LMFDB - Embedded newform 160.4.u.a.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(43,160)]

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([4, 5, 6]))

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

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

chi := DirichletCharacter("160.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.u (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			43.6
Character	$\chi$	$=$	160.43
Dual form			160.4.u.a.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.71454 + 0.794525i) q^{2} +(1.40505 - 3.39208i) q^{3} +(6.73746 - 4.31354i) q^{4} +(10.5782 + 3.61974i) q^{5} +(-1.11896 + 10.3243i) q^{6} +12.0132i q^{7} +(-14.8619 + 17.0624i) q^{8} +(9.55980 + 9.55980i) q^{9} +(-31.5908 - 1.42133i) q^{10} +(-1.26189 + 3.04648i) q^{11} +(-5.16544 - 28.9148i) q^{12} +(-16.2323 + 39.1882i) q^{13} +(-9.54482 - 32.6104i) q^{14} +(27.1413 - 30.7961i) q^{15} +(26.7868 - 58.1246i) q^{16} +(4.97489 + 4.97489i) q^{17} +(-33.5460 - 18.3550i) q^{18} +(-9.00445 - 21.7387i) q^{19} +(86.8838 - 21.2414i) q^{20} +(40.7499 + 16.8792i) q^{21} +(1.00496 - 9.27239i) q^{22} +74.1079i q^{23} +(36.9953 + 74.3862i) q^{24} +(98.7949 + 76.5804i) q^{25} +(12.9272 - 119.275i) q^{26} +(137.446 - 56.9320i) q^{27} +(51.8196 + 80.9388i) q^{28} +(45.2125 + 109.153i) q^{29} +(-49.2079 + 105.162i) q^{30} -11.2948i q^{31} +(-26.5323 + 179.064i) q^{32} +(8.56089 + 8.56089i) q^{33} +(-17.4572 - 9.55187i) q^{34} +(-43.4849 + 127.078i) q^{35} +(105.645 + 23.1722i) q^{36} +(108.970 + 263.076i) q^{37} +(41.7148 + 51.8562i) q^{38} +(110.122 + 110.122i) q^{39} +(-218.973 + 126.692i) q^{40} +(285.959 - 285.959i) q^{41} +(-124.028 - 13.4424i) q^{42} +(-351.832 + 145.734i) q^{43} +(4.63915 + 25.9687i) q^{44} +(66.5211 + 135.729i) q^{45} +(-58.8806 - 201.169i) q^{46} +(285.478 - 285.478i) q^{47} +(-159.527 - 172.531i) q^{48} +198.682 q^{49} +(-329.028 - 129.386i) q^{50} +(23.8652 - 9.88529i) q^{51} +(59.6754 + 334.047i) q^{52} +(-76.5523 - 184.814i) q^{53} +(-327.869 + 263.748i) q^{54} +(-24.3760 + 27.6584i) q^{55} +(-204.974 - 178.540i) q^{56} -86.3911 q^{57} +(-209.456 - 260.377i) q^{58} +(326.805 - 788.976i) q^{59} +(50.0232 - 324.563i) q^{60} +(-251.331 + 104.105i) q^{61} +(8.97396 + 30.6601i) q^{62} +(-114.844 + 114.844i) q^{63} +(-70.2480 - 507.158i) q^{64} +(-313.559 + 355.782i) q^{65} +(-30.0407 - 16.4370i) q^{66} +(295.823 + 122.534i) q^{67} +(54.9775 + 12.0587i) q^{68} +(251.380 + 104.125i) q^{69} +(17.0748 - 379.508i) q^{70} +(166.176 - 166.176i) q^{71} +(-305.190 + 21.0359i) q^{72} -411.925 q^{73} +(-504.823 - 627.552i) q^{74} +(398.579 - 227.522i) q^{75} +(-154.438 - 107.622i) q^{76} +(-36.5981 - 15.1594i) q^{77} +(-386.427 - 211.437i) q^{78} -119.435i q^{79} +(493.751 - 517.890i) q^{80} -181.191i q^{81} +(-549.046 + 1003.45i) q^{82} +(-882.907 - 365.712i) q^{83} +(347.360 - 62.0537i) q^{84} +(34.6174 + 70.6330i) q^{85} +(839.273 - 675.139i) q^{86} +433.781 q^{87} +(-33.2260 - 66.8073i) q^{88} +(-625.108 + 625.108i) q^{89} +(-288.414 - 315.590i) q^{90} +(-470.777 - 195.002i) q^{91} +(319.667 + 499.299i) q^{92} +(-38.3128 - 15.8697i) q^{93} +(-548.122 + 1001.76i) q^{94} +(-16.5621 - 262.549i) q^{95} +(570.122 + 341.594i) q^{96} +(-998.946 + 998.946i) q^{97} +(-539.330 + 157.858i) q^{98} +(-41.1871 + 17.0603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} + 80 q^{8} + 8 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} + 64 q^{14} - 8 q^{15} - 8 q^{16} + 28 q^{18} - 48 q^{19} - 312 q^{20} - 8 q^{21} - 436 q^{22} + 736 q^{24}+ \cdots + 3480 q^{98}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 + 80 * q^8 + 8 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 + 64 * q^14 - 8 * q^15 - 8 * q^16 + 28 * q^18 - 48 * q^19 - 312 * q^20 - 8 * q^21 - 436 * q^22 + 736 * q^24 - 4 * q^25 - 8 * q^26 - 112 * q^27 + 252 * q^28 - 1696 * q^30 - 344 * q^32 - 8 * q^33 + 696 * q^34 + 952 * q^35 - 8 * q^36 - 4 * q^37 - 172 * q^38 + 816 * q^40 - 8 * q^41 - 460 * q^42 + 860 * q^43 + 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 3496 * q^48 - 11368 * q^49 - 36 * q^50 + 1480 * q^51 - 328 * q^52 - 4 * q^53 + 2968 * q^54 - 292 * q^55 - 344 * q^56 - 8 * q^57 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 - 440 * q^62 + 2744 * q^63 + 816 * q^64 - 8 * q^65 + 552 * q^66 + 1844 * q^67 + 1224 * q^68 + 216 * q^69 + 1764 * q^70 - 232 * q^71 - 3432 * q^72 - 8 * q^73 + 104 * q^75 + 824 * q^76 + 1368 * q^77 - 5968 * q^78 - 1800 * q^80 + 588 * q^82 + 2676 * q^83 + 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 2568 * q^87 - 5880 * q^88 - 84 * q^90 - 8 * q^91 - 3284 * q^92 + 104 * q^93 + 416 * q^94 + 6168 * q^96 - 8 * q^97 + 3480 * q^98

Character values

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

$n$	$31$	$97$	$101$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−2.71454	+	0.794525i	−0.959735	+	0.280907i
$2$	−2.71454	+	0.794525i	−0.959735	+	0.280907i
$3$	1.40505	−	3.39208i	0.270402	−	0.652807i	−0.729099	−	0.684408i	$-0.760061\pi$
$3$	1.40505	−	3.39208i	0.270402	−	0.652807i	0.999501	+	0.0316012i	$0.0100606\pi$
$4$	6.73746	−	4.31354i	0.842183	−	0.539192i
$5$	10.5782	+	3.61974i	0.946139	+	0.323760i
$5$	10.5782	+	3.61974i	0.946139	+	0.323760i
$6$	−1.11896	+	10.3243i	−0.0761358	+	0.702479i
$7$			12.0132i			0.648654i	0.945945	+	0.324327i	$0.105138\pi$
$7$			12.0132i			0.648654i	−0.945945	+	0.324327i	$0.894862\pi$
$8$	−14.8619	+	17.0624i	−0.656809	+	0.754057i
$9$	9.55980	+	9.55980i	0.354067	+	0.354067i
$10$	−31.5908	−	1.42133i	−0.998989	−	0.0449464i
$11$	−1.26189	+	3.04648i	−0.0345886	+	0.0835043i	−0.940230	−	0.340540i	$-0.889390\pi$
$11$	−1.26189	+	3.04648i	−0.0345886	+	0.0835043i	0.905641	+	0.424045i	$0.139390\pi$
$12$	−5.16544	−	28.9148i	−0.124261	−	0.695581i
$13$	−16.2323	+	39.1882i	−0.346309	+	0.836065i	0.650740	+	0.759301i	$0.274459\pi$
$13$	−16.2323	+	39.1882i	−0.346309	+	0.836065i	−0.997049	+	0.0767641i	$0.975541\pi$
$14$	−9.54482	−	32.6104i	−0.182211	−	0.622536i
$15$	27.1413	−	30.7961i	0.467190	−	0.530101i
$16$	26.7868	−	58.1246i	0.418543	−	0.908197i
$17$	4.97489	+	4.97489i	0.0709758	+	0.0709758i	0.741704	−	0.670728i	$-0.234018\pi$
$17$	4.97489	+	4.97489i	0.0709758	+	0.0709758i	−0.670728	+	0.741704i	$0.734018\pi$
$18$	−33.5460	−	18.3550i	−0.439270	−	0.240350i
$19$	−9.00445	−	21.7387i	−0.108724	−	0.262484i	0.860148	−	0.510044i	$-0.170371\pi$
$19$	−9.00445	−	21.7387i	−0.108724	−	0.262484i	−0.968872	+	0.247561i	$0.920371\pi$
$20$	86.8838	−	21.2414i	0.971391	−	0.237486i
$21$	40.7499	+	16.8792i	0.423446	+	0.175397i
$22$	1.00496	−	9.27239i	0.00973897	−	0.0898582i
$23$			74.1079i			0.671851i	0.941889	+	0.335925i	$0.109049\pi$
$23$			74.1079i			0.671851i	−0.941889	+	0.335925i	$0.890951\pi$
$24$	36.9953	+	74.3862i	0.314651	+	0.632668i
$25$	98.7949	+	76.5804i	0.790359	+	0.612644i
$26$	12.9272	−	119.275i	0.0975089	−	0.899681i
$27$	137.446	−	56.9320i	0.979684	−	0.405799i
$28$	51.8196	+	80.9388i	0.349749	+	0.546285i
$29$	45.2125	+	109.153i	0.289509	+	0.698936i	0.999989	−	0.00478173i	$-0.00152208\pi$
$29$	45.2125	+	109.153i	0.289509	+	0.698936i	−0.710480	+	0.703718i	$0.751522\pi$
$30$	−49.2079	+	105.162i	−0.299470	+	0.639994i
$31$		−	11.2948i		−	0.0654386i	−0.999465	−	0.0327193i	$-0.989583\pi$
$31$		−	11.2948i		−	0.0654386i	0.999465	−	0.0327193i	$-0.0104167\pi$
$32$	−26.5323	+	179.064i	−0.146572	+	0.989200i
$33$	8.56089	+	8.56089i	0.0451594	+	0.0451594i
$34$	−17.4572	−	9.55187i	−0.0880555	−	0.0481803i
$35$	−43.4849	+	127.078i	−0.210008	+	0.613717i
$36$	105.645	+	23.1722i	0.489099	+	0.107279i
$37$	108.970	+	263.076i	0.484176	+	1.16890i	0.957608	+	0.288074i	$0.0930148\pi$
$37$	108.970	+	263.076i	0.484176	+	1.16890i	−0.473432	+	0.880830i	$0.656985\pi$
$38$	41.7148	+	51.8562i	0.178080	+	0.221373i
$39$	110.122	+	110.122i	0.452146	+	0.452146i
$40$	−218.973	+	126.692i	−0.865566	+	0.500794i
$41$	285.959	−	285.959i	1.08925	−	1.08925i	0.0936464	−	0.995606i	$-0.470148\pi$
$41$	285.959	−	285.959i	1.08925	−	1.08925i	0.995606	−	0.0936464i	$-0.0298523\pi$
$42$	−124.028	−	13.4424i	−0.455666	−	0.0493858i
$43$	−351.832	+	145.734i	−1.24776	+	0.516841i	−0.906133	−	0.422993i	$-0.860980\pi$
$43$	−351.832	+	145.734i	−1.24776	+	0.516841i	−0.341632	+	0.939834i	$0.610980\pi$
$44$	4.63915	+	25.9687i	0.0158949	+	0.0889758i
$45$	66.5211	+	135.729i	0.220364	+	0.449629i
$46$	−58.8806	−	201.169i	−0.188727	−	0.644799i
$47$	285.478	−	285.478i	0.885984	−	0.885984i	−0.108151	−	0.994135i	$-0.534493\pi$
$47$	285.478	−	285.478i	0.885984	−	0.885984i	0.994135	+	0.108151i	$0.0344929\pi$
$48$	−159.527	−	172.531i	−0.479703	−	0.518806i
$49$	198.682			0.579248
$50$	−329.028	−	129.386i	−0.930631	−	0.365958i
$51$	23.8652	−	9.88529i	0.0655254	−	0.0271415i
$52$	59.6754	+	334.047i	0.159144	+	0.890847i
$53$	−76.5523	−	184.814i	−0.198401	−	0.478983i	0.793098	−	0.609094i	$-0.208467\pi$
$53$	−76.5523	−	184.814i	−0.198401	−	0.478983i	−0.991499	+	0.130111i	$0.958467\pi$
$54$	−327.869	+	263.748i	−0.826246	+	0.664659i
$55$	−24.3760	+	27.6584i	−0.0597610	+	0.0678083i
$56$	−204.974	−	178.540i	−0.489122	−	0.426042i
$57$	−86.3911			−0.200750
$58$	−209.456	−	260.377i	−0.474188	−	0.589468i
$59$	326.805	−	788.976i	0.721124	−	1.74095i	0.0510005	−	0.998699i	$-0.483759\pi$
$59$	326.805	−	788.976i	0.721124	−	1.74095i	0.670124	−	0.742249i	$-0.266241\pi$
$60$	50.0232	−	324.563i	0.107633	−	0.698347i
$61$	−251.331	+	104.105i	−0.527535	+	0.218512i	−0.630523	−	0.776170i	$-0.717160\pi$
$61$	−251.331	+	104.105i	−0.527535	+	0.218512i	0.102988	+	0.994683i	$0.467160\pi$
$62$	8.97396	+	30.6601i	0.0183822	+	0.0628037i
$63$	−114.844	+	114.844i	−0.229667	+	0.229667i
$64$	−70.2480	−	507.158i	−0.137203	−	0.990543i
$65$	−313.559	+	355.782i	−0.598341	+	0.678913i
$66$	−30.0407	−	16.4370i	−0.0560266	−	0.0306555i
$67$	295.823	+	122.534i	0.539411	+	0.223431i	0.635719	−	0.771920i	$-0.280704\pi$
$67$	295.823	+	122.534i	0.539411	+	0.223431i	−0.0963085	+	0.995352i	$0.530704\pi$
$68$	54.9775	+	12.0587i	0.0980441	+	0.0215050i
$69$	251.380	+	104.125i	0.438589	+	0.181669i
$70$	17.0748	−	379.508i	0.0291547	−	0.647999i
$71$	166.176	−	166.176i	0.277766	−	0.277766i	−0.554450	−	0.832217i	$-0.687071\pi$
$71$	166.176	−	166.176i	0.277766	−	0.277766i	0.832217	+	0.554450i	$0.187071\pi$
$72$	−305.190	+	21.0359i	−0.499541	+	0.0344321i
$73$	−411.925			−0.660441			−0.330220	−	0.943904i	$-0.607123\pi$
$73$	−411.925			−0.660441			−0.330220	+	0.943904i	$0.607123\pi$
$74$	−504.823	−	627.552i	−0.793034	−	0.985830i
$75$	398.579	−	227.522i	0.613652	−	0.350292i
$76$	−154.438	−	107.622i	−0.233095	−	0.162436i
$77$	−36.5981	−	15.1594i	−0.0541654	−	0.0224360i
$78$	−386.427	−	211.437i	−0.560952	−	0.306930i
$79$		−	119.435i		−	0.170095i	−0.996377	−	0.0850473i	$-0.972896\pi$
$79$		−	119.435i		−	0.170095i	0.996377	−	0.0850473i	$-0.0271041\pi$
$80$	493.751	−	517.890i	0.690038	−	0.723773i
$81$		−	181.191i		−	0.248548i
$82$	−549.046	+	1003.45i	−0.739415	+	1.35137i
$83$	−882.907	−	365.712i	−1.16761	−	0.483640i	−0.287208	−	0.957868i	$-0.592727\pi$
$83$	−882.907	−	365.712i	−1.16761	−	0.483640i	−0.880402	+	0.474228i	$0.842727\pi$
$84$	347.360	−	62.0537i	0.451192	−	0.0806025i
$85$	34.6174	+	70.6330i	0.0441739	+	0.0901320i
$86$	839.273	−	675.139i	1.05234	−	0.846536i
$87$	433.781			0.534554
$88$	−33.2260	−	66.8073i	−0.0402488	−	0.0809282i
$89$	−625.108	+	625.108i	−0.744509	+	0.744509i	−0.973442	−	0.228933i	$-0.926476\pi$
$89$	−625.108	+	625.108i	−0.744509	+	0.744509i	0.228933	+	0.973442i	$0.426476\pi$
$90$	−288.414	−	315.590i	−0.337795	−	0.369623i
$91$	−470.777	−	195.002i	−0.542317	−	0.224635i
$92$	319.667	+	499.299i	0.362257	+	0.565821i
$93$	−38.3128	−	15.8697i	−0.0427188	−	0.0176947i
$94$	−548.122	+	1001.76i	−0.601431	+	1.09919i
$95$	−16.5621	−	262.549i	−0.0178867	−	0.283547i
$96$	570.122	+	341.594i	0.606124	+	0.363164i
$97$	−998.946	+	998.946i	−1.04565	+	1.04565i	−0.0467378	+	0.998907i	$0.514883\pi$
$97$	−998.946	+	998.946i	−1.04565	+	1.04565i	−0.998907	+	0.0467378i	$0.985117\pi$
$98$	−539.330	+	157.858i	−0.555924	+	0.162715i
$99$	−41.1871	+	17.0603i	−0.0418128	+	0.0173194i
$100$	995.960	+	89.8020i	0.995960	+	0.0898020i
$101$	147.259	−	355.516i	0.145078	−	0.350249i	−0.834591	−	0.550870i	$-0.814296\pi$
$101$	147.259	−	355.516i	0.145078	−	0.350249i	0.979669	+	0.200621i	$0.0642960\pi$
$102$	−56.9290	+	45.7955i	−0.0552628	+	0.0444552i
$103$	571.762			0.546964			0.273482	−	0.961877i	$-0.411825\pi$
$103$	571.762			0.546964			0.273482	+	0.961877i	$0.411825\pi$
$104$	−427.400	−	859.371i	−0.402981	−	0.810272i
$105$	369.961	+	326.055i	0.343852	+	0.303045i
$106$	354.643	+	440.861i	0.324962	+	0.403964i
$107$	−579.924	−	1400.06i	−0.523957	−	1.26494i	−0.935427	−	0.353520i	$-0.884985\pi$
$107$	−579.924	−	1400.06i	−0.523957	−	1.26494i	0.411470	−	0.911423i	$-0.365015\pi$
$108$	680.458	−	976.455i	0.606270	−	0.869995i
$109$	233.187	−	96.5892i	0.204911	−	0.0848767i	−0.277868	−	0.960619i	$-0.589628\pi$
$109$	233.187	−	96.5892i	0.204911	−	0.0848767i	0.482778	+	0.875743i	$0.339628\pi$
$110$	44.1942	−	94.4471i	0.0383069	−	0.0818653i
$111$	1045.48			0.893991
$112$	698.265	+	321.796i	0.589106	+	0.271490i
$113$	−1025.32	+	1025.32i	−0.853575	+	0.853575i	−0.990571	−	0.136997i	$-0.956255\pi$
$113$	−1025.32	+	1025.32i	−0.853575	+	0.853575i	0.136997	+	0.990571i	$0.456255\pi$
$114$	234.512	−	68.6398i	0.192667	−	0.0563922i
$115$	−268.252	+	783.925i	−0.217518	+	0.635664i
$116$	775.452	+	540.386i	0.620680	+	0.432531i
$117$	−529.808	+	219.454i	−0.418639	+	0.173406i
$118$	−260.263	+	2401.36i	−0.203044	+	1.87342i
$119$	−59.7646	+	59.7646i	−0.0460387	+	0.0460387i
$120$	122.083	+	920.783i	0.0928717	+	0.700463i
$121$	933.470	+	933.470i	0.701330	+	0.701330i
$122$	599.534	−	482.285i	0.444912	−	0.357902i
$123$	−568.212	−	1371.78i	−0.416536	−	1.00561i
$124$	−48.7204	−	76.0980i	−0.0352840	−	0.0551113i
$125$	767.867	+	1167.69i	0.549441	+	0.835533i
$126$	220.503	−	402.996i	0.155904	−	0.284934i
$127$	555.699	+	555.699i	0.388270	+	0.388270i	0.874070	−	0.485800i	$-0.161472\pi$
$127$	555.699	+	555.699i	0.388270	+	0.388270i	−0.485800	+	0.874070i	$0.661472\pi$
$128$	593.641	+	1320.89i	0.409929	+	0.912117i
$129$			1398.21i			0.954304i
$130$	568.490	−	1214.91i	0.383538	−	0.819655i
$131$	−108.947	−	263.020i	−0.0726619	−	0.175421i	0.883376	−	0.468666i	$-0.155265\pi$
$131$	−108.947	−	263.020i	−0.0726619	−	0.175421i	−0.956038	+	0.293244i	$0.905265\pi$
$132$	94.6064	+	20.7509i	0.0623820	+	0.0136828i
$133$	261.152	−	108.173i	0.170261	−	0.0705245i
$134$	−900.380	−	97.5846i	−0.580455	−	0.0629106i
$135$	1660.00	−	104.717i	1.05830	−	0.0667597i
$136$	−158.820	+	10.9470i	−0.100137	+	0.00690221i
$137$		−	1326.19i		−	0.827038i	−0.910496	−	0.413519i	$-0.864300\pi$
$137$		−	1326.19i		−	0.827038i	0.910496	−	0.413519i	$-0.135700\pi$
$138$	−765.112	−	82.9240i	−0.471961	−	0.0511519i
$139$	−1346.20	−	557.613i	−0.821460	−	0.340260i	−0.0679438	−	0.997689i	$-0.521644\pi$
$139$	−1346.20	−	557.613i	−0.821460	−	0.340260i	−0.753516	+	0.657429i	$0.771644\pi$
$140$	255.178	+	1043.76i	0.154047	+	0.630097i
$141$	−567.255	−	1369.48i	−0.338805	−	0.817948i
$142$	−319.060	+	583.121i	−0.188556	+	0.344609i
$143$	−98.9025	−	98.9025i	−0.0578366	−	0.0578366i
$144$	811.736	−	299.584i	0.469755	−	0.173370i
$145$	83.1606	+	1318.29i	0.0476283	+	0.755022i
$146$	1118.19	−	327.285i	0.633848	−	0.185522i
$147$	279.158	−	673.946i	0.156629	−	0.378137i
$148$	1868.97	+	1302.42i	1.03803	+	0.723367i
$149$	37.2039	−	89.8182i	0.0204555	−	0.0493838i	−0.913322	−	0.407239i	$-0.866492\pi$
$149$	37.2039	−	89.8182i	0.0204555	−	0.0493838i	0.933777	+	0.357855i	$0.116492\pi$
$150$	−901.187	+	934.297i	−0.490544	+	0.508567i
$151$	−1086.61	−	1086.61i	−0.585607	−	0.585607i	0.350831	−	0.936439i	$-0.385899\pi$
$151$	−1086.61	−	1086.61i	−0.585607	−	0.585607i	−0.936439	+	0.350831i	$0.885899\pi$
$152$	504.736	+	169.441i	0.269339	+	0.0904174i
$153$			95.1179i			0.0502603i
$154$	111.391	+	12.0728i	0.0582869	+	0.00631722i
$155$	40.8841	−	119.478i	0.0211864	−	0.0619141i
$156$	1216.96	+	266.928i	0.624584	+	0.136996i
$157$	823.704	−	1988.60i	0.418718	−	1.01087i	−0.564001	−	0.825774i	$-0.690739\pi$
$157$	823.704	−	1988.60i	0.418718	−	1.01087i	0.982719	−	0.185101i	$-0.0592612\pi$
$158$	94.8940	+	324.211i	0.0477807	+	0.163246i
$159$	−734.463			−0.366331
$160$	−928.830	+	1798.13i	−0.458940	+	0.888467i
$161$	−890.276			−0.435799
$162$	143.961	+	491.851i	0.0698187	+	0.238540i
$163$	−751.240	+	1813.65i	−0.360992	+	0.871511i	0.634164	+	0.773199i	$0.281344\pi$
$163$	−751.240	+	1813.65i	−0.360992	+	0.871511i	−0.995156	+	0.0983126i	$0.968656\pi$
$164$	693.143	−	3160.14i	0.330033	−	1.50467i
$165$	59.5702	+	121.547i	0.0281063	+	0.0573478i
$166$	2687.25	+	291.249i	1.25645	+	0.136176i
$167$		−	797.200i		−	0.369396i	−0.982795	−	0.184698i	$-0.940869\pi$
$167$		−	797.200i		−	0.369396i	0.982795	−	0.184698i	$-0.0591308\pi$
$168$	−893.620	+	444.433i	−0.410383	+	0.204100i
$169$	281.288	+	281.288i	0.128033	+	0.128033i
$170$	−150.090	−	164.232i	−0.0677139	−	0.0740941i
$171$	121.737	−	293.898i	0.0544411	−	0.131432i
$172$	−1741.83	+	2499.52i	−0.772169	+	1.10806i
$173$	1433.28	−	3460.25i	0.629887	−	1.52068i	−0.209875	−	0.977728i	$-0.567306\pi$
$173$	1433.28	−	3460.25i	0.629887	−	1.52068i	0.839763	−	0.542954i	$-0.182694\pi$
$174$	−1177.52	+	344.650i	−0.513030	+	0.150160i
$175$	−919.979	+	1186.85i	−0.397394	+	0.512670i
$176$	143.273	+	154.952i	0.0613615	+	0.0663634i
$177$	−2217.10	−	2217.10i	−0.941510	−	0.941510i
$178$	1200.22	−	2193.54i	0.505394	−	0.923669i
$179$	−1627.35	−	3928.78i	−0.679520	−	1.64051i	−0.764892	−	0.644158i	$-0.777208\pi$
$179$	−1627.35	−	3928.78i	−0.679520	−	1.64051i	0.0853719	−	0.996349i	$-0.472792\pi$
$180$	1033.66	+	627.528i	0.428023	+	0.259851i
$181$	−2673.84	−	1107.54i	−1.09804	−	0.454822i	−0.241234	−	0.970467i	$-0.577552\pi$
$181$	−2673.84	−	1107.54i	−1.09804	−	0.454822i	−0.856802	+	0.515645i	$0.827552\pi$
$182$	1432.88	+	155.297i	0.583582	+	0.0632495i
$183$			998.808i			0.403464i
$184$	−1264.46	−	1101.38i	−0.506614	−	0.441278i
$185$	200.431	+	3177.30i	0.0796539	+	1.26270i
$186$	116.610	+	12.6384i	0.0459693	+	0.00498222i
$187$	−21.4337	+	8.87811i	−0.00838173	+	0.00347183i
$188$	691.976	−	3154.82i	0.268444	−	1.22388i
$189$	683.938	+	1651.17i	0.263223	+	0.635476i
$190$	253.560	+	699.540i	0.0968167	+	0.267105i
$191$			2743.59i			1.03937i	0.854359	+	0.519684i	$0.173950\pi$
$191$			2743.59i			1.03937i	−0.854359	+	0.519684i	$0.826050\pi$
$192$	−1819.02	−	474.294i	−0.683733	−	0.178277i
$193$	−2581.44	−	2581.44i	−0.962778	−	0.962778i	0.0365538	−	0.999332i	$-0.488362\pi$
$193$	−2581.44	−	2581.44i	−0.962778	−	0.962778i	−0.999332	+	0.0365538i	$0.988362\pi$
$194$	1917.99	−	3505.37i	0.709813	−	1.29727i
$195$	766.278	+	1563.51i	0.281407	+	0.574180i
$196$	1338.61	−	857.022i	0.487832	−	0.312326i
$197$	219.259	+	529.339i	0.0792974	+	0.191441i	0.958556	−	0.284904i	$-0.0919616\pi$
$197$	219.259	+	529.339i	0.0792974	+	0.191441i	−0.879259	+	0.476344i	$0.841962\pi$
$198$	98.2494	−	79.0350i	0.0352640	−	0.0283675i
$199$	1280.95	+	1280.95i	0.456301	+	0.456301i	0.897439	−	0.441139i	$-0.145425\pi$
$199$	1280.95	+	1280.95i	0.456301	+	0.456301i	−0.441139	+	0.897439i	$0.645425\pi$
$200$	−2774.92	+	547.543i	−0.981083	+	0.193586i
$201$	831.291	−	831.291i	0.291715	−	0.291715i
$202$	−117.276	+	1082.06i	−0.0408489	+	0.376899i
$203$	−1311.28	+	543.149i	−0.453368	+	0.187791i
$204$	118.150	−	169.545i	0.0405499	−	0.0581889i
$205$	4060.02	−	1989.82i	1.38324	−	0.677928i
$206$	−1552.07	+	454.279i	−0.524941	+	0.153646i
$207$	−708.457	+	708.457i	−0.237880	+	0.237880i
$208$	1842.99	+	1993.22i	0.614366	+	0.664446i
$209$	77.5889			0.0256791
$210$	−1263.33	−	591.146i	−0.415135	−	0.194252i
$211$	−1468.19	+	608.145i	−0.479026	+	0.198419i	−0.609113	−	0.793084i	$-0.708474\pi$
$211$	−1468.19	+	608.145i	−0.479026	+	0.198419i	0.130087	+	0.991503i	$0.458474\pi$
$212$	−1312.97	−	914.963i	−0.425354	−	0.296415i
$213$	−330.197	−	797.167i	−0.106219	−	0.256436i
$214$	2686.61	+	3339.76i	0.858191	+	1.06683i
$215$	−4249.25	+	268.052i	−1.34789	+	0.0850278i
$216$	−1071.31	+	3191.27i	−0.337471	+	1.00527i
$217$	135.687			0.0424470
$218$	−556.253	+	447.468i	−0.172817	+	0.139020i
$219$	−578.774	+	1397.28i	−0.178584	+	0.431140i
$220$	−44.9265	+	291.494i	−0.0137679	+	0.0893296i
$221$	−275.711	+	114.203i	−0.0839199	+	0.0347608i
$222$	−2838.01	+	830.663i	−0.857994	+	0.251128i
$223$	1719.35	−	1719.35i	0.516307	−	0.516307i	−0.400145	−	0.916452i	$-0.631040\pi$
$223$	1719.35	−	1719.35i	0.516307	−	0.516307i	0.916452	+	0.400145i	$0.131040\pi$
$224$	−2151.14	−	318.739i	−0.641649	−	0.0950744i
$225$	212.366	+	1676.55i	0.0629233	+	0.496757i
$226$	1968.63	−	3597.91i	0.579430	−	1.05898i
$227$	4349.50	+	1801.62i	1.27175	+	0.526775i	0.913495	−	0.406850i	$-0.133373\pi$
$227$	4349.50	+	1801.62i	1.27175	+	0.526775i	0.358252	+	0.933625i	$0.383373\pi$
$228$	−582.056	+	372.651i	−0.169069	+	0.108243i
$229$	−893.817	−	370.231i	−0.257926	−	0.106836i	0.249974	−	0.968253i	$-0.419578\pi$
$229$	−893.817	−	370.231i	−0.257926	−	0.106836i	−0.507900	+	0.861416i	$0.669578\pi$
$230$	105.332	−	2341.13i	0.0301973	−	0.671172i
$231$	−102.844	+	102.844i	−0.0292928	+	0.0292928i
$232$	−2534.34	−	850.784i	−0.717189	−	0.240762i
$233$	−620.995			−0.174604			−0.0873021	−	0.996182i	$-0.527825\pi$
$233$	−620.995			−0.174604			−0.0873021	+	0.996182i	$0.527825\pi$
$234$	1263.82	−	1016.66i	0.353072	−	0.284023i
$235$	4053.19	−	1986.47i	1.12511	−	0.551418i
$236$	−1201.45	−	6725.38i	−0.331388	−	1.85502i
$237$	−405.133	−	167.812i	−0.111039	−	0.0459938i
$238$	114.749	−	209.718i	0.0312524	−	0.0571176i
$239$			3556.78i			0.962633i	0.876547	+	0.481316i	$0.159841\pi$
$239$			3556.78i			0.962633i	−0.876547	+	0.481316i	$0.840159\pi$
$240$	−1062.98	−	2402.50i	−0.285897	−	0.646171i
$241$			2502.17i			0.668793i	0.942433	+	0.334396i	$0.108532\pi$
$241$			2502.17i			0.668793i	−0.942433	+	0.334396i	$0.891468\pi$
$242$	−3275.61	−	1792.28i	−0.870100	−	0.476083i
$243$	3096.42	+	1282.58i	0.817431	+	0.338591i
$244$	−1244.27	+	1785.53i	−0.326461	+	0.468470i
$245$	2101.69	+	719.178i	0.548049	+	0.187537i
$246$	2632.35	+	3272.31i	0.682246	+	0.848108i
$247$	998.061			0.257106
$248$	192.715	+	167.861i	0.0493444	+	0.0429807i
$249$	−2481.05	+	2481.05i	−0.631447	+	0.631447i
$250$	−3012.17	−	2559.66i	−0.762025	−	0.647548i
$251$	−4121.90	−	1707.35i	−1.03654	−	0.429349i	−0.201472	−	0.979494i	$-0.564572\pi$
$251$	−4121.90	−	1707.35i	−1.03654	−	0.429349i	−0.835069	+	0.550145i	$0.814572\pi$
$252$	−278.373	+	1269.14i	−0.0695868	+	0.317256i
$253$	−225.768	−	93.5161i	−0.0561024	−	0.0232384i
$254$	−1949.99	−	1066.95i	−0.481705	−	0.263569i
$255$	288.232	−	18.1823i	0.0707835	−	0.00446517i
$256$	−2660.94	−	3113.94i	−0.649643	−	0.760239i
$257$	4484.98	−	4484.98i	1.08858	−	1.08858i	0.0929061	−	0.995675i	$-0.470384\pi$
$257$	4484.98	−	4484.98i	1.08858	−	1.08858i	0.995675	−	0.0929061i	$-0.0296156\pi$
$258$	−1110.91	−	3795.49i	−0.268071	−	0.915879i
$259$	−3160.40	+	1309.08i	−0.758214	+	0.314063i
$260$	−577.909	+	3749.62i	−0.137848	+	0.894390i
$261$	−611.255	+	1475.70i	−0.144965	+	0.349975i
$262$	504.716	+	627.419i	0.119013	+	0.147947i
$263$	4897.27			1.14821			0.574104	−	0.818783i	$-0.305351\pi$
$263$	4897.27			1.14821			0.574104	+	0.818783i	$0.305351\pi$
$264$	−273.300	+	18.8379i	−0.0637138	+	0.00439163i
$265$	−140.805	−	2232.09i	−0.0326398	−	0.517419i
$266$	−622.961	+	501.131i	−0.143595	+	0.115512i
$267$	1242.11	+	2998.73i	0.284704	+	0.687337i
$268$	2521.65	−	450.477i	0.574755	−	0.102676i
$269$	5017.63	−	2078.37i	1.13729	−	0.471080i	0.267036	−	0.963687i	$-0.413956\pi$
$269$	5017.63	−	2078.37i	1.13729	−	0.471080i	0.870252	+	0.492607i	$0.163956\pi$
$270$	−4422.95	+	1603.17i	−0.996934	+	0.361355i
$271$	−6941.79			−1.55603			−0.778015	−	0.628246i	$-0.783773\pi$
$271$	−6941.79			−1.55603			−0.778015	+	0.628246i	$0.783773\pi$
$272$	422.425	−	155.902i	0.0941664	−	0.0347535i
$273$	−1322.93	+	1322.93i	−0.293287	+	0.293287i
$274$	1053.69	+	3600.00i	0.232321	+	0.793737i
$275$	−357.969	+	204.340i	−0.0784958	+	0.0448079i
$276$	2142.81	−	382.800i	0.467327	−	0.0834849i
$277$	6660.67	−	2758.94i	1.44477	−	0.598442i	0.483819	−	0.875168i	$-0.339249\pi$
$277$	6660.67	−	2758.94i	1.44477	−	0.598442i	0.960949	+	0.276726i	$0.0892494\pi$
$278$	4097.34	+	444.077i	0.883965	+	0.0958055i
$279$	107.976	−	107.976i	0.0231696	−	0.0231696i
$280$	−1521.98	−	2630.57i	−0.324842	−	0.561453i
$281$	5299.69	+	5299.69i	1.12510	+	1.12510i	0.990963	+	0.134136i	$0.0428260\pi$
$281$	5299.69	+	5299.69i	1.12510	+	1.12510i	0.134136	+	0.990963i	$0.457174\pi$
$282$	2627.92	+	3266.80i	0.554930	+	0.689840i
$283$	−2363.06	−	5704.94i	−0.496359	−	1.19832i	−0.951431	−	0.307861i	$-0.900387\pi$
$283$	−2363.06	−	5704.94i	−0.496359	−	1.19832i	0.455073	−	0.890454i	$-0.349613\pi$
$284$	402.797	−	1836.41i	0.0841605	−	0.383700i
$285$	−913.858	−	312.713i	−0.189938	−	0.0649949i
$286$	347.055	+	189.894i	0.0717546	+	0.0392611i
$287$	3435.30	+	3435.30i	0.706548	+	0.706548i
$288$	−1965.46	+	1458.18i	−0.402139	+	0.298347i
$289$		−	4863.50i		−	0.989925i
$290$	−1273.16	−	3512.48i	−0.257801	−	0.711242i
$291$	1984.94	+	4792.07i	0.399860	+	0.965348i
$292$	−2775.33	+	1776.85i	−0.556212	+	0.356105i
$293$	−4666.87	+	1933.08i	−0.930518	+	0.385433i	−0.795875	−	0.605461i	$-0.792989\pi$
$293$	−4666.87	+	1933.08i	−0.930518	+	0.385433i	−0.134643	+	0.990894i	$0.542989\pi$
$294$	−222.318	+	2051.25i	−0.0441015	+	0.406910i
$295$	6312.88	−	7162.97i	1.24593	−	1.41371i
$296$	−6108.19	−	2050.53i	−1.19943	−	0.402651i
$297$			490.568i			0.0958439i
$298$	−29.6287	+	273.374i	−0.00575956	+	0.0531415i
$299$	−2904.15	−	1202.94i	−0.561711	−	0.232668i
$300$	1703.99	−	3252.20i	0.327932	−	0.625887i
$301$	−1750.73	−	4226.64i	−0.335251	−	0.809368i
$302$	3812.97	+	2086.30i	0.726529	+	0.397527i
$303$	−999.033	−	999.033i	−0.189416	−	0.189416i
$304$	−1504.75	−	58.9284i	−0.283893	−	0.0111177i
$305$	−3035.45	+	191.483i	−0.569867	+	0.0359484i
$306$	−75.5735	−	258.201i	−0.0141185	−	0.0482366i
$307$	862.973	−	2083.40i	0.160431	−	0.387316i	−0.823139	−	0.567840i	$-0.807779\pi$
$307$	862.973	−	2083.40i	0.160431	−	0.387316i	0.983571	+	0.180524i	$0.0577793\pi$
$308$	−311.969	+	55.7312i	−0.0577145	+	0.0103103i
$309$	803.352	−	1939.46i	0.147900	−	0.357062i
$310$	−16.0536	+	356.810i	−0.00294123	+	0.0653725i
$311$	4929.83	+	4929.83i	0.898858	+	0.898858i	0.995335	−	0.0964774i	$-0.0307576\pi$
$311$	4929.83	+	4929.83i	0.898858	+	0.898858i	−0.0964774	+	0.995335i	$0.530758\pi$
$312$	−3515.58	+	242.320i	−0.637918	+	0.0439701i
$313$			302.961i			0.0547105i	0.999626	+	0.0273552i	$0.00870853\pi$
$313$			302.961i			0.0547105i	−0.999626	+	0.0273552i	$0.991291\pi$
$314$	−655.988	+	6052.58i	−0.117897	+	1.08779i
$315$	−1630.55	+	799.134i	−0.291654	+	0.142940i
$316$	−515.187	−	804.688i	−0.0917137	−	0.143251i
$317$	3629.48	−	8762.33i	0.643065	−	1.55250i	−0.179458	−	0.983766i	$-0.557434\pi$
$317$	3629.48	−	8762.33i	0.643065	−	1.55250i	0.822523	−	0.568731i	$-0.192566\pi$
$318$	1993.73	−	583.549i	0.351581	−	0.102905i
$319$	−389.584			−0.0683778
$320$	1092.69	−	5619.08i	0.190885	−	0.981612i
$321$	−5563.94			−0.967443
$322$	2416.69	−	707.346i	0.418251	−	0.122419i
$323$	63.3513	−	152.944i	0.0109132	−	0.0263468i
$324$	−781.575	−	1220.77i	−0.134015	−	0.209322i
$325$	−4604.71	+	2628.52i	−0.785919	+	0.448627i
$326$	598.279	−	5520.12i	0.101643	−	0.937825i
$327$		−	926.702i		−	0.156718i
$328$	629.241	+	9129.04i	0.105927	+	1.53679i
$329$	3429.52	+	3429.52i	0.574697	+	0.574697i
$330$	−258.278	−	282.613i	−0.0430840	−	0.0471435i
$331$	−1900.28	+	4587.67i	−0.315555	+	0.761816i	0.683925	+	0.729553i	$0.260272\pi$
$331$	−1900.28	+	4587.67i	−0.315555	+	0.761816i	−0.999479	+	0.0322637i	$0.989728\pi$
$332$	−7526.07	+	1344.48i	−1.24412	+	0.222253i
$333$	−1473.23	+	3556.68i	−0.242439	+	0.585300i
$334$	633.395	+	2164.03i	0.103766	+	0.354523i
$335$	2685.72	+	2366.99i	0.438020	+	0.386037i
$336$	2072.65	−	1916.44i	0.336526	−	0.311161i
$337$	715.985	+	715.985i	0.115733	+	0.115733i	0.762602	−	0.646868i	$-0.223922\pi$
$337$	715.985	+	715.985i	0.115733	+	0.115733i	−0.646868	+	0.762602i	$0.723922\pi$
$338$	−987.056	−	540.077i	−0.158843	−	0.0869121i
$339$	2037.35	+	4918.59i	0.326412	+	0.788027i
$340$	537.911	+	326.564i	0.0858010	+	0.0520894i
$341$	34.4092	+	14.2528i	0.00546441	+	0.00226343i
$342$	−96.9495	+	894.521i	−0.0153287	+	0.141433i
$343$			6507.36i			1.02439i
$344$	2742.33	−	8168.96i	0.429816	−	1.28035i
$345$	2282.23	+	2011.38i	0.356149	+	0.313882i
$346$	−1141.45	+	10531.8i	−0.177355	+	1.63639i
$347$	−2394.57	+	991.865i	−0.370454	+	0.153447i	−0.560140	−	0.828398i	$-0.689253\pi$
$347$	−2394.57	+	991.865i	−0.370454	+	0.153447i	0.189687	+	0.981845i	$0.439253\pi$
$348$	2922.58	−	1871.13i	0.450192	−	0.288227i
$349$	−69.2537	−	167.193i	−0.0106220	−	0.0256437i	0.918480	−	0.395468i	$-0.129418\pi$
$349$	−69.2537	−	167.193i	−0.0106220	−	0.0256437i	−0.929102	+	0.369825i	$0.879418\pi$
$350$	1554.34	−	3952.69i	0.237380	−	0.603658i
$351$			6310.39i			0.959612i
$352$	−512.034	−	306.790i	−0.0775327	−	0.0464544i
$353$	−5731.93	−	5731.93i	−0.864248	−	0.864248i	0.127580	−	0.991828i	$-0.459279\pi$
$353$	−5731.93	−	5731.93i	−0.864248	−	0.864248i	−0.991828	+	0.127580i	$0.959279\pi$
$354$	7779.94	+	4256.86i	1.16808	+	0.639123i
$355$	2359.35	−	1156.32i	0.352735	−	0.172876i
$356$	−1515.21	+	6908.07i	−0.225579	+	1.02845i
$357$	118.754	+	286.699i	0.0176055	+	0.0425033i
$358$	7539.03	+	9371.86i	1.11299	+	1.38357i
$359$	6048.49	+	6048.49i	0.889212	+	0.889212i	0.994447	−	0.105236i	$-0.0335597\pi$
$359$	6048.49	+	6048.49i	0.889212	+	0.889212i	−0.105236	+	0.994447i	$0.533560\pi$
$360$	−3304.49	−	882.186i	−0.483783	−	0.129154i
$361$	4458.56	−	4458.56i	0.650030	−	0.650030i
$362$	8138.20	+	882.031i	1.18159	+	0.128062i
$363$	4477.98	−	1854.84i	0.647474	−	0.268193i
$364$	−4012.99	+	716.895i	−0.577851	+	0.103229i
$365$	−4357.41	−	1491.06i	−0.624869	−	0.213824i
$366$	−793.578	−	2711.30i	−0.113336	−	0.387219i
$367$	391.822	−	391.822i	0.0557301	−	0.0557301i	−0.678692	−	0.734423i	$-0.737453\pi$
$367$	391.822	−	391.822i	0.0557301	−	0.0557301i	0.734423	+	0.678692i	$0.237453\pi$
$368$	4307.49	+	1985.11i	0.610173	+	0.281198i
$369$	5467.43			0.771336
$370$	−3068.52	−	8465.67i	−0.431148	−	1.18948i
$371$	2220.21	−	919.641i	0.310694	−	0.128694i
$372$	−326.585	+	58.3423i	−0.0455179	+	0.00813148i
$373$	2834.72	+	6843.62i	0.393502	+	0.949997i	0.989171	+	0.146767i	$0.0468869\pi$
$373$	2834.72	+	6843.62i	0.393502	+	0.949997i	−0.595669	+	0.803230i	$0.703113\pi$
$374$	51.1286	−	41.1296i	0.00706898	−	0.00568652i
$375$	5039.80	−	964.007i	0.694011	−	0.132750i
$376$	628.182	+	9113.67i	0.0861596	+	1.25000i
$377$	−5011.39			−0.684615
$378$	−3168.47	−	3938.77i	−0.431134	−	0.535948i
$379$	−701.841	+	1694.39i	−0.0951218	+	0.229644i	−0.964277	−	0.264894i	$-0.914663\pi$
$379$	−701.841	+	1694.39i	−0.0951218	+	0.229644i	0.869156	+	0.494539i	$0.164663\pi$
$380$	−1244.10	−	1697.47i	−0.167950	−	0.229154i
$381$	2665.76	−	1104.20i	0.358455	−	0.148477i
$382$	−2179.85	−	7447.59i	−0.291966	−	0.997518i
$383$	−2861.48	+	2861.48i	−0.381762	+	0.381762i	−0.871737	−	0.489975i	$-0.837006\pi$
$383$	−2861.48	+	2861.48i	−0.381762	+	0.381762i	0.489975	+	0.871737i	$0.337006\pi$
$384$	5314.65	−	157.770i	0.706282	−	0.0209665i
$385$	−332.267	−	292.834i	−0.0439841	−	0.0387642i
$386$	9058.44	+	4956.41i	1.19446	+	0.653561i
$387$	−4756.63	−	1970.26i	−0.624788	−	0.258796i
$388$	−2421.37	+	11039.3i	−0.316820	+	1.44443i
$389$	11410.7	+	4726.46i	1.48726	+	0.616044i	0.970719	−	0.240218i	$-0.0772189\pi$
$389$	11410.7	+	4726.46i	1.48726	+	0.616044i	0.516542	+	0.856262i	$0.327219\pi$
$390$	−3322.34	−	3635.38i	−0.431367	−	0.472012i
$391$	−368.679	+	368.679i	−0.0476851	+	0.0476851i
$392$	−2952.79	+	3389.98i	−0.380455	+	0.436786i
$393$	−1045.26			−0.134164
$394$	−1015.76	−	1262.71i	−0.129882	−	0.161457i
$395$	432.324	−	1263.40i	0.0550698	−	0.160933i
$396$	−203.907	+	292.605i	−0.0258755	+	0.0371312i
$397$	−12573.3	−	5208.01i	−1.58950	−	0.658395i	−0.599622	−	0.800283i	$-0.704683\pi$
$397$	−12573.3	−	5208.01i	−1.58950	−	0.658395i	−0.989883	+	0.141889i	$0.954683\pi$
$398$	−4494.92	−	2459.44i	−0.566106	−	0.309750i
$399$		−	1037.84i		−	0.130218i
$400$	7097.60	−	3691.07i	0.887200	−	0.461384i
$401$		−	13793.5i		−	1.71775i	−0.512189	−	0.858873i	$-0.671165\pi$
$401$		−	13793.5i		−	1.71775i	0.512189	−	0.858873i	$-0.328835\pi$
$402$	−1596.09	+	2917.05i	−0.198024	+	0.361914i
$403$	442.621	+	183.339i	0.0547109	+	0.0226620i
$404$	−541.376	−	3030.48i	−0.0666695	−	0.373198i
$405$	655.865	−	1916.67i	0.0804697	−	0.235161i
$406$	3127.97	−	2516.24i	0.382361	−	0.307584i
$407$	−938.963			−0.114355
$408$	−186.016	+	554.111i	−0.0225715	+	0.0672367i
$409$	7402.41	−	7402.41i	0.894928	−	0.894928i	−0.100054	−	0.994982i	$-0.531902\pi$
$409$	7402.41	−	7402.41i	0.894928	−	0.894928i	0.994982	+	0.100054i	$0.0319016\pi$
$410$	−9440.13	+	8627.24i	−1.13711	+	1.03919i
$411$	−4498.55	−	1863.36i	−0.539896	−	0.223632i
$412$	3852.22	−	2466.32i	0.460644	−	0.294919i
$413$	9478.16	+	3925.98i	1.12927	+	0.467760i
$414$	1360.25	−	2486.02i	0.161480	−	0.295124i
$415$	−8015.75	−	7064.46i	−0.948139	−	0.835616i
$416$	−6586.52	−	3946.37i	−0.776276	−	0.465113i
$417$	−3782.94	+	3782.94i	−0.444248	+	0.444248i
$418$	−210.618	+	61.6463i	−0.0246452	+	0.00721345i
$419$	−13020.6	+	5393.31i	−1.51813	+	0.628832i	−0.977217	−	0.212243i	$-0.931923\pi$
$419$	−13020.6	+	5393.31i	−1.51813	+	0.628832i	−0.540918	+	0.841075i	$0.681923\pi$
$420$	3899.05	+	600.941i	0.452986	+	0.0698165i
$421$	−4952.26	+	11955.8i	−0.573298	+	1.38406i	0.325435	+	0.945565i	$0.394489\pi$
$421$	−4952.26	+	11955.8i	−0.573298	+	1.38406i	−0.898732	+	0.438498i	$0.855511\pi$
$422$	3502.28	−	2817.35i	0.404001	−	0.324991i
$423$	5458.22			0.627395
$424$	4291.07	+	1440.52i	0.491492	+	0.164995i
$425$	110.515	+	872.473i	0.0126135	+	0.0995792i
$426$	1529.70	+	1901.59i	0.173977	+	0.216273i
$427$	−1250.63	−	3019.30i	−0.141739	−	0.342188i
$428$	−9946.43	−	6931.33i	−1.12331	−	0.782800i
$429$	−474.448	+	196.523i	−0.0533953	+	0.0221170i
$430$	11321.8	−	4103.77i	1.26973	−	0.460236i
$431$	−10639.1			−1.18902			−0.594509	−	0.804089i	$-0.702653\pi$
$431$	−10639.1			−1.18902			−0.594509	+	0.804089i	$0.702653\pi$
$432$	372.583	−	9514.01i	0.0414952	−	1.05959i
$433$	1433.14	−	1433.14i	0.159059	−	0.159059i	−0.623091	−	0.782150i	$-0.714123\pi$
$433$	1433.14	−	1433.14i	0.159059	−	0.159059i	0.782150	+	0.623091i	$0.214123\pi$
$434$	−368.327	+	107.806i	−0.0407379	+	0.0119237i
$435$	4588.60	+	1570.17i	0.505762	+	0.173067i
$436$	1154.45	−	1656.63i	0.126807	−	0.181968i
$437$	1611.01	−	667.301i	0.176350	−	0.0730465i
$438$	460.929	−	4252.84i	0.0502832	−	0.463946i
$439$	4484.72	−	4484.72i	0.487572	−	0.487572i	−0.419967	−	0.907539i	$-0.637958\pi$
$439$	4484.72	−	4484.72i	0.487572	−	0.487572i	0.907539	+	0.419967i	$0.137958\pi$
$440$	−109.644	−	826.967i	−0.0118797	−	0.0896003i
$441$	1899.36	+	1899.36i	0.205092	+	0.205092i
$442$	657.690	−	529.068i	0.0707763	−	0.0569348i
$443$	−4858.96	−	11730.6i	−0.521120	−	1.25810i	−0.937208	−	0.348771i	$-0.886599\pi$
$443$	−4858.96	−	11730.6i	−0.521120	−	1.25810i	0.416088	−	0.909325i	$-0.363401\pi$
$444$	7043.91	−	4509.74i	0.752903	−	0.482033i
$445$	−8875.22	+	4349.76i	−0.945451	+	0.463367i
$446$	−3301.19	+	6033.33i	−0.350484	+	0.640552i
$447$	−252.398	−	252.398i	−0.0267069	−	0.0267069i
$448$	6092.61	−	843.906i	0.642520	−	0.0889974i
$449$			10769.6i			1.13195i	0.824421	+	0.565977i	$0.191501\pi$
$449$			10769.6i			1.13195i	−0.824421	+	0.565977i	$0.808499\pi$
$450$	−1908.54	−	4382.34i	−0.199932	−	0.459079i
$451$	510.318	+	1232.02i	0.0532815	+	0.128633i
$452$	−2485.29	+	11330.8i	−0.258625	+	1.17911i
$453$	−5212.59	+	2159.13i	−0.540638	+	0.223939i
$454$	−13238.3	−	1434.79i	−1.36851	−	0.148322i
$455$	−4274.10	−	3766.86i	−0.440380	−	0.388116i
$456$	1283.94	−	1474.03i	0.131855	−	0.151377i
$457$		−	5003.28i		−	0.512130i	−0.966660	−	0.256065i	$-0.917574\pi$
$457$		−	5003.28i		−	0.512130i	0.966660	−	0.256065i	$-0.0824262\pi$
$458$	2720.46	+	294.848i	0.277552	+	0.0300815i
$459$	967.009	+	400.548i	0.0983357	+	0.0407320i
$460$	1574.16	+	6438.78i	0.159555	+	0.652630i
$461$	−6353.32	−	15338.3i	−0.641874	−	1.54962i	−0.824149	−	0.566373i	$-0.808346\pi$
$461$	−6353.32	−	15338.3i	−0.641874	−	1.54962i	0.182276	−	0.983247i	$-0.441654\pi$
$462$	197.462	−	360.886i	0.0198848	−	0.0363419i
$463$	−12644.4	−	12644.4i	−1.26919	−	1.26919i	−0.946507	−	0.322684i	$-0.895415\pi$
$463$	−12644.4	−	12644.4i	−1.26919	−	1.26919i	−0.322684	−	0.946507i	$-0.604585\pi$
$464$	7555.55	+	295.887i	0.755943	+	0.0296039i
$465$	−347.834	−	306.554i	−0.0346891	−	0.0305723i
$466$	1685.72	−	493.396i	0.167574	−	0.0490475i
$467$	−3859.29	+	9317.15i	−0.382413	+	0.923225i	0.609086	+	0.793104i	$0.291537\pi$
$467$	−3859.29	+	9317.15i	−0.382413	+	0.923225i	−0.991498	+	0.130121i	$0.958463\pi$
$468$	−2622.94	+	3763.91i	−0.259072	+	0.371767i
$469$	−1472.03	+	3553.79i	−0.144930	+	0.349891i
$470$	−9424.24	+	8612.72i	−0.924910	+	0.845267i
$471$	−5588.15	−	5588.15i	−0.546684	−	0.546684i
$472$	8604.85	+	17301.7i	0.839132	+	1.68724i
$473$		−	1255.75i		−	0.122071i
$474$	1233.08	+	133.643i	0.119488	+	0.0129503i
$475$	775.162	−	2837.23i	0.0748777	−	0.274066i
$476$	−144.865	+	660.458i	−0.0139493	+	0.0635967i
$477$	1034.96	−	2498.60i	0.0993446	−	0.239839i
$478$	−2825.95	−	9655.03i	−0.270410	−	0.923872i
$479$	−10719.2			−1.02249			−0.511245	−	0.859435i	$-0.670816\pi$
$479$	−10719.2			−1.02249			−0.511245	+	0.859435i	$0.670816\pi$
$480$	4794.36	+	5677.13i	0.455899	+	0.539842i
$481$	−12078.3			−1.14495
$482$	−1988.04	−	6792.25i	−0.187869	−	0.641864i
$483$	−1250.88	+	3019.89i	−0.117841	+	0.284492i
$484$	10315.8	+	2262.66i	0.968800	+	0.212496i
$485$	−14182.9	+	6951.08i	−1.32786	+	0.650788i
$486$	−9424.41	−	1021.43i	−0.879630	−	0.0953356i
$487$		−	6357.86i		−	0.591585i	−0.955252	−	0.295793i	$-0.904416\pi$
$487$		−	6357.86i		−	0.591585i	0.955252	−	0.295793i	$-0.0955837\pi$
$488$	1958.98	−	5835.49i	0.181719	−	0.541312i
$489$	5096.54	+	5096.54i	0.471316	+	0.471316i
$490$	−6276.53	−	282.393i	−0.578662	−	0.0260351i
$491$	−1004.38	+	2424.78i	−0.0923153	+	0.222869i	−0.963292	−	0.268455i	$-0.913487\pi$
$491$	−1004.38	+	2424.78i	−0.0923153	+	0.222869i	0.870977	+	0.491324i	$0.163487\pi$
$492$	−9745.55	−	6791.34i	−0.893015	−	0.622312i
$493$	−318.095	+	767.950i	−0.0290594	+	0.0701556i
$494$	−2709.28	+	792.984i	−0.246753	+	0.0722227i
$495$	−497.438	+	31.3794i	−0.0451680	+	0.00284929i
$496$	−656.503	−	302.550i	−0.0594312	−	0.0273889i
$497$	1996.31	+	1996.31i	0.180174	+	0.180174i
$498$	4763.66	−	8706.18i	0.428644	−	0.783400i
$499$	−6137.21	−	14816.5i	−0.550580	−	1.32922i	−0.917044	−	0.398785i	$-0.869432\pi$
$499$	−6137.21	−	14816.5i	−0.550580	−	1.32922i	0.366465	−	0.930432i	$-0.380568\pi$
$500$	10210.4	+	4555.06i	0.913242	+	0.407417i
$501$	−2704.17	−	1120.10i	−0.241145	−	0.0998854i
$502$	12545.6	+	1359.71i	1.11541	+	0.120890i
$503$		−	248.276i		−	0.0220081i	−0.999939	−	0.0110041i	$-0.996497\pi$
$503$		−	248.276i		−	0.0220081i	0.999939	−	0.0110041i	$-0.00350277\pi$
$504$	−252.710	−	3666.32i	−0.0223345	−	0.324029i
$505$	2844.61	−	3227.66i	0.250660	−	0.284414i
$506$	687.157	+	74.4752i	0.0603713	+	0.00654313i
$507$	1349.37	−	558.929i	0.118201	−	0.0489604i
$508$	6141.03	+	1346.97i	0.536347	+	0.117642i
$509$	1291.12	+	3117.03i	0.112432	+	0.271434i	0.970073	−	0.242815i	$-0.0780708\pi$
$509$	1291.12	+	3117.03i	0.112432	+	0.271434i	−0.857641	+	0.514249i	$0.828071\pi$
$510$	−767.972	+	278.364i	−0.0666791	+	0.0241690i
$511$		−	4948.56i		−	0.428398i
$512$	9697.33	+	6338.73i	0.837042	+	0.547139i
$513$	−2475.25	−	2475.25i	−0.213031	−	0.213031i
$514$	−8611.23	+	15738.1i	−0.738959	+	1.35054i
$515$	6048.19	+	2069.63i	0.517505	+	0.177085i
$516$	6031.22	+	9420.36i	0.514554	+	0.803699i
$517$	509.459	+	1229.94i	0.0433385	+	0.104628i
$518$	7538.93	−	6064.56i	0.639462	−	0.514405i
$519$	−9723.63	−	9723.63i	−0.822389	−	0.822389i
$520$	−1410.40	−	10637.6i	−0.118943	−	0.897099i
$521$	8649.79	−	8649.79i	0.727360	−	0.727360i	−0.242733	−	0.970093i	$-0.578044\pi$
$521$	8649.79	−	8649.79i	0.727360	−	0.727360i	0.970093	+	0.242733i	$0.0780440\pi$
$522$	486.796	−	4491.51i	0.0408170	−	0.376605i
$523$	19033.9	−	7884.10i	1.59138	−	0.659173i	0.601221	−	0.799083i	$-0.294681\pi$
$523$	19033.9	−	7884.10i	1.59138	−	0.659173i	0.990164	+	0.139910i	$0.0446813\pi$
$524$	−1868.57	−	1302.14i	−0.155780	−	0.108558i
$525$	2733.27	+	4788.23i	0.227219	+	0.398048i
$526$	−13293.8	+	3891.00i	−1.10197	+	0.322539i
$527$	56.1901	−	56.1901i	0.00464456	−	0.00464456i
$528$	726.917	−	268.280i	0.0599147	−	0.0221125i
$529$	6675.02			0.548617
$530$	2155.67	+	5947.22i	0.176672	+	0.487416i
$531$	10666.6	−	4418.27i	0.871738	−	0.361086i
$532$	1292.89	−	1855.30i	0.105365	−	0.151198i
$533$	6564.45	+	15848.0i	0.533467	+	1.28790i
$534$	−5754.33	−	7153.27i	−0.466319	−	0.579686i
$535$	−1066.67	−	16909.2i	−0.0861984	−	1.36645i
$536$	−6487.21	+	3226.35i	−0.522770	+	0.259995i
$537$	−15613.3			−1.25468
$538$	−11969.2	+	9628.46i	−0.959165	+	0.771584i
$539$	−250.715	+	605.280i	−0.0200354	+	0.0483697i
$540$	10732.5	−	7866.02i	0.855285	−	0.626851i
$541$	−3342.03	+	1384.31i	−0.265591	+	0.110012i	−0.511505	−	0.859280i	$-0.670912\pi$
$541$	−3342.03	+	1384.31i	−0.265591	+	0.110012i	0.245914	+	0.969292i	$0.420912\pi$
$542$	18843.8	−	5515.43i	1.49338	−	0.437099i
$543$	−7513.73	+	7513.73i	−0.593822	+	0.593822i
$544$	−1022.82	+	758.830i	−0.0806123	+	0.0598062i
$545$	2816.32	−	177.659i	0.221354	−	0.0139634i
$546$	2540.04	−	4642.24i	0.199091	−	0.363864i
$547$	12556.2	+	5200.96i	0.981472	+	0.406539i	0.814971	−	0.579502i	$-0.196753\pi$
$547$	12556.2	+	5200.96i	0.981472	+	0.406539i	0.166501	+	0.986041i	$0.446753\pi$
$548$	−5720.58	−	8935.16i	−0.445933	−	0.696517i
$549$	−3397.89	−	1407.45i	−0.264150	−	0.109415i
$550$	809.368	−	839.105i	0.0627483	−	0.0650537i
$551$	1965.72	−	1965.72i	0.151983	−	0.151983i
$552$	−5512.61	+	2741.64i	−0.425058	+	0.211399i
$553$	1434.80			0.110333
$554$	−15888.6	+	12781.3i	−1.21849	+	0.980191i
$555$	11059.3	+	3784.38i	0.845840	+	0.289438i
$556$	−11475.2	+	2049.98i	−0.875285	+	0.156364i
$557$	−3309.42	−	1370.80i	−0.251749	−	0.104278i	0.253240	−	0.967403i	$-0.418504\pi$
$557$	−3309.42	−	1370.80i	−0.251749	−	0.104278i	−0.504990	+	0.863125i	$0.668504\pi$
$558$	−207.315	+	378.893i	−0.0157282	+	0.0287452i
$559$		−	16153.2i		−	1.22220i
$560$	6221.54	+	5931.55i	0.469479	+	0.447596i
$561$			85.1789i			0.00641044i
$562$	−18596.9	−	10175.5i	−1.39585	−	0.763749i
$563$	18580.6	+	7696.35i	1.39091	+	0.576132i	0.947375	−	0.320126i	$-0.103725\pi$
$563$	18580.6	+	7696.35i	1.39091	+	0.576132i	0.443532	+	0.896259i	$0.353725\pi$
$564$	−9729.15	−	6779.91i	−0.726367	−	0.506180i
$565$	−14557.4	+	7134.60i	−1.08395	+	0.531247i
$566$	10947.3	+	13608.8i	0.812988	+	1.01063i
$567$	2176.69			0.161221
$568$	365.662	+	5305.03i	0.0270121	+	0.391891i
$569$	2801.08	−	2801.08i	0.206375	−	0.206375i	−0.596350	−	0.802725i	$-0.703383\pi$
$569$	2801.08	−	2801.08i	0.206375	−	0.206375i	0.802725	+	0.596350i	$0.203383\pi$
$570$	2729.16	+	122.790i	0.200548	+	0.00902301i
$571$	16021.3	+	6636.24i	1.17420	+	0.486372i	0.882581	−	0.470161i	$-0.155804\pi$
$571$	16021.3	+	6636.24i	1.17420	+	0.486372i	0.291624	+	0.956533i	$0.405804\pi$
$572$	−1092.97	−	239.732i	−0.0798941	−	0.0175239i
$573$	9306.50	+	3854.88i	0.678507	+	0.281047i
$574$	−12054.7	−	6595.83i	−0.876573	−	0.479625i
$575$	−5675.22	+	7321.48i	−0.411605	+	0.531003i
$576$	4176.77	−	5519.89i	0.302139	−	0.399297i
$577$	−568.339	+	568.339i	−0.0410056	+	0.0410056i	−0.727312	−	0.686307i	$-0.759231\pi$
$577$	−568.339	+	568.339i	−0.0410056	+	0.0410056i	0.686307	+	0.727312i	$0.259231\pi$
$578$	3864.17	+	13202.2i	0.278077	+	0.950066i
$579$	−12383.5	+	5129.42i	−0.888845	+	0.368172i
$580$	6246.79	+	8523.22i	0.447214	+	0.610185i
$581$	4393.39	−	10606.6i	0.313715	−	0.757375i
$582$	−9195.63	−	11431.2i	−0.654933	−	0.814155i
$583$	659.631			0.0468595
$584$	6121.99	−	7028.41i	0.433784	−	0.498010i
$585$	−6398.76	+	403.647i	−0.452233	+	0.0285278i
$586$	11132.5	−	8955.38i	0.784780	−	0.631303i
$587$	−3809.50	−	9196.94i	−0.267862	−	0.646675i	0.731521	−	0.681819i	$-0.238811\pi$
$587$	−3809.50	−	9196.94i	−0.267862	−	0.646675i	−0.999382	+	0.0351441i	$0.988811\pi$
$588$	−1026.28	−	5744.84i	−0.0719780	−	0.402914i
$589$	−245.533	+	101.703i	−0.0171766	+	0.00711477i
$590$	−11445.4	+	24459.9i	−0.798645	+	1.70678i
$591$	2103.63			0.146416
$592$	18210.1	+	713.137i	1.26424	+	0.0495097i
$593$	6443.67	−	6443.67i	0.446222	−	0.446222i	−0.447874	−	0.894097i	$-0.647819\pi$
$593$	6443.67	−	6443.67i	0.446222	−	0.446222i	0.894097	+	0.447874i	$0.147819\pi$
$594$	−389.768	−	1331.67i	−0.0269232	−	0.0919847i
$595$	−848.531	+	415.867i	−0.0584645	+	0.0286536i
$596$	−136.774	−	765.627i	−0.00940016	−	0.0526196i
$597$	6144.86	−	2545.29i	0.421261	−	0.174492i
$598$	8839.21	+	958.007i	0.604452	+	0.0655114i
$599$	−301.285	+	301.285i	−0.0205512	+	0.0205512i	−0.717308	−	0.696757i	$-0.754626\pi$
$599$	−301.285	+	301.285i	−0.0205512	+	0.0205512i	0.696757	+	0.717308i	$0.254626\pi$
$600$	−2041.58	+	10182.1i	−0.138912	+	0.692804i
$601$	9472.78	+	9472.78i	0.642933	+	0.642933i	0.951275	−	0.308343i	$-0.0997743\pi$
$601$	9472.78	+	9472.78i	0.642933	+	0.642933i	−0.308343	+	0.951275i	$0.599774\pi$
$602$	8110.61	+	10082.4i	0.549109	+	0.682604i
$603$	1656.61	+	3999.41i	0.111878	+	0.270097i
$604$	−12008.1	−	2633.85i	−0.808943	−	0.177433i
$605$	6495.48	+	13253.3i	0.436494	+	0.890619i
$606$	3505.67	+	1918.16i	0.234997	+	0.128581i
$607$	13559.4	+	13559.4i	0.906686	+	0.906686i	0.996003	−	0.0893168i	$-0.0284684\pi$
$607$	13559.4	+	13559.4i	0.906686	+	0.906686i	−0.0893168	+	0.996003i	$0.528468\pi$
$608$	4131.53	−	1035.60i	0.275585	−	0.0690774i
$609$			5211.11i			0.346741i
$610$	8087.72	−	2931.53i	0.536823	−	0.194580i
$611$	6553.40	+	15821.3i	0.433915	+	1.04756i
$612$	410.295	+	640.853i	0.0271000	+	0.0423284i
$613$	174.614	−	72.3275i	0.0115050	−	0.00476554i	−0.376923	−	0.926244i	$-0.623018\pi$
$613$	174.614	−	72.3275i	0.0115050	−	0.00476554i	0.388429	+	0.921479i	$0.373018\pi$
$614$	−687.261	+	6341.13i	−0.0451720	+	0.416787i
$615$	−1045.13	−	16567.7i	−0.0685262	−	1.08630i
$616$	802.572	−	399.151i	0.0524944	−	0.0261076i
$617$			20159.2i			1.31537i	0.753295	+	0.657683i	$0.228463\pi$
$617$			20159.2i			1.31537i	−0.753295	+	0.657683i	$0.771537\pi$
$618$	−639.780	+	5903.04i	−0.0416436	+	0.384231i
$619$	−3799.70	−	1573.89i	−0.246725	−	0.102197i	0.255894	−	0.966705i	$-0.417630\pi$
$619$	−3799.70	−	1573.89i	−0.246725	−	0.102197i	−0.502619	+	0.864508i	$0.667630\pi$
$620$	−239.917	−	981.331i	−0.0155408	−	0.0635665i
$621$	4219.11	+	10185.8i	0.272636	+	0.658202i
$622$	−17299.1	−	9465.34i	−1.11516	−	0.610170i
$623$	−7509.57	−	7509.57i	−0.482929	−	0.482929i
$624$	9350.65	−	3451.00i	0.599881	−	0.221395i
$625$	3895.87	+	15131.5i	0.249336	+	0.968417i
$626$	−240.710	−	822.401i	−0.0153686	−	0.0525076i
$627$	109.016	−	263.188i	0.00694368	−	0.0167635i
$628$	−3028.22	−	16951.2i	−0.192419	−	1.07711i
$629$	−766.662	+	1850.89i	−0.0485991	+	0.117329i
$630$	3791.25	−	3464.79i	0.239757	−	0.219112i
$631$	15825.2	+	15825.2i	0.998400	+	0.998400i	0.999999	−	0.00159865i	$-0.000508866\pi$
$631$	15825.2	+	15825.2i	0.998400	+	0.998400i	−0.00159865	+	0.999999i	$0.500509\pi$
$632$	2037.84	+	1775.03i	0.128261	+	0.111720i
$633$			5834.70i			0.366364i
$634$	−2890.47	+	26669.4i	−0.181065	+	1.67063i
$635$	3866.79	+	7889.77i	0.241652	+	0.493064i
$636$	−4948.41	+	3168.13i	−0.308518	+	0.197523i
$637$	−3225.06	+	7785.98i	−0.200599	+	0.484289i
$638$	1057.54	−	309.534i	0.0656246	−	0.0192078i
$639$	3177.21			0.196696
$640$	1498.35	+	16121.4i	0.0925431	+	0.995709i
$641$	9340.81			0.575569			0.287785	−	0.957695i	$-0.407081\pi$
$641$	9340.81			0.575569			0.287785	+	0.957695i	$0.407081\pi$
$642$	15103.6	−	4420.69i	0.928489	−	0.271761i
$643$	5543.38	−	13382.9i	0.339984	−	0.820794i	−0.657732	−	0.753252i	$-0.728484\pi$
$643$	5543.38	−	13382.9i	0.339984	−	0.820794i	0.997716	−	0.0675422i	$-0.0215157\pi$
$644$	−5998.20	+	3840.24i	−0.367022	+	0.234979i
$645$	−5061.15	+	14790.5i	−0.308965	+	0.902905i
$646$	−50.4522	+	465.506i	−0.00307278	+	0.0283515i
$647$			31085.6i			1.88887i	0.328692	+	0.944437i	$0.393392\pi$
$647$			31085.6i			1.88887i	−0.328692	+	0.944437i	$0.606608\pi$
$648$	3091.55	+	2692.84i	0.187419	+	0.163248i
$649$	1991.20	+	1991.20i	0.120434	+	0.120434i
$650$	10411.3	−	10793.8i	0.628251	−	0.651333i
$651$	190.646	−	460.260i	0.0114777	−	0.0277097i
$652$	2761.82	+	15459.9i	0.165891	+	0.928616i
$653$	−10153.9	+	24513.6i	−0.608502	+	1.46905i	0.256127	+	0.966643i	$0.417553\pi$
$653$	−10153.9	+	24513.6i	−0.608502	+	1.46905i	−0.864629	+	0.502411i	$0.832447\pi$
$654$	736.288	+	2515.57i	0.0440231	+	0.150408i
$655$	−200.388	−	3176.63i	−0.0119539	−	0.189498i
$656$	−8961.35	−	24281.2i	−0.533356	−	1.44515i
$657$	−3937.92	−	3937.92i	−0.233840	−	0.233840i
$658$	−12034.4	−	6584.73i	−0.712993	−	0.390121i
$659$	993.473	+	2398.45i	0.0587256	+	0.141776i	0.950519	−	0.310667i	$-0.100552\pi$
$659$	993.473	+	2398.45i	0.0587256	+	0.141776i	−0.891793	+	0.452443i	$0.850552\pi$
$660$	925.648	+	561.957i	0.0545921	+	0.0331427i
$661$	2395.53	+	992.262i	0.140961	+	0.0583881i	0.452049	−	0.891993i	$-0.350693\pi$
$661$	2395.53	+	992.262i	0.140961	+	0.0583881i	−0.311088	+	0.950381i	$0.600693\pi$
$662$	1513.36	−	13963.2i	0.0888494	−	0.819783i
$663$			1095.69i			0.0641829i
$664$	19361.6	−	9629.30i	1.13159	−	0.562785i
$665$	3154.06	−	198.965i	0.183924	−	0.0116023i
$666$	1173.26	−	10825.3i	0.0682626	−	0.629836i
$667$	−8089.07	+	3350.60i	−0.469580	+	0.194507i
$668$	−3438.75	−	5371.11i	−0.199176	−	0.311099i
$669$	−3416.42	−	8247.97i	−0.197439	−	0.476659i
$670$	−9171.13	−	4291.41i	−0.528823	−	0.247450i
$671$		−	897.042i		−	0.0516094i
$672$	−4103.65	+	6849.02i	−0.235568	+	0.393165i
$673$	−18388.0	−	18388.0i	−1.05320	−	1.05320i	−0.998503	−	0.0546986i	$-0.982580\pi$
$673$	−18388.0	−	18388.0i	−1.05320	−	1.05320i	−0.0546986	−	0.998503i	$-0.517420\pi$
$674$	−2512.44	−	1374.70i	−0.143584	−	0.0785631i
$675$	17938.8	+	4901.08i	1.02291	+	0.279471i
$676$	3108.51	+	681.819i	0.176861	+	0.0387926i
$677$	−3735.71	−	9018.79i	−0.212075	−	0.511995i	0.781667	−	0.623696i	$-0.214370\pi$
$677$	−3735.71	−	9018.79i	−0.212075	−	0.511995i	−0.993742	+	0.111702i	$0.964370\pi$
$678$	−9438.41	−	11733.0i	−0.534631	−	0.664606i
$679$	−12000.6	−	12000.6i	−0.678262	−	0.678262i
$680$	−1719.64	−	459.087i	−0.0969785	−	0.0258900i
$681$	12222.5	−	12222.5i	0.687765	−	0.687765i
$682$	−104.729	−	11.3507i	−0.00588019	−	0.000637305i
$683$	750.661	−	310.934i	0.0420545	−	0.0174196i	−0.361557	−	0.932350i	$-0.617755\pi$
$683$	750.661	−	310.934i	0.0420545	−	0.0174196i	0.403612	+	0.914930i	$0.367755\pi$
$684$	−447.545	−	2505.24i	−0.0250180	−	0.140044i
$685$	4800.47	−	14028.7i	0.267762	−	0.782493i
$686$	−5170.26	−	17664.5i	−0.287757	−	0.983139i
$687$	−2511.71	+	2511.71i	−0.139487	+	0.139487i
$688$	−953.733	+	24353.8i	−0.0528499	+	1.34954i
$689$	8485.12			0.469169
$690$	−7793.31	−	3646.69i	−0.429980	−	0.201199i
$691$	6012.82	−	2490.59i	0.331025	−	0.137115i	−0.210980	−	0.977490i	$-0.567665\pi$
$691$	6012.82	−	2490.59i	0.331025	−	0.137115i	0.542005	+	0.840375i	$0.317665\pi$
$692$	−5269.24	−	29495.8i	−0.289460	−	1.62032i
$693$	−204.949	−	494.791i	−0.0112343	−	0.0271220i
$694$	5712.10	−	4595.00i	0.312433	−	0.251331i
$695$	−12221.9	−	10771.4i	−0.667053	−	0.587889i
$696$	−6446.81	+	7401.32i	−0.351100	+	0.403084i
$697$	2845.23			0.154621
$698$	320.831	+	398.829i	0.0173978	+	0.0216274i
$699$	−872.528	+	2106.47i	−0.0472132	+	0.113983i
$700$	−1078.81	+	11964.7i	−0.0582504	+	0.646033i
$701$	14746.9	−	6108.35i	0.794553	−	0.329115i	0.0517805	−	0.998658i	$-0.483510\pi$
$701$	14746.9	−	6108.35i	0.794553	−	0.329115i	0.742773	+	0.669544i	$0.233510\pi$
$702$	−5013.76	−	17129.8i	−0.269562	−	0.920973i
$703$	4737.71	−	4737.71i	0.254177	−	0.254177i
$704$	1633.69	+	425.970i	0.0874602	+	0.0228045i
$705$	−1043.37	−	16539.8i	−0.0557383	−	0.883584i
$706$	20113.7	+	11005.4i	1.07222	+	0.586676i
$707$	4270.90	+	1769.06i	0.227190	+	0.0941053i
$708$	−24501.1	−	5374.07i	−1.30058	−	0.285268i
$709$	−22896.1	−	9483.89i	−1.21281	−	0.502363i	−0.317693	−	0.948194i	$-0.602908\pi$
$709$	−22896.1	−	9483.89i	−1.21281	−	0.502363i	−0.895117	+	0.445831i	$0.852908\pi$
$710$	−5485.81	+	5013.43i	−0.289970	+	0.265001i
$711$	1141.77	−	1141.77i	0.0602248	−	0.0602248i
$712$	−1375.52	−	19956.1i	−0.0724016	−	1.05040i
$713$	837.030			0.0439650
$714$	−550.153	−	683.901i	−0.0288361	−	0.0358465i
$715$	−688.204	−	1404.21i	−0.0359963	−	0.0734467i
$716$	−27911.2	−	19450.3i	−1.45683	−	1.01521i
$717$	12064.9	+	4997.45i	0.628413	+	0.260297i
$718$	−21224.5	−	11613.2i	−1.10319	−	0.603622i
$719$		−	26068.2i		−	1.35213i	−0.736844	−	0.676063i	$-0.763685\pi$
$719$		−	26068.2i		−	1.35213i	0.736844	−	0.676063i	$-0.236315\pi$
$720$	9671.09	−	230.768i	0.500583	−	0.0119447i
$721$			6868.71i			0.354791i
$722$	−8560.50	+	15645.4i	−0.441259	+	0.806455i
$723$	8487.58	+	3515.67i	0.436593	+	0.180843i
$724$	−22792.3	+	4071.69i	−1.16998	+	0.209010i
$725$	−3892.19	+	14246.1i	−0.199383	+	0.729776i
$726$	−10681.9	+	8592.91i	−0.546066	+	0.439274i
$727$	−8760.58			−0.446922			−0.223461	−	0.974713i	$-0.571735\pi$
$727$	−8760.58			−0.446922			−0.223461	+	0.974713i	$0.571735\pi$
$728$	10323.8	−	5134.46i	0.525586	−	0.261395i
$729$	12160.5	−	12160.5i	0.617819	−	0.617819i
$730$	13013.1	+	585.482i	0.659773	+	0.0296844i
$731$	−2475.33	−	1025.32i	−0.125244	−	0.0518779i
$732$	4308.40	+	6729.43i	0.217545	+	0.339791i
$733$	−18305.1	−	7582.20i	−0.922391	−	0.382067i	−0.129604	−	0.991566i	$-0.541371\pi$
$733$	−18305.1	−	7582.20i	−0.922391	−	0.382067i	−0.792787	+	0.609499i	$0.791371\pi$
$734$	−752.305	+	1374.93i	−0.0378312	+	0.0691411i
$735$	5392.49	−	6118.63i	0.270619	−	0.307060i
$736$	−13270.1	−	1966.25i	−0.664595	−	0.0984743i
$737$	−746.593	+	746.593i	−0.0373149	+	0.0373149i
$738$	−14841.6	+	4344.01i	−0.740278	+	0.216674i
$739$	−3928.92	+	1627.41i	−0.195572	+	0.0810086i	−0.478320	−	0.878186i	$-0.658754\pi$
$739$	−3928.92	+	1627.41i	−0.195572	+	0.0810086i	0.282748	+	0.959194i	$0.408754\pi$
$740$	15055.8	+	20542.4i	0.747923	+	1.02048i
$741$	1402.32	−	3385.51i	0.0695218	−	0.167840i
$742$	−5296.17	+	4260.41i	−0.262033	+	0.210788i
$743$	−23675.4			−1.16900			−0.584499	−	0.811394i	$-0.698709\pi$
$743$	−23675.4			−1.16900			−0.584499	+	0.811394i	$0.698709\pi$
$744$	840.174	−	417.853i	0.0414009	−	0.0205903i
$745$	718.667	−	815.442i	0.0353422	−	0.0401013i
$746$	−13132.4	−	16325.0i	−0.644518	−	0.801208i
$747$	−4944.28	−	11936.6i	−0.242171	−	0.584653i
$748$	−106.112	+	152.271i	−0.00518697	+	0.00744328i
$749$	16819.3	−	6966.77i	0.820511	−	0.339867i
$750$	−12914.8	+	6621.08i	−0.628777	+	0.322357i
$751$	27311.1			1.32703			0.663513	−	0.748165i	$-0.269065\pi$
$751$	27311.1			1.32703			0.663513	+	0.748165i	$0.269065\pi$
$752$	−8946.26	−	24240.3i	−0.433825	−	1.17547i
$753$	−11582.9	+	11582.9i	−0.560565	+	0.560565i
$754$	13603.6	−	3981.68i	0.657049	−	0.192313i
$755$	−7561.05	−	15427.5i	−0.364470	−	0.743662i
$756$	11730.4	+	8174.51i	0.564326	+	0.393259i
$757$	−13190.9	+	5463.86i	−0.633332	+	0.262335i	−0.676168	−	0.736747i	$-0.736361\pi$
$757$	−13190.9	+	5463.86i	−0.633332	+	0.262335i	0.0428359	+	0.999082i	$0.486361\pi$
$758$	558.938	−	5157.13i	0.0267830	−	0.247118i
$759$	−634.429	+	634.429i	−0.0303404	+	0.0303404i
$760$	4725.85	+	3619.38i	0.225558	+	0.172749i
$761$	2564.19	+	2564.19i	0.122144	+	0.122144i	0.765537	−	0.643392i	$-0.222474\pi$
$761$	2564.19	+	2564.19i	0.122144	+	0.122144i	−0.643392	+	0.765537i	$0.722474\pi$
$762$	−6359.01	+	5115.40i	−0.302313	+	0.243191i
$763$	1160.35	+	2801.33i	0.0550557	+	0.132916i
$764$	11834.6	+	18484.8i	0.560419	+	0.875338i
$765$	−344.302	+	1006.17i	−0.0162723	+	0.0475533i
$766$	5494.08	−	10041.1i	0.259151	−	0.473629i
$767$	25613.7	+	25613.7i	1.20581	+	1.20581i
$768$	−14301.5	+	4650.90i	−0.671954	+	0.218522i
$769$			18959.2i			0.889060i	0.895764	+	0.444530i	$0.146629\pi$
$769$			18959.2i			0.889060i	−0.895764	+	0.444530i	$0.853371\pi$
$770$	1134.62	+	530.916i	0.0531022	+	0.0248479i
$771$	−8911.82	−	21515.0i	−0.416279	−	1.00499i
$772$	−28527.5	−	6257.21i	−1.32996	−	0.291712i
$773$	38728.0	−	16041.6i	1.80200	−	0.746414i	0.816366	−	0.577535i	$-0.195985\pi$
$773$	38728.0	−	16041.6i	1.80200	−	0.746414i	0.985637	−	0.168879i	$-0.0540146\pi$
$774$	14477.5	+	1569.09i	0.672329	+	0.0728680i
$775$	864.957	−	1115.86i	0.0400905	−	0.0517200i
$776$	−2198.14	−	31890.6i	−0.101686	−	1.47527i
$777$			12559.7i			0.579891i
$778$	−34730.1	−	3764.10i	−1.60043	−	0.173457i
$779$	−8791.28	−	3641.47i	−0.404339	−	0.167483i
$780$	11907.0	+	7228.71i	0.546590	+	0.331832i
$781$	296.554	+	715.946i	0.0135871	+	0.0328022i
$782$	707.869	−	1293.72i	0.0323700	−	0.0591601i
$783$	12428.5	+	12428.5i	0.567254	+	0.567254i
$784$	5322.05	−	11548.3i	0.242440	−	0.526071i
$785$	15911.5	−	18054.1i	0.723446	−	0.820864i
$786$	2837.41	−	830.487i	0.128762	−	0.0376876i
$787$	−15031.1	+	36288.3i	−0.680814	+	1.64363i	0.0816990	+	0.996657i	$0.473965\pi$
$787$	−15031.1	+	36288.3i	−0.680814	+	1.64363i	−0.762513	+	0.646973i	$0.776035\pi$
$788$	3760.58	+	2620.62i	0.170006	+	0.118472i
$789$	6880.90	−	16612.0i	0.310477	−	0.749558i
$790$	−169.756	+	3773.05i	−0.00764514	+	0.169923i
$791$	−12317.4	−	12317.4i	−0.553675	−	0.553675i
$792$	321.031	−	956.298i	0.0144032	−	0.0429047i
$793$		−	11539.1i		−	0.516726i
$794$	38268.5	+	4147.60i	1.71045	+	0.185381i
$795$	−7769.26	−	2658.57i	−0.346600	−	0.118603i
$796$	14155.7	+	3104.91i	0.630322	+	0.138255i
$797$	213.394	−	515.178i	0.00948405	−	0.0228965i	−0.919067	−	0.394102i	$-0.871056\pi$
$797$	213.394	−	515.178i	0.00948405	−	0.0228965i	0.928551	+	0.371206i	$0.121056\pi$
$798$	824.587	+	2817.25i	0.0365790	+	0.124974i
$799$	2840.44			0.125767
$800$	−16334.1	+	15658.8i	−0.721871	+	0.692027i
$801$	−11951.8			−0.527212
$802$	10959.3	+	37443.1i	0.482527	+	1.64858i
$803$	519.805	−	1254.92i	0.0228437	−	0.0551496i
$804$	2014.98	−	9186.60i	0.0883868	−	0.402968i
$805$	−9417.48	−	3222.57i	−0.412326	−	0.141094i
$806$	−1347.18	−	146.009i	−0.0588739	−	0.00638085i
$807$		−	19940.4i		−	0.869810i
$808$	3877.38	+	7796.23i	0.168819	+	0.339444i
$809$	4038.32	+	4038.32i	0.175501	+	0.175501i	0.789391	−	0.613891i	$-0.210396\pi$
$809$	4038.32	+	4038.32i	0.175501	+	0.175501i	−0.613891	+	0.789391i	$0.710396\pi$
$810$	−257.532	+	5723.98i	−0.0111713	+	0.248296i
$811$	−9185.54	+	22175.9i	−0.397716	+	0.960172i	0.590490	+	0.807045i	$0.298934\pi$
$811$	−9185.54	+	22175.9i	−0.397716	+	0.960172i	−0.988206	+	0.153127i	$0.951066\pi$
$812$	−6491.79	+	9315.69i	−0.280563	+	0.402607i
$813$	−9753.55	+	23547.2i	−0.420753	+	1.01579i
$814$	2548.85	−	746.029i	0.109751	−	0.0321232i
$815$	−14511.7	+	16465.8i	−0.623709	+	0.707697i
$816$	64.6929	−	1651.95i	0.00277537	−	0.0708699i
$817$	6336.11	+	6336.11i	0.271325	+	0.271325i
$818$	−14212.7	+	25975.5i	−0.607502	+	1.11028i
$819$	−2636.35	−	6364.72i	−0.112481	−	0.271552i
$820$	18771.1	−	30919.4i	0.799407	−	1.31677i
$821$	−4251.62	−	1761.08i	−0.180734	−	0.0748625i	0.290481	−	0.956881i	$-0.406185\pi$
$821$	−4251.62	−	1761.08i	−0.180734	−	0.0748625i	−0.471215	+	0.882018i	$0.656185\pi$
$822$	13692.0	+	1483.96i	0.580977	+	0.0629672i
$823$			22557.7i			0.955420i	0.878518	+	0.477710i	$0.158533\pi$
$823$			22557.7i			0.955420i	−0.878518	+	0.477710i	$0.841467\pi$
$824$	−8497.46	+	9755.60i	−0.359251	+	0.412442i
$825$	190.176	+	1501.37i	0.00802554	+	0.0633587i
$826$	−28848.1	−	3126.61i	−1.21520	−	0.131705i
$827$	−13778.6	+	5707.30i	−0.579359	+	0.239978i	−0.653065	−	0.757302i	$-0.726517\pi$
$827$	−13778.6	+	5707.30i	−0.579359	+	0.239978i	0.0737061	+	0.997280i	$0.476517\pi$
$828$	−1717.24	+	7829.16i	−0.0720753	+	0.328601i
$829$	−11953.8	−	28859.0i	−0.500811	−	1.20906i	−0.949043	−	0.315147i	$-0.897946\pi$
$829$	−11953.8	−	28859.0i	−0.500811	−	1.20906i	0.448232	−	0.893917i	$-0.352054\pi$
$830$	27372.0	+	12808.0i	1.14469	+	0.535631i
$831$		−	26470.0i		−	1.10497i
$832$	21014.9	+	5479.44i	0.875673	+	0.228324i
$833$	988.421	+	988.421i	0.0411125	+	0.0411125i
$834$	7263.31	−	13274.6i	0.301568	−	0.551153i
$835$	2885.66	−	8432.91i	0.119596	−	0.349501i
$836$	522.752	−	334.683i	0.0216265	−	0.0138460i
$837$	−643.032	−	1552.42i	−0.0265549	−	0.0641092i
$838$	31059.9	−	24985.6i	1.28036	−	1.02997i
$839$	21571.6	+	21571.6i	0.887644	+	0.887644i	0.994296	−	0.106653i	$-0.0340132\pi$
$839$	21571.6	+	21571.6i	0.887644	+	0.887644i	−0.106653	+	0.994296i	$0.534013\pi$
$840$	−11061.6	+	1466.61i	−0.454358	+	0.0602416i
$841$	7375.50	−	7375.50i	0.302411	−	0.302411i
$842$	3943.92	−	36389.2i	0.161421	−	1.48938i
$843$	25423.3	−	10530.7i	1.03870	−	0.430244i
$844$	−7268.63	+	10430.5i	−0.296441	+	0.425392i
$845$	1957.32	+	3993.69i	0.0796849	+	0.162588i
$846$	−14816.6	+	4336.69i	−0.602133	+	0.176240i
$847$	−11214.0	+	11214.0i	−0.454921	+	0.454921i
$848$	−12792.8	−	500.986i	−0.518050	−	0.0202876i
$849$	−22671.8			−0.916485
$850$	−993.198	−	2280.56i	−0.0400781	−	0.0920264i
$851$	−19496.0	+	8075.51i	−0.785329	+	0.325294i
$852$	−5663.30	−	3946.56i	−0.227725	−	0.158694i
$853$	5227.98	+	12621.5i	0.209851	+	0.506624i	0.993399	−	0.114706i	$-0.0365926\pi$
$853$	5227.98	+	12621.5i	0.209851	+	0.506624i	−0.783549	+	0.621330i	$0.786593\pi$
$854$	5793.81	+	7202.35i	0.232155	+	0.288594i
$855$	2351.58	−	2668.24i	0.0940614	−	0.106728i
$856$	32507.1	+	10912.7i	1.29798	+	0.435733i
$857$	−17770.4			−0.708315			−0.354157	−	0.935186i	$-0.615232\pi$
$857$	−17770.4			−0.708315			−0.354157	+	0.935186i	$0.615232\pi$
$858$	1131.77	−	910.430i	0.0450325	−	0.0362256i
$859$	−782.573	+	1889.30i	−0.0310839	+	0.0750431i	−0.938659	−	0.344846i	$-0.887931\pi$
$859$	−782.573	+	1889.30i	−0.0310839	+	0.0750431i	0.907575	+	0.419889i	$0.137931\pi$
$860$	−27472.9	+	20135.3i	−1.08932	+	0.798382i
$861$	16479.6	−	6826.07i	0.652291	−	0.270188i
$862$	28880.2	−	8453.01i	1.14114	−	0.334003i
$863$	−33081.3	+	33081.3i	−1.30487	+	1.30487i	−0.379799	+	0.925069i	$0.624007\pi$
$863$	−33081.3	+	33081.3i	−1.30487	+	1.30487i	−0.925069	+	0.379799i	$0.875993\pi$
$864$	6547.73	+	26122.2i	0.257822	+	1.02858i
$865$	27686.7	−	31415.0i	1.08830	−	1.23485i
$866$	−2751.66	+	5028.99i	−0.107974	+	0.197335i
$867$	−16497.4	−	6833.45i	−0.646230	−	0.267677i
$868$	914.183	−	585.289i	0.0357482	−	0.0228871i
$869$	363.855	+	150.714i	0.0142036	+	0.00588333i
$870$	−13703.5	−	616.546i	−0.534014	−	0.0240263i
$871$	−9603.76	+	9603.76i	−0.373606	+	0.373606i
$872$	−1817.56	+	5414.22i	−0.0705853	+	0.210262i
$873$	−19099.4			−0.740456
$874$	−3842.96	+	3091.40i	−0.148730	+	0.119643i
$875$	−14027.8	+	9224.57i	−0.541972	+	0.356397i
$876$	2127.77	+	11910.7i	0.0820671	+	0.459390i
$877$	4253.56	+	1761.88i	0.163777	+	0.0678387i	0.463066	−	0.886324i	$-0.346749\pi$
$877$	4253.56	+	1761.88i	0.163777	+	0.0678387i	−0.299289	+	0.954163i	$0.596749\pi$
$878$	−8610.74	+	15737.2i	−0.330978	+	0.604902i
$879$			18546.5i			0.711670i
$880$	954.680	+	2157.72i	0.0365707	+	0.0826554i
$881$		−	35372.9i		−	1.35272i	−0.736573	−	0.676358i	$-0.763557\pi$
$881$		−	35372.9i		−	1.35272i	0.736573	−	0.676358i	$-0.236443\pi$
$882$	−6664.98	−	3646.80i	−0.254446	−	0.139222i
$883$	−5043.94	−	2089.27i	−0.192233	−	0.0796257i	0.284490	−	0.958679i	$-0.408176\pi$
$883$	−5043.94	−	2089.27i	−0.192233	−	0.0796257i	−0.476724	+	0.879053i	$0.658176\pi$
$884$	−1364.97	+	1958.73i	−0.0519332	+	0.0745239i
$885$	−15427.5	−	31478.1i	−0.585977	−	1.19562i
$886$	22510.1	+	27982.6i	0.853545	+	1.06105i
$887$	14546.7			0.550655			0.275327	−	0.961351i	$-0.411214\pi$
$887$	14546.7			0.550655			0.275327	+	0.961351i	$0.411214\pi$
$888$	−15537.9	+	17838.4i	−0.587181	+	0.674120i
$889$	−6675.75	+	6675.75i	−0.251853	+	0.251853i
$890$	20636.2	−	18859.2i	0.777220	−	0.710294i
$891$	551.994	+	228.644i	0.0207548	+	0.00859691i
$892$	4167.58	−	19000.6i	0.156436	−	0.713214i
$893$	−8776.48	−	3635.34i	−0.328884	−	0.136228i
$894$	885.680	+	484.607i	0.0331337	+	0.0181294i
$895$	−2993.24	−	47449.9i	−0.111791	−	1.77215i
$896$	−15868.1	+	7131.55i	−0.591649	+	0.265902i
$897$	−8160.95	+	8160.95i	−0.303775	+	0.303775i
$898$	−8556.69	−	29234.4i	−0.317974	−	1.08638i
$899$	1232.85	−	510.664i	0.0457374	−	0.0189450i
$900$	8662.69	+	10379.7i	0.320840	+	0.384432i
$901$	538.588	−	1300.27i	0.0199145	−	0.0480778i
$902$	−2364.15	−	2938.90i	−0.0872700	−	0.108486i
$903$	−16797.0			−0.619013
$904$	−2256.17	−	32732.6i	−0.0830079	−	1.20428i
$905$	−24275.3	−	21394.3i	−0.891643	−	0.785825i
$906$	12434.3	−	10002.6i	0.455963	−	0.366791i
$907$	−9383.82	−	22654.5i	−0.343533	−	0.829363i	−0.997353	−	0.0727122i	$-0.976835\pi$
$907$	−9383.82	−	22654.5i	−0.343533	−	0.829363i	0.653820	−	0.756650i	$-0.273165\pi$
$908$	37076.0	−	6623.38i	1.35508	−	0.242076i
$909$	4806.43	−	1990.89i	0.175379	−	0.0726442i
$910$	14595.1	+	6829.41i	0.531672	+	0.248783i
$911$	33980.0			1.23579			0.617897	−	0.786259i	$-0.287985\pi$
$911$	33980.0			1.23579			0.617897	+	0.786259i	$0.287985\pi$
$912$	−2314.14	+	5021.45i	−0.0840227	+	0.182321i
$913$	2228.27	−	2228.27i	0.0807720	−	0.0807720i
$914$	3975.23	+	13581.6i	0.143861	+	0.491510i
$915$	−3615.43	+	10565.5i	−0.130626	+	0.381734i
$916$	−7619.06	+	1361.10i	−0.274826	+	0.0490960i
$917$	3159.73	−	1308.80i	0.113788	−	0.0471324i
$918$	−2943.23	−	318.992i	−0.105818	−	0.0114687i
$919$	−19873.9	+	19873.9i	−0.713362	+	0.713362i	−0.967237	−	0.253875i	$-0.918295\pi$
$919$	−19873.9	+	19873.9i	−0.713362	+	0.713362i	0.253875	+	0.967237i	$0.418295\pi$
$920$	−9388.88	−	16227.6i	−0.336459	−	0.581531i
$921$	−5854.55	−	5854.55i	−0.209462	−	0.209462i
$922$	29433.0	+	36588.5i	1.05133	+	1.30692i
$923$	3814.71	+	9209.53i	0.136038	+	0.328424i
$924$	−249.286	+	1136.53i	−0.00887544	+	0.0404644i
$925$	−9380.83	+	34335.5i	−0.333448	+	1.22048i
$926$	44370.0	+	24277.5i	1.57461	+	0.861562i
$927$	5465.93	+	5465.93i	0.193662	+	0.193662i
$928$	−20744.9	+	5199.87i	−0.733821	+	0.183938i
$929$			31232.0i			1.10300i	0.834174	+	0.551502i	$0.185945\pi$
$929$			31232.0i			1.10300i	−0.834174	+	0.551502i	$0.814055\pi$
$930$	1187.78	+	555.791i	0.0418803	+	0.0195969i
$931$	−1789.02	−	4319.08i	−0.0629783	−	0.152043i
$932$	−4183.93	+	2678.69i	−0.147049	+	0.0941452i
$933$	23649.0	−	9795.75i	0.829833	−	0.343728i
$934$	3073.49	−	28358.1i	0.107674	−	0.993474i
$935$	−258.865	+	16.3297i	−0.00905432	+	0.000571166i
$936$	4129.56	−	12301.3i	0.144208	−	0.429573i
$937$		−	19550.2i		−	0.681619i	−0.940132	−	0.340809i	$-0.889299\pi$
$937$		−	19550.2i		−	0.681619i	0.940132	−	0.340809i	$-0.110701\pi$
$938$	1172.31	−	10816.5i	0.0408072	−	0.376515i
$939$	1027.67	+	425.675i	0.0357154	+	0.0147938i
$940$	18739.5	−	30867.4i	0.650227	−	1.07105i
$941$	9743.57	+	23523.0i	0.337546	+	0.814909i	0.997950	+	0.0639983i	$0.0203852\pi$
$941$	9743.57	+	23523.0i	0.337546	+	0.814909i	−0.660404	+	0.750911i	$0.729615\pi$
$942$	19609.2	+	10729.3i	0.678239	+	0.371105i
$943$	21191.8	+	21191.8i	0.731815	+	0.731815i
$944$	−37104.9	−	40129.5i	−1.27930	−	1.38358i
$945$	1257.98	+	19942.0i	0.0433040	+	0.686470i
$946$	997.723	+	3408.78i	0.0342905	+	0.117155i
$947$	−4823.11	+	11644.0i	−0.165501	+	0.399556i	−0.984772	−	0.173851i	$-0.944379\pi$
$947$	−4823.11	+	11644.0i	−0.165501	+	0.399556i	0.819270	+	0.573407i	$0.194379\pi$
$948$	−3453.43	+	616.933i	−0.118315	+	0.0211361i
$949$	6686.48	−	16142.6i	0.228717	−	0.552171i
$950$	150.043	+	8317.67i	0.00512423	+	0.284064i
$951$	−24623.0	−	24623.0i	−0.839595	−	0.839595i
$952$	−131.509	−	1907.94i	−0.00447715	−	0.0649545i
$953$		−	49123.9i		−	1.66976i	−0.550434	−	0.834879i	$-0.685538\pi$
$953$		−	49123.9i		−	1.66976i	0.550434	−	0.834879i	$-0.314462\pi$
$954$	−824.227	+	7604.86i	−0.0279720	+	0.258089i
$955$	−9931.10	+	29022.1i	−0.336505	+	0.983387i
$956$	15342.3	+	23963.7i	0.519044	+	0.810713i
$957$	−547.384	+	1321.50i	−0.0184895	+	0.0446375i
$958$	29097.7	−	8516.68i	0.981320	−	0.287225i
$959$	15931.9			0.536462
$960$	−17525.1	−	11601.6i	−0.589188	−	0.390040i
$961$	29663.4			0.995718
$962$	32787.0	−	9596.50i	1.09885	−	0.321625i
$963$	7840.34	−	18928.3i	0.262359	−	0.633390i
$964$	10793.2	+	16858.3i	0.360608	+	0.563246i
$965$	−17962.7	−	36651.0i	−0.599213	−	1.22263i
$966$	996.187	−	9191.48i	0.0331799	−	0.306140i
$967$			12099.9i			0.402387i	0.979552	+	0.201193i	$0.0644819\pi$
$967$			12099.9i			0.402387i	−0.979552	+	0.201193i	$0.935518\pi$
$968$	−29800.3	+	2054.06i	−0.989483	+	0.0682026i
$969$	−429.786	−	429.786i	−0.0142484	−	0.0142484i
$970$	32977.3	−	30137.7i	1.09159	−	0.997590i
$971$	−19863.0	+	47953.6i	−0.656472	+	1.58486i	0.146743	+	0.989175i	$0.453121\pi$
$971$	−19863.0	+	47953.6i	−0.656472	+	1.58486i	−0.803215	+	0.595689i	$0.796879\pi$
$972$	26394.5	−	4715.21i	0.870992	−	0.155597i
$973$	6698.74	−	16172.2i	0.220711	−	0.532844i
$974$	5051.47	+	17258.7i	0.166180	+	0.567765i
$975$	2446.31	+	19312.8i	0.0803536	+	0.634363i
$976$	−681.299	+	17397.1i	−0.0223441	+	0.570562i
$977$	−6969.87	−	6969.87i	−0.228235	−	0.228235i	0.583720	−	0.811955i	$-0.301597\pi$
$977$	−6969.87	−	6969.87i	−0.228235	−	0.228235i	−0.811955	+	0.583720i	$0.801597\pi$
$978$	−17884.1	−	9785.44i	−0.584734	−	0.319943i
$979$	−1115.56	−	2693.19i	−0.0364182	−	0.0879212i
$980$	17262.3	−	4220.29i	0.562676	−	0.137563i
$981$	3152.59	+	1305.85i	0.102604	+	0.0425000i
$982$	799.873	−	7380.15i	0.0259928	−	0.239827i
$983$			26451.0i			0.858247i	0.903246	+	0.429124i	$0.141178\pi$
$983$			26451.0i			0.858247i	−0.903246	+	0.429124i	$0.858822\pi$
$984$	31850.6	+	10692.3i	1.03187	+	0.346400i
$985$	403.290	+	6393.10i	0.0130456	+	0.206803i
$986$	253.327	−	2337.36i	0.00818213	−	0.0754938i
$987$	16451.8	−	6814.58i	0.530565	−	0.219767i
$988$	6724.40	−	4305.17i	0.216530	−	0.138629i
$989$	−10800.0	−	26073.5i	−0.347240	−	0.838312i
$990$	1325.38	−	480.407i	0.0425490	−	0.0154226i
$991$		−	49389.7i		−	1.58316i	−0.611064	−	0.791581i	$-0.709258\pi$
$991$		−	49389.7i		−	1.58316i	0.611064	−	0.791581i	$-0.290742\pi$
$992$	2022.49	+	299.676i	0.0647319	+	0.00959145i
$993$	12891.8	+	12891.8i	0.411993	+	0.411993i
$994$	−7005.18	−	3832.94i	−0.223532	−	0.122307i
$995$	8913.35	+	18186.7i	0.283992	+	0.579456i
$996$	−6013.88	+	27418.1i	−0.191322	+	0.872265i
$997$	3886.07	+	9381.79i	0.123443	+	0.298018i	0.973505	−	0.228664i	$-0.0734357\pi$
$997$	3886.07	+	9381.79i	0.123443	+	0.298018i	−0.850062	+	0.526682i	$0.823436\pi$
$998$	28431.8	+	35343.9i	0.901797	+	1.12103i
$999$	29954.9	+	29954.9i	0.948679	+	0.948679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.4.u.a.43.6	✓	280
5.2	odd	4		160.4.ba.a.107.30	yes	280
32.3	odd	8		160.4.ba.a.3.30	yes	280
160.67	even	8	inner	160.4.u.a.67.6	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.u.a.43.6	✓	280	1.1	even	1	trivial
160.4.u.a.67.6	yes	280	160.67	even	8	inner
160.4.ba.a.3.30	yes	280	32.3	odd	8
160.4.ba.a.107.30	yes	280	5.2	odd	4

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.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.71454 + 0.794525i) q^{2} +(1.40505 - 3.39208i) q^{3} +(6.73746 - 4.31354i) q^{4} +(10.5782 + 3.61974i) q^{5} +(-1.11896 + 10.3243i) q^{6} +12.0132i q^{7} +(-14.8619 + 17.0624i) q^{8} +(9.55980 + 9.55980i) q^{9} +(-31.5908 - 1.42133i) q^{10} +(-1.26189 + 3.04648i) q^{11} +(-5.16544 - 28.9148i) q^{12} +(-16.2323 + 39.1882i) q^{13} +(-9.54482 - 32.6104i) q^{14} +(27.1413 - 30.7961i) q^{15} +(26.7868 - 58.1246i) q^{16} +(4.97489 + 4.97489i) q^{17} +(-33.5460 - 18.3550i) q^{18} +(-9.00445 - 21.7387i) q^{19} +(86.8838 - 21.2414i) q^{20} +(40.7499 + 16.8792i) q^{21} +(1.00496 - 9.27239i) q^{22} +74.1079i q^{23} +(36.9953 + 74.3862i) q^{24} +(98.7949 + 76.5804i) q^{25} +(12.9272 - 119.275i) q^{26} +(137.446 - 56.9320i) q^{27} +(51.8196 + 80.9388i) q^{28} +(45.2125 + 109.153i) q^{29} +(-49.2079 + 105.162i) q^{30} -11.2948i q^{31} +(-26.5323 + 179.064i) q^{32} +(8.56089 + 8.56089i) q^{33} +(-17.4572 - 9.55187i) q^{34} +(-43.4849 + 127.078i) q^{35} +(105.645 + 23.1722i) q^{36} +(108.970 + 263.076i) q^{37} +(41.7148 + 51.8562i) q^{38} +(110.122 + 110.122i) q^{39} +(-218.973 + 126.692i) q^{40} +(285.959 - 285.959i) q^{41} +(-124.028 - 13.4424i) q^{42} +(-351.832 + 145.734i) q^{43} +(4.63915 + 25.9687i) q^{44} +(66.5211 + 135.729i) q^{45} +(-58.8806 - 201.169i) q^{46} +(285.478 - 285.478i) q^{47} +(-159.527 - 172.531i) q^{48} +198.682 q^{49} +(-329.028 - 129.386i) q^{50} +(23.8652 - 9.88529i) q^{51} +(59.6754 + 334.047i) q^{52} +(-76.5523 - 184.814i) q^{53} +(-327.869 + 263.748i) q^{54} +(-24.3760 + 27.6584i) q^{55} +(-204.974 - 178.540i) q^{56} -86.3911 q^{57} +(-209.456 - 260.377i) q^{58} +(326.805 - 788.976i) q^{59} +(50.0232 - 324.563i) q^{60} +(-251.331 + 104.105i) q^{61} +(8.97396 + 30.6601i) q^{62} +(-114.844 + 114.844i) q^{63} +(-70.2480 - 507.158i) q^{64} +(-313.559 + 355.782i) q^{65} +(-30.0407 - 16.4370i) q^{66} +(295.823 + 122.534i) q^{67} +(54.9775 + 12.0587i) q^{68} +(251.380 + 104.125i) q^{69} +(17.0748 - 379.508i) q^{70} +(166.176 - 166.176i) q^{71} +(-305.190 + 21.0359i) q^{72} -411.925 q^{73} +(-504.823 - 627.552i) q^{74} +(398.579 - 227.522i) q^{75} +(-154.438 - 107.622i) q^{76} +(-36.5981 - 15.1594i) q^{77} +(-386.427 - 211.437i) q^{78} -119.435i q^{79} +(493.751 - 517.890i) q^{80} -181.191i q^{81} +(-549.046 + 1003.45i) q^{82} +(-882.907 - 365.712i) q^{83} +(347.360 - 62.0537i) q^{84} +(34.6174 + 70.6330i) q^{85} +(839.273 - 675.139i) q^{86} +433.781 q^{87} +(-33.2260 - 66.8073i) q^{88} +(-625.108 + 625.108i) q^{89} +(-288.414 - 315.590i) q^{90} +(-470.777 - 195.002i) q^{91} +(319.667 + 499.299i) q^{92} +(-38.3128 - 15.8697i) q^{93} +(-548.122 + 1001.76i) q^{94} +(-16.5621 - 262.549i) q^{95} +(570.122 + 341.594i) q^{96} +(-998.946 + 998.946i) q^{97} +(-539.330 + 157.858i) q^{98} +(-41.1871 + 17.0603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} + 80 q^{8} + 8 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} + 64 q^{14} - 8 q^{15} - 8 q^{16} + 28 q^{18} - 48 q^{19} - 312 q^{20} - 8 q^{21} - 436 q^{22} + 736 q^{24}+ \cdots + 3480 q^{98}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 + 80 * q^8 + 8 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 + 64 * q^14 - 8 * q^15 - 8 * q^16 + 28 * q^18 - 48 * q^19 - 312 * q^20 - 8 * q^21 - 436 * q^22 + 736 * q^24 - 4 * q^25 - 8 * q^26 - 112 * q^27 + 252 * q^28 - 1696 * q^30 - 344 * q^32 - 8 * q^33 + 696 * q^34 + 952 * q^35 - 8 * q^36 - 4 * q^37 - 172 * q^38 + 816 * q^40 - 8 * q^41 - 460 * q^42 + 860 * q^43 + 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 3496 * q^48 - 11368 * q^49 - 36 * q^50 + 1480 * q^51 - 328 * q^52 - 4 * q^53 + 2968 * q^54 - 292 * q^55 - 344 * q^56 - 8 * q^57 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 - 440 * q^62 + 2744 * q^63 + 816 * q^64 - 8 * q^65 + 552 * q^66 + 1844 * q^67 + 1224 * q^68 + 216 * q^69 + 1764 * q^70 - 232 * q^71 - 3432 * q^72 - 8 * q^73 + 104 * q^75 + 824 * q^76 + 1368 * q^77 - 5968 * q^78 - 1800 * q^80 + 588 * q^82 + 2676 * q^83 + 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 2568 * q^87 - 5880 * q^88 - 84 * q^90 - 8 * q^91 - 3284 * q^92 + 104 * q^93 + 416 * q^94 + 6168 * q^96 - 8 * q^97 + 3480 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more