LMFDB - Embedded newform 19.2.e.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,2,Mod(4,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("19.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	19.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.151715763840$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			9.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	19.9
Dual form			19.2.e.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.233956 - 1.32683i) q^{2} +(-2.20574 + 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-0.173648 + 0.300767i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +O(q^{10})$	\(q+(-0.233956 - 1.32683i) q^{2} +(-2.20574 + 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-0.173648 + 0.300767i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +(-0.205737 + 1.16679i) q^{10} +(1.11334 + 1.92836i) q^{11} +(-0.266044 + 0.460802i) q^{12} +(1.97178 + 1.65452i) q^{13} +(0.439693 + 0.160035i) q^{14} +(2.37939 - 0.866025i) q^{15} +(-2.75490 + 2.31164i) q^{16} +(0.0812519 + 0.460802i) q^{17} -7.12836 q^{18} +(-4.29813 - 0.725293i) q^{19} -0.162504 q^{20} +(-0.173648 - 0.984808i) q^{21} +(2.29813 - 1.92836i) q^{22} +(2.53209 - 0.921605i) q^{23} +(7.96451 + 2.89884i) q^{24} +(-3.23783 - 2.71686i) q^{25} +(1.73396 - 3.00330i) q^{26} +(3.29813 + 5.71253i) q^{27} +(-0.0111444 + 0.0632028i) q^{28} +(-1.19459 + 6.77487i) q^{29} +(-1.70574 - 2.95442i) q^{30} +(3.55303 - 6.15403i) q^{31} +(-0.798133 - 0.669713i) q^{32} +(-6.02481 - 2.19285i) q^{33} +(0.592396 - 0.215615i) q^{34} +(0.233956 - 0.196312i) q^{35} +(-0.169778 - 0.962858i) q^{36} +4.94356 q^{37} +(0.0432332 + 5.87257i) q^{38} -7.41147 q^{39} +(0.449493 + 2.54920i) q^{40} +(1.89646 - 1.59132i) q^{41} +(-1.26604 + 0.460802i) q^{42} +(-3.66637 - 1.33445i) q^{43} +(0.315207 + 0.264490i) q^{44} +(-2.32635 + 4.02936i) q^{45} +(-1.81521 - 3.14403i) q^{46} +(-1.26604 + 7.18009i) q^{47} +(1.79813 - 10.1977i) q^{48} +(3.43969 + 5.95772i) q^{49} +(-2.84730 + 4.93166i) q^{50} +(-1.03209 - 0.866025i) q^{51} +(0.446967 + 0.162683i) q^{52} +(2.66637 - 0.970481i) q^{53} +(6.80793 - 5.71253i) q^{54} +(-0.340022 - 1.92836i) q^{55} +1.02229 q^{56} +(10.8229 - 6.35532i) q^{57} +9.26857 q^{58} +(-1.09492 - 6.20961i) q^{59} +(0.358441 - 0.300767i) q^{60} +(-8.57785 + 3.12208i) q^{61} +(-8.99660 - 3.27449i) q^{62} +(1.40760 + 1.18112i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-1.13176 - 1.96026i) q^{65} +(-1.50000 + 8.50692i) q^{66} +(1.33275 - 7.55839i) q^{67} +(0.0432332 + 0.0748822i) q^{68} +(-3.87939 + 6.71929i) q^{69} +(-0.315207 - 0.264490i) q^{70} +(8.74422 + 3.18264i) q^{71} +(-14.6348 + 5.32661i) q^{72} +(1.06418 - 0.892951i) q^{73} +(-1.15657 - 6.55926i) q^{74} +12.1702 q^{75} +(-0.792204 + 0.145708i) q^{76} -0.773318 q^{77} +(1.73396 + 9.83375i) q^{78} +(-9.07398 + 7.61397i) q^{79} +(2.97178 - 1.08164i) q^{80} +(-2.93242 - 1.06731i) q^{81} +(-2.55509 - 2.14398i) q^{82} +(7.41534 - 12.8438i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(0.0714517 - 0.405223i) q^{85} +(-0.912818 + 5.17685i) q^{86} +(-9.90420 - 17.1546i) q^{87} +(3.27719 - 5.67626i) q^{88} +(-7.88326 - 6.61484i) q^{89} +(5.89053 + 2.14398i) q^{90} +(-0.840022 + 0.305743i) q^{91} +(0.381445 - 0.320070i) q^{92} +(3.55303 + 20.1503i) q^{93} +9.82295 q^{94} +(3.33363 + 1.89209i) q^{95} +3.00000 q^{96} +(1.64156 + 9.30975i) q^{97} +(7.10014 - 5.95772i) q^{98} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9	$ 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + 9 q^{10} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{15} - 18 q^{16} + 3 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} + 6 q^{23} + 15 q^{24} + 15 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 24 q^{36} - 15 q^{38} - 24 q^{39} + 21 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} - 15 q^{45} - 18 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} - 15 q^{50} + 3 q^{51} + 15 q^{52} - 3 q^{53} + 30 q^{54} + 18 q^{55} - 6 q^{56} + 24 q^{57} + 36 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 12 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{65} - 9 q^{66} - 30 q^{67} - 15 q^{68} - 12 q^{69} - 9 q^{70} - 6 q^{71} - 12 q^{72} - 12 q^{73} + 15 q^{74} + 30 q^{75} + 36 q^{76} - 18 q^{77} + 15 q^{78} - 39 q^{79} + 3 q^{80} + 6 q^{81} - 54 q^{82} + 3 q^{84} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 12 q^{89} + 18 q^{90} + 15 q^{91} + 42 q^{92} + 9 q^{93} + 18 q^{94} + 39 q^{95} + 18 q^{96} + 18 q^{97} - 9 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9 + 9 * q^10 + 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^15 - 18 * q^16 + 3 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 + 6 * q^23 + 15 * q^24 + 15 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 24 * q^36 - 15 * q^38 - 24 * q^39 + 21 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 - 15 * q^45 - 18 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 - 15 * q^50 + 3 * q^51 + 15 * q^52 - 3 * q^53 + 30 * q^54 + 18 * q^55 - 6 * q^56 + 24 * q^57 + 36 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^65 - 9 * q^66 - 30 * q^67 - 15 * q^68 - 12 * q^69 - 9 * q^70 - 6 * q^71 - 12 * q^72 - 12 * q^73 + 15 * q^74 + 30 * q^75 + 36 * q^76 - 18 * q^77 + 15 * q^78 - 39 * q^79 + 3 * q^80 + 6 * q^81 - 54 * q^82 + 3 * q^84 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 12 * q^89 + 18 * q^90 + 15 * q^91 + 42 * q^92 + 9 * q^93 + 18 * q^94 + 39 * q^95 + 18 * q^96 + 18 * q^97 - 9 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

Coefficient data

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

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

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

$2$	−0.233956	−	1.32683i	−0.165432	−	0.938209i	−0.948618	−	0.316423i	$-0.897518\pi$
$2$	−0.233956	−	1.32683i	−0.165432	−	0.938209i	0.783187	−	0.621786i	$-0.213593\pi$
$3$	−2.20574	+	1.85083i	−1.27348	+	1.06858i	−0.279375	+	0.960182i	$0.590127\pi$
$3$	−2.20574	+	1.85083i	−1.27348	+	1.06858i	−0.994108	+	0.108397i	$0.965428\pi$
$4$	0.173648	−	0.0632028i	0.0868241	−	0.0316014i
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	0.150565	−	0.988600i	$-0.451891\pi$
$5$	−0.826352	−	0.300767i	−0.369556	−	0.134507i	−0.520121	+	0.854093i	$0.674113\pi$
$6$	2.97178	+	2.49362i	1.21322	+	1.01802i
$7$	−0.173648	+	0.300767i	−0.0656328	+	0.113679i	−0.896975	−	0.442082i	$-0.854240\pi$
$7$	−0.173648	+	0.300767i	−0.0656328	+	0.113679i	0.831342	+	0.555762i	$0.187573\pi$
$8$	−1.47178	−	2.54920i	−0.520353	−	0.901278i
$9$	0.918748	−	5.21048i	0.306249	−	1.73683i
$10$	−0.205737	+	1.16679i	−0.0650598	+	0.368972i
$11$	1.11334	+	1.92836i	0.335685	+	0.581423i	0.983616	−	0.180276i	$-0.0576989\pi$
$11$	1.11334	+	1.92836i	0.335685	+	0.581423i	−0.647931	+	0.761699i	$0.724366\pi$
$12$	−0.266044	+	0.460802i	−0.0768004	+	0.133022i
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	0.873881	−	0.486140i	$-0.161596\pi$
$13$	1.97178	+	1.65452i	0.546874	+	0.458882i	−0.327007	+	0.945022i	$0.606040\pi$
$14$	0.439693	+	0.160035i	0.117513	+	0.0427712i
$15$	2.37939	−	0.866025i	0.614355	−	0.223607i
$16$	−2.75490	+	2.31164i	−0.688725	+	0.577909i
$17$	0.0812519	+	0.460802i	0.0197065	+	0.111761i	0.993074	−	0.117488i	$-0.0374841\pi$
$17$	0.0812519	+	0.460802i	0.0197065	+	0.111761i	−0.973368	+	0.229249i	$0.926373\pi$
$18$	−7.12836			−1.68017
$19$	−4.29813	−	0.725293i	−0.986059	−	0.166394i
$19$	−4.29813	−	0.725293i	−0.986059	−	0.166394i
$20$	−0.162504			−0.0363370
$21$	−0.173648	−	0.984808i	−0.0378931	−	0.214903i
$22$	2.29813	−	1.92836i	0.489964	−	0.411128i
$23$	2.53209	−	0.921605i	0.527977	−	0.192168i	−0.0642578	−	0.997933i	$-0.520468\pi$
$23$	2.53209	−	0.921605i	0.527977	−	0.192168i	0.592235	+	0.805765i	$0.298246\pi$
$24$	7.96451	+	2.89884i	1.62575	+	0.591724i
$25$	−3.23783	−	2.71686i	−0.647565	−	0.543372i
$26$	1.73396	−	3.00330i	0.340057	−	0.588995i
$27$	3.29813	+	5.71253i	0.634726	+	1.09938i
$28$	−0.0111444	+	0.0632028i	−0.00210608	+	0.0119442i
$29$	−1.19459	+	6.77487i	−0.221830	+	1.25806i	0.646822	+	0.762641i	$0.276097\pi$
$29$	−1.19459	+	6.77487i	−0.221830	+	1.25806i	−0.868653	+	0.495421i	$0.835014\pi$
$30$	−1.70574	−	2.95442i	−0.311424	−	0.539401i
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	−0.347696	−	0.937607i	$-0.613036\pi$
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	0.985840	−	0.167690i	$-0.0536307\pi$
$32$	−0.798133	−	0.669713i	−0.141091	−	0.118390i
$33$	−6.02481	−	2.19285i	−1.04879	−	0.381727i
$34$	0.592396	−	0.215615i	0.101595	−	0.0369776i
$35$	0.233956	−	0.196312i	0.0395457	−	0.0331828i
$36$	−0.169778	−	0.962858i	−0.0282963	−	0.160476i
$37$	4.94356			0.812717			0.406358	−	0.913714i	$-0.366798\pi$
$37$	4.94356			0.812717			0.406358	+	0.913714i	$0.366798\pi$
$38$	0.0432332	+	5.87257i	0.00701336	+	0.952657i
$39$	−7.41147			−1.18679
$40$	0.449493	+	2.54920i	0.0710711	+	0.403064i
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	−0.482574	−	0.875855i	$-0.660298\pi$
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	0.778751	+	0.627333i	$0.215854\pi$
$42$	−1.26604	+	0.460802i	−0.195355	+	0.0711034i
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	0.0469757	−	0.998896i	$-0.485042\pi$
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	−0.606093	+	0.795394i	$0.707264\pi$
$44$	0.315207	+	0.264490i	0.0475193	+	0.0398734i
$45$	−2.32635	+	4.02936i	−0.346792	+	0.600661i
$46$	−1.81521	−	3.14403i	−0.267638	−	0.463562i
$47$	−1.26604	+	7.18009i	−0.184672	+	1.04732i	0.741705	+	0.670726i	$0.234017\pi$
$47$	−1.26604	+	7.18009i	−0.184672	+	1.04732i	−0.926377	+	0.376598i	$0.877094\pi$
$48$	1.79813	−	10.1977i	0.259538	−	1.47191i
$49$	3.43969	+	5.95772i	0.491385	+	0.851103i
$50$	−2.84730	+	4.93166i	−0.402669	+	0.697442i
$51$	−1.03209	−	0.866025i	−0.144521	−	0.121268i
$52$	0.446967	+	0.162683i	0.0619831	+	0.0225600i
$53$	2.66637	−	0.970481i	0.366255	−	0.133306i	−0.152335	−	0.988329i	$-0.548679\pi$
$53$	2.66637	−	0.970481i	0.366255	−	0.133306i	0.518590	+	0.855023i	$0.326457\pi$
$54$	6.80793	−	5.71253i	0.926442	−	0.777377i
$55$	−0.340022	−	1.92836i	−0.0458486	−	0.260020i
$56$	1.02229			0.136609
$57$	10.8229	−	6.35532i	1.43353	−	0.841783i
$58$	9.26857			1.21702
$59$	−1.09492	−	6.20961i	−0.142547	−	0.808423i	−0.969304	−	0.245864i	$-0.920928\pi$
$59$	−1.09492	−	6.20961i	−0.142547	−	0.808423i	0.826757	−	0.562559i	$-0.190183\pi$
$60$	0.358441	−	0.300767i	0.0462745	−	0.0388289i
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.826682	−	0.562669i	$-0.809775\pi$
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.271599	+	0.962411i	$0.587552\pi$
$62$	−8.99660	−	3.27449i	−1.14257	−	0.415861i
$63$	1.40760	+	1.18112i	0.177341	+	0.148807i
$64$	−4.29813	+	7.44459i	−0.537267	+	0.930573i
$65$	−1.13176	−	1.96026i	−0.140377	−	0.243141i
$66$	−1.50000	+	8.50692i	−0.184637	+	1.04713i
$67$	1.33275	−	7.55839i	0.162821	−	0.923405i	−0.788461	−	0.615084i	$-0.789122\pi$
$67$	1.33275	−	7.55839i	0.162821	−	0.923405i	0.951283	−	0.308320i	$-0.0997669\pi$
$68$	0.0432332	+	0.0748822i	0.00524280	+	0.00908080i
$69$	−3.87939	+	6.71929i	−0.467023	+	0.808908i
$70$	−0.315207	−	0.264490i	−0.0376745	−	0.0316127i
$71$	8.74422	+	3.18264i	1.03775	+	0.377709i	0.804026	−	0.594594i	$-0.202687\pi$
$71$	8.74422	+	3.18264i	1.03775	+	0.377709i	0.233722	+	0.972303i	$0.424909\pi$
$72$	−14.6348	+	5.32661i	−1.72472	+	0.627748i
$73$	1.06418	−	0.892951i	0.124553	−	0.104512i	−0.578384	−	0.815765i	$-0.696316\pi$
$73$	1.06418	−	0.892951i	0.124553	−	0.104512i	0.702936	+	0.711253i	$0.251872\pi$
$74$	−1.15657	−	6.55926i	−0.134449	−	0.762498i
$75$	12.1702			1.40530
$76$	−0.792204	+	0.145708i	−0.0908720	+	0.0167139i
$77$	−0.773318			−0.0881278
$78$	1.73396	+	9.83375i	0.196332	+	1.11345i
$79$	−9.07398	+	7.61397i	−1.02090	+	0.856639i	−0.989741	−	0.142876i	$-0.954365\pi$
$79$	−9.07398	+	7.61397i	−1.02090	+	0.856639i	−0.0311616	+	0.999514i	$0.509921\pi$
$80$	2.97178	−	1.08164i	0.332255	−	0.120931i
$81$	−2.93242	−	1.06731i	−0.325824	−	0.118590i
$82$	−2.55509	−	2.14398i	−0.282163	−	0.236763i
$83$	7.41534	−	12.8438i	0.813940	−	1.40979i	−0.0961469	−	0.995367i	$-0.530652\pi$
$83$	7.41534	−	12.8438i	0.813940	−	1.40979i	0.910087	−	0.414418i	$-0.136015\pi$
$84$	−0.0923963	−	0.160035i	−0.0100813	−	0.0174613i
$85$	0.0714517	−	0.405223i	0.00775003	−	0.0439526i
$86$	−0.912818	+	5.17685i	−0.0984317	+	0.558234i
$87$	−9.90420	−	17.1546i	−1.06184	−	1.83916i
$88$	3.27719	−	5.67626i	0.349349	−	0.605091i
$89$	−7.88326	−	6.61484i	−0.835623	−	0.701171i	0.120951	−	0.992658i	$-0.461406\pi$
$89$	−7.88326	−	6.61484i	−0.835623	−	0.701171i	−0.956575	+	0.291487i	$0.905850\pi$
$90$	5.89053	+	2.14398i	0.620916	+	0.225995i
$91$	−0.840022	+	0.305743i	−0.0880583	+	0.0320506i
$92$	0.381445	−	0.320070i	0.0397684	−	0.0333696i
$93$	3.55303	+	20.1503i	0.368432	+	2.08948i
$94$	9.82295			1.01316
$95$	3.33363	+	1.89209i	0.342023	+	0.194124i
$96$	3.00000			0.306186
$97$	1.64156	+	9.30975i	0.166675	+	0.945261i	0.947320	+	0.320287i	$0.103779\pi$
$97$	1.64156	+	9.30975i	0.166675	+	0.945261i	−0.780645	+	0.624974i	$0.785109\pi$
$98$	7.10014	−	5.95772i	0.717222	−	0.601821i
$99$	11.0706	−	4.02936i	1.11263	−	0.404966i
$100$	−0.733956	−	0.267138i	−0.0733956	−	0.0267138i
$101$	−7.08512	−	5.94512i	−0.704996	−	0.591562i	0.218194	−	0.975905i	$-0.429983\pi$
$101$	−7.08512	−	5.94512i	−0.704996	−	0.591562i	−0.923190	+	0.384343i	$0.874428\pi$
$102$	−0.907604	+	1.57202i	−0.0898662	+	0.155653i
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	0.969233	−	0.246145i	$-0.0791640\pi$
$103$	2.75490	+	4.77163i	0.271448	+	0.470162i	−0.697785	+	0.716308i	$0.745831\pi$
$104$	1.31567	−	7.46156i	0.129012	−	0.731666i
$105$	−0.152704	+	0.866025i	−0.0149023	+	0.0845154i
$106$	−1.91147	−	3.31077i	−0.185659	−	0.321570i
$107$	−5.11721	+	8.86327i	−0.494699	+	0.856845i	−0.999981	−	0.00610974i	$-0.998055\pi$
$107$	−5.11721	+	8.86327i	−0.494699	+	0.856845i	0.505282	+	0.862954i	$0.331389\pi$
$108$	0.933763	+	0.783520i	0.0898514	+	0.0753943i
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	0.422753	−	0.906245i	$-0.361064\pi$
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	−0.258676	+	0.965964i	$0.583286\pi$
$110$	−2.47906	+	0.902302i	−0.236369	+	0.0860312i
$111$	−10.9042	+	9.14971i	−1.03498	+	0.868452i
$112$	−0.216881	−	1.23000i	−0.0204934	−	0.116224i
$113$	−17.6878			−1.66393			−0.831963	−	0.554830i	$-0.812783\pi$
$113$	−17.6878			−1.66393			−0.831963	+	0.554830i	$0.812783\pi$
$114$	−10.9645	−	12.8733i	−1.02692	−	1.20570i
$115$	−2.36959			−0.220965
$116$	0.220752	+	1.25195i	0.0204963	+	0.116240i
$117$	10.4324	−	8.75384i	0.964477	−	0.809293i
$118$	−7.98293	+	2.90555i	−0.734888	+	0.267477i
$119$	−0.152704	−	0.0555796i	−0.0139983	−	0.00509497i
$120$	−5.70961	−	4.79093i	−0.521213	−	0.437350i
$121$	3.02094	−	5.23243i	0.274631	−	0.475675i
$122$	6.14930	+	10.6509i	0.556731	+	0.964287i
$123$	−1.23783	+	7.02006i	−0.111611	+	0.632977i
$124$	0.228026	−	1.29320i	0.0204773	−	0.116133i
$125$	4.05690	+	7.02676i	0.362861	+	0.628493i
$126$	1.23783	−	2.14398i	0.110274	−	0.191001i
$127$	8.88919	+	7.45891i	0.788788	+	0.661871i	0.945445	−	0.325782i	$-0.105627\pi$
$127$	8.88919	+	7.45891i	0.788788	+	0.661871i	−0.156657	+	0.987653i	$0.550072\pi$
$128$	8.92514	+	3.24849i	0.788879	+	0.287128i
$129$	10.5569	−	3.84240i	0.929484	−	0.338304i
$130$	−2.33615	+	1.96026i	−0.204894	+	0.171927i
$131$	0.320422	+	1.81720i	0.0279954	+	0.158770i	0.995601	−	0.0936982i	$-0.0298689\pi$
$131$	0.320422	+	1.81720i	0.0279954	+	0.158770i	−0.967605	+	0.252468i	$0.918758\pi$
$132$	−1.18479			−0.103123
$133$	0.964508	−	1.16679i	0.0836334	−	0.101174i
$134$	−10.3405			−0.893282
$135$	−1.00727	−	5.71253i	−0.0866923	−	0.491657i
$136$	1.05509	−	0.885328i	0.0904735	−	0.0759162i
$137$	−0.240352	+	0.0874810i	−0.0205347	+	0.00747401i	−0.352267	−	0.935900i	$-0.614589\pi$
$137$	−0.240352	+	0.0874810i	−0.0205347	+	0.00747401i	0.331732	+	0.943374i	$0.392367\pi$
$138$	9.82295	+	3.57526i	0.836185	+	0.304346i
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	0.770704	−	0.637193i	$-0.219905\pi$
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	−0.493682	+	0.869643i	$0.664349\pi$
$140$	0.0282185	−	0.0488759i	0.00238490	−	0.00413076i
$141$	−10.4966	−	18.1806i	−0.883973	−	1.53109i
$142$	2.17705	−	12.3467i	0.182694	−	1.03611i
$143$	−0.995252	+	5.64436i	−0.0832272	+	0.472005i
$144$	9.51367	+	16.4782i	0.792806	+	1.37318i
$145$	3.02481	−	5.23913i	0.251197	−	0.435086i
$146$	−1.43376	−	1.20307i	−0.118659	−	0.0995668i
$147$	−18.6138	−	6.77487i	−1.53524	−	0.558782i
$148$	0.858441	−	0.312447i	0.0705634	−	0.0256830i
$149$	12.6853	−	10.6442i	1.03922	−	0.872007i	0.0472981	−	0.998881i	$-0.484939\pi$
$149$	12.6853	−	10.6442i	1.03922	−	0.872007i	0.991919	+	0.126874i	$0.0404945\pi$
$150$	−2.84730	−	16.1478i	−0.232481	−	1.31846i
$151$	−4.36184			−0.354962			−0.177481	−	0.984124i	$-0.556795\pi$
$151$	−4.36184			−0.354962			−0.177481	+	0.984124i	$0.556795\pi$
$152$	4.47700	+	12.0243i	0.363132	+	0.975298i
$153$	2.47565			0.200145
$154$	0.180922	+	1.02606i	0.0145791	+	0.0826823i
$155$	−4.78699	+	4.01676i	−0.384500	+	0.322634i
$156$	−1.28699	+	0.468426i	−0.103042	+	0.0375041i
$157$	9.03849	+	3.28974i	0.721350	+	0.262550i	0.676499	−	0.736444i	$-0.263496\pi$
$157$	9.03849	+	3.28974i	0.721350	+	0.262550i	0.0448510	+	0.998994i	$0.485719\pi$
$158$	12.2253	+	10.2583i	0.972596	+	0.816105i
$159$	−4.08512	+	7.07564i	−0.323971	+	0.561135i
$160$	0.458111	+	0.793471i	0.0362168	+	0.0627294i
$161$	−0.162504	+	0.921605i	−0.0128071	+	0.0726326i
$162$	−0.730085	+	4.14052i	−0.0573609	+	0.325310i
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	0.654748	−	0.755847i	$-0.272775\pi$
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	−0.981957	+	0.189105i	$0.939441\pi$
$164$	0.228741	−	0.396191i	0.0178617	−	0.0309373i
$165$	4.31908	+	3.62414i	0.336240	+	0.282139i
$166$	−18.7763	−	6.83402i	−1.45732	−	0.530423i
$167$	−3.79174	+	1.38008i	−0.293413	+	0.106794i	−0.484533	−	0.874773i	$-0.661010\pi$
$167$	−3.79174	+	1.38008i	−0.293413	+	0.106794i	0.191120	+	0.981567i	$0.438788\pi$
$168$	−2.25490	+	1.89209i	−0.173969	+	0.145978i
$169$	−1.10694	−	6.27779i	−0.0851496	−	0.482907i
$170$	−0.554378			−0.0425188
$171$	−7.72803	+	21.7290i	−0.590977	+	1.66166i
$172$	−0.721000			−0.0549758
$173$	−3.49794	−	19.8378i	−0.265943	−	1.50824i	−0.766335	−	0.642441i	$-0.777922\pi$
$173$	−3.49794	−	19.8378i	−0.265943	−	1.50824i	0.500391	−	0.865799i	$-0.333189\pi$
$174$	−20.4440	+	17.1546i	−1.54986	+	1.30049i
$175$	1.37939	−	0.502055i	0.104272	−	0.0379518i
$176$	−7.52481	−	2.73881i	−0.567204	−	0.206445i
$177$	13.9081	+	11.6703i	1.04539	+	0.877190i
$178$	−6.93242	+	12.0073i	−0.519607	+	0.899985i
$179$	5.75624	+	9.97011i	0.430242	+	0.745201i	0.996894	−	0.0787564i	$-0.0250949\pi$
$179$	5.75624	+	9.97011i	0.430242	+	0.745201i	−0.566652	+	0.823957i	$0.691762\pi$
$180$	−0.149300	+	0.846723i	−0.0111282	+	0.0631110i
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	−0.878829	−	0.477136i	$-0.841675\pi$
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	0.989020	−	0.147784i	$-0.0472141\pi$
$182$	0.602196	+	1.04303i	0.0446378	+	0.0773149i
$183$	13.1420	−	22.7627i	0.971487	−	1.68266i
$184$	−6.07604	−	5.09840i	−0.447931	−	0.375859i
$185$	−4.08512	−	1.48686i	−0.300344	−	0.109316i
$186$	25.9047	−	9.42853i	1.89942	−	0.691333i
$187$	−0.798133	+	0.669713i	−0.0583653	+	0.0489743i
$188$	0.233956	+	1.32683i	0.0170630	+	0.0967689i
$189$	−2.29086			−0.166635
$190$	1.73055	−	4.86581i	0.125547	−	0.353003i
$191$	18.3354			1.32671			0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354			1.32671			0.663353	+	0.748307i	$0.269133\pi$
$192$	−4.29813	−	24.3759i	−0.310191	−	1.75918i
$193$	0.228026	−	0.191336i	0.0164137	−	0.0137727i	−0.634544	−	0.772887i	$-0.718812\pi$
$193$	0.228026	−	0.191336i	0.0164137	−	0.0137727i	0.650958	+	0.759114i	$0.274368\pi$
$194$	11.9684	−	4.35613i	0.859279	−	0.312752i
$195$	6.12449	+	2.22913i	0.438583	+	0.159631i
$196$	0.973841	+	0.817150i	0.0695601	+	0.0583678i
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	−0.999337	−	0.0364128i	$-0.988407\pi$
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	0.531203	+	0.847245i	$0.321740\pi$
$198$	−7.93629	−	13.7461i	−0.564008	−	0.976890i
$199$	−0.0445774	+	0.252811i	−0.00316001	+	0.0179213i	−0.986347	−	0.164680i	$-0.947341\pi$
$199$	−0.0445774	+	0.252811i	−0.00316001	+	0.0179213i	0.983187	+	0.182602i	$0.0584519\pi$
$200$	−2.16044	+	12.2525i	−0.152766	+	0.866382i
$201$	11.0496	+	19.1385i	0.779381	+	1.34993i
$202$	−6.23055	+	10.7916i	−0.438380	+	0.759297i
$203$	−1.83022	−	1.53574i	−0.128456	−	0.107788i
$204$	−0.233956	−	0.0851529i	−0.0163802	−	0.00596189i
$205$	−2.04576	+	0.744596i	−0.142882	+	0.0520048i
$206$	5.68660	−	4.77163i	0.396204	−	0.332455i
$207$	−2.47565	−	14.0401i	−0.172070	−	0.975856i
$208$	−9.25671			−0.641837
$209$	−3.38666	−	9.09586i	−0.234260	−	0.629174i
$210$	1.18479			0.0817585
$211$	0.425145	+	2.41112i	0.0292682	+	0.165988i	0.995938	−	0.0900364i	$-0.0286983\pi$
$211$	0.425145	+	2.41112i	0.0292682	+	0.165988i	−0.966670	+	0.256024i	$0.917587\pi$
$212$	0.401674	−	0.337044i	0.0275871	−	0.0231483i
$213$	−25.1780	+	9.16404i	−1.72517	+	0.627909i
$214$	12.9572	+	4.71605i	0.885738	+	0.322382i
$215$	2.62836	+	2.20545i	0.179252	+	0.150411i
$216$	9.70826	−	16.8152i	0.660564	−	1.14413i
$217$	1.23396	+	2.13727i	0.0837664	+	0.145088i
$218$	0.426489	−	2.41874i	0.0288855	−	0.163818i
$219$	−0.694593	+	3.93923i	−0.0469362	+	0.266189i
$220$	−0.180922	−	0.313366i	−0.0121978	−	0.0211272i
$221$	−0.602196	+	1.04303i	−0.0405081	+	0.0701621i
$222$	14.6912	+	12.3274i	0.986008	+	0.827359i
$223$	7.99660	+	2.91052i	0.535492	+	0.194903i	0.595589	−	0.803289i	$-0.296919\pi$
$223$	7.99660	+	2.91052i	0.535492	+	0.194903i	−0.0600971	+	0.998193i	$0.519141\pi$
$224$	0.340022	−	0.123758i	0.0227187	−	0.00826893i
$225$	−17.1309	+	14.3745i	−1.14206	+	0.958301i
$226$	4.13816	+	23.4686i	0.275266	+	1.56111i
$227$	−14.1506			−0.939211			−0.469606	−	0.882876i	$-0.655604\pi$
$227$	−14.1506			−0.939211			−0.469606	+	0.882876i	$0.655604\pi$
$228$	1.47771	−	1.78763i	0.0978638	−	0.118389i
$229$	−20.5330			−1.35686			−0.678430	−	0.734665i	$-0.737339\pi$
$229$	−20.5330			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$230$	0.554378	+	3.14403i	0.0365546	+	0.207311i
$231$	1.70574	−	1.43128i	0.112229	−	0.0941715i
$232$	19.0287	−	6.92588i	1.24929	−	0.454706i
$233$	−16.5865	−	6.03698i	−1.08662	−	0.395496i	−0.264249	−	0.964454i	$-0.585124\pi$
$233$	−16.5865	−	6.03698i	−1.08662	−	0.395496i	−0.822366	+	0.568959i	$0.807346\pi$
$234$	−14.0556	−	11.7940i	−0.918841	−	0.770999i
$235$	3.20574	−	5.55250i	0.209119	−	0.362205i
$236$	−0.582596	−	1.00909i	−0.0379238	−	0.0656859i
$237$	5.92262	−	33.5888i	0.384715	−	2.18183i
$238$	−0.0380187	+	0.215615i	−0.00246438	+	0.0139762i
$239$	−1.17617	−	2.03719i	−0.0760804	−	0.131775i	0.825475	−	0.564438i	$-0.190907\pi$
$239$	−1.17617	−	2.03719i	−0.0760804	−	0.131775i	−0.901556	+	0.432663i	$0.857574\pi$
$240$	−4.55303	+	7.88609i	−0.293897	+	0.509045i
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	0.916298	−	0.400498i	$-0.131163\pi$
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	−0.235300	+	0.971923i	$0.575607\pi$
$242$	−7.64930	−	2.78412i	−0.491716	−	0.178970i
$243$	−10.1518	+	3.69496i	−0.651240	+	0.237032i
$244$	−1.29220	+	1.08429i	−0.0827249	+	0.0694144i
$245$	−1.05051	−	5.95772i	−0.0671144	−	0.380625i
$246$	9.60401			0.612329
$247$	−7.27497	−	8.54147i	−0.462895	−	0.543481i
$248$	−20.9172			−1.32824
$249$	7.41534	+	42.0545i	0.469928	+	2.66510i
$250$	8.37417	−	7.02676i	0.529629	−	0.444412i
$251$	3.91400	−	1.42458i	0.247050	−	0.0899187i	−0.215528	−	0.976498i	$-0.569147\pi$
$251$	3.91400	−	1.42458i	0.247050	−	0.0899187i	0.462577	+	0.886579i	$0.346925\pi$
$252$	0.319078	+	0.116135i	0.0201000	+	0.00731581i
$253$	4.59627	+	3.85673i	0.288965	+	0.242470i
$254$	7.81702	−	13.5395i	0.490483	−	0.849542i
$255$	0.592396	+	1.02606i	0.0370973	+	0.0642544i
$256$	−0.763356	+	4.32921i	−0.0477098	+	0.270575i
$257$	0.115867	−	0.657115i	0.00722759	−	0.0409897i	−0.980981	−	0.194105i	$-0.937820\pi$
$257$	0.115867	−	0.657115i	0.00722759	−	0.0409897i	0.988208	+	0.153116i	$0.0489307\pi$
$258$	−7.56805	−	13.1082i	−0.471166	−	0.816084i
$259$	−0.858441	+	1.48686i	−0.0533409	+	0.0923892i
$260$	−0.320422	−	0.268866i	−0.0198717	−	0.0166744i
$261$	34.2028	+	12.4488i	2.11710	+	0.770561i
$262$	2.33615	−	0.850290i	0.144328	−	0.0525311i
$263$	8.73261	−	7.32753i	0.538476	−	0.451835i	−0.332540	−	0.943089i	$-0.607906\pi$
$263$	8.73261	−	7.32753i	0.538476	−	0.451835i	0.871016	+	0.491254i	$0.163461\pi$
$264$	3.27719	+	18.5859i	0.201697	+	1.14388i
$265$	−2.49525			−0.153282
$266$	−1.77379	−	1.00676i	−0.108758	−	0.0617283i
$267$	29.6313			1.81341
$268$	−0.246282	−	1.39673i	−0.0150441	−	0.0853191i
$269$	14.8537	−	12.4637i	0.905646	−	0.759927i	−0.0656400	−	0.997843i	$-0.520909\pi$
$269$	14.8537	−	12.4637i	0.905646	−	0.759927i	0.971286	+	0.237916i	$0.0764644\pi$
$270$	−7.34389	+	2.67296i	−0.446935	+	0.162671i
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.694725	−	0.719276i	$-0.255526\pi$
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.0698486	+	0.997558i	$0.477748\pi$
$272$	−1.28905	−	1.08164i	−0.0781600	−	0.0655841i
$273$	1.28699	−	2.22913i	0.0778921	−	0.134913i
$274$	0.172304	+	0.298439i	0.0104093	+	0.0180294i
$275$	1.63429	−	9.26849i	0.0985511	−	0.558911i
$276$	−0.248970	+	1.41198i	−0.0149863	+	0.0849913i
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	−0.999250	−	0.0387161i	$-0.987673\pi$
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	0.466096	−	0.884734i	$-0.345660\pi$
$278$	2.87211	−	4.97464i	0.172258	−	0.298359i
$279$	−28.8011	−	24.1670i	−1.72428	−	1.44684i
$280$	−0.844770	−	0.307471i	−0.0504847	−	0.0183749i
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.799050	−	0.601265i	$-0.794664\pi$
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.225622	+	0.974215i	$0.572442\pi$
$282$	−21.6668	+	18.1806i	−1.29024	+	1.08264i
$283$	1.33497	+	7.57099i	0.0793557	+	0.450049i	0.998432	+	0.0559700i	$0.0178251\pi$
$283$	1.33497	+	7.57099i	0.0793557	+	0.450049i	−0.919077	+	0.394079i	$0.871064\pi$
$284$	1.71957			0.102038
$285$	−10.8550	+	1.99654i	−0.642997	+	0.118265i
$286$	7.72193			0.456608
$287$	0.149300	+	0.846723i	0.00881290	+	0.0499805i
$288$	−4.22281	+	3.54336i	−0.248832	+	0.208794i
$289$	15.7690	−	5.73946i	0.927590	−	0.337615i
$290$	−7.65910	−	2.78768i	−0.449758	−	0.163698i
$291$	−20.8516	−	17.4966i	−1.22234	−	1.02567i
$292$	0.128356	−	0.222318i	0.00751144	−	0.0130102i
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	0.977660	−	0.210195i	$-0.0674098\pi$
$293$	5.25150	+	9.09586i	0.306796	+	0.531386i	−0.670864	+	0.741581i	$0.734076\pi$
$294$	−4.63429	+	26.2823i	−0.270277	+	1.53282i
$295$	−0.962859	+	5.46064i	−0.0560598	+	0.317931i
$296$	−7.27584	−	12.6021i	−0.422900	−	0.732484i
$297$	−7.34389	+	12.7200i	−0.426136	+	0.738089i
$298$	−17.0908	−	14.3409i	−0.990044	−	0.830745i
$299$	6.51754	+	2.37219i	0.376919	+	0.137187i
$300$	2.11334	−	0.769193i	0.122014	−	0.0444094i
$301$	1.03802	−	0.871001i	0.0598304	−	0.0502037i
$302$	1.02048	+	5.78742i	0.0587219	+	0.333028i
$303$	26.6313			1.52993
$304$	13.5175	−	7.93761i	0.775284	−	0.455253i
$305$	8.02734			0.459644
$306$	−0.579193	−	3.28476i	−0.0331102	−	0.187777i
$307$	−8.95929	+	7.51774i	−0.511334	+	0.429060i	−0.861598	−	0.507591i	$-0.830536\pi$
$307$	−8.95929	+	7.51774i	−0.511334	+	0.429060i	0.350264	+	0.936651i	$0.386092\pi$
$308$	−0.134285	+	0.0488759i	−0.00765162	+	0.00278496i
$309$	−14.9081	−	5.42609i	−0.848091	−	0.308680i
$310$	6.44949	+	5.41177i	0.366307	+	0.307368i
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	−0.998551	−	0.0538151i	$-0.982862\pi$
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	0.545881	+	0.837863i	$0.316195\pi$
$312$	10.9081	+	18.8933i	0.617548	+	1.06962i
$313$	−4.62402	+	26.2241i	−0.261365	+	1.48227i	0.517825	+	0.855487i	$0.326742\pi$
$313$	−4.62402	+	26.2241i	−0.261365	+	1.48227i	−0.779190	+	0.626788i	$0.784369\pi$
$314$	2.25031	−	12.7622i	0.126993	−	0.720211i
$315$	−0.807934	−	1.39938i	−0.0455219	−	0.0788462i
$316$	−1.09446	+	1.89565i	−0.0615679	+	0.106639i
$317$	22.6229	+	18.9829i	1.27063	+	1.06618i	0.994465	+	0.105073i	$0.0335077\pi$
$317$	22.6229	+	18.9829i	1.27063	+	1.06618i	0.276164	+	0.961111i	$0.410937\pi$
$318$	10.3439	+	3.76487i	0.580057	+	0.211123i
$319$	−14.3944	+	5.23913i	−0.805932	+	0.293335i
$320$	5.79086	−	4.85911i	0.323719	−	0.271632i
$321$	−5.11721	−	29.0211i	−0.285615	−	1.61980i
$322$	1.26083			0.0702633
$323$	−0.0150147	−	2.03952i	−0.000835443	−	0.113482i
$324$	−0.576666			−0.0320370
$325$	−1.88919	−	10.7141i	−0.104793	−	0.594311i
$326$	−8.62314	+	7.23567i	−0.477592	+	0.400747i
$327$	−4.93242	+	1.79525i	−0.272763	+	0.0992777i
$328$	−6.84776	−	2.49238i	−0.378104	−	0.137619i
$329$	−1.93969	−	1.62760i	−0.106939	−	0.0897322i
$330$	3.79813	−	6.57856i	0.209080	−	0.362138i
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	−0.942687	−	0.333677i	$-0.891710\pi$
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	0.182371	−	0.983230i	$-0.441623\pi$
$332$	0.475900	−	2.69896i	0.0261184	−	0.148125i
$333$	4.54189	−	25.7583i	0.248894	−	1.41155i
$334$	2.71823	+	4.70810i	0.148735	+	0.257616i
$335$	−3.37464	+	5.84504i	−0.184376	+	0.319349i
$336$	2.75490	+	2.31164i	0.150292	+	0.126110i
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.158279	−	0.987394i	$-0.550594\pi$
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.755934	+	0.654648i	$0.772817\pi$
$338$	−8.07057	+	2.93745i	−0.438981	+	0.159776i
$339$	39.0146	−	32.7371i	2.11898	−	1.77804i
$340$	−0.0132037	−	0.0748822i	−0.000716074	−	0.00406106i
$341$	15.8229			0.856861
$342$	30.6386	+	5.17015i	1.65675	+	0.279569i
$343$	−4.82026			−0.260270
$344$	1.99432	+	11.3103i	0.107526	+	0.609813i
$345$	5.22668	−	4.38571i	0.281395	−	0.236119i
$346$	−25.5030	+	9.28233i	−1.37105	+	0.499021i
$347$	5.45084	+	1.98394i	0.292616	+	0.106504i	0.484157	−	0.874981i	$-0.339126\pi$
$347$	5.45084	+	1.98394i	0.292616	+	0.106504i	−0.191541	+	0.981485i	$0.561348\pi$
$348$	−2.80406	−	2.35289i	−0.150314	−	0.126128i
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	−0.928919	−	0.370282i	$-0.879261\pi$
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	0.785134	+	0.619326i	$0.212594\pi$
$350$	−0.988856	−	1.71275i	−0.0528566	−	0.0915502i
$351$	−2.94831	+	16.7207i	−0.157369	+	0.892485i
$352$	0.402856	−	2.28471i	0.0214723	−	0.121775i
$353$	12.6172	+	21.8537i	0.671546	+	1.16315i	0.977466	+	0.211095i	$0.0677029\pi$
$353$	12.6172	+	21.8537i	0.671546	+	1.16315i	−0.305919	+	0.952057i	$0.598964\pi$
$354$	12.2306	−	21.1839i	0.650047	−	1.12591i
$355$	−6.26857	−	5.25996i	−0.332701	−	0.279169i
$356$	−1.78699	−	0.650411i	−0.0947102	−	0.0344717i
$357$	0.439693	−	0.160035i	0.0232710	−	0.00846995i
$358$	11.8819	−	9.97011i	0.627979	−	0.526937i
$359$	1.16116	+	6.58526i	0.0612837	+	0.347557i	0.999996	+	0.00285518i	$0.000908833\pi$
$359$	1.16116	+	6.58526i	0.0612837	+	0.347557i	−0.938712	+	0.344702i	$0.887980\pi$
$360$	13.6955			0.721818
$361$	17.9479	+	6.23481i	0.944626	+	0.328148i
$362$	−11.5021			−0.604535
$363$	3.02094	+	17.1326i	0.158558	+	0.899230i
$364$	−0.126545	+	0.106183i	−0.00663274	+	0.00556553i
$365$	−1.14796	+	0.417822i	−0.0600868	+	0.0218698i
$366$	−33.2768	−	12.1118i	−1.73941	−	0.633092i
$367$	6.21941	+	5.21870i	0.324650	+	0.272414i	0.790516	−	0.612441i	$-0.209812\pi$
$367$	6.21941	+	5.21870i	0.324650	+	0.272414i	−0.465865	+	0.884856i	$0.654257\pi$
$368$	−4.84524	+	8.39220i	−0.252575	+	0.437473i
$369$	−6.54916	−	11.3435i	−0.340936	−	0.590518i
$370$	−1.01707	+	5.76811i	−0.0528752	+	0.299870i
$371$	−0.171122	+	0.970481i	−0.00888421	+	0.0503849i
$372$	1.89053	+	3.27449i	0.0980194	+	0.169775i
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.0804968	+	0.996755i	$0.525651\pi$
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.822967	+	0.568090i	$0.807683\pi$
$374$	1.07532	+	0.902302i	0.0556036	+	0.0466569i
$375$	−21.9538	−	7.99054i	−1.13369	−	0.412630i
$376$	20.1668	−	7.34013i	1.04003	−	0.378538i
$377$	−13.5646	+	11.3821i	−0.698615	+	0.586207i
$378$	0.535959	+	3.03958i	0.0275668	+	0.156339i
$379$	1.70140			0.0873950			0.0436975	−	0.999045i	$-0.486086\pi$
$379$	1.70140			0.0873950			0.0436975	+	0.999045i	$0.486086\pi$
$380$	0.698463	+	0.117863i	0.0358304	+	0.00604624i
$381$	−33.4124			−1.71177
$382$	−4.28968	−	24.3280i	−0.219479	−	1.24473i
$383$	2.24969	−	1.88771i	0.114954	−	0.0964575i	−0.583499	−	0.812114i	$-0.698317\pi$
$383$	2.24969	−	1.88771i	0.114954	−	0.0964575i	0.698453	+	0.715656i	$0.253872\pi$
$384$	−25.6989	+	9.35365i	−1.31144	+	0.477326i
$385$	0.639033	+	0.232589i	0.0325681	+	0.0118538i
$386$	−0.307218	−	0.257787i	−0.0156370	−	0.0131210i
$387$	−10.3216	+	17.8775i	−0.524677	+	0.908767i
$388$	0.873455	+	1.51287i	0.0443430	+	0.0768043i
$389$	−4.26604	+	24.1939i	−0.216297	+	1.22668i	0.662344	+	0.749199i	$0.269562\pi$
$389$	−4.26604	+	24.1939i	−0.216297	+	1.22668i	−0.878642	+	0.477482i	$0.841550\pi$
$390$	1.52481	−	8.64766i	0.0772120	−	0.437891i
$391$	0.630415	+	1.09191i	0.0318815	+	0.0552203i
$392$	10.1250	−	17.5369i	0.511387	−	0.885749i
$393$	−4.07011	−	3.41523i	−0.205310	−	0.172275i
$394$	16.6373	+	6.05547i	0.838174	+	0.305070i
$395$	9.78833	−	3.56266i	0.492504	−	0.179257i
$396$	1.66772	−	1.39938i	0.0838060	−	0.0703216i
$397$	−5.52822	−	31.3521i	−0.277453	−	1.57352i	−0.731059	−	0.682314i	$-0.760974\pi$
$397$	−5.52822	−	31.3521i	−0.277453	−	1.57352i	0.453606	−	0.891202i	$-0.350137\pi$
$398$	0.345866			0.0173367
$399$	0.0320889	+	4.35878i	0.00160645	+	0.218212i
$400$	15.2003			0.760014
$401$	−0.0150147	−	0.0851529i	−0.000749801	−	0.00425233i	0.984431	−	0.175774i	$-0.0562428\pi$
$401$	−0.0150147	−	0.0851529i	−0.000749801	−	0.00425233i	−0.985180	+	0.171522i	$0.945132\pi$
$402$	22.8084	−	19.1385i	1.13758	−	0.954543i
$403$	17.1878	−	6.25584i	0.856185	−	0.311626i
$404$	−1.60607	−	0.584561i	−0.0799048	−	0.0290830i
$405$	2.10220	+	1.76395i	0.104459	+	0.0876515i
$406$	−1.60947	+	2.78768i	−0.0798767	+	0.138350i
$407$	5.50387	+	9.53298i	0.272817	+	0.472532i
$408$	−0.688663	+	3.90560i	−0.0340939	+	0.193356i
$409$	3.47400	−	19.7021i	0.171778	−	0.974204i	−0.770019	−	0.638021i	$-0.779753\pi$
$409$	3.47400	−	19.7021i	0.171778	−	0.974204i	0.941797	−	0.336182i	$-0.109136\pi$
$410$	1.46657	+	2.54017i	0.0724286	+	0.125450i
$411$	0.368241	−	0.637812i	0.0181640	−	0.0314609i
$412$	0.779963	+	0.654467i	0.0384260	+	0.0322433i
$413$	2.05778	+	0.748971i	0.101257	+	0.0368545i
$414$	−18.0496	+	6.56953i	−0.887091	+	0.322875i
$415$	−9.99067	+	8.38316i	−0.490423	+	0.411513i
$416$	−0.465690	−	2.64106i	−0.0228323	−	0.129488i
$417$	−12.2763			−0.601174
$418$	−11.2763	+	6.62154i	−0.551542	+	0.323870i
$419$	25.4097			1.24135			0.620673	−	0.784070i	$-0.286859\pi$
$419$	25.4097			1.24135			0.620673	+	0.784070i	$0.286859\pi$
$420$	0.0282185	+	0.160035i	0.00137692	+	0.00780891i
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	−0.557565	−	0.830134i	$-0.688264\pi$
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	0.720702	+	0.693245i	$0.243820\pi$
$422$	3.09967	−	1.12819i	0.150890	−	0.0549193i
$423$	36.2486	+	13.1934i	1.76247	+	0.641485i
$424$	−6.39827	−	5.36879i	−0.310727	−	0.260731i
$425$	0.988856	−	1.71275i	0.0479665	−	0.0830805i
$426$	18.0496	+	31.2629i	0.874507	+	1.51469i
$427$	0.550507	−	3.12208i	0.0266409	−	0.151088i
$428$	−0.328411	+	1.86251i	−0.0158744	+	0.0900279i
$429$	−8.25150	−	14.2920i	−0.398386	−	0.690025i
$430$	2.31134	−	4.00335i	0.111463	−	0.193059i
$431$	−29.3444	−	24.6228i	−1.41347	−	1.18604i	−0.954732	−	0.297468i	$-0.903858\pi$
$431$	−29.3444	−	24.6228i	−1.41347	−	1.18604i	−0.458736	−	0.888572i	$-0.651698\pi$
$432$	−22.2913	−	8.11338i	−1.07249	−	0.390355i
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.101532	−	0.994832i	$-0.467626\pi$
$433$	17.0376	−	6.20118i	0.818775	−	0.298010i	0.717244	+	0.696823i	$0.245403\pi$
$434$	2.54710	−	2.13727i	0.122265	−	0.102592i
$435$	3.02481	+	17.1546i	0.145029	+	0.822499i
$436$	0.336867			0.0161330
$437$	−11.5517	+	2.12467i	−0.552592	+	0.101637i
$438$	5.38919			0.257505
$439$	−1.05762	−	5.99806i	−0.0504774	−	0.286272i	0.949112	−	0.314940i	$-0.101984\pi$
$439$	−1.05762	−	5.99806i	−0.0504774	−	0.286272i	−0.999589	+	0.0286685i	$0.990873\pi$
$440$	−4.41534	+	3.70491i	−0.210493	+	0.176625i
$441$	34.2028	−	12.4488i	1.62870	−	0.592800i
$442$	1.52481	+	0.554987i	0.0725280	+	0.0263981i
$443$	−22.8995	−	19.2149i	−1.08799	−	0.912928i	−0.0914266	−	0.995812i	$-0.529143\pi$
$443$	−22.8995	−	19.2149i	−1.08799	−	0.912928i	−0.996559	+	0.0828833i	$0.973587\pi$
$444$	−1.31521	+	2.27801i	−0.0624170	+	0.108109i
$445$	4.52481	+	7.83721i	0.214497	+	0.371519i
$446$	1.99092	−	11.2910i	0.0942726	−	0.534646i
$447$	−8.27972	+	46.9566i	−0.391617	+	2.22097i
$448$	−1.49273	−	2.58548i	−0.0705247	−	0.122152i
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	−0.702226	−	0.711955i	$-0.747810\pi$
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	0.967683	+	0.252168i	$0.0811435\pi$
$450$	23.0804	+	19.3667i	1.08802	+	0.912957i
$451$	5.18004	+	1.88538i	0.243919	+	0.0887792i
$452$	−3.07145	+	1.11792i	−0.144469	+	0.0525824i
$453$	9.62108	−	8.07305i	0.452038	−	0.379305i
$454$	3.31062	+	18.7755i	0.155375	+	0.881176i
$455$	0.786112			0.0368535
$456$	−32.1300	−	18.2362i	−1.50463	−	0.853989i
$457$	−23.3901			−1.09414			−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901			−1.09414			−0.547072	+	0.837086i	$0.684258\pi$
$458$	4.80381	+	27.2438i	0.224468	+	1.27302i
$459$	−2.36437	+	1.98394i	−0.110359	+	0.0926025i
$460$	−0.411474	+	0.149764i	−0.0191851	+	0.00698280i
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.980011	−	0.198945i	$-0.0637514\pi$
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.622853	+	0.782339i	$0.285974\pi$
$462$	−2.29813	−	1.92836i	−0.106919	−	0.0897156i
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.458340	−	0.888777i	$-0.348444\pi$
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.540534	−	0.841322i	$-0.318222\pi$
$464$	−12.3701	−	21.4256i	−0.574265	−	0.994657i
$465$	3.12449	−	17.7198i	0.144895	−	0.821738i
$466$	−4.12954	+	23.4198i	−0.191297	+	1.08490i
$467$	−12.7981	−	22.1670i	−0.592227	−	1.02577i	−0.993932	−	0.109998i	$-0.964916\pi$
$467$	−12.7981	−	22.1670i	−0.592227	−	1.02577i	0.401705	−	0.915769i	$-0.368418\pi$
$468$	1.25830	−	2.17945i	0.0581651	−	0.100745i
$469$	2.04189	+	1.71335i	0.0942857	+	0.0791151i
$470$	−8.11721	−	2.95442i	−0.374419	−	0.136277i
$471$	−26.0253	+	9.47243i	−1.19918	+	0.436466i
$472$	−14.2181	+	11.9304i	−0.654439	+	0.549140i
$473$	−1.50862	−	8.55580i	−0.0693663	−	0.393396i
$474$	−45.9522			−2.11066
$475$	11.9461	+	14.0258i	0.548124	+	0.643548i
$476$	−0.0300295			−0.00137640
$477$	−2.60694	−	14.7847i	−0.119364	−	0.676946i
$478$	−2.42783	+	2.03719i	−0.111046	+	0.0931791i
$479$	−35.8739	+	13.0570i	−1.63912	+	0.596591i	−0.986885	−	0.161424i	$-0.948391\pi$
$479$	−35.8739	+	13.0570i	−1.63912	+	0.596591i	−0.652236	+	0.758016i	$0.726169\pi$
$480$	−2.47906	−	0.902302i	−0.113153	−	0.0411843i
$481$	9.74763	+	8.17923i	0.444453	+	0.372941i
$482$	9.29679	−	16.1025i	0.423457	−	0.733449i
$483$	−1.34730	−	2.33359i	−0.0613041	−	0.106182i
$484$	0.193877	−	1.09953i	0.00881261	−	0.0499788i
$485$	1.44356	−	8.18685i	0.0655488	−	0.371746i
$486$	7.27766	+	12.6053i	0.330121	+	0.571787i
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	−0.940475	−	0.339864i	$-0.889619\pi$
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	0.764568	+	0.644543i	$0.222952\pi$
$488$	20.5835	+	17.2716i	0.931773	+	0.781850i
$489$	22.6065	+	8.22811i	1.02230	+	0.372088i
$490$	−7.65910	+	2.78768i	−0.346003	+	0.125935i
$491$	−28.1313	+	23.6050i	−1.26955	+	1.06528i	−0.274954	+	0.961457i	$0.588663\pi$
$491$	−28.1313	+	23.6050i	−1.26955	+	1.06528i	−0.994596	+	0.103822i	$0.966893\pi$
$492$	0.228741	+	1.29725i	0.0103124	+	0.0584848i
$493$	−3.21894			−0.144974
$494$	−9.63104	+	11.6510i	−0.433321	+	0.524201i
$495$	−10.3601			−0.465651
$496$	4.43763	+	25.1671i	0.199256	+	1.13003i
$497$	−2.47565	+	2.07732i	−0.111048	+	0.0931805i
$498$	54.0642	−	19.6778i	2.42268	−	0.881782i
$499$	−4.62923	−	1.68490i	−0.207233	−	0.0754266i	0.236318	−	0.971676i	$-0.424059\pi$
$499$	−4.62923	−	1.68490i	−0.207233	−	0.0754266i	−0.443551	+	0.896249i	$0.646281\pi$
$500$	1.14858	+	0.963777i	0.0513663	+	0.0431014i
$501$	5.80928	−	10.0620i	0.259539	−	0.449535i
$502$	−2.80587	−	4.85992i	−0.125232	−	0.216909i
$503$	5.72163	−	32.4490i	0.255115	−	1.44683i	−0.540663	−	0.841239i	$-0.681827\pi$
$503$	5.72163	−	32.4490i	0.255115	−	1.44683i	0.795778	−	0.605589i	$-0.207062\pi$
$504$	0.939226	−	5.32661i	0.0418364	−	0.237266i
$505$	4.06670	+	7.04374i	0.180966	+	0.313442i
$506$	4.04189	−	7.00076i	0.179684	−	0.311222i
$507$	14.0608	+	11.7984i	0.624461	+	0.523985i
$508$	2.01501	+	0.733405i	0.0894018	+	0.0325396i
$509$	34.7075	−	12.6325i	1.53839	−	0.559926i	0.572728	−	0.819746i	$-0.305885\pi$
$509$	34.7075	−	12.6325i	1.53839	−	0.559926i	0.965657	+	0.259819i	$0.0836630\pi$
$510$	1.22281	−	1.02606i	0.0541470	−	0.0454347i
$511$	0.0837781	+	0.475129i	0.00370613	+	0.0210185i
$512$	24.9186			1.10126
$513$	−10.0326	−	26.9453i	−0.442948	−	1.18967i
$514$	−0.898986			−0.0396526
$515$	−0.841367	−	4.77163i	−0.0370750	−	0.210263i
$516$	1.59034	−	1.33445i	0.0700107	−	0.0587459i
$517$	−15.2554	+	5.55250i	−0.670930	+	0.244199i
$518$	2.17365	+	0.791143i	0.0955046	+	0.0347608i
$519$	44.4320	+	37.2829i	1.95035	+	1.63654i
$520$	−3.33140	+	5.77016i	−0.146092	+	0.253038i
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	0.746126	−	0.665804i	$-0.231912\pi$
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	−0.949667	+	0.313262i	$0.898578\pi$
$522$	8.51548	−	48.2937i	0.372713	−	2.11376i
$523$	−4.93423	+	27.9834i	−0.215759	+	1.22363i	0.663826	+	0.747887i	$0.268932\pi$
$523$	−4.93423	+	27.9834i	−0.215759	+	1.22363i	−0.879585	+	0.475742i	$0.842180\pi$
$524$	0.170493	+	0.295303i	0.00744802	+	0.0129004i
$525$	−2.11334	+	3.66041i	−0.0922338	+	0.159754i
$526$	−11.7654	−	9.87236i	−0.512996	−	0.430455i
$527$	3.12449	+	1.13722i	0.136105	+	0.0495381i
$528$	21.6668	−	7.88609i	0.942928	−	0.343198i
$529$	−12.0569	+	10.1169i	−0.524213	+	0.439867i
$530$	0.583778	+	3.31077i	0.0253577	+	0.143811i
$531$	−33.3610			−1.44775
$532$	0.0937404	−	0.263571i	0.00406416	−	0.0114273i
$533$	6.37227			0.276014
$534$	−6.93242	−	39.3157i	−0.299995	−	1.70136i
$535$	6.89440	−	5.78509i	0.298071	−	0.250111i
$536$	−21.2294	+	7.72686i	−0.916969	+	0.333749i
$537$	−31.1498	−	11.3376i	−1.34421	−	0.489253i
$538$	−20.0123	−	16.7923i	−0.862793	−	0.723969i
$539$	−7.65910	+	13.2660i	−0.329901	+	0.571405i
$540$	−0.535959	−	0.928309i	−0.0230640	−	0.0399480i
$541$	2.60220	−	14.7578i	0.111877	−	0.634487i	−0.876372	−	0.481635i	$-0.840043\pi$
$541$	2.60220	−	14.7578i	0.111877	−	0.634487i	0.988249	−	0.152852i	$-0.0488458\pi$
$542$	3.13366	−	17.7718i	0.134602	−	0.763366i
$543$	12.2909	+	21.2884i	0.527451	+	0.913572i
$544$	0.243756	−	0.422197i	0.0104509	−	0.0181016i
$545$	−1.22803	−	1.03044i	−0.0526028	−	0.0441390i
$546$	−3.25877	−	1.18610i	−0.139463	−	0.0507602i
$547$	3.65270	−	1.32948i	0.156178	−	0.0568443i	−0.262748	−	0.964864i	$-0.584629\pi$
$547$	3.65270	−	1.32948i	0.156178	−	0.0568443i	0.418926	+	0.908020i	$0.362407\pi$
$548$	−0.0362077	+	0.0303818i	−0.00154672	+	0.00129785i
$549$	8.38666	+	47.5631i	0.357934	+	2.02994i
$550$	−12.6800			−0.540679
$551$	10.0483	−	28.2529i	0.428071	−	1.20361i
$552$	22.8384			0.972068
$553$	−0.714355	−	4.05131i	−0.0303775	−	0.172279i
$554$	−18.3164	+	15.3693i	−0.778189	+	0.652978i
$555$	11.7626	−	4.28125i	0.499296	−	0.181729i
$556$	0.740352	+	0.269466i	0.0313979	+	0.0114279i
$557$	10.1152	+	8.48762i	0.428593	+	0.359632i	0.831420	−	0.555644i	$-0.187528\pi$
$557$	10.1152	+	8.48762i	0.428593	+	0.359632i	−0.402828	+	0.915276i	$0.631973\pi$
$558$	−25.3273	+	43.8681i	−1.07219	+	1.85709i
$559$	−5.02141	−	8.69734i	−0.212383	−	0.367858i
$560$	−0.190722	+	1.08164i	−0.00805949	+	0.0457076i
$561$	0.520945	−	2.95442i	0.0219943	−	0.124736i
$562$	12.3136	+	21.3278i	0.519418	+	0.899659i
$563$	−5.35638	+	9.27752i	−0.225745	+	0.391001i	−0.956543	−	0.291593i	$-0.905815\pi$
$563$	−5.35638	+	9.27752i	−0.225745	+	0.391001i	0.730798	+	0.682594i	$0.239148\pi$
$564$	−2.97178	−	2.49362i	−0.125135	−	0.105000i
$565$	14.6163	+	5.31991i	0.614914	+	0.223810i
$566$	9.73308	−	3.54255i	0.409112	−	0.148905i
$567$	0.830222	−	0.696639i	0.0348661	−	0.0292561i
$568$	−4.75641	−	26.9749i	−0.199574	−	1.13184i
$569$	−13.4706			−0.564717			−0.282358	−	0.959309i	$-0.591117\pi$
$569$	−13.4706			−0.564717			−0.282358	+	0.959309i	$0.591117\pi$
$570$	5.18866	+	13.9357i	0.217329	+	0.583701i
$571$	12.6655			0.530035			0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655			0.530035			0.265017	+	0.964244i	$0.414622\pi$
$572$	0.183915	+	1.04303i	0.00768988	+	0.0436115i
$573$	−40.4432	+	33.9358i	−1.68954	+	1.41769i
$574$	1.08853	−	0.396191i	0.0454342	−	0.0165367i
$575$	−10.7023	−	3.89533i	−0.446318	−	0.162447i
$576$	34.8410	+	29.2350i	1.45171	+	1.21813i
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	−0.735022	−	0.678044i	$-0.762828\pi$
$577$	5.27719	−	9.14036i	0.219692	−	0.380518i	0.954714	+	0.297526i	$0.0961613\pi$
$578$	−11.3045	−	19.5800i	−0.470206	−	0.814421i
$579$	−0.148833	+	0.844075i	−0.00618530	+	0.0350786i
$580$	0.194126	−	1.10094i	0.00806064	−	0.0457142i
$581$	2.57532	+	4.46059i	0.106842	+	0.185056i
$582$	−18.3366	+	31.7600i	−0.760077	+	1.31649i
$583$	4.84002	+	4.06126i	0.200453	+	0.168200i
$584$	−3.84255	−	1.39857i	−0.159006	−	0.0578734i
$585$	−11.2537	+	4.09602i	−0.465284	+	0.169350i
$586$	10.8400	−	9.09586i	0.447797	−	0.375746i
$587$	−3.32619	−	18.8638i	−0.137287	−	0.778591i	−0.973240	−	0.229791i	$-0.926196\pi$
$587$	−3.32619	−	18.8638i	−0.137287	−	0.778591i	0.835954	−	0.548800i	$-0.184915\pi$
$588$	−3.66044			−0.150954
$589$	−19.7349	+	23.8739i	−0.813162	+	0.983706i
$590$	7.47060			0.307560
$591$	−6.57057	−	37.2636i	−0.270277	−	1.53282i
$592$	−13.6190	+	11.4277i	−0.559738	+	0.469676i
$593$	8.17024	−	2.97373i	0.335512	−	0.122116i	−0.168770	−	0.985655i	$-0.553980\pi$
$593$	8.17024	−	2.97373i	0.335512	−	0.122116i	0.504282	+	0.863539i	$0.331757\pi$
$594$	18.5954	+	6.76817i	0.762978	+	0.277701i
$595$	0.109470	+	0.0918566i	0.00448785	+	0.00376575i
$596$	1.53003	−	2.65009i	0.0626724	−	0.108552i
$597$	−0.369585	−	0.640140i	−0.0151261	−	0.0261992i
$598$	1.62267	−	9.20264i	0.0663561	−	0.376324i
$599$	3.44373	−	19.5303i	0.140707	−	0.797988i	−0.830008	−	0.557752i	$-0.811664\pi$
$599$	3.44373	−	19.5303i	0.140707	−	0.797988i	0.970715	−	0.240236i	$-0.0772248\pi$
$600$	−17.9119	−	31.0244i	−0.731252	−	1.26657i
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	−0.283718	−	0.958908i	$-0.591568\pi$
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	0.972298	−	0.233747i	$-0.0750986\pi$
$602$	−1.39852	−	1.17350i	−0.0569994	−	0.0478282i
$603$	−38.1584	−	13.8885i	−1.55393	−	0.565584i
$604$	−0.757426	+	0.275681i	−0.0308192	+	0.0112173i
$605$	−4.07011	+	3.41523i	−0.165473	+	0.138849i
$606$	−6.23055	−	35.3352i	−0.253099	−	1.43540i
$607$	35.2850			1.43217			0.716087	−	0.698011i	$-0.245932\pi$
$607$	35.2850			1.43217			0.716087	+	0.698011i	$0.245932\pi$
$608$	2.94475	+	3.45740i	0.119425	+	0.140216i
$609$	6.87939			0.278767
$610$	−1.87804	−	10.6509i	−0.0760397	−	0.431242i
$611$	−14.3760	+	12.0629i	−0.581590	+	0.488012i
$612$	0.429892	−	0.156468i	0.0173774	−	0.00632485i
$613$	−17.3405	−	6.31142i	−0.700376	−	0.254916i	−0.0328044	−	0.999462i	$-0.510444\pi$
$613$	−17.3405	−	6.31142i	−0.700376	−	0.254916i	−0.667571	+	0.744546i	$0.732666\pi$
$614$	12.0708	+	10.1286i	0.487139	+	0.408758i
$615$	3.13429	−	5.42874i	0.126387	−	0.218908i
$616$	1.13816	+	1.97134i	0.0458576	+	0.0794277i
$617$	−6.19671	+	35.1433i	−0.249470	+	1.41482i	0.560408	+	0.828217i	$0.310644\pi$
$617$	−6.19671	+	35.1433i	−0.249470	+	1.41482i	−0.809878	+	0.586598i	$0.800467\pi$
$618$	−3.71167	+	21.0499i	−0.149305	+	0.846752i
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	0.826908	−	0.562337i	$-0.190098\pi$
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	−0.900452	+	0.434955i	$0.856764\pi$
$620$	−0.577382	+	1.00005i	−0.0231882	+	0.0401631i
$621$	13.6159	+	11.4251i	0.546386	+	0.458472i
$622$	20.2135	+	7.35710i	0.810487	+	0.294993i
$623$	3.35844	−	1.22237i	0.134553	−	0.0489733i
$624$	20.4179	−	17.1326i	0.817369	−	0.685854i
$625$	2.43077	+	13.7856i	0.0972308	+	0.551423i
$626$	35.8767			1.43392
$627$	24.3050	+	13.7949i	0.970648	+	0.550917i
$628$	1.77744			0.0709275
$629$	0.401674	+	2.27801i	0.0160158	+	0.0908301i
$630$	−1.66772	+	1.39938i	−0.0664435	+	0.0557527i
$631$	0.745977	−	0.271514i	0.0296969	−	0.0108088i	−0.327129	−	0.944980i	$-0.606081\pi$
$631$	0.745977	−	0.271514i	0.0296969	−	0.0108088i	0.356826	+	0.934171i	$0.383859\pi$
$632$	32.7645	+	11.9253i	1.30330	+	0.474362i
$633$	−5.40033	−	4.53141i	−0.214644	−	0.180108i
$634$	19.8942	−	34.4578i	0.790101	−	1.36850i
$635$	−5.10220	−	8.83726i	−0.202474	−	0.350696i
$636$	−0.262174	+	1.48686i	−0.0103959	+	0.0589579i
$637$	−3.07486	+	17.4384i	−0.121830	+	0.690933i
$638$	10.3191	+	17.8732i	0.408536	+	0.707605i
$639$	24.6168	−	42.6375i	0.973826	−	1.68672i
$640$	−6.39827	−	5.36879i	−0.252914	−	0.212220i
$641$	−27.6104	−	10.0494i	−1.09055	−	0.396926i	−0.266723	−	0.963773i	$-0.585941\pi$
$641$	−27.6104	−	10.0494i	−1.09055	−	0.396926i	−0.823823	+	0.566847i	$0.808163\pi$
$642$	−37.3089	+	13.5793i	−1.47246	+	0.535933i
$643$	17.0168	−	14.2788i	0.671078	−	0.563101i	−0.242306	−	0.970200i	$-0.577904\pi$
$643$	17.0168	−	14.2788i	0.671078	−	0.563101i	0.913384	+	0.407098i	$0.133459\pi$
$644$	0.0300295	+	0.170306i	0.00118333	+	0.00671099i
$645$	−9.87939			−0.389000
$646$	−2.70258	+	0.497079i	−0.106332	+	0.0195573i
$647$	11.2591			0.442640			0.221320	−	0.975201i	$-0.428963\pi$
$647$	11.2591			0.442640			0.221320	+	0.975201i	$0.428963\pi$
$648$	1.59508	+	9.04617i	0.0626608	+	0.355367i
$649$	10.7554	−	9.02482i	0.422185	−	0.354255i
$650$	−13.7738	+	5.01325i	−0.540252	+	0.196636i
$651$	−6.67752	−	2.43042i	−0.261713	−	0.0952556i
$652$	−1.18273	−	0.992431i	−0.0463194	−	0.0388666i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	3.53596	+	6.12446i	0.138267	+	0.239485i
$655$	0.281774	−	1.59802i	0.0110098	−	0.0624399i
$656$	−1.54601	+	8.76785i	−0.0603615	+	0.342327i
$657$	−3.67499	−	6.36527i	−0.143375	−	0.248333i
$658$	−1.70574	+	2.95442i	−0.0664966	+	0.115175i
$659$	21.4691	+	18.0147i	0.836317	+	0.701753i	0.956732	−	0.290970i	$-0.0939781\pi$
$659$	21.4691	+	18.0147i	0.836317	+	0.701753i	−0.120415	+	0.992724i	$0.538423\pi$
$660$	0.979055	+	0.356347i	0.0381097	+	0.0138708i
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	−0.541303	−	0.840827i	$-0.682069\pi$
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	0.125811	+	0.992054i	$0.459847\pi$
$662$	−28.5533	+	23.9590i	−1.10975	+	0.931194i
$663$	−0.602196	−	3.41523i	−0.0233874	−	0.132636i
$664$	−43.6551			−1.69415
$665$	−1.14796	+	0.674089i	−0.0445158	+	0.0261400i
$666$	−35.2395			−1.36550
$667$	3.21894	+	18.2555i	0.124638	+	0.706857i
$668$	−0.571203	+	0.479297i	−0.0221005	+	0.0185445i
$669$	−23.0253	+	8.38052i	−0.890209	+	0.324010i
$670$	8.54488	+	3.11008i	0.330118	+	0.120153i
$671$	−15.5706	−	13.0653i	−0.601095	−	0.504379i
$672$	−0.520945	+	0.902302i	−0.0200959	+	0.0348071i
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	0.980344	−	0.197296i	$-0.0632160\pi$
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	−0.661035	+	0.750355i	$0.729883\pi$
$674$	−4.17840	+	23.6969i	−0.160946	+	0.912769i
$675$	4.84137	−	27.4568i	0.186344	−	1.05681i
$676$	−0.588993	−	1.02017i	−0.0226536	−	0.0392371i
$677$	4.52481	−	7.83721i	0.173903	−	0.301208i	−0.765878	−	0.642986i	$-0.777695\pi$
$677$	4.52481	−	7.83721i	0.173903	−	0.301208i	0.939781	+	0.341777i	$0.111029\pi$
$678$	−52.5642	−	44.1066i	−2.01872	−	1.69390i
$679$	−3.08512	−	1.12289i	−0.118396	−	0.0430927i
$680$	−1.13816	+	0.414255i	−0.0436463	+	0.0158859i
$681$	31.2126	−	26.1905i	1.19607	−	1.00362i
$682$	−3.70187	−	20.9943i	−0.141752	−	0.803914i
$683$	8.73143			0.334099			0.167049	−	0.985949i	$-0.446576\pi$
$683$	8.73143			0.334099			0.167049	+	0.985949i	$0.446576\pi$
$684$	0.0313737	+	4.26163i	0.00119960	+	0.162947i
$685$	0.224927			0.00859402
$686$	1.12773	+	6.39566i	0.0430568	+	0.244187i
$687$	45.2904	−	38.0032i	1.72794	−	1.44991i
$688$	13.1853	−	4.79904i	0.502683	−	0.182962i
$689$	6.86319	+	2.49800i	0.261467	+	0.0951661i
$690$	−7.04189	−	5.90885i	−0.268080	−	0.224946i
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	0.320099	+	0.947384i	$0.396284\pi$
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	−0.980508	+	0.196478i	$0.937050\pi$
$692$	−1.86122	−	3.22372i	−0.0707528	−	0.122547i
$693$	−0.710485	+	4.02936i	−0.0269891	+	0.153063i
$694$	1.35710	−	7.69648i	0.0515147	−	0.292154i
$695$	−1.87464	−	3.24697i	−0.0711091	−	0.123164i
$696$	−29.1536	+	50.4956i	−1.10507	+	1.91403i
$697$	0.887374	+	0.744596i	0.0336117	+	0.0282036i
$698$	6.80154	+	2.47556i	0.257442	+	0.0937012i
$699$	47.7588	−	17.3828i	1.80640	−	0.657478i
$700$	0.207796	−	0.174362i	0.00785397	−	0.00659026i
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	0.786905	+	0.617074i	$0.211682\pi$
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	−0.528397	+	0.848997i	$0.677207\pi$
$702$	22.8753			0.863371
$703$	−21.2481	−	3.58553i	−0.801387	−	0.135231i
$704$	−19.1411			−0.721409
$705$	3.20574	+	18.1806i	0.120735	+	0.684722i
$706$	26.0442	−	21.8537i	0.980185	−	0.822473i
$707$	3.01842	−	1.09861i	0.113519	−	0.0413176i
$708$	3.15270	+	1.14749i	0.118486	+	0.0431253i
$709$	−31.5009	−	26.4324i	−1.18304	−	0.992690i	−0.999954	−	0.00959399i	$-0.996946\pi$
$709$	−31.5009	−	26.4324i	−1.18304	−	0.992690i	−0.183088	−	0.983096i	$-0.558609\pi$
$710$	−5.51249	+	9.54791i	−0.206880	+	0.358327i
$711$	31.3357	+	54.2751i	1.17518	+	2.03548i
$712$	−5.26011	+	29.8316i	−0.197131	+	1.11799i
$713$	3.32501	−	18.8571i	0.124523	−	0.706202i
$714$	−0.315207	−	0.545955i	−0.0117963	−	0.0204319i
$715$	2.52007	−	4.36488i	0.0942452	−	0.163237i
$716$	1.62970	+	1.36748i	0.0609047	+	0.0511051i
$717$	6.36484	+	2.31661i	0.237699	+	0.0865154i
$718$	8.46585	−	3.08132i	0.315943	−	0.114994i
$719$	−32.4768	+	27.2513i	−1.21118	+	1.01630i	−0.211943	+	0.977282i	$0.567979\pi$
$719$	−32.4768	+	27.2513i	−1.21118	+	1.01630i	−0.999238	+	0.0390200i	$0.987576\pi$
$720$	−2.90554	−	16.4782i	−0.108283	−	0.614105i
$721$	−1.91353			−0.0712637
$722$	4.07351	−	25.2724i	0.151600	−	0.940543i
$723$	−39.7374			−1.47785
$724$	−0.273947	−	1.55363i	−0.0101812	−	0.0577403i
$725$	22.2743	−	18.6903i	0.827245	−	0.694141i
$726$	22.0253	−	8.01655i	0.817435	−	0.297522i
$727$	−48.5411	−	17.6675i	−1.80029	−	0.655251i	−0.998324	−	0.0578805i	$-0.981566\pi$
$727$	−48.5411	−	17.6675i	−1.80029	−	0.655251i	−0.801965	−	0.597371i	$-0.796212\pi$
$728$	2.01573	+	1.69140i	0.0747079	+	0.0626874i
$729$	20.2344	−	35.0470i	0.749423	−	1.29804i
$730$	0.822948	+	1.42539i	0.0304587	+	0.0527560i
$731$	0.317018	−	1.79790i	0.0117254	−	0.0664978i
$732$	0.843426	−	4.78331i	0.0311739	−	0.176796i
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	0.996252	−	0.0864997i	$-0.0275682\pi$
$733$	11.4581	+	19.8460i	0.423215	+	0.733030i	−0.573037	+	0.819530i	$0.694235\pi$
$734$	5.46926	−	9.47303i	0.201874	−	0.349656i
$735$	13.3439	+	11.1969i	0.492197	+	0.413002i
$736$	−2.63816	−	0.960210i	−0.0972437	−	0.0353938i
$737$	16.0591	−	5.84504i	0.591545	−	0.215305i
$738$	−13.5186	+	11.3435i	−0.497628	+	0.417559i
$739$	4.88413	+	27.6993i	0.179666	+	1.01894i	0.932619	+	0.360862i	$0.117517\pi$
$739$	4.88413	+	27.6993i	0.179666	+	1.01894i	−0.752954	+	0.658074i	$0.771372\pi$
$740$	−0.803348			−0.0295317
$741$	31.8555	+	5.37549i	1.17024	+	0.197474i
$742$	1.32770			0.0487413
$743$	1.06489	+	6.03931i	0.0390671	+	0.221561i	0.998091	−	0.0617657i	$-0.0196731\pi$
$743$	1.06489	+	6.03931i	0.0390671	+	0.221561i	−0.959024	+	0.283326i	$0.908562\pi$
$744$	46.1377	−	38.7142i	1.69149	−	1.41933i
$745$	−13.6839	+	4.98054i	−0.501340	+	0.182473i
$746$	44.1819	+	16.0809i	1.61761	+	0.588763i
$747$	−60.1093	−	50.4377i	−2.19928	−	1.84542i
$748$	−0.0962667	+	0.166739i	−0.00351986	+	0.00609657i
$749$	−1.77719	−	3.07818i	−0.0649371	−	0.112474i
$750$	−5.46585	+	30.9984i	−0.199585	+	1.13190i
$751$	0.979522	−	5.55515i	0.0357433	−	0.202710i	−0.961707	−	0.274081i	$-0.911626\pi$
$751$	0.979522	−	5.55515i	0.0357433	−	0.202710i	0.997450	+	0.0713710i	$0.0227374\pi$
$752$	−13.1099	−	22.7071i	−0.478070	−	0.828042i
$753$	−5.99660	+	10.3864i	−0.218528	+	0.378502i
$754$	18.2756	+	15.3350i	0.665558	+	0.558469i
$755$	3.60442	+	1.31190i	0.131178	+	0.0477450i
$756$	−0.397804	+	0.144789i	−0.0144680	+	0.00526591i
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	−0.397648	−	0.917538i	$-0.630173\pi$
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	0.834548	+	0.550936i	$0.185729\pi$
$758$	−0.398052	−	2.25746i	−0.0144579	−	0.0819948i
$759$	−17.2763			−0.627090
$760$	−0.0830629	−	11.2828i	−0.00301301	−	0.409271i
$761$	4.86484			0.176350			0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484			0.176350			0.0881751	+	0.996105i	$0.471896\pi$
$762$	7.81702	+	44.3325i	0.283181	+	1.60600i
$763$	−0.484985	+	0.406951i	−0.0175576	+	0.0147326i
$764$	3.18392	−	1.15885i	0.115190	−	0.0419257i
$765$	−2.04576	−	0.744596i	−0.0739646	−	0.0269209i
$766$	−3.03099	−	2.54331i	−0.109514	−	0.0918934i
$767$	8.11499	−	14.0556i	0.293015	−	0.507517i
$768$	−6.32888	−	10.9619i	−0.228374	−	0.395555i
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	−0.829327	−	0.558764i	$-0.811276\pi$
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	0.970421	−	0.241420i	$-0.0776131\pi$
$770$	0.159100	−	0.902302i	0.00573358	−	0.0325167i
$771$	0.960637	+	1.66387i	0.0345965	+	0.0599229i
$772$	0.0275033	−	0.0476371i	0.000989864	−	0.00171450i
$773$	−20.2481	−	16.9902i	−0.728273	−	0.611094i	0.201387	−	0.979512i	$-0.435455\pi$
$773$	−20.2481	−	16.9902i	−0.728273	−	0.611094i	−0.929660	+	0.368418i	$0.879900\pi$
$774$	26.1352	+	9.51244i	0.939411	+	0.341918i
$775$	−28.2237	+	10.2726i	−1.01383	+	0.369003i
$776$	21.3164	−	17.8866i	0.765214	−	0.642091i
$777$	−0.858441	−	4.86846i	−0.0307964	−	0.174655i
$778$	33.0993			1.18667
$779$	−9.30541	+	5.46421i	−0.333401	+	0.195776i
$780$	1.20439			0.0431242
$781$	3.59802	+	20.4054i	0.128747	+	0.730162i
$782$	1.30129	−	1.09191i	0.0465340	−	0.0390466i
$783$	−42.6416	+	15.5203i	−1.52389	+	0.554650i
$784$	−23.2481	−	8.46161i	−0.830289	−	0.302200i
$785$	−6.47952	−	5.43696i	−0.231264	−	0.194054i
$786$	−3.57919	+	6.19934i	−0.127666	+	0.221123i
$787$	7.77884	+	13.4733i	0.277286	+	0.480273i	0.970709	−	0.240257i	$-0.0772318\pi$
$787$	7.77884	+	13.4733i	0.277286	+	0.480273i	−0.693424	+	0.720530i	$0.743899\pi$
$788$	−0.421685	+	2.39149i	−0.0150219	+	0.0851934i
$789$	−5.69981	+	32.3252i	−0.202919	+	1.15081i
$790$	−7.01707	−	12.1539i	−0.249656	−	0.432417i
$791$	3.07145	−	5.31991i	0.109208	−	0.189154i
$792$	−26.5651	−	22.2908i	−0.943950	−	0.792068i
$793$	−22.0792	−	8.03617i	−0.784055	−	0.285373i
$794$	−40.3055	+	14.6700i	−1.43039	+	0.520618i
$795$	5.50387	−	4.61830i	0.195202	−	0.163794i
$796$	0.00823757	+	0.0467176i	0.000291973	+	0.00165586i
$797$	33.4935			1.18640			0.593200	−	0.805055i	$-0.297864\pi$
$797$	33.4935			1.18640			0.593200	+	0.805055i	$0.297864\pi$
$798$	5.77584	−	1.06234i	0.204463	−	0.0376063i
$799$	−3.41147			−0.120689
$800$	0.764700	+	4.33683i	0.0270362	+	0.153330i
$801$	−41.7092	+	34.9982i	−1.47372	+	1.23660i
$802$	−0.109470	+	0.0398440i	−0.00386553	+	0.00140694i
$803$	2.90673	+	1.05796i	0.102576	+	0.0373347i
$804$	3.12836	+	2.62500i	0.110329	+	0.0925767i
$805$	0.411474	−	0.712694i	0.0145026	−	0.0251192i
$806$	−12.3216	−	21.3416i	−0.434010	−	0.751727i
$807$	−9.69506	+	54.9834i	−0.341282	+	1.93551i
$808$	−4.72756	+	26.8113i	−0.166315	+	0.943219i
$809$	−20.5581	−	35.6076i	−0.722784	−	1.25190i	−0.959880	−	0.280412i	$-0.909529\pi$
$809$	−20.5581	−	35.6076i	−0.722784	−	1.25190i	0.237096	−	0.971486i	$-0.423804\pi$
$810$	1.84864	−	3.20194i	0.0649546	−	0.112505i
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	0.839025	−	0.544093i	$-0.183126\pi$
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	−0.390132	+	0.920759i	$0.627571\pi$
$812$	−0.414878	−	0.151003i	−0.0145594	−	0.00529917i
$813$	−36.2413	+	13.1907i	−1.27104	+	0.462620i
$814$	11.3610	−	9.53298i	0.398202	−	0.334131i
$815$	1.27584	+	7.23567i	0.0446909	+	0.253455i
$816$	4.84524			0.169617
$817$	14.7907	+	8.39484i	0.517461	+	0.293698i
$818$	−26.9540			−0.942424
$819$	0.821299	+	4.65782i	0.0286985	+	0.162757i
$820$	−0.308182	+	0.258595i	−0.0107622	+	0.00903054i
$821$	29.4971	−	10.7361i	1.02945	−	0.374691i	0.228581	−	0.973525i	$-0.426591\pi$
$821$	29.4971	−	10.7361i	1.02945	−	0.374691i	0.800873	+	0.598834i	$0.204369\pi$
$822$	−0.932419	−	0.339373i	−0.0325218	−	0.0118370i
$823$	35.4877	+	29.7777i	1.23702	+	1.03799i	0.997751	+	0.0670347i	$0.0213538\pi$
$823$	35.4877	+	29.7777i	1.23702	+	1.03799i	0.239274	+	0.970952i	$0.423091\pi$
$824$	8.10922	−	14.0456i	0.282498	−	0.489301i
$825$	13.5496	+	23.4686i	0.471738	+	0.817073i
$826$	0.512326	−	2.90555i	0.0178261	−	0.101097i
$827$	7.07769	−	40.1396i	0.246115	−	1.39579i	−0.571773	−	0.820412i	$-0.693744\pi$
$827$	7.07769	−	40.1396i	0.246115	−	1.39579i	0.817888	−	0.575377i	$-0.195145\pi$
$828$	−1.31727	−	2.28157i	−0.0457782	−	0.0792901i
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	−0.373979	−	0.927437i	$-0.622007\pi$
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	0.990174	−	0.139843i	$-0.0446598\pi$
$830$	13.4604	+	11.2946i	0.467217	+	0.392042i
$831$	48.0185	+	17.4773i	1.66574	+	0.606281i
$832$	−20.7922	+	7.56774i	−0.720840	+	0.262364i
$833$	−2.46585	+	2.06910i	−0.0854367	+	0.0716899i
$834$	2.87211	+	16.2886i	0.0994531	+	0.564026i
$835$	3.54839			0.122797
$836$	−1.16297	−	1.36543i	−0.0402222	−	0.0472245i
$837$	46.8735			1.62019
$838$	−5.94475	−	33.7143i	−0.205358	−	1.16464i
$839$	−29.2649	+	24.5562i	−1.01034	+	0.847774i	−0.988383	−	0.151985i	$-0.951433\pi$
$839$	−29.2649	+	24.5562i	−1.01034	+	0.847774i	−0.0219545	+	0.999759i	$0.506989\pi$
$840$	2.43242	−	0.885328i	0.0839264	−	0.0305467i
$841$	−17.2208	−	6.26784i	−0.593819	−	0.216132i
$842$	−4.50980	−	3.78417i	−0.155418	−	0.130411i
$843$	26.3161	−	45.5809i	0.906376	−	1.56989i
$844$	0.226215	+	0.391815i	0.00778663	+	0.0134868i
$845$	−0.973430	+	5.52060i	−0.0334870	+	0.189914i
$846$	9.02481	−	51.1823i	0.310280	−	1.75968i
$847$	1.04916	+	1.81720i	0.0360497	+	0.0624399i
$848$	−5.10220	+	8.83726i	−0.175210	+	0.303473i
$849$	−16.9572	−	14.2288i	−0.581971	−	0.488331i
$850$	−2.50387	−	0.911334i	−0.0858820	−	0.0312585i
$851$	12.5175	−	4.55601i	0.429096	−	0.156178i
$852$	−3.79292	+	3.18264i	−0.129943	+	0.109035i
$853$	−4.44568	−	25.2127i	−0.152217	−	0.863266i	−0.961286	−	0.275552i	$-0.911139\pi$
$853$	−4.44568	−	25.2127i	−0.152217	−	0.863266i	0.809069	−	0.587714i	$-0.199972\pi$
$854$	−4.27126			−0.146159
$855$	12.9214	−	15.6314i	0.441904	−	0.534584i
$856$	30.1257			1.02967
$857$	−3.66163	−	20.7661i	−0.125079	−	0.709357i	−0.981261	−	0.192683i	$-0.938281\pi$
$857$	−3.66163	−	20.7661i	−0.125079	−	0.709357i	0.856182	−	0.516674i	$-0.172830\pi$
$858$	−17.0326	+	14.2920i	−0.581482	+	0.487921i
$859$	18.3871	−	6.69237i	0.627361	−	0.228341i	−0.00872148	−	0.999962i	$-0.502776\pi$
$859$	18.3871	−	6.69237i	0.627361	−	0.228341i	0.636082	+	0.771621i	$0.280554\pi$
$860$	0.595800	+	0.216853i	0.0203166	+	0.00739464i
$861$	−1.89646	−	1.59132i	−0.0646312	−	0.0542320i
$862$	−25.8050	+	44.6956i	−0.878922	+	1.52234i
$863$	−2.47447	−	4.28591i	−0.0842319	−	0.145894i	0.820832	−	0.571170i	$-0.193510\pi$
$863$	−2.47447	−	4.28591i	−0.0842319	−	0.145894i	−0.905064	+	0.425276i	$0.860177\pi$
$864$	1.19341	−	6.76817i	0.0406007	−	0.230258i
$865$	−3.07604	+	17.4451i	−0.104588	+	0.593150i
$866$	−12.2139	−	21.1552i	−0.415047	−	0.718882i
$867$	−24.1596	+	41.8456i	−0.820502	+	1.42115i
$868$	0.349356	+	0.293144i	0.0118579	+	0.00994997i
$869$	−24.7849	−	9.02098i	−0.840771	−	0.306016i
$870$	22.0535	−	8.02682i	0.747684	−	0.272135i
$871$	15.1334	−	12.6984i	0.512776	−	0.430270i
$872$	−0.931790	−	5.28444i	−0.0315544	−	0.178954i
$873$	50.0164			1.69280
$874$	5.52166	+	14.8300i	0.186773	+	0.501633i
$875$	−2.81790			−0.0952623
$876$	0.128356	+	0.727940i	0.00433673	+	0.0245948i
$877$	0.934478	−	0.784120i	0.0315551	−	0.0264779i	−0.626874	−	0.779121i	$-0.715666\pi$
$877$	0.934478	−	0.784120i	0.0315551	−	0.0264779i	0.658429	+	0.752643i	$0.271221\pi$
$878$	−7.71095	+	2.80656i	−0.260232	+	0.0947167i
$879$	−28.4183	−	10.3434i	−0.958527	−	0.348875i
$880$	5.39440	+	4.52644i	0.181845	+	0.152586i
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	0.146609	+	0.989194i	$0.453164\pi$
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	−0.929972	+	0.367630i	$0.880169\pi$
$882$	−24.5194	−	42.4688i	−0.825610	−	1.43000i
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	−0.923472	−	0.383667i	$-0.874661\pi$
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	0.999001	−	0.0446828i	$-0.0142277\pi$
$884$	−0.0386476	+	0.219182i	−0.00129986	+	0.00737187i
$885$	−7.98293	−	13.8268i	−0.268343	−	0.464784i
$886$	−20.1374	+	34.8791i	−0.676531	+	1.17179i
$887$	−17.7909	−	14.9283i	−0.597359	−	0.501243i	0.293237	−	0.956040i	$-0.405268\pi$
$887$	−17.7909	−	14.9283i	−0.597359	−	0.501243i	−0.890595	+	0.454796i	$0.849712\pi$
$888$	39.3730	+	14.3306i	1.32127	+	0.480904i
$889$	−3.78699	+	1.37835i	−0.127012	+	0.0462284i
$890$	9.34002	−	7.83721i	0.313078	−	0.262704i
$891$	−1.20661	−	6.84305i	−0.0404231	−	0.229251i
$892$	1.57255			0.0526528
$893$	10.6493	−	29.9428i	0.356365	−	1.00200i
$894$	64.2404			2.14852
$895$	−1.75800	−	9.97011i	−0.0587634	−	0.333264i
$896$	−2.52687	+	2.12030i	−0.0844169	+	0.0708342i
$897$	−18.7665	+	6.83045i	−0.626596	+	0.228062i
$898$	−14.2429	−	5.18398i	−0.475291	−	0.172992i
$899$	37.4484	+	31.4229i	1.24897	+	1.04801i
$900$	−2.06624	+	3.57883i	−0.0688746	+	0.119294i
$901$	0.663848	+	1.14982i	0.0221160	+	0.0383060i
$902$	1.28968	−	7.31412i	0.0429416	−	0.243534i
$903$	−0.677519	+	3.84240i	−0.0225464	+	0.127867i
$904$	26.0326	+	45.0897i	0.865830	+	1.49966i
$905$	−3.75372	+	6.50163i	−0.124778	+	0.216122i
$906$	−12.9624	−	10.8768i	−0.430648	−	0.361357i
$907$	37.5847	+	13.6797i	1.24798	+	0.454228i	0.879719	−	0.475495i	$-0.157731\pi$
$907$	37.5847	+	13.6797i	1.24798	+	0.454228i	0.368261	+	0.929722i	$0.379953\pi$
$908$	−2.45723	+	0.894360i	−0.0815462	+	0.0296804i
$909$	−37.4864	+	31.4548i	−1.24334	+	1.04329i
$910$	−0.183915	−	1.04303i	−0.00609673	−	0.0345763i
$911$	−18.7997			−0.622863			−0.311431	−	0.950269i	$-0.600808\pi$
$911$	−18.7997			−0.622863			−0.311431	+	0.950269i	$0.600808\pi$
$912$	−15.1250	+	42.5270i	−0.500837	+	1.40821i
$913$	33.0232			1.09291
$914$	5.47225	+	31.0347i	0.181006	+	1.02654i
$915$	−17.7062	+	14.8573i	−0.585349	+	0.491166i
$916$	−3.56552	+	1.29774i	−0.117808	+	0.0428787i
$917$	−0.602196	−	0.219182i	−0.0198863	−	0.00723801i
$918$	3.18551	+	2.67296i	0.105137	+	0.0882208i
$919$	−19.9158	+	34.4952i	−0.656962	+	1.13789i	0.324436	+	0.945908i	$0.394825\pi$
$919$	−19.9158	+	34.4952i	−0.656962	+	1.13789i	−0.981398	+	0.191984i	$0.938508\pi$
$920$	3.48751	+	6.04055i	0.114980	+	0.199151i
$921$	5.84776	−	33.1643i	0.192690	−	1.09280i
$922$	8.56830	−	48.5932i	0.282182	−	1.60033i
$923$	11.9760	+	20.7430i	0.394193	+	0.682763i
$924$	0.205737	−	0.356347i	0.00676825	−	0.0117230i
$925$	−16.0064	−	13.4310i	−0.526287	−	0.441607i
$926$	−54.4227	−	19.8082i	−1.78844	−	0.650939i
$927$	27.3935	−	9.97043i	0.899721	−	0.327472i
$928$	5.49067	−	4.60722i	0.180240	−	0.151239i
$929$	4.68051	+	26.5445i	0.153563	+	0.870897i	0.960088	+	0.279698i	$0.0902342\pi$
$929$	4.68051	+	26.5445i	0.153563	+	0.870897i	−0.806526	+	0.591199i	$0.798655\pi$
$930$	−24.2422			−0.794932
$931$	−10.4632	−	28.1019i	−0.342916	−	0.921002i
$932$	−3.26176			−0.106843
$933$	−7.98293	−	45.2734i	−0.261349	−	1.48219i
$934$	−26.4176	+	22.1670i	−0.864411	+	0.725327i
$935$	0.860967	−	0.313366i	0.0281566	−	0.0102482i
$936$	−37.6695	−	13.7106i	−1.23127	−	0.448145i
$937$	2.00980	+	1.68642i	0.0656573	+	0.0550930i	0.675026	−	0.737794i	$-0.264133\pi$
$937$	2.00980	+	1.68642i	0.0656573	+	0.0550930i	−0.609368	+	0.792887i	$0.708577\pi$
$938$	1.79561	−	3.11008i	0.0586287	−	0.101548i
$939$	−38.3371	−	66.4018i	−1.25108	−	2.16694i
$940$	0.205737	−	1.16679i	0.00671040	−	0.0380566i
$941$	−3.24194	+	18.3860i	−0.105684	+	0.599366i	0.885260	+	0.465096i	$0.153980\pi$
$941$	−3.24194	+	18.3860i	−0.105684	+	0.599366i	−0.990945	+	0.134270i	$0.957131\pi$
$942$	18.6570	+	32.3149i	0.607879	+	1.05288i
$943$	3.33544	−	5.77715i	0.108617	−	0.188130i
$944$	17.3708	+	14.5758i	0.565370	+	0.474402i
$945$	1.89306	+	0.689016i	0.0615811	+	0.0224137i
$946$	−10.9991	+	4.00335i	−0.357612	+	0.130160i
$947$	6.43448	−	5.39917i	0.209092	−	0.175449i	−0.532227	−	0.846602i	$-0.678645\pi$
$947$	6.43448	−	5.39917i	0.209092	−	0.175449i	0.741320	+	0.671152i	$0.234200\pi$
$948$	−1.09446	−	6.20697i	−0.0355463	−	0.201593i
$949$	3.57573			0.116073
$950$	15.8150	−	19.1318i	0.513105	−	0.620718i
$951$	−85.0343			−2.75742
$952$	0.0830629	+	0.471073i	0.00269208	+	0.0152676i
$953$	25.8102	−	21.6573i	0.836075	−	0.701550i	−0.120602	−	0.992701i	$-0.538483\pi$
$953$	25.8102	−	21.6573i	0.836075	−	0.701550i	0.956677	+	0.291151i	$0.0940382\pi$
$954$	−19.0069	+	6.91793i	−0.615370	+	0.223976i
$955$	−15.1515	−	5.51470i	−0.490292	−	0.178452i
$956$	−0.332997	−	0.279418i	−0.0107699	−	0.00903701i
$957$	22.0535	−	38.1978i	0.712888	−	1.23476i
$958$	25.7173	+	44.5438i	0.830890	+	1.43914i
$959$	0.0154253	−	0.0874810i	0.000498108	−	0.00282491i
$960$	−3.77972	+	21.4358i	−0.121990	+	0.691838i
$961$	−9.74809	−	16.8842i	−0.314455	−	0.544651i
$962$	8.57192	−	14.8470i	0.276370	−	0.478686i
$963$	41.4805	+	34.8062i	1.33669	+	1.12162i
$964$	2.39646	+	0.872240i	0.0771848	+	0.0280930i
$965$	−0.245977	+	0.0895284i	−0.00791829	+	0.00288202i
$966$	−2.78106	+	2.33359i	−0.0894791	+	0.0750819i
$967$	2.03920	+	11.5649i	0.0655763	+	0.371902i	0.999881	+	0.0154262i	$0.00491051\pi$
$967$	2.03920	+	11.5649i	0.0655763	+	0.371902i	−0.934305	+	0.356475i	$0.883978\pi$
$968$	−17.7847			−0.571621
$969$	3.80793	+	4.47086i	0.122328	+	0.143625i
$970$	−11.2003			−0.359619
$971$	2.22432	+	12.6147i	0.0713817	+	0.404826i	0.999473	+	0.0324723i	$0.0103381\pi$
$971$	2.22432	+	12.6147i	0.0713817	+	0.404826i	−0.928091	+	0.372354i	$0.878551\pi$
$972$	−1.52931	+	1.28325i	−0.0490528	+	0.0411602i
$973$	−1.39141	+	0.506431i	−0.0446065	+	0.0162354i
$974$	9.82934	+	3.57759i	0.314953	+	0.114633i
$975$	23.9971	+	20.1359i	0.768521	+	0.644866i
$976$	16.4140	−	28.4299i	0.525399	−	0.910018i
$977$	−7.26382	−	12.5813i	−0.232390	−	0.402512i	0.726121	−	0.687567i	$-0.241321\pi$
$977$	−7.26382	−	12.5813i	−0.232390	−	0.402512i	−0.958511	+	0.285055i	$0.907988\pi$
$978$	5.62836	−	31.9200i	0.179975	−	1.02069i
$979$	3.97906	−	22.5663i	0.127171	−	0.721224i
$980$	−0.558963	−	0.968153i	−0.0178554	−	0.0309265i
$981$	4.82248	−	8.35278i	0.153970	−	0.266684i
$982$	37.9013	+	31.8029i	1.20948	+	1.01487i
$983$	34.8158	+	12.6719i	1.11045	+	0.404172i	0.831159	−	0.556034i	$-0.187678\pi$
$983$	34.8158	+	12.6719i	1.11045	+	0.404172i	0.279293	+	0.960206i	$0.409900\pi$
$984$	19.7173	−	7.17653i	0.628566	−	0.228779i
$985$	8.85251	−	7.42814i	0.282064	−	0.236680i
$986$	0.753089	+	4.27098i	0.0239832	+	0.136016i
$987$	7.29086			0.232071
$988$	−1.80313	−	1.02341i	−0.0573652	−	0.0325591i
$989$	−10.5134			−0.334307
$990$	2.42380	+	13.7461i	0.0770334	+	0.436878i
$991$	2.62860	−	2.20566i	0.0835004	−	0.0700651i	−0.600082	−	0.799938i	$-0.704865\pi$
$991$	2.62860	−	2.20566i	0.0835004	−	0.0700651i	0.683582	+	0.729873i	$0.260421\pi$
$992$	−6.95723	+	2.53223i	−0.220892	+	0.0803983i
$993$	74.8556	+	27.2452i	2.37547	+	0.864600i
$994$	3.33544	+	2.79876i	0.105794	+	0.0887714i
$995$	0.112874	−	0.195503i	0.00357835	−	0.00619788i
$996$	3.94562	+	6.83402i	0.125022	+	0.216544i
$997$	2.21853	−	12.5819i	0.0702616	−	0.398473i	−0.929313	−	0.369294i	$-0.879600\pi$
$997$	2.21853	−	12.5819i	0.0702616	−	0.398473i	0.999574	−	0.0291792i	$-0.00928933\pi$
$998$	−1.15254	+	6.53639i	−0.0364831	+	0.206906i
$999$	16.3045	+	28.2403i	0.515852	+	0.893483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.2.e.a.9.1	✓	6
3.2	odd	2		171.2.u.c.28.1		6
4.3	odd	2		304.2.u.b.161.1		6
5.2	odd	4		475.2.u.a.199.2		12
5.3	odd	4		475.2.u.a.199.1		12
5.4	even	2		475.2.l.a.351.1		6
7.2	even	3		931.2.x.a.655.1		6
7.3	odd	6		931.2.v.a.275.1		6
7.4	even	3		931.2.v.b.275.1		6
7.5	odd	6		931.2.x.b.655.1		6
7.6	odd	2		931.2.w.a.883.1		6
19.2	odd	18		361.2.e.h.245.1		6
19.3	odd	18		361.2.e.b.62.1		6
19.4	even	9		361.2.c.i.68.2		6
19.5	even	9		361.2.e.g.54.1		6
19.6	even	9		361.2.a.g.1.2		3
19.7	even	3		361.2.e.f.99.1		6
19.8	odd	6		361.2.e.a.234.1		6
19.9	even	9		361.2.c.i.292.2		6
19.10	odd	18		361.2.c.h.292.2		6
19.11	even	3		361.2.e.g.234.1		6
19.12	odd	6		361.2.e.b.99.1		6
19.13	odd	18		361.2.a.h.1.2		3
19.14	odd	18		361.2.e.a.54.1		6
19.15	odd	18		361.2.c.h.68.2		6
19.16	even	9		361.2.e.f.62.1		6
19.17	even	9	inner	19.2.e.a.17.1	yes	6
19.18	odd	2		361.2.e.h.28.1		6
57.17	odd	18		171.2.u.c.55.1		6
57.32	even	18		3249.2.a.s.1.2		3
57.44	odd	18		3249.2.a.z.1.2		3
76.51	even	18		5776.2.a.bi.1.1		3
76.55	odd	18		304.2.u.b.17.1		6
76.63	odd	18		5776.2.a.br.1.3		3
95.17	odd	36		475.2.u.a.74.1		12
95.44	even	18		9025.2.a.bd.1.2		3
95.74	even	18		475.2.l.a.226.1		6
95.89	odd	18		9025.2.a.x.1.2		3
95.93	odd	36		475.2.u.a.74.2		12
133.17	odd	18		931.2.x.b.226.1		6
133.55	odd	18		931.2.w.a.834.1		6
133.74	even	9		931.2.x.a.226.1		6
133.93	even	9		931.2.v.b.606.1		6
133.131	odd	18		931.2.v.a.606.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	1.1	even	1	trivial
19.2.e.a.17.1	yes	6	19.17	even	9	inner
171.2.u.c.28.1		6	3.2	odd	2
171.2.u.c.55.1		6	57.17	odd	18
304.2.u.b.17.1		6	76.55	odd	18
304.2.u.b.161.1		6	4.3	odd	2
361.2.a.g.1.2		3	19.6	even	9
361.2.a.h.1.2		3	19.13	odd	18
361.2.c.h.68.2		6	19.15	odd	18
361.2.c.h.292.2		6	19.10	odd	18
361.2.c.i.68.2		6	19.4	even	9
361.2.c.i.292.2		6	19.9	even	9
361.2.e.a.54.1		6	19.14	odd	18
361.2.e.a.234.1		6	19.8	odd	6
361.2.e.b.62.1		6	19.3	odd	18
361.2.e.b.99.1		6	19.12	odd	6
361.2.e.f.62.1		6	19.16	even	9
361.2.e.f.99.1		6	19.7	even	3
361.2.e.g.54.1		6	19.5	even	9
361.2.e.g.234.1		6	19.11	even	3
361.2.e.h.28.1		6	19.18	odd	2
361.2.e.h.245.1		6	19.2	odd	18
475.2.l.a.226.1		6	95.74	even	18
475.2.l.a.351.1		6	5.4	even	2
475.2.u.a.74.1		12	95.17	odd	36
475.2.u.a.74.2		12	95.93	odd	36
475.2.u.a.199.1		12	5.3	odd	4
475.2.u.a.199.2		12	5.2	odd	4
931.2.v.a.275.1		6	7.3	odd	6
931.2.v.a.606.1		6	133.131	odd	18
931.2.v.b.275.1		6	7.4	even	3
931.2.v.b.606.1		6	133.93	even	9
931.2.w.a.834.1		6	133.55	odd	18
931.2.w.a.883.1		6	7.6	odd	2
931.2.x.a.226.1		6	133.74	even	9
931.2.x.a.655.1		6	7.2	even	3
931.2.x.b.226.1		6	133.17	odd	18
931.2.x.b.655.1		6	7.5	odd	6
3249.2.a.s.1.2		3	57.32	even	18
3249.2.a.z.1.2		3	57.44	odd	18
5776.2.a.bi.1.1		3	76.51	even	18
5776.2.a.br.1.3		3	76.63	odd	18
9025.2.a.x.1.2		3	95.89	odd	18
9025.2.a.bd.1.2		3	95.44	even	18

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	19.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.233956 - 1.32683i) q^{2} +(-2.20574 + 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-0.173648 + 0.300767i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +O(q^{10})\)	\(q+(-0.233956 - 1.32683i) q^{2} +(-2.20574 + 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(-0.826352 - 0.300767i) q^{5} +(2.97178 + 2.49362i) q^{6} +(-0.173648 + 0.300767i) q^{7} +(-1.47178 - 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +(-0.205737 + 1.16679i) q^{10} +(1.11334 + 1.92836i) q^{11} +(-0.266044 + 0.460802i) q^{12} +(1.97178 + 1.65452i) q^{13} +(0.439693 + 0.160035i) q^{14} +(2.37939 - 0.866025i) q^{15} +(-2.75490 + 2.31164i) q^{16} +(0.0812519 + 0.460802i) q^{17} -7.12836 q^{18} +(-4.29813 - 0.725293i) q^{19} -0.162504 q^{20} +(-0.173648 - 0.984808i) q^{21} +(2.29813 - 1.92836i) q^{22} +(2.53209 - 0.921605i) q^{23} +(7.96451 + 2.89884i) q^{24} +(-3.23783 - 2.71686i) q^{25} +(1.73396 - 3.00330i) q^{26} +(3.29813 + 5.71253i) q^{27} +(-0.0111444 + 0.0632028i) q^{28} +(-1.19459 + 6.77487i) q^{29} +(-1.70574 - 2.95442i) q^{30} +(3.55303 - 6.15403i) q^{31} +(-0.798133 - 0.669713i) q^{32} +(-6.02481 - 2.19285i) q^{33} +(0.592396 - 0.215615i) q^{34} +(0.233956 - 0.196312i) q^{35} +(-0.169778 - 0.962858i) q^{36} +4.94356 q^{37} +(0.0432332 + 5.87257i) q^{38} -7.41147 q^{39} +(0.449493 + 2.54920i) q^{40} +(1.89646 - 1.59132i) q^{41} +(-1.26604 + 0.460802i) q^{42} +(-3.66637 - 1.33445i) q^{43} +(0.315207 + 0.264490i) q^{44} +(-2.32635 + 4.02936i) q^{45} +(-1.81521 - 3.14403i) q^{46} +(-1.26604 + 7.18009i) q^{47} +(1.79813 - 10.1977i) q^{48} +(3.43969 + 5.95772i) q^{49} +(-2.84730 + 4.93166i) q^{50} +(-1.03209 - 0.866025i) q^{51} +(0.446967 + 0.162683i) q^{52} +(2.66637 - 0.970481i) q^{53} +(6.80793 - 5.71253i) q^{54} +(-0.340022 - 1.92836i) q^{55} +1.02229 q^{56} +(10.8229 - 6.35532i) q^{57} +9.26857 q^{58} +(-1.09492 - 6.20961i) q^{59} +(0.358441 - 0.300767i) q^{60} +(-8.57785 + 3.12208i) q^{61} +(-8.99660 - 3.27449i) q^{62} +(1.40760 + 1.18112i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-1.13176 - 1.96026i) q^{65} +(-1.50000 + 8.50692i) q^{66} +(1.33275 - 7.55839i) q^{67} +(0.0432332 + 0.0748822i) q^{68} +(-3.87939 + 6.71929i) q^{69} +(-0.315207 - 0.264490i) q^{70} +(8.74422 + 3.18264i) q^{71} +(-14.6348 + 5.32661i) q^{72} +(1.06418 - 0.892951i) q^{73} +(-1.15657 - 6.55926i) q^{74} +12.1702 q^{75} +(-0.792204 + 0.145708i) q^{76} -0.773318 q^{77} +(1.73396 + 9.83375i) q^{78} +(-9.07398 + 7.61397i) q^{79} +(2.97178 - 1.08164i) q^{80} +(-2.93242 - 1.06731i) q^{81} +(-2.55509 - 2.14398i) q^{82} +(7.41534 - 12.8438i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(0.0714517 - 0.405223i) q^{85} +(-0.912818 + 5.17685i) q^{86} +(-9.90420 - 17.1546i) q^{87} +(3.27719 - 5.67626i) q^{88} +(-7.88326 - 6.61484i) q^{89} +(5.89053 + 2.14398i) q^{90} +(-0.840022 + 0.305743i) q^{91} +(0.381445 - 0.320070i) q^{92} +(3.55303 + 20.1503i) q^{93} +9.82295 q^{94} +(3.33363 + 1.89209i) q^{95} +3.00000 q^{96} +(1.64156 + 9.30975i) q^{97} +(7.10014 - 5.95772i) q^{98} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9	\( 6 q - 6 q^{2} - 3 q^{3} - 6 q^{5} + 3 q^{6} + 6 q^{8} + 3 q^{9} + 9 q^{10} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 3 q^{15} - 18 q^{16} + 3 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} + 6 q^{23} + 15 q^{24} + 15 q^{26} + 6 q^{27} + 6 q^{28} - 3 q^{29} + 9 q^{31} + 9 q^{32} - 9 q^{33} + 6 q^{35} - 24 q^{36} - 15 q^{38} - 24 q^{39} + 21 q^{41} - 3 q^{42} - 3 q^{43} + 9 q^{44} - 15 q^{45} - 18 q^{46} - 3 q^{47} - 3 q^{48} + 15 q^{49} - 15 q^{50} + 3 q^{51} + 15 q^{52} - 3 q^{53} + 30 q^{54} + 18 q^{55} - 6 q^{56} + 24 q^{57} + 36 q^{58} + 12 q^{59} - 6 q^{60} - 12 q^{61} - 12 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{65} - 9 q^{66} - 30 q^{67} - 15 q^{68} - 12 q^{69} - 9 q^{70} - 6 q^{71} - 12 q^{72} - 12 q^{73} + 15 q^{74} + 30 q^{75} + 36 q^{76} - 18 q^{77} + 15 q^{78} - 39 q^{79} + 3 q^{80} + 6 q^{81} - 54 q^{82} + 3 q^{84} + 24 q^{86} - 21 q^{87} + 9 q^{88} - 12 q^{89} + 18 q^{90} + 15 q^{91} + 42 q^{92} + 9 q^{93} + 18 q^{94} + 39 q^{95} + 18 q^{96} + 18 q^{97} - 9 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 3 * q^3 - 6 * q^5 + 3 * q^6 + 6 * q^8 + 3 * q^9 + 9 * q^10 + 3 * q^12 - 3 * q^13 - 3 * q^14 + 3 * q^15 - 18 * q^16 + 3 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 + 6 * q^23 + 15 * q^24 + 15 * q^26 + 6 * q^27 + 6 * q^28 - 3 * q^29 + 9 * q^31 + 9 * q^32 - 9 * q^33 + 6 * q^35 - 24 * q^36 - 15 * q^38 - 24 * q^39 + 21 * q^41 - 3 * q^42 - 3 * q^43 + 9 * q^44 - 15 * q^45 - 18 * q^46 - 3 * q^47 - 3 * q^48 + 15 * q^49 - 15 * q^50 + 3 * q^51 + 15 * q^52 - 3 * q^53 + 30 * q^54 + 18 * q^55 - 6 * q^56 + 24 * q^57 + 36 * q^58 + 12 * q^59 - 6 * q^60 - 12 * q^61 - 12 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^65 - 9 * q^66 - 30 * q^67 - 15 * q^68 - 12 * q^69 - 9 * q^70 - 6 * q^71 - 12 * q^72 - 12 * q^73 + 15 * q^74 + 30 * q^75 + 36 * q^76 - 18 * q^77 + 15 * q^78 - 39 * q^79 + 3 * q^80 + 6 * q^81 - 54 * q^82 + 3 * q^84 + 24 * q^86 - 21 * q^87 + 9 * q^88 - 12 * q^89 + 18 * q^90 + 15 * q^91 + 42 * q^92 + 9 * q^93 + 18 * q^94 + 39 * q^95 + 18 * q^96 + 18 * q^97 - 9 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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