LMFDB - Embedded newform 135.3.h.a.44.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(44,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.44"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{12} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.8
Root			$1.72886 + 0.105167i$ of defining polynomial
Character	$\chi$	$=$	135.44
Dual form			135.3.h.a.89.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14670 + 1.98614i) q^{2} +(-0.629835 + 1.09091i) q^{4} +(3.96090 - 3.05143i) q^{5} +(6.04559 - 3.49042i) q^{7} +6.28466 q^{8} +(10.6025 + 4.36783i) q^{10} +(-15.8064 + 9.12584i) q^{11} +(3.66955 + 2.11862i) q^{13} +(13.8649 + 8.00492i) q^{14} +(9.72596 + 16.8458i) q^{16} -17.3066 q^{17} -3.96601 q^{19} +(0.834115 + 6.24287i) q^{20} +(-36.2504 - 20.9292i) q^{22} +(0.287675 - 0.498269i) q^{23} +(6.37749 - 24.1729i) q^{25} +9.71765i q^{26} +8.79356i q^{28} +(18.1762 - 10.4940i) q^{29} +(-16.7326 + 28.9818i) q^{31} +(-9.73615 + 16.8635i) q^{32} +(-19.8455 - 34.3734i) q^{34} +(13.2952 - 32.2729i) q^{35} +21.4222i q^{37} +(-4.54782 - 7.87705i) q^{38} +(24.8929 - 19.1772i) q^{40} +(-44.1003 - 25.4613i) q^{41} +(7.15514 - 4.13102i) q^{43} -22.9911i q^{44} +1.31951 q^{46} +(-7.57789 - 13.1253i) q^{47} +(-0.133907 + 0.231934i) q^{49} +(55.3238 - 15.0524i) q^{50} +(-4.62242 + 2.66876i) q^{52} +24.5806 q^{53} +(-34.7608 + 84.3789i) q^{55} +(37.9945 - 21.9361i) q^{56} +(41.6853 + 24.0670i) q^{58} +(-43.1589 - 24.9178i) q^{59} +(-31.4674 - 54.5031i) q^{61} -76.7492 q^{62} +33.1499 q^{64} +(20.9995 - 2.80576i) q^{65} +(-103.545 - 59.7818i) q^{67} +(10.9003 - 18.8799i) q^{68} +(79.3442 - 10.6012i) q^{70} +66.8256i q^{71} -48.9419i q^{73} +(-42.5475 + 24.5648i) q^{74} +(2.49793 - 4.32654i) q^{76} +(-63.7061 + 110.342i) q^{77} +(58.9661 + 102.132i) q^{79} +(89.9276 + 37.0466i) q^{80} -116.786i q^{82} +(3.66063 + 6.34040i) q^{83} +(-68.5499 + 52.8101i) q^{85} +(16.4096 + 9.47408i) q^{86} +(-99.3381 + 57.3529i) q^{88} +100.624i q^{89} +29.5794 q^{91} +(0.362376 + 0.627654i) q^{92} +(17.3791 - 30.1015i) q^{94} +(-15.7090 + 12.1020i) q^{95} +(3.59238 - 2.07406i) q^{97} -0.614205 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) $ 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.14670	+	1.98614i	0.573349	+	0.993070i	0.996219	+	0.0868795i	$0.0276895\pi$
$2$	1.14670	+	1.98614i	0.573349	+	0.993070i	−0.422870	+	0.906191i	$0.638977\pi$
$3$		0			0
$3$		0			0
$4$	−0.629835	+	1.09091i	−0.157459	+	0.272727i
$5$	3.96090	−	3.05143i	0.792180	−	0.610287i
$5$	3.96090	−	3.05143i	0.792180	−	0.610287i
$6$		0			0
$7$	6.04559	−	3.49042i	0.863655	−	0.498632i	−0.00157923	−	0.999999i	$-0.500503\pi$
$7$	6.04559	−	3.49042i	0.863655	−	0.498632i	0.865235	+	0.501367i	$0.167169\pi$
$8$	6.28466			0.785583
$9$		0			0
$10$	10.6025	+	4.36783i	1.06025	+	0.436783i
$11$	−15.8064	+	9.12584i	−1.43695	+	0.829622i	−0.997636	−	0.0687126i	$-0.978111\pi$
$11$	−15.8064	+	9.12584i	−1.43695	+	0.829622i	−0.439311	+	0.898335i	$0.644778\pi$
$12$		0			0
$13$	3.66955	+	2.11862i	0.282273	+	0.162970i	0.634452	−	0.772962i	$-0.281226\pi$
$13$	3.66955	+	2.11862i	0.282273	+	0.162970i	−0.352179	+	0.935933i	$0.614559\pi$
$14$	13.8649	+	8.00492i	0.990352	+	0.571780i
$15$		0			0
$16$	9.72596	+	16.8458i	0.607872	+	1.05287i
$17$	−17.3066			−1.01804			−0.509019	−	0.860756i	$-0.669992\pi$
$17$	−17.3066			−1.01804			−0.509019	+	0.860756i	$0.669992\pi$
$18$		0			0
$19$	−3.96601			−0.208737			−0.104369	−	0.994539i	$-0.533282\pi$
$19$	−3.96601			−0.208737			−0.104369	+	0.994539i	$0.533282\pi$
$20$	0.834115	+	6.24287i	0.0417057	+	0.312144i
$21$		0			0
$22$	−36.2504	−	20.9292i	−1.64775	−	0.951327i
$23$	0.287675	−	0.498269i	0.0125076	−	0.0216639i	−0.859704	−	0.510793i	$-0.829352\pi$
$23$	0.287675	−	0.498269i	0.0125076	−	0.0216639i	0.872211	+	0.489129i	$0.162685\pi$
$24$		0			0
$25$	6.37749	−	24.1729i	0.255100	−	0.966915i
$26$			9.71765i			0.373756i
$27$		0			0
$28$			8.79356i			0.314056i
$29$	18.1762	−	10.4940i	0.626766	−	0.361863i	−0.152733	−	0.988268i	$-0.548807\pi$
$29$	18.1762	−	10.4940i	0.626766	−	0.361863i	0.779498	+	0.626404i	$0.215474\pi$
$30$		0			0
$31$	−16.7326	+	28.9818i	−0.539763	+	0.934897i	0.459154	+	0.888357i	$0.348153\pi$
$31$	−16.7326	+	28.9818i	−0.539763	+	0.934897i	−0.998916	+	0.0465398i	$0.985181\pi$
$32$	−9.73615	+	16.8635i	−0.304255	+	0.526985i
$33$		0			0
$34$	−19.8455	−	34.3734i	−0.583691	−	1.01098i
$35$	13.2952	−	32.2729i	0.379863	−	0.922084i
$36$		0			0
$37$			21.4222i			0.578978i	0.957181	+	0.289489i	$0.0934854\pi$
$37$			21.4222i			0.578978i	−0.957181	+	0.289489i	$0.906515\pi$
$38$	−4.54782	−	7.87705i	−0.119679	−	0.207291i
$39$		0			0
$40$	24.8929	−	19.1772i	0.622323	−	0.479431i
$41$	−44.1003	−	25.4613i	−1.07562	−	0.621008i	−0.145907	−	0.989298i	$-0.546610\pi$
$41$	−44.1003	−	25.4613i	−1.07562	−	0.621008i	−0.929711	+	0.368290i	$0.879943\pi$
$42$		0			0
$43$	7.15514	−	4.13102i	0.166399	−	0.0960703i	−0.414488	−	0.910055i	$-0.636039\pi$
$43$	7.15514	−	4.13102i	0.166399	−	0.0960703i	0.580887	+	0.813984i	$0.302706\pi$
$44$		−	22.9911i		−	0.522525i
$45$		0			0
$46$	1.31951			0.0286850
$47$	−7.57789	−	13.1253i	−0.161232	−	0.279262i	0.774079	−	0.633089i	$-0.218213\pi$
$47$	−7.57789	−	13.1253i	−0.161232	−	0.279262i	−0.935311	+	0.353828i	$0.884880\pi$
$48$		0			0
$49$	−0.133907	+	0.231934i	−0.00273280	+	0.00473335i
$50$	55.3238	−	15.0524i	1.10648	−	0.301048i
$51$		0			0
$52$	−4.62242	+	2.66876i	−0.0888927	+	0.0513222i
$53$	24.5806			0.463784			0.231892	−	0.972741i	$-0.425508\pi$
$53$	24.5806			0.463784			0.231892	+	0.972741i	$0.425508\pi$
$54$		0			0
$55$	−34.7608	+	84.3789i	−0.632014	+	1.53416i
$56$	37.9945	−	21.9361i	0.678473	−	0.391717i
$57$		0			0
$58$	41.6853	+	24.0670i	0.718711	+	0.414948i
$59$	−43.1589	−	24.9178i	−0.731506	−	0.422335i	0.0874668	−	0.996167i	$-0.472123\pi$
$59$	−43.1589	−	24.9178i	−0.731506	−	0.422335i	−0.818973	+	0.573832i	$0.805456\pi$
$60$		0			0
$61$	−31.4674	−	54.5031i	−0.515858	−	0.893493i	−0.999831	−	0.0184097i	$-0.994140\pi$
$61$	−31.4674	−	54.5031i	−0.515858	−	0.893493i	0.483972	−	0.875083i	$-0.339194\pi$
$62$	−76.7492			−1.23789
$63$		0			0
$64$	33.1499			0.517968
$65$	20.9995	−	2.80576i	0.323070	−	0.0431656i
$66$		0			0
$67$	−103.545	−	59.7818i	−1.54545	−	0.892266i	−0.998480	−	0.0551129i	$-0.982448\pi$
$67$	−103.545	−	59.7818i	−1.54545	−	0.892266i	−0.546969	−	0.837153i	$-0.684219\pi$
$68$	10.9003	−	18.8799i	0.160299	−	0.277646i
$69$		0			0
$70$	79.3442	−	10.6012i	1.13349	−	0.151446i
$71$			66.8256i			0.941205i	0.882345	+	0.470603i	$0.155963\pi$
$71$			66.8256i			0.941205i	−0.882345	+	0.470603i	$0.844037\pi$
$72$		0			0
$73$		−	48.9419i		−	0.670437i	−0.942140	−	0.335218i	$-0.891190\pi$
$73$		−	48.9419i		−	0.670437i	0.942140	−	0.335218i	$-0.108810\pi$
$74$	−42.5475	+	24.5648i	−0.574966	+	0.331957i
$75$		0			0
$76$	2.49793	−	4.32654i	0.0328675	−	0.0569282i
$77$	−63.7061	+	110.342i	−0.827352	+	1.43302i
$78$		0			0
$79$	58.9661	+	102.132i	0.746407	+	1.29281i	0.949535	+	0.313662i	$0.101556\pi$
$79$	58.9661	+	102.132i	0.746407	+	1.29281i	−0.203128	+	0.979152i	$0.565111\pi$
$80$	89.9276	+	37.0466i	1.12409	+	0.463083i
$81$		0			0
$82$		−	116.786i		−	1.42422i
$83$	3.66063	+	6.34040i	0.0441040	+	0.0763904i	0.887235	−	0.461318i	$-0.152623\pi$
$83$	3.66063	+	6.34040i	0.0441040	+	0.0763904i	−0.843131	+	0.537709i	$0.819290\pi$
$84$		0			0
$85$	−68.5499	+	52.8101i	−0.806469	+	0.621295i
$86$	16.4096	+	9.47408i	0.190809	+	0.110164i
$87$		0			0
$88$	−99.3381	+	57.3529i	−1.12884	+	0.651737i
$89$			100.624i			1.13060i	0.824884	+	0.565302i	$0.191241\pi$
$89$			100.624i			1.13060i	−0.824884	+	0.565302i	$0.808759\pi$
$90$		0			0
$91$	29.5794			0.325049
$92$	0.362376	+	0.627654i	0.00393887	+	0.00682233i
$93$		0			0
$94$	17.3791	−	30.1015i	0.184884	−	0.320229i
$95$	−15.7090	+	12.1020i	−0.165358	+	0.127390i
$96$		0			0
$97$	3.59238	−	2.07406i	0.0370349	−	0.0213821i	−0.481368	−	0.876518i	$-0.659860\pi$
$97$	3.59238	−	2.07406i	0.0370349	−	0.0213821i	0.518403	+	0.855136i	$0.326527\pi$
$98$	−0.614205			−0.00626740
$99$		0			0
$100$	22.3536	+	22.1822i	0.223536	+	0.221822i
$101$	140.266	−	80.9826i	1.38877	−	0.801808i	0.395595	−	0.918425i	$-0.370538\pi$
$101$	140.266	−	80.9826i	1.38877	−	0.801808i	0.993177	+	0.116617i	$0.0372050\pi$
$102$		0			0
$103$	142.152	+	82.0717i	1.38012	+	0.796813i	0.992173	−	0.124869i	$-0.0398509\pi$
$103$	142.152	+	82.0717i	1.38012	+	0.796813i	0.387947	+	0.921682i	$0.373184\pi$
$104$	23.0619	+	13.3148i	0.221749	+	0.128027i
$105$		0			0
$106$	28.1865	+	48.8205i	0.265910	+	0.460570i
$107$	48.4086			0.452416			0.226208	−	0.974079i	$-0.427367\pi$
$107$	48.4086			0.452416			0.226208	+	0.974079i	$0.427367\pi$
$108$		0			0
$109$	23.7458			0.217851			0.108925	−	0.994050i	$-0.465259\pi$
$109$	23.7458			0.217851			0.108925	+	0.994050i	$0.465259\pi$
$110$	−207.448	+	27.7173i	−1.88589	+	0.251976i
$111$		0			0
$112$	117.598	+	67.8954i	1.04998	+	0.606209i
$113$	56.3972	−	97.6828i	0.499090	−	0.864449i	−0.500909	−	0.865500i	$-0.667001\pi$
$113$	56.3972	−	97.6828i	0.499090	−	0.864449i	0.999999	+	0.00105049i	$0.000334381\pi$
$114$		0			0
$115$	−0.380980	−	2.85142i	−0.00331287	−	0.0247949i
$116$			26.4381i			0.227914i
$117$		0			0
$118$		−	114.293i		−	0.968582i
$119$	−104.629	+	60.4074i	−0.879233	+	0.507626i
$120$		0			0
$121$	106.062	−	183.705i	0.876546	−	1.51822i
$122$	72.1672	−	124.997i	0.591534	−	1.02457i
$123$		0			0
$124$	−21.0776	−	36.5075i	−0.169981	−	0.294415i
$125$	−48.5013	−	115.207i	−0.388011	−	0.921655i
$126$		0			0
$127$			97.5047i			0.767754i	0.923384	+	0.383877i	$0.125411\pi$
$127$			97.5047i			0.767754i	−0.923384	+	0.383877i	$0.874589\pi$
$128$	76.9576	+	133.294i	0.601231	+	1.04136i
$129$		0			0
$130$	29.6528	+	38.4907i	0.228098	+	0.296082i
$131$	−17.7898	−	10.2709i	−0.135800	−	0.0784041i	0.430561	−	0.902562i	$-0.358316\pi$
$131$	−17.7898	−	10.2709i	−0.135800	−	0.0784041i	−0.566361	+	0.824157i	$0.691649\pi$
$132$		0			0
$133$	−23.9769	+	13.8430i	−0.180277	+	0.104083i
$134$		−	274.207i		−	2.04632i
$135$		0			0
$136$	−108.766			−0.799753
$137$	−9.83571	−	17.0360i	−0.0717935	−	0.124350i	0.827894	−	0.560885i	$-0.189539\pi$
$137$	−9.83571	−	17.0360i	−0.0717935	−	0.124350i	−0.899687	+	0.436535i	$0.856206\pi$
$138$		0			0
$139$	−54.0215	+	93.5679i	−0.388644	+	0.673150i	−0.992267	−	0.124119i	$-0.960390\pi$
$139$	−54.0215	+	93.5679i	−0.388644	+	0.673150i	0.603624	+	0.797269i	$0.293723\pi$
$140$	26.8330	+	34.8304i	0.191664	+	0.248789i
$141$		0			0
$142$	−132.725	+	76.6288i	−0.934683	+	0.539639i
$143$	−77.3366			−0.540816
$144$		0			0
$145$	39.9723	−	97.0294i	0.275671	−	0.669168i
$146$	97.2054	−	56.1216i	0.665791	−	0.384394i
$147$		0			0
$148$	−23.3696	−	13.4925i	−0.157903	−	0.0911652i
$149$	196.553	+	113.480i	1.31915	+	0.761612i	0.983592	−	0.180408i	$-0.0577417\pi$
$149$	196.553	+	113.480i	1.31915	+	0.761612i	0.335558	+	0.942019i	$0.391075\pi$
$150$		0			0
$151$	−27.9141	−	48.3486i	−0.184862	−	0.320190i	0.758668	−	0.651477i	$-0.225850\pi$
$151$	−27.9141	−	48.3486i	−0.184862	−	0.320190i	−0.943530	+	0.331288i	$0.892517\pi$
$152$	−24.9250			−0.163980
$153$		0			0
$154$	−292.207			−1.89745
$155$	22.1597	+	165.853i	0.142966	+	1.07002i
$156$		0			0
$157$	−59.2359	−	34.1999i	−0.377299	−	0.217833i	0.299344	−	0.954145i	$-0.403232\pi$
$157$	−59.2359	−	34.1999i	−0.377299	−	0.217833i	−0.676642	+	0.736312i	$0.736566\pi$
$158$	−135.233	+	234.230i	−0.855904	+	1.48247i
$159$		0			0
$160$	12.8940	+	96.5039i	0.0805872	+	0.603150i
$161$		−	4.01644i		−	0.0249468i
$162$		0			0
$163$		−	80.5043i		−	0.493892i	−0.969029	−	0.246946i	$-0.920573\pi$
$163$		−	80.5043i		−	0.493892i	0.969029	−	0.246946i	$-0.0794269\pi$
$164$	55.5519	−	32.0729i	0.338731	−	0.195566i
$165$		0			0
$166$	−8.39529	+	14.5411i	−0.0505740	+	0.0875968i
$167$	37.4114	−	64.7985i	0.224020	−	0.388015i	−0.732005	−	0.681300i	$-0.761415\pi$
$167$	37.4114	−	64.7985i	0.224020	−	0.388015i	0.956025	+	0.293285i	$0.0947484\pi$
$168$		0			0
$169$	−75.5229	−	130.810i	−0.446881	−	0.774021i
$170$	−183.494	−	75.5924i	−1.07938	−	0.444661i
$171$		0			0
$172$			10.4075i			0.0605085i
$173$	−159.212	−	275.763i	−0.920301	−	1.59401i	−0.798950	−	0.601398i	$-0.794611\pi$
$173$	−159.212	−	275.763i	−0.920301	−	1.59401i	−0.121351	−	0.992610i	$-0.538723\pi$
$174$		0			0
$175$	−45.8178	−	168.399i	−0.261816	−	0.962282i
$176$	−307.465	−	177.515i	−1.74696	−	1.00861i
$177$		0			0
$178$	−199.853	+	115.385i	−1.12277	+	0.648232i
$179$		−	3.14738i		−	0.0175831i	−0.999961	−	0.00879155i	$-0.997202\pi$
$179$		−	3.14738i		−	0.0175831i	0.999961	−	0.00879155i	$-0.00279847\pi$
$180$		0			0
$181$	−0.833264			−0.00460367			−0.00230183	−	0.999997i	$-0.500733\pi$
$181$	−0.833264			−0.00460367			−0.00230183	+	0.999997i	$0.500733\pi$
$182$	33.9187	+	58.7489i	0.186367	+	0.322796i
$183$		0			0
$184$	1.80794	−	3.13145i	0.00982578	−	0.0170188i
$185$	65.3684	+	84.8512i	0.353343	+	0.458655i
$186$		0			0
$187$	273.556	−	157.938i	1.46287	−	0.844586i
$188$	19.0913			0.101549
$189$		0			0
$190$	−42.0498	−	17.3229i	−0.221315	−	0.0911729i
$191$	−49.8127	+	28.7594i	−0.260799	+	0.150573i	−0.624699	−	0.780866i	$-0.714778\pi$
$191$	−49.8127	+	28.7594i	−0.260799	+	0.150573i	0.363900	+	0.931438i	$0.381445\pi$
$192$		0			0
$193$	−31.4897	−	18.1806i	−0.163159	−	0.0941999i	0.416197	−	0.909274i	$-0.363363\pi$
$193$	−31.4897	−	18.1806i	−0.163159	−	0.0941999i	−0.579356	+	0.815075i	$0.696696\pi$
$194$	8.23876	+	4.75665i	0.0424678	+	0.0245188i
$195$		0			0
$196$	−0.168679	−	0.292161i	−0.000860607	−	0.00149062i
$197$	151.285			0.767943			0.383972	−	0.923345i	$-0.374556\pi$
$197$	151.285			0.767943			0.383972	+	0.923345i	$0.374556\pi$
$198$		0			0
$199$	268.742			1.35046			0.675232	−	0.737605i	$-0.264043\pi$
$199$	268.742			1.35046			0.675232	+	0.737605i	$0.264043\pi$
$200$	40.0804	−	151.918i	0.200402	−	0.759592i
$201$		0			0
$202$	321.686	+	185.725i	1.59250	+	0.919432i
$203$	73.2573	−	126.885i	0.360873	−	0.625051i
$204$		0			0
$205$	−252.371	+	33.7194i	−1.23108	+	0.164485i
$206$			376.446i			1.82741i
$207$		0			0
$208$			82.4222i			0.396261i
$209$	62.6884	−	36.1932i	0.299945	−	0.173173i
$210$		0			0
$211$	−178.833	+	309.747i	−0.847548	+	1.46800i	0.0358410	+	0.999358i	$0.488589\pi$
$211$	−178.833	+	309.747i	−0.847548	+	1.46800i	−0.883389	+	0.468640i	$0.844744\pi$
$212$	−15.4817	+	26.8151i	−0.0730269	+	0.126486i
$213$		0			0
$214$	55.5100	+	96.1462i	0.259393	+	0.449281i
$215$	15.7353	−	38.1960i	0.0731873	−	0.177656i
$216$		0			0
$217$			233.616i			1.07657i
$218$	27.2292	+	47.1624i	0.124905	+	0.216341i
$219$		0			0
$220$	−70.1559	−	91.0655i	−0.318890	−	0.413934i
$221$	−63.5075	−	36.6661i	−0.287364	−	0.165910i
$222$		0			0
$223$	309.408	−	178.637i	1.38748	−	0.801062i	0.394449	−	0.918918i	$-0.370936\pi$
$223$	309.408	−	178.637i	1.38748	−	0.801062i	0.993031	+	0.117856i	$0.0376023\pi$
$224$			135.933i			0.606844i
$225$		0			0
$226$	258.682			1.14461
$227$	64.4002	+	111.544i	0.283701	+	0.491385i	0.972293	−	0.233764i	$-0.0751042\pi$
$227$	64.4002	+	111.544i	0.283701	+	0.491385i	−0.688592	+	0.725149i	$0.741771\pi$
$228$		0			0
$229$	126.552	−	219.195i	0.552631	−	0.957184i	−0.445453	−	0.895305i	$-0.646957\pi$
$229$	126.552	−	219.195i	0.552631	−	0.957184i	0.998084	−	0.0618791i	$-0.0197093\pi$
$230$	5.22644	−	4.02639i	0.0227237	−	0.0175061i
$231$		0			0
$232$	114.231	−	65.9515i	0.492377	−	0.284274i
$233$	96.3566			0.413548			0.206774	−	0.978389i	$-0.433704\pi$
$233$	96.3566			0.413548			0.206774	+	0.978389i	$0.433704\pi$
$234$		0			0
$235$	−70.0663	−	28.8646i	−0.298154	−	0.122828i
$236$	54.3659	−	31.3882i	0.230364	−	0.133001i
$237$		0			0
$238$	−239.955	−	138.538i	−1.00822	−	0.582094i
$239$	−94.7361	−	54.6959i	−0.396385	−	0.228853i	0.288538	−	0.957469i	$-0.406831\pi$
$239$	−94.7361	−	54.6959i	−0.396385	−	0.228853i	−0.684923	+	0.728615i	$0.740164\pi$
$240$		0			0
$241$	156.812	+	271.606i	0.650672	+	1.12700i	0.982960	+	0.183819i	$0.0588460\pi$
$241$	156.812	+	271.606i	0.650672	+	1.12700i	−0.332288	+	0.943178i	$0.607821\pi$
$242$	486.485			2.01027
$243$		0			0
$244$	79.2770			0.324906
$245$	0.177338	+	1.32728i	0.000723830	+	0.00541746i
$246$		0			0
$247$	−14.5535	−	8.40245i	−0.0589209	−	0.0340180i
$248$	−105.159	+	182.141i	−0.424029	+	0.734439i
$249$		0			0
$250$	173.201	−	228.438i	0.692802	−	0.913752i
$251$			192.888i			0.768478i	0.923234	+	0.384239i	$0.125536\pi$
$251$			192.888i			0.768478i	−0.923234	+	0.384239i	$0.874464\pi$
$252$		0			0
$253$			10.5011i			0.0415064i
$254$	−193.658	+	111.809i	−0.762433	+	0.440191i
$255$		0			0
$256$	−110.194	+	190.862i	−0.430447	+	0.745556i
$257$	186.757	−	323.472i	0.726680	−	1.25865i	−0.231599	−	0.972811i	$-0.574396\pi$
$257$	186.757	−	323.472i	0.726680	−	1.25865i	0.958279	−	0.285835i	$-0.0922710\pi$
$258$		0			0
$259$	74.7725	+	129.510i	0.288697	+	0.500038i
$260$	−10.1654	+	24.6757i	−0.0390978	+	0.0949066i
$261$		0			0
$262$		−	47.1107i		−	0.179812i
$263$	100.790	+	174.573i	0.383230	+	0.663774i	0.991522	−	0.129939i	$-0.0414783\pi$
$263$	100.790	+	174.573i	0.383230	+	0.663774i	−0.608292	+	0.793713i	$0.708145\pi$
$264$		0			0
$265$	97.3612	−	75.0060i	0.367401	−	0.283042i
$266$	−54.9885	−	31.7476i	−0.206724	−	0.119352i
$267$		0			0
$268$	130.433	−	75.3054i	0.486689	−	0.280990i
$269$		−	7.31695i		−	0.0272006i	−0.999908	−	0.0136003i	$-0.995671\pi$
$269$		−	7.31695i		−	0.0272006i	0.999908	−	0.0136003i	$-0.00432924\pi$
$270$		0			0
$271$	−93.8451			−0.346292			−0.173146	−	0.984896i	$-0.555393\pi$
$271$	−93.8451			−0.346292			−0.173146	+	0.984896i	$0.555393\pi$
$272$	−168.324	−	291.545i	−0.618837	−	1.07186i
$273$		0			0
$274$	22.5572	−	39.0702i	0.0823255	−	0.142592i
$275$	119.793	+	440.287i	0.435609	+	1.60104i
$276$		0			0
$277$	−231.116	+	133.435i	−0.834353	+	0.481714i	−0.855341	−	0.518066i	$-0.826652\pi$
$277$	−231.116	+	133.435i	−0.834353	+	0.481714i	0.0209878	+	0.999780i	$0.493319\pi$
$278$	−247.785			−0.891314
$279$		0			0
$280$	83.5558	−	202.825i	0.298414	−	0.724374i
$281$	−5.46813	+	3.15703i	−0.0194595	+	0.0112350i	−0.509698	−	0.860353i	$-0.670243\pi$
$281$	−5.46813	+	3.15703i	−0.0194595	+	0.0112350i	0.490239	+	0.871588i	$0.336910\pi$
$282$		0			0
$283$	−300.060	−	173.240i	−1.06028	−	0.612155i	−0.134773	−	0.990877i	$-0.543030\pi$
$283$	−300.060	−	173.240i	−1.06028	−	0.612155i	−0.925511	+	0.378722i	$0.876364\pi$
$284$	−72.9004	−	42.0891i	−0.256692	−	0.148201i
$285$		0			0
$286$	−88.6818	−	153.601i	−0.310076	−	0.537068i
$287$	−355.483			−1.23862
$288$		0			0
$289$	10.5195			0.0363996
$290$	238.550	−	31.8728i	0.822587	−	0.109906i
$291$		0			0
$292$	53.3910	+	30.8253i	0.182846	+	0.105566i
$293$	−53.3460	+	92.3980i	−0.182068	+	0.315352i	−0.942585	−	0.333967i	$-0.891613\pi$
$293$	−53.3460	+	92.3980i	−0.182068	+	0.315352i	0.760516	+	0.649319i	$0.224946\pi$
$294$		0			0
$295$	−246.983	+	32.9996i	−0.837231	+	0.111863i
$296$			134.631i			0.454835i
$297$		0			0
$298$			520.510i			1.74668i
$299$	2.11128	−	1.21895i	0.00706113	−	0.00407675i
$300$		0			0
$301$	28.8380	−	49.9489i	0.0958074	−	0.165943i
$302$	64.0181	−	110.883i	0.211980	−	0.367161i
$303$		0			0
$304$	−38.5732	−	66.8108i	−0.126886	−	0.219772i
$305$	−290.952	−	119.861i	−0.953940	−	0.392986i
$306$		0			0
$307$			161.083i			0.524702i	0.964973	+	0.262351i	$0.0844978\pi$
$307$			161.083i			0.524702i	−0.964973	+	0.262351i	$0.915502\pi$
$308$	−80.2487	−	138.995i	−0.260548	−	0.451282i
$309$		0			0
$310$	−303.996	+	234.195i	−0.980633	+	0.755469i
$311$	−15.0468	−	8.68727i	−0.0483820	−	0.0279333i	0.475614	−	0.879654i	$-0.342226\pi$
$311$	−15.0468	−	8.68727i	−0.0483820	−	0.0279333i	−0.523996	+	0.851721i	$0.675559\pi$
$312$		0			0
$313$	301.788	−	174.238i	0.964180	−	0.556670i	0.0667232	−	0.997772i	$-0.478746\pi$
$313$	301.788	−	174.238i	0.964180	−	0.556670i	0.897457	+	0.441102i	$0.145412\pi$
$314$		−	156.868i		−	0.499579i
$315$		0			0
$316$	−148.556			−0.470113
$317$	148.425	+	257.080i	0.468218	+	0.810978i	0.999340	−	0.0363175i	$-0.0115628\pi$
$317$	148.425	+	257.080i	0.468218	+	0.810978i	−0.531122	+	0.847295i	$0.678229\pi$
$318$		0			0
$319$	−191.534	+	331.747i	−0.600420	+	1.03996i
$320$	131.304	−	101.155i	0.410324	−	0.316109i
$321$		0			0
$322$	7.97720	−	4.60564i	0.0247739	−	0.0143032i
$323$	68.6383			0.212502
$324$		0			0
$325$	74.6155	−	75.1921i	0.229586	−	0.231360i
$326$	159.893	−	92.3142i	0.490469	−	0.283172i
$327$		0			0
$328$	−277.156	−	160.016i	−0.844987	−	0.487853i
$329$	−91.6256	−	52.9001i	−0.278497	−	0.160791i
$330$		0			0
$331$	−101.347	−	175.538i	−0.306184	−	0.530326i	0.671341	−	0.741149i	$-0.265719\pi$
$331$	−101.347	−	175.538i	−0.306184	−	0.530326i	−0.977524	+	0.210823i	$0.932385\pi$
$332$	−9.22238			−0.0277783
$333$		0			0
$334$	171.598			0.513768
$335$	−592.552	+	79.1713i	−1.76881	+	0.236332i
$336$		0			0
$337$	28.3716	+	16.3804i	0.0841888	+	0.0486064i	0.541503	−	0.840699i	$-0.317855\pi$
$337$	28.3716	+	16.3804i	0.0841888	+	0.0486064i	−0.457315	+	0.889305i	$0.651189\pi$
$338$	173.204	−	299.998i	0.512438	−	0.887569i
$339$		0			0
$340$	−14.4357	−	108.043i	−0.0424580	−	0.317774i
$341$		−	610.798i		−	1.79120i
$342$		0			0
$343$			343.931i			1.00271i
$344$	44.9677	−	25.9621i	0.130720	−	0.0754712i
$345$		0			0
$346$	365.136	−	632.435i	1.05531	−	1.82785i
$347$	−334.696	+	579.710i	−0.964540	+	1.67063i	−0.253696	+	0.967284i	$0.581646\pi$
$347$	−334.696	+	579.710i	−0.964540	+	1.67063i	−0.710845	+	0.703349i	$0.751687\pi$
$348$		0			0
$349$	−274.137	−	474.819i	−0.785492	−	1.36051i	−0.928705	−	0.370821i	$-0.879076\pi$
$349$	−274.137	−	474.819i	−0.785492	−	1.36051i	0.143212	−	0.989692i	$-0.454257\pi$
$350$	281.925	−	284.104i	0.805501	−	0.811726i
$351$		0			0
$352$		−	355.402i		−	1.00967i
$353$	−10.0056	−	17.3302i	−0.0283444	−	0.0490939i	0.851505	−	0.524346i	$-0.175690\pi$
$353$	−10.0056	−	17.3302i	−0.0283444	−	0.0490939i	−0.879850	+	0.475252i	$0.842357\pi$
$354$		0			0
$355$	203.914	+	264.690i	0.574405	+	0.745604i
$356$	−109.771	−	63.3764i	−0.308346	−	0.178024i
$357$		0			0
$358$	6.25113	−	3.60909i	0.0174613	−	0.0100813i
$359$		−	224.934i		−	0.626556i	−0.949661	−	0.313278i	$-0.898573\pi$
$359$		−	224.934i		−	0.626556i	0.949661	−	0.313278i	$-0.101427\pi$
$360$		0			0
$361$	−345.271			−0.956429
$362$	−0.955502	−	1.65498i	−0.00263951	−	0.00457176i
$363$		0			0
$364$	−18.6302	+	32.2684i	−0.0511818	+	0.0886495i
$365$	−149.343	−	193.854i	−0.409159	−	0.531107i
$366$		0			0
$367$	43.7972	−	25.2863i	0.119338	−	0.0689000i	−0.439143	−	0.898417i	$-0.644718\pi$
$367$	43.7972	−	25.2863i	0.119338	−	0.0689000i	0.558481	+	0.829517i	$0.311384\pi$
$368$	11.1917			0.0304122
$369$		0			0
$370$	−93.5685	+	227.130i	−0.252888	+	0.613864i
$371$	148.604	−	85.7966i	0.400550	−	0.231258i
$372$		0			0
$373$	244.861	+	141.371i	0.656464	+	0.379010i	0.790928	−	0.611909i	$-0.209598\pi$
$373$	244.861	+	141.371i	0.656464	+	0.379010i	−0.134464	+	0.990918i	$0.542931\pi$
$374$	627.373	+	362.214i	1.67747	+	0.968486i
$375$		0			0
$376$	−47.6245	−	82.4881i	−0.126661	−	0.219383i
$377$	88.9313			0.235892
$378$		0			0
$379$	−435.602			−1.14935			−0.574673	−	0.818383i	$-0.694871\pi$
$379$	−435.602			−1.14935			−0.574673	+	0.818383i	$0.694871\pi$
$380$	−3.30811	−	24.7593i	−0.00870554	−	0.0651560i
$381$		0			0
$382$	−114.240	−	65.9566i	−0.299058	−	0.172661i
$383$	156.225	−	270.589i	0.407897	−	0.706499i	−0.586757	−	0.809763i	$-0.699595\pi$
$383$	156.225	−	270.589i	0.407897	−	0.706499i	0.994654	+	0.103265i	$0.0329288\pi$
$384$		0			0
$385$	84.3684	+	631.450i	0.219139	+	1.64013i
$386$		−	83.3905i		−	0.216038i
$387$		0			0
$388$			5.22527i			0.0134672i
$389$	217.725	−	125.703i	0.559704	−	0.323145i	−0.193323	−	0.981135i	$-0.561926\pi$
$389$	217.725	−	125.703i	0.559704	−	0.323145i	0.753027	+	0.657990i	$0.228593\pi$
$390$		0			0
$391$	−4.97869	+	8.62335i	−0.0127332	+	0.0220546i
$392$	−0.841562	+	1.45763i	−0.00214684	+	0.00371844i
$393$		0			0
$394$	173.478	+	300.473i	0.440300	+	0.762622i
$395$	545.209	+	224.605i	1.38028	+	0.568620i
$396$		0			0
$397$		−	237.163i		−	0.597388i	−0.954349	−	0.298694i	$-0.903449\pi$
$397$		−	237.163i		−	0.597388i	0.954349	−	0.298694i	$-0.0965510\pi$
$398$	308.167	+	533.760i	0.774288	+	1.34111i
$399$		0			0
$400$	469.240	−	127.670i	1.17310	−	0.319175i
$401$	464.967	+	268.449i	1.15952	+	0.669448i	0.951188	−	0.308611i	$-0.0998640\pi$
$401$	464.967	+	268.449i	1.15952	+	0.669448i	0.208330	+	0.978059i	$0.433197\pi$
$402$		0			0
$403$	−122.803	+	70.9001i	−0.304721	+	0.175931i
$404$			204.023i			0.505007i
$405$		0			0
$406$	336.016			0.827626
$407$	−195.496	−	338.608i	−0.480333	−	0.831962i
$408$		0			0
$409$	20.7517	−	35.9430i	0.0507376	−	0.0878801i	−0.839541	−	0.543296i	$-0.817176\pi$
$409$	20.7517	−	35.9430i	0.0507376	−	0.0878801i	0.890279	+	0.455416i	$0.150509\pi$
$410$	−356.364	−	462.577i	−0.869182	−	1.12824i
$411$		0			0
$412$	−179.065	+	103.383i	−0.434624	+	0.250930i
$413$	−347.894			−0.842359
$414$		0			0
$415$	33.8467	+	13.9435i	0.0815584	+	0.0335989i
$416$	−71.4546	+	41.2543i	−0.171766	+	0.0991690i
$417$		0			0
$418$	143.769	+	83.0053i	0.343946	+	0.198577i
$419$	−636.413	−	367.433i	−1.51889	−	0.876929i	−0.999753	−	0.0222364i	$-0.992921\pi$
$419$	−636.413	−	367.433i	−1.51889	−	0.876929i	−0.519134	−	0.854693i	$-0.673745\pi$
$420$		0			0
$421$	7.65881	+	13.2655i	0.0181920	+	0.0315094i	0.874978	−	0.484163i	$-0.160876\pi$
$421$	7.65881	+	13.2655i	0.0181920	+	0.0315094i	−0.856786	+	0.515672i	$0.827542\pi$
$422$	−820.269			−1.94377
$423$		0			0
$424$	154.481			0.364341
$425$	−110.373	+	418.351i	−0.259701	+	0.984355i
$426$		0			0
$427$	−380.478	−	219.669i	−0.891048	−	0.514447i
$428$	−30.4894	+	52.8092i	−0.0712369	+	0.123386i
$429$		0			0
$430$	93.9063	−	12.5469i	0.218387	−	0.0291788i
$431$		−	98.8622i		−	0.229379i	−0.993401	−	0.114689i	$-0.963413\pi$
$431$		−	98.8622i		−	0.229379i	0.993401	−	0.114689i	$-0.0365872\pi$
$432$		0			0
$433$		−	573.821i		−	1.32522i	−0.748964	−	0.662610i	$-0.769449\pi$
$433$		−	573.821i		−	1.32522i	0.748964	−	0.662610i	$-0.230551\pi$
$434$	−463.994	+	267.887i	−1.06911	+	0.617252i
$435$		0			0
$436$	−14.9559	+	25.9044i	−0.0343025	+	0.0594137i
$437$	−1.14092	+	1.97614i	−0.00261081	+	0.00452205i
$438$		0			0
$439$	119.927	+	207.719i	0.273182	+	0.473165i	0.969675	−	0.244399i	$-0.0785906\pi$
$439$	119.927	+	207.719i	0.273182	+	0.473165i	−0.696493	+	0.717564i	$0.745257\pi$
$440$	−218.460	+	530.293i	−0.496500	+	1.20521i
$441$		0			0
$442$		−	168.180i		−	0.380497i
$443$	−183.257	−	317.411i	−0.413673	−	0.716503i	0.581615	−	0.813464i	$-0.302421\pi$
$443$	−183.257	−	317.411i	−0.413673	−	0.716503i	−0.995288	+	0.0969610i	$0.969088\pi$
$444$		0			0
$445$	307.047	+	398.561i	0.689993	+	0.895643i
$446$	709.595	+	409.685i	1.59102	+	0.918576i
$447$		0			0
$448$	200.411	−	115.707i	0.447346	−	0.258275i
$449$			623.682i			1.38905i	0.719470	+	0.694523i	$0.244385\pi$
$449$			623.682i			1.38905i	−0.719470	+	0.694523i	$0.755615\pi$
$450$		0			0
$451$	929.424			2.06081
$452$	71.0418	+	123.048i	0.157172	+	0.272230i
$453$		0			0
$454$	−147.695	+	255.816i	−0.325320	+	0.563471i
$455$	117.161	−	90.2598i	0.257497	−	0.198373i
$456$		0			0
$457$	−336.409	+	194.226i	−0.736126	+	0.425002i	−0.820659	−	0.571418i	$-0.806393\pi$
$457$	−336.409	+	194.226i	−0.736126	+	0.425002i	0.0845333	+	0.996421i	$0.473060\pi$
$458$	580.470			1.26740
$459$		0			0
$460$	3.35058	+	1.38031i	0.00728387	+	0.00300067i
$461$	−328.964	+	189.927i	−0.713588	+	0.411990i	−0.812388	−	0.583117i	$-0.801833\pi$
$461$	−328.964	+	189.927i	−0.713588	+	0.411990i	0.0988003	+	0.995107i	$0.468499\pi$
$462$		0			0
$463$	331.040	+	191.126i	0.714990	+	0.412800i	0.812906	−	0.582395i	$-0.197884\pi$
$463$	331.040	+	191.126i	0.714990	+	0.412800i	−0.0979160	+	0.995195i	$0.531218\pi$
$464$	353.562	+	204.129i	0.761987	+	0.439933i
$465$		0			0
$466$	110.492	+	191.378i	0.237107	+	0.410682i
$467$	35.3515			0.0756992			0.0378496	−	0.999283i	$-0.487949\pi$
$467$	35.3515			0.0756992			0.0378496	+	0.999283i	$0.487949\pi$
$468$		0			0
$469$	−834.655			−1.77965
$470$	−23.0158	−	172.260i	−0.0489698	−	0.366511i
$471$		0			0
$472$	−271.239	−	156.600i	−0.574659	−	0.331779i
$473$	−75.3982	+	130.593i	−0.159404	+	0.276096i
$474$		0			0
$475$	−25.2932	+	95.8698i	−0.0532488	+	0.201831i
$476$		−	152.187i		−	0.319720i
$477$		0			0
$478$		−	250.879i		−	0.524851i
$479$	501.226	−	289.383i	1.04640	−	0.604139i	0.124761	−	0.992187i	$-0.460184\pi$
$479$	501.226	−	289.383i	1.04640	−	0.604139i	0.921639	+	0.388047i	$0.126850\pi$
$480$		0			0
$481$	−45.3854	+	78.6098i	−0.0943563	+	0.163430i
$482$	−359.632	+	622.901i	−0.746124	+	1.29233i
$483$		0			0
$484$	133.603	+	231.408i	0.276040	+	0.478115i
$485$	7.90020	−	19.1771i	0.0162891	−	0.0395404i
$486$		0			0
$487$		−	424.778i		−	0.872235i	−0.899890	−	0.436117i	$-0.856353\pi$
$487$		−	424.778i		−	0.872235i	0.899890	−	0.436117i	$-0.143647\pi$
$488$	−197.762	−	342.534i	−0.405250	−	0.701913i
$489$		0			0
$490$	−2.43281	+	1.87421i	−0.00496491	+	0.00382491i
$491$	−337.754	−	195.002i	−0.687890	−	0.397154i	0.114931	−	0.993373i	$-0.463335\pi$
$491$	−337.754	−	195.002i	−0.687890	−	0.397154i	−0.802821	+	0.596220i	$0.796669\pi$
$492$		0			0
$493$	−314.569	+	181.616i	−0.638071	+	0.368390i
$494$		−	38.5403i		−	0.0780168i
$495$		0			0
$496$	−650.964			−1.31243
$497$	233.249	+	404.000i	0.469315	+	0.812877i
$498$		0			0
$499$	308.776	−	534.816i	0.618790	−	1.07178i	−0.370916	−	0.928666i	$-0.620956\pi$
$499$	308.776	−	534.816i	0.618790	−	1.07178i	0.989707	−	0.143110i	$-0.0457103\pi$
$500$	156.228	+	19.6509i	0.312455	+	0.0393019i
$501$		0			0
$502$	−383.102	+	221.184i	−0.763152	+	0.440606i
$503$	551.752			1.09692			0.548461	−	0.836176i	$-0.315214\pi$
$503$	551.752			1.09692			0.548461	+	0.836176i	$0.315214\pi$
$504$		0			0
$505$	308.467	−	748.777i	0.610825	−	1.48273i
$506$	−20.8567	+	12.0416i	−0.0412188	+	0.0237977i
$507$		0			0
$508$	−106.369	−	61.4119i	−0.209387	−	0.120890i
$509$	−383.782	−	221.577i	−0.753992	−	0.435317i	0.0731427	−	0.997321i	$-0.476697\pi$
$509$	−383.782	−	221.577i	−0.753992	−	0.435317i	−0.827134	+	0.562004i	$0.810030\pi$
$510$		0			0
$511$	−170.828	−	295.882i	−0.334301	−	0.579026i
$512$	110.221			0.215276
$513$		0			0
$514$	856.615			1.66657
$515$	813.488	−	108.691i	1.57959	−	0.211050i
$516$		0			0
$517$	239.559	+	138.309i	0.463363	+	0.267523i
$518$	−171.483	+	297.017i	−0.331048	+	0.573393i
$519$		0			0
$520$	131.975	−	17.6333i	0.253798	−	0.0339101i
$521$			716.733i			1.37569i	0.725859	+	0.687843i	$0.241442\pi$
$521$			716.733i			1.37569i	−0.725859	+	0.687843i	$0.758558\pi$
$522$		0			0
$523$			417.591i			0.798453i	0.916852	+	0.399227i	$0.130721\pi$
$523$			417.591i			0.798453i	−0.916852	+	0.399227i	$0.869279\pi$
$524$	22.4093	−	12.9380i	0.0427658	−	0.0246908i
$525$		0			0
$526$	−231.150	+	400.364i	−0.439449	+	0.761149i
$527$	289.586	−	501.577i	0.549499	−	0.951760i
$528$		0			0
$529$	264.334	+	457.841i	0.499687	+	0.865483i
$530$	260.616	+	107.364i	0.491729	+	0.202573i
$531$		0			0
$532$		−	34.8753i		−	0.0655552i
$533$	−107.886	−	186.863i	−0.202412	−	0.350588i
$534$		0			0
$535$	191.742	−	147.716i	0.358395	−	0.276104i
$536$	−650.746	−	375.709i	−1.21408	−	0.700949i
$537$		0			0
$538$	14.5325	−	8.39034i	0.0270121	−	0.0155954i
$539$		−	4.88807i		−	0.00906877i
$540$		0			0
$541$	−365.297			−0.675225			−0.337612	−	0.941285i	$-0.609619\pi$
$541$	−365.297			−0.675225			−0.337612	+	0.941285i	$0.609619\pi$
$542$	−107.612	−	186.389i	−0.198546	−	0.343892i
$543$		0			0
$544$	168.500	−	291.851i	0.309743	−	0.536490i
$545$	94.0546	−	72.4586i	0.172577	−	0.132952i
$546$		0			0
$547$	529.651	−	305.794i	0.968283	−	0.559039i	0.0695708	−	0.997577i	$-0.477837\pi$
$547$	529.651	−	305.794i	0.968283	−	0.559039i	0.898712	+	0.438538i	$0.144504\pi$
$548$	24.7795			0.0452181
$549$		0			0
$550$	−737.105	+	742.801i	−1.34019	+	1.35055i
$551$	−72.0870	+	41.6195i	−0.130829	+	0.0755344i
$552$		0			0
$553$	712.970	+	411.633i	1.28928	+	0.744364i
$554$	−530.040	−	306.019i	−0.956751	−	0.552381i
$555$		0			0
$556$	−68.0492	−	117.865i	−0.122391	−	0.211987i
$557$	−510.888			−0.917214			−0.458607	−	0.888639i	$-0.651651\pi$
$557$	−510.888			−0.917214			−0.458607	+	0.888639i	$0.651651\pi$
$558$		0			0
$559$	35.0082			0.0626265
$560$	672.974	−	89.9164i	1.20174	−	0.160565i
$561$		0			0
$562$	−12.5406	−	7.24031i	−0.0223142	−	0.0128831i
$563$	78.8759	−	136.617i	0.140099	−	0.242659i	−0.787435	−	0.616398i	$-0.788591\pi$
$563$	78.8759	−	136.617i	0.140099	−	0.242659i	0.927534	+	0.373739i	$0.121924\pi$
$564$		0			0
$565$	−74.6889	−	559.004i	−0.132193	−	0.989388i
$566$		−	794.615i		−	1.40391i
$567$		0			0
$568$			419.976i			0.739395i
$569$	152.312	−	87.9374i	0.267684	−	0.154547i	−0.360151	−	0.932894i	$-0.617275\pi$
$569$	152.312	−	87.9374i	0.267684	−	0.154547i	0.627835	+	0.778347i	$0.283941\pi$
$570$		0			0
$571$	294.258	−	509.670i	0.515338	−	0.892591i	−0.484504	−	0.874789i	$-0.661000\pi$
$571$	294.258	−	509.670i	0.515338	−	0.892591i	0.999842	−	0.0178020i	$-0.00566685\pi$
$572$	48.7093	−	84.3670i	0.0851562	−	0.147495i
$573$		0			0
$574$	−407.632	−	706.039i	−0.710160	−	1.23003i
$575$	−10.2099	−	10.1316i	−0.0177564	−	0.0176203i
$576$		0			0
$577$			323.853i			0.561270i	0.959815	+	0.280635i	$0.0905451\pi$
$577$			323.853i			0.561270i	−0.959815	+	0.280635i	$0.909455\pi$
$578$	12.0627	+	20.8932i	0.0208697	+	0.0361474i
$579$		0			0
$580$	80.6740	+	104.719i	0.139093	+	0.180549i
$581$	44.2614	+	25.5543i	0.0761814	+	0.0439833i
$582$		0			0
$583$	−388.531	+	224.318i	−0.666434	+	0.384766i
$584$		−	307.583i		−	0.526684i
$585$		0			0
$586$	−244.687			−0.417555
$587$	−515.537	−	892.937i	−0.878258	−	1.52119i	−0.853251	−	0.521500i	$-0.825373\pi$
$587$	−515.537	−	892.937i	−0.878258	−	1.52119i	−0.0250065	−	0.999687i	$-0.507961\pi$
$588$		0			0
$589$	66.3618	−	114.942i	0.112669	−	0.195148i
$590$	−348.757	−	452.702i	−0.591113	−	0.767292i
$591$		0			0
$592$	−360.875	+	208.351i	−0.609586	+	0.351945i
$593$	193.131			0.325685			0.162842	−	0.986652i	$-0.447934\pi$
$593$	193.131			0.325685			0.162842	+	0.986652i	$0.447934\pi$
$594$		0			0
$595$	−230.095	+	558.536i	−0.386714	+	0.938716i
$596$	−247.592	+	142.948i	−0.415424	+	0.239845i
$597$		0			0
$598$	4.84200	+	2.79553i	0.00809699	+	0.00467480i
$599$	354.438	+	204.635i	0.591716	+	0.341627i	0.765776	−	0.643108i	$-0.222355\pi$
$599$	354.438	+	204.635i	0.591716	+	0.341627i	−0.174060	+	0.984735i	$0.555689\pi$
$600$		0			0
$601$	520.432	+	901.414i	0.865943	+	1.49986i	0.866108	+	0.499857i	$0.166614\pi$
$601$	520.432	+	901.414i	0.865943	+	1.49986i	−0.000165360		1.00000i	$0.500053\pi$
$602$	132.274			0.219724
$603$		0			0
$604$	70.3251			0.116432
$605$	−140.462	−	1051.28i	−0.232169	−	1.73765i
$606$		0			0
$607$	−589.637	−	340.427i	−0.971396	−	0.560836i	−0.0717342	−	0.997424i	$-0.522853\pi$
$607$	−589.637	−	340.427i	−0.971396	−	0.560836i	−0.899661	+	0.436588i	$0.856187\pi$
$608$	38.6137	−	66.8808i	0.0635093	−	0.110001i
$609$		0			0
$610$	−95.5737	−	715.315i	−0.156678	−	1.17265i
$611$		−	64.2185i		−	0.105104i
$612$		0			0
$613$		−	1024.19i		−	1.67079i	−0.549651	−	0.835395i	$-0.685239\pi$
$613$		−	1024.19i		−	1.67079i	0.549651	−	0.835395i	$-0.314761\pi$
$614$	−319.934	+	184.714i	−0.521066	+	0.300837i
$615$		0			0
$616$	−400.371	+	693.464i	−0.649954	+	1.12575i
$617$	−555.636	+	962.389i	−0.900544	+	1.55979i	−0.0737542	+	0.997276i	$0.523498\pi$
$617$	−555.636	+	962.389i	−0.900544	+	1.55979i	−0.826790	+	0.562511i	$0.809835\pi$
$618$		0			0
$619$	−400.940	−	694.448i	−0.647722	−	1.12189i	−0.983666	−	0.180005i	$-0.942389\pi$
$619$	−400.940	−	694.448i	−0.647722	−	1.12189i	0.335944	−	0.941882i	$-0.390945\pi$
$620$	−194.887	−	80.2857i	−0.314333	−	0.129493i
$621$		0			0
$622$		−	39.8467i		−	0.0640622i
$623$	351.220	+	608.330i	0.563755	+	0.976453i
$624$		0			0
$625$	−543.655	−	308.325i	−0.869848	−	0.493319i
$626$	692.121	+	399.596i	1.10562	+	0.638332i
$627$		0			0
$628$	74.6177	−	43.0805i	0.118818	−	0.0685996i
$629$		−	370.746i		−	0.589421i
$630$		0			0
$631$	−564.192			−0.894124			−0.447062	−	0.894503i	$-0.647530\pi$
$631$	−564.192			−0.894124			−0.447062	+	0.894503i	$0.647530\pi$
$632$	370.582	+	641.868i	0.586365	+	1.01561i
$633$		0			0
$634$	−340.398	+	589.587i	−0.536905	+	0.929947i
$635$	297.529	+	386.207i	0.468550	+	0.608200i
$636$		0			0
$637$	−0.982759	+	0.567396i	−0.00154279	+	0.000890731i
$638$	−878.527			−1.37700
$639$		0			0
$640$	711.561	+	293.135i	1.11181	+	0.458024i
$641$	−1043.99	+	602.749i	−1.62869	+	0.940327i	−0.644210	+	0.764848i	$0.722814\pi$
$641$	−1043.99	+	602.749i	−1.62869	+	0.940327i	−0.984483	+	0.175478i	$0.943853\pi$
$642$		0			0
$643$	−402.110	−	232.158i	−0.625365	−	0.361055i	0.153590	−	0.988135i	$-0.450917\pi$
$643$	−402.110	−	232.158i	−0.625365	−	0.361055i	−0.778955	+	0.627080i	$0.784250\pi$
$644$	4.38156	+	2.52969i	0.00680366	+	0.00392809i
$645$		0			0
$646$	78.7074	+	136.325i	0.121838	+	0.211030i
$647$	−372.702			−0.576046			−0.288023	−	0.957624i	$-0.592998\pi$
$647$	−372.702			−0.576046			−0.288023	+	0.957624i	$0.592998\pi$
$648$		0			0
$649$	909.583			1.40151
$650$	234.904	+	61.9742i	0.361390	+	0.0953450i
$651$		0			0
$652$	87.8227	+	50.7044i	0.134697	+	0.0777676i
$653$	−110.705	+	191.747i	−0.169533	+	0.293639i	−0.938256	−	0.345943i	$-0.887559\pi$
$653$	−110.705	+	191.747i	−0.169533	+	0.293639i	0.768723	+	0.639582i	$0.220893\pi$
$654$		0			0
$655$	−101.805	+	13.6022i	−0.155427	+	0.0207667i
$656$		−	990.543i		−	1.50997i
$657$		0			0
$658$		−	242.642i		−	0.368757i
$659$	541.098	−	312.403i	0.821090	−	0.474057i	−0.0297021	−	0.999559i	$-0.509456\pi$
$659$	541.098	−	312.403i	0.821090	−	0.474057i	0.850792	+	0.525502i	$0.176123\pi$
$660$		0			0
$661$	−167.257	+	289.698i	−0.253037	+	0.438273i	−0.964360	−	0.264592i	$-0.914763\pi$
$661$	−167.257	+	289.698i	−0.253037	+	0.438273i	0.711324	+	0.702865i	$0.248096\pi$
$662$	232.428	−	402.578i	0.351100	−	0.608124i
$663$		0			0
$664$	23.0059	+	39.8473i	0.0346474	+	0.0600110i
$665$	−52.7288	+	127.995i	−0.0792915	+	0.192473i
$666$		0			0
$667$		−	12.0755i		−	0.0181042i
$668$	47.1260	+	81.6247i	0.0705480	+	0.122193i
$669$		0			0
$670$	−836.724	−	1086.11i	−1.24884	−	1.62105i
$671$	994.773	+	574.333i	1.48252	+	0.855935i
$672$		0			0
$673$	−820.344	+	473.626i	−1.21894	+	0.703753i	−0.964690	−	0.263387i	$-0.915160\pi$
$673$	−820.344	+	473.626i	−1.21894	+	0.703753i	−0.254245	+	0.967140i	$0.581827\pi$
$674$			75.1334i			0.111474i
$675$		0			0
$676$	190.268			0.281462
$677$	504.620	+	874.028i	0.745377	+	1.29103i	0.950018	+	0.312194i	$0.101064\pi$
$677$	504.620	+	874.028i	0.745377	+	1.29103i	−0.204641	+	0.978837i	$0.565603\pi$
$678$		0			0
$679$	14.4787	−	25.0778i	0.0213236	−	0.0369335i
$680$	−430.813	+	331.893i	−0.633548	+	0.488079i
$681$		0			0
$682$	1213.13	−	700.401i	1.77878	−	1.02698i
$683$	−697.555			−1.02131			−0.510655	−	0.859786i	$-0.670597\pi$
$683$	−697.555			−1.02131			−0.510655	+	0.859786i	$0.670597\pi$
$684$		0			0
$685$	−90.9424	−	37.4647i	−0.132763	−	0.0546930i
$686$	−683.095	+	394.385i	−0.995765	+	0.574905i
$687$		0			0
$688$	139.181	+	80.3563i	0.202298	+	0.116797i
$689$	90.1996	+	52.0768i	0.130914	+	0.0755831i
$690$		0			0
$691$	89.5928	+	155.179i	0.129657	+	0.224572i	0.923544	−	0.383493i	$-0.125279\pi$
$691$	89.5928	+	155.179i	0.129657	+	0.224572i	−0.793887	+	0.608066i	$0.791946\pi$
$692$	401.109			0.579638
$693$		0			0
$694$	−1535.18			−2.21207
$695$	71.5427	+	535.456i	0.102939	+	0.770441i
$696$		0			0
$697$	763.228	+	440.650i	1.09502	+	0.632209i
$698$	628.705	−	1088.95i	0.900723	−	1.56010i
$699$		0			0
$700$	212.566	+	56.0809i	0.303665	+	0.0801155i
$701$		−	211.499i		−	0.301710i	−0.988556	−	0.150855i	$-0.951797\pi$
$701$		−	211.499i		−	0.301710i	0.988556	−	0.150855i	$-0.0482026\pi$
$702$		0			0
$703$		−	84.9606i		−	0.120854i
$704$	−523.982	+	302.521i	−0.744292	+	0.429717i
$705$		0			0
$706$	22.9468	−	39.7449i	0.0325025	−	0.0562960i
$707$	565.327	−	979.175i	0.799614	−	1.38497i
$708$		0			0
$709$	216.625	+	375.205i	0.305536	+	0.529203i	0.977380	−	0.211489i	$-0.0678312\pi$
$709$	216.625	+	375.205i	0.305536	+	0.529203i	−0.671845	+	0.740692i	$0.734498\pi$
$710$	−291.883	+	708.521i	−0.411103	+	0.997916i
$711$		0			0
$712$			632.387i			0.888184i
$713$	9.62715	+	16.6747i	0.0135023	+	0.0233867i
$714$		0			0
$715$	−306.323	+	235.988i	−0.428423	+	0.330053i
$716$	3.43349	+	1.98233i	0.00479538	+	0.00276861i
$717$		0			0
$718$	446.750	−	257.931i	0.622214	−	0.359236i
$719$			588.734i			0.818824i	0.912350	+	0.409412i	$0.134266\pi$
$719$			588.734i			0.818824i	−0.912350	+	0.409412i	$0.865734\pi$
$720$		0			0
$721$	1145.86			1.58927
$722$	−395.921	−	685.756i	−0.548368	−	0.949801i
$723$		0			0
$724$	0.524819	−	0.909013i	0.000724888	−	0.00125554i
$725$	−137.752	−	506.297i	−0.190003	−	0.698340i
$726$		0			0
$727$	218.273	−	126.020i	0.300238	−	0.173343i	−0.342312	−	0.939587i	$-0.611210\pi$
$727$	218.273	−	126.020i	0.300238	−	0.173343i	0.642550	+	0.766244i	$0.277876\pi$
$728$	185.897			0.255353
$729$		0			0
$730$	213.770	−	518.908i	0.292835	−	0.710833i
$731$	−123.831	+	71.4941i	−0.169400	+	0.0978031i
$732$		0			0
$733$	−166.687	−	96.2366i	−0.227403	−	0.131291i	0.381970	−	0.924175i	$-0.375246\pi$
$733$	−166.687	−	96.2366i	−0.227403	−	0.131291i	−0.609374	+	0.792883i	$0.708579\pi$
$734$	100.444	+	57.9916i	0.136845	+	0.0790076i
$735$		0			0
$736$	5.60170	+	9.70244i	0.00761101	+	0.0131827i
$737$	2182.24			2.96097
$738$		0			0
$739$	811.337			1.09788			0.548942	−	0.835860i	$-0.315031\pi$
$739$	811.337			1.09788			0.548942	+	0.835860i	$0.315031\pi$
$740$	−133.736	+	17.8686i	−0.180724	+	0.0241467i
$741$		0			0
$742$	340.808	+	196.766i	0.459310	+	0.265183i
$743$	−510.716	+	884.586i	−0.687370	+	1.19056i	0.285315	+	0.958434i	$0.407902\pi$
$743$	−510.716	+	884.586i	−0.687370	+	1.19056i	−0.972686	+	0.232126i	$0.925432\pi$
$744$		0			0
$745$	1124.81	−	150.286i	1.50981	−	0.201726i
$746$			648.438i			0.869219i
$747$		0			0
$748$			397.899i			0.531950i
$749$	292.658	−	168.966i	0.390732	−	0.225589i
$750$		0			0
$751$	477.189	−	826.515i	0.635404	−	1.10055i	−0.351025	−	0.936366i	$-0.614167\pi$
$751$	477.189	−	826.515i	0.635404	−	1.10055i	0.986429	−	0.164186i	$-0.0524999\pi$
$752$	147.404	−	255.312i	0.196017	−	0.339511i
$753$		0			0
$754$	101.977	+	176.630i	0.135249	+	0.234257i
$755$	−258.098	−	106.326i	−0.341851	−	0.140829i
$756$		0			0
$757$			1462.32i			1.93173i	0.259040	+	0.965866i	$0.416594\pi$
$757$			1462.32i			1.93173i	−0.259040	+	0.965866i	$0.583406\pi$
$758$	−499.504	−	865.166i	−0.658976	−	1.14138i
$759$		0			0
$760$	−98.7256	+	76.0571i	−0.129902	+	0.100075i
$761$	33.0469	+	19.0796i	0.0434256	+	0.0250718i	0.521556	−	0.853217i	$-0.325352\pi$
$761$	33.0469	+	19.0796i	0.0434256	+	0.0250718i	−0.478130	+	0.878289i	$0.658685\pi$
$762$		0			0
$763$	143.557	−	82.8827i	0.188148	−	0.108627i
$764$		−	72.4546i		−	0.0948359i
$765$		0			0
$766$	716.570			0.935470
$767$	−105.582	−	182.874i	−0.137656	−	0.238428i
$768$		0			0
$769$	−301.249	+	521.778i	−0.391741	+	0.678515i	−0.992679	−	0.120781i	$-0.961460\pi$
$769$	−301.249	+	521.778i	−0.391741	+	0.678515i	0.600939	+	0.799295i	$0.294794\pi$
$770$	−1157.40	+	891.650i	−1.50312	+	1.15799i
$771$		0			0
$772$	39.6666	−	22.9015i	0.0513816	−	0.0296652i
$773$	394.816			0.510758			0.255379	−	0.966841i	$-0.417800\pi$
$773$	394.816			0.510758			0.255379	+	0.966841i	$0.417800\pi$
$774$		0			0
$775$	593.861	+	589.307i	0.766272	+	0.760397i
$776$	22.5769	−	13.0348i	0.0290940	−	0.0167974i
$777$		0			0
$778$	499.329	+	288.288i	0.641811	+	0.370550i
$779$	174.902	+	100.980i	0.224521	+	0.129628i
$780$		0			0
$781$	−609.840	−	1056.27i	−0.780845	−	1.35246i
$782$	−22.8362			−0.0292024
$783$		0			0
$784$	−5.20950			−0.00664478
$785$	−338.986	+	45.2922i	−0.431830	+	0.0576970i
$786$		0			0
$787$	−713.353	−	411.855i	−0.906421	−	0.523322i	−0.0271429	−	0.999632i	$-0.508641\pi$
$787$	−713.353	−	411.855i	−0.906421	−	0.523322i	−0.879278	+	0.476309i	$0.841974\pi$
$788$	−95.2845	+	165.038i	−0.120919	+	0.209439i
$789$		0			0
$790$	179.094	+	1340.42i	0.226701	+	1.69673i
$791$		−	787.400i		−	0.995448i
$792$		0			0
$793$		−	266.669i		−	0.336279i
$794$	471.039	−	271.955i	0.593248	−	0.342512i
$795$		0			0
$796$	−169.263	+	293.173i	−0.212642	+	0.368308i
$797$	459.750	−	796.310i	0.576850	−	0.999134i	−0.418988	−	0.907992i	$-0.637615\pi$
$797$	459.750	−	796.310i	0.576850	−	0.999134i	0.995838	−	0.0911420i	$-0.0290517\pi$
$798$		0			0
$799$	131.148	+	227.155i	0.164140	+	0.284299i
$800$	345.547	+	342.898i	0.431934	+	0.428622i
$801$		0			0
$802$			1231.32i			1.53531i
$803$	446.636	+	773.596i	0.556209	+	0.963383i
$804$		0			0
$805$	−12.2559	−	15.9087i	−0.0152247	−	0.0197624i
$806$	−281.635	−	162.602i	−0.349423	−	0.201740i
$807$		0			0
$808$	881.525	−	508.948i	1.09100	−	0.629887i
$809$			1432.18i			1.77031i	0.465300	+	0.885153i	$0.345946\pi$
$809$			1432.18i			1.77031i	−0.465300	+	0.885153i	$0.654054\pi$
$810$		0			0
$811$	−422.921			−0.521481			−0.260740	−	0.965409i	$-0.583967\pi$
$811$	−422.921			−0.521481			−0.260740	+	0.965409i	$0.583967\pi$
$812$	92.2800	+	159.834i	0.113645	+	0.196839i
$813$		0			0
$814$	448.349	−	776.563i	0.550797	−	0.954009i
$815$	−245.654	−	318.870i	−0.301416	−	0.391251i
$816$		0			0
$817$	−28.3774	+	16.3837i	−0.0347336	+	0.0200535i
$818$	95.1837			0.116362
$819$		0			0
$820$	122.167	−	296.550i	0.148984	−	0.361647i
$821$	151.022	−	87.1926i	0.183949	−	0.106203i	−0.405198	−	0.914229i	$-0.632797\pi$
$821$	151.022	−	87.1926i	0.183949	−	0.106203i	0.589147	+	0.808026i	$0.299464\pi$
$822$		0			0
$823$	−777.136	−	448.680i	−0.944272	−	0.545176i	−0.0529754	−	0.998596i	$-0.516870\pi$
$823$	−777.136	−	448.680i	−0.944272	−	0.545176i	−0.891297	+	0.453420i	$0.850204\pi$
$824$	893.380	+	515.793i	1.08420	+	0.625963i
$825$		0			0
$826$	−398.930	−	690.967i	−0.482966	−	0.836522i
$827$	−233.440			−0.282273			−0.141137	−	0.989990i	$-0.545076\pi$
$827$	−233.440			−0.282273			−0.141137	+	0.989990i	$0.545076\pi$
$828$		0			0
$829$	−990.934			−1.19534			−0.597668	−	0.801744i	$-0.703906\pi$
$829$	−990.934			−1.19534			−0.597668	+	0.801744i	$0.703906\pi$
$830$	11.1182	+	83.2134i	0.0133954	+	0.100257i
$831$		0			0
$832$	121.645	+	70.2319i	0.146208	+	0.0844134i
$833$	2.31748	−	4.01400i	0.00278209	−	0.00481873i
$834$		0			0
$835$	−49.5453	−	370.819i	−0.0593357	−	0.444094i
$836$			91.1829i			0.109071i
$837$		0			0
$838$		−	1685.34i		−	2.01115i
$839$	301.025	−	173.797i	0.358790	−	0.207148i	−0.309760	−	0.950815i	$-0.600249\pi$
$839$	301.025	−	173.797i	0.358790	−	0.207148i	0.668550	+	0.743667i	$0.266915\pi$
$840$		0			0
$841$	−200.250	+	346.844i	−0.238110	+	0.412418i
$842$	−17.5647	+	30.4229i	−0.0208607	+	0.0361318i
$843$		0			0
$844$	−225.270	−	390.180i	−0.266908	−	0.462298i
$845$	−698.296	−	287.671i	−0.826386	−	0.340439i
$846$		0			0
$847$		−	1480.81i		−	1.74829i
$848$	239.070	+	414.081i	0.281922	+	0.488303i
$849$		0			0
$850$	−957.468	+	260.506i	−1.12643	+	0.306478i
$851$	10.6740	+	6.16264i	0.0125429	+	0.00724165i
$852$		0			0
$853$	−1070.74	+	618.192i	−1.25526	+	0.724727i	−0.972150	−	0.234359i	$-0.924701\pi$
$853$	−1070.74	+	618.192i	−1.25526	+	0.724727i	−0.283114	+	0.959086i	$0.591368\pi$
$854$		−	1007.58i		−	1.17983i
$855$		0			0
$856$	304.231			0.355411
$857$	−457.353	−	792.158i	−0.533667	−	0.924338i	−0.999227	−	0.0393219i	$-0.987480\pi$
$857$	−457.353	−	792.158i	−0.533667	−	0.924338i	0.465560	−	0.885017i	$-0.345853\pi$
$858$		0			0
$859$	−571.510	+	989.884i	−0.665320	+	1.15237i	0.313879	+	0.949463i	$0.398371\pi$
$859$	−571.510	+	989.884i	−0.665320	+	1.15237i	−0.979199	+	0.202905i	$0.934962\pi$
$860$	31.7577	+	41.2229i	0.0369275	+	0.0479336i
$861$		0			0
$862$	196.354	−	113.365i	0.227789	−	0.131514i
$863$	−1228.14			−1.42311			−0.711554	−	0.702632i	$-0.752008\pi$
$863$	−1228.14			−1.42311			−0.711554	+	0.702632i	$0.752008\pi$
$864$		0			0
$865$	−1472.10	−	606.446i	−1.70185	−	0.701094i
$866$	1139.69	−	657.999i	1.31604	−	0.759814i
$867$		0			0
$868$	−254.853	−	147.140i	−0.293610	−	0.169516i
$869$	−1864.09	−	1076.23i	−2.14510	−	1.23847i
$870$		0			0
$871$	−253.309	−	438.745i	−0.290826	−	0.503725i
$872$	149.234			0.171140
$873$		0			0
$874$	−5.23318			−0.00598762
$875$	−695.340	−	527.203i	−0.794674	−	0.602518i
$876$		0			0
$877$	1193.15	+	688.864i	1.36049	+	0.785478i	0.989689	−	0.143235i	$-0.0457504\pi$
$877$	1193.15	+	688.864i	1.36049	+	0.785478i	0.370799	+	0.928713i	$0.379084\pi$
$878$	−275.040	+	476.383i	−0.313257	+	0.542578i
$879$		0			0
$880$	−1759.52	+	235.090i	−1.99945	+	0.267148i
$881$		−	1087.45i		−	1.23434i	−0.786831	−	0.617168i	$-0.788280\pi$
$881$		−	1087.45i		−	1.23434i	0.786831	−	0.617168i	$-0.211720\pi$
$882$		0			0
$883$			922.151i			1.04434i	0.852842	+	0.522170i	$0.174877\pi$
$883$			922.151i			1.04434i	−0.852842	+	0.522170i	$0.825123\pi$
$884$	79.9986	−	46.1872i	0.0904961	−	0.0522480i
$885$		0			0
$886$	420.282	−	727.949i	0.474359	−	0.821613i
$887$	−530.496	+	918.846i	−0.598079	+	1.03590i	0.395026	+	0.918670i	$0.370736\pi$
$887$	−530.496	+	918.846i	−0.598079	+	1.03590i	−0.993104	+	0.117233i	$0.962598\pi$
$888$		0			0
$889$	340.333	+	589.473i	0.382826	+	0.663075i
$890$	−439.508	+	1066.87i	−0.493829	+	1.19873i
$891$		0			0
$892$			450.047i			0.504537i
$893$	30.0540	+	52.0550i	0.0336551	+	0.0582923i
$894$		0			0
$895$	−9.60401	−	12.4664i	−0.0107307	−	0.0139290i
$896$	930.508	+	537.229i	1.03851	+	0.599586i
$897$		0			0
$898$	−1238.72	+	715.175i	−1.37942	+	0.796409i
$899$			702.372i			0.781282i
$900$		0			0
$901$	−425.407			−0.472150
$902$	1065.77	+	1845.97i	1.18156	+	2.04653i
$903$		0			0
$904$	354.437	−	613.903i	0.392077	−	0.679097i
$905$	−3.30048	+	2.54265i	−0.00364693	+	0.00280956i
$906$		0			0
$907$	1208.95	−	697.990i	1.33292	−	0.769559i	0.347170	−	0.937802i	$-0.387143\pi$
$907$	1208.95	−	697.990i	1.33292	−	0.769559i	0.985745	+	0.168243i	$0.0538095\pi$
$908$	−162.246			−0.178685
$909$		0			0
$910$	313.617	+	129.198i	0.344634	+	0.141976i
$911$	1100.06	−	635.123i	1.20754	−	0.697171i	0.245315	−	0.969443i	$-0.421109\pi$
$911$	1100.06	−	635.123i	1.20754	−	0.697171i	0.962220	+	0.272272i	$0.0877752\pi$
$912$		0			0
$913$	−115.723	−	66.8128i	−0.126750	−	0.0731794i
$914$	−771.520	−	445.438i	−0.844114	−	0.487350i
$915$		0			0
$916$	159.414	+	276.114i	0.174033	+	0.301434i
$917$	−143.400			−0.156379
$918$		0			0
$919$	269.489			0.293242			0.146621	−	0.989193i	$-0.453160\pi$
$919$	269.489			0.293242			0.146621	+	0.989193i	$0.453160\pi$
$920$	−2.39433	−	17.9202i	−0.00260253	−	0.0194785i
$921$		0			0
$922$	−754.445	−	435.579i	−0.818270	−	0.472428i
$923$	−141.578	+	245.220i	−0.153389	+	0.265677i
$924$		0			0
$925$	517.836	+	136.620i	0.559823	+	0.147697i
$926$			876.657i			0.946713i
$927$		0			0
$928$			408.686i			0.440395i
$929$	−958.120	+	553.171i	−1.03135	+	0.595447i	−0.917370	−	0.398036i	$-0.869692\pi$
$929$	−958.120	+	553.171i	−1.03135	+	0.595447i	−0.113976	+	0.993484i	$0.536359\pi$
$930$		0			0
$931$	0.531077	−	0.919853i	0.000570438	−	0.000988027i
$932$	−60.6888	+	105.116i	−0.0651167	+	0.112785i
$933$		0			0
$934$	40.5375	+	70.2131i	0.0434021	+	0.0751746i
$935$	601.592	−	1460.31i	0.643414	−	1.56183i
$936$		0			0
$937$		−	130.956i		−	0.139761i	−0.997555	−	0.0698805i	$-0.977738\pi$
$937$		−	130.956i		−	0.139761i	0.997555	−	0.0698805i	$-0.0222618\pi$
$938$	−957.097	−	1657.74i	−1.02036	−	1.76731i
$939$		0			0
$940$	75.6187	−	58.2558i	0.0804455	−	0.0619743i
$941$	308.082	+	177.871i	0.327398	+	0.189023i	0.654685	−	0.755901i	$-0.272801\pi$
$941$	308.082	+	177.871i	0.327398	+	0.189023i	−0.327287	+	0.944925i	$0.606134\pi$
$942$		0			0
$943$	−25.3732	+	14.6492i	−0.0269068	+	0.0155347i
$944$		−	969.397i		−	1.02690i
$945$		0			0
$946$	−345.836			−0.365577
$947$	−511.335	−	885.658i	−0.539953	−	0.935225i	−0.998906	−	0.0467648i	$-0.985109\pi$
$947$	−511.335	−	885.658i	−0.539953	−	0.935225i	0.458953	−	0.888460i	$-0.348224\pi$
$948$		0			0
$949$	103.689	−	179.595i	0.109261	−	0.189246i
$950$	−219.415	+	59.6980i	−0.230963	+	0.0628400i
$951$		0			0
$952$	−657.557	+	379.641i	−0.690711	+	0.398782i
$953$	475.336			0.498778			0.249389	−	0.968403i	$-0.419770\pi$
$953$	475.336			0.498778			0.249389	+	0.968403i	$0.419770\pi$
$954$		0			0
$955$	−109.546	+	265.913i	−0.114708	+	0.278443i
$956$	119.336	−	68.8988i	0.124829	−	0.0720699i
$957$		0			0
$958$	1149.51	+	663.670i	1.19991	+	0.692766i
$959$	−118.925	−	68.6616i	−0.124010	−	0.0715971i
$960$		0			0
$961$	−79.4631	−	137.634i	−0.0826880	−	0.143220i
$962$	−208.173			−0.216397
$963$		0			0
$964$	−395.063			−0.409816
$965$	−180.204	+	24.0772i	−0.186740	+	0.0249505i
$966$		0			0
$967$	1084.58	+	626.185i	1.12160	+	0.647554i	0.941808	−	0.336151i	$-0.109125\pi$
$967$	1084.58	+	626.185i	1.12160	+	0.647554i	0.179788	+	0.983705i	$0.442459\pi$
$968$	666.565	−	1154.52i	0.688600	−	1.19269i
$969$		0			0
$970$	47.1475	−	6.29941i	0.0486057	−	0.00649424i
$971$		−	280.624i		−	0.289005i	−0.989504	−	0.144502i	$-0.953842\pi$
$971$		−	280.624i		−	0.289005i	0.989504	−	0.144502i	$-0.0461581\pi$
$972$		0			0
$973$			754.231i			0.775160i
$974$	843.669	−	487.093i	0.866190	−	0.500095i
$975$		0			0
$976$	612.100	−	1060.19i	0.627152	−	1.08626i
$977$	165.797	−	287.169i	0.169700	−	0.293929i	−0.768614	−	0.639712i	$-0.779053\pi$
$977$	165.797	−	287.169i	0.169700	−	0.293929i	0.938314	+	0.345783i	$0.112387\pi$
$978$		0			0
$979$	−918.278	−	1590.50i	−0.937975	−	1.62462i
$980$	−1.55963	−	0.642507i	−0.00159146	−	0.000655619i
$981$		0			0
$982$		−	894.436i		−	0.910831i
$983$	6.49145	+	11.2435i	0.00660372	+	0.0114380i	0.869308	−	0.494270i	$-0.164565\pi$
$983$	6.49145	+	11.2435i	0.00660372	+	0.0114380i	−0.862705	+	0.505708i	$0.831231\pi$
$984$		0			0
$985$	599.225	−	461.636i	0.608350	−	0.468666i
$986$	−721.432	−	416.519i	−0.731675	−	0.422433i
$987$		0			0
$988$	18.3326	−	10.5843i	0.0185552	−	0.0107129i
$989$		−	4.75358i		−	0.00480645i
$990$		0			0
$991$	−1366.83			−1.37924			−0.689619	−	0.724172i	$-0.742222\pi$
$991$	−1366.83			−1.37924			−0.689619	+	0.724172i	$0.742222\pi$
$992$	−325.823	−	564.342i	−0.328451	−	0.568893i
$993$		0			0
$994$	−534.934	+	926.532i	−0.538163	+	0.932125i
$995$	1064.46	−	820.050i	1.06981	−	0.824171i
$996$		0			0
$997$	−890.111	+	513.906i	−0.892789	+	0.515452i	−0.874854	−	0.484387i	$-0.839043\pi$
$997$	−890.111	+	513.906i	−0.892789	+	0.515452i	−0.0179352	+	0.999839i	$0.505709\pi$
$998$	1416.29			1.41913
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.h.a.44.8		20
3.2	odd	2		45.3.h.a.14.3	✓	20
5.2	odd	4		675.3.j.e.476.3		20
5.3	odd	4		675.3.j.e.476.8		20
5.4	even	2	inner	135.3.h.a.44.3		20
9.2	odd	6	inner	135.3.h.a.89.3		20
9.4	even	3		405.3.d.a.404.5		20
9.5	odd	6		405.3.d.a.404.16		20
9.7	even	3		45.3.h.a.29.8	yes	20
15.2	even	4		225.3.j.e.176.8		20
15.8	even	4		225.3.j.e.176.3		20
15.14	odd	2		45.3.h.a.14.8	yes	20
45.2	even	12		675.3.j.e.251.3		20
45.4	even	6		405.3.d.a.404.15		20
45.7	odd	12		225.3.j.e.101.8		20
45.14	odd	6		405.3.d.a.404.6		20
45.29	odd	6	inner	135.3.h.a.89.8		20
45.34	even	6		45.3.h.a.29.3	yes	20
45.38	even	12		675.3.j.e.251.8		20
45.43	odd	12		225.3.j.e.101.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.3	✓	20	3.2	odd	2
45.3.h.a.14.8	yes	20	15.14	odd	2
45.3.h.a.29.3	yes	20	45.34	even	6
45.3.h.a.29.8	yes	20	9.7	even	3
135.3.h.a.44.3		20	5.4	even	2	inner
135.3.h.a.44.8		20	1.1	even	1	trivial
135.3.h.a.89.3		20	9.2	odd	6	inner
135.3.h.a.89.8		20	45.29	odd	6	inner
225.3.j.e.101.3		20	45.43	odd	12
225.3.j.e.101.8		20	45.7	odd	12
225.3.j.e.176.3		20	15.8	even	4
225.3.j.e.176.8		20	15.2	even	4
405.3.d.a.404.5		20	9.4	even	3
405.3.d.a.404.6		20	45.14	odd	6
405.3.d.a.404.15		20	45.4	even	6
405.3.d.a.404.16		20	9.5	odd	6
675.3.j.e.251.3		20	45.2	even	12
675.3.j.e.251.8		20	45.38	even	12
675.3.j.e.476.3		20	5.2	odd	4
675.3.j.e.476.8		20	5.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.14670 + 1.98614i) q^{2} +(-0.629835 + 1.09091i) q^{4} +(3.96090 - 3.05143i) q^{5} +(6.04559 - 3.49042i) q^{7} +6.28466 q^{8} +(10.6025 + 4.36783i) q^{10} +(-15.8064 + 9.12584i) q^{11} +(3.66955 + 2.11862i) q^{13} +(13.8649 + 8.00492i) q^{14} +(9.72596 + 16.8458i) q^{16} -17.3066 q^{17} -3.96601 q^{19} +(0.834115 + 6.24287i) q^{20} +(-36.2504 - 20.9292i) q^{22} +(0.287675 - 0.498269i) q^{23} +(6.37749 - 24.1729i) q^{25} +9.71765i q^{26} +8.79356i q^{28} +(18.1762 - 10.4940i) q^{29} +(-16.7326 + 28.9818i) q^{31} +(-9.73615 + 16.8635i) q^{32} +(-19.8455 - 34.3734i) q^{34} +(13.2952 - 32.2729i) q^{35} +21.4222i q^{37} +(-4.54782 - 7.87705i) q^{38} +(24.8929 - 19.1772i) q^{40} +(-44.1003 - 25.4613i) q^{41} +(7.15514 - 4.13102i) q^{43} -22.9911i q^{44} +1.31951 q^{46} +(-7.57789 - 13.1253i) q^{47} +(-0.133907 + 0.231934i) q^{49} +(55.3238 - 15.0524i) q^{50} +(-4.62242 + 2.66876i) q^{52} +24.5806 q^{53} +(-34.7608 + 84.3789i) q^{55} +(37.9945 - 21.9361i) q^{56} +(41.6853 + 24.0670i) q^{58} +(-43.1589 - 24.9178i) q^{59} +(-31.4674 - 54.5031i) q^{61} -76.7492 q^{62} +33.1499 q^{64} +(20.9995 - 2.80576i) q^{65} +(-103.545 - 59.7818i) q^{67} +(10.9003 - 18.8799i) q^{68} +(79.3442 - 10.6012i) q^{70} +66.8256i q^{71} -48.9419i q^{73} +(-42.5475 + 24.5648i) q^{74} +(2.49793 - 4.32654i) q^{76} +(-63.7061 + 110.342i) q^{77} +(58.9661 + 102.132i) q^{79} +(89.9276 + 37.0466i) q^{80} -116.786i q^{82} +(3.66063 + 6.34040i) q^{83} +(-68.5499 + 52.8101i) q^{85} +(16.4096 + 9.47408i) q^{86} +(-99.3381 + 57.3529i) q^{88} +100.624i q^{89} +29.5794 q^{91} +(0.362376 + 0.627654i) q^{92} +(17.3791 - 30.1015i) q^{94} +(-15.7090 + 12.1020i) q^{95} +(3.59238 - 2.07406i) q^{97} -0.614205 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) \) 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

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