LMFDB - Embedded newform 171.2.v.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(25,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([12, 14]))

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

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

chi := DirichletCharacter("171.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.v (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	171.25
Dual form			171.2.v.a.130.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.351652 - 1.99432i) q^{2} +(-0.903452 + 1.47776i) q^{3} +(-1.97425 + 0.718570i) q^{4} +(1.25384 - 1.05209i) q^{5} +(3.26482 + 1.28211i) q^{6} +(-1.67092 - 2.89412i) q^{7} +(0.102224 + 0.177058i) q^{8} +(-1.36755 - 2.67017i) q^{9} +O(q^{10})$	\(q+(-0.351652 - 1.99432i) q^{2} +(-0.903452 + 1.47776i) q^{3} +(-1.97425 + 0.718570i) q^{4} +(1.25384 - 1.05209i) q^{5} +(3.26482 + 1.28211i) q^{6} +(-1.67092 - 2.89412i) q^{7} +(0.102224 + 0.177058i) q^{8} +(-1.36755 - 2.67017i) q^{9} +(-2.53912 - 2.13058i) q^{10} +4.59858 q^{11} +(0.721770 - 3.56667i) q^{12} +(-4.60962 - 3.86793i) q^{13} +(-5.18420 + 4.35006i) q^{14} +(0.421961 + 2.80339i) q^{15} +(-2.90169 + 2.43481i) q^{16} +(2.52648 - 2.11996i) q^{17} +(-4.84426 + 3.66630i) q^{18} +(1.24581 + 4.17707i) q^{19} +(-1.71939 + 2.97807i) q^{20} +(5.78640 + 0.145477i) q^{21} +(-1.61710 - 9.17102i) q^{22} +(3.34469 - 1.21737i) q^{23} +(-0.354004 - 0.00890010i) q^{24} +(-0.403036 + 2.28573i) q^{25} +(-6.09289 + 10.5532i) q^{26} +(5.18139 + 0.391460i) q^{27} +(5.37844 + 4.51305i) q^{28} +(-5.37998 + 1.95815i) q^{29} +(5.44246 - 1.82734i) q^{30} +4.21052 q^{31} +(6.18940 + 5.19352i) q^{32} +(-4.15459 + 6.79560i) q^{33} +(-5.11632 - 4.29310i) q^{34} +(-5.13994 - 1.87079i) q^{35} +(4.61860 + 4.28892i) q^{36} +5.19847 q^{37} +(7.89232 - 3.95342i) q^{38} +(9.88044 - 3.31742i) q^{39} +(0.314454 + 0.114452i) q^{40} +(-0.770270 - 4.36842i) q^{41} +(-1.74467 - 11.5911i) q^{42} +(-1.63995 - 0.596894i) q^{43} +(-9.07877 + 3.30440i) q^{44} +(-4.52395 - 1.90917i) q^{45} +(-3.60398 - 6.24228i) q^{46} +(3.47002 - 1.26298i) q^{47} +(-0.976525 - 6.48774i) q^{48} +(-2.08394 + 3.60949i) q^{49} +4.70020 q^{50} +(0.850250 + 5.64881i) q^{51} +(11.8799 + 4.32394i) q^{52} +(-1.03632 + 5.87728i) q^{53} +(-1.04135 - 10.4710i) q^{54} +(5.76587 - 4.83814i) q^{55} +(0.341617 - 0.591698i) q^{56} +(-7.29824 - 1.93278i) q^{57} +(5.79706 + 10.0408i) q^{58} +(7.28192 + 2.65040i) q^{59} +(-2.84749 - 5.23139i) q^{60} +(0.905056 + 0.759432i) q^{61} +(-1.48064 - 8.39710i) q^{62} +(-5.44272 + 8.41948i) q^{63} +(4.39313 - 7.60912i) q^{64} -9.84913 q^{65} +(15.0135 + 5.89589i) q^{66} +(-2.62337 + 14.8778i) q^{67} +(-3.46456 + 6.00080i) q^{68} +(-1.22279 + 6.04249i) q^{69} +(-1.92347 + 10.9085i) q^{70} +(-0.582229 - 3.30198i) q^{71} +(0.332977 - 0.515092i) q^{72} +(3.14639 + 1.14519i) q^{73} +(-1.82805 - 10.3674i) q^{74} +(-3.01364 - 2.66064i) q^{75} +(-5.46107 - 7.35141i) q^{76} +(-7.68385 - 13.3088i) q^{77} +(-10.0905 - 18.5381i) q^{78} +(-5.33963 + 4.48048i) q^{79} +(-1.07660 + 6.10571i) q^{80} +(-5.25962 + 7.30318i) q^{81} +(-8.44114 + 3.07232i) q^{82} +(3.00716 + 5.20856i) q^{83} +(-11.5284 + 3.87073i) q^{84} +(0.937386 - 5.31618i) q^{85} +(-0.613703 + 3.48048i) q^{86} +(1.96687 - 9.71942i) q^{87} +(0.470087 + 0.814214i) q^{88} +(3.61385 - 1.31534i) q^{89} +(-2.21663 + 9.69356i) q^{90} +(-3.49194 + 19.8038i) q^{91} +(-5.72851 + 4.80679i) q^{92} +(-3.80400 + 6.22213i) q^{93} +(-3.73903 - 6.47619i) q^{94} +(5.95672 + 3.92666i) q^{95} +(-13.2666 + 4.45435i) q^{96} +(-1.96859 - 11.1645i) q^{97} +(7.93128 + 2.88675i) q^{98} +(-6.28879 - 12.2790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 3 q^{2} - 12 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} + 3 q^{7} + 12 q^{8} - 24 q^{9}+O(q^{10}) $ 108 * q - 3 * q^2 - 12 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 + 3 * q^7 + 12 * q^8 - 24 * q^9	\( 108 q - 3 q^{2} - 12 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} + 3 q^{7} + 12 q^{8} - 24 q^{9} - 12 q^{10} - 6 q^{11} - 3 q^{12} + 9 q^{14} - 12 q^{15} - 9 q^{16} - 21 q^{17} - 24 q^{18} - 9 q^{19} - 6 q^{20} + 3 q^{21} - 36 q^{22} - 15 q^{23} + 39 q^{24} - 3 q^{25} - 30 q^{26} - 6 q^{27} - 12 q^{28} + 15 q^{29} + 63 q^{30} - 6 q^{31} + 21 q^{32} - 42 q^{33} - 39 q^{34} - 9 q^{35} - 102 q^{36} - 24 q^{37} + 3 q^{38} - 6 q^{39} + 39 q^{40} + 39 q^{41} + 75 q^{42} + 9 q^{43} - 39 q^{44} - 3 q^{45} - 6 q^{46} + 15 q^{47} + 63 q^{48} - 15 q^{49} - 138 q^{50} + 45 q^{51} - 15 q^{52} + 12 q^{53} + 51 q^{54} - 27 q^{55} + 87 q^{56} - 60 q^{57} - 6 q^{58} + 48 q^{59} - 9 q^{60} + 18 q^{61} + 18 q^{62} + 63 q^{63} - 36 q^{64} - 42 q^{65} - 33 q^{66} - 27 q^{67} + 24 q^{68} + 15 q^{69} + 39 q^{70} + 30 q^{71} - 3 q^{72} + 63 q^{73} - 9 q^{74} + 72 q^{75} - 3 q^{76} - 48 q^{77} - 111 q^{78} - 9 q^{79} + 18 q^{80} - 84 q^{81} - 21 q^{82} - 9 q^{83} + 3 q^{84} - 3 q^{85} - 57 q^{86} + 3 q^{87} - 45 q^{88} - 30 q^{89} + 147 q^{90} - 57 q^{91} + 147 q^{92} + 54 q^{93} - 6 q^{94} - 15 q^{95} - 87 q^{96} + 51 q^{97} - 9 q^{98} - 21 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 12 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 + 3 * q^7 + 12 * q^8 - 24 * q^9 - 12 * q^10 - 6 * q^11 - 3 * q^12 + 9 * q^14 - 12 * q^15 - 9 * q^16 - 21 * q^17 - 24 * q^18 - 9 * q^19 - 6 * q^20 + 3 * q^21 - 36 * q^22 - 15 * q^23 + 39 * q^24 - 3 * q^25 - 30 * q^26 - 6 * q^27 - 12 * q^28 + 15 * q^29 + 63 * q^30 - 6 * q^31 + 21 * q^32 - 42 * q^33 - 39 * q^34 - 9 * q^35 - 102 * q^36 - 24 * q^37 + 3 * q^38 - 6 * q^39 + 39 * q^40 + 39 * q^41 + 75 * q^42 + 9 * q^43 - 39 * q^44 - 3 * q^45 - 6 * q^46 + 15 * q^47 + 63 * q^48 - 15 * q^49 - 138 * q^50 + 45 * q^51 - 15 * q^52 + 12 * q^53 + 51 * q^54 - 27 * q^55 + 87 * q^56 - 60 * q^57 - 6 * q^58 + 48 * q^59 - 9 * q^60 + 18 * q^61 + 18 * q^62 + 63 * q^63 - 36 * q^64 - 42 * q^65 - 33 * q^66 - 27 * q^67 + 24 * q^68 + 15 * q^69 + 39 * q^70 + 30 * q^71 - 3 * q^72 + 63 * q^73 - 9 * q^74 + 72 * q^75 - 3 * q^76 - 48 * q^77 - 111 * q^78 - 9 * q^79 + 18 * q^80 - 84 * q^81 - 21 * q^82 - 9 * q^83 + 3 * q^84 - 3 * q^85 - 57 * q^86 + 3 * q^87 - 45 * q^88 - 30 * q^89 + 147 * q^90 - 57 * q^91 + 147 * q^92 + 54 * q^93 - 6 * q^94 - 15 * q^95 - 87 * q^96 + 51 * q^97 - 9 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.351652	−	1.99432i	−0.248655	−	1.41019i	−0.811848	−	0.583869i	$-0.801538\pi$
$2$	−0.351652	−	1.99432i	−0.248655	−	1.41019i	0.563192	−	0.826326i	$-0.309573\pi$
$3$	−0.903452	+	1.47776i	−0.521608	+	0.853185i
$3$	−0.903452	+	1.47776i	−0.521608	+	0.853185i
$4$	−1.97425	+	0.718570i	−0.987127	+	0.359285i
$5$	1.25384	−	1.05209i	0.560733	−	0.470511i	−0.317823	−	0.948150i	$-0.602952\pi$
$5$	1.25384	−	1.05209i	0.560733	−	0.470511i	0.878556	+	0.477639i	$0.158507\pi$
$6$	3.26482	+	1.28211i	1.33286	+	0.523420i
$7$	−1.67092	−	2.89412i	−0.631548	−	1.09387i	−0.987235	−	0.159268i	$-0.949087\pi$
$7$	−1.67092	−	2.89412i	−0.631548	−	1.09387i	0.355688	−	0.934605i	$-0.384247\pi$
$8$	0.102224	+	0.177058i	0.0361418	+	0.0625994i
$9$	−1.36755	−	2.67017i	−0.455850	−	0.890057i
$10$	−2.53912	−	2.13058i	−0.802941	−	0.673748i
$11$	4.59858			1.38652			0.693262	−	0.720686i	$-0.256173\pi$
$11$	4.59858			1.38652			0.693262	+	0.720686i	$0.256173\pi$
$12$	0.721770	−	3.56667i	0.208357	−	1.02961i
$13$	−4.60962	−	3.86793i	−1.27848	−	1.07277i	−0.993452	−	0.114251i	$-0.963553\pi$
$13$	−4.60962	−	3.86793i	−1.27848	−	1.07277i	−0.285026	−	0.958520i	$-0.592002\pi$
$14$	−5.18420	+	4.35006i	−1.38554	+	1.16260i
$15$	0.421961	+	2.80339i	0.108950	+	0.723831i
$16$	−2.90169	+	2.43481i	−0.725423	+	0.608702i
$17$	2.52648	−	2.11996i	0.612760	−	0.514167i	−0.282758	−	0.959191i	$-0.591249\pi$
$17$	2.52648	−	2.11996i	0.612760	−	0.514167i	0.895519	+	0.445024i	$0.146805\pi$
$18$	−4.84426	+	3.66630i	−1.14180	+	0.864155i
$19$	1.24581	+	4.17707i	0.285809	+	0.958287i
$19$	1.24581	+	4.17707i	0.285809	+	0.958287i
$20$	−1.71939	+	2.97807i	−0.384467	+	0.665917i
$21$	5.78640	+	0.145477i	1.26270	+	0.0317458i
$22$	−1.61710	−	9.17102i	−0.344767	−	1.95527i
$23$	3.34469	−	1.21737i	0.697416	−	0.253839i	0.0311090	−	0.999516i	$-0.490096\pi$
$23$	3.34469	−	1.21737i	0.697416	−	0.253839i	0.666307	+	0.745677i	$0.267874\pi$
$24$	−0.354004	−	0.00890010i	−0.0722607	−	0.00181672i
$25$	−0.403036	+	2.28573i	−0.0806072	+	0.457146i
$26$	−6.09289	+	10.5532i	−1.19491	+	2.06965i
$27$	5.18139	+	0.391460i	0.997158	+	0.0753364i
$28$	5.37844	+	4.51305i	1.01643	+	0.852886i
$29$	−5.37998	+	1.95815i	−0.999038	+	0.363620i	−0.789213	−	0.614119i	$-0.789511\pi$
$29$	−5.37998	+	1.95815i	−0.999038	+	0.363620i	−0.209824	+	0.977739i	$0.567289\pi$
$30$	5.44246	−	1.82734i	0.993652	−	0.333625i
$31$	4.21052			0.756231			0.378115	−	0.925758i	$-0.376572\pi$
$31$	4.21052			0.756231			0.378115	+	0.925758i	$0.376572\pi$
$32$	6.18940	+	5.19352i	1.09414	+	0.918094i
$33$	−4.15459	+	6.79560i	−0.723222	+	1.18296i
$34$	−5.11632	−	4.29310i	−0.877442	−	0.736261i
$35$	−5.13994	−	1.87079i	−0.868809	−	0.316220i
$36$	4.61860	+	4.28892i	0.769766	+	0.714819i
$37$	5.19847			0.854623			0.427312	−	0.904104i	$-0.359461\pi$
$37$	5.19847			0.854623			0.427312	+	0.904104i	$0.359461\pi$
$38$	7.89232	−	3.95342i	1.28030	−	0.641329i
$39$	9.88044	−	3.31742i	1.58214	−	0.531213i
$40$	0.314454	+	0.114452i	0.0497196	+	0.0180964i
$41$	−0.770270	−	4.36842i	−0.120296	−	0.682232i	−0.983991	−	0.178218i	$-0.942967\pi$
$41$	−0.770270	−	4.36842i	−0.120296	−	0.682232i	0.863695	−	0.504015i	$-0.168144\pi$
$42$	−1.74467	−	11.5911i	−0.269209	−	1.78854i
$43$	−1.63995	−	0.596894i	−0.250090	−	0.0910254i	0.213933	−	0.976848i	$-0.431372\pi$
$43$	−1.63995	−	0.596894i	−0.250090	−	0.0910254i	−0.464024	+	0.885823i	$0.653595\pi$
$44$	−9.07877	+	3.30440i	−1.36868	+	0.498157i
$45$	−4.52395	−	1.90917i	−0.674391	−	0.284602i
$46$	−3.60398	−	6.24228i	−0.531379	−	0.920375i
$47$	3.47002	−	1.26298i	0.506155	−	0.184225i	−0.0763055	−	0.997084i	$-0.524312\pi$
$47$	3.47002	−	1.26298i	0.506155	−	0.184225i	0.582460	+	0.812859i	$0.302090\pi$
$48$	−0.976525	−	6.48774i	−0.140949	−	0.936424i
$49$	−2.08394	+	3.60949i	−0.297705	+	0.515641i
$50$	4.70020			0.664708
$51$	0.850250	+	5.64881i	0.119059	+	0.790992i
$52$	11.8799	+	4.32394i	1.64745	+	0.599623i
$53$	−1.03632	+	5.87728i	−0.142350	+	0.807306i	0.827107	+	0.562044i	$0.189985\pi$
$53$	−1.03632	+	5.87728i	−0.142350	+	0.807306i	−0.969457	+	0.245262i	$0.921126\pi$
$54$	−1.04135	−	10.4710i	−0.141710	−	1.42492i
$55$	5.76587	−	4.83814i	0.777469	−	0.652374i
$56$	0.341617	−	0.591698i	0.0456505	−	0.0790690i
$57$	−7.29824	−	1.93278i	−0.966676	−	0.256002i
$58$	5.79706	+	10.0408i	0.761191	+	1.31842i
$59$	7.28192	+	2.65040i	0.948026	+	0.345053i	0.769330	−	0.638851i	$-0.220590\pi$
$59$	7.28192	+	2.65040i	0.948026	+	0.345053i	0.178695	+	0.983904i	$0.442812\pi$
$60$	−2.84749	−	5.23139i	−0.367609	−	0.675370i
$61$	0.905056	+	0.759432i	0.115881	+	0.0972354i	0.698887	−	0.715232i	$-0.253679\pi$
$61$	0.905056	+	0.759432i	0.115881	+	0.0972354i	−0.583006	+	0.812468i	$0.698124\pi$
$62$	−1.48064	−	8.39710i	−0.188041	−	1.06643i
$63$	−5.44272	+	8.41948i	−0.685718	+	1.06076i
$64$	4.39313	−	7.60912i	0.549141	−	0.951140i
$65$	−9.84913			−1.22163
$66$	15.0135	+	5.89589i	1.84804	+	0.725734i
$67$	−2.62337	+	14.8778i	−0.320495	+	1.81762i	0.219111	+	0.975700i	$0.429684\pi$
$67$	−2.62337	+	14.8778i	−0.320495	+	1.81762i	−0.539606	+	0.841918i	$0.681427\pi$
$68$	−3.46456	+	6.00080i	−0.420140	+	0.727704i
$69$	−1.22279	+	6.04249i	−0.147207	+	0.727430i
$70$	−1.92347	+	10.9085i	−0.229899	+	1.30382i
$71$	−0.582229	−	3.30198i	−0.0690978	−	0.391873i	−0.999668	−	0.0257600i	$-0.991799\pi$
$71$	−0.582229	−	3.30198i	−0.0690978	−	0.391873i	0.930570	−	0.366113i	$-0.119312\pi$
$72$	0.332977	−	0.515092i	0.0392418	−	0.0607041i
$73$	3.14639	+	1.14519i	0.368257	+	0.134035i	0.519519	−	0.854459i	$-0.326111\pi$
$73$	3.14639	+	1.14519i	0.368257	+	0.134035i	−0.151261	+	0.988494i	$0.548333\pi$
$74$	−1.82805	−	10.3674i	−0.212507	−	1.20519i
$75$	−3.01364	−	2.66064i	−0.347985	−	0.307224i
$76$	−5.46107	−	7.35141i	−0.626428	−	0.843264i
$77$	−7.68385	−	13.3088i	−0.875656	−	1.51668i
$78$	−10.0905	−	18.5381i	−1.14252	−	2.09903i
$79$	−5.33963	+	4.48048i	−0.600755	+	0.504094i	−0.891688	−	0.452650i	$-0.850479\pi$
$79$	−5.33963	+	4.48048i	−0.600755	+	0.504094i	0.290933	+	0.956743i	$0.406034\pi$
$80$	−1.07660	+	6.10571i	−0.120368	+	0.682639i
$81$	−5.25962	+	7.30318i	−0.584402	+	0.811464i
$82$	−8.44114	+	3.07232i	−0.932168	+	0.339281i
$83$	3.00716	+	5.20856i	0.330079	+	0.571714i	0.982527	−	0.186120i	$-0.0595913\pi$
$83$	3.00716	+	5.20856i	0.330079	+	0.571714i	−0.652448	+	0.757833i	$0.726258\pi$
$84$	−11.5284	+	3.87073i	−1.25785	+	0.422331i
$85$	0.937386	−	5.31618i	0.101674	−	0.576621i
$86$	−0.613703	+	3.48048i	−0.0661773	+	0.375310i
$87$	1.96687	−	9.71942i	0.210871	−	1.04203i
$88$	0.470087	+	0.814214i	0.0501114	+	0.0867955i
$89$	3.61385	−	1.31534i	0.383068	−	0.139425i	−0.143306	−	0.989678i	$-0.545773\pi$
$89$	3.61385	−	1.31534i	0.383068	−	0.139425i	0.526374	+	0.850253i	$0.323551\pi$
$90$	−2.21663	+	9.69356i	−0.233653	+	1.02179i
$91$	−3.49194	+	19.8038i	−0.366055	+	2.07600i
$92$	−5.72851	+	4.80679i	−0.597238	+	0.501143i
$93$	−3.80400	+	6.22213i	−0.394456	+	0.645205i
$94$	−3.73903	−	6.47619i	−0.385652	−	0.667968i
$95$	5.95672	+	3.92666i	0.611146	+	0.402867i
$96$	−13.2666	+	4.45435i	−1.35402	+	0.454620i
$97$	−1.96859	−	11.1645i	−0.199880	−	1.13358i	−0.905295	−	0.424783i	$-0.860350\pi$
$97$	−1.96859	−	11.1645i	−0.199880	−	1.13358i	0.705415	−	0.708795i	$-0.250761\pi$
$98$	7.93128	+	2.88675i	0.801180	+	0.291606i
$99$	−6.28879	−	12.2790i	−0.632047	−	1.23408i
$100$	−0.846762	−	4.80222i	−0.0846762	−	0.480222i
$101$	2.50110	−	14.1844i	0.248869	−	1.41140i	−0.562465	−	0.826821i	$-0.690147\pi$
$101$	2.50110	−	14.1844i	0.248869	−	1.41140i	0.811334	−	0.584583i	$-0.198742\pi$
$102$	10.9665	−	3.68208i	1.08585	−	0.364581i
$103$	8.05650	−	13.9543i	0.793830	−	1.37495i	−0.129749	−	0.991547i	$-0.541417\pi$
$103$	8.05650	−	13.9543i	0.793830	−	1.37495i	0.923579	−	0.383408i	$-0.125250\pi$
$104$	0.213632	−	1.21157i	0.0209483	−	0.118804i
$105$	7.40826	−	5.90543i	0.722972	−	0.576311i
$106$	12.0856			1.17385
$107$	2.96510	−	5.13570i	0.286647	−	0.496487i	−0.686360	−	0.727261i	$-0.740793\pi$
$107$	2.96510	−	5.13570i	0.286647	−	0.496487i	0.973007	+	0.230775i	$0.0741261\pi$
$108$	−10.5107	+	2.95035i	−1.01139	+	0.283897i
$109$	−0.684068	−	3.87954i	−0.0655219	−	0.371593i	−0.999883	−	0.0152667i	$-0.995140\pi$
$109$	−0.684068	−	3.87954i	−0.0655219	−	0.371593i	0.934362	−	0.356326i	$-0.115971\pi$
$110$	−11.6764	−	9.79763i	−1.11330	−	0.934167i
$111$	−4.69657	+	7.68209i	−0.445778	+	0.729152i
$112$	11.8951	+	4.32947i	1.12398	+	0.409096i
$113$	−2.64486	−	4.58103i	−0.248808	−	0.430947i	0.714388	−	0.699750i	$-0.246705\pi$
$113$	−2.64486	−	4.58103i	−0.248808	−	0.430947i	−0.963195	+	0.268803i	$0.913372\pi$
$114$	−1.28813	+	15.2347i	−0.120644	+	1.42686i
$115$	2.91291	−	5.04531i	0.271630	−	0.470478i
$116$	9.21439	−	7.73179i	0.855534	−	0.717878i
$117$	−4.02415	+	17.5980i	−0.372032	+	1.62694i
$118$	2.72504	−	15.4545i	0.250860	−	1.42270i
$119$	−10.3570	−	3.76962i	−0.949421	−	0.345561i
$120$	−0.453227	+	0.361286i	−0.0413737	+	0.0329807i
$121$	10.1469			0.922448
$122$	1.19628	−	2.07202i	0.108306	−	0.187592i
$123$	7.15138	+	2.80838i	0.644818	+	0.253223i
$124$	−8.31263	+	3.02555i	−0.746496	+	0.271702i
$125$	5.99138	+	10.3774i	0.535885	+	0.928181i
$126$	18.7051	+	7.89377i	1.66638	+	0.703233i
$127$	−17.4043	+	6.33463i	−1.54438	+	0.562108i	−0.967090	−	0.254433i	$-0.918111\pi$
$127$	−17.4043	+	6.33463i	−1.54438	+	0.562108i	−0.577288	+	0.816541i	$0.695889\pi$
$128$	−1.53499	−	0.558692i	−0.135676	−	0.0493819i
$129$	2.36368	−	1.88419i	0.208111	−	0.165894i
$130$	3.46347	+	19.6423i	0.303766	+	1.72274i
$131$	9.50535	+	3.45967i	0.830487	+	0.302272i	0.722059	−	0.691832i	$-0.243196\pi$
$131$	9.50535	+	3.45967i	0.830487	+	0.302272i	0.108428	+	0.994104i	$0.465418\pi$
$132$	3.31912	−	16.4016i	0.288892	−	1.42758i
$133$	10.0073	−	10.5851i	0.867742	−	0.917842i
$134$	30.5936			2.64289
$135$	6.90846	−	4.96048i	0.594586	−	0.426930i
$136$	0.633624	+	0.230620i	0.0543328	+	0.0197755i
$137$	2.28559	+	1.91784i	0.195271	+	0.163852i	0.735181	−	0.677871i	$-0.237097\pi$
$137$	2.28559	+	1.91784i	0.195271	+	0.163852i	−0.539910	+	0.841723i	$0.681542\pi$
$138$	12.4806	+	0.313779i	1.06242	+	0.0267106i
$139$	−9.96119	−	8.35843i	−0.844897	−	0.708953i	0.113762	−	0.993508i	$-0.463710\pi$
$139$	−9.96119	−	8.35843i	−0.844897	−	0.708953i	−0.958660	+	0.284555i	$0.908154\pi$
$140$	11.4918			0.971238
$141$	−1.26861	+	6.26891i	−0.106836	+	0.527937i
$142$	−6.38046	+	2.32230i	−0.535436	+	0.194883i
$143$	−21.1977	−	17.7870i	−1.77264	−	1.48742i
$144$	10.4696	+	4.41829i	0.872464	+	0.368191i
$145$	−4.68546	+	8.11545i	−0.389106	+	0.673952i
$146$	1.17744	−	6.67761i	0.0974459	−	0.552643i
$147$	−3.45122	−	6.34056i	−0.284652	−	0.522960i
$148$	−10.2631	+	3.73547i	−0.843622	+	0.307053i
$149$	−1.50450	−	8.53242i	−0.123253	−	0.699003i	−0.982330	−	0.187157i	$-0.940073\pi$
$149$	−1.50450	−	8.53242i	−0.123253	−	0.699003i	0.859077	−	0.511847i	$-0.171038\pi$
$150$	−4.24640	+	6.94577i	−0.346717	+	0.567119i
$151$	−2.80454	+	4.85761i	−0.228230	+	0.395307i	−0.957284	−	0.289150i	$-0.906627\pi$
$151$	−2.80454	+	4.85761i	−0.228230	+	0.395307i	0.729053	+	0.684457i	$0.239961\pi$
$152$	−0.612231	+	0.647579i	−0.0496585	+	0.0525256i
$153$	−9.11575	−	3.84696i	−0.736964	−	0.311008i
$154$	−23.8400	+	20.0041i	−1.92108	+	1.61198i
$155$	5.27930	−	4.42986i	0.424044	−	0.355815i
$156$	−17.1227	+	13.6492i	−1.37091	+	1.09281i
$157$	1.54137	−	1.29336i	0.123015	−	0.103222i	−0.579205	−	0.815182i	$-0.696637\pi$
$157$	1.54137	−	1.29336i	0.123015	−	0.103222i	0.702220	+	0.711960i	$0.252192\pi$
$158$	10.8132	+	9.07335i	0.860251	+	0.721837i
$159$	−7.74894	−	6.84127i	−0.614531	−	0.542548i
$160$	13.2246			1.04549
$161$	−9.11191	−	7.64580i	−0.718119	−	0.602574i
$162$	16.4144	+	7.92116i	1.28964	+	0.622345i
$163$	−4.29730	−	7.44314i	−0.336590	−	0.582991i	0.647199	−	0.762321i	$-0.275940\pi$
$163$	−4.29730	−	7.44314i	−0.336590	−	0.582991i	−0.983789	+	0.179330i	$0.942607\pi$
$164$	4.65972	+	8.07088i	0.363863	+	0.630230i
$165$	1.94042	+	12.8916i	0.151062	+	1.00361i
$166$	9.33004	−	7.82883i	0.724152	−	0.607635i
$167$	−5.39635	+	1.96411i	−0.417582	+	0.151988i	−0.542262	−	0.840210i	$-0.682432\pi$
$167$	−5.39635	+	1.96411i	−0.417582	+	0.151988i	0.124680	+	0.992197i	$0.460210\pi$
$168$	0.565753	+	1.03940i	0.0436488	+	0.0801914i
$169$	4.03028	+	22.8568i	0.310021	+	1.75822i
$170$	−10.9318			−0.838429
$171$	9.44979	−	9.03888i	0.722644	−	0.691221i
$172$	3.66659			0.279575
$173$	−0.955522	−	5.41903i	−0.0726470	−	0.412001i	−0.999345	−	0.0361941i	$-0.988477\pi$
$173$	−0.955522	−	5.41903i	−0.0726470	−	0.412001i	0.926698	−	0.375807i	$-0.122635\pi$
$174$	−20.0753	−	0.504717i	−1.52190	−	0.0382625i
$175$	7.28861	−	2.65284i	0.550967	−	0.200536i
$176$	−13.3437	+	11.1967i	−1.00582	+	0.843980i
$177$	−10.4955	+	8.36642i	−0.788892	+	0.628859i
$178$	−3.89401	−	6.74463i	−0.291869	−	0.505531i
$179$	12.1665	+	21.0730i	0.909368	+	1.57507i	0.814945	+	0.579539i	$0.196767\pi$
$179$	12.1665	+	21.0730i	0.909368	+	1.57507i	0.0944228	+	0.995532i	$0.469899\pi$
$180$	10.3033	+	0.518404i	0.767963	+	0.0386395i
$181$	−2.37856	−	1.99585i	−0.176797	−	0.148350i	0.550095	−	0.835102i	$-0.314591\pi$
$181$	−2.37856	−	1.99585i	−0.176797	−	0.148350i	−0.726892	+	0.686752i	$0.759036\pi$
$182$	40.7229			3.01858
$183$	−1.93993	+	0.651345i	−0.143404	+	0.0481488i
$184$	0.557453	+	0.467759i	0.0410960	+	0.0344836i
$185$	6.51803	−	5.46928i	0.479215	−	0.402109i
$186$	13.7466	+	5.39835i	1.00795	+	0.395826i
$187$	11.6182	−	9.74883i	0.849607	−	0.712905i
$188$	−5.94317	+	4.98691i	−0.433450	+	0.363708i
$189$	−7.52474	−	15.6496i	−0.547345	−	1.13834i
$190$	5.73631	−	13.2604i	0.416156	−	0.962011i
$191$	−0.406195	+	0.703551i	−0.0293913	+	0.0509072i	−0.880347	−	0.474330i	$-0.842690\pi$
$191$	−0.406195	+	0.703551i	−0.0293913	+	0.0509072i	0.850956	+	0.525238i	$0.176024\pi$
$192$	7.27547	+	13.3665i	0.525062	+	0.964641i
$193$	4.54920	+	25.7998i	0.327458	+	1.85711i	0.491804	+	0.870706i	$0.336338\pi$
$193$	4.54920	+	25.7998i	0.327458	+	1.85711i	−0.164346	+	0.986403i	$0.552551\pi$
$194$	−21.5732	+	7.85200i	−1.54886	+	0.563741i
$195$	8.89822	−	14.5547i	0.637215	−	1.04228i
$196$	1.52056	−	8.62350i	0.108611	−	0.615964i
$197$	−7.51807	+	13.0217i	−0.535641	+	0.927757i	0.463492	+	0.886101i	$0.346596\pi$
$197$	−7.51807	+	13.0217i	−0.535641	+	0.927757i	−0.999132	+	0.0416552i	$0.986737\pi$
$198$	−22.2767	+	16.8598i	−1.58314	+	1.19817i
$199$	10.9480	+	9.18644i	0.776081	+	0.651209i	0.942258	−	0.334887i	$-0.108698\pi$
$199$	10.9480	+	9.18644i	0.776081	+	0.651209i	−0.166178	+	0.986096i	$0.553142\pi$
$200$	−0.445906	+	0.162297i	−0.0315303	+	0.0114761i
$201$	−19.6158	−	17.3181i	−1.38359	−	1.22153i
$202$	−29.1678			−2.05224
$203$	14.6566	+	12.2984i	1.02869	+	0.863177i
$204$	−5.73768	−	10.5412i	−0.401718	−	0.738034i
$205$	−5.56178	−	4.66689i	−0.388452	−	0.325950i
$206$	−30.6623	−	11.1602i	−2.13634	−	0.777566i
$207$	−7.82461	−	7.26608i	−0.543848	−	0.505028i
$208$	22.7934			1.58044
$209$	5.72896	+	19.2086i	0.396280	+	1.32869i
$210$	−14.3824	−	12.6978i	−0.992482	−	0.876229i
$211$	19.0858	+	6.94665i	1.31392	+	0.478227i	0.901504	−	0.432770i	$-0.142464\pi$
$211$	19.0858	+	6.94665i	1.31392	+	0.478227i	0.412413	+	0.910997i	$0.364686\pi$
$212$	−2.17727	−	12.3479i	−0.149536	−	0.848058i
$213$	5.40555	+	2.12279i	0.370382	+	0.145451i
$214$	−11.2849	−	4.10736i	−0.771419	−	0.280774i
$215$	−2.68422	+	0.976976i	−0.183062	+	0.0666292i
$216$	0.460353	+	0.957421i	0.0313230	+	0.0651443i
$217$	−7.03543	−	12.1857i	−0.477596	−	0.827221i
$218$	−7.49649	+	2.72850i	−0.507726	+	0.184797i
$219$	−4.53493	+	3.61499i	−0.306442	+	0.244278i
$220$	−7.90675	+	13.6949i	−0.533073	+	0.923310i
$221$	−19.8460			−1.33498
$222$	16.9721	+	6.66502i	1.13909	+	0.447327i
$223$	−1.36957	−	0.498481i	−0.0917130	−	0.0333808i	0.295756	−	0.955263i	$-0.404428\pi$
$223$	−1.36957	−	0.498481i	−0.0917130	−	0.0333808i	−0.387469	+	0.921883i	$0.626651\pi$
$224$	4.68867	−	26.5908i	0.313275	−	1.77667i
$225$	6.65446	−	2.04968i	0.443631	−	0.136645i
$226$	−8.20596	+	6.88562i	−0.545853	+	0.458025i
$227$	−1.44297	+	2.49930i	−0.0957736	+	0.165885i	−0.909931	−	0.414759i	$-0.863866\pi$
$227$	−1.44297	+	2.49930i	−0.0957736	+	0.165885i	0.814158	+	0.580644i	$0.197199\pi$
$228$	15.7974	−	1.42851i	1.04621	−	0.0946051i
$229$	−1.93456	−	3.35075i	−0.127839	−	0.221424i	0.795000	−	0.606609i	$-0.207471\pi$
$229$	−1.93456	−	3.35075i	−0.127839	−	0.221424i	−0.922839	+	0.385186i	$0.874137\pi$
$230$	−11.0863	−	4.03508i	−0.731008	−	0.266065i
$231$	26.6092	+	0.668989i	1.75076	+	0.0440163i
$232$	−0.896671	−	0.752397i	−0.0588694	−	0.0493973i
$233$	0.460293	+	2.61045i	0.0301548	+	0.171016i	0.996166	−	0.0874843i	$-0.0278828\pi$
$233$	0.460293	+	2.61045i	0.0301548	+	0.171016i	−0.966011	+	0.258500i	$0.916772\pi$
$234$	36.5112	+	1.83703i	2.38681	+	0.120091i
$235$	3.02206	−	5.23437i	0.197138	−	0.341452i
$236$	−16.2809			−1.05979
$237$	−1.79698	−	11.9386i	−0.116726	−	0.775495i
$238$	−3.87578	+	21.9807i	−0.251230	+	1.42479i
$239$	8.49579	−	14.7151i	0.549547	−	0.951844i	−0.448758	−	0.893653i	$-0.648134\pi$
$239$	8.49579	−	14.7151i	0.549547	−	0.951844i	0.998305	−	0.0581905i	$-0.0185331\pi$
$240$	−8.05011	−	7.10717i	−0.519633	−	0.458766i
$241$	0.669875	−	3.79905i	0.0431504	−	0.244718i	−0.955602	−	0.294662i	$-0.904793\pi$
$241$	0.669875	−	3.79905i	0.0431504	−	0.244718i	0.998752	+	0.0499436i	$0.0159041\pi$
$242$	−3.56819	−	20.2362i	−0.229372	−	1.30083i
$243$	−6.04054	−	14.3705i	−0.387501	−	0.921869i
$244$	−2.33252	−	0.848967i	−0.149324	−	0.0543495i
$245$	1.18460	+	6.71820i	0.0756814	+	0.429210i
$246$	3.08601	−	15.2497i	0.196757	−	0.972284i
$247$	10.4139	−	24.0734i	0.662622	−	1.53176i
$248$	0.430417	+	0.745505i	0.0273315	+	0.0473396i
$249$	−10.4138	−	0.261817i	−0.659949	−	0.0165920i
$250$	18.5889	−	15.5979i	1.17566	−	0.986500i
$251$	−2.30066	+	13.0477i	−0.145216	+	0.823563i	0.821977	+	0.569521i	$0.192871\pi$
$251$	−2.30066	+	13.0477i	−0.145216	+	0.823563i	−0.967193	+	0.254042i	$0.918240\pi$
$252$	4.69532	−	20.5332i	0.295777	−	1.29347i
$253$	15.3808	−	5.59816i	0.966984	−	0.351954i
$254$	18.7535	+	32.4820i	1.17670	+	2.03810i
$255$	7.00915	+	6.18814i	0.438930	+	0.387517i
$256$	2.47701	−	14.0478i	0.154813	−	0.877988i
$257$	−3.46893	+	19.6733i	−0.216386	+	1.22718i	0.662100	+	0.749416i	$0.269665\pi$
$257$	−3.46893	+	19.6733i	−0.216386	+	1.22718i	−0.878486	+	0.477769i	$0.841446\pi$
$258$	−4.58887	−	4.05135i	−0.285690	−	0.252226i
$259$	−8.68622	−	15.0450i	−0.539736	−	0.934849i
$260$	19.4447	−	7.07729i	1.20591	−	0.438915i
$261$	12.5860	+	11.6876i	0.779054	+	0.723444i
$262$	3.55709	−	20.1733i	0.219758	−	1.24631i
$263$	−19.8676	+	16.6709i	−1.22509	+	1.02797i	−0.226549	+	0.974000i	$0.572744\pi$
$263$	−19.8676	+	16.6709i	−1.22509	+	1.02797i	−0.998542	+	0.0539737i	$0.982811\pi$
$264$	−1.62791	−	0.0409278i	−0.100191	−	0.00251893i
$265$	4.88407	+	8.45945i	0.300026	+	0.519660i
$266$	−24.6291	−	16.2354i	−1.51011	−	0.995459i
$267$	−1.32119	+	6.52875i	−0.0808557	+	0.399553i
$268$	−5.51158	−	31.2577i	−0.336673	−	1.90937i
$269$	26.0172	+	9.46950i	1.58630	+	0.577366i	0.976562	−	0.215237i	$-0.0690525\pi$
$269$	26.0172	+	9.46950i	1.58630	+	0.577366i	0.609738	+	0.792603i	$0.291275\pi$
$270$	−12.3221	−	12.0333i	−0.749902	−	0.732324i
$271$	1.86555	+	10.5801i	0.113324	+	0.642694i	0.987566	+	0.157203i	$0.0502478\pi$
$271$	1.86555	+	10.5801i	0.113324	+	0.642694i	−0.874242	+	0.485490i	$0.838641\pi$
$272$	−2.16935	+	12.3030i	−0.131536	+	0.745977i
$273$	−26.1104	−	23.0520i	−1.58027	−	1.39517i
$274$	3.02104	−	5.23260i	0.182508	−	0.316113i
$275$	−1.85339	+	10.5111i	−0.111764	+	0.633844i
$276$	−1.92785	−	12.8081i	−0.116043	−	0.770955i
$277$	−6.45947			−0.388112			−0.194056	−	0.980990i	$-0.562164\pi$
$277$	−6.45947			−0.388112			−0.194056	+	0.980990i	$0.562164\pi$
$278$	−13.1665	+	22.8050i	−0.789674	+	1.36775i
$279$	−5.75809	−	11.2428i	−0.344728	−	0.673088i
$280$	−0.194190	−	1.10131i	−0.0116051	−	0.0658156i
$281$	−20.7110	−	17.3786i	−1.23551	−	1.03672i	−0.997861	−	0.0653686i	$-0.979178\pi$
$281$	−20.7110	−	17.3786i	−1.23551	−	1.03672i	−0.237652	−	0.971350i	$-0.576378\pi$
$282$	12.9483	+	0.325536i	0.771060	+	0.0193854i
$283$	−15.1225	−	5.50414i	−0.898939	−	0.327187i	−0.149111	−	0.988820i	$-0.547641\pi$
$283$	−15.1225	−	5.50414i	−0.898939	−	0.327187i	−0.749827	+	0.661633i	$0.769864\pi$
$284$	3.52217	+	6.10058i	0.209003	+	0.362003i
$285$	−11.1843	+	5.25505i	−0.662499	+	0.311282i
$286$	−28.0187	+	48.5297i	−1.65678	+	2.86962i
$287$	−11.3556	+	9.52852i	−0.670303	+	0.562451i
$288$	5.40328	−	23.6292i	0.318391	−	1.39236i
$289$	−1.06319	+	6.02965i	−0.0625406	+	0.354686i
$290$	17.8324	+	6.49047i	1.04716	+	0.381134i
$291$	18.2769	+	7.17743i	1.07141	+	0.420749i
$292$	−7.03468			−0.411674
$293$	4.68904	−	8.12165i	0.273936	−	0.474472i	−0.695930	−	0.718110i	$-0.745008\pi$
$293$	4.68904	−	8.12165i	0.273936	−	0.474472i	0.969866	+	0.243638i	$0.0783409\pi$
$294$	−11.4314	+	9.11249i	−0.666696	+	0.531451i
$295$	11.9188	−	4.33809i	0.693940	−	0.252574i
$296$	0.531410	+	0.920430i	0.0308876	+	0.0534989i
$297$	23.8270	+	1.80016i	1.38258	+	0.104456i
$298$	−16.4873	+	6.00088i	−0.955083	+	0.347622i
$299$	−20.1264	−	7.32543i	−1.16394	−	0.423640i
$300$	7.86154	+	3.08727i	0.453886	+	0.178243i
$301$	1.01275	+	5.74357i	0.0583738	+	0.331054i
$302$	10.6738	+	3.88496i	0.614210	+	0.223554i
$303$	18.7016	+	16.5110i	1.07438	+	0.948531i
$304$	−13.7853	−	9.08728i	−0.790644	−	0.521191i
$305$	1.93379			0.110728
$306$	−4.46649	+	19.5325i	−0.255332	+	1.11660i
$307$	−11.3250	−	4.12198i	−0.646354	−	0.235254i	−0.00202016	−	0.999998i	$-0.500643\pi$
$307$	−11.3250	−	4.12198i	−0.646354	−	0.235254i	−0.644334	+	0.764744i	$0.722865\pi$
$308$	24.7332	+	20.7536i	1.40930	+	1.18255i
$309$	13.3424	+	24.5126i	0.759023	+	1.39447i
$310$	−10.6910	−	8.97083i	−0.607209	−	0.509509i
$311$	−31.7215			−1.79876			−0.899381	−	0.437166i	$-0.855982\pi$
$311$	−31.7215			−1.79876			−0.899381	+	0.437166i	$0.855982\pi$
$312$	1.59740	+	1.41029i	0.0904348	+	0.0798418i
$313$	7.60149	−	2.76672i	0.429662	−	0.156384i	−0.118131	−	0.992998i	$-0.537690\pi$
$313$	7.60149	−	2.76672i	0.429662	−	0.156384i	0.547793	+	0.836614i	$0.315468\pi$
$314$	−3.12140	−	2.61917i	−0.176151	−	0.147808i
$315$	2.03381	+	16.2829i	0.114592	+	0.917438i
$316$	7.32225	−	12.6825i	0.411909	−	0.713447i
$317$	4.59433	−	26.0557i	0.258043	−	1.46344i	−0.530095	−	0.847938i	$-0.677844\pi$
$317$	4.59433	−	26.0557i	0.258043	−	1.46344i	0.788139	−	0.615498i	$-0.211045\pi$
$318$	−10.9187	+	17.8596i	−0.612292	+	1.00152i
$319$	−24.7403	+	9.00472i	−1.38519	+	0.504168i
$320$	−2.49724	−	14.1626i	−0.139600	−	0.791712i
$321$	4.91051	+	9.02156i	0.274078	+	0.503534i
$322$	−12.0439	+	20.8607i	−0.671182	+	1.16252i
$323$	12.0028	+	7.91220i	0.667852	+	0.440247i
$324$	5.13598	−	18.1977i	0.285332	−	1.01099i
$325$	10.6989	−	8.97743i	0.593467	−	0.497978i
$326$	−13.3328	+	11.1876i	−0.738436	+	0.619622i
$327$	6.35106	+	2.49409i	0.351214	+	0.137924i
$328$	0.694722	−	0.582941i	0.0383596	−	0.0321875i
$329$	−9.45335	−	7.93230i	−0.521180	−	0.437322i
$330$	25.0276	−	8.40317i	1.37772	−	0.462579i
$331$	−6.28296			−0.345343			−0.172671	−	0.984979i	$-0.555240\pi$
$331$	−6.28296			−0.345343			−0.172671	+	0.984979i	$0.555240\pi$
$332$	−9.67962	−	8.12217i	−0.531238	−	0.445762i
$333$	−7.10917	−	13.8808i	−0.389580	−	0.760663i
$334$	5.81470	+	10.0714i	0.318166	+	0.551080i
$335$	12.3636	+	21.4144i	0.675497	+	1.16999i
$336$	−17.1446	+	13.6667i	−0.935313	+	0.745577i
$337$	4.68091	−	3.92775i	0.254986	−	0.213958i	−0.506330	−	0.862340i	$-0.668998\pi$
$337$	4.68091	−	3.92775i	0.254986	−	0.213958i	0.761316	+	0.648382i	$0.224554\pi$
$338$	44.1665	−	16.0753i	2.40234	−	0.874381i
$339$	9.15917	+	0.230273i	0.497458	+	0.0125067i
$340$	1.96941	+	11.1691i	0.106806	+	0.605728i
$341$	19.3624			1.04853
$342$	−21.3494	−	15.6673i	−1.15445	−	0.847193i
$343$	−9.46450			−0.511035
$344$	−0.0619584	−	0.351383i	−0.00334057	−	0.0189453i
$345$	4.82408	+	8.86278i	0.259720	+	0.477156i
$346$	−10.4713	+	3.81123i	−0.562938	+	0.204893i
$347$	22.5449	−	18.9174i	1.21027	−	1.01554i	0.210996	−	0.977487i	$-0.432329\pi$
$347$	22.5449	−	18.9174i	1.21027	−	1.01554i	0.999276	−	0.0380516i	$-0.0121151\pi$
$348$	3.10097	+	20.6019i	0.166230	+	1.10438i
$349$	14.5857	+	25.2632i	0.780756	+	1.35231i	0.931502	+	0.363737i	$0.118499\pi$
$349$	14.5857	+	25.2632i	0.780756	+	1.35231i	−0.150745	+	0.988573i	$0.548167\pi$
$350$	−7.85365	−	13.6029i	−0.419795	−	0.727107i
$351$	−22.3701	−	21.8457i	−1.19403	−	1.16604i
$352$	28.4624	+	23.8828i	1.51705	+	1.27296i
$353$	−26.6830			−1.42019			−0.710097	−	0.704104i	$-0.751349\pi$
$353$	−26.6830			−1.42019			−0.710097	+	0.704104i	$0.751349\pi$
$354$	20.3761	+	17.9893i	1.08298	+	0.956123i
$355$	−4.20401	−	3.52759i	−0.223126	−	0.187225i
$356$	−6.18951	+	5.19361i	−0.328043	+	0.275261i
$357$	14.9276	−	11.8994i	0.790053	−	0.629784i
$358$	37.7479	−	31.6742i	1.99504	−	1.67404i
$359$	−6.12301	+	5.13781i	−0.323160	+	0.271163i	−0.789906	−	0.613228i	$-0.789871\pi$
$359$	−6.12301	+	5.13781i	−0.323160	+	0.271163i	0.466746	+	0.884391i	$0.345426\pi$
$360$	−0.124425	−	0.996165i	−0.00655780	−	0.0525025i
$361$	−15.8959	+	10.4077i	−0.836627	+	0.547773i
$362$	−3.14393	+	5.44545i	−0.165241	+	0.286206i
$363$	−9.16726	+	14.9947i	−0.481157	+	0.787019i
$364$	−7.33641	−	41.6069i	−0.384533	−	2.18079i
$365$	5.14991	−	1.87442i	0.269559	−	0.0981114i
$366$	1.98117	+	3.63980i	0.103557	+	0.190255i
$367$	−2.58777	+	14.6760i	−0.135080	+	0.766079i	0.839723	+	0.543014i	$0.182717\pi$
$367$	−2.58777	+	14.6760i	−0.135080	+	0.766079i	−0.974804	+	0.223064i	$0.928394\pi$
$368$	−6.74121	+	11.6761i	−0.351410	+	0.608660i
$369$	−10.6110	+	8.03078i	−0.552388	+	0.418066i
$370$	−13.1996	−	11.0757i	−0.686212	−	0.575800i
$371$	18.7411	−	6.82121i	0.972991	−	0.354140i
$372$	3.03902	−	15.0175i	0.157566	−	0.778622i
$373$	11.2528			0.582646			0.291323	−	0.956625i	$-0.405904\pi$
$373$	11.2528			0.582646			0.291323	+	0.956625i	$0.405904\pi$
$374$	−23.5278	−	19.7422i	−1.21659	−	1.02084i
$375$	−20.7482	−	0.521636i	−1.07143	−	0.0269371i
$376$	0.578342	+	0.485287i	0.0298257	+	0.0250267i
$377$	32.3737	+	11.7830i	1.66733	+	0.606858i
$378$	−28.5642	+	20.5099i	−1.46919	+	1.05492i
$379$	2.59739			0.133419			0.0667094	−	0.997772i	$-0.478750\pi$
$379$	2.59739			0.133419			0.0667094	+	0.997772i	$0.478750\pi$
$380$	−14.5817	−	3.47191i	−0.748023	−	0.178105i
$381$	6.36284	−	31.4423i	0.325978	−	1.61084i
$382$	1.54594	+	0.562677i	0.0790973	+	0.0287891i
$383$	0.317839	+	1.80256i	0.0162408	+	0.0921063i	0.991851	−	0.127405i	$-0.0406648\pi$
$383$	0.317839	+	1.80256i	0.0162408	+	0.0921063i	−0.975610	+	0.219511i	$0.929554\pi$
$384$	2.21241	−	1.76360i	0.112901	−	0.0899984i
$385$	−23.6364	−	8.60296i	−1.20462	−	0.438447i
$386$	49.8532	−	18.1451i	2.53746	−	0.923560i
$387$	0.648908	+	5.19523i	0.0329859	+	0.264089i
$388$	11.9089	+	20.6269i	0.604585	+	1.04717i
$389$	7.69606	−	2.80114i	0.390206	−	0.142023i	−0.139464	−	0.990227i	$-0.544538\pi$
$389$	7.69606	−	2.80114i	0.390206	−	0.142023i	0.529670	+	0.848204i	$0.322316\pi$
$390$	−32.1557	−	12.6277i	−1.62827	−	0.639428i
$391$	5.86950	−	10.1663i	0.296834	−	0.514131i
$392$	−0.852117			−0.0430384
$393$	−13.7002	+	10.9210i	−0.691083	+	0.550891i
$394$	28.6131	+	10.4143i	1.44151	+	0.524666i
$395$	−1.98114	+	11.2356i	−0.0996818	+	0.565324i
$396$	21.2390	+	19.7229i	1.06730	+	0.991114i
$397$	−13.1457	+	11.0305i	−0.659763	+	0.553607i	−0.910016	−	0.414574i	$-0.863931\pi$
$397$	−13.1457	+	11.0305i	−0.659763	+	0.553607i	0.250253	+	0.968181i	$0.419486\pi$
$398$	14.4708	−	25.0641i	0.725355	−	1.25635i
$399$	6.60109	+	24.3515i	0.330468	+	1.21910i
$400$	−4.39583	−	7.61380i	−0.219792	−	0.380690i
$401$	−20.9894	−	7.63953i	−1.04816	−	0.381500i	−0.240194	−	0.970725i	$-0.577211\pi$
$401$	−20.9894	−	7.63953i	−1.04816	−	0.381500i	−0.807969	+	0.589225i	$0.799433\pi$
$402$	−27.6399	+	45.2101i	−1.37855	+	2.25487i
$403$	−19.4089	−	16.2860i	−0.966825	−	0.811262i
$404$	5.25470	+	29.8009i	0.261431	+	1.48265i
$405$	1.08893	+	14.6906i	0.0541095	+	0.729982i
$406$	19.3728	−	33.5547i	0.961457	−	1.66529i
$407$	23.9056			1.18496
$408$	−0.913250	+	0.727989i	−0.0452126	+	0.0360408i
$409$	−2.66303	+	15.1028i	−0.131678	+	0.746785i	0.845437	+	0.534075i	$0.179340\pi$
$409$	−2.66303	+	15.1028i	−0.131678	+	0.746785i	−0.977115	+	0.212710i	$0.931771\pi$
$410$	−7.35144	+	12.7331i	−0.363062	+	0.628841i
$411$	−4.89902	+	1.64488i	−0.241651	+	0.0811359i
$412$	−5.87847	+	33.3384i	−0.289611	+	1.64247i
$413$	−4.49693	−	25.5033i	−0.221279	−	1.25494i
$414$	−11.7393	+	18.1599i	−0.576957	+	0.892510i
$415$	9.25039	+	3.36686i	0.454084	+	0.165273i
$416$	−8.44259	−	47.8803i	−0.413932	−	2.34753i
$417$	21.3512	−	7.16881i	1.04557	−	0.351058i
$418$	36.2935	−	18.1801i	1.77517	−	0.889218i
$419$	0.548528	+	0.950079i	0.0267974	+	0.0464144i	0.879113	−	0.476613i	$-0.158136\pi$
$419$	0.548528	+	0.950079i	0.0267974	+	0.0464144i	−0.852316	+	0.523028i	$0.824802\pi$
$420$	−10.3823	+	16.9822i	−0.506606	+	0.828646i
$421$	6.85756	−	5.75418i	0.334217	−	0.280441i	−0.460198	−	0.887816i	$-0.652222\pi$
$421$	6.85756	−	5.75418i	0.334217	−	0.280441i	0.794416	+	0.607375i	$0.207777\pi$
$422$	7.14227	−	40.5058i	0.347680	−	1.97179i
$423$	−8.11781	−	7.53835i	−0.394702	−	0.366527i
$424$	−1.14655	+	0.417312i	−0.0556816	+	0.0202665i
$425$	3.82741	+	6.62926i	0.185657	+	0.321567i
$426$	2.33264	−	11.5269i	0.113017	−	0.558478i
$427$	0.685610	−	3.88829i	0.0331790	−	0.188167i
$428$	−2.16350	+	12.2698i	−0.104577	+	0.593083i
$429$	45.4360	−	15.2554i	2.19367	−	0.736539i
$430$	2.89231	+	5.00963i	0.139480	+	0.241586i
$431$	34.1549	−	12.4314i	1.64518	−	0.598798i	0.657249	−	0.753673i	$-0.271720\pi$
$431$	34.1549	−	12.4314i	1.64518	−	0.598798i	0.987934	+	0.154876i	$0.0494977\pi$
$432$	−15.9879	+	11.4798i	−0.769219	+	0.552322i
$433$	0.729991	−	4.13999i	0.0350811	−	0.198955i	−0.962230	−	0.272238i	$-0.912236\pi$
$433$	0.729991	−	4.13999i	0.0350811	−	0.198955i	0.997311	+	0.0732825i	$0.0233475\pi$
$434$	−21.8282	+	18.3160i	−1.04779	+	0.879196i
$435$	−7.75960	−	14.2559i	−0.372045	−	0.683518i
$436$	4.13825	+	7.16766i	0.198186	+	0.343269i
$437$	9.25189	+	12.4544i	0.442578	+	0.595776i
$438$	8.80415	+	7.77288i	0.420678	+	0.371403i
$439$	4.67537	+	26.5154i	0.223143	+	1.26551i	0.866203	+	0.499692i	$0.166554\pi$
$439$	4.67537	+	26.5154i	0.223143	+	1.26551i	−0.643060	+	0.765816i	$0.722335\pi$
$440$	1.44604	+	0.526316i	0.0689373	+	0.0250911i
$441$	12.4878	+	0.628316i	0.594658	+	0.0299198i
$442$	6.97887	+	39.5791i	0.331951	+	1.88259i
$443$	−4.31989	+	24.4993i	−0.205244	+	1.16400i	0.691811	+	0.722079i	$0.256813\pi$
$443$	−4.31989	+	24.4993i	−0.205244	+	1.16400i	−0.897055	+	0.441919i	$0.854298\pi$
$444$	3.75210	−	18.5412i	0.178067	−	0.879927i
$445$	3.14733	−	5.45133i	0.149198	−	0.258418i
$446$	−0.512519	+	2.90664i	−0.0242685	+	0.137633i
$447$	13.9681	+	5.48535i	0.660669	+	0.259448i
$448$	−29.3622			−1.38723
$449$	11.2639	−	19.5096i	0.531576	−	0.920717i	−0.467744	−	0.883864i	$-0.654933\pi$
$449$	11.2639	−	19.5096i	0.531576	−	0.920717i	0.999321	−	0.0368534i	$-0.0117334\pi$
$450$	−6.42776	−	12.5503i	−0.303007	−	0.591628i
$451$	−3.54215	−	20.0885i	−0.166793	−	0.945931i
$452$	8.51342	+	7.14361i	0.400438	+	0.336007i
$453$	−4.64461	−	8.53306i	−0.218223	−	0.400918i
$454$	5.49183	+	1.99886i	0.257744	+	0.0938113i
$455$	16.4571	+	28.5045i	0.771521	+	1.33631i
$456$	−0.403845	−	1.48979i	−0.0189118	−	0.0697657i
$457$	−7.75163	+	13.4262i	−0.362606	+	0.628052i	−0.988389	−	0.151945i	$-0.951446\pi$
$457$	−7.75163	+	13.4262i	−0.362606	+	0.628052i	0.625783	+	0.779997i	$0.284780\pi$
$458$	−6.00216	+	5.03641i	−0.280463	+	0.235336i
$459$	13.9205	−	9.99534i	0.649754	−	0.466543i
$460$	−2.12542	+	12.0539i	−0.0990983	+	0.562014i
$461$	4.72252	+	1.71886i	0.219949	+	0.0800551i	0.449645	−	0.893208i	$-0.351551\pi$
$461$	4.72252	+	1.71886i	0.219949	+	0.0800551i	−0.229695	+	0.973263i	$0.573773\pi$
$462$	−8.02301	−	53.3025i	−0.373264	−	2.47986i
$463$	−37.0578			−1.72222			−0.861111	−	0.508417i	$-0.830231\pi$
$463$	−37.0578			−1.72222			−0.861111	+	0.508417i	$0.830231\pi$
$464$	10.8433	−	18.7812i	0.503389	−	0.871895i
$465$	1.77668	+	11.8037i	0.0823913	+	0.547384i
$466$	5.04420	−	1.83594i	0.233668	−	0.0850482i
$467$	−1.35903	−	2.35390i	−0.0628882	−	0.108926i	0.832867	−	0.553473i	$-0.186698\pi$
$467$	−1.35903	−	2.35390i	−0.0628882	−	0.108926i	−0.895755	+	0.444547i	$0.853364\pi$
$468$	−4.70074	−	37.6347i	−0.217292	−	1.73966i
$469$	47.4416	−	17.2673i	2.19065	−	0.797332i
$470$	−11.5017	−	4.18628i	−0.530534	−	0.193098i
$471$	0.518727	+	3.44626i	0.0239017	+	0.158796i
$472$	0.275115	+	1.56026i	0.0126632	+	0.0718166i
$473$	−7.54145	−	2.74486i	−0.346756	−	0.126209i
$474$	−23.1774	+	7.78197i	−1.06457	+	0.357438i
$475$	−10.0498	+	1.16408i	−0.461115	+	0.0534115i
$476$	23.1560			1.06135
$477$	17.1106	−	5.27031i	0.783438	−	0.241311i
$478$	−32.3342	−	11.7687i	−1.47893	−	0.538288i
$479$	11.2511	+	9.44078i	0.514075	+	0.431360i	0.862561	−	0.505954i	$-0.168859\pi$
$479$	11.2511	+	9.44078i	0.514075	+	0.431360i	−0.348485	+	0.937314i	$0.613304\pi$
$480$	−11.9478	+	19.5427i	−0.545338	+	0.892000i
$481$	−23.9630	−	20.1073i	−1.09262	−	0.916815i
$482$	−7.81207			−0.355830
$483$	19.5308	−	6.55761i	0.888684	−	0.298381i
$484$	−20.0326	+	7.29128i	−0.910574	+	0.331422i
$485$	−14.2143	−	11.9273i	−0.645440	−	0.541589i
$486$	−26.5352	+	17.1002i	−1.20366	+	0.775679i
$487$	−7.61907	+	13.1966i	−0.345253	+	0.597996i	−0.985400	−	0.170257i	$-0.945540\pi$
$487$	−7.61907	+	13.1966i	−0.345253	+	0.597996i	0.640147	+	0.768253i	$0.278874\pi$
$488$	−0.0419446	+	0.237880i	−0.00189874	+	0.0107683i
$489$	14.8816	+	0.374141i	0.672968	+	0.0169193i
$490$	12.9817	−	4.72494i	0.586452	−	0.213451i
$491$	1.96727	+	11.1569i	0.0887817	+	0.503506i	0.996476	+	0.0838747i	$0.0267295\pi$
$491$	1.96727	+	11.1569i	0.0887817	+	0.503506i	−0.907695	+	0.419631i	$0.862159\pi$
$492$	−16.1367	−	0.405696i	−0.727497	−	0.0182902i
$493$	−9.44118	+	16.3526i	−0.425209	+	0.736484i
$494$	−51.6721	−	12.3032i	−2.32484	−	0.553546i
$495$	−20.8038	−	8.77945i	−0.935060	−	0.394607i
$496$	−12.2176	+	10.2518i	−0.548587	+	0.460320i
$497$	−8.58346	+	7.20238i	−0.385021	+	0.323071i
$498$	3.13990	+	20.8605i	0.140702	+	0.934783i
$499$	−19.7458	+	16.5687i	−0.883944	+	0.741717i	−0.966986	−	0.254829i	$-0.917981\pi$
$499$	−19.7458	+	16.5687i	−0.883944	+	0.741717i	0.0830421	+	0.996546i	$0.473536\pi$
$500$	−19.2854	−	16.1824i	−0.862469	−	0.723697i
$501$	1.97286	−	9.74900i	0.0881408	−	0.435553i
$502$	26.8303			1.19749
$503$	−1.07674	−	0.903490i	−0.0480094	−	0.0402846i	0.618467	−	0.785811i	$-0.287754\pi$
$503$	−1.07674	−	0.903490i	−0.0480094	−	0.0402846i	−0.666477	+	0.745526i	$0.732198\pi$
$504$	−2.04711	−	0.102999i	−0.0911857	−	0.00458794i
$505$	−11.7874	−	20.4164i	−0.524532	−	0.908516i
$506$	−16.5732	−	28.7056i	−0.736769	−	1.27612i
$507$	−37.4181	−	14.6943i	−1.66180	−	0.652596i
$508$	29.8086	−	25.0124i	1.32254	−	1.10974i
$509$	−9.39441	+	3.41929i	−0.416400	+	0.151557i	−0.541720	−	0.840559i	$-0.682227\pi$
$509$	−9.39441	+	3.41929i	−0.416400	+	0.151557i	0.125320	+	0.992116i	$0.460004\pi$
$510$	9.87634	−	16.1545i	0.437331	−	0.715335i
$511$	−1.94304	−	11.0195i	−0.0859552	−	0.487476i
$512$	−32.1538			−1.42101
$513$	4.81987	+	22.1307i	0.212802	+	0.977095i
$514$	40.4546			1.78437
$515$	−4.57966	−	25.9726i	−0.201804	−	1.14449i
$516$	−3.31259	+	5.41835i	−0.145829	+	0.238529i
$517$	15.9572	−	5.80794i	0.701796	−	0.255433i
$518$	−26.9499	+	22.6137i	−1.18411	+	0.993588i
$519$	8.87130	+	3.48380i	0.389407	+	0.152922i
$520$	−1.00682	−	1.74387i	−0.0441520	−	0.0764736i
$521$	−19.1561	−	33.1793i	−0.839242	−	1.45361i	−0.890529	−	0.454926i	$-0.849666\pi$
$521$	−19.1561	−	33.1793i	−0.839242	−	1.45361i	0.0512868	−	0.998684i	$-0.483668\pi$
$522$	18.8829	−	29.2104i	0.826481	−	1.27851i
$523$	−29.7406	−	24.9553i	−1.30046	−	1.09122i	−0.990065	−	0.140612i	$-0.955093\pi$
$523$	−29.7406	−	24.9553i	−1.30046	−	1.09122i	−0.310399	−	0.950606i	$-0.600463\pi$
$524$	−21.2520			−0.928398
$525$	−2.66465	+	13.1675i	−0.116295	+	0.574678i
$526$	40.2336	+	33.7600i	1.75427	+	1.47201i
$527$	10.6378	−	8.92614i	0.463388	−	0.388829i
$528$	−4.49063	−	29.8344i	−0.195429	−	1.29837i
$529$	−7.91405	+	6.64067i	−0.344089	+	0.288725i
$530$	15.1533	−	12.7152i	0.658219	−	0.552311i
$531$	−2.88136	−	23.0685i	−0.125041	−	1.00109i
$532$	−12.1508	+	28.0886i	−0.526805	+	1.21779i
$533$	−13.3461	+	23.1161i	−0.578083	+	1.00127i
$534$	13.4850	+	0.339030i	0.583553	+	0.0146713i
$535$	−1.68549	−	9.55889i	−0.0728701	−	0.413267i
$536$	−2.90241	+	1.05639i	−0.125365	+	0.0456291i
$537$	−42.1327	−	1.05927i	−1.81816	−	0.0457108i
$538$	9.73618	−	55.2166i	0.419756	−	2.38056i
$539$	−9.58315	+	16.5985i	−0.412776	+	0.714948i
$540$	−10.0746	+	14.7575i	−0.433543	+	0.635060i
$541$	13.5447	+	11.3654i	0.582332	+	0.488635i	0.885712	−	0.464235i	$-0.153671\pi$
$541$	13.5447	+	11.3654i	0.582332	+	0.488635i	−0.303380	+	0.952870i	$0.598115\pi$
$542$	20.4440	−	7.44101i	0.878145	−	0.319619i
$543$	5.09830	−	1.71179i	0.218789	−	0.0734598i
$544$	26.6475			1.14250
$545$	−4.93936	−	4.14461i	−0.211579	−	0.177536i
$546$	−36.7912	+	60.1787i	−1.57452	+	2.57541i
$547$	9.66841	+	8.11276i	0.413391	+	0.346877i	0.825642	−	0.564194i	$-0.190813\pi$
$547$	9.66841	+	8.11276i	0.413391	+	0.346877i	−0.412251	+	0.911070i	$0.635257\pi$
$548$	−5.89043	−	2.14394i	−0.251627	−	0.0915847i
$549$	0.790104	−	3.45522i	0.0337208	−	0.147465i
$550$	21.6142			0.921634
$551$	−14.8818	−	20.0331i	−0.633986	−	0.853439i
$552$	−1.19487	+	0.401185i	−0.0508570	+	0.0170756i
$553$	21.8891	+	7.96699i	0.930820	+	0.338791i
$554$	2.27148	+	12.8822i	0.0965061	+	0.547313i
$555$	2.19355	+	14.5733i	0.0931112	+	0.618603i
$556$	25.6721	+	9.34386i	1.08874	+	0.396268i
$557$	−31.6129	+	11.5061i	−1.33948	+	0.487531i	−0.909649	−	0.415378i	$-0.863649\pi$
$557$	−31.6129	+	11.5061i	−1.33948	+	0.487531i	−0.429832	+	0.902909i	$0.641427\pi$
$558$	−20.3968	+	15.4370i	−0.863467	+	0.653500i
$559$	5.25081	+	9.09467i	0.222086	+	0.384664i
$560$	19.4695	−	7.08633i	0.822738	−	0.299452i
$561$	3.90994	+	25.9765i	0.165078	+	1.09673i
$562$	−27.3753	+	47.4155i	−1.15476	+	2.00010i
$563$	14.4652			0.609636			0.304818	−	0.952411i	$-0.401404\pi$
$563$	14.4652			0.609636			0.304818	+	0.952411i	$0.401404\pi$
$564$	−2.00009	−	13.2880i	−0.0842190	−	0.559526i
$565$	−8.13590	−	2.96123i	−0.342280	−	0.124580i
$566$	−5.65914	+	32.0946i	−0.237871	+	1.34904i
$567$	29.9246	+	3.01892i	1.25672	+	0.126783i
$568$	0.525124	−	0.440631i	0.0220337	−	0.0184885i
$569$	6.70002	−	11.6048i	0.280880	−	0.486498i	−0.690722	−	0.723120i	$-0.742707\pi$
$569$	6.70002	−	11.6048i	0.280880	−	0.486498i	0.971602	+	0.236623i	$0.0760405\pi$
$570$	14.4132	+	20.4570i	0.603703	+	0.856851i
$571$	4.34004	+	7.51717i	0.181625	+	0.314584i	0.942434	−	0.334392i	$-0.108531\pi$
$571$	4.34004	+	7.51717i	0.181625	+	0.314584i	−0.760809	+	0.648976i	$0.775198\pi$
$572$	54.6308	+	19.8840i	2.28423	+	0.831392i
$573$	−0.672701	−	1.23588i	−0.0281025	−	0.0516298i
$574$	22.9961	+	19.2960i	0.959840	+	0.805401i
$575$	1.43454	+	8.13571i	0.0598246	+	0.339282i
$576$	−26.3255	−	1.32455i	−1.09689	−	0.0551895i
$577$	20.5166	−	35.5357i	0.854116	−	1.47937i	−0.0233465	−	0.999727i	$-0.507432\pi$
$577$	20.5166	−	35.5357i	0.854116	−	1.47937i	0.877463	−	0.479645i	$-0.159235\pi$
$578$	12.3989			0.515727
$579$	−42.2359	−	16.5862i	−1.75526	−	0.689300i
$580$	3.41877	−	19.3888i	0.141957	−	0.805076i
$581$	10.0494	−	17.4062i	0.416921	−	0.722129i
$582$	7.88697	−	38.9739i	0.326925	−	1.61552i
$583$	−4.76561	+	27.0271i	−0.197371	+	1.11935i
$584$	0.118873	+	0.674160i	0.00491898	+	0.0278969i
$585$	13.4692	+	26.2989i	0.556882	+	1.08732i
$586$	−17.8460	−	6.49543i	−0.737213	−	0.268324i
$587$	4.47368	+	25.3715i	0.184649	+	1.04719i	0.926406	+	0.376526i	$0.122881\pi$
$587$	4.47368	+	25.3715i	0.184649	+	1.04719i	−0.741757	+	0.670668i	$0.766007\pi$
$588$	11.3697	+	10.0379i	0.468879	+	0.413957i
$589$	5.24551	+	17.5876i	0.216137	+	0.724686i
$590$	−12.8428	−	22.2444i	−0.528730	−	0.915787i
$591$	−12.4507	−	22.8744i	−0.512154	−	0.940926i
$592$	−15.0844	+	12.6573i	−0.619964	+	0.520211i
$593$	−1.82372	+	10.3428i	−0.0748912	+	0.424729i	0.924192	+	0.381927i	$0.124740\pi$
$593$	−1.82372	+	10.3428i	−0.0748912	+	0.424729i	−0.999084	+	0.0428020i	$0.986372\pi$
$594$	−4.78873	−	48.1516i	−0.196484	−	1.97569i
$595$	−16.9519	+	6.17000i	−0.694962	+	0.252945i
$596$	9.10140	+	15.7641i	0.372808	+	0.645722i
$597$	−23.4663	+	7.87897i	−0.960412	+	0.322465i
$598$	−7.53172	+	42.7145i	−0.307995	+	1.74673i
$599$	5.45448	−	30.9339i	0.222864	−	1.26393i	−0.643862	−	0.765141i	$-0.722669\pi$
$599$	5.45448	−	30.9339i	0.222864	−	1.26393i	0.866726	−	0.498784i	$-0.166220\pi$
$600$	0.163019	−	0.805570i	0.00665524	−	0.0328873i
$601$	−20.3671	−	35.2768i	−0.830791	−	1.43897i	−0.897412	−	0.441194i	$-0.854555\pi$
$601$	−20.3671	−	35.2768i	−0.830791	−	1.43897i	0.0666205	−	0.997778i	$-0.478778\pi$
$602$	11.0984	−	4.03948i	0.452336	−	0.164637i
$603$	43.3140	−	13.3414i	1.76388	−	0.543302i
$604$	2.04635	−	11.6054i	0.0832648	−	0.472218i
$605$	12.7226	−	10.6755i	0.517247	−	0.434022i
$606$	26.3517	−	43.1030i	1.07046	−	1.75094i
$607$	−4.47022	−	7.74264i	−0.181441	−	0.314264i	0.760931	−	0.648833i	$-0.224743\pi$
$607$	−4.47022	−	7.74264i	−0.181441	−	0.314264i	−0.942371	+	0.334569i	$0.891409\pi$
$608$	−13.9829	+	32.3237i	−0.567082	+	1.31090i
$609$	−31.4156	+	10.5480i	−1.27302	+	0.427426i
$610$	−0.680020	−	3.85658i	−0.0275332	−	0.156149i
$611$	−20.8806	−	7.59992i	−0.844739	−	0.307460i
$612$	20.7611	+	1.04458i	0.839219	+	0.0422247i
$613$	−0.199162	−	1.12950i	−0.00804406	−	0.0456201i	0.980522	−	0.196412i	$-0.0629289\pi$
$613$	−0.199162	−	1.12950i	−0.00804406	−	0.0456201i	−0.988566	+	0.150792i	$0.951818\pi$
$614$	−4.23806	+	24.0352i	−0.171034	+	0.969982i
$615$	11.9213	−	4.00267i	0.480715	−	0.161403i
$616$	1.57095	−	2.72097i	0.0632955	−	0.109631i
$617$	−3.43968	+	19.5074i	−0.138476	+	0.785337i	0.833900	+	0.551916i	$0.186103\pi$
$617$	−3.43968	+	19.5074i	−0.138476	+	0.785337i	−0.972376	+	0.233421i	$0.925008\pi$
$618$	44.1940	−	35.2289i	1.77774	−	1.41711i
$619$	−2.75811			−0.110858			−0.0554289	−	0.998463i	$-0.517653\pi$
$619$	−2.75811			−0.110858			−0.0554289	+	0.998463i	$0.517653\pi$
$620$	−7.23952	+	12.5392i	−0.290746	+	0.503587i
$621$	17.8067	−	4.99834i	0.714558	−	0.200577i
$622$	11.1549	+	63.2627i	0.447272	+	2.53660i
$623$	−9.84519	−	8.26109i	−0.394439	−	0.330974i
$624$	−20.5927	+	33.6831i	−0.824368	+	1.34840i
$625$	7.52510	+	2.73891i	0.301004	+	0.109556i
$626$	−8.19079	−	14.1869i	−0.327370	−	0.567021i
$627$	−33.5616	−	8.88803i	−1.34032	−	0.354954i
$628$	−2.11368	+	3.66101i	−0.0843452	+	0.146090i
$629$	13.1338	−	11.0206i	0.523679	−	0.439419i
$630$	31.7581	−	9.78197i	1.26527	−	0.389723i
$631$	7.95077	−	45.0910i	0.316515	−	1.79505i	−0.247081	−	0.968995i	$-0.579471\pi$
$631$	7.95077	−	45.0910i	0.316515	−	1.79505i	0.563596	−	0.826051i	$-0.309418\pi$
$632$	−1.33914	−	0.487409i	−0.0532683	−	0.0193881i
$633$	−27.5085	+	21.9282i	−1.09337	+	0.871568i
$634$	−53.5790			−2.12789
$635$	−15.1575	+	26.2535i	−0.601506	+	1.04184i
$636$	20.2143	+	7.93826i	0.801550	+	0.314773i
$637$	23.5674	−	8.57783i	0.933774	−	0.339866i
$638$	26.6582	+	46.1734i	1.05541	+	1.82802i
$639$	−8.02063	+	6.07027i	−0.317291	+	0.240136i
$640$	−2.51243	+	0.914449i	−0.0993124	+	0.0361468i
$641$	5.99804	+	2.18311i	0.236908	+	0.0862275i	0.457746	−	0.889083i	$-0.348657\pi$
$641$	5.99804	+	2.18311i	0.236908	+	0.0862275i	−0.220838	+	0.975311i	$0.570879\pi$
$642$	16.2651	−	12.9656i	0.641930	−	0.511710i
$643$	−2.66069	−	15.0895i	−0.104927	−	0.595072i	−0.991249	−	0.132003i	$-0.957859\pi$
$643$	−2.66069	−	15.0895i	−0.104927	−	0.595072i	0.886322	−	0.463069i	$-0.153252\pi$
$644$	23.4833	+	8.54721i	0.925371	+	0.336807i
$645$	0.981327	−	4.84929i	0.0386397	−	0.190940i
$646$	11.5586	−	26.7197i	0.454769	−	1.05127i
$647$	16.8690			0.663190			0.331595	−	0.943422i	$-0.392413\pi$
$647$	16.8690			0.663190			0.331595	+	0.943422i	$0.392413\pi$
$648$	−1.83075	−	0.184693i	−0.0719185	−	0.00725542i
$649$	33.4865	+	12.1881i	1.31446	+	0.478424i
$650$	−21.6661	−	18.1800i	−0.849815	−	0.713080i
$651$	24.3637	+	0.612535i	0.954890	+	0.0240071i
$652$	13.8324	+	11.6067i	0.541718	+	0.454555i
$653$	15.6246			0.611437			0.305718	−	0.952122i	$-0.401103\pi$
$653$	15.6246			0.611437			0.305718	+	0.952122i	$0.401103\pi$
$654$	2.74065	−	13.5431i	0.107168	−	0.529576i
$655$	15.5581	−	5.66267i	0.607904	−	0.221259i
$656$	12.8714	+	10.8003i	0.502542	+	0.421683i
$657$	−1.24499	−	9.96751i	−0.0485716	−	0.388870i
$658$	−12.4952	+	21.6424i	−0.487115	+	0.843708i
$659$	3.61092	−	20.4785i	0.140661	−	0.797731i	−0.830087	−	0.557633i	$-0.811709\pi$
$659$	3.61092	−	20.4785i	0.140661	−	0.797731i	0.970749	−	0.240097i	$-0.0771794\pi$
$660$	−13.0944	−	24.0570i	−0.509699	−	0.936416i
$661$	28.1355	−	10.2405i	1.09434	−	0.398308i	0.269115	−	0.963108i	$-0.413269\pi$
$661$	28.1355	−	10.2405i	1.09434	−	0.398308i	0.825228	+	0.564800i	$0.191047\pi$
$662$	2.20942	+	12.5302i	0.0858714	+	0.487001i
$663$	17.9299	−	29.3276i	0.696338	−	1.13899i
$664$	−0.614811	+	1.06488i	−0.0238593	+	0.0413255i
$665$	1.41102	−	23.8006i	0.0547169	−	0.922946i
$666$	−25.1828	+	19.0591i	−0.975812	+	0.738527i
$667$	−15.6106	+	13.0988i	−0.604444	+	0.507189i
$668$	9.24242	−	7.75531i	0.357600	−	0.300062i
$669$	1.97397	−	1.57354i	0.0763182	−	0.0608365i
$670$	38.3594	−	32.1874i	1.48195	−	1.24351i
$671$	4.16197	+	3.49231i	0.160671	+	0.134819i
$672$	35.0588	+	30.9522i	1.35242	+	1.19401i
$673$	21.3235			0.821960			0.410980	−	0.911644i	$-0.365187\pi$
$673$	21.3235			0.821960			0.410980	+	0.911644i	$0.365187\pi$
$674$	−9.47923	−	7.95402i	−0.365126	−	0.306377i
$675$	−2.98306	+	11.6855i	−0.114818	+	0.449774i
$676$	−24.3810	−	42.2292i	−0.937732	−	1.62420i
$677$	12.7705	+	22.1191i	0.490808	+	0.850105i	0.999944	−	0.0105812i	$-0.00336815\pi$
$677$	12.7705	+	22.1191i	0.490808	+	0.850105i	−0.509136	+	0.860686i	$0.670035\pi$
$678$	−2.76160	−	18.3473i	−0.106059	−	0.704623i
$679$	−29.0219	+	24.3522i	−1.11376	+	0.934553i
$680$	1.03709	−	0.377472i	0.0397708	−	0.0144754i
$681$	−2.38972	−	4.39037i	−0.0915741	−	0.168239i
$682$	−6.80882	−	38.6147i	−0.260723	−	1.47863i
$683$	−11.6108			−0.444275			−0.222138	−	0.975015i	$-0.571303\pi$
$683$	−11.6108			−0.444275			−0.222138	+	0.975015i	$0.571303\pi$
$684$	−12.1612	+	24.6354i	−0.464996	+	0.941958i
$685$	4.88350			0.186589
$686$	3.32821	+	18.8752i	0.127072	+	0.720659i
$687$	6.69938	+	0.168431i	0.255597	+	0.00642604i
$688$	6.21196	−	2.26097i	0.236829	−	0.0861986i
$689$	27.5099	−	23.0836i	1.04805	−	0.879414i
$690$	15.9788	−	12.7374i	0.608302	−	0.484903i
$691$	12.9765	+	22.4760i	0.493651	+	0.855029i	0.999973	−	0.00731577i	$-0.00232870\pi$
$691$	12.9765	+	22.4760i	0.493651	+	0.855029i	−0.506322	+	0.862344i	$0.668995\pi$
$692$	5.78040	+	10.0119i	0.219738	+	0.380597i
$693$	−25.0288	+	38.7177i	−0.950764	+	1.47076i
$694$	−45.6552	−	38.3093i	−1.73305	−	1.45420i
$695$	−21.2836			−0.807332
$696$	1.92196	−	0.645311i	0.0728517	−	0.0244605i
$697$	−11.2070	−	9.40376i	−0.424494	−	0.356193i
$698$	45.2538	−	37.9724i	1.71288	−	1.43728i
$699$	−4.27347	−	1.67821i	−0.161637	−	0.0634758i
$700$	−12.4833	+	10.4748i	−0.471825	+	0.395908i
$701$	6.57464	−	5.51678i	0.248321	−	0.208366i	−0.510128	−	0.860098i	$-0.670402\pi$
$701$	6.57464	−	5.51678i	0.248321	−	0.208366i	0.758449	+	0.651733i	$0.225958\pi$
$702$	−35.7008	+	52.2951i	−1.34744	+	1.97375i
$703$	6.47631	+	21.7144i	0.244259	+	0.818974i
$704$	20.2021	−	34.9911i	0.761397	−	1.31878i
$705$	5.00485	+	9.19488i	0.188494	+	0.346299i
$706$	9.38314	+	53.2144i	0.353139	+	2.00275i
$707$	−45.2305	+	16.4626i	−1.70107	+	0.619139i
$708$	14.7090	−	24.0592i	0.552798	−	0.904201i
$709$	−0.167217	+	0.948336i	−0.00627997	+	0.0356155i	−0.987787	−	0.155812i	$-0.950201\pi$
$709$	−0.167217	+	0.948336i	−0.00627997	+	0.0356155i	0.981507	+	0.191428i	$0.0613117\pi$
$710$	−5.55678	+	9.62462i	−0.208542	+	0.361206i
$711$	19.2659	+	8.13044i	0.722526	+	0.304915i
$712$	0.602314	+	0.505402i	0.0225727	+	0.0189407i
$713$	14.0829	−	5.12575i	0.527408	−	0.191961i
$714$	−28.9805	−	25.5859i	−1.08457	−	0.957529i
$715$	−45.2920			−1.69383
$716$	−39.1622	−	32.8610i	−1.46356	−	1.22807i
$717$	14.0699	+	25.8492i	0.525451	+	0.965355i
$718$	12.3996	+	10.4045i	0.462749	+	0.388292i
$719$	−17.6880	−	6.43790i	−0.659650	−	0.240093i	−0.00956499	−	0.999954i	$-0.503045\pi$
$719$	−17.6880	−	6.43790i	−0.659650	−	0.240093i	−0.650085	+	0.759861i	$0.725267\pi$
$720$	17.7756	−	5.47515i	0.662457	−	0.204047i
$721$	−53.8470			−2.00537
$722$	26.3461	+	28.0416i	0.980499	+	1.04360i
$723$	5.00888	+	4.42217i	0.186282	+	0.164462i
$724$	6.13004	+	2.23115i	0.227821	+	0.0829201i
$725$	−2.30748	−	13.0864i	−0.0856978	−	0.486016i
$726$	33.1279	+	13.0095i	1.22949	+	0.482828i
$727$	−7.38625	−	2.68837i	−0.273941	−	0.0997063i	0.201397	−	0.979510i	$-0.435452\pi$
$727$	−7.38625	−	2.68837i	−0.273941	−	0.0997063i	−0.475338	+	0.879803i	$0.657674\pi$
$728$	−3.86337	+	1.40615i	−0.143186	+	0.0521155i
$729$	26.6935	+	4.05661i	0.988649	+	0.150245i
$730$	−5.54915	−	9.61142i	−0.205383	−	0.355734i
$731$	−5.40869	+	1.96860i	−0.200048	+	0.0728114i
$732$	3.36189	−	2.67990i	0.124259	−	0.0990520i
$733$	−13.4417	+	23.2817i	−0.496481	+	0.859930i	−0.999992	−	0.00405915i	$-0.998708\pi$
$733$	−13.4417	+	23.2817i	−0.496481	+	0.859930i	0.503511	+	0.863989i	$0.332041\pi$
$734$	30.1785			1.11391
$735$	−10.9981	−	4.31902i	−0.405672	−	0.159309i
$736$	27.0241	+	9.83596i	0.996120	+	0.362558i
$737$	−12.0638	+	68.4169i	−0.444374	+	2.52017i
$738$	19.7473	+	18.3377i	0.726909	+	0.675021i
$739$	16.8603	−	14.1474i	0.620215	−	0.520422i	−0.277656	−	0.960680i	$-0.589558\pi$
$739$	16.8603	−	14.1474i	0.620215	−	0.520422i	0.897871	+	0.440259i	$0.145113\pi$
$740$	−8.93820	+	15.4814i	−0.328575	+	0.569108i
$741$	26.1663	+	37.1385i	0.961242	+	1.36432i
$742$	−20.1940	−	34.9771i	−0.741346	−	1.28405i
$743$	14.1896	+	5.16458i	0.520565	+	0.189470i	0.588921	−	0.808191i	$-0.299553\pi$
$743$	14.1896	+	5.16458i	0.520565	+	0.189470i	−0.0683556	+	0.997661i	$0.521775\pi$
$744$	−1.49054	−	0.0374740i	−0.0546458	−	0.00137386i
$745$	−10.8633	−	9.11539i	−0.398001	−	0.333962i
$746$	−3.95706	−	22.4416i	−0.144878	−	0.821645i
$747$	9.79529	−	15.1526i	0.358391	−	0.554405i
$748$	−15.9321	+	27.5952i	−0.582534	+	1.00898i
$749$	−19.8177			−0.724124
$750$	6.25584	+	41.5619i	0.228431	+	1.51763i
$751$	−1.03504	+	5.87003i	−0.0377693	+	0.214200i	−0.997851	−	0.0655180i	$-0.979130\pi$
$751$	−1.03504	+	5.87003i	−0.0377693	+	0.214200i	0.960082	+	0.279718i	$0.0902411\pi$
$752$	−6.99381	+	12.1136i	−0.255038	+	0.441739i
$753$	−17.2028	−	15.1878i	−0.626906	−	0.553474i
$754$	12.1149	−	68.7069i	0.441198	−	2.50216i
$755$	1.59422	+	9.04129i	0.0580198	+	0.329046i
$756$	26.1011	+	25.4893i	0.949288	+	0.927037i
$757$	−41.7714	−	15.2035i	−1.51821	−	0.552582i	−0.557507	−	0.830172i	$-0.688242\pi$
$757$	−41.7714	−	15.2035i	−1.51821	−	0.552582i	−0.960700	+	0.277590i	$0.910464\pi$
$758$	−0.913376	−	5.18001i	−0.0331753	−	0.188147i
$759$	−5.62309	+	27.7868i	−0.204105	+	1.00860i
$760$	−0.0863240	+	1.45608i	−0.00313130	+	0.0528177i
$761$	0.124644	+	0.215890i	0.00451835	+	0.00782602i	0.868276	−	0.496082i	$-0.165228\pi$
$761$	0.124644	+	0.215890i	0.00451835	+	0.00782602i	−0.863757	+	0.503908i	$0.831895\pi$
$762$	−64.9435	−	1.63276i	−2.35266	−	0.0591487i
$763$	−10.0848	+	8.46218i	−0.365095	+	0.306351i
$764$	0.296382	−	1.68087i	0.0107227	−	0.0608117i
$765$	−15.4770	+	4.76716i	−0.559573	+	0.172357i
$766$	3.48310	−	1.26774i	0.125849	−	0.0458055i
$767$	−23.3153	−	40.3833i	−0.841867	−	1.45816i
$768$	18.5214	+	16.3519i	0.668335	+	0.590050i
$769$	7.05924	−	40.0349i	0.254563	−	1.44370i	−0.542630	−	0.839972i	$-0.682572\pi$
$769$	7.05924	−	40.0349i	0.254563	−	1.44370i	0.797193	−	0.603725i	$-0.206317\pi$
$770$	−8.84523	+	50.1638i	−0.318760	+	1.80778i
$771$	−25.9383	−	22.9001i	−0.934147	−	0.824726i
$772$	−27.5202	−	47.6664i	−0.990475	−	1.71555i
$773$	−10.8974	+	3.96632i	−0.391951	+	0.142659i	−0.530475	−	0.847700i	$-0.677986\pi$
$773$	−10.8974	+	3.96632i	−0.391951	+	0.142659i	0.138524	+	0.990359i	$0.455764\pi$
$774$	10.1328	−	3.12104i	0.364214	−	0.112184i
$775$	−1.69699	+	9.62410i	−0.0609577	+	0.345708i
$776$	1.77551	−	1.48983i	0.0637373	−	0.0534819i
$777$	30.0804	+	0.756260i	1.07913	+	0.0271307i
$778$	−8.29269	−	14.3634i	−0.297307	−	0.514951i
$779$	17.2876	−	8.65970i	0.619393	−	0.310266i
$780$	−7.10881	+	35.1286i	−0.254536	+	1.25781i
$781$	−2.67742	−	15.1844i	−0.0958058	−	0.543342i
$782$	−22.3388	−	8.13066i	−0.798834	−	0.290752i
$783$	−28.6423	+	8.03990i	−1.02359	+	0.287323i
$784$	−2.74146	−	15.5476i	−0.0979094	−	0.555272i
$785$	0.571887	−	3.24333i	0.0204115	−	0.115759i
$786$	26.5976	+	23.4821i	0.948705	+	0.837580i
$787$	−26.1852	+	45.3542i	−0.933403	+	1.61670i	−0.155945	+	0.987766i	$0.549842\pi$
$787$	−26.1852	+	45.3542i	−0.933403	+	1.61670i	−0.777458	+	0.628935i	$0.783491\pi$
$788$	5.48560	−	31.1104i	0.195416	−	1.10826i
$789$	−6.68618	−	44.4210i	−0.238034	−	1.58143i
$790$	23.1040			0.822003
$791$	−8.83870	+	15.3091i	−0.314268	+	0.544328i
$792$	1.53122	−	2.36869i	0.0544097	−	0.0841677i
$793$	−1.23453	−	7.00139i	−0.0438396	−	0.248627i
$794$	26.6211	+	22.3378i	0.944747	+	0.792737i
$795$	−16.9136	−	0.425228i	−0.599862	−	0.0150813i
$796$	−28.2152	−	10.2695i	−1.00006	−	0.363992i
$797$	6.28491	+	10.8858i	0.222623	+	0.385594i	0.955604	−	0.294655i	$-0.0952048\pi$
$797$	6.28491	+	10.8858i	0.222623	+	0.385594i	−0.732981	+	0.680249i	$0.761871\pi$
$798$	46.2433	−	21.7279i	1.63699	−	0.769160i
$799$	6.08944	−	10.5472i	0.215429	−	0.373134i
$800$	−14.3655	+	12.0541i	−0.507899	+	0.426178i
$801$	−8.45429	−	7.85082i	−0.298718	−	0.277395i
$802$	−7.85467	+	44.5461i	−0.277358	+	1.57298i
$803$	14.4689	+	5.26626i	0.510598	+	0.185842i
$804$	51.1709	+	20.0951i	1.80466	+	0.708698i
$805$	−19.4690			−0.686190
$806$	−25.6542	+	44.4344i	−0.903632	+	1.56514i
$807$	−37.4990	+	29.8920i	−1.32003	+	1.05225i
$808$	2.76714	−	1.00716i	0.0973476	−	0.0354316i
$809$	14.8222	+	25.6727i	0.521119	+	0.902605i	0.999698	+	0.0245605i	$0.00781864\pi$
$809$	14.8222	+	25.6727i	0.521119	+	0.902605i	−0.478579	+	0.878044i	$0.658848\pi$
$810$	28.9148	−	7.33766i	1.01596	−	0.257819i
$811$	−6.44816	+	2.34694i	−0.226426	+	0.0824122i	−0.452742	−	0.891642i	$-0.649554\pi$
$811$	−6.44816	+	2.34694i	−0.226426	+	0.0824122i	0.226316	+	0.974054i	$0.427332\pi$
$812$	−37.7732	−	13.7483i	−1.32558	−	0.482471i
$813$	−17.3202	−	6.80175i	−0.607448	−	0.238548i
$814$	−8.40644	−	47.6753i	−0.294646	−	1.67102i
$815$	−13.2190	−	4.81132i	−0.463041	−	0.168533i
$816$	−16.2209	−	14.3209i	−0.567847	−	0.501332i
$817$	0.450200	−	7.59382i	0.0157505	−	0.265674i
$818$	31.0562			1.08586
$819$	57.6548	−	17.7586i	2.01462	−	0.620534i
$820$	14.3339	+	5.21710i	0.500560	+	0.182189i
$821$	10.3304	+	8.66820i	0.360532	+	0.302522i	0.805003	−	0.593271i	$-0.202164\pi$
$821$	10.3304	+	8.66820i	0.360532	+	0.302522i	−0.444471	+	0.895793i	$0.646608\pi$
$822$	5.00316	+	9.19177i	0.174505	+	0.320600i
$823$	9.61267	+	8.06599i	0.335077	+	0.281163i	0.794765	−	0.606918i	$-0.207594\pi$
$823$	9.61267	+	8.06599i	0.335077	+	0.281163i	−0.459688	+	0.888080i	$0.652039\pi$
$824$	3.29428			0.114762
$825$	−13.8585	−	12.2352i	−0.482489	−	0.425973i
$826$	−49.2804	+	17.9366i	−1.71468	+	0.624094i
$827$	13.2010	+	11.0770i	0.459044	+	0.385184i	0.842779	−	0.538260i	$-0.180918\pi$
$827$	13.2010	+	11.0770i	0.459044	+	0.385184i	−0.383735	+	0.923443i	$0.625362\pi$
$828$	20.6690	+	8.72257i	0.718296	+	0.303130i
$829$	−3.36576	+	5.82966i	−0.116898	+	0.202473i	−0.918537	−	0.395336i	$-0.870628\pi$
$829$	−3.36576	+	5.82966i	−0.116898	+	0.202473i	0.801639	+	0.597808i	$0.203962\pi$
$830$	3.46168	−	19.6322i	0.120157	−	0.681442i
$831$	5.83582	−	9.54554i	0.202442	−	0.331131i
$832$	−49.6822	+	18.0828i	−1.72242	+	0.626909i
$833$	2.38696	+	13.5372i	0.0827034	+	0.469034i
$834$	−21.8051	−	40.0602i	−0.755048	−	1.38717i
$835$	−4.69972	+	8.14015i	−0.162640	+	0.281701i
$836$	−25.1132	−	33.8060i	−0.868557	−	1.16921i
$837$	21.8163	+	1.64825i	0.754082	+	0.0569717i
$838$	1.70187	−	1.42804i	0.0587900	−	0.0493307i
$839$	−25.0718	+	21.0377i	−0.865574	+	0.726303i	−0.963161	−	0.268924i	$-0.913332\pi$
$839$	−25.0718	+	21.0377i	−0.865574	+	0.726303i	0.0975873	+	0.995227i	$0.468887\pi$
$840$	1.80291	+	0.708011i	0.0622062	+	0.0244287i
$841$	2.89455	−	2.42882i	0.0998121	−	0.0837523i
$842$	−13.8871	−	11.6527i	−0.478582	−	0.401578i
$843$	44.3927	−	14.9052i	1.52897	−	0.513361i
$844$	−42.6718			−1.46882
$845$	29.1009	+	24.4185i	1.00110	+	0.840023i
$846$	−12.1792	+	18.8404i	−0.418730	+	0.647745i
$847$	−16.9547	−	29.3664i	−0.582570	−	1.00904i
$848$	−11.3030	−	19.5773i	−0.388145	−	0.672287i
$849$	21.7962	−	17.3747i	0.748045	−	0.596298i
$850$	11.8749	−	9.96426i	0.407307	−	0.341771i
$851$	17.3873	−	6.32845i	0.596028	−	0.216937i
$852$	−12.1973	−	0.306656i	−0.417873	−	0.0105058i
$853$	7.65866	+	43.4344i	0.262228	+	1.48717i	0.776815	+	0.629729i	$0.216834\pi$
$853$	7.65866	+	43.4344i	0.262228	+	1.48717i	−0.514588	+	0.857438i	$0.672055\pi$
$854$	−7.99557			−0.273603
$855$	2.33874	−	21.2754i	0.0799833	−	0.727602i
$856$	1.21242			0.0414397
$857$	−2.04661	−	11.6069i	−0.0699109	−	0.396484i	−0.999604	−	0.0281486i	$-0.991039\pi$
$857$	−2.04661	−	11.6069i	−0.0699109	−	0.396484i	0.929693	−	0.368336i	$-0.120072\pi$
$858$	−46.4018	−	85.2491i	−1.58413	−	2.91036i
$859$	11.6015	−	4.22262i	0.395840	−	0.144074i	−0.136428	−	0.990650i	$-0.543562\pi$
$859$	11.6015	−	4.22262i	0.395840	−	0.144074i	0.532268	+	0.846576i	$0.321340\pi$
$860$	4.59731	−	3.85760i	0.156767	−	0.131543i
$861$	−3.82159	−	25.3895i	−0.130239	−	0.865271i
$862$	−36.8027	−	63.7441i	−1.25351	−	2.17113i
$863$	−13.9436	−	24.1510i	−0.474645	−	0.822110i	0.524933	−	0.851143i	$-0.324090\pi$
$863$	−13.9436	−	24.1510i	−0.474645	−	0.822110i	−0.999578	+	0.0290338i	$0.990757\pi$
$864$	30.0366	+	29.3325i	1.02187	+	0.997914i
$865$	−6.89940	−	5.78928i	−0.234587	−	0.196842i
$866$	−8.51315			−0.289289
$867$	−7.94984	−	7.01864i	−0.269991	−	0.238366i
$868$	22.6460	+	19.0023i	0.768656	+	0.644979i
$869$	−24.5547	+	20.6039i	−0.832962	+	0.698938i
$870$	−25.7021	+	20.4882i	−0.871383	+	0.694616i
$871$	69.6391	−	58.4342i	2.35963	−	1.97997i
$872$	0.616975	−	0.517704i	0.0208934	−	0.0175317i
$873$	−27.1188	+	20.5244i	−0.917833	+	0.694646i
$874$	21.5846	−	22.8308i	0.730110	−	0.772264i
$875$	20.0222	−	34.6795i	0.676875	−	1.17238i
$876$	6.35550	−	10.3956i	0.214732	−	0.351234i
$877$	−2.35231	−	13.3406i	−0.0794317	−	0.450480i	−0.998420	−	0.0561945i	$-0.982103\pi$
$877$	−2.35231	−	13.3406i	−0.0794317	−	0.450480i	0.918988	−	0.394285i	$-0.129008\pi$
$878$	51.2359	−	18.6483i	1.72913	−	0.629351i
$879$	7.76553	+	14.2668i	0.261925	+	0.481207i
$880$	−4.95083	+	28.0776i	−0.166893	+	0.946495i
$881$	22.9782	−	39.7993i	0.774154	−	1.34087i	−0.161115	−	0.986936i	$-0.551509\pi$
$881$	22.9782	−	39.7993i	0.774154	−	1.34087i	0.935269	−	0.353938i	$-0.115158\pi$
$882$	−3.13831	−	25.1256i	−0.105672	−	0.846024i
$883$	28.1694	+	23.6369i	0.947976	+	0.795446i	0.978955	−	0.204074i	$-0.0654183\pi$
$883$	28.1694	+	23.6369i	0.947976	+	0.795446i	−0.0309797	+	0.999520i	$0.509863\pi$
$884$	39.1810	−	14.2607i	1.31780	−	0.479640i
$885$	−4.35741	+	21.5324i	−0.146473	+	0.723804i
$886$	50.3785			1.69250
$887$	11.4007	+	9.56629i	0.382797	+	0.321205i	0.813799	−	0.581146i	$-0.197396\pi$
$887$	11.4007	+	9.56629i	0.382797	+	0.321205i	−0.431002	+	0.902351i	$0.641840\pi$
$888$	−1.84028	−	0.0462669i	−0.0617557	−	0.00155262i
$889$	47.4143	+	39.7853i	1.59022	+	1.33436i
$890$	−11.9784	−	4.35980i	−0.401518	−	0.146141i
$891$	−24.1868	+	33.5843i	−0.810287	+	1.12511i
$892$	3.06207			0.102526
$893$	9.59857	+	12.9211i	0.321204	+	0.432388i
$894$	6.02761	−	29.7858i	0.201593	−	0.996185i
$895$	37.4256	+	13.6218i	1.25100	+	0.455327i
$896$	0.947930	+	5.37598i	0.0316681	+	0.179599i
$897$	29.0085	−	23.1239i	0.968565	−	0.772084i
$898$	−42.8694	−	15.6032i	−1.43057	−	0.520685i
$899$	−22.6525	+	8.24483i	−0.755503	+	0.274981i
$900$	−11.6648	+	8.82828i	−0.388826	+	0.294276i
$901$	9.84138	+	17.0458i	0.327864	+	0.567877i
$902$	−38.8173	+	14.1283i	−1.29247	+	0.470422i
$903$	−9.40259	−	3.69244i	−0.312899	−	0.122877i
$904$	0.540738	−	0.936586i	0.0179847	−	0.0311504i
$905$	−5.08215			−0.168936
$906$	−15.3843	+	12.2635i	−0.511110	+	0.407427i
$907$	−28.5039	−	10.3746i	−0.946456	−	0.344482i	−0.177744	−	0.984077i	$-0.556880\pi$
$907$	−28.5039	−	10.3746i	−0.946456	−	0.344482i	−0.768712	+	0.639595i	$0.779102\pi$
$908$	1.05287	−	5.97114i	0.0349408	−	0.198159i
$909$	−41.2952	+	12.7196i	−1.36968	+	0.421881i
$910$	51.0599	−	42.8443i	1.69262	−	1.42028i
$911$	−11.0550	+	19.1478i	−0.366269	+	0.634396i	−0.988979	−	0.148057i	$-0.952698\pi$
$911$	−11.0550	+	19.1478i	−0.366269	+	0.634396i	0.622710	+	0.782453i	$0.286032\pi$
$912$	25.8832	−	12.1615i	0.857079	−	0.402708i
$913$	13.8287	+	23.9520i	0.457662	+	0.792695i
$914$	29.5020	+	10.7379i	0.975839	+	0.355177i
$915$	−1.74708	+	2.85767i	−0.0577568	+	0.0944718i
$916$	6.22705	+	5.22512i	0.205748	+	0.172643i
$917$	−5.87000	−	33.2904i	−0.193844	−	1.09935i
$918$	−24.8291	−	24.2471i	−0.819481	−	0.800272i
$919$	−10.9848	+	19.0262i	−0.362355	+	0.627618i	−0.988348	−	0.152211i	$-0.951361\pi$
$919$	−10.9848	+	19.0262i	−0.362355	+	0.627618i	0.625993	+	0.779829i	$0.284694\pi$
$920$	1.19108			0.0392688
$921$	16.3229	−	13.0117i	0.537858	−	0.428749i
$922$	1.76726	−	10.0226i	0.0582016	−	0.330078i
$923$	−10.0880	+	17.4729i	−0.332050	+	0.575127i
$924$	−53.0141	+	17.7998i	−1.74404	+	0.585572i
$925$	−2.09517	+	11.8823i	−0.0688888	+	0.390688i
$926$	13.0314	+	73.9050i	0.428240	+	2.42867i
$927$	−48.2779	−	2.42907i	−1.58566	−	0.0797811i
$928$	−43.4686	−	15.8213i	−1.42693	−	0.519359i
$929$	−9.22044	−	52.2917i	−0.302513	−	1.71564i	−0.634987	−	0.772523i	$-0.718994\pi$
$929$	−9.22044	−	52.2917i	−0.302513	−	1.71564i	0.332474	−	0.943113i	$-0.392117\pi$
$930$	22.9155	−	7.69405i	0.751430	−	0.252298i
$931$	−17.6733	−	4.20803i	−0.579218	−	0.137913i
$932$	−2.78453	−	4.82294i	−0.0912102	−	0.157981i
$933$	28.6589	−	46.8768i	0.938249	−	1.53468i
$934$	−4.21652	+	3.53808i	−0.137969	+	0.115770i
$935$	4.31064	−	24.4469i	0.140973	−	0.799498i
$936$	−3.52724	+	1.08644i	−0.115291	+	0.0355115i
$937$	44.7864	−	16.3009i	1.46311	−	0.532527i	0.516887	−	0.856053i	$-0.327091\pi$
$937$	44.7864	−	16.3009i	1.46311	−	0.532527i	0.946219	+	0.323526i	$0.104868\pi$
$938$	−51.1195	−	88.5415i	−1.66911	−	2.89098i
$939$	−2.77904	+	13.7328i	−0.0906905	+	0.448152i
$940$	−2.20506	+	12.5055i	−0.0719212	+	0.407886i
$941$	−0.0481674	+	0.273171i	−0.00157021	+	0.00890511i	−0.985583	−	0.169194i	$-0.945884\pi$
$941$	−0.0481674	+	0.273171i	−0.00157021	+	0.00890511i	0.984013	+	0.178099i	$0.0569947\pi$
$942$	6.69053	−	2.24639i	0.217989	−	0.0731914i
$943$	−7.89429	−	13.6733i	−0.257073	−	0.445264i
$944$	−27.5831	+	10.0394i	−0.897755	+	0.326756i
$945$	−25.8997	−	11.7053i	−0.842517	−	0.380775i
$946$	−2.82216	+	16.0053i	−0.0917564	+	0.520376i
$947$	36.9997	−	31.0465i	1.20233	−	1.00887i	0.202769	−	0.979227i	$-0.435006\pi$
$947$	36.9997	−	31.0465i	1.20233	−	1.00887i	0.999560	−	0.0296477i	$-0.00943853\pi$
$948$	12.1264	+	22.2786i	0.393848	+	0.723574i
$949$	−10.0741	−	17.4489i	−0.327020	−	0.566416i
$950$	5.85556	+	19.6331i	0.189979	+	0.636981i
$951$	34.3534	+	30.3294i	1.11398	+	0.983499i
$952$	−0.391292	−	2.21913i	−0.0126818	−	0.0719223i
$953$	0.146928	+	0.0534775i	0.00475947	+	0.00173231i	0.344399	−	0.938823i	$-0.388083\pi$
$953$	0.146928	+	0.0534775i	0.00475947	+	0.00173231i	−0.339639	+	0.940556i	$0.610305\pi$
$954$	−16.5276	−	32.2705i	−0.535102	−	1.04480i
$955$	0.230899	+	1.30949i	0.00747172	+	0.0423742i
$956$	−6.19900	+	35.1563i	−0.200490	+	1.13704i
$957$	9.04482	−	44.6955i	0.292378	−	1.44480i
$958$	14.8714	−	25.7581i	0.480475	−	0.832206i
$959$	1.73141	−	9.81930i	0.0559101	−	0.317082i
$960$	23.1850	+	9.10487i	0.748293	+	0.293859i
$961$	−13.2716			−0.428115
$962$	−31.6737	+	54.8605i	−1.02120	+	1.76877i
$963$	−17.7681	−	0.893990i	−0.572569	−	0.0288084i
$964$	1.40738	+	7.98164i	0.0453286	+	0.257071i
$965$	32.8477	+	27.5625i	1.05741	+	0.887269i
$966$	−19.9460	−	36.6447i	−0.641752	−	1.17902i
$967$	37.6205	+	13.6928i	1.20980	+	0.440329i	0.866633	−	0.498947i	$-0.166280\pi$
$967$	37.6205	+	13.6928i	1.20980	+	0.440329i	0.343163	+	0.939276i	$0.388502\pi$
$968$	1.03726	+	1.79659i	0.0333389	+	0.0577447i
$969$	−22.5363	+	10.5889i	−0.723969	+	0.340165i
$970$	−18.7882	+	32.5422i	−0.603253	+	1.04487i
$971$	−34.3716	+	28.8412i	−1.10304	+	0.925557i	−0.997626	−	0.0688716i	$-0.978060\pi$
$971$	−34.3716	+	28.8412i	−1.10304	+	0.925557i	−0.105411	+	0.994429i	$0.533616\pi$
$972$	22.2518	+	24.0305i	0.713727	+	0.770779i
$973$	−7.54593	+	42.7951i	−0.241911	+	1.37195i
$974$	28.9975	+	10.5542i	0.929140	+	0.338179i
$975$	3.60056	+	23.9211i	0.115310	+	0.766087i
$976$	−4.47527			−0.143250
$977$	23.3962	−	40.5235i	0.748512	−	1.29646i	−0.200024	−	0.979791i	$-0.564102\pi$
$977$	23.3962	−	40.5235i	0.748512	−	1.29646i	0.948536	−	0.316670i	$-0.102565\pi$
$978$	−4.48698	−	29.8101i	−0.143478	−	0.953223i
$979$	16.6186	−	6.04867i	0.531133	−	0.193316i
$980$	−7.16620	−	12.4122i	−0.228916	−	0.396494i
$981$	−9.42355	+	7.13205i	−0.300871	+	0.227709i
$982$	21.5587	−	7.84672i	0.687966	−	0.250399i
$983$	−1.79749	−	0.654233i	−0.0573310	−	0.0208668i	0.313195	−	0.949689i	$-0.398601\pi$
$983$	−1.79749	−	0.654233i	−0.0573310	−	0.0208668i	−0.370526	+	0.928822i	$0.620823\pi$
$984$	0.233799	+	1.55329i	0.00745324	+	0.0495171i
$985$	4.27360	+	24.2368i	0.136168	+	0.772248i
$986$	35.9323	+	13.0783i	1.14432	+	0.416497i
$987$	20.2627	−	6.80333i	0.644968	−	0.216552i
$988$	−3.26128	+	55.0102i	−0.103755	+	1.75011i
$989$	−6.21177			−0.197523
$990$	−10.1933	+	44.5766i	−0.323965	+	1.41674i
$991$	39.9043	+	14.5240i	1.26760	+	0.461370i	0.886313	−	0.463086i	$-0.153258\pi$
$991$	39.9043	+	14.5240i	1.26760	+	0.461370i	0.381289	+	0.924456i	$0.375480\pi$
$992$	26.0606	+	21.8674i	0.827424	+	0.694291i
$993$	5.67635	−	9.28471i	0.180134	−	0.294641i
$994$	17.3822	+	14.5854i	0.551330	+	0.462621i
$995$	23.3920			0.741575
$996$	20.7477	−	6.96617i	0.657416	−	0.220732i
$997$	56.9057	−	20.7120i	1.80222	−	0.655955i	0.804113	−	0.594477i	$-0.202641\pi$
$997$	56.9057	−	20.7120i	1.80222	−	0.655955i	0.998108	−	0.0614784i	$-0.0195815\pi$
$998$	39.9869	+	33.5530i	1.26576	+	1.06210i
$999$	26.9353	+	2.03499i	0.852195	+	0.0643843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.v.a.25.4	✓	108
3.2	odd	2		513.2.z.a.424.15		108
9.4	even	3		171.2.w.a.139.15	yes	108
9.5	odd	6		513.2.bd.a.253.4		108
19.16	even	9		171.2.w.a.16.15	yes	108
57.35	odd	18		513.2.bd.a.73.4		108
171.130	even	9	inner	171.2.v.a.130.4	yes	108
171.149	odd	18		513.2.z.a.415.15		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.v.a.25.4	✓	108	1.1	even	1	trivial
171.2.v.a.130.4	yes	108	171.130	even	9	inner
171.2.w.a.16.15	yes	108	19.16	even	9
171.2.w.a.139.15	yes	108	9.4	even	3
513.2.z.a.415.15		108	171.149	odd	18
513.2.z.a.424.15		108	3.2	odd	2
513.2.bd.a.73.4		108	57.35	odd	18
513.2.bd.a.253.4		108	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.351652 - 1.99432i) q^{2} +(-0.903452 + 1.47776i) q^{3} +(-1.97425 + 0.718570i) q^{4} +(1.25384 - 1.05209i) q^{5} +(3.26482 + 1.28211i) q^{6} +(-1.67092 - 2.89412i) q^{7} +(0.102224 + 0.177058i) q^{8} +(-1.36755 - 2.67017i) q^{9} +O(q^{10})\)	\(q+(-0.351652 - 1.99432i) q^{2} +(-0.903452 + 1.47776i) q^{3} +(-1.97425 + 0.718570i) q^{4} +(1.25384 - 1.05209i) q^{5} +(3.26482 + 1.28211i) q^{6} +(-1.67092 - 2.89412i) q^{7} +(0.102224 + 0.177058i) q^{8} +(-1.36755 - 2.67017i) q^{9} +(-2.53912 - 2.13058i) q^{10} +4.59858 q^{11} +(0.721770 - 3.56667i) q^{12} +(-4.60962 - 3.86793i) q^{13} +(-5.18420 + 4.35006i) q^{14} +(0.421961 + 2.80339i) q^{15} +(-2.90169 + 2.43481i) q^{16} +(2.52648 - 2.11996i) q^{17} +(-4.84426 + 3.66630i) q^{18} +(1.24581 + 4.17707i) q^{19} +(-1.71939 + 2.97807i) q^{20} +(5.78640 + 0.145477i) q^{21} +(-1.61710 - 9.17102i) q^{22} +(3.34469 - 1.21737i) q^{23} +(-0.354004 - 0.00890010i) q^{24} +(-0.403036 + 2.28573i) q^{25} +(-6.09289 + 10.5532i) q^{26} +(5.18139 + 0.391460i) q^{27} +(5.37844 + 4.51305i) q^{28} +(-5.37998 + 1.95815i) q^{29} +(5.44246 - 1.82734i) q^{30} +4.21052 q^{31} +(6.18940 + 5.19352i) q^{32} +(-4.15459 + 6.79560i) q^{33} +(-5.11632 - 4.29310i) q^{34} +(-5.13994 - 1.87079i) q^{35} +(4.61860 + 4.28892i) q^{36} +5.19847 q^{37} +(7.89232 - 3.95342i) q^{38} +(9.88044 - 3.31742i) q^{39} +(0.314454 + 0.114452i) q^{40} +(-0.770270 - 4.36842i) q^{41} +(-1.74467 - 11.5911i) q^{42} +(-1.63995 - 0.596894i) q^{43} +(-9.07877 + 3.30440i) q^{44} +(-4.52395 - 1.90917i) q^{45} +(-3.60398 - 6.24228i) q^{46} +(3.47002 - 1.26298i) q^{47} +(-0.976525 - 6.48774i) q^{48} +(-2.08394 + 3.60949i) q^{49} +4.70020 q^{50} +(0.850250 + 5.64881i) q^{51} +(11.8799 + 4.32394i) q^{52} +(-1.03632 + 5.87728i) q^{53} +(-1.04135 - 10.4710i) q^{54} +(5.76587 - 4.83814i) q^{55} +(0.341617 - 0.591698i) q^{56} +(-7.29824 - 1.93278i) q^{57} +(5.79706 + 10.0408i) q^{58} +(7.28192 + 2.65040i) q^{59} +(-2.84749 - 5.23139i) q^{60} +(0.905056 + 0.759432i) q^{61} +(-1.48064 - 8.39710i) q^{62} +(-5.44272 + 8.41948i) q^{63} +(4.39313 - 7.60912i) q^{64} -9.84913 q^{65} +(15.0135 + 5.89589i) q^{66} +(-2.62337 + 14.8778i) q^{67} +(-3.46456 + 6.00080i) q^{68} +(-1.22279 + 6.04249i) q^{69} +(-1.92347 + 10.9085i) q^{70} +(-0.582229 - 3.30198i) q^{71} +(0.332977 - 0.515092i) q^{72} +(3.14639 + 1.14519i) q^{73} +(-1.82805 - 10.3674i) q^{74} +(-3.01364 - 2.66064i) q^{75} +(-5.46107 - 7.35141i) q^{76} +(-7.68385 - 13.3088i) q^{77} +(-10.0905 - 18.5381i) q^{78} +(-5.33963 + 4.48048i) q^{79} +(-1.07660 + 6.10571i) q^{80} +(-5.25962 + 7.30318i) q^{81} +(-8.44114 + 3.07232i) q^{82} +(3.00716 + 5.20856i) q^{83} +(-11.5284 + 3.87073i) q^{84} +(0.937386 - 5.31618i) q^{85} +(-0.613703 + 3.48048i) q^{86} +(1.96687 - 9.71942i) q^{87} +(0.470087 + 0.814214i) q^{88} +(3.61385 - 1.31534i) q^{89} +(-2.21663 + 9.69356i) q^{90} +(-3.49194 + 19.8038i) q^{91} +(-5.72851 + 4.80679i) q^{92} +(-3.80400 + 6.22213i) q^{93} +(-3.73903 - 6.47619i) q^{94} +(5.95672 + 3.92666i) q^{95} +(-13.2666 + 4.45435i) q^{96} +(-1.96859 - 11.1645i) q^{97} +(7.93128 + 2.88675i) q^{98} +(-6.28879 - 12.2790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 12 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} + 3 q^{7} + 12 q^{8} - 24 q^{9}+O(q^{10}) \) 108 * q - 3 * q^2 - 12 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 + 3 * q^7 + 12 * q^8 - 24 * q^9	\( 108 q - 3 q^{2} - 12 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} + 3 q^{7} + 12 q^{8} - 24 q^{9} - 12 q^{10} - 6 q^{11} - 3 q^{12} + 9 q^{14} - 12 q^{15} - 9 q^{16} - 21 q^{17} - 24 q^{18} - 9 q^{19} - 6 q^{20} + 3 q^{21} - 36 q^{22} - 15 q^{23} + 39 q^{24} - 3 q^{25} - 30 q^{26} - 6 q^{27} - 12 q^{28} + 15 q^{29} + 63 q^{30} - 6 q^{31} + 21 q^{32} - 42 q^{33} - 39 q^{34} - 9 q^{35} - 102 q^{36} - 24 q^{37} + 3 q^{38} - 6 q^{39} + 39 q^{40} + 39 q^{41} + 75 q^{42} + 9 q^{43} - 39 q^{44} - 3 q^{45} - 6 q^{46} + 15 q^{47} + 63 q^{48} - 15 q^{49} - 138 q^{50} + 45 q^{51} - 15 q^{52} + 12 q^{53} + 51 q^{54} - 27 q^{55} + 87 q^{56} - 60 q^{57} - 6 q^{58} + 48 q^{59} - 9 q^{60} + 18 q^{61} + 18 q^{62} + 63 q^{63} - 36 q^{64} - 42 q^{65} - 33 q^{66} - 27 q^{67} + 24 q^{68} + 15 q^{69} + 39 q^{70} + 30 q^{71} - 3 q^{72} + 63 q^{73} - 9 q^{74} + 72 q^{75} - 3 q^{76} - 48 q^{77} - 111 q^{78} - 9 q^{79} + 18 q^{80} - 84 q^{81} - 21 q^{82} - 9 q^{83} + 3 q^{84} - 3 q^{85} - 57 q^{86} + 3 q^{87} - 45 q^{88} - 30 q^{89} + 147 q^{90} - 57 q^{91} + 147 q^{92} + 54 q^{93} - 6 q^{94} - 15 q^{95} - 87 q^{96} + 51 q^{97} - 9 q^{98} - 21 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 12 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 + 3 * q^7 + 12 * q^8 - 24 * q^9 - 12 * q^10 - 6 * q^11 - 3 * q^12 + 9 * q^14 - 12 * q^15 - 9 * q^16 - 21 * q^17 - 24 * q^18 - 9 * q^19 - 6 * q^20 + 3 * q^21 - 36 * q^22 - 15 * q^23 + 39 * q^24 - 3 * q^25 - 30 * q^26 - 6 * q^27 - 12 * q^28 + 15 * q^29 + 63 * q^30 - 6 * q^31 + 21 * q^32 - 42 * q^33 - 39 * q^34 - 9 * q^35 - 102 * q^36 - 24 * q^37 + 3 * q^38 - 6 * q^39 + 39 * q^40 + 39 * q^41 + 75 * q^42 + 9 * q^43 - 39 * q^44 - 3 * q^45 - 6 * q^46 + 15 * q^47 + 63 * q^48 - 15 * q^49 - 138 * q^50 + 45 * q^51 - 15 * q^52 + 12 * q^53 + 51 * q^54 - 27 * q^55 + 87 * q^56 - 60 * q^57 - 6 * q^58 + 48 * q^59 - 9 * q^60 + 18 * q^61 + 18 * q^62 + 63 * q^63 - 36 * q^64 - 42 * q^65 - 33 * q^66 - 27 * q^67 + 24 * q^68 + 15 * q^69 + 39 * q^70 + 30 * q^71 - 3 * q^72 + 63 * q^73 - 9 * q^74 + 72 * q^75 - 3 * q^76 - 48 * q^77 - 111 * q^78 - 9 * q^79 + 18 * q^80 - 84 * q^81 - 21 * q^82 - 9 * q^83 + 3 * q^84 - 3 * q^85 - 57 * q^86 + 3 * q^87 - 45 * q^88 - 30 * q^89 + 147 * q^90 - 57 * q^91 + 147 * q^92 + 54 * q^93 - 6 * q^94 - 15 * q^95 - 87 * q^96 + 51 * q^97 - 9 * q^98 - 21 * q^99

Introduction

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