LMFDB - Embedded newform 16.4.e.a.5.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [16,4,Mod(5,16)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("16.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(16, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.944030560092$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 $ x^10 - 2x^9 - x^8 + 6x^7 + 14x^6 - 80x^5 + 56x^4 + 96x^3 - 64x^2 - 512x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.3
Root			$-1.62580 - 1.16481i$ of defining polynomial
Character	$\chi$	$=$	16.5
Dual form			16.4.e.a.13.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.460984 - 2.79061i) q^{2} +(0.756776 - 0.756776i) q^{3} +(-7.57499 - 2.57285i) q^{4} +(8.22587 + 8.22587i) q^{5} +(-1.76300 - 2.46073i) q^{6} +2.67171i q^{7} +(-10.6718 + 19.9528i) q^{8} +25.8546i q^{9} +(26.7472 - 19.1632i) q^{10} +(-45.2213 - 45.2213i) q^{11} +(-7.67964 + 3.78550i) q^{12} +(35.3968 - 35.3968i) q^{13} +(7.45568 + 1.23161i) q^{14} +12.4503 q^{15} +(50.7609 + 38.9786i) q^{16} -72.4991 q^{17} +(72.1500 + 11.9185i) q^{18} +(19.4427 - 19.4427i) q^{19} +(-41.1470 - 83.4748i) q^{20} +(2.02188 + 2.02188i) q^{21} +(-147.041 + 105.349i) q^{22} +139.462i q^{23} +(7.02366 + 23.1759i) q^{24} +10.3299i q^{25} +(-82.4612 - 115.096i) q^{26} +(39.9991 + 39.9991i) q^{27} +(6.87389 - 20.2381i) q^{28} +(66.0434 - 66.0434i) q^{29} +(5.73937 - 34.7439i) q^{30} +188.682 q^{31} +(132.174 - 123.685i) q^{32} -68.4447 q^{33} +(-33.4209 + 202.317i) q^{34} +(-21.9771 + 21.9771i) q^{35} +(66.5199 - 195.848i) q^{36} +(-84.0653 - 84.0653i) q^{37} +(-45.2941 - 63.2196i) q^{38} -53.5748i q^{39} +(-251.914 + 76.3445i) q^{40} -104.629i q^{41} +(6.57434 - 4.71023i) q^{42} +(-31.4857 - 31.4857i) q^{43} +(226.203 + 458.898i) q^{44} +(-212.676 + 212.676i) q^{45} +(389.183 + 64.2896i) q^{46} -488.151 q^{47} +(67.9127 - 8.91656i) q^{48} +335.862 q^{49} +(28.8266 + 4.76190i) q^{50} +(-54.8656 + 54.8656i) q^{51} +(-359.201 + 177.060i) q^{52} +(149.560 + 149.560i) q^{53} +(130.061 - 93.1828i) q^{54} -743.968i q^{55} +(-53.3080 - 28.5118i) q^{56} -29.4275i q^{57} +(-153.856 - 214.746i) q^{58} +(284.698 + 284.698i) q^{59} +(-94.3107 - 32.0327i) q^{60} +(-228.069 + 228.069i) q^{61} +(86.9792 - 526.537i) q^{62} -69.0758 q^{63} +(-284.227 - 425.863i) q^{64} +582.338 q^{65} +(-31.5519 + 191.002i) q^{66} +(139.151 - 139.151i) q^{67} +(549.180 + 186.529i) q^{68} +(105.541 + 105.541i) q^{69} +(51.1984 + 71.4606i) q^{70} +453.655i q^{71} +(-515.871 - 275.914i) q^{72} +259.747i q^{73} +(-273.346 + 195.841i) q^{74} +(7.81740 + 7.81740i) q^{75} +(-197.301 + 97.2550i) q^{76} +(120.818 - 120.818i) q^{77} +(-149.506 - 24.6971i) q^{78} +323.190 q^{79} +(96.9197 + 738.185i) q^{80} -637.533 q^{81} +(-291.979 - 48.2323i) q^{82} +(-563.897 + 563.897i) q^{83} +(-10.1137 - 20.5177i) q^{84} +(-596.368 - 596.368i) q^{85} +(-102.379 + 73.3499i) q^{86} -99.9602i q^{87} +(1384.88 - 419.700i) q^{88} -866.853i q^{89} +(495.456 + 691.537i) q^{90} +(94.5697 + 94.5697i) q^{91} +(358.814 - 1056.42i) q^{92} +(142.790 - 142.790i) q^{93} +(-225.030 + 1362.24i) q^{94} +319.866 q^{95} +(6.42400 - 193.628i) q^{96} -936.077 q^{97} +(154.827 - 937.259i) q^{98} +(1169.18 - 1169.18i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} - 68 q^{10} + 18 q^{11} + 100 q^{12} - 2 q^{13} + 188 q^{14} - 124 q^{15} + 280 q^{16} - 4 q^{17} + 174 q^{18} - 26 q^{19} - 196 q^{20}+ \cdots + 4958 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 32 * q^6 - 44 * q^8 - 68 * q^10 + 18 * q^11 + 100 * q^12 - 2 * q^13 + 188 * q^14 - 124 * q^15 + 280 * q^16 - 4 * q^17 + 174 * q^18 - 26 * q^19 - 196 * q^20 + 52 * q^21 - 588 * q^22 - 848 * q^24 - 264 * q^26 + 184 * q^27 + 280 * q^28 - 202 * q^29 + 1236 * q^30 + 368 * q^31 + 968 * q^32 - 4 * q^33 + 436 * q^34 + 476 * q^35 - 596 * q^36 - 10 * q^37 - 1232 * q^38 - 1336 * q^40 - 680 * q^42 - 838 * q^43 + 868 * q^44 + 194 * q^45 + 1132 * q^46 - 944 * q^47 + 1768 * q^48 + 94 * q^49 + 726 * q^50 - 1500 * q^51 - 236 * q^52 - 378 * q^53 - 1376 * q^54 - 488 * q^56 + 8 * q^58 + 1706 * q^59 - 192 * q^60 + 910 * q^61 - 80 * q^62 + 2628 * q^63 + 512 * q^64 - 492 * q^65 - 428 * q^66 + 1942 * q^67 - 880 * q^68 + 580 * q^69 + 160 * q^70 + 1092 * q^72 - 452 * q^74 - 2954 * q^75 - 1228 * q^76 - 268 * q^77 - 772 * q^78 - 4416 * q^79 - 2648 * q^80 + 482 * q^81 - 704 * q^82 - 2562 * q^83 + 1960 * q^84 - 12 * q^85 + 3764 * q^86 + 1528 * q^88 + 1896 * q^90 + 3332 * q^91 + 632 * q^92 - 2192 * q^93 - 3248 * q^94 + 6900 * q^95 - 4432 * q^96 - 4 * q^97 + 314 * q^98 + 4958 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.460984	−	2.79061i	0.162982	−	0.986629i
$2$	0.460984	−	2.79061i	0.162982	−	0.986629i
$3$	0.756776	−	0.756776i	0.145642	−	0.145642i	−0.630526	−	0.776168i	$-0.717161\pi$
$3$	0.756776	−	0.756776i	0.145642	−	0.145642i	0.776168	+	0.630526i	$0.217161\pi$
$4$	−7.57499	−	2.57285i	−0.946874	−	0.321606i
$5$	8.22587	+	8.22587i	0.735744	+	0.735744i	0.971751	−	0.236007i	$-0.0758389\pi$
$5$	8.22587	+	8.22587i	0.735744	+	0.735744i	−0.236007	+	0.971751i	$0.575839\pi$
$6$	−1.76300	−	2.46073i	−0.119957	−	0.167431i
$7$			2.67171i			0.144259i	0.997395	+	0.0721293i	$0.0229794\pi$
$7$			2.67171i			0.144259i	−0.997395	+	0.0721293i	$0.977021\pi$
$8$	−10.6718	+	19.9528i	−0.471630	+	0.881797i
$9$			25.8546i			0.957577i
$10$	26.7472	−	19.1632i	0.845820	−	0.605993i
$11$	−45.2213	−	45.2213i	−1.23952	−	1.23952i	−0.960197	−	0.279323i	$-0.909890\pi$
$11$	−45.2213	−	45.2213i	−1.23952	−	1.23952i	−0.279323	−	0.960197i	$-0.590110\pi$
$12$	−7.67964	+	3.78550i	−0.184743	+	0.0910650i
$13$	35.3968	−	35.3968i	0.755176	−	0.755176i	−0.220264	−	0.975440i	$-0.570692\pi$
$13$	35.3968	−	35.3968i	0.755176	−	0.755176i	0.975440	+	0.220264i	$0.0706918\pi$
$14$	7.45568	+	1.23161i	0.142330	+	0.0235116i
$15$	12.4503			0.214310
$16$	50.7609	+	38.9786i	0.793139	+	0.609041i
$17$	−72.4991			−1.03433			−0.517165	−	0.855886i	$-0.673013\pi$
$17$	−72.4991			−1.03433			−0.517165	+	0.855886i	$0.673013\pi$
$18$	72.1500	+	11.9185i	0.944773	+	0.156068i
$19$	19.4427	−	19.4427i	0.234761	−	0.234761i	−0.579916	−	0.814676i	$-0.696915\pi$
$19$	19.4427	−	19.4427i	0.234761	−	0.234761i	0.814676	+	0.579916i	$0.196915\pi$
$20$	−41.1470	−	83.4748i	−0.460037	−	0.933277i
$21$	2.02188	+	2.02188i	0.0210100	+	0.0210100i
$22$	−147.041	+	105.349i	−1.42497	+	1.02093i
$23$			139.462i			1.26434i	0.774830	+	0.632170i	$0.217835\pi$
$23$			139.462i			1.26434i	−0.774830	+	0.632170i	$0.782165\pi$
$24$	7.02366	+	23.1759i	0.0597374	+	0.197115i
$25$			10.3299i			0.0826390i
$26$	−82.4612	−	115.096i	−0.621999	−	0.868159i
$27$	39.9991	+	39.9991i	0.285105	+	0.285105i
$28$	6.87389	−	20.2381i	0.0463944	−	0.136595i
$29$	66.0434	−	66.0434i	0.422895	−	0.422895i	−0.463304	−	0.886199i	$-0.653336\pi$
$29$	66.0434	−	66.0434i	0.422895	−	0.422895i	0.886199	+	0.463304i	$0.153336\pi$
$30$	5.73937	−	34.7439i	0.0349287	−	0.211444i
$31$	188.682			1.09317			0.546584	−	0.837404i	$-0.315928\pi$
$31$	188.682			1.09317			0.546584	+	0.837404i	$0.315928\pi$
$32$	132.174	−	123.685i	0.730165	−	0.683271i
$33$	−68.4447			−0.361051
$34$	−33.4209	+	202.317i	−0.168577	+	1.02050i
$35$	−21.9771	+	21.9771i	−0.106137	+	0.106137i
$36$	66.5199	−	195.848i	0.307963	−	0.906704i
$37$	−84.0653	−	84.0653i	−0.373520	−	0.373520i	0.495237	−	0.868758i	$-0.335081\pi$
$37$	−84.0653	−	84.0653i	−0.373520	−	0.373520i	−0.868758	+	0.495237i	$0.835081\pi$
$38$	−45.2941	−	63.2196i	−0.193360	−	0.269884i
$39$		−	53.5748i		−	0.219970i
$40$	−251.914	+	76.3445i	−0.995776	+	0.301778i
$41$		−	104.629i		−	0.398545i	−0.979944	−	0.199272i	$-0.936142\pi$
$41$		−	104.629i		−	0.398545i	0.979944	−	0.199272i	$-0.0638578\pi$
$42$	6.57434	−	4.71023i	0.0241534	−	0.0173049i
$43$	−31.4857	−	31.4857i	−0.111663	−	0.111663i	0.649067	−	0.760731i	$-0.275159\pi$
$43$	−31.4857	−	31.4857i	−0.111663	−	0.111663i	−0.760731	+	0.649067i	$0.775159\pi$
$44$	226.203	+	458.898i	0.775032	+	1.57231i
$45$	−212.676	+	212.676i	−0.704532	+	0.704532i
$46$	389.183	+	64.2896i	1.24743	+	0.206065i
$47$	−488.151			−1.51498			−0.757491	−	0.652846i	$-0.773575\pi$
$47$	−488.151			−1.51498			−0.757491	+	0.652846i	$0.773575\pi$
$48$	67.9127	−	8.91656i	0.204216	−	0.0268124i
$49$	335.862			0.979189
$50$	28.8266	+	4.76190i	0.0815341	+	0.0134687i
$51$	−54.8656	+	54.8656i	−0.150641	+	0.150641i
$52$	−359.201	+	177.060i	−0.957926	+	0.472187i
$53$	149.560	+	149.560i	0.387617	+	0.387617i	0.873837	−	0.486220i	$-0.161624\pi$
$53$	149.560	+	149.560i	0.387617	+	0.387617i	−0.486220	+	0.873837i	$0.661624\pi$
$54$	130.061	−	93.1828i	0.327760	−	0.234826i
$55$		−	743.968i		−	1.82394i
$56$	−53.3080	−	28.5118i	−0.127207	−	0.0680366i
$57$		−	29.4275i		−	0.0683819i
$58$	−153.856	−	214.746i	−0.348316	−	0.486165i
$59$	284.698	+	284.698i	0.628212	+	0.628212i	0.947618	−	0.319406i	$-0.103483\pi$
$59$	284.698	+	284.698i	0.628212	+	0.628212i	−0.319406	+	0.947618i	$0.603483\pi$
$60$	−94.3107	−	32.0327i	−0.202924	−	0.0689234i
$61$	−228.069	+	228.069i	−0.478709	+	0.478709i	−0.904719	−	0.426010i	$-0.859919\pi$
$61$	−228.069	+	228.069i	−0.478709	+	0.478709i	0.426010	+	0.904719i	$0.359919\pi$
$62$	86.9792	−	526.537i	0.178167	−	1.07855i
$63$	−69.0758			−0.138139
$64$	−284.227	−	425.863i	−0.555131	−	0.831763i
$65$	582.338			1.11123
$66$	−31.5519	+	191.002i	−0.0588450	+	0.356224i
$67$	139.151	−	139.151i	0.253730	−	0.253730i	−0.568768	−	0.822498i	$-0.692580\pi$
$67$	139.151	−	139.151i	0.253730	−	0.253730i	0.822498	+	0.568768i	$0.192580\pi$
$68$	549.180	+	186.529i	0.979380	+	0.332647i
$69$	105.541	+	105.541i	0.184140	+	0.184140i
$70$	51.1984	+	71.4606i	0.0874197	+	0.122017i
$71$			453.655i			0.758294i	0.925336	+	0.379147i	$0.123783\pi$
$71$			453.655i			0.758294i	−0.925336	+	0.379147i	$0.876217\pi$
$72$	−515.871	−	275.914i	−0.844388	−	0.451622i
$73$			259.747i			0.416454i	0.978081	+	0.208227i	$0.0667692\pi$
$73$			259.747i			0.416454i	−0.978081	+	0.208227i	$0.933231\pi$
$74$	−273.346	+	195.841i	−0.429403	+	0.307649i
$75$	7.81740	+	7.81740i	0.0120357	+	0.0120357i
$76$	−197.301	+	97.2550i	−0.297789	+	0.146788i
$77$	120.818	−	120.818i	0.178811	−	0.178811i
$78$	−149.506	−	24.6971i	−0.217029	−	0.0358512i
$79$	323.190			0.460275			0.230138	−	0.973158i	$-0.426082\pi$
$79$	323.190			0.460275			0.230138	+	0.973158i	$0.426082\pi$
$80$	96.9197	+	738.185i	0.135449	+	1.03165i
$81$	−637.533			−0.874531
$82$	−291.979	−	48.2323i	−0.393216	−	0.0649557i
$83$	−563.897	+	563.897i	−0.745732	+	0.745732i	−0.973674	−	0.227943i	$-0.926800\pi$
$83$	−563.897	+	563.897i	−0.745732	+	0.745732i	0.227943	+	0.973674i	$0.426800\pi$
$84$	−10.1137	−	20.5177i	−0.0131369	−	0.0266508i
$85$	−596.368	−	596.368i	−0.761002	−	0.761002i
$86$	−102.379	+	73.3499i	−0.128369	+	0.0919711i
$87$		−	99.9602i		−	0.123182i
$88$	1384.88	−	419.700i	1.67760	−	0.508411i
$89$		−	866.853i		−	1.03243i	−0.856459	−	0.516215i	$-0.827341\pi$
$89$		−	866.853i		−	1.03243i	0.856459	−	0.516215i	$-0.172659\pi$
$90$	495.456	+	691.537i	0.580285	+	0.809938i
$91$	94.5697	+	94.5697i	0.108941	+	0.108941i
$92$	358.814	−	1056.42i	0.406619	−	1.19717i
$93$	142.790	−	142.790i	0.159211	−	0.159211i
$94$	−225.030	+	1362.24i	−0.246915	+	1.49472i
$95$	319.866			0.345448
$96$	6.42400	−	193.628i	0.00682966	−	0.205855i
$97$	−936.077			−0.979837			−0.489919	−	0.871768i	$-0.662974\pi$
$97$	−936.077			−0.979837			−0.489919	+	0.871768i	$0.662974\pi$
$98$	154.827	−	937.259i	0.159591	−	0.966097i
$99$	1169.18	−	1169.18i	1.18694	−	1.18694i
$100$	26.5772	−	78.2487i	0.0265772	−	0.0782487i
$101$	−1.58844	−	1.58844i	−0.00156491	−	0.00156491i	0.706324	−	0.707889i	$-0.250352\pi$
$101$	−1.58844	−	1.58844i	−0.00156491	−	0.00156491i	−0.707889	+	0.706324i	$0.750352\pi$
$102$	127.816	+	178.400i	0.124075	+	0.173179i
$103$			1388.28i			1.32807i	0.747700	+	0.664036i	$0.231158\pi$
$103$			1388.28i			1.32807i	−0.747700	+	0.664036i	$0.768842\pi$
$104$	328.518	+	1084.01i	0.309749	+	1.02208i
$105$			33.2635i			0.0309160i
$106$	486.310	−	348.420i	0.445609	−	0.319260i
$107$	−821.526	−	821.526i	−0.742243	−	0.742243i	0.230767	−	0.973009i	$-0.425877\pi$
$107$	−821.526	−	821.526i	−0.742243	−	0.742243i	−0.973009	+	0.230767i	$0.925877\pi$
$108$	−200.081	−	405.904i	−0.178267	−	0.361649i
$109$	532.797	−	532.797i	0.468190	−	0.468190i	−0.433138	−	0.901328i	$-0.642594\pi$
$109$	532.797	−	532.797i	0.468190	−	0.468190i	0.901328	+	0.433138i	$0.142594\pi$
$110$	−2076.12	−	342.957i	−1.79955	−	0.297270i
$111$	−127.237			−0.108800
$112$	−104.139	+	135.618i	−0.0878593	+	0.114417i
$113$	−67.2680			−0.0560003			−0.0280002	−	0.999608i	$-0.508914\pi$
$113$	−67.2680			−0.0560003			−0.0280002	+	0.999608i	$0.508914\pi$
$114$	−82.1206	−	13.5656i	−0.0674675	−	0.0111450i
$115$	−1147.19	+	1147.19i	−0.930230	+	0.930230i
$116$	−670.198	+	330.359i	−0.536434	+	0.264423i
$117$	915.168	+	915.168i	0.723140	+	0.723140i
$118$	925.722	−	663.240i	0.722200	−	0.517425i
$119$		−	193.696i		−	0.149211i
$120$	−132.866	+	248.418i	−0.101075	+	0.188978i
$121$			2758.92i			2.07282i
$122$	531.315	+	741.587i	0.394287	+	0.550329i
$123$	−79.1808	−	79.1808i	−0.0580447	−	0.0580447i
$124$	−1429.26	−	485.449i	−1.03509	−	0.351570i
$125$	943.262	−	943.262i	0.674943	−	0.674943i
$126$	−31.8428	+	192.764i	−0.0225142	+	0.136292i
$127$	1903.59			1.33005			0.665026	−	0.746820i	$-0.268421\pi$
$127$	1903.59			1.33005			0.665026	+	0.746820i	$0.268421\pi$
$128$	−1319.44	+	596.851i	−0.911118	+	0.412146i
$129$	−47.6552			−0.0325257
$130$	268.448	−	1625.08i	0.181111	−	1.09638i
$131$	918.430	−	918.430i	0.612546	−	0.612546i	−0.331062	−	0.943609i	$-0.607407\pi$
$131$	918.430	−	918.430i	0.612546	−	0.612546i	0.943609	+	0.331062i	$0.107407\pi$
$132$	518.468	+	176.098i	0.341870	+	0.116116i
$133$	51.9451	+	51.9451i	0.0338662	+	0.0338662i
$134$	−324.169	−	452.461i	−0.208984	−	0.291691i
$135$			658.054i			0.419528i
$136$	773.693	−	1446.56i	0.487821	−	0.912069i
$137$		−	477.234i		−	0.297612i	−0.988866	−	0.148806i	$-0.952457\pi$
$137$		−	477.234i		−	0.297612i	0.988866	−	0.148806i	$-0.0475430\pi$
$138$	343.177	−	245.872i	0.211690	−	0.151667i
$139$	−1513.89	−	1513.89i	−0.923788	−	0.923788i	0.0735064	−	0.997295i	$-0.476581\pi$
$139$	−1513.89	−	1513.89i	−0.923788	−	0.923788i	−0.997295	+	0.0735064i	$0.976581\pi$
$140$	223.020	−	109.933i	0.134633	−	0.0663642i
$141$	−369.421	+	369.421i	−0.220644	+	0.220644i
$142$	1265.97	+	209.127i	0.748155	+	0.123589i
$143$	−3201.37			−1.87211
$144$	−1007.78	+	1312.40i	−0.583203	+	0.759492i
$145$	1086.53			0.622285
$146$	724.853	+	119.739i	0.410885	+	0.0678746i
$147$	254.172	−	254.172i	0.142611	−	0.142611i
$148$	420.507	+	853.081i	0.233550	+	0.473803i
$149$	375.353	+	375.353i	0.206377	+	0.206377i	0.802725	−	0.596349i	$-0.203382\pi$
$149$	375.353	+	375.353i	0.206377	+	0.206377i	−0.596349	+	0.802725i	$0.703382\pi$
$150$	25.4190	−	18.2116i	0.0138364	−	0.00991315i
$151$		−	2997.52i		−	1.61546i	−0.589553	−	0.807730i	$-0.700696\pi$
$151$		−	2997.52i		−	1.61546i	0.589553	−	0.807730i	$-0.299304\pi$
$152$	180.448	+	595.423i	0.0962912	+	0.317731i
$153$		−	1874.43i		−	0.990451i
$154$	−281.460	−	392.850i	−0.147277	−	0.205564i
$155$	1552.07	+	1552.07i	0.804293	+	0.804293i
$156$	−137.840	+	405.829i	−0.0707438	+	0.208284i
$157$	−1509.01	+	1509.01i	−0.767082	+	0.767082i	−0.977592	−	0.210510i	$-0.932488\pi$
$157$	−1509.01	+	1509.01i	−0.767082	+	0.767082i	0.210510	+	0.977592i	$0.432488\pi$
$158$	148.985	−	901.897i	0.0750167	−	0.454121i
$159$	226.368			0.112906
$160$	2104.66	+	69.8265i	1.03993	+	0.0345017i
$161$	−372.601			−0.182392
$162$	−293.892	+	1779.10i	−0.142533	+	0.862837i
$163$	−1425.19	+	1425.19i	−0.684844	+	0.684844i	−0.961088	−	0.276244i	$-0.910910\pi$
$163$	−1425.19	+	1425.19i	−0.684844	+	0.684844i	0.276244	+	0.961088i	$0.410910\pi$
$164$	−269.195	+	792.565i	−0.128174	+	0.377371i
$165$	−563.017	−	563.017i	−0.265641	−	0.265641i
$166$	1313.67	+	1833.56i	0.614219	+	0.857301i
$167$			792.415i			0.367179i	0.983003	+	0.183590i	$0.0587717\pi$
$167$			792.415i			0.367179i	−0.983003	+	0.183590i	$0.941228\pi$
$168$	−61.9192	+	18.7651i	−0.0284355	+	0.00861763i
$169$		−	308.861i		−	0.140583i
$170$	−1939.15	+	1389.31i	−0.874857	+	0.626797i
$171$	502.682	+	502.682i	0.224802	+	0.224802i
$172$	157.496	+	319.512i	0.0698195	+	0.141643i
$173$	−773.594	+	773.594i	−0.339972	+	0.339972i	−0.856357	−	0.516384i	$-0.827278\pi$
$173$	−773.594	+	773.594i	−0.339972	+	0.339972i	0.516384	+	0.856357i	$0.327278\pi$
$174$	−278.950	−	46.0800i	−0.121535	−	0.0200765i
$175$	−27.5984			−0.0119214
$176$	−532.810	−	4058.13i	−0.228194	−	1.73803i
$177$	430.905			0.182988
$178$	−2419.05	−	399.605i	−1.01862	−	0.168268i
$179$	426.050	−	426.050i	0.177902	−	0.177902i	−0.612539	−	0.790441i	$-0.709852\pi$
$179$	426.050	−	426.050i	0.177902	−	0.177902i	0.790441	+	0.612539i	$0.209852\pi$
$180$	2158.21	−	1063.84i	0.893684	−	0.440521i
$181$	−2618.06	−	2618.06i	−1.07513	−	1.07513i	−0.996938	−	0.0781951i	$-0.975084\pi$
$181$	−2618.06	−	2618.06i	−1.07513	−	1.07513i	−0.0781951	−	0.996938i	$-0.524916\pi$
$182$	307.502	−	220.312i	0.125239	−	0.0897286i
$183$			345.194i			0.139440i
$184$	−2782.65	−	1488.30i	−1.11489	−	0.596300i
$185$		−	1383.02i		−	0.549631i
$186$	−332.647	−	464.294i	−0.131134	−	0.183031i
$187$	3278.50	+	3278.50i	1.28207	+	1.28207i
$188$	3697.74	+	1255.94i	1.43450	+	0.487227i
$189$	−106.866	+	106.866i	−0.0411288	+	0.0411288i
$190$	147.453	−	892.620i	0.0563019	−	0.340829i
$191$	3216.39			1.21848			0.609240	−	0.792986i	$-0.291475\pi$
$191$	3216.39			1.21848			0.609240	+	0.792986i	$0.291475\pi$
$192$	−537.379	−	107.186i	−0.201989	−	0.0402891i
$193$	2852.57			1.06390			0.531950	−	0.846776i	$-0.321459\pi$
$193$	2852.57			1.06390			0.531950	+	0.846776i	$0.321459\pi$
$194$	−431.516	+	2612.22i	−0.159696	+	0.966736i
$195$	440.700	−	440.700i	0.161842	−	0.161842i
$196$	−2544.15	−	864.122i	−0.927169	−	0.314913i
$197$	1609.02	+	1609.02i	0.581918	+	0.581918i	0.935430	−	0.353512i	$-0.115013\pi$
$197$	1609.02	+	1609.02i	0.581918	+	0.581918i	−0.353512	+	0.935430i	$0.615013\pi$
$198$	−2723.74	−	3801.68i	−0.977616	−	1.36451i
$199$		−	747.136i		−	0.266146i	−0.991106	−	0.133073i	$-0.957516\pi$
$199$		−	747.136i		−	0.266146i	0.991106	−	0.133073i	$-0.0424845\pi$
$200$	−206.110	−	110.238i	−0.0728708	−	0.0389750i
$201$		−	210.612i		−	0.0739074i
$202$	−5.16496	+	3.70047i	−0.00179904	+	0.00128893i
$203$	176.449	+	176.449i	0.0610062	+	0.0610062i
$204$	556.767	−	274.445i	0.191086	−	0.0941912i
$205$	860.666	−	860.666i	0.293227	−	0.293227i
$206$	3874.15	+	639.975i	1.31032	+	0.216452i
$207$	−3605.73			−1.21070
$208$	3176.49	−	417.055i	1.05889	−	0.139027i
$209$	−1758.44			−0.581981
$210$	92.8254	+	15.3339i	0.0305027	+	0.00503877i
$211$	−2227.13	+	2227.13i	−0.726645	+	0.726645i	−0.969950	−	0.243305i	$-0.921769\pi$
$211$	−2227.13	+	2227.13i	−0.726645	+	0.726645i	0.243305	+	0.969950i	$0.421769\pi$
$212$	−748.122	−	1517.72i	−0.242364	−	0.491684i
$213$	343.315	+	343.315i	0.110439	+	0.110439i
$214$	−2671.27	+	1913.85i	−0.853290	+	0.611346i
$215$		−	517.995i		−	0.164311i
$216$	−1224.95	+	371.232i	−0.385868	+	0.116941i
$217$			504.102i			0.157699i
$218$	−1241.22	−	1732.44i	−0.385623	−	0.538237i
$219$	196.570	+	196.570i	0.0606530	+	0.0606530i
$220$	−1914.12	+	5635.55i	−0.586590	+	1.72704i
$221$	−2566.23	+	2566.23i	−0.781102	+	0.781102i
$222$	−58.6543	+	355.069i	−0.0177325	+	0.107345i
$223$	−358.053			−0.107520			−0.0537601	−	0.998554i	$-0.517121\pi$
$223$	−358.053			−0.107520			−0.0537601	+	0.998554i	$0.517121\pi$
$224$	330.451	+	353.130i	0.0985677	+	0.105332i
$225$	−267.075			−0.0791332
$226$	−31.0094	+	187.719i	−0.00912706	+	0.0552516i
$227$	3455.40	−	3455.40i	1.01032	−	1.01032i	0.0103741	−	0.999946i	$-0.496698\pi$
$227$	3455.40	−	3455.40i	1.01032	−	1.01032i	0.999946	−	0.0103741i	$-0.00330223\pi$
$228$	−75.7125	+	222.913i	−0.0219920	+	0.0647490i
$229$	−1430.03	−	1430.03i	−0.412659	−	0.412659i	0.470005	−	0.882664i	$-0.344252\pi$
$229$	−1430.03	−	1430.03i	−0.412659	−	0.412659i	−0.882664	+	0.470005i	$0.844252\pi$
$230$	2672.53	+	3730.21i	0.766181	+	1.06940i
$231$		−	182.864i		−	0.0520847i
$232$	612.951	+	2022.55i	0.173458	+	0.572357i
$233$			926.479i			0.260496i	0.991481	+	0.130248i	$0.0415774\pi$
$233$			926.479i			0.260496i	−0.991481	+	0.130248i	$0.958423\pi$
$234$	2975.75	−	2132.00i	0.831330	−	0.595612i
$235$	−4015.47	−	4015.47i	−1.11464	−	1.11464i
$236$	−1424.10	−	2889.07i	−0.392801	−	0.796875i
$237$	244.583	−	244.583i	0.0670352	−	0.0670352i
$238$	−540.530	−	89.2908i	−0.147216	−	0.0243187i
$239$	−792.472			−0.214480			−0.107240	−	0.994233i	$-0.534201\pi$
$239$	−792.472			−0.214480			−0.107240	+	0.994233i	$0.534201\pi$
$240$	631.987	+	485.295i	0.169978	+	0.130523i
$241$	1449.01			0.387299			0.193650	−	0.981071i	$-0.437967\pi$
$241$	1449.01			0.387299			0.193650	+	0.981071i	$0.437967\pi$
$242$	7699.07	+	1271.82i	2.04510	+	0.337833i
$243$	−1562.44	+	1562.44i	−0.412473	+	0.412473i
$244$	2314.41	−	1140.83i	0.607233	−	0.299321i
$245$	2762.76	+	2762.76i	0.720433	+	0.720433i
$246$	−257.464	+	184.462i	−0.0667288	+	0.0478083i
$247$		−	1376.42i		−	0.354572i
$248$	−2013.57	+	3764.73i	−0.515571	+	0.963953i
$249$			853.487i			0.217219i
$250$	−2197.45	−	3067.10i	−0.555915	−	0.775922i
$251$	−3580.04	−	3580.04i	−0.900280	−	0.900280i	0.0951802	−	0.995460i	$-0.469657\pi$
$251$	−3580.04	−	3580.04i	−0.900280	−	0.900280i	−0.995460	+	0.0951802i	$0.969657\pi$
$252$	523.249	+	177.722i	0.130800	+	0.0444262i
$253$	6306.64	−	6306.64i	1.56717	−	1.56717i
$254$	877.525	−	5312.18i	0.216775	−	1.31227i
$255$	−902.634			−0.221667
$256$	1057.34	+	3957.18i	0.258139	+	0.966108i
$257$	−4708.87			−1.14292			−0.571461	−	0.820629i	$-0.693623\pi$
$257$	−4708.87			−1.14292			−0.571461	+	0.820629i	$0.693623\pi$
$258$	−21.9683	+	132.987i	−0.00530111	+	0.0320908i
$259$	224.598	−	224.598i	0.0538835	−	0.0538835i
$260$	−4411.21	−	1498.27i	−1.05220	−	0.357379i
$261$	1707.53	+	1707.53i	0.404955	+	0.404955i
$262$	−2139.60	−	2986.36i	−0.504522	−	0.704190i
$263$			2967.82i			0.695830i	0.937526	+	0.347915i	$0.113110\pi$
$263$			2967.82i			0.695830i	−0.937526	+	0.347915i	$0.886890\pi$
$264$	730.425	−	1365.66i	0.170282	−	0.318374i
$265$			2460.53i			0.570374i
$266$	168.904	−	121.013i	0.0389330	−	0.0278938i
$267$	−656.013	−	656.013i	−0.150365	−	0.150365i
$268$	−1412.08	+	696.050i	−0.321852	+	0.158649i
$269$	−663.633	+	663.633i	−0.150418	+	0.150418i	−0.778305	−	0.627887i	$-0.783920\pi$
$269$	−663.633	+	663.633i	−0.150418	+	0.150418i	0.627887	+	0.778305i	$0.283920\pi$
$270$	1836.37	+	303.352i	0.413919	+	0.0683757i
$271$	8058.74			1.80640			0.903199	−	0.429223i	$-0.141212\pi$
$271$	8058.74			1.80640			0.903199	+	0.429223i	$0.141212\pi$
$272$	−3680.12	−	2825.91i	−0.820368	−	0.629949i
$273$	143.136			0.0317326
$274$	−1331.77	−	219.997i	−0.293633	−	0.0485055i
$275$	467.130	−	467.130i	0.102433	−	0.102433i
$276$	−527.933	−	1071.02i	−0.115137	−	0.233578i
$277$	482.477	+	482.477i	0.104654	+	0.104654i	0.757495	−	0.652841i	$-0.226423\pi$
$277$	482.477	+	482.477i	0.104654	+	0.104654i	−0.652841	+	0.757495i	$0.726423\pi$
$278$	−4922.56	+	3526.80i	−1.06200	+	0.760875i
$279$			4878.29i			1.04679i
$280$	−203.970	−	673.039i	−0.0435341	−	0.143649i
$281$			5899.10i			1.25235i	0.779682	+	0.626175i	$0.215381\pi$
$281$			5899.10i			1.25235i	−0.779682	+	0.626175i	$0.784619\pi$
$282$	860.612	+	1201.21i	0.181733	+	0.253655i
$283$	−679.897	−	679.897i	−0.142812	−	0.142812i	0.632086	−	0.774898i	$-0.282199\pi$
$283$	−679.897	−	679.897i	−0.142812	−	0.142812i	−0.774898	+	0.632086i	$0.782199\pi$
$284$	1167.18	−	3436.43i	0.243872	−	0.718009i
$285$	242.067	−	242.067i	0.0503116	−	0.0503116i
$286$	−1475.78	+	8933.77i	−0.305121	+	1.84708i
$287$	279.538			0.0574935
$288$	3197.83	+	3417.30i	0.654285	+	0.699189i
$289$	343.118			0.0698388
$290$	500.872	−	3032.08i	0.101421	−	0.613965i
$291$	−708.401	+	708.401i	−0.142705	+	0.142705i
$292$	668.290	−	1967.58i	0.133934	−	0.394329i
$293$	−3552.87	−	3552.87i	−0.708398	−	0.708398i	0.257800	−	0.966198i	$-0.417002\pi$
$293$	−3552.87	−	3552.87i	−0.708398	−	0.708398i	−0.966198	+	0.257800i	$0.917002\pi$
$294$	−592.126	−	826.464i	−0.117461	−	0.163947i
$295$			4683.78i			0.924407i
$296$	2574.46	−	780.213i	0.505532	−	0.153206i
$297$		−	3617.62i		−	0.706786i
$298$	1220.49	−	874.432i	0.237253	−	0.169981i
$299$	4936.50	+	4936.50i	0.954799	+	0.954799i
$300$	−39.1037	−	79.3297i	−0.00752552	−	0.0152670i
$301$	84.1205	−	84.1205i	0.0161084	−	0.0161084i
$302$	−8364.89	−	1381.81i	−1.59386	−	0.263291i
$303$	−2.40419			−0.000455831
$304$	1744.78	−	229.079i	0.329177	−	0.0432191i
$305$	−3752.13			−0.704415
$306$	−5230.81	−	864.083i	−0.977207	−	0.161426i
$307$	2735.56	−	2735.56i	0.508556	−	0.508556i	−0.405527	−	0.914083i	$-0.632912\pi$
$307$	2735.56	−	2735.56i	0.508556	−	0.508556i	0.914083	+	0.405527i	$0.132912\pi$
$308$	−1226.04	+	604.348i	−0.226819	+	0.111805i
$309$	1050.62	+	1050.62i	0.193423	+	0.193423i
$310$	5046.70	−	3615.74i	0.924624	−	0.662453i
$311$		−	5796.70i		−	1.05692i	−0.848960	−	0.528458i	$-0.822771\pi$
$311$		−	5796.70i		−	1.05692i	0.848960	−	0.528458i	$-0.177229\pi$
$312$	1068.97	+	571.738i	0.193969	+	0.103744i
$313$		−	8362.62i		−	1.51017i	−0.655627	−	0.755085i	$-0.727596\pi$
$313$		−	8362.62i		−	1.51017i	0.655627	−	0.755085i	$-0.272404\pi$
$314$	3515.42	+	4906.67i	0.631804	+	0.881846i
$315$	−568.209	−	568.209i	−0.101635	−	0.101635i
$316$	−2448.16	−	831.519i	−0.435822	−	0.148027i
$317$	−344.406	+	344.406i	−0.0610214	+	0.0610214i	−0.736959	−	0.675938i	$-0.763739\pi$
$317$	−344.406	+	344.406i	−0.0610214	+	0.0610214i	0.675938	+	0.736959i	$0.263739\pi$
$318$	104.352	−	631.703i	0.0184017	−	0.111397i
$319$	−5973.13			−1.04837
$320$	1165.07	−	5841.11i	0.203530	−	1.02040i
$321$	−1243.42			−0.216203
$322$	−171.763	+	1039.78i	−0.0297266	+	0.179953i
$323$	−1409.58	+	1409.58i	−0.242820	+	0.242820i
$324$	4829.30	+	1640.28i	0.828070	+	0.281254i
$325$	365.644	+	365.644i	0.0624071	+	0.0624071i
$326$	3320.16	+	4634.14i	0.564069	+	0.787304i
$327$		−	806.416i		−	0.136376i
$328$	2087.64	+	1116.58i	0.351435	+	0.187965i
$329$		−	1304.20i		−	0.218549i
$330$	−1830.70	+	1311.62i	−0.305384	+	0.218795i
$331$	2687.86	+	2687.86i	0.446339	+	0.446339i	0.894135	−	0.447797i	$-0.147791\pi$
$331$	2687.86	+	2687.86i	0.446339	+	0.446339i	−0.447797	+	0.894135i	$0.647791\pi$
$332$	5722.33	−	2820.69i	0.945945	−	0.466282i
$333$	2173.47	−	2173.47i	0.357675	−	0.357675i
$334$	2211.32	+	365.290i	0.362270	+	0.0598437i
$335$	2289.27			0.373361
$336$	23.8224	+	181.443i	0.00386792	+	0.0294599i
$337$	−1795.31			−0.290199			−0.145099	−	0.989417i	$-0.546350\pi$
$337$	−1795.31			−0.290199			−0.145099	+	0.989417i	$0.546350\pi$
$338$	−861.910	−	142.380i	−0.138703	−	0.0229125i
$339$	−50.9068	+	50.9068i	−0.00815598	+	0.00815598i
$340$	2983.12	+	6051.85i	0.475830	+	0.965316i
$341$	−8532.42	−	8532.42i	−1.35500	−	1.35500i
$342$	1634.52	−	1171.06i	0.258434	−	0.185157i
$343$			1813.72i			0.285515i
$344$	964.235	−	292.220i	0.151128	−	0.0458007i
$345$			1736.34i			0.270960i
$346$	1802.18	+	2515.41i	0.280017	+	0.390836i
$347$	−1967.33	−	1967.33i	−0.304357	−	0.304357i	0.538359	−	0.842716i	$-0.319045\pi$
$347$	−1967.33	−	1967.33i	−0.304357	−	0.304357i	−0.842716	+	0.538359i	$0.819045\pi$
$348$	−257.182	+	757.197i	−0.0396162	+	0.116638i
$349$	−7363.37	+	7363.37i	−1.12938	+	1.12938i	−0.139097	+	0.990279i	$0.544420\pi$
$349$	−7363.37	+	7363.37i	−1.12938	+	1.12938i	−0.990279	+	0.139097i	$0.955580\pi$
$350$	−12.7224	+	77.0163i	−0.00194297	+	0.0117620i
$351$	2831.68			0.430609
$352$	−11570.3	−	383.867i	−1.75198	−	0.0581255i
$353$	10644.3			1.60493			0.802466	−	0.596698i	$-0.203521\pi$
$353$	10644.3			1.60493			0.802466	+	0.596698i	$0.203521\pi$
$354$	198.640	−	1202.49i	0.0298238	−	0.180541i
$355$	−3731.70	+	3731.70i	−0.557911	+	0.557911i
$356$	−2230.28	+	6566.40i	−0.332036	+	0.977580i
$357$	−146.585	−	146.585i	−0.0217313	−	0.0217313i
$358$	−992.537	−	1385.34i	−0.146529	−	0.204518i
$359$		−	7459.42i		−	1.09664i	−0.836269	−	0.548319i	$-0.815268\pi$
$359$		−	7459.42i		−	1.09664i	0.836269	−	0.548319i	$-0.184732\pi$
$360$	−1973.86	−	6513.12i	−0.288976	−	0.953532i
$361$			6102.96i			0.889775i
$362$	−8512.87	+	6099.10i	−1.23599	+	0.885530i
$363$	2087.89	+	2087.89i	0.301889	+	0.301889i
$364$	−473.051	−	959.678i	−0.0681170	−	0.138189i
$365$	−2136.65	+	2136.65i	−0.306403	+	0.306403i
$366$	963.302	+	159.129i	0.137575	+	0.0227262i
$367$	−6251.35			−0.889149			−0.444574	−	0.895742i	$-0.646645\pi$
$367$	−6251.35			−0.889149			−0.444574	+	0.895742i	$0.646645\pi$
$368$	−5436.03	+	7079.21i	−0.770034	+	1.00280i
$369$	2705.14			0.381637
$370$	−3859.47	−	637.550i	−0.542282	−	0.0895801i
$371$	−399.582	+	399.582i	−0.0559171	+	0.0559171i
$372$	−1449.01	+	714.254i	−0.201956	+	0.0995494i
$373$	8911.86	+	8911.86i	1.23710	+	1.23710i	0.961180	+	0.275921i	$0.0889827\pi$
$373$	8911.86	+	8911.86i	1.23710	+	1.23710i	0.275921	+	0.961180i	$0.411017\pi$
$374$	10660.3	−	7637.67i	1.47389	−	1.05598i
$375$		−	1427.68i		−	0.196600i
$376$	5209.43	−	9739.97i	0.714510	−	1.33591i
$377$		−	4675.45i		−	0.638721i
$378$	248.957	+	347.484i	0.0338756	+	0.0472821i
$379$	1184.03	+	1184.03i	0.160473	+	0.160473i	0.782776	−	0.622303i	$-0.213803\pi$
$379$	1184.03	+	1184.03i	0.160473	+	0.160473i	−0.622303	+	0.782776i	$0.713803\pi$
$380$	−2422.98	−	822.966i	−0.327095	−	0.111098i
$381$	1440.59	−	1440.59i	0.193711	−	0.193711i
$382$	1482.70	−	8975.67i	0.198591	−	1.20219i
$383$	−2880.38			−0.384283			−0.192142	−	0.981367i	$-0.561543\pi$
$383$	−2880.38			−0.384283			−0.192142	+	0.981367i	$0.561543\pi$
$384$	−546.838	+	1450.20i	−0.0726711	+	0.192722i
$385$	1987.66			0.263119
$386$	1314.99	−	7960.42i	0.173397	−	1.04968i
$387$	814.050	−	814.050i	0.106926	−	0.106926i
$388$	7090.77	+	2408.38i	0.927782	+	0.315122i
$389$	9244.24	+	9244.24i	1.20489	+	1.20489i	0.972662	+	0.232226i	$0.0746009\pi$
$389$	9244.24	+	9244.24i	1.20489	+	1.20489i	0.232226	+	0.972662i	$0.425399\pi$
$390$	−1026.66	−	1432.98i	−0.133300	−	0.186055i
$391$		−	10110.9i		−	1.30774i
$392$	−3584.24	+	6701.38i	−0.461815	+	0.863446i
$393$		−	1390.09i		−	0.178424i
$394$	5231.87	−	3748.41i	0.668979	−	0.479295i
$395$	2658.52	+	2658.52i	0.338645	+	0.338645i
$396$	−11864.6	+	5848.38i	−1.50560	+	0.742152i
$397$	−4257.80	+	4257.80i	−0.538270	+	0.538270i	−0.923020	−	0.384751i	$-0.874287\pi$
$397$	−4257.80	+	4257.80i	−0.538270	+	0.538270i	0.384751	+	0.923020i	$0.374287\pi$
$398$	−2084.96	−	344.417i	−0.262587	−	0.0433771i
$399$	78.6216			0.00986467
$400$	−402.644	+	524.354i	−0.0503305	+	0.0655442i
$401$	12722.6			1.58437			0.792187	−	0.610278i	$-0.208942\pi$
$401$	12722.6			1.58437			0.792187	+	0.610278i	$0.208942\pi$
$402$	−587.734	−	97.0884i	−0.0729192	−	0.0120456i
$403$	6678.72	−	6678.72i	0.825535	−	0.825535i
$404$	7.94560	+	16.1192i	0.000978486	+	0.00198505i
$405$	−5244.26	−	5244.26i	−0.643431	−	0.643431i
$406$	573.739	−	411.059i	0.0701335	−	0.0502476i
$407$			7603.08i			0.925972i
$408$	−509.209	−	1680.23i	−0.0617882	−	0.203882i
$409$		−	232.991i		−	0.0281678i	−0.999901	−	0.0140839i	$-0.995517\pi$
$409$		−	232.991i		−	0.0281678i	0.999901	−	0.0140839i	$-0.00448320\pi$
$410$	−2005.03	−	2798.53i	−0.241515	−	0.337097i
$411$	−361.159	−	361.159i	−0.0433447	−	0.0433447i
$412$	3571.84	−	10516.2i	0.427116	−	1.25752i
$413$	−760.629	+	760.629i	−0.0906250	+	0.0906250i
$414$	−1662.18	+	10062.2i	−0.197323	+	1.19451i
$415$	−9277.08			−1.09734
$416$	300.471	−	9056.59i	0.0354129	−	1.06739i
$417$	−2291.35			−0.269084
$418$	−810.614	+	4907.13i	−0.0948527	+	0.574200i
$419$	−6125.69	+	6125.69i	−0.714223	+	0.714223i	−0.967416	−	0.253193i	$-0.918519\pi$
$419$	−6125.69	+	6125.69i	−0.714223	+	0.714223i	0.253193	+	0.967416i	$0.418519\pi$
$420$	85.5819	−	251.971i	0.00994279	−	0.0292736i
$421$	−8308.44	−	8308.44i	−0.961825	−	0.961825i	0.0374725	−	0.999298i	$-0.488069\pi$
$421$	−8308.44	−	8308.44i	−0.961825	−	0.961825i	−0.999298	+	0.0374725i	$0.988069\pi$
$422$	5188.38	+	7241.73i	0.598499	+	0.835360i
$423$		−	12620.9i		−	1.45071i
$424$	−4580.22	+	1388.07i	−0.524611	+	0.158988i
$425$		−	748.907i		−	0.0854760i
$426$	1116.32	−	799.795i	0.126962	−	0.0909629i
$427$	−609.333	−	609.333i	−0.0690579	−	0.0690579i
$428$	4109.39	+	8336.72i	0.464100	+	0.941520i
$429$	−2422.72	+	2422.72i	−0.272657	+	0.272657i
$430$	−1445.52	−	238.787i	−0.162114	−	0.0267798i
$431$	8737.57			0.976506			0.488253	−	0.872702i	$-0.337634\pi$
$431$	8737.57			0.976506			0.488253	+	0.872702i	$0.337634\pi$
$432$	471.281	+	3589.50i	0.0524873	+	0.399768i
$433$	−11627.5			−1.29049			−0.645247	−	0.763974i	$-0.723245\pi$
$433$	−11627.5			−1.29049			−0.645247	+	0.763974i	$0.723245\pi$
$434$	1406.75	+	232.383i	0.155590	+	0.0257021i
$435$	822.260	−	822.260i	0.0906306	−	0.0906306i
$436$	−5406.74	+	2665.13i	−0.593890	+	0.292744i
$437$	2711.51	+	2711.51i	0.296817	+	0.296817i
$438$	639.167	−	457.935i	0.0697273	−	0.0499566i
$439$			17631.8i			1.91690i	0.285261	+	0.958450i	$0.407920\pi$
$439$			17631.8i			1.91690i	−0.285261	+	0.958450i	$0.592080\pi$
$440$	14844.2	+	7939.45i	1.60834	+	0.860224i
$441$			8683.57i			0.937649i
$442$	5978.36	+	8344.34i	0.643352	+	0.897963i
$443$	−4549.81	−	4549.81i	−0.487964	−	0.487964i	0.419699	−	0.907663i	$-0.362136\pi$
$443$	−4549.81	−	4549.81i	−0.487964	−	0.487964i	−0.907663	+	0.419699i	$0.862136\pi$
$444$	963.821	+	327.362i	0.103020	+	0.0349908i
$445$	7130.62	−	7130.62i	0.759604	−	0.759604i
$446$	−165.057	+	999.186i	−0.0175239	+	0.106083i
$447$	568.116			0.0601140
$448$	1137.78	−	759.371i	0.119989	−	0.0800824i
$449$	−12926.5			−1.35867			−0.679334	−	0.733830i	$-0.737731\pi$
$449$	−12926.5			−1.35867			−0.679334	+	0.733830i	$0.737731\pi$
$450$	−123.117	+	745.301i	−0.0128973	+	0.0780751i
$451$	−4731.46	+	4731.46i	−0.494004	+	0.494004i
$452$	509.554	+	173.070i	0.0530252	+	0.0180101i
$453$	−2268.45	−	2268.45i	−0.235278	−	0.235278i
$454$	−8049.78	−	11235.5i	−0.832147	−	1.16148i
$455$			1555.84i			0.160305i
$456$	587.160	+	314.043i	0.0602989	+	0.0322509i
$457$		−	9320.32i		−	0.954018i	−0.878898	−	0.477009i	$-0.841721\pi$
$457$		−	9320.32i		−	0.954018i	0.878898	−	0.477009i	$-0.158279\pi$
$458$	−4649.87	+	3331.43i	−0.474398	+	0.339886i
$459$	−2899.90	−	2899.90i	−0.294892	−	0.294892i
$460$	11641.5	−	5738.43i	1.17998	−	0.581643i
$461$	12885.0	−	12885.0i	1.30177	−	1.30177i	0.374566	−	0.927200i	$-0.377792\pi$
$461$	12885.0	−	12885.0i	1.30177	−	1.30177i	0.927200	−	0.374566i	$-0.122208\pi$
$462$	−510.302	−	84.2973i	−0.0513883	−	0.00848889i
$463$	7038.37			0.706482			0.353241	−	0.935532i	$-0.385080\pi$
$463$	7038.37			0.706482			0.353241	+	0.935532i	$0.385080\pi$
$464$	5926.71	−	778.144i	0.592975	−	0.0778543i
$465$	2349.14			0.234277
$466$	2585.44	+	427.091i	0.257013	+	0.0424563i
$467$	6001.76	−	6001.76i	0.594707	−	0.594707i	−0.344192	−	0.938899i	$-0.611847\pi$
$467$	6001.76	−	6001.76i	0.594707	−	0.594707i	0.938899	+	0.344192i	$0.111847\pi$
$468$	−4577.80	−	9286.98i	−0.452156	−	0.917288i
$469$	371.769	+	371.769i	0.0366028	+	0.0366028i
$470$	−13056.7	+	9354.53i	−1.28140	+	0.918069i
$471$			2283.96i			0.223438i
$472$	−8718.75	+	2642.29i	−0.850239	+	0.257672i
$473$			2847.65i			0.276818i
$474$	−569.786	−	795.283i	−0.0552133	−	0.0770644i
$475$	200.840	+	200.840i	0.0194004	+	0.0194004i
$476$	−498.351	+	1467.25i	−0.0479872	+	0.141284i
$477$	−3866.82	+	3866.82i	−0.371173	+	0.371173i
$478$	−365.317	+	2211.48i	−0.0349565	+	0.211612i
$479$	−587.317			−0.0560234			−0.0280117	−	0.999608i	$-0.508918\pi$
$479$	−587.317			−0.0560234			−0.0280117	+	0.999608i	$0.508918\pi$
$480$	1645.60	−	1539.92i	0.156482	−	0.146432i
$481$	−5951.28			−0.564148
$482$	667.971	−	4043.63i	0.0631229	−	0.382121i
$483$	−281.975	+	281.975i	−0.0265638	+	0.0265638i
$484$	7098.29	−	20898.8i	0.666631	−	1.96270i
$485$	−7700.05	−	7700.05i	−0.720910	−	0.720910i
$486$	3639.91	+	5080.43i	0.339732	+	0.474183i
$487$			8366.45i			0.778481i	0.921136	+	0.389240i	$0.127262\pi$
$487$			8366.45i			0.778481i	−0.921136	+	0.389240i	$0.872738\pi$
$488$	−2116.71	−	6984.51i	−0.196351	−	0.647897i
$489$			2157.10i			0.199483i
$490$	8983.36	−	6436.19i	0.828218	−	0.593382i
$491$	1529.30	+	1529.30i	0.140563	+	0.140563i	0.773887	−	0.633324i	$-0.218310\pi$
$491$	1529.30	+	1529.30i	0.140563	+	0.140563i	−0.633324	+	0.773887i	$0.718310\pi$
$492$	396.074	+	803.514i	0.0362935	+	0.0736285i
$493$	−4788.09	+	4788.09i	−0.437413	+	0.437413i
$494$	−3841.04	−	634.505i	−0.349831	−	0.0577889i
$495$	19235.0			1.74656
$496$	9577.65	+	7354.55i	0.867035	+	0.665784i
$497$	−1212.03			−0.109390
$498$	2381.75	+	393.444i	0.214315	+	0.0354029i
$499$	11364.5	−	11364.5i	1.01952	−	1.01952i	0.0197191	−	0.999806i	$-0.493723\pi$
$499$	11364.5	−	11364.5i	1.01952	−	1.01952i	0.999806	−	0.0197191i	$-0.00627718\pi$
$500$	−9572.06	+	4718.33i	−0.856151	+	0.422020i
$501$	599.681	+	599.681i	0.0534766	+	0.0534766i
$502$	−11640.8	+	8340.15i	−1.03497	+	0.741513i
$503$			12570.2i			1.11427i	0.830421	+	0.557137i	$0.188100\pi$
$503$			12570.2i			1.11427i	−0.830421	+	0.557137i	$0.811900\pi$
$504$	737.160	−	1378.25i	0.0651503	−	0.121810i
$505$		−	26.1326i		−	0.00230274i
$506$	−14692.1	−	20506.6i	−1.29080	−	1.80164i
$507$	−233.738	−	233.738i	−0.0204747	−	0.0204747i
$508$	−14419.7	−	4897.66i	−1.25939	−	0.427753i
$509$	11880.4	−	11880.4i	1.03456	−	1.03456i	0.0351750	−	0.999381i	$-0.488801\pi$
$509$	11880.4	−	11880.4i	1.03456	−	1.03456i	0.999381	−	0.0351750i	$-0.0111989\pi$
$510$	−416.099	+	2518.90i	−0.0361278	+	0.218703i
$511$	−693.968			−0.0600770
$512$	11530.3	−	1126.42i	0.995262	−	0.0972291i
$513$	1555.38			0.133863
$514$	−2170.71	+	13140.6i	−0.186276	+	1.12764i
$515$	−11419.8	+	11419.8i	−0.977122	+	0.977122i
$516$	360.988	+	122.610i	0.0307977	+	0.0104604i
$517$	22074.8	+	22074.8i	1.87785	+	1.87785i
$518$	−523.229	−	730.300i	−0.0443810	−	0.0619451i
$519$			1170.87i			0.0990283i
$520$	−6214.57	+	11619.3i	−0.524090	+	0.979882i
$521$			6612.98i			0.556085i	0.960569	+	0.278042i	$0.0896856\pi$
$521$			6612.98i			0.556085i	−0.960569	+	0.278042i	$0.910314\pi$
$522$	5552.18	−	3977.89i	0.465541	−	0.333540i
$523$	5129.30	+	5129.30i	0.428850	+	0.428850i	0.888236	−	0.459387i	$-0.151931\pi$
$523$	5129.30	+	5129.30i	0.428850	+	0.428850i	−0.459387	+	0.888236i	$0.651931\pi$
$524$	−9320.07	+	4594.11i	−0.777003	+	0.383005i
$525$	−20.8858	+	20.8858i	−0.00173625	+	0.00173625i
$526$	8282.01	+	1368.11i	0.686526	+	0.113408i
$527$	−13679.3			−1.13070
$528$	−3474.32	−	2667.88i	−0.286364	−	0.219895i
$529$	−7282.60			−0.598553
$530$	6866.38	+	1134.26i	0.562748	+	0.0929609i
$531$	−7360.75	+	7360.75i	−0.601562	+	0.601562i
$532$	−259.837	−	527.130i	−0.0211755	−	0.0429586i
$533$	−3703.53	−	3703.53i	−0.300972	−	0.300972i
$534$	−2133.09	+	1528.26i	−0.172861	+	0.123847i
$535$		−	13515.5i		−	1.09220i
$536$	1291.46	+	4261.42i	0.104072	+	0.343406i
$537$		−	644.849i		−	0.0518199i
$538$	1546.02	+	2157.86i	0.123891	+	0.172922i
$539$	−15188.1	−	15188.1i	−1.21372	−	1.21372i
$540$	1693.07	−	4984.75i	0.134923	−	0.397240i
$541$	−10968.5	+	10968.5i	−0.871672	+	0.871672i	−0.992655	−	0.120983i	$-0.961395\pi$
$541$	−10968.5	+	10968.5i	−0.871672	+	0.871672i	0.120983	+	0.992655i	$0.461395\pi$
$542$	3714.95	−	22488.8i	0.294411	−	1.78224i
$543$	−3962.57			−0.313168
$544$	−9582.49	+	8967.07i	−0.755231	+	0.706728i
$545$	8765.44			0.688936
$546$	65.9834	−	399.437i	0.00517185	−	0.0313083i
$547$	13088.8	−	13088.8i	1.02311	−	1.02311i	0.0233784	−	0.999727i	$-0.492558\pi$
$547$	13088.8	−	13088.8i	1.02311	−	1.02311i	0.999727	−	0.0233784i	$-0.00744226\pi$
$548$	−1227.85	+	3615.04i	−0.0957138	+	0.281801i
$549$	−5896.63	−	5896.63i	−0.458401	−	0.458401i
$550$	−1088.24	−	1518.92i	−0.0843684	−	0.117758i
$551$		−	2568.12i		−	0.198558i
$552$	−3232.16	+	979.532i	−0.249220	+	0.0755284i
$553$			863.469i			0.0663986i
$554$	1568.82	−	1123.99i	0.120312	−	0.0861981i
$555$	−1046.64	−	1046.64i	−0.0800491	−	0.0800491i
$556$	7572.70	+	15362.7i	0.577615	+	1.17181i
$557$	5049.87	−	5049.87i	0.384147	−	0.384147i	−0.488447	−	0.872594i	$-0.662436\pi$
$557$	5049.87	−	5049.87i	0.384147	−	0.384147i	0.872594	+	0.488447i	$0.162436\pi$
$558$	13613.4	+	2248.81i	1.03280	+	0.170609i
$559$	−2228.98			−0.168651
$560$	−1972.21	+	258.941i	−0.148824	+	0.0195397i
$561$	4962.18			0.373446
$562$	16462.1	+	2719.39i	1.23561	+	0.204111i
$563$	−3249.06	+	3249.06i	−0.243217	+	0.243217i	−0.818180	−	0.574962i	$-0.805017\pi$
$563$	−3249.06	+	3249.06i	−0.243217	+	0.243217i	0.574962	+	0.818180i	$0.305017\pi$
$564$	3748.82	−	1847.90i	0.279883	−	0.137962i
$565$	−553.338	−	553.338i	−0.0412019	−	0.0412019i
$566$	−2210.75	+	1583.90i	−0.164178	+	0.117626i
$567$		−	1703.30i		−	0.126159i
$568$	−9051.67	−	4841.29i	−0.668661	−	0.357634i
$569$		−	2806.05i		−	0.206741i	−0.994643	−	0.103371i	$-0.967037\pi$
$569$		−	2806.05i		−	0.206741i	0.994643	−	0.103371i	$-0.0329628\pi$
$570$	−563.925	−	787.102i	−0.0414390	−	0.0578387i
$571$	−12038.8	−	12038.8i	−0.882324	−	0.882324i	0.111446	−	0.993770i	$-0.464452\pi$
$571$	−12038.8	−	12038.8i	−0.882324	−	0.882324i	−0.993770	+	0.111446i	$0.964452\pi$
$572$	24250.3	+	8236.64i	1.77265	+	0.602083i
$573$	2434.08	−	2434.08i	0.177461	−	0.177461i
$574$	128.863	−	780.082i	0.00937042	−	0.0567247i
$575$	−1440.62			−0.104484
$576$	11010.5	−	7348.57i	0.796477	−	0.531581i
$577$	7206.84			0.519973			0.259987	−	0.965612i	$-0.416282\pi$
$577$	7206.84			0.519973			0.259987	+	0.965612i	$0.416282\pi$
$578$	158.172	−	957.508i	0.0113825	−	0.0689050i
$579$	2158.76	−	2158.76i	0.154948	−	0.154948i
$580$	−8230.45	−	2795.48i	−0.589226	−	0.200131i
$581$	−1506.57	−	1506.57i	−0.107578	−	0.107578i
$582$	1650.31	+	2303.43i	0.117539	+	0.164055i
$583$		−	13526.6i		−	0.960918i
$584$	−5182.68	−	2771.96i	−0.367227	−	0.196412i
$585$			15056.1i			1.06409i
$586$	−11552.5	+	8276.84i	−0.814382	+	0.583470i
$587$	10377.0	+	10377.0i	0.729647	+	0.729647i	0.970549	−	0.240903i	$-0.0774435\pi$
$587$	10377.0	+	10377.0i	0.729647	+	0.729647i	−0.240903	+	0.970549i	$0.577443\pi$
$588$	−2579.30	+	1271.41i	−0.180899	+	0.0891698i
$589$	3668.48	−	3668.48i	0.256633	−	0.256633i
$590$	13070.6	+	2159.14i	0.912047	+	0.150662i
$591$	2435.33			0.169503
$592$	−990.483	−	7543.98i	−0.0687645	−	0.523743i
$593$	−4758.60			−0.329531			−0.164766	−	0.986333i	$-0.552687\pi$
$593$	−4758.60			−0.329531			−0.164766	+	0.986333i	$0.552687\pi$
$594$	−10095.4	−	1667.66i	−0.697335	−	0.115194i
$595$	1593.32	−	1593.32i	0.109781	−	0.109781i
$596$	−1877.57	−	3809.02i	−0.129041	−	0.261785i
$597$	−565.414	−	565.414i	−0.0387619	−	0.0387619i
$598$	16051.5	−	11500.2i	1.09765	−	0.786417i
$599$		−	14256.4i		−	0.972455i	−0.873832	−	0.486227i	$-0.838373\pi$
$599$		−	14256.4i		−	0.972455i	0.873832	−	0.486227i	$-0.161627\pi$
$600$	−239.404	+	72.5535i	−0.0162894	+	0.00493664i
$601$		−	10385.2i		−	0.704862i	−0.935838	−	0.352431i	$-0.885355\pi$
$601$		−	10385.2i		−	0.704862i	0.935838	−	0.352431i	$-0.114645\pi$
$602$	−195.969	−	273.526i	−0.0132676	−	0.0185184i
$603$	3597.68	+	3597.68i	0.242966	+	0.242966i
$604$	−7712.16	+	22706.2i	−0.519542	+	1.52964i
$605$	−22694.5	+	22694.5i	−1.52506	+	1.52506i
$606$	−1.10829	+	6.70914i	−7.42924e−5	+	0.000449737i
$607$	−16243.6			−1.08618			−0.543088	−	0.839676i	$-0.682745\pi$
$607$	−16243.6			−1.08618			−0.543088	+	0.839676i	$0.682745\pi$
$608$	165.042	−	4974.59i	0.0110088	−	0.331819i
$609$	267.064			0.0177701
$610$	−1729.67	+	10470.7i	−0.114807	+	0.694996i
$611$	−17279.0	+	17279.0i	−1.14408	+	1.14408i
$612$	−4822.63	+	14198.8i	−0.318535	+	0.937832i
$613$	−500.502	−	500.502i	−0.0329773	−	0.0329773i	0.690426	−	0.723403i	$-0.257423\pi$
$613$	−500.502	−	500.502i	−0.0329773	−	0.0329773i	−0.723403	+	0.690426i	$0.757423\pi$
$614$	−6372.83	−	8894.92i	−0.418870	−	0.584642i
$615$		−	1302.66i		−	0.0854121i
$616$	1121.31	+	3699.99i	0.0733426	+	0.242008i
$617$		−	11575.9i		−	0.755316i	−0.925945	−	0.377658i	$-0.876729\pi$
$617$		−	11575.9i		−	0.755316i	0.925945	−	0.377658i	$-0.123271\pi$
$618$	3416.18	−	2447.55i	0.222361	−	0.159312i
$619$	18356.1	+	18356.1i	1.19191	+	1.19191i	0.976530	+	0.215380i	$0.0690992\pi$
$619$	18356.1	+	18356.1i	1.19191	+	1.19191i	0.215380	+	0.976530i	$0.430901\pi$
$620$	−7763.68	−	15750.2i	−0.502898	−	1.02023i
$621$	−5578.34	+	5578.34i	−0.360469	+	0.360469i
$622$	−16176.3	−	2672.18i	−1.04278	−	0.172258i
$623$	2315.98			0.148937
$624$	2088.27	−	2719.51i	0.133971	−	0.174467i
$625$	16809.5			1.07581
$626$	−23336.8	−	3855.03i	−1.48998	−	0.246131i
$627$	−1330.75	+	1330.75i	−0.0847607	+	0.0847607i
$628$	15313.2	−	7548.26i	0.973027	−	0.479631i
$629$	6094.66	+	6094.66i	0.386343	+	0.386343i
$630$	−1847.58	+	1323.71i	−0.116840	+	0.0837111i
$631$			10224.8i			0.645079i	0.946556	+	0.322539i	$0.104537\pi$
$631$			10224.8i			0.645079i	−0.946556	+	0.322539i	$0.895463\pi$
$632$	−3449.01	+	6448.54i	−0.217079	+	0.405869i
$633$			3370.88i			0.211660i
$634$	802.338	+	1119.87i	0.0502601	+	0.0701509i
$635$	15658.7	+	15658.7i	0.978578	+	0.978578i
$636$	−1714.73	−	582.409i	−0.106908	−	0.0363114i
$637$	11888.4	−	11888.4i	0.739461	−	0.739461i
$638$	−2753.52	+	16668.7i	−0.170866	+	1.03436i
$639$	−11729.0			−0.726125
$640$	−15763.2	−	5943.92i	−0.973584	−	0.367116i
$641$	19804.4			1.22032			0.610162	−	0.792277i	$-0.291104\pi$
$641$	19804.4			1.22032			0.610162	+	0.792277i	$0.291104\pi$
$642$	−573.197	+	3469.91i	−0.0352372	+	0.213312i
$643$	15680.7	−	15680.7i	0.961723	−	0.961723i	−0.0375712	−	0.999294i	$-0.511962\pi$
$643$	15680.7	−	15680.7i	0.961723	−	0.961723i	0.999294	+	0.0375712i	$0.0119621\pi$
$644$	2822.45	+	958.646i	0.172702	+	0.0586583i
$645$	−392.006	−	392.006i	−0.0239306	−	0.0239306i
$646$	3283.78	+	4583.37i	0.199998	+	0.279149i
$647$			9232.26i			0.560985i	0.959856	+	0.280493i	$0.0904978\pi$
$647$			9232.26i			0.560985i	−0.959856	+	0.280493i	$0.909502\pi$
$648$	6803.60	−	12720.6i	0.412455	−	0.771159i
$649$		−	25748.8i		−	1.55736i
$650$	1188.93	−	851.814i	0.0717438	−	0.0514014i
$651$	381.492	+	381.492i	0.0229675	+	0.0229675i
$652$	14462.6	−	7129.00i	0.868710	−	0.428210i
$653$	−19697.9	+	19697.9i	−1.18046	+	1.18046i	−0.200833	+	0.979626i	$0.564365\pi$
$653$	−19697.9	+	19697.9i	−1.18046	+	1.18046i	−0.979626	+	0.200833i	$0.935635\pi$
$654$	−2250.39	−	371.745i	−0.134552	−	0.0222269i
$655$	15109.8			0.901355
$656$	4078.30	−	5311.07i	0.242730	−	0.316101i
$657$	−6715.66			−0.398786
$658$	−3639.50	−	601.213i	−0.215627	−	0.0356196i
$659$	3888.06	−	3888.06i	0.229829	−	0.229829i	−0.582792	−	0.812621i	$-0.698040\pi$
$659$	3888.06	−	3888.06i	0.229829	−	0.229829i	0.812621	+	0.582792i	$0.198040\pi$
$660$	2816.29	+	5713.41i	0.166097	+	0.336961i
$661$	−8110.20	−	8110.20i	−0.477232	−	0.477232i	0.427013	−	0.904245i	$-0.359566\pi$
$661$	−8110.20	−	8110.20i	−0.477232	−	0.477232i	−0.904245	+	0.427013i	$0.859566\pi$
$662$	8739.82	−	6261.70i	0.513116	−	0.367625i
$663$			3884.13i			0.227522i
$664$	−5233.54	−	17269.1i	−0.305875	−	1.00929i
$665$			854.587i			0.0498338i
$666$	−5063.38	−	7067.25i	−0.294597	−	0.411187i
$667$	9210.54	+	9210.54i	0.534683	+	0.534683i
$668$	2038.76	−	6002.54i	0.118087	−	0.347672i
$669$	−270.966	+	270.966i	−0.0156594	+	0.0156594i
$670$	1055.31	−	6388.45i	0.0608513	−	0.368369i
$671$	20627.1			1.18674
$672$	517.317	+	17.1630i	0.0296964	+	0.000985236i
$673$	−28428.2			−1.62827			−0.814135	−	0.580676i	$-0.802788\pi$
$673$	−28428.2			−1.62827			−0.814135	+	0.580676i	$0.802788\pi$
$674$	−827.610	+	5010.02i	−0.0472972	+	0.286318i
$675$	−413.186	+	413.186i	−0.0235608	+	0.0235608i
$676$	−794.652	+	2339.62i	−0.0452124	+	0.133114i
$677$	−16967.4	−	16967.4i	−0.963235	−	0.963235i	0.0361128	−	0.999348i	$-0.488502\pi$
$677$	−16967.4	−	16967.4i	−0.963235	−	0.963235i	−0.999348	+	0.0361128i	$0.988502\pi$
$678$	118.594	+	165.528i	0.00671765	+	0.00937621i
$679$		−	2500.92i		−	0.141350i
$680$	18263.5	−	5534.91i	1.02996	−	0.312138i
$681$		−	5229.92i		−	0.294289i
$682$	−27744.0	+	19877.3i	−1.55773	+	1.11605i
$683$	−9550.16	−	9550.16i	−0.535032	−	0.535032i	0.387034	−	0.922066i	$-0.373500\pi$
$683$	−9550.16	−	9550.16i	−0.535032	−	0.535032i	−0.922066	+	0.387034i	$0.873500\pi$
$684$	−2514.49	−	5101.14i	−0.140561	−	0.285156i
$685$	3925.66	−	3925.66i	0.218966	−	0.218966i
$686$	5061.38	+	836.095i	0.281697	+	0.0465339i
$687$	−2164.42			−0.120201
$688$	−370.974	−	2825.51i	−0.0205570	−	0.156572i
$689$	10587.9			0.585439
$690$	4845.44	+	800.424i	0.267337	+	0.0441617i
$691$	−20859.7	+	20859.7i	−1.14839	+	1.14839i	−0.161527	+	0.986868i	$0.551642\pi$
$691$	−20859.7	+	20859.7i	−1.14839	+	1.14839i	−0.986868	+	0.161527i	$0.948358\pi$
$692$	7850.30	−	3869.62i	0.431248	−	0.212574i
$693$	3123.70	+	3123.70i	0.171226	+	0.171226i
$694$	−6396.96	+	4583.14i	−0.349892	+	0.250683i
$695$		−	24906.1i		−	1.35934i
$696$	1994.48	+	1066.75i	0.108622	+	0.0580964i
$697$			7585.52i			0.412227i
$698$	17153.9	+	23942.7i	0.930207	+	1.29834i
$699$	701.137	+	701.137i	0.0379391	+	0.0379391i
$700$	209.058	+	71.0065i	0.0112880	+	0.00383399i
$701$	23495.4	−	23495.4i	1.26592	−	1.26592i	0.317740	−	0.948178i	$-0.397076\pi$
$701$	23495.4	−	23495.4i	1.26592	−	1.26592i	0.948178	−	0.317740i	$-0.102924\pi$
$702$	1305.36	−	7902.10i	0.0701816	−	0.424851i
$703$	−3268.91			−0.175376
$704$	−6404.93	+	32111.1i	−0.342890	+	1.71908i
$705$	−6077.62			−0.324676
$706$	4906.86	−	29704.2i	0.261575	−	1.58347i
$707$	4.24384	−	4.24384i	0.000225751	−	0.000225751i
$708$	−3264.10	−	1108.65i	−0.173266	−	0.0588500i
$709$	4559.45	+	4559.45i	0.241515	+	0.241515i	0.817477	−	0.575962i	$-0.195372\pi$
$709$	4559.45	+	4559.45i	0.241515	+	0.241515i	−0.575962	+	0.817477i	$0.695372\pi$
$710$	8693.47	+	12134.0i	0.459521	+	0.641380i
$711$			8355.95i			0.440749i
$712$	17296.1	+	9250.84i	0.910393	+	0.486924i
$713$			26313.9i			1.38214i
$714$	−476.633	+	341.487i	−0.0249826	+	0.0178989i
$715$	−26334.1	−	26334.1i	−1.37740	−	1.37740i
$716$	−4323.49	+	2131.16i	−0.225665	+	0.111236i
$717$	−599.724	+	599.724i	−0.0312372	+	0.0312372i
$718$	−20816.3	−	3438.67i	−1.08198	−	0.178733i
$719$	−6494.67			−0.336871			−0.168436	−	0.985713i	$-0.553872\pi$
$719$	−6494.67			−0.336871			−0.168436	+	0.985713i	$0.553872\pi$
$720$	−19085.5	+	2505.82i	−0.987880	+	0.129703i
$721$	−3709.08			−0.191586
$722$	17031.0	+	2813.37i	0.877878	+	0.145018i
$723$	1096.58	−	1096.58i	0.0564069	−	0.0564069i
$724$	13095.9	+	26567.7i	0.672246	+	1.36378i
$725$	682.221	+	682.221i	0.0349476	+	0.0349476i
$726$	6788.95	−	4863.99i	0.347055	−	0.248650i
$727$			24866.4i			1.26856i	0.773103	+	0.634280i	$0.218704\pi$
$727$			24866.4i			1.26856i	−0.773103	+	0.634280i	$0.781296\pi$
$728$	−2896.15	+	877.704i	−0.147443	+	0.0446839i
$729$		−	14848.5i		−	0.754384i
$730$	4977.59	+	6947.50i	0.252368	+	0.352245i
$731$	2282.68	+	2282.68i	0.115497	+	0.115497i
$732$	888.133	−	2614.84i	0.0448447	−	0.132032i
$733$	−14914.3	+	14914.3i	−0.751533	+	0.751533i	−0.974765	−	0.223232i	$-0.928339\pi$
$733$	−14914.3	+	14914.3i	−0.751533	+	0.751533i	0.223232	+	0.974765i	$0.428339\pi$
$734$	−2881.77	+	17445.1i	−0.144916	+	0.877260i
$735$	4181.58			0.209850
$736$	17249.4	+	18433.2i	0.863886	+	0.923176i
$737$	−12585.1			−0.629008
$738$	1247.03	−	7548.99i	0.0622001	−	0.376534i
$739$	8451.86	−	8451.86i	0.420713	−	0.420713i	−0.464737	−	0.885449i	$-0.653851\pi$
$739$	8451.86	−	8451.86i	0.420713	−	0.420713i	0.885449	+	0.464737i	$0.153851\pi$
$740$	−3558.30	+	10476.4i	−0.176765	+	0.520431i
$741$	−1041.64	−	1041.64i	−0.0516404	−	0.0516404i
$742$	930.875	+	1299.28i	0.0460559	+	0.0642829i
$743$			5622.43i			0.277614i	0.990319	+	0.138807i	$0.0443267\pi$
$743$			5622.43i			0.277614i	−0.990319	+	0.138807i	$0.955673\pi$
$744$	1325.24	+	4372.87i	0.0653031	+	0.215480i
$745$			6175.21i			0.303681i
$746$	28977.7	−	20761.3i	1.42219	−	1.01893i
$747$	−14579.3	−	14579.3i	−0.714095	−	0.714095i
$748$	−16399.5	−	33269.7i	−0.801638	−	1.62628i
$749$	2194.88	−	2194.88i	0.107075	−	0.107075i
$750$	−3984.08	−	658.135i	−0.193971	−	0.0320422i
$751$	−32314.9			−1.57016			−0.785079	−	0.619396i	$-0.787378\pi$
$751$	−32314.9			−1.57016			−0.785079	+	0.619396i	$0.787378\pi$
$752$	−24779.0	−	19027.4i	−1.20159	−	0.922685i
$753$	−5418.58			−0.262236
$754$	−13047.3	−	2155.30i	−0.630181	−	0.104100i
$755$	24657.2	−	24657.2i	1.18857	−	1.18857i
$756$	1084.46	−	534.557i	0.0521710	−	0.0257165i
$757$	12692.8	+	12692.8i	0.609418	+	0.609418i	0.942794	−	0.333376i	$-0.108188\pi$
$757$	12692.8	+	12692.8i	0.609418	+	0.609418i	−0.333376	+	0.942794i	$0.608188\pi$
$758$	3849.97	−	2758.34i	0.184482	−	0.132173i
$759$		−	9545.42i		−	0.456491i
$760$	−3413.53	+	6382.21i	−0.162923	+	0.304615i
$761$			13108.2i			0.624404i	0.950016	+	0.312202i	$0.101067\pi$
$761$			13108.2i			0.624404i	−0.950016	+	0.312202i	$0.898933\pi$
$762$	−3356.04	−	4684.22i	−0.159549	−	0.222692i
$763$	1423.48	+	1423.48i	0.0675404	+	0.0675404i
$764$	−24364.1	−	8275.27i	−1.15375	−	0.391870i
$765$	15418.8	−	15418.8i	0.728718	−	0.728718i
$766$	−1327.81	+	8038.01i	−0.0626314	+	0.379145i
$767$	20154.8			0.948822
$768$	3794.86	+	2194.53i	0.178301	+	0.103110i
$769$	23661.2			1.10955			0.554776	−	0.832000i	$-0.312804\pi$
$769$	23661.2			1.10955			0.554776	+	0.832000i	$0.312804\pi$
$770$	916.280	−	5546.79i	0.0428837	−	0.259601i
$771$	−3563.56	+	3563.56i	−0.166457	+	0.166457i
$772$	−21608.2	−	7339.24i	−1.00738	−	0.342157i
$773$	21370.5	+	21370.5i	0.994362	+	0.994362i	0.999984	−	0.00562228i	$-0.00178964\pi$
$773$	21370.5	+	21370.5i	0.994362	+	0.994362i	−0.00562228	+	0.999984i	$0.501790\pi$
$774$	−1896.43	−	2646.96i	−0.0880695	−	0.122924i
$775$			1949.06i			0.0903384i
$776$	9989.59	−	18677.3i	0.462120	−	0.864018i
$777$		−	339.940i		−	0.0156954i
$778$	30058.5	−	21535.6i	1.38515	−	0.992402i
$779$	−2034.27	−	2034.27i	−0.0935627	−	0.0935627i
$780$	−4472.15	+	2204.44i	−0.205293	+	0.101194i
$781$	20514.8	−	20514.8i	0.939921	−	0.939921i
$782$	−28215.4	−	4660.94i	−1.29026	−	0.213139i
$783$	5283.35			0.241139
$784$	17048.7	+	13091.4i	0.776633	+	0.596366i
$785$	−24825.8			−1.12875
$786$	−3879.20	−	640.809i	−0.176039	−	0.0290800i
$787$	−20890.9	+	20890.9i	−0.946226	+	0.946226i	−0.998626	−	0.0524002i	$-0.983313\pi$
$787$	−20890.9	+	20890.9i	−0.946226	+	0.946226i	0.0524002	+	0.998626i	$0.483313\pi$
$788$	−8048.54	−	16328.1i	−0.363854	−	0.738151i
$789$	2245.97	+	2245.97i	0.101342	+	0.101342i
$790$	8644.42	−	6193.35i	0.389310	−	0.278924i
$791$		−	179.720i		−	0.00807853i
$792$	10851.2	+	35805.5i	0.486842	+	1.60643i
$793$			16145.8i			0.723020i
$794$	9919.09	+	13844.6i	0.443344	+	0.618801i
$795$	1862.07	+	1862.07i	0.0830702	+	0.0830702i
$796$	−1922.27	+	5659.54i	−0.0855942	+	0.252007i
$797$	−6834.83	+	6834.83i	−0.303767	+	0.303767i	−0.842486	−	0.538719i	$-0.818908\pi$
$797$	−6834.83	+	6834.83i	−0.303767	+	0.303767i	0.538719	+	0.842486i	$0.318908\pi$
$798$	36.2433	−	219.402i	0.00160777	−	0.00973277i
$799$	35390.5			1.56699
$800$	1277.65	+	1365.34i	0.0564649	+	0.0603401i
$801$	22412.1			0.988631
$802$	5864.89	−	35503.7i	0.258225	−	1.56319i
$803$	11746.1	−	11746.1i	0.516203	−	0.516203i
$804$	−541.872	+	1595.38i	−0.0237691	+	0.0699810i
$805$	−3064.97	−	3064.97i	−0.134194	−	0.134194i
$806$	−15558.9	−	21716.5i	−0.679950	−	0.949045i
$807$			1004.44i			0.0438142i
$808$	48.6453	−	14.7424i	0.00211799	−	0.000641874i
$809$			15807.0i			0.686952i	0.939162	+	0.343476i	$0.111604\pi$
$809$			15807.0i			0.686952i	−0.939162	+	0.343476i	$0.888396\pi$
$810$	−17052.2	+	12217.2i	−0.739696	+	0.529960i
$811$	−11522.7	−	11522.7i	−0.498910	−	0.498910i	0.412189	−	0.911099i	$-0.364764\pi$
$811$	−11522.7	−	11522.7i	−0.498910	−	0.498910i	−0.911099	+	0.412189i	$0.864764\pi$
$812$	−882.621	−	1790.57i	−0.0381452	−	0.0773852i
$813$	6098.66	−	6098.66i	0.263087	−	0.263087i
$814$	21217.2	+	3504.89i	0.913591	+	0.150917i
$815$	−23446.9			−1.00774
$816$	−4923.61	+	646.443i	−0.211226	+	0.0277329i
$817$	−1224.33			−0.0524284
$818$	−650.185	−	107.405i	−0.0277912	−	0.00459086i
$819$	−2445.06	+	2445.06i	−0.104319	+	0.104319i
$820$	−8733.90	+	4305.17i	−0.371952	+	0.183345i
$821$	308.824	+	308.824i	0.0131279	+	0.0131279i	0.713640	−	0.700512i	$-0.247045\pi$
$821$	308.824	+	308.824i	0.0131279	+	0.0131279i	−0.700512	+	0.713640i	$0.747045\pi$
$822$	−1174.34	+	841.365i	−0.0498295	+	0.0357007i
$823$			5633.49i			0.238604i	0.992858	+	0.119302i	$0.0380656\pi$
$823$			5633.49i			0.238604i	−0.992858	+	0.119302i	$0.961934\pi$
$824$	−27700.1	−	14815.4i	−1.17109	−	0.626358i
$825$		−	707.026i		−	0.0298369i
$826$	1771.98	+	2473.26i	0.0746430	+	0.104184i
$827$	−15835.5	−	15835.5i	−0.665844	−	0.665844i	0.290908	−	0.956751i	$-0.406043\pi$
$827$	−15835.5	−	15835.5i	−0.665844	−	0.665844i	−0.956751	+	0.290908i	$0.906043\pi$
$828$	27313.3	+	9276.99i	1.14638	+	0.389369i
$829$	−6200.19	+	6200.19i	−0.259761	+	0.259761i	−0.824957	−	0.565196i	$-0.808801\pi$
$829$	−6200.19	+	6200.19i	−0.259761	+	0.259761i	0.565196	+	0.824957i	$0.308801\pi$
$830$	−4276.58	+	25888.7i	−0.178846	+	1.08266i
$831$	730.253			0.0304840
$832$	−25134.9	−	5013.43i	−1.04735	−	0.208906i
$833$	−24349.7			−1.01281
$834$	−1056.28	+	6394.27i	−0.0438559	+	0.265486i
$835$	−6518.30	+	6518.30i	−0.270150	+	0.270150i
$836$	13320.2	+	4524.21i	0.551063	+	0.187169i
$837$	7547.09	+	7547.09i	0.311668	+	0.311668i
$838$	14270.6	+	19918.2i	0.588267	+	0.821079i
$839$			30644.3i			1.26098i	0.776199	+	0.630488i	$0.217145\pi$
$839$			30644.3i			1.26098i	−0.776199	+	0.630488i	$0.782855\pi$
$840$	−663.699	−	354.980i	−0.0272617	−	0.0145809i
$841$			15665.5i			0.642319i
$842$	−27015.6	+	19355.5i	−1.10573	+	0.792204i
$843$	4464.29	+	4464.29i	0.182394	+	0.182394i
$844$	22600.6	−	11140.4i	0.921735	−	0.454348i
$845$	2540.65	−	2540.65i	0.103433	−	0.103433i
$846$	−35220.1	−	5818.04i	−1.43131	−	0.236440i
$847$	−7371.03			−0.299022
$848$	1762.17	+	13421.5i	0.0713597	+	0.543509i
$849$	−1029.06			−0.0415986
$850$	−2089.91	−	345.234i	−0.0843331	−	0.0139311i
$851$	11723.9	−	11723.9i	0.472256	−	0.472256i
$852$	−1717.31	−	3483.90i	−0.0690540	−	0.140090i
$853$	−30801.0	−	30801.0i	−1.23635	−	1.23635i	−0.961482	−	0.274869i	$-0.911365\pi$
$853$	−30801.0	−	30801.0i	−1.23635	−	1.23635i	−0.274869	−	0.961482i	$-0.588635\pi$
$854$	−1981.30	+	1419.52i	−0.0793897	+	0.0568793i
$855$			8270.00i			0.330793i
$856$	25158.9	−	7624.61i	1.00457	−	0.304444i
$857$		−	41788.5i		−	1.66566i	−0.553533	−	0.832828i	$-0.686721\pi$
$857$		−	41788.5i		−	1.66566i	0.553533	−	0.832828i	$-0.313279\pi$
$858$	5644.03	+	7877.70i	0.224573	+	0.313450i
$859$	11914.5	+	11914.5i	0.473243	+	0.473243i	0.902963	−	0.429719i	$-0.141388\pi$
$859$	11914.5	+	11914.5i	0.473243	+	0.473243i	−0.429719	+	0.902963i	$0.641388\pi$
$860$	−1332.72	+	3923.80i	−0.0528435	+	0.155582i
$861$	211.548	−	211.548i	0.00837344	−	0.00837344i
$862$	4027.88	−	24383.1i	0.159153	−	0.963449i
$863$	27636.7			1.09011			0.545054	−	0.838401i	$-0.316509\pi$
$863$	27636.7			1.09011			0.545054	+	0.838401i	$0.316509\pi$
$864$	10234.1	+	339.538i	0.402977	+	0.0133696i
$865$	−12727.0			−0.500266
$866$	−5360.10	+	32447.9i	−0.210328	+	1.27324i
$867$	259.664	−	259.664i	0.0101714	−	0.0101714i
$868$	1296.98	−	3818.57i	0.0507169	−	0.149321i
$869$	−14615.1	−	14615.1i	−0.570520	−	0.570520i
$870$	−1915.56	−	2673.65i	−0.0746476	−	0.104190i
$871$		−	9850.95i		−	0.383223i
$872$	4944.90	+	16316.7i	0.192036	+	0.633661i
$873$		−	24201.9i		−	0.938270i
$874$	8816.73	−	6316.80i	0.341224	−	0.244473i
$875$	2520.12	+	2520.12i	0.0973663	+	0.0973663i
$876$	−983.273	−	1994.77i	−0.0379243	−	0.0769371i
$877$	−11918.3	+	11918.3i	−0.458896	+	0.458896i	−0.898293	−	0.439397i	$-0.855192\pi$
$877$	−11918.3	+	11918.3i	−0.458896	+	0.458896i	0.439397	+	0.898293i	$0.355192\pi$
$878$	49203.4	+	8127.96i	1.89127	+	0.312421i
$879$	−5377.45			−0.206344
$880$	28998.8	−	37764.5i	1.11085	−	1.44664i
$881$	−13330.0			−0.509759			−0.254880	−	0.966973i	$-0.582036\pi$
$881$	−13330.0			−0.509759			−0.254880	+	0.966973i	$0.582036\pi$
$882$	24232.4	+	4002.98i	0.925112	+	0.152820i
$883$	−25172.1	+	25172.1i	−0.959353	+	0.959353i	−0.999206	−	0.0398530i	$-0.987311\pi$
$883$	−25172.1	+	25172.1i	−0.959353	+	0.959353i	0.0398530	+	0.999206i	$0.487311\pi$
$884$	26041.7	−	12836.7i	0.990812	−	0.488398i
$885$	3544.57	+	3544.57i	0.134632	+	0.134632i
$886$	−14794.1	+	10599.4i	−0.560969	+	0.401910i
$887$		−	48821.3i		−	1.84810i	−0.382278	−	0.924048i	$-0.624860\pi$
$887$		−	48821.3i		−	1.84810i	0.382278	−	0.924048i	$-0.375140\pi$
$888$	1357.84	−	2538.74i	0.0513134	−	0.0959397i
$889$			5085.84i			0.191871i
$890$	−16611.7	−	23185.9i	−0.625645	−	0.873249i
$891$	28830.0	+	28830.0i	1.08400	+	1.08400i
$892$	2712.25	+	921.217i	0.101808	+	0.0345792i
$893$	−9490.96	+	9490.96i	−0.355658	+	0.355658i
$894$	261.892	−	1585.39i	0.00979752	−	0.0593103i
$895$	7009.27			0.261781
$896$	−1594.61	−	3525.15i	−0.0594556	−	0.131437i
$897$	7471.64			0.278117
$898$	−5958.93	+	36072.9i	−0.221439	+	1.34050i
$899$	12461.2	−	12461.2i	0.462296	−	0.462296i
$900$	2023.09	+	687.143i	0.0749292	+	0.0254497i
$901$	−10843.0	−	10843.0i	−0.400924	−	0.400924i
$902$	11022.5	+	15384.8i	0.406885	+	0.567913i
$903$		−	127.321i		−	0.00469210i
$904$	717.868	−	1342.18i	0.0264114	−	0.0493809i
$905$		−	43071.7i		−	1.58205i
$906$	−7376.07	+	5284.63i	−0.270478	+	0.193786i
$907$	5320.20	+	5320.20i	0.194768	+	0.194768i	0.797753	−	0.602985i	$-0.206022\pi$
$907$	5320.20	+	5320.20i	0.194768	+	0.194768i	−0.602985	+	0.797753i	$0.706022\pi$
$908$	−35064.8	+	17284.4i	−1.28157	+	0.631720i
$909$	41.0685	−	41.0685i	0.00149852	−	0.00149852i
$910$	4341.73	+	717.215i	0.158161	+	0.0261269i
$911$	−26016.0			−0.946155			−0.473077	−	0.881021i	$-0.656857\pi$
$911$	−26016.0			−0.946155			−0.473077	+	0.881021i	$0.656857\pi$
$912$	1147.04	−	1493.77i	0.0416473	−	0.0542363i
$913$	51000.2			1.84870
$914$	−26009.4	−	4296.52i	−0.941262	−	0.155488i
$915$	−2839.52	+	2839.52i	−0.102592	+	0.102592i
$916$	7153.21	+	14511.7i	0.258023	+	0.523450i
$917$	2453.77	+	2453.77i	0.0883650	+	0.0883650i
$918$	−9429.28	+	6755.67i	−0.339012	+	0.242887i
$919$		−	24082.1i		−	0.864413i	−0.901775	−	0.432206i	$-0.857735\pi$
$919$		−	24082.1i		−	0.864413i	0.901775	−	0.432206i	$-0.142265\pi$
$920$	−10647.1	−	35132.3i	−0.381550	−	1.25900i
$921$		−	4140.41i		−	0.148134i
$922$	−30017.2	−	41896.8i	−1.07220	−	1.49653i
$923$	16057.9	+	16057.9i	0.572646	+	0.572646i
$924$	−470.482	+	1385.19i	−0.0167508	+	0.0493177i
$925$	868.385	−	868.385i	0.0308674	−	0.0308674i
$926$	3244.57	−	19641.3i	0.115144	−	0.697035i
$927$	−35893.5			−1.27173
$928$	560.619	−	16897.8i	0.0198311	−	0.597735i
$929$	9324.93			0.329323			0.164661	−	0.986350i	$-0.447347\pi$
$929$	9324.93			0.329323			0.164661	+	0.986350i	$0.447347\pi$
$930$	1082.91	−	6555.53i	0.0381830	−	0.231144i
$931$	6530.06	−	6530.06i	0.229875	−	0.229875i
$932$	2383.69	−	7018.07i	0.0837772	−	0.246657i
$933$	−4386.80	−	4386.80i	−0.153931	−	0.153931i
$934$	−13981.8	−	19515.3i	−0.489829	−	0.683682i
$935$			53937.0i			1.88656i
$936$	−28026.6	+	8493.70i	−0.978716	+	0.296608i
$937$			15535.2i			0.541636i	0.962631	+	0.270818i	$0.0872941\pi$
$937$			15535.2i			0.541636i	−0.962631	+	0.270818i	$0.912706\pi$
$938$	1208.84	−	866.083i	0.0420790	−	0.0301478i
$939$	−6328.63	−	6328.63i	−0.219944	−	0.219944i
$940$	20085.9	+	40748.3i	0.696947	+	1.41390i
$941$	−34024.8	+	34024.8i	−1.17872	+	1.17872i	−0.198651	+	0.980070i	$0.563656\pi$
$941$	−34024.8	+	34024.8i	−1.17872	+	1.17872i	−0.980070	+	0.198651i	$0.936344\pi$
$942$	6373.64	+	1052.87i	0.220450	+	0.0364164i
$943$	14591.8			0.503896
$944$	3354.40	+	25548.7i	0.115653	+	0.880867i
$945$	−1758.13			−0.0605205
$946$	7946.66	+	1312.72i	0.273117	+	0.0451164i
$947$	−3816.02	+	3816.02i	−0.130944	+	0.130944i	−0.769541	−	0.638597i	$-0.779515\pi$
$947$	−3816.02	+	3816.02i	−0.130944	+	0.130944i	0.638597	+	0.769541i	$0.279515\pi$
$948$	−2481.98	+	1223.44i	−0.0850328	+	0.0419149i
$949$	9194.21	+	9194.21i	0.314496	+	0.314496i
$950$	653.051	−	467.883i	0.0223029	−	0.0159791i
$951$			521.277i			0.0177745i
$952$	3864.78	+	2067.08i	0.131574	+	0.0703723i
$953$			21759.7i			0.739629i	0.929106	+	0.369815i	$0.120579\pi$
$953$			21759.7i			0.739629i	−0.929106	+	0.369815i	$0.879421\pi$
$954$	9008.25	+	12573.3i	0.305716	+	0.426705i
$955$	26457.6	+	26457.6i	0.896489	+	0.896489i
$956$	6002.97	+	2038.91i	0.203086	+	0.0689781i
$957$	−4520.32	+	4520.32i	−0.152687	+	0.152687i
$958$	−270.744	+	1638.97i	−0.00913082	+	0.0552743i
$959$	1275.03			0.0429331
$960$	−3538.71	−	5302.11i	−0.118970	−	0.178255i
$961$	5809.78			0.195018
$962$	−2743.44	+	16607.7i	−0.0919461	+	0.556604i
$963$	21240.2	−	21240.2i	0.710754	−	0.710754i
$964$	−10976.3	−	3728.09i	−0.366723	−	0.124558i
$965$	23464.9	+	23464.9i	0.782759	+	0.782759i
$966$	656.897	+	916.869i	0.0218792	+	0.0305381i
$967$		−	19338.5i		−	0.643108i	−0.946891	−	0.321554i	$-0.895795\pi$
$967$		−	19338.5i		−	0.643108i	0.946891	−	0.321554i	$-0.104205\pi$
$968$	−55048.2	−	29442.6i	−1.82781	−	0.977603i
$969$			2133.47i			0.0707294i
$970$	−25037.4	+	17938.2i	−0.828766	+	0.593775i
$971$	4184.92	+	4184.92i	0.138311	+	0.138311i	0.772873	−	0.634561i	$-0.218819\pi$
$971$	4184.92	+	4184.92i	0.138311	+	0.138311i	−0.634561	+	0.772873i	$0.718819\pi$
$972$	15855.4	−	7815.57i	0.523213	−	0.257906i
$973$	4044.67	−	4044.67i	0.133264	−	0.133264i
$974$	23347.5	+	3856.80i	0.768072	+	0.126879i
$975$	553.421			0.0181781
$976$	−20466.8	+	2687.18i	−0.671236	+	0.0881296i
$977$	17841.9			0.584249			0.292125	−	0.956380i	$-0.405638\pi$
$977$	17841.9			0.584249			0.292125	+	0.956380i	$0.405638\pi$
$978$	6019.62	+	994.387i	0.196816	+	0.0325123i
$979$	−39200.2	+	39200.2i	−1.27972	+	1.27972i
$980$	−13819.7	−	28036.0i	−0.450463	−	0.913855i
$981$	13775.2	+	13775.2i	0.448328	+	0.448328i
$982$	4972.66	−	3562.69i	0.161593	−	0.115774i
$983$		−	61512.0i		−	1.99586i	−0.0643304	−	0.997929i	$-0.520491\pi$
$983$		−	61512.0i		−	1.99586i	0.0643304	−	0.997929i	$-0.479509\pi$
$984$	2424.88	−	734.879i	0.0785592	−	0.0238080i
$985$			26471.2i			0.856286i
$986$	11154.5	+	15568.9i	0.360274	+	0.502855i
$987$	−986.984	−	986.984i	−0.0318298	−	0.0318298i
$988$	−3541.31	+	10426.3i	−0.114032	+	0.335735i
$989$	4391.05	−	4391.05i	0.141180	−	0.141180i
$990$	8867.01	−	53677.3i	0.284659	−	1.72321i
$991$	1827.73			0.0585870			0.0292935	−	0.999571i	$-0.490674\pi$
$991$	1827.73			0.0585870			0.0292935	+	0.999571i	$0.490674\pi$
$992$	24938.8	−	23337.2i	0.798193	−	0.746931i
$993$	4068.21			0.130011
$994$	−558.726	+	3382.30i	−0.0178287	+	0.107928i
$995$	6145.84	−	6145.84i	0.195815	−	0.195815i
$996$	2195.89	−	6465.16i	0.0698590	−	0.205679i
$997$	−25017.0	−	25017.0i	−0.794681	−	0.794681i	0.187570	−	0.982251i	$-0.439939\pi$
$997$	−25017.0	−	25017.0i	−0.794681	−	0.794681i	−0.982251	+	0.187570i	$0.939939\pi$
$998$	−26474.9	−	36952.6i	−0.839728	−	1.17206i
$999$		−	6725.07i		−	0.212985i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.4.e.a.5.3	✓	10
3.2	odd	2		144.4.k.a.37.3		10
4.3	odd	2		64.4.e.a.49.3		10
8.3	odd	2		128.4.e.a.97.3		10
8.5	even	2		128.4.e.b.97.3		10
12.11	even	2		576.4.k.a.433.2		10
16.3	odd	4		64.4.e.a.17.3		10
16.5	even	4		128.4.e.b.33.3		10
16.11	odd	4		128.4.e.a.33.3		10
16.13	even	4	inner	16.4.e.a.13.3	yes	10
32.3	odd	8		1024.4.a.m.1.5		10
32.5	even	8		1024.4.b.j.513.6		10
32.11	odd	8		1024.4.b.k.513.6		10
32.13	even	8		1024.4.a.n.1.5		10
32.19	odd	8		1024.4.a.m.1.6		10
32.21	even	8		1024.4.b.j.513.5		10
32.27	odd	8		1024.4.b.k.513.5		10
32.29	even	8		1024.4.a.n.1.6		10
48.29	odd	4		144.4.k.a.109.3		10
48.35	even	4		576.4.k.a.145.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.4.e.a.5.3	✓	10	1.1	even	1	trivial
16.4.e.a.13.3	yes	10	16.13	even	4	inner
64.4.e.a.17.3		10	16.3	odd	4
64.4.e.a.49.3		10	4.3	odd	2
128.4.e.a.33.3		10	16.11	odd	4
128.4.e.a.97.3		10	8.3	odd	2
128.4.e.b.33.3		10	16.5	even	4
128.4.e.b.97.3		10	8.5	even	2
144.4.k.a.37.3		10	3.2	odd	2
144.4.k.a.109.3		10	48.29	odd	4
576.4.k.a.145.2		10	48.35	even	4
576.4.k.a.433.2		10	12.11	even	2
1024.4.a.m.1.5		10	32.3	odd	8
1024.4.a.m.1.6		10	32.19	odd	8
1024.4.a.n.1.5		10	32.13	even	8
1024.4.a.n.1.6		10	32.29	even	8
1024.4.b.j.513.5		10	32.21	even	8
1024.4.b.j.513.6		10	32.5	even	8
1024.4.b.k.513.5		10	32.27	odd	8
1024.4.b.k.513.6		10	32.11	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.460984 - 2.79061i) q^{2} +(0.756776 - 0.756776i) q^{3} +(-7.57499 - 2.57285i) q^{4} +(8.22587 + 8.22587i) q^{5} +(-1.76300 - 2.46073i) q^{6} +2.67171i q^{7} +(-10.6718 + 19.9528i) q^{8} +25.8546i q^{9} +(26.7472 - 19.1632i) q^{10} +(-45.2213 - 45.2213i) q^{11} +(-7.67964 + 3.78550i) q^{12} +(35.3968 - 35.3968i) q^{13} +(7.45568 + 1.23161i) q^{14} +12.4503 q^{15} +(50.7609 + 38.9786i) q^{16} -72.4991 q^{17} +(72.1500 + 11.9185i) q^{18} +(19.4427 - 19.4427i) q^{19} +(-41.1470 - 83.4748i) q^{20} +(2.02188 + 2.02188i) q^{21} +(-147.041 + 105.349i) q^{22} +139.462i q^{23} +(7.02366 + 23.1759i) q^{24} +10.3299i q^{25} +(-82.4612 - 115.096i) q^{26} +(39.9991 + 39.9991i) q^{27} +(6.87389 - 20.2381i) q^{28} +(66.0434 - 66.0434i) q^{29} +(5.73937 - 34.7439i) q^{30} +188.682 q^{31} +(132.174 - 123.685i) q^{32} -68.4447 q^{33} +(-33.4209 + 202.317i) q^{34} +(-21.9771 + 21.9771i) q^{35} +(66.5199 - 195.848i) q^{36} +(-84.0653 - 84.0653i) q^{37} +(-45.2941 - 63.2196i) q^{38} -53.5748i q^{39} +(-251.914 + 76.3445i) q^{40} -104.629i q^{41} +(6.57434 - 4.71023i) q^{42} +(-31.4857 - 31.4857i) q^{43} +(226.203 + 458.898i) q^{44} +(-212.676 + 212.676i) q^{45} +(389.183 + 64.2896i) q^{46} -488.151 q^{47} +(67.9127 - 8.91656i) q^{48} +335.862 q^{49} +(28.8266 + 4.76190i) q^{50} +(-54.8656 + 54.8656i) q^{51} +(-359.201 + 177.060i) q^{52} +(149.560 + 149.560i) q^{53} +(130.061 - 93.1828i) q^{54} -743.968i q^{55} +(-53.3080 - 28.5118i) q^{56} -29.4275i q^{57} +(-153.856 - 214.746i) q^{58} +(284.698 + 284.698i) q^{59} +(-94.3107 - 32.0327i) q^{60} +(-228.069 + 228.069i) q^{61} +(86.9792 - 526.537i) q^{62} -69.0758 q^{63} +(-284.227 - 425.863i) q^{64} +582.338 q^{65} +(-31.5519 + 191.002i) q^{66} +(139.151 - 139.151i) q^{67} +(549.180 + 186.529i) q^{68} +(105.541 + 105.541i) q^{69} +(51.1984 + 71.4606i) q^{70} +453.655i q^{71} +(-515.871 - 275.914i) q^{72} +259.747i q^{73} +(-273.346 + 195.841i) q^{74} +(7.81740 + 7.81740i) q^{75} +(-197.301 + 97.2550i) q^{76} +(120.818 - 120.818i) q^{77} +(-149.506 - 24.6971i) q^{78} +323.190 q^{79} +(96.9197 + 738.185i) q^{80} -637.533 q^{81} +(-291.979 - 48.2323i) q^{82} +(-563.897 + 563.897i) q^{83} +(-10.1137 - 20.5177i) q^{84} +(-596.368 - 596.368i) q^{85} +(-102.379 + 73.3499i) q^{86} -99.9602i q^{87} +(1384.88 - 419.700i) q^{88} -866.853i q^{89} +(495.456 + 691.537i) q^{90} +(94.5697 + 94.5697i) q^{91} +(358.814 - 1056.42i) q^{92} +(142.790 - 142.790i) q^{93} +(-225.030 + 1362.24i) q^{94} +319.866 q^{95} +(6.42400 - 193.628i) q^{96} -936.077 q^{97} +(154.827 - 937.259i) q^{98} +(1169.18 - 1169.18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} - 68 q^{10} + 18 q^{11} + 100 q^{12} - 2 q^{13} + 188 q^{14} - 124 q^{15} + 280 q^{16} - 4 q^{17} + 174 q^{18} - 26 q^{19} - 196 q^{20}+ \cdots + 4958 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 - 2 * q^5 - 32 * q^6 - 44 * q^8 - 68 * q^10 + 18 * q^11 + 100 * q^12 - 2 * q^13 + 188 * q^14 - 124 * q^15 + 280 * q^16 - 4 * q^17 + 174 * q^18 - 26 * q^19 - 196 * q^20 + 52 * q^21 - 588 * q^22 - 848 * q^24 - 264 * q^26 + 184 * q^27 + 280 * q^28 - 202 * q^29 + 1236 * q^30 + 368 * q^31 + 968 * q^32 - 4 * q^33 + 436 * q^34 + 476 * q^35 - 596 * q^36 - 10 * q^37 - 1232 * q^38 - 1336 * q^40 - 680 * q^42 - 838 * q^43 + 868 * q^44 + 194 * q^45 + 1132 * q^46 - 944 * q^47 + 1768 * q^48 + 94 * q^49 + 726 * q^50 - 1500 * q^51 - 236 * q^52 - 378 * q^53 - 1376 * q^54 - 488 * q^56 + 8 * q^58 + 1706 * q^59 - 192 * q^60 + 910 * q^61 - 80 * q^62 + 2628 * q^63 + 512 * q^64 - 492 * q^65 - 428 * q^66 + 1942 * q^67 - 880 * q^68 + 580 * q^69 + 160 * q^70 + 1092 * q^72 - 452 * q^74 - 2954 * q^75 - 1228 * q^76 - 268 * q^77 - 772 * q^78 - 4416 * q^79 - 2648 * q^80 + 482 * q^81 - 704 * q^82 - 2562 * q^83 + 1960 * q^84 - 12 * q^85 + 3764 * q^86 + 1528 * q^88 + 1896 * q^90 + 3332 * q^91 + 632 * q^92 - 2192 * q^93 - 3248 * q^94 + 6900 * q^95 - 4432 * q^96 - 4 * q^97 + 314 * q^98 + 4958 * q^99

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