LMFDB - Embedded newform 19.2.e.a.17.1

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			17.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	19.17
Dual form			19.2.e.a.9.1

$q$-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 $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	0.783187	+	0.621786i	$0.213593\pi$
$2$	−0.233956	+	1.32683i	−0.165432	+	0.938209i	−0.948618	+	0.316423i	$0.897518\pi$
$3$	−2.20574	−	1.85083i	−1.27348	−	1.06858i	−0.994108	−	0.108397i	$-0.965428\pi$
$3$	−2.20574	−	1.85083i	−1.27348	−	1.06858i	−0.279375	−	0.960182i	$-0.590127\pi$
$4$	0.173648	+	0.0632028i	0.0868241	+	0.0316014i
$5$	−0.826352	+	0.300767i	−0.369556	+	0.134507i	−0.520121	−	0.854093i	$-0.674113\pi$
$5$	−0.826352	+	0.300767i	−0.369556	+	0.134507i	0.150565	+	0.988600i	$0.451891\pi$
$6$	2.97178	−	2.49362i	1.21322	−	1.01802i
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	0.831342	−	0.555762i	$-0.187573\pi$
$7$	−0.173648	−	0.300767i	−0.0656328	−	0.113679i	−0.896975	+	0.442082i	$0.854240\pi$
$8$	−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	−0.647931	−	0.761699i	$-0.724366\pi$
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	0.983616	+	0.180276i	$0.0576989\pi$
$12$	−0.266044	−	0.460802i	−0.0768004	−	0.133022i
$13$	1.97178	−	1.65452i	0.546874	−	0.458882i	−0.327007	−	0.945022i	$-0.606040\pi$
$13$	1.97178	−	1.65452i	0.546874	−	0.458882i	0.873881	+	0.486140i	$0.161596\pi$
$14$	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	−0.973368	−	0.229249i	$-0.926373\pi$
$17$	0.0812519	−	0.460802i	0.0197065	−	0.111761i	0.993074	+	0.117488i	$0.0374841\pi$
$18$	−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	0.592235	−	0.805765i	$-0.298246\pi$
$23$	2.53209	+	0.921605i	0.527977	+	0.192168i	−0.0642578	+	0.997933i	$0.520468\pi$
$24$	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	−0.868653	−	0.495421i	$-0.835014\pi$
$29$	−1.19459	−	6.77487i	−0.221830	−	1.25806i	0.646822	−	0.762641i	$-0.276097\pi$
$30$	−1.70574	+	2.95442i	−0.311424	+	0.539401i
$31$	3.55303	+	6.15403i	0.638144	+	1.10530i	0.985840	+	0.167690i	$0.0536307\pi$
$31$	3.55303	+	6.15403i	0.638144	+	1.10530i	−0.347696	+	0.937607i	$0.613036\pi$
$32$	−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	0.778751	−	0.627333i	$-0.215854\pi$
$41$	1.89646	+	1.59132i	0.296177	+	0.248522i	−0.482574	+	0.875855i	$0.660298\pi$
$42$	−1.26604	−	0.460802i	−0.195355	−	0.0711034i
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	−0.606093	−	0.795394i	$-0.707264\pi$
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	0.0469757	+	0.998896i	$0.485042\pi$
$44$	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	−0.926377	−	0.376598i	$-0.877094\pi$
$47$	−1.26604	−	7.18009i	−0.184672	−	1.04732i	0.741705	−	0.670726i	$-0.234017\pi$
$48$	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	0.518590	−	0.855023i	$-0.326457\pi$
$53$	2.66637	+	0.970481i	0.366255	+	0.133306i	−0.152335	+	0.988329i	$0.548679\pi$
$54$	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	0.826757	+	0.562559i	$0.190183\pi$
$59$	−1.09492	+	6.20961i	−0.142547	+	0.808423i	−0.969304	+	0.245864i	$0.920928\pi$
$60$	0.358441	+	0.300767i	0.0462745	+	0.0388289i
$61$	−8.57785	−	3.12208i	−1.09828	−	0.399742i	−0.271599	−	0.962411i	$-0.587552\pi$
$61$	−8.57785	−	3.12208i	−1.09828	−	0.399742i	−0.826682	+	0.562669i	$0.809775\pi$
$62$	−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	0.951283	+	0.308320i	$0.0997669\pi$
$67$	1.33275	+	7.55839i	0.162821	+	0.923405i	−0.788461	+	0.615084i	$0.789122\pi$
$68$	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	0.233722	−	0.972303i	$-0.424909\pi$
$71$	8.74422	−	3.18264i	1.03775	−	0.377709i	0.804026	+	0.594594i	$0.202687\pi$
$72$	−14.6348	−	5.32661i	−1.72472	−	0.627748i
$73$	1.06418	+	0.892951i	0.124553	+	0.104512i	0.702936	−	0.711253i	$-0.251872\pi$
$73$	1.06418	+	0.892951i	0.124553	+	0.104512i	−0.578384	+	0.815765i	$0.696316\pi$
$74$	−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	−0.0311616	−	0.999514i	$-0.509921\pi$
$79$	−9.07398	−	7.61397i	−1.02090	−	0.856639i	−0.989741	+	0.142876i	$0.954365\pi$
$80$	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	0.910087	+	0.414418i	$0.136015\pi$
$83$	7.41534	+	12.8438i	0.813940	+	1.40979i	−0.0961469	+	0.995367i	$0.530652\pi$
$84$	−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	−0.956575	−	0.291487i	$-0.905850\pi$
$89$	−7.88326	+	6.61484i	−0.835623	+	0.701171i	0.120951	+	0.992658i	$0.461406\pi$
$90$	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	−0.780645	−	0.624974i	$-0.785109\pi$
$97$	1.64156	−	9.30975i	0.166675	−	0.945261i	0.947320	−	0.320287i	$-0.103779\pi$
$98$	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	−0.923190	−	0.384343i	$-0.874428\pi$
$101$	−7.08512	+	5.94512i	−0.704996	+	0.591562i	0.218194	+	0.975905i	$0.429983\pi$
$102$	−0.907604	−	1.57202i	−0.0898662	−	0.155653i
$103$	2.75490	−	4.77163i	0.271448	−	0.470162i	−0.697785	−	0.716308i	$-0.745831\pi$
$103$	2.75490	−	4.77163i	0.271448	−	0.470162i	0.969233	+	0.246145i	$0.0791640\pi$
$104$	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	0.505282	−	0.862954i	$-0.331389\pi$
$107$	−5.11721	−	8.86327i	−0.494699	−	0.856845i	−0.999981	+	0.00610974i	$0.998055\pi$
$108$	0.933763	−	0.783520i	0.0898514	−	0.0753943i
$109$	1.71301	−	0.623485i	0.164077	−	0.0597190i	−0.258676	−	0.965964i	$-0.583286\pi$
$109$	1.71301	−	0.623485i	0.164077	−	0.0597190i	0.422753	+	0.906245i	$0.361064\pi$
$110$	−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	−0.156657	−	0.987653i	$-0.550072\pi$
$127$	8.88919	−	7.45891i	0.788788	−	0.661871i	0.945445	+	0.325782i	$0.105627\pi$
$128$	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	−0.967605	−	0.252468i	$-0.918758\pi$
$131$	0.320422	−	1.81720i	0.0279954	−	0.158770i	0.995601	+	0.0936982i	$0.0298689\pi$
$132$	−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	0.331732	−	0.943374i	$-0.392367\pi$
$137$	−0.240352	−	0.0874810i	−0.0205347	−	0.00747401i	−0.352267	+	0.935900i	$0.614589\pi$
$138$	9.82295	−	3.57526i	0.836185	−	0.304346i
$139$	3.26604	−	2.74054i	0.277022	−	0.232449i	−0.493682	−	0.869643i	$-0.664349\pi$
$139$	3.26604	−	2.74054i	0.277022	−	0.232449i	0.770704	+	0.637193i	$0.219905\pi$
$140$	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	0.991919	−	0.126874i	$-0.0404945\pi$
$149$	12.6853	+	10.6442i	1.03922	+	0.872007i	0.0472981	+	0.998881i	$0.484939\pi$
$150$	−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	0.0448510	−	0.998994i	$-0.485719\pi$
$157$	9.03849	−	3.28974i	0.721350	−	0.262550i	0.676499	+	0.736444i	$0.263496\pi$
$158$	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	−0.981957	−	0.189105i	$-0.939441\pi$
$163$	−4.17752	+	7.23567i	−0.327209	+	0.566742i	0.654748	+	0.755847i	$0.272775\pi$
$164$	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	0.191120	−	0.981567i	$-0.438788\pi$
$167$	−3.79174	−	1.38008i	−0.293413	−	0.106794i	−0.484533	+	0.874773i	$0.661010\pi$
$168$	−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	0.500391	+	0.865799i	$0.333189\pi$
$173$	−3.49794	+	19.8378i	−0.265943	+	1.50824i	−0.766335	+	0.642441i	$0.777922\pi$
$174$	−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	−0.566652	−	0.823957i	$-0.691762\pi$
$179$	5.75624	−	9.97011i	0.430242	−	0.745201i	0.996894	+	0.0787564i	$0.0250949\pi$
$180$	−0.149300	−	0.846723i	−0.0111282	−	0.0631110i
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	0.989020	+	0.147784i	$0.0472141\pi$
$181$	1.48246	+	8.40744i	0.110190	+	0.624920i	−0.878829	+	0.477136i	$0.841675\pi$
$182$	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	0.650958	−	0.759114i	$-0.274368\pi$
$193$	0.228026	+	0.191336i	0.0164137	+	0.0137727i	−0.634544	+	0.772887i	$0.718812\pi$
$194$	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	0.531203	−	0.847245i	$-0.321740\pi$
$197$	−6.57057	−	11.3806i	−0.468134	−	0.810832i	−0.999337	+	0.0364128i	$0.988407\pi$
$198$	−7.93629	+	13.7461i	−0.564008	+	0.976890i
$199$	−0.0445774	−	0.252811i	−0.00316001	−	0.0179213i	0.983187	−	0.182602i	$-0.0584519\pi$
$199$	−0.0445774	−	0.252811i	−0.00316001	−	0.0179213i	−0.986347	+	0.164680i	$0.947341\pi$
$200$	−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	−0.966670	−	0.256024i	$-0.917587\pi$
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	0.995938	+	0.0900364i	$0.0286983\pi$
$212$	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	−0.0600971	−	0.998193i	$-0.519141\pi$
$223$	7.99660	−	2.91052i	0.535492	−	0.194903i	0.595589	+	0.803289i	$0.296919\pi$
$224$	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	−0.822366	−	0.568959i	$-0.807346\pi$
$233$	−16.5865	+	6.03698i	−1.08662	+	0.395496i	−0.264249	+	0.964454i	$0.585124\pi$
$234$	−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	−0.901556	−	0.432663i	$-0.857574\pi$
$239$	−1.17617	+	2.03719i	−0.0760804	+	0.131775i	0.825475	+	0.564438i	$0.190907\pi$
$240$	−4.55303	−	7.88609i	−0.293897	−	0.509045i
$241$	10.5719	−	8.87089i	0.680997	−	0.571424i	−0.235300	−	0.971923i	$-0.575607\pi$
$241$	10.5719	−	8.87089i	0.680997	−	0.571424i	0.916298	+	0.400498i	$0.131163\pi$
$242$	−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	0.462577	−	0.886579i	$-0.346925\pi$
$251$	3.91400	+	1.42458i	0.247050	+	0.0899187i	−0.215528	+	0.976498i	$0.569147\pi$
$252$	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	0.988208	−	0.153116i	$-0.0489307\pi$
$257$	0.115867	+	0.657115i	0.00722759	+	0.0409897i	−0.980981	+	0.194105i	$0.937820\pi$
$258$	−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	0.871016	−	0.491254i	$-0.163461\pi$
$263$	8.73261	+	7.32753i	0.538476	+	0.451835i	−0.332540	+	0.943089i	$0.607906\pi$
$264$	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	0.971286	−	0.237916i	$-0.0764644\pi$
$269$	14.8537	+	12.4637i	0.905646	+	0.759927i	−0.0656400	+	0.997843i	$0.520909\pi$
$270$	−7.34389	−	2.67296i	−0.446935	−	0.162671i
$271$	12.5865	−	4.58110i	0.764573	−	0.278282i	0.0698486	−	0.997558i	$-0.477748\pi$
$271$	12.5865	−	4.58110i	0.764573	−	0.278282i	0.694725	+	0.719276i	$0.255526\pi$
$272$	−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	0.466096	+	0.884734i	$0.345660\pi$
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	−0.999250	+	0.0387161i	$0.987673\pi$
$278$	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	−0.225622	−	0.974215i	$-0.572442\pi$
$281$	−17.1766	−	6.25179i	−1.02467	−	0.372950i	−0.799050	+	0.601265i	$0.794664\pi$
$282$	−21.6668	−	18.1806i	−1.29024	−	1.08264i
$283$	1.33497	−	7.57099i	0.0793557	−	0.450049i	−0.919077	−	0.394079i	$-0.871064\pi$
$283$	1.33497	−	7.57099i	0.0793557	−	0.450049i	0.998432	−	0.0559700i	$-0.0178251\pi$
$284$	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	−0.670864	−	0.741581i	$-0.734076\pi$
$293$	5.25150	−	9.09586i	0.306796	−	0.531386i	0.977660	+	0.210195i	$0.0674098\pi$
$294$	−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	0.350264	−	0.936651i	$-0.386092\pi$
$307$	−8.95929	−	7.51774i	−0.511334	−	0.429060i	−0.861598	+	0.507591i	$0.830536\pi$
$308$	−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	0.545881	−	0.837863i	$-0.316195\pi$
$311$	−7.98293	−	13.8268i	−0.452670	−	0.784048i	−0.998551	+	0.0538151i	$0.982862\pi$
$312$	10.9081	−	18.8933i	0.617548	−	1.06962i
$313$	−4.62402	−	26.2241i	−0.261365	−	1.48227i	−0.779190	−	0.626788i	$-0.784369\pi$
$313$	−4.62402	−	26.2241i	−0.261365	−	1.48227i	0.517825	−	0.855487i	$-0.326742\pi$
$314$	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	0.276164	−	0.961111i	$-0.410937\pi$
$317$	22.6229	−	18.9829i	1.27063	−	1.06618i	0.994465	−	0.105073i	$-0.0335077\pi$
$318$	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	0.182371	+	0.983230i	$0.441623\pi$
$331$	−13.8327	+	23.9590i	−0.760317	+	1.31691i	−0.942687	+	0.333677i	$0.891710\pi$
$332$	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	−0.755934	−	0.654648i	$-0.772817\pi$
$337$	−16.7827	+	6.10841i	−0.914212	+	0.332746i	−0.158279	+	0.987394i	$0.550594\pi$
$338$	−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	−0.191541	−	0.981485i	$-0.561348\pi$
$347$	5.45084	−	1.98394i	0.292616	−	0.106504i	0.484157	+	0.874981i	$0.339126\pi$
$348$	−2.80406	+	2.35289i	−0.150314	+	0.126128i
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	0.785134	−	0.619326i	$-0.212594\pi$
$349$	−2.68614	−	4.65253i	−0.143786	−	0.249044i	−0.928919	+	0.370282i	$0.879261\pi$
$350$	−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	−0.305919	−	0.952057i	$-0.598964\pi$
$353$	12.6172	−	21.8537i	0.671546	−	1.16315i	0.977466	−	0.211095i	$-0.0677029\pi$
$354$	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	−0.938712	−	0.344702i	$-0.887980\pi$
$359$	1.16116	−	6.58526i	0.0612837	−	0.347557i	0.999996	−	0.00285518i	$-0.000908833\pi$
$360$	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	−0.465865	−	0.884856i	$-0.654257\pi$
$367$	6.21941	−	5.21870i	0.324650	−	0.272414i	0.790516	+	0.612441i	$0.209812\pi$
$368$	−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	−0.822967	−	0.568090i	$-0.807683\pi$
$373$	−17.4488	−	30.2222i	−0.903463	−	1.56484i	−0.0804968	−	0.996755i	$-0.525651\pi$
$374$	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	0.698453	−	0.715656i	$-0.253872\pi$
$383$	2.24969	+	1.88771i	0.114954	+	0.0964575i	−0.583499	+	0.812114i	$0.698317\pi$
$384$	−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	−0.878642	−	0.477482i	$-0.841550\pi$
$389$	−4.26604	−	24.1939i	−0.216297	−	1.22668i	0.662344	−	0.749199i	$-0.269562\pi$
$390$	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	0.453606	+	0.891202i	$0.350137\pi$
$397$	−5.52822	+	31.3521i	−0.277453	+	1.57352i	−0.731059	+	0.682314i	$0.760974\pi$
$398$	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	−0.985180	−	0.171522i	$-0.945132\pi$
$401$	−0.0150147	+	0.0851529i	−0.000749801	+	0.00425233i	0.984431	+	0.175774i	$0.0562428\pi$
$402$	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	0.941797	+	0.336182i	$0.109136\pi$
$409$	3.47400	+	19.7021i	0.171778	+	0.974204i	−0.770019	+	0.638021i	$0.779753\pi$
$410$	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	0.720702	−	0.693245i	$-0.243820\pi$
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	−0.557565	+	0.830134i	$0.688264\pi$
$422$	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	−0.458736	+	0.888572i	$0.651698\pi$
$431$	−29.3444	+	24.6228i	−1.41347	+	1.18604i	−0.954732	+	0.297468i	$0.903858\pi$
$432$	−22.2913	+	8.11338i	−1.07249	+	0.390355i
$433$	17.0376	+	6.20118i	0.818775	+	0.298010i	0.717244	−	0.696823i	$-0.245403\pi$
$433$	17.0376	+	6.20118i	0.818775	+	0.298010i	0.101532	+	0.994832i	$0.467626\pi$
$434$	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	−0.999589	−	0.0286685i	$-0.990873\pi$
$439$	−1.05762	+	5.99806i	−0.0504774	+	0.286272i	0.949112	+	0.314940i	$0.101984\pi$
$440$	−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	−0.996559	−	0.0828833i	$-0.973587\pi$
$443$	−22.8995	+	19.2149i	−1.08799	+	0.912928i	−0.0914266	+	0.995812i	$0.529143\pi$
$444$	−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	0.967683	−	0.252168i	$-0.0811435\pi$
$449$	5.62495	+	9.74270i	0.265458	+	0.459787i	−0.702226	+	0.711955i	$0.747810\pi$
$450$	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	0.622853	−	0.782339i	$-0.285974\pi$
$461$	34.4149	−	12.5260i	1.60286	−	0.583395i	0.980011	+	0.198945i	$0.0637514\pi$
$462$	−2.29813	+	1.92836i	−0.106919	+	0.0897156i
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.540534	+	0.841322i	$0.318222\pi$
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.458340	+	0.888777i	$0.348444\pi$
$464$	−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	0.401705	+	0.915769i	$0.368418\pi$
$467$	−12.7981	+	22.1670i	−0.592227	+	1.02577i	−0.993932	+	0.109998i	$0.964916\pi$
$468$	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	−0.652236	−	0.758016i	$-0.726169\pi$
$479$	−35.8739	−	13.0570i	−1.63912	−	0.596591i	−0.986885	+	0.161424i	$0.948391\pi$
$480$	−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	0.764568	−	0.644543i	$-0.222952\pi$
$487$	−3.88191	−	6.72367i	−0.175906	−	0.304678i	−0.940475	+	0.339864i	$0.889619\pi$
$488$	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	−0.994596	−	0.103822i	$-0.966893\pi$
$491$	−28.1313	−	23.6050i	−1.26955	−	1.06528i	−0.274954	−	0.961457i	$-0.588663\pi$
$492$	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	−0.443551	−	0.896249i	$-0.646281\pi$
$499$	−4.62923	+	1.68490i	−0.207233	+	0.0754266i	0.236318	+	0.971676i	$0.424059\pi$
$500$	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	0.795778	+	0.605589i	$0.207062\pi$
$503$	5.72163	+	32.4490i	0.255115	+	1.44683i	−0.540663	+	0.841239i	$0.681827\pi$
$504$	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	0.965657	−	0.259819i	$-0.0836630\pi$
$509$	34.7075	+	12.6325i	1.53839	+	0.559926i	0.572728	+	0.819746i	$0.305885\pi$
$510$	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	−0.949667	−	0.313262i	$-0.898578\pi$
$521$	−4.64590	+	8.04693i	−0.203540	+	0.352542i	0.746126	+	0.665804i	$0.231912\pi$
$522$	8.51548	+	48.2937i	0.372713	+	2.11376i
$523$	−4.93423	−	27.9834i	−0.215759	−	1.22363i	−0.879585	−	0.475742i	$-0.842180\pi$
$523$	−4.93423	−	27.9834i	−0.215759	−	1.22363i	0.663826	−	0.747887i	$-0.268932\pi$
$524$	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	0.988249	+	0.152852i	$0.0488458\pi$
$541$	2.60220	+	14.7578i	0.111877	+	0.634487i	−0.876372	+	0.481635i	$0.840043\pi$
$542$	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	0.418926	−	0.908020i	$-0.362407\pi$
$547$	3.65270	+	1.32948i	0.156178	+	0.0568443i	−0.262748	+	0.964864i	$0.584629\pi$
$548$	−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	−0.402828	−	0.915276i	$-0.631973\pi$
$557$	10.1152	−	8.48762i	0.428593	−	0.359632i	0.831420	+	0.555644i	$0.187528\pi$
$558$	−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	0.730798	−	0.682594i	$-0.239148\pi$
$563$	−5.35638	−	9.27752i	−0.225745	−	0.391001i	−0.956543	+	0.291593i	$0.905815\pi$
$564$	−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	0.954714	−	0.297526i	$-0.0961613\pi$
$577$	5.27719	+	9.14036i	0.219692	+	0.380518i	−0.735022	+	0.678044i	$0.762828\pi$
$578$	−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	0.835954	+	0.548800i	$0.184915\pi$
$587$	−3.32619	+	18.8638i	−0.137287	+	0.778591i	−0.973240	+	0.229791i	$0.926196\pi$
$588$	−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	0.504282	−	0.863539i	$-0.331757\pi$
$593$	8.17024	+	2.97373i	0.335512	+	0.122116i	−0.168770	+	0.985655i	$0.553980\pi$
$594$	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	0.970715	+	0.240236i	$0.0772248\pi$
$599$	3.44373	+	19.5303i	0.140707	+	0.797988i	−0.830008	+	0.557752i	$0.811664\pi$
$600$	−17.9119	+	31.0244i	−0.731252	+	1.26657i
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	0.972298	+	0.233747i	$0.0750986\pi$
$601$	16.8807	+	29.2383i	0.688579	+	1.19265i	−0.283718	+	0.958908i	$0.591568\pi$
$602$	−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	−0.667571	−	0.744546i	$-0.732666\pi$
$613$	−17.3405	+	6.31142i	−0.700376	+	0.254916i	−0.0328044	+	0.999462i	$0.510444\pi$
$614$	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	−0.809878	−	0.586598i	$-0.800467\pi$
$617$	−6.19671	−	35.1433i	−0.249470	−	1.41482i	0.560408	−	0.828217i	$-0.310644\pi$
$618$	−3.71167	−	21.0499i	−0.149305	−	0.846752i
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	−0.900452	−	0.434955i	$-0.856764\pi$
$619$	−1.82976	+	3.16923i	−0.0735441	+	0.127382i	0.826908	+	0.562337i	$0.190098\pi$
$620$	−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	0.356826	−	0.934171i	$-0.383859\pi$
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	−0.327129	+	0.944980i	$0.606081\pi$
$632$	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	−0.823823	−	0.566847i	$-0.808163\pi$
$641$	−27.6104	+	10.0494i	−1.09055	+	0.396926i	−0.266723	+	0.963773i	$0.585941\pi$
$642$	−37.3089	−	13.5793i	−1.47246	−	0.535933i
$643$	17.0168	+	14.2788i	0.671078	+	0.563101i	0.913384	−	0.407098i	$-0.133459\pi$
$643$	17.0168	+	14.2788i	0.671078	+	0.563101i	−0.242306	+	0.970200i	$0.577904\pi$
$644$	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	−0.999456	−	0.0329874i	$-0.989498\pi$
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	0.471160	−	0.882048i	$-0.343835\pi$
$654$	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	−0.120415	−	0.992724i	$-0.538423\pi$
$659$	21.4691	−	18.0147i	0.836317	−	0.701753i	0.956732	+	0.290970i	$0.0939781\pi$
$660$	0.979055	−	0.356347i	0.0381097	−	0.0138708i
$661$	−10.6823	−	3.88803i	−0.415492	−	0.151227i	0.125811	−	0.992054i	$-0.459847\pi$
$661$	−10.6823	−	3.88803i	−0.415492	−	0.151227i	−0.541303	+	0.840827i	$0.682069\pi$
$662$	−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	−0.661035	−	0.750355i	$-0.729883\pi$
$673$	8.28359	−	14.3476i	0.319309	−	0.553059i	0.980344	+	0.197296i	$0.0632160\pi$
$674$	−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	0.939781	−	0.341777i	$-0.111029\pi$
$677$	4.52481	+	7.83721i	0.173903	+	0.301208i	−0.765878	+	0.642986i	$0.777695\pi$
$678$	−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	−0.980508	−	0.196478i	$-0.937050\pi$
$691$	−17.3601	−	30.0686i	−0.660409	−	1.14386i	0.320099	−	0.947384i	$-0.396284\pi$
$692$	−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	−0.528397	−	0.848997i	$-0.677207\pi$
$701$	6.84436	−	38.8163i	0.258508	−	1.46607i	0.786905	−	0.617074i	$-0.211682\pi$
$702$	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	−0.183088	+	0.983096i	$0.558609\pi$
$709$	−31.5009	+	26.4324i	−1.18304	+	0.992690i	−0.999954	+	0.00959399i	$0.996946\pi$
$710$	−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	−0.999238	−	0.0390200i	$-0.987576\pi$
$719$	−32.4768	−	27.2513i	−1.21118	−	1.01630i	−0.211943	−	0.977282i	$-0.567979\pi$
$720$	−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	−0.801965	+	0.597371i	$0.796212\pi$
$727$	−48.5411	+	17.6675i	−1.80029	+	0.655251i	−0.998324	+	0.0578805i	$0.981566\pi$
$728$	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	−0.573037	−	0.819530i	$-0.694235\pi$
$733$	11.4581	−	19.8460i	0.423215	−	0.733030i	0.996252	+	0.0864997i	$0.0275682\pi$
$734$	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	−0.752954	−	0.658074i	$-0.771372\pi$
$739$	4.88413	−	27.6993i	0.179666	−	1.01894i	0.932619	−	0.360862i	$-0.117517\pi$
$740$	−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	−0.959024	−	0.283326i	$-0.908562\pi$
$743$	1.06489	−	6.03931i	0.0390671	−	0.221561i	0.998091	+	0.0617657i	$0.0196731\pi$
$744$	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	0.997450	−	0.0713710i	$-0.0227374\pi$
$751$	0.979522	+	5.55515i	0.0357433	+	0.202710i	−0.961707	+	0.274081i	$0.911626\pi$
$752$	−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	0.834548	−	0.550936i	$-0.185729\pi$
$757$	12.0207	+	10.0866i	0.436900	+	0.366602i	−0.397648	+	0.917538i	$0.630173\pi$
$758$	−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	0.970421	+	0.241420i	$0.0776131\pi$
$769$	3.91266	+	22.1898i	0.141094	+	0.800184i	−0.829327	+	0.558764i	$0.811276\pi$
$770$	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	−0.929660	−	0.368418i	$-0.879900\pi$
$773$	−20.2481	+	16.9902i	−0.728273	+	0.611094i	0.201387	+	0.979512i	$0.435455\pi$
$774$	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	−0.693424	−	0.720530i	$-0.743899\pi$
$787$	7.77884	−	13.4733i	0.277286	−	0.480273i	0.970709	+	0.240257i	$0.0772318\pi$
$788$	−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	0.237096	+	0.971486i	$0.423804\pi$
$809$	−20.5581	+	35.6076i	−0.722784	+	1.25190i	−0.959880	+	0.280412i	$0.909529\pi$
$810$	1.84864	+	3.20194i	0.0649546	+	0.112505i
$811$	12.7836	−	10.7267i	0.448892	−	0.376665i	−0.390132	−	0.920759i	$-0.627571\pi$
$811$	12.7836	−	10.7267i	0.448892	−	0.376665i	0.839025	+	0.544093i	$0.183126\pi$
$812$	−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	0.800873	−	0.598834i	$-0.204369\pi$
$821$	29.4971	+	10.7361i	1.02945	+	0.374691i	0.228581	+	0.973525i	$0.426591\pi$
$822$	−0.932419	+	0.339373i	−0.0325218	+	0.0118370i
$823$	35.4877	−	29.7777i	1.23702	−	1.03799i	0.239274	−	0.970952i	$-0.423091\pi$
$823$	35.4877	−	29.7777i	1.23702	−	1.03799i	0.997751	−	0.0670347i	$-0.0213538\pi$
$824$	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	0.817888	+	0.575377i	$0.195145\pi$
$827$	7.07769	+	40.1396i	0.246115	+	1.39579i	−0.571773	+	0.820412i	$0.693744\pi$
$828$	−1.31727	+	2.28157i	−0.0457782	+	0.0792901i
$829$	17.7417	+	30.7295i	0.616195	+	1.06728i	0.990174	+	0.139843i	$0.0446598\pi$
$829$	17.7417	+	30.7295i	0.616195	+	1.06728i	−0.373979	+	0.927437i	$0.622007\pi$
$830$	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	−0.0219545	−	0.999759i	$-0.506989\pi$
$839$	−29.2649	−	24.5562i	−1.01034	−	0.847774i	−0.988383	+	0.151985i	$0.951433\pi$
$840$	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	0.809069	+	0.587714i	$0.199972\pi$
$853$	−4.44568	+	25.2127i	−0.152217	+	0.863266i	−0.961286	+	0.275552i	$0.911139\pi$
$854$	−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	0.856182	+	0.516674i	$0.172830\pi$
$857$	−3.66163	+	20.7661i	−0.125079	+	0.709357i	−0.981261	+	0.192683i	$0.938281\pi$
$858$	−17.0326	−	14.2920i	−0.581482	−	0.487921i
$859$	18.3871	+	6.69237i	0.627361	+	0.228341i	0.636082	−	0.771621i	$-0.280554\pi$
$859$	18.3871	+	6.69237i	0.627361	+	0.228341i	−0.00872148	+	0.999962i	$0.502776\pi$
$860$	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	−0.905064	−	0.425276i	$-0.860177\pi$
$863$	−2.47447	+	4.28591i	−0.0842319	+	0.145894i	0.820832	+	0.571170i	$0.193510\pi$
$864$	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	0.658429	−	0.752643i	$-0.271221\pi$
$877$	0.934478	+	0.784120i	0.0315551	+	0.0264779i	−0.626874	+	0.779121i	$0.715666\pi$
$878$	−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	−0.929972	−	0.367630i	$-0.880169\pi$
$881$	−23.2515	−	40.2728i	−0.783363	−	1.35682i	0.146609	−	0.989194i	$-0.453164\pi$
$882$	−24.5194	+	42.4688i	−0.825610	+	1.43000i
$883$	2.24438	+	12.7285i	0.0755296	+	0.428349i	0.999001	+	0.0446828i	$0.0142277\pi$
$883$	2.24438	+	12.7285i	0.0755296	+	0.428349i	−0.923472	+	0.383667i	$0.874661\pi$
$884$	−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	−0.890595	−	0.454796i	$-0.849712\pi$
$887$	−17.7909	+	14.9283i	−0.597359	+	0.501243i	0.293237	+	0.956040i	$0.405268\pi$
$888$	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	0.368261	−	0.929722i	$-0.379953\pi$
$907$	37.5847	−	13.6797i	1.24798	−	0.454228i	0.879719	+	0.475495i	$0.157731\pi$
$908$	−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	−0.981398	−	0.191984i	$-0.938508\pi$
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	0.324436	−	0.945908i	$-0.394825\pi$
$920$	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	−0.806526	−	0.591199i	$-0.798655\pi$
$929$	4.68051	−	26.5445i	0.153563	−	0.870897i	0.960088	−	0.279698i	$-0.0902342\pi$
$930$	−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	−0.609368	−	0.792887i	$-0.708577\pi$
$937$	2.00980	−	1.68642i	0.0656573	−	0.0550930i	0.675026	+	0.737794i	$0.264133\pi$
$938$	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	−0.990945	−	0.134270i	$-0.957131\pi$
$941$	−3.24194	−	18.3860i	−0.105684	−	0.599366i	0.885260	−	0.465096i	$-0.153980\pi$
$942$	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	0.741320	−	0.671152i	$-0.234200\pi$
$947$	6.43448	+	5.39917i	0.209092	+	0.175449i	−0.532227	+	0.846602i	$0.678645\pi$
$948$	−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	0.956677	−	0.291151i	$-0.0940382\pi$
$953$	25.8102	+	21.6573i	0.836075	+	0.701550i	−0.120602	+	0.992701i	$0.538483\pi$
$954$	−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	−0.934305	−	0.356475i	$-0.883978\pi$
$967$	2.03920	−	11.5649i	0.0655763	−	0.371902i	0.999881	−	0.0154262i	$-0.00491051\pi$
$968$	−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	−0.928091	−	0.372354i	$-0.878551\pi$
$971$	2.22432	−	12.6147i	0.0713817	−	0.404826i	0.999473	−	0.0324723i	$-0.0103381\pi$
$972$	−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	−0.958511	−	0.285055i	$-0.907988\pi$
$977$	−7.26382	+	12.5813i	−0.232390	+	0.402512i	0.726121	+	0.687567i	$0.241321\pi$
$978$	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	0.279293	−	0.960206i	$-0.409900\pi$
$983$	34.8158	−	12.6719i	1.11045	−	0.404172i	0.831159	+	0.556034i	$0.187678\pi$
$984$	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	0.683582	−	0.729873i	$-0.260421\pi$
$991$	2.62860	+	2.20566i	0.0835004	+	0.0700651i	−0.600082	+	0.799938i	$0.704865\pi$
$992$	−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	0.999574	+	0.0291792i	$0.00928933\pi$
$997$	2.21853	+	12.5819i	0.0702616	+	0.398473i	−0.929313	+	0.369294i	$0.879600\pi$
$998$	−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.17.1	yes	6
3.2	odd	2		171.2.u.c.55.1		6
4.3	odd	2		304.2.u.b.17.1		6
5.2	odd	4		475.2.u.a.74.1		12
5.3	odd	4		475.2.u.a.74.2		12
5.4	even	2		475.2.l.a.226.1		6
7.2	even	3		931.2.v.b.606.1		6
7.3	odd	6		931.2.x.b.226.1		6
7.4	even	3		931.2.x.a.226.1		6
7.5	odd	6		931.2.v.a.606.1		6
7.6	odd	2		931.2.w.a.834.1		6
19.2	odd	18		361.2.c.h.68.2		6
19.3	odd	18		361.2.a.h.1.2		3
19.4	even	9		361.2.e.g.234.1		6
19.5	even	9		361.2.c.i.292.2		6
19.6	even	9		361.2.e.f.99.1		6
19.7	even	3		361.2.e.g.54.1		6
19.8	odd	6		361.2.e.b.62.1		6
19.9	even	9	inner	19.2.e.a.9.1	✓	6
19.10	odd	18		361.2.e.h.28.1		6
19.11	even	3		361.2.e.f.62.1		6
19.12	odd	6		361.2.e.a.54.1		6
19.13	odd	18		361.2.e.b.99.1		6
19.14	odd	18		361.2.c.h.292.2		6
19.15	odd	18		361.2.e.a.234.1		6
19.16	even	9		361.2.a.g.1.2		3
19.17	even	9		361.2.c.i.68.2		6
19.18	odd	2		361.2.e.h.245.1		6
57.35	odd	18		3249.2.a.z.1.2		3
57.41	even	18		3249.2.a.s.1.2		3
57.47	odd	18		171.2.u.c.28.1		6
76.3	even	18		5776.2.a.bi.1.1		3
76.35	odd	18		5776.2.a.br.1.3		3
76.47	odd	18		304.2.u.b.161.1		6
95.9	even	18		475.2.l.a.351.1		6
95.28	odd	36		475.2.u.a.199.1		12
95.47	odd	36		475.2.u.a.199.2		12
95.54	even	18		9025.2.a.bd.1.2		3
95.79	odd	18		9025.2.a.x.1.2		3
133.9	even	9		931.2.x.a.655.1		6
133.47	odd	18		931.2.x.b.655.1		6
133.66	odd	18		931.2.v.a.275.1		6
133.104	odd	18		931.2.w.a.883.1		6
133.123	even	9		931.2.v.b.275.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	19.9	even	9	inner
19.2.e.a.17.1	yes	6	1.1	even	1	trivial
171.2.u.c.28.1		6	57.47	odd	18
171.2.u.c.55.1		6	3.2	odd	2
304.2.u.b.17.1		6	4.3	odd	2
304.2.u.b.161.1		6	76.47	odd	18
361.2.a.g.1.2		3	19.16	even	9
361.2.a.h.1.2		3	19.3	odd	18
361.2.c.h.68.2		6	19.2	odd	18
361.2.c.h.292.2		6	19.14	odd	18
361.2.c.i.68.2		6	19.17	even	9
361.2.c.i.292.2		6	19.5	even	9
361.2.e.a.54.1		6	19.12	odd	6
361.2.e.a.234.1		6	19.15	odd	18
361.2.e.b.62.1		6	19.8	odd	6
361.2.e.b.99.1		6	19.13	odd	18
361.2.e.f.62.1		6	19.11	even	3
361.2.e.f.99.1		6	19.6	even	9
361.2.e.g.54.1		6	19.7	even	3
361.2.e.g.234.1		6	19.4	even	9
361.2.e.h.28.1		6	19.10	odd	18
361.2.e.h.245.1		6	19.18	odd	2
475.2.l.a.226.1		6	5.4	even	2
475.2.l.a.351.1		6	95.9	even	18
475.2.u.a.74.1		12	5.2	odd	4
475.2.u.a.74.2		12	5.3	odd	4
475.2.u.a.199.1		12	95.28	odd	36
475.2.u.a.199.2		12	95.47	odd	36
931.2.v.a.275.1		6	133.66	odd	18
931.2.v.a.606.1		6	7.5	odd	6
931.2.v.b.275.1		6	133.123	even	9
931.2.v.b.606.1		6	7.2	even	3
931.2.w.a.834.1		6	7.6	odd	2
931.2.w.a.883.1		6	133.104	odd	18
931.2.x.a.226.1		6	7.4	even	3
931.2.x.a.655.1		6	133.9	even	9
931.2.x.b.226.1		6	7.3	odd	6
931.2.x.b.655.1		6	133.47	odd	18
3249.2.a.s.1.2		3	57.41	even	18
3249.2.a.z.1.2		3	57.35	odd	18
5776.2.a.bi.1.1		3	76.3	even	18
5776.2.a.br.1.3		3	76.35	odd	18
9025.2.a.x.1.2		3	95.79	odd	18
9025.2.a.bd.1.2		3	95.54	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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