LMFDB - Embedded newform 153.3.i.a.50.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(50,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.50"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.i (of order $6$, 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:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			50.20
Character	$\chi$	$=$	153.50
Dual form			153.3.i.a.101.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.542321 - 0.313109i) q^{2} +(2.45367 - 1.72612i) q^{3} +(-1.80392 + 3.12449i) q^{4} +(-3.87159 + 6.70579i) q^{5} +(0.790215 - 1.70438i) q^{6} +(10.9773 - 6.33772i) q^{7} +4.76418i q^{8} +(3.04102 - 8.47067i) q^{9} +4.84893i q^{10} +(8.44140 + 14.6209i) q^{11} +(0.967004 + 10.7803i) q^{12} +(-4.57710 + 7.92777i) q^{13} +(3.96880 - 6.87416i) q^{14} +(2.07539 + 23.1366i) q^{15} +(-5.72399 - 9.91424i) q^{16} +(16.8414 - 2.31664i) q^{17} +(-1.00304 - 5.54600i) q^{18} -10.9564 q^{19} +(-13.9681 - 24.1935i) q^{20} +(15.9949 - 34.4988i) q^{21} +(9.15591 + 5.28617i) q^{22} +(4.67192 - 8.09201i) q^{23} +(8.22355 + 11.6897i) q^{24} +(-17.4784 - 30.2735i) q^{25} +5.73253i q^{26} +(-7.15973 - 26.0334i) q^{27} +45.7311i q^{28} +(-5.93786 - 10.2847i) q^{29} +(8.36983 + 11.8977i) q^{30} +(-35.3634 - 20.4171i) q^{31} +(-22.7121 - 13.1128i) q^{32} +(45.9499 + 21.3041i) q^{33} +(8.40810 - 6.52957i) q^{34} +98.1483i q^{35} +(20.9807 + 24.7821i) q^{36} -32.8577i q^{37} +(-5.94189 + 3.43055i) q^{38} +(2.45358 + 27.3528i) q^{39} +(-31.9476 - 18.4450i) q^{40} +(-8.44003 + 14.6186i) q^{41} +(-2.12750 - 23.7176i) q^{42} +(7.58448 + 13.1367i) q^{43} -60.9106 q^{44} +(45.0290 + 53.1874i) q^{45} -5.85129i q^{46} +(-15.6837 + 9.05501i) q^{47} +(-31.1580 - 14.4460i) q^{48} +(55.8334 - 96.7063i) q^{49} +(-18.9579 - 10.9453i) q^{50} +(37.3245 - 34.7546i) q^{51} +(-16.5135 - 28.6022i) q^{52} -21.5435i q^{53} +(-12.0342 - 11.8767i) q^{54} -130.727 q^{55} +(30.1940 + 52.2976i) q^{56} +(-26.8834 + 18.9121i) q^{57} +(-6.44046 - 3.71840i) q^{58} +(-5.02914 - 2.90357i) q^{59} +(-76.0341 - 35.2523i) q^{60} +(65.6535 - 37.9051i) q^{61} -25.5711 q^{62} +(-20.3027 - 112.258i) q^{63} +29.3689 q^{64} +(-35.4413 - 61.3862i) q^{65} +(31.5902 - 2.83368i) q^{66} +(-16.9553 + 29.3674i) q^{67} +(-23.1423 + 56.7999i) q^{68} +(-2.50441 - 27.9194i) q^{69} +(30.7311 + 53.2279i) q^{70} +32.6164 q^{71} +(40.3558 + 14.4880i) q^{72} +73.7502i q^{73} +(-10.2880 - 17.8194i) q^{74} +(-95.1421 - 44.1114i) q^{75} +(19.7645 - 34.2331i) q^{76} +(185.327 + 106.999i) q^{77} +(9.89504 + 14.0658i) q^{78} +(67.6514 - 39.0586i) q^{79} +88.6438 q^{80} +(-62.5044 - 51.5189i) q^{81} +10.5706i q^{82} +(-86.4969 + 49.9390i) q^{83} +(78.9374 + 112.209i) q^{84} +(-49.6682 + 121.904i) q^{85} +(8.22645 + 4.74955i) q^{86} +(-32.3222 - 14.9858i) q^{87} +(-69.6568 + 40.2164i) q^{88} -100.949i q^{89} +(41.0736 + 14.7457i) q^{90} +116.034i q^{91} +(16.8556 + 29.1948i) q^{92} +(-122.013 + 10.9447i) q^{93} +(-5.67041 + 9.82145i) q^{94} +(42.4187 - 73.4713i) q^{95} +(-78.3623 + 7.02920i) q^{96} +(-6.59417 + 3.80715i) q^{97} -69.9279i q^{98} +(149.520 - 27.0418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) $ 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.542321	−	0.313109i	0.271161	−	0.156555i	−0.358254	−	0.933624i	$-0.616628\pi$
$2$	0.542321	−	0.313109i	0.271161	−	0.156555i	0.629415	+	0.777069i	$0.283295\pi$
$3$	2.45367	−	1.72612i	0.817891	−	0.575373i
$3$	2.45367	−	1.72612i	0.817891	−	0.575373i
$4$	−1.80392	+	3.12449i	−0.450981	+	0.781122i
$5$	−3.87159	+	6.70579i	−0.774318	+	1.34116i	0.160859	+	0.986977i	$0.448574\pi$
$5$	−3.87159	+	6.70579i	−0.774318	+	1.34116i	−0.935177	+	0.354181i	$0.884760\pi$
$6$	0.790215	−	1.70438i	0.131702	−	0.284063i
$7$	10.9773	−	6.33772i	1.56818	−	0.905389i	0.571798	−	0.820394i	$-0.306246\pi$
$7$	10.9773	−	6.33772i	1.56818	−	0.905389i	0.996381	−	0.0849943i	$-0.0270872\pi$
$8$			4.76418i			0.595522i
$9$	3.04102	−	8.47067i	0.337891	−	0.941185i
$10$			4.84893i			0.484893i
$11$	8.44140	+	14.6209i	0.767400	+	1.32918i	0.938968	+	0.344004i	$0.111783\pi$
$11$	8.44140	+	14.6209i	0.767400	+	1.32918i	−0.171568	+	0.985172i	$0.554883\pi$
$12$	0.967004	+	10.7803i	0.0805836	+	0.898356i
$13$	−4.57710	+	7.92777i	−0.352085	+	0.609829i	−0.986615	−	0.163070i	$-0.947860\pi$
$13$	−4.57710	+	7.92777i	−0.352085	+	0.609829i	0.634530	+	0.772898i	$0.281194\pi$
$14$	3.96880	−	6.87416i	0.283486	−	0.491012i
$15$	2.07539	+	23.1366i	0.138359	+	1.54244i
$16$	−5.72399	−	9.91424i	−0.357749	−	0.619640i
$17$	16.8414	−	2.31664i	0.990671	−	0.136273i
$17$	16.8414	−	2.31664i	0.990671	−	0.136273i
$18$	−1.00304	−	5.54600i	−0.0557243	−	0.308111i
$19$	−10.9564			−0.576652			−0.288326	−	0.957532i	$-0.593099\pi$
$19$	−10.9564			−0.576652			−0.288326	+	0.957532i	$0.593099\pi$
$20$	−13.9681	−	24.1935i	−0.698406	−	1.20967i
$21$	15.9949	−	34.4988i	0.761663	−	1.64280i
$22$	9.15591	+	5.28617i	0.416178	+	0.240280i
$23$	4.67192	−	8.09201i	0.203127	−	0.351826i	−0.746407	−	0.665489i	$-0.768223\pi$
$23$	4.67192	−	8.09201i	0.203127	−	0.351826i	0.949534	+	0.313663i	$0.101556\pi$
$24$	8.22355	+	11.6897i	0.342648	+	0.487072i
$25$	−17.4784	−	30.2735i	−0.699137	−	1.21094i
$26$			5.73253i			0.220482i
$27$	−7.15973	−	26.0334i	−0.265175	−	0.964200i
$28$			45.7311i			1.63325i
$29$	−5.93786	−	10.2847i	−0.204754	−	0.354644i	0.745300	−	0.666729i	$-0.232306\pi$
$29$	−5.93786	−	10.2847i	−0.204754	−	0.354644i	−0.950054	+	0.312085i	$0.898973\pi$
$30$	8.36983	+	11.8977i	0.278994	+	0.396589i
$31$	−35.3634	−	20.4171i	−1.14076	−	0.658616i	−0.194138	−	0.980974i	$-0.562191\pi$
$31$	−35.3634	−	20.4171i	−1.14076	−	0.658616i	−0.946618	+	0.322358i	$0.895524\pi$
$32$	−22.7121	−	13.1128i	−0.709753	−	0.409776i
$33$	45.9499	+	21.3041i	1.39242	+	0.645579i
$34$	8.40810	−	6.52957i	0.247297	−	0.192046i
$35$			98.1483i			2.80424i
$36$	20.9807	+	24.7821i	0.582799	+	0.688391i
$37$		−	32.8577i		−	0.888046i	−0.896016	−	0.444023i	$-0.853551\pi$
$37$		−	32.8577i		−	0.888046i	0.896016	−	0.444023i	$-0.146449\pi$
$38$	−5.94189	+	3.43055i	−0.156365	+	0.0902776i
$39$	2.45358	+	27.3528i	0.0629123	+	0.701353i
$40$	−31.9476	−	18.4450i	−0.798690	−	0.461124i
$41$	−8.44003	+	14.6186i	−0.205854	+	0.356550i	−0.950405	−	0.311016i	$-0.899331\pi$
$41$	−8.44003	+	14.6186i	−0.205854	+	0.356550i	0.744550	+	0.667566i	$0.232664\pi$
$42$	−2.12750	−	23.7176i	−0.0506547	−	0.564704i
$43$	7.58448	+	13.1367i	0.176383	+	0.305505i	0.940639	−	0.339408i	$-0.110227\pi$
$43$	7.58448	+	13.1367i	0.176383	+	0.305505i	−0.764256	+	0.644913i	$0.776894\pi$
$44$	−60.9106			−1.38433
$45$	45.0290	+	53.1874i	1.00064	+	1.18194i
$46$		−	5.85129i		−	0.127202i
$47$	−15.6837	+	9.05501i	−0.333696	+	0.192660i	−0.657481	−	0.753471i	$-0.728378\pi$
$47$	−15.6837	+	9.05501i	−0.333696	+	0.192660i	0.323785	+	0.946131i	$0.395045\pi$
$48$	−31.1580	−	14.4460i	−0.649124	−	0.300959i
$49$	55.8334	−	96.7063i	1.13946	−	1.97360i
$50$	−18.9579	−	10.9453i	−0.379157	−	0.218906i
$51$	37.3245	−	34.7546i	0.731853	−	0.681462i
$52$	−16.5135	−	28.6022i	−0.317567	−	0.550043i
$53$		−	21.5435i		−	0.406481i	−0.979129	−	0.203240i	$-0.934853\pi$
$53$		−	21.5435i		−	0.406481i	0.979129	−	0.203240i	$-0.0651473\pi$
$54$	−12.0342	−	11.8767i	−0.222855	−	0.219939i
$55$	−130.727			−2.37685
$56$	30.1940	+	52.2976i	0.539179	+	0.933886i
$57$	−26.8834	+	18.9121i	−0.471639	+	0.331790i
$58$	−6.44046	−	3.71840i	−0.111042	−	0.0641103i
$59$	−5.02914	−	2.90357i	−0.0852396	−	0.0492131i	0.456774	−	0.889583i	$-0.349005\pi$
$59$	−5.02914	−	2.90357i	−0.0852396	−	0.0492131i	−0.542014	+	0.840369i	$0.682338\pi$
$60$	−76.0341	−	35.2523i	−1.26723	−	0.587538i
$61$	65.6535	−	37.9051i	1.07629	−	0.621395i	0.146395	−	0.989226i	$-0.453233\pi$
$61$	65.6535	−	37.9051i	1.07629	−	0.621395i	0.929892	+	0.367831i	$0.119900\pi$
$62$	−25.5711			−0.412438
$63$	−20.3027	−	112.258i	−0.322265	−	1.78187i
$64$	29.3689			0.458889
$65$	−35.4413	−	61.3862i	−0.545251	−	0.944403i
$66$	31.5902	−	2.83368i	0.478639	−	0.0429345i
$67$	−16.9553	+	29.3674i	−0.253064	+	0.438319i	−0.964368	−	0.264565i	$-0.914772\pi$
$67$	−16.9553	+	29.3674i	−0.253064	+	0.438319i	0.711304	+	0.702885i	$0.248105\pi$
$68$	−23.1423	+	56.7999i	−0.340329	+	0.835292i
$69$	−2.50441	−	27.9194i	−0.0362958	−	0.404630i
$70$	30.7311	+	53.2279i	0.439016	+	0.760399i
$71$	32.6164			0.459385			0.229693	−	0.973263i	$-0.426228\pi$
$71$	32.6164			0.459385			0.229693	+	0.973263i	$0.426228\pi$
$72$	40.3558	+	14.4880i	0.560497	+	0.201222i
$73$			73.7502i			1.01028i	0.863038	+	0.505138i	$0.168558\pi$
$73$			73.7502i			1.01028i	−0.863038	+	0.505138i	$0.831442\pi$
$74$	−10.2880	−	17.8194i	−0.139028	−	0.240803i
$75$	−95.1421	−	44.1114i	−1.26856	−	0.588153i
$76$	19.7645	−	34.2331i	0.260059	−	0.450436i
$77$	185.327	+	106.999i	2.40684	+	1.38959i
$78$	9.89504	+	14.0658i	0.126860	+	0.180330i
$79$	67.6514	−	39.0586i	0.856347	−	0.494412i	−0.00644008	−	0.999979i	$-0.502050\pi$
$79$	67.6514	−	39.0586i	0.856347	−	0.494412i	0.862787	+	0.505567i	$0.168717\pi$
$80$	88.6438			1.10805
$81$	−62.5044	−	51.5189i	−0.771660	−	0.636036i
$82$			10.5706i			0.128910i
$83$	−86.4969	+	49.9390i	−1.04213	+	0.601675i	−0.920436	−	0.390893i	$-0.872166\pi$
$83$	−86.4969	+	49.9390i	−1.04213	+	0.601675i	−0.121695	+	0.992568i	$0.538833\pi$
$84$	78.9374	+	112.209i	0.939731	+	1.33582i
$85$	−49.6682	+	121.904i	−0.584331	+	1.43417i
$86$	8.22645	+	4.74955i	0.0956564	+	0.0552273i
$87$	−32.3222	−	14.9858i	−0.371519	−	0.172250i
$88$	−69.6568	+	40.2164i	−0.791554	+	0.457004i
$89$		−	100.949i		−	1.13425i	−0.823631	−	0.567127i	$-0.808055\pi$
$89$		−	100.949i		−	1.13425i	0.823631	−	0.567127i	$-0.191945\pi$
$90$	41.0736	+	14.7457i	0.456374	+	0.163841i
$91$			116.034i			1.27509i
$92$	16.8556	+	29.1948i	0.183213	+	0.317334i
$93$	−122.013	+	10.9447i	−1.31196	+	0.117685i
$94$	−5.67041	+	9.82145i	−0.0603236	+	0.104483i
$95$	42.4187	−	73.4713i	0.446512	−	0.773382i
$96$	−78.3623	+	7.02920i	−0.816274	+	0.0732209i
$97$	−6.59417	+	3.80715i	−0.0679812	+	0.0392489i	−0.533605	−	0.845734i	$-0.679163\pi$
$97$	−6.59417	+	3.80715i	−0.0679812	+	0.0392489i	0.465624	+	0.884983i	$0.345830\pi$
$98$		−	69.9279i		−	0.713550i
$99$	149.520	−	27.0418i	1.51030	−	0.273149i
$100$	126.119			1.26119
$101$	−30.8119	+	17.7893i	−0.305069	+	0.176131i	−0.644718	−	0.764421i	$-0.723025\pi$
$101$	−30.8119	+	17.7893i	−0.305069	+	0.176131i	0.339649	+	0.940552i	$0.389692\pi$
$102$	9.35990	−	30.5348i	0.0917637	−	0.299361i
$103$	80.5139	−	139.454i	0.781688	−	1.35392i	−0.149269	−	0.988797i	$-0.547692\pi$
$103$	80.5139	−	139.454i	0.781688	−	1.35392i	0.930958	−	0.365127i	$-0.118975\pi$
$104$	−37.7693	−	21.8061i	−0.363167	−	0.209674i
$105$	169.416	+	240.824i	1.61348	+	2.29356i
$106$	−6.74547	−	11.6835i	−0.0636365	−	0.110222i
$107$	9.34659			0.0873513			0.0436756	−	0.999046i	$-0.486093\pi$
$107$	9.34659			0.0873513			0.0436756	+	0.999046i	$0.486093\pi$
$108$	94.2567	+	24.5918i	0.872747	+	0.227702i
$109$		−	142.540i		−	1.30770i	−0.756623	−	0.653851i	$-0.773152\pi$
$109$		−	142.540i		−	1.30770i	0.756623	−	0.653851i	$-0.226848\pi$
$110$	−70.8958	+	40.9317i	−0.644508	+	0.372107i
$111$	−56.7163	−	80.6220i	−0.510958	−	0.726324i
$112$	−125.667	−	72.5541i	−1.12203	−	0.647805i
$113$	−3.13589	+	5.43153i	−0.0277513	+	0.0480666i	−0.879568	−	0.475774i	$-0.842168\pi$
$113$	−3.13589	+	5.43153i	−0.0277513	+	0.0480666i	0.851816	+	0.523841i	$0.175501\pi$
$114$	−8.65790	+	18.6739i	−0.0759465	+	0.163806i
$115$	36.1755	+	62.6579i	0.314570	+	0.544851i
$116$	42.8458			0.369361
$117$	53.2345	+	62.8796i	0.454996	+	0.537433i
$118$	−3.63654			−0.0308182
$119$	170.190	−	132.166i	1.43017	−	1.11064i
$120$	−110.227	+	9.88752i	−0.918559	+	0.0823960i
$121$	−82.0146	+	142.053i	−0.677806	+	1.17399i
$122$	23.7369	−	41.1135i	0.194565	−	0.336996i
$123$	4.52432	+	50.4376i	0.0367831	+	0.410062i
$124$	127.586	−	73.6618i	1.02892	−	0.594047i
$125$	77.0977			0.616782
$126$	−46.1596	−	54.5228i	−0.366346	−	0.432721i
$127$	15.5272			0.122261			0.0611307	−	0.998130i	$-0.480529\pi$
$127$	15.5272			0.122261			0.0611307	+	0.998130i	$0.480529\pi$
$128$	106.776	−	61.6470i	0.834185	−	0.481617i
$129$	41.2854	+	19.1415i	0.320042	+	0.148383i
$130$	−38.4412	−	22.1940i	−0.295701	−	0.170723i
$131$	−80.0490	+	138.649i	−0.611061	+	1.05839i	0.380001	+	0.924986i	$0.375924\pi$
$131$	−80.0490	+	138.649i	−0.611061	+	1.05839i	−0.991062	+	0.133403i	$0.957410\pi$
$132$	−149.455	+	105.139i	−1.13223	+	0.796508i
$133$	−120.271	+	69.4386i	−0.904294	+	0.522095i
$134$			21.2354i			0.158473i
$135$	202.294	+	52.7790i	1.49848	+	0.390956i
$136$	11.0369	+	80.2355i	0.0811535	+	0.589967i
$137$	−113.030	+	65.2577i	−0.825034	+	0.476334i	−0.852149	−	0.523298i	$-0.824701\pi$
$137$	−113.030	+	65.2577i	−0.825034	+	0.476334i	0.0271150	+	0.999632i	$0.491368\pi$
$138$	−10.1000	−	14.3572i	−0.0731887	−	0.104037i
$139$	120.090	+	69.3341i	0.863958	+	0.498806i	0.865336	−	0.501193i	$-0.167105\pi$
$139$	120.090	+	69.3341i	0.863958	+	0.498806i	−0.00137798	+	0.999999i	$0.500439\pi$
$140$	−306.663	−	177.052i	−2.19045	−	1.26466i
$141$	−22.8527	+	49.2900i	−0.162076	+	0.349575i
$142$	17.6886	−	10.2125i	0.124567	−	0.0719190i
$143$	−154.549			−1.08076
$144$	−101.387	+	18.3366i	−0.704076	+	0.127338i
$145$	91.9559			0.634178
$146$	23.0919	+	39.9963i	0.158164	+	0.273947i
$147$	−29.9298	−	333.661i	−0.203604	−	2.26980i
$148$	102.663	+	59.2728i	0.693672	+	0.400492i
$149$	−45.3375	−	26.1756i	−0.304279	−	0.175675i	0.340085	−	0.940395i	$-0.389544\pi$
$149$	−45.3375	−	26.1756i	−0.304279	−	0.175675i	−0.644363	+	0.764719i	$0.722878\pi$
$150$	−65.4093	+	5.86730i	−0.436062	+	0.0391153i
$151$	−30.8174	−	53.3773i	−0.204089	−	0.353492i	0.745753	−	0.666222i	$-0.232090\pi$
$151$	−30.8174	−	53.3773i	−0.204089	−	0.353492i	−0.949842	+	0.312730i	$0.898756\pi$
$152$		−	52.1982i		−	0.343409i
$153$	31.5916	−	149.703i	0.206481	−	0.978451i
$154$	134.009			0.870188
$155$	273.825	−	158.093i	1.76662	−	1.01996i
$156$	−89.8896	−	41.6762i	−0.576215	−	0.267155i
$157$	−30.0503	+	52.0487i	−0.191403	+	0.331520i	−0.945715	−	0.324996i	$-0.894637\pi$
$157$	−30.0503	+	52.0487i	−0.191403	+	0.331520i	0.754312	+	0.656516i	$0.227970\pi$
$158$	24.4592	−	42.3646i	0.154805	−	0.268130i
$159$	−37.1866	−	52.8606i	−0.233878	−	0.332457i
$160$	175.864	−	101.535i	1.09915	−	0.634594i
$161$		−	118.437i		−	0.735636i
$162$	−50.0285	−	8.36908i	−0.308818	−	0.0516610i
$163$			270.408i			1.65895i	0.558546	+	0.829474i	$0.311360\pi$
$163$			270.408i			1.65895i	−0.558546	+	0.829474i	$0.688640\pi$
$164$	−30.4504	−	52.7416i	−0.185673	−	0.321595i
$165$	−320.760	+	225.650i	−1.94400	+	1.36757i
$166$	−31.2727	+	54.1660i	−0.188390	+	0.326301i
$167$	−17.9365	+	31.0669i	−0.107404	+	0.186029i	−0.914718	−	0.404093i	$-0.867587\pi$
$167$	−17.9365	+	31.0669i	−0.107404	+	0.186029i	0.807314	+	0.590122i	$0.200921\pi$
$168$	164.358	+	76.2027i	0.978323	+	0.453587i
$169$	42.6003	+	73.7859i	0.252073	+	0.436603i
$170$	11.2332	+	81.6628i	0.0660776	+	0.480369i
$171$	−33.3186	+	92.8080i	−0.194846	+	0.542737i
$172$	−54.7274			−0.318182
$173$	88.3600	+	153.044i	0.510752	+	0.884648i	0.999922	+	0.0124597i	$0.00396616\pi$
$173$	88.3600	+	153.044i	0.510752	+	0.884648i	−0.489171	+	0.872188i	$0.662701\pi$
$174$	−22.2212	+	1.99327i	−0.127708	+	0.0114556i
$175$	−383.730	−	221.547i	−2.19274	−	1.26598i
$176$	96.6370	−	167.380i	0.549074	−	0.951024i
$177$	−17.3518	+	1.55648i	−0.0980326	+	0.00879365i
$178$	−31.6079	−	54.7465i	−0.177573	−	0.307565i
$179$			3.13712i			0.0175258i	0.999962	+	0.00876292i	$0.00278936\pi$
$179$			3.13712i			0.0175258i	−0.999962	+	0.00876292i	$0.997211\pi$
$180$	−247.412	+	44.7465i	−1.37451	+	0.248591i
$181$			109.859i			0.606953i	0.952839	+	0.303477i	$0.0981475\pi$
$181$			109.859i			0.606953i	−0.952839	+	0.303477i	$0.901853\pi$
$182$	36.3312	+	62.9275i	0.199622	+	0.345755i
$183$	95.6635	−	206.333i	0.522752	−	1.12750i
$184$	38.5518	+	22.2579i	0.209521	+	0.120967i
$185$	220.337	+	127.212i	1.19101	+	0.687630i
$186$	−62.7432	+	44.1388i	−0.337329	+	0.237306i
$187$	176.037	+	226.682i	0.941372	+	1.21220i
$188$		−	65.3382i		−	0.347544i
$189$	−243.587	−	240.399i	−1.28882	−	1.27195i
$190$		−	53.1267i		−	0.279614i
$191$	−76.5270	+	44.1829i	−0.400665	+	0.231324i	−0.686771	−	0.726874i	$-0.740972\pi$
$191$	−76.5270	+	44.1829i	−0.400665	+	0.231324i	0.286106	+	0.958198i	$0.407639\pi$
$192$	72.0617	−	50.6943i	0.375322	−	0.264033i
$193$	−270.243	−	156.025i	−1.40022	−	0.808420i	−0.405809	−	0.913958i	$-0.633010\pi$
$193$	−270.243	−	156.025i	−1.40022	−	0.808420i	−0.994415	+	0.105538i	$0.966344\pi$
$194$	−2.38411	+	4.12940i	−0.0122892	+	0.0212855i
$195$	−192.921	−	89.4456i	−0.989340	−	0.458695i
$196$	201.439	+	348.902i	1.02775	+	1.78011i
$197$	−153.242			−0.777879			−0.388940	−	0.921263i	$-0.627159\pi$
$197$	−153.242			−0.777879			−0.388940	+	0.921263i	$0.627159\pi$
$198$	72.6206	−	61.4813i	0.366771	−	0.310512i
$199$		−	166.292i		−	0.835639i	−0.908530	−	0.417819i	$-0.862795\pi$
$199$		−	166.292i		−	0.835639i	0.908530	−	0.417819i	$-0.137205\pi$
$200$	144.228	−	83.2704i	0.721142	−	0.416352i
$201$	9.08897	+	101.325i	0.0452188	+	0.504104i
$202$	−11.1400	+	19.2950i	−0.0551484	+	0.0955198i
$203$	−130.363	−	75.2650i	−0.642181	−	0.370764i
$204$	41.2597	+	179.315i	0.202253	+	0.878994i
$205$	−65.3527	−	113.194i	−0.318793	−	0.552166i
$206$		−	100.839i		−	0.489508i
$207$	−54.3373	−	64.1823i	−0.262499	−	0.310059i
$208$	104.797			0.503832
$209$	−92.4873	−	160.193i	−0.442523	−	0.766473i
$210$	167.282	+	77.5582i	0.796581	+	0.369325i
$211$	96.5019	+	55.7154i	0.457355	+	0.264054i	0.710931	−	0.703261i	$-0.248274\pi$
$211$	96.5019	+	55.7154i	0.457355	+	0.264054i	−0.253577	+	0.967315i	$0.581607\pi$
$212$	67.3124	+	38.8628i	0.317511	+	0.183315i
$213$	80.0299	−	56.2998i	0.375727	−	0.264318i
$214$	5.06885	−	2.92650i	0.0236862	−	0.0136753i
$215$	−117.456			−0.546307
$216$	124.028	−	34.1102i	0.574203	−	0.157918i
$217$	−517.591			−2.38521
$218$	−44.6305	−	77.3023i	−0.204727	−	0.354598i
$219$	127.302	+	180.959i	0.581286	+	0.826296i
$220$	235.821	−	408.454i	1.07191	−	1.85661i
$221$	−58.7191	+	144.118i	−0.265697	+	0.652119i
$222$	−56.0020	−	25.9646i	−0.252261	−	0.116958i
$223$	−53.0210	−	91.8351i	−0.237762	−	0.411817i	0.722309	−	0.691570i	$-0.243081\pi$
$223$	−53.0210	−	91.8351i	−0.237762	−	0.411817i	−0.960072	+	0.279753i	$0.909747\pi$
$224$	−332.422			−1.48403
$225$	−309.589	+	55.9916i	−1.37595	+	0.248852i
$226$			3.92751i			0.0173784i
$227$	−185.930	−	322.040i	−0.819074	−	1.41868i	−0.906366	−	0.422494i	$-0.861155\pi$
$227$	−185.930	−	322.040i	−0.819074	−	1.41868i	0.0872920	−	0.996183i	$-0.472179\pi$
$228$	−10.5949	−	118.113i	−0.0464688	−	0.518039i
$229$	−134.192	+	232.428i	−0.585993	+	1.01497i	0.408758	+	0.912643i	$0.365962\pi$
$229$	−134.192	+	232.428i	−0.585993	+	1.01497i	−0.994751	+	0.102326i	$0.967371\pi$
$230$	39.2375	+	22.6538i	0.170598	+	0.0984948i
$231$	639.424	−	57.3571i	2.76807	−	0.248299i
$232$	48.9980	−	28.2890i	0.211198	−	0.121935i
$233$	386.512			1.65885			0.829426	−	0.558617i	$-0.188668\pi$
$233$	386.512			1.65885			0.829426	+	0.558617i	$0.188668\pi$
$234$	48.5584	+	17.4327i	0.207515	+	0.0744989i
$235$		−	140.229i		−	0.596720i
$236$	18.1444	−	10.4757i	0.0768829	−	0.0443884i
$237$	98.5747	−	212.611i	0.415927	−	0.897095i
$238$	50.9153	−	124.965i	0.213930	−	0.525063i
$239$	−293.670	−	169.550i	−1.22874	−	0.709416i	−0.261977	−	0.965074i	$-0.584374\pi$
$239$	−293.670	−	169.550i	−1.22874	−	0.709416i	−0.966767	+	0.255658i	$0.917708\pi$
$240$	217.503	−	153.010i	0.906262	−	0.637541i
$241$	−263.515	+	152.141i	−1.09342	+	0.631289i	−0.934486	−	0.356000i	$-0.884140\pi$
$241$	−263.515	+	152.141i	−1.09342	+	0.631289i	−0.158938	+	0.987289i	$0.550807\pi$
$242$			102.718i			0.424455i
$243$	−242.293	−	18.5204i	−0.997091	−	0.0762155i
$244$			273.512i			1.12095i
$245$	432.328	+	748.815i	1.76461	+	3.05639i
$246$	18.2461	+	25.9368i	0.0741713	+	0.105434i
$247$	50.1485	−	86.8598i	0.203030	−	0.351659i
$248$	97.2707	−	168.478i	0.392220	−	0.679346i
$249$	−126.034	+	271.838i	−0.506162	+	1.09172i
$250$	41.8118	−	24.1400i	0.167247	−	0.0965601i
$251$			265.520i			1.05785i	0.848669	+	0.528924i	$0.177404\pi$
$251$			265.520i			1.05785i	−0.848669	+	0.528924i	$0.822596\pi$
$252$	387.373	+	139.069i	1.53719	+	0.551861i
$253$	157.750			0.623519
$254$	8.42073	−	4.86171i	0.0331525	−	0.0191406i
$255$	88.5517	+	384.846i	0.347261	+	1.50920i
$256$	−20.1333	+	34.8720i	−0.0786459	+	0.136219i
$257$	323.082	+	186.532i	1.25713	+	0.725804i	0.972516	−	0.232838i	$-0.0748012\pi$
$257$	323.082	+	186.532i	1.25713	+	0.725804i	0.284614	+	0.958642i	$0.408135\pi$
$258$	28.3833	−	2.54602i	0.110013	−	0.00986829i
$259$	−208.243	−	360.687i	−0.804026	−	1.39261i
$260$	255.734			0.983592
$261$	−105.175	+	19.0218i	−0.402970	+	0.0728803i
$262$			100.256i			0.382658i
$263$	−291.372	+	168.224i	−1.10788	+	0.639634i	−0.938279	−	0.345879i	$-0.887581\pi$
$263$	−291.372	+	168.224i	−1.10788	+	0.639634i	−0.169599	+	0.985513i	$0.554247\pi$
$264$	−101.497	+	218.914i	−0.384457	+	0.829219i
$265$	144.466	+	83.4075i	0.545155	+	0.314745i
$266$	−43.4837	+	75.3161i	−0.163473	+	0.283143i
$267$	−174.249	−	247.695i	−0.652619	−	0.927695i
$268$	−61.1721	−	105.953i	−0.228254	−	0.395348i
$269$	−78.2251			−0.290799			−0.145400	−	0.989373i	$-0.546447\pi$
$269$	−78.2251			−0.290799			−0.145400	+	0.989373i	$0.546447\pi$
$270$	126.234	−	34.7170i	0.467534	−	0.128581i
$271$	174.512			0.643956			0.321978	−	0.946747i	$-0.395652\pi$
$271$	174.512			0.643956			0.321978	+	0.946747i	$0.395652\pi$
$272$	−119.368	−	153.709i	−0.438852	−	0.565108i
$273$	200.288	+	284.708i	0.733655	+	1.04289i
$274$	−40.8656	+	70.7813i	−0.149145	+	0.258326i
$275$	295.085	−	511.102i	1.07304	−	1.85855i
$276$	91.7518	+	42.5396i	0.332434	+	0.154129i
$277$	335.011	−	193.419i	1.20943	−	0.698263i	0.246793	−	0.969068i	$-0.420623\pi$
$277$	335.011	−	193.419i	1.20943	−	0.698263i	0.962634	+	0.270805i	$0.0872898\pi$
$278$	86.8366			0.312362
$279$	−280.487	+	237.463i	−1.00533	+	0.851122i
$280$	−467.596			−1.66999
$281$	−36.0547	+	20.8162i	−0.128309	+	0.0740790i	−0.562780	−	0.826606i	$-0.690268\pi$
$281$	−36.0547	+	20.8162i	−0.128309	+	0.0740790i	0.434472	+	0.900685i	$0.356935\pi$
$282$	3.03966	+	33.8864i	0.0107789	+	0.120165i
$283$	439.568	+	253.785i	1.55324	+	0.896766i	0.997875	+	0.0651627i	$0.0207567\pi$
$283$	439.568	+	253.785i	1.55324	+	0.896766i	0.555370	+	0.831603i	$0.312577\pi$
$284$	−58.8375	+	101.910i	−0.207174	+	0.358836i
$285$	−22.7388	−	253.494i	−0.0797851	−	0.889454i
$286$	−83.8150	+	48.3906i	−0.293060	+	0.169198i
$287$			213.962i			0.745513i
$288$	−180.142	+	152.510i	−0.625494	+	0.529549i
$289$	278.266	−	78.0309i	0.962859	−	0.270003i
$290$	49.8696	−	28.7922i	0.171964	−	0.0992836i
$291$	−9.60835	+	20.7238i	−0.0330184	+	0.0712159i
$292$	−230.432	−	133.040i	−0.789150	−	0.455616i
$293$	169.676	+	97.9624i	0.579098	+	0.334343i	0.760775	−	0.649016i	$-0.224819\pi$
$293$	169.676	+	97.9624i	0.579098	+	0.334343i	−0.181677	+	0.983358i	$0.558152\pi$
$294$	−120.704	−	171.580i	−0.410558	−	0.583606i
$295$	38.9415	−	22.4829i	0.132005	−	0.0762132i
$296$	156.540			0.528851
$297$	320.195	−	324.440i	1.07810	−	1.09239i
$298$	−32.7833			−0.110011
$299$	42.7677	+	74.0759i	0.143036	+	0.247745i
$300$	309.455	−	217.697i	1.03152	−	0.725656i
$301$	166.514	+	96.1367i	0.553201	+	0.319391i
$302$	−33.4258	−	19.2984i	−0.110682	−	0.0639021i
$303$	−44.8960	+	96.8341i	−0.148171	+	0.319585i
$304$	62.7143	+	108.624i	0.206297	+	0.357317i
$305$			587.012i			1.92463i
$306$	−29.7406	−	91.0787i	−0.0971915	−	0.297643i
$307$	−381.679			−1.24325			−0.621626	−	0.783314i	$-0.713528\pi$
$307$	−381.679			−1.24325			−0.621626	+	0.783314i	$0.713528\pi$
$308$	−668.632	+	386.035i	−2.17088	+	1.25336i
$309$	−43.1599	−	481.152i	−0.139676	−	1.55712i
$310$	99.0009	−	171.475i	0.319358	−	0.553144i
$311$	−248.756	+	430.858i	−0.799858	+	1.38540i	0.119849	+	0.992792i	$0.461759\pi$
$311$	−248.756	+	430.858i	−0.799858	+	1.38540i	−0.919708	+	0.392603i	$0.871575\pi$
$312$	−130.314	+	11.6893i	−0.417672	+	0.0374657i
$313$	251.129	−	144.989i	0.802327	−	0.463224i	−0.0419569	−	0.999119i	$-0.513359\pi$
$313$	251.129	−	144.989i	0.802327	−	0.463224i	0.844284	+	0.535895i	$0.180026\pi$
$314$			37.6361i			0.119860i
$315$	831.381	+	298.471i	2.63931	+	0.947526i
$316$			281.835i			0.891883i
$317$	−135.434	−	234.579i	−0.427237	−	0.739997i	0.569389	−	0.822068i	$-0.307180\pi$
$317$	−135.434	−	234.579i	−0.427237	−	0.739997i	−0.996626	+	0.0820714i	$0.973846\pi$
$318$	−36.7183	−	17.0240i	−0.115466	−	0.0535345i
$319$	100.248	−	173.634i	0.314256	−	0.544308i
$320$	−113.704	+	196.942i	−0.355326	+	0.615443i
$321$	22.9335	−	16.1333i	0.0714438	−	0.0502596i
$322$	−37.0839	−	64.2311i	−0.115167	−	0.199476i
$323$	−184.521	+	25.3820i	−0.571273	+	0.0785820i
$324$	273.724	−	102.358i	0.844826	−	0.315920i
$325$	320.002			0.984622
$326$	84.6674	+	146.648i	0.259716	+	0.449841i
$327$	−246.041	−	349.746i	−0.752417	−	1.06956i
$328$	−69.6454	−	40.2098i	−0.212334	−	0.122591i
$329$	−114.776	+	198.798i	−0.348864	+	0.604250i
$330$	−103.302	+	222.808i	−0.313037	+	0.675175i
$331$	−112.717	−	195.231i	−0.340533	−	0.589821i	0.643999	−	0.765027i	$-0.277274\pi$
$331$	−112.717	−	195.231i	−0.340533	−	0.589821i	−0.984532	+	0.175206i	$0.943941\pi$
$332$		−	360.345i		−	1.08538i
$333$	−278.327	−	99.9208i	−0.835815	−	0.300062i
$334$			22.4643i			0.0672584i
$335$	−131.288	−	227.397i	−0.391904	−	0.678797i
$336$	−433.584	+	38.8930i	−1.29043	+	0.115753i
$337$	288.134	+	166.354i	0.854996	+	0.493632i	0.862334	−	0.506341i	$-0.169002\pi$
$337$	288.134	+	166.354i	0.854996	+	0.493632i	−0.00733716	+	0.999973i	$0.502336\pi$
$338$	46.2061	+	26.6771i	0.136704	+	0.0789263i
$339$	1.68101	+	18.7401i	0.00495874	+	0.0552806i
$340$	−291.290	−	375.094i	−0.856736	−	1.10322i
$341$		−	689.395i		−	2.02169i
$342$	10.9897	+	60.7641i	0.0321335	+	0.177673i
$343$		−	794.330i		−	2.31583i
$344$	−62.5856	+	36.1338i	−0.181935	+	0.105040i
$345$	196.918	+	91.2986i	0.570777	+	0.264634i
$346$	95.8391	+	55.3327i	0.276992	+	0.159921i
$347$	30.1175	−	52.1651i	0.0867940	−	0.150332i	−0.819360	−	0.573279i	$-0.805671\pi$
$347$	30.1175	−	52.1651i	0.0867940	−	0.150332i	0.906154	+	0.422947i	$0.139004\pi$
$348$	105.130	−	73.9570i	0.302097	−	0.212520i
$349$	−139.901	−	242.315i	−0.400862	−	0.694313i	0.592969	−	0.805226i	$-0.297956\pi$
$349$	−139.901	−	242.315i	−0.400862	−	0.694313i	−0.993830	+	0.110913i	$0.964623\pi$
$350$	−277.474			−0.792782
$351$	239.158	+	62.3968i	0.681361	+	0.177769i
$352$		−	442.763i		−	1.25785i
$353$	−142.595	+	82.3272i	−0.403951	+	0.233222i	−0.688188	−	0.725533i	$-0.741593\pi$
$353$	−142.595	+	82.3272i	−0.403951	+	0.233222i	0.284236	+	0.958754i	$0.408260\pi$
$354$	−8.92289	+	6.27711i	−0.0252059	+	0.0177320i
$355$	−126.277	+	218.719i	−0.355710	+	0.616109i
$356$	315.413	+	182.104i	0.885990	+	0.511527i
$357$	189.456	−	618.062i	0.530689	−	1.73127i
$358$	0.982263	+	1.70133i	0.00274375	+	0.00475232i
$359$			187.993i			0.523657i	0.965114	+	0.261828i	$0.0843254\pi$
$359$			187.993i			0.523657i	−0.965114	+	0.261828i	$0.915675\pi$
$360$	−253.394	+	214.526i	−0.703873	+	0.595906i
$361$	−240.957			−0.667472
$362$	34.3978	+	59.5787i	0.0950214	+	0.164582i
$363$	43.9643	+	490.119i	0.121114	+	1.35019i
$364$	−362.546	−	209.316i	−0.996005	−	0.575044i
$365$	−494.553	−	285.531i	−1.35494	−	0.782275i
$366$	−12.7243	−	141.852i	−0.0347658	−	0.387573i
$367$	−277.801	+	160.389i	−0.756952	+	0.437026i	−0.828200	−	0.560432i	$-0.810635\pi$
$367$	−277.801	+	160.389i	−0.756952	+	0.437026i	0.0712484	+	0.997459i	$0.477302\pi$
$368$	−106.968			−0.290674
$369$	98.1627	+	115.948i	0.266023	+	0.314222i
$370$	159.324			0.430607
$371$	−136.537	−	236.488i	−0.368023	−	0.637435i
$372$	185.905	−	400.971i	0.499745	−	1.07788i
$373$	−233.696	+	404.773i	−0.626530	+	1.08518i	0.361713	+	0.932289i	$0.382192\pi$
$373$	−233.696	+	404.773i	−0.626530	+	1.08518i	−0.988243	+	0.152892i	$0.951141\pi$
$374$	166.445	+	67.8156i	0.445039	+	0.181325i
$375$	189.173	−	133.080i	0.504460	−	0.354880i
$376$	−43.1397	−	74.7201i	−0.114733	−	0.198724i
$377$	108.713			0.288363
$378$	−207.373	−	54.1042i	−0.548607	−	0.143133i
$379$		−	169.143i		−	0.446287i	−0.974786	−	0.223144i	$-0.928368\pi$
$379$		−	169.143i		−	0.446287i	0.974786	−	0.223144i	$-0.0716319\pi$
$380$	153.040	+	265.073i	0.402737	+	0.697562i
$381$	38.0986	−	26.8018i	0.0999964	−	0.0703459i
$382$	−27.6681	+	47.9226i	−0.0724297	+	0.125452i
$383$	64.7447	+	37.3804i	0.169046	+	0.0975989i	0.582136	−	0.813091i	$-0.302217\pi$
$383$	64.7447	+	37.3804i	0.169046	+	0.0975989i	−0.413090	+	0.910690i	$0.635550\pi$
$384$	155.583	−	335.569i	0.405163	−	0.873878i
$385$	−1435.02	+	828.509i	−3.72732	+	2.15197i
$386$	−195.412			−0.506248
$387$	134.341	−	24.2967i	0.347135	−	0.0627821i
$388$		−	27.4712i		−	0.0708022i
$389$	373.746	−	215.782i	0.960787	−	0.554711i	0.0643719	−	0.997926i	$-0.479496\pi$
$389$	373.746	−	215.782i	0.960787	−	0.554711i	0.896415	+	0.443215i	$0.146162\pi$
$390$	−132.632	+	11.8972i	−0.340081	+	0.0305057i
$391$	59.9355	−	147.104i	0.153288	−	0.376225i
$392$	460.726	+	266.000i	1.17532	+	0.678573i
$393$	42.9107	+	478.373i	0.109188	+	1.21724i
$394$	−83.1065	+	47.9816i	−0.210930	+	0.121781i
$395$			604.875i			1.53133i
$396$	−185.230	+	515.954i	−0.467753	+	1.30291i
$397$			301.697i			0.759942i	0.924998	+	0.379971i	$0.124066\pi$
$397$			301.697i			0.759942i	−0.924998	+	0.379971i	$0.875934\pi$
$398$	−52.0676	−	90.1838i	−0.130823	−	0.226592i
$399$	−175.247	+	377.982i	−0.439215	+	0.947323i
$400$	−200.093	+	346.571i	−0.500232	+	0.866427i
$401$	153.158	−	265.277i	0.381939	−	0.661538i	−0.609400	−	0.792863i	$-0.708590\pi$
$401$	153.158	−	265.277i	0.381939	−	0.661538i	0.991339	+	0.131325i	$0.0419230\pi$
$402$	36.6549	+	52.1048i	0.0911814	+	0.129614i
$403$	323.724	−	186.902i	0.803285	−	0.463777i
$404$		−	128.362i		−	0.317728i
$405$	587.467	−	219.682i	1.45053	−	0.542424i
$406$	−94.2647			−0.232179
$407$	480.410	−	277.365i	1.18037	−	0.681486i
$408$	165.577	+	177.821i	0.405826	+	0.435835i
$409$	−398.853	+	690.833i	−0.975190	+	1.68908i	−0.295883	+	0.955224i	$0.595614\pi$
$409$	−398.853	+	690.833i	−0.975190	+	1.68908i	−0.679307	+	0.733854i	$0.737719\pi$
$410$	−70.8843	−	40.9251i	−0.172889	−	0.0998172i
$411$	−164.695	+	355.224i	−0.400718	+	0.864292i
$412$	290.482	+	503.130i	0.705054	+	1.22119i
$413$	−73.6081			−0.178228
$414$	−49.5644	−	17.7939i	−0.119721	−	0.0429804i
$415$		−	773.373i		−	1.86355i
$416$	207.911	−	120.037i	0.499786	−	0.288552i
$417$	414.341	−	37.1669i	0.993623	−	0.0891292i
$418$	−100.316	−	57.9173i	−0.239990	−	0.138558i
$419$	329.737	−	571.121i	0.786962	−	1.36306i	−0.140858	−	0.990030i	$-0.544986\pi$
$419$	329.737	−	571.121i	0.786962	−	1.36306i	0.927820	−	0.373028i	$-0.121681\pi$
$420$	−1058.06	+	94.9097i	−2.51920	+	0.225976i
$421$	−68.8883	−	119.318i	−0.163630	−	0.283416i	0.772538	−	0.634969i	$-0.218987\pi$
$421$	−68.8883	−	119.318i	−0.163630	−	0.283416i	−0.936168	+	0.351553i	$0.885654\pi$
$422$	69.7800			0.165356
$423$	29.0074	+	160.388i	0.0685755	+	0.379168i
$424$	102.637			0.242068
$425$	−364.494	−	469.358i	−0.857633	−	1.10437i
$426$	25.7739	−	55.5907i	0.0605022	−	0.130495i
$427$	480.464	−	832.188i	1.12521	−	1.94892i
$428$	−16.8605	+	29.2033i	−0.0393938	+	0.0682321i
$429$	−379.212	+	266.770i	−0.883943	+	0.621840i
$430$	−63.6989	+	36.7766i	−0.148137	+	0.0855270i
$431$	306.231			0.710514			0.355257	−	0.934769i	$-0.384393\pi$
$431$	306.231			0.710514			0.355257	+	0.934769i	$0.384393\pi$
$432$	−217.119	+	219.998i	−0.502591	+	0.509255i
$433$	550.337			1.27099			0.635493	−	0.772107i	$-0.280797\pi$
$433$	550.337			1.27099			0.635493	+	0.772107i	$0.280797\pi$
$434$	−280.701	+	162.063i	−0.646776	+	0.373416i
$435$	225.630	−	158.727i	0.518689	−	0.364889i
$436$	445.364	+	257.131i	1.02148	+	0.589749i
$437$	−51.1874	+	88.6592i	−0.117134	+	0.202882i
$438$	125.698	+	58.2785i	0.286982	+	0.133056i
$439$	−593.822	+	342.843i	−1.35267	+	0.780964i	−0.988623	−	0.150416i	$-0.951939\pi$
$439$	−593.822	+	342.843i	−1.35267	+	0.780964i	−0.364047	+	0.931381i	$0.618605\pi$
$440$		−	622.805i		−	1.41547i
$441$	−649.377	−	767.032i	−1.47251	−	1.73930i
$442$	13.2802	+	96.5440i	0.0300457	+	0.218425i
$443$	−398.061	+	229.821i	−0.898557	+	0.518782i	−0.876732	−	0.480979i	$-0.840281\pi$
$443$	−398.061	+	229.821i	−0.898557	+	0.518782i	−0.0218256	+	0.999762i	$0.506948\pi$
$444$	354.215	−	31.7735i	0.797781	−	0.0715619i
$445$	676.940	+	390.831i	1.52121	+	0.878273i
$446$	−57.5089	−	33.2028i	−0.128944	−	0.0744456i
$447$	−156.426	+	14.0316i	−0.349946	+	0.0313906i
$448$	322.390	−	186.132i	0.719621	−	0.415473i
$449$	376.390			0.838284			0.419142	−	0.907921i	$-0.362331\pi$
$449$	376.390			0.838284			0.419142	+	0.907921i	$0.362331\pi$
$450$	−150.365	+	127.301i	−0.334145	+	0.282891i
$451$	−284.983			−0.631891
$452$	−11.3138	−	19.5961i	−0.0250306	−	0.0433543i
$453$	−167.751	−	77.7758i	−0.370312	−	0.171691i
$454$	−201.667	−	116.433i	−0.444201	−	0.256460i
$455$	−778.097	−	449.235i	−1.71010	−	0.987329i
$456$	−90.1004	−	128.077i	−0.197589	−	0.280871i
$457$	218.885	+	379.120i	0.478960	+	0.829583i	0.999709	−	0.0241267i	$-0.00768051\pi$
$457$	218.885	+	379.120i	0.478960	+	0.829583i	−0.520749	+	0.853710i	$0.674347\pi$
$458$			168.068i			0.366960i
$459$	−180.890	−	421.853i	−0.394096	−	0.919069i
$460$	−261.032			−0.567461
$461$	348.000	−	200.918i	0.754880	−	0.435830i	−0.0725746	−	0.997363i	$-0.523122\pi$
$461$	348.000	−	200.918i	0.754880	−	0.435830i	0.827454	+	0.561533i	$0.189788\pi$
$462$	328.814	−	231.316i	0.711719	−	0.500683i
$463$	188.028	−	325.675i	0.406109	−	0.703401i	−0.588341	−	0.808613i	$-0.700219\pi$
$463$	188.028	−	325.675i	0.406109	−	0.703401i	0.994450	+	0.105212i	$0.0335520\pi$
$464$	−67.9765	+	117.739i	−0.146501	+	0.253747i
$465$	398.990	−	860.565i	0.858043	−	1.85068i
$466$	209.614	−	121.021i	0.449815	−	0.259701i
$467$		−	906.421i		−	1.94094i	−0.241215	−	0.970472i	$-0.577546\pi$
$467$		−	906.421i		−	1.94094i	0.241215	−	0.970472i	$-0.422454\pi$
$468$	−292.498	+	52.9005i	−0.624995	+	0.113035i
$469$			429.831i			0.916485i
$470$	−43.9070	−	76.0492i	−0.0934193	−	0.161807i
$471$	16.1086	+	179.581i	0.0342009	+	0.381276i
$472$	13.8331	−	23.9597i	0.0293075	−	0.0507621i
$473$	−128.047	+	221.784i	−0.270713	+	0.468889i
$474$	−13.1115	−	146.168i	−0.0276614	−	0.308372i
$475$	191.501	+	331.689i	0.403159	+	0.698292i
$476$	105.942	+	770.176i	0.222568	+	1.61802i
$477$	−182.488	−	65.5141i	−0.382574	−	0.137346i
$478$	−212.351			−0.444250
$479$	226.867	+	392.945i	0.473626	+	0.820344i	0.999544	−	0.0301908i	$-0.00961149\pi$
$479$	226.867	+	392.945i	0.473626	+	0.820344i	−0.525918	+	0.850535i	$0.676278\pi$
$480$	256.251	−	552.696i	0.533855	−	1.15145i
$481$	260.488	+	150.393i	0.541556	+	0.312667i
$482$	−95.2733	+	165.018i	−0.197662	+	0.342361i
$483$	−204.437	−	290.607i	−0.423265	−	0.601670i
$484$	−295.896	−	512.507i	−0.611356	−	1.05890i
$485$		−	58.9589i		−	0.121565i
$486$	−137.200	+	65.8203i	−0.282304	+	0.135433i
$487$		−	442.969i		−	0.909588i	−0.890597	−	0.454794i	$-0.849713\pi$
$487$		−	442.969i		−	0.909588i	0.890597	−	0.454794i	$-0.150287\pi$
$488$	180.587	+	312.785i	0.370055	+	0.640953i
$489$	466.757	+	663.494i	0.954514	+	1.35684i
$490$	468.922	+	270.732i	0.956983	+	0.552515i
$491$	186.614	+	107.741i	0.380068	+	0.219433i	0.677848	−	0.735202i	$-0.262913\pi$
$491$	186.614	+	107.741i	0.380068	+	0.219433i	−0.297780	+	0.954635i	$0.596246\pi$
$492$	−165.753	−	76.8495i	−0.336897	−	0.156198i
$493$	−123.828	−	159.453i	−0.251172	−	0.323433i
$494$		−	62.8079i		−	0.127142i
$495$	−397.542	+	1107.34i	−0.803115	+	2.23705i
$496$			467.469i			0.942478i
$497$	358.038	−	206.713i	0.720399	−	0.415922i
$498$	16.7639	+	186.886i	0.0336625	+	0.375273i
$499$	438.298	+	253.051i	0.878352	+	0.507117i	0.870115	−	0.492849i	$-0.164045\pi$
$499$	438.298	+	253.051i	0.878352	+	0.507117i	0.00823740	+	0.999966i	$0.497378\pi$
$500$	−139.079	+	240.891i	−0.278157	+	0.481782i
$501$	9.61495	+	107.188i	0.0191915	+	0.213949i
$502$	83.1367	+	143.997i	0.165611	+	0.286847i
$503$	−607.803			−1.20836			−0.604178	−	0.796849i	$-0.706499\pi$
$503$	−607.803			−1.20836			−0.604178	+	0.796849i	$0.706499\pi$
$504$	534.816	−	96.7257i	1.06114	−	0.191916i
$505$		−	275.491i		−	0.545527i
$506$	85.5514	−	49.3931i	0.169074	−	0.0976149i
$507$	231.890	+	107.513i	0.457377	+	0.212057i
$508$	−28.0099	+	48.5145i	−0.0551376	+	0.0955011i
$509$	−441.976	−	255.175i	−0.868321	−	0.501326i	−0.00153126	−	0.999999i	$-0.500487\pi$
$509$	−441.976	−	255.175i	−0.868321	−	0.501326i	−0.866790	+	0.498673i	$0.833821\pi$
$510$	168.522	+	180.984i	0.330436	+	0.354870i
$511$	467.408	+	809.575i	0.914693	+	1.58429i
$512$			518.392i			1.01248i
$513$	78.4448	+	285.232i	0.152914	+	0.556008i
$514$	233.619			0.454512
$515$	623.434	+	1079.82i	1.21055	+	2.09674i
$516$	−134.283	+	94.4660i	−0.260238	+	0.183074i
$517$	−264.785	−	152.874i	−0.512157	−	0.295694i
$518$	−225.869	−	130.406i	−0.436041	−	0.251748i
$519$	480.979	+	223.000i	0.926742	+	0.429672i
$520$	292.455	−	168.849i	0.562413	−	0.324709i
$521$	−878.914			−1.68698			−0.843488	−	0.537149i	$-0.819501\pi$
$521$	−878.914			−1.68698			−0.843488	+	0.537149i	$0.819501\pi$
$522$	−51.0829	+	43.2473i	−0.0978599	+	0.0828491i
$523$	953.748			1.82361			0.911805	−	0.410624i	$-0.134689\pi$
$523$	953.748			1.82361			0.911805	+	0.410624i	$0.134689\pi$
$524$	−288.805	−	500.225i	−0.551154	−	0.954627i
$525$	−1323.97	+	118.761i	−2.52184	+	0.226212i
$526$	−105.345	+	182.463i	−0.200275	+	0.346887i
$527$	−642.869	−	261.928i	−1.21987	−	0.497018i
$528$	−51.8028	−	577.503i	−0.0981114	−	1.09376i
$529$	220.846	+	382.517i	0.417479	+	0.723094i
$530$	104.463			0.197099
$531$	−39.8889	+	33.7703i	−0.0751203	+	0.0635976i
$532$		−	501.048i		−	0.941819i
$533$	−77.2617	−	133.821i	−0.144956	−	0.251072i
$534$	−172.055	−	79.7710i	−0.322200	−	0.149384i
$535$	−36.1862	+	62.6763i	−0.0676377	+	0.117152i
$536$	−139.912	−	80.7780i	−0.261029	−	0.150705i
$537$	5.41505	+	7.69748i	0.0100839	+	0.0143342i
$538$	−42.4231	+	24.4930i	−0.0788534	+	0.0455260i
$539$	1885.25			3.49768
$540$	−529.831	+	536.857i	−0.981169	+	0.994179i
$541$		−	755.200i		−	1.39593i	−0.716131	−	0.697966i	$-0.754089\pi$
$541$		−	755.200i		−	1.39593i	0.716131	−	0.697966i	$-0.245911\pi$
$542$	94.6416	−	54.6414i	0.174616	−	0.100814i
$543$	189.629	+	269.557i	0.349225	+	0.496422i
$544$	−412.881	−	168.223i	−0.758973	−	0.309233i
$545$	955.841	+	551.855i	1.75384	+	1.01258i
$546$	197.765	+	91.6914i	0.362208	+	0.167933i
$547$	207.072	−	119.553i	0.378559	−	0.218561i	−0.298632	−	0.954368i	$-0.596530\pi$
$547$	207.072	−	119.553i	0.378559	−	0.218561i	0.677191	+	0.735807i	$0.263197\pi$
$548$		−	470.880i		−	0.859271i
$549$	−121.428	−	671.399i	−0.221180	−	1.22295i
$550$		−	369.575i		−	0.671955i
$551$	65.0575	+	112.683i	0.118072	+	0.204506i
$552$	133.013	−	11.9315i	0.240966	−	0.0216150i
$553$	495.085	−	857.512i	0.895271	−	1.55065i
$554$	121.123	−	209.790i	0.218633	−	0.378683i
$555$	760.217	−	68.1924i	1.36976	−	0.122869i
$556$	−433.267	+	250.147i	−0.779257	+	0.449904i
$557$			101.467i			0.182167i	0.995843	+	0.0910835i	$0.0290330\pi$
$557$			101.467i			0.182167i	−0.995843	+	0.0910835i	$0.970967\pi$
$558$	−77.7623	+	216.605i	−0.139359	+	0.388180i
$559$	−138.860			−0.248407
$560$	973.066	−	561.800i	1.73762	−	1.00321i
$561$	823.216	+	252.342i	1.46741	+	0.449808i
$562$	−13.0355	+	22.5781i	−0.0231948	+	0.0401746i
$563$	−781.603	−	451.259i	−1.38828	−	0.801525i	−0.395161	−	0.918612i	$-0.629311\pi$
$563$	−781.603	−	451.259i	−1.38828	−	0.801525i	−0.993122	+	0.117087i	$0.962645\pi$
$564$	−112.782	−	160.319i	−0.199967	−	0.284253i
$565$	−24.2818	−	42.0573i	−0.0429766	−	0.0744377i
$566$	317.850			0.561572
$567$	−1012.64	−	169.401i	−1.78596	−	0.298766i
$568$			155.390i			0.273574i
$569$	337.392	−	194.793i	0.592956	−	0.342344i	−0.173309	−	0.984867i	$-0.555446\pi$
$569$	337.392	−	194.793i	0.592956	−	0.342344i	0.766266	+	0.642524i	$0.222113\pi$
$570$	−91.7032	−	130.356i	−0.160883	−	0.228694i
$571$	−115.995	−	66.9697i	−0.203144	−	0.117285i	0.394977	−	0.918691i	$-0.370752\pi$
$571$	−115.995	−	66.9697i	−0.203144	−	0.117285i	−0.598121	+	0.801406i	$0.704086\pi$
$572$	278.794	−	482.886i	0.487402	−	0.844206i
$573$	−111.507	+	240.505i	−0.194602	+	0.419730i
$574$	66.9936	+	116.036i	0.116714	+	0.202154i
$575$	−326.631			−0.568055
$576$	89.3114	−	248.774i	0.155055	−	0.431900i
$577$	−595.553			−1.03215			−0.516077	−	0.856542i	$-0.672608\pi$
$577$	−595.553			−1.03215			−0.516077	+	0.856542i	$0.672608\pi$
$578$	126.478	−	129.446i	0.218819	−	0.223954i
$579$	−932.407	+	83.6381i	−1.61037	+	0.144453i
$580$	−165.881	+	287.315i	−0.286003	+	0.495371i
$581$	−632.999	+	1096.39i	−1.08950	+	1.88707i
$582$	1.27801	+	14.2474i	0.00219590	+	0.0244801i
$583$	314.986	−	181.857i	0.540284	−	0.311933i
$584$	−351.359			−0.601642
$585$	−627.760	+	113.535i	−1.07309	+	0.194077i
$586$	122.692			0.209372
$587$	−645.818	+	372.863i	−1.10020	+	0.635202i	−0.936274	−	0.351271i	$-0.885750\pi$
$587$	−645.818	+	372.863i	−1.10020	+	0.635202i	−0.163927	+	0.986472i	$0.552416\pi$
$588$	1096.51	+	508.384i	1.86481	+	0.864598i
$589$	387.456	+	223.698i	0.657820	+	0.379792i
$590$	14.0792	−	24.3859i	0.0238631	−	0.0413320i
$591$	−376.006	+	264.515i	−0.636220	+	0.447571i
$592$	−325.759	+	188.077i	−0.550269	+	0.317698i
$593$		−	480.309i		−	0.809965i	−0.914324	−	0.404983i	$-0.867278\pi$
$593$		−	480.309i		−	0.809965i	0.914324	−	0.404983i	$-0.132722\pi$
$594$	72.0631	−	276.207i	0.121318	−	0.464995i
$595$	227.374	+	1652.96i	0.382141	+	2.77808i
$596$	163.571	−	94.4377i	0.274448	−	0.158453i
$597$	−287.040	−	408.026i	−0.480804	−	0.683461i
$598$	46.3877	+	26.7820i	0.0775714	+	0.0447859i
$599$	658.300	+	380.070i	1.09900	+	0.634507i	0.935958	−	0.352112i	$-0.114536\pi$
$599$	658.300	+	380.070i	1.09900	+	0.634507i	0.163041	+	0.986619i	$0.447870\pi$
$600$	210.155	−	453.274i	0.350258	−	0.755456i
$601$	56.5025	−	32.6217i	0.0940141	−	0.0542790i	−0.452256	−	0.891888i	$-0.649381\pi$
$601$	56.5025	−	32.6217i	0.0940141	−	0.0542790i	0.546270	+	0.837609i	$0.316047\pi$
$602$	120.405			0.200009
$603$	197.200	+	232.929i	0.327032	+	0.386284i
$604$	222.369			0.368161
$605$	−635.054	−	1099.94i	−1.04968	−	1.81809i
$606$	5.97165	+	66.5726i	0.00985420	+	0.109856i
$607$	−235.188	−	135.786i	−0.387460	−	0.223700i	0.293599	−	0.955929i	$-0.405147\pi$
$607$	−235.188	−	135.786i	−0.387460	−	0.223700i	−0.681059	+	0.732229i	$0.738480\pi$
$608$	248.843	+	143.669i	0.409281	+	0.236298i
$609$	−449.784	+	40.3462i	−0.738562	+	0.0662499i
$610$	183.799	+	318.349i	0.301310	+	0.521884i
$611$		−	165.783i		−	0.271330i
$612$	410.756	+	368.760i	0.671171	+	0.602550i
$613$	348.795			0.568997			0.284499	−	0.958676i	$-0.408173\pi$
$613$	348.795			0.568997			0.284499	+	0.958676i	$0.408173\pi$
$614$	−206.992	+	119.507i	−0.337121	+	0.194637i
$615$	−355.741	−	164.935i	−0.578440	−	0.268187i
$616$	−509.760	+	882.930i	−0.827533	+	1.43333i
$617$	528.808	−	915.922i	0.857063	−	1.48448i	−0.0176549	−	0.999844i	$-0.505620\pi$
$617$	528.808	−	915.922i	0.857063	−	1.48448i	0.874718	−	0.484632i	$-0.161047\pi$
$618$	−174.060	−	247.425i	−0.281650	−	0.400364i
$619$	−331.287	+	191.269i	−0.535197	+	0.308996i	−0.743130	−	0.669147i	$-0.766660\pi$
$619$	−331.287	+	191.269i	−0.535197	+	0.308996i	0.207933	+	0.978143i	$0.433326\pi$
$620$			1140.75i			1.83992i
$621$	−244.112	−	63.6895i	−0.393095	−	0.102560i
$622$			311.551i			0.500886i
$623$	−639.784	−	1108.14i	−1.02694	−	1.77871i
$624$	257.138	−	180.892i	0.412080	−	0.289892i
$625$	138.470	−	239.837i	0.221552	−	0.383739i
$626$	90.7949	−	157.261i	0.145040	−	0.251216i
$627$	−503.446	−	233.416i	−0.802944	−	0.372275i
$628$	−108.417	−	187.784i	−0.172639	−	0.299019i
$629$	−76.1193	−	553.370i	−0.121016	−	0.879761i
$630$	544.330	−	98.4463i	0.864016	−	0.156264i
$631$	423.245			0.670753			0.335376	−	0.942084i	$-0.391137\pi$
$631$	423.245			0.670753			0.335376	+	0.942084i	$0.391137\pi$
$632$	186.082	+	322.304i	0.294434	+	0.509974i
$633$	332.955	−	29.8665i	0.525996	−	0.0471825i
$634$	−146.898	−	84.8115i	−0.231700	−	0.133772i
$635$	−60.1149	+	104.122i	−0.0946691	+	0.163972i
$636$	232.244	−	20.8326i	0.365164	−	0.0327557i
$637$	511.111	+	885.269i	0.802371	+	1.38975i
$638$		−	125.554i		−	0.196793i
$639$	99.1870	−	276.282i	0.155222	−	0.432367i
$640$			954.688i			1.49170i
$641$	493.641	+	855.012i	0.770111	+	1.33387i	0.937502	+	0.347981i	$0.113133\pi$
$641$	493.641	+	855.012i	0.770111	+	1.33387i	−0.167391	+	0.985891i	$0.553534\pi$
$642$	7.38581	−	15.9301i	0.0115044	−	0.0248133i
$643$	−238.189	−	137.519i	−0.370435	−	0.213871i	0.303214	−	0.952923i	$-0.401940\pi$
$643$	−238.189	−	137.519i	−0.370435	−	0.213871i	−0.673648	+	0.739052i	$0.735274\pi$
$644$	370.056	+	213.652i	0.574622	+	0.331758i
$645$	−288.199	+	202.743i	−0.446820	+	0.314331i
$646$	−92.1224	+	71.5405i	−0.142604	+	0.110744i
$647$		−	110.251i		−	0.170403i	−0.996364	−	0.0852016i	$-0.972847\pi$
$647$		−	110.251i		−	0.170403i	0.996364	−	0.0852016i	$-0.0271534\pi$
$648$	245.445	−	297.782i	0.378774	−	0.459540i
$649$		−	98.0409i		−	0.151065i
$650$	173.544	−	100.196i	0.266991	−	0.154147i
$651$	−1270.00	+	893.425i	−1.95084	+	1.37239i
$652$	−844.888	−	487.797i	−1.29584	−	0.748154i
$653$	239.347	−	414.561i	0.366534	−	0.634856i	−0.622487	−	0.782630i	$-0.713878\pi$
$653$	239.347	−	414.561i	0.366534	−	0.634856i	0.989021	+	0.147774i	$0.0472109\pi$
$654$	−242.942	−	112.637i	−0.371470	−	0.172228i
$655$	−619.834	−	1073.58i	−0.946311	−	1.63906i
$656$	193.243			0.294577
$657$	624.713	+	224.276i	0.950857	+	0.341363i
$658$			143.750i			0.218465i
$659$	−326.952	+	188.766i	−0.496133	+	0.286443i	−0.727115	−	0.686515i	$-0.759139\pi$
$659$	−326.952	+	188.766i	−0.496133	+	0.286443i	0.230982	+	0.972958i	$0.425806\pi$
$660$	−126.413	−	1409.27i	−0.191535	−	2.13525i
$661$	−342.084	+	592.506i	−0.517524	+	0.896378i	0.482268	+	0.876023i	$0.339813\pi$
$661$	−342.084	+	592.506i	−0.517524	+	0.896378i	−0.999793	+	0.0203550i	$0.993520\pi$
$662$	−122.257	−	70.5852i	−0.184679	−	0.106624i
$663$	104.688	+	454.976i	0.157901	+	0.686238i
$664$	−237.918	−	412.087i	−0.358311	−	0.620612i
$665$		−	1075.35i		−	1.61707i
$666$	−182.229	+	32.9575i	−0.273616	+	0.0494857i
$667$	−110.965			−0.166364
$668$	−64.7121	−	112.085i	−0.0968744	−	0.167791i
$669$	−288.615	−	133.813i	−0.431412	−	0.200019i
$670$	−142.400	−	82.2149i	−0.212538	−	0.122709i
$671$	1108.42	+	639.944i	1.65189	+	0.953717i
$672$	−815.654	+	573.800i	−1.21377	+	0.853869i
$673$	−448.160	+	258.746i	−0.665914	+	0.384466i	−0.794527	−	0.607229i	$-0.792281\pi$
$673$	−448.160	+	258.746i	−0.665914	+	0.384466i	0.128612	+	0.991695i	$0.458948\pi$
$674$	208.348			0.309122
$675$	−662.982	+	671.773i	−0.982196	+	0.995220i
$676$	−307.391			−0.454720
$677$	246.745	+	427.374i	0.364468	+	0.631276i	0.988691	−	0.149970i	$-0.0479177\pi$
$677$	246.745	+	427.374i	0.364468	+	0.631276i	−0.624223	+	0.781246i	$0.714584\pi$
$678$	6.77936	+	9.63683i	0.00999906	+	0.0142136i
$679$	−48.2573	+	83.5841i	−0.0710711	+	0.123099i
$680$	−580.773	−	236.628i	−0.854078	−	0.347982i
$681$	−1012.09	−	469.243i	−1.48618	−	0.689050i
$682$	−215.856	−	373.874i	−0.316505	−	0.548202i
$683$	−157.726			−0.230931			−0.115465	−	0.993312i	$-0.536836\pi$
$683$	−157.726			−0.230931			−0.115465	+	0.993312i	$0.536836\pi$
$684$	−229.873	−	271.522i	−0.336072	−	0.396962i
$685$		−	1010.61i		−	1.47534i
$686$	−248.712	−	430.782i	−0.362554	−	0.627962i
$687$	71.9345	+	801.934i	0.104708	+	1.16730i
$688$	86.8270	−	150.389i	0.126202	−	0.218588i
$689$	170.792	+	98.6067i	0.247884	+	0.143116i
$690$	135.379	−	12.1437i	0.196202	−	0.0175996i
$691$	−721.851	+	416.761i	−1.04465	+	0.603127i	−0.921146	−	0.389217i	$-0.872745\pi$
$691$	−721.851	+	416.761i	−1.04465	+	0.603127i	−0.123501	+	0.992344i	$0.539412\pi$
$692$	−637.579			−0.921358
$693$	1469.93	−	1244.46i	2.12111	−	1.79575i
$694$		−	37.7203i		−	0.0543520i
$695$	−929.879	+	536.866i	−1.33796	+	0.772469i
$696$	71.3949	−	153.989i	0.102579	−	0.221248i
$697$	−108.276	+	265.750i	−0.155346	+	0.381276i
$698$	−151.742	−	87.6084i	−0.217396	−	0.125514i
$699$	948.375	−	667.167i	1.35676	−	0.954459i
$700$	1384.44	−	799.308i	1.97777	−	1.14187i
$701$		−	703.002i		−	1.00286i	−0.865199	−	0.501428i	$-0.832808\pi$
$701$		−	703.002i		−	1.00286i	0.865199	−	0.501428i	$-0.167192\pi$
$702$	149.237	−	41.0434i	0.212589	−	0.0584664i
$703$			360.002i			0.512094i
$704$	247.915	+	429.401i	0.352152	+	0.609945i
$705$	−242.052	−	344.076i	−0.343337	−	0.488051i
$706$	−51.5548	+	89.2956i	−0.0730238	+	0.126481i
$707$	−225.487	+	390.555i	−0.318935	+	0.552411i
$708$	26.4381	−	57.0232i	0.0373419	−	0.0805412i
$709$	753.932	−	435.283i	1.06337	−	0.613939i	0.137010	−	0.990570i	$-0.456251\pi$
$709$	753.932	−	435.283i	1.06337	−	0.613939i	0.926363	+	0.376631i	$0.122918\pi$
$710$			158.154i			0.222753i
$711$	−125.123	−	691.831i	−0.175982	−	0.973039i
$712$	480.937			0.675473
$713$	−330.430	+	190.774i	−0.463437	+	0.267565i
$714$	−90.7751	−	394.509i	−0.127136	−	0.552533i
$715$	598.349	−	1036.37i	0.836852	−	1.44947i
$716$	−9.80191	−	5.65914i	−0.0136898	−	0.00790382i
$717$	−1013.23	+	90.8884i	−1.41316	+	0.126762i
$718$	58.8623	+	101.952i	0.0819809	+	0.141995i
$719$	−404.861			−0.563089			−0.281545	−	0.959548i	$-0.590847\pi$
$719$	−404.861			−0.563089			−0.281545	+	0.959548i	$0.590847\pi$
$720$	269.567	−	750.872i	0.374399	−	1.04288i
$721$		−	2041.10i		−	2.83093i
$722$	−130.676	+	75.4460i	−0.180992	+	0.104496i
$723$	−383.967	+	828.162i	−0.531075	+	1.14545i
$724$	−343.252	−	198.177i	−0.474105	−	0.273725i
$725$	−207.569	+	359.520i	−0.286302	+	0.495890i
$726$	177.304	+	252.037i	0.244220	+	0.347158i
$727$	−116.655	−	202.052i	−0.160461	−	0.277926i	0.774573	−	0.632484i	$-0.217965\pi$
$727$	−116.655	−	202.052i	−0.160461	−	0.277926i	−0.935034	+	0.354558i	$0.884631\pi$
$728$	−552.805			−0.759347
$729$	−626.477	+	372.784i	−0.859364	+	0.511364i
$730$	−357.609			−0.489876
$731$	158.166	+	203.670i	0.216370	+	0.278619i
$732$	472.114	+	671.108i	0.644965	+	0.916814i
$733$	−41.4135	+	71.7302i	−0.0564986	+	0.0978584i	−0.892891	−	0.450272i	$-0.851327\pi$
$733$	−41.4135	+	71.7302i	−0.0564986	+	0.0978584i	0.836393	+	0.548131i	$0.184660\pi$
$734$	−100.438	+	173.964i	−0.136837	+	0.237009i
$735$	2353.34	+	1091.10i	3.20182	+	1.48448i
$736$	−212.218	+	122.524i	−0.288340	+	0.166473i
$737$	−572.505			−0.776805
$738$	89.5401	+	32.1454i	0.121328	+	0.0435575i
$739$	256.558			0.347169			0.173585	−	0.984819i	$-0.444465\pi$
$739$	256.558			0.347169			0.173585	+	0.984819i	$0.444465\pi$
$740$	−794.942	+	458.960i	−1.07425	+	0.620216i
$741$	−26.8824	−	299.688i	−0.0362785	−	0.404437i
$742$	−148.093	−	85.5018i	−0.199587	−	0.115231i
$743$	−211.289	+	365.963i	−0.284373	+	0.492548i	−0.972457	−	0.233083i	$-0.925119\pi$
$743$	−211.289	+	365.963i	−0.284373	+	0.492548i	0.688084	+	0.725631i	$0.258452\pi$
$744$	−52.1425	−	581.290i	−0.0700840	−	0.781304i
$745$	351.057	−	202.683i	0.471217	−	0.272057i
$746$			292.689i			0.392345i
$747$	159.978	+	884.552i	0.214161	+	1.18414i
$748$	−1025.82	+	141.108i	−1.37142	+	0.188647i
$749$	102.600	−	59.2361i	0.136982	−	0.0790869i
$750$	60.9238	−	131.404i	0.0812317	−	0.175205i
$751$	−555.896	−	320.946i	−0.740207	−	0.427359i	0.0819375	−	0.996637i	$-0.473889\pi$
$751$	−555.896	−	320.946i	−0.740207	−	0.427359i	−0.822145	+	0.569279i	$0.807223\pi$
$752$	179.547	+	103.662i	0.238759	+	0.137848i
$753$	458.319	+	651.499i	0.608657	+	0.865204i
$754$	58.9573	−	34.0390i	0.0781926	−	0.0451445i
$755$	477.249			0.632118
$756$	1190.54	−	327.422i	1.57478	−	0.433098i
$757$	750.494			0.991406			0.495703	−	0.868492i	$-0.334910\pi$
$757$	750.494			0.991406			0.495703	+	0.868492i	$0.334910\pi$
$758$	−52.9602	−	91.7298i	−0.0698684	−	0.121016i
$759$	387.068	−	272.296i	0.509971	−	0.358756i
$760$	350.030	+	202.090i	0.460566	+	0.265908i
$761$	768.666	+	443.789i	1.01007	+	0.583166i	0.911213	−	0.411935i	$-0.135147\pi$
$761$	768.666	+	443.789i	1.01007	+	0.583166i	0.0988601	+	0.995101i	$0.468480\pi$
$762$	12.2698	−	26.4642i	0.0161021	−	0.0347300i
$763$	−903.376	−	1564.69i	−1.18398	−	2.05071i
$764$		−	318.810i		−	0.417291i
$765$	881.567	+	791.435i	1.15238	+	1.03456i
$766$	46.8166			0.0611183
$767$	46.0377	−	26.5799i	0.0600231	−	0.0346544i
$768$	10.7926	+	120.317i	0.0140528	+	0.156663i
$769$	−281.200	+	487.053i	−0.365670	+	0.633358i	−0.988883	−	0.148693i	$-0.952493\pi$
$769$	−281.200	+	487.053i	−0.365670	+	0.633358i	0.623214	+	0.782052i	$0.285827\pi$
$770$	−518.828	+	898.636i	−0.673802	+	1.16706i
$771$	1114.71	−	99.9913i	1.44580	−	0.129690i
$772$	974.997	−	562.915i	1.26295	−	0.729164i
$773$			1383.76i			1.79011i	0.445951	+	0.895057i	$0.352866\pi$
$773$			1383.76i			1.79011i	−0.445951	+	0.895057i	$0.647134\pi$
$774$	65.2486	−	55.2401i	0.0843005	−	0.0713696i
$775$			1427.43i			1.84185i
$776$	−18.1379	−	31.4158i	−0.0233736	−	0.0404843i
$777$	−1133.55	−	525.556i	−1.45888	−	0.676391i
$778$	135.127	−	234.047i	0.173685	−	0.300831i
$779$	92.4723	−	160.167i	0.118706	−	0.205605i
$780$	627.487	−	441.428i	0.804471	−	0.565933i
$781$	275.328	+	476.882i	0.352532	+	0.610604i
$782$	−13.5553	−	98.5440i	−0.0173342	−	0.126015i
$783$	−225.232	+	228.218i	−0.287652	+	0.291466i
$784$	−1278.36			−1.63056
$785$	−232.685	−	403.022i	−0.296414	−	0.513404i
$786$	173.055	+	245.996i	0.220171	+	0.312972i
$787$	553.909	+	319.799i	0.703823	+	0.406353i	0.808770	−	0.588125i	$-0.200134\pi$
$787$	553.909	+	319.799i	0.703823	+	0.406353i	−0.104947	+	0.994478i	$0.533467\pi$
$788$	276.438	−	478.804i	0.350809	−	0.607619i
$789$	−424.557	+	915.709i	−0.538095	+	1.16059i
$790$	189.392	+	328.037i	0.239737	+	0.415236i
$791$			79.4977i			0.100503i
$792$	128.832	+	712.338i	0.162667	+	0.899417i
$793$			693.982i			0.875135i
$794$	94.4641	+	163.617i	0.118972	+	0.206066i
$795$	498.444	−	44.7111i	0.626973	−	0.0562403i
$796$	519.578	+	299.978i	0.652736	+	0.376857i
$797$	−398.507	−	230.078i	−0.500009	−	0.288680i	0.228708	−	0.973495i	$-0.426550\pi$
$797$	−398.507	−	230.078i	−0.500009	−	0.288680i	−0.728717	+	0.684815i	$0.759883\pi$
$798$	23.3097	+	259.859i	0.0292101	+	0.325638i
$799$	−243.159	+	188.833i	−0.304329	+	0.236336i
$800$			916.767i			1.14596i
$801$	−855.101	−	306.986i	−1.06754	−	0.383254i
$802$		−	191.820i		−	0.239178i
$803$	−1078.30	+	622.555i	−1.34284	+	0.775286i
$804$	−332.984	−	154.384i	−0.414160	−	0.192020i
$805$	794.216	+	458.541i	0.986604	+	0.569616i
$806$	117.042	−	202.722i	0.145213	−	0.251516i
$807$	−191.939	+	135.026i	−0.237842	+	0.167318i
$808$	−84.7513	−	146.794i	−0.104890	−	0.181675i
$809$	−258.934			−0.320066			−0.160033	−	0.987112i	$-0.551160\pi$
$809$	−258.934			−0.320066			−0.160033	+	0.987112i	$0.551160\pi$
$810$	249.811	−	303.079i	0.308409	−	0.374172i
$811$		−	506.320i		−	0.624315i	−0.950030	−	0.312158i	$-0.898948\pi$
$811$		−	506.320i		−	0.624315i	0.950030	−	0.312158i	$-0.101052\pi$
$812$	470.329	−	271.545i	0.579224	−	0.334415i
$813$	428.196	−	301.229i	0.526686	−	0.370515i
$814$	173.691	−	300.842i	0.213380	−	0.369585i
$815$	−1813.30	−	1046.91i	−2.22491	−	1.28455i
$816$	−558.210	−	171.110i	−0.684081	−	0.209693i
$817$	−83.0986	−	143.931i	−0.101712	−	0.176170i
$818$			499.538i			0.610682i
$819$	982.882	+	352.860i	1.20010	+	0.430843i
$820$	471.565			0.575079
$821$	493.929	+	855.510i	0.601619	+	1.04203i	0.992576	+	0.121625i	$0.0388106\pi$
$821$	493.929	+	855.510i	0.601619	+	1.04203i	−0.390958	+	0.920409i	$0.627856\pi$
$822$	21.9062	+	244.213i	0.0266499	+	0.297096i
$823$	209.432	+	120.916i	0.254474	+	0.146921i	0.621811	−	0.783167i	$-0.286397\pi$
$823$	209.432	+	120.916i	0.254474	+	0.146921i	−0.367337	+	0.930088i	$0.619730\pi$
$824$	664.385	+	383.583i	0.806292	+	0.465513i
$825$	−158.182	−	1763.43i	−0.191736	−	2.13749i
$826$	−39.9193	+	23.0474i	−0.0483284	+	0.0279024i
$827$	640.794			0.774841			0.387421	−	0.921903i	$-0.373366\pi$
$827$	640.794			0.774841			0.387421	+	0.921903i	$0.373366\pi$
$828$	298.557	−	53.9964i	0.360576	−	0.0652131i
$829$	−1193.22			−1.43934			−0.719671	−	0.694315i	$-0.755708\pi$
$829$	−1193.22			−1.43934			−0.719671	+	0.694315i	$0.755708\pi$
$830$	−242.150	−	419.417i	−0.291748	−	0.505322i
$831$	488.144	−	1052.86i	0.587417	−	1.26698i
$832$	−134.425	+	232.830i	−0.161568	+	0.279844i
$833$	716.280	−	1758.02i	0.859880	−	2.11046i
$834$	213.069	−	149.890i	0.255478	−	0.179725i
$835$	−138.885	−	240.557i	−0.166330	−	0.288092i
$836$	667.361			0.798279
$837$	−278.334	+	1066.81i	−0.332537	+	1.27457i
$838$		−	412.975i		−	0.492810i
$839$	692.652	+	1199.71i	0.825569	+	1.42993i	0.901484	+	0.432813i	$0.142479\pi$
$839$	692.652	+	1199.71i	0.825569	+	1.42993i	−0.0759153	+	0.997114i	$0.524188\pi$
$840$	−1147.33	+	807.127i	−1.36587	+	0.960865i
$841$	349.984	−	606.189i	0.416152	−	0.720796i
$842$	−74.7192	−	43.1392i	−0.0887402	−	0.0512342i
$843$	−52.5352	+	113.311i	−0.0623193	+	0.134414i
$844$	−348.164	+	201.013i	−0.412517	+	0.238167i
$845$	−659.723			−0.780738
$846$	65.9504	+	77.8994i	0.0779555	+	0.0920797i
$847$			2079.14i			2.45471i
$848$	−213.587	+	123.315i	−0.251872	+	0.145418i
$849$	1516.62	−	136.043i	1.78636	−	0.160239i
$850$	−344.633	−	140.416i	−0.405451	−	0.165196i
$851$	−265.885	−	153.509i	−0.312438	−	0.180386i
$852$	31.5401	+	351.613i	0.0370190	+	0.412691i
$853$	−65.7506	+	37.9611i	−0.0770816	+	0.0445031i	−0.538045	−	0.842916i	$-0.680837\pi$
$853$	−65.7506	+	37.9611i	−0.0770816	+	0.0445031i	0.460964	+	0.887419i	$0.347504\pi$
$854$		−	601.751i		−	0.704626i
$855$	−493.355	−	582.742i	−0.577023	−	0.681570i
$856$			44.5288i			0.0520196i
$857$	147.012	+	254.633i	0.171543	+	0.297121i	0.938959	−	0.344028i	$-0.111791\pi$
$857$	147.012	+	254.633i	0.171543	+	0.297121i	−0.767417	+	0.641149i	$0.778458\pi$
$858$	−122.127	+	263.410i	−0.142339	+	0.307004i
$859$	33.7179	−	58.4010i	0.0392525	−	0.0679872i	−0.845732	−	0.533608i	$-0.820836\pi$
$859$	33.7179	−	58.4010i	0.0392525	−	0.0679872i	0.884984	+	0.465621i	$0.154169\pi$
$860$	211.882	−	366.990i	0.246374	−	0.426733i
$861$	369.324	+	524.993i	0.428948	+	0.609748i
$862$	166.076	−	95.8840i	0.192663	−	0.111234i
$863$			885.719i			1.02633i	0.858291	+	0.513163i	$0.171526\pi$
$863$			885.719i			1.02633i	−0.858291	+	0.513163i	$0.828474\pi$
$864$	−178.759	+	685.157i	−0.206897	+	0.793006i
$865$	−1368.38			−1.58194
$866$	298.460	−	172.316i	0.344642	−	0.198979i
$867$	548.084	−	671.783i	0.632161	−	0.774837i
$868$	933.696	−	1617.21i	1.07569	−	1.86314i
$869$	1142.15	+	659.418i	1.31432	+	0.758824i
$870$	72.6649	−	156.728i	0.0835228	−	0.180147i
$871$	−155.212	−	268.835i	−0.178200	−	0.308651i
$872$	679.084			0.778766
$873$	12.1961	+	67.4347i	0.0139703	+	0.0772447i
$874$			64.1091i			0.0733513i
$875$	846.322	−	488.624i	0.967225	−	0.558427i
$876$	−795.047	+	71.3167i	−0.907587	+	0.0814118i
$877$	−453.960	−	262.094i	−0.517628	−	0.298853i	0.218335	−	0.975874i	$-0.429937\pi$
$877$	−453.960	−	262.094i	−0.517628	−	0.298853i	−0.735964	+	0.677021i	$0.763271\pi$
$878$	−214.695	+	371.863i	−0.244527	+	0.423534i
$879$	585.424	−	52.5133i	0.666011	−	0.0597421i
$880$	748.278	+	1296.06i	0.850316	+	1.47279i
$881$	417.401			0.473781			0.236891	−	0.971536i	$-0.423872\pi$
$881$	417.401			0.473781			0.236891	+	0.971536i	$0.423872\pi$
$882$	−592.336	−	212.652i	−0.671583	−	0.241102i
$883$	−916.666			−1.03813			−0.519063	−	0.854736i	$-0.673719\pi$
$883$	−916.666			−1.03813			−0.519063	+	0.854736i	$0.673719\pi$
$884$	−344.372	−	443.446i	−0.389561	−	0.501636i
$885$	56.7415	−	122.383i	0.0641147	−	0.138286i
$886$	−143.918	+	249.273i	−0.162436	+	0.281347i
$887$	489.915	−	848.557i	0.552328	−	0.956660i	−0.445778	−	0.895143i	$-0.647073\pi$
$887$	489.915	−	848.557i	0.552328	−	0.956660i	0.998106	−	0.0615166i	$-0.0195937\pi$
$888$	384.098	−	270.207i	0.432542	−	0.304287i
$889$	170.446	−	98.4070i	0.191728	−	0.110694i
$890$	489.492			0.549991
$891$	225.630	−	1348.77i	0.253232	−	1.51377i
$892$	382.584			0.428906
$893$	171.837	−	99.2102i	0.192427	−	0.111098i
$894$	−80.4396	+	56.5880i	−0.0899771	+	0.0632975i
$895$	−21.0369	−	12.1457i	−0.0235049	−	0.0135706i
$896$	781.403	−	1353.43i	0.872102	−	1.51052i
$897$	232.802	+	107.936i	0.259534	+	0.120330i
$898$	204.124	−	117.851i	0.227310	−	0.131237i
$899$			484.935i			0.539416i
$900$	383.530	−	1068.31i	0.426145	−	1.18701i
$901$	−49.9084	−	362.823i	−0.0553922	−	0.402689i
$902$	−154.552	+	89.2307i	−0.171344	+	0.0989254i
$903$	574.513	−	51.5346i	0.636227	−	0.0570704i
$904$	−25.8768	−	14.9400i	−0.0286248	−	0.0165265i
$905$	−736.689	−	425.327i	−0.814021	−	0.469975i
$906$	−115.327	+	10.3450i	−0.127293	+	0.0114183i
$907$	203.562	−	117.527i	0.224435	−	0.129577i	−0.383567	−	0.923513i	$-0.625305\pi$
$907$	203.562	−	117.527i	0.224435	−	0.129577i	0.608002	+	0.793935i	$0.291971\pi$
$908$	1341.61			1.47755
$909$	56.9874	+	315.095i	0.0626924	+	0.346639i
$910$	−562.638			−0.618284
$911$	−744.537	−	1289.58i	−0.817275	−	1.41556i	−0.907683	−	0.419657i	$-0.862150\pi$
$911$	−744.537	−	1289.58i	−0.817275	−	1.41556i	0.0904082	−	0.995905i	$-0.471183\pi$
$912$	341.379	+	158.276i	0.374319	+	0.173548i
$913$	−1460.31	−	843.110i	−1.59946	−	0.923450i
$914$	237.412	+	137.070i	0.259750	+	0.149967i
$915$	1013.25	+	1440.33i	1.10738	+	1.57414i
$916$	−484.146	−	838.565i	−0.528543	−	0.915464i
$917$			2029.31i			2.21299i
$918$	−230.187	−	172.142i	−0.250748	−	0.187518i
$919$	1002.45			1.09081			0.545404	−	0.838174i	$-0.316376\pi$
$919$	1002.45			1.09081			0.545404	+	0.838174i	$0.316376\pi$
$920$	−298.513	+	172.347i	−0.324471	+	0.187333i
$921$	−936.514	+	658.823i	−1.01685	+	0.715335i
$922$	125.818	−	217.924i	0.136462	−	0.236360i
$923$	−149.288	+	258.575i	−0.161743	+	0.280146i
$924$	−974.261	+	2101.34i	−1.05439	+	2.27418i
$925$	−994.718	+	574.301i	−1.07537	+	0.620866i
$926$		−	235.494i		−	0.254313i
$927$	−936.426	−	1106.09i	−1.01017	−	1.19319i
$928$			311.449i			0.335613i
$929$	−567.885	−	983.606i	−0.611286	−	1.05878i	−0.991024	−	0.133685i	$-0.957319\pi$
$929$	−567.885	−	983.606i	−0.611286	−	1.05878i	0.379737	−	0.925094i	$-0.376014\pi$
$930$	−53.0700	−	591.630i	−0.0570645	−	0.636161i
$931$	−611.733	+	1059.55i	−0.657071	+	1.13808i
$932$	−697.239	+	1207.65i	−0.748111	+	1.29577i
$933$	133.347	+	1486.57i	0.142923	+	1.59332i
$934$	−283.809	−	491.571i	−0.303864	−	0.526308i
$935$	−2201.62	+	302.846i	−2.35467	+	0.323900i
$936$	−299.570	+	253.619i	−0.320053	+	0.270960i
$937$	−1088.25			−1.16142			−0.580709	−	0.814111i	$-0.697225\pi$
$937$	−1088.25			−1.16142			−0.580709	+	0.814111i	$0.697225\pi$
$938$	134.584	+	233.107i	0.143480	+	0.248515i
$939$	365.918	−	789.234i	0.389690	−	0.840505i
$940$	438.144	+	252.963i	0.466111	+	0.269109i
$941$	−269.063	+	466.031i	−0.285933	+	0.495251i	−0.972835	−	0.231499i	$-0.925637\pi$
$941$	−269.063	+	466.031i	−0.285933	+	0.495251i	0.686902	+	0.726750i	$0.258970\pi$
$942$	64.9645	+	92.3467i	0.0689644	+	0.0980326i
$943$	78.8623	+	136.594i	0.0836292	+	0.144850i
$944$			66.4801i			0.0704238i
$945$	2555.13	−	702.715i	2.70384	−	0.743614i
$946$			160.371i			0.169526i
$947$	334.288	+	579.004i	0.352997	+	0.611409i	0.986773	−	0.162108i	$-0.0518292\pi$
$947$	334.288	+	579.004i	0.352997	+	0.611409i	−0.633776	+	0.773517i	$0.718496\pi$
$948$	486.481	+	691.531i	0.513166	+	0.729463i
$949$	−584.675	−	337.562i	−0.616096	−	0.355703i
$950$	207.710	+	119.921i	0.218642	+	0.126233i
$951$	−737.223	−	341.804i	−0.775208	−	0.359416i
$952$	629.665	+	810.817i	0.661413	+	0.851699i
$953$			355.805i			0.373353i	0.982421	+	0.186676i	$0.0597716\pi$
$953$			355.805i			0.373353i	−0.982421	+	0.186676i	$0.940228\pi$
$954$	−119.480	+	21.6089i	−0.125241	+	0.0226508i
$955$		−	684.232i		−	0.716473i
$956$	1059.52	−	611.712i	1.10828	−	0.639866i
$957$	−53.7383	−	599.081i	−0.0561529	−	0.625999i
$958$	246.070	+	142.068i	0.256858	+	0.148297i
$959$	−827.171	+	1432.70i	−0.862535	+	1.49395i
$960$	60.9519	+	679.499i	0.0634916	+	0.707811i
$961$	353.215	+	611.786i	0.367549	+	0.636614i
$962$	188.358			0.195798
$963$	28.4231	−	79.1718i	0.0295152	−	0.0822138i
$964$		−	1097.80i		−	1.13880i
$965$	2092.54	−	1208.13i	2.16844	−	1.25195i
$966$	−201.862	−	93.5910i	−0.208967	−	0.0968851i
$967$	−318.302	+	551.315i	−0.329164	+	0.570129i	−0.982346	−	0.187072i	$-0.940100\pi$
$967$	−318.302	+	551.315i	−0.329164	+	0.570129i	0.653182	+	0.757201i	$0.273434\pi$
$968$	−676.768	−	390.732i	−0.699140	−	0.403649i
$969$	−408.942	+	380.785i	−0.422025	+	0.392967i
$970$	−18.4606	−	31.9747i	−0.0190315	−	0.0329636i
$971$		−	1713.07i		−	1.76423i	−0.471032	−	0.882116i	$-0.656119\pi$
$971$		−	1713.07i		−	1.76423i	0.471032	−	0.882116i	$-0.343881\pi$
$972$	494.945	−	723.633i	0.509203	−	0.744479i
$973$	1757.68			1.80645
$974$	−138.698	−	240.232i	−0.142400	−	0.246644i
$975$	785.181	−	552.362i	0.805313	−	0.566525i
$976$	−751.600	−	433.937i	−0.770082	−	0.444607i
$977$	−167.944	−	96.9625i	−0.171898	−	0.0992451i	0.411583	−	0.911372i	$-0.364976\pi$
$977$	−167.944	−	96.9625i	−0.171898	−	0.0992451i	−0.583480	+	0.812127i	$0.698309\pi$
$978$	460.879	+	213.681i	0.471246	+	0.218487i
$979$	1475.96	−	852.147i	1.50762	−	0.870426i
$980$	−3119.55			−3.18322
$981$	−1207.41	−	433.466i	−1.23079	−	0.441861i
$982$	134.939			0.137413
$983$	284.702	+	493.119i	0.289626	+	0.501647i	0.973720	−	0.227747i	$-0.0731358\pi$
$983$	284.702	+	493.119i	0.289626	+	0.501647i	−0.684095	+	0.729393i	$0.739802\pi$
$984$	−240.294	+	21.5547i	−0.244201	+	0.0219052i
$985$	593.291	−	1027.61i	0.602326	−	1.04326i
$986$	−117.081	−	47.7029i	−0.118743	−	0.0483802i
$987$	61.5264	+	685.903i	0.0623368	+	0.694937i
$988$	180.928	+	313.377i	0.183126	+	0.317183i
$989$	141.736			0.143313
$990$	131.124	+	725.009i	0.132448	+	0.732333i
$991$			1077.67i			1.08746i	0.839261	+	0.543729i	$0.182988\pi$
$991$			1077.67i			1.08746i	−0.839261	+	0.543729i	$0.817012\pi$
$992$	535.452	+	927.429i	0.539770	+	0.934908i
$993$	−613.561	−	284.470i	−0.617886	−	0.286475i
$994$	129.448	−	224.210i	0.130229	−	0.225564i
$995$	1115.12	+	643.815i	1.12072	+	0.647050i
$996$	−621.998	−	884.168i	−0.624496	−	0.887719i
$997$	456.054	−	263.303i	0.457426	−	0.264095i	−0.253535	−	0.967326i	$-0.581593\pi$
$997$	456.054	−	263.303i	0.457426	−	0.264095i	0.710962	+	0.703231i	$0.248260\pi$
$998$	316.931			0.317566
$999$	−855.397	+	235.252i	−0.856254	+	0.235488i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.i.a.50.20	yes	68
3.2	odd	2		459.3.i.a.152.16		68
9.2	odd	6	inner	153.3.i.a.101.19	yes	68
9.7	even	3		459.3.i.a.305.15		68
17.16	even	2	inner	153.3.i.a.50.19	✓	68
51.50	odd	2		459.3.i.a.152.15		68
153.16	even	6		459.3.i.a.305.16		68
153.101	odd	6	inner	153.3.i.a.101.20	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.3.i.a.50.19	✓	68	17.16	even	2	inner
153.3.i.a.50.20	yes	68	1.1	even	1	trivial
153.3.i.a.101.19	yes	68	9.2	odd	6	inner
153.3.i.a.101.20	yes	68	153.101	odd	6	inner
459.3.i.a.152.15		68	51.50	odd	2
459.3.i.a.152.16		68	3.2	odd	2
459.3.i.a.305.15		68	9.7	even	3
459.3.i.a.305.16		68	153.16	even	6

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.542321 - 0.313109i) q^{2} +(2.45367 - 1.72612i) q^{3} +(-1.80392 + 3.12449i) q^{4} +(-3.87159 + 6.70579i) q^{5} +(0.790215 - 1.70438i) q^{6} +(10.9773 - 6.33772i) q^{7} +4.76418i q^{8} +(3.04102 - 8.47067i) q^{9} +4.84893i q^{10} +(8.44140 + 14.6209i) q^{11} +(0.967004 + 10.7803i) q^{12} +(-4.57710 + 7.92777i) q^{13} +(3.96880 - 6.87416i) q^{14} +(2.07539 + 23.1366i) q^{15} +(-5.72399 - 9.91424i) q^{16} +(16.8414 - 2.31664i) q^{17} +(-1.00304 - 5.54600i) q^{18} -10.9564 q^{19} +(-13.9681 - 24.1935i) q^{20} +(15.9949 - 34.4988i) q^{21} +(9.15591 + 5.28617i) q^{22} +(4.67192 - 8.09201i) q^{23} +(8.22355 + 11.6897i) q^{24} +(-17.4784 - 30.2735i) q^{25} +5.73253i q^{26} +(-7.15973 - 26.0334i) q^{27} +45.7311i q^{28} +(-5.93786 - 10.2847i) q^{29} +(8.36983 + 11.8977i) q^{30} +(-35.3634 - 20.4171i) q^{31} +(-22.7121 - 13.1128i) q^{32} +(45.9499 + 21.3041i) q^{33} +(8.40810 - 6.52957i) q^{34} +98.1483i q^{35} +(20.9807 + 24.7821i) q^{36} -32.8577i q^{37} +(-5.94189 + 3.43055i) q^{38} +(2.45358 + 27.3528i) q^{39} +(-31.9476 - 18.4450i) q^{40} +(-8.44003 + 14.6186i) q^{41} +(-2.12750 - 23.7176i) q^{42} +(7.58448 + 13.1367i) q^{43} -60.9106 q^{44} +(45.0290 + 53.1874i) q^{45} -5.85129i q^{46} +(-15.6837 + 9.05501i) q^{47} +(-31.1580 - 14.4460i) q^{48} +(55.8334 - 96.7063i) q^{49} +(-18.9579 - 10.9453i) q^{50} +(37.3245 - 34.7546i) q^{51} +(-16.5135 - 28.6022i) q^{52} -21.5435i q^{53} +(-12.0342 - 11.8767i) q^{54} -130.727 q^{55} +(30.1940 + 52.2976i) q^{56} +(-26.8834 + 18.9121i) q^{57} +(-6.44046 - 3.71840i) q^{58} +(-5.02914 - 2.90357i) q^{59} +(-76.0341 - 35.2523i) q^{60} +(65.6535 - 37.9051i) q^{61} -25.5711 q^{62} +(-20.3027 - 112.258i) q^{63} +29.3689 q^{64} +(-35.4413 - 61.3862i) q^{65} +(31.5902 - 2.83368i) q^{66} +(-16.9553 + 29.3674i) q^{67} +(-23.1423 + 56.7999i) q^{68} +(-2.50441 - 27.9194i) q^{69} +(30.7311 + 53.2279i) q^{70} +32.6164 q^{71} +(40.3558 + 14.4880i) q^{72} +73.7502i q^{73} +(-10.2880 - 17.8194i) q^{74} +(-95.1421 - 44.1114i) q^{75} +(19.7645 - 34.2331i) q^{76} +(185.327 + 106.999i) q^{77} +(9.89504 + 14.0658i) q^{78} +(67.6514 - 39.0586i) q^{79} +88.6438 q^{80} +(-62.5044 - 51.5189i) q^{81} +10.5706i q^{82} +(-86.4969 + 49.9390i) q^{83} +(78.9374 + 112.209i) q^{84} +(-49.6682 + 121.904i) q^{85} +(8.22645 + 4.74955i) q^{86} +(-32.3222 - 14.9858i) q^{87} +(-69.6568 + 40.2164i) q^{88} -100.949i q^{89} +(41.0736 + 14.7457i) q^{90} +116.034i q^{91} +(16.8556 + 29.1948i) q^{92} +(-122.013 + 10.9447i) q^{93} +(-5.67041 + 9.82145i) q^{94} +(42.4187 - 73.4713i) q^{95} +(-78.3623 + 7.02920i) q^{96} +(-6.59417 + 3.80715i) q^{97} -69.9279i q^{98} +(149.520 - 27.0418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} + 62 q^{4} - 8 q^{9} - 2 q^{13} - 106 q^{16} - 2 q^{18} - 32 q^{19} - 28 q^{21} - 132 q^{25} + 180 q^{30} - 98 q^{33} - 27 q^{34} + 158 q^{36} - 102 q^{38} + 110 q^{42} + 58 q^{43} - 312 q^{47}+ \cdots - 18 q^{94}+O(q^{100}) \) 68 * q - 6 * q^2 + 62 * q^4 - 8 * q^9 - 2 * q^13 - 106 * q^16 - 2 * q^18 - 32 * q^19 - 28 * q^21 - 132 * q^25 + 180 * q^30 - 98 * q^33 - 27 * q^34 + 158 * q^36 - 102 * q^38 + 110 * q^42 + 58 * q^43 - 312 * q^47 + 152 * q^49 - 90 * q^50 - 17 * q^51 + 70 * q^52 + 92 * q^55 - 258 * q^59 - 126 * q^60 - 16 * q^64 + 400 * q^66 + 82 * q^67 - 333 * q^68 + 404 * q^69 + 204 * q^70 + 474 * q^72 + 34 * q^76 - 60 * q^77 - 88 * q^81 - 690 * q^83 - 200 * q^84 - 44 * q^85 - 1248 * q^86 + 114 * q^87 + 50 * q^93 - 18 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more