LMFDB - Embedded newform 798.2.cj.a.649.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(241,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.241"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cj (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			649.9
Character	$\chi$	$=$	798.649
Dual form			798.2.cj.a.241.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.342020 + 0.939693i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.636249 + 0.758252i) q^{5} +(-0.342020 + 0.939693i) q^{6} +(2.63863 + 0.194020i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.930134 - 0.338541i) q^{10} +3.02124 q^{11} -1.00000 q^{12} +(5.58523 + 2.03286i) q^{13} +(0.720145 + 2.54586i) q^{14} +(-0.974791 + 0.171882i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.37756 - 0.242901i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-1.05772 - 4.22862i) q^{19} -0.989828i q^{20} +(1.89659 + 1.84470i) q^{21} +(1.03333 + 2.83904i) q^{22} +(-5.59152 - 2.03515i) q^{23} +(-0.342020 - 0.939693i) q^{24} +(0.698107 + 3.95916i) q^{25} +5.94367i q^{26} +(-0.500000 + 0.866025i) q^{27} +(-2.14602 + 1.54745i) q^{28} +(1.50432 + 1.79277i) q^{29} +(-0.494914 - 0.857216i) q^{30} +(-2.79867 + 4.84744i) q^{31} +(0.984808 - 0.173648i) q^{32} +(2.31441 + 1.94202i) q^{33} +(-0.242901 - 1.37756i) q^{34} +(-1.82594 + 1.87730i) q^{35} +(-0.766044 - 0.642788i) q^{36} +(-2.19310 - 1.26619i) q^{37} +(3.61184 - 2.44020i) q^{38} +(2.97184 + 5.14737i) q^{39} +(0.930134 - 0.338541i) q^{40} +(-6.80561 + 2.47704i) q^{41} +(-1.08478 + 2.41314i) q^{42} +(-1.21794 + 6.90726i) q^{43} +(-2.31441 + 1.94202i) q^{44} +(-0.857216 - 0.494914i) q^{45} -5.95037i q^{46} +(6.70988 - 1.18313i) q^{47} +(0.766044 - 0.642788i) q^{48} +(6.92471 + 1.02389i) q^{49} +(-3.48163 + 2.01012i) q^{50} +(-0.899139 - 1.07155i) q^{51} +(-5.58523 + 2.03286i) q^{52} +(-4.69201 - 5.59172i) q^{53} +(-0.984808 - 0.173648i) q^{54} +(-1.92226 + 2.29087i) q^{55} +(-2.18811 - 1.48734i) q^{56} +(1.90784 - 3.91920i) q^{57} +(-1.17015 + 2.02676i) q^{58} +(-0.265323 + 1.50472i) q^{59} +(0.636249 - 0.758252i) q^{60} +(3.75476 - 10.3161i) q^{61} +(-5.51230 - 0.971968i) q^{62} +(0.267121 + 2.63223i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.09501 + 2.94161i) q^{65} +(-1.03333 + 2.83904i) q^{66} +(1.18712 - 3.26159i) q^{67} +(1.21141 - 0.699406i) q^{68} +(-2.97519 - 5.15317i) q^{69} +(-2.38859 - 1.07375i) q^{70} +(-7.98583 - 1.40812i) q^{71} +(0.342020 - 0.939693i) q^{72} +(1.35401 - 1.61365i) q^{73} +(0.439742 - 2.49390i) q^{74} +(-2.01012 + 3.48163i) q^{75} +(3.52836 + 2.55942i) q^{76} +(7.97194 + 0.586181i) q^{77} +(-3.82052 + 4.55312i) q^{78} +(8.81286 + 1.55394i) q^{79} +(0.636249 + 0.758252i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-4.65531 - 5.54799i) q^{82} +(3.46857 - 2.00258i) q^{83} +(-2.63863 - 0.194020i) q^{84} +(1.06065 - 0.889993i) q^{85} +(-6.90726 + 1.21794i) q^{86} +2.34030i q^{87} +(-2.61647 - 1.51062i) q^{88} +(13.8061 - 11.5847i) q^{89} +(0.171882 - 0.974791i) q^{90} +(14.3429 + 6.44759i) q^{91} +(5.59152 - 2.03515i) q^{92} +(-5.25978 + 1.91440i) q^{93} +(3.40670 + 5.90057i) q^{94} +(3.87934 + 1.88844i) q^{95} +(0.866025 + 0.500000i) q^{96} +(4.48053 + 3.75961i) q^{97} +(1.40625 + 6.85729i) q^{98} +(0.524634 + 2.97535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 12 q^{7} + 12 q^{10} - 12 q^{11} - 72 q^{12} - 30 q^{13} - 18 q^{14} + 36 q^{19} - 6 q^{21} + 12 q^{22} - 6 q^{23} - 30 q^{25} - 36 q^{27} - 12 q^{28} - 6 q^{31} - 12 q^{33} - 6 q^{34} - 6 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) $ 72 * q + 12 * q^7 + 12 * q^10 - 12 * q^11 - 72 * q^12 - 30 * q^13 - 18 * q^14 + 36 * q^19 - 6 * q^21 + 12 * q^22 - 6 * q^23 - 30 * q^25 - 36 * q^27 - 12 * q^28 - 6 * q^31 - 12 * q^33 - 6 * q^34 - 6 * q^35 - 18 * q^37 - 12 * q^38 - 12 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 18 * q^45 - 18 * q^47 - 24 * q^49 - 18 * q^51 + 30 * q^52 - 48 * q^53 + 30 * q^55 - 18 * q^56 + 6 * q^57 - 48 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^63 + 36 * q^64 - 72 * q^65 - 12 * q^66 + 84 * q^67 - 6 * q^69 + 54 * q^70 + 6 * q^71 + 60 * q^73 - 18 * q^74 + 6 * q^75 + 18 * q^76 + 48 * q^77 - 12 * q^78 + 60 * q^79 + 6 * q^82 - 18 * q^83 - 12 * q^84 + 84 * q^85 - 12 * q^86 + 24 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 - 42 * q^93 + 18 * q^94 + 60 * q^95 - 30 * q^97 - 24 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$2$	0.342020	+	0.939693i	0.241845	+	0.664463i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$3$	0.766044	+	0.642788i	0.442276	+	0.371114i
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$	−0.636249	+	0.758252i	−0.284539	+	0.339101i	−0.889315	−	0.457295i	$-0.848818\pi$
$5$	−0.636249	+	0.758252i	−0.284539	+	0.339101i	0.604776	+	0.796396i	$0.293263\pi$
$6$	−0.342020	+	0.939693i	−0.139629	+	0.383628i
$7$	2.63863	+	0.194020i	0.997308	+	0.0733325i
$7$	2.63863	+	0.194020i	0.997308	+	0.0733325i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.930134	−	0.338541i	−0.294134	−	0.107056i
$11$	3.02124			0.910939			0.455470	−	0.890251i	$-0.349471\pi$
$11$	3.02124			0.910939			0.455470	+	0.890251i	$0.349471\pi$
$12$	−1.00000			−0.288675
$13$	5.58523	+	2.03286i	1.54906	+	0.563813i	0.968198	−	0.250187i	$-0.0804921\pi$
$13$	5.58523	+	2.03286i	1.54906	+	0.563813i	0.580865	+	0.814000i	$0.302714\pi$
$14$	0.720145	+	2.54586i	0.192467	+	0.680409i
$15$	−0.974791	+	0.171882i	−0.251690	+	0.0443797i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.37756	−	0.242901i	−0.334108	−	0.0589122i	0.00407783	−	0.999992i	$-0.498702\pi$
$17$	−1.37756	−	0.242901i	−0.334108	−	0.0589122i	−0.338185	+	0.941080i	$0.609813\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−1.05772	−	4.22862i	−0.242657	−	0.970112i
$19$	−1.05772	−	4.22862i	−0.242657	−	0.970112i
$20$		−	0.989828i		−	0.221332i
$21$	1.89659	+	1.84470i	0.413870	+	0.402548i
$22$	1.03333	+	2.83904i	0.220306	+	0.605286i
$23$	−5.59152	−	2.03515i	−1.16591	−	0.424358i	−0.314707	−	0.949189i	$-0.601906\pi$
$23$	−5.59152	−	2.03515i	−1.16591	−	0.424358i	−0.851206	+	0.524831i	$0.824128\pi$
$24$	−0.342020	−	0.939693i	−0.0698146	−	0.191814i
$25$	0.698107	+	3.95916i	0.139621	+	0.791833i
$26$			5.94367i			1.16565i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	−2.14602	+	1.54745i	−0.405560	+	0.292440i
$29$	1.50432	+	1.79277i	0.279344	+	0.332910i	0.887413	−	0.460975i	$-0.152500\pi$
$29$	1.50432	+	1.79277i	0.279344	+	0.332910i	−0.608069	+	0.793884i	$0.708056\pi$
$30$	−0.494914	−	0.857216i	−0.0903585	−	0.156506i
$31$	−2.79867	+	4.84744i	−0.502656	+	0.870625i	0.497339	+	0.867556i	$0.334310\pi$
$31$	−2.79867	+	4.84744i	−0.502656	+	0.870625i	−0.999995	+	0.00306941i	$0.999023\pi$
$32$	0.984808	−	0.173648i	0.174091	−	0.0306970i
$33$	2.31441	+	1.94202i	0.402887	+	0.338062i
$34$	−0.242901	−	1.37756i	−0.0416572	−	0.236250i
$35$	−1.82594	+	1.87730i	−0.308640	+	0.317322i
$36$	−0.766044	−	0.642788i	−0.127674	−	0.107131i
$37$	−2.19310	−	1.26619i	−0.360543	−	0.208160i	0.308776	−	0.951135i	$-0.400081\pi$
$37$	−2.19310	−	1.26619i	−0.360543	−	0.208160i	−0.669319	+	0.742975i	$0.733414\pi$
$38$	3.61184	−	2.44020i	0.585918	−	0.395853i
$39$	2.97184	+	5.14737i	0.475875	+	0.824239i
$40$	0.930134	−	0.338541i	0.147067	−	0.0535281i
$41$	−6.80561	+	2.47704i	−1.06286	+	0.386849i	−0.813501	−	0.581563i	$-0.802441\pi$
$41$	−6.80561	+	2.47704i	−1.06286	+	0.386849i	−0.249357	+	0.968412i	$0.580219\pi$
$42$	−1.08478	+	2.41314i	−0.167386	+	0.372356i
$43$	−1.21794	+	6.90726i	−0.185734	+	1.05335i	0.739276	+	0.673403i	$0.235168\pi$
$43$	−1.21794	+	6.90726i	−0.185734	+	1.05335i	−0.925009	+	0.379945i	$0.875943\pi$
$44$	−2.31441	+	1.94202i	−0.348910	+	0.292770i
$45$	−0.857216	−	0.494914i	−0.127786	−	0.0737774i
$46$		−	5.95037i		−	0.877335i
$47$	6.70988	−	1.18313i	0.978737	−	0.172578i	0.338677	−	0.940903i	$-0.390021\pi$
$47$	6.70988	−	1.18313i	0.978737	−	0.172578i	0.640060	+	0.768325i	$0.278909\pi$
$48$	0.766044	−	0.642788i	0.110569	−	0.0927784i
$49$	6.92471	+	1.02389i	0.989245	+	0.146270i
$50$	−3.48163	+	2.01012i	−0.492377	+	0.284274i
$51$	−0.899139	−	1.07155i	−0.125905	−	0.150047i
$52$	−5.58523	+	2.03286i	−0.774531	+	0.281906i
$53$	−4.69201	−	5.59172i	−0.644497	−	0.768082i	0.340576	−	0.940217i	$-0.389378\pi$
$53$	−4.69201	−	5.59172i	−0.644497	−	0.768082i	−0.985073	+	0.172135i	$0.944933\pi$
$54$	−0.984808	−	0.173648i	−0.134015	−	0.0236305i
$55$	−1.92226	+	2.29087i	−0.259198	+	0.308900i
$56$	−2.18811	−	1.48734i	−0.292398	−	0.198754i
$57$	1.90784	−	3.91920i	0.252700	−	0.519111i
$58$	−1.17015	+	2.02676i	−0.153648	+	0.266126i
$59$	−0.265323	+	1.50472i	−0.0345421	+	0.195898i	−0.997196	−	0.0748381i	$-0.976156\pi$
$59$	−0.265323	+	1.50472i	−0.0345421	+	0.195898i	0.962654	+	0.270736i	$0.0872671\pi$
$60$	0.636249	−	0.758252i	0.0821394	−	0.0978900i
$61$	3.75476	−	10.3161i	0.480748	−	1.32084i	−0.428106	−	0.903729i	$-0.640819\pi$
$61$	3.75476	−	10.3161i	0.480748	−	1.32084i	0.908854	−	0.417115i	$-0.136959\pi$
$62$	−5.51230	−	0.971968i	−0.700063	−	0.123440i
$63$	0.267121	+	2.63223i	0.0336541	+	0.331630i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−5.09501	+	2.94161i	−0.631959	+	0.364862i
$66$	−1.03333	+	2.83904i	−0.127194	+	0.349462i
$67$	1.18712	−	3.26159i	0.145030	−	0.398466i	−0.845814	−	0.533478i	$-0.820885\pi$
$67$	1.18712	−	3.26159i	0.145030	−	0.398466i	0.990844	+	0.135011i	$0.0431071\pi$
$68$	1.21141	−	0.699406i	0.146905	−	0.0848154i
$69$	−2.97519	−	5.15317i	−0.358170	−	0.620369i
$70$	−2.38859	−	1.07375i	−0.285492	−	0.128337i
$71$	−7.98583	−	1.40812i	−0.947743	−	0.167113i	−0.321648	−	0.946859i	$-0.604237\pi$
$71$	−7.98583	−	1.40812i	−0.947743	−	0.167113i	−0.626095	+	0.779747i	$0.715348\pi$
$72$	0.342020	−	0.939693i	0.0403075	−	0.110744i
$73$	1.35401	−	1.61365i	0.158475	−	0.188863i	−0.680964	−	0.732317i	$-0.738439\pi$
$73$	1.35401	−	1.61365i	0.158475	−	0.188863i	0.839439	+	0.543453i	$0.182884\pi$
$74$	0.439742	−	2.49390i	0.0511190	−	0.289910i
$75$	−2.01012	+	3.48163i	−0.232109	+	0.402024i
$76$	3.52836	+	2.55942i	0.404731	+	0.293586i
$77$	7.97194	+	0.586181i	0.908487	+	0.0668015i
$78$	−3.82052	+	4.55312i	−0.432589	+	0.515539i
$79$	8.81286	+	1.55394i	0.991524	+	0.174832i	0.645802	−	0.763505i	$-0.276523\pi$
$79$	8.81286	+	1.55394i	0.991524	+	0.174832i	0.345722	+	0.938337i	$0.387634\pi$
$80$	0.636249	+	0.758252i	0.0711348	+	0.0847752i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−4.65531	−	5.54799i	−0.514093	−	0.612673i
$83$	3.46857	−	2.00258i	0.380725	−	0.219812i	−0.297408	−	0.954750i	$-0.596122\pi$
$83$	3.46857	−	2.00258i	0.380725	−	0.219812i	0.678134	+	0.734938i	$0.262789\pi$
$84$	−2.63863	−	0.194020i	−0.287898	−	0.0211693i
$85$	1.06065	−	0.889993i	0.115044	−	0.0965333i
$86$	−6.90726	+	1.21794i	−0.744829	+	0.131333i
$87$			2.34030i			0.250906i
$88$	−2.61647	−	1.51062i	−0.278917	−	0.161033i
$89$	13.8061	−	11.5847i	1.46344	−	1.22798i	0.541472	−	0.840719i	$-0.317867\pi$
$89$	13.8061	−	11.5847i	1.46344	−	1.22798i	0.921972	−	0.387256i	$-0.126577\pi$
$90$	0.171882	−	0.974791i	0.0181179	−	0.102752i
$91$	14.3429	+	6.44759i	1.50355	+	0.675891i
$92$	5.59152	−	2.03515i	0.582956	−	0.212179i
$93$	−5.25978	+	1.91440i	−0.545414	+	0.198514i
$94$	3.40670	+	5.90057i	0.351374	+	0.608598i
$95$	3.87934	+	1.88844i	0.398011	+	0.193750i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	4.48053	+	3.75961i	0.454929	+	0.381731i	0.841261	−	0.540629i	$-0.181814\pi$
$97$	4.48053	+	3.75961i	0.454929	+	0.381731i	−0.386332	+	0.922360i	$0.626258\pi$
$98$	1.40625	+	6.85729i	0.142053	+	0.692691i
$99$	0.524634	+	2.97535i	0.0527277	+	0.299033i
$100$	−3.07968	−	2.58416i	−0.307968	−	0.258416i
$101$	−12.6555	+	2.23150i	−1.25927	+	0.222043i	−0.763155	−	0.646216i	$-0.776351\pi$
$101$	−12.6555	+	2.23150i	−1.25927	+	0.222043i	−0.496112	+	0.868259i	$0.665239\pi$
$102$	0.699406	−	1.21141i	0.0692515	−	0.119947i
$103$	−6.88379	−	11.9231i	−0.678280	−	1.17482i	−0.975498	−	0.220006i	$-0.929392\pi$
$103$	−6.88379	−	11.9231i	−0.678280	−	1.17482i	0.297218	−	0.954810i	$-0.403941\pi$
$104$	−3.82052	−	4.55312i	−0.374633	−	0.446470i
$105$	−2.60546	+	0.264404i	−0.254267	+	0.0258032i
$106$	3.64974	−	6.32153i	0.354494	−	0.614001i
$107$		−	10.2996i		−	0.995697i	−0.867264	−	0.497848i	$-0.834124\pi$
$107$		−	10.2996i		−	0.995697i	0.867264	−	0.497848i	$-0.165876\pi$
$108$	−0.173648	−	0.984808i	−0.0167093	−	0.0947632i
$109$	−0.168587	−	0.463189i	−0.0161477	−	0.0443654i	0.931357	−	0.364108i	$-0.118626\pi$
$109$	−0.168587	−	0.463189i	−0.0161477	−	0.0443654i	−0.947505	+	0.319742i	$0.896404\pi$
$110$	−2.81016	−	1.02282i	−0.267939	−	0.0975217i
$111$	−0.866123	−	2.37965i	−0.0822087	−	0.225867i
$112$	0.649265	−	2.56485i	0.0613498	−	0.242356i
$113$			4.15837i			0.391187i	0.980685	+	0.195593i	$0.0626633\pi$
$113$			4.15837i			0.391187i	−0.980685	+	0.195593i	$0.937337\pi$
$114$	4.33536	+	0.452342i	0.406044	+	0.0423657i
$115$	5.10076	−	2.94492i	0.475648	−	0.274616i
$116$	−2.30474	−	0.406389i	−0.213990	−	0.0377322i
$117$	−1.03211	+	5.85337i	−0.0954184	+	0.541145i
$118$	−1.50472	+	0.265323i	−0.138521	+	0.0244250i
$119$	−3.58774	−	0.908199i	−0.328888	−	0.0832545i
$120$	0.930134	+	0.338541i	0.0849093	+	0.0309044i
$121$	−1.87208			−0.170189
$122$	10.9782			0.993918
$123$	−6.80561	−	2.47704i	−0.613641	−	0.223347i
$124$	−0.971968	−	5.51230i	−0.0872853	−	0.495019i
$125$	−7.73230	−	4.46424i	−0.691598	−	0.399294i
$126$	−2.38213	+	1.15129i	−0.212217	+	0.102565i
$127$	−4.33082	+	11.8988i	−0.384298	+	1.05585i	0.585229	+	0.810868i	$0.301005\pi$
$127$	−4.33082	+	11.8988i	−0.384298	+	1.05585i	−0.969527	+	0.244983i	$0.921218\pi$
$128$	−0.642788	+	0.766044i	−0.0568149	+	0.0677094i
$129$	−5.37290	+	4.50840i	−0.473057	+	0.396942i
$130$	−4.50680	−	3.78166i	−0.395273	−	0.331673i
$131$	−3.56983	−	9.80802i	−0.311897	−	0.856931i	−0.992274	−	0.124068i	$-0.960406\pi$
$131$	−3.56983	−	9.80802i	−0.311897	−	0.856931i	0.680376	−	0.732863i	$-0.261816\pi$
$132$	−3.02124			−0.262966
$133$	−1.97049	−	11.3630i	−0.170863	−	0.985295i
$134$	3.47091			0.299841
$135$	−0.338541	−	0.930134i	−0.0291370	−	0.0800532i
$136$	1.07155	+	0.899139i	0.0918848	+	0.0771005i
$137$	2.20160	−	1.84736i	0.188095	−	0.157831i	−0.543877	−	0.839165i	$-0.683044\pi$
$137$	2.20160	−	1.84736i	0.188095	−	0.157831i	0.731973	+	0.681334i	$0.238600\pi$
$138$	3.82483	−	4.55825i	0.325591	−	0.388024i
$139$	7.55913	−	20.7685i	0.641157	−	1.76156i	−0.00690462	−	0.999976i	$-0.502198\pi$
$139$	7.55913	−	20.7685i	0.641157	−	1.76156i	0.648062	−	0.761588i	$-0.275580\pi$
$140$	0.192046	−	2.61179i	0.0162309	−	0.220736i
$141$	5.90057	+	3.40670i	0.496918	+	0.286896i
$142$	−1.40812	−	7.98583i	−0.118167	−	0.670156i
$143$	16.8743	+	6.14175i	1.41110	+	0.513599i
$144$	1.00000			0.0833333
$145$	−2.31649			−0.192374
$146$	1.97943	+	0.720454i	0.163819	+	0.0596252i
$147$	4.64649	+	5.23547i	0.383236	+	0.431814i
$148$	2.49390	−	0.439742i	0.204997	−	0.0361466i
$149$	−4.10325	+	23.2707i	−0.336151	+	1.90641i	0.0794090	+	0.996842i	$0.474697\pi$
$149$	−4.10325	+	23.2707i	−0.336151	+	1.90641i	−0.415560	+	0.909566i	$0.636414\pi$
$150$	−3.95916	−	0.698107i	−0.323264	−	0.0570002i
$151$	16.7477	−	9.66927i	1.36291	−	0.786874i	0.372896	−	0.927873i	$-0.378365\pi$
$151$	16.7477	−	9.66927i	1.36291	−	0.786874i	0.990010	+	0.140999i	$0.0450315\pi$
$152$	−1.19830	+	4.19095i	−0.0971948	+	0.339931i
$153$		−	1.39881i		−	0.113087i
$154$	2.17573	+	7.69166i	0.175326	+	0.619811i
$155$	−1.89493	−	5.20628i	−0.152204	−	0.418178i
$156$	−5.58523	−	2.03286i	−0.447176	−	0.162759i
$157$	2.66761	+	7.32920i	0.212899	+	0.584934i	0.999470	−	0.0325658i	$-0.0103679\pi$
$157$	2.66761	+	7.32920i	0.212899	+	0.584934i	−0.786571	+	0.617500i	$0.788146\pi$
$158$	1.55394	+	8.81286i	0.123625	+	0.701113i
$159$		−	7.29947i		−	0.578886i
$160$	−0.494914	+	0.857216i	−0.0391264	+	0.0677689i
$161$	−14.3591	−	6.45486i	−1.13165	−	0.508714i
$162$	−0.642788	−	0.766044i	−0.0505022	−	0.0601861i
$163$	−9.13444	−	15.8213i	−0.715465	−	1.23922i	−0.962780	−	0.270286i	$-0.912882\pi$
$163$	−9.13444	−	15.8213i	−0.715465	−	1.23922i	0.247315	−	0.968935i	$-0.420452\pi$
$164$	3.62119	−	6.27209i	0.282768	−	0.489768i
$165$	−2.94508	+	0.519297i	−0.229274	+	0.0404272i
$166$	3.06813	+	2.57447i	0.238133	+	0.199818i
$167$	−0.497398	−	2.82088i	−0.0384898	−	0.218287i	0.959496	−	0.281722i	$-0.0909055\pi$
$167$	−0.497398	−	2.82088i	−0.0384898	−	0.218287i	−0.997986	+	0.0634352i	$0.979794\pi$
$168$	−0.720145	−	2.54586i	−0.0555604	−	0.196417i
$169$	17.1037	+	14.3517i	1.31567	+	1.10397i
$170$	1.19908	+	0.692292i	0.0919656	+	0.0530964i
$171$	3.98071	−	1.77594i	0.304412	−	0.135810i
$172$	−3.50691	−	6.07414i	−0.267399	−	0.463149i
$173$	−14.1923	+	5.16558i	−1.07902	+	0.392732i	−0.819543	−	0.573017i	$-0.805773\pi$
$173$	−14.1923	+	5.16558i	−1.07902	+	0.392732i	−0.259478	+	0.965749i	$0.583551\pi$
$174$	−2.19916	+	0.800429i	−0.166718	+	0.0606804i
$175$	1.07389	+	10.5822i	0.0811785	+	0.799940i
$176$	0.524634	−	2.97535i	0.0395457	−	0.224275i
$177$	−1.17047	+	0.982138i	−0.0879776	+	0.0738220i
$178$	15.6080	+	9.01129i	1.16987	+	0.675425i
$179$			16.8757i			1.26135i	0.776046	+	0.630676i	$0.217222\pi$
$179$			16.8757i			1.26135i	−0.776046	+	0.630676i	$0.782778\pi$
$180$	0.974791	−	0.171882i	0.0726566	−	0.0128113i
$181$	7.73092	−	6.48701i	0.574635	−	0.482176i	−0.308546	−	0.951210i	$-0.599842\pi$
$181$	7.73092	−	6.48701i	0.574635	−	0.482176i	0.883180	+	0.469034i	$0.155398\pi$
$182$	−1.15319	+	15.6831i	−0.0854801	+	1.16251i
$183$	9.50739	−	5.48909i	0.702806	−	0.405765i
$184$	3.82483	+	4.55825i	0.281970	+	0.336039i
$185$	2.35545	−	0.857313i	0.173176	−	0.0630309i
$186$	−3.59790	−	4.28781i	−0.263811	−	0.314397i
$187$	−4.16195	−	0.733864i	−0.304352	−	0.0536654i
$188$	−4.37957	+	5.21936i	−0.319413	+	0.380661i
$189$	−1.48734	+	2.18811i	−0.108188	+	0.159161i
$190$	−0.447741	+	4.29127i	−0.0324826	+	0.311321i
$191$	2.58448	−	4.47645i	0.187007	−	0.323905i	−0.757244	−	0.653132i	$-0.773455\pi$
$191$	2.58448	−	4.47645i	0.187007	−	0.323905i	0.944251	+	0.329227i	$0.106788\pi$
$192$	−0.173648	+	0.984808i	−0.0125320	+	0.0710724i
$193$	−0.605125	+	0.721160i	−0.0435579	+	0.0519102i	−0.787384	−	0.616463i	$-0.788565\pi$
$193$	−0.605125	+	0.721160i	−0.0435579	+	0.0519102i	0.743826	+	0.668374i	$0.233009\pi$
$194$	−2.00045	+	5.49619i	−0.143624	+	0.394603i
$195$	−5.79384	−	1.02161i	−0.414905	−	0.0731590i
$196$	−5.96278	+	3.66677i	−0.425913	+	0.261912i
$197$	6.31478	+	10.9375i	0.449909	+	0.779266i	0.998380	−	0.0569044i	$-0.0181230\pi$
$197$	6.31478	+	10.9375i	0.449909	+	0.779266i	−0.548470	+	0.836170i	$0.684790\pi$
$198$	−2.61647	+	1.51062i	−0.185945	+	0.107355i
$199$	4.60219	−	12.6444i	0.326241	−	0.896339i	−0.662813	−	0.748785i	$-0.730638\pi$
$199$	4.60219	−	12.6444i	0.326241	−	0.896339i	0.989054	−	0.147554i	$-0.0471402\pi$
$200$	1.37500	−	3.77779i	0.0972274	−	0.267130i
$201$	3.00590	−	1.73545i	0.212019	−	0.122410i
$202$	−6.42535	−	11.1290i	−0.452086	−	0.783036i
$203$	3.62149	+	5.02233i	0.254179	+	0.352498i
$204$	1.37756	+	0.242901i	0.0964485	+	0.0170065i
$205$	2.45184	−	6.73639i	0.171244	−	0.470490i
$206$	8.84963	−	10.5466i	0.616583	−	0.734815i
$207$	1.03327	−	5.85997i	0.0718173	−	0.407296i
$208$	2.97184	−	5.14737i	0.206060	−	0.356906i
$209$	−3.19563	−	12.7757i	−0.221046	−	0.883713i
$210$	−1.13958	−	2.35790i	−0.0786383	−	0.162710i
$211$	−3.20684	+	3.82176i	−0.220768	+	0.263101i	−0.865049	−	0.501688i	$-0.832712\pi$
$211$	−3.20684	+	3.82176i	−0.220768	+	0.263101i	0.644281	+	0.764789i	$0.277157\pi$
$212$	7.18858	+	1.26754i	0.493714	+	0.0870550i
$213$	−5.21238	−	6.21187i	−0.357146	−	0.425630i
$214$	9.67843	−	3.52266i	0.661604	−	0.240804i
$215$	−4.46254	−	5.31824i	−0.304343	−	0.362701i
$216$	0.866025	−	0.500000i	0.0589256	−	0.0340207i
$217$	−8.32514	+	12.2476i	−0.565148	+	0.831420i
$218$	0.377595	−	0.316840i	0.0255740	−	0.0214591i
$219$	2.07447	−	0.365784i	0.140179	−	0.0247174i
$220$		−	2.99051i		−	0.201620i
$221$	−7.20020	−	4.15704i	−0.484338	−	0.279633i
$222$	1.93991	−	1.62778i	0.130198	−	0.109249i
$223$	0.864794	−	4.90449i	0.0579109	−	0.328429i	−0.942065	−	0.335432i	$-0.891118\pi$
$223$	0.864794	−	4.90449i	0.0579109	−	0.328429i	0.999975	+	0.00700249i	$0.00222898\pi$
$224$	2.63223	−	0.267121i	0.175873	−	0.0178478i
$225$	−3.77779	+	1.37500i	−0.251853	+	0.0916669i
$226$	−3.90759	+	1.42225i	−0.259929	+	0.0946065i
$227$	1.12532	+	1.94912i	0.0746903	+	0.129367i	0.900952	−	0.433920i	$-0.142870\pi$
$227$	1.12532	+	1.94912i	0.0746903	+	0.129367i	−0.826261	+	0.563287i	$0.809537\pi$
$228$	1.05772	+	4.22862i	0.0700492	+	0.280047i
$229$	14.5499	+	8.40041i	0.961486	+	0.555114i	0.896630	−	0.442780i	$-0.146008\pi$
$229$	14.5499	+	8.40041i	0.961486	+	0.555114i	0.0648562	+	0.997895i	$0.479341\pi$
$230$	4.51188	+	3.78592i	0.297505	+	0.249636i
$231$	5.73007	+	5.57330i	0.377011	+	0.366697i
$232$	−0.406389	−	2.30474i	−0.0266807	−	0.151314i
$233$	−14.5076	−	12.1733i	−0.950425	−	0.797501i	0.0289439	−	0.999581i	$-0.490786\pi$
$233$	−14.5076	−	12.1733i	−0.950425	−	0.797501i	−0.979369	+	0.202080i	$0.935230\pi$
$234$	−5.85337	+	1.03211i	−0.382647	+	0.0674710i
$235$	−3.37204	+	5.84055i	−0.219968	+	0.380996i
$236$	−0.763967	−	1.32323i	−0.0497300	−	0.0861350i
$237$	5.75218	+	6.85518i	0.373644	+	0.445292i
$238$	−0.373652	−	3.68200i	−0.0242203	−	0.238668i
$239$	1.91994	−	3.32543i	0.124191	−	0.215104i	−0.797226	−	0.603681i	$-0.793700\pi$
$239$	1.91994	−	3.32543i	0.124191	−	0.215104i	0.921416	+	0.388577i	$0.127033\pi$
$240$			0.989828i			0.0638931i
$241$	−3.20624	−	18.1835i	−0.206532	−	1.17130i	−0.895010	−	0.446045i	$-0.852832\pi$
$241$	−3.20624	−	18.1835i	−0.206532	−	1.17130i	0.688478	−	0.725257i	$-0.258279\pi$
$242$	−0.640290	−	1.75918i	−0.0411594	−	0.113084i
$243$	−0.939693	−	0.342020i	−0.0602813	−	0.0219406i
$244$	3.75476	+	10.3161i	0.240374	+	0.660422i
$245$	−5.18221	+	4.59923i	−0.331079	+	0.293834i
$246$		−	7.24238i		−	0.461757i
$247$	2.68857	−	25.7680i	0.171070	−	1.63958i
$248$	4.84744	−	2.79867i	0.307813	−	0.177716i
$249$	3.94432	+	0.695489i	0.249961	+	0.0440749i
$250$	1.55042	−	8.79284i	0.0980569	−	0.556108i
$251$	22.4915	−	3.96586i	1.41965	−	0.250323i	0.589459	−	0.807798i	$-0.299341\pi$
$251$	22.4915	−	3.96586i	1.41965	−	0.250323i	0.830194	+	0.557475i	$0.188230\pi$
$252$	−1.89659	−	1.84470i	−0.119474	−	0.116205i
$253$	−16.8934	−	6.14868i	−1.06208	−	0.386564i
$254$	−12.6625			−0.794514
$255$	1.38458			0.0867060
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−3.87286	−	21.9641i	−0.241582	−	1.37008i	−0.828297	−	0.560289i	$-0.810690\pi$
$257$	−3.87286	−	21.9641i	−0.241582	−	1.37008i	0.586715	−	0.809794i	$-0.300421\pi$
$258$	−6.07414	−	3.50691i	−0.378160	−	0.218331i
$259$	−5.54111	−	3.76650i	−0.344308	−	0.234039i
$260$	2.01218	−	5.52841i	0.124790	−	0.342858i
$261$	−1.50432	+	1.79277i	−0.0931148	+	0.110970i
$262$	7.99557	−	6.70908i	0.493968	−	0.414488i
$263$	−1.14335	−	0.959381i	−0.0705017	−	0.0591580i	0.606856	−	0.794812i	$-0.292431\pi$
$263$	−1.14335	−	0.959381i	−0.0705017	−	0.0591580i	−0.677358	+	0.735654i	$0.736875\pi$
$264$	−1.03333	−	2.83904i	−0.0635968	−	0.174731i
$265$	7.22522			0.443842
$266$	10.0038	−	5.73802i	0.613370	−	0.351821i
$267$	18.0226			1.10296
$268$	1.18712	+	3.26159i	0.0725149	+	0.199233i
$269$	9.95083	+	8.34974i	0.606713	+	0.509092i	0.893595	−	0.448873i	$-0.148175\pi$
$269$	9.95083	+	8.34974i	0.606713	+	0.509092i	−0.286883	+	0.957966i	$0.592619\pi$
$270$	0.758252	−	0.636249i	0.0461458	−	0.0387209i
$271$	9.15562	−	10.9112i	0.556164	−	0.662811i	−0.412566	−	0.910928i	$-0.635367\pi$
$271$	9.15562	−	10.9112i	0.556164	−	0.662811i	0.968730	+	0.248117i	$0.0798118\pi$
$272$	−0.478422	+	1.31445i	−0.0290086	+	0.0797004i
$273$	6.84288	+	14.1586i	0.414150	+	0.856917i
$274$	2.48894	+	1.43699i	0.150363	+	0.0868119i
$275$	2.10915	+	11.9616i	0.127187	+	0.721312i
$276$	5.59152	+	2.03515i	0.336570	+	0.122501i
$277$	−8.07075			−0.484924			−0.242462	−	0.970161i	$-0.577955\pi$
$277$	−8.07075			−0.484924			−0.242462	+	0.970161i	$0.577955\pi$
$278$	22.1014			1.32555
$279$	−5.25978	−	1.91440i	−0.314895	−	0.114612i
$280$	2.51996	−	0.712820i	0.150597	−	0.0425991i
$281$	−20.1102	+	3.54597i	−1.19967	+	0.211535i	−0.737557	−	0.675285i	$-0.764021\pi$
$281$	−20.1102	+	3.54597i	−1.19967	+	0.211535i	−0.462116	+	0.886819i	$0.652910\pi$
$282$	−1.18313	+	6.70988i	−0.0704546	+	0.399568i
$283$	7.92977	+	1.39823i	0.471376	+	0.0831162i	0.404290	−	0.914631i	$-0.367519\pi$
$283$	7.92977	+	1.39823i	0.471376	+	0.0831162i	0.0670859	+	0.997747i	$0.478630\pi$
$284$	7.02262	−	4.05451i	0.416716	−	0.240591i
$285$	1.75788	+	3.94022i	0.104128	+	0.233398i
$286$			17.9573i			1.06184i
$287$	−18.4381	+	5.21557i	−1.08837	+	0.307865i
$288$	0.342020	+	0.939693i	0.0201537	+	0.0553719i
$289$	−14.1361	−	5.14512i	−0.831535	−	0.302654i
$290$	−0.792288	−	2.17679i	−0.0465247	−	0.127826i
$291$	1.01565	+	5.76006i	0.0595387	+	0.337661i
$292$			2.10647i			0.123272i
$293$	−8.27402	+	14.3310i	−0.483373	+	0.837227i	−0.999818	−	0.0190937i	$-0.993922\pi$
$293$	−8.27402	+	14.3310i	−0.483373	+	0.837227i	0.516445	+	0.856321i	$0.327255\pi$
$294$	−3.33053	+	6.15691i	−0.194241	+	0.359078i
$295$	−0.972148	−	1.15856i	−0.0566006	−	0.0674540i
$296$	1.26619	+	2.19310i	0.0735956	+	0.127471i
$297$	−1.51062	+	2.61647i	−0.0876552	+	0.151823i
$298$	−23.2707	+	4.10325i	−1.34803	+	0.237695i
$299$	−27.0927	−	22.7335i	−1.56681	−	1.31471i
$300$	−0.698107	−	3.95916i	−0.0403052	−	0.228582i
$301$	−4.55383	+	17.9894i	−0.262478	+	1.03689i
$302$	14.8142	+	12.4306i	0.852460	+	0.715299i
$303$	−11.1290	−	6.42535i	−0.639346	−	0.369127i
$304$	−4.34805	+	0.307358i	−0.249378	+	0.0176282i
$305$	5.43326	+	9.41068i	0.311107	+	0.538854i
$306$	1.31445	−	0.478422i	0.0751423	−	0.0273496i
$307$	2.62352	−	0.954883i	0.149732	−	0.0544981i	−0.266067	−	0.963955i	$-0.585724\pi$
$307$	2.62352	−	0.954883i	0.149732	−	0.0544981i	0.415799	+	0.909457i	$0.363502\pi$
$308$	−6.48365	+	4.67522i	−0.369440	+	0.266396i
$309$	2.39072	−	13.5584i	0.136003	−	0.771312i
$310$	4.24420	−	3.56130i	0.241054	−	0.202268i
$311$	16.5896	+	9.57801i	0.940710	+	0.543119i	0.890183	−	0.455604i	$-0.150577\pi$
$311$	16.5896	+	9.57801i	0.940710	+	0.543119i	0.0505271	+	0.998723i	$0.483910\pi$
$312$		−	5.94367i		−	0.336494i
$313$	−12.1902	+	2.14946i	−0.689031	+	0.121495i	−0.507191	−	0.861834i	$-0.669316\pi$
$313$	−12.1902	+	2.14946i	−0.689031	+	0.121495i	−0.181839	+	0.983328i	$0.558205\pi$
$314$	−5.97482	+	5.01347i	−0.337179	+	0.282926i
$315$	−2.16585	−	1.47221i	−0.122032	−	0.0829497i
$316$	−7.74990	+	4.47440i	−0.435966	+	0.251705i
$317$	3.85184	+	4.59045i	0.216341	+	0.257825i	0.863290	−	0.504708i	$-0.168400\pi$
$317$	3.85184	+	4.59045i	0.216341	+	0.257825i	−0.646949	+	0.762533i	$0.723955\pi$
$318$	6.85926	−	2.49657i	0.384648	−	0.140001i
$319$	4.54490	+	5.41641i	0.254466	+	0.303260i
$320$	−0.974791	−	0.171882i	−0.0544924	−	0.00960849i
$321$	6.62043	−	7.88993i	0.369517	−	0.440373i
$322$	1.15449	−	15.7008i	0.0643372	−	0.874972i
$323$	0.429936	+	6.08210i	0.0239223	+	0.338417i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−4.14932	+	23.5320i	−0.230163	+	1.30532i
$326$	11.7430	−	13.9948i	0.650385	−	0.775099i
$327$	0.168587	−	0.463189i	0.00932288	−	0.0256144i
$328$	7.13235	+	1.25763i	0.393818	+	0.0694408i
$329$	17.9344	−	1.82000i	0.988757	−	0.100340i
$330$	−1.49526	−	2.58986i	−0.0823112	−	0.142567i
$331$	−28.1134	+	16.2313i	−1.54525	+	0.892150i	−0.546756	+	0.837292i	$0.684137\pi$
$331$	−28.1134	+	16.2313i	−1.54525	+	0.892150i	−0.998494	+	0.0548581i	$0.982529\pi$
$332$	−1.36985	+	3.76362i	−0.0751801	+	0.206556i
$333$	0.866123	−	2.37965i	0.0474632	−	0.130404i
$334$	2.48064	−	1.43220i	0.135735	−	0.0783665i
$335$	1.71780	+	2.97532i	0.0938535	+	0.162559i
$336$	2.14602	−	1.54745i	0.117075	−	0.0844203i
$337$	−29.4827	−	5.19860i	−1.60603	−	0.283186i	−0.702489	−	0.711694i	$-0.747928\pi$
$337$	−29.4827	−	5.19860i	−1.60603	−	0.283186i	−0.903538	+	0.428509i	$0.859039\pi$
$338$	−7.63637	+	20.9807i	−0.415364	+	1.14120i
$339$	−2.67295	+	3.18550i	−0.145175	+	0.173012i
$340$	−0.240430	+	1.36355i	−0.0130392	+	0.0739488i
$341$	−8.45546	+	14.6453i	−0.457889	+	0.793087i
$342$	3.03032	+	3.13323i	0.163861	+	0.169426i
$343$	18.0731	+	4.04520i	0.975855	+	0.218420i
$344$	4.50840	−	5.37290i	0.243076	−	0.289687i
$345$	5.80037	+	1.02276i	0.312281	+	0.0550636i
$346$	−9.70811	−	11.5697i	−0.521911	−	0.621990i
$347$	20.2294	−	7.36291i	1.08597	−	0.395262i	0.263845	−	0.964565i	$-0.415009\pi$
$347$	20.2294	−	7.36291i	1.08597	−	0.395262i	0.822128	+	0.569303i	$0.192787\pi$
$348$	−1.50432	−	1.79277i	−0.0806398	−	0.0961027i
$349$	−10.4983	+	6.06122i	−0.561964	+	0.324450i	−0.753933	−	0.656951i	$-0.771846\pi$
$349$	−10.4983	+	6.06122i	−0.561964	+	0.324450i	0.191970	+	0.981401i	$0.438512\pi$
$350$	−9.57673	+	4.62845i	−0.511898	+	0.247401i
$351$	−4.55312	+	3.82052i	−0.243027	+	0.203924i
$352$	2.97535	−	0.524634i	0.158586	−	0.0279631i
$353$		−	33.8531i		−	1.80182i	−0.434005	−	0.900910i	$-0.642900\pi$
$353$		−	33.8531i		−	1.80182i	0.434005	−	0.900910i	$-0.357100\pi$
$354$	−1.32323	−	0.763967i	−0.0703289	−	0.0406044i
$355$	6.14869	−	5.15936i	0.326338	−	0.273830i
$356$	−3.12959	+	17.7488i	−0.165868	+	0.940684i
$357$	−2.16459	−	3.00188i	−0.114562	−	0.158876i
$358$	−15.8580	+	5.77185i	−0.838122	+	0.305052i
$359$	8.86075	−	3.22505i	0.467652	−	0.170212i	−0.0974362	−	0.995242i	$-0.531064\pi$
$359$	8.86075	−	3.22505i	0.467652	−	0.170212i	0.565089	+	0.825030i	$0.308842\pi$
$360$	0.494914	+	0.857216i	0.0260843	+	0.0451793i
$361$	−16.7625	+	8.94539i	−0.882235	+	0.470810i
$362$	8.73992	+	5.04600i	0.459360	+	0.265212i
$363$	−1.43410	−	1.20335i	−0.0752706	−	0.0631595i
$364$	−15.1317	+	4.28031i	−0.793119	+	0.224349i
$365$	0.362064	+	2.05336i	0.0189513	+	0.107478i
$366$	8.40978	+	7.05664i	0.439586	+	0.368856i
$367$	−0.321356	+	0.0566637i	−0.0167746	+	0.00295782i	−0.182029	−	0.983293i	$-0.558267\pi$
$367$	−0.321356	+	0.0566637i	−0.0167746	+	0.00295782i	0.165255	+	0.986251i	$0.447155\pi$
$368$	−2.97519	+	5.15317i	−0.155092	+	0.268628i
$369$	−3.62119	−	6.27209i	−0.188512	−	0.326512i
$370$	1.61122	+	1.92018i	0.0837634	+	0.0998253i
$371$	−11.2956	−	15.6648i	−0.586437	−	0.813276i
$372$	2.79867	−	4.84744i	0.145104	−	0.251328i
$373$			33.4145i			1.73014i	0.501655	+	0.865068i	$0.332725\pi$
$373$			33.4145i			1.73014i	−0.501655	+	0.865068i	$0.667275\pi$
$374$	−0.733864	−	4.16195i	−0.0379472	−	0.215209i
$375$	−3.05372	−	8.39003i	−0.157694	−	0.433260i
$376$	−6.40250	−	2.33032i	−0.330184	−	0.120177i
$377$	4.75749	+	13.0711i	0.245023	+	0.673196i
$378$	−2.56485	−	0.649265i	−0.131922	−	0.0333946i
$379$			23.4266i			1.20334i	0.798744	+	0.601671i	$0.205498\pi$
$379$			23.4266i			1.20334i	−0.798744	+	0.601671i	$0.794502\pi$
$380$	−4.18561	+	1.04696i	−0.214717	+	0.0537079i
$381$	−10.9660	+	6.33124i	−0.561806	+	0.324359i
$382$	5.09044	+	0.897581i	0.260449	+	0.0459242i
$383$	0.152316	−	0.863829i	0.00778300	−	0.0441396i	−0.980669	−	0.195674i	$-0.937310\pi$
$383$	0.152316	−	0.863829i	0.00778300	−	0.0441396i	0.988452	+	0.151535i	$0.0484216\pi$
$384$	−0.984808	+	0.173648i	−0.0502558	+	0.00886145i
$385$	−5.51661	+	5.67179i	−0.281153	+	0.289061i
$386$	−0.884634	−	0.321980i	−0.0450267	−	0.0163884i
$387$	−7.01382			−0.356532
$388$	−5.84892			−0.296934
$389$	5.77835	+	2.10315i	0.292974	+	0.106634i	0.484326	−	0.874888i	$-0.339065\pi$
$389$	5.77835	+	2.10315i	0.292974	+	0.106634i	−0.191352	+	0.981522i	$0.561287\pi$
$390$	−1.02161	−	5.79384i	−0.0517312	−	0.293382i
$391$	7.20832	+	4.16173i	0.364540	+	0.210468i
$392$	−5.48503	−	4.34907i	−0.277036	−	0.219661i
$393$	3.56983	−	9.80802i	0.180074	−	0.494749i
$394$	−8.11812	+	9.67480i	−0.408985	+	0.487409i
$395$	−6.78546	+	5.69367i	−0.341413	+	0.286480i
$396$	−2.31441	−	1.94202i	−0.116303	−	0.0975901i
$397$	3.73436	+	10.2601i	0.187422	+	0.514938i	0.997443	−	0.0714626i	$-0.0227667\pi$
$397$	3.73436	+	10.2601i	0.187422	+	0.514938i	−0.810021	+	0.586401i	$0.800544\pi$
$398$	13.4559			0.674484
$399$	5.79449	−	9.97115i	0.290088	−	0.499182i
$400$	4.02024			0.201012
$401$	4.61652	+	12.6838i	0.230538	+	0.633398i	0.999986	−	0.00531186i	$-0.00169083\pi$
$401$	4.61652	+	12.6838i	0.230538	+	0.633398i	−0.769448	+	0.638709i	$0.779469\pi$
$402$	2.65887	+	2.23106i	0.132612	+	0.111275i
$403$	−25.4853	+	21.3847i	−1.26952	+	1.06525i
$404$	8.26027	−	9.84421i	0.410964	−	0.489768i
$405$	0.338541	−	0.930134i	0.0168222	−	0.0462187i
$406$	−3.48082	+	5.12083i	−0.172750	+	0.254142i
$407$	−6.62589	−	3.82546i	−0.328433	−	0.189621i
$408$	0.242901	+	1.37756i	0.0120254	+	0.0681994i
$409$	−4.70410	−	1.71215i	−0.232603	−	0.0846605i	0.223089	−	0.974798i	$-0.428386\pi$
$409$	−4.70410	−	1.71215i	−0.232603	−	0.0846605i	−0.455692	+	0.890138i	$0.650608\pi$
$410$	7.16871			0.354038
$411$	2.87398			0.141763
$412$	12.9373	+	4.70879i	0.637375	+	0.231986i
$413$	−0.992035	+	3.91892i	−0.0488148	+	0.192838i
$414$	5.85997	−	1.03327i	0.288002	−	0.0507825i
$415$	−0.688415	+	3.90420i	−0.0337930	+	0.191649i
$416$	5.85337	+	1.03211i	0.286985	+	0.0506033i
$417$	19.1404	−	11.0507i	0.937309	−	0.541155i
$418$	10.9123	−	7.37245i	0.533736	−	0.360599i
$419$		−	24.8730i		−	1.21512i	−0.794272	−	0.607562i	$-0.792148\pi$
$419$		−	24.8730i		−	1.21512i	0.794272	−	0.607562i	$-0.207852\pi$
$420$	1.82594	−	1.87730i	0.0890968	−	0.0916029i
$421$	2.58967	+	7.11507i	0.126213	+	0.346767i	0.986665	−	0.162764i	$-0.0520410\pi$
$421$	2.58967	+	7.11507i	0.126213	+	0.346767i	−0.860452	+	0.509531i	$0.829819\pi$
$422$	−4.68809	−	1.70632i	−0.228212	−	0.0830626i
$423$	2.33032	+	6.40250i	0.113304	+	0.311300i
$424$	1.26754	+	7.18858i	0.0615572	+	0.349108i
$425$		−	5.62356i		−	0.272783i
$426$	4.05451	−	7.02262i	0.196442	−	0.340247i
$427$	11.9089	−	26.4919i	0.576314	−	1.28203i
$428$	6.62043	+	7.88993i	0.320011	+	0.381374i
$429$	8.97864	+	15.5515i	0.433493	+	0.750832i
$430$	3.47124	−	6.01236i	0.167398	−	0.289942i
$431$	2.78079	−	0.490329i	0.133946	−	0.0236183i	−0.106273	−	0.994337i	$-0.533892\pi$
$431$	2.78079	−	0.490329i	0.133946	−	0.0236183i	0.240219	+	0.970719i	$0.422781\pi$
$432$	0.766044	+	0.642788i	0.0368563	+	0.0309261i
$433$	0.873300	+	4.95273i	0.0419681	+	0.238013i	0.998575	−	0.0533691i	$-0.0169960\pi$
$433$	0.873300	+	4.95273i	0.0419681	+	0.238013i	−0.956607	+	0.291382i	$0.905885\pi$
$434$	−14.3563	−	3.63416i	−0.689126	−	0.174445i
$435$	−1.77454	−	1.48901i	−0.0850826	−	0.0713927i
$436$	0.426877	+	0.246458i	0.0204437	+	0.0118032i
$437$	−2.69160	+	25.7970i	−0.128757	+	1.23404i
$438$	1.05323	+	1.82425i	0.0503255	+	0.0871662i
$439$	−20.8526	+	7.58974i	−0.995242	+	0.362238i	−0.787748	−	0.615998i	$-0.788753\pi$
$439$	−20.8526	+	7.58974i	−0.995242	+	0.362238i	−0.207494	+	0.978236i	$0.566531\pi$
$440$	2.81016	−	1.02282i	0.133969	−	0.0487608i
$441$	0.194128	+	6.99731i	0.00924419	+	0.333205i
$442$	1.44372	−	8.18777i	0.0686710	−	0.389452i
$443$	−20.1872	+	16.9390i	−0.959121	+	0.804798i	−0.980810	−	0.194966i	$-0.937540\pi$
$443$	−20.1872	+	16.9390i	−0.959121	+	0.804798i	0.0216885	+	0.999765i	$0.493096\pi$
$444$	2.19310	+	1.26619i	0.104080	+	0.0600906i
$445$			17.8393i			0.845662i
$446$	4.90449	−	0.864794i	0.232234	−	0.0409492i
$447$	−18.1014	+	15.1889i	−0.856165	+	0.718408i
$448$	1.15129	+	2.38213i	0.0543932	+	0.112545i
$449$	32.8811	−	18.9839i	1.55175	−	0.895905i	0.553754	−	0.832680i	$-0.313195\pi$
$449$	32.8811	−	18.9839i	1.55175	−	0.895905i	0.997999	−	0.0632249i	$-0.0201386\pi$
$450$	−2.58416	−	3.07968i	−0.121818	−	0.145178i
$451$	−20.5614	+	7.48375i	−0.968200	+	0.352396i
$452$	−2.67295	−	3.18550i	−0.125725	−	0.149833i
$453$	19.0447	+	3.35810i	0.894800	+	0.157777i
$454$	−1.44669	+	1.72409i	−0.0678963	+	0.0809157i
$455$	−14.0146	+	6.77327i	−0.657013	+	0.317536i
$456$	−3.61184	+	2.44020i	−0.169140	+	0.114273i
$457$	−3.38158	+	5.85707i	−0.158184	+	0.273982i	−0.934214	−	0.356714i	$-0.883897\pi$
$457$	−3.38158	+	5.85707i	−0.158184	+	0.273982i	0.776030	+	0.630696i	$0.217230\pi$
$458$	−2.91743	+	16.5456i	−0.136323	+	0.773124i
$459$	0.899139	−	1.07155i	0.0419682	−	0.0500158i
$460$	−2.01445	+	5.53465i	−0.0939240	+	0.258054i
$461$	−35.9052	−	6.33106i	−1.67227	−	0.294867i	−0.744392	−	0.667743i	$-0.767260\pi$
$461$	−35.9052	−	6.33106i	−1.67227	−	0.294867i	−0.927881	+	0.372876i	$0.878372\pi$
$462$	−3.27739	+	7.29069i	−0.152478	+	0.339193i
$463$	4.81957	+	8.34774i	0.223984	+	0.387952i	0.956014	−	0.293320i	$-0.0947602\pi$
$463$	4.81957	+	8.34774i	0.223984	+	0.387952i	−0.732030	+	0.681273i	$0.761427\pi$
$464$	2.02676	−	1.17015i	0.0940899	−	0.0543228i
$465$	1.89493	−	5.20628i	0.0878753	−	0.241435i
$466$	6.47729	−	17.7962i	0.300055	−	0.824394i
$467$	23.8816	−	13.7881i	1.10511	−	0.638035i	0.167551	−	0.985863i	$-0.446414\pi$
$467$	23.8816	−	13.7881i	1.10511	−	0.638035i	0.937558	+	0.347828i	$0.113081\pi$
$468$	−2.97184	−	5.14737i	−0.137373	−	0.237937i
$469$	3.76518	−	8.37579i	0.173860	−	0.386758i
$470$	−6.64163	−	1.17110i	−0.306356	−	0.0540188i
$471$	−2.66761	+	7.32920i	−0.122917	+	0.337712i
$472$	0.982138	−	1.17047i	0.0452065	−	0.0538751i
$473$	−3.67968	+	20.8685i	−0.169192	+	0.959536i
$474$	−4.47440	+	7.74990i	−0.205516	+	0.355964i
$475$	16.0034	−	7.13971i	0.734286	−	0.327593i
$476$	3.33215	−	1.61044i	0.152729	−	0.0738142i
$477$	4.69201	−	5.59172i	0.214832	−	0.256027i
$478$	3.78154	+	0.666788i	0.172964	+	0.0304982i
$479$	11.6952	+	13.9379i	0.534369	+	0.636837i	0.963916	−	0.266208i	$-0.0857709\pi$
$479$	11.6952	+	13.9379i	0.534369	+	0.636837i	−0.429546	+	0.903045i	$0.641326\pi$
$480$	−0.930134	+	0.338541i	−0.0424546	+	0.0154522i
$481$	−9.67498	−	11.5302i	−0.441141	−	0.525732i
$482$	15.9903	−	9.23200i	0.728338	−	0.420506i
$483$	−6.85059	−	14.1746i	−0.311713	−	0.644964i
$484$	1.43410	−	1.20335i	0.0651863	−	0.0546978i
$485$	−5.70147	+	1.00532i	−0.258891	+	0.0456494i
$486$		−	1.00000i		−	0.0453609i
$487$	−11.0205	−	6.36271i	−0.499388	−	0.288322i	0.229073	−	0.973409i	$-0.426431\pi$
$487$	−11.0205	−	6.36271i	−0.499388	−	0.288322i	−0.728461	+	0.685087i	$0.759764\pi$
$488$	−8.40978	+	7.05664i	−0.380693	+	0.319439i
$489$	3.17236	−	17.9913i	0.143459	−	0.813597i
$490$	−6.09428	−	3.29666i	−0.275312	−	0.148928i
$491$	−32.1452	+	11.6999i	−1.45069	+	0.528008i	−0.942784	−	0.333404i	$-0.891803\pi$
$491$	−32.1452	+	11.6999i	−1.45069	+	0.528008i	−0.507907	+	0.861412i	$0.669581\pi$
$492$	6.80561	−	2.47704i	0.306821	−	0.111674i
$493$	−1.63682	−	2.83505i	−0.0737186	−	0.127684i
$494$	25.1335	−	6.28674i	1.13081	−	0.282854i
$495$	−2.58986	−	1.49526i	−0.116406	−	0.0672068i
$496$	4.28781	+	3.59790i	0.192528	+	0.161550i
$497$	−20.7984	−	5.26490i	−0.932937	−	0.236163i
$498$	0.695489	+	3.94432i	0.0311656	+	0.176749i
$499$	−22.9840	−	19.2859i	−1.02891	−	0.863355i	−0.0381860	−	0.999271i	$-0.512158\pi$
$499$	−22.9840	−	19.2859i	−1.02891	−	0.863355i	−0.990720	+	0.135916i	$0.956602\pi$
$500$	8.79284	−	1.55042i	0.393228	−	0.0693367i
$501$	1.43220	−	2.48064i	0.0639860	−	0.110827i
$502$	11.4192	+	19.7787i	0.509666	+	0.882767i
$503$	3.60699	+	4.29864i	0.160828	+	0.191667i	0.840440	−	0.541904i	$-0.182296\pi$
$503$	3.60699	+	4.29864i	0.160828	+	0.191667i	−0.679612	+	0.733571i	$0.737852\pi$
$504$	1.08478	−	2.41314i	0.0483201	−	0.107490i
$505$	6.35999	−	11.0158i	0.283016	−	0.490198i
$506$		−	17.9775i		−	0.799199i
$507$	3.87708	+	21.9880i	0.172187	+	0.976523i
$508$	−4.33082	−	11.8988i	−0.192149	−	0.527925i
$509$	−25.3552	−	9.22854i	−1.12385	−	0.409048i	−0.287794	−	0.957692i	$-0.592922\pi$
$509$	−25.3552	−	9.22854i	−1.12385	−	0.409048i	−0.836056	+	0.548645i	$0.815144\pi$
$510$	0.473555	+	1.30108i	0.0209694	+	0.0576129i
$511$	3.88581	−	3.99511i	0.171898	−	0.176733i
$512$		−	1.00000i		−	0.0441942i
$513$	4.19095	+	1.19830i	0.185035	+	0.0529062i
$514$	19.3149	−	11.1515i	0.851944	−	0.491870i
$515$	13.4205	+	2.36640i	0.591379	+	0.104276i
$516$	1.21794	−	6.90726i	0.0536167	−	0.304075i
$517$	20.2722	−	3.57454i	0.891570	−	0.157208i
$518$	1.64418	−	6.49516i	0.0722412	−	0.285381i
$519$	−14.1923	−	5.16558i	−0.622973	−	0.226744i
$520$	5.88322			0.257996
$521$	−27.8253			−1.21905			−0.609525	−	0.792767i	$-0.708640\pi$
$521$	−27.8253			−1.21905			−0.609525	+	0.792767i	$0.708640\pi$
$522$	−2.19916	−	0.800429i	−0.0962547	−	0.0350338i
$523$	7.72620	+	43.8175i	0.337843	+	1.91600i	0.397129	+	0.917763i	$0.370007\pi$
$523$	7.72620	+	43.8175i	0.337843	+	1.91600i	−0.0592856	+	0.998241i	$0.518882\pi$
$524$	9.03912	+	5.21874i	0.394876	+	0.227982i
$525$	−5.97946	+	8.79672i	−0.260965	+	0.383920i
$526$	0.510476	−	1.40252i	0.0222578	−	0.0611529i
$527$	5.03278	−	5.99784i	0.219232	−	0.261270i
$528$	2.31441	−	1.94202i	0.100722	−	0.0845155i
$529$	9.50426	+	7.97502i	0.413229	+	0.346740i
$530$	2.47117	+	6.78949i	0.107341	+	0.294917i
$531$	−1.52793			−0.0663067
$532$	8.81346	+	7.43793i	0.382112	+	0.322475i
$533$	−43.0463			−1.86454
$534$	6.16409	+	16.9357i	0.266746	+	0.732879i
$535$	7.80967	+	6.55309i	0.337642	+	0.283315i
$536$	−2.65887	+	2.23106i	−0.114846	+	0.0963670i
$537$	−10.8475	+	12.9276i	−0.468105	+	0.557866i
$538$	−4.44280	+	12.2065i	−0.191543	+	0.526260i
$539$	20.9213	+	3.09343i	0.901142	+	0.133243i
$540$	0.857216	+	0.494914i	0.0368887	+	0.0212977i
$541$	−7.67816	−	43.5450i	−0.330110	−	1.87215i	−0.471018	−	0.882124i	$-0.656113\pi$
$541$	−7.67816	−	43.5450i	−0.330110	−	1.87215i	0.140908	−	0.990023i	$-0.454998\pi$
$542$	13.3846	+	4.87160i	0.574919	+	0.209253i
$543$	10.0920			0.433089
$544$	−1.39881			−0.0599736
$545$	0.458477	+	0.166872i	0.0196390	+	0.00714802i
$546$	−10.9643	+	11.2727i	−0.469230	+	0.482428i
$547$	0.754786	−	0.133089i	0.0322723	−	0.00569048i	−0.157489	−	0.987521i	$-0.550340\pi$
$547$	0.754786	−	0.133089i	0.0322723	−	0.00569048i	0.189761	+	0.981830i	$0.439229\pi$
$548$	−0.499062	+	2.83032i	−0.0213189	+	0.120905i
$549$	10.8114	+	1.90634i	0.461419	+	0.0813607i
$550$	−10.5189	+	6.07306i	−0.448525	+	0.258956i
$551$	5.98981	−	8.25743i	0.255175	−	0.351778i
$552$			5.95037i			0.253265i
$553$	22.9523	+	5.81015i	0.976033	+	0.247073i
$554$	−2.76036	−	7.58403i	−0.117276	−	0.322214i
$555$	2.35545	+	0.857313i	0.0999832	+	0.0363909i
$556$	7.55913	+	20.7685i	0.320578	+	0.880782i
$557$	7.25194	+	41.1278i	0.307274	+	1.74264i	0.612601	+	0.790392i	$0.290123\pi$
$557$	7.25194	+	41.1278i	0.307274	+	1.74264i	−0.305326	+	0.952248i	$0.598766\pi$
$558$		−	5.59734i		−	0.236954i
$559$	−20.8439	+	36.1027i	−0.881604	+	1.52698i
$560$	1.53171	+	2.12419i	0.0647265	+	0.0897634i
$561$	−2.71652	−	3.23742i	−0.114692	−	0.136684i
$562$	−10.2102	−	17.6846i	−0.430692	−	0.745980i
$563$	14.7853	−	25.6089i	0.623125	−	1.07928i	−0.365775	−	0.930703i	$-0.619196\pi$
$563$	14.7853	−	25.6089i	0.623125	−	1.07928i	0.988900	−	0.148581i	$-0.0474706\pi$
$564$	−6.70988	+	1.18313i	−0.282537	+	0.0498189i
$565$	−3.15310	−	2.64576i	−0.132652	−	0.111308i
$566$	1.39823	+	7.92977i	0.0587721	+	0.333313i
$567$	−2.54586	+	0.720145i	−0.106916	+	0.0302432i
$568$	6.21187	+	5.21238i	0.260644	+	0.218707i
$569$	−0.648170	−	0.374221i	−0.0271727	−	0.0156882i	0.486352	−	0.873763i	$-0.338327\pi$
$569$	−0.648170	−	0.374221i	−0.0271727	−	0.0156882i	−0.513525	+	0.858075i	$0.671661\pi$
$570$	−3.10136	+	2.99950i	−0.129902	+	0.125635i
$571$	−14.1768	−	24.5550i	−0.593281	−	1.02759i	−0.993787	−	0.111299i	$-0.964499\pi$
$571$	−14.1768	−	24.5550i	−0.593281	−	1.02759i	0.400506	−	0.916294i	$-0.368835\pi$
$572$	−16.8743	+	6.14175i	−0.705551	+	0.256800i
$573$	4.85724	−	1.76789i	0.202914	−	0.0738546i
$574$	−11.2072	−	15.5423i	−0.467780	−	0.648723i
$575$	4.15400	−	23.5585i	0.173234	−	0.982457i
$576$	−0.766044	+	0.642788i	−0.0319185	+	0.0267828i
$577$	6.77855	+	3.91360i	0.282195	+	0.162925i	0.634417	−	0.772991i	$-0.281240\pi$
$577$	6.77855	+	3.91360i	0.282195	+	0.162925i	−0.352222	+	0.935917i	$0.614574\pi$
$578$		−	15.0433i		−	0.625720i
$579$	−0.927106	+	0.163474i	−0.0385292	+	0.00679374i
$580$	1.77454	−	1.48901i	0.0736837	−	0.0618279i
$581$	9.54082	−	4.61110i	0.395820	−	0.191301i
$582$	−5.06531	+	2.92446i	−0.209964	+	0.121223i
$583$	−14.1757	−	16.8940i	−0.587098	−	0.699676i
$584$	−1.97943	+	0.720454i	−0.0819095	+	0.0298126i
$585$	−3.78166	−	4.50680i	−0.156352	−	0.186333i
$586$	−16.2966	−	2.87354i	−0.673208	−	0.118705i
$587$	30.3696	−	36.1931i	1.25349	−	1.49385i	0.456663	−	0.889640i	$-0.349044\pi$
$587$	30.3696	−	36.1931i	1.25349	−	1.49385i	0.796825	−	0.604210i	$-0.206511\pi$
$588$	−6.92471	−	1.02389i	−0.285570	−	0.0422246i
$589$	23.4582	+	6.70728i	0.966577	+	0.276369i
$590$	0.756197	−	1.30977i	0.0311321	−	0.0539224i
$591$	−2.19310	+	12.4377i	−0.0902120	+	0.511618i
$592$	−1.62778	+	1.93991i	−0.0669013	+	0.0797298i
$593$	−8.65489	+	23.7791i	−0.355414	+	0.976491i	0.625187	+	0.780475i	$0.285023\pi$
$593$	−8.65489	+	23.7791i	−0.355414	+	0.976491i	−0.980601	+	0.196016i	$0.937199\pi$
$594$	−2.97535	−	0.524634i	−0.122080	−	0.0215260i
$595$	2.97134	−	2.14257i	0.121813	−	0.0878369i
$596$	−11.8148	−	20.4639i	−0.483954	−	0.838233i
$597$	11.6532	−	6.72796i	0.476932	−	0.275357i
$598$	12.0962	−	33.2342i	0.494652	−	1.35905i
$599$	−11.0374	+	30.3250i	−0.450976	+	1.23905i	0.481062	+	0.876686i	$0.340251\pi$
$599$	−11.0374	+	30.3250i	−0.450976	+	1.23905i	−0.932038	+	0.362360i	$0.881971\pi$
$600$	3.48163	−	2.01012i	0.142137	−	0.0820628i
$601$	−6.06800	−	10.5101i	−0.247519	−	0.428715i	0.715318	−	0.698799i	$-0.246282\pi$
$601$	−6.06800	−	10.5101i	−0.247519	−	0.428715i	−0.962837	+	0.270084i	$0.912949\pi$
$602$	−18.4620	+	1.87354i	−0.752455	+	0.0763597i
$603$	3.41818	+	0.602717i	0.139199	+	0.0245445i
$604$	−6.61417	+	18.1723i	−0.269127	+	0.739420i
$605$	1.19111	−	1.41951i	0.0484255	−	0.0577113i
$606$	2.23150	−	12.6555i	0.0906485	−	0.514093i
$607$	−16.6355	+	28.8136i	−0.675216	+	1.16951i	0.301190	+	0.953564i	$0.402616\pi$
$607$	−16.6355	+	28.8136i	−0.675216	+	1.16951i	−0.976406	+	0.215944i	$0.930717\pi$
$608$	−1.77594	−	3.98071i	−0.0720240	−	0.161439i
$609$	−0.454064	+	6.17518i	−0.0183996	+	0.250231i
$610$	−6.98486	+	8.32423i	−0.282809	+	0.337038i
$611$	39.8813	+	7.03216i	1.61343	+	0.284491i
$612$	0.899139	+	1.07155i	0.0363455	+	0.0433149i
$613$	16.6947	−	6.07638i	0.674294	−	0.245423i	0.0178981	−	0.999840i	$-0.494303\pi$
$613$	16.6947	−	6.07638i	0.674294	−	0.245423i	0.656395	+	0.754417i	$0.272080\pi$
$614$	1.79459	+	2.13871i	0.0724239	+	0.0863114i
$615$	6.20829	−	3.58436i	0.250342	−	0.144535i
$616$	−6.61081	−	4.49362i	−0.266357	−	0.181053i
$617$	18.8857	−	15.8470i	0.760309	−	0.637975i	−0.177899	−	0.984049i	$-0.556930\pi$
$617$	18.8857	−	15.8470i	0.760309	−	0.637975i	0.938207	+	0.346074i	$0.112485\pi$
$618$	13.5584	−	2.39072i	0.545400	−	0.0961687i
$619$		−	12.9393i		−	0.520075i	−0.965598	−	0.260038i	$-0.916265\pi$
$619$		−	12.9393i		−	0.520075i	0.965598	−	0.260038i	$-0.0837350\pi$
$620$	4.79813	+	2.77020i	0.192698	+	0.111254i
$621$	4.55825	−	3.82483i	0.182916	−	0.153485i
$622$	−3.32641	+	18.8650i	−0.133377	+	0.756417i
$623$	38.6768	−	27.8890i	1.54955	−	1.11735i
$624$	5.58523	−	2.03286i	0.223588	−	0.0813794i
$625$	−10.5843	+	3.85235i	−0.423370	+	0.154094i
$626$	−6.18913	−	10.7199i	−0.247367	−	0.428453i
$627$	5.76407	−	11.8409i	0.230195	−	0.472878i
$628$	−6.75463	−	3.89979i	−0.269539	−	0.155618i
$629$	2.71357	+	2.27696i	0.108197	+	0.0907882i
$630$	0.642661	−	2.53876i	0.0256042	−	0.101147i
$631$	−1.79319	−	10.1697i	−0.0713859	−	0.404849i	−0.999472	−	0.0324844i	$-0.989658\pi$
$631$	−1.79319	−	10.1697i	−0.0713859	−	0.404849i	0.928086	−	0.372365i	$-0.121453\pi$
$632$	−6.85518	−	5.75218i	−0.272685	−	0.228810i
$633$	−4.91316	+	0.866323i	−0.195281	+	0.0344333i
$634$	−2.99620	+	5.18958i	−0.118994	+	0.206104i
$635$	−6.26684	−	10.8545i	−0.248692	−	0.430747i
$636$	4.69201	+	5.59172i	0.186050	+	0.221726i
$637$	36.5947	+	19.7956i	1.44993	+	0.784330i
$638$	−3.53531	+	6.12333i	−0.139964	+	0.242425i
$639$		−	8.10902i		−	0.320788i
$640$	−0.171882	−	0.974791i	−0.00679423	−	0.0385320i
$641$	−7.43737	−	20.4340i	−0.293758	−	0.807094i	−0.995509	−	0.0946713i	$-0.969820\pi$
$641$	−7.43737	−	20.4340i	−0.293758	−	0.807094i	0.701750	−	0.712423i	$-0.252402\pi$
$642$	9.67843	+	3.52266i	0.381977	+	0.139028i
$643$	15.6384	+	42.9660i	0.616717	+	1.69441i	0.714882	+	0.699245i	$0.246480\pi$
$643$	15.6384	+	42.9660i	0.616717	+	1.69441i	−0.0981658	+	0.995170i	$0.531298\pi$
$644$	15.1488	−	4.28513i	0.596946	−	0.168858i
$645$		−	6.94248i		−	0.273360i
$646$	−5.56826	+	2.48421i	−0.219080	+	0.0977399i
$647$	11.0110	−	6.35719i	0.432886	−	0.249927i	−0.267689	−	0.963505i	$-0.586260\pi$
$647$	11.0110	−	6.35719i	0.432886	−	0.249927i	0.700576	+	0.713578i	$0.252927\pi$
$648$	0.984808	+	0.173648i	0.0386869	+	0.00682154i
$649$	−0.801606	+	4.54613i	−0.0314658	+	0.178451i
$650$	−23.5320	+	4.14932i	−0.923000	+	0.162750i
$651$	−14.2500	+	4.03090i	−0.558503	+	0.157983i
$652$	17.1671	+	6.24833i	0.672317	+	0.244703i
$653$	16.2214			0.634793			0.317397	−	0.948293i	$-0.397191\pi$
$653$	16.2214			0.634793			0.317397	+	0.948293i	$0.397191\pi$
$654$	0.492915			0.0192745
$655$	9.70826	+	3.53352i	0.379333	+	0.138066i
$656$	1.25763	+	7.13235i	0.0491021	+	0.278472i
$657$	1.82425	+	1.05323i	0.0711709	+	0.0410906i
$658$	7.84418	+	16.2304i	0.305798	+	0.632726i
$659$	6.51942	−	17.9120i	0.253961	−	0.697751i	−0.745549	−	0.666450i	$-0.767813\pi$
$659$	6.51942	−	17.9120i	0.253961	−	0.697751i	0.999510	−	0.0313007i	$-0.00996494\pi$
$660$	1.92226	−	2.29087i	0.0748241	−	0.0891718i
$661$	−29.4066	+	24.6751i	−1.14378	+	0.959749i	−0.999556	−	0.0297949i	$-0.990515\pi$
$661$	−29.4066	+	24.6751i	−1.14378	+	0.959749i	−0.144229	+	0.989544i	$0.546070\pi$
$662$	−24.8677	−	20.8665i	−0.966511	−	0.810999i
$663$	−2.84358	−	7.81268i	−0.110436	−	0.303419i
$664$	−4.00516			−0.155431
$665$	9.86973	+	5.73555i	0.382732	+	0.222415i
$666$	2.53237			0.0981275
$667$	−4.76285	−	13.0858i	−0.184418	−	0.506685i
$668$	2.19426	+	1.84120i	0.0848984	+	0.0712382i
$669$	3.81502	−	3.20118i	0.147497	−	0.123765i
$670$	−2.20836	+	2.63183i	−0.0853165	+	0.101676i
$671$	11.3440	−	31.1675i	0.437932	−	1.20321i
$672$	2.18811	+	1.48734i	0.0844081	+	0.0573754i
$673$	13.4325	+	7.75526i	0.517785	+	0.298943i	0.736028	−	0.676951i	$-0.236699\pi$
$673$	13.4325	+	7.75526i	0.517785	+	0.298943i	−0.218243	+	0.975894i	$0.570033\pi$
$674$	−5.19860	−	29.4827i	−0.200243	−	1.13563i
$675$	−3.77779	−	1.37500i	−0.145407	−	0.0529239i
$676$	−22.3272			−0.858740
$677$	−2.42918			−0.0933609			−0.0466805	−	0.998910i	$-0.514864\pi$
$677$	−2.42918			−0.0933609			−0.0466805	+	0.998910i	$0.514864\pi$
$678$	−3.90759	−	1.42225i	−0.150070	−	0.0546211i
$679$	11.0930	+	10.7895i	0.425711	+	0.414064i
$680$	−1.36355	+	0.240430i	−0.0522897	+	0.00922009i
$681$	−0.390820	+	2.21645i	−0.0149763	+	0.0849346i
$682$	−16.6540	−	2.93655i	−0.637715	−	0.112446i
$683$	4.36598	−	2.52070i	0.167060	−	0.0964519i	−0.414139	−	0.910214i	$-0.635917\pi$
$683$	4.36598	−	2.52070i	0.167060	−	0.0964519i	0.581199	+	0.813762i	$0.302584\pi$
$684$	−1.90784	+	3.91920i	−0.0729483	+	0.149854i
$685$			2.84475i			0.108692i
$686$	2.38012	+	18.3667i	0.0908733	+	0.701243i
$687$	5.74622	+	15.7876i	0.219232	+	0.602334i
$688$	6.59083	+	2.39887i	0.251273	+	0.0914559i
$689$	−14.8388	−	40.7692i	−0.565312	−	1.55318i
$690$	1.02276	+	5.80037i	0.0389359	+	0.220816i
$691$		−	27.3303i		−	1.03969i	−0.854259	−	0.519847i	$-0.825989\pi$
$691$		−	27.3303i		−	1.03969i	0.854259	−	0.519847i	$-0.174011\pi$
$692$	7.55157	−	13.0797i	0.287068	−	0.497216i
$693$	0.807038	+	7.95262i	0.0306568	+	0.302095i
$694$	13.8378	+	16.4912i	0.525274	+	0.625997i
$695$	10.9383	+	18.9457i	0.414913	+	0.718651i
$696$	1.17015	−	2.02676i	0.0443544	−	0.0768241i
$697$	9.97682	−	1.75918i	0.377899	−	0.0666338i
$698$	−9.28633	−	7.79216i	−0.351493	−	0.294938i
$699$	−3.28861	−	18.6506i	−0.124387	−	0.705431i
$700$	−7.62476	−	7.41616i	−0.288189	−	0.280304i
$701$	16.5573	+	13.8933i	0.625362	+	0.524741i	0.899484	−	0.436954i	$-0.143943\pi$
$701$	16.5573	+	13.8933i	0.625362	+	0.524741i	−0.274122	+	0.961695i	$0.588387\pi$
$702$	−5.14737	−	2.97184i	−0.194275	−	0.112165i
$703$	−3.03454	+	10.6131i	−0.114450	+	0.400279i
$704$	1.51062	+	2.61647i	0.0569337	+	0.0986121i
$705$	−6.33737	+	2.30661i	−0.238679	+	0.0868721i
$706$	31.8115	−	11.5785i	1.19724	−	0.435761i
$707$	−33.8260	+	3.43269i	−1.27216	+	0.129100i
$708$	0.265323	−	1.50472i	0.00997145	−	0.0565509i
$709$	28.2382	−	23.6947i	1.06051	−	0.889871i	0.0663484	−	0.997797i	$-0.478865\pi$
$709$	28.2382	−	23.6947i	1.06051	−	0.889871i	0.994159	+	0.107925i	$0.0344207\pi$
$710$	6.95119	+	4.01327i	0.260873	+	0.150615i
$711$			8.94881i			0.335607i
$712$	−17.7488	+	3.12959i	−0.665164	+	0.117286i
$713$	25.5141	−	21.4088i	0.955509	−	0.801768i
$714$	2.08051	−	3.06075i	0.0778611	−	0.114546i
$715$	−15.3933	+	8.88732i	−0.575676	+	0.332367i
$716$	−10.8475	−	12.9276i	−0.405391	−	0.483126i
$717$	3.60830	−	1.31332i	0.134755	−	0.0490467i
$718$	6.06111	+	7.22335i	0.226199	+	0.269573i
$719$	35.9530	+	6.33949i	1.34082	+	0.236423i	0.797611	−	0.603173i	$-0.206097\pi$
$719$	35.9530	+	6.33949i	1.34082	+	0.236423i	0.543212	+	0.839596i	$0.317208\pi$
$720$	−0.636249	+	0.758252i	−0.0237116	+	0.0282584i
$721$	−15.8505	−	32.7962i	−0.590302	−	1.22139i
$722$	−14.1390	−	12.6921i	−0.526200	−	0.472349i
$723$	9.23200	−	15.9903i	0.343342	−	0.594686i
$724$	−1.75246	+	9.93867i	−0.0651295	+	0.369368i
$725$	−6.04771	+	7.20738i	−0.224606	+	0.267675i
$726$	0.640290	−	1.75918i	0.0237634	−	0.0652893i
$727$	8.10242	+	1.42868i	0.300502	+	0.0529866i	0.321866	−	0.946785i	$-0.395690\pi$
$727$	8.10242	+	1.42868i	0.300502	+	0.0529866i	−0.0213642	+	0.999772i	$0.506801\pi$
$728$	−9.19753	−	12.7552i	−0.340883	−	0.472741i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−1.80570	+	1.04252i	−0.0668319	+	0.0385854i
$731$	3.35556	−	9.21934i	0.124110	−	0.340989i
$732$	−3.75476	+	10.3161i	−0.138780	+	0.381295i
$733$	−36.5091	+	21.0785i	−1.34849	+	0.778554i	−0.988036	−	0.154221i	$-0.950713\pi$
$733$	−36.5091	+	21.0785i	−1.34849	+	0.778554i	−0.360458	+	0.932775i	$0.617380\pi$
$734$	−0.163157	−	0.282595i	−0.00602222	−	0.0104308i
$735$	−6.92613	+	0.192153i	−0.255474	+	0.00708768i
$736$	−5.85997	−	1.03327i	−0.216001	−	0.0380869i
$737$	3.58658	−	9.85405i	0.132113	−	0.362979i
$738$	4.65531	−	5.54799i	0.171364	−	0.204224i
$739$	5.75989	−	32.6660i	0.211881	−	1.20164i	−0.674356	−	0.738406i	$-0.735579\pi$
$739$	5.75989	−	32.6660i	0.211881	−	1.20164i	0.886237	−	0.463231i	$-0.153310\pi$
$740$	−1.25331	+	2.17079i	−0.0460725	+	0.0797999i
$741$	18.6229	−	18.0112i	0.684130	−	0.661659i
$742$	10.8568	−	15.9720i	0.398566	−	0.586352i
$743$	27.0330	−	32.2167i	0.991745	−	1.18192i	0.00843761	−	0.999964i	$-0.497314\pi$
$743$	27.0330	−	32.2167i	0.991745	−	1.18192i	0.983308	−	0.181951i	$-0.0582414\pi$
$744$	5.51230	+	0.971968i	0.202091	+	0.0356341i
$745$	−15.0344	−	17.9172i	−0.550816	−	0.656437i
$746$	−31.3993	+	11.4284i	−1.14961	+	0.418424i
$747$	2.57447	+	3.06813i	0.0941949	+	0.112257i
$748$	3.65996	−	2.11308i	0.133821	−	0.0772617i
$749$	1.99832	−	27.1767i	0.0730170	−	0.993016i
$750$	6.83962	−	5.73912i	0.249748	−	0.209563i
$751$	−29.8827	+	5.26912i	−1.09043	+	0.192273i	−0.689825	−	0.723976i	$-0.742313\pi$
$751$	−29.8827	+	5.26912i	−1.09043	+	0.192273i	−0.400609	+	0.916249i	$0.631201\pi$
$752$		−	6.81339i		−	0.248459i
$753$	19.7787	+	11.4192i	0.720777	+	0.416141i
$754$	−10.6557	+	8.94116i	−0.388056	+	0.325618i
$755$	−3.32394	+	18.8510i	−0.120971	+	0.686059i
$756$	−0.267121	−	2.63223i	−0.00971509	−	0.0957334i
$757$	−31.3944	+	11.4266i	−1.14105	+	0.415308i	−0.842292	−	0.539022i	$-0.818794\pi$
$757$	−31.3944	+	11.4266i	−1.14105	+	0.415308i	−0.298756	+	0.954329i	$0.596572\pi$
$758$	−22.0138	+	8.01236i	−0.799577	+	0.291022i
$759$	−8.98877	−	15.5690i	−0.326272	−	0.565119i
$760$	−2.41538	−	3.57510i	−0.0876152	−	0.129683i
$761$	−4.41710	−	2.55022i	−0.160120	−	0.0924452i	0.417799	−	0.908540i	$-0.362802\pi$
$761$	−4.41710	−	2.55022i	−0.160120	−	0.0924452i	−0.577919	+	0.816094i	$0.696135\pi$
$762$	−9.70002	−	8.13928i	−0.351395	−	0.294855i
$763$	−0.354970	−	1.25489i	−0.0128508	−	0.0454301i
$764$	0.897581	+	5.09044i	0.0324733	+	0.184165i
$765$	1.06065	+	0.889993i	0.0383480	+	0.0321778i
$766$	0.863829	−	0.152316i	0.0312114	−	0.00550341i
$767$	−4.54077	+	7.86485i	−0.163958	+	0.283983i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	16.5228	+	19.6911i	0.595827	+	0.710079i	0.976715	−	0.214543i	$-0.0688260\pi$
$769$	16.5228	+	19.6911i	0.595827	+	0.710079i	−0.380888	+	0.924621i	$0.624382\pi$
$770$	−7.21653	−	3.24406i	−0.260066	−	0.116908i
$771$	11.1515	−	19.3149i	0.401610	−	0.695609i
$772$		−	0.941408i		−	0.0338820i
$773$	3.11264	+	17.6527i	0.111954	+	0.634922i	0.988213	+	0.153083i	$0.0489201\pi$
$773$	3.11264	+	17.6527i	0.111954	+	0.634922i	−0.876259	+	0.481840i	$0.839969\pi$
$774$	−2.39887	−	6.59083i	−0.0862255	−	0.236903i
$775$	−21.1456	−	7.69636i	−0.759571	−	0.276461i
$776$	−2.00045	−	5.49619i	−0.0718119	−	0.197302i
$777$	−1.82368	−	6.44706i	−0.0654240	−	0.231287i
$778$			6.14919i			0.220459i
$779$	17.6729	+	26.1583i	0.633197	+	0.937220i
$780$	5.09501	−	2.94161i	0.182431	−	0.105326i
$781$	−24.1271	−	4.25427i	−0.863337	−	0.152230i
$782$	−1.44535	+	8.19700i	−0.0516857	+	0.293124i
$783$	−2.30474	+	0.406389i	−0.0823649	+	0.0145231i
$784$	2.21080	−	6.64171i	0.0789571	−	0.237204i
$785$	−7.25465	−	2.64048i	−0.258930	−	0.0942427i
$786$	10.4375			0.372293
$787$	−28.4461			−1.01400			−0.506998	−	0.861947i	$-0.669245\pi$
$787$	−28.4461			−1.01400			−0.506998	+	0.861947i	$0.669245\pi$
$788$	−11.8679	−	4.31956i	−0.422776	−	0.153878i
$789$	−0.259176	−	1.46986i	−0.00922689	−	0.0523283i
$790$	−7.67107	−	4.42889i	−0.272924	−	0.157573i
$791$	−0.806806	+	10.9724i	−0.0286867	+	0.390133i
$792$	1.03333	−	2.83904i	0.0367177	−	0.100881i
$793$	41.9424	−	49.9850i	1.48942	−	1.77502i
$794$	−8.36408	+	7.01830i	−0.296830	+	0.249070i
$795$	5.53484	+	4.64428i	0.196301	+	0.164716i
$796$	4.60219	+	12.6444i	0.163120	+	0.448170i
$797$	−44.0799			−1.56139			−0.780695	−	0.624912i	$-0.785135\pi$
$797$	−44.0799			−1.56139			−0.780695	+	0.624912i	$0.785135\pi$
$798$	11.3517	+	2.03471i	0.401844	+	0.0720279i
$799$	−9.53066			−0.337170
$800$	1.37500	+	3.77779i	0.0486137	+	0.133565i
$801$	13.8061	+	11.5847i	0.487815	+	0.409325i
$802$	−10.3399	+	8.67621i	−0.365115	+	0.306368i
$803$	4.09080	−	4.87522i	0.144361	−	0.172043i
$804$	−1.18712	+	3.26159i	−0.0418665	+	0.115027i
$805$	14.0304	−	6.78091i	0.494506	−	0.238996i
$806$	−28.8116	−	16.6344i	−1.01484	−	0.585921i
$807$	2.25567	+	12.7925i	0.0794033	+	0.450319i
$808$	12.0757	+	4.39520i	0.424822	+	0.154623i
$809$	21.4749			0.755018			0.377509	−	0.926006i	$-0.376781\pi$
$809$	21.4749			0.755018			0.377509	+	0.926006i	$0.376781\pi$
$810$	0.989828			0.0347790
$811$	−0.405235	−	0.147493i	−0.0142297	−	0.00517920i	0.334895	−	0.942255i	$-0.391299\pi$
$811$	−0.405235	−	0.147493i	−0.0142297	−	0.00517920i	−0.349125	+	0.937076i	$0.613521\pi$
$812$	−6.00252	−	1.51947i	−0.210647	−	0.0533231i
$813$	14.0272	−	2.47338i	0.491956	−	0.0867451i
$814$	1.32857	−	7.53469i	0.0465663	−	0.264091i
$815$	17.8083	+	3.14009i	0.623799	+	0.109993i
$816$	−1.21141	+	0.699406i	−0.0424077	+	0.0244841i
$817$	30.4964	−	2.15575i	1.06693	−	0.0754203i
$818$		−	5.00600i		−	0.175031i
$819$	−3.85902	+	15.2446i	−0.134845	+	0.532690i
$820$	2.45184	+	6.73639i	0.0856221	+	0.235245i
$821$	15.3500	+	5.58695i	0.535720	+	0.194986i	0.595690	−	0.803214i	$-0.296879\pi$
$821$	15.3500	+	5.58695i	0.535720	+	0.194986i	−0.0599708	+	0.998200i	$0.519101\pi$
$822$	0.982961	+	2.70066i	0.0342847	+	0.0941964i
$823$	−2.24398	−	12.7262i	−0.0782202	−	0.443609i	−0.998615	−	0.0526177i	$-0.983244\pi$
$823$	−2.24398	−	12.7262i	−0.0782202	−	0.443609i	0.920395	−	0.390991i	$-0.127868\pi$
$824$			13.7676i			0.479617i
$825$	−6.07306	+	10.5189i	−0.211437	+	0.366220i
$826$	−4.02188	+	0.408143i	−0.139939	+	0.0142011i
$827$	27.0273	+	32.2099i	0.939832	+	1.12005i	0.992599	+	0.121441i	$0.0387514\pi$
$827$	27.0273	+	32.2099i	0.939832	+	1.12005i	−0.0527672	+	0.998607i	$0.516804\pi$
$828$	2.97519	+	5.15317i	0.103395	+	0.179085i
$829$	−12.1921	+	21.1173i	−0.423448	+	0.733434i	−0.996274	−	0.0862431i	$-0.972514\pi$
$829$	−12.1921	+	21.1173i	−0.423448	+	0.733434i	0.572826	+	0.819677i	$0.305847\pi$
$830$	−3.90420	+	0.688415i	−0.135517	+	0.0238952i
$831$	−6.18255	−	5.18778i	−0.214470	−	0.179962i
$832$	1.03211	+	5.85337i	0.0357819	+	0.202929i
$833$	−9.29051	−	3.09249i	−0.321897	−	0.107149i
$834$	16.9307	+	14.2065i	0.586261	+	0.491931i
$835$	2.45541	+	1.41763i	0.0849730	+	0.0490592i
$836$	10.6601	+	7.73264i	0.368686	+	0.267439i
$837$	−2.79867	−	4.84744i	−0.0967362	−	0.167552i
$838$	23.3729	−	8.50706i	0.807405	−	0.293871i
$839$	14.5040	−	5.27902i	0.500733	−	0.182252i	−0.0792907	−	0.996852i	$-0.525266\pi$
$839$	14.5040	−	5.27902i	0.500733	−	0.182252i	0.580024	+	0.814600i	$0.303043\pi$
$840$	2.38859	+	1.07375i	0.0824143	+	0.0370478i
$841$	4.08473	−	23.1656i	0.140853	−	0.798815i
$842$	−5.80026	+	4.86700i	−0.199890	+	0.167728i
$843$	−17.6846	−	10.2102i	−0.609090	−	0.351658i
$844$		−	4.98896i		−	0.171727i
$845$	−21.7644	+	3.83765i	−0.748718	+	0.132019i
$846$	−5.21936	+	4.37957i	−0.179445	+	0.150573i
$847$	−4.93973	−	0.363221i	−0.169731	−	0.0124804i
$848$	−6.32153	+	3.64974i	−0.217082	+	0.125332i
$849$	5.17579	+	6.16826i	0.177633	+	0.211694i
$850$	5.28442	−	1.92337i	0.181254	−	0.0659711i
$851$	9.68589	+	11.5432i	0.332028	+	0.395696i
$852$	7.98583	+	1.40812i	0.273590	+	0.0482413i
$853$	−5.80417	+	6.91715i	−0.198731	+	0.236839i	−0.856202	−	0.516642i	$-0.827182\pi$
$853$	−5.80417	+	6.91715i	−0.198731	+	0.236839i	0.657471	+	0.753480i	$0.271626\pi$
$854$	28.9673	+	2.12998i	0.991242	+	0.0728865i
$855$	−1.18611	+	4.14832i	−0.0405641	+	0.141870i
$856$	−5.14978	+	8.91969i	−0.176016	+	0.304869i
$857$	−8.93351	+	50.6644i	−0.305163	+	1.73066i	0.317575	+	0.948233i	$0.397132\pi$
$857$	−8.93351	+	50.6644i	−0.305163	+	1.73066i	−0.622737	+	0.782431i	$0.713980\pi$
$858$	−11.5427	+	13.7561i	−0.394062	+	0.469625i
$859$	7.82503	−	21.4991i	0.266987	−	0.733539i	−0.731667	−	0.681662i	$-0.761257\pi$
$859$	7.82503	−	21.4991i	0.266987	−	0.733539i	0.998653	−	0.0518772i	$-0.0165204\pi$
$860$	6.83700	+	1.20555i	0.233140	+	0.0411089i
$861$	−17.4769	−	7.85641i	−0.595611	−	0.267746i
$862$	1.41185	+	2.44539i	0.0480877	+	0.0832903i
$863$	24.0319	−	13.8748i	0.818055	−	0.472304i	−0.0316901	−	0.999498i	$-0.510089\pi$
$863$	24.0319	−	13.8748i	0.818055	−	0.472304i	0.849745	+	0.527193i	$0.176756\pi$
$864$	−0.342020	+	0.939693i	−0.0116358	+	0.0319690i
$865$	5.11304	−	14.0480i	0.173848	−	0.477645i
$866$	−4.35536	+	2.51457i	−0.148001	+	0.0854485i
$867$	−7.52166	−	13.0279i	−0.255449	−	0.442451i
$868$	−1.49517	−	14.7335i	−0.0507492	−	0.500087i
$869$	26.6258	+	4.69485i	0.903218	+	0.159262i
$870$	0.792288	−	2.17679i	0.0268611	−	0.0738002i
$871$	13.2607	−	15.8035i	0.449321	−	0.535480i
$872$	−0.0855938	+	0.485427i	−0.00289857	+	0.0164386i
$873$	−2.92446	+	5.06531i	−0.0989780	+	0.171435i
$874$	−25.1619	+	6.29382i	−0.851113	+	0.212892i
$875$	−19.5365	−	13.2797i	−0.660454	−	0.448936i
$876$	−1.35401	+	1.61365i	−0.0457478	+	0.0545201i
$877$	34.0200	+	5.99864i	1.14877	+	0.202560i	0.715440	−	0.698674i	$-0.246226\pi$
$877$	34.0200	+	5.99864i	1.14877	+	0.202560i	0.433333	+	0.901234i	$0.357337\pi$
$878$	−14.2640	−	16.9992i	−0.481388	−	0.573696i
$879$	−15.5501	+	5.65976i	−0.524491	+	0.190899i
$880$	1.92226	+	2.29087i	0.0647995	+	0.0772251i
$881$	−18.8648	+	10.8916i	−0.635571	+	0.366947i	−0.782906	−	0.622140i	$-0.786264\pi$
$881$	−18.8648	+	10.8916i	−0.635571	+	0.366947i	0.147336	+	0.989087i	$0.452930\pi$
$882$	−6.50892	+	2.57564i	−0.219167	+	0.0867263i
$883$	−2.61200	+	2.19173i	−0.0879008	+	0.0737576i	−0.685679	−	0.727904i	$-0.740495\pi$
$883$	−2.61200	+	2.19173i	−0.0879008	+	0.0737576i	0.597778	+	0.801661i	$0.296050\pi$
$884$	8.18777	−	1.44372i	0.275385	−	0.0485577i
$885$		−	1.51239i		−	0.0508385i
$886$	−22.8219	−	13.1762i	−0.766717	−	0.442664i
$887$	15.2325	−	12.7816i	0.511458	−	0.429164i	−0.350184	−	0.936681i	$-0.613881\pi$
$887$	15.2325	−	12.7816i	0.511458	−	0.429164i	0.861642	+	0.507517i	$0.169436\pi$
$888$	−0.439742	+	2.49390i	−0.0147568	+	0.0836899i
$889$	−13.7360	+	30.5563i	−0.460692	+	1.02483i
$890$	−16.7634	+	6.10139i	−0.561911	+	0.204519i
$891$	−2.83904	+	1.03333i	−0.0951115	+	0.0346177i
$892$	2.49008	+	4.31294i	0.0833739	+	0.144408i
$893$	−12.1002	−	27.1221i	−0.404918	−	0.907607i
$894$	−20.4639	−	11.8148i	−0.684415	−	0.395147i
$895$	−12.7961	−	10.7372i	−0.427726	−	0.358905i
$896$	−1.84470	+	1.89659i	−0.0616273	+	0.0633607i
$897$	−6.14143	−	34.8298i	−0.205056	−	1.16293i
$898$	29.0850	+	24.4052i	0.970579	+	0.814413i
$899$	−12.9004	+	2.27469i	−0.430254	+	0.0758653i
$900$	2.01012	−	3.48163i	0.0670040	−	0.116054i
$901$	5.10529	+	8.84263i	0.170082	+	0.294591i
$902$	−14.0648	−	16.7618i	−0.468308	−	0.558108i
$903$	−15.0518	+	10.8535i	−0.500892	+	0.361183i
$904$	2.07919	−	3.60126i	0.0691527	−	0.119776i
$905$			9.98934i			0.332057i
$906$	3.35810	+	19.0447i	0.111565	+	0.632719i
$907$	13.0617	+	35.8868i	0.433708	+	1.19160i	0.943520	+	0.331316i	$0.107493\pi$
$907$	13.0617	+	35.8868i	0.433708	+	1.19160i	−0.509812	+	0.860286i	$0.670285\pi$
$908$	−2.11491	−	0.769766i	−0.0701859	−	0.0255456i
$909$	−4.39520	−	12.0757i	−0.145780	−	0.400526i
$910$	−11.1581	−	10.8528i	−0.369886	−	0.359767i
$911$		−	17.2717i		−	0.572237i	−0.958194	−	0.286119i	$-0.907635\pi$
$911$		−	17.2717i		−	0.572237i	0.958194	−	0.286119i	$-0.0923652\pi$
$912$	−3.52836	−	2.55942i	−0.116836	−	0.0847509i
$913$	10.4794	−	6.05029i	0.346818	−	0.200235i
$914$	−6.66041	−	1.17441i	−0.220307	−	0.0388460i
$915$	−1.88695	+	10.7014i	−0.0623807	+	0.353778i
$916$	−16.5456	+	2.91743i	−0.546681	+	0.0963946i
$917$	−7.51650	−	26.5723i	−0.248217	−	0.877496i
$918$	1.31445	+	0.478422i	0.0433834	+	0.0157903i
$919$	−30.2535			−0.997971			−0.498985	−	0.866610i	$-0.666294\pi$
$919$	−30.2535			−0.997971			−0.498985	+	0.866610i	$0.666294\pi$
$920$	−5.88985			−0.194183
$921$	2.62352	+	0.954883i	0.0864479	+	0.0314645i
$922$	−6.33106	−	35.9052i	−0.208502	−	1.18248i
$923$	−41.7401	−	24.0987i	−1.37389	−	0.793218i
$924$	−7.97194	−	0.586181i	−0.262258	−	0.0192839i
$925$	3.48202	−	9.56678i	0.114488	−	0.314554i
$926$	−6.19592	+	7.38401i	−0.203611	+	0.242654i
$927$	10.5466	−	8.84963i	0.346395	−	0.290660i
$928$	1.79277	+	1.50432i	0.0588507	+	0.0493816i
$929$	1.06289	+	2.92026i	0.0348722	+	0.0958107i	0.955907	−	0.293670i	$-0.0948767\pi$
$929$	1.06289	+	2.92026i	0.0348722	+	0.0958107i	−0.921035	+	0.389481i	$0.872654\pi$
$930$	5.54040			0.181677
$931$	−2.99476	−	30.3650i	−0.0981492	−	0.995172i
$932$	18.9383			0.620346
$933$	6.55174	+	18.0008i	0.214494	+	0.589319i
$934$	21.1245	+	17.7256i	0.691216	+	0.579999i
$935$	3.20449	−	2.68889i	0.104798	−	0.0879360i
$936$	3.82052	−	4.55312i	0.124878	−	0.148823i
$937$	16.0703	−	44.1527i	0.524992	−	1.44240i	−0.339907	−	0.940459i	$-0.610396\pi$
$937$	16.0703	−	44.1527i	0.524992	−	1.44240i	0.864899	−	0.501945i	$-0.167382\pi$
$938$	9.15844	+	0.673424i	0.299034	+	0.0219881i
$939$	−10.7199	−	6.18913i	−0.349830	−	0.201974i
$940$	−1.17110	−	6.64163i	−0.0381970	−	0.216626i
$941$	−35.9807	−	13.0959i	−1.17294	−	0.426914i	−0.319234	−	0.947676i	$-0.603426\pi$
$941$	−35.9807	−	13.0959i	−1.17294	−	0.426914i	−0.853702	+	0.520762i	$0.825648\pi$
$942$	−7.79957			−0.254124
$943$	43.0949			1.40336
$944$	1.43579	+	0.522585i	0.0467310	+	0.0170087i
$945$	−0.712820	−	2.51996i	−0.0231880	−	0.0819744i
$946$	−20.8685	+	3.67968i	−0.678494	+	0.119637i
$947$	−6.75694	+	38.3205i	−0.219571	+	1.24525i	0.653225	+	0.757164i	$0.273416\pi$
$947$	−6.75694	+	38.3205i	−0.219571	+	1.24525i	−0.872796	+	0.488085i	$0.837695\pi$
$948$	−8.81286	−	1.55394i	−0.286228	−	0.0504698i
$949$	10.8428	−	6.26008i	0.351971	−	0.203211i
$950$	12.1826	+	12.5963i	0.395256	+	0.408679i
$951$			5.99241i			0.194317i
$952$	2.65298	+	2.58040i	0.0859835	+	0.0836311i
$953$	−3.01378	−	8.28030i	−0.0976260	−	0.268225i	0.881260	−	0.472632i	$-0.156696\pi$
$953$	−3.01378	−	8.28030i	−0.0976260	−	0.268225i	−0.978886	+	0.204406i	$0.934474\pi$
$954$	6.85926	+	2.49657i	0.222077	+	0.0808293i
$955$	1.74991	+	4.80783i	0.0566257	+	0.155578i
$956$	0.666788	+	3.78154i	0.0215655	+	0.122304i
$957$			7.07062i			0.228561i
$958$	−9.09729	+	15.7570i	−0.293920	+	0.509084i
$959$	6.16763	−	4.44735i	0.199163	−	0.143612i
$960$	−0.636249	−	0.758252i	−0.0205349	−	0.0244725i
$961$	−0.165099	−	0.285959i	−0.00532577	−	0.00922450i
$962$	7.52580	−	13.0351i	0.242642	−	0.420267i
$963$	10.1431	−	1.78850i	0.326857	−	0.0576336i
$964$	14.1442	+	11.8684i	0.455556	+	0.382257i
$965$	−0.161811	−	0.917675i	−0.00520888	−	0.0295410i
$966$	10.9767	−	11.2854i	0.353169	−	0.363103i
$967$	−20.7001	−	17.3694i	−0.665670	−	0.558564i	0.246110	−	0.969242i	$-0.420848\pi$
$967$	−20.7001	−	17.3694i	−0.665670	−	0.558564i	−0.911780	+	0.410678i	$0.865292\pi$
$968$	1.62127	+	0.936041i	0.0521096	+	0.0300855i
$969$	−3.58015	+	4.93552i	−0.115011	+	0.158552i
$970$	−2.89471	−	5.01379i	−0.0929437	−	0.160983i
$971$	26.0665	−	9.48744i	0.836514	−	0.304466i	0.111985	−	0.993710i	$-0.464279\pi$
$971$	26.0665	−	9.48744i	0.836514	−	0.304466i	0.724530	+	0.689244i	$0.242057\pi$
$972$	0.939693	−	0.342020i	0.0301407	−	0.0109703i
$973$	23.9752	−	53.3338i	0.768611	−	1.70980i
$974$	2.20975	−	12.5321i	0.0708048	−	0.401554i
$975$	−18.3046	+	15.3594i	−0.586217	+	0.491895i
$976$	−9.50739	−	5.48909i	−0.304324	−	0.175702i
$977$			42.3186i			1.35389i	0.736033	+	0.676946i	$0.236697\pi$
$977$			42.3186i			1.35389i	−0.736033	+	0.676946i	$0.763303\pi$
$978$	17.9913	−	3.17236i	0.575300	−	0.101441i
$979$	41.7116	−	35.0002i	1.33311	−	1.11861i
$980$	1.01348	−	6.85428i	0.0323743	−	0.218952i
$981$	0.426877	−	0.246458i	0.0136291	−	0.00786879i
$982$	−21.9886	−	26.2050i	−0.701684	−	0.836235i
$983$	−44.0511	+	16.0333i	−1.40501	+	0.511383i	−0.929662	−	0.368414i	$-0.879901\pi$
$983$	−44.0511	+	16.0333i	−1.40501	+	0.511383i	−0.475351	+	0.879796i	$0.657679\pi$
$984$	4.65531	+	5.54799i	0.148406	+	0.176863i
$985$	−12.3112	−	2.17079i	−0.392266	−	0.0691672i
$986$	2.10425	−	2.50775i	0.0670131	−	0.0798631i
$987$	14.9084	+	10.1338i	0.474541	+	0.322563i
$988$	14.5038	+	21.4676i	0.461427	+	0.682976i
$989$	20.8674	−	36.1434i	0.663545	−	1.14929i
$990$	0.519297	−	2.94508i	0.0165043	−	0.0936008i
$991$	−29.9198	+	35.6571i	−0.950435	+	1.13268i	0.0406130	+	0.999175i	$0.487069\pi$
$991$	−29.9198	+	35.6571i	−0.950435	+	1.13268i	−0.991048	+	0.133509i	$0.957376\pi$
$992$	−1.91440	+	5.25978i	−0.0607823	+	0.166998i
$993$	−31.9693	−	5.63706i	−1.01452	−	0.178887i
$994$	−2.16609	−	21.3448i	−0.0687042	−	0.677017i
$995$	6.65952	+	11.5346i	0.211121	+	0.365672i
$996$	−3.46857	+	2.00258i	−0.109906	+	0.0634542i
$997$	13.6800	−	37.5854i	0.433249	−	1.19034i	−0.510558	−	0.859843i	$-0.670561\pi$
$997$	13.6800	−	37.5854i	0.433249	−	1.19034i	0.943807	−	0.330497i	$-0.107217\pi$
$998$	10.2618	−	28.1941i	0.324832	−	0.892468i
$999$	2.19310	−	1.26619i	0.0693866	−	0.0400604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cj.a.649.9	yes	72
7.3	odd	6		798.2.ca.a.535.4	yes	72
19.13	odd	18		798.2.ca.a.355.4	✓	72
133.108	even	18	inner	798.2.cj.a.241.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.ca.a.355.4	✓	72	19.13	odd	18
798.2.ca.a.535.4	yes	72	7.3	odd	6
798.2.cj.a.241.9	yes	72	133.108	even	18	inner
798.2.cj.a.649.9	yes	72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.342020 + 0.939693i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.636249 + 0.758252i) q^{5} +(-0.342020 + 0.939693i) q^{6} +(2.63863 + 0.194020i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.930134 - 0.338541i) q^{10} +3.02124 q^{11} -1.00000 q^{12} +(5.58523 + 2.03286i) q^{13} +(0.720145 + 2.54586i) q^{14} +(-0.974791 + 0.171882i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.37756 - 0.242901i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-1.05772 - 4.22862i) q^{19} -0.989828i q^{20} +(1.89659 + 1.84470i) q^{21} +(1.03333 + 2.83904i) q^{22} +(-5.59152 - 2.03515i) q^{23} +(-0.342020 - 0.939693i) q^{24} +(0.698107 + 3.95916i) q^{25} +5.94367i q^{26} +(-0.500000 + 0.866025i) q^{27} +(-2.14602 + 1.54745i) q^{28} +(1.50432 + 1.79277i) q^{29} +(-0.494914 - 0.857216i) q^{30} +(-2.79867 + 4.84744i) q^{31} +(0.984808 - 0.173648i) q^{32} +(2.31441 + 1.94202i) q^{33} +(-0.242901 - 1.37756i) q^{34} +(-1.82594 + 1.87730i) q^{35} +(-0.766044 - 0.642788i) q^{36} +(-2.19310 - 1.26619i) q^{37} +(3.61184 - 2.44020i) q^{38} +(2.97184 + 5.14737i) q^{39} +(0.930134 - 0.338541i) q^{40} +(-6.80561 + 2.47704i) q^{41} +(-1.08478 + 2.41314i) q^{42} +(-1.21794 + 6.90726i) q^{43} +(-2.31441 + 1.94202i) q^{44} +(-0.857216 - 0.494914i) q^{45} -5.95037i q^{46} +(6.70988 - 1.18313i) q^{47} +(0.766044 - 0.642788i) q^{48} +(6.92471 + 1.02389i) q^{49} +(-3.48163 + 2.01012i) q^{50} +(-0.899139 - 1.07155i) q^{51} +(-5.58523 + 2.03286i) q^{52} +(-4.69201 - 5.59172i) q^{53} +(-0.984808 - 0.173648i) q^{54} +(-1.92226 + 2.29087i) q^{55} +(-2.18811 - 1.48734i) q^{56} +(1.90784 - 3.91920i) q^{57} +(-1.17015 + 2.02676i) q^{58} +(-0.265323 + 1.50472i) q^{59} +(0.636249 - 0.758252i) q^{60} +(3.75476 - 10.3161i) q^{61} +(-5.51230 - 0.971968i) q^{62} +(0.267121 + 2.63223i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-5.09501 + 2.94161i) q^{65} +(-1.03333 + 2.83904i) q^{66} +(1.18712 - 3.26159i) q^{67} +(1.21141 - 0.699406i) q^{68} +(-2.97519 - 5.15317i) q^{69} +(-2.38859 - 1.07375i) q^{70} +(-7.98583 - 1.40812i) q^{71} +(0.342020 - 0.939693i) q^{72} +(1.35401 - 1.61365i) q^{73} +(0.439742 - 2.49390i) q^{74} +(-2.01012 + 3.48163i) q^{75} +(3.52836 + 2.55942i) q^{76} +(7.97194 + 0.586181i) q^{77} +(-3.82052 + 4.55312i) q^{78} +(8.81286 + 1.55394i) q^{79} +(0.636249 + 0.758252i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-4.65531 - 5.54799i) q^{82} +(3.46857 - 2.00258i) q^{83} +(-2.63863 - 0.194020i) q^{84} +(1.06065 - 0.889993i) q^{85} +(-6.90726 + 1.21794i) q^{86} +2.34030i q^{87} +(-2.61647 - 1.51062i) q^{88} +(13.8061 - 11.5847i) q^{89} +(0.171882 - 0.974791i) q^{90} +(14.3429 + 6.44759i) q^{91} +(5.59152 - 2.03515i) q^{92} +(-5.25978 + 1.91440i) q^{93} +(3.40670 + 5.90057i) q^{94} +(3.87934 + 1.88844i) q^{95} +(0.866025 + 0.500000i) q^{96} +(4.48053 + 3.75961i) q^{97} +(1.40625 + 6.85729i) q^{98} +(0.524634 + 2.97535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 12 q^{7} + 12 q^{10} - 12 q^{11} - 72 q^{12} - 30 q^{13} - 18 q^{14} + 36 q^{19} - 6 q^{21} + 12 q^{22} - 6 q^{23} - 30 q^{25} - 36 q^{27} - 12 q^{28} - 6 q^{31} - 12 q^{33} - 6 q^{34} - 6 q^{35}+ \cdots + 6 q^{99}+O(q^{100}) \) 72 * q + 12 * q^7 + 12 * q^10 - 12 * q^11 - 72 * q^12 - 30 * q^13 - 18 * q^14 + 36 * q^19 - 6 * q^21 + 12 * q^22 - 6 * q^23 - 30 * q^25 - 36 * q^27 - 12 * q^28 - 6 * q^31 - 12 * q^33 - 6 * q^34 - 6 * q^35 - 18 * q^37 - 12 * q^38 - 12 * q^40 - 6 * q^42 + 6 * q^43 + 12 * q^44 - 18 * q^45 - 18 * q^47 - 24 * q^49 - 18 * q^51 + 30 * q^52 - 48 * q^53 + 30 * q^55 - 18 * q^56 + 6 * q^57 - 48 * q^59 + 6 * q^61 + 12 * q^62 + 12 * q^63 + 36 * q^64 - 72 * q^65 - 12 * q^66 + 84 * q^67 - 6 * q^69 + 54 * q^70 + 6 * q^71 + 60 * q^73 - 18 * q^74 + 6 * q^75 + 18 * q^76 + 48 * q^77 - 12 * q^78 + 60 * q^79 + 6 * q^82 - 18 * q^83 - 12 * q^84 + 84 * q^85 - 12 * q^86 + 24 * q^89 - 6 * q^90 + 24 * q^91 + 6 * q^92 - 42 * q^93 + 18 * q^94 + 60 * q^95 - 30 * q^97 - 24 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more