LMFDB - Embedded newform 18.3.d.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,3,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.490464475849$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.3.d.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(2.44949 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-4.50000 + 2.59808i) q^{5} +(-4.22474 + 0.389270i) q^{6} +(-3.17423 + 5.49794i) q^{7} -2.82843i q^{8} +(3.00000 - 8.48528i) q^{9} +7.34847 q^{10} +(8.17423 + 4.71940i) q^{11} +(5.44949 + 2.51059i) q^{12} +(-9.84847 - 17.0580i) q^{13} +(7.77526 - 4.48905i) q^{14} +(-6.52270 + 14.1582i) q^{15} +(-2.00000 + 3.46410i) q^{16} -1.90702i q^{17} +(-9.67423 + 8.27098i) q^{18} +4.69694 q^{19} +(-9.00000 - 5.19615i) q^{20} +(1.74745 + 18.9651i) q^{21} +(-6.67423 - 11.5601i) q^{22} +(8.17423 - 4.71940i) q^{23} +(-4.89898 - 6.92820i) q^{24} +(1.00000 - 1.73205i) q^{25} +27.8557i q^{26} +(-7.34847 - 25.9808i) q^{27} -12.6969 q^{28} +(-2.84847 - 1.64456i) q^{29} +(18.0000 - 12.7279i) q^{30} +(20.5227 + 35.5464i) q^{31} +(4.89898 - 2.82843i) q^{32} +(28.1969 - 2.59808i) q^{33} +(-1.34847 + 2.33562i) q^{34} -32.9876i q^{35} +(17.6969 - 3.28913i) q^{36} +17.3031 q^{37} +(-5.75255 - 3.32124i) q^{38} +(-53.6691 - 24.7255i) q^{39} +(7.34847 + 12.7279i) q^{40} +(-53.5454 + 30.9145i) q^{41} +(11.2702 - 24.4630i) q^{42} +(-0.477296 + 0.826701i) q^{43} +18.8776i q^{44} +(8.54541 + 45.9780i) q^{45} -13.3485 q^{46} +(-12.2196 - 7.05501i) q^{47} +(1.10102 + 11.9494i) q^{48} +(4.34847 + 7.53177i) q^{49} +(-2.44949 + 1.41421i) q^{50} +(-3.30306 - 4.67123i) q^{51} +(19.6969 - 34.1161i) q^{52} -9.53512i q^{53} +(-9.37117 + 37.0160i) q^{54} -49.0454 q^{55} +(15.5505 + 8.97809i) q^{56} +(11.5051 - 8.13534i) q^{57} +(2.32577 + 4.02834i) q^{58} +(79.2650 - 45.7637i) q^{59} +(-31.0454 + 2.86054i) q^{60} +(37.5454 - 65.0306i) q^{61} -58.0470i q^{62} +(37.1288 + 43.4281i) q^{63} -8.00000 q^{64} +(88.6362 + 51.1741i) q^{65} +(-36.3712 - 16.7563i) q^{66} +(-15.4773 - 26.8075i) q^{67} +(3.30306 - 1.90702i) q^{68} +(11.8485 - 25.7183i) q^{69} +(-23.3258 + 40.4014i) q^{70} +85.9026i q^{71} +(-24.0000 - 8.48528i) q^{72} -96.0908 q^{73} +(-21.1918 - 12.2351i) q^{74} +(-0.550510 - 5.97469i) q^{75} +(4.69694 + 8.13534i) q^{76} +(-51.8939 + 29.9609i) q^{77} +(48.2474 + 68.2322i) q^{78} +(-14.8712 + 25.7576i) q^{79} -20.7846i q^{80} +(-63.0000 - 50.9117i) q^{81} +87.4393 q^{82} +(-76.1288 - 43.9530i) q^{83} +(-31.1010 + 21.9917i) q^{84} +(4.95459 + 8.58161i) q^{85} +(1.16913 - 0.674999i) q^{86} +(-9.82577 + 0.905350i) q^{87} +(13.3485 - 23.1202i) q^{88} -41.3766i q^{89} +(22.0454 - 62.3538i) q^{90} +125.045 q^{91} +(16.3485 + 9.43879i) q^{92} +(111.838 + 51.5241i) q^{93} +(9.97730 + 17.2812i) q^{94} +(-21.1362 + 12.2030i) q^{95} +(7.10102 - 15.4135i) q^{96} +(-47.9393 + 83.0333i) q^{97} -12.2993i q^{98} +(64.5681 - 55.2025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} - 18 q^{5} - 12 q^{6} + 2 q^{7} + 12 q^{9} + 18 q^{11} + 12 q^{12} - 10 q^{13} + 36 q^{14} + 18 q^{15} - 8 q^{16} - 24 q^{18} - 40 q^{19} - 36 q^{20} - 42 q^{21} - 12 q^{22} + 18 q^{23} + 4 q^{25}+ \cdots + 126 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 - 18 * q^5 - 12 * q^6 + 2 * q^7 + 12 * q^9 + 18 * q^11 + 12 * q^12 - 10 * q^13 + 36 * q^14 + 18 * q^15 - 8 * q^16 - 24 * q^18 - 40 * q^19 - 36 * q^20 - 42 * q^21 - 12 * q^22 + 18 * q^23 + 4 * q^25 + 8 * q^28 + 18 * q^29 + 72 * q^30 + 38 * q^31 + 54 * q^33 + 24 * q^34 + 12 * q^36 + 128 * q^37 - 72 * q^38 - 102 * q^39 - 126 * q^41 - 48 * q^42 - 46 * q^43 - 54 * q^45 - 24 * q^46 + 54 * q^47 + 24 * q^48 - 12 * q^49 - 72 * q^51 + 20 * q^52 + 36 * q^54 - 108 * q^55 + 72 * q^56 + 144 * q^57 + 24 * q^58 + 126 * q^59 - 36 * q^60 + 62 * q^61 + 222 * q^63 - 32 * q^64 + 90 * q^65 - 72 * q^66 - 106 * q^67 + 72 * q^68 + 18 * q^69 - 108 * q^70 - 96 * q^72 - 208 * q^73 + 72 * q^74 - 12 * q^75 - 40 * q^76 - 90 * q^77 + 144 * q^78 + 14 * q^79 - 252 * q^81 + 144 * q^82 - 378 * q^83 - 144 * q^84 + 108 * q^85 - 108 * q^86 - 54 * q^87 + 24 * q^88 + 412 * q^91 + 36 * q^92 + 222 * q^93 + 84 * q^94 + 180 * q^95 + 48 * q^96 + 14 * q^97 + 126 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	2.44949	−	1.73205i	0.816497	−	0.577350i
$3$	2.44949	−	1.73205i	0.816497	−	0.577350i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−4.50000	+	2.59808i	−0.900000	+	0.519615i	−0.877200	−	0.480125i	$-0.840591\pi$
$5$	−4.50000	+	2.59808i	−0.900000	+	0.519615i	−0.0227998	+	0.999740i	$0.507258\pi$
$6$	−4.22474	+	0.389270i	−0.704124	+	0.0648783i
$7$	−3.17423	+	5.49794i	−0.453462	+	0.785419i	−0.998598	−	0.0529281i	$-0.983145\pi$
$7$	−3.17423	+	5.49794i	−0.453462	+	0.785419i	0.545136	+	0.838347i	$0.316478\pi$
$8$		−	2.82843i		−	0.353553i
$9$	3.00000	−	8.48528i	0.333333	−	0.942809i
$10$	7.34847			0.734847
$11$	8.17423	+	4.71940i	0.743112	+	0.429036i	0.823200	−	0.567752i	$-0.192187\pi$
$11$	8.17423	+	4.71940i	0.743112	+	0.429036i	−0.0800876	+	0.996788i	$0.525520\pi$
$12$	5.44949	+	2.51059i	0.454124	+	0.209216i
$13$	−9.84847	−	17.0580i	−0.757575	−	1.31216i	−0.944084	−	0.329704i	$-0.893051\pi$
$13$	−9.84847	−	17.0580i	−0.757575	−	1.31216i	0.186510	−	0.982453i	$-0.440282\pi$
$14$	7.77526	−	4.48905i	0.555375	−	0.320646i
$15$	−6.52270	+	14.1582i	−0.434847	+	0.943879i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$		−	1.90702i		−	0.112178i	−0.998426	−	0.0560889i	$-0.982137\pi$
$17$		−	1.90702i		−	0.112178i	0.998426	−	0.0560889i	$-0.0178630\pi$
$18$	−9.67423	+	8.27098i	−0.537457	+	0.459499i
$19$	4.69694			0.247207			0.123604	−	0.992332i	$-0.460555\pi$
$19$	4.69694			0.247207			0.123604	+	0.992332i	$0.460555\pi$
$20$	−9.00000	−	5.19615i	−0.450000	−	0.259808i
$21$	1.74745	+	18.9651i	0.0832118	+	0.903099i
$22$	−6.67423	−	11.5601i	−0.303374	−	0.525460i
$23$	8.17423	−	4.71940i	0.355402	−	0.205191i	−0.311660	−	0.950194i	$-0.600885\pi$
$23$	8.17423	−	4.71940i	0.355402	−	0.205191i	0.667062	+	0.745002i	$0.267552\pi$
$24$	−4.89898	−	6.92820i	−0.204124	−	0.288675i
$25$	1.00000	−	1.73205i	0.0400000	−	0.0692820i
$26$			27.8557i			1.07137i
$27$	−7.34847	−	25.9808i	−0.272166	−	0.962250i
$28$	−12.6969			−0.453462
$29$	−2.84847	−	1.64456i	−0.0982231	−	0.0567091i	0.450084	−	0.892986i	$-0.351394\pi$
$29$	−2.84847	−	1.64456i	−0.0982231	−	0.0567091i	−0.548307	+	0.836277i	$0.684727\pi$
$30$	18.0000	−	12.7279i	0.600000	−	0.424264i
$31$	20.5227	+	35.5464i	0.662023	+	1.14666i	0.980083	+	0.198587i	$0.0636351\pi$
$31$	20.5227	+	35.5464i	0.662023	+	1.14666i	−0.318061	+	0.948070i	$0.603032\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	28.1969	−	2.59808i	0.854453	−	0.0787296i
$34$	−1.34847	+	2.33562i	−0.0396609	+	0.0686946i
$35$		−	32.9876i		−	0.942503i
$36$	17.6969	−	3.28913i	0.491582	−	0.0913647i
$37$	17.3031			0.467650			0.233825	−	0.972279i	$-0.424876\pi$
$37$	17.3031			0.467650			0.233825	+	0.972279i	$0.424876\pi$
$38$	−5.75255	−	3.32124i	−0.151383	−	0.0874010i
$39$	−53.6691	−	24.7255i	−1.37613	−	0.633986i
$40$	7.34847	+	12.7279i	0.183712	+	0.318198i
$41$	−53.5454	+	30.9145i	−1.30599	+	0.754011i	−0.981424	−	0.191853i	$-0.938550\pi$
$41$	−53.5454	+	30.9145i	−1.30599	+	0.754011i	−0.324562	+	0.945864i	$0.605217\pi$
$42$	11.2702	−	24.4630i	0.268337	−	0.582453i
$43$	−0.477296	+	0.826701i	−0.0110999	+	0.0192256i	−0.871522	−	0.490356i	$-0.836867\pi$
$43$	−0.477296	+	0.826701i	−0.0110999	+	0.0192256i	0.860422	+	0.509582i	$0.170200\pi$
$44$			18.8776i			0.429036i
$45$	8.54541	+	45.9780i	0.189898	+	1.02173i
$46$	−13.3485			−0.290184
$47$	−12.2196	−	7.05501i	−0.259992	−	0.150107i	0.364339	−	0.931267i	$-0.381295\pi$
$47$	−12.2196	−	7.05501i	−0.259992	−	0.150107i	−0.624331	+	0.781160i	$0.714628\pi$
$48$	1.10102	+	11.9494i	0.0229379	+	0.248945i
$49$	4.34847	+	7.53177i	0.0887443	+	0.153710i
$50$	−2.44949	+	1.41421i	−0.0489898	+	0.0282843i
$51$	−3.30306	−	4.67123i	−0.0647659	−	0.0915928i
$52$	19.6969	−	34.1161i	0.378787	−	0.656079i
$53$		−	9.53512i		−	0.179908i	−0.995946	−	0.0899539i	$-0.971328\pi$
$53$		−	9.53512i		−	0.179908i	0.995946	−	0.0899539i	$-0.0286720\pi$
$54$	−9.37117	+	37.0160i	−0.173540	+	0.685481i
$55$	−49.0454			−0.891735
$56$	15.5505	+	8.97809i	0.277688	+	0.160323i
$57$	11.5051	−	8.13534i	0.201844	−	0.142725i
$58$	2.32577	+	4.02834i	0.0400994	+	0.0694542i
$59$	79.2650	−	45.7637i	1.34348	−	0.775656i	0.356160	−	0.934425i	$-0.384086\pi$
$59$	79.2650	−	45.7637i	1.34348	−	0.775656i	0.987316	+	0.158769i	$0.0507526\pi$
$60$	−31.0454	+	2.86054i	−0.517423	+	0.0476756i
$61$	37.5454	−	65.0306i	0.615498	−	1.06607i	−0.374798	−	0.927106i	$-0.622288\pi$
$61$	37.5454	−	65.0306i	0.615498	−	1.06607i	0.990297	−	0.138968i	$-0.0443786\pi$
$62$		−	58.0470i		−	0.936241i
$63$	37.1288	+	43.4281i	0.589346	+	0.689335i
$64$	−8.00000			−0.125000
$65$	88.6362	+	51.1741i	1.36363	+	0.787295i
$66$	−36.3712	−	16.7563i	−0.551078	−	0.253883i
$67$	−15.4773	−	26.8075i	−0.231004	−	0.400111i	0.727100	−	0.686532i	$-0.240868\pi$
$67$	−15.4773	−	26.8075i	−0.231004	−	0.400111i	−0.958104	+	0.286421i	$0.907535\pi$
$68$	3.30306	−	1.90702i	0.0485744	−	0.0280445i
$69$	11.8485	−	25.7183i	0.171717	−	0.372729i
$70$	−23.3258	+	40.4014i	−0.333225	+	0.577163i
$71$			85.9026i			1.20990i	0.796265	+	0.604948i	$0.206806\pi$
$71$			85.9026i			1.20990i	−0.796265	+	0.604948i	$0.793194\pi$
$72$	−24.0000	−	8.48528i	−0.333333	−	0.117851i
$73$	−96.0908			−1.31631			−0.658156	−	0.752881i	$-0.728663\pi$
$73$	−96.0908			−1.31631			−0.658156	+	0.752881i	$0.728663\pi$
$74$	−21.1918	−	12.2351i	−0.286376	−	0.165339i
$75$	−0.550510	−	5.97469i	−0.00734014	−	0.0796626i
$76$	4.69694	+	8.13534i	0.0618018	+	0.107044i
$77$	−51.8939	+	29.9609i	−0.673946	+	0.389103i
$78$	48.2474	+	68.2322i	0.618557	+	0.874772i
$79$	−14.8712	+	25.7576i	−0.188243	+	0.326046i	−0.944664	−	0.328038i	$-0.893612\pi$
$79$	−14.8712	+	25.7576i	−0.188243	+	0.326046i	0.756422	+	0.654084i	$0.226946\pi$
$80$		−	20.7846i		−	0.259808i
$81$	−63.0000	−	50.9117i	−0.777778	−	0.628539i
$82$	87.4393			1.06633
$83$	−76.1288	−	43.9530i	−0.917215	−	0.529554i	−0.0344693	−	0.999406i	$-0.510974\pi$
$83$	−76.1288	−	43.9530i	−0.917215	−	0.529554i	−0.882745	+	0.469852i	$0.844307\pi$
$84$	−31.1010	+	21.9917i	−0.370250	+	0.261806i
$85$	4.95459	+	8.58161i	0.0582893	+	0.100960i
$86$	1.16913	−	0.674999i	0.0135946	−	0.00784882i
$87$	−9.82577	+	0.905350i	−0.112940	+	0.0104063i
$88$	13.3485	−	23.1202i	0.151687	−	0.262730i
$89$		−	41.3766i		−	0.464905i	−0.972608	−	0.232453i	$-0.925325\pi$
$89$		−	41.3766i		−	0.464905i	0.972608	−	0.232453i	$-0.0746751\pi$
$90$	22.0454	−	62.3538i	0.244949	−	0.692820i
$91$	125.045			1.37413
$92$	16.3485	+	9.43879i	0.177701	+	0.102596i
$93$	111.838	+	51.5241i	1.20256	+	0.554023i
$94$	9.97730	+	17.2812i	0.106141	+	0.183842i
$95$	−21.1362	+	12.2030i	−0.222487	+	0.128453i
$96$	7.10102	−	15.4135i	0.0739690	−	0.160557i
$97$	−47.9393	+	83.0333i	−0.494219	+	0.856013i	−0.999978	−	0.00666202i	$-0.997879\pi$
$97$	−47.9393	+	83.0333i	−0.494219	+	0.856013i	0.505758	+	0.862675i	$0.331213\pi$
$98$		−	12.2993i		−	0.125503i
$99$	64.5681	−	55.2025i	0.652203	−	0.557601i
$100$	4.00000			0.0400000
$101$	−136.772	−	78.9656i	−1.35418	−	0.781838i	−0.365350	−	0.930870i	$-0.619051\pi$
$101$	−136.772	−	78.9656i	−1.35418	−	0.781838i	−0.988832	+	0.149032i	$0.952384\pi$
$102$	0.742346	+	8.05669i	0.00727790	+	0.0789871i
$103$	−14.5681	−	25.2327i	−0.141438	−	0.244978i	0.786600	−	0.617462i	$-0.211839\pi$
$103$	−14.5681	−	25.2327i	−0.141438	−	0.244978i	−0.928038	+	0.372485i	$0.878506\pi$
$104$	−48.2474	+	27.8557i	−0.463918	+	0.267843i
$105$	−57.1362	−	80.8028i	−0.544155	−	0.769551i
$106$	−6.74235	+	11.6781i	−0.0636070	+	0.110171i
$107$			171.805i			1.60566i	0.596210	+	0.802829i	$0.296673\pi$
$107$			171.805i			1.60566i	−0.596210	+	0.802829i	$0.703327\pi$
$108$	37.6515	−	38.7087i	0.348625	−	0.358414i
$109$	116.272			1.06672			0.533360	−	0.845888i	$-0.320929\pi$
$109$	116.272			1.06672			0.533360	+	0.845888i	$0.320929\pi$
$110$	60.0681	+	34.6803i	0.546074	+	0.315276i
$111$	42.3837	−	29.9698i	0.381835	−	0.269998i
$112$	−12.6969	−	21.9917i	−0.113366	−	0.196355i
$113$	175.166	−	101.132i	1.55014	−	0.894976i	0.552015	−	0.833834i	$-0.313859\pi$
$113$	175.166	−	101.132i	1.55014	−	0.894976i	0.998129	−	0.0611424i	$-0.0194744\pi$
$114$	−19.8434	+	1.82838i	−0.174065	+	0.0160384i
$115$	−24.5227	+	42.4746i	−0.213241	+	0.369344i
$116$		−	6.57826i		−	0.0567091i
$117$	−174.288	+	32.3929i	−1.48964	+	0.276862i
$118$	−129.439			−1.09694
$119$	10.4847	+	6.05334i	0.0881067	+	0.0508684i
$120$	40.0454	+	18.4490i	0.333712	+	0.153742i
$121$	−15.9546	−	27.6342i	−0.131856	−	0.228382i
$122$	−91.9671	+	53.0972i	−0.753829	+	0.435223i
$123$	−77.6135	+	168.468i	−0.631004	+	1.36966i
$124$	−41.0454	+	71.0927i	−0.331011	+	0.573328i
$125$		−	119.512i		−	0.956092i
$126$	−14.7650	−	79.4424i	−0.117183	−	0.630495i
$127$	10.0908			0.0794552			0.0397276	−	0.999211i	$-0.487351\pi$
$127$	10.0908			0.0794552			0.0397276	+	0.999211i	$0.487351\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	0.262756	+	2.85170i	0.00203687	+	0.0221062i
$130$	−72.3712	−	125.351i	−0.556701	−	0.964235i
$131$	4.29567	−	2.48010i	0.0327913	−	0.0189321i	−0.483515	−	0.875336i	$-0.660640\pi$
$131$	4.29567	−	2.48010i	0.0327913	−	0.0189321i	0.516306	+	0.856404i	$0.327307\pi$
$132$	32.6969	+	46.2405i	0.247704	+	0.350306i
$133$	−14.9092	+	25.8235i	−0.112099	+	0.194161i
$134$			43.7764i			0.326690i
$135$	100.568	+	97.8215i	0.744949	+	0.724604i
$136$	−5.39388			−0.0396609
$137$	203.242	+	117.342i	1.48352	+	0.856511i	0.999825	−	0.0187249i	$-0.00596067\pi$
$137$	203.242	+	117.342i	1.48352	+	0.856511i	0.483696	+	0.875236i	$0.339294\pi$
$138$	−32.6969	+	23.1202i	−0.236934	+	0.167538i
$139$	−53.2650	−	92.2578i	−0.383202	−	0.663725i	0.608316	−	0.793695i	$-0.291845\pi$
$139$	−53.2650	−	92.2578i	−0.383202	−	0.663725i	−0.991518	+	0.129970i	$0.958512\pi$
$140$	57.1362	−	32.9876i	0.408116	−	0.235626i
$141$	−42.1515	+	3.88386i	−0.298947	+	0.0275451i
$142$	60.7423	−	105.209i	0.427763	−	0.740907i
$143$		−	185.915i		−	1.30011i
$144$	23.3939	+	27.3629i	0.162457	+	0.190020i
$145$	17.0908			0.117868
$146$	117.687	+	67.9465i	0.806074	+	0.465387i
$147$	23.6969	+	10.9172i	0.161204	+	0.0742668i
$148$	17.3031	+	29.9698i	0.116913	+	0.202499i
$149$	−91.0301	+	52.5563i	−0.610940	+	0.352727i	−0.773333	−	0.634000i	$-0.781412\pi$
$149$	−91.0301	+	52.5563i	−0.610940	+	0.352727i	0.162393	+	0.986726i	$0.448079\pi$
$150$	−3.55051	+	7.70674i	−0.0236701	+	0.0513783i
$151$	142.614	−	247.014i	0.944460	−	1.63585i	0.187632	−	0.982239i	$-0.439919\pi$
$151$	142.614	−	247.014i	0.944460	−	1.63585i	0.756828	−	0.653614i	$-0.226748\pi$
$152$		−	13.2849i		−	0.0874010i
$153$	−16.1816	−	5.72107i	−0.105762	−	0.0373926i
$154$	84.7423			0.550275
$155$	−184.704	−	106.639i	−1.19164	−	0.687994i
$156$	−10.8434	−	117.683i	−0.0695088	−	0.754379i
$157$	98.5908	+	170.764i	0.627967	+	1.08767i	0.987959	+	0.154715i	$0.0494460\pi$
$157$	98.5908	+	170.764i	0.627967	+	1.08767i	−0.359992	+	0.932955i	$0.617221\pi$
$158$	36.4268	−	21.0310i	0.230549	−	0.133108i
$159$	−16.5153	−	23.3562i	−0.103870	−	0.146894i
$160$	−14.6969	+	25.4558i	−0.0918559	+	0.159099i
$161$			59.9219i			0.372186i
$162$	41.1589	+	106.902i	0.254067	+	0.659886i
$163$	−249.060			−1.52798			−0.763988	−	0.645230i	$-0.776762\pi$
$163$	−249.060			−1.52798			−0.763988	+	0.645230i	$0.776762\pi$
$164$	−107.091	−	61.8289i	−0.652993	−	0.377006i
$165$	−120.136	+	84.9491i	−0.728098	+	0.514843i
$166$	62.1589	+	107.662i	0.374451	+	0.648569i
$167$	−41.9472	+	24.2182i	−0.251181	+	0.145019i	−0.620305	−	0.784361i	$-0.712991\pi$
$167$	−41.9472	+	24.2182i	−0.251181	+	0.145019i	0.369124	+	0.929380i	$0.379658\pi$
$168$	53.6413	−	4.94253i	0.319294	−	0.0294198i
$169$	−109.485	+	189.633i	−0.647838	+	1.12209i
$170$		−	14.0137i		−	0.0824335i
$171$	14.0908	−	39.8548i	0.0824024	−	0.233069i
$172$	−1.90918			−0.0110999
$173$	86.9847	+	50.2206i	0.502802	+	0.290293i	0.729870	−	0.683586i	$-0.239581\pi$
$173$	86.9847	+	50.2206i	0.502802	+	0.290293i	−0.227068	+	0.973879i	$0.572914\pi$
$174$	12.6742	+	5.83904i	0.0728404	+	0.0335577i
$175$	6.34847	+	10.9959i	0.0362770	+	0.0628336i
$176$	−32.6969	+	18.8776i	−0.185778	+	0.107259i
$177$	114.894	−	249.389i	0.649118	−	1.40898i
$178$	−29.2577	+	50.6757i	−0.164369	+	0.284695i
$179$			285.071i			1.59257i	0.604919	+	0.796287i	$0.293206\pi$
$179$			285.071i			1.59257i	−0.604919	+	0.796287i	$0.706794\pi$
$180$	−71.0908	+	60.7791i	−0.394949	+	0.337662i
$181$	37.1214			0.205091			0.102545	−	0.994728i	$-0.467301\pi$
$181$	37.1214			0.205091			0.102545	+	0.994728i	$0.467301\pi$
$182$	−153.149	−	88.4205i	−0.841476	−	0.485827i
$183$	−20.6691	−	224.322i	−0.112946	−	1.22580i
$184$	−13.3485	−	23.1202i	−0.0725460	−	0.125653i
$185$	−77.8638	+	44.9547i	−0.420885	+	0.242998i
$186$	−100.540	−	142.185i	−0.540539	−	0.764438i
$187$	9.00000	−	15.5885i	0.0481283	−	0.0833607i
$188$		−	28.2201i		−	0.150107i
$189$	166.166	+	42.0676i	0.879187	+	0.222580i
$190$	34.5153			0.181660
$191$	−15.5227	−	8.96204i	−0.0812707	−	0.0469217i	0.458814	−	0.888532i	$-0.348274\pi$
$191$	−15.5227	−	8.96204i	−0.0812707	−	0.0469217i	−0.540085	+	0.841611i	$0.681608\pi$
$192$	−19.5959	+	13.8564i	−0.102062	+	0.0721688i
$193$	47.7270	+	82.6657i	0.247290	+	0.428319i	0.962773	−	0.270311i	$-0.0871265\pi$
$193$	47.7270	+	82.6657i	0.247290	+	0.428319i	−0.715483	+	0.698630i	$0.753793\pi$
$194$	117.427	−	67.7964i	0.605293	−	0.349466i
$195$	305.750	−	28.1719i	1.56795	−	0.144471i
$196$	−8.69694	+	15.0635i	−0.0443721	+	0.0768548i
$197$		−	160.363i		−	0.814026i	−0.913422	−	0.407013i	$-0.866570\pi$
$197$		−	160.363i		−	0.814026i	0.913422	−	0.407013i	$-0.133430\pi$
$198$	−118.114	+	21.9524i	−0.596533	+	0.110871i
$199$	6.51531			0.0327402			0.0163701	−	0.999866i	$-0.494789\pi$
$199$	6.51531			0.0327402			0.0163701	+	0.999866i	$0.494789\pi$
$200$	−4.89898	−	2.82843i	−0.0244949	−	0.0141421i
$201$	−84.3434	−	38.8571i	−0.419619	−	0.193319i
$202$	111.674	+	193.425i	0.552843	+	0.957552i
$203$	18.0834	−	10.4405i	0.0890809	−	0.0514309i
$204$	4.78775	−	10.3923i	0.0234694	−	0.0509427i
$205$	160.636	−	278.230i	0.783591	−	1.35722i
$206$			41.2048i			0.200024i
$207$	−15.5227	−	83.5189i	−0.0749889	−	0.403473i
$208$	78.7878			0.378787
$209$	38.3939	+	22.1667i	0.183703	+	0.106061i
$210$	12.8411	+	139.364i	0.0611480	+	0.663639i
$211$	77.2196	+	133.748i	0.365970	+	0.633878i	0.988931	−	0.148374i	$-0.0474040\pi$
$211$	77.2196	+	133.748i	0.365970	+	0.633878i	−0.622961	+	0.782253i	$0.714071\pi$
$212$	16.5153	−	9.53512i	0.0779024	−	0.0449770i
$213$	148.788	+	210.418i	0.698534	+	0.987876i
$214$	121.485	−	210.418i	0.567685	−	0.983260i
$215$		−	4.96021i		−	0.0230707i
$216$	−73.4847	+	20.7846i	−0.340207	+	0.0962250i
$217$	−260.576			−1.20081
$218$	−142.404	−	82.2170i	−0.653230	−	0.377142i
$219$	−235.373	+	166.434i	−1.07476	+	0.759973i
$220$	−49.0454	−	84.9491i	−0.222934	−	0.386132i
$221$	−32.5301	+	18.7813i	−0.147195	+	0.0849831i
$222$	−73.1010	+	6.73555i	−0.329284	+	0.0303403i
$223$	−46.3865	+	80.3437i	−0.208011	+	0.360286i	−0.951088	−	0.308920i	$-0.900032\pi$
$223$	−46.3865	+	80.3437i	−0.208011	+	0.360286i	0.743077	+	0.669206i	$0.233366\pi$
$224$			35.9124i			0.160323i
$225$	−11.6969	−	13.6814i	−0.0519864	−	0.0608064i
$226$	−286.045			−1.26569
$227$	147.053	+	84.9010i	0.647810	+	0.374013i	0.787617	−	0.616166i	$-0.211315\pi$
$227$	147.053	+	84.9010i	0.647810	+	0.374013i	−0.139807	+	0.990179i	$0.544648\pi$
$228$	25.5959	+	11.7921i	0.112263	+	0.0517197i
$229$	−203.772	−	352.944i	−0.889836	−	1.54124i	−0.840068	−	0.542480i	$-0.817485\pi$
$229$	−203.772	−	352.944i	−0.889836	−	1.54124i	−0.0497675	−	0.998761i	$-0.515848\pi$
$230$	60.0681	−	34.6803i	0.261166	−	0.150784i
$231$	−75.2196	+	163.272i	−0.325626	+	0.706805i
$232$	−4.65153	+	8.05669i	−0.0200497	+	0.0347271i
$233$		−	15.2562i		−	0.0654772i	−0.999464	−	0.0327386i	$-0.989577\pi$
$233$		−	15.2562i		−	0.0654772i	0.999464	−	0.0327386i	$-0.0104229\pi$
$234$	236.363	+	83.5670i	1.01010	+	0.357124i
$235$	73.3179			0.311991
$236$	158.530	+	91.5274i	0.671738	+	0.387828i
$237$	8.18673	+	88.8507i	0.0345432	+	0.374897i
$238$	−8.56072	−	14.8276i	−0.0359694	−	0.0623008i
$239$	48.9620	−	28.2682i	0.204862	−	0.118277i	−0.394059	−	0.919085i	$-0.628930\pi$
$239$	48.9620	−	28.2682i	0.204862	−	0.118277i	0.598921	+	0.800808i	$0.295596\pi$
$240$	−36.0000	−	50.9117i	−0.150000	−	0.212132i
$241$	−42.1061	+	72.9299i	−0.174714	+	0.302614i	−0.940062	−	0.341003i	$-0.889233\pi$
$241$	−42.1061	+	72.9299i	−0.174714	+	0.302614i	0.765348	+	0.643617i	$0.222567\pi$
$242$			45.1264i			0.186473i
$243$	−242.499	−	15.5885i	−0.997940	−	0.0641500i
$244$	150.182			0.615498
$245$	−39.1362	−	22.5953i	−0.159740	−	0.0922258i
$246$	214.182	−	151.449i	0.870657	−	0.615647i
$247$	−46.2577	−	80.1206i	−0.187278	−	0.324375i
$248$	100.540	−	58.0470i	0.405404	−	0.234060i
$249$	−262.606	+	24.1966i	−1.05464	+	0.0971750i
$250$	−84.5074	+	146.371i	−0.338030	+	0.585484i
$251$		−	218.903i		−	0.872123i	−0.899917	−	0.436062i	$-0.856373\pi$
$251$		−	218.903i		−	0.872123i	0.899917	−	0.436062i	$-0.143627\pi$
$252$	−38.0908	+	107.737i	−0.151154	+	0.427528i
$253$	89.0908			0.352138
$254$	−12.3587	−	7.13528i	−0.0486562	−	0.0280917i
$255$	27.0000	+	12.4389i	0.105882	+	0.0487802i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−11.1061	+	6.41212i	−0.0432145	+	0.0249499i	−0.521452	−	0.853281i	$-0.674609\pi$
$257$	−11.1061	+	6.41212i	−0.0432145	+	0.0249499i	0.478237	+	0.878231i	$0.341276\pi$
$258$	1.69464	−	3.67840i	0.00656839	−	0.0142574i
$259$	−54.9240	+	95.1311i	−0.212062	+	0.367302i
$260$			204.697i			0.787295i
$261$	−22.5000	+	19.2364i	−0.0862069	+	0.0737026i
$262$	−7.01479			−0.0267740
$263$	291.386	+	168.232i	1.10793	+	0.639666i	0.938293	−	0.345840i	$-0.112406\pi$
$263$	291.386	+	168.232i	1.10793	+	0.639666i	0.169640	+	0.985506i	$0.445739\pi$
$264$	−7.34847	−	79.7530i	−0.0278351	−	0.302095i
$265$	24.7730	+	42.9080i	0.0934829	+	0.161917i
$266$	36.5199	−	21.0848i	0.137293	−	0.0792661i
$267$	−71.6663	−	101.351i	−0.268413	−	0.379594i
$268$	30.9546	−	53.6149i	0.115502	−	0.200056i
$269$		−	60.4468i		−	0.224709i	−0.993668	−	0.112355i	$-0.964161\pi$
$269$		−	60.4468i		−	0.224709i	0.993668	−	0.112355i	$-0.0358393\pi$
$270$	−54.0000	−	190.919i	−0.200000	−	0.707107i
$271$	274.636			1.01342			0.506708	−	0.862118i	$-0.330862\pi$
$271$	274.636			1.01342			0.506708	+	0.862118i	$0.330862\pi$
$272$	6.60612	+	3.81405i	0.0242872	+	0.0140222i
$273$	306.297	−	216.585i	1.12197	−	0.793352i
$274$	−165.947	−	287.428i	−0.605645	−	1.04901i
$275$	16.3485	−	9.43879i	0.0594490	−	0.0343229i
$276$	56.3939	−	5.19615i	0.204326	−	0.0188266i
$277$	24.5000	−	42.4352i	0.0884477	−	0.153196i	−0.818407	−	0.574638i	$-0.805143\pi$
$277$	24.5000	−	42.4352i	0.0884477	−	0.153196i	0.906855	+	0.421442i	$0.138476\pi$
$278$			150.656i			0.541929i
$279$	363.189	−	67.5018i	1.30175	−	0.241942i
$280$	−93.3031			−0.333225
$281$	−297.121	−	171.543i	−1.05737	−	0.610473i	−0.132666	−	0.991161i	$-0.542354\pi$
$281$	−297.121	−	171.543i	−1.05737	−	0.610473i	−0.924704	+	0.380688i	$0.875687\pi$
$282$	54.3712	+	25.0489i	0.192806	+	0.0888259i
$283$	171.704	+	297.401i	0.606729	+	1.05089i	0.991776	+	0.127988i	$0.0408521\pi$
$283$	171.704	+	297.401i	0.606729	+	1.05089i	−0.385047	+	0.922897i	$0.625815\pi$
$284$	−148.788	+	85.9026i	−0.523901	+	0.302474i
$285$	−30.6367	+	66.5001i	−0.107497	+	0.233334i
$286$	−131.462	+	227.699i	−0.459657	+	0.796150i
$287$		−	392.519i		−	1.36766i
$288$	−9.30306	−	50.0545i	−0.0323023	−	0.173800i
$289$	285.363			0.987416
$290$	−20.9319	−	12.0850i	−0.0721789	−	0.0416725i
$291$	26.3911	+	286.422i	0.0906910	+	0.984270i
$292$	−96.0908	−	166.434i	−0.329078	−	0.569980i
$293$	−248.076	+	143.226i	−0.846674	+	0.488828i	−0.859527	−	0.511090i	$-0.829242\pi$
$293$	−248.076	+	143.226i	−0.846674	+	0.488828i	0.0128532	+	0.999917i	$0.495909\pi$
$294$	−21.3031	−	30.1271i	−0.0724594	−	0.102473i
$295$	−237.795	+	411.873i	−0.806085	+	1.39618i
$296$		−	48.9404i		−	0.165339i
$297$	62.5454	−	247.053i	0.210591	−	0.831829i
$298$	148.652			0.498831
$299$	−161.007	−	92.9577i	−0.538486	−	0.310895i
$300$	9.79796	−	6.92820i	0.0326599	−	0.0230940i
$301$	−3.03010	−	5.24829i	−0.0100668	−	0.0174362i
$302$	−349.330	+	201.686i	−1.15672	+	0.667834i
$303$	−471.795	+	43.4714i	−1.55708	+	0.143470i
$304$	−9.39388	+	16.2707i	−0.0309009	+	0.0535219i
$305$			390.183i			1.27929i
$306$	15.7730	+	18.4490i	0.0515456	+	0.0602908i
$307$	154.091			0.501924			0.250962	−	0.967997i	$-0.419253\pi$
$307$	154.091			0.501924			0.250962	+	0.967997i	$0.419253\pi$
$308$	−103.788	−	59.9219i	−0.336973	−	0.194552i
$309$	−79.3888	−	36.5746i	−0.256922	−	0.118364i
$310$	150.810	+	261.211i	0.486485	+	0.842617i
$311$	−62.3411	+	35.9926i	−0.200454	+	0.115732i	−0.596867	−	0.802340i	$-0.703588\pi$
$311$	−62.3411	+	35.9926i	−0.200454	+	0.115732i	0.396413	+	0.918072i	$0.370255\pi$
$312$	−69.9342	+	151.799i	−0.224148	+	0.486536i
$313$	183.803	−	318.356i	0.587230	−	1.01711i	−0.407363	−	0.913266i	$-0.633552\pi$
$313$	183.803	−	318.356i	0.587230	−	1.01711i	0.994593	−	0.103846i	$-0.0331150\pi$
$314$		−	278.857i		−	0.888079i
$315$	−279.909	−	98.9628i	−0.888601	−	0.314168i
$316$	−59.4847			−0.188243
$317$	−93.1821	−	53.7987i	−0.293950	−	0.169712i	0.345772	−	0.938319i	$-0.387617\pi$
$317$	−93.1821	−	53.7987i	−0.293950	−	0.169712i	−0.639722	+	0.768607i	$0.720950\pi$
$318$	3.71173	+	40.2834i	0.0116721	+	0.126677i
$319$	−15.5227	−	26.8861i	−0.0486605	−	0.0842825i
$320$	36.0000	−	20.7846i	0.112500	−	0.0649519i
$321$	297.576	+	420.835i	0.927027	+	1.31101i
$322$	42.3712	−	73.3890i	0.131587	−	0.227916i
$323$		−	8.95717i		−	0.0277312i
$324$	25.1816	−	160.031i	0.0777211	−	0.493922i
$325$	−39.3939			−0.121212
$326$	305.035	+	176.112i	0.935691	+	0.540221i
$327$	284.808	−	201.390i	0.870973	−	0.615871i
$328$	87.4393	+	151.449i	0.266583	+	0.461736i
$329$	77.5760	−	44.7885i	0.235793	−	0.136135i
$330$	207.204	−	19.0919i	0.627892	−	0.0578542i
$331$	−8.59873	+	14.8934i	−0.0259780	+	0.0449953i	−0.878722	−	0.477334i	$-0.841603\pi$
$331$	−8.59873	+	14.8934i	−0.0259780	+	0.0449953i	0.852744	+	0.522329i	$0.174937\pi$
$332$		−	175.812i		−	0.529554i
$333$	51.9092	−	146.821i	0.155883	−	0.440905i
$334$	68.4995			0.205088
$335$	139.296	+	80.4224i	0.415808	+	0.240067i
$336$	−69.1918	−	31.8768i	−0.205928	−	0.0948714i
$337$	−182.197	−	315.574i	−0.540644	−	0.936422i	−0.998867	−	0.0475854i	$-0.984847\pi$
$337$	−182.197	−	315.574i	−0.540644	−	0.936422i	0.458223	−	0.888837i	$-0.348486\pi$
$338$	268.182	−	154.835i	0.793437	−	0.458091i
$339$	253.902	−	551.120i	0.748973	−	1.62572i
$340$	−9.90918	+	17.1632i	−0.0291447	+	0.0504800i
$341$			387.419i			1.13613i
$342$	−45.4393	+	38.8483i	−0.132863	+	0.113592i
$343$	−366.287			−1.06789
$344$	2.33826	+	1.35000i	0.00679728	+	0.00392441i
$345$	13.5000	+	146.516i	0.0391304	+	0.424683i
$346$	−71.0227	−	123.015i	−0.205268	−	0.355534i
$347$	505.234	−	291.697i	1.45601	−	0.840626i	0.457196	−	0.889366i	$-0.348854\pi$
$347$	505.234	−	291.697i	1.45601	−	0.840626i	0.998811	+	0.0487402i	$0.0155206\pi$
$348$	−11.3939	−	16.1134i	−0.0327410	−	0.0463028i
$349$	−156.379	+	270.856i	−0.448076	+	0.776091i	−0.998261	−	0.0589524i	$-0.981224\pi$
$349$	−156.379	+	270.856i	−0.448076	+	0.776091i	0.550185	+	0.835043i	$0.314557\pi$
$350$		−	17.9562i		−	0.0513034i
$351$	−370.810	+	381.221i	−1.05644	+	1.08610i
$352$	53.3939			0.151687
$353$	−32.5760	−	18.8078i	−0.0922834	−	0.0532798i	0.453148	−	0.891435i	$-0.350301\pi$
$353$	−32.5760	−	18.8078i	−0.0922834	−	0.0532798i	−0.545431	+	0.838155i	$0.683634\pi$
$354$	−317.060	+	224.195i	−0.895650	+	0.633320i
$355$	−223.182	−	386.562i	−0.628681	−	1.08891i
$356$	71.6663	−	41.3766i	0.201310	−	0.116226i
$357$	36.1668	−	3.33243i	0.101308	−	0.00933453i
$358$	201.576	−	349.139i	0.563060	−	0.975249i
$359$			294.028i			0.819019i	0.912306	+	0.409510i	$0.134300\pi$
$359$			294.028i			0.819019i	−0.912306	+	0.409510i	$0.865700\pi$
$360$	130.045	−	24.1701i	0.361237	−	0.0671391i
$361$	−338.939			−0.938889
$362$	−45.4643	−	26.2488i	−0.125592	−	0.0725105i
$363$	−86.9444	−	40.0554i	−0.239516	−	0.110346i
$364$	125.045	+	216.585i	0.343531	+	0.595014i
$365$	432.409	−	249.651i	1.18468	−	0.683976i
$366$	−133.305	+	289.353i	−0.364222	+	0.790581i
$367$	16.6135	−	28.7755i	0.0452684	−	0.0784072i	−0.842503	−	0.538691i	$-0.818919\pi$
$367$	16.6135	−	28.7755i	0.0452684	−	0.0784072i	0.887772	+	0.460284i	$0.152252\pi$
$368$			37.7552i			0.102596i
$369$	101.682	+	547.091i	0.275560	+	1.48263i
$370$	127.151			0.343651
$371$	52.4235	+	30.2667i	0.141303	+	0.0815814i
$372$	22.5959	+	245.234i	0.0607417	+	0.659230i
$373$	112.515	+	194.881i	0.301648	+	0.522470i	0.976509	−	0.215475i	$-0.0691299\pi$
$373$	112.515	+	194.881i	0.301648	+	0.522470i	−0.674861	+	0.737945i	$0.735797\pi$
$374$	−22.0454	+	12.7279i	−0.0589449	+	0.0340319i
$375$	−207.000	−	292.742i	−0.552000	−	0.780646i
$376$	−19.9546	+	34.5624i	−0.0530707	+	0.0919212i
$377$			64.7858i			0.171846i
$378$	−173.765	−	169.019i	−0.459696	−	0.447141i
$379$	−166.334			−0.438875			−0.219438	−	0.975627i	$-0.570422\pi$
$379$	−166.334			−0.438875			−0.219438	+	0.975627i	$0.570422\pi$
$380$	−42.2724	−	24.4060i	−0.111243	−	0.0642263i
$381$	24.7173	−	17.4778i	0.0648749	−	0.0458735i
$382$	12.6742	+	21.9524i	0.0331786	+	0.0574671i
$383$	−638.249	+	368.493i	−1.66645	+	0.962124i	−0.696917	+	0.717152i	$0.745445\pi$
$383$	−638.249	+	368.493i	−1.66645	+	0.962124i	−0.969530	+	0.244972i	$0.921221\pi$
$384$	33.7980	−	3.11416i	0.0880155	−	0.00810978i
$385$	155.682	−	269.648i	0.404368	−	0.700386i
$386$		−	134.992i		−	0.349721i
$387$	5.58290	+	6.53010i	0.0144261	+	0.0168736i
$388$	−191.757			−0.494219
$389$	−146.682	−	84.6867i	−0.377074	−	0.217704i	0.299471	−	0.954106i	$-0.403190\pi$
$389$	−146.682	−	84.6867i	−0.377074	−	0.217704i	−0.676544	+	0.736402i	$0.736523\pi$
$390$	−394.386	−	181.694i	−1.01125	−	0.465883i
$391$	−9.00000	−	15.5885i	−0.0230179	−	0.0398682i
$392$	21.3031	−	12.2993i	0.0543445	−	0.0313758i
$393$	6.22652	−	13.5153i	0.0158436	−	0.0343901i
$394$	−113.394	+	196.404i	−0.287802	+	0.498487i
$395$		−	154.546i		−	0.391255i
$396$	160.182	+	56.6328i	0.404499	+	0.143012i
$397$	−256.272			−0.645523			−0.322761	−	0.946480i	$-0.604611\pi$
$397$	−256.272			−0.645523			−0.322761	+	0.946480i	$0.604611\pi$
$398$	−7.97959	−	4.60702i	−0.0200492	−	0.0115754i
$399$	8.20766	+	89.0778i	0.0205706	+	0.223253i
$400$	4.00000	+	6.92820i	0.0100000	+	0.0173205i
$401$	226.364	−	130.691i	0.564498	−	0.325913i	−0.190451	−	0.981697i	$-0.560995\pi$
$401$	226.364	−	130.691i	0.564498	−	0.325913i	0.754949	+	0.655784i	$0.227662\pi$
$402$	75.8230	+	107.230i	0.188614	+	0.266741i
$403$	404.234	−	700.155i	1.00306	−	1.73736i
$404$		−	315.862i		−	0.781838i
$405$	415.772	+	65.4238i	1.02660	+	0.161540i
$406$	−29.5301			−0.0727342
$407$	141.439	+	81.6600i	0.347517	+	0.200639i
$408$	−13.2122	+	9.34247i	−0.0323830	+	0.0228982i
$409$	221.894	+	384.331i	0.542528	+	0.939686i	0.998758	+	0.0498240i	$0.0158660\pi$
$409$	221.894	+	384.331i	0.542528	+	0.939686i	−0.456230	+	0.889862i	$0.650801\pi$
$410$	−393.477	+	227.174i	−0.959699	+	0.554083i
$411$	701.082	−	64.5980i	1.70580	−	0.157173i
$412$	29.1362	−	50.4654i	0.0707190	−	0.122489i
$413$			581.059i			1.40692i
$414$	−40.0454	+	113.266i	−0.0967280	+	0.273588i
$415$	456.773			1.10066
$416$	−96.4949	−	55.7114i	−0.231959	−	0.133922i
$417$	−290.267	−	133.727i	−0.696085	−	0.320688i
$418$	−31.3485	−	54.2971i	−0.0749963	−	0.129897i
$419$	9.32525	−	5.38394i	0.0222560	−	0.0128495i	−0.488831	−	0.872379i	$-0.662576\pi$
$419$	9.32525	−	5.38394i	0.0222560	−	0.0128495i	0.511087	+	0.859529i	$0.329243\pi$
$420$	82.8184	−	179.766i	0.197187	−	0.428013i
$421$	−127.152	+	220.233i	−0.302023	+	0.523119i	−0.976594	−	0.215091i	$-0.930995\pi$
$421$	−127.152	+	220.233i	−0.302023	+	0.523119i	0.674571	+	0.738210i	$0.264328\pi$
$422$		−	218.410i		−	0.517560i
$423$	−96.5227	+	82.5221i	−0.228186	+	0.195088i
$424$	−26.9694			−0.0636070
$425$	−3.30306	−	1.90702i	−0.00777191	−	0.00448711i
$426$	−33.4393	−	362.917i	−0.0784960	−	0.851917i
$427$	238.356	+	412.844i	0.558210	+	0.966849i
$428$	−297.576	+	171.805i	−0.695270	+	0.401414i
$429$	−322.015	−	455.398i	−0.750617	−	1.06153i
$430$	−3.50740	+	6.07499i	−0.00815674	+	0.0141279i
$431$		−	698.663i		−	1.62103i	−0.585719	−	0.810514i	$-0.699188\pi$
$431$		−	698.663i		−	1.62103i	0.585719	−	0.810514i	$-0.300812\pi$
$432$	104.697	+	26.5057i	0.242354	+	0.0613557i
$433$	211.728			0.488978			0.244489	−	0.969652i	$-0.421380\pi$
$433$	211.728			0.488978			0.244489	+	0.969652i	$0.421380\pi$
$434$	319.139	+	184.255i	0.735342	+	0.424550i
$435$	41.8638	−	29.6022i	0.0962386	−	0.0680509i
$436$	116.272	+	201.390i	0.266680	+	0.461903i
$437$	38.3939	−	22.1667i	0.0878578	−	0.0507247i
$438$	405.959	−	37.4052i	0.926847	−	0.0854001i
$439$	−139.931	+	242.368i	−0.318750	+	0.552092i	−0.980228	−	0.197874i	$-0.936596\pi$
$439$	−139.931	+	242.368i	−0.318750	+	0.552092i	0.661477	+	0.749965i	$0.269930\pi$
$440$			138.721i			0.315276i
$441$	76.9546	−	14.3027i	0.174500	−	0.0324324i
$442$	53.1214			0.120184
$443$	−477.400	−	275.627i	−1.07765	−	0.622183i	−0.147391	−	0.989078i	$-0.547087\pi$
$443$	−477.400	−	275.627i	−1.07765	−	0.622183i	−0.930262	+	0.366895i	$0.880421\pi$
$444$	94.2929	+	43.4409i	0.212371	+	0.0978398i
$445$	107.499	+	186.195i	0.241572	+	0.418415i
$446$	113.623	−	65.6004i	0.254761	−	0.147086i
$447$	−131.947	+	286.405i	−0.295184	+	0.640727i
$448$	25.3939	−	43.9835i	0.0566828	−	0.0981774i
$449$		−	542.865i		−	1.20905i	−0.796585	−	0.604527i	$-0.793362\pi$
$449$		−	542.865i		−	1.20905i	0.796585	−	0.604527i	$-0.206638\pi$
$450$	4.65153	+	25.0273i	0.0103367	+	0.0556161i
$451$	−583.590			−1.29399
$452$	350.333	+	202.265i	0.775072	+	0.447488i
$453$	−78.5102	−	852.072i	−0.173312	−	1.88095i
$454$	−120.068	−	207.964i	−0.264467	−	0.458071i
$455$	−562.704	+	324.877i	−1.23671	+	0.714016i
$456$	−23.0102	−	32.5413i	−0.0504610	−	0.0713626i
$457$	−46.1821	+	79.9898i	−0.101055	+	0.175032i	−0.912120	−	0.409924i	$-0.865555\pi$
$457$	−46.1821	+	79.9898i	−0.101055	+	0.175032i	0.811065	+	0.584957i	$0.198888\pi$
$458$			576.356i			1.25842i
$459$	−49.5459	+	14.0137i	−0.107943	+	0.0305309i
$460$	−98.0908			−0.213241
$461$	−199.030	−	114.910i	−0.431736	−	0.249263i	0.268350	−	0.963321i	$-0.413522\pi$
$461$	−199.030	−	114.910i	−0.431736	−	0.249263i	−0.700086	+	0.714059i	$0.746855\pi$
$462$	207.576	−	146.778i	0.449298	−	0.317701i
$463$	255.401	+	442.368i	0.551623	+	0.955438i	0.998158	+	0.0606723i	$0.0193245\pi$
$463$	255.401	+	442.368i	0.551623	+	0.955438i	−0.446535	+	0.894766i	$0.647342\pi$
$464$	11.3939	−	6.57826i	0.0245558	−	0.0141773i
$465$	−637.136	+	58.7059i	−1.37018	+	0.126249i
$466$	−10.7878	+	18.6849i	−0.0231497	+	0.0400964i
$467$			833.657i			1.78513i	0.450915	+	0.892567i	$0.351098\pi$
$467$			833.657i			1.78513i	−0.450915	+	0.892567i	$0.648902\pi$
$468$	−230.394	−	269.482i	−0.492295	−	0.575817i
$469$	196.514			0.419007
$470$	−89.7957	−	51.8436i	−0.191055	−	0.110305i
$471$	537.270	+	247.521i	1.14070	+	0.525523i
$472$	−129.439	−	224.195i	−0.274236	−	0.474990i
$473$	−7.80306	+	4.50510i	−0.0164970	+	0.00952452i
$474$	52.8003	−	114.608i	0.111393	−	0.241790i
$475$	4.69694	−	8.13534i	0.00988829	−	0.0171270i
$476$			24.2134i			0.0508684i
$477$	−80.9082	−	28.6054i	−0.169619	−	0.0599693i
$478$	−79.9546			−0.167269
$479$	569.144	+	328.595i	1.18819	+	0.686003i	0.957895	−	0.287118i	$-0.0926972\pi$
$479$	569.144	+	328.595i	1.18819	+	0.686003i	0.230296	+	0.973121i	$0.426031\pi$
$480$	8.09082	+	87.8097i	0.0168559	+	0.182937i
$481$	−170.409	−	295.156i	−0.354280	−	0.613631i
$482$	103.139	−	59.5471i	0.213980	−	0.123542i
$483$	103.788	+	146.778i	0.214881	+	0.303888i
$484$	31.9092	−	55.2683i	0.0659281	−	0.114191i
$485$		−	498.200i		−	1.02722i
$486$	285.977	+	190.565i	0.588431	+	0.392109i
$487$	−351.666			−0.722107			−0.361054	−	0.932545i	$-0.617583\pi$
$487$	−351.666			−0.722107			−0.361054	+	0.932545i	$0.617583\pi$
$488$	−183.934	−	106.194i	−0.376914	−	0.217612i
$489$	−610.070	+	431.385i	−1.24759	+	0.882178i
$490$	31.9546	+	55.3470i	0.0652135	+	0.112953i
$491$	212.539	−	122.709i	0.432869	−	0.249917i	−0.267699	−	0.963503i	$-0.586263\pi$
$491$	212.539	−	122.709i	0.432869	−	0.249917i	0.700568	+	0.713586i	$0.252930\pi$
$492$	−369.409	+	34.0374i	−0.750831	+	0.0691818i
$493$	−3.13622	+	5.43210i	−0.00636151	+	0.0110185i
$494$			130.836i			0.264851i
$495$	−147.136	+	416.164i	−0.297245	+	0.840736i
$496$	−164.182			−0.331011
$497$	−472.287	−	272.675i	−0.950276	−	0.548642i
$498$	338.734	+	156.056i	0.680190	+	0.313365i
$499$	−315.113	−	545.792i	−0.631489	−	1.09377i	−0.987247	−	0.159193i	$-0.949111\pi$
$499$	−315.113	−	545.792i	−0.631489	−	1.09377i	0.355758	−	0.934578i	$-0.384223\pi$
$500$	207.000	−	119.512i	0.414000	−	0.239023i
$501$	−60.8020	+	131.977i	−0.121361	+	0.263427i
$502$	−154.788	+	268.100i	−0.308342	+	0.534064i
$503$		−	286.891i		−	0.570360i	−0.958474	−	0.285180i	$-0.907947\pi$
$503$		−	286.891i		−	0.570360i	0.958474	−	0.285180i	$-0.0920534\pi$
$504$	122.833	−	105.016i	0.243717	−	0.208365i
$505$	820.635			1.62502
$506$	−109.114	−	62.9967i	−0.215639	−	0.124499i
$507$	60.2724	+	654.137i	0.118881	+	1.29021i
$508$	10.0908	+	17.4778i	0.0198638	+	0.0344051i
$509$	755.454	−	436.161i	1.48419	−	0.856898i	0.484353	−	0.874873i	$-0.339055\pi$
$509$	755.454	−	436.161i	1.48419	−	0.856898i	0.999838	+	0.0179741i	$0.00572163\pi$
$510$	−24.2724	−	34.3264i	−0.0475930	−	0.0673067i
$511$	305.015	−	528.301i	0.596898	−	1.03386i
$512$			22.6274i			0.0441942i
$513$	−34.5153	−	122.030i	−0.0672813	−	0.237875i
$514$	18.1362			0.0352845
$515$	131.113	+	75.6981i	0.254588	+	0.146987i
$516$	−4.67653	+	3.30680i	−0.00906304	+	0.00640854i
$517$	−66.5908	−	115.339i	−0.128802	−	0.223092i
$518$	134.536	−	77.6742i	0.259721	−	0.149950i
$519$	300.053	−	27.6470i	0.578136	−	0.0532697i
$520$	144.742	−	250.701i	0.278351	−	0.482117i
$521$		−	206.132i		−	0.395646i	−0.980238	−	0.197823i	$-0.936613\pi$
$521$		−	206.132i		−	0.395646i	0.980238	−	0.197823i	$-0.0633872\pi$
$522$	41.1589	−	7.64974i	0.0788485	−	0.0146547i
$523$	884.817			1.69181			0.845906	−	0.533333i	$-0.179061\pi$
$523$	884.817			1.69181			0.845906	+	0.533333i	$0.179061\pi$
$524$	8.59133	+	4.96021i	0.0163957	+	0.00946604i
$525$	34.5959	+	15.9384i	0.0658970	+	0.0303589i
$526$	−237.916	−	412.083i	−0.452312	−	0.783427i
$527$	67.7878	−	39.1373i	0.128630	−	0.0742643i
$528$	−47.3939	+	102.873i	−0.0897611	+	0.194836i
$529$	−219.955	+	380.973i	−0.415793	+	0.720175i
$530$		−	70.0685i		−	0.132205i
$531$	−150.523	−	809.877i	−0.283470	−	1.52519i
$532$	−59.6367			−0.112099
$533$	1054.68	+	608.920i	1.97876	+	1.14244i
$534$	16.1066	+	174.805i	0.0301622	+	0.327351i
$535$	−446.363	−	773.124i	−0.834324	−	1.44509i
$536$	−75.8230	+	43.7764i	−0.141461	+	0.0816724i
$537$	493.757	+	698.278i	0.919473	+	1.30033i
$538$	−42.7423	+	74.0319i	−0.0794467	+	0.137606i
$539$			82.0886i			0.152298i
$540$	−68.8638	+	272.011i	−0.127526	+	0.503723i
$541$	−509.151			−0.941129			−0.470565	−	0.882365i	$-0.655950\pi$
$541$	−509.151			−0.941129			−0.470565	+	0.882365i	$0.655950\pi$
$542$	−336.359	−	194.197i	−0.620588	−	0.358297i
$543$	90.9286	−	64.2962i	0.167456	−	0.118409i
$544$	−5.39388	−	9.34247i	−0.00991521	−	0.0171737i
$545$	−523.226	+	302.085i	−0.960048	+	0.554284i
$546$	−528.285	+	48.6764i	−0.967555	+	0.0891509i
$547$	−274.022	+	474.620i	−0.500955	+	0.867679i	0.499045	+	0.866576i	$0.333684\pi$
$547$	−274.022	+	474.620i	−0.500955	+	0.867679i	−0.999999	+	0.00110267i	$0.999649\pi$
$548$			469.368i			0.856511i
$549$	−439.166	−	513.675i	−0.799939	−	0.935656i
$550$	−26.6969			−0.0485399
$551$	−13.3791	−	7.72442i	−0.0242815	−	0.0140189i
$552$	−72.7423	−	33.5125i	−0.131780	−	0.0607111i
$553$	−94.4092	−	163.522i	−0.170722	−	0.295699i
$554$	−60.0125	+	34.6482i	−0.108326	+	0.0625419i
$555$	−112.863	+	244.980i	−0.203356	+	0.441405i
$556$	106.530	−	184.516i	0.191601	−	0.331862i
$557$			406.542i			0.729879i	0.931031	+	0.364939i	$0.118910\pi$
$557$			406.542i			0.729879i	−0.931031	+	0.364939i	$0.881090\pi$
$558$	−492.545	−	174.141i	−0.882697	−	0.312080i
$559$	18.8025			0.0336360
$560$	114.272	+	65.9752i	0.204058	+	0.117813i
$561$	−4.95459	−	53.7722i	−0.00883172	−	0.0958507i
$562$	242.598	+	420.192i	0.431669	+	0.747673i
$563$	−525.220	+	303.236i	−0.932895	+	0.538607i	−0.887726	−	0.460372i	$-0.847716\pi$
$563$	−525.220	+	303.236i	−0.932895	+	0.538607i	−0.0451687	+	0.998979i	$0.514383\pi$
$564$	−48.8786	−	69.1247i	−0.0866641	−	0.122562i
$565$	−525.499	+	910.191i	−0.930087	+	1.61096i
$566$		−	485.653i		−	0.858045i
$567$	479.886	−	184.764i	0.846360	−	0.325863i
$568$	242.969			0.427763
$569$	−224.954	−	129.877i	−0.395350	−	0.228255i	0.289126	−	0.957291i	$-0.406635\pi$
$569$	−224.954	−	129.877i	−0.395350	−	0.228255i	−0.684476	+	0.729036i	$0.739969\pi$
$570$	84.5449	−	59.7823i	0.148324	−	0.104881i
$571$	43.9166	+	76.0657i	0.0769117	+	0.133215i	0.901916	−	0.431911i	$-0.142161\pi$
$571$	43.9166	+	76.0657i	0.0769117	+	0.133215i	−0.825004	+	0.565126i	$0.808827\pi$
$572$	322.015	−	185.915i	0.562963	−	0.325027i
$573$	−53.5454	+	4.93369i	−0.0934475	+	0.00861029i
$574$	−277.553	+	480.736i	−0.483541	+	0.837518i
$575$		−	18.8776i		−	0.0328306i
$576$	−24.0000	+	67.8823i	−0.0416667	+	0.117851i
$577$	−132.091			−0.228927			−0.114463	−	0.993427i	$-0.536515\pi$
$577$	−132.091			−0.228927			−0.114463	+	0.993427i	$0.536515\pi$
$578$	−349.497	−	201.782i	−0.604666	−	0.349104i
$579$	260.088	+	119.823i	0.449202	+	0.206948i
$580$	17.0908	+	29.6022i	0.0294669	+	0.0510382i
$581$	483.302	−	279.034i	0.831844	−	0.480266i
$582$	170.209	−	369.456i	0.292455	−	0.634804i
$583$	45.0000	−	77.9423i	0.0771870	−	0.133692i
$584$			271.786i			0.465387i
$585$	700.136	−	598.581i	1.19681	−	1.02322i
$586$	405.106			0.691306
$587$	−491.614	−	283.833i	−0.837502	−	0.483532i	0.0189125	−	0.999821i	$-0.493980\pi$
$587$	−491.614	−	283.833i	−0.837502	−	0.483532i	−0.856414	+	0.516289i	$0.827313\pi$
$588$	4.78775	+	51.9615i	0.00814244	+	0.0883699i
$589$	96.3939	+	166.959i	0.163657	+	0.283462i
$590$	582.477	−	336.293i	0.987249	−	0.569988i
$591$	−277.757	−	392.808i	−0.469978	−	0.664650i
$592$	−34.6061	+	59.9396i	−0.0584563	+	0.101249i
$593$			77.0321i			0.129902i	0.997888	+	0.0649512i	$0.0206892\pi$
$593$			77.0321i			0.129902i	−0.997888	+	0.0649512i	$0.979311\pi$
$594$	−251.295	+	258.351i	−0.423056	+	0.434934i
$595$	−62.9082			−0.105728
$596$	−182.060	−	105.113i	−0.305470	−	0.176363i
$597$	15.9592	−	11.2848i	0.0267323	−	0.0189026i
$598$	131.462	+	227.699i	0.219836	+	0.380767i
$599$	−764.917	+	441.625i	−1.27699	+	0.737270i	−0.976294	−	0.216450i	$-0.930552\pi$
$599$	−764.917	+	441.625i	−1.27699	+	0.737270i	−0.300696	+	0.953720i	$0.597219\pi$
$600$	−16.8990	+	1.55708i	−0.0281650	+	0.00259513i
$601$	397.545	−	688.569i	0.661473	−	1.14571i	−0.318755	−	0.947837i	$-0.603265\pi$
$601$	397.545	−	688.569i	0.661473	−	1.14571i	0.980229	−	0.197868i	$-0.0634018\pi$
$602$			8.57042i			0.0142366i
$603$	−273.901	+	50.9068i	−0.454230	+	0.0844226i
$604$	570.454			0.944460
$605$	143.591	+	82.9025i	0.237341	+	0.137029i
$606$	608.568	+	280.368i	1.00424	+	0.462654i
$607$	148.372	+	256.987i	0.244434	+	0.423373i	0.961972	−	0.273147i	$-0.0880644\pi$
$607$	148.372	+	256.987i	0.244434	+	0.423373i	−0.717538	+	0.696519i	$0.754731\pi$
$608$	23.0102	−	13.2849i	0.0378457	−	0.0218502i
$609$	26.2117	−	56.8952i	0.0430406	−	0.0934240i
$610$	275.901	−	477.875i	0.452297	−	0.783402i
$611$			277.924i			0.454868i
$612$	−6.27245	−	33.7485i	−0.0102491	−	0.0551446i
$613$	−517.181			−0.843688			−0.421844	−	0.906668i	$-0.638617\pi$
$613$	−517.181			−0.843688			−0.421844	+	0.906668i	$0.638617\pi$
$614$	−188.722	−	108.959i	−0.307365	−	0.177457i
$615$	−88.4319	−	959.752i	−0.143792	−	1.56057i
$616$	84.7423	+	146.778i	0.137569	+	0.238276i
$617$	−229.909	+	132.738i	−0.372623	+	0.215134i	−0.674604	−	0.738180i	$-0.735686\pi$
$617$	−229.909	+	132.738i	−0.372623	+	0.215134i	0.301981	+	0.953314i	$0.402352\pi$
$618$	71.3689	+	100.931i	0.115484	+	0.163319i
$619$	98.5227	−	170.646i	0.159164	−	0.275681i	−0.775403	−	0.631466i	$-0.782453\pi$
$619$	98.5227	−	170.646i	0.159164	−	0.275681i	0.934568	+	0.355786i	$0.115787\pi$
$620$		−	426.556i		−	0.687994i
$621$	−182.682	−	177.693i	−0.294173	−	0.286139i
$622$	101.803			0.163670
$623$	227.486	+	131.339i	0.365146	+	0.210817i
$624$	192.990	−	136.464i	0.309279	−	0.218693i
$625$	335.500	+	581.103i	0.536800	+	0.929765i
$626$	−450.224	+	259.937i	−0.719207	+	0.415234i
$627$	132.439	−	12.2030i	0.211227	−	0.0194625i
$628$	−197.182	+	341.529i	−0.313983	+	0.543835i
$629$		−	32.9973i		−	0.0524600i
$630$	272.840	+	319.130i	0.433079	+	0.506555i
$631$	−160.879			−0.254958			−0.127479	−	0.991841i	$-0.540689\pi$
$631$	−160.879			−0.254958			−0.127479	+	0.991841i	$0.540689\pi$
$632$	72.8536	+	42.0620i	0.115275	+	0.0665538i
$633$	420.808	+	193.867i	0.664783	+	0.306267i
$634$	76.0829	+	131.779i	0.120005	+	0.207854i
$635$	−45.4087	+	26.2167i	−0.0715097	+	0.0412862i
$636$	23.9388	−	51.9615i	0.0376396	−	0.0817005i
$637$	85.6515	−	148.353i	0.134461	−	0.232893i
$638$			43.9048i			0.0688164i
$639$	728.908	+	257.708i	1.14070	+	0.403299i
$640$	−58.7878			−0.0918559
$641$	−267.894	−	154.669i	−0.417931	−	0.241293i	0.276261	−	0.961083i	$-0.410905\pi$
$641$	−267.894	−	154.669i	−0.417931	−	0.241293i	−0.694192	+	0.719790i	$0.744238\pi$
$642$	−66.8786	−	725.834i	−0.104172	−	1.13058i
$643$	−197.296	−	341.726i	−0.306836	−	0.531456i	0.670832	−	0.741609i	$-0.265937\pi$
$643$	−197.296	−	341.726i	−0.306836	−	0.531456i	−0.977668	+	0.210153i	$0.932604\pi$
$644$	−103.788	+	59.9219i	−0.161161	+	0.0930464i
$645$	−8.59133	−	12.1500i	−0.0133199	−	0.0188372i
$646$	−6.33368	+	10.9703i	−0.00980445	+	0.0169818i
$647$		−	418.736i		−	0.647196i	−0.946195	−	0.323598i	$-0.895108\pi$
$647$		−	418.736i		−	0.647196i	0.946195	−	0.323598i	$-0.104892\pi$
$648$	−144.000	+	178.191i	−0.222222	+	0.274986i
$649$	863.908			1.33114
$650$	48.2474	+	27.8557i	0.0742268	+	0.0428549i
$651$	−638.277	+	451.330i	−0.980456	+	0.693287i
$652$	−249.060	−	431.385i	−0.381994	−	0.661633i
$653$	−459.621	+	265.363i	−0.703861	+	0.406375i	−0.808784	−	0.588106i	$-0.799874\pi$
$653$	−459.621	+	265.363i	−0.703861	+	0.406375i	0.104923	+	0.994480i	$0.466540\pi$
$654$	−491.221	+	45.2613i	−0.751103	+	0.0692069i
$655$	−12.8870	+	22.3209i	−0.0196748	+	0.0340778i
$656$		−	247.316i		−	0.377006i
$657$	−288.272	+	815.358i	−0.438771	+	1.24103i
$658$	−126.681			−0.192524
$659$	310.204	+	179.096i	0.470719	+	0.271770i	0.716541	−	0.697545i	$-0.245724\pi$
$659$	310.204	+	179.096i	0.470719	+	0.271770i	−0.245822	+	0.969315i	$0.579058\pi$
$660$	−267.272	−	123.133i	−0.404958	−	0.186565i
$661$	111.136	+	192.493i	0.168133	+	0.291214i	0.937763	−	0.347275i	$-0.112893\pi$
$661$	111.136	+	192.493i	0.168133	+	0.291214i	−0.769631	+	0.638489i	$0.779560\pi$
$662$	21.0625	−	12.1604i	0.0318165	−	0.0183692i
$663$	−47.1520	+	102.348i	−0.0711192	+	0.154371i
$664$	−124.318	+	215.325i	−0.187226	+	0.324284i
$665$		−	154.941i		−	0.232994i
$666$	−167.394	+	143.113i	−0.251342	+	0.214885i
$667$	−31.0454			−0.0465448
$668$	−83.8944	−	48.4365i	−0.125590	−	0.0725097i
$669$	25.5362	+	277.145i	0.0381708	+	0.414267i
$670$	−113.734	−	196.994i	−0.169753	−	0.294021i
$671$	613.810	−	354.383i	0.914769	−	0.528142i
$672$	62.2020	+	87.9670i	0.0925626	+	0.130903i
$673$	144.606	−	250.464i	0.214867	−	0.372161i	−0.738364	−	0.674402i	$-0.764401\pi$
$673$	144.606	−	250.464i	0.214867	−	0.372161i	0.953231	+	0.302241i	$0.0977348\pi$
$674$			515.331i			0.764586i
$675$	−52.3485	−	13.2528i	−0.0775533	−	0.0196338i
$676$	−437.939			−0.647838
$677$	402.227	+	232.226i	0.594131	+	0.343022i	0.766729	−	0.641971i	$-0.221883\pi$
$677$	402.227	+	232.226i	0.594131	+	0.343022i	−0.172598	+	0.984992i	$0.555216\pi$
$678$	−700.665	+	495.445i	−1.03343	+	0.730745i
$679$	−304.341	−	527.134i	−0.448220	−	0.776339i
$680$	24.2724	−	14.0137i	0.0356948	−	0.0206084i
$681$	507.257	−	46.7389i	0.744871	−	0.0686327i
$682$	273.947	−	474.490i	0.401681	−	0.695733i
$683$		−	1126.36i		−	1.64913i	−0.565767	−	0.824565i	$-0.691420\pi$
$683$		−	1126.36i		−	1.64913i	0.565767	−	0.824565i	$-0.308580\pi$
$684$	83.1214	−	15.4488i	0.121523	−	0.0225860i
$685$	−1219.45			−1.78022
$686$	448.608	+	259.004i	0.653948	+	0.377557i
$687$	−1110.46	−	511.589i	−1.61638	−	0.744671i
$688$	−1.90918	−	3.30680i	−0.00277498	−	0.00480640i
$689$	−162.650	+	93.9063i	−0.236067	+	0.136294i
$690$	87.0681	−	188.990i	0.126186	−	0.273899i
$691$	−518.841	+	898.658i	−0.750855	+	1.30052i	0.196554	+	0.980493i	$0.437025\pi$
$691$	−518.841	+	898.658i	−0.750855	+	1.30052i	−0.947409	+	0.320025i	$0.896309\pi$
$692$			200.883i			0.290293i
$693$	98.5454	+	530.217i	0.142201	+	0.765104i
$694$	−825.044			−1.18882
$695$	479.385	+	276.773i	0.689763	+	0.398235i
$696$	2.56072	+	27.7915i	0.00367919	+	0.0399303i
$697$	58.9546	+	102.112i	0.0845833	+	0.146503i
$698$	383.048	−	221.153i	0.548779	−	0.316838i
$699$	−26.4245	−	37.3699i	−0.0378033	−	0.0534619i
$700$	−12.6969	+	21.9917i	−0.0181385	+	0.0314168i
$701$			778.180i			1.11010i	0.831817	+	0.555050i	$0.187301\pi$
$701$			778.180i			1.11010i	−0.831817	+	0.555050i	$0.812699\pi$
$702$	723.712	−	204.697i	1.03093	−	0.291591i
$703$	81.2714			0.115607
$704$	−65.3939	−	37.7552i	−0.0928890	−	0.0536295i
$705$	179.591	−	126.990i	0.254739	−	0.180128i
$706$	26.5982	+	46.0695i	0.0376745	+	0.0652542i
$707$	868.296	−	501.311i	1.22814	−	0.709068i
$708$	546.848	−	50.3868i	0.772384	−	0.0711678i
$709$	586.014	−	1015.01i	0.826536	−	1.43160i	−0.0742031	−	0.997243i	$-0.523641\pi$
$709$	586.014	−	1015.01i	0.826536	−	1.43160i	0.900739	−	0.434360i	$-0.143025\pi$
$710$			631.253i			0.889089i
$711$	173.947	+	203.459i	0.244651	+	0.286159i
$712$	−117.031			−0.164369
$713$	335.515	+	193.710i	0.470568	+	0.271682i
$714$	−46.6515	−	21.4924i	−0.0653383	−	0.0301015i
$715$	483.022	+	836.619i	0.675556	+	1.17010i
$716$	−493.757	+	285.071i	−0.689605	+	0.398144i
$717$	70.9699	−	154.047i	0.0989817	−	0.214850i
$718$	207.909	−	360.109i	0.289567	−	0.501545i
$719$		−	515.416i		−	0.716851i	−0.933558	−	0.358426i	$-0.883314\pi$
$719$		−	515.416i		−	0.716851i	0.933558	−	0.358426i	$-0.116686\pi$
$720$	−176.363	−	62.3538i	−0.244949	−	0.0866025i
$721$	184.970			0.256547
$722$	415.114	+	239.666i	0.574949	+	0.331947i
$723$	23.1799	+	251.571i	0.0320607	+	0.347954i
$724$	37.1214	+	64.2962i	0.0512727	+	0.0888069i
$725$	−5.69694	+	3.28913i	−0.00785785	+	0.00453673i
$726$	78.1612	+	110.537i	0.107660	+	0.152254i
$727$	420.704	−	728.681i	0.578685	−	1.00231i	−0.416945	−	0.908932i	$-0.636899\pi$
$727$	420.704	−	728.681i	0.578685	−	1.00231i	0.995630	−	0.0933809i	$-0.0297674\pi$
$728$		−	353.682i		−	0.485827i
$729$	−621.000	+	381.838i	−0.851852	+	0.523783i
$730$	−706.120			−0.967288
$731$	1.57654	+	0.910215i	0.00215669	+	0.00124516i
$732$	367.868	−	260.122i	0.502552	−	0.355358i
$733$	−303.181	−	525.125i	−0.413617	−	0.716405i	0.581665	−	0.813428i	$-0.302401\pi$
$733$	−303.181	−	525.125i	−0.413617	−	0.716405i	−0.995282	+	0.0970229i	$0.969068\pi$
$734$	−40.6946	+	23.4951i	−0.0554423	+	0.0320096i
$735$	−135.000	+	12.4389i	−0.183673	+	0.0169237i
$736$	26.6969	−	46.2405i	0.0362730	−	0.0628267i
$737$		−	292.174i		−	0.396437i
$738$	262.318	−	741.947i	0.355444	−	1.00535i
$739$	−389.362			−0.526877			−0.263439	−	0.964676i	$-0.584857\pi$
$739$	−389.362			−0.526877			−0.263439	+	0.964676i	$0.584857\pi$
$740$	−155.728	−	89.9093i	−0.210443	−	0.121499i
$741$	−252.081	−	116.134i	−0.340190	−	0.156726i
$742$	−42.8036	−	74.1380i	−0.0576868	−	0.0999164i
$743$	904.779	−	522.375i	1.21774	−	0.703061i	0.253304	−	0.967387i	$-0.418483\pi$
$743$	904.779	−	522.375i	1.21774	−	0.703061i	0.964434	+	0.264325i	$0.0851492\pi$
$744$	145.732	−	316.326i	0.195877	−	0.425170i
$745$	273.090	−	473.006i	0.366564	−	0.634908i
$746$		−	318.240i		−	0.426595i
$747$	−601.340	+	514.116i	−0.805007	+	0.688240i
$748$	36.0000			0.0481283
$749$	−944.574	−	545.350i	−1.26111	−	0.728105i
$750$	46.5222	+	504.906i	0.0620296	+	0.673207i
$751$	645.916	+	1118.76i	0.860074	+	1.48969i	0.871857	+	0.489761i	$0.162916\pi$
$751$	645.916	+	1118.76i	0.860074	+	1.48969i	−0.0117826	+	0.999931i	$0.503751\pi$
$752$	48.8786	−	28.2201i	0.0649981	−	0.0375267i
$753$	−379.151	−	536.201i	−0.503521	−	0.712086i
$754$	45.8105	−	79.3460i	0.0607566	−	0.105233i
$755$			1482.08i			1.96302i
$756$	93.3031	+	329.876i	0.123417	+	0.436344i
$757$	1042.36			1.37697			0.688483	−	0.725252i	$-0.258277\pi$
$757$	1042.36			1.37697			0.688483	+	0.725252i	$0.258277\pi$
$758$	203.716	+	117.616i	0.268755	+	0.155166i
$759$	218.227	−	154.310i	0.287519	−	0.203307i
$760$	34.5153	+	59.7823i	0.0454149	+	0.0786609i
$761$	−281.607	+	162.586i	−0.370048	+	0.213647i	−0.673479	−	0.739206i	$-0.735201\pi$
$761$	−281.607	+	162.586i	−0.370048	+	0.213647i	0.303431	+	0.952853i	$0.401868\pi$
$762$	−42.6311	+	3.92805i	−0.0559464	+	0.00515492i
$763$	−369.076	+	639.258i	−0.483717	+	0.837822i
$764$		−	35.8481i		−	0.0469217i
$765$	87.6811	−	16.2963i	0.114616	−	0.0213023i
$766$	1042.26			1.36065
$767$	−1561.28	−	901.405i	−2.03557	−	1.17523i
$768$	−43.5959	−	20.0847i	−0.0567655	−	0.0261520i
$769$	−171.348	−	296.783i	−0.222819	−	0.385934i	0.732844	−	0.680397i	$-0.238193\pi$
$769$	−171.348	−	296.783i	−0.222819	−	0.385934i	−0.955663	+	0.294463i	$0.904859\pi$
$770$	−381.341	+	220.167i	−0.495247	+	0.285931i
$771$	−16.0982	+	34.9428i	−0.0208797	+	0.0453214i
$772$	−95.4541	+	165.331i	−0.123645	+	0.214160i
$773$		−	532.579i		−	0.688977i	−0.938791	−	0.344488i	$-0.888052\pi$
$773$		−	532.579i		−	0.688977i	0.938791	−	0.344488i	$-0.111948\pi$
$774$	−2.22016	−	11.9454i	−0.00286842	−	0.0154333i
$775$	82.0908			0.105924
$776$	234.854	+	135.593i	0.302646	+	0.174733i
$777$	30.2362	+	328.154i	0.0389140	+	0.422334i
$778$	119.765	+	207.439i	0.153940	+	0.266631i
$779$	−251.499	+	145.203i	−0.322849	+	0.186397i
$780$	354.545	+	501.402i	0.454545	+	0.642823i
$781$	−405.409	+	702.188i	−0.519089	+	0.899089i
$782$			25.4558i			0.0325522i
$783$	−21.7951	+	86.0904i	−0.0278354	+	0.109949i
$784$	−34.7878			−0.0443721
$785$	−887.317	−	512.293i	−1.13034	−	0.652602i
$786$	−17.1827	+	12.1500i	−0.0218609	+	0.0154580i
$787$	51.9768	+	90.0264i	0.0660442	+	0.114392i	0.897157	−	0.441712i	$-0.145629\pi$
$787$	51.9768	+	90.0264i	0.0660442	+	0.114392i	−0.831113	+	0.556104i	$0.812296\pi$
$788$	277.757	−	160.363i	0.352484	−	0.203507i
$789$	1005.13	−	92.6135i	1.27393	−	0.117381i
$790$	−109.280	+	189.279i	−0.138330	+	0.239594i
$791$			1284.07i			1.62335i
$792$	−156.136	−	182.626i	−0.197142	−	0.230589i
$793$	−1479.06			−1.86514
$794$	313.868	+	181.212i	0.395300	+	0.228227i
$795$	135.000	+	62.1947i	0.169811	+	0.0782324i
$796$	6.51531	+	11.2848i	0.00818506	+	0.0141769i
$797$	−956.331	+	552.138i	−1.19991	+	0.692770i	−0.960536	−	0.278156i	$-0.910277\pi$
$797$	−956.331	+	552.138i	−1.19991	+	0.692770i	−0.239378	+	0.970927i	$0.576943\pi$
$798$	52.9352	−	114.901i	0.0663349	−	0.143987i
$799$	−13.4541	+	23.3031i	−0.0168386	+	0.0291654i
$800$		−	11.3137i		−	0.0141421i
$801$	−351.092	−	124.130i	−0.438317	−	0.154968i
$802$	−369.650			−0.460911
$803$	−785.469	−	453.491i	−0.978168	−	0.564746i
$804$	−17.0408	−	184.944i	−0.0211951	−	0.230030i
$805$	−155.682	−	269.648i	−0.193393	−	0.334967i
$806$	−990.168	+	571.674i	−1.22850	+	0.709273i
$807$	−104.697	−	148.064i	−0.129736	−	0.183474i
$808$	−223.348	+	386.851i	−0.276421	+	0.478776i
$809$		−	256.465i		−	0.317015i	−0.987358	−	0.158508i	$-0.949332\pi$
$809$		−	256.465i		−	0.317015i	0.987358	−	0.158508i	$-0.0506683\pi$
$810$	−462.954	−	374.123i	−0.571548	−	0.461880i
$811$	735.362			0.906735			0.453368	−	0.891324i	$-0.350222\pi$
$811$	735.362			0.906735			0.453368	+	0.891324i	$0.350222\pi$
$812$	36.1668	+	20.8809i	0.0445404	+	0.0257154i
$813$	672.717	−	475.683i	0.827451	−	0.585096i
$814$	−115.485	−	200.025i	−0.141873	−	0.245731i
$815$	1120.77	−	647.077i	1.37518	−	0.793960i
$816$	22.7878	−	2.09967i	0.0279262	−	0.00257313i
$817$	−2.24183	+	3.88296i	−0.00274398	+	0.00475271i
$818$		−	627.611i		−	0.767250i
$819$	375.136	−	1061.05i	0.458042	−	1.29554i
$820$	642.545			0.783591
$821$	1078.45	+	622.645i	1.31358	+	0.758398i	0.982688	−	0.185269i	$-0.0593157\pi$
$821$	1078.45	+	622.645i	1.31358	+	0.758398i	0.330896	+	0.943667i	$0.392649\pi$
$822$	−904.325	−	416.624i	−1.10015	−	0.506842i
$823$	771.129	+	1335.63i	0.936973	+	1.62288i	0.771077	+	0.636742i	$0.219718\pi$
$823$	771.129	+	1335.63i	0.936973	+	1.62288i	0.165896	+	0.986143i	$0.446948\pi$
$824$	−71.3689	+	41.2048i	−0.0866127	+	0.0500059i
$825$	23.6969	−	51.4366i	0.0287236	−	0.0623474i
$826$	410.871	−	711.649i	0.497422	−	0.861560i
$827$			955.707i			1.15563i	0.816167	+	0.577815i	$0.196095\pi$
$827$			955.707i			1.15563i	−0.816167	+	0.577815i	$0.803905\pi$
$828$	129.136	−	110.405i	0.155962	−	0.133339i
$829$	1082.88			1.30625			0.653123	−	0.757252i	$-0.273458\pi$
$829$	1082.88			1.30625			0.653123	+	0.757252i	$0.273458\pi$
$830$	−559.430	−	322.987i	−0.674012	−	0.389141i
$831$	−13.4875	−	146.380i	−0.0162304	−	0.176149i
$832$	78.7878	+	136.464i	0.0946968	+	0.164020i
$833$	14.3633	−	8.29263i	0.0172428	−	0.00995514i
$834$	260.944	+	369.031i	0.312883	+	0.442483i
$835$	125.842	−	217.964i	0.150708	−	0.261035i
$836$			88.6669i			0.106061i
$837$	772.711	−	794.407i	0.923191	−	0.949112i
$838$	−15.2281			−0.0181719
$839$	903.778	+	521.797i	1.07721	+	0.621927i	0.930142	−	0.367200i	$-0.119683\pi$
$839$	903.778	+	521.797i	1.07721	+	0.621927i	0.147067	+	0.989127i	$0.453017\pi$
$840$	−228.545	+	161.606i	−0.272077	+	0.192388i
$841$	−415.091	−	718.958i	−0.493568	−	0.854885i
$842$	311.456	−	179.819i	0.369901	−	0.213562i
$843$	−1024.92	+	94.4361i	−1.21580	+	0.112024i
$844$	−154.439	+	267.497i	−0.182985	+	0.316939i
$845$		−	1137.80i		−	1.34651i
$846$	176.568	−	32.8166i	0.208709	−	0.0387903i
$847$	202.574			0.239167
$848$	33.0306	+	19.0702i	0.0389512	+	0.0224885i
$849$	935.701	+	431.079i	1.10212	+	0.507749i
$850$	2.69694	+	4.67123i	0.00317287	+	0.00549557i
$851$	141.439	−	81.6600i	0.166204	−	0.0959577i
$852$	−215.666	+	468.126i	−0.253129	+	0.549443i
$853$	−236.909	+	410.338i	−0.277736	+	0.481053i	−0.970822	−	0.239802i	$-0.922917\pi$
$853$	−236.909	+	410.338i	−0.277736	+	0.481053i	0.693086	+	0.720855i	$0.256251\pi$
$854$		−	674.172i		−	0.789429i
$855$	40.1373	+	215.956i	0.0469442	+	0.252580i
$856$	485.939			0.567685
$857$	793.939	+	458.381i	0.926417	+	0.534867i	0.885677	−	0.464303i	$-0.153695\pi$
$857$	793.939	+	458.381i	0.926417	+	0.534867i	0.0407403	+	0.999170i	$0.487028\pi$
$858$	72.3712	+	785.445i	0.0843487	+	0.915437i
$859$	−478.901	−	829.480i	−0.557510	−	0.965635i	−0.997704	−	0.0677322i	$-0.978424\pi$
$859$	−478.901	−	829.480i	−0.557510	−	0.965635i	0.440194	−	0.897903i	$-0.354910\pi$
$860$	8.59133	−	4.96021i	0.00998992	−	0.00576768i
$861$	−679.863	−	961.471i	−0.789620	−	1.11669i
$862$	−494.030	+	855.684i	−0.573120	+	0.992673i
$863$		−	524.200i		−	0.607416i	−0.952765	−	0.303708i	$-0.901775\pi$
$863$		−	524.200i		−	0.607416i	0.952765	−	0.303708i	$-0.0982247\pi$
$864$	−109.485	−	106.495i	−0.126718	−	0.123258i
$865$	−521.908			−0.603362
$866$	−259.312	−	149.714i	−0.299437	−	0.172880i
$867$	698.994	−	494.264i	0.806222	−	0.570085i
$868$	−260.576	−	451.330i	−0.300202	−	0.519965i
$869$	−243.121	+	140.366i	−0.279771	+	0.161526i
$870$	−72.2043	+	6.65293i	−0.0829935	+	0.00764705i
$871$	−304.855	+	528.025i	−0.350006	+	0.606228i
$872$		−	328.868i		−	0.377142i
$873$	560.743	+	655.878i	0.642317	+	0.751292i
$874$	−62.6969			−0.0717356
$875$	657.067	+	379.358i	0.750933	+	0.433551i
$876$	−523.646	−	241.245i	−0.597769	−	0.275393i
$877$	−503.878	−	872.742i	−0.574547	−	0.995145i	−0.996091	−	0.0883370i	$-0.971845\pi$
$877$	−503.878	−	872.742i	−0.574547	−	0.995145i	0.421543	−	0.906808i	$-0.361489\pi$
$878$	342.760	−	197.893i	0.390388	−	0.225390i
$879$	−359.583	+	780.511i	−0.409082	+	0.887954i
$880$	98.0908	−	169.898i	0.111467	−	0.193066i
$881$			1536.71i			1.74428i	0.489254	+	0.872141i	$0.337269\pi$
$881$			1536.71i			1.74428i	−0.489254	+	0.872141i	$0.662731\pi$
$882$	−104.363	−	36.8980i	−0.118326	−	0.0418345i
$883$	−294.213			−0.333197			−0.166599	−	0.986025i	$-0.553278\pi$
$883$	−294.213			−0.333197			−0.166599	+	0.986025i	$0.553278\pi$
$884$	−65.0602	−	37.5625i	−0.0735975	−	0.0424915i
$885$	130.909	+	1420.75i	0.147919	+	1.60537i
$886$	389.796	+	675.146i	0.439950	+	0.762016i
$887$	−497.794	+	287.402i	−0.561211	+	0.324015i	−0.753631	−	0.657297i	$-0.771700\pi$
$887$	−497.794	+	287.402i	−0.561211	+	0.324015i	0.192420	+	0.981313i	$0.438366\pi$
$888$	−84.7673	−	119.879i	−0.0954587	−	0.134999i
$889$	−32.0306	+	55.4787i	−0.0360299	+	0.0624057i
$890$		−	304.054i		−	0.341634i
$891$	−274.704	−	713.486i	−0.308310	−	0.800770i
$892$	−185.546			−0.208011
$893$	−57.3949	−	33.1370i	−0.0642720	−	0.0371075i
$894$	364.120	−	257.472i	0.407294	−	0.288000i
$895$	−740.636	−	1282.82i	−0.827526	−	1.43332i
$896$	−62.2020	+	35.9124i	−0.0694219	+	0.0400808i
$897$	−555.393	+	51.1741i	−0.619168	+	0.0570503i
$898$	−383.864	+	664.872i	−0.427465	+	0.740391i
$899$		−	135.004i		−	0.150171i
$900$	12.0000	−	33.9411i	0.0133333	−	0.0377124i
$901$	−18.1837			−0.0201817
$902$	714.749	+	412.661i	0.792405	+	0.457495i
$903$	−16.5125	−	7.60734i	−0.0182863	−	0.00842452i
$904$	−286.045	−	495.445i	−0.316422	−	0.548059i
$905$	−167.046	+	96.4443i	−0.184582	+	0.106568i
$906$	−506.351	+	1099.09i	−0.558886	+	1.21312i
$907$	255.037	−	441.737i	0.281187	−	0.487031i	−0.690490	−	0.723342i	$-0.742605\pi$
$907$	255.037	−	441.737i	0.281187	−	0.487031i	0.971677	+	0.236311i	$0.0759384\pi$
$908$			339.604i			0.374013i
$909$	−1080.36	+	923.656i	−1.18852	+	1.01612i
$910$	918.892			1.00977
$911$	−803.127	−	463.685i	−0.881588	−	0.508985i	−0.0104064	−	0.999946i	$-0.503313\pi$
$911$	−803.127	−	463.685i	−0.881588	−	0.508985i	−0.871182	+	0.490961i	$0.836646\pi$
$912$	5.17143	+	56.1255i	0.00567042	+	0.0615411i
$913$	−414.863	−	718.564i	−0.454396	−	0.787036i
$914$	113.123	−	65.3114i	0.123767	−	0.0714567i
$915$	675.817	+	955.750i	0.738598	+	1.04454i
$916$	407.545	−	705.888i	0.444918	−	0.770621i
$917$			31.4897i			0.0343399i
$918$	70.5903	+	17.8710i	0.0768958	+	0.0194674i
$919$	−1240.63			−1.34998			−0.674991	−	0.737826i	$-0.735853\pi$
$919$	−1240.63			−1.34998			−0.674991	+	0.737826i	$0.735853\pi$
$920$	120.136	+	69.3607i	0.130583	+	0.0753920i
$921$	377.444	−	266.893i	0.409820	−	0.289786i
$922$	162.507	+	281.471i	0.176255	+	0.305283i
$923$	1465.33	−	846.010i	1.58757	−	0.916587i
$924$	−358.015	+	32.9876i	−0.387462	+	0.0357009i
$925$	17.3031	−	29.9698i	0.0187060	−	0.0323998i
$926$		−	722.384i		−	0.780112i
$927$	−257.811	+	47.9164i	−0.278113	+	0.0516897i
$928$	−18.6061			−0.0200497
$929$	293.576	+	169.496i	0.316013	+	0.182450i	0.649614	−	0.760264i	$-0.274931\pi$
$929$	293.576	+	169.496i	0.316013	+	0.182450i	−0.333601	+	0.942714i	$0.608264\pi$
$930$	821.840	+	378.623i	0.883699	+	0.407122i
$931$	20.4245	+	35.3763i	0.0219382	+	0.0379981i
$932$	26.4245	−	15.2562i	0.0283525	−	0.0163693i
$933$	−90.3627	+	196.141i	−0.0968518	+	0.210227i
$934$	589.485	−	1021.02i	0.631140	−	1.09317i
$935$			93.5307i			0.100033i
$936$	91.6209	+	492.960i	0.0978856	+	0.526667i
$937$	1322.21			1.41111			0.705556	−	0.708655i	$-0.250698\pi$
$937$	1322.21			1.41111			0.705556	+	0.708655i	$0.250698\pi$
$938$	−240.680	−	138.957i	−0.256588	−	0.148141i
$939$	−101.185	−	1098.17i	−0.107759	−	1.16951i
$940$	73.3179	+	126.990i	0.0779977	+	0.135096i
$941$	−310.984	+	179.547i	−0.330482	+	0.190804i	−0.656055	−	0.754713i	$-0.727776\pi$
$941$	−310.984	+	179.547i	−0.330482	+	0.190804i	0.325573	+	0.945517i	$0.394443\pi$
$942$	−482.994	−	683.057i	−0.512733	−	0.725114i
$943$	−291.795	+	505.404i	−0.309433	+	0.535953i
$944$			366.110i			0.387828i
$945$	−857.043	+	242.408i	−0.906924	+	0.256517i
$946$	12.7423			0.0134697
$947$	−671.855	−	387.896i	−0.709457	−	0.409605i	0.101403	−	0.994845i	$-0.467667\pi$
$947$	−671.855	−	387.896i	−0.709457	−	0.409605i	−0.810860	+	0.585240i	$0.801000\pi$
$948$	−145.707	+	103.031i	−0.153700	+	0.108682i
$949$	946.347	+	1639.12i	0.997205	+	1.72721i
$950$	−11.5051	+	6.64247i	−0.0121106	+	0.00699208i
$951$	−321.431	+	29.6168i	−0.337992	+	0.0311428i
$952$	17.1214	−	29.6552i	0.0179847	−	0.0311504i
$953$		−	465.082i		−	0.488019i	−0.969773	−	0.244010i	$-0.921537\pi$
$953$		−	465.082i		−	0.488019i	0.969773	−	0.244010i	$-0.0784628\pi$
$954$	78.8648	+	92.2450i	0.0826675	+	0.0966928i
$955$	93.1362			0.0975248
$956$	97.9240	+	56.5364i	0.102431	+	0.0591385i
$957$	−84.5908	−	38.9711i	−0.0883917	−	0.0407222i
$958$	−464.704	−	804.891i	−0.485077	−	0.840178i
$959$	−1290.28	+	744.942i	−1.34544	+	0.776791i
$960$	52.1816	−	113.266i	0.0543559	−	0.117985i
$961$	−361.863	+	626.765i	−0.376548	+	0.652200i
$962$			481.989i			0.501028i
$963$	1457.82	+	515.416i	1.51383	+	0.535219i
$964$	−168.424			−0.174714
$965$	−429.543	−	247.997i	−0.445123	−	0.256992i
$966$	−23.3258	−	253.155i	−0.0241468	−	0.262065i
$967$	−612.113	−	1060.21i	−0.633002	−	1.09639i	−0.986935	−	0.161121i	$-0.948489\pi$
$967$	−612.113	−	1060.21i	−0.633002	−	1.09639i	0.353933	−	0.935271i	$-0.384844\pi$
$968$	−78.1612	+	45.1264i	−0.0807451	+	0.0466182i
$969$	−15.5143	−	21.9405i	−0.0160106	−	0.0226424i
$970$	−352.280	+	610.167i	−0.363176	+	0.629039i
$971$		−	658.702i		−	0.678375i	−0.940719	−	0.339188i	$-0.889848\pi$
$971$		−	658.702i		−	0.678375i	0.940719	−	0.339188i	$-0.110152\pi$
$972$	−215.499	−	435.610i	−0.221707	−	0.448158i
$973$	676.303			0.695070
$974$	430.702	+	248.666i	0.442199	+	0.255304i
$975$	−96.4949	+	68.2322i	−0.0989691	+	0.0699817i
$976$	150.182	+	260.122i	0.153875	+	0.266519i
$977$	1314.92	−	759.170i	1.34588	−	0.777042i	0.358214	−	0.933639i	$-0.383386\pi$
$977$	1314.92	−	759.170i	1.34588	−	0.777042i	0.987663	+	0.156597i	$0.0500525\pi$
$978$	1052.22	−	96.9515i	1.07589	−	0.0991325i
$979$	195.272	−	338.222i	0.199461	−	0.345477i
$980$		−	90.3812i		−	0.0922258i
$981$	348.817	−	986.604i	0.355573	−	1.00571i
$982$	−347.074			−0.353436
$983$	716.930	+	413.920i	0.729329	+	0.421078i	0.818177	−	0.574967i	$-0.194985\pi$
$983$	716.930	+	413.920i	0.729329	+	0.421078i	−0.0888477	+	0.996045i	$0.528318\pi$
$984$	476.499	+	219.524i	0.484247	+	0.223094i
$985$	416.636	+	721.634i	0.422980	+	0.732624i
$986$	7.68215	−	4.43529i	0.00779122	−	0.00449826i
$987$	112.446	−	244.075i	0.113927	−	0.247289i
$988$	92.5153	−	160.241i	0.0936390	−	0.162187i
$989$			9.01020i			0.00911041i
$990$	474.477	−	405.654i	0.479269	−	0.409751i
$991$	429.546			0.433447			0.216723	−	0.976233i	$-0.430463\pi$
$991$	429.546			0.433447			0.216723	+	0.976233i	$0.430463\pi$
$992$	201.081	+	116.094i	0.202702	+	0.117030i
$993$	4.73369	+	51.3747i	0.00476706	+	0.0517369i
$994$	385.621	+	667.915i	0.387949	+	0.671947i
$995$	−29.3189	+	16.9273i	−0.0294662	+	0.0170123i
$996$	−304.515	−	430.650i	−0.305738	−	0.432379i
$997$	347.499	−	601.886i	0.348545	−	0.603697i	−0.637447	−	0.770495i	$-0.720009\pi$
$997$	347.499	−	601.886i	0.348545	−	0.603697i	0.985991	+	0.166798i	$0.0533427\pi$
$998$			891.274i			0.893060i
$999$	−127.151	−	449.547i	−0.127278	−	0.449997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.3.d.a.11.1	yes	4
3.2	odd	2		54.3.d.a.35.2		4
4.3	odd	2		144.3.q.c.65.1		4
5.2	odd	4		450.3.k.a.299.3		8
5.3	odd	4		450.3.k.a.299.2		8
5.4	even	2		450.3.i.b.101.2		4
8.3	odd	2		576.3.q.e.65.2		4
8.5	even	2		576.3.q.f.65.1		4
9.2	odd	6		162.3.b.a.161.2		4
9.4	even	3		54.3.d.a.17.2		4
9.5	odd	6	inner	18.3.d.a.5.1	✓	4
9.7	even	3		162.3.b.a.161.3		4
12.11	even	2		432.3.q.d.305.2		4
15.2	even	4		1350.3.k.a.899.2		8
15.8	even	4		1350.3.k.a.899.3		8
15.14	odd	2		1350.3.i.b.251.1		4
24.5	odd	2		1728.3.q.d.1601.1		4
24.11	even	2		1728.3.q.c.1601.2		4
36.7	odd	6		1296.3.e.g.161.1		4
36.11	even	6		1296.3.e.g.161.3		4
36.23	even	6		144.3.q.c.113.1		4
36.31	odd	6		432.3.q.d.17.2		4
45.4	even	6		1350.3.i.b.1151.1		4
45.13	odd	12		1350.3.k.a.449.2		8
45.14	odd	6		450.3.i.b.401.2		4
45.22	odd	12		1350.3.k.a.449.3		8
45.23	even	12		450.3.k.a.149.3		8
45.32	even	12		450.3.k.a.149.2		8
72.5	odd	6		576.3.q.f.257.1		4
72.13	even	6		1728.3.q.d.449.1		4
72.59	even	6		576.3.q.e.257.2		4
72.67	odd	6		1728.3.q.c.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.1	✓	4	9.5	odd	6	inner
18.3.d.a.11.1	yes	4	1.1	even	1	trivial
54.3.d.a.17.2		4	9.4	even	3
54.3.d.a.35.2		4	3.2	odd	2
144.3.q.c.65.1		4	4.3	odd	2
144.3.q.c.113.1		4	36.23	even	6
162.3.b.a.161.2		4	9.2	odd	6
162.3.b.a.161.3		4	9.7	even	3
432.3.q.d.17.2		4	36.31	odd	6
432.3.q.d.305.2		4	12.11	even	2
450.3.i.b.101.2		4	5.4	even	2
450.3.i.b.401.2		4	45.14	odd	6
450.3.k.a.149.2		8	45.32	even	12
450.3.k.a.149.3		8	45.23	even	12
450.3.k.a.299.2		8	5.3	odd	4
450.3.k.a.299.3		8	5.2	odd	4
576.3.q.e.65.2		4	8.3	odd	2
576.3.q.e.257.2		4	72.59	even	6
576.3.q.f.65.1		4	8.5	even	2
576.3.q.f.257.1		4	72.5	odd	6
1296.3.e.g.161.1		4	36.7	odd	6
1296.3.e.g.161.3		4	36.11	even	6
1350.3.i.b.251.1		4	15.14	odd	2
1350.3.i.b.1151.1		4	45.4	even	6
1350.3.k.a.449.2		8	45.13	odd	12
1350.3.k.a.449.3		8	45.22	odd	12
1350.3.k.a.899.2		8	15.2	even	4
1350.3.k.a.899.3		8	15.8	even	4
1728.3.q.c.449.2		4	72.67	odd	6
1728.3.q.c.1601.2		4	24.11	even	2
1728.3.q.d.449.1		4	72.13	even	6
1728.3.q.d.1601.1		4	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(2.44949 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-4.50000 + 2.59808i) q^{5} +(-4.22474 + 0.389270i) q^{6} +(-3.17423 + 5.49794i) q^{7} -2.82843i q^{8} +(3.00000 - 8.48528i) q^{9} +7.34847 q^{10} +(8.17423 + 4.71940i) q^{11} +(5.44949 + 2.51059i) q^{12} +(-9.84847 - 17.0580i) q^{13} +(7.77526 - 4.48905i) q^{14} +(-6.52270 + 14.1582i) q^{15} +(-2.00000 + 3.46410i) q^{16} -1.90702i q^{17} +(-9.67423 + 8.27098i) q^{18} +4.69694 q^{19} +(-9.00000 - 5.19615i) q^{20} +(1.74745 + 18.9651i) q^{21} +(-6.67423 - 11.5601i) q^{22} +(8.17423 - 4.71940i) q^{23} +(-4.89898 - 6.92820i) q^{24} +(1.00000 - 1.73205i) q^{25} +27.8557i q^{26} +(-7.34847 - 25.9808i) q^{27} -12.6969 q^{28} +(-2.84847 - 1.64456i) q^{29} +(18.0000 - 12.7279i) q^{30} +(20.5227 + 35.5464i) q^{31} +(4.89898 - 2.82843i) q^{32} +(28.1969 - 2.59808i) q^{33} +(-1.34847 + 2.33562i) q^{34} -32.9876i q^{35} +(17.6969 - 3.28913i) q^{36} +17.3031 q^{37} +(-5.75255 - 3.32124i) q^{38} +(-53.6691 - 24.7255i) q^{39} +(7.34847 + 12.7279i) q^{40} +(-53.5454 + 30.9145i) q^{41} +(11.2702 - 24.4630i) q^{42} +(-0.477296 + 0.826701i) q^{43} +18.8776i q^{44} +(8.54541 + 45.9780i) q^{45} -13.3485 q^{46} +(-12.2196 - 7.05501i) q^{47} +(1.10102 + 11.9494i) q^{48} +(4.34847 + 7.53177i) q^{49} +(-2.44949 + 1.41421i) q^{50} +(-3.30306 - 4.67123i) q^{51} +(19.6969 - 34.1161i) q^{52} -9.53512i q^{53} +(-9.37117 + 37.0160i) q^{54} -49.0454 q^{55} +(15.5505 + 8.97809i) q^{56} +(11.5051 - 8.13534i) q^{57} +(2.32577 + 4.02834i) q^{58} +(79.2650 - 45.7637i) q^{59} +(-31.0454 + 2.86054i) q^{60} +(37.5454 - 65.0306i) q^{61} -58.0470i q^{62} +(37.1288 + 43.4281i) q^{63} -8.00000 q^{64} +(88.6362 + 51.1741i) q^{65} +(-36.3712 - 16.7563i) q^{66} +(-15.4773 - 26.8075i) q^{67} +(3.30306 - 1.90702i) q^{68} +(11.8485 - 25.7183i) q^{69} +(-23.3258 + 40.4014i) q^{70} +85.9026i q^{71} +(-24.0000 - 8.48528i) q^{72} -96.0908 q^{73} +(-21.1918 - 12.2351i) q^{74} +(-0.550510 - 5.97469i) q^{75} +(4.69694 + 8.13534i) q^{76} +(-51.8939 + 29.9609i) q^{77} +(48.2474 + 68.2322i) q^{78} +(-14.8712 + 25.7576i) q^{79} -20.7846i q^{80} +(-63.0000 - 50.9117i) q^{81} +87.4393 q^{82} +(-76.1288 - 43.9530i) q^{83} +(-31.1010 + 21.9917i) q^{84} +(4.95459 + 8.58161i) q^{85} +(1.16913 - 0.674999i) q^{86} +(-9.82577 + 0.905350i) q^{87} +(13.3485 - 23.1202i) q^{88} -41.3766i q^{89} +(22.0454 - 62.3538i) q^{90} +125.045 q^{91} +(16.3485 + 9.43879i) q^{92} +(111.838 + 51.5241i) q^{93} +(9.97730 + 17.2812i) q^{94} +(-21.1362 + 12.2030i) q^{95} +(7.10102 - 15.4135i) q^{96} +(-47.9393 + 83.0333i) q^{97} -12.2993i q^{98} +(64.5681 - 55.2025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} - 18 q^{5} - 12 q^{6} + 2 q^{7} + 12 q^{9} + 18 q^{11} + 12 q^{12} - 10 q^{13} + 36 q^{14} + 18 q^{15} - 8 q^{16} - 24 q^{18} - 40 q^{19} - 36 q^{20} - 42 q^{21} - 12 q^{22} + 18 q^{23} + 4 q^{25}+ \cdots + 126 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 - 18 * q^5 - 12 * q^6 + 2 * q^7 + 12 * q^9 + 18 * q^11 + 12 * q^12 - 10 * q^13 + 36 * q^14 + 18 * q^15 - 8 * q^16 - 24 * q^18 - 40 * q^19 - 36 * q^20 - 42 * q^21 - 12 * q^22 + 18 * q^23 + 4 * q^25 + 8 * q^28 + 18 * q^29 + 72 * q^30 + 38 * q^31 + 54 * q^33 + 24 * q^34 + 12 * q^36 + 128 * q^37 - 72 * q^38 - 102 * q^39 - 126 * q^41 - 48 * q^42 - 46 * q^43 - 54 * q^45 - 24 * q^46 + 54 * q^47 + 24 * q^48 - 12 * q^49 - 72 * q^51 + 20 * q^52 + 36 * q^54 - 108 * q^55 + 72 * q^56 + 144 * q^57 + 24 * q^58 + 126 * q^59 - 36 * q^60 + 62 * q^61 + 222 * q^63 - 32 * q^64 + 90 * q^65 - 72 * q^66 - 106 * q^67 + 72 * q^68 + 18 * q^69 - 108 * q^70 - 96 * q^72 - 208 * q^73 + 72 * q^74 - 12 * q^75 - 40 * q^76 - 90 * q^77 + 144 * q^78 + 14 * q^79 - 252 * q^81 + 144 * q^82 - 378 * q^83 - 144 * q^84 + 108 * q^85 - 108 * q^86 - 54 * q^87 + 24 * q^88 + 412 * q^91 + 36 * q^92 + 222 * q^93 + 84 * q^94 + 180 * q^95 + 48 * q^96 + 14 * q^97 + 126 * q^99

Introduction

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