LMFDB - Embedded newform 430.2.b.a.259.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(259,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("430.259");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			259.3
Root			$-0.854638 - 0.854638i$ of defining polynomial
Character	$\chi$	$=$	430.259
Dual form			430.2.b.a.259.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.17009i q^{3} -1.00000 q^{4} +(2.17009 - 0.539189i) q^{5} +1.17009 q^{6} +2.70928i q^{7} +1.00000i q^{8} +1.63090 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.17009i q^{3} -1.00000 q^{4} +(2.17009 - 0.539189i) q^{5} +1.17009 q^{6} +2.70928i q^{7} +1.00000i q^{8} +1.63090 q^{9} +(-0.539189 - 2.17009i) q^{10} -2.53919 q^{11} -1.17009i q^{12} +0.0783777i q^{13} +2.70928 q^{14} +(0.630898 + 2.53919i) q^{15} +1.00000 q^{16} +5.51026i q^{17} -1.63090i q^{18} +3.29072 q^{19} +(-2.17009 + 0.539189i) q^{20} -3.17009 q^{21} +2.53919i q^{22} -1.46081i q^{23} -1.17009 q^{24} +(4.41855 - 2.34017i) q^{25} +0.0783777 q^{26} +5.41855i q^{27} -2.70928i q^{28} +5.87936 q^{29} +(2.53919 - 0.630898i) q^{30} -4.61757 q^{31} -1.00000i q^{32} -2.97107i q^{33} +5.51026 q^{34} +(1.46081 + 5.87936i) q^{35} -1.63090 q^{36} -9.95774i q^{37} -3.29072i q^{38} -0.0917087 q^{39} +(0.539189 + 2.17009i) q^{40} +7.83710 q^{41} +3.17009i q^{42} -1.00000i q^{43} +2.53919 q^{44} +(3.53919 - 0.879362i) q^{45} -1.46081 q^{46} +1.12064i q^{47} +1.17009i q^{48} -0.340173 q^{49} +(-2.34017 - 4.41855i) q^{50} -6.44748 q^{51} -0.0783777i q^{52} +5.89269i q^{53} +5.41855 q^{54} +(-5.51026 + 1.36910i) q^{55} -2.70928 q^{56} +3.85043i q^{57} -5.87936i q^{58} -12.4969 q^{59} +(-0.630898 - 2.53919i) q^{60} -11.4319 q^{61} +4.61757i q^{62} +4.41855i q^{63} -1.00000 q^{64} +(0.0422604 + 0.170086i) q^{65} -2.97107 q^{66} -7.38243i q^{67} -5.51026i q^{68} +1.70928 q^{69} +(5.87936 - 1.46081i) q^{70} -2.98667 q^{71} +1.63090i q^{72} -11.4547i q^{73} -9.95774 q^{74} +(2.73820 + 5.17009i) q^{75} -3.29072 q^{76} -6.87936i q^{77} +0.0917087i q^{78} +8.51026 q^{79} +(2.17009 - 0.539189i) q^{80} -1.44748 q^{81} -7.83710i q^{82} -12.9444i q^{83} +3.17009 q^{84} +(2.97107 + 11.9577i) q^{85} -1.00000 q^{86} +6.87936i q^{87} -2.53919i q^{88} -16.3968 q^{89} +(-0.879362 - 3.53919i) q^{90} -0.212347 q^{91} +1.46081i q^{92} -5.40295i q^{93} +1.12064 q^{94} +(7.14116 - 1.77432i) q^{95} +1.17009 q^{96} -3.51026i q^{97} +0.340173i q^{98} -4.14116 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	$ 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 34 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} - 2 q^{25} - 6 q^{26} + 10 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{35} - 2 q^{36} + 4 q^{39} - 10 q^{41} + 12 q^{44} + 18 q^{45} - 12 q^{46} + 20 q^{49} + 8 q^{50} - 40 q^{51} + 4 q^{54} - 2 q^{56} - 40 q^{59} + 4 q^{60} - 42 q^{61} - 6 q^{64} + 32 q^{65} + 12 q^{66} - 4 q^{69} + 10 q^{70} - 16 q^{71} - 28 q^{74} + 32 q^{75} - 34 q^{76} + 18 q^{79} + 2 q^{80} - 10 q^{81} + 8 q^{84} - 12 q^{85} - 6 q^{86} + 28 q^{89} + 20 q^{90} - 22 q^{91} + 32 q^{94} + 2 q^{95} - 4 q^{96} + 16 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 34 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 - 2 * q^25 - 6 * q^26 + 10 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^35 - 2 * q^36 + 4 * q^39 - 10 * q^41 + 12 * q^44 + 18 * q^45 - 12 * q^46 + 20 * q^49 + 8 * q^50 - 40 * q^51 + 4 * q^54 - 2 * q^56 - 40 * q^59 + 4 * q^60 - 42 * q^61 - 6 * q^64 + 32 * q^65 + 12 * q^66 - 4 * q^69 + 10 * q^70 - 16 * q^71 - 28 * q^74 + 32 * q^75 - 34 * q^76 + 18 * q^79 + 2 * q^80 - 10 * q^81 + 8 * q^84 - 12 * q^85 - 6 * q^86 + 28 * q^89 + 20 * q^90 - 22 * q^91 + 32 * q^94 + 2 * q^95 - 4 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			1.17009i			0.675550i	0.941227	+	0.337775i	$0.109674\pi$
$3$			1.17009i			0.675550i	−0.941227	+	0.337775i	$0.890326\pi$
$4$	−1.00000			−0.500000
$5$	2.17009	−	0.539189i	0.970492	−	0.241133i
$5$	2.17009	−	0.539189i	0.970492	−	0.241133i
$6$	1.17009			0.477686
$7$			2.70928i			1.02401i	0.858983	+	0.512005i	$0.171097\pi$
$7$			2.70928i			1.02401i	−0.858983	+	0.512005i	$0.828903\pi$
$8$			1.00000i			0.353553i
$9$	1.63090			0.543633
$10$	−0.539189	−	2.17009i	−0.170506	−	0.686242i
$11$	−2.53919			−0.765594			−0.382797	−	0.923832i	$-0.625039\pi$
$11$	−2.53919			−0.765594			−0.382797	+	0.923832i	$0.625039\pi$
$12$		−	1.17009i		−	0.337775i
$13$			0.0783777i			0.0217381i	0.999941	+	0.0108690i	$0.00345979\pi$
$13$			0.0783777i			0.0217381i	−0.999941	+	0.0108690i	$0.996540\pi$
$14$	2.70928			0.724084
$15$	0.630898	+	2.53919i	0.162897	+	0.655616i
$16$	1.00000			0.250000
$17$			5.51026i			1.33643i	0.743966	+	0.668217i	$0.232942\pi$
$17$			5.51026i			1.33643i	−0.743966	+	0.668217i	$0.767058\pi$
$18$		−	1.63090i		−	0.384406i
$19$	3.29072			0.754944			0.377472	−	0.926021i	$-0.376793\pi$
$19$	3.29072			0.754944			0.377472	+	0.926021i	$0.376793\pi$
$20$	−2.17009	+	0.539189i	−0.485246	+	0.120566i
$21$	−3.17009			−0.691770
$22$			2.53919i			0.541357i
$23$		−	1.46081i		−	0.304600i	−0.988334	−	0.152300i	$-0.951332\pi$
$23$		−	1.46081i		−	0.304600i	0.988334	−	0.152300i	$-0.0486680\pi$
$24$	−1.17009			−0.238843
$25$	4.41855	−	2.34017i	0.883710	−	0.468035i
$26$	0.0783777			0.0153711
$27$			5.41855i			1.04280i
$28$		−	2.70928i		−	0.512005i
$29$	5.87936			1.09177			0.545885	−	0.837860i	$-0.316194\pi$
$29$	5.87936			1.09177			0.545885	+	0.837860i	$0.316194\pi$
$30$	2.53919	−	0.630898i	0.463590	−	0.115186i
$31$	−4.61757			−0.829339			−0.414670	−	0.909972i	$-0.636103\pi$
$31$	−4.61757			−0.829339			−0.414670	+	0.909972i	$0.636103\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	2.97107i		−	0.517197i
$34$	5.51026			0.945002
$35$	1.46081	+	5.87936i	0.246922	+	0.993794i
$36$	−1.63090			−0.271816
$37$		−	9.95774i		−	1.63704i	−0.574476	−	0.818521i	$-0.694794\pi$
$37$		−	9.95774i		−	1.63704i	0.574476	−	0.818521i	$-0.305206\pi$
$38$		−	3.29072i		−	0.533826i
$39$	−0.0917087			−0.0146852
$40$	0.539189	+	2.17009i	0.0852532	+	0.343121i
$41$	7.83710			1.22395			0.611975	−	0.790877i	$-0.290375\pi$
$41$	7.83710			1.22395			0.611975	+	0.790877i	$0.290375\pi$
$42$			3.17009i			0.489155i
$43$		−	1.00000i		−	0.152499i
$43$		−	1.00000i		−	0.152499i
$44$	2.53919			0.382797
$45$	3.53919	−	0.879362i	0.527591	−	0.131088i
$46$	−1.46081			−0.215385
$47$			1.12064i			0.163462i	0.996654	+	0.0817309i	$0.0260448\pi$
$47$			1.12064i			0.163462i	−0.996654	+	0.0817309i	$0.973955\pi$
$48$			1.17009i			0.168887i
$49$	−0.340173			−0.0485961
$50$	−2.34017	−	4.41855i	−0.330950	−	0.624877i
$51$	−6.44748			−0.902828
$52$		−	0.0783777i		−	0.0108690i
$53$			5.89269i			0.809424i	0.914444	+	0.404712i	$0.132628\pi$
$53$			5.89269i			0.809424i	−0.914444	+	0.404712i	$0.867372\pi$
$54$	5.41855			0.737371
$55$	−5.51026	+	1.36910i	−0.743003	+	0.184610i
$56$	−2.70928			−0.362042
$57$			3.85043i			0.510002i
$58$		−	5.87936i		−	0.771998i
$59$	−12.4969			−1.62696			−0.813481	−	0.581592i	$-0.802430\pi$
$59$	−12.4969			−1.62696			−0.813481	+	0.581592i	$0.802430\pi$
$60$	−0.630898	−	2.53919i	−0.0814485	−	0.327808i
$61$	−11.4319			−1.46370			−0.731851	−	0.681464i	$-0.761343\pi$
$61$	−11.4319			−1.46370			−0.731851	+	0.681464i	$0.761343\pi$
$62$			4.61757i			0.586432i
$63$			4.41855i			0.556685i
$64$	−1.00000			−0.125000
$65$	0.0422604	+	0.170086i	0.00524176	+	0.0210966i
$66$	−2.97107			−0.365714
$67$		−	7.38243i		−	0.901908i	−0.892547	−	0.450954i	$-0.851084\pi$
$67$		−	7.38243i		−	0.901908i	0.892547	−	0.450954i	$-0.148916\pi$
$68$		−	5.51026i		−	0.668217i
$69$	1.70928			0.205773
$70$	5.87936	−	1.46081i	0.702718	−	0.174600i
$71$	−2.98667			−0.354452			−0.177226	−	0.984170i	$-0.556712\pi$
$71$	−2.98667			−0.354452			−0.177226	+	0.984170i	$0.556712\pi$
$72$			1.63090i			0.192203i
$73$		−	11.4547i		−	1.34067i	−0.742060	−	0.670334i	$-0.766151\pi$
$73$		−	11.4547i		−	1.34067i	0.742060	−	0.670334i	$-0.233849\pi$
$74$	−9.95774			−1.15756
$75$	2.73820	+	5.17009i	0.316181	+	0.596990i
$76$	−3.29072			−0.377472
$77$		−	6.87936i		−	0.783976i
$78$			0.0917087i			0.0103840i
$79$	8.51026			0.957479			0.478739	−	0.877957i	$-0.341094\pi$
$79$	8.51026			0.957479			0.478739	+	0.877957i	$0.341094\pi$
$80$	2.17009	−	0.539189i	0.242623	−	0.0602831i
$81$	−1.44748			−0.160831
$82$		−	7.83710i		−	0.865463i
$83$		−	12.9444i		−	1.42083i	−0.703781	−	0.710417i	$-0.748506\pi$
$83$		−	12.9444i		−	1.42083i	0.703781	−	0.710417i	$-0.251494\pi$
$84$	3.17009			0.345885
$85$	2.97107	+	11.9577i	0.322258	+	1.29700i
$86$	−1.00000			−0.107833
$87$			6.87936i			0.737545i
$88$		−	2.53919i		−	0.270678i
$89$	−16.3968			−1.73806			−0.869029	−	0.494761i	$-0.835256\pi$
$89$	−16.3968			−1.73806			−0.869029	+	0.494761i	$0.835256\pi$
$90$	−0.879362	−	3.53919i	−0.0926929	−	0.373063i
$91$	−0.212347			−0.0222600
$92$			1.46081i			0.152300i
$93$		−	5.40295i		−	0.560260i
$94$	1.12064			0.115585
$95$	7.14116	−	1.77432i	0.732667	−	0.182042i
$96$	1.17009			0.119421
$97$		−	3.51026i		−	0.356413i	−0.983993	−	0.178206i	$-0.942971\pi$
$97$		−	3.51026i		−	0.356413i	0.983993	−	0.178206i	$-0.0570295\pi$
$98$			0.340173i			0.0343627i
$99$	−4.14116			−0.416202
$100$	−4.41855	+	2.34017i	−0.441855	+	0.234017i
$101$	−15.1122			−1.50372			−0.751861	−	0.659321i	$-0.770844\pi$
$101$	−15.1122			−1.50372			−0.751861	+	0.659321i	$0.770844\pi$
$102$			6.44748i			0.638396i
$103$			7.75872i			0.764490i	0.924061	+	0.382245i	$0.124849\pi$
$103$			7.75872i			0.764490i	−0.924061	+	0.382245i	$0.875151\pi$
$104$	−0.0783777			−0.00768557
$105$	−6.87936	+	1.70928i	−0.671357	+	0.166808i
$106$	5.89269			0.572349
$107$		−	1.40522i		−	0.135848i	−0.997691	−	0.0679239i	$-0.978363\pi$
$107$		−	1.40522i		−	0.135848i	0.997691	−	0.0679239i	$-0.0216375\pi$
$108$		−	5.41855i		−	0.521400i
$109$	−2.18342			−0.209133			−0.104567	−	0.994518i	$-0.533346\pi$
$109$	−2.18342			−0.209133			−0.104567	+	0.994518i	$0.533346\pi$
$110$	1.36910	+	5.51026i	0.130539	+	0.525383i
$111$	11.6514			1.10590
$112$			2.70928i			0.256002i
$113$			11.1906i			1.05272i	0.850261	+	0.526362i	$0.176444\pi$
$113$			11.1906i			1.05272i	−0.850261	+	0.526362i	$0.823556\pi$
$114$	3.85043			0.360626
$115$	−0.787653	−	3.17009i	−0.0734490	−	0.295612i
$116$	−5.87936			−0.545885
$117$			0.127826i			0.0118175i
$118$			12.4969i			1.15044i
$119$	−14.9288			−1.36852
$120$	−2.53919	+	0.630898i	−0.231795	+	0.0575928i
$121$	−4.55252			−0.413865
$122$			11.4319i			1.03499i
$123$			9.17009i			0.826839i
$124$	4.61757			0.414670
$125$	8.32684	−	7.46081i	0.744775	−	0.667315i
$126$	4.41855			0.393636
$127$		−	4.15676i		−	0.368852i	−0.982846	−	0.184426i	$-0.940957\pi$
$127$		−	4.15676i		−	0.368852i	0.982846	−	0.184426i	$-0.0590427\pi$
$128$			1.00000i			0.0883883i
$129$	1.17009			0.103020
$130$	0.170086	−	0.0422604i	0.0149176	−	0.00370648i
$131$	−6.23287			−0.544568			−0.272284	−	0.962217i	$-0.587779\pi$
$131$	−6.23287			−0.544568			−0.272284	+	0.962217i	$0.587779\pi$
$132$			2.97107i			0.258599i
$133$			8.91548i			0.773070i
$134$	−7.38243			−0.637745
$135$	2.92162	+	11.7587i	0.251453	+	1.01203i
$136$	−5.51026			−0.472501
$137$		−	7.00719i		−	0.598664i	−0.954149	−	0.299332i	$-0.903236\pi$
$137$		−	7.00719i		−	0.598664i	0.954149	−	0.299332i	$-0.0967639\pi$
$138$		−	1.70928i		−	0.145503i
$139$	18.4547			1.56530			0.782652	−	0.622459i	$-0.213866\pi$
$139$	18.4547			1.56530			0.782652	+	0.622459i	$0.213866\pi$
$140$	−1.46081	−	5.87936i	−0.123461	−	0.496897i
$141$	−1.31124			−0.110427
$142$			2.98667i			0.250636i
$143$		−	0.199016i		−	0.0166425i
$144$	1.63090			0.135908
$145$	12.7587	−	3.17009i	1.05955	−	0.263261i
$146$	−11.4547			−0.947995
$147$		−	0.398032i		−	0.0328291i
$148$			9.95774i			0.818521i
$149$	10.6670			0.873876			0.436938	−	0.899492i	$-0.356063\pi$
$149$	10.6670			0.873876			0.436938	+	0.899492i	$0.356063\pi$
$150$	5.17009	−	2.73820i	0.422136	−	0.223573i
$151$	−2.24128			−0.182392			−0.0911962	−	0.995833i	$-0.529069\pi$
$151$	−2.24128			−0.182392			−0.0911962	+	0.995833i	$0.529069\pi$
$152$			3.29072i			0.266913i
$153$			8.98667i			0.726529i
$154$	−6.87936			−0.554355
$155$	−10.0205	+	2.48974i	−0.804867	+	0.199981i
$156$	0.0917087			0.00734258
$157$		−	18.0833i		−	1.44320i	−0.692308	−	0.721602i	$-0.743406\pi$
$157$		−	18.0833i		−	1.44320i	0.692308	−	0.721602i	$-0.256594\pi$
$158$		−	8.51026i		−	0.677040i
$159$	−6.89496			−0.546806
$160$	−0.539189	−	2.17009i	−0.0426266	−	0.171560i
$161$	3.95774			0.311914
$162$			1.44748i			0.113725i
$163$			9.26180i			0.725440i	0.931898	+	0.362720i	$0.118152\pi$
$163$			9.26180i			0.725440i	−0.931898	+	0.362720i	$0.881848\pi$
$164$	−7.83710			−0.611975
$165$	−1.60197	−	6.44748i	−0.124713	−	0.501936i
$166$	−12.9444			−1.00468
$167$		−	9.40295i		−	0.727622i	−0.931473	−	0.363811i	$-0.881475\pi$
$167$		−	9.40295i		−	0.727622i	0.931473	−	0.363811i	$-0.118525\pi$
$168$		−	3.17009i		−	0.244577i
$169$	12.9939			0.999527
$170$	11.9577	−	2.97107i	0.917117	−	0.227871i
$171$	5.36683			0.410412
$172$			1.00000i			0.0762493i
$173$		−	5.68035i		−	0.431869i	−0.976408	−	0.215934i	$-0.930720\pi$
$173$		−	5.68035i		−	0.431869i	0.976408	−	0.215934i	$-0.0692797\pi$
$174$	6.87936			0.521523
$175$	6.34017	+	11.9711i	0.479272	+	0.904928i
$176$	−2.53919			−0.191399
$177$		−	14.6225i		−	1.09909i
$178$			16.3968i			1.22899i
$179$	15.7298			1.17570			0.587850	−	0.808970i	$-0.299975\pi$
$179$	15.7298			1.17570			0.587850	+	0.808970i	$0.299975\pi$
$180$	−3.53919	+	0.879362i	−0.263796	+	0.0655438i
$181$	5.32684			0.395941			0.197971	−	0.980208i	$-0.436565\pi$
$181$	5.32684			0.395941			0.197971	+	0.980208i	$0.436565\pi$
$182$			0.212347i			0.0157402i
$183$		−	13.3763i		−	0.988804i
$184$	1.46081			0.107692
$185$	−5.36910	−	21.6092i	−0.394744	−	1.58874i
$186$	−5.40295			−0.396164
$187$		−	13.9916i		−	1.02317i
$188$		−	1.12064i		−	0.0817309i
$189$	−14.6803			−1.06784
$190$	−1.77432	−	7.14116i	−0.128723	−	0.518074i
$191$	−14.1906			−1.02680			−0.513398	−	0.858151i	$-0.671614\pi$
$191$	−14.1906			−1.02680			−0.513398	+	0.858151i	$0.671614\pi$
$192$		−	1.17009i		−	0.0844437i
$193$		−	6.49693i		−	0.467659i	−0.972278	−	0.233830i	$-0.924874\pi$
$193$		−	6.49693i		−	0.467659i	0.972278	−	0.233830i	$-0.0751258\pi$
$194$	−3.51026			−0.252022
$195$	−0.199016	+	0.0494483i	−0.0142518	+	0.00354107i
$196$	0.340173			0.0242981
$197$		−	8.18568i		−	0.583206i	−0.956539	−	0.291603i	$-0.905811\pi$
$197$		−	8.18568i		−	0.583206i	0.956539	−	0.291603i	$-0.0941886\pi$
$198$			4.14116i			0.294299i
$199$	−1.48360			−0.105169			−0.0525847	−	0.998616i	$-0.516746\pi$
$199$	−1.48360			−0.105169			−0.0525847	+	0.998616i	$0.516746\pi$
$200$	2.34017	+	4.41855i	0.165475	+	0.312439i
$201$	8.63809			0.609284
$202$			15.1122i			1.06329i
$203$			15.9288i			1.11798i
$204$	6.44748			0.451414
$205$	17.0072	−	4.22568i	1.18783	−	0.295134i
$206$	7.75872			0.540576
$207$		−	2.38243i		−	0.165591i
$208$			0.0783777i			0.00543452i
$209$	−8.35577			−0.577981
$210$	1.70928	+	6.87936i	0.117951	+	0.474721i
$211$	19.1506			1.31838			0.659191	−	0.751975i	$-0.270899\pi$
$211$	19.1506			1.31838			0.659191	+	0.751975i	$0.270899\pi$
$212$		−	5.89269i		−	0.404712i
$213$		−	3.49466i		−	0.239450i
$214$	−1.40522			−0.0960588
$215$	−0.539189	−	2.17009i	−0.0367724	−	0.147999i
$216$	−5.41855			−0.368686
$217$		−	12.5103i		−	0.849252i
$218$			2.18342i			0.147880i
$219$	13.4030			0.905688
$220$	5.51026	−	1.36910i	0.371502	−	0.0923049i
$221$	−0.431882			−0.0290515
$222$		−	11.6514i		−	0.781992i
$223$		−	9.55252i		−	0.639684i	−0.947471	−	0.319842i	$-0.896370\pi$
$223$		−	9.55252i		−	0.639684i	0.947471	−	0.319842i	$-0.103630\pi$
$224$	2.70928			0.181021
$225$	7.20620	−	3.81658i	0.480414	−	0.254439i
$226$	11.1906			0.744388
$227$			13.8576i			0.919763i	0.887980	+	0.459881i	$0.152108\pi$
$227$			13.8576i			0.919763i	−0.887980	+	0.459881i	$0.847892\pi$
$228$		−	3.85043i		−	0.255001i
$229$	23.1773			1.53160			0.765799	−	0.643080i	$-0.222344\pi$
$229$	23.1773			1.53160			0.765799	+	0.643080i	$0.222344\pi$
$230$	−3.17009	+	0.787653i	−0.209029	+	0.0519363i
$231$	8.04945			0.529615
$232$			5.87936i			0.385999i
$233$			19.1278i			1.25311i	0.779379	+	0.626553i	$0.215535\pi$
$233$			19.1278i			1.25311i	−0.779379	+	0.626553i	$0.784465\pi$
$234$	0.127826			0.00835625
$235$	0.604236	+	2.43188i	0.0394160	+	0.158638i
$236$	12.4969			0.813481
$237$			9.95774i			0.646825i
$238$			14.9288i			0.967691i
$239$	12.1434			0.785493			0.392746	−	0.919647i	$-0.371525\pi$
$239$	12.1434			0.785493			0.392746	+	0.919647i	$0.371525\pi$
$240$	0.630898	+	2.53919i	0.0407243	+	0.163904i
$241$	−13.1929			−0.849828			−0.424914	−	0.905234i	$-0.639696\pi$
$241$	−13.1929			−0.849828			−0.424914	+	0.905234i	$0.639696\pi$
$242$			4.55252i			0.292647i
$243$			14.5620i			0.934151i
$244$	11.4319			0.731851
$245$	−0.738205	+	0.183417i	−0.0471622	+	0.0117181i
$246$	9.17009			0.584663
$247$			0.257920i			0.0164110i
$248$		−	4.61757i		−	0.293216i
$249$	15.1461			0.959844
$250$	−7.46081	−	8.32684i	−0.471863	−	0.526636i
$251$	−15.8888			−1.00289			−0.501447	−	0.865189i	$-0.667199\pi$
$251$	−15.8888			−1.00289			−0.501447	+	0.865189i	$0.667199\pi$
$252$		−	4.41855i		−	0.278343i
$253$			3.70928i			0.233200i
$254$	−4.15676			−0.260818
$255$	−13.9916	+	3.47641i	−0.876187	+	0.217701i
$256$	1.00000			0.0625000
$257$			17.5041i			1.09188i	0.837825	+	0.545938i	$0.183827\pi$
$257$			17.5041i			1.09188i	−0.837825	+	0.545938i	$0.816173\pi$
$258$		−	1.17009i		−	0.0728464i
$259$	26.9783			1.67635
$260$	−0.0422604	−	0.170086i	−0.00262088	−	0.0105483i
$261$	9.58864			0.593522
$262$			6.23287i			0.385068i
$263$		−	25.3812i		−	1.56507i	−0.622605	−	0.782536i	$-0.713926\pi$
$263$		−	25.3812i		−	1.56507i	0.622605	−	0.782536i	$-0.286074\pi$
$264$	2.97107			0.182857
$265$	3.17727	+	12.7877i	0.195178	+	0.785539i
$266$	8.91548			0.546643
$267$		−	19.1857i		−	1.17414i
$268$			7.38243i			0.450954i
$269$	−23.3874			−1.42595			−0.712976	−	0.701188i	$-0.752653\pi$
$269$	−23.3874			−1.42595			−0.712976	+	0.701188i	$0.752653\pi$
$270$	11.7587	−	2.92162i	0.715613	−	0.177804i
$271$	3.05664			0.185677			0.0928387	−	0.995681i	$-0.470406\pi$
$271$	3.05664			0.185677			0.0928387	+	0.995681i	$0.470406\pi$
$272$			5.51026i			0.334109i
$273$		−	0.248464i		−	0.0150377i
$274$	−7.00719			−0.423320
$275$	−11.2195	+	5.94214i	−0.676563	+	0.358325i
$276$	−1.70928			−0.102886
$277$		−	18.6803i		−	1.12239i	−0.827683	−	0.561197i	$-0.810341\pi$
$277$		−	18.6803i		−	1.12239i	0.827683	−	0.561197i	$-0.189659\pi$
$278$		−	18.4547i		−	1.10684i
$279$	−7.53078			−0.450856
$280$	−5.87936	+	1.46081i	−0.351359	+	0.0873002i
$281$	−8.85762			−0.528401			−0.264201	−	0.964468i	$-0.585108\pi$
$281$	−8.85762			−0.528401			−0.264201	+	0.964468i	$0.585108\pi$
$282$			1.31124i			0.0780834i
$283$		−	9.19061i		−	0.546325i	−0.961968	−	0.273162i	$-0.911930\pi$
$283$		−	9.19061i		−	0.546325i	0.961968	−	0.273162i	$-0.0880696\pi$
$284$	2.98667			0.177226
$285$	2.07611	+	8.35577i	0.122978	+	0.494953i
$286$	−0.199016			−0.0117681
$287$			21.2329i			1.25334i
$288$		−	1.63090i		−	0.0961016i
$289$	−13.3630			−0.786056
$290$	−3.17009	−	12.7587i	−0.186154	−	0.749218i
$291$	4.10731			0.240775
$292$			11.4547i			0.670334i
$293$			3.56093i			0.208032i	0.994576	+	0.104016i	$0.0331693\pi$
$293$			3.56093i			0.208032i	−0.994576	+	0.104016i	$0.966831\pi$
$294$	−0.398032			−0.0232137
$295$	−27.1194	+	6.73820i	−1.57895	+	0.392313i
$296$	9.95774			0.578782
$297$		−	13.7587i		−	0.798362i
$298$		−	10.6670i		−	0.617924i
$299$	0.114495			0.00662142
$300$	−2.73820	−	5.17009i	−0.158090	−	0.298495i
$301$	2.70928			0.156160
$302$			2.24128i			0.128971i
$303$		−	17.6826i		−	1.01584i
$304$	3.29072			0.188736
$305$	−24.8082	+	6.16394i	−1.42051	+	0.352946i
$306$	8.98667			0.513734
$307$			32.6092i			1.86110i	0.366161	+	0.930551i	$0.380672\pi$
$307$			32.6092i			1.86110i	−0.366161	+	0.930551i	$0.619328\pi$
$308$			6.87936i			0.391988i
$309$	−9.07838			−0.516451
$310$	2.48974	+	10.0205i	0.141408	+	0.569127i
$311$	7.33299			0.415815			0.207908	−	0.978148i	$-0.433335\pi$
$311$	7.33299			0.415815			0.207908	+	0.978148i	$0.433335\pi$
$312$		−	0.0917087i		−	0.00519199i
$313$			4.73820i			0.267819i	0.990994	+	0.133910i	$0.0427532\pi$
$313$			4.73820i			0.267819i	−0.990994	+	0.133910i	$0.957247\pi$
$314$	−18.0833			−1.02050
$315$	2.38243	+	9.58864i	0.134235	+	0.540259i
$316$	−8.51026			−0.478739
$317$			6.86603i			0.385635i	0.981235	+	0.192817i	$0.0617625\pi$
$317$			6.86603i			0.385635i	−0.981235	+	0.192817i	$0.938238\pi$
$318$			6.89496i			0.386650i
$319$	−14.9288			−0.835853
$320$	−2.17009	+	0.539189i	−0.121312	+	0.0301416i
$321$	1.64423			0.0917719
$322$		−	3.95774i		−	0.220556i
$323$			18.1327i			1.00893i
$324$	1.44748			0.0804156
$325$	0.183417	+	0.346316i	0.0101742	+	0.0192102i
$326$	9.26180			0.512963
$327$		−	2.55479i		−	0.141280i
$328$			7.83710i			0.432732i
$329$	−3.03612			−0.167387
$330$	−6.44748	+	1.60197i	−0.354922	+	0.0881854i
$331$	16.9711			0.932814			0.466407	−	0.884570i	$-0.345548\pi$
$331$	16.9711			0.932814			0.466407	+	0.884570i	$0.345548\pi$
$332$			12.9444i			0.710417i
$333$		−	16.2401i		−	0.889949i
$334$	−9.40295			−0.514507
$335$	−3.98053	−	16.0205i	−0.217479	−	0.875294i
$336$	−3.17009			−0.172942
$337$			17.0472i			0.928619i	0.885673	+	0.464310i	$0.153697\pi$
$337$			17.0472i			0.928619i	−0.885673	+	0.464310i	$0.846303\pi$
$338$		−	12.9939i		−	0.706773i
$339$	−13.0940			−0.711167
$340$	−2.97107	−	11.9577i	−0.161129	−	0.648499i
$341$	11.7249			0.634938
$342$		−	5.36683i		−	0.290205i
$343$			18.0433i			0.974247i
$344$	1.00000			0.0539164
$345$	3.70928	−	0.921622i	0.199701	−	0.0496185i
$346$	−5.68035			−0.305377
$347$		−	8.37856i		−	0.449785i	−0.974384	−	0.224892i	$-0.927797\pi$
$347$		−	8.37856i		−	0.449785i	0.974384	−	0.224892i	$-0.0722030\pi$
$348$		−	6.87936i		−	0.368773i
$349$	0.241276			0.0129152			0.00645761	−	0.999979i	$-0.497944\pi$
$349$	0.241276			0.0129152			0.00645761	+	0.999979i	$0.497944\pi$
$350$	11.9711	−	6.34017i	0.639881	−	0.338897i
$351$	−0.424694			−0.0226685
$352$			2.53919i			0.135339i
$353$			35.2378i			1.87552i	0.347287	+	0.937759i	$0.387103\pi$
$353$			35.2378i			1.87552i	−0.347287	+	0.937759i	$0.612897\pi$
$354$	−14.6225			−0.777176
$355$	−6.48133	+	1.61038i	−0.343993	+	0.0854700i
$356$	16.3968			0.869029
$357$		−	17.4680i		−	0.924505i
$358$		−	15.7298i		−	0.831345i
$359$	−2.65264			−0.140001			−0.0700005	−	0.997547i	$-0.522300\pi$
$359$	−2.65264			−0.140001			−0.0700005	+	0.997547i	$0.522300\pi$
$360$	0.879362	+	3.53919i	0.0463464	+	0.186532i
$361$	−8.17113			−0.430060
$362$		−	5.32684i		−	0.279973i
$363$		−	5.32684i		−	0.279587i
$364$	0.212347			0.0111300
$365$	−6.17623	−	24.8576i	−0.323279	−	1.30111i
$366$	−13.3763			−0.699190
$367$		−	2.13009i		−	0.111190i	−0.998453	−	0.0555950i	$-0.982294\pi$
$367$		−	2.13009i		−	0.111190i	0.998453	−	0.0555950i	$-0.0177056\pi$
$368$		−	1.46081i		−	0.0761500i
$369$	12.7815			0.665379
$370$	−21.6092	+	5.36910i	−1.12341	+	0.279126i
$371$	−15.9649			−0.828858
$372$			5.40295i			0.280130i
$373$		−	2.53919i		−	0.131474i	−0.997837	−	0.0657371i	$-0.979060\pi$
$373$		−	2.53919i		−	0.131474i	0.997837	−	0.0657371i	$-0.0209399\pi$
$374$	−13.9916			−0.723488
$375$	8.72979	+	9.74313i	0.450805	+	0.503133i
$376$	−1.12064			−0.0577925
$377$			0.460811i			0.0237330i
$378$			14.6803i			0.755076i
$379$	−26.0410			−1.33764			−0.668819	−	0.743425i	$-0.733200\pi$
$379$	−26.0410			−1.33764			−0.668819	+	0.743425i	$0.733200\pi$
$380$	−7.14116	+	1.77432i	−0.366334	+	0.0910208i
$381$	4.86376			0.249178
$382$			14.1906i			0.726055i
$383$			25.0144i			1.27817i	0.769134	+	0.639087i	$0.220688\pi$
$383$			25.0144i			1.27817i	−0.769134	+	0.639087i	$0.779312\pi$
$384$	−1.17009			−0.0597107
$385$	−3.70928	−	14.9288i	−0.189042	−	0.760843i
$386$	−6.49693			−0.330685
$387$		−	1.63090i		−	0.0829032i
$388$			3.51026i			0.178206i
$389$	15.3074			0.776114			0.388057	−	0.921635i	$-0.373146\pi$
$389$	15.3074			0.776114			0.388057	+	0.921635i	$0.373146\pi$
$390$	0.0494483	+	0.199016i	0.00250391	+	0.0100776i
$391$	8.04945			0.407078
$392$		−	0.340173i		−	0.0171813i
$393$		−	7.29299i		−	0.367883i
$394$	−8.18568			−0.412389
$395$	18.4680	−	4.58864i	0.929226	−	0.230879i
$396$	4.14116			0.208101
$397$		−	14.2907i		−	0.717231i	−0.933485	−	0.358615i	$-0.883249\pi$
$397$		−	14.2907i		−	0.717231i	0.933485	−	0.358615i	$-0.116751\pi$
$398$			1.48360i			0.0743660i
$399$	−10.4319			−0.522247
$400$	4.41855	−	2.34017i	0.220928	−	0.117009i
$401$	−6.62863			−0.331018			−0.165509	−	0.986208i	$-0.552927\pi$
$401$	−6.62863			−0.331018			−0.165509	+	0.986208i	$0.552927\pi$
$402$		−	8.63809i		−	0.430829i
$403$		−	0.361914i		−	0.0180282i
$404$	15.1122			0.751861
$405$	−3.14116	+	0.780465i	−0.156085	+	0.0387816i
$406$	15.9288			0.790534
$407$			25.2846i			1.25331i
$408$		−	6.44748i		−	0.319198i
$409$	13.2462			0.654982			0.327491	−	0.944854i	$-0.393797\pi$
$409$	13.2462			0.654982			0.327491	+	0.944854i	$0.393797\pi$
$410$	−4.22568	−	17.0072i	−0.208691	−	0.839925i
$411$	8.19902			0.404428
$412$		−	7.75872i		−	0.382245i
$413$		−	33.8576i		−	1.66602i
$414$	−2.38243			−0.117090
$415$	−6.97948	−	28.0905i	−0.342609	−	1.37891i
$416$	0.0783777			0.00384279
$417$			21.5936i			1.05744i
$418$			8.35577i			0.408694i
$419$	29.3318			1.43295			0.716475	−	0.697613i	$-0.245754\pi$
$419$	29.3318			1.43295			0.716475	+	0.697613i	$0.245754\pi$
$420$	6.87936	−	1.70928i	0.335678	−	0.0834041i
$421$	−35.6525			−1.73759			−0.868797	−	0.495168i	$-0.835107\pi$
$421$	−35.6525			−1.73759			−0.868797	+	0.495168i	$0.835107\pi$
$422$		−	19.1506i		−	0.932237i
$423$			1.82765i			0.0888632i
$424$	−5.89269			−0.286174
$425$	12.8950	+	24.3474i	0.625497	+	1.18102i
$426$	−3.49466			−0.169317
$427$		−	30.9721i		−	1.49885i
$428$			1.40522i			0.0679239i
$429$	0.232866			0.0112429
$430$	−2.17009	+	0.539189i	−0.104651	+	0.0260020i
$431$	20.2472			0.975275			0.487638	−	0.873046i	$-0.337859\pi$
$431$	20.2472			0.975275			0.487638	+	0.873046i	$0.337859\pi$
$432$			5.41855i			0.260700i
$433$			4.42961i			0.212874i	0.994319	+	0.106437i	$0.0339442\pi$
$433$			4.42961i			0.212874i	−0.994319	+	0.106437i	$0.966056\pi$
$434$	−12.5103			−0.600512
$435$	3.70928	+	14.9288i	0.177846	+	0.715782i
$436$	2.18342			0.104567
$437$		−	4.80713i		−	0.229956i
$438$		−	13.4030i		−	0.640418i
$439$	−26.4534			−1.26255			−0.631277	−	0.775557i	$-0.717469\pi$
$439$	−26.4534			−1.26255			−0.631277	+	0.775557i	$0.717469\pi$
$440$	−1.36910	−	5.51026i	−0.0652694	−	0.262691i
$441$	−0.554787			−0.0264184
$442$			0.431882i			0.0205425i
$443$		−	21.0072i		−	0.998082i	−0.866578	−	0.499041i	$-0.833686\pi$
$443$		−	21.0072i		−	0.998082i	0.866578	−	0.499041i	$-0.166314\pi$
$444$	−11.6514			−0.552952
$445$	−35.5825	+	8.84098i	−1.68677	+	0.419103i
$446$	−9.55252			−0.452325
$447$			12.4813i			0.590347i
$448$		−	2.70928i		−	0.128001i
$449$	0.167819			0.00791987			0.00395994	−	0.999992i	$-0.498740\pi$
$449$	0.167819			0.00791987			0.00395994	+	0.999992i	$0.498740\pi$
$450$	−3.81658	−	7.20620i	−0.179915	−	0.339704i
$451$	−19.8999			−0.937049
$452$		−	11.1906i		−	0.526362i
$453$		−	2.62249i		−	0.123215i
$454$	13.8576			0.650370
$455$	−0.460811	+	0.114495i	−0.0216032	+	0.00536761i
$456$	−3.85043			−0.180313
$457$			16.3545i			0.765034i	0.923949	+	0.382517i	$0.124943\pi$
$457$			16.3545i			0.765034i	−0.923949	+	0.382517i	$0.875057\pi$
$458$		−	23.1773i		−	1.08300i
$459$	−29.8576			−1.39363
$460$	0.787653	+	3.17009i	0.0367245	+	0.147806i
$461$	30.0027			1.39736			0.698681	−	0.715433i	$-0.253770\pi$
$461$	30.0027			1.39736			0.698681	+	0.715433i	$0.253770\pi$
$462$		−	8.04945i		−	0.374494i
$463$		−	28.6925i		−	1.33345i	−0.745303	−	0.666726i	$-0.767695\pi$
$463$		−	28.6925i		−	1.33345i	0.745303	−	0.666726i	$-0.232305\pi$
$464$	5.87936			0.272943
$465$	−2.91321	−	11.7249i	−0.135097	−	0.543728i
$466$	19.1278			0.886079
$467$			15.6092i			0.722306i	0.932507	+	0.361153i	$0.117617\pi$
$467$			15.6092i			0.722306i	−0.932507	+	0.361153i	$0.882383\pi$
$468$		−	0.127826i		−	0.00590876i
$469$	20.0010			0.923562
$470$	2.43188	−	0.604236i	0.112174	−	0.0278713i
$471$	21.1590			0.974956
$472$		−	12.4969i		−	0.575218i
$473$			2.53919i			0.116752i
$474$	9.95774			0.457374
$475$	14.5402	−	7.70086i	0.667152	−	0.353340i
$476$	14.9288			0.684261
$477$			9.61038i			0.440029i
$478$		−	12.1434i		−	0.555427i
$479$	−31.2495			−1.42783			−0.713913	−	0.700234i	$-0.753079\pi$
$479$	−31.2495			−1.42783			−0.713913	+	0.700234i	$0.753079\pi$
$480$	2.53919	−	0.630898i	0.115898	−	0.0287964i
$481$	0.780465			0.0355861
$482$			13.1929i			0.600919i
$483$			4.63090i			0.210713i
$484$	4.55252			0.206933
$485$	−1.89269	−	7.61757i	−0.0859428	−	0.345896i
$486$	14.5620			0.660545
$487$		−	13.8420i		−	0.627242i	−0.949548	−	0.313621i	$-0.898458\pi$
$487$		−	13.8420i		−	0.627242i	0.949548	−	0.313621i	$-0.101542\pi$
$488$		−	11.4319i		−	0.517497i
$489$	−10.8371			−0.490071
$490$	0.183417	+	0.738205i	0.00828596	+	0.0333487i
$491$	−4.97107			−0.224341			−0.112171	−	0.993689i	$-0.535780\pi$
$491$	−4.97107			−0.224341			−0.112171	+	0.993689i	$0.535780\pi$
$492$		−	9.17009i		−	0.413419i
$493$			32.3968i			1.45908i
$494$	0.257920			0.0116044
$495$	−8.98667	+	2.23287i	−0.403921	+	0.100360i
$496$	−4.61757			−0.207335
$497$		−	8.09171i		−	0.362963i
$498$		−	15.1461i		−	0.678712i
$499$	−15.4475			−0.691524			−0.345762	−	0.938322i	$-0.612380\pi$
$499$	−15.4475			−0.691524			−0.345762	+	0.938322i	$0.612380\pi$
$500$	−8.32684	+	7.46081i	−0.372388	+	0.333658i
$501$	11.0023			0.491545
$502$			15.8888i			0.709153i
$503$			31.2411i			1.39297i	0.717571	+	0.696486i	$0.245254\pi$
$503$			31.2411i			1.39297i	−0.717571	+	0.696486i	$0.754746\pi$
$504$	−4.41855			−0.196818
$505$	−32.7948	+	8.14834i	−1.45935	+	0.362597i
$506$	3.70928			0.164897
$507$			15.2039i			0.675231i
$508$			4.15676i			0.184426i
$509$	−12.4391			−0.551352			−0.275676	−	0.961251i	$-0.588902\pi$
$509$	−12.4391			−0.551352			−0.275676	+	0.961251i	$0.588902\pi$
$510$	3.47641	+	13.9916i	0.153938	+	0.619558i
$511$	31.0338			1.37286
$512$		−	1.00000i		−	0.0441942i
$513$			17.8310i			0.787256i
$514$	17.5041			0.772073
$515$	4.18342	+	16.8371i	0.184343	+	0.741931i
$516$	−1.17009			−0.0515102
$517$		−	2.84551i		−	0.125145i
$518$		−	26.9783i		−	1.18536i
$519$	6.64650			0.291749
$520$	−0.170086	+	0.0422604i	−0.00745879	+	0.00185324i
$521$	−5.89988			−0.258478			−0.129239	−	0.991613i	$-0.541254\pi$
$521$	−5.89988			−0.258478			−0.129239	+	0.991613i	$0.541254\pi$
$522$		−	9.58864i		−	0.419683i
$523$		−	40.8710i		−	1.78716i	−0.448902	−	0.893581i	$-0.648185\pi$
$523$		−	40.8710i		−	1.78716i	0.448902	−	0.893581i	$-0.351815\pi$
$524$	6.23287			0.272284
$525$	−14.0072	+	7.41855i	−0.611324	+	0.323772i
$526$	−25.3812			−1.10667
$527$		−	25.4440i		−	1.10836i
$528$		−	2.97107i		−	0.129299i
$529$	20.8660			0.907219
$530$	12.7877	−	3.17727i	0.555460	−	0.138012i
$531$	−20.3812			−0.884469
$532$		−	8.91548i		−	0.386535i
$533$			0.614254i			0.0266063i
$534$	−19.1857			−0.830246
$535$	−0.757679	−	3.04945i	−0.0327573	−	0.131839i
$536$	7.38243			0.318873
$537$			18.4052i			0.794244i
$538$			23.3874i			1.00830i
$539$	0.863763			0.0372049
$540$	−2.92162	−	11.7587i	−0.125727	−	0.506015i
$541$	−18.4924			−0.795050			−0.397525	−	0.917591i	$-0.630131\pi$
$541$	−18.4924			−0.795050			−0.397525	+	0.917591i	$0.630131\pi$
$542$		−	3.05664i		−	0.131294i
$543$			6.23287i			0.267478i
$544$	5.51026			0.236250
$545$	−4.73820	+	1.17727i	−0.202962	+	0.0504289i
$546$	−0.248464			−0.0106333
$547$			14.9216i			0.638002i	0.947754	+	0.319001i	$0.103347\pi$
$547$			14.9216i			0.638002i	−0.947754	+	0.319001i	$0.896653\pi$
$548$			7.00719i			0.299332i
$549$	−18.6442			−0.795716
$550$	5.94214	+	11.2195i	0.253374	+	0.478403i
$551$	19.3474			0.824225
$552$			1.70928i			0.0727516i
$553$			23.0566i			0.980468i
$554$	−18.6803			−0.793652
$555$	25.2846	−	6.28231i	1.07327	−	0.266669i
$556$	−18.4547			−0.782652
$557$		−	43.8515i		−	1.85805i	−0.370021	−	0.929023i	$-0.620650\pi$
$557$		−	43.8515i		−	1.85805i	0.370021	−	0.929023i	$-0.379350\pi$
$558$			7.53078i			0.318803i
$559$	0.0783777			0.00331503
$560$	1.46081	+	5.87936i	0.0617305	+	0.248448i
$561$	16.3714			0.691200
$562$			8.85762i			0.373636i
$563$		−	26.1617i		−	1.10258i	−0.834313	−	0.551292i	$-0.814135\pi$
$563$		−	26.1617i		−	1.10258i	0.834313	−	0.551292i	$-0.185865\pi$
$564$	1.31124			0.0552133
$565$	6.03385	+	24.2846i	0.253846	+	1.02166i
$566$	−9.19061			−0.386310
$567$		−	3.92162i		−	0.164693i
$568$		−	2.98667i		−	0.125318i
$569$	−27.7610			−1.16380			−0.581901	−	0.813260i	$-0.697691\pi$
$569$	−27.7610			−1.16380			−0.581901	+	0.813260i	$0.697691\pi$
$570$	8.35577	−	2.07611i	0.349985	−	0.0869587i
$571$	45.6102			1.90873			0.954364	−	0.298647i	$-0.0965352\pi$
$571$	45.6102			1.90873			0.954364	+	0.298647i	$0.0965352\pi$
$572$			0.199016i			0.00832127i
$573$		−	16.6042i		−	0.693652i
$574$	21.2329			0.886243
$575$	−3.41855	−	6.45467i	−0.142563	−	0.269178i
$576$	−1.63090			−0.0679541
$577$			33.8215i			1.40801i	0.710196	+	0.704004i	$0.248606\pi$
$577$			33.8215i			1.40801i	−0.710196	+	0.704004i	$0.751394\pi$
$578$			13.3630i			0.555826i
$579$	7.60197			0.315927
$580$	−12.7587	+	3.17009i	−0.529777	+	0.131631i
$581$	35.0700			1.45495
$582$		−	4.10731i		−	0.170253i
$583$		−	14.9627i		−	0.619690i
$584$	11.4547			0.473998
$585$	0.0689224	+	0.277394i	0.00284959	+	0.0114688i
$586$	3.56093			0.147101
$587$			43.3991i			1.79127i	0.444788	+	0.895636i	$0.353279\pi$
$587$			43.3991i			1.79127i	−0.444788	+	0.895636i	$0.646721\pi$
$588$			0.398032i			0.0164146i
$589$	−15.1951			−0.626105
$590$	6.73820	+	27.1194i	0.277408	+	1.11649i
$591$	9.57796			0.393985
$592$		−	9.95774i		−	0.409261i
$593$			41.8404i			1.71818i	0.511825	+	0.859090i	$0.328970\pi$
$593$			41.8404i			1.71818i	−0.511825	+	0.859090i	$0.671030\pi$
$594$	−13.7587			−0.564527
$595$	−32.3968	+	8.04945i	−1.32814	+	0.329995i
$596$	−10.6670			−0.436938
$597$		−	1.73594i		−	0.0710472i
$598$		−	0.114495i		−	0.00468205i
$599$	−4.94828			−0.202181			−0.101091	−	0.994877i	$-0.532233\pi$
$599$	−4.94828			−0.202181			−0.101091	+	0.994877i	$0.532233\pi$
$600$	−5.17009	+	2.73820i	−0.211068	+	0.111787i
$601$	13.4140			0.547169			0.273585	−	0.961848i	$-0.411791\pi$
$601$	13.4140			0.547169			0.273585	+	0.961848i	$0.411791\pi$
$602$		−	2.70928i		−	0.110422i
$603$		−	12.0400i		−	0.490306i
$604$	2.24128			0.0911962
$605$	−9.87936	+	2.45467i	−0.401653	+	0.0997964i
$606$	−17.6826			−0.718307
$607$			38.3773i			1.55769i	0.627218	+	0.778844i	$0.284194\pi$
$607$			38.3773i			1.55769i	−0.627218	+	0.778844i	$0.715806\pi$
$608$		−	3.29072i		−	0.133457i
$609$	−18.6381			−0.755253
$610$	6.16394	+	24.8082i	0.249571	+	1.00445i
$611$	−0.0878331			−0.00355335
$612$		−	8.98667i		−	0.363265i
$613$		−	11.5548i		−	0.466693i	−0.972394	−	0.233347i	$-0.925032\pi$
$613$		−	11.5548i		−	0.466693i	0.972394	−	0.233347i	$-0.0749677\pi$
$614$	32.6092			1.31600
$615$	4.94441	+	19.8999i	0.199378	+	0.802441i
$616$	6.87936			0.277177
$617$		−	9.10504i		−	0.366555i	−0.983061	−	0.183278i	$-0.941329\pi$
$617$		−	9.10504i		−	0.366555i	0.983061	−	0.183278i	$-0.0586707\pi$
$618$			9.07838i			0.365186i
$619$	26.7103			1.07358			0.536789	−	0.843716i	$-0.319637\pi$
$619$	26.7103			1.07358			0.536789	+	0.843716i	$0.319637\pi$
$620$	10.0205	−	2.48974i	0.402434	−	0.0999904i
$621$	7.91548			0.317637
$622$		−	7.33299i		−	0.294026i
$623$		−	44.4235i		−	1.77979i
$624$	−0.0917087			−0.00367129
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	4.73820			0.189377
$627$		−	9.77698i		−	0.390455i
$628$			18.0833i			0.721602i
$629$	54.8697			2.18780
$630$	9.58864	−	2.38243i	0.382020	−	0.0949184i
$631$	−33.2255			−1.32269			−0.661343	−	0.750083i	$-0.730013\pi$
$631$	−33.2255			−1.32269			−0.661343	+	0.750083i	$0.730013\pi$
$632$			8.51026i			0.338520i
$633$			22.4079i			0.890633i
$634$	6.86603			0.272685
$635$	−2.24128	−	9.02052i	−0.0889423	−	0.357968i
$636$	6.89496			0.273403
$637$		−	0.0266620i		−	0.00105639i
$638$			14.9288i			0.591037i
$639$	−4.87095			−0.192692
$640$	0.539189	+	2.17009i	0.0213133	+	0.0857802i
$641$	27.3028			1.07840			0.539199	−	0.842179i	$-0.318727\pi$
$641$	27.3028			1.07840			0.539199	+	0.842179i	$0.318727\pi$
$642$		−	1.64423i		−	0.0648925i
$643$		−	33.5886i		−	1.32461i	−0.749236	−	0.662303i	$-0.769579\pi$
$643$		−	33.5886i		−	1.32461i	0.749236	−	0.662303i	$-0.230421\pi$
$644$	−3.95774			−0.155957
$645$	2.53919	−	0.630898i	0.0999805	−	0.0248416i
$646$	18.1327			0.713423
$647$			8.22076i			0.323191i	0.986857	+	0.161596i	$0.0516640\pi$
$647$			8.22076i			0.323191i	−0.986857	+	0.161596i	$0.948336\pi$
$648$		−	1.44748i		−	0.0568624i
$649$	31.7321			1.24559
$650$	0.346316	−	0.183417i	0.0135836	−	0.00719423i
$651$	14.6381			0.573712
$652$		−	9.26180i		−	0.362720i
$653$			37.3763i			1.46265i	0.682031	+	0.731324i	$0.261097\pi$
$653$			37.3763i			1.46265i	−0.682031	+	0.731324i	$0.738903\pi$
$654$	−2.55479			−0.0999001
$655$	−13.5259	+	3.36069i	−0.528499	+	0.131313i
$656$	7.83710			0.305987
$657$		−	18.6814i		−	0.728830i
$658$			3.03612i			0.118360i
$659$	5.31843			0.207177			0.103588	−	0.994620i	$-0.466968\pi$
$659$	5.31843			0.207177			0.103588	+	0.994620i	$0.466968\pi$
$660$	1.60197	+	6.44748i	0.0623565	+	0.250968i
$661$	10.1061			0.393081			0.196541	−	0.980496i	$-0.437029\pi$
$661$	10.1061			0.393081			0.196541	+	0.980496i	$0.437029\pi$
$662$		−	16.9711i		−	0.659599i
$663$		−	0.505339i		−	0.0196257i
$664$	12.9444			0.502340
$665$	4.80713	+	19.3474i	0.186412	+	0.750258i
$666$	−16.2401			−0.629289
$667$		−	8.58864i		−	0.332553i
$668$			9.40295i			0.363811i
$669$	11.1773			0.432138
$670$	−16.0205	+	3.98053i	−0.618927	+	0.153781i
$671$	29.0277			1.12060
$672$			3.17009i			0.122289i
$673$			38.6007i			1.48795i	0.668208	+	0.743975i	$0.267062\pi$
$673$			38.6007i			1.48795i	−0.668208	+	0.743975i	$0.732938\pi$
$674$	17.0472			0.656633
$675$	12.6803	+	23.9421i	0.488067	+	0.921533i
$676$	−12.9939			−0.499764
$677$		−	25.7731i		−	0.990541i	−0.868739	−	0.495270i	$-0.835069\pi$
$677$		−	25.7731i		−	0.990541i	0.868739	−	0.495270i	$-0.164931\pi$
$678$			13.0940i			0.502871i
$679$	9.51026			0.364970
$680$	−11.9577	+	2.97107i	−0.458558	+	0.113935i
$681$	−16.2146			−0.621345
$682$		−	11.7249i		−	0.448969i
$683$		−	40.6803i		−	1.55659i	−0.627899	−	0.778295i	$-0.716085\pi$
$683$		−	40.6803i		−	1.55659i	0.627899	−	0.778295i	$-0.283915\pi$
$684$	−5.36683			−0.205206
$685$	−3.77820	−	15.2062i	−0.144358	−	0.580999i
$686$	18.0433			0.688897
$687$			27.1194i			1.03467i
$688$		−	1.00000i		−	0.0381246i
$689$	−0.461856			−0.0175953
$690$	−0.921622	−	3.70928i	−0.0350856	−	0.141210i
$691$	−33.1857			−1.26244			−0.631221	−	0.775603i	$-0.717446\pi$
$691$	−33.1857			−1.26244			−0.631221	+	0.775603i	$0.717446\pi$
$692$			5.68035i			0.215934i
$693$		−	11.2195i		−	0.426195i
$694$	−8.37856			−0.318046
$695$	40.0482	−	9.95055i	1.51912	−	0.377446i
$696$	−6.87936			−0.260762
$697$			43.1845i			1.63573i
$698$		−	0.241276i		−	0.00913244i
$699$	−22.3812			−0.846535
$700$	−6.34017	−	11.9711i	−0.239636	−	0.452464i
$701$	3.94933			0.149164			0.0745821	−	0.997215i	$-0.476238\pi$
$701$	3.94933			0.149164			0.0745821	+	0.997215i	$0.476238\pi$
$702$			0.424694i			0.0160290i
$703$		−	32.7682i		−	1.23588i
$704$	2.53919			0.0956993
$705$	−2.84551	+	0.707008i	−0.107168	+	0.0266275i
$706$	35.2378			1.32619
$707$		−	40.9432i		−	1.53983i
$708$			14.6225i			0.549547i
$709$	22.9021			0.860108			0.430054	−	0.902803i	$-0.358494\pi$
$709$	22.9021			0.860108			0.430054	+	0.902803i	$0.358494\pi$
$710$	1.61038	+	6.48133i	0.0604364	+	0.243240i
$711$	13.8794			0.520517
$712$		−	16.3968i		−	0.614496i
$713$			6.74539i			0.252617i
$714$	−17.4680			−0.653723
$715$	−0.107307	−	0.431882i	−0.00401306	−	0.0161515i
$716$	−15.7298			−0.587850
$717$			14.2089i			0.530639i
$718$			2.65264i			0.0989956i
$719$	−40.0950			−1.49529			−0.747646	−	0.664097i	$-0.768816\pi$
$719$	−40.0950			−1.49529			−0.747646	+	0.664097i	$0.768816\pi$
$720$	3.53919	−	0.879362i	0.131898	−	0.0327719i
$721$	−21.0205			−0.782845
$722$			8.17113i			0.304098i
$723$		−	15.4368i		−	0.574101i
$724$	−5.32684			−0.197971
$725$	25.9783	−	13.7587i	0.964808	−	0.510986i
$726$	−5.32684			−0.197698
$727$		−	30.6986i		−	1.13855i	−0.822148	−	0.569274i	$-0.807224\pi$
$727$		−	30.6986i		−	1.13855i	0.822148	−	0.569274i	$-0.192776\pi$
$728$		−	0.212347i		−	0.00787010i
$729$	−21.3812			−0.791897
$730$	−24.8576	+	6.17623i	−0.920022	+	0.228593i
$731$	5.51026			0.203804
$732$			13.3763i			0.494402i
$733$		−	25.2729i		−	0.933474i	−0.884396	−	0.466737i	$-0.845429\pi$
$733$		−	25.2729i		−	0.933474i	0.884396	−	0.466737i	$-0.154571\pi$
$734$	−2.13009			−0.0786232
$735$	−0.214614	−	0.863763i	−0.00791617	−	0.0318604i
$736$	−1.46081			−0.0538462
$737$			18.7454i			0.690495i
$738$		−	12.7815i		−	0.470494i
$739$	0.194095			0.00713991			0.00356996	−	0.999994i	$-0.498864\pi$
$739$	0.194095			0.00713991			0.00356996	+	0.999994i	$0.498864\pi$
$740$	5.36910	+	21.6092i	0.197372	+	0.794368i
$741$	−0.301788			−0.0110865
$742$			15.9649i			0.586091i
$743$		−	43.0782i		−	1.58039i	−0.612858	−	0.790193i	$-0.709980\pi$
$743$		−	43.0782i		−	1.58039i	0.612858	−	0.790193i	$-0.290020\pi$
$744$	5.40295			0.198082
$745$	23.1483	−	5.75154i	0.848090	−	0.210720i
$746$	−2.53919			−0.0929663
$747$		−	21.1110i		−	0.772411i
$748$			13.9916i			0.511583i
$749$	3.80713			0.139109
$750$	9.74313	−	8.72979i	0.355769	−	0.318767i
$751$	15.2690			0.557173			0.278587	−	0.960411i	$-0.410134\pi$
$751$	15.2690			0.557173			0.278587	+	0.960411i	$0.410134\pi$
$752$			1.12064i			0.0408655i
$753$		−	18.5913i		−	0.677504i
$754$	0.460811			0.0167818
$755$	−4.86376	+	1.20847i	−0.177010	+	0.0439808i
$756$	14.6803			0.533919
$757$			41.4863i			1.50784i	0.656964	+	0.753922i	$0.271840\pi$
$757$			41.4863i			1.50784i	−0.656964	+	0.753922i	$0.728160\pi$
$758$			26.0410i			0.945853i
$759$	−4.34017			−0.157538
$760$	1.77432	+	7.14116i	0.0643614	+	0.259037i
$761$	−35.4740			−1.28593			−0.642965	−	0.765895i	$-0.722296\pi$
$761$	−35.4740			−1.28593			−0.642965	+	0.765895i	$0.722296\pi$
$762$		−	4.86376i		−	0.176196i
$763$		−	5.91548i		−	0.214155i
$764$	14.1906			0.513398
$765$	4.84551	+	19.5018i	0.175190	+	0.705091i
$766$	25.0144			0.903806
$767$		−	0.979481i		−	0.0353670i
$768$			1.17009i			0.0422219i
$769$	−21.3318			−0.769243			−0.384622	−	0.923074i	$-0.625668\pi$
$769$	−21.3318			−0.769243			−0.384622	+	0.923074i	$0.625668\pi$
$770$	−14.9288	+	3.70928i	−0.537997	+	0.133673i
$771$	−20.4813			−0.737617
$772$			6.49693i			0.233830i
$773$			18.0300i			0.648493i	0.945973	+	0.324247i	$0.105111\pi$
$773$			18.0300i			0.648493i	−0.945973	+	0.324247i	$0.894889\pi$
$774$	−1.63090			−0.0586214
$775$	−20.4030	+	10.8059i	−0.732896	+	0.388160i
$776$	3.51026			0.126011
$777$			31.5669i			1.13246i
$778$		−	15.3074i		−	0.548796i
$779$	25.7897			0.924013
$780$	0.199016	−	0.0494483i	0.00712591	−	0.00177053i
$781$	7.58372			0.271367
$782$		−	8.04945i		−	0.287848i
$783$			31.8576i			1.13850i
$784$	−0.340173			−0.0121490
$785$	−9.75031	−	39.2423i	−0.348004	−	1.40062i
$786$	−7.29299			−0.260132
$787$		−	43.0977i		−	1.53627i	−0.640290	−	0.768133i	$-0.721186\pi$
$787$		−	43.0977i		−	1.53627i	0.640290	−	0.768133i	$-0.278814\pi$
$788$			8.18568i			0.291603i
$789$	29.6982			1.05728
$790$	−4.58864	−	18.4680i	−0.163256	−	0.657062i
$791$	−30.3184			−1.07800
$792$		−	4.14116i		−	0.147150i
$793$		−	0.896005i		−	0.0318181i
$794$	−14.2907			−0.507159
$795$	−14.9627	+	3.71769i	−0.530671	+	0.131853i
$796$	1.48360			0.0525847
$797$			0.0289294i			0.00102473i	1.00000		0.000512366i	$0.000163091\pi$
$797$			0.0289294i			0.00102473i	−1.00000		0.000512366i	$0.999837\pi$
$798$			10.4319i			0.369285i
$799$	−6.17501			−0.218456
$800$	−2.34017	−	4.41855i	−0.0827376	−	0.156219i
$801$	−26.7415			−0.944865
$802$			6.62863i			0.234065i
$803$			29.0856i			1.02641i
$804$	−8.63809			−0.304642
$805$	8.58864	−	2.13397i	0.302710	−	0.0752125i
$806$	−0.361914			−0.0127479
$807$		−	27.3652i		−	0.963302i
$808$		−	15.1122i		−	0.531646i
$809$	−35.9132			−1.26264			−0.631321	−	0.775522i	$-0.717487\pi$
$809$	−35.9132			−1.26264			−0.631321	+	0.775522i	$0.717487\pi$
$810$	0.780465	+	3.14116i	0.0274228	+	0.110369i
$811$	−24.8843			−0.873805			−0.436903	−	0.899509i	$-0.643925\pi$
$811$	−24.8843			−0.873805			−0.436903	+	0.899509i	$0.643925\pi$
$812$		−	15.9288i		−	0.558992i
$813$			3.57653i			0.125434i
$814$	25.2846			0.886224
$815$	4.99386	+	20.0989i	0.174927	+	0.704034i
$816$	−6.44748			−0.225707
$817$		−	3.29072i		−	0.115128i
$818$		−	13.2462i		−	0.463142i
$819$	−0.346316			−0.0121013
$820$	−17.0072	+	4.22568i	−0.593917	+	0.147567i
$821$	33.2183			1.15933			0.579664	−	0.814856i	$-0.303184\pi$
$821$	33.2183			1.15933			0.579664	+	0.814856i	$0.303184\pi$
$822$		−	8.19902i		−	0.285974i
$823$		−	45.9155i		−	1.60051i	−0.599658	−	0.800256i	$-0.704697\pi$
$823$		−	45.9155i		−	1.60051i	0.599658	−	0.800256i	$-0.295303\pi$
$824$	−7.75872			−0.270288
$825$	−6.95282	−	13.1278i	−0.242066	−	0.457052i
$826$	−33.8576			−1.17806
$827$		−	29.3656i		−	1.02114i	−0.859835	−	0.510571i	$-0.829434\pi$
$827$		−	29.3656i		−	1.02114i	0.859835	−	0.510571i	$-0.170566\pi$
$828$			2.38243i			0.0827953i
$829$	−29.3123			−1.01806			−0.509029	−	0.860749i	$-0.669995\pi$
$829$	−29.3123			−1.01806			−0.509029	+	0.860749i	$0.669995\pi$
$830$	−28.0905	+	6.97948i	−0.975035	+	0.242261i
$831$	21.8576			0.758232
$832$		−	0.0783777i		−	0.00271726i
$833$		−	1.87444i		−	0.0649455i
$834$	21.5936			0.747724
$835$	−5.06997	−	20.4052i	−0.175453	−	0.706152i
$836$	8.35577			0.288990
$837$		−	25.0205i		−	0.864836i
$838$		−	29.3318i		−	1.01325i
$839$	23.3412			0.805828			0.402914	−	0.915238i	$-0.367997\pi$
$839$	23.3412			0.805828			0.402914	+	0.915238i	$0.367997\pi$
$840$	−1.70928	−	6.87936i	−0.0589756	−	0.237361i
$841$	5.56690			0.191962
$842$			35.6525i			1.22866i
$843$		−	10.3642i		−	0.356961i
$844$	−19.1506			−0.659191
$845$	28.1978	−	7.00614i	0.970034	−	0.241019i
$846$	1.82765			0.0628358
$847$		−	12.3340i		−	0.423802i
$848$			5.89269i			0.202356i
$849$	10.7538			0.369070
$850$	24.3474	−	12.8950i	0.835108	−	0.442293i
$851$	−14.5464			−0.498643
$852$			3.49466i			0.119725i
$853$			6.76487i			0.231625i	0.993271	+	0.115812i	$0.0369471\pi$
$853$			6.76487i			0.231625i	−0.993271	+	0.115812i	$0.963053\pi$
$854$	−30.9721			−1.05984
$855$	11.6465	−	2.89374i	0.398302	−	0.0989637i
$856$	1.40522			0.0480294
$857$			27.2423i			0.930580i	0.885158	+	0.465290i	$0.154050\pi$
$857$			27.2423i			0.930580i	−0.885158	+	0.465290i	$0.845950\pi$
$858$		−	0.232866i		−	0.00794991i
$859$	46.6430			1.59144			0.795719	−	0.605665i	$-0.207093\pi$
$859$	46.6430			1.59144			0.795719	+	0.605665i	$0.207093\pi$
$860$	0.539189	+	2.17009i	0.0183862	+	0.0739993i
$861$	−24.8443			−0.846691
$862$		−	20.2472i		−	0.689624i
$863$			29.7815i			1.01377i	0.862012	+	0.506887i	$0.169204\pi$
$863$			29.7815i			1.01377i	−0.862012	+	0.506887i	$0.830796\pi$
$864$	5.41855			0.184343
$865$	−3.06278	−	12.3268i	−0.104138	−	0.419125i
$866$	4.42961			0.150524
$867$		−	15.6358i		−	0.531020i
$868$			12.5103i			0.424626i
$869$	−21.6092			−0.733040
$870$	14.9288	−	3.70928i	0.506134	−	0.125756i
$871$	0.578618			0.0196057
$872$		−	2.18342i		−	0.0739398i
$873$		−	5.72487i		−	0.193758i
$874$	−4.80713			−0.162604
$875$	20.2134	+	22.5597i	0.683337	+	0.762657i
$876$	−13.4030			−0.452844
$877$		−	33.5402i		−	1.13257i	−0.824208	−	0.566287i	$-0.808380\pi$
$877$		−	33.5402i		−	1.13257i	0.824208	−	0.566287i	$-0.191620\pi$
$878$			26.4534i			0.892761i
$879$	−4.16660			−0.140536
$880$	−5.51026	+	1.36910i	−0.185751	+	0.0461524i
$881$	13.1034			0.441466			0.220733	−	0.975334i	$-0.429155\pi$
$881$	13.1034			0.441466			0.220733	+	0.975334i	$0.429155\pi$
$882$			0.554787i			0.0186807i
$883$			21.4729i			0.722621i	0.932446	+	0.361311i	$0.117671\pi$
$883$			21.4729i			0.722621i	−0.932446	+	0.361311i	$0.882329\pi$
$884$	0.431882			0.0145258
$885$	−7.88428	−	31.7321i	−0.265027	−	1.06666i
$886$	−21.0072			−0.705750
$887$			33.8059i			1.13509i	0.823342	+	0.567546i	$0.192107\pi$
$887$			33.8059i			1.13509i	−0.823342	+	0.567546i	$0.807893\pi$
$888$			11.6514i			0.390996i
$889$	11.2618			0.377708
$890$	8.84098	+	35.5825i	0.296350	+	1.19273i
$891$	3.67543			0.123131
$892$			9.55252i			0.319842i
$893$			3.68771i			0.123405i
$894$	12.4813			0.417438
$895$	34.1350	−	8.48133i	1.14101	−	0.283500i
$896$	−2.70928			−0.0905105
$897$			0.133969i			0.00447310i
$898$		−	0.167819i		−	0.00560019i
$899$	−27.1483			−0.905448
$900$	−7.20620	+	3.81658i	−0.240207	+	0.127219i
$901$	−32.4703			−1.08174
$902$			19.8999i			0.662594i
$903$			3.17009i			0.105494i
$904$	−11.1906			−0.372194
$905$	11.5597	−	2.87217i	0.384258	−	0.0954743i
$906$	−2.62249			−0.0871263
$907$			49.7514i			1.65197i	0.563694	+	0.825983i	$0.309380\pi$
$907$			49.7514i			1.65197i	−0.563694	+	0.825983i	$0.690620\pi$
$908$		−	13.8576i		−	0.459881i
$909$	−24.6465			−0.817473
$910$	0.114495	+	0.460811i	0.00379548	+	0.0152757i
$911$	−13.2956			−0.440504			−0.220252	−	0.975443i	$-0.570688\pi$
$911$	−13.2956			−0.440504			−0.220252	+	0.975443i	$0.570688\pi$
$912$			3.85043i			0.127501i
$913$			32.8683i			1.08778i
$914$	16.3545			0.540960
$915$	−7.21235	−	29.0277i	−0.238433	−	0.959626i
$916$	−23.1773			−0.765799
$917$		−	16.8865i		−	0.557643i
$918$			29.8576i			0.985448i
$919$	29.2856			0.966044			0.483022	−	0.875608i	$-0.339539\pi$
$919$	29.2856			0.966044			0.483022	+	0.875608i	$0.339539\pi$
$920$	3.17009	−	0.787653i	0.104515	−	0.0259682i
$921$	−38.1555			−1.25727
$922$		−	30.0027i		−	0.988085i
$923$		−	0.234088i		−	0.00770511i
$924$	−8.04945			−0.264807
$925$	−23.3028	−	43.9988i	−0.766192	−	1.44667i
$926$	−28.6925			−0.942893
$927$			12.6537i			0.415602i
$928$		−	5.87936i		−	0.193000i
$929$	47.9565			1.57340			0.786701	−	0.617334i	$-0.211787\pi$
$929$	47.9565			1.57340			0.786701	+	0.617334i	$0.211787\pi$
$930$	−11.7249	+	2.91321i	−0.384474	+	0.0955280i
$931$	−1.11942			−0.0366874
$932$		−	19.1278i		−	0.626553i
$933$			8.58023i			0.280904i
$934$	15.6092			0.510747
$935$	−7.54411	−	30.3630i	−0.246719	−	0.992975i
$936$	−0.127826			−0.00417813
$937$			1.14011i			0.0372458i	0.999827	+	0.0186229i	$0.00592820\pi$
$937$			1.14011i			0.0372458i	−0.999827	+	0.0186229i	$0.994072\pi$
$938$		−	20.0010i		−	0.653057i
$939$	−5.54411			−0.180925
$940$	−0.604236	−	2.43188i	−0.0197080	−	0.0793192i
$941$	26.4606			0.862592			0.431296	−	0.902210i	$-0.358056\pi$
$941$	26.4606			0.862592			0.431296	+	0.902210i	$0.358056\pi$
$942$		−	21.1590i		−	0.689398i
$943$		−	11.4485i		−	0.372815i
$944$	−12.4969			−0.406740
$945$	−31.8576	+	7.91548i	−1.03633	+	0.257491i
$946$	2.53919			0.0825562
$947$			54.4317i			1.76879i	0.466737	+	0.884396i	$0.345430\pi$
$947$			54.4317i			1.76879i	−0.466737	+	0.884396i	$0.654570\pi$
$948$		−	9.95774i		−	0.323412i
$949$	0.897791			0.0291435
$950$	−7.70086	−	14.5402i	−0.249849	−	0.471747i
$951$	−8.03385			−0.260515
$952$		−	14.9288i		−	0.483846i
$953$			27.4319i			0.888606i	0.895877	+	0.444303i	$0.146549\pi$
$953$			27.4319i			0.888606i	−0.895877	+	0.444303i	$0.853451\pi$
$954$	9.61038			0.311147
$955$	−30.7948	+	7.65142i	−0.996498	+	0.247594i
$956$	−12.1434			−0.392746
$957$		−	17.4680i		−	0.564660i
$958$			31.2495i			1.00963i
$959$	18.9844			0.613038
$960$	−0.630898	−	2.53919i	−0.0203621	−	0.0819520i
$961$	−9.67808			−0.312196
$962$		−	0.780465i		−	0.0251632i
$963$		−	2.29177i		−	0.0738512i
$964$	13.1929			0.424914
$965$	−3.50307	−	14.0989i	−0.112768	−	0.453860i
$966$	4.63090			0.148997
$967$		−	50.5536i		−	1.62569i	−0.582478	−	0.812847i	$-0.697917\pi$
$967$		−	50.5536i		−	1.62569i	0.582478	−	0.812847i	$-0.302083\pi$
$968$		−	4.55252i		−	0.146324i
$969$	−21.2169			−0.681584
$970$	−7.61757	+	1.89269i	−0.244585	+	0.0607707i
$971$	−13.8010			−0.442895			−0.221447	−	0.975172i	$-0.571078\pi$
$971$	−13.8010			−0.442895			−0.221447	+	0.975172i	$0.571078\pi$
$972$		−	14.5620i		−	0.467076i
$973$			49.9988i			1.60289i
$974$	−13.8420			−0.443527
$975$	−0.405220	+	0.214614i	−0.0129774	+	0.00687316i
$976$	−11.4319			−0.365926
$977$			58.7819i			1.88060i	0.340348	+	0.940300i	$0.389455\pi$
$977$			58.7819i			1.88060i	−0.340348	+	0.940300i	$0.610545\pi$
$978$			10.8371i			0.346532i
$979$	41.6346			1.33065
$980$	0.738205	−	0.183417i	0.0235811	−	0.00585906i
$981$	−3.56093			−0.113692
$982$			4.97107i			0.158633i
$983$			40.6970i			1.29803i	0.760775	+	0.649016i	$0.224819\pi$
$983$			40.6970i			1.29803i	−0.760775	+	0.649016i	$0.775181\pi$
$984$	−9.17009			−0.292332
$985$	−4.41363	−	17.7636i	−0.140630	−	0.565997i
$986$	32.3968			1.03172
$987$		−	3.55252i		−	0.113078i
$988$		−	0.257920i		−	0.00820551i
$989$	−1.46081			−0.0464511
$990$	2.23287	+	8.98667i	0.0709651	+	0.285615i
$991$	−60.4489			−1.92022			−0.960111	−	0.279618i	$-0.909792\pi$
$991$	−60.4489			−1.92022			−0.960111	+	0.279618i	$0.909792\pi$
$992$			4.61757i			0.146608i
$993$			19.8576i			0.630163i
$994$	−8.09171			−0.256653
$995$	−3.21953	+	0.799939i	−0.102066	+	0.0253598i
$996$	−15.1461			−0.479922
$997$			7.79976i			0.247021i	0.992343	+	0.123510i	$0.0394153\pi$
$997$			7.79976i			0.247021i	−0.992343	+	0.123510i	$0.960585\pi$
$998$			15.4475i			0.488981i
$999$	53.9565			1.70711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.b.a.259.3	✓	6
5.2	odd	4		2150.2.a.bd.1.3		3
5.3	odd	4		2150.2.a.bc.1.1		3
5.4	even	2	inner	430.2.b.a.259.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.b.a.259.3	✓	6	1.1	even	1	trivial
430.2.b.a.259.4	yes	6	5.4	even	2	inner
2150.2.a.bc.1.1		3	5.3	odd	4
2150.2.a.bd.1.3		3	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.17009i q^{3} -1.00000 q^{4} +(2.17009 - 0.539189i) q^{5} +1.17009 q^{6} +2.70928i q^{7} +1.00000i q^{8} +1.63090 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.17009i q^{3} -1.00000 q^{4} +(2.17009 - 0.539189i) q^{5} +1.17009 q^{6} +2.70928i q^{7} +1.00000i q^{8} +1.63090 q^{9} +(-0.539189 - 2.17009i) q^{10} -2.53919 q^{11} -1.17009i q^{12} +0.0783777i q^{13} +2.70928 q^{14} +(0.630898 + 2.53919i) q^{15} +1.00000 q^{16} +5.51026i q^{17} -1.63090i q^{18} +3.29072 q^{19} +(-2.17009 + 0.539189i) q^{20} -3.17009 q^{21} +2.53919i q^{22} -1.46081i q^{23} -1.17009 q^{24} +(4.41855 - 2.34017i) q^{25} +0.0783777 q^{26} +5.41855i q^{27} -2.70928i q^{28} +5.87936 q^{29} +(2.53919 - 0.630898i) q^{30} -4.61757 q^{31} -1.00000i q^{32} -2.97107i q^{33} +5.51026 q^{34} +(1.46081 + 5.87936i) q^{35} -1.63090 q^{36} -9.95774i q^{37} -3.29072i q^{38} -0.0917087 q^{39} +(0.539189 + 2.17009i) q^{40} +7.83710 q^{41} +3.17009i q^{42} -1.00000i q^{43} +2.53919 q^{44} +(3.53919 - 0.879362i) q^{45} -1.46081 q^{46} +1.12064i q^{47} +1.17009i q^{48} -0.340173 q^{49} +(-2.34017 - 4.41855i) q^{50} -6.44748 q^{51} -0.0783777i q^{52} +5.89269i q^{53} +5.41855 q^{54} +(-5.51026 + 1.36910i) q^{55} -2.70928 q^{56} +3.85043i q^{57} -5.87936i q^{58} -12.4969 q^{59} +(-0.630898 - 2.53919i) q^{60} -11.4319 q^{61} +4.61757i q^{62} +4.41855i q^{63} -1.00000 q^{64} +(0.0422604 + 0.170086i) q^{65} -2.97107 q^{66} -7.38243i q^{67} -5.51026i q^{68} +1.70928 q^{69} +(5.87936 - 1.46081i) q^{70} -2.98667 q^{71} +1.63090i q^{72} -11.4547i q^{73} -9.95774 q^{74} +(2.73820 + 5.17009i) q^{75} -3.29072 q^{76} -6.87936i q^{77} +0.0917087i q^{78} +8.51026 q^{79} +(2.17009 - 0.539189i) q^{80} -1.44748 q^{81} -7.83710i q^{82} -12.9444i q^{83} +3.17009 q^{84} +(2.97107 + 11.9577i) q^{85} -1.00000 q^{86} +6.87936i q^{87} -2.53919i q^{88} -16.3968 q^{89} +(-0.879362 - 3.53919i) q^{90} -0.212347 q^{91} +1.46081i q^{92} -5.40295i q^{93} +1.12064 q^{94} +(7.14116 - 1.77432i) q^{95} +1.17009 q^{96} -3.51026i q^{97} +0.340173i q^{98} -4.14116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9	\( 6 q - 6 q^{4} + 2 q^{5} - 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 34 q^{19} - 2 q^{20} - 8 q^{21} + 4 q^{24} - 2 q^{25} - 6 q^{26} + 10 q^{29} + 12 q^{30} - 18 q^{31} + 12 q^{35} - 2 q^{36} + 4 q^{39} - 10 q^{41} + 12 q^{44} + 18 q^{45} - 12 q^{46} + 20 q^{49} + 8 q^{50} - 40 q^{51} + 4 q^{54} - 2 q^{56} - 40 q^{59} + 4 q^{60} - 42 q^{61} - 6 q^{64} + 32 q^{65} + 12 q^{66} - 4 q^{69} + 10 q^{70} - 16 q^{71} - 28 q^{74} + 32 q^{75} - 34 q^{76} + 18 q^{79} + 2 q^{80} - 10 q^{81} + 8 q^{84} - 12 q^{85} - 6 q^{86} + 28 q^{89} + 20 q^{90} - 22 q^{91} + 32 q^{94} + 2 q^{95} - 4 q^{96} + 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 2 * q^5 - 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 34 * q^19 - 2 * q^20 - 8 * q^21 + 4 * q^24 - 2 * q^25 - 6 * q^26 + 10 * q^29 + 12 * q^30 - 18 * q^31 + 12 * q^35 - 2 * q^36 + 4 * q^39 - 10 * q^41 + 12 * q^44 + 18 * q^45 - 12 * q^46 + 20 * q^49 + 8 * q^50 - 40 * q^51 + 4 * q^54 - 2 * q^56 - 40 * q^59 + 4 * q^60 - 42 * q^61 - 6 * q^64 + 32 * q^65 + 12 * q^66 - 4 * q^69 + 10 * q^70 - 16 * q^71 - 28 * q^74 + 32 * q^75 - 34 * q^76 + 18 * q^79 + 2 * q^80 - 10 * q^81 + 8 * q^84 - 12 * q^85 - 6 * q^86 + 28 * q^89 + 20 * q^90 - 22 * q^91 + 32 * q^94 + 2 * q^95 - 4 * q^96 + 16 * q^99

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