LMFDB - Embedded newform 189.2.ba.a.38.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			38.4
Character	$\chi$	$=$	189.38
Dual form			189.2.ba.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27453 - 0.401061i) q^{2} +(1.22609 - 1.22340i) q^{3} +(3.13325 + 1.14041i) q^{4} +(-0.595188 - 3.37548i) q^{5} +(-3.27944 + 2.29092i) q^{6} +(-2.64569 - 0.0174348i) q^{7} +(-2.66893 - 1.54091i) q^{8} +(0.00659757 - 2.99999i) q^{9} +O(q^{10})$	\(q+(-2.27453 - 0.401061i) q^{2} +(1.22609 - 1.22340i) q^{3} +(3.13325 + 1.14041i) q^{4} +(-0.595188 - 3.37548i) q^{5} +(-3.27944 + 2.29092i) q^{6} +(-2.64569 - 0.0174348i) q^{7} +(-2.66893 - 1.54091i) q^{8} +(0.00659757 - 2.99999i) q^{9} +7.91633i q^{10} +(1.05044 + 0.185221i) q^{11} +(5.23683 - 2.43497i) q^{12} +(2.65013 + 3.15830i) q^{13} +(6.01072 + 1.10074i) q^{14} +(-4.85931 - 3.41049i) q^{15} +(0.344058 + 0.288699i) q^{16} -6.74438 q^{17} +(-1.21819 + 6.82093i) q^{18} -3.89053i q^{19} +(1.98456 - 11.2550i) q^{20} +(-3.26519 + 3.21536i) q^{21} +(-2.31497 - 0.842581i) q^{22} +(0.748519 + 0.892051i) q^{23} +(-5.15749 + 1.37587i) q^{24} +(-6.34114 + 2.30799i) q^{25} +(-4.76112 - 8.24651i) q^{26} +(-3.66209 - 3.68634i) q^{27} +(-8.26975 - 3.07181i) q^{28} +(-1.58160 + 1.88488i) q^{29} +(9.68482 + 9.70615i) q^{30} +(3.16020 - 8.68256i) q^{31} +(3.29512 + 3.92697i) q^{32} +(1.51453 - 1.05801i) q^{33} +(15.3403 + 2.70491i) q^{34} +(1.51583 + 8.94086i) q^{35} +(3.44190 - 9.39221i) q^{36} +(-0.357225 + 0.618733i) q^{37} +(-1.56034 + 8.84913i) q^{38} +(7.11315 + 0.630202i) q^{39} +(-3.61278 + 9.92604i) q^{40} +(5.44308 - 4.56728i) q^{41} +(8.71633 - 6.00389i) q^{42} +(3.59373 - 1.30801i) q^{43} +(3.08007 + 1.77828i) q^{44} +(-10.1303 + 1.76329i) q^{45} +(-1.34476 - 2.32920i) q^{46} +(-1.83909 + 0.669375i) q^{47} +(0.775040 - 0.0669486i) q^{48} +(6.99939 + 0.0922545i) q^{49} +(15.3488 - 2.70640i) q^{50} +(-8.26923 + 8.25106i) q^{51} +(4.70176 + 12.9180i) q^{52} +(6.35643 + 3.66989i) q^{53} +(6.85110 + 9.85340i) q^{54} -3.65598i q^{55} +(7.03430 + 4.12330i) q^{56} +(-4.75966 - 4.77014i) q^{57} +(4.35336 - 3.65290i) q^{58} +(4.57964 - 3.84278i) q^{59} +(-11.3361 - 16.2275i) q^{60} +(2.34201 + 6.43463i) q^{61} +(-10.6702 + 18.4813i) q^{62} +(-0.0697595 + 7.93695i) q^{63} +(-6.36903 - 11.0315i) q^{64} +(9.08344 - 10.8252i) q^{65} +(-3.86918 + 1.79905i) q^{66} +(-0.361541 - 2.05040i) q^{67} +(-21.1319 - 7.69137i) q^{68} +(2.00909 + 0.177999i) q^{69} +(0.138020 - 20.9442i) q^{70} +(1.33942 - 0.773313i) q^{71} +(-4.64032 + 7.99660i) q^{72} +(9.58401 - 5.53333i) q^{73} +(1.06067 - 1.26406i) q^{74} +(-4.95123 + 10.5875i) q^{75} +(4.43680 - 12.1900i) q^{76} +(-2.77591 - 0.508352i) q^{77} +(-15.9263 - 4.28622i) q^{78} +(-0.698202 + 3.95970i) q^{79} +(0.769718 - 1.33319i) q^{80} +(-8.99991 - 0.0395853i) q^{81} +(-14.2122 + 8.20542i) q^{82} +(-6.13413 - 5.14714i) q^{83} +(-13.8975 + 6.35087i) q^{84} +(4.01418 + 22.7655i) q^{85} +(-8.69865 + 1.53381i) q^{86} +(0.366770 + 4.24596i) q^{87} +(-2.51814 - 2.11297i) q^{88} +11.1246 q^{89} +(23.7489 + 0.0522286i) q^{90} +(-6.95636 - 8.40209i) q^{91} +(1.32800 + 3.64864i) q^{92} +(-6.74754 - 14.5118i) q^{93} +(4.45153 - 0.784926i) q^{94} +(-13.1324 + 2.31560i) q^{95} +(8.84436 + 0.783582i) q^{96} +(-0.832291 - 2.28670i) q^{97} +(-15.8833 - 3.01702i) q^{98} +(0.562592 - 3.15009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−2.27453	−	0.401061i	−1.60834	−	0.283593i	−0.703931	−	0.710268i	$-0.748574\pi$
$2$	−2.27453	−	0.401061i	−1.60834	−	0.283593i	−0.904405	+	0.426675i	$0.859685\pi$
$3$	1.22609	−	1.22340i	0.707884	−	0.706329i
$3$	1.22609	−	1.22340i	0.707884	−	0.706329i
$4$	3.13325	+	1.14041i	1.56663	+	0.570205i
$5$	−0.595188	−	3.37548i	−0.266176	−	1.50956i	−0.765665	−	0.643239i	$-0.777590\pi$
$5$	−0.595188	−	3.37548i	−0.266176	−	1.50956i	0.499489	−	0.866320i	$-0.333521\pi$
$6$	−3.27944	+	2.29092i	−1.33882	+	0.935263i
$7$	−2.64569	−	0.0174348i	−0.999978	−	0.00658975i
$7$	−2.64569	−	0.0174348i	−0.999978	−	0.00658975i
$8$	−2.66893	−	1.54091i	−0.943609	−	0.544793i
$9$	0.00659757	−	2.99999i	0.00219919	−	0.999998i
$10$			7.91633i			2.50336i
$11$	1.05044	+	0.185221i	0.316720	+	0.0558462i	0.329748	−	0.944069i	$-0.393036\pi$
$11$	1.05044	+	0.185221i	0.316720	+	0.0558462i	−0.0130286	+	0.999915i	$0.504147\pi$
$12$	5.23683	−	2.43497i	1.51174	−	0.702914i
$13$	2.65013	+	3.15830i	0.735013	+	0.875954i	0.995997	−	0.0893890i	$-0.0284914\pi$
$13$	2.65013	+	3.15830i	0.735013	+	0.875954i	−0.260984	+	0.965343i	$0.584047\pi$
$14$	6.01072	+	1.10074i	1.60643	+	0.294185i
$15$	−4.85931	−	3.41049i	−1.25467	−	0.880585i
$16$	0.344058	+	0.288699i	0.0860145	+	0.0721748i
$17$	−6.74438			−1.63575			−0.817877	−	0.575393i	$-0.804849\pi$
$17$	−6.74438			−1.63575			−0.817877	+	0.575393i	$0.804849\pi$
$18$	−1.21819	+	6.82093i	−0.287129	+	1.60771i
$19$		−	3.89053i		−	0.892549i	−0.894896	−	0.446274i	$-0.852751\pi$
$19$		−	3.89053i		−	0.892549i	0.894896	−	0.446274i	$-0.147249\pi$
$20$	1.98456	−	11.2550i	0.443761	−	2.51669i
$21$	−3.26519	+	3.21536i	−0.712523	+	0.701649i
$22$	−2.31497	−	0.842581i	−0.493554	−	0.179639i
$23$	0.748519	+	0.892051i	0.156077	+	0.186005i	0.838416	−	0.545030i	$-0.183482\pi$
$23$	0.748519	+	0.892051i	0.156077	+	0.186005i	−0.682339	+	0.731036i	$0.739037\pi$
$24$	−5.15749	+	1.37587i	−1.05277	+	0.280848i
$25$	−6.34114	+	2.30799i	−1.26823	+	0.461597i
$26$	−4.76112	−	8.24651i	−0.933733	−	1.61727i
$27$	−3.66209	−	3.68634i	−0.704770	−	0.709436i
$28$	−8.26975	−	3.07181i	−1.56284	−	0.580517i
$29$	−1.58160	+	1.88488i	−0.293696	+	0.350014i	−0.892634	−	0.450782i	$-0.851145\pi$
$29$	−1.58160	+	1.88488i	−0.293696	+	0.350014i	0.598938	+	0.800796i	$0.295590\pi$
$30$	9.68482	+	9.70615i	1.76820	+	1.77209i
$31$	3.16020	−	8.68256i	0.567588	−	1.55943i	−0.240671	−	0.970607i	$-0.577367\pi$
$31$	3.16020	−	8.68256i	0.567588	−	1.55943i	0.808258	−	0.588828i	$-0.200410\pi$
$32$	3.29512	+	3.92697i	0.582500	+	0.694196i
$33$	1.51453	−	1.05801i	0.263647	−	0.184176i
$34$	15.3403	+	2.70491i	2.63084	+	0.463888i
$35$	1.51583	+	8.94086i	0.256223	+	1.51128i
$36$	3.44190	−	9.39221i	0.573649	−	1.56537i
$37$	−0.357225	+	0.618733i	−0.0587275	+	0.101719i	−0.893894	−	0.448278i	$-0.852038\pi$
$37$	−0.357225	+	0.618733i	−0.0587275	+	0.101719i	0.835167	+	0.549997i	$0.185371\pi$
$38$	−1.56034	+	8.84913i	−0.253121	+	1.43552i
$39$	7.11315	+	0.630202i	1.13902	+	0.100913i
$40$	−3.61278	+	9.92604i	−0.571231	+	1.56944i
$41$	5.44308	−	4.56728i	0.850066	−	0.713290i	−0.109738	−	0.993961i	$-0.535001\pi$
$41$	5.44308	−	4.56728i	0.850066	−	0.713290i	0.959804	+	0.280671i	$0.0905569\pi$
$42$	8.71633	−	6.00389i	1.34496	−	0.926420i
$43$	3.59373	−	1.30801i	0.548039	−	0.199470i	−0.0531360	−	0.998587i	$-0.516922\pi$
$43$	3.59373	−	1.30801i	0.548039	−	0.199470i	0.601175	+	0.799117i	$0.294699\pi$
$44$	3.08007	+	1.77828i	0.464338	+	0.268085i
$45$	−10.1303	+	1.76329i	−1.51014	+	0.262856i
$46$	−1.34476	−	2.32920i	−0.198275	−	0.343422i
$47$	−1.83909	+	0.669375i	−0.268259	+	0.0976384i	−0.472648	−	0.881251i	$-0.656702\pi$
$47$	−1.83909	+	0.669375i	−0.268259	+	0.0976384i	0.204388	+	0.978890i	$0.434479\pi$
$48$	0.775040	−	0.0669486i	0.111867	−	0.00966319i
$49$	6.99939	+	0.0922545i	0.999913	+	0.0131792i
$50$	15.3488	−	2.70640i	2.17064	−	0.382743i
$51$	−8.26923	+	8.25106i	−1.15792	+	1.15538i
$52$	4.70176	+	12.9180i	0.652017	+	1.79140i
$53$	6.35643	+	3.66989i	0.873123	+	0.504098i	0.868385	−	0.495891i	$-0.165158\pi$
$53$	6.35643	+	3.66989i	0.873123	+	0.504098i	0.00473813	+	0.999989i	$0.498492\pi$
$54$	6.85110	+	9.85340i	0.932316	+	1.34088i
$55$		−	3.65598i		−	0.492972i
$56$	7.03430	+	4.12330i	0.939998	+	0.550999i
$57$	−4.75966	−	4.77014i	−0.630433	−	0.631821i
$58$	4.35336	−	3.65290i	0.571624	−	0.479649i
$59$	4.57964	−	3.84278i	0.596219	−	0.500287i	−0.294009	−	0.955803i	$-0.594990\pi$
$59$	4.57964	−	3.84278i	0.596219	−	0.500287i	0.890228	+	0.455516i	$0.150545\pi$
$60$	−11.3361	−	16.2275i	−1.46348	−	2.09497i
$61$	2.34201	+	6.43463i	0.299864	+	0.823870i	0.994522	+	0.104529i	$0.0333336\pi$
$61$	2.34201	+	6.43463i	0.299864	+	0.823870i	−0.694658	+	0.719340i	$0.744444\pi$
$62$	−10.6702	+	18.4813i	−1.35512	+	2.34713i
$63$	−0.0697595	+	7.93695i	−0.00878888	+	0.999961i
$64$	−6.36903	−	11.0315i	−0.796128	−	1.37893i
$65$	9.08344	−	10.8252i	1.12666	−	1.34270i
$66$	−3.86918	+	1.79905i	−0.476263	+	0.221448i
$67$	−0.361541	−	2.05040i	−0.0441692	−	0.250496i	0.954726	−	0.297486i	$-0.0961482\pi$
$67$	−0.361541	−	2.05040i	−0.0441692	−	0.250496i	−0.998895	+	0.0469900i	$0.985037\pi$
$68$	−21.1319	−	7.69137i	−2.56261	−	0.932716i
$69$	2.00909	+	0.177999i	0.241865	+	0.0214285i
$70$	0.138020	−	20.9442i	0.0164965	−	2.50331i
$71$	1.33942	−	0.773313i	0.158960	−	0.0917754i	−0.418410	−	0.908258i	$-0.637412\pi$
$71$	1.33942	−	0.773313i	0.158960	−	0.0917754i	0.577370	+	0.816483i	$0.304079\pi$
$72$	−4.64032	+	7.99660i	−0.546867	+	0.942408i
$73$	9.58401	−	5.53333i	1.12172	−	0.647627i	0.179883	−	0.983688i	$-0.442428\pi$
$73$	9.58401	−	5.53333i	1.12172	−	0.647627i	0.941840	+	0.336061i	$0.109095\pi$
$74$	1.06067	−	1.26406i	0.123300	−	0.146944i
$75$	−4.95123	+	10.5875i	−0.571719	+	1.22254i
$76$	4.43680	−	12.1900i	0.508936	−	1.39829i
$77$	−2.77591	−	0.508352i	−0.316345	−	0.0579321i
$78$	−15.9263	−	4.28622i	−1.80330	−	0.485319i
$79$	−0.698202	+	3.95970i	−0.0785539	+	0.445501i	0.920008	+	0.391899i	$0.128182\pi$
$79$	−0.698202	+	3.95970i	−0.0785539	+	0.445501i	−0.998562	+	0.0536028i	$0.982930\pi$
$80$	0.769718	−	1.33319i	0.0860571	−	0.149055i
$81$	−8.99991	−	0.0395853i	−0.999990	−	0.00439837i
$82$	−14.2122	+	8.20542i	−1.56948	+	0.906137i
$83$	−6.13413	−	5.14714i	−0.673308	−	0.564972i	0.240735	−	0.970591i	$-0.422612\pi$
$83$	−6.13413	−	5.14714i	−0.673308	−	0.564972i	−0.914042	+	0.405619i	$0.867056\pi$
$84$	−13.8975	+	6.35087i	−1.51634	+	0.692937i
$85$	4.01418	+	22.7655i	0.435398	+	2.46927i
$86$	−8.69865	+	1.53381i	−0.937999	+	0.165395i
$87$	0.366770	+	4.24596i	0.0393218	+	0.455215i
$88$	−2.51814	−	2.11297i	−0.268435	−	0.225244i
$89$	11.1246			1.17920			0.589601	−	0.807695i	$-0.299285\pi$
$89$	11.1246			1.17920			0.589601	+	0.807695i	$0.299285\pi$
$90$	23.7489	+	0.0522286i	2.50336	+	0.00550537i
$91$	−6.95636	−	8.40209i	−0.729224	−	0.880779i
$92$	1.32800	+	3.64864i	0.138453	+	0.380397i
$93$	−6.74754	−	14.5118i	−0.699687	−	1.50480i
$94$	4.45153	−	0.784926i	0.459141	−	0.0809589i
$95$	−13.1324	+	2.31560i	−1.34736	+	0.237575i
$96$	8.84436	+	0.783582i	0.902673	+	0.0799740i
$97$	−0.832291	−	2.28670i	−0.0845063	−	0.232179i	0.890241	−	0.455490i	$-0.150536\pi$
$97$	−0.832291	−	2.28670i	−0.0845063	−	0.232179i	−0.974747	+	0.223311i	$0.928314\pi$
$98$	−15.8833	−	3.01702i	−1.60446	−	0.304765i
$99$	0.562592	−	3.15009i	0.0565426	−	0.316596i
$100$	−22.5005			−2.25005
$101$	6.45368	+	5.41528i	0.642165	+	0.538840i	0.904682	−	0.426087i	$-0.140108\pi$
$101$	6.45368	+	5.41528i	0.642165	+	0.538840i	−0.262517	+	0.964927i	$0.584553\pi$
$102$	22.1178	−	15.4508i	2.18999	−	1.52986i
$103$	−4.33276	+	0.763983i	−0.426920	+	0.0752775i	−0.382980	−	0.923757i	$-0.625102\pi$
$103$	−4.33276	+	0.763983i	−0.426920	+	0.0752775i	−0.0439399	+	0.999034i	$0.513991\pi$
$104$	−2.20636	−	12.5129i	−0.216351	−	1.22699i
$105$	12.7968	+	9.10784i	1.24884	+	0.888834i
$106$	−12.9860	−	10.8966i	−1.26132	−	1.05837i
$107$	5.59193	−	3.22850i	0.540592	−	0.312111i	−0.204727	−	0.978819i	$-0.565631\pi$
$107$	5.59193	−	3.22850i	0.540592	−	0.312111i	0.745319	+	0.666708i	$0.232297\pi$
$108$	−7.27033	−	15.7265i	−0.699588	−	1.51328i
$109$	2.16059	−	3.74226i	0.206947	−	0.358443i	−0.743804	−	0.668398i	$-0.766980\pi$
$109$	2.16059	−	3.74226i	0.206947	−	0.358443i	0.950751	+	0.309954i	$0.100314\pi$
$110$	−1.46627	+	8.31564i	−0.139803	+	0.792865i
$111$	0.318965	+	1.19565i	0.0302748	+	0.113486i
$112$	−0.905239	−	0.769808i	−0.0855371	−	0.0727400i
$113$	−1.44517	+	3.97057i	−0.135950	+	0.373519i	−0.988922	−	0.148438i	$-0.952576\pi$
$113$	−1.44517	+	3.97057i	−0.135950	+	0.373519i	0.852972	+	0.521957i	$0.174798\pi$
$114$	8.91288	+	12.7587i	0.834768	+	1.19497i
$115$	2.56559	−	3.05755i	0.239242	−	0.285118i
$116$	−7.10510	+	4.10213i	−0.659692	+	0.380873i
$117$	9.49235	−	7.92952i	0.877568	−	0.733085i
$118$	−11.9577	+	6.90380i	−1.10080	+	0.635546i
$119$	17.8436	+	0.117587i	1.63572	+	0.0107792i
$120$	7.71389	+	16.5901i	0.704179	+	1.51446i
$121$	−9.26750	−	3.37309i	−0.842500	−	0.306645i
$122$	−2.74630	−	15.5750i	−0.248638	−	1.41010i
$123$	1.08610	−	12.2590i	0.0979307	−	1.10535i
$124$	19.8034	−	23.6008i	1.77840	−	2.11941i
$125$	2.99585	+	5.18897i	0.267957	+	0.464116i
$126$	3.34187	−	18.0249i	0.297718	−	1.60578i
$127$	2.73727	−	4.74109i	0.242893	−	0.420704i	−0.718644	−	0.695378i	$-0.755237\pi$
$127$	2.73727	−	4.74109i	0.242893	−	0.420704i	0.961537	+	0.274675i	$0.0885701\pi$
$128$	6.55566	+	18.0115i	0.579444	+	1.59201i
$129$	2.80602	−	6.00030i	0.247057	−	0.528297i
$130$	−25.0021	+	20.9793i	−2.19283	+	1.84001i
$131$	12.4171	−	10.4192i	1.08489	−	0.910331i	0.0885726	−	0.996070i	$-0.471769\pi$
$131$	12.4171	−	10.4192i	1.08489	−	0.910331i	0.996318	+	0.0857387i	$0.0273250\pi$
$132$	5.95198	−	1.58782i	0.518054	−	0.138202i
$133$	−0.0678307	+	10.2931i	−0.00588167	+	0.892529i
$134$			4.80870i			0.415408i
$135$	−10.2635	+	14.5554i	−0.883342	+	1.25273i
$136$	18.0003	+	10.3925i	1.54351	+	0.891147i
$137$	3.02771	+	8.31857i	0.258675	+	0.710703i	0.999250	+	0.0387294i	$0.0123310\pi$
$137$	3.02771	+	8.31857i	0.258675	+	0.710703i	−0.740575	+	0.671974i	$0.765447\pi$
$138$	−4.49834	−	1.21063i	−0.382924	−	0.103056i
$139$	−22.0614	+	3.89002i	−1.87123	+	0.329948i	−0.989810	−	0.142394i	$-0.954520\pi$
$139$	−22.0614	+	3.89002i	−1.87123	+	0.329948i	−0.881416	+	0.472341i	$0.843409\pi$
$140$	−5.44676	+	29.7426i	−0.460335	+	2.51371i
$141$	−1.43598	+	3.07066i	−0.120932	+	0.258596i
$142$	−3.35669	+	1.22174i	−0.281687	+	0.102526i
$143$	2.19882	+	3.80846i	0.183874	+	0.318480i
$144$	0.868365	−	1.03027i	0.0723638	−	0.0858556i
$145$	7.30373	+	4.21681i	0.606541	+	0.350187i
$146$	−24.0183	+	8.74195i	−1.98777	+	0.723489i
$147$	8.69475	−	8.44993i	0.717131	−	0.696938i
$148$	−1.82489	+	1.53126i	−0.150005	+	0.125869i
$149$	−5.51505	+	15.1525i	−0.451811	+	1.24134i	0.479638	+	0.877466i	$0.340768\pi$
$149$	−5.51505	+	15.1525i	−0.451811	+	1.24134i	−0.931449	+	0.363873i	$0.881454\pi$
$150$	15.5080	−	22.0959i	1.26622	−	1.80413i
$151$	−1.76751	+	10.0241i	−0.143838	+	0.815747i	0.824455	+	0.565928i	$0.191482\pi$
$151$	−1.76751	+	10.0241i	−0.143838	+	0.815747i	−0.968293	+	0.249818i	$0.919629\pi$
$152$	−5.99494	+	10.3835i	−0.486254	+	0.842217i
$153$	−0.0444965	+	20.2331i	−0.00359733	+	1.63575i
$154$	6.11002	+	2.26957i	0.492360	+	0.182887i
$155$	−31.1887	−	5.49941i	−2.50514	−	0.441723i
$156$	21.5686	+	10.0865i	1.72687	+	0.807566i
$157$	7.17325	+	8.54875i	0.572488	+	0.682264i	0.972140	−	0.234403i	$-0.0753135\pi$
$157$	7.17325	+	8.54875i	0.572488	+	0.682264i	−0.399652	+	0.916667i	$0.630869\pi$
$158$	3.17617	−	8.72644i	0.252682	−	0.694238i
$159$	12.2833	−	3.27683i	0.974128	−	0.259869i
$160$	11.2942	−	13.4599i	0.892883	−	1.06410i
$161$	−1.96480	−	2.37314i	−0.154848	−	0.187030i
$162$	20.4547	+	3.69955i	1.60707	+	0.290664i
$163$	−6.62402	−	11.4731i	−0.518833	−	0.898645i	−0.999761	−	0.0218848i	$-0.993033\pi$
$163$	−6.62402	−	11.4731i	−0.518833	−	0.898645i	0.480927	−	0.876760i	$-0.340300\pi$
$164$	22.2631	−	8.10311i	1.73846	−	0.632747i
$165$	−4.47272	−	4.48256i	−0.348200	−	0.348967i
$166$	11.8879	+	14.1675i	0.922683	+	1.09961i
$167$	5.35496	+	1.94905i	0.414379	+	0.150822i	0.540793	−	0.841156i	$-0.318124\pi$
$167$	5.35496	+	1.94905i	0.414379	+	0.150822i	−0.126413	+	0.991978i	$0.540347\pi$
$168$	13.6691	−	3.55021i	1.05460	−	0.273904i
$169$	−0.694247	+	3.93727i	−0.0534037	+	0.302867i
$170$		−	53.3908i		−	4.09489i
$171$	−11.6716	−	0.0256680i	−0.892546	−	0.00196288i
$172$	12.7517			0.972311
$173$	−10.5337	−	8.83880i	−0.800860	−	0.672002i	0.147547	−	0.989055i	$-0.452862\pi$
$173$	−10.5337	−	8.83880i	−0.800860	−	0.672002i	−0.948408	+	0.317053i	$0.897307\pi$
$174$	0.868662	−	9.80467i	0.0658531	−	0.743290i
$175$	16.8170	−	5.99567i	1.27124	−	0.453230i
$176$	0.307939	+	0.366988i	0.0232118	+	0.0276628i
$177$	0.913816	−	10.3143i	0.0686866	−	0.775272i
$178$	−25.3032	−	4.46163i	−1.89655	−	0.334413i
$179$		−	2.15435i		−	0.161023i	−0.996754	−	0.0805117i	$-0.974345\pi$
$179$		−	2.15435i		−	0.161023i	0.996754	−	0.0805117i	$-0.0256554\pi$
$180$	−33.7518	−	6.02791i	−2.51571	−	0.449294i
$181$	21.9924	+	12.6973i	1.63468	+	0.943786i	0.982621	+	0.185621i	$0.0594297\pi$
$181$	21.9924	+	12.6973i	1.63468	+	0.943786i	0.652063	+	0.758164i	$0.273904\pi$
$182$	12.4527	+	21.9007i	0.923055	+	1.62339i
$183$	10.7436	+	5.02423i	0.794192	+	0.371401i
$184$	−0.623178	−	3.53422i	−0.0459413	−	0.260546i
$185$	2.30113	+	0.837545i	0.169183	+	0.0615775i
$186$	9.52737	+	35.7137i	0.698581	+	2.61865i
$187$	−7.08457	−	1.24920i	−0.518075	−	0.0913507i
$188$	−6.52571			−0.475936
$189$	9.62451	+	9.81676i	0.700080	+	0.714064i
$190$	30.7987			2.23437
$191$	−13.4162	−	2.36564i	−0.970765	−	0.171172i	−0.334291	−	0.942470i	$-0.608497\pi$
$191$	−13.4162	−	2.36564i	−0.970765	−	0.171172i	−0.636474	+	0.771298i	$0.719608\pi$
$192$	−21.3049	−	5.73374i	−1.53755	−	0.413797i
$193$	−17.8457	−	6.49531i	−1.28456	−	0.467543i	−0.392624	−	0.919699i	$-0.628433\pi$
$193$	−17.8457	−	6.49531i	−1.28456	−	0.467543i	−0.891939	+	0.452156i	$0.850655\pi$
$194$	0.975964	+	5.53497i	0.0700701	+	0.397388i
$195$	−2.10643	−	24.3854i	−0.150844	−	1.74627i
$196$	21.8257	+	8.27124i	1.55898	+	0.590803i
$197$	−16.5034	−	9.52825i	−1.17582	−	0.678860i	−0.220776	−	0.975325i	$-0.570859\pi$
$197$	−16.5034	−	9.52825i	−1.17582	−	0.678860i	−0.955044	+	0.296465i	$0.904192\pi$
$198$	−2.54301	+	6.93934i	−0.180724	+	0.493158i
$199$			7.54509i			0.534857i	0.963578	+	0.267429i	$0.0861740\pi$
$199$			7.54509i			0.534857i	−0.963578	+	0.267429i	$0.913826\pi$
$200$	20.4804	+	3.61125i	1.44819	+	0.255354i
$201$	−2.95174	−	2.07167i	−0.208199	−	0.146124i
$202$	−12.5072	−	14.9055i	−0.880005	−	1.04875i
$203$	4.21730	−	4.95924i	0.295996	−	0.348071i
$204$	−35.3192	+	16.4223i	−2.47284	+	1.14979i
$205$	−18.6564	−	15.6546i	−1.30302	−	1.09336i
$206$	10.1614			0.707978
$207$	2.68108	−	2.23967i	0.186348	−	0.155668i
$208$			1.85173i			0.128394i
$209$	0.720608	−	4.08677i	0.0498455	−	0.282688i
$210$	−25.4539	−	25.8483i	−1.75648	−	1.78371i
$211$	22.8365	+	8.31180i	1.57213	+	0.572208i	0.973474	−	0.228799i	$-0.0734798\pi$
$211$	22.8365	+	8.31180i	1.57213	+	0.572208i	0.598655	+	0.801007i	$0.295702\pi$
$212$	15.7311	+	18.7476i	1.08042	+	1.28759i
$213$	0.696179	−	2.58679i	0.0477014	−	0.177244i
$214$	−14.0138	+	5.10062i	−0.957966	+	0.348671i
$215$	−6.55411	−	11.3521i	−0.446987	−	0.774204i
$216$	4.09357	+	15.4815i	0.278532	+	1.05338i
$217$	−8.51229	+	22.9163i	−0.577852	+	1.55566i
$218$	−6.41521	+	7.64535i	−0.434493	+	0.517809i
$219$	4.98140	−	18.5094i	0.336612	−	1.25075i
$220$	4.16932	−	11.4551i	0.281095	−	0.772303i
$221$	−17.8735	−	21.3008i	−1.20230	−	1.43284i
$222$	−0.245967	−	2.84747i	−0.0165082	−	0.191110i
$223$	5.30044	+	0.934610i	0.354944	+	0.0625861i	0.348277	−	0.937392i	$-0.386767\pi$
$223$	5.30044	+	0.934610i	0.354944	+	0.0625861i	0.00666651	+	0.999978i	$0.497878\pi$
$224$	−8.64941	−	10.4470i	−0.577913	−	0.698020i
$225$	6.88211	+	19.0386i	0.458807	+	1.26924i
$226$	4.87952	−	8.45157i	0.324581	−	0.562190i
$227$	2.73469	−	15.5092i	0.181508	−	1.02938i	−0.748853	−	0.662736i	$-0.769395\pi$
$227$	2.73469	−	15.5092i	0.181508	−	1.02938i	0.930361	−	0.366645i	$-0.119494\pi$
$228$	−9.47331	−	20.3740i	−0.627385	−	1.34930i
$229$	−5.49184	+	15.0887i	−0.362911	+	0.997091i	0.615084	+	0.788462i	$0.289122\pi$
$229$	−5.49184	+	15.0887i	−0.362911	+	0.997091i	−0.977995	+	0.208629i	$0.933100\pi$
$230$	−7.06177	+	5.92553i	−0.465639	+	0.390718i
$231$	−4.02544	+	2.77276i	−0.264855	+	0.182434i
$232$	7.12561	−	2.59351i	0.467819	−	0.170272i
$233$	21.4007	+	12.3557i	1.40201	+	0.809449i	0.994598	−	0.103797i	$-0.0330994\pi$
$233$	21.4007	+	12.3557i	1.40201	+	0.809449i	0.407408	+	0.913246i	$0.366433\pi$
$234$	−24.7709	+	14.2289i	−1.61932	+	0.930174i
$235$	3.35407	+	5.80942i	0.218795	+	0.378965i
$236$	18.7315	−	6.81772i	1.21932	−	0.443796i
$237$	3.98823	+	5.70913i	0.259063	+	0.370848i
$238$	−40.5386	−	7.42382i	−2.62773	−	0.481215i
$239$	1.41814	−	0.250057i	0.0917321	−	0.0161748i	−0.127594	−	0.991827i	$-0.540725\pi$
$239$	1.41814	−	0.250057i	0.0917321	−	0.0161748i	0.219326	+	0.975652i	$0.429614\pi$
$240$	−0.687278	−	2.57628i	−0.0443636	−	0.166298i
$241$	2.10423	+	5.78133i	0.135546	+	0.372408i	0.988832	−	0.149034i	$-0.0476164\pi$
$241$	2.10423	+	5.78133i	0.135546	+	0.372408i	−0.853286	+	0.521442i	$0.825394\pi$
$242$	19.7264	+	11.3890i	1.26806	+	0.732115i
$243$	−11.0831	+	10.9619i	−0.710984	+	0.703208i
$244$			22.8322i			1.46168i
$245$	−3.85455	−	23.6812i	−0.246258	−	1.51294i
$246$	−7.38696	+	27.4478i	−0.470976	+	1.75001i
$247$	12.2874	−	10.3104i	0.781832	−	0.656035i
$248$	−21.8134	+	18.3036i	−1.38515	+	1.16228i
$249$	−13.8180	+	1.19361i	−0.875680	+	0.0756419i
$250$	−4.73306	−	13.0040i	−0.299345	−	0.822444i
$251$	−7.90667	+	13.6947i	−0.499064	+	0.864405i	−0.999999	−	0.00108000i	$-0.999656\pi$
$251$	−7.90667	+	13.6947i	−0.499064	+	0.864405i	0.500935	+	0.865485i	$0.332990\pi$
$252$	−9.26996	+	24.7889i	−0.583952	+	1.56155i
$253$	0.621049	+	1.07569i	0.0390450	+	0.0676279i
$254$	−8.12747	+	9.68594i	−0.509963	+	0.607750i
$255$	32.7730	+	23.0017i	2.05233	+	1.44042i
$256$	−3.26344	−	18.5079i	−0.203965	−	1.15674i
$257$	9.32649	+	3.39457i	0.581771	+	0.211747i	0.616106	−	0.787663i	$-0.288709\pi$
$257$	9.32649	+	3.39457i	0.581771	+	0.211747i	−0.0343355	+	0.999410i	$0.510931\pi$
$258$	−8.78888	+	12.5225i	−0.547171	+	0.779616i
$259$	0.955897	−	1.63075i	0.0593965	−	0.101330i
$260$	40.8059	−	23.5593i	2.53068	−	1.46109i
$261$	5.64420	+	4.75723i	0.349367	+	0.294465i
$262$	−32.4219	+	18.7188i	−2.00303	+	1.15645i
$263$	0.314400	−	0.374688i	0.0193867	−	0.0231042i	−0.756264	−	0.654267i	$-0.772977\pi$
$263$	0.314400	−	0.374688i	0.0193867	−	0.0231042i	0.775651	+	0.631162i	$0.217422\pi$
$264$	−5.67248	+	0.489993i	−0.349117	+	0.0301570i
$265$	8.60435	−	23.6403i	0.528561	−	1.45221i
$266$	4.28246	−	23.3849i	0.262575	−	1.43382i
$267$	13.6397	−	13.6098i	0.834738	−	0.832904i
$268$	1.20550	−	6.83673i	0.0736376	−	0.417620i
$269$	−3.71312	+	6.43131i	−0.226393	+	0.392124i	−0.956736	−	0.290956i	$-0.906027\pi$
$269$	−3.71312	+	6.43131i	−0.226393	+	0.392124i	0.730344	+	0.683080i	$0.239360\pi$
$270$	29.1823	−	28.9904i	1.77598	−	1.76430i
$271$	5.27042	−	3.04288i	0.320155	−	0.184842i	−0.331306	−	0.943523i	$-0.607489\pi$
$271$	5.27042	−	3.04288i	0.320155	−	0.184842i	0.651462	+	0.758681i	$0.274156\pi$
$272$	−2.32046	−	1.94710i	−0.140699	−	0.118060i
$273$	−18.8082	−	1.79134i	−1.13833	−	0.108417i
$274$	−3.55037	−	20.1351i	−0.214486	−	1.21641i
$275$	−7.08848	+	1.24989i	−0.427451	+	0.0753712i
$276$	6.09198	+	2.84890i	0.366694	+	0.171483i
$277$	10.7274	+	9.00133i	0.644545	+	0.540838i	0.905410	−	0.424538i	$-0.139563\pi$
$277$	10.7274	+	9.00133i	0.644545	+	0.540838i	−0.260865	+	0.965375i	$0.584008\pi$
$278$	51.7395			3.10313
$279$	−26.0268	−	9.53785i	−1.55818	−	0.571016i
$280$	9.73138	−	26.1983i	0.581561	−	1.56565i
$281$	6.49576	+	17.8470i	0.387505	+	1.06466i	0.968121	+	0.250483i	$0.0805894\pi$
$281$	6.49576	+	17.8470i	0.387505	+	1.06466i	−0.580616	+	0.814177i	$0.697188\pi$
$282$	4.49771	−	6.40839i	0.267835	−	0.381614i
$283$	−13.1434	+	2.31753i	−0.781292	+	0.137763i	−0.550048	−	0.835133i	$-0.685391\pi$
$283$	−13.1434	+	2.31753i	−0.781292	+	0.137763i	−0.231244	+	0.972896i	$0.574279\pi$
$284$	5.07863	−	0.895500i	0.301361	−	0.0531381i
$285$	−13.2686	+	18.9053i	−0.785965	+	1.11985i
$286$	−3.47385	−	9.54432i	−0.205413	−	0.564368i
$287$	−14.4803	+	11.9887i	−0.854748	+	0.707673i
$288$	11.8026	−	9.85942i	0.695476	−	0.580972i
$289$	28.4867			1.67569
$290$	−14.9213	−	12.5205i	−0.876212	−	0.735229i
$291$	−3.81801	−	1.78548i	−0.223816	−	0.104667i
$292$	36.3394	−	6.40761i	2.12660	−	0.374977i
$293$	4.14559	+	23.5108i	0.242188	+	1.37351i	0.826934	+	0.562299i	$0.190083\pi$
$293$	4.14559	+	23.5108i	0.242188	+	1.37351i	−0.584747	+	0.811216i	$0.698806\pi$
$294$	−23.1654	+	15.7325i	−1.35103	+	0.917537i
$295$	−15.6970	−	13.1713i	−0.913913	−	0.766864i
$296$	1.90682	−	1.10090i	0.110832	−	0.0639886i
$297$	−3.16402	−	4.55057i	−0.183595	−	0.264051i
$298$	18.6212	−	32.2529i	1.07870	−	1.86836i
$299$	−0.833691	+	4.72809i	−0.0482136	+	0.273433i
$300$	−27.5876	+	27.5270i	−1.59277	+	1.58927i
$301$	−9.53072	+	3.39794i	−0.549342	+	0.195854i
$302$	8.04052	−	22.0912i	0.462680	−	1.27120i
$303$	14.5378	−	1.25579i	0.835177	−	0.0721432i
$304$	1.12319	−	1.33857i	0.0644195	−	0.0767722i
$305$	20.3260	−	11.7352i	1.16386	−	0.671957i
$306$	8.21592	−	46.0030i	0.469673	−	2.62981i
$307$	9.91518	−	5.72453i	0.565889	−	0.326716i	−0.189617	−	0.981858i	$-0.560725\pi$
$307$	9.91518	−	5.72453i	0.565889	−	0.326716i	0.755506	+	0.655142i	$0.227391\pi$
$308$	−8.11791	−	4.75848i	−0.462561	−	0.271140i
$309$	−4.37770	+	6.23740i	−0.249039	+	0.354833i
$310$	68.7341	+	25.0172i	3.90383	+	1.42088i
$311$	−1.33764	−	7.58615i	−0.0758508	−	0.430171i	−0.998958	−	0.0456295i	$-0.985471\pi$
$311$	−1.33764	−	7.58615i	−0.0758508	−	0.430171i	0.923108	−	0.384542i	$-0.125640\pi$
$312$	−18.0134	−	12.6427i	−1.01981	−	0.715750i
$313$	−13.5087	+	16.0991i	−0.763559	+	0.909974i	−0.998067	−	0.0621404i	$-0.980207\pi$
$313$	−13.5087	+	16.0991i	−0.763559	+	0.909974i	0.234509	+	0.972114i	$0.424652\pi$
$314$	−12.8872	−	22.3213i	−0.727267	−	1.25966i
$315$	26.8325	−	4.48850i	1.51184	−	0.252898i
$316$	−6.70333	+	11.6105i	−0.377092	+	0.653142i
$317$	3.11317	+	8.55336i	0.174853	+	0.480404i	0.995901	−	0.0904554i	$-0.0288323\pi$
$317$	3.11317	+	8.55336i	0.174853	+	0.480404i	−0.821048	+	0.570860i	$0.806610\pi$
$318$	−29.2529	+	2.52689i	−1.64042	+	0.141701i
$319$	−2.01050	+	1.68701i	−0.112566	+	0.0944544i
$320$	−33.4457	+	28.0643i	−1.86967	+	1.56884i
$321$	2.90647	−	10.7996i	0.162223	−	0.602774i
$322$	3.51722	+	6.18579i	0.196007	+	0.344721i
$323$			26.2392i			1.45999i
$324$	−28.1539	−	10.3876i	−1.56410	−	0.577091i
$325$	−24.0941	−	13.9108i	−1.33650	−	0.771630i
$326$	10.4651	+	28.7526i	0.579608	+	1.59246i
$327$	−1.92919	−	7.23162i	−0.106684	−	0.399909i
$328$	−21.5649	+	3.80248i	−1.19072	+	0.209957i
$329$	4.87735	−	1.73890i	0.268897	−	0.0958685i
$330$	8.37555	+	11.9896i	0.461059	+	0.660003i
$331$	−19.6845	+	7.16458i	−1.08196	+	0.393801i	−0.820637	−	0.571450i	$-0.806381\pi$
$331$	−19.6845	+	7.16458i	−1.08196	+	0.393801i	−0.261323	+	0.965251i	$0.584159\pi$
$332$	−13.3499	−	23.1227i	−0.732672	−	1.26902i
$333$	1.85384	+	1.07576i	0.101590	+	0.0589511i
$334$	−11.3983	−	6.58083i	−0.623689	−	0.360087i
$335$	−6.70589	+	2.44075i	−0.366382	+	0.133352i
$336$	−2.05169	+	0.163613i	−0.111929	+	0.00892581i
$337$	−24.6263	+	20.6639i	−1.34148	+	1.12564i	−0.360237	+	0.932861i	$0.617304\pi$
$337$	−24.6263	+	20.6639i	−1.34148	+	1.12564i	−0.981243	+	0.192775i	$0.938251\pi$
$338$	3.15817	−	8.67701i	0.171782	−	0.471967i
$339$	3.08567	+	6.63629i	0.167591	+	0.360434i
$340$	−13.3846	+	75.9080i	−0.725883	+	4.11669i
$341$	4.92779	−	8.53518i	0.266855	−	0.462206i
$342$	26.5370	+	4.73939i	1.43496	+	0.256277i
$343$	−18.5166	−	0.366110i	−0.999805	−	0.0197681i
$344$	−11.6069	−	2.04662i	−0.625804	−	0.110346i
$345$	−0.594953	−	6.88757i	−0.0320312	−	0.370814i
$346$	20.4143	+	24.3288i	1.09748	+	1.30792i
$347$	6.86008	−	18.8479i	0.368269	−	1.01181i	−0.607751	−	0.794128i	$-0.707928\pi$
$347$	6.86008	−	18.8479i	0.368269	−	1.01181i	0.976020	−	0.217682i	$-0.0698496\pi$
$348$	−3.69296	+	13.7220i	−0.197964	+	0.735574i
$349$	0.359264	−	0.428154i	0.0192310	−	0.0229186i	−0.756343	−	0.654175i	$-0.773016\pi$
$349$	0.359264	−	0.428154i	0.0192310	−	0.0229186i	0.775574	+	0.631256i	$0.217460\pi$
$350$	−40.6553	+	6.89270i	−2.17312	+	0.368431i
$351$	1.93753	−	21.3352i	0.103418	−	1.13879i
$352$	2.73397	+	4.73537i	0.145721	+	0.252396i
$353$	22.8349	−	8.31122i	1.21538	−	0.442361i	0.346812	−	0.937935i	$-0.387264\pi$
$353$	22.8349	−	8.31122i	1.21538	−	0.442361i	0.868566	+	0.495573i	$0.165042\pi$
$354$	−6.21517	+	23.0937i	−0.330333	+	1.22742i
$355$	−3.40751	−	4.06091i	−0.180852	−	0.215531i
$356$	34.8561	+	12.6866i	1.84737	+	0.672387i
$357$	22.0217	−	21.6856i	1.16551	−	1.14772i
$358$	−0.864024	+	4.90012i	−0.0456651	+	0.258980i
$359$			13.4381i			0.709238i	0.935011	+	0.354619i	$0.115389\pi$
$359$			13.4381i			0.709238i	−0.935011	+	0.354619i	$0.884611\pi$
$360$	29.7542	+	10.9038i	1.56818	+	0.574681i
$361$	3.86378			0.203357
$362$	−44.9301	−	37.7008i	−2.36147	−	1.98151i
$363$	−15.4894	+	7.20212i	−0.812984	+	0.378013i
$364$	−12.2142	−	34.2590i	−0.640198	−	1.79566i
$365$	−24.3819	−	29.0572i	−1.27621	−	1.52093i
$366$	−22.4217	−	15.7366i	−1.17200	−	0.822566i
$367$	24.0521	+	4.24104i	1.25551	+	0.221380i	0.761551	−	0.648105i	$-0.224438\pi$
$367$	24.0521	+	4.24104i	1.25551	+	0.221380i	0.493959	+	0.869485i	$0.335549\pi$
$368$			0.523014i			0.0272640i
$369$	−13.6659	−	16.3593i	−0.711419	−	0.851632i
$370$	−4.89809	−	2.82792i	−0.254640	−	0.147016i
$371$	−16.7532	−	9.82022i	−0.869782	−	0.509840i
$372$	−4.59235	−	53.1641i	−0.238102	−	2.75643i
$373$	−1.13896	−	6.45937i	−0.0589732	−	0.334453i	0.941019	−	0.338353i	$-0.109870\pi$
$373$	−1.13896	−	6.45937i	−0.0589732	−	0.334453i	−0.999992	+	0.00389965i	$0.998759\pi$
$374$	15.6131	+	5.68269i	0.807333	+	0.293845i
$375$	10.0214	+	2.69703i	0.517501	+	0.139274i
$376$	5.93985	+	1.04736i	0.306325	+	0.0540133i
$377$	−10.1445			−0.522466
$378$	−17.9541	−	26.1885i	−0.923460	−	1.34699i
$379$	2.78708			0.143163			0.0715813	−	0.997435i	$-0.477195\pi$
$379$	2.78708			0.143163			0.0715813	+	0.997435i	$0.477195\pi$
$380$	−43.7879	−	7.72098i	−2.24627	−	0.396078i
$381$	−2.44410	−	9.16178i	−0.125215	−	0.469372i
$382$	29.5669	+	10.7615i	1.51277	+	0.550604i
$383$	5.80403	+	32.9163i	0.296572	+	1.68194i	0.660743	+	0.750612i	$0.270241\pi$
$383$	5.80403	+	32.9163i	0.296572	+	1.68194i	−0.364171	+	0.931332i	$0.618648\pi$
$384$	30.0731	+	14.0636i	1.53466	+	0.717679i
$385$	−0.0637414	+	9.67260i	−0.00324856	+	0.492961i
$386$	37.9856	+	21.9310i	1.93342	+	1.11626i
$387$	−3.90032	−	10.7898i	−0.198264	−	0.548476i
$388$		−	8.11396i		−	0.411924i
$389$	6.13392	+	1.08158i	0.311002	+	0.0548380i	0.326971	−	0.945034i	$-0.393972\pi$
$389$	6.13392	+	1.08158i	0.311002	+	0.0548380i	−0.0159688	+	0.999872i	$0.505083\pi$
$390$	−4.98889	+	56.3101i	−0.252622	+	2.85137i
$391$	−5.04830	−	6.01633i	−0.255304	−	0.304259i
$392$	−18.5387	−	11.0316i	−0.936347	−	0.557181i
$393$	2.47770	−	27.9660i	0.124983	−	1.41070i
$394$	33.7161	+	28.2912i	1.69859	+	1.42529i
$395$	13.7815			0.693420
$396$	5.35514	−	9.22845i	0.269106	−	0.463747i
$397$		−	4.38660i		−	0.220157i	−0.993923	−	0.110078i	$-0.964890\pi$
$397$		−	4.38660i		−	0.220157i	0.993923	−	0.110078i	$-0.0351102\pi$
$398$	3.02604	−	17.1615i	0.151682	−	0.860230i
$399$	12.5094	+	12.7033i	0.626256	+	0.635961i
$400$	−2.84804	−	1.03660i	−0.142402	−	0.0518300i
$401$	−16.4534	−	19.6084i	−0.821643	−	0.979196i	0.178346	−	0.983968i	$-0.442925\pi$
$401$	−16.4534	−	19.6084i	−0.821643	−	0.979196i	−0.999989	+	0.00477226i	$0.998481\pi$
$402$	5.88295	+	5.89590i	0.293415	+	0.294061i
$403$	35.7970	−	13.0291i	1.78318	−	0.649024i
$404$	14.0454	+	24.3273i	0.698783	+	1.21033i
$405$	5.22302	+	30.4026i	0.259534	+	1.51072i
$406$	−11.5813	+	9.58856i	−0.574772	+	0.475872i
$407$	−0.489846	+	0.583776i	−0.0242808	+	0.0289367i
$408$	34.7841	−	9.27939i	1.72207	−	0.459398i
$409$	6.22876	−	17.1134i	0.307992	−	0.846202i	−0.685056	−	0.728491i	$-0.740222\pi$
$409$	6.22876	−	17.1134i	0.307992	−	0.846202i	0.993048	−	0.117711i	$-0.0375556\pi$
$410$	36.1561	+	43.0892i	1.78562	+	2.12802i
$411$	13.8892	+	6.49523i	0.685102	+	0.320386i
$412$	−14.4469	−	2.54738i	−0.711747	−	0.125500i
$413$	−12.1833	+	10.0870i	−0.599503	+	0.496347i
$414$	−6.99645	+	4.01891i	−0.343857	+	0.197519i
$415$	−13.7231	+	23.7691i	−0.673641	+	1.16678i
$416$	−3.67006	+	20.8139i	−0.179939	+	1.02049i
$417$	−22.2903	+	31.7594i	−1.09156	+	1.55527i
$418$	−3.27809	+	9.00647i	−0.160337	+	0.440521i
$419$	17.2171	−	14.4469i	0.841111	−	0.705776i	−0.116702	−	0.993167i	$-0.537232\pi$
$419$	17.2171	−	14.4469i	0.841111	−	0.705776i	0.957813	+	0.287391i	$0.0927879\pi$
$420$	29.7089	+	43.1307i	1.44964	+	2.10456i
$421$	−0.972055	+	0.353799i	−0.0473750	+	0.0172431i	−0.365599	−	0.930772i	$-0.619136\pi$
$421$	−0.972055	+	0.353799i	−0.0473750	+	0.0172431i	0.318224	+	0.948016i	$0.396914\pi$
$422$	−48.6088	−	28.0643i	−2.36624	−	1.36615i
$423$	1.99599	+	5.52168i	0.0970482	+	0.268473i
$424$	−11.3099	−	19.5893i	−0.549258	−	0.951342i
$425$	42.7671	−	15.5659i	2.07451	−	0.755059i
$426$	−2.62094	+	5.60453i	−0.126985	+	0.271540i
$427$	−6.08406	−	17.0649i	−0.294428	−	0.825828i
$428$	21.2027	−	3.73862i	1.02487	−	0.180713i
$429$	7.35521	+	1.97949i	0.355113	+	0.0955709i
$430$	10.3547	+	28.4492i	0.499346	+	1.37194i
$431$	−11.0227	−	6.36393i	−0.530943	−	0.306540i	0.210458	−	0.977603i	$-0.432505\pi$
$431$	−11.0227	−	6.36393i	−0.530943	−	0.306540i	−0.741400	+	0.671063i	$0.765838\pi$
$432$	−0.195732	−	2.32556i	−0.00941715	−	0.111888i
$433$		−	33.5621i		−	1.61289i	−0.591309	−	0.806445i	$-0.701388\pi$
$433$		−	33.5621i		−	1.61289i	0.591309	−	0.806445i	$-0.298612\pi$
$434$	28.5523	−	48.7099i	1.37055	−	2.33815i
$435$	14.1139	−	3.76517i	0.676708	−	0.180526i
$436$	11.0374	−	9.26148i	0.528596	−	0.443545i
$437$	3.47055	−	2.91214i	0.166019	−	0.139306i
$438$	−18.7538	+	40.1024i	−0.896089	+	1.91617i
$439$	−8.37354	−	23.0061i	−0.399647	−	1.09802i	−0.962457	−	0.271435i	$-0.912502\pi$
$439$	−8.37354	−	23.0061i	−0.399647	−	1.09802i	0.562810	−	0.826587i	$-0.309720\pi$
$440$	−5.63352	+	9.75755i	−0.268568	+	0.465173i
$441$	0.322942	−	20.9975i	0.0153782	−	0.999882i
$442$	32.1108	+	55.6176i	1.52736	+	2.64546i
$443$	5.70047	−	6.79356i	0.270838	−	0.322772i	−0.613433	−	0.789747i	$-0.710212\pi$
$443$	5.70047	−	6.79356i	0.270838	−	0.322772i	0.884270	+	0.466975i	$0.154656\pi$
$444$	−0.364135	+	4.11003i	−0.0172811	+	0.195053i
$445$	−6.62121	−	37.5507i	−0.313875	−	1.78008i
$446$	−11.6812	−	4.25160i	−0.553119	−	0.201319i
$447$	11.7755	+	25.3254i	0.556964	+	1.19785i
$448$	16.6582	+	29.2970i	0.787024	+	1.38415i
$449$	−6.55230	+	3.78297i	−0.309222	+	0.178529i	−0.646578	−	0.762848i	$-0.723801\pi$
$449$	−6.55230	+	3.78297i	−0.309222	+	0.178529i	0.337356	+	0.941377i	$0.390467\pi$
$450$	−8.01792	−	46.0640i	−0.377968	−	2.17148i
$451$	6.56358	−	3.78949i	0.309067	−	0.178440i
$452$	−9.05615	+	10.7927i	−0.425966	+	0.507646i
$453$	10.0963	+	14.4528i	0.474365	+	0.679051i
$454$	−12.4403	+	34.1794i	−0.583851	+	1.60412i
$455$	−24.2207	+	28.4819i	−1.13549	+	1.33525i
$456$	5.35286	+	20.0654i	0.250671	+	0.939647i
$457$	−3.15444	+	17.8897i	−0.147559	+	0.836846i	0.817719	+	0.575618i	$0.195239\pi$
$457$	−3.15444	+	17.8897i	−0.147559	+	0.836846i	−0.965277	+	0.261228i	$0.915873\pi$
$458$	18.5429	−	32.1172i	0.866451	−	1.50074i
$459$	24.6986	+	24.8621i	1.15283	+	1.16046i
$460$	11.5255	−	6.65425i	0.537379	−	0.310256i
$461$	−8.23081	−	6.90647i	−0.383347	−	0.321666i	0.430668	−	0.902511i	$-0.358278\pi$
$461$	−8.23081	−	6.90647i	−0.383347	−	0.321666i	−0.814015	+	0.580844i	$0.802723\pi$
$462$	10.2680	−	4.69228i	0.477712	−	0.218305i
$463$	−1.72699	−	9.79424i	−0.0802600	−	0.455177i	−0.998279	−	0.0586410i	$-0.981323\pi$
$463$	−1.72699	−	9.79424i	−0.0802600	−	0.455177i	0.918019	−	0.396536i	$-0.129788\pi$
$464$	−1.08833	+	0.191901i	−0.0505243	+	0.00890880i
$465$	−44.9682	+	31.4134i	−2.08535	+	1.45676i
$466$	−43.7212	−	36.6864i	−2.02534	−	1.69946i
$467$	−20.6390			−0.955059			−0.477530	−	0.878616i	$-0.658468\pi$
$467$	−20.6390			−0.955059			−0.477530	+	0.878616i	$0.658468\pi$
$468$	38.7849	−	14.0200i	1.79283	−	0.648076i
$469$	0.920778	+	5.43103i	0.0425176	+	0.250782i
$470$	−5.29900	−	14.5589i	−0.244425	−	0.671551i
$471$	19.2536	+	1.70580i	0.887158	+	0.0785993i
$472$	−18.1441	+	3.19930i	−0.835150	+	0.147260i
$473$	4.01727	−	0.708354i	0.184714	−	0.0325701i
$474$	−6.78164	−	14.5851i	−0.311491	−	0.669917i
$475$	8.97929	+	24.6704i	0.411998	+	1.13196i
$476$	55.7743	+	20.7174i	2.55641	+	0.949582i
$477$	11.0516	−	19.0450i	0.506017	−	0.872012i
$478$	−3.32590			−0.152123
$479$	−31.0077	−	26.0185i	−1.41678	−	1.18882i	−0.953041	−	0.302842i	$-0.902064\pi$
$479$	−31.0077	−	26.0185i	−1.41678	−	1.18882i	−0.463735	−	0.885974i	$-0.653491\pi$
$480$	−2.61909	−	30.3203i	−0.119545	−	1.38393i
$481$	−2.90083	+	0.511495i	−0.132267	+	0.0233222i
$482$	−2.46748	−	13.9937i	−0.112390	−	0.637398i
$483$	−5.31232	−	0.505958i	−0.241719	−	0.0230219i
$484$	−25.1907	−	21.1375i	−1.14503	−	0.960796i
$485$	−7.22334	+	4.17039i	−0.327995	+	0.189368i
$486$	29.6053	−	20.4882i	1.34293	−	0.929365i
$487$	−16.0436	+	27.7883i	−0.727004	+	1.25921i	0.231140	+	0.972921i	$0.425754\pi$
$487$	−16.0436	+	27.7883i	−0.727004	+	1.25921i	−0.958144	+	0.286287i	$0.907579\pi$
$488$	3.66450	−	20.7824i	0.165884	−	0.940774i
$489$	−22.1578	−	5.96330i	−1.00201	−	0.269670i
$490$	−0.730317	+	55.4095i	−0.0329924	+	2.50315i
$491$	−11.1829	+	30.7246i	−0.504675	+	1.38658i	0.381988	+	0.924167i	$0.375240\pi$
$491$	−11.1829	+	30.7246i	−0.504675	+	1.38658i	−0.886663	+	0.462416i	$0.846983\pi$
$492$	17.3833	−	37.1718i	0.783699	−	1.67583i
$493$	10.6669	−	12.7124i	0.480415	−	0.572536i
$494$	−32.0833	+	18.5233i	−1.44349	+	0.833402i
$495$	−10.9679	−	0.0241206i	−0.492971	−	0.00108414i
$496$	3.59394	−	2.07496i	0.161373	−	0.0931685i
$497$	−3.55717	+	2.02260i	−0.159561	+	0.0907259i
$498$	31.9082	+	2.82696i	1.42984	+	0.126679i
$499$	21.0760	+	7.67104i	0.943492	+	0.343403i	0.767544	−	0.640996i	$-0.221479\pi$
$499$	21.0760	+	7.67104i	0.943492	+	0.343403i	0.175948	+	0.984399i	$0.443701\pi$
$500$	3.46921	+	19.6749i	0.155148	+	0.879886i
$501$	8.95012	−	4.16154i	0.399862	−	0.185924i
$502$	23.4764	−	27.9781i	1.04780	−	1.24872i
$503$	4.42934	+	7.67184i	0.197495	+	0.342071i	0.947715	−	0.319117i	$-0.103386\pi$
$503$	4.42934	+	7.67184i	0.197495	+	0.342071i	−0.750221	+	0.661187i	$0.770053\pi$
$504$	12.4163	−	21.0757i	0.553065	−	0.938784i
$505$	14.4380	−	25.0074i	0.642483	−	1.11281i
$506$	−0.981177	−	2.69576i	−0.0436187	−	0.119841i
$507$	3.96564	+	5.67680i	0.176120	+	0.252115i
$508$	13.9834	−	11.7334i	0.620411	−	0.520587i
$509$	9.75926	−	8.18899i	0.432572	−	0.362971i	−0.400349	−	0.916363i	$-0.631111\pi$
$509$	9.75926	−	8.18899i	0.432572	−	0.362971i	0.832921	+	0.553392i	$0.186667\pi$
$510$	−65.3182	−	65.4620i	−2.89234	−	2.89870i
$511$	−25.4528	+	14.4724i	−1.12597	+	0.640221i
$512$			5.07071i			0.224096i
$513$	−14.3418	+	14.2475i	−0.633206	+	0.629042i
$514$	−19.8520	−	11.4615i	−0.875633	−	0.505547i
$515$	5.15761	+	14.1704i	0.227272	+	0.624424i
$516$	15.6348	−	15.6004i	0.688284	−	0.686772i
$517$	−2.05584	+	0.362500i	−0.0904158	+	0.0159427i
$518$	−2.82825	+	3.32582i	−0.124266	+	0.146128i
$519$	−23.7286	+	2.04969i	−1.04157	+	0.0899716i
$520$	−40.9237	+	14.8950i	−1.79462	+	0.653190i
$521$	2.09954	+	3.63652i	0.0919827	+	0.159319i	0.908345	−	0.418221i	$-0.137346\pi$
$521$	2.09954	+	3.63652i	0.0919827	+	0.159319i	−0.816363	+	0.577540i	$0.804013\pi$
$522$	−10.9300	−	13.0841i	−0.478391	−	0.572677i
$523$	−18.4606	−	10.6582i	−0.807225	−	0.466052i	0.0387660	−	0.999248i	$-0.487657\pi$
$523$	−18.4606	−	10.6582i	−0.807225	−	0.466052i	−0.845991	+	0.533196i	$0.820991\pi$
$524$	50.7882	−	18.4854i	2.21869	−	0.807538i
$525$	13.2840	−	27.9251i	0.579763	−	1.21875i
$526$	−0.865385	+	0.726144i	−0.0377326	+	0.0316614i
$527$	−21.3136	+	58.5586i	−0.928434	+	2.55085i
$528$	0.826534	+	0.0732282i	0.0359703	+	0.00318685i
$529$	3.75843	−	21.3151i	0.163410	−	0.926745i
$530$	−29.0521	+	50.3196i	−1.26194	+	2.18574i
$531$	−11.4981	−	13.7643i	−0.498975	−	0.597318i
$532$	−11.9510	+	32.1737i	−0.518139	+	1.39491i
$533$	28.8497	+	5.08698i	1.24962	+	0.220341i
$534$	−36.4823	+	25.4855i	−1.57874	+	1.10286i
$535$	−14.2260	−	16.9539i	−0.615043	−	0.732979i
$536$	−2.19455	+	6.02947i	−0.0947900	+	0.260433i
$537$	−2.63562	−	2.64142i	−0.113735	−	0.113986i
$538$	11.0249	−	13.1390i	0.475319	−	0.566463i
$539$	7.33536	+	1.39334i	0.315956	+	0.0600155i
$540$	−48.7573	+	33.9011i	−2.09818	+	1.45887i
$541$	−8.53158	−	14.7771i	−0.366801	−	0.635318i	0.622262	−	0.782809i	$-0.286214\pi$
$541$	−8.53158	−	14.7771i	−0.366801	−	0.635318i	−0.989063	+	0.147491i	$0.952880\pi$
$542$	−13.2081	+	4.80736i	−0.567337	+	0.206494i
$543$	42.4986	−	11.3374i	1.82379	−	0.486534i
$544$	−22.2235	−	26.4850i	−0.952826	−	1.13553i
$545$	−13.9179	−	5.06569i	−0.596176	−	0.216990i
$546$	42.0614	+	11.6177i	1.80006	+	0.497192i
$547$	0.589590	−	3.34373i	0.0252090	−	0.142968i	−0.969605	−	0.244674i	$-0.921319\pi$
$547$	0.589590	−	3.34373i	0.0252090	−	0.142968i	0.994814	+	0.101706i	$0.0324302\pi$
$548$			29.5170i			1.26090i
$549$	19.3193	−	6.98357i	0.824527	−	0.298051i
$550$	16.6242			0.708860
$551$	7.33318	+	6.15327i	0.312404	+	0.262138i
$552$	−5.08783	−	3.57088i	−0.216552	−	0.151987i
$553$	1.91627	−	10.4640i	0.0814879	−	0.444974i
$554$	−20.7896	−	24.7761i	−0.883267	−	1.05264i
$555$	3.84605	−	1.78830i	0.163256	−	0.0759090i
$556$	−73.5603	−	12.9707i	−3.11965	−	0.550078i
$557$		−	12.3208i		−	0.522050i	−0.965332	−	0.261025i	$-0.915940\pi$
$557$		−	12.3208i		−	0.522050i	0.965332	−	0.261025i	$-0.0840605\pi$
$558$	55.3734	+	32.1325i	2.34414	+	1.36028i
$559$	13.6549	+	7.88368i	0.577542	+	0.333444i
$560$	−2.05968	+	3.51380i	−0.0870375	+	0.148485i
$561$	−10.2146	+	7.13561i	−0.431261	+	0.301266i
$562$	−7.61708	−	43.1986i	−0.321307	−	1.82222i
$563$	10.0489	+	3.65751i	0.423512	+	0.154146i	0.544979	−	0.838450i	$-0.316538\pi$
$563$	10.0489	+	3.65751i	0.423512	+	0.154146i	−0.121467	+	0.992595i	$0.538760\pi$
$564$	−8.00111	+	7.98354i	−0.336908	+	0.336167i
$565$	14.2627	+	2.51490i	0.600037	+	0.105803i
$566$	30.8244			1.29565
$567$	23.8103	+	0.261643i	0.999940	+	0.0109880i
$568$	−4.76641			−0.199994
$569$	8.87372	+	1.56468i	0.372006	+	0.0655947i	0.356526	−	0.934286i	$-0.383961\pi$
$569$	8.87372	+	1.56468i	0.372006	+	0.0655947i	0.0154801	+	0.999880i	$0.495072\pi$
$570$	37.7620	−	37.6791i	1.58168	−	1.57820i
$571$	29.3684	+	10.6892i	1.22903	+	0.447330i	0.873265	−	0.487246i	$-0.161999\pi$
$571$	29.3684	+	10.6892i	1.22903	+	0.447330i	0.355764	+	0.934576i	$0.384221\pi$
$572$	2.54624	+	14.4404i	0.106464	+	0.603785i
$573$	−19.3436	+	13.5129i	−0.808092	+	0.564509i
$574$	37.7442	−	21.4612i	1.57541	−	0.895775i
$575$	−6.80531	−	3.92905i	−0.283801	−	0.163853i
$576$	−33.1364	+	19.0343i	−1.38068	+	0.793094i
$577$			13.3322i			0.555028i	0.960722	+	0.277514i	$0.0895105\pi$
$577$			13.3322i			0.555028i	−0.960722	+	0.277514i	$0.910489\pi$
$578$	−64.7939	−	11.4249i	−2.69507	−	0.475214i
$579$	−29.8268	+	13.8686i	−1.23956	+	0.576358i
$580$	18.0755	+	21.5416i	0.750546	+	0.894465i
$581$	16.1393	+	13.7247i	0.669570	+	0.569397i
$582$	7.96809	+	5.59238i	0.330288	+	0.231812i
$583$	5.99731	+	5.03234i	0.248383	+	0.208418i
$584$	−34.1054			−1.41129
$585$	−32.4157	−	27.3217i	−1.34022	−	1.12961i
$586$		−	55.1386i		−	2.27776i
$587$	−0.186169	+	1.05582i	−0.00768403	+	0.0435783i	−0.988409	−	0.151817i	$-0.951488\pi$
$587$	−0.186169	+	1.05582i	−0.00768403	+	0.0435783i	0.980725	+	0.195395i	$0.0625988\pi$
$588$	36.8793	−	16.5602i	1.52087	−	0.682930i
$589$	−33.7798	−	12.2948i	−1.39187	−	0.506600i
$590$	30.4207	+	36.2540i	1.25240	+	1.49255i
$591$	−31.8915	+	8.50773i	−1.31184	+	0.349961i
$592$	−0.301534	+	0.109749i	−0.0123930	+	0.00451067i
$593$	19.5768	+	33.9081i	0.803925	+	1.39244i	0.917015	+	0.398854i	$0.130592\pi$
$593$	19.5768	+	33.9081i	0.803925	+	1.39244i	−0.113090	+	0.993585i	$0.536075\pi$
$594$	5.37161	+	11.6194i	0.220400	+	0.476749i
$595$	−10.2234	−	60.3006i	−0.419117	−	2.47208i
$596$	−34.5601	+	41.1871i	−1.41564	+	1.68709i
$597$	9.23064	+	9.25097i	0.377785	+	0.378617i
$598$	3.79251	−	10.4198i	0.155087	−	0.426099i
$599$	−9.15034	−	10.9049i	−0.373873	−	0.445564i	0.545998	−	0.837787i	$-0.316151\pi$
$599$	−9.15034	−	10.9049i	−0.373873	−	0.445564i	−0.919870	+	0.392223i	$0.871706\pi$
$600$	29.5289	−	20.6280i	1.20551	−	0.842134i
$601$	−10.2398	−	1.80556i	−0.417691	−	0.0736502i	−0.0391471	−	0.999233i	$-0.512464\pi$
$601$	−10.2398	−	1.80556i	−0.417691	−	0.0736502i	−0.378544	+	0.925583i	$0.623575\pi$
$602$	23.0407	−	3.90632i	0.939069	−	0.159210i
$603$	−6.15357	+	1.07109i	−0.250593	+	0.0436182i
$604$	−16.9696	+	29.3922i	−0.690484	+	1.19595i
$605$	−5.86990	+	33.2899i	−0.238645	+	1.35343i
$606$	−33.5704	−	2.97423i	−1.36370	−	0.120820i
$607$	4.69066	−	12.8875i	0.190388	−	0.523087i	−0.807367	−	0.590049i	$-0.799108\pi$
$607$	4.69066	−	12.8875i	0.190388	−	0.523087i	0.997756	+	0.0669619i	$0.0213306\pi$
$608$	15.2780	−	12.8198i	0.619604	−	0.519910i
$609$	−0.896332	−	11.2399i	−0.0363212	−	0.455464i
$610$	−50.9387	+	18.5402i	−2.06245	+	0.750669i
$611$	−6.98792	−	4.03448i	−0.282701	−	0.163217i
$612$	−23.2135	+	63.3447i	−0.938349	+	2.56056i
$613$	−6.94113	−	12.0224i	−0.280350	−	0.485580i	0.691121	−	0.722739i	$-0.257117\pi$
$613$	−6.94113	−	12.0224i	−0.280350	−	0.485580i	−0.971471	+	0.237159i	$0.923784\pi$
$614$	−24.8483	+	9.04403i	−1.00279	+	0.364987i
$615$	−42.0263	+	3.63026i	−1.69466	+	0.146386i
$616$	6.62539	+	5.63418i	0.266945	+	0.227008i
$617$	8.55178	−	1.50791i	0.344282	−	0.0607062i	0.00116607	−	0.999999i	$-0.499629\pi$
$617$	8.55178	−	1.50791i	0.344282	−	0.0607062i	0.343116	+	0.939293i	$0.388518\pi$
$618$	12.4588	−	12.4314i	0.501166	−	0.500066i
$619$	−9.06062	−	24.8939i	−0.364177	−	1.00057i	−0.977537	−	0.210765i	$-0.932405\pi$
$619$	−9.06062	−	24.8939i	−0.364177	−	1.00057i	0.613360	−	0.789804i	$-0.289818\pi$
$620$	−91.4506	−	52.7990i	−3.67274	−	2.12046i
$621$	0.547249	−	6.02607i	0.0219604	−	0.241818i
$622$			17.7914i			0.713370i
$623$	−29.4322	−	0.193955i	−1.17918	−	0.00777064i
$624$	2.26540	+	2.27039i	0.0906885	+	0.0908882i
$625$	−10.1146	+	8.48713i	−0.404583	+	0.339485i
$626$	37.1827	−	31.2000i	1.48612	−	1.24700i
$627$	−4.11621	−	5.89234i	−0.164386	−	0.235317i
$628$	12.7265	+	34.9658i	0.507844	+	1.39529i
$629$	2.40927	−	4.17297i	0.0960637	−	0.166387i
$630$	−62.8315	−	0.552240i	−2.50327	−	0.0220018i
$631$	15.1131	+	26.1767i	0.601643	+	1.04208i	0.992572	+	0.121655i	$0.0388203\pi$
$631$	15.1131	+	26.1767i	0.601643	+	1.04208i	−0.390930	+	0.920421i	$0.627846\pi$
$632$	7.96498	−	9.49230i	0.316830	−	0.377583i
$633$	38.1683	−	17.7471i	1.51705	−	0.705383i
$634$	−3.65057	−	20.7034i	−0.144983	−	0.822239i
$635$	−17.6326	−	6.41776i	−0.699730	−	0.254681i
$636$	42.2236	+	3.74087i	1.67427	+	0.148335i
$637$	18.2579	+	22.3506i	0.723405	+	0.885565i
$638$	5.24954	−	3.03082i	0.207831	−	0.119991i
$639$	−2.31110	−	4.02335i	−0.0914256	−	0.159161i
$640$	56.8957	−	32.8487i	2.24900	−	1.29846i
$641$	−21.7096	+	25.8725i	−0.857477	+	1.02190i	0.142010	+	0.989865i	$0.454644\pi$
$641$	−21.7096	+	25.8725i	−0.857477	+	1.02190i	−0.999487	+	0.0320360i	$0.989801\pi$
$642$	−10.9421	+	23.3983i	−0.431852	+	0.923458i
$643$	3.76068	−	10.3324i	0.148307	−	0.407469i	−0.843188	−	0.537619i	$-0.819324\pi$
$643$	3.76068	−	10.3324i	0.148307	−	0.407469i	0.991494	+	0.130150i	$0.0415459\pi$
$644$	−3.44986	−	9.67634i	−0.135943	−	0.381301i
$645$	−21.9240	−	5.90037i	−0.863257	−	0.232327i
$646$	10.5235	−	59.6819i	0.414043	−	2.34815i
$647$	15.6788	−	27.1565i	0.616399	−	1.06763i	−0.373739	−	0.927534i	$-0.621924\pi$
$647$	15.6788	−	27.1565i	0.616399	−	1.06763i	0.990137	−	0.140100i	$-0.0447424\pi$
$648$	23.9591	+	13.9737i	0.941203	+	0.548938i
$649$	5.52241	−	3.18836i	0.216773	−	0.125154i
$650$	49.2238	+	41.3037i	1.93072	+	1.62006i
$651$	17.5989	+	38.5114i	0.689756	+	1.50938i
$652$	−7.67063	−	43.5023i	−0.300405	−	1.70368i
$653$	5.01148	−	0.883658i	0.196114	−	0.0345802i	−0.0747281	−	0.997204i	$-0.523809\pi$
$653$	5.01148	−	0.883658i	0.196114	−	0.0345802i	0.270842	+	0.962624i	$0.412698\pi$
$654$	1.48767	+	17.2223i	0.0581726	+	0.673443i
$655$	−42.5604	−	35.7124i	−1.66297	−	1.39540i
$656$	3.19131			0.124600
$657$	−16.5367	−	28.7885i	−0.645159	−	1.12314i
$658$	−11.7911	+	1.99906i	−0.459664	+	0.0779315i
$659$	8.93801	+	24.5570i	0.348176	+	0.956605i	0.982944	+	0.183903i	$0.0588731\pi$
$659$	8.93801	+	24.5570i	0.348176	+	0.956605i	−0.634769	+	0.772702i	$0.718905\pi$
$660$	−8.90219	−	19.1457i	−0.346517	−	0.745247i
$661$	−10.3360	+	1.82252i	−0.402025	+	0.0708878i	−0.371005	−	0.928631i	$-0.620987\pi$
$661$	−10.3360	+	1.82252i	−0.402025	+	0.0708878i	−0.0310200	+	0.999519i	$0.509876\pi$
$662$	47.6465	−	8.40136i	1.85183	−	0.326528i
$663$	−47.9738	−	4.25032i	−1.86315	−	0.165069i
$664$	8.44028	+	23.1895i	0.327546	+	0.899926i
$665$	34.7847	−	5.89740i	1.34889	−	0.228691i
$666$	−3.78516	−	3.19034i	−0.146672	−	0.123623i
$667$	−2.86527			−0.110944
$668$	14.5557	+	12.2137i	0.563178	+	0.472563i
$669$	7.64222	−	5.33862i	0.295465	−	0.206403i
$670$	16.2316	−	2.86208i	0.627083	−	0.110572i
$671$	1.26832	+	7.19298i	0.0489628	+	0.277682i
$672$	−23.3858	−	2.22732i	−0.902127	−	0.0859206i
$673$	22.4416	+	18.8308i	0.865061	+	0.725873i	0.963052	−	0.269315i	$-0.0867972\pi$
$673$	22.4416	+	18.8308i	0.865061	+	0.725873i	−0.0979910	+	0.995187i	$0.531242\pi$
$674$	64.3008	−	37.1241i	2.47677	−	1.42997i
$675$	31.7299	+	14.9235i	1.22128	+	0.574406i
$676$	−6.66536	+	11.5447i	−0.256360	+	0.444029i
$677$	2.10665	−	11.9474i	0.0809652	−	0.459176i	−0.917189	−	0.398452i	$-0.869548\pi$
$677$	2.10665	−	11.9474i	0.0809652	−	0.459176i	0.998155	−	0.0607248i	$-0.0193412\pi$
$678$	−4.35690	−	16.3320i	−0.167326	−	0.627226i
$679$	2.16212	+	6.06442i	0.0829745	+	0.232731i
$680$	24.3660	−	66.9450i	0.934393	−	2.56722i
$681$	−15.6209	−	22.3613i	−0.598596	−	0.856887i
$682$	−14.6315	+	17.4372i	−0.560270	+	0.667704i
$683$	29.2693	−	16.8986i	1.11996	−	0.646608i	0.178568	−	0.983928i	$-0.442854\pi$
$683$	29.2693	−	16.8986i	1.11996	−	0.646608i	0.941390	+	0.337320i	$0.109520\pi$
$684$	−36.5407	−	13.3908i	−1.39717	−	0.512010i
$685$	26.2771	−	15.1711i	1.00400	−	0.579657i
$686$	41.9698	+	8.25903i	1.60242	+	0.315331i
$687$	11.7260	+	25.2188i	0.447375	+	0.962159i
$688$	1.61407	+	0.587475i	0.0615360	+	0.0223973i
$689$	5.25475	+	29.8012i	0.200190	+	1.13533i
$690$	−1.40910	+	15.9046i	−0.0536434	+	0.605477i
$691$	−19.0529	+	22.7063i	−0.724806	+	0.863790i	−0.995088	−	0.0989914i	$-0.968438\pi$
$691$	−19.0529	+	22.7063i	−0.724806	+	0.863790i	0.270283	+	0.962781i	$0.412883\pi$
$692$	−22.9248	−	39.7069i	−0.871470	−	1.50943i
$693$	−1.54337	+	8.32437i	−0.0586277	+	0.316217i
$694$	−23.1626	+	40.1189i	−0.879242	+	1.52289i
$695$	26.2614	+	72.1526i	0.996151	+	2.73690i
$696$	5.56375	−	11.8973i	0.210894	−	0.450967i
$697$	−36.7102	+	30.8035i	−1.39050	+	1.16677i
$698$	−0.988873	+	0.829763i	−0.0374294	+	0.0314070i
$699$	41.3551	−	11.0323i	1.56419	−	0.417282i
$700$	59.5293	+	0.392292i	2.25000	+	0.0148272i
$701$		−	46.4472i		−	1.75429i	−0.480229	−	0.877143i	$-0.659446\pi$
$701$		−	46.4472i		−	1.75429i	0.480229	−	0.877143i	$-0.340554\pi$
$702$	−12.9637	+	47.7506i	−0.489284	+	1.80223i
$703$	2.40720	+	1.38980i	0.0907892	+	0.0524172i
$704$	−4.64702	−	12.7676i	−0.175141	−	0.481197i
$705$	11.2196	+	3.01951i	0.422555	+	0.113721i
$706$	−55.2719	+	9.74593i	−2.08019	+	0.366793i
$707$	−16.9800	−	14.4397i	−0.638600	−	0.543060i
$708$	14.6258	−	31.2753i	0.549670	−	1.17540i
$709$	9.76292	−	3.55341i	0.366654	−	0.133451i	−0.152121	−	0.988362i	$-0.548610\pi$
$709$	9.76292	−	3.55341i	0.366654	−	0.133451i	0.518775	+	0.854911i	$0.326388\pi$
$710$	6.12181	+	10.6033i	0.229747	+	0.397934i
$711$	11.8745	+	2.12073i	0.445328	+	0.0795335i
$712$	−29.6907	−	17.1419i	−1.11270	−	0.642421i
$713$	10.1108	−	3.68001i	0.378651	−	0.137818i
$714$	−58.7863	+	40.4925i	−2.20002	+	1.51540i
$715$	11.5467	−	9.68881i	0.431821	−	0.362341i
$716$	2.45684	−	6.75011i	0.0918164	−	0.252263i
$717$	1.43285	−	2.04155i	0.0535109	−	0.0762429i
$718$	5.38951	−	30.5655i	0.201135	−	1.14069i
$719$	6.92962	−	12.0025i	0.258431	−	0.447616i	−0.707390	−	0.706823i	$-0.750128\pi$
$719$	6.92962	−	12.0025i	0.258431	−	0.447616i	0.965822	+	0.259207i	$0.0834611\pi$
$720$	−3.99449	−	2.31795i	−0.148866	−	0.0863847i
$721$	11.4765	−	1.94572i	0.427406	−	0.0724625i
$722$	−8.78829	−	1.54961i	−0.327066	−	0.0576706i
$723$	9.65285	+	4.51413i	0.358993	+	0.167882i
$724$	54.4277	+	64.8644i	2.02279	+	2.41067i
$725$	5.67889	−	15.6026i	0.210909	−	0.579467i
$726$	38.1197	−	10.1692i	1.41475	−	0.377415i
$727$	25.7069	−	30.6363i	0.953416	−	1.13624i	−0.0371652	−	0.999309i	$-0.511833\pi$
$727$	25.7069	−	30.6363i	0.953416	−	1.13624i	0.990581	−	0.136928i	$-0.0437228\pi$
$728$	5.61918	+	33.1437i	0.208261	+	1.22839i
$729$	−0.178133	+	26.9994i	−0.00659753	+	0.999978i
$730$	43.8037	+	75.8702i	1.62125	+	2.80808i
$731$	−24.2375	+	8.82173i	−0.896457	+	0.326284i
$732$	27.9328	+	27.9943i	1.03243	+	1.03470i
$733$	17.5321	+	20.8940i	0.647563	+	0.771736i	0.985544	−	0.169417i	$-0.0541884\pi$
$733$	17.5321	+	20.8940i	0.647563	+	0.771736i	−0.337981	+	0.941153i	$0.609744\pi$
$734$	−53.0064	−	19.2927i	−1.95650	−	0.712108i
$735$	−33.6976	−	24.3197i	−1.24295	−	0.897044i
$736$	−1.03660	+	5.87882i	−0.0382094	+	0.216696i
$737$		−	2.22079i		−	0.0818038i
$738$	24.5224	+	42.6906i	0.902683	+	1.57146i
$739$	2.75414			0.101313			0.0506564	−	0.998716i	$-0.483869\pi$
$739$	2.75414			0.101313			0.0506564	+	0.998716i	$0.483869\pi$
$740$	6.25489	+	5.24848i	0.229934	+	0.192938i
$741$	2.45182	−	27.6739i	0.0900698	−	1.01663i
$742$	34.1671	+	29.0554i	1.25431	+	1.06666i
$743$	24.2232	+	28.8681i	0.888662	+	1.05907i	0.997882	+	0.0650490i	$0.0207204\pi$
$743$	24.2232	+	28.8681i	0.888662	+	1.05907i	−0.109220	+	0.994018i	$0.534835\pi$
$744$	−4.35261	+	49.1283i	−0.159574	+	1.80113i
$745$	54.4294	+	9.59736i	1.99414	+	0.351620i
$746$			15.1488i			0.554638i
$747$	−15.4819	+	18.3684i	−0.566452	+	0.672064i
$748$	−20.7732	−	11.9934i	−0.759542	−	0.438522i
$749$	−14.8508	+	8.44413i	−0.542637	+	0.308542i
$750$	−21.7122	−	10.1537i	−0.792818	−	0.370759i
$751$	7.13696	+	40.4757i	0.260431	+	1.47698i	0.781737	+	0.623609i	$0.214334\pi$
$751$	7.13696	+	40.4757i	0.260431	+	1.47698i	−0.521305	+	0.853370i	$0.674555\pi$
$752$	−0.826003	−	0.300641i	−0.0301212	−	0.0109632i
$753$	7.05983	+	26.4640i	0.257274	+	0.964402i
$754$	23.0739	+	4.06855i	0.840302	+	0.148168i
$755$	34.8880			1.26970
$756$	18.9609	+	41.7343i	0.689601	+	1.51786i
$757$	23.0506			0.837788			0.418894	−	0.908035i	$-0.362418\pi$
$757$	23.0506			0.837788			0.418894	+	0.908035i	$0.362418\pi$
$758$	−6.33929	−	1.11779i	−0.230253	−	0.0405999i
$759$	2.07746	+	0.559102i	0.0754068	+	0.0202941i
$760$	38.6175	+	14.0556i	1.40081	+	0.509851i
$761$	−5.65233	−	32.0560i	−0.204897	−	1.16203i	−0.897602	−	0.440807i	$-0.854692\pi$
$761$	−5.65233	−	32.0560i	−0.204897	−	1.16203i	0.692705	−	0.721221i	$-0.256419\pi$
$762$	1.88474	+	21.8190i	0.0682769	+	0.790418i
$763$	−5.78152	+	9.86320i	−0.209305	+	0.357072i
$764$	−39.3387	−	22.7122i	−1.42322	−	0.821698i
$765$	68.3229	−	11.8923i	2.47022	−	0.429967i
$766$		−	77.1969i		−	2.78924i
$767$	24.2733	+	4.28003i	0.876457	+	0.154543i
$768$	−26.6438	−	18.6999i	−0.961425	−	0.674774i
$769$	24.7226	+	29.4632i	0.891519	+	1.06247i	0.997677	+	0.0681217i	$0.0217006\pi$
$769$	24.7226	+	29.4632i	0.891519	+	1.06247i	−0.106158	+	0.994349i	$0.533855\pi$
$770$	4.02429	−	21.9751i	0.145025	−	0.791926i
$771$	15.5880	−	7.24796i	0.561389	−	0.261029i
$772$	−48.5078	−	40.7029i	−1.74584	−	1.46493i
$773$	−52.4225			−1.88551			−0.942754	−	0.333489i	$-0.891774\pi$
$773$	−52.4225			−1.88551			−0.942754	+	0.333489i	$0.891774\pi$
$774$	4.54402	+	26.1060i	0.163331	+	0.938361i
$775$			62.3511i			2.23972i
$776$	−1.30227	+	7.38552i	−0.0467486	+	0.265125i
$777$	−0.823038	−	3.16889i	−0.0295263	−	0.113683i
$778$	−13.5180	−	4.92015i	−0.484644	−	0.176396i
$779$	−17.7692	−	21.1764i	−0.636646	−	0.758725i
$780$	21.2094	−	78.8077i	0.759417	−	2.82177i
$781$	1.55021	−	0.564231i	0.0554710	−	0.0201898i
$782$	9.06960	+	15.7090i	0.324328	+	0.561753i
$783$	12.7403	−	1.07229i	0.455301	−	0.0383206i
$784$	2.38156	+	2.05246i	0.0850559	+	0.0733021i
$785$	24.5867	−	29.3013i	0.877536	−	1.04581i
$786$	−16.8517	+	62.6158i	−0.601079	+	2.23343i
$787$	11.8238	−	32.4855i	0.421472	−	1.15798i	−0.529393	−	0.848377i	$-0.677580\pi$
$787$	11.8238	−	32.4855i	0.421472	−	1.15798i	0.950864	−	0.309607i	$-0.100198\pi$
$788$	−40.8432	−	48.6751i	−1.45498	−	1.73398i
$789$	−0.0729086	−	0.844037i	−0.00259561	−	0.0300485i
$790$	−31.3463	−	5.52720i	−1.11525	−	0.196649i
$791$	3.89270	−	10.4797i	0.138408	−	0.372615i
$792$	−6.35551	+	7.54047i	−0.225833	+	0.267939i
$793$	−14.1158	+	24.4494i	−0.501268	+	0.868222i
$794$	−1.75929	+	9.97745i	−0.0624350	+	0.354086i
$795$	−18.3717	−	39.5117i	−0.651578	−	1.40133i
$796$	−8.60450	+	23.6407i	−0.304979	+	0.837922i
$797$	−15.5543	+	13.0516i	−0.550963	+	0.462313i	−0.875267	−	0.483640i	$-0.839314\pi$
$797$	−15.5543	+	13.0516i	−0.550963	+	0.462313i	0.324304	+	0.945953i	$0.394870\pi$
$798$	−23.3583	−	33.9111i	−0.826875	−	1.20044i
$799$	12.4036	−	4.51452i	0.438806	−	0.159712i
$800$	−29.9582	−	17.2964i	−1.05918	−	0.611519i
$801$	0.0733951	−	33.3736i	0.00259329	−	1.17920i
$802$	29.5596	+	51.1987i	1.04378	+	1.80789i
$803$	11.0923	−	4.03727i	0.391439	−	0.142472i
$804$	−6.88598	−	9.85725i	−0.242850	−	0.347638i
$805$	−6.84107	+	8.04461i	−0.241116	+	0.283535i
$806$	−86.6469	+	15.2782i	−3.05201	+	0.538151i
$807$	3.31543	+	12.4280i	0.116708	+	0.437486i
$808$	−8.87996	−	24.3975i	−0.312396	−	0.858301i
$809$	−5.69185	−	3.28619i	−0.200115	−	0.115536i	0.396594	−	0.917994i	$-0.370192\pi$
$809$	−5.69185	−	3.28619i	−0.200115	−	0.115536i	−0.596709	+	0.802458i	$0.703525\pi$
$810$	0.313371	−	71.2463i	0.0110107	−	2.50334i
$811$			28.5329i			1.00192i	0.865469	+	0.500962i	$0.167020\pi$
$811$			28.5329i			1.00192i	−0.865469	+	0.500962i	$0.832980\pi$
$812$	18.8694	−	10.7291i	0.662188	−	0.376518i
$813$	2.73937	−	10.1787i	0.0960737	−	0.356981i
$814$	1.34830	−	1.13136i	0.0472579	−	0.0396541i
$815$	−34.7848	+	29.1879i	−1.21846	+	1.02241i
$816$	−5.22717	+	0.451527i	−0.182988	+	0.0158066i
$817$	−5.08886	−	13.9815i	−0.178037	−	0.489151i
$818$	−21.0310	+	36.4268i	−0.735332	+	1.27363i
$819$	−25.2521	+	20.8136i	−0.882380	+	0.727286i
$820$	−40.6026	−	70.3258i	−1.41790	−	2.45588i
$821$	12.9283	−	15.4073i	0.451200	−	0.537720i	−0.491713	−	0.870757i	$-0.663629\pi$
$821$	12.9283	−	15.4073i	0.451200	−	0.537720i	0.942914	+	0.333038i	$0.108074\pi$
$822$	−28.9863	−	20.3440i	−1.01101	−	0.709578i
$823$	−3.83170	−	21.7306i	−0.133565	−	0.757482i	−0.975849	−	0.218448i	$-0.929900\pi$
$823$	−3.83170	−	21.7306i	−0.133565	−	0.757482i	0.842284	−	0.539034i	$-0.181211\pi$
$824$	12.7411	+	4.63737i	0.443856	+	0.161550i
$825$	−7.16201	+	10.2045i	−0.249349	+	0.355275i
$826$	31.7569	−	18.0569i	1.10496	−	0.628278i
$827$	−18.3858	+	10.6150i	−0.639337	+	0.369121i	−0.784359	−	0.620307i	$-0.787008\pi$
$827$	−18.3858	+	10.6150i	−0.639337	+	0.369121i	0.145022	+	0.989428i	$0.453675\pi$
$828$	10.9547	−	3.95991i	0.380701	−	0.137616i
$829$	−35.9600	+	20.7615i	−1.24894	+	0.721078i	−0.970899	−	0.239491i	$-0.923020\pi$
$829$	−35.9600	+	20.7615i	−1.24894	+	0.721078i	−0.278044	+	0.960568i	$0.589686\pi$
$830$	40.7465	−	48.5598i	1.41433	−	1.68553i
$831$	24.1649	−	2.08739i	0.838272	−	0.0724106i
$832$	17.9620	−	49.3501i	0.622719	−	1.71091i
$833$	−47.2066	−	0.622200i	−1.63561	−	0.0215579i
$834$	63.4374	−	63.2980i	2.19666	−	2.19183i
$835$	3.39175	−	19.2356i	0.117377	−	0.665675i
$836$	6.91844	−	11.9831i	0.239279	−	0.414444i
$837$	−43.5798	+	20.1468i	−1.50634	+	0.696376i
$838$	−44.9549	+	25.9547i	−1.55294	+	0.896592i
$839$	2.39490	+	2.00956i	0.0826813	+	0.0693778i	0.683192	−	0.730239i	$-0.260591\pi$
$839$	2.39490	+	2.00956i	0.0826813	+	0.0693778i	−0.600510	+	0.799617i	$0.705036\pi$
$840$	−20.1193	−	44.0268i	−0.694183	−	1.51907i
$841$	3.98449	+	22.5972i	0.137396	+	0.779212i
$842$	2.35286	−	0.414873i	0.0810850	−	0.0142975i
$843$	29.7983	+	13.9351i	1.02631	+	0.479950i
$844$	62.0736	+	52.0860i	2.13666	+	1.79287i
$845$	13.7034			0.471411
$846$	−2.32540	−	13.3597i	−0.0799490	−	0.459318i
$847$	24.4602	+	9.08575i	0.840461	+	0.312190i
$848$	1.12749	+	3.09775i	0.0387181	+	0.106377i
$849$	−13.2797	+	18.9211i	−0.455758	+	0.649369i
$850$	−103.518	+	18.2530i	−3.55064	+	0.626073i
$851$	−0.819331	+	0.144470i	−0.0280863	+	0.00495237i
$852$	5.13131	−	7.31115i	0.175796	−	0.250476i
$853$	−7.99913	−	21.9774i	−0.273885	−	0.752493i	−0.998024	−	0.0628387i	$-0.979985\pi$
$853$	−7.99913	−	21.9774i	−0.273885	−	0.752493i	0.724139	−	0.689654i	$-0.242238\pi$
$854$	6.99432	+	41.2547i	0.239341	+	1.41171i
$855$	6.86013	+	39.4124i	0.234611	+	1.34787i
$856$	−19.8993			−0.680143
$857$	−19.8435	−	16.6506i	−0.677840	−	0.568775i	0.237534	−	0.971379i	$-0.423661\pi$
$857$	−19.8435	−	16.6506i	−0.677840	−	0.568775i	−0.915374	+	0.402604i	$0.868105\pi$
$858$	−15.9358	−	7.45231i	−0.544038	−	0.254418i
$859$	7.99184	−	1.40918i	0.272678	−	0.0480805i	−0.0356370	−	0.999365i	$-0.511346\pi$
$859$	7.99184	−	1.40918i	0.272678	−	0.0480805i	0.308315	+	0.951284i	$0.400235\pi$
$860$	−7.58968	−	43.0432i	−0.258806	−	1.46776i
$861$	−3.08723	+	32.4145i	−0.105213	+	1.10468i
$862$	22.5190	+	18.8957i	0.767002	+	0.643591i
$863$	41.7341	−	24.0952i	1.42065	−	0.820211i	0.424292	−	0.905525i	$-0.360523\pi$
$863$	41.7341	−	24.0952i	1.42065	−	0.820211i	0.996354	+	0.0853147i	$0.0271896\pi$
$864$	2.40909	−	26.5278i	0.0819589	−	0.902495i
$865$	−23.5657	+	40.8169i	−0.801257	+	1.38782i
$866$	−13.4604	+	76.3380i	−0.457405	+	2.59407i
$867$	34.9273	−	34.8506i	1.18619	−	1.18359i
$868$	−52.8052	+	62.0951i	−1.79232	+	2.10765i
$869$	−1.46684	+	4.03011i	−0.0497591	+	0.136712i
$870$	−33.6125	+	2.90347i	−1.13957	+	0.0984369i
$871$	5.51764	−	6.57567i	0.186958	−	0.222808i
$872$	−11.5329	+	6.65855i	−0.390555	+	0.225487i
$873$	−6.86557	+	2.48178i	−0.232364	+	0.0839955i
$874$	−9.06181	+	5.23184i	−0.306520	+	0.176970i
$875$	−7.83564	−	13.7807i	−0.264893	−	0.465871i
$876$	36.7163	−	52.3138i	1.24053	−	1.76752i
$877$	−34.1273	−	12.4213i	−1.15240	−	0.419438i	−0.306022	−	0.952025i	$-0.598998\pi$
$877$	−34.1273	−	12.4213i	−1.15240	−	0.419438i	−0.846376	+	0.532586i	$0.821220\pi$
$878$	9.81901	+	55.6864i	0.331376	+	1.87932i
$879$	33.8459	+	23.7547i	1.14159	+	0.801225i
$880$	1.05548	−	1.25787i	0.0355802	−	0.0424028i
$881$	−2.17755	−	3.77162i	−0.0733634	−	0.127069i	0.827010	−	0.562187i	$-0.190040\pi$
$881$	−2.17755	−	3.77162i	−0.0733634	−	0.127069i	−0.900373	+	0.435118i	$0.856707\pi$
$882$	−9.15583	+	47.6300i	−0.308293	+	1.60378i
$883$	22.4381	−	38.8639i	0.755101	−	1.30787i	−0.190223	−	0.981741i	$-0.560921\pi$
$883$	22.4381	−	38.8639i	0.755101	−	1.30787i	0.945324	−	0.326133i	$-0.105746\pi$
$884$	−31.7105	−	87.1238i	−1.06654	−	2.93029i
$885$	−35.3597	+	3.05439i	−1.18860	+	0.102672i
$886$	−15.6905	+	13.1659i	−0.527134	+	0.442318i
$887$	−23.7720	+	19.9471i	−0.798186	+	0.669758i	−0.947757	−	0.318993i	$-0.896655\pi$
$887$	−23.7720	+	19.9471i	−0.798186	+	0.669758i	0.149571	+	0.988751i	$0.452211\pi$
$888$	0.991092	−	3.68260i	0.0332589	−	0.123580i
$889$	−7.32464	+	12.4958i	−0.245661	+	0.419094i
$890$			88.0658i			2.95197i
$891$	−9.44654	−	1.70855i	−0.316471	−	0.0572387i
$892$	15.5418	+	8.97305i	0.520377	+	0.300440i
$893$	2.60422	+	7.15505i	0.0871470	+	0.239435i
$894$	−16.6268	−	62.3261i	−0.556084	−	2.08450i
$895$	−7.27195	+	1.28224i	−0.243074	+	0.0428606i
$896$	−17.0302	−	47.7673i	−0.568940	−	1.59579i
$897$	4.76216	+	6.81701i	0.159004	+	0.227613i
$898$	16.4206	−	5.97661i	0.547963	−	0.199442i
$899$	11.3674	+	19.6890i	0.379125	+	0.656664i
$900$	−0.148448	+	67.5012i	−0.00494828	+	2.25004i
$901$	−42.8702	−	24.7511i	−1.42821	−	0.824580i
$902$	−16.4489	+	5.98691i	−0.547688	+	0.199342i
$903$	−7.52850	+	15.8260i	−0.250533	+	0.526658i
$904$	9.97532	−	8.37029i	0.331774	−	0.278392i
$905$	29.7700	−	81.7923i	0.989587	−	2.71887i
$906$	−17.1678	−	36.9225i	−0.570364	−	1.22667i
$907$	0.0302728	−	0.171686i	0.00100519	−	0.00570072i	−0.984301	−	0.176498i	$-0.943523\pi$
$907$	0.0302728	−	0.171686i	0.00100519	−	0.00570072i	0.985306	+	0.170797i	$0.0546343\pi$
$908$	26.2553	−	45.4756i	0.871314	−	1.50916i
$909$	16.2884	−	19.3253i	0.540251	−	0.640978i
$910$	66.5138	−	55.0689i	2.20491	−	1.82551i
$911$	48.1931	+	8.49774i	1.59671	+	0.281543i	0.900025	−	0.435838i	$-0.143548\pi$
$911$	48.1931	+	8.49774i	1.59671	+	0.281543i	0.696682	+	0.717380i	$0.254659\pi$
$912$	−0.260465	−	3.01532i	−0.00862487	−	0.0998471i
$913$	−5.49017	−	6.54293i	−0.181698	−	0.216540i
$914$	14.3497	−	39.4256i	0.474647	−	1.30408i
$915$	10.5647	−	39.2552i	0.349258	−	1.29774i
$916$	−34.4147	+	41.0138i	−1.13709	+	1.35513i
$917$	−33.0336	+	27.3496i	−1.09087	+	0.903162i
$918$	−46.2064	−	66.4551i	−1.52504	−	2.19335i
$919$	−9.29027	−	16.0912i	−0.306458	−	0.530800i	0.671127	−	0.741342i	$-0.265810\pi$
$919$	−9.29027	−	16.0912i	−0.306458	−	0.530800i	−0.977585	+	0.210542i	$0.932477\pi$
$920$	−11.5588	+	4.20705i	−0.381081	+	0.138702i
$921$	5.15353	−	19.1490i	0.169815	−	0.630981i
$922$	15.9513	+	19.0100i	0.525328	+	0.626062i
$923$	5.99198	+	2.18090i	0.197228	+	0.0717853i
$924$	−15.7748	+	4.09710i	−0.518953	+	0.134785i
$925$	0.837190	−	4.74794i	0.0275267	−	0.156111i
$926$			22.9699i			0.754839i
$927$	2.26336	+	13.0033i	0.0743384	+	0.427084i
$928$	−12.6134			−0.414056
$929$	23.4946	+	19.7143i	0.770831	+	0.646804i	0.940922	−	0.338624i	$-0.109962\pi$
$929$	23.4946	+	19.7143i	0.770831	+	0.646804i	−0.170090	+	0.985428i	$0.554406\pi$
$930$	114.880	−	53.4158i	3.76707	−	1.75157i
$931$	0.358919	−	27.2313i	0.0117631	−	0.892471i
$932$	52.9632	+	63.1191i	1.73487	+	2.06754i
$933$	−10.9209	−	7.66484i	−0.357536	−	0.250936i
$934$	46.9440	+	8.27750i	1.53606	+	0.270848i
$935$			24.6573i			0.806381i
$936$	−37.5531	+	6.53650i	−1.22746	+	0.213652i
$937$	−27.4918	−	15.8724i	−0.898117	−	0.518528i	−0.0215283	−	0.999768i	$-0.506853\pi$
$937$	−27.4918	−	15.8724i	−0.898117	−	0.518528i	−0.876589	+	0.481240i	$0.840187\pi$
$938$	0.0838388	−	12.7223i	0.00273744	−	0.415399i
$939$	3.13264	+	36.2655i	0.102230	+	1.18348i
$940$	3.88402	+	22.0274i	0.126683	+	0.718454i
$941$	−21.5805	−	7.85468i	−0.703506	−	0.256055i	−0.0345988	−	0.999401i	$-0.511015\pi$
$941$	−21.5805	−	7.85468i	−0.703506	−	0.256055i	−0.668907	+	0.743346i	$0.733238\pi$
$942$	−43.1087	−	11.6018i	−1.40456	−	0.378006i
$943$	8.14850	+	1.43680i	0.265352	+	0.0467886i
$944$	2.68507			0.0873916
$945$	27.4079	−	38.3301i	0.891578	−	1.24688i
$946$	−9.42150			−0.306319
$947$	17.2292	+	3.03797i	0.559874	+	0.0987209i	0.446422	−	0.894823i	$-0.352698\pi$
$947$	17.2292	+	3.03797i	0.559874	+	0.0987209i	0.113452	+	0.993543i	$0.463809\pi$
$948$	5.98538	+	22.4364i	0.194396	+	0.728700i
$949$	42.8747	+	15.6051i	1.39177	+	0.506564i
$950$	−10.5293	−	59.7148i	−0.341617	−	1.93740i
$951$	14.2812	+	6.67855i	0.463099	+	0.216567i
$952$	−47.4420	−	27.8091i	−1.53761	−	0.901299i
$953$	−49.0691	−	28.3301i	−1.58950	−	0.917701i	−0.993388	−	0.114803i	$-0.963376\pi$
$953$	−49.0691	−	28.3301i	−1.58950	−	0.917701i	−0.596116	−	0.802898i	$-0.703290\pi$
$954$	−32.7754	+	38.8862i	−1.06114	+	1.25899i
$955$			46.6942i			1.51099i
$956$	4.72857	+	0.833774i	0.152933	+	0.0269662i
$957$	−0.401172	+	4.52807i	−0.0129681	+	0.146372i
$958$	60.0928	+	71.6159i	1.94151	+	2.31380i
$959$	−7.86536	−	22.0612i	−0.253986	−	0.712392i
$960$	−6.67372	+	75.3268i	−0.215393	+	2.43116i
$961$	−41.6527	−	34.9508i	−1.34364	−	1.12744i
$962$	6.80318			0.219343
$963$	−9.64858	−	16.7970i	−0.310921	−	0.541277i
$964$			20.5141i			0.660714i
$965$	−11.3032	+	64.1038i	−0.363864	+	2.06357i
$966$	11.8801	+	3.28138i	0.382236	+	0.105577i
$967$	−7.44352	−	2.70922i	−0.239367	−	0.0871226i	0.219551	−	0.975601i	$-0.429541\pi$
$967$	−7.44352	−	2.70922i	−0.239367	−	0.0871226i	−0.458918	+	0.888478i	$0.651763\pi$
$968$	19.5367	+	23.2829i	0.627932	+	0.748341i
$969$	32.1010	+	32.1717i	1.03123	+	1.03350i
$970$	18.1023	−	6.58869i	0.581229	−	0.211550i
$971$	−24.8663	−	43.0696i	−0.797996	−	1.38217i	−0.920919	−	0.389753i	$-0.872560\pi$
$971$	−24.8663	−	43.0696i	−0.797996	−	1.38217i	0.122923	−	0.992416i	$-0.460773\pi$
$972$	−47.2274	+	21.7072i	−1.51482	+	0.696258i
$973$	58.4356	−	9.90718i	1.87336	−	0.317610i
$974$	47.6364	−	56.7709i	1.52637	−	1.81906i
$975$	−46.5600	+	12.4209i	−1.49111	+	0.397786i
$976$	−1.05188	+	2.89002i	−0.0336699	+	0.0925074i
$977$	0.500646	+	0.596647i	0.0160171	+	0.0190884i	0.773994	−	0.633194i	$-0.218256\pi$
$977$	0.500646	+	0.596647i	0.0160171	+	0.0190884i	−0.757976	+	0.652282i	$0.773812\pi$
$978$	48.0070	+	22.4504i	1.53510	+	0.717883i
$979$	11.6857	+	2.06050i	0.373476	+	0.0658540i
$980$	14.9290	−	78.5950i	0.476890	−	2.51062i
$981$	−11.2125	−	6.50646i	−0.357988	−	0.207735i
$982$	37.7582	−	65.3991i	1.20491	−	2.08697i
$983$	6.00596	−	34.0615i	0.191560	−	1.08639i	−0.725672	−	0.688041i	$-0.758471\pi$
$983$	6.00596	−	34.0615i	0.191560	−	1.08639i	0.917233	−	0.398352i	$-0.130418\pi$
$984$	−21.7886	+	31.0447i	−0.694596	+	0.989668i
$985$	−22.3398	+	61.3780i	−0.711804	+	1.95567i
$986$	−29.3607	+	24.6366i	−0.935036	+	0.784588i
$987$	3.85271	−	8.09898i	0.122633	−	0.257793i
$988$	50.2578	−	18.2923i	1.59891	−	0.581957i
$989$	3.85679	+	2.22672i	0.122639	+	0.0708056i
$990$	24.9372	+	4.45367i	0.792556	+	0.141547i
$991$	14.9430	+	25.8821i	0.474681	+	0.822172i	0.999580	−	0.0289930i	$-0.00923006\pi$
$991$	14.9430	+	25.8821i	0.474681	+	0.822172i	−0.524899	+	0.851165i	$0.675897\pi$
$992$	44.5094	−	16.2001i	1.41317	−	0.514353i
$993$	−15.3699	+	32.8664i	−0.487749	+	1.04298i
$994$	8.90208	−	3.17382i	0.282357	−	0.100667i
$995$	25.4683	−	4.49075i	0.807399	−	0.142366i
$996$	−44.6565	−	12.0183i	−1.41499	−	0.380815i
$997$	9.49742	+	26.0939i	0.300786	+	0.826403i	0.994364	+	0.106021i	$0.0338112\pi$
$997$	9.49742	+	26.0939i	0.300786	+	0.826403i	−0.693578	+	0.720382i	$0.743967\pi$
$998$	−44.8615	−	25.9008i	−1.42007	−	0.819875i
$999$	3.58905	−	0.949004i	0.113552	−	0.0300252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.38.4	yes	132
3.2	odd	2		567.2.ba.a.521.19		132
7.5	odd	6		189.2.bd.a.173.19	yes	132
21.5	even	6		567.2.bd.a.278.4		132
27.5	odd	18		189.2.bd.a.59.19	yes	132
27.22	even	9		567.2.bd.a.206.4		132
189.5	even	18	inner	189.2.ba.a.5.4	✓	132
189.103	odd	18		567.2.ba.a.530.19		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.4	✓	132	189.5	even	18	inner
189.2.ba.a.38.4	yes	132	1.1	even	1	trivial
189.2.bd.a.59.19	yes	132	27.5	odd	18
189.2.bd.a.173.19	yes	132	7.5	odd	6
567.2.ba.a.521.19		132	3.2	odd	2
567.2.ba.a.530.19		132	189.103	odd	18
567.2.bd.a.206.4		132	27.22	even	9
567.2.bd.a.278.4		132	21.5	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27453 - 0.401061i) q^{2} +(1.22609 - 1.22340i) q^{3} +(3.13325 + 1.14041i) q^{4} +(-0.595188 - 3.37548i) q^{5} +(-3.27944 + 2.29092i) q^{6} +(-2.64569 - 0.0174348i) q^{7} +(-2.66893 - 1.54091i) q^{8} +(0.00659757 - 2.99999i) q^{9} +O(q^{10})\)	\(q+(-2.27453 - 0.401061i) q^{2} +(1.22609 - 1.22340i) q^{3} +(3.13325 + 1.14041i) q^{4} +(-0.595188 - 3.37548i) q^{5} +(-3.27944 + 2.29092i) q^{6} +(-2.64569 - 0.0174348i) q^{7} +(-2.66893 - 1.54091i) q^{8} +(0.00659757 - 2.99999i) q^{9} +7.91633i q^{10} +(1.05044 + 0.185221i) q^{11} +(5.23683 - 2.43497i) q^{12} +(2.65013 + 3.15830i) q^{13} +(6.01072 + 1.10074i) q^{14} +(-4.85931 - 3.41049i) q^{15} +(0.344058 + 0.288699i) q^{16} -6.74438 q^{17} +(-1.21819 + 6.82093i) q^{18} -3.89053i q^{19} +(1.98456 - 11.2550i) q^{20} +(-3.26519 + 3.21536i) q^{21} +(-2.31497 - 0.842581i) q^{22} +(0.748519 + 0.892051i) q^{23} +(-5.15749 + 1.37587i) q^{24} +(-6.34114 + 2.30799i) q^{25} +(-4.76112 - 8.24651i) q^{26} +(-3.66209 - 3.68634i) q^{27} +(-8.26975 - 3.07181i) q^{28} +(-1.58160 + 1.88488i) q^{29} +(9.68482 + 9.70615i) q^{30} +(3.16020 - 8.68256i) q^{31} +(3.29512 + 3.92697i) q^{32} +(1.51453 - 1.05801i) q^{33} +(15.3403 + 2.70491i) q^{34} +(1.51583 + 8.94086i) q^{35} +(3.44190 - 9.39221i) q^{36} +(-0.357225 + 0.618733i) q^{37} +(-1.56034 + 8.84913i) q^{38} +(7.11315 + 0.630202i) q^{39} +(-3.61278 + 9.92604i) q^{40} +(5.44308 - 4.56728i) q^{41} +(8.71633 - 6.00389i) q^{42} +(3.59373 - 1.30801i) q^{43} +(3.08007 + 1.77828i) q^{44} +(-10.1303 + 1.76329i) q^{45} +(-1.34476 - 2.32920i) q^{46} +(-1.83909 + 0.669375i) q^{47} +(0.775040 - 0.0669486i) q^{48} +(6.99939 + 0.0922545i) q^{49} +(15.3488 - 2.70640i) q^{50} +(-8.26923 + 8.25106i) q^{51} +(4.70176 + 12.9180i) q^{52} +(6.35643 + 3.66989i) q^{53} +(6.85110 + 9.85340i) q^{54} -3.65598i q^{55} +(7.03430 + 4.12330i) q^{56} +(-4.75966 - 4.77014i) q^{57} +(4.35336 - 3.65290i) q^{58} +(4.57964 - 3.84278i) q^{59} +(-11.3361 - 16.2275i) q^{60} +(2.34201 + 6.43463i) q^{61} +(-10.6702 + 18.4813i) q^{62} +(-0.0697595 + 7.93695i) q^{63} +(-6.36903 - 11.0315i) q^{64} +(9.08344 - 10.8252i) q^{65} +(-3.86918 + 1.79905i) q^{66} +(-0.361541 - 2.05040i) q^{67} +(-21.1319 - 7.69137i) q^{68} +(2.00909 + 0.177999i) q^{69} +(0.138020 - 20.9442i) q^{70} +(1.33942 - 0.773313i) q^{71} +(-4.64032 + 7.99660i) q^{72} +(9.58401 - 5.53333i) q^{73} +(1.06067 - 1.26406i) q^{74} +(-4.95123 + 10.5875i) q^{75} +(4.43680 - 12.1900i) q^{76} +(-2.77591 - 0.508352i) q^{77} +(-15.9263 - 4.28622i) q^{78} +(-0.698202 + 3.95970i) q^{79} +(0.769718 - 1.33319i) q^{80} +(-8.99991 - 0.0395853i) q^{81} +(-14.2122 + 8.20542i) q^{82} +(-6.13413 - 5.14714i) q^{83} +(-13.8975 + 6.35087i) q^{84} +(4.01418 + 22.7655i) q^{85} +(-8.69865 + 1.53381i) q^{86} +(0.366770 + 4.24596i) q^{87} +(-2.51814 - 2.11297i) q^{88} +11.1246 q^{89} +(23.7489 + 0.0522286i) q^{90} +(-6.95636 - 8.40209i) q^{91} +(1.32800 + 3.64864i) q^{92} +(-6.74754 - 14.5118i) q^{93} +(4.45153 - 0.784926i) q^{94} +(-13.1324 + 2.31560i) q^{95} +(8.84436 + 0.783582i) q^{96} +(-0.832291 - 2.28670i) q^{97} +(-15.8833 - 3.01702i) q^{98} +(0.562592 - 3.15009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

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