LMFDB - Embedded newform 324.2.p.a.23.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(11,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([27, 13]))

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

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

chi := DirichletCharacter("324.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.p (of order $54$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$936$
Relative dimension:	$52$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			23.50
Character	$\chi$	$=$	324.23
Dual form			324.2.p.a.155.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37313 + 0.338405i) q^{2} +(0.288087 + 1.70792i) q^{3} +(1.77096 + 0.929346i) q^{4} +(1.00330 - 1.52545i) q^{5} +(-0.182388 + 2.44269i) q^{6} +(-2.48232 + 2.34195i) q^{7} +(2.11727 + 1.87541i) q^{8} +(-2.83401 + 0.984063i) q^{9} +O(q^{10})$	\(q+(1.37313 + 0.338405i) q^{2} +(0.288087 + 1.70792i) q^{3} +(1.77096 + 0.929346i) q^{4} +(1.00330 - 1.52545i) q^{5} +(-0.182388 + 2.44269i) q^{6} +(-2.48232 + 2.34195i) q^{7} +(2.11727 + 1.87541i) q^{8} +(-2.83401 + 0.984063i) q^{9} +(1.89388 - 1.75511i) q^{10} +(0.697519 + 0.350307i) q^{11} +(-1.07706 + 3.29241i) q^{12} +(0.923085 - 2.13995i) q^{13} +(-4.20108 + 2.37577i) q^{14} +(2.89439 + 1.27410i) q^{15} +(2.27263 + 3.29168i) q^{16} +(3.49809 - 4.16886i) q^{17} +(-4.22447 + 0.392203i) q^{18} +(-2.77306 - 3.30481i) q^{19} +(3.19448 - 1.76910i) q^{20} +(-4.71500 - 3.56493i) q^{21} +(0.839238 + 0.717061i) q^{22} +(0.0510191 - 0.0540770i) q^{23} +(-2.59311 + 4.15642i) q^{24} +(0.660026 + 1.53011i) q^{25} +(1.99168 - 2.62605i) q^{26} +(-2.49715 - 4.55678i) q^{27} +(-6.57259 + 1.84058i) q^{28} +(-0.385867 + 3.30130i) q^{29} +(3.54320 + 2.72898i) q^{30} +(1.52199 - 6.42177i) q^{31} +(2.00670 + 5.28897i) q^{32} +(-0.397352 + 1.29223i) q^{33} +(6.21409 - 4.54061i) q^{34} +(1.08200 + 6.13634i) q^{35} +(-5.93347 - 0.891037i) q^{36} +(1.01074 - 5.73217i) q^{37} +(-2.68941 - 5.47635i) q^{38} +(3.92081 + 0.960066i) q^{39} +(4.98510 - 1.34817i) q^{40} +(-9.21489 + 6.86023i) q^{41} +(-5.26791 - 6.49069i) q^{42} +(-4.53525 + 0.264148i) q^{43} +(0.909725 + 1.26862i) q^{44} +(-1.34223 + 5.31045i) q^{45} +(0.0883556 - 0.0569896i) q^{46} +(6.34059 - 1.50275i) q^{47} +(-4.96722 + 4.82977i) q^{48} +(0.270180 - 4.63881i) q^{49} +(0.388504 + 2.32440i) q^{50} +(8.12786 + 4.77348i) q^{51} +(3.62351 - 2.93191i) q^{52} +(-5.60215 - 3.23440i) q^{53} +(-1.88687 - 7.10209i) q^{54} +(1.23420 - 0.712564i) q^{55} +(-9.64787 + 0.303152i) q^{56} +(4.84548 - 5.68826i) q^{57} +(-1.64702 + 4.40253i) q^{58} +(4.33408 - 2.17666i) q^{59} +(3.94177 + 4.94628i) q^{60} +(1.69812 - 5.67212i) q^{61} +(4.26304 - 8.30286i) q^{62} +(4.73031 - 9.07988i) q^{63} +(0.965641 + 7.94151i) q^{64} +(-2.33825 - 3.55514i) q^{65} +(-0.982911 + 1.63993i) q^{66} +(-0.718219 - 6.14476i) q^{67} +(10.0693 - 4.13197i) q^{68} +(0.107057 + 0.0715578i) q^{69} +(-0.590837 + 8.79214i) q^{70} +(5.57405 - 2.02879i) q^{71} +(-7.84589 - 3.23142i) q^{72} +(8.85743 + 3.22384i) q^{73} +(3.32767 - 7.52897i) q^{74} +(-2.42317 + 1.56808i) q^{75} +(-1.83969 - 8.42984i) q^{76} +(-2.55187 + 0.763980i) q^{77} +(5.05888 + 2.64511i) q^{78} +(-9.61276 - 7.15644i) q^{79} +(7.30142 - 0.164230i) q^{80} +(7.06324 - 5.57769i) q^{81} +(-14.9748 + 6.30162i) q^{82} +(-7.63379 + 10.2540i) q^{83} +(-5.03704 - 10.6952i) q^{84} +(-2.84973 - 9.51878i) q^{85} +(-6.31687 - 1.17204i) q^{86} +(-5.74954 + 0.292032i) q^{87} +(0.819863 + 2.04983i) q^{88} +(-4.72291 + 12.9761i) q^{89} +(-3.64014 + 6.83771i) q^{90} +(2.72027 + 7.47387i) q^{91} +(0.140609 - 0.0483542i) q^{92} +(11.4064 + 0.749408i) q^{93} +(9.21499 + 0.0822194i) q^{94} +(-7.82353 + 0.914440i) q^{95} +(-8.45505 + 4.95097i) q^{96} +(-14.7662 + 9.71187i) q^{97} +(1.94079 - 6.27825i) q^{98} +(-2.32150 - 0.306372i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	$ 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) $ 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{54}\right)$

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 $

$2$	1.37313	+	0.338405i	0.970949	+	0.239288i
$2$	1.37313	+	0.338405i	0.970949	+	0.239288i
$3$	0.288087	+	1.70792i	0.166327	+	0.986071i
$3$	0.288087	+	1.70792i	0.166327	+	0.986071i
$4$	1.77096	+	0.929346i	0.885482	+	0.464673i
$5$	1.00330	−	1.52545i	0.448690	−	0.682200i	−0.538341	−	0.842727i	$-0.680949\pi$
$5$	1.00330	−	1.52545i	0.448690	−	0.682200i	0.987032	+	0.160526i	$0.0513192\pi$
$6$	−0.182388	+	2.44269i	−0.0744598	+	0.997224i
$7$	−2.48232	+	2.34195i	−0.938230	+	0.885175i	−0.993562	−	0.113294i	$-0.963860\pi$
$7$	−2.48232	+	2.34195i	−0.938230	+	0.885175i	0.0553314	+	0.998468i	$0.482378\pi$
$8$	2.11727	+	1.87541i	0.748567	+	0.663059i
$9$	−2.83401	+	0.984063i	−0.944670	+	0.328021i
$10$	1.89388	−	1.75511i	0.598898	−	0.555015i
$11$	0.697519	+	0.350307i	0.210310	+	0.105622i	0.550836	−	0.834613i	$-0.314309\pi$
$11$	0.697519	+	0.350307i	0.210310	+	0.105622i	−0.340526	+	0.940235i	$0.610605\pi$
$12$	−1.07706	+	3.29241i	−0.310921	+	0.950436i
$13$	0.923085	−	2.13995i	0.256018	−	0.593516i	−0.740930	−	0.671582i	$-0.765615\pi$
$13$	0.923085	−	2.13995i	0.256018	−	0.593516i	0.996948	+	0.0780659i	$0.0248745\pi$
$14$	−4.20108	+	2.37577i	−1.12279	+	0.634952i
$15$	2.89439	+	1.27410i	0.747327	+	0.328972i
$16$	2.27263	+	3.29168i	0.568158	+	0.822920i
$17$	3.49809	−	4.16886i	0.848412	−	1.01110i	−0.151333	−	0.988483i	$-0.548356\pi$
$17$	3.49809	−	4.16886i	0.848412	−	1.01110i	0.999744	−	0.0226146i	$-0.00719906\pi$
$18$	−4.22447	+	0.392203i	−0.995718	+	0.0924430i
$19$	−2.77306	−	3.30481i	−0.636185	−	0.758175i	0.347578	−	0.937651i	$-0.387004\pi$
$19$	−2.77306	−	3.30481i	−0.636185	−	0.758175i	−0.983762	+	0.179476i	$0.942560\pi$
$20$	3.19448	−	1.76910i	0.714308	−	0.395582i
$21$	−4.71500	−	3.56493i	−1.02890	−	0.777932i
$22$	0.839238	+	0.717061i	0.178926	+	0.152878i
$23$	0.0510191	−	0.0540770i	0.0106382	−	0.0112758i	−0.722033	−	0.691859i	$-0.756792\pi$
$23$	0.0510191	−	0.0540770i	0.0106382	−	0.0112758i	0.732671	+	0.680583i	$0.238273\pi$
$24$	−2.59311	+	4.15642i	−0.529316	+	0.848425i
$25$	0.660026	+	1.53011i	0.132005	+	0.306023i
$26$	1.99168	−	2.62605i	0.390601	−	0.515011i
$27$	−2.49715	−	4.55678i	−0.480576	−	0.876953i
$28$	−6.57259	+	1.84058i	−1.24210	+	0.347836i
$29$	−0.385867	+	3.30130i	−0.0716537	+	0.613037i	0.908932	+	0.416945i	$0.136899\pi$
$29$	−0.385867	+	3.30130i	−0.0716537	+	0.613037i	−0.980586	+	0.196092i	$0.937175\pi$
$30$	3.54320	+	2.72898i	0.646897	+	0.498241i
$31$	1.52199	−	6.42177i	0.273357	−	1.15338i	−0.647058	−	0.762441i	$-0.724001\pi$
$31$	1.52199	−	6.42177i	0.273357	−	1.15338i	0.920415	−	0.390943i	$-0.127851\pi$
$32$	2.00670	+	5.28897i	0.354737	+	0.934966i
$33$	−0.397352	+	1.29223i	−0.0691701	+	0.224948i
$34$	6.21409	−	4.54061i	1.06571	−	0.778709i
$35$	1.08200	+	6.13634i	0.182892	+	1.03723i
$36$	−5.93347	−	0.891037i	−0.988911	−	0.148506i
$37$	1.01074	−	5.73217i	0.166164	−	0.942364i	−0.781692	−	0.623665i	$-0.785643\pi$
$37$	1.01074	−	5.73217i	0.166164	−	0.942364i	0.947856	−	0.318699i	$-0.103246\pi$
$38$	−2.68941	−	5.47635i	−0.436280	−	0.888381i
$39$	3.92081	+	0.960066i	0.627831	+	0.153734i
$40$	4.98510	−	1.34817i	0.788214	−	0.213165i
$41$	−9.21489	+	6.86023i	−1.43912	+	1.07139i	−0.455686	+	0.890141i	$0.650606\pi$
$41$	−9.21489	+	6.86023i	−1.43912	+	1.07139i	−0.983438	+	0.181247i	$0.941987\pi$
$42$	−5.26791	−	6.49069i	−0.812857	−	1.00154i
$43$	−4.53525	+	0.264148i	−0.691619	+	0.0402822i	−0.400354	−	0.916360i	$-0.631113\pi$
$43$	−4.53525	+	0.264148i	−0.691619	+	0.0402822i	−0.291264	+	0.956643i	$0.594076\pi$
$44$	0.909725	+	1.26862i	0.137146	+	0.191251i
$45$	−1.34223	+	5.31045i	−0.200088	+	0.791634i
$46$	0.0883556	−	0.0569896i	0.0130273	−	0.00840266i
$47$	6.34059	−	1.50275i	0.924871	−	0.219198i	0.259527	−	0.965736i	$-0.416433\pi$
$47$	6.34059	−	1.50275i	0.924871	−	0.219198i	0.665343	+	0.746537i	$0.268285\pi$
$48$	−4.96722	+	4.82977i	−0.716957	+	0.697118i
$49$	0.270180	−	4.63881i	0.0385971	−	0.662687i
$50$	0.388504	+	2.32440i	0.0549427	+	0.328719i
$51$	8.12786	+	4.77348i	1.13813	+	0.668420i
$52$	3.62351	−	2.93191i	0.502490	−	0.406583i
$53$	−5.60215	−	3.23440i	−0.769515	−	0.444279i	0.0631869	−	0.998002i	$-0.479874\pi$
$53$	−5.60215	−	3.23440i	−0.769515	−	0.444279i	−0.832701	+	0.553722i	$0.813207\pi$
$54$	−1.88687	−	7.10209i	−0.256770	−	0.966472i
$55$	1.23420	−	0.712564i	0.166419	−	0.0960821i
$56$	−9.64787	+	0.303152i	−1.28925	+	0.0405104i
$57$	4.84548	−	5.68826i	0.641799	−	0.753428i
$58$	−1.64702	+	4.40253i	−0.216264	+	0.578081i
$59$	4.33408	−	2.17666i	0.564250	−	0.283377i	−0.143721	−	0.989618i	$-0.545907\pi$
$59$	4.33408	−	2.17666i	0.564250	−	0.283377i	0.707971	+	0.706241i	$0.249611\pi$
$60$	3.94177	+	4.94628i	0.508881	+	0.638562i
$61$	1.69812	−	5.67212i	0.217422	−	0.726241i	−0.777792	−	0.628522i	$-0.783660\pi$
$61$	1.69812	−	5.67212i	0.217422	−	0.726241i	0.995214	−	0.0977187i	$-0.0311545\pi$
$62$	4.26304	−	8.30286i	0.541406	−	1.05446i
$63$	4.73031	−	9.07988i	0.595963	−	1.14396i
$64$	0.965641	+	7.94151i	0.120705	+	0.992688i
$65$	−2.33825	−	3.55514i	−0.290024	−	0.440960i
$66$	−0.982911	+	1.63993i	−0.120988	+	0.201862i
$67$	−0.718219	−	6.14476i	−0.0877445	−	0.750702i	−0.963456	−	0.267867i	$-0.913681\pi$
$67$	−0.718219	−	6.14476i	−0.0877445	−	0.750702i	0.875711	−	0.482835i	$-0.160393\pi$
$68$	10.0693	−	4.13197i	1.22108	−	0.501075i
$69$	0.107057	+	0.0715578i	0.0128882	+	0.00861454i
$70$	−0.590837	+	8.79214i	−0.0706185	+	1.05086i
$71$	5.57405	−	2.02879i	0.661518	−	0.240773i	0.0106263	−	0.999944i	$-0.496617\pi$
$71$	5.57405	−	2.02879i	0.661518	−	0.240773i	0.650891	+	0.759171i	$0.274395\pi$
$72$	−7.84589	−	3.23142i	−0.924646	−	0.380827i
$73$	8.85743	+	3.22384i	1.03668	+	0.377322i	0.803622	−	0.595140i	$-0.202903\pi$
$73$	8.85743	+	3.22384i	1.03668	+	0.377322i	0.233062	+	0.972462i	$0.425126\pi$
$74$	3.32767	−	7.52897i	0.386833	−	0.875225i
$75$	−2.42317	+	1.56808i	−0.279804	+	0.181066i
$76$	−1.83969	−	8.42984i	−0.211027	−	0.966969i
$77$	−2.55187	+	0.763980i	−0.290813	+	0.0870636i
$78$	5.05888	+	2.64511i	0.572805	+	0.299500i
$79$	−9.61276	−	7.15644i	−1.08152	−	0.805162i	−0.0997081	−	0.995017i	$-0.531791\pi$
$79$	−9.61276	−	7.15644i	−1.08152	−	0.805162i	−0.981812	+	0.189855i	$0.939198\pi$
$80$	7.30142	−	0.164230i	0.816323	−	0.0183615i
$81$	7.06324	−	5.57769i	0.784804	−	0.619743i
$82$	−14.9748	+	6.30162i	−1.65369	+	0.695897i
$83$	−7.63379	+	10.2540i	−0.837917	+	1.12552i	0.152622	+	0.988285i	$0.451228\pi$
$83$	−7.63379	+	10.2540i	−0.837917	+	1.12552i	−0.990539	+	0.137233i	$0.956179\pi$
$84$	−5.03704	−	10.6952i	−0.549587	−	1.16695i
$85$	−2.84973	−	9.51878i	−0.309097	−	1.03246i
$86$	−6.31687	−	1.17204i	−0.681165	−	0.126384i
$87$	−5.74954	+	0.292032i	−0.616415	+	0.0313091i
$88$	0.819863	+	2.04983i	0.0873977	+	0.218513i
$89$	−4.72291	+	12.9761i	−0.500628	+	1.37546i	0.390036	+	0.920800i	$0.372463\pi$
$89$	−4.72291	+	12.9761i	−0.500628	+	1.37546i	−0.890663	+	0.454663i	$0.849760\pi$
$90$	−3.64014	+	6.83771i	−0.383704	+	0.720758i
$91$	2.72027	+	7.47387i	0.285162	+	0.783475i
$92$	0.140609	−	0.0483542i	0.0146595	−	0.00504127i
$93$	11.4064	+	0.749408i	1.18278	+	0.0777100i
$94$	9.21499	+	0.0822194i	0.950453	+	0.00848028i
$95$	−7.82353	+	0.914440i	−0.802677	+	0.0938195i
$96$	−8.45505	+	4.95097i	−0.862940	+	0.505306i
$97$	−14.7662	+	9.71187i	−1.49928	+	0.986091i	−0.507016	+	0.861937i	$0.669252\pi$
$97$	−14.7662	+	9.71187i	−1.49928	+	0.986091i	−0.992263	+	0.124155i	$0.960378\pi$
$98$	1.94079	−	6.27825i	0.196049	−	0.634199i
$99$	−2.32150	−	0.306372i	−0.233320	−	0.0307915i
$100$	−0.253121	+	3.32317i	−0.0253121	+	0.332317i
$101$	18.7553	+	5.61498i	1.86622	+	0.558711i	0.998048	+	0.0624559i	$0.0198933\pi$
$101$	18.7553	+	5.61498i	1.86622	+	0.558711i	0.868177	+	0.496255i	$0.165292\pi$
$102$	9.54523	+	9.30510i	0.945118	+	0.921342i
$103$	−1.81117	−	3.60633i	−0.178460	−	0.355342i	0.786563	−	0.617511i	$-0.211859\pi$
$103$	−1.81117	−	3.60633i	−0.178460	−	0.355342i	−0.965022	+	0.262168i	$0.915562\pi$
$104$	5.96771	−	2.79968i	0.585183	−	0.274531i
$105$	−10.1687	+	3.61578i	−0.992362	+	0.352864i
$106$	−6.59794	−	6.33705i	−0.640848	−	0.615508i
$107$	6.10860	+	10.5804i	0.590541	+	1.02285i	0.994160	+	0.107919i	$0.0344189\pi$
$107$	6.10860	+	10.5804i	0.590541	+	1.02285i	−0.403619	+	0.914927i	$0.632248\pi$
$108$	−0.187534	−	10.3906i	−0.0180455	−	0.999837i
$109$	−3.96518	+	6.86790i	−0.379796	+	0.657825i	−0.991032	−	0.133623i	$-0.957339\pi$
$109$	−3.96518	+	6.86790i	−0.379796	+	0.657825i	0.611237	+	0.791448i	$0.290672\pi$
$110$	1.93585	−	0.560784i	0.184576	−	0.0534687i
$111$	10.0813	+	0.0748952i	0.956875	+	0.00710874i
$112$	−13.3504	−	2.84862i	−1.26149	−	0.269169i
$113$	−16.8021	−	0.978611i	−1.58061	−	0.0920600i	−0.754779	−	0.655979i	$-0.772256\pi$
$113$	−16.8021	−	0.978611i	−1.58061	−	0.0920600i	−0.825830	+	0.563919i	$0.809293\pi$
$114$	8.57840	−	6.17098i	0.803441	−	0.577965i
$115$	−0.0313041	−	0.132082i	−0.00291912	−	0.0123168i
$116$	−3.75141	+	5.48789i	−0.348310	+	0.509538i
$117$	−0.510186	+	6.97302i	−0.0471667	+	0.644656i
$118$	6.68785	−	1.52216i	0.615666	−	0.140126i
$119$	1.07988	+	18.5408i	0.0989924	+	1.69963i
$120$	3.73872	+	8.12579i	0.341297	+	0.741780i
$121$	−6.20493	−	8.33466i	−0.564084	−	0.757697i
$122$	4.25121	−	7.21390i	0.384887	−	0.653116i
$123$	−14.3714	−	13.7620i	−1.29583	−	1.24088i
$124$	8.66343	−	9.95827i	0.777999	−	0.894279i
$125$	11.9867	+	2.11358i	1.07212	+	0.189044i
$126$	9.56799	−	10.8671i	0.852384	−	0.968117i
$127$	−21.0422	+	3.71030i	−1.86719	+	0.329236i	−0.988863	−	0.148826i	$-0.952451\pi$
$127$	−21.0422	+	3.71030i	−1.86719	+	0.329236i	−0.878326	+	0.478062i	$0.841340\pi$
$128$	−1.36149	+	11.2315i	−0.120340	+	0.992733i
$129$	−1.75769	−	7.66976i	−0.154756	−	0.675285i
$130$	−2.00764	−	5.67293i	−0.176082	−	0.497549i
$131$	−1.21045	−	0.286883i	−0.105758	−	0.0250651i	0.177396	−	0.984140i	$-0.443233\pi$
$131$	−1.21045	−	0.286883i	−0.105758	−	0.0250651i	−0.283154	+	0.959074i	$0.591381\pi$
$132$	−1.90462	+	1.91921i	−0.165776	+	0.167046i
$133$	14.6233	+	1.70922i	1.26800	+	0.148209i
$134$	1.09321	−	8.68059i	0.0944387	−	0.749889i
$135$	−9.45652	−	0.762562i	−0.813888	−	0.0656308i
$136$	15.2247	−	2.26623i	1.30551	−	0.194327i
$137$	4.09702	−	1.76728i	0.350032	−	0.150989i	−0.213803	−	0.976877i	$-0.568585\pi$
$137$	4.09702	−	1.76728i	0.350032	−	0.150989i	0.563834	+	0.825888i	$0.309326\pi$
$138$	0.122788	+	0.134487i	0.0104524	+	0.0114483i
$139$	8.34749	+	7.87545i	0.708025	+	0.667987i	0.953492	−	0.301418i	$-0.0974599\pi$
$139$	8.34749	+	7.87545i	0.708025	+	0.667987i	−0.245467	+	0.969405i	$0.578941\pi$
$140$	−3.78659	+	11.8728i	−0.320026	+	1.00343i
$141$	4.39323	+	10.3963i	0.369976	+	0.875529i
$142$	8.34044	−	0.899503i	0.699914	−	0.0754846i
$143$	1.39351	−	1.16929i	0.116531	−	0.0977813i
$144$	−9.67988	−	7.09224i	−0.806657	−	0.591020i
$145$	4.64882	+	3.90082i	0.386064	+	0.323946i
$146$	11.0714	+	7.42414i	0.916278	+	0.614426i
$147$	8.00057	−	0.874935i	0.659876	−	0.0721635i
$148$	7.11715	−	9.21215i	0.585026	−	0.757234i
$149$	7.84460	+	3.38383i	0.642655	+	0.277214i	0.692363	−	0.721550i	$-0.256570\pi$
$149$	7.84460	+	3.38383i	0.642655	+	0.277214i	−0.0497079	+	0.998764i	$0.515829\pi$
$150$	−3.85797	+	1.33316i	−0.315002	+	0.108852i
$151$	−0.527119	+	1.04958i	−0.0428963	+	0.0854136i	−0.914060	−	0.405580i	$-0.867070\pi$
$151$	−0.527119	+	1.04958i	−0.0428963	+	0.0854136i	0.871163	+	0.490993i	$0.163366\pi$
$152$	0.326569	−	12.1978i	0.0264882	−	0.989373i
$153$	−5.81121	+	15.2569i	−0.469808	+	1.23345i
$154$	−3.76258	+	0.185478i	−0.303197	+	0.0149462i
$155$	−8.26905	−	8.76468i	−0.664186	−	0.703996i
$156$	6.05137	+	5.34403i	0.484498	+	0.427865i
$157$	3.49826	+	2.30084i	0.279191	+	0.183627i	0.681380	−	0.731930i	$-0.261380\pi$
$157$	3.49826	+	2.30084i	0.279191	+	0.183627i	−0.402189	+	0.915557i	$0.631750\pi$
$158$	−10.7778	−	13.0797i	−0.857435	−	1.04057i
$159$	3.91021	−	10.4998i	0.310100	−	0.832691i
$160$	10.0814	+	2.24532i	0.797001	+	0.177508i
$161$			0.253721i			0.0199960i
$162$	11.5863	−	5.26865i	0.910302	−	0.413945i
$163$			12.5416i			0.982330i	0.871066	+	0.491165i	$0.163429\pi$
$163$			12.5416i			0.982330i	−0.871066	+	0.491165i	$0.836571\pi$
$164$	−22.6948	+	3.58540i	−1.77216	+	0.279973i
$165$	1.57256	+	1.90263i	0.122424	+	0.148120i
$166$	−13.9522	+	11.4967i	−1.08290	+	0.892317i
$167$	−7.47838	−	4.91861i	−0.578695	−	0.380613i	0.226156	−	0.974091i	$-0.427384\pi$
$167$	−7.47838	−	4.91861i	−0.578695	−	0.380613i	−0.804850	+	0.593478i	$0.797755\pi$
$168$	−3.29719	−	16.3905i	−0.254384	−	1.26455i
$169$	5.19383	+	5.50514i	0.399526	+	0.423472i
$170$	−0.691854	−	14.0349i	−0.0530628	−	1.07643i
$171$	11.1110	+	6.63700i	0.849682	+	0.507544i
$172$	−8.27725	−	3.74702i	−0.631134	−	0.285707i
$173$	5.28367	−	10.5207i	0.401710	−	0.799870i	−0.598289	−	0.801280i	$-0.704153\pi$
$173$	5.28367	−	10.5207i	0.401710	−	0.799870i	0.999999	+	0.00141007i	$0.000448838\pi$
$174$	−7.99368	−	1.54467i	−0.606000	−	0.117101i
$175$	−5.22185	−	2.25249i	−0.394735	−	0.170272i
$176$	0.432105	+	3.09213i	0.0325711	+	0.233078i
$177$	4.96616	+	6.77522i	0.373280	+	0.509257i
$178$	−10.8763	+	16.2196i	−0.815216	+	1.21571i
$179$	−4.68689	−	3.93277i	−0.350315	−	0.293949i	0.450602	−	0.892725i	$-0.351209\pi$
$179$	−4.68689	−	3.93277i	−0.350315	−	0.293949i	−0.800916	+	0.598776i	$0.795654\pi$
$180$	−7.31229	+	8.15721i	−0.545026	+	0.608003i
$181$	4.24409	−	3.56121i	0.315461	−	0.264703i	−0.471284	−	0.881981i	$-0.656209\pi$
$181$	4.24409	−	3.56121i	0.315461	−	0.264703i	0.786745	+	0.617279i	$0.211765\pi$
$182$	1.20608	+	11.1831i	0.0894009	+	0.828950i
$183$	10.1768	+	1.26620i	0.752288	+	0.0935999i
$184$	0.209438	−	0.0188137i	0.0154400	−	0.00138696i
$185$	−7.73005	−	7.29293i	−0.568325	−	0.536187i
$186$	15.4088	+	4.88900i	1.12983	+	0.358479i
$187$	3.90037	−	1.68245i	0.285223	−	0.123033i
$188$	12.6255	+	3.23129i	0.920812	+	0.235666i
$189$	16.8705	+	5.46321i	1.22715	+	0.397390i
$190$	−11.0522	−	1.39188i	−0.801808	−	0.100977i
$191$	13.4244	+	1.56909i	0.971358	+	0.113535i	0.586946	−	0.809626i	$-0.300330\pi$
$191$	13.4244	+	1.56909i	0.971358	+	0.113535i	0.384412	+	0.923162i	$0.374404\pi$
$192$	−13.2853	+	3.93709i	−0.958784	+	0.284135i
$193$	−18.9616	−	4.49399i	−1.36489	−	0.323485i	−0.518058	−	0.855346i	$-0.673345\pi$
$193$	−18.9616	−	4.49399i	−1.36489	−	0.323485i	−0.846832	+	0.531861i	$0.821493\pi$
$194$	−23.5624	+	8.33871i	−1.69168	+	0.598684i
$195$	5.39828	−	5.01774i	0.386579	−	0.359328i
$196$	4.78954	−	7.96407i	0.342110	−	0.568862i
$197$	−4.89735	+	0.863534i	−0.348921	+	0.0615243i	−0.345362	−	0.938469i	$-0.612244\pi$
$197$	−4.89735	+	0.863534i	−0.348921	+	0.0615243i	−0.00355902	+	0.999994i	$0.501133\pi$
$198$	−3.08404	−	1.20629i	−0.219173	−	0.0857276i
$199$	−24.0219	−	4.23571i	−1.70287	−	0.300262i	−0.764174	−	0.645010i	$-0.776853\pi$
$199$	−24.0219	−	4.23571i	−1.70287	−	0.300262i	−0.938695	+	0.344749i	$0.887964\pi$
$200$	−1.47214	+	4.47748i	−0.104096	+	0.316606i
$201$	10.2879	−	2.99689i	0.725651	−	0.211384i
$202$	23.8533	+	14.0570i	1.67832	+	0.989045i
$203$	−6.77365	−	9.09859i	−0.475417	−	0.638595i
$204$	9.95793	+	16.0073i	0.697195	+	1.12073i
$205$	1.21960	+	20.9397i	0.0851805	+	1.46249i
$206$	−1.26657	−	5.56486i	−0.0882459	−	0.387722i
$207$	−0.0913734	+	0.203461i	−0.00635089	+	0.0141415i
$208$	9.14187	−	1.82482i	0.633874	−	0.126529i
$209$	−0.776566	−	3.27659i	−0.0537162	−	0.226647i
$210$	−15.1865	+	1.52380i	−1.04797	+	0.105152i
$211$	27.0717	+	1.57675i	1.86369	+	0.108548i	0.952707	−	0.303890i	$-0.0982854\pi$
$211$	27.0717	+	1.57675i	1.86369	+	0.108548i	0.910986	+	0.412437i	$0.135322\pi$
$212$	−6.91533	−	10.9344i	−0.474947	−	0.750974i
$213$	5.07083	+	8.93558i	0.347447	+	0.612256i
$214$	4.80744	+	16.5954i	0.328630	+	1.13444i
$215$	−4.14728	+	7.18330i	−0.282842	+	0.489897i
$216$	3.25872	−	14.3311i	0.221728	−	0.975109i
$217$	11.2614	+	19.5053i	0.764474	+	1.32411i
$218$	−7.76883	+	8.08867i	−0.526172	+	0.547834i
$219$	−2.95436	+	16.0566i	−0.199637	+	1.08500i
$220$	2.84794	−	0.114929i	0.192008	−	0.00774854i
$221$	−5.69213	−	11.3340i	−0.382894	−	0.762405i
$222$	13.8176	+	3.51440i	0.927375	+	0.235871i
$223$	9.59494	+	2.87254i	0.642525	+	0.192359i	0.591458	−	0.806336i	$-0.298553\pi$
$223$	9.59494	+	2.87254i	0.642525	+	0.192359i	0.0510670	+	0.998695i	$0.483738\pi$
$224$	−17.3678	−	8.42934i	−1.16043	−	0.563209i
$225$	−3.37625	−	3.68685i	−0.225083	−	0.245790i
$226$	−22.7403	−	7.02967i	−1.51266	−	0.467607i
$227$	−12.0010	+	7.89315i	−0.796532	+	0.523887i	−0.881324	−	0.472512i	$-0.843348\pi$
$227$	−12.0010	+	7.89315i	−0.796532	+	0.523887i	0.0847929	+	0.996399i	$0.472977\pi$
$228$	13.8675	−	5.57058i	0.918400	−	0.368920i
$229$	−6.20655	+	0.725442i	−0.410141	+	0.0479386i	−0.318662	−	0.947868i	$-0.603233\pi$
$229$	−6.20655	+	0.725442i	−0.410141	+	0.0479386i	−0.0914788	+	0.995807i	$0.529159\pi$
$230$	0.00171273	−	0.191960i	0.000112934	−	0.0126574i
$231$	−2.03998	−	4.13831i	−0.134221	−	0.272281i
$232$	−7.00830	+	6.26608i	−0.460117	+	0.411388i
$233$	4.11037	+	11.2932i	0.269279	+	0.739839i	0.998458	+	0.0555154i	$0.0176802\pi$
$233$	4.11037	+	11.2932i	0.269279	+	0.739839i	−0.729178	+	0.684324i	$0.760098\pi$
$234$	−3.06025	+	9.40221i	−0.200055	+	0.614641i
$235$	4.06917	−	11.1799i	0.265443	−	0.729299i
$236$	9.69838	+	0.173079i	0.631311	+	0.0112665i
$237$	9.45334	−	18.4796i	0.614060	−	1.20038i
$238$	−4.79149	+	25.8244i	−0.310586	+	1.67395i
$239$	3.11712	+	10.4119i	0.201630	+	0.673491i	0.997669	+	0.0682452i	$0.0217400\pi$
$239$	3.11712	+	10.4119i	0.201630	+	0.673491i	−0.796039	+	0.605246i	$0.793075\pi$
$240$	2.38394	+	12.4230i	0.153883	+	0.801898i
$241$	10.5142	−	14.1230i	0.677280	−	0.909745i	−0.322036	−	0.946728i	$-0.604367\pi$
$241$	10.5142	−	14.1230i	0.677280	−	0.909745i	0.999316	+	0.0369824i	$0.0117745\pi$
$242$	−5.69967	−	13.5443i	−0.366389	−	0.870663i
$243$	11.5611	+	10.4566i	0.741645	+	0.670792i
$244$	8.27868	−	8.46698i	0.529988	−	0.542043i
$245$	−6.80518	−	5.06627i	−0.434767	−	0.323672i
$246$	−15.0767	−	23.7603i	−0.961257	−	1.51490i
$247$	−9.63191	+	2.88360i	−0.612864	+	0.183479i
$248$	15.2659	−	10.7422i	0.969387	−	0.682133i
$249$	−19.7122	−	10.0839i	−1.24921	−	0.639041i
$250$	15.7440	+	6.95857i	0.995740	+	0.440099i
$251$	−6.97387	−	2.53828i	−0.440187	−	0.160215i	0.112413	−	0.993662i	$-0.464142\pi$
$251$	−6.97387	−	2.53828i	−0.440187	−	0.160215i	−0.552600	+	0.833447i	$0.686364\pi$
$252$	16.8156	−	11.6841i	1.05928	−	0.736026i
$253$	0.0545303	−	0.0198474i	0.00342829	−	0.00124780i
$254$	−30.1492	−	2.02604i	−1.89173	−	0.127125i
$255$	15.4364	−	7.60937i	0.966664	−	0.476517i
$256$	−5.67029	+	14.9615i	−0.354393	+	0.935096i
$257$	−2.44966	−	20.9582i	−0.152805	−	1.30733i	−0.824228	−	0.566259i	$-0.808390\pi$
$257$	−2.44966	−	20.9582i	−0.152805	−	1.30733i	0.671422	−	0.741075i	$-0.265684\pi$
$258$	0.181945	−	11.1264i	0.0113274	−	0.692698i
$259$	10.9155	+	16.5962i	0.678256	+	1.03124i
$260$	−0.837005	−	8.46906i	−0.0519089	−	0.525229i
$261$	−2.15514	−	9.73565i	−0.133400	−	0.602621i
$262$	−1.56503	−	0.803550i	−0.0966877	−	0.0496435i
$263$	2.30120	−	7.68654i	0.141898	−	0.473972i	−0.857265	−	0.514875i	$-0.827838\pi$
$263$	2.30120	−	7.68654i	0.141898	−	0.473972i	0.999163	+	0.0409028i	$0.0130234\pi$
$264$	−3.26476	+	1.99079i	−0.200932	+	0.122525i
$265$	−10.5546	+	5.30070i	−0.648361	+	0.325619i
$266$	19.5013	+	7.29559i	1.19570	+	0.447321i
$267$	−23.5228	−	4.32813i	−1.43957	−	0.264877i
$268$	4.43867	−	11.5496i	0.271135	−	0.705506i
$269$	−9.69671	+	5.59840i	−0.591219	+	0.341340i	−0.765579	−	0.643342i	$-0.777547\pi$
$269$	−9.69671	+	5.59840i	−0.591219	+	0.341340i	0.174361	+	0.984682i	$0.444214\pi$
$270$	−12.7270	−	4.24723i	−0.774538	−	0.258478i
$271$	27.7242	+	16.0065i	1.68412	+	0.972328i	0.958870	+	0.283845i	$0.0916101\pi$
$271$	27.7242	+	16.0065i	1.68412	+	0.972328i	0.725252	+	0.688483i	$0.241723\pi$
$272$	21.6724	+	2.04030i	1.31408	+	0.123711i
$273$	−11.9811	+	6.79914i	−0.725131	+	0.411503i
$274$	6.22378	−	1.04025i	0.375993	−	0.0628440i
$275$	−0.0756287	+	1.29849i	−0.00456058	+	0.0783022i
$276$	0.123093	+	0.226220i	0.00740933	+	0.0136168i
$277$	−19.7533	+	4.68162i	−1.18686	+	0.281291i	−0.776194	−	0.630495i	$-0.782852\pi$
$277$	−19.7533	+	4.68162i	−1.18686	+	0.281291i	−0.410666	+	0.911786i	$0.634704\pi$
$278$	8.79709	+	13.6388i	0.527614	+	0.818003i
$279$	2.00609	+	19.6971i	0.120102	+	1.17923i
$280$	−9.21729	+	15.0215i	−0.550838	+	0.897704i
$281$	9.63800	−	0.561349i	0.574955	−	0.0334873i	0.231795	−	0.972765i	$-0.425540\pi$
$281$	9.63800	−	0.561349i	0.574955	−	0.0334873i	0.343159	+	0.939277i	$0.388503\pi$
$282$	2.51430	+	15.7622i	0.149724	+	0.938625i
$283$	−0.0388301	+	0.0289079i	−0.00230821	+	0.00171840i	−0.598312	−	0.801263i	$-0.704162\pi$
$283$	−0.0388301	+	0.0289079i	−0.00230821	+	0.00171840i	0.596004	+	0.802982i	$0.296754\pi$
$284$	11.7569	+	1.58731i	0.697643	+	0.0941895i
$285$	−3.81565	−	13.0986i	−0.226020	−	0.775892i
$286$	2.30916	−	1.13402i	0.136544	−	0.0670560i
$287$	6.80801	−	38.6101i	0.401864	−	2.27908i
$288$	−10.8917	−	13.0143i	−0.641798	−	0.766874i
$289$	−2.19075	−	12.4244i	−0.128868	−	0.730846i
$290$	5.06337	+	6.92952i	0.297331	+	0.406915i
$291$	−20.8411	−	22.4217i	−1.22173	−	1.31438i
$292$	12.6901	+	13.9409i	0.742634	+	0.815831i
$293$	−1.39755	+	5.89673i	−0.0816458	+	0.344491i	−0.998501	−	0.0547286i	$-0.982571\pi$
$293$	−1.39755	+	5.89673i	−0.0816458	+	0.344491i	0.916855	+	0.399219i	$0.130719\pi$
$294$	11.2819	+	1.50603i	0.657973	+	0.0878335i
$295$	1.02802	−	8.79526i	0.0598536	−	0.512080i
$296$	12.8902	−	10.2410i	0.749228	−	0.595246i
$297$	−0.145535	−	4.05321i	−0.00844480	−	0.235191i
$298$	9.62655	+	7.30109i	0.557651	+	0.422941i
$299$	−0.0686273	−	0.159096i	−0.00396882	−	0.00920076i
$300$	−5.74864	+	0.525051i	−0.331898	+	0.0303138i
$301$	10.6393	−	11.2770i	0.613241	−	0.649997i
$302$	−1.07898	+	1.26283i	−0.0620886	+	0.0726676i
$303$	−4.18678	+	33.6503i	−0.240524	+	1.93316i
$304$	4.57622	−	16.6386i	0.262464	−	0.954292i
$305$	−6.94879	−	8.28124i	−0.397886	−	0.474183i
$306$	−13.1426	+	18.9832i	−0.751310	+	1.08520i
$307$	20.0195	−	23.8584i	1.14258	−	1.36167i	0.220163	−	0.975463i	$-0.429341\pi$
$307$	20.0195	−	23.8584i	1.14258	−	1.36167i	0.922413	−	0.386205i	$-0.126214\pi$
$308$	−5.22927	−	1.01859i	−0.297966	−	0.0580395i
$309$	5.63756	−	4.13227i	0.320710	−	0.235077i
$310$	−8.38846	−	14.8333i	−0.476433	−	0.842476i
$311$	2.63378	−	6.10578i	0.149348	−	0.346227i	−0.827076	−	0.562090i	$-0.809997\pi$
$311$	2.63378	−	6.10578i	0.149348	−	0.346227i	0.976424	+	0.215863i	$0.0692566\pi$
$312$	6.50087	+	9.38585i	0.368039	+	0.531369i
$313$	−24.1433	−	12.1252i	−1.36466	−	0.685357i	−0.392516	−	0.919745i	$-0.628395\pi$
$313$	−24.1433	−	12.1252i	−1.36466	−	0.685357i	−0.972143	+	0.234388i	$0.924691\pi$
$314$	4.02494	+	4.34318i	0.227141	+	0.245100i
$315$	−9.10495	−	16.3257i	−0.513006	−	0.919849i
$316$	−10.3731	−	21.6074i	−0.583530	−	1.21551i
$317$	14.4273	−	13.6115i	0.810319	−	0.764496i	−0.164765	−	0.986333i	$-0.552687\pi$
$317$	14.4273	−	13.6115i	0.810319	−	0.764496i	0.975084	+	0.221837i	$0.0712051\pi$
$318$	8.92241	−	13.0944i	0.500344	−	0.734297i
$319$	−1.42562	+	2.16755i	−0.0798194	+	0.121359i
$320$	13.0832	+	6.49470i	0.731372	+	0.363065i
$321$	−16.3107	+	13.4811i	−0.910376	+	0.752442i
$322$	−0.0858603	+	0.348391i	−0.00478481	+	0.0194151i
$323$	−23.4777			−1.30634
$324$	17.6924	−	3.31370i	0.982909	−	0.184094i
$325$	3.88363			0.215425
$326$	−4.24412	+	17.2212i	−0.235060	+	0.953792i
$327$	−12.8722	−	4.79368i	−0.711833	−	0.265091i
$328$	−32.3762	−	2.75679i	−1.78767	−	0.152218i
$329$	−12.2200	+	18.5797i	−0.673713	+	1.02433i
$330$	1.51547	+	3.14472i	0.0834239	+	0.173111i
$331$	−10.8984	+	10.2821i	−0.599028	+	0.565154i	−0.924876	−	0.380268i	$-0.875832\pi$
$331$	−10.8984	+	10.2821i	−0.599028	+	0.565154i	0.325848	+	0.945422i	$0.394350\pi$
$332$	−23.0486	+	11.0650i	−1.26496	+	0.607269i
$333$	2.77638	+	17.2397i	0.152145	+	0.944728i
$334$	−8.60430	−	9.28460i	−0.470806	−	0.508031i
$335$	−10.0941	−	5.06944i	−0.551499	−	0.276973i
$336$	1.01915	−	23.6221i	0.0555994	−	1.28869i
$337$	−0.288857	+	0.669645i	−0.0157350	+	0.0364779i	−0.925902	−	0.377763i	$-0.876694\pi$
$337$	−0.288857	+	0.669645i	−0.0157350	+	0.0364779i	0.910167	+	0.414241i	$0.135953\pi$
$338$	5.26884	+	9.31689i	0.286587	+	0.506772i
$339$	−3.16908	−	28.9787i	−0.172121	−	1.57390i
$340$	3.79946	−	19.5058i	0.206055	−	1.05785i
$341$	3.31121	−	3.94614i	0.179312	−	0.213696i
$342$	13.0109	+	12.8735i	0.703548	+	0.696118i
$343$	−5.16240	−	6.15230i	−0.278743	−	0.332193i
$344$	−10.0977	−	7.94619i	−0.544432	−	0.428430i
$345$	0.216569	−	0.0915163i	0.0116597	−	0.00492707i
$346$	10.8154	−	12.6582i	0.581439	−	0.680508i
$347$	12.7595	−	13.5242i	0.684964	−	0.726019i	−0.287833	−	0.957681i	$-0.592935\pi$
$347$	12.7595	−	13.5242i	0.684964	−	0.726019i	0.972796	+	0.231662i	$0.0744162\pi$
$348$	−10.4536	−	4.82613i	−0.560373	−	0.258708i
$349$	3.94684	+	9.14980i	0.211269	+	0.489778i	0.990593	−	0.136845i	$-0.0436962\pi$
$349$	3.94684	+	9.14980i	0.211269	+	0.489778i	−0.779323	+	0.626622i	$0.784437\pi$
$350$	−6.40802	−	4.86005i	−0.342523	−	0.259781i
$351$	−12.0564	+	1.13748i	−0.643522	+	0.0607142i
$352$	−0.453054	+	4.39212i	−0.0241479	+	0.234101i
$353$	1.69705	−	14.5192i	0.0903249	−	0.772779i	−0.869838	−	0.493337i	$-0.835777\pi$
$353$	1.69705	−	14.5192i	0.0903249	−	0.772779i	0.960163	−	0.279441i	$-0.0901492\pi$
$354$	4.52642	+	10.9838i	0.240576	+	0.583784i
$355$	2.49765	−	10.5384i	0.132561	−	0.559320i
$356$	−20.4234	+	18.5910i	−1.08244	+	0.985320i
$357$	−31.3552	+	7.18573i	−1.65949	+	0.380309i
$358$	−5.10484	−	6.98626i	−0.269799	−	0.369235i
$359$	2.18442	+	12.3885i	0.115289	+	0.653838i	0.986607	+	0.163118i	$0.0521551\pi$
$359$	2.18442	+	12.3885i	0.115289	+	0.653838i	−0.871317	+	0.490720i	$0.836734\pi$
$360$	−12.8012	+	8.72639i	−0.674680	+	0.459921i
$361$	0.0674366	−	0.382452i	0.00354930	−	0.0201291i
$362$	7.03281	−	3.45378i	0.369636	−	0.181527i
$363$	12.4474	−	12.9987i	0.653320	−	0.682253i
$364$	−2.12832	+	15.7640i	−0.111554	+	0.826260i
$365$	13.8045	−	10.2771i	0.722559	−	0.537925i
$366$	13.5455	+	5.18251i	0.708035	+	0.270894i
$367$	24.5762	−	1.43140i	1.28286	−	0.0747184i	0.596878	−	0.802332i	$-0.296408\pi$
$367$	24.5762	−	1.43140i	1.28286	−	0.0747184i	0.685987	+	0.727614i	$0.259371\pi$
$368$	0.293952	+	0.0450411i	0.0153233	+	0.00234793i
$369$	19.3642	−	28.5100i	1.00806	−	1.48417i
$370$	−8.14639	−	12.6300i	−0.423511	−	0.656603i
$371$	21.4812	−	5.09113i	1.11525	−	0.264318i
$372$	19.5038	+	11.9276i	1.01122	+	0.618419i
$373$	0.777530	−	13.3497i	0.0402590	−	0.691220i	−0.916446	−	0.400159i	$-0.868955\pi$
$373$	0.777530	−	13.3497i	0.0402590	−	0.691220i	0.956705	−	0.291061i	$-0.0940082\pi$
$374$	5.92506	−	0.990324i	0.306377	−	0.0512084i
$375$	−0.156615	+	21.0813i	−0.00808758	+	1.08863i
$376$	16.2430	+	8.70952i	0.837669	+	0.449159i
$377$	6.70844	+	3.87312i	0.345502	+	0.199476i
$378$	21.3166	+	13.2107i	1.09641	+	0.679487i
$379$	2.06197	−	1.19048i	0.105916	−	0.0611507i	−0.446106	−	0.894980i	$-0.647190\pi$
$379$	2.06197	−	1.19048i	0.105916	−	0.0611507i	0.552022	+	0.833829i	$0.313856\pi$
$380$	−14.7050	−	5.65133i	−0.754352	−	0.289907i
$381$	−12.3989	−	34.8695i	−0.635215	−	1.78642i
$382$	17.9025	+	6.69745i	0.915971	+	0.342672i
$383$	31.2085	−	15.6735i	1.59468	−	0.800879i	0.594687	−	0.803958i	$-0.297276\pi$
$383$	31.2085	−	15.6735i	1.59468	−	0.800879i	0.999995	+	0.00307833i	$0.000979863\pi$
$384$	−19.5748	+	0.910323i	−0.998920	+	0.0464547i
$385$	−1.39489	+	4.65925i	−0.0710900	+	0.237457i
$386$	−24.5160	−	12.5875i	−1.24783	−	0.640689i
$387$	12.5930	−	5.21157i	0.640138	−	0.264919i
$388$	−35.1761	+	3.47649i	−1.78580	+	0.176492i
$389$	−3.32389	−	5.05373i	−0.168528	−	0.256234i	0.741342	−	0.671127i	$-0.234189\pi$
$389$	−3.32389	−	5.05373i	−0.168528	−	0.256234i	−0.909870	+	0.414893i	$0.863819\pi$
$390$	9.11056	−	5.06320i	0.461331	−	0.256385i
$391$	−0.0469704	−	0.401858i	−0.00237540	−	0.0203228i
$392$	9.27173	−	9.31490i	0.468293	−	0.470473i
$393$	0.141258	−	2.15001i	0.00712551	−	0.108454i
$394$	−7.01691	−	0.471541i	−0.353507	−	0.0237559i
$395$	−20.5613	+	7.48369i	−1.03455	+	0.376545i
$396$	−3.82657	−	2.70005i	−0.192292	−	0.135683i
$397$	−5.87994	−	2.14012i	−0.295106	−	0.107410i	0.190225	−	0.981741i	$-0.439078\pi$
$397$	−5.87994	−	2.14012i	−0.295106	−	0.107410i	−0.485330	+	0.874331i	$0.661301\pi$
$398$	−31.5518	−	13.9453i	−1.58155	−	0.699015i
$399$	1.29358	+	25.4680i	0.0647598	+	1.27499i
$400$	−3.53664	+	5.64998i	−0.176832	+	0.282499i
$401$	5.41733	−	1.62184i	0.270528	−	0.0809909i	−0.148666	−	0.988888i	$-0.547498\pi$
$401$	5.41733	−	1.62184i	0.270528	−	0.0809909i	0.419194	+	0.907897i	$0.362313\pi$
$402$	15.1407	−	0.633654i	0.755151	−	0.0316038i
$403$	−12.3373	−	9.18481i	−0.614567	−	0.457528i
$404$	27.9968	+	27.3741i	1.39289	+	1.36191i
$405$	−1.42191	−	16.3707i	−0.0706551	−	0.813467i
$406$	−6.22208	−	14.7858i	−0.308797	−	0.733805i
$407$	2.71303	−	3.64423i	0.134480	−	0.180638i
$408$	8.25660	+	25.3498i	0.408762	+	1.25500i
$409$	−1.99127	−	6.65129i	−0.0984618	−	0.328885i	0.894539	−	0.446989i	$-0.147504\pi$
$409$	−1.99127	−	6.65129i	−0.0984618	−	0.328885i	−0.993001	+	0.118104i	$0.962318\pi$
$410$	−5.41143	+	29.1656i	−0.267251	+	1.44039i
$411$	4.19868	+	6.48826i	0.207106	+	0.320042i
$412$	0.144016	−	8.06988i	0.00709517	−	0.397575i
$413$	−5.66097	+	15.5534i	−0.278558	+	0.765332i
$414$	−0.194319	+	0.248457i	−0.00955028	+	0.0122110i
$415$	7.98287	+	21.9328i	0.391864	+	1.07664i
$416$	13.1705	+	0.587933i	0.645736	+	0.0288258i
$417$	−11.0459	+	16.5257i	−0.540918	+	0.809267i
$418$	0.0424880	−	4.76198i	0.00207816	−	0.232916i
$419$	5.67756	−	0.663612i	0.277367	−	0.0324196i	0.0237278	−	0.999718i	$-0.492446\pi$
$419$	5.67756	−	0.663612i	0.277367	−	0.0324196i	0.253639	+	0.967299i	$0.418372\pi$
$420$	−21.3687	−	3.04682i	−1.04269	−	0.148669i
$421$	23.3082	−	15.3300i	1.13597	−	0.747140i	0.164990	−	0.986295i	$-0.447241\pi$
$421$	23.3082	−	15.3300i	1.13597	−	0.747140i	0.970981	+	0.239155i	$0.0768703\pi$
$422$	36.6394	+	11.3263i	1.78358	+	0.551354i
$423$	−16.4905	+	10.4983i	−0.801796	+	0.510447i
$424$	−5.79540	−	17.3544i	−0.281450	−	0.842807i
$425$	8.68766	+	2.60091i	0.421413	+	0.126163i
$426$	3.93906	+	13.9857i	0.190848	+	0.677609i
$427$	9.06854	+	18.0570i	0.438858	+	0.873837i
$428$	0.985256	+	24.4145i	0.0476241	+	1.18012i
$429$	2.39852	+	2.04315i	0.115802	+	0.0986443i
$430$	−8.12561	+	8.46013i	−0.391852	+	0.407984i
$431$	0.130048	+	0.225250i	0.00626419	+	0.0108499i	0.869141	−	0.494565i	$-0.164673\pi$
$431$	0.130048	+	0.225250i	0.00626419	+	0.0108499i	−0.862876	+	0.505415i	$0.831339\pi$
$432$	9.32436	−	18.5757i	0.448618	−	0.893723i
$433$	−10.7349	+	18.5933i	−0.515885	+	0.893539i	0.483945	+	0.875099i	$0.339204\pi$
$433$	−10.7349	+	18.5933i	−0.515885	+	0.893539i	−0.999830	+	0.0184408i	$0.994130\pi$
$434$	8.86266	+	30.5942i	0.425421	+	1.46857i
$435$	−5.32305	+	9.06361i	−0.255220	+	0.434567i
$436$	−13.4049	+	8.47778i	−0.641976	+	0.406012i
$437$	−0.320193	−	0.0186491i	−0.0153169	−	0.000892109i
$438$	−9.49034	+	21.0480i	−0.453466	+	1.00571i
$439$	1.30903	+	5.52323i	0.0624765	+	0.263609i	0.995315	−	0.0966858i	$-0.0308242\pi$
$439$	1.30903	+	5.52323i	0.0624765	+	0.263609i	−0.932838	+	0.360295i	$0.882676\pi$
$440$	3.94948	+	0.805943i	0.188284	+	0.0384218i
$441$	3.79919	+	13.4123i	0.180914	+	0.638681i
$442$	−3.98056	−	17.4892i	−0.189336	−	0.831878i
$443$	0.731471	+	12.5589i	0.0347533	+	0.596690i	0.970062	+	0.242858i	$0.0780848\pi$
$443$	0.731471	+	12.5589i	0.0347533	+	0.596690i	−0.935309	+	0.353833i	$0.884878\pi$
$444$	17.7840	+	9.50165i	0.843992	+	0.450929i
$445$	15.0558	+	20.2235i	0.713715	+	0.958685i
$446$	12.2030	+	7.19134i	0.577829	+	0.340520i
$447$	−3.51940	+	14.3728i	−0.166462	+	0.679811i
$448$	−20.9957	−	17.4519i	−0.991952	−	0.824525i
$449$	8.28292	+	1.46050i	0.390895	+	0.0689254i	0.365642	−	0.930756i	$-0.380850\pi$
$449$	8.28292	+	1.46050i	0.390895	+	0.0689254i	0.0252536	+	0.999681i	$0.491961\pi$
$450$	−3.38838	−	6.20506i	−0.159730	−	0.292509i
$451$	−8.83075	+	1.55710i	−0.415824	+	0.0733209i
$452$	−28.8465	−	17.3481i	−1.35682	−	0.815984i
$453$	−1.94446	−	0.597908i	−0.0913587	−	0.0280922i
$454$	−19.1499	+	6.77714i	−0.898751	+	0.318067i
$455$	14.1302	+	3.34893i	0.662436	+	0.157000i
$456$	20.9270	−	2.95628i	0.979997	−	0.138440i
$457$	−28.5445	−	3.33638i	−1.33526	−	0.156069i	−0.581674	−	0.813422i	$-0.697602\pi$
$457$	−28.5445	−	3.33638i	−1.33526	−	0.156069i	−0.753583	+	0.657353i	$0.771676\pi$
$458$	−8.76789	−	1.10420i	−0.409697	−	0.0515959i
$459$	−27.7318	−	5.52977i	−1.29441	−	0.258107i
$460$	0.0673118	−	0.263006i	0.00313843	−	0.0122627i
$461$	−4.64327	+	2.00291i	−0.216259	+	0.0932849i	−0.501453	−	0.865185i	$-0.667201\pi$
$461$	−4.64327	+	2.00291i	−0.216259	+	0.0932849i	0.285194	+	0.958470i	$0.407942\pi$
$462$	−1.40073	−	6.37277i	−0.0651681	−	0.296488i
$463$	−13.6692	−	12.8962i	−0.635260	−	0.599337i	0.299724	−	0.954026i	$-0.403105\pi$
$463$	−13.6692	−	12.8962i	−0.635260	−	0.599337i	−0.934984	+	0.354689i	$0.884587\pi$
$464$	−11.7438	+	6.23250i	−0.545190	+	0.289336i
$465$	12.5872	−	16.6479i	0.583717	−	0.772028i
$466$	1.82241	+	16.8979i	0.0844217	+	0.782781i
$467$	3.34797	−	2.80928i	0.154926	−	0.129998i	−0.562030	−	0.827117i	$-0.689979\pi$
$467$	3.34797	−	2.80928i	0.154926	−	0.129998i	0.716956	+	0.697119i	$0.245535\pi$
$468$	−7.38387	+	11.8748i	−0.341320	+	0.548914i
$469$	16.1736	+	13.5712i	0.746827	+	0.626662i
$470$	9.37084	−	13.9745i	0.432245	−	0.644595i
$471$	−2.92186	+	6.63760i	−0.134632	+	0.305845i
$472$	13.2586	+	3.51964i	0.610274	+	0.162004i
$473$	−3.25595	−	1.40448i	−0.149709	−	0.0645781i
$474$	19.2342	−	22.1757i	0.883457	−	1.01857i
$475$	3.22644	−	6.42436i	0.148039	−	0.294770i
$476$	−15.3184	+	33.8387i	−0.702118	+	1.55100i
$477$	19.0594	+	3.65347i	0.872671	+	0.167281i
$478$	0.756771	+	15.3518i	0.0346139	+	0.702173i
$479$	16.4946	+	17.4833i	0.753658	+	0.798830i	0.984727	−	0.174107i	$-0.0557038\pi$
$479$	16.4946	+	17.4833i	0.753658	+	0.798830i	−0.231069	+	0.972937i	$0.574222\pi$
$480$	−0.930530	+	17.8650i	−0.0424727	+	0.815424i
$481$	−11.3336	−	7.45421i	−0.516767	−	0.339883i
$482$	19.2167	−	15.8347i	0.875295	−	0.721251i
$483$	−0.433336	+	0.0730938i	−0.0197175	+	0.00332588i
$484$	−3.24292	−	20.5269i	−0.147405	−	0.933042i
$485$			32.2690i			1.46526i
$486$	12.3363	+	18.2706i	0.559587	+	0.828772i
$487$		−	14.9714i		−	0.678421i	−0.940711	−	0.339210i	$-0.889840\pi$
$487$		−	14.9714i		−	0.678421i	0.940711	−	0.339210i	$-0.110160\pi$
$488$	14.2330	−	8.82471i	0.644295	−	0.399476i
$489$	−21.4200	+	3.61306i	−0.968647	+	0.163388i
$490$	−7.62994	−	9.25955i	−0.344686	−	0.418304i
$491$	10.5104	+	6.91278i	0.474326	+	0.311969i	0.764068	−	0.645136i	$-0.223199\pi$
$491$	10.5104	+	6.91278i	0.474326	+	0.311969i	−0.289742	+	0.957105i	$0.593569\pi$
$492$	−12.6617	−	37.7280i	−0.570832	−	1.70091i
$493$	12.4129	+	13.1569i	0.559048	+	0.592556i
$494$	−14.2017	+	0.700077i	−0.638963	+	0.0314980i
$495$	−2.79652	+	3.23394i	−0.125694	+	0.145355i
$496$	24.5973	−	9.58442i	1.10445	−	0.430353i
$497$	−9.08527	+	18.0903i	−0.407530	+	0.811459i
$498$	−23.6549	−	20.5172i	−1.06000	−	0.919397i
$499$	12.6434	+	5.45383i	0.565996	+	0.244147i	0.659797	−	0.751444i	$-0.270642\pi$
$499$	12.6434	+	5.45383i	0.565996	+	0.244147i	−0.0938006	+	0.995591i	$0.529902\pi$
$500$	19.2638	+	14.8829i	0.861502	+	0.665582i
$501$	6.24619	−	14.1895i	0.279059	−	0.633940i
$502$	−8.71706	−	5.84538i	−0.389061	−	0.260892i
$503$	−23.7244	−	19.9071i	−1.05782	−	0.887615i	−0.0639243	−	0.997955i	$-0.520362\pi$
$503$	−23.7244	−	19.9071i	−1.05782	−	0.887615i	−0.993894	+	0.110340i	$0.964806\pi$
$504$	27.0439	−	10.3532i	1.20463	−	0.461170i
$505$	27.3826	−	22.9767i	1.21851	−	1.02245i
$506$	0.0815936	−	0.00879974i	0.00362728	−	0.000391196i
$507$	−7.90609	+	10.4566i	−0.351122	+	0.464396i
$508$	−40.7131	−	12.9846i	−1.80635	−	0.576100i
$509$	8.86560	+	8.36426i	0.392961	+	0.370739i	0.857212	−	0.514964i	$-0.172195\pi$
$509$	8.86560	+	8.36426i	0.392961	+	0.370739i	−0.464251	+	0.885704i	$0.653676\pi$
$510$	23.7712	−	5.22490i	1.05261	−	0.231363i
$511$	−29.5371	+	12.7411i	−1.30664	+	0.563631i
$512$	−12.8491	+	18.6253i	−0.567855	+	0.823128i
$513$	−8.13454	+	20.8888i	−0.359149	+	0.922265i
$514$	3.72864	−	29.6072i	0.164463	−	1.30592i
$515$	−7.31841	−	0.855400i	−0.322488	−	0.0376934i
$516$	4.01505	−	15.2164i	0.176753	−	0.669864i
$517$	4.94911	+	1.17296i	0.217662	+	0.0515867i
$518$	9.37215	+	26.4826i	0.411789	+	1.16358i
$519$	19.4906	+	5.99324i	0.855544	+	0.263074i
$520$	1.71665	−	11.9124i	0.0752802	−	0.522391i
$521$	18.1550	−	3.20122i	0.795385	−	0.140248i	0.238833	−	0.971061i	$-0.423235\pi$
$521$	18.1550	−	3.20122i	0.795385	−	0.140248i	0.556552	+	0.830813i	$0.312124\pi$
$522$	0.335306	−	14.0976i	0.0146759	−	0.617035i
$523$	17.1639	+	3.02645i	0.750523	+	0.132337i	0.535809	−	0.844340i	$-0.320007\pi$
$523$	17.1639	+	3.02645i	0.750523	+	0.132337i	0.214714	+	0.976677i	$0.431118\pi$
$524$	−1.87706	−	1.63299i	−0.0819997	−	0.0713375i
$525$	2.34273	−	9.56744i	0.102245	−	0.417557i
$526$	5.76100	−	9.77587i	0.251192	−	0.426248i
$527$	−21.4474	−	28.8089i	−0.934264	−	1.25493i
$528$	−5.15664	+	1.62881i	−0.224414	+	0.0708847i
$529$	1.33701	+	22.9556i	0.0581309	+	0.998068i
$530$	−16.2865	+	3.70683i	−0.707442	+	0.161014i
$531$	−10.1409	+	10.4337i	−0.440077	+	0.452784i
$532$	24.3090	+	16.6171i	1.05393	+	0.720444i
$533$	6.17444	+	26.0520i	0.267444	+	1.12844i
$534$	−30.8352	−	13.9033i	−1.33437	−	0.601654i
$535$	22.2686	+	1.29700i	0.962756	+	0.0560742i
$536$	10.0033	−	14.3571i	0.432077	−	0.620130i
$537$	5.36664	−	9.13783i	0.231587	−	0.394327i
$538$	−15.2093	+	4.40591i	−0.655722	+	0.189952i
$539$	1.81346	−	3.14101i	0.0781114	−	0.135293i
$540$	−16.0385	−	10.1389i	−0.690186	−	0.436307i
$541$	−9.30910	−	16.1238i	−0.400230	−	0.693218i	0.593524	−	0.804816i	$-0.297736\pi$
$541$	−9.30910	−	16.1238i	−0.400230	−	0.693218i	−0.993753	+	0.111598i	$0.964403\pi$
$542$	32.6521	+	31.3610i	1.40253	+	1.34707i
$543$	7.30495	+	6.22264i	0.313485	+	0.267039i
$544$	29.0686	+	10.1356i	1.24630	+	0.434562i
$545$	6.49834	+	12.9393i	0.278358	+	0.554257i
$546$	−18.7525	+	5.28162i	−0.802533	+	0.226033i
$547$	4.68254	+	1.40186i	0.200211	+	0.0599392i	0.385339	−	0.922775i	$-0.374085\pi$
$547$	4.68254	+	1.40186i	0.200211	+	0.0599392i	−0.185128	+	0.982714i	$0.559270\pi$
$548$	8.89808	+	0.677755i	0.380107	+	0.0289523i
$549$	0.769228	+	17.7459i	0.0328299	+	0.757377i
$550$	−0.543265	+	1.75741i	−0.0231649	+	0.0749361i
$551$	11.9802	−	7.87951i	0.510374	−	0.335678i
$552$	0.0924687	+	0.352284i	0.00393573	+	0.0149942i
$553$	40.6220	−	4.74803i	1.72742	−	0.201907i
$554$	−28.7081	−	0.256144i	−1.21969	−	0.0108825i
$555$	10.2288	−	15.3033i	0.434190	−	0.649591i
$556$	7.46409	+	21.7049i	0.316548	+	0.920491i
$557$	14.2222	+	39.0751i	0.602612	+	1.65566i	0.745959	+	0.665992i	$0.231991\pi$
$557$	14.2222	+	39.0751i	0.602612	+	1.65566i	−0.143347	+	0.989673i	$0.545786\pi$
$558$	−3.91096	+	27.7255i	−0.165564	+	1.17371i
$559$	−3.62115	+	9.94904i	−0.153159	+	0.420800i
$560$	−17.7399	+	17.5072i	−0.749646	+	0.739816i
$561$	3.99715	+	6.17684i	0.168760	+	0.260786i
$562$	13.4242	+	2.49074i	0.566265	+	0.105065i
$563$	0.563742	+	1.88303i	0.0237589	+	0.0793603i	0.969047	−	0.246877i	$-0.0794044\pi$
$563$	0.563742	+	1.88303i	0.0237589	+	0.0793603i	−0.945288	+	0.326237i	$0.894219\pi$
$564$	−1.88154	+	22.4944i	−0.0792273	+	0.947184i
$565$	−18.3504	+	24.6489i	−0.772007	+	1.03699i
$566$	−0.0631012	+	0.0265540i	−0.00265234	+	0.00111615i
$567$	−4.47057	+	30.3874i	−0.187746	+	1.27615i
$568$	15.6066	+	6.15816i	0.654837	+	0.258391i
$569$	10.4066	+	7.74744i	0.436268	+	0.324790i	0.792787	−	0.609498i	$-0.208629\pi$
$569$	10.4066	+	7.74744i	0.436268	+	0.324790i	−0.356519	+	0.934288i	$0.616037\pi$
$570$	−0.806771	−	19.2772i	−0.0337919	−	0.807435i
$571$	−32.7794	+	9.81350i	−1.37177	+	0.410682i	−0.886115	−	0.463466i	$-0.846606\pi$
$571$	−32.7794	+	9.81350i	−1.37177	+	0.410682i	−0.485660	+	0.874148i	$0.661421\pi$
$572$	3.55454	−	0.775725i	0.148623	−	0.0324347i
$573$	1.18752	+	23.3799i	0.0496094	+	0.976711i
$574$	22.4141	−	50.7128i	0.935547	−	2.11671i
$575$	0.116418	+	0.0423726i	0.00485496	+	0.00176706i
$576$	−10.5516	−	21.5561i	−0.439649	−	0.898170i
$577$	8.38296	−	3.05115i	0.348987	−	0.127021i	−0.161578	−	0.986860i	$-0.551658\pi$
$577$	8.38296	−	3.05115i	0.348987	−	0.127021i	0.510565	+	0.859839i	$0.329436\pi$
$578$	1.19628	−	17.8016i	0.0497587	−	0.740450i
$579$	2.21279	−	33.6797i	0.0919604	−	1.39968i
$580$	4.60768	+	11.2286i	0.191324	+	0.466242i
$581$	−5.06474	−	43.3316i	−0.210121	−	1.79770i
$582$	−21.0299	−	37.8405i	−0.871718	−	1.56854i
$583$	−2.77457	−	4.21853i	−0.114911	−	0.174714i
$584$	12.7075	+	23.4371i	0.525840	+	0.969833i
$585$	10.1251	+	7.77431i	0.418621	+	0.321428i
$586$	−3.91450	+	7.62403i	−0.161706	+	0.314946i
$587$	8.17413	−	27.3035i	0.337382	−	1.12694i	−0.606066	−	0.795415i	$-0.707253\pi$
$587$	8.17413	−	27.3035i	0.337382	−	1.12694i	0.943448	−	0.331521i	$-0.107562\pi$
$588$	14.9818	+	5.88582i	0.617841	+	0.242727i
$589$	−25.4433	+	12.7781i	−1.04837	+	0.526512i
$590$	4.38796	−	11.7291i	0.180649	−	0.482881i
$591$	−2.88571	−	8.11552i	−0.118702	−	0.333828i
$592$	21.1655	−	9.70010i	0.869897	−	0.398672i
$593$	6.29274	−	3.63311i	0.258412	−	0.149194i	−0.365198	−	0.930930i	$-0.618999\pi$
$593$	6.29274	−	3.63311i	0.258412	−	0.149194i	0.623610	+	0.781736i	$0.285665\pi$
$594$	1.17179	−	5.61483i	0.0480790	−	0.230379i
$595$	29.3665	+	16.9547i	1.20391	+	0.695077i
$596$	10.7478	+	13.2830i	0.440246	+	0.544093i
$597$	0.313865	−	42.2479i	0.0128456	−	1.72909i
$598$	−0.0403953	−	0.241683i	−0.00165189	−	0.00988316i
$599$	0.757499	−	13.0057i	0.0309506	−	0.531400i	−0.946825	−	0.321748i	$-0.895730\pi$
$599$	0.757499	−	13.0057i	0.0309506	−	0.531400i	0.977776	−	0.209653i	$-0.0672333\pi$
$600$	−8.07130	−	1.22440i	−0.329510	−	0.0499861i
$601$	−24.2080	+	5.73741i	−0.987467	+	0.234034i	−0.692456	−	0.721460i	$-0.743471\pi$
$601$	−24.2080	+	5.73741i	−0.987467	+	0.234034i	−0.295011	+	0.955494i	$0.595323\pi$
$602$	18.4254	−	11.8844i	0.750962	−	0.484373i
$603$	8.08227	+	16.7075i	0.329136	+	0.680384i
$604$	−1.90893	+	1.36889i	−0.0776733	+	0.0556995i
$605$	−18.9395	+	1.10310i	−0.770000	+	0.0448474i
$606$	−17.1364	+	44.7893i	−0.696119	+	1.81944i
$607$	−30.7174	+	22.8683i	−1.24678	+	0.928194i	−0.999173	−	0.0406661i	$-0.987052\pi$
$607$	−30.7174	+	22.8683i	−1.24678	+	0.928194i	−0.247608	+	0.968860i	$0.579645\pi$
$608$	11.9143	−	21.2984i	0.483190	−	0.863764i
$609$	13.5883	−	14.1901i	0.550625	−	0.575010i
$610$	−6.73917	−	13.7227i	−0.272861	−	0.555616i
$611$	2.63710	−	14.9557i	0.106686	−	0.605044i
$612$	−24.4704	+	21.6189i	−0.989158	+	0.873892i
$613$	−4.72457	−	26.7944i	−0.190824	−	1.08222i	−0.918242	−	0.396021i	$-0.870391\pi$
$613$	−4.72457	−	26.7944i	−0.190824	−	1.08222i	0.727418	−	0.686195i	$-0.240720\pi$
$614$	35.5632	−	25.9859i	1.43521	−	1.04871i
$615$	−35.4121	+	8.11545i	−1.42795	+	0.327246i
$616$	−6.83577	−	3.16827i	−0.275421	−	0.127653i
$617$	−5.63074	+	23.7580i	−0.226685	+	0.956459i	0.734073	+	0.679071i	$0.237617\pi$
$617$	−5.63074	+	23.7580i	−0.226685	+	0.956459i	−0.960758	+	0.277389i	$0.910531\pi$
$618$	9.13948	−	3.76637i	0.367644	−	0.151505i
$619$	4.80891	−	41.1429i	0.193287	−	1.65367i	−0.453688	−	0.891161i	$-0.649892\pi$
$619$	4.80891	−	41.1429i	0.193287	−	1.65367i	0.646975	−	0.762512i	$-0.276034\pi$
$620$	−6.49877	−	23.2067i	−0.260997	−	0.932005i
$621$	−0.373819	−	0.0974443i	−0.0150009	−	0.00391030i
$622$	5.68274	−	7.49274i	0.227857	−	0.300431i
$623$	−18.6656	−	43.2717i	−0.747821	−	1.73364i
$624$	5.75032	+	15.0879i	0.230197	+	0.604000i
$625$	9.53267	−	10.1040i	0.381307	−	0.404162i
$626$	−29.0486	−	24.8197i	−1.16102	−	0.991994i
$627$	5.37245	−	2.27026i	0.214555	−	0.0906655i
$628$	4.05701	+	7.32580i	0.161892	+	0.292331i
$629$	−20.3610	−	24.2653i	−0.811846	−	0.967520i
$630$	−6.97758	−	25.4984i	−0.277993	−	1.01588i
$631$	−4.34867	+	5.18255i	−0.173118	+	0.206314i	−0.845626	−	0.533776i	$-0.820773\pi$
$631$	−4.34867	+	5.18255i	−0.173118	+	0.206314i	0.672508	+	0.740090i	$0.265217\pi$
$632$	−6.93150	−	33.1800i	−0.275720	−	1.31983i
$633$	5.10605	+	46.6907i	0.202947	+	1.85579i
$634$	24.4167	−	13.8080i	0.969713	−	0.548387i
$635$	−15.4518	+	35.8212i	−0.613185	+	1.42152i
$636$	16.6828	−	14.9609i	0.661517	−	0.593239i
$637$	−9.67743	−	4.86019i	−0.383434	−	0.192568i
$638$	−2.69107	+	2.49389i	−0.106540	+	0.0987340i
$639$	−13.8005	+	11.2348i	−0.545938	+	0.444443i
$640$	15.7670	+	13.3455i	0.623247	+	0.527526i
$641$	3.68305	−	3.47478i	0.145472	−	0.137246i	−0.610066	−	0.792351i	$-0.708857\pi$
$641$	3.68305	−	3.47478i	0.145472	−	0.137246i	0.755538	+	0.655105i	$0.227376\pi$
$642$	−26.9588	+	12.9917i	−1.06398	+	0.512741i
$643$	−8.65690	+	13.1622i	−0.341395	+	0.519066i	−0.964853	−	0.262791i	$-0.915357\pi$
$643$	−8.65690	+	13.1622i	−0.341395	+	0.519066i	0.623458	+	0.781857i	$0.285727\pi$
$644$	−0.235795	+	0.449331i	−0.00929161	+	0.0177061i
$645$	−13.4633	−	5.01382i	−0.530117	−	0.197419i
$646$	−32.2379	−	7.94497i	−1.26838	−	0.312591i
$647$	19.7833			0.777761			0.388881	−	0.921288i	$-0.372862\pi$
$647$	19.7833			0.777761			0.388881	+	0.921288i	$0.372862\pi$
$648$	25.4152	+	1.43704i	0.998405	+	0.0564523i
$649$	3.78561			0.148598
$650$	5.33272	+	1.31424i	0.209167	+	0.0515486i
$651$	−30.0693	+	24.8529i	−1.17851	+	0.974060i
$652$	−11.6554	+	22.2106i	−0.456462	+	0.869836i
$653$	4.39766	−	6.68632i	0.172094	−	0.261656i	−0.739134	−	0.673558i	$-0.764765\pi$
$653$	4.39766	−	6.68632i	0.172094	−	0.261656i	0.911228	+	0.411902i	$0.135135\pi$
$654$	−16.0529	−	10.9383i	−0.627720	−	0.427723i
$655$	−1.65208	+	1.55865i	−0.0645519	+	0.0609016i
$656$	−43.5237	−	14.7417i	−1.69932	−	0.575566i
$657$	−28.2745	−	0.420133i	−1.10309	−	0.0163909i
$658$	−23.0671	+	21.3770i	−0.899251	+	0.833361i
$659$	−4.28936	−	2.15420i	−0.167090	−	0.0839157i	0.363289	−	0.931677i	$-0.381654\pi$
$659$	−4.28936	−	2.15420i	−0.167090	−	0.0839157i	−0.530378	+	0.847761i	$0.677950\pi$
$660$	1.01675	+	4.83095i	0.0395768	+	0.188045i
$661$	13.5682	−	31.4547i	0.527743	−	1.22345i	−0.420903	−	0.907106i	$-0.638287\pi$
$661$	13.5682	−	31.4547i	0.527743	−	1.22345i	0.948646	−	0.316340i	$-0.102454\pi$
$662$	−18.4444	+	10.4306i	−0.716861	+	0.405395i
$663$	17.7177	−	12.9869i	0.688099	−	0.504369i
$664$	−35.3932	+	7.39385i	−1.37352	+	0.286937i
$665$	17.2790	−	20.5923i	0.670049	−	0.798534i
$666$	−2.02166	+	24.6118i	−0.0783377	+	0.953689i
$667$	0.158838	+	0.189296i	0.00615024	+	0.00732957i
$668$	−8.67286	−	15.6607i	−0.335563	−	0.605930i
$669$	−2.14189	+	17.2150i	−0.0828104	+	0.665570i
$670$	−12.1450	−	10.3769i	−0.469201	−	0.400894i
$671$	3.17146	−	3.36155i	0.122433	−	0.129771i
$672$	9.39324	−	32.0912i	0.362352	−	1.23795i
$673$	−10.3724	−	24.0460i	−0.399827	−	0.926904i	−0.992588	−	0.121525i	$-0.961221\pi$
$673$	−10.3724	−	24.0460i	−0.399827	−	0.926904i	0.592761	−	0.805378i	$-0.298038\pi$
$674$	−0.623248	+	0.821758i	−0.0240066	+	0.0316529i
$675$	5.32421	−	6.82851i	0.204929	−	0.262830i
$676$	4.08191	+	14.5763i	0.156997	+	0.560626i
$677$	0.540250	−	4.62213i	0.0207635	−	0.177643i	−0.978877	−	0.204449i	$-0.934460\pi$
$677$	0.540250	−	4.62213i	0.0207635	−	0.177643i	0.999641	+	0.0268063i	$0.00853374\pi$
$678$	5.45495	−	40.8638i	0.209496	−	1.56937i
$679$	13.9097	−	58.6897i	0.533806	−	2.25230i
$680$	11.8180	−	25.4982i	0.453200	−	0.977813i
$681$	−16.9382	−	18.2228i	−0.649075	−	0.698300i
$682$	5.88210	−	4.29803i	0.225237	−	0.164580i
$683$	8.69623	+	49.3187i	0.332752	+	1.88713i	0.448390	+	0.893838i	$0.351998\pi$
$683$	8.69623	+	49.3187i	0.332752	+	1.88713i	−0.115638	+	0.993291i	$0.536891\pi$
$684$	13.5092	+	22.0799i	0.516537	+	0.844245i
$685$	1.41465	−	8.02289i	0.0540511	−	0.306539i
$686$	−5.00667	−	10.1949i	−0.191155	−	0.389243i
$687$	−3.02703	−	10.3913i	−0.115488	−	0.396454i
$688$	−11.1764	−	14.3283i	−0.426098	−	0.546260i
$689$	−12.0927	+	9.00270i	−0.460696	+	0.342976i
$690$	0.328346	−	0.0523759i	0.0124999	−	0.00199392i
$691$	9.06206	−	0.527805i	0.344737	−	0.0200786i	0.115097	−	0.993354i	$-0.463282\pi$
$691$	9.06206	−	0.527805i	0.344737	−	0.0200786i	0.229640	+	0.973276i	$0.426245\pi$
$692$	19.1345	−	13.7213i	0.727385	−	0.521607i
$693$	6.48023	−	4.67633i	0.246163	−	0.177639i
$694$	22.0970	−	14.2527i	0.838792	−	0.541023i
$695$	20.3886	−	4.83219i	0.773385	−	0.183296i
$696$	−12.7210	−	10.1645i	−0.482188	−	0.385283i
$697$	−3.63516	+	62.4133i	−0.137692	+	2.36407i
$698$	2.32318	+	13.8995i	0.0879337	+	0.526103i
$699$	−18.1037	+	10.2736i	−0.684745	+	0.388584i
$700$	−7.15437	−	8.84198i	−0.270410	−	0.334195i
$701$	−9.30476	−	5.37211i	−0.351436	−	0.202902i	0.313882	−	0.949462i	$-0.398371\pi$
$701$	−9.30476	−	5.37211i	−0.351436	−	0.202902i	−0.665318	+	0.746560i	$0.731704\pi$
$702$	−16.9399	−	2.51803i	−0.639355	−	0.0950368i
$703$	−21.7466	+	12.5554i	−0.820188	+	0.473536i
$704$	−2.10841	+	5.87762i	−0.0794638	+	0.221521i
$705$	20.2668	+	3.72903i	0.763291	+	0.140443i
$706$	7.24363	−	19.3624i	0.272618	−	0.728715i
$707$	−59.7068	+	29.9859i	−2.24550	+	1.12773i
$708$	2.49838	+	16.6140i	0.0938947	+	0.624391i
$709$	−2.47824	+	8.27789i	−0.0930722	+	0.310883i	−0.991831	−	0.127561i	$-0.959285\pi$
$709$	−2.47824	+	8.27789i	−0.0930722	+	0.310883i	0.898759	+	0.438444i	$0.144470\pi$
$710$	6.99583	−	13.6254i	0.262549	−	0.511351i
$711$	34.2851	+	10.8219i	1.28579	+	0.405851i
$712$	−34.3352	+	18.6164i	−1.28677	+	0.697681i
$713$	−0.269620	−	0.409937i	−0.0100973	−	0.0153523i
$714$	−45.4864	−	0.743820i	−1.70229	−	0.0278368i
$715$	−0.385584	−	3.29888i	−0.0144200	−	0.123371i
$716$	−4.64541	−	11.3205i	−0.173607	−	0.423068i
$717$	−16.8848	+	8.32335i	−0.630573	+	0.310841i
$718$	−1.19282	+	17.7502i	−0.0445157	+	0.662430i
$719$	−8.92843	+	3.24968i	−0.332974	+	0.121193i	−0.503096	−	0.864230i	$-0.667806\pi$
$719$	−8.92843	+	3.24968i	−0.332974	+	0.121193i	0.170122	+	0.985423i	$0.445584\pi$
$720$	−20.5307	+	7.65048i	−0.765133	+	0.285117i
$721$	12.9418	+	4.71041i	0.481976	+	0.175425i
$722$	0.222023	−	0.502335i	0.00826283	−	0.0186950i
$723$	27.1501	+	13.8888i	1.00972	+	0.516531i
$724$	10.8257	−	2.36255i	0.402335	−	0.0878036i
$725$	−5.30605	+	1.58853i	−0.197062	+	0.0589964i
$726$	21.4907	−	13.6366i	0.797595	−	0.506100i
$727$	−24.8313	−	18.4862i	−0.920942	−	0.685616i	0.0284884	−	0.999594i	$-0.490931\pi$
$727$	−24.8313	−	18.4862i	−0.920942	−	0.685616i	−0.949430	+	0.313978i	$0.898338\pi$
$728$	−8.25708	+	20.9258i	−0.306028	+	0.775562i
$729$	−14.5285	+	22.7579i	−0.538093	+	0.842886i
$730$	22.4331	−	9.44022i	0.830287	−	0.349398i
$731$	−14.7635	+	19.8308i	−0.546048	+	0.733470i
$732$	16.8459	+	11.7001i	0.622644	+	0.432449i
$733$	11.8288	+	39.5109i	0.436906	+	1.45937i	0.839182	+	0.543850i	$0.183034\pi$
$733$	11.8288	+	39.5109i	0.436906	+	1.45937i	−0.402276	+	0.915518i	$0.631781\pi$
$734$	34.2306	+	6.35119i	1.26347	+	0.234427i
$735$	6.69232	−	13.0823i	0.246850	−	0.482547i
$736$	0.388391	+	0.161322i	0.0143163	+	0.00594640i
$737$	1.65158	−	4.53768i	0.0608368	−	0.167148i
$738$	36.2375	−	32.5950i	1.33392	−	1.19984i
$739$	−3.06933	−	8.43292i	−0.112907	−	0.310210i	0.870350	−	0.492434i	$-0.163893\pi$
$739$	−3.06933	−	8.43292i	−0.112907	−	0.310210i	−0.983257	+	0.182224i	$0.941670\pi$
$740$	−6.91199	−	20.0994i	−0.254090	−	0.738869i
$741$	−7.69981	−	15.6198i	−0.282860	−	0.573809i
$742$	31.2193	+	0.278549i	1.14610	+	0.0102259i
$743$	−46.3178	+	5.41377i	−1.69924	+	0.198612i	−0.909750	−	0.415157i	$-0.863727\pi$
$743$	−46.3178	+	5.41377i	−1.69924	+	0.198612i	−0.789485	+	0.613769i	$0.789652\pi$
$744$	22.7449	+	22.9783i	0.833867	+	0.842427i
$745$	13.0324	−	8.57152i	0.477469	−	0.314036i
$746$	5.58524	−	18.0677i	0.204490	−	0.661506i
$747$	11.5437	−	36.5720i	0.422362	−	1.33810i
$748$	8.47099	+	0.645224i	0.309730	+	0.0235917i
$749$	−39.9423	−	11.9579i	−1.45946	−	0.436934i
$750$	−7.34905	+	28.8943i	−0.268349	+	1.05507i
$751$	11.0537	+	22.0097i	0.403355	+	0.803145i	1.00000		0.000640082i	$0.000203744\pi$
$751$	11.0537	+	22.0097i	0.403355	+	0.803145i	−0.596645	+	0.802505i	$0.703500\pi$
$752$	19.3564	+	17.4560i	0.705855	+	0.636555i
$753$	2.32611	−	12.6421i	0.0847681	−	0.460704i
$754$	7.90087	+	7.58846i	0.287733	+	0.276355i
$755$	1.07222	+	1.85714i	0.0390220	+	0.0675881i
$756$	24.7998	+	25.3537i	0.901961	+	0.922104i
$757$	6.06705	−	10.5084i	0.220511	−	0.381935i	−0.734453	−	0.678660i	$-0.762561\pi$
$757$	6.06705	−	10.5084i	0.220511	−	0.381935i	0.954963	+	0.296725i	$0.0958943\pi$
$758$	3.23421	−	0.936899i	0.117472	−	0.0340297i
$759$	0.0496074	+	0.0874159i	0.00180063	+	0.00317300i
$760$	−18.2795	−	12.7363i	−0.663066	−	0.461992i
$761$	46.7436	+	2.72251i	1.69446	+	0.0986908i	0.877982	−	0.478693i	$-0.158889\pi$
$761$	46.7436	+	2.72251i	1.69446	+	0.0986908i	0.816473	+	0.577384i	$0.195926\pi$
$762$	−5.22527	−	52.0762i	−0.189291	−	1.88652i
$763$	−6.24142	−	26.3346i	−0.225955	−	0.953377i
$764$	22.3160	+	15.2547i	0.807363	+	0.551897i
$765$	17.4433	+	24.1720i	0.630662	+	0.873941i
$766$	48.1573	−	10.9606i	1.74000	−	0.396024i
$767$	−0.657217	−	11.2840i	−0.0237307	−	0.407441i
$768$	−27.1867	−	5.37420i	−0.981016	−	0.193925i
$769$	−2.09204	−	2.81010i	−0.0754409	−	0.101335i	0.762801	−	0.646633i	$-0.223824\pi$
$769$	−2.09204	−	2.81010i	−0.0754409	−	0.101335i	−0.838242	+	0.545299i	$0.816416\pi$
$770$	−3.49207	+	5.92571i	−0.125845	+	0.213548i
$771$	35.0892	−	10.2216i	1.26371	−	0.368122i
$772$	−29.4039	−	25.5806i	−1.05827	−	0.920667i
$773$	−19.8347	−	3.49740i	−0.713406	−	0.125793i	−0.194846	−	0.980834i	$-0.562421\pi$
$773$	−19.8347	−	3.49740i	−0.713406	−	0.125793i	−0.518560	+	0.855041i	$0.673532\pi$
$774$	19.0554	−	2.89462i	0.684933	−	0.104045i
$775$	10.8306	−	1.90972i	0.389046	−	0.0685993i
$776$	−49.4778	−	7.13009i	−1.77615	−	0.255955i
$777$	−25.2005	+	23.4240i	−0.904061	+	0.840331i
$778$	−2.85392	−	8.06424i	−0.102318	−	0.289117i
$779$	48.2252	+	11.4296i	1.72785	+	0.409507i
$780$	14.2234	−	3.86937i	0.509279	−	0.138546i
$781$	4.59870	+	0.537511i	0.164555	+	0.0192337i
$782$	0.0714941	−	0.567697i	0.00255662	−	0.0203008i
$783$	16.0069	−	6.48553i	0.572039	−	0.231774i
$784$	15.8835	−	9.65296i	0.567267	−	0.344748i
$785$	7.01962	−	3.02797i	0.250541	−	0.108073i
$786$	0.921539	−	2.90444i	0.0328702	−	0.103598i
$787$	12.0626	+	11.3804i	0.429984	+	0.405669i	0.870573	−	0.492040i	$-0.163749\pi$
$787$	12.0626	+	11.3804i	0.429984	+	0.405669i	−0.440588	+	0.897709i	$0.645230\pi$
$788$	−9.47555	−	3.02204i	−0.337552	−	0.107656i
$789$	13.7910	+	1.71588i	0.490972	+	0.0610869i
$790$	−30.7658	+	3.31804i	−1.09460	+	0.118051i
$791$	44.0001	−	36.9205i	1.56446	−	1.31274i
$792$	−4.34066	−	5.00245i	−0.154239	−	0.177754i
$793$	−10.5706	−	8.86975i	−0.375371	−	0.314974i
$794$	−7.34968	−	4.92846i	−0.260830	−	0.174905i
$795$	−12.0938	−	16.4993i	−0.428924	−	0.585171i
$796$	−38.6055	−	29.8260i	−1.36834	−	1.05715i
$797$	20.1403	+	8.68767i	0.713406	+	0.307733i	0.721674	−	0.692233i	$-0.243373\pi$
$797$	20.1403	+	8.68767i	0.713406	+	0.307733i	−0.00826870	+	0.999966i	$0.502632\pi$
$798$	−6.84223	+	35.4086i	−0.242212	+	1.25345i
$799$	15.9152	−	31.6898i	0.563040	−	1.12110i
$800$	−6.76824	+	6.56133i	−0.239294	+	0.231978i
$801$	0.615493	−	41.4220i	0.0217474	−	1.46358i
$802$	7.98753	−	0.393748i	0.282049	−	0.0139037i
$803$	5.04889	+	5.35151i	0.178172	+	0.188851i
$804$	21.0046	+	4.25361i	0.740776	+	0.150013i
$805$	0.387038	+	0.254559i	0.0136413	+	0.00897201i
$806$	−13.8326	−	16.7869i	−0.487232	−	0.591295i
$807$	−12.3551	−	14.9484i	−0.434921	−	0.526209i
$808$	29.1796	+	47.0624i	1.02654	+	1.65565i
$809$		−	7.04073i		−	0.247539i	−0.992311	−	0.123769i	$-0.960502\pi$
$809$		−	7.04073i		−	0.247539i	0.992311	−	0.123769i	$-0.0394983\pi$
$810$	3.58746	−	22.9603i	0.126051	−	0.806741i
$811$			25.3893i			0.891541i	0.895147	+	0.445770i	$0.147070\pi$
$811$			25.3893i			0.891541i	−0.895147	+	0.445770i	$0.852930\pi$
$812$	−3.54015	−	22.4083i	−0.124235	−	0.786378i
$813$	−19.3510	+	51.9620i	−0.678669	+	1.82239i
$814$	4.95856	−	4.08590i	0.173798	−	0.143211i
$815$	19.1315	+	12.5830i	0.670146	+	0.440762i
$816$	2.75887	+	37.6026i	0.0965798	+	1.31636i
$817$	13.4495	+	14.2556i	0.470538	+	0.498741i
$818$	−0.483437	−	9.80693i	−0.0169030	−	0.342891i
$819$	−15.0640	−	18.5041i	−0.526380	−	0.646587i
$820$	−17.3004	+	38.2169i	−0.604155	+	1.33459i
$821$	16.6517	−	33.1562i	0.581148	−	1.15716i	−0.390473	−	0.920614i	$-0.627688\pi$
$821$	16.6517	−	33.1562i	0.581148	−	1.15716i	0.971620	−	0.236546i	$-0.0760152\pi$
$822$	3.56967	+	10.3301i	0.124506	+	0.360303i
$823$	−12.1664	−	5.24809i	−0.424096	−	0.182937i	0.173326	−	0.984865i	$-0.444549\pi$
$823$	−12.1664	−	5.24809i	−0.424096	−	0.182937i	−0.597421	+	0.801928i	$0.703808\pi$
$824$	2.92864	−	11.0323i	0.102024	−	0.384327i
$825$	−2.23952	+	0.244912i	−0.0779700	+	0.00852674i
$826$	−13.0366	+	19.4411i	−0.453601	+	0.676443i
$827$	29.8125	+	25.0156i	1.03668	+	0.869879i	0.991631	−	0.129106i	$-0.0412108\pi$
$827$	29.8125	+	25.0156i	1.03668	+	0.869879i	0.0450501	+	0.998985i	$0.485655\pi$
$828$	−0.350905	+	0.275405i	−0.0121948	+	0.00957097i
$829$	−11.1237	+	9.33393i	−0.386344	+	0.324181i	−0.815187	−	0.579198i	$-0.803366\pi$
$829$	−11.1237	+	9.33393i	−0.386344	+	0.324181i	0.428843	+	0.903379i	$0.358921\pi$
$830$	3.53936	+	32.8179i	0.122853	+	1.13913i
$831$	−13.6865	−	32.3884i	−0.474780	−	1.12354i
$832$	17.8858	+	5.26426i	0.620079	+	0.182505i
$833$	−18.3934	−	17.3533i	−0.637295	−	0.601257i
$834$	−20.7598	+	18.9539i	−0.718852	+	0.656321i
$835$	−15.0062	+	6.47302i	−0.519309	+	0.224008i
$836$	1.66982	−	6.52443i	0.0577518	−	0.225652i
$837$	−33.0632	+	9.10074i	−1.14283	+	0.314568i
$838$	8.02059	+	1.01009i	0.277067	+	0.0348929i
$839$	−28.1897	−	3.29490i	−0.973215	−	0.113753i	−0.385402	−	0.922749i	$-0.625937\pi$
$839$	−28.1897	−	3.29490i	−0.973215	−	0.113753i	−0.587814	+	0.808996i	$0.700011\pi$
$840$	−28.3109	−	11.4149i	−0.976819	−	0.393853i
$841$	17.4686	+	4.14013i	0.602365	+	0.142763i
$842$	37.1929	−	13.1625i	1.28175	−	0.453610i
$843$	3.73533	+	16.2993i	0.128652	+	0.561376i
$844$	46.4777	+	27.9514i	1.59983	+	0.962125i
$845$	13.6088	−	2.39960i	0.468156	−	0.0825486i
$846$	−26.1963	+	8.83512i	−0.900647	+	0.303758i
$847$	34.9220	+	6.15769i	1.19993	+	0.211581i
$848$	−2.08501	−	25.7911i	−0.0715995	−	0.885669i
$849$	−0.0605590	−	0.0579908i	−0.00207838	−	0.00199024i
$850$	11.0491	+	6.51134i	0.378981	+	0.223337i
$851$	−0.258412	−	0.347108i	−0.00885825	−	0.0118987i
$852$	0.676007	+	20.5372i	0.0231596	+	0.703591i
$853$	1.78876	+	30.7118i	0.0612460	+	1.05155i	0.879256	+	0.476349i	$0.158040\pi$
$853$	1.78876	+	30.7118i	0.0612460	+	1.05155i	−0.818010	+	0.575204i	$0.804923\pi$
$854$	6.34172	+	27.8634i	0.217009	+	0.953465i
$855$	21.2721	−	10.2904i	0.727491	−	0.351924i
$856$	−6.90911	+	33.8577i	−0.236148	+	1.15723i
$857$	2.55925	+	10.7983i	0.0874224	+	0.368864i	0.999117	−	0.0420034i	$-0.0133740\pi$
$857$	2.55925	+	10.7983i	0.0874224	+	0.368864i	−0.911695	+	0.410868i	$0.865226\pi$
$858$	2.60206	+	3.61718i	0.0888329	+	0.123488i
$859$	28.7444	+	1.67417i	0.980745	+	0.0571219i	0.541019	−	0.841010i	$-0.318039\pi$
$859$	28.7444	+	1.67417i	0.980745	+	0.0571219i	0.439726	+	0.898132i	$0.355076\pi$
$860$	−14.0205	+	8.86711i	−0.478093	+	0.302366i
$861$	67.9045	+	0.504471i	2.31418	+	0.0171923i
$862$	0.102347	+	0.353306i	0.00348596	+	0.0120336i
$863$	−18.7682	+	32.5075i	−0.638877	+	1.10657i	0.346802	+	0.937938i	$0.387268\pi$
$863$	−18.7682	+	32.5075i	−0.638877	+	1.10657i	−0.985679	+	0.168630i	$0.946066\pi$
$864$	19.0896	−	22.3514i	0.649443	−	0.760410i
$865$	−10.7476	−	18.6153i	−0.365429	−	0.632941i
$866$	−21.0324	+	21.8983i	−0.714711	+	0.744136i
$867$	20.5888	−	7.32095i	0.699231	−	0.248632i
$868$	1.81635	+	45.0090i	0.0616509	+	1.52770i
$869$	−4.19813	−	8.35917i	−0.142412	−	0.283565i
$870$	−10.3764	+	10.6442i	−0.351793	+	0.360871i
$871$	−13.8125	−	4.13518i	−0.468018	−	0.140115i
$872$	−21.2755	+	7.10482i	−0.720480	+	0.240599i
$873$	32.2904	−	42.0544i	1.09287	−	1.42333i
$874$	−0.433356	−	0.133963i	−0.0146585	−	0.00453135i
$875$	−34.7048	+	22.8257i	−1.17324	+	0.771649i
$876$	−20.1542	+	25.6900i	−0.680947	+	0.867984i
$877$	−38.5415	+	4.50485i	−1.30145	+	0.152118i	−0.738434	−	0.674325i	$-0.764435\pi$
$877$	−38.5415	+	4.50485i	−1.30145	+	0.152118i	−0.563020	+	0.826444i	$0.690360\pi$
$878$	−0.0716205	+	8.02708i	−0.00241707	+	0.270901i
$879$	−10.4738	−	0.688137i	−0.353272	−	0.0232103i
$880$	5.15041	+	2.44318i	0.173620	+	0.0823597i
$881$	−13.3039	−	36.5522i	−0.448221	−	1.23148i	−0.933962	−	0.357373i	$-0.883672\pi$
$881$	−13.3039	−	36.5522i	−0.448221	−	1.23148i	0.485741	−	0.874103i	$-0.338550\pi$
$882$	0.677985	+	19.7025i	0.0228289	+	0.663417i
$883$	−3.53345	+	9.70807i	−0.118910	+	0.326703i	−0.984841	−	0.173461i	$-0.944505\pi$
$883$	−3.53345	+	9.70807i	−0.118910	+	0.326703i	0.865931	+	0.500164i	$0.166727\pi$
$884$	0.452614	−	25.3620i	0.0152230	−	0.853016i
$885$	15.3178	−	0.778026i	0.514902	−	0.0261531i
$886$	−3.24558	+	17.4925i	−0.109037	+	0.587672i
$887$	11.8901	+	39.7158i	0.399232	+	1.33353i	0.887490	+	0.460828i	$0.152447\pi$
$887$	11.8901	+	39.7158i	0.399232	+	1.33353i	−0.488258	+	0.872700i	$0.662367\pi$
$888$	21.2043	+	19.0652i	0.711571	+	0.639786i
$889$	43.5441	−	58.4899i	1.46042	−	1.96169i
$890$	13.8299	+	32.8644i	0.463578	+	1.10162i
$891$	6.88065	−	1.41624i	0.230510	−	0.0474459i
$892$	14.3227	+	14.0042i	0.479560	+	0.468895i
$893$	−22.5492	−	16.7872i	−0.754579	−	0.561763i
$894$	−9.69642	+	18.5448i	−0.324297	+	0.620230i
$895$	−10.7016	+	3.20385i	−0.357715	+	0.107093i
$896$	−22.9239	−	31.0687i	−0.765835	−	1.03793i
$897$	0.251953	−	0.163044i	0.00841248	−	0.00544388i
$898$	10.8793	+	4.80844i	0.363046	+	0.160460i
$899$	20.6129	+	7.50249i	0.687479	+	0.250222i
$900$	−2.55286	−	9.66699i	−0.0850953	−	0.322233i
$901$	−33.0806	+	12.0404i	−1.10207	+	0.401122i
$902$	−12.6527	−	0.850268i	−0.421288	−	0.0283108i
$903$	22.3254	+	14.9224i	0.742942	+	0.496586i
$904$	−33.7392	−	33.5829i	−1.12215	−	1.11695i
$905$	−1.17434	−	10.0471i	−0.0390363	−	0.333977i
$906$	−2.46766	−	1.47902i	−0.0819824	−	0.0491371i
$907$	29.3516	+	44.6269i	0.974603	+	1.48181i	0.873434	+	0.486943i	$0.161888\pi$
$907$	29.3516	+	44.6269i	0.974603	+	1.48181i	0.101170	+	0.994869i	$0.467741\pi$
$908$	−28.5887	+	2.82545i	−0.948751	+	0.0937660i
$909$	−58.6783	+	2.54352i	−1.94624	+	0.0843631i
$910$	18.2694	+	9.38025i	0.605623	+	0.310952i
$911$	1.90644	−	6.36796i	0.0631633	−	0.210980i	−0.920582	−	0.390549i	$-0.872285\pi$
$911$	1.90644	−	6.36796i	0.0631633	−	0.210980i	0.983745	+	0.179569i	$0.0574703\pi$
$912$	29.7359	+	3.02245i	0.984654	+	0.100083i
$913$	−8.91675	+	4.47816i	−0.295101	+	0.148205i
$914$	−38.0663	−	14.2409i	−1.25912	−	0.471046i
$915$	12.1419	−	14.2537i	0.401398	−	0.471214i
$916$	−11.6658	−	4.48330i	−0.385448	−	0.148133i
$917$	3.67660	−	2.12269i	0.121412	−	0.0700974i
$918$	−36.2081	−	16.9777i	−1.19504	−	0.560346i
$919$	−24.9414	−	14.3999i	−0.822740	−	0.475009i	0.0286205	−	0.999590i	$-0.490889\pi$
$919$	−24.9414	−	14.3999i	−0.822740	−	0.475009i	−0.851360	+	0.524581i	$0.824222\pi$
$920$	0.181430	−	0.338362i	0.00598157	−	0.0111555i
$921$	46.5157	+	27.3186i	1.53274	+	0.900177i
$922$	−7.05361	+	1.17895i	−0.232298	+	0.0388267i
$923$	0.803813	−	13.8009i	0.0264578	−	0.454263i
$924$	0.233186	−	9.22465i	0.00767126	−	0.303469i
$925$	9.43799	−	2.23684i	0.310319	−	0.0735470i
$926$	−14.4054	−	22.3338i	−0.473390	−	0.733935i
$927$	8.68172	+	8.43808i	0.285145	+	0.277143i
$928$	−18.2348	+	4.58387i	−0.598587	+	0.150473i
$929$	−47.0358	+	2.73953i	−1.54320	+	0.0898809i	−0.808492	−	0.588507i	$-0.799716\pi$
$929$	−47.0358	+	2.73953i	−1.54320	+	0.0898809i	−0.734704	+	0.678388i	$0.762679\pi$
$930$	22.9176	−	18.6001i	0.751497	−	0.609923i
$931$	−16.0796	+	11.9708i	−0.526988	+	0.392328i
$932$	−3.21593	+	23.8197i	−0.105341	+	0.780241i
$933$	11.1870	+	2.73929i	0.366245	+	0.0896804i
$934$	5.54787	−	2.72454i	0.181532	−	0.0891496i
$935$	1.34675	−	7.63781i	0.0440435	−	0.249783i
$936$	−14.1575	+	13.8069i	−0.462753	+	0.451294i
$937$	4.72013	+	26.7692i	0.154200	+	0.874512i	0.959513	+	0.281663i	$0.0908859\pi$
$937$	4.72013	+	26.7692i	0.154200	+	0.874512i	−0.805313	+	0.592849i	$0.798003\pi$
$938$	17.6158	+	24.1083i	0.575177	+	0.787163i
$939$	13.7536	−	44.7280i	0.448831	−	1.45964i
$940$	17.5964	−	16.0176i	0.573931	−	0.522437i
$941$	−8.28995	+	34.9780i	−0.270245	+	1.14025i	0.653404	+	0.757010i	$0.273340\pi$
$941$	−8.28995	+	34.9780i	−0.270245	+	1.14025i	−0.923648	+	0.383242i	$0.874808\pi$
$942$	−6.25828	+	8.12551i	−0.203906	+	0.264744i
$943$	−0.0991539	+	0.848316i	−0.00322890	+	0.0276250i
$944$	17.0146	+	9.31967i	0.553779	+	0.303329i
$945$	25.2600	−	20.2538i	0.821709	−	0.658856i
$946$	−3.99556	−	3.03036i	−0.129907	−	0.0985256i
$947$	−7.77671	−	18.0284i	−0.252709	−	0.585845i	0.743885	−	0.668307i	$-0.232981\pi$
$947$	−7.77671	−	18.0284i	−0.252709	−	0.585845i	−0.996594	+	0.0824621i	$0.973722\pi$
$948$	33.9154	−	23.9412i	1.10152	−	0.777574i
$949$	15.0750	−	15.9786i	0.489356	−	0.518687i
$950$	6.60435	−	7.72963i	0.214273	−	0.250782i
$951$	27.4037	+	20.7195i	0.888625	+	0.671875i
$952$	−32.4853	+	41.2811i	−1.05286	+	1.33793i
$953$	1.08747	+	1.29599i	0.0352266	+	0.0419814i	0.783370	−	0.621556i	$-0.213499\pi$
$953$	1.08747	+	1.29599i	0.0352266	+	0.0419814i	−0.748144	+	0.663537i	$0.769055\pi$
$954$	24.9347	+	11.4665i	0.807290	+	0.371241i
$955$	15.8623	−	18.9040i	0.513293	−	0.611719i
$956$	−4.15596	+	21.3360i	−0.134413	+	0.690056i
$957$	−4.11271	−	1.81041i	−0.132945	−	0.0585222i
$958$	16.7328	+	29.5886i	0.540612	+	0.955965i
$959$	−6.03123	+	13.9820i	−0.194759	+	0.451501i
$960$	−7.32335	+	24.2161i	−0.236360	+	0.781572i
$961$	−11.2200	−	5.63490i	−0.361936	−	0.181771i
$962$	−13.0399	−	14.0709i	−0.420424	−	0.453665i
$963$	−27.7236	−	23.9737i	−0.893382	−	0.772543i
$964$	31.7455	−	15.2401i	1.02245	−	0.490849i
$965$	−25.8796	+	24.4161i	−0.833094	+	0.785984i
$966$	−0.619761	−	0.0462758i	−0.0199405	−	0.00148890i
$967$	−21.0982	+	32.0783i	−0.678473	+	1.03157i	0.318036	+	0.948079i	$0.396977\pi$
$967$	−21.0982	+	32.0783i	−0.678473	+	1.03157i	−0.996509	+	0.0834893i	$0.973394\pi$
$968$	2.49346	−	29.2835i	0.0801428	−	0.941208i
$969$	−6.76364	−	40.0982i	−0.217279	−	1.28814i
$970$	−10.9200	+	44.3095i	−0.350619	+	1.42269i
$971$	−55.6763			−1.78674			−0.893368	−	0.449325i	$-0.851665\pi$
$971$	−55.6763			−1.78674			−0.893368	+	0.449325i	$0.851665\pi$
$972$	10.7565	+	29.2626i	0.345015	+	0.938597i
$973$	−39.1651			−1.25558
$974$	5.06641	−	20.5577i	0.162338	−	0.658712i
$975$	1.11882	+	6.63294i	0.0358311	+	0.212424i
$976$	22.5300	−	7.30097i	0.721168	−	0.233698i
$977$	−2.37909	+	3.61722i	−0.0761137	+	0.115725i	−0.871539	−	0.490327i	$-0.836877\pi$
$977$	−2.37909	+	3.61722i	−0.0761137	+	0.115725i	0.795425	+	0.606052i	$0.207248\pi$
$978$	−30.6351	−	2.28743i	−0.979603	−	0.0731441i
$979$	−7.83994	+	7.39660i	−0.250566	+	0.236396i
$980$	−7.34342	−	15.2966i	−0.234577	−	0.488631i
$981$	4.47893	−	23.3657i	0.143001	−	0.746009i
$982$	12.0928	+	13.0489i	0.385896	+	0.416407i
$983$	17.3809	+	8.72902i	0.554365	+	0.278412i	0.703847	−	0.710352i	$-0.251464\pi$
$983$	17.3809	+	8.72902i	0.554365	+	0.278412i	−0.149482	+	0.988764i	$0.547761\pi$
$984$	−4.61877	−	56.0902i	−0.147241	−	1.78809i
$985$	−3.59624	+	8.33702i	−0.114586	+	0.265640i
$986$	12.5921	+	22.2667i	0.401015	+	0.709115i
$987$	−35.2531	−	15.5183i	−1.12212	−	0.493954i
$988$	−19.7376	−	3.84462i	−0.627938	−	0.122314i
$989$	−0.217100	+	0.258729i	−0.00690337	+	0.00822711i
$990$	−4.93436	+	3.49426i	−0.156824	+	0.111055i
$991$	−25.7301	−	30.6640i	−0.817344	−	0.974073i	0.182615	−	0.983185i	$-0.441544\pi$
$991$	−25.7301	−	30.6640i	−0.817344	−	0.974073i	−0.999958	+	0.00911199i	$0.997100\pi$
$992$	37.0187	−	4.83680i	1.17534	−	0.153568i
$993$	−20.7007	−	15.6514i	−0.656917	−	0.496684i
$994$	−18.5971	+	21.7658i	−0.589863	+	0.690368i
$995$	−30.5626	+	32.3945i	−0.968899	+	1.02697i
$996$	−25.5381	−	36.1777i	−0.809207	−	1.14633i
$997$	−4.85047	−	11.2447i	−0.153616	−	0.356122i	0.823978	−	0.566622i	$-0.191750\pi$
$997$	−4.85047	−	11.2447i	−0.153616	−	0.356122i	−0.977594	+	0.210500i	$0.932491\pi$
$998$	15.5154	+	11.7674i	0.491132	+	0.372490i
$999$	−28.6442	+	9.70838i	−0.906263	+	0.307160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.23.50	yes	936
3.2	odd	2		972.2.p.a.503.3		936
4.3	odd	2	inner	324.2.p.a.23.35	✓	936
12.11	even	2		972.2.p.a.503.18		936
81.7	even	27		972.2.p.a.143.18		936
81.74	odd	54	inner	324.2.p.a.155.35	yes	936
324.7	odd	54		972.2.p.a.143.3		936
324.155	even	54	inner	324.2.p.a.155.50	yes	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.23.35	✓	936	4.3	odd	2	inner
324.2.p.a.23.50	yes	936	1.1	even	1	trivial
324.2.p.a.155.35	yes	936	81.74	odd	54	inner
324.2.p.a.155.50	yes	936	324.155	even	54	inner
972.2.p.a.143.3		936	324.7	odd	54
972.2.p.a.143.18		936	81.7	even	27
972.2.p.a.503.3		936	3.2	odd	2
972.2.p.a.503.18		936	12.11	even	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.p (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37313 + 0.338405i) q^{2} +(0.288087 + 1.70792i) q^{3} +(1.77096 + 0.929346i) q^{4} +(1.00330 - 1.52545i) q^{5} +(-0.182388 + 2.44269i) q^{6} +(-2.48232 + 2.34195i) q^{7} +(2.11727 + 1.87541i) q^{8} +(-2.83401 + 0.984063i) q^{9} +O(q^{10})\)	\(q+(1.37313 + 0.338405i) q^{2} +(0.288087 + 1.70792i) q^{3} +(1.77096 + 0.929346i) q^{4} +(1.00330 - 1.52545i) q^{5} +(-0.182388 + 2.44269i) q^{6} +(-2.48232 + 2.34195i) q^{7} +(2.11727 + 1.87541i) q^{8} +(-2.83401 + 0.984063i) q^{9} +(1.89388 - 1.75511i) q^{10} +(0.697519 + 0.350307i) q^{11} +(-1.07706 + 3.29241i) q^{12} +(0.923085 - 2.13995i) q^{13} +(-4.20108 + 2.37577i) q^{14} +(2.89439 + 1.27410i) q^{15} +(2.27263 + 3.29168i) q^{16} +(3.49809 - 4.16886i) q^{17} +(-4.22447 + 0.392203i) q^{18} +(-2.77306 - 3.30481i) q^{19} +(3.19448 - 1.76910i) q^{20} +(-4.71500 - 3.56493i) q^{21} +(0.839238 + 0.717061i) q^{22} +(0.0510191 - 0.0540770i) q^{23} +(-2.59311 + 4.15642i) q^{24} +(0.660026 + 1.53011i) q^{25} +(1.99168 - 2.62605i) q^{26} +(-2.49715 - 4.55678i) q^{27} +(-6.57259 + 1.84058i) q^{28} +(-0.385867 + 3.30130i) q^{29} +(3.54320 + 2.72898i) q^{30} +(1.52199 - 6.42177i) q^{31} +(2.00670 + 5.28897i) q^{32} +(-0.397352 + 1.29223i) q^{33} +(6.21409 - 4.54061i) q^{34} +(1.08200 + 6.13634i) q^{35} +(-5.93347 - 0.891037i) q^{36} +(1.01074 - 5.73217i) q^{37} +(-2.68941 - 5.47635i) q^{38} +(3.92081 + 0.960066i) q^{39} +(4.98510 - 1.34817i) q^{40} +(-9.21489 + 6.86023i) q^{41} +(-5.26791 - 6.49069i) q^{42} +(-4.53525 + 0.264148i) q^{43} +(0.909725 + 1.26862i) q^{44} +(-1.34223 + 5.31045i) q^{45} +(0.0883556 - 0.0569896i) q^{46} +(6.34059 - 1.50275i) q^{47} +(-4.96722 + 4.82977i) q^{48} +(0.270180 - 4.63881i) q^{49} +(0.388504 + 2.32440i) q^{50} +(8.12786 + 4.77348i) q^{51} +(3.62351 - 2.93191i) q^{52} +(-5.60215 - 3.23440i) q^{53} +(-1.88687 - 7.10209i) q^{54} +(1.23420 - 0.712564i) q^{55} +(-9.64787 + 0.303152i) q^{56} +(4.84548 - 5.68826i) q^{57} +(-1.64702 + 4.40253i) q^{58} +(4.33408 - 2.17666i) q^{59} +(3.94177 + 4.94628i) q^{60} +(1.69812 - 5.67212i) q^{61} +(4.26304 - 8.30286i) q^{62} +(4.73031 - 9.07988i) q^{63} +(0.965641 + 7.94151i) q^{64} +(-2.33825 - 3.55514i) q^{65} +(-0.982911 + 1.63993i) q^{66} +(-0.718219 - 6.14476i) q^{67} +(10.0693 - 4.13197i) q^{68} +(0.107057 + 0.0715578i) q^{69} +(-0.590837 + 8.79214i) q^{70} +(5.57405 - 2.02879i) q^{71} +(-7.84589 - 3.23142i) q^{72} +(8.85743 + 3.22384i) q^{73} +(3.32767 - 7.52897i) q^{74} +(-2.42317 + 1.56808i) q^{75} +(-1.83969 - 8.42984i) q^{76} +(-2.55187 + 0.763980i) q^{77} +(5.05888 + 2.64511i) q^{78} +(-9.61276 - 7.15644i) q^{79} +(7.30142 - 0.164230i) q^{80} +(7.06324 - 5.57769i) q^{81} +(-14.9748 + 6.30162i) q^{82} +(-7.63379 + 10.2540i) q^{83} +(-5.03704 - 10.6952i) q^{84} +(-2.84973 - 9.51878i) q^{85} +(-6.31687 - 1.17204i) q^{86} +(-5.74954 + 0.292032i) q^{87} +(0.819863 + 2.04983i) q^{88} +(-4.72291 + 12.9761i) q^{89} +(-3.64014 + 6.83771i) q^{90} +(2.72027 + 7.47387i) q^{91} +(0.140609 - 0.0483542i) q^{92} +(11.4064 + 0.749408i) q^{93} +(9.21499 + 0.0822194i) q^{94} +(-7.82353 + 0.914440i) q^{95} +(-8.45505 + 4.95097i) q^{96} +(-14.7662 + 9.71187i) q^{97} +(1.94079 - 6.27825i) q^{98} +(-2.32150 - 0.306372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9}+O(q^{10}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9	\( 936 q - 18 q^{2} - 18 q^{4} - 36 q^{5} - 18 q^{6} - 18 q^{8} - 36 q^{9} - 18 q^{10} - 18 q^{12} - 36 q^{13} - 18 q^{14} - 18 q^{16} - 36 q^{17} - 18 q^{18} - 18 q^{20} - 36 q^{21} - 18 q^{22} - 18 q^{24} - 36 q^{25} - 27 q^{26} - 9 q^{28} - 36 q^{29} - 18 q^{30} - 18 q^{32} - 36 q^{33} - 18 q^{34} - 18 q^{36} - 36 q^{37} - 18 q^{38} - 18 q^{40} - 36 q^{41} - 63 q^{42} - 90 q^{44} - 36 q^{45} - 18 q^{46} - 117 q^{48} - 36 q^{49} - 135 q^{50} - 18 q^{52} - 54 q^{53} - 144 q^{54} - 144 q^{56} - 36 q^{57} - 18 q^{58} - 135 q^{60} - 36 q^{61} - 117 q^{62} - 18 q^{64} - 36 q^{65} - 90 q^{66} - 63 q^{68} - 36 q^{69} - 18 q^{70} - 18 q^{72} - 36 q^{73} - 18 q^{74} - 18 q^{76} - 36 q^{77} + 9 q^{78} - 36 q^{81} - 36 q^{82} - 45 q^{84} - 36 q^{85} - 18 q^{86} - 18 q^{88} - 54 q^{89} + 45 q^{90} + 72 q^{92} - 144 q^{93} - 18 q^{94} + 99 q^{96} - 36 q^{97} + 153 q^{98}+O(q^{100}) \) 936 * q - 18 * q^2 - 18 * q^4 - 36 * q^5 - 18 * q^6 - 18 * q^8 - 36 * q^9 - 18 * q^10 - 18 * q^12 - 36 * q^13 - 18 * q^14 - 18 * q^16 - 36 * q^17 - 18 * q^18 - 18 * q^20 - 36 * q^21 - 18 * q^22 - 18 * q^24 - 36 * q^25 - 27 * q^26 - 9 * q^28 - 36 * q^29 - 18 * q^30 - 18 * q^32 - 36 * q^33 - 18 * q^34 - 18 * q^36 - 36 * q^37 - 18 * q^38 - 18 * q^40 - 36 * q^41 - 63 * q^42 - 90 * q^44 - 36 * q^45 - 18 * q^46 - 117 * q^48 - 36 * q^49 - 135 * q^50 - 18 * q^52 - 54 * q^53 - 144 * q^54 - 144 * q^56 - 36 * q^57 - 18 * q^58 - 135 * q^60 - 36 * q^61 - 117 * q^62 - 18 * q^64 - 36 * q^65 - 90 * q^66 - 63 * q^68 - 36 * q^69 - 18 * q^70 - 18 * q^72 - 36 * q^73 - 18 * q^74 - 18 * q^76 - 36 * q^77 + 9 * q^78 - 36 * q^81 - 36 * q^82 - 45 * q^84 - 36 * q^85 - 18 * q^86 - 18 * q^88 - 54 * q^89 + 45 * q^90 + 72 * q^92 - 144 * q^93 - 18 * q^94 + 99 * q^96 - 36 * q^97 + 153 * q^98

Introduction

L-functions

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