4258.17	+	4258.17i	0.776395	+	0.776395i	−0.202821	+	0.979216i	$0.565011\pi$
$312$	1297.21	+	2256.02i	0.235385	+	0.409364i
$313$	−1466.99	−	1466.99i	−0.264917	−	0.264917i	0.562131	−	0.827048i	$-0.309982\pi$
$313$	−1466.99	−	1466.99i	−0.264917	−	0.264917i	−0.827048	+	0.562131i	$0.809982\pi$
$314$	−591.317	+	376.222i	−0.106274	+	0.0676160i
$315$	−23.8523	+	11097.9i	−0.00426644	+	1.98507i
$316$	4367.14	−	1583.70i	0.777439	−	0.281930i
$317$	2791.39	−	6739.02i	0.494575	−	1.19401i	−0.457793	−	0.889059i	$-0.651360\pi$
$317$	2791.39	−	6739.02i	0.494575	−	1.19401i	0.952368	−	0.304951i	$-0.0986402\pi$
$318$	7854.56	+	5506.70i	1.38510	+	0.971071i
$319$	11060.3			1.94124
$320$	−4941.09	−	2890.26i	−0.863174	−	0.504907i
$321$	4533.10			0.788202
$322$	−2960.20	−	2075.35i	−0.512315	−	0.359176i
$323$	408.257	−	985.619i	0.0703282	−	0.169787i
$324$	4952.88	−	1796.11i	0.849260	−	0.307975i
$325$	1765.46	+	740.184i	0.301323	+	0.126332i
$326$	−3044.95	+	1937.33i	−0.517313	+	0.329138i
$327$	1525.13	+	1525.13i	0.257921	+	0.257921i
$328$	−7645.38	+	4396.11i	−1.28703	+	0.740044i
$329$	−9803.71	−	9803.71i	−1.64285	−	1.64285i
$330$	7139.03	−	10136.4i	1.19088	−	1.69089i
$331$	−3081.63	+	1276.45i	−0.511728	+	0.211965i	−0.623579	−	0.781760i	$-0.714322\pi$
$331$	−3081.63	+	1276.45i	−0.511728	+	0.211965i	0.111851	+	0.993725i	$0.464322\pi$
$332$	217.353	−	4847.44i	0.0359300	−	0.801318i
$333$	−7939.43	−	3288.62i	−1.30654	−	0.541187i
$334$	−1992.00	−	11336.2i	−0.326340	−	1.85715i
$335$	−2820.46	+	6768.02i	−0.459995	+	1.10381i
$336$	−7527.72	+	14378.0i	−1.22223	+	2.33448i
$337$	−1372.41			−0.221839			−0.110920	−	0.993829i	$-0.535380\pi$
$337$	−1372.41			−0.221839			−0.110920	+	0.993829i	$0.535380\pi$
$338$	960.651	+	5466.91i	0.154593	+	0.879765i
$339$	5905.87	−	14258.0i	0.946203	−	2.28434i
$340$	1149.61	+	3191.51i	0.183372	+	0.509071i
$341$	562.349	−	232.932i	0.0893046	−	0.0369912i
$342$	2283.03	+	507.543i	0.360971	+	0.0802479i
$343$	10845.9	−	10845.9i	1.70736	−	1.70736i
$344$	182.367	−	23.6821i	0.0285831	−	0.00371178i
$345$	−1209.91	−	2938.82i	−0.188809	−	0.458611i
$346$	−227.322	−	357.288i	−0.0353206	−	0.0555142i
$347$	−10058.3	+	4166.30i	−1.55608	+	0.644549i	−0.984403	−	0.175930i	$-0.943707\pi$
$347$	−10058.3	+	4166.30i	−1.55608	+	0.644549i	−0.571676	+	0.820479i	$0.693707\pi$
$348$	−11528.9	−	5392.51i	−1.77590	−	0.830658i
$349$	6096.27	+	2525.16i	0.935031	+	0.387302i	0.797585	−	0.603207i	$-0.206111\pi$
$349$	6096.27	+	2525.16i	0.935031	+	0.387302i	0.137446	+	0.990509i	$0.456111\pi$
$350$	2015.64	+	11767.2i	0.307830	+	1.79709i
$351$	275.582			0.0419074
$352$	8395.50	−	4339.11i	1.27125	−	0.657033i
$353$			2154.74i			0.324887i	0.986718	+	0.162443i	$0.0519375\pi$
$353$			2154.74i			0.324887i	−0.986718	+	0.162443i	$0.948062\pi$
$354$	−7446.36	−	5220.52i	−1.11799	−	0.783807i
$355$	1531.93	−	1525.35i	0.229031	−	0.228049i
$356$	387.940	+	181.455i	0.0577551	+	0.0270143i
$357$	8885.47	−	3680.48i	1.31728	−	0.545635i
$358$	−1861.84	+	1184.59i	−0.274865	+	0.174881i
$359$	−5082.09	+	5082.09i	−0.747138	+	0.747138i	−0.973941	−	0.226803i	$-0.927173\pi$
$359$	−5082.09	+	5082.09i	−0.747138	+	0.747138i	0.226803	+	0.973941i	$0.427173\pi$
$360$	−6454.87	+	3693.13i	−0.945005	+	0.540680i
$361$	4290.56	+	4290.56i	0.625538	+	0.625538i
$362$	7499.21	+	1667.16i	1.08881	+	0.242055i
$363$	4007.86	+	9675.83i	0.579499	+	1.39903i
$364$	3053.49	−	2791.41i	0.439688	−	0.401950i
$365$	8363.56	−	8327.68i	1.19937	−	1.19422i
$366$	10885.1	−	1912.73i	1.55457	−	0.273170i
$367$	6998.29			0.995389			0.497695	−	0.867352i	$-0.334180\pi$
$367$	6998.29			0.995389			0.497695	+	0.867352i	$0.334180\pi$
$368$	216.812	−	2412.83i	0.0307122	−	0.341786i
$369$			11457.3i			1.61638i
$370$	−9019.86	−	2025.57i	−1.26735	−	0.284606i
$371$	5835.84	−	14089.0i	0.816663	−	1.97160i
$372$	−699.742	−	31.3755i	−0.0975268	−	0.00437297i
$373$	−1119.83	−	2703.52i	−0.155450	−	0.375289i	0.826898	−	0.562352i	$-0.190103\pi$
$373$	−1119.83	−	2703.52i	−0.155450	−	0.375289i	−0.982348	+	0.187062i	$0.940103\pi$
$374$	−5466.93	−	1215.36i	−0.755850	−	0.168034i
$375$	−4078.77	+	9670.18i	−0.561671	+	1.33164i
$376$	2420.40	−	8969.76i	0.331975	−	1.23027i
$377$	2294.20	+	2294.20i	0.313414	+	0.313414i
$378$	922.569	+	1450.02i	0.125534	+	0.197305i
$379$	1114.72	+	2691.17i	0.151080	+	0.364739i	0.981241	−	0.192784i	$-0.0617517\pi$
$379$	1114.72	+	2691.17i	0.151080	+	0.364739i	−0.830161	+	0.557523i	$0.811752\pi$
$380$	2513.14	+	118.099i	0.339267	+	0.0159430i
$381$	10366.8	+	4294.06i	1.39398	+	0.577406i
$382$	6448.20	+	4520.73i	0.863661	+	0.605499i
$383$			3303.01i			0.440668i	0.975425	+	0.220334i	$0.0707147\pi$
$383$			3303.01i			0.440668i	−0.975425	+	0.220334i	$0.929285\pi$
$384$	−10866.8	+	429.671i	−1.44412	+	0.0571005i
$385$	−18193.3	−	7581.75i	−2.40835	−	1.00364i
$386$	320.377	−	456.975i	0.0422456	−	0.0602575i
$387$	91.4268	−	220.724i	0.0120090	−	0.0289923i
$388$	4399.00	−	1595.25i	0.575581	−	0.208728i
$389$	−4298.88	−	10378.4i	−0.560313	−	1.35272i	−0.909516	−	0.415669i	$-0.863547\pi$
$389$	−4298.88	−	10378.4i	−0.560313	−	1.35272i	0.349203	−	0.937047i	$-0.386453\pi$
$390$	3583.39	−	621.742i	0.465262	−	0.0807259i
$391$	−1015.13	+	1015.13i	−0.131297	+	0.131297i
$392$	17416.5	+	4699.66i	2.24404	+	0.605532i
$393$	−9258.04	+	9258.04i	−1.18831	+	1.18831i
$394$	5693.13	+	1265.65i	0.727959	+	0.161834i
$395$	13.9534	−	6492.17i	0.00177739	−	0.826978i
$396$	549.955	−	12265.2i	0.0697886	−	1.55644i
$397$	8597.35	+	3561.14i	1.08687	+	0.450197i	0.852915	−	0.522049i	$-0.174832\pi$
$397$	8597.35	+	3561.14i	1.08687	+	0.450197i	0.233957	+	0.972247i	$0.424832\pi$
$398$	−1317.31	+	231.479i	−0.165907	+	0.0291533i
$399$		−	7133.02i		−	0.894981i
$400$	−6162.41	+	5101.44i	−0.770302	+	0.637680i
$401$		−	1358.61i		−	0.169192i	−0.996415	−	0.0845960i	$-0.973040\pi$
$401$		−	1358.61i		−	0.169192i	0.996415	−	0.0845960i	$-0.0269600\pi$
$402$	2410.84	+	13719.7i	0.299109	+	1.70218i
$403$	164.963	+	68.3297i	0.0203905	+	0.00844602i
$404$	6439.73	−	5887.01i	0.793041	−	0.724975i
$405$	15.8249	−	7362.93i	0.00194159	−	0.903375i
$406$	−4391.01	+	19751.6i	−0.536754	+	2.41442i
$407$	10791.9	−	10791.9i	1.31434	−	1.31434i
$408$	5106.00	+	3932.29i	0.619570	+	0.477151i
$409$	−5582.13	+	5582.13i	−0.674861	+	0.674861i	−0.958833	−	0.283971i	$-0.908348\pi$
$409$	−5582.13	+	5582.13i	−0.674861	+	0.674861i	0.283971	+	0.958833i	$0.408348\pi$
$410$	2107.01	+	12143.7i	0.253800	+	1.46277i
$411$	−4772.46	−	11521.7i	−0.572769	−	1.38279i
$412$	−4692.93	+	10033.2i	−0.561175	+	1.19976i
$413$	−5532.56	+	13356.8i	−0.659175	+	1.59139i
$414$	−2577.00	−	1806.69i	−0.305924	−	0.214478i
$415$	−6259.52	−	2608.55i	−0.740404	−	0.308551i
$416$	2641.50	+	841.403i	0.311323	+	0.0991663i
$417$		−	4992.72i		−	0.586317i
$418$	−2384.42	+	3401.04i	−0.279009	+	0.397968i
$419$	−5151.19	−	2133.69i	−0.600602	−	0.248778i	0.0616023	−	0.998101i	$-0.480379\pi$
$419$	−5151.19	−	2133.69i	−0.600602	−	0.248778i	−0.662204	+	0.749323i	$0.730379\pi$
$420$	15267.6	+	16773.2i	1.77376	+	1.94869i
$421$	409.749	+	989.222i	0.0474346	+	0.114517i	0.945821	−	0.324689i	$-0.105260\pi$
$421$	409.749	+	989.222i	0.0474346	+	0.114517i	−0.898386	+	0.439206i	$0.855260\pi$
$422$	6809.71	−	4332.64i	0.785525	−	0.499786i
$423$	−8534.61	−	8534.61i	−0.981009	−	0.981009i
$424$	10133.7	−	1315.96i	1.16070	−	0.150728i
$425$	4740.77	+	20.3784i	0.541085	+	0.00232587i
$426$	891.297	−	4009.23i	0.101370	−	0.455981i
$427$	−6723.60	−	16232.2i	−0.762009	−	1.83965i
$428$	3564.17	−	3258.26i	0.402525	−	0.367977i
$429$	−2297.76	+	5547.30i	−0.258595	+	0.624303i
$430$	56.3128	−	250.761i	0.00631545	−	0.0281227i
$431$			16629.0i			1.85844i	0.369524	+	0.929221i	$0.379521\pi$
$431$			16629.0i			1.85844i	−0.369524	+	0.929221i	$0.620479\pi$
$432$	−534.173	+	1020.27i	−0.0594916	+	0.113629i
$433$	4720.06			0.523861			0.261930	−	0.965087i	$-0.415641\pi$
$433$	4720.06			0.523861			0.261930	+	0.965087i	$0.415641\pi$
$434$	192.718	+	1096.73i	0.0213151	+	0.121301i
$435$	−12604.7	+	12550.6i	−1.38930	+	1.38335i
$436$	2295.37	+	102.921i	0.252129	+	0.0113051i
$437$	407.459	+	983.692i	0.0446027	+	0.107680i
$438$	4866.04	−	21888.4i	0.530841	−	2.38783i
$439$	−3658.76	−	3658.76i	−0.397775	−	0.397775i	0.479673	−	0.877447i	$-0.340755\pi$
$439$	−3658.76	−	3658.76i	−0.397775	−	0.397775i	−0.877447	+	0.479673i	$0.840755\pi$
$440$	−1672.68	−	13101.2i	−0.181232	−	1.41948i
$441$	16571.6	−	16571.6i	1.78939	−	1.78939i
$442$	−881.889	−	1386.09i	−0.0949031	−	0.149161i
$443$	−380.201	+	157.484i	−0.0407763	+	0.0168901i	−0.402978	−	0.915209i	$-0.632025\pi$
$443$	−380.201	+	157.484i	−0.0407763	+	0.0168901i	0.362202	+	0.932100i	$0.382025\pi$
$444$	−16510.9	+	5987.49i	−1.76480	+	0.639986i
$445$	424.140	−	422.321i	0.0451824	−	0.0449886i
$446$	−2432.63	+	3469.82i	−0.258270	+	0.368387i
$447$			4795.66i			0.507443i
$448$	4415.78	+	16715.5i	0.465683	+	1.76279i
$449$	−7966.77			−0.837361			−0.418680	−	0.908134i	$-0.637507\pi$
$449$	−7966.77			−0.837361			−0.418680	+	0.908134i	$0.637507\pi$
$450$	1754.71	+	10243.9i	0.183818	+	1.07312i
$451$	−18799.2	−	7786.86i	−1.96279	−	0.813014i
$452$	−5604.75	−	15455.4i	−0.583242	−	1.60832i
$453$	−20061.0	+	8309.53i	−2.08068	+	0.861845i
$454$	−6004.83	+	3820.54i	−0.620750	+	0.394949i
$455$	−2201.11	−	5346.43i	−0.226791	−	0.550867i
$456$	4143.65	−	2382.60i	0.425535	−	0.244683i
$457$	−9546.56	+	9546.56i	−0.977176	+	0.977176i	−0.999745	−	0.0225694i	$-0.992815\pi$
$457$	−9546.56	+	9546.56i	−0.977176	+	0.977176i	0.0225694	+	0.999745i	$0.492815\pi$
$458$	−900.546	+	4050.83i	−0.0918772	+	0.413282i
$459$	630.519	−	261.170i	0.0641179	−	0.0265585i
$460$	−3063.64	−	1441.02i	−0.310528	−	0.146060i
$461$	−2105.48	+	5083.09i	−0.212716	+	0.513542i	−0.993839	−	0.110835i	$-0.964647\pi$
$461$	−2105.48	+	5083.09i	−0.212716	+	0.513542i	0.781123	+	0.624378i	$0.214647\pi$
$462$	−36880.3	+	6480.65i	−3.71391	+	0.652612i
$463$	−7242.62			−0.726983			−0.363492	−	0.931598i	$-0.618415\pi$
$463$	−7242.62			−0.726983			−0.363492	+	0.931598i	$0.618415\pi$
$464$	−12940.6	+	4046.74i	−1.29473	+	0.404882i
$465$	−376.553	+	903.581i	−0.0375531	+	0.0901130i
$466$	−8535.50	+	1499.87i	−0.848497	+	0.149099i
$467$	4331.95	+	1794.35i	0.429248	+	0.177800i	0.586838	−	0.809704i	$-0.300373\pi$
$467$	4331.95	+	1794.35i	0.429248	+	0.177800i	−0.157590	+	0.987505i	$0.550373\pi$
$468$	2658.21	−	2430.06i	0.262555	−	0.240020i
$469$	20459.3	−	8474.54i	2.01434	−	0.834366i
$470$	−10615.4	−	7476.39i	−1.04182	−	0.733745i
$471$	1315.81	+	1315.81i	0.128725	+	0.128725i
$472$	−9607.10	+	1247.57i	−0.936870	+	0.121661i
$473$	300.026	+	300.026i	0.0291653	+	0.0291653i
$474$	−6620.96	−	10406.3i	−0.641584	−	1.00839i
$475$	1359.50	−	3242.64i	0.131323	−	0.313226i
$476$	4340.82	−	9280.42i	0.417985	−	0.893629i
$477$	5080.39	−	12265.1i	0.487662	−	1.17732i
$478$	−2206.27	+	3146.94i	−0.211114	+	0.301125i
$479$	−2239.80			−0.213651			−0.106826	−	0.994278i	$-0.534069\pi$
$479$	−2239.80			−0.213651			−0.106826	+	0.994278i	$0.534069\pi$
$480$	−4644.01	+	14471.8i	−0.441602	+	1.37613i
$481$	4477.07			0.424401
$482$	4547.60	−	6486.53i	0.429746	−	0.612974i
$483$	−3673.29	+	8868.10i	−0.346046	+	0.835430i
$484$	10105.9	+	4726.93i	0.949090	+	0.443927i
$485$	14.0551	−	6539.53i	0.00131590	−	0.612257i
$486$	−8246.68	−	12961.5i	−0.769705	−	1.20976i
$487$	−14249.0	−	14249.0i	−1.32584	−	1.32584i	−0.908960	−	0.416884i	$-0.863122\pi$
$487$	−14249.0	−	14249.0i	−1.32584	−	1.32584i	−0.416884	−	0.908960i	$-0.636878\pi$
$488$	7183.61	−	9327.76i	0.666366	−	0.865262i
$489$	6775.68	+	6775.68i	0.626599	+	0.626599i
$490$	14516.8	−	20611.9i	1.33837	−	1.90030i
$491$	−1746.66	+	723.490i	−0.160541	+	0.0664983i	−0.461507	−	0.887137i	$-0.652691\pi$
$491$	−1746.66	+	723.490i	−0.160541	+	0.0664983i	0.300966	+	0.953635i	$0.402691\pi$
$492$	15799.1	+	17282.4i	1.44772	+	1.58364i
$493$	7423.23	+	3074.80i	0.678145	+	0.280897i
$494$	−1200.06	+	210.876i	−0.109298	+	0.0192060i
$495$	−15838.1	−	6600.28i	−1.43812	−	0.599314i
$496$	−572.728	+	478.286i	−0.0518472	+	0.0432977i
$497$	−6529.26			−0.589290
$498$	−12688.9	+	2229.71i	−1.14177	+	0.200634i
$499$	−2812.40	+	6789.73i	−0.252305	+	0.609118i	−0.998389	−	0.0567331i	$-0.981932\pi$
$499$	−2812.40	+	6789.73i	−0.252305	+	0.609118i	0.746084	+	0.665852i	$0.231932\pi$
$500$	3743.70	+	10534.9i	0.334847	+	0.942273i
$501$	−28233.5	+	11694.7i	−2.51772	+	1.04288i
$502$	326.603	−	1469.13i	0.0290379	−	0.130618i
$503$	6031.16	−	6031.16i	0.534625	−	0.534625i	−0.387320	−	0.921945i	$-0.626599\pi$
$503$	6031.16	−	6031.16i	0.534625	−	0.534625i	0.921945	+	0.387320i	$0.126599\pi$
$504$	21685.1	+	5851.50i	1.91653	+	0.517156i
$505$	−4642.09	−	11275.5i	−0.409050	−	0.993570i
$506$	4715.85	−	3000.43i	0.414319	−	0.263608i
$507$	13615.7	−	5639.81i	1.19269	−	0.494029i
$508$	11237.4	−	4075.12i	0.981454	−	0.355914i
$509$	454.287	+	188.172i	0.0395598	+	0.0163862i	0.402376	−	0.915475i	$-0.368185\pi$
$509$	454.287	+	188.172i	0.0395598	+	0.0163862i	−0.362816	+	0.931861i	$0.618185\pi$
$510$	7609.42	−	4818.51i	0.660688	−	0.418367i
$511$	−35646.5			−3.08593
$512$	−8235.22	+	8148.56i	−0.710837	+	0.703357i
$513$		−	506.164i		−	0.0435628i
$514$	12250.9	−	17474.2i	1.05129	−	1.49952i
$515$	10922.4	+	10969.4i	0.934558	+	0.938584i
$516$	−166.458	−	459.017i	−0.0142014	−	0.0391611i
$517$	19804.1	−	8203.11i	1.68468	−	0.697819i
$518$	14987.9	+	23556.9i	1.27130	+	1.99813i
$519$	−795.044	+	795.044i	−0.0672419	+	0.0672419i
$520$	2370.57	−	3064.49i	0.199916	−	0.258436i
$521$	2675.89	+	2675.89i	0.225015	+	0.225015i	0.810606	−	0.585592i	$-0.199138\pi$
$521$	2675.89	+	2675.89i	0.225015	+	0.225015i	−0.585592	+	0.810606i	$0.699138\pi$
$522$	−3822.59	+	17194.7i	−0.320517	+	1.44175i
$523$	7180.03	+	17334.1i	0.600307	+	1.44927i	0.873266	+	0.487244i	$0.161998\pi$
$523$	7180.03	+	17334.1i	0.600307	+	1.44927i	−0.272958	+	0.962026i	$0.588002\pi$
$524$	−624.764	+	13933.6i	−0.0520857	+	1.16163i
$525$	29337.0	−	12004.3i	2.43881	−	0.997927i
$526$	2354.39	+	13398.4i	0.195164	+	1.11065i
$527$	442.183			0.0365499
$528$	−16083.6	−	19259.5i	−1.32566	−	1.58742i
$529$			10734.2i			0.882239i
$530$	3129.18	−	13934.2i	0.256458	−	1.14201i
$531$	−4816.36	+	11627.7i	−0.393620	+	0.950283i
$532$	−5127.01	−	5608.37i	−0.417827	−	0.457056i
$533$	−2284.24	−	5514.65i	−0.185631	−	0.448154i
$534$	246.771	−	1110.02i	0.0199978	−	0.0899540i
$535$	−2569.24	−	6240.60i	−0.207622	−	0.504308i
$536$	11756.9	+	9054.34i	0.947425	+	0.729642i
$537$	4143.02	+	4143.02i	0.332932	+	0.332932i
$538$	7712.41	−	4906.98i	0.618040	−	0.393225i
$539$	15927.9	+	38453.3i	1.27284	+	3.07291i
$540$	1083.40	+	1190.24i	0.0863370	+	0.0948515i
$541$	8117.74	+	3362.48i	0.645118	+	0.267217i	0.681161	−	0.732134i	$-0.261475\pi$
$541$	8117.74	+	3362.48i	0.645118	+	0.267217i	−0.0360432	+	0.999350i	$0.511475\pi$
$542$	6736.46	−	9608.64i	0.533867	−	0.761488i
$543$		−	20397.2i		−	1.61202i
$544$	6841.03	−	578.262i	0.539167	−	0.0455749i
$545$	1235.21	−	2964.02i	0.0970834	−	0.232963i
$546$	−8994.22	−	6305.70i	−0.704976	−	0.494248i
$547$	−8904.35	+	21497.0i	−0.696019	+	1.68034i	0.0362680	+	0.999342i	$0.488453\pi$
$547$	−8904.35	+	21497.0i	−0.696019	+	1.68034i	−0.732287	+	0.680996i	$0.761547\pi$
$548$	−12033.9	−	5628.72i	−0.938069	−	0.438772i
$549$	−5853.22	−	14130.9i	−0.455026	−	1.09853i
$550$	−18000.8	−	4083.06i	−1.39556	−	0.316549i
$551$	4213.77	−	4213.77i	0.325794	−	0.325794i
$552$	−6378.54	+	828.312i	−0.491827	+	0.0638683i
$553$	−13864.9	+	13864.9i	−1.06618	+	1.06618i
$554$	−3385.17	+	15227.2i	−0.259607	+	1.16776i
$555$	−52.7535	+	24545.0i	−0.00403470	+	1.87725i
$556$	−3588.62	−	3925.55i	−0.273726	−	0.299425i
$557$	−11513.0	−	4768.85i	−0.875804	−	0.362770i	−0.100936	−	0.994893i	$-0.532184\pi$
$557$	−11513.0	−	4768.85i	−0.875804	−	0.362770i	−0.774868	+	0.632123i	$0.782184\pi$
$558$	167.770	+	954.754i	0.0127281	+	0.0724336i
$559$			124.467i			0.00941751i
$560$	24060.3	+	2214.15i	1.81560	+	0.167080i
$561$			14869.6i			1.11906i
$562$	14306.0	−	2513.86i	1.07377	−	0.188685i
$563$	13204.3	+	5469.38i	0.988442	+	0.409426i	0.817546	−	0.575863i	$-0.195334\pi$
$563$	13204.3	+	5469.38i	0.988442	+	0.409426i	0.170896	+	0.985289i	$0.445334\pi$
$564$	−24642.6	−	1104.94i	−1.83979	−	0.0824936i
$565$	−22976.0	−	49.3813i	−1.71081	−	0.00367697i
$566$	−7061.91	−	1569.94i	−0.524442	−	0.116589i
$567$	−15724.6	+	15724.6i	−1.16468	+	1.16468i
$568$	−2180.93	−	3792.91i	−0.161109	−	0.280189i
$569$	5145.32	−	5145.32i	0.379091	−	0.379091i	−0.491683	−	0.870774i	$-0.663618\pi$
$569$	5145.32	−	5145.32i	0.379091	−	0.379091i	0.870774	+	0.491683i	$0.163618\pi$
$570$	−1141.96	−	6581.66i	−0.0839147	−	0.483641i
$571$	−3154.74	−	7616.22i	−0.231212	−	0.558194i	0.765109	−	0.643901i	$-0.222685\pi$
$571$	−3154.74	−	7616.22i	−0.231212	−	0.558194i	−0.996320	+	0.0857070i	$0.972685\pi$
$572$	2180.61	+	6013.16i	0.159398	+	0.439550i
$573$	8001.52	−	19317.4i	0.583365	−	1.40837i
$574$	21369.3	−	30480.4i	1.55390	−	2.21642i
$575$	−3360.06	+	3331.29i	−0.243694	+	0.241608i
$576$	3844.15	+	14551.6i	0.278078	+	1.05264i
$577$		−	7606.07i		−	0.548778i	−0.961619	−	0.274389i	$-0.911524\pi$
$577$		−	7606.07i		−	0.548778i	0.961619	−	0.274389i	$-0.0884755\pi$
$578$	8046.98	+	5641.61i	0.579084	+	0.405986i
$579$	−1368.99	−	567.056i	−0.0982616	−	0.0407013i
$580$	−889.465	+	18927.8i	−0.0636777	+	1.35506i
$581$	7837.83	+	18922.2i	0.559669	+	1.35116i
$582$	−6669.26	−	10482.2i	−0.475000	−	0.746568i
$583$	16671.8	+	16671.8i	1.18435	+	1.18435i
$584$	−11906.8	−	20707.4i	−0.843677	−	1.46726i
$585$	−1916.18	−	4654.33i	−0.135426	−	0.328945i
$586$	23764.1	+	5283.03i	1.67523	+	0.372423i
$587$	302.717	+	730.823i	0.0212853	+	0.0513872i	0.934165	−	0.356842i	$-0.116146\pi$
$587$	302.717	+	730.823i	0.0212853	+	0.0513872i	−0.912880	+	0.408229i	$0.866146\pi$
$588$	2145.45	−	47848.3i	0.150471	−	3.35583i
$589$	125.502	−	302.988i	0.00877965	−	0.0211960i
$590$	−2966.56	+	13210.1i	−0.207002	+	0.921780i
$591$		−	15484.8i		−	1.07777i
$592$	−8678.10	+	16575.2i	−0.602479	+	1.15074i
$593$	−13365.9			−0.925586			−0.462793	−	0.886466i	$-0.653153\pi$
$593$	−13365.9			−0.925586			−0.462793	+	0.886466i	$0.653153\pi$
$594$	−2617.05	+	459.871i	−0.180773	+	0.0317656i
$595$	−10102.9	−	10146.4i	−0.696097	−	0.699095i
$596$	3446.98	+	3770.61i	0.236903	+	0.259145i
$597$	1358.97	+	3280.86i	0.0931644	+	0.224919i
$598$	1600.56	+	355.824i	0.109451	+	0.0243323i
$599$	−675.268	−	675.268i	−0.0460613	−	0.0460613i	0.683701	−	0.729762i	$-0.260369\pi$
$599$	−675.268	−	675.268i	−0.0460613	−	0.0460613i	−0.729762	+	0.683701i	$0.760369\pi$
$600$	16772.7	+	13032.5i	1.14124	+	0.886746i
$601$	13854.9	−	13854.9i	0.940357	−	0.940357i	−0.0579614	−	0.998319i	$-0.518460\pi$
$601$	13854.9	−	13854.9i	0.940357	−	0.940357i	0.998319	+	0.0579614i	$0.0184600\pi$
$602$	−654.904	+	416.679i	−0.0443387	+	0.0282102i
$603$	17810.9	−	7377.50i	1.20284	−	0.498234i
$604$	−9800.38	+	20952.7i	−0.660219	+	1.41151i
$605$	11048.9	−	11001.5i	0.742483	−	0.739298i
$606$	−18968.6	−	13298.6i	−1.27153	−	0.891448i
$607$			1630.11i			0.109002i	0.998514	+	0.0545011i	$0.0173568\pi$
$607$			1630.11i			0.109002i	−0.998514	+	0.0545011i	$0.982643\pi$
$608$	1545.41	−	4851.67i	0.103084	−	0.323620i
$609$	53722.7			3.57463
$610$	−8802.57	−	13901.1i	−0.584272	−	0.922686i
$611$	5809.44	+	2406.35i	0.384656	+	0.159330i
$612$	3778.89	−	8079.06i	0.249596	−	0.533622i
$613$	20862.9	−	8641.68i	1.37462	−	0.569387i	0.431584	−	0.902073i	$-0.357955\pi$
$613$	20862.9	−	8641.68i	1.37462	−	0.569387i	0.943038	+	0.332686i	$0.107955\pi$
$614$	6472.43	+	10172.9i	0.425417	+	0.668638i
$615$	30260.3	−	12458.1i	1.98408	−	0.816843i
$616$	−24339.2	+	31603.9i	−1.59197	+	2.06714i
$617$	7882.74	−	7882.74i	0.514339	−	0.514339i	−0.401514	−	0.915853i	$-0.631516\pi$
$617$	7882.74	−	7882.74i	0.514339	−	0.514339i	0.915853	+	0.401514i	$0.131516\pi$
$618$	28708.3	+	6382.18i	1.86864	+	0.415419i
$619$	14617.9	−	6054.92i	0.949179	−	0.393163i	0.146257	−	0.989247i	$-0.453277\pi$
$619$	14617.9	−	6054.92i	0.949179	−	0.393163i	0.802922	+	0.596084i	$0.203277\pi$
$620$	353.402	+	981.100i	0.0228919	+	0.0635515i
$621$	−260.659	+	629.287i	−0.0168436	+	0.0406641i
$622$	−2947.84	−	16775.7i	−0.190028	−	1.08142i
$623$	−1807.74			−0.116253
$624$	658.757	−	7331.10i	0.0422619	−	0.470318i
$625$	15624.4	+	134.327i	0.999963	+	0.00859692i
$626$	1015.56	+	5779.41i	0.0648404	+	0.368996i
$627$	10188.8	+	4220.33i	0.648964	+	0.268810i
$628$	1980.33	+	88.7953i	0.125834	+	0.00564222i
$629$	10243.3	−	4242.93i	0.649330	−	0.268961i
$630$	18074.7	−	25663.6i	1.14304	−	1.62296i
$631$	−13721.0	−	13721.0i	−0.865647	−	0.865647i	0.126340	−	0.991987i	$-0.459677\pi$
$631$	−13721.0	−	13721.0i	−0.865647	−	0.865647i	−0.991987	+	0.126340i	$0.959677\pi$
$632$	−12685.5	−	3423.06i	−0.798423	−	0.215446i
$633$	−15153.1	−	15153.1i	−0.951473	−	0.951473i
$634$	−17406.8	+	11075.0i	−1.09040	+	0.693758i
$635$	35.9043	−	16705.4i	0.00224381	−	1.04399i
$636$	−9249.70	−	25506.6i	−0.576690	−	1.59026i
$637$	−4672.38	+	11280.1i	−0.290622	+	0.701624i
$638$	−25615.1	−	17958.3i	−1.58952	−	1.11439i
$639$	−5684.03			−0.351889
$640$	6750.52	+	14716.5i	0.416934	+	0.908937i
$641$	−11996.5			−0.739207			−0.369604	−	0.929190i	$-0.620506\pi$
$641$	−11996.5			−0.739207			−0.369604	+	0.929190i	$0.620506\pi$
$642$	−10498.5	−	7360.31i	−0.645392	−	0.452474i
$643$	6461.34	−	15599.0i	0.396283	−	0.956713i	−0.592256	−	0.805750i	$-0.701763\pi$
$643$	6461.34	−	15599.0i	0.396283	−	0.956713i	0.988539	−	0.150963i	$-0.0482374\pi$
$644$	3486.00	+	9612.84i	0.213304	+	0.588197i
$645$	−682.373	−	1.46660i	−0.0416565	−	8.95305e-5i
$646$	−2545.84	+	1619.77i	−0.155054	+	0.0986519i
$647$	−7211.47	−	7211.47i	−0.438195	−	0.438195i	0.453209	−	0.891404i	$-0.350279\pi$
$647$	−7211.47	−	7211.47i	−0.438195	−	0.438195i	−0.891404	+	0.453209i	$0.850279\pi$
$648$	−14387.0	−	3882.18i	−0.872182	−	0.235349i
$649$	−15805.4	−	15805.4i	−0.955955	−	0.955955i
$650$	−2886.91	−	4580.78i	−0.174206	−	0.276420i
$651$	2731.48	−	1131.41i	0.164447	−	0.0681162i
$652$	10197.6	+	457.246i	0.612528	+	0.0274649i
$653$	−8495.94	−	3519.13i	−0.509145	−	0.210895i	0.113296	−	0.993561i	$-0.463859\pi$
$653$	−8495.94	−	3519.13i	−0.509145	−	0.210895i	−0.622441	+	0.782666i	$0.713859\pi$
$654$	−1055.82	−	6008.48i	−0.0631279	−	0.359251i
$655$	17992.5	+	7498.09i	1.07332	+	0.447290i
$656$	24844.3	+	2232.45i	1.47867	+	0.132870i
$657$	−31032.0			−1.84273
$658$	6786.89	+	38623.1i	0.402098	+	2.28827i
$659$	9309.67	−	22475.5i	0.550309	−	1.32856i	−0.366939	−	0.930245i	$-0.619594\pi$
$659$	9309.67	−	22475.5i	0.550309	−	1.32856i	0.917248	−	0.398318i	$-0.130406\pi$
$660$	−32992.0	+	11884.0i	−1.94578	+	0.700888i
$661$	8384.43	−	3472.95i	0.493369	−	0.204360i	−0.122105	−	0.992517i	$-0.538965\pi$
$661$	8384.43	−	3472.95i	0.493369	−	0.204360i	0.615474	+	0.788157i	$0.288965\pi$
$662$	9209.49	+	2047.37i	0.540690	+	0.120202i
$663$	−3084.35	+	3084.35i	−0.180673	+	0.180673i
$664$	−8374.07	+	10873.6i	−0.489423	+	0.635505i
$665$	−9819.84	+	4042.81i	−0.572627	+	0.235749i
$666$	13047.7	+	20507.4i	0.759142	+	1.19316i
$667$	−7408.72	+	3068.79i	−0.430085	+	0.178147i
$668$	−13792.9	+	29488.4i	−0.798898	+	1.70800i
$669$	10394.8	+	4305.67i	0.600726	+	0.248829i
$670$	17521.2	−	11094.9i	1.01030	−	0.639752i
$671$	27164.1			1.56283
$672$	40779.2	−	21076.2i	2.34091	−	1.20987i
$673$		−	6709.46i		−	0.384295i	−0.981366	−	0.192148i	$-0.938455\pi$
$673$		−	6709.46i		−	0.384295i	0.981366	−	0.192148i	$-0.0615453\pi$
$674$	3178.44	+	2228.35i	0.181645	+	0.127349i
$675$	2081.78	−	851.835i	0.118708	−	0.0485736i
$676$	6651.68	−	14220.9i	0.378453	−	0.809110i
$677$	−22806.9	+	9446.91i	−1.29474	+	0.536299i	−0.920395	−	0.390991i	$-0.872132\pi$
$677$	−22806.9	+	9446.91i	−1.29474	+	0.536299i	−0.374345	+	0.927289i	$0.622132\pi$
$678$	−36828.2	+	23431.8i	−2.08611	+	1.32727i
$679$	−13966.1	+	13966.1i	−0.789352	+	0.789352i
$680$	2519.54	−	9258.01i	0.142088	−	0.522101i
$681$	13362.1	+	13362.1i	0.751888	+	0.751888i
$682$	−1680.58	−	373.613i	−0.0943590	−	0.0209771i
$683$	936.902	+	2261.88i	0.0524884	+	0.126718i	0.947949	−	0.318423i	$-0.103153\pi$
$683$	936.902	+	2261.88i	0.0524884	+	0.126718i	−0.895460	+	0.445142i	$0.853153\pi$
$684$	−4463.31	−	4882.36i	−0.249501	−	0.272926i
$685$	−13156.8	+	13100.3i	−0.733861	+	0.730713i
$686$	−42728.9	+	7508.37i	−2.37813	+	0.417888i
$687$	11017.9			0.611877
$688$	−460.807	−	241.259i	−0.0255350	−	0.0133691i
$689$			6916.35i			0.382427i
$690$	−1969.62	+	8770.69i	−0.108670	+	0.483905i
$691$	8660.58	−	20908.5i	0.476793	−	1.15108i	−0.484312	−	0.874895i	$-0.660930\pi$
$691$	8660.58	−	20908.5i	0.476793	−	1.15108i	0.961105	−	0.276184i	$-0.0890700\pi$
$692$	−53.6522	+	1196.56i	−0.00294733	+	0.0657319i
$693$	19831.6	+	47877.8i	1.08707	+	2.62443i
$694$	30059.4	+	6682.54i	1.64415	+	0.365513i
$695$	−6873.34	+	2829.74i	−0.375138	+	0.154443i
$696$	17944.7	+	31208.1i	0.977287	+	1.69962i
$697$	−10452.5	−	10452.5i	−0.568029	−	0.568029i
$698$	−10018.7	−	15746.5i	−0.543283	−	0.853891i
$699$	8805.46	+	21258.3i	0.476471	+	1.15030i
$700$	14438.0	−	30525.1i	0.779580	−	1.64820i
$701$	−20528.9	−	8503.35i	−1.10609	−	0.458155i	−0.246497	−	0.969143i	$-0.579280\pi$
$701$	−20528.9	−	8503.35i	−1.10609	−	0.458155i	−0.859588	+	0.510988i	$0.829280\pi$
$702$	−638.236	−	447.457i	−0.0343144	−	0.0240572i
$703$		−	8223.08i		−	0.441165i
$704$	−26489.0	−	3582.41i	−1.41810	−	0.191785i
$705$	−13260.9	+	31821.1i	−0.708419	+	1.69993i
$706$	3498.60	−	4990.28i	0.186504	−	0.266022i
$707$	−14093.4	+	34024.6i	−0.749700	+	1.80994i
$708$	8769.00	+	24181.0i	0.465479	+	1.28359i
$709$	−4035.51	−	9742.59i	−0.213761	−	0.516066i	0.780234	−	0.625488i	$-0.215100\pi$
$709$	−4035.51	−	9742.59i	−0.213761	−	0.516066i	−0.993995	+	0.109422i	$0.965100\pi$
$710$	−6024.56	+	1045.30i	−0.318448	+	0.0552527i
$711$	−12070.1	+	12070.1i	−0.636659	+	0.636659i
$712$	−603.829	−	1050.13i	−0.0317829	−	0.0552745i
$713$	−312.060	+	312.060i	−0.0163909	+	0.0163909i
$714$	−26554.3	−	5903.32i	−1.39183	−	0.309421i
$715$	8939.13	+	19.2125i	0.467559	+	0.00100490i
$716$	6235.35	+	279.584i	0.325455	+	0.0145930i
$717$	9427.52	+	3905.01i	0.491042	+	0.203396i
$718$	20021.6	−	3518.22i	1.04067	−	0.182867i
$719$			17857.7i			0.926261i	0.886290	+	0.463130i	$0.153274\pi$
$719$			17857.7i			0.926261i	−0.886290	+	0.463130i	$0.846726\pi$
$720$	20945.7	+	1927.53i	1.08417	+	0.0997703i
$721$		−	46753.1i		−	2.41495i
$722$	−2970.26	−	16903.3i	−0.153105	−	0.871294i
$723$	−19432.2	−	8049.08i	−0.999573	−	0.414037i
$724$	−14660.9	−	16037.4i	−0.752581	−	0.823239i
$725$	24422.1	+	10239.2i	1.25105	+	0.524515i
$726$	6428.42	−	28916.3i	0.328624	−	1.47822i
$727$	−6491.49	+	6491.49i	−0.331164	+	0.331164i	−0.853028	−	0.521865i	$-0.825237\pi$
$727$	−6491.49	+	6491.49i	−0.331164	+	0.331164i	0.521865	+	0.853028i	$0.325237\pi$
$728$	−11604.1	+	1506.90i	−0.590765	+	0.0767163i
$729$	−16269.0	+	16269.0i	−0.826550	+	0.826550i
$730$	−32891.1	+	5706.82i	−1.66761	+	0.289341i
$731$	117.957	+	284.775i	0.00596828	+	0.0144087i
$732$	−28315.0	−	13244.0i	−1.42972	−	0.668735i
$733$	2792.37	−	6741.37i	0.140707	−	0.339697i	−0.837779	−	0.546010i	$-0.816146\pi$
$733$	2792.37	−	6741.37i	0.140707	−	0.339697i	0.978486	+	0.206312i	$0.0661462\pi$
$734$	−16207.8	−	11363.0i	−0.815040	−	0.571411i
$735$	−61786.7	−	25748.6i	−3.10073	−	1.29218i
$736$	−4419.79	+	5235.98i	−0.221353	+	0.262229i
$737$			34238.1i			1.71123i
$738$	18603.0	−	26534.7i	0.927895	−	1.32352i
$739$	24199.5	+	10023.8i	1.20459	+	0.498959i	0.892480	−	0.451086i	$-0.148963\pi$
$739$	24199.5	+	10023.8i	1.20459	+	0.498959i	0.312113	+	0.950045i	$0.398963\pi$
$740$	17600.7	+	19336.5i	0.874346	+	0.960573i
$741$	1238.02	+	2988.83i	0.0613760	+	0.148175i
$742$	−36391.6	+	23153.9i	−1.80051	+	1.14556i
$743$	14791.1	+	14791.1i	0.730328	+	0.730328i	0.970685	−	0.240357i	$-0.0772644\pi$
$743$	14791.1	+	14791.1i	0.730328	+	0.730328i	−0.240357	+	0.970685i	$0.577264\pi$
$744$	1569.63	+	1208.82i	0.0773460	+	0.0595666i
$745$	6602.06	−	2718.05i	0.324672	−	0.133667i
$746$	−1796.16	+	8079.49i	−0.0881531	+	0.396530i
$747$	6823.21	+	16472.7i	0.334201	+	0.806833i
$748$	10687.8	+	11691.3i	0.522440	+	0.571491i
$749$	−7800.24	+	18831.4i	−0.380527	+	0.918673i
$750$	25147.5	−	15773.1i	1.22434	−	0.767937i
$751$			19579.5i			0.951352i	0.879621	+	0.475676i	$0.157797\pi$
$751$			19579.5i			0.951352i	−0.879621	+	0.475676i	$0.842203\pi$
$752$	−20169.6	+	16843.6i	−0.978070	+	0.816788i
$753$	−3995.89			−0.193384
$754$	−1588.22	−	9038.31i	−0.0767103	−	0.436546i
$755$	22809.5	+	22907.8i	1.09950	+	1.10424i
$756$	217.743	−	4856.15i	0.0104752	−	0.233620i
$757$	4916.36	+	11869.1i	0.236048	+	0.569870i	0.996867	−	0.0790938i	$-0.0252027\pi$
$757$	4916.36	+	11869.1i	0.236048	+	0.569870i	−0.760819	+	0.648964i	$0.775203\pi$
$758$	1787.96	−	8042.59i	0.0856749	−	0.385383i
$759$	−10493.8	−	10493.8i	−0.501846	−	0.501846i
$760$	−5628.58	−	4354.05i	−0.268645	−	0.207813i
$761$	2443.31	−	2443.31i	0.116386	−	0.116386i	−0.646515	−	0.762901i	$-0.723774\pi$
$761$	2443.31	−	2443.31i	0.116386	−	0.116386i	0.762901	+	0.646515i	$0.223774\pi$
$762$	−17036.9	−	26777.2i	−0.809948	−	1.27301i
$763$	−8960.07	+	3711.38i	−0.425133	+	0.176096i
$764$	−7593.54	−	20939.6i	−0.359587	−	0.991583i
$765$	−8795.04	−	8832.93i	−0.415667	−	0.417458i
$766$	5363.03	−	7649.62i	0.252969	−	0.360825i
$767$		−	6556.91i		−	0.308678i
$768$	25864.6	+	16649.1i	1.21525	+	0.782254i
$769$	8065.67			0.378226			0.189113	−	0.981955i	$-0.439439\pi$
$769$	8065.67			0.378226			0.189113	+	0.981955i	$0.439439\pi$
$770$	29824.5	+	47099.1i	1.39585	+	2.20433i
$771$	−52348.8	−	21683.6i	−2.44526	−	1.01286i
$772$	−1483.96	+	538.143i	−0.0691826	+	0.0250883i
$773$	35384.1	−	14656.6i	1.64641	−	0.681967i	0.649492	−	0.760368i	$-0.274982\pi$
$773$	35384.1	−	14656.6i	1.64641	−	0.681967i	0.996922	+	0.0784015i	$0.0249816\pi$
$774$	−570.125	+	362.739i	−0.0264764	+	0.0168455i
$775$	1457.36	+	6.26450i	0.0675481	+	0.000290358i
$776$	−12778.1	−	3448.03i	−0.591116	−	0.159507i
$777$	52419.2	−	52419.2i	2.42024	−	2.42024i
$778$	−6895.21	+	31016.0i	−0.317744	+	1.42928i
$779$	−10128.8	+	4195.49i	−0.465857	+	0.192964i
$780$	−9308.50	−	4378.36i	−0.427305	−	0.200988i
$781$	3863.10	−	9326.36i	0.176995	−	0.427303i
$782$	3999.24	−	702.750i	0.182880	−	0.0321359i
$783$	3812.20			0.173993
$784$	−32705.1	−	39163.0i	−1.48985	−	1.78403i
$785$	1065.68	−	2557.21i	0.0484530	−	0.116268i
$786$	36473.3	−	6409.13i	1.65517	−	0.290848i
$787$	−21220.9	−	8789.98i	−0.961173	−	0.398131i	−0.153754	−	0.988109i	$-0.549136\pi$
$787$	−21220.9	−	8789.98i	−0.961173	−	0.398131i	−0.807419	+	0.589978i	$0.799136\pi$
$788$	−11130.0	−	12175.0i	−0.503162	−	0.550402i
$789$	33369.8	−	13822.2i	1.50570	−	0.623680i
$790$	−10573.5	+	15012.9i	−0.476189	+	0.676122i
$791$	49068.4	+	49068.4i	2.20565	+	2.20565i
$792$	−21188.5	+	27512.8i	−0.950630	+	1.23437i
$793$	5634.56	+	5634.56i	0.252319	+	0.252319i
$794$	−14128.9	−	22206.8i	−0.631508	−	0.992556i
$795$	−37918.0	−	81.4956i	−1.69159	−	0.00363566i
$796$	3426.69	+	1602.80i	0.152582	+	0.0713688i
$797$	−5370.41	+	12965.3i	−0.238682	+	0.576229i	−0.997147	−	0.0754845i	$-0.975950\pi$
$797$	−5370.41	+	12965.3i	−0.238682	+	0.576229i	0.758465	+	0.651714i	$0.225950\pi$
$798$	−11581.7	+	16519.8i	−0.513771	+	0.732824i
$799$	15572.2			0.689494
$800$	22555.0	−	1808.93i	0.996799	−	0.0799441i
$801$	−1573.72			−0.0694192
$802$	−2205.96	+	3146.49i	−0.0971259	+	0.138537i
$803$	21090.6	−	50917.3i	0.926865	−	2.23765i
$804$	16693.0	−	35688.7i	0.732235	−	1.56548i
$805$	14290.4	+	30.7138i	0.625678	+	0.00134474i
$806$	−271.101	−	426.095i	−0.0118475	−	0.0186211i
$807$	−17161.8	−	17161.8i	−0.748605	−	0.748605i
$808$	−24472.8	+	3178.02i	−1.06553	+	0.138369i
$809$	−19100.9	−	19100.9i	−0.830103	−	0.830103i	0.157428	−	0.987531i	$-0.449680\pi$
$809$	−19100.9	−	19100.9i	−0.830103	−	0.830103i	−0.987531	+	0.157428i	$0.949680\pi$
$810$	−11991.7	+	17026.5i	−0.520179	+	0.738583i
$811$	1627.13	−	673.979i	0.0704516	−	0.0291820i	−0.347179	−	0.937799i	$-0.612860\pi$
$811$	1627.13	−	673.979i	0.0704516	−	0.0291820i	0.417631	+	0.908617i	$0.362860\pi$
$812$	42239.7	−	38614.3i	1.82552	−	1.66884i
$813$	−28785.3	−	11923.3i	−1.24175	−	0.514351i
$814$	−42516.3	+	7471.01i	−1.83071	+	0.321694i
$815$	5487.63	−	13168.2i	0.235857	−	0.565965i
$816$	−5440.49	−	17397.5i	−0.233401	−	0.746367i
$817$	228.609			0.00978951
$818$	21991.6	−	3864.38i	0.939996	−	0.165177i
$819$	−5817.53	+	14044.8i	−0.248206	+	0.599223i
$820$	14837.8	−	31545.5i	0.631899	−	1.34343i
$821$	−37614.9	+	15580.6i	−1.59899	+	0.662323i	−0.991272	−	0.131830i	$-0.957915\pi$
$821$	−37614.9	+	15580.6i	−1.59899	+	0.662323i	−0.607717	+	0.794154i	$0.707915\pi$
$822$	−7654.81	+	34432.8i	−0.324808	+	1.46105i
$823$	9314.07	−	9314.07i	0.394493	−	0.394493i	−0.481792	−	0.876285i	$-0.660014\pi$
$823$	9314.07	−	9314.07i	0.394493	−	0.394493i	0.876285	+	0.481792i	$0.160014\pi$
$824$	27159.4	−	15616.7i	1.14823	−	0.660234i
$825$	−210.660	+	49007.4i	−0.00888999	+	2.06814i
$826$	34500.3	−	21950.6i	1.45329	−	0.924649i
$827$	1706.08	−	706.680i	0.0717365	−	0.0297142i	−0.346527	−	0.938040i	$-0.612639\pi$
$827$	1706.08	−	706.680i	0.0717365	−	0.0297142i	0.418263	+	0.908326i	$0.362639\pi$
$828$	3034.73	+	8368.44i	0.127372	+	0.351236i
$829$	13582.7	+	5626.14i	0.569055	+	0.235710i	0.648611	−	0.761120i	$-0.275350\pi$
$829$	13582.7	+	5626.14i	0.569055	+	0.235710i	−0.0795561	+	0.996830i	$0.525350\pi$
$830$	10261.3	+	16204.8i	0.429127	+	0.677681i
$831$	41416.6			1.72891
$832$	−4751.43	−	6237.61i	−0.197988	−	0.259916i
$833$			30236.4i			1.25766i
$834$	−8106.58	+	11562.9i	−0.336580	+	0.480085i
$835$	32101.8	+	32240.1i	1.33045	+	1.33618i
$836$	11044.4	−	4005.15i	0.456913	−	0.165695i
$837$	193.827	−	80.2860i	0.00800437	−	0.00331552i
$838$	8465.51	+	13305.4i	0.348969	+	0.548483i
$839$	−1345.87	+	1345.87i	−0.0553810	+	0.0553810i	−0.734255	−	0.678874i	$-0.762468\pi$
$839$	−1345.87	+	1345.87i	−0.0553810	+	0.0553810i	0.678874	+	0.734255i	$0.262468\pi$
$840$	−8124.66	−	63635.8i	−0.333723	−	2.61386i
$841$	14490.6	+	14490.6i	0.594145	+	0.594145i
$842$	657.219	−	2956.30i	0.0268994	−	0.120999i
$843$	−14758.4	−	35630.0i	−0.602974	−	1.45571i
$844$	−22805.8	−	1022.58i	−0.930106	−	0.0417047i
$845$	−15481.2	−	15547.9i	−0.630260	−	0.632975i
$846$	5908.32	+	33623.3i	0.240109	+	1.36642i
$847$	−47091.8			−1.91038
$848$	−25606.0	−	13406.3i	−1.03693	−	0.542893i
$849$			19207.8i			0.776454i
$850$	−10946.3	−	7744.69i	−0.441713	−	0.312518i
$851$	−4234.63	+	10223.3i	−0.170577	+	0.411810i
$852$	−8573.91	+	7838.02i	−0.344762	+	0.315172i
$853$	−1540.40	−	3718.85i	−0.0618314	−	0.149274i	0.889944	−	0.456070i	$-0.150743\pi$
$853$	−1540.40	−	3718.85i	−0.0618314	−	0.149274i	−0.951775	+	0.306796i	$0.900743\pi$
$854$	−10784.3	+	48510.1i	−0.432122	+	1.94377i
$855$	−8548.65	+	3519.46i	−0.341939	+	0.140775i
$856$	−13544.8	+	1758.92i	−0.540833	+	0.0702322i
$857$	9584.03	+	9584.03i	0.382012	+	0.382012i	0.871827	−	0.489815i	$-0.162936\pi$
$857$	9584.03	+	9584.03i	0.382012	+	0.382012i	−0.489815	+	0.871827i	$0.662936\pi$
$858$	14328.6	−	9116.47i	0.570127	−	0.362740i
$859$	−14206.8	−	34298.2i	−0.564295	−	1.36233i	−0.906302	−	0.422631i	$-0.861107\pi$
$859$	−14206.8	−	34298.2i	−0.564295	−	1.36233i	0.342007	−	0.939697i	$-0.388893\pi$
$860$	−537.573	+	489.317i	−0.0213152	+	0.0194018i
$861$	−91312.5	−	37822.9i	−3.61431	−	1.49710i
$862$	27000.1	−	38512.0i	1.06685	−	1.52172i
$863$			11129.9i			0.439011i	0.975611	+	0.219506i	$0.0704444\pi$
$863$			11129.9i			0.439011i	−0.975611	+	0.219506i	$0.929556\pi$
$864$	2893.72	−	1495.58i	0.113942	−	0.0588898i
$865$	1545.13	+	643.906i	0.0607351	+	0.0253104i
$866$	−10931.5	−	7663.87i	−0.428945	−	0.300726i
$867$	9985.43	−	24107.0i	0.391145	−	0.944309i
$868$	1334.41	−	2852.89i	0.0521806	−	0.111559i
$869$	−11601.3	−	28008.0i	−0.452873	−	1.09333i
$870$	49570.0	−	8600.71i	1.93170	−	0.335163i
$871$	−7101.90	+	7101.90i	−0.276278	+	0.276278i
$872$	−5148.86	−	3965.30i	−0.199957	−	0.153993i
$873$	−12158.2	+	12158.2i	−0.471353	+	0.471353i
$874$	653.545	−	2939.77i	0.0252935	−	0.113775i
$875$	−33153.5	−	33583.8i	−1.28091	−	1.29753i
$876$	−46809.3	+	42791.7i	−1.80541	+	1.65046i
$877$	−2229.68	−	923.563i	−0.0858505	−	0.0355604i	0.339345	−	0.940662i	$-0.389795\pi$
$877$	−2229.68	−	923.563i	−0.0858505	−	0.0355604i	−0.425195	+	0.905102i	$0.639795\pi$
$878$	2532.88	+	14414.2i	0.0973582	+	0.554050i
$879$		−	64636.3i		−	2.48024i
$880$	−17398.2	+	33057.6i	−0.666471	+	1.26633i
$881$			19256.3i			0.736393i	0.929748	+	0.368196i	$0.120025\pi$
$881$			19256.3i			0.736393i	−0.929748	+	0.368196i	$0.879975\pi$
$882$	−65285.9	+	11472.1i	−2.49239	+	0.437966i
$883$	4585.72	+	1899.47i	0.174770	+	0.0723921i	0.468353	−	0.883542i	$-0.344848\pi$
$883$	4585.72	+	1899.47i	0.174770	+	0.0723921i	−0.293583	+	0.955934i	$0.594848\pi$
$884$	−208.142	+	4642.02i	−0.00791920	+	0.176615i
$885$	35947.4	+	77.2603i	1.36538	+	0.00293455i
$886$	1136.23	+	252.598i	0.0430841	+	0.00957809i
$887$	22700.5	−	22700.5i	0.859312	−	0.859312i	−0.131945	−	0.991257i	$-0.542122\pi$
$887$	22700.5	−	22700.5i	0.859312	−	0.859312i	0.991257	+	0.131945i	$0.0421222\pi$
$888$	47960.2	+	12941.6i	1.81243	+	0.489066i
$889$	−35676.9	+	35676.9i	−1.34597	+	1.34597i
$890$	−1668.00	+	289.409i	−0.0628221	+	0.0109000i
$891$	−13157.3	−	31764.6i	−0.494710	−	1.19434i
$892$	11267.7	−	4086.13i	0.422951	−	0.153379i
$893$	4419.76	−	10670.2i	0.165623	−	0.399850i
$894$	7786.62	−	11106.5i	0.291301	−	0.415502i
$895$	3355.43	−	8051.73i	0.125318	−	0.300715i
$896$	16913.8	−	45882.2i	0.630638	−	1.71073i
$897$		−	4353.40i		−	0.162046i
$898$	18450.7	+	12935.5i	0.685643	+	0.480693i
$899$	2281.97	+	945.223i	0.0846585	+	0.0350667i
$900$	12569.0	−	26573.6i	0.465519	−	0.984206i
$901$	6554.64	+	15824.3i	0.242360	+	0.585110i
$902$	30894.7	+	48557.9i	1.14044	+	1.79246i
$903$	1457.31	+	1457.31i	0.0537055	+	0.0537055i
$904$	−12114.3	+	44894.4i	−0.445703	+	1.65173i
$905$	−28080.3	+	11560.6i	−1.03140	+	0.424627i
$906$	59952.4	+	13328.1i	2.19844	+	0.488738i
$907$	17172.1	+	41457.1i	0.628655	+	1.51771i	0.841294	+	0.540577i	$0.181794\pi$
$907$	17172.1	+	41457.1i	0.628655	+	1.51771i	−0.212639	+	0.977131i	$0.568206\pi$
$908$	20110.3	+	901.717i	0.735003	+	0.0329565i
$909$	−12269.0	+	29620.0i	−0.447676	+	1.08079i
$910$	−3583.21	+	15956.0i	−0.130530	+	0.581249i
$911$		−	5334.65i		−	0.194012i	−0.995284	−	0.0970060i	$-0.969073\pi$
$911$		−	5334.65i		−	0.194012i	0.995284	−	0.0970060i	$-0.0309266\pi$
$912$	−13465.1	−	1209.95i	−0.488897	−	0.0439313i
$913$	−31665.7			−1.14784
$914$	37610.0	−	6608.87i	1.36108	−	0.239171i
$915$	−30957.1	+	30824.3i	−1.11848	+	1.11368i
$916$	8662.88	−	7919.36i	0.312478	−	0.285658i
$917$	−22529.2	−	54390.4i	−0.811321	−	1.95870i
$918$	−1884.31	−	418.904i	−0.0677468	−	0.0150609i
$919$	5388.05	+	5388.05i	0.193401	+	0.193401i	0.797164	−	0.603763i	$-0.206333\pi$
$919$	5388.05	+	5388.05i	0.193401	+	0.193401i	−0.603763	+	0.797164i	$0.706333\pi$
$920$	4755.50	+	8311.70i	0.170418	+	0.297857i
$921$	22636.9	−	22636.9i	0.809892	−	0.809892i
$922$	13129.5	−	8353.59i	0.468978	−	0.298385i
$923$	2735.85	−	1133.23i	0.0975640	−	0.0404123i
$924$	95935.7	+	44872.9i	3.41564	+	1.59763i
$925$	33820.3	−	13838.8i	1.20217	−	0.491910i
$926$	16773.6	+	11759.7i	0.595265	+	0.417330i
$927$		−	40700.8i		−	1.44206i
$928$	36540.6	+	11639.4i	1.29257	+	0.411725i
$929$	5580.00			0.197066			0.0985328	−	0.995134i	$-0.468585\pi$
$929$	5580.00			0.197066			0.0985328	+	0.995134i	$0.468585\pi$
$930$	2339.21	−	1481.25i	0.0824791	−	0.0522282i
$931$	20718.3	+	8581.80i	0.729339	+	0.302102i
$932$	22203.2	+	10385.3i	0.780353	+	0.365002i
$933$	−41781.0	+	17306.2i	−1.46607	+	0.607268i
$934$	−7119.16	−	11189.3i	−0.249407	−	0.391999i
$935$	20470.5	−	8427.67i	0.715998	−	0.294775i
$936$	−10101.9	+	1311.83i	−0.352769	+	0.0458104i
$937$	−3422.12	+	3422.12i	−0.119312	+	0.119312i	−0.764242	−	0.644930i	$-0.776887\pi$
$937$	−3422.12	+	3422.12i	−0.119312	+	0.119312i	0.644930	+	0.764242i	$0.276887\pi$
$938$	−61142.9	−	13592.8i	−2.12834	−	0.473155i
$939$	14394.0	−	5962.20i	0.500246	−	0.207209i
$940$	12445.6	+	34551.1i	0.431842	+	1.19886i
$941$	12684.0	−	30621.9i	0.439412	−	1.06084i	−0.536740	−	0.843748i	$-0.680344\pi$
$941$	12684.0	−	30621.9i	0.439412	−	1.06084i	0.976152	−	0.217087i	$-0.0696557\pi$
$942$	−910.906	−	5183.82i	−0.0315063	−	0.179297i
$943$	14753.2			0.509469
$944$	24275.3	+	12709.5i	0.836964	+	0.438200i
$945$	−6270.77	−	2613.24i	−0.215860	−	0.0899563i
$946$	−207.701	−	1181.99i	−0.00713842	−	0.0406236i
$947$	−3642.40	−	1508.73i	−0.124986	−	0.0517711i	0.319314	−	0.947649i	$-0.396548\pi$
$947$	−3642.40	−	1508.73i	−0.124986	−	0.0517711i	−0.444300	+	0.895878i	$0.646548\pi$
$948$	−1562.67	+	34850.9i	−0.0535370	+	1.19399i
$949$	14936.4	−	6186.85i	0.510912	−	0.211627i
$950$	−8413.56	+	5302.41i	−0.287339	+	0.181087i
$951$	38733.9	+	38733.9i	1.32075	+	1.32075i
$952$	−25121.6	+	14445.0i	−0.855247	+	0.491769i
$953$	−30829.8	−	30829.8i	−1.04793	−	1.04793i	−0.998792	−	0.0491343i	$-0.984354\pi$
$953$	−30829.8	−	30829.8i	−1.04793	−	1.04793i	−0.0491343	−	0.998792i	$-0.515646\pi$
$954$	−31680.6	+	20156.6i	−1.07516	+	0.684061i
$955$	−31128.8	−	66.9038i	−1.05477	−	0.00226697i
$956$	10219.2	−	3705.90i	0.345726	−	0.125374i
$957$	−31785.6	+	76737.2i	−1.07365	+	2.59202i
$958$	5187.28	+	3636.72i	0.174941	+	0.122648i
$959$	56075.8			1.88820
$960$	34252.8	−	25975.6i	1.15157	−	0.873291i
$961$	−29655.1			−0.995437
$962$	−10368.7	−	7269.33i	−0.347506	−	0.243631i
$963$	−6790.48	+	16393.7i	−0.227228	+	0.548576i
$964$	−21064.1	+	7638.68i	−0.703765	+	0.255213i
$965$	−4.74137	+	2206.05i	−0.000158166	+	0.0735910i
$966$	22906.1	−	14573.9i	0.762933	−	0.485412i
$967$	1507.94	+	1507.94i	0.0501468	+	0.0501468i	0.731735	−	0.681589i	$-0.238711\pi$
$967$	1507.94	+	1507.94i	0.0501468	+	0.0501468i	−0.681589	+	0.731735i	$0.738711\pi$
$968$	−15729.8	−	27356.1i	−0.522289	−	0.908326i
$969$	5665.05	+	5665.05i	0.187810	+	0.187810i
$970$	−10650.7	+	15122.5i	−0.352548	+	0.500570i
$971$	13941.0	−	5774.55i	0.460749	−	0.190849i	−0.140221	−	0.990120i	$-0.544781\pi$
$971$	13941.0	−	5774.55i	0.460749	−	0.190849i	0.600970	+	0.799272i	$0.294781\pi$
$972$	−1946.37	+	43408.2i	−0.0642281	+	1.43243i
$973$	20740.8	+	8591.11i	0.683370	+	0.283061i
$974$	9864.29	+	56136.1i	0.324510	+	1.84673i
$975$	−10209.1	+	10121.7i	−0.335338	+	0.332467i
$976$	−31782.2	+	9938.82i	−1.04234	+	0.325957i
$977$	34209.7			1.12023			0.560115	−	0.828415i	$-0.310757\pi$
$977$	34209.7			1.12023			0.560115	+	0.828415i	$0.310757\pi$
$978$	−4690.65	−	26693.7i	−0.153365	−	0.872773i
$979$	1069.57	−	2582.16i	0.0349168	−	0.0842965i
$980$	−67087.4	+	24165.5i	−2.18676	+	0.787694i
$981$	−7800.17	+	3230.94i	−0.253864	+	0.105154i
$982$	5219.91	+	1160.44i	0.169627	+	0.0377101i
$983$	−23923.7	+	23923.7i	−0.776242	+	0.776242i	−0.979190	−	0.202947i	$-0.934948\pi$
$983$	−23923.7	+	23923.7i	−0.776242	+	0.776242i	0.202947	+	0.979190i	$0.434948\pi$
$984$	−8528.91	−	65678.1i	−0.276313	−	2.12779i
$985$	−21317.6	+	8776.39i	−0.689577	+	0.283897i
$986$	−12199.4	−	19174.1i	−0.394024	−	0.619297i
$987$	96193.5	−	39844.7i	3.10220	−	1.28497i
$988$	3121.68	+	1460.13i	0.100520	+	0.0470173i
$989$	−284.218	−	117.727i	−0.00913812	−	0.00378513i
$990$	25963.7	+	41002.0i	0.833515	+	1.31629i
$991$	53208.8			1.70558			0.852791	−	0.522252i	$-0.174908\pi$
$991$	53208.8			1.70558			0.852791	+	0.522252i	$0.174908\pi$
$992$	2103.00	−	177.763i	0.0673087	−	0.00568950i
$993$		−	25049.0i		−	0.800510i
$994$	15121.5	+	10601.4i	0.482519	+	0.338287i
$995$	3746.44	−	3730.37i	0.119367	−	0.118855i
$996$	33007.3	+	15438.8i	1.05008	+	0.491163i
$997$	−26266.2	+	10879.8i	−0.834361	+	0.345604i	−0.758628	−	0.651524i	$-0.774130\pi$
$997$	−26266.2	+	10879.8i	−0.834361	+	0.345604i	−0.0757336	+	0.997128i	$0.524130\pi$
$998$	17537.7	−	11158.3i	0.556260	−	0.353917i
$999$	3719.71	−	3719.71i	0.117804	−	0.117804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.z.a.29.14	✓	280
5.4	even	2	inner	160.4.z.a.29.57	yes	280
32.21	even	8	inner	160.4.z.a.149.57	yes	280
160.149	even	8	inner	160.4.z.a.149.14	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.z.a.29.14	✓	280	1.1	even	1	trivial
160.4.z.a.29.57	yes	280	5.4	even	2	inner
160.4.z.a.149.14	yes	280	160.149	even	8	inner
160.4.z.a.149.57	yes	280	32.21	even	8	inner

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.31596 - 1.62368i) q^{2} +(-2.87385 + 6.93809i) q^{3} +(2.72732 + 7.52075i) q^{4} +(11.1803 + 0.0240294i) q^{5} +(17.9210 - 11.4021i) q^{6} +(-23.8772 - 23.8772i) q^{7} +(5.89493 - 21.8460i) q^{8} +(-20.7862 - 20.7862i) q^{9} +(-25.8541 - 18.2089i) q^{10} +(48.2332 - 19.9788i) q^{11} +(-60.0176 - 2.69111i) q^{12} +(14.1490 + 5.86071i) q^{13} +(16.5296 + 94.0674i) q^{14} +(-32.2973 + 77.5010i) q^{15} +(-49.1234 + 41.0230i) q^{16} +37.9265 q^{17} +(14.3898 + 81.8902i) q^{18} +(10.7644 - 25.9876i) q^{19} +(30.3116 + 84.1499i) q^{20} +(234.281 - 97.0425i) q^{21} +(-144.145 - 32.0451i) q^{22} +(-26.7657 + 26.7657i) q^{23} +(134.629 + 103.682i) q^{24} +(124.999 + 0.537312i) q^{25} +(-23.2526 - 36.5466i) q^{26} +(16.6248 - 6.88621i) q^{27} +(114.453 - 244.695i) q^{28} +(195.727 + 81.0727i) q^{29} +(200.636 - 127.049i) q^{30} +11.6590 q^{31} +(180.376 - 15.2469i) q^{32} +392.063i q^{33} +(-87.8362 - 61.5805i) q^{34} +(-266.380 - 267.528i) q^{35} +(99.6373 - 213.019i) q^{36} +(270.084 - 111.872i) q^{37} +(-67.1255 + 42.7082i) q^{38} +(-81.3243 + 81.3243i) q^{39} +(66.4321 - 244.104i) q^{40} +(-275.599 - 275.599i) q^{41} +(-700.152 - 155.652i) q^{42} +(3.11016 + 7.50859i) q^{43} +(281.803 + 308.261i) q^{44} +(-231.897 - 232.896i) q^{45} +(105.447 - 18.5293i) q^{46} +410.590 q^{47} +(-143.448 - 458.717i) q^{48} +797.237i q^{49} +(-288.620 - 204.203i) q^{50} +(-108.995 + 263.138i) q^{51} +(-5.48803 + 122.395i) q^{52} +(172.825 + 417.236i) q^{53} +(-49.6833 - 11.0452i) q^{54} +(539.742 - 222.211i) q^{55} +(-662.376 + 380.867i) q^{56} +(149.369 + 149.369i) q^{57} +(-321.659 - 505.559i) q^{58} +(-163.843 - 395.553i) q^{59} +(-670.951 - 31.5296i) q^{60} +(480.706 + 199.115i) q^{61} +(-27.0017 - 18.9304i) q^{62} +992.632i q^{63} +(-442.500 - 257.562i) q^{64} +(158.049 + 65.8646i) q^{65} +(636.584 - 908.001i) q^{66} +(-250.968 + 605.890i) q^{67} +(103.438 + 285.236i) q^{68} +(-108.782 - 262.623i) q^{69} +(182.546 + 1052.10i) q^{70} +(136.726 - 136.726i) q^{71} +(-576.630 + 331.563i) q^{72} +(746.457 - 746.457i) q^{73} +(-807.148 - 179.438i) q^{74} +(-362.956 + 865.709i) q^{75} +(224.804 + 10.0799i) q^{76} +(-1628.71 - 674.634i) q^{77} +(320.388 - 56.2990i) q^{78} -580.678i q^{79} +(-550.201 + 457.470i) q^{80} -658.562i q^{81} +(190.791 + 1085.76i) q^{82} +(-560.369 - 232.112i) q^{83} +(1368.79 + 1497.31i) q^{84} +(424.030 + 0.911351i) q^{85} +(4.98855 - 22.4395i) q^{86} +(-1124.98 + 1124.98i) q^{87} +(-152.127 - 1171.48i) q^{88} +(37.8550 - 37.8550i) q^{89} +(158.915 + 915.904i) q^{90} +(-197.901 - 477.775i) q^{91} +(-274.296 - 128.299i) q^{92} +(-33.5061 + 80.8909i) q^{93} +(-950.908 - 666.666i) q^{94} +(120.974 - 290.291i) q^{95} +(-412.590 + 1295.28i) q^{96} -584.915i q^{97} +(1294.46 - 1846.37i) q^{98} +(-1417.87 - 587.301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} + 200 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 464 q^{24} - 4 q^{25} - 48 q^{26} - 8 q^{29} + 1124 q^{30} + 1472 q^{31} - 72 q^{34}+ \cdots + 5520 q^{99}+O(q^{100}) \) 280 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 + 200 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 464 * q^24 - 4 * q^25 - 48 * q^26 - 8 * q^29 + 1124 * q^30 + 1472 * q^31 - 72 * q^34 - 460 * q^35 - 888 * q^36 - 8 * q^39 - 1112 * q^40 - 8 * q^41 - 8 * q^44 - 112 * q^45 - 8 * q^46 + 3556 * q^50 - 1712 * q^51 + 856 * q^54 + 284 * q^55 + 328 * q^56 - 1384 * q^59 - 5248 * q^60 - 1832 * q^61 + 832 * q^64 - 8 * q^65 + 6088 * q^66 + 1048 * q^69 - 616 * q^70 + 216 * q^71 - 2064 * q^74 + 2204 * q^75 - 5128 * q^76 - 656 * q^80 - 6904 * q^84 - 504 * q^85 - 1192 * q^86 - 8 * q^89 + 2720 * q^90 - 8 * q^91 - 920 * q^94 - 8 * q^95 - 4152 * q^96 + 5520 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more