LMFDB - Embedded newform 324.2.p.a.275.22

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			275.22
Character	$\chi$	$=$	324.275
Dual form			324.2.p.a.119.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483712 + 1.32892i) q^{2} +(0.996582 + 1.41662i) q^{3} +(-1.53204 - 1.28563i) q^{4} +(1.06564 + 0.459673i) q^{5} +(-2.36464 + 0.639137i) q^{6} +(4.92386 - 0.286782i) q^{7} +(2.44956 - 1.41409i) q^{8} +(-1.01365 + 2.82356i) q^{9} +O(q^{10})$	\(q+(-0.483712 + 1.32892i) q^{2} +(0.996582 + 1.41662i) q^{3} +(-1.53204 - 1.28563i) q^{4} +(1.06564 + 0.459673i) q^{5} +(-2.36464 + 0.639137i) q^{6} +(4.92386 - 0.286782i) q^{7} +(2.44956 - 1.41409i) q^{8} +(-1.01365 + 2.82356i) q^{9} +(-1.12633 + 1.19380i) q^{10} +(0.474450 - 0.637297i) q^{11} +(0.294444 - 3.45157i) q^{12} +(2.24814 - 2.38289i) q^{13} +(-2.00062 + 6.68212i) q^{14} +(0.410816 + 1.96772i) q^{15} +(0.694320 + 3.93928i) q^{16} +(-6.53434 - 1.15218i) q^{17} +(-3.26197 - 2.71285i) q^{18} +(-0.197362 + 0.0348003i) q^{19} +(-1.04164 - 2.07426i) q^{20} +(5.31329 + 6.68945i) q^{21} +(0.617418 + 0.938773i) q^{22} +(-0.288498 + 4.95332i) q^{23} +(4.44442 + 2.06086i) q^{24} +(-2.50691 - 2.65717i) q^{25} +(2.07921 + 4.14022i) q^{26} +(-5.01011 + 1.37795i) q^{27} +(-7.91226 - 5.89088i) q^{28} +(-0.423200 - 1.78562i) q^{29} +(-2.81365 - 0.405869i) q^{30} +(-2.28835 - 4.55649i) q^{31} +(-5.57083 - 0.982784i) q^{32} +(1.37564 + 0.0369987i) q^{33} +(4.69190 - 8.12628i) q^{34} +(5.37889 + 1.95776i) q^{35} +(5.18301 - 3.02265i) q^{36} +(-7.20460 + 2.62226i) q^{37} +(0.0492198 - 0.279111i) q^{38} +(5.61611 + 0.810024i) q^{39} +(3.26038 - 0.380912i) q^{40} +(-1.45225 + 0.434774i) q^{41} +(-11.4598 + 3.82515i) q^{42} +(0.229169 - 1.96067i) q^{43} +(-1.54620 + 0.366401i) q^{44} +(-2.37810 + 2.54296i) q^{45} +(-6.44300 - 2.77937i) q^{46} +(3.61195 + 1.81399i) q^{47} +(-4.88853 + 4.90941i) q^{48} +(17.2094 - 2.01150i) q^{49} +(4.74379 - 2.04617i) q^{50} +(-4.87980 - 10.4050i) q^{51} +(-6.50775 + 0.760419i) q^{52} +(-8.16877 - 4.71624i) q^{53} +(0.592267 - 7.32456i) q^{54} +(0.798542 - 0.461038i) q^{55} +(11.6558 - 7.66525i) q^{56} +(-0.245986 - 0.244907i) q^{57} +(2.57765 + 0.301330i) q^{58} +(4.93857 + 6.63365i) q^{59} +(1.90036 - 3.54279i) q^{60} +(0.282422 - 0.185752i) q^{61} +(7.16210 - 0.837004i) q^{62} +(-4.18131 + 14.1935i) q^{63} +(4.00072 - 6.92779i) q^{64} +(3.49106 - 1.50590i) q^{65} +(-0.714582 + 1.81021i) q^{66} +(-2.08847 + 8.81193i) q^{67} +(8.52963 + 10.1659i) q^{68} +(-7.30450 + 4.52769i) q^{69} +(-5.20354 + 6.20112i) q^{70} +(8.80081 + 7.38476i) q^{71} +(1.50977 + 8.34989i) q^{72} +(9.58287 - 8.04098i) q^{73} +(0.000187394 - 10.8427i) q^{74} +(1.26587 - 6.19945i) q^{75} +(0.347108 + 0.200419i) q^{76} +(2.15336 - 3.27402i) q^{77} +(-3.79304 + 7.07153i) q^{78} +(-11.8559 - 3.54943i) q^{79} +(-1.07088 + 4.51702i) q^{80} +(-6.94503 - 5.72420i) q^{81} +(0.124691 - 2.14022i) q^{82} +(2.32762 - 7.77478i) q^{83} +(0.459954 - 17.0795i) q^{84} +(-6.43365 - 4.23148i) q^{85} +(2.49471 + 1.25295i) q^{86} +(2.10780 - 2.37904i) q^{87} +(0.261002 - 2.23201i) q^{88} +(1.27548 + 1.52006i) q^{89} +(-2.22907 - 4.39037i) q^{90} +(10.3861 - 12.3777i) q^{91} +(6.81011 - 7.21780i) q^{92} +(4.17430 - 7.78265i) q^{93} +(-4.15778 + 3.92253i) q^{94} +(-0.226314 - 0.0536375i) q^{95} +(-4.15955 - 8.87120i) q^{96} +(2.82572 + 6.55075i) q^{97} +(-5.65131 + 23.8429i) q^{98} +(1.31852 + 1.98563i) 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{5}{54}\right)$

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 $

$2$	−0.483712	+	1.32892i	−0.342036	+	0.939687i
$2$	−0.483712	+	1.32892i	−0.342036	+	0.939687i
$3$	0.996582	+	1.41662i	0.575377	+	0.817888i
$3$	0.996582	+	1.41662i	0.575377	+	0.817888i
$4$	−1.53204	−	1.28563i	−0.766022	−	0.642814i
$5$	1.06564	+	0.459673i	0.476570	+	0.205572i	0.620795	−	0.783973i	$-0.286810\pi$
$5$	1.06564	+	0.459673i	0.476570	+	0.205572i	−0.144226	+	0.989545i	$0.546069\pi$
$6$	−2.36464	+	0.639137i	−0.965359	+	0.260926i
$7$	4.92386	−	0.286782i	1.86104	−	0.108393i	0.909461	−	0.415790i	$-0.136495\pi$
$7$	4.92386	−	0.286782i	1.86104	−	0.108393i	0.951582	+	0.307396i	$0.0994577\pi$
$8$	2.44956	−	1.41409i	0.866051	−	0.499955i
$9$	−1.01365	+	2.82356i	−0.337883	+	0.941188i
$10$	−1.12633	+	1.19380i	−0.356178	+	0.377513i
$11$	0.474450	−	0.637297i	0.143052	−	0.192152i	−0.724823	−	0.688936i	$-0.758078\pi$
$11$	0.474450	−	0.637297i	0.143052	−	0.192152i	0.867875	+	0.496783i	$0.165486\pi$
$12$	0.294444	−	3.45157i	0.0849987	−	0.996381i
$13$	2.24814	−	2.38289i	0.623521	−	0.660894i	−0.336219	−	0.941784i	$-0.609148\pi$
$13$	2.24814	−	2.38289i	0.623521	−	0.660894i	0.959740	+	0.280890i	$0.0906297\pi$
$14$	−2.00062	+	6.68212i	−0.534688	+	1.78587i
$15$	0.410816	+	1.96772i	0.106072	+	0.508062i
$16$	0.694320	+	3.93928i	0.173580	+	0.984820i
$17$	−6.53434	−	1.15218i	−1.58481	−	0.279445i	−0.689297	−	0.724478i	$-0.742081\pi$
$17$	−6.53434	−	1.15218i	−1.58481	−	0.279445i	−0.895514	+	0.445033i	$0.853192\pi$
$18$	−3.26197	−	2.71285i	−0.768854	−	0.639425i
$19$	−0.197362	+	0.0348003i	−0.0452780	+	0.00798373i	−0.196241	−	0.980556i	$-0.562874\pi$
$19$	−0.197362	+	0.0348003i	−0.0452780	+	0.00798373i	0.150963	+	0.988539i	$0.451762\pi$
$20$	−1.04164	−	2.07426i	−0.232918	−	0.463819i
$21$	5.31329	+	6.68945i	1.15945	+	1.45976i
$22$	0.617418	+	0.938773i	0.131634	+	0.200147i
$23$	−0.288498	+	4.95332i	−0.0601559	+	1.03284i	0.824282	+	0.566180i	$0.191579\pi$
$23$	−0.288498	+	4.95332i	−0.0601559	+	1.03284i	−0.884438	+	0.466658i	$0.845458\pi$
$24$	4.44442	+	2.06086i	0.907213	+	0.420671i
$25$	−2.50691	−	2.65717i	−0.501383	−	0.531435i
$26$	2.07921	+	4.14022i	0.407766	+	0.811964i
$27$	−5.01011	+	1.37795i	−0.964197	+	0.265187i
$28$	−7.91226	−	5.89088i	−1.49528	−	1.11327i
$29$	−0.423200	−	1.78562i	−0.0785863	−	0.331582i	0.919524	−	0.393035i	$-0.128575\pi$
$29$	−0.423200	−	1.78562i	−0.0785863	−	0.331582i	−0.998110	+	0.0614529i	$0.980427\pi$
$30$	−2.81365	−	0.405869i	−0.513700	−	0.0741012i
$31$	−2.28835	−	4.55649i	−0.411000	−	0.818369i	−0.999948	−	0.0101978i	$-0.996754\pi$
$31$	−2.28835	−	4.55649i	−0.411000	−	0.818369i	0.588948	−	0.808171i	$-0.299542\pi$
$32$	−5.57083	−	0.982784i	−0.984793	−	0.173733i
$33$	1.37564	+	0.0369987i	0.239468	+	0.00644064i
$34$	4.69190	−	8.12628i	0.804654	−	1.39365i
$35$	5.37889	+	1.95776i	0.909199	+	0.330921i
$36$	5.18301	−	3.02265i	0.863835	−	0.503775i
$37$	−7.20460	+	2.62226i	−1.18443	+	0.431097i	−0.857764	−	0.514044i	$-0.828147\pi$
$37$	−7.20460	+	2.62226i	−1.18443	+	0.431097i	−0.326664	+	0.945140i	$0.605925\pi$
$38$	0.0492198	−	0.279111i	0.00798451	−	0.0452778i
$39$	5.61611	+	0.810024i	0.899297	+	0.129708i
$40$	3.26038	−	0.380912i	0.515511	−	0.0602275i
$41$	−1.45225	+	0.434774i	−0.226803	+	0.0679003i	−0.398188	−	0.917304i	$-0.630361\pi$
$41$	−1.45225	+	0.434774i	−0.226803	+	0.0679003i	0.171385	+	0.985204i	$0.445176\pi$
$42$	−11.4598	+	3.82515i	−1.76829	+	0.590234i
$43$	0.229169	−	1.96067i	0.0349480	−	0.298999i	−0.964449	−	0.264270i	$-0.914869\pi$
$43$	0.229169	−	1.96067i	0.0349480	−	0.298999i	0.999397	−	0.0347292i	$-0.0110569\pi$
$44$	−1.54620	+	0.366401i	−0.233099	+	0.0552370i
$45$	−2.37810	+	2.54296i	−0.354507	+	0.379082i
$46$	−6.44300	−	2.77937i	−0.949968	−	0.409796i
$47$	3.61195	+	1.81399i	0.526856	+	0.264597i	0.692285	−	0.721625i	$-0.256604\pi$
$47$	3.61195	+	1.81399i	0.526856	+	0.264597i	−0.165428	+	0.986222i	$0.552901\pi$
$48$	−4.88853	+	4.90941i	−0.705599	+	0.708612i
$49$	17.2094	−	2.01150i	2.45849	−	0.287356i
$50$	4.74379	−	2.04617i	0.670873	−	0.289373i
$51$	−4.87980	−	10.4050i	−0.683309	−	1.45699i
$52$	−6.50775	+	0.760419i	−0.902463	+	0.105451i
$53$	−8.16877	−	4.71624i	−1.12207	−	0.647826i	−0.180139	−	0.983641i	$-0.557655\pi$
$53$	−8.16877	−	4.71624i	−1.12207	−	0.647826i	−0.941928	+	0.335815i	$0.890988\pi$
$54$	0.592267	−	7.32456i	0.0805973	−	0.996747i
$55$	0.798542	−	0.461038i	0.107675	−	0.0621664i
$56$	11.6558	−	7.66525i	1.55757	−	1.02431i
$57$	−0.245986	−	0.244907i	−0.0325817	−	0.0324387i
$58$	2.57765	+	0.301330i	0.338462	+	0.0395665i
$59$	4.93857	+	6.63365i	0.642947	+	0.863628i	0.997446	−	0.0714285i	$-0.0227558\pi$
$59$	4.93857	+	6.63365i	0.642947	+	0.863628i	−0.354498	+	0.935057i	$0.615348\pi$
$60$	1.90036	−	3.54279i	0.245336	−	0.457372i
$61$	0.282422	−	0.185752i	0.0361604	−	0.0237831i	−0.531300	−	0.847184i	$-0.678296\pi$
$61$	0.282422	−	0.185752i	0.0361604	−	0.0237831i	0.567461	+	0.823401i	$0.307926\pi$
$62$	7.16210	−	0.837004i	0.909588	−	0.106300i
$63$	−4.18131	+	14.1935i	−0.526796	+	1.78822i
$64$	4.00072	−	6.92779i	0.500090	−	0.865974i
$65$	3.49106	−	1.50590i	0.433013	−	0.186783i
$66$	−0.714582	+	1.81021i	−0.0879589	+	0.222822i
$67$	−2.08847	+	8.81193i	−0.255147	+	1.07655i	0.683030	+	0.730391i	$0.260662\pi$
$67$	−2.08847	+	8.81193i	−0.255147	+	1.07655i	−0.938176	+	0.346158i	$0.887486\pi$
$68$	8.52963	+	10.1659i	1.03437	+	1.23280i
$69$	−7.30450	+	4.52769i	−0.879358	+	0.545070i
$70$	−5.20354	+	6.20112i	−0.621942	+	0.741175i
$71$	8.80081	+	7.38476i	1.04446	+	0.876409i	0.992501	−	0.122239i	$-0.0390076\pi$
$71$	8.80081	+	7.38476i	1.04446	+	0.876409i	0.0519635	+	0.998649i	$0.483452\pi$
$72$	1.50977	+	8.34989i	0.177928	+	0.984044i
$73$	9.58287	−	8.04098i	1.12159	−	0.941126i	0.122906	−	0.992418i	$-0.460779\pi$
$73$	9.58287	−	8.04098i	1.12159	−	0.941126i	0.998684	+	0.0512925i	$0.0163341\pi$
$74$	0.000187394	−	10.8427i	2.17841e−5	−	1.26044i
$75$	1.26587	−	6.19945i	0.146170	−	0.715850i
$76$	0.347108	+	0.200419i	0.0398160	+	0.0229896i
$77$	2.15336	−	3.27402i	0.245398	−	0.373109i
$78$	−3.79304	+	7.07153i	−0.429477	+	0.800693i
$79$	−11.8559	−	3.54943i	−1.33390	−	0.399342i	−0.461065	−	0.887366i	$-0.652533\pi$
$79$	−11.8559	−	3.54943i	−1.33390	−	0.399342i	−0.872830	+	0.488024i	$0.837718\pi$
$80$	−1.07088	+	4.51702i	−0.119728	+	0.505019i
$81$	−6.94503	−	5.72420i	−0.771670	−	0.636023i
$82$	0.124691	−	2.14022i	0.0137698	−	0.236348i
$83$	2.32762	−	7.77478i	0.255489	−	0.853393i	−0.729970	−	0.683479i	$-0.760466\pi$
$83$	2.32762	−	7.77478i	0.255489	−	0.853393i	0.985459	−	0.169914i	$-0.0543489\pi$
$84$	0.459954	−	17.0795i	0.0501851	−	1.86352i
$85$	−6.43365	−	4.23148i	−0.697827	−	0.458968i
$86$	2.49471	+	1.25295i	0.269012	+	0.135109i
$87$	2.10780	−	2.37904i	0.225980	−	0.255059i
$88$	0.261002	−	2.23201i	0.0278229	−	0.237933i
$89$	1.27548	+	1.52006i	0.135201	+	0.161126i	0.829397	−	0.558660i	$-0.188684\pi$
$89$	1.27548	+	1.52006i	0.135201	+	0.161126i	−0.694196	+	0.719786i	$0.744240\pi$
$90$	−2.22907	−	4.39037i	−0.234965	−	0.462785i
$91$	10.3861	−	12.3777i	1.08876	−	1.29754i
$92$	6.81011	−	7.21780i	0.710003	−	0.752508i
$93$	4.17430	−	7.78265i	0.432854	−	0.807023i
$94$	−4.15778	+	3.92253i	−0.428843	+	0.404578i
$95$	−0.226314	−	0.0536375i	−0.0232193	−	0.00550309i
$96$	−4.15955	−	8.87120i	−0.424533	−	0.905413i
$97$	2.82572	+	6.55075i	0.286908	+	0.665128i	0.999329	−	0.0366242i	$-0.0116605\pi$
$97$	2.82572	+	6.55075i	0.286908	+	0.665128i	−0.712421	+	0.701753i	$0.752401\pi$
$98$	−5.65131	+	23.8429i	−0.570869	+	2.40850i
$99$	1.31852	+	1.98563i	0.132517	+	0.199564i
$100$	0.424566	+	7.29387i	0.0424566	+	0.729387i
$101$	−4.86524	−	7.39724i	−0.484110	−	0.736053i	0.508009	−	0.861352i	$-0.330382\pi$
$101$	−4.86524	−	7.39724i	−0.484110	−	0.736053i	−0.992119	+	0.125298i	$0.960011\pi$
$102$	16.1877	−	1.45185i	1.60283	−	0.143755i
$103$	8.24899	−	6.14115i	0.812797	−	0.605105i	−0.108441	−	0.994103i	$-0.534586\pi$
$103$	8.24899	−	6.14115i	0.812797	−	0.605105i	0.921239	+	0.388998i	$0.127179\pi$
$104$	2.13735	−	9.01609i	0.209584	−	0.884100i
$105$	2.58710	+	9.57094i	0.252475	+	0.934028i
$106$	10.2188	−	8.57432i	0.992541	−	0.832811i
$107$	−9.57835	−	16.5902i	−0.925975	−	1.60383i	−0.789986	−	0.613124i	$-0.789912\pi$
$107$	−9.57835	−	16.5902i	−0.925975	−	1.60383i	−0.135988	−	0.990710i	$-0.543421\pi$
$108$	9.44725	+	4.33006i	0.909062	+	0.416660i
$109$	5.43542	−	9.41442i	0.520619	−	0.901738i	−0.479094	−	0.877764i	$-0.659035\pi$
$109$	5.43542	−	9.41442i	0.520619	−	0.901738i	0.999713	−	0.0239745i	$-0.00763205\pi$
$110$	0.226417	+	1.28421i	0.0215881	+	0.122444i
$111$	−10.8947	−	7.59291i	−1.03408	−	0.720687i
$112$	4.54845	+	19.1973i	0.429788	+	1.81398i
$113$	0.599299	+	5.12733i	0.0563773	+	0.482338i	0.991703	+	0.128551i	$0.0410325\pi$
$113$	0.599299	+	5.12733i	0.0563773	+	0.482338i	−0.935326	+	0.353788i	$0.884893\pi$
$114$	0.444448	−	0.208431i	0.0416263	−	0.0195214i
$115$	−2.58434	+	5.14585i	−0.240991	+	0.479853i
$116$	−1.64728	+	3.27973i	−0.152947	+	0.304515i
$117$	4.44941	+	8.76317i	0.411348	+	0.810155i
$118$	−11.2044	+	3.35417i	−1.03145	+	0.308777i
$119$	−32.5046	−	3.79924i	−2.97969	−	0.348276i
$120$	3.78884	+	4.23912i	0.345872	+	0.386977i
$121$	2.97379	+	9.93315i	0.270345	+	0.903014i
$122$	0.110238	+	0.465166i	0.00998047	+	0.0421142i
$123$	−2.06319	−	1.62400i	−0.186032	−	0.146431i
$124$	−2.35209	+	9.92271i	−0.211224	+	0.891086i
$125$	−3.43471	−	9.43679i	−0.307210	−	0.844052i
$126$	−16.8395	−	12.4222i	−1.50018	−	1.10666i
$127$	−3.37183	+	9.26404i	−0.299202	+	0.822050i	0.695432	+	0.718592i	$0.255213\pi$
$127$	−3.37183	+	9.26404i	−0.299202	+	0.822050i	−0.994634	+	0.103458i	$0.967009\pi$
$128$	7.27126	+	8.66768i	0.642695	+	0.766122i
$129$	3.00591	−	1.62932i	0.264656	−	0.143454i
$130$	0.312543	+	5.36775i	0.0274118	+	0.470783i
$131$	−4.26026	+	2.13958i	−0.372220	+	0.186936i	−0.625068	−	0.780570i	$-0.714929\pi$
$131$	−4.26026	+	2.13958i	−0.372220	+	0.186936i	0.252848	+	0.967506i	$0.418633\pi$
$132$	−2.05997	−	1.82524i	−0.179298	−	0.158867i
$133$	−0.961803	+	0.227951i	−0.0833989	+	0.0197659i
$134$	−10.7001	−	7.03784i	−0.924349	−	0.607977i
$135$	−5.97240	−	0.834609i	−0.514022	−	0.0718317i
$136$	−17.6356	+	6.41779i	−1.51224	+	0.550321i
$137$	0.884331	−	0.834323i	0.0755535	−	0.0712810i	−0.647539	−	0.762033i	$-0.724202\pi$
$137$	0.884331	−	0.834323i	0.0755535	−	0.0712810i	0.723092	+	0.690751i	$0.242720\pi$
$138$	−2.48365	−	11.8972i	−0.211423	−	1.01276i
$139$	−10.9835	−	0.639719i	−0.931612	−	0.0542602i	−0.414379	−	0.910105i	$-0.636001\pi$
$139$	−10.9835	−	0.639719i	−0.931612	−	0.0542602i	−0.517234	+	0.855844i	$0.673038\pi$
$140$	−5.72376	−	9.91463i	−0.483746	−	0.837939i
$141$	1.02986	+	6.92456i	0.0867300	+	0.583153i
$142$	−14.0708	+	8.12345i	−1.18080	+	0.681705i
$143$	−0.451977	−	2.56329i	−0.0377962	−	0.214353i
$144$	−11.8266	−	2.03259i	−0.985550	−	0.169382i
$145$	0.369823	−	2.09737i	0.0307121	−	0.174177i
$146$	6.05045	+	16.6244i	0.500739	+	1.37584i
$147$	20.0002	+	22.3747i	1.64958	+	1.84543i
$148$	14.4090	+	5.24502i	1.18441	+	0.431138i
$149$	6.09546	+	5.75077i	0.499360	+	0.471122i	0.894225	−	0.447617i	$-0.147727\pi$
$149$	6.09546	+	5.75077i	0.499360	+	0.471122i	−0.394865	+	0.918739i	$0.629209\pi$
$150$	7.62624	+	4.68099i	0.622680	+	0.382201i
$151$	14.5009	+	10.7955i	1.18007	+	0.878527i	0.994565	−	0.104117i	$-0.0332017\pi$
$151$	14.5009	+	10.7955i	1.18007	+	0.878527i	0.185501	+	0.982644i	$0.440609\pi$
$152$	−0.434240	+	0.364333i	−0.0352216	+	0.0295513i
$153$	9.87679	−	17.2822i	0.798491	−	1.39719i
$154$	3.30930	+	4.44532i	0.266671	+	0.358214i
$155$	−0.344071	−	5.90748i	−0.0276365	−	0.474500i
$156$	−7.56274	−	8.46122i	−0.605504	−	0.677440i
$157$	−9.15770	+	21.2299i	−0.730864	+	1.69433i	−0.0112711	+	0.999936i	$0.503588\pi$
$157$	−9.15770	+	21.2299i	−0.730864	+	1.69433i	−0.719593	+	0.694396i	$0.755671\pi$
$158$	10.4518	−	14.0386i	0.831497	−	1.11685i
$159$	−1.45971	−	16.2722i	−0.115762	−	1.29047i
$160$	−5.48475	−	3.60806i	−0.433608	−	0.285242i
$161$			24.4721i			1.92868i
$162$	10.9664	−	6.46051i	0.861601	−	0.507585i
$163$			3.18483i			0.249455i	0.992191	+	0.124727i	$0.0398057\pi$
$163$			3.18483i			0.249455i	−0.992191	+	0.124727i	$0.960194\pi$
$164$	2.78386	+	1.20096i	0.217383	+	0.0937789i
$165$	1.44893	+	0.671771i	0.112799	+	0.0522973i
$166$	9.20615	+	6.85397i	0.714536	+	0.531971i
$167$	−2.32169	+	5.38228i	−0.179658	+	0.416494i	−0.984119	−	0.177512i	$-0.943195\pi$
$167$	−2.32169	+	5.38228i	−0.179658	+	0.416494i	0.804461	+	0.594006i	$0.202454\pi$
$168$	22.4747	+	8.87278i	1.73396	+	0.684550i
$169$	0.131857	+	2.26389i	0.0101428	+	0.174146i
$170$	8.73532	−	6.50297i	0.669968	−	0.498755i
$171$	0.101795	−	0.592540i	0.00778446	−	0.0453127i
$172$	−2.87179	+	2.70920i	−0.218972	+	0.206575i
$173$	−13.1708	−	9.80527i	−1.00135	−	0.745481i	−0.0341338	−	0.999417i	$-0.510867\pi$
$173$	−13.1708	−	9.80527i	−1.00135	−	0.745481i	−0.967221	+	0.253936i	$0.918275\pi$
$174$	2.14197	+	3.95186i	0.162382	+	0.299590i
$175$	−13.1057	−	12.3646i	−0.990699	−	0.934676i
$176$	2.83991	+	1.42650i	0.214066	+	0.107527i
$177$	−4.47570	+	13.6071i	−0.336414	+	1.02277i
$178$	−2.63700	+	0.959739i	−0.197652	+	0.0719355i
$179$	1.80860	−	10.2571i	0.135181	−	0.766649i	−0.839553	−	0.543278i	$-0.817183\pi$
$179$	1.80860	−	10.2571i	0.135181	−	0.766649i	0.974734	−	0.223371i	$-0.0717061\pi$
$180$	6.91267	−	0.838575i	0.515240	−	0.0625037i
$181$	−0.478446	−	2.71340i	−0.0355626	−	0.201686i	0.961850	−	0.273578i	$-0.0882072\pi$
$181$	−0.478446	−	2.71340i	−0.0355626	−	0.201686i	−0.997412	+	0.0718926i	$0.977096\pi$
$182$	11.4251	+	19.7896i	0.846882	+	1.46690i
$183$	0.544597	+	0.214969i	0.0402578	+	0.0158910i
$184$	6.29772	+	12.5414i	0.464274	+	0.924566i
$185$	−8.88291	−	0.517370i	−0.653084	−	0.0380378i
$186$	8.32334	+	9.31186i	0.610297	+	0.682779i
$187$	−3.83450	+	3.61766i	−0.280406	+	0.264550i
$188$	−3.20155	−	7.42273i	−0.233497	−	0.541358i
$189$	−24.2739	+	8.22166i	−1.76567	+	0.598038i
$190$	0.180751	−	0.274808i	0.0131130	−	0.0199367i
$191$	−8.35069	+	1.97915i	−0.604235	+	0.143206i	−0.521336	−	0.853352i	$-0.674566\pi$
$191$	−8.35069	+	1.97915i	−0.604235	+	0.143206i	−0.0828990	+	0.996558i	$0.526418\pi$
$192$	13.8011	−	1.23659i	0.996010	−	0.0892435i
$193$	18.5267	−	9.30446i	1.33358	−	0.669750i	0.367994	−	0.929828i	$-0.380045\pi$
$193$	18.5267	−	9.30446i	1.33358	−	0.669750i	0.965587	+	0.260079i	$0.0837485\pi$
$194$	−10.0722	+	0.586467i	−0.723145	+	0.0421059i
$195$	5.61242	+	3.44477i	0.401913	+	0.246685i
$196$	−28.9517	−	19.0432i	−2.06798	−	1.36023i
$197$	0.965221	−	2.65192i	0.0687692	−	0.188942i	−0.900547	−	0.434758i	$-0.856834\pi$
$197$	0.965221	−	2.65192i	0.0687692	−	0.188942i	0.969316	+	0.245816i	$0.0790561\pi$
$198$	−3.27653	+	0.791732i	−0.232853	+	0.0562660i
$199$	−2.21656	−	6.08995i	−0.157128	−	0.431705i	0.836001	−	0.548727i	$-0.184887\pi$
$199$	−2.21656	−	6.08995i	−0.157128	−	0.431705i	−0.993129	+	0.117022i	$0.962665\pi$
$200$	−9.89832	−	2.96392i	−0.699917	−	0.209581i
$201$	−14.5645	+	5.82324i	−1.02730	+	0.410740i
$202$	12.1837	−	2.88737i	0.857242	−	0.203155i
$203$	−2.59586	−	8.67078i	−0.182194	−	0.608570i
$204$	−5.90083	+	22.2145i	−0.413141	+	1.55532i
$205$	−1.74743	−	0.204245i	−0.122046	−	0.0142651i
$206$	4.17094	+	13.9328i	0.290603	+	0.970743i
$207$	−13.6936	−	5.83551i	−0.951769	−	0.405596i
$208$	10.9478	+	7.20155i	0.759092	+	0.499338i
$209$	−0.0714603	+	0.142289i	−0.00494302	+	0.00984235i
$210$	−13.9704	−	1.19154i	−0.964049	−	0.0822238i
$211$	−1.40055	−	11.9825i	−0.0964179	−	0.824908i	−0.951760	−	0.306844i	$-0.900727\pi$
$211$	−1.40055	−	11.9825i	−0.0964179	−	0.824908i	0.855342	−	0.518064i	$-0.173347\pi$
$212$	6.45159	+	17.7275i	0.443097	+	1.21753i
$213$	−1.69070	+	19.8270i	−0.115845	+	1.35852i
$214$	26.6802	−	4.70396i	1.82382	−	0.321556i
$215$	1.14548	−	1.98403i	0.0781210	−	0.135310i
$216$	−10.3240	+	10.4601i	−0.702462	+	0.711721i
$217$	−12.5742	−	21.7792i	−0.853595	−	1.47847i
$218$	9.88181	+	11.7771i	0.669281	+	0.797646i
$219$	20.9412	+	5.56183i	1.41507	+	0.375833i
$220$	−1.81613	−	0.320297i	−0.122443	−	0.0215944i
$221$	−17.4356	+	12.9803i	−1.17285	+	0.873152i
$222$	15.3603	−	10.8054i	1.03091	−	0.725212i
$223$	14.5501	+	22.1223i	0.974345	+	1.48142i	0.873681	+	0.486499i	$0.161726\pi$
$223$	14.5501	+	22.1223i	0.974345	+	1.48142i	0.100664	+	0.994920i	$0.467903\pi$
$224$	−27.7118	−	3.24147i	−1.85157	−	0.216580i
$225$	10.0438	−	4.38499i	0.669589	−	0.292333i
$226$	−7.10368	−	1.68373i	−0.472530	−	0.112000i
$227$	6.06372	+	14.0573i	0.402463	+	0.933015i	0.992112	+	0.125355i	$0.0400070\pi$
$227$	6.06372	+	14.0573i	0.402463	+	0.933015i	−0.589649	+	0.807660i	$0.700734\pi$
$228$	0.0620033	+	0.691455i	0.00410627	+	0.0457927i
$229$	−15.1303	−	3.58594i	−0.999836	−	0.236965i	−0.302066	−	0.953287i	$-0.597676\pi$
$229$	−15.1303	−	3.58594i	−0.999836	−	0.236965i	−0.697770	+	0.716322i	$0.745824\pi$
$230$	−5.58833	−	5.92349i	−0.368484	−	0.390583i
$231$	6.78405	−	0.212332i	0.446358	−	0.0139704i
$232$	−3.56168	−	3.77555i	−0.233836	−	0.247877i
$233$	16.8260	−	20.0525i	1.10231	−	1.31368i	0.156966	−	0.987604i	$-0.449829\pi$
$233$	16.8260	−	20.0525i	1.10231	−	1.31368i	0.945343	−	0.326077i	$-0.105727\pi$
$234$	−13.7978	+	1.67405i	−0.901988	+	0.109436i
$235$	3.01520	+	3.59338i	0.196690	+	0.234406i
$236$	0.962300	−	16.5122i	0.0626404	−	1.07485i
$237$	−6.78719	−	20.3327i	−0.440875	−	1.32075i
$238$	20.7718	−	41.3582i	1.34643	−	2.68085i
$239$	16.6368	+	10.9422i	1.07614	+	0.707791i	0.958450	−	0.285259i	$-0.0920797\pi$
$239$	16.6368	+	10.9422i	1.07614	+	0.707791i	0.117693	+	0.993050i	$0.462450\pi$
$240$	−7.46615	+	2.98454i	−0.481938	+	0.192651i
$241$	−2.70755	+	9.04385i	−0.174409	+	0.582566i	0.825428	+	0.564507i	$0.190934\pi$
$241$	−2.70755	+	9.04385i	−0.174409	+	0.582566i	−0.999837	+	0.0180586i	$0.994251\pi$
$242$	−14.6388	−	0.852867i	−0.941018	−	0.0548244i
$243$	1.18775	−	15.5431i	0.0761943	−	0.997093i
$244$	−0.671491	−	0.0785096i	−0.0429878	−	0.00502606i
$245$	19.2637	+	5.76718i	1.23072	+	0.368452i
$246$	3.15615	−	1.95627i	0.201229	−	0.124727i
$247$	−0.360772	+	0.548527i	−0.0229554	+	0.0349020i
$248$	−12.0487	−	7.92547i	−0.765095	−	0.503268i
$249$	13.3336	−	4.45085i	0.844983	−	0.282061i
$250$	14.2021		0.000245455i	0.898222		1.55239e-5i
$251$	17.1780	−	14.4140i	1.08426	−	0.909805i	0.0879961	−	0.996121i	$-0.471954\pi$
$251$	17.1780	−	14.4140i	1.08426	−	0.909805i	0.996268	+	0.0863154i	$0.0275093\pi$
$252$	24.6535	−	16.3695i	1.55303	−	1.03118i
$253$	3.01985	+	2.53396i	0.189857	+	0.159309i
$254$	−10.6801	−	8.96202i	−0.670132	−	0.562327i
$255$	−0.417245	−	13.3311i	−0.0261289	−	0.834824i
$256$	−15.0358	+	5.47024i	−0.939740	+	0.341890i
$257$	3.34716	−	14.1228i	0.208790	−	0.880956i	−0.763243	−	0.646112i	$-0.776394\pi$
$257$	3.34716	−	14.1228i	0.208790	−	0.880956i	0.972033	−	0.234844i	$-0.0754579\pi$
$258$	0.711233	+	4.78274i	0.0442794	+	0.297760i
$259$	−34.7224	+	14.9778i	−2.15754	+	0.930673i
$260$	−7.28448	−	2.18110i	−0.451764	−	0.135266i
$261$	5.47080	+	0.615060i	0.338634	+	0.0380713i
$262$	−0.782588	−	6.69647i	−0.0483484	−	0.413709i
$263$	−5.39588	+	3.54892i	−0.332724	+	0.218836i	−0.704867	−	0.709339i	$-0.748993\pi$
$263$	−5.39588	+	3.54892i	−0.332724	+	0.218836i	0.372143	+	0.928175i	$0.378623\pi$
$264$	3.42203	−	1.85464i	0.210612	−	0.114145i
$265$	−6.53706	−	8.78079i	−0.401568	−	0.539400i
$266$	0.162307	−	1.38842i	0.00995170	−	0.0851295i
$267$	−0.882232	+	3.32174i	−0.0539917	+	0.203287i
$268$	14.5285	−	10.8153i	0.887468	−	0.660648i
$269$	−17.1539	+	9.90384i	−1.04589	+	0.603848i	−0.921497	−	0.388385i	$-0.873033\pi$
$269$	−17.1539	+	9.90384i	−1.04589	+	0.603848i	−0.124397	+	0.992232i	$0.539700\pi$
$270$	3.99805	−	7.53311i	0.243314	−	0.458451i
$271$	−0.465351	−	0.268671i	−0.0282681	−	0.0163206i	0.485799	−	0.874070i	$-0.338529\pi$
$271$	−0.465351	−	0.268671i	−0.0282681	−	0.0163206i	−0.514067	+	0.857750i	$0.671862\pi$
$272$	0.00183480	−	26.5406i	0.000111251	−	1.60926i
$273$	27.8852	+	2.37784i	1.68769	+	0.143914i
$274$	0.680985	+	1.57878i	0.0411398	+	0.0953773i
$275$	−2.88281	+	0.336953i	−0.173840	+	0.0203190i
$276$	17.0117	+	2.45424i	1.02399	+	0.147728i
$277$	3.81140	+	1.91416i	0.229005	+	0.115011i	0.559602	−	0.828761i	$-0.310954\pi$
$277$	3.81140	+	1.91416i	0.229005	+	0.115011i	−0.330597	+	0.943772i	$0.607250\pi$
$278$	6.16301	−	14.2868i	0.369633	−	0.856865i
$279$	15.1851	−	1.84264i	0.909109	−	0.110316i
$280$	15.9444	−	2.81057i	0.952859	−	0.167964i
$281$	2.10570	−	18.0154i	0.125616	−	1.07471i	−0.772519	−	0.634991i	$-0.781004\pi$
$281$	2.10570	−	18.0154i	0.125616	−	1.07471i	0.898135	−	0.439720i	$-0.144922\pi$
$282$	−9.70032	−	1.98089i	−0.577646	−	0.117960i
$283$	−9.19261	+	2.75209i	−0.546444	+	0.163595i	−0.548113	−	0.836404i	$-0.684654\pi$
$283$	−9.19261	+	2.75209i	−0.546444	+	0.163595i	0.00166960	+	0.999999i	$0.499469\pi$
$284$	−3.98918	−	22.6283i	−0.236714	−	1.34275i
$285$	−0.149557	−	0.374056i	−0.00885897	−	0.0221572i
$286$	3.62503	+	0.639255i	0.214352	+	0.0377999i
$287$	−7.02596	+	2.55724i	−0.414730	+	0.150949i
$288$	8.42182	−	14.7334i	0.496260	−	0.868174i
$289$	25.3954	+	9.24316i	1.49384	+	0.543715i
$290$	2.60834	+	1.50599i	0.153167	+	0.0884346i
$291$	−6.46390	+	10.5313i	−0.378920	+	0.617358i
$292$	−25.0191		0.000864807i	−1.46413		5.06090e-5i
$293$	6.90157	+	13.7422i	0.403194	+	0.802825i	1.00000		0.000439526i	$0.000139906\pi$
$293$	6.90157	+	13.7422i	0.403194	+	0.802825i	−0.596806	+	0.802386i	$0.703564\pi$
$294$	−39.4084	+	15.7556i	−2.29835	+	0.918887i
$295$	2.21344	+	9.33923i	0.128871	+	0.543751i
$296$	−13.9400	+	16.6113i	−0.810247	+	0.965513i
$297$	−1.49888	+	3.84670i	−0.0869739	+	0.223208i
$298$	−10.5908	+	5.31865i	−0.613506	+	0.308101i
$299$	11.1546	+	11.8232i	0.645087	+	0.683753i
$300$	−9.90955	+	7.87039i	−0.572128	+	0.454397i
$301$	0.566112	−	9.71976i	0.0326301	−	0.560238i
$302$	−21.3606	+	14.0486i	−1.22917	+	0.808404i
$303$	5.63050	−	14.2642i	0.323464	−	0.819456i
$304$	−0.274121	−	0.753302i	−0.0157219	−	0.0432048i
$305$	0.386346	−	0.0681232i	0.0221221	−	0.00390072i
$306$	18.1891	+	21.4851i	1.03980	+	1.22822i
$307$	14.9336	+	2.63319i	0.852305	+	0.150284i	0.582701	−	0.812687i	$-0.301996\pi$
$307$	14.9336	+	2.63319i	0.852305	+	0.150284i	0.269604	+	0.962971i	$0.413107\pi$
$308$	−7.50821	+	2.24753i	−0.427820	+	0.128065i
$309$	16.9205	+	5.56557i	0.962573	+	0.316614i
$310$	8.01698	+	2.40028i	0.455334	+	0.136327i
$311$	13.7256	−	14.5483i	0.778307	−	0.824957i	−0.209958	−	0.977710i	$-0.567333\pi$
$311$	13.7256	−	14.5483i	0.778307	−	0.824957i	0.988264	+	0.152754i	$0.0488141\pi$
$312$	14.9025	−	5.95746i	0.843685	−	0.337275i
$313$	−2.17623	+	2.92318i	−0.123008	+	0.165228i	−0.859361	−	0.511369i	$-0.829139\pi$
$313$	−2.17623	+	2.92318i	−0.123008	+	0.165228i	0.736354	+	0.676597i	$0.236546\pi$
$314$	−23.7831	−	22.4390i	−1.34216	−	1.26631i
$315$	−10.9802	+	13.2032i	−0.618662	+	0.743915i
$316$	13.6005	+	20.6802i	0.765091	+	1.16335i
$317$	−10.9358	+	0.636937i	−0.614215	+	0.0357739i	−0.362433	−	0.932010i	$-0.618054\pi$
$317$	−10.9358	+	0.636937i	−0.614215	+	0.0357739i	−0.251782	+	0.967784i	$0.581017\pi$
$318$	22.3305	+	5.93124i	1.25223	+	0.332607i
$319$	−1.33876	−	0.577484i	−0.0749561	−	0.0323329i
$320$	7.44785	−	5.54352i	0.416348	−	0.309892i
$321$	13.9565	−	30.1024i	0.778974	−	1.68015i
$322$	−32.5215	−	11.8375i	−1.81235	−	0.659677i
$323$	1.32973			0.0739881
$324$	3.28090	+	17.6985i	0.182272	+	0.983248i
$325$	−11.9676			−0.663845
$326$	−4.23237	−	1.54054i	−0.234410	−	0.0853227i
$327$	18.7535	−	1.68230i	1.03707	−	0.0930313i
$328$	−2.94256	+	3.11861i	−0.162476	+	0.172196i
$329$	18.3049	+	7.89597i	1.00918	+	0.435319i
$330$	−1.59359	+	1.60057i	−0.0877245	+	0.0881082i
$331$	−1.62215	+	0.0944792i	−0.0891612	+	0.00519305i	−0.102667	−	0.994716i	$-0.532738\pi$
$331$	−1.62215	+	0.0944792i	−0.0891612	+	0.00519305i	0.0135062	+	0.999909i	$0.495701\pi$
$332$	−13.5615	+	8.91886i	−0.744284	+	0.489486i
$333$	−0.101188	−	23.0007i	−0.00554505	−	1.26043i
$334$	−6.02958	−	5.68881i	−0.329924	−	0.311278i
$335$	−6.27616	+	8.43035i	−0.342903	+	0.460599i
$336$	−22.6625	+	25.5751i	−1.23634	+	1.39524i
$337$	−8.86472	+	9.39606i	−0.482892	+	0.511836i	−0.922312	−	0.386446i	$-0.873703\pi$
$337$	−8.86472	+	9.39606i	−0.482892	+	0.511836i	0.439420	+	0.898282i	$0.355184\pi$
$338$	−3.07231	−	0.919847i	−0.167112	−	0.0500331i
$339$	−6.66625	+	5.95878i	−0.362061	+	0.323637i
$340$	4.41653	+	14.7541i	0.239520	+	0.800153i
$341$	−3.98954	−	0.703464i	−0.216046	−	0.0380947i
$342$	0.738197	+	0.421896i	0.0399171	+	0.0228135i
$343$	50.1591	−	8.84440i	2.70833	−	0.477552i
$344$	−2.21119	−	5.12684i	−0.119219	−	0.276421i
$345$	−9.86524	+	1.46722i	−0.531127	+	0.0789924i
$346$	19.4013	−	12.7599i	1.04302	−	0.685978i
$347$	−1.34837	+	23.1507i	−0.0723846	+	1.24279i	0.745143	+	0.666905i	$0.232381\pi$
$347$	−1.34837	+	23.1507i	−0.0723846	+	1.24279i	−0.817527	+	0.575890i	$0.804656\pi$
$348$	−6.28780	+	0.934937i	−0.337062	+	0.0501179i
$349$	2.93245	+	3.10822i	0.156971	+	0.166379i	0.801086	−	0.598549i	$-0.204256\pi$
$349$	2.93245	+	3.10822i	0.156971	+	0.166379i	−0.644115	+	0.764928i	$0.722774\pi$
$350$	22.7709	−	11.4355i	1.21716	−	0.611253i
$351$	−7.97992	+	15.0364i	−0.425936	+	0.802582i
$352$	−3.26940	+	3.08399i	−0.174260	+	0.164377i
$353$	6.28900	+	26.5354i	0.334730	+	1.41234i	0.836800	+	0.547509i	$0.184424\pi$
$353$	6.28900	+	26.5354i	0.334730	+	1.41234i	−0.502070	+	0.864827i	$0.667428\pi$
$354$	−15.9177	−	12.5298i	−0.846018	−	0.665949i
$355$	5.98394	+	11.9150i	0.317595	+	0.632383i
$356$	0.000137178	−	3.96860i	7.27042e−6	−	0.210335i
$357$	−27.0114	−	49.8331i	−1.42959	−	2.63744i
$358$	12.7560	+	7.36495i	0.674173	+	0.389250i
$359$	8.40764	+	3.06013i	0.443738	+	0.161507i	0.554219	−	0.832371i	$-0.313017\pi$
$359$	8.40764	+	3.06013i	0.443738	+	0.161507i	−0.110481	+	0.993878i	$0.535239\pi$
$360$	−2.22935	+	9.59199i	−0.117497	+	0.505542i
$361$	−17.8164	+	6.48465i	−0.937706	+	0.341297i
$362$	3.83732	+	0.676691i	0.201685	+	0.0355661i
$363$	−11.1079	+	14.1119i	−0.583015	+	0.740685i
$364$	−31.8252	+	5.61050i	−1.66809	+	0.294070i
$365$	13.9081	−	4.16382i	0.727985	−	0.217944i
$366$	−0.549105	+	0.619742i	−0.0287022	+	0.0323944i
$367$	−1.62461	+	13.8994i	−0.0848038	+	0.725543i	0.882217	+	0.470844i	$0.156050\pi$
$367$	−1.62461	+	13.8994i	−0.0848038	+	0.725543i	−0.967020	+	0.254699i	$0.918024\pi$
$368$	−19.7128	+	2.30271i	−1.02760	+	0.120037i
$369$	0.244455	−	4.54122i	0.0127258	−	0.236406i
$370$	4.98432	−	11.5544i	0.259122	−	0.600684i
$371$	−41.5744	−	20.8794i	−2.15843	−	1.08401i
$372$	−16.4008	+	6.55677i	−0.850342	+	0.339953i
$373$	20.1490	−	2.35508i	1.04328	−	0.121941i	0.422844	−	0.906202i	$-0.361032\pi$
$373$	20.1490	−	2.35508i	1.04328	−	0.121941i	0.620431	+	0.784261i	$0.286958\pi$
$374$	−2.95278	−	6.84564i	−0.152685	−	0.353980i
$375$	9.94542	−	14.2702i	0.513579	−	0.736912i
$376$	11.4128	−	0.664127i	0.588571	−	0.0342498i
$377$	−5.20635	−	3.00589i	−0.268141	−	0.154811i
$378$	0.815683	−	36.2349i	0.0419542	−	1.86372i
$379$	−0.591307	+	0.341391i	−0.0303734	+	0.0175361i	−0.515110	−	0.857124i	$-0.672249\pi$
$379$	−0.591307	+	0.341391i	−0.0303734	+	0.0175361i	0.484736	+	0.874660i	$0.338916\pi$
$380$	0.277766	+	0.373131i	0.0142491	+	0.0191412i
$381$	−16.4840	+	4.45575i	−0.844499	+	0.228275i
$382$	1.40921	−	12.0547i	0.0721012	−	0.616773i
$383$	−3.73842	−	5.02157i	−0.191024	−	0.256590i	0.696285	−	0.717766i	$-0.254835\pi$
$383$	−3.73842	−	5.02157i	−0.191024	−	0.256590i	−0.887309	+	0.461176i	$0.847428\pi$
$384$	−5.03244	+	18.9387i	−0.256811	+	0.966462i
$385$	3.79969	−	2.49909i	0.193650	−	0.127366i
$386$	3.40326	+	29.1211i	0.173222	+	1.48223i
$387$	5.30377	+	2.63450i	0.269606	+	0.133919i
$388$	4.09271	−	13.6689i	0.207776	−	0.693932i
$389$	11.0798	−	4.77937i	0.561769	−	0.242324i	−0.0962082	−	0.995361i	$-0.530671\pi$
$389$	11.0798	−	4.77937i	0.561769	−	0.242324i	0.657977	+	0.753038i	$0.271412\pi$
$390$	−7.29261	+	5.79216i	−0.369276	+	0.293297i
$391$	7.59226	−	32.0343i	0.383957	−	1.62004i
$392$	39.3112	−	29.2629i	1.98551	−	1.47800i
$393$	−7.27668	−	3.90291i	−0.367060	−	0.196876i
$394$	3.05730	+	2.56547i	0.154024	+	0.129246i
$395$	−11.0026	−	9.23227i	−0.553600	−	0.464526i
$396$	0.532752	−	4.73721i	0.0267718	−	0.238054i
$397$	−13.5521	+	11.3715i	−0.680159	+	0.570721i	−0.916053	−	0.401058i	$-0.868643\pi$
$397$	−13.5521	+	11.3715i	−0.680159	+	0.570721i	0.235894	+	0.971779i	$0.424198\pi$
$398$	9.16523		0.000158402i	0.459411		7.93997e-6i
$399$	−1.28144	−	1.13534i	−0.0641521	−	0.0568381i
$400$	8.72675	−	11.7204i	0.436337	−	0.586018i
$401$	12.2597	−	18.6400i	0.612221	−	0.930837i	−0.387738	−	0.921770i	$-0.626743\pi$
$401$	12.2597	−	18.6400i	0.612221	−	0.930837i	0.999959	−	0.00906738i	$-0.00288628\pi$
$402$	−0.693565	−	22.1718i	−0.0345919	−	1.10583i
$403$	−16.0021	−	4.79072i	−0.797122	−	0.238643i
$404$	−2.05633	+	17.5878i	−0.102306	+	0.875026i
$405$	−4.76966	−	9.29240i	−0.237006	−	0.461743i
$406$	12.7784	+	0.744479i	0.634182	+	0.0369479i
$407$	−1.74706	+	5.83560i	−0.0865987	+	0.289260i
$408$	−26.6669	−	18.5871i	−1.32021	−	0.920200i
$409$	−2.06903	−	1.36082i	−0.102307	−	0.0672883i	0.497325	−	0.867565i	$-0.334316\pi$
$409$	−2.06903	−	1.36082i	−0.102307	−	0.0672883i	−0.599632	+	0.800276i	$0.704686\pi$
$410$	1.11668	−	2.22339i	0.0551488	−	0.109806i
$411$	2.06323	+	0.421293i	0.101772	+	0.0207809i
$412$	−20.5331	−	1.19663i	−1.01159	−	0.0589535i
$413$	26.2192	+	31.2469i	1.29016	+	1.53756i
$414$	14.3787	−	15.3749i	0.706673	−	0.755636i
$415$	6.05427	−	7.21519i	0.297192	−	0.354180i
$416$	−14.8659	+	11.0652i	−0.728858	+	0.542517i
$417$	−10.0398	−	16.1971i	−0.491649	−	0.793175i
$418$	−0.154524	−	0.163792i	−0.00755804	−	0.00801133i
$419$	26.8878	+	6.37253i	1.31356	+	0.311319i	0.826937	−	0.562295i	$-0.190082\pi$
$419$	26.8878	+	6.37253i	1.31356	+	0.311319i	0.486620	+	0.873614i	$0.338230\pi$
$420$	8.34111	−	17.9892i	0.407005	−	0.877781i
$421$	−12.6757	−	29.3855i	−0.617774	−	1.43216i	−0.883647	−	0.468154i	$-0.844919\pi$
$421$	−12.6757	−	29.3855i	−0.617774	−	1.43216i	0.265873	−	0.964008i	$-0.414340\pi$
$422$	16.6012	+	3.93486i	0.808133	+	0.191546i
$423$	−8.78315	+	8.35982i	−0.427052	+	0.406468i
$424$	−26.6791	−	0.00138328i	−1.29565	−	6.71780e-5i
$425$	13.3195	+	20.2513i	0.646090	+	0.982333i
$426$	−25.5306	−	11.8373i	−1.23696	−	0.573521i
$427$	1.33733	−	0.995609i	0.0647182	−	0.0481809i
$428$	−6.65436	+	37.7311i	−0.321651	+	1.82380i
$429$	3.18079	−	3.19481i	0.153570	−	0.154247i
$430$	2.08253	+	2.48195i	0.100428	+	0.119690i
$431$	3.89954	+	6.75421i	0.187834	+	0.325339i	0.944528	−	0.328431i	$-0.106520\pi$
$431$	3.89954	+	6.75421i	0.187834	+	0.325339i	−0.756694	+	0.653770i	$0.773187\pi$
$432$	−8.90677	−	18.7795i	−0.428527	−	0.903529i
$433$	−12.7081	+	22.0112i	−0.610715	+	1.05779i	0.380406	+	0.924820i	$0.375784\pi$
$433$	−12.7081	+	22.0112i	−0.610715	+	1.05779i	−0.991120	+	0.132969i	$0.957549\pi$
$434$	35.0251	−	6.17525i	1.68126	−	0.296421i
$435$	3.33974	−	1.56630i	0.160128	−	0.0750983i
$436$	−20.4308	+	7.43539i	−0.978456	+	0.356090i
$437$	−0.115438	−	0.987637i	−0.00552216	−	0.0472451i
$438$	−17.5207	+	25.1388i	−0.837172	+	1.20118i
$439$	0.480874	−	0.957499i	0.0229509	−	0.0456989i	−0.881865	−	0.471502i	$-0.843712\pi$
$439$	0.480874	−	0.957499i	0.0229509	−	0.0456989i	0.904816	+	0.425803i	$0.140008\pi$
$440$	1.30413	−	2.25855i	0.0621720	−	0.107672i
$441$	−11.7647	+	50.6309i	−0.560226	+	2.41100i
$442$	−8.81597	−	29.4493i	−0.419333	−	1.40076i
$443$	15.9850	+	1.86838i	0.759470	+	0.0887693i	0.487008	−	0.873397i	$-0.338088\pi$
$443$	15.9850	+	1.86838i	0.759470	+	0.0887693i	0.272462	+	0.962167i	$0.412162\pi$
$444$	6.92955	+	25.6392i	0.328862	+	1.21678i
$445$	0.660477	+	2.20615i	0.0313096	+	0.104581i
$446$	−36.4368	+	8.63501i	−1.72533	+	0.408880i
$447$	−2.07206	+	14.3661i	−0.0980048	+	0.679493i
$448$	17.7122	−	35.2588i	0.836823	−	1.66582i
$449$	−6.64750	−	18.2639i	−0.313715	−	0.861925i	−0.991899	−	0.127032i	$-0.959455\pi$
$449$	−6.64750	−	18.2639i	−0.313715	−	0.861925i	0.678184	−	0.734892i	$-0.262767\pi$
$450$	0.968969	+	15.4685i	0.0456776	+	0.729192i
$451$	−0.411938	+	1.13179i	−0.0193974	+	0.0532939i
$452$	5.67368	−	8.62577i	0.266868	−	0.405722i
$453$	−0.841859	+	31.3009i	−0.0395540	+	1.47065i
$454$	−21.6141	+	1.25850i	−1.01440	+	0.0590644i
$455$	16.7576	−	8.41599i	0.785609	−	0.394548i
$456$	−0.948879	−	0.252068i	−0.0444353	−	0.0118042i
$457$	−24.6914	+	5.85198i	−1.15502	+	0.273744i	−0.763115	−	0.646263i	$-0.776331\pi$
$457$	−24.6914	+	5.85198i	−1.15502	+	0.273744i	−0.391902	+	0.920007i	$0.628183\pi$
$458$	12.0841	−	18.3723i	0.564654	−	0.858482i
$459$	34.3255	−	3.23147i	1.60218	−	0.150832i
$460$	10.5750	−	4.56116i	0.493061	−	0.212665i
$461$	−6.83555	+	6.44900i	−0.318363	+	0.300360i	−0.828789	−	0.559562i	$-0.810969\pi$
$461$	−6.83555	+	6.44900i	−0.318363	+	0.300360i	0.510425	+	0.859922i	$0.329488\pi$
$462$	−2.99936	+	9.11816i	−0.139543	+	0.424215i
$463$	7.42996	+	0.432746i	0.345300	+	0.0201114i	0.229918	−	0.973210i	$-0.426154\pi$
$463$	7.42996	+	0.432746i	0.345300	+	0.0201114i	0.115381	+	0.993321i	$0.463191\pi$
$464$	6.74023	−	2.90690i	0.312907	−	0.134949i
$465$	8.02578	−	6.37471i	0.372187	−	0.295620i
$466$	18.5091	+	32.0600i	0.857419	+	1.48515i
$467$	−4.05342	−	22.9881i	−0.187570	−	1.06376i	−0.922609	−	0.385737i	$-0.873947\pi$
$467$	−4.05342	−	22.9881i	−0.187570	−	1.06376i	0.735039	−	0.678025i	$-0.237164\pi$
$468$	4.44948	−	19.1459i	0.205677	−	0.885018i
$469$	−7.75620	+	43.9876i	−0.358148	+	2.03116i
$470$	−6.23379	+	2.26879i	−0.287543	+	0.104652i
$471$	−39.2012	+	8.18435i	−1.80630	+	0.377115i
$472$	21.4779	+	9.26598i	0.988601	+	0.426501i
$473$	−1.14080	−	1.07629i	−0.0524539	−	0.0494877i
$474$	30.3035	+	0.815557i	1.39189	+	0.0374598i
$475$	0.587240	+	0.437184i	0.0269444	+	0.0200594i
$476$	44.9141	+	47.6094i	2.05863	+	2.18217i
$477$	21.5969	−	18.2844i	0.988853	−	0.837187i
$478$	−22.5887	+	16.8160i	−1.03318	+	0.769148i
$479$	−0.188629	−	3.23864i	−0.00861868	−	0.147977i	−0.999872	−	0.0160036i	$-0.994906\pi$
$479$	−0.188629	−	3.23864i	−0.00861868	−	0.147977i	0.991253	−	0.131973i	$-0.0421314\pi$
$480$	−0.354744	−	11.3656i	−0.0161918	−	0.518764i
$481$	−9.94838	+	23.0629i	−0.453607	+	1.05158i
$482$	−10.7089	−	7.97274i	−0.487775	−	0.363148i
$483$	−34.6678	+	24.3885i	−1.57744	+	1.10972i
$484$	8.21436	−	19.0412i	0.373380	−	0.865510i
$485$			8.27967i			0.375960i
$486$	20.0810	+	9.09684i	0.910894	+	0.412641i
$487$			8.36821i			0.379200i	0.981861	+	0.189600i	$0.0607191\pi$
$487$			8.36821i			0.379200i	−0.981861	+	0.189600i	$0.939281\pi$
$488$	0.429141	−	0.854380i	0.0194263	−	0.0386760i
$489$	−4.51170	+	3.17394i	−0.204026	+	0.143531i
$490$	−16.9822	+	22.8103i	−0.767179	+	1.03046i
$491$	−3.88151	+	8.99836i	−0.175170	+	0.406090i	−0.983070	−	0.183229i	$-0.941345\pi$
$491$	−3.88151	+	8.99836i	−0.175170	+	0.406090i	0.807900	+	0.589320i	$0.200604\pi$
$492$	1.07305	+	5.14054i	0.0483766	+	0.231753i
$493$	0.707976	+	12.1555i	0.0318856	+	0.547455i
$494$	−0.554438	−	0.744766i	−0.0249453	−	0.0335086i
$495$	0.492331	+	2.72207i	0.0221286	+	0.122348i
$496$	16.3604	−	12.1781i	0.734604	−	0.546814i
$497$	45.4517	+	33.8376i	2.03879	+	1.51782i
$498$	−0.534819	+	19.8722i	−0.0239658	+	0.890494i
$499$	−18.5566	−	17.5072i	−0.830707	−	0.783731i	0.148002	−	0.988987i	$-0.452716\pi$
$499$	−18.5566	−	17.5072i	−0.830707	−	0.783731i	−0.978708	+	0.205256i	$0.934197\pi$
$500$	−6.87008	+	18.8733i	−0.307239	+	0.844042i
$501$	−9.93843	+	2.07492i	−0.444016	+	0.0927008i
$502$	10.8459	+	29.8004i	0.484074	+	1.33005i
$503$	−6.48865	+	36.7990i	−0.289315	+	1.64079i	0.400138	+	0.916455i	$0.368962\pi$
$503$	−6.48865	+	36.7990i	−0.289315	+	1.64079i	−0.689453	+	0.724331i	$0.742149\pi$
$504$	9.82848	+	40.6807i	0.437795	+	1.81206i
$505$	−1.78429	−	10.1192i	−0.0794001	−	0.450300i
$506$	−4.82816	+	2.78743i	−0.214638	+	0.123916i
$507$	−3.07568	+	2.44295i	−0.136596	+	0.108495i
$508$	17.0759	−	9.85799i	0.757621	−	0.437378i
$509$	−32.3814	−	1.88600i	−1.43528	−	0.0835956i	−0.677220	−	0.735780i	$-0.736816\pi$
$509$	−32.3814	−	1.88600i	−1.43528	−	0.0835956i	−0.758060	+	0.652185i	$0.773853\pi$
$510$	17.9177	+	5.89392i	0.793410	+	0.260987i
$511$	44.8787	−	42.3408i	1.98531	−	1.87305i
$512$	0.00351961	−	22.6274i	0.000155546	−	1.00000i
$513$	0.940854	−	0.446309i	0.0415397	−	0.0197050i
$514$	17.1490	+	11.2795i	0.756409	+	0.497516i
$515$	11.6134	−	2.75243i	0.511747	−	0.121286i
$516$	−6.69989	−	1.36830i	−0.294946	−	0.0602360i
$517$	2.86974	−	1.44124i	0.126211	−	0.0633854i
$518$	−3.10858	−	53.3881i	−0.136583	−	2.34574i
$519$	0.764638	−	28.4298i	0.0335639	−	1.24793i
$520$	6.42210	−	8.62545i	0.281628	−	0.378251i
$521$	7.27070	−	19.9761i	0.318535	−	0.875168i	−0.672323	−	0.740258i	$-0.734703\pi$
$521$	7.27070	−	19.9761i	0.318535	−	0.875168i	0.990858	−	0.134910i	$-0.0430744\pi$
$522$	−3.46366	+	6.97273i	−0.151600	+	0.305188i
$523$	3.96976	+	10.9068i	0.173586	+	0.476922i	0.995725	−	0.0923632i	$-0.0294421\pi$
$523$	3.96976	+	10.9068i	0.173586	+	0.476922i	−0.822140	+	0.569286i	$0.807220\pi$
$524$	9.27761	+	2.19917i	0.405294	+	0.0960713i
$525$	4.45508	−	30.8882i	0.194436	−	1.34807i
$526$	−2.10617	−	8.88733i	−0.0918336	−	0.387506i
$527$	9.70299	+	32.4102i	0.422669	+	1.41181i
$528$	0.809386	+	5.44471i	0.0352240	+	0.236951i
$529$	−1.60762	−	0.187904i	−0.0698965	−	0.00816973i
$530$	14.8310	−	4.43983i	0.644218	−	0.192854i
$531$	−23.7365	+	7.22018i	−1.03008	+	0.313329i
$532$	1.76659	+	0.887289i	0.0765912	+	0.0384689i
$533$	−2.22883	+	4.43797i	−0.0965414	+	0.192230i
$534$	−3.98758	−	2.77918i	−0.172559	−	0.120267i
$535$	−2.58103	−	22.0821i	−0.111588	−	0.954694i
$536$	7.34500	+	24.5386i	0.317256	+	1.05991i
$537$	16.3328	−	7.65991i	0.704814	−	0.330549i
$538$	−4.86380	−	27.5868i	−0.209693	−	1.18935i
$539$	6.88310	−	11.9219i	0.296476	−	0.513511i
$540$	8.07698	+	8.95694i	0.347578	+	0.385445i
$541$	3.88855	+	6.73517i	0.167182	+	0.289568i	0.937428	−	0.348179i	$-0.113200\pi$
$541$	3.88855	+	6.73517i	0.167182	+	0.289568i	−0.770246	+	0.637747i	$0.779867\pi$
$542$	0.582137	−	0.488454i	0.0250049	−	0.0209809i
$543$	3.36706	−	3.38191i	0.144494	−	0.145131i
$544$	35.2694	+	12.8405i	1.51216	+	0.550530i
$545$	10.1198	−	7.53389i	0.433483	−	0.322716i
$546$	−16.6484	+	35.9069i	−0.712485	+	1.53668i
$547$	−13.2104	−	20.0855i	−0.564836	−	0.858792i	0.434282	−	0.900777i	$-0.357002\pi$
$547$	−13.2104	−	20.0855i	−0.564836	−	0.858792i	−0.999118	+	0.0419851i	$0.986632\pi$
$548$	−2.42746	+	0.141299i	−0.103696	+	0.00603601i
$549$	0.238206	+	0.985724i	0.0101664	+	0.0420697i
$550$	0.946671	−	3.99401i	0.0403662	−	0.170305i
$551$	0.145664	+	0.337687i	0.00620549	+	0.0143859i
$552$	−11.4903	+	21.4201i	−0.489059	+	0.911698i
$553$	−59.3947	−	14.0768i	−2.52572	−	0.598607i
$554$	−4.38738	+	4.13914i	−0.186402	+	0.175855i
$555$	−8.11962	−	13.0993i	−0.344659	−	0.556036i
$556$	16.0048	+	15.1008i	0.678756	+	0.640418i
$557$	−17.3912	+	20.7260i	−0.736889	+	0.878190i	−0.996154	−	0.0876163i	$-0.972075\pi$
$557$	−17.3912	+	20.7260i	−0.736889	+	0.878190i	0.259266	+	0.965806i	$0.416520\pi$
$558$	−4.89652	+	21.0711i	−0.207286	+	0.892010i
$559$	−4.15684	−	4.95393i	−0.175816	−	0.209529i
$560$	−3.97748	+	22.5483i	−0.168079	+	0.952839i
$561$	−8.94627	−	1.82675i	−0.377712	−	0.0771253i
$562$	22.9225	+	11.5126i	0.966927	+	0.485630i
$563$	−0.386837	−	0.254427i	−0.0163033	−	0.0107228i	0.541331	−	0.840809i	$-0.317921\pi$
$563$	−0.386837	−	0.254427i	−0.0163033	−	0.0107228i	−0.557634	+	0.830087i	$0.688291\pi$
$564$	7.32461	−	11.9327i	0.308422	−	0.502459i
$565$	−1.71826	+	5.73938i	−0.0722876	+	0.241457i
$566$	0.789283	−	13.5474i	0.0331760	−	0.569441i
$567$	−35.8379	−	26.1934i	−1.50505	−	1.10002i
$568$	32.0008	+	5.64432i	1.34272	+	0.236830i
$569$	−31.8893	−	9.54703i	−1.33687	−	0.400232i	−0.462985	−	0.886366i	$-0.653222\pi$
$569$	−31.8893	−	9.54703i	−1.33687	−	0.400232i	−0.873884	+	0.486134i	$0.838407\pi$
$570$	0.569432	−	0.0178126i	0.0238509	−	0.000746089i
$571$	−19.0932	+	29.0299i	−0.799027	+	1.21486i	0.174131	+	0.984723i	$0.444288\pi$
$571$	−19.0932	+	29.0299i	−0.799027	+	1.21486i	−0.973158	+	0.230139i	$0.926082\pi$
$572$	−2.60299	+	4.50815i	−0.108836	+	0.188495i
$573$	−11.1259	−	9.85740i	−0.464789	−	0.411799i
$574$	0.000182748	−	10.5739i	7.62775e−6	−	0.441346i
$575$	13.8851	−	11.6509i	0.579047	−	0.485878i
$576$	15.5057	+	18.3186i	0.646072	+	0.763276i
$577$	−2.94900	−	2.47451i	−0.122769	−	0.103015i	0.579336	−	0.815089i	$-0.303312\pi$
$577$	−2.94900	−	2.47451i	−0.122769	−	0.103015i	−0.702105	+	0.712074i	$0.747756\pi$
$578$	−24.5674	+	29.2773i	−1.02187	+	1.21778i
$579$	31.6443	+	16.9727i	1.31509	+	0.705362i
$580$	−3.26302	+	2.73781i	−0.135490	+	0.113681i
$581$	9.23118	−	38.9494i	0.382974	−	1.61589i
$582$	−10.8686	−	13.6841i	−0.450519	−	0.567225i
$583$	−6.88132	+	2.96831i	−0.284995	+	0.122935i
$584$	12.1032	−	33.2479i	0.500834	−	1.37581i
$585$	0.713287	+	11.3837i	0.0294908	+	0.470657i
$586$	−21.6006	+	2.52437i	−0.892311	+	0.104281i
$587$	25.1725	−	16.5562i	1.03898	−	0.683348i	0.0891194	−	0.996021i	$-0.471595\pi$
$587$	25.1725	−	16.5562i	1.03898	−	0.683348i	0.949861	+	0.312673i	$0.101224\pi$
$588$	−1.87559	−	59.9918i	−0.0773480	−	2.47402i
$589$	0.610201	+	0.819643i	0.0251429	+	0.0337728i
$590$	−13.4817	−	1.57603i	−0.555034	−	0.0648839i
$591$	4.71870	−	1.27550i	0.194101	−	0.0524672i
$592$	−15.3321	−	26.5602i	−0.630146	−	1.09162i
$593$	23.9809	−	13.8454i	0.984776	−	0.568561i	0.0810674	−	0.996709i	$-0.474167\pi$
$593$	23.9809	−	13.8454i	0.984776	−	0.568561i	0.903709	+	0.428148i	$0.140834\pi$
$594$	−4.38692	−	3.85259i	−0.179997	−	0.158074i
$595$	−32.8919	−	18.9901i	−1.34843	−	0.778519i
$596$	−1.94516	−	16.6469i	−0.0796770	−	0.681885i
$597$	6.41819	−	9.20917i	0.262679	−	0.376906i
$598$	−21.1077	+	9.10453i	−0.863157	+	0.372312i
$599$	−42.6824	+	4.98886i	−1.74396	+	0.203839i	−0.927566	−	0.373660i	$-0.878103\pi$
$599$	−42.6824	+	4.98886i	−1.74396	+	0.203839i	−0.816391	+	0.577499i	$0.804029\pi$
$600$	−5.66572	−	16.9760i	−0.231302	−	0.693042i
$601$	25.5776	+	12.8455i	1.04333	+	0.523980i	0.886058	−	0.463575i	$-0.153433\pi$
$601$	25.5776	+	12.8455i	1.04333	+	0.523980i	0.157273	+	0.987555i	$0.449730\pi$
$602$	12.6429	+	5.45389i	0.515287	+	0.222284i
$603$	−22.7641	−	14.8291i	−0.927025	−	0.603888i
$604$	−8.33700	−	35.1820i	−0.339228	−	1.43153i
$605$	−1.39701	+	11.9522i	−0.0567964	+	0.485924i
$606$	16.2324	+	14.3822i	0.659395	+	0.584238i
$607$	−14.1455	+	4.23489i	−0.574148	+	0.171889i	−0.560697	−	0.828021i	$-0.689467\pi$
$607$	−14.1455	+	4.23489i	−0.574148	+	0.171889i	−0.0134509	+	0.999910i	$0.504282\pi$
$608$	1.13367		9.79659e-5i	0.0459765		3.97304e-6i
$609$	9.69625	−	12.3185i	0.392912	−	0.499171i
$610$	−0.0963502	+	0.546374i	−0.00390111	+	0.0221220i
$611$	12.4427	−	4.52876i	0.503377	−	0.183214i
$612$	−37.3502	+	13.7793i	−1.50979	+	0.556994i
$613$	8.86507	+	3.22662i	0.358057	+	0.130322i	0.514784	−	0.857320i	$-0.327872\pi$
$613$	8.86507	+	3.22662i	0.358057	+	0.130322i	−0.156727	+	0.987642i	$0.550094\pi$
$614$	−10.7229	+	18.5718i	−0.432740	+	0.749497i
$615$	−1.45212	−	2.67900i	−0.0585550	−	0.108028i
$616$	0.645036	−	11.0650i	0.0259892	−	0.445820i
$617$	−0.962502	−	1.91650i	−0.0387489	−	0.0771554i	0.873425	−	0.486958i	$-0.161894\pi$
$617$	−0.962502	−	1.91650i	−0.0387489	−	0.0771554i	−0.912174	+	0.409803i	$0.865597\pi$
$618$	−15.5808	+	19.7938i	−0.626753	+	0.796224i
$619$	7.02374	+	29.6355i	0.282308	+	1.19115i	0.910638	+	0.413204i	$0.135591\pi$
$619$	7.02374	+	29.6355i	0.282308	+	1.19115i	−0.628330	+	0.777947i	$0.716261\pi$
$620$	−7.06769	+	9.49287i	−0.283845	+	0.381243i
$621$	−5.38004	−	25.2142i	−0.215893	−	1.01181i
$622$	12.6942	+	25.2774i	0.508992	+	1.01353i
$623$	6.71622	+	7.11877i	0.269080	+	0.285208i
$624$	0.708467	+	22.6858i	0.0283614	+	0.908160i
$625$	−0.384380	+	6.59954i	−0.0153752	+	0.263982i
$626$	−2.83200	−	4.30601i	−0.113190	−	0.172103i
$627$	−0.272786	+	0.0405704i	−0.0108940	+	0.00162023i
$628$	41.3238	−	20.7518i	1.64900	−	0.828087i
$629$	50.0986	−	8.83374i	1.99756	−	0.352224i
$630$	−12.2347	−	20.9783i	−0.487442	−	0.835795i
$631$	−43.1971	−	7.61682i	−1.71965	−	0.303221i	−0.775161	−	0.631763i	$-0.782331\pi$
$631$	−43.1971	−	7.61682i	−1.71965	−	0.303221i	−0.944489	+	0.328542i	$0.893443\pi$
$632$	−34.0610	+	8.07075i	−1.35487	+	0.321037i
$633$	15.5789	−	13.9256i	0.619206	−	0.553492i
$634$	4.44334	−	14.8409i	0.176468	−	0.589406i
$635$	−7.85160	+	8.32221i	−0.311581	+	0.330257i
$636$	−18.6837	+	26.8064i	−0.740855	+	1.06294i
$637$	33.8960	−	45.5303i	1.34301	−	1.80397i
$638$	1.41500	−	1.49976i	0.0560205	−	0.0593762i
$639$	−29.7723	+	17.3641i	−1.17777	+	0.686914i
$640$	3.76426	+	12.5791i	0.148796	+	0.497231i
$641$	−40.2482	+	2.34419i	−1.58971	+	0.0925900i	−0.830034	−	0.557713i	$-0.811679\pi$
$641$	−40.2482	+	2.34419i	−1.58971	+	0.0925900i	−0.759675	+	0.650303i	$0.774642\pi$
$642$	33.2527	+	33.1079i	1.31238	+	1.30666i
$643$	−3.14694	−	1.35746i	−0.124103	−	0.0535329i	0.333123	−	0.942883i	$-0.391898\pi$
$643$	−3.14694	−	1.35746i	−0.124103	−	0.0535329i	−0.457226	+	0.889351i	$0.651157\pi$
$644$	31.4621	−	37.4924i	1.23978	−	1.47741i
$645$	3.95218	−	0.354533i	0.155617	−	0.0139597i
$646$	−0.643206	+	1.76710i	−0.0253066	+	0.0695256i
$647$	4.02096			0.158080			0.0790401	−	0.996871i	$-0.474814\pi$
$647$	4.02096			0.158080			0.0790401	+	0.996871i	$0.474814\pi$
$648$	−25.1068	−	4.20092i	−0.986289	−	0.165028i
$649$	6.57071			0.257923
$650$	5.78889	−	15.9040i	0.227059	−	0.623806i
$651$	18.3217	−	39.5177i	0.718084	−	1.54882i
$652$	4.09450	−	4.87930i	0.160353	−	0.191088i
$653$	32.6914	+	14.1017i	1.27931	+	0.551842i	0.923816	−	0.382836i	$-0.125053\pi$
$653$	32.6914	+	14.1017i	1.27931	+	0.551842i	0.355496	+	0.934678i	$0.384312\pi$
$654$	−6.83569	+	25.7357i	−0.267297	+	1.00634i
$655$	−5.52342	+	0.321702i	−0.215818	+	0.0125700i
$656$	−2.72102	−	5.41893i	−0.106238	−	0.211574i
$657$	12.9906	+	35.2086i	0.506810	+	1.37362i
$658$	−19.3474	+	20.5063i	−0.754241	+	0.799421i
$659$	−4.25244	+	5.71202i	−0.165651	+	0.222509i	−0.877196	−	0.480132i	$-0.840589\pi$
$659$	−4.25244	+	5.71202i	−0.165651	+	0.222509i	0.711545	+	0.702641i	$0.247996\pi$
$660$	−1.35618	−	2.89197i	−0.0527892	−	0.112570i
$661$	4.61960	−	4.89649i	0.179682	−	0.190451i	−0.631273	−	0.775561i	$-0.717467\pi$
$661$	4.61960	−	4.89649i	0.179682	−	0.190451i	0.810954	+	0.585110i	$0.198949\pi$
$662$	0.659097	−	2.20140i	0.0256165	−	0.0855598i
$663$	−35.7643	−	11.7638i	−1.38897	−	0.456866i
$664$	−5.29257	−	22.3363i	−0.205392	−	0.866815i
$665$	−1.12972	−	0.199200i	−0.0438087	−	0.00772465i
$666$	30.6150	+	10.9913i	1.18631	+	0.425902i
$667$	8.96684	−	1.58110i	0.347198	−	0.0612203i
$668$	10.4765	−	5.26107i	0.405350	−	0.203557i
$669$	−16.8387	+	42.6587i	−0.651020	+	1.64928i
$670$	−8.16738	−	12.4184i	−0.315534	−	0.479764i
$671$	0.0156160	−	0.268117i	0.000602850	−	0.0103505i
$672$	−23.0251	−	42.4876i	−0.888214	−	1.63899i
$673$	−21.8540	−	23.1639i	−0.842411	−	0.892903i	0.153036	−	0.988221i	$-0.451095\pi$
$673$	−21.8540	−	23.1639i	−0.842411	−	0.892903i	−0.995447	+	0.0953172i	$0.969613\pi$
$674$	−8.19861	−	16.3255i	−0.315799	−	0.628834i
$675$	16.2214	+	9.85833i	0.624362	+	0.379447i
$676$	2.70852	−	3.63791i	0.104174	−	0.139919i
$677$	3.79225	+	16.0008i	0.145748	+	0.614960i	0.996060	+	0.0886808i	$0.0282651\pi$
$677$	3.79225	+	16.0008i	0.145748	+	0.614960i	−0.850312	+	0.526279i	$0.823587\pi$
$678$	−4.69419	−	11.7412i	−0.180279	−	0.450919i
$679$	15.7921	+	31.4446i	0.606044	+	1.20673i
$680$	−21.7433	−	1.26753i	−0.833817	−	0.0486077i
$681$	−13.8709	+	22.5993i	−0.531534	+	0.866005i
$682$	2.86464	−	4.96150i	0.109693	−	0.189986i
$683$	−14.6395	−	5.32833i	−0.560163	−	0.203883i	0.0463931	−	0.998923i	$-0.485227\pi$
$683$	−14.6395	−	5.32833i	−0.560163	−	0.203883i	−0.606556	+	0.795041i	$0.707450\pi$
$684$	−0.917741	+	0.776927i	−0.0350907	+	0.0297065i
$685$	1.32590	−	0.482587i	0.0506599	−	0.0184387i
$686$	−12.5091	+	70.9354i	−0.477599	+	2.70833i
$687$	−9.99862	−	25.0076i	−0.381471	−	0.954099i
$688$	7.88273	−	0.458570i	0.300526	−	0.0174828i
$689$	−29.6028	+	8.86249i	−1.12778	+	0.337634i
$690$	2.82213	−	13.8198i	0.107437	−	0.526111i
$691$	0.0748857	−	0.640688i	0.00284878	−	0.0243729i	−0.991739	−	0.128271i	$-0.959057\pi$
$691$	0.0748857	−	0.640688i	0.00284878	−	0.0243729i	0.994588	+	0.103898i	$0.0331315\pi$
$692$	7.57226	+	31.9548i	0.287854	+	1.21474i
$693$	7.06166	+	9.39885i	0.268250	+	0.357033i
$694$	−30.1132	−	12.9902i	−1.14308	−	0.493100i
$695$	−11.4105	−	5.73055i	−0.432824	−	0.217372i
$696$	1.79903	−	8.80821i	0.0681922	−	0.333874i
$697$	9.99041	−	1.16771i	0.378414	−	0.0442302i
$698$	−5.54903	+	2.39350i	−0.210034	+	0.0905955i
$699$	45.1753	+	3.85222i	1.70869	+	0.145704i
$700$	4.18225	+	35.7922i	0.158074	+	1.35282i
$701$	−2.73892	−	1.58132i	−0.103448	−	0.0597254i	0.447384	−	0.894342i	$-0.352356\pi$
$701$	−2.73892	−	1.58132i	−0.103448	−	0.0597254i	−0.550831	+	0.834617i	$0.685689\pi$
$702$	−16.1221	−	17.8779i	−0.608490	−	0.674759i
$703$	1.33066	−	0.768257i	0.0501868	−	0.0289753i
$704$	−2.51692	−	5.83653i	−0.0948599	−	0.219973i
$705$	−2.08557	+	7.85250i	−0.0785471	+	0.295742i
$706$	−38.3054	−	4.47793i	−1.44164	−	0.168529i
$707$	−26.0771	−	35.0277i	−0.980732	−	1.31735i
$708$	24.3506	−	15.0926i	0.915152	−	0.567213i
$709$	17.6148	−	11.5855i	0.661539	−	0.435101i	−0.173841	−	0.984774i	$-0.555618\pi$
$709$	17.6148	−	11.5855i	0.661539	−	0.435101i	0.835380	+	0.549673i	$0.185248\pi$
$710$	−18.7286	+	2.18873i	−0.702871	+	0.0821415i
$711$	22.0398	−	29.8781i	0.826556	−	1.12052i
$712$	5.27387	+	1.91984i	0.197647	+	0.0719491i
$713$	23.2299	−	10.0204i	0.869966	−	0.375267i
$714$	79.2898	−	11.7911i	2.96735	−	0.441269i
$715$	0.696630	−	2.93931i	0.0260525	−	0.109924i
$716$	−15.9576	+	13.3891i	−0.596365	+	0.500374i
$717$	1.07895	+	34.4728i	0.0402943	+	1.28741i
$718$	−8.13354	+	9.69283i	−0.303541	+	0.361733i
$719$	−18.2673	−	15.3281i	−0.681254	−	0.571640i	0.235118	−	0.971967i	$-0.424452\pi$
$719$	−18.2673	−	15.3281i	−0.681254	−	0.571640i	−0.916373	+	0.400327i	$0.868897\pi$
$720$	−11.6686	−	7.60238i	−0.434863	−	0.283324i
$721$	38.8557	−	32.6038i	1.44706	−	1.21423i
$722$	0.000463412	−	26.8133i	1.72464e−5	−	0.997886i
$723$	−15.5100	+	5.17736i	−0.576824	+	0.192548i
$724$	−2.75543	+	4.77216i	−0.102405	+	0.177356i
$725$	−3.68378	+	5.60092i	−0.136812	+	0.208013i
$726$	−13.3806	−	21.5876i	−0.496600	−	0.801192i
$727$	−3.30106	−	0.988272i	−0.122429	−	0.0366530i	0.225002	−	0.974358i	$-0.427761\pi$
$727$	−3.30106	−	0.988272i	−0.122429	−	0.0366530i	−0.347432	+	0.937705i	$0.612946\pi$
$728$	7.93833	−	45.0069i	0.294214	−	1.66807i
$729$	23.2025	−	13.8074i	0.859351	−	0.511386i
$730$	−1.19416	+	20.4969i	−0.0441979	+	0.758623i
$731$	−3.75651	+	12.5476i	−0.138940	+	0.464091i
$732$	−0.557977	−	1.02949i	−0.0206234	−	0.0380511i
$733$	−21.0643	−	13.8542i	−0.778028	−	0.511717i	0.0972954	−	0.995256i	$-0.468981\pi$
$733$	−21.0643	−	13.8542i	−0.778028	−	0.511717i	−0.875323	+	0.483539i	$0.839351\pi$
$734$	−17.6853	−	8.88228i	−0.652777	−	0.327851i
$735$	11.0280	+	33.0370i	0.406773	+	1.21859i
$736$	6.47521	−	27.3105i	0.238679	−	1.00668i
$737$	4.62494	+	5.51179i	0.170362	+	0.203029i
$738$	5.91666	+	2.52150i	0.217795	+	0.0928179i
$739$	13.8693	−	16.5288i	0.510192	−	0.608023i	−0.448041	−	0.894013i	$-0.647878\pi$
$739$	13.8693	−	16.5288i	0.510192	−	0.608023i	0.958233	+	0.285990i	$0.0923225\pi$
$740$	12.9439	+	12.2127i	0.475826	+	0.448950i
$741$	−1.13660	+	0.0355740i	−0.0417539	+	0.00130684i
$742$	47.8571	−	45.1493i	1.75689	−	1.65748i
$743$	−35.4265	−	8.39623i	−1.29967	−	0.308028i	−0.478186	−	0.878258i	$-0.658706\pi$
$743$	−35.4265	−	8.39623i	−1.29967	−	0.308028i	−0.821485	+	0.570231i	$0.806854\pi$
$744$	−0.780136	−	24.9669i	−0.0286012	−	0.915331i
$745$	3.85211	+	8.93019i	0.141130	+	0.327177i
$746$	−6.61661	+	27.9155i	−0.242251	+	1.02206i
$747$	19.5932	+	14.4531i	0.716878	+	0.528810i
$748$	10.5256	−	0.612681i	0.384854	−	0.0224018i
$749$	−51.9202	−	78.9408i	−1.89712	−	2.88444i
$750$	14.1532	+	20.1193i	0.516803	+	0.734654i
$751$	−6.30665	+	4.69513i	−0.230133	+	0.171328i	−0.706049	−	0.708163i	$-0.749524\pi$
$751$	−6.30665	+	4.69513i	−0.230133	+	0.171328i	0.475916	+	0.879491i	$0.342117\pi$
$752$	−4.63795	+	15.4879i	−0.169129	+	0.564787i
$753$	37.5385	+	9.96997i	1.36798	+	0.363326i
$754$	6.51295	−	5.46482i	0.237188	−	0.199017i
$755$	10.4904	+	18.1698i	0.381783	+	0.661268i
$756$	47.7587	+	18.6113i	1.73697	+	0.676885i
$757$	15.7668	−	27.3089i	0.573054	−	0.992559i	−0.423196	−	0.906038i	$-0.639092\pi$
$757$	15.7668	−	27.3089i	0.573054	−	0.992559i	0.996250	−	0.0865205i	$-0.0275748\pi$
$758$	−0.167658	−	0.950933i	−0.00608962	−	0.0345395i
$759$	−0.580135	+	6.80330i	−0.0210576	+	0.246944i
$760$	−0.630219	+	0.188640i	−0.0228604	+	0.00684268i
$761$	0.267982	+	2.29273i	0.00971434	+	0.0831115i	0.997226	−	0.0744355i	$-0.0237155\pi$
$761$	0.267982	+	2.29273i	0.00971434	+	0.0831115i	−0.987511	+	0.157547i	$0.949641\pi$
$762$	2.05218	−	24.0611i	0.0743425	−	0.871643i
$763$	24.0633	−	47.9140i	0.871151	−	1.73460i
$764$	15.3381	+	7.70373i	0.554912	+	0.278711i
$765$	18.4693	−	13.8766i	0.667759	−	0.501709i
$766$	8.48157	−	2.53906i	0.306452	−	0.0917398i
$767$	26.9098	+	3.14531i	0.971658	+	0.113570i
$768$	−22.7337	−	15.8486i	−0.820333	−	0.571887i
$769$	−1.23028	−	4.10942i	−0.0443650	−	0.148190i	0.932937	−	0.360039i	$-0.117237\pi$
$769$	−1.23028	−	4.10942i	−0.0443650	−	0.148190i	−0.977302	+	0.211849i	$0.932051\pi$
$770$	1.48313	+	6.25832i	0.0534484	+	0.225534i
$771$	23.3424	−	9.33285i	0.840657	−	0.336114i
$772$	−40.3458	−	9.56361i	−1.45208	−	0.344202i
$773$	9.58055	+	26.3223i	0.344588	+	0.946749i	0.984045	+	0.177922i	$0.0569373\pi$
$773$	9.58055	+	26.3223i	0.344588	+	0.946749i	−0.639456	+	0.768828i	$0.720840\pi$
$774$	−6.06654	+	5.77394i	−0.218057	+	0.207540i
$775$	−6.37067	+	17.5033i	−0.228841	+	0.628736i
$776$	16.1851	+	12.0507i	0.581012	+	0.432594i
$777$	−55.8216	−	34.2620i	−2.00259	−	1.22914i
$778$	0.991939	+	17.0360i	0.0355627	+	0.610771i
$779$	0.271488	−	0.136346i	0.00972707	−	0.00488512i
$780$	−4.16978	−	12.4930i	−0.149302	−	0.447322i
$781$	8.88183	−	2.10503i	0.317817	−	0.0753239i
$782$	38.8984	+	25.5849i	1.39101	+	0.914913i
$783$	4.58079	+	8.36302i	0.163704	+	0.298870i
$784$	19.8727	+	66.3962i	0.709740	+	2.37129i
$785$	−19.5177	+	18.4140i	−0.696615	+	0.657223i
$786$	8.70647	−	7.78222i	0.310550	−	0.277582i
$787$	23.2836	+	1.35612i	0.829971	+	0.0483403i	0.467869	−	0.883798i	$-0.345022\pi$
$787$	23.2836	+	1.35612i	0.829971	+	0.0483403i	0.362102	+	0.932138i	$0.382059\pi$
$788$	−4.88815	+	2.82195i	−0.174133	+	0.100528i
$789$	−10.4049	−	4.10714i	−0.370425	−	0.146218i
$790$	17.5910	−	10.1558i	0.625860	−	0.361326i
$791$	4.42129	+	25.0744i	0.157203	+	0.891541i
$792$	6.03766	+	2.99943i	0.214539	+	0.106580i
$793$	0.192298	−	1.09058i	0.00682870	−	0.0387275i
$794$	−8.55653	−	23.5101i	−0.303660	−	0.834343i
$795$	5.92437	−	18.0113i	0.210116	−	0.638796i
$796$	−4.43354	+	12.1798i	−0.157143	+	0.431700i
$797$	−16.4708	−	15.5394i	−0.583427	−	0.550435i	0.336922	−	0.941532i	$-0.390614\pi$
$797$	−16.4708	−	15.5394i	−0.583427	−	0.550435i	−0.920349	+	0.391098i	$0.872095\pi$
$798$	2.12862	−	1.15375i	0.0753524	−	0.0408421i
$799$	−21.5117	−	16.0148i	−0.761028	−	0.566564i
$800$	11.3542	+	17.2664i	0.401430	+	0.610460i
$801$	−5.58488	+	2.06060i	−0.197332	+	0.0728077i
$802$	18.8408	+	25.3086i	0.665293	+	0.893676i
$803$	−0.577901	−	9.92217i	−0.0203937	−	0.350146i
$804$	29.8000	+	9.80309i	1.05097	+	0.345728i
$805$	−11.2492	+	26.0786i	−0.396482	+	0.919148i
$806$	14.1069	−	18.9482i	0.496894	−	0.667421i
$807$	−31.1253	−	14.4307i	−1.09566	−	0.507985i
$808$	−22.3781	−	11.2401i	−0.787257	−	0.395427i
$809$		−	0.881588i		−	0.0309950i	−0.999880	−	0.0154975i	$-0.995067\pi$
$809$		−	0.881588i		−	0.0309950i	0.999880	−	0.0154975i	$-0.00493320\pi$
$810$	14.6560	−	1.84363i	0.514959	−	0.0647786i
$811$			7.04559i			0.247404i	0.992319	+	0.123702i	$0.0394767\pi$
$811$			7.04559i			0.247404i	−0.992319	+	0.123702i	$0.960523\pi$
$812$	−7.17043	+	16.6213i	−0.251633	+	0.583295i
$813$	−0.0831553	−	0.926980i	−0.00291638	−	0.0325106i
$814$	−6.90995	−	5.14445i	−0.242194	−	0.180313i
$815$	−1.46398	+	3.39389i	−0.0512810	+	0.118883i
$816$	37.5999	−	26.4473i	1.31626	−	0.925840i
$817$	0.0230024	+	0.394937i	0.000804754	+	0.0138171i
$818$	2.80924	−	2.09132i	0.0982226	−	0.0731214i
$819$	24.4214	+	41.8726i	0.853352	+	1.46315i
$820$	2.41455	+	2.55946i	0.0843199	+	0.0893801i
$821$	−4.72332	−	3.51638i	−0.164845	−	0.122722i	0.511575	−	0.859239i	$-0.329062\pi$
$821$	−4.72332	−	3.51638i	−0.164845	−	0.122722i	−0.676420	+	0.736516i	$0.736470\pi$
$822$	−1.55787	+	2.53808i	−0.0543371	+	0.0885257i
$823$	33.0524	+	31.1833i	1.15213	+	1.08698i	0.995048	+	0.0993969i	$0.0316914\pi$
$823$	33.0524	+	31.1833i	1.15213	+	1.08698i	0.157086	+	0.987585i	$0.449790\pi$
$824$	11.5223	−	26.7079i	0.401399	−	0.930414i
$825$	−3.35029	−	3.74806i	−0.116642	−	0.130491i
$826$	−54.2071	+	19.7287i	−1.88611	+	0.686449i
$827$	−3.54747	+	20.1187i	−0.123358	+	0.699596i	0.858912	+	0.512123i	$0.171141\pi$
$827$	−3.54747	+	20.1187i	−0.123358	+	0.699596i	−0.982270	+	0.187473i	$0.939970\pi$
$828$	13.4769	+	26.5451i	0.468353	+	0.922506i
$829$	2.64823	+	15.0188i	0.0919767	+	0.521626i	0.995632	+	0.0933650i	$0.0297624\pi$
$829$	2.64823	+	15.0188i	0.0919767	+	0.521626i	−0.903655	+	0.428261i	$0.859127\pi$
$830$	6.65987	+	11.5357i	0.231168	+	0.400410i
$831$	1.08673	+	7.30694i	0.0376983	+	0.253475i
$832$	−7.51397	−	25.1079i	−0.260500	−	0.870459i
$833$	−114.770	−	6.68459i	−3.97655	−	0.231607i
$834$	26.3810	−	5.50728i	0.913498	−	0.190702i
$835$	−4.94818	+	4.66837i	−0.171239	+	0.161556i
$836$	0.292411	−	0.126122i	0.0101133	−	0.00436202i
$837$	17.7435	+	19.6753i	0.613306	+	0.680077i
$838$	−21.4746	+	32.6492i	−0.741826	+	1.12785i
$839$	3.84439	−	0.911137i	0.132723	−	0.0314559i	−0.163717	−	0.986507i	$-0.552349\pi$
$839$	3.84439	−	0.911137i	0.132723	−	0.0314559i	0.296440	+	0.955051i	$0.404200\pi$
$840$	19.8714	+	19.7862i	0.685629	+	0.682690i
$841$	22.9060	−	11.5038i	0.789862	−	0.396684i
$842$	45.1823	−	2.63079i	1.55708	−	0.0906628i
$843$	27.6196	−	14.9709i	0.951270	−	0.515624i
$844$	−13.2593	+	20.1583i	−0.456404	+	0.693876i
$845$	−0.900139	+	2.47311i	−0.0309657	+	0.0850777i
$846$	−6.86099	−	15.7158i	−0.235886	−	0.540322i
$847$	17.4912	+	48.0566i	0.601004	+	1.65124i
$848$	12.9068	−	35.4537i	0.443223	−	1.21748i
$849$	−13.0599	−	10.2798i	−0.448213	−	0.352801i
$850$	−33.3551	+	7.90470i	−1.14407	+	0.271129i
$851$	−10.9104	−	36.4432i	−0.374003	−	1.24926i
$852$	28.0803	−	28.2022i	0.962016	−	0.966191i
$853$	−0.561038	−	0.0655759i	−0.0192096	−	0.00224528i	0.106483	−	0.994315i	$-0.466041\pi$
$853$	−0.561038	−	0.0655759i	−0.0192096	−	0.00224528i	−0.125692	+	0.992069i	$0.540115\pi$
$854$	0.676197	+	2.25880i	0.0231390	+	0.0772944i
$855$	0.380852	−	0.584643i	0.0130249	−	0.0199944i
$856$	−46.9228	−	27.0941i	−1.60379	−	0.926058i
$857$	−4.16942	+	8.30199i	−0.142425	+	0.283591i	−0.953524	−	0.301318i	$-0.902573\pi$
$857$	−4.16942	+	8.30199i	−0.142425	+	0.283591i	0.811099	+	0.584909i	$0.198870\pi$
$858$	2.70705	+	5.77237i	0.0924173	+	0.197066i
$859$	4.58098	+	39.1928i	0.156301	+	1.33724i	0.812636	+	0.582771i	$0.198032\pi$
$859$	4.58098	+	39.1928i	0.156301	+	1.33724i	−0.656335	+	0.754469i	$0.727894\pi$
$860$	−4.30565	+	1.56696i	−0.146821	+	0.0534328i
$861$	−10.6246	−	7.40465i	−0.362085	−	0.252350i
$862$	−10.8620	+	1.91508i	−0.369963	+	0.0652278i
$863$	−4.09417	+	7.09131i	−0.139367	+	0.241391i	−0.927257	−	0.374425i	$-0.877840\pi$
$863$	−4.09417	+	7.09131i	−0.139367	+	0.241391i	0.787890	+	0.615816i	$0.211173\pi$
$864$	29.2647	−	2.75249i	0.995606	−	0.0936416i
$865$	−9.52810	−	16.5032i	−0.323965	−	0.561124i
$866$	−23.1039	−	27.5352i	−0.785103	−	0.935683i
$867$	12.2145	+	45.1873i	0.414826	+	1.53464i
$868$	−8.73569	+	49.5325i	−0.296509	+	1.68124i
$869$	−7.88708	+	5.87171i	−0.267551	+	0.199184i
$870$	0.466009	+	5.19588i	0.0157992	+	0.176157i
$871$	16.3027	+	24.7870i	0.552395	+	0.839875i
$872$	0.00159421	−	30.7474i	5.39869e−5	−	1.04124i
$873$	−21.3608	+	1.33844i	−0.722952	+	0.0452993i
$874$	1.36833	+	0.324324i	0.0462843	+	0.0109704i
$875$	−19.6183	−	45.4804i	−0.663220	−	1.53752i
$876$	−24.9324	−	35.4435i	−0.842386	−	1.19753i
$877$	6.25112	+	1.48154i	0.211085	+	0.0500281i	0.334798	−	0.942290i	$-0.391332\pi$
$877$	6.25112	+	1.48154i	0.211085	+	0.0500281i	−0.123713	+	0.992318i	$0.539480\pi$
$878$	1.03983	+	1.10220i	0.0350926	+	0.0371973i
$879$	−12.5895	+	23.4721i	−0.424633	+	0.791695i
$880$	2.37060	+	2.82557i	0.0799130	+	0.0952500i
$881$	24.1391	−	28.7679i	0.813267	−	0.969214i	−0.186646	−	0.982427i	$-0.559762\pi$
$881$	24.1391	−	28.7679i	0.813267	−	0.969214i	0.999913	+	0.0132137i	$0.00420617\pi$
$882$	−61.5936	−	40.1252i	−2.07396	−	1.35108i
$883$	−30.1777	−	35.9644i	−1.01556	−	1.21030i	−0.977481	−	0.211023i	$-0.932321\pi$
$883$	−30.1777	−	35.9644i	−1.01556	−	1.21030i	−0.0380792	−	0.999275i	$-0.512124\pi$
$884$	43.4000	+	2.52927i	1.45970	+	0.0850685i
$885$	−11.0243	+	12.4429i	−0.370578	+	0.418264i
$886$	−10.2151	+	20.3390i	−0.343182	+	0.683302i
$887$	6.74527	+	4.43643i	0.226484	+	0.148961i	0.657680	−	0.753297i	$-0.271538\pi$
$887$	6.74527	+	4.43643i	0.226484	+	0.148961i	−0.431196	+	0.902258i	$0.641908\pi$
$888$	−37.4244	−	3.19323i	−1.25588	−	0.107158i
$889$	−13.9457	+	46.5818i	−0.467723	+	1.56230i
$890$	−3.25127	−	0.189421i	−0.108983	−	0.00634941i
$891$	−6.94309	+	1.71020i	−0.232602	+	0.0572938i
$892$	6.14971	−	52.5984i	0.205907	−	1.76112i
$893$	−0.775989	−	0.232316i	−0.0259675	−	0.00777415i
$894$	−18.0891	−	9.70265i	−0.604989	−	0.324505i
$895$	6.64222	−	10.0990i	0.222025	−	0.337572i
$896$	38.2884	+	40.5932i	1.27913	+	1.35612i
$897$	−5.63254	+	27.5847i	−0.188065	+	0.921025i
$898$	27.4866		0.000475050i	0.917241		1.58526e-5i
$899$	−7.16773	+	6.01444i	−0.239057	+	0.200593i
$900$	−21.0251	−	6.19463i	−0.700836	−	0.206488i
$901$	47.9436	+	40.2295i	1.59723	+	1.34024i
$902$	−1.30480	−	1.09489i	−0.0434450	−	0.0364559i
$903$	14.3334	−	8.88457i	0.476987	−	0.295660i
$904$	8.71851	+	11.7123i	0.289973	+	0.389544i
$905$	0.737426	−	3.11145i	0.0245129	−	0.103428i
$906$	−41.1892	−	16.2594i	−1.36842	−	0.540183i
$907$	9.44954	−	4.07614i	0.313767	−	0.135346i	−0.233372	−	0.972387i	$-0.574976\pi$
$907$	9.44954	−	4.07614i	0.313767	−	0.135346i	0.547139	+	0.837042i	$0.315717\pi$
$908$	8.78255	−	29.3321i	0.291459	−	0.973419i
$909$	25.8182	−	6.23912i	0.856337	−	0.206939i
$910$	3.07829	+	26.3404i	0.102044	+	0.873176i
$911$	14.9392	−	9.82569i	0.494959	−	0.325540i	−0.277369	−	0.960763i	$-0.589462\pi$
$911$	14.9392	−	9.82569i	0.494959	−	0.325540i	0.772328	+	0.635224i	$0.219092\pi$
$912$	0.793962	−	1.13905i	0.0262907	−	0.0377178i
$913$	−3.85051	−	5.17213i	−0.127433	−	0.171172i
$914$	4.16676	−	35.6436i	0.137824	−	1.17898i
$915$	0.481531	+	0.479417i	0.0159189	+	0.0158490i
$916$	18.5701	+	24.9457i	0.613572	+	0.824229i
$917$	−20.3633	+	11.7568i	−0.672455	+	0.388242i
$918$	−12.3093	+	47.1788i	−0.406267	+	1.55713i
$919$	−1.16882	−	0.674819i	−0.0385558	−	0.0222602i	0.480598	−	0.876941i	$-0.340420\pi$
$919$	−1.16882	−	0.674819i	−0.0385558	−	0.0222602i	−0.519154	+	0.854681i	$0.673753\pi$
$920$	0.946166	+	16.2596i	0.0311942	+	0.536062i
$921$	11.1523	+	23.7795i	0.367481	+	0.783560i
$922$	−5.26376	−	12.2033i	−0.173353	−	0.401896i
$923$	37.3825	−	4.36938i	1.23046	−	0.143820i
$924$	−10.6665	−	8.39647i	−0.350901	−	0.276224i
$925$	25.0291	+	12.5701i	0.822952	+	0.413302i
$926$	−4.16905	+	9.66448i	−0.137003	+	0.317595i
$927$	8.97835	+	29.5165i	0.294888	+	0.969450i
$928$	0.602696	+	10.3633i	0.0197845	+	0.340192i
$929$	−1.09032	+	9.32826i	−0.0357722	+	0.306050i	0.963493	+	0.267732i	$0.0862742\pi$
$929$	−1.09032	+	9.32826i	−0.0357722	+	0.306050i	−0.999266	+	0.0383184i	$0.987800\pi$
$930$	4.58929	+	13.7491i	0.150489	+	0.450852i
$931$	−3.32649	+	0.995886i	−0.109021	+	0.0326389i
$932$	−51.5582	+	9.08927i	−1.68885	+	0.297729i
$933$	34.2881	+	4.94545i	1.12254	+	0.161907i
$934$	32.5100	+	5.73296i	1.06376	+	0.187588i
$935$	−5.74915	+	2.09252i	−0.188017	+	0.0684327i
$936$	23.2910	+	15.1741i	0.761290	+	0.495980i
$937$	−17.8490	−	6.49649i	−0.583100	−	0.212231i	0.0335917	−	0.999436i	$-0.489305\pi$
$937$	−17.8490	−	6.49649i	−0.583100	−	0.212231i	−0.616692	+	0.787204i	$0.711528\pi$
$938$	−54.7041	−	31.5847i	−1.78615	−	1.03128i
$939$	−6.30984	−	0.169707i	−0.205914	−	0.00553819i
$940$	0.000324284	−	9.38164i	1.05770e−5	−	0.305995i
$941$	22.0334	+	43.8722i	0.718270	+	1.43019i	0.895061	+	0.445944i	$0.147132\pi$
$941$	22.0334	+	43.8722i	0.718270	+	1.43019i	−0.176791	+	0.984248i	$0.556572\pi$
$942$	8.08580	−	56.0541i	0.263450	−	1.82634i
$943$	−1.73460	−	7.31886i	−0.0564864	−	0.238335i
$944$	−22.7029	+	24.0603i	−0.738915	+	0.783096i
$945$	−29.6466	−	2.39672i	−0.964403	−	0.0779652i
$946$	1.98212	−	0.995413i	0.0644441	−	0.0323637i
$947$	−11.4049	−	12.0885i	−0.370610	−	0.392824i	0.515048	−	0.857161i	$-0.327774\pi$
$947$	−11.4049	−	12.0885i	−0.370610	−	0.392824i	−0.885658	+	0.464337i	$0.846293\pi$
$948$	−15.7420	+	39.8764i	−0.511276	+	1.29512i
$949$	2.38286	−	40.9121i	0.0773509	−	1.32806i
$950$	−0.865037	+	0.568923i	−0.0280655	+	0.0184583i
$951$	−11.8007	−	14.8571i	−0.382664	−	0.481776i
$952$	−84.9945	+	36.6578i	−2.75469	+	1.18809i
$953$	−20.8198	+	3.67110i	−0.674420	+	0.118918i	−0.500361	−	0.865817i	$-0.666799\pi$
$953$	−20.8198	+	3.67110i	−0.674420	+	0.118918i	−0.174059	+	0.984735i	$0.555688\pi$
$954$	13.8518	+	37.5449i	0.448470	+	1.21556i
$955$	−9.80861	−	1.72952i	−0.317399	−	0.0559660i
$956$	−11.4207	−	38.1526i	−0.369372	−	1.23394i
$957$	−0.516105	−	2.47203i	−0.0166833	−	0.0799093i
$958$	4.39512	+	1.31590i	0.142000	+	0.0425147i
$959$	4.11505	−	4.36170i	0.132882	−	0.140847i
$960$	15.2755	+	5.02624i	0.493014	+	0.162221i
$961$	2.98691	−	4.01212i	0.0963521	−	0.129423i
$962$	−25.8366	−	24.3764i	−0.833005	−	0.785927i
$963$	56.5526	−	10.2285i	1.82238	−	0.329608i
$964$	15.7751	−	10.3747i	0.508082	−	0.334146i
$965$	24.0198	−	1.39900i	0.773226	−	0.0450353i
$966$	−15.6410	−	57.8677i	−0.503242	−	1.86186i
$967$	50.0331	+	21.5822i	1.60895	+	0.694035i	0.995417	−	0.0956298i	$-0.0304865\pi$
$967$	50.0331	+	21.5822i	1.60895	+	0.694035i	0.613538	+	0.789665i	$0.289746\pi$
$968$	21.3308	+	20.1267i	0.685599	+	0.646896i
$969$	1.32518	+	1.88373i	0.0425710	+	0.0605140i
$970$	−11.0030	−	4.00498i	−0.353285	−	0.128592i
$971$	−27.8157			−0.892648			−0.446324	−	0.894872i	$-0.647267\pi$
$971$	−27.8157			−0.892648			−0.446324	+	0.894872i	$0.647267\pi$
$972$	−21.8024	+	22.2858i	−0.699312	+	0.714817i
$973$	−54.2649			−1.73965
$974$	−11.1207	−	4.04781i	−0.356329	−	0.129700i
$975$	−11.9267	−	16.9536i	−0.381961	−	0.542951i
$976$	0.927820	+	0.983568i	0.0296988	+	0.0314832i
$977$	33.0040	+	14.2365i	1.05589	+	0.455467i	0.852009	−	0.523528i	$-0.175384\pi$
$977$	33.0040	+	14.2365i	1.05589	+	0.455467i	0.203883	+	0.978995i	$0.434644\pi$
$978$	−2.03554	−	7.53096i	−0.0650894	−	0.240814i
$979$	1.57388	−	0.0916682i	0.0503015	−	0.00292973i
$980$	−22.0984	−	33.6016i	−0.705909	−	1.07336i
$981$	21.0726	+	24.8902i	0.672797	+	0.794682i
$982$	−10.0805	−	9.51083i	−0.321683	−	0.303503i
$983$	−7.30812	+	9.81651i	−0.233093	+	0.313098i	−0.903245	−	0.429126i	$-0.858822\pi$
$983$	−7.30812	+	9.81651i	−0.233093	+	0.313098i	0.670152	+	0.742224i	$0.266229\pi$
$984$	−7.35040	−	1.06055i	−0.234322	−	0.0338092i
$985$	2.24760	−	2.38232i	0.0716145	−	0.0759069i
$986$	−16.4961	−	4.93891i	−0.525342	−	0.157287i
$987$	7.05673	+	33.8002i	0.224618	+	1.07587i
$988$	1.25792	−	0.376550i	0.0400198	−	0.0119796i
$989$	9.64569	+	1.70080i	0.306715	+	0.0540821i
$990$	−3.85555	−	0.662430i	−0.122537	−	0.0210534i
$991$	18.3445	−	3.23463i	0.582732	−	0.102751i	0.125492	−	0.992095i	$-0.459949\pi$
$991$	18.3445	−	3.23463i	0.582732	−	0.102751i	0.457240	+	0.889343i	$0.348838\pi$
$992$	8.26998	+	27.6324i	0.262572	+	0.877328i
$993$	−1.75044	−	2.20381i	−0.0555486	−	0.0699359i
$994$	−66.9529	+	44.0340i	−2.12362	+	1.39667i
$995$	0.437327	−	7.50861i	0.0138642	−	0.238039i
$996$	−26.1498	−	10.3232i	−0.828589	−	0.327102i
$997$	24.7687	+	26.2533i	0.784434	+	0.831451i	0.989079	−	0.147385i	$-0.0470857\pi$
$997$	24.7687	+	26.2533i	0.784434	+	0.831451i	−0.204646	+	0.978836i	$0.565604\pi$
$998$	32.2417	−	16.1917i	1.02059	−	0.512539i
$999$	32.4825	−	23.0654i	1.02770	−	0.729758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.p.a.275.22	yes	936
3.2	odd	2		972.2.p.a.935.31		936
4.3	odd	2	inner	324.2.p.a.275.31	yes	936
12.11	even	2		972.2.p.a.935.22		936
81.38	odd	54	inner	324.2.p.a.119.31	yes	936
81.43	even	27		972.2.p.a.683.22		936
324.43	odd	54		972.2.p.a.683.31		936
324.119	even	54	inner	324.2.p.a.119.22	✓	936

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.p.a.119.22	✓	936	324.119	even	54	inner
324.2.p.a.119.31	yes	936	81.38	odd	54	inner
324.2.p.a.275.22	yes	936	1.1	even	1	trivial
324.2.p.a.275.31	yes	936	4.3	odd	2	inner
972.2.p.a.683.22		936	81.43	even	27
972.2.p.a.683.31		936	324.43	odd	54
972.2.p.a.935.22		936	12.11	even	2
972.2.p.a.935.31		936	3.2	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.483712 + 1.32892i) q^{2} +(0.996582 + 1.41662i) q^{3} +(-1.53204 - 1.28563i) q^{4} +(1.06564 + 0.459673i) q^{5} +(-2.36464 + 0.639137i) q^{6} +(4.92386 - 0.286782i) q^{7} +(2.44956 - 1.41409i) q^{8} +(-1.01365 + 2.82356i) q^{9} +O(q^{10})\)	\(q+(-0.483712 + 1.32892i) q^{2} +(0.996582 + 1.41662i) q^{3} +(-1.53204 - 1.28563i) q^{4} +(1.06564 + 0.459673i) q^{5} +(-2.36464 + 0.639137i) q^{6} +(4.92386 - 0.286782i) q^{7} +(2.44956 - 1.41409i) q^{8} +(-1.01365 + 2.82356i) q^{9} +(-1.12633 + 1.19380i) q^{10} +(0.474450 - 0.637297i) q^{11} +(0.294444 - 3.45157i) q^{12} +(2.24814 - 2.38289i) q^{13} +(-2.00062 + 6.68212i) q^{14} +(0.410816 + 1.96772i) q^{15} +(0.694320 + 3.93928i) q^{16} +(-6.53434 - 1.15218i) q^{17} +(-3.26197 - 2.71285i) q^{18} +(-0.197362 + 0.0348003i) q^{19} +(-1.04164 - 2.07426i) q^{20} +(5.31329 + 6.68945i) q^{21} +(0.617418 + 0.938773i) q^{22} +(-0.288498 + 4.95332i) q^{23} +(4.44442 + 2.06086i) q^{24} +(-2.50691 - 2.65717i) q^{25} +(2.07921 + 4.14022i) q^{26} +(-5.01011 + 1.37795i) q^{27} +(-7.91226 - 5.89088i) q^{28} +(-0.423200 - 1.78562i) q^{29} +(-2.81365 - 0.405869i) q^{30} +(-2.28835 - 4.55649i) q^{31} +(-5.57083 - 0.982784i) q^{32} +(1.37564 + 0.0369987i) q^{33} +(4.69190 - 8.12628i) q^{34} +(5.37889 + 1.95776i) q^{35} +(5.18301 - 3.02265i) q^{36} +(-7.20460 + 2.62226i) q^{37} +(0.0492198 - 0.279111i) q^{38} +(5.61611 + 0.810024i) q^{39} +(3.26038 - 0.380912i) q^{40} +(-1.45225 + 0.434774i) q^{41} +(-11.4598 + 3.82515i) q^{42} +(0.229169 - 1.96067i) q^{43} +(-1.54620 + 0.366401i) q^{44} +(-2.37810 + 2.54296i) q^{45} +(-6.44300 - 2.77937i) q^{46} +(3.61195 + 1.81399i) q^{47} +(-4.88853 + 4.90941i) q^{48} +(17.2094 - 2.01150i) q^{49} +(4.74379 - 2.04617i) q^{50} +(-4.87980 - 10.4050i) q^{51} +(-6.50775 + 0.760419i) q^{52} +(-8.16877 - 4.71624i) q^{53} +(0.592267 - 7.32456i) q^{54} +(0.798542 - 0.461038i) q^{55} +(11.6558 - 7.66525i) q^{56} +(-0.245986 - 0.244907i) q^{57} +(2.57765 + 0.301330i) q^{58} +(4.93857 + 6.63365i) q^{59} +(1.90036 - 3.54279i) q^{60} +(0.282422 - 0.185752i) q^{61} +(7.16210 - 0.837004i) q^{62} +(-4.18131 + 14.1935i) q^{63} +(4.00072 - 6.92779i) q^{64} +(3.49106 - 1.50590i) q^{65} +(-0.714582 + 1.81021i) q^{66} +(-2.08847 + 8.81193i) q^{67} +(8.52963 + 10.1659i) q^{68} +(-7.30450 + 4.52769i) q^{69} +(-5.20354 + 6.20112i) q^{70} +(8.80081 + 7.38476i) q^{71} +(1.50977 + 8.34989i) q^{72} +(9.58287 - 8.04098i) q^{73} +(0.000187394 - 10.8427i) q^{74} +(1.26587 - 6.19945i) q^{75} +(0.347108 + 0.200419i) q^{76} +(2.15336 - 3.27402i) q^{77} +(-3.79304 + 7.07153i) q^{78} +(-11.8559 - 3.54943i) q^{79} +(-1.07088 + 4.51702i) q^{80} +(-6.94503 - 5.72420i) q^{81} +(0.124691 - 2.14022i) q^{82} +(2.32762 - 7.77478i) q^{83} +(0.459954 - 17.0795i) q^{84} +(-6.43365 - 4.23148i) q^{85} +(2.49471 + 1.25295i) q^{86} +(2.10780 - 2.37904i) q^{87} +(0.261002 - 2.23201i) q^{88} +(1.27548 + 1.52006i) q^{89} +(-2.22907 - 4.39037i) q^{90} +(10.3861 - 12.3777i) q^{91} +(6.81011 - 7.21780i) q^{92} +(4.17430 - 7.78265i) q^{93} +(-4.15778 + 3.92253i) q^{94} +(-0.226314 - 0.0536375i) q^{95} +(-4.15955 - 8.87120i) q^{96} +(2.82572 + 6.55075i) q^{97} +(-5.65131 + 23.8429i) q^{98} +(1.31852 + 1.98563i) 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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