LMFDB - Embedded newform 225.2.w.a.2.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			2.21
Character	$\chi$	$=$	225.2
Dual form			225.2.w.a.113.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.861819 + 0.697887i) q^{2} +(0.923545 + 1.46529i) q^{3} +(-0.160138 - 0.753391i) q^{4} +(1.74579 + 1.39722i) q^{5} +(-0.226676 + 1.90734i) q^{6} +(-2.43080 + 0.651331i) q^{7} +(1.39468 - 2.73721i) q^{8} +(-1.29413 + 2.70652i) q^{9} +O(q^{10})$	\(q+(0.861819 + 0.697887i) q^{2} +(0.923545 + 1.46529i) q^{3} +(-0.160138 - 0.753391i) q^{4} +(1.74579 + 1.39722i) q^{5} +(-0.226676 + 1.90734i) q^{6} +(-2.43080 + 0.651331i) q^{7} +(1.39468 - 2.73721i) q^{8} +(-1.29413 + 2.70652i) q^{9} +(0.529449 + 2.42251i) q^{10} +(2.42792 - 0.255185i) q^{11} +(0.956039 - 0.930439i) q^{12} +(-0.0493002 - 0.0608806i) q^{13} +(-2.54947 - 1.13510i) q^{14} +(-0.435017 + 3.84848i) q^{15} +(1.70496 - 0.759098i) q^{16} +(-5.10587 - 2.60157i) q^{17} +(-3.00415 + 1.42937i) q^{18} +(1.99615 - 0.648587i) q^{19} +(0.773087 - 1.53901i) q^{20} +(-3.19934 - 2.96029i) q^{21} +(2.27052 + 1.47449i) q^{22} +(-2.24534 - 5.84931i) q^{23} +(5.29885 - 0.484335i) q^{24} +(1.09554 + 4.87850i) q^{25} -0.0868740i q^{26} +(-5.16101 + 0.603320i) q^{27} +(0.879971 + 1.72704i) q^{28} +(3.64845 + 4.05202i) q^{29} +(-3.06071 + 3.01310i) q^{30} +(1.74472 - 1.93771i) q^{31} +(-3.93561 - 1.05454i) q^{32} +(2.61621 + 3.32192i) q^{33} +(-2.58473 - 5.80540i) q^{34} +(-5.15372 - 2.25928i) q^{35} +(2.24630 + 0.541568i) q^{36} +(-1.17452 - 7.41562i) q^{37} +(2.17296 + 0.834120i) q^{38} +(0.0436766 - 0.128465i) q^{39} +(6.25931 - 2.82992i) q^{40} +(2.37741 + 0.249876i) q^{41} +(-0.691307 - 4.78401i) q^{42} +(0.621435 + 2.31923i) q^{43} +(-0.581057 - 1.78831i) q^{44} +(-6.04088 + 2.91682i) q^{45} +(2.14708 - 6.60804i) q^{46} +(-9.33330 - 0.489138i) q^{47} +(2.68691 + 1.79720i) q^{48} +(-0.577613 + 0.333485i) q^{49} +(-2.46048 + 4.96895i) q^{50} +(-0.903455 - 9.88423i) q^{51} +(-0.0379721 + 0.0468916i) q^{52} +(11.3074 - 5.76140i) q^{53} +(-4.86890 - 3.08185i) q^{54} +(4.59518 + 2.94684i) q^{55} +(-1.60736 + 7.56202i) q^{56} +(2.79390 + 2.32593i) q^{57} +(0.316455 + 6.03832i) q^{58} +(1.02042 - 9.70861i) q^{59} +(2.96907 - 0.288550i) q^{60} +(1.14035 + 10.8497i) q^{61} +(2.85593 - 0.452335i) q^{62} +(1.38293 - 7.42191i) q^{63} +(-4.84981 - 6.67519i) q^{64} +(-0.00100385 - 0.175168i) q^{65} +(-0.0636269 + 4.68872i) q^{66} +(4.83915 - 0.253609i) q^{67} +(-1.14236 + 4.26333i) q^{68} +(6.49724 - 8.69217i) q^{69} +(-2.86485 - 5.54380i) q^{70} +(-5.52847 - 1.79631i) q^{71} +(5.60342 + 7.31703i) q^{72} +(-2.05016 + 12.9442i) q^{73} +(4.16304 - 7.21060i) q^{74} +(-6.13662 + 6.11080i) q^{75} +(-0.808299 - 1.40002i) q^{76} +(-5.73558 + 2.20168i) q^{77} +(0.127295 - 0.0802321i) q^{78} +(-5.54923 + 4.99655i) q^{79} +(4.03713 + 1.05699i) q^{80} +(-5.65046 - 7.00516i) q^{81} +(1.87451 + 1.87451i) q^{82} +(-0.731245 - 1.12602i) q^{83} +(-1.71792 + 2.88441i) q^{84} +(-5.27879 - 11.6758i) q^{85} +(-1.08299 + 2.43244i) q^{86} +(-2.56786 + 9.08825i) q^{87} +(2.68768 - 7.00164i) q^{88} +(-6.60723 + 4.80043i) q^{89} +(-7.24175 - 1.70208i) q^{90} +(0.159492 + 0.115878i) q^{91} +(-4.04725 + 2.62832i) q^{92} +(4.45062 + 0.766954i) q^{93} +(-7.70225 - 6.93514i) q^{94} +(4.39107 + 1.65676i) q^{95} +(-2.08950 - 6.74071i) q^{96} +(-1.00911 + 19.2549i) q^{97} +(-0.730533 - 0.115705i) q^{98} +(-2.45138 + 6.90145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	0.861819	+	0.697887i	0.609398	+	0.493481i	0.883632	−	0.468182i	$-0.155091\pi$
$2$	0.861819	+	0.697887i	0.609398	+	0.493481i	−0.274234	+	0.961663i	$0.588424\pi$
$3$	0.923545	+	1.46529i	0.533209	+	0.845984i
$3$	0.923545	+	1.46529i	0.533209	+	0.845984i
$4$	−0.160138	−	0.753391i	−0.0800691	−	0.376695i
$5$	1.74579	+	1.39722i	0.780740	+	0.624856i
$5$	1.74579	+	1.39722i	0.780740	+	0.624856i
$6$	−0.226676	+	1.90734i	−0.0925401	+	0.778669i
$7$	−2.43080	+	0.651331i	−0.918757	+	0.246180i	−0.687054	−	0.726607i	$-0.741096\pi$
$7$	−2.43080	+	0.651331i	−0.918757	+	0.246180i	−0.231703	+	0.972787i	$0.574430\pi$
$8$	1.39468	−	2.73721i	0.493094	−	0.967751i
$9$	−1.29413	+	2.70652i	−0.431376	+	0.902172i
$10$	0.529449	+	2.42251i	0.167427	+	0.766066i
$11$	2.42792	−	0.255185i	0.732046	−	0.0769411i	0.268831	−	0.963187i	$-0.413363\pi$
$11$	2.42792	−	0.255185i	0.732046	−	0.0769411i	0.463214	+	0.886246i	$0.346696\pi$
$12$	0.956039	−	0.930439i	0.275985	−	0.268595i
$13$	−0.0493002	−	0.0608806i	−0.0136734	−	0.0168852i	0.770263	−	0.637726i	$-0.220125\pi$
$13$	−0.0493002	−	0.0608806i	−0.0136734	−	0.0168852i	−0.783937	+	0.620841i	$0.786791\pi$
$14$	−2.54947	−	1.13510i	−0.681374	−	0.303367i
$15$	−0.435017	+	3.84848i	−0.112321	+	0.993672i
$16$	1.70496	−	0.759098i	0.426241	−	0.189775i
$17$	−5.10587	−	2.60157i	−1.23836	−	0.630974i	−0.292719	−	0.956199i	$-0.594560\pi$
$17$	−5.10587	−	2.60157i	−1.23836	−	0.630974i	−0.945637	+	0.325225i	$0.894560\pi$
$18$	−3.00415	+	1.42937i	−0.708084	+	0.336906i
$19$	1.99615	−	0.648587i	0.457947	−	0.148796i	−0.0709536	−	0.997480i	$-0.522604\pi$
$19$	1.99615	−	0.648587i	0.457947	−	0.148796i	0.528901	+	0.848683i	$0.322604\pi$
$20$	0.773087	−	1.53901i	0.172867	−	0.344133i
$21$	−3.19934	−	2.96029i	−0.698154	−	0.645988i
$22$	2.27052	+	1.47449i	0.484076	+	0.314363i
$23$	−2.24534	−	5.84931i	−0.468186	−	1.21967i	−0.940971	−	0.338488i	$-0.890085\pi$
$23$	−2.24534	−	5.84931i	−0.468186	−	1.21967i	0.472785	−	0.881178i	$-0.343249\pi$
$24$	5.29885	−	0.484335i	1.08162	−	0.0988644i
$25$	1.09554	+	4.87850i	0.219109	+	0.975700i
$26$		−	0.0868740i		−	0.0170374i
$27$	−5.16101	+	0.603320i	−0.993236	+	0.116109i
$28$	0.879971	+	1.72704i	0.166299	+	0.326380i
$29$	3.64845	+	4.05202i	0.677501	+	0.752441i	0.979627	−	0.200827i	$-0.0643629\pi$
$29$	3.64845	+	4.05202i	0.677501	+	0.752441i	−0.302126	+	0.953268i	$0.597696\pi$
$30$	−3.06071	+	3.01310i	−0.558806	+	0.550113i
$31$	1.74472	−	1.93771i	0.313361	−	0.348023i	−0.565804	−	0.824540i	$-0.691434\pi$
$31$	1.74472	−	1.93771i	0.313361	−	0.348023i	0.879165	+	0.476517i	$0.158101\pi$
$32$	−3.93561	−	1.05454i	−0.695724	−	0.186419i
$33$	2.61621	+	3.32192i	0.455424	+	0.578273i
$34$	−2.58473	−	5.80540i	−0.443278	−	0.995619i
$35$	−5.15372	−	2.25928i	−0.871137	−	0.381888i
$36$	2.24630	+	0.541568i	0.374384	+	0.0902614i
$37$	−1.17452	−	7.41562i	−0.193090	−	1.21912i	−0.873696	−	0.486472i	$-0.838284\pi$
$37$	−1.17452	−	7.41562i	−0.193090	−	1.21912i	0.680607	−	0.732649i	$-0.261716\pi$
$38$	2.17296	+	0.834120i	0.352500	+	0.135312i
$39$	0.0436766	−	0.128465i	0.00699386	−	0.0205708i
$40$	6.25931	−	2.82992i	0.989684	−	0.447449i
$41$	2.37741	+	0.249876i	0.371289	+	0.0390240i	0.288336	−	0.957529i	$-0.406898\pi$
$41$	2.37741	+	0.249876i	0.371289	+	0.0390240i	0.0829532	+	0.996553i	$0.473565\pi$
$42$	−0.691307	−	4.78401i	−0.106671	−	0.738189i
$43$	0.621435	+	2.31923i	0.0947679	+	0.353679i	0.996984	−	0.0776054i	$-0.0247274\pi$
$43$	0.621435	+	2.31923i	0.0947679	+	0.353679i	−0.902216	+	0.431284i	$0.858061\pi$
$44$	−0.581057	−	1.78831i	−0.0875976	−	0.269598i
$45$	−6.04088	+	2.91682i	−0.900521	+	0.434813i
$46$	2.14708	−	6.60804i	0.316570	−	0.974302i
$47$	−9.33330	−	0.489138i	−1.36140	−	0.0713480i	−0.642407	−	0.766364i	$-0.722064\pi$
$47$	−9.33330	−	0.489138i	−1.36140	−	0.0713480i	−0.718995	+	0.695016i	$0.755397\pi$
$48$	2.68691	+	1.79720i	0.387822	+	0.259403i
$49$	−0.577613	+	0.333485i	−0.0825162	+	0.0476408i
$50$	−2.46048	+	4.96895i	−0.347965	+	0.702716i
$51$	−0.903455	−	9.88423i	−0.126509	−	1.38407i
$52$	−0.0379721	+	0.0468916i	−0.00526578	+	0.00650270i
$53$	11.3074	−	5.76140i	1.55319	−	0.791389i	0.554033	−	0.832495i	$-0.313088\pi$
$53$	11.3074	−	5.76140i	1.55319	−	0.791389i	0.999155	+	0.0411062i	$0.0130882\pi$
$54$	−4.86890	−	3.08185i	−0.662574	−	0.419386i
$55$	4.59518	+	2.94684i	0.619614	+	0.397352i
$56$	−1.60736	+	7.56202i	−0.214792	+	1.01052i
$57$	2.79390	+	2.32593i	0.370061	+	0.308077i
$58$	0.316455	+	6.03832i	0.0415525	+	0.792870i
$59$	1.02042	−	9.70861i	0.132847	−	1.26395i	−0.701482	−	0.712687i	$-0.747478\pi$
$59$	1.02042	−	9.70861i	0.132847	−	1.26395i	0.834329	−	0.551267i	$-0.185855\pi$
$60$	2.96907	−	0.288550i	0.383305	−	0.0372516i
$61$	1.14035	+	10.8497i	0.146007	+	1.38917i	0.784781	+	0.619773i	$0.212775\pi$
$61$	1.14035	+	10.8497i	0.146007	+	1.38917i	−0.638773	+	0.769395i	$0.720558\pi$
$62$	2.85593	−	0.452335i	0.362704	−	0.0574466i
$63$	1.38293	−	7.42191i	0.174233	−	0.935073i
$64$	−4.84981	−	6.67519i	−0.606226	−	0.834399i
$65$	−0.00100385	−	0.175168i	−0.000124513	−	0.0217269i
$66$	−0.0636269	+	4.68872i	−0.00783193	+	0.577141i
$67$	4.83915	−	0.253609i	0.591196	−	0.0309833i	0.245607	−	0.969369i	$-0.421013\pi$
$67$	4.83915	−	0.253609i	0.591196	−	0.0309833i	0.345589	+	0.938386i	$0.387679\pi$
$68$	−1.14236	+	4.26333i	−0.138531	+	0.517004i
$69$	6.49724	−	8.69217i	0.782176	−	1.04641i
$70$	−2.86485	−	5.54380i	−0.342414	−	0.662611i
$71$	−5.52847	−	1.79631i	−0.656109	−	0.213183i	−0.0380030	−	0.999278i	$-0.512100\pi$
$71$	−5.52847	−	1.79631i	−0.656109	−	0.213183i	−0.618106	+	0.786095i	$0.712100\pi$
$72$	5.60342	+	7.31703i	0.660369	+	0.862321i
$73$	−2.05016	+	12.9442i	−0.239953	+	1.51501i	0.513835	+	0.857889i	$0.328224\pi$
$73$	−2.05016	+	12.9442i	−0.239953	+	1.51501i	−0.753789	+	0.657117i	$0.771776\pi$
$74$	4.16304	−	7.21060i	0.483944	−	0.838216i
$75$	−6.13662	+	6.11080i	−0.708596	+	0.705615i
$76$	−0.808299	−	1.40002i	−0.0927183	−	0.160593i
$77$	−5.73558	+	2.20168i	−0.653630	+	0.250905i
$78$	0.127295	−	0.0802321i	0.0144134	−	0.00908449i
$79$	−5.54923	+	4.99655i	−0.624337	+	0.562155i	−0.919401	−	0.393322i	$-0.871326\pi$
$79$	−5.54923	+	4.99655i	−0.624337	+	0.562155i	0.295064	+	0.955477i	$0.404659\pi$
$80$	4.03713	+	1.05699i	0.451365	+	0.118175i
$81$	−5.65046	−	7.00516i	−0.627829	−	0.778351i
$82$	1.87451	+	1.87451i	0.207005	+	0.207005i
$83$	−0.731245	−	1.12602i	−0.0802646	−	0.123597i	0.796258	−	0.604957i	$-0.206810\pi$
$83$	−0.731245	−	1.12602i	−0.0802646	−	0.123597i	−0.876523	+	0.481360i	$0.840143\pi$
$84$	−1.71792	+	2.88441i	−0.187440	+	0.314715i
$85$	−5.27879	−	11.6758i	−0.572565	−	1.26642i
$86$	−1.08299	+	2.43244i	−0.116782	+	0.262297i
$87$	−2.56786	+	9.08825i	−0.275303	+	0.974363i
$88$	2.68768	−	7.00164i	0.286507	−	0.746377i
$89$	−6.60723	+	4.80043i	−0.700365	+	0.508845i	−0.880051	−	0.474879i	$-0.842492\pi$
$89$	−6.60723	+	4.80043i	−0.700365	+	0.508845i	0.179686	+	0.983724i	$0.442492\pi$
$90$	−7.24175	−	1.70208i	−0.763347	−	0.179415i
$91$	0.159492	+	0.115878i	0.0167193	+	0.0121473i
$92$	−4.04725	+	2.62832i	−0.421955	+	0.274021i
$93$	4.45062	+	0.766954i	0.461508	+	0.0795294i
$94$	−7.70225	−	6.93514i	−0.794426	−	0.715305i
$95$	4.39107	+	1.65676i	0.450514	+	0.169980i
$96$	−2.08950	−	6.74071i	−0.213259	−	0.687971i
$97$	−1.00911	+	19.2549i	−0.102459	+	1.95504i	0.153015	+	0.988224i	$0.451102\pi$
$97$	−1.00911	+	19.2549i	−0.102459	+	1.95504i	−0.255475	+	0.966816i	$0.582232\pi$
$98$	−0.730533	−	0.115705i	−0.0737950	−	0.0116880i
$99$	−2.45138	+	6.90145i	−0.246373	+	0.693622i
$100$	3.49998	−	1.60661i	0.349998	−	0.160661i
$101$	6.85621	+	3.95844i	0.682219	+	0.393879i	0.800690	−	0.599078i	$-0.204466\pi$
$101$	6.85621	+	3.95844i	0.682219	+	0.393879i	−0.118472	+	0.992957i	$0.537800\pi$
$102$	6.11946	−	9.14893i	0.605917	−	0.905879i
$103$	−5.32595	+	8.20124i	−0.524781	+	0.808092i	−0.997316	−	0.0732200i	$-0.976672\pi$
$103$	−5.32595	+	8.20124i	−0.524781	+	0.808092i	0.472535	+	0.881312i	$0.343339\pi$
$104$	−0.235401	+	0.0500361i	−0.0230830	+	0.00490644i
$105$	−1.44919	−	9.63822i	−0.141427	−	0.940594i
$106$	13.7657	+	2.92599i	1.33704	+	0.284198i
$107$	8.05906	−	8.05906i	0.779098	−	0.779098i	−0.200579	−	0.979678i	$-0.564282\pi$
$107$	8.05906	−	8.05906i	0.779098	−	0.779098i	0.979678	+	0.200579i	$0.0642824\pi$
$108$	1.28101	+	3.79164i	0.123265	+	0.364851i
$109$	−0.0328738	+	0.0452469i	−0.00314874	+	0.00433387i	−0.810588	−	0.585616i	$-0.800853\pi$
$109$	−0.0328738	+	0.0452469i	−0.00314874	+	0.00433387i	0.807440	+	0.589950i	$0.200853\pi$
$110$	1.90365	+	5.74656i	0.181506	+	0.547913i
$111$	9.78129	−	8.56967i	0.928399	−	0.813397i
$112$	−3.65000	+	2.95571i	−0.344893	+	0.279289i
$113$	−8.08525	+	6.54730i	−0.760596	+	0.615919i	−0.929120	−	0.369779i	$-0.879433\pi$
$113$	−8.08525	+	6.54730i	−0.760596	+	0.615919i	0.168524	+	0.985698i	$0.446100\pi$
$114$	0.784599	+	3.95435i	0.0734844	+	0.370359i
$115$	4.25290	−	13.3489i	0.396585	−	1.24479i
$116$	2.46850	−	3.39759i	0.229194	−	0.315459i
$117$	0.228575	−	0.0546443i	0.0211318	−	0.00505187i
$118$	7.65493	−	7.65493i	0.704693	−	0.704693i
$119$	14.1058	+	2.99829i	1.29308	+	0.274853i
$120$	9.92739	+	6.55813i	0.906243	+	0.598672i
$121$	−4.92994	+	1.04789i	−0.448177	+	0.0952629i
$122$	−6.58912	+	10.1464i	−0.596551	+	0.918608i
$123$	1.82950	+	3.71436i	0.164961	+	0.334912i
$124$	−1.73925	−	1.00415i	−0.156189	−	0.0901758i
$125$	−4.90376	+	10.0475i	−0.438606	+	0.898680i
$126$	6.37149	−	5.43121i	0.567618	−	0.483851i
$127$	10.0760	+	1.59589i	0.894104	+	0.141612i	0.586545	−	0.809917i	$-0.300488\pi$
$127$	10.0760	+	1.59589i	0.894104	+	0.141612i	0.307559	+	0.951529i	$0.400488\pi$
$128$	0.0523929	−	0.999716i	0.00463092	−	0.0883632i
$129$	−2.82441	+	3.05249i	−0.248675	+	0.268757i
$130$	0.121382	−	0.151664i	0.0106459	−	0.0133018i
$131$	5.54448	+	4.99227i	0.484424	+	0.436177i	0.874804	−	0.484477i	$-0.160990\pi$
$131$	5.54448	+	4.99227i	0.484424	+	0.436177i	−0.390381	+	0.920654i	$0.627657\pi$
$132$	2.08375	−	2.50300i	0.181367	−	0.217858i
$133$	−4.42979	+	2.87674i	−0.384112	+	0.249445i
$134$	4.34746	+	3.15861i	0.375563	+	0.272863i
$135$	−9.85299	−	6.15780i	−0.848011	−	0.529979i
$136$	−14.2421	+	10.3475i	−1.22125	+	0.887291i
$137$	−3.09633	+	8.06621i	−0.264537	+	0.689143i	0.735397	+	0.677637i	$0.236996\pi$
$137$	−3.09633	+	8.06621i	−0.264537	+	0.689143i	−0.999934	+	0.0115061i	$0.996337\pi$
$138$	11.6656	−	2.95673i	0.993041	−	0.251694i
$139$	−5.07734	+	11.4039i	−0.430655	+	0.967266i	0.559698	+	0.828697i	$0.310917\pi$
$139$	−5.07734	+	11.4039i	−0.430655	+	0.967266i	−0.990353	+	0.138569i	$0.955750\pi$
$140$	−0.876816	+	4.24456i	−0.0741045	+	0.358731i
$141$	−7.90300	−	14.1277i	−0.665552	−	1.18977i
$142$	−3.51092	−	5.40634i	−0.294630	−	0.453690i
$143$	−0.135233	−	0.135233i	−0.0113087	−	0.0113087i
$144$	−0.151930	+	5.59688i	−0.0126608	+	0.466407i
$145$	0.707856	+	12.1717i	0.0587842	+	1.01080i
$146$	−10.8005	+	9.72478i	−0.893853	+	0.804829i
$147$	−1.02210	−	0.538380i	−0.0843017	−	0.0444049i
$148$	−5.39878	+	2.07240i	−0.443777	+	0.170350i
$149$	5.76176	+	9.97966i	0.472022	+	0.817566i	0.999488	−	0.0320105i	$-0.0101910\pi$
$149$	5.76176	+	9.97966i	0.472022	+	0.817566i	−0.527466	+	0.849576i	$0.676858\pi$
$150$	−9.55330	+	0.983737i	−0.780024	+	0.0803218i
$151$	5.11749	−	8.86375i	0.416455	−	0.721322i	−0.579125	−	0.815239i	$-0.696606\pi$
$151$	5.11749	−	8.86375i	0.416455	−	0.721322i	0.995580	+	0.0939173i	$0.0299389\pi$
$152$	1.00866	−	6.36845i	0.0818135	−	0.516550i
$153$	13.6488	−	10.4524i	1.10344	−	0.845023i
$154$	−6.47956	−	2.10534i	−0.522138	−	0.169653i
$155$	5.75331	−	0.945064i	0.462117	−	0.0759094i
$156$	−0.103779	−	0.0123335i	−0.00830893	−	0.000987466i
$157$	1.83277	−	6.84001i	0.146271	−	0.545892i	−0.853424	−	0.521217i	$-0.825478\pi$
$157$	1.83277	−	6.84001i	0.146271	−	0.545892i	0.999696	−	0.0246750i	$-0.00785511\pi$
$158$	−8.26945	+	0.433384i	−0.657882	+	0.0344781i
$159$	18.8850	+	11.2476i	1.49768	+	0.891996i
$160$	−5.39730	−	7.33992i	−0.426694	−	0.580272i
$161$	9.26781	+	12.7561i	0.730406	+	1.00532i
$162$	0.0191389	−	9.98056i	0.00150370	−	0.784147i
$163$	−20.1209	+	3.18684i	−1.57599	+	0.249613i	−0.882310	−	0.470668i	$-0.844013\pi$
$163$	−20.1209	+	3.18684i	−1.57599	+	0.249613i	−0.693682	+	0.720281i	$0.744013\pi$
$164$	−0.192460	−	1.83113i	−0.0150286	−	0.142987i
$165$	−0.0741143	+	9.45480i	−0.00576979	+	0.736055i
$166$	0.155633	−	1.48075i	0.0120795	−	0.114929i
$167$	−0.426316	−	8.13460i	−0.0329893	−	0.629474i	−0.964230	−	0.265068i	$-0.914605\pi$
$167$	−0.426316	−	8.13460i	−0.0329893	−	0.629474i	0.931240	−	0.364406i	$-0.118728\pi$
$168$	−12.5650	+	4.62863i	−0.969411	+	0.357107i
$169$	2.70158	−	12.7099i	0.207814	−	0.977686i
$170$	3.59904	−	13.7464i	0.276034	−	1.05430i
$171$	−0.827859	+	6.24196i	−0.0633080	+	0.477335i
$172$	1.64777	−	0.839580i	0.125641	−	0.0640173i
$173$	13.7011	−	16.9194i	1.04167	−	1.28636i	0.0846312	−	0.996412i	$-0.473029\pi$
$173$	13.7011	−	16.9194i	1.04167	−	1.28636i	0.957043	−	0.289948i	$-0.0936379\pi$
$174$	−8.55560	+	6.04035i	−0.648598	+	0.457918i
$175$	−5.84057	−	11.1451i	−0.441506	−	0.842491i
$176$	3.94580	−	2.27811i	0.297426	−	0.171719i
$177$	15.1683	−	7.47114i	1.14012	−	0.561565i
$178$	−9.04439	−	0.473997i	−0.677906	−	0.0355276i
$179$	3.03093	−	9.32825i	0.226542	−	0.697226i	−0.771589	−	0.636122i	$-0.780538\pi$
$179$	3.03093	−	9.32825i	0.226542	−	0.697226i	0.998131	−	0.0611045i	$-0.0194623\pi$
$180$	3.16488	+	4.08405i	0.235896	+	0.304407i
$181$	−2.45627	−	7.55961i	−0.182573	−	0.561902i	0.817325	−	0.576177i	$-0.195456\pi$
$181$	−2.45627	−	7.55961i	−0.182573	−	0.561902i	−0.999898	+	0.0142750i	$0.995456\pi$
$182$	0.0565838	+	0.211173i	0.00419427	+	0.0156532i
$183$	−14.8448	+	11.6912i	−1.09736	+	0.864237i
$184$	−19.1423	−	2.01194i	−1.41119	−	0.148322i
$185$	8.31081	−	14.5872i	0.611023	−	1.07247i
$186$	3.30038	+	3.76701i	0.241996	+	0.276210i
$187$	−13.0605	−	5.01347i	−0.955081	−	0.366621i
$188$	1.12611	+	7.10995i	0.0821297	+	0.518547i
$189$	12.1524	−	4.82808i	0.883959	−	0.351191i
$190$	2.62807	+	4.49230i	0.190660	+	0.325906i
$191$	−6.80592	−	15.2863i	−0.492459	−	1.10608i	−0.973355	−	0.229303i	$-0.926355\pi$
$191$	−6.80592	−	15.2863i	−0.492459	−	1.10608i	0.480896	−	0.876778i	$-0.340311\pi$
$192$	5.30205	−	13.2712i	0.382643	−	0.957767i
$193$	10.7069	+	2.86891i	0.770701	+	0.206509i	0.622681	−	0.782476i	$-0.286043\pi$
$193$	10.7069	+	2.86891i	0.770701	+	0.206509i	0.148020	+	0.988984i	$0.452710\pi$
$194$	−14.3074	+	15.8900i	−1.02721	+	1.14084i
$195$	0.255744	−	0.163246i	0.0183142	−	0.0116903i
$196$	0.343743	+	0.381765i	0.0245531	+	0.0272689i
$197$	6.74976	+	13.2471i	0.480900	+	0.943820i	0.996224	+	0.0868242i	$0.0276718\pi$
$197$	6.74976	+	13.2471i	0.480900	+	0.943820i	−0.515323	+	0.856996i	$0.672328\pi$
$198$	−6.92908	+	4.23701i	−0.492428	+	0.301111i
$199$		−	2.33837i		−	0.165763i	−0.996559	−	0.0828814i	$-0.973588\pi$
$199$		−	2.33837i		−	0.165763i	0.996559	−	0.0828814i	$-0.0264123\pi$
$200$	14.8814	+	3.80521i	1.05228	+	0.269069i
$201$	4.84078	+	6.85652i	0.341442	+	0.483622i
$202$	3.14627	+	8.19632i	0.221371	+	0.576691i
$203$	−11.5079	−	7.47330i	−0.807695	−	0.524523i
$204$	−7.30201	+	2.26350i	−0.511243	+	0.158477i
$205$	3.80132	+	3.75800i	0.265496	+	0.262470i
$206$	−10.3135	+	3.35107i	−0.718578	+	0.233480i
$207$	18.7370	+	1.49271i	1.30231	+	0.103751i
$208$	−0.130269	−	0.0663755i	−0.00903255	−	0.00460231i
$209$	4.68098	−	2.08411i	0.323790	−	0.144161i
$210$	5.47745	−	9.31777i	0.377980	−	0.642987i
$211$	20.2718	+	9.02561i	1.39557	+	0.621348i	0.960305	−	0.278953i	$-0.0899875\pi$
$211$	20.2718	+	9.02561i	1.39557	+	0.621348i	0.435266	+	0.900302i	$0.356654\pi$
$212$	−6.15133	−	7.59625i	−0.422475	−	0.521713i
$213$	−2.47368	−	9.75977i	−0.169494	−	0.668728i
$214$	12.5698	−	1.32113i	0.859251	−	0.0903109i
$215$	−2.15558	+	4.91715i	−0.147009	+	0.335347i
$216$	−5.54654	+	14.9682i	−0.377394	+	1.01846i
$217$	−2.97898	+	5.84657i	−0.202226	+	0.396891i
$218$	−0.0599085	+	0.0160524i	−0.00405752	+	0.00108721i
$219$	−20.8604	+	8.95049i	−1.40962	+	0.604818i
$220$	1.48426	−	3.93387i	0.100069	−	0.265221i
$221$	0.0933350	+	0.439106i	0.00627839	+	0.0295375i
$222$	14.4104	−	0.559266i	0.967160	−	0.0375354i
$223$	−18.1749	−	14.7177i	−1.21708	−	0.985571i	−0.999956	−	0.00942684i	$-0.996999\pi$
$223$	−18.1749	−	14.7177i	−1.21708	−	0.985571i	−0.217123	−	0.976144i	$-0.569667\pi$
$224$	10.2535			0.685093
$225$	−14.6215	−	3.34830i	−0.974768	−	0.223220i
$226$	−11.5373			−0.767450
$227$	−4.69373	−	3.80090i	−0.311534	−	0.252275i	0.460783	−	0.887513i	$-0.347569\pi$
$227$	−4.69373	−	3.80090i	−0.311534	−	0.252275i	−0.772316	+	0.635238i	$0.780902\pi$
$228$	1.30492	−	2.47737i	0.0864206	−	0.164068i
$229$	−1.80107	−	8.47337i	−0.119018	−	0.559936i	−0.996734	−	0.0807545i	$-0.974267\pi$
$229$	−1.80107	−	8.47337i	−0.119018	−	0.559936i	0.877716	−	0.479181i	$-0.159066\pi$
$230$	12.9812	−	8.53628i	0.855958	−	0.562865i
$231$	−8.52317	−	6.37092i	−0.560783	−	0.419176i
$232$	16.1797	−	4.33533i	1.06225	−	0.284628i
$233$	10.4578	−	20.5247i	0.685116	−	1.34462i	−0.242159	−	0.970236i	$-0.577856\pi$
$233$	10.4578	−	20.5247i	0.685116	−	1.34462i	0.927276	−	0.374380i	$-0.122144\pi$
$234$	0.235126	+	0.112426i	0.0153707	+	0.00734953i
$235$	−15.6105	−	13.8946i	−1.01832	−	0.906385i
$236$	−7.47779	+	0.785947i	−0.486762	+	0.0511608i
$237$	−12.4463	−	3.51667i	−0.808476	−	0.228432i
$238$	10.0642	+	12.4283i	0.652366	+	0.805605i
$239$	−4.28074	−	1.90591i	−0.276898	−	0.123283i	0.263590	−	0.964635i	$-0.415094\pi$
$239$	−4.28074	−	1.90591i	−0.276898	−	0.123283i	−0.540488	+	0.841352i	$0.681760\pi$
$240$	2.17968	+	6.89173i	0.140698	+	0.444859i
$241$	9.72247	−	4.32872i	0.626279	−	0.278837i	−0.0689560	−	0.997620i	$-0.521967\pi$
$241$	9.72247	−	4.32872i	0.626279	−	0.278837i	0.695235	+	0.718782i	$0.255300\pi$
$242$	−4.98003	−	2.53745i	−0.320128	−	0.163114i
$243$	5.04611	−	14.7491i	0.323708	−	0.946157i
$244$	7.99149	−	2.59659i	0.511603	−	0.166230i
$245$	−1.47434	−	0.224860i	−0.0941923	−	0.0143658i
$246$	−1.01550	+	4.47789i	−0.0647459	+	0.285500i
$247$	−0.137897	−	0.0895512i	−0.00877416	−	0.00569801i
$248$	−2.87059	−	7.47815i	−0.182283	−	0.474863i
$249$	0.974602	−	2.11141i	0.0617629	−	0.133805i
$250$	−11.2382	+	5.23689i	−0.710766	+	0.331210i
$251$			14.6220i			0.922931i	0.887158	+	0.461466i	$0.152676\pi$
$251$			14.6220i			0.922931i	−0.887158	+	0.461466i	$0.847324\pi$
$252$	−5.81306	+	0.146643i	−0.366188	+	0.00923764i
$253$	−6.94416	−	13.6287i	−0.436576	−	0.856828i
$254$	7.56997	+	8.40731i	0.474982	+	0.527521i
$255$	12.2332	−	18.5181i	0.766074	−	1.15965i
$256$	−10.2991	+	11.4384i	−0.643696	+	0.714897i
$257$	17.9660	+	4.81396i	1.12069	+	0.300287i	0.771161	−	0.636640i	$-0.219676\pi$
$257$	17.9660	+	4.81396i	1.12069	+	0.300287i	0.349525	+	0.936927i	$0.386343\pi$
$258$	−4.56442	+	0.659575i	−0.284168	+	0.0410634i
$259$	7.68505	+	17.2609i	0.477526	+	1.07254i
$260$	−0.131809	+	0.0288074i	−0.00817445	+	0.00178656i
$261$	−15.6884	+	4.63077i	−0.971089	+	0.286637i
$262$	1.29430	+	8.17186i	0.0799618	+	0.504859i
$263$	−16.5813	−	6.36495i	−1.02245	−	0.392480i	−0.211360	−	0.977408i	$-0.567789\pi$
$263$	−16.5813	−	6.36495i	−1.02245	−	0.392480i	−0.811085	+	0.584928i	$0.801123\pi$
$264$	12.7416	−	2.52811i	0.784191	−	0.155595i
$265$	27.7902	+	5.74074i	1.70714	+	0.352651i
$266$	−5.82532	−	0.612266i	−0.357173	−	0.0375404i
$267$	−13.1361	−	5.24807i	−0.803915	−	0.321177i
$268$	−0.965999	−	3.60516i	−0.0590078	−	0.220220i
$269$	−2.10939	−	6.49203i	−0.128612	−	0.395826i	0.865930	−	0.500165i	$-0.166727\pi$
$269$	−2.10939	−	6.49203i	−0.128612	−	0.395826i	−0.994542	+	0.104339i	$0.966727\pi$
$270$	−4.19404	−	12.1832i	−0.255241	−	0.741445i
$271$	8.03831	−	24.7394i	0.488293	−	1.50281i	−0.338862	−	0.940836i	$-0.610042\pi$
$271$	8.03831	−	24.7394i	0.488293	−	1.50281i	0.827155	−	0.561974i	$-0.189958\pi$
$272$	−10.6802	−	0.559724i	−0.647580	−	0.0339382i
$273$	−0.0224961	+	0.340721i	−0.00136152	+	0.0206213i
$274$	−8.29778	+	4.79073i	−0.501287	+	0.289418i
$275$	3.90481	+	11.5651i	0.235469	+	0.697399i
$276$	−7.58905	−	3.50301i	−0.456807	−	0.210857i
$277$	−8.10057	+	10.0034i	−0.486716	+	0.601044i	−0.960046	−	0.279841i	$-0.909718\pi$
$277$	−8.10057	+	10.0034i	−0.486716	+	0.601044i	0.473330	+	0.880885i	$0.343052\pi$
$278$	−12.3344	+	6.28468i	−0.739767	+	0.376930i
$279$	2.98654	+	7.22975i	0.178800	+	0.432834i
$280$	−13.3719	+	10.9558i	−0.799126	+	0.654737i
$281$	0.621223	−	2.92262i	0.0370590	−	0.174349i	−0.955726	−	0.294259i	$-0.904927\pi$
$281$	0.621223	−	2.92262i	0.0370590	−	0.174349i	0.992785	+	0.119910i	$0.0382605\pi$
$282$	3.04859	−	17.6909i	0.181541	−	1.05348i
$283$	−0.373657	−	7.12980i	−0.0222116	−	0.423823i	−0.986992	−	0.160767i	$-0.948603\pi$
$283$	−0.373657	−	7.12980i	−0.0222116	−	0.423823i	0.964781	−	0.263055i	$-0.0847302\pi$
$284$	−0.468004	+	4.45276i	−0.0277709	+	0.264223i
$285$	1.62771	+	7.96427i	0.0964175	+	0.471762i
$286$	−0.0221689	−	0.210923i	−0.00131088	−	0.0124722i
$287$	−5.94176	+	0.941083i	−0.350731	+	0.0555503i
$288$	7.94732	−	9.28707i	0.468300	−	0.547246i
$289$	9.30939	+	12.8133i	0.547611	+	0.753722i
$290$	−7.88440	+	10.9838i	−0.462988	+	0.644989i
$291$	−29.1459	+	16.3041i	−1.70856	+	0.955766i
$292$	10.0804	−	0.528289i	0.589909	−	0.0309158i
$293$	−0.790416	+	2.94987i	−0.0461766	+	0.172333i	−0.985163	−	0.171621i	$-0.945100\pi$
$293$	−0.790416	+	2.94987i	−0.0461766	+	0.172333i	0.938987	+	0.343954i	$0.111766\pi$
$294$	−0.505139	−	1.17730i	−0.0294603	−	0.0686615i
$295$	15.3465	−	15.5234i	0.893508	−	0.903808i
$296$	−21.9362	−	7.12751i	−1.27502	−	0.414278i
$297$	−12.3766	+	2.78182i	−0.718161	+	0.161418i
$298$	−1.99908	+	12.6217i	−0.115804	+	0.731157i
$299$	−0.245414	+	0.425070i	−0.0141927	+	0.0245824i
$300$	5.58653	+	3.64470i	0.322538	+	0.210427i
$301$	−3.02117	−	5.23282i	−0.174137	−	0.301615i
$302$	10.5962	−	4.06752i	0.609745	−	0.234059i
$303$	0.531778	+	13.7021i	0.0305499	+	0.787166i
$304$	2.91101	−	2.62109i	0.166958	−	0.150330i
$305$	−13.1687	+	20.5347i	−0.754037	+	1.17581i
$306$	19.0574	+	0.517321i	1.08944	+	0.0295733i
$307$	19.5469	+	19.5469i	1.11560	+	1.11560i	0.992379	+	0.123224i	$0.0393235\pi$
$307$	19.5469	+	19.5469i	1.11560	+	1.11560i	0.123224	+	0.992379i	$0.460676\pi$
$308$	2.57721	+	3.96856i	0.146850	+	0.226130i
$309$	−16.9359	−	0.229824i	−0.963451	−	0.0130742i
$310$	5.61786	+	3.20069i	0.319073	+	0.181787i
$311$	−4.49755	+	10.1017i	−0.255033	+	0.572813i	−0.995005	−	0.0998245i	$-0.968172\pi$
$311$	−4.49755	+	10.1017i	−0.255033	+	0.572813i	0.739972	+	0.672637i	$0.234839\pi$
$312$	−0.290721	−	0.298720i	−0.0164588	−	0.0169117i
$313$	−1.94403	+	5.06437i	−0.109883	+	0.286255i	−0.977485	−	0.211004i	$-0.932327\pi$
$313$	−1.94403	+	5.06437i	−0.109883	+	0.286255i	0.867602	+	0.497259i	$0.165660\pi$
$314$	6.35307	−	4.61578i	0.358525	−	0.260483i
$315$	12.7844	−	11.0248i	0.720317	−	0.621178i
$316$	4.65299	+	3.38060i	0.261751	+	0.190174i
$317$	−3.45299	+	2.24240i	−0.193939	+	0.125946i	−0.637956	−	0.770073i	$-0.720220\pi$
$317$	−3.45299	+	2.24240i	−0.193939	+	0.125946i	0.444017	+	0.896019i	$0.353553\pi$
$318$	8.42584	+	22.8730i	0.472498	+	1.28265i
$319$	9.89217	+	8.90695i	0.553855	+	0.498694i
$320$	0.859986	−	18.4297i	0.0480747	−	1.03025i
$321$	19.2517	+	4.36592i	1.07453	+	0.243682i
$322$	−0.915107	+	17.4613i	−0.0509969	+	0.973080i
$323$	−11.8794	−	1.88151i	−0.660988	−	0.104690i
$324$	−4.37277	+	5.37880i	−0.242932	+	0.298822i
$325$	0.242996	−	0.307208i	0.0134790	−	0.0170409i
$326$	−19.5646	−	11.2957i	−1.08359	−	0.625608i
$327$	−0.0966602	−	0.00638198i	−0.00534532	−	0.000352925i
$328$	3.99969	−	6.15898i	0.220846	−	0.340073i
$329$	23.0060	−	4.89007i	1.26836	−	0.269599i
$330$	−6.66226	+	8.09660i	−0.366745	+	0.445703i
$331$	13.7965	+	2.93254i	0.758325	+	0.161187i	0.570818	−	0.821076i	$-0.306626\pi$
$331$	13.7965	+	2.93254i	0.758325	+	0.161187i	0.187507	+	0.982263i	$0.439959\pi$
$332$	−0.731232	+	0.731232i	−0.0401316	+	0.0401316i
$333$	21.5905	+	6.41792i	1.18315	+	0.351700i
$334$	5.30962	−	7.30807i	0.290530	−	0.399880i
$335$	8.80247	+	6.31862i	0.480930	+	0.345223i
$336$	−7.70191	−	2.61856i	−0.420173	−	0.142854i
$337$	−2.08573	+	1.68899i	−0.113617	+	0.0920053i	−0.684445	−	0.729064i	$-0.739956\pi$
$337$	−2.08573	+	1.68899i	−0.113617	+	0.0920053i	0.570828	+	0.821070i	$0.306622\pi$
$338$	11.1984	−	9.06825i	0.609110	−	0.493248i
$339$	−17.0608	−	5.80047i	−0.926614	−	0.315038i
$340$	−7.95112	+	5.84674i	−0.431210	+	0.317084i
$341$	3.74157	−	5.14983i	0.202617	−	0.278879i
$342$	−5.06965	+	4.80169i	−0.274135	+	0.259645i
$343$	13.6431	−	13.6431i	0.736661	−	0.736661i
$344$	7.21492	+	1.53358i	0.389002	+	0.0826850i
$345$	23.4877	−	6.09658i	1.26453	−	0.328229i
$346$	23.6157	−	5.01967i	1.26959	−	0.269859i
$347$	9.10192	−	14.0157i	0.488617	−	0.752403i	−0.505252	−	0.862972i	$-0.668600\pi$
$347$	9.10192	−	14.0157i	0.488617	−	0.752403i	0.993869	+	0.110568i	$0.0352671\pi$
$348$	7.25822	+	0.479223i	0.389081	+	0.0256891i
$349$	24.6896	+	14.2546i	1.32161	+	0.763030i	0.983985	−	0.178252i	$-0.0570443\pi$
$349$	24.6896	+	14.2546i	1.32161	+	0.763030i	0.337621	+	0.941282i	$0.390378\pi$
$350$	2.74451	−	13.6811i	0.146700	−	0.731287i
$351$	0.291169	+	0.284462i	0.0155415	+	0.0151834i
$352$	−9.82444	−	1.55604i	−0.523645	−	0.0829372i
$353$	−1.15505	+	22.0396i	−0.0614769	+	1.17305i	0.777501	+	0.628882i	$0.216487\pi$
$353$	−1.15505	+	22.0396i	−0.0614769	+	1.17305i	−0.838977	+	0.544166i	$0.816846\pi$
$354$	18.2863	+	4.14699i	0.971908	+	0.220410i
$355$	−7.14169	−	10.8605i	−0.379042	−	0.576414i
$356$	4.67467	+	4.20909i	0.247757	+	0.223082i
$357$	8.63403	+	23.4382i	0.456961	+	1.24048i
$358$	9.12218	−	5.92401i	0.482122	−	0.313094i
$359$	−10.0097	−	7.27249i	−0.528293	−	0.383827i	0.291426	−	0.956593i	$-0.405870\pi$
$359$	−10.0097	−	7.27249i	−0.528293	−	0.383827i	−0.819719	+	0.572766i	$0.805870\pi$
$360$	−0.441141	+	20.6032i	−0.0232502	+	1.08588i
$361$	−11.8074	+	8.57857i	−0.621441	+	0.451504i
$362$	3.15890	−	8.22921i	0.166028	−	0.432518i
$363$	−6.08849	−	6.25600i	−0.319563	−	0.328355i
$364$	0.0617606	−	0.138717i	0.00323714	−	0.00727072i
$365$	−21.6651	+	19.7333i	−1.13400	+	1.03289i
$366$	−20.9527	−	0.284332i	−1.09521	−	0.0148623i
$367$	2.32423	+	3.57899i	0.121324	+	0.186822i	0.894114	−	0.447839i	$-0.147806\pi$
$367$	2.32423	+	3.57899i	0.121324	+	0.186822i	−0.772790	+	0.634661i	$0.781140\pi$
$368$	−8.26842	−	8.26842i	−0.431021	−	0.431021i
$369$	−3.75297	+	6.11112i	−0.195372	+	0.318132i
$370$	17.3426	−	6.77148i	0.901599	−	0.352033i
$371$	−23.7334	+	21.3697i	−1.23218	+	1.10946i
$372$	−0.134899	−	3.47588i	−0.00699417	−	0.180216i
$373$	−1.66350	+	0.638559i	−0.0861330	+	0.0330633i	−0.401053	−	0.916055i	$-0.631356\pi$
$373$	−1.66350	+	0.638559i	−0.0861330	+	0.0330633i	0.314920	+	0.949118i	$0.398022\pi$
$374$	−7.75698	−	13.4355i	−0.401104	−	0.694732i
$375$	−19.2514	+	2.09394i	−0.994137	+	0.108131i
$376$	−14.3558	+	24.8651i	−0.740346	+	1.28232i
$377$	0.0668201	−	0.421885i	0.00344141	−	0.0217282i
$378$	13.8426	+	4.32009i	0.711989	+	0.222202i
$379$	20.1539	+	6.54841i	1.03524	+	0.336369i	0.776859	−	0.629674i	$-0.216812\pi$
$379$	20.1539	+	6.54841i	1.03524	+	0.336369i	0.258379	+	0.966044i	$0.416812\pi$
$380$	0.545013	−	3.57350i	0.0279586	−	0.183317i
$381$	6.96725	+	16.2382i	0.356943	+	0.831906i
$382$	4.80267	−	17.9238i	0.245726	−	0.917062i
$383$	24.5165	−	1.28485i	1.25273	−	0.0656530i	0.585606	−	0.810596i	$-0.300857\pi$
$383$	24.5165	−	1.28485i	1.25273	−	0.0656530i	0.667128	+	0.744943i	$0.267523\pi$
$384$	1.51326	−	0.846512i	0.0772231	−	0.0431984i
$385$	−13.0893	−	4.17021i	−0.667095	−	0.212534i
$386$	7.22525	+	9.94471i	0.367756	+	0.506172i
$387$	−7.08124	−	1.31945i	−0.359960	−	0.0670716i
$388$	14.6681	−	2.32319i	0.744658	−	0.117942i
$389$	−3.09234	−	29.4217i	−0.156788	−	1.49174i	−0.736234	−	0.676727i	$-0.763398\pi$
$389$	−3.09234	−	29.4217i	−0.156788	−	1.49174i	0.579446	−	0.815011i	$-0.303269\pi$
$390$	0.334332	+	0.0377917i	0.0169296	+	0.00191366i
$391$	−3.75298	+	35.7072i	−0.189796	+	1.80579i
$392$	0.107235	+	2.04616i	0.00541616	+	0.103347i
$393$	−2.19453	+	12.7348i	−0.110700	+	0.642388i
$394$	−3.42794	+	16.1272i	−0.172697	+	0.812477i
$395$	−16.6690	+	0.969406i	−0.838711	+	0.0487761i
$396$	5.59205	+	0.741662i	0.281011	+	0.0372699i
$397$	19.3203	−	9.84417i	0.969656	−	0.494065i	0.103931	−	0.994584i	$-0.466858\pi$
$397$	19.3203	−	9.84417i	0.969656	−	0.494065i	0.865725	+	0.500520i	$0.166858\pi$
$398$	1.63192	−	2.01525i	0.0818007	−	0.101015i
$399$	−8.30636	−	3.83411i	−0.415838	−	0.191946i
$400$	5.57112	+	7.48604i	0.278556	+	0.374302i
$401$	26.7982	−	15.4719i	1.33824	−	0.772631i	0.351691	−	0.936116i	$-0.385607\pi$
$401$	26.7982	−	15.4719i	1.33824	−	0.772631i	0.986546	+	0.163485i	$0.0522736\pi$
$402$	−0.613200	+	9.28740i	−0.0305836	+	0.463213i
$403$	−0.203984	−	0.0106903i	−0.0101612	−	0.000532524i
$404$	1.88431	−	5.79930i	0.0937478	−	0.288526i
$405$	−0.0767374	−	20.1245i	−0.00381311	−	0.999993i
$406$	−4.70218	−	14.4718i	−0.233365	−	0.718225i
$407$	−4.74399	−	17.7048i	−0.235151	−	0.877595i
$408$	−28.3153	−	11.3124i	−1.40182	−	0.560047i
$409$	−14.1544	−	1.48768i	−0.699889	−	0.0735613i	−0.252101	−	0.967701i	$-0.581121\pi$
$409$	−14.1544	−	1.48768i	−0.699889	−	0.0735613i	−0.447788	+	0.894140i	$0.647788\pi$
$410$	0.653390	+	5.89160i	0.0322686	+	0.290965i
$411$	−14.6789	+	2.91250i	−0.724057	+	0.143663i
$412$	7.03163	+	2.69919i	0.346423	+	0.132979i
$413$	3.84309	+	24.2643i	0.189106	+	1.19397i
$414$	15.1062	+	14.3628i	0.742427	+	0.705891i
$415$	0.296699	−	2.98750i	0.0145644	−	0.146651i
$416$	0.129825	+	0.291591i	0.00636519	+	0.0142964i
$417$	−21.3991	+	3.09225i	−1.04792	+	0.151428i
$418$	5.48862	+	1.47067i	0.268457	+	0.0719329i
$419$	−8.17059	+	9.07436i	−0.399159	+	0.443312i	−0.908898	−	0.417018i	$-0.863075\pi$
$419$	−8.17059	+	9.07436i	−0.399159	+	0.443312i	0.509739	+	0.860329i	$0.329742\pi$
$420$	−7.02928	+	2.63526i	−0.342994	+	0.128587i
$421$	−16.8057	−	18.6647i	−0.819061	−	0.909660i	0.178172	−	0.983999i	$-0.442982\pi$
$421$	−16.8057	−	18.6647i	−0.819061	−	0.909660i	−0.997233	+	0.0743397i	$0.976315\pi$
$422$	11.1718	+	21.9259i	0.543835	+	1.06734i
$423$	13.4024	−	24.6277i	0.651645	−	1.19744i
$424$		−	38.9860i		−	1.89333i
$425$	7.09806	−	27.7591i	0.344307	−	1.34652i
$426$	4.67935	−	10.1375i	0.226715	−	0.491164i
$427$	−9.83876	−	25.6308i	−0.476131	−	1.24036i
$428$	−7.36218	−	4.78106i	−0.355864	−	0.231101i
$429$	0.0732611	−	0.323048i	0.00353708	−	0.0155969i
$430$	−5.28934	+	2.73335i	−0.255074	+	0.131814i
$431$	17.4861	−	5.68157i	0.842275	−	0.273672i	0.144068	−	0.989568i	$-0.453982\pi$
$431$	17.4861	−	5.68157i	0.842275	−	0.273672i	0.698207	+	0.715896i	$0.253982\pi$
$432$	−8.34135	+	4.94635i	−0.401323	+	0.237981i
$433$	−28.8691	−	14.7095i	−1.38736	−	0.706895i	−0.408755	−	0.912644i	$-0.634037\pi$
$433$	−28.8691	−	14.7095i	−1.38736	−	0.706895i	−0.978605	+	0.205749i	$0.934037\pi$
$434$	−6.64759	+	2.95970i	−0.319094	+	0.142070i
$435$	−17.1812	+	12.2783i	−0.823777	+	0.588699i
$436$	0.0393530	+	0.0175211i	0.00188467	+	0.000839107i
$437$	−8.27582	−	10.2198i	−0.395886	−	0.488878i
$438$	−24.2243	−	6.84450i	−1.15748	−	0.327043i
$439$	−13.7845	+	1.44881i	−0.657899	+	0.0691479i	−0.427594	−	0.903971i	$-0.640639\pi$
$439$	−13.7845	+	1.44881i	−0.657899	+	0.0691479i	−0.230304	+	0.973119i	$0.573972\pi$
$440$	14.4750	−	8.46809i	0.690066	−	0.403700i
$441$	−0.155077	−	1.99489i	−0.00738462	−	0.0949949i
$442$	−0.226009	+	0.443567i	−0.0107501	+	0.0210984i
$443$	−33.0995	+	8.86899i	−1.57261	+	0.421379i	−0.936627	−	0.350327i	$-0.886070\pi$
$443$	−33.0995	+	8.86899i	−1.57261	+	0.421379i	−0.635979	+	0.771706i	$0.719404\pi$
$444$	−8.02267	−	5.99680i	−0.380739	−	0.284596i
$445$	−18.2421	−	0.851230i	−0.864758	−	0.0403522i
$446$	−5.39214	−	25.3680i	−0.255325	−	1.20121i
$447$	−9.30182	+	17.6593i	−0.439961	+	0.835256i
$448$	16.1367	+	13.0672i	0.762387	+	0.617369i
$449$	−27.6968			−1.30709			−0.653546	−	0.756887i	$-0.726719\pi$
$449$	−27.6968			−1.30709			−0.653546	+	0.756887i	$0.726719\pi$
$450$	−10.2644	−	13.0898i	−0.483867	−	0.617059i
$451$	5.83592			0.274803
$452$	6.22744	+	5.04288i	0.292914	+	0.237197i
$453$	17.7142	−	0.687486i	0.832284	−	0.0323009i
$454$	−1.39254	−	6.55138i	−0.0653551	−	0.307472i
$455$	0.116532	+	0.425144i	0.00546313	+	0.0199311i
$456$	10.2632	−	4.40357i	0.480616	−	0.206216i
$457$	−24.4276	+	6.54536i	−1.14268	+	0.306179i	−0.780026	−	0.625747i	$-0.784794\pi$
$457$	−24.4276	+	6.54536i	−1.14268	+	0.306179i	−0.362649	+	0.931926i	$0.618128\pi$
$458$	4.36126	−	8.55945i	0.203788	−	0.399957i
$459$	27.9210	+	10.3463i	1.30324	+	0.482922i
$460$	−10.7380	−	1.06643i	−0.500661	−	0.0497224i
$461$	25.0844	−	2.63648i	1.16830	−	0.122793i	0.499551	−	0.866284i	$-0.333498\pi$
$461$	25.0844	−	2.63648i	1.16830	−	0.122793i	0.668745	+	0.743492i	$0.266832\pi$
$462$	−2.89924	−	11.4388i	−0.134885	−	0.532181i
$463$	8.31244	+	10.2650i	0.386312	+	0.477055i	0.932791	−	0.360417i	$-0.117366\pi$
$463$	8.31244	+	10.2650i	0.386312	+	0.477055i	−0.546479	+	0.837472i	$0.684032\pi$
$464$	9.29636	+	4.13901i	0.431573	+	0.192149i
$465$	6.69824	+	7.55744i	0.310623	+	0.350468i
$466$	23.3367	−	10.3902i	1.08105	−	0.481315i
$467$	26.1256	+	13.3117i	1.20895	+	0.615990i	0.938011	−	0.346606i	$-0.112666\pi$
$467$	26.1256	+	13.3117i	1.20895	+	0.615990i	0.270938	+	0.962597i	$0.412666\pi$
$468$	−0.0777721	−	0.163456i	−0.00359502	−	0.00755575i
$469$	−11.5978	+	3.76836i	−0.535538	+	0.174007i
$470$	−3.75656	−	22.8690i	−0.173277	−	1.05487i
$471$	11.7152	−	3.63152i	0.539809	−	0.167331i
$472$	−25.1514	−	16.3335i	−1.15769	−	0.751811i
$473$	2.10062	+	5.47231i	0.0965868	+	0.251617i
$474$	−8.27224	−	11.7169i	−0.379957	−	0.538174i
$475$	5.35100	+	9.02765i	0.245521	+	0.414217i
$476$		−	11.1074i		−	0.509105i
$477$	0.960109	+	38.0596i	0.0439604	+	1.74263i
$478$	−2.35911	−	4.63002i	−0.107903	−	0.211772i
$479$	−12.3413	−	13.7064i	−0.563888	−	0.626261i	0.392009	−	0.919961i	$-0.371780\pi$
$479$	−12.3413	−	13.7064i	−0.563888	−	0.626261i	−0.955898	+	0.293700i	$0.905113\pi$
$480$	5.77044	−	14.6873i	0.263383	−	0.670382i
$481$	−0.393564	+	0.437097i	−0.0179450	+	0.0199299i
$482$	11.4000	+	3.05461i	0.519254	+	0.139134i
$483$	−10.1320	+	25.3608i	−0.461023	+	1.15396i
$484$	1.57894	+	3.54637i	0.0717702	+	0.161198i
$485$	−28.6651	+	32.2050i	−1.30161	+	1.46235i
$486$	14.6421	−	9.18946i	0.664177	−	0.416842i
$487$	−1.29525	−	8.17789i	−0.0586934	−	0.370576i	−0.999500	−	0.0316307i	$-0.989930\pi$
$487$	−1.29525	−	8.17789i	−0.0586934	−	0.370576i	0.940806	−	0.338945i	$-0.110070\pi$
$488$	31.2885	+	12.0105i	1.41636	+	0.543692i
$489$	−23.2522	−	26.5397i	−1.05150	−	1.20017i
$490$	−1.11369	−	1.22271i	−0.0503114	−	0.0552365i
$491$	−7.15961	−	0.752505i	−0.323109	−	0.0339601i	−0.0584142	−	0.998292i	$-0.518604\pi$
$491$	−7.15961	−	0.752505i	−0.323109	−	0.0339601i	−0.264694	+	0.964332i	$0.585271\pi$
$492$	2.50539	−	1.97314i	0.112952	−	0.0889561i
$493$	−8.08692	−	30.1808i	−0.364217	−	1.35927i
$494$	−0.0563454	−	0.173413i	−0.00253510	−	0.00780223i
$495$	−13.9224	+	8.62334i	−0.625767	+	0.387590i
$496$	1.50377	−	4.62813i	0.0675213	−	0.207809i
$497$	14.6086	+	0.765605i	0.655286	+	0.0343421i
$498$	2.31346	−	1.13949i	0.103669	−	0.0510619i
$499$	−10.2532	+	5.91969i	−0.458996	+	0.265002i	−0.711622	−	0.702562i	$-0.752039\pi$
$499$	−10.2532	+	5.91969i	−0.458996	+	0.265002i	0.252626	+	0.967564i	$0.418706\pi$
$500$	8.35501	+	2.08545i	0.373647	+	0.0932643i
$501$	11.5258	−	8.13735i	0.514935	−	0.363550i
$502$	−10.2045	+	12.6015i	−0.455449	+	0.562432i
$503$	−20.6249	+	10.5089i	−0.919621	+	0.468570i	−0.848678	−	0.528910i	$-0.822601\pi$
$503$	−20.6249	+	10.5089i	−0.919621	+	0.468570i	−0.0709429	+	0.997480i	$0.522601\pi$
$504$	−18.3866	−	14.1366i	−0.819005	−	0.629693i
$505$	6.43867	+	16.4902i	0.286517	+	0.733806i
$506$	3.52667	−	16.5917i	0.156780	−	0.737591i
$507$	21.1187	−	7.77960i	0.937914	−	0.345504i
$508$	−0.411231	−	7.84676i	−0.0182454	−	0.348144i
$509$	2.65175	−	25.2297i	0.117537	−	1.11829i	−0.763686	−	0.645588i	$-0.776612\pi$
$509$	2.65175	−	25.2297i	0.117537	−	1.11829i	0.881223	−	0.472701i	$-0.156721\pi$
$510$	23.4664	−	7.42183i	1.03911	−	0.328644i
$511$	−3.44743	−	32.8002i	−0.152506	−	1.45099i
$512$	−18.8362	+	2.98336i	−0.832450	+	0.131847i
$513$	−9.91082	+	4.55168i	−0.437574	+	0.200962i
$514$	12.1238	+	16.6870i	0.534758	+	0.736031i
$515$	−20.7569	+	6.87609i	−0.914659	+	0.302997i
$516$	2.75201	+	1.63906i	0.121151	+	0.0721557i
$517$	−22.7853	+	1.19413i	−1.00210	+	0.0525177i
$518$	−5.42304	+	20.2391i	−0.238275	+	0.889254i
$519$	37.4454	+	4.45016i	1.64367	+	0.195340i
$520$	−0.480872	−	0.241555i	−0.0210876	−	0.0105929i
$521$	−4.24963	−	1.38079i	−0.186179	−	0.0604934i	0.214443	−	0.976736i	$-0.431206\pi$
$521$	−4.24963	−	1.38079i	−0.186179	−	0.0604934i	−0.400623	+	0.916243i	$0.631206\pi$
$522$	−16.7523	−	6.95787i	−0.733230	−	0.304538i
$523$	−6.97403	+	44.0323i	−0.304953	+	1.92540i	0.0682899	+	0.997666i	$0.478246\pi$
$523$	−6.97403	+	44.0323i	−0.304953	+	1.92540i	−0.373243	+	0.927734i	$0.621754\pi$
$524$	2.87325	−	4.97662i	0.125519	−	0.217404i
$525$	10.9367	−	18.8511i	0.477319	−	0.822730i
$526$	−9.84803	−	17.0573i	−0.429395	−	0.743733i
$527$	−13.9494	+	5.35467i	−0.607645	+	0.233253i
$528$	6.98221	+	3.67779i	0.303862	+	0.160055i
$529$	−12.0805	+	10.8774i	−0.525241	+	0.472929i
$530$	19.9437	+	24.3419i	0.866301	+	1.05734i
$531$	24.9560	+	15.3260i	1.08300	+	0.665090i
$532$	2.87669	+	2.87669i	0.124720	+	0.124720i
$533$	−0.101994	−	0.157057i	−0.00441785	−	0.00680290i
$534$	−7.65837	−	13.6904i	−0.331410	−	0.592441i
$535$	25.3297	−	2.80911i	1.09510	−	0.121448i
$536$	6.05488	−	13.5995i	0.261531	−	0.587409i
$537$	16.4678	−	4.17388i	0.710636	−	0.180116i
$538$	2.71279	−	7.06707i	0.116957	−	0.304683i
$539$	−1.31730	+	0.957074i	−0.0567401	+	0.0412241i
$540$	−3.06139	+	8.40925i	−0.131741	+	0.361877i
$541$	21.4770	+	15.6039i	0.923368	+	0.670866i	0.944360	−	0.328914i	$-0.106682\pi$
$541$	21.4770	+	15.6039i	0.923368	+	0.670866i	−0.0209921	+	0.999780i	$0.506682\pi$
$542$	24.1929	−	15.7110i	1.03917	−	0.674847i
$543$	8.80853	−	10.5808i	0.378010	−	0.454065i
$544$	17.3512	+	15.6231i	0.743928	+	0.669836i
$545$	−0.120611	+	0.0330595i	−0.00516639	+	0.00141611i
$546$	−0.257172	+	0.277940i	−0.0110059	+	0.0118947i
$547$	0.354658	−	6.76728i	0.0151641	−	0.289348i	−0.980512	−	0.196458i	$-0.937056\pi$
$547$	0.354658	−	6.76728i	0.0151641	−	0.289348i	0.995676	−	0.0928902i	$-0.0296106\pi$
$548$	6.57285	+	1.04104i	0.280778	+	0.0444709i
$549$	−30.8408	−	10.9546i	−1.31625	−	0.467530i
$550$	−4.70586	+	12.6921i	−0.200658	+	0.541193i
$551$	9.91094	+	5.72208i	0.422220	+	0.243769i
$552$	−14.7307	−	29.9071i	−0.626982	−	1.27293i
$553$	10.2347	−	15.7600i	0.435222	−	0.670183i
$554$	−13.9624	+	2.96781i	−0.593207	+	0.126090i
$555$	29.0498	−	1.29419i	1.23309	−	0.0549352i
$556$	9.40467	+	1.99902i	0.398847	+	0.0847775i
$557$	4.04978	−	4.04978i	0.171595	−	0.171595i	−0.616085	−	0.787680i	$-0.711282\pi$
$557$	4.04978	−	4.04978i	0.171595	−	0.171595i	0.787680	+	0.616085i	$0.211282\pi$
$558$	−2.47169	+	8.31501i	−0.104635	+	0.352002i
$559$	0.110559	−	0.152171i	0.00467615	−	0.00643617i
$560$	−10.5019	+	0.0601844i	−0.443787	+	0.00254325i
$561$	−4.71582	−	23.7676i	−0.199102	−	1.00347i
$562$	2.57504	−	2.08523i	0.108622	−	0.0879601i
$563$	4.23752	−	3.43148i	0.178590	−	0.144620i	−0.535857	−	0.844309i	$-0.680011\pi$
$563$	4.23752	−	3.43148i	0.178590	−	0.144620i	0.714448	+	0.699689i	$0.246678\pi$
$564$	−9.37811	+	8.21643i	−0.394890	+	0.345974i
$565$	−23.2632	+	0.133317i	−0.978688	+	0.00560867i
$566$	4.65377	−	6.40537i	0.195613	−	0.269238i
$567$	18.2978	+	13.3478i	0.768437	+	0.560556i
$568$	−12.6273	+	12.6273i	−0.529831	+	0.529831i
$569$	−38.1019	−	8.09881i	−1.59731	−	0.339520i	−0.678620	−	0.734489i	$-0.737422\pi$
$569$	−38.1019	−	8.09881i	−1.59731	−	0.339520i	−0.918694	+	0.394970i	$0.870755\pi$
$570$	−4.15536	+	7.99972i	−0.174049	+	0.335071i
$571$	−15.4090	+	3.27529i	−0.644848	+	0.137067i	−0.518716	−	0.854947i	$-0.673590\pi$
$571$	−15.4090	+	3.27529i	−0.644848	+	0.137067i	−0.126132	+	0.992013i	$0.540256\pi$
$572$	−0.0802272	+	0.123539i	−0.00335447	+	0.00516542i
$573$	16.1133	−	24.0902i	0.673143	−	1.00638i
$574$	−5.77749	−	3.33564i	−0.241148	−	0.139227i
$575$	26.0760	−	17.3621i	1.08744	−	0.724048i
$576$	24.3428	−	4.48753i	1.01428	−	0.186981i
$577$	−11.6182	−	1.84015i	−0.483673	−	0.0766063i	−0.0901640	−	0.995927i	$-0.528739\pi$
$577$	−11.6182	−	1.84015i	−0.483673	−	0.0766063i	−0.393509	+	0.919321i	$0.628739\pi$
$578$	−0.919213	+	17.5396i	−0.0382342	+	0.729553i
$579$	5.68455	+	18.3383i	0.236242	+	0.762113i
$580$	9.05666	−	2.48244i	0.376057	−	0.103078i
$581$	2.51092	+	2.26085i	0.104171	+	0.0937957i
$582$	−36.4969	−	6.28934i	−1.51285	−	0.260701i
$583$	25.9832	−	16.8737i	1.07611	−	0.698837i
$584$	32.5718	+	23.6648i	1.34783	+	0.979255i
$585$	0.475394	+	0.223973i	0.0196551	+	0.00926014i
$586$	−2.73987	+	1.99063i	−0.113183	+	0.0822323i
$587$	−1.57637	+	4.10658i	−0.0650636	+	0.169497i	−0.962258	−	0.272140i	$-0.912269\pi$
$587$	−1.57637	+	4.10658i	−0.0650636	+	0.169497i	0.897194	+	0.441637i	$0.145602\pi$
$588$	−0.241933	+	0.856259i	−0.00997715	+	0.0353115i
$589$	2.22594	−	4.99955i	0.0917184	−	0.206003i
$590$	24.0595	−	2.66824i	0.990514	−	0.109850i
$591$	−13.1772	+	22.1247i	−0.542036	+	0.910087i
$592$	−7.63170	−	11.7518i	−0.313661	−	0.482995i
$593$	13.2498	+	13.2498i	0.544103	+	0.544103i	0.924729	−	0.380626i	$-0.124292\pi$
$593$	13.2498	+	13.2498i	0.544103	+	0.544103i	−0.380626	+	0.924729i	$0.624292\pi$
$594$	−12.6078	−	6.24001i	−0.517302	−	0.256031i
$595$	20.4365	+	24.9434i	0.837816	+	1.02258i
$596$	6.59591	−	5.93898i	0.270179	−	0.243270i
$597$	3.42638	−	2.15959i	0.140233	−	0.0883862i
$598$	−0.508153	+	0.195062i	−0.0207799	+	0.00797666i
$599$	8.89838	+	15.4124i	0.363578	+	0.629735i	0.988547	−	0.150914i	$-0.0482217\pi$
$599$	8.89838	+	15.4124i	0.363578	+	0.629735i	−0.624969	+	0.780650i	$0.714888\pi$
$600$	8.16795	+	25.3199i	0.333455	+	1.03368i
$601$	13.7336	−	23.7874i	0.560207	−	0.970307i	−0.437271	−	0.899330i	$-0.644055\pi$
$601$	13.7336	−	23.7874i	0.560207	−	0.970307i	0.997478	−	0.0709770i	$-0.0226117\pi$
$602$	1.04822	−	6.61817i	0.0427221	−	0.269737i
$603$	−5.57609	+	13.4254i	−0.227076	+	0.546726i
$604$	−7.49737	−	2.43604i	−0.305064	−	0.0991212i
$605$	−10.0708	−	5.05883i	−0.409435	−	0.205671i
$606$	−9.10423	+	12.1799i	−0.369834	+	0.494773i
$607$	3.64809	−	13.6149i	0.148071	−	0.552610i	−0.851528	−	0.524309i	$-0.824324\pi$
$607$	3.64809	−	13.6149i	0.148071	−	0.552610i	0.999599	−	0.0283011i	$-0.00900971\pi$
$608$	−8.54001	+	0.447563i	−0.346343	+	0.0181511i
$609$	0.322486	−	23.7643i	0.0130678	−	0.962977i
$610$	−25.6799	+	8.50692i	−1.03975	+	0.344435i
$611$	0.430354	+	0.592332i	0.0174103	+	0.0239632i
$612$	−10.0604	−	8.60910i	−0.406668	−	0.348002i
$613$	−27.0483	+	4.28402i	−1.09247	+	0.173030i	−0.676568	−	0.736380i	$-0.736534\pi$
$613$	−27.0483	+	4.28402i	−1.09247	+	0.173030i	−0.415901	+	0.909410i	$0.636534\pi$
$614$	3.20436	+	30.4875i	0.129318	+	1.23037i
$615$	−1.99585	+	9.04070i	−0.0804806	+	0.364556i
$616$	−1.97282	+	18.7702i	−0.0794874	+	0.756272i
$617$	0.575624	+	10.9836i	0.0231738	+	0.442182i	0.985435	+	0.170054i	$0.0543941\pi$
$617$	0.575624	+	10.9836i	0.0231738	+	0.442182i	−0.962261	+	0.272128i	$0.912273\pi$
$618$	−14.4353	−	12.0174i	−0.580673	−	0.483412i
$619$	−1.02089	+	4.80292i	−0.0410331	+	0.193046i	−0.993890	−	0.110374i	$-0.964795\pi$
$619$	−1.02089	+	4.80292i	−0.0410331	+	0.193046i	0.952857	+	0.303420i	$0.0981285\pi$
$620$	−1.63333	−	4.18315i	−0.0655960	−	0.168000i
$621$	15.1172	+	28.8337i	0.606633	+	1.15706i
$622$	−10.9259	+	5.56702i	−0.438088	+	0.223217i
$623$	12.9342	−	15.9724i	0.518197	−	0.639921i
$624$	−0.0230504	−	0.252183i	−0.000922755	−	0.0100954i
$625$	−22.5996	+	10.6892i	−0.903983	+	0.427569i
$626$	−5.20976	+	3.00786i	−0.208224	+	0.120218i
$627$	7.37690	+	4.93421i	0.294605	+	0.197053i
$628$	−5.44670	−	0.285449i	−0.217347	−	0.0113907i
$629$	−13.2953	+	40.9188i	−0.530119	+	1.63154i
$630$	18.7119	−	0.579353i	0.745499	−	0.0230820i
$631$	−2.72168	−	8.37647i	−0.108348	−	0.333462i	0.882153	−	0.470962i	$-0.156093\pi$
$631$	−2.72168	−	8.37647i	−0.108348	−	0.333462i	−0.990502	+	0.137500i	$0.956093\pi$
$632$	5.93722	+	22.1580i	0.236170	+	0.881398i
$633$	5.49686	+	38.0396i	0.218481	+	1.51194i
$634$	−4.54079	−	0.477256i	−0.180338	−	0.0189543i
$635$	15.3608	+	16.8645i	0.609575	+	0.669249i
$636$	5.44966	−	16.0289i	0.216093	−	0.635589i
$637$	0.0487792	+	0.0187246i	0.00193270	+	0.000741895i
$638$	2.30921	+	14.5798i	0.0914226	+	0.577220i
$639$	12.0163	−	12.6382i	0.475357	−	0.499961i
$640$	1.48829	−	1.67209i	0.0588299	−	0.0660950i
$641$	−13.5150	−	30.3552i	−0.533811	−	1.19896i	−0.956245	−	0.292566i	$-0.905491\pi$
$641$	−13.5150	−	30.3552i	−0.533811	−	1.19896i	0.422434	−	0.906394i	$-0.361176\pi$
$642$	13.5446	+	17.1982i	0.534562	+	0.678758i
$643$	21.8724	+	5.86068i	0.862562	+	0.231123i	0.662869	−	0.748736i	$-0.269339\pi$
$643$	21.8724	+	5.86068i	0.862562	+	0.231123i	0.199693	+	0.979858i	$0.436005\pi$
$644$	8.12616	−	9.02502i	0.320216	−	0.355635i
$645$	−9.19581	+	1.38267i	−0.362085	+	0.0544427i
$646$	−8.92482	−	9.91201i	−0.351142	−	0.389983i
$647$	−2.77041	−	5.43724i	−0.108916	−	0.213760i	0.830115	−	0.557592i	$-0.188275\pi$
$647$	−2.77041	−	5.43724i	−0.108916	−	0.213760i	−0.939031	+	0.343832i	$0.888275\pi$
$648$	−27.0552	+	5.69656i	−1.06283	+	0.223782i
$649$		−	23.8321i		−	0.935493i
$650$	0.423815	−	0.0951743i	0.0166234	−	0.00373304i
$651$	−11.3181	+	1.03452i	−0.443592	+	0.0405460i
$652$	5.62306	+	14.6486i	0.220216	+	0.573683i
$653$	24.0662	+	15.6288i	0.941783	+	0.611601i	0.921577	−	0.388195i	$-0.126901\pi$
$653$	24.0662	+	15.6288i	0.941783	+	0.611601i	0.0202058	+	0.999796i	$0.493568\pi$
$654$	−0.0788497	−	0.0729580i	−0.00308327	−	0.00285288i
$655$	2.70417	+	16.4623i	0.105661	+	0.643236i
$656$	4.24307	−	1.37866i	0.165664	−	0.0538276i
$657$	−32.3806	−	22.3003i	−1.26329	−	0.870017i
$658$	23.2397	+	11.8412i	0.905978	+	0.461619i
$659$	−26.3915	+	11.7503i	−1.02807	+	0.457725i	−0.850273	−	0.526342i	$-0.823563\pi$
$659$	−26.3915	+	11.7503i	−1.02807	+	0.457725i	−0.177795	+	0.984068i	$0.556896\pi$
$660$	7.13503	−	1.45824i	0.277731	−	0.0567618i
$661$	−43.8555	−	19.5257i	−1.70578	−	0.759463i	−0.998626	−	0.0524044i	$-0.983312\pi$
$661$	−43.8555	−	19.5257i	−1.70578	−	0.759463i	−0.707155	−	0.707058i	$-0.750022\pi$
$662$	9.84351	+	12.1557i	0.382579	+	0.472446i
$663$	−0.557218	+	0.542297i	−0.0216405	+	0.0210611i
$664$	−4.10201	+	0.431138i	−0.159189	+	0.0167314i
$665$	−11.7529	−	1.16722i	−0.455759	−	0.0452630i
$666$	14.1281	+	20.5988i	0.547453	+	0.798187i
$667$	15.5095	−	30.4391i	0.600530	−	1.17861i
$668$	−6.06026	+	1.62384i	−0.234479	+	0.0628284i
$669$	4.78036	−	40.2239i	0.184819	−	1.55514i
$670$	3.17645	+	11.5886i	0.122717	+	0.447708i
$671$	5.53738	+	26.0513i	0.213768	+	1.00570i
$672$	9.46960	+	15.0244i	0.365298	+	0.579578i
$673$	31.6057	+	25.5938i	1.21831	+	0.986568i	0.999943	+	0.0107009i	$0.00340627\pi$
$673$	31.6057	+	25.5938i	1.21831	+	0.986568i	0.218367	+	0.975867i	$0.429927\pi$
$674$	−2.97625			−0.114641
$675$	−8.59741	−	24.5170i	−0.330914	−	0.943661i
$676$	−10.0082			−0.384929
$677$	19.4307	+	15.7347i	0.746784	+	0.604733i	0.925314	−	0.379201i	$-0.123801\pi$
$677$	19.4307	+	15.7347i	0.746784	+	0.604733i	−0.178531	+	0.983934i	$0.557134\pi$
$678$	−10.6552	−	16.9054i	−0.409211	−	0.649250i
$679$	−10.0884	−	47.4621i	−0.387157	−	1.82143i
$680$	−39.3215	−	1.83486i	−1.50791	−	0.0703635i
$681$	1.23455	−	10.3880i	0.0473079	−	0.398067i
$682$	6.81855	−	1.82702i	0.261096	−	0.0699604i
$683$	15.4432	−	30.3089i	0.590916	−	1.15974i	−0.381036	−	0.924560i	$-0.624433\pi$
$683$	15.4432	−	30.3089i	0.590916	−	1.15974i	0.971952	−	0.235178i	$-0.0755674\pi$
$684$	4.83521	−	0.375875i	0.184879	−	0.0143719i
$685$	−16.6758	+	9.75563i	−0.637150	+	0.372744i
$686$	21.2793	−	2.23654i	0.812447	−	0.0853917i
$687$	10.7525	−	10.4646i	0.410235	−	0.399250i
$688$	2.82004	+	3.48246i	0.107513	+	0.132768i
$689$	−0.908213	−	0.404362i	−0.0346002	−	0.0154050i
$690$	24.4969	+	11.1376i	0.932579	+	0.424001i
$691$	−13.0977	+	5.83146i	−0.498259	+	0.221839i	−0.640450	−	0.768000i	$-0.721252\pi$
$691$	−13.0977	+	5.83146i	−0.498259	+	0.221839i	0.142191	+	0.989839i	$0.454585\pi$
$692$	−14.9410	−	7.61282i	−0.567972	−	0.289396i
$693$	1.46369	−	18.3727i	0.0556010	−	0.697922i
$694$	17.6256	−	5.72690i	0.669058	−	0.217390i
$695$	−24.7977	+	12.8146i	−0.940632	+	0.486086i
$696$	21.2952	+	19.7040i	0.807191	+	0.746878i
$697$	−11.4887	−	7.46083i	−0.435164	−	0.282599i
$698$	11.3299	+	29.5154i	0.428844	+	1.11718i
$699$	39.7328	−	3.63172i	1.50283	−	0.137364i
$700$	−7.46132	+	6.18499i	−0.282012	+	0.233771i
$701$			25.6509i			0.968822i	0.874841	+	0.484411i	$0.160966\pi$
$701$			25.6509i			0.968822i	−0.874841	+	0.484411i	$0.839034\pi$
$702$	0.0524128	+	0.448357i	0.00197820	+	0.0169222i
$703$	−7.15419	−	14.0409i	−0.269825	−	0.529562i
$704$	−13.4784	−	14.9692i	−0.507985	−	0.564175i
$705$	5.94258	−	35.7062i	0.223810	−	1.34477i
$706$	−16.3766	+	18.1880i	−0.616341	+	0.684516i
$707$	−19.2443	−	5.15651i	−0.723758	−	0.193930i
$708$	−8.05771	−	10.2312i	−0.302827	−	0.384514i
$709$	−0.990744	−	2.22525i	−0.0372082	−	0.0835710i	0.893985	−	0.448096i	$-0.147898\pi$
$709$	−0.990744	−	2.22525i	−0.0372082	−	0.0835710i	−0.931193	+	0.364525i	$0.881231\pi$
$710$	1.42454	−	14.3439i	0.0534620	−	0.538315i
$711$	−6.34182	−	21.4852i	−0.237837	−	0.805760i
$712$	3.92484	+	24.7805i	0.147090	+	0.928688i
$713$	−15.2517	−	5.85459i	−0.571182	−	0.219256i
$714$	−8.91622	+	26.2250i	−0.333681	+	0.981447i
$715$	−0.0471374	−	0.425037i	−0.00176284	−	0.0158955i
$716$	−7.51318	−	0.789668i	−0.280781	−	0.0295113i
$717$	−1.16076	−	8.03270i	−0.0433492	−	0.299987i
$718$	−3.55119	−	13.2532i	−0.132529	−	0.494606i
$719$	−2.53963	−	7.81619i	−0.0947123	−	0.291495i	0.892466	−	0.451114i	$-0.148973\pi$
$719$	−2.53963	−	7.81619i	−0.0947123	−	0.291495i	−0.987179	+	0.159620i	$0.948973\pi$
$720$	−8.08532	+	9.55868i	−0.301322	+	0.356231i
$721$	7.60460	−	23.4045i	0.283210	−	0.871631i
$722$	−16.1627	−	0.847051i	−0.601513	−	0.0315240i
$723$	15.3220	+	10.2484i	0.569830	+	0.381143i
$724$	−5.30200	+	3.06111i	−0.197047	+	0.113765i
$725$	−15.7707	+	22.2382i	−0.585711	+	0.825904i
$726$	−0.881188	−	9.64062i	−0.0327039	−	0.357797i
$727$	11.8991	−	14.6942i	0.441315	−	0.544978i	−0.507151	−	0.861857i	$-0.669301\pi$
$727$	11.8991	−	14.6942i	0.441315	−	0.544978i	0.948466	+	0.316879i	$0.102635\pi$
$728$	0.539624	−	0.274952i	0.0199998	−	0.0101904i
$729$	26.2720	−	6.22748i	0.973037	−	0.230647i
$730$	−32.4430	+	1.88676i	−1.20077	+	0.0698320i
$731$	2.86066	−	13.4584i	0.105806	−	0.497776i
$732$	11.1852	+	9.31175i	0.413419	+	0.344172i
$733$	0.539693	+	10.2980i	0.0199340	+	0.380364i	0.990320	+	0.138804i	$0.0443257\pi$
$733$	0.539693	+	10.2980i	0.0199340	+	0.380364i	−0.970386	+	0.241560i	$0.922341\pi$
$734$	−0.494672	+	4.70649i	−0.0182587	+	0.173720i
$735$	−1.03214	−	2.36800i	−0.0380710	−	0.0873451i
$736$	2.66843	+	25.3884i	0.0983595	+	0.935828i
$737$	11.6844	−	1.85062i	0.430399	−	0.0681685i
$738$	−7.49925	+	2.64753i	−0.276051	+	0.0974571i
$739$	−3.28609	−	4.52292i	−0.120881	−	0.166378i	0.744288	−	0.667859i	$-0.232789\pi$
$739$	−3.28609	−	4.52292i	−0.120881	−	0.166378i	−0.865169	+	0.501480i	$0.832789\pi$
$740$	−12.3207	−	3.92532i	−0.452918	−	0.144298i
$741$	0.00386429	−	0.284763i	0.000141958	−	0.0104610i
$742$	−35.3675	+	1.85353i	−1.29838	+	0.0680453i
$743$	6.96402	−	25.9901i	0.255485	−	0.953484i	−0.712335	−	0.701840i	$-0.752362\pi$
$743$	6.96402	−	25.9901i	0.255485	−	0.953484i	0.967820	−	0.251644i	$-0.0809712\pi$
$744$	8.30651	−	11.1127i	0.304532	−	0.407410i
$745$	−3.88499	+	25.4728i	−0.142335	+	0.933252i
$746$	−1.87928	−	0.610615i	−0.0688054	−	0.0223562i
$747$	3.99391	−	0.521913i	0.146130	−	0.0190958i
$748$	−1.68561	+	10.6425i	−0.0616321	+	0.389129i
$749$	−14.3409	+	24.8391i	−0.524003	+	0.907600i
$750$	−18.0525	−	11.6307i	−0.659185	−	0.424693i
$751$	14.9521	+	25.8979i	0.545611	+	0.945026i	0.998568	+	0.0534937i	$0.0170357\pi$
$751$	14.9521	+	25.8979i	0.545611	+	0.945026i	−0.452957	+	0.891532i	$0.649631\pi$
$752$	−16.2842	+	6.25093i	−0.593825	+	0.227948i
$753$	−21.4254	+	13.5041i	−0.780785	+	0.492115i
$754$	0.352015	−	0.316956i	0.0128196	−	0.0115429i
$755$	21.3187	−	8.32395i	0.775866	−	0.302940i
$756$	−5.58350	−	8.38237i	−0.203070	−	0.304864i
$757$	−9.07256	−	9.07256i	−0.329748	−	0.329748i	0.522743	−	0.852491i	$-0.324909\pi$
$757$	−9.07256	−	9.07256i	−0.329748	−	0.329748i	−0.852491	+	0.522743i	$0.824909\pi$
$758$	12.7990	+	19.7087i	0.464880	+	0.715853i
$759$	13.5567	−	22.7619i	0.492076	−	0.826204i
$760$	10.6591	−	9.70864i	0.386644	−	0.352169i
$761$	1.33957	−	3.00873i	0.0485595	−	0.109067i	−0.887637	−	0.460545i	$-0.847654\pi$
$761$	1.33957	−	3.00873i	0.0485595	−	0.109067i	0.936196	+	0.351478i	$0.114321\pi$
$762$	−5.32790	+	18.8567i	−0.193010	+	0.683106i
$763$	0.0504390	−	0.131398i	0.00182601	−	0.00475693i
$764$	−10.4267	+	7.57544i	−0.377225	+	0.274070i
$765$	38.4322	+	0.822883i	1.38952	+	0.0297514i
$766$	22.0255	+	16.0024i	0.795812	+	0.578191i
$767$	−0.641373	+	0.416513i	−0.0231586	+	0.0150394i
$768$	−26.2722	−	4.52736i	−0.948016	−	0.163367i
$769$	21.1156	+	19.0125i	0.761447	+	0.685610i	0.955372	−	0.295407i	$-0.0954551\pi$
$769$	21.1156	+	19.0125i	0.761447	+	0.685610i	−0.193925	+	0.981016i	$0.562122\pi$
$770$	−8.37031	−	12.7289i	−0.301645	−	0.458716i
$771$	9.53854	+	30.7712i	0.343522	+	1.10820i
$772$	0.446825	−	8.52592i	0.0160816	−	0.306855i
$773$	9.64385	+	1.52744i	0.346865	+	0.0549381i	0.327437	−	0.944873i	$-0.393815\pi$
$773$	9.64385	+	1.52744i	0.346865	+	0.0549381i	0.0194288	+	0.999811i	$0.493815\pi$
$774$	−5.18191	−	6.07903i	−0.186260	−	0.218506i
$775$	11.3645	+	6.38877i	0.408226	+	0.229492i
$776$	51.2974	+	29.6166i	1.84147	+	1.06317i
$777$	−18.1947	+	27.2020i	−0.652730	+	0.975867i
$778$	17.8680	−	27.5143i	0.640598	−	0.986434i
$779$	4.90772	−	1.04317i	0.175837	−	0.0373754i
$780$	−0.163943	−	0.166533i	−0.00587009	−	0.00596285i
$781$	−13.8811	−	2.95051i	−0.496704	−	0.105578i
$782$	−28.1540	+	28.1540i	−1.00679	+	1.00679i
$783$	−21.2744	−	18.7113i	−0.760284	−	0.668688i
$784$	−0.731661	+	1.00705i	−0.0261308	+	0.0359659i
$785$	12.7566	−	9.38040i	0.455304	−	0.334801i
$786$	−10.7788	+	9.44359i	−0.384466	+	0.336842i
$787$	1.20821	−	0.978390i	0.0430681	−	0.0348758i	−0.607545	−	0.794285i	$-0.707845\pi$
$787$	1.20821	−	0.978390i	0.0430681	−	0.0348758i	0.650613	+	0.759410i	$0.274512\pi$
$788$	8.89938	−	7.20658i	0.317027	−	0.256724i
$789$	−5.98707	−	30.1746i	−0.213145	−	1.07425i
$790$	−15.0422	−	10.7977i	−0.535179	−	0.384164i
$791$	15.3892	−	21.1814i	0.547176	−	0.753123i
$792$	15.4719	+	16.3353i	0.549768	+	0.580449i
$793$	0.604320	−	0.604320i	0.0214600	−	0.0214600i
$794$	23.5207	+	4.99948i	0.834718	+	0.177425i
$795$	17.2537	+	46.0225i	0.611925	+	1.63225i
$796$	−1.76171	+	0.374463i	−0.0624421	+	0.0132725i
$797$	6.15577	−	9.47905i	0.218049	−	0.335765i	−0.712671	−	0.701498i	$-0.752515\pi$
$797$	6.15577	−	9.47905i	0.218049	−	0.335765i	0.930720	+	0.365733i	$0.119182\pi$
$798$	−4.48280	−	9.10121i	−0.158689	−	0.322179i
$799$	46.3821	+	26.7787i	1.64088	+	0.947363i
$800$	0.832958	−	20.3552i	0.0294495	−	0.719664i
$801$	−4.44184	−	24.0950i	−0.156945	−	0.851353i
$802$	33.8928	+	5.36809i	1.19680	+	0.189554i
$803$	−1.67446	+	31.9507i	−0.0590906	+	1.12752i
$804$	4.39045	−	4.74499i	0.154839	−	0.167343i
$805$	−1.64340	+	35.2185i	−0.0579223	+	1.24129i
$806$	−0.168336	−	0.151571i	−0.00592940	−	0.00533885i
$807$	7.56457	−	9.08654i	0.266285	−	0.319861i
$808$	20.3973	−	13.2462i	0.717575	−	0.465999i
$809$	−12.7934	−	9.29496i	−0.449793	−	0.326793i	0.339721	−	0.940526i	$-0.389667\pi$
$809$	−12.7934	−	9.29496i	−0.449793	−	0.326793i	−0.789514	+	0.613733i	$0.789667\pi$
$810$	13.9785	−	17.3972i	0.491153	−	0.611275i
$811$	−28.2443	+	20.5207i	−0.991790	+	0.720577i	−0.960312	−	0.278927i	$-0.910021\pi$
$811$	−28.2443	+	20.5207i	−0.991790	+	0.720577i	−0.0314775	+	0.999504i	$0.510021\pi$
$812$	−3.78747	+	9.86669i	−0.132914	+	0.346253i
$813$	43.6740	−	11.0695i	1.53172	−	0.388225i
$814$	8.26750	−	18.5691i	0.289776	−	0.650847i
$815$	−39.5796	−	22.5498i	−1.38641	−	0.789887i
$816$	−9.04346	−	16.1664i	−0.316584	−	0.565938i
$817$	2.74469	+	4.22646i	0.0960247	+	0.147865i
$818$	−11.1603	−	11.1603i	−0.390210	−	0.390210i
$819$	−0.520029	+	0.281708i	−0.0181713	+	0.00984366i
$820$	2.22250	−	3.46568i	0.0776132	−	0.121027i
$821$	15.1514	−	13.6424i	0.528787	−	0.476122i	−0.360957	−	0.932583i	$-0.617550\pi$
$821$	15.1514	−	13.6424i	0.528787	−	0.476122i	0.889744	+	0.456461i	$0.150883\pi$
$822$	−14.6832	−	7.73417i	−0.512134	−	0.269760i
$823$	−16.8859	+	6.48188i	−0.588605	+	0.225944i	−0.634398	−	0.773007i	$-0.718752\pi$
$823$	−16.8859	+	6.48188i	−0.588605	+	0.225944i	0.0457931	+	0.998951i	$0.485418\pi$
$824$	15.0206	+	26.0164i	0.523266	+	0.906323i
$825$	−13.3398	+	16.4025i	−0.464434	+	0.571062i
$826$	−13.6217	+	23.5935i	−0.473960	+	0.820923i
$827$	2.04739	−	12.9267i	0.0711949	−	0.449507i	−0.926179	−	0.377084i	$-0.876927\pi$
$827$	2.04739	−	12.9267i	0.0711949	−	0.449507i	0.997374	−	0.0724230i	$-0.0230732\pi$
$828$	−1.87591	−	14.3553i	−0.0651925	−	0.498882i
$829$	6.38932	+	2.07602i	0.221910	+	0.0721030i	0.417862	−	0.908511i	$-0.362780\pi$
$829$	6.38932	+	2.07602i	0.221910	+	0.0721030i	−0.195952	+	0.980614i	$0.562780\pi$
$830$	2.34064	−	2.36762i	0.0812448	−	0.0821813i
$831$	−22.1390	−	2.63109i	−0.767995	−	0.0912715i
$832$	−0.167293	+	0.624348i	−0.00579986	+	0.0216454i
$833$	3.81681	−	0.200030i	0.132244	−	0.00693064i
$834$	−20.6002	−	12.2692i	−0.713327	−	0.424848i
$835$	10.6216	−	14.7969i	0.367575	−	0.512069i
$836$	−2.31975	−	3.19286i	−0.0802302	−	0.110427i
$837$	−7.83545	+	11.0531i	−0.270833	+	0.382053i
$838$	−13.3744	+	2.11830i	−0.462013	+	0.0731756i
$839$	2.80458	+	26.6838i	0.0968248	+	0.921227i	0.929837	+	0.367972i	$0.119948\pi$
$839$	2.80458	+	26.6838i	0.0968248	+	0.921227i	−0.833012	+	0.553255i	$0.813386\pi$
$840$	−28.4030	−	9.47548i	−0.979998	−	0.326935i
$841$	−0.0763138	+	0.726077i	−0.00263151	+	0.0250371i
$842$	−1.45767	−	27.8141i	−0.0502347	−	0.958536i
$843$	4.85621	−	1.78891i	0.167257	−	0.0616132i
$844$	3.55351	−	16.7180i	0.122317	−	0.575456i
$845$	22.4749	−	18.4141i	0.773162	−	0.633464i
$846$	28.7378	−	11.8713i	0.988025	−	0.408144i
$847$	11.3012	−	5.75824i	0.388314	−	0.197856i
$848$	14.9052	−	18.4064i	0.511846	−	0.632077i
$849$	10.1021	−	7.13221i	0.346704	−	0.244777i
$850$	25.4900	−	18.9697i	0.874299	−	0.650655i
$851$	−40.7391	+	23.5207i	−1.39652	+	0.806280i
$852$	−6.95679	+	3.42656i	−0.238336	+	0.117392i
$853$	30.1394	+	1.57954i	1.03195	+	0.0540824i	0.560786	−	0.827961i	$-0.310499\pi$
$853$	30.1394	+	1.57954i	1.03195	+	0.0540824i	0.471168	+	0.882043i	$0.343832\pi$
$854$	9.40821	−	28.9555i	0.321942	−	0.990836i
$855$	−10.1667	+	9.74043i	−0.347693	+	0.333116i
$856$	−10.8196	−	33.2992i	−0.369805	−	1.13814i
$857$	1.09759	+	4.09627i	0.0374931	+	0.139926i	0.982135	−	0.188176i	$-0.0602576\pi$
$857$	1.09759	+	4.09627i	0.0374931	+	0.139926i	−0.944642	+	0.328102i	$0.893591\pi$
$858$	0.288589	−	0.227281i	0.00985226	−	0.00775924i
$859$	47.2410	+	4.96523i	1.61184	+	0.169412i	0.867168	−	0.498015i	$-0.165938\pi$
$859$	47.2410	+	4.96523i	1.61184	+	0.169412i	0.744675	+	0.667427i	$0.232604\pi$
$860$	4.04973	+	0.836569i	0.138095	+	0.0285268i
$861$	−6.86644	−	7.83725i	−0.234008	−	0.267093i
$862$	19.0349	+	7.30683i	0.648332	+	0.248872i
$863$	2.64928	+	16.7269i	0.0901824	+	0.569389i	0.990859	+	0.134900i	$0.0430713\pi$
$863$	2.64928	+	16.7269i	0.0901824	+	0.569389i	−0.900677	+	0.434490i	$0.856929\pi$
$864$	20.9479	+	3.06807i	0.712663	+	0.104378i
$865$	47.5593	−	10.3943i	1.61707	−	0.353416i
$866$	−14.6143	−	32.8243i	−0.496615	−	1.11542i
$867$	−10.1775	+	25.4746i	−0.345645	+	0.865162i
$868$	4.88180	+	1.30807i	0.165699	+	0.0443990i
$869$	−12.1980	+	13.5473i	−0.413790	+	0.459560i
$870$	−23.3760	−	1.40890i	−0.792520	−	0.0477662i
$871$	−0.254011	−	0.282107i	−0.00860682	−	0.00955885i
$872$	0.0780021	+	0.153088i	0.00264148	+	0.00518421i
$873$	−50.8078	−	27.6495i	−1.71958	−	0.935794i
$874$		−	14.5832i		−	0.493284i
$875$	5.37579	−	27.6176i	0.181735	−	0.933644i
$876$	10.0838	+	14.2827i	0.340699	+	0.482568i
$877$	−14.9458	−	38.9352i	−0.504684	−	1.31475i	−0.915239	−	0.402912i	$-0.867998\pi$
$877$	−14.9458	−	38.9352i	−0.504684	−	1.31475i	0.410555	−	0.911836i	$-0.365335\pi$
$878$	−12.8909	−	8.37142i	−0.435045	−	0.282522i
$879$	−5.05239	+	1.56615i	−0.170413	+	0.0528251i
$880$	10.0716	+	1.53607i	0.339512	+	0.0517808i
$881$	−22.1224	+	7.18801i	−0.745323	+	0.242170i	−0.656968	−	0.753919i	$-0.728161\pi$
$881$	−22.1224	+	7.18801i	−0.745323	+	0.242170i	−0.0883555	+	0.996089i	$0.528161\pi$
$882$	1.25856	−	1.82746i	0.0423780	−	0.0615339i
$883$	29.2404	+	14.8987i	0.984019	+	0.501383i	0.870508	−	0.492154i	$-0.163790\pi$
$883$	29.2404	+	14.8987i	0.984019	+	0.501383i	0.113511	+	0.993537i	$0.463790\pi$
$884$	0.315872	−	0.140635i	0.0106239	−	0.00473008i
$885$	36.9195	+	8.15046i	1.24103	+	0.273975i
$886$	−34.7154	−	15.4563i	−1.16629	−	0.519264i
$887$	6.39760	+	7.90037i	0.214810	+	0.265269i	0.873149	−	0.487453i	$-0.162074\pi$
$887$	6.39760	+	7.90037i	0.214810	+	0.265269i	−0.658339	+	0.752722i	$0.728741\pi$
$888$	−9.81525	−	38.7254i	−0.329378	−	1.29954i
$889$	−25.5323	+	2.68355i	−0.856326	+	0.0900035i
$890$	−15.1273	−	13.4645i	−0.507069	−	0.451332i
$891$	−15.5065	−	15.5661i	−0.519487	−	0.521483i
$892$	−8.17770	+	16.0496i	−0.273810	+	0.537382i
$893$	−18.9479	+	5.07707i	−0.634067	+	0.169898i
$894$	−20.3407	+	8.72750i	−0.680294	+	0.291891i
$895$	18.3250	−	12.0503i	0.612537	−	0.402795i
$896$	0.523790	+	2.46424i	0.0174986	+	0.0823243i
$897$	−0.849500	+	0.0329691i	−0.0283640	+	0.00110080i
$898$	−23.8696	−	19.3292i	−0.796539	−	0.645025i
$899$	14.2172			0.474169
$900$	−0.181117	+	11.5519i	−0.00603724	+	0.385064i
$901$	−72.7227			−2.42274
$902$	5.02951	+	4.07282i	0.167464	+	0.135610i
$903$	4.87739	−	9.25962i	0.162309	−	0.308141i
$904$	6.64504	+	31.2625i	0.221011	+	1.03977i
$905$	6.27433	−	16.6294i	0.208566	−	0.552781i
$906$	15.7462	+	11.7700i	0.523132	+	0.391032i
$907$	−40.4383	+	10.8354i	−1.34273	+	0.359784i	−0.857447	−	0.514573i	$-0.827951\pi$
$907$	−40.4383	+	10.8354i	−1.34273	+	0.359784i	−0.485284	+	0.874356i	$0.661284\pi$
$908$	−2.11192	+	4.14488i	−0.0700866	+	0.137553i
$909$	−19.5864	+	13.4337i	−0.649640	+	0.445568i
$910$	−0.196273	+	0.447724i	−0.00650639	+	0.0148419i
$911$	46.1397	−	4.84947i	1.52868	−	0.160670i	0.697461	−	0.716623i	$-0.254313\pi$
$911$	46.1397	−	4.84947i	1.52868	−	0.160670i	0.831214	+	0.555953i	$0.187646\pi$
$912$	6.52910	+	1.84478i	0.216200	+	0.0610866i
$913$	−2.06275	−	2.54728i	−0.0682670	−	0.0843027i
$914$	−25.6201	−	11.4068i	−0.847437	−	0.377303i
$915$	−42.2511	−	0.331197i	−1.39678	−	0.0109490i
$916$	−6.09534	+	2.71382i	−0.201396	+	0.0896671i
$917$	−16.7292	−	8.52393i	−0.552446	−	0.281485i
$918$	16.8423	+	28.4023i	0.555880	+	0.937416i
$919$	−37.0383	+	12.0345i	−1.22178	+	0.396981i	−0.847731	−	0.530427i	$-0.822032\pi$
$919$	−37.0383	+	12.0345i	−1.22178	+	0.396981i	−0.374051	+	0.927408i	$0.622032\pi$
$920$	−30.6073	−	30.2585i	−1.00909	−	0.997594i
$921$	−10.5894	+	46.6944i	−0.348932	+	1.53863i
$922$	23.4582	+	15.2339i	0.772553	+	0.501702i
$923$	0.163194	+	0.425135i	0.00537160	+	0.0139935i
$924$	−3.43491	+	7.44150i	−0.113000	+	0.244808i
$925$	34.8904	−	13.8540i	1.14719	−	0.455518i
$926$			14.6477i			0.481354i
$927$	−15.3043	−	25.0282i	−0.502660	−	0.822035i
$928$	−10.0859	−	19.7946i	−0.331084	−	0.649790i
$929$	8.17144	+	9.07530i	0.268096	+	0.297751i	0.862128	−	0.506691i	$-0.169131\pi$
$929$	8.17144	+	9.07530i	0.268096	+	0.297751i	−0.594032	+	0.804442i	$0.702465\pi$
$930$	0.498422	+	11.1878i	0.0163439	+	0.366861i
$931$	−0.936707	+	1.04032i	−0.0306993	+	0.0340951i
$932$	−17.1378	−	4.59206i	−0.561367	−	0.150418i
$933$	−18.9555	+	2.73914i	−0.620576	+	0.0896755i
$934$	13.2255	+	29.7050i	0.432752	+	0.971976i
$935$	−15.7960	−	27.0009i	−0.516584	−	0.883024i
$936$	0.169216	−	0.701871i	0.00553100	−	0.0229414i
$937$	−7.75367	−	48.9547i	−0.253301	−	1.59928i	−0.706395	−	0.707818i	$-0.749680\pi$
$937$	−7.75367	−	48.9547i	−0.253301	−	1.59928i	0.453093	−	0.891463i	$-0.350320\pi$
$938$	−12.6251	−	4.84633i	−0.412225	−	0.158238i
$939$	−9.21615	+	1.82861i	−0.300758	+	0.0596745i
$940$	−7.96824	+	13.9859i	−0.259895	+	0.456169i
$941$	−24.2657	−	2.55043i	−0.791040	−	0.0831417i	−0.299614	−	0.954061i	$-0.596858\pi$
$941$	−24.2657	−	2.55043i	−0.791040	−	0.0831417i	−0.491427	+	0.870919i	$0.663524\pi$
$942$	12.6308	+	5.04619i	0.411533	+	0.164414i
$943$	−3.87649	−	14.4673i	−0.126236	−	0.471119i
$944$	−5.63002	−	17.3274i	−0.183242	−	0.563959i
$945$	27.9614	+	8.55084i	0.909586	+	0.278159i
$946$	−2.00870	+	6.18214i	−0.0653085	+	0.200999i
$947$	37.0928	+	1.94395i	1.20536	+	0.0631700i	0.644408	−	0.764682i	$-0.277104\pi$
$947$	37.0928	+	1.94395i	1.20536	+	0.0631700i	0.560947	+	0.827852i	$0.310437\pi$
$948$	−0.656295	+	9.94011i	−0.0213155	+	0.322840i
$949$	0.889125	−	0.513337i	0.0288622	−	0.0166636i
$950$	−1.68869	+	11.5146i	−0.0547882	+	0.373583i
$951$	−6.47474	−	2.98866i	−0.209958	−	0.0969140i
$952$	27.8801	−	34.4291i	0.903599	−	1.11585i
$953$	−8.86706	+	4.51799i	−0.287232	+	0.146352i	−0.591670	−	0.806180i	$-0.701531\pi$
$953$	−8.86706	+	4.51799i	−0.287232	+	0.146352i	0.304438	+	0.952532i	$0.401531\pi$
$954$	−25.7339	+	33.4705i	−0.833164	+	1.08365i
$955$	9.47672	−	36.1961i	0.306660	−	1.17128i
$956$	−0.750384	+	3.53028i	−0.0242692	+	0.114177i
$957$	−3.91537	+	22.7208i	−0.126566	+	0.734460i
$958$	−1.07044	−	20.4253i	−0.0345844	−	0.659910i
$959$	2.27278	−	21.6241i	0.0733920	−	0.698279i
$960$	27.7991	−	15.7606i	0.897211	−	0.508670i
$961$	2.52972	+	24.0687i	0.0816038	+	0.776409i
$962$	−0.644225	+	0.102035i	−0.0207706	+	0.00328975i
$963$	11.3825	+	32.2414i	0.366796	+	1.03897i
$964$	−4.81816	−	6.63163i	−0.155182	−	0.213590i
$965$	14.6835	+	19.9685i	0.472679	+	0.642807i
$966$	−26.4309	+	14.7854i	−0.850401	+	0.475712i
$967$	38.9070	−	2.03903i	1.25117	−	0.0655708i	0.584789	−	0.811186i	$-0.301177\pi$
$967$	38.9070	−	2.03903i	1.25117	−	0.0655708i	0.666377	+	0.745615i	$0.267844\pi$
$968$	−4.00739	+	14.9558i	−0.128802	+	0.480697i
$969$	−8.21422	−	19.1444i	−0.263879	−	0.615007i
$970$	−47.1796	+	7.74992i	−1.51484	+	0.248835i
$971$	0.613375	+	0.199297i	0.0196841	+	0.00639576i	0.318843	−	0.947808i	$-0.396706\pi$
$971$	0.613375	+	0.199297i	0.0196841	+	0.00639576i	−0.299158	+	0.954203i	$0.596706\pi$
$972$	−11.9199	−	1.43980i	−0.382332	−	0.0461815i
$973$	4.91430	−	31.0276i	0.157545	−	0.994701i
$974$	4.59097	−	7.95180i	0.147104	−	0.254792i
$975$	0.674566	+	0.0723377i	0.0216034	+	0.00231666i
$976$	10.1803	+	17.6328i	0.325863	+	0.564411i
$977$	21.4230	−	8.22352i	0.685383	−	0.263094i	0.00934010	−	0.999956i	$-0.497027\pi$
$977$	21.4230	−	8.22352i	0.685383	−	0.263094i	0.676042	+	0.736863i	$0.263694\pi$
$978$	−1.51746	−	39.0999i	−0.0485232	−	1.25028i
$979$	−14.8168	+	13.3411i	−0.473548	+	0.426385i
$980$	0.0666913	+	1.14676i	0.00213038	+	0.0366321i
$981$	−0.0799186	−	0.147529i	−0.00255161	−	0.00471024i
$982$	−5.64512	−	5.64512i	−0.180143	−	0.180143i
$983$	−5.77273	−	8.88923i	−0.184122	−	0.283522i	0.734542	−	0.678563i	$-0.237397\pi$
$983$	−5.77273	−	8.88923i	−0.184122	−	0.283522i	−0.918664	+	0.395041i	$0.870730\pi$
$984$	12.7186	+	0.172594i	0.405453	+	0.00550208i
$985$	−6.72556	+	32.5576i	−0.214294	+	1.03737i
$986$	14.0933	−	31.6541i	0.448823	−	1.00807i
$987$	28.4124	+	29.1942i	0.904378	+	0.929261i
$988$	−0.0453845	+	0.118231i	−0.00144387	+	0.00376142i
$989$	12.1705	−	8.84241i	0.387000	−	0.281172i
$990$	−18.0167	−	2.28454i	−0.572609	−	0.0726074i
$991$	10.0219	+	7.28132i	0.318356	+	0.231299i	0.735473	−	0.677554i	$-0.236960\pi$
$991$	10.0219	+	7.28132i	0.318356	+	0.231299i	−0.417118	+	0.908852i	$0.636960\pi$
$992$	−8.90992	+	5.78617i	−0.282890	+	0.183711i
$993$	8.44469	+	22.9242i	0.267984	+	0.727477i
$994$	12.0557	+	10.8550i	0.382383	+	0.344299i
$995$	3.26722	−	4.08230i	0.103578	−	0.129418i
$996$	−1.74679	−	0.396139i	−0.0553491	−	0.0125521i
$997$	1.71794	−	32.7803i	0.0544078	−	1.03816i	−0.825917	−	0.563791i	$-0.809342\pi$
$997$	1.71794	−	32.7803i	0.0544078	−	1.03816i	0.880325	−	0.474371i	$-0.157324\pi$
$998$	−12.9677	−	2.05388i	−0.410485	−	0.0650144i
$999$	10.5357	+	37.5635i	0.333335	+	1.18846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.2.21	✓	448
3.2	odd	2		675.2.bd.a.602.8		448
9.4	even	3		675.2.bd.a.152.8		448
9.5	odd	6	inner	225.2.w.a.77.21	yes	448
25.13	odd	20	inner	225.2.w.a.38.21	yes	448
75.38	even	20		675.2.bd.a.413.8		448
225.13	odd	60		675.2.bd.a.638.8		448
225.113	even	60	inner	225.2.w.a.113.21	yes	448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.2.21	✓	448	1.1	even	1	trivial
225.2.w.a.38.21	yes	448	25.13	odd	20	inner
225.2.w.a.77.21	yes	448	9.5	odd	6	inner
225.2.w.a.113.21	yes	448	225.113	even	60	inner
675.2.bd.a.152.8		448	9.4	even	3
675.2.bd.a.413.8		448	75.38	even	20
675.2.bd.a.602.8		448	3.2	odd	2
675.2.bd.a.638.8		448	225.13	odd	60

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.861819 + 0.697887i) q^{2} +(0.923545 + 1.46529i) q^{3} +(-0.160138 - 0.753391i) q^{4} +(1.74579 + 1.39722i) q^{5} +(-0.226676 + 1.90734i) q^{6} +(-2.43080 + 0.651331i) q^{7} +(1.39468 - 2.73721i) q^{8} +(-1.29413 + 2.70652i) q^{9} +O(q^{10})\)	\(q+(0.861819 + 0.697887i) q^{2} +(0.923545 + 1.46529i) q^{3} +(-0.160138 - 0.753391i) q^{4} +(1.74579 + 1.39722i) q^{5} +(-0.226676 + 1.90734i) q^{6} +(-2.43080 + 0.651331i) q^{7} +(1.39468 - 2.73721i) q^{8} +(-1.29413 + 2.70652i) q^{9} +(0.529449 + 2.42251i) q^{10} +(2.42792 - 0.255185i) q^{11} +(0.956039 - 0.930439i) q^{12} +(-0.0493002 - 0.0608806i) q^{13} +(-2.54947 - 1.13510i) q^{14} +(-0.435017 + 3.84848i) q^{15} +(1.70496 - 0.759098i) q^{16} +(-5.10587 - 2.60157i) q^{17} +(-3.00415 + 1.42937i) q^{18} +(1.99615 - 0.648587i) q^{19} +(0.773087 - 1.53901i) q^{20} +(-3.19934 - 2.96029i) q^{21} +(2.27052 + 1.47449i) q^{22} +(-2.24534 - 5.84931i) q^{23} +(5.29885 - 0.484335i) q^{24} +(1.09554 + 4.87850i) q^{25} -0.0868740i q^{26} +(-5.16101 + 0.603320i) q^{27} +(0.879971 + 1.72704i) q^{28} +(3.64845 + 4.05202i) q^{29} +(-3.06071 + 3.01310i) q^{30} +(1.74472 - 1.93771i) q^{31} +(-3.93561 - 1.05454i) q^{32} +(2.61621 + 3.32192i) q^{33} +(-2.58473 - 5.80540i) q^{34} +(-5.15372 - 2.25928i) q^{35} +(2.24630 + 0.541568i) q^{36} +(-1.17452 - 7.41562i) q^{37} +(2.17296 + 0.834120i) q^{38} +(0.0436766 - 0.128465i) q^{39} +(6.25931 - 2.82992i) q^{40} +(2.37741 + 0.249876i) q^{41} +(-0.691307 - 4.78401i) q^{42} +(0.621435 + 2.31923i) q^{43} +(-0.581057 - 1.78831i) q^{44} +(-6.04088 + 2.91682i) q^{45} +(2.14708 - 6.60804i) q^{46} +(-9.33330 - 0.489138i) q^{47} +(2.68691 + 1.79720i) q^{48} +(-0.577613 + 0.333485i) q^{49} +(-2.46048 + 4.96895i) q^{50} +(-0.903455 - 9.88423i) q^{51} +(-0.0379721 + 0.0468916i) q^{52} +(11.3074 - 5.76140i) q^{53} +(-4.86890 - 3.08185i) q^{54} +(4.59518 + 2.94684i) q^{55} +(-1.60736 + 7.56202i) q^{56} +(2.79390 + 2.32593i) q^{57} +(0.316455 + 6.03832i) q^{58} +(1.02042 - 9.70861i) q^{59} +(2.96907 - 0.288550i) q^{60} +(1.14035 + 10.8497i) q^{61} +(2.85593 - 0.452335i) q^{62} +(1.38293 - 7.42191i) q^{63} +(-4.84981 - 6.67519i) q^{64} +(-0.00100385 - 0.175168i) q^{65} +(-0.0636269 + 4.68872i) q^{66} +(4.83915 - 0.253609i) q^{67} +(-1.14236 + 4.26333i) q^{68} +(6.49724 - 8.69217i) q^{69} +(-2.86485 - 5.54380i) q^{70} +(-5.52847 - 1.79631i) q^{71} +(5.60342 + 7.31703i) q^{72} +(-2.05016 + 12.9442i) q^{73} +(4.16304 - 7.21060i) q^{74} +(-6.13662 + 6.11080i) q^{75} +(-0.808299 - 1.40002i) q^{76} +(-5.73558 + 2.20168i) q^{77} +(0.127295 - 0.0802321i) q^{78} +(-5.54923 + 4.99655i) q^{79} +(4.03713 + 1.05699i) q^{80} +(-5.65046 - 7.00516i) q^{81} +(1.87451 + 1.87451i) q^{82} +(-0.731245 - 1.12602i) q^{83} +(-1.71792 + 2.88441i) q^{84} +(-5.27879 - 11.6758i) q^{85} +(-1.08299 + 2.43244i) q^{86} +(-2.56786 + 9.08825i) q^{87} +(2.68768 - 7.00164i) q^{88} +(-6.60723 + 4.80043i) q^{89} +(-7.24175 - 1.70208i) q^{90} +(0.159492 + 0.115878i) q^{91} +(-4.04725 + 2.62832i) q^{92} +(4.45062 + 0.766954i) q^{93} +(-7.70225 - 6.93514i) q^{94} +(4.39107 + 1.65676i) q^{95} +(-2.08950 - 6.74071i) q^{96} +(-1.00911 + 19.2549i) q^{97} +(-0.730533 - 0.115705i) q^{98} +(-2.45138 + 6.90145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

Modular forms

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