LMFDB - Embedded newform 54.3.d.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(17,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, 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("54.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	54.d (of order $6$, degree $2$, not 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:	$1.47139342755$
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:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	54.17
Dual form			54.3.d.a.35.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(-3.17423 - 5.49794i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(-3.17423 - 5.49794i) q^{7} -2.82843i q^{8} +7.34847 q^{10} +(-8.17423 + 4.71940i) q^{11} +(-9.84847 + 17.0580i) q^{13} +(-7.77526 - 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702i q^{17} +4.69694 q^{19} +(9.00000 - 5.19615i) q^{20} +(-6.67423 + 11.5601i) q^{22} +(-8.17423 - 4.71940i) q^{23} +(1.00000 + 1.73205i) q^{25} +27.8557i q^{26} -12.6969 q^{28} +(2.84847 - 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-1.34847 - 2.33562i) q^{34} -32.9876i q^{35} +17.3031 q^{37} +(5.75255 - 3.32124i) q^{38} +(7.34847 - 12.7279i) q^{40} +(53.5454 + 30.9145i) q^{41} +(-0.477296 - 0.826701i) q^{43} +18.8776i q^{44} -13.3485 q^{46} +(12.2196 - 7.05501i) q^{47} +(4.34847 - 7.53177i) q^{49} +(2.44949 + 1.41421i) q^{50} +(19.6969 + 34.1161i) q^{52} -9.53512i q^{53} -49.0454 q^{55} +(-15.5505 + 8.97809i) q^{56} +(2.32577 - 4.02834i) q^{58} +(-79.2650 - 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470i q^{62} -8.00000 q^{64} +(-88.6362 + 51.1741i) q^{65} +(-15.4773 + 26.8075i) q^{67} +(-3.30306 - 1.90702i) q^{68} +(-23.3258 - 40.4014i) q^{70} +85.9026i q^{71} -96.0908 q^{73} +(21.1918 - 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(51.8939 + 29.9609i) q^{77} +(-14.8712 - 25.7576i) q^{79} -20.7846i q^{80} +87.4393 q^{82} +(76.1288 - 43.9530i) q^{83} +(4.95459 - 8.58161i) q^{85} +(-1.16913 - 0.674999i) q^{86} +(13.3485 + 23.1202i) q^{88} -41.3766i q^{89} +125.045 q^{91} +(-16.3485 + 9.43879i) q^{92} +(9.97730 - 17.2812i) q^{94} +(21.1362 + 12.2030i) q^{95} +(-47.9393 - 83.0333i) q^{97} -12.2993i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7}+O(q^{10}) $ 4 * q + 4 * q^4 + 18 * q^5 + 2 * q^7	$ 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7} - 18 q^{11} - 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 36 q^{20} - 12 q^{22} - 18 q^{23} + 4 q^{25} + 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} + 128 q^{37} + 72 q^{38} + 126 q^{41} - 46 q^{43} - 24 q^{46} - 54 q^{47} - 12 q^{49} + 20 q^{52} - 108 q^{55} - 72 q^{56} + 24 q^{58} - 126 q^{59} + 62 q^{61} - 32 q^{64} - 90 q^{65} - 106 q^{67} - 72 q^{68} - 108 q^{70} - 208 q^{73} - 72 q^{74} - 40 q^{76} + 90 q^{77} + 14 q^{79} + 144 q^{82} + 378 q^{83} + 108 q^{85} + 108 q^{86} + 24 q^{88} + 412 q^{91} - 36 q^{92} + 84 q^{94} - 180 q^{95} + 14 q^{97}+O(q^{100}) $ 4 * q + 4 * q^4 + 18 * q^5 + 2 * q^7 - 18 * q^11 - 10 * q^13 - 36 * q^14 - 8 * q^16 - 40 * q^19 + 36 * q^20 - 12 * q^22 - 18 * q^23 + 4 * q^25 + 8 * q^28 - 18 * q^29 + 38 * q^31 + 24 * q^34 + 128 * q^37 + 72 * q^38 + 126 * q^41 - 46 * q^43 - 24 * q^46 - 54 * q^47 - 12 * q^49 + 20 * q^52 - 108 * q^55 - 72 * q^56 + 24 * q^58 - 126 * q^59 + 62 * q^61 - 32 * q^64 - 90 * q^65 - 106 * q^67 - 72 * q^68 - 108 * q^70 - 208 * q^73 - 72 * q^74 - 40 * q^76 + 90 * q^77 + 14 * q^79 + 144 * q^82 + 378 * q^83 + 108 * q^85 + 108 * q^86 + 24 * q^88 + 412 * q^91 - 36 * q^92 + 84 * q^94 - 180 * q^95 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.877200	−	0.480125i	$-0.159409\pi$
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.0227998	+	0.999740i	$0.492742\pi$
$6$		0			0
$7$	−3.17423	−	5.49794i	−0.453462	−	0.785419i	0.545136	−	0.838347i	$-0.316478\pi$
$7$	−3.17423	−	5.49794i	−0.453462	−	0.785419i	−0.998598	+	0.0529281i	$0.983145\pi$
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	7.34847			0.734847
$11$	−8.17423	+	4.71940i	−0.743112	+	0.429036i	−0.823200	−	0.567752i	$-0.807813\pi$
$11$	−8.17423	+	4.71940i	−0.743112	+	0.429036i	0.0800876	+	0.996788i	$0.474480\pi$
$12$		0			0
$13$	−9.84847	+	17.0580i	−0.757575	+	1.31216i	0.186510	+	0.982453i	$0.440282\pi$
$13$	−9.84847	+	17.0580i	−0.757575	+	1.31216i	−0.944084	+	0.329704i	$0.893051\pi$
$14$	−7.77526	−	4.48905i	−0.555375	−	0.320646i
$15$		0			0
$16$	−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	$-0.0178630\pi$
$18$		0			0
$19$	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
$21$		0			0
$22$	−6.67423	+	11.5601i	−0.303374	+	0.525460i
$23$	−8.17423	−	4.71940i	−0.355402	−	0.205191i	0.311660	−	0.950194i	$-0.399115\pi$
$23$	−8.17423	−	4.71940i	−0.355402	−	0.205191i	−0.667062	+	0.745002i	$0.732448\pi$
$24$		0			0
$25$	1.00000	+	1.73205i	0.0400000	+	0.0692820i
$26$			27.8557i			1.07137i
$27$		0			0
$28$	−12.6969			−0.453462
$29$	2.84847	−	1.64456i	0.0982231	−	0.0567091i	−0.450084	−	0.892986i	$-0.648606\pi$
$29$	2.84847	−	1.64456i	0.0982231	−	0.0567091i	0.548307	+	0.836277i	$0.315273\pi$
$30$		0			0
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	−0.318061	−	0.948070i	$-0.603032\pi$
$31$	20.5227	−	35.5464i	0.662023	−	1.14666i	0.980083	−	0.198587i	$-0.0636351\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−1.34847	−	2.33562i	−0.0396609	−	0.0686946i
$35$		−	32.9876i		−	0.942503i
$36$		0			0
$37$	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
$39$		0			0
$40$	7.34847	−	12.7279i	0.183712	−	0.318198i
$41$	53.5454	+	30.9145i	1.30599	+	0.754011i	0.981424	−	0.191853i	$-0.0614498\pi$
$41$	53.5454	+	30.9145i	1.30599	+	0.754011i	0.324562	+	0.945864i	$0.394783\pi$
$42$		0			0
$43$	−0.477296	−	0.826701i	−0.0110999	−	0.0192256i	0.860422	−	0.509582i	$-0.170200\pi$
$43$	−0.477296	−	0.826701i	−0.0110999	−	0.0192256i	−0.871522	+	0.490356i	$0.836867\pi$
$44$			18.8776i			0.429036i
$45$		0			0
$46$	−13.3485			−0.290184
$47$	12.2196	−	7.05501i	0.259992	−	0.150107i	−0.364339	−	0.931267i	$-0.618705\pi$
$47$	12.2196	−	7.05501i	0.259992	−	0.150107i	0.624331	+	0.781160i	$0.285372\pi$
$48$		0			0
$49$	4.34847	−	7.53177i	0.0887443	−	0.153710i
$50$	2.44949	+	1.41421i	0.0489898	+	0.0282843i
$51$		0			0
$52$	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	$-0.0286720\pi$
$54$		0			0
$55$	−49.0454			−0.891735
$56$	−15.5505	+	8.97809i	−0.277688	+	0.160323i
$57$		0			0
$58$	2.32577	−	4.02834i	0.0400994	−	0.0694542i
$59$	−79.2650	−	45.7637i	−1.34348	−	0.775656i	−0.356160	−	0.934425i	$-0.615914\pi$
$59$	−79.2650	−	45.7637i	−1.34348	−	0.775656i	−0.987316	+	0.158769i	$0.949247\pi$
$60$		0			0
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	0.990297	+	0.138968i	$0.0443786\pi$
$61$	37.5454	+	65.0306i	0.615498	+	1.06607i	−0.374798	+	0.927106i	$0.622288\pi$
$62$		−	58.0470i		−	0.936241i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−88.6362	+	51.1741i	−1.36363	+	0.787295i
$66$		0			0
$67$	−15.4773	+	26.8075i	−0.231004	+	0.400111i	−0.958104	−	0.286421i	$-0.907535\pi$
$67$	−15.4773	+	26.8075i	−0.231004	+	0.400111i	0.727100	+	0.686532i	$0.240868\pi$
$68$	−3.30306	−	1.90702i	−0.0485744	−	0.0280445i
$69$		0			0
$70$	−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	$0.793194\pi$
$72$		0			0
$73$	−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			0
$76$	4.69694	−	8.13534i	0.0618018	−	0.107044i
$77$	51.8939	+	29.9609i	0.673946	+	0.389103i
$78$		0			0
$79$	−14.8712	−	25.7576i	−0.188243	−	0.326046i	0.756422	−	0.654084i	$-0.226946\pi$
$79$	−14.8712	−	25.7576i	−0.188243	−	0.326046i	−0.944664	+	0.328038i	$0.893612\pi$
$80$		−	20.7846i		−	0.259808i
$81$		0			0
$82$	87.4393			1.06633
$83$	76.1288	−	43.9530i	0.917215	−	0.529554i	0.0344693	−	0.999406i	$-0.489026\pi$
$83$	76.1288	−	43.9530i	0.917215	−	0.529554i	0.882745	+	0.469852i	$0.155693\pi$
$84$		0			0
$85$	4.95459	−	8.58161i	0.0582893	−	0.100960i
$86$	−1.16913	−	0.674999i	−0.0135946	−	0.00784882i
$87$		0			0
$88$	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	$-0.0746751\pi$
$90$		0			0
$91$	125.045			1.37413
$92$	−16.3485	+	9.43879i	−0.177701	+	0.102596i
$93$		0			0
$94$	9.97730	−	17.2812i	0.106141	−	0.183842i
$95$	21.1362	+	12.2030i	0.222487	+	0.128453i
$96$		0			0
$97$	−47.9393	−	83.0333i	−0.494219	−	0.856013i	0.505758	−	0.862675i	$-0.331213\pi$
$97$	−47.9393	−	83.0333i	−0.494219	−	0.856013i	−0.999978	+	0.00666202i	$0.997879\pi$
$98$		−	12.2993i		−	0.125503i
$99$		0			0
$100$	4.00000			0.0400000
$101$	136.772	−	78.9656i	1.35418	−	0.781838i	0.365350	−	0.930870i	$-0.380949\pi$
$101$	136.772	−	78.9656i	1.35418	−	0.781838i	0.988832	+	0.149032i	$0.0476159\pi$
$102$		0			0
$103$	−14.5681	+	25.2327i	−0.141438	+	0.244978i	−0.928038	−	0.372485i	$-0.878506\pi$
$103$	−14.5681	+	25.2327i	−0.141438	+	0.244978i	0.786600	+	0.617462i	$0.211839\pi$
$104$	48.2474	+	27.8557i	0.463918	+	0.267843i
$105$		0			0
$106$	−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	$0.703327\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−12.6969	+	21.9917i	−0.113366	+	0.196355i
$113$	−175.166	−	101.132i	−1.55014	−	0.894976i	−0.998129	−	0.0611424i	$-0.980526\pi$
$113$	−175.166	−	101.132i	−1.55014	−	0.894976i	−0.552015	−	0.833834i	$-0.686141\pi$
$114$		0			0
$115$	−24.5227	−	42.4746i	−0.213241	−	0.369344i
$116$		−	6.57826i		−	0.0567091i
$117$		0			0
$118$	−129.439			−1.09694
$119$	−10.4847	+	6.05334i	−0.0881067	+	0.0508684i
$120$		0			0
$121$	−15.9546	+	27.6342i	−0.131856	+	0.228382i
$122$	91.9671	+	53.0972i	0.753829	+	0.435223i
$123$		0			0
$124$	−41.0454	−	71.0927i	−0.331011	−	0.573328i
$125$		−	119.512i		−	0.956092i
$126$		0			0
$127$	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			0
$130$	−72.3712	+	125.351i	−0.556701	+	0.964235i
$131$	−4.29567	−	2.48010i	−0.0327913	−	0.0189321i	0.483515	−	0.875336i	$-0.339360\pi$
$131$	−4.29567	−	2.48010i	−0.0327913	−	0.0189321i	−0.516306	+	0.856404i	$0.672693\pi$
$132$		0			0
$133$	−14.9092	−	25.8235i	−0.112099	−	0.194161i
$134$			43.7764i			0.326690i
$135$		0			0
$136$	−5.39388			−0.0396609
$137$	−203.242	+	117.342i	−1.48352	+	0.856511i	−0.999825	−	0.0187249i	$-0.994039\pi$
$137$	−203.242	+	117.342i	−1.48352	+	0.856511i	−0.483696	+	0.875236i	$0.660706\pi$
$138$		0			0
$139$	−53.2650	+	92.2578i	−0.383202	+	0.663725i	−0.991518	−	0.129970i	$-0.958512\pi$
$139$	−53.2650	+	92.2578i	−0.383202	+	0.663725i	0.608316	+	0.793695i	$0.291845\pi$
$140$	−57.1362	−	32.9876i	−0.408116	−	0.235626i
$141$		0			0
$142$	60.7423	+	105.209i	0.427763	+	0.740907i
$143$		−	185.915i		−	1.30011i
$144$		0			0
$145$	17.0908			0.117868
$146$	−117.687	+	67.9465i	−0.806074	+	0.465387i
$147$		0			0
$148$	17.3031	−	29.9698i	0.116913	−	0.202499i
$149$	91.0301	+	52.5563i	0.610940	+	0.352727i	0.773333	−	0.634000i	$-0.218588\pi$
$149$	91.0301	+	52.5563i	0.610940	+	0.352727i	−0.162393	+	0.986726i	$0.551921\pi$
$150$		0			0
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.756828	+	0.653614i	$0.226748\pi$
$151$	142.614	+	247.014i	0.944460	+	1.63585i	0.187632	+	0.982239i	$0.439919\pi$
$152$		−	13.2849i		−	0.0874010i
$153$		0			0
$154$	84.7423			0.550275
$155$	184.704	−	106.639i	1.19164	−	0.687994i
$156$		0			0
$157$	98.5908	−	170.764i	0.627967	−	1.08767i	−0.359992	−	0.932955i	$-0.617221\pi$
$157$	98.5908	−	170.764i	0.627967	−	1.08767i	0.987959	−	0.154715i	$-0.0494460\pi$
$158$	−36.4268	−	21.0310i	−0.230549	−	0.133108i
$159$		0			0
$160$	−14.6969	−	25.4558i	−0.0918559	−	0.159099i
$161$			59.9219i			0.372186i
$162$		0			0
$163$	−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
$165$		0			0
$166$	62.1589	−	107.662i	0.374451	−	0.648569i
$167$	41.9472	+	24.2182i	0.251181	+	0.145019i	0.620305	−	0.784361i	$-0.287009\pi$
$167$	41.9472	+	24.2182i	0.251181	+	0.145019i	−0.369124	+	0.929380i	$0.620342\pi$
$168$		0			0
$169$	−109.485	−	189.633i	−0.647838	−	1.12209i
$170$		−	14.0137i		−	0.0824335i
$171$		0			0
$172$	−1.90918			−0.0110999
$173$	−86.9847	+	50.2206i	−0.502802	+	0.290293i	−0.729870	−	0.683586i	$-0.760419\pi$
$173$	−86.9847	+	50.2206i	−0.502802	+	0.290293i	0.227068	+	0.973879i	$0.427086\pi$
$174$		0			0
$175$	6.34847	−	10.9959i	0.0362770	−	0.0628336i
$176$	32.6969	+	18.8776i	0.185778	+	0.107259i
$177$		0			0
$178$	−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	$0.706794\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$	−13.3485	+	23.1202i	−0.0725460	+	0.125653i
$185$	77.8638	+	44.9547i	0.420885	+	0.242998i
$186$		0			0
$187$	9.00000	+	15.5885i	0.0481283	+	0.0833607i
$188$		−	28.2201i		−	0.150107i
$189$		0			0
$190$	34.5153			0.181660
$191$	15.5227	−	8.96204i	0.0812707	−	0.0469217i	−0.458814	−	0.888532i	$-0.651726\pi$
$191$	15.5227	−	8.96204i	0.0812707	−	0.0469217i	0.540085	+	0.841611i	$0.318392\pi$
$192$		0			0
$193$	47.7270	−	82.6657i	0.247290	−	0.428319i	−0.715483	−	0.698630i	$-0.753793\pi$
$193$	47.7270	−	82.6657i	0.247290	−	0.428319i	0.962773	+	0.270311i	$0.0871265\pi$
$194$	−117.427	−	67.7964i	−0.605293	−	0.349466i
$195$		0			0
$196$	−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	$-0.133430\pi$
$198$		0			0
$199$	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
$201$		0			0
$202$	111.674	−	193.425i	0.552843	−	0.957552i
$203$	−18.0834	−	10.4405i	−0.0890809	−	0.0514309i
$204$		0			0
$205$	160.636	+	278.230i	0.783591	+	1.35722i
$206$			41.2048i			0.200024i
$207$		0			0
$208$	78.7878			0.378787
$209$	−38.3939	+	22.1667i	−0.183703	+	0.106061i
$210$		0			0
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	−0.622961	−	0.782253i	$-0.714071\pi$
$211$	77.2196	−	133.748i	0.365970	−	0.633878i	0.988931	+	0.148374i	$0.0474040\pi$
$212$	−16.5153	−	9.53512i	−0.0779024	−	0.0449770i
$213$		0			0
$214$	121.485	+	210.418i	0.567685	+	0.983260i
$215$		−	4.96021i		−	0.0230707i
$216$		0			0
$217$	−260.576			−1.20081
$218$	142.404	−	82.2170i	0.653230	−	0.377142i
$219$		0			0
$220$	−49.0454	+	84.9491i	−0.222934	+	0.386132i
$221$	32.5301	+	18.7813i	0.147195	+	0.0849831i
$222$		0			0
$223$	−46.3865	−	80.3437i	−0.208011	−	0.360286i	0.743077	−	0.669206i	$-0.233366\pi$
$223$	−46.3865	−	80.3437i	−0.208011	−	0.360286i	−0.951088	+	0.308920i	$0.900032\pi$
$224$			35.9124i			0.160323i
$225$		0			0
$226$	−286.045			−1.26569
$227$	−147.053	+	84.9010i	−0.647810	+	0.374013i	−0.787617	−	0.616166i	$-0.788685\pi$
$227$	−147.053	+	84.9010i	−0.647810	+	0.374013i	0.139807	+	0.990179i	$0.455352\pi$
$228$		0			0
$229$	−203.772	+	352.944i	−0.889836	+	1.54124i	−0.0497675	+	0.998761i	$0.515848\pi$
$229$	−203.772	+	352.944i	−0.889836	+	1.54124i	−0.840068	+	0.542480i	$0.817485\pi$
$230$	−60.0681	−	34.6803i	−0.261166	−	0.150784i
$231$		0			0
$232$	−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	$-0.0104229\pi$
$234$		0			0
$235$	73.3179			0.311991
$236$	−158.530	+	91.5274i	−0.671738	+	0.387828i
$237$		0			0
$238$	−8.56072	+	14.8276i	−0.0359694	+	0.0623008i
$239$	−48.9620	−	28.2682i	−0.204862	−	0.118277i	0.394059	−	0.919085i	$-0.371070\pi$
$239$	−48.9620	−	28.2682i	−0.204862	−	0.118277i	−0.598921	+	0.800808i	$0.704404\pi$
$240$		0			0
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	0.765348	−	0.643617i	$-0.222567\pi$
$241$	−42.1061	−	72.9299i	−0.174714	−	0.302614i	−0.940062	+	0.341003i	$0.889233\pi$
$242$			45.1264i			0.186473i
$243$		0			0
$244$	150.182			0.615498
$245$	39.1362	−	22.5953i	0.159740	−	0.0922258i
$246$		0			0
$247$	−46.2577	+	80.1206i	−0.187278	+	0.324375i
$248$	−100.540	−	58.0470i	−0.405404	−	0.234060i
$249$		0			0
$250$	−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	$-0.143627\pi$
$252$		0			0
$253$	89.0908			0.352138
$254$	12.3587	−	7.13528i	0.0486562	−	0.0280917i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	11.1061	+	6.41212i	0.0432145	+	0.0249499i	0.521452	−	0.853281i	$-0.325391\pi$
$257$	11.1061	+	6.41212i	0.0432145	+	0.0249499i	−0.478237	+	0.878231i	$0.658724\pi$
$258$		0			0
$259$	−54.9240	−	95.1311i	−0.212062	−	0.367302i
$260$			204.697i			0.787295i
$261$		0			0
$262$	−7.01479			−0.0267740
$263$	−291.386	+	168.232i	−1.10793	+	0.639666i	−0.938293	−	0.345840i	$-0.887594\pi$
$263$	−291.386	+	168.232i	−1.10793	+	0.639666i	−0.169640	+	0.985506i	$0.554261\pi$
$264$		0			0
$265$	24.7730	−	42.9080i	0.0934829	−	0.161917i
$266$	−36.5199	−	21.0848i	−0.137293	−	0.0792661i
$267$		0			0
$268$	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	$-0.0358393\pi$
$270$		0			0
$271$	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
$273$		0			0
$274$	−165.947	+	287.428i	−0.605645	+	1.04901i
$275$	−16.3485	−	9.43879i	−0.0594490	−	0.0343229i
$276$		0			0
$277$	24.5000	+	42.4352i	0.0884477	+	0.153196i	0.906855	−	0.421442i	$-0.138476\pi$
$277$	24.5000	+	42.4352i	0.0884477	+	0.153196i	−0.818407	+	0.574638i	$0.805143\pi$
$278$			150.656i			0.541929i
$279$		0			0
$280$	−93.3031			−0.333225
$281$	297.121	−	171.543i	1.05737	−	0.610473i	0.132666	−	0.991161i	$-0.457646\pi$
$281$	297.121	−	171.543i	1.05737	−	0.610473i	0.924704	+	0.380688i	$0.124313\pi$
$282$		0			0
$283$	171.704	−	297.401i	0.606729	−	1.05089i	−0.385047	−	0.922897i	$-0.625815\pi$
$283$	171.704	−	297.401i	0.606729	−	1.05089i	0.991776	−	0.127988i	$-0.0408521\pi$
$284$	148.788	+	85.9026i	0.523901	+	0.302474i
$285$		0			0
$286$	−131.462	−	227.699i	−0.459657	−	0.796150i
$287$		−	392.519i		−	1.36766i
$288$		0			0
$289$	285.363			0.987416
$290$	20.9319	−	12.0850i	0.0721789	−	0.0416725i
$291$		0			0
$292$	−96.0908	+	166.434i	−0.329078	+	0.569980i
$293$	248.076	+	143.226i	0.846674	+	0.488828i	0.859527	−	0.511090i	$-0.170758\pi$
$293$	248.076	+	143.226i	0.846674	+	0.488828i	−0.0128532	+	0.999917i	$0.504091\pi$
$294$		0			0
$295$	−237.795	−	411.873i	−0.806085	−	1.39618i
$296$		−	48.9404i		−	0.165339i
$297$		0			0
$298$	148.652			0.498831
$299$	161.007	−	92.9577i	0.538486	−	0.310895i
$300$		0			0
$301$	−3.03010	+	5.24829i	−0.0100668	+	0.0174362i
$302$	349.330	+	201.686i	1.15672	+	0.667834i
$303$		0			0
$304$	−9.39388	−	16.2707i	−0.0309009	−	0.0535219i
$305$			390.183i			1.27929i
$306$		0			0
$307$	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
$309$		0			0
$310$	150.810	−	261.211i	0.486485	−	0.842617i
$311$	62.3411	+	35.9926i	0.200454	+	0.115732i	0.596867	−	0.802340i	$-0.296412\pi$
$311$	62.3411	+	35.9926i	0.200454	+	0.115732i	−0.396413	+	0.918072i	$0.629745\pi$
$312$		0			0
$313$	183.803	+	318.356i	0.587230	+	1.01711i	0.994593	+	0.103846i	$0.0331150\pi$
$313$	183.803	+	318.356i	0.587230	+	1.01711i	−0.407363	+	0.913266i	$0.633552\pi$
$314$		−	278.857i		−	0.888079i
$315$		0			0
$316$	−59.4847			−0.188243
$317$	93.1821	−	53.7987i	0.293950	−	0.169712i	−0.345772	−	0.938319i	$-0.612383\pi$
$317$	93.1821	−	53.7987i	0.293950	−	0.169712i	0.639722	+	0.768607i	$0.279050\pi$
$318$		0			0
$319$	−15.5227	+	26.8861i	−0.0486605	+	0.0842825i
$320$	−36.0000	−	20.7846i	−0.112500	−	0.0649519i
$321$		0			0
$322$	42.3712	+	73.3890i	0.131587	+	0.227916i
$323$		−	8.95717i		−	0.0277312i
$324$		0			0
$325$	−39.3939			−0.121212
$326$	−305.035	+	176.112i	−0.935691	+	0.540221i
$327$		0			0
$328$	87.4393	−	151.449i	0.266583	−	0.461736i
$329$	−77.5760	−	44.7885i	−0.235793	−	0.136135i
$330$		0			0
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	0.852744	−	0.522329i	$-0.174937\pi$
$331$	−8.59873	−	14.8934i	−0.0259780	−	0.0449953i	−0.878722	+	0.477334i	$0.841603\pi$
$332$		−	175.812i		−	0.529554i
$333$		0			0
$334$	68.4995			0.205088
$335$	−139.296	+	80.4224i	−0.415808	+	0.240067i
$336$		0			0
$337$	−182.197	+	315.574i	−0.540644	+	0.936422i	0.458223	+	0.888837i	$0.348486\pi$
$337$	−182.197	+	315.574i	−0.540644	+	0.936422i	−0.998867	+	0.0475854i	$0.984847\pi$
$338$	−268.182	−	154.835i	−0.793437	−	0.458091i
$339$		0			0
$340$	−9.90918	−	17.1632i	−0.0291447	−	0.0504800i
$341$			387.419i			1.13613i
$342$		0			0
$343$	−366.287			−1.06789
$344$	−2.33826	+	1.35000i	−0.00679728	+	0.00392441i
$345$		0			0
$346$	−71.0227	+	123.015i	−0.205268	+	0.355534i
$347$	−505.234	−	291.697i	−1.45601	−	0.840626i	−0.457196	−	0.889366i	$-0.651146\pi$
$347$	−505.234	−	291.697i	−1.45601	−	0.840626i	−0.998811	+	0.0487402i	$0.984479\pi$
$348$		0			0
$349$	−156.379	−	270.856i	−0.448076	−	0.776091i	0.550185	−	0.835043i	$-0.314557\pi$
$349$	−156.379	−	270.856i	−0.448076	−	0.776091i	−0.998261	+	0.0589524i	$0.981224\pi$
$350$		−	17.9562i		−	0.0513034i
$351$		0			0
$352$	53.3939			0.151687
$353$	32.5760	−	18.8078i	0.0922834	−	0.0532798i	−0.453148	−	0.891435i	$-0.649699\pi$
$353$	32.5760	−	18.8078i	0.0922834	−	0.0532798i	0.545431	+	0.838155i	$0.316366\pi$
$354$		0			0
$355$	−223.182	+	386.562i	−0.628681	+	1.08891i
$356$	−71.6663	−	41.3766i	−0.201310	−	0.116226i
$357$		0			0
$358$	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	$0.865700\pi$
$360$		0			0
$361$	−338.939			−0.938889
$362$	45.4643	−	26.2488i	0.125592	−	0.0725105i
$363$		0			0
$364$	125.045	−	216.585i	0.343531	−	0.595014i
$365$	−432.409	−	249.651i	−1.18468	−	0.683976i
$366$		0			0
$367$	16.6135	+	28.7755i	0.0452684	+	0.0784072i	0.887772	−	0.460284i	$-0.152252\pi$
$367$	16.6135	+	28.7755i	0.0452684	+	0.0784072i	−0.842503	+	0.538691i	$0.818919\pi$
$368$			37.7552i			0.102596i
$369$		0			0
$370$	127.151			0.343651
$371$	−52.4235	+	30.2667i	−0.141303	+	0.0815814i
$372$		0			0
$373$	112.515	−	194.881i	0.301648	−	0.522470i	−0.674861	−	0.737945i	$-0.735797\pi$
$373$	112.515	−	194.881i	0.301648	−	0.522470i	0.976509	+	0.215475i	$0.0691299\pi$
$374$	22.0454	+	12.7279i	0.0589449	+	0.0340319i
$375$		0			0
$376$	−19.9546	−	34.5624i	−0.0530707	−	0.0919212i
$377$			64.7858i			0.171846i
$378$		0			0
$379$	−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
$381$		0			0
$382$	12.6742	−	21.9524i	0.0331786	−	0.0574671i
$383$	638.249	+	368.493i	1.66645	+	0.962124i	0.969530	+	0.244972i	$0.0787787\pi$
$383$	638.249	+	368.493i	1.66645	+	0.962124i	0.696917	+	0.717152i	$0.254555\pi$
$384$		0			0
$385$	155.682	+	269.648i	0.404368	+	0.700386i
$386$		−	134.992i		−	0.349721i
$387$		0			0
$388$	−191.757			−0.494219
$389$	146.682	−	84.6867i	0.377074	−	0.217704i	−0.299471	−	0.954106i	$-0.596810\pi$
$389$	146.682	−	84.6867i	0.377074	−	0.217704i	0.676544	+	0.736402i	$0.263477\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.0230179	+	0.0398682i
$392$	−21.3031	−	12.2993i	−0.0543445	−	0.0313758i
$393$		0			0
$394$	−113.394	−	196.404i	−0.287802	−	0.498487i
$395$		−	154.546i		−	0.391255i
$396$		0			0
$397$	−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
$399$		0			0
$400$	4.00000	−	6.92820i	0.0100000	−	0.0173205i
$401$	−226.364	−	130.691i	−0.564498	−	0.325913i	0.190451	−	0.981697i	$-0.439005\pi$
$401$	−226.364	−	130.691i	−0.564498	−	0.325913i	−0.754949	+	0.655784i	$0.772338\pi$
$402$		0			0
$403$	404.234	+	700.155i	1.00306	+	1.73736i
$404$		−	315.862i		−	0.781838i
$405$		0			0
$406$	−29.5301			−0.0727342
$407$	−141.439	+	81.6600i	−0.347517	+	0.200639i
$408$		0			0
$409$	221.894	−	384.331i	0.542528	−	0.939686i	−0.456230	−	0.889862i	$-0.650801\pi$
$409$	221.894	−	384.331i	0.542528	−	0.939686i	0.998758	−	0.0498240i	$-0.0158660\pi$
$410$	393.477	+	227.174i	0.959699	+	0.554083i
$411$		0			0
$412$	29.1362	+	50.4654i	0.0707190	+	0.122489i
$413$			581.059i			1.40692i
$414$		0			0
$415$	456.773			1.10066
$416$	96.4949	−	55.7114i	0.231959	−	0.133922i
$417$		0			0
$418$	−31.3485	+	54.2971i	−0.0749963	+	0.129897i
$419$	−9.32525	−	5.38394i	−0.0222560	−	0.0128495i	0.488831	−	0.872379i	$-0.337424\pi$
$419$	−9.32525	−	5.38394i	−0.0222560	−	0.0128495i	−0.511087	+	0.859529i	$0.670757\pi$
$420$		0			0
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	0.674571	−	0.738210i	$-0.264328\pi$
$421$	−127.152	−	220.233i	−0.302023	−	0.523119i	−0.976594	+	0.215091i	$0.930995\pi$
$422$		−	218.410i		−	0.517560i
$423$		0			0
$424$	−26.9694			−0.0636070
$425$	3.30306	−	1.90702i	0.00777191	−	0.00448711i
$426$		0			0
$427$	238.356	−	412.844i	0.558210	−	0.966849i
$428$	297.576	+	171.805i	0.695270	+	0.401414i
$429$		0			0
$430$	−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	$-0.300812\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	116.272	−	201.390i	0.266680	−	0.461903i
$437$	−38.3939	−	22.1667i	−0.0878578	−	0.0507247i
$438$		0			0
$439$	−139.931	−	242.368i	−0.318750	−	0.552092i	0.661477	−	0.749965i	$-0.269930\pi$
$439$	−139.931	−	242.368i	−0.318750	−	0.552092i	−0.980228	+	0.197874i	$0.936596\pi$
$440$			138.721i			0.315276i
$441$		0			0
$442$	53.1214			0.120184
$443$	477.400	−	275.627i	1.07765	−	0.622183i	0.147391	−	0.989078i	$-0.452913\pi$
$443$	477.400	−	275.627i	1.07765	−	0.622183i	0.930262	+	0.366895i	$0.119579\pi$
$444$		0			0
$445$	107.499	−	186.195i	0.241572	−	0.418415i
$446$	−113.623	−	65.6004i	−0.254761	−	0.147086i
$447$		0			0
$448$	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	$-0.206638\pi$
$450$		0			0
$451$	−583.590			−1.29399
$452$	−350.333	+	202.265i	−0.775072	+	0.447488i
$453$		0			0
$454$	−120.068	+	207.964i	−0.264467	+	0.458071i
$455$	562.704	+	324.877i	1.23671	+	0.714016i
$456$		0			0
$457$	−46.1821	−	79.9898i	−0.101055	−	0.175032i	0.811065	−	0.584957i	$-0.198888\pi$
$457$	−46.1821	−	79.9898i	−0.101055	−	0.175032i	−0.912120	+	0.409924i	$0.865555\pi$
$458$			576.356i			1.25842i
$459$		0			0
$460$	−98.0908			−0.213241
$461$	199.030	−	114.910i	0.431736	−	0.249263i	−0.268350	−	0.963321i	$-0.586478\pi$
$461$	199.030	−	114.910i	0.431736	−	0.249263i	0.700086	+	0.714059i	$0.253145\pi$
$462$		0			0
$463$	255.401	−	442.368i	0.551623	−	0.955438i	−0.446535	−	0.894766i	$-0.647342\pi$
$463$	255.401	−	442.368i	0.551623	−	0.955438i	0.998158	−	0.0606723i	$-0.0193245\pi$
$464$	−11.3939	−	6.57826i	−0.0245558	−	0.0141773i
$465$		0			0
$466$	−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	$0.648902\pi$
$468$		0			0
$469$	196.514			0.419007
$470$	89.7957	−	51.8436i	0.191055	−	0.110305i
$471$		0			0
$472$	−129.439	+	224.195i	−0.274236	+	0.474990i
$473$	7.80306	+	4.50510i	0.0164970	+	0.00952452i
$474$		0			0
$475$	4.69694	+	8.13534i	0.00988829	+	0.0171270i
$476$			24.2134i			0.0508684i
$477$		0			0
$478$	−79.9546			−0.167269
$479$	−569.144	+	328.595i	−1.18819	+	0.686003i	−0.957895	−	0.287118i	$-0.907303\pi$
$479$	−569.144	+	328.595i	−1.18819	+	0.686003i	−0.230296	+	0.973121i	$0.573969\pi$
$480$		0			0
$481$	−170.409	+	295.156i	−0.354280	+	0.613631i
$482$	−103.139	−	59.5471i	−0.213980	−	0.123542i
$483$		0			0
$484$	31.9092	+	55.2683i	0.0659281	+	0.114191i
$485$		−	498.200i		−	1.02722i
$486$		0			0
$487$	−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
$489$		0			0
$490$	31.9546	−	55.3470i	0.0652135	−	0.112953i
$491$	−212.539	−	122.709i	−0.432869	−	0.249917i	0.267699	−	0.963503i	$-0.413737\pi$
$491$	−212.539	−	122.709i	−0.432869	−	0.249917i	−0.700568	+	0.713586i	$0.747070\pi$
$492$		0			0
$493$	−3.13622	−	5.43210i	−0.00636151	−	0.0110185i
$494$			130.836i			0.264851i
$495$		0			0
$496$	−164.182			−0.331011
$497$	472.287	−	272.675i	0.950276	−	0.548642i
$498$		0			0
$499$	−315.113	+	545.792i	−0.631489	+	1.09377i	0.355758	+	0.934578i	$0.384223\pi$
$499$	−315.113	+	545.792i	−0.631489	+	1.09377i	−0.987247	+	0.159193i	$0.949111\pi$
$500$	−207.000	−	119.512i	−0.414000	−	0.239023i
$501$		0			0
$502$	−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	$-0.0920534\pi$
$504$		0			0
$505$	820.635			1.62502
$506$	109.114	−	62.9967i	0.215639	−	0.124499i
$507$		0			0
$508$	10.0908	−	17.4778i	0.0198638	−	0.0344051i
$509$	−755.454	−	436.161i	−1.48419	−	0.856898i	−0.484353	−	0.874873i	$-0.660945\pi$
$509$	−755.454	−	436.161i	−1.48419	−	0.856898i	−0.999838	+	0.0179741i	$0.994278\pi$
$510$		0			0
$511$	305.015	+	528.301i	0.596898	+	1.03386i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	18.1362			0.0352845
$515$	−131.113	+	75.6981i	−0.254588	+	0.146987i
$516$		0			0
$517$	−66.5908	+	115.339i	−0.128802	+	0.223092i
$518$	−134.536	−	77.6742i	−0.259721	−	0.149950i
$519$		0			0
$520$	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	$-0.0633872\pi$
$522$		0			0
$523$	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
$525$		0			0
$526$	−237.916	+	412.083i	−0.452312	+	0.783427i
$527$	−67.7878	−	39.1373i	−0.128630	−	0.0742643i
$528$		0			0
$529$	−219.955	−	380.973i	−0.415793	−	0.720175i
$530$		−	70.0685i		−	0.132205i
$531$		0			0
$532$	−59.6367			−0.112099
$533$	−1054.68	+	608.920i	−1.97876	+	1.14244i
$534$		0			0
$535$	−446.363	+	773.124i	−0.834324	+	1.44509i
$536$	75.8230	+	43.7764i	0.141461	+	0.0816724i
$537$		0			0
$538$	−42.7423	−	74.0319i	−0.0794467	−	0.137606i
$539$			82.0886i			0.152298i
$540$		0			0
$541$	−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
$543$		0			0
$544$	−5.39388	+	9.34247i	−0.00991521	+	0.0171737i
$545$	523.226	+	302.085i	0.960048	+	0.554284i
$546$		0			0
$547$	−274.022	−	474.620i	−0.500955	−	0.867679i	−0.999999	−	0.00110267i	$-0.999649\pi$
$547$	−274.022	−	474.620i	−0.500955	−	0.867679i	0.499045	−	0.866576i	$-0.333684\pi$
$548$			469.368i			0.856511i
$549$		0			0
$550$	−26.6969			−0.0485399
$551$	13.3791	−	7.72442i	0.0242815	−	0.0140189i
$552$		0			0
$553$	−94.4092	+	163.522i	−0.170722	+	0.295699i
$554$	60.0125	+	34.6482i	0.108326	+	0.0625419i
$555$		0			0
$556$	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	$0.881090\pi$
$558$		0			0
$559$	18.8025			0.0336360
$560$	−114.272	+	65.9752i	−0.204058	+	0.117813i
$561$		0			0
$562$	242.598	−	420.192i	0.431669	−	0.747673i
$563$	525.220	+	303.236i	0.932895	+	0.538607i	0.887726	−	0.460372i	$-0.152284\pi$
$563$	525.220	+	303.236i	0.932895	+	0.538607i	0.0451687	+	0.998979i	$0.485617\pi$
$564$		0			0
$565$	−525.499	−	910.191i	−0.930087	−	1.61096i
$566$		−	485.653i		−	0.858045i
$567$		0			0
$568$	242.969			0.427763
$569$	224.954	−	129.877i	0.395350	−	0.228255i	−0.289126	−	0.957291i	$-0.593365\pi$
$569$	224.954	−	129.877i	0.395350	−	0.228255i	0.684476	+	0.729036i	$0.260031\pi$
$570$		0			0
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	−0.825004	−	0.565126i	$-0.808827\pi$
$571$	43.9166	−	76.0657i	0.0769117	−	0.133215i	0.901916	+	0.431911i	$0.142161\pi$
$572$	−322.015	−	185.915i	−0.562963	−	0.325027i
$573$		0			0
$574$	−277.553	−	480.736i	−0.483541	−	0.837518i
$575$		−	18.8776i		−	0.0328306i
$576$		0			0
$577$	−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
$579$		0			0
$580$	17.0908	−	29.6022i	0.0294669	−	0.0510382i
$581$	−483.302	−	279.034i	−0.831844	−	0.480266i
$582$		0			0
$583$	45.0000	+	77.9423i	0.0771870	+	0.133692i
$584$			271.786i			0.465387i
$585$		0			0
$586$	405.106			0.691306
$587$	491.614	−	283.833i	0.837502	−	0.483532i	−0.0189125	−	0.999821i	$-0.506020\pi$
$587$	491.614	−	283.833i	0.837502	−	0.483532i	0.856414	+	0.516289i	$0.172687\pi$
$588$		0			0
$589$	96.3939	−	166.959i	0.163657	−	0.283462i
$590$	−582.477	−	336.293i	−0.987249	−	0.569988i
$591$		0			0
$592$	−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	$0.979311\pi$
$594$		0			0
$595$	−62.9082			−0.105728
$596$	182.060	−	105.113i	0.305470	−	0.176363i
$597$		0			0
$598$	131.462	−	227.699i	0.219836	−	0.380767i
$599$	764.917	+	441.625i	1.27699	+	0.737270i	0.976294	−	0.216450i	$-0.0694479\pi$
$599$	764.917	+	441.625i	1.27699	+	0.737270i	0.300696	+	0.953720i	$0.402781\pi$
$600$		0			0
$601$	397.545	+	688.569i	0.661473	+	1.14571i	0.980229	+	0.197868i	$0.0634018\pi$
$601$	397.545	+	688.569i	0.661473	+	1.14571i	−0.318755	+	0.947837i	$0.603265\pi$
$602$			8.57042i			0.0142366i
$603$		0			0
$604$	570.454			0.944460
$605$	−143.591	+	82.9025i	−0.237341	+	0.137029i
$606$		0			0
$607$	148.372	−	256.987i	0.244434	−	0.423373i	−0.717538	−	0.696519i	$-0.754731\pi$
$607$	148.372	−	256.987i	0.244434	−	0.423373i	0.961972	+	0.273147i	$0.0880644\pi$
$608$	−23.0102	−	13.2849i	−0.0378457	−	0.0218502i
$609$		0			0
$610$	275.901	+	477.875i	0.452297	+	0.783402i
$611$			277.924i			0.454868i
$612$		0			0
$613$	−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
$615$		0			0
$616$	84.7423	−	146.778i	0.137569	−	0.238276i
$617$	229.909	+	132.738i	0.372623	+	0.215134i	0.674604	−	0.738180i	$-0.264314\pi$
$617$	229.909	+	132.738i	0.372623	+	0.215134i	−0.301981	+	0.953314i	$0.597648\pi$
$618$		0			0
$619$	98.5227	+	170.646i	0.159164	+	0.275681i	0.934568	−	0.355786i	$-0.115787\pi$
$619$	98.5227	+	170.646i	0.159164	+	0.275681i	−0.775403	+	0.631466i	$0.782453\pi$
$620$		−	426.556i		−	0.687994i
$621$		0			0
$622$	101.803			0.163670
$623$	−227.486	+	131.339i	−0.365146	+	0.210817i
$624$		0			0
$625$	335.500	−	581.103i	0.536800	−	0.929765i
$626$	450.224	+	259.937i	0.719207	+	0.415234i
$627$		0			0
$628$	−197.182	−	341.529i	−0.313983	−	0.543835i
$629$		−	32.9973i		−	0.0524600i
$630$		0			0
$631$	−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
$633$		0			0
$634$	76.0829	−	131.779i	0.120005	−	0.207854i
$635$	45.4087	+	26.2167i	0.0715097	+	0.0412862i
$636$		0			0
$637$	85.6515	+	148.353i	0.134461	+	0.232893i
$638$			43.9048i			0.0688164i
$639$		0			0
$640$	−58.7878			−0.0918559
$641$	267.894	−	154.669i	0.417931	−	0.241293i	−0.276261	−	0.961083i	$-0.589095\pi$
$641$	267.894	−	154.669i	0.417931	−	0.241293i	0.694192	+	0.719790i	$0.255762\pi$
$642$		0			0
$643$	−197.296	+	341.726i	−0.306836	+	0.531456i	−0.977668	−	0.210153i	$-0.932604\pi$
$643$	−197.296	+	341.726i	−0.306836	+	0.531456i	0.670832	+	0.741609i	$0.265937\pi$
$644$	103.788	+	59.9219i	0.161161	+	0.0930464i
$645$		0			0
$646$	−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	$-0.104892\pi$
$648$		0			0
$649$	863.908			1.33114
$650$	−48.2474	+	27.8557i	−0.0742268	+	0.0428549i
$651$		0			0
$652$	−249.060	+	431.385i	−0.381994	+	0.661633i
$653$	459.621	+	265.363i	0.703861	+	0.406375i	0.808784	−	0.588106i	$-0.200126\pi$
$653$	459.621	+	265.363i	0.703861	+	0.406375i	−0.104923	+	0.994480i	$0.533460\pi$
$654$		0			0
$655$	−12.8870	−	22.3209i	−0.0196748	−	0.0340778i
$656$		−	247.316i		−	0.377006i
$657$		0			0
$658$	−126.681			−0.192524
$659$	−310.204	+	179.096i	−0.470719	+	0.271770i	−0.716541	−	0.697545i	$-0.754276\pi$
$659$	−310.204	+	179.096i	−0.470719	+	0.271770i	0.245822	+	0.969315i	$0.420942\pi$
$660$		0			0
$661$	111.136	−	192.493i	0.168133	−	0.291214i	−0.769631	−	0.638489i	$-0.779560\pi$
$661$	111.136	−	192.493i	0.168133	−	0.291214i	0.937763	+	0.347275i	$0.112893\pi$
$662$	−21.0625	−	12.1604i	−0.0318165	−	0.0183692i
$663$		0			0
$664$	−124.318	−	215.325i	−0.187226	−	0.324284i
$665$		−	154.941i		−	0.232994i
$666$		0			0
$667$	−31.0454			−0.0465448
$668$	83.8944	−	48.4365i	0.125590	−	0.0725097i
$669$		0			0
$670$	−113.734	+	196.994i	−0.169753	+	0.294021i
$671$	−613.810	−	354.383i	−0.914769	−	0.528142i
$672$		0			0
$673$	144.606	+	250.464i	0.214867	+	0.372161i	0.953231	−	0.302241i	$-0.0977348\pi$
$673$	144.606	+	250.464i	0.214867	+	0.372161i	−0.738364	+	0.674402i	$0.764401\pi$
$674$			515.331i			0.764586i
$675$		0			0
$676$	−437.939			−0.647838
$677$	−402.227	+	232.226i	−0.594131	+	0.343022i	−0.766729	−	0.641971i	$-0.778117\pi$
$677$	−402.227	+	232.226i	−0.594131	+	0.343022i	0.172598	+	0.984992i	$0.444784\pi$
$678$		0			0
$679$	−304.341	+	527.134i	−0.448220	+	0.776339i
$680$	−24.2724	−	14.0137i	−0.0356948	−	0.0206084i
$681$		0			0
$682$	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	$-0.308580\pi$
$684$		0			0
$685$	−1219.45			−1.78022
$686$	−448.608	+	259.004i	−0.653948	+	0.377557i
$687$		0			0
$688$	−1.90918	+	3.30680i	−0.00277498	+	0.00480640i
$689$	162.650	+	93.9063i	0.236067	+	0.136294i
$690$		0			0
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	−0.947409	−	0.320025i	$-0.896309\pi$
$691$	−518.841	−	898.658i	−0.750855	−	1.30052i	0.196554	−	0.980493i	$-0.437025\pi$
$692$			200.883i			0.290293i
$693$		0			0
$694$	−825.044			−1.18882
$695$	−479.385	+	276.773i	−0.689763	+	0.398235i
$696$		0			0
$697$	58.9546	−	102.112i	0.0845833	−	0.146503i
$698$	−383.048	−	221.153i	−0.548779	−	0.316838i
$699$		0			0
$700$	−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	$0.812699\pi$
$702$		0			0
$703$	81.2714			0.115607
$704$	65.3939	−	37.7552i	0.0928890	−	0.0536295i
$705$		0			0
$706$	26.5982	−	46.0695i	0.0376745	−	0.0652542i
$707$	−868.296	−	501.311i	−1.22814	−	0.709068i
$708$		0			0
$709$	586.014	+	1015.01i	0.826536	+	1.43160i	0.900739	+	0.434360i	$0.143025\pi$
$709$	586.014	+	1015.01i	0.826536	+	1.43160i	−0.0742031	+	0.997243i	$0.523641\pi$
$710$			631.253i			0.889089i
$711$		0			0
$712$	−117.031			−0.164369
$713$	−335.515	+	193.710i	−0.470568	+	0.271682i
$714$		0			0
$715$	483.022	−	836.619i	0.675556	−	1.17010i
$716$	493.757	+	285.071i	0.689605	+	0.398144i
$717$		0			0
$718$	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	$-0.116686\pi$
$720$		0			0
$721$	184.970			0.256547
$722$	−415.114	+	239.666i	−0.574949	+	0.331947i
$723$		0			0
$724$	37.1214	−	64.2962i	0.0512727	−	0.0888069i
$725$	5.69694	+	3.28913i	0.00785785	+	0.00453673i
$726$		0			0
$727$	420.704	+	728.681i	0.578685	+	1.00231i	0.995630	+	0.0933809i	$0.0297674\pi$
$727$	420.704	+	728.681i	0.578685	+	1.00231i	−0.416945	+	0.908932i	$0.636899\pi$
$728$		−	353.682i		−	0.485827i
$729$		0			0
$730$	−706.120			−0.967288
$731$	−1.57654	+	0.910215i	−0.00215669	+	0.00124516i
$732$		0			0
$733$	−303.181	+	525.125i	−0.413617	+	0.716405i	−0.995282	−	0.0970229i	$-0.969068\pi$
$733$	−303.181	+	525.125i	−0.413617	+	0.716405i	0.581665	+	0.813428i	$0.302401\pi$
$734$	40.6946	+	23.4951i	0.0554423	+	0.0320096i
$735$		0			0
$736$	26.6969	+	46.2405i	0.0362730	+	0.0628267i
$737$		−	292.174i		−	0.396437i
$738$		0			0
$739$	−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
$741$		0			0
$742$	−42.8036	+	74.1380i	−0.0576868	+	0.0999164i
$743$	−904.779	−	522.375i	−1.21774	−	0.703061i	−0.253304	−	0.967387i	$-0.581517\pi$
$743$	−904.779	−	522.375i	−1.21774	−	0.703061i	−0.964434	+	0.264325i	$0.914851\pi$
$744$		0			0
$745$	273.090	+	473.006i	0.366564	+	0.634908i
$746$		−	318.240i		−	0.426595i
$747$		0			0
$748$	36.0000			0.0481283
$749$	944.574	−	545.350i	1.26111	−	0.728105i
$750$		0			0
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	−0.0117826	−	0.999931i	$-0.503751\pi$
$751$	645.916	−	1118.76i	0.860074	−	1.48969i	0.871857	−	0.489761i	$-0.162916\pi$
$752$	−48.8786	−	28.2201i	−0.0649981	−	0.0375267i
$753$		0			0
$754$	45.8105	+	79.3460i	0.0607566	+	0.105233i
$755$			1482.08i			1.96302i
$756$		0			0
$757$	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
$759$		0			0
$760$	34.5153	−	59.7823i	0.0454149	−	0.0786609i
$761$	281.607	+	162.586i	0.370048	+	0.213647i	0.673479	−	0.739206i	$-0.264799\pi$
$761$	281.607	+	162.586i	0.370048	+	0.213647i	−0.303431	+	0.952853i	$0.598132\pi$
$762$		0			0
$763$	−369.076	−	639.258i	−0.483717	−	0.837822i
$764$		−	35.8481i		−	0.0469217i
$765$		0			0
$766$	1042.26			1.36065
$767$	1561.28	−	901.405i	2.03557	−	1.17523i
$768$		0			0
$769$	−171.348	+	296.783i	−0.222819	+	0.385934i	−0.955663	−	0.294463i	$-0.904859\pi$
$769$	−171.348	+	296.783i	−0.222819	+	0.385934i	0.732844	+	0.680397i	$0.238193\pi$
$770$	381.341	+	220.167i	0.495247	+	0.285931i
$771$		0			0
$772$	−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	$-0.111948\pi$
$774$		0			0
$775$	82.0908			0.105924
$776$	−234.854	+	135.593i	−0.302646	+	0.174733i
$777$		0			0
$778$	119.765	−	207.439i	0.153940	−	0.266631i
$779$	251.499	+	145.203i	0.322849	+	0.186397i
$780$		0			0
$781$	−405.409	−	702.188i	−0.519089	−	0.899089i
$782$			25.4558i			0.0325522i
$783$		0			0
$784$	−34.7878			−0.0443721
$785$	887.317	−	512.293i	1.13034	−	0.652602i
$786$		0			0
$787$	51.9768	−	90.0264i	0.0660442	−	0.114392i	−0.831113	−	0.556104i	$-0.812296\pi$
$787$	51.9768	−	90.0264i	0.0660442	−	0.114392i	0.897157	+	0.441712i	$0.145629\pi$
$788$	−277.757	−	160.363i	−0.352484	−	0.203507i
$789$		0			0
$790$	−109.280	−	189.279i	−0.138330	−	0.239594i
$791$			1284.07i			1.62335i
$792$		0			0
$793$	−1479.06			−1.86514
$794$	−313.868	+	181.212i	−0.395300	+	0.228227i
$795$		0			0
$796$	6.51531	−	11.2848i	0.00818506	−	0.0141769i
$797$	956.331	+	552.138i	1.19991	+	0.692770i	0.960536	−	0.278156i	$-0.0897233\pi$
$797$	956.331	+	552.138i	1.19991	+	0.692770i	0.239378	+	0.970927i	$0.423057\pi$
$798$		0			0
$799$	−13.4541	−	23.3031i	−0.0168386	−	0.0291654i
$800$		−	11.3137i		−	0.0141421i
$801$		0			0
$802$	−369.650			−0.460911
$803$	785.469	−	453.491i	0.978168	−	0.564746i
$804$		0			0
$805$	−155.682	+	269.648i	−0.193393	+	0.334967i
$806$	990.168	+	571.674i	1.22850	+	0.709273i
$807$		0			0
$808$	−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	$-0.0506683\pi$
$810$		0			0
$811$	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
$813$		0			0
$814$	−115.485	+	200.025i	−0.141873	+	0.245731i
$815$	−1120.77	−	647.077i	−1.37518	−	0.793960i
$816$		0			0
$817$	−2.24183	−	3.88296i	−0.00274398	−	0.00475271i
$818$		−	627.611i		−	0.767250i
$819$		0			0
$820$	642.545			0.783591
$821$	−1078.45	+	622.645i	−1.31358	+	0.758398i	−0.982688	−	0.185269i	$-0.940684\pi$
$821$	−1078.45	+	622.645i	−1.31358	+	0.758398i	−0.330896	+	0.943667i	$0.607351\pi$
$822$		0			0
$823$	771.129	−	1335.63i	0.936973	−	1.62288i	0.165896	−	0.986143i	$-0.446948\pi$
$823$	771.129	−	1335.63i	0.936973	−	1.62288i	0.771077	−	0.636742i	$-0.219718\pi$
$824$	71.3689	+	41.2048i	0.0866127	+	0.0500059i
$825$		0			0
$826$	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	$0.803905\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	78.7878	−	136.464i	0.0946968	−	0.164020i
$833$	−14.3633	−	8.29263i	−0.0172428	−	0.00995514i
$834$		0			0
$835$	125.842	+	217.964i	0.150708	+	0.261035i
$836$			88.6669i			0.106061i
$837$		0			0
$838$	−15.2281			−0.0181719
$839$	−903.778	+	521.797i	−1.07721	+	0.621927i	−0.930142	−	0.367200i	$-0.880317\pi$
$839$	−903.778	+	521.797i	−1.07721	+	0.621927i	−0.147067	+	0.989127i	$0.546983\pi$
$840$		0			0
$841$	−415.091	+	718.958i	−0.493568	+	0.854885i
$842$	−311.456	−	179.819i	−0.369901	−	0.213562i
$843$		0			0
$844$	−154.439	−	267.497i	−0.182985	−	0.316939i
$845$		−	1137.80i		−	1.34651i
$846$		0			0
$847$	202.574			0.239167
$848$	−33.0306	+	19.0702i	−0.0389512	+	0.0224885i
$849$		0			0
$850$	2.69694	−	4.67123i	0.00317287	−	0.00549557i
$851$	−141.439	−	81.6600i	−0.166204	−	0.0959577i
$852$		0			0
$853$	−236.909	−	410.338i	−0.277736	−	0.481053i	0.693086	−	0.720855i	$-0.256251\pi$
$853$	−236.909	−	410.338i	−0.277736	−	0.481053i	−0.970822	+	0.239802i	$0.922917\pi$
$854$		−	674.172i		−	0.789429i
$855$		0			0
$856$	485.939			0.567685
$857$	−793.939	+	458.381i	−0.926417	+	0.534867i	−0.885677	−	0.464303i	$-0.846305\pi$
$857$	−793.939	+	458.381i	−0.926417	+	0.534867i	−0.0407403	+	0.999170i	$0.512972\pi$
$858$		0			0
$859$	−478.901	+	829.480i	−0.557510	+	0.965635i	0.440194	+	0.897903i	$0.354910\pi$
$859$	−478.901	+	829.480i	−0.557510	+	0.965635i	−0.997704	+	0.0677322i	$0.978424\pi$
$860$	−8.59133	−	4.96021i	−0.00998992	−	0.00576768i
$861$		0			0
$862$	−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	$-0.0982247\pi$
$864$		0			0
$865$	−521.908			−0.603362
$866$	259.312	−	149.714i	0.299437	−	0.172880i
$867$		0			0
$868$	−260.576	+	451.330i	−0.300202	+	0.519965i
$869$	243.121	+	140.366i	0.279771	+	0.161526i
$870$		0			0
$871$	−304.855	−	528.025i	−0.350006	−	0.606228i
$872$		−	328.868i		−	0.377142i
$873$		0			0
$874$	−62.6969			−0.0717356
$875$	−657.067	+	379.358i	−0.750933	+	0.433551i
$876$		0			0
$877$	−503.878	+	872.742i	−0.574547	+	0.995145i	0.421543	+	0.906808i	$0.361489\pi$
$877$	−503.878	+	872.742i	−0.574547	+	0.995145i	−0.996091	+	0.0883370i	$0.971845\pi$
$878$	−342.760	−	197.893i	−0.390388	−	0.225390i
$879$		0			0
$880$	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	$0.662731\pi$
$882$		0			0
$883$	−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
$885$		0			0
$886$	389.796	−	675.146i	0.439950	−	0.762016i
$887$	497.794	+	287.402i	0.561211	+	0.324015i	0.753631	−	0.657297i	$-0.228300\pi$
$887$	497.794	+	287.402i	0.561211	+	0.324015i	−0.192420	+	0.981313i	$0.561634\pi$
$888$		0			0
$889$	−32.0306	−	55.4787i	−0.0360299	−	0.0624057i
$890$		−	304.054i		−	0.341634i
$891$		0			0
$892$	−185.546			−0.208011
$893$	57.3949	−	33.1370i	0.0642720	−	0.0371075i
$894$		0			0
$895$	−740.636	+	1282.82i	−0.827526	+	1.43332i
$896$	62.2020	+	35.9124i	0.0694219	+	0.0400808i
$897$		0			0
$898$	−383.864	−	664.872i	−0.427465	−	0.740391i
$899$		−	135.004i		−	0.150171i
$900$		0			0
$901$	−18.1837			−0.0201817
$902$	−714.749	+	412.661i	−0.792405	+	0.457495i
$903$		0			0
$904$	−286.045	+	495.445i	−0.316422	+	0.548059i
$905$	167.046	+	96.4443i	0.184582	+	0.106568i
$906$		0			0
$907$	255.037	+	441.737i	0.281187	+	0.487031i	0.971677	−	0.236311i	$-0.0759384\pi$
$907$	255.037	+	441.737i	0.281187	+	0.487031i	−0.690490	+	0.723342i	$0.742605\pi$
$908$			339.604i			0.374013i
$909$		0			0
$910$	918.892			1.00977
$911$	803.127	−	463.685i	0.881588	−	0.508985i	0.0104064	−	0.999946i	$-0.496687\pi$
$911$	803.127	−	463.685i	0.881588	−	0.508985i	0.871182	+	0.490961i	$0.163354\pi$
$912$		0			0
$913$	−414.863	+	718.564i	−0.454396	+	0.787036i
$914$	−113.123	−	65.3114i	−0.123767	−	0.0714567i
$915$		0			0
$916$	407.545	+	705.888i	0.444918	+	0.770621i
$917$			31.4897i			0.0343399i
$918$		0			0
$919$	−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
$921$		0			0
$922$	162.507	−	281.471i	0.176255	−	0.305283i
$923$	−1465.33	−	846.010i	−1.58757	−	0.916587i
$924$		0			0
$925$	17.3031	+	29.9698i	0.0187060	+	0.0323998i
$926$		−	722.384i		−	0.780112i
$927$		0			0
$928$	−18.6061			−0.0200497
$929$	−293.576	+	169.496i	−0.316013	+	0.182450i	−0.649614	−	0.760264i	$-0.725069\pi$
$929$	−293.576	+	169.496i	−0.316013	+	0.182450i	0.333601	+	0.942714i	$0.391736\pi$
$930$		0			0
$931$	20.4245	−	35.3763i	0.0219382	−	0.0379981i
$932$	−26.4245	−	15.2562i	−0.0283525	−	0.0163693i
$933$		0			0
$934$	589.485	+	1021.02i	0.631140	+	1.09317i
$935$			93.5307i			0.100033i
$936$		0			0
$937$	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
$939$		0			0
$940$	73.3179	−	126.990i	0.0779977	−	0.135096i
$941$	310.984	+	179.547i	0.330482	+	0.190804i	0.656055	−	0.754713i	$-0.272224\pi$
$941$	310.984	+	179.547i	0.330482	+	0.190804i	−0.325573	+	0.945517i	$0.605557\pi$
$942$		0			0
$943$	−291.795	−	505.404i	−0.309433	−	0.535953i
$944$			366.110i			0.387828i
$945$		0			0
$946$	12.7423			0.0134697
$947$	671.855	−	387.896i	0.709457	−	0.409605i	−0.101403	−	0.994845i	$-0.532333\pi$
$947$	671.855	−	387.896i	0.709457	−	0.409605i	0.810860	+	0.585240i	$0.199000\pi$
$948$		0			0
$949$	946.347	−	1639.12i	0.997205	−	1.72721i
$950$	11.5051	+	6.64247i	0.0121106	+	0.00699208i
$951$		0			0
$952$	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	$-0.0784628\pi$
$954$		0			0
$955$	93.1362			0.0975248
$956$	−97.9240	+	56.5364i	−0.102431	+	0.0591385i
$957$		0			0
$958$	−464.704	+	804.891i	−0.485077	+	0.840178i
$959$	1290.28	+	744.942i	1.34544	+	0.776791i
$960$		0			0
$961$	−361.863	−	626.765i	−0.376548	−	0.652200i
$962$			481.989i			0.501028i
$963$		0			0
$964$	−168.424			−0.174714
$965$	429.543	−	247.997i	0.445123	−	0.256992i
$966$		0			0
$967$	−612.113	+	1060.21i	−0.633002	+	1.09639i	0.353933	+	0.935271i	$0.384844\pi$
$967$	−612.113	+	1060.21i	−0.633002	+	1.09639i	−0.986935	+	0.161121i	$0.948489\pi$
$968$	78.1612	+	45.1264i	0.0807451	+	0.0466182i
$969$		0			0
$970$	−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	$-0.110152\pi$
$972$		0			0
$973$	676.303			0.695070
$974$	−430.702	+	248.666i	−0.442199	+	0.255304i
$975$		0			0
$976$	150.182	−	260.122i	0.153875	−	0.266519i
$977$	−1314.92	−	759.170i	−1.34588	−	0.777042i	−0.358214	−	0.933639i	$-0.616614\pi$
$977$	−1314.92	−	759.170i	−1.34588	−	0.777042i	−0.987663	+	0.156597i	$0.949948\pi$
$978$		0			0
$979$	195.272	+	338.222i	0.199461	+	0.345477i
$980$		−	90.3812i		−	0.0922258i
$981$		0			0
$982$	−347.074			−0.353436
$983$	−716.930	+	413.920i	−0.729329	+	0.421078i	−0.818177	−	0.574967i	$-0.805015\pi$
$983$	−716.930	+	413.920i	−0.729329	+	0.421078i	0.0888477	+	0.996045i	$0.471682\pi$
$984$		0			0
$985$	416.636	−	721.634i	0.422980	−	0.732624i
$986$	−7.68215	−	4.43529i	−0.00779122	−	0.00449826i
$987$		0			0
$988$	92.5153	+	160.241i	0.0936390	+	0.162187i
$989$			9.01020i			0.00911041i
$990$		0			0
$991$	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
$993$		0			0
$994$	385.621	−	667.915i	0.387949	−	0.671947i
$995$	29.3189	+	16.9273i	0.0294662	+	0.0170123i
$996$		0			0
$997$	347.499	+	601.886i	0.348545	+	0.603697i	0.985991	−	0.166798i	$-0.0533427\pi$
$997$	347.499	+	601.886i	0.348545	+	0.603697i	−0.637447	+	0.770495i	$0.720009\pi$
$998$			891.274i			0.893060i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.1	✓	4	3.2	odd	2
18.3.d.a.11.1	yes	4	9.7	even	3
54.3.d.a.17.2		4	1.1	even	1	trivial
54.3.d.a.35.2		4	9.2	odd	6	inner
144.3.q.c.65.1		4	36.7	odd	6
144.3.q.c.113.1		4	12.11	even	2
162.3.b.a.161.2		4	9.5	odd	6
162.3.b.a.161.3		4	9.4	even	3
432.3.q.d.17.2		4	4.3	odd	2
432.3.q.d.305.2		4	36.11	even	6
450.3.i.b.101.2		4	45.34	even	6
450.3.i.b.401.2		4	15.14	odd	2
450.3.k.a.149.2		8	15.2	even	4
450.3.k.a.149.3		8	15.8	even	4
450.3.k.a.299.2		8	45.43	odd	12
450.3.k.a.299.3		8	45.7	odd	12
576.3.q.e.65.2		4	72.43	odd	6
576.3.q.e.257.2		4	24.11	even	2
576.3.q.f.65.1		4	72.61	even	6
576.3.q.f.257.1		4	24.5	odd	2
1296.3.e.g.161.1		4	36.31	odd	6
1296.3.e.g.161.3		4	36.23	even	6
1350.3.i.b.251.1		4	45.29	odd	6
1350.3.i.b.1151.1		4	5.4	even	2
1350.3.k.a.449.2		8	5.3	odd	4
1350.3.k.a.449.3		8	5.2	odd	4
1350.3.k.a.899.2		8	45.2	even	12
1350.3.k.a.899.3		8	45.38	even	12
1728.3.q.c.449.2		4	8.3	odd	2
1728.3.q.c.1601.2		4	72.11	even	6
1728.3.q.d.449.1		4	8.5	even	2
1728.3.q.d.1601.1		4	72.29	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(-3.17423 - 5.49794i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.50000 + 2.59808i) q^{5} +(-3.17423 - 5.49794i) q^{7} -2.82843i q^{8} +7.34847 q^{10} +(-8.17423 + 4.71940i) q^{11} +(-9.84847 + 17.0580i) q^{13} +(-7.77526 - 4.48905i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.90702i q^{17} +4.69694 q^{19} +(9.00000 - 5.19615i) q^{20} +(-6.67423 + 11.5601i) q^{22} +(-8.17423 - 4.71940i) q^{23} +(1.00000 + 1.73205i) q^{25} +27.8557i q^{26} -12.6969 q^{28} +(2.84847 - 1.64456i) q^{29} +(20.5227 - 35.5464i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-1.34847 - 2.33562i) q^{34} -32.9876i q^{35} +17.3031 q^{37} +(5.75255 - 3.32124i) q^{38} +(7.34847 - 12.7279i) q^{40} +(53.5454 + 30.9145i) q^{41} +(-0.477296 - 0.826701i) q^{43} +18.8776i q^{44} -13.3485 q^{46} +(12.2196 - 7.05501i) q^{47} +(4.34847 - 7.53177i) q^{49} +(2.44949 + 1.41421i) q^{50} +(19.6969 + 34.1161i) q^{52} -9.53512i q^{53} -49.0454 q^{55} +(-15.5505 + 8.97809i) q^{56} +(2.32577 - 4.02834i) q^{58} +(-79.2650 - 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} -58.0470i q^{62} -8.00000 q^{64} +(-88.6362 + 51.1741i) q^{65} +(-15.4773 + 26.8075i) q^{67} +(-3.30306 - 1.90702i) q^{68} +(-23.3258 - 40.4014i) q^{70} +85.9026i q^{71} -96.0908 q^{73} +(21.1918 - 12.2351i) q^{74} +(4.69694 - 8.13534i) q^{76} +(51.8939 + 29.9609i) q^{77} +(-14.8712 - 25.7576i) q^{79} -20.7846i q^{80} +87.4393 q^{82} +(76.1288 - 43.9530i) q^{83} +(4.95459 - 8.58161i) q^{85} +(-1.16913 - 0.674999i) q^{86} +(13.3485 + 23.1202i) q^{88} -41.3766i q^{89} +125.045 q^{91} +(-16.3485 + 9.43879i) q^{92} +(9.97730 - 17.2812i) q^{94} +(21.1362 + 12.2030i) q^{95} +(-47.9393 - 83.0333i) q^{97} -12.2993i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7}+O(q^{10}) \) 4 * q + 4 * q^4 + 18 * q^5 + 2 * q^7	\( 4 q + 4 q^{4} + 18 q^{5} + 2 q^{7} - 18 q^{11} - 10 q^{13} - 36 q^{14} - 8 q^{16} - 40 q^{19} + 36 q^{20} - 12 q^{22} - 18 q^{23} + 4 q^{25} + 8 q^{28} - 18 q^{29} + 38 q^{31} + 24 q^{34} + 128 q^{37} + 72 q^{38} + 126 q^{41} - 46 q^{43} - 24 q^{46} - 54 q^{47} - 12 q^{49} + 20 q^{52} - 108 q^{55} - 72 q^{56} + 24 q^{58} - 126 q^{59} + 62 q^{61} - 32 q^{64} - 90 q^{65} - 106 q^{67} - 72 q^{68} - 108 q^{70} - 208 q^{73} - 72 q^{74} - 40 q^{76} + 90 q^{77} + 14 q^{79} + 144 q^{82} + 378 q^{83} + 108 q^{85} + 108 q^{86} + 24 q^{88} + 412 q^{91} - 36 q^{92} + 84 q^{94} - 180 q^{95} + 14 q^{97}+O(q^{100}) \) 4 * q + 4 * q^4 + 18 * q^5 + 2 * q^7 - 18 * q^11 - 10 * q^13 - 36 * q^14 - 8 * q^16 - 40 * q^19 + 36 * q^20 - 12 * q^22 - 18 * q^23 + 4 * q^25 + 8 * q^28 - 18 * q^29 + 38 * q^31 + 24 * q^34 + 128 * q^37 + 72 * q^38 + 126 * q^41 - 46 * q^43 - 24 * q^46 - 54 * q^47 - 12 * q^49 + 20 * q^52 - 108 * q^55 - 72 * q^56 + 24 * q^58 - 126 * q^59 + 62 * q^61 - 32 * q^64 - 90 * q^65 - 106 * q^67 - 72 * q^68 - 108 * q^70 - 208 * q^73 - 72 * q^74 - 40 * q^76 + 90 * q^77 + 14 * q^79 + 144 * q^82 + 378 * q^83 + 108 * q^85 + 108 * q^86 + 24 * q^88 + 412 * q^91 - 36 * q^92 + 84 * q^94 - 180 * q^95 + 14 * q^97

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