LMFDB - Embedded newform 273.2.cg.b.262.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			262.2
Character	$\chi$	$=$	273.262
Dual form			273.2.cg.b.124.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.604879 - 2.25744i) q^{2} +1.00000i q^{3} +(-2.99811 + 1.73096i) q^{4} +(0.721604 - 2.69306i) q^{5} +(2.25744 - 0.604879i) q^{6} +(-1.83932 + 1.90181i) q^{7} +(2.41591 + 2.41591i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.604879 - 2.25744i) q^{2} +1.00000i q^{3} +(-2.99811 + 1.73096i) q^{4} +(0.721604 - 2.69306i) q^{5} +(2.25744 - 0.604879i) q^{6} +(-1.83932 + 1.90181i) q^{7} +(2.41591 + 2.41591i) q^{8} -1.00000 q^{9} -6.51591 q^{10} +(-4.28455 - 4.28455i) q^{11} +(-1.73096 - 2.99811i) q^{12} +(-0.711416 - 3.53467i) q^{13} +(5.40580 + 3.00179i) q^{14} +(2.69306 + 0.721604i) q^{15} +(0.530515 - 0.918879i) q^{16} +(0.641993 + 1.11196i) q^{17} +(0.604879 + 2.25744i) q^{18} +(-1.37301 - 1.37301i) q^{19} +(2.49813 + 9.32315i) q^{20} +(-1.90181 - 1.83932i) q^{21} +(-7.08048 + 12.2637i) q^{22} +(-1.85691 - 1.07209i) q^{23} +(-2.41591 + 2.41591i) q^{24} +(-2.40174 - 1.38664i) q^{25} +(-7.54898 + 3.74403i) q^{26} -1.00000i q^{27} +(2.22253 - 8.88563i) q^{28} +(2.48648 + 4.30672i) q^{29} -6.51591i q^{30} +(-1.92572 + 0.515996i) q^{31} +(4.20516 + 1.12677i) q^{32} +(4.28455 - 4.28455i) q^{33} +(2.12187 - 2.12187i) q^{34} +(3.79444 + 6.32576i) q^{35} +(2.99811 - 1.73096i) q^{36} +(11.4000 - 3.05463i) q^{37} +(-2.26899 + 3.93000i) q^{38} +(3.53467 - 0.711416i) q^{39} +(8.24951 - 4.76285i) q^{40} +(1.19027 - 4.44214i) q^{41} +(-3.00179 + 5.40580i) q^{42} +(-2.94613 - 1.70095i) q^{43} +(20.2619 + 5.42916i) q^{44} +(-0.721604 + 2.69306i) q^{45} +(-1.29697 + 4.84036i) q^{46} +(-9.99804 - 2.67897i) q^{47} +(0.918879 + 0.530515i) q^{48} +(-0.233788 - 6.99609i) q^{49} +(-1.67751 + 6.26054i) q^{50} +(-1.11196 + 0.641993i) q^{51} +(8.25127 + 9.36589i) q^{52} +(4.30659 - 7.45923i) q^{53} +(-2.25744 + 0.604879i) q^{54} +(-14.6303 + 8.44680i) q^{55} +(-9.03823 + 0.150973i) q^{56} +(1.37301 - 1.37301i) q^{57} +(8.21813 - 8.21813i) q^{58} +(11.2322 + 3.00965i) q^{59} +(-9.32315 + 2.49813i) q^{60} +3.67019i q^{61} +(2.32966 + 4.03509i) q^{62} +(1.83932 - 1.90181i) q^{63} -12.2965i q^{64} +(-10.0324 - 0.634743i) q^{65} +(-12.2637 - 7.08048i) q^{66} +(1.20496 - 1.20496i) q^{67} +(-3.84953 - 2.22253i) q^{68} +(1.07209 - 1.85691i) q^{69} +(11.9849 - 12.3920i) q^{70} +(-1.73527 - 6.47610i) q^{71} +(-2.41591 - 2.41591i) q^{72} +(-1.17111 - 4.37064i) q^{73} +(-13.7913 - 23.8872i) q^{74} +(1.38664 - 2.40174i) q^{75} +(6.49307 + 1.73981i) q^{76} +(16.0291 - 0.267747i) q^{77} +(-3.74403 - 7.54898i) q^{78} +(0.418084 + 0.724143i) q^{79} +(-2.09178 - 2.09178i) q^{80} +1.00000 q^{81} -10.7478 q^{82} +(-2.01023 - 2.01023i) q^{83} +(8.88563 + 2.22253i) q^{84} +(3.45785 - 0.926529i) q^{85} +(-2.05774 + 7.67959i) q^{86} +(-4.30672 + 2.48648i) q^{87} -20.7021i q^{88} +(1.29112 + 4.81854i) q^{89} +6.51591 q^{90} +(8.03080 + 5.14841i) q^{91} +7.42297 q^{92} +(-0.515996 - 1.92572i) q^{93} +24.1904i q^{94} +(-4.68838 + 2.70684i) q^{95} +(-1.12677 + 4.20516i) q^{96} +(-6.27512 + 1.68141i) q^{97} +(-15.6519 + 4.75956i) q^{98} +(4.28455 + 4.28455i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.604879	−	2.25744i	−0.427714	−	1.59625i	−0.757923	−	0.652344i	$-0.773786\pi$
$2$	−0.604879	−	2.25744i	−0.427714	−	1.59625i	0.330209	−	0.943908i	$-0.392881\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−2.99811	+	1.73096i	−1.49905	+	0.865479i
$5$	0.721604	−	2.69306i	0.322711	−	1.20437i	−0.593882	−	0.804552i	$-0.702405\pi$
$5$	0.721604	−	2.69306i	0.322711	−	1.20437i	0.916593	−	0.399821i	$-0.130928\pi$
$6$	2.25744	−	0.604879i	0.921596	−	0.246941i
$7$	−1.83932	+	1.90181i	−0.695198	+	0.718818i
$7$	−1.83932	+	1.90181i	−0.695198	+	0.718818i
$8$	2.41591	+	2.41591i	0.854152	+	0.854152i
$9$	−1.00000			−0.333333
$10$	−6.51591			−2.06051
$11$	−4.28455	−	4.28455i	−1.29184	−	1.29184i	−0.933648	−	0.358192i	$-0.883393\pi$
$11$	−4.28455	−	4.28455i	−1.29184	−	1.29184i	−0.358192	−	0.933648i	$-0.616607\pi$
$12$	−1.73096	−	2.99811i	−0.499685	−	0.865479i
$13$	−0.711416	−	3.53467i	−0.197311	−	0.980341i
$13$	−0.711416	−	3.53467i	−0.197311	−	0.980341i
$14$	5.40580	+	3.00179i	1.44476	+	0.802263i
$15$	2.69306	+	0.721604i	0.695345	+	0.186317i
$16$	0.530515	−	0.918879i	0.132629	−	0.229720i
$17$	0.641993	+	1.11196i	0.155706	+	0.269691i	0.933316	−	0.359056i	$-0.116901\pi$
$17$	0.641993	+	1.11196i	0.155706	+	0.269691i	−0.777610	+	0.628747i	$0.783568\pi$
$18$	0.604879	+	2.25744i	0.142571	+	0.532084i
$19$	−1.37301	−	1.37301i	−0.314991	−	0.314991i	0.531849	−	0.846839i	$-0.321498\pi$
$19$	−1.37301	−	1.37301i	−0.314991	−	0.314991i	−0.846839	+	0.531849i	$0.821498\pi$
$20$	2.49813	+	9.32315i	0.558599	+	2.08472i
$21$	−1.90181	−	1.83932i	−0.415010	−	0.401373i
$22$	−7.08048	+	12.2637i	−1.50956	+	2.61464i
$23$	−1.85691	−	1.07209i	−0.387194	−	0.223546i	0.293750	−	0.955882i	$-0.405097\pi$
$23$	−1.85691	−	1.07209i	−0.387194	−	0.223546i	−0.680943	+	0.732336i	$0.738430\pi$
$24$	−2.41591	+	2.41591i	−0.493145	+	0.493145i
$25$	−2.40174	−	1.38664i	−0.480348	−	0.277329i
$26$	−7.54898	+	3.74403i	−1.48048	+	0.734264i
$27$		−	1.00000i		−	0.192450i
$28$	2.22253	−	8.88563i	0.420018	−	1.67923i
$29$	2.48648	+	4.30672i	0.461728	+	0.799737i	0.999047	−	0.0436422i	$-0.0138961\pi$
$29$	2.48648	+	4.30672i	0.461728	+	0.799737i	−0.537319	+	0.843379i	$0.680563\pi$
$30$		−	6.51591i		−	1.18964i
$31$	−1.92572	+	0.515996i	−0.345870	+	0.0926757i	−0.427572	−	0.903981i	$-0.640631\pi$
$31$	−1.92572	+	0.515996i	−0.345870	+	0.0926757i	0.0817020	+	0.996657i	$0.473964\pi$
$32$	4.20516	+	1.12677i	0.743375	+	0.199187i
$33$	4.28455	−	4.28455i	0.745844	−	0.745844i
$34$	2.12187	−	2.12187i	0.363897	−	0.363897i
$35$	3.79444	+	6.32576i	0.641377	+	1.06925i
$36$	2.99811	−	1.73096i	0.499685	−	0.288493i
$37$	11.4000	−	3.05463i	1.87416	−	0.502179i	0.874297	−	0.485392i	$-0.161323\pi$
$37$	11.4000	−	3.05463i	1.87416	−	0.502179i	0.999859	−	0.0167870i	$-0.00534370\pi$
$38$	−2.26899	+	3.93000i	−0.368078	+	0.637531i
$39$	3.53467	−	0.711416i	0.566000	−	0.113918i
$40$	8.24951	−	4.76285i	1.30436	−	0.753073i
$41$	1.19027	−	4.44214i	0.185889	−	0.693746i	−0.808550	−	0.588427i	$-0.799747\pi$
$41$	1.19027	−	4.44214i	0.185889	−	0.693746i	0.994439	−	0.105318i	$-0.0335861\pi$
$42$	−3.00179	+	5.40580i	−0.463187	+	0.834133i
$43$	−2.94613	−	1.70095i	−0.449281	−	0.259393i	0.258245	−	0.966079i	$-0.416856\pi$
$43$	−2.94613	−	1.70095i	−0.449281	−	0.259393i	−0.707527	+	0.706687i	$0.750189\pi$
$44$	20.2619	+	5.42916i	3.05460	+	0.818477i
$45$	−0.721604	+	2.69306i	−0.107570	+	0.401458i
$46$	−1.29697	+	4.84036i	−0.191228	+	0.713672i
$47$	−9.99804	−	2.67897i	−1.45836	−	0.390768i	−0.559440	−	0.828871i	$-0.688984\pi$
$47$	−9.99804	−	2.67897i	−1.45836	−	0.390768i	−0.898925	+	0.438103i	$0.855650\pi$
$48$	0.918879	+	0.530515i	0.132629	+	0.0765732i
$49$	−0.233788	−	6.99609i	−0.0333984	−	0.999442i
$50$	−1.67751	+	6.26054i	−0.237235	+	0.885373i
$51$	−1.11196	+	0.641993i	−0.155706	+	0.0898970i
$52$	8.25127	+	9.36589i	1.14424	+	1.29881i
$53$	4.30659	−	7.45923i	0.591556	−	1.02460i	−0.402468	−	0.915434i	$-0.631847\pi$
$53$	4.30659	−	7.45923i	0.591556	−	1.02460i	0.994023	−	0.109170i	$-0.0348193\pi$
$54$	−2.25744	+	0.604879i	−0.307199	+	0.0823136i
$55$	−14.6303	+	8.44680i	−1.97275	+	1.13897i
$56$	−9.03823	+	0.150973i	−1.20778	+	0.0201746i
$57$	1.37301	−	1.37301i	0.181860	−	0.181860i
$58$	8.21813	−	8.21813i	1.07909	−	1.07909i
$59$	11.2322	+	3.00965i	1.46230	+	0.391823i	0.900285	−	0.435302i	$-0.143358\pi$
$59$	11.2322	+	3.00965i	1.46230	+	0.391823i	0.562018	+	0.827125i	$0.310025\pi$
$60$	−9.32315	+	2.49813i	−1.20361	+	0.322507i
$61$			3.67019i			0.469919i	0.972005	+	0.234960i	$0.0754958\pi$
$61$			3.67019i			0.469919i	−0.972005	+	0.234960i	$0.924504\pi$
$62$	2.32966	+	4.03509i	0.295867	+	0.512457i
$63$	1.83932	−	1.90181i	0.231733	−	0.239606i
$64$		−	12.2965i		−	1.53707i
$65$	−10.0324	−	0.634743i	−1.24437	−	0.0787302i
$66$	−12.2637	−	7.08048i	−1.50956	−	0.871546i
$67$	1.20496	−	1.20496i	0.147209	−	0.147209i	−0.629661	−	0.776870i	$-0.716806\pi$
$67$	1.20496	−	1.20496i	0.147209	−	0.147209i	0.776870	+	0.629661i	$0.216806\pi$
$68$	−3.84953	−	2.22253i	−0.466824	−	0.269521i
$69$	1.07209	−	1.85691i	0.129065	−	0.223546i
$70$	11.9849	−	12.3920i	1.43246	−	1.48113i
$71$	−1.73527	−	6.47610i	−0.205938	−	0.768572i	−0.989162	−	0.146831i	$-0.953093\pi$
$71$	−1.73527	−	6.47610i	−0.205938	−	0.768572i	0.783223	−	0.621740i	$-0.213574\pi$
$72$	−2.41591	−	2.41591i	−0.284717	−	0.284717i
$73$	−1.17111	−	4.37064i	−0.137068	−	0.511544i	−0.999981	−	0.00619171i	$-0.998029\pi$
$73$	−1.17111	−	4.37064i	−0.137068	−	0.511544i	0.862913	−	0.505353i	$-0.168638\pi$
$74$	−13.7913	−	23.8872i	−1.60321	−	2.77684i
$75$	1.38664	−	2.40174i	0.160116	−	0.277329i
$76$	6.49307	+	1.73981i	0.744806	+	0.199570i
$77$	16.0291	−	0.267747i	1.82668	−	0.0305126i
$78$	−3.74403	−	7.54898i	−0.423928	−	0.854754i
$79$	0.418084	+	0.724143i	0.0470382	+	0.0814725i	0.888586	−	0.458710i	$-0.151688\pi$
$79$	0.418084	+	0.724143i	0.0470382	+	0.0814725i	−0.841548	+	0.540183i	$0.818355\pi$
$80$	−2.09178	−	2.09178i	−0.233868	−	0.233868i
$81$	1.00000			0.111111
$82$	−10.7478			−1.18690
$83$	−2.01023	−	2.01023i	−0.220651	−	0.220651i	0.588121	−	0.808773i	$-0.299868\pi$
$83$	−2.01023	−	2.01023i	−0.220651	−	0.220651i	−0.808773	+	0.588121i	$0.799868\pi$
$84$	8.88563	+	2.22253i	0.969502	+	0.242497i
$85$	3.45785	−	0.926529i	0.375057	−	0.100496i
$86$	−2.05774	+	7.67959i	−0.221892	+	0.828112i
$87$	−4.30672	+	2.48648i	−0.461728	+	0.266579i
$88$		−	20.7021i		−	2.20685i
$89$	1.29112	+	4.81854i	0.136859	+	0.510764i	0.999983	+	0.00577306i	$0.00183763\pi$
$89$	1.29112	+	4.81854i	0.136859	+	0.510764i	−0.863124	+	0.504991i	$0.831496\pi$
$90$	6.51591			0.686837
$91$	8.03080	+	5.14841i	0.841857	+	0.539701i
$92$	7.42297			0.773898
$93$	−0.515996	−	1.92572i	−0.0535063	−	0.199688i
$94$			24.1904i			2.49505i
$95$	−4.68838	+	2.70684i	−0.481018	+	0.277716i
$96$	−1.12677	+	4.20516i	−0.115001	+	0.429188i
$97$	−6.27512	+	1.68141i	−0.637142	+	0.170722i	−0.562909	−	0.826519i	$-0.690318\pi$
$97$	−6.27512	+	1.68141i	−0.637142	+	0.170722i	−0.0742335	+	0.997241i	$0.523651\pi$
$98$	−15.6519	+	4.75956i	−1.58108	+	0.480788i
$99$	4.28455	+	4.28455i	0.430613	+	0.430613i
$100$	9.60089			0.960089
$101$	−10.8179			−1.07642			−0.538212	−	0.842809i	$-0.680900\pi$
$101$	−10.8179			−1.07642			−0.538212	+	0.842809i	$0.680900\pi$
$102$	2.12187	+	2.12187i	0.210096	+	0.210096i
$103$	4.92483	+	8.53006i	0.485258	+	0.840491i	0.999857	−	0.0169399i	$-0.00539239\pi$
$103$	4.92483	+	8.53006i	0.485258	+	0.840491i	−0.514599	+	0.857431i	$0.672059\pi$
$104$	6.82071	−	10.2581i	0.668826	−	1.00589i
$105$	−6.32576	+	3.79444i	−0.617331	+	0.370299i
$106$	−19.4437	−	5.20993i	−1.88854	−	0.506033i
$107$	8.92371	−	15.4563i	0.862688	−	1.49422i	−0.00663727	−	0.999978i	$-0.502113\pi$
$107$	8.92371	−	15.4563i	0.862688	−	1.49422i	0.869325	−	0.494241i	$-0.164554\pi$
$108$	1.73096	+	2.99811i	0.166562	+	0.288493i
$109$	4.54330	+	16.9558i	0.435169	+	1.62407i	0.740661	+	0.671879i	$0.234513\pi$
$109$	4.54330	+	16.9558i	0.435169	+	1.62407i	−0.305491	+	0.952195i	$0.598821\pi$
$110$	27.9177	+	27.9177i	2.66185	+	2.66185i
$111$	3.05463	+	11.4000i	0.289933	+	1.08204i
$112$	0.771748	+	2.69905i	0.0729234	+	0.255037i
$113$	6.75649	−	11.7026i	0.635597	−	1.10089i	−0.350792	−	0.936454i	$-0.614087\pi$
$113$	6.75649	−	11.7026i	0.635597	−	1.10089i	0.986388	−	0.164432i	$-0.0525792\pi$
$114$	−3.93000	−	2.26899i	−0.368078	−	0.212510i
$115$	−4.22716	+	4.22716i	−0.394185	+	0.394185i
$116$	−14.9095	−	8.60800i	−1.38431	−	0.799232i
$117$	0.711416	+	3.53467i	0.0657704	+	0.326780i
$118$		−	27.1764i		−	2.50179i
$119$	−3.29558	−	0.824310i	−0.302105	−	0.0755644i
$120$	4.76285	+	8.24951i	0.434787	+	0.753073i
$121$			25.7147i			2.33770i
$122$	8.28522	−	2.22002i	0.750109	−	0.200991i
$123$	4.44214	+	1.19027i	0.400534	+	0.107323i
$124$	4.88036	−	4.88036i	0.438269	−	0.438269i
$125$	4.38987	−	4.38987i	0.392641	−	0.392641i
$126$	−5.40580	−	3.00179i	−0.481587	−	0.267421i
$127$	13.1985	−	7.62018i	1.17118	−	0.676182i	0.217223	−	0.976122i	$-0.430300\pi$
$127$	13.1985	−	7.62018i	1.17118	−	0.676182i	0.953958	+	0.299940i	$0.0969667\pi$
$128$	−19.3483	+	5.18437i	−1.71017	+	0.458238i
$129$	1.70095	−	2.94613i	0.149760	−	0.259393i
$130$	4.63552	+	23.0316i	0.406562	+	2.02000i
$131$	−7.39124	+	4.26734i	−0.645776	+	0.372839i	−0.786836	−	0.617162i	$-0.788282\pi$
$131$	−7.39124	+	4.26734i	−0.645776	+	0.372839i	0.141060	+	0.990001i	$0.454949\pi$
$132$	−5.42916	+	20.2619i	−0.472548	+	1.76357i
$133$	5.13663	−	0.0858014i	0.445402	−	0.00743992i
$134$	−3.44898	−	1.99127i	−0.297947	−	0.172020i
$135$	−2.69306	−	0.721604i	−0.231782	−	0.0621057i
$136$	−1.13541	+	4.23739i	−0.0973603	+	0.363354i
$137$	−1.15681	+	4.31726i	−0.0988326	+	0.368848i	−0.997573	−	0.0696336i	$-0.977817\pi$
$137$	−1.15681	+	4.31726i	−0.0988326	+	0.368848i	0.898740	+	0.438482i	$0.144484\pi$
$138$	−4.84036	−	1.29697i	−0.412039	−	0.110405i
$139$	12.7644	+	7.36955i	1.08267	+	0.625077i	0.931614	−	0.363448i	$-0.118401\pi$
$139$	12.7644	+	7.36955i	1.08267	+	0.625077i	0.151052	+	0.988526i	$0.451734\pi$
$140$	−22.3258	−	12.3973i	−1.88687	−	1.04776i
$141$	2.67897	−	9.99804i	0.225610	−	0.841987i
$142$	−13.5698	+	7.83452i	−1.13875	+	0.657458i
$143$	−12.0964	+	18.1926i	−1.01155	+	1.52134i
$144$	−0.530515	+	0.918879i	−0.0442096	+	0.0765732i
$145$	13.3925	−	3.58851i	1.11219	−	0.298010i
$146$	−9.15807	+	5.28742i	−0.757927	+	0.437590i
$147$	6.99609	−	0.233788i	0.577028	−	0.0192825i
$148$	−28.8911	+	28.8911i	−2.37484	+	2.37484i
$149$	−4.04274	+	4.04274i	−0.331194	+	0.331194i	−0.853040	−	0.521846i	$-0.825244\pi$
$149$	−4.04274	+	4.04274i	−0.331194	+	0.331194i	0.521846	+	0.853040i	$0.325244\pi$
$150$	−6.26054	−	1.67751i	−0.511171	−	0.136968i
$151$	1.23844	−	0.331838i	0.100783	−	0.0270046i	−0.208075	−	0.978113i	$-0.566720\pi$
$151$	1.23844	−	0.331838i	0.100783	−	0.0270046i	0.308858	+	0.951108i	$0.400053\pi$
$152$		−	6.63414i		−	0.538100i
$153$	−0.641993	−	1.11196i	−0.0519021	−	0.0898970i
$154$	−10.3001	−	36.0227i	−0.830004	−	2.90279i
$155$			5.55844i			0.446465i
$156$	−9.36589	+	8.25127i	−0.749871	+	0.660630i
$157$	−15.9387	−	9.20223i	−1.27205	−	0.734418i	−0.296676	−	0.954978i	$-0.595878\pi$
$157$	−15.9387	−	9.20223i	−1.27205	−	0.734418i	−0.975373	+	0.220561i	$0.929211\pi$
$158$	1.38182	−	1.38182i	0.109932	−	0.109932i
$159$	7.45923	+	4.30659i	0.591556	+	0.341535i
$160$	6.06892	−	10.5117i	0.479790	−	0.831021i
$161$	5.45438	−	1.55959i	0.429865	−	0.122913i
$162$	−0.604879	−	2.25744i	−0.0475238	−	0.177361i
$163$	2.96534	+	2.96534i	0.232263	+	0.232263i	0.813637	−	0.581374i	$-0.197484\pi$
$163$	2.96534	+	2.96534i	0.232263	+	0.232263i	−0.581374	+	0.813637i	$0.697484\pi$
$164$	4.12061	+	15.3783i	0.321765	+	1.20084i
$165$	−8.44680	−	14.6303i	−0.657583	−	1.13897i
$166$	−3.32202	+	5.75392i	−0.257839	+	0.446590i
$167$	−17.0124	−	4.55845i	−1.31646	−	0.352743i	−0.468807	−	0.883301i	$-0.655316\pi$
$167$	−17.0124	−	4.55845i	−1.31646	−	0.352743i	−0.847649	+	0.530557i	$0.821983\pi$
$168$	−0.150973	−	9.03823i	−0.0116478	−	0.697315i
$169$	−11.9878	+	5.02924i	−0.922136	+	0.386865i
$170$	−4.18317	−	7.24546i	−0.320834	−	0.555701i
$171$	1.37301	+	1.37301i	0.104997	+	0.104997i
$172$	11.7771			0.897995
$173$	3.85466			0.293064			0.146532	−	0.989206i	$-0.453189\pi$
$173$	3.85466			0.293064			0.146532	+	0.989206i	$0.453189\pi$
$174$	8.21813	+	8.21813i	0.623015	+	0.623015i
$175$	7.05471	−	2.01717i	0.533286	−	0.152484i
$176$	−6.21000	+	1.66396i	−0.468096	+	0.125426i
$177$	−3.00965	+	11.2322i	−0.226219	+	0.844261i
$178$	10.0966	−	5.82927i	0.756772	−	0.436922i
$179$			8.72984i			0.652499i	0.945284	+	0.326249i	$0.105785\pi$
$179$			8.72984i			0.652499i	−0.945284	+	0.326249i	$0.894215\pi$
$180$	−2.49813	−	9.32315i	−0.186200	−	0.694907i
$181$	−15.8824			−1.18053			−0.590266	−	0.807209i	$-0.700977\pi$
$181$	−15.8824			−1.18053			−0.590266	+	0.807209i	$0.700977\pi$
$182$	6.76457	−	21.2432i	0.501423	−	1.57465i
$183$	−3.67019			−0.271308
$184$	−1.89606	−	7.07620i	−0.139780	−	0.521664i
$185$		−	32.9053i		−	2.41924i
$186$	−4.03509	+	2.32966i	−0.295867	+	0.170819i
$187$	2.01362	−	7.51491i	0.147250	−	0.549545i
$188$	34.6124	−	9.27436i	2.52437	−	0.676402i
$189$	1.90181	+	1.83932i	0.138337	+	0.133791i
$190$	8.94643	+	8.94643i	0.649042	+	0.649042i
$191$	20.8859			1.51125			0.755626	−	0.655003i	$-0.227333\pi$
$191$	20.8859			1.51125			0.755626	+	0.655003i	$0.227333\pi$
$192$	12.2965			0.887425
$193$	3.01587	+	3.01587i	0.217087	+	0.217087i	0.807270	−	0.590183i	$-0.200944\pi$
$193$	3.01587	+	3.01587i	0.217087	+	0.217087i	−0.590183	+	0.807270i	$0.700944\pi$
$194$	7.59138	+	13.1487i	0.545029	+	0.944019i
$195$	0.634743	−	10.0324i	0.0454549	−	0.718438i
$196$	12.8109	+	20.5704i	0.915062	+	1.46931i
$197$	−16.6951	−	4.47344i	−1.18948	−	0.318719i	−0.390798	−	0.920476i	$-0.627801\pi$
$197$	−16.6951	−	4.47344i	−1.18948	−	0.318719i	−0.798679	+	0.601757i	$0.794468\pi$
$198$	7.08048	−	12.2637i	0.503188	−	0.871546i
$199$	−8.10511	−	14.0385i	−0.574556	−	0.995160i	−0.996090	−	0.0883471i	$-0.971842\pi$
$199$	−8.10511	−	14.0385i	−0.574556	−	0.995160i	0.421534	−	0.906813i	$-0.361492\pi$
$200$	−2.45237	−	9.15238i	−0.173409	−	0.647171i
$201$	1.20496	+	1.20496i	0.0849914	+	0.0849914i
$202$	6.54354	+	24.4208i	0.460402	+	1.71824i
$203$	−12.7640	−	3.19261i	−0.895858	−	0.224077i
$204$	2.22253	−	3.84953i	0.155608	−	0.269521i
$205$	−11.1041	−	6.41093i	−0.775541	−	0.447759i
$206$	16.2772	−	16.2772i	1.13408	−	1.13408i
$207$	1.85691	+	1.07209i	0.129065	+	0.0745154i
$208$	−3.62535	−	1.22149i	−0.251373	−	0.0846951i
$209$			11.7655i			0.813835i
$210$	12.3920	+	11.9849i	0.855132	+	0.827033i
$211$	0.261775	+	0.453408i	0.0180213	+	0.0312139i	0.874895	−	0.484312i	$-0.160930\pi$
$211$	0.261775	+	0.453408i	0.0180213	+	0.0312139i	−0.856874	+	0.515526i	$0.827597\pi$
$212$			29.8181i			2.04792i
$213$	6.47610	−	1.73527i	0.443735	−	0.118898i
$214$	−40.2895	−	10.7955i	−2.75413	−	0.737968i
$215$	−6.70671	+	6.70671i	−0.457393	+	0.457393i
$216$	2.41591	−	2.41591i	0.164382	−	0.164382i
$217$	2.56070	−	4.61145i	0.173832	−	0.313046i
$218$	35.5286	−	20.5125i	2.40630	−	1.38928i
$219$	4.37064	−	1.17111i	0.295340	−	0.0791362i
$220$	29.2421	−	50.6488i	1.97150	−	3.41474i
$221$	3.47370	−	3.06030i	0.233667	−	0.205858i
$222$	23.8872	−	13.7913i	1.60321	−	0.925612i
$223$	5.87188	−	21.9142i	0.393210	−	1.46748i	−0.431596	−	0.902067i	$-0.642050\pi$
$223$	5.87188	−	21.9142i	0.393210	−	1.46748i	0.824807	−	0.565414i	$-0.191284\pi$
$224$	−9.87756	+	5.92494i	−0.659972	+	0.395877i
$225$	2.40174	+	1.38664i	0.160116	+	0.0924430i
$226$	−30.5047	−	8.17372i	−2.02914	−	0.543708i
$227$	−0.605263	+	2.25887i	−0.0401727	+	0.149927i	−0.983099	−	0.183075i	$-0.941395\pi$
$227$	−0.605263	+	2.25887i	−0.0401727	+	0.149927i	0.942926	+	0.333002i	$0.108062\pi$
$228$	−1.73981	+	6.49307i	−0.115222	+	0.430014i
$229$	−9.39632	−	2.51774i	−0.620927	−	0.166377i	−0.0653776	−	0.997861i	$-0.520825\pi$
$229$	−9.39632	−	2.51774i	−0.620927	−	0.166377i	−0.555549	+	0.831484i	$0.687492\pi$
$230$	12.0995	+	6.98564i	0.797817	+	0.460620i
$231$	0.267747	+	16.0291i	0.0176165	+	1.05464i
$232$	−4.39751	+	16.4117i	−0.288711	+	1.07748i
$233$	−2.70246	+	1.56026i	−0.177044	+	0.102216i	−0.585903	−	0.810381i	$-0.699260\pi$
$233$	−2.70246	+	1.56026i	−0.177044	+	0.102216i	0.408859	+	0.912597i	$0.365927\pi$
$234$	7.54898	−	3.74403i	0.493493	−	0.244755i
$235$	−14.4292	+	24.9922i	−0.941260	+	1.63031i
$236$	−38.8848	+	10.4192i	−2.53119	+	0.678229i
$237$	−0.724143	+	0.418084i	−0.0470382	+	0.0271575i
$238$	0.132598	+	7.93818i	0.00859506	+	0.514556i
$239$	−5.27158	+	5.27158i	−0.340990	+	0.340990i	−0.856739	−	0.515749i	$-0.827514\pi$
$239$	−5.27158	+	5.27158i	−0.340990	+	0.340990i	0.515749	+	0.856739i	$0.327514\pi$
$240$	2.09178	−	2.09178i	0.135024	−	0.135024i
$241$	−14.2707	−	3.82383i	−0.919259	−	0.246315i	−0.231990	−	0.972718i	$-0.574524\pi$
$241$	−14.2707	−	3.82383i	−0.919259	−	0.246315i	−0.687268	+	0.726404i	$0.741190\pi$
$242$	58.0494	−	15.5543i	3.73156	−	0.999868i
$243$			1.00000i			0.0641500i
$244$	−6.35294	−	11.0036i	−0.406705	−	0.704434i
$245$	−19.0096	−	4.41880i	−1.21448	−	0.282307i
$246$		−	10.7478i		−	0.685257i
$247$	−3.87636	+	5.82993i	−0.246647	+	0.370950i
$248$	−5.89897	−	3.40577i	−0.374585	−	0.216267i
$249$	2.01023	−	2.01023i	0.127393	−	0.127393i
$250$	−12.5652	−	7.25452i	−0.794693	−	0.458816i
$251$	0.406821	−	0.704635i	0.0256783	−	0.0444762i	−0.852901	−	0.522073i	$-0.825159\pi$
$251$	0.406821	−	0.704635i	0.0256783	−	0.0444762i	0.878579	+	0.477597i	$0.158492\pi$
$252$	−2.22253	+	8.88563i	−0.140006	+	0.559742i
$253$	3.36262	+	12.5495i	0.211406	+	0.788978i
$254$	−25.1856	−	25.1856i	−1.58029	−	1.58029i
$255$	0.926529	+	3.45785i	0.0580215	+	0.216539i
$256$	11.1103	+	19.2436i	0.694394	+	1.20273i
$257$	4.95468	−	8.58176i	0.309065	−	0.535315i	−0.669093	−	0.743178i	$-0.733317\pi$
$257$	4.95468	−	8.58176i	0.309065	−	0.535315i	0.978158	+	0.207863i	$0.0666508\pi$
$258$	−7.67959	−	2.05774i	−0.478110	−	0.128109i
$259$	−15.1590	+	27.2992i	−0.941935	+	1.69629i
$260$	31.1770	−	15.4627i	1.93352	−	0.958956i
$261$	−2.48648	−	4.30672i	−0.153909	−	0.266579i
$262$	14.1041	+	14.1041i	0.871352	+	0.871352i
$263$	−2.58615			−0.159469			−0.0797345	−	0.996816i	$-0.525407\pi$
$263$	−2.58615			−0.159469			−0.0797345	+	0.996816i	$0.525407\pi$
$264$	20.7021			1.27413
$265$	−16.9805	−	16.9805i	−1.04310	−	1.04310i
$266$	−3.30073	−	11.5437i	−0.202381	−	0.707792i
$267$	−4.81854	+	1.29112i	−0.294890	+	0.0790155i
$268$	−1.52686	+	5.69834i	−0.0932681	+	0.348081i
$269$	−11.5928	+	6.69308i	−0.706823	+	0.408084i	−0.809884	−	0.586591i	$-0.800470\pi$
$269$	−11.5928	+	6.69308i	−0.706823	+	0.408084i	0.103061	+	0.994675i	$0.467136\pi$
$270$			6.51591i			0.396546i
$271$	3.60441	+	13.4518i	0.218952	+	0.817141i	0.984738	+	0.174045i	$0.0556837\pi$
$271$	3.60441	+	13.4518i	0.218952	+	0.817141i	−0.765786	+	0.643096i	$0.777650\pi$
$272$	1.36235			0.0826045
$273$	−5.14841	+	8.03080i	−0.311596	+	0.486046i
$274$	10.4457			0.631047
$275$	4.34922	+	16.2315i	0.262268	+	0.978797i
$276$			7.42297i			0.446810i
$277$	−6.18606	+	3.57152i	−0.371684	+	0.214592i	−0.674194	−	0.738554i	$-0.735509\pi$
$277$	−6.18606	+	3.57152i	−0.371684	+	0.214592i	0.302510	+	0.953146i	$0.402176\pi$
$278$	8.91538	−	33.2727i	0.534709	−	1.99556i
$279$	1.92572	−	0.515996i	0.115290	−	0.0308919i
$280$	−6.11544	+	24.4494i	−0.365467	+	1.46113i
$281$	7.93911	+	7.93911i	0.473608	+	0.473608i	0.903080	−	0.429472i	$-0.141300\pi$
$281$	7.93911	+	7.93911i	0.473608	+	0.473608i	−0.429472	+	0.903080i	$0.641300\pi$
$282$	−24.1904			−1.44052
$283$	24.1164			1.43357			0.716784	−	0.697295i	$-0.245613\pi$
$283$	24.1164			1.43357			0.716784	+	0.697295i	$0.245613\pi$
$284$	16.4124	+	16.4124i	0.973895	+	0.973895i
$285$	−2.70684	−	4.68838i	−0.160339	−	0.277716i
$286$	48.3855	+	16.3025i	2.86109	+	0.963988i
$287$	6.25883	+	10.4342i	0.369447	+	0.615911i
$288$	−4.20516	−	1.12677i	−0.247792	−	0.0663956i
$289$	7.67569	−	13.2947i	0.451511	−	0.782040i
$290$	−16.2017	−	28.0622i	−0.951396	−	1.64787i
$291$	−1.68141	−	6.27512i	−0.0985662	−	0.367854i
$292$	11.0765	+	11.0765i	0.648203	+	0.648203i
$293$	−4.31028	−	16.0862i	−0.251809	−	0.939765i	−0.969838	−	0.243751i	$-0.921622\pi$
$293$	−4.31028	−	16.0862i	−0.251809	−	0.939765i	0.718029	−	0.696013i	$-0.245045\pi$
$294$	−4.75956	−	15.6519i	−0.277583	−	0.912835i
$295$	16.2103	−	28.0771i	0.943802	−	1.63471i
$296$	34.9211	+	20.1617i	2.02975	+	1.17188i
$297$	−4.28455	+	4.28455i	−0.248615	+	0.248615i
$298$	11.5716	+	6.68088i	0.670326	+	0.387013i
$299$	−2.46845	+	7.32628i	−0.142754	+	0.423690i
$300$			9.60089i			0.554308i
$301$	8.65378	−	2.47440i	0.498796	−	0.142622i
$302$	−1.49821	−	2.59497i	−0.0862122	−	0.149324i
$303$		−	10.8179i		−	0.621474i
$304$	−1.99004	+	0.533229i	−0.114136	+	0.0305828i
$305$	9.88403	+	2.64842i	0.565958	+	0.151648i
$306$	−2.12187	+	2.12187i	−0.121299	+	0.121299i
$307$	3.38448	−	3.38448i	0.193163	−	0.193163i	−0.603899	−	0.797061i	$-0.706387\pi$
$307$	3.38448	−	3.38448i	0.193163	−	0.193163i	0.797061	+	0.603899i	$0.206387\pi$
$308$	−47.5934	+	28.5484i	−2.71189	+	1.62670i
$309$	−8.53006	+	4.92483i	−0.485258	+	0.280164i
$310$	12.5478	−	3.36219i	0.712670	−	0.190959i
$311$	−11.5078	+	19.9321i	−0.652549	+	1.13025i	0.329953	+	0.943997i	$0.392967\pi$
$311$	−11.5078	+	19.9321i	−0.652549	+	1.13025i	−0.982502	+	0.186251i	$0.940366\pi$
$312$	10.2581	+	6.82071i	0.580753	+	0.386147i
$313$	10.4564	−	6.03699i	0.591029	−	0.341231i	−0.174475	−	0.984662i	$-0.555823\pi$
$313$	10.4564	−	6.03699i	0.591029	−	0.341231i	0.765504	+	0.643431i	$0.222489\pi$
$314$	−11.1325	+	41.5470i	−0.628242	+	2.34463i
$315$	−3.79444	−	6.32576i	−0.213792	−	0.356416i
$316$	−2.50692	−	1.44737i	−0.141025	−	0.0814211i
$317$	−4.21491	−	1.12938i	−0.236733	−	0.0634325i	0.138502	−	0.990362i	$-0.455771\pi$
$317$	−4.21491	−	1.12938i	−0.236733	−	0.0634325i	−0.375235	+	0.926930i	$0.622438\pi$
$318$	5.20993	−	19.4437i	0.292159	−	1.09035i
$319$	7.79887	−	29.1058i	0.436653	−	1.62961i
$320$	−33.1153	−	8.87322i	−1.85120	−	0.496028i
$321$	15.4563	+	8.92371i	0.862688	+	0.498073i
$322$	−6.81992	−	11.3696i	−0.380059	−	0.633602i
$323$	0.645277	−	2.40821i	0.0359042	−	0.133996i
$324$	−2.99811	+	1.73096i	−0.166562	+	0.0961643i
$325$	−3.19269	+	9.47583i	−0.177099	+	0.525625i
$326$	4.90040	−	8.48775i	0.271408	−	0.470093i
$327$	−16.9558	+	4.54330i	−0.937660	+	0.251245i
$328$	13.6074	−	7.85621i	0.751341	−	0.433787i
$329$	23.4845	−	14.0869i	1.29474	−	0.776637i
$330$	−27.9177	+	27.9177i	−1.53682	+	1.53682i
$331$	9.48746	−	9.48746i	0.521478	−	0.521478i	−0.396540	−	0.918018i	$-0.629789\pi$
$331$	9.48746	−	9.48746i	0.521478	−	0.521478i	0.918018	+	0.396540i	$0.129789\pi$
$332$	9.50650	+	2.54726i	0.521737	+	0.139799i
$333$	−11.4000	+	3.05463i	−0.624719	+	0.167393i
$334$			41.1617i			2.25227i
$335$	−2.37553	−	4.11454i	−0.129789	−	0.224801i
$336$	−2.69905	+	0.771748i	−0.147246	+	0.0421023i
$337$			19.8421i			1.08087i	0.841386	+	0.540435i	$0.181740\pi$
$337$			19.8421i			1.08087i	−0.841386	+	0.540435i	$0.818260\pi$
$338$	18.6044	+	24.0196i	1.01194	+	1.30649i
$339$	11.7026	+	6.75649i	0.635597	+	0.366962i
$340$	−8.76323	+	8.76323i	−0.475253	+	0.475253i
$341$	10.4617	+	6.04005i	0.566531	+	0.327087i
$342$	2.26899	−	3.93000i	0.122693	−	0.212510i
$343$	13.7353	+	12.4234i	0.741635	+	0.670803i
$344$	−3.00824	−	11.2269i	−0.162194	−	0.605315i
$345$	−4.22716	−	4.22716i	−0.227583	−	0.227583i
$346$	−2.33160	−	8.70166i	−0.125348	−	0.467804i
$347$	−7.43077	−	12.8705i	−0.398905	−	0.690923i	0.594686	−	0.803958i	$-0.297276\pi$
$347$	−7.43077	−	12.8705i	−0.398905	−	0.690923i	−0.993591	+	0.113035i	$0.963943\pi$
$348$	8.60800	−	14.9095i	0.461437	−	0.799232i
$349$	−5.71985	−	1.53263i	−0.306177	−	0.0820398i	0.102459	−	0.994737i	$-0.467329\pi$
$349$	−5.71985	−	1.53263i	−0.306177	−	0.0820398i	−0.408636	+	0.912697i	$0.633995\pi$
$350$	−8.82090	−	14.7054i	−0.471497	−	0.786039i
$351$	−3.53467	+	0.711416i	−0.188667	+	0.0379726i
$352$	−13.1895	−	22.8449i	−0.703004	−	1.21764i
$353$	20.7636	+	20.7636i	1.10514	+	1.10514i	0.993781	+	0.111354i	$0.0355189\pi$
$353$	20.7636	+	20.7636i	1.10514	+	1.10514i	0.111354	+	0.993781i	$0.464481\pi$
$354$	27.1764			1.44441
$355$	−18.6927			−0.992106
$356$	−12.2116	−	12.2116i	−0.647215	−	0.647215i
$357$	0.824310	−	3.29558i	0.0436271	−	0.174421i
$358$	19.7071	−	5.28050i	1.04155	−	0.279083i
$359$	1.36716	−	5.10230i	0.0721558	−	0.269289i	−0.920418	−	0.390937i	$-0.872151\pi$
$359$	1.36716	−	5.10230i	0.0721558	−	0.269289i	0.992573	+	0.121648i	$0.0388178\pi$
$360$	−8.24951	+	4.76285i	−0.434787	+	0.251024i
$361$		−	15.2297i		−	0.801562i
$362$	9.60696	+	35.8536i	0.504930	+	1.88443i
$363$	−25.7147			−1.34967
$364$	−32.9889	−	1.53451i	−1.72909	−	0.0804304i
$365$	−12.6155			−0.660324
$366$	2.22002	+	8.28522i	0.116042	+	0.433076i
$367$		−	3.08464i		−	0.161017i	−0.996754	−	0.0805084i	$-0.974346\pi$
$367$		−	3.08464i		−	0.161017i	0.996754	−	0.0805084i	$-0.0256544\pi$
$368$	−1.97024	+	1.13752i	−0.102706	+	0.0592973i
$369$	−1.19027	+	4.44214i	−0.0619629	+	0.231249i
$370$	−74.2816	+	19.9037i	−3.86172	+	1.03474i
$371$	6.26486	+	21.9103i	0.325255	+	1.13752i
$372$	4.88036	+	4.88036i	0.253035	+	0.253035i
$373$	25.7754			1.33460			0.667300	−	0.744789i	$-0.267450\pi$
$373$	25.7754			1.33460			0.667300	+	0.744789i	$0.267450\pi$
$374$	−18.1825			−0.940193
$375$	4.38987	+	4.38987i	0.226692	+	0.226692i
$376$	−17.6822	−	30.6265i	−0.911889	−	1.57944i
$377$	13.4539	−	11.8528i	0.692911	−	0.610448i
$378$	3.00179	−	5.40580i	0.154396	−	0.278044i
$379$	15.7457	+	4.21904i	0.808801	+	0.216717i	0.639444	−	0.768837i	$-0.279164\pi$
$379$	15.7457	+	4.21904i	0.808801	+	0.216717i	0.169356	+	0.985555i	$0.445831\pi$
$380$	9.37084	−	16.2308i	0.480714	−	0.832621i
$381$	7.62018	+	13.1985i	0.390394	+	0.676182i
$382$	−12.6335	−	47.1487i	−0.646384	−	2.41234i
$383$	−1.16542	−	1.16542i	−0.0595502	−	0.0595502i	0.676705	−	0.736255i	$-0.263407\pi$
$383$	−1.16542	−	1.16542i	−0.0595502	−	0.0595502i	−0.736255	+	0.676705i	$0.763407\pi$
$384$	−5.18437	−	19.3483i	−0.264564	−	0.987366i
$385$	10.8456	−	43.3605i	0.552742	−	2.20985i
$386$	4.98390	−	8.63238i	0.253674	−	0.439376i
$387$	2.94613	+	1.70095i	0.149760	+	0.0864642i
$388$	15.9030	−	15.9030i	0.807354	−	0.807354i
$389$	−7.18251	−	4.14683i	−0.364168	−	0.210252i	0.306740	−	0.951793i	$-0.400762\pi$
$389$	−7.18251	−	4.14683i	−0.364168	−	0.210252i	−0.670908	+	0.741541i	$0.734095\pi$
$390$	−23.0316	+	4.63552i	−1.16625	+	0.234729i
$391$		−	2.75310i		−	0.139230i
$392$	16.3371	−	17.4667i	0.825148	−	0.882202i
$393$	−4.26734	−	7.39124i	−0.215259	−	0.372839i
$394$			40.3941i			2.03503i
$395$	2.25185	−	0.603382i	0.113303	−	0.0303595i
$396$	−20.2619	−	5.42916i	−1.01820	−	0.272826i
$397$	23.9543	−	23.9543i	1.20223	−	1.20223i	0.228747	−	0.973486i	$-0.426537\pi$
$397$	23.9543	−	23.9543i	1.20223	−	1.20223i	0.973486	−	0.228747i	$-0.0734628\pi$
$398$	−26.7884	+	26.7884i	−1.34278	+	1.34278i
$399$	0.0858014	+	5.13663i	0.00429544	+	0.257153i
$400$	−2.54832	+	1.47127i	−0.127416	+	0.0735636i
$401$	15.1688	−	4.06446i	0.757492	−	0.202969i	0.140654	−	0.990059i	$-0.455080\pi$
$401$	15.1688	−	4.06446i	0.757492	−	0.202969i	0.616839	+	0.787089i	$0.288413\pi$
$402$	1.99127	−	3.44898i	0.0993156	−	0.172020i
$403$	3.19387	+	6.43971i	0.159098	+	0.320785i
$404$	32.4333	−	18.7254i	1.61362	−	0.931622i
$405$	0.721604	−	2.69306i	0.0358568	−	0.133819i
$406$	0.513562	+	30.7451i	0.0254876	+	1.52586i
$407$	−61.9318	−	35.7563i	−3.06984	−	1.77238i
$408$	−4.23739	−	1.13541i	−0.209782	−	0.0562110i
$409$	−1.56976	+	5.85843i	−0.0776197	+	0.289681i	−0.993815	−	0.111052i	$-0.964578\pi$
$409$	−1.56976	+	5.85843i	−0.0776197	+	0.289681i	0.916195	+	0.400733i	$0.131245\pi$
$410$	−7.75567	+	28.9446i	−0.383025	+	1.42947i
$411$	−4.31726	−	1.15681i	−0.212955	−	0.0570610i
$412$	−29.5303	−	17.0493i	−1.45486	−	0.839961i
$413$	−26.3834	+	15.8258i	−1.29824	+	0.778735i
$414$	1.29697	−	4.84036i	0.0637426	−	0.237891i
$415$	−6.86425	+	3.96308i	−0.336953	+	0.194540i
$416$	0.991139	−	15.6655i	0.0485946	−	0.768063i
$417$	−7.36955	+	12.7644i	−0.360889	+	0.625077i
$418$	26.5599	−	7.11670i	1.29909	−	0.348089i
$419$	2.76236	−	1.59485i	0.134950	−	0.0779134i	−0.431005	−	0.902350i	$-0.641841\pi$
$419$	2.76236	−	1.59485i	0.134950	−	0.0779134i	0.565955	+	0.824436i	$0.308508\pi$
$420$	12.3973	−	22.3258i	0.604926	−	1.08939i
$421$	11.3351	−	11.3351i	0.552438	−	0.552438i	−0.374706	−	0.927144i	$-0.622256\pi$
$421$	11.3351	−	11.3351i	0.552438	−	0.552438i	0.927144	+	0.374706i	$0.122256\pi$
$422$	0.865198	−	0.865198i	0.0421172	−	0.0421172i
$423$	9.99804	+	2.67897i	0.486121	+	0.130256i
$424$	28.4251	−	7.61648i	1.38045	−	0.369889i
$425$		−	3.56086i		−	0.172727i
$426$	−7.83452	−	13.5698i	−0.379584	−	0.657458i
$427$	−6.98001	−	6.75065i	−0.337786	−	0.326687i
$428$			61.7863i			2.98655i
$429$	−18.1926	−	12.0964i	−0.878345	−	0.584018i
$430$	19.1967	+	11.0832i	0.925749	+	0.534481i
$431$	−23.7258	+	23.7258i	−1.14283	+	1.14283i	−0.154901	+	0.987930i	$0.549506\pi$
$431$	−23.7258	+	23.7258i	−1.14283	+	1.14283i	−0.987930	+	0.154901i	$0.950494\pi$
$432$	−0.918879	−	0.530515i	−0.0442096	−	0.0255244i
$433$	−4.68210	+	8.10963i	−0.225007	+	0.389724i	−0.956322	−	0.292317i	$-0.905574\pi$
$433$	−4.68210	+	8.10963i	−0.225007	+	0.389724i	0.731314	+	0.682040i	$0.238907\pi$
$434$	−11.9590	−	2.99125i	−0.574050	−	0.143585i
$435$	3.58851	+	13.3925i	0.172056	+	0.642121i
$436$	−42.9711	−	42.9711i	−2.05794	−	2.05794i
$437$	1.07757	+	4.02156i	0.0515474	+	0.192377i
$438$	−5.28742	−	9.15807i	−0.252642	−	0.437590i
$439$	−0.461604	+	0.799522i	−0.0220312	+	0.0381591i	−0.876831	−	0.480799i	$-0.840347\pi$
$439$	−0.461604	+	0.799522i	−0.0220312	+	0.0381591i	0.854800	+	0.518958i	$0.173680\pi$
$440$	−55.7521	−	14.9387i	−2.65788	−	0.712176i
$441$	0.233788	+	6.99609i	0.0111328	+	0.333147i
$442$	−9.00962	−	5.99056i	−0.428544	−	0.284942i
$443$	10.2398	+	17.7358i	0.486505	+	0.842652i	0.999880	−	0.0155128i	$-0.00493806\pi$
$443$	10.2398	+	17.7358i	0.486505	+	0.842652i	−0.513374	+	0.858165i	$0.671605\pi$
$444$	−28.8911	−	28.8911i	−1.37111	−	1.37111i
$445$	13.9083			0.659317
$446$	−53.0217			−2.51065
$447$	−4.04274	−	4.04274i	−0.191215	−	0.191215i
$448$	23.3857	+	22.6173i	1.10487	+	1.06857i
$449$	5.20881	−	1.39570i	0.245819	−	0.0658670i	−0.133806	−	0.991008i	$-0.542720\pi$
$449$	5.20881	−	1.39570i	0.245819	−	0.0658670i	0.379625	+	0.925141i	$0.376053\pi$
$450$	1.67751	−	6.26054i	0.0790784	−	0.295124i
$451$	−24.1323	+	13.9328i	−1.13635	+	0.656070i
$452$			46.7808i			2.20038i
$453$	0.331838	+	1.23844i	0.0155911	+	0.0581868i
$454$	5.46538			0.256503
$455$	19.6601	−	17.9123i	0.921677	−	0.839743i
$456$	6.63414			0.310672
$457$	5.39681	+	20.1412i	0.252452	+	0.942165i	0.969490	+	0.245130i	$0.0788308\pi$
$457$	5.39681	+	20.1412i	0.252452	+	0.942165i	−0.717038	+	0.697034i	$0.754503\pi$
$458$			22.7346i			1.06232i
$459$	1.11196	−	0.641993i	0.0519021	−	0.0299657i
$460$	5.35644	−	19.9905i	0.249745	−	0.932063i
$461$	−20.0777	+	5.37980i	−0.935112	+	0.250562i	−0.694033	−	0.719943i	$-0.744168\pi$
$461$	−20.0777	+	5.37980i	−0.935112	+	0.250562i	−0.241079	+	0.970506i	$0.577501\pi$
$462$	36.0227	−	10.3001i	1.67593	−	0.479203i
$463$	−12.2033	−	12.2033i	−0.567134	−	0.567134i	0.364190	−	0.931325i	$-0.381346\pi$
$463$	−12.2033	−	12.2033i	−0.567134	−	0.567134i	−0.931325	+	0.364190i	$0.881346\pi$
$464$	5.27647			0.244954
$465$	−5.55844			−0.257766
$466$	5.15686	+	5.15686i	0.238887	+	0.238887i
$467$	1.92605	+	3.33601i	0.0891268	+	0.154372i	0.907142	−	0.420824i	$-0.138259\pi$
$467$	1.92605	+	3.33601i	0.0891268	+	0.154372i	−0.818015	+	0.575196i	$0.804926\pi$
$468$	−8.25127	−	9.36589i	−0.381415	−	0.432938i
$469$	0.0752996	+	4.50792i	0.00347701	+	0.208156i
$470$	65.1463	+	17.4559i	3.00498	+	0.805181i
$471$	9.20223	−	15.9387i	0.424016	−	0.734418i
$472$	19.8648	+	34.4069i	0.914352	+	1.58370i
$473$	5.33504	+	19.9107i	0.245306	+	0.915493i
$474$	1.38182	+	1.38182i	0.0634691	+	0.0634691i
$475$	1.39374	+	5.20150i	0.0639491	+	0.238661i
$476$	11.3073	−	3.23314i	0.518272	−	0.148191i
$477$	−4.30659	+	7.45923i	−0.197185	+	0.341535i
$478$	15.0889	+	8.71160i	0.690152	+	0.398459i
$479$	17.0011	−	17.0011i	0.776799	−	0.776799i	−0.202486	−	0.979285i	$-0.564902\pi$
$479$	17.0011	−	17.0011i	0.776799	−	0.776799i	0.979285	+	0.202486i	$0.0649022\pi$
$480$	10.5117	+	6.06892i	0.479790	+	0.277007i
$481$	−18.9073	−	38.1223i	−0.862098	−	1.73823i
$482$			34.5283i			1.57272i
$483$	1.55959	+	5.45438i	0.0709636	+	0.248183i
$484$	−44.5111	−	77.0954i	−2.02323	−	3.50434i
$485$			18.1126i			0.822451i
$486$	2.25744	−	0.604879i	0.102400	−	0.0274379i
$487$	36.1238	+	9.67933i	1.63692	+	0.438612i	0.955910	−	0.293659i	$-0.0948728\pi$
$487$	36.1238	+	9.67933i	1.63692	+	0.438612i	0.681013	+	0.732271i	$0.261540\pi$
$488$	−8.86682	+	8.86682i	−0.401382	+	0.401382i
$489$	−2.96534	+	2.96534i	−0.134097	+	0.134097i
$490$	1.52334	+	45.5859i	0.0688177	+	2.05936i
$491$	6.19382	−	3.57600i	0.279523	−	0.161383i	−0.353684	−	0.935365i	$-0.615071\pi$
$491$	6.19382	−	3.57600i	0.279523	−	0.161383i	0.633208	+	0.773982i	$0.281738\pi$
$492$	−15.3783	+	4.12061i	−0.693308	+	0.185771i
$493$	−3.19261	+	5.52976i	−0.143788	+	0.249048i
$494$	15.5055	+	5.22425i	0.697623	+	0.235050i
$495$	14.6303	−	8.44680i	0.657583	−	0.379656i
$496$	−0.547488	+	2.04325i	−0.0245829	+	0.0917447i
$497$	15.5080	+	8.61148i	0.695631	+	0.386278i
$498$	−5.75392	−	3.32202i	−0.257839	−	0.148863i
$499$	8.70707	+	2.33305i	0.389782	+	0.104442i	0.448387	−	0.893839i	$-0.351999\pi$
$499$	8.70707	+	2.33305i	0.389782	+	0.104442i	−0.0586050	+	0.998281i	$0.518665\pi$
$500$	−5.56261	+	20.7600i	−0.248768	+	0.928414i
$501$	4.55845	−	17.0124i	0.203657	−	0.760056i
$502$	−1.83675	−	0.492156i	−0.0819781	−	0.0219660i
$503$	−32.8329	−	18.9561i	−1.46395	−	0.845209i	−0.464755	−	0.885439i	$-0.653857\pi$
$503$	−32.8329	−	18.9561i	−1.46395	−	0.845209i	−0.999190	+	0.0402304i	$0.987191\pi$
$504$	9.03823	−	0.150973i	0.402595	−	0.00672488i
$505$	−7.80626	+	29.1333i	−0.347374	+	1.29642i
$506$	26.2957	−	15.1818i	1.16899	−	0.674914i
$507$	−5.02924	−	11.9878i	−0.223356	−	0.532396i
$508$	−26.3804	+	45.6923i	−1.17044	+	2.02727i
$509$	37.6080	−	10.0770i	1.66694	−	0.446656i	0.702660	−	0.711525i	$-0.251995\pi$
$509$	37.6080	−	10.0770i	1.66694	−	0.446656i	0.964284	+	0.264869i	$0.0853287\pi$
$510$	7.24546	−	4.18317i	0.320834	−	0.185234i
$511$	10.4662	+	5.81178i	0.462997	+	0.257098i
$512$	8.39296	−	8.39296i	0.370920	−	0.370920i
$513$	−1.37301	+	1.37301i	−0.0606200	+	0.0606200i
$514$	−22.3698	−	5.99397i	−0.986689	−	0.264383i
$515$	26.5257	−	7.10755i	1.16886	−	0.313196i
$516$			11.7771i			0.518458i
$517$	31.3589	+	54.3153i	1.37916	+	2.38878i
$518$	70.7957	+	17.7078i	3.11059	+	0.778038i
$519$			3.85466i			0.169201i
$520$	−22.7039	−	25.7709i	−0.995634	−	1.13013i
$521$	−24.6719	−	14.2443i	−1.08089	−	0.624054i	−0.149757	−	0.988723i	$-0.547849\pi$
$521$	−24.6719	−	14.2443i	−1.08089	−	0.624054i	−0.931137	+	0.364668i	$0.881182\pi$
$522$	−8.21813	+	8.21813i	−0.359698	+	0.359698i
$523$	22.5632	+	13.0269i	0.986621	+	0.569626i	0.904263	−	0.426977i	$-0.140421\pi$
$523$	22.5632	+	13.0269i	0.986621	+	0.569626i	0.0823584	+	0.996603i	$0.473755\pi$
$524$	14.7732	−	25.5879i	0.645369	−	1.11781i
$525$	2.01717	+	7.05471i	0.0880367	+	0.307893i
$526$	1.56431	+	5.83808i	0.0682071	+	0.254552i
$527$	−1.81007	−	1.81007i	−0.0788480	−	0.0788480i
$528$	−1.66396	−	6.21000i	−0.0724147	−	0.270255i
$529$	−9.20124	−	15.9370i	−0.400054	−	0.692914i
$530$	−28.0613	+	48.6037i	−1.21891	+	2.11121i
$531$	−11.2322	−	3.00965i	−0.487434	−	0.130608i
$532$	−15.2516	+	9.14853i	−0.661243	+	0.396639i
$533$	−16.5483	−	1.04699i	−0.716785	−	0.0453503i
$534$	5.82927	+	10.0966i	0.252257	+	0.436922i
$535$	−35.1854	−	35.1854i	−1.52120	−	1.52120i
$536$	5.82214			0.251478
$537$	−8.72984			−0.376720
$538$	22.1215	+	22.1215i	0.953724	+	0.953724i
$539$	−28.9734	+	30.9768i	−1.24797	+	1.33426i
$540$	9.32315	−	2.49813i	0.401205	−	0.107502i
$541$	8.76662	−	32.7175i	0.376906	−	1.40663i	−0.473633	−	0.880722i	$-0.657058\pi$
$541$	8.76662	−	32.7175i	0.376906	−	1.40663i	0.850539	−	0.525912i	$-0.176276\pi$
$542$	28.1865	−	16.2735i	1.21071	−	0.699005i
$543$		−	15.8824i		−	0.681580i
$544$	1.44676	+	5.39937i	0.0620292	+	0.231496i
$545$	48.9416			2.09643
$546$	21.2432	+	6.76457i	0.909126	+	0.289497i
$547$	22.5824			0.965553			0.482776	−	0.875744i	$-0.339628\pi$
$547$	22.5824			0.965553			0.482776	+	0.875744i	$0.339628\pi$
$548$	−4.00477	−	14.9460i	−0.171075	−	0.638461i
$549$		−	3.67019i		−	0.156640i
$550$	34.0109	−	19.6362i	1.45023	−	0.837291i
$551$	2.49920	−	9.32715i	0.106470	−	0.397350i
$552$	7.07620	−	1.89606i	0.301183	−	0.0807018i
$553$	−2.14618	−	0.536814i	−0.0912647	−	0.0228277i
$554$	11.8043	+	11.8043i	0.501518	+	0.501518i
$555$	32.9053			1.39675
$556$	−51.0256			−2.16397
$557$	−16.7351	−	16.7351i	−0.709087	−	0.709087i	0.257256	−	0.966343i	$-0.417182\pi$
$557$	−16.7351	−	16.7351i	−0.709087	−	0.709087i	−0.966343	+	0.257256i	$0.917182\pi$
$558$	−2.32966	−	4.03509i	−0.0986225	−	0.170819i
$559$	−3.91637	+	11.6237i	−0.165645	+	0.491630i
$560$	7.82562	−	0.130718i	0.330693	−	0.00552384i
$561$	7.51491	+	2.01362i	0.317280	+	0.0850149i
$562$	13.1199	−	22.7243i	0.553428	−	0.958566i
$563$	16.1634	+	27.9958i	0.681204	+	1.17988i	0.974614	+	0.223894i	$0.0718768\pi$
$563$	16.1634	+	27.9958i	0.681204	+	1.17988i	−0.293409	+	0.955987i	$0.594790\pi$
$564$	9.27436	+	34.6124i	0.390521	+	1.45744i
$565$	−26.6402	−	26.6402i	−1.12076	−	1.12076i
$566$	−14.5875	−	54.4412i	−0.613158	−	2.28834i
$567$	−1.83932	+	1.90181i	−0.0772443	+	0.0798687i
$568$	11.4534	−	19.8379i	0.480574	−	0.832379i
$569$	31.5625	+	18.2226i	1.32317	+	0.763931i	0.984233	−	0.176879i	$-0.0566001\pi$
$569$	31.5625	+	18.2226i	1.32317	+	0.763931i	0.338935	+	0.940810i	$0.389933\pi$
$570$	−8.94643	+	8.94643i	−0.374725	+	0.374725i
$571$	−0.112930	−	0.0652004i	−0.00472599	−	0.00272855i	0.497635	−	0.867386i	$-0.334202\pi$
$571$	−0.112930	−	0.0652004i	−0.00472599	−	0.00272855i	−0.502361	+	0.864658i	$0.667535\pi$
$572$	4.77564	−	75.4815i	0.199680	−	3.15604i
$573$			20.8859i			0.872522i
$574$	19.7687	−	20.4404i	0.825131	−	0.853165i
$575$	2.97322	+	5.14976i	0.123992	+	0.214760i
$576$			12.2965i			0.512355i
$577$	2.75663	−	0.738638i	0.114760	−	0.0307499i	−0.200982	−	0.979595i	$-0.564413\pi$
$577$	2.75663	−	0.738638i	0.114760	−	0.0307499i	0.315742	+	0.948845i	$0.397747\pi$
$578$	−34.6548	−	9.28573i	−1.44145	−	0.386236i
$579$	−3.01587	+	3.01587i	−0.125335	+	0.125335i
$580$	−33.9406	+	33.9406i	−1.40931	+	1.40931i
$581$	7.52054	−	0.125622i	0.312004	−	0.00521167i
$582$	−13.1487	+	7.59138i	−0.545029	+	0.314673i
$583$	−50.4112	+	13.5076i	−2.08782	+	0.559430i
$584$	7.72976	−	13.3883i	0.319860	−	0.554013i
$585$	10.0324	+	0.634743i	0.414790	+	0.0262434i
$586$	−33.7064	+	19.4604i	−1.39240	+	0.803901i
$587$	9.87906	−	36.8692i	0.407753	−	1.52175i	−0.391169	−	0.920319i	$-0.627929\pi$
$587$	9.87906	−	36.8692i	0.407753	−	1.52175i	0.798922	−	0.601435i	$-0.205404\pi$
$588$	−20.5704	+	12.8109i	−0.848308	+	0.528311i
$589$	3.35252	+	1.93558i	0.138138	+	0.0797540i
$590$	−73.1877	−	19.6106i	−3.01309	−	0.807355i
$591$	4.47344	−	16.6951i	0.184013	−	0.686745i
$592$	3.24106	−	12.0958i	0.133207	−	0.497134i
$593$	−32.7224	−	8.76795i	−1.34375	−	0.360057i	−0.485925	−	0.874000i	$-0.661517\pi$
$593$	−32.7224	−	8.76795i	−1.34375	−	0.360057i	−0.857824	+	0.513944i	$0.828184\pi$
$594$	12.2637	+	7.08048i	0.503188	+	0.290515i
$595$	−4.59802	+	8.28037i	−0.188500	+	0.339462i
$596$	5.12276	−	19.1184i	0.209836	−	0.783120i
$597$	14.0385	−	8.10511i	0.574556	−	0.331720i
$598$	18.0318	+	1.14085i	0.737373	+	0.0466529i
$599$	12.5220	−	21.6888i	0.511637	−	0.886181i	−0.488272	−	0.872691i	$-0.662373\pi$
$599$	12.5220	−	21.6888i	0.511637	−	0.886181i	0.999909	−	0.0134895i	$-0.00429397\pi$
$600$	9.15238	−	2.45237i	0.373644	−	0.100118i
$601$	−15.0841	+	8.70880i	−0.615292	+	0.355239i	−0.775034	−	0.631920i	$-0.782267\pi$
$601$	−15.0841	+	8.70880i	−0.615292	+	0.355239i	0.159741	+	0.987159i	$0.448934\pi$
$602$	−10.8203	−	18.0387i	−0.441003	−	0.735202i
$603$	−1.20496	+	1.20496i	−0.0490698	+	0.0490698i
$604$	−3.13857	+	3.13857i	−0.127706	+	0.127706i
$605$	69.2513	+	18.5558i	2.81546	+	0.754401i
$606$	−24.4208	+	6.54354i	−0.992028	+	0.265813i
$607$			21.9453i			0.890732i	0.895349	+	0.445366i	$0.146926\pi$
$607$			21.9453i			0.890732i	−0.895349	+	0.445366i	$0.853074\pi$
$608$	−4.22667	−	7.32082i	−0.171414	−	0.296898i
$609$	3.19261	−	12.7640i	0.129371	−	0.517224i
$610$		−	23.9146i		−	0.968273i
$611$	−2.35650	+	37.2456i	−0.0953336	+	1.50680i
$612$	3.84953	+	2.22253i	0.155608	+	0.0898403i
$613$	−29.6440	+	29.6440i	−1.19731	+	1.19731i	−0.222342	+	0.974969i	$0.571370\pi$
$613$	−29.6440	+	29.6440i	−1.19731	+	1.19731i	−0.974969	+	0.222342i	$0.928630\pi$
$614$	−9.68747	−	5.59306i	−0.390954	−	0.225718i
$615$	6.41093	−	11.1041i	0.258514	−	0.447759i
$616$	39.3716	+	38.0779i	1.58633	+	1.53420i
$617$	4.55227	+	16.9893i	0.183267	+	0.683963i	0.994995	+	0.0999269i	$0.0318609\pi$
$617$	4.55227	+	16.9893i	0.183267	+	0.683963i	−0.811727	+	0.584037i	$0.801472\pi$
$618$	16.2772	+	16.2772i	0.654764	+	0.654764i
$619$	3.06113	+	11.4243i	0.123037	+	0.459181i	0.999762	−	0.0218110i	$-0.00694322\pi$
$619$	3.06113	+	11.4243i	0.123037	+	0.459181i	−0.876725	+	0.480992i	$0.840277\pi$
$620$	−9.62143	−	16.6648i	−0.386406	−	0.669274i
$621$	−1.07209	+	1.85691i	−0.0430215	+	0.0745154i
$622$	51.9565	+	13.9217i	2.08327	+	0.558209i
$623$	−11.5388	−	6.40737i	−0.462291	−	0.256706i
$624$	1.22149	−	3.62535i	0.0488987	−	0.145130i
$625$	−15.5877	−	26.9986i	−0.623506	−	1.07994i
$626$	−19.9530	−	19.9530i	−0.797482	−	0.797482i
$627$	−11.7655			−0.469868
$628$	63.7147			2.54249
$629$	10.7154	+	10.7154i	0.427251	+	0.427251i
$630$	−11.9849	+	12.3920i	−0.477488	+	0.493711i
$631$	4.79799	−	1.28562i	0.191005	−	0.0511796i	−0.162048	−	0.986783i	$-0.551810\pi$
$631$	4.79799	−	1.28562i	0.191005	−	0.0511796i	0.353053	+	0.935603i	$0.385143\pi$
$632$	−0.739410	+	2.75951i	−0.0294121	+	0.109768i
$633$	−0.453408	+	0.261775i	−0.0180213	+	0.0104046i
$634$			10.1981i			0.405017i
$635$	−10.9975	−	41.0432i	−0.436423	−	1.62875i
$636$	−29.8181			−1.18236
$637$	−24.5626	+	5.80350i	−0.973204	+	0.229943i
$638$	−70.4220			−2.78803
$639$	1.73527	+	6.47610i	0.0686461	+	0.256191i
$640$			55.8473i			2.20756i
$641$	21.7102	−	12.5344i	0.857501	−	0.495078i	−0.00567382	−	0.999984i	$-0.501806\pi$
$641$	21.7102	−	12.5344i	0.857501	−	0.495078i	0.863175	+	0.504906i	$0.168473\pi$
$642$	10.7955	−	40.2895i	0.426066	−	1.59010i
$643$	−1.76030	+	0.471670i	−0.0694193	+	0.0186008i	−0.293362	−	0.956002i	$-0.594774\pi$
$643$	−1.76030	+	0.471670i	−0.0694193	+	0.0186008i	0.223942	+	0.974602i	$0.428107\pi$
$644$	−13.6532	+	14.1171i	−0.538013	+	0.556292i
$645$	−6.70671	−	6.70671i	−0.264076	−	0.264076i
$646$	−5.82670			−0.229248
$647$	−0.270022			−0.0106157			−0.00530784	−	0.999986i	$-0.501690\pi$
$647$	−0.270022			−0.0106157			−0.00530784	+	0.999986i	$0.501690\pi$
$648$	2.41591	+	2.41591i	0.0949057	+	0.0949057i
$649$	−35.2298	−	61.0197i	−1.38289	−	2.39523i
$650$	23.3223	+	1.47558i	0.914777	+	0.0578771i
$651$	4.61145	+	2.56070i	0.180737	+	0.100362i
$652$	−14.0233	−	3.75753i	−0.549194	−	0.147156i
$653$	−10.0230	+	17.3603i	−0.392230	+	0.679363i	−0.992743	−	0.120252i	$-0.961630\pi$
$653$	−10.0230	+	17.3603i	−0.392230	+	0.679363i	0.600513	+	0.799615i	$0.294963\pi$
$654$	20.5125	+	35.5286i	0.802101	+	1.38928i
$655$	6.15865	+	22.9844i	0.240638	+	0.898075i
$656$	−3.45033	−	3.45033i	−0.134713	−	0.134713i
$657$	1.17111	+	4.37064i	0.0456893	+	0.170515i
$658$	−46.0057	−	44.4940i	−1.79349	−	1.73456i
$659$	3.60803	−	6.24930i	0.140549	−	0.243438i	−0.787155	−	0.616756i	$-0.788447\pi$
$659$	3.60803	−	6.24930i	0.140549	−	0.243438i	0.927703	+	0.373318i	$0.121780\pi$
$660$	50.6488	+	29.2421i	1.97150	+	1.13825i
$661$	−11.5312	+	11.5312i	−0.448512	+	0.448512i	−0.894860	−	0.446347i	$-0.852725\pi$
$661$	−11.5312	+	11.5312i	−0.448512	+	0.448512i	0.446347	+	0.894860i	$0.352725\pi$
$662$	−27.1561	−	15.6786i	−1.05545	−	0.609366i
$663$	3.06030	+	3.47370i	0.118852	+	0.134907i
$664$		−	9.71304i		−	0.376939i
$665$	3.47554	−	13.8952i	0.134776	−	0.538831i
$666$	13.7913	+	23.8872i	0.534402	+	0.925612i
$667$		−	10.6629i		−	0.412871i
$668$	58.8954	−	15.7810i	2.27873	−	0.610584i
$669$	21.9142	+	5.87188i	0.847251	+	0.227020i
$670$	−7.85141	+	7.85141i	−0.303327	+	0.303327i
$671$	15.7251	−	15.7251i	0.607060	−	0.607060i
$672$	−5.92494	−	9.87756i	−0.228560	−	0.381035i
$673$	26.8777	−	15.5179i	1.03606	−	0.598169i	0.117345	−	0.993091i	$-0.462562\pi$
$673$	26.8777	−	15.5179i	1.03606	−	0.598169i	0.918715	+	0.394922i	$0.129228\pi$
$674$	44.7924	−	12.0021i	1.72534	−	0.462303i
$675$	−1.38664	+	2.40174i	−0.0533720	+	0.0924430i
$676$	27.2352	−	35.8285i	1.04751	−	1.37802i
$677$	19.5160	−	11.2676i	0.750062	−	0.433049i	−0.0756542	−	0.997134i	$-0.524104\pi$
$677$	19.5160	−	11.2676i	0.750062	−	0.433049i	0.825716	+	0.564085i	$0.190771\pi$
$678$	8.17372	−	30.5047i	0.313910	−	1.17153i
$679$	8.34423	−	15.0268i	0.320222	−	0.576675i
$680$	10.5922	+	6.11544i	0.406194	+	0.234516i
$681$	−2.25887	−	0.605263i	−0.0865602	−	0.0231937i
$682$	7.30700	−	27.2701i	0.279800	−	1.04423i
$683$	−2.51045	+	9.36913i	−0.0960597	+	0.358500i	−0.997178	−	0.0750737i	$-0.976081\pi$
$683$	−2.51045	+	9.36913i	−0.0960597	+	0.358500i	0.901118	+	0.433573i	$0.142747\pi$
$684$	−6.49307	−	1.73981i	−0.248269	−	0.0665234i
$685$	10.7919	+	6.23070i	0.412337	+	0.238063i
$686$	19.7370	−	38.5213i	0.753563	−	1.47075i
$687$	2.51774	−	9.39632i	0.0960577	−	0.358492i
$688$	−3.12594	+	1.80476i	−0.119175	+	0.0688058i
$689$	−29.4297	−	9.91575i	−1.12118	−	0.377760i
$690$	−6.98564	+	12.0995i	−0.265939	+	0.460620i
$691$	15.4875	−	4.14987i	0.589174	−	0.157869i	0.0480982	−	0.998843i	$-0.484684\pi$
$691$	15.4875	−	4.14987i	0.589174	−	0.157869i	0.541076	+	0.840974i	$0.318017\pi$
$692$	−11.5567	+	6.67225i	−0.439319	+	0.253641i
$693$	−16.0291	+	0.267747i	−0.608894	+	0.0101709i
$694$	−24.5596	+	24.5596i	−0.932270	+	0.932270i
$695$	29.0575	−	29.0575i	1.10221	−	1.10221i
$696$	−16.4117	−	4.39751i	−0.622085	−	0.166687i
$697$	5.70364	−	1.52829i	0.216041	−	0.0578880i
$698$			13.8393i			0.523824i
$699$	−1.56026	−	2.70246i	−0.0590146	−	0.102216i
$700$	−17.6591	+	18.2591i	−0.667453	+	0.690130i
$701$			38.8560i			1.46757i	0.679381	+	0.733785i	$0.262248\pi$
$701$			38.8560i			1.46757i	−0.679381	+	0.733785i	$0.737752\pi$
$702$	3.74403	+	7.54898i	0.141309	+	0.284918i
$703$	−19.8465	−	11.4584i	−0.748523	−	0.432160i
$704$	−52.6851	+	52.6851i	−1.98564	+	1.98564i
$705$	−24.9922	−	14.4292i	−0.941260	−	0.543437i
$706$	34.3131	−	59.4321i	1.29139	−	2.23676i
$707$	19.8977	−	20.5737i	0.748328	−	0.773753i
$708$	−10.4192	−	38.8848i	−0.391576	−	1.46138i
$709$	14.1404	+	14.1404i	0.531053	+	0.531053i	0.920886	−	0.389833i	$-0.127467\pi$
$709$	14.1404	+	14.1404i	0.531053	+	0.531053i	−0.389833	+	0.920886i	$0.627467\pi$
$710$	11.3068	+	42.1977i	0.424338	+	1.58365i
$711$	−0.418084	−	0.724143i	−0.0156794	−	0.0271575i
$712$	−8.52191	+	14.7604i	−0.319372	+	0.553168i
$713$	4.12910	+	1.10639i	0.154636	+	0.0414346i
$714$	−7.93818	+	0.132598i	−0.297079	+	0.00496236i
$715$	40.2649	+	45.7041i	1.50582	+	1.70923i
$716$	−15.1110	−	26.1730i	−0.564724	−	0.978131i
$717$	−5.27158	−	5.27158i	−0.196871	−	0.196871i
$718$	−12.3451			−0.460715
$719$	11.4034			0.425275			0.212638	−	0.977131i	$-0.431795\pi$
$719$	11.4034			0.425275			0.212638	+	0.977131i	$0.431795\pi$
$720$	2.09178	+	2.09178i	0.0779559	+	0.0779559i
$721$	−25.2809	−	6.32341i	−0.941511	−	0.235496i
$722$	−34.3801	+	9.21211i	−1.27949	+	0.342839i
$723$	3.82383	−	14.2707i	0.142210	−	0.530734i
$724$	47.6172	−	27.4918i	1.76968	−	1.02173i
$725$		−	13.7915i		−	0.512203i
$726$	15.5543	+	58.0494i	0.577274	+	2.15442i
$727$	51.3939			1.90609			0.953046	−	0.302824i	$-0.0979295\pi$
$727$	51.3939			1.90609			0.953046	+	0.302824i	$0.0979295\pi$
$728$	6.96358	+	31.8397i	0.258087	+	1.18006i
$729$	−1.00000			−0.0370370
$730$	7.63083	+	28.4787i	0.282430	+	1.05404i
$731$		−	4.36799i		−	0.161556i
$732$	11.0036	−	6.35294i	0.406705	−	0.234811i
$733$	−3.46789	+	12.9424i	−0.128090	+	0.478037i	−0.999931	−	0.0117516i	$-0.996259\pi$
$733$	−3.46789	+	12.9424i	−0.128090	+	0.478037i	0.871841	+	0.489788i	$0.162926\pi$
$734$	−6.96339	+	1.86583i	−0.257023	+	0.0688692i
$735$	4.41880	−	19.0096i	0.162990	−	0.701180i
$736$	−6.60063	−	6.60063i	−0.243303	−	0.243303i
$737$	−10.3254			−0.380342
$738$	10.7478			0.395633
$739$	−16.8507	−	16.8507i	−0.619862	−	0.619862i	0.325634	−	0.945496i	$-0.394422\pi$
$739$	−16.8507	−	16.8507i	−0.619862	−	0.619862i	−0.945496	+	0.325634i	$0.894422\pi$
$740$	56.9576	+	98.6535i	2.09380	+	3.62657i
$741$	−5.82993	−	3.87636i	−0.214168	−	0.142402i
$742$	45.6716	−	27.3956i	1.67666	−	1.00572i
$743$	16.7746	+	4.49474i	0.615400	+	0.164896i	0.553036	−	0.833158i	$-0.313469\pi$
$743$	16.7746	+	4.49474i	0.615400	+	0.164896i	0.0623643	+	0.998053i	$0.480136\pi$
$744$	3.40577	−	5.89897i	0.124862	−	0.216267i
$745$	7.97010	+	13.8046i	0.292002	+	0.505762i
$746$	−15.5910	−	58.1865i	−0.570828	−	2.13036i
$747$	2.01023	+	2.01023i	0.0735504	+	0.0735504i
$748$	6.97097	+	26.0160i	0.254884	+	0.951239i
$749$	12.9815	+	45.4004i	0.474332	+	1.65889i
$750$	7.25452	−	12.5652i	0.264898	−	0.458816i
$751$	−15.1620	−	8.75381i	−0.553271	−	0.319431i	0.197169	−	0.980369i	$-0.436825\pi$
$751$	−15.1620	−	8.75381i	−0.553271	−	0.319431i	−0.750440	+	0.660938i	$0.770158\pi$
$752$	−7.76576	+	7.76576i	−0.283188	+	0.283188i
$753$	0.704635	+	0.406821i	0.0256783	+	0.0148254i
$754$	−34.8949	−	23.2019i	−1.27080	−	0.844962i
$755$		−	3.57464i		−	0.130094i
$756$	−8.88563	−	2.22253i	−0.323167	−	0.0808325i
$757$	−10.0522	−	17.4109i	−0.365352	−	0.632809i	0.623480	−	0.781839i	$-0.285718\pi$
$757$	−10.0522	−	17.4109i	−0.365352	−	0.632809i	−0.988833	+	0.149030i	$0.952385\pi$
$758$		−	38.0969i		−	1.38374i
$759$	−12.5495	+	3.36262i	−0.455517	+	0.122055i
$760$	−17.8661	−	4.78722i	−0.648073	−	0.173651i
$761$	−8.04624	+	8.04624i	−0.291676	+	0.291676i	−0.837742	−	0.546066i	$-0.816125\pi$
$761$	−8.04624	+	8.04624i	−0.291676	+	0.291676i	0.546066	+	0.837742i	$0.316125\pi$
$762$	25.1856	−	25.1856i	0.912379	−	0.912379i
$763$	−40.6034	−	22.5467i	−1.46994	−	0.816246i
$764$	−62.6182	+	36.1526i	−2.26545	+	1.30796i
$765$	−3.45785	+	0.926529i	−0.125019	+	0.0334987i
$766$	−1.92593	+	3.33581i	−0.0695866	+	0.120528i
$767$	2.64737	−	41.8431i	0.0955911	−	1.51087i
$768$	−19.2436	+	11.1103i	−0.694394	+	0.400909i
$769$	−9.54507	+	35.6227i	−0.344204	+	1.28459i	0.549335	+	0.835602i	$0.314881\pi$
$769$	−9.54507	+	35.6227i	−0.344204	+	1.28459i	−0.893539	+	0.448985i	$0.851786\pi$
$770$	−104.444	+	1.74462i	−3.76390	+	0.0628716i
$771$	8.58176	+	4.95468i	0.309065	+	0.178438i
$772$	−14.2622	−	3.82155i	−0.513309	−	0.137541i
$773$	5.17760	−	19.3231i	0.186225	−	0.695002i	−0.808140	−	0.588991i	$-0.799525\pi$
$773$	5.17760	−	19.3231i	0.186225	−	0.695002i	0.994365	−	0.106011i	$-0.0338079\pi$
$774$	2.05774	−	7.67959i	0.0739639	−	0.276037i
$775$	5.34059	+	1.43101i	0.191840	+	0.0514033i
$776$	−19.2222	−	11.0980i	−0.690038	−	0.398394i
$777$	−27.2992	−	15.1590i	−0.979354	−	0.543827i
$778$	−5.01666	+	18.7224i	−0.179856	+	0.671231i
$779$	−7.73337	+	4.46486i	−0.277077	+	0.159970i
$780$	15.4627	+	31.1770i	0.553654	+	1.11632i
$781$	−20.3123	+	35.1820i	−0.726832	+	1.25891i
$782$	−6.21495	+	1.66529i	−0.222246	+	0.0595507i
$783$	4.30672	−	2.48648i	0.153909	−	0.0888597i
$784$	−6.55259	−	3.49671i	−0.234021	−	0.124883i
$785$	−36.2836	+	36.2836i	−1.29502	+	1.29502i
$786$	−14.1041	+	14.1041i	−0.503076	+	0.503076i
$787$	−43.7381	−	11.7196i	−1.55910	−	0.417759i	−0.626719	−	0.779245i	$-0.715603\pi$
$787$	−43.7381	−	11.7196i	−1.55910	−	0.417759i	−0.932377	+	0.361487i	$0.882269\pi$
$788$	57.7971	−	15.4867i	2.05894	−	0.551690i
$789$		−	2.58615i		−	0.0920694i
$790$	−2.72420	−	4.71845i	−0.0969227	−	0.167875i
$791$	9.82876	+	34.3744i	0.349471	+	1.22221i
$792$			20.7021i			0.735618i
$793$	12.9729	−	2.61103i	0.460681	−	0.0927204i
$794$	−68.5649	−	39.5860i	−2.43328	−	1.40485i
$795$	16.9805	−	16.9805i	0.602237	−	0.602237i
$796$	48.5999	+	28.0592i	1.72258	+	0.994532i
$797$	−16.0952	+	27.8777i	−0.570122	+	0.987480i	0.426431	+	0.904520i	$0.359771\pi$
$797$	−16.0952	+	27.8777i	−0.570122	+	0.987480i	−0.996553	+	0.0829596i	$0.973563\pi$
$798$	11.5437	−	3.30073i	0.408644	−	0.116845i
$799$	−3.43976	−	12.8373i	−0.121690	−	0.454153i
$800$	−8.53728	−	8.53728i	−0.301838	−	0.301838i
$801$	−1.29112	−	4.81854i	−0.0456196	−	0.170255i
$802$	−18.3506	−	31.7841i	−0.647981	−	1.12234i
$803$	−13.7085	+	23.7439i	−0.483764	+	0.837903i
$804$	−5.69834	−	1.52686i	−0.200965	−	0.0538484i
$805$	−0.264161	−	15.8144i	−0.00931045	−	0.557384i
$806$	12.6054	−	11.1052i	0.444005	−	0.391165i
$807$	−6.69308	−	11.5928i	−0.235608	−	0.408084i
$808$	−26.1351	−	26.1351i	−0.919429	−	0.919429i
$809$	13.1284			0.461569			0.230784	−	0.973005i	$-0.425871\pi$
$809$	13.1284			0.461569			0.230784	+	0.973005i	$0.425871\pi$
$810$	−6.51591			−0.228946
$811$	−2.21060	−	2.21060i	−0.0776246	−	0.0776246i	0.667228	−	0.744853i	$-0.267480\pi$
$811$	−2.21060	−	2.21060i	−0.0776246	−	0.0776246i	−0.744853	+	0.667228i	$0.767480\pi$
$812$	43.7942	−	12.5222i	1.53687	−	0.439443i
$813$	−13.4518	+	3.60441i	−0.471776	+	0.126412i
$814$	−43.2565	+	161.436i	−1.51614	+	5.65831i
$815$	10.1256	−	5.84604i	0.354686	−	0.204778i
$816$			1.36235i			0.0476917i
$817$	1.70965	+	6.38051i	0.0598131	+	0.223226i
$818$	14.1746			0.495602
$819$	−8.03080	−	5.14841i	−0.280619	−	0.179900i
$820$	44.3882			1.55010
$821$	−14.0027	−	52.2589i	−0.488699	−	1.82385i	−0.562793	−	0.826598i	$-0.690273\pi$
$821$	−14.0027	−	52.2589i	−0.488699	−	1.82385i	0.0740935	−	0.997251i	$-0.476394\pi$
$822$			10.4457i			0.364335i
$823$	−37.2404	+	21.5008i	−1.29812	+	0.749469i	−0.980079	−	0.198608i	$-0.936358\pi$
$823$	−37.2404	+	21.5008i	−1.29812	+	0.749469i	−0.318040	+	0.948077i	$0.603025\pi$
$824$	−8.70988	+	32.5057i	−0.303423	+	1.13239i
$825$	−16.2315	+	4.34922i	−0.565109	+	0.151420i
$826$	51.6845	+	49.9862i	1.79833	+	1.73924i
$827$	7.69342	+	7.69342i	0.267526	+	0.267526i	0.828103	−	0.560576i	$-0.189420\pi$
$827$	7.69342	+	7.69342i	0.267526	+	0.267526i	−0.560576	+	0.828103i	$0.689420\pi$
$828$	−7.42297			−0.257966
$829$	26.6776			0.926552			0.463276	−	0.886214i	$-0.346674\pi$
$829$	26.6776			0.926552			0.463276	+	0.886214i	$0.346674\pi$
$830$	13.0985	+	13.0985i	0.454654	+	0.454654i
$831$	−3.57152	−	6.18606i	−0.123895	−	0.214592i
$832$	−43.4642	+	8.74795i	−1.50685	+	0.303280i
$833$	7.62932	−	4.75141i	0.264340	−	0.164627i
$834$	33.2727	+	8.91538i	1.15214	+	0.308714i
$835$	−24.5524	+	42.5259i	−0.849670	+	1.47167i
$836$	−20.3656	−	35.2742i	−0.704357	−	1.21998i
$837$	0.515996	+	1.92572i	0.0178354	+	0.0665628i
$838$	−5.27117	−	5.27117i	−0.182089	−	0.182089i
$839$	−6.71331	−	25.0544i	−0.231769	−	0.864974i	−0.979579	−	0.201061i	$-0.935561\pi$
$839$	−6.71331	−	25.0544i	−0.231769	−	0.864974i	0.747810	−	0.663913i	$-0.231106\pi$
$840$	−24.4494	−	6.11544i	−0.843586	−	0.211003i
$841$	2.13480	−	3.69758i	0.0736138	−	0.127503i
$842$	−32.4446	−	18.7319i	−1.11812	−	0.645544i
$843$	−7.93911	+	7.93911i	−0.273438	+	0.273438i
$844$	−1.56966	−	0.906243i	−0.0540299	−	0.0311942i
$845$	4.89363	+	35.9129i	0.168346	+	1.23544i
$846$		−	24.1904i		−	0.831684i
$847$	−48.9046	−	47.2976i	−1.68038	−	1.62517i
$848$	−4.56942	−	7.91447i	−0.156915	−	0.271784i
$849$			24.1164i			0.827671i
$850$	−8.03844	+	2.15389i	−0.275716	+	0.0738779i
$851$	−24.4438	−	6.54969i	−0.837921	−	0.224520i
$852$	−16.4124	+	16.4124i	−0.562278	+	0.562278i
$853$	24.3606	−	24.3606i	0.834092	−	0.834092i	−0.153982	−	0.988074i	$-0.549210\pi$
$853$	24.3606	−	24.3606i	0.834092	−	0.834092i	0.988074	+	0.153982i	$0.0492097\pi$
$854$	−11.0171	+	19.8403i	−0.376999	+	0.678920i
$855$	4.68838	−	2.70684i	0.160339	−	0.0925719i
$856$	58.8998	−	15.7822i	2.01316	−	0.539423i
$857$	−0.627594	+	1.08703i	−0.0214382	+	0.0371321i	−0.876545	−	0.481319i	$-0.840158\pi$
$857$	−0.627594	+	1.08703i	−0.0214382	+	0.0371321i	0.855107	+	0.518451i	$0.173491\pi$
$858$	−16.3025	+	48.3855i	−0.556559	+	1.65185i
$859$	24.0206	−	13.8683i	0.819574	−	0.473181i	−0.0306958	−	0.999529i	$-0.509772\pi$
$859$	24.0206	−	13.8683i	0.819574	−	0.473181i	0.850269	+	0.526348i	$0.176439\pi$
$860$	8.49840	−	31.7164i	0.289793	−	1.08152i
$861$	−10.4342	+	6.25883i	−0.355596	+	0.213300i
$862$	67.9108	+	39.2083i	2.31305	+	1.33544i
$863$	−39.3806	−	10.5520i	−1.34053	−	0.359194i	−0.483900	−	0.875123i	$-0.660780\pi$
$863$	−39.3806	−	10.5520i	−1.34053	−	0.359194i	−0.856632	+	0.515929i	$0.827447\pi$
$864$	1.12677	−	4.20516i	0.0383335	−	0.143063i
$865$	2.78153	−	10.3808i	0.0945750	−	0.352959i
$866$	21.1391	+	5.66421i	0.718336	+	0.192478i
$867$	13.2947	+	7.67569i	0.451511	+	0.260680i
$868$	0.304980	+	18.2581i	0.0103517	+	0.619720i
$869$	1.31132	−	4.89393i	0.0444836	−	0.166015i
$870$	28.0622	−	16.2017i	0.951396	−	0.549289i
$871$	−5.11637	−	3.40191i	−0.173361	−	0.115269i
$872$	−29.9875	+	51.9399i	−1.01550	+	1.75891i
$873$	6.27512	−	1.68141i	0.212381	−	0.0569072i
$874$	8.42663	−	4.86512i	0.285035	−	0.164565i
$875$	0.274328	+	16.4231i	0.00927399	+	0.555201i
$876$	−11.0765	+	11.0765i	−0.374240	+	0.374240i
$877$	29.1522	−	29.1522i	0.984399	−	0.984399i	−0.0154809	−	0.999880i	$-0.504928\pi$
$877$	29.1522	−	29.1522i	0.984399	−	0.984399i	0.999880	+	0.0154809i	$0.00492792\pi$
$878$	2.08409	+	0.558430i	0.0703346	+	0.0188461i
$879$	16.0862	−	4.31028i	0.542573	−	0.145382i
$880$			17.9246i			0.604239i
$881$	6.36240	+	11.0200i	0.214355	+	0.371273i	0.953073	−	0.302741i	$-0.0979018\pi$
$881$	6.36240	+	11.0200i	0.214355	+	0.371273i	−0.738718	+	0.674015i	$0.764568\pi$
$882$	15.6519	−	4.75956i	0.527025	−	0.160263i
$883$			5.97448i			0.201057i	0.994934	+	0.100529i	$0.0320534\pi$
$883$			5.97448i			0.201057i	−0.994934	+	0.100529i	$0.967947\pi$
$884$	−5.11728	+	15.1879i	−0.172113	+	0.510826i
$885$	28.0771	+	16.2103i	0.943802	+	0.544905i
$886$	33.8436	−	33.8436i	1.13700	−	1.13700i
$887$	−30.4672	−	17.5902i	−1.02299	−	0.590622i	−0.108020	−	0.994149i	$-0.534451\pi$
$887$	−30.4672	−	17.5902i	−1.02299	−	0.590622i	−0.914968	+	0.403527i	$0.867784\pi$
$888$	−20.1617	+	34.9211i	−0.676583	+	1.17188i
$889$	−9.78421	+	39.1171i	−0.328152	+	1.31195i
$890$	−8.41285	−	31.3972i	−0.281999	−	1.05244i
$891$	−4.28455	−	4.28455i	−0.143538	−	0.143538i
$892$	20.3280	+	75.8650i	0.680631	+	2.54015i
$893$	10.0492	+	17.4057i	0.336283	+	0.582460i
$894$	−6.68088	+	11.5716i	−0.223442	+	0.387013i
$895$	23.5100	+	6.29948i	0.785852	+	0.210569i
$896$	25.7281	−	46.3327i	0.859517	−	1.54787i
$897$	−7.32628	−	2.46845i	−0.244617	−	0.0824190i
$898$	−6.30141	−	10.9144i	−0.210281	−	0.364217i
$899$	−7.01053	−	7.01053i	−0.233814	−	0.233814i
$900$	−9.60089			−0.320030
$901$	11.0592			0.368435
$902$	46.0496	+	46.0496i	1.53328	+	1.53328i
$903$	2.47440	+	8.65378i	0.0823429	+	0.287980i
$904$	44.5953	−	11.9493i	1.48322	−	0.397427i
$905$	−11.4608	+	42.7724i	−0.380971	+	1.42180i
$906$	2.59497	−	1.49821i	0.0862122	−	0.0497747i
$907$		−	24.5393i		−	0.814813i	−0.913247	−	0.407406i	$-0.866433\pi$
$907$		−	24.5393i		−	0.814813i	0.913247	−	0.407406i	$-0.133567\pi$
$908$	−2.09537	−	7.82003i	−0.0695373	−	0.259517i
$909$	10.8179			0.358808
$910$	−52.3280	−	33.5466i	−1.73466	−	1.11206i
$911$	12.4045			0.410981			0.205490	−	0.978659i	$-0.434121\pi$
$911$	12.4045			0.410981			0.205490	+	0.978659i	$0.434121\pi$
$912$	−0.533229	−	1.99004i	−0.0176570	−	0.0658967i
$913$			17.2258i			0.570092i
$914$	42.2031	−	24.3660i	1.39595	−	0.805955i
$915$	−2.64842	+	9.88403i	−0.0875540	+	0.326756i
$916$	32.5293	−	8.71620i	1.07480	−	0.287991i
$917$	5.47920	−	21.9058i	0.180939	−	0.723392i
$918$	−2.12187	−	2.12187i	−0.0700320	−	0.0700320i
$919$	32.8106			1.08232			0.541161	−	0.840919i	$-0.317985\pi$
$919$	32.8106			1.08232			0.541161	+	0.840919i	$0.317985\pi$
$920$	−20.4248			−0.673387
$921$	3.38448	+	3.38448i	0.111522	+	0.111522i
$922$	24.2892	+	42.0701i	0.799921	+	1.38550i
$923$	−21.6564	+	10.7408i	−0.712828	+	0.353537i
$924$	−28.5484	−	47.5934i	−0.939173	−	1.56571i
$925$	−31.6156	−	8.47138i	−1.03952	−	0.278537i
$926$	−20.1667	+	34.9297i	−0.662717	+	1.14786i
$927$	−4.92483	−	8.53006i	−0.161753	−	0.280164i
$928$	5.60339	+	20.9121i	0.183940	+	0.686475i
$929$	29.9167	+	29.9167i	0.981536	+	0.981536i	0.999833	−	0.0182968i	$-0.00582439\pi$
$929$	29.9167	+	29.9167i	0.981536	+	0.981536i	−0.0182968	+	0.999833i	$0.505824\pi$
$930$	3.36219	+	12.5478i	0.110250	+	0.411460i
$931$	−9.28473	+	9.92672i	−0.304295	+	0.325335i
$932$	5.40150	−	9.35568i	0.176932	−	0.306455i
$933$	−19.9321	−	11.5078i	−0.652549	−	0.376749i
$934$	6.36582	−	6.36582i	0.208296	−	0.208296i
$935$	−18.7851	−	10.8456i	−0.614338	−	0.354688i
$936$	−6.82071	+	10.2581i	−0.222942	+	0.335298i
$937$			43.3342i			1.41567i	0.706380	+	0.707833i	$0.250327\pi$
$937$			43.3342i			1.41567i	−0.706380	+	0.707833i	$0.749673\pi$
$938$	10.1308	−	2.89673i	0.330783	−	0.0945817i
$939$	6.03699	+	10.4564i	0.197010	+	0.341231i
$940$		−	99.9057i		−	3.25856i
$941$	30.1218	−	8.07110i	0.981941	−	0.263110i	0.268079	−	0.963397i	$-0.413611\pi$
$941$	30.1218	−	8.07110i	0.981941	−	0.263110i	0.713862	+	0.700286i	$0.246944\pi$
$942$	−41.5470	−	11.1325i	−1.35367	−	0.362716i
$943$	−6.97260	+	6.97260i	−0.227059	+	0.227059i
$944$	8.72433	−	8.72433i	0.283953	−	0.283953i
$945$	6.32576	−	3.79444i	0.205777	−	0.123433i
$946$	41.7201	−	24.0871i	1.35644	−	0.783139i
$947$	−15.5947	+	4.17860i	−0.506761	+	0.135786i	−0.503136	−	0.864207i	$-0.667821\pi$
$947$	−15.5947	+	4.17860i	−0.506761	+	0.135786i	−0.00362489	+	0.999993i	$0.501154\pi$
$948$	1.44737	−	2.50692i	0.0470085	−	0.0814211i
$949$	−14.6156	+	7.24882i	−0.474443	+	0.235307i
$950$	10.8990	−	6.29256i	0.353611	−	0.204158i
$951$	1.12938	−	4.21491i	0.0366227	−	0.136678i
$952$	−5.97036	−	9.95327i	−0.193500	−	0.322587i
$953$	8.83857	+	5.10295i	0.286309	+	0.165301i	0.636276	−	0.771461i	$-0.280474\pi$
$953$	8.83857	+	5.10295i	0.286309	+	0.165301i	−0.349967	+	0.936762i	$0.613807\pi$
$954$	19.4437	+	5.20993i	0.629514	+	0.168678i
$955$	15.0714	−	56.2470i	0.487697	−	1.82011i
$956$	6.67987	−	24.9296i	0.216043	−	0.806282i
$957$	29.1058	+	7.79887i	0.940857	+	0.252102i
$958$	−48.6625	−	28.0953i	−1.57221	−	0.907718i
$959$	−6.08288	−	10.1409i	−0.196426	−	0.327465i
$960$	8.87322	−	33.1153i	0.286382	−	1.06879i
$961$	−23.4046	+	13.5127i	−0.754988	+	0.435892i
$962$	−74.6221	+	65.7415i	−2.40591	+	2.11959i
$963$	−8.92371	+	15.4563i	−0.287563	+	0.498073i
$964$	49.4041	−	13.2378i	1.59120	−	0.426360i
$965$	10.2982	−	5.94565i	0.331510	−	0.191397i
$966$	11.3696	−	6.81992i	0.365810	−	0.219427i
$967$	39.7846	−	39.7846i	1.27939	−	1.27939i	0.338374	−	0.941012i	$-0.390123\pi$
$967$	39.7846	−	39.7846i	1.27939	−	1.27939i	0.941012	−	0.338374i	$-0.109877\pi$
$968$	−62.1243	+	62.1243i	−1.99675	+	1.99675i
$969$	2.40821	+	0.645277i	0.0773627	+	0.0207293i
$970$	40.8881	−	10.9559i	1.31284	−	0.351774i
$971$			6.24940i			0.200553i	0.994960	+	0.100276i	$0.0319727\pi$
$971$			6.24940i			0.200553i	−0.994960	+	0.100276i	$0.968027\pi$
$972$	−1.73096	−	2.99811i	−0.0555205	−	0.0961643i
$973$	−37.4934	+	10.7206i	−1.20198	+	0.343687i
$974$		−	87.4021i		−	2.80054i
$975$	−9.47583	−	3.19269i	−0.303470	−	0.102248i
$976$	3.37246	+	1.94709i	0.107950	+	0.0623248i
$977$	27.9340	−	27.9340i	0.893689	−	0.893689i	−0.101179	−	0.994868i	$-0.532261\pi$
$977$	27.9340	−	27.9340i	0.893689	−	0.893689i	0.994868	+	0.101179i	$0.0322614\pi$
$978$	8.48775	+	4.90040i	0.271408	+	0.156698i
$979$	15.1134	−	26.1772i	0.483026	−	0.836626i
$980$	64.6416	−	19.6568i	2.06490	−	0.627914i
$981$	−4.54330	−	16.9558i	−0.145056	−	0.541358i
$982$	−11.8191	−	11.8191i	−0.377164	−	0.377164i
$983$	−6.50777	−	24.2873i	−0.207566	−	0.774646i	−0.988652	−	0.150223i	$-0.952001\pi$
$983$	−6.50777	−	24.2873i	−0.207566	−	0.774646i	0.781086	−	0.624423i	$-0.214666\pi$
$984$	7.85621	+	13.6074i	0.250447	+	0.433787i
$985$	−24.0945	+	41.7329i	−0.767715	+	1.32972i
$986$	14.4143	+	3.86229i	0.459043	+	0.123000i
$987$	14.0869	+	23.4845i	0.448392	+	0.747520i
$988$	1.53039	−	24.1886i	0.0486881	−	0.769541i
$989$	3.64715	+	6.31704i	0.115973	+	0.200870i
$990$	−27.9177	−	27.9177i	−0.887283	−	0.887283i
$991$	−2.50217			−0.0794841			−0.0397420	−	0.999210i	$-0.512654\pi$
$991$	−2.50217			−0.0794841			−0.0397420	+	0.999210i	$0.512654\pi$
$992$	−8.67940			−0.275571
$993$	9.48746	+	9.48746i	0.301075	+	0.301075i
$994$	10.0594	−	40.2174i	0.319065	−	1.27562i
$995$	−43.6551	+	11.6973i	−1.38396	+	0.370831i
$996$	−2.54726	+	9.50650i	−0.0807130	+	0.301225i
$997$	−6.31728	+	3.64728i	−0.200070	+	0.115511i	−0.596688	−	0.802473i	$-0.703517\pi$
$997$	−6.31728	+	3.64728i	−0.200070	+	0.115511i	0.396618	+	0.917984i	$0.370184\pi$
$998$		−	21.0669i		−	0.666862i
$999$	−3.05463	−	11.4000i	−0.0966443	−	0.360681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.262.2	yes	40
3.2	odd	2		819.2.gh.d.262.9		40
7.5	odd	6		273.2.bt.b.145.2	✓	40
13.7	odd	12		273.2.bt.b.241.2	yes	40
21.5	even	6		819.2.et.d.145.9		40
39.20	even	12		819.2.et.d.514.9		40
91.33	even	12	inner	273.2.cg.b.124.2	yes	40
273.215	odd	12		819.2.gh.d.397.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.2	✓	40	7.5	odd	6
273.2.bt.b.241.2	yes	40	13.7	odd	12
273.2.cg.b.124.2	yes	40	91.33	even	12	inner
273.2.cg.b.262.2	yes	40	1.1	even	1	trivial
819.2.et.d.145.9		40	21.5	even	6
819.2.et.d.514.9		40	39.20	even	12
819.2.gh.d.262.9		40	3.2	odd	2
819.2.gh.d.397.9		40	273.215	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.604879 - 2.25744i) q^{2} +1.00000i q^{3} +(-2.99811 + 1.73096i) q^{4} +(0.721604 - 2.69306i) q^{5} +(2.25744 - 0.604879i) q^{6} +(-1.83932 + 1.90181i) q^{7} +(2.41591 + 2.41591i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.604879 - 2.25744i) q^{2} +1.00000i q^{3} +(-2.99811 + 1.73096i) q^{4} +(0.721604 - 2.69306i) q^{5} +(2.25744 - 0.604879i) q^{6} +(-1.83932 + 1.90181i) q^{7} +(2.41591 + 2.41591i) q^{8} -1.00000 q^{9} -6.51591 q^{10} +(-4.28455 - 4.28455i) q^{11} +(-1.73096 - 2.99811i) q^{12} +(-0.711416 - 3.53467i) q^{13} +(5.40580 + 3.00179i) q^{14} +(2.69306 + 0.721604i) q^{15} +(0.530515 - 0.918879i) q^{16} +(0.641993 + 1.11196i) q^{17} +(0.604879 + 2.25744i) q^{18} +(-1.37301 - 1.37301i) q^{19} +(2.49813 + 9.32315i) q^{20} +(-1.90181 - 1.83932i) q^{21} +(-7.08048 + 12.2637i) q^{22} +(-1.85691 - 1.07209i) q^{23} +(-2.41591 + 2.41591i) q^{24} +(-2.40174 - 1.38664i) q^{25} +(-7.54898 + 3.74403i) q^{26} -1.00000i q^{27} +(2.22253 - 8.88563i) q^{28} +(2.48648 + 4.30672i) q^{29} -6.51591i q^{30} +(-1.92572 + 0.515996i) q^{31} +(4.20516 + 1.12677i) q^{32} +(4.28455 - 4.28455i) q^{33} +(2.12187 - 2.12187i) q^{34} +(3.79444 + 6.32576i) q^{35} +(2.99811 - 1.73096i) q^{36} +(11.4000 - 3.05463i) q^{37} +(-2.26899 + 3.93000i) q^{38} +(3.53467 - 0.711416i) q^{39} +(8.24951 - 4.76285i) q^{40} +(1.19027 - 4.44214i) q^{41} +(-3.00179 + 5.40580i) q^{42} +(-2.94613 - 1.70095i) q^{43} +(20.2619 + 5.42916i) q^{44} +(-0.721604 + 2.69306i) q^{45} +(-1.29697 + 4.84036i) q^{46} +(-9.99804 - 2.67897i) q^{47} +(0.918879 + 0.530515i) q^{48} +(-0.233788 - 6.99609i) q^{49} +(-1.67751 + 6.26054i) q^{50} +(-1.11196 + 0.641993i) q^{51} +(8.25127 + 9.36589i) q^{52} +(4.30659 - 7.45923i) q^{53} +(-2.25744 + 0.604879i) q^{54} +(-14.6303 + 8.44680i) q^{55} +(-9.03823 + 0.150973i) q^{56} +(1.37301 - 1.37301i) q^{57} +(8.21813 - 8.21813i) q^{58} +(11.2322 + 3.00965i) q^{59} +(-9.32315 + 2.49813i) q^{60} +3.67019i q^{61} +(2.32966 + 4.03509i) q^{62} +(1.83932 - 1.90181i) q^{63} -12.2965i q^{64} +(-10.0324 - 0.634743i) q^{65} +(-12.2637 - 7.08048i) q^{66} +(1.20496 - 1.20496i) q^{67} +(-3.84953 - 2.22253i) q^{68} +(1.07209 - 1.85691i) q^{69} +(11.9849 - 12.3920i) q^{70} +(-1.73527 - 6.47610i) q^{71} +(-2.41591 - 2.41591i) q^{72} +(-1.17111 - 4.37064i) q^{73} +(-13.7913 - 23.8872i) q^{74} +(1.38664 - 2.40174i) q^{75} +(6.49307 + 1.73981i) q^{76} +(16.0291 - 0.267747i) q^{77} +(-3.74403 - 7.54898i) q^{78} +(0.418084 + 0.724143i) q^{79} +(-2.09178 - 2.09178i) q^{80} +1.00000 q^{81} -10.7478 q^{82} +(-2.01023 - 2.01023i) q^{83} +(8.88563 + 2.22253i) q^{84} +(3.45785 - 0.926529i) q^{85} +(-2.05774 + 7.67959i) q^{86} +(-4.30672 + 2.48648i) q^{87} -20.7021i q^{88} +(1.29112 + 4.81854i) q^{89} +6.51591 q^{90} +(8.03080 + 5.14841i) q^{91} +7.42297 q^{92} +(-0.515996 - 1.92572i) q^{93} +24.1904i q^{94} +(-4.68838 + 2.70684i) q^{95} +(-1.12677 + 4.20516i) q^{96} +(-6.27512 + 1.68141i) q^{97} +(-15.6519 + 4.75956i) q^{98} +(4.28455 + 4.28455i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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