LMFDB - Embedded newform 144.3.q.c.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.q (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:	$3.92371580679$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	144.113
Dual form			144.3.q.c.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(3.17423 + 5.49794i) q^{7} +(3.00000 + 8.48528i) q^{9} +O(q^{10})$	\(q+(-2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(3.17423 + 5.49794i) q^{7} +(3.00000 + 8.48528i) q^{9} +(-8.17423 + 4.71940i) q^{11} +(-9.84847 + 17.0580i) q^{13} +(6.52270 + 14.1582i) q^{15} +1.90702i q^{17} -4.69694 q^{19} +(1.74745 - 18.9651i) q^{21} +(-8.17423 - 4.71940i) q^{23} +(1.00000 + 1.73205i) q^{25} +(7.34847 - 25.9808i) q^{27} +(-2.84847 + 1.64456i) q^{29} +(-20.5227 + 35.5464i) q^{31} +(28.1969 + 2.59808i) q^{33} -32.9876i q^{35} +17.3031 q^{37} +(53.6691 - 24.7255i) q^{39} +(-53.5454 - 30.9145i) q^{41} +(0.477296 + 0.826701i) q^{43} +(8.54541 - 45.9780i) q^{45} +(12.2196 - 7.05501i) q^{47} +(4.34847 - 7.53177i) q^{49} +(3.30306 - 4.67123i) q^{51} +9.53512i q^{53} +49.0454 q^{55} +(11.5051 + 8.13534i) q^{57} +(-79.2650 - 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} +(-37.1288 + 43.4281i) q^{63} +(88.6362 - 51.1741i) q^{65} +(15.4773 - 26.8075i) q^{67} +(11.8485 + 25.7183i) q^{69} +85.9026i q^{71} -96.0908 q^{73} +(0.550510 - 5.97469i) q^{75} +(-51.8939 - 29.9609i) q^{77} +(14.8712 + 25.7576i) q^{79} +(-63.0000 + 50.9117i) q^{81} +(76.1288 - 43.9530i) q^{83} +(4.95459 - 8.58161i) q^{85} +(9.82577 + 0.905350i) q^{87} +41.3766i q^{89} -125.045 q^{91} +(111.838 - 51.5241i) q^{93} +(21.1362 + 12.2030i) q^{95} +(-47.9393 - 83.0333i) q^{97} +(-64.5681 - 55.2025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9	$ 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9} - 18 q^{11} - 10 q^{13} - 18 q^{15} + 40 q^{19} - 42 q^{21} - 18 q^{23} + 4 q^{25} + 18 q^{29} - 38 q^{31} + 54 q^{33} + 128 q^{37} + 102 q^{39} - 126 q^{41} + 46 q^{43} - 54 q^{45} - 54 q^{47} - 12 q^{49} + 72 q^{51} + 108 q^{55} + 144 q^{57} - 126 q^{59} + 62 q^{61} - 222 q^{63} + 90 q^{65} + 106 q^{67} + 18 q^{69} - 208 q^{73} + 12 q^{75} - 90 q^{77} - 14 q^{79} - 252 q^{81} + 378 q^{83} + 108 q^{85} + 54 q^{87} - 412 q^{91} + 222 q^{93} - 180 q^{95} + 14 q^{97} - 126 q^{99}+O(q^{100}) $ 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9 - 18 * q^11 - 10 * q^13 - 18 * q^15 + 40 * q^19 - 42 * q^21 - 18 * q^23 + 4 * q^25 + 18 * q^29 - 38 * q^31 + 54 * q^33 + 128 * q^37 + 102 * q^39 - 126 * q^41 + 46 * q^43 - 54 * q^45 - 54 * q^47 - 12 * q^49 + 72 * q^51 + 108 * q^55 + 144 * q^57 - 126 * q^59 + 62 * q^61 - 222 * q^63 + 90 * q^65 + 106 * q^67 + 18 * q^69 - 208 * q^73 + 12 * q^75 - 90 * q^77 - 14 * q^79 - 252 * q^81 + 378 * q^83 + 108 * q^85 + 54 * q^87 - 412 * q^91 + 222 * q^93 - 180 * q^95 + 14 * q^97 - 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.44949	−	1.73205i	−0.816497	−	0.577350i
$3$	−2.44949	−	1.73205i	−0.816497	−	0.577350i
$4$		0			0
$5$	−4.50000	−	2.59808i	−0.900000	−	0.519615i	−0.0227998	−	0.999740i	$-0.507258\pi$
$5$	−4.50000	−	2.59808i	−0.900000	−	0.519615i	−0.877200	+	0.480125i	$0.840591\pi$
$6$		0			0
$7$	3.17423	+	5.49794i	0.453462	+	0.785419i	0.998598	−	0.0529281i	$-0.0168554\pi$
$7$	3.17423	+	5.49794i	0.453462	+	0.785419i	−0.545136	+	0.838347i	$0.683522\pi$
$8$		0			0
$9$	3.00000	+	8.48528i	0.333333	+	0.942809i
$10$		0			0
$11$	−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	$0.893051\pi$
$14$		0			0
$15$	6.52270	+	14.1582i	0.434847	+	0.943879i
$16$		0			0
$17$			1.90702i			0.112178i	0.998426	+	0.0560889i	$0.0178630\pi$
$17$			1.90702i			0.112178i	−0.998426	+	0.0560889i	$0.982137\pi$
$18$		0			0
$19$	−4.69694			−0.247207			−0.123604	−	0.992332i	$-0.539445\pi$
$19$	−4.69694			−0.247207			−0.123604	+	0.992332i	$0.539445\pi$
$20$		0			0
$21$	1.74745	−	18.9651i	0.0832118	−	0.903099i
$22$		0			0
$23$	−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
$26$		0			0
$27$	7.34847	−	25.9808i	0.272166	−	0.962250i
$28$		0			0
$29$	−2.84847	+	1.64456i	−0.0982231	+	0.0567091i	−0.548307	−	0.836277i	$-0.684727\pi$
$29$	−2.84847	+	1.64456i	−0.0982231	+	0.0567091i	0.450084	+	0.892986i	$0.351394\pi$
$30$		0			0
$31$	−20.5227	+	35.5464i	−0.662023	+	1.14666i	0.318061	+	0.948070i	$0.396968\pi$
$31$	−20.5227	+	35.5464i	−0.662023	+	1.14666i	−0.980083	+	0.198587i	$0.936365\pi$
$32$		0			0
$33$	28.1969	+	2.59808i	0.854453	+	0.0787296i
$34$		0			0
$35$		−	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	$0.424876\pi$
$38$		0			0
$39$	53.6691	−	24.7255i	1.37613	−	0.633986i
$40$		0			0
$41$	−53.5454	−	30.9145i	−1.30599	−	0.754011i	−0.324562	−	0.945864i	$-0.605217\pi$
$41$	−53.5454	−	30.9145i	−1.30599	−	0.754011i	−0.981424	+	0.191853i	$0.938550\pi$
$42$		0			0
$43$	0.477296	+	0.826701i	0.0110999	+	0.0192256i	0.871522	−	0.490356i	$-0.163133\pi$
$43$	0.477296	+	0.826701i	0.0110999	+	0.0192256i	−0.860422	+	0.509582i	$0.829800\pi$
$44$		0			0
$45$	8.54541	−	45.9780i	0.189898	−	1.02173i
$46$		0			0
$47$	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
$50$		0			0
$51$	3.30306	−	4.67123i	0.0647659	−	0.0915928i
$52$		0			0
$53$			9.53512i			0.179908i	0.995946	+	0.0899539i	$0.0286720\pi$
$53$			9.53512i			0.179908i	−0.995946	+	0.0899539i	$0.971328\pi$
$54$		0			0
$55$	49.0454			0.891735
$56$		0			0
$57$	11.5051	+	8.13534i	0.201844	+	0.142725i
$58$		0			0
$59$	−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	$0.622288\pi$
$62$		0			0
$63$	−37.1288	+	43.4281i	−0.589346	+	0.689335i
$64$		0			0
$65$	88.6362	−	51.1741i	1.36363	−	0.787295i
$66$		0			0
$67$	15.4773	−	26.8075i	0.231004	−	0.400111i	−0.727100	−	0.686532i	$-0.759132\pi$
$67$	15.4773	−	26.8075i	0.231004	−	0.400111i	0.958104	+	0.286421i	$0.0924655\pi$
$68$		0			0
$69$	11.8485	+	25.7183i	0.171717	+	0.372729i
$70$		0			0
$71$			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	$0.728663\pi$
$74$		0			0
$75$	0.550510	−	5.97469i	0.00734014	−	0.0796626i
$76$		0			0
$77$	−51.8939	−	29.9609i	−0.673946	−	0.389103i
$78$		0			0
$79$	14.8712	+	25.7576i	0.188243	+	0.326046i	0.944664	−	0.328038i	$-0.106388\pi$
$79$	14.8712	+	25.7576i	0.188243	+	0.326046i	−0.756422	+	0.654084i	$0.773054\pi$
$80$		0			0
$81$	−63.0000	+	50.9117i	−0.777778	+	0.628539i
$82$		0			0
$83$	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
$86$		0			0
$87$	9.82577	+	0.905350i	0.112940	+	0.0104063i
$88$		0			0
$89$			41.3766i			0.464905i	0.972608	+	0.232453i	$0.0746751\pi$
$89$			41.3766i			0.464905i	−0.972608	+	0.232453i	$0.925325\pi$
$90$		0			0
$91$	−125.045			−1.37413
$92$		0			0
$93$	111.838	−	51.5241i	1.20256	−	0.554023i
$94$		0			0
$95$	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	$0.997879\pi$
$98$		0			0
$99$	−64.5681	−	55.2025i	−0.652203	−	0.557601i
$100$		0			0
$101$	−136.772	+	78.9656i	−1.35418	+	0.781838i	−0.988832	−	0.149032i	$-0.952384\pi$
$101$	−136.772	+	78.9656i	−1.35418	+	0.781838i	−0.365350	+	0.930870i	$0.619051\pi$
$102$		0			0
$103$	14.5681	−	25.2327i	0.141438	−	0.244978i	−0.786600	−	0.617462i	$-0.788161\pi$
$103$	14.5681	−	25.2327i	0.141438	−	0.244978i	0.928038	+	0.372485i	$0.121494\pi$
$104$		0			0
$105$	−57.1362	+	80.8028i	−0.544155	+	0.769551i
$106$		0			0
$107$			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	$0.320929\pi$
$110$		0			0
$111$	−42.3837	−	29.9698i	−0.381835	−	0.269998i
$112$		0			0
$113$	175.166	+	101.132i	1.55014	+	0.894976i	0.998129	+	0.0611424i	$0.0194744\pi$
$113$	175.166	+	101.132i	1.55014	+	0.894976i	0.552015	+	0.833834i	$0.313859\pi$
$114$		0			0
$115$	24.5227	+	42.4746i	0.213241	+	0.369344i
$116$		0			0
$117$	−174.288	−	32.3929i	−1.48964	−	0.276862i
$118$		0			0
$119$	−10.4847	+	6.05334i	−0.0881067	+	0.0508684i
$120$		0			0
$121$	−15.9546	+	27.6342i	−0.131856	+	0.228382i
$122$		0			0
$123$	77.6135	+	168.468i	0.631004	+	1.36966i
$124$		0			0
$125$			119.512i			0.956092i
$126$		0			0
$127$	−10.0908			−0.0794552			−0.0397276	−	0.999211i	$-0.512649\pi$
$127$	−10.0908			−0.0794552			−0.0397276	+	0.999211i	$0.512649\pi$
$128$		0			0
$129$	0.262756	−	2.85170i	0.00203687	−	0.0221062i
$130$		0			0
$131$	−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
$134$		0			0
$135$	−100.568	+	97.8215i	−0.744949	+	0.724604i
$136$		0			0
$137$	203.242	−	117.342i	1.48352	−	0.856511i	0.483696	−	0.875236i	$-0.339294\pi$
$137$	203.242	−	117.342i	1.48352	−	0.856511i	0.999825	+	0.0187249i	$0.00596067\pi$
$138$		0			0
$139$	53.2650	−	92.2578i	0.383202	−	0.663725i	−0.608316	−	0.793695i	$-0.708155\pi$
$139$	53.2650	−	92.2578i	0.383202	−	0.663725i	0.991518	+	0.129970i	$0.0414881\pi$
$140$		0			0
$141$	−42.1515	−	3.88386i	−0.298947	−	0.0275451i
$142$		0			0
$143$		−	185.915i		−	1.30011i
$144$		0			0
$145$	17.0908			0.117868
$146$		0			0
$147$	−23.6969	+	10.9172i	−0.161204	+	0.0742668i
$148$		0			0
$149$	−91.0301	−	52.5563i	−0.610940	−	0.352727i	0.162393	−	0.986726i	$-0.448079\pi$
$149$	−91.0301	−	52.5563i	−0.610940	−	0.352727i	−0.773333	+	0.634000i	$0.781412\pi$
$150$		0			0
$151$	−142.614	−	247.014i	−0.944460	−	1.63585i	−0.756828	−	0.653614i	$-0.773252\pi$
$151$	−142.614	−	247.014i	−0.944460	−	1.63585i	−0.187632	−	0.982239i	$-0.560081\pi$
$152$		0			0
$153$	−16.1816	+	5.72107i	−0.105762	+	0.0373926i
$154$		0			0
$155$	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	$-0.0494460\pi$
$158$		0			0
$159$	16.5153	−	23.3562i	0.103870	−	0.146894i
$160$		0			0
$161$		−	59.9219i		−	0.372186i
$162$		0			0
$163$	249.060			1.52798			0.763988	−	0.645230i	$-0.223238\pi$
$163$	249.060			1.52798			0.763988	+	0.645230i	$0.223238\pi$
$164$		0			0
$165$	−120.136	−	84.9491i	−0.728098	−	0.514843i
$166$		0			0
$167$	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
$170$		0			0
$171$	−14.0908	−	39.8548i	−0.0824024	−	0.233069i
$172$		0			0
$173$	86.9847	−	50.2206i	0.502802	−	0.290293i	−0.227068	−	0.973879i	$-0.572914\pi$
$173$	86.9847	−	50.2206i	0.502802	−	0.290293i	0.729870	+	0.683586i	$0.239581\pi$
$174$		0			0
$175$	−6.34847	+	10.9959i	−0.0362770	+	0.0628336i
$176$		0			0
$177$	114.894	+	249.389i	0.649118	+	1.40898i
$178$		0			0
$179$			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	$0.467301\pi$
$182$		0			0
$183$	20.6691	−	224.322i	0.112946	−	1.22580i
$184$		0			0
$185$	−77.8638	−	44.9547i	−0.420885	−	0.242998i
$186$		0			0
$187$	−9.00000	−	15.5885i	−0.0481283	−	0.0833607i
$188$		0			0
$189$	166.166	−	42.0676i	0.879187	−	0.222580i
$190$		0			0
$191$	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	$0.0871265\pi$
$194$		0			0
$195$	−305.750	−	28.1719i	−1.56795	−	0.144471i
$196$		0			0
$197$			160.363i			0.814026i	0.913422	+	0.407013i	$0.133430\pi$
$197$			160.363i			0.814026i	−0.913422	+	0.407013i	$0.866570\pi$
$198$		0			0
$199$	−6.51531			−0.0327402			−0.0163701	−	0.999866i	$-0.505211\pi$
$199$	−6.51531			−0.0327402			−0.0163701	+	0.999866i	$0.505211\pi$
$200$		0			0
$201$	−84.3434	+	38.8571i	−0.419619	+	0.193319i
$202$		0			0
$203$	−18.0834	−	10.4405i	−0.0890809	−	0.0514309i
$204$		0			0
$205$	160.636	+	278.230i	0.783591	+	1.35722i
$206$		0			0
$207$	15.5227	−	83.5189i	0.0749889	−	0.403473i
$208$		0			0
$209$	38.3939	−	22.1667i	0.183703	−	0.106061i
$210$		0			0
$211$	−77.2196	+	133.748i	−0.365970	+	0.633878i	−0.988931	−	0.148374i	$-0.952596\pi$
$211$	−77.2196	+	133.748i	−0.365970	+	0.633878i	0.622961	+	0.782253i	$0.285929\pi$
$212$		0			0
$213$	148.788	−	210.418i	0.698534	−	0.987876i
$214$		0			0
$215$		−	4.96021i		−	0.0230707i
$216$		0			0
$217$	−260.576			−1.20081
$218$		0			0
$219$	235.373	+	166.434i	1.07476	+	0.759973i
$220$		0			0
$221$	−32.5301	−	18.7813i	−0.147195	−	0.0849831i
$222$		0			0
$223$	46.3865	+	80.3437i	0.208011	+	0.360286i	0.951088	−	0.308920i	$-0.0999676\pi$
$223$	46.3865	+	80.3437i	0.208011	+	0.360286i	−0.743077	+	0.669206i	$0.766634\pi$
$224$		0			0
$225$	−11.6969	+	13.6814i	−0.0519864	+	0.0608064i
$226$		0			0
$227$	−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	$0.817485\pi$
$230$		0			0
$231$	75.2196	+	163.272i	0.325626	+	0.706805i
$232$		0			0
$233$			15.2562i			0.0654772i	0.999464	+	0.0327386i	$0.0104229\pi$
$233$			15.2562i			0.0654772i	−0.999464	+	0.0327386i	$0.989577\pi$
$234$		0			0
$235$	−73.3179			−0.311991
$236$		0			0
$237$	8.18673	−	88.8507i	0.0345432	−	0.374897i
$238$		0			0
$239$	−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	$0.889233\pi$
$242$		0			0
$243$	242.499	−	15.5885i	0.997940	−	0.0641500i
$244$		0			0
$245$	−39.1362	+	22.5953i	−0.159740	+	0.0922258i
$246$		0			0
$247$	46.2577	−	80.1206i	0.187278	−	0.324375i
$248$		0			0
$249$	−262.606	−	24.1966i	−1.05464	−	0.0971750i
$250$		0			0
$251$		−	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
$254$		0			0
$255$	−27.0000	+	12.4389i	−0.105882	+	0.0487802i
$256$		0			0
$257$	−11.1061	−	6.41212i	−0.0432145	−	0.0249499i	0.478237	−	0.878231i	$-0.341276\pi$
$257$	−11.1061	−	6.41212i	−0.0432145	−	0.0249499i	−0.521452	+	0.853281i	$0.674609\pi$
$258$		0			0
$259$	54.9240	+	95.1311i	0.212062	+	0.367302i
$260$		0			0
$261$	−22.5000	−	19.2364i	−0.0862069	−	0.0737026i
$262$		0			0
$263$	−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
$266$		0			0
$267$	71.6663	−	101.351i	0.268413	−	0.379594i
$268$		0			0
$269$			60.4468i			0.224709i	0.993668	+	0.112355i	$0.0358393\pi$
$269$			60.4468i			0.224709i	−0.993668	+	0.112355i	$0.964161\pi$
$270$		0			0
$271$	−274.636			−1.01342			−0.506708	−	0.862118i	$-0.669138\pi$
$271$	−274.636			−1.01342			−0.506708	+	0.862118i	$0.669138\pi$
$272$		0			0
$273$	306.297	+	216.585i	1.12197	+	0.793352i
$274$		0			0
$275$	−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	$0.805143\pi$
$278$		0			0
$279$	−363.189	−	67.5018i	−1.30175	−	0.241942i
$280$		0			0
$281$	−297.121	+	171.543i	−1.05737	+	0.610473i	−0.924704	−	0.380688i	$-0.875687\pi$
$281$	−297.121	+	171.543i	−1.05737	+	0.610473i	−0.132666	+	0.991161i	$0.542354\pi$
$282$		0			0
$283$	−171.704	+	297.401i	−0.606729	+	1.05089i	0.385047	+	0.922897i	$0.374185\pi$
$283$	−171.704	+	297.401i	−0.606729	+	1.05089i	−0.991776	+	0.127988i	$0.959148\pi$
$284$		0			0
$285$	−30.6367	−	66.5001i	−0.107497	−	0.233334i
$286$		0			0
$287$		−	392.519i		−	1.36766i
$288$		0			0
$289$	285.363			0.987416
$290$		0			0
$291$	−26.3911	+	286.422i	−0.0906910	+	0.984270i
$292$		0			0
$293$	−248.076	−	143.226i	−0.846674	−	0.488828i	0.0128532	−	0.999917i	$-0.495909\pi$
$293$	−248.076	−	143.226i	−0.846674	−	0.488828i	−0.859527	+	0.511090i	$0.829242\pi$
$294$		0			0
$295$	237.795	+	411.873i	0.806085	+	1.39618i
$296$		0			0
$297$	62.5454	+	247.053i	0.210591	+	0.831829i
$298$		0			0
$299$	161.007	−	92.9577i	0.538486	−	0.310895i
$300$		0			0
$301$	−3.03010	+	5.24829i	−0.0100668	+	0.0174362i
$302$		0			0
$303$	471.795	+	43.4714i	1.55708	+	0.143470i
$304$		0			0
$305$		−	390.183i		−	1.27929i
$306$		0			0
$307$	−154.091			−0.501924			−0.250962	−	0.967997i	$-0.580747\pi$
$307$	−154.091			−0.501924			−0.250962	+	0.967997i	$0.580747\pi$
$308$		0			0
$309$	−79.3888	+	36.5746i	−0.256922	+	0.118364i
$310$		0			0
$311$	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	$0.633552\pi$
$314$		0			0
$315$	279.909	−	98.9628i	0.888601	−	0.314168i
$316$		0			0
$317$	−93.1821	+	53.7987i	−0.293950	+	0.169712i	−0.639722	−	0.768607i	$-0.720950\pi$
$317$	−93.1821	+	53.7987i	−0.293950	+	0.169712i	0.345772	+	0.938319i	$0.387617\pi$
$318$		0			0
$319$	15.5227	−	26.8861i	0.0486605	−	0.0842825i
$320$		0			0
$321$	297.576	−	420.835i	0.927027	−	1.31101i
$322$		0			0
$323$		−	8.95717i		−	0.0277312i
$324$		0			0
$325$	−39.3939			−0.121212
$326$		0			0
$327$	−284.808	−	201.390i	−0.870973	−	0.615871i
$328$		0			0
$329$	77.5760	+	44.7885i	0.235793	+	0.136135i
$330$		0			0
$331$	8.59873	+	14.8934i	0.0259780	+	0.0449953i	0.878722	−	0.477334i	$-0.158397\pi$
$331$	8.59873	+	14.8934i	0.0259780	+	0.0449953i	−0.852744	+	0.522329i	$0.825063\pi$
$332$		0			0
$333$	51.9092	+	146.821i	0.155883	+	0.440905i
$334$		0			0
$335$	−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	$0.984847\pi$
$338$		0			0
$339$	−253.902	−	551.120i	−0.748973	−	1.62572i
$340$		0			0
$341$		−	387.419i		−	1.13613i
$342$		0			0
$343$	366.287			1.06789
$344$		0			0
$345$	13.5000	−	146.516i	0.0391304	−	0.424683i
$346$		0			0
$347$	−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	$0.981224\pi$
$350$		0			0
$351$	370.810	+	381.221i	1.05644	+	1.08610i
$352$		0			0
$353$	−32.5760	+	18.8078i	−0.0922834	+	0.0532798i	−0.545431	−	0.838155i	$-0.683634\pi$
$353$	−32.5760	+	18.8078i	−0.0922834	+	0.0532798i	0.453148	+	0.891435i	$0.350301\pi$
$354$		0			0
$355$	223.182	−	386.562i	0.628681	−	1.08891i
$356$		0			0
$357$	36.1668	+	3.33243i	0.101308	+	0.00933453i
$358$		0			0
$359$			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
$362$		0			0
$363$	86.9444	−	40.0554i	0.239516	−	0.110346i
$364$		0			0
$365$	432.409	+	249.651i	1.18468	+	0.683976i
$366$		0			0
$367$	−16.6135	−	28.7755i	−0.0452684	−	0.0784072i	0.842503	−	0.538691i	$-0.181081\pi$
$367$	−16.6135	−	28.7755i	−0.0452684	−	0.0784072i	−0.887772	+	0.460284i	$0.847748\pi$
$368$		0			0
$369$	101.682	−	547.091i	0.275560	−	1.48263i
$370$		0			0
$371$	−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	$0.0691299\pi$
$374$		0			0
$375$	207.000	−	292.742i	0.552000	−	0.780646i
$376$		0			0
$377$		−	64.7858i		−	0.171846i
$378$		0			0
$379$	166.334			0.438875			0.219438	−	0.975627i	$-0.429578\pi$
$379$	166.334			0.438875			0.219438	+	0.975627i	$0.429578\pi$
$380$		0			0
$381$	24.7173	+	17.4778i	0.0648749	+	0.0458735i
$382$		0			0
$383$	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
$386$		0			0
$387$	−5.58290	+	6.53010i	−0.0144261	+	0.0168736i
$388$		0			0
$389$	−146.682	+	84.6867i	−0.377074	+	0.217704i	−0.676544	−	0.736402i	$-0.736523\pi$
$389$	−146.682	+	84.6867i	−0.377074	+	0.217704i	0.299471	+	0.954106i	$0.403190\pi$
$390$		0			0
$391$	9.00000	−	15.5885i	0.0230179	−	0.0398682i
$392$		0			0
$393$	6.22652	+	13.5153i	0.0158436	+	0.0343901i
$394$		0			0
$395$		−	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	$0.604611\pi$
$398$		0			0
$399$	−8.20766	+	89.0778i	−0.0205706	+	0.223253i
$400$		0			0
$401$	226.364	+	130.691i	0.564498	+	0.325913i	0.754949	−	0.655784i	$-0.227662\pi$
$401$	226.364	+	130.691i	0.564498	+	0.325913i	−0.190451	+	0.981697i	$0.560995\pi$
$402$		0			0
$403$	−404.234	−	700.155i	−1.00306	−	1.73736i
$404$		0			0
$405$	415.772	−	65.4238i	1.02660	−	0.161540i
$406$		0			0
$407$	−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	$-0.0158660\pi$
$410$		0			0
$411$	−701.082	−	64.5980i	−1.70580	−	0.157173i
$412$		0			0
$413$		−	581.059i		−	1.40692i
$414$		0			0
$415$	−456.773			−1.10066
$416$		0			0
$417$	−290.267	+	133.727i	−0.696085	+	0.320688i
$418$		0			0
$419$	−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	$0.930995\pi$
$422$		0			0
$423$	96.5227	+	82.5221i	0.228186	+	0.195088i
$424$		0			0
$425$	−3.30306	+	1.90702i	−0.00777191	+	0.00448711i
$426$		0			0
$427$	−238.356	+	412.844i	−0.558210	+	0.966849i
$428$		0			0
$429$	−322.015	+	455.398i	−0.750617	+	1.06153i
$430$		0			0
$431$		−	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	$0.421380\pi$
$434$		0			0
$435$	−41.8638	−	29.6022i	−0.0962386	−	0.0680509i
$436$		0			0
$437$	38.3939	+	22.1667i	0.0878578	+	0.0507247i
$438$		0			0
$439$	139.931	+	242.368i	0.318750	+	0.552092i	0.980228	−	0.197874i	$-0.0634035\pi$
$439$	139.931	+	242.368i	0.318750	+	0.552092i	−0.661477	+	0.749965i	$0.730070\pi$
$440$		0			0
$441$	76.9546	+	14.3027i	0.174500	+	0.0324324i
$442$		0			0
$443$	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
$446$		0			0
$447$	131.947	+	286.405i	0.295184	+	0.640727i
$448$		0			0
$449$			542.865i			1.20905i	0.796585	+	0.604527i	$0.206638\pi$
$449$			542.865i			1.20905i	−0.796585	+	0.604527i	$0.793362\pi$
$450$		0			0
$451$	583.590			1.29399
$452$		0			0
$453$	−78.5102	+	852.072i	−0.173312	+	1.88095i
$454$		0			0
$455$	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	$0.865555\pi$
$458$		0			0
$459$	49.5459	+	14.0137i	0.107943	+	0.0305309i
$460$		0			0
$461$	−199.030	+	114.910i	−0.431736	+	0.249263i	−0.700086	−	0.714059i	$-0.746855\pi$
$461$	−199.030	+	114.910i	−0.431736	+	0.249263i	0.268350	+	0.963321i	$0.413522\pi$
$462$		0			0
$463$	−255.401	+	442.368i	−0.551623	+	0.955438i	0.446535	+	0.894766i	$0.352658\pi$
$463$	−255.401	+	442.368i	−0.551623	+	0.955438i	−0.998158	+	0.0606723i	$0.980676\pi$
$464$		0			0
$465$	−637.136	−	58.7059i	−1.37018	−	0.126249i
$466$		0			0
$467$			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
$470$		0			0
$471$	−537.270	+	247.521i	−1.14070	+	0.525523i
$472$		0			0
$473$	−7.80306	−	4.50510i	−0.0164970	−	0.00952452i
$474$		0			0
$475$	−4.69694	−	8.13534i	−0.00988829	−	0.0171270i
$476$		0			0
$477$	−80.9082	+	28.6054i	−0.169619	+	0.0599693i
$478$		0			0
$479$	−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
$482$		0			0
$483$	−103.788	+	146.778i	−0.214881	+	0.303888i
$484$		0			0
$485$			498.200i			1.02722i
$486$		0			0
$487$	351.666			0.722107			0.361054	−	0.932545i	$-0.382417\pi$
$487$	351.666			0.722107			0.361054	+	0.932545i	$0.382417\pi$
$488$		0			0
$489$	−610.070	−	431.385i	−1.24759	−	0.882178i
$490$		0			0
$491$	−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
$494$		0			0
$495$	147.136	+	416.164i	0.297245	+	0.840736i
$496$		0			0
$497$	−472.287	+	272.675i	−0.950276	+	0.548642i
$498$		0			0
$499$	315.113	−	545.792i	0.631489	−	1.09377i	−0.355758	−	0.934578i	$-0.615777\pi$
$499$	315.113	−	545.792i	0.631489	−	1.09377i	0.987247	−	0.159193i	$-0.0508892\pi$
$500$		0			0
$501$	−60.8020	−	131.977i	−0.121361	−	0.263427i
$502$		0			0
$503$		−	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
$506$		0			0
$507$	−60.2724	+	654.137i	−0.118881	+	1.29021i
$508$		0			0
$509$	755.454	+	436.161i	1.48419	+	0.856898i	0.999838	−	0.0179741i	$-0.00572163\pi$
$509$	755.454	+	436.161i	1.48419	+	0.856898i	0.484353	+	0.874873i	$0.339055\pi$
$510$		0			0
$511$	−305.015	−	528.301i	−0.596898	−	1.03386i
$512$		0			0
$513$	−34.5153	+	122.030i	−0.0672813	+	0.237875i
$514$		0			0
$515$	−131.113	+	75.6981i	−0.254588	+	0.146987i
$516$		0			0
$517$	−66.5908	+	115.339i	−0.128802	+	0.223092i
$518$		0			0
$519$	−300.053	−	27.6470i	−0.578136	−	0.0532697i
$520$		0			0
$521$			206.132i			0.395646i	0.980238	+	0.197823i	$0.0633872\pi$
$521$			206.132i			0.395646i	−0.980238	+	0.197823i	$0.936613\pi$
$522$		0			0
$523$	−884.817			−1.69181			−0.845906	−	0.533333i	$-0.820939\pi$
$523$	−884.817			−1.69181			−0.845906	+	0.533333i	$0.820939\pi$
$524$		0			0
$525$	34.5959	−	15.9384i	0.0658970	−	0.0303589i
$526$		0			0
$527$	−67.7878	−	39.1373i	−0.128630	−	0.0742643i
$528$		0			0
$529$	−219.955	−	380.973i	−0.415793	−	0.720175i
$530$		0			0
$531$	150.523	−	809.877i	0.283470	−	1.52519i
$532$		0			0
$533$	1054.68	−	608.920i	1.97876	−	1.14244i
$534$		0			0
$535$	446.363	−	773.124i	0.834324	−	1.44509i
$536$		0			0
$537$	493.757	−	698.278i	0.919473	−	1.30033i
$538$		0			0
$539$			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	$0.655950\pi$
$542$		0			0
$543$	−90.9286	−	64.2962i	−0.167456	−	0.118409i
$544$		0			0
$545$	−523.226	−	302.085i	−0.960048	−	0.554284i
$546$		0			0
$547$	274.022	+	474.620i	0.500955	+	0.867679i	0.999999	+	0.00110267i	$0.000350992\pi$
$547$	274.022	+	474.620i	0.500955	+	0.867679i	−0.499045	+	0.866576i	$0.666316\pi$
$548$		0			0
$549$	−439.166	+	513.675i	−0.799939	+	0.935656i
$550$		0			0
$551$	13.3791	−	7.72442i	0.0242815	−	0.0140189i
$552$		0			0
$553$	−94.4092	+	163.522i	−0.170722	+	0.295699i
$554$		0			0
$555$	112.863	+	244.980i	0.203356	+	0.441405i
$556$		0			0
$557$		−	406.542i		−	0.729879i	−0.931031	−	0.364939i	$-0.881090\pi$
$557$		−	406.542i		−	0.729879i	0.931031	−	0.364939i	$-0.118910\pi$
$558$		0			0
$559$	−18.8025			−0.0336360
$560$		0			0
$561$	−4.95459	+	53.7722i	−0.00883172	+	0.0958507i
$562$		0			0
$563$	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
$566$		0			0
$567$	−479.886	−	184.764i	−0.846360	−	0.325863i
$568$		0			0
$569$	−224.954	+	129.877i	−0.395350	+	0.228255i	−0.684476	−	0.729036i	$-0.739969\pi$
$569$	−224.954	+	129.877i	−0.395350	+	0.228255i	0.289126	+	0.957291i	$0.406635\pi$
$570$		0			0
$571$	−43.9166	+	76.0657i	−0.0769117	+	0.133215i	−0.901916	−	0.431911i	$-0.857839\pi$
$571$	−43.9166	+	76.0657i	−0.0769117	+	0.133215i	0.825004	+	0.565126i	$0.191173\pi$
$572$		0			0
$573$	−53.5454	−	4.93369i	−0.0934475	−	0.00861029i
$574$		0			0
$575$		−	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	$0.536515\pi$
$578$		0			0
$579$	−260.088	+	119.823i	−0.449202	+	0.206948i
$580$		0			0
$581$	483.302	+	279.034i	0.831844	+	0.480266i
$582$		0			0
$583$	−45.0000	−	77.9423i	−0.0771870	−	0.133692i
$584$		0			0
$585$	700.136	+	598.581i	1.19681	+	1.02322i
$586$		0			0
$587$	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
$590$		0			0
$591$	277.757	−	392.808i	0.469978	−	0.664650i
$592$		0			0
$593$		−	77.0321i		−	0.129902i	−0.997888	−	0.0649512i	$-0.979311\pi$
$593$		−	77.0321i		−	0.129902i	0.997888	−	0.0649512i	$-0.0206892\pi$
$594$		0			0
$595$	62.9082			0.105728
$596$		0			0
$597$	15.9592	+	11.2848i	0.0267323	+	0.0189026i
$598$		0			0
$599$	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	$0.603265\pi$
$602$		0			0
$603$	273.901	+	50.9068i	0.454230	+	0.0844226i
$604$		0			0
$605$	143.591	−	82.9025i	0.237341	−	0.137029i
$606$		0			0
$607$	−148.372	+	256.987i	−0.244434	+	0.423373i	−0.961972	−	0.273147i	$-0.911936\pi$
$607$	−148.372	+	256.987i	−0.244434	+	0.423373i	0.717538	+	0.696519i	$0.245269\pi$
$608$		0			0
$609$	26.2117	+	56.8952i	0.0430406	+	0.0934240i
$610$		0			0
$611$			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	$0.638617\pi$
$614$		0			0
$615$	88.4319	−	959.752i	0.143792	−	1.56057i
$616$		0			0
$617$	−229.909	−	132.738i	−0.372623	−	0.215134i	0.301981	−	0.953314i	$-0.402352\pi$
$617$	−229.909	−	132.738i	−0.372623	−	0.215134i	−0.674604	+	0.738180i	$0.735686\pi$
$618$		0			0
$619$	−98.5227	−	170.646i	−0.159164	−	0.275681i	0.775403	−	0.631466i	$-0.217547\pi$
$619$	−98.5227	−	170.646i	−0.159164	−	0.275681i	−0.934568	+	0.355786i	$0.884213\pi$
$620$		0			0
$621$	−182.682	+	177.693i	−0.294173	+	0.286139i
$622$		0			0
$623$	−227.486	+	131.339i	−0.365146	+	0.210817i
$624$		0			0
$625$	335.500	−	581.103i	0.536800	−	0.929765i
$626$		0			0
$627$	−132.439	−	12.2030i	−0.211227	−	0.0194625i
$628$		0			0
$629$			32.9973i			0.0524600i
$630$		0			0
$631$	160.879			0.254958			0.127479	−	0.991841i	$-0.459311\pi$
$631$	160.879			0.254958			0.127479	+	0.991841i	$0.459311\pi$
$632$		0			0
$633$	420.808	−	193.867i	0.664783	−	0.306267i
$634$		0			0
$635$	45.4087	+	26.2167i	0.0715097	+	0.0412862i
$636$		0			0
$637$	85.6515	+	148.353i	0.134461	+	0.232893i
$638$		0			0
$639$	−728.908	+	257.708i	−1.14070	+	0.403299i
$640$		0			0
$641$	−267.894	+	154.669i	−0.417931	+	0.241293i	−0.694192	−	0.719790i	$-0.744238\pi$
$641$	−267.894	+	154.669i	−0.417931	+	0.241293i	0.276261	+	0.961083i	$0.410905\pi$
$642$		0			0
$643$	197.296	−	341.726i	0.306836	−	0.531456i	−0.670832	−	0.741609i	$-0.734063\pi$
$643$	197.296	−	341.726i	0.306836	−	0.531456i	0.977668	+	0.210153i	$0.0673963\pi$
$644$		0			0
$645$	−8.59133	+	12.1500i	−0.0133199	+	0.0188372i
$646$		0			0
$647$		−	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
$650$		0			0
$651$	638.277	+	451.330i	0.980456	+	0.693287i
$652$		0			0
$653$	−459.621	−	265.363i	−0.703861	−	0.406375i	0.104923	−	0.994480i	$-0.466540\pi$
$653$	−459.621	−	265.363i	−0.703861	−	0.406375i	−0.808784	+	0.588106i	$0.799874\pi$
$654$		0			0
$655$	12.8870	+	22.3209i	0.0196748	+	0.0340778i
$656$		0			0
$657$	−288.272	−	815.358i	−0.438771	−	1.24103i
$658$		0			0
$659$	−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	$0.112893\pi$
$662$		0			0
$663$	47.1520	+	102.348i	0.0711192	+	0.154371i
$664$		0			0
$665$			154.941i			0.232994i
$666$		0			0
$667$	31.0454			0.0465448
$668$		0			0
$669$	25.5362	−	277.145i	0.0381708	−	0.414267i
$670$		0			0
$671$	−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	$0.764401\pi$
$674$		0			0
$675$	52.3485	−	13.2528i	0.0775533	−	0.0196338i
$676$		0			0
$677$	402.227	−	232.226i	0.594131	−	0.343022i	−0.172598	−	0.984992i	$-0.555216\pi$
$677$	402.227	−	232.226i	0.594131	−	0.343022i	0.766729	+	0.641971i	$0.221883\pi$
$678$		0			0
$679$	304.341	−	527.134i	0.448220	−	0.776339i
$680$		0			0
$681$	507.257	+	46.7389i	0.744871	+	0.0686327i
$682$		0			0
$683$		−	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
$686$		0			0
$687$	1110.46	−	511.589i	1.61638	−	0.744671i
$688$		0			0
$689$	−162.650	−	93.9063i	−0.236067	−	0.136294i
$690$		0			0
$691$	518.841	+	898.658i	0.750855	+	1.30052i	0.947409	+	0.320025i	$0.103691\pi$
$691$	518.841	+	898.658i	0.750855	+	1.30052i	−0.196554	+	0.980493i	$0.562975\pi$
$692$		0			0
$693$	98.5454	−	530.217i	0.142201	−	0.765104i
$694$		0			0
$695$	−479.385	+	276.773i	−0.689763	+	0.398235i
$696$		0			0
$697$	58.9546	−	102.112i	0.0845833	−	0.146503i
$698$		0			0
$699$	26.4245	−	37.3699i	0.0378033	−	0.0534619i
$700$		0			0
$701$		−	778.180i		−	1.11010i	−0.831817	−	0.555050i	$-0.812699\pi$
$701$		−	778.180i		−	1.11010i	0.831817	−	0.555050i	$-0.187301\pi$
$702$		0			0
$703$	−81.2714			−0.115607
$704$		0			0
$705$	179.591	+	126.990i	0.254739	+	0.180128i
$706$		0			0
$707$	−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	$0.523641\pi$
$710$		0			0
$711$	−173.947	+	203.459i	−0.244651	+	0.286159i
$712$		0			0
$713$	335.515	−	193.710i	0.470568	−	0.271682i
$714$		0			0
$715$	−483.022	+	836.619i	−0.675556	+	1.17010i
$716$		0			0
$717$	70.9699	+	154.047i	0.0989817	+	0.214850i
$718$		0			0
$719$		−	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
$722$		0			0
$723$	−23.1799	+	251.571i	−0.0320607	+	0.347954i
$724$		0			0
$725$	−5.69694	−	3.28913i	−0.00785785	−	0.00453673i
$726$		0			0
$727$	−420.704	−	728.681i	−0.578685	−	1.00231i	−0.995630	−	0.0933809i	$-0.970233\pi$
$727$	−420.704	−	728.681i	−0.578685	−	1.00231i	0.416945	−	0.908932i	$-0.363101\pi$
$728$		0			0
$729$	−621.000	−	381.838i	−0.851852	−	0.523783i
$730$		0			0
$731$	−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	$0.302401\pi$
$734$		0			0
$735$	135.000	+	12.4389i	0.183673	+	0.0169237i
$736$		0			0
$737$			292.174i			0.396437i
$738$		0			0
$739$	389.362			0.526877			0.263439	−	0.964676i	$-0.415143\pi$
$739$	389.362			0.526877			0.263439	+	0.964676i	$0.415143\pi$
$740$		0			0
$741$	−252.081	+	116.134i	−0.340190	+	0.156726i
$742$		0			0
$743$	−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
$746$		0			0
$747$	601.340	+	514.116i	0.805007	+	0.688240i
$748$		0			0
$749$	−944.574	+	545.350i	−1.26111	+	0.728105i
$750$		0			0
$751$	−645.916	+	1118.76i	−0.860074	+	1.48969i	0.0117826	+	0.999931i	$0.496249\pi$
$751$	−645.916	+	1118.76i	−0.860074	+	1.48969i	−0.871857	+	0.489761i	$0.837084\pi$
$752$		0			0
$753$	−379.151	+	536.201i	−0.503521	+	0.712086i
$754$		0			0
$755$			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	$0.258277\pi$
$758$		0			0
$759$	−218.227	−	154.310i	−0.287519	−	0.203307i
$760$		0			0
$761$	−281.607	−	162.586i	−0.370048	−	0.213647i	0.303431	−	0.952853i	$-0.401868\pi$
$761$	−281.607	−	162.586i	−0.370048	−	0.213647i	−0.673479	+	0.739206i	$0.735201\pi$
$762$		0			0
$763$	369.076	+	639.258i	0.483717	+	0.837822i
$764$		0			0
$765$	87.6811	+	16.2963i	0.114616	+	0.0213023i
$766$		0			0
$767$	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	$0.238193\pi$
$770$		0			0
$771$	16.0982	+	34.9428i	0.0208797	+	0.0453214i
$772$		0			0
$773$			532.579i			0.688977i	0.938791	+	0.344488i	$0.111948\pi$
$773$			532.579i			0.688977i	−0.938791	+	0.344488i	$0.888052\pi$
$774$		0			0
$775$	−82.0908			−0.105924
$776$		0			0
$777$	30.2362	−	328.154i	0.0389140	−	0.422334i
$778$		0			0
$779$	251.499	+	145.203i	0.322849	+	0.186397i
$780$		0			0
$781$	−405.409	−	702.188i	−0.519089	−	0.899089i
$782$		0			0
$783$	21.7951	+	86.0904i	0.0278354	+	0.109949i
$784$		0			0
$785$	−887.317	+	512.293i	−1.13034	+	0.652602i
$786$		0			0
$787$	−51.9768	+	90.0264i	−0.0660442	+	0.114392i	−0.897157	−	0.441712i	$-0.854371\pi$
$787$	−51.9768	+	90.0264i	−0.0660442	+	0.114392i	0.831113	+	0.556104i	$0.187704\pi$
$788$		0			0
$789$	1005.13	+	92.6135i	1.27393	+	0.117381i
$790$		0			0
$791$			1284.07i			1.62335i
$792$		0			0
$793$	−1479.06			−1.86514
$794$		0			0
$795$	−135.000	+	62.1947i	−0.169811	+	0.0782324i
$796$		0			0
$797$	−956.331	−	552.138i	−1.19991	−	0.692770i	−0.239378	−	0.970927i	$-0.576943\pi$
$797$	−956.331	−	552.138i	−1.19991	−	0.692770i	−0.960536	+	0.278156i	$0.910277\pi$
$798$		0			0
$799$	13.4541	+	23.3031i	0.0168386	+	0.0291654i
$800$		0			0
$801$	−351.092	+	124.130i	−0.438317	+	0.154968i
$802$		0			0
$803$	785.469	−	453.491i	0.978168	−	0.564746i
$804$		0			0
$805$	−155.682	+	269.648i	−0.193393	+	0.334967i
$806$		0			0
$807$	104.697	−	148.064i	0.129736	−	0.183474i
$808$		0			0
$809$			256.465i			0.317015i	0.987358	+	0.158508i	$0.0506683\pi$
$809$			256.465i			0.317015i	−0.987358	+	0.158508i	$0.949332\pi$
$810$		0			0
$811$	−735.362			−0.906735			−0.453368	−	0.891324i	$-0.649778\pi$
$811$	−735.362			−0.906735			−0.453368	+	0.891324i	$0.649778\pi$
$812$		0			0
$813$	672.717	+	475.683i	0.827451	+	0.585096i
$814$		0			0
$815$	−1120.77	−	647.077i	−1.37518	−	0.793960i
$816$		0			0
$817$	−2.24183	−	3.88296i	−0.00274398	−	0.00475271i
$818$		0			0
$819$	−375.136	−	1061.05i	−0.458042	−	1.29554i
$820$		0			0
$821$	1078.45	−	622.645i	1.31358	−	0.758398i	0.330896	−	0.943667i	$-0.392649\pi$
$821$	1078.45	−	622.645i	1.31358	−	0.758398i	0.982688	+	0.185269i	$0.0593157\pi$
$822$		0			0
$823$	−771.129	+	1335.63i	−0.936973	+	1.62288i	−0.165896	+	0.986143i	$0.553052\pi$
$823$	−771.129	+	1335.63i	−0.936973	+	1.62288i	−0.771077	+	0.636742i	$0.780282\pi$
$824$		0			0
$825$	23.6969	+	51.4366i	0.0287236	+	0.0623474i
$826$		0			0
$827$			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	$0.273458\pi$
$830$		0			0
$831$	13.4875	−	146.380i	0.0162304	−	0.176149i
$832$		0			0
$833$	14.3633	+	8.29263i	0.0172428	+	0.00995514i
$834$		0			0
$835$	−125.842	−	217.964i	−0.150708	−	0.261035i
$836$		0			0
$837$	772.711	+	794.407i	0.923191	+	0.949112i
$838$		0			0
$839$	−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
$842$		0			0
$843$	1024.92	+	94.4361i	1.21580	+	0.112024i
$844$		0			0
$845$			1137.80i			1.34651i
$846$		0			0
$847$	−202.574			−0.239167
$848$		0			0
$849$	935.701	−	431.079i	1.10212	−	0.507749i
$850$		0			0
$851$	−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	$0.922917\pi$
$854$		0			0
$855$	−40.1373	+	215.956i	−0.0469442	+	0.252580i
$856$		0			0
$857$	793.939	−	458.381i	0.926417	−	0.534867i	0.0407403	−	0.999170i	$-0.487028\pi$
$857$	793.939	−	458.381i	0.926417	−	0.534867i	0.885677	+	0.464303i	$0.153695\pi$
$858$		0			0
$859$	478.901	−	829.480i	0.557510	−	0.965635i	−0.440194	−	0.897903i	$-0.645090\pi$
$859$	478.901	−	829.480i	0.557510	−	0.965635i	0.997704	−	0.0677322i	$-0.0215764\pi$
$860$		0			0
$861$	−679.863	+	961.471i	−0.789620	+	1.11669i
$862$		0			0
$863$		−	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
$866$		0			0
$867$	−698.994	−	494.264i	−0.806222	−	0.570085i
$868$		0			0
$869$	−243.121	−	140.366i	−0.279771	−	0.161526i
$870$		0			0
$871$	304.855	+	528.025i	0.350006	+	0.606228i
$872$		0			0
$873$	560.743	−	655.878i	0.642317	−	0.751292i
$874$		0			0
$875$	−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	$0.971845\pi$
$878$		0			0
$879$	359.583	+	780.511i	0.409082	+	0.887954i
$880$		0			0
$881$		−	1536.71i		−	1.74428i	−0.489254	−	0.872141i	$-0.662731\pi$
$881$		−	1536.71i		−	1.74428i	0.489254	−	0.872141i	$-0.337269\pi$
$882$		0			0
$883$	294.213			0.333197			0.166599	−	0.986025i	$-0.446722\pi$
$883$	294.213			0.333197			0.166599	+	0.986025i	$0.446722\pi$
$884$		0			0
$885$	130.909	−	1420.75i	0.147919	−	1.60537i
$886$		0			0
$887$	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
$890$		0			0
$891$	274.704	−	713.486i	0.308310	−	0.800770i
$892$		0			0
$893$	−57.3949	+	33.1370i	−0.0642720	+	0.0371075i
$894$		0			0
$895$	740.636	−	1282.82i	0.827526	−	1.43332i
$896$		0			0
$897$	−555.393	−	51.1741i	−0.619168	−	0.0570503i
$898$		0			0
$899$		−	135.004i		−	0.150171i
$900$		0			0
$901$	−18.1837			−0.0201817
$902$		0			0
$903$	16.5125	−	7.60734i	0.0182863	−	0.00842452i
$904$		0			0
$905$	−167.046	−	96.4443i	−0.184582	−	0.106568i
$906$		0			0
$907$	−255.037	−	441.737i	−0.281187	−	0.487031i	0.690490	−	0.723342i	$-0.257395\pi$
$907$	−255.037	−	441.737i	−0.281187	−	0.487031i	−0.971677	+	0.236311i	$0.924062\pi$
$908$		0			0
$909$	−1080.36	−	923.656i	−1.18852	−	1.01612i
$910$		0			0
$911$	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
$914$		0			0
$915$	−675.817	+	955.750i	−0.738598	+	1.04454i
$916$		0			0
$917$		−	31.4897i		−	0.0343399i
$918$		0			0
$919$	1240.63			1.34998			0.674991	−	0.737826i	$-0.264147\pi$
$919$	1240.63			1.34998			0.674991	+	0.737826i	$0.264147\pi$
$920$		0			0
$921$	377.444	+	266.893i	0.409820	+	0.289786i
$922$		0			0
$923$	−1465.33	−	846.010i	−1.58757	−	0.916587i
$924$		0			0
$925$	17.3031	+	29.9698i	0.0187060	+	0.0323998i
$926$		0			0
$927$	257.811	+	47.9164i	0.278113	+	0.0516897i
$928$		0			0
$929$	293.576	−	169.496i	0.316013	−	0.182450i	−0.333601	−	0.942714i	$-0.608264\pi$
$929$	293.576	−	169.496i	0.316013	−	0.182450i	0.649614	+	0.760264i	$0.274931\pi$
$930$		0			0
$931$	−20.4245	+	35.3763i	−0.0219382	+	0.0379981i
$932$		0			0
$933$	−90.3627	−	196.141i	−0.0968518	−	0.210227i
$934$		0			0
$935$			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	$0.250698\pi$
$938$		0			0
$939$	101.185	−	1098.17i	0.107759	−	1.16951i
$940$		0			0
$941$	−310.984	−	179.547i	−0.330482	−	0.190804i	0.325573	−	0.945517i	$-0.394443\pi$
$941$	−310.984	−	179.547i	−0.330482	−	0.190804i	−0.656055	+	0.754713i	$0.727776\pi$
$942$		0			0
$943$	291.795	+	505.404i	0.309433	+	0.535953i
$944$		0			0
$945$	−857.043	−	242.408i	−0.906924	−	0.256517i
$946$		0			0
$947$	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
$950$		0			0
$951$	321.431	+	29.6168i	0.337992	+	0.0311428i
$952$		0			0
$953$			465.082i			0.488019i	0.969773	+	0.244010i	$0.0784628\pi$
$953$			465.082i			0.488019i	−0.969773	+	0.244010i	$0.921537\pi$
$954$		0			0
$955$	−93.1362			−0.0975248
$956$		0			0
$957$	−84.5908	+	38.9711i	−0.0883917	+	0.0407222i
$958$		0			0
$959$	1290.28	+	744.942i	1.34544	+	0.776791i
$960$		0			0
$961$	−361.863	−	626.765i	−0.376548	−	0.652200i
$962$		0			0
$963$	−1457.82	+	515.416i	−1.51383	+	0.535219i
$964$		0			0
$965$	−429.543	+	247.997i	−0.445123	+	0.256992i
$966$		0			0
$967$	612.113	−	1060.21i	0.633002	−	1.09639i	−0.353933	−	0.935271i	$-0.615156\pi$
$967$	612.113	−	1060.21i	0.633002	−	1.09639i	0.986935	−	0.161121i	$-0.0515109\pi$
$968$		0			0
$969$	−15.5143	+	21.9405i	−0.0160106	+	0.0226424i
$970$		0			0
$971$		−	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
$974$		0			0
$975$	96.4949	+	68.2322i	0.0989691	+	0.0699817i
$976$		0			0
$977$	1314.92	+	759.170i	1.34588	+	0.777042i	0.987663	−	0.156597i	$-0.0500525\pi$
$977$	1314.92	+	759.170i	1.34588	+	0.777042i	0.358214	+	0.933639i	$0.383386\pi$
$978$		0			0
$979$	−195.272	−	338.222i	−0.199461	−	0.345477i
$980$		0			0
$981$	348.817	+	986.604i	0.355573	+	1.00571i
$982$		0			0
$983$	−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
$986$		0			0
$987$	−112.446	−	244.075i	−0.113927	−	0.247289i
$988$		0			0
$989$		−	9.01020i		−	0.00911041i
$990$		0			0
$991$	−429.546			−0.433447			−0.216723	−	0.976233i	$-0.569537\pi$
$991$	−429.546			−0.433447			−0.216723	+	0.976233i	$0.569537\pi$
$992$		0			0
$993$	4.73369	−	51.3747i	0.00476706	−	0.0517369i
$994$		0			0
$995$	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	$0.720009\pi$
$998$		0			0
$999$	127.151	−	449.547i	0.127278	−	0.449997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.q.c.113.1		4
3.2	odd	2		432.3.q.d.17.2		4
4.3	odd	2		18.3.d.a.5.1	✓	4
8.3	odd	2		576.3.q.f.257.1		4
8.5	even	2		576.3.q.e.257.2		4
9.2	odd	6	inner	144.3.q.c.65.1		4
9.4	even	3		1296.3.e.g.161.3		4
9.5	odd	6		1296.3.e.g.161.1		4
9.7	even	3		432.3.q.d.305.2		4
12.11	even	2		54.3.d.a.17.2		4
20.3	even	4		450.3.k.a.149.3		8
20.7	even	4		450.3.k.a.149.2		8
20.19	odd	2		450.3.i.b.401.2		4
24.5	odd	2		1728.3.q.c.449.2		4
24.11	even	2		1728.3.q.d.449.1		4
36.7	odd	6		54.3.d.a.35.2		4
36.11	even	6		18.3.d.a.11.1	yes	4
36.23	even	6		162.3.b.a.161.3		4
36.31	odd	6		162.3.b.a.161.2		4
60.23	odd	4		1350.3.k.a.449.2		8
60.47	odd	4		1350.3.k.a.449.3		8
60.59	even	2		1350.3.i.b.1151.1		4
72.11	even	6		576.3.q.f.65.1		4
72.29	odd	6		576.3.q.e.65.2		4
72.43	odd	6		1728.3.q.d.1601.1		4
72.61	even	6		1728.3.q.c.1601.2		4
180.7	even	12		1350.3.k.a.899.2		8
180.43	even	12		1350.3.k.a.899.3		8
180.47	odd	12		450.3.k.a.299.3		8
180.79	odd	6		1350.3.i.b.251.1		4
180.83	odd	12		450.3.k.a.299.2		8
180.119	even	6		450.3.i.b.101.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.3.d.a.5.1	✓	4	4.3	odd	2
18.3.d.a.11.1	yes	4	36.11	even	6
54.3.d.a.17.2		4	12.11	even	2
54.3.d.a.35.2		4	36.7	odd	6
144.3.q.c.65.1		4	9.2	odd	6	inner
144.3.q.c.113.1		4	1.1	even	1	trivial
162.3.b.a.161.2		4	36.31	odd	6
162.3.b.a.161.3		4	36.23	even	6
432.3.q.d.17.2		4	3.2	odd	2
432.3.q.d.305.2		4	9.7	even	3
450.3.i.b.101.2		4	180.119	even	6
450.3.i.b.401.2		4	20.19	odd	2
450.3.k.a.149.2		8	20.7	even	4
450.3.k.a.149.3		8	20.3	even	4
450.3.k.a.299.2		8	180.83	odd	12
450.3.k.a.299.3		8	180.47	odd	12
576.3.q.e.65.2		4	72.29	odd	6
576.3.q.e.257.2		4	8.5	even	2
576.3.q.f.65.1		4	72.11	even	6
576.3.q.f.257.1		4	8.3	odd	2
1296.3.e.g.161.1		4	9.5	odd	6
1296.3.e.g.161.3		4	9.4	even	3
1350.3.i.b.251.1		4	180.79	odd	6
1350.3.i.b.1151.1		4	60.59	even	2
1350.3.k.a.449.2		8	60.23	odd	4
1350.3.k.a.449.3		8	60.47	odd	4
1350.3.k.a.899.2		8	180.7	even	12
1350.3.k.a.899.3		8	180.43	even	12
1728.3.q.c.449.2		4	24.5	odd	2
1728.3.q.c.1601.2		4	72.61	even	6
1728.3.q.d.449.1		4	24.11	even	2
1728.3.q.d.1601.1		4	72.43	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(3.17423 + 5.49794i) q^{7} +(3.00000 + 8.48528i) q^{9} +O(q^{10})\)	\(q+(-2.44949 - 1.73205i) q^{3} +(-4.50000 - 2.59808i) q^{5} +(3.17423 + 5.49794i) q^{7} +(3.00000 + 8.48528i) q^{9} +(-8.17423 + 4.71940i) q^{11} +(-9.84847 + 17.0580i) q^{13} +(6.52270 + 14.1582i) q^{15} +1.90702i q^{17} -4.69694 q^{19} +(1.74745 - 18.9651i) q^{21} +(-8.17423 - 4.71940i) q^{23} +(1.00000 + 1.73205i) q^{25} +(7.34847 - 25.9808i) q^{27} +(-2.84847 + 1.64456i) q^{29} +(-20.5227 + 35.5464i) q^{31} +(28.1969 + 2.59808i) q^{33} -32.9876i q^{35} +17.3031 q^{37} +(53.6691 - 24.7255i) q^{39} +(-53.5454 - 30.9145i) q^{41} +(0.477296 + 0.826701i) q^{43} +(8.54541 - 45.9780i) q^{45} +(12.2196 - 7.05501i) q^{47} +(4.34847 - 7.53177i) q^{49} +(3.30306 - 4.67123i) q^{51} +9.53512i q^{53} +49.0454 q^{55} +(11.5051 + 8.13534i) q^{57} +(-79.2650 - 45.7637i) q^{59} +(37.5454 + 65.0306i) q^{61} +(-37.1288 + 43.4281i) q^{63} +(88.6362 - 51.1741i) q^{65} +(15.4773 - 26.8075i) q^{67} +(11.8485 + 25.7183i) q^{69} +85.9026i q^{71} -96.0908 q^{73} +(0.550510 - 5.97469i) q^{75} +(-51.8939 - 29.9609i) q^{77} +(14.8712 + 25.7576i) q^{79} +(-63.0000 + 50.9117i) q^{81} +(76.1288 - 43.9530i) q^{83} +(4.95459 - 8.58161i) q^{85} +(9.82577 + 0.905350i) q^{87} +41.3766i q^{89} -125.045 q^{91} +(111.838 - 51.5241i) q^{93} +(21.1362 + 12.2030i) q^{95} +(-47.9393 - 83.0333i) q^{97} +(-64.5681 - 55.2025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9	\( 4 q - 18 q^{5} - 2 q^{7} + 12 q^{9} - 18 q^{11} - 10 q^{13} - 18 q^{15} + 40 q^{19} - 42 q^{21} - 18 q^{23} + 4 q^{25} + 18 q^{29} - 38 q^{31} + 54 q^{33} + 128 q^{37} + 102 q^{39} - 126 q^{41} + 46 q^{43} - 54 q^{45} - 54 q^{47} - 12 q^{49} + 72 q^{51} + 108 q^{55} + 144 q^{57} - 126 q^{59} + 62 q^{61} - 222 q^{63} + 90 q^{65} + 106 q^{67} + 18 q^{69} - 208 q^{73} + 12 q^{75} - 90 q^{77} - 14 q^{79} - 252 q^{81} + 378 q^{83} + 108 q^{85} + 54 q^{87} - 412 q^{91} + 222 q^{93} - 180 q^{95} + 14 q^{97} - 126 q^{99}+O(q^{100}) \) 4 * q - 18 * q^5 - 2 * q^7 + 12 * q^9 - 18 * q^11 - 10 * q^13 - 18 * q^15 + 40 * q^19 - 42 * q^21 - 18 * q^23 + 4 * q^25 + 18 * q^29 - 38 * q^31 + 54 * q^33 + 128 * q^37 + 102 * q^39 - 126 * q^41 + 46 * q^43 - 54 * q^45 - 54 * q^47 - 12 * q^49 + 72 * q^51 + 108 * q^55 + 144 * q^57 - 126 * q^59 + 62 * q^61 - 222 * q^63 + 90 * q^65 + 106 * q^67 + 18 * q^69 - 208 * q^73 + 12 * q^75 - 90 * q^77 - 14 * q^79 - 252 * q^81 + 378 * q^83 + 108 * q^85 + 54 * q^87 - 412 * q^91 + 222 * q^93 - 180 * q^95 + 14 * q^97 - 126 * q^99

Introduction

L-functions

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