LMFDB - Embedded newform 160.4.ba.a.107.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,4,Mod(3,160)]

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, 3, 6]))

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

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

chi := DirichletCharacter("160.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	160.ba (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			107.30
Character	$\chi$	$=$	160.107
Dual form			160.4.ba.a.3.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.794525 - 2.71454i) q^{2} +(-3.39208 - 1.40505i) q^{3} +(-6.73746 + 4.31354i) q^{4} +(-10.0394 - 4.92034i) q^{5} +(-1.11896 + 10.3243i) q^{6} -12.0132 q^{7} +(17.0624 + 14.8619i) q^{8} +(-9.55980 - 9.55980i) q^{9} +(-5.37989 + 31.1618i) q^{10} +(-1.26189 + 3.04648i) q^{11} +(28.9148 - 5.16544i) q^{12} +(39.1882 + 16.2323i) 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} +(-18.3550 + 33.5460i) q^{18} +(9.00445 + 21.7387i) q^{19} +(88.8644 - 10.1549i) q^{20} +(40.7499 + 16.8792i) q^{21} +(9.27239 + 1.00496i) q^{22} +74.1079 q^{23} +(-36.9953 - 74.3862i) q^{24} +(76.5804 + 98.7949i) q^{25} +(12.9272 - 119.275i) q^{26} +(56.9320 + 137.446i) q^{27} +(80.9388 - 51.8196i) q^{28} +(-45.2125 - 109.153i) q^{29} +(62.0328 - 98.1444i) q^{30} -11.2948i q^{31} +(-179.064 - 26.5323i) q^{32} +(8.56089 - 8.56089i) q^{33} +(17.4572 + 9.55187i) q^{34} +(120.606 + 59.1093i) q^{35} +(105.645 + 23.1722i) q^{36} +(-263.076 + 108.970i) q^{37} +(51.8562 - 41.7148i) q^{38} +(-110.122 - 110.122i) q^{39} +(-98.1707 - 233.158i) q^{40} +(285.959 - 285.959i) q^{41} +(13.4424 - 124.028i) q^{42} +(145.734 + 351.832i) q^{43} +(-4.63915 - 25.9687i) q^{44} +(48.9375 + 143.012i) q^{45} +(-58.8806 - 201.169i) q^{46} +(285.478 + 285.478i) q^{47} +(-172.531 + 159.527i) q^{48} -198.682 q^{49} +(207.338 - 286.376i) q^{50} +(23.8652 - 9.88529i) q^{51} +(-334.047 + 59.6754i) q^{52} +(-184.814 + 76.5523i) q^{53} +(327.869 - 263.748i) q^{54} +(27.6584 - 24.3760i) q^{55} +(-204.974 - 178.540i) q^{56} -86.3911i q^{57} +(-260.377 + 209.456i) q^{58} +(-326.805 + 788.976i) q^{59} +(-315.704 - 90.4125i) q^{60} +(-251.331 + 104.105i) q^{61} +(-30.6601 + 8.97396i) 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} +(-122.534 + 295.823i) q^{67} +(12.0587 - 54.9775i) q^{68} +(-251.380 - 104.125i) q^{69} +(64.6300 - 374.354i) q^{70} +(166.176 - 166.176i) q^{71} +(-21.0359 - 305.190i) q^{72} +411.925i q^{73} +(504.823 + 627.552i) q^{74} +(-120.956 - 442.720i) q^{75} +(-154.438 - 107.622i) q^{76} +(15.1594 - 36.5981i) q^{77} +(-211.437 + 386.427i) q^{78} +119.435i q^{79} +(-554.917 + 451.738i) q^{80} -181.191i q^{81} +(-1003.45 - 549.046i) q^{82} +(-365.712 + 882.907i) q^{83} +(-347.360 + 62.0537i) q^{84} +(74.4232 - 25.4669i) q^{85} +(839.273 - 675.139i) q^{86} +433.781i q^{87} +(-66.8073 + 33.2260i) q^{88} +(625.108 - 625.108i) q^{89} +(349.331 - 246.470i) q^{90} +(-470.777 - 195.002i) q^{91} +(-499.299 + 319.667i) q^{92} +(-15.8697 + 38.3128i) 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} +(157.858 + 539.330i) 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} - 8 q^{7} - 88 q^{8} - 16 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} - 64 q^{14} - 8 q^{15} - 8 q^{16} - 36 q^{18} + 48 q^{19} + 304 q^{20} - 8 q^{21} - 436 q^{22}+ \cdots + 2760 q^{98}+O(q^{100}) $ 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 - 88 * q^8 - 16 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 - 64 * q^14 - 8 * q^15 - 8 * q^16 - 36 * q^18 + 48 * q^19 + 304 * q^20 - 8 * q^21 - 436 * q^22 - 8 * q^23 - 736 * q^24 - 4 * q^25 - 8 * q^26 + 104 * q^27 - 260 * q^28 - 632 * q^30 + 336 * q^32 - 8 * q^33 - 696 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 2244 * q^38 + 816 * q^40 - 8 * q^41 + 452 * q^42 - 868 * q^43 - 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 1384 * q^48 + 11368 * q^49 + 28 * q^50 + 1480 * q^51 + 320 * q^52 - 4 * q^53 - 2968 * q^54 + 284 * q^55 - 344 * q^56 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 + 496 * q^62 - 2744 * q^63 - 816 * q^64 - 8 * q^65 + 552 * q^66 - 1852 * q^67 + 1224 * q^68 - 216 * q^69 - 980 * q^70 - 232 * q^71 + 664 * q^72 - 112 * q^75 + 824 * q^76 - 1376 * q^77 - 5744 * q^78 - 4528 * q^80 + 524 * q^82 - 2684 * q^83 - 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 5256 * q^88 + 2068 * q^90 - 8 * q^91 - 3796 * q^92 + 104 * q^93 - 416 * q^94 + 6168 * q^96 - 8 * q^97 + 2760 * q^98

Character values

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

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

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 $

$2$	−0.794525	−	2.71454i	−0.280907	−	0.959735i
$2$	−0.794525	−	2.71454i	−0.280907	−	0.959735i
$3$	−3.39208	−	1.40505i	−0.652807	−	0.270402i	0.0316012	−	0.999501i	$-0.489939\pi$
$3$	−3.39208	−	1.40505i	−0.652807	−	0.270402i	−0.684408	+	0.729099i	$0.739939\pi$
$4$	−6.73746	+	4.31354i	−0.842183	+	0.539192i
$5$	−10.0394	−	4.92034i	−0.897954	−	0.440089i
$5$	−10.0394	−	4.92034i	−0.897954	−	0.440089i
$6$	−1.11896	+	10.3243i	−0.0761358	+	0.702479i
$7$	−12.0132			−0.648654			−0.324327	−	0.945945i	$-0.605138\pi$
$7$	−12.0132			−0.648654			−0.324327	+	0.945945i	$0.605138\pi$
$8$	17.0624	+	14.8619i	0.754057	+	0.656809i
$9$	−9.55980	−	9.55980i	−0.354067	−	0.354067i
$10$	−5.37989	+	31.1618i	−0.170127	+	0.985422i
$11$	−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	$0.139390\pi$
$12$	28.9148	−	5.16544i	0.695581	−	0.124261i
$13$	39.1882	+	16.2323i	0.836065	+	0.346309i	0.759301	−	0.650740i	$-0.225541\pi$
$13$	39.1882	+	16.2323i	0.836065	+	0.346309i	0.0767641	+	0.997049i	$0.475541\pi$
$14$	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	$-0.765982\pi$
$17$	−4.97489	+	4.97489i	−0.0709758	+	0.0709758i	0.670728	+	0.741704i	$0.265982\pi$
$18$	−18.3550	+	33.5460i	−0.240350	+	0.439270i
$19$	9.00445	+	21.7387i	0.108724	+	0.262484i	0.968872	−	0.247561i	$-0.0796290\pi$
$19$	9.00445	+	21.7387i	0.108724	+	0.262484i	−0.860148	+	0.510044i	$0.829629\pi$
$20$	88.8644	−	10.1549i	0.993534	−	0.113535i
$21$	40.7499	+	16.8792i	0.423446	+	0.175397i
$22$	9.27239	+	1.00496i	0.0898582	+	0.00973897i
$23$	74.1079			0.671851			0.335925	−	0.941889i	$-0.390951\pi$
$23$	74.1079			0.671851			0.335925	+	0.941889i	$0.390951\pi$
$24$	−36.9953	−	74.3862i	−0.314651	−	0.632668i
$25$	76.5804	+	98.7949i	0.612644	+	0.790359i
$26$	12.9272	−	119.275i	0.0975089	−	0.899681i
$27$	56.9320	+	137.446i	0.405799	+	0.979684i
$28$	80.9388	−	51.8196i	0.546285	−	0.349749i
$29$	−45.2125	−	109.153i	−0.289509	−	0.698936i	0.710480	−	0.703718i	$-0.248478\pi$
$29$	−45.2125	−	109.153i	−0.289509	−	0.698936i	−0.999989	+	0.00478173i	$0.998478\pi$
$30$	62.0328	−	98.1444i	0.377520	−	0.597288i
$31$		−	11.2948i		−	0.0654386i	−0.999465	−	0.0327193i	$-0.989583\pi$
$31$		−	11.2948i		−	0.0654386i	0.999465	−	0.0327193i	$-0.0104167\pi$
$32$	−179.064	−	26.5323i	−0.989200	−	0.146572i
$33$	8.56089	−	8.56089i	0.0451594	−	0.0451594i
$34$	17.4572	+	9.55187i	0.0880555	+	0.0481803i
$35$	120.606	+	59.1093i	0.582462	+	0.285466i
$36$	105.645	+	23.1722i	0.489099	+	0.107279i
$37$	−263.076	+	108.970i	−1.16890	+	0.484176i	−0.880830	−	0.473432i	$-0.843015\pi$
$37$	−263.076	+	108.970i	−1.16890	+	0.484176i	−0.288074	+	0.957608i	$0.593015\pi$
$38$	51.8562	−	41.7148i	0.221373	−	0.178080i
$39$	−110.122	−	110.122i	−0.452146	−	0.452146i
$40$	−98.1707	−	233.158i	−0.388054	−	0.921637i
$41$	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	$-0.0298523\pi$
$42$	13.4424	−	124.028i	0.0493858	−	0.455666i
$43$	145.734	+	351.832i	0.516841	+	1.24776i	0.939834	+	0.341632i	$0.110980\pi$
$43$	145.734	+	351.832i	0.516841	+	1.24776i	−0.422993	+	0.906133i	$0.639020\pi$
$44$	−4.63915	−	25.9687i	−0.0158949	−	0.0889758i
$45$	48.9375	+	143.012i	0.162115	+	0.473757i
$46$	−58.8806	−	201.169i	−0.188727	−	0.644799i
$47$	285.478	+	285.478i	0.885984	+	0.885984i	0.994135	−	0.108151i	$-0.0344929\pi$
$47$	285.478	+	285.478i	0.885984	+	0.885984i	−0.108151	+	0.994135i	$0.534493\pi$
$48$	−172.531	+	159.527i	−0.518806	+	0.479703i
$49$	−198.682			−0.579248
$50$	207.338	−	286.376i	0.586440	−	0.809993i
$51$	23.8652	−	9.88529i	0.0655254	−	0.0271415i
$52$	−334.047	+	59.6754i	−0.890847	+	0.159144i
$53$	−184.814	+	76.5523i	−0.478983	+	0.198401i	−0.609094	−	0.793098i	$-0.708467\pi$
$53$	−184.814	+	76.5523i	−0.478983	+	0.198401i	0.130111	+	0.991499i	$0.458467\pi$
$54$	327.869	−	263.748i	0.826246	−	0.664659i
$55$	27.6584	−	24.3760i	0.0678083	−	0.0597610i
$56$	−204.974	−	178.540i	−0.489122	−	0.426042i
$57$		−	86.3911i		−	0.200750i
$58$	−260.377	+	209.456i	−0.589468	+	0.474188i
$59$	−326.805	+	788.976i	−0.721124	+	1.74095i	−0.0510005	+	0.998699i	$0.516241\pi$
$59$	−326.805	+	788.976i	−0.721124	+	1.74095i	−0.670124	+	0.742249i	$0.733759\pi$
$60$	−315.704	−	90.4125i	−0.679286	−	0.194537i
$61$	−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	$0.467160\pi$
$62$	−30.6601	+	8.97396i	−0.0628037	+	0.0183822i
$63$	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
$67$	−122.534	+	295.823i	−0.223431	+	0.539411i	−0.995352	−	0.0963085i	$-0.969296\pi$
$67$	−122.534	+	295.823i	−0.223431	+	0.539411i	0.771920	+	0.635719i	$0.219296\pi$
$68$	12.0587	−	54.9775i	0.0215050	−	0.0980441i
$69$	−251.380	−	104.125i	−0.438589	−	0.181669i
$70$	64.6300	−	374.354i	0.110354	−	0.639198i
$71$	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	$0.187071\pi$
$72$	−21.0359	−	305.190i	−0.0344321	−	0.499541i
$73$			411.925i			0.660441i	0.943904	+	0.330220i	$0.107123\pi$
$73$			411.925i			0.660441i	−0.943904	+	0.330220i	$0.892877\pi$
$74$	504.823	+	627.552i	0.793034	+	0.985830i
$75$	−120.956	−	442.720i	−0.186224	−	0.681612i
$76$	−154.438	−	107.622i	−0.233095	−	0.162436i
$77$	15.1594	−	36.5981i	0.0224360	−	0.0541654i
$78$	−211.437	+	386.427i	−0.306930	+	0.560952i
$79$			119.435i			0.170095i	0.996377	+	0.0850473i	$0.0271041\pi$
$79$			119.435i			0.170095i	−0.996377	+	0.0850473i	$0.972896\pi$
$80$	−554.917	+	451.738i	−0.775520	+	0.631323i
$81$		−	181.191i		−	0.248548i
$82$	−1003.45	−	549.046i	−1.35137	−	0.739415i
$83$	−365.712	+	882.907i	−0.483640	+	1.16761i	0.474228	+	0.880402i	$0.342727\pi$
$83$	−365.712	+	882.907i	−0.483640	+	1.16761i	−0.957868	+	0.287208i	$0.907273\pi$
$84$	−347.360	+	62.0537i	−0.451192	+	0.0806025i
$85$	74.4232	−	25.4669i	0.0949686	−	0.0324973i
$86$	839.273	−	675.139i	1.05234	−	0.846536i
$87$			433.781i			0.534554i
$88$	−66.8073	+	33.2260i	−0.0809282	+	0.0402488i
$89$	625.108	−	625.108i	0.744509	−	0.744509i	−0.228933	−	0.973442i	$-0.573524\pi$
$89$	625.108	−	625.108i	0.744509	−	0.744509i	0.973442	+	0.228933i	$0.0735237\pi$
$90$	349.331	−	246.470i	0.409142	−	0.288669i
$91$	−470.777	−	195.002i	−0.542317	−	0.224635i
$92$	−499.299	+	319.667i	−0.565821	+	0.362257i
$93$	−15.8697	+	38.3128i	−0.0176947	+	0.0427188i
$94$	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	−0.998907	−	0.0467378i	$-0.985117\pi$
$97$	−998.946	−	998.946i	−1.04565	−	1.04565i	−0.0467378	−	0.998907i	$-0.514883\pi$
$98$	157.858	+	539.330i	0.162715	+	0.555924i
$99$	41.1871	−	17.0603i	0.0418128	−	0.0173194i
$100$	−942.113	−	335.294i	−0.942113	−	0.335294i
$101$	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	$0.0642960\pi$
$102$	−45.7955	−	56.9290i	−0.0444552	−	0.0552628i
$103$		−	571.762i		−	0.546964i	−0.961877	−	0.273482i	$-0.911825\pi$
$103$		−	571.762i		−	0.546964i	0.961877	−	0.273482i	$-0.0881755\pi$
$104$	427.400	+	859.371i	0.402981	+	0.810272i
$105$	−326.055	−	369.961i	−0.303045	−	0.343852i
$106$	354.643	+	440.861i	0.324962	+	0.403964i
$107$	1400.06	−	579.924i	1.26494	−	0.523957i	0.353520	−	0.935427i	$-0.384985\pi$
$107$	1400.06	−	579.924i	1.26494	−	0.523957i	0.911423	+	0.411470i	$0.134985\pi$
$108$	−976.455	−	680.458i	−0.869995	−	0.606270i
$109$	−233.187	+	96.5892i	−0.204911	+	0.0848767i	−0.482778	−	0.875743i	$-0.660372\pi$
$109$	−233.187	+	96.5892i	−0.204911	+	0.0848767i	0.277868	+	0.960619i	$0.410372\pi$
$110$	−88.1448	−	55.7125i	−0.0764025	−	0.0482907i
$111$	1045.48			0.893991
$112$	−321.796	+	698.265i	−0.271490	+	0.589106i
$113$	1025.32	+	1025.32i	0.853575	+	0.853575i	0.990571	−	0.136997i	$-0.0437451\pi$
$113$	1025.32	+	1025.32i	0.853575	+	0.853575i	−0.136997	+	0.990571i	$0.543745\pi$
$114$	−234.512	+	68.6398i	−0.192667	+	0.0563922i
$115$	−744.001	−	364.636i	−0.603291	−	0.295674i
$116$	775.452	+	540.386i	0.620680	+	0.432531i
$117$	−219.454	−	529.808i	−0.173406	−	0.418639i
$118$	2401.36	+	260.263i	1.87342	+	0.203044i
$119$	59.7646	−	59.7646i	0.0460387	−	0.0460387i
$120$	5.40584	+	928.825i	0.00411236	+	0.706581i
$121$	933.470	+	933.470i	0.701330	+	0.701330i
$122$	482.285	+	599.534i	0.357902	+	0.444912i
$123$	−1371.78	+	568.212i	−1.00561	+	0.416536i
$124$	48.7204	+	76.0980i	0.0352840	+	0.0551113i
$125$	−282.719	−	1368.65i	−0.202297	−	0.979324i
$126$	220.503	−	402.996i	0.155904	−	0.284934i
$127$	−555.699	+	555.699i	−0.388270	+	0.388270i	−0.874070	−	0.485800i	$-0.838528\pi$
$127$	−555.699	+	555.699i	−0.388270	+	0.388270i	0.485800	+	0.874070i	$0.338528\pi$
$128$	1320.89	−	593.641i	0.912117	−	0.409929i
$129$		−	1398.21i		−	0.954304i
$130$	−716.655	+	1133.85i	−0.483498	+	0.764960i
$131$	−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	$0.905265\pi$
$132$	−20.7509	+	94.6064i	−0.0136828	+	0.0623820i
$133$	−108.173	−	261.152i	−0.0705245	−	0.170261i
$134$	900.380	+	97.5846i	0.580455	+	0.0629106i
$135$	104.717	−	1660.00i	0.0667597	−	1.05830i
$136$	−158.820	+	10.9470i	−0.100137	+	0.00690221i
$137$	1326.19			0.827038			0.413519	−	0.910496i	$-0.364300\pi$
$137$	1326.19			0.827038			0.413519	+	0.910496i	$0.364300\pi$
$138$	−82.9240	+	765.112i	−0.0511519	+	0.471961i
$139$	1346.20	+	557.613i	0.821460	+	0.340260i	0.753516	−	0.657429i	$-0.228356\pi$
$139$	1346.20	+	557.613i	0.821460	+	0.340260i	0.0679438	+	0.997689i	$0.478356\pi$
$140$	−1067.55	+	121.993i	−0.644460	+	0.0736448i
$141$	−567.255	−	1369.48i	−0.338805	−	0.817948i
$142$	−583.121	−	319.060i	−0.344609	−	0.188556i
$143$	−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
$147$	673.946	+	279.158i	0.378137	+	0.156629i
$148$	1302.42	−	1868.97i	0.723367	−	1.03803i
$149$	−37.2039	+	89.8182i	−0.0204555	+	0.0493838i	−0.933777	−	0.357855i	$-0.883508\pi$
$149$	−37.2039	+	89.8182i	−0.0204555	+	0.0493838i	0.913322	+	0.407239i	$0.133508\pi$
$150$	−1105.68	+	680.091i	−0.601855	+	0.370195i
$151$	−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	$0.885899\pi$
$152$	−169.441	+	504.736i	−0.0904174	+	0.269339i
$153$	95.1179			0.0502603
$154$	−111.391	−	12.0728i	−0.0582869	−	0.00631722i
$155$	−55.5741	+	113.393i	−0.0287988	+	0.0587609i
$156$	1216.96	+	266.928i	0.624584	+	0.136996i
$157$	1988.60	+	823.704i	1.01087	+	0.418718i	0.825774	−	0.564001i	$-0.190739\pi$
$157$	1988.60	+	823.704i	1.01087	+	0.418718i	0.185101	+	0.982719i	$0.440739\pi$
$158$	324.211	−	94.8940i	0.163246	−	0.0477807i
$159$	734.463			0.366331
$160$	1667.16	+	1147.43i	0.823752	+	0.566951i
$161$	−890.276			−0.435799
$162$	−491.851	+	143.961i	−0.238540	+	0.0698187i
$163$	1813.65	+	751.240i	0.871511	+	0.360992i	0.773199	−	0.634164i	$-0.218656\pi$
$163$	1813.65	+	751.240i	0.871511	+	0.360992i	0.0983126	+	0.995156i	$0.468656\pi$
$164$	−693.143	+	3160.14i	−0.330033	+	1.50467i
$165$	−128.069	+	43.8239i	−0.0604252	+	0.0206769i
$166$	2687.25	+	291.249i	1.25645	+	0.136176i
$167$	797.200			0.369396			0.184698	−	0.982795i	$-0.440869\pi$
$167$	797.200			0.369396			0.184698	+	0.982795i	$0.440869\pi$
$168$	444.433	+	893.620i	0.204100	+	0.410383i
$169$	−281.288	−	281.288i	−0.128033	−	0.128033i
$170$	−128.262	−	181.791i	−0.0578662	−	0.0820160i
$171$	121.737	−	293.898i	0.0544411	−	0.131432i
$172$	−2499.52	−	1741.83i	−1.10806	−	0.772169i
$173$	−3460.25	−	1433.28i	−1.52068	−	0.629887i	−0.542954	−	0.839763i	$-0.682694\pi$
$173$	−3460.25	−	1433.28i	−1.52068	−	0.629887i	−0.977728	+	0.209875i	$0.932694\pi$
$174$	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
$178$	−2193.54	−	1200.22i	−0.923669	−	0.505394i
$179$	1627.35	+	3928.78i	0.679520	+	1.64051i	0.764892	+	0.644158i	$0.222792\pi$
$179$	1627.35	+	3928.78i	0.679520	+	1.64051i	−0.0853719	+	0.996349i	$0.527208\pi$
$180$	−946.604	−	752.447i	−0.391976	−	0.311578i
$181$	−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	$0.827552\pi$
$182$	−155.297	+	1432.88i	−0.0632495	+	0.583582i
$183$	998.808			0.403464
$184$	1264.46	+	1101.38i	0.506614	+	0.441278i
$185$	3177.30	+	200.431i	1.26270	+	0.0796539i
$186$	116.610	+	12.6384i	0.0459693	+	0.00498222i
$187$	−8.87811	−	21.4337i	−0.00347183	−	0.00838173i
$188$	−3154.82	−	691.976i	−1.22388	−	0.268444i
$189$	−683.938	−	1651.17i	−0.263223	−	0.635476i
$190$	−725.858	+	163.643i	−0.277154	+	0.0624837i
$191$			2743.59i			1.03937i	0.854359	+	0.519684i	$0.173950\pi$
$191$			2743.59i			1.03937i	−0.854359	+	0.519684i	$0.826050\pi$
$192$	474.294	−	1819.02i	0.178277	−	0.683733i
$193$	−2581.44	+	2581.44i	−0.962778	+	0.962778i	−0.999332	−	0.0365538i	$-0.988362\pi$
$193$	−2581.44	+	2581.44i	−0.962778	+	0.962778i	0.0365538	+	0.999332i	$0.488362\pi$
$194$	−1917.99	+	3505.37i	−0.709813	+	1.29727i
$195$	563.727	+	1647.41i	0.207022	+	0.604991i
$196$	1338.61	−	857.022i	0.487832	−	0.312326i
$197$	−529.339	+	219.259i	−0.191441	+	0.0792974i	−0.476344	−	0.879259i	$-0.658038\pi$
$197$	−529.339	+	219.259i	−0.191441	+	0.0792974i	0.284904	+	0.958556i	$0.408038\pi$
$198$	−79.0350	−	98.2494i	−0.0283675	−	0.0352640i
$199$	−1280.95	−	1280.95i	−0.456301	−	0.456301i	0.441139	−	0.897439i	$-0.354575\pi$
$199$	−1280.95	−	1280.95i	−0.456301	−	0.456301i	−0.897439	+	0.441139i	$0.854575\pi$
$200$	−161.637	+	2823.80i	−0.0571474	+	0.998366i
$201$	831.291	−	831.291i	0.291715	−	0.291715i
$202$	−1082.06	−	117.276i	−0.376899	−	0.0408489i
$203$	543.149	+	1311.28i	0.187791	+	0.453368i
$204$	−118.150	+	169.545i	−0.0405499	+	0.0581889i
$205$	−4277.89	+	1463.85i	−1.45747	+	0.498731i
$206$	−1552.07	+	454.279i	−0.524941	+	0.153646i
$207$	−708.457	−	708.457i	−0.237880	−	0.237880i
$208$	1993.22	−	1842.99i	0.664446	−	0.614366i
$209$	−77.5889			−0.0256791
$210$	−745.216	+	1179.03i	−0.244880	+	0.387433i
$211$	−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	$0.458474\pi$
$212$	914.963	−	1312.97i	0.296415	−	0.425354i
$213$	−797.167	+	330.197i	−0.256436	+	0.106219i
$214$	−2686.61	−	3339.76i	−0.858191	−	1.06683i
$215$	268.052	−	4249.25i	0.0850278	−	1.34789i
$216$	−1071.31	+	3191.27i	−0.337471	+	1.00527i
$217$			135.687i			0.0424470i
$218$	447.468	+	556.253i	0.139020	+	0.172817i
$219$	578.774	−	1397.28i	0.178584	−	0.431140i
$220$	−81.2007	+	283.538i	−0.0248843	+	0.0868914i
$221$	−275.711	+	114.203i	−0.0839199	+	0.0347608i
$222$	−830.663	−	2838.01i	−0.251128	−	0.857994i
$223$	−1719.35	−	1719.35i	−0.516307	−	0.516307i	0.400145	−	0.916452i	$-0.368960\pi$
$223$	−1719.35	−	1719.35i	−0.516307	−	0.516307i	−0.916452	+	0.400145i	$0.868960\pi$
$224$	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
$227$	−1801.62	+	4349.50i	−0.526775	+	1.27175i	0.406850	+	0.913495i	$0.366627\pi$
$227$	−1801.62	+	4349.50i	−0.526775	+	1.27175i	−0.933625	+	0.358252i	$0.883373\pi$
$228$	372.651	+	582.056i	0.108243	+	0.169069i
$229$	893.817	+	370.231i	0.257926	+	0.106836i	0.507900	−	0.861416i	$-0.330422\pi$
$229$	893.817	+	370.231i	0.257926	+	0.106836i	−0.249974	+	0.968253i	$0.580422\pi$
$230$	−398.693	+	2309.33i	−0.114300	+	0.662056i
$231$	−102.844	+	102.844i	−0.0292928	+	0.0292928i
$232$	850.784	−	2534.34i	0.240762	−	0.717189i
$233$			620.995i			0.174604i	0.996182	+	0.0873021i	$0.0278245\pi$
$233$			620.995i			0.174604i	−0.996182	+	0.0873021i	$0.972175\pi$
$234$	−1263.82	+	1016.66i	−0.353072	+	0.284023i
$235$	−1461.39	−	4270.69i	−0.405661	−	1.18548i
$236$	−1201.45	−	6725.38i	−0.331388	−	1.85502i
$237$	167.812	−	405.133i	0.0459938	−	0.111039i
$238$	−209.718	−	114.749i	−0.0571176	−	0.0312524i
$239$		−	3556.78i		−	0.962633i	−0.876547	−	0.481316i	$-0.840159\pi$
$239$		−	3556.78i		−	0.962633i	0.876547	−	0.481316i	$-0.159841\pi$
$240$	2517.04	−	752.649i	0.676976	−	0.202430i
$241$			2502.17i			0.668793i	0.942433	+	0.334396i	$0.108532\pi$
$241$			2502.17i			0.668793i	−0.942433	+	0.334396i	$0.891468\pi$
$242$	1792.28	−	3275.61i	0.476083	−	0.870100i
$243$	1282.58	−	3096.42i	0.338591	−	0.817431i
$244$	1244.27	−	1785.53i	0.326461	−	0.468470i
$245$	1994.65	+	977.584i	0.520138	+	0.254921i
$246$	2632.35	+	3272.31i	0.682246	+	0.848108i
$247$			998.061i			0.257106i
$248$	167.861	−	192.715i	0.0429807	−	0.0493444i
$249$	2481.05	−	2481.05i	0.631447	−	0.631447i
$250$	−3490.62	+	1854.88i	−0.883065	+	0.469251i
$251$	−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	$0.814572\pi$
$252$	−1269.14	−	278.373i	−0.317256	−	0.0695868i
$253$	−93.5161	+	225.768i	−0.0232384	+	0.0561024i
$254$	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	0.995675	+	0.0929061i	$0.0296156\pi$
$257$	4484.98	+	4484.98i	1.08858	+	1.08858i	0.0929061	+	0.995675i	$0.470384\pi$
$258$	−3795.49	+	1110.91i	−0.915879	+	0.268071i
$259$	3160.40	−	1309.08i	0.758214	−	0.314063i
$260$	3647.27	+	1044.52i	0.869977	+	0.249148i
$261$	−611.255	+	1475.70i	−0.144965	+	0.349975i
$262$	−627.419	+	504.716i	−0.147947	+	0.119013i
$263$		−	4897.27i		−	1.14821i	−0.818783	−	0.574104i	$-0.805351\pi$
$263$		−	4897.27i		−	1.14821i	0.818783	−	0.574104i	$-0.194649\pi$
$264$	273.300	−	18.8379i	0.0637138	−	0.00439163i
$265$	2232.09	+	140.805i	0.517419	+	0.0326398i
$266$	−622.961	+	501.131i	−0.143595	+	0.115512i
$267$	−2998.73	+	1242.11i	−0.687337	+	0.284704i
$268$	−450.477	−	2521.65i	−0.102676	−	0.574755i
$269$	−5017.63	+	2078.37i	−1.13729	+	0.471080i	−0.870252	−	0.492607i	$-0.836044\pi$
$269$	−5017.63	+	2078.37i	−1.13729	+	0.471080i	−0.267036	+	0.963687i	$0.586044\pi$
$270$	−4589.35	+	1034.66i	−1.03444	+	0.233212i
$271$	−6941.79			−1.55603			−0.778015	−	0.628246i	$-0.783773\pi$
$271$	−6941.79			−1.55603			−0.778015	+	0.628246i	$0.783773\pi$
$272$	155.902	+	422.425i	0.0347535	+	0.0941664i
$273$	1322.93	+	1322.93i	0.293287	+	0.293287i
$274$	−1053.69	−	3600.00i	−0.232321	−	0.793737i
$275$	−397.613	+	108.632i	−0.0871889	+	0.0238209i
$276$	2142.81	−	382.800i	0.467327	−	0.0834849i
$277$	2758.94	+	6660.67i	0.598442	+	1.44477i	0.875168	+	0.483819i	$0.160751\pi$
$277$	2758.94	+	6660.67i	0.598442	+	1.44477i	−0.276726	+	0.960949i	$0.589249\pi$
$278$	444.077	−	4097.34i	0.0958055	−	0.883965i
$279$	−107.976	+	107.976i	−0.0231696	+	0.0231696i
$280$	1179.35	+	2800.98i	0.251713	+	0.597823i
$281$	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	$0.457174\pi$
$282$	−3266.80	+	2627.92i	−0.689840	+	0.554930i
$283$	−5704.94	+	2363.06i	−1.19832	+	0.496359i	−0.890454	−	0.455073i	$-0.849613\pi$
$283$	−5704.94	+	2363.06i	−1.19832	+	0.496359i	−0.307861	+	0.951431i	$0.599613\pi$
$284$	−402.797	+	1836.41i	−0.0841605	+	0.383700i
$285$	−425.074	+	867.317i	−0.0883480	+	0.180265i
$286$	347.055	+	189.894i	0.0717546	+	0.0392611i
$287$	−3435.30	+	3435.30i	−0.706548	+	0.706548i
$288$	1458.18	+	1965.46i	0.298347	+	0.402139i
$289$			4863.50i			0.989925i
$290$	3644.63	−	821.673i	0.738000	−	0.166380i
$291$	1984.94	+	4792.07i	0.399860	+	0.965348i
$292$	−1776.85	−	2775.33i	−0.356105	−	0.556212i
$293$	1933.08	+	4666.87i	0.385433	+	0.930518i	0.990894	+	0.134643i	$0.0429887\pi$
$293$	1933.08	+	4666.87i	0.385433	+	0.930518i	−0.605461	+	0.795875i	$0.707011\pi$
$294$	222.318	−	2051.25i	0.0441015	−	0.406910i
$295$	7162.97	−	6312.88i	1.41371	−	1.24593i
$296$	−6108.19	−	2050.53i	−1.19943	−	0.402651i
$297$	−490.568			−0.0958439
$298$	273.374	+	29.6287i	0.0531415	+	0.00575956i
$299$	2904.15	+	1202.94i	0.561711	+	0.232668i
$300$	2724.62	+	2461.06i	0.524354	+	0.473631i
$301$	−1750.73	−	4226.64i	−0.335251	−	0.809368i
$302$	−2086.30	+	3812.97i	−0.397527	+	0.726529i
$303$	−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
$307$	2083.40	+	862.973i	0.387316	+	0.160431i	0.567840	−	0.823139i	$-0.307779\pi$
$307$	2083.40	+	862.973i	0.387316	+	0.160431i	−0.180524	+	0.983571i	$0.557779\pi$
$308$	55.7312	+	311.969i	0.0103103	+	0.0577145i
$309$	−803.352	+	1939.46i	−0.147900	+	0.357062i
$310$	351.965	+	60.7646i	0.0644847	+	0.0111329i
$311$	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	$0.530758\pi$
$312$	−242.320	−	3515.58i	−0.0439701	−	0.637918i
$313$	302.961			0.0547105			0.0273552	−	0.999626i	$-0.491291\pi$
$313$	302.961			0.0547105			0.0273552	+	0.999626i	$0.491291\pi$
$314$	655.988	−	6052.58i	0.117897	−	1.08779i
$315$	−587.898	−	1718.04i	−0.105156	−	0.307304i
$316$	−515.187	−	804.688i	−0.0917137	−	0.143251i
$317$	8762.33	+	3629.48i	1.55250	+	0.643065i	0.983766	−	0.179458i	$-0.0574344\pi$
$317$	8762.33	+	3629.48i	1.55250	+	0.643065i	0.568731	+	0.822523i	$0.307434\pi$
$318$	−583.549	−	1993.73i	−0.102905	−	0.351581i
$319$	389.584			0.0683778
$320$	1790.14	−	5437.22i	0.312725	−	0.949844i
$321$	−5563.94			−0.967443
$322$	707.346	+	2416.69i	0.122419	+	0.418251i
$323$	−152.944	−	63.3513i	−0.0263468	−	0.0109132i
$324$	781.575	+	1220.77i	0.134015	+	0.209322i
$325$	1397.38	+	5114.67i	0.238501	+	0.872956i
$326$	598.279	−	5520.12i	0.101643	−	0.937825i
$327$	926.702			0.156718
$328$	9129.04	−	629.241i	1.53679	−	0.105927i
$329$	−3429.52	−	3429.52i	−0.574697	−	0.574697i
$330$	220.716	+	312.829i	0.0368182	+	0.0521839i
$331$	−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	$0.989728\pi$
$332$	−1344.48	−	7526.07i	−0.222253	−	1.24412i
$333$	3556.68	+	1473.23i	0.585300	+	0.242439i
$334$	−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	$-0.776078\pi$
$337$	−715.985	+	715.985i	−0.115733	+	0.115733i	0.646868	+	0.762602i	$0.276078\pi$
$338$	−540.077	+	987.056i	−0.0869121	+	0.158843i
$339$	−2037.35	−	4918.59i	−0.326412	−	0.788027i
$340$	−391.571	+	492.610i	−0.0624586	+	0.0785751i
$341$	34.4092	+	14.2528i	0.00546441	+	0.00226343i
$342$	−894.521	−	96.9495i	−0.141433	−	0.0153287i
$343$	6507.36			1.02439
$344$	−2742.33	+	8168.96i	−0.429816	+	1.28035i
$345$	2011.38	+	2282.23i	0.313882	+	0.356149i
$346$	−1141.45	+	10531.8i	−0.177355	+	1.63639i
$347$	−991.865	−	2394.57i	−0.153447	−	0.370454i	0.828398	−	0.560140i	$-0.189253\pi$
$347$	−991.865	−	2394.57i	−0.153447	−	0.370454i	−0.981845	+	0.189687i	$0.939253\pi$
$348$	−1871.13	−	2922.58i	−0.288227	−	0.450192i
$349$	69.2537	+	167.193i	0.0106220	+	0.0256437i	0.929102	−	0.369825i	$-0.120582\pi$
$349$	69.2537	+	167.193i	0.0106220	+	0.0256437i	−0.918480	+	0.395468i	$0.870582\pi$
$350$	−2490.80	+	3440.30i	−0.380397	+	0.525405i
$351$			6310.39i			0.959612i
$352$	306.790	−	512.034i	0.0464544	−	0.0775327i
$353$	−5731.93	+	5731.93i	−0.864248	+	0.864248i	−0.991828	−	0.127580i	$-0.959279\pi$
$353$	−5731.93	+	5731.93i	−0.864248	+	0.864248i	0.127580	+	0.991828i	$0.459279\pi$
$354$	−7779.94	−	4256.86i	−1.16808	−	0.639123i
$355$	−2485.95	+	850.668i	−0.371664	+	0.127180i
$356$	−1515.21	+	6908.07i	−0.225579	+	1.02845i
$357$	−286.699	+	118.754i	−0.0425033	+	0.0176055i
$358$	9371.86	−	7539.03i	1.38357	−	1.11299i
$359$	−6048.49	−	6048.49i	−0.889212	−	0.889212i	0.105236	−	0.994447i	$-0.466440\pi$
$359$	−6048.49	−	6048.49i	−0.889212	−	0.889212i	−0.994447	+	0.105236i	$0.966440\pi$
$360$	−1290.45	+	3167.43i	−0.188924	+	0.463718i
$361$	4458.56	−	4458.56i	0.650030	−	0.650030i
$362$	−882.031	+	8138.20i	−0.128062	+	1.18159i
$363$	−1854.84	−	4477.98i	−0.268193	−	0.647474i
$364$	4012.99	−	716.895i	0.577851	−	0.103229i
$365$	2026.81	−	4135.49i	0.290653	−	0.593046i
$366$	−793.578	−	2711.30i	−0.113336	−	0.387219i
$367$	391.822	+	391.822i	0.0557301	+	0.0557301i	0.734423	−	0.678692i	$-0.237453\pi$
$367$	391.822	+	391.822i	0.0557301	+	0.0557301i	−0.678692	+	0.734423i	$0.737453\pi$
$368$	1985.11	−	4307.49i	0.281198	−	0.610173i
$369$	−5467.43			−0.771336
$370$	−1980.37	−	8784.17i	−0.278255	−	1.23424i
$371$	2220.21	−	919.641i	0.310694	−	0.128694i
$372$	−58.3423	−	326.585i	−0.00813148	−	0.0455179i
$373$	6843.62	−	2834.72i	0.949997	−	0.393502i	0.146767	−	0.989171i	$-0.453113\pi$
$373$	6843.62	−	2834.72i	0.949997	−	0.393502i	0.803230	+	0.595669i	$0.203113\pi$
$374$	−51.1286	+	41.1296i	−0.00706898	+	0.00568652i
$375$	−964.007	+	5039.80i	−0.132750	+	0.694011i
$376$	628.182	+	9113.67i	0.0861596	+	1.25000i
$377$		−	5011.39i		−	0.684615i
$378$	−3938.77	+	3168.47i	−0.535948	+	0.431134i
$379$	701.841	−	1694.39i	0.0951218	−	0.229644i	−0.869156	−	0.494539i	$-0.835337\pi$
$379$	701.841	−	1694.39i	0.0951218	−	0.229644i	0.964277	+	0.264894i	$0.0853370\pi$
$380$	1020.93	+	1840.35i	0.137822	+	0.248442i
$381$	2665.76	−	1104.20i	0.358455	−	0.148477i
$382$	7447.59	−	2179.85i	0.997518	−	0.291966i
$383$	2861.48	+	2861.48i	0.381762	+	0.381762i	0.871737	−	0.489975i	$-0.162994\pi$
$383$	2861.48	+	2861.48i	0.381762	+	0.381762i	−0.489975	+	0.871737i	$0.662994\pi$
$384$	−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
$387$	1970.26	−	4756.63i	0.258796	−	0.624788i
$388$	11039.3	+	2421.37i	1.44443	+	0.316820i
$389$	−11410.7	−	4726.46i	−1.48726	−	0.616044i	−0.516542	−	0.856262i	$-0.672781\pi$
$389$	−11410.7	−	4726.46i	−1.48726	−	0.616044i	−0.970719	+	0.240218i	$0.922781\pi$
$390$	4024.06	−	2839.17i	0.522477	−	0.368633i
$391$	−368.679	+	368.679i	−0.0476851	+	0.0476851i
$392$	−3389.98	−	2952.79i	−0.436786	−	0.380455i
$393$			1045.26i			0.134164i
$394$	1015.76	+	1262.71i	0.129882	+	0.161457i
$395$	587.661	−	1199.06i	0.0748567	−	0.152737i
$396$	−203.907	+	292.605i	−0.0258755	+	0.0371312i
$397$	5208.01	−	12573.3i	0.658395	−	1.58950i	−0.141889	−	0.989883i	$-0.545317\pi$
$397$	5208.01	−	12573.3i	0.658395	−	1.58950i	0.800283	−	0.599622i	$-0.204683\pi$
$398$	−2459.44	+	4494.92i	−0.309750	+	0.566106i
$399$			1037.84i			0.130218i
$400$	7793.76	−	1804.81i	0.974220	−	0.225601i
$401$		−	13793.5i		−	1.71775i	−0.512189	−	0.858873i	$-0.671165\pi$
$401$		−	13793.5i		−	1.71775i	0.512189	−	0.858873i	$-0.328835\pi$
$402$	−2917.05	−	1596.09i	−0.361914	−	0.198024i
$403$	183.339	−	442.621i	0.0226620	−	0.0547109i
$404$	541.376	+	3030.48i	0.0666695	+	0.373198i
$405$	−891.523	+	1819.06i	−0.109383	+	0.223184i
$406$	3127.97	−	2516.24i	0.382361	−	0.307584i
$407$		−	938.963i		−	0.114355i
$408$	554.111	+	186.016i	0.0672367	+	0.0225715i
$409$	−7402.41	+	7402.41i	−0.894928	+	0.894928i	−0.994982	−	0.100054i	$-0.968098\pi$
$409$	−7402.41	+	7402.41i	−0.894928	+	0.894928i	0.100054	+	0.994982i	$0.468098\pi$
$410$	7372.57	+	10449.4i	0.888062	+	1.25868i
$411$	−4498.55	−	1863.36i	−0.539896	−	0.223632i
$412$	2466.32	+	3852.22i	0.294919	+	0.460644i
$413$	3925.98	−	9478.16i	0.467760	−	1.12927i
$414$	−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
$418$	61.6463	+	210.618i	0.00721345	+	0.0246452i
$419$	13020.6	−	5393.31i	1.51813	−	0.628832i	0.540918	−	0.841075i	$-0.318077\pi$
$419$	13020.6	−	5393.31i	1.51813	−	0.628832i	0.977217	+	0.212243i	$0.0680770\pi$
$420$	3792.62	+	1086.15i	0.440622	+	0.126187i
$421$	−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	$0.855511\pi$
$422$	2817.35	+	3502.28i	0.324991	+	0.404001i
$423$		−	5458.22i		−	0.627395i
$424$	−4291.07	−	1440.52i	−0.491492	−	0.164995i
$425$	−872.473	−	110.515i	−0.0995792	−	0.0126135i
$426$	1529.70	+	1901.59i	0.173977	+	0.216273i
$427$	3019.30	−	1250.63i	0.342188	−	0.141739i
$428$	−6931.33	+	9946.43i	−0.782800	+	1.12331i
$429$	474.448	−	196.523i	0.0533953	−	0.0221170i
$430$	−11747.7	+	2648.50i	−1.31750	+	0.297028i
$431$	−10639.1			−1.18902			−0.594509	−	0.804089i	$-0.702653\pi$
$431$	−10639.1			−1.18902			−0.594509	+	0.804089i	$0.702653\pi$
$432$	9514.01	+	372.583i	1.05959	+	0.0414952i
$433$	−1433.14	−	1433.14i	−0.159059	−	0.159059i	0.623091	−	0.782150i	$-0.285877\pi$
$433$	−1433.14	−	1433.14i	−0.159059	−	0.159059i	−0.782150	+	0.623091i	$0.785877\pi$
$434$	368.327	−	107.806i	0.0407379	−	0.0119237i
$435$	2134.35	−	4354.91i	0.235251	−	0.480005i
$436$	1154.45	−	1656.63i	0.126807	−	0.181968i
$437$	667.301	+	1611.01i	0.0730465	+	0.176350i
$438$	−4252.84	−	460.929i	−0.463946	−	0.0502832i
$439$	−4484.72	+	4484.72i	−0.487572	+	0.487572i	−0.907539	−	0.419967i	$-0.862042\pi$
$439$	−4484.72	+	4484.72i	−0.487572	+	0.487572i	0.419967	+	0.907539i	$0.362042\pi$
$440$	834.190	−	4.85506i	0.0903828	−	0.000526036i
$441$	1899.36	+	1899.36i	0.205092	+	0.205092i
$442$	529.068	+	657.690i	0.0569348	+	0.0707763i
$443$	−11730.6	+	4858.96i	−1.25810	+	0.521120i	−0.909325	−	0.416088i	$-0.863401\pi$
$443$	−11730.6	+	4858.96i	−1.25810	+	0.521120i	−0.348771	+	0.937208i	$0.613401\pi$
$444$	−7043.91	+	4509.74i	−0.752903	+	0.482033i
$445$	−9351.48	+	3199.98i	−0.996185	+	0.340885i
$446$	−3301.19	+	6033.33i	−0.350484	+	0.640552i
$447$	252.398	−	252.398i	0.0267069	−	0.0267069i
$448$	−843.906	−	6092.61i	−0.0889974	−	0.642520i
$449$		−	10769.6i		−	1.13195i	−0.824421	−	0.565977i	$-0.808499\pi$
$449$		−	10769.6i		−	1.13195i	0.824421	−	0.565977i	$-0.191501\pi$
$450$	−4719.80	+	755.587i	−0.494430	+	0.0791527i
$451$	510.318	+	1232.02i	0.0532815	+	0.128633i
$452$	−11330.8	−	2485.29i	−1.17911	−	0.258625i
$453$	2159.13	+	5212.59i	0.223939	+	0.540638i
$454$	13238.3	+	1434.79i	1.36851	+	0.148322i
$455$	3766.86	+	4274.10i	0.388116	+	0.440380i
$456$	1283.94	−	1474.03i	0.131855	−	0.151377i
$457$	5003.28			0.512130			0.256065	−	0.966660i	$-0.417574\pi$
$457$	5003.28			0.512130			0.256065	+	0.966660i	$0.417574\pi$
$458$	294.848	−	2720.46i	0.0300815	−	0.277552i
$459$	−967.009	−	400.548i	−0.0983357	−	0.0407320i
$460$	6585.55	−	752.556i	0.667506	−	0.0762785i
$461$	−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	$-0.441654\pi$
$462$	360.886	+	197.462i	0.0363419	+	0.0198848i
$463$	−12644.4	+	12644.4i	−1.26919	+	1.26919i	−0.322684	+	0.946507i	$0.604585\pi$
$463$	−12644.4	+	12644.4i	−1.26919	+	1.26919i	−0.946507	+	0.322684i	$0.895415\pi$
$464$	−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
$467$	−9317.15	−	3859.29i	−0.923225	−	0.382413i	−0.130121	−	0.991498i	$-0.541537\pi$
$467$	−9317.15	−	3859.29i	−0.923225	−	0.382413i	−0.793104	+	0.609086i	$0.791537\pi$
$468$	3763.91	+	2622.94i	0.371767	+	0.259072i
$469$	1472.03	−	3553.79i	0.144930	−	0.349891i
$470$	−10431.8	+	7360.16i	−1.02380	+	0.722338i
$471$	−5588.15	−	5588.15i	−0.546684	−	0.546684i
$472$	−17301.7	+	8604.85i	−1.68724	+	0.839132i
$473$	−1255.75			−0.122071
$474$	−1233.08	−	133.643i	−0.119488	−	0.0129503i
$475$	−1458.10	+	2554.35i	−0.140847	+	0.246740i
$476$	−144.865	+	660.458i	−0.0139493	+	0.0635967i
$477$	2498.60	+	1034.96i	0.239839	+	0.0993446i
$478$	−9655.03	+	2825.95i	−0.923872	+	0.270410i
$479$	10719.2			1.02249			0.511245	−	0.859435i	$-0.329184\pi$
$479$	10719.2			1.02249			0.511245	+	0.859435i	$0.329184\pi$
$480$	−4042.95	−	6234.61i	−0.384447	−	0.592853i
$481$	−12078.3			−1.14495
$482$	6792.25	−	1988.04i	0.641864	−	0.187869i
$483$	3019.89	+	1250.88i	0.284492	+	0.117841i
$484$	−10315.8	−	2262.66i	−0.968800	−	0.212496i
$485$	5113.69	+	14944.0i	0.478765	+	1.39912i
$486$	−9424.41	−	1021.43i	−0.879630	−	0.0953356i
$487$	6357.86			0.591585			0.295793	−	0.955252i	$-0.404416\pi$
$487$	6357.86			0.591585			0.295793	+	0.955252i	$0.404416\pi$
$488$	−5835.49	−	1958.98i	−0.541312	−	0.181719i
$489$	−5096.54	−	5096.54i	−0.471316	−	0.471316i
$490$	1068.89	−	6191.28i	0.0985458	−	0.570804i
$491$	−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	$0.163487\pi$
$492$	6791.34	−	9745.55i	0.622312	−	0.893015i
$493$	767.950	+	318.095i	0.0701556	+	0.0290594i
$494$	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
$498$	−8706.18	−	4763.66i	−0.783400	−	0.428644i
$499$	6137.21	+	14816.5i	0.550580	+	1.32922i	0.917044	+	0.398785i	$0.130568\pi$
$499$	6137.21	+	14816.5i	0.550580	+	1.32922i	−0.366465	+	0.930432i	$0.619432\pi$
$500$	7808.52	+	8001.69i	0.698415	+	0.715693i
$501$	−2704.17	−	1120.10i	−0.241145	−	0.0998854i
$502$	−1359.71	+	12545.6i	−0.120890	+	1.11541i
$503$	−248.276			−0.0220081			−0.0110041	−	0.999939i	$-0.503503\pi$
$503$	−248.276			−0.0220081			−0.0110041	+	0.999939i	$0.503503\pi$
$504$	252.710	+	3666.32i	0.0223345	+	0.324029i
$505$	−3227.66	+	2844.61i	−0.284414	+	0.250660i
$506$	687.157	+	74.4752i	0.0603713	+	0.00654313i
$507$	558.929	+	1349.37i	0.0489604	+	0.118201i
$508$	1346.97	−	6141.03i	0.117642	−	0.536347i
$509$	−1291.12	−	3117.03i	−0.112432	−	0.271434i	0.857641	−	0.514249i	$-0.171929\pi$
$509$	−1291.12	−	3117.03i	−0.112432	−	0.271434i	−0.970073	+	0.242815i	$0.921929\pi$
$510$	179.651	+	796.864i	0.0155982	+	0.0691877i
$511$		−	4948.56i		−	0.428398i
$512$	−6338.73	+	9697.33i	−0.547139	+	0.837042i
$513$	−2475.25	+	2475.25i	−0.213031	+	0.213031i
$514$	8611.23	−	15738.1i	0.738959	−	1.35054i
$515$	−2813.26	+	5740.16i	−0.240713	+	0.491149i
$516$	6031.22	+	9420.36i	0.514554	+	0.803699i
$517$	−1229.94	+	509.459i	−0.104628	+	0.0433385i
$518$	−6064.56	−	7538.93i	−0.514405	−	0.639462i
$519$	9723.63	+	9723.63i	0.822389	+	0.822389i
$520$	−62.4527	−	10730.6i	−0.00526680	−	0.904935i
$521$	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	$0.0780440\pi$
$522$	4491.51	+	486.796i	0.376605	+	0.0408170i
$523$	−7884.10	−	19033.9i	−0.659173	−	1.59138i	−0.799083	−	0.601221i	$-0.794681\pi$
$523$	−7884.10	−	19033.9i	−0.659173	−	1.59138i	0.139910	−	0.990164i	$-0.455319\pi$
$524$	1868.57	+	1302.14i	0.155780	+	0.108558i
$525$	1453.07	+	5318.50i	0.120795	+	0.442130i
$526$	−13293.8	+	3891.00i	−1.10197	+	0.322539i
$527$	56.1901	+	56.1901i	0.00464456	+	0.00464456i
$528$	−268.280	−	726.917i	−0.0221125	−	0.0599147i
$529$	−6675.02			−0.548617
$530$	−1391.23	−	6170.96i	−0.114021	−	0.505754i
$531$	10666.6	−	4418.27i	0.871738	−	0.361086i
$532$	1855.30	+	1292.89i	0.151198	+	0.105365i
$533$	15848.0	−	6564.45i	1.28790	−	0.533467i
$534$	5754.33	+	7153.27i	0.466319	+	0.579686i
$535$	−16909.2	−	1066.67i	−1.36645	−	0.0861984i
$536$	−6487.21	+	3226.35i	−0.522770	+	0.259995i
$537$		−	15613.3i		−	1.25468i
$538$	9628.46	+	11969.2i	0.771584	+	0.959165i
$539$	250.715	−	605.280i	0.0200354	−	0.0483697i
$540$	6454.97	+	11635.9i	0.514403	+	0.927278i
$541$	−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	$0.420912\pi$
$542$	5515.43	+	18843.8i	0.437099	+	1.49338i
$543$	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
$547$	−5200.96	+	12556.2i	−0.406539	+	0.981472i	0.579502	+	0.814971i	$0.303247\pi$
$547$	−5200.96	+	12556.2i	−0.406539	+	0.981472i	−0.986041	+	0.166501i	$0.946753\pi$
$548$	−8935.16	+	5720.58i	−0.696517	+	0.445933i
$549$	3397.89	+	1407.45i	0.264150	+	0.109415i
$550$	610.799	+	993.025i	0.0473537	+	0.0769868i
$551$	1965.72	−	1965.72i	0.151983	−	0.151983i
$552$	−2741.64	−	5512.61i	−0.211399	−	0.425058i
$553$		−	1434.80i		−	0.110333i
$554$	15888.6	−	12781.3i	1.21849	−	0.980191i
$555$	−10496.1	−	5144.14i	−0.802763	−	0.393435i
$556$	−11475.2	+	2049.98i	−0.875285	+	0.156364i
$557$	1370.80	−	3309.42i	0.104278	−	0.251749i	−0.863125	−	0.504990i	$-0.831496\pi$
$557$	1370.80	−	3309.42i	0.104278	−	0.251749i	0.967403	+	0.253240i	$0.0814963\pi$
$558$	378.893	+	207.315i	0.0287452	+	0.0157282i
$559$			16153.2i			1.22220i
$560$	6666.35	−	5426.84i	0.503044	−	0.409510i
$561$			85.1789i			0.00641044i
$562$	10175.5	−	18596.9i	0.763749	−	1.39585i
$563$	7696.35	−	18580.6i	0.576132	−	1.39091i	−0.320126	−	0.947375i	$-0.603725\pi$
$563$	7696.35	−	18580.6i	0.576132	−	1.39091i	0.896259	−	0.443532i	$-0.146275\pi$
$564$	9729.15	+	6779.91i	0.726367	+	0.506180i
$565$	−5248.70	−	15338.5i	−0.390822	−	1.14212i
$566$	10947.3	+	13608.8i	0.812988	+	1.01063i
$567$			2176.69i			0.161221i
$568$	5305.03	−	365.662i	0.391891	−	0.0270121i
$569$	−2801.08	+	2801.08i	−0.206375	+	0.206375i	−0.802725	−	0.596350i	$-0.796617\pi$
$569$	−2801.08	+	2801.08i	−0.206375	+	0.206375i	0.596350	+	0.802725i	$0.296617\pi$
$570$	2692.10	+	464.775i	0.197824	+	0.0341531i
$571$	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	$0.405804\pi$
$572$	239.732	−	1092.97i	0.0175239	−	0.0798941i
$573$	3854.88	−	9306.50i	0.281047	−	0.678507i
$574$	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	0.686307	−	0.727312i	$-0.259231\pi$
$577$	−568.339	−	568.339i	−0.0410056	−	0.0410056i	−0.727312	+	0.686307i	$0.759231\pi$
$578$	13202.2	−	3864.17i	0.950066	−	0.278077i
$579$	12383.5	−	5129.42i	0.888845	−	0.368172i
$580$	−5126.21	−	9240.66i	−0.366990	−	0.661547i
$581$	4393.39	−	10606.6i	0.313715	−	0.757375i
$582$	11431.2	−	9195.63i	0.814155	−	0.654933i
$583$		−	659.631i		−	0.0468595i
$584$	−6121.99	+	7028.41i	−0.433784	+	0.498010i
$585$	−403.647	+	6398.76i	−0.0285278	+	0.452233i
$586$	11132.5	−	8955.38i	0.784780	−	0.631303i
$587$	9196.94	−	3809.50i	0.646675	−	0.267862i	−0.0351441	−	0.999382i	$-0.511189\pi$
$587$	9196.94	−	3809.50i	0.646675	−	0.267862i	0.681819	+	0.731521i	$0.261189\pi$
$588$	−5744.84	+	1026.28i	−0.402914	+	0.0719780i
$589$	245.533	−	101.703i	0.0171766	−	0.00711477i
$590$	−22827.7	−	14428.4i	−1.59289	−	1.00679i
$591$	2103.63			0.146416
$592$	−713.137	+	18210.1i	−0.0495097	+	1.26424i
$593$	−6443.67	−	6443.67i	−0.446222	−	0.446222i	0.447874	−	0.894097i	$-0.352181\pi$
$593$	−6443.67	−	6443.67i	−0.446222	−	0.446222i	−0.894097	+	0.447874i	$0.852181\pi$
$594$	389.768	+	1331.67i	0.0269232	+	0.0919847i
$595$	−894.064	+	305.940i	−0.0616018	+	0.0210795i
$596$	−136.774	−	765.627i	−0.00940016	−	0.0526196i
$597$	2545.29	+	6144.86i	0.174492	+	0.421261i
$598$	958.007	−	8839.21i	0.0655114	−	0.604452i
$599$	301.285	−	301.285i	0.0205512	−	0.0205512i	−0.696757	−	0.717308i	$-0.745374\pi$
$599$	301.285	−	301.285i	0.0205512	−	0.0205512i	0.717308	+	0.696757i	$0.245374\pi$
$600$	4515.87	−	9351.48i	0.307266	−	0.636287i
$601$	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	$0.599774\pi$
$602$	−10082.4	+	8110.61i	−0.682604	+	0.549109i
$603$	3999.41	−	1656.61i	0.270097	−	0.111878i
$604$	12008.1	+	2633.85i	0.808943	+	0.177433i
$605$	−4778.52	−	13964.5i	−0.321115	−	0.938410i
$606$	3505.67	+	1918.16i	0.234997	+	0.128581i
$607$	−13559.4	+	13559.4i	−0.906686	+	0.906686i	−0.996003	−	0.0893168i	$-0.971532\pi$
$607$	−13559.4	+	13559.4i	−0.906686	+	0.906686i	0.0893168	+	0.996003i	$0.471532\pi$
$608$	−1035.60	−	4131.53i	−0.0690774	−	0.275585i
$609$		−	5211.11i		−	0.346741i
$610$	−1891.95	−	8391.99i	−0.125579	−	0.557019i
$611$	6553.40	+	15821.3i	0.433915	+	1.04756i
$612$	−640.853	+	410.295i	−0.0423284	+	0.0271000i
$613$	−72.3275	−	174.614i	−0.00476554	−	0.0115050i	0.921479	−	0.388429i	$-0.126982\pi$
$613$	−72.3275	−	174.614i	−0.00476554	−	0.0115050i	−0.926244	+	0.376923i	$0.876982\pi$
$614$	687.261	−	6341.13i	0.0451720	−	0.416787i
$615$	16567.7	+	1045.13i	1.08630	+	0.0685262i
$616$	802.572	−	399.151i	0.0524944	−	0.0261076i
$617$	−20159.2			−1.31537			−0.657683	−	0.753295i	$-0.728463\pi$
$617$	−20159.2			−1.31537			−0.657683	+	0.753295i	$0.728463\pi$
$618$	5903.04	+	639.780i	0.384231	+	0.0416436i
$619$	3799.70	+	1573.89i	0.246725	+	0.102197i	0.502619	−	0.864508i	$-0.332370\pi$
$619$	3799.70	+	1573.89i	0.246725	+	0.102197i	−0.255894	+	0.966705i	$0.582370\pi$
$620$	−114.697	−	1003.70i	−0.00742956	−	0.0650155i
$621$	4219.11	+	10185.8i	0.272636	+	0.658202i
$622$	9465.34	−	17299.1i	0.610170	−	1.11516i
$623$	−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
$627$	263.188	+	109.016i	0.0167635	+	0.00694368i
$628$	−16951.2	+	3028.22i	−1.07711	+	0.192419i
$629$	766.662	−	1850.89i	0.0485991	−	0.117329i
$630$	−4196.60	+	2960.90i	−0.265391	+	0.187246i
$631$	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	$0.500509\pi$
$632$	−1775.03	+	2037.84i	−0.111720	+	0.128261i
$633$	5834.70			0.366364
$634$	2890.47	−	26669.4i	0.181065	−	1.67063i
$635$	8313.14	−	2844.67i	0.519523	−	0.177776i
$636$	−4948.41	+	3168.13i	−0.308518	+	0.197523i
$637$	−7785.98	−	3225.06i	−0.484289	−	0.200599i
$638$	−309.534	−	1057.54i	−0.0192078	−	0.0656246i
$639$	−3177.21			−0.196696
$640$	−16181.9	−	539.404i	−0.999445	−	0.0333154i
$641$	9340.81			0.575569			0.287785	−	0.957695i	$-0.407081\pi$
$641$	9340.81			0.575569			0.287785	+	0.957695i	$0.407081\pi$
$642$	4420.69	+	15103.6i	0.271761	+	0.928489i
$643$	−13382.9	−	5543.38i	−0.820794	−	0.339984i	−0.0675422	−	0.997716i	$-0.521516\pi$
$643$	−13382.9	−	5543.38i	−0.820794	−	0.339984i	−0.753252	+	0.657732i	$0.771516\pi$
$644$	5998.20	−	3840.24i	0.367022	−	0.234979i
$645$	−6879.66	+	14037.2i	−0.419979	+	0.856922i
$646$	−50.4522	+	465.506i	−0.00307278	+	0.0283515i
$647$	−31085.6			−1.88887			−0.944437	−	0.328692i	$-0.893392\pi$
$647$	−31085.6			−1.88887			−0.944437	+	0.328692i	$0.893392\pi$
$648$	2692.84	−	3091.55i	0.163248	−	0.187419i
$649$	−1991.20	−	1991.20i	−0.120434	−	0.120434i
$650$	12773.7	−	7856.98i	0.770810	−	0.474117i
$651$	190.646	−	460.260i	0.0114777	−	0.0277097i
$652$	−15459.9	+	2761.82i	−0.928616	+	0.165891i
$653$	24513.6	+	10153.9i	1.46905	+	0.608502i	0.966643	−	0.256127i	$-0.0824466\pi$
$653$	24513.6	+	10153.9i	1.46905	+	0.608502i	0.502411	+	0.864629i	$0.332447\pi$
$654$	−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
$658$	−6584.73	+	12034.4i	−0.390121	+	0.712993i
$659$	−993.473	−	2398.45i	−0.0587256	−	0.141776i	0.891793	−	0.452443i	$-0.149448\pi$
$659$	−993.473	−	2398.45i	−0.0587256	−	0.141776i	−0.950519	+	0.310667i	$0.899448\pi$
$660$	673.823	−	847.693i	0.0397402	−	0.0499945i
$661$	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	$0.600693\pi$
$662$	13963.2	+	1513.36i	0.819783	+	0.0888494i
$663$	1095.69			0.0641829
$664$	−19361.6	+	9629.30i	−1.13159	+	0.562785i
$665$	−198.965	+	3154.06i	−0.0116023	+	0.183924i
$666$	1173.26	−	10825.3i	0.0682626	−	0.629836i
$667$	−3350.60	−	8089.07i	−0.194507	−	0.469580i
$668$	−5371.11	+	3438.75i	−0.311099	+	0.199176i
$669$	3416.42	+	8247.97i	0.197439	+	0.476659i
$670$	−8559.15	−	5409.87i	−0.493536	−	0.311943i
$671$		−	897.042i		−	0.0516094i
$672$	−6849.02	−	4103.65i	−0.393165	−	0.235568i
$673$	−18388.0	+	18388.0i	−1.05320	+	1.05320i	−0.0546986	+	0.998503i	$0.517420\pi$
$673$	−18388.0	+	18388.0i	−1.05320	+	1.05320i	−0.998503	+	0.0546986i	$0.982580\pi$
$674$	2512.44	+	1374.70i	0.143584	+	0.0785631i
$675$	−9219.08	+	16150.3i	−0.525693	+	0.920924i
$676$	3108.51	+	681.819i	0.176861	+	0.0387926i
$677$	9018.79	−	3735.71i	0.511995	−	0.212075i	−0.111702	−	0.993742i	$-0.535630\pi$
$677$	9018.79	−	3735.71i	0.511995	−	0.212075i	0.623696	+	0.781667i	$0.285630\pi$
$678$	−11733.0	+	9438.41i	−0.664606	+	0.534631i
$679$	12000.6	+	12000.6i	0.678262	+	0.678262i
$680$	1648.32	+	671.545i	0.0929563	+	0.0378714i
$681$	12222.5	−	12222.5i	0.687765	−	0.687765i
$682$	11.3507	−	104.729i	0.000637305	−	0.00588019i
$683$	−310.934	−	750.661i	−0.0174196	−	0.0420545i	0.914930	−	0.403612i	$-0.132245\pi$
$683$	−310.934	−	750.661i	−0.0174196	−	0.0420545i	−0.932350	+	0.361557i	$0.882245\pi$
$684$	447.545	+	2505.24i	0.0250180	+	0.140044i
$685$	−13314.2	−	6525.32i	−0.742642	−	0.363970i
$686$	−5170.26	−	17664.5i	−0.287757	−	0.983139i
$687$	−2511.71	−	2511.71i	−0.139487	−	0.139487i
$688$	24353.8	+	953.733i	1.34954	+	0.0528499i
$689$	−8485.12			−0.469169
$690$	4597.12	−	7273.28i	0.253637	−	0.401288i
$691$	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	$0.317665\pi$
$692$	29495.8	−	5269.24i	1.62032	−	0.289460i
$693$	−494.791	+	204.949i	−0.0271220	+	0.0112343i
$694$	−5712.10	+	4595.00i	−0.312433	+	0.251331i
$695$	−10771.4	−	12221.9i	−0.587889	−	0.667053i
$696$	−6446.81	+	7401.32i	−0.351100	+	0.403084i
$697$			2845.23i			0.154621i
$698$	398.829	−	320.831i	0.0216274	−	0.0173978i
$699$	872.528	−	2106.47i	0.0472132	−	0.113983i
$700$	11317.8	+	4027.97i	0.611106	+	0.217490i
$701$	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	$0.233510\pi$
$702$	17129.8	−	5013.76i	0.920973	−	0.269562i
$703$	−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
$707$	−1769.06	+	4270.90i	−0.0941053	+	0.227190i
$708$	−5374.07	+	24501.1i	−0.285268	+	1.30058i
$709$	22896.1	+	9483.89i	1.21281	+	0.502363i	0.895117	−	0.445831i	$-0.147092\pi$
$709$	22896.1	+	9483.89i	1.21281	+	0.502363i	0.317693	+	0.948194i	$0.397092\pi$
$710$	4284.32	+	6072.34i	0.226462	+	0.320973i
$711$	1141.77	−	1141.77i	0.0602248	−	0.0602248i
$712$	19956.1	−	1375.52i	1.05040	−	0.0724016i
$713$		−	837.030i		−	0.0439650i
$714$	550.153	+	683.901i	0.0288361	+	0.0358465i
$715$	1479.56	−	506.291i	0.0773879	−	0.0264814i
$716$	−27911.2	−	19450.3i	−1.45683	−	1.01521i
$717$	−4997.45	+	12064.9i	−0.260297	+	0.628413i
$718$	−11613.2	+	21224.5i	−0.603622	+	1.10319i
$719$			26068.2i			1.35213i	0.736844	+	0.676063i	$0.236315\pi$
$719$			26068.2i			1.35213i	−0.736844	+	0.676063i	$0.763685\pi$
$720$	9623.42	+	986.370i	0.498116	+	0.0510553i
$721$			6868.71i			0.354791i
$722$	−15645.4	−	8560.50i	−0.806455	−	0.441259i
$723$	3515.67	−	8487.58i	0.180843	−	0.436593i
$724$	22792.3	−	4071.69i	1.16998	−	0.209010i
$725$	7321.33	−	12825.7i	0.375045	−	0.657014i
$726$	−10681.9	+	8592.91i	−0.546066	+	0.439274i
$727$		−	8760.58i		−	0.446922i	−0.974713	−	0.223461i	$-0.928265\pi$
$727$		−	8760.58i		−	0.446922i	0.974713	−	0.223461i	$-0.0717355\pi$
$728$	−5134.46	−	10323.8i	−0.261395	−	0.525586i
$729$	−12160.5	+	12160.5i	−0.617819	+	0.617819i
$730$	−12836.3	−	2216.11i	−0.650813	−	0.112359i
$731$	−2475.33	−	1025.32i	−0.125244	−	0.0518779i
$732$	−6729.43	+	4308.40i	−0.339791	+	0.217545i
$733$	−7582.20	+	18305.1i	−0.382067	+	0.922391i	0.609499	+	0.792787i	$0.291371\pi$
$733$	−7582.20	+	18305.1i	−0.382067	+	0.922391i	−0.991566	+	0.129604i	$0.958629\pi$
$734$	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
$738$	4344.01	+	14841.6i	0.216674	+	0.740278i
$739$	3928.92	−	1627.41i	0.195572	−	0.0810086i	−0.282748	−	0.959194i	$-0.591246\pi$
$739$	3928.92	−	1627.41i	0.195572	−	0.0810086i	0.478320	+	0.878186i	$0.341246\pi$
$740$	−22271.5	+	12355.0i	−1.10637	+	0.613756i
$741$	1402.32	−	3385.51i	0.0695218	−	0.167840i
$742$	−4260.41	−	5296.17i	−0.210788	−	0.262033i
$743$			23675.4i			1.16900i	0.811394	+	0.584499i	$0.198709\pi$
$743$			23675.4i			1.16900i	−0.811394	+	0.584499i	$0.801291\pi$
$744$	−840.174	+	417.853i	−0.0414009	+	0.0205903i
$745$	815.442	−	718.667i	0.0401013	−	0.0353422i
$746$	−13132.4	−	16325.0i	−0.644518	−	0.801208i
$747$	11936.6	−	4944.28i	0.584653	−	0.242171i
$748$	152.271	+	106.112i	0.00744328	+	0.00518697i
$749$	−16819.3	+	6966.77i	−0.820511	+	0.339867i
$750$	14446.7	−	1387.41i	0.703357	−	0.0675481i
$751$	27311.1			1.32703			0.663513	−	0.748165i	$-0.269065\pi$
$751$	27311.1			1.32703			0.663513	+	0.748165i	$0.269065\pi$
$752$	24240.3	−	8946.26i	1.17547	−	0.433825i
$753$	11582.9	+	11582.9i	0.560565	+	0.560565i
$754$	−13603.6	+	3981.68i	−0.657049	+	0.192313i
$755$	5562.43	+	16255.4i	0.268129	+	0.783568i
$756$	11730.4	+	8174.51i	0.564326	+	0.393259i
$757$	−5463.86	−	13190.9i	−0.262335	−	0.633332i	0.736747	−	0.676168i	$-0.236361\pi$
$757$	−5463.86	−	13190.9i	−0.262335	−	0.633332i	−0.999082	+	0.0428359i	$0.986361\pi$
$758$	−5157.13	−	558.938i	−0.247118	−	0.0267830i
$759$	634.429	−	634.429i	0.0303404	−	0.0303404i
$760$	4184.56	−	4233.56i	0.199724	−	0.202062i
$761$	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	$0.722474\pi$
$762$	−5115.40	−	6359.01i	−0.243191	−	0.302313i
$763$	2801.33	−	1160.35i	0.132916	−	0.0550557i
$764$	−11834.6	−	18484.8i	−0.560419	−	0.875338i
$765$	−954.930	−	468.013i	−0.0451315	−	0.0221190i
$766$	5494.08	−	10041.1i	0.259151	−	0.473629i
$767$	−25613.7	+	25613.7i	−1.20581	+	1.20581i
$768$	4650.90	+	14301.5i	0.218522	+	0.671954i
$769$		−	18959.2i		−	0.889060i	−0.895764	−	0.444530i	$-0.853371\pi$
$769$		−	18959.2i		−	0.889060i	0.895764	−	0.444530i	$-0.146629\pi$
$770$	1058.90	+	669.288i	0.0495588	+	0.0313240i
$771$	−8911.82	−	21515.0i	−0.416279	−	1.00499i
$772$	6257.21	−	28527.5i	0.291712	−	1.32996i
$773$	−16041.6	−	38728.0i	−0.746414	−	1.80200i	−0.577535	−	0.816366i	$-0.695985\pi$
$773$	−16041.6	−	38728.0i	−0.746414	−	1.80200i	−0.168879	−	0.985637i	$-0.554015\pi$
$774$	−14477.5	−	1569.09i	−0.672329	−	0.0728680i
$775$	1115.86	−	864.957i	0.0517200	−	0.0400905i
$776$	−2198.14	−	31890.6i	−0.101686	−	1.47527i
$777$	−12559.7			−0.579891
$778$	−3764.10	+	34730.1i	−0.173457	+	1.60043i
$779$	8791.28	+	3641.47i	0.404339	+	0.167483i
$780$	−10904.2	−	8667.69i	−0.500557	−	0.397888i
$781$	296.554	+	715.946i	0.0135871	+	0.0328022i
$782$	1293.72	+	707.869i	0.0591601	+	0.0323700i
$783$	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
$787$	−36288.3	−	15031.1i	−1.64363	−	0.680814i	−0.646973	−	0.762513i	$-0.723965\pi$
$787$	−36288.3	−	15031.1i	−1.64363	−	0.680814i	−0.996657	+	0.0816990i	$0.973965\pi$
$788$	2620.62	−	3760.58i	0.118472	−	0.170006i
$789$	−6880.90	+	16612.0i	−0.310477	+	0.749558i
$790$	−3721.80	−	642.547i	−0.167615	−	0.0289377i
$791$	−12317.4	−	12317.4i	−0.553675	−	0.553675i
$792$	956.298	+	321.031i	0.0429047	+	0.0144032i
$793$	−11539.1			−0.516726
$794$	−38268.5	−	4147.60i	−1.71045	−	0.185381i
$795$	−7373.59	−	3613.81i	−0.328949	−	0.161218i
$796$	14155.7	+	3104.91i	0.630322	+	0.138255i
$797$	515.178	+	213.394i	0.0228965	+	0.00948405i	0.394102	−	0.919067i	$-0.371056\pi$
$797$	515.178	+	213.394i	0.0228965	+	0.00948405i	−0.371206	+	0.928551i	$0.621056\pi$
$798$	2817.25	−	824.587i	0.124974	−	0.0365790i
$799$	−2840.44			−0.125767
$800$	−11091.6	−	19722.5i	−0.490183	−	0.871620i
$801$	−11951.8			−0.527212
$802$	−37443.1	+	10959.3i	−1.64858	+	0.482527i
$803$	−1254.92	−	519.805i	−0.0551496	−	0.0228437i
$804$	−2014.98	+	9186.60i	−0.0883868	+	0.402968i
$805$	8937.87	+	4380.46i	0.391327	+	0.191790i
$806$	−1347.18	−	146.009i	−0.0588739	−	0.00638085i
$807$	19940.4			0.869810
$808$	7796.23	−	3877.38i	0.339444	−	0.168819i
$809$	−4038.32	−	4038.32i	−0.175501	−	0.175501i	0.613891	−	0.789391i	$-0.289604\pi$
$809$	−4038.32	−	4038.32i	−0.175501	−	0.175501i	−0.789391	+	0.613891i	$0.789604\pi$
$810$	5646.24	+	974.789i	0.244924	+	0.0422847i
$811$	−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	$0.951066\pi$
$812$	−9315.69	−	6491.79i	−0.402607	−	0.280563i
$813$	23547.2	+	9753.55i	1.01579	+	0.420753i
$814$	−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
$818$	25975.5	+	14212.7i	1.11028	+	0.607502i
$819$	2636.35	+	6364.72i	0.112481	+	0.271552i
$820$	22507.7	−	28315.5i	0.958541	−	1.20588i
$821$	−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	$0.656185\pi$
$822$	−1483.96	+	13692.0i	−0.0629672	+	0.580977i
$823$	22557.7			0.955420			0.477710	−	0.878518i	$-0.341467\pi$
$823$	22557.7			0.955420			0.477710	+	0.878518i	$0.341467\pi$
$824$	8497.46	−	9755.60i	0.359251	−	0.412442i
$825$	1501.37	+	190.176i	0.0633587	+	0.00802554i
$826$	−28848.1	−	3126.61i	−1.21520	−	0.131705i
$827$	−5707.30	−	13778.6i	−0.239978	−	0.579359i	0.757302	−	0.653065i	$-0.226517\pi$
$827$	−5707.30	−	13778.6i	−0.239978	−	0.579359i	−0.997280	+	0.0737061i	$0.976517\pi$
$828$	7829.16	+	1717.24i	0.328601	+	0.0720753i
$829$	11953.8	+	28859.0i	0.500811	+	1.20906i	0.949043	+	0.315147i	$0.102054\pi$
$829$	11953.8	+	28859.0i	0.500811	+	1.20906i	−0.448232	+	0.893917i	$0.647946\pi$
$830$	−25545.5	−	16146.2i	−1.06831	−	0.675232i
$831$		−	26470.0i		−	1.10497i
$832$	−5479.44	+	21014.9i	−0.228324	+	0.875673i
$833$	988.421	−	988.421i	0.0411125	−	0.0411125i
$834$	−7263.31	+	13274.6i	−0.301568	+	0.551153i
$835$	−8003.44	−	3922.50i	−0.331701	−	0.162567i
$836$	522.752	−	334.683i	0.0216265	−	0.0138460i
$837$	1552.42	−	643.032i	0.0641092	−	0.0265549i
$838$	−24985.6	−	31059.9i	−1.02997	−	1.28036i
$839$	−21571.6	−	21571.6i	−0.887644	−	0.887644i	0.106653	−	0.994296i	$-0.465987\pi$
$839$	−21571.6	−	21571.6i	−0.887644	−	0.887644i	−0.994296	+	0.106653i	$0.965987\pi$
$840$	−64.9417	−	11158.2i	−0.00266750	−	0.458327i
$841$	7375.50	−	7375.50i	0.302411	−	0.302411i
$842$	36389.2	+	3943.92i	1.48938	+	0.161421i
$843$	−10530.7	−	25423.3i	−0.430244	−	1.03870i
$844$	7268.63	−	10430.5i	0.296441	−	0.425392i
$845$	1439.94	+	4208.00i	0.0586217	+	0.171313i
$846$	−14816.6	+	4336.69i	−0.602133	+	0.176240i
$847$	−11214.0	−	11214.0i	−0.454921	−	0.454921i
$848$	−500.986	+	12792.8i	−0.0202876	+	0.518050i
$849$	22671.8			0.916485
$850$	393.205	+	2456.17i	0.0158668	+	0.0991129i
$851$	−19496.0	+	8075.51i	−0.785329	+	0.325294i
$852$	3946.56	−	5663.30i	0.158694	−	0.227725i
$853$	12621.5	−	5227.98i	0.506624	−	0.209851i	−0.114706	−	0.993399i	$-0.536593\pi$
$853$	12621.5	−	5227.98i	0.506624	−	0.209851i	0.621330	+	0.783549i	$0.286593\pi$
$854$	−5793.81	−	7202.35i	−0.232155	−	0.288594i
$855$	−2668.24	+	2351.58i	−0.106728	+	0.0940614i
$856$	32507.1	+	10912.7i	1.29798	+	0.435733i
$857$		−	17770.4i		−	0.708315i	−0.935186	−	0.354157i	$-0.884768\pi$
$857$		−	17770.4i		−	0.708315i	0.935186	−	0.354157i	$-0.115232\pi$
$858$	−910.430	−	1131.77i	−0.0362256	−	0.0450325i
$859$	782.573	−	1889.30i	0.0310839	−	0.0750431i	−0.907575	−	0.419889i	$-0.862069\pi$
$859$	782.573	−	1889.30i	0.0310839	−	0.0750431i	0.938659	+	0.344846i	$0.112069\pi$
$860$	16523.3	+	29785.4i	0.655164	+	1.18102i
$861$	16479.6	−	6826.07i	0.652291	−	0.270188i
$862$	8453.01	+	28880.2i	0.334003	+	1.14114i
$863$	33081.3	+	33081.3i	1.30487	+	1.30487i	0.925069	+	0.379799i	$0.124007\pi$
$863$	33081.3	+	33081.3i	1.30487	+	1.30487i	0.379799	+	0.925069i	$0.375993\pi$
$864$	−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
$867$	6833.45	−	16497.4i	0.267677	−	0.646230i
$868$	−585.289	−	914.183i	−0.0228871	−	0.0357482i
$869$	−363.855	−	150.714i	−0.0142036	−	0.00588333i
$870$	−13517.4	−	2333.69i	−0.526761	−	0.0909421i
$871$	−9603.76	+	9603.76i	−0.373606	+	0.373606i
$872$	−5414.22	−	1817.56i	−0.210262	−	0.0705853i
$873$			19099.4i			0.740456i
$874$	3842.96	−	3091.40i	0.148730	−	0.119643i
$875$	3396.38	+	16441.9i	0.131221	+	0.635243i
$876$	2127.77	+	11910.7i	0.0820671	+	0.459390i
$877$	−1761.88	+	4253.56i	−0.0678387	+	0.163777i	−0.954163	−	0.299289i	$-0.903251\pi$
$877$	−1761.88	+	4253.56i	−0.0678387	+	0.163777i	0.886324	+	0.463066i	$0.153251\pi$
$878$	15737.2	+	8610.74i	0.604902	+	0.330978i
$879$		−	18546.5i		−	0.711670i
$880$	−675.964	−	2260.59i	−0.0258940	−	0.0865958i
$881$		−	35372.9i		−	1.35272i	−0.736573	−	0.676358i	$-0.763557\pi$
$881$		−	35372.9i		−	1.35272i	0.736573	−	0.676358i	$-0.236443\pi$
$882$	3646.80	−	6664.98i	0.139222	−	0.254446i
$883$	−2089.27	+	5043.94i	−0.0796257	+	0.192233i	−0.958679	−	0.284490i	$-0.908176\pi$
$883$	−2089.27	+	5043.94i	−0.0796257	+	0.192233i	0.879053	+	0.476724i	$0.158176\pi$
$884$	1364.97	−	1958.73i	0.0519332	−	0.0745239i
$885$	−33167.3	+	11349.5i	−1.25978	+	0.431085i
$886$	22510.1	+	27982.6i	0.853545	+	1.06105i
$887$			14546.7i			0.550655i	0.961351	+	0.275327i	$0.0887863\pi$
$887$			14546.7i			0.550655i	−0.961351	+	0.275327i	$0.911214\pi$
$888$	17838.4	+	15537.9i	0.674120	+	0.587181i
$889$	6675.75	−	6675.75i	0.251853	−	0.251853i
$890$	16116.5	+	22842.5i	0.606994	+	0.860317i
$891$	551.994	+	228.644i	0.0207548	+	0.00859691i
$892$	19000.6	+	4167.58i	0.713214	+	0.156436i
$893$	−3635.34	+	8776.48i	−0.136228	+	0.328884i
$894$	−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
$898$	−29234.4	+	8556.69i	−1.08638	+	0.317974i
$899$	−1232.85	+	510.664i	−0.0457374	+	0.0189450i
$900$	5801.07	+	12211.8i	0.214855	+	0.452288i
$901$	538.588	−	1300.27i	0.0199145	−	0.0480778i
$902$	2938.90	−	2364.15i	0.108486	−	0.0872700i
$903$			16797.0i			0.619013i
$904$	2256.17	+	32732.6i	0.0830079	+	1.20428i
$905$	21394.3	+	24275.3i	0.785825	+	0.891643i
$906$	12434.3	−	10002.6i	0.455963	−	0.366791i
$907$	22654.5	−	9383.82i	0.829363	−	0.343533i	0.0727122	−	0.997353i	$-0.476835\pi$
$907$	22654.5	−	9383.82i	0.829363	−	0.343533i	0.756650	+	0.653820i	$0.226835\pi$
$908$	−6623.38	−	37076.0i	−0.242076	−	1.35508i
$909$	−4806.43	+	1990.89i	−0.175379	+	0.0726442i
$910$	8609.35	−	13621.2i	0.313623	−	0.496195i
$911$	33980.0			1.23579			0.617897	−	0.786259i	$-0.287985\pi$
$911$	33980.0			1.23579			0.617897	+	0.786259i	$0.287985\pi$
$912$	−5021.45	−	2314.14i	−0.182321	−	0.0840227i
$913$	−2228.27	−	2228.27i	−0.0807720	−	0.0807720i
$914$	−3975.23	−	13581.6i	−0.143861	−	0.491510i
$915$	−10027.5	−	4914.48i	−0.362293	−	0.177560i
$916$	−7619.06	+	1361.10i	−0.274826	+	0.0490960i
$917$	1308.80	+	3159.73i	0.0471324	+	0.113788i
$918$	−318.992	+	2943.23i	−0.0114687	+	0.105818i
$919$	19873.9	−	19873.9i	0.713362	−	0.713362i	−0.253875	−	0.967237i	$-0.581705\pi$
$919$	19873.9	−	19873.9i	0.713362	−	0.713362i	0.967237	+	0.253875i	$0.0817051\pi$
$920$	−7275.23	−	17278.8i	−0.260714	−	0.619202i
$921$	−5854.55	−	5854.55i	−0.209462	−	0.209462i
$922$	−36588.5	+	29433.0i	−1.30692	+	1.05133i
$923$	9209.53	−	3814.71i	0.328424	−	0.136038i
$924$	249.286	−	1136.53i	0.00887544	−	0.0404644i
$925$	−30912.1	−	17645.6i	−1.09879	−	0.627227i
$926$	44370.0	+	24277.5i	1.57461	+	0.861562i
$927$	−5465.93	+	5465.93i	−0.193662	+	0.193662i
$928$	5199.87	+	20744.9i	0.183938	+	0.733821i
$929$		−	31232.0i		−	1.10300i	−0.834174	−	0.551502i	$-0.814055\pi$
$929$		−	31232.0i		−	1.10300i	0.834174	−	0.551502i	$-0.185945\pi$
$930$	−1108.52	−	700.646i	−0.0390857	−	0.0247044i
$931$	−1789.02	−	4319.08i	−0.0629783	−	0.152043i
$932$	−2678.69	−	4183.93i	−0.0941452	−	0.147049i
$933$	−9795.75	−	23649.0i	−0.343728	−	0.829833i
$934$	−3073.49	+	28358.1i	−0.107674	+	0.993474i
$935$	−16.3297	+	258.865i	−0.000571166	+	0.00905432i
$936$	4129.56	−	12301.3i	0.144208	−	0.429573i
$937$	19550.2			0.681619			0.340809	−	0.940132i	$-0.389299\pi$
$937$	19550.2			0.681619			0.340809	+	0.940132i	$0.389299\pi$
$938$	−10816.5	−	1172.31i	−0.376515	−	0.0408072i
$939$	−1027.67	−	425.675i	−0.0357154	−	0.0147938i
$940$	28267.8	+	22469.8i	0.980845	+	0.779665i
$941$	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	$0.729615\pi$
$942$	−10729.3	+	19609.2i	−0.371105	+	0.678239i
$943$	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
$947$	−11644.0	−	4823.11i	−0.399556	−	0.165501i	0.173851	−	0.984772i	$-0.444379\pi$
$947$	−11644.0	−	4823.11i	−0.399556	−	0.165501i	−0.573407	+	0.819270i	$0.694379\pi$
$948$	616.933	+	3453.43i	0.0211361	+	0.118315i
$949$	−6686.48	+	16142.6i	−0.228717	+	0.552171i
$950$	8092.39	+	1928.59i	0.276370	+	0.0658650i
$951$	−24623.0	−	24623.0i	−0.839595	−	0.839595i
$952$	1907.94	−	131.509i	0.0649545	−	0.00447715i
$953$	−49123.9			−1.66976			−0.834879	−	0.550434i	$-0.814462\pi$
$953$	−49123.9			−1.66976			−0.834879	+	0.550434i	$0.814462\pi$
$954$	824.227	−	7604.86i	0.0279720	−	0.258089i
$955$	13499.4	−	27544.1i	0.457414	−	0.933305i
$956$	15342.3	+	23963.7i	0.519044	+	0.810713i
$957$	−1321.50	−	547.384i	−0.0446375	−	0.0184895i
$958$	−8516.68	−	29097.7i	−0.287225	−	0.981320i
$959$	−15931.9			−0.536462
$960$	−13711.9	+	15928.3i	−0.460988	+	0.535503i
$961$	29663.4			0.995718
$962$	9596.50	+	32787.0i	0.321625	+	1.09885i
$963$	−18928.3	−	7840.34i	−0.633390	−	0.262359i
$964$	−10793.2	−	16858.3i	−0.360608	−	0.563246i
$965$	38617.8	−	13214.6i	1.28824	−	0.440823i
$966$	996.187	−	9191.48i	0.0331799	−	0.306140i
$967$	−12099.9			−0.402387			−0.201193	−	0.979552i	$-0.564482\pi$
$967$	−12099.9			−0.402387			−0.201193	+	0.979552i	$0.564482\pi$
$968$	2054.06	+	29800.3i	0.0682026	+	0.989483i
$969$	429.786	+	429.786i	0.0142484	+	0.0142484i
$970$	36503.2	−	25754.7i	1.20829	−	0.852509i
$971$	−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	$0.796879\pi$
$972$	4715.21	+	26394.5i	0.155597	+	0.870992i
$973$	−16172.2	−	6698.74i	−0.532844	−	0.220711i
$974$	−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	$-0.698403\pi$
$977$	6969.87	−	6969.87i	0.228235	−	0.228235i	0.811955	+	0.583720i	$0.198403\pi$
$978$	−9785.44	+	17884.1i	−0.319943	+	0.584734i
$979$	1115.56	+	2693.19i	0.0364182	+	0.0879212i
$980$	−17655.8	+	2017.59i	−0.575502	+	0.0657648i
$981$	3152.59	+	1305.85i	0.102604	+	0.0425000i
$982$	7380.15	+	799.873i	0.239827	+	0.0259928i
$983$	26451.0			0.858247			0.429124	−	0.903246i	$-0.358822\pi$
$983$	26451.0			0.858247			0.429124	+	0.903246i	$0.358822\pi$
$984$	−31850.6	−	10692.3i	−1.03187	−	0.346400i
$985$	6393.10	+	403.290i	0.206803	+	0.0130456i
$986$	253.327	−	2337.36i	0.00818213	−	0.0754938i
$987$	6814.58	+	16451.8i	0.219767	+	0.530565i
$988$	−4305.17	−	6724.40i	−0.138629	−	0.216530i
$989$	10800.0	+	26073.5i	0.347240	+	0.838312i
$990$	310.046	+	1375.25i	0.00995344	+	0.0441497i
$991$		−	49389.7i		−	1.58316i	−0.611064	−	0.791581i	$-0.709258\pi$
$991$		−	49389.7i		−	1.58316i	0.611064	−	0.791581i	$-0.290742\pi$
$992$	−299.676	+	2022.49i	−0.00959145	+	0.0647319i
$993$	12891.8	−	12891.8i	0.411993	−	0.411993i
$994$	7005.18	+	3832.94i	0.223532	+	0.122307i
$995$	6557.27	+	19162.7i	0.208924	+	0.610550i
$996$	−6013.88	+	27418.1i	−0.191322	+	0.872265i
$997$	−9381.79	+	3886.07i	−0.298018	+	0.123443i	−0.526682	−	0.850062i	$-0.676564\pi$
$997$	−9381.79	+	3886.07i	−0.298018	+	0.123443i	0.228664	+	0.973505i	$0.426564\pi$
$998$	35343.9	−	28431.8i	1.12103	−	0.901797i
$999$	−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.ba.a.107.30	yes	280
5.3	odd	4		160.4.u.a.43.6	✓	280
32.3	odd	8		160.4.u.a.67.6	yes	280
160.3	even	8	inner	160.4.ba.a.3.30	yes	280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.4.u.a.43.6	✓	280	5.3	odd	4
160.4.u.a.67.6	yes	280	32.3	odd	8
160.4.ba.a.3.30	yes	280	160.3	even	8	inner
160.4.ba.a.107.30	yes	280	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.794525 - 2.71454i) q^{2} +(-3.39208 - 1.40505i) q^{3} +(-6.73746 + 4.31354i) q^{4} +(-10.0394 - 4.92034i) q^{5} +(-1.11896 + 10.3243i) q^{6} -12.0132 q^{7} +(17.0624 + 14.8619i) q^{8} +(-9.55980 - 9.55980i) q^{9} +(-5.37989 + 31.1618i) q^{10} +(-1.26189 + 3.04648i) q^{11} +(28.9148 - 5.16544i) q^{12} +(39.1882 + 16.2323i) 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} +(-18.3550 + 33.5460i) q^{18} +(9.00445 + 21.7387i) q^{19} +(88.8644 - 10.1549i) q^{20} +(40.7499 + 16.8792i) q^{21} +(9.27239 + 1.00496i) q^{22} +74.1079 q^{23} +(-36.9953 - 74.3862i) q^{24} +(76.5804 + 98.7949i) q^{25} +(12.9272 - 119.275i) q^{26} +(56.9320 + 137.446i) q^{27} +(80.9388 - 51.8196i) q^{28} +(-45.2125 - 109.153i) q^{29} +(62.0328 - 98.1444i) q^{30} -11.2948i q^{31} +(-179.064 - 26.5323i) q^{32} +(8.56089 - 8.56089i) q^{33} +(17.4572 + 9.55187i) q^{34} +(120.606 + 59.1093i) q^{35} +(105.645 + 23.1722i) q^{36} +(-263.076 + 108.970i) q^{37} +(51.8562 - 41.7148i) q^{38} +(-110.122 - 110.122i) q^{39} +(-98.1707 - 233.158i) q^{40} +(285.959 - 285.959i) q^{41} +(13.4424 - 124.028i) q^{42} +(145.734 + 351.832i) q^{43} +(-4.63915 - 25.9687i) q^{44} +(48.9375 + 143.012i) q^{45} +(-58.8806 - 201.169i) q^{46} +(285.478 + 285.478i) q^{47} +(-172.531 + 159.527i) q^{48} -198.682 q^{49} +(207.338 - 286.376i) q^{50} +(23.8652 - 9.88529i) q^{51} +(-334.047 + 59.6754i) q^{52} +(-184.814 + 76.5523i) q^{53} +(327.869 - 263.748i) q^{54} +(27.6584 - 24.3760i) q^{55} +(-204.974 - 178.540i) q^{56} -86.3911i q^{57} +(-260.377 + 209.456i) q^{58} +(-326.805 + 788.976i) q^{59} +(-315.704 - 90.4125i) q^{60} +(-251.331 + 104.105i) q^{61} +(-30.6601 + 8.97396i) 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} +(-122.534 + 295.823i) q^{67} +(12.0587 - 54.9775i) q^{68} +(-251.380 - 104.125i) q^{69} +(64.6300 - 374.354i) q^{70} +(166.176 - 166.176i) q^{71} +(-21.0359 - 305.190i) q^{72} +411.925i q^{73} +(504.823 + 627.552i) q^{74} +(-120.956 - 442.720i) q^{75} +(-154.438 - 107.622i) q^{76} +(15.1594 - 36.5981i) q^{77} +(-211.437 + 386.427i) q^{78} +119.435i q^{79} +(-554.917 + 451.738i) q^{80} -181.191i q^{81} +(-1003.45 - 549.046i) q^{82} +(-365.712 + 882.907i) q^{83} +(-347.360 + 62.0537i) q^{84} +(74.4232 - 25.4669i) q^{85} +(839.273 - 675.139i) q^{86} +433.781i q^{87} +(-66.8073 + 33.2260i) q^{88} +(625.108 - 625.108i) q^{89} +(349.331 - 246.470i) q^{90} +(-470.777 - 195.002i) q^{91} +(-499.299 + 319.667i) q^{92} +(-15.8697 + 38.3128i) 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} +(157.858 + 539.330i) q^{98} +(41.1871 - 17.0603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 280 q - 4 q^{2} - 4 q^{3} - 4 q^{5} - 8 q^{6} - 8 q^{7} - 88 q^{8} - 16 q^{10} - 8 q^{11} + 44 q^{12} - 4 q^{13} - 64 q^{14} - 8 q^{15} - 8 q^{16} - 36 q^{18} + 48 q^{19} + 304 q^{20} - 8 q^{21} - 436 q^{22}+ \cdots + 2760 q^{98}+O(q^{100}) \) 280 * q - 4 * q^2 - 4 * q^3 - 4 * q^5 - 8 * q^6 - 8 * q^7 - 88 * q^8 - 16 * q^10 - 8 * q^11 + 44 * q^12 - 4 * q^13 - 64 * q^14 - 8 * q^15 - 8 * q^16 - 36 * q^18 + 48 * q^19 + 304 * q^20 - 8 * q^21 - 436 * q^22 - 8 * q^23 - 736 * q^24 - 4 * q^25 - 8 * q^26 + 104 * q^27 - 260 * q^28 - 632 * q^30 + 336 * q^32 - 8 * q^33 - 696 * q^34 - 48 * q^35 - 8 * q^36 - 4 * q^37 - 2244 * q^38 + 816 * q^40 - 8 * q^41 + 452 * q^42 - 868 * q^43 - 1232 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 1384 * q^48 + 11368 * q^49 + 28 * q^50 + 1480 * q^51 + 320 * q^52 - 4 * q^53 - 2968 * q^54 + 284 * q^55 - 344 * q^56 - 2020 * q^58 + 252 * q^60 + 1816 * q^61 + 496 * q^62 - 2744 * q^63 - 816 * q^64 - 8 * q^65 + 552 * q^66 - 1852 * q^67 + 1224 * q^68 - 216 * q^69 - 980 * q^70 - 232 * q^71 + 664 * q^72 - 112 * q^75 + 824 * q^76 - 1376 * q^77 - 5744 * q^78 - 4528 * q^80 + 524 * q^82 - 2684 * q^83 - 2744 * q^84 - 4 * q^85 - 1192 * q^86 + 5256 * q^88 + 2068 * q^90 - 8 * q^91 - 3796 * q^92 + 104 * q^93 - 416 * q^94 + 6168 * q^96 - 8 * q^97 + 2760 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more