LMFDB - Embedded newform 900.3.p.e.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 $ x^16 - 2x^15 + 10x^14 - 12x^13 + 6x^12 - 27x^11 - 585x^10 + 3618x^9 - 12150x^8 + 32562x^7 - 47385x^6 - 19683x^5 + 39366x^4 - 708588x^3 + 5314410x^2 - 9565938*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Root			$1.13333 + 2.77769i$ of defining polynomial
Character	$\chi$	$=$	900.101
Dual form			900.3.p.e.401.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.83888 - 2.37034i) q^{3} +(-4.13058 + 7.15437i) q^{7} +(-2.23701 - 8.71756i) q^{9} +O(q^{10})$	\(q+(1.83888 - 2.37034i) q^{3} +(-4.13058 + 7.15437i) q^{7} +(-2.23701 - 8.71756i) q^{9} +(-1.19023 - 0.687179i) q^{11} +(10.7805 + 18.6723i) q^{13} -25.3117i q^{17} -2.49216 q^{19} +(9.36262 + 22.9469i) q^{21} +(33.1892 - 19.1618i) q^{23} +(-24.7772 - 10.7281i) q^{27} +(37.0732 + 21.4042i) q^{29} +(10.9499 + 18.9658i) q^{31} +(-3.81754 + 1.55760i) q^{33} +30.5877 q^{37} +(64.0837 + 8.78288i) q^{39} +(7.29574 - 4.21220i) q^{41} +(35.5905 - 61.6445i) q^{43} +(42.1375 + 24.3281i) q^{47} +(-9.62335 - 16.6681i) q^{49} +(-59.9974 - 46.5454i) q^{51} -1.96485i q^{53} +(-4.58279 + 5.90725i) q^{57} +(3.77749 - 2.18094i) q^{59} +(-18.4907 + 32.0268i) q^{61} +(71.6088 + 20.0042i) q^{63} +(-8.06346 - 13.9663i) q^{67} +(15.6112 - 113.906i) q^{69} +71.5235i q^{71} +122.276 q^{73} +(9.83266 - 5.67689i) q^{77} +(3.98462 - 6.90157i) q^{79} +(-70.9916 + 39.0024i) q^{81} +(-90.2806 - 52.1235i) q^{83} +(118.909 - 48.5161i) q^{87} -9.37245i q^{89} -178.118 q^{91} +(65.0910 + 8.92094i) q^{93} +(-6.86481 + 11.8902i) q^{97} +(-3.32797 + 11.9131i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} - q^{7} + 14 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 - q^7 + 14 * q^9	$ 16 q + 2 q^{3} - q^{7} + 14 q^{9} - 10 q^{13} + 2 q^{19} + q^{21} + 27 q^{23} - 16 q^{27} + 9 q^{29} + 8 q^{31} + 36 q^{33} - 22 q^{37} + 19 q^{39} + 54 q^{41} + 44 q^{43} - 108 q^{47} - 45 q^{49} + 90 q^{51} - 68 q^{57} + 9 q^{59} - 55 q^{61} - 107 q^{63} - 28 q^{67} - 147 q^{69} + 86 q^{73} + 342 q^{77} + 11 q^{79} - 130 q^{81} - 306 q^{83} + 375 q^{87} - 134 q^{91} - 83 q^{93} + 41 q^{97} + 252 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 - q^7 + 14 * q^9 - 10 * q^13 + 2 * q^19 + q^21 + 27 * q^23 - 16 * q^27 + 9 * q^29 + 8 * q^31 + 36 * q^33 - 22 * q^37 + 19 * q^39 + 54 * q^41 + 44 * q^43 - 108 * q^47 - 45 * q^49 + 90 * q^51 - 68 * q^57 + 9 * q^59 - 55 * q^61 - 107 * q^63 - 28 * q^67 - 147 * q^69 + 86 * q^73 + 342 * q^77 + 11 * q^79 - 130 * q^81 - 306 * q^83 + 375 * q^87 - 134 * q^91 - 83 * q^93 + 41 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	1.83888	−	2.37034i	0.612962	−	0.790113i
$3$	1.83888	−	2.37034i	0.612962	−	0.790113i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.13058	+	7.15437i	−0.590083	+	1.02205i	0.404138	+	0.914698i	$0.367571\pi$
$7$	−4.13058	+	7.15437i	−0.590083	+	1.02205i	−0.994221	+	0.107355i	$0.965762\pi$
$8$		0			0
$9$	−2.23701	−	8.71756i	−0.248556	−	0.968617i
$10$		0			0
$11$	−1.19023	−	0.687179i	−0.108203	−	0.0624708i	0.444922	−	0.895569i	$-0.353231\pi$
$11$	−1.19023	−	0.687179i	−0.108203	−	0.0624708i	−0.553125	+	0.833098i	$0.686565\pi$
$12$		0			0
$13$	10.7805	+	18.6723i	0.829266	+	1.43633i	0.898615	+	0.438739i	$0.144575\pi$
$13$	10.7805	+	18.6723i	0.829266	+	1.43633i	−0.0693484	+	0.997593i	$0.522092\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	25.3117i		−	1.48893i	−0.667664	−	0.744463i	$-0.732706\pi$
$17$		−	25.3117i		−	1.48893i	0.667664	−	0.744463i	$-0.267294\pi$
$18$		0			0
$19$	−2.49216			−0.131166			−0.0655831	−	0.997847i	$-0.520891\pi$
$19$	−2.49216			−0.131166			−0.0655831	+	0.997847i	$0.520891\pi$
$20$		0			0
$21$	9.36262	+	22.9469i	0.445839	+	1.09271i
$22$		0			0
$23$	33.1892	−	19.1618i	1.44301	−	0.833122i	0.444961	−	0.895550i	$-0.353218\pi$
$23$	33.1892	−	19.1618i	1.44301	−	0.833122i	0.998049	+	0.0624276i	$0.0198843\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−24.7772	−	10.7281i	−0.917672	−	0.397338i
$28$		0			0
$29$	37.0732	+	21.4042i	1.27839	+	0.738076i	0.976551	−	0.215284i	$-0.0690678\pi$
$29$	37.0732	+	21.4042i	1.27839	+	0.738076i	0.301834	+	0.953360i	$0.402401\pi$
$30$		0			0
$31$	10.9499	+	18.9658i	0.353223	+	0.611800i	0.986812	−	0.161869i	$-0.0517523\pi$
$31$	10.9499	+	18.9658i	0.353223	+	0.611800i	−0.633589	+	0.773670i	$0.718419\pi$
$32$		0			0
$33$	−3.81754	+	1.55760i	−0.115683	+	0.0472000i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	30.5877			0.826693			0.413347	−	0.910574i	$-0.364360\pi$
$37$	30.5877			0.826693			0.413347	+	0.910574i	$0.364360\pi$
$38$		0			0
$39$	64.0837	+	8.78288i	1.64317	+	0.225202i
$40$		0			0
$41$	7.29574	−	4.21220i	0.177945	−	0.102736i	−0.408382	−	0.912811i	$-0.633907\pi$
$41$	7.29574	−	4.21220i	0.177945	−	0.102736i	0.586327	+	0.810075i	$0.300573\pi$
$42$		0			0
$43$	35.5905	−	61.6445i	0.827686	−	1.43359i	−0.0721636	−	0.997393i	$-0.522990\pi$
$43$	35.5905	−	61.6445i	0.827686	−	1.43359i	0.899849	−	0.436201i	$-0.143676\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	42.1375	+	24.3281i	0.896544	+	0.517620i	0.876077	−	0.482171i	$-0.160152\pi$
$47$	42.1375	+	24.3281i	0.896544	+	0.517620i	0.0204664	+	0.999791i	$0.493485\pi$
$48$		0			0
$49$	−9.62335	−	16.6681i	−0.196395	−	0.340166i
$50$		0			0
$51$	−59.9974	−	46.5454i	−1.17642	−	0.912654i
$52$		0			0
$53$		−	1.96485i		−	0.0370727i	−0.999828	−	0.0185363i	$-0.994099\pi$
$53$		−	1.96485i		−	0.0370727i	0.999828	−	0.0185363i	$-0.00590064\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.58279	+	5.90725i	−0.0803998	+	0.103636i
$58$		0			0
$59$	3.77749	−	2.18094i	0.0640253	−	0.0369650i	−0.467646	−	0.883916i	$-0.654898\pi$
$59$	3.77749	−	2.18094i	0.0640253	−	0.0369650i	0.531671	+	0.846951i	$0.321564\pi$
$60$		0			0
$61$	−18.4907	+	32.0268i	−0.303126	+	0.525030i	−0.976842	−	0.213960i	$-0.931364\pi$
$61$	−18.4907	+	32.0268i	−0.303126	+	0.525030i	0.673716	+	0.738990i	$0.264697\pi$
$62$		0			0
$63$	71.6088	+	20.0042i	1.13665	+	0.317527i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.06346	−	13.9663i	−0.120350	−	0.208453i	0.799556	−	0.600592i	$-0.205068\pi$
$67$	−8.06346	−	13.9663i	−0.120350	−	0.208453i	−0.919906	+	0.392139i	$0.871735\pi$
$68$		0			0
$69$	15.6112	−	113.906i	0.226249	−	1.65081i
$70$		0			0
$71$			71.5235i			1.00737i	0.863886	+	0.503687i	$0.168023\pi$
$71$			71.5235i			1.00737i	−0.863886	+	0.503687i	$0.831977\pi$
$72$		0			0
$73$	122.276			1.67502			0.837510	−	0.546422i	$-0.184011\pi$
$73$	122.276			1.67502			0.837510	+	0.546422i	$0.184011\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.83266	−	5.67689i	0.127697	−	0.0737259i
$78$		0			0
$79$	3.98462	−	6.90157i	0.0504382	−	0.0873616i	−0.839704	−	0.543044i	$-0.817272\pi$
$79$	3.98462	−	6.90157i	0.0504382	−	0.0873616i	0.890142	+	0.455683i	$0.150605\pi$
$80$		0			0
$81$	−70.9916	+	39.0024i	−0.876440	+	0.481512i
$82$		0			0
$83$	−90.2806	−	52.1235i	−1.08772	−	0.627994i	−0.154750	−	0.987954i	$-0.549457\pi$
$83$	−90.2806	−	52.1235i	−1.08772	−	0.627994i	−0.932968	+	0.359960i	$0.882790\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	118.909	−	48.5161i	1.36676	−	0.557656i
$88$		0			0
$89$		−	9.37245i		−	0.105308i	−0.998613	−	0.0526542i	$-0.983232\pi$
$89$		−	9.37245i		−	0.105308i	0.998613	−	0.0526542i	$-0.0167681\pi$
$90$		0			0
$91$	−178.118			−1.95734
$92$		0			0
$93$	65.0910	+	8.92094i	0.699903	+	0.0959241i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.86481	+	11.8902i	−0.0707713	+	0.122579i	−0.899240	−	0.437457i	$-0.855879\pi$
$97$	−6.86481	+	11.8902i	−0.0707713	+	0.122579i	0.828468	+	0.560036i	$0.189213\pi$
$98$		0			0
$99$	−3.32797	+	11.9131i	−0.0336159	+	0.120334i
$100$		0			0
$101$	−103.509	−	59.7611i	−1.02484	−	0.591694i	−0.109341	−	0.994004i	$-0.534874\pi$
$101$	−103.509	−	59.7611i	−1.02484	−	0.591694i	−0.915503	+	0.402310i	$0.868207\pi$
$102$		0			0
$103$	−40.2560	−	69.7254i	−0.390835	−	0.676945i	0.601725	−	0.798703i	$-0.294480\pi$
$103$	−40.2560	−	69.7254i	−0.390835	−	0.676945i	−0.992560	+	0.121758i	$0.961147\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			74.6987i			0.698119i	0.937101	+	0.349060i	$0.113499\pi$
$107$			74.6987i			0.698119i	−0.937101	+	0.349060i	$0.886501\pi$
$108$		0			0
$109$	−88.2427			−0.809566			−0.404783	−	0.914413i	$-0.632653\pi$
$109$	−88.2427			−0.809566			−0.404783	+	0.914413i	$0.632653\pi$
$110$		0			0
$111$	56.2472	−	72.5031i	0.506731	−	0.653181i
$112$		0			0
$113$	137.822	−	79.5718i	1.21967	−	0.704175i	0.254821	−	0.966988i	$-0.417984\pi$
$113$	137.822	−	79.5718i	1.21967	−	0.704175i	0.964847	+	0.262813i	$0.0846502\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	138.661	−	135.749i	1.18514	−	1.16025i
$118$		0			0
$119$	181.090	+	104.552i	1.52176	+	0.878589i
$120$		0			0
$121$	−59.5556	−	103.153i	−0.492195	−	0.852506i
$122$		0			0
$123$	3.43169	−	25.0391i	0.0278999	−	0.203570i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−210.083			−1.65420			−0.827100	−	0.562055i	$-0.810011\pi$
$127$	−210.083			−1.65420			−0.827100	+	0.562055i	$0.810011\pi$
$128$		0			0
$129$	−80.6716	−	197.719i	−0.625361	−	1.53270i
$130$		0			0
$131$	−5.70580	+	3.29424i	−0.0435557	+	0.0251469i	−0.521620	−	0.853178i	$-0.674672\pi$
$131$	−5.70580	+	3.29424i	−0.0435557	+	0.0251469i	0.478064	+	0.878325i	$0.341339\pi$
$132$		0			0
$133$	10.2940	−	17.8298i	0.0773988	−	0.134059i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	185.816	+	107.281i	1.35632	+	0.783072i	0.989126	−	0.147072i	$-0.0469849\pi$
$137$	185.816	+	107.281i	1.35632	+	0.783072i	0.367195	+	0.930144i	$0.380318\pi$
$138$		0			0
$139$	40.7194	+	70.5281i	0.292946	+	0.507397i	0.974505	−	0.224366i	$-0.0720312\pi$
$139$	40.7194	+	70.5281i	0.292946	+	0.507397i	−0.681559	+	0.731763i	$0.738698\pi$
$140$		0			0
$141$	135.152	−	55.1436i	0.958525	−	0.391089i
$142$		0			0
$143$		−	29.6324i		−	0.207220i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−57.2053	−	7.84018i	−0.389152	−	0.0533346i
$148$		0			0
$149$	234.181	−	135.204i	1.57168	−	0.907412i	0.575721	−	0.817646i	$-0.304721\pi$
$149$	234.181	−	135.204i	1.57168	−	0.907412i	0.995963	−	0.0897663i	$-0.0286120\pi$
$150$		0			0
$151$	−52.7441	+	91.3555i	−0.349299	+	0.605003i	−0.986125	−	0.166004i	$-0.946914\pi$
$151$	−52.7441	+	91.3555i	−0.349299	+	0.605003i	0.636826	+	0.771007i	$0.280247\pi$
$152$		0			0
$153$	−220.657	+	56.6225i	−1.44220	+	0.370082i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.36152	−	9.28642i	−0.0341498	−	0.0591492i	0.848445	−	0.529283i	$-0.177539\pi$
$157$	−5.36152	−	9.28642i	−0.0341498	−	0.0591492i	−0.882595	+	0.470134i	$0.844206\pi$
$158$		0			0
$159$	−4.65737	−	3.61314i	−0.0292916	−	0.0227241i
$160$		0			0
$161$			316.597i			1.96644i
$162$		0			0
$163$	155.005			0.950950			0.475475	−	0.879729i	$-0.342276\pi$
$163$	155.005			0.950950			0.475475	+	0.879729i	$0.342276\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	65.8848	−	38.0386i	0.394519	−	0.227776i	−0.289597	−	0.957149i	$-0.593521\pi$
$167$	65.8848	−	38.0386i	0.394519	−	0.227776i	0.684117	+	0.729373i	$0.260188\pi$
$168$		0			0
$169$	−147.937	+	256.234i	−0.875365	+	1.51618i
$170$		0			0
$171$	5.57497	+	21.7255i	0.0326021	+	0.127050i
$172$		0			0
$173$	−53.0935	−	30.6536i	−0.306899	−	0.177188i	0.338639	−	0.940916i	$-0.390033\pi$
$173$	−53.0935	−	30.6536i	−0.306899	−	0.177188i	−0.645538	+	0.763728i	$0.723367\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.77682	−	12.9644i	0.0100385	−	0.0732453i
$178$		0			0
$179$			294.705i			1.64640i	0.567752	+	0.823200i	$0.307813\pi$
$179$			294.705i			1.64640i	−0.567752	+	0.823200i	$0.692187\pi$
$180$		0			0
$181$	219.086			1.21042			0.605209	−	0.796067i	$-0.293090\pi$
$181$	219.086			1.21042			0.605209	+	0.796067i	$0.293090\pi$
$182$		0			0
$183$	41.9121	+	102.723i	0.229028	+	0.561327i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−17.3937	+	30.1268i	−0.0930144	+	0.161106i
$188$		0			0
$189$	179.097	−	132.952i	0.947603	−	0.703448i
$190$		0			0
$191$	146.319	+	84.4770i	0.766066	+	0.442288i	0.831469	−	0.555571i	$-0.187500\pi$
$191$	146.319	+	84.4770i	0.766066	+	0.442288i	−0.0654037	+	0.997859i	$0.520834\pi$
$192$		0			0
$193$	101.314	+	175.481i	0.524942	+	0.909226i	0.999578	+	0.0290438i	$0.00924622\pi$
$193$	101.314	+	175.481i	0.524942	+	0.909226i	−0.474636	+	0.880182i	$0.657420\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			345.227i			1.75242i	0.481929	+	0.876211i	$0.339936\pi$
$197$			345.227i			1.75242i	−0.481929	+	0.876211i	$0.660064\pi$
$198$		0			0
$199$	−313.067			−1.57320			−0.786601	−	0.617462i	$-0.788161\pi$
$199$	−313.067			−1.57320			−0.786601	+	0.617462i	$0.788161\pi$
$200$		0			0
$201$	−47.9327	−	6.56933i	−0.238471	−	0.0326832i
$202$		0			0
$203$	−306.267	+	176.824i	−1.50871	+	0.871052i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−241.289	−	246.464i	−1.16565	−	1.19065i
$208$		0			0
$209$	2.96624	+	1.71256i	0.0141925	+	0.00819405i
$210$		0			0
$211$	−17.2115	−	29.8111i	−0.0815710	−	0.141285i	0.822354	−	0.568976i	$-0.192660\pi$
$211$	−17.2115	−	29.8111i	−0.0815710	−	0.141285i	−0.903925	+	0.427691i	$0.859327\pi$
$212$		0			0
$213$	169.535	+	131.524i	0.795939	+	0.617481i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−180.918			−0.833723
$218$		0			0
$219$	224.852	−	289.837i	1.02672	−	1.32345i
$220$		0			0
$221$	472.628	−	272.872i	2.13859	−	1.23472i
$222$		0			0
$223$	107.220	−	185.711i	0.480808	−	0.832785i	−0.518949	−	0.854805i	$-0.673677\pi$
$223$	107.220	−	185.711i	0.480808	−	0.832785i	0.999758	+	0.0220206i	$0.00700994\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−377.705	−	218.068i	−1.66390	−	0.960653i	−0.970825	−	0.239789i	$-0.922922\pi$
$227$	−377.705	−	218.068i	−1.66390	−	0.960653i	−0.693076	−	0.720865i	$-0.743745\pi$
$228$		0			0
$229$	−181.933	−	315.117i	−0.794466	−	1.37605i	−0.923178	−	0.384373i	$-0.874418\pi$
$229$	−181.933	−	315.117i	−0.794466	−	1.37605i	0.128712	−	0.991682i	$-0.458916\pi$
$230$		0			0
$231$	4.62499	−	33.7459i	0.0200216	−	0.146086i
$232$		0			0
$233$		−	192.385i		−	0.825685i	−0.910802	−	0.412843i	$-0.864536\pi$
$233$		−	192.385i		−	0.825685i	0.910802	−	0.412843i	$-0.135464\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.03179	−	22.1361i	−0.0381088	−	0.0934012i
$238$		0			0
$239$	−229.644	+	132.585i	−0.960853	+	0.554749i	−0.896436	−	0.443174i	$-0.853852\pi$
$239$	−229.644	+	132.585i	−0.960853	+	0.554749i	−0.0644178	+	0.997923i	$0.520519\pi$
$240$		0			0
$241$	−61.4106	+	106.366i	−0.254816	+	0.441354i	−0.964845	−	0.262818i	$-0.915348\pi$
$241$	−61.4106	+	106.366i	−0.254816	+	0.441354i	0.710030	+	0.704172i	$0.248681\pi$
$242$		0			0
$243$	−38.0964	+	239.995i	−0.156775	+	0.987634i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−26.8666	−	46.5343i	−0.108772	−	0.188398i
$248$		0			0
$249$	−289.566	+	118.146i	−1.16292	+	0.474483i
$250$		0			0
$251$		−	218.969i		−	0.872388i	−0.899853	−	0.436194i	$-0.856326\pi$
$251$		−	218.969i		−	0.872388i	0.899853	−	0.436194i	$-0.143674\pi$
$252$		0			0
$253$	−52.6704			−0.208183
$254$		0			0
$255$		0			0
$256$		0			0
$257$	356.703	−	205.943i	1.38795	−	0.801334i	0.394867	−	0.918738i	$-0.370791\pi$
$257$	356.703	−	205.943i	1.38795	−	0.801334i	0.993084	+	0.117404i	$0.0374574\pi$
$258$		0			0
$259$	−126.345	+	218.835i	−0.487817	+	0.844925i
$260$		0			0
$261$	103.660	−	371.069i	0.397163	−	1.42172i
$262$		0			0
$263$	−356.886	−	206.048i	−1.35698	−	0.783453i	−0.367765	−	0.929919i	$-0.619877\pi$
$263$	−356.886	−	206.048i	−1.35698	−	0.783453i	−0.989216	+	0.146466i	$0.953210\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−22.2159	−	17.2349i	−0.0832055	−	0.0645500i
$268$		0			0
$269$			384.725i			1.43020i	0.699020	+	0.715102i	$0.253620\pi$
$269$			384.725i			1.43020i	−0.699020	+	0.715102i	$0.746380\pi$
$270$		0			0
$271$	−148.889			−0.549405			−0.274702	−	0.961529i	$-0.588579\pi$
$271$	−148.889			−0.549405			−0.274702	+	0.961529i	$0.588579\pi$
$272$		0			0
$273$	−327.539	+	422.200i	−1.19978	+	1.54652i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−264.867	+	458.764i	−0.956200	+	1.65619i	−0.224602	+	0.974451i	$0.572108\pi$
$277$	−264.867	+	458.764i	−0.956200	+	1.65619i	−0.731598	+	0.681737i	$0.761225\pi$
$278$		0			0
$279$	140.841	−	137.883i	0.504805	−	0.494205i
$280$		0			0
$281$	81.2085	+	46.8857i	0.288998	+	0.166853i	0.637490	−	0.770459i	$-0.279973\pi$
$281$	81.2085	+	46.8857i	0.288998	+	0.166853i	−0.348492	+	0.937312i	$0.613306\pi$
$282$		0			0
$283$	−25.2312	−	43.7017i	−0.0891561	−	0.154423i	0.817999	−	0.575220i	$-0.195084\pi$
$283$	−25.2312	−	43.7017i	−0.0891561	−	0.154423i	−0.907155	+	0.420797i	$0.861750\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			69.5952i			0.242492i
$288$		0			0
$289$	−351.684			−1.21690
$290$		0			0
$291$	15.5602	+	38.1367i	0.0534715	+	0.131054i
$292$		0			0
$293$	−204.410	+	118.016i	−0.697643	+	0.402785i	−0.806469	−	0.591276i	$-0.798624\pi$
$293$	−204.410	+	118.016i	−0.697643	+	0.402785i	0.108826	+	0.994061i	$0.465291\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	22.1183	+	29.7953i	0.0744725	+	0.100321i
$298$		0			0
$299$	715.591	+	413.146i	2.39328	+	1.38176i
$300$		0			0
$301$	294.019	+	509.255i	0.976806	+	1.69188i
$302$		0			0
$303$	−331.996	+	135.458i	−1.09570	+	0.447057i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	78.3780			0.255303			0.127651	−	0.991819i	$-0.459256\pi$
$307$	78.3780			0.255303			0.127651	+	0.991819i	$0.459256\pi$
$308$		0			0
$309$	−239.299	−	32.7967i	−0.774430	−	0.106138i
$310$		0			0
$311$	−217.139	+	125.365i	−0.698195	+	0.403103i	−0.806675	−	0.590995i	$-0.798735\pi$
$311$	−217.139	+	125.365i	−0.698195	+	0.403103i	0.108480	+	0.994099i	$0.465402\pi$
$312$		0			0
$313$	−62.7902	+	108.756i	−0.200608	+	0.347463i	−0.948724	−	0.316104i	$-0.897625\pi$
$313$	−62.7902	+	108.756i	−0.200608	+	0.347463i	0.748117	+	0.663567i	$0.230958\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	137.255	+	79.2443i	0.432982	+	0.249982i	0.700616	−	0.713538i	$-0.252909\pi$
$317$	137.255	+	79.2443i	0.432982	+	0.249982i	−0.267634	+	0.963521i	$0.586242\pi$
$318$		0			0
$319$	−29.4170	−	50.9518i	−0.0922164	−	0.159724i
$320$		0			0
$321$	177.061	+	137.362i	0.551593	+	0.427920i
$322$		0			0
$323$			63.0808i			0.195297i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−162.268	+	209.165i	−0.496233	+	0.639648i
$328$		0			0
$329$	−348.105	+	200.978i	−1.05807	+	0.610877i
$330$		0			0
$331$	235.780	−	408.383i	0.712327	−	1.23379i	−0.251655	−	0.967817i	$-0.580975\pi$
$331$	235.780	−	408.383i	0.712327	−	1.23379i	0.963982	−	0.265969i	$-0.0856919\pi$
$332$		0			0
$333$	−68.4247	−	266.650i	−0.205480	−	0.800750i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	48.0857	+	83.2869i	0.142688	+	0.247142i	0.928508	−	0.371313i	$-0.121092\pi$
$337$	48.0857	+	83.2869i	0.142688	+	0.247142i	−0.785820	+	0.618455i	$0.787759\pi$
$338$		0			0
$339$	64.8275	−	473.009i	0.191231	−	1.39531i
$340$		0			0
$341$		−	30.0982i		−	0.0882645i
$342$		0			0
$343$	−245.797			−0.716608
$344$		0			0
$345$		0			0
$346$		0			0
$347$	235.376	−	135.894i	0.678317	−	0.391626i	−0.120904	−	0.992664i	$-0.538579\pi$
$347$	235.376	−	135.894i	0.678317	−	0.391626i	0.799220	+	0.601038i	$0.205246\pi$
$348$		0			0
$349$	−166.723	+	288.773i	−0.477717	+	0.827430i	−0.999674	−	0.0255418i	$-0.991869\pi$
$349$	−166.723	+	288.773i	−0.477717	+	0.827430i	0.521957	+	0.852972i	$0.325202\pi$
$350$		0			0
$351$	−66.7903	−	578.301i	−0.190286	−	1.64758i
$352$		0			0
$353$	−292.339	−	168.782i	−0.828156	−	0.478136i	0.0250648	−	0.999686i	$-0.492021\pi$
$353$	−292.339	−	168.782i	−0.828156	−	0.478136i	−0.853221	+	0.521550i	$0.825354\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	580.827	−	236.984i	1.62697	−	0.663821i
$358$		0			0
$359$		−	638.638i		−	1.77894i	−0.456997	−	0.889468i	$-0.651075\pi$
$359$		−	638.638i		−	1.77894i	0.456997	−	0.889468i	$-0.348925\pi$
$360$		0			0
$361$	−354.789			−0.982795
$362$		0			0
$363$	−354.024	−	48.5202i	−0.975273	−	0.133664i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−59.7781	+	103.539i	−0.162883	+	0.282122i	−0.935902	−	0.352262i	$-0.885413\pi$
$367$	−59.7781	+	103.539i	−0.162883	+	0.282122i	0.773018	+	0.634384i	$0.218746\pi$
$368$		0			0
$369$	−53.0407	−	54.1783i	−0.143742	−	0.146825i
$370$		0			0
$371$	14.0573	+	8.11598i	0.0378903	+	0.0218760i
$372$		0			0
$373$	51.3932	+	89.0157i	0.137783	+	0.238648i	0.926657	−	0.375907i	$-0.122669\pi$
$373$	51.3932	+	89.0157i	0.137783	+	0.238648i	−0.788874	+	0.614555i	$0.789336\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			922.989i			2.44825i
$378$		0			0
$379$	−546.990			−1.44325			−0.721623	−	0.692286i	$-0.756604\pi$
$379$	−546.990			−1.44325			−0.721623	+	0.692286i	$0.756604\pi$
$380$		0			0
$381$	−386.319	+	497.969i	−1.01396	+	1.30700i
$382$		0			0
$383$	207.029	−	119.529i	0.540547	−	0.312085i	−0.204754	−	0.978814i	$-0.565639\pi$
$383$	207.029	−	119.529i	0.540547	−	0.312085i	0.745301	+	0.666729i	$0.232306\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−617.006	−	172.363i	−1.59433	−	0.445382i
$388$		0			0
$389$	124.222	+	71.7196i	0.319337	+	0.184369i	0.651097	−	0.758995i	$-0.274309\pi$
$389$	124.222	+	71.7196i	0.319337	+	0.184369i	−0.331760	+	0.943364i	$0.607643\pi$
$390$		0			0
$391$	−485.019	−	840.077i	−1.24046	−	2.14853i
$392$		0			0
$393$	−2.68383	+	19.5824i	−0.00682909	+	0.0498280i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−184.077			−0.463671			−0.231836	−	0.972755i	$-0.574473\pi$
$397$	−184.077			−0.463671			−0.231836	+	0.972755i	$0.574473\pi$
$398$		0			0
$399$	−23.3331	−	57.1873i	−0.0584790	−	0.143327i
$400$		0			0
$401$	102.303	−	59.0645i	0.255119	−	0.147293i	−0.366987	−	0.930226i	$-0.619611\pi$
$401$	102.303	−	59.0645i	0.255119	−	0.147293i	0.622106	+	0.782933i	$0.286277\pi$
$402$		0			0
$403$	−236.090	+	408.920i	−0.585832	+	1.01469i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−36.4063	−	21.0192i	−0.0894504	−	0.0516442i
$408$		0			0
$409$	307.520	+	532.640i	0.751882	+	1.30230i	0.946910	+	0.321499i	$0.104187\pi$
$409$	307.520	+	532.640i	0.751882	+	1.30230i	−0.195028	+	0.980798i	$0.562480\pi$
$410$		0			0
$411$	595.986	−	243.169i	1.45009	−	0.591653i
$412$		0			0
$413$			36.0341i			0.0872496i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	242.054	+	33.1743i	0.580465	+	0.0795547i
$418$		0			0
$419$	−128.125	+	73.9729i	−0.305787	+	0.176546i	−0.645040	−	0.764149i	$-0.723159\pi$
$419$	−128.125	+	73.9729i	−0.305787	+	0.176546i	0.339253	+	0.940695i	$0.389826\pi$
$420$		0			0
$421$	42.4834	−	73.5835i	0.100911	−	0.174783i	−0.811149	−	0.584839i	$-0.801158\pi$
$421$	42.4834	−	73.5835i	0.100911	−	0.174783i	0.912060	+	0.410056i	$0.134491\pi$
$422$		0			0
$423$	117.820	−	421.759i	0.278534	−	0.997065i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−152.754	−	264.578i	−0.357739	−	0.619622i
$428$		0			0
$429$	−70.2388	−	54.4906i	−0.163727	−	0.127018i
$430$		0			0
$431$			422.458i			0.980180i	0.871672	+	0.490090i	$0.163036\pi$
$431$			422.458i			0.980180i	−0.871672	+	0.490090i	$0.836964\pi$
$432$		0			0
$433$	534.169			1.23365			0.616823	−	0.787102i	$-0.288419\pi$
$433$	534.169			1.23365			0.616823	+	0.787102i	$0.288419\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−82.7128	+	47.7542i	−0.189274	+	0.109277i
$438$		0			0
$439$	29.5206	−	51.1312i	0.0672452	−	0.116472i	−0.830443	−	0.557104i	$-0.811912\pi$
$439$	29.5206	−	51.1312i	0.0672452	−	0.116472i	0.897688	+	0.440632i	$0.145246\pi$
$440$		0			0
$441$	−123.778	+	121.179i	−0.280676	+	0.274782i
$442$		0			0
$443$	56.2191	+	32.4581i	0.126905	+	0.0732689i	0.562109	−	0.827063i	$-0.309990\pi$
$443$	56.2191	+	32.4581i	0.126905	+	0.0732689i	−0.435203	+	0.900332i	$0.643324\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	110.152	−	803.713i	0.246424	−	1.79802i
$448$		0			0
$449$		−	543.268i		−	1.20995i	−0.796244	−	0.604976i	$-0.793183\pi$
$449$		−	543.268i		−	1.20995i	0.796244	−	0.604976i	$-0.206817\pi$
$450$		0			0
$451$	−11.5781			−0.0256721
$452$		0			0
$453$	119.553	+	293.014i	0.263914	+	0.646829i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	357.935	−	619.962i	0.783228	−	1.35659i	−0.146825	−	0.989163i	$-0.546905\pi$
$457$	357.935	−	619.962i	0.783228	−	1.35659i	0.930052	−	0.367427i	$-0.119761\pi$
$458$		0			0
$459$	−271.547	+	627.153i	−0.591607	+	1.36635i
$460$		0			0
$461$	130.777	+	75.5039i	0.283680	+	0.163783i	0.635088	−	0.772440i	$-0.280964\pi$
$461$	130.777	+	75.5039i	0.283680	+	0.163783i	−0.351408	+	0.936222i	$0.614297\pi$
$462$		0			0
$463$	−164.074	−	284.185i	−0.354372	−	0.613790i	0.632639	−	0.774447i	$-0.281972\pi$
$463$	−164.074	−	284.185i	−0.354372	−	0.613790i	−0.987010	+	0.160658i	$0.948639\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	30.8948i		−	0.0661558i	−0.999453	−	0.0330779i	$-0.989469\pi$
$467$		−	30.8948i		−	0.0661558i	0.999453	−	0.0330779i	$-0.0105309\pi$
$468$		0			0
$469$	133.227			0.284066
$470$		0			0
$471$	−31.8712	−	4.36805i	−0.0676671	−	0.00927399i
$472$		0			0
$473$	−84.7216	+	48.9141i	−0.179115	+	0.103412i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−17.1287	+	4.39539i	−0.0359093	+	0.00921465i
$478$		0			0
$479$	420.016	+	242.497i	0.876861	+	0.506256i	0.869622	−	0.493718i	$-0.164362\pi$
$479$	420.016	+	242.497i	0.876861	+	0.506256i	0.00723877	+	0.999974i	$0.497696\pi$
$480$		0			0
$481$	329.749	+	571.142i	0.685549	+	1.18741i
$482$		0			0
$483$	750.443	+	582.186i	1.55371	+	1.20535i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−764.340			−1.56949			−0.784743	−	0.619821i	$-0.787205\pi$
$487$	−764.340			−1.56949			−0.784743	+	0.619821i	$0.787205\pi$
$488$		0			0
$489$	285.036	−	367.414i	0.582896	−	0.751358i
$490$		0			0
$491$	−387.463	+	223.702i	−0.789129	+	0.455604i	−0.839656	−	0.543119i	$-0.817243\pi$
$491$	−387.463	+	223.702i	−0.789129	+	0.455604i	0.0505265	+	0.998723i	$0.483910\pi$
$492$		0			0
$493$	541.778	−	938.386i	1.09894	−	1.90342i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−511.706	−	295.433i	−1.02959	−	0.594434i
$498$		0			0
$499$	−158.431	−	274.410i	−0.317497	−	0.549920i	0.662468	−	0.749090i	$-0.269509\pi$
$499$	−158.431	−	274.410i	−0.317497	−	0.549920i	−0.979965	+	0.199170i	$0.936176\pi$
$500$		0			0
$501$	30.9902	−	226.118i	0.0618566	−	0.451333i
$502$		0			0
$503$			630.817i			1.25411i	0.778976	+	0.627054i	$0.215740\pi$
$503$			630.817i			1.25411i	−0.778976	+	0.627054i	$0.784260\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	335.322	+	821.845i	0.661385	+	1.62100i
$508$		0			0
$509$	−138.696	+	80.0759i	−0.272486	+	0.157320i	−0.630017	−	0.776581i	$-0.716952\pi$
$509$	−138.696	+	80.0759i	−0.272486	+	0.157320i	0.357531	+	0.933901i	$0.383619\pi$
$510$		0			0
$511$	−505.072	+	874.811i	−0.988400	+	1.71196i
$512$		0			0
$513$	61.7485	+	26.7362i	0.120368	+	0.0521173i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−33.4355	−	57.9121i	−0.0646722	−	0.112016i
$518$		0			0
$519$	−170.292	+	69.4812i	−0.328116	+	0.133875i
$520$		0			0
$521$		−	269.377i		−	0.517039i	−0.966006	−	0.258519i	$-0.916765\pi$
$521$		−	269.377i		−	0.517039i	0.966006	−	0.258519i	$-0.0832346\pi$
$522$		0			0
$523$	−224.057			−0.428407			−0.214204	−	0.976789i	$-0.568716\pi$
$523$	−224.057			−0.428407			−0.214204	+	0.976789i	$0.568716\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	480.058	−	277.161i	0.910925	−	0.525923i
$528$		0			0
$529$	469.850	−	813.805i	0.888186	−	1.53838i
$530$		0			0
$531$	−27.4627	−	28.0517i	−0.0517188	−	0.0528281i
$532$		0			0
$533$	157.303	+	90.8188i	0.295127	+	0.170392i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	698.552	+	541.929i	1.30084	+	1.00918i
$538$		0			0
$539$			26.4519i			0.0490758i
$540$		0			0
$541$	705.258			1.30362			0.651809	−	0.758383i	$-0.274010\pi$
$541$	705.258			1.30362			0.651809	+	0.758383i	$0.274010\pi$
$542$		0			0
$543$	402.873	−	519.307i	0.741939	−	0.956366i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−153.882	+	266.531i	−0.281319	+	0.487259i	−0.971710	−	0.236178i	$-0.924105\pi$
$547$	−153.882	+	266.531i	−0.281319	+	0.487259i	0.690391	+	0.723437i	$0.257439\pi$
$548$		0			0
$549$	320.559	+	89.5495i	0.583897	+	0.163114i
$550$		0			0
$551$	−92.3921	−	53.3426i	−0.167681	−	0.0968106i
$552$		0			0
$553$	32.9176	+	57.0149i	0.0595255	+	0.103101i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			530.424i			0.952287i	0.879368	+	0.476143i	$0.157966\pi$
$557$			530.424i			0.952287i	−0.879368	+	0.476143i	$0.842034\pi$
$558$		0			0
$559$	1534.73			2.74549
$560$		0			0
$561$	39.4256	+	96.6285i	0.0702774	+	0.172243i
$562$		0			0
$563$	741.240	−	427.955i	1.31659	−	0.760133i	0.333411	−	0.942781i	$-0.391800\pi$
$563$	741.240	−	427.955i	1.31659	−	0.760133i	0.983178	+	0.182648i	$0.0584669\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	14.1985	−	669.003i	0.0250414	−	1.17990i
$568$		0			0
$569$	218.351	+	126.065i	0.383746	+	0.221556i	0.679447	−	0.733725i	$-0.262220\pi$
$569$	218.351	+	126.065i	0.383746	+	0.221556i	−0.295701	+	0.955281i	$0.595553\pi$
$570$		0			0
$571$	−185.624	−	321.511i	−0.325087	−	0.563066i	0.656443	−	0.754375i	$-0.272060\pi$
$571$	−185.624	−	321.511i	−0.325087	−	0.563066i	−0.981530	+	0.191309i	$0.938727\pi$
$572$		0			0
$573$	469.302	−	191.481i	0.819026	−	0.334172i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	752.555			1.30425			0.652127	−	0.758109i	$-0.273877\pi$
$577$	752.555			1.30425			0.652127	+	0.758109i	$0.273877\pi$
$578$		0			0
$579$	602.253	+	82.5407i	1.04016	+	0.142557i
$580$		0			0
$581$	745.822	−	430.600i	1.28369	−	0.741137i
$582$		0			0
$583$	−1.35021	+	2.33862i	−0.00231596	+	0.00401136i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−691.767	−	399.392i	−1.17848	−	0.680395i	−0.222816	−	0.974860i	$-0.571525\pi$
$587$	−691.767	−	399.392i	−1.17848	−	0.680395i	−0.955662	+	0.294466i	$0.904858\pi$
$588$		0			0
$589$	−27.2889	−	47.2658i	−0.0463309	−	0.0802475i
$590$		0			0
$591$	818.305	+	634.833i	1.38461	+	1.07417i
$592$		0			0
$593$		−	684.110i		−	1.15364i	−0.816871	−	0.576821i	$-0.804293\pi$
$593$		−	684.110i		−	1.15364i	0.816871	−	0.576821i	$-0.195707\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−575.694	+	742.075i	−0.964312	+	1.24301i
$598$		0			0
$599$	−112.311	+	64.8430i	−0.187498	+	0.108252i	−0.590811	−	0.806810i	$-0.701192\pi$
$599$	−112.311	+	64.8430i	−0.187498	+	0.108252i	0.403313	+	0.915062i	$0.367859\pi$
$600$		0			0
$601$	−110.390	+	191.201i	−0.183677	+	0.318139i	−0.943130	−	0.332424i	$-0.892133\pi$
$601$	−110.390	+	191.201i	−0.183677	+	0.318139i	0.759453	+	0.650563i	$0.225467\pi$
$602$		0			0
$603$	−103.714	+	101.536i	−0.171997	+	0.168385i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	252.519	+	437.376i	0.416011	+	0.720553i	0.995534	−	0.0944034i	$-0.0300943\pi$
$607$	252.519	+	437.376i	0.416011	+	0.720553i	−0.579523	+	0.814956i	$0.696761\pi$
$608$		0			0
$609$	−144.059	+	1051.12i	−0.236550	+	1.72597i
$610$		0			0
$611$			1049.07i			1.71698i
$612$		0			0
$613$	582.009			0.949444			0.474722	−	0.880136i	$-0.342549\pi$
$613$	582.009			0.949444			0.474722	+	0.880136i	$0.342549\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	522.504	−	301.668i	0.846846	−	0.488927i	−0.0127394	−	0.999919i	$-0.504055\pi$
$617$	522.504	−	301.668i	0.846846	−	0.488927i	0.859585	+	0.510992i	$0.170722\pi$
$618$		0			0
$619$	−160.899	+	278.685i	−0.259933	+	0.450218i	−0.966224	−	0.257704i	$-0.917034\pi$
$619$	−160.899	+	278.685i	−0.259933	+	0.450218i	0.706290	+	0.707922i	$0.250367\pi$
$620$		0			0
$621$	−1027.91	+	118.717i	−1.65524	+	0.191171i
$622$		0			0
$623$	67.0540	+	38.7136i	0.107631	+	0.0621407i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	9.51390	−	3.88179i	0.0151737	−	0.00619105i
$628$		0			0
$629$		−	774.227i		−	1.23088i
$630$		0			0
$631$	−453.251			−0.718306			−0.359153	−	0.933279i	$-0.616934\pi$
$631$	−453.251			−0.718306			−0.359153	+	0.933279i	$0.616934\pi$
$632$		0			0
$633$	−102.312	−	14.0223i	−0.161631	−	0.0221521i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	207.488	−	359.380i	0.325727	−	0.564176i
$638$		0			0
$639$	623.510	−	159.998i	0.975760	−	0.250389i
$640$		0			0
$641$	−1098.13	−	634.006i	−1.71315	−	0.989089i	−0.930236	−	0.366963i	$-0.880398\pi$
$641$	−1098.13	−	634.006i	−1.71315	−	0.989089i	−0.782917	−	0.622126i	$-0.786269\pi$
$642$		0			0
$643$	170.352	+	295.058i	0.264933	+	0.458877i	0.967546	−	0.252695i	$-0.0813169\pi$
$643$	170.352	+	295.058i	0.264933	+	0.458877i	−0.702613	+	0.711572i	$0.747984\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	460.508i		−	0.711759i	−0.934532	−	0.355879i	$-0.884181\pi$
$647$		−	460.508i		−	0.711759i	0.934532	−	0.355879i	$-0.115819\pi$
$648$		0			0
$649$	−5.99477			−0.00923693
$650$		0			0
$651$	−332.687	+	428.837i	−0.511040	+	0.658735i
$652$		0			0
$653$	729.367	−	421.100i	1.11695	−	0.644870i	0.176328	−	0.984331i	$-0.443578\pi$
$653$	729.367	−	421.100i	1.11695	−	0.644870i	0.940620	+	0.339461i	$0.110245\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−273.533	−	1065.95i	−0.416336	−	1.62245i
$658$		0			0
$659$	−651.160	−	375.948i	−0.988104	−	0.570482i	−0.0833967	−	0.996516i	$-0.526577\pi$
$659$	−651.160	−	375.948i	−0.988104	−	0.570482i	−0.904707	+	0.426035i	$0.859910\pi$
$660$		0			0
$661$	−45.6212	−	79.0183i	−0.0690185	−	0.119544i	0.829451	−	0.558579i	$-0.188653\pi$
$661$	−45.6212	−	79.0183i	−0.0690185	−	0.119544i	−0.898470	+	0.439036i	$0.855320\pi$
$662$		0			0
$663$	222.310	−	1622.07i	0.335309	−	2.44656i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1640.57			2.45963
$668$		0			0
$669$	−243.032	−	595.649i	−0.363277	−	0.890358i
$670$		0			0
$671$	44.0163	−	25.4128i	0.0655981	−	0.0378731i
$672$		0			0
$673$	−543.046	+	940.583i	−0.806903	+	1.39760i	0.108096	+	0.994140i	$0.465525\pi$
$673$	−543.046	+	940.583i	−0.806903	+	1.39760i	−0.914999	+	0.403456i	$0.867809\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−666.823	−	384.990i	−0.984967	−	0.568671i	−0.0812011	−	0.996698i	$-0.525876\pi$
$677$	−666.823	−	384.990i	−0.984967	−	0.568671i	−0.903766	+	0.428027i	$0.859209\pi$
$678$		0			0
$679$	−56.7113	−	98.2269i	−0.0835218	−	0.144664i
$680$		0			0
$681$	−1211.45	+	494.287i	−1.77893	+	0.725825i
$682$		0			0
$683$			993.247i			1.45424i	0.686510	+	0.727121i	$0.259142\pi$
$683$			993.247i			1.45424i	−0.686510	+	0.727121i	$0.740858\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1081.49	−	148.221i	−1.57422	−	0.215751i
$688$		0			0
$689$	36.6883	−	21.1820i	0.0532487	−	0.0307431i
$690$		0			0
$691$	461.866	−	799.975i	0.668402	−	1.15771i	−0.309949	−	0.950753i	$-0.600312\pi$
$691$	461.866	−	799.975i	0.668402	−	1.15771i	0.978351	−	0.206953i	$-0.0663547\pi$
$692$		0			0
$693$	−71.4843	−	73.0176i	−0.103152	−	0.105364i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−106.618	−	184.668i	−0.152967	−	0.264947i
$698$		0			0
$699$	−456.017	−	353.773i	−0.652384	−	0.506113i
$700$		0			0
$701$		−	163.654i		−	0.233458i	−0.993164	−	0.116729i	$-0.962759\pi$
$701$		−	163.654i		−	0.233458i	0.993164	−	0.116729i	$-0.0372409\pi$
$702$		0			0
$703$	−76.2292			−0.108434
$704$		0			0
$705$		0			0
$706$		0			0
$707$	855.106	−	493.696i	1.20949	−	0.698297i
$708$		0			0
$709$	11.5863	−	20.0680i	0.0163417	−	0.0283047i	−0.857739	−	0.514086i	$-0.828131\pi$
$709$	11.5863	−	20.0680i	0.0163417	−	0.0283047i	0.874081	+	0.485781i	$0.161465\pi$
$710$		0			0
$711$	−69.0784	−	19.2973i	−0.0971567	−	0.0271411i
$712$		0			0
$713$	726.839	+	419.641i	1.01941	+	0.588556i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−108.018	+	788.142i	−0.150652	+	1.09922i
$718$		0			0
$719$		−	122.596i		−	0.170509i	−0.996359	−	0.0852545i	$-0.972830\pi$
$719$		−	122.596i		−	0.170509i	0.996359	−	0.0852545i	$-0.0271703\pi$
$720$		0			0
$721$	665.122			0.922499
$722$		0			0
$723$	139.197	+	341.159i	0.192527	+	0.471866i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	191.983	−	332.525i	0.264076	−	0.457393i	−0.703245	−	0.710947i	$-0.748266\pi$
$727$	191.983	−	332.525i	0.264076	−	0.457393i	0.967321	+	0.253554i	$0.0815997\pi$
$728$		0			0
$729$	498.815	+	531.625i	0.684245	+	0.729252i
$730$		0			0
$731$	−1560.33	−	900.857i	−2.13451	−	1.23236i
$732$		0			0
$733$	5.47425	+	9.48169i	0.00746829	+	0.0129355i	0.869735	−	0.493518i	$-0.164289\pi$
$733$	5.47425	+	9.48169i	0.00746829	+	0.0129355i	−0.862267	+	0.506454i	$0.830956\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			22.1642i			0.0300735i
$738$		0			0
$739$	429.537			0.581241			0.290621	−	0.956838i	$-0.406138\pi$
$739$	429.537			0.581241			0.290621	+	0.956838i	$0.406138\pi$
$740$		0			0
$741$	−159.707	−	21.8883i	−0.215528	−	0.0295389i
$742$		0			0
$743$	848.213	−	489.716i	1.14161	−	0.659106i	0.194778	−	0.980847i	$-0.437601\pi$
$743$	848.213	−	489.716i	1.14161	−	0.659106i	0.946828	+	0.321741i	$0.104268\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−252.432	+	903.626i	−0.337927	+	1.20967i
$748$		0			0
$749$	−534.423	−	308.549i	−0.713515	−	0.411948i
$750$		0			0
$751$	50.7936	+	87.9772i	0.0676347	+	0.117147i	0.897860	−	0.440282i	$-0.145121\pi$
$751$	50.7936	+	87.9772i	0.0676347	+	0.117147i	−0.830225	+	0.557428i	$0.811788\pi$
$752$		0			0
$753$	−519.031	−	402.659i	−0.689284	−	0.534740i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−264.365			−0.349227			−0.174614	−	0.984637i	$-0.555868\pi$
$757$	−264.365			−0.349227			−0.174614	+	0.984637i	$0.555868\pi$
$758$		0			0
$759$	−96.8548	+	124.847i	−0.127608	+	0.164488i
$760$		0			0
$761$	217.673	−	125.674i	0.286036	−	0.165143i	−0.350117	−	0.936706i	$-0.613858\pi$
$761$	217.673	−	125.674i	0.286036	−	0.165143i	0.636153	+	0.771563i	$0.280525\pi$
$762$		0			0
$763$	364.493	−	631.321i	0.477711	−	0.827419i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	81.4462	+	47.0230i	0.106188	+	0.0613077i
$768$		0			0
$769$	−179.852	−	311.512i	−0.233878	−	0.405088i	0.725068	−	0.688677i	$-0.241808\pi$
$769$	−179.852	−	311.512i	−0.233878	−	0.405088i	−0.958946	+	0.283589i	$0.908475\pi$
$770$		0			0
$771$	167.782	−	1224.21i	0.217617	−	1.58782i
$772$		0			0
$773$		−	455.149i		−	0.588808i	−0.955681	−	0.294404i	$-0.904879\pi$
$773$		−	455.149i		−	0.588808i	0.955681	−	0.294404i	$-0.0951211\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	286.381	+	701.893i	0.368572	+	0.903337i
$778$		0			0
$779$	−18.1821	+	10.4974i	−0.0233403	+	0.0134755i
$780$		0			0
$781$	49.1494	−	85.1293i	0.0629314	−	0.109000i
$782$		0			0
$783$	−688.941	−	928.061i	−0.879873	−	1.18526i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	656.715	+	1137.46i	0.834454	+	1.44532i	0.894474	+	0.447120i	$0.147550\pi$
$787$	656.715	+	1137.46i	0.834454	+	1.44532i	−0.0600202	+	0.998197i	$0.519117\pi$
$788$		0			0
$789$	−1144.68	+	467.041i	−1.45079	+	0.591941i
$790$		0			0
$791$			1314.71i			1.66209i
$792$		0			0
$793$	−797.353			−1.00549
$794$		0			0
$795$		0			0
$796$		0			0
$797$	385.136	−	222.359i	0.483233	−	0.278995i	−0.238530	−	0.971135i	$-0.576666\pi$
$797$	385.136	−	222.359i	0.483233	−	0.278995i	0.721763	+	0.692141i	$0.243332\pi$
$798$		0			0
$799$	615.787	−	1066.57i	0.770697	−	1.33489i
$800$		0			0
$801$	−81.7049	+	20.9662i	−0.102004	+	0.0261751i
$802$		0			0
$803$	−145.537	−	84.0258i	−0.181242	−	0.104640i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	911.928	+	707.465i	1.13002	+	0.876660i
$808$		0			0
$809$		−	718.402i		−	0.888012i	−0.896024	−	0.444006i	$-0.853557\pi$
$809$		−	718.402i		−	0.888012i	0.896024	−	0.444006i	$-0.146443\pi$
$810$		0			0
$811$	−899.465			−1.10908			−0.554541	−	0.832157i	$-0.687106\pi$
$811$	−899.465			−1.10908			−0.554541	+	0.832157i	$0.687106\pi$
$812$		0			0
$813$	−273.789	+	352.916i	−0.336764	+	0.434092i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−88.6970	+	153.628i	−0.108564	+	0.188039i
$818$		0			0
$819$	398.451	+	1552.76i	0.486509	+	1.89592i
$820$		0			0
$821$	−1327.63	−	766.507i	−1.61709	−	0.933626i	−0.987669	−	0.156559i	$-0.949960\pi$
$821$	−1327.63	−	766.507i	−1.61709	−	0.933626i	−0.629418	−	0.777067i	$-0.716707\pi$
$822$		0			0
$823$	−395.140	−	684.403i	−0.480122	−	0.831595i	0.519618	−	0.854399i	$-0.326074\pi$
$823$	−395.140	−	684.403i	−0.480122	−	0.831595i	−0.999740	+	0.0228034i	$0.992741\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			608.168i			0.735390i	0.929946	+	0.367695i	$0.119853\pi$
$827$			608.168i			0.735390i	−0.929946	+	0.367695i	$0.880147\pi$
$828$		0			0
$829$	1293.97			1.56088			0.780441	−	0.625229i	$-0.214994\pi$
$829$	1293.97			1.56088			0.780441	+	0.625229i	$0.214994\pi$
$830$		0			0
$831$	600.365	+	1471.44i	0.722461	+	1.77068i
$832$		0			0
$833$	−421.899	+	243.584i	−0.506482	+	0.292417i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−67.8401	−	587.391i	−0.0810515	−	0.701781i
$838$		0			0
$839$	−1075.31	−	620.832i	−1.28166	−	0.739966i	−0.304508	−	0.952510i	$-0.598492\pi$
$839$	−1075.31	−	620.832i	−1.28166	−	0.739966i	−0.977152	+	0.212543i	$0.931825\pi$
$840$		0			0
$841$	495.780	+	858.717i	0.589513	+	1.02107i
$842$		0			0
$843$	260.468	−	106.274i	0.308978	−	0.126067i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	983.996			1.16174
$848$		0			0
$849$	−149.985	−	20.5559i	−0.176661	−	0.0242119i
$850$		0			0
$851$	1015.18	−	586.115i	1.19293	−	0.688737i
$852$		0			0
$853$	−575.580	+	996.935i	−0.674772	+	1.16874i	0.301764	+	0.953383i	$0.402425\pi$
$853$	−575.580	+	996.935i	−0.674772	+	1.16874i	−0.976536	+	0.215356i	$0.930909\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1427.38	−	824.101i	−1.66556	−	0.961611i	−0.969987	−	0.243155i	$-0.921818\pi$
$857$	−1427.38	−	824.101i	−1.66556	−	0.961611i	−0.695572	−	0.718456i	$-0.744849\pi$
$858$		0			0
$859$	279.406	+	483.945i	0.325269	+	0.563382i	0.981567	−	0.191120i	$-0.0612119\pi$
$859$	279.406	+	483.945i	0.325269	+	0.563382i	−0.656298	+	0.754502i	$0.727879\pi$
$860$		0			0
$861$	164.964	+	127.978i	0.191596	+	0.148638i
$862$		0			0
$863$			1222.64i			1.41673i	0.705846	+	0.708365i	$0.250567\pi$
$863$			1222.64i			1.41673i	−0.705846	+	0.708365i	$0.749433\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−646.706	+	833.610i	−0.745913	+	0.961488i
$868$		0			0
$869$	−9.48522	+	5.47629i	−0.0109151	+	0.00630184i
$870$		0			0
$871$	173.856	−	301.127i	0.199605	−	0.345725i
$872$		0			0
$873$	119.010	+	33.2460i	0.136323	+	0.0380824i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−594.086	−	1028.99i	−0.677407	−	1.17330i	−0.975759	−	0.218848i	$-0.929770\pi$
$877$	−594.086	−	1028.99i	−0.677407	−	1.17330i	0.298352	−	0.954456i	$-0.403563\pi$
$878$		0			0
$879$	−96.1480	+	701.537i	−0.109383	+	0.798108i
$880$		0			0
$881$		−	663.144i		−	0.752717i	−0.926474	−	0.376359i	$-0.877176\pi$
$881$		−	663.144i		−	0.752717i	0.926474	−	0.376359i	$-0.122824\pi$
$882$		0			0
$883$	−1447.52			−1.63932			−0.819659	−	0.572852i	$-0.805837\pi$
$883$	−1447.52			−1.63932			−0.819659	+	0.572852i	$0.805837\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−559.739	+	323.166i	−0.631047	+	0.364335i	−0.781158	−	0.624334i	$-0.785370\pi$
$887$	−559.739	+	323.166i	−0.631047	+	0.364335i	0.150110	+	0.988669i	$0.452037\pi$
$888$		0			0
$889$	867.766	−	1503.01i	0.976114	−	1.69068i
$890$		0			0
$891$	111.298	+	2.36211i	0.124913	+	0.00265108i
$892$		0			0
$893$	−105.013	−	60.6295i	−0.117596	−	0.0678942i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2295.19	−	936.463i	2.55874	−	1.04399i
$898$		0			0
$899$			937.497i			1.04282i
$900$		0			0
$901$	−49.7338			−0.0551985
$902$		0			0
$903$	1747.77	+	239.538i	1.93552	+	0.265269i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	361.322	−	625.829i	0.398371	−	0.689999i	−0.595154	−	0.803612i	$-0.702909\pi$
$907$	361.322	−	625.829i	0.398371	−	0.689999i	0.993525	+	0.113613i	$0.0362424\pi$
$908$		0			0
$909$	−289.420	+	1036.03i	−0.318394	+	1.13975i
$910$		0			0
$911$	1278.01	+	737.862i	1.40287	+	0.809947i	0.994686	−	0.102952i	$-0.0328289\pi$
$911$	1278.01	+	737.862i	1.40287	+	0.809947i	0.408184	+	0.912900i	$0.366162\pi$
$912$		0			0
$913$	71.6363	+	124.078i	0.0784626	+	0.135901i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	54.4285i		−	0.0593550i
$918$		0			0
$919$	−1283.57			−1.39670			−0.698351	−	0.715755i	$-0.746083\pi$
$919$	−1283.57			−1.39670			−0.698351	+	0.715755i	$0.746083\pi$
$920$		0			0
$921$	144.128	−	185.782i	0.156491	−	0.201718i
$922$		0			0
$923$	−1335.51	+	771.057i	−1.44692	+	0.835381i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−517.782	+	506.910i	−0.558557	+	0.546828i
$928$		0			0
$929$	−486.909	−	281.117i	−0.524121	−	0.302601i	0.214498	−	0.976724i	$-0.431188\pi$
$929$	−486.909	−	281.117i	−0.524121	−	0.302601i	−0.738619	+	0.674123i	$0.764522\pi$
$930$		0			0
$931$	23.9829	+	41.5396i	0.0257604	+	0.0446182i
$932$		0			0
$933$	−102.135	+	745.224i	−0.109470	+	0.798740i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1337.27			−1.42718			−0.713592	−	0.700562i	$-0.752933\pi$
$937$	−1337.27			−1.42718			−0.713592	+	0.700562i	$0.752933\pi$
$938$		0			0
$939$	142.324	+	348.824i	0.151570	+	0.371484i
$940$		0			0
$941$	918.441	−	530.262i	0.976026	−	0.563509i	0.0749581	−	0.997187i	$-0.476118\pi$
$941$	918.441	−	530.262i	0.976026	−	0.563509i	0.901068	+	0.433678i	$0.142784\pi$
$942$		0			0
$943$	161.427	−	279.599i	0.171184	−	0.296500i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1250.43	−	721.938i	−1.32042	−	0.762342i	−0.336621	−	0.941640i	$-0.609284\pi$
$947$	−1250.43	−	721.938i	−1.32042	−	0.762342i	−0.983795	+	0.179298i	$0.942617\pi$
$948$		0			0
$949$	1318.20	+	2283.18i	1.38904	+	2.40588i
$950$		0			0
$951$	440.232	−	179.620i	0.462915	−	0.188875i
$952$		0			0
$953$			854.631i			0.896780i	0.893838	+	0.448390i	$0.148002\pi$
$953$			854.631i			0.896780i	−0.893838	+	0.448390i	$0.851998\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−174.868	−	23.9662i	−0.182725	−	0.0250430i
$958$		0			0
$959$	−1535.05	+	886.264i	−1.60068	+	0.924154i
$960$		0			0
$961$	240.699	−	416.902i	0.250467	−	0.433821i
$962$		0			0
$963$	651.191	−	167.101i	0.676210	−	0.173522i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−62.9165	−	108.975i	−0.0650636	−	0.112693i	0.831659	−	0.555287i	$-0.187392\pi$
$967$	−62.9165	−	108.975i	−0.0650636	−	0.112693i	−0.896722	+	0.442594i	$0.854058\pi$
$968$		0			0
$969$	149.523	+	115.998i	0.154306	+	0.119709i
$970$		0			0
$971$			20.0762i			0.0206758i	0.999947	+	0.0103379i	$0.00329072\pi$
$971$			20.0762i			0.0206758i	−0.999947	+	0.0103379i	$0.996709\pi$
$972$		0			0
$973$	−672.779			−0.691449
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1131.72	+	653.401i	−1.15837	+	0.668783i	−0.950912	−	0.309461i	$-0.899851\pi$
$977$	−1131.72	+	653.401i	−1.15837	+	0.668783i	−0.207455	+	0.978245i	$0.566518\pi$
$978$		0			0
$979$	−6.44055	+	11.1554i	−0.00657870	+	0.0113946i
$980$		0			0
$981$	197.399	+	769.261i	0.201223	+	0.784160i
$982$		0			0
$983$	−1107.19	−	639.237i	−1.12634	−	0.650292i	−0.183327	−	0.983052i	$-0.558687\pi$
$983$	−1107.19	−	639.237i	−1.12634	−	0.650292i	−0.943011	+	0.332760i	$0.892020\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−163.738	+	1194.70i	−0.165895	+	1.21044i
$988$		0			0
$989$		−	2727.91i		−	2.75825i
$990$		0			0
$991$	1017.87			1.02711			0.513557	−	0.858055i	$-0.328327\pi$
$991$	1017.87			1.02711			0.513557	+	0.858055i	$0.328327\pi$
$992$		0			0
$993$	−534.434	−	1309.85i	−0.538201	−	1.31908i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	206.181	−	357.116i	0.206802	−	0.358191i	−0.743904	−	0.668287i	$-0.767028\pi$
$997$	206.181	−	357.116i	0.206802	−	0.358191i	0.950705	+	0.310096i	$0.100361\pi$
$998$		0			0
$999$	−757.875	−	328.148i	−0.758634	−	0.328477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.e.101.6	yes	16
3.2	odd	2		2700.3.p.d.1601.2		16
5.2	odd	4		900.3.u.d.749.4		32
5.3	odd	4		900.3.u.d.749.13		32
5.4	even	2		900.3.p.d.101.3	✓	16
9.4	even	3		2700.3.p.d.2501.2		16
9.5	odd	6	inner	900.3.p.e.401.6	yes	16
15.2	even	4		2700.3.u.d.2249.4		32
15.8	even	4		2700.3.u.d.2249.13		32
15.14	odd	2		2700.3.p.e.1601.7		16
45.4	even	6		2700.3.p.e.2501.7		16
45.13	odd	12		2700.3.u.d.449.4		32
45.14	odd	6		900.3.p.d.401.3	yes	16
45.22	odd	12		2700.3.u.d.449.13		32
45.23	even	12		900.3.u.d.149.4		32
45.32	even	12		900.3.u.d.149.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.3	✓	16	5.4	even	2
900.3.p.d.401.3	yes	16	45.14	odd	6
900.3.p.e.101.6	yes	16	1.1	even	1	trivial
900.3.p.e.401.6	yes	16	9.5	odd	6	inner
900.3.u.d.149.4		32	45.23	even	12
900.3.u.d.149.13		32	45.32	even	12
900.3.u.d.749.4		32	5.2	odd	4
900.3.u.d.749.13		32	5.3	odd	4
2700.3.p.d.1601.2		16	3.2	odd	2
2700.3.p.d.2501.2		16	9.4	even	3
2700.3.p.e.1601.7		16	15.14	odd	2
2700.3.p.e.2501.7		16	45.4	even	6
2700.3.u.d.449.4		32	45.13	odd	12
2700.3.u.d.449.13		32	45.22	odd	12
2700.3.u.d.2249.4		32	15.2	even	4
2700.3.u.d.2249.13		32	15.8	even	4

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.83888 - 2.37034i) q^{3} +(-4.13058 + 7.15437i) q^{7} +(-2.23701 - 8.71756i) q^{9} +O(q^{10})\)	\(q+(1.83888 - 2.37034i) q^{3} +(-4.13058 + 7.15437i) q^{7} +(-2.23701 - 8.71756i) q^{9} +(-1.19023 - 0.687179i) q^{11} +(10.7805 + 18.6723i) q^{13} -25.3117i q^{17} -2.49216 q^{19} +(9.36262 + 22.9469i) q^{21} +(33.1892 - 19.1618i) q^{23} +(-24.7772 - 10.7281i) q^{27} +(37.0732 + 21.4042i) q^{29} +(10.9499 + 18.9658i) q^{31} +(-3.81754 + 1.55760i) q^{33} +30.5877 q^{37} +(64.0837 + 8.78288i) q^{39} +(7.29574 - 4.21220i) q^{41} +(35.5905 - 61.6445i) q^{43} +(42.1375 + 24.3281i) q^{47} +(-9.62335 - 16.6681i) q^{49} +(-59.9974 - 46.5454i) q^{51} -1.96485i q^{53} +(-4.58279 + 5.90725i) q^{57} +(3.77749 - 2.18094i) q^{59} +(-18.4907 + 32.0268i) q^{61} +(71.6088 + 20.0042i) q^{63} +(-8.06346 - 13.9663i) q^{67} +(15.6112 - 113.906i) q^{69} +71.5235i q^{71} +122.276 q^{73} +(9.83266 - 5.67689i) q^{77} +(3.98462 - 6.90157i) q^{79} +(-70.9916 + 39.0024i) q^{81} +(-90.2806 - 52.1235i) q^{83} +(118.909 - 48.5161i) q^{87} -9.37245i q^{89} -178.118 q^{91} +(65.0910 + 8.92094i) q^{93} +(-6.86481 + 11.8902i) q^{97} +(-3.32797 + 11.9131i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} - q^{7} + 14 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 - q^7 + 14 * q^9	\( 16 q + 2 q^{3} - q^{7} + 14 q^{9} - 10 q^{13} + 2 q^{19} + q^{21} + 27 q^{23} - 16 q^{27} + 9 q^{29} + 8 q^{31} + 36 q^{33} - 22 q^{37} + 19 q^{39} + 54 q^{41} + 44 q^{43} - 108 q^{47} - 45 q^{49} + 90 q^{51} - 68 q^{57} + 9 q^{59} - 55 q^{61} - 107 q^{63} - 28 q^{67} - 147 q^{69} + 86 q^{73} + 342 q^{77} + 11 q^{79} - 130 q^{81} - 306 q^{83} + 375 q^{87} - 134 q^{91} - 83 q^{93} + 41 q^{97} + 252 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 - q^7 + 14 * q^9 - 10 * q^13 + 2 * q^19 + q^21 + 27 * q^23 - 16 * q^27 + 9 * q^29 + 8 * q^31 + 36 * q^33 - 22 * q^37 + 19 * q^39 + 54 * q^41 + 44 * q^43 - 108 * q^47 - 45 * q^49 + 90 * q^51 - 68 * q^57 + 9 * q^59 - 55 * q^61 - 107 * q^63 - 28 * q^67 - 147 * q^69 + 86 * q^73 + 342 * q^77 + 11 * q^79 - 130 * q^81 - 306 * q^83 + 375 * q^87 - 134 * q^91 - 83 * q^93 + 41 * q^97 + 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more